LMFDB - Embedded newform 552.2.b.c.413.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [552,2,Mod(413,552)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(552, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("552.413");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 552 = 2^{3} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	552.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$4.40774219157$
Analytic rank:	$0$
Dimension:	$80$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			413.8
Character	$\chi$	$=$	552.413
Dual form			552.2.b.c.413.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.36401 + 0.373449i) q^{2} +(1.13395 + 1.30925i) q^{3} +(1.72107 - 1.01878i) q^{4} +0.395927i q^{5} +(-2.03567 - 1.36237i) q^{6} +4.71612i q^{7} +(-1.96710 + 2.03236i) q^{8} +(-0.428296 + 2.96927i) q^{9} +O(q^{10})$	\(q+(-1.36401 + 0.373449i) q^{2} +(1.13395 + 1.30925i) q^{3} +(1.72107 - 1.01878i) q^{4} +0.395927i q^{5} +(-2.03567 - 1.36237i) q^{6} +4.71612i q^{7} +(-1.96710 + 2.03236i) q^{8} +(-0.428296 + 2.96927i) q^{9} +(-0.147859 - 0.540050i) q^{10} -2.82419i q^{11} +(3.28546 + 1.09807i) q^{12} +2.21325i q^{13} +(-1.76123 - 6.43286i) q^{14} +(-0.518369 + 0.448963i) q^{15} +(1.92417 - 3.50679i) q^{16} -1.31355 q^{17} +(-0.524670 - 4.21007i) q^{18} -5.28976 q^{19} +(0.403363 + 0.681419i) q^{20} +(-6.17461 + 5.34787i) q^{21} +(1.05469 + 3.85224i) q^{22} +(-4.02325 - 2.61027i) q^{23} +(-4.89149 - 0.270830i) q^{24} +4.84324 q^{25} +(-0.826538 - 3.01891i) q^{26} +(-4.37320 + 2.80627i) q^{27} +(4.80470 + 8.11678i) q^{28} +4.04998 q^{29} +(0.539398 - 0.805977i) q^{30} +5.38084 q^{31} +(-1.31499 + 5.50189i) q^{32} +(3.69759 - 3.20251i) q^{33} +(1.79171 - 0.490546i) q^{34} -1.86724 q^{35} +(2.28791 + 5.54666i) q^{36} +5.90978 q^{37} +(7.21531 - 1.97546i) q^{38} +(-2.89771 + 2.50973i) q^{39} +(-0.804668 - 0.778829i) q^{40} -5.67578i q^{41} +(6.42510 - 9.60047i) q^{42} -9.26919 q^{43} +(-2.87723 - 4.86064i) q^{44} +(-1.17561 - 0.169574i) q^{45} +(6.46257 + 2.05796i) q^{46} +7.65682i q^{47} +(6.77320 - 1.45731i) q^{48} -15.2418 q^{49} +(-6.60625 + 1.80871i) q^{50} +(-1.48951 - 1.71978i) q^{51} +(2.25482 + 3.80917i) q^{52} +11.9238i q^{53} +(4.91711 - 5.46096i) q^{54} +1.11817 q^{55} +(-9.58488 - 9.27710i) q^{56} +(-5.99834 - 6.92564i) q^{57} +(-5.52424 + 1.51246i) q^{58} +0.688356 q^{59} +(-0.434756 + 1.30080i) q^{60} -1.56462 q^{61} +(-7.33954 + 2.00947i) q^{62} +(-14.0034 - 2.01990i) q^{63} +(-0.261012 - 7.99574i) q^{64} -0.876287 q^{65} +(-3.84759 + 5.74913i) q^{66} +13.0480 q^{67} +(-2.26072 + 1.33822i) q^{68} +(-1.14467 - 8.22738i) q^{69} +(2.54694 - 0.697320i) q^{70} +8.34009i q^{71} +(-5.19214 - 6.71131i) q^{72} -2.50041 q^{73} +(-8.06103 + 2.20701i) q^{74} +(5.49201 + 6.34104i) q^{75} +(-9.10405 + 5.38910i) q^{76} +13.3192 q^{77} +(3.01526 - 4.50545i) q^{78} -7.94045i q^{79} +(1.38843 + 0.761832i) q^{80} +(-8.63313 - 2.54345i) q^{81} +(2.11962 + 7.74185i) q^{82} +3.48249i q^{83} +(-5.17863 + 15.4946i) q^{84} -0.520071i q^{85} +(12.6433 - 3.46157i) q^{86} +(4.59250 + 5.30246i) q^{87} +(5.73979 + 5.55548i) q^{88} +10.6029 q^{89} +(1.66688 - 0.207731i) q^{90} -10.4380 q^{91} +(-9.58358 - 0.393646i) q^{92} +(6.10163 + 7.04489i) q^{93} +(-2.85943 - 10.4440i) q^{94} -2.09436i q^{95} +(-8.69451 + 4.51723i) q^{96} -14.1265i q^{97} +(20.7901 - 5.69205i) q^{98} +(8.38579 + 1.20959i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 12 q^{6} - 4 q^{9}+O(q^{10}) $ 80 * q - 12 * q^6 - 4 * q^9	$ 80 q - 12 q^{6} - 4 q^{9} + 16 q^{12} + 8 q^{16} + 20 q^{18} - 8 q^{24} - 144 q^{25} - 24 q^{31} + 40 q^{36} + 68 q^{39} - 24 q^{46} + 92 q^{48} - 160 q^{49} - 48 q^{52} - 32 q^{54} + 32 q^{55} - 40 q^{58} + 48 q^{64} + 72 q^{70} + 68 q^{72} - 8 q^{73} + 64 q^{78} + 12 q^{81} - 48 q^{82} + 92 q^{87} - 144 q^{94} + 68 q^{96}+O(q^{100}) $ 80 * q - 12 * q^6 - 4 * q^9 + 16 * q^12 + 8 * q^16 + 20 * q^18 - 8 * q^24 - 144 * q^25 - 24 * q^31 + 40 * q^36 + 68 * q^39 - 24 * q^46 + 92 * q^48 - 160 * q^49 - 48 * q^52 - 32 * q^54 + 32 * q^55 - 40 * q^58 + 48 * q^64 + 72 * q^70 + 68 * q^72 - 8 * q^73 + 64 * q^78 + 12 * q^81 - 48 * q^82 + 92 * q^87 - 144 * q^94 + 68 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/552\mathbb{Z}\right)^\times$.

$n$	$97$	$185$	$277$	$415$
$\chi(n)$	$-1$	$-1$	$-1$	$1$

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 $

$2$	−1.36401	+	0.373449i	−0.964504	+	0.264069i
$2$	−1.36401	+	0.373449i	−0.964504	+	0.264069i
$3$	1.13395	+	1.30925i	0.654689	+	0.755899i
$3$	1.13395	+	1.30925i	0.654689	+	0.755899i
$4$	1.72107	−	1.01878i	0.860536	−	0.509390i
$5$			0.395927i			0.177064i	0.996073	+	0.0885320i	$0.0282176\pi$
$5$			0.395927i			0.177064i	−0.996073	+	0.0885320i	$0.971782\pi$
$6$	−2.03567	−	1.36237i	−0.831059	−	0.556184i
$7$			4.71612i			1.78253i	0.453486	+	0.891264i	$0.350180\pi$
$7$			4.71612i			1.78253i	−0.453486	+	0.891264i	$0.649820\pi$
$8$	−1.96710	+	2.03236i	−0.695476	+	0.718549i
$9$	−0.428296	+	2.96927i	−0.142765	+	0.989757i
$10$	−0.147859	−	0.540050i	−0.0467570	−	0.170779i
$11$		−	2.82419i		−	0.851526i	−0.904835	−	0.425763i	$-0.860006\pi$
$11$		−	2.82419i		−	0.851526i	0.904835	−	0.425763i	$-0.139994\pi$
$12$	3.28546	+	1.09807i	0.948430	+	0.316985i
$13$			2.21325i			0.613846i	0.951734	+	0.306923i	$0.0992994\pi$
$13$			2.21325i			0.613846i	−0.951734	+	0.306923i	$0.900701\pi$
$14$	−1.76123	−	6.43286i	−0.470709	−	1.71925i
$15$	−0.518369	+	0.448963i	−0.133842	+	0.115922i
$16$	1.92417	−	3.50679i	0.481043	−	0.876697i
$17$	−1.31355			−0.318583			−0.159292	−	0.987232i	$-0.550921\pi$
$17$	−1.31355			−0.318583			−0.159292	+	0.987232i	$0.550921\pi$
$18$	−0.524670	−	4.21007i	−0.123666	−	0.992324i
$19$	−5.28976			−1.21355			−0.606777	−	0.794872i	$-0.707538\pi$
$19$	−5.28976			−1.21355			−0.606777	+	0.794872i	$0.707538\pi$
$20$	0.403363	+	0.681419i	0.0901947	+	0.152370i
$21$	−6.17461	+	5.34787i	−1.34741	+	1.16700i
$22$	1.05469	+	3.85224i	0.224861	+	0.821301i
$23$	−4.02325	−	2.61027i	−0.838905	−	0.544278i
$23$	−4.02325	−	2.61027i	−0.838905	−	0.544278i
$24$	−4.89149	−	0.270830i	−0.998471	−	0.0552830i
$25$	4.84324			0.968648
$26$	−0.826538	−	3.01891i	−0.162097	−	0.592057i
$27$	−4.37320	+	2.80627i	−0.841622	+	0.540066i
$28$	4.80470	+	8.11678i	0.908002	+	1.53393i
$29$	4.04998			0.752063			0.376032	−	0.926607i	$-0.377288\pi$
$29$	4.04998			0.752063			0.376032	+	0.926607i	$0.377288\pi$
$30$	0.539398	−	0.805977i	0.0984802	−	0.147151i
$31$	5.38084			0.966427			0.483214	−	0.875502i	$-0.339469\pi$
$31$	5.38084			0.966427			0.483214	+	0.875502i	$0.339469\pi$
$32$	−1.31499	+	5.50189i	−0.232460	+	0.972606i
$33$	3.69759	−	3.20251i	0.643668	−	0.557485i
$34$	1.79171	−	0.490546i	0.307275	−	0.0841279i
$35$	−1.86724			−0.315621
$36$	2.28791	+	5.54666i	0.381318	+	0.924444i
$37$	5.90978			0.971562			0.485781	−	0.874080i	$-0.338535\pi$
$37$	5.90978			0.971562			0.485781	+	0.874080i	$0.338535\pi$
$38$	7.21531	−	1.97546i	1.17048	−	0.320461i
$39$	−2.89771	+	2.50973i	−0.464005	+	0.401878i
$40$	−0.804668	−	0.778829i	−0.127229	−	0.123144i
$41$		−	5.67578i		−	0.886409i	−0.896421	−	0.443204i	$-0.853842\pi$
$41$		−	5.67578i		−	0.886409i	0.896421	−	0.443204i	$-0.146158\pi$
$42$	6.42510	−	9.60047i	0.991414	−	1.48138i
$43$	−9.26919			−1.41354			−0.706769	−	0.707445i	$-0.749848\pi$
$43$	−9.26919			−1.41354			−0.706769	+	0.707445i	$0.749848\pi$
$44$	−2.87723	−	4.86064i	−0.433759	−	0.732769i
$45$	−1.17561	−	0.169574i	−0.175250	−	0.0252786i
$46$	6.46257	+	2.05796i	0.952854	+	0.303430i
$47$			7.65682i			1.11686i	0.829551	+	0.558431i	$0.188596\pi$
$47$			7.65682i			1.11686i	−0.829551	+	0.558431i	$0.811404\pi$
$48$	6.77320	−	1.45731i	0.977627	−	0.210344i
$49$	−15.2418			−2.17740
$50$	−6.60625	+	1.80871i	−0.934265	+	0.255790i
$51$	−1.48951	−	1.71978i	−0.208573	−	0.240817i
$52$	2.25482	+	3.80917i	0.312687	+	0.528236i
$53$			11.9238i			1.63786i	0.573896	+	0.818928i	$0.305431\pi$
$53$			11.9238i			1.63786i	−0.573896	+	0.818928i	$0.694569\pi$
$54$	4.91711	−	5.46096i	0.669133	−	0.743142i
$55$	1.11817			0.150775
$56$	−9.58488	−	9.27710i	−1.28083	−	1.23970i
$57$	−5.99834	−	6.92564i	−0.794500	−	0.917323i
$58$	−5.52424	+	1.51246i	−0.725368	+	0.198596i
$59$	0.688356			0.0896163			0.0448082	−	0.998996i	$-0.485732\pi$
$59$	0.688356			0.0896163			0.0448082	+	0.998996i	$0.485732\pi$
$60$	−0.434756	+	1.30080i	−0.0561267	+	0.167933i
$61$	−1.56462			−0.200330			−0.100165	−	0.994971i	$-0.531937\pi$
$61$	−1.56462			−0.200330			−0.100165	+	0.994971i	$0.531937\pi$
