LMFDB - Embedded newform 187.2.h.a.100.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [187,2,Mod(100,187)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(187, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 3]))

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

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

chi := DirichletCharacter("187.100");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 187 = 11 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	187.h (of order $8$, degree $4$, 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:	$1.49320251780$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			100.14
Character	$\chi$	$=$	187.100
Dual form			187.2.h.a.144.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.82043 + 1.82043i) q^{2} +(-0.100390 - 0.242362i) q^{3} +4.62792i q^{4} +(-1.17236 + 0.485606i) q^{5} +(0.258451 - 0.623955i) q^{6} +(-0.180288 - 0.0746777i) q^{7} +(-4.78394 + 4.78394i) q^{8} +(2.07266 - 2.07266i) q^{9} +O(q^{10})$	\(q+(1.82043 + 1.82043i) q^{2} +(-0.100390 - 0.242362i) q^{3} +4.62792i q^{4} +(-1.17236 + 0.485606i) q^{5} +(0.258451 - 0.623955i) q^{6} +(-0.180288 - 0.0746777i) q^{7} +(-4.78394 + 4.78394i) q^{8} +(2.07266 - 2.07266i) q^{9} +(-3.01820 - 1.25018i) q^{10} +(0.382683 - 0.923880i) q^{11} +(1.12163 - 0.464596i) q^{12} +0.389335i q^{13} +(-0.192256 - 0.464147i) q^{14} +(0.235385 + 0.235385i) q^{15} -8.16181 q^{16} +(0.148839 - 4.12042i) q^{17} +7.54626 q^{18} +(1.58378 + 1.58378i) q^{19} +(-2.24735 - 5.42557i) q^{20} +0.0511919i q^{21} +(2.37850 - 0.985209i) q^{22} +(0.417847 - 1.00877i) q^{23} +(1.63971 + 0.679188i) q^{24} +(-2.39693 + 2.39693i) q^{25} +(-0.708757 + 0.708757i) q^{26} +(-1.43749 - 0.595430i) q^{27} +(0.345602 - 0.834358i) q^{28} +(4.19159 - 1.73622i) q^{29} +0.857004i q^{30} +(-1.21699 - 2.93806i) q^{31} +(-5.29010 - 5.29010i) q^{32} -0.262331 q^{33} +(7.77188 - 7.22998i) q^{34} +0.247626 q^{35} +(9.59210 + 9.59210i) q^{36} +(-2.10950 - 5.09279i) q^{37} +5.76632i q^{38} +(0.0943601 - 0.0390852i) q^{39} +(3.28538 - 7.93160i) q^{40} +(-8.90123 - 3.68701i) q^{41} +(-0.0931911 + 0.0931911i) q^{42} +(-8.28078 + 8.28078i) q^{43} +(4.27564 + 1.77103i) q^{44} +(-1.42340 + 3.43639i) q^{45} +(2.59705 - 1.07574i) q^{46} +3.65052i q^{47} +(0.819362 + 1.97811i) q^{48} +(-4.92282 - 4.92282i) q^{49} -8.72687 q^{50} +(-1.01358 + 0.377575i) q^{51} -1.80181 q^{52} +(8.80526 + 8.80526i) q^{53} +(-1.53292 - 3.70079i) q^{54} +1.26895i q^{55} +(1.21974 - 0.505233i) q^{56} +(0.224853 - 0.542844i) q^{57} +(10.7912 + 4.46984i) q^{58} +(5.20490 - 5.20490i) q^{59} +(-1.08934 + 1.08934i) q^{60} +(-2.86655 - 1.18736i) q^{61} +(3.13310 - 7.56397i) q^{62} +(-0.528457 + 0.218894i) q^{63} -2.93690i q^{64} +(-0.189064 - 0.456440i) q^{65} +(-0.477555 - 0.477555i) q^{66} +2.40497 q^{67} +(19.0690 + 0.688817i) q^{68} -0.286435 q^{69} +(0.450785 + 0.450785i) q^{70} +(3.65041 + 8.81286i) q^{71} +19.8310i q^{72} +(-2.33531 + 0.967317i) q^{73} +(5.43086 - 13.1113i) q^{74} +(0.821551 + 0.340298i) q^{75} +(-7.32961 + 7.32961i) q^{76} +(-0.137986 + 0.137986i) q^{77} +(0.242928 + 0.100624i) q^{78} +(-5.20111 + 12.5566i) q^{79} +(9.56855 - 3.96342i) q^{80} -8.38538i q^{81} +(-9.49211 - 22.9160i) q^{82} +(-5.09341 - 5.09341i) q^{83} -0.236912 q^{84} +(1.82641 + 4.90288i) q^{85} -30.1491 q^{86} +(-0.841586 - 0.841586i) q^{87} +(2.58905 + 6.25052i) q^{88} -7.05766i q^{89} +(-8.84690 + 3.66451i) q^{90} +(0.0290747 - 0.0701924i) q^{91} +(4.66851 + 1.93376i) q^{92} +(-0.589903 + 0.589903i) q^{93} +(-6.64551 + 6.64551i) q^{94} +(-2.62585 - 1.08766i) q^{95} +(-0.751049 + 1.81319i) q^{96} +(-14.8335 + 6.14424i) q^{97} -17.9233i q^{98} +(-1.12171 - 2.70806i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 16 q^{6}+O(q^{10}) $ 56 * q - 16 * q^6	$ 56 q - 16 q^{6} - 16 q^{10} - 16 q^{14} + 24 q^{15} - 32 q^{16} + 8 q^{17} - 24 q^{19} + 16 q^{20} - 24 q^{24} - 8 q^{25} - 48 q^{27} - 40 q^{32} + 16 q^{33} + 64 q^{34} + 32 q^{35} + 64 q^{36} + 8 q^{37} - 32 q^{39} + 96 q^{40} - 24 q^{41} - 8 q^{42} - 32 q^{43} + 16 q^{44} - 32 q^{45} - 16 q^{46} - 24 q^{48} - 112 q^{50} - 48 q^{51} + 8 q^{53} - 72 q^{54} + 64 q^{56} + 40 q^{57} + 16 q^{58} + 16 q^{59} - 8 q^{60} - 64 q^{61} + 56 q^{62} + 16 q^{63} + 56 q^{65} + 24 q^{67} - 88 q^{68} - 64 q^{69} - 96 q^{70} - 16 q^{71} + 8 q^{73} - 48 q^{74} + 40 q^{75} + 88 q^{76} + 136 q^{78} - 32 q^{80} + 104 q^{82} - 56 q^{83} + 80 q^{84} - 8 q^{85} - 32 q^{86} + 56 q^{87} - 32 q^{91} + 40 q^{92} + 8 q^{93} + 16 q^{94} + 48 q^{95} + 64 q^{96} - 16 q^{97}+O(q^{100}) $ 56 * q - 16 * q^6 - 16 * q^10 - 16 * q^14 + 24 * q^15 - 32 * q^16 + 8 * q^17 - 24 * q^19 + 16 * q^20 - 24 * q^24 - 8 * q^25 - 48 * q^27 - 40 * q^32 + 16 * q^33 + 64 * q^34 + 32 * q^35 + 64 * q^36 + 8 * q^37 - 32 * q^39 + 96 * q^40 - 24 * q^41 - 8 * q^42 - 32 * q^43 + 16 * q^44 - 32 * q^45 - 16 * q^46 - 24 * q^48 - 112 * q^50 - 48 * q^51 + 8 * q^53 - 72 * q^54 + 64 * q^56 + 40 * q^57 + 16 * q^58 + 16 * q^59 - 8 * q^60 - 64 * q^61 + 56 * q^62 + 16 * q^63 + 56 * q^65 + 24 * q^67 - 88 * q^68 - 64 * q^69 - 96 * q^70 - 16 * q^71 + 8 * q^73 - 48 * q^74 + 40 * q^75 + 88 * q^76 + 136 * q^78 - 32 * q^80 + 104 * q^82 - 56 * q^83 + 80 * q^84 - 8 * q^85 - 32 * q^86 + 56 * q^87 - 32 * q^91 + 40 * q^92 + 8 * q^93 + 16 * q^94 + 48 * q^95 + 64 * q^96 - 16 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/187\mathbb{Z}\right)^\times$.

$n$	$35$	$122$
$\chi(n)$	$1$	$e\left(\frac{3}{8}\right)$

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 $

$2$	1.82043	+	1.82043i	1.28724	+	1.28724i	0.936458	+	0.350779i	$0.114083\pi$
$2$	1.82043	+	1.82043i	1.28724	+	1.28724i	0.350779	+	0.936458i	$0.385917\pi$
$3$	−0.100390	−	0.242362i	−0.0579600	−	0.139928i	0.892247	−	0.451548i	$-0.149128\pi$
$3$	−0.100390	−	0.242362i	−0.0579600	−	0.139928i	−0.950207	+	0.311621i	$0.899128\pi$
$4$			4.62792i			2.31396i
$5$	−1.17236	+	0.485606i	−0.524294	+	0.217170i	−0.629102	−	0.777323i	$-0.716577\pi$
$5$	−1.17236	+	0.485606i	−0.524294	+	0.217170i	0.104808	+	0.994492i	$0.466577\pi$
$6$	0.258451	−	0.623955i	0.105512	−	0.254729i
$7$	−0.180288	−	0.0746777i	−0.0681424	−	0.0282255i	0.348352	−	0.937364i	$-0.386741\pi$
$7$	−0.180288	−	0.0746777i	−0.0681424	−	0.0282255i	−0.416494	+	0.909138i	$0.636741\pi$
$8$	−4.78394	+	4.78394i	−1.69138	+	1.69138i
$9$	2.07266	−	2.07266i	0.690886	−	0.690886i
$10$	−3.01820	−	1.25018i	−0.954440	−	0.395342i
$11$	0.382683	−	0.923880i	0.115383	−	0.278560i
$11$	0.382683	−	0.923880i	0.115383	−	0.278560i
$12$	1.12163	−	0.464596i	0.323788	−	0.134117i
$13$			0.389335i			0.107982i	0.998541	+	0.0539911i	$0.0171942\pi$
$13$			0.389335i			0.107982i	−0.998541	+	0.0539911i	$0.982806\pi$
$14$	−0.192256	−	0.464147i	−0.0513825	−	0.124048i
$15$	0.235385	+	0.235385i	0.0607762	+	0.0607762i
$16$	−8.16181			−2.04045
$17$	0.148839	−	4.12042i	0.0360989	−	0.999348i
$17$	0.148839	−	4.12042i	0.0360989	−	0.999348i
$18$	7.54626			1.77867
$19$	1.58378	+	1.58378i	0.363344	+	0.363344i	0.865043	−	0.501698i	$-0.167291\pi$
$19$	1.58378	+	1.58378i	0.363344	+	0.363344i	−0.501698	+	0.865043i	$0.667291\pi$
$20$	−2.24735	−	5.42557i	−0.502522	−	1.21320i
$21$			0.0511919i			0.0111710i
$22$	2.37850	−	0.985209i	0.507099	−	0.210047i
$23$	0.417847	−	1.00877i	0.0871270	−	0.210343i	−0.874310	−	0.485367i	$-0.838686\pi$
$23$	0.417847	−	1.00877i	0.0871270	−	0.210343i	0.961437	+	0.275024i	$0.0886859\pi$
$24$	1.63971	+	0.679188i	0.334703	+	0.138639i
$25$	−2.39693	+	2.39693i	−0.479385	+	0.479385i
$26$	−0.708757	+	0.708757i	−0.138999	+	0.138999i
$27$	−1.43749	−	0.595430i	−0.276646	−	0.114591i
$28$	0.345602	−	0.834358i	0.0653127	−	0.157679i
$29$	4.19159	−	1.73622i	0.778360	−	0.322407i	0.0421063	−	0.999113i	$-0.486593\pi$
$29$	4.19159	−	1.73622i	0.778360	−	0.322407i	0.736253	+	0.676706i	$0.236593\pi$
$30$			0.857004i			0.156467i
$31$	−1.21699	−	2.93806i	−0.218577	−	0.527692i	0.776115	−	0.630592i	$-0.217188\pi$
$31$	−1.21699	−	2.93806i	−0.218577	−	0.527692i	−0.994692	+	0.102900i	$0.967188\pi$
$32$	−5.29010	−	5.29010i	−0.935167	−	0.935167i
$33$	−0.262331			−0.0456660
$34$	7.77188	−	7.22998i	1.33287	−	1.23993i
$35$	0.247626			0.0418564
$36$	9.59210	+	9.59210i	1.59868	+	1.59868i
$37$	−2.10950	−	5.09279i	−0.346800	−	0.837250i	−0.996994	−	0.0774814i	$-0.975312\pi$
$37$	−2.10950	−	5.09279i	−0.346800	−	0.837250i	0.650193	−	0.759769i	$-0.274688\pi$
$38$			5.76632i			0.935421i
$39$	0.0943601	−	0.0390852i	0.0151097	−	0.00625865i
$40$	3.28538	−	7.93160i	0.519464	−	1.25410i
$41$	−8.90123	−	3.68701i	−1.39014	−	0.575814i	−0.442966	−	0.896539i	$-0.646074\pi$
$41$	−8.90123	−	3.68701i	−1.39014	−	0.575814i	−0.947173	+	0.320724i	$0.896074\pi$
$42$	−0.0931911	+	0.0931911i	−0.0143797	+	0.0143797i
$43$	−8.28078	+	8.28078i	−1.26281	+	1.26281i	−0.313081	+	0.949727i	$0.601361\pi$
$43$	−8.28078	+	8.28078i	−1.26281	+	1.26281i	−0.949727	+	0.313081i	$0.898639\pi$
$44$	4.27564	+	1.77103i	0.644577	+	0.266993i
$45$	−1.42340	+	3.43639i	−0.212188	+	0.512267i
$46$	2.59705	−	1.07574i	0.382915	−	0.158609i
$47$			3.65052i			0.532483i	0.963906	+	0.266242i	$0.0857819\pi$
$47$			3.65052i			0.532483i	−0.963906	+	0.266242i	$0.914218\pi$
$48$	0.819362	+	1.97811i	0.118265	+	0.285516i
$49$	−4.92282	−	4.92282i	−0.703260	−	0.703260i
