LMFDB - Embedded newform 804.2.c.b.671.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [804,2,Mod(671,804)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(804, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("804.671");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 804 = 2^{2} \cdot 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	804.c (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:	$6.41997232251$
Analytic rank:	$0$
Dimension:	$128$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			671.6
Character	$\chi$	$=$	804.671
Dual form			804.2.c.b.671.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.40536 + 0.157993i) q^{2} +(1.10632 - 1.33268i) q^{3} +(1.95008 - 0.444075i) q^{4} -1.25971i q^{5} +(-1.34423 + 2.04769i) q^{6} +4.86310i q^{7} +(-2.67040 + 0.932185i) q^{8} +(-0.552098 - 2.94876i) q^{9} +O(q^{10})$	\(q+(-1.40536 + 0.157993i) q^{2} +(1.10632 - 1.33268i) q^{3} +(1.95008 - 0.444075i) q^{4} -1.25971i q^{5} +(-1.34423 + 2.04769i) q^{6} +4.86310i q^{7} +(-2.67040 + 0.932185i) q^{8} +(-0.552098 - 2.94876i) q^{9} +(0.199026 + 1.77035i) q^{10} +2.77221 q^{11} +(1.56560 - 3.09013i) q^{12} -0.427783 q^{13} +(-0.768337 - 6.83441i) q^{14} +(-1.67880 - 1.39365i) q^{15} +(3.60559 - 1.73196i) q^{16} -6.13077i q^{17} +(1.24178 + 4.05684i) q^{18} +5.50865i q^{19} +(-0.559407 - 2.45653i) q^{20} +(6.48098 + 5.38016i) q^{21} +(-3.89595 + 0.437991i) q^{22} +7.85942 q^{23} +(-1.71202 + 4.59010i) q^{24} +3.41313 q^{25} +(0.601189 - 0.0675869i) q^{26} +(-4.54057 - 2.52651i) q^{27} +(2.15958 + 9.48341i) q^{28} +5.86394i q^{29} +(2.57950 + 1.69334i) q^{30} -6.21018i q^{31} +(-4.79352 + 3.00369i) q^{32} +(3.06696 - 3.69448i) q^{33} +(0.968620 + 8.61594i) q^{34} +6.12610 q^{35} +(-2.38610 - 5.50513i) q^{36} +9.87650 q^{37} +(-0.870330 - 7.74164i) q^{38} +(-0.473266 + 0.570100i) q^{39} +(1.17428 + 3.36393i) q^{40} +2.42494i q^{41} +(-9.95814 - 6.53711i) q^{42} -3.59689i q^{43} +(5.40602 - 1.23107i) q^{44} +(-3.71459 + 0.695484i) q^{45} +(-11.0453 + 1.24174i) q^{46} +2.24122 q^{47} +(1.68079 - 6.72123i) q^{48} -16.6497 q^{49} +(-4.79667 + 0.539251i) q^{50} +(-8.17038 - 6.78261i) q^{51} +(-0.834209 + 0.189968i) q^{52} -6.38222i q^{53} +(6.78031 + 2.83328i) q^{54} -3.49218i q^{55} +(-4.53331 - 12.9864i) q^{56} +(7.34129 + 6.09435i) q^{57} +(-0.926465 - 8.24096i) q^{58} -14.1971 q^{59} +(-3.89267 - 1.97221i) q^{60} +11.5337 q^{61} +(0.981168 + 8.72754i) q^{62} +(14.3401 - 2.68491i) q^{63} +(6.26206 - 4.97861i) q^{64} +0.538883i q^{65} +(-3.72648 + 5.67664i) q^{66} -1.00000i q^{67} +(-2.72252 - 11.9555i) q^{68} +(8.69506 - 10.4741i) q^{69} +(-8.60938 + 0.967883i) q^{70} -1.23130 q^{71} +(4.22311 + 7.35971i) q^{72} +1.24895 q^{73} +(-13.8800 + 1.56042i) q^{74} +(3.77602 - 4.54862i) q^{75} +(2.44626 + 10.7423i) q^{76} +13.4815i q^{77} +(0.575038 - 0.875969i) q^{78} -2.27216i q^{79} +(-2.18177 - 4.54201i) q^{80} +(-8.39038 + 3.25601i) q^{81} +(-0.383125 - 3.40792i) q^{82} +5.12319 q^{83} +(15.0276 + 7.61368i) q^{84} -7.72300 q^{85} +(0.568285 + 5.05493i) q^{86} +(7.81479 + 6.48742i) q^{87} +(-7.40291 + 2.58421i) q^{88} +7.91523i q^{89} +(5.11045 - 1.56429i) q^{90} -2.08035i q^{91} +(15.3265 - 3.49017i) q^{92} +(-8.27622 - 6.87047i) q^{93} +(-3.14972 + 0.354098i) q^{94} +6.93931 q^{95} +(-1.30021 + 9.71131i) q^{96} +10.0240 q^{97} +(23.3989 - 2.63055i) q^{98} +(-1.53053 - 8.17458i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q + 4 q^{4} - 6 q^{6} - 4 q^{9}+O(q^{10}) $ 128 * q + 4 * q^4 - 6 * q^6 - 4 * q^9	$ 128 q + 4 q^{4} - 6 q^{6} - 4 q^{9} - 4 q^{10} + 4 q^{12} - 8 q^{13} - 4 q^{16} + 18 q^{18} - 8 q^{21} - 8 q^{22} - 24 q^{24} - 136 q^{25} + 14 q^{30} - 32 q^{33} + 34 q^{36} - 48 q^{37} + 16 q^{40} - 28 q^{42} - 16 q^{45} - 28 q^{46} - 22 q^{48} - 152 q^{49} + 8 q^{52} - 16 q^{54} - 32 q^{57} - 20 q^{58} - 14 q^{60} + 8 q^{61} + 16 q^{64} + 14 q^{66} + 56 q^{69} - 4 q^{70} - 8 q^{72} - 48 q^{73} - 36 q^{76} + 40 q^{78} + 44 q^{81} + 60 q^{82} + 46 q^{84} + 64 q^{85} - 28 q^{88} - 14 q^{90} + 32 q^{93} - 8 q^{96} + 64 q^{97}+O(q^{100}) $ 128 * q + 4 * q^4 - 6 * q^6 - 4 * q^9 - 4 * q^10 + 4 * q^12 - 8 * q^13 - 4 * q^16 + 18 * q^18 - 8 * q^21 - 8 * q^22 - 24 * q^24 - 136 * q^25 + 14 * q^30 - 32 * q^33 + 34 * q^36 - 48 * q^37 + 16 * q^40 - 28 * q^42 - 16 * q^45 - 28 * q^46 - 22 * q^48 - 152 * q^49 + 8 * q^52 - 16 * q^54 - 32 * q^57 - 20 * q^58 - 14 * q^60 + 8 * q^61 + 16 * q^64 + 14 * q^66 + 56 * q^69 - 4 * q^70 - 8 * q^72 - 48 * q^73 - 36 * q^76 + 40 * q^78 + 44 * q^81 + 60 * q^82 + 46 * q^84 + 64 * q^85 - 28 * q^88 - 14 * q^90 + 32 * q^93 - 8 * q^96 + 64 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/804\mathbb{Z}\right)^\times$.

$n$	$269$	$337$	$403$
$\chi(n)$	$-1$	$1$	$-1$

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 $

$2$	−1.40536	+	0.157993i	−0.993740	+	0.111718i
$2$	−1.40536	+	0.157993i	−0.993740	+	0.111718i
$3$	1.10632	−	1.33268i	0.638736	−	0.769426i
$3$	1.10632	−	1.33268i	0.638736	−	0.769426i
$4$	1.95008	−	0.444075i	0.975038	−	0.222038i
$5$		−	1.25971i		−	0.563360i	−0.959508	−	0.281680i	$-0.909108\pi$
$5$		−	1.25971i		−	0.563360i	0.959508	−	0.281680i	$-0.0908917\pi$
$6$	−1.34423	+	2.04769i	−0.548779	+	0.835968i
$7$			4.86310i			1.83808i	0.394166	+	0.919039i	$0.371033\pi$
$7$			4.86310i			1.83808i	−0.394166	+	0.919039i	$0.628967\pi$
$8$	−2.67040	+	0.932185i	−0.944129	+	0.329577i
$9$	−0.552098	−	2.94876i	−0.184033	−	0.982920i
$10$	0.199026	+	1.77035i	0.0629376	+	0.559833i
$11$	2.77221			0.835853			0.417926	−	0.908481i	$-0.362757\pi$
$11$	2.77221			0.835853			0.417926	+	0.908481i	$0.362757\pi$
$12$	1.56560	−	3.09013i	0.451950	−	0.892043i
$13$	−0.427783			−0.118646			−0.0593228	−	0.998239i	$-0.518894\pi$
$13$	−0.427783			−0.118646			−0.0593228	+	0.998239i	$0.518894\pi$
$14$	−0.768337	−	6.83441i	−0.205347	−	1.82657i
$15$	−1.67880	−	1.39365i	−0.433464	−	0.359838i
$16$	3.60559	−	1.73196i	0.901399	−	0.432990i
$17$		−	6.13077i		−	1.48693i	−0.668775	−	0.743465i	$-0.733181\pi$
$17$		−	6.13077i		−	1.48693i	0.668775	−	0.743465i	$-0.266819\pi$
$18$	1.24178	+	4.05684i	0.292691	+	0.956207i
$19$			5.50865i			1.26377i	0.775062	+	0.631885i	$0.217719\pi$
$19$			5.50865i			1.26377i	−0.775062	+	0.631885i	$0.782281\pi$
$20$	−0.559407	−	2.45653i	−0.125087	−	0.549298i
$21$	6.48098	+	5.38016i	1.41427	+	1.17405i
$22$	−3.89595	+	0.437991i	−0.830620	+	0.0933799i
$23$	7.85942			1.63880			0.819401	−	0.573221i	$-0.194306\pi$
$23$	7.85942			1.63880			0.819401	+	0.573221i	$0.194306\pi$
$24$	−1.71202	+	4.59010i	−0.349464	+	0.936950i
$25$	3.41313			0.682625
$26$	0.601189	−	0.0675869i	0.117903	−	0.0132549i
$27$	−4.54057	−	2.52651i	−0.873833	−	0.486227i
$28$	2.15958	+	9.48341i	0.408123	+	1.79220i
$29$			5.86394i			1.08891i	0.838791	+	0.544454i	$0.183263\pi$
$29$			5.86394i			1.08891i	−0.838791	+	0.544454i	$0.816737\pi$
$30$	2.57950	+	1.69334i	0.470951	+	0.309160i
$31$		−	6.21018i		−	1.11538i	−0.830049	−	0.557691i	$-0.811688\pi$
$31$		−	6.21018i		−	1.11538i	0.830049	−	0.557691i	$-0.188312\pi$
$32$	−4.79352	+	3.00369i	−0.847383	+	0.530982i
$33$	3.06696	−	3.69448i	0.533889	−	0.643127i
$34$	0.968620	+	8.61594i	0.166117	+	1.47762i
$35$	6.12610			1.03550
$36$	−2.38610	−	5.50513i	−0.397684	−	0.917522i
$37$	9.87650			1.62369			0.811844	−	0.583875i	$-0.198464\pi$
$37$	9.87650			1.62369			0.811844	+	0.583875i	$0.198464\pi$
$38$	−0.870330	−	7.74164i	−0.141186	−	1.25586i
$39$	−0.473266	+	0.570100i	−0.0757833	+	0.0912891i
$40$	1.17428	+	3.36393i	0.185671	+	0.531884i
$41$			2.42494i			0.378713i	0.981908	+	0.189356i	$0.0606401\pi$
$41$			2.42494i			0.378713i	−0.981908	+	0.189356i	$0.939360\pi$
$42$	−9.95814	−	6.53711i	−1.53657	−	1.00870i
$43$		−	3.59689i		−	0.548521i	−0.961655	−	0.274260i	$-0.911567\pi$
$43$		−	3.59689i		−	0.548521i	0.961655	−	0.274260i	$-0.0884330\pi$
$44$	5.40602	−	1.23107i	0.814988	−	0.185591i
$45$	−3.71459	+	0.695484i	−0.553738	+	0.103677i
$46$	−11.0453	+	1.24174i	−1.62854	+	0.183084i
$47$	2.24122			0.326915			0.163458	−	0.986550i	$-0.447735\pi$
$47$	2.24122			0.326915			0.163458	+	0.986550i	$0.447735\pi$
$48$	1.68079	−	6.72123i	0.242602	−	0.970126i
$49$	−16.6497			−2.37853
$50$	−4.79667	+	0.539251i	−0.678352	+	0.0762617i
$51$	−8.17038	−	6.78261i	−1.14408	−	0.949755i
$52$	−0.834209	+	0.189968i	−0.115684	+	0.0263438i
$53$		−	6.38222i		−	0.876665i	−0.898813	−	0.438333i	$-0.855569\pi$
$53$		−	6.38222i		−	0.876665i	0.898813	−	0.438333i	$-0.144431\pi$
$54$	6.78031	+	2.83328i	0.922683	+	0.385560i