$62$	−7.33954	+	2.00947i	−0.932123	+	0.255203i
$63$	−14.0034	−	2.01990i	−1.76427	−	0.254483i
$64$	−0.261012	−	7.99574i	−0.0326265	−	0.999468i
$65$	−0.876287			−0.108690
$66$	−3.84759	+	5.74913i	−0.473606	+	0.707669i
$67$	13.0480			1.59406			0.797032	−	0.603938i	$-0.206402\pi$
$67$	13.0480			1.59406			0.797032	+	0.603938i	$0.206402\pi$
$68$	−2.26072	+	1.33822i	−0.274152	+	0.162283i
$69$	−1.14467	−	8.22738i	−0.137803	−	0.990460i
$70$	2.54694	−	0.697320i	0.304418	−	0.0833457i
$71$			8.34009i			0.989787i	0.868954	+	0.494894i	$0.164793\pi$
$71$			8.34009i			0.989787i	−0.868954	+	0.494894i	$0.835207\pi$
$72$	−5.19214	−	6.71131i	−0.611899	−	0.790936i
$73$	−2.50041			−0.292651			−0.146326	−	0.989236i	$-0.546745\pi$
$73$	−2.50041			−0.292651			−0.146326	+	0.989236i	$0.546745\pi$
$74$	−8.06103	+	2.20701i	−0.937076	+	0.256559i
$75$	5.49201	+	6.34104i	0.634163	+	0.732200i
$76$	−9.10405	+	5.38910i	−1.04431	+	0.618173i
$77$	13.3192			1.51787
$78$	3.01526	−	4.50545i	0.341412	−	0.510142i
$79$		−	7.94045i		−	0.893370i	−0.894691	−	0.446685i	$-0.852604\pi$
$79$		−	7.94045i		−	0.893370i	0.894691	−	0.446685i	$-0.147396\pi$
$80$	1.38843	+	0.761832i	0.155231	+	0.0851754i
$81$	−8.63313	−	2.54345i	−0.959236	−	0.282606i
$82$	2.11962	+	7.74185i	0.234073	+	0.854944i
$83$			3.48249i			0.382253i	0.981565	+	0.191126i	$0.0612141\pi$
$83$			3.48249i			0.382253i	−0.981565	+	0.191126i	$0.938786\pi$
$84$	−5.17863	+	15.4946i	−0.565035	+	1.69060i
$85$		−	0.520071i		−	0.0564096i
$86$	12.6433	−	3.46157i	1.36336	−	0.373271i
$87$	4.59250	+	5.30246i	0.492367	+	0.568483i
$88$	5.73979	+	5.55548i	0.611864	+	0.592216i
$89$	10.6029			1.12391			0.561954	−	0.827168i	$-0.310050\pi$
$89$	10.6029			1.12391			0.561954	+	0.827168i	$0.310050\pi$
$90$	1.66688	−	0.207731i	0.175705	−	0.0218968i
$91$	−10.4380			−1.09420
$92$	−9.58358	−	0.393646i	−0.999157	−	0.0410405i
$93$	6.10163	+	7.04489i	0.632709	+	0.730521i
$94$	−2.85943	−	10.4440i	−0.294928	−	1.07722i
$95$		−	2.09436i		−	0.214877i
$96$	−8.69451	+	4.51723i	−0.887380	+	0.461038i
$97$		−	14.1265i		−	1.43433i	−0.696902	−	0.717166i	$-0.745439\pi$
$97$		−	14.1265i		−	1.43433i	0.696902	−	0.717166i	$-0.254561\pi$
$98$	20.7901	−	5.69205i	2.10011	−	0.574984i
$99$	8.38579	+	1.20959i	0.842804	+	0.121568i
$100$	8.33556	−	4.93420i	0.833556	−	0.493420i
$101$	−14.4330			−1.43614			−0.718068	−	0.695973i	$-0.754973\pi$
$101$	−14.4330			−1.43614			−0.718068	+	0.695973i	$0.754973\pi$
$102$	2.67396	+	1.78954i	0.264762	+	0.177191i
$103$			7.11129i			0.700696i	0.936620	+	0.350348i	$0.113937\pi$
$103$			7.11129i			0.700696i	−0.936620	+	0.350348i	$0.886063\pi$
$104$	−4.49814	−	4.35370i	−0.441079	−	0.426915i
$105$	−2.11737	−	2.44469i	−0.206634	−	0.238578i
$106$	−4.45292	−	16.2642i	−0.432506	−	1.57972i
$107$			11.5678i			1.11830i	0.829065	+	0.559152i	$0.188873\pi$
$107$			11.5678i			1.11830i	−0.829065	+	0.559152i	$0.811127\pi$
$108$	−4.66761	+	9.28512i	−0.449141	+	0.893461i
$109$	16.2589			1.55732			0.778659	−	0.627447i	$-0.215900\pi$
$109$	16.2589			1.55732			0.778659	+	0.627447i	$0.215900\pi$
$110$	−1.52521	+	0.417582i	−0.145423	+	0.0398149i
$111$	6.70142	+	7.73741i	0.636071	+	0.734403i
$112$	16.5384	+	9.07463i	1.56274	+	0.857472i
$113$	6.11939			0.575664			0.287832	−	0.957681i	$-0.407066\pi$
$113$	6.11939			0.575664			0.287832	+	0.957681i	$0.407066\pi$
$114$	10.7682	+	7.20660i	1.00853	+	0.674960i
$115$	1.03347	−	1.59291i	0.0963720	−	0.148540i
$116$	6.97031	−	4.12605i	0.647177	−	0.383094i
$117$	−6.57175	−	0.947927i	−0.607558	−	0.0876359i
$118$	−0.938928	+	0.257066i	−0.0864353	+	0.0236649i
$119$		−	6.19488i		−	0.567883i
$120$	0.107229	−	1.93667i	0.00978863	−	0.176793i
$121$	3.02393			0.274903
$122$	2.13417	−	0.584308i	0.193219	−	0.0529007i
$123$	7.43105	−	6.43608i	0.670035	−	0.580322i
$124$	9.26081	−	5.48190i	0.831645	−	0.492289i
$125$			3.89721i			0.348577i
$126$	19.8552	−	2.47441i	1.76884	−	0.220438i
$127$	0.720794			0.0639601			0.0319800	−	0.999489i	$-0.489819\pi$
$127$	0.720794			0.0639601			0.0319800	+	0.999489i	$0.489819\pi$
$128$	3.34203	+	10.8088i	0.295396	+	0.955375i
$129$	−10.5108	−	12.1357i	−0.925427	−	1.06849i
$130$	1.19527	−	0.327249i	0.104832	−	0.0287016i
$131$	9.14850			0.799308			0.399654	−	0.916666i	$-0.369130\pi$
$131$	9.14850			0.799308			0.399654	+	0.916666i	$0.369130\pi$
$132$	3.10116	−	9.27877i	0.269921	−	0.807614i
$133$		−	24.9471i		−	2.16319i
$134$	−17.7976	+	4.87276i	−1.53748	+	0.420942i
$135$	−1.11108	−	1.73147i	−0.0956263	−	0.149021i
$136$	2.58389	−	2.66962i	0.221567	−	0.228918i
$137$	17.6096			1.50449			0.752244	−	0.658885i	$-0.228972\pi$
$137$	17.6096			1.50449			0.752244	+	0.658885i	$0.228972\pi$
$138$	4.63386	+	10.7948i	0.394461	+	0.918913i
$139$			10.9631i			0.929876i	0.885343	+	0.464938i	$0.153923\pi$
$139$			10.9631i			0.929876i	−0.885343	+	0.464938i	$0.846077\pi$
$140$	−3.21365	+	1.90231i	−0.271603	+	0.160774i
$141$	−10.0247	+	8.68248i	−0.844234	+	0.731197i
$142$	−3.11460	−	11.3760i	−0.261372	−	0.954653i
$143$	6.25065			0.522706
$144$	9.58849	+	7.21533i	0.799040	+	0.601277i
$145$			1.60350i			0.133163i
$146$	3.41060	−	0.933778i	0.282263	−	0.0772800i
$147$	−17.2835	−	19.9554i	−1.42552	−	1.64590i
$148$	10.1712	−	6.02077i	0.836064	−	0.494905i
$149$		−	9.16188i		−	0.750571i	−0.926909	−	0.375285i	$-0.877545\pi$
$149$		−	9.16188i		−	0.750571i	0.926909	−	0.375285i	$-0.122455\pi$
$150$	−9.85924	−	6.59828i	−0.805004	−	0.538747i
$151$	1.95851			0.159381			0.0796906	−	0.996820i	$-0.474607\pi$
$151$	1.95851			0.159381			0.0796906	+	0.996820i	$0.474607\pi$
$152$	10.4055	−	10.7507i	0.843997	−	0.871998i
$153$	0.562589	−	3.90029i	0.0454826	−	0.315320i
$154$	−18.1676	+	4.97406i	−1.46399	+	0.400821i
$155$			2.13042i			0.171119i
$156$	−2.43031	+	7.27155i	−0.194580	+	0.582190i
$157$	10.3146			0.823191			0.411596	−	0.911367i	$-0.364972\pi$
$157$	10.3146			0.823191			0.411596	+	0.911367i	$0.364972\pi$
$158$	2.96536	+	10.8309i	0.235911	+	0.861659i
$159$	−15.6113	+	13.5210i	−1.23805	+	1.07229i
$160$	−2.17835	−	0.520640i	−0.172214	−	0.0411602i
$161$	12.3103	−	18.9741i	0.970190	−	1.49537i
$162$	12.7256	+	0.245269i	0.999814	+	0.0192702i
$163$		−	3.72439i		−	0.291717i	−0.989305	−	0.145858i	$-0.953406\pi$
$163$		−	3.72439i		−	0.291717i	0.989305	−	0.145858i	$-0.0465944\pi$
$164$	−5.78238	−	9.76843i	−0.451528	−	0.762786i
$165$	1.26796	+	1.46398i	0.0987105	+	0.113970i
$166$	−1.30053	−	4.75017i	−0.100941	−	0.368684i
$167$		−	21.6834i		−	1.67792i	−0.544196	−	0.838958i	$-0.683165\pi$
$167$		−	21.6834i		−	1.67792i	0.544196	−	0.838958i	$-0.316835\pi$
$168$	1.27727	−	23.0689i	0.0985435	−	1.77980i
$169$	8.10151			0.623193
$170$	0.194220	+	0.709385i	0.0148960	+	0.0544073i
$171$	2.26558	−	15.7067i	0.173253	−	1.20112i
$172$	−15.9529	+	9.44327i	−1.21640	+	0.720042i
$173$	−2.79889			−0.212796			−0.106398	−	0.994324i	$-0.533932\pi$
$173$	−2.79889			−0.212796			−0.106398	+	0.994324i	$0.533932\pi$
$174$	−8.24443	−	5.51757i	−0.625009	−	0.418286i
$175$			22.8413i			1.72664i
$176$	−9.90385	−	5.43423i	−0.746531	−	0.409621i
$177$	0.780564	+	0.901234i	0.0586708	+	0.0677409i
$178$	−14.4626	+	3.95966i	−1.08401	+	0.296789i
$179$	3.24790			0.242760			0.121380	−	0.992606i	$-0.461268\pi$
$179$	3.24790			0.242760			0.121380	+	0.992606i	$0.461268\pi$
$180$	−2.19607	+	0.905845i	−0.163686	+	0.0675177i
$181$	−3.36533			−0.250143			−0.125072	−	0.992148i	$-0.539916\pi$
$181$	−3.36533			−0.250143			−0.125072	+	0.992148i	$0.539916\pi$
$182$	14.2375	−	3.89805i	1.05536	−	0.288943i
$183$	−1.77421	−	2.04849i	−0.131153	−	0.151429i
$184$	13.2192	−	3.04204i	0.974529	−	0.224262i
$185$			2.33984i			0.172029i
$186$	−10.9536	−	7.33068i	−0.803158	−	0.537512i
$187$			3.70973i			0.271282i
$188$	7.80062	+	13.1779i	0.568918	+	0.961099i
$189$	−13.2347	−	20.6245i	−0.962683	−	1.50021i
$190$	0.782137	+	2.85674i	0.0567422	+	0.207249i
$191$	5.27217			0.381481			0.190740	−	0.981641i	$-0.438911\pi$
$191$	5.27217			0.381481			0.190740	+	0.981641i	$0.438911\pi$
$192$	10.1725	−	9.40853i	0.734136	−	0.679003i
$193$	14.4630			1.04107			0.520534	−	0.853841i	$-0.325733\pi$
$193$	14.4630			1.04107			0.520534	+	0.853841i	$0.325733\pi$
$194$	5.27555	+	19.2688i	0.378762	+	1.38342i
$195$	−0.993669	−	1.14728i	−0.0711581	−	0.0821586i
$196$	−26.2323	+	15.5281i	−1.87373	+	1.10915i
$197$	4.79829			0.341864			0.170932	−	0.985283i	$-0.445322\pi$
$197$	4.79829			0.341864			0.170932	+	0.985283i	$0.445322\pi$
$198$	−11.8901	+	1.48177i	−0.844990	+	0.105305i
$199$			7.73815i			0.548543i	0.961652	+	0.274271i	$0.0884366\pi$
$199$			7.73815i			0.548543i	−0.961652	+	0.274271i	$0.911563\pi$