$50$	−8.72687			−1.23417
$51$	−1.01358	+	0.377575i	−0.141929	+	0.0528710i
$52$	−1.80181			−0.249866
$53$	8.80526	+	8.80526i	1.20950	+	1.20950i	0.971190	+	0.238306i	$0.0765920\pi$
$53$	8.80526	+	8.80526i	1.20950	+	1.20950i	0.238306	+	0.971190i	$0.423408\pi$
$54$	−1.53292	−	3.70079i	−0.208604	−	0.503614i
$55$			1.26895i			0.171105i
$56$	1.21974	−	0.505233i	0.162995	−	0.0675146i
$57$	0.224853	−	0.542844i	0.0297826	−	0.0719015i
$58$	10.7912	+	4.46984i	1.41695	+	0.586919i
$59$	5.20490	−	5.20490i	0.677620	−	0.677620i	−0.281841	−	0.959461i	$-0.590945\pi$
$59$	5.20490	−	5.20490i	0.677620	−	0.677620i	0.959461	+	0.281841i	$0.0909451\pi$
$60$	−1.08934	+	1.08934i	−0.140634	+	0.140634i
$61$	−2.86655	−	1.18736i	−0.367024	−	0.152026i	0.191546	−	0.981484i	$-0.438650\pi$
$61$	−2.86655	−	1.18736i	−0.367024	−	0.152026i	−0.558570	+	0.829457i	$0.688650\pi$
$62$	3.13310	−	7.56397i	0.397904	−	0.960626i
$63$	−0.528457	+	0.218894i	−0.0665793	+	0.0275780i
$64$		−	2.93690i		−	0.367112i
$65$	−0.189064	−	0.456440i	−0.0234504	−	0.0566144i
$66$	−0.477555	−	0.477555i	−0.0587829	−	0.0587829i
$67$	2.40497			0.293814			0.146907	−	0.989150i	$-0.453068\pi$
$67$	2.40497			0.293814			0.146907	+	0.989150i	$0.453068\pi$
$68$	19.0690	+	0.688817i	2.31245	+	0.0835314i
$69$	−0.286435			−0.0344828
$70$	0.450785	+	0.450785i	0.0538791	+	0.0538791i
$71$	3.65041	+	8.81286i	0.433224	+	1.04589i	0.978241	+	0.207470i	$0.0665228\pi$
$71$	3.65041	+	8.81286i	0.433224	+	1.04589i	−0.545018	+	0.838424i	$0.683477\pi$
$72$			19.8310i			2.33710i
$73$	−2.33531	+	0.967317i	−0.273327	+	0.113216i	−0.515137	−	0.857108i	$-0.672259\pi$
$73$	−2.33531	+	0.967317i	−0.273327	+	0.113216i	0.241810	+	0.970324i	$0.422259\pi$
$74$	5.43086	−	13.1113i	0.631325	−	1.52415i
$75$	0.821551	+	0.340298i	0.0948646	+	0.0392942i
$76$	−7.32961	+	7.32961i	−0.840764	+	0.840764i
$77$	−0.137986	+	0.137986i	−0.0157250	+	0.0157250i
$78$	0.242928	+	0.100624i	0.0275061	+	0.0113934i
$79$	−5.20111	+	12.5566i	−0.585171	+	1.41273i	0.302900	+	0.953022i	$0.402045\pi$
$79$	−5.20111	+	12.5566i	−0.585171	+	1.41273i	−0.888071	+	0.459706i	$0.847955\pi$
$80$	9.56855	−	3.96342i	1.06980	−	0.443124i
$81$		−	8.38538i		−	0.931709i
$82$	−9.49211	−	22.9160i	−1.04823	−	2.53065i
$83$	−5.09341	−	5.09341i	−0.559074	−	0.559074i	0.369970	−	0.929044i	$-0.379368\pi$
$83$	−5.09341	−	5.09341i	−0.559074	−	0.559074i	−0.929044	+	0.369970i	$0.879368\pi$
$84$	−0.236912			−0.0258492
$85$	1.82641	+	4.90288i	0.198102	+	0.531792i
$86$	−30.1491			−3.25107
$87$	−0.841586	−	0.841586i	−0.0902275	−	0.0902275i
$88$	2.58905	+	6.25052i	0.275994	+	0.666308i
$89$		−	7.05766i		−	0.748110i	−0.927406	−	0.374055i	$-0.877967\pi$
$89$		−	7.05766i		−	0.748110i	0.927406	−	0.374055i	$-0.122033\pi$
$90$	−8.84690	+	3.66451i	−0.932546	+	0.386273i
$91$	0.0290747	−	0.0701924i	0.00304785	−	0.00735816i
$92$	4.66851	+	1.93376i	0.486726	+	0.201608i
$93$	−0.589903	+	0.589903i	−0.0611701	+	0.0611701i
$94$	−6.64551	+	6.64551i	−0.685432	+	0.685432i
$95$	−2.62585	−	1.08766i	−0.269407	−	0.111592i
$96$	−0.751049	+	1.81319i	−0.0766536	+	0.185058i
$97$	−14.8335	+	6.14424i	−1.50611	+	0.623853i	−0.974752	−	0.223292i	$-0.928320\pi$
$97$	−14.8335	+	6.14424i	−1.50611	+	0.623853i	−0.531362	+	0.847145i	$0.678320\pi$
$98$		−	17.9233i		−	1.81053i
$99$	−1.12171	−	2.70806i	−0.112737	−	0.272170i
$100$	−11.0928	−	11.0928i	−1.10928	−	1.10928i
$101$	7.32255			0.728621			0.364310	−	0.931278i	$-0.381305\pi$
$101$	7.32255			0.728621			0.364310	+	0.931278i	$0.381305\pi$
$102$	−2.53249	−	1.15779i	−0.250754	−	0.114639i
$103$	−6.99931			−0.689662			−0.344831	−	0.938665i	$-0.612064\pi$
$103$	−6.99931			−0.689662			−0.344831	+	0.938665i	$0.612064\pi$
$104$	−1.86256	−	1.86256i	−0.182639	−	0.182639i
$105$	−0.0248591	−	0.0600151i	−0.00242600	−	0.00585688i
$106$			32.0587i			3.11382i
$107$	−9.65594	+	3.99962i	−0.933475	+	0.386658i	−0.796996	−	0.603985i	$-0.793579\pi$
$107$	−9.65594	+	3.99962i	−0.933475	+	0.386658i	−0.136479	+	0.990643i	$0.543579\pi$
$108$	2.75560	−	6.65261i	0.265158	−	0.640148i
$109$	13.3278	+	5.52054i	1.27657	+	0.528772i	0.914955	−	0.403557i	$-0.132226\pi$
$109$	13.3278	+	5.52054i	1.27657	+	0.528772i	0.361613	+	0.932328i	$0.382226\pi$
$110$	−2.31003	+	2.31003i	−0.220253	+	0.220253i
$111$	−1.02253	+	1.02253i	−0.0970541	+	0.0970541i
$112$	1.47148	+	0.609505i	0.139041	+	0.0575928i
$113$	5.70865	−	13.7819i	0.537024	−	1.29649i	−0.389766	−	0.920914i	$-0.627444\pi$
$113$	5.70865	−	13.7819i	0.537024	−	1.29649i	0.926791	−	0.375578i	$-0.122556\pi$
$114$	1.39754	−	0.578879i	0.130891	−	0.0542170i
$115$			1.38555i			0.129203i
$116$	8.03507	+	19.3984i	0.746037	+	1.80109i
$117$	0.806959	+	0.806959i	0.0746034	+	0.0746034i
$118$	18.9503			1.74452
$119$	−0.334537	+	0.731747i	−0.0306670	+	0.0670791i
$120$	−2.25214			−0.205591
$121$	−0.707107	−	0.707107i	−0.0642824	−	0.0642824i
$122$	−3.05684	−	7.37987i	−0.276753	−	0.668142i
$123$			2.52746i			0.227893i
$124$	13.5971	−	5.63212i	1.22106	−	0.505779i
$125$	4.07412	−	9.83580i	0.364401	−	0.879741i
$126$	−1.36050	−	0.563537i	−0.121203	−	0.0502039i
$127$	2.95566	−	2.95566i	0.262273	−	0.262273i	−0.563704	−	0.825977i	$-0.690624\pi$
$127$	2.95566	−	2.95566i	0.262273	−	0.262273i	0.825977	+	0.563704i	$0.190624\pi$
$128$	−5.23379	+	5.23379i	−0.462606	+	0.462606i
$129$	2.83825	+	1.17564i	0.249894	+	0.103510i
$130$	0.486739	−	1.17509i	0.0426899	−	0.103062i
$131$	5.53320	−	2.29193i	0.483438	−	0.200247i	−0.127634	−	0.991821i	$-0.540738\pi$
$131$	5.53320	−	2.29193i	0.483438	−	0.200247i	0.611072	+	0.791575i	$0.290738\pi$
$132$		−	1.21405i		−	0.105669i
$133$	−0.167263	−	0.403810i	−0.0145036	−	0.0350147i
$134$	4.37807	+	4.37807i	0.378208	+	0.378208i
$135$	1.97440			0.169929
$136$	18.9998	+	20.4239i	1.62922	+	1.75133i
$137$	10.3153			0.881293			0.440647	−	0.897681i	$-0.354749\pi$
$137$	10.3153			0.881293			0.440647	+	0.897681i	$0.354749\pi$
$138$	−0.521435	−	0.521435i	−0.0443875	−	0.0443875i
$139$	7.77099	+	18.7608i	0.659127	+	1.59127i	0.799154	+	0.601126i	$0.205281\pi$
$139$	7.77099	+	18.7608i	0.659127	+	1.59127i	−0.140027	+	0.990148i	$0.544719\pi$
$140$			1.14599i			0.0968540i
$141$	0.884748	−	0.366475i	0.0745092	−	0.0308627i
$142$	−9.39788	+	22.6885i	−0.788653	+	1.90398i
$143$	0.359699	+	0.148992i	0.0300795	+	0.0124593i
$144$	−16.9166	+	16.9166i	−1.40972	+	1.40972i
$145$	−4.07093	+	4.07093i	−0.338072	+	0.338072i
$146$	−6.01220	−	2.49033i	−0.497573	−	0.206101i
$147$	−0.698905	+	1.68731i	−0.0576447	+	0.139167i
$148$	23.5690	−	9.76262i	1.93736	−	0.802482i
$149$		−	3.86695i		−	0.316793i	−0.987376	−	0.158396i	$-0.949368\pi$
$149$		−	3.86695i		−	0.316793i	0.987376	−	0.158396i	$-0.0506324\pi$
$150$	0.876088	+	2.11506i	0.0715323	+	0.172694i
$151$	2.21198	+	2.21198i	0.180008	+	0.180008i	0.791359	−	0.611351i	$-0.209374\pi$
$151$	2.21198	+	2.21198i	0.180008	+	0.180008i	−0.611351	+	0.791359i	$0.709374\pi$
$152$	−15.1534			−1.22911
$153$	−8.23173	−	8.84872i	−0.665496	−	0.715376i
$154$	−0.502389			−0.0404836
$155$	2.85348	+	2.85348i	0.229197	+	0.229197i
$156$	0.180883	+	0.436691i	0.0144823	+	0.0349633i
$157$		−	16.7161i		−	1.33409i	−0.745017	−	0.667045i	$-0.767559\pi$
$157$		−	16.7161i		−	1.33409i	0.745017	−	0.667045i	$-0.232441\pi$
$158$	−32.3267	+	13.3901i	−2.57177	+	1.06526i
$159$	1.25011	−	3.01802i	0.0991398	−	0.239345i
$160$	8.77080	+	3.63298i	0.693392	+	0.287213i
$161$	−0.150665	+	0.150665i	−0.0118741	+	0.0118741i
$162$	15.2650	−	15.2650i	1.19933	−	1.19933i
$163$	13.8207	+	5.72471i	1.08252	+	0.448394i	0.851392	−	0.524530i	$-0.175759\pi$
$163$	13.8207	+	5.72471i	1.08252	+	0.448394i	0.231127	+	0.972924i	$0.425759\pi$
$164$	17.0632	−	41.1942i	1.33241	−	3.21672i
$165$	0.307546	−	0.127390i	0.0239424	−	0.00991726i
$166$		−	18.5444i		−	1.43932i
$167$	7.27523	+	17.5640i	0.562974	+	1.35914i	0.907377	+	0.420318i	$0.138081\pi$
$167$	7.27523	+	17.5640i	0.562974	+	1.35914i	−0.344403	+	0.938822i	$0.611919\pi$
$168$	−0.244899	−	0.244899i	−0.0188944	−	0.0188944i
$169$	12.8484			0.988340
$170$	−5.60050	+	12.2502i	−0.429538	+	0.939546i
$171$	6.56528			0.502059
$172$	−38.3228	−	38.3228i	−2.92209	−	2.92209i
$173$	2.20321	+	5.31903i	0.167507	+	0.404398i	0.985235	−	0.171207i	$-0.0547666\pi$
$173$	2.20321	+	5.31903i	0.167507	+	0.404398i	−0.817728	+	0.575605i	$0.804767\pi$
$174$		−	3.06409i		−	0.232288i
$175$	0.611134	−	0.253140i	0.0461974	−	0.0191356i
$176$	−3.12339	+	7.54053i	−0.235434	+	0.568389i
$177$	−1.78399	−	0.738952i	−0.134093	−	0.0555431i
$178$	12.8480	−	12.8480i	0.962995	−	0.962995i
$179$	−8.89864	+	8.89864i	−0.665115	+	0.665115i	−0.956581	−	0.291466i	$-0.905857\pi$
$179$	−8.89864	+	8.89864i	−0.665115	+	0.665115i	0.291466	+	0.956581i	$0.405857\pi$
$180$	−15.9033	−	6.58738i	−1.18537	−	0.490995i
$181$	5.08798	−	12.2835i	0.378186	−	0.913022i	−0.614120	−	0.789213i	$-0.710489\pi$
$181$	5.08798	−	12.2835i	0.378186	−	0.913022i	0.992306	−	0.123809i	$-0.0395112\pi$
$182$	0.180709	−	0.0748520i	0.0133950	−	0.00554840i
$183$			0.813943i			0.0601684i
$184$	2.82695	+	6.82485i	0.208405	+	0.503135i
$185$	4.94618	+	4.94618i	0.363651	+	0.363651i
$186$	−2.14775			−0.157481
$187$	−3.74981	−	1.71433i	−0.274213	−	0.125364i
$188$	−16.8943			−1.23214
$189$	0.214698	+	0.214698i	0.0156170	+	0.0156170i
$190$	−2.80016	−	6.76019i	−0.203145	−	0.490436i