$55$		−	3.49218i		−	0.470886i
$56$	−4.53331	−	12.9864i	−0.605789	−	1.73538i
$57$	7.34129	+	6.09435i	0.972378	+	0.807216i
$58$	−0.926465	−	8.24096i	−0.121651	−	1.08209i
$59$	−14.1971			−1.84830			−0.924151	−	0.382027i	$-0.875226\pi$
$59$	−14.1971			−1.84830			−0.924151	+	0.382027i	$0.875226\pi$
$60$	−3.89267	−	1.97221i	−0.502542	−	0.254611i
$61$	11.5337			1.47674			0.738368	−	0.674398i	$-0.235597\pi$
$61$	11.5337			1.47674			0.738368	+	0.674398i	$0.235597\pi$
$62$	0.981168	+	8.72754i	0.124608	+	1.10840i
$63$	14.3401	−	2.68491i	1.80668	−	0.338266i
$64$	6.26206	−	4.97861i	0.782758	−	0.622327i
$65$			0.538883i			0.0668402i
$66$	−3.72648	+	5.67664i	−0.458698	+	0.698746i
$67$		−	1.00000i		−	0.122169i
$67$		−	1.00000i		−	0.122169i
$68$	−2.72252	−	11.9555i	−0.330154	−	1.44981i
$69$	8.69506	−	10.4741i	1.04676	−	1.26094i
$70$	−8.60938	+	0.967883i	−1.02902	+	0.115684i
$71$	−1.23130			−0.146128			−0.0730639	−	0.997327i	$-0.523278\pi$
$71$	−1.23130			−0.146128			−0.0730639	+	0.997327i	$0.523278\pi$
$72$	4.22311	+	7.35971i	0.497699	+	0.867350i
$73$	1.24895			0.146179			0.0730895	−	0.997325i	$-0.476714\pi$
$73$	1.24895			0.146179			0.0730895	+	0.997325i	$0.476714\pi$
$74$	−13.8800	+	1.56042i	−1.61352	+	0.181395i
$75$	3.77602	−	4.54862i	0.436017	−	0.525230i
$76$	2.44626	+	10.7423i	0.280605	+	1.23222i
$77$			13.4815i			1.53636i
$78$	0.575038	−	0.875969i	0.0651102	−	0.0991839i
$79$		−	2.27216i		−	0.255638i	−0.991797	−	0.127819i	$-0.959202\pi$
$79$		−	2.27216i		−	0.255638i	0.991797	−	0.127819i	$-0.0407977\pi$
$80$	−2.18177	−	4.54201i	−0.243930	−	0.507812i
$81$	−8.39038	+	3.25601i	−0.932264	+	0.361779i
$82$	−0.383125	−	3.40792i	−0.0423091	−	0.376342i
$83$	5.12319			0.562343			0.281172	−	0.959657i	$-0.409277\pi$
$83$	5.12319			0.562343			0.281172	+	0.959657i	$0.409277\pi$
$84$	15.0276	+	7.61368i	1.63964	+	0.830720i
$85$	−7.72300			−0.837677
$86$	0.568285	+	5.05493i	0.0612797	+	0.545087i
$87$	7.81479	+	6.48742i	0.837834	+	0.695524i
$88$	−7.40291	+	2.58421i	−0.789152	+	0.275478i
$89$			7.91523i			0.839012i	0.907752	+	0.419506i	$0.137797\pi$
$89$			7.91523i			0.839012i	−0.907752	+	0.419506i	$0.862203\pi$
$90$	5.11045	−	1.56429i	0.538689	−	0.164890i
$91$		−	2.08035i		−	0.218080i
$92$	15.3265	−	3.49017i	1.59789	−	0.363876i
$93$	−8.27622	−	6.87047i	−0.858204	−	0.712434i
$94$	−3.14972	+	0.354098i	−0.324869	+	0.0365224i
$95$	6.93931			0.711958
$96$	−1.30021	+	9.71131i	−0.132702	+	0.991156i
$97$	10.0240			1.01778			0.508890	−	0.860831i	$-0.330056\pi$
$97$	10.0240			1.01778			0.508890	+	0.860831i	$0.330056\pi$
$98$	23.3989	−	2.63055i	2.36364	−	0.265725i
$99$	−1.53053	−	8.17458i	−0.153824	−	0.821576i
$100$	6.65586	−	1.51569i	0.665586	−	0.151569i
$101$		−	14.1039i		−	1.40339i	−0.712478	−	0.701695i	$-0.752427\pi$
$101$		−	14.1039i		−	1.40339i	0.712478	−	0.701695i	$-0.247573\pi$
$102$	12.5539	+	8.24114i	1.24302	+	0.815995i
$103$			10.8924i			1.07326i	0.843818	+	0.536629i	$0.180303\pi$
$103$			10.8924i			1.07326i	−0.843818	+	0.536629i	$0.819697\pi$
$104$	1.14235	−	0.398773i	0.112017	−	0.0391029i
$105$	6.77745	−	8.16416i	0.661411	−	0.796741i
$106$	1.00835	+	8.96932i	0.0979395	+	0.871177i
$107$	2.87635			0.278067			0.139034	−	0.990288i	$-0.455600\pi$
$107$	2.87635			0.278067			0.139034	+	0.990288i	$0.455600\pi$
$108$	−9.97641	−	2.91053i	−0.959981	−	0.280066i
$109$	−18.3966			−1.76208			−0.881038	−	0.473045i	$-0.843155\pi$
$109$	−18.3966			−1.76208			−0.881038	+	0.473045i	$0.843155\pi$
$110$	0.551742	+	4.90778i	0.0526065	+	0.467938i
$111$	10.9266	−	13.1623i	1.03711	−	1.24931i
$112$	8.42270	+	17.5344i	0.795870	+	1.65684i
$113$			6.39464i			0.601557i	0.953694	+	0.300779i	$0.0972466\pi$
$113$			6.39464i			0.601557i	−0.953694	+	0.300779i	$0.902753\pi$
$114$	−11.2800	−	7.40488i	−1.05647	−	0.693530i
$115$		−	9.90060i		−	0.923236i
$116$	2.60403	+	11.4351i	0.241778	+	1.06173i
$117$	0.236178	+	1.26143i	0.0218347	+	0.116619i
$118$	19.9520	−	2.24305i	1.83673	−	0.206489i
$119$	29.8145			2.73309
$120$	5.78220	+	2.15665i	0.527840	+	0.196874i
$121$	−3.31485			−0.301350
$122$	−16.2090	+	1.82225i	−1.46749	+	0.164978i
$123$	3.23169	+	2.68277i	0.291391	+	0.241897i
$124$	−2.75779	−	12.1103i	−0.247657	−	1.08754i
$125$		−	10.5981i		−	0.947924i
$126$	−19.7288	+	6.03890i	−1.75758	+	0.537988i
$127$			0.300709i			0.0266836i	0.999911	+	0.0133418i	$0.00424696\pi$
$127$			0.300709i			0.0266836i	−0.999911	+	0.0133418i	$0.995753\pi$
$128$	−8.01387	+	7.98611i	−0.708332	+	0.705879i
$129$	−4.79352	−	3.97932i	−0.422046	−	0.350360i
$130$	−0.0851400	−	0.757325i	−0.00746727	−	0.0664218i
$131$	−1.25125			−0.109322			−0.0546609	−	0.998505i	$-0.517408\pi$
$131$	−1.25125			−0.109322			−0.0546609	+	0.998505i	$0.517408\pi$
$132$	4.34018	−	8.56648i	0.377764	−	0.745617i
$133$	−26.7891			−2.32291
$134$	0.157993	+	1.40536i	0.0136486	+	0.121405i
$135$	−3.18267	+	5.71981i	−0.273921	+	0.492282i
$136$	5.71501	+	16.3716i	0.490058	+	1.40385i
$137$		−	1.25825i		−	0.107500i	−0.998554	−	0.0537498i	$-0.982883\pi$
$137$		−	1.25825i		−	0.107500i	0.998554	−	0.0537498i	$-0.0171173\pi$
$138$	−10.5648	+	16.0937i	−0.899339	+	1.36999i
$139$		−	20.8734i		−	1.77046i	−0.465157	−	0.885228i	$-0.654002\pi$
$139$		−	20.8734i		−	1.77046i	0.465157	−	0.885228i	$-0.345998\pi$
$140$	11.9464	−	2.72045i	1.00965	−	0.229920i
$141$	2.47951	−	2.98684i	0.208813	−	0.251537i
$142$	1.73041	−	0.194537i	0.145213	−	0.0163251i
$143$	−1.18590			−0.0991703
$144$	−7.09778	−	9.67582i	−0.591482	−	0.806318i
$145$	7.38688			0.613447
$146$	−1.75523	+	0.197326i	−0.145264	+	0.0163309i
$147$	−18.4200	+	22.1888i	−1.51925	+	1.83010i
$148$	19.2599	−	4.38591i	1.58316	−	0.360520i
$149$			10.2635i			0.840821i	0.907334	+	0.420410i	$0.138114\pi$
$149$			10.2635i			0.840821i	−0.907334	+	0.420410i	$0.861886\pi$
$150$	−4.58802	+	6.98904i	−0.374610	+	0.570653i
$151$			23.0493i			1.87573i	0.347004	+	0.937864i	$0.387199\pi$
$151$			23.0493i			1.87573i	−0.347004	+	0.937864i	$0.612801\pi$
$152$	−5.13508	−	14.7103i	−0.416510	−	1.19316i
$153$	−18.0782	+	3.38478i	−1.46153	+	0.273644i
$154$	−2.12999	−	18.9464i	−0.171640	−	1.52674i
$155$	−7.82304			−0.628362
$156$	−0.669738	+	1.32190i	−0.0536220	+	0.105837i
$157$	10.2970			0.821791			0.410895	−	0.911683i	$-0.365216\pi$
$157$	10.2970			0.821791			0.410895	+	0.911683i	$0.365216\pi$
$158$	0.358987	+	3.19321i	0.0285594	+	0.254038i
$159$	−8.50549	−	7.06080i	−0.674529	−	0.559958i
$160$	3.78378	+	6.03845i	0.299134	+	0.477382i
$161$			38.2211i			3.01225i
$162$	11.2771	−	5.90149i	0.886011	−	0.463665i
$163$			2.16912i			0.169898i	0.996385	+	0.0849491i	$0.0270728\pi$
$163$			2.16912i			0.169898i	−0.996385	+	0.0849491i	$0.972927\pi$
$164$	1.07686	+	4.72883i	0.0840885	+	0.369259i
$165$	−4.65398	−	3.86348i	−0.362312	−	0.300772i
$166$	−7.19993	+	0.809431i	−0.558823	+	0.0628240i
$167$	−14.9163			−1.15426			−0.577130	−	0.816652i	$-0.695828\pi$
$167$	−14.9163			−1.15426			−0.577130	+	0.816652i	$0.695828\pi$
$168$	−22.3221	−	8.32570i	−1.72219	−	0.642342i
$169$	−12.8170			−0.985923
$170$	10.8536	−	1.22018i	0.832433	−	0.0935837i
$171$	16.2437	−	3.04131i	1.24219	−	0.232575i
$172$	−1.59729	−	7.01421i	−0.121792	−	0.534829i
$173$			4.41053i			0.335327i	0.985844	+	0.167663i	$0.0536222\pi$
$173$			4.41053i			0.335327i	−0.985844	+	0.167663i	$0.946378\pi$
$174$	−12.0076	−	7.88248i	−0.910291	−	0.597569i
$175$			16.5984i			1.25472i
$176$	9.99546	−	4.80136i	0.753436	−	0.361916i
$177$	−15.7066	+	18.9202i	−1.18058	+	1.42213i
$178$	−1.25055	−	11.1237i	−0.0937330	−	0.833760i
$179$	−20.9886			−1.56876			−0.784382	−	0.620278i	$-0.787020\pi$
$179$	−20.9886			−1.56876			−0.784382	+	0.620278i	$0.787020\pi$
$180$	−6.93488	+	3.00580i	−0.516896	+	0.224039i
$181$	1.59101			0.118259			0.0591293	−	0.998250i	$-0.481168\pi$
$181$	1.59101			0.118259			0.0591293	+	0.998250i	$0.481168\pi$
$182$	0.328682	+	2.92364i	0.0243635	+	0.216715i
$183$	12.7600	−	15.3708i	0.943245	−	1.13624i
$184$	−20.9878	+	7.32643i	−1.54724	+	0.540112i
$185$		−	12.4415i		−	0.914721i
$186$	12.7166	+	8.34790i	0.932423	+	0.612097i
$187$		−	16.9958i		−	1.24285i
$188$	4.37055	−	0.995270i	0.318755	−	0.0725875i
$189$	12.2867	−	22.0812i	0.893723	−	1.60617i
$190$	−9.75223	+	1.09637i	−0.707501	+	0.0795387i
$191$	3.47535			0.251467			0.125734	−	0.992064i	$-0.459872\pi$
$191$	3.47535			0.251467			0.125734	+	0.992064i	$0.459872\pi$
$192$	0.292943	−	13.8533i	0.0211413	−	0.999776i
$193$	−5.09586			−0.366808			−0.183404	−	0.983038i	$-0.558712\pi$
$193$	−5.09586			−0.366808			−0.183404	+	0.983038i	$0.558712\pi$