$200$	−9.52716	+	9.84323i	−0.673672	+	0.696022i
$201$	14.7958	+	17.0831i	1.04362	+	1.20495i
$202$	19.6868	−	5.38999i	1.38516	−	0.379238i
$203$			19.1002i			1.34057i
$204$	−4.31562	−	1.44237i	−0.302154	−	0.100986i
$205$	2.24720			0.156951
$206$	−2.65571	−	9.69990i	−0.185032	−	0.675824i
$207$	9.47372	−	10.8281i	0.658469	−	0.752608i
$208$	7.76141	+	4.25868i	0.538157	+	0.295286i
$209$			14.9393i			1.03337i
$210$	3.80109	+	2.54387i	0.262300	+	0.175544i
$211$			11.7355i			0.807905i	0.914780	+	0.403952i	$0.132364\pi$
$211$			11.7355i			0.807905i	−0.914780	+	0.403952i	$0.867636\pi$
$212$	12.1477	+	20.5217i	0.834308	+	1.40943i
$213$	−10.9193	+	9.45728i	−0.748179	+	0.648002i
$214$	−4.32000	−	15.7787i	−0.295309	−	1.07861i
$215$		−	3.66992i		−	0.250287i
$216$	2.89917	−	14.4082i	0.197264	−	0.980350i
$217$			25.3767i			1.72268i
$218$	−22.1773	+	6.07187i	−1.50204	+	0.411239i
$219$	−2.83535	−	3.27368i	−0.191595	−	0.221215i
$220$	1.92446	−	1.13917i	0.129747	−	0.0768032i
$221$		−	2.90722i		−	0.195561i
$222$	−12.0304	−	8.05130i	−0.807426	−	0.540368i
$223$	−21.0590			−1.41021			−0.705107	−	0.709101i	$-0.749101\pi$
$223$	−21.0590			−1.41021			−0.705107	+	0.709101i	$0.749101\pi$
$224$	−25.9476	−	6.20166i	−1.73370	−	0.414366i
$225$	−2.07434	+	14.3809i	−0.138289	+	0.958726i
$226$	−8.34694	+	2.28528i	−0.555230	+	0.152015i
$227$		−	24.7131i		−	1.64027i	−0.572171	−	0.820134i	$-0.693899\pi$
$227$		−	24.7131i		−	1.64027i	0.572171	−	0.820134i	$-0.306101\pi$
$228$	−17.3793	−	5.80852i	−1.15097	−	0.384679i
$229$	2.62314			0.173342			0.0866709	−	0.996237i	$-0.472377\pi$
$229$	2.62314			0.173342			0.0866709	+	0.996237i	$0.472377\pi$
$230$	−0.814803	+	2.55871i	−0.0537265	+	0.168716i
$231$	15.1034	+	17.4383i	0.993732	+	1.14735i
$232$	−7.96674	+	8.23104i	−0.523042	+	0.540395i
$233$		−	4.28438i		−	0.280679i	−0.990103	−	0.140340i	$-0.955181\pi$
$233$		−	4.28438i		−	0.280679i	0.990103	−	0.140340i	$-0.0448194\pi$
$234$	9.31796	−	1.16123i	0.609134	−	0.0759118i
$235$	−3.03154			−0.197756
$236$	1.18471	−	0.701284i	0.0771181	−	0.0456497i
$237$	10.3961	−	9.00411i	0.675297	−	0.584880i
$238$	2.31347	+	8.44990i	0.149960	+	0.547726i
$239$			16.7614i			1.08421i	0.840312	+	0.542103i	$0.182372\pi$
$239$			16.7614i			1.08421i	−0.840312	+	0.542103i	$0.817628\pi$
$240$	0.576987	+	2.68169i	0.0372444	+	0.173103i
$241$		−	11.4070i		−	0.734792i	−0.930065	−	0.367396i	$-0.880249\pi$
$241$		−	11.4070i		−	0.734792i	0.930065	−	0.367396i	$-0.119751\pi$
$242$	−4.12469	+	1.12929i	−0.265145	+	0.0725932i
$243$	−6.45954	−	14.1871i	−0.414380	−	0.910104i
$244$	−2.69283	+	1.59401i	−0.172391	+	0.102046i
$245$		−	6.03465i		−	0.385540i
$246$	−7.73251	+	11.5540i	−0.493007	+	0.736658i
$247$		−	11.7076i		−	0.744935i
$248$	−10.5847	+	10.9358i	−0.672127	+	0.694426i
$249$	−4.55947	+	3.94898i	−0.288944	+	0.250257i
$250$	−1.45541	−	5.31585i	−0.0920482	−	0.336204i
$251$			2.66337i			0.168110i	0.996461	+	0.0840551i	$0.0267872\pi$
$251$			2.66337i			0.168110i	−0.996461	+	0.0840551i	$0.973213\pi$
$252$	−26.1588	+	10.7901i	−1.64785	+	0.679709i
$253$	−7.37190	+	11.3624i	−0.463467	+	0.714350i
$254$	−0.983173	+	0.269180i	−0.0616898	+	0.0168899i
$255$	0.680906	−	0.589737i	0.0426400	−	0.0369308i
$256$	−8.59513	−	13.4953i	−0.537195	−	0.843458i
$257$		−	27.1697i		−	1.69480i	−0.530957	−	0.847399i	$-0.678167\pi$
$257$		−	27.1697i		−	1.69480i	0.530957	−	0.847399i	$-0.321833\pi$
$258$	18.8690	+	12.6280i	1.17473	+	0.786188i
$259$			27.8713i			1.73184i
$260$	−1.50815	+	0.892744i	−0.0935316	+	0.0553656i
$261$	−1.73459	+	12.0255i	−0.107368	+	0.744359i
$262$	−12.4787	+	3.41650i	−0.770936	+	0.211072i
$263$	−26.3132			−1.62254			−0.811270	−	0.584672i	$-0.801223\pi$
$263$	−26.3132			−1.62254			−0.811270	+	0.584672i	$0.801223\pi$
$264$	−0.764878	+	13.8145i	−0.0470750	+	0.850224i
$265$	−4.72094			−0.290005
$266$	9.31650	+	34.0283i	0.571231	+	2.08641i
$267$	12.0232	+	13.8819i	0.735810	+	0.849561i
$268$	22.4565	−	13.2930i	1.37175	−	0.812000i
$269$	6.21379			0.378861			0.189431	−	0.981894i	$-0.439336\pi$
$269$	6.21379			0.378861			0.189431	+	0.981894i	$0.439336\pi$
$270$	2.16214	+	1.94682i	0.131584	+	0.118479i
$271$	22.0807			1.34131			0.670654	−	0.741770i	$-0.266014\pi$
$271$	22.0807			1.34131			0.670654	+	0.741770i	$0.266014\pi$
$272$	−2.52750	+	4.60635i	−0.153252	+	0.279301i
$273$	−11.8362	−	13.6660i	−0.716358	−	0.827102i
$274$	−24.0197	+	6.57629i	−1.45108	+	0.397288i
$275$		−	13.6783i		−	0.824830i
$276$	−10.3520	−	12.9937i	−0.623115	−	0.782130i
$277$		−	9.81512i		−	0.589733i	−0.955538	−	0.294867i	$-0.904725\pi$
$277$		−	9.81512i		−	0.589733i	0.955538	−	0.294867i	$-0.0952752\pi$
$278$	−4.09415	−	14.9538i	−0.245551	−	0.896869i
$279$	−2.30459	+	15.9772i	−0.137972	+	0.956528i
$280$	3.67306	−	3.79491i	0.219507	−	0.226790i
$281$	−19.4657			−1.16122			−0.580612	−	0.814181i	$-0.697187\pi$
$281$	−19.4657			−1.16122			−0.580612	+	0.814181i	$0.697187\pi$
$282$	10.4314	−	15.5868i	0.621181	−	0.928178i
$283$	−10.4791			−0.622920			−0.311460	−	0.950259i	$-0.600818\pi$
$283$	−10.4791			−0.622920			−0.311460	+	0.950259i	$0.600818\pi$
$284$	8.49673	+	14.3539i	0.504188	+	0.851747i
$285$	2.74205	−	2.37491i	0.162425	−	0.140677i
$286$	−8.52598	+	2.33430i	−0.504152	+	0.138030i
$287$	26.7677			1.58005
$288$	−15.7734	−	6.26100i	−0.929456	−	0.368933i
$289$	−15.2746			−0.898505
$290$	−0.598826	−	2.18720i	−0.0351642	−	0.128437i
$291$	18.4952	−	16.0188i	1.08421	−	0.939041i
$292$	−4.30339	+	2.54737i	−0.251837	+	0.149074i
$293$			14.8006i			0.864661i	0.901715	+	0.432330i	$0.142309\pi$
$293$			14.8006i			0.864661i	−0.901715	+	0.432330i	$0.857691\pi$
$294$	31.0273	+	20.7650i	1.80955	+	1.21104i
$295$			0.272539i			0.0158678i
$296$	−11.6252	+	12.0108i	−0.675698	+	0.698116i
$297$	7.92544	+	12.3508i	0.459881	+	0.716664i
$298$	3.42150	+	12.4969i	0.198202	+	0.723928i
$299$	5.77718	−	8.90446i	0.334103	−	0.514958i
$300$	15.9123	+	5.31822i	0.918696	+	0.307047i
$301$		−	43.7146i		−	2.51967i
$302$	−2.67144	+	0.731404i	−0.153724	+	0.0420876i
$303$	−16.3663	−	18.8965i	−0.940222	−	1.08557i
$304$	−10.1784	+	18.5501i	−0.583771	+	1.06392i
$305$		−	0.619477i		−	0.0354711i
$306$	0.689182	+	5.53015i	0.0393979	+	0.316138i
$307$		−	26.8958i		−	1.53502i	−0.641034	−	0.767512i	$-0.721494\pi$
$307$		−	26.8958i		−	1.53502i	0.641034	−	0.767512i	$-0.278506\pi$
$308$	22.9234	−	13.5694i	1.30618	−	0.773188i
$309$	−9.31049	+	8.06388i	−0.529655	+	0.458738i
$310$	−0.795604	−	2.90592i	−0.0451873	−	0.165045i
$311$		−	4.82552i		−	0.273630i	−0.990597	−	0.136815i	$-0.956313\pi$
$311$		−	4.82552i		−	0.273630i	0.990597	−	0.136815i	$-0.0436866\pi$
$312$	0.599416	−	10.8261i	0.0339353	−	0.612907i
$313$			3.75108i			0.212024i	0.994365	+	0.106012i	$0.0338082\pi$
$313$			3.75108i			0.212024i	−0.994365	+	0.106012i	$0.966192\pi$
$314$	−14.0692	+	3.85197i	−0.793971	+	0.217379i
$315$	0.799732	−	5.54434i	0.0450598	−	0.312388i
$316$	−8.08958	−	13.6661i	−0.455074	−	0.768777i
$317$	−18.4220			−1.03468			−0.517342	−	0.855779i	$-0.673079\pi$
$317$	−18.4220			−1.03468			−0.517342	+	0.855779i	$0.673079\pi$
$318$	16.2446	−	24.2729i	0.910950	−	1.36115i
$319$		−	11.4379i		−	0.640402i
$320$	3.16573	−	0.103342i	0.176970	−	0.00577698i
$321$	−15.1452	+	13.1174i	−0.845325	+	0.732141i
$322$	−9.70560	+	30.4783i	−0.540872	+	1.69849i
$323$	6.94838			0.386618
$324$	−17.4494	+	4.41780i	−0.969413	+	0.245433i
$325$			10.7193i			0.594601i
$326$	1.39087	+	5.08012i	0.0770332	+	0.281362i
$327$	18.4368	+	21.2870i	1.01956	+	1.17717i
$328$	11.5353	+	11.1649i	0.636928	+	0.616476i
$329$	−36.1105			−1.99084
$330$	−2.27624	−	1.52337i	−0.125303	−	0.0838585i
$331$			8.34800i			0.458848i	0.973327	+	0.229424i	$0.0736842\pi$
$331$			8.34800i			0.458848i	−0.973327	+	0.229424i	$0.926316\pi$
$332$	3.54789	+	5.99361i	0.194716	+	0.328942i
$333$	−2.53114	+	17.5477i	−0.138705	+	0.961610i
$334$	8.09767	+	29.5765i	0.443085	+	1.61836i
$335$			5.16605i			0.282251i
$336$	6.87284	+	31.9433i	0.374944	+	1.74265i
$337$			7.74577i			0.421939i	0.977493	+	0.210969i	$0.0676620\pi$
$337$			7.74577i			0.421939i	−0.977493	+	0.210969i	$0.932338\pi$
$338$	−11.0506	+	3.02550i	−0.601072	+	0.164566i
$339$	6.93911	+	8.01185i	0.376881	+	0.435144i
$340$	−0.529839	−	0.895080i	−0.0287345	−	0.0485425i
$341$		−	15.1965i		−	0.822938i
$342$	2.77538	+	22.2703i	0.150075	+	1.20424i
$343$		−	38.8694i		−	2.09875i
$344$	18.2334	−	18.8384i	0.983081	−	1.01570i
$345$	3.25744	−	0.453208i	0.175375	−	0.0243999i
$346$	3.81773	−	1.04524i	0.205242	−	0.0561926i
