LMFDB - Embedded newform 272.2.l.c.205.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [272,2,Mod(69,272)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(272, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 1, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("272.69"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 272 = 2^{4} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	272.l (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [32] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.17193093498$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			205.8
Character	$\chi$	$=$	272.205
Dual form			272.2.l.c.69.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.0578728 - 1.41303i) q^{2} +(1.71777 + 1.71777i) q^{3} +(-1.99330 + 0.163552i) q^{4} +(-1.50377 + 1.50377i) q^{5} +(2.32785 - 2.52667i) q^{6} +1.59335i q^{7} +(0.346462 + 2.80713i) q^{8} +2.90147i q^{9} +(2.21190 + 2.03785i) q^{10} +(1.13260 - 1.13260i) q^{11} +(-3.70498 - 3.14309i) q^{12} +(3.39887 + 3.39887i) q^{13} +(2.25145 - 0.0922118i) q^{14} -5.16627 q^{15} +(3.94650 - 0.652017i) q^{16} +1.00000 q^{17} +(4.09986 - 0.167916i) q^{18} +(-1.08254 - 1.08254i) q^{19} +(2.75153 - 3.24342i) q^{20} +(-2.73701 + 2.73701i) q^{21} +(-1.66595 - 1.53486i) q^{22} +3.36256i q^{23} +(-4.22686 + 5.41714i) q^{24} +0.477333i q^{25} +(4.60600 - 4.99940i) q^{26} +(0.169248 - 0.169248i) q^{27} +(-0.260596 - 3.17603i) q^{28} +(-3.98811 - 3.98811i) q^{29} +(0.298987 + 7.30010i) q^{30} -6.88063 q^{31} +(-1.14971 - 5.53879i) q^{32} +3.89111 q^{33} +(-0.0578728 - 1.41303i) q^{34} +(-2.39604 - 2.39604i) q^{35} +(-0.474542 - 5.78351i) q^{36} +(4.91619 - 4.91619i) q^{37} +(-1.46701 + 1.59231i) q^{38} +11.6770i q^{39} +(-4.74228 - 3.70028i) q^{40} -11.7839i q^{41} +(4.02588 + 3.70908i) q^{42} +(5.00347 - 5.00347i) q^{43} +(-2.07238 + 2.44286i) q^{44} +(-4.36316 - 4.36316i) q^{45} +(4.75139 - 0.194601i) q^{46} -3.77271 q^{47} +(7.89920 + 5.65917i) q^{48} +4.46123 q^{49} +(0.674485 - 0.0276246i) q^{50} +(1.71777 + 1.71777i) q^{51} +(-7.33087 - 6.21908i) q^{52} +(5.02004 - 5.02004i) q^{53} +(-0.248947 - 0.229357i) q^{54} +3.40636i q^{55} +(-4.47274 + 0.552035i) q^{56} -3.71911i q^{57} +(-5.40451 + 5.86611i) q^{58} +(0.0625800 - 0.0625800i) q^{59} +(10.2979 - 0.844955i) q^{60} +(-1.34466 - 1.34466i) q^{61} +(0.398201 + 9.72252i) q^{62} -4.62307 q^{63} +(-7.75993 + 1.94512i) q^{64} -10.2223 q^{65} +(-0.225190 - 5.49825i) q^{66} +(5.61932 + 5.61932i) q^{67} +(-1.99330 + 0.163552i) q^{68} +(-5.77610 + 5.77610i) q^{69} +(-3.24701 + 3.52434i) q^{70} +9.90234i q^{71} +(-8.14480 + 1.00525i) q^{72} +10.7806i q^{73} +(-7.23123 - 6.66221i) q^{74} +(-0.819948 + 0.819948i) q^{75} +(2.33488 + 1.98078i) q^{76} +(1.80464 + 1.80464i) q^{77} +(16.4999 - 0.675779i) q^{78} -5.17541 q^{79} +(-4.95416 + 6.91513i) q^{80} +9.28588 q^{81} +(-16.6510 + 0.681970i) q^{82} +(-3.56034 - 3.56034i) q^{83} +(5.00805 - 5.90334i) q^{84} +(-1.50377 + 1.50377i) q^{85} +(-7.35962 - 6.78049i) q^{86} -13.7013i q^{87} +(3.57177 + 2.78696i) q^{88} -15.4509i q^{89} +(-5.91276 + 6.41777i) q^{90} +(-5.41560 + 5.41560i) q^{91} +(-0.549953 - 6.70259i) q^{92} +(-11.8193 - 11.8193i) q^{93} +(0.218337 + 5.33095i) q^{94} +3.25579 q^{95} +(7.53942 - 11.4893i) q^{96} -0.773938 q^{97} +(-0.258184 - 6.30385i) q^{98} +(3.28622 + 3.28622i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 2 q^{4} - 16 q^{6} - 18 q^{8} - 6 q^{10} - 4 q^{11} + 2 q^{12} + 14 q^{14} + 24 q^{15} + 26 q^{16} + 32 q^{17} + 10 q^{18} - 14 q^{20} - 8 q^{22} - 50 q^{24} - 6 q^{26} + 12 q^{27} - 8 q^{29} + 36 q^{30}+ \cdots - 24 q^{99}+O(q^{100}) $ 32 * q - 2 * q^4 - 16 * q^6 - 18 * q^8 - 6 * q^10 - 4 * q^11 + 2 * q^12 + 14 * q^14 + 24 * q^15 + 26 * q^16 + 32 * q^17 + 10 * q^18 - 14 * q^20 - 8 * q^22 - 50 * q^24 - 6 * q^26 + 12 * q^27 - 8 * q^29 + 36 * q^30 - 24 * q^31 + 10 * q^32 + 12 * q^35 + 16 * q^36 - 8 * q^37 - 34 * q^38 - 38 * q^40 - 12 * q^42 - 12 * q^43 + 38 * q^44 - 40 * q^45 + 26 * q^46 + 32 * q^47 + 30 * q^48 - 32 * q^49 - 2 * q^50 - 54 * q^52 + 8 * q^53 - 52 * q^54 - 36 * q^56 - 26 * q^58 - 12 * q^59 + 28 * q^60 + 6 * q^62 - 40 * q^63 + 10 * q^64 + 28 * q^66 + 8 * q^67 - 2 * q^68 - 32 * q^70 - 32 * q^72 - 14 * q^74 + 8 * q^75 + 30 * q^76 + 56 * q^77 + 108 * q^78 + 48 * q^79 + 90 * q^80 - 64 * q^81 + 32 * q^82 + 4 * q^83 - 8 * q^84 - 54 * q^86 - 66 * q^88 - 66 * q^90 - 28 * q^91 + 24 * q^92 - 24 * q^93 + 12 * q^94 - 40 * q^95 + 70 * q^96 + 12 * q^98 - 24 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/272\mathbb{Z}\right)^\times$.

$n$	$69$	$239$	$241$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$1$

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 $

$2$	−0.0578728	−	1.41303i	−0.0409223	−	0.999162i
$2$	−0.0578728	−	1.41303i	−0.0409223	−	0.999162i
$3$	1.71777	+	1.71777i	0.991755	+	0.991755i	0.999966	−	0.00821092i	$-0.00261365\pi$
$3$	1.71777	+	1.71777i	0.991755	+	0.991755i	−0.00821092	+	0.999966i	$0.502614\pi$
$4$	−1.99330	+	0.163552i	−0.996651	+	0.0817760i
$5$	−1.50377	+	1.50377i	−0.672508	+	0.672508i	−0.958294	−	0.285786i	$-0.907745\pi$
$5$	−1.50377	+	1.50377i	−0.672508	+	0.672508i	0.285786	+	0.958294i	$0.407745\pi$
$6$	2.32785	−	2.52667i	0.950340	−	1.03151i
$7$			1.59335i			0.602230i	0.953588	+	0.301115i	$0.0973589\pi$
$7$			1.59335i			0.602230i	−0.953588	+	0.301115i	$0.902641\pi$
$8$	0.346462	+	2.80713i	0.122493	+	0.992469i
$9$			2.90147i			0.967157i
$10$	2.21190	+	2.03785i	0.699465	+	0.644424i
$11$	1.13260	−	1.13260i	0.341493	−	0.341493i	−0.515435	−	0.856928i	$-0.672370\pi$
$11$	1.13260	−	1.13260i	0.341493	−	0.341493i	0.856928	+	0.515435i	$0.172370\pi$
$12$	−3.70498	−	3.14309i	−1.06954	−	0.907332i
$13$	3.39887	+	3.39887i	0.942677	+	0.942677i	0.998444	−	0.0557667i	$-0.0177603\pi$
$13$	3.39887	+	3.39887i	0.942677	+	0.942677i	−0.0557667	+	0.998444i	$0.517760\pi$
$14$	2.25145	−	0.0922118i	0.601726	−	0.0246446i
$15$	−5.16627			−1.33393
$16$	3.94650	−	0.652017i	0.986625	−	0.163004i
$17$	1.00000			0.242536
$17$	1.00000			0.242536
$18$	4.09986	−	0.167916i	0.966347	−	0.0395783i
$19$	−1.08254	−	1.08254i	−0.248352	−	0.248352i	0.571942	−	0.820294i	$-0.306190\pi$
$19$	−1.08254	−	1.08254i	−0.248352	−	0.248352i	−0.820294	+	0.571942i	$0.806190\pi$
$20$	2.75153	−	3.24342i	0.615260	−	0.725250i
$21$	−2.73701	+	2.73701i	−0.597265	+	0.597265i
$22$	−1.66595	−	1.53486i	−0.355182	−	0.327232i
$23$			3.36256i			0.701141i	0.936536	+	0.350571i	$0.114012\pi$
$23$			3.36256i			0.701141i	−0.936536	+	0.350571i	$0.885988\pi$
$24$	−4.22686	+	5.41714i	−0.862804	+	1.10577i
$25$			0.477333i			0.0954665i
$26$	4.60600	−	4.99940i	0.903311	−	0.980464i
$27$	0.169248	−	0.169248i	0.0325718	−	0.0325718i
$28$	−0.260596	−	3.17603i	−0.0492480	−	0.600213i
$29$	−3.98811	−	3.98811i	−0.740573	−	0.740573i	0.232116	−	0.972688i	$-0.425435\pi$
$29$	−3.98811	−	3.98811i	−0.740573	−	0.740573i	−0.972688	+	0.232116i	$0.925435\pi$
$30$	0.298987	+	7.30010i	0.0545873	+	1.33281i
$31$	−6.88063			−1.23580			−0.617898	−	0.786258i	$-0.712016\pi$
$31$	−6.88063			−1.23580			−0.617898	+	0.786258i	$0.712016\pi$
$32$	−1.14971	−	5.53879i	−0.203243	−	0.979128i
$33$	3.89111			0.677355
$34$	−0.0578728	−	1.41303i	−0.00992511	−	0.242332i
$35$	−2.39604	−	2.39604i	−0.405005	−	0.405005i
$36$	−0.474542	−	5.78351i	−0.0790903	−	0.963918i
$37$	4.91619	−	4.91619i	0.808217	−	0.808217i	−0.176147	−	0.984364i	$-0.556363\pi$
$37$	4.91619	−	4.91619i	0.808217	−	0.808217i	0.984364	+	0.176147i	$0.0563634\pi$
$38$	−1.46701	+	1.59231i	−0.237980	+	0.258307i
$39$			11.6770i			1.86981i
$40$	−4.74228	−	3.70028i	−0.749821	−	0.585066i
$41$		−	11.7839i		−	1.84034i	−0.391517	−	0.920171i	$-0.628050\pi$
$41$		−	11.7839i		−	1.84034i	0.391517	−	0.920171i	$-0.371950\pi$
$42$	4.02588	+	3.70908i	0.621206	+	0.572323i
$43$	5.00347	−	5.00347i	0.763023	−	0.763023i	−0.213845	−	0.976868i	$-0.568599\pi$
$43$	5.00347	−	5.00347i	0.763023	−	0.763023i	0.976868	+	0.213845i	$0.0685987\pi$
$44$	−2.07238	+	2.44286i	−0.312423	+	0.368275i
$45$	−4.36316	−	4.36316i	−0.650421	−	0.650421i
$46$	4.75139	−	0.194601i	0.700554	−	0.0286923i
$47$	−3.77271			−0.550306			−0.275153	−	0.961400i	$-0.588729\pi$
$47$	−3.77271			−0.550306			−0.275153	+	0.961400i	$0.588729\pi$
$48$	7.89920	+	5.65917i	1.14015	+	0.816831i
$49$	4.46123			0.637319
$50$	0.674485	−	0.0276246i	0.0953865	−	0.00390671i
$51$	1.71777	+	1.71777i	0.240536	+	0.240536i
$52$	−7.33087	−	6.21908i	−1.01661	−	0.862431i
$53$	5.02004	−	5.02004i	0.689555	−	0.689555i	−0.272579	−	0.962134i	$-0.587876\pi$
$53$	5.02004	−	5.02004i	0.689555	−	0.689555i	0.962134	+	0.272579i	$0.0878764\pi$
$54$	−0.248947	−	0.229357i	−0.0338774	−	0.0312116i
$55$			3.40636i			0.459314i
$56$	−4.47274	+	0.552035i	−0.597695	+	0.0737688i
$57$		−	3.71911i		−	0.492608i
$58$	−5.40451	+	5.86611i	−0.709646	+	0.770258i
$59$	0.0625800	−	0.0625800i	0.00814723	−	0.00814723i	−0.703021	−	0.711169i	$-0.748166\pi$