$194$	−14.0873	+	1.58372i	−1.01141	+	0.113705i
$195$	0.718162	+	0.596179i	0.0514286	+	0.0426933i
$196$	−32.4682	+	7.39373i	−2.31916	+	0.528124i
$197$			2.07682i			0.147967i	0.997259	+	0.0739836i	$0.0235713\pi$
$197$			2.07682i			0.147967i	−0.997259	+	0.0739836i	$0.976429\pi$
$198$	3.44248	+	11.2464i	0.244646	+	0.799248i
$199$			3.56635i			0.252812i	0.991979	+	0.126406i	$0.0403441\pi$
$199$			3.56635i			0.252812i	−0.991979	+	0.126406i	$0.959656\pi$
$200$	−9.11441	+	3.18167i	−0.644486	+	0.224978i
$201$	−1.33268	−	1.10632i	−0.0940003	−	0.0780340i
$202$	2.22832	+	19.8210i	0.156784	+	1.39460i
$203$	−28.5169			−2.00150
$204$	−18.9448	−	9.59834i	−1.32640	−	0.672018i
$205$	3.05473			0.213352
$206$	−1.72092	−	15.3077i	−0.119902	−	1.06654i
$207$	−4.33917	−	23.1755i	−0.301593	−	1.61081i
$208$	−1.54241	+	0.740904i	−0.106947	+	0.0513724i
$209$			15.2711i			1.05633i
$210$	−8.23487	+	12.5444i	−0.568260	+	0.865645i
$211$			1.25689i			0.0865278i	0.999064	+	0.0432639i	$0.0137756\pi$
$211$			1.25689i			0.0865278i	−0.999064	+	0.0432639i	$0.986224\pi$
$212$	−2.83419	−	12.4458i	−0.194653	−	0.854782i
$213$	−1.36221	+	1.64093i	−0.0933371	+	0.112435i
$214$	−4.04231	+	0.454444i	−0.276326	+	0.0310652i
$215$	−4.53104			−0.309015
$216$	14.4803	+	2.51414i	0.985260	+	0.171065i
$217$	30.2007			2.05016
$218$	25.8539	−	2.90654i	1.75105	−	0.196856i
$219$	1.38175	−	1.66446i	0.0933698	−	0.112474i
$220$	−1.55079	−	6.81003i	−0.104554	−	0.459132i
$221$			2.62264i			0.176418i
$222$	−13.2763	+	20.2241i	−0.891045	+	1.35735i
$223$			1.37687i			0.0922018i	0.998937	+	0.0461009i	$0.0146796\pi$
$223$			1.37687i			0.0922018i	−0.998937	+	0.0461009i	$0.985320\pi$
$224$	−14.6072	−	23.3114i	−0.975987	−	1.55756i
$225$	−1.88438	−	10.0645i	−0.125625	−	0.670966i
$226$	−1.01031	−	8.98678i	−0.0672049	−	0.597792i
$227$	9.52868			0.632441			0.316220	−	0.948686i	$-0.397586\pi$
$227$	9.52868			0.632441			0.316220	+	0.948686i	$0.397586\pi$
$228$	17.0224	+	8.62435i	1.12734	+	0.571162i
$229$	7.49602			0.495351			0.247675	−	0.968843i	$-0.420333\pi$
$229$	7.49602			0.495351			0.247675	+	0.968843i	$0.420333\pi$
$230$	1.56423	+	13.9139i	0.103142	+	0.917456i
$231$	17.9666	+	14.9149i	1.18212	+	0.981330i
$232$	−5.46628	−	15.6591i	−0.358879	−	1.02807i
$233$			4.31409i			0.282625i	0.989965	+	0.141313i	$0.0451323\pi$
$233$			4.31409i			0.282625i	−0.989965	+	0.141313i	$0.954868\pi$
$234$	−0.531213	−	1.73545i	−0.0347265	−	0.113450i
$235$		−	2.82329i		−	0.184171i
$236$	−27.6854	+	6.30457i	−1.80217	+	0.410393i
$237$	−3.02808	−	2.51375i	−0.196695	−	0.163285i
$238$	−41.9001	+	4.71050i	−2.71598	+	0.305336i
$239$	−11.8383			−0.765755			−0.382878	−	0.923799i	$-0.625067\pi$
$239$	−11.8383			−0.765755			−0.382878	+	0.923799i	$0.625067\pi$
$240$	−8.46681	−	2.11732i	−0.546530	−	0.136672i
$241$	−0.457915			−0.0294969			−0.0147484	−	0.999891i	$-0.504695\pi$
$241$	−0.457915			−0.0294969			−0.0147484	+	0.999891i	$0.504695\pi$
$242$	4.65857	−	0.523725i	0.299464	−	0.0336663i
$243$	−4.94323	+	14.7839i	−0.317108	+	0.948389i
$244$	22.4916	−	5.12182i	1.43987	−	0.327891i
$245$			20.9738i			1.33997i
$246$	−4.96555	−	3.25968i	−0.316592	−	0.207829i
$247$		−	2.35651i		−	0.149941i
$248$	5.78904	+	16.5837i	0.367604	+	1.05306i
$249$	5.66791	−	6.82760i	0.359189	−	0.432682i
$250$	1.67443	+	14.8942i	0.105900	+	0.941990i
$251$	−16.5781			−1.04640			−0.523201	−	0.852209i	$-0.675262\pi$
$251$	−16.5781			−1.04640			−0.523201	+	0.852209i	$0.675262\pi$
$252$	26.7720	−	11.6039i	1.68648	−	0.730975i
$253$	21.7879			1.36980
$254$	−0.0475101	−	0.422605i	−0.00298105	−	0.0265166i
$255$	−8.54413	+	10.2923i	−0.535054	+	0.644530i
$256$	10.0006	−	12.4895i	0.625039	−	0.780594i
$257$		−	0.0721774i		−	0.00450230i	−0.999997	−	0.00225115i	$-0.999283\pi$
$257$		−	0.0721774i		−	0.00450230i	0.999997	−	0.00225115i	$-0.000716564\pi$
$258$	7.36533	+	4.83504i	0.458546	+	0.301016i
$259$			48.0304i			2.98446i
$260$	0.239305	+	1.05086i	0.0148411	+	0.0651718i
$261$	17.2914	−	3.23747i	1.07031	−	0.200395i
$262$	1.75845	−	0.197688i	0.108637	−	0.0122132i
$263$	−20.1693			−1.24369			−0.621846	−	0.783139i	$-0.713617\pi$
$263$	−20.1693			−1.24369			−0.621846	+	0.783139i	$0.713617\pi$
$264$	−4.74607	+	12.7247i	−0.292100	+	0.783152i
$265$	−8.03976			−0.493878
$266$	37.6483	−	4.23250i	2.30837	−	0.259511i
$267$	10.5485	+	8.75680i	0.645558	+	0.535907i
$268$	−0.444075	−	1.95008i	−0.0271262	−	0.119120i
$269$		−	7.29380i		−	0.444711i	−0.974966	−	0.222355i	$-0.928625\pi$
$269$		−	7.29380i		−	0.444711i	0.974966	−	0.222355i	$-0.0713745\pi$
$270$	3.56911	−	8.54123i	0.217209	−	0.519803i
$271$			12.9899i			0.789083i	0.918878	+	0.394541i	$0.129096\pi$
$271$			12.9899i			0.789083i	−0.918878	+	0.394541i	$0.870904\pi$
$272$	−10.6182	−	22.1051i	−0.643826	−	1.34032i
$273$	−2.77245	−	2.30154i	−0.167796	−	0.139296i
$274$	0.198795	+	1.76830i	0.0120097	+	0.106827i
$275$	9.46190			0.570574
$276$	12.3047	−	24.2866i	0.740657	−	1.46188i
$277$	−14.0622			−0.844918			−0.422459	−	0.906382i	$-0.638833\pi$
$277$	−14.0622			−0.844918			−0.422459	+	0.906382i	$0.638833\pi$
$278$	3.29786	+	29.3346i	0.197792	+	1.75937i
$279$	−18.3123	+	3.42863i	−1.09633	+	0.205267i
$280$	−16.3591	+	5.71066i	−0.977645	+	0.341277i
$281$			19.9722i			1.19144i	0.803192	+	0.595720i	$0.203133\pi$
$281$			19.9722i			1.19144i	−0.803192	+	0.595720i	$0.796867\pi$
$282$	−3.01271	+	4.58933i	−0.179404	+	0.273291i
$283$			3.20880i			0.190743i	0.995442	+	0.0953716i	$0.0304039\pi$
$283$			3.20880i			0.190743i	−0.995442	+	0.0953716i	$0.969596\pi$
$284$	−2.40112	+	0.546788i	−0.142480	+	0.0324459i
$285$	7.67712	−	9.24791i	0.454753	−	0.547799i
$286$	1.66662	−	0.187365i	0.0985495	−	0.0110791i
$287$	−11.7927			−0.696104
$288$	11.5037	+	12.4766i	0.677859	+	0.735192i
$289$	−20.5863			−1.21096
$290$	−10.3812	+	1.16708i	−0.609607	+	0.0685332i
$291$	11.0898	−	13.3588i	0.650093	−	0.783107i
$292$	2.43556	−	0.554630i	0.142530	−	0.0324572i
$293$			2.12004i			0.123854i	0.998081	+	0.0619270i	$0.0197246\pi$
$293$			2.12004i			0.123854i	−0.998081	+	0.0619270i	$0.980275\pi$
$294$	22.3810	−	34.0935i	1.30529	−	1.98838i
$295$			17.8842i			1.04126i
$296$	−26.3742	+	9.20673i	−1.53297	+	0.535130i
$297$	−12.5874	−	7.00401i	−0.730395	−	0.406414i
$298$	−1.62157	−	14.4239i	−0.0939350	−	0.835557i
$299$	−3.36213			−0.194437
$300$	5.34360	−	10.5470i	0.308513	−	0.608931i
$301$	17.4920			1.00822
$302$	−3.64164	−	32.3926i	−0.209553	−	1.86399i
$303$	−18.7960	−	15.6035i	−1.07980	−	0.896395i
$304$	9.54077	+	19.8620i	0.547201	+	1.13916i
$305$		−	14.5291i		−	0.831935i
$306$	24.8716	−	7.61307i	1.42181	−	0.435210i
$307$		−	7.78622i		−	0.444383i	−0.975003	−	0.222192i	$-0.928679\pi$
$307$		−	7.78622i		−	0.444383i	0.975003	−	0.222192i	$-0.0713210\pi$
$308$	5.98681	+	26.2900i	0.341130	+	1.49801i
$309$	14.5161	+	12.0505i	0.825793	+	0.685529i
$310$	10.9942	−	1.23599i	0.624428	−	0.0701994i
$311$	−9.43231			−0.534857			−0.267429	−	0.963578i	$-0.586174\pi$
$311$	−9.43231			−0.534857			−0.267429	+	0.963578i	$0.586174\pi$
$312$	0.732371	−	1.96357i	0.0414624	−	0.111165i
$313$	20.1611			1.13957			0.569786	−	0.821793i	$-0.307026\pi$
$313$	20.1611			1.13957			0.569786	+	0.821793i	$0.307026\pi$
$314$	−14.4710	+	1.62686i	−0.816646	+	0.0918090i
$315$	−3.38221	−	18.0644i	−0.190566	−	1.01781i
$316$	−1.00901	−	4.43089i	−0.0567613	−	0.249257i
$317$			10.4607i			0.587531i	0.955877	+	0.293766i	$0.0949085\pi$
$317$			10.4607i			0.587531i	−0.955877	+	0.293766i	$0.905091\pi$
$318$	13.0688	+	8.57916i	0.732864	+	0.481095i
$319$			16.2561i			0.910166i
$320$	−6.27162	−	7.88839i	−0.350594	−	0.440975i
$321$	3.18217	−	3.83327i	0.177611	−	0.213952i
$322$	−6.03868	−	53.7144i	−0.336523	−	2.99339i
$323$	33.7722			1.87914
$324$	−14.9160	+	10.0754i	−0.828664	+	0.559746i
$325$	−1.46008			−0.0809905
$326$	−0.342706	−	3.04839i	−0.0189807	−	0.168835i
$327$	−20.3526	+	24.5169i	−1.12550	+	1.35579i
$328$	−2.26050	−	6.47557i	−0.124815	−	0.357553i
$329$			10.8993i			0.600896i
$330$	7.15093	+	4.69429i	0.393646	+	0.258412i
$331$			1.38752i			0.0762652i	0.999273	+	0.0381326i	$0.0121409\pi$
$331$			1.38752i			0.0762652i	−0.999273	+	0.0381326i	$0.987859\pi$
$332$	9.99062	−	2.27508i	0.548306	−	0.124861i
$333$	−5.45280	−	29.1234i	−0.298812	−	1.59596i
$334$	20.9628	−	2.35668i	1.14704	−	0.128952i
$335$	−1.25971			−0.0688254
$336$	32.6860	+	8.17386i	1.78317	+	0.445921i
$337$	22.9907			1.25239			0.626193	−	0.779668i	$-0.284612\pi$
$337$	22.9907			1.25239			0.626193	+	0.779668i	$0.284612\pi$
$338$	18.0125	−	2.02500i	0.979751	−	0.110146i