$347$	−12.2180			−0.655899			−0.327949	−	0.944695i	$-0.606358\pi$
$347$	−12.2180			−0.655899			−0.327949	+	0.944695i	$0.606358\pi$
$348$	13.3061	+	4.44717i	0.713280	+	0.238393i
$349$			5.84864i			0.313071i	0.987672	+	0.156535i	$0.0500325\pi$
$349$			5.84864i			0.313071i	−0.987672	+	0.156535i	$0.949967\pi$
$350$	−8.53008	−	31.1559i	−0.455952	−	1.66535i
$351$	−6.21098	−	9.67899i	−0.331518	−	0.516626i
$352$	15.5384	+	3.71379i	0.828200	+	0.197946i
$353$			19.8507i			1.05655i	0.849075	+	0.528273i	$0.177160\pi$
$353$			19.8507i			1.05655i	−0.849075	+	0.528273i	$0.822840\pi$
$354$	−1.40127	−	0.937794i	−0.0744765	−	0.0498432i
$355$	−3.30207			−0.175256
$356$	18.2484	−	10.8021i	0.967164	−	0.572508i
$357$	8.11067	−	7.02471i	0.429262	−	0.371787i
$358$	−4.43019	+	1.21293i	−0.234143	+	0.0641052i
$359$	33.0184			1.74264			0.871321	−	0.490714i	$-0.163264\pi$
$359$	33.0184			1.74264			0.871321	+	0.490714i	$0.163264\pi$
$360$	2.65719	−	2.05571i	0.140046	−	0.108345i
$361$	8.98154			0.472713
$362$	4.59037	−	1.25678i	0.241264	−	0.0660550i
$363$	3.42900	+	3.95910i	0.179976	+	0.207799i
$364$	−17.9645	+	10.6340i	−0.941595	+	0.557373i
$365$		−	0.989981i		−	0.0518180i
$366$	3.18506	+	2.13159i	0.166486	+	0.111420i
$367$		−	18.7443i		−	0.978447i	−0.872159	−	0.489223i	$-0.837280\pi$
$367$		−	18.7443i		−	0.978447i	0.872159	−	0.489223i	$-0.162720\pi$
$368$	−16.8951	+	9.08607i	−0.880716	+	0.473644i
$369$	16.8529	+	2.43091i	0.877329	+	0.126548i
$370$	−0.873813	−	3.19158i	−0.0454274	−	0.165922i
$371$	−56.2340			−2.91952
$372$	17.6785	+	5.90854i	0.916589	+	0.306343i
$373$	9.72608			0.503597			0.251799	−	0.967780i	$-0.418978\pi$
$373$	9.72608			0.503597			0.251799	+	0.967780i	$0.418978\pi$
$374$	−1.38540	−	5.06012i	−0.0716371	−	0.261653i
$375$	−5.10244	+	4.41925i	−0.263489	+	0.228209i
$376$	−15.5614	−	15.0617i	−0.802520	−	0.776750i
$377$			8.96364i			0.461651i
$378$	25.7545	+	23.1897i	1.32467	+	1.19275i
$379$	−22.0300			−1.13161			−0.565803	−	0.824540i	$-0.691434\pi$
$379$	−22.0300			−1.13161			−0.565803	+	0.824540i	$0.691434\pi$
$380$	−2.13369	−	3.60454i	−0.109456	−	0.184909i
$381$	0.817347	+	0.943702i	0.0418740	+	0.0483473i
$382$	−7.19131	+	1.96889i	−0.367940	+	0.100737i
$383$	−2.89411			−0.147882			−0.0739410	−	0.997263i	$-0.523558\pi$
$383$	−2.89411			−0.147882			−0.0739410	+	0.997263i	$0.523558\pi$
$384$	−10.3618	+	16.6323i	−0.528774	+	0.848763i
$385$			5.27345i			0.268760i
$386$	−19.7277	+	5.40119i	−1.00411	+	0.274913i
$387$	3.96995	−	27.5227i	0.201804	−	1.39906i
$388$	−14.3918	−	24.3128i	−0.730635	−	1.23429i
$389$		−	13.8535i		−	0.702403i	−0.936300	−	0.351201i	$-0.885773\pi$
$389$		−	13.8535i		−	0.702403i	0.936300	−	0.351201i	$-0.114227\pi$
$390$	1.78383	+	1.19383i	0.0903278	+	0.0604517i
$391$	5.28475	+	3.42872i	0.267261	+	0.173398i
$392$	29.9822	−	30.9769i	1.51433	−	1.56457i
$393$	10.3740	+	11.9777i	0.523298	+	0.604196i
$394$	−6.54493	+	1.79192i	−0.329729	+	0.0902755i
$395$	3.14384			0.158184
$396$	15.6649	−	6.46149i	0.787188	−	0.324702i
$397$			2.79933i			0.140495i	0.997530	+	0.0702473i	$0.0223788\pi$
$397$			2.79933i			0.140495i	−0.997530	+	0.0702473i	$0.977621\pi$
$398$	−2.88981	−	10.5549i	−0.144853	−	0.529072i
$399$	32.6622	−	28.2889i	1.63515	−	1.41622i
$400$	9.31923	−	16.9842i	0.465961	−	0.849211i
$401$	32.3349			1.61473			0.807365	−	0.590053i	$-0.200893\pi$
$401$	32.3349			1.61473			0.807365	+	0.590053i	$0.200893\pi$
$402$	−26.5614	−	17.7761i	−1.32476	−	0.886593i
$403$			11.9092i			0.593237i
$404$	−24.8402	+	14.7040i	−1.23585	+	0.731554i
$405$	1.00702	−	3.41809i	0.0500393	−	0.169846i
$406$	−7.13297	−	26.0530i	−0.354003	−	1.29299i
$407$		−	16.6904i		−	0.827311i
$408$	6.42523	+	0.355750i	0.318096	+	0.0176123i
$409$	5.89621			0.291549			0.145775	−	0.989318i	$-0.453433\pi$
$409$	5.89621			0.291549			0.145775	+	0.989318i	$0.453433\pi$
$410$	−3.06521	+	0.839214i	−0.151380	+	0.0414458i
$411$	19.9685	+	23.0554i	0.984971	+	1.13724i
$412$	7.24485	+	12.2390i	0.356928	+	0.602974i
$413$			3.24637i			0.159744i
$414$	−8.87853	+	18.3077i	−0.436356	+	0.899774i
$415$	−1.37881			−0.0676832
$416$	−12.1771	−	2.91041i	−0.597030	−	0.142694i
$417$	−14.3535	+	12.4316i	−0.702892	+	0.608779i
$418$	−5.57907	−	20.3774i	−0.272881	−	0.996692i
$419$		−	3.95202i		−	0.193069i	−0.995330	−	0.0965343i	$-0.969224\pi$
$419$		−	3.95202i		−	0.193069i	0.995330	−	0.0965343i	$-0.0307758\pi$
$420$	−6.13474	−	2.05036i	−0.299345	−	0.100047i
$421$	18.6997			0.911366			0.455683	−	0.890142i	$-0.349395\pi$
$421$	18.6997			0.911366			0.455683	+	0.890142i	$0.349395\pi$
$422$	−4.38261	−	16.0074i	−0.213342	−	0.779227i
$423$	−22.7352	−	3.27938i	−1.10542	−	0.159449i
$424$	−24.2334	−	23.4553i	−1.17688	−	1.13909i
$425$	−6.36185			−0.308595
$426$	11.3623	−	16.9777i	0.550504	−	0.822571i
$427$		−	7.37896i		−	0.357093i
$428$	11.7851	+	19.9091i	0.569653	+	0.962341i
$429$	7.08796	+	8.18370i	0.342210	+	0.395113i
$430$	1.37053	+	5.00583i	0.0660928	+	0.241402i
$431$	−1.08062			−0.0520516			−0.0260258	−	0.999661i	$-0.508285\pi$
$431$	−1.08062			−0.0520516			−0.0260258	+	0.999661i	$0.508285\pi$
$432$	1.42620	+	20.7356i	0.0686182	+	0.997643i
$433$		−	33.2111i		−	1.59602i	−0.602641	−	0.798012i	$-0.705885\pi$
$433$		−	33.2111i		−	1.59602i	0.602641	−	0.798012i	$-0.294115\pi$
$434$	−9.47691	−	34.6142i	−0.454906	−	1.66153i
$435$	−2.09939	+	1.81829i	−0.100658	+	0.0871805i
$436$	27.9827	−	16.5642i	1.34013	−	0.793283i
$437$	21.2820	+	13.8077i	1.01806	+	0.660511i
$438$	5.09002	+	3.40648i	0.243210	+	0.162768i
$439$	−34.0435			−1.62481			−0.812405	−	0.583094i	$-0.801842\pi$
$439$	−34.0435			−1.62481			−0.812405	+	0.583094i	$0.801842\pi$
$440$	−2.19956	+	2.27254i	−0.104860	+	0.108339i
$441$	6.52801	−	45.2571i	0.310857	−	2.15510i
$442$	1.08570	+	3.96550i	0.0516415	+	0.188619i
$443$	14.9546			0.710515			0.355257	−	0.934769i	$-0.384393\pi$
$443$	14.9546			0.710515			0.355257	+	0.934769i	$0.384393\pi$
$444$	19.4164	+	6.48936i	0.921459	+	0.307971i
$445$			4.19799i			0.199004i
$446$	28.7247	−	7.86446i	1.36016	−	0.372393i
$447$	11.9952	−	10.3892i	0.567355	−	0.491390i
$448$	37.7089	−	1.23096i	1.78158	−	0.0581576i
$449$			28.7060i			1.35472i	0.735653	+	0.677359i	$0.236876\pi$
$449$			28.7060i			1.35472i	−0.735653	+	0.677359i	$0.763124\pi$
$450$	−2.54110	−	20.3904i	−0.119789	−	0.961213i
$451$	−16.0295			−0.754800
$452$	10.5319	−	6.23432i	0.495379	−	0.293238i
$453$	2.22086	+	2.56419i	0.104345	+	0.120476i
$454$	9.22910	+	33.7091i	0.433143	+	1.58205i
$455$		−	4.13268i		−	0.193743i
$456$	25.8748	+	1.43263i	1.21170	+	0.0670889i
$457$			28.8806i			1.35098i	0.737370	+	0.675489i	$0.236067\pi$
$457$			28.8806i			1.35098i	−0.737370	+	0.675489i	$0.763933\pi$
$458$	−3.57800	+	0.979608i	−0.167189	+	0.0457741i
$459$	5.74443	−	3.68618i	0.268127	−	0.172056i
$460$	0.155855	−	3.79440i	0.00726679	−	0.176915i
$461$	11.9977			0.558788			0.279394	−	0.960177i	$-0.409866\pi$
$461$	11.9977			0.558788			0.279394	+	0.960177i	$0.409866\pi$
$462$	−27.1136	−	18.1457i	−1.26144	−	0.844215i
$463$	−18.6391			−0.866230			−0.433115	−	0.901339i	$-0.642586\pi$
$463$	−18.6391			−0.866230			−0.433115	+	0.901339i	$0.642586\pi$
$464$	7.79286	−	14.2024i	0.361775	−	0.659332i
$465$	−2.78926	+	2.41580i	−0.129349	+	0.112030i
$466$	1.60000	+	5.84396i	0.0741186	+	0.270716i
$467$		−	15.9366i		−	0.737458i	−0.929537	−	0.368729i	$-0.879793\pi$
$467$		−	15.9366i		−	0.737458i	0.929537	−	0.368729i	$-0.120207\pi$
$468$	−12.2762	+	5.06372i	−0.567466	+	0.234070i
$469$			61.5358i			2.84146i
$470$	4.13507	−	1.13213i	0.190736	−	0.0522211i
$471$	11.6962	+	13.5044i	0.538934	+	0.622249i
$472$	−1.35407	+	1.39899i	−0.0623260	+	0.0643938i
$473$			26.1780i			1.20366i
$474$	−10.8178	+	16.1641i	−0.496879	+	0.742443i
$475$	−25.6196			−1.17551
$476$	−6.31122	−	10.6618i	−0.289274	−	0.488684i
$477$	−35.4049	−	5.10690i	−1.62108	−	0.233829i
$478$	−6.25954	−	22.8628i	−0.286305	−	1.04572i
$479$	9.43400			0.431050			0.215525	−	0.976498i	$-0.430854\pi$
$479$	9.43400			0.431050			0.215525	+	0.976498i	$0.430854\pi$
$480$	−1.78850	−	3.44239i	−0.0816333	−	0.157123i
$481$			13.0798i			0.596390i
$482$	4.25995	+	15.5594i	0.194036	+	0.708710i
$483$	38.8013	−	5.39843i	1.76552	−	0.245637i
$484$	5.20440	−	3.08072i	0.236564	−	0.140033i
$485$	5.59308			0.253969
$486$	14.1091	+	16.9391i	0.640001	+	0.768374i
$487$	−42.0425			−1.90513			−0.952563	−	0.304340i	$-0.901564\pi$
$487$	−42.0425			−1.90513			−0.952563	+	0.304340i	$0.901564\pi$
$488$	3.07778	−	3.17989i	0.139324	−	0.143947i
$489$	4.87617	−	4.22329i	0.220508	−	0.190984i
$490$	2.25364	+	8.23135i	0.101809	+	0.371854i