$59$	0.0625800	−	0.0625800i	0.00814723	−	0.00814723i	0.711169	+	0.703021i	$0.248166\pi$
$60$	10.2979	−	0.844955i	1.32946	−	0.109083i
$61$	−1.34466	−	1.34466i	−0.172167	−	0.172167i	0.615764	−	0.787931i	$-0.288847\pi$
$61$	−1.34466	−	1.34466i	−0.172167	−	0.172167i	−0.787931	+	0.615764i	$0.788847\pi$
$62$	0.398201	+	9.72252i	0.0505716	+	1.23476i
$63$	−4.62307			−0.582452
$64$	−7.75993	+	1.94512i	−0.969991	+	0.243141i
$65$	−10.2223			−1.26792
$66$	−0.225190	−	5.49825i	−0.0277189	−	0.676788i
$67$	5.61932	+	5.61932i	0.686510	+	0.686510i	0.961459	−	0.274949i	$-0.0886610\pi$
$67$	5.61932	+	5.61932i	0.686510	+	0.686510i	−0.274949	+	0.961459i	$0.588661\pi$
$68$	−1.99330	+	0.163552i	−0.241723	+	0.0198336i
$69$	−5.77610	+	5.77610i	−0.695361	+	0.695361i
$70$	−3.24701	+	3.52434i	−0.388092	+	0.421239i
$71$			9.90234i			1.17519i	0.809155	+	0.587596i	$0.199925\pi$
$71$			9.90234i			1.17519i	−0.809155	+	0.587596i	$0.800075\pi$
$72$	−8.14480	+	1.00525i	−0.959874	+	0.118470i
$73$			10.7806i			1.26177i	0.775876	+	0.630885i	$0.217308\pi$
$73$			10.7806i			1.26177i	−0.775876	+	0.630885i	$0.782692\pi$
$74$	−7.23123	−	6.66221i	−0.840614	−	0.774466i
$75$	−0.819948	+	0.819948i	−0.0946794	+	0.0946794i
$76$	2.33488	+	1.98078i	0.267829	+	0.227211i
$77$	1.80464	+	1.80464i	0.205658	+	0.205658i
$78$	16.4999	−	0.675779i	1.86824	−	0.0765169i
$79$	−5.17541			−0.582280			−0.291140	−	0.956681i	$-0.594034\pi$
$79$	−5.17541			−0.582280			−0.291140	+	0.956681i	$0.594034\pi$
$80$	−4.95416	+	6.91513i	−0.553892	+	0.773135i
$81$	9.28588			1.03176
$82$	−16.6510	+	0.681970i	−1.83880	+	0.0753110i
$83$	−3.56034	−	3.56034i	−0.390798	−	0.390798i	0.484174	−	0.874972i	$-0.339120\pi$
$83$	−3.56034	−	3.56034i	−0.390798	−	0.390798i	−0.874972	+	0.484174i	$0.839120\pi$
$84$	5.00805	−	5.90334i	0.546423	−	0.644107i
$85$	−1.50377	+	1.50377i	−0.163107	+	0.163107i
$86$	−7.35962	−	6.78049i	−0.793608	−	0.731159i
$87$		−	13.7013i		−	1.46893i
$88$	3.57177	+	2.78696i	0.380752	+	0.297091i
$89$		−	15.4509i		−	1.63780i	−0.573938	−	0.818898i	$-0.694585\pi$
$89$		−	15.4509i		−	1.63780i	0.573938	−	0.818898i	$-0.305415\pi$
$90$	−5.91276	+	6.41777i	−0.623259	+	0.676493i
$91$	−5.41560	+	5.41560i	−0.567709	+	0.567709i
$92$	−0.549953	−	6.70259i	−0.0573365	−	0.698793i
$93$	−11.8193	−	11.8193i	−1.22561	−	1.22561i
$94$	0.218337	+	5.33095i	0.0225198	+	0.549845i
$95$	3.25579			0.334037
$96$	7.53942	−	11.4893i	0.769489	−	1.17262i
$97$	−0.773938			−0.0785815			−0.0392908	−	0.999228i	$-0.512510\pi$
$97$	−0.773938			−0.0785815			−0.0392908	+	0.999228i	$0.512510\pi$
$98$	−0.258184	−	6.30385i	−0.0260805	−	0.636785i
$99$	3.28622	+	3.28622i	0.330278	+	0.330278i
$100$	−0.0780687	−	0.951468i	−0.00780687	−	0.0951468i
$101$	9.49495	−	9.49495i	0.944783	−	0.944783i	−0.0537701	−	0.998553i	$-0.517124\pi$
$101$	9.49495	−	9.49495i	0.944783	−	0.944783i	0.998553	+	0.0537701i	$0.0171238\pi$
$102$	2.32785	−	2.52667i	0.230491	−	0.250178i
$103$			15.2564i			1.50326i	0.659585	+	0.751630i	$0.270732\pi$
$103$			15.2564i			1.50326i	−0.659585	+	0.751630i	$0.729268\pi$
$104$	−8.36348	+	10.7186i	−0.820107	+	1.05105i
$105$		−	8.23169i		−	0.803331i
$106$	−7.38398	−	6.80293i	−0.717196	−	0.660759i
$107$	−5.70294	+	5.70294i	−0.551324	+	0.551324i	−0.926823	−	0.375499i	$-0.877471\pi$
$107$	−5.70294	+	5.70294i	−0.551324	+	0.551324i	0.375499	+	0.926823i	$0.377471\pi$
$108$	−0.309681	+	0.365043i	−0.0297991	+	0.0351263i
$109$	11.0145	+	11.0145i	1.05500	+	1.05500i	0.998397	+	0.0566059i	$0.0180279\pi$
$109$	11.0145	+	11.0145i	1.05500	+	1.05500i	0.0566059	+	0.998397i	$0.481972\pi$
$110$	4.81329	−	0.197136i	0.458929	−	0.0187962i
$111$	16.8898			1.60311
$112$	1.03889	+	6.28817i	0.0981661	+	0.594176i
$113$	6.67002			0.627462			0.313731	−	0.949512i	$-0.398421\pi$
$113$	6.67002			0.627462			0.313731	+	0.949512i	$0.398421\pi$
$114$	−5.25521	+	0.215235i	−0.492196	+	0.0201586i
$115$	−5.05652	−	5.05652i	−0.471523	−	0.471523i
$116$	8.60176	+	7.29724i	0.798653	+	0.677531i
$117$	−9.86173	+	9.86173i	−0.911717	+	0.911717i
$118$	−0.0920491	−	0.0848057i	−0.00847381	−	0.00780700i
$119$			1.59335i			0.146062i
$120$	−1.78992	−	14.5024i	−0.163396	−	1.32388i
$121$			8.43441i			0.766765i
$122$	−1.82223	+	1.97787i	−0.164977	+	0.179068i
$123$	20.2421	−	20.2421i	1.82517	−	1.82517i
$124$	13.7152	−	1.12534i	1.23166	−	0.101059i
$125$	−8.23667	−	8.23667i	−0.736710	−	0.736710i
$126$	0.267550	+	6.53253i	0.0238352	+	0.581964i
$127$	15.4224			1.36852			0.684260	−	0.729238i	$-0.260125\pi$
$127$	15.4224			1.36852			0.684260	+	0.729238i	$0.260125\pi$
$128$	3.19761	+	10.8524i	0.282631	+	0.959229i
$129$	17.1896			1.51346
$130$	0.591591	+	14.4444i	0.0518860	+	1.26685i
$131$	−9.40807	−	9.40807i	−0.821987	−	0.821987i	0.164406	−	0.986393i	$-0.447429\pi$
$131$	−9.40807	−	9.40807i	−0.821987	−	0.821987i	−0.986393	+	0.164406i	$0.947429\pi$
$132$	−7.75615	+	0.636399i	−0.675087	+	0.0553914i
$133$	1.72487	−	1.72487i	0.149565	−	0.149565i
$134$	7.61506	−	8.26547i	0.657841	−	0.714028i
$135$			0.509021i			0.0438096i
$136$	0.346462	+	2.80713i	0.0297088	+	0.240709i
$137$			18.7861i			1.60501i	0.596646	+	0.802504i	$0.296500\pi$
$137$			18.7861i			1.60501i	−0.596646	+	0.802504i	$0.703500\pi$
$138$	8.49607	+	7.82752i	0.723234	+	0.666322i
$139$	−8.63911	+	8.63911i	−0.732759	+	0.732759i	−0.971166	−	0.238406i	$-0.923375\pi$
$139$	−8.63911	+	8.63911i	−0.732759	+	0.732759i	0.238406	+	0.971166i	$0.423375\pi$
$140$	5.16791	+	4.38415i	0.436768	+	0.370528i
$141$	−6.48065	−	6.48065i	−0.545769	−	0.545769i
$142$	13.9923	−	0.573077i	1.17421	−	0.0480915i
$143$	7.69915			0.643835
$144$	1.89181	+	11.4507i	0.157651	+	0.954222i
$145$	11.9944			0.996082
$146$	15.2333	−	0.623903i	1.26071	−	0.0516345i
$147$	7.66337	+	7.66337i	0.632064	+	0.632064i
$148$	−8.99540	+	10.6035i	−0.739417	+	0.871603i
$149$	7.46149	−	7.46149i	0.611269	−	0.611269i	−0.332007	−	0.943277i	$-0.607726\pi$
$149$	7.46149	−	7.46149i	0.611269	−	0.611269i	0.943277	+	0.332007i	$0.107726\pi$
$150$	1.20606	+	1.11116i	0.0984746	+	0.0907256i
$151$		−	20.3702i		−	1.65770i	−0.559470	−	0.828851i	$-0.688995\pi$
$151$		−	20.3702i		−	1.65770i	0.559470	−	0.828851i	$-0.311005\pi$
$152$	2.66377	−	3.41389i	0.216060	−	0.276903i
$153$			2.90147i			0.234570i
$154$	2.44557	−	2.65444i	0.197069	−	0.213901i
$155$	10.3469	−	10.3469i	0.831083	−	0.831083i
$156$	−1.90979	−	23.2757i	−0.152906	−	1.86355i
$157$	−8.11617	−	8.11617i	−0.647741	−	0.647741i	0.304705	−	0.952447i	$-0.401442\pi$
$157$	−8.11617	−	8.11617i	−0.647741	−	0.647741i	−0.952447	+	0.304705i	$0.901442\pi$
$158$	0.299516	+	7.31301i	0.0238282	+	0.581792i
$159$	17.2465			1.36774
$160$	10.0580	+	6.60017i	0.795154	+	0.521789i
$161$	−5.35773			−0.422249
$162$	−0.537400	−	13.1212i	−0.0422221	−	1.03090i
$163$	−17.3935	−	17.3935i	−1.36237	−	1.36237i	−0.870894	−	0.491471i	$-0.836459\pi$
$163$	−17.3935	−	17.3935i	−1.36237	−	1.36237i	−0.491471	−	0.870894i	$-0.663541\pi$
$164$	1.92729	+	23.4889i	0.150496	+	1.83418i
$165$	−5.85135	+	5.85135i	−0.455527	+	0.455527i
$166$	−4.82481	+	5.23690i	−0.374478	+	0.406463i
$167$		−	10.6538i		−	0.824413i	−0.911090	−	0.412207i	$-0.864758\pi$
$167$		−	10.6538i		−	0.824413i	0.911090	−	0.412207i	$-0.135242\pi$
$168$	−8.63141	−	6.73487i	−0.665928	−	0.519607i
$169$			10.1046i			0.777280i
$170$	2.21190	+	2.03785i	0.169645	+	0.156296i
$171$	3.14096	−	3.14096i	0.240195	−	0.240195i
$172$	−9.15511	+	10.7918i	−0.698070	+	0.822864i
$173$	−11.0797	−	11.0797i	−0.842374	−	0.842374i	0.146793	−	0.989167i	$-0.453105\pi$
$173$	−11.0797	−	11.0797i	−0.842374	−	0.842374i	−0.989167	+	0.146793i	$0.953105\pi$
$174$	−19.3603	+	0.792933i	−1.46770	+	0.0601121i
$175$	−0.760559			−0.0574928
$176$	3.73135	−	5.20830i	0.281261	−	0.392591i
$177$	0.214996			0.0161601
$178$	−21.8326	+	0.894190i	−1.63643	+	0.0670224i
$179$	5.71254	+	5.71254i	0.426975	+	0.426975i	0.887597	−	0.460622i	$-0.152373\pi$
$179$	5.71254	+	5.71254i	0.426975	+	0.426975i	−0.460622	+	0.887597i	$0.652373\pi$
$180$	9.41069	+	7.98348i	0.701431	+	0.595054i
$181$	0.685997	−	0.685997i	0.0509898	−	0.0509898i	−0.681152	−	0.732142i	$-0.738521\pi$
$181$	0.685997	−	0.685997i	0.0509898	−	0.0509898i	0.732142	+	0.681152i	$0.238521\pi$
$182$	7.96581	+	7.33898i	0.590465	+	0.544001i
$183$		−	4.61965i		−	0.341494i
$184$	−9.43912	+	1.16500i	−0.695861	+	0.0858847i
$185$			14.7857i			1.08706i
$186$	−16.0170	+	17.3851i	−1.17443	+	1.27474i
$187$	1.13260	−	1.13260i	0.0828242	−	0.0828242i
$188$	7.52015	−	0.617034i	0.548463	−	0.0450019i
$189$	0.269672	+	0.269672i	0.0196157	+	0.0196157i
$190$	−0.188422	−	4.60052i	−0.0136695	−	0.333757i
$191$	−20.5013			−1.48342			−0.741711	−	0.670720i	$-0.765985\pi$
$191$	−20.5013			−1.48342			−0.741711	+	0.670720i	$0.765985\pi$
$192$	−16.6711	−	9.98850i	−1.20313	−	0.720858i
$193$	5.04363			0.363049			0.181524	−	0.983386i	$-0.441897\pi$
$193$	5.04363			0.363049			0.181524	+	0.983386i	$0.441897\pi$