$339$	8.52204	+	7.07454i	0.462854	+	0.384236i
$340$	−15.0604	+	3.42959i	−0.816767	+	0.185996i
$341$		−	17.2159i		−	0.932295i
$342$	−22.3477	+	6.84054i	−1.20843	+	0.369894i
$343$		−	46.9275i		−	2.53385i
$344$	3.35297	+	9.60513i	0.180780	+	0.517874i
$345$	−13.1944	−	10.9533i	−0.710361	−	0.589704i
$346$	−0.696835	−	6.19839i	−0.0374621	−	0.333228i
$347$	0.285568			0.0153301			0.00766504	−	0.999971i	$-0.497560\pi$
$347$	0.285568			0.0153301			0.00766504	+	0.999971i	$0.497560\pi$
$348$	18.1203	+	9.18060i	0.971352	+	0.492132i
$349$	−33.2446			−1.77954			−0.889770	−	0.456409i	$-0.849136\pi$
$349$	−33.2446			−1.77954			−0.889770	+	0.456409i	$0.849136\pi$
$350$	−2.62243	−	23.3267i	−0.140175	−	1.24686i
$351$	1.94238	+	1.08080i	0.103676	+	0.0576887i
$352$	−13.2886	+	8.32686i	−0.708287	+	0.443823i
$353$		−	14.1619i		−	0.753762i	−0.926262	−	0.376881i	$-0.876997\pi$
$353$		−	14.1619i		−	0.753762i	0.926262	−	0.376881i	$-0.123003\pi$
$354$	19.0841	−	29.0713i	1.01431	−	1.54512i
$355$			1.55108i			0.0823226i
$356$	3.51496	+	15.4353i	0.186292	+	0.818069i
$357$	32.9845	−	39.7333i	1.74572	−	2.10291i
$358$	29.4966	−	3.31607i	1.55894	−	0.175260i
$359$	13.7325			0.724773			0.362386	−	0.932028i	$-0.381962\pi$
$359$	13.7325			0.724773			0.362386	+	0.932028i	$0.381962\pi$
$360$	9.27111	−	5.31990i	0.488630	−	0.280384i
$361$	−11.3452			−0.597117
$362$	−2.23594	+	0.251369i	−0.117518	+	0.0132116i
$363$	−3.66730	+	4.41766i	−0.192483	+	0.231867i
$364$	−0.923832	−	4.05684i	−0.0484220	−	0.212636i
$365$		−	1.57332i		−	0.0823514i
$366$	−15.5039	+	23.6175i	−0.810402	+	1.23450i
$367$		−	10.3004i		−	0.537675i	−0.963185	−	0.268838i	$-0.913360\pi$
$367$		−	10.3004i		−	0.537675i	0.963185	−	0.268838i	$-0.0866395\pi$
$368$	28.3379	−	13.6122i	1.47721	−	0.709585i
$369$	7.15058	−	1.33881i	0.372244	−	0.0696955i
$370$	1.96568	+	17.4849i	0.102191	+	0.908995i
$371$	31.0374			1.61138
$372$	−19.1903	−	9.72267i	−0.994968	−	0.504097i
$373$	−10.7157			−0.554836			−0.277418	−	0.960749i	$-0.589479\pi$
$373$	−10.7157			−0.554836			−0.277418	+	0.960749i	$0.589479\pi$
$374$	2.68522	+	23.8852i	0.138849	+	1.23507i
$375$	−14.1239	−	11.7249i	−0.729357	−	0.605473i
$376$	−5.98495	+	2.08923i	−0.308650	+	0.107744i
$377$		−	2.50850i		−	0.129194i
$378$	−13.7785	+	32.9733i	−0.708690	+	1.69596i
$379$		−	26.8420i		−	1.37878i	−0.724390	−	0.689391i	$-0.757878\pi$
$379$		−	26.8420i		−	1.37878i	0.724390	−	0.689391i	$-0.242122\pi$
$380$	13.5322	−	3.08158i	0.694186	−	0.158082i
$381$	0.400751	+	0.332682i	0.0205311	+	0.0170438i
$382$	−4.88412	+	0.549082i	−0.249893	+	0.0280935i
$383$	3.61111			0.184519			0.0922596	−	0.995735i	$-0.470591\pi$
$383$	3.61111			0.184519			0.0922596	+	0.995735i	$0.470591\pi$
$384$	1.77704	+	19.5152i	0.0906842	+	0.995880i
$385$	16.9828			0.865525
$386$	7.16152	−	0.805112i	0.364512	−	0.0409791i
$387$	−10.6064	+	1.98584i	−0.539152	+	0.100946i
$388$	19.5475	−	4.45140i	0.992375	−	0.225986i
$389$			28.8138i			1.46092i	0.682958	+	0.730458i	$0.260693\pi$
$389$			28.8138i			1.46092i	−0.682958	+	0.730458i	$0.739307\pi$
$390$	−1.10347	−	0.724382i	−0.0558763	−	0.0366805i
$391$		−	48.1842i		−	2.43678i
$392$	44.4614	−	15.5206i	2.24564	−	0.783910i
$393$	−1.38428	+	1.66752i	−0.0698278	+	0.0841150i
$394$	−0.328124	−	2.91868i	−0.0165306	−	0.147041i
$395$	−2.86227			−0.144016
$396$	−6.61478	−	15.2614i	−0.332405	−	0.766913i
$397$	12.1436			0.609471			0.304736	−	0.952437i	$-0.401432\pi$
$397$	12.1436			0.609471			0.304736	+	0.952437i	$0.401432\pi$
$398$	−0.563459	−	5.01200i	−0.0282437	−	0.251229i
$399$	−29.6374	+	35.7014i	−1.48373	+	1.78731i
$400$	12.3063	−	5.91140i	0.615317	−	0.295570i
$401$			34.5972i			1.72770i	0.503746	+	0.863852i	$0.331955\pi$
$401$			34.5972i			1.72770i	−0.503746	+	0.863852i	$0.668045\pi$
$402$	2.04769	+	1.34423i	0.102130	+	0.0670440i
$403$			2.65661i			0.132335i
$404$	−6.26319	−	27.5037i	−0.311605	−	1.36836i
$405$	4.10163	+	10.5695i	0.203812	+	0.525200i
$406$	40.0766	−	4.50549i	1.98897	−	0.223604i
$407$	27.3797			1.35716
$408$	28.1408	+	10.4960i	1.39318	+	0.519628i
$409$	−19.5900			−0.968663			−0.484331	−	0.874885i	$-0.660937\pi$
$409$	−19.5900			−0.968663			−0.484331	+	0.874885i	$0.660937\pi$
$410$	−4.29300	+	0.482627i	−0.212016	+	0.0238353i
$411$	−1.67685	−	1.39203i	−0.0827130	−	0.0686639i
$412$	4.83704	+	21.2410i	0.238304	+	1.04647i
$413$		−	69.0418i		−	3.39732i
$414$	9.75968	+	31.8844i	0.479662	+	1.56703i
$415$		−	6.45375i		−	0.316802i
$416$	2.05059	−	1.28493i	0.100538	−	0.0629988i
$417$	−27.8176	−	23.0927i	−1.36224	−	1.13085i
$418$	−2.41274	−	21.4614i	−0.118011	−	1.04971i
$419$	−24.5940			−1.20150			−0.600748	−	0.799439i	$-0.705130\pi$
$419$	−24.5940			−1.20150			−0.600748	+	0.799439i	$0.705130\pi$
$420$	9.59104	−	18.9304i	0.467995	−	0.923711i
$421$	−11.6977			−0.570112			−0.285056	−	0.958511i	$-0.592012\pi$
$421$	−11.6977			−0.570112			−0.285056	+	0.958511i	$0.592012\pi$
$422$	−0.198580	−	1.76638i	−0.00966673	−	0.0859861i
$423$	−1.23737	−	6.60882i	−0.0601631	−	0.321332i
$424$	5.94941	+	17.0431i	0.288929	+	0.827685i
$425$		−	20.9251i		−	1.01502i
$426$	1.65514	−	2.52132i	0.0801918	−	0.122158i
$427$			56.0894i			2.71436i
$428$	5.60910	−	1.27732i	0.271126	−	0.0617414i
$429$	−1.31199	+	1.58044i	−0.0633436	+	0.0763042i
$430$	6.36775	−	0.715875i	0.307080	−	0.0345226i
$431$	31.6932			1.52661			0.763304	−	0.646040i	$-0.223576\pi$
$431$	31.6932			1.52661			0.763304	+	0.646040i	$0.223576\pi$
$432$	−20.7473	−	1.24548i	−0.998203	−	0.0599232i
$433$	−12.7355			−0.612030			−0.306015	−	0.952027i	$-0.598996\pi$
$433$	−12.7355			−0.612030			−0.306015	+	0.952027i	$0.598996\pi$
$434$	−42.4429	+	4.77151i	−2.03732	+	0.229040i
$435$	8.17228	−	9.84438i	0.391831	−	0.472002i
$436$	−35.8748	+	8.16948i	−1.71809	+	0.391247i
$437$			43.2948i			2.07107i
$438$	−1.67888	+	2.55748i	−0.0802199	+	0.122201i
$439$			31.4270i			1.49993i	0.661479	+	0.749964i	$0.269929\pi$
$439$			31.4270i			1.49993i	−0.661479	+	0.749964i	$0.730071\pi$
$440$	3.25536	+	9.32553i	0.155193	+	0.444577i
$441$	9.19228	+	49.0960i	0.437727	+	2.33791i
$442$	−0.414359	−	3.68575i	−0.0197091	−	0.175313i
$443$	−22.3976			−1.06414			−0.532071	−	0.846700i	$-0.678586\pi$
$443$	−22.3976			−1.06414			−0.532071	+	0.846700i	$0.678586\pi$
$444$	15.4627	−	30.5197i	0.733826	−	1.44840i
$445$	9.97090			0.472666
$446$	−0.217536	−	1.93499i	−0.0103006	−	0.0916247i
$447$	13.6780	+	11.3548i	0.646949	+	0.537062i
$448$	24.2115	+	30.4530i	1.14388	+	1.43877i
$449$		−	3.63676i		−	0.171629i	−0.996311	−	0.0858146i	$-0.972651\pi$
$449$		−	3.63676i		−	0.171629i	0.996311	−	0.0858146i	$-0.0273493\pi$
$450$	4.23836	+	13.8465i	0.199798	+	0.652731i
$451$			6.72245i			0.316548i
$452$	2.83970	+	12.4700i	0.133568	+	0.586541i
$453$	30.7175	+	25.5000i	1.44323	+	1.19809i
$454$	−13.3912	+	1.50547i	−0.628482	+	0.0706551i
$455$	−2.62064			−0.122858
$456$	−25.2852	−	9.43089i	−1.18409	−	0.441642i
$457$	−0.261403			−0.0122279			−0.00611396	−	0.999981i	$-0.501946\pi$
$457$	−0.261403			−0.0122279			−0.00611396	+	0.999981i	$0.501946\pi$
$458$	−10.5346	+	1.18432i	−0.492250	+	0.0553397i
$459$	−15.4894	+	27.8372i	−0.722985	+	1.29933i
$460$	−4.39661	−	19.3069i	−0.204993	−	0.900190i
$461$		−	7.20352i		−	0.335501i	−0.985829	−	0.167751i	$-0.946350\pi$
$461$		−	7.20352i		−	0.335501i	0.985829	−	0.167751i	$-0.0536504\pi$
$462$	−27.6060	−	18.1222i	−1.28435	−	0.843123i
$463$		−	17.3328i		−	0.805522i	−0.915305	−	0.402761i	$-0.868051\pi$
$463$		−	17.3328i		−	0.805522i	0.915305	−	0.402761i	$-0.131949\pi$
$464$	10.1561	+	21.1430i	0.471486	+	0.981539i
$465$	−8.65481	+	10.4256i	−0.401357	+	0.483478i
$466$	−0.681597	−	6.06285i	−0.0315744	−	0.280856i
$467$	−31.0393			−1.43633			−0.718164	−	0.695874i	$-0.755017\pi$
$467$	−31.0393			−1.43633			−0.718164	+	0.695874i	$0.755017\pi$
$468$	1.02074	+	2.35500i	0.0471835	+	0.108860i
$469$	4.86310			0.224557
$470$	0.446061	+	3.96774i	0.0205753	+	0.183018i
$471$	11.3918	−	13.7227i	0.524907	−	0.632307i
$472$	37.9119	−	13.2343i	1.74504	−	0.609158i
$473$		−	9.97133i		−	0.458482i
$474$	4.65269	+	3.05430i	0.213705	+	0.140289i
$475$			18.8017i			0.862682i
$476$	58.1406	−	13.2399i	2.66487	−	0.606849i
$477$	−18.8196	+	3.52361i	−0.861692	+	0.161335i
$478$	16.6371	−	1.87037i	0.760962	−	0.0855488i
$479$	11.6813			0.533731			0.266865	−	0.963734i	$-0.414012\pi$
$479$	11.6813			0.533731			0.266865	+	0.963734i	$0.414012\pi$
$480$	12.2334	+	1.63789i	0.558378	+	0.0747591i
$481$	−4.22500			−0.192643
$482$	0.643535	−	0.0723475i	0.0293122	−	0.00329534i