$191$		−	22.4693i		−	1.62582i	−0.582388	−	0.812911i	$-0.697882\pi$
$191$		−	22.4693i		−	1.62582i	0.582388	−	0.812911i	$-0.302118\pi$
$192$	−0.711793	+	0.294834i	−0.0513693	+	0.0212778i
$193$	3.04095	−	7.34150i	0.218892	−	0.528453i	−0.775844	−	0.630925i	$-0.782675\pi$
$193$	3.04095	−	7.34150i	0.218892	−	0.528453i	0.994736	+	0.102473i	$0.0326754\pi$
$194$	−38.1885	−	15.8182i	−2.74177	−	1.13568i
$195$	−0.0916437	+	0.0916437i	−0.00656274	+	0.00656274i
$196$	22.7824	−	22.7824i	1.62732	−	1.62732i
$197$	7.18754	+	2.97718i	0.512091	+	0.212115i	0.623739	−	0.781633i	$-0.285613\pi$
$197$	7.18754	+	2.97718i	0.512091	+	0.212115i	−0.111648	+	0.993748i	$0.535613\pi$
$198$	2.88783	−	6.97183i	0.205229	−	0.495466i
$199$	−20.4800	+	8.48308i	−1.45179	+	0.601349i	−0.962623	−	0.270844i	$-0.912697\pi$
$199$	−20.4800	+	8.48308i	−1.45179	+	0.601349i	−0.489162	+	0.872193i	$0.662697\pi$
$200$		−	22.9335i		−	1.62164i
$201$	−0.241434	−	0.582873i	−0.0170294	−	0.0411127i
$202$	13.3302	+	13.3302i	0.937908	+	0.937908i
$203$	−0.885351			−0.0621394
$204$	−1.74739	−	4.69075i	−0.122341	−	0.328418i
$205$	12.2259			0.853890
$206$	−12.7417	−	12.7417i	−0.887759	−	0.887759i
$207$	−1.22478	−	2.95689i	−0.0851284	−	0.205518i
$208$		−	3.17768i		−	0.220332i
$209$	2.06931	−	0.857136i	0.143137	−	0.0592894i
$210$	0.0639991	−	0.154507i	0.00441636	−	0.0106620i
$211$	−0.866765	−	0.359026i	−0.0596706	−	0.0247164i	0.352649	−	0.935756i	$-0.385281\pi$
$211$	−0.866765	−	0.359026i	−0.0596706	−	0.0247164i	−0.412319	+	0.911039i	$0.635281\pi$
$212$	−40.7501	+	40.7501i	−2.79873	+	2.79873i
$213$	1.76944	−	1.76944i	0.121240	−	0.121240i
$214$	−24.8590	−	10.2969i	−1.69932	−	0.703883i
$215$	5.68683	−	13.7292i	0.387839	−	0.936326i
$216$	9.72539	−	4.02839i	0.661729	−	0.274097i
$217$			0.620579i			0.0421277i
$218$	14.2125	+	34.3120i	0.962591	+	2.32390i
$219$	0.468882	+	0.468882i	0.0316841	+	0.0316841i
$220$	−5.87260			−0.395931
$221$	1.60422	+	0.0579484i	0.107912	+	0.00389803i
$222$	−3.72288			−0.249863
$223$	20.0690	+	20.0690i	1.34392	+	1.34392i	0.892117	+	0.451804i	$0.149219\pi$
$223$	20.0690	+	20.0690i	1.34392	+	1.34392i	0.451804	+	0.892117i	$0.350781\pi$
$224$	0.558689	+	1.34879i	0.0373290	+	0.0901201i
$225$			9.93602i			0.662401i
$226$	35.4811	−	14.6968i	2.36017	−	0.977615i
$227$	6.81993	−	16.4648i	0.452655	−	1.09280i	−0.518654	−	0.854984i	$-0.673567\pi$
$227$	6.81993	−	16.4648i	0.452655	−	1.09280i	0.971309	−	0.237821i	$-0.0764331\pi$
$228$	2.51224	+	1.04060i	0.166377	+	0.0689157i
$229$	10.8416	−	10.8416i	0.716435	−	0.716435i	−0.251439	−	0.967873i	$-0.580904\pi$
$229$	10.8416	−	10.8416i	0.716435	−	0.716435i	0.967873	+	0.251439i	$0.0809036\pi$
$230$	−2.52229	+	2.52229i	−0.166315	+	0.166315i
$231$	0.0472951	+	0.0195903i	0.00311179	+	0.00128895i
$232$	−11.7464	+	28.3583i	−0.771188	+	1.86181i
$233$	−20.1496	+	8.34622i	−1.32004	+	0.546779i	−0.927798	−	0.373082i	$-0.878301\pi$
$233$	−20.1496	+	8.34622i	−1.32004	+	0.546779i	−0.392244	+	0.919861i	$0.628301\pi$
$234$			2.93802i			0.192065i
$235$	−1.77272	−	4.27971i	−0.115639	−	0.279178i
$236$	24.0879	+	24.0879i	1.56799	+	1.56799i
$237$	3.56538			0.231597
$238$	−1.94109	+	0.723091i	−0.125822	+	0.0468710i
$239$	−0.993928			−0.0642919			−0.0321459	−	0.999483i	$-0.510234\pi$
$239$	−0.993928			−0.0642919			−0.0321459	+	0.999483i	$0.510234\pi$
$240$	−1.92117	−	1.92117i	−0.124011	−	0.124011i
$241$	9.99440	+	24.1286i	0.643796	+	1.55426i	0.821519	+	0.570181i	$0.193127\pi$
$241$	9.99440	+	24.1286i	0.643796	+	1.55426i	−0.177723	+	0.984081i	$0.556873\pi$
$242$		−	2.57447i		−	0.165494i
$243$	−6.34478	+	2.62809i	−0.407018	+	0.168592i
$244$	5.49503	−	13.2662i	0.351783	−	0.849280i
$245$	8.16185	+	3.38075i	0.521442	+	0.215988i
$246$	−4.60106	+	4.60106i	−0.293353	+	0.293353i
$247$	−0.616622	+	0.616622i	−0.0392347	+	0.0392347i
$248$	19.8775	+	8.23354i	1.26222	+	0.522830i
$249$	−0.723124	+	1.74577i	−0.0458261	+	0.110634i
$250$	25.3220	−	10.4887i	1.60151	−	0.663365i
$251$		−	20.6831i		−	1.30551i	−0.757570	−	0.652754i	$-0.773614\pi$
$251$		−	20.6831i		−	1.30551i	0.757570	−	0.652754i	$-0.226386\pi$
$252$	−1.01302	−	2.44566i	−0.0638145	−	0.154062i
$253$	−0.772080	−	0.772080i	−0.0485402	−	0.0485402i
$254$	10.7611			0.675214
$255$	1.00492	−	0.934851i	0.0629305	−	0.0585426i
$256$	−24.9293			−1.55808
$257$	−9.49576	−	9.49576i	−0.592329	−	0.592329i	0.345931	−	0.938260i	$-0.387563\pi$
$257$	−9.49576	−	9.49576i	−0.592329	−	0.592329i	−0.938260	+	0.345931i	$0.887563\pi$
$258$	3.02666	+	7.30701i	0.188432	+	0.454915i
$259$			1.07570i			0.0668409i
$260$	2.11237	−	0.874971i	0.131003	−	0.0542634i
$261$	5.08916	−	12.2863i	0.315011	−	0.760505i
$262$	14.2451	+	5.90051i	0.880064	+	0.364535i
$263$	−6.27416	+	6.27416i	−0.386882	+	0.386882i	−0.873574	−	0.486692i	$-0.838203\pi$
$263$	−6.27416	+	6.27416i	−0.386882	+	0.386882i	0.486692	+	0.873574i	$0.338203\pi$
$264$	1.25498	−	1.25498i	0.0772384	−	0.0772384i
$265$	−14.5988	−	6.04702i	−0.896797	−	0.371466i
$266$	0.430616	−	1.03960i	0.0264027	−	0.0637419i
$267$	−1.71051	+	0.708516i	−0.104681	+	0.0433605i
$268$			11.1300i			0.679873i
$269$	−3.07245	−	7.41756i	−0.187331	−	0.452257i	0.802113	−	0.597172i	$-0.203709\pi$
$269$	−3.07245	−	7.41756i	−0.187331	−	0.452257i	−0.989444	+	0.144915i	$0.953709\pi$
$270$	3.59426	+	3.59426i	0.218739	+	0.218739i
$271$	−3.18943			−0.193744			−0.0968721	−	0.995297i	$-0.530884\pi$
$271$	−3.18943			−0.193744			−0.0968721	+	0.995297i	$0.530884\pi$
$272$	−1.21480	+	33.6301i	−0.0736580	+	2.03912i
$273$	−0.0199308			−0.00120627
$274$	18.7782	+	18.7782i	1.13443	+	1.13443i
$275$	1.29721	+	3.13174i	0.0782245	+	0.188851i
$276$		−	1.32560i		−	0.0797918i
$277$	−5.91807	+	2.45135i	−0.355583	+	0.147287i	−0.553322	−	0.832968i	$-0.686640\pi$
$277$	−5.91807	+	2.45135i	−0.355583	+	0.147287i	0.197739	+	0.980255i	$0.436640\pi$
$278$	−20.0062	+	48.2993i	−1.19989	+	2.89680i
$279$	−8.61200	−	3.56721i	−0.515587	−	0.213563i
$280$	−1.18463	+	1.18463i	−0.0707950	+	0.0707950i
$281$	8.67977	−	8.67977i	0.517791	−	0.517791i	−0.399111	−	0.916903i	$-0.630681\pi$
$281$	8.67977	−	8.67977i	0.517791	−	0.517791i	0.916903	+	0.399111i	$0.130681\pi$
$282$	2.27776	+	0.943480i	0.135639	+	0.0561834i
$283$	−10.4369	+	25.1969i	−0.620408	+	1.49780i	0.230817	+	0.972997i	$0.425860\pi$
$283$	−10.4369	+	25.1969i	−0.620408	+	1.49780i	−0.851225	+	0.524801i	$0.824140\pi$
$284$	−40.7852	+	16.8938i	−2.42016	+	1.00246i
$285$			0.745597i			0.0441654i
$286$	0.383576	+	0.926035i	0.0226813	+	0.0547576i
$287$	1.32945	+	1.32945i	0.0784747	+	0.0784747i
$288$	−21.9292			−1.29219
$289$	−16.9557	−	1.22656i	−0.997394	−	0.0721507i
$290$	−14.8217			−0.870358
$291$	2.97826	+	2.97826i	0.174589	+	0.174589i
$292$	−4.47667	−	10.8076i	−0.261977	−	0.632469i
$293$			21.6665i			1.26577i	0.774247	+	0.632884i	$0.218129\pi$
$293$			21.6665i			1.26577i	−0.774247	+	0.632884i	$0.781871\pi$
$294$	−4.34393	+	1.79931i	−0.253343	+	0.104938i
$295$	−3.57447	+	8.62953i	−0.208114	+	0.502431i
$296$	34.4554	+	14.2719i	2.00268	+	0.829536i
$297$	−1.10021	+	1.10021i	−0.0638407	+	0.0638407i
$298$	7.03950	−	7.03950i	0.407787	−	0.407787i
$299$	0.392750	+	0.162682i	0.0227133	+	0.00940816i
$300$	−1.57487	+	3.80207i	−0.0909252	+	0.219513i
$301$	2.11131	−	0.874535i	0.121694	−	0.0504074i
$302$			8.05349i			0.463427i
$303$	−0.735108	−	1.77471i	−0.0422309	−	0.101954i
$304$	−12.9265	−	12.9265i	−0.741387	−	0.741387i
$305$	3.93721			0.225444
$306$	1.12318	−	31.0937i	0.0642080	−	1.77751i
$307$	−13.4648			−0.768479			−0.384239	−	0.923233i	$-0.625536\pi$
$307$	−13.4648			−0.768479			−0.384239	+	0.923233i	$0.625536\pi$
$308$	−0.638590	−	0.638590i	−0.0363870	−	0.0363870i
$309$	0.702658	+	1.69637i	0.0399728	+	0.0965030i
$310$			10.3891i			0.590063i
$311$	22.6522	−	9.38283i	1.28449	−	0.532051i	0.367148	−	0.930162i	$-0.380334\pi$
$311$	22.6522	−	9.38283i	1.28449	−	0.532051i	0.917337	+	0.398111i	$0.130334\pi$
$312$	−0.264432	+	0.638395i	−0.0149705	+	0.0361420i
$313$	−7.51572	−	3.11312i	−0.424814	−	0.175964i	0.160025	−	0.987113i	$-0.448842\pi$
$313$	−7.51572	−	3.11312i	−0.424814	−	0.175964i	−0.584839	+	0.811149i	$0.698842\pi$
$314$	30.4305	−	30.4305i	1.71729	−	1.71729i
$315$	0.513244	−	0.513244i	0.0289180	−	0.0289180i
$316$	−58.1110	−	24.0703i	−3.26900	−	1.35406i
$317$	−5.75849	+	13.9022i	−0.323429	+	0.780827i	0.675621	+	0.737249i	$0.263876\pi$
$317$	−5.75849	+	13.9022i	−0.323429	+	0.780827i	−0.999050	+	0.0435776i	$0.986124\pi$
$318$	7.76982	−	3.21836i	0.435710	−	0.180477i
$319$		−	4.53695i		−	0.254020i
$320$	1.42618	+	3.44309i	0.0797257	+	0.192475i
$321$	1.93871	+	1.93871i	0.108208	+	0.108208i
$322$	−0.548551			−0.0305696
$323$	6.76157	−	6.29011i	0.376224	−	0.349991i
$324$	38.8069			2.15594
$325$	−0.933208	−	0.933208i	−0.0517650	−	0.0517650i
$326$	14.7381	+	35.5810i	0.816269	+	1.97065i
$327$		−	3.78435i		−	0.209275i
$328$	60.2214	−	24.9445i	3.32517	−	1.37733i
$329$	0.272612	−	0.658145i	0.0150296	−	0.0362847i
$330$	0.791768	+	0.327961i	0.0435854	+	0.0180537i
$331$	9.84004	−	9.84004i	0.540857	−	0.540857i	−0.382923	−	0.923780i	$-0.625082\pi$
$331$	9.84004	−	9.84004i	0.540857	−	0.540857i	0.923780	+	0.382923i	$0.125082\pi$
$332$	23.5719	−	23.5719i	1.29367	−	1.29367i
$333$	−14.9279	−	6.18334i	−0.818044	−	0.338845i
$334$	−18.7299	+	45.2180i	−1.02485	+	2.47422i
