LMFDB - Embedded newform 42.28.d.a.41.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [42,28,Mod(41,42)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("42.41"); S:= CuspForms(chi, 28); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(42, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1])) N = Newforms(chi, 28, names="a")

Level:	$ N $	$=$	$ 42 = 2 \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 28 $
Character orbit:	$[\chi]$	$=$	42.d (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$193.979341432$
Analytic rank:	$0$
Dimension:	$72$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			41.11
Character	$\chi$	$=$	42.41
Dual form			42.28.d.a.41.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-8192.00i q^{2} +(-2.76049e6 + 72866.3i) q^{3} -6.71089e7 q^{4} +5.43718e9 q^{5} +(5.96921e8 + 2.26139e10i) q^{6} +(2.02300e11 - 1.57440e11i) q^{7} +5.49756e11i q^{8} +(7.61498e12 - 4.02293e11i) q^{9} -4.45414e13i q^{10} +1.42065e14i q^{11} +(1.85253e14 - 4.88998e12i) q^{12} +1.72209e15i q^{13} +(-1.28975e15 - 1.65724e15i) q^{14} +(-1.50093e16 + 3.96187e14i) q^{15} +4.50360e15 q^{16} +3.48884e16 q^{17} +(-3.29558e15 - 6.23819e16i) q^{18} -9.58862e16i q^{19} -3.64883e17 q^{20} +(-5.46973e17 + 4.49351e17i) q^{21} +1.16380e18 q^{22} -3.80211e18i q^{23} +(-4.00587e16 - 1.51759e18i) q^{24} +2.21123e19 q^{25} +1.41074e19 q^{26} +(-2.09917e19 + 1.66540e18i) q^{27} +(-1.35761e19 + 1.05656e19i) q^{28} -3.14510e19i q^{29} +(3.24557e18 + 1.22956e20i) q^{30} -4.59128e19i q^{31} -3.68935e19i q^{32} +(-1.03518e19 - 3.92169e20i) q^{33} -2.85806e20i q^{34} +(1.09994e21 - 8.56028e20i) q^{35} +(-5.11033e20 + 2.69974e19i) q^{36} -1.14939e20 q^{37} -7.85499e20 q^{38} +(-1.25483e20 - 4.75382e21i) q^{39} +2.98912e21i q^{40} -8.22935e20 q^{41} +(3.68108e21 + 4.48080e21i) q^{42} -6.76183e20 q^{43} -9.53383e21i q^{44} +(4.14040e22 - 2.18734e21i) q^{45} -3.11469e22 q^{46} +4.92175e22 q^{47} +(-1.24321e22 + 3.28161e20i) q^{48} +(1.61379e22 - 6.37000e22i) q^{49} -1.81144e23i q^{50} +(-9.63089e22 + 2.54219e21i) q^{51} -1.15568e23i q^{52} -1.33298e23i q^{53} +(1.36430e22 + 1.71964e23i) q^{54} +7.72433e23i q^{55} +(8.65534e22 + 1.11215e23i) q^{56} +(6.98687e21 + 2.64692e23i) q^{57} -2.57647e23 q^{58} -7.27488e23 q^{59} +(1.00725e24 - 2.65877e22i) q^{60} +9.98024e22i q^{61} -3.76118e23 q^{62} +(1.47717e24 - 1.28028e24i) q^{63} -3.02231e23 q^{64} +9.36333e24i q^{65} +(-3.21265e24 + 8.48016e22i) q^{66} -3.30747e24 q^{67} -2.34132e24 q^{68} +(2.77046e23 + 1.04957e25i) q^{69} +(-7.01258e24 - 9.01070e24i) q^{70} +9.60512e24i q^{71} +(2.21163e23 + 4.18638e24i) q^{72} -1.61000e25i q^{73} +9.41583e23i q^{74} +(-6.10408e25 + 1.61124e24i) q^{75} +6.43481e24i q^{76} +(2.23667e25 + 2.87397e25i) q^{77} +(-3.89433e25 + 1.02795e24i) q^{78} -1.96386e25 q^{79} +2.44869e25 q^{80} +(5.78261e25 - 6.12691e24i) q^{81} +6.74148e24i q^{82} +4.28555e24 q^{83} +(3.67068e25 - 3.01554e25i) q^{84} +1.89694e26 q^{85} +5.53929e24i q^{86} +(2.29172e24 + 8.68200e25i) q^{87} -7.81011e25 q^{88} +2.31808e26 q^{89} +(-1.79187e25 - 3.39182e26i) q^{90} +(2.71126e26 + 3.48379e26i) q^{91} +2.55155e26i q^{92} +(3.34550e24 + 1.26742e26i) q^{93} -4.03190e26i q^{94} -5.21350e26i q^{95} +(2.68829e24 + 1.01844e26i) q^{96} -8.59553e26i q^{97} +(-5.21830e26 - 1.32201e26i) q^{98} +(5.71518e25 + 1.08182e27i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - 4831838208 q^{4} + 173098572084 q^{7} + 10931690833860 q^{9} - 26\!\cdots\!68 q^{15} + 32\!\cdots\!12 q^{16} - 24\!\cdots\!00 q^{18} + 10\!\cdots\!36 q^{21} - 26\!\cdots\!80 q^{22} + 11\!\cdots\!60 q^{25}+ \cdots - 59\!\cdots\!40 q^{99}+O(q^{100}) $ 72 * q - 4831838208 * q^4 + 173098572084 * q^7 + 10931690833860 * q^9 - 26442633448919268 * q^15 + 324259173170675712 * q^16 - 242698684300492800 * q^18 + 1081562836793204136 * q^21 - 2684750441896673280 * q^22 + 112067860522999462560 * q^25 - 11616448532579352576 * q^28 - 400382102997890531328 * q^30 - 733613353459557335040 * q^36 + 2987518151389179781008 * q^37 + 5509242802593360042396 * q^39 + 7342334144630240477184 * q^42 + 38276543559094928933184 * q^43 - 47129436388964590682112 * q^46 - 246837558232318243206960 * q^49 + 180152926647992184062232 * q^51 + 2549537180400127603920132 * q^57 - 463456938429255032045568 * q^58 + 1774535091925374103191552 * q^60 + 1839194856473813675870064 * q^63 - 21760664753063325144711168 * q^64 - 5521386041924492099769264 * q^67 - 899114292517766427574272 * q^70 + 16287232997700706448179200 * q^72 - 127774240517705488068280320 * q^78 + 91626681768773661319484520 * q^79 + 25422207502947578014228992 * q^81 - 72582453321809332487061504 * q^84 - 112192359350687429664946176 * q^85 + 180170552279183749199953920 * q^88 + 1190684031659173062666572472 * q^91 + 1605040757349523360531558488 * q^93 - 5985962449271479573968162240 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/42\mathbb{Z}\right)^\times$.

$n$	$29$	$31$
$\chi(n)$	$-1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		−	8192.00i		−	0.707107i
$2$		−	8192.00i		−	0.707107i
$3$	−2.76049e6	+	72866.3i	−0.999652	+	0.0263870i
$3$	−2.76049e6	+	72866.3i	−0.999652	+	0.0263870i
$4$	−6.71089e7			−0.500000
$5$	5.43718e9			1.99195			0.995975	−	0.0896285i	$-0.0285680\pi$
$5$	5.43718e9			1.99195			0.995975	+	0.0896285i	$0.0285680\pi$
$6$	5.96921e8	+	2.26139e10i	0.0186584	+	0.706861i
$7$	2.02300e11	−	1.57440e11i	0.789172	−	0.614173i
$7$	2.02300e11	−	1.57440e11i	0.789172	−	0.614173i