$491$	29.6102			1.33629			0.668144	−	0.744032i	$-0.267089\pi$
$491$	29.6102			1.33629			0.668144	+	0.744032i	$0.267089\pi$
$492$	6.23241	−	18.6476i	0.280979	−	0.840697i
$493$	−5.31987			−0.239595
$494$	4.37219	+	15.9693i	0.196714	+	0.718493i
$495$	−0.478910	+	3.32016i	−0.0215254	+	0.149230i
$496$	10.3537	−	18.8695i	0.464893	−	0.847264i
$497$	−39.3329			−1.76432
$498$	4.74443	−	7.08920i	0.212603	−	0.317675i
$499$		−	37.9030i		−	1.69677i	−0.529380	−	0.848385i	$-0.677575\pi$
$499$		−	37.9030i		−	1.69677i	0.529380	−	0.848385i	$-0.322425\pi$
$500$	3.97040	+	6.70737i	0.177562	+	0.299963i
$501$	28.3892	−	24.5880i	1.26833	−	1.09851i
$502$	−0.994633	−	3.63287i	−0.0443926	−	0.162143i
$503$	−4.48302			−0.199888			−0.0999440	−	0.994993i	$-0.531866\pi$
$503$	−4.48302			−0.199888			−0.0999440	+	0.994993i	$0.531866\pi$
$504$	31.6514	−	24.4868i	1.40986	−	1.09073i
$505$		−	5.71441i		−	0.254288i
$506$	5.81208	−	18.2515i	0.258378	−	0.811380i
$507$	9.18674	+	10.6069i	0.407998	+	0.471071i
$508$	1.24054	−	0.734331i	0.0550399	−	0.0325807i
$509$	−43.4158			−1.92437			−0.962187	−	0.272391i	$-0.912186\pi$
$509$	−43.4158			−1.92437			−0.962187	+	0.272391i	$0.912186\pi$
$510$	−0.708528	+	1.05869i	−0.0313742	+	0.0468797i
$511$		−	11.7923i		−	0.521659i
$512$	16.7637	+	15.1980i	0.740858	+	0.671662i
$513$	23.1332	−	14.8445i	1.02135	−	0.655400i
$514$	10.1465	+	37.0598i	0.447543	+	1.63464i
$515$	−2.81555			−0.124068
$516$	−30.4535	−	10.1782i	−1.34064	−	0.448071i
$517$	21.6243			0.951037
$518$	−10.4085	−	38.0168i	−0.457324	−	1.67036i
$519$	−3.17381	−	3.66446i	−0.139315	−	0.160852i
$520$	1.72375	−	1.78093i	0.0755913	−	0.0780991i
$521$	−6.51277			−0.285330			−0.142665	−	0.989771i	$-0.545567\pi$
$521$	−6.51277			−0.285330			−0.142665	+	0.989771i	$0.545567\pi$
$522$	−2.12491	−	17.0507i	−0.0930046	−	0.746290i
$523$	14.0480			0.614276			0.307138	−	0.951665i	$-0.400629\pi$
$523$	14.0480			0.614276			0.307138	+	0.951665i	$0.400629\pi$
$524$	15.7452	−	9.32032i	0.687833	−	0.407160i
$525$	−29.9051	+	25.9010i	−1.30517	+	1.13041i
$526$	35.8916	−	9.82664i	1.56495	−	0.428462i
$527$	−7.06802			−0.307888
$528$	−4.11572	−	19.1288i	−0.179114	−	0.832476i
$529$	9.37303	+	21.0035i	0.407523	+	0.913195i
$530$	6.43944	−	1.76303i	0.279711	−	0.0765813i
$531$	−0.294820	+	2.04392i	−0.0127941	+	0.0886984i
$532$	−25.4157	−	42.9358i	−1.10191	−	1.86150i
$533$	12.5619			0.544118
$534$	−21.5841	−	14.4451i	−0.934034	−	0.625101i
$535$	−4.58002			−0.198011
$536$	−25.6667	+	26.5182i	−1.10863	+	1.14541i
$537$	3.68297	+	4.25233i	0.158932	+	0.183502i
$538$	−8.47570	+	2.32054i	−0.365413	+	0.100045i
$539$			43.0458i			1.85412i
$540$	−3.67623	−	1.84803i	−0.158200	−	0.0795268i
$541$		−	5.52534i		−	0.237553i	−0.992921	−	0.118776i	$-0.962103\pi$
$541$		−	5.52534i		−	0.237553i	0.992921	−	0.118776i	$-0.0378972\pi$
$542$	−30.1184	+	8.24603i	−1.29370	+	0.354197i
$543$	−3.81614	−	4.40608i	−0.163766	−	0.189083i
$544$	1.72731	−	7.22702i	0.0740578	−	0.309856i
$545$			6.43733i			0.275745i
$546$	21.2483	+	14.2204i	0.909342	+	0.608575i
$547$			35.6835i			1.52572i	0.646566	+	0.762858i	$0.276204\pi$
$547$			35.6835i			1.52572i	−0.646566	+	0.762858i	$0.723796\pi$
$548$	30.3073	−	17.9403i	1.29467	−	0.766371i
$549$	0.670122	−	4.64579i	0.0286001	−	0.198277i
$550$	5.10813	+	18.6573i	0.217812	+	0.795551i
$551$	−21.4234			−0.912669
$552$	18.9727	+	13.8577i	0.807533	+	0.589823i
$553$	37.4481			1.59246
$554$	3.66545	+	13.3880i	0.155730	+	0.568800i
$555$	−3.06345	+	2.65328i	−0.130036	+	0.112625i
$556$	11.1690	+	18.8682i	0.473670	+	0.800191i
$557$			34.0487i			1.44269i	0.692576	+	0.721345i	$0.256476\pi$
$557$			34.0487i			1.44269i	−0.692576	+	0.721345i	$0.743524\pi$
$558$	−2.82317	−	22.6537i	−0.119514	−	0.959009i
$559$		−	20.5151i		−	0.867694i
$560$	−3.59289	+	6.54802i	−0.151827	+	0.276704i
$561$	−4.85698	+	4.20666i	−0.205062	+	0.177605i
$562$	26.5514	−	7.26944i	1.12000	−	0.306643i
$563$			27.3094i			1.15095i	0.817819	+	0.575476i	$0.195183\pi$
$563$			27.3094i			1.15095i	−0.817819	+	0.575476i	$0.804817\pi$
$564$	−8.40772	+	25.1562i	−0.354029	+	1.05927i
$565$			2.42283i			0.101929i
$566$	14.2937	−	3.91343i	0.600809	−	0.164494i
$567$	11.9952	−	40.7149i	0.503752	−	1.70986i
$568$	−16.9501	−	16.4058i	−0.711211	−	0.688373i
$569$	9.58502			0.401825			0.200912	−	0.979609i	$-0.435609\pi$
$569$	9.58502			0.401825			0.200912	+	0.979609i	$0.435609\pi$
$570$	−2.85329	+	4.26342i	−0.119511	+	0.178575i
$571$	16.3004			0.682150			0.341075	−	0.940036i	$-0.389209\pi$
$571$	16.3004			0.682150			0.341075	+	0.940036i	$0.389209\pi$
$572$	10.7578	−	6.36805i	0.449807	−	0.266261i
$573$	5.97840	+	6.90261i	0.249751	+	0.288361i
$574$	−36.5115	+	9.99638i	−1.52396	+	0.417241i
$575$	−19.4856	−	12.6421i	−0.812604	−	0.527214i
$576$	23.8533	+	2.64953i	0.993888	+	0.110397i
$577$	1.23178			0.0512799			0.0256399	−	0.999671i	$-0.491838\pi$
$577$	1.23178			0.0512799			0.0256399	+	0.999671i	$0.491838\pi$
$578$	20.8347	−	5.70428i	0.866611	−	0.237267i
$579$	16.4004	+	18.9357i	0.681575	+	0.786942i
$580$	1.63361	+	2.75974i	0.0678321	+	0.114592i
$581$	−16.4239			−0.681376
$582$	−19.2455	+	28.7570i	−0.797753	+	1.19201i
$583$	33.6750			1.39468
$584$	4.91857	−	5.08175i	0.203532	−	0.210284i
$585$	0.375310	−	2.60193i	0.0155172	−	0.107577i
$586$	−5.52728	−	20.1882i	−0.228330	−	0.833969i
$587$	35.3693			1.45985			0.729924	−	0.683528i	$-0.239555\pi$
$587$	35.3693			1.45985			0.729924	+	0.683528i	$0.239555\pi$
$588$	−50.0764	−	16.7366i	−2.06511	−	0.690205i
$589$	−28.4633			−1.17281
$590$	−0.101779	−	0.371747i	−0.00419020	−	0.0153046i
$591$	5.44104	+	6.28218i	0.223814	+	0.258414i
$592$	11.3714	−	20.7244i	0.467363	−	0.851766i
$593$		−	11.3915i		−	0.467792i	−0.972262	−	0.233896i	$-0.924852\pi$
$593$		−	11.3915i		−	0.467792i	0.972262	−	0.233896i	$-0.0751476\pi$
$594$	−15.4228	−	13.8869i	−0.632805	−	0.569785i
$595$	2.45272			0.100552
$596$	−9.33395	−	15.7683i	−0.382333	−	0.645893i
$597$	−10.1312	+	8.77470i	−0.414643	+	0.359125i
$598$	−4.55479	+	14.3033i	−0.186259	+	0.584905i
$599$			13.2344i			0.540744i	0.962756	+	0.270372i	$0.0871467\pi$
$599$			13.2344i			0.540744i	−0.962756	+	0.270372i	$0.912853\pi$
$600$	−23.6907	−	1.31170i	−0.967167	−	0.0535498i
$601$	−37.9482			−1.54794			−0.773969	−	0.633223i	$-0.781732\pi$
$601$	−37.9482			−1.54794			−0.773969	+	0.633223i	$0.781732\pi$
$602$	16.3252	+	59.6274i	0.665365	+	2.43023i
$603$	−5.58839	+	38.7429i	−0.227577	+	1.57773i
$604$	3.37074	−	1.99529i	0.137153	−	0.0811873i
$605$			1.19726i			0.0486754i
$606$	29.3808	+	19.6630i	1.19351	+	0.798756i
$607$	1.13190			0.0459423			0.0229711	−	0.999736i	$-0.492687\pi$
$607$	1.13190			0.0459423			0.0229711	+	0.999736i	$0.492687\pi$
$608$	6.95598	−	29.1037i	0.282102	−	1.18031i
$609$	−25.0071	+	21.6588i	−1.01334	+	0.877658i
$610$	0.231343	+	0.844975i	0.00936681	+	0.0342121i
$611$	−16.9465			−0.685581
$612$	−3.00529	−	7.28584i	−0.121482	−	0.294512i
$613$	−1.81100			−0.0731455			−0.0365728	−	0.999331i	$-0.511644\pi$
$613$	−1.81100			−0.0731455			−0.0365728	+	0.999331i	$0.511644\pi$
$614$	10.0442	+	36.6863i	0.405352	+	1.48054i
$615$	2.54822	+	2.94215i	0.102754	+	0.118639i
$616$	−26.2003	+	27.0696i	−1.05564	+	1.09066i
$617$	−27.8553			−1.12141			−0.560707	−	0.828014i	$-0.689471\pi$
$617$	−27.8553			−1.12141			−0.560707	+	0.828014i	$0.689471\pi$
$618$	9.68819	−	14.4762i	0.389716	−	0.582320i
$619$	−26.8676			−1.07990			−0.539951	−	0.841697i	$-0.681557\pi$
$619$	−26.8676			−1.07990			−0.539951	+	0.841697i	$0.681557\pi$
$620$	2.17043	+	3.66661i	0.0871666	+	0.147254i
$621$	24.9196	+	0.124902i	0.999987	+	0.00501214i
$622$	1.80209	+	6.58208i	0.0722571	+	0.263917i
$623$			50.0047i			2.00340i
$624$	3.22539	+	14.9908i	0.129119	+	0.600113i
$625$	22.6732			0.906928
$626$	−1.40084	−	5.11653i	−0.0559888	−	0.204498i
$627$	−19.5593	+	16.9405i	−0.781125	+	0.676538i
$628$	17.7521	−	10.5083i	0.708385	−	0.419326i
$629$	−7.76281			−0.309524
$630$	0.979686	+	7.86122i	0.0390316	+	0.313199i
$631$		−	9.81304i		−	0.390651i	−0.980738	−	0.195326i	$-0.937424\pi$
$631$		−	9.81304i		−	0.390651i	0.980738	−	0.195326i	$-0.0625764\pi$
$632$	16.1379	+	15.6197i	0.641931	+	0.621318i
$633$	−15.3647	+	13.3075i	−0.610694	+	0.528926i
$634$	25.1279	−	6.87970i	0.997957	−	0.273228i
$635$			0.285382i			0.0113250i
$636$	−13.0931	+	39.1751i	−0.519176	+	1.55339i
$637$		−	33.7340i		−	1.33659i
$638$	4.27149	+	15.6015i	0.169110	+	0.617670i
$639$	−24.7640	−	3.57203i	−0.979648	−	0.141307i
$640$	−4.27951	+	1.32320i	−0.169162	+	0.0523041i