$335$	−2.81948	+	1.16787i	−0.154045	+	0.0638074i
$336$		−	0.417818i		−	0.0227938i
$337$	−4.02985	−	9.72891i	−0.219520	−	0.529968i	0.775303	−	0.631589i	$-0.217597\pi$
$337$	−4.02985	−	9.72891i	−0.219520	−	0.529968i	−0.994823	+	0.101621i	$0.967597\pi$
$338$	23.3896	+	23.3896i	1.27223	+	1.27223i
$339$	−3.91330			−0.212541
$340$	−22.6901	+	8.45247i	−1.23055	+	0.458399i
$341$	−3.18014			−0.172214
$342$	11.9516	+	11.9516i	0.646270	+	0.646270i
$343$	1.04264	+	2.51717i	0.0562975	+	0.135914i
$344$		−	79.2295i		−	4.27177i
$345$	0.335805	−	0.139095i	0.0180791	−	0.00748861i
$346$	−5.67212	+	13.6937i	−0.304935	+	0.736178i
$347$	−2.47828	−	1.02654i	−0.133041	−	0.0551074i	0.315170	−	0.949035i	$-0.397939\pi$
$347$	−2.47828	−	1.02654i	−0.133041	−	0.0551074i	−0.448211	+	0.893928i	$0.647939\pi$
$348$	3.89479	−	3.89479i	0.208783	−	0.208783i
$349$	−21.7990	+	21.7990i	−1.16688	+	1.16688i	−0.183937	+	0.982938i	$0.558884\pi$
$349$	−21.7990	+	21.7990i	−1.16688	+	1.16688i	−0.982938	+	0.183937i	$0.941116\pi$
$350$	1.57335	+	0.651702i	0.0840990	+	0.0348350i
$351$	0.231822	−	0.559667i	0.0123737	−	0.0298728i
$352$	−6.91185	+	2.86298i	−0.368403	+	0.152598i
$353$			13.3717i			0.711704i	0.934542	+	0.355852i	$0.115809\pi$
$353$			13.3717i			0.711704i	−0.934542	+	0.355852i	$0.884191\pi$
$354$	−1.90241	−	4.59283i	−0.101112	−	0.244106i
$355$	−8.55916	−	8.55916i	−0.454273	−	0.454273i
$356$	32.6623			1.73110
$357$	0.210932	+	0.00761937i	0.0111637	+	0.000403260i
$358$	−32.3987			−1.71232
$359$	−20.3167	−	20.3167i	−1.07228	−	1.07228i	−0.997176	−	0.0750993i	$-0.976073\pi$
$359$	−20.3167	−	20.3167i	−1.07228	−	1.07228i	−0.0750993	−	0.997176i	$-0.523927\pi$
$360$	−9.63004	−	23.2490i	−0.507547	−	1.22533i
$361$		−	13.9833i		−	0.735962i
$362$	31.6235	−	13.0989i	1.66209	−	0.688461i
$363$	−0.100390	+	0.242362i	−0.00526909	+	0.0127207i
$364$	0.324845	+	0.134555i	0.0170265	+	0.00705261i
$365$	2.26808	−	2.26808i	0.118717	−	0.118717i
$366$	−1.48173	+	1.48173i	−0.0774510	+	0.0774510i
$367$	4.88256	+	2.02242i	0.254867	+	0.105569i	0.506459	−	0.862264i	$-0.330954\pi$
$367$	4.88256	+	2.02242i	0.254867	+	0.105569i	−0.251592	+	0.967833i	$0.580954\pi$
$368$	−3.41038	+	8.23339i	−0.177779	+	0.429195i
$369$	−26.0911	+	10.8073i	−1.35825	+	0.562605i
$370$			18.0083i			0.936209i
$371$	−0.929926	−	2.24504i	−0.0482793	−	0.116557i
$372$	−2.73002	−	2.73002i	−0.141545	−	0.141545i
$373$	−16.6266			−0.860895			−0.430448	−	0.902616i	$-0.641644\pi$
$373$	−16.6266			−0.860895			−0.430448	+	0.902616i	$0.641644\pi$
$374$	−3.70546	−	9.94707i	−0.191605	−	0.514351i
$375$	−2.79283			−0.144221
$376$	−17.4639	−	17.4639i	−0.900631	−	0.900631i
$377$	0.675970	+	1.63194i	0.0348142	+	0.0840489i
$378$			0.781683i			0.0402054i
$379$	4.48810	−	1.85903i	0.230538	−	0.0954921i	−0.264424	−	0.964407i	$-0.585182\pi$
$379$	4.48810	−	1.85903i	0.230538	−	0.0954921i	0.494962	+	0.868914i	$0.335182\pi$
$380$	5.03362	−	12.1522i	0.258219	−	0.623396i
$381$	−1.01306	−	0.419623i	−0.0519006	−	0.0214979i
$382$	40.9038	−	40.9038i	2.09282	−	2.09282i
$383$	−16.8297	+	16.8297i	−0.859957	+	0.859957i	−0.991333	−	0.131376i	$-0.958061\pi$
$383$	−16.8297	+	16.8297i	−0.859957	+	0.859957i	0.131376	+	0.991333i	$0.458061\pi$
$384$	1.79389	+	0.743055i	0.0915442	+	0.0379189i
$385$	0.0947623	−	0.228776i	0.00482953	−	0.0116595i
$386$	18.9005	−	7.82884i	0.962010	−	0.398478i
$387$			34.3265i			1.74491i
$388$	−28.4350	−	68.6483i	−1.44357	−	3.48509i
$389$	−0.989584	−	0.989584i	−0.0501739	−	0.0501739i	0.681575	−	0.731749i	$-0.261295\pi$
$389$	−0.989584	−	0.989584i	−0.0501739	−	0.0501739i	−0.731749	+	0.681575i	$0.761295\pi$
$390$	−0.333662			−0.0168956
$391$	−4.09437	−	1.87185i	−0.207061	−	0.0946634i
$392$	47.1010			2.37896
$393$	−1.11095	−	1.11095i	−0.0560402	−	0.0560402i
$394$	7.66467	+	18.5041i	0.386140	+	0.932225i
$395$		−	17.2465i		−	0.867766i
$396$	12.5327	−	5.19121i	0.629791	−	0.260868i
$397$	−7.14165	+	17.2415i	−0.358429	+	0.865324i	0.637092	+	0.770788i	$0.280137\pi$
$397$	−7.14165	+	17.2415i	−0.358429	+	0.865324i	−0.995521	+	0.0945368i	$0.969863\pi$
$398$	−52.7251	−	21.8395i	−2.64287	−	1.09471i
$399$	−0.0810767	+	0.0810767i	−0.00405891	+	0.00405891i
$400$	19.5633	−	19.5633i	0.978163	−	0.978163i
$401$	−26.0402	−	10.7862i	−1.30038	−	0.538637i	−0.378320	−	0.925675i	$-0.623498\pi$
$401$	−26.0402	−	10.7862i	−1.30038	−	0.538637i	−0.922064	+	0.387038i	$0.873498\pi$
$402$	0.621566	−	1.50059i	0.0310009	−	0.0748428i
$403$	1.14389	−	0.473815i	0.0569813	−	0.0236024i
$404$			33.8882i			1.68600i
$405$	4.07199	+	9.83066i	0.202339	+	0.488489i
$406$	−1.61172	−	1.61172i	−0.0799882	−	0.0799882i
$407$	−5.51240			−0.273239
$408$	3.04259	−	6.65518i	0.150631	−	0.329481i
$409$	1.28004			0.0632940			0.0316470	−	0.999499i	$-0.489925\pi$
$409$	1.28004			0.0632940			0.0316470	+	0.999499i	$0.489925\pi$
$410$	22.2563	+	22.2563i	1.09916	+	1.09916i
$411$	−1.03555	−	2.50003i	−0.0510798	−	0.123317i
$412$		−	32.3922i		−	1.59585i
$413$	−1.32707	+	0.549690i	−0.0653009	+	0.0270485i
$414$	3.15318	−	7.61244i	0.154970	−	0.374131i
$415$	8.44468	+	3.49790i	0.414533	+	0.171705i
$416$	2.05962	−	2.05962i	0.100981	−	0.100981i
$417$	3.76679	−	3.76679i	0.184461	−	0.184461i
$418$	5.32739	+	2.20668i	0.260571	+	0.107932i
$419$	5.74422	−	13.8678i	0.280624	−	0.677485i	−0.719227	−	0.694775i	$-0.755504\pi$
$419$	5.74422	−	13.8678i	0.280624	−	0.677485i	0.999851	+	0.0172900i	$0.00550385\pi$
$420$	0.277745	−	0.115046i	0.0135526	−	0.00561366i
$421$		−	2.48731i		−	0.121224i	−0.998161	−	0.0606120i	$-0.980695\pi$
$421$		−	2.48731i		−	0.121224i	0.998161	−	0.0606120i	$-0.0193052\pi$
$422$	−0.924303	−	2.23146i	−0.0449944	−	0.108626i
$423$	7.56628	+	7.56628i	0.367885	+	0.367885i
$424$	−84.2477			−4.09143
$425$	9.51958	+	10.2331i	0.461768	+	0.496378i
$426$	6.44228			0.312130
$427$	0.428135	+	0.428135i	0.0207189	+	0.0207189i
$428$	−18.5099	−	44.6869i	−0.894711	−	2.16002i
$429$		−	0.102135i		−	0.00493111i
$430$	35.3456	−	14.6406i	1.70451	−	0.706033i
$431$	12.8077	−	30.9206i	0.616927	−	1.48939i	−0.238327	−	0.971185i	$-0.576599\pi$
$431$	12.8077	−	30.9206i	0.616927	−	1.48939i	0.855254	−	0.518209i	$-0.173401\pi$
$432$	11.7326	+	4.85978i	0.564483	+	0.233816i
$433$	6.53442	−	6.53442i	0.314024	−	0.314024i	−0.532442	−	0.846466i	$-0.678726\pi$
$433$	6.53442	−	6.53442i	0.314024	−	0.314024i	0.846466	+	0.532442i	$0.178726\pi$
$434$	−1.12972	+	1.12972i	−0.0542283	+	0.0542283i
$435$	1.39532	+	0.577960i	0.0669004	+	0.0277111i
$436$	−25.5486	+	61.6798i	−1.22356	+	2.95393i
$437$	2.25945	−	0.935895i	0.108084	−	0.0447699i
$438$			1.70713i			0.0815700i
$439$	−8.95870	−	21.6282i	−0.427576	−	1.03226i	−0.980054	−	0.198732i	$-0.936318\pi$
$439$	−8.95870	−	21.6282i	−0.427576	−	1.03226i	0.552478	−	0.833527i	$-0.313682\pi$
$440$	−6.07058	−	6.07058i	−0.289404	−	0.289404i
$441$	−20.4067			−0.971746
$442$	2.81488	+	3.02587i	0.133890	+	0.143926i
$443$	5.69673			0.270660			0.135330	−	0.990801i	$-0.456791\pi$
$443$	5.69673			0.270660			0.135330	+	0.990801i	$0.456791\pi$
$444$	−4.73218	−	4.73218i	−0.224579	−	0.224579i
$445$	3.42724	+	8.27409i	0.162467	+	0.392230i
$446$			73.0685i			3.45989i
$447$	−0.937202	+	0.388202i	−0.0443281	+	0.0183613i
$448$	−0.219321	+	0.529487i	−0.0103619	+	0.0250159i
$449$	6.67598	+	2.76528i	0.315059	+	0.130502i	0.534609	−	0.845100i	$-0.320459\pi$
$449$	6.67598	+	2.76528i	0.315059	+	0.130502i	−0.219550	+	0.975601i	$0.570459\pi$
$450$	−18.0878	+	18.0878i	−0.852668	+	0.852668i
$451$	−6.81270	+	6.81270i	−0.320798	+	0.320798i
$452$	63.7815	+	26.4192i	3.00003	+	1.24265i
$453$	0.314040	−	0.758160i	0.0147549	−	0.0356214i
$454$	42.3881	−	17.5577i	1.98937	−	0.824025i
$455$			0.0964094i			0.00451974i
$456$	1.52125	+	3.67262i	0.0712390	+	0.171986i
$457$	−15.3218	−	15.3218i	−0.716724	−	0.716724i	0.251209	−	0.967933i	$-0.419172\pi$
$457$	−15.3218	−	15.3218i	−0.716724	−	0.716724i	−0.967933	+	0.251209i	$0.919172\pi$
$458$	39.4728			1.84444
$459$	−2.66738	+	5.83446i	−0.124502	+	0.272329i
$460$	−6.41221			−0.298971
$461$	27.0213	+	27.0213i	1.25851	+	1.25851i	0.951805	+	0.306704i	$0.0992263\pi$
$461$	27.0213	+	27.0213i	1.25851	+	1.25851i	0.306704	+	0.951805i	$0.400774\pi$
$462$	0.0504347	+	0.121760i	0.00234643	+	0.00566479i
$463$			0.465764i			0.0216459i	0.999941	+	0.0108230i	$0.00344512\pi$
$463$			0.465764i			0.0216459i	−0.999941	+	0.0108230i	$0.996555\pi$
$464$	−34.2110	+	14.1707i	−1.58821	+	0.657856i
$465$	0.405116	−	0.978037i	0.0187868	−	0.0453554i
$466$	−51.8746	−	21.4871i	−2.40304	−	0.995373i
$467$	−5.52249	+	5.52249i	−0.255550	+	0.255550i	−0.823242	−	0.567691i	$-0.807837\pi$
$467$	−5.52249	+	5.52249i	−0.255550	+	0.255550i	0.567691	+	0.823242i	$0.307837\pi$
$468$	−3.73454	+	3.73454i	−0.172629	+	0.172629i
$469$	−0.433587	−	0.179597i	−0.0200212	−	0.00829304i
$470$	4.56381	−	11.0180i	0.210513	−	0.508223i
$471$	−4.05135	+	1.67812i	−0.186676	+	0.0773239i
$472$			49.7999i			2.29222i
$473$	4.48153	+	10.8194i	0.206061	+	0.497475i
$474$	6.49053	+	6.49053i	0.298120	+	0.298120i
$475$	−7.59241			−0.348364
$476$	−3.38647	−	1.54821i	−0.155218	−	0.0709622i
$477$	36.5006			1.67125
$478$	−1.80938	−	1.80938i	−0.0827589	−	0.0827589i
$479$	13.3302	+	32.1820i	0.609073	+	1.47043i	0.864010	+	0.503474i	$0.167945\pi$
$479$	13.3302	+	32.1820i	0.609073	+	1.47043i	−0.254938	+	0.966957i	$0.582055\pi$