$483$	50.9367	+	42.2849i	2.31770	+	1.92403i
$484$	−6.46422	+	1.47205i	−0.293828	+	0.0669112i
$485$		−	12.6273i		−	0.573377i
$486$	4.61126	−	21.5577i	0.209171	−	0.977879i
$487$		−	18.6601i		−	0.845569i	−0.906230	−	0.422785i	$-0.861053\pi$
$487$		−	18.6601i		−	0.845569i	0.906230	−	0.422785i	$-0.138947\pi$
$488$	−30.7995	+	10.7515i	−1.39423	+	0.486699i
$489$	2.89075	+	2.39974i	0.130724	+	0.108520i
$490$	−3.31373	−	29.4758i	−0.149699	−	1.33158i
$491$	20.4643			0.923542			0.461771	−	0.886999i	$-0.347214\pi$
$491$	20.4643			0.923542			0.461771	+	0.886999i	$0.347214\pi$
$492$	7.49339	+	3.79650i	0.337828	+	0.171159i
$493$	35.9505			1.61913
$494$	0.372313	+	3.31174i	0.0167511	+	0.149002i
$495$	−10.2976	+	1.92803i	−0.462843	+	0.0866584i
$496$	−10.7558	−	22.3914i	−0.482949	−	1.00540i
$497$		−	5.98791i		−	0.268594i
$498$	−6.88674	+	10.4907i	−0.308602	+	0.470101i
$499$		−	6.33076i		−	0.283404i	−0.989909	−	0.141702i	$-0.954743\pi$
$499$		−	6.33076i		−	0.283404i	0.989909	−	0.141702i	$-0.0452574\pi$
$500$	−4.70636	−	20.6671i	−0.210475	−	0.924262i
$501$	−16.5023	+	19.8788i	−0.737268	+	0.888118i
$502$	23.2983	−	2.61924i	1.03985	−	0.116902i
$503$	37.7123			1.68151			0.840755	−	0.541416i	$-0.182112\pi$
$503$	37.7123			1.68151			0.840755	+	0.541416i	$0.182112\pi$
$504$	−35.7910	+	20.5374i	−1.59426	+	0.914809i
$505$	−17.7668			−0.790614
$506$	−30.6199	+	3.44235i	−1.36122	+	0.153031i
$507$	−14.1797	+	17.0810i	−0.629745	+	0.758595i
$508$	0.133538	+	0.586406i	0.00592477	+	0.0260176i
$509$		−	7.74429i		−	0.343260i	−0.985162	−	0.171630i	$-0.945097\pi$
$509$		−	7.74429i		−	0.343260i	0.985162	−	0.171630i	$-0.0549033\pi$
$510$	10.3815	−	15.8143i	0.459699	−	0.700271i
$511$			6.07379i			0.268688i
$512$	−12.0812	+	19.1323i	−0.533919	+	0.845535i
$513$	13.9177	−	25.0124i	0.614479	−	1.10432i
$514$	0.0114036	+	0.101435i	0.000502989	+	0.00447412i
$515$	13.7213			0.604631
$516$	−11.1149	−	5.63130i	−0.489304	−	0.247904i
$517$	6.21313			0.273253
$518$	−7.58849	−	67.5000i	−0.333419	−	2.96578i
$519$	5.87785	+	4.87948i	0.258009	+	0.214185i
$520$	−0.502339	−	1.43903i	−0.0220290	−	0.0631058i
$521$		−	9.29493i		−	0.407218i	−0.979052	−	0.203609i	$-0.934733\pi$
$521$		−	9.29493i		−	0.407218i	0.979052	−	0.203609i	$-0.0652672\pi$
$522$	−23.7891	+	7.28174i	−1.04122	+	0.318713i
$523$		−	1.17970i		−	0.0515845i	−0.999667	−	0.0257922i	$-0.991789\pi$
$523$		−	1.17970i		−	0.0515845i	0.999667	−	0.0257922i	$-0.00821084\pi$
$524$	−2.44002	+	0.555647i	−0.106593	+	0.0242736i
$525$	22.1204	+	18.3632i	0.965413	+	0.801434i
$526$	28.3451	−	3.18662i	1.23591	−	0.138943i
$527$	−38.0732			−1.65849
$528$	4.65951	−	18.6327i	0.202779	−	0.810882i
$529$	38.7704			1.68567
$530$	11.2988	−	1.27023i	0.490787	−	0.0551752i
$531$	7.83818	+	41.8638i	0.340148	+	1.81673i
$532$	−52.2408	+	11.8964i	−2.26493	+	0.515773i
$533$		−	1.03735i		−	0.0449326i
$534$	−16.2080	−	10.6399i	−0.701387	−	0.460432i
$535$		−	3.62337i		−	0.156652i
$536$	0.932185	+	2.67040i	0.0402643	+	0.115344i
$537$	−23.2202	+	27.9712i	−1.00203	+	1.20705i
$538$	1.15237	+	10.2504i	0.0496823	+	0.441927i
$539$	−46.1565			−1.98810
$540$	−3.66643	+	12.5674i	−0.157778	+	0.540815i
$541$	−6.50510			−0.279676			−0.139838	−	0.990174i	$-0.544658\pi$
$541$	−6.50510			−0.279676			−0.139838	+	0.990174i	$0.544658\pi$
$542$	−2.05232	−	18.2555i	−0.0881549	−	0.784143i
$543$	1.76017	−	2.12031i	0.0755360	−	0.0909913i
$544$	18.4149	+	29.3880i	0.789533	+	1.26000i
$545$			23.1744i			0.992684i
$546$	4.25992	+	2.79646i	0.182308	+	0.119678i
$547$			1.65898i			0.0709327i	0.999371	+	0.0354664i	$0.0112917\pi$
$547$			1.65898i			0.0709327i	−0.999371	+	0.0354664i	$0.988708\pi$
$548$	−0.558758	−	2.45368i	−0.0238690	−	0.104816i
$549$	−6.36772	−	34.0101i	−0.271768	−	1.45151i
$550$	−13.2974	+	1.49492i	−0.567002	+	0.0637435i
$551$	−32.3024			−1.37613
$552$	−13.4554	+	36.0755i	−0.572702	+	1.53548i
$553$	11.0497			0.469883
$554$	19.7625	−	2.22174i	0.839629	−	0.0943927i
$555$	−16.5807	−	13.7644i	−0.703810	−	0.584265i
$556$	−9.26935	−	40.7047i	−0.393108	−	1.72626i
$557$		−	14.5839i		−	0.617942i	−0.951071	−	0.308971i	$-0.900015\pi$
$557$		−	14.5839i		−	0.617942i	0.951071	−	0.308971i	$-0.0999846\pi$
$558$	25.1937	−	7.71169i	1.06654	−	0.326462i
$559$			1.53869i			0.0650796i
$560$	22.0882	−	10.6102i	0.933398	−	0.448362i
$561$	−22.6500	−	18.8028i	−0.956284	−	0.793855i
$562$	−3.15547	−	28.0681i	−0.133106	−	1.18398i
$563$	−20.4654			−0.862512			−0.431256	−	0.902230i	$-0.641929\pi$
$563$	−20.4654			−0.862512			−0.431256	+	0.902230i	$0.641929\pi$
$564$	3.50886	−	6.92565i	0.147750	−	0.291623i
$565$	8.05541			0.338893
$566$	−0.506969	−	4.50952i	−0.0213095	−	0.189549i
$567$	−15.8343	−	40.8032i	−0.664978	−	1.71357i
$568$	3.28805	−	1.14780i	0.137963	−	0.0481604i
$569$		−	8.56768i		−	0.359176i	−0.983742	−	0.179588i	$-0.942524\pi$
$569$		−	8.56768i		−	0.359176i	0.983742	−	0.179588i	$-0.0574764\pi$
$570$	−9.32801	+	14.2096i	−0.390707	+	0.595174i
$571$		−	19.2420i		−	0.805254i	−0.915364	−	0.402627i	$-0.868097\pi$
$571$		−	19.2420i		−	0.805254i	0.915364	−	0.402627i	$-0.131903\pi$
$572$	−2.31260	+	0.526631i	−0.0966948	+	0.0220195i
$573$	3.84486	−	4.63154i	0.160621	−	0.193485i
$574$	16.5731	−	1.86318i	0.691746	−	0.0777674i
$575$	26.8252			1.11869
$576$	−18.1380	−	15.7166i	−0.755750	−	0.654860i
$577$	−24.9578			−1.03901			−0.519503	−	0.854469i	$-0.673883\pi$
$577$	−24.9578			−1.03901			−0.519503	+	0.854469i	$0.673883\pi$
$578$	28.9312	−	3.25250i	1.20338	−	0.135286i
$579$	−5.63767	+	6.79117i	−0.234293	+	0.282232i
$580$	14.4050	−	3.28033i	0.598134	−	0.136208i
$581$			24.9146i			1.03363i
$582$	−13.4745	+	20.5260i	−0.558536	+	0.850832i
$583$		−	17.6928i		−	0.732763i
$584$	−3.33521	+	1.16426i	−0.138012	+	0.0481773i
$585$	1.58904	−	0.297516i	0.0656986	−	0.0123008i
$586$	−0.334952	−	2.97942i	−0.0138368	−	0.123079i
$587$	−12.7221			−0.525098			−0.262549	−	0.964919i	$-0.584563\pi$
$587$	−12.7221			−0.525098			−0.262549	+	0.964919i	$0.584563\pi$
$588$	−26.0668	+	51.4498i	−1.07498	+	2.12175i
$589$	34.2097			1.40959
$590$	−2.82559	−	25.1338i	−0.116328	−	1.03474i
$591$	2.76775	+	2.29763i	0.113850	+	0.0945120i
$592$	35.6107	−	17.1057i	1.46359	−	0.703041i
$593$		−	15.4614i		−	0.634924i	−0.948271	−	0.317462i	$-0.897169\pi$
$593$		−	15.4614i		−	0.634924i	0.948271	−	0.317462i	$-0.102831\pi$
$594$	18.7964	+	7.85444i	0.771227	+	0.322271i
$595$		−	37.5577i		−	1.53972i
$596$	4.55778	+	20.0147i	0.186694	+	0.819832i
$597$	4.75282	+	3.94553i	0.194520	+	0.161480i
$598$	4.72500	−	0.531194i	0.193220	−	0.0217221i
$599$	−15.5594			−0.635740			−0.317870	−	0.948134i	$-0.602968\pi$
$599$	−15.5594			−0.635740			−0.317870	+	0.948134i	$0.602968\pi$
$600$	−5.84333	+	15.6666i	−0.238553	+	0.639586i
$601$	−25.0477			−1.02172			−0.510858	−	0.859665i	$-0.670672\pi$
$601$	−25.0477			−1.02172			−0.510858	+	0.859665i	$0.670672\pi$
$602$	−24.5826	+	2.76363i	−1.00191	+	0.112637i
$603$	−2.94876	+	0.552098i	−0.120083	+	0.0224832i
$604$	10.2356	+	44.9479i	0.416482	+	1.82891i
$605$			4.17576i			0.169769i
$606$	28.8804	+	18.9588i	1.17319	+	0.770150i
$607$		−	34.6017i		−	1.40444i	−0.711959	−	0.702221i	$-0.752192\pi$
$607$		−	34.6017i		−	1.40444i	0.711959	−	0.702221i	$-0.247808\pi$
$608$	−16.5463	−	26.4058i	−0.671040	−	1.07090i
$609$	−31.5489	+	38.0041i	−1.27843	+	1.54000i
$610$	2.29550	+	20.4186i	0.0929422	+	0.826727i
$611$	−0.958755			−0.0387871
$612$	−33.7507	+	14.6286i	−1.36429	+	0.591328i
$613$	−38.2221			−1.54378			−0.771889	−	0.635758i	$-0.780688\pi$
$613$	−38.2221			−1.54378			−0.771889	+	0.635758i	$0.780688\pi$
$614$	1.23017	+	10.9424i	0.0496457	+	0.441601i
$615$	3.37952	−	4.07099i	0.136275	−	0.164158i
$616$	−12.5673	−	36.0011i	−0.506350	−	1.45052i
$617$		−	19.3234i		−	0.777930i	−0.921253	−	0.388965i	$-0.872833\pi$
$617$		−	19.3234i		−	0.777930i	0.921253	−	0.388965i	$-0.127167\pi$
$618$	−22.3043	−	14.6418i	−0.897209	−	0.588981i
$619$		−	34.2281i		−	1.37574i	−0.725832	−	0.687872i	$-0.758545\pi$
$619$		−	34.2281i		−	1.37574i	0.725832	−	0.687872i	$-0.241455\pi$
$620$	−15.2555	+	3.47402i	−0.612676	+	0.139520i
$621$	−35.6862	−	19.8569i	−1.43204	−	0.796830i
$622$	13.2558	−	1.49024i	0.531509	−	0.0597533i
$623$	−38.4925			−1.54217
$624$	−0.719015	+	2.87523i	−0.0287836	+	0.115101i
$625$	3.71507			0.148603
$626$	−28.3336	+	3.18532i	−1.13244	+	0.127311i
$627$	20.3516	+	16.8948i	0.812765	+	0.674714i
$628$	20.0799	−	4.57265i	0.801277	−	0.182468i
$629$		−	60.5505i		−	2.41431i
$630$	7.60728	+	24.8526i	0.303081	+	0.990153i
