LMFDB - Embedded newform 150.8.e.b.107.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [150,8,Mod(107,150)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(150, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1]))

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("150.107");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 150 = 2 \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	150.e (of order $4$, degree $2$, 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:	$46.8577538226$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 30)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			107.7
Character	$\chi$	$=$	150.107
Dual form			150.8.e.b.143.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-5.65685 + 5.65685i) q^{2} +(-0.750092 - 46.7594i) q^{3} -64.0000i q^{4} +(268.754 + 260.268i) q^{6} +(661.697 + 661.697i) q^{7} +(362.039 + 362.039i) q^{8} +(-2185.87 + 70.1477i) q^{9} -6676.11i q^{11} +(-2992.60 + 48.0059i) q^{12} +(4252.25 - 4252.25i) q^{13} -7486.24 q^{14} -4096.00 q^{16} +(11523.1 - 11523.1i) q^{17} +(11968.4 - 12762.0i) q^{18} +56529.5i q^{19} +(30444.2 - 31436.8i) q^{21} +(37765.8 + 37765.8i) q^{22} +(36833.1 + 36833.1i) q^{23} +(16657.1 - 17200.3i) q^{24} +48108.7i q^{26} +(4919.67 + 102157. i) q^{27} +(42348.6 - 42348.6i) q^{28} -34373.4 q^{29} +154212. q^{31} +(23170.5 - 23170.5i) q^{32} +(-312171. + 5007.70i) q^{33} +130370. i q^{34} +(4489.45 + 139896. i) q^{36} +(-86338.1 - 86338.1i) q^{37} +(-319779. - 319779. i) q^{38} +(-202022. - 195643. i) q^{39} -520858. i q^{41} +(5615.37 + 350052. i) q^{42} +(499651. - 499651. i) q^{43} -427271. q^{44} -416719. q^{46} +(47164.4 - 47164.4i) q^{47} +(3072.38 + 191526. i) q^{48} +52142.1i q^{49} +(-547458. - 530171. i) q^{51} +(-272144. - 272144. i) q^{52} +(315618. + 315618. i) q^{53} +(-605720. - 550060. i) q^{54} +479120. i q^{56} +(2.64328e6 - 42402.3i) q^{57} +(194445. - 194445. i) q^{58} -1.04851e6 q^{59} -1.20134e6 q^{61} +(-872352. + 872352. i) q^{62} +(-1.49280e6 - 1.39997e6i) q^{63} +262144. i q^{64} +(1.73758e6 - 1.79423e6i) q^{66} +(-242323. - 242323. i) q^{67} +(-737481. - 737481. i) q^{68} +(1.69466e6 - 1.74992e6i) q^{69} +34141.9i q^{71} +(-816767. - 765975. i) q^{72} +(2.31111e6 - 2.31111e6i) q^{73} +976804. q^{74} +3.61789e6 q^{76} +(4.41756e6 - 4.41756e6i) q^{77} +(2.24953e6 - 36085.9i) q^{78} -7.82727e6i q^{79} +(4.77313e6 - 306668. i) q^{81} +(2.94642e6 + 2.94642e6i) q^{82} +(-5.24218e6 - 5.24218e6i) q^{83} +(-2.01196e6 - 1.94843e6i) q^{84} +5.65291e6i q^{86} +(25783.2 + 1.60728e6i) q^{87} +(2.41701e6 - 2.41701e6i) q^{88} -5.17995e6 q^{89} +5.62739e6 q^{91} +(2.35732e6 - 2.35732e6i) q^{92} +(-115673. - 7.21083e6i) q^{93} +533605. i q^{94} +(-1.10082e6 - 1.06606e6i) q^{96} +(-114183. - 114183. i) q^{97} +(-294960. - 294960. i) q^{98} +(468314. + 1.45931e7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 52 q^{3} - 928 q^{6} + 1348 q^{7} - 3328 q^{12} + 21840 q^{13} - 114688 q^{16} - 50624 q^{18} - 142744 q^{21} + 47008 q^{22} - 212972 q^{27} + 86272 q^{28} - 44936 q^{31} - 1398788 q^{33} + 50432 q^{36}+ \cdots - 82948404 q^{97}+O(q^{100}) $ 28 * q + 52 * q^3 - 928 * q^6 + 1348 * q^7 - 3328 * q^12 + 21840 * q^13 - 114688 * q^16 - 50624 * q^18 - 142744 * q^21 + 47008 * q^22 - 212972 * q^27 + 86272 * q^28 - 44936 * q^31 - 1398788 * q^33 + 50432 * q^36 - 608088 * q^37 + 624032 * q^42 + 1288968 * q^43 - 1486208 * q^46 - 212992 * q^48 + 4263064 * q^51 - 1397760 * q^52 + 9921952 * q^57 + 416480 * q^58 - 14602248 * q^61 - 4050428 * q^63 + 10106816 * q^66 - 22755248 * q^67 + 3239936 * q^72 + 522380 * q^73 - 4901888 * q^76 - 8835840 * q^78 + 33339556 * q^81 - 22502528 * q^82 + 38505100 * q^87 + 3008512 * q^88 - 77623680 * q^91 - 70200824 * q^93 + 3801088 * q^96 - 82948404 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/150\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−5.65685	+	5.65685i	−0.500000	+	0.500000i
$2$	−5.65685	+	5.65685i	−0.500000	+	0.500000i
$3$	−0.750092	−	46.7594i	−0.0160395	−	0.999871i
$3$	−0.750092	−	46.7594i	−0.0160395	−	0.999871i
$4$		−	64.0000i		−	0.500000i
$5$		0			0
$5$		0			0
$6$	268.754	+	260.268i	0.507955	+	0.491916i
$7$	661.697	+	661.697i	0.729148	+	0.729148i	0.970450	−	0.241302i	$-0.0775744\pi$
$7$	661.697	+	661.697i	0.729148	+	0.729148i	−0.241302	+	0.970450i	$0.577574\pi$
$8$	362.039	+	362.039i	0.250000	+	0.250000i
$9$	−2185.87	+	70.1477i	−0.999485	+	0.0320748i
$10$		0			0
$11$		−	6676.11i		−	1.51234i	−0.654376	−	0.756170i	$-0.727069\pi$
$11$		−	6676.11i		−	1.51234i	0.654376	−	0.756170i	$-0.272931\pi$
$12$	−2992.60	+	48.0059i	−0.499936	+	0.00801974i
$13$	4252.25	−	4252.25i	0.536805	−	0.536805i	−0.385784	−	0.922589i	$-0.626069\pi$
$13$	4252.25	−	4252.25i	0.536805	−	0.536805i	0.922589	+	0.385784i	$0.126069\pi$
$14$	−7486.24			−0.729148
$15$		0			0
$16$	−4096.00			−0.250000
$17$	11523.1	−	11523.1i	0.568853	−	0.568853i	−0.362954	−	0.931807i	$-0.618232\pi$
$17$	11523.1	−	11523.1i	0.568853	−	0.568853i	0.931807	+	0.362954i	$0.118232\pi$
$18$	11968.4	−	12762.0i	0.483705	−	0.515780i
$19$			56529.5i			1.89076i	0.325965	+	0.945382i	$0.394311\pi$
$19$			56529.5i			1.89076i	−0.325965	+	0.945382i	$0.605689\pi$
$20$		0			0
$21$	30444.2	−	31436.8i	0.717359	−	0.740750i
$22$	37765.8	+	37765.8i	0.756170	+	0.756170i
$23$	36833.1	+	36833.1i	0.631235	+	0.631235i	0.948378	−	0.317143i	$-0.102723\pi$
$23$	36833.1	+	36833.1i	0.631235	+	0.631235i	−0.317143	+	0.948378i	$0.602723\pi$
$24$	16657.1	−	17200.3i	0.245958	−	0.253978i
$25$		0			0
$26$			48108.7i			0.536805i
$27$	4919.67	+	102157.i	0.0481019	+	0.998842i
$28$	42348.6	−	42348.6i	0.364574	−	0.364574i
$29$	−34373.4			−0.261715			−0.130858	−	0.991401i	$-0.541773\pi$
$29$	−34373.4			−0.261715			−0.130858	+	0.991401i	$0.541773\pi$
$30$		0			0
$31$	154212.			0.929717			0.464859	−	0.885385i	$-0.346105\pi$
$31$	154212.			0.929717			0.464859	+	0.885385i	$0.346105\pi$
$32$	23170.5	−	23170.5i	0.125000	−	0.125000i
$33$	−312171.	+	5007.70i	−1.51214	+	0.0242571i
$34$			130370.i			0.568853i
$35$		0			0
$36$	4489.45	+	139896.i	0.0160374	+	0.499743i
$37$	−86338.1	−	86338.1i	−0.280218	−	0.280218i	0.552978	−	0.833196i	$-0.313491\pi$
$37$	−86338.1	−	86338.1i	−0.280218	−	0.280218i	−0.833196	+	0.552978i	$0.813491\pi$
$38$	−319779.	−	319779.i	−0.945382	−	0.945382i
$39$	−202022.	−	195643.i	−0.545346	−	0.528126i
$40$		0			0
$41$		−	520858.i		−	1.18026i	−0.807310	−	0.590128i	$-0.799077\pi$
$41$		−	520858.i		−	1.18026i	0.807310	−	0.590128i	$-0.200923\pi$
$42$	5615.37	+	350052.i	0.0116952	+	0.729054i
$43$	499651.	−	499651.i	0.958357	−	0.958357i	−0.0408103	−	0.999167i	$-0.512994\pi$
$43$	499651.	−	499651.i	0.958357	−	0.958357i	0.999167	+	0.0408103i	$0.0129939\pi$
$44$	−427271.			−0.756170
$45$		0			0
$46$	−416719.			−0.631235
$47$	47164.4	−	47164.4i	0.0662631	−	0.0662631i	−0.673199	−	0.739462i	$-0.735080\pi$
$47$	47164.4	−	47164.4i	0.0662631	−	0.0662631i	0.739462	+	0.673199i	$0.235080\pi$
$48$	3072.38	+	191526.i	0.00400987	+	0.249968i
$49$			52142.1i			0.0633144i
$50$		0			0
$51$	−547458.	−	530171.i	−0.577904	−	0.559655i
$52$	−272144.	−	272144.i	−0.268403	−	0.268403i
$53$	315618.	+	315618.i	0.291203	+	0.291203i	0.837555	−	0.546352i	$-0.183984\pi$
$53$	315618.	+	315618.i	0.291203	+	0.291203i	−0.546352	+	0.837555i	$0.683984\pi$
$54$	−605720.	−	550060.i	−0.523472	−	0.475370i
$55$		0			0
$56$			479120.i			0.364574i
$57$	2.64328e6	−	42402.3i	1.89052	−	0.0303269i
$58$	194445.	−	194445.i	0.130858	−	0.130858i
$59$	−1.04851e6			−0.664648			−0.332324	−	0.943165i	$-0.607833\pi$
$59$	−1.04851e6			−0.664648			−0.332324	+	0.943165i	$0.607833\pi$
$60$		0			0
$61$	−1.20134e6			−0.677658			−0.338829	−	0.940848i	$-0.610031\pi$
$61$	−1.20134e6			−0.677658			−0.338829	+	0.940848i	$0.610031\pi$
$62$	−872352.	+	872352.i	−0.464859	+	0.464859i
$63$	−1.49280e6	−	1.39997e6i	−0.752160	−	0.705386i
$64$			262144.i			0.125000i
$65$		0			0
$66$	1.73758e6	−	1.79423e6i	0.743944	−	0.768201i
$67$	−242323.	−	242323.i	−0.0984314	−	0.0984314i	0.656176	−	0.754608i	$-0.272173\pi$
$67$	−242323.	−	242323.i	−0.0984314	−	0.0984314i	−0.754608	+	0.656176i	$0.772173\pi$
$68$	−737481.	−	737481.i	−0.284426	−	0.284426i