$480$		−	2.49042i		−	0.113672i
$481$	1.98280	−	0.821304i	0.0904080	−	0.0374482i
$482$	−25.7303	+	62.1185i	−1.17198	+	2.82942i
$483$	0.0516408	+	0.0213903i	0.00234974	+	0.000973294i
$484$	3.27243	−	3.27243i	0.148747	−	0.148747i
$485$	14.4065	−	14.4065i	0.654165	−	0.654165i
$486$	−16.3345	−	6.76596i	−0.740947	−	0.306910i
$487$	−1.77037	+	4.27404i	−0.0802229	+	0.193675i	−0.958902	−	0.283738i	$-0.908425\pi$
$487$	−1.77037	+	4.27404i	−0.0802229	+	0.193675i	0.878679	+	0.477413i	$0.158425\pi$
$488$	19.3937	−	8.03313i	0.877911	−	0.363643i
$489$		−	3.92431i		−	0.177463i
$490$	8.70366	+	21.0125i	0.393191	+	0.949248i
$491$	7.99785	+	7.99785i	0.360938	+	0.360938i	0.864158	−	0.503220i	$-0.167852\pi$
$491$	7.99785	+	7.99785i	0.360938	+	0.360938i	−0.503220	+	0.864158i	$0.667852\pi$
$492$	−11.6969			−0.527336
$493$	−6.53006	−	17.5295i	−0.294099	−	0.789491i
$494$	−2.24503			−0.101009
$495$	2.63010	+	2.63010i	0.118214	+	0.118214i
$496$	9.93281	+	23.9799i	0.445996	+	1.07673i
$497$		−	1.86146i		−	0.0834977i
$498$	−4.49445	+	1.86166i	−0.201401	+	0.0834231i
$499$	12.4621	−	30.0861i	0.557878	−	1.34684i	−0.353564	−	0.935410i	$-0.615030\pi$
$499$	12.4621	−	30.0861i	0.557878	−	1.34684i	0.911443	−	0.411427i	$-0.134970\pi$
$500$	45.5193	+	18.8547i	2.03569	+	0.843208i
$501$	3.52648	−	3.52648i	0.157552	−	0.157552i
$502$	37.6522	−	37.6522i	1.68050	−	1.68050i
$503$	−23.4052	−	9.69475i	−1.04359	−	0.432267i	−0.205988	−	0.978555i	$-0.566041\pi$
$503$	−23.4052	−	9.69475i	−1.04359	−	0.432267i	−0.837598	+	0.546287i	$0.816041\pi$
$504$	1.48093	−	3.57528i	0.0659659	−	0.159256i
$505$	−8.58464	+	3.55587i	−0.382011	+	0.158234i
$506$		−	2.81103i		−	0.124966i
$507$	−1.28985	−	3.11397i	−0.0572842	−	0.138296i
$508$	13.6786	+	13.6786i	0.606889	+	0.606889i
$509$	35.9402			1.59302			0.796510	−	0.604626i	$-0.206677\pi$
$509$	35.9402			1.59302			0.796510	+	0.604626i	$0.206677\pi$
$510$	3.53121	+	0.127556i	0.156365	+	0.00564827i
$511$	0.493265			0.0218208
$512$	−34.9144	−	34.9144i	−1.54301	−	1.54301i
$513$	−1.33365	−	3.21971i	−0.0588819	−	0.142154i
$514$		−	34.5727i		−	1.52494i
$515$	8.20568	−	3.39891i	0.361586	−	0.149774i
$516$	−5.44078	+	13.1352i	−0.239517	+	0.578245i
$517$	3.37264	+	1.39699i	0.148329	+	0.0614397i
$518$	−1.95824	+	1.95824i	−0.0860401	+	0.0860401i
$519$	1.06795	−	1.06795i	0.0468779	−	0.0468779i
$520$	3.08805	+	1.27911i	0.135420	+	0.0560928i
$521$	−2.74867	+	6.63588i	−0.120422	+	0.290723i	−0.972583	−	0.232555i	$-0.925291\pi$
$521$	−2.74867	+	6.63588i	−0.120422	+	0.290723i	0.852162	+	0.523279i	$0.175291\pi$
$522$	31.6308	−	13.1019i	1.38444	−	0.573456i
$523$			14.6695i			0.641451i	0.947172	+	0.320726i	$0.103927\pi$
$523$			14.6695i			0.641451i	−0.947172	+	0.320726i	$0.896073\pi$
$524$	10.6069	+	25.6072i	0.463363	+	1.11866i
$525$	−0.122703	−	0.122703i	−0.00535520	−	0.00535520i
$526$	−22.8433			−0.996017
$527$	−12.2872	+	4.57719i	−0.535238	+	0.199386i
$528$	2.14109			0.0931792
$529$	15.4204	+	15.4204i	0.670454	+	0.670454i
$530$	−15.5679	−	37.5842i	−0.676227	−	1.63256i
$531$		−	21.5760i		−	0.936317i
$532$	1.86880	−	0.774082i	0.0810227	−	0.0335607i
$533$	1.43548	−	3.46556i	0.0621776	−	0.150110i
$534$	−4.40366	−	1.82406i	−0.190565	−	0.0789347i
$535$	9.37797	−	9.37797i	0.405445	−	0.405445i
$536$	−11.5052	+	11.5052i	−0.496950	+	0.496950i
$537$	3.05003	+	1.26336i	0.131618	+	0.0545181i
$538$	7.90996	−	19.0963i	0.341022	−	0.823301i
$539$	−6.43197	+	2.66421i	−0.277045	+	0.114756i
$540$			9.13737i			0.393210i
$541$	−0.508943	−	1.22870i	−0.0218812	−	0.0528258i	0.912561	−	0.408940i	$-0.134101\pi$
$541$	−0.508943	−	1.22870i	−0.0218812	−	0.0528258i	−0.934442	+	0.356114i	$0.884101\pi$
$542$	−5.80613	−	5.80613i	−0.249395	−	0.249395i
$543$	−3.48783			−0.149677
$544$	−22.5848	+	21.0101i	−0.968316	+	0.900799i
$545$	−18.3057			−0.784130
$546$	−0.0362826	−	0.0362826i	−0.00155275	−	0.00155275i
$547$	−9.34015	−	22.5491i	−0.399356	−	0.964131i	−0.987819	−	0.155607i	$-0.950267\pi$
$547$	−9.34015	−	22.5491i	−0.399356	−	0.964131i	0.588463	−	0.808524i	$-0.299733\pi$
$548$			47.7383i			2.03928i
$549$	−8.40239	+	3.48038i	−0.358605	+	0.148539i
$550$	−3.33963	+	8.06257i	−0.142402	+	0.343789i
$551$	9.38836	+	3.88878i	0.399957	+	0.165668i
$552$	1.37029	−	1.37029i	0.0583234	−	0.0583234i
$553$	1.87540	−	1.87540i	0.0797500	−	0.0797500i
$554$	−15.2359	−	6.31093i	−0.647313	−	0.268126i
$555$	0.702222	−	1.69531i	0.0298077	−	0.0719621i
$556$	−86.8237	+	35.9635i	−3.68214	+	1.52519i
$557$		−	36.2718i		−	1.53688i	−0.639920	−	0.768442i	$-0.721032\pi$
$557$		−	36.2718i		−	1.53688i	0.639920	−	0.768442i	$-0.278968\pi$
$558$	−9.18369	−	22.1714i	−0.388777	−	0.938590i
$559$	−3.22400	−	3.22400i	−0.136361	−	0.136361i
$560$	−2.02107			−0.0854059
$561$	−0.0390452	+	1.08091i	−0.00164849	+	0.0456362i
$562$	31.6018			1.33304
$563$	−5.89498	−	5.89498i	−0.248444	−	0.248444i	0.571888	−	0.820332i	$-0.306211\pi$
$563$	−5.89498	−	5.89498i	−0.248444	−	0.248444i	−0.820332	+	0.571888i	$0.806211\pi$
$564$	1.69602	+	4.09454i	0.0714152	+	0.172411i
$565$			18.9295i			0.796368i
$566$	−64.8687	+	26.8695i	−2.72663	+	1.12941i
$567$	−0.626201	+	1.51178i	−0.0262980	+	0.0634889i
$568$	−59.6235	−	24.6969i	−2.50175	−	1.03626i
$569$	−13.3178	+	13.3178i	−0.558310	+	0.558310i	−0.928826	−	0.370516i	$-0.879181\pi$
$569$	−13.3178	+	13.3178i	−0.558310	+	0.558310i	0.370516	+	0.928826i	$0.379181\pi$
$570$	−1.35731	+	1.35731i	−0.0568513	+	0.0568513i
$571$	0.150528	+	0.0623509i	0.00629942	+	0.00260931i	0.385831	−	0.922570i	$-0.373915\pi$
$571$	0.150528	+	0.0623509i	0.00629942	+	0.00260931i	−0.379531	+	0.925179i	$0.623915\pi$
$572$	−0.689524	+	1.66466i	−0.0288304	+	0.0696028i
$573$	−5.44571	+	2.25569i	−0.227498	+	0.0942327i
$574$			4.84032i			0.202031i
$575$	1.41640	+	3.41950i	0.0590680	+	0.142603i
$576$	−6.08719	−	6.08719i	−0.253633	−	0.253633i
$577$	4.30328			0.179148			0.0895740	−	0.995980i	$-0.471449\pi$
$577$	4.30328			0.179148			0.0895740	+	0.995980i	$0.471449\pi$
$578$	−28.6338	−	33.0995i	−1.19101	−	1.37676i
$579$	−2.08458			−0.0866322
$580$	−18.8399	−	18.8399i	−0.782286	−	0.782286i
$581$	0.537916	+	1.29864i	0.0223165	+	0.0538768i
$582$			10.8434i			0.449474i
$583$	11.5046	−	4.76537i	0.476473	−	0.197362i
$584$	6.54440	−	15.7996i	0.270809	−	0.653791i
$585$	−1.33791	−	0.554180i	−0.0553157	−	0.0229125i
$586$	−39.4422	+	39.4422i	−1.62934	+	1.62934i
$587$	−0.198167	+	0.198167i	−0.00817924	+	0.00817924i	−0.711185	−	0.703005i	$-0.751841\pi$
$587$	−0.198167	+	0.198167i	−0.00817924	+	0.00817924i	0.703005	+	0.711185i	$0.251841\pi$
$588$	−7.80872	−	3.23448i	−0.322026	−	0.133388i
$589$	2.72581	−	6.58069i	0.112315	−	0.271153i
$590$	−22.2165	+	9.20238i	−0.914639	+	0.378856i
$591$		−	2.04087i		−	0.0839500i
$592$	17.2174	+	41.5664i	0.707629	+	1.70837i
$593$	15.5137	+	15.5137i	0.637069	+	0.637069i	0.949832	−	0.312762i	$-0.101254\pi$
$593$	15.5137	+	15.5137i	0.637069	+	0.637069i	−0.312762	+	0.949832i	$0.601254\pi$
$594$	−4.00571			−0.164356
$595$	0.0368565	−	1.02032i	0.00151097	−	0.0418291i
$596$	17.8959			0.733046
$597$	4.11195	+	4.11195i	0.168291	+	0.168291i
$598$	0.418822	+	1.01112i	0.0171269	+	0.0413480i
$599$		−	28.1990i		−	1.15218i	−0.817386	−	0.576090i	$-0.804578\pi$
$599$		−	28.1990i		−	1.15218i	0.817386	−	0.576090i	$-0.195422\pi$
$600$	−5.55822	+	2.30229i	−0.226913	+	0.0939905i
$601$	9.60064	−	23.1780i	0.391618	−	0.945450i	−0.597970	−	0.801519i	$-0.704026\pi$
$601$	9.60064	−	23.1780i	0.391618	−	0.945450i	0.989588	−	0.143931i	$-0.0459743\pi$
$602$	5.43553	+	2.25147i	0.221535	+	0.0917630i
$603$	4.98468	−	4.98468i	0.202992	−	0.202992i
$604$	−10.2369	+	10.2369i	−0.416532	+	0.416532i
$605$	1.17236	+	0.485606i	0.0476631	+	0.0197427i
$606$	1.89252	−	4.56894i	0.0768783	−	0.185601i
$607$	33.6064	−	13.9202i	1.36404	−	0.565005i	0.423876	−	0.905720i	$-0.360669\pi$
$607$	33.6064	−	13.9202i	1.36404	−	0.565005i	0.940166	+	0.340716i	$0.110669\pi$
$608$		−	16.7567i		−	0.679575i
$609$	0.0888801	+	0.214576i	0.00360160	+	0.00869504i
$610$	7.16742	+	7.16742i	0.290200	+	0.290200i
$611$	−1.42128			−0.0574987
$612$	40.9512	−	38.0958i	1.65535	−	1.53993i
$613$	33.9213			1.37007			0.685034	−	0.728511i	$-0.259788\pi$
$613$	33.9213			1.37007			0.685034	+	0.728511i	$0.259788\pi$
$614$	−24.5118	−	24.5118i	−0.989215	−	0.989215i
$615$	−1.22735	−	2.96308i	−0.0494915	−	0.119483i
$616$		−	1.32024i		−	0.0531939i
$617$	−27.6591	+	11.4568i	−1.11351	+	0.461232i	−0.862146	−	0.506660i	$-0.830880\pi$
$617$	−27.6591	+	11.4568i	−1.11351	+	0.461232i	−0.251366	+	0.967892i	$0.580880\pi$
$618$	−1.80898	+	4.36725i	−0.0727677	+	0.175677i
$619$	13.3032	+	5.51036i	0.534700	+	0.221480i	0.633660	−	0.773611i	$-0.281552\pi$
$619$	13.3032	+	5.51036i	0.534700	+	0.221480i	−0.0989603	+	0.995091i	$0.531552\pi$
$620$	−13.2057	+	13.2057i	−0.530354	+	0.530354i
$621$	−1.20130	+	1.20130i	−0.0482067	+	0.0482067i
$622$	58.3174	+	24.1559i	2.33831	+	0.968562i
$623$	−0.527050	+	1.27241i	−0.0211158	+	0.0509780i
$624$	−0.770149	+	0.319006i	−0.0308306	+	0.0127705i
$625$		−	3.43934i		−	0.137574i
$626$	−8.01464	−	19.3490i	−0.320329	−	0.773343i
$627$	−0.415475	−	0.415475i	−0.0165925	−	0.0165925i
$628$	77.3608			3.08703
$629$	−21.2984	+	7.93403i	−0.849223	+	0.316350i
$630$	1.86865			0.0744487