$194$	0.0447900	+	1.09360i	0.00321574	+	0.0785157i
$195$	−17.5595	−	17.5595i	−1.25746	−	1.25746i
$196$	−8.89258	+	0.729643i	−0.635184	+	0.0521174i
$197$	2.31874	−	2.31874i	0.165204	−	0.165204i	−0.619664	−	0.784867i	$-0.712731\pi$
$197$	2.31874	−	2.31874i	0.165204	−	0.165204i	0.784867	+	0.619664i	$0.212731\pi$
$198$	4.45334	−	4.83371i	0.316485	−	0.343517i
$199$		−	3.89446i		−	0.276071i	−0.990427	−	0.138035i	$-0.955921\pi$
$199$		−	3.89446i		−	0.276071i	0.990427	−	0.138035i	$-0.0440788\pi$
$200$	−1.33993	+	0.165377i	−0.0947476	+	0.0116940i
$201$			19.3054i			1.36170i
$202$	−13.9661	−	12.8671i	−0.982654	−	0.905329i
$203$	6.35446	−	6.35446i	0.445995	−	0.445995i
$204$	−3.70498	−	3.14309i	−0.259400	−	0.220060i
$205$	17.7204	+	17.7204i	1.23764	+	1.23764i
$206$	21.5578	−	0.882932i	1.50200	−	0.0615168i
$207$	−9.75636			−0.678114
$208$	15.6298	+	11.1975i	1.08373	+	0.776409i
$209$	−2.45218			−0.169621
$210$	−11.6316	+	0.476391i	−0.802658	+	0.0328741i
$211$	3.05348	+	3.05348i	0.210210	+	0.210210i	0.804357	−	0.594147i	$-0.202510\pi$
$211$	3.05348	+	3.05348i	0.210210	+	0.210210i	−0.594147	+	0.804357i	$0.702510\pi$
$212$	−9.18541	+	10.8275i	−0.630856	+	0.743635i
$213$	−17.0100	+	17.0100i	−1.16550	+	1.16550i
$214$	8.38846	+	7.72837i	0.573424	+	0.528301i
$215$			15.0482i			1.02628i
$216$	0.533739	+	0.416463i	0.0363163	+	0.0283367i
$217$		−	10.9633i		−	0.744234i
$218$	14.9264	−	16.2013i	1.01095	−	1.09729i
$219$	−18.5186	+	18.5186i	−1.25137	+	1.25137i
$220$	−0.557117	−	6.78990i	−0.0375608	−	0.457775i
$221$	3.39887	+	3.39887i	0.228633	+	0.228633i
$222$	−0.977459	−	23.8657i	−0.0656028	−	1.60176i
$223$	−27.4512			−1.83827			−0.919134	−	0.393945i	$-0.871110\pi$
$223$	−27.4512			−1.83827			−0.919134	+	0.393945i	$0.871110\pi$
$224$	8.82524	−	1.83190i	0.589661	−	0.122399i
$225$	−1.38497			−0.0923311
$226$	−0.386013	−	9.42493i	−0.0256772	−	0.626937i
$227$	0.0235126	+	0.0235126i	0.00156059	+	0.00156059i	0.707887	−	0.706326i	$-0.249649\pi$
$227$	0.0235126	+	0.0235126i	0.00156059	+	0.00156059i	−0.706326	+	0.707887i	$0.749649\pi$
$228$	0.608268	+	7.41331i	0.0402835	+	0.490958i
$229$	−3.10655	+	3.10655i	−0.205287	+	0.205287i	−0.802261	−	0.596974i	$-0.796370\pi$
$229$	−3.10655	+	3.10655i	−0.205287	+	0.205287i	0.596974	+	0.802261i	$0.296370\pi$
$230$	−6.85237	+	7.43764i	−0.451832	+	0.490424i
$231$			6.19991i			0.407924i
$232$	9.81340	−	12.5768i	0.644281	−	0.825711i
$233$			21.1230i			1.38382i	0.721985	+	0.691908i	$0.243230\pi$
$233$			21.1230i			1.38382i	−0.721985	+	0.691908i	$0.756770\pi$
$234$	14.5056	+	13.3642i	0.948263	+	0.873644i
$235$	5.67330	−	5.67330i	0.370085	−	0.370085i
$236$	−0.114506	+	0.134976i	−0.00745369	+	0.00878619i
$237$	−8.89017	−	8.89017i	−0.577479	−	0.577479i
$238$	2.25145	−	0.0922118i	0.145940	−	0.00597720i
$239$	−6.22498			−0.402660			−0.201330	−	0.979523i	$-0.564526\pi$
$239$	−6.22498			−0.402660			−0.201330	+	0.979523i	$0.564526\pi$
$240$	−20.3887	+	3.36850i	−1.31609	+	0.217436i
$241$	−14.9765			−0.964722			−0.482361	−	0.875972i	$-0.660221\pi$
$241$	−14.9765			−0.964722			−0.482361	+	0.875972i	$0.660221\pi$
$242$	11.9181	−	0.488123i	0.766123	−	0.0313778i
$243$	15.4433	+	15.4433i	0.990686	+	0.990686i
$244$	2.90024	+	2.46040i	0.185669	+	0.157511i
$245$	−6.70868	+	6.70868i	−0.428602	+	0.428602i
$246$	−29.7741	−	27.4312i	−1.89833	−	1.74895i
$247$		−	7.35882i		−	0.468231i
$248$	−2.38387	−	19.3148i	−0.151376	−	1.22649i
$249$		−	12.2317i		−	0.775151i
$250$	−11.1620	+	12.1153i	−0.705945	+	0.766241i
$251$	−4.63061	+	4.63061i	−0.292282	+	0.292282i	−0.837981	−	0.545699i	$-0.816264\pi$
$251$	−4.63061	+	4.63061i	−0.292282	+	0.292282i	0.545699	+	0.837981i	$0.316264\pi$
$252$	9.21516	−	0.756112i	0.580501	−	0.0476306i
$253$	3.80845	+	3.80845i	0.239435	+	0.239435i
$254$	−0.892541	−	21.7924i	−0.0560030	−	1.36737i
$255$	−5.16627			−0.323525
$256$	15.1497	−	5.14637i	0.946859	−	0.321648i
$257$	−7.53821			−0.470220			−0.235110	−	0.971969i	$-0.575545\pi$
$257$	−7.53821			−0.470220			−0.235110	+	0.971969i	$0.575545\pi$
$258$	−0.994814	−	24.2895i	−0.0619344	−	1.51220i
$259$	7.83322	+	7.83322i	0.486733	+	0.486733i
$260$	20.3760	−	1.67187i	1.26367	−	0.103685i
$261$	11.5714	−	11.5714i	0.716250	−	0.716250i
$262$	−12.7494	+	13.8383i	−0.787661	+	0.854936i
$263$		−	19.2671i		−	1.18806i	−0.804443	−	0.594030i	$-0.797536\pi$
$263$		−	19.2671i		−	1.18806i	0.804443	−	0.594030i	$-0.202464\pi$
$264$	1.34812	+	10.9228i	0.0829711	+	0.672254i
$265$			15.0980i			0.927462i
$266$	−2.53711	−	2.33746i	−0.155560	−	0.143319i
$267$	26.5412	−	26.5412i	1.62429	−	1.62429i
$268$	−12.1201	−	10.2820i	−0.740350	−	0.628070i
$269$	7.37045	+	7.37045i	0.449384	+	0.449384i	0.895150	−	0.445766i	$-0.147068\pi$
$269$	7.37045	+	7.37045i	0.449384	+	0.449384i	−0.445766	+	0.895150i	$0.647068\pi$
$270$	0.719262	−	0.0294585i	0.0437729	−	0.00179279i
$271$	3.25204			0.197548			0.0987738	−	0.995110i	$-0.468508\pi$
$271$	3.25204			0.197548			0.0987738	+	0.995110i	$0.468508\pi$
$272$	3.94650	−	0.652017i	0.239292	−	0.0395343i
$273$	−18.6055			−1.12606
$274$	26.5454	−	1.08721i	1.60366	−	0.0656806i
$275$	0.540629	+	0.540629i	0.0326012	+	0.0326012i
$276$	10.5688	−	12.4582i	0.636168	−	0.749895i
$277$	12.1549	−	12.1549i	0.730315	−	0.730315i	−0.240367	−	0.970682i	$-0.577268\pi$
$277$	12.1549	−	12.1549i	0.730315	−	0.730315i	0.970682	+	0.240367i	$0.0772677\pi$
$278$	12.7073	+	11.7073i	0.762132	+	0.702159i
$279$		−	19.9639i		−	1.19521i
$280$	5.89585	−	7.55612i	0.352345	−	0.451565i
$281$			19.4903i			1.16270i	0.813655	+	0.581348i	$0.197475\pi$
$281$			19.4903i			1.16270i	−0.813655	+	0.581348i	$0.802525\pi$
$282$	−8.78229	+	9.53240i	−0.522978	+	0.567646i
$283$	−14.7428	+	14.7428i	−0.876366	+	0.876366i	−0.993157	−	0.116791i	$-0.962739\pi$
$283$	−14.7428	+	14.7428i	−0.876366	+	0.876366i	0.116791	+	0.993157i	$0.462739\pi$
$284$	−1.61955	−	19.7384i	−0.0961025	−	1.17126i
$285$	5.59270	+	5.59270i	0.331283	+	0.331283i
$286$	−0.445572	−	10.8791i	−0.0263472	−	0.643296i
$287$	18.7760			1.10831
$288$	16.0706	−	3.33586i	0.946971	−	0.196568i
$289$	1.00000			0.0588235
$290$	−0.694151	−	16.9485i	−0.0407619	−	0.995247i
$291$	−1.32945	−	1.32945i	−0.0779337	−	0.0779337i
$292$	−1.76318	−	21.4889i	−0.103183	−	1.25754i
$293$	−0.755302	+	0.755302i	−0.0441252	+	0.0441252i	−0.728825	−	0.684700i	$-0.759933\pi$
$293$	−0.755302	+	0.755302i	−0.0441252	+	0.0441252i	0.684700	+	0.728825i	$0.259933\pi$
$294$	10.3851	−	11.2721i	0.605669	−	0.657400i
$295$			0.188212i			0.0109581i
$296$	15.5036	+	12.0971i	0.901131	+	0.703130i
$297$		−	0.383382i		−	0.0222461i
$298$	−10.9751	−	10.1115i	−0.635772	−	0.585743i
$299$	−11.4289	+	11.4289i	−0.660950	+	0.660950i
$300$	1.50030	−	1.76851i	0.0866198	−	0.102105i
$301$	7.97230	+	7.97230i	0.459515	+	0.459515i
$302$	−28.7837	+	1.17888i	−1.65631	+	0.0678369i
$303$	32.6203			1.87399
$304$	−4.97808	−	3.56641i	−0.285512	−	0.204548i
$305$	4.04414			0.231567
$306$	4.09986	−	0.167916i	0.234374	−	0.00959914i
$307$	4.94578	+	4.94578i	0.282270	+	0.282270i	0.834014	−	0.551743i	$-0.186037\pi$
$307$	4.94578	+	4.94578i	0.282270	+	0.282270i	−0.551743	+	0.834014i	$0.686037\pi$
$308$	−3.89234	−	3.30203i	−0.221787	−	0.188151i
$309$	−26.2070	+	26.2070i	−1.49087	+	1.49087i
$310$	−15.2193	−	14.0217i	−0.864397	−	0.796377i
$311$			13.2594i			0.751873i	0.926645	+	0.375937i	$0.122679\pi$
$311$			13.2594i			0.751873i	−0.926645	+	0.375937i	$0.877321\pi$
$312$	−32.7787	+	4.04562i	−1.85573	+	0.229038i
$313$		−	33.0375i		−	1.86739i	−0.358070	−	0.933695i	$-0.616565\pi$
$313$		−	33.0375i		−	1.86739i	0.358070	−	0.933695i	$-0.383435\pi$
$314$	−10.9987	+	11.9381i	−0.620691	+	0.673706i
$315$	6.95204	−	6.95204i	0.391703	−	0.391703i
$316$	10.3162	−	0.846449i	0.580329	−	0.0476165i
$317$	−12.2342	−	12.2342i	−0.687143	−	0.687143i	0.274457	−	0.961599i	$-0.411502\pi$
$317$	−12.2342	−	12.2342i	−0.687143	−	0.687143i	−0.961599	+	0.274457i	$0.911502\pi$
$318$	−0.998106	−	24.3699i	−0.0559710	−	1.36659i
$319$	−9.03389			−0.505801
$320$	8.74415	−	14.5942i	0.488813	−	0.815840i
$321$	−19.5927			−1.09356
$322$	0.310067	+	7.57063i	0.0172794	+	0.421895i
$323$	−1.08254	−	1.08254i	−0.0602341	−	0.0602341i
$324$	−18.5095	+	1.51872i	−1.02831	+	0.0843735i
$325$	−1.62239	+	1.62239i	−0.0899941	+	0.0899941i
$326$	−23.5709	+	25.5842i	−1.30547	+	1.41698i
$327$			37.8409i			2.09261i
$328$	33.0790	−	4.08268i	1.82648	−	0.225428i
$329$		−	6.01126i		−	0.331411i
$330$	8.60676	+	7.92949i	0.473786	+	0.436504i
$331$	1.27352	−	1.27352i	0.0699990	−	0.0699990i	−0.671241	−	0.741240i	$-0.734238\pi$
$331$	1.27352	−	1.27352i	0.0699990	−	0.0699990i	0.741240	+	0.671241i	$0.234238\pi$
$332$	7.67912	+	6.51452i	0.421447	+	0.357531i
$333$	14.2642	+	14.2642i	0.781673	+	0.781673i
$334$	−15.0541	+	0.616564i	−0.823723	+	0.0337369i
$335$	−16.9004			−0.923366
$336$	−9.01705	+	12.5862i	−0.491920	+	0.686634i
$337$	−19.9367			−1.08602			−0.543012	−	0.839725i	$-0.682716\pi$