$631$			18.3626i			0.731005i	0.930810	+	0.365503i	$0.119103\pi$
$631$			18.3626i			0.731005i	−0.930810	+	0.365503i	$0.880897\pi$
$632$	2.11808	+	6.06758i	0.0842525	+	0.241355i
$633$	1.67504	+	1.39053i	0.0665767	+	0.0552684i
$634$	−1.65272	−	14.7010i	−0.0656379	−	0.583853i
$635$	0.378807			0.0150325
$636$	−19.7219	−	9.99202i	−0.782023	−	0.396209i
$637$	7.12247			0.282202
$638$	−2.56835	−	22.8457i	−0.101682	−	0.904468i
$639$	0.679796	+	3.63079i	0.0268923	+	0.143632i
$640$	10.0602	+	10.0952i	0.397664	+	0.399046i
$641$			37.4540i			1.47935i	0.672967	+	0.739673i	$0.265020\pi$
$641$			37.4540i			1.47935i	−0.672967	+	0.739673i	$0.734980\pi$
$642$	−3.86647	+	5.88988i	−0.152597	+	0.232455i
$643$		−	4.93520i		−	0.194625i	−0.995254	−	0.0973126i	$-0.968975\pi$
$643$		−	4.93520i		−	0.194625i	0.995254	−	0.0973126i	$-0.0310246\pi$
$644$	16.9731	+	74.5341i	0.668832	+	2.93705i
$645$	−5.01280	+	6.03845i	−0.197379	+	0.237764i
$646$	−47.4622	+	5.33579i	−1.86737	+	0.209934i
$647$	−12.0200			−0.472557			−0.236278	−	0.971685i	$-0.575928\pi$
$647$	−12.0200			−0.472557			−0.236278	+	0.971685i	$0.575928\pi$
$648$	19.3704	−	16.5162i	0.760943	−	0.648819i
$649$	−39.3573			−1.54491
$650$	2.05194	−	0.230683i	0.0804835	−	0.00904812i
$651$	33.4118	−	40.2480i	1.30951	−	1.57745i
$652$	0.963251	+	4.22994i	0.0377238	+	0.165657i
$653$		−	18.3299i		−	0.717302i	−0.933472	−	0.358651i	$-0.883237\pi$
$653$		−	18.3299i		−	0.717302i	0.933472	−	0.358651i	$-0.116763\pi$
$654$	24.7292	−	37.6707i	0.966990	−	1.47304i
$655$			1.57621i			0.0615875i
$656$	4.19991	+	8.74337i	0.163979	+	0.341371i
$657$	−0.689545	−	3.68287i	−0.0269017	−	0.143682i
$658$	−1.72201	−	15.3174i	−0.0671310	−	0.597134i
$659$	28.3163			1.10305			0.551524	−	0.834159i	$-0.314047\pi$
$659$	28.3163			1.10305			0.551524	+	0.834159i	$0.314047\pi$
$660$	−10.7913	−	5.46737i	−0.420051	−	0.212817i
$661$	31.1455			1.21142			0.605710	−	0.795685i	$-0.292889\pi$
$661$	31.1455			1.21142			0.605710	+	0.795685i	$0.292889\pi$
$662$	−0.219220	−	1.94997i	−0.00852021	−	0.0757878i
$663$	3.49515	+	2.90148i	0.135740	+	0.112684i
$664$	−13.6810	+	4.77576i	−0.530925	+	0.185336i
$665$			33.7465i			1.30863i
$666$	12.2645	+	40.0674i	0.475238	+	1.55258i
$667$			46.0872i			1.78450i
$668$	−29.0880	+	6.62398i	−1.12545	+	0.256289i
$669$	1.83493	+	1.52326i	0.0709425	+	0.0588926i
$670$	1.77035	−	0.199026i	0.0683945	−	0.00768905i
$671$	31.9738			1.23433
$672$	−47.2270	−	6.32305i	−1.82182	−	0.243917i
$673$	−22.0469			−0.849846			−0.424923	−	0.905230i	$-0.639699\pi$
$673$	−22.0469			−0.849846			−0.424923	+	0.905230i	$0.639699\pi$
$674$	−32.3103	+	3.63239i	−1.24455	+	0.139914i
$675$	−15.4975	−	8.62330i	−0.596500	−	0.331911i
$676$	−24.9941	+	5.69171i	−0.961313	+	0.218912i
$677$		−	13.9075i		−	0.534509i	−0.963626	−	0.267255i	$-0.913883\pi$
$677$		−	13.9075i		−	0.534509i	0.963626	−	0.267255i	$-0.0861165\pi$
$678$	−13.0943	−	8.59586i	−0.502883	−	0.330122i
$679$			48.7476i			1.87076i
$680$	20.6235	−	7.19926i	0.790874	−	0.276079i
$681$	10.5418	−	12.6987i	0.403963	−	0.486616i
$682$	2.72000	+	24.1946i	0.104154	+	0.926458i
$683$	2.95966			0.113248			0.0566240	−	0.998396i	$-0.481966\pi$
$683$	2.95966			0.113248			0.0566240	+	0.998396i	$0.481966\pi$
$684$	30.3259	−	13.1442i	1.15954	−	0.502582i
$685$	−1.58503			−0.0605610
$686$	7.41424	+	65.9501i	0.283077	+	2.51799i
$687$	8.29302	−	9.98983i	0.316398	−	0.381136i
$688$	−6.22968	−	12.9689i	−0.237504	−	0.494436i
$689$			2.73021i			0.104013i
$690$	20.2734	+	13.3087i	0.771795	+	0.506652i
$691$		−	3.91167i		−	0.148807i	−0.997228	−	0.0744035i	$-0.976295\pi$
$691$		−	3.91167i		−	0.148807i	0.997228	−	0.0744035i	$-0.0237053\pi$
$692$	1.95861	+	8.60088i	0.0744552	+	0.326956i
$693$	39.7538	−	7.44312i	1.51012	−	0.282741i
$694$	−0.401325	+	0.0451178i	−0.0152341	+	0.00171265i
$695$	−26.2944			−0.997405
$696$	−26.9161	−	10.0392i	−1.02025	−	0.380534i
$697$	14.8668			0.563119
$698$	46.7206	−	5.25242i	1.76840	−	0.198807i
$699$	5.74932	+	4.77277i	0.217459	+	0.180523i
$700$	7.37093	+	32.3681i	0.278595	+	1.22340i
$701$		−	19.2085i		−	0.725494i	−0.931888	−	0.362747i	$-0.881839\pi$
$701$		−	19.2085i		−	0.725494i	0.931888	−	0.362747i	$-0.118161\pi$
$702$	−2.90050	−	1.21203i	−0.109472	−	0.0457450i
$703$			54.4062i			2.05197i
$704$	17.3597	−	13.8018i	0.654270	−	0.520173i
$705$	−3.76256	−	3.12347i	−0.141706	−	0.117637i
$706$	2.23749	+	19.9026i	0.0842089	+	0.749043i
$707$	68.5886			2.57954
$708$	−22.2270	+	43.8708i	−0.835341	+	1.64877i
$709$	−8.33169			−0.312903			−0.156452	−	0.987686i	$-0.550005\pi$
$709$	−8.33169			−0.312903			−0.156452	+	0.987686i	$0.550005\pi$
$710$	−0.245060	−	2.17982i	−0.00919693	−	0.0818073i
$711$	−6.70006	+	1.25446i	−0.251272	+	0.0470458i
$712$	−7.37846	−	21.1368i	−0.276519	−	0.792136i
$713$		−	48.8084i		−	1.82789i
$714$	−40.0775	+	61.0510i	−1.49986	+	2.28478i
$715$			1.49390i			0.0558686i
$716$	−40.9295	+	9.32054i	−1.52961	+	0.348325i
$717$	−13.0970	+	15.7767i	−0.489116	+	0.589192i
$718$	−19.2991	+	2.16964i	−0.720235	+	0.0809703i
$719$	32.2204			1.20162			0.600809	−	0.799393i	$-0.294845\pi$
$719$	32.2204			1.20162			0.600809	+	0.799393i	$0.294845\pi$
$720$	−12.1887	+	8.94116i	−0.454248	+	0.333217i
$721$	−52.9707			−1.97273
$722$	15.9441	−	1.79247i	0.593379	−	0.0667088i
$723$	−0.506602	+	0.610256i	−0.0188407	+	0.0226957i
$724$	3.10259	−	0.706527i	0.115307	−	0.0262579i
$725$			20.0144i			0.743316i
$726$	4.45592	−	6.78781i	0.165375	−	0.251919i
$727$			36.0565i			1.33726i	0.743594	+	0.668632i	$0.233120\pi$
$727$			36.0565i			1.33726i	−0.743594	+	0.668632i	$0.766880\pi$
$728$	1.93927	+	5.55537i	0.0718742	+	0.205896i
$729$	14.2335	+	22.9436i	0.527167	+	0.849762i
$730$	0.248574	+	2.21108i	0.00920015	+	0.0818359i
$731$	−22.0517			−0.815611
$732$	18.0572	−	35.6406i	0.667412	−	1.31731i
$733$	1.54846			0.0571936			0.0285968	−	0.999591i	$-0.490896\pi$
$733$	1.54846			0.0571936			0.0285968	+	0.999591i	$0.490896\pi$
$734$	1.62739	+	14.4757i	0.0600681	+	0.534310i
$735$	27.9515	+	23.2039i	1.03101	+	0.855887i
$736$	−37.6743	+	23.6073i	−1.38869	+	0.870175i
$737$		−	2.77221i		−	0.102116i
$738$	−9.83762	+	3.01125i	−0.362128	+	0.110846i
$739$		−	39.3655i		−	1.44808i	−0.689756	−	0.724041i	$-0.742282\pi$
$739$		−	39.3655i		−	1.44808i	0.689756	−	0.724041i	$-0.257718\pi$
$740$	−5.52498	−	24.2620i	−0.203102	−	0.891888i
$741$	−3.14048	−	2.60706i	−0.115368	−	0.0957727i
$742$	−43.6187	+	4.90370i	−1.60129	+	0.180020i
$743$	−31.8855			−1.16976			−0.584882	−	0.811118i	$-0.698859\pi$
$743$	−31.8855			−1.16976			−0.584882	+	0.811118i	$0.698859\pi$
$744$	28.5053	+	10.6319i	1.04506	+	0.389785i
$745$	12.9291			0.473685
$746$	15.0594	−	1.69300i	0.551362	−	0.0619852i
$747$	−2.82850	−	15.1071i	−0.103490	−	0.552739i
$748$	−7.54740	−	33.1430i	−0.275960	−	1.21183i
$749$			13.9880i			0.511109i
$750$	21.7017	+	14.2463i	0.792434	+	0.520200i
$751$		−	40.4301i		−	1.47531i	−0.675175	−	0.737657i	$-0.735932\pi$
$751$		−	40.4301i		−	1.47531i	0.675175	−	0.737657i	$-0.264068\pi$
$752$	8.08093	−	3.88171i	0.294681	−	0.141551i
$753$	−18.3408	+	22.0934i	−0.668375	+	0.805130i
$754$	0.396326	+	3.52534i	0.0144333	+	0.128385i
$755$	29.0355			1.05671
$756$	14.1542	−	48.5163i	0.514783	−	1.76452i
$757$	22.6047			0.821582			0.410791	−	0.911729i	$-0.365253\pi$
$757$	22.6047			0.821582			0.410791	+	0.911729i	$0.365253\pi$
$758$	4.24086	+	37.7227i	0.154035	+	1.37015i
$759$	24.1045	−	29.0365i	0.874938	−	1.05396i
$760$	−18.5307	+	6.46872i	−0.672180	+	0.234645i
$761$		−	6.14774i		−	0.222855i	−0.993773	−	0.111428i	$-0.964458\pi$
$761$		−	6.14774i		−	0.222855i	0.993773	−	0.111428i	$-0.0355423\pi$
$762$	−0.615761	−	0.404222i	−0.0223067	−	0.0146434i
$763$		−	89.4646i		−	3.23883i
$764$	6.77719	−	1.54332i	0.245190	−	0.0558352i
$765$	4.26385	+	22.7733i	0.154160	+	0.823369i
$766$	−5.07491	+	0.570532i	−0.183364	+	0.0206142i
$767$	6.07327			0.219293
$768$	−5.58065	−	27.1451i	−0.201374	−	0.979514i
$769$	−42.5351			−1.53385			−0.766927	−	0.641734i	$-0.778215\pi$
$769$	−42.5351			−1.53385			−0.766927	+	0.641734i	$0.778215\pi$
$770$	−23.8670	+	2.68318i	−0.860107	+	0.0966949i
$771$	−0.0961897	−	0.0798515i	−0.00346419	−	0.00287578i
$772$	−9.93731	+	2.26295i	−0.357652	+	0.0814452i
$773$			23.0500i			0.829052i	0.910037	+	0.414526i	$0.136053\pi$
$773$			23.0500i			0.829052i	−0.910037	+	0.414526i	$0.863947\pi$
$774$	14.5920	−	4.46655i	0.524499	−	0.160547i
$775$		−	21.1961i		−	0.761388i
$776$	−26.7680	+	9.34420i	−0.960916	+	0.335437i
$777$	64.0094	+	53.1372i	2.29632	+	1.90628i
$778$	−4.55239	−	40.4937i	−0.163211	−	1.45177i