$8$			5.49756e11i			0.353553i
$9$	7.61498e12	−	4.02293e11i	0.998607	−	0.0527556i
$10$		−	4.45414e13i		−	1.40852i
$11$			1.42065e14i			1.24076i	0.784303	+	0.620378i	$0.213021\pi$
$11$			1.42065e14i			1.24076i	−0.784303	+	0.620378i	$0.786979\pi$
$12$	1.85253e14	−	4.88998e12i	0.499826	−	0.0131935i
$13$			1.72209e15i			1.57696i	0.615058	+	0.788482i	$0.289133\pi$
$13$			1.72209e15i			1.57696i	−0.615058	+	0.788482i	$0.710867\pi$
$14$	−1.28975e15	−	1.65724e15i	−0.434286	−	0.558029i
$15$	−1.50093e16	+	3.96187e14i	−1.99126	+	0.0525616i
$16$	4.50360e15			0.250000
$17$	3.48884e16			0.854319			0.427160	−	0.904176i	$-0.359514\pi$
$17$	3.48884e16			0.854319			0.427160	+	0.904176i	$0.359514\pi$
$18$	−3.29558e15	−	6.23819e16i	−0.0373038	−	0.706122i
$19$		−	9.58862e16i		−	0.523097i	−0.965190	−	0.261549i	$-0.915767\pi$
$19$		−	9.58862e16i		−	0.523097i	0.965190	−	0.261549i	$-0.0842332\pi$
$20$	−3.64883e17			−0.995975
$21$	−5.46973e17	+	4.49351e17i	−0.772691	+	0.634783i
$22$	1.16380e18			0.877347
$23$		−	3.80211e18i		−	1.57289i	−0.617659	−	0.786446i	$-0.711919\pi$
$23$		−	3.80211e18i		−	1.57289i	0.617659	−	0.786446i	$-0.288081\pi$
$24$	−4.00587e16	−	1.51759e18i	−0.00932921	−	0.353430i
$25$	2.21123e19			2.96787
$26$	1.41074e19			1.11508
$27$	−2.09917e19	+	1.66540e18i	−0.996868	+	0.0790875i
$28$	−1.35761e19	+	1.05656e19i	−0.394586	+	0.307086i
$29$		−	3.14510e19i		−	0.569195i	−0.958647	−	0.284598i	$-0.908140\pi$
$29$		−	3.14510e19i		−	0.569195i	0.958647	−	0.284598i	$-0.0918600\pi$
$30$	3.24557e18	+	1.22956e20i	0.0371666	+	1.40803i
$31$		−	4.59128e19i		−	0.337716i	−0.985640	−	0.168858i	$-0.945992\pi$
$31$		−	4.59128e19i		−	0.337716i	0.985640	−	0.168858i	$-0.0540079\pi$
$32$		−	3.68935e19i		−	0.176777i
$33$	−1.03518e19	−	3.92169e20i	−0.0327398	−	1.24032i
$34$		−	2.85806e20i		−	0.604095i
$35$	1.09994e21	−	8.56028e20i	1.57199	−	1.22340i
$36$	−5.11033e20	+	2.69974e19i	−0.499304	+	0.0263778i
$37$	−1.14939e20			−0.0775792			−0.0387896	−	0.999247i	$-0.512350\pi$
$37$	−1.14939e20			−0.0775792			−0.0387896	+	0.999247i	$0.512350\pi$
$38$	−7.85499e20			−0.369886
$39$	−1.25483e20	−	4.75382e21i	−0.0416113	−	1.57641i
$40$			2.98912e21i			0.704261i
$41$	−8.22935e20			−0.138926			−0.0694630	−	0.997585i	$-0.522129\pi$
$41$	−8.22935e20			−0.138926			−0.0694630	+	0.997585i	$0.522129\pi$
$42$	3.68108e21	+	4.48080e21i	0.448859	+	0.546375i
$43$	−6.76183e20			−0.0600123			−0.0300061	−	0.999550i	$-0.509553\pi$
$43$	−6.76183e20			−0.0600123			−0.0300061	+	0.999550i	$0.509553\pi$
$44$		−	9.53383e21i		−	0.620378i
$45$	4.14040e22	−	2.18734e21i	1.98918	−	0.105087i
$46$	−3.11469e22			−1.11220
$47$	4.92175e22			1.31462			0.657308	−	0.753622i	$-0.271695\pi$
$47$	4.92175e22			1.31462			0.657308	+	0.753622i	$0.271695\pi$