$337$	−19.9367			−1.08602			−0.543012	+	0.839725i	$0.682716\pi$
$338$	14.2782	−	0.584784i	0.776629	−	0.0318081i
$339$	11.4576	+	11.4576i	0.622289	+	0.622289i
$340$	2.75153	−	3.24342i	0.149223	−	0.175899i
$341$	−7.79303	+	7.79303i	−0.422016	+	0.422016i
$342$	−4.62004	−	4.25649i	−0.249823	−	0.230165i
$343$			18.2618i			0.986043i
$344$	15.7789	+	12.3119i	0.850741	+	0.663812i
$345$		−	17.3719i		−	0.935271i
$346$	−15.0147	+	16.2971i	−0.807196	+	0.876140i
$347$	19.4382	−	19.4382i	1.04350	−	1.04350i	0.0444868	−	0.999010i	$-0.485835\pi$
$347$	19.4382	−	19.4382i	1.04350	−	1.04350i	0.999010	−	0.0444868i	$-0.0141653\pi$
$348$	2.24088	+	27.3108i	0.120124	+	1.46401i
$349$	8.74693	+	8.74693i	0.468212	+	0.468212i	0.901335	−	0.433123i	$-0.142588\pi$
$349$	8.74693	+	8.74693i	0.468212	+	0.468212i	−0.433123	+	0.901335i	$0.642588\pi$
$350$	0.0440157	+	1.07469i	0.00235274	+	0.0574447i
$351$	1.15050			0.0614094
$352$	−7.57543	−	4.97108i	−0.403772	−	0.264960i
$353$	−26.3858			−1.40437			−0.702186	−	0.711993i	$-0.747793\pi$
$353$	−26.3858			−1.40437			−0.702186	+	0.711993i	$0.747793\pi$
$354$	−0.0124424	−	0.303796i	−0.000661309	−	0.0161466i
$355$	−14.8909	−	14.8909i	−0.790326	−	0.790326i
$356$	2.52703	+	30.7984i	0.133932	+	1.63231i
$357$	−2.73701	+	2.73701i	−0.144858	+	0.144858i
$358$	7.74138	−	8.40258i	0.409145	−	0.444090i
$359$			4.76485i			0.251479i	0.992063	+	0.125740i	$0.0401304\pi$
$359$			4.76485i			0.251479i	−0.992063	+	0.125740i	$0.959870\pi$
$360$	10.7363	−	13.7596i	0.565851	−	0.725195i
$361$		−	16.6562i		−	0.876643i
$362$	−1.00903	−	0.929633i	−0.0530337	−	0.0488604i
$363$	−14.4884	+	14.4884i	−0.760443	+	0.760443i
$364$	9.90918	−	11.6806i	0.519382	−	0.612232i
$365$	−16.2115	−	16.2115i	−0.848551	−	0.848551i
$366$	−6.52770	+	0.267352i	−0.341208	+	0.0139747i
$367$	22.8633			1.19346			0.596728	−	0.802444i	$-0.296467\pi$
$367$	22.8633			1.19346			0.596728	+	0.802444i	$0.296467\pi$
$368$	2.19244	+	13.2703i	0.114289	+	0.691764i
$369$	34.1908			1.77990
$370$	20.8926	−	0.855689i	1.08615	−	0.0444851i
$371$	7.99868	+	7.99868i	0.415271	+	0.415271i
$372$	25.4926	+	21.6264i	1.32173	+	1.12128i
$373$	8.23959	−	8.23959i	0.426630	−	0.426630i	−0.460849	−	0.887479i	$-0.652455\pi$
$373$	8.23959	−	8.23959i	0.426630	−	0.426630i	0.887479	+	0.460849i	$0.152455\pi$
$374$	−1.66595	−	1.53486i	−0.0861442	−	0.0793655i
$375$		−	28.2974i		−	1.46127i
$376$	−1.30710	−	10.5905i	−0.0674085	−	0.546162i
$377$		−	27.1101i		−	1.39624i
$378$	0.365447	−	0.396660i	0.0187966	−	0.0204020i
$379$	−7.16457	+	7.16457i	−0.368019	+	0.368019i	−0.866754	−	0.498735i	$-0.833798\pi$
$379$	−7.16457	+	7.16457i	−0.368019	+	0.368019i	0.498735	+	0.866754i	$0.333798\pi$
$380$	−6.48977	+	0.532491i	−0.332918	+	0.0273162i
$381$	26.4922	+	26.4922i	1.35724	+	1.35724i
$382$	1.18647	+	28.9689i	0.0607050	+	1.48218i
$383$	−22.4883			−1.14910			−0.574549	−	0.818470i	$-0.694822\pi$
$383$	−22.4883			−1.14910			−0.574549	+	0.818470i	$0.694822\pi$
$384$	−13.1492	+	24.1347i	−0.671019	+	1.23162i
$385$	−5.42753			−0.276613
$386$	−0.291889	−	7.12680i	−0.0148568	−	0.362745i
$387$	14.5174	+	14.5174i	0.737963	+	0.737963i
$388$	1.54269	−	0.126579i	0.0783183	−	0.00642608i
$389$	−3.73953	+	3.73953i	−0.189602	+	0.189602i	−0.795524	−	0.605922i	$-0.792804\pi$
$389$	−3.73953	+	3.73953i	−0.189602	+	0.189602i	0.605922	+	0.795524i	$0.292804\pi$
$390$	−23.7959	+	25.8283i	−1.20495	+	1.30787i
$391$			3.36256i			0.170052i
$392$	1.54565	+	12.5232i	0.0780669	+	0.632519i
$393$		−	32.3218i		−	1.63042i
$394$	−3.41065	−	3.14226i	−0.171826	−	0.158305i
$395$	7.78265	−	7.78265i	0.391588	−	0.391588i
$396$	−7.08790	−	6.01296i	−0.356180	−	0.302163i
$397$	−7.04883	−	7.04883i	−0.353771	−	0.353771i	0.507740	−	0.861510i	$-0.330481\pi$
$397$	−7.04883	−	7.04883i	−0.353771	−	0.353771i	−0.861510	+	0.507740i	$0.830481\pi$
$398$	−5.50298	+	0.225383i	−0.275840	+	0.0112975i
$399$	5.92585			0.296664
$400$	0.311229	+	1.88379i	0.0155614	+	0.0941897i
$401$	2.74065			0.136861			0.0684307	−	0.997656i	$-0.478201\pi$
$401$	2.74065			0.136861			0.0684307	+	0.997656i	$0.478201\pi$
$402$	27.2791	−	1.11726i	1.36056	−	0.0557238i
$403$	−23.3864	−	23.3864i	−1.16496	−	1.16496i
$404$	−17.3734	+	20.4792i	−0.864358	+	1.01888i
$405$	−13.9639	+	13.9639i	−0.693869	+	0.693869i
$406$	−9.34678	−	8.61128i	−0.463873	−	0.427371i
$407$		−	11.1362i		−	0.552001i
$408$	−4.22686	+	5.41714i	−0.209261	+	0.268189i
$409$		−	22.3601i		−	1.10563i	−0.833303	−	0.552817i	$-0.813553\pi$
$409$		−	22.3601i		−	1.10563i	0.833303	−	0.552817i	$-0.186447\pi$
$410$	24.0139	−	26.0649i	1.18596	−	1.28725i
$411$	−32.2703	+	32.2703i	−1.59178	+	1.59178i
$412$	−2.49522	−	30.4106i	−0.122931	−	1.49822i
$413$	0.0997120	+	0.0997120i	0.00490651	+	0.00490651i
$414$	0.564628	+	13.7860i	0.0277500	+	0.677546i
$415$	10.7079			0.525629
$416$	14.9179	−	22.7333i	0.731410	−	1.11459i
$417$	−29.6800			−1.45344
$418$	0.141915	+	3.46500i	0.00694127	+	0.169479i
$419$	12.2019	+	12.2019i	0.596101	+	0.596101i	0.939273	−	0.343172i	$-0.111501\pi$
$419$	12.2019	+	12.2019i	0.596101	+	0.596101i	−0.343172	+	0.939273i	$0.611501\pi$
$420$	1.34631	+	16.4082i	0.0656932	+	0.800640i
$421$	15.9302	−	15.9302i	0.776388	−	0.776388i	−0.202826	−	0.979215i	$-0.565013\pi$
$421$	15.9302	−	15.9302i	0.776388	−	0.776388i	0.979215	+	0.202826i	$0.0650127\pi$
$422$	4.13794	−	4.49137i	0.201432	−	0.218636i
$423$		−	10.9464i		−	0.532233i
$424$	15.8311	+	12.3526i	0.768828	+	0.599897i
$425$			0.477333i			0.0231540i
$426$	25.0200	+	23.0511i	1.21222	+	1.11683i
$427$	2.14252	−	2.14252i	0.103684	−	0.103684i
$428$	10.4350	−	12.3004i	0.504392	−	0.594563i
$429$	13.2254	+	13.2254i	0.638527	+	0.638527i
$430$	21.2635	−	0.870881i	1.02542	−	0.0419976i
$431$	12.9631			0.624408			0.312204	−	0.950015i	$-0.398933\pi$
$431$	12.9631			0.624408			0.312204	+	0.950015i	$0.398933\pi$
$432$	0.557585	−	0.778290i	0.0268268	−	0.0374455i
$433$	16.3983			0.788051			0.394026	−	0.919099i	$-0.371082\pi$
$433$	16.3983			0.788051			0.394026	+	0.919099i	$0.371082\pi$
$434$	−15.4914	+	0.634475i	−0.743611	+	0.0304558i
$435$	20.6037	+	20.6037i	0.987870	+	0.987870i
$436$	−23.7568	−	20.1539i	−1.13774	−	0.965195i
$437$	3.64010	−	3.64010i	0.174130	−	0.174130i
$438$	27.2390	+	25.0955i	1.30153	+	1.19911i
$439$			16.8265i			0.803084i	0.915841	+	0.401542i	$0.131526\pi$
$439$			16.8265i			0.803084i	−0.915841	+	0.401542i	$0.868474\pi$
$440$	−9.56209	+	1.18017i	−0.455855	+	0.0562626i
$441$			12.9441i			0.616387i
$442$	4.60600	−	4.99940i	0.219085	−	0.237797i
$443$	−11.7630	+	11.7630i	−0.558878	+	0.558878i	−0.928988	−	0.370110i	$-0.879320\pi$
$443$	−11.7630	+	11.7630i	−0.558878	+	0.558878i	0.370110	+	0.928988i	$0.379320\pi$
$444$	−33.6664	+	2.76236i	−1.59774	+	0.131096i
$445$	23.2347	+	23.2347i	1.10143	+	1.10143i
$446$	1.58868	+	38.7893i	0.0752261	+	1.83673i
$447$	25.6343			1.21246
$448$	−3.09927	−	12.3643i	−0.146427	−	0.584158i
$449$	−30.1205			−1.42147			−0.710737	−	0.703458i	$-0.751638\pi$
$449$	−30.1205			−1.42147			−0.710737	+	0.703458i	$0.751638\pi$
$450$	0.0801520	+	1.95700i	0.00377840	+	0.0922538i
$451$	−13.3465	−	13.3465i	−0.628464	−	0.628464i
$452$	−13.2954	+	1.09089i	−0.625361	+	0.0513114i
$453$	34.9913	−	34.9913i	1.64403	−	1.64403i
$454$	0.0318632	−	0.0345847i	0.00149542	−	0.00162314i
$455$		−	16.2877i		−	0.763577i
$456$	10.4400	−	1.28853i	0.488899	−	0.0603409i
$457$			19.0863i			0.892819i	0.894829	+	0.446409i	$0.147298\pi$
$457$			19.0863i			0.892819i	−0.894829	+	0.446409i	$0.852702\pi$
$458$	4.56943	+	4.20986i	0.213516	+	0.196714i
$459$	0.169248	−	0.169248i	0.00789982	−	0.00789982i
$460$	10.9062	+	9.25217i	0.508503	+	0.431384i
$461$	27.8285	+	27.8285i	1.29610	+	1.29610i	0.930948	+	0.365153i	$0.118983\pi$
$461$	27.8285	+	27.8285i	1.29610	+	1.29610i	0.365153	+	0.930948i	$0.381017\pi$
$462$	8.76065	−	0.358806i	0.407582	−	0.0166932i
$463$	−23.5223			−1.09318			−0.546588	−	0.837402i	$-0.684073\pi$
$463$	−23.5223			−1.09318			−0.546588	+	0.837402i	$0.684073\pi$
$464$	−18.3394	−	13.1388i	−0.851384	−	0.609951i
$465$	35.5472			1.64846
$466$	29.8475	−	1.22245i	1.38266	−	0.0566289i
$467$	28.6466	+	28.6466i	1.32561	+	1.32561i	0.909159	+	0.416449i	$0.136725\pi$
$467$	28.6466	+	28.6466i	1.32561	+	1.32561i	0.416449	+	0.909159i	$0.363275\pi$
$468$	18.0445	−	21.2703i	0.834107	−	0.983220i
$469$	−8.95356	+	8.95356i	−0.413437	+	0.413437i
$470$	−8.34487	−	7.68821i	−0.384920	−	0.354631i
$471$		−	27.8834i		−	1.28480i
$472$	0.197352	+	0.153989i	0.00908385	+	0.00708790i
$473$		−	11.3339i		−	0.521134i
$474$	−12.0476	+	13.0766i	−0.553363	+	0.600627i
$475$	0.516731	−	0.516731i	0.0237093	−	0.0237093i
$476$	−0.260596	−	3.17603i	−0.0119444	−	0.145573i
$477$	14.5655	+	14.5655i	0.666908	+	0.666908i
$478$	0.360257	+	8.79607i	0.0164778	+	0.402323i
$479$	−31.8615			−1.45579			−0.727895	−	0.685689i	$-0.759501\pi$
$479$	−31.8615			−1.45579			−0.727895	+	0.685689i	$0.759501\pi$