$69$	1.69466e6	−	1.74992e6i	0.621029	−	0.641279i
$70$		0			0
$71$			34141.9i			0.0113210i	0.999984	+	0.00566048i	$0.00180180\pi$
$71$			34141.9i			0.0113210i	−0.999984	+	0.00566048i	$0.998198\pi$
$72$	−816767.	−	765975.i	−0.257890	−	0.241853i
$73$	2.31111e6	−	2.31111e6i	0.695330	−	0.695330i	−0.268070	−	0.963399i	$-0.586386\pi$
$73$	2.31111e6	−	2.31111e6i	0.695330	−	0.695330i	0.963399	+	0.268070i	$0.0863858\pi$
$74$	976804.			0.280218
$75$		0			0
$76$	3.61789e6			0.945382
$77$	4.41756e6	−	4.41756e6i	1.10272	−	1.10272i
$78$	2.24953e6	−	36085.9i	0.536736	−	0.00861008i
$79$		−	7.82727e6i		−	1.78614i	−0.449917	−	0.893070i	$-0.648546\pi$
$79$		−	7.82727e6i		−	1.78614i	0.449917	−	0.893070i	$-0.351454\pi$
$80$		0			0
$81$	4.77313e6	−	306668.i	0.997942	−	0.0641167i
$82$	2.94642e6	+	2.94642e6i	0.590128	+	0.590128i
$83$	−5.24218e6	−	5.24218e6i	−1.00633	−	1.00633i	−0.999980	−	0.00634664i	$-0.997980\pi$
$83$	−5.24218e6	−	5.24218e6i	−1.00633	−	1.00633i	−0.00634664	−	0.999980i	$-0.502020\pi$
$84$	−2.01196e6	−	1.94843e6i	−0.370375	−	0.358680i
$85$		0			0
$86$			5.65291e6i			0.958357i
$87$	25783.2	+	1.60728e6i	0.00419778	+	0.261682i
$88$	2.41701e6	−	2.41701e6i	0.378085	−	0.378085i
$89$	−5.17995e6			−0.778862			−0.389431	−	0.921056i	$-0.627328\pi$
$89$	−5.17995e6			−0.778862			−0.389431	+	0.921056i	$0.627328\pi$
$90$		0			0
$91$	5.62739e6			0.782821
$92$	2.35732e6	−	2.35732e6i	0.315618	−	0.315618i
$93$	−115673.	−	7.21083e6i	−0.0149122	−	0.929598i
$94$			533605.i			0.0662631i
$95$		0			0
$96$	−1.10082e6	−	1.06606e6i	−0.126989	−	0.122979i
$97$	−114183.	−	114183.i	−0.0127028	−	0.0127028i	0.700727	−	0.713430i	$-0.252859\pi$
$97$	−114183.	−	114183.i	−0.0127028	−	0.0127028i	−0.713430	+	0.700727i	$0.752859\pi$
$98$	−294960.	−	294960.i	−0.0316572	−	0.0316572i
$99$	468314.	+	1.45931e7i	0.0485080	+	1.51156i
$100$		0			0
$101$		−	1.20718e7i		−	1.16586i	−0.812522	−	0.582931i	$-0.801906\pi$
$101$		−	1.20718e7i		−	1.16586i	0.812522	−	0.582931i	$-0.198094\pi$
$102$	6.09599e6	−	97789.2i	0.568780	−	0.00912410i
$103$	6.07066e6	−	6.07066e6i	0.547401	−	0.547401i	−0.378287	−	0.925688i	$-0.623487\pi$
$103$	6.07066e6	−	6.07066e6i	0.547401	−	0.547401i	0.925688	+	0.378287i	$0.123487\pi$
$104$	3.07896e6			0.268403
$105$		0			0
$106$	−3.57081e6			−0.291203
$107$	−2.24222e6	+	2.24222e6i	−0.176943	+	0.176943i	−0.790022	−	0.613079i	$-0.789931\pi$
$107$	−2.24222e6	+	2.24222e6i	−0.176943	+	0.176943i	0.613079	+	0.790022i	$0.289931\pi$
$108$	6.53808e6	−	314859.i	0.499421	−	0.0240510i
$109$		−	2.08031e7i		−	1.53863i	−0.638869	−	0.769316i	$-0.720597\pi$
$109$		−	2.08031e7i		−	1.53863i	0.638869	−	0.769316i	$-0.279403\pi$
$110$		0			0
$111$	−3.97235e6	+	4.10187e6i	−0.275688	+	0.284677i
$112$	−2.71031e6	−	2.71031e6i	−0.182287	−	0.182287i
$113$	1.18546e7	+	1.18546e7i	0.772882	+	0.772882i	0.978609	−	0.205727i	$-0.0659560\pi$
$113$	1.18546e7	+	1.18546e7i	0.772882	+	0.772882i	−0.205727	+	0.978609i	$0.565956\pi$
$114$	−1.47128e7	+	1.51925e7i	−0.930097	+	0.960424i
$115$		0			0
$116$			2.19990e6i			0.130858i
$117$	−8.99659e6	+	9.59316e6i	−0.519311	+	0.553747i
$118$	5.93128e6	−	5.93128e6i	0.332324	−	0.332324i
$119$	1.52497e7			0.829556
$120$		0			0
$121$	−2.50833e7			−1.28717
$122$	6.79579e6	−	6.79579e6i	0.338829	−	0.338829i
$123$	−2.43550e7	+	390692.i	−1.18010	+	0.0189307i
$124$		−	9.86954e6i		−	0.464859i
$125$		0			0
$126$	1.63640e7	−	525143.i	0.728773	−	0.0233873i
$127$	−8.44428e6	−	8.44428e6i	−0.365805	−	0.365805i	0.500140	−	0.865945i	$-0.333282\pi$
$127$	−8.44428e6	−	8.44428e6i	−0.365805	−	0.365805i	−0.865945	+	0.500140i	$0.833282\pi$
$128$	−1.48291e6	−	1.48291e6i	−0.0625000	−	0.0625000i
$129$	−2.37381e7	−	2.29886e7i	−0.973605	−	0.942862i
$130$		0			0
$131$		−	1.45441e7i		−	0.565244i	−0.959231	−	0.282622i	$-0.908796\pi$
$131$		−	1.45441e7i		−	0.565244i	0.959231	−	0.282622i	$-0.0912042\pi$
$132$	320493.	+	1.99789e7i	0.0121286	+	0.756072i
$133$	−3.74054e7	+	3.74054e7i	−1.37865	+	1.37865i
$134$	2.74158e6			0.0984314
$135$		0			0
$136$	8.34365e6			0.284426
$137$	5.62961e6	−	5.62961e6i	0.187049	−	0.187049i	−0.607370	−	0.794419i	$-0.707775\pi$
$137$	5.62961e6	−	5.62961e6i	0.187049	−	0.187049i	0.794419	+	0.607370i	$0.207775\pi$
$138$	312578.	+	1.94855e7i	0.0101247	+	0.631154i
$139$			4.74278e7i			1.49789i	0.662630	+	0.748947i	$0.269440\pi$
$139$			4.74278e7i			1.49789i	−0.662630	+	0.748947i	$0.730560\pi$
$140$		0			0
$141$	−2.24076e6	−	2.17000e6i	−0.0673174	−	0.0651918i
$142$	−193136.	−	193136.i	−0.00566048	−	0.00566048i
$143$	−2.83885e7	−	2.83885e7i	−0.811831	−	0.811831i
$144$	8.95334e6	−	287325.i	0.249871	−	0.00801871i
$145$		0			0
$146$			2.61472e7i			0.695330i
$147$	2.43813e6	−	39111.4i	0.0633062	−	0.00101553i
$148$	−5.52564e6	+	5.52564e6i	−0.140109	+	0.140109i
$149$	4.33349e7			1.07321			0.536607	−	0.843832i	$-0.319706\pi$
$149$	4.33349e7			1.07321			0.536607	+	0.843832i	$0.319706\pi$
$150$		0			0
$151$	−6.29581e7			−1.48810			−0.744050	−	0.668124i	$-0.767098\pi$
$151$	−6.29581e7			−1.48810			−0.744050	+	0.668124i	$0.767098\pi$
$152$	−2.04659e7	+	2.04659e7i	−0.472691	+	0.472691i
$153$	−2.43798e7	+	2.59965e7i	−0.550314	+	0.586806i
$154$			4.99790e7i			1.10272i
$155$		0			0
$156$	−1.25211e7	+	1.29294e7i	−0.264063	+	0.272673i
$157$	−2.02698e7	−	2.02698e7i	−0.418024	−	0.418024i	0.466498	−	0.884522i	$-0.345515\pi$
$157$	−2.02698e7	−	2.02698e7i	−0.418024	−	0.418024i	−0.884522	+	0.466498i	$0.845515\pi$
$158$	4.42777e7	+	4.42777e7i	0.893070	+	0.893070i
$159$	1.45213e7	−	1.49948e7i	0.286495	−	0.295836i
$160$		0			0
$161$			4.87447e7i			0.920528i
$162$	−2.52661e7	+	2.87357e7i	−0.466913	+	0.531030i
$163$	3.74541e7	−	3.74541e7i	0.677396	−	0.677396i	−0.282014	−	0.959410i	$-0.591003\pi$
$163$	3.74541e7	−	3.74541e7i	0.677396	−	0.677396i	0.959410	+	0.282014i	$0.0910026\pi$
$164$	−3.33349e7			−0.590128
$165$		0			0
$166$	5.93085e7			1.00633
$167$	2.57050e7	−	2.57050e7i	0.427081	−	0.427081i	−0.460552	−	0.887633i	$-0.652348\pi$
$167$	2.57050e7	−	2.57050e7i	0.427081	−	0.427081i	0.887633	+	0.460552i	$0.152348\pi$
$168$	2.24033e7	−	359384.i	0.364527	−	0.00584758i
$169$			2.65853e7i			0.423680i
$170$		0			0
$171$	−3.96541e6	−	1.23566e8i	−0.0606459	−	1.88979i
$172$	−3.19777e7	−	3.19777e7i	−0.479178	−	0.479178i
$173$	8.41199e7	+	8.41199e7i	1.23520	+	1.23520i	0.961940	+	0.273261i	$0.0881021\pi$
$173$	8.41199e7	+	8.41199e7i	1.23520	+	1.23520i	0.273261	+	0.961940i	$0.411898\pi$
$174$	−9.23798e6	−	8.94628e6i	−0.132940	−	0.128742i
$175$		0			0
$176$			2.73454e7i			0.378085i
$177$	786481.	+	4.90278e7i	0.0106606	+	0.664563i
$178$	2.93022e7	−	2.93022e7i	0.389431	−	0.389431i
$179$	8.83756e7			1.15172			0.575860	−	0.817548i	$-0.304667\pi$
$179$	8.83756e7			1.15172			0.575860	+	0.817548i	$0.304667\pi$
$180$		0			0
$181$	−2.85699e7			−0.358124			−0.179062	−	0.983838i	$-0.557306\pi$
$181$	−2.85699e7			−0.358124			−0.179062	+	0.983838i	$0.557306\pi$
$182$	−3.18334e7	+	3.18334e7i	−0.391411	+	0.391411i
$183$	901114.	+	5.61738e7i	0.0108693	+	0.677571i
$184$			2.66700e7i			0.315618i
$185$		0			0
$186$	4.14450e7	+	4.01363e7i	0.472255	+	0.457343i
$187$	−7.69298e7	−	7.69298e7i	−0.860298	−	0.860298i
$188$	−3.01852e6	−	3.01852e6i	−0.0331316	−	0.0331316i
$189$	−6.43419e7	+	7.08526e7i	−0.693231	+	0.763378i
$190$		0			0
$191$			8.58776e7i			0.891791i	0.895085	+	0.445896i	$0.147115\pi$
$191$			8.58776e7i			0.891791i	−0.895085	+	0.445896i	$0.852885\pi$
$192$	1.22577e7	−	196632.i	0.124984	−	0.00200494i
$193$	−3.39490e7	+	3.39490e7i	−0.339920	+	0.339920i	−0.856337	−	0.516417i	$-0.827265\pi$
$193$	−3.39490e7	+	3.39490e7i	−0.339920	+	0.339920i	0.516417	+	0.856337i	$0.327265\pi$
$194$	1.29183e6			0.0127028
$195$		0			0
$196$	3.33710e6			0.0316572
$197$	2.12932e7	−	2.12932e7i	0.198431	−	0.198431i	−0.600896	−	0.799327i	$-0.705190\pi$
$197$	2.12932e7	−	2.12932e7i	0.198431	−	0.198431i	0.799327	+	0.600896i	$0.205190\pi$
$198$	−8.52005e7	−	7.99021e7i	−0.780035	−	0.731526i
$199$		−	1.09790e8i		−	0.987594i	−0.869577	−	0.493797i	$-0.835609\pi$
$199$		−	1.09790e8i		−	0.987594i	0.869577	−	0.493797i	$-0.164391\pi$
$200$		0			0
$201$	−1.11491e7	+	1.15127e7i	−0.0968399	+	0.0999975i
$202$	6.82884e7	+	6.82884e7i	0.582931	+	0.582931i