$631$	4.14068	+	4.14068i	0.164838	+	0.164838i	0.784706	−	0.619868i	$-0.212814\pi$
$631$	4.14068	+	4.14068i	0.164838	+	0.164838i	−0.619868	+	0.784706i	$0.712814\pi$
$632$	−35.1882	−	84.9519i	−1.39971	−	3.37920i
$633$			0.246114i			0.00978214i
$634$	−35.7909	+	14.8251i	−1.42144	+	0.588779i
$635$	−2.02980	+	4.90038i	−0.0805503	+	0.194466i
$636$	13.9672	+	5.78539i	0.553834	+	0.229406i
$637$	1.91663	−	1.91663i	0.0759395	−	0.0759395i
$638$	8.25919	−	8.25919i	0.326985	−	0.326985i
$639$	25.8321	+	10.7000i	1.02190	+	0.423286i
$640$	3.59431	−	8.67744i	0.142078	−	0.343006i
$641$	5.71060	−	2.36541i	0.225555	−	0.0934281i	−0.267044	−	0.963684i	$-0.586047\pi$
$641$	5.71060	−	2.36541i	0.225555	−	0.0934281i	0.492599	+	0.870256i	$0.336047\pi$
$642$			7.05858i			0.278580i
$643$	4.41664	+	10.6627i	0.174175	+	0.420496i	0.986726	−	0.162394i	$-0.0519216\pi$
$643$	4.41664	+	10.6627i	0.174175	+	0.420496i	−0.812551	+	0.582891i	$0.801922\pi$
$644$	−0.697267	−	0.697267i	−0.0274762	−	0.0274762i
$645$	−3.89835			−0.153497
$646$	23.7597	+	0.858256i	0.934811	+	0.0337676i
$647$	28.7841			1.13162			0.565810	−	0.824535i	$-0.308563\pi$
$647$	28.7841			1.13162			0.565810	+	0.824535i	$0.308563\pi$
$648$	40.1152	+	40.1152i	1.57587	+	1.57587i
$649$	−2.81687	−	6.80053i	−0.110572	−	0.266944i
$650$		−	3.39768i		−	0.133268i
$651$	0.150405	−	0.0622998i	0.00589484	−	0.00244172i
$652$	−26.4935	+	63.9610i	−1.03757	+	2.50491i
$653$	23.3800	+	9.68433i	0.914932	+	0.378977i	0.789942	−	0.613181i	$-0.210110\pi$
$653$	23.3800	+	9.68433i	0.914932	+	0.378977i	0.124989	+	0.992158i	$0.460110\pi$
$654$	6.88914	−	6.88914i	0.269387	−	0.269387i
$655$	−5.37391	+	5.37391i	−0.209976	+	0.209976i
$656$	72.6501	+	30.0927i	2.83651	+	1.17492i
$657$	−2.83538	+	6.84522i	−0.110619	+	0.267057i
$658$	1.69438	−	0.701834i	0.0660537	−	0.0273603i
$659$		−	31.9134i		−	1.24317i	−0.783347	−	0.621585i	$-0.786489\pi$
$659$		−	31.9134i		−	1.24317i	0.783347	−	0.621585i	$-0.213511\pi$
$660$	0.589549	+	1.42330i	0.0229481	+	0.0554017i
$661$	−7.12369	−	7.12369i	−0.277080	−	0.277080i	0.554862	−	0.831942i	$-0.312771\pi$
$661$	−7.12369	−	7.12369i	−0.277080	−	0.277080i	−0.831942	+	0.554862i	$0.812771\pi$
$662$	35.8262			1.39242
$663$	−0.147003	−	0.394621i	−0.00570912	−	0.0153258i
$664$	48.7331			1.89121
$665$	0.392185	+	0.392185i	0.0152083	+	0.0152083i
$666$	−15.9189	−	38.4315i	−0.616843	−	1.48919i
$667$		−	4.95383i		−	0.191813i
$668$	−81.2846	+	33.6692i	−3.14500	+	1.30270i
$669$	2.84925	−	6.87870i	0.110158	−	0.265946i
$670$	−7.25868	−	3.00664i	−0.280427	−	0.116157i
$671$	−2.19396	+	2.19396i	−0.0846970	+	0.0846970i
$672$	0.270810	−	0.270810i	0.0104467	−	0.0104467i
$673$	7.20911	+	2.98611i	0.277891	+	0.115106i	0.517276	−	0.855818i	$-0.326946\pi$
$673$	7.20911	+	2.98611i	0.277891	+	0.115106i	−0.239385	+	0.970925i	$0.576946\pi$
$674$	10.3747	−	25.0468i	0.399620	−	0.964768i
$675$	4.87277	−	2.01837i	0.187553	−	0.0776870i
$676$			59.4615i			2.28698i
$677$	10.8285	+	26.1424i	0.416175	+	1.00474i	0.983446	+	0.181204i	$0.0579993\pi$
$677$	10.8285	+	26.1424i	0.416175	+	1.00474i	−0.567271	+	0.823531i	$0.692001\pi$
$678$	−7.12388	−	7.12388i	−0.273591	−	0.273591i
$679$	3.13314			0.120239
$680$	−32.1925	−	14.7177i	−1.23453	−	0.564396i
$681$	−4.67509			−0.179150
$682$	−5.78921	−	5.78921i	−0.221680	−	0.221680i
$683$	16.0565	+	38.7638i	0.614384	+	1.48325i	0.858139	+	0.513418i	$0.171621\pi$
$683$	16.0565	+	38.7638i	0.614384	+	1.48325i	−0.243755	+	0.969837i	$0.578379\pi$
$684$			30.3836i			1.16175i
$685$	−12.0932	+	5.00916i	−0.462057	+	0.191390i
$686$	−2.68426	+	6.48038i	−0.102486	+	0.247422i
$687$	−3.71599	−	1.53921i	−0.141774	−	0.0587246i
$688$	67.5861	−	67.5861i	2.57670	−	2.57670i
$689$	−3.42820	+	3.42820i	−0.130604	+	0.130604i
$690$	0.864520	+	0.358096i	0.0329117	+	0.0136325i
$691$	18.2355	−	44.0245i	0.693713	−	1.67477i	−0.0434500	−	0.999056i	$-0.513835\pi$
$691$	18.2355	−	44.0245i	0.693713	−	1.67477i	0.737163	−	0.675715i	$-0.236165\pi$
$692$	−24.6160	+	10.1963i	−0.935761	+	0.387605i
$693$			0.571998i			0.0217284i
$694$	−2.64280	−	6.38027i	−0.100319	−	0.242192i
$695$	−18.2208	−	18.2208i	−0.691153	−	0.691153i
$696$	8.05220			0.305218
$697$	−16.5169	+	36.1280i	−0.625621	+	1.36845i
$698$	−79.3671			−3.00409
$699$	4.04562	+	4.04562i	0.153019	+	0.153019i
$700$	1.17151	+	2.82828i	0.0442790	+	0.106899i
$701$			28.6868i			1.08349i	0.840544	+	0.541743i	$0.182236\pi$
$701$			28.6868i			1.08349i	−0.840544	+	0.541743i	$0.817764\pi$
$702$	1.44085	−	0.596819i	0.0543813	−	0.0225255i
$703$	4.72488	−	11.4069i	0.178202	−	0.430218i
$704$	−2.71334	−	1.12390i	−0.102263	−	0.0423587i
$705$	−0.859278	+	0.859278i	−0.0323623	+	0.0323623i
$706$	−24.3422	+	24.3422i	−0.916132	+	0.916132i
$707$	−1.32017	−	0.546831i	−0.0496500	−	0.0205657i
$708$	3.41981	−	8.25616i	0.128524	−	0.310285i
$709$	−18.4469	+	7.64096i	−0.692789	+	0.286962i	−0.701161	−	0.713003i	$-0.747335\pi$
$709$	−18.4469	+	7.64096i	−0.692789	+	0.286962i	0.00837290	+	0.999965i	$0.497335\pi$
$710$		−	31.1627i		−	1.16951i
$711$	15.2454	+	36.8057i	0.571748	+	1.38032i
$712$	33.7634	+	33.7634i	1.26534	+	1.26534i
$713$	−3.47235			−0.130040
$714$	0.370116	+	0.397857i	0.0138512	+	0.0148894i
$715$	−0.494047			−0.0184763
$716$	−41.1822	−	41.1822i	−1.53905	−	1.53905i
$717$	0.0997802	+	0.240891i	0.00372636	+	0.00899623i
$718$		−	73.9703i		−	2.76055i
$719$	−41.4790	+	17.1812i	−1.54691	+	0.640749i	−0.982753	−	0.184921i	$-0.940797\pi$
$719$	−41.4790	+	17.1812i	−1.54691	+	0.640749i	−0.564152	+	0.825671i	$0.690797\pi$
$720$	11.6175	−	28.0472i	0.432959	−	1.04526i
$721$	1.26189	+	0.522692i	0.0469953	+	0.0194661i
$722$	25.4556	−	25.4556i	0.947358	−	0.947358i
$723$	4.84453	−	4.84453i	0.180170	−	0.180170i
$724$	56.8469	+	23.5467i	2.11270	+	0.875108i
$725$	−5.88536	+	14.2085i	−0.218577	+	0.527691i
$726$	−0.623955	+	0.258451i	−0.0231572	+	0.00959201i
$727$		−	7.40307i		−	0.274565i	−0.990532	−	0.137282i	$-0.956163\pi$
$727$		−	7.40307i		−	0.274565i	0.990532	−	0.137282i	$-0.0438368\pi$
$728$	0.196705	+	0.474888i	0.00729037	+	0.0176005i
$729$	−16.5142	−	16.5142i	−0.611636	−	0.611636i
$730$	8.25776			0.305633
$731$	32.8878	+	35.3528i	1.21640	+	1.30757i
$732$	−3.76686			−0.139227
$733$	12.1822	+	12.1822i	0.449959	+	0.449959i	0.895341	−	0.445382i	$-0.146932\pi$
$733$	12.1822	+	12.1822i	0.449959	+	0.449959i	−0.445382	+	0.895341i	$0.646932\pi$
$734$	5.20667	+	12.5700i	0.192182	+	0.463968i
$735$		−	2.31752i		−	0.0854829i
$736$	−7.54695	+	3.12605i	−0.278184	+	0.115228i
$737$	0.920341	−	2.22190i	0.0339012	−	0.0818448i
$738$	−67.1709	−	27.8231i	−2.47260	−	1.02418i
$739$	−1.09274	+	1.09274i	−0.0401970	+	0.0401970i	−0.726920	−	0.686723i	$-0.759049\pi$
$739$	−1.09274	+	1.09274i	−0.0401970	+	0.0401970i	0.686723	+	0.726920i	$0.259049\pi$
$740$	−22.8905	+	22.8905i	−0.841473	+	0.841473i
$741$	0.211348	+	0.0875433i	0.00776407	+	0.00321598i
$742$	2.39407	−	5.77980i	0.0878891	−	0.212183i
$743$	14.0480	−	5.81889i	0.515373	−	0.213474i	−0.109810	−	0.993953i	$-0.535024\pi$
$743$	14.0480	−	5.81889i	0.515373	−	0.213474i	0.625183	+	0.780478i	$0.285024\pi$
$744$		−	5.64412i		−	0.206924i
$745$	1.87781	+	4.53344i	0.0687978	+	0.166092i
$746$	−30.2676	−	30.2676i	−1.10818	−	1.10818i
$747$	−21.1138			−0.772513
$748$	7.93376	−	17.3538i	0.290087	−	0.634519i
$749$	2.03953			0.0745229
$750$	−5.08414	−	5.08414i	−0.185647	−	0.185647i
$751$	−6.74565	−	16.2854i	−0.246152	−	0.594264i	0.751719	−	0.659484i	$-0.229225\pi$
$751$	−6.74565	−	16.2854i	−0.246152	−	0.594264i	−0.997871	+	0.0652199i	$0.979225\pi$
$752$		−	29.7948i		−	1.08651i
$753$	−5.01281	+	2.07637i	−0.182677	+	0.0756672i
$754$	−1.74027	+	4.20138i	−0.0633768	+	0.153005i
$755$	−3.66738	−	1.51908i	−0.133470	−	0.0552849i
$756$	−0.993603	+	0.993603i	−0.0361370	+	0.0361370i
$757$	8.74227	−	8.74227i	0.317743	−	0.317743i	−0.530157	−	0.847900i	$-0.677867\pi$
$757$	8.74227	−	8.74227i	0.317743	−	0.317743i	0.847900	+	0.530157i	$0.177867\pi$
$758$	11.5545	+	4.78603i	0.419679	+	0.173837i
$759$	−0.109614	+	0.264632i	−0.00397874	+	0.00960553i
$760$	17.7652	−	7.35860i	0.644413	−	0.266925i
$761$		−	18.7170i		−	0.678491i	−0.940698	−	0.339245i	$-0.889828\pi$
$761$		−	18.7170i		−	0.678491i	0.940698	−	0.339245i	$-0.110172\pi$
$762$	−1.08031	−	2.60810i	−0.0391354	−	0.0944813i
$763$	−1.99057	−	1.99057i	−0.0720636	−	0.0720636i
$764$	103.986			3.76209
$765$	13.9475	+	6.37648i	0.504273	+	0.230542i
$766$	−61.2745			−2.21394
$767$	2.02645	+	2.02645i	0.0731709	+	0.0731709i
$768$	2.50264	+	6.04192i	0.0903064	+	0.218019i
$769$		−	22.0209i		−	0.794094i	−0.917798	−	0.397047i	$-0.870035\pi$
$769$		−	22.0209i		−	0.794094i	0.917798	−	0.397047i	$-0.129965\pi$
$770$	0.588979	−	0.243963i	0.0212253	−	0.00879182i
$771$	−1.34814	+	3.25469i	−0.0485520	+	0.117215i
$772$	33.9759	+	14.0733i	1.22282	+	0.506508i
$773$	−22.3811	+	22.3811i	−0.804993	+	0.804993i	−0.983871	−	0.178878i	$-0.942753\pi$
$773$	−22.3811	+	22.3811i	−0.804993	+	0.804993i	0.178878	+	0.983871i	$0.442753\pi$
$774$	−62.4889	+	62.4889i	−2.24612	+	2.24612i
$775$	9.95935	+	4.12530i	0.357750	+	0.148185i
$776$	41.5689	−	100.356i	1.49224	−	3.60258i
$777$	0.260710	−	0.107989i	0.00935290	−	0.00387410i
$778$		−	3.60293i		−	0.129171i
$779$	−8.25818	−	19.9370i	−0.295880	−	0.714318i
$780$	−0.424120	−	0.424120i	−0.0151859	−	0.0151859i