$480$	5.93974	+	28.6149i	0.271111	+	1.30609i
$481$	33.4190			1.52378
$482$	0.866733	+	21.1622i	0.0394786	+	0.963914i
$483$	−9.20336	−	9.20336i	−0.418767	−	0.418767i
$484$	−1.37947	−	16.8123i	−0.0627030	−	0.764197i
$485$	1.16383	−	1.16383i	0.0528467	−	0.0528467i
$486$	20.9280	−	22.7155i	0.949315	−	1.03040i
$487$		−	15.1869i		−	0.688183i	−0.938936	−	0.344092i	$-0.888187\pi$
$487$		−	15.1869i		−	0.688183i	0.938936	−	0.344092i	$-0.111813\pi$
$488$	3.30877	−	4.24052i	0.149781	−	0.191959i
$489$		−	59.7561i		−	2.70227i
$490$	9.86781	+	9.09131i	0.445782	+	0.410703i
$491$	−4.06438	+	4.06438i	−0.183423	+	0.183423i	−0.792846	−	0.609423i	$-0.791401\pi$
$491$	−4.06438	+	4.06438i	−0.183423	+	0.183423i	0.609423	+	0.792846i	$0.291401\pi$
$492$	−37.0380	+	43.6592i	−1.66980	+	1.96831i
$493$	−3.98811	−	3.98811i	−0.179615	−	0.179615i
$494$	−10.3982	+	0.425876i	−0.467839	+	0.0191611i
$495$	−9.88346			−0.444229
$496$	−27.1544	+	4.48628i	−1.21927	+	0.201440i
$497$	−15.7779			−0.707736
$498$	−17.2837	+	0.707882i	−0.774502	+	0.0317210i
$499$	−16.7030	−	16.7030i	−0.747731	−	0.747731i	0.226322	−	0.974053i	$-0.427330\pi$
$499$	−16.7030	−	16.7030i	−0.747731	−	0.747731i	−0.974053	+	0.226322i	$0.927330\pi$
$500$	17.7653	+	15.0710i	0.794488	+	0.673997i
$501$	18.3007	−	18.3007i	0.817616	−	0.817616i
$502$	6.81118	+	6.27520i	0.303998	+	0.280076i
$503$			1.97642i			0.0881241i	0.999029	+	0.0440621i	$0.0140299\pi$
$503$			1.97642i			0.0881241i	−0.999029	+	0.0440621i	$0.985970\pi$
$504$	−1.60172	−	12.9775i	−0.0713461	−	0.578065i
$505$			28.5565i			1.27075i
$506$	5.16104	−	5.60185i	0.229436	−	0.249033i
$507$	−17.3575	+	17.3575i	−0.770872	+	0.770872i
$508$	−30.7416	+	2.52237i	−1.36394	+	0.111912i
$509$	−23.0549	−	23.0549i	−1.02189	−	1.02189i	−0.999755	−	0.0221346i	$-0.992954\pi$
$509$	−23.0549	−	23.0549i	−1.02189	−	1.02189i	−0.0221346	−	0.999755i	$-0.507046\pi$
$510$	0.298987	+	7.30010i	0.0132394	+	0.323254i
$511$	−17.1772			−0.759877
$512$	−8.14873	−	21.1092i	−0.360126	−	0.932904i
$513$	−0.366435			−0.0161785
$514$	0.436257	+	10.6517i	0.0192425	+	0.469827i
$515$	−22.9422	−	22.9422i	−1.01095	−	1.01095i
$516$	−34.2641	+	2.81140i	−1.50839	+	0.123765i
$517$	−4.27299	+	4.27299i	−0.187926	+	0.187926i
$518$	10.6152	−	11.5219i	0.466407	−	0.506243i
$519$		−	38.0648i		−	1.67086i
$520$	−3.54162	−	28.6952i	−0.155310	−	1.25837i
$521$			31.6278i			1.38564i	0.721112	+	0.692819i	$0.243631\pi$
$521$			31.6278i			1.38564i	−0.721112	+	0.692819i	$0.756369\pi$
$522$	−17.0204	−	15.6810i	−0.744961	−	0.686340i
$523$	24.8469	−	24.8469i	1.08648	−	1.08648i	0.0905930	−	0.995888i	$-0.471124\pi$
$523$	24.8469	−	24.8469i	1.08648	−	1.08648i	0.995888	−	0.0905930i	$-0.0288762\pi$
$524$	20.2918	+	17.2144i	0.886452	+	0.752015i
$525$	−1.30647	−	1.30647i	−0.0570188	−	0.0570188i
$526$	−27.2250	+	1.11504i	−1.18707	+	0.0486182i
$527$	−6.88063			−0.299725
$528$	15.3563	−	2.53707i	0.668296	−	0.110412i
$529$	11.6932			0.508401
$530$	21.3339	−	0.873764i	0.926685	−	0.0379539i
$531$	0.181574	+	0.181574i	0.00787965	+	0.00787965i
$532$	−3.15607	+	3.72028i	−0.136833	+	0.161295i
$533$	40.0521	−	40.0521i	1.73485	−	1.73485i
$534$	−39.0395	−	35.9674i	−1.68940	−	1.55646i
$535$		−	17.1519i		−	0.741539i
$536$	−13.8273	+	17.7210i	−0.597247	+	0.765432i
$537$			19.6257i			0.846909i
$538$	9.98811	−	10.8412i	0.430618	−	0.467398i
$539$	5.05281	−	5.05281i	0.217640	−	0.217640i
$540$	−0.0832514	−	1.01463i	−0.00358257	−	0.0436628i
$541$	−3.65961	−	3.65961i	−0.157339	−	0.157339i	0.624047	−	0.781386i	$-0.285487\pi$
$541$	−3.65961	−	3.65961i	−0.157339	−	0.157339i	−0.781386	+	0.624047i	$0.785487\pi$
$542$	−0.188205	−	4.59523i	−0.00808410	−	0.197382i
$543$	2.35677			0.101139
$544$	−1.14971	−	5.53879i	−0.0492936	−	0.237474i
$545$	−33.1268			−1.41899
$546$	1.07675	+	26.2901i	0.0460808	+	1.12511i
$547$	32.0388	+	32.0388i	1.36988	+	1.36988i	0.860601	+	0.509280i	$0.170088\pi$
$547$	32.0388	+	32.0388i	1.36988	+	1.36988i	0.509280	+	0.860601i	$0.329912\pi$
$548$	−3.07251	−	37.4464i	−0.131251	−	1.59963i
$549$	3.90150	−	3.90150i	0.166512	−	0.166512i
$550$	0.732637	−	0.795212i	0.0312397	−	0.0339080i
$551$			8.63457i			0.367845i
$552$	−18.2154	−	14.2130i	−0.775301	−	0.604948i
$553$		−	8.24625i		−	0.350666i
$554$	−17.8786	−	16.4717i	−0.759590	−	0.699818i
$555$	−25.3984	+	25.3984i	−1.07810	+	1.07810i
$556$	15.8074	−	18.6333i	0.670383	−	0.790227i
$557$	9.02235	+	9.02235i	0.382289	+	0.382289i	0.871926	−	0.489637i	$-0.162871\pi$
$557$	9.02235	+	9.02235i	0.382289	+	0.382289i	−0.489637	+	0.871926i	$0.662871\pi$
$558$	−28.2096	+	1.15537i	−1.19421	+	0.0489107i
$559$	34.0123			1.43857
$560$	−11.0182	−	7.89372i	−0.465605	−	0.333570i
$561$	3.89111			0.164283
$562$	27.5404	−	1.12796i	1.16172	−	0.0475802i
$563$	2.59414	+	2.59414i	0.109330	+	0.109330i	0.759656	−	0.650326i	$-0.225368\pi$
$563$	2.59414	+	2.59414i	0.109330	+	0.109330i	−0.650326	+	0.759656i	$0.725368\pi$
$564$	13.9778	+	11.8580i	0.588572	+	0.499311i
$565$	−10.0302	+	10.0302i	−0.421973	+	0.421973i
$566$	21.6851	+	19.9787i	0.911495	+	0.839769i
$567$			14.7957i			0.621360i
$568$	−27.7971	+	3.43078i	−1.16634	+	0.143952i
$569$			22.4094i			0.939450i	0.882813	+	0.469725i	$0.155647\pi$
$569$			22.4094i			0.939450i	−0.882813	+	0.469725i	$0.844353\pi$
$570$	7.57898	−	8.22631i	0.317448	−	0.344562i
$571$	−12.7315	+	12.7315i	−0.532797	+	0.532797i	−0.921404	−	0.388607i	$-0.872956\pi$
$571$	−12.7315	+	12.7315i	−0.532797	+	0.532797i	0.388607	+	0.921404i	$0.372956\pi$
$572$	−15.3467	+	1.25921i	−0.641679	+	0.0526503i
$573$	−35.2165	−	35.2165i	−1.47119	−	1.47119i
$574$	−1.08662	−	26.5310i	−0.0453546	−	1.10738i
$575$	−1.60506			−0.0669355
$576$	−5.64372	−	22.5152i	−0.235155	−	0.938134i
$577$	6.07021			0.252706			0.126353	−	0.991985i	$-0.459673\pi$
$577$	6.07021			0.252706			0.126353	+	0.991985i	$0.459673\pi$
$578$	−0.0578728	−	1.41303i	−0.00240719	−	0.0587743i
$579$	8.66381	+	8.66381i	0.360056	+	0.360056i
$580$	−23.9085	+	1.96171i	−0.992746	+	0.0814556i
$581$	5.67287	−	5.67287i	0.235350	−	0.235350i
$582$	−1.80161	+	1.95549i	−0.0746791	+	0.0810576i
$583$		−	11.3714i		−	0.470957i
$584$	−30.2624	+	3.73506i	−1.25227	+	0.154558i
$585$		−	29.6596i		−	1.22627i
$586$	1.11097	+	1.02355i	0.0458939	+	0.0422825i
$587$	15.9119	−	15.9119i	0.656753	−	0.656753i	−0.297858	−	0.954610i	$-0.596272\pi$
$587$	15.9119	−	15.9119i	0.656753	−	0.656753i	0.954610	+	0.297858i	$0.0962721\pi$
$588$	−16.5288	−	14.0220i	−0.681635	−	0.578260i
$589$	7.44855	+	7.44855i	0.306912	+	0.306912i
$590$	0.265950	−	0.0108924i	0.0109490	−	0.000448432i
$591$	7.96614			0.327683
$592$	16.1963	−	22.6072i	0.665665	−	0.929150i
$593$	−37.3707			−1.53463			−0.767315	−	0.641271i	$-0.778408\pi$
$593$	−37.3707			−1.53463			−0.767315	+	0.641271i	$0.778408\pi$
$594$	−0.541730	+	0.0221874i	−0.0222274	+	0.000910360i
$595$	−2.39604	−	2.39604i	−0.0982280	−	0.0982280i
$596$	−13.6527	+	16.0933i	−0.559235	+	0.659209i
$597$	6.68979	−	6.68979i	0.273795	−	0.273795i
$598$	16.8108	+	15.4879i	0.687444	+	0.633349i
$599$		−	26.9527i		−	1.10126i	−0.834750	−	0.550628i	$-0.814388\pi$
$599$		−	26.9527i		−	1.10126i	0.834750	−	0.550628i	$-0.185612\pi$
$600$	−2.58578	−	2.01762i	−0.105564	−	0.0823689i
$601$		−	11.5256i		−	0.470139i	−0.971979	−	0.235070i	$-0.924468\pi$
$601$		−	11.5256i		−	0.470139i	0.971979	−	0.235070i	$-0.0755318\pi$
$602$	10.8037	−	11.7265i	0.440326	−	0.477935i
$603$	−16.3043	+	16.3043i	−0.663963	+	0.663963i
$604$	3.33158	+	40.6039i	0.135560	+	1.65215i
$605$	−12.6834	−	12.6834i	−0.515655	−	0.515655i
$606$	−1.88783	−	46.0934i	−0.0766878	−	1.87242i
$607$	26.2561			1.06570			0.532852	−	0.846209i	$-0.321120\pi$
$607$	26.2561			1.06570			0.532852	+	0.846209i	$0.321120\pi$
$608$	−4.75135	+	7.24057i	−0.192693	+	0.293644i
$609$	21.8310			0.884637
$610$	−0.234046	−	5.71448i	−0.00947624	−	0.231373i
$611$	−12.8230	−	12.8230i	−0.518761	−	0.518761i
$612$	−0.474542	−	5.78351i	−0.0191822	−	0.233784i
$613$	1.48845	−	1.48845i	0.0601181	−	0.0601181i	−0.676409	−	0.736527i	$-0.736465\pi$
$613$	1.48845	−	1.48845i	0.0601181	−	0.0601181i	0.736527	+	0.676409i	$0.236465\pi$
$614$	6.70230	−	7.27475i	0.270483	−	0.293585i
$615$			60.8791i			2.45488i
$616$	−4.44061	+	5.69108i	−0.178917	+	0.229300i
$617$			11.0405i			0.444474i	0.974993	+	0.222237i	$0.0713358\pi$
$617$			11.0405i			0.444474i	−0.974993	+	0.222237i	$0.928664\pi$
$618$	38.5480	+	35.5146i	1.55063	+	1.42861i
$619$	−16.0499	+	16.0499i	−0.645100	+	0.645100i	−0.951805	−	0.306705i	$-0.900774\pi$
$619$	−16.0499	+	16.0499i	−0.645100	+	0.645100i	0.306705	+	0.951805i	$0.400774\pi$
$620$	−18.9322	+	22.3167i	−0.760337	+	0.896262i
$621$	0.569106	+	0.569106i	0.0228374	+	0.0228374i
$622$	18.7360	−	0.767361i	0.751244	−	0.0307684i
$623$	24.6188			0.986331
$624$	7.61358	+	46.0831i	0.304787	+	1.84480i
$625$	22.3855			0.895420
$626$	−46.6829	+	1.91197i	−1.86583	+	0.0764178i