$203$	−2.27447e7	−	2.27447e7i	−0.190829	−	0.190829i
$204$	−3.39310e7	+	3.50373e7i	−0.279828	+	0.288952i
$205$		0			0
$206$			6.86816e7i			0.547401i
$207$	−8.30963e7	−	7.79288e7i	−0.651157	−	0.610663i
$208$	−1.74172e7	+	1.74172e7i	−0.134201	+	0.134201i
$209$	3.77397e8			2.85948
$210$		0			0
$211$	1.88528e8			1.38161			0.690807	−	0.723039i	$-0.257255\pi$
$211$	1.88528e8			1.38161			0.690807	+	0.723039i	$0.257255\pi$
$212$	2.01995e7	−	2.01995e7i	0.145601	−	0.145601i
$213$	1.59645e6	−	25609.6i	0.0113195	−	0.000181582i
$214$		−	2.53678e7i		−	0.176943i
$215$		0			0
$216$	−3.52038e7	+	3.87661e7i	−0.237685	+	0.261736i
$217$	1.02041e8	+	1.02041e8i	0.677902	+	0.677902i
$218$	1.17680e8	+	1.17680e8i	0.769316	+	0.769316i
$219$	−1.09800e8	−	1.06332e8i	−0.706393	−	0.684087i
$220$		0			0
$221$		−	9.79985e7i		−	0.610726i
$222$	−732693.	−	4.56747e7i	−0.00449456	−	0.280182i
$223$	−1.69582e8	+	1.69582e8i	−1.02403	+	1.02403i	−0.0243277	+	0.999704i	$0.507745\pi$
$223$	−1.69582e8	+	1.69582e8i	−1.02403	+	1.02403i	−0.999704	+	0.0243277i	$0.992255\pi$
$224$	3.06637e7			0.182287
$225$		0			0
$226$	−1.34120e8			−0.772882
$227$	1.85495e8	−	1.85495e8i	1.05255	−	1.05255i	0.0540048	−	0.998541i	$-0.482801\pi$
$227$	1.85495e8	−	1.85495e8i	1.05255	−	1.05255i	0.998541	−	0.0540048i	$-0.0171986\pi$
$228$	−2.71375e6	−	1.69170e8i	−0.0151634	−	0.945260i
$229$		−	1.00981e8i		−	0.555670i	−0.960629	−	0.277835i	$-0.910383\pi$
$229$		−	1.00981e8i		−	0.555670i	0.960629	−	0.277835i	$-0.0896169\pi$
$230$		0			0
$231$	−2.09876e8	−	2.03249e8i	−1.12026	−	1.08489i
$232$	−1.24445e7	−	1.24445e7i	−0.0654288	−	0.0654288i
$233$	−7.25267e7	−	7.25267e7i	−0.375623	−	0.375623i	0.493897	−	0.869520i	$-0.335572\pi$
$233$	−7.25267e7	−	7.25267e7i	−0.375623	−	0.375623i	−0.869520	+	0.493897i	$0.835572\pi$
$234$	−3.37471e6	−	1.05160e8i	−0.0172179	−	0.536529i
$235$		0			0
$236$			6.71048e7i			0.332324i
$237$	−3.65998e8	+	5.87118e6i	−1.78591	+	0.0286488i
$238$	−8.62651e7	+	8.62651e7i	−0.414778	+	0.414778i
$239$	−3.76628e8			−1.78452			−0.892258	−	0.451526i	$-0.850880\pi$
$239$	−3.76628e8			−1.78452			−0.892258	+	0.451526i	$0.850880\pi$
$240$		0			0
$241$	−6.94841e7			−0.319761			−0.159881	−	0.987136i	$-0.551111\pi$
$241$	−6.94841e7			−0.319761			−0.159881	+	0.987136i	$0.551111\pi$
$242$	1.41893e8	−	1.41893e8i	0.643585	−	0.643585i
$243$	−1.79199e7	−	2.22958e8i	−0.0801149	−	0.996786i
$244$			7.68856e7i			0.338829i
$245$		0			0
$246$	1.35563e8	−	1.39983e8i	0.580587	−	0.599517i
$247$	2.40377e8	+	2.40377e8i	1.01497	+	1.01497i
$248$	5.58305e7	+	5.58305e7i	0.232429	+	0.232429i
$249$	−2.41189e8	+	2.49053e8i	−0.990056	+	1.02234i
$250$		0			0
$251$			1.90916e8i			0.762052i	0.924564	+	0.381026i	$0.124429\pi$
$251$			1.90916e8i			0.762052i	−0.924564	+	0.381026i	$0.875571\pi$
$252$	−8.95981e7	+	9.55394e7i	−0.352693	+	0.376080i
$253$	2.45902e8	−	2.45902e8i	0.954641	−	0.954641i
$254$	9.55361e7			0.365805
$255$		0			0
$256$	1.67772e7			0.0625000
$257$	−1.16268e8	+	1.16268e8i	−0.427264	+	0.427264i	−0.887695	−	0.460432i	$-0.847695\pi$
$257$	−1.16268e8	+	1.16268e8i	−0.427264	+	0.427264i	0.460432	+	0.887695i	$0.347695\pi$
$258$	2.64326e8	−	4.24020e6i	0.958233	−	0.0153715i
$259$		−	1.14259e8i		−	0.408641i
$260$		0			0
$261$	7.51359e7	−	2.41121e6i	0.261581	−	0.00839448i
$262$	8.22736e7	+	8.22736e7i	0.282622	+	0.282622i
$263$	−2.94044e7	−	2.94044e7i	−0.0996705	−	0.0996705i	0.655513	−	0.755184i	$-0.272452\pi$
$263$	−2.94044e7	−	2.94044e7i	−0.0996705	−	0.0996705i	−0.755184	+	0.655513i	$0.772452\pi$
$264$	−1.14831e8	−	1.11205e8i	−0.384100	−	0.371972i
$265$		0			0
$266$		−	4.23193e8i		−	1.37865i
$267$	3.88544e6	+	2.42211e8i	0.0124925	+	0.778762i
$268$	−1.55087e7	+	1.55087e7i	−0.0492157	+	0.0492157i
$269$	9.05736e6			0.0283706			0.0141853	−	0.999899i	$-0.495485\pi$
$269$	9.05736e6			0.0283706			0.0141853	+	0.999899i	$0.495485\pi$
$270$		0			0
$271$	3.20432e7			0.0978010			0.0489005	−	0.998804i	$-0.484428\pi$
$271$	3.20432e7			0.0978010			0.0489005	+	0.998804i	$0.484428\pi$
$272$	−4.71988e7	+	4.71988e7i	−0.142213	+	0.142213i
$273$	−4.22107e6	−	2.63133e8i	−0.0125560	−	0.782720i
$274$			6.36917e7i			0.187049i
$275$		0			0
$276$	−1.11995e8	−	1.08459e8i	−0.320639	−	0.310515i
$277$	4.31831e6	+	4.31831e6i	0.0122077	+	0.0122077i	0.713184	−	0.700977i	$-0.247252\pi$
$277$	4.31831e6	+	4.31831e6i	0.0122077	+	0.0122077i	−0.700977	+	0.713184i	$0.747252\pi$
$278$	−2.68292e8	−	2.68292e8i	−0.748947	−	0.748947i
$279$	−3.37087e8	+	1.08176e7i	−0.929239	+	0.0298205i
$280$		0			0
$281$			2.39886e8i			0.644960i	0.946576	+	0.322480i	$0.104516\pi$
$281$			2.39886e8i			0.644960i	−0.946576	+	0.322480i	$0.895484\pi$
$282$	2.49510e7	−	400253.i	0.0662546	−	0.00106283i
$283$	3.38724e8	−	3.38724e8i	0.888370	−	0.888370i	−0.105997	−	0.994366i	$-0.533803\pi$
$283$	3.38724e8	−	3.38724e8i	0.888370	−	0.888370i	0.994366	+	0.105997i	$0.0338033\pi$
$284$	2.18508e6			0.00566048
$285$		0			0
$286$	3.21179e8			0.811831
$287$	3.44650e8	−	3.44650e8i	0.860581	−	0.860581i
$288$	−4.90224e7	+	5.22731e7i	−0.120926	+	0.128945i
$289$			1.44773e8i			0.352813i
$290$		0			0
$291$	−5.25347e6	+	5.42476e6i	−0.0124974	+	0.0129049i
$292$	−1.47911e8	−	1.47911e8i	−0.347665	−	0.347665i
$293$	−1.40487e8	−	1.40487e8i	−0.326286	−	0.326286i	0.524886	−	0.851172i	$-0.324108\pi$
$293$	−1.40487e8	−	1.40487e8i	−0.326286	−	0.326286i	−0.851172	+	0.524886i	$0.824108\pi$
$294$	−1.35709e7	+	1.40134e7i	−0.0311454	+	0.0321609i
$295$		0			0
$296$		−	6.25155e7i		−	0.140109i
$297$	6.82015e8	−	3.28442e7i	1.51059	−	0.0727464i
$298$	−2.45139e8	+	2.45139e8i	−0.536607	+	0.536607i
$299$	3.13247e8			0.677700
$300$		0			0
$301$	6.61235e8			1.39757
$302$	3.56145e8	−	3.56145e8i	0.744050	−	0.744050i
$303$	−5.64469e8	+	9.05496e6i	−1.16571	+	0.0186998i
$304$		−	2.31545e8i		−	0.472691i
$305$		0			0
$306$	−9.14512e6	−	2.84971e8i	−0.0182459	−	0.568560i
$307$	4.65228e8	+	4.65228e8i	0.917660	+	0.917660i	0.996859	−	0.0791992i	$-0.0252363\pi$
$307$	4.65228e8	+	4.65228e8i	0.917660	+	0.917660i	−0.0791992	+	0.996859i	$0.525236\pi$
$308$	−2.82724e8	−	2.82724e8i	−0.551360	−	0.551360i
$309$	−2.88414e8	−	2.79306e8i	−0.556110	−	0.538550i
$310$		0			0
$311$			3.33690e8i			0.629046i	0.949250	+	0.314523i	$0.101845\pi$
$311$			3.33690e8i			0.629046i	−0.949250	+	0.314523i	$0.898155\pi$
$312$	−2.30950e6	−	1.43970e8i	−0.00430504	−	0.268368i
$313$	1.68738e8	−	1.68738e8i	0.311034	−	0.311034i	−0.534276	−	0.845310i	$-0.679416\pi$
$313$	1.68738e8	−	1.68738e8i	0.311034	−	0.311034i	0.845310	+	0.534276i	$0.179416\pi$
$314$	2.29327e8			0.418024
$315$		0			0
$316$	−5.00946e8			−0.893070
$317$	−5.32238e8	+	5.32238e8i	−0.938423	+	0.938423i	−0.998211	−	0.0597877i	$-0.980958\pi$
$317$	−5.32238e8	+	5.32238e8i	−0.938423	+	0.938423i	0.0597877	+	0.998211i	$0.480958\pi$
$318$	2.67843e6	+	1.66969e8i	0.00467074	+	0.291166i
$319$			2.29480e8i			0.395802i
$320$		0			0
$321$	1.06527e8	+	1.03163e8i	0.179759	+	0.174083i
$322$	−2.75742e8	−	2.75742e8i	−0.460264	−	0.460264i
$323$	6.51397e8	+	6.51397e8i	1.07557	+	1.07557i
$324$	−1.96268e7	−	3.05480e8i	−0.0320583	−	0.498971i
$325$		0			0
$326$			4.23744e8i			0.677396i
$327$	−9.72738e8	+	1.56042e7i	−1.53843	+	0.0246788i
$328$	1.88571e8	−	1.88571e8i	0.295064	−	0.295064i
$329$	6.24171e7			0.0966313
$330$		0			0
$331$	8.98588e8			1.36195			0.680977	−	0.732305i	$-0.261555\pi$
$331$	8.98588e8			1.36195			0.680977	+	0.732305i	$0.261555\pi$
$332$	−3.35500e8	+	3.35500e8i	−0.503163	+	0.503163i
$333$	1.94781e8	+	1.82668e8i	0.289062	+	0.271086i
$334$			2.90819e8i			0.427081i
$335$		0			0
$336$	−1.24699e8	+	1.28765e8i	−0.179340	+	0.185187i
$337$	−4.32152e8	−	4.32152e8i	−0.615081	−	0.615081i	0.329185	−	0.944266i	$-0.393226\pi$
$337$	−4.32152e8	−	4.32152e8i	−0.615081	−	0.615081i	−0.944266	+	0.329185i	$0.893226\pi$
$338$	−1.50389e8	−	1.50389e8i	−0.211840	−	0.211840i
$339$	5.45422e8	−	5.63207e8i	0.760386	−	0.785179i
$340$		0			0
$341$		−	1.02953e9i		−	1.40605i
$342$	7.21428e8	+	6.76565e8i	0.975218	+	0.914572i
$343$	5.10433e8	−	5.10433e8i	0.682983	−	0.682983i
$344$	3.61786e8			0.479178
$345$		0			0
$346$	−9.51708e8			−1.23520
$347$	7.18768e8	−	7.18768e8i	0.923497	−	0.923497i	−0.0737780	−	0.997275i	$-0.523506\pi$