$779$	−13.3582			−0.478606
$780$	1.66522	+	0.843677i	0.0596244	+	0.0302085i
$781$	−3.41341			−0.122141
$782$	7.61279	+	67.7162i	0.272233	+	2.42153i
$783$	14.8153	−	26.6256i	0.529456	−	0.951523i
$784$	−60.0321	+	28.8367i	−2.14400	+	1.02988i
$785$		−	12.9713i		−	0.462964i
$786$	1.68196	−	2.56217i	0.0599935	−	0.0913895i
$787$		−	46.8216i		−	1.66901i	−0.551000	−	0.834505i	$-0.685754\pi$
$787$		−	46.8216i		−	1.66901i	0.551000	−	0.834505i	$-0.314246\pi$
$788$	0.922264	+	4.04996i	0.0328543	+	0.144274i
$789$	−22.3138	+	26.8793i	−0.794391	+	0.956929i
$790$	4.02252	−	0.452220i	0.143115	−	0.0160892i
$791$	−31.0978			−1.10571
$792$	11.7074	+	20.4027i	0.416003	+	0.724977i
$793$	−4.93391			−0.175208
$794$	−17.0662	+	1.91861i	−0.605656	+	0.0680890i
$795$	−8.89457	+	10.7145i	−0.315458	+	0.380003i
$796$	1.58373	+	6.95465i	0.0561337	+	0.246501i
$797$		−	30.8071i		−	1.09124i	−0.838031	−	0.545622i	$-0.816293\pi$
$797$		−	30.8071i		−	1.09124i	0.838031	−	0.545622i	$-0.183707\pi$
$798$	36.0106	−	54.8559i	1.27476	−	1.94188i
$799$		−	13.7404i		−	0.486100i
$800$	−16.3609	+	10.2520i	−0.578445	+	0.362462i
$801$	23.3401	−	4.36998i	0.824682	−	0.154406i
$802$	−5.46613	−	48.6216i	−0.193016	−	1.71689i
$803$	3.46236			0.122184
$804$	−3.09013	−	1.56560i	−0.108980	−	0.0552145i
$805$	48.1476			1.69698
$806$	−0.419727	−	3.73350i	−0.0147842	−	0.131507i
$807$	−9.72034	−	8.06930i	−0.342172	−	0.284053i
$808$	13.1474	+	37.6630i	0.462525	+	1.32498i
$809$		−	22.0560i		−	0.775446i	−0.921776	−	0.387723i	$-0.873262\pi$
$809$		−	22.0560i		−	0.775446i	0.921776	−	0.387723i	$-0.126738\pi$
$810$	−7.43418	−	14.2059i	−0.261210	−	0.499143i
$811$		−	36.8446i		−	1.29379i	−0.762579	−	0.646895i	$-0.776067\pi$
$811$		−	36.8446i		−	1.29379i	0.762579	−	0.646895i	$-0.223933\pi$
$812$	−55.6102	+	12.6637i	−1.95154	+	0.444408i
$813$	17.3115	+	14.3711i	0.607141	+	0.504015i
$814$	−38.4784	+	4.32582i	−1.34867	+	0.151620i
$815$	2.73246			0.0957139
$816$	−41.2063	−	10.3046i	−1.44251	−	0.360731i
$817$	19.8140			0.693204
$818$	27.5310	−	3.09509i	0.962599	−	0.108217i
$819$	−6.13446	+	1.14856i	−0.214355	+	0.0401338i
$820$	5.95696	−	1.35653i	0.208026	−	0.0473721i
$821$			11.0514i			0.385696i	0.981229	+	0.192848i	$0.0617725\pi$
$821$			11.0514i			0.385696i	−0.981229	+	0.192848i	$0.938228\pi$
$822$	2.57651	+	1.69138i	0.0898662	+	0.0589935i
$823$			39.2047i			1.36659i	0.730142	+	0.683295i	$0.239454\pi$
$823$			39.2047i			1.36659i	−0.730142	+	0.683295i	$0.760546\pi$
$824$	−10.1537	−	29.0870i	−0.353721	−	1.01329i
$825$	10.4679	−	12.6097i	0.364446	−	0.439015i
$826$	10.9081	+	97.0286i	0.379543	+	3.37606i
$827$	−34.3086			−1.19303			−0.596514	−	0.802603i	$-0.703448\pi$
$827$	−34.3086			−1.19303			−0.596514	+	0.802603i	$0.703448\pi$
$828$	−18.7534	−	43.2671i	−0.651725	−	1.50364i
$829$	−13.1640			−0.457204			−0.228602	−	0.973520i	$-0.573415\pi$
$829$	−13.1640			−0.457204			−0.228602	+	0.973520i	$0.573415\pi$
$830$	1.01965	+	9.06984i	0.0353925	+	0.314819i
$831$	−15.5574	+	18.7405i	−0.539680	+	0.650102i
$832$	−2.67880	+	2.12977i	−0.0928708	+	0.0738363i
$833$			102.076i			3.53671i
$834$	42.7423	+	28.0586i	1.48004	+	0.971589i
$835$			18.7903i			0.650265i
$836$	6.78153	+	29.7799i	0.234544	+	1.02996i
$837$	−15.6901	+	28.1977i	−0.542329	+	0.974657i
$838$	34.5634	−	3.88569i	1.19397	−	0.134229i
$839$	47.2405			1.63092			0.815461	−	0.578811i	$-0.196483\pi$
$839$	47.2405			1.63092			0.815461	+	0.578811i	$0.196483\pi$
$840$	−10.4880	+	28.1194i	−0.361870	+	0.970212i
$841$	−5.38585			−0.185719
$842$	16.4395	−	1.84816i	0.566543	−	0.0636919i
$843$	26.6166	+	22.0957i	0.916726	+	0.761016i
$844$	0.558153	+	2.45103i	0.0192124	+	0.0843679i
$845$			16.1457i			0.555430i
$846$	2.78310	+	9.09227i	0.0956851	+	0.312599i
$847$		−	16.1205i		−	0.553906i
$848$	−11.0538	−	23.0117i	−0.379588	−	0.790225i
$849$	4.27632	+	3.54997i	0.146763	+	0.121835i
$850$	3.30602	+	29.4073i	0.113396	+	1.00866i
$851$	77.6236			2.66090
$852$	−1.92772	+	3.80486i	−0.0660425	+	0.130352i
$853$	1.69453			0.0580195			0.0290097	−	0.999579i	$-0.490765\pi$
$853$	1.69453			0.0580195			0.0290097	+	0.999579i	$0.490765\pi$
$854$	−8.86176	−	78.8259i	−0.303243	−	2.69737i
$855$	−3.83118	−	20.4624i	−0.131024	−	0.699798i
$856$	−7.68100	+	2.68129i	−0.262531	+	0.0916446i
$857$			2.23693i			0.0764122i	0.999270	+	0.0382061i	$0.0121643\pi$
$857$			2.23693i			0.0764122i	−0.999270	+	0.0382061i	$0.987836\pi$
$858$	1.59412	−	2.42837i	0.0544225	−	0.0829032i
$859$		−	32.2361i		−	1.09988i	−0.835203	−	0.549941i	$-0.814650\pi$
$859$		−	32.2361i		−	1.09988i	0.835203	−	0.549941i	$-0.185350\pi$
$860$	−8.83588	+	2.01213i	−0.301301	+	0.0686129i
$861$	−13.0466	+	15.7160i	−0.444626	+	0.535600i
$862$	−44.5404	+	5.00731i	−1.51705	+	0.170550i
$863$	16.0637			0.546814			0.273407	−	0.961898i	$-0.411849\pi$
$863$	16.0637			0.546814			0.273407	+	0.961898i	$0.411849\pi$
$864$	29.3542	−	1.52758i	0.998649	−	0.0519694i
$865$	5.55600			0.188910
$866$	17.8980	−	2.01213i	0.608199	−	0.0683749i
$867$	−22.7751	+	27.4350i	−0.773482	+	0.931742i
$868$	58.8937	−	13.4114i	1.99898	−	0.455212i
$869$		−	6.29891i		−	0.213676i
$870$	−9.92965	+	15.1261i	−0.336647	+	0.512822i
$871$			0.427783i			0.0144949i
$872$	49.1263	−	17.1491i	1.66363	−	0.580740i
$873$	−5.53422	−	29.5583i	−0.187305	−	1.00040i
$874$	−6.84029	−	60.8448i	−0.231376	−	2.05810i
$875$	51.5397			1.74236
$876$	1.95537	−	3.85943i	0.0660657	−	0.130398i
$877$	40.8025			1.37780			0.688902	−	0.724855i	$-0.258093\pi$
$877$	40.8025			1.37780			0.688902	+	0.724855i	$0.258093\pi$
$878$	−4.96525	−	44.1662i	−0.167569	−	1.49054i
$879$	2.82535	+	2.34545i	0.0952966	+	0.0791101i
$880$	−6.04833	−	12.5914i	−0.203889	−	0.424456i
$881$		−	0.00929461i		−	0.000313143i	−1.00000		0.000156572i	$-0.999950\pi$
$881$		−	0.00929461i		−	0.000313143i	1.00000		0.000156572i	$-4.98383e-5\pi$
$882$	−20.6753	−	67.5453i	−0.696174	−	2.27437i
$883$			4.16092i			0.140026i	0.997546	+	0.0700131i	$0.0223041\pi$
$883$			4.16092i			0.140026i	−0.997546	+	0.0700131i	$0.977696\pi$
$884$	1.16465	+	5.11434i	0.0391714	+	0.172014i
$885$	23.8340	+	19.7857i	0.801173	+	0.665090i
$886$	31.4767	−	3.53867i	1.05748	−	0.118884i
$887$	−11.1118			−0.373099			−0.186550	−	0.982446i	$-0.559730\pi$
$887$	−11.1118			−0.373099			−0.186550	+	0.982446i	$0.559730\pi$
$888$	−16.9087	+	45.3341i	−0.567420	+	1.52131i
$889$	−1.46238			−0.0490466
$890$	−14.0127	+	1.57534i	−0.469707	+	0.0528054i
$891$	−23.2599	+	9.02634i	−0.779235	+	0.302394i
$892$	0.611433	+	2.68500i	0.0204723	+	0.0899003i
$893$			12.3461i			0.413146i
$894$	−21.0166	−	13.7965i	−0.702899	−	0.461424i
$895$			26.4396i			0.883780i
$896$	−38.8372	−	38.9722i	−1.29746	−	1.30197i
$897$	−3.71960	+	4.48065i	−0.124194	+	0.149605i
$898$	0.574584	+	5.11096i	0.0191741	+	0.170555i
$899$	36.4162			1.21455
$900$	−8.14408	−	18.7897i	−0.271469	−	0.626324i
$901$	−39.1279			−1.30354
$902$	−1.06210	−	9.44747i	−0.0353642	−	0.314566i
$903$	19.3518	−	23.3114i	0.643989	−	0.775754i
$904$	−5.96099	−	17.0762i	−0.198260	−	0.567948i
$905$		−	2.00421i		−	0.0666222i
$906$	−47.1980	−	30.9835i	−1.56805	−	1.02936i
$907$			41.5172i			1.37855i	0.724497	+	0.689277i	$0.242072\pi$
$907$			41.5172i			1.37855i	−0.724497	+	0.689277i	$0.757928\pi$
$908$	18.5817	−	4.23145i	0.616654	−	0.140426i
$909$	−41.5890	+	7.78673i	−1.37942	+	0.258269i
$910$	3.68295	−	0.414044i	0.122088	−	0.0137254i
$911$	−5.56297			−0.184309			−0.0921547	−	0.995745i	$-0.529375\pi$
$911$	−5.56297			−0.184309			−0.0921547	+	0.995745i	$0.529375\pi$
$912$	37.0249	+	9.25890i	1.22602	+	0.306593i
$913$	14.2026			0.470036
$914$	0.367365	−	0.0412999i	0.0121514	−	0.00136608i
$915$	−19.3627	−	16.0739i	−0.640112	−	0.531387i
$916$	14.6178	−	3.32880i	0.482986	−	0.109987i
$917$		−	6.08493i		−	0.200942i
$918$	17.3702	−	41.5685i	0.573301	−	1.37196i
$919$			36.0619i			1.18957i	0.803884	+	0.594786i	$0.202763\pi$
$919$			36.0619i			1.18957i	−0.803884	+	0.594786i	$0.797237\pi$
$920$	9.22919	+	26.4385i	0.304277	+	0.871653i
$921$	−10.3766	−	8.61408i	−0.341920	−	0.283843i
$922$	1.13811	+	10.1235i	0.0374816	+	0.333401i
$923$	0.526727			0.0173374
$924$	41.6596	+	21.1067i	1.37050	+	0.694360i
$925$	33.7098			1.10837
$926$	2.73846	+	24.3588i	0.0899915	+	0.800480i
$927$	32.1190	−	6.01366i	1.05493	−	0.197515i
$928$	−17.6135	−	28.1089i	−0.578191	−	0.922721i
$929$		−	30.7440i		−	1.00868i	−0.863505	−	0.504340i	$-0.831736\pi$
$929$		−	30.7440i		−	1.00868i	0.863505	−	0.504340i	$-0.168264\pi$
$930$	10.5159	−	16.0192i	0.344831	−	0.525290i