$627$	−4.21228	−	4.21228i	−0.168222	−	0.168222i
$628$	17.5054	+	14.8506i	0.698541	+	0.592602i
$629$	4.91619	−	4.91619i	0.196021	−	0.196021i
$630$	−10.2258	−	9.42110i	−0.407404	−	0.375346i
$631$			33.0601i			1.31610i	0.752973	+	0.658051i	$0.228619\pi$
$631$			33.0601i			1.31610i	−0.752973	+	0.658051i	$0.771381\pi$
$632$	−1.79308	−	14.5280i	−0.0713250	−	0.577895i
$633$			10.4904i			0.416954i
$634$	−16.5793	+	17.9954i	−0.658448	+	0.714687i
$635$	−23.1919	+	23.1919i	−0.920341	+	0.920341i
$636$	−34.3776	+	2.82071i	−1.36316	+	0.111848i
$637$	15.1631	+	15.1631i	0.600786	+	0.600786i
$638$	0.522817	+	12.7652i	0.0206985	+	0.505377i
$639$	−28.7314			−1.13660
$640$	−21.1281	−	11.5111i	−0.835160	−	0.455017i
$641$	9.72183			0.383989			0.191995	−	0.981396i	$-0.438504\pi$
$641$	9.72183			0.383989			0.191995	+	0.981396i	$0.438504\pi$
$642$	1.13388	+	27.6850i	0.0447508	+	1.09264i
$643$	−31.4019	−	31.4019i	−1.23837	−	1.23837i	−0.960667	−	0.277704i	$-0.910426\pi$
$643$	−31.4019	−	31.4019i	−1.23837	−	1.23837i	−0.277704	−	0.960667i	$-0.589574\pi$
$644$	10.6796	−	0.876268i	0.420834	−	0.0345298i
$645$	−25.8493	+	25.8493i	−1.01782	+	1.01782i
$646$	−1.46701	+	1.59231i	−0.0577187	+	0.0626486i
$647$		−	16.6269i		−	0.653670i	−0.945081	−	0.326835i	$-0.894018\pi$
$647$		−	16.6269i		−	0.653670i	0.945081	−	0.326835i	$-0.105982\pi$
$648$	3.21720	+	26.0666i	0.126384	+	1.02399i
$649$		−	0.141757i		−	0.00556444i
$650$	2.38638	+	2.19859i	0.0936015	+	0.0862359i
$651$	18.8324	−	18.8324i	0.738099	−	0.738099i
$652$	37.5153	+	31.8258i	1.46921	+	1.24639i
$653$	6.25098	+	6.25098i	0.244620	+	0.244620i	0.818758	−	0.574139i	$-0.194663\pi$
$653$	6.25098	+	6.25098i	0.244620	+	0.244620i	−0.574139	+	0.818758i	$0.694663\pi$
$654$	53.4703	−	2.18996i	2.09086	−	0.0856343i
$655$	28.2952			1.10558
$656$	−7.68333	−	46.5053i	−0.299983	−	1.81573i
$657$	−31.2795			−1.22033
$658$	−8.49408	+	0.347888i	−0.331134	+	0.0135621i
$659$	9.99625	+	9.99625i	0.389399	+	0.389399i	0.874473	−	0.485074i	$-0.161207\pi$
$659$	9.99625	+	9.99625i	0.389399	+	0.389399i	−0.485074	+	0.874473i	$0.661207\pi$
$660$	10.7065	−	12.6205i	0.416750	−	0.491252i
$661$	14.3803	−	14.3803i	0.559330	−	0.559330i	−0.369787	−	0.929117i	$-0.620569\pi$
$661$	14.3803	−	14.3803i	0.559330	−	0.559330i	0.929117	+	0.369787i	$0.120569\pi$
$662$	−1.87322	−	1.72582i	−0.0728049	−	0.0670759i
$663$			11.6770i			0.453496i
$664$	8.76080	−	11.2278i	0.339985	−	0.435725i
$665$			5.18762i			0.201167i
$666$	19.3302	−	20.9812i	0.749030	−	0.813006i
$667$	13.4102	−	13.4102i	0.519246	−	0.519246i
$668$	1.74245	+	21.2362i	0.0674172	+	0.821652i
$669$	−47.1549	−	47.1549i	−1.82311	−	1.82311i
$670$	0.978073	+	23.8807i	0.0377862	+	0.922593i
$671$	−3.04594			−0.117587
$672$	18.3065	+	12.0129i	0.706189	+	0.463410i
$673$	−26.6392			−1.02687			−0.513433	−	0.858129i	$-0.671627\pi$
$673$	−26.6392			−1.02687			−0.513433	+	0.858129i	$0.671627\pi$
$674$	1.15380	+	28.1712i	0.0444426	+	1.08511i
$675$	0.0807876	+	0.0807876i	0.00310951	+	0.00310951i
$676$	−1.65263	−	20.1416i	−0.0635629	−	0.774677i
$677$	−7.71971	+	7.71971i	−0.296693	+	0.296693i	−0.839717	−	0.543024i	$-0.817279\pi$
$677$	−7.71971	+	7.71971i	−0.296693	+	0.296693i	0.543024	+	0.839717i	$0.317279\pi$
$678$	15.5268	−	16.8529i	0.596302	−	0.647233i
$679$		−	1.23316i		−	0.0473242i
$680$	−4.74228	−	3.70028i	−0.181858	−	0.141899i
$681$			0.0807785i			0.00309544i
$682$	11.4628	+	10.5608i	0.438933	+	0.404393i
$683$	32.0068	−	32.0068i	1.22471	−	1.22471i	0.258768	−	0.965939i	$-0.416683\pi$
$683$	32.0068	−	32.0068i	1.22471	−	1.22471i	0.965939	−	0.258768i	$-0.0833167\pi$
$684$	−5.74717	+	6.77459i	−0.219748	+	0.259033i
$685$	−28.2501	−	28.2501i	−1.07938	−	1.07938i
$686$	25.8044	−	1.05686i	0.985217	−	0.0403511i
$687$	−10.6727			−0.407188
$688$	16.4839	−	23.0086i	0.628442	−	0.877194i
$689$	34.1249			1.30006
$690$	−24.5470	+	1.00536i	−0.934487	+	0.0382734i
$691$	−2.27124	−	2.27124i	−0.0864022	−	0.0864022i	0.662585	−	0.748987i	$-0.269459\pi$
$691$	−2.27124	−	2.27124i	−0.0864022	−	0.0864022i	−0.748987	+	0.662585i	$0.769459\pi$
$692$	23.8973	+	20.2731i	0.908438	+	0.770666i
$693$	−5.23611	+	5.23611i	−0.198903	+	0.198903i
$694$	−28.5917	−	26.3418i	−1.08532	−	0.999920i
$695$		−	25.9825i		−	0.985573i
$696$	38.4613	−	4.74698i	1.45787	−	0.179934i
$697$		−	11.7839i		−	0.446348i
$698$	11.8535	−	12.8659i	0.448660	−	0.486980i
$699$	−36.2846	+	36.2846i	−1.37241	+	1.37241i
$700$	1.51602	−	0.124391i	0.0573003	−	0.00470153i
$701$	14.1367	+	14.1367i	0.533934	+	0.533934i	0.921741	−	0.387807i	$-0.126767\pi$
$701$	14.1367	+	14.1367i	0.533934	+	0.533934i	−0.387807	+	0.921741i	$0.626767\pi$
$702$	−0.0665829	−	1.62570i	−0.00251301	−	0.0613579i
$703$	−10.6439			−0.401444
$704$	−6.58587	+	10.9920i	−0.248214	+	0.414276i
$705$	19.4909			0.734068
$706$	1.52702	+	37.2838i	0.0574701	+	1.40320i
$707$	15.1288	+	15.1288i	0.568977	+	0.568977i
$708$	−0.428553	+	0.0351631i	−0.0161060	+	0.00132151i
$709$	−19.0113	+	19.0113i	−0.713986	+	0.713986i	−0.967367	−	0.253381i	$-0.918458\pi$
$709$	−19.0113	+	19.0113i	−0.713986	+	0.713986i	0.253381	+	0.967367i	$0.418458\pi$
$710$	−20.1795	+	21.9030i	−0.757322	+	0.822005i
$711$		−	15.0163i		−	0.563156i
$712$	43.3728	−	5.35316i	1.62546	−	0.200618i
$713$		−	23.1365i		−	0.866468i
$714$	4.02588	+	3.70908i	0.150665	+	0.138809i
$715$	−11.5778	+	11.5778i	−0.432984	+	0.432984i
$716$	−12.3211	−	10.4525i	−0.460461	−	0.390629i
$717$	−10.6931	−	10.6931i	−0.399341	−	0.399341i
$718$	6.73287	−	0.275756i	0.251269	−	0.0102911i
$719$	−25.0655			−0.934785			−0.467393	−	0.884050i	$-0.654807\pi$
$719$	−25.0655			−0.934785			−0.467393	+	0.884050i	$0.654807\pi$
$720$	−20.0641	−	14.3744i	−0.747743	−	0.535700i
$721$	−24.3088			−0.905308
$722$	−23.5357	+	0.963943i	−0.875909	+	0.0358742i
$723$	−25.7262	−	25.7262i	−0.956768	−	0.956768i
$724$	−1.25520	+	1.47960i	−0.0466492	+	0.0549887i
$725$	1.90365	−	1.90365i	0.0706999	−	0.0706999i
$726$	21.3110	+	19.6340i	0.790925	+	0.728687i
$727$		−	15.3521i		−	0.569379i	−0.958620	−	0.284689i	$-0.908110\pi$
$727$		−	15.3521i		−	0.569379i	0.958620	−	0.284689i	$-0.0918904\pi$
$728$	−17.0786	−	13.3260i	−0.632974	−	0.493893i
$729$			25.1983i			0.933272i
$730$	−21.9692	+	23.8456i	−0.813115	+	0.882565i
$731$	5.00347	−	5.00347i	0.185060	−	0.185060i
$732$	0.755553	+	9.20835i	0.0279260	+	0.340350i
$733$	9.88115	+	9.88115i	0.364969	+	0.364969i	0.865638	−	0.500670i	$-0.166913\pi$
$733$	9.88115	+	9.88115i	0.364969	+	0.364969i	−0.500670	+	0.865638i	$0.666913\pi$
$734$	−1.32316	−	32.3065i	−0.0488389	−	1.19246i
$735$	−23.0479			−0.850136
$736$	18.6245	−	3.86598i	0.686507	−	0.142502i
$737$	12.7289			0.468877
$738$	−1.97872	−	48.3125i	−0.0728376	−	1.77841i
$739$	7.88121	+	7.88121i	0.289915	+	0.289915i	0.837047	−	0.547132i	$-0.184280\pi$
$739$	7.88121	+	7.88121i	0.289915	+	0.289915i	−0.547132	+	0.837047i	$0.684280\pi$
$740$	−2.41823	−	29.4723i	−0.0888958	−	1.08342i
$741$	12.6408	−	12.6408i	0.464370	−	0.464370i
$742$	10.8395	−	11.7653i	0.397929	−	0.431917i
$743$			51.5709i			1.89195i	0.324235	+	0.945977i	$0.394893\pi$
$743$			51.5709i			1.89195i	−0.324235	+	0.945977i	$0.605107\pi$
$744$	29.0834	−	37.2733i	1.06625	−	1.36651i
$745$			22.4408i			0.822167i
$746$	−12.1196	−	11.1659i	−0.443731	−	0.408814i
$747$	10.3302	−	10.3302i	0.377963	−	0.377963i
$748$	−2.07238	+	2.44286i	−0.0757738	+	0.0893199i
$749$	−9.08679	−	9.08679i	−0.332024	−	0.332024i
$750$	−39.9851	+	1.63765i	−1.46005	+	0.0597986i
$751$	16.1881			0.590712			0.295356	−	0.955387i	$-0.404562\pi$
$751$	16.1881			0.590712			0.295356	+	0.955387i	$0.404562\pi$
$752$	−14.8890	+	2.45987i	−0.542946	+	0.0897023i
$753$	−15.9087			−0.579744
$754$	−38.3074	+	1.56894i	−1.39507	+	0.0571374i
$755$	30.6321	+	30.6321i	1.11482	+	1.11482i
$756$	−0.581642	−	0.493431i	−0.0211541	−	0.0179459i
$757$	−15.8949	+	15.8949i	−0.577712	+	0.577712i	−0.934272	−	0.356561i	$-0.883949\pi$
$757$	−15.8949	+	15.8949i	−0.577712	+	0.577712i	0.356561	+	0.934272i	$0.383949\pi$
$758$	10.5384	+	9.70911i	0.382771	+	0.352651i
$759$			13.0841i			0.474922i
$760$	1.12801	+	9.13941i	0.0409171	+	0.331521i
$761$		−	34.1373i		−	1.23748i	−0.785598	−	0.618738i	$-0.787644\pi$
$761$		−	34.1373i		−	1.23748i	0.785598	−	0.618738i	$-0.212356\pi$
$762$	35.9011	−	38.9675i	1.30056	−	1.41164i
$763$	−17.5501	+	17.5501i	−0.635355	+	0.635355i
$764$	40.8653	−	3.35303i	1.47845	−	0.121308i
$765$	−4.36316	−	4.36316i	−0.157750	−	0.157750i
$766$	1.30146	+	31.7766i	0.0470237	+	1.14814i
$767$	0.425403			0.0153604
$768$	34.8641	+	17.1835i	1.25805	+	0.620056i
$769$	0.762415			0.0274934			0.0137467	−	0.999906i	$-0.495624\pi$
$769$	0.762415			0.0274934			0.0137467	+	0.999906i	$0.495624\pi$
$770$	0.314107	+	7.66926i	0.0113196	+	0.276381i
$771$	−12.9489	−	12.9489i	−0.466344	−	0.466344i
$772$	−10.0535	+	0.824896i	−0.361833	+	0.0296887i
$773$	14.6272	−	14.6272i	0.526106	−	0.526106i	−0.393303	−	0.919409i	$-0.628668\pi$