$347$	7.18768e8	−	7.18768e8i	0.923497	−	0.923497i	0.997275	+	0.0737780i	$0.0235056\pi$
$348$	1.02866e8	−	1.65012e6i	0.130841	−	0.00209889i
$349$			3.24847e8i			0.409063i	0.978860	+	0.204531i	$0.0655670\pi$
$349$			3.24847e8i			0.409063i	−0.978860	+	0.204531i	$0.934433\pi$
$350$		0			0
$351$	4.55318e8	+	4.13479e8i	0.562005	+	0.510362i
$352$	−1.54689e8	−	1.54689e8i	−0.189042	−	0.189042i
$353$	8.23396e8	+	8.23396e8i	0.996316	+	0.996316i	0.999993	−	0.00367700i	$-0.00117043\pi$
$353$	8.23396e8	+	8.23396e8i	0.996316	+	0.996316i	−0.00367700	+	0.999993i	$0.501170\pi$
$354$	−2.81792e8	−	2.72894e8i	−0.337612	−	0.326951i
$355$		0			0
$356$			3.31517e8i			0.389431i
$357$	−1.14386e7	−	7.13064e8i	−0.0133056	−	0.829449i
$358$	−4.99928e8	+	4.99928e8i	−0.575860	+	0.575860i
$359$	−2.51163e8			−0.286500			−0.143250	−	0.989687i	$-0.545755\pi$
$359$	−2.51163e8			−0.286500			−0.143250	+	0.989687i	$0.545755\pi$
$360$		0			0
$361$	−2.30171e9			−2.57499
$362$	1.61616e8	−	1.61616e8i	0.179062	−	0.179062i
$363$	1.88148e7	+	1.17288e9i	0.0206455	+	1.28700i
$364$		−	3.60153e8i		−	0.391411i
$365$		0			0
$366$	−3.22864e8	−	3.12669e8i	−0.344220	−	0.333351i
$367$	−5.77098e8	−	5.77098e8i	−0.609423	−	0.609423i	0.333373	−	0.942795i	$-0.391813\pi$
$367$	−5.77098e8	−	5.77098e8i	−0.609423	−	0.609423i	−0.942795	+	0.333373i	$0.891813\pi$
$368$	−1.50868e8	−	1.50868e8i	−0.157809	−	0.157809i
$369$	3.65370e7	+	1.13853e9i	0.0378565	+	1.17965i
$370$		0			0
$371$			4.17686e8i			0.424660i
$372$	−4.61493e8	+	7.40307e6i	−0.464799	+	0.00745609i
$373$	−1.14505e9	+	1.14505e9i	−1.14247	+	1.14247i	−0.154470	+	0.987997i	$0.549367\pi$
$373$	−1.14505e9	+	1.14505e9i	−1.14247	+	1.14247i	−0.987997	+	0.154470i	$0.950633\pi$
$374$	8.70361e8			0.860298
$375$		0			0
$376$	3.41507e7			0.0331316
$377$	−1.46164e8	+	1.46164e8i	−0.140490	+	0.140490i
$378$	−3.68298e7	−	7.64776e8i	−0.0350734	−	0.728304i
$379$		−	6.24053e8i		−	0.588822i	−0.955679	−	0.294411i	$-0.904876\pi$
$379$		−	6.24053e8i		−	0.588822i	0.955679	−	0.294411i	$-0.0951235\pi$
$380$		0			0
$381$	−3.88515e8	+	4.01183e8i	−0.359891	+	0.371625i
$382$	−4.85797e8	−	4.85797e8i	−0.445896	−	0.445896i
$383$	1.12571e8	+	1.12571e8i	0.102383	+	0.102383i	0.756443	−	0.654060i	$-0.226935\pi$
$383$	1.12571e8	+	1.12571e8i	0.102383	+	0.102383i	−0.654060	+	0.756443i	$0.726935\pi$
$384$	−6.82276e7	+	7.04523e7i	−0.0614895	+	0.0634944i
$385$		0			0
$386$		−	3.84090e8i		−	0.339920i
$387$	−1.05713e9	+	1.12722e9i	−0.927124	+	0.988603i
$388$	−7.30770e6	+	7.30770e6i	−0.00635141	+	0.00635141i
$389$	−5.19958e8			−0.447862			−0.223931	−	0.974605i	$-0.571889\pi$
$389$	−5.19958e8			−0.447862			−0.223931	+	0.974605i	$0.571889\pi$
$390$		0			0
$391$	8.48867e8			0.718160
$392$	−1.88775e7	+	1.88775e7i	−0.0158286	+	0.0158286i
$393$	−6.80071e8	+	1.09094e7i	−0.565171	+	0.00906622i
$394$			2.40905e8i			0.198431i
$395$		0			0
$396$	9.33961e8	−	2.99721e7i	0.755781	−	0.0242540i
$397$	8.77781e8	+	8.77781e8i	0.704076	+	0.704076i	0.965283	−	0.261207i	$-0.0841206\pi$
$397$	8.77781e8	+	8.77781e8i	0.704076	+	0.704076i	−0.261207	+	0.965283i	$0.584121\pi$
$398$	6.21068e8	+	6.21068e8i	0.493797	+	0.493797i
$399$	1.77711e9	+	1.72099e9i	1.40058	+	1.35636i
$400$		0			0
$401$			1.79053e9i			1.38668i	0.720612	+	0.693338i	$0.243861\pi$
$401$			1.79053e9i			1.38668i	−0.720612	+	0.693338i	$0.756139\pi$
$402$	−2.05644e6	−	1.28194e8i	−0.00157879	−	0.0984187i
$403$	6.55745e8	−	6.55745e8i	0.499077	−	0.499077i
$404$	−7.72594e8			−0.582931
$405$		0			0
$406$	2.57327e8			0.190829
$407$	−5.76403e8	+	5.76403e8i	−0.423785	+	0.423785i
$408$	−6.25851e6	−	3.90144e8i	−0.00456205	−	0.284390i
$409$		−	4.81089e8i		−	0.347692i	−0.984773	−	0.173846i	$-0.944381\pi$
$409$		−	4.81089e8i		−	0.347692i	0.984773	−	0.173846i	$-0.0556194\pi$
$410$		0			0
$411$	−2.67459e8	−	2.59014e8i	−0.190025	−	0.184025i
$412$	−3.88522e8	−	3.88522e8i	−0.273700	−	0.273700i
$413$	−6.93798e8	−	6.93798e8i	−0.484627	−	0.484627i
$414$	9.10896e8	−	2.92319e7i	0.630910	−	0.0202468i
$415$		0			0
$416$		−	1.97053e8i		−	0.134201i
$417$	2.21769e9	−	3.55752e7i	1.49770	−	0.0240255i
$418$	−2.13488e9	+	2.13488e9i	−1.42974	+	1.42974i
$419$	1.06990e9			0.710549			0.355275	−	0.934762i	$-0.384387\pi$
$419$	1.06990e9			0.710549			0.355275	+	0.934762i	$0.384387\pi$
$420$		0			0
$421$	2.63062e9			1.71819			0.859095	−	0.511817i	$-0.171027\pi$
$421$	2.63062e9			1.71819			0.859095	+	0.511817i	$0.171027\pi$
$422$	−1.06647e9	+	1.06647e9i	−0.690807	+	0.690807i
$423$	−9.97871e7	+	1.06404e8i	−0.0641037	+	0.0683544i
$424$			2.28532e8i			0.145601i
$425$		0			0
$426$	−8.88604e6	+	9.17577e6i	−0.00556896	+	0.00575055i
$427$	−7.94921e8	−	7.94921e8i	−0.494113	−	0.494113i
$428$	1.43502e8	+	1.43502e8i	0.0884717	+	0.0884717i
$429$	−1.30613e9	+	1.34872e9i	−0.798706	+	0.824748i
$430$		0			0
$431$			3.33688e8i			0.200757i	0.994949	+	0.100378i	$0.0320053\pi$
$431$			3.33688e8i			0.200757i	−0.994949	+	0.100378i	$0.967995\pi$
$432$	−2.01510e7	−	4.18437e8i	−0.0120255	−	0.249711i
$433$	1.12847e9	−	1.12847e9i	0.668008	−	0.668008i	−0.289247	−	0.957255i	$-0.593405\pi$
$433$	1.12847e9	−	1.12847e9i	0.668008	−	0.668008i	0.957255	+	0.289247i	$0.0934048\pi$
$434$	−1.15447e9			−0.677902
$435$		0			0
$436$	−1.33140e9			−0.769316
$437$	−2.08216e9	+	2.08216e9i	−1.19352	+	1.19352i
$438$	1.22263e9	−	1.96128e7i	0.695240	−	0.0111527i
$439$		−	4.51964e8i		−	0.254963i	−0.991841	−	0.127482i	$-0.959311\pi$
$439$		−	4.51964e8i		−	0.254963i	0.991841	−	0.127482i	$-0.0406894\pi$
$440$		0			0
$441$	−3.65765e6	−	1.13976e8i	−0.00203080	−	0.0632818i
$442$	5.54363e8	+	5.54363e8i	0.305363	+	0.305363i
$443$	6.00898e8	+	6.00898e8i	0.328388	+	0.328388i	0.851973	−	0.523585i	$-0.175406\pi$
$443$	6.00898e8	+	6.00898e8i	0.328388	+	0.328388i	−0.523585	+	0.851973i	$0.675406\pi$
$444$	2.62520e8	+	2.54231e8i	0.142338	+	0.137844i
$445$		0			0
$446$		−	1.91860e9i		−	1.02403i
$447$	−3.25052e7	−	2.02631e9i	−0.0172138	−	1.07308i
$448$	−1.73460e8	+	1.73460e8i	−0.0911435	+	0.0911435i
$449$	−3.08560e9			−1.60871			−0.804354	−	0.594150i	$-0.797488\pi$
$449$	−3.08560e9			−1.60871			−0.804354	+	0.594150i	$0.797488\pi$
$450$		0			0
$451$	−3.47731e9			−1.78495
$452$	7.58696e8	−	7.58696e8i	0.386441	−	0.386441i
$453$	4.72244e7	+	2.94388e9i	0.0238683	+	1.48791i
$454$			2.09863e9i			1.05255i
$455$		0			0
$456$	9.72321e8	+	9.41619e8i	0.480212	+	0.465048i
$457$	2.13005e9	+	2.13005e9i	1.04396	+	1.04396i	0.998988	+	0.0449691i	$0.0143189\pi$
$457$	2.13005e9	+	2.13005e9i	1.04396	+	1.04396i	0.0449691	+	0.998988i	$0.485681\pi$
$458$	5.71237e8	+	5.71237e8i	0.277835	+	0.277835i
$459$	1.23387e9	+	1.12049e9i	0.595557	+	0.540831i
$460$		0			0
$461$		−	3.55188e9i		−	1.68852i	−0.535936	−	0.844259i	$-0.680041\pi$
$461$		−	3.55188e9i		−	1.68852i	0.535936	−	0.844259i	$-0.319959\pi$
$462$	2.33699e9	−	3.74889e7i	1.10258	−	0.0176870i
$463$	5.49134e8	−	5.49134e8i	0.257126	−	0.257126i	−0.566758	−	0.823884i	$-0.691803\pi$
$463$	5.49134e8	−	5.49134e8i	0.257126	−	0.257126i	0.823884	+	0.566758i	$0.191803\pi$
$464$	1.40793e8			0.0654288
$465$		0			0
$466$	8.20546e8			0.375623
$467$	−2.58849e8	+	2.58849e8i	−0.117608	+	0.117608i	−0.763462	−	0.645853i	$-0.776502\pi$
$467$	−2.58849e8	+	2.58849e8i	−0.117608	+	0.117608i	0.645853	+	0.763462i	$0.276502\pi$
$468$	6.13962e8	+	5.75782e8i	0.276873	+	0.259655i
$469$		−	3.20689e8i		−	0.143542i
$470$		0			0
$471$	−9.32599e8	+	9.63007e8i	−0.411265	+	0.424675i
$472$	−3.79602e8	−	3.79602e8i	−0.166162	−	0.166162i
$473$	−3.33573e9	−	3.33573e9i	−1.44936	−	1.44936i
$474$	2.03719e9	−	2.10361e9i	0.878631	−	0.907280i
$475$		0			0
$476$		−	9.75978e8i		−	0.414778i
$477$	−7.12041e8	−	6.67761e8i	−0.300393	−	0.281713i
$478$	2.13053e9	−	2.13053e9i	0.892258	−	0.892258i
$479$	1.55118e9			0.644892			0.322446	−	0.946588i	$-0.395495\pi$
$479$	1.55118e9			0.644892			0.322446	+	0.946588i	$0.395495\pi$
$480$		0			0
$481$	−7.34262e8			−0.300845
$482$	3.93062e8	−	3.93062e8i	0.159881	−	0.159881i
$483$	2.27927e9	−	3.65630e7i	0.920409	−	0.0147648i
$484$			1.60533e9i			0.643585i
$485$		0			0
$486$	1.36261e9	+	1.15987e9i	0.538450	+	0.458335i
$487$	−1.50250e9	−	1.50250e9i	−0.589470	−	0.589470i	0.348018	−	0.937488i	$-0.386855\pi$
$487$	−1.50250e9	−	1.50250e9i	−0.589470	−	0.589470i	−0.937488	+	0.348018i	$0.886855\pi$