$641$	−6.52799			−0.257840			−0.128920	−	0.991655i	$-0.541151\pi$
$641$	−6.52799			−0.257840			−0.128920	+	0.991655i	$0.541151\pi$
$642$	15.7596	−	23.5483i	0.621983	−	0.929377i
$643$	28.1486			1.11007			0.555037	−	0.831826i	$-0.312704\pi$
$643$	28.1486			1.11007			0.555037	+	0.831826i	$0.312704\pi$
$644$	1.85649	−	45.1974i	0.0731558	−	1.78103i
$645$	4.80486	−	4.16152i	0.189191	−	0.163860i
$646$	−9.47769	+	2.59487i	−0.372895	+	0.102094i
$647$		−	21.8960i		−	0.860822i	−0.902633	−	0.430411i	$-0.858369\pi$
$647$		−	21.8960i		−	0.860822i	0.902633	−	0.430411i	$-0.141631\pi$
$648$	22.1515	−	12.5424i	0.870192	−	0.492713i
$649$		−	1.94405i		−	0.0763107i
$650$	−4.00312	−	14.6213i	−0.157015	−	0.573495i
$651$	−33.2246	+	28.7760i	−1.30217	+	1.12782i
$652$	−3.79434	−	6.40994i	−0.148598	−	0.251033i
$653$	26.5566			1.03924			0.519620	−	0.854397i	$-0.326073\pi$
$653$	26.5566			1.03924			0.519620	+	0.854397i	$0.326073\pi$
$654$	−33.0977	−	22.1506i	−1.29422	−	0.866156i
$655$			3.62214i			0.141529i
$656$	−19.9038	−	10.9212i	−0.777112	−	0.426401i
$657$	1.07092	−	7.42440i	0.0417804	−	0.289653i
$658$	49.2552	−	13.4854i	1.92017	−	0.525717i
$659$			15.0532i			0.586391i	0.956052	+	0.293196i	$0.0947187\pi$
$659$			15.0532i			0.586391i	−0.956052	+	0.293196i	$0.905281\pi$
$660$	3.67372	+	1.22783i	0.142999	+	0.0477934i
$661$	−40.8683			−1.58959			−0.794797	−	0.606875i	$-0.792423\pi$
$661$	−40.8683			−1.58959			−0.794797	+	0.606875i	$0.792423\pi$
$662$	−3.11756	−	11.3868i	−0.121167	−	0.442560i
$663$	3.80630	−	3.29666i	0.147824	−	0.128032i
$664$	−7.07769	−	6.85042i	−0.274668	−	0.265848i
$665$	9.87725			0.383023
$666$	−3.10069	−	24.8806i	−0.120149	−	0.964105i
$667$	−16.2941	−	10.5715i	−0.630910	−	0.409331i
$668$	−22.0907	−	37.3188i	−0.854714	−	1.44391i
$669$	−23.8799	−	27.5716i	−0.923251	−	1.06598i
$670$	−1.92926	−	7.04656i	−0.0745337	−	0.272232i
$671$			4.41880i			0.170586i
$672$	−21.3038	−	41.0044i	−0.821813	−	1.58178i
$673$	−23.6230			−0.910599			−0.455300	−	0.890338i	$-0.650468\pi$
$673$	−23.6230			−0.910599			−0.455300	+	0.890338i	$0.650468\pi$
$674$	−2.89265	−	10.5653i	−0.111421	−	0.406962i
$675$	−21.1805	+	13.5914i	−0.815236	+	0.523134i
$676$	13.9433	−	8.25366i	0.536280	−	0.317449i
$677$		−	35.7529i		−	1.37409i	−0.726613	−	0.687047i	$-0.758907\pi$
$677$		−	35.7529i		−	1.37409i	0.726613	−	0.687047i	$-0.241093\pi$
$678$	−12.4571	−	8.33687i	−0.478411	−	0.320175i
$679$	66.6225			2.55674
$680$	1.05697	+	1.02303i	0.0405331	+	0.0392316i
$681$	32.3558	−	28.0236i	1.23988	−	1.07387i
$682$	5.67514	+	20.7283i	0.217312	+	0.793727i
$683$	8.95042			0.342478			0.171239	−	0.985229i	$-0.445223\pi$
$683$	8.95042			0.342478			0.171239	+	0.985229i	$0.445223\pi$
$684$	−12.1025	−	29.3405i	−0.462750	−	1.12186i
$685$			6.97211i			0.266391i
$686$	14.5158	+	53.0185i	0.554214	+	2.02425i
$687$	2.97452	+	3.43435i	0.113485	+	0.131029i
$688$	−17.8355	+	32.5051i	−0.679972	+	1.23924i
$689$	−26.3903			−1.00539
$690$	−4.27395	+	1.83467i	−0.162706	+	0.0698448i
$691$		−	26.7410i		−	1.01728i	−0.860981	−	0.508638i	$-0.830149\pi$
$691$		−	26.7410i		−	1.01728i	0.860981	−	0.508638i	$-0.169851\pi$
$692$	−4.81709	+	2.85145i	−0.183118	+	0.108396i
$693$	−5.70458	+	39.5484i	−0.216699	+	1.50232i
$694$	16.6656	−	4.56282i	0.632617	−	0.173202i
$695$	−4.34058			−0.164648
$696$	−19.8104	−	1.09686i	−0.750913	−	0.0415763i
$697$			7.45544i			0.282395i
$698$	−2.18417	−	7.97764i	−0.0826722	−	0.301958i
$699$	5.60935	−	4.85829i	0.212165	−	0.183758i
$700$	23.2703	+	39.3115i	0.879535	+	1.48584i
$701$		−	27.8508i		−	1.05191i	−0.850512	−	0.525956i	$-0.823708\pi$
$701$		−	27.8508i		−	1.05191i	0.850512	−	0.525956i	$-0.176292\pi$
$702$	12.0865	+	10.8828i	0.456175	+	0.410745i
$703$	−31.2613			−1.17904
$704$	−22.5815	+	0.737148i	−0.851073	+	0.0277823i
$705$	−3.43763	−	3.96906i	−0.129469	−	0.149483i
$706$	−7.41323	−	27.0766i	−0.279001	−	1.01904i
$707$		−	68.0677i		−	2.55995i
$708$	2.26157	+	0.755863i	0.0849949	+	0.0284071i
$709$	−0.598769			−0.0224872			−0.0112436	−	0.999937i	$-0.503579\pi$
$709$	−0.598769			−0.0224872			−0.0112436	+	0.999937i	$0.503579\pi$
$710$	4.50407	−	1.23316i	0.169035	−	0.0462795i
$711$	23.5773	+	3.40086i	0.884219	+	0.127542i
$712$	−20.8571	+	21.5490i	−0.781652	+	0.807584i
$713$	−21.6484	−	14.0454i	−0.810741	−	0.526005i
$714$	−8.43970	+	12.6107i	−0.315848	+	0.471945i
$715$			2.47480i			0.0925524i
$716$	5.58987	−	3.30890i	0.208903	−	0.123659i
$717$	−21.9450	+	19.0067i	−0.819550	+	0.709818i
$718$	−45.0375	+	12.3307i	−1.68078	+	0.460177i
$719$		−	20.7659i		−	0.774437i	−0.921988	−	0.387219i	$-0.873436\pi$
$719$		−	20.7659i		−	0.774437i	0.921988	−	0.387219i	$-0.126564\pi$
$720$	−2.85674	+	3.79634i	−0.106465	+	0.141481i
$721$	−33.5377			−1.24901
$722$	−12.2509	+	3.35415i	−0.455933	+	0.124829i
$723$	14.9347	−	12.9351i	0.555429	−	0.481060i
$724$	−5.79198	+	3.42854i	−0.215257	+	0.127421i
$725$	19.6151			0.728485
$726$	−6.15573	−	4.11971i	−0.228460	−	0.152897i
$727$		−	13.1588i		−	0.488032i	−0.969771	−	0.244016i	$-0.921535\pi$
$727$		−	13.1588i		−	0.488032i	0.969771	−	0.244016i	$-0.0784650\pi$
$728$	20.5326	−	21.2138i	0.760988	−	0.786235i
$729$	11.2497	−	24.5447i	0.416656	−	0.909064i
$730$	0.369708	+	1.35035i	0.0136835	+	0.0499787i
$731$	12.1756			0.450330
$732$	−5.14051	−	1.71807i	−0.189999	−	0.0635015i
$733$	6.22994			0.230108			0.115054	−	0.993359i	$-0.463296\pi$
$733$	6.22994			0.230108			0.115054	+	0.993359i	$0.463296\pi$
$734$	7.00006	+	25.5676i	0.258377	+	0.943716i
$735$	7.90089	−	6.84302i	0.291429	−	0.252408i
$736$	19.6519	−	18.7030i	0.724380	−	0.689401i
$737$		−	36.8500i		−	1.35739i
$738$	−23.8955	+	2.97791i	−0.879604	+	0.109619i
$739$		−	34.0856i		−	1.25386i	−0.779076	−	0.626929i	$-0.784312\pi$
$739$		−	34.0856i		−	1.25386i	0.779076	−	0.626929i	$-0.215688\pi$
$740$	2.38379	+	4.02704i	0.0876298	+	0.148037i
$741$	15.3282	−	13.2759i	0.563095	−	0.487701i
$742$	76.7039	−	21.0005i	2.81589	−	0.770954i
$743$	30.0894			1.10387			0.551936	−	0.833887i	$-0.313889\pi$
$743$	30.0894			1.10387			0.551936	+	0.833887i	$0.313889\pi$
$744$	−26.3203	−	1.45730i	−0.964949	−	0.0534270i
$745$	3.62744			0.132899
$746$	−13.2665	+	3.63220i	−0.485721	+	0.132984i
$747$	−10.3405	−	1.49154i	−0.378337	−	0.0545724i
$748$	3.77940	+	6.38471i	0.138189	+	0.233448i
$749$	−54.5553			−1.99341
$750$	5.30943	−	7.93343i	0.193873	−	0.289688i
$751$			43.8899i			1.60156i	0.598956	+	0.800782i	$0.295582\pi$
$751$			43.8899i			1.60156i	−0.598956	+	0.800782i	$0.704418\pi$
$752$	26.8508	+	14.7330i	0.979149	+	0.537258i
$753$	−3.48703	+	3.02014i	−0.127074	+	0.110060i
$754$	−3.34747	−	12.2265i	−0.121908	−	0.445264i
$755$			0.775427i			0.0282207i
$756$	−43.7898	−	22.0130i	−1.59262	−	0.800607i
$757$	6.82566			0.248083			0.124041	−	0.992277i	$-0.460414\pi$
$757$	6.82566			0.248083			0.124041	+	0.992277i	$0.460414\pi$
$758$	30.0493	−	8.22710i	1.09144	−	0.298822i
$759$	−23.2357	+	3.23278i	−0.843403	+	0.117343i
$760$	4.25650	+	4.11982i	0.154399	+	0.149442i
$761$			31.9286i			1.15741i	0.815537	+	0.578705i	$0.196442\pi$
$761$			31.9286i			1.15741i	−0.815537	+	0.578705i	$0.803558\pi$
$762$	−1.46730	−	0.981986i	−0.0531546	−	0.0355736i
$763$			76.6789i			2.77596i
$764$	9.07378	−	5.37118i	0.328278	−	0.194323i
$765$	1.54423	+	0.222744i	0.0558318	+	0.00805334i
$766$	3.94761	−	1.08080i	0.142633	−	0.0390510i
$767$			1.52351i			0.0550106i
$768$	7.92234	−	26.5563i	0.285873	−	0.958268i
$769$			4.82086i			0.173845i	0.996215	+	0.0869223i	$0.0277032\pi$
$769$			4.82086i			0.173845i	−0.996215	+	0.0869223i	$0.972297\pi$
$770$	−1.96937	−	7.19306i	−0.0709710	−	0.259220i
$771$	35.5720	−	30.8092i	1.28110	−	1.10956i
$772$	24.8918	−	14.7346i	0.895876	−	0.530310i
$773$		−	13.2817i		−	0.477710i	−0.971055	−	0.238855i	$-0.923228\pi$
$773$		−	13.2817i		−	0.477710i	0.971055	−	0.238855i	$-0.0767720\pi$
$774$	4.86327	+	39.0240i	0.174806	+	1.40269i
$775$	26.0607			0.936128
$776$	28.7103	+	27.7883i	1.03064	+	0.997544i
$777$	−36.4906	+	31.6047i	−1.30909	+	1.13381i
$778$	5.17360	+	18.8964i	0.185483	+	0.677470i
$779$			30.0235i			1.07570i
$780$	−2.87900	−	0.962224i	−0.103085	−	0.0344532i
$781$	23.5540			0.842830
$782$	−8.48893	−	2.70324i	−0.303563	−	0.0966677i
$783$	−17.7114	+	11.3653i	−0.632953	+	0.406164i
$784$	−29.3279	+	53.4498i	−1.04742	+	1.90892i
$785$			4.08381i			0.145758i
$786$	−18.6233	−	12.4636i	−0.664272	−	0.444563i
$787$	26.2992			0.937465			0.468733	−	0.883340i	$-0.344711\pi$
$787$	26.2992			0.937465			0.468733	+	0.883340i	$0.344711\pi$
$788$	8.25819	−	4.88840i	0.294186	−	0.174142i
$789$	−29.8379	−	34.4507i	−1.06226	−	1.22648i