$773$	14.6272	−	14.6272i	0.526106	−	0.526106i	0.919409	+	0.393303i	$0.128668\pi$
$774$	19.6734	−	21.3537i	0.707146	−	0.767544i
$775$		−	3.28435i		−	0.117977i
$776$	−0.268140	−	2.17254i	−0.00962566	−	0.0779898i
$777$			26.9114i			0.965440i
$778$	5.50048	+	5.06764i	0.197202	+	0.181684i
$779$	−12.7566	+	12.7566i	−0.457052	+	0.457052i
$780$	37.8733	+	32.1295i	1.35608	+	1.15042i
$781$	11.2154	+	11.2154i	0.401320	+	0.401320i
$782$	4.75139	−	0.194601i	0.169909	−	0.00695890i
$783$	−1.34996			−0.0482436
$784$	17.6063	−	2.90880i	0.628795	−	0.103886i
$785$	24.4098			0.871222
$786$	−45.6716	+	1.87055i	−1.62905	+	0.0667205i
$787$	−0.673156	−	0.673156i	−0.0239954	−	0.0239954i	0.695007	−	0.719003i	$-0.255401\pi$
$787$	−0.673156	−	0.673156i	−0.0239954	−	0.0239954i	−0.719003	+	0.695007i	$0.755401\pi$
$788$	−4.24272	+	5.00119i	−0.151141	+	0.178160i
$789$	33.0965	−	33.0965i	1.17827	−	1.17827i
$790$	−11.4475	−	10.5467i	−0.407284	−	0.375235i
$791$			10.6277i			0.377877i
$792$	−8.08629	+	10.3634i	−0.287334	+	0.368247i
$793$		−	9.14068i		−	0.324595i
$794$	−9.55227	+	10.3681i	−0.338997	+	0.367951i
$795$	−25.9349	+	25.9349i	−0.919816	+	0.919816i
$796$	0.636947	+	7.76283i	0.0225760	+	0.275146i
$797$	19.6102	+	19.6102i	0.694629	+	0.694629i	0.963247	−	0.268618i	$-0.0865668\pi$
$797$	19.6102	+	19.6102i	0.694629	+	0.694629i	−0.268618	+	0.963247i	$0.586567\pi$
$798$	−0.342946	−	8.37340i	−0.0121401	−	0.296415i
$799$	−3.77271			−0.133469
$800$	2.64384	−	0.548796i	0.0934740	−	0.0194029i
$801$	44.8305			1.58401
$802$	−0.158609	−	3.87261i	−0.00560068	−	0.136747i
$803$	12.2101	+	12.2101i	0.430886	+	0.430886i
$804$	−3.15744	−	38.4815i	−0.111354	−	1.35714i
$805$	8.05682	−	8.05682i	0.283965	−	0.283965i
$806$	−31.6922	+	34.3990i	−1.11631	+	1.21165i
$807$			25.3215i			0.891358i
$808$	29.9432	+	23.3639i	1.05340	+	0.821939i
$809$			17.0604i			0.599810i	0.953969	+	0.299905i	$0.0969550\pi$
$809$			17.0604i			0.599810i	−0.953969	+	0.299905i	$0.903045\pi$
$810$	20.5395	+	18.9232i	0.721683	+	0.664893i
$811$	38.2674	−	38.2674i	1.34375	−	1.34375i	0.451458	−	0.892292i	$-0.350904\pi$
$811$	38.2674	−	38.2674i	1.34375	−	1.34375i	0.892292	−	0.451458i	$-0.149096\pi$
$812$	−11.6271	+	13.7056i	−0.408030	+	0.480973i
$813$	5.58627	+	5.58627i	0.195919	+	0.195919i
$814$	−15.7358	+	0.644484i	−0.551539	+	0.0225891i
$815$	52.3118			1.83240
$816$	7.89920	+	5.65917i	0.276527	+	0.198111i
$817$	−10.8329			−0.378996
$818$	−31.5954	+	1.29404i	−1.10471	+	0.0452451i
$819$	−15.7132	−	15.7132i	−0.549064	−	0.549064i
$820$	−38.2202	−	32.4238i	−1.33471	−	1.13229i
$821$	−12.4187	+	12.4187i	−0.433416	+	0.433416i	−0.889789	−	0.456373i	$-0.849148\pi$
$821$	−12.4187	+	12.4187i	−0.433416	+	0.433416i	0.456373	+	0.889789i	$0.349148\pi$
$822$	47.4664	+	43.7313i	1.65558	+	1.52530i
$823$		−	20.4049i		−	0.711271i	−0.934625	−	0.355635i	$-0.884264\pi$
$823$		−	20.4049i		−	0.711271i	0.934625	−	0.355635i	$-0.115736\pi$
$824$	−42.8267	+	5.28576i	−1.49194	+	0.184138i
$825$			1.85735i			0.0646647i
$826$	0.135125	−	0.146667i	0.00470161	−	0.00510318i
$827$	−14.8596	+	14.8596i	−0.516721	+	0.516721i	−0.916578	−	0.399857i	$-0.869060\pi$
$827$	−14.8596	+	14.8596i	−0.516721	+	0.516721i	0.399857	+	0.916578i	$0.369060\pi$
$828$	19.4474	−	1.59567i	0.675843	−	0.0554534i
$829$	1.04893	+	1.04893i	0.0364308	+	0.0364308i	0.725088	−	0.688657i	$-0.241799\pi$
$829$	1.04893	+	1.04893i	0.0364308	+	0.0364308i	−0.688657	+	0.725088i	$0.741799\pi$
$830$	−0.619695	−	15.1305i	−0.0215099	−	0.525189i
$831$	41.7586			1.44859
$832$	−32.9862	−	19.7638i	−1.14359	−	0.685185i
$833$	4.46123			0.154572
$834$	1.71767	+	41.9387i	0.0594779	+	1.45222i
$835$	16.0209	+	16.0209i	0.554424	+	0.554424i
$836$	4.88793	−	0.401059i	0.169053	−	0.0138709i
$837$	−1.16453	+	1.16453i	−0.0402521	+	0.0402521i
$838$	16.5355	−	17.9478i	0.571208	−	0.619996i
$839$			25.3130i			0.873902i	0.899485	+	0.436951i	$0.143942\pi$
$839$			25.3130i			0.873902i	−0.899485	+	0.436951i	$0.856058\pi$
$840$	23.1074	−	2.85197i	0.797281	−	0.0984022i
$841$			2.80998i			0.0968959i
$842$	−23.4317	−	21.5879i	−0.807510	−	0.743967i
$843$	−33.4799	+	33.4799i	−1.15311	+	1.15311i
$844$	−6.58591	−	5.58710i	−0.226696	−	0.192316i
$845$	−15.1951	−	15.1951i	−0.522727	−	0.522727i
$846$	−15.4676	+	0.633500i	−0.531787	+	0.0217802i
$847$	−13.4390			−0.461769
$848$	16.5384	−	23.0847i	0.567932	−	0.792733i
$849$	−50.6493			−1.73828
$850$	0.674485	−	0.0276246i	0.0231346	−	0.000947516i
$851$	16.5310	+	16.5310i	0.566674	+	0.566674i
$852$	31.1239	−	36.6880i	1.06629	−	1.25691i
$853$	−13.4083	+	13.4083i	−0.459093	+	0.459093i	−0.898358	−	0.439265i	$-0.855239\pi$
$853$	−13.4083	+	13.4083i	−0.459093	+	0.459093i	0.439265	+	0.898358i	$0.355239\pi$
$854$	−3.15144	−	2.90345i	−0.107840	−	0.0993541i
$855$			9.44658i			0.323066i
$856$	−17.9847	−	14.0330i	−0.614705	−	0.479639i
$857$			46.2915i			1.58129i	0.612277	+	0.790643i	$0.290254\pi$
$857$			46.2915i			1.58129i	−0.612277	+	0.790643i	$0.709746\pi$
$858$	17.9225	−	19.4532i	0.611862	−	0.664122i
$859$	23.3453	−	23.3453i	0.796532	−	0.796532i	−0.186015	−	0.982547i	$-0.559557\pi$
$859$	23.3453	−	23.3453i	0.796532	−	0.796532i	0.982547	+	0.186015i	$0.0595574\pi$
$860$	−2.46116	−	29.9956i	−0.0839249	−	1.02284i
$861$	32.2528	+	32.2528i	1.09917	+	1.09917i
$862$	−0.750209	−	18.3172i	−0.0255522	−	0.623885i
$863$	16.0384			0.545952			0.272976	−	0.962021i	$-0.411992\pi$
$863$	16.0384			0.545952			0.272976	+	0.962021i	$0.411992\pi$
$864$	−1.13202	−	0.742842i	−0.0385119	−	0.0252720i
$865$	33.3227			1.13301
$866$	−0.949015	−	23.1712i	−0.0322488	−	0.787391i
$867$	1.71777	+	1.71777i	0.0583386	+	0.0583386i
$868$	1.79306	+	21.8531i	0.0608605	+	0.741742i
$869$	−5.86170	+	5.86170i	−0.198844	+	0.198844i
$870$	27.9212	−	30.3059i	0.946616	−	1.02747i
$871$			38.1987i			1.29431i
$872$	−27.1031	+	34.7354i	−0.917828	+	1.17629i
$873$		−	2.24556i		−	0.0760007i
$874$	−5.35423	−	4.93290i	−0.181109	−	0.166858i
$875$	13.1239	−	13.1239i	0.443669	−	0.443669i
$876$	33.8843	−	39.9418i	1.14485	−	1.34951i
$877$	−37.9010	−	37.9010i	−1.27983	−	1.27983i	−0.940764	−	0.339062i	$-0.889890\pi$
$877$	−37.9010	−	37.9010i	−1.27983	−	1.27983i	−0.339062	−	0.940764i	$-0.610110\pi$
$878$	23.7763	−	0.973796i	0.802412	−	0.0328640i
$879$	−2.59487			−0.0875228
$880$	2.22100	+	13.4432i	0.0748700	+	0.453170i
$881$	5.98657			0.201693			0.100846	−	0.994902i	$-0.467845\pi$
$881$	5.98657			0.201693			0.100846	+	0.994902i	$0.467845\pi$
$882$	18.2904	−	0.749114i	0.615871	−	0.0252240i
$883$	−35.5929	−	35.5929i	−1.19780	−	1.19780i	−0.974825	−	0.222972i	$-0.928424\pi$
$883$	−35.5929	−	35.5929i	−1.19780	−	1.19780i	−0.222972	−	0.974825i	$-0.571576\pi$
$884$	−7.33087	−	6.21908i	−0.246564	−	0.209170i
$885$	−0.323306	+	0.323306i	−0.0108678	+	0.0108678i
$886$	17.3023	+	15.9407i	0.581281	+	0.535540i
$887$		−	21.3432i		−	0.716633i	−0.933600	−	0.358317i	$-0.883351\pi$
$887$		−	21.3432i		−	0.716633i	0.933600	−	0.358317i	$-0.116649\pi$
$888$	5.85166	+	47.4118i	0.196369	+	1.59103i
$889$			24.5734i			0.824165i
$890$	31.4867	−	34.1760i	1.05544	−	1.14558i
$891$	10.5172	−	10.5172i	0.352340	−	0.352340i
$892$	54.7185	−	4.48970i	1.83211	−	0.150326i
$893$	4.08411	+	4.08411i	0.136669	+	0.136669i
$894$	−1.48353	−	36.2220i	−0.0496166	−	1.21144i
$895$	−17.1807			−0.574288
$896$	−17.2917	+	5.09491i	−0.577677	+	0.170209i
$897$	−39.2644			−1.31100
$898$	1.74316	+	42.5611i	0.0581699	+	1.42028i
$899$	27.4407	+	27.4407i	0.915198	+	0.915198i
$900$	2.76066	−	0.226514i	0.0920219	−	0.00755047i
$901$	5.02004	−	5.02004i	0.167242	−	0.167242i
$902$	−18.0866	+	19.6314i	−0.602219	+	0.653656i
$903$			27.3892i			0.911454i
$904$	2.31091	+	18.7236i	0.0768596	+	0.622737i
$905$			2.06317i			0.0685820i
$906$	−51.4688	−	47.4187i	−1.70994	−	1.57538i
$907$	−23.3789	+	23.3789i	−0.776285	+	0.776285i	−0.979197	−	0.202912i	$-0.934960\pi$
$907$	−23.3789	+	23.3789i	−0.776285	+	0.776285i	0.202912	+	0.979197i	$0.434960\pi$
$908$	−0.0507132	−	0.0430222i	−0.00168298	−	0.00142774i
$909$	27.5493	+	27.5493i	0.913754	+	0.913754i
$910$	−23.0149	+	0.942613i	−0.762938	+	0.0312473i
$911$	7.05642			0.233790			0.116895	−	0.993144i	$-0.462706\pi$
$911$	7.05642			0.233790			0.116895	+	0.993144i	$0.462706\pi$
$912$	−2.42492	−	14.6775i	−0.0802972	−	0.486020i
$913$	−8.06491			−0.266909
$914$	26.9695	−	1.10458i	0.892071	−	0.0365362i
$915$	6.94690	+	6.94690i	0.229657	+	0.229657i
$916$	5.68421	−	6.70038i	0.187812	−	0.221387i
$917$	14.9904	−	14.9904i	0.495025	−	0.495025i
$918$	−0.248947	−	0.229357i	−0.00821648	−	0.00756992i
$919$		−	32.8796i		−	1.08460i	−0.840186	−	0.542299i	$-0.817554\pi$
$919$		−	32.8796i		−	1.08460i	0.840186	−	0.542299i	$-0.182446\pi$
$920$	12.4424	−	15.9462i	0.410214	−	0.525730i
$921$			16.9914i			0.559886i
$922$	37.7119	−	40.9329i	1.24198	−	1.34805i
$923$	−33.6568	+	33.6568i	−1.10783	+	1.10783i
$924$	−1.01401	−	12.3583i	−0.0333584	−	0.406558i