$488$	−4.34931e8	−	4.34931e8i	−0.169415	−	0.169415i
$489$	−1.77942e9	−	1.72323e9i	−0.688174	−	0.666444i
$490$		0			0
$491$			2.41834e9i			0.922004i	0.887399	+	0.461002i	$0.152510\pi$
$491$			2.41834e9i			0.922004i	−0.887399	+	0.461002i	$0.847490\pi$
$492$	2.50043e7	+	1.55872e9i	0.00946534	+	0.590052i
$493$	−3.96089e8	+	3.96089e8i	−0.148877	+	0.148877i
$494$	−2.71956e9			−1.01497
$495$		0			0
$496$	−6.31650e8			−0.232429
$497$	−2.25916e7	+	2.25916e7i	−0.00825466	+	0.00825466i
$498$	−4.44869e7	−	2.77323e9i	−0.0161410	−	1.00620i
$499$		−	3.02016e9i		−	1.08812i	−0.839046	−	0.544061i	$-0.816886\pi$
$499$		−	3.02016e9i		−	1.08812i	0.839046	−	0.544061i	$-0.183114\pi$
$500$		0			0
$501$	−1.22123e9	−	1.18267e9i	−0.433876	−	0.420176i
$502$	−1.07998e9	−	1.07998e9i	−0.381026	−	0.381026i
$503$	−1.26473e9	−	1.26473e9i	−0.443107	−	0.443107i	0.449948	−	0.893055i	$-0.351442\pi$
$503$	−1.26473e9	−	1.26473e9i	−0.443107	−	0.443107i	−0.893055	+	0.449948i	$0.851442\pi$
$504$	−3.36091e7	−	1.04730e9i	−0.0116937	−	0.364387i
$505$		0			0
$506$			2.78206e9i			0.954641i
$507$	1.24311e9	−	1.99414e7i	0.423626	−	0.00679562i
$508$	−5.40434e8	+	5.40434e8i	−0.182903	+	0.182903i
$509$	−2.77528e9			−0.932812			−0.466406	−	0.884571i	$-0.654451\pi$
$509$	−2.77528e9			−0.932812			−0.466406	+	0.884571i	$0.654451\pi$
$510$		0			0
$511$	3.05851e9			1.01400
$512$	−9.49063e7	+	9.49063e7i	−0.0312500	+	0.0312500i
$513$	−5.77491e9	+	2.78106e8i	−1.88857	+	0.0909494i
$514$		−	1.31543e9i		−	0.427264i
$515$		0			0
$516$	−1.47127e9	+	1.51924e9i	−0.471431	+	0.486802i
$517$	−3.14875e8	−	3.14875e8i	−0.100212	−	0.100212i
$518$	6.46348e8	+	6.46348e8i	0.204321	+	0.204321i
$519$	3.87030e9	−	3.99649e9i	1.21523	−	1.25485i
$520$		0			0
$521$		−	5.35817e9i		−	1.65991i	−0.557831	−	0.829955i	$-0.688366\pi$
$521$		−	5.35817e9i		−	1.65991i	0.557831	−	0.829955i	$-0.311634\pi$
$522$	−4.11393e8	+	4.38673e8i	−0.126593	+	0.134988i
$523$	−7.09968e7	+	7.09968e7i	−0.0217012	+	0.0217012i	−0.717874	−	0.696173i	$-0.754885\pi$
$523$	−7.09968e7	+	7.09968e7i	−0.0217012	+	0.0217012i	0.696173	+	0.717874i	$0.254885\pi$
$524$	−9.30820e8			−0.282622
$525$		0			0
$526$	3.32672e8			0.0996705
$527$	1.77700e9	−	1.77700e9i	0.528872	−	0.528872i
$528$	1.27865e9	−	2.05115e7i	0.378036	−	0.00606428i
$529$		−	6.91468e8i		−	0.203085i
$530$		0			0
$531$	2.29192e9	−	7.35507e7i	0.664306	−	0.0213185i
$532$	2.39394e9	+	2.39394e9i	0.689324	+	0.689324i
$533$	−2.21482e9	−	2.21482e9i	−0.633567	−	0.633567i
$534$	−1.39213e9	−	1.34817e9i	−0.395627	−	0.383135i
$535$		0			0
$536$		−	1.75461e8i		−	0.0492157i
$537$	−6.62899e7	−	4.13239e9i	−0.0184730	−	1.15157i
$538$	−5.12362e7	+	5.12362e7i	−0.0141853	+	0.0141853i
$539$	3.48107e8			0.0957528
$540$		0			0
$541$	2.08295e8			0.0565573			0.0282787	−	0.999600i	$-0.490997\pi$
$541$	2.08295e8			0.0565573			0.0282787	+	0.999600i	$0.490997\pi$
$542$	−1.81264e8	+	1.81264e8i	−0.0489005	+	0.0489005i
$543$	2.14300e7	+	1.33591e9i	0.00574412	+	0.358078i
$544$		−	5.33994e8i		−	0.142213i
$545$		0			0
$546$	1.51238e9	+	1.46463e9i	0.397638	+	0.385082i
$547$	−1.59142e9	−	1.59142e9i	−0.415747	−	0.415747i	0.467988	−	0.883735i	$-0.344979\pi$
$547$	−1.59142e9	−	1.59142e9i	−0.415747	−	0.415747i	−0.883735	+	0.467988i	$0.844979\pi$
$548$	−3.60295e8	−	3.60295e8i	−0.0935246	−	0.0935246i
$549$	2.62597e9	−	8.42710e7i	0.677309	−	0.0217358i
$550$		0			0
$551$		−	1.94311e9i		−	0.494842i
$552$	1.24707e9	−	2.00050e7i	0.315577	−	0.00506234i
$553$	5.17928e9	−	5.17928e9i	1.30236	−	1.30236i
$554$	−4.88561e7			−0.0122077
$555$		0			0
$556$	3.03538e9			0.748947
$557$	1.70195e9	−	1.70195e9i	0.417305	−	0.417305i	−0.466969	−	0.884274i	$-0.654654\pi$
$557$	1.70195e9	−	1.70195e9i	0.417305	−	0.417305i	0.884274	+	0.466969i	$0.154654\pi$
$558$	1.84566e9	−	1.96805e9i	0.449709	−	0.479530i
$559$		−	4.24928e9i		−	1.02890i
$560$		0			0
$561$	−3.53948e9	+	3.65489e9i	−0.846389	+	0.873986i
$562$	−1.35700e9	−	1.35700e9i	−0.322480	−	0.322480i
$563$	1.21787e9	+	1.21787e9i	0.287622	+	0.287622i	0.836139	−	0.548517i	$-0.184808\pi$
$563$	1.21787e9	+	1.21787e9i	0.287622	+	0.287622i	−0.548517	+	0.836139i	$0.684808\pi$
$564$	−1.38880e8	+	1.43408e8i	−0.0325959	+	0.0336587i
$565$		0			0
$566$			3.83223e9i			0.888370i
$567$	3.36128e9	+	2.95544e9i	0.774399	+	0.680897i
$568$	−1.23607e7	+	1.23607e7i	−0.00283024	+	0.00283024i
$569$	1.05145e9			0.239274			0.119637	−	0.992818i	$-0.461827\pi$
$569$	1.05145e9			0.239274			0.119637	+	0.992818i	$0.461827\pi$
$570$		0			0
$571$	4.36857e9			0.982004			0.491002	−	0.871159i	$-0.336631\pi$
$571$	4.36857e9			0.982004			0.491002	+	0.871159i	$0.336631\pi$
$572$	−1.81686e9	+	1.81686e9i	−0.405916	+	0.405916i
$573$	4.01558e9	−	6.44162e7i	0.891677	−	0.0143039i
$574$			3.89927e9i			0.860581i
$575$		0			0
$576$	−1.83888e7	−	5.73014e8i	−0.00400935	−	0.124936i
$577$	5.02534e9	+	5.02534e9i	1.08906	+	1.08906i	0.995626	+	0.0934291i	$0.0297828\pi$
$577$	5.02534e9	+	5.02534e9i	1.08906	+	1.08906i	0.0934291	+	0.995626i	$0.470217\pi$
$578$	−8.18959e8	−	8.18959e8i	−0.176407	−	0.176407i
$579$	1.61290e9	+	1.56197e9i	0.345329	+	0.334424i
$580$		0			0
$581$		−	6.93747e9i		−	1.46752i
$582$	−968993.	−	6.04052e7i	−0.000203747	−	0.0127012i
$583$	2.10710e9	−	2.10710e9i	0.440398	−	0.440398i
$584$	1.67342e9			0.347665
$585$		0			0
$586$	1.58942e9			0.326286
$587$	2.79539e9	−	2.79539e9i	0.570438	−	0.570438i	−0.361813	−	0.932251i	$-0.617842\pi$
$587$	2.79539e9	−	2.79539e9i	0.570438	−	0.570438i	0.932251	+	0.361813i	$0.117842\pi$
$588$	−2.50313e6	−	1.56040e8i	−0.000507765	−	0.0316531i
$589$			8.71750e9i			1.75788i
$590$		0			0
$591$	−1.01163e9	−	9.79684e8i	−0.201588	−	0.195222i
$592$	3.53641e8	+	3.53641e8i	0.0700546	+	0.0700546i
$593$	1.16539e8	+	1.16539e8i	0.0229499	+	0.0229499i	0.718489	−	0.695539i	$-0.244834\pi$
$593$	1.16539e8	+	1.16539e8i	0.0229499	+	0.0229499i	−0.695539	+	0.718489i	$0.744834\pi$
$594$	−3.67226e9	+	4.04385e9i	−0.718921	+	0.791667i
$595$		0			0
$596$		−	2.77344e9i		−	0.536607i
$597$	−5.13373e9	+	8.23529e7i	−0.987467	+	0.0158405i
$598$	−1.77199e9	+	1.77199e9i	−0.338850	+	0.338850i
$599$	−6.39357e9			−1.21548			−0.607742	−	0.794134i	$-0.707925\pi$
$599$	−6.39357e9			−1.21548			−0.607742	+	0.794134i	$0.707925\pi$
$600$		0			0
$601$	−4.56178e9			−0.857183			−0.428592	−	0.903498i	$-0.640990\pi$
$601$	−4.56178e9			−0.857183			−0.428592	+	0.903498i	$0.640990\pi$
$602$	−3.74051e9	+	3.74051e9i	−0.698784	+	0.698784i
$603$	5.46687e8	+	5.12690e8i	0.101538	+	0.0952236i
$604$			4.02932e9i			0.744050i
$605$		0			0
$606$	3.14190e9	−	3.24434e9i	0.573506	−	0.592205i
$607$	6.56778e9	+	6.56778e9i	1.19195	+	1.19195i	0.976519	+	0.215433i	$0.0691161\pi$
$607$	6.56778e9	+	6.56778e9i	1.19195	+	1.19195i	0.215433	+	0.976519i	$0.430884\pi$
$608$	1.30981e9	+	1.30981e9i	0.236345	+	0.236345i
$609$	−1.04647e9	+	1.08059e9i	−0.187744	+	0.193866i
$610$		0			0
$611$		−	4.01109e8i		−	0.0711408i
$612$	1.66377e9	+	1.56031e9i	0.293403	+	0.275157i
$613$	−4.99817e9	+	4.99817e9i	−0.876394	+	0.876394i	−0.993159	−	0.116766i	$-0.962747\pi$
$613$	−4.99817e9	+	4.99817e9i	−0.876394	+	0.876394i	0.116766	+	0.993159i	$0.462747\pi$
$614$	−5.26346e9			−0.917660
$615$		0			0
$616$	3.19866e9			0.551360
$617$	−2.34903e9	+	2.34903e9i	−0.402615	+	0.402615i	−0.879154	−	0.476539i	$-0.841891\pi$
$617$	−2.34903e9	+	2.34903e9i	−0.402615	+	0.402615i	0.476539	+	0.879154i	$0.341891\pi$
$618$	3.21151e9	−	5.15176e7i	0.547330	−	0.00878002i
$619$		−	8.82741e9i		−	1.49595i	−0.663729	−	0.747973i	$-0.731027\pi$
$619$		−	8.82741e9i		−	1.49595i	0.663729	−	0.747973i	$-0.268973\pi$
$620$		0			0
$621$	−3.58157e9	+	3.94399e9i	−0.600141	+	0.660868i
$622$	−1.88764e9	−	1.88764e9i	−0.314523	−	0.314523i
$623$	−3.42756e9	−	3.42756e9i	−0.567906	−	0.567906i
$624$	8.27482e8	+	8.01353e8i	0.136337	+	0.132032i
$625$		0			0
$626$			1.90905e9i			0.311034i
$627$	−2.83083e8	−	1.76468e10i	−0.0458645	−	2.85911i
$628$	−1.29727e9	+	1.29727e9i	−0.209012	+	0.209012i
$629$	−1.98977e9			−0.318806
$630$		0			0
$631$	−2.05327e9			−0.325345			−0.162672	−	0.986680i	$-0.552011\pi$
$631$	−2.05327e9			−0.325345			−0.162672	+	0.986680i	$0.552011\pi$
$632$	2.83378e9	−	2.83378e9i	0.446535	−	0.446535i