$790$	−4.28824	+	1.17406i	−0.152569	+	0.0417714i
$791$			28.8598i			1.02614i
$792$	−18.9540	+	14.6636i	−0.673503	+	0.521048i
$793$		−	3.46291i		−	0.122971i
$794$	−1.04541	−	3.81833i	−0.0371002	−	0.135508i
$795$	−5.35333	−	6.18092i	−0.189863	−	0.219215i
$796$	7.88347	+	13.3179i	0.279422	+	0.472040i
$797$		−	12.3127i		−	0.436139i	−0.975933	−	0.218069i	$-0.930024\pi$
$797$		−	12.3127i		−	0.436139i	0.975933	−	0.218069i	$-0.0699759\pi$
$798$	−33.9872	+	50.7842i	−1.20313	+	1.79774i
$799$		−	10.0576i		−	0.355814i
$800$	−6.36882	+	26.6470i	−0.225172	+	0.942113i
$801$	−4.54119	+	31.4830i	−0.160455	+	1.11240i
$802$	−44.1053	+	12.0755i	−1.55741	+	0.426399i
$803$			7.06165i			0.249200i
$804$	42.8686	+	14.3276i	1.51186	+	0.505295i
$805$	7.51237	+	4.87400i	0.264776	+	0.171786i
$806$	−4.44747	−	16.2443i	−0.156655	−	0.572180i
$807$	7.04615	+	8.13543i	0.248036	+	0.286381i
$808$	28.3912	−	29.3331i	0.998798	−	1.03193i
$809$		−	16.3532i		−	0.574947i	−0.957789	−	0.287474i	$-0.907185\pi$
$809$		−	16.3532i		−	0.574947i	0.957789	−	0.287474i	$-0.0928154\pi$
$810$	−0.0971088	+	5.03839i	−0.00341206	+	0.177031i
$811$			36.0686i			1.26654i	0.773931	+	0.633270i	$0.218288\pi$
$811$			36.0686i			1.26654i	−0.773931	+	0.633270i	$0.781712\pi$
$812$	19.4589	+	32.8728i	0.682875	+	1.15361i
$813$	25.0385	+	28.9093i	0.878139	+	1.01389i
$814$	6.23301	+	22.7659i	0.218467	+	0.797945i
$815$	1.47459			0.0516525
$816$	−8.89696	+	1.91425i	−0.311456	+	0.0670121i
$817$	49.0318			1.71540
$818$	−8.04252	+	2.20194i	−0.281200	+	0.0769889i
$819$	4.47054	−	30.9932i	0.156213	−	1.08299i
$820$	3.86759	−	2.28940i	0.135062	−	0.0799493i
$821$	37.9900			1.32586			0.662929	−	0.748682i	$-0.269313\pi$
$821$	37.9900			1.32586			0.662929	+	0.748682i	$0.269313\pi$
$822$	−35.8473	−	23.9907i	−1.25032	−	0.836772i
$823$	−19.7154			−0.687237			−0.343618	−	0.939109i	$-0.611653\pi$
$823$	−19.7154			−0.687237			−0.343618	+	0.939109i	$0.611653\pi$
$824$	−14.4527	−	13.9886i	−0.503485	−	0.487317i
$825$	17.9083	−	15.5105i	0.623488	−	0.540007i
$826$	−1.21236	−	4.42810i	−0.0421833	−	0.154073i
$827$			27.6385i			0.961086i	0.876971	+	0.480543i	$0.159560\pi$
$827$			27.6385i			0.961086i	−0.876971	+	0.480543i	$0.840440\pi$
$828$	5.27345	−	28.2876i	0.183265	−	0.983064i
$829$		−	1.47448i		−	0.0512107i	−0.999672	−	0.0256054i	$-0.991849\pi$
$829$		−	1.47448i		−	0.0512107i	0.999672	−	0.0256054i	$-0.00815133\pi$
$830$	1.88072	−	0.514917i	0.0652807	−	0.0178730i
$831$	12.8505	−	11.1299i	0.445778	−	0.386092i
$832$	17.6966	−	0.577685i	0.613519	−	0.0200276i
$833$	20.0209			0.693684
$834$	14.9357	−	22.3172i	0.517182	−	0.772782i
$835$	8.58507			0.297098
$836$	15.2199	+	25.7116i	0.526390	+	0.889254i
$837$	−23.5315	+	15.1001i	−0.813367	+	0.521935i
$838$	1.47588	+	5.39061i	0.0509834	+	0.186215i
$839$	−55.9255			−1.93076			−0.965382	−	0.260840i	$-0.916001\pi$
$839$	−55.9255			−1.93076			−0.965382	+	0.260840i	$0.916001\pi$
$840$	9.13359	+	0.505706i	0.315139	+	0.0174485i
$841$	−12.5976			−0.434401
$842$	−25.5066	+	6.98338i	−0.879016	+	0.240663i
$843$	−22.0732	−	25.4855i	−0.760240	−	0.877767i
$844$	11.9559	+	20.1976i	0.411539	+	0.695231i
$845$			3.20761i			0.110345i
$846$	32.2358	−	4.01730i	1.10829	−	0.138118i
$847$			14.2612i			0.490022i
$848$	41.8141	+	22.9434i	1.43590	+	0.787879i
$849$	−11.8829	−	13.7199i	−0.407819	−	0.470865i
$850$	8.67766	−	2.37583i	0.297641	−	0.0814903i
$851$	−23.7765	−	15.4261i	−0.815049	−	0.528800i
$852$	−9.15801	+	27.4010i	−0.313748	+	0.938744i
$853$		−	39.5431i		−	1.35393i	−0.736016	−	0.676964i	$-0.763295\pi$
$853$		−	39.5431i		−	1.35393i	0.736016	−	0.676964i	$-0.236705\pi$
$854$	2.75567	+	10.0650i	0.0942970	+	0.344417i
$855$	6.21872	+	0.897005i	0.212676	+	0.0306769i
$856$	−23.5100	−	22.7551i	−0.803557	−	0.777754i
$857$			36.6030i			1.25033i	0.780491	+	0.625167i	$0.214969\pi$
$857$			36.6030i			1.25033i	−0.780491	+	0.625167i	$0.785031\pi$
$858$	−12.7243	−	8.51569i	−0.434399	−	0.290721i
$859$		−	26.6830i		−	0.910414i	−0.890386	−	0.455207i	$-0.849565\pi$
$859$		−	26.6830i		−	0.910414i	0.890386	−	0.455207i	$-0.150435\pi$
$860$	−3.73885	−	6.31620i	−0.127494	−	0.215381i
$861$	30.3533	+	35.0457i	1.03444	+	1.19436i
$862$	1.47398	−	0.403556i	0.0502040	−	0.0137452i
$863$		−	30.8021i		−	1.04851i	−0.851560	−	0.524257i	$-0.824343\pi$
$863$		−	30.8021i		−	1.04851i	0.851560	−	0.524257i	$-0.175657\pi$
$864$	−9.68906	−	27.7511i	−0.329629	−	0.944111i
$865$		−	1.10816i		−	0.0376784i
$866$	12.4027	+	45.3004i	0.421460	+	1.53937i
$867$	−17.3207	−	19.9983i	−0.588241	−	0.679178i
$868$	25.8533	+	43.6751i	0.877518	+	1.48243i
$869$	−22.4254			−0.760728
$870$	2.18456	−	3.26419i	0.0740634	−	0.110667i
$871$			28.8785i			0.978509i
$872$	−31.9829	+	33.0440i	−1.08308	+	1.11901i
$873$	41.9455	+	6.05034i	1.41964	+	0.204773i
$874$	−34.1854	−	10.8861i	−1.15634	−	0.368228i
$875$	−18.3797			−0.621347
$876$	−8.21501	−	2.74563i	−0.277559	−	0.0927662i
$877$		−	0.867456i		−	0.0292919i	−0.999893	−	0.0146460i	$-0.995338\pi$
$877$		−	0.867456i		−	0.0292919i	0.999893	−	0.0146460i	$-0.00466212\pi$
$878$	46.4359	−	12.7135i	1.56714	−	0.429061i
$879$	−19.3778	+	16.7832i	−0.653596	+	0.566084i
$880$	2.15156	−	3.92120i	0.0725291	−	0.132184i
$881$	46.7065			1.57358			0.786790	−	0.617220i	$-0.211741\pi$
$881$	46.7065			1.57358			0.786790	+	0.617220i	$0.211741\pi$
$882$	7.99693	+	64.1692i	0.269271	+	2.16069i
$883$		−	6.23955i		−	0.209978i	−0.994473	−	0.104989i	$-0.966519\pi$
$883$		−	6.23955i		−	0.209978i	0.994473	−	0.104989i	$-0.0334807\pi$
$884$	−2.96182	−	5.00354i	−0.0996169	−	0.168287i
$885$	−0.356823	+	0.309047i	−0.0119945	+	0.0103885i
$886$	−20.3983	+	5.58479i	−0.685294	+	0.187625i
$887$			15.4951i			0.520273i	0.965572	+	0.260137i	$0.0837676\pi$
$887$			15.4951i			0.520273i	−0.965572	+	0.260137i	$0.916232\pi$
$888$	−28.9076	−	1.60055i	−0.970077	−	0.0537109i
$889$			3.39935i			0.114011i
$890$	−1.56774	−	5.72612i	−0.0525506	−	0.191940i
$891$	−7.18320	+	24.3816i	−0.240646	+	0.816815i
$892$	−36.2440	+	21.4545i	−1.21354	+	0.718349i
$893$		−	40.5027i		−	1.35537i
$894$	−12.4819	+	18.6506i	−0.417456	+	0.623769i
$895$			1.28593i			0.0429840i
$896$	−50.9758	+	15.7614i	−1.70298	+	0.526552i
$897$	18.2093	−	2.53346i	0.607990	−	0.0845896i
$898$	−10.7202	−	39.1554i	−0.357739	−	1.30663i
$899$	21.7923			0.726814
$900$	11.0809	+	26.8638i	0.369363	+	0.895461i
$901$		−	15.6625i		−	0.521794i
$902$	21.8645	−	5.98621i	0.728008	−	0.199319i
$903$	57.2336	−	49.5704i	1.90461	−	1.64960i
$904$	−12.0375	+	12.4368i	−0.400361	+	0.413643i
$905$		−	1.33243i		−	0.0442914i
$906$	−3.98688	−	2.66821i	−0.132455	−	0.0886454i
$907$	4.85413			0.161179			0.0805894	−	0.996747i	$-0.474320\pi$
$907$	4.85413			0.161179			0.0805894	+	0.996747i	$0.474320\pi$
$908$	−25.1773	−	42.5331i	−0.835537	−	1.41151i
$909$	6.18159	−	42.8554i	0.205030	−	1.42142i
$910$	1.54335	+	5.63703i	0.0511614	+	0.186866i
$911$	−20.4767			−0.678425			−0.339212	−	0.940710i	$-0.610161\pi$
$911$	−20.4767			−0.678425			−0.339212	+	0.940710i	$0.610161\pi$
$912$	−35.8286	+	7.70880i	−1.18640	+	0.255264i
$913$	9.83523			0.325498
$914$	−10.7854	−	39.3936i	−0.356751	−	1.30302i
$915$	0.811053	−	0.702458i	0.0268126	−	0.0232226i
$916$	4.51460	−	2.67240i	0.149167	−	0.0882986i
$917$			43.1455i			1.42479i
$918$	−6.45888	+	7.17326i	−0.213175	+	0.236753i
$919$			43.3874i			1.43122i	0.698501	+	0.715609i	$0.253851\pi$
$919$			43.3874i			1.43122i	−0.698501	+	0.715609i	$0.746149\pi$
$920$	1.20443	+	5.23382i	0.0397088	+	0.172554i
$921$	35.2135	−	30.4986i	1.16032	−	1.00496i
$922$	−16.3650	+	4.48053i	−0.538953	+	0.147558i
$923$	−18.4587			−0.607577
$924$	43.7598	+	14.6255i	1.43959	+	0.481142i
$925$	28.6225			0.941102
$926$	25.4239	−	6.96074i	0.835482	−	0.228744i
$927$	−21.1153	−	3.04574i	−0.693519	−	0.100035i
$928$	−5.32569	+	22.2826i	−0.174824	+	0.731461i
$929$		−	31.0888i		−	1.01999i	−0.860178	−	0.509995i	$-0.829647\pi$
$929$		−	31.0888i		−	1.01999i	0.860178	−	0.509995i	$-0.170353\pi$
$930$	2.90242	−	4.33683i	0.0951740	−	0.142210i
$931$	80.6255			2.64239
$932$	−4.36485	−	7.37373i	−0.142975	−	0.241534i
$933$	6.31783	−	5.47192i	0.206836	−	0.179142i
$934$	5.95152	+	21.7378i	0.194740	+	0.711281i
$935$	−1.46878			−0.0480343
$936$	14.8538	−	11.4915i	0.485513	−	0.375612i
$937$		−	52.2497i		−	1.70692i	−0.521155	−	0.853462i	$-0.674499\pi$
$937$		−	52.2497i		−	1.70692i	0.521155	−	0.853462i	$-0.325501\pi$
$938$	−22.9805	−	83.9358i	−0.750341	−	2.74060i
$939$	−4.91112	+	4.25356i	−0.160268	+	0.138810i
$940$	−5.21750	+	3.08848i	−0.170176	+	0.100735i