$48$	−1.24321e22	+	3.28161e20i	−0.249913	+	0.00659675i
$49$	1.61379e22	−	6.37000e22i	0.245583	−	0.969375i
$50$		−	1.81144e23i		−	2.09860i
$51$	−9.63089e22	+	2.54219e21i	−0.854022	+	0.0225429i
$52$		−	1.15568e23i		−	0.788482i
$53$		−	1.33298e23i		−	0.703235i	−0.936144	−	0.351618i	$-0.885632\pi$
$53$		−	1.33298e23i		−	0.703235i	0.936144	−	0.351618i	$-0.114368\pi$
$54$	1.36430e22	+	1.71964e23i	0.0559233	+	0.704892i
$55$			7.72433e23i			2.47152i
$56$	8.65534e22	+	1.11215e23i	0.217143	+	0.279014i
$57$	6.98687e21	+	2.64692e23i	0.0138030	+	0.522915i
$58$	−2.57647e23			−0.402482
$59$	−7.27488e23			−0.902243			−0.451122	−	0.892463i	$-0.648976\pi$
$59$	−7.27488e23			−0.902243			−0.451122	+	0.892463i	$0.648976\pi$
$60$	1.00725e24	−	2.65877e22i	0.995628	−	0.0262808i
$61$			9.98024e22i			0.0789202i	0.999221	+	0.0394601i	$0.0125638\pi$
$61$			9.98024e22i			0.0789202i	−0.999221	+	0.0394601i	$0.987436\pi$
$62$	−3.76118e23			−0.238801
$63$	1.47717e24	−	1.28028e24i	0.755672	−	0.654951i
$64$	−3.02231e23			−0.125000
$65$			9.36333e24i			3.14123i
$66$	−3.21265e24	+	8.48016e22i	−0.877041	+	0.0231505i
$67$	−3.30747e24			−0.737032			−0.368516	−	0.929621i	$-0.620134\pi$
$67$	−3.30747e24			−0.737032			−0.368516	+	0.929621i	$0.620134\pi$
$68$	−2.34132e24			−0.427160
$69$	2.77046e23	+	1.04957e25i	0.0415039	+	1.57234i
$70$	−7.01258e24	−	9.01070e24i	−0.865076	−	1.11157i
$71$			9.60512e24i			0.978397i	0.872172	+	0.489199i	$0.162711\pi$
$71$			9.60512e24i			0.978397i	−0.872172	+	0.489199i	$0.837289\pi$
$72$	2.21163e23	+	4.18638e24i	0.0186519	+	0.353061i
$73$		−	1.61000e25i		−	1.12711i	−0.826078	−	0.563556i	$-0.809433\pi$
$73$		−	1.61000e25i		−	1.12711i	0.826078	−	0.563556i	$-0.190567\pi$
$74$			9.41583e23i			0.0548568i
$75$	−6.10408e25	+	1.61124e24i	−2.96683	+	0.0783131i
$76$			6.43481e24i			0.261549i
$77$	2.23667e25	+	2.87397e25i	0.762038	+	0.979169i
$78$	−3.89433e25	+	1.02795e24i	−1.11469	+	0.0294237i
$79$	−1.96386e25			−0.473308			−0.236654	−	0.971594i	$-0.576051\pi$
$79$	−1.96386e25			−0.473308			−0.236654	+	0.971594i	$0.576051\pi$
$80$	2.44869e25			0.497988
$81$	5.78261e25	−	6.12691e24i	0.994434	−	0.105364i
$82$			6.74148e24i			0.0982355i
$83$	4.28555e24			0.0530215			0.0265108	−	0.999649i	$-0.491560\pi$
$83$	4.28555e24			0.0530215			0.0265108	+	0.999649i	$0.491560\pi$
$84$	3.67068e25	−	3.01554e25i	0.386345	−	0.317391i
$85$	1.89694e26			1.70176
$86$			5.53929e24i			0.0424351i
$87$	2.29172e24	+	8.68200e25i	0.0150194	+	0.568997i
$88$	−7.81011e25			−0.438673
$89$	2.31808e26			1.11780			0.558899	−	0.829236i	$-0.311224\pi$
$89$	2.31808e26			1.11780			0.558899	+	0.829236i	$0.311224\pi$
$90$	−1.79187e25	−	3.39182e26i	−0.0743074	−	1.40656i
$91$	2.71126e26	+	3.48379e26i	0.968528	+	1.24449i