$633$	−1.41413e8	−	8.81544e9i	−0.0221604	−	1.38144i
$634$		−	6.02159e9i		−	0.938423i
$635$		0			0
$636$	−9.59669e8	−	9.29366e8i	−0.147918	−	0.143247i
$637$	2.21721e8	+	2.21721e8i	0.0339875	+	0.0339875i
$638$	−1.29814e9	−	1.29814e9i	−0.197901	−	0.197901i
$639$	−2.39498e6	−	7.46299e7i	−0.000363118	−	0.0113151i
$640$		0			0
$641$			4.55381e9i			0.682923i	0.939896	+	0.341461i	$0.110922\pi$
$641$			4.55381e9i			0.682923i	−0.939896	+	0.341461i	$0.889078\pi$
$642$	−1.18618e9	+	1.90282e7i	−0.176921	+	0.00283808i
$643$	−6.29461e9	+	6.29461e9i	−0.933750	+	0.933750i	−0.997938	−	0.0641883i	$-0.979554\pi$
$643$	−6.29461e9	+	6.29461e9i	−0.933750	+	0.933750i	0.0641883	+	0.997938i	$0.479554\pi$
$644$	3.11966e9			0.460264
$645$		0			0
$646$	−7.36972e9			−1.07557
$647$	−7.40915e9	+	7.40915e9i	−1.07548	+	1.07548i	−0.0785738	+	0.996908i	$0.525037\pi$
$647$	−7.40915e9	+	7.40915e9i	−1.07548	+	1.07548i	−0.996908	+	0.0785738i	$0.974963\pi$
$648$	1.83908e9	+	1.61703e9i	0.265515	+	0.233456i
$649$			6.99999e9i			1.00517i
$650$		0			0
$651$	4.69484e9	−	4.84792e9i	0.666941	−	0.688688i
$652$	−2.39706e9	−	2.39706e9i	−0.338698	−	0.338698i
$653$	7.12337e9	+	7.12337e9i	1.00113	+	1.00113i	0.999999	+	0.00112784i	$0.000359002\pi$
$653$	7.12337e9	+	7.12337e9i	1.00113	+	1.00113i	0.00112784	+	0.999999i	$0.499641\pi$
$654$	5.41436e9	−	5.59091e9i	0.756877	−	0.781556i
$655$		0			0
$656$			2.13344e9i			0.295064i
$657$	−4.88968e9	+	5.21392e9i	−0.672669	+	0.717274i
$658$	−3.53084e8	+	3.53084e8i	−0.0483157	+	0.0483157i
$659$	4.96125e9			0.675294			0.337647	−	0.941273i	$-0.390369\pi$
$659$	4.96125e9			0.675294			0.337647	+	0.941273i	$0.390369\pi$
$660$		0			0
$661$	−2.47575e7			−0.00333428			−0.00166714	−	0.999999i	$-0.500531\pi$
$661$	−2.47575e7			−0.00333428			−0.00166714	+	0.999999i	$0.500531\pi$
$662$	−5.08318e9	+	5.08318e9i	−0.680977	+	0.680977i
$663$	−4.58235e9	+	7.35079e7i	−0.610648	+	0.00979573i
$664$		−	3.79575e9i		−	0.503163i
$665$		0			0
$666$	−2.13517e9	+	6.85205e7i	−0.280074	+	0.00898795i
$667$	−1.26608e9	−	1.26608e9i	−0.165204	−	0.165204i
$668$	−1.64512e9	−	1.64512e9i	−0.213540	−	0.213540i
$669$	8.05676e9	+	7.80236e9i	1.04032	+	1.00748i
$670$		0			0
$671$			8.02026e9i			1.02485i
$672$	−2.30006e7	−	1.43381e9i	−0.00292379	−	0.182264i
$673$	−7.83270e9	+	7.83270e9i	−0.990510	+	0.990510i	−0.999955	−	0.00944549i	$-0.996993\pi$
$673$	−7.83270e9	+	7.83270e9i	−0.990510	+	0.990510i	0.00944549	+	0.999955i	$0.496993\pi$
$674$	4.88925e9			0.615081
$675$		0			0
$676$	1.70146e9			0.211840
$677$	−5.20965e9	+	5.20965e9i	−0.645280	+	0.645280i	−0.951849	−	0.306568i	$-0.900819\pi$
$677$	−5.20965e9	+	5.20965e9i	−0.645280	+	0.645280i	0.306568	+	0.951849i	$0.400819\pi$
$678$	1.00602e8	+	6.27135e9i	0.0123966	+	0.772783i
$679$		−	1.51109e8i		−	0.0185245i
$680$		0			0
$681$	−8.81275e9	−	8.53447e9i	−1.06929	−	1.03553i
$682$	5.82392e9	+	5.82392e9i	0.703024	+	0.703024i
$683$	3.27856e9	+	3.27856e9i	0.393741	+	0.393741i	0.876019	−	0.482277i	$-0.160190\pi$
$683$	3.27856e9	+	3.27856e9i	0.393741	+	0.393741i	−0.482277	+	0.876019i	$0.660190\pi$
$684$	−7.90824e9	+	2.53786e8i	−0.944895	+	0.0303230i
$685$		0			0
$686$			5.77490e9i			0.682983i
$687$	−4.72183e9	+	7.57454e7i	−0.555599	+	0.00891266i
$688$	−2.04657e9	+	2.04657e9i	−0.239589	+	0.239589i
$689$	2.68417e9			0.312639
$690$		0			0
$691$	−4.22632e9			−0.487292			−0.243646	−	0.969864i	$-0.578343\pi$
$691$	−4.22632e9			−0.487292			−0.243646	+	0.969864i	$0.578343\pi$
$692$	5.38367e9	−	5.38367e9i	0.617600	−	0.617600i
$693$	−9.34635e9	+	9.96612e9i	−1.06678	+	1.13752i
$694$			8.13193e9i			0.923497i
$695$		0			0
$696$	−5.72562e8	+	5.91231e8i	−0.0643710	+	0.0664699i
$697$	−6.00193e9	−	6.00193e9i	−0.671392	−	0.671392i
$698$	−1.83761e9	−	1.83761e9i	−0.204531	−	0.204531i
$699$	−3.33690e9	+	3.44570e9i	−0.369550	+	0.381600i
$700$		0			0
$701$			8.01143e9i			0.878410i	0.898387	+	0.439205i	$0.144740\pi$
$701$			8.01143e9i			0.878410i	−0.898387	+	0.439205i	$0.855260\pi$
$702$	−4.91466e9	+	2.36679e8i	−0.536184	+	0.0258214i
$703$	4.88065e9	−	4.88065e9i	0.529826	−	0.529826i
$704$	1.75010e9			0.189042
$705$		0			0
$706$	−9.31566e9			−0.996316
$707$	7.98786e9	−	7.98786e9i	0.850086	−	0.850086i
$708$	3.13778e9	−	5.03348e7i	0.332281	−	0.00533031i
$709$		−	6.28682e9i		−	0.662474i	−0.943548	−	0.331237i	$-0.892534\pi$
$709$		−	6.28682e9i		−	0.662474i	0.943548	−	0.331237i	$-0.107466\pi$
$710$		0			0
$711$	5.49065e8	+	1.71094e10i	0.0572902	+	1.78522i
$712$	−1.87534e9	−	1.87534e9i	−0.194715	−	0.194715i
$713$	5.68009e9	+	5.68009e9i	0.586870	+	0.586870i
$714$	4.09841e9	+	3.96899e9i	0.421377	+	0.408072i
$715$		0			0
$716$		−	5.65604e9i		−	0.575860i
$717$	2.82506e8	+	1.76109e10i	0.0286227	+	1.78429i
$718$	1.42079e9	−	1.42079e9i	0.143250	−	0.143250i
$719$	2.58283e9			0.259146			0.129573	−	0.991570i	$-0.458639\pi$
$719$	2.58283e9			0.259146			0.129573	+	0.991570i	$0.458639\pi$
$720$		0			0
$721$	8.03387e9			0.798273
$722$	1.30204e10	−	1.30204e10i	1.28749	−	1.28749i
$723$	5.21195e7	+	3.24903e9i	0.00512881	+	0.319720i
$724$			1.82847e9i			0.179062i
$725$		0			0
$726$	−6.74124e9	−	6.52837e9i	−0.653825	−	0.633179i
$727$	−1.10330e10	−	1.10330e10i	−1.06494	−	1.06494i	−0.997740	−	0.0671994i	$-0.978594\pi$
$727$	−1.10330e10	−	1.10330e10i	−1.06494	−	1.06494i	−0.0671994	−	0.997740i	$-0.521406\pi$
$728$	2.03733e9	+	2.03733e9i	0.195705	+	0.195705i
$729$	−1.04119e10	+	1.00516e9i	−0.995372	+	0.0960925i
$730$		0			0
$731$		−	1.15151e10i		−	1.09033i
$732$	3.59512e9	−	5.76713e7i	0.338785	−	0.00543464i
$733$	8.27693e9	−	8.27693e9i	0.776257	−	0.776257i	−0.202935	−	0.979192i	$-0.565048\pi$
$733$	8.27693e9	−	8.27693e9i	0.776257	−	0.776257i	0.979192	+	0.202935i	$0.0650481\pi$
$734$	6.52912e9			0.609423
$735$		0			0
$736$	1.70688e9			0.157809
$737$	−1.61778e9	+	1.61778e9i	−0.148862	+	0.148862i
$738$	−6.64719e9	−	6.23382e9i	−0.608752	−	0.570896i
$739$			2.90689e9i			0.264955i	0.991186	+	0.132478i	$0.0422933\pi$
$739$			2.90689e9i			0.264955i	−0.991186	+	0.132478i	$0.957707\pi$
$740$		0			0
$741$	1.10596e10	−	1.14202e10i	0.998561	−	1.03112i
$742$	−2.36279e9	−	2.36279e9i	−0.212330	−	0.212330i
$743$	1.41461e10	+	1.41461e10i	1.26524	+	1.26524i	0.948516	+	0.316728i	$0.102584\pi$
$743$	1.41461e10	+	1.41461e10i	1.26524	+	1.26524i	0.316728	+	0.948516i	$0.397416\pi$
$744$	2.56872e9	−	2.65248e9i	0.228671	−	0.236127i
$745$		0			0
$746$		−	1.29548e10i		−	1.14247i
$747$	1.18265e10	+	1.10910e10i	1.03809	+	0.973531i
$748$	−4.92351e9	+	4.92351e9i	−0.430149	+	0.430149i
$749$	−2.96734e9			−0.258036
$750$		0			0
$751$	6.52059e9			0.561756			0.280878	−	0.959744i	$-0.409374\pi$
$751$	6.52059e9			0.561756			0.280878	+	0.959744i	$0.409374\pi$
$752$	−1.93185e8	+	1.93185e8i	−0.0165658	+	0.0165658i
$753$	8.92711e9	−	1.43205e8i	0.761954	−	0.0122229i
$754$		−	1.65366e9i		−	0.140490i
$755$		0			0
$756$	4.53457e9	+	4.11788e9i	0.381689	+	0.346615i
$757$	−3.49234e9	−	3.49234e9i	−0.292604	−	0.292604i	0.545504	−	0.838108i	$-0.316338\pi$
$757$	−3.49234e9	−	3.49234e9i	−0.292604	−	0.292604i	−0.838108	+	0.545504i	$0.816338\pi$
$758$	3.53018e9	+	3.53018e9i	0.294411	+	0.294411i
$759$	−1.16827e10	−	1.13138e10i	−0.969831	−	0.939207i
$760$		0			0
$761$			1.40877e10i			1.15876i	0.815058	+	0.579379i	$0.196705\pi$
$761$			1.40877e10i			1.15876i	−0.815058	+	0.579379i	$0.803295\pi$
$762$	−7.16609e7	−	4.46721e9i	−0.00586732	−	0.365758i
$763$	1.37653e10	−	1.37653e10i	1.12189	−	1.12189i
$764$	5.49617e9			0.445896
$765$		0			0
$766$	−1.27359e9			−0.102383
$767$	−4.45854e9	+	4.45854e9i	−0.356787	+	0.356787i
$768$	−1.25845e7	−	7.84492e8i	−0.00100247	−	0.0624920i
$769$			1.74258e10i			1.38182i	0.722941	+	0.690910i	$0.242790\pi$
$769$			1.74258e10i			1.38182i	−0.722941	+	0.690910i	$0.757210\pi$
$770$		0			0
$771$	5.52385e9	+	5.34943e9i	0.434062	+	0.420356i
$772$	2.17274e9	+	2.17274e9i	0.169960	+	0.169960i
$773$	−9.20009e9	−	9.20009e9i	−0.716414	−	0.716414i	0.251455	−	0.967869i	$-0.419091\pi$
$773$	−9.20009e9	−	9.20009e9i	−0.716414	−	0.716414i	−0.967869	+	0.251455i	$0.919091\pi$
$774$	−3.96538e8	−	1.23565e10i	−0.0307391	−	0.957864i
$775$		0			0
$776$		−	8.26772e7i		−	0.00635141i
$777$	−5.34269e9	+	8.57050e7i	−0.408589	+	0.00655439i