$781$	9.53897			0.341331
$782$	−4.04594	−	10.8611i	−0.144682	−	0.388391i
$783$	−7.05919			−0.252275
$784$	40.1791	+	40.1791i	1.43497	+	1.43497i
$785$	8.11744	+	19.5972i	0.289724	+	0.699456i
$786$		−	4.04482i		−	0.144274i
$787$	22.7612	−	9.42801i	0.811350	−	0.336072i	0.0618578	−	0.998085i	$-0.480297\pi$
$787$	22.7612	−	9.42801i	0.811350	−	0.336072i	0.749493	+	0.662013i	$0.230297\pi$
$788$	−13.7781	+	33.2634i	−0.490826	+	1.18496i
$789$	2.15048	+	0.890759i	0.0765592	+	0.0317119i
$790$	31.3960	−	31.3960i	1.11702	−	1.11702i
$791$	−2.05840	+	2.05840i	−0.0731883	+	0.0731883i
$792$	18.3214	+	7.58898i	0.651023	+	0.269663i
$793$	0.462283	−	1.11605i	0.0164161	−	0.0396321i
$794$	−44.3877	+	18.3860i	−1.57526	+	0.652495i
$795$			4.14526i			0.147017i
$796$	−39.2590	−	94.7796i	−1.39150	−	3.35937i
$797$	−9.39013	−	9.39013i	−0.332615	−	0.332615i	0.520964	−	0.853579i	$-0.325573\pi$
$797$	−9.39013	−	9.39013i	−0.332615	−	0.332615i	−0.853579	+	0.520964i	$0.825573\pi$
$798$	−0.295189			−0.0104496
$799$	15.0417	+	0.543342i	0.532136	+	0.0192220i
$800$	25.3600			0.896611
$801$	−14.6281	−	14.6281i	−0.516859	−	0.516859i
$802$	−27.7688	−	67.0397i	−0.980549	−	2.36726i
$803$			2.52772i			0.0892013i
$804$	2.69749	−	1.11734i	0.0951332	−	0.0394055i
$805$	0.103470	−	0.249798i	0.00364682	−	0.00880421i
$806$	2.94492	+	1.21983i	0.103730	+	0.0429665i
$807$	−1.48929	+	1.48929i	−0.0524256	+	0.0524256i
$808$	−35.0306	+	35.0306i	−1.23237	+	1.23237i
$809$	12.9656	+	5.37052i	0.455845	+	0.188817i	0.598778	−	0.800915i	$-0.295653\pi$
$809$	12.9656	+	5.37052i	0.455845	+	0.188817i	−0.142933	+	0.989732i	$0.545653\pi$
$810$	−10.4832	+	25.3088i	−0.368343	+	0.889260i
$811$	−1.59682	+	0.661423i	−0.0560718	+	0.0232257i	−0.410543	−	0.911841i	$-0.634661\pi$
$811$	−1.59682	+	0.661423i	−0.0560718	+	0.0232257i	0.354471	+	0.935067i	$0.384661\pi$
$812$		−	4.09733i		−	0.143788i
$813$	0.320186	+	0.772998i	0.0112294	+	0.0271102i
$814$	−10.0349	−	10.0349i	−0.351724	−	0.351724i
$815$	−18.9827			−0.664936
$816$	8.27261	−	3.08169i	0.289599	−	0.107881i
$817$	−26.2299			−0.917668
$818$	2.33022	+	2.33022i	0.0814744	+	0.0814744i
$819$	−0.0852231	−	0.205747i	−0.00297794	−	0.00718937i
$820$			56.5803i			1.97587i
$821$	−1.98615	+	0.822688i	−0.0693169	+	0.0287120i	−0.417073	−	0.908873i	$-0.636944\pi$
$821$	−1.98615	+	0.822688i	−0.0693169	+	0.0287120i	0.347756	+	0.937585i	$0.386944\pi$
$822$	2.66599	−	6.43627i	0.0929871	−	0.224491i
$823$	−27.1235	−	11.2349i	−0.945466	−	0.391625i	−0.143941	−	0.989586i	$-0.545978\pi$
$823$	−27.1235	−	11.2349i	−0.945466	−	0.391625i	−0.801525	+	0.597961i	$0.795978\pi$
$824$	33.4843	−	33.4843i	1.16648	−	1.16648i
$825$	0.628788	−	0.628788i	0.0218916	−	0.0218916i
$826$	−3.41651	−	1.41516i	−0.118876	−	0.0492399i
$827$	−2.30990	+	5.57659i	−0.0803230	+	0.193917i	−0.958939	−	0.283612i	$-0.908467\pi$
$827$	−2.30990	+	5.57659i	−0.0803230	+	0.193917i	0.878616	+	0.477529i	$0.158467\pi$
$828$	13.6843	−	5.66821i	0.475561	−	0.196984i
$829$			46.8982i			1.62884i	0.580276	+	0.814420i	$0.302945\pi$
$829$			46.8982i			1.62884i	−0.580276	+	0.814420i	$0.697055\pi$
$830$	9.00526	+	21.7406i	0.312577	+	0.754628i
$831$	1.18823	+	1.18823i	0.0412192	+	0.0412192i
$832$	1.14344			0.0396416
$833$	−21.0168	+	19.5514i	−0.728189	+	0.677415i
$834$	13.7143			0.474889
$835$	−17.0583	−	17.0583i	−0.590328	−	0.590328i
$836$	3.96676	+	9.57660i	0.137193	+	0.331214i
$837$			4.94808i			0.171031i
$838$	35.7022	−	14.7884i	1.23331	−	0.510855i
$839$	9.94137	−	24.0006i	0.343214	−	0.828593i	−0.654172	−	0.756345i	$-0.726983\pi$
$839$	9.94137	−	24.0006i	0.343214	−	0.828593i	0.997387	−	0.0722473i	$-0.0230171\pi$
$840$	0.406033	+	0.168184i	0.0140095	+	0.00580292i
$841$	−5.95107	+	5.95107i	−0.205209	+	0.205209i
$842$	4.52797	−	4.52797i	0.156044	−	0.156044i
$843$	−2.97501	−	1.23229i	−0.102465	−	0.0424423i
$844$	1.66154	−	4.01132i	0.0571927	−	0.138075i
$845$	−15.0629	+	6.23927i	−0.518181	+	0.214637i
$846$			27.5478i			0.947112i
$847$	0.0746777	+	0.180288i	0.00256596	+	0.00619477i
$848$	−71.8669	−	71.8669i	−2.46792	−	2.46792i
$849$	7.15452			0.245543
$850$	−1.29890	+	35.9583i	−0.0445520	+	1.23336i
$851$	−6.01891			−0.206326
$852$	8.18883	+	8.18883i	0.280545	+	0.280545i
$853$	−7.39959	−	17.8642i	−0.253357	−	0.611659i	0.745114	−	0.666938i	$-0.232395\pi$
$853$	−7.39959	−	17.8642i	−0.253357	−	0.611659i	−0.998471	+	0.0552789i	$0.982395\pi$
$854$			1.55878i			0.0533403i
$855$	−7.69685	+	3.18814i	−0.263227	+	0.109032i
$856$	27.0595	−	65.3274i	0.924874	−	2.23284i
$857$	39.3371	+	16.2940i	1.34373	+	0.556591i	0.934540	−	0.355858i	$-0.115811\pi$
$857$	39.3371	+	16.2940i	1.34373	+	0.556591i	0.409190	+	0.912449i	$0.365811\pi$
$858$	0.185929	−	0.185929i	0.00634751	−	0.00634751i
$859$	−25.5420	+	25.5420i	−0.871481	+	0.871481i	−0.992634	−	0.121153i	$-0.961341\pi$
$859$	−25.5420	+	25.5420i	−0.871481	+	0.871481i	0.121153	+	0.992634i	$0.461341\pi$
$860$	63.5378	+	26.3182i	2.16662	+	0.897443i
$861$	0.188745	−	0.455670i	0.00643241	−	0.0155292i
$862$	79.6044	−	32.9732i	2.71134	−	1.12307i
$863$		−	30.1763i		−	1.02721i	−0.858025	−	0.513607i	$-0.828309\pi$
$863$		−	30.1763i		−	1.02721i	0.858025	−	0.513607i	$-0.171691\pi$
$864$	4.45461	+	10.7544i	0.151549	+	0.365871i
$865$	−5.16591	−	5.16591i	−0.175646	−	0.175646i
$866$	23.7909			0.808448
$867$	1.40491	+	4.23255i	0.0477131	+	0.143745i
$868$	−2.87199			−0.0974817
$869$	9.61041	+	9.61041i	0.326011	+	0.326011i
$870$	1.48794	+	3.59221i	0.0504460	+	0.121787i
$871$			0.936338i			0.0317266i
$872$	−90.1692	+	37.3493i	−3.05351	+	1.26481i
$873$	−18.0099	+	43.4797i	−0.609542	+	1.47156i
$874$	5.81690	+	2.40944i	0.196759	+	0.0815004i
$875$	−1.46903	+	1.46903i	−0.0496623	+	0.0496623i
$876$	−2.16995	+	2.16995i	−0.0733158	+	0.0733158i
$877$	−1.00784	−	0.417459i	−0.0340322	−	0.0140966i	0.365602	−	0.930771i	$-0.380863\pi$
$877$	−1.00784	−	0.417459i	−0.0340322	−	0.0140966i	−0.399635	+	0.916675i	$0.630863\pi$
$878$	23.0640	−	55.6813i	0.778371	−	1.87915i
$879$	5.25113	−	2.17509i	0.177116	−	0.0733639i
$880$		−	10.3569i		−	0.349132i
$881$	−13.9431	−	33.6616i	−0.469754	−	1.13409i	−0.964271	−	0.264919i	$-0.914655\pi$
$881$	−13.9431	−	33.6616i	−0.469754	−	1.13409i	0.494516	−	0.869168i	$-0.335345\pi$
$882$	−37.1489	−	37.1489i	−1.25087	−	1.25087i
$883$	23.7707			0.799949			0.399974	−	0.916526i	$-0.369019\pi$
$883$	23.7707			0.799949			0.399974	+	0.916526i	$0.369019\pi$
$884$	−0.268181	+	7.42422i	−0.00901989	+	0.249703i
$885$	2.45031			0.0823663
$886$	10.3705	+	10.3705i	0.348403	+	0.348403i
$887$	−21.0234	−	50.7550i	−0.705896	−	1.70418i	−0.710008	−	0.704193i	$-0.751309\pi$
$887$	−21.0234	−	50.7550i	−0.705896	−	1.70418i	0.00411193	−	0.999992i	$-0.498691\pi$
$888$		−	9.78343i		−	0.328310i
$889$	−0.753592	+	0.312148i	−0.0252747	+	0.0104691i
$890$	−8.82335	+	21.3014i	−0.295759	+	0.714026i
$891$	−7.74708	−	3.20895i	−0.259537	−	0.107504i
$892$	−92.8779	+	92.8779i	−3.10978	+	3.10978i
$893$	−5.78163	+	5.78163i	−0.193475	+	0.193475i
$894$	−2.41280	−	0.999416i	−0.0806962	−	0.0334255i
$895$	6.11115	−	14.7536i	0.204273	−	0.493159i
$896$	1.33444	−	0.552742i	0.0445804	−	0.0184658i
$897$		−	0.111519i		−	0.00372352i
$898$	7.11915	+	17.1872i	0.237569	+	0.573543i
$899$	−10.2022	−	10.2022i	−0.340263	−	0.340263i
$900$	−45.9831			−1.53277
$901$	37.5919	−	34.9708i	1.25237	−	1.16505i
$902$	−24.8041			−0.825886
$903$	−0.423908	−	0.423908i	−0.0141068	−	0.0141068i
$904$	38.6219	+	93.2416i	1.28455	+	3.10117i
$905$			16.8714i			0.560823i
$906$	1.95186	−	0.808488i	0.0648463	−	0.0268602i
$907$	−7.72678	+	18.6541i	−0.256563	+	0.619399i	−0.998707	−	0.0508424i	$-0.983809\pi$
$907$	−7.72678	+	18.6541i	−0.256563	+	0.619399i	0.742143	+	0.670241i	$0.233809\pi$
$908$	76.1976	+	31.5621i	2.52871	+	1.04742i
$909$	15.1771	−	15.1771i	0.503394	−	0.503394i
$910$	−0.175506	+	0.175506i	−0.00581798	+	0.00581798i
$911$	31.5005	+	13.0479i	1.04366	+	0.432297i	0.837624	−	0.546248i	$-0.183944\pi$
$911$	31.5005	+	13.0479i	1.04366	+	0.432297i	0.206034	+	0.978545i	$0.433944\pi$
$912$	−1.83521	+	4.43059i	−0.0607699	+	0.146711i
$913$	−6.65486	+	2.75653i	−0.220244	+	0.0912279i
$914$		−	55.7845i		−	1.84519i
$915$	−0.395256	−	0.954232i	−0.0130668	−	0.0315459i
$916$	50.1742	+	50.1742i	1.65780	+	1.65780i
$917$	−1.16873			−0.0385947
$918$	−15.4770	+	5.76544i	−0.510816	+	0.190288i
$919$	20.8562			0.687983			0.343991	−	0.938973i	$-0.388221\pi$
$919$	20.8562			0.687983			0.343991	+	0.938973i	$0.388221\pi$
$920$	−6.62838	−	6.62838i	−0.218531	−	0.218531i
$921$	1.35173	+	3.26337i	0.0445411	+	0.107532i
$922$			98.3808i			3.24000i
$923$	−3.43116	+	1.42123i	−0.112938	+	0.0467804i
$924$	−0.0906622	+	0.218878i	−0.00298257	+	0.00720056i
$925$	17.2634	+	7.15072i	0.567616	+	0.235114i
$926$	−0.847891	+	0.847891i	−0.0278634	+	0.0278634i
$927$	−14.5072	+	14.5072i	−0.476478	+	0.476478i
$928$	−31.3587	−	12.9892i	−1.02940	−	0.426392i
$929$	−14.3011	+	34.5259i	−0.469204	+	1.13276i	0.495307	+	0.868718i	$0.335055\pi$
$929$	−14.3011	+	34.5259i	−0.469204	+	1.13276i	−0.964511	+	0.264041i	$0.914945\pi$
$930$	2.51793	−	1.04296i	0.0825662	−	0.0342001i
$931$		−	15.5933i		−	0.511051i
$932$	−38.6257	−	93.2506i	−1.26523	−	3.05452i
$933$	−4.54809	−	4.54809i	−0.148898	−	0.148898i
$934$	−20.1066			−0.657908
$935$	5.22860	+	0.188870i	0.170994	+	0.00617670i