$931$		−	91.7175i		−	3.00592i
$932$	1.91578	+	8.41280i	0.0627535	+	0.275570i
$933$	−10.4352	+	12.5703i	−0.341633	+	0.411533i
$934$	43.6214	−	4.90400i	1.42734	−	0.160464i
$935$	−21.4098			−0.700174
$936$	−1.80658	−	3.14836i	−0.0590498	−	0.102907i
$937$	−7.33731			−0.239699			−0.119850	−	0.992792i	$-0.538241\pi$
$937$	−7.33731			−0.239699			−0.119850	+	0.992792i	$0.538241\pi$
$938$	−6.83441	+	0.768337i	−0.223151	+	0.0250871i
$939$	22.3047	−	26.8684i	0.727885	−	0.876816i
$940$	−1.25375	−	5.50563i	−0.0408929	−	0.179574i
$941$		−	46.3582i		−	1.51124i	−0.655013	−	0.755618i	$-0.727337\pi$
$941$		−	46.3582i		−	1.51124i	0.655013	−	0.755618i	$-0.272663\pi$
$942$	−13.8415	+	21.0851i	−0.450981	+	0.686990i
$943$			19.0586i			0.620635i
$944$	−51.1889	+	24.5888i	−1.66606	+	0.800297i
$945$	−27.8160	−	15.4777i	−0.904854	−	0.503488i
$946$	1.57540	+	14.0133i	0.0512208	+	0.455612i
$947$	−29.9982			−0.974811			−0.487405	−	0.873176i	$-0.662057\pi$
$947$	−29.9982			−0.974811			−0.487405	+	0.873176i	$0.662057\pi$
$948$	−7.02127	−	3.55730i	−0.228040	−	0.115536i
$949$	−0.534281			−0.0173435
$950$	−2.97055	−	26.4232i	−0.0963773	−	0.857282i
$951$	13.9408	+	11.5729i	0.452062	+	0.375277i
$952$	−79.6166	+	27.7926i	−2.58039	+	0.900765i
$953$			52.3336i			1.69525i	0.530594	+	0.847626i	$0.321969\pi$
$953$			52.3336i			1.69525i	−0.530594	+	0.847626i	$0.678031\pi$
$954$	25.8917	−	7.92532i	0.838274	−	0.256592i
$955$		−	4.37794i		−	0.141667i
$956$	−23.0856	+	5.25709i	−0.746641	+	0.170027i
$957$	21.6642	+	17.9845i	0.700305	+	0.581356i
$958$	−16.4164	+	1.84556i	−0.530389	+	0.0596274i
$959$	6.11900			0.197593
$960$	−17.4512	−	0.369024i	−0.563234	−	0.0119102i
$961$	−7.56636			−0.244076
$962$	5.93765	−	0.667522i	0.191438	−	0.0215218i
$963$	−1.58803	−	8.48166i	−0.0511734	−	0.273318i
$964$	−0.892968	+	0.203349i	−0.0287606	+	0.00654942i
$965$			6.41931i			0.206645i
$966$	−78.2652	−	51.3779i	−2.51814	−	1.65306i
$967$			29.4612i			0.947407i	0.880684	+	0.473704i	$0.157083\pi$
$967$			29.4612i			0.947407i	−0.880684	+	0.473704i	$0.842917\pi$
$968$	8.85199	−	3.09006i	0.284514	−	0.0993182i
$969$	37.3630	−	45.0078i	1.20027	−	1.44586i
$970$	1.99503	+	17.7459i	0.0640566	+	0.569788i
$971$	43.9396			1.41009			0.705044	−	0.709163i	$-0.250927\pi$
$971$	43.9396			1.41009			0.705044	+	0.709163i	$0.250927\pi$
$972$	−3.07450	+	31.0249i	−0.0986147	+	0.995126i
$973$	101.509			3.25424
$974$	2.94817	+	26.2242i	0.0944655	+	0.840276i
$975$	−1.61532	+	1.94582i	−0.0517316	+	0.0623162i
$976$	41.5858	−	19.9759i	1.33113	−	0.639413i
$977$		−	18.5481i		−	0.593408i	−0.954970	−	0.296704i	$-0.904113\pi$
$977$		−	18.5481i		−	0.593408i	0.954970	−	0.296704i	$-0.0958874\pi$
$978$	−4.44168	−	2.91578i	−0.142029	−	0.0932365i
$979$			21.9427i			0.701291i
$980$	9.31397	+	40.9006i	0.297524	+	1.30652i
$981$	10.1567	+	54.2472i	0.324280	+	1.73198i
$982$	−28.7598	+	3.23323i	−0.917761	+	0.103176i
$983$	34.9003			1.11315			0.556573	−	0.830799i	$-0.312116\pi$
$983$	34.9003			1.11315			0.556573	+	0.830799i	$0.312116\pi$
$984$	−11.1307	−	4.15154i	−0.354835	−	0.132346i
$985$	2.61619			0.0833589
$986$	−50.5234	+	5.67994i	−1.60899	+	0.180886i
$987$	14.5253	+	12.0581i	0.462345	+	0.383814i
$988$	−1.04647	−	4.59537i	−0.0332925	−	0.146198i
$989$		−	28.2695i		−	0.898917i
$990$	14.1672	−	4.33653i	0.450265	−	0.137824i
$991$			18.3425i			0.582669i	0.956621	+	0.291335i	$0.0940993\pi$
$991$			18.3425i			0.582669i	−0.956621	+	0.291335i	$0.905901\pi$
$992$	18.6535	+	29.7686i	0.592248	+	0.945155i
$993$	1.84913	+	1.53505i	0.0586804	+	0.0487133i
$994$	0.946050	+	8.41517i	0.0300069	+	0.266913i
$995$	4.49257			0.142424
$996$	8.02088	−	15.8313i	0.254151	−	0.501635i
$997$	−45.1969			−1.43140			−0.715700	−	0.698408i	$-0.753892\pi$
$997$	−45.1969			−1.43140			−0.715700	+	0.698408i	$0.753892\pi$
$998$	1.00022	+	8.89700i	0.0316614	+	0.281630i
$999$	−44.8449	−	24.9531i	−1.41883	−	0.789481i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.c.b.671.6	yes	128
3.2	odd	2	inner	804.2.c.b.671.123	yes	128
4.3	odd	2	inner	804.2.c.b.671.124	yes	128
12.11	even	2	inner	804.2.c.b.671.5	✓	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.c.b.671.5	✓	128	12.11	even	2	inner
804.2.c.b.671.6	yes	128	1.1	even	1	trivial
804.2.c.b.671.123	yes	128	3.2	odd	2	inner
804.2.c.b.671.124	yes	128	4.3	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	804.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.40536 + 0.157993i) q^{2} +(1.10632 - 1.33268i) q^{3} +(1.95008 - 0.444075i) q^{4} -1.25971i q^{5} +(-1.34423 + 2.04769i) q^{6} +4.86310i q^{7} +(-2.67040 + 0.932185i) q^{8} +(-0.552098 - 2.94876i) q^{9} +O(q^{10})\)	\(q+(-1.40536 + 0.157993i) q^{2} +(1.10632 - 1.33268i) q^{3} +(1.95008 - 0.444075i) q^{4} -1.25971i q^{5} +(-1.34423 + 2.04769i) q^{6} +4.86310i q^{7} +(-2.67040 + 0.932185i) q^{8} +(-0.552098 - 2.94876i) q^{9} +(0.199026 + 1.77035i) q^{10} +2.77221 q^{11} +(1.56560 - 3.09013i) q^{12} -0.427783 q^{13} +(-0.768337 - 6.83441i) q^{14} +(-1.67880 - 1.39365i) q^{15} +(3.60559 - 1.73196i) q^{16} -6.13077i q^{17} +(1.24178 + 4.05684i) q^{18} +5.50865i q^{19} +(-0.559407 - 2.45653i) q^{20} +(6.48098 + 5.38016i) q^{21} +(-3.89595 + 0.437991i) q^{22} +7.85942 q^{23} +(-1.71202 + 4.59010i) q^{24} +3.41313 q^{25} +(0.601189 - 0.0675869i) q^{26} +(-4.54057 - 2.52651i) q^{27} +(2.15958 + 9.48341i) q^{28} +5.86394i q^{29} +(2.57950 + 1.69334i) q^{30} -6.21018i q^{31} +(-4.79352 + 3.00369i) q^{32} +(3.06696 - 3.69448i) q^{33} +(0.968620 + 8.61594i) q^{34} +6.12610 q^{35} +(-2.38610 - 5.50513i) q^{36} +9.87650 q^{37} +(-0.870330 - 7.74164i) q^{38} +(-0.473266 + 0.570100i) q^{39} +(1.17428 + 3.36393i) q^{40} +2.42494i q^{41} +(-9.95814 - 6.53711i) q^{42} -3.59689i q^{43} +(5.40602 - 1.23107i) q^{44} +(-3.71459 + 0.695484i) q^{45} +(-11.0453 + 1.24174i) q^{46} +2.24122 q^{47} +(1.68079 - 6.72123i) q^{48} -16.6497 q^{49} +(-4.79667 + 0.539251i) q^{50} +(-8.17038 - 6.78261i) q^{51} +(-0.834209 + 0.189968i) q^{52} -6.38222i q^{53} +(6.78031 + 2.83328i) q^{54} -3.49218i q^{55} +(-4.53331 - 12.9864i) q^{56} +(7.34129 + 6.09435i) q^{57} +(-0.926465 - 8.24096i) q^{58} -14.1971 q^{59} +(-3.89267 - 1.97221i) q^{60} +11.5337 q^{61} +(0.981168 + 8.72754i) q^{62} +(14.3401 - 2.68491i) q^{63} +(6.26206 - 4.97861i) q^{64} +0.538883i q^{65} +(-3.72648 + 5.67664i) q^{66} -1.00000i q^{67} +(-2.72252 - 11.9555i) q^{68} +(8.69506 - 10.4741i) q^{69} +(-8.60938 + 0.967883i) q^{70} -1.23130 q^{71} +(4.22311 + 7.35971i) q^{72} +1.24895 q^{73} +(-13.8800 + 1.56042i) q^{74} +(3.77602 - 4.54862i) q^{75} +(2.44626 + 10.7423i) q^{76} +13.4815i q^{77} +(0.575038 - 0.875969i) q^{78} -2.27216i q^{79} +(-2.18177 - 4.54201i) q^{80} +(-8.39038 + 3.25601i) q^{81} +(-0.383125 - 3.40792i) q^{82} +5.12319 q^{83} +(15.0276 + 7.61368i) q^{84} -7.72300 q^{85} +(0.568285 + 5.05493i) q^{86} +(7.81479 + 6.48742i) q^{87} +(-7.40291 + 2.58421i) q^{88} +7.91523i q^{89} +(5.11045 - 1.56429i) q^{90} -2.08035i q^{91} +(15.3265 - 3.49017i) q^{92} +(-8.27622 - 6.87047i) q^{93} +(-3.14972 + 0.354098i) q^{94} +6.93931 q^{95} +(-1.30021 + 9.71131i) q^{96} +10.0240 q^{97} +(23.3989 - 2.63055i) q^{98} +(-1.53053 - 8.17458i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q + 4 q^{4} - 6 q^{6} - 4 q^{9}+O(q^{10}) \) 128 * q + 4 * q^4 - 6 * q^6 - 4 * q^9	\( 128 q + 4 q^{4} - 6 q^{6} - 4 q^{9} - 4 q^{10} + 4 q^{12} - 8 q^{13} - 4 q^{16} + 18 q^{18} - 8 q^{21} - 8 q^{22} - 24 q^{24} - 136 q^{25} + 14 q^{30} - 32 q^{33} + 34 q^{36} - 48 q^{37} + 16 q^{40} - 28 q^{42} - 16 q^{45} - 28 q^{46} - 22 q^{48} - 152 q^{49} + 8 q^{52} - 16 q^{54} - 32 q^{57} - 20 q^{58} - 14 q^{60} + 8 q^{61} + 16 q^{64} + 14 q^{66} + 56 q^{69} - 4 q^{70} - 8 q^{72} - 48 q^{73} - 36 q^{76} + 40 q^{78} + 44 q^{81} + 60 q^{82} + 46 q^{84} + 64 q^{85} - 28 q^{88} - 14 q^{90} + 32 q^{93} - 8 q^{96} + 64 q^{97}+O(q^{100}) \) 128 * q + 4 * q^4 - 6 * q^6 - 4 * q^9 - 4 * q^10 + 4 * q^12 - 8 * q^13 - 4 * q^16 + 18 * q^18 - 8 * q^21 - 8 * q^22 - 24 * q^24 - 136 * q^25 + 14 * q^30 - 32 * q^33 + 34 * q^36 - 48 * q^37 + 16 * q^40 - 28 * q^42 - 16 * q^45 - 28 * q^46 - 22 * q^48 - 152 * q^49 + 8 * q^52 - 16 * q^54 - 32 * q^57 - 20 * q^58 - 14 * q^60 + 8 * q^61 + 16 * q^64 + 14 * q^66 + 56 * q^69 - 4 * q^70 - 8 * q^72 - 48 * q^73 - 36 * q^76 + 40 * q^78 + 44 * q^81 + 60 * q^82 + 46 * q^84 + 64 * q^85 - 28 * q^88 - 14 * q^90 + 32 * q^93 - 8 * q^96 + 64 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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