$778$	2.94133e9	−	2.94133e9i	0.223931	−	0.223931i
$779$	2.94438e10			2.23158
$780$		0			0
$781$	2.27935e8			0.0171211
$782$	−4.80192e9	+	4.80192e9i	−0.359080	+	0.359080i
$783$	−1.69106e8	−	3.51150e9i	−0.0125890	−	0.261412i
$784$		−	2.13574e8i		−	0.0158286i
$785$		0			0
$786$	3.78535e9	−	3.90877e9i	0.278053	−	0.287119i
$787$	−1.64623e9	−	1.64623e9i	−0.120387	−	0.120387i	0.644347	−	0.764733i	$-0.277129\pi$
$787$	−1.64623e9	−	1.64623e9i	−0.120387	−	0.120387i	−0.764733	+	0.644347i	$0.777129\pi$
$788$	−1.36276e9	−	1.36276e9i	−0.0992153	−	0.0992153i
$789$	−1.35287e9	+	1.39699e9i	−0.0980590	+	0.101256i
$790$		0			0
$791$			1.56883e10i			1.12709i
$792$	−5.11373e9	+	5.45283e9i	−0.365763	+	0.390017i
$793$	−5.10838e9	+	5.10838e9i	−0.363770	+	0.363770i
$794$	−9.93096e9			−0.704076
$795$		0			0
$796$	−7.02659e9			−0.493797
$797$	1.45349e10	−	1.45349e10i	1.01697	−	1.01697i	0.0171143	−	0.999854i	$-0.494552\pi$
$797$	1.45349e10	−	1.45349e10i	1.01697	−	1.01697i	0.999854	−	0.0171143i	$-0.00544791\pi$
$798$	−1.97882e10	+	3.17434e8i	−1.37847	+	0.0221128i
$799$		−	1.08697e9i		−	0.0753879i
$800$		0			0
$801$	1.13227e10	−	3.63361e8i	0.778461	−	0.0249819i
$802$	−1.01287e10	−	1.01287e10i	−0.693338	−	0.693338i
$803$	−1.54292e10	−	1.54292e10i	−1.05157	−	1.05157i
$804$	7.36810e8	+	7.13544e8i	0.0499988	+	0.0484200i
$805$		0			0
$806$			7.41891e9i			0.499077i
$807$	−6.79386e6	−	4.23516e8i	−0.000455050	−	0.0283670i
$808$	4.37045e9	−	4.37045e9i	0.291465	−	0.291465i
$809$	−1.44299e9			−0.0958174			−0.0479087	−	0.998852i	$-0.515256\pi$
$809$	−1.44299e9			−0.0958174			−0.0479087	+	0.998852i	$0.515256\pi$
$810$		0			0
$811$	4.73097e9			0.311442			0.155721	−	0.987801i	$-0.450230\pi$
$811$	4.73097e9			0.311442			0.155721	+	0.987801i	$0.450230\pi$
$812$	−1.45566e9	+	1.45566e9i	−0.0954146	+	0.0954146i
$813$	−2.40354e7	−	1.49832e9i	−0.00156868	−	0.0977884i
$814$		−	6.52125e9i		−	0.423785i
$815$		0			0
$816$	2.24239e9	+	2.17158e9i	0.144476	+	0.139914i
$817$	2.82450e10	+	2.82450e10i	1.81203	+	1.81203i
$818$	2.72145e9	+	2.72145e9i	0.173846	+	0.173846i
$819$	−1.23008e10	+	3.94749e8i	−0.782418	+	0.0251089i
$820$		0			0
$821$			5.46533e9i			0.344679i	0.985038	+	0.172340i	$0.0551327\pi$
$821$			5.46533e9i			0.344679i	−0.985038	+	0.172340i	$0.944867\pi$
$822$	2.97818e9	−	4.77747e7i	0.187025	−	0.00300017i
$823$	−3.47565e9	+	3.47565e9i	−0.217338	+	0.217338i	−0.807376	−	0.590038i	$-0.799113\pi$
$823$	−3.47565e9	+	3.47565e9i	−0.217338	+	0.217338i	0.590038	+	0.807376i	$0.299113\pi$
$824$	4.39563e9			0.273700
$825$		0			0
$826$	7.84942e9			0.484627
$827$	2.27169e10	−	2.27169e10i	1.39662	−	1.39662i	0.587132	−	0.809491i	$-0.300257\pi$
$827$	2.27169e10	−	2.27169e10i	1.39662	−	1.39662i	0.809491	−	0.587132i	$-0.199743\pi$
$828$	−4.98745e9	+	5.31817e9i	−0.305332	+	0.325578i
$829$		−	6.24125e9i		−	0.380479i	−0.981738	−	0.190240i	$-0.939074\pi$
$829$		−	6.24125e9i		−	0.380479i	0.981738	−	0.190240i	$-0.0609265\pi$
$830$		0			0
$831$	1.98682e8	−	2.05161e8i	0.0120103	−	0.0124020i
$832$	1.11470e9	+	1.11470e9i	0.0671006	+	0.0671006i
$833$	6.00841e8	+	6.00841e8i	0.0360166	+	0.0360166i
$834$	−1.23439e10	+	1.27464e10i	−0.736838	+	0.760864i
$835$		0			0
$836$		−	2.41534e10i		−	1.42974i
$837$	7.58670e8	+	1.57539e10i	0.0447212	+	0.928641i
$838$	−6.05227e9	+	6.05227e9i	−0.355275	+	0.355275i
$839$	1.93981e10			1.13395			0.566973	−	0.823736i	$-0.308114\pi$
$839$	1.93981e10			1.13395			0.566973	+	0.823736i	$0.308114\pi$
$840$		0			0
$841$	−1.60683e10			−0.931505
$842$	−1.48810e10	+	1.48810e10i	−0.859095	+	0.859095i
$843$	1.12169e10	−	1.79937e8i	0.644877	−	0.0103448i
$844$		−	1.20658e10i		−	0.690807i
$845$		0			0
$846$	−3.74311e7	−	1.16639e9i	−0.00212538	−	0.0662291i
$847$	−1.65975e10	−	1.65975e10i	−0.938538	−	0.938538i
$848$	−1.29277e9	−	1.29277e9i	−0.0728007	−	0.0728007i
$849$	−1.60926e10	−	1.55845e10i	−0.902504	−	0.874006i
$850$		0			0
$851$		−	6.36020e9i		−	0.353767i
$852$	−1.63901e6	−	1.02173e8i	−9.07912e−5	−	0.00565976i
$853$	1.82356e10	−	1.82356e10i	1.00600	−	1.00600i	0.00601662	−	0.999982i	$-0.498085\pi$
$853$	1.82356e10	−	1.82356e10i	1.00600	−	1.00600i	0.999982	−	0.00601662i	$-0.00191516\pi$
$854$	8.99351e9			0.494113
$855$		0			0
$856$	−1.62354e9			−0.0884717
$857$	−7.54295e9	+	7.54295e9i	−0.409363	+	0.409363i	−0.881516	−	0.472154i	$-0.843477\pi$
$857$	−7.54295e9	+	7.54295e9i	−0.409363	+	0.409363i	0.472154	+	0.881516i	$0.343477\pi$
$858$	−2.40914e8	−	1.50181e10i	−0.0130214	−	0.811727i
$859$			2.51811e9i			0.135550i	0.997701	+	0.0677748i	$0.0215899\pi$
$859$			2.51811e9i			0.135550i	−0.997701	+	0.0677748i	$0.978410\pi$
$860$		0			0
$861$	−1.63741e10	−	1.58571e10i	−0.874274	−	0.846667i
$862$	−1.88762e9	−	1.88762e9i	−0.100378	−	0.100378i
$863$	−5.60021e9	−	5.60021e9i	−0.296597	−	0.296597i	0.543082	−	0.839679i	$-0.317257\pi$
$863$	−5.60021e9	−	5.60021e9i	−0.296597	−	0.296597i	−0.839679	+	0.543082i	$0.817257\pi$
$864$	2.48103e9	+	2.25305e9i	0.130868	+	0.118843i
$865$		0			0
$866$			1.27672e10i			0.668008i
$867$	6.76949e9	−	1.08593e8i	0.352768	−	0.00565894i
$868$	6.53064e9	−	6.53064e9i	0.338951	−	0.338951i
$869$	−5.22558e10			−2.70125
$870$		0			0
$871$	−2.06084e9			−0.105677
$872$	7.53151e9	−	7.53151e9i	0.384658	−	0.384658i
$873$	2.57599e8	+	2.41580e8i	0.0131037	+	0.0122888i
$874$		−	2.35569e10i		−	1.19352i
$875$		0			0
$876$	−6.80528e9	+	7.02717e9i	−0.342044	+	0.353196i
$877$	−1.05803e8	−	1.05803e8i	−0.00529661	−	0.00529661i	0.704454	−	0.709750i	$-0.251192\pi$
$877$	−1.05803e8	−	1.05803e8i	−0.00529661	−	0.00529661i	−0.709750	+	0.704454i	$0.751192\pi$
$878$	2.55669e9	+	2.55669e9i	0.127482	+	0.127482i
$879$	−6.46369e9	+	6.67444e9i	−0.321011	+	0.331477i
$880$		0			0
$881$		−	9.68685e8i		−	0.0477273i	−0.999715	−	0.0238637i	$-0.992403\pi$
$881$		−	9.68685e8i		−	0.0477273i	0.999715	−	0.0238637i	$-0.00759676\pi$
$882$	6.65437e8	+	6.24056e8i	0.0326563	+	0.0306255i
$883$	−5.01947e9	+	5.01947e9i	−0.245355	+	0.245355i	−0.819061	−	0.573706i	$-0.805505\pi$
$883$	−5.01947e9	+	5.01947e9i	−0.245355	+	0.245355i	0.573706	+	0.819061i	$0.305505\pi$
$884$	−6.27190e9			−0.305363
$885$		0			0
$886$	−6.79839e9			−0.328388
$887$	−5.70163e9	+	5.70163e9i	−0.274326	+	0.274326i	−0.830839	−	0.556513i	$-0.812139\pi$
$887$	−5.70163e9	+	5.70163e9i	−0.274326	+	0.274326i	0.556513	+	0.830839i	$0.312139\pi$
$888$	−2.92318e9	+	4.68924e7i	−0.140091	+	0.00224728i
$889$		−	1.11751e10i		−	0.533452i
$890$		0			0
$891$	−2.04735e9	−	3.18659e10i	−0.0969661	−	1.50923i
$892$	1.08533e10	+	1.08533e10i	0.512016	+	0.512016i
$893$	2.66618e9	+	2.66618e9i	0.125288	+	0.125288i
$894$	1.16464e10	+	1.12787e10i	0.545145	+	0.527931i
$895$		0			0
$896$		−	1.96247e9i		−	0.0911435i
$897$	−2.34964e8	−	1.46472e10i	−0.0108700	−	0.677613i
$898$	1.74548e10	−	1.74548e10i	0.804354	−	0.804354i
$899$	−5.30077e9			−0.243321
$900$		0			0
$901$	7.27382e9			0.331303
$902$	1.96706e10	−	1.96706e10i	0.892473	−	0.892473i
$903$	−4.95987e8	−	3.09189e10i	−0.0224163	−	1.39739i
$904$			8.58366e9i			0.386441i
$905$		0			0
$906$	−1.69202e10	−	1.63860e10i	−0.755888	−	0.732020i
$907$	7.14355e9	+	7.14355e9i	0.317898	+	0.317898i	0.847959	−	0.530061i	$-0.177831\pi$
$907$	7.14355e9	+	7.14355e9i	0.317898	+	0.317898i	−0.530061	+	0.847959i	$0.677831\pi$
$908$	−1.18717e10	−	1.18717e10i	−0.526273	−	0.526273i
$909$	8.46808e8	+	2.63874e10i	0.0373948	+	1.16526i
$910$		0			0
$911$		−	7.12663e9i		−	0.312298i	−0.987733	−	0.156149i	$-0.950092\pi$
$911$		−	7.12663e9i		−	0.312298i	0.987733	−	0.156149i	$-0.0499081\pi$
$912$	−1.08269e10	+	1.73680e8i	−0.472630	+	0.00758172i
$913$	−3.49974e10	+	3.49974e10i	−1.52191	+	1.52191i
$914$	−2.40987e10			−1.04396
$915$		0			0
$916$	−6.46281e9			−0.277835
$917$	9.62375e9	−	9.62375e9i	0.412147	−	0.412147i
$918$	−1.33182e10	+	6.41375e8i	−0.568194	+	0.0273629i
$919$		−	7.47046e9i		−	0.317500i	−0.987319	−	0.158750i	$-0.949254\pi$
$919$		−	7.47046e9i		−	0.317500i	0.987319	−	0.158750i	$-0.0507463\pi$
$920$		0			0
$921$	2.14048e10	−	2.21027e10i	0.902823	−	0.932260i
$922$	2.00925e10	+	2.00925e10i	0.844259	+	0.844259i
$923$	1.45180e8	+	1.45180e8i	0.00607715	+	0.00607715i
$924$	−1.30079e10	+	1.34321e10i	−0.542445	+	0.560132i
$925$		0			0
$926$			6.21275e9i			0.257126i