$925$	2.34666	+	2.34666i	0.0771576	+	0.0771576i
$926$	1.36130	+	33.2377i	0.0447352	+	1.09226i
$927$	−44.2661			−1.45389
$928$	−17.5041	+	26.6745i	−0.574600	+	0.875632i
$929$	9.46044			0.310387			0.155194	−	0.987884i	$-0.450400\pi$
$929$	9.46044			0.310387			0.155194	+	0.987884i	$0.450400\pi$
$930$	−2.05722	−	50.2292i	−0.0674588	−	1.64708i
$931$	−4.82946	−	4.82946i	−0.158279	−	0.158279i
$932$	−3.45472	−	42.1046i	−0.113163	−	1.37918i
$933$	−22.7767	+	22.7767i	−0.745674	+	0.745674i
$934$	38.8207	−	42.1364i	1.27025	−	1.37874i
$935$			3.40636i			0.111400i
$936$	−31.0998	−	24.2664i	−1.01653	−	0.793173i
$937$		−	35.9085i		−	1.17308i	−0.809921	−	0.586539i	$-0.800490\pi$
$937$		−	35.9085i		−	1.17308i	0.809921	−	0.586539i	$-0.199510\pi$
$938$	13.1698	+	12.1335i	0.430009	+	0.396172i
$939$	56.7508	−	56.7508i	1.85199	−	1.85199i
$940$	−10.3807	+	12.2365i	−0.338582	+	0.399110i
$941$	−16.2449	−	16.2449i	−0.529568	−	0.529568i	0.390876	−	0.920443i	$-0.372172\pi$
$941$	−16.2449	−	16.2449i	−0.529568	−	0.529568i	−0.920443	+	0.390876i	$0.872172\pi$
$942$	−39.4001	+	1.61369i	−1.28373	+	0.0525770i
$943$	39.6241			1.29034
$944$	0.206169	−	0.287775i	0.00671023	−	0.00936629i
$945$	−0.811050			−0.0263834
$946$	−16.0152	+	0.655926i	−0.520698	+	0.0213260i
$947$	37.2255	+	37.2255i	1.20967	+	1.20967i	0.971134	+	0.238533i	$0.0766666\pi$
$947$	37.2255	+	37.2255i	1.20967	+	1.20967i	0.238533	+	0.971134i	$0.423333\pi$
$948$	19.1748	+	16.2668i	0.622769	+	0.528321i
$949$	−36.6418	+	36.6418i	−1.18944	+	1.18944i
$950$	−0.760061	−	0.700252i	−0.0246596	−	0.0227192i
$951$		−	42.0312i		−	1.36296i
$952$	−4.47274	+	0.552035i	−0.144962	+	0.0178916i
$953$		−	8.64749i		−	0.280120i	−0.990143	−	0.140060i	$-0.955271\pi$
$953$		−	8.64749i		−	0.280120i	0.990143	−	0.140060i	$-0.0447295\pi$
$954$	19.7385	−	21.4244i	0.639058	−	0.693641i
$955$	30.8293	−	30.8293i	0.997613	−	0.997613i
$956$	12.4083	−	1.01811i	0.401312	−	0.0329280i
$957$	−15.5182	−	15.5182i	−0.501631	−	0.501631i
$958$	1.84392	+	45.0212i	0.0595742	+	1.45457i
$959$	−29.9329			−0.966585
$960$	40.0899	−	10.0490i	1.29390	−	0.324332i
$961$	16.3430			0.527194
$962$	−1.93405	−	47.2220i	−0.0623563	−	1.52250i
$963$	−16.5469	−	16.5469i	−0.533217	−	0.533217i
$964$	29.8527	−	2.44944i	0.961491	−	0.0788911i
$965$	−7.58448	+	7.58448i	−0.244153	+	0.244153i
$966$	−12.4720	+	13.5372i	−0.401280	+	0.435553i
$967$			15.5070i			0.498671i	0.968417	+	0.249336i	$0.0802122\pi$
$967$			15.5070i			0.498671i	−0.968417	+	0.249336i	$0.919788\pi$
$968$	−23.6765	+	2.92220i	−0.760991	+	0.0939231i
$969$		−	3.71911i		−	0.119475i
$970$	−1.71188	−	1.57717i	−0.0549650	−	0.0506398i
$971$	−3.46337	+	3.46337i	−0.111145	+	0.111145i	−0.760492	−	0.649347i	$-0.775042\pi$
$971$	−3.46337	+	3.46337i	−0.111145	+	0.111145i	0.649347	+	0.760492i	$0.275042\pi$
$972$	−33.3089	−	28.2573i	−1.06838	−	0.906353i
$973$	−13.7651	−	13.7651i	−0.441290	−	0.441290i
$974$	−21.4595	+	0.878908i	−0.687607	+	0.0281620i
$975$	−5.57379			−0.178504
$976$	−6.18346	−	4.42997i	−0.197928	−	0.141800i
$977$	−48.8549			−1.56301			−0.781503	−	0.623902i	$-0.785547\pi$
$977$	−48.8549			−1.56301			−0.781503	+	0.623902i	$0.785547\pi$
$978$	−84.4371	+	3.45826i	−2.70000	+	0.110583i
$979$	−17.4998	−	17.4998i	−0.559296	−	0.559296i
$980$	12.2752	−	14.4696i	0.392117	−	0.462216i
$981$	−31.9584	+	31.9584i	−1.02035	+	1.02035i
$982$	5.97830	+	5.50787i	0.190775	+	0.175763i
$983$		−	27.5385i		−	0.878341i	−0.898404	−	0.439171i	$-0.855272\pi$
$983$		−	27.5385i		−	0.878341i	0.898404	−	0.439171i	$-0.144728\pi$
$984$	63.8353	+	49.8090i	2.03499	+	1.58785i
$985$			6.97373i			0.222202i
$986$	−5.40451	+	5.86611i	−0.172115	+	0.186815i
$987$	10.3260	−	10.3260i	0.328679	−	0.328679i
$988$	1.20355	+	14.6684i	0.0382900	+	0.466663i
$989$	16.8245	+	16.8245i	0.534987	+	0.534987i
$990$	0.571984	+	13.9656i	0.0181788	+	0.443856i
$991$	−28.4457			−0.903606			−0.451803	−	0.892118i	$-0.649219\pi$
$991$	−28.4457			−0.903606			−0.451803	+	0.892118i	$0.649219\pi$
$992$	7.91075	+	38.1103i	0.251167	+	1.21000i
$993$	4.37523			0.138844
$994$	0.913113	+	22.2946i	0.0289622	+	0.707143i
$995$	5.85638	+	5.85638i	0.185660	+	0.185660i
$996$	2.00052	+	24.3814i	0.0633888	+	0.772555i
$997$	−18.1160	+	18.1160i	−0.573739	+	0.573739i	−0.933171	−	0.359432i	$-0.882970\pi$
$997$	−18.1160	+	18.1160i	−0.573739	+	0.573739i	0.359432	+	0.933171i	$0.382970\pi$
$998$	−22.6352	+	24.5685i	−0.716506	+	0.777704i
$999$		−	1.66411i		−	0.0526501i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	272.2.l.c.205.8	yes	32
4.3	odd	2		1088.2.l.c.273.4		32
16.5	even	4	inner	272.2.l.c.69.8	✓	32
16.11	odd	4		1088.2.l.c.817.4		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
272.2.l.c.69.8	✓	32	16.5	even	4	inner
272.2.l.c.205.8	yes	32	1.1	even	1	trivial
1088.2.l.c.273.4		32	4.3	odd	2
1088.2.l.c.817.4		32	16.11	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 272 = 2^{4} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	272.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0578728 - 1.41303i) q^{2} +(1.71777 + 1.71777i) q^{3} +(-1.99330 + 0.163552i) q^{4} +(-1.50377 + 1.50377i) q^{5} +(2.32785 - 2.52667i) q^{6} +1.59335i q^{7} +(0.346462 + 2.80713i) q^{8} +2.90147i q^{9} +(2.21190 + 2.03785i) q^{10} +(1.13260 - 1.13260i) q^{11} +(-3.70498 - 3.14309i) q^{12} +(3.39887 + 3.39887i) q^{13} +(2.25145 - 0.0922118i) q^{14} -5.16627 q^{15} +(3.94650 - 0.652017i) q^{16} +1.00000 q^{17} +(4.09986 - 0.167916i) q^{18} +(-1.08254 - 1.08254i) q^{19} +(2.75153 - 3.24342i) q^{20} +(-2.73701 + 2.73701i) q^{21} +(-1.66595 - 1.53486i) q^{22} +3.36256i q^{23} +(-4.22686 + 5.41714i) q^{24} +0.477333i q^{25} +(4.60600 - 4.99940i) q^{26} +(0.169248 - 0.169248i) q^{27} +(-0.260596 - 3.17603i) q^{28} +(-3.98811 - 3.98811i) q^{29} +(0.298987 + 7.30010i) q^{30} -6.88063 q^{31} +(-1.14971 - 5.53879i) q^{32} +3.89111 q^{33} +(-0.0578728 - 1.41303i) q^{34} +(-2.39604 - 2.39604i) q^{35} +(-0.474542 - 5.78351i) q^{36} +(4.91619 - 4.91619i) q^{37} +(-1.46701 + 1.59231i) q^{38} +11.6770i q^{39} +(-4.74228 - 3.70028i) q^{40} -11.7839i q^{41} +(4.02588 + 3.70908i) q^{42} +(5.00347 - 5.00347i) q^{43} +(-2.07238 + 2.44286i) q^{44} +(-4.36316 - 4.36316i) q^{45} +(4.75139 - 0.194601i) q^{46} -3.77271 q^{47} +(7.89920 + 5.65917i) q^{48} +4.46123 q^{49} +(0.674485 - 0.0276246i) q^{50} +(1.71777 + 1.71777i) q^{51} +(-7.33087 - 6.21908i) q^{52} +(5.02004 - 5.02004i) q^{53} +(-0.248947 - 0.229357i) q^{54} +3.40636i q^{55} +(-4.47274 + 0.552035i) q^{56} -3.71911i q^{57} +(-5.40451 + 5.86611i) q^{58} +(0.0625800 - 0.0625800i) q^{59} +(10.2979 - 0.844955i) q^{60} +(-1.34466 - 1.34466i) q^{61} +(0.398201 + 9.72252i) q^{62} -4.62307 q^{63} +(-7.75993 + 1.94512i) q^{64} -10.2223 q^{65} +(-0.225190 - 5.49825i) q^{66} +(5.61932 + 5.61932i) q^{67} +(-1.99330 + 0.163552i) q^{68} +(-5.77610 + 5.77610i) q^{69} +(-3.24701 + 3.52434i) q^{70} +9.90234i q^{71} +(-8.14480 + 1.00525i) q^{72} +10.7806i q^{73} +(-7.23123 - 6.66221i) q^{74} +(-0.819948 + 0.819948i) q^{75} +(2.33488 + 1.98078i) q^{76} +(1.80464 + 1.80464i) q^{77} +(16.4999 - 0.675779i) q^{78} -5.17541 q^{79} +(-4.95416 + 6.91513i) q^{80} +9.28588 q^{81} +(-16.6510 + 0.681970i) q^{82} +(-3.56034 - 3.56034i) q^{83} +(5.00805 - 5.90334i) q^{84} +(-1.50377 + 1.50377i) q^{85} +(-7.35962 - 6.78049i) q^{86} -13.7013i q^{87} +(3.57177 + 2.78696i) q^{88} -15.4509i q^{89} +(-5.91276 + 6.41777i) q^{90} +(-5.41560 + 5.41560i) q^{91} +(-0.549953 - 6.70259i) q^{92} +(-11.8193 - 11.8193i) q^{93} +(0.218337 + 5.33095i) q^{94} +3.25579 q^{95} +(7.53942 - 11.4893i) q^{96} -0.773938 q^{97} +(-0.258184 - 6.30385i) q^{98} +(3.28622 + 3.28622i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 2 q^{4} - 16 q^{6} - 18 q^{8} - 6 q^{10} - 4 q^{11} + 2 q^{12} + 14 q^{14} + 24 q^{15} + 26 q^{16} + 32 q^{17} + 10 q^{18} - 14 q^{20} - 8 q^{22} - 50 q^{24} - 6 q^{26} + 12 q^{27} - 8 q^{29} + 36 q^{30}+ \cdots - 24 q^{99}+O(q^{100}) \) 32 * q - 2 * q^4 - 16 * q^6 - 18 * q^8 - 6 * q^10 - 4 * q^11 + 2 * q^12 + 14 * q^14 + 24 * q^15 + 26 * q^16 + 32 * q^17 + 10 * q^18 - 14 * q^20 - 8 * q^22 - 50 * q^24 - 6 * q^26 + 12 * q^27 - 8 * q^29 + 36 * q^30 - 24 * q^31 + 10 * q^32 + 12 * q^35 + 16 * q^36 - 8 * q^37 - 34 * q^38 - 38 * q^40 - 12 * q^42 - 12 * q^43 + 38 * q^44 - 40 * q^45 + 26 * q^46 + 32 * q^47 + 30 * q^48 - 32 * q^49 - 2 * q^50 - 54 * q^52 + 8 * q^53 - 52 * q^54 - 36 * q^56 - 26 * q^58 - 12 * q^59 + 28 * q^60 + 6 * q^62 - 40 * q^63 + 10 * q^64 + 28 * q^66 + 8 * q^67 - 2 * q^68 - 32 * q^70 - 32 * q^72 - 14 * q^74 + 8 * q^75 + 30 * q^76 + 56 * q^77 + 108 * q^78 + 48 * q^79 + 90 * q^80 - 64 * q^81 + 32 * q^82 + 4 * q^83 - 8 * q^84 - 54 * q^86 - 66 * q^88 - 66 * q^90 - 28 * q^91 + 24 * q^92 - 24 * q^93 + 12 * q^94 - 40 * q^95 + 70 * q^96 + 12 * q^98 - 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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