$936$	−7.72089			−0.252365
$937$	−38.0643	−	38.0643i	−1.24351	−	1.24351i	−0.958536	−	0.284972i	$-0.908016\pi$
$937$	−38.0643	−	38.0643i	−1.24351	−	1.24351i	−0.284972	−	0.958536i	$-0.591984\pi$
$938$	−0.462369	−	1.11626i	−0.0150969	−	0.0364471i
$939$			2.13405i			0.0696422i
$940$	19.8062	−	8.20399i	0.646006	−	0.267585i
$941$	−0.734097	+	1.77227i	−0.0239309	+	0.0577742i	−0.935393	−	0.353609i	$-0.884954\pi$
$941$	−0.734097	+	1.77227i	−0.0239309	+	0.0577742i	0.911462	+	0.411383i	$0.134954\pi$
$942$	−10.4301	−	4.32029i	−0.339831	−	0.140763i
$943$	−7.43869	+	7.43869i	−0.242237	+	0.242237i
$944$	−42.4814	+	42.4814i	−1.38265	+	1.38265i
$945$	−0.355961	−	0.147444i	−0.0115794	−	0.00479634i
$946$	−11.5376	+	27.8542i	−0.375119	+	0.905617i
$947$	11.4148	−	4.72818i	0.370932	−	0.153645i	−0.189427	−	0.981895i	$-0.560663\pi$
$947$	11.4148	−	4.72818i	0.370932	−	0.153645i	0.560359	+	0.828250i	$0.310663\pi$
$948$			16.5003i			0.535905i
$949$	−0.376610	−	0.909218i	−0.0122253	−	0.0295145i
$950$	−13.8214	−	13.8214i	−0.448427	−	0.448427i
$951$	3.94747			0.128005
$952$	−1.90023	−	5.10104i	−0.0615867	−	0.165326i
$953$	−23.2373			−0.752731			−0.376366	−	0.926471i	$-0.622826\pi$
$953$	−23.2373			−0.752731			−0.376366	+	0.926471i	$0.622826\pi$
$954$	66.4468	+	66.4468i	2.15129	+	2.15129i
$955$	10.9112	+	26.3420i	0.353079	+	0.852408i
$956$		−	4.59982i		−	0.148769i
$957$	−1.09959	+	0.455463i	−0.0355445	+	0.0147230i
$958$	−34.3183	+	82.8517i	−1.10877	+	2.67682i
$959$	−1.85972	−	0.770321i	−0.0600534	−	0.0248750i
$960$	0.691302	−	0.691302i	0.0223117	−	0.0223117i
$961$	14.7691	−	14.7691i	0.476424	−	0.476424i
$962$	5.10468	+	2.11443i	0.164581	+	0.0681718i
$963$	−11.7236	+	28.3033i	−0.377788	+	0.912062i
$964$	−111.665	+	46.2533i	−3.59650	+	1.48972i
$965$			10.0836i			0.324601i
$966$	0.0550689	+	0.132948i	0.00177181	+	0.00427753i
$967$	−6.72756	−	6.72756i	−0.216344	−	0.216344i	0.590612	−	0.806956i	$-0.298886\pi$
$967$	−6.72756	−	6.72756i	−0.216344	−	0.216344i	−0.806956	+	0.590612i	$0.798886\pi$
$968$	6.76552			0.217452
$969$	−2.20328	−	1.00729i	−0.0707795	−	0.0323587i
$970$	52.4519			1.68413
$971$	−11.8335	−	11.8335i	−0.379755	−	0.379755i	0.491259	−	0.871014i	$-0.336537\pi$
$971$	−11.8335	−	11.8335i	−0.379755	−	0.379755i	−0.871014	+	0.491259i	$0.836537\pi$
$972$	−12.1626	−	29.3631i	−0.390116	−	0.941823i
$973$		−	3.96267i		−	0.127037i
$974$	−11.0034	+	4.55776i	−0.352572	+	0.146040i
$975$	−0.132490	+	0.319859i	−0.00424307	+	0.0102437i
$976$	23.3962	+	9.69104i	0.748895	+	0.310203i
$977$	2.67911	−	2.67911i	0.0857124	−	0.0857124i	−0.662951	−	0.748663i	$-0.730696\pi$
$977$	2.67911	−	2.67911i	0.0857124	−	0.0857124i	0.748663	+	0.662951i	$0.230696\pi$
$978$	7.14393	−	7.14393i	0.228438	−	0.228438i
$979$	−6.52043	−	2.70085i	−0.208394	−	0.0863195i
$980$	−15.6458	+	37.7724i	−0.499788	+	1.20660i
$981$	39.0661	−	16.1817i	1.24728	−	0.516642i
$982$			29.1190i			0.929226i
$983$	6.88714	+	16.6270i	0.219666	+	0.530320i	0.994843	−	0.101423i	$-0.0323397\pi$
$983$	6.88714	+	16.6270i	0.219666	+	0.530320i	−0.775178	+	0.631743i	$0.782340\pi$
$984$	−12.0912	−	12.0912i	−0.385454	−	0.385454i
$985$	−9.87210			−0.314551
$986$	20.0238	−	43.7988i	0.637687	−	1.39484i
$987$	−0.186877			−0.00594836
$988$	−2.85368	−	2.85368i	−0.0907875	−	0.0907875i
$989$	4.89331	+	11.8135i	0.155598	+	0.375648i
$990$			9.57582i			0.304340i
$991$	−14.0938	+	5.83786i	−0.447705	+	0.185446i	−0.595133	−	0.803627i	$-0.702901\pi$
$991$	−14.0938	+	5.83786i	−0.447705	+	0.185446i	0.147428	+	0.989073i	$0.452901\pi$
$992$	−9.10468	+	21.9807i	−0.289074	+	0.697886i
$993$	−3.37269	−	1.39701i	−0.107029	−	0.0443329i
$994$	3.38865	−	3.38865i	0.107481	−	0.107481i
$995$	19.8904	−	19.8904i	0.630568	−	0.630568i
$996$	−8.07931	−	3.34656i	−0.256003	−	0.106040i
$997$	−4.48640	+	10.8311i	−0.142086	+	0.343025i	−0.978863	−	0.204519i	$-0.934437\pi$
$997$	−4.48640	+	10.8311i	−0.142086	+	0.343025i	0.836777	+	0.547544i	$0.184437\pi$
$998$	77.4558	−	32.0833i	2.45182	−	1.01558i
$999$			8.57692i			0.271362i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	187.2.h.a.100.14	✓	56
17.5	odd	16		3179.2.a.bh.1.1		28
17.8	even	8	inner	187.2.h.a.144.14	yes	56
17.12	odd	16		3179.2.a.bi.1.1		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
187.2.h.a.100.14	✓	56	1.1	even	1	trivial
187.2.h.a.144.14	yes	56	17.8	even	8	inner
3179.2.a.bh.1.1		28	17.5	odd	16
3179.2.a.bi.1.1		28	17.12	odd	16

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:	\( N \)	\(=\)	\( 187 = 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	187.h (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.82043 + 1.82043i) q^{2} +(-0.100390 - 0.242362i) q^{3} +4.62792i q^{4} +(-1.17236 + 0.485606i) q^{5} +(0.258451 - 0.623955i) q^{6} +(-0.180288 - 0.0746777i) q^{7} +(-4.78394 + 4.78394i) q^{8} +(2.07266 - 2.07266i) q^{9} +O(q^{10})\)	\(q+(1.82043 + 1.82043i) q^{2} +(-0.100390 - 0.242362i) q^{3} +4.62792i q^{4} +(-1.17236 + 0.485606i) q^{5} +(0.258451 - 0.623955i) q^{6} +(-0.180288 - 0.0746777i) q^{7} +(-4.78394 + 4.78394i) q^{8} +(2.07266 - 2.07266i) q^{9} +(-3.01820 - 1.25018i) q^{10} +(0.382683 - 0.923880i) q^{11} +(1.12163 - 0.464596i) q^{12} +0.389335i q^{13} +(-0.192256 - 0.464147i) q^{14} +(0.235385 + 0.235385i) q^{15} -8.16181 q^{16} +(0.148839 - 4.12042i) q^{17} +7.54626 q^{18} +(1.58378 + 1.58378i) q^{19} +(-2.24735 - 5.42557i) q^{20} +0.0511919i q^{21} +(2.37850 - 0.985209i) q^{22} +(0.417847 - 1.00877i) q^{23} +(1.63971 + 0.679188i) q^{24} +(-2.39693 + 2.39693i) q^{25} +(-0.708757 + 0.708757i) q^{26} +(-1.43749 - 0.595430i) q^{27} +(0.345602 - 0.834358i) q^{28} +(4.19159 - 1.73622i) q^{29} +0.857004i q^{30} +(-1.21699 - 2.93806i) q^{31} +(-5.29010 - 5.29010i) q^{32} -0.262331 q^{33} +(7.77188 - 7.22998i) q^{34} +0.247626 q^{35} +(9.59210 + 9.59210i) q^{36} +(-2.10950 - 5.09279i) q^{37} +5.76632i q^{38} +(0.0943601 - 0.0390852i) q^{39} +(3.28538 - 7.93160i) q^{40} +(-8.90123 - 3.68701i) q^{41} +(-0.0931911 + 0.0931911i) q^{42} +(-8.28078 + 8.28078i) q^{43} +(4.27564 + 1.77103i) q^{44} +(-1.42340 + 3.43639i) q^{45} +(2.59705 - 1.07574i) q^{46} +3.65052i q^{47} +(0.819362 + 1.97811i) q^{48} +(-4.92282 - 4.92282i) q^{49} -8.72687 q^{50} +(-1.01358 + 0.377575i) q^{51} -1.80181 q^{52} +(8.80526 + 8.80526i) q^{53} +(-1.53292 - 3.70079i) q^{54} +1.26895i q^{55} +(1.21974 - 0.505233i) q^{56} +(0.224853 - 0.542844i) q^{57} +(10.7912 + 4.46984i) q^{58} +(5.20490 - 5.20490i) q^{59} +(-1.08934 + 1.08934i) q^{60} +(-2.86655 - 1.18736i) q^{61} +(3.13310 - 7.56397i) q^{62} +(-0.528457 + 0.218894i) q^{63} -2.93690i q^{64} +(-0.189064 - 0.456440i) q^{65} +(-0.477555 - 0.477555i) q^{66} +2.40497 q^{67} +(19.0690 + 0.688817i) q^{68} -0.286435 q^{69} +(0.450785 + 0.450785i) q^{70} +(3.65041 + 8.81286i) q^{71} +19.8310i q^{72} +(-2.33531 + 0.967317i) q^{73} +(5.43086 - 13.1113i) q^{74} +(0.821551 + 0.340298i) q^{75} +(-7.32961 + 7.32961i) q^{76} +(-0.137986 + 0.137986i) q^{77} +(0.242928 + 0.100624i) q^{78} +(-5.20111 + 12.5566i) q^{79} +(9.56855 - 3.96342i) q^{80} -8.38538i q^{81} +(-9.49211 - 22.9160i) q^{82} +(-5.09341 - 5.09341i) q^{83} -0.236912 q^{84} +(1.82641 + 4.90288i) q^{85} -30.1491 q^{86} +(-0.841586 - 0.841586i) q^{87} +(2.58905 + 6.25052i) q^{88} -7.05766i q^{89} +(-8.84690 + 3.66451i) q^{90} +(0.0290747 - 0.0701924i) q^{91} +(4.66851 + 1.93376i) q^{92} +(-0.589903 + 0.589903i) q^{93} +(-6.64551 + 6.64551i) q^{94} +(-2.62585 - 1.08766i) q^{95} +(-0.751049 + 1.81319i) q^{96} +(-14.8335 + 6.14424i) q^{97} -17.9233i q^{98} +(-1.12171 - 2.70806i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 16 q^{6}+O(q^{10}) \) 56 * q - 16 * q^6	\( 56 q - 16 q^{6} - 16 q^{10} - 16 q^{14} + 24 q^{15} - 32 q^{16} + 8 q^{17} - 24 q^{19} + 16 q^{20} - 24 q^{24} - 8 q^{25} - 48 q^{27} - 40 q^{32} + 16 q^{33} + 64 q^{34} + 32 q^{35} + 64 q^{36} + 8 q^{37} - 32 q^{39} + 96 q^{40} - 24 q^{41} - 8 q^{42} - 32 q^{43} + 16 q^{44} - 32 q^{45} - 16 q^{46} - 24 q^{48} - 112 q^{50} - 48 q^{51} + 8 q^{53} - 72 q^{54} + 64 q^{56} + 40 q^{57} + 16 q^{58} + 16 q^{59} - 8 q^{60} - 64 q^{61} + 56 q^{62} + 16 q^{63} + 56 q^{65} + 24 q^{67} - 88 q^{68} - 64 q^{69} - 96 q^{70} - 16 q^{71} + 8 q^{73} - 48 q^{74} + 40 q^{75} + 88 q^{76} + 136 q^{78} - 32 q^{80} + 104 q^{82} - 56 q^{83} + 80 q^{84} - 8 q^{85} - 32 q^{86} + 56 q^{87} - 32 q^{91} + 40 q^{92} + 8 q^{93} + 16 q^{94} + 48 q^{95} + 64 q^{96} - 16 q^{97}+O(q^{100}) \) 56 * q - 16 * q^6 - 16 * q^10 - 16 * q^14 + 24 * q^15 - 32 * q^16 + 8 * q^17 - 24 * q^19 + 16 * q^20 - 24 * q^24 - 8 * q^25 - 48 * q^27 - 40 * q^32 + 16 * q^33 + 64 * q^34 + 32 * q^35 + 64 * q^36 + 8 * q^37 - 32 * q^39 + 96 * q^40 - 24 * q^41 - 8 * q^42 - 32 * q^43 + 16 * q^44 - 32 * q^45 - 16 * q^46 - 24 * q^48 - 112 * q^50 - 48 * q^51 + 8 * q^53 - 72 * q^54 + 64 * q^56 + 40 * q^57 + 16 * q^58 + 16 * q^59 - 8 * q^60 - 64 * q^61 + 56 * q^62 + 16 * q^63 + 56 * q^65 + 24 * q^67 - 88 * q^68 - 64 * q^69 - 96 * q^70 - 16 * q^71 + 8 * q^73 - 48 * q^74 + 40 * q^75 + 88 * q^76 + 136 * q^78 - 32 * q^80 + 104 * q^82 - 56 * q^83 + 80 * q^84 - 8 * q^85 - 32 * q^86 + 56 * q^87 - 32 * q^91 + 40 * q^92 + 8 * q^93 + 16 * q^94 + 48 * q^95 + 64 * q^96 - 16 * q^97

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