$927$	−1.28439e10	+	1.36955e10i	−0.529561	+	0.564677i
$928$	−7.96447e8	+	7.96447e8i	−0.0327144	+	0.0327144i
$929$	2.65804e10			1.08769			0.543847	−	0.839184i	$-0.316967\pi$
$929$	2.65804e10			1.08769			0.543847	+	0.839184i	$0.316967\pi$
$930$		0			0
$931$	−2.94757e9			−0.119713
$932$	−4.64171e9	+	4.64171e9i	−0.187812	+	0.187812i
$933$	1.56031e10	−	2.50299e8i	0.628965	−	0.0100896i
$934$		−	2.92854e9i		−	0.117608i
$935$		0			0
$936$	−6.73021e9	+	2.15982e8i	−0.268264	+	0.00860897i
$937$	−4.69611e9	−	4.69611e9i	−0.186488	−	0.186488i	0.607688	−	0.794176i	$-0.292097\pi$
$937$	−4.69611e9	−	4.69611e9i	−0.186488	−	0.186488i	−0.794176	+	0.607688i	$0.792097\pi$
$938$	1.81409e9	+	1.81409e9i	0.0717711	+	0.0717711i
$939$	−8.01664e9	−	7.76350e9i	−0.315982	−	0.306005i
$940$		0			0
$941$			1.48675e10i			0.581668i	0.956774	+	0.290834i	$0.0939327\pi$
$941$			1.48675e10i			0.581668i	−0.956774	+	0.290834i	$0.906067\pi$
$942$	−1.72016e8	−	1.07232e10i	−0.00670488	−	0.417970i
$943$	1.91848e10	−	1.91848e10i	0.745019	−	0.745019i
$944$	4.29471e9			0.166162
$945$		0			0
$946$	3.77394e10			1.44936
$947$	−2.02863e10	+	2.02863e10i	−0.776209	+	0.776209i	−0.979184	−	0.202975i	$-0.934939\pi$
$947$	−2.02863e10	+	2.02863e10i	−0.776209	+	0.776209i	0.202975	+	0.979184i	$0.434939\pi$
$948$	3.75755e8	+	2.34239e10i	0.0143244	+	0.892956i
$949$		−	1.96548e10i		−	0.746513i
$950$		0			0
$951$	2.52864e10	+	2.44879e10i	0.953355	+	0.923251i
$952$	5.52097e9	+	5.52097e9i	0.207389	+	0.207389i
$953$	9.35730e9	+	9.35730e9i	0.350208	+	0.350208i	0.860187	−	0.509979i	$-0.170347\pi$
$953$	9.35730e9	+	9.35730e9i	0.350208	+	0.350208i	−0.509979	+	0.860187i	$0.670347\pi$
$954$	7.80534e9	−	2.50484e8i	0.291053	−	0.00934029i
$955$		0			0
$956$			2.41042e10i			0.892258i
$957$	1.07304e10	−	1.72132e8i	0.395751	−	0.00634846i
$958$	−8.77478e9	+	8.77478e9i	−0.322446	+	0.322446i
$959$	7.45018e9			0.272773
$960$		0			0
$961$	−3.73141e9			−0.135626
$962$	4.15361e9	−	4.15361e9i	0.150423	−	0.150423i
$963$	4.74392e9	−	5.05849e9i	0.171177	−	0.182528i
$964$			4.44698e9i			0.159881i
$965$		0			0
$966$	−1.26867e10	+	1.31003e10i	−0.452822	+	0.467587i
$967$	1.14031e10	+	1.14031e10i	0.405537	+	0.405537i	0.880179	−	0.474642i	$-0.157423\pi$
$967$	1.14031e10	+	1.14031e10i	0.405537	+	0.405537i	−0.474642	+	0.880179i	$0.657423\pi$
$968$	−9.08112e9	−	9.08112e9i	−0.321792	−	0.321792i
$969$	2.99703e10	−	3.09475e10i	1.05818	−	1.09268i
$970$		0			0
$971$		−	3.89442e9i		−	0.136513i	−0.997668	−	0.0682567i	$-0.978256\pi$
$971$		−	3.89442e9i		−	0.136513i	0.997668	−	0.0682567i	$-0.0217437\pi$
$972$	−1.42693e10	+	1.14687e9i	−0.498393	+	0.0400574i
$973$	−3.13828e10	+	3.13828e10i	−1.09219	+	1.09219i
$974$	1.69988e10			0.589470
$975$		0			0
$976$	4.92068e9			0.169415
$977$	2.04105e10	−	2.04105e10i	0.700202	−	0.700202i	−0.264252	−	0.964454i	$-0.585125\pi$
$977$	2.04105e10	−	2.04105e10i	0.700202	−	0.700202i	0.964454	+	0.264252i	$0.0851250\pi$
$978$	1.98140e10	−	3.17847e8i	0.677309	−	0.0108651i
$979$			3.45819e10i			1.17790i
$980$		0			0
$981$	1.45929e9	+	4.54729e10i	0.0493513	+	1.53784i
$982$	−1.36802e10	−	1.36802e10i	−0.461002	−	0.461002i
$983$	2.15633e10	+	2.15633e10i	0.724066	+	0.724066i	0.969431	−	0.245365i	$-0.0789079\pi$
$983$	2.15633e10	+	2.15633e10i	0.724066	+	0.724066i	−0.245365	+	0.969431i	$0.578908\pi$
$984$	−8.95890e9	−	8.67600e9i	−0.299759	−	0.290293i
$985$		0			0
$986$		−	4.48124e9i		−	0.148877i
$987$	−4.68186e7	−	2.91858e9i	−0.00154992	−	0.0966189i
$988$	1.53841e10	−	1.53841e10i	0.507486	−	0.507486i
$989$	3.68074e10			1.20990
$990$		0			0
$991$	1.91180e10			0.623999			0.312000	−	0.950082i	$-0.399001\pi$
$991$	1.91180e10			0.623999			0.312000	+	0.950082i	$0.399001\pi$
$992$	3.57315e9	−	3.57315e9i	0.116215	−	0.116215i
$993$	−6.74024e8	−	4.20174e10i	−0.0218450	−	1.36178i
$994$		−	2.55595e8i		−	0.00825466i
$995$		0			0
$996$	1.59394e10	+	1.54361e10i	0.511169	+	0.495028i
$997$	3.08953e9	+	3.08953e9i	0.0987322	+	0.0987322i	0.754748	−	0.656015i	$-0.227759\pi$
$997$	3.08953e9	+	3.08953e9i	0.0987322	+	0.0987322i	−0.656015	+	0.754748i	$0.727759\pi$
$998$	1.70846e10	+	1.70846e10i	0.544061	+	0.544061i
$999$	8.39533e9	−	9.24484e9i	0.266415	−	0.293373i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	150.8.e.b.107.7		28
3.2	odd	2	inner	150.8.e.b.107.14		28
5.2	odd	4		30.8.e.a.23.1	yes	28
5.3	odd	4	inner	150.8.e.b.143.14		28
5.4	even	2		30.8.e.a.17.12	yes	28
15.2	even	4		30.8.e.a.23.12	yes	28
15.8	even	4	inner	150.8.e.b.143.7		28
15.14	odd	2		30.8.e.a.17.1	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
30.8.e.a.17.1	✓	28	15.14	odd	2
30.8.e.a.17.12	yes	28	5.4	even	2
30.8.e.a.23.1	yes	28	5.2	odd	4
30.8.e.a.23.12	yes	28	15.2	even	4
150.8.e.b.107.7		28	1.1	even	1	trivial
150.8.e.b.107.14		28	3.2	odd	2	inner
150.8.e.b.143.7		28	15.8	even	4	inner
150.8.e.b.143.14		28	5.3	odd	4	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:	\( N \)	\(=\)	\( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	150.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-5.65685 + 5.65685i) q^{2} +(-0.750092 - 46.7594i) q^{3} -64.0000i q^{4} +(268.754 + 260.268i) q^{6} +(661.697 + 661.697i) q^{7} +(362.039 + 362.039i) q^{8} +(-2185.87 + 70.1477i) q^{9} -6676.11i q^{11} +(-2992.60 + 48.0059i) q^{12} +(4252.25 - 4252.25i) q^{13} -7486.24 q^{14} -4096.00 q^{16} +(11523.1 - 11523.1i) q^{17} +(11968.4 - 12762.0i) q^{18} +56529.5i q^{19} +(30444.2 - 31436.8i) q^{21} +(37765.8 + 37765.8i) q^{22} +(36833.1 + 36833.1i) q^{23} +(16657.1 - 17200.3i) q^{24} +48108.7i q^{26} +(4919.67 + 102157. i) q^{27} +(42348.6 - 42348.6i) q^{28} -34373.4 q^{29} +154212. q^{31} +(23170.5 - 23170.5i) q^{32} +(-312171. + 5007.70i) q^{33} +130370. i q^{34} +(4489.45 + 139896. i) q^{36} +(-86338.1 - 86338.1i) q^{37} +(-319779. - 319779. i) q^{38} +(-202022. - 195643. i) q^{39} -520858. i q^{41} +(5615.37 + 350052. i) q^{42} +(499651. - 499651. i) q^{43} -427271. q^{44} -416719. q^{46} +(47164.4 - 47164.4i) q^{47} +(3072.38 + 191526. i) q^{48} +52142.1i q^{49} +(-547458. - 530171. i) q^{51} +(-272144. - 272144. i) q^{52} +(315618. + 315618. i) q^{53} +(-605720. - 550060. i) q^{54} +479120. i q^{56} +(2.64328e6 - 42402.3i) q^{57} +(194445. - 194445. i) q^{58} -1.04851e6 q^{59} -1.20134e6 q^{61} +(-872352. + 872352. i) q^{62} +(-1.49280e6 - 1.39997e6i) q^{63} +262144. i q^{64} +(1.73758e6 - 1.79423e6i) q^{66} +(-242323. - 242323. i) q^{67} +(-737481. - 737481. i) q^{68} +(1.69466e6 - 1.74992e6i) q^{69} +34141.9i q^{71} +(-816767. - 765975. i) q^{72} +(2.31111e6 - 2.31111e6i) q^{73} +976804. q^{74} +3.61789e6 q^{76} +(4.41756e6 - 4.41756e6i) q^{77} +(2.24953e6 - 36085.9i) q^{78} -7.82727e6i q^{79} +(4.77313e6 - 306668. i) q^{81} +(2.94642e6 + 2.94642e6i) q^{82} +(-5.24218e6 - 5.24218e6i) q^{83} +(-2.01196e6 - 1.94843e6i) q^{84} +5.65291e6i q^{86} +(25783.2 + 1.60728e6i) q^{87} +(2.41701e6 - 2.41701e6i) q^{88} -5.17995e6 q^{89} +5.62739e6 q^{91} +(2.35732e6 - 2.35732e6i) q^{92} +(-115673. - 7.21083e6i) q^{93} +533605. i q^{94} +(-1.10082e6 - 1.06606e6i) q^{96} +(-114183. - 114183. i) q^{97} +(-294960. - 294960. i) q^{98} +(468314. + 1.45931e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 52 q^{3} - 928 q^{6} + 1348 q^{7} - 3328 q^{12} + 21840 q^{13} - 114688 q^{16} - 50624 q^{18} - 142744 q^{21} + 47008 q^{22} - 212972 q^{27} + 86272 q^{28} - 44936 q^{31} - 1398788 q^{33} + 50432 q^{36}+ \cdots - 82948404 q^{97}+O(q^{100}) \) 28 * q + 52 * q^3 - 928 * q^6 + 1348 * q^7 - 3328 * q^12 + 21840 * q^13 - 114688 * q^16 - 50624 * q^18 - 142744 * q^21 + 47008 * q^22 - 212972 * q^27 + 86272 * q^28 - 44936 * q^31 - 1398788 * q^33 + 50432 * q^36 - 608088 * q^37 + 624032 * q^42 + 1288968 * q^43 - 1486208 * q^46 - 212992 * q^48 + 4263064 * q^51 - 1397760 * q^52 + 9921952 * q^57 + 416480 * q^58 - 14602248 * q^61 - 4050428 * q^63 + 10106816 * q^66 - 22755248 * q^67 + 3239936 * q^72 + 522380 * q^73 - 4901888 * q^76 - 8835840 * q^78 + 33339556 * q^81 - 22502528 * q^82 + 38505100 * q^87 + 3008512 * q^88 - 77623680 * q^91 - 70200824 * q^93 + 3801088 * q^96 - 82948404 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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