$941$		−	3.84298i		−	0.125278i	−0.998036	−	0.0626388i	$-0.980048\pi$
$941$		−	3.84298i		−	0.125278i	0.998036	−	0.0626388i	$-0.0199516\pi$
$942$	−20.9970	−	14.0522i	−0.684121	−	0.457846i
$943$	−14.8153	+	22.8351i	−0.482453	+	0.743612i
$944$	1.32452	−	2.41392i	0.0431093	−	0.0785664i
$945$	8.16582	−	5.23998i	0.265634	−	0.170457i
$946$	−9.77615	−	35.7071i	−0.317850	−	1.16094i
$947$	−49.4587			−1.60719			−0.803596	−	0.595175i	$-0.797083\pi$
$947$	−49.4587			−1.60719			−0.803596	+	0.595175i	$0.797083\pi$
$948$	8.71917	−	26.0880i	0.283185	−	0.847300i
$949$		−	5.53405i		−	0.179643i
$950$	34.9455	−	9.56761i	1.13378	−	0.310414i
$951$	−20.8897	−	24.1191i	−0.677396	−	0.782116i
$952$	12.5902	+	12.1860i	0.408052	+	0.394949i
$953$	−38.9441			−1.26152			−0.630761	−	0.775977i	$-0.717257\pi$
$953$	−38.9441			−1.26152			−0.630761	+	0.775977i	$0.717257\pi$
$954$	50.1999	−	6.25605i	1.62528	−	0.202547i
$955$			2.08739i			0.0675465i
$956$	17.0762	+	28.8476i	0.552284	+	0.932998i
$957$	14.9752	−	12.9701i	0.484079	−	0.419264i
$958$	−12.8681	+	3.52312i	−0.415750	+	0.113827i
$959$			83.0489i			2.68179i
$960$	3.72509	+	4.02756i	0.120227	+	0.129989i
$961$	−2.04656			−0.0660182
$962$	−4.88466	−	17.8411i	−0.157488	−	0.575220i
$963$	−34.3480	−	4.95445i	−1.10685	−	0.159655i
$964$	−11.6213	−	19.6323i	−0.374296	−	0.632315i
$965$			5.72629i			0.184336i
$966$	−50.9095	+	21.8539i	−1.63799	+	0.703137i
$967$	−25.4511			−0.818453			−0.409227	−	0.912433i	$-0.634201\pi$
$967$	−25.4511			−0.818453			−0.409227	+	0.912433i	$0.634201\pi$
$968$	−5.94838	+	6.14573i	−0.191188	+	0.197531i
$969$	7.87914	+	9.09720i	0.253114	+	0.292244i
$970$	−7.62904	+	2.08873i	−0.244954	+	0.0670651i
$971$		−	36.6730i		−	1.17689i	−0.808536	−	0.588447i	$-0.799740\pi$
$971$		−	36.6730i		−	1.17689i	0.808536	−	0.588447i	$-0.200260\pi$
$972$	−25.5709	−	17.8362i	−0.820187	−	0.572096i
$973$	−51.7032			−1.65753
$974$	57.3466	−	15.7007i	1.83750	−	0.503084i
$975$	−14.0343	+	12.1552i	−0.449458	+	0.389278i
$976$	−3.01060	+	5.48680i	−0.0963671	+	0.175628i
$977$	12.1650			0.389194			0.194597	−	0.980883i	$-0.437660\pi$
$977$	12.1650			0.389194			0.194597	+	0.980883i	$0.437660\pi$
$978$	−5.07399	+	7.58163i	−0.162248	+	0.242434i
$979$		−	29.9447i		−	0.957038i
$980$	−6.14798	−	10.3861i	−0.196390	−	0.331771i
$981$	−6.96361	+	48.2770i	−0.222331	+	1.54137i
$982$	−40.3887	+	11.0579i	−1.28886	+	0.352872i
$983$	5.40024			0.172241			0.0861204	−	0.996285i	$-0.472553\pi$
$983$	5.40024			0.172241			0.0861204	+	0.996285i	$0.472553\pi$
$984$	−1.53718	+	27.7630i	−0.0490034	+	0.885053i
$985$			1.89977i			0.0605317i
$986$	7.25638	−	1.98670i	0.231090	−	0.0632695i
$987$	−40.9476	−	47.2778i	−1.30338	−	1.50487i
$988$	−11.9274	−	20.1496i	−0.379463	−	0.641043i
$989$	37.2922	+	24.1950i	1.18582	+	0.769357i
$990$	−0.586673	−	4.70760i	−0.0186457	−	0.149617i
$991$	17.4881			0.555528			0.277764	−	0.960649i	$-0.410407\pi$
$991$	17.4881			0.555528			0.277764	+	0.960649i	$0.410407\pi$
$992$	−7.07575	+	29.6048i	−0.224655	+	0.939953i
$993$	−10.9297	+	9.46625i	−0.346842	+	0.300402i
$994$	53.6507	−	14.6889i	1.70170	−	0.465902i
$995$	−3.06374			−0.0971272
$996$	−3.82402	+	11.4416i	−0.121169	+	0.362540i
$997$		−	3.42160i		−	0.108363i	−0.998531	−	0.0541816i	$-0.982745\pi$
$997$		−	3.42160i		−	0.108363i	0.998531	−	0.0541816i	$-0.0172550\pi$
$998$	14.1548	+	51.7002i	0.448064	+	1.63654i
$999$	−25.8447	+	16.5844i	−0.817689	+	0.524708i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.b.c.413.8	yes	80
3.2	odd	2	inner	552.2.b.c.413.73	yes	80
4.3	odd	2		2208.2.b.c.689.22		80
8.3	odd	2		2208.2.b.c.689.59		80
8.5	even	2	inner	552.2.b.c.413.75	yes	80
12.11	even	2		2208.2.b.c.689.57		80
23.22	odd	2	inner	552.2.b.c.413.7	yes	80
24.5	odd	2	inner	552.2.b.c.413.6	yes	80
24.11	even	2		2208.2.b.c.689.24		80
69.68	even	2	inner	552.2.b.c.413.74	yes	80
92.91	even	2		2208.2.b.c.689.21		80
184.45	odd	2	inner	552.2.b.c.413.76	yes	80
184.91	even	2		2208.2.b.c.689.60		80
276.275	odd	2		2208.2.b.c.689.58		80
552.275	odd	2		2208.2.b.c.689.23		80
552.413	even	2	inner	552.2.b.c.413.5	✓	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.b.c.413.5	✓	80	552.413	even	2	inner
552.2.b.c.413.6	yes	80	24.5	odd	2	inner
552.2.b.c.413.7	yes	80	23.22	odd	2	inner
552.2.b.c.413.8	yes	80	1.1	even	1	trivial
552.2.b.c.413.73	yes	80	3.2	odd	2	inner
552.2.b.c.413.74	yes	80	69.68	even	2	inner
552.2.b.c.413.75	yes	80	8.5	even	2	inner
552.2.b.c.413.76	yes	80	184.45	odd	2	inner
2208.2.b.c.689.21		80	92.91	even	2
2208.2.b.c.689.22		80	4.3	odd	2
2208.2.b.c.689.23		80	552.275	odd	2
2208.2.b.c.689.24		80	24.11	even	2
2208.2.b.c.689.57		80	12.11	even	2
2208.2.b.c.689.58		80	276.275	odd	2
2208.2.b.c.689.59		80	8.3	odd	2
2208.2.b.c.689.60		80	184.91	even	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	552.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.36401 + 0.373449i) q^{2} +(1.13395 + 1.30925i) q^{3} +(1.72107 - 1.01878i) q^{4} +0.395927i q^{5} +(-2.03567 - 1.36237i) q^{6} +4.71612i q^{7} +(-1.96710 + 2.03236i) q^{8} +(-0.428296 + 2.96927i) q^{9} +O(q^{10})\)	\(q+(-1.36401 + 0.373449i) q^{2} +(1.13395 + 1.30925i) q^{3} +(1.72107 - 1.01878i) q^{4} +0.395927i q^{5} +(-2.03567 - 1.36237i) q^{6} +4.71612i q^{7} +(-1.96710 + 2.03236i) q^{8} +(-0.428296 + 2.96927i) q^{9} +(-0.147859 - 0.540050i) q^{10} -2.82419i q^{11} +(3.28546 + 1.09807i) q^{12} +2.21325i q^{13} +(-1.76123 - 6.43286i) q^{14} +(-0.518369 + 0.448963i) q^{15} +(1.92417 - 3.50679i) q^{16} -1.31355 q^{17} +(-0.524670 - 4.21007i) q^{18} -5.28976 q^{19} +(0.403363 + 0.681419i) q^{20} +(-6.17461 + 5.34787i) q^{21} +(1.05469 + 3.85224i) q^{22} +(-4.02325 - 2.61027i) q^{23} +(-4.89149 - 0.270830i) q^{24} +4.84324 q^{25} +(-0.826538 - 3.01891i) q^{26} +(-4.37320 + 2.80627i) q^{27} +(4.80470 + 8.11678i) q^{28} +4.04998 q^{29} +(0.539398 - 0.805977i) q^{30} +5.38084 q^{31} +(-1.31499 + 5.50189i) q^{32} +(3.69759 - 3.20251i) q^{33} +(1.79171 - 0.490546i) q^{34} -1.86724 q^{35} +(2.28791 + 5.54666i) q^{36} +5.90978 q^{37} +(7.21531 - 1.97546i) q^{38} +(-2.89771 + 2.50973i) q^{39} +(-0.804668 - 0.778829i) q^{40} -5.67578i q^{41} +(6.42510 - 9.60047i) q^{42} -9.26919 q^{43} +(-2.87723 - 4.86064i) q^{44} +(-1.17561 - 0.169574i) q^{45} +(6.46257 + 2.05796i) q^{46} +7.65682i q^{47} +(6.77320 - 1.45731i) q^{48} -15.2418 q^{49} +(-6.60625 + 1.80871i) q^{50} +(-1.48951 - 1.71978i) q^{51} +(2.25482 + 3.80917i) q^{52} +11.9238i q^{53} +(4.91711 - 5.46096i) q^{54} +1.11817 q^{55} +(-9.58488 - 9.27710i) q^{56} +(-5.99834 - 6.92564i) q^{57} +(-5.52424 + 1.51246i) q^{58} +0.688356 q^{59} +(-0.434756 + 1.30080i) q^{60} -1.56462 q^{61} +(-7.33954 + 2.00947i) q^{62} +(-14.0034 - 2.01990i) q^{63} +(-0.261012 - 7.99574i) q^{64} -0.876287 q^{65} +(-3.84759 + 5.74913i) q^{66} +13.0480 q^{67} +(-2.26072 + 1.33822i) q^{68} +(-1.14467 - 8.22738i) q^{69} +(2.54694 - 0.697320i) q^{70} +8.34009i q^{71} +(-5.19214 - 6.71131i) q^{72} -2.50041 q^{73} +(-8.06103 + 2.20701i) q^{74} +(5.49201 + 6.34104i) q^{75} +(-9.10405 + 5.38910i) q^{76} +13.3192 q^{77} +(3.01526 - 4.50545i) q^{78} -7.94045i q^{79} +(1.38843 + 0.761832i) q^{80} +(-8.63313 - 2.54345i) q^{81} +(2.11962 + 7.74185i) q^{82} +3.48249i q^{83} +(-5.17863 + 15.4946i) q^{84} -0.520071i q^{85} +(12.6433 - 3.46157i) q^{86} +(4.59250 + 5.30246i) q^{87} +(5.73979 + 5.55548i) q^{88} +10.6029 q^{89} +(1.66688 - 0.207731i) q^{90} -10.4380 q^{91} +(-9.58358 - 0.393646i) q^{92} +(6.10163 + 7.04489i) q^{93} +(-2.85943 - 10.4440i) q^{94} -2.09436i q^{95} +(-8.69451 + 4.51723i) q^{96} -14.1265i q^{97} +(20.7901 - 5.69205i) q^{98} +(8.38579 + 1.20959i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 12 q^{6} - 4 q^{9}+O(q^{10}) \) 80 * q - 12 * q^6 - 4 * q^9	\( 80 q - 12 q^{6} - 4 q^{9} + 16 q^{12} + 8 q^{16} + 20 q^{18} - 8 q^{24} - 144 q^{25} - 24 q^{31} + 40 q^{36} + 68 q^{39} - 24 q^{46} + 92 q^{48} - 160 q^{49} - 48 q^{52} - 32 q^{54} + 32 q^{55} - 40 q^{58} + 48 q^{64} + 72 q^{70} + 68 q^{72} - 8 q^{73} + 64 q^{78} + 12 q^{81} - 48 q^{82} + 92 q^{87} - 144 q^{94} + 68 q^{96}+O(q^{100}) \) 80 * q - 12 * q^6 - 4 * q^9 + 16 * q^12 + 8 * q^16 + 20 * q^18 - 8 * q^24 - 144 * q^25 - 24 * q^31 + 40 * q^36 + 68 * q^39 - 24 * q^46 + 92 * q^48 - 160 * q^49 - 48 * q^52 - 32 * q^54 + 32 * q^55 - 40 * q^58 + 48 * q^64 + 72 * q^70 + 68 * q^72 - 8 * q^73 + 64 * q^78 + 12 * q^81 - 48 * q^82 + 92 * q^87 - 144 * q^94 + 68 * q^96

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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