$92$			2.55155e26i			0.786446i
$93$	3.34550e24	+	1.26742e26i	0.00891130	+	0.337598i
$94$		−	4.03190e26i		−	0.929573i
$95$		−	5.21350e26i		−	1.04198i
$96$	2.68829e24	+	1.01844e26i	0.00466460	+	0.176715i
$97$		−	8.59553e26i		−	1.29674i	−0.761324	−	0.648372i	$-0.775450\pi$
$97$		−	8.59553e26i		−	1.29674i	0.761324	−	0.648372i	$-0.224550\pi$
$98$	−5.21830e26	−	1.32201e26i	−0.685452	−	0.173654i
$99$	5.71518e25	+	1.08182e27i	0.0654568	+	1.23903i
$100$	−1.48393e27			−1.48393
$101$	6.59181e26			0.576323			0.288161	−	0.957582i	$-0.406956\pi$
$101$	6.59181e26			0.576323			0.288161	+	0.957582i	$0.406956\pi$
$102$	2.08256e25	+	7.88962e26i	0.0159402	+	0.603885i
$103$			2.35868e27i			1.58258i	0.611441	+	0.791290i	$0.290590\pi$
$103$			2.35868e27i			1.58258i	−0.611441	+	0.791290i	$0.709410\pi$
$104$	−9.46731e26			−0.557541
$105$	−2.97399e27	+	2.44320e27i	−1.53916	+	1.26446i
$106$	−1.09198e27			−0.497262
$107$			2.14191e27i			0.859251i	0.903007	+	0.429625i	$0.141354\pi$
$107$			2.14191e27i			0.859251i	−0.903007	+	0.429625i	$0.858646\pi$
$108$	1.40873e27	−	1.11763e26i	0.498434	−	0.0395437i
$109$	5.92026e27			1.84962			0.924812	−	0.380425i	$-0.124222\pi$
$109$	5.92026e27			1.84962			0.924812	+	0.380425i	$0.124222\pi$
$110$	6.32777e27			1.74763
$111$	3.17289e26	−	8.37521e24i	0.0775522	−	0.00204708i
$112$	9.11076e26	−	7.09045e26i	0.197293	−	0.153543i
$113$		−	2.28156e27i		−	0.438200i	−0.975702	−	0.219100i	$-0.929688\pi$
$113$		−	2.28156e27i		−	0.438200i	0.975702	−	0.219100i	$-0.0703121\pi$
$114$	2.16836e27	−	5.72364e25i	0.369757	−	0.00976017i
$115$		−	2.06728e28i		−	3.13312i
$116$			2.11064e27i			0.284598i
$117$	6.92787e26	+	1.31137e28i	0.0831937	+	1.57477i
$118$			5.95958e27i			0.637982i
$119$	7.05790e27	−	5.49281e27i	0.674204	−	0.524700i
$120$	−2.17806e26	−	8.25143e27i	−0.0185833	−	0.704016i
$121$	−7.07250e27			−0.539474
$122$	8.17581e26			0.0558050
$123$	2.27170e27	−	5.99642e25i	0.138878	−	0.00366584i
$124$			3.08116e27i			0.168858i
$125$	7.97186e28			3.91989
$126$	−1.04881e28	−	1.21010e28i	−0.463120	−	0.534340i
$127$	2.33112e27			0.0925157			0.0462578	−	0.998930i	$-0.485270\pi$
$127$	2.33112e27			0.0925157			0.0462578	+	0.998930i	$0.485270\pi$
$128$			2.47588e27i			0.0883883i
$129$	1.86659e27	−	4.92709e25i	0.0599914	−	0.00158354i
$130$	7.67044e28			2.22119
$131$	−5.34607e28			−1.39596			−0.697978	−	0.716119i	$-0.745917\pi$
$131$	−5.34607e28			−1.39596			−0.697978	+	0.716119i	$0.745917\pi$
$132$	6.94695e26	+	2.63180e28i	0.0163699	+	0.620162i
$133$	−1.50963e28	−	1.93977e28i	−0.321272	−	0.412813i
$134$			2.70948e28i			0.521160i
$135$	−1.14136e29	+	9.05508e27i	−1.98571	+	0.157538i
$136$			1.91801e28i			0.302047i
$137$			1.09241e29i			1.55833i	0.626819	+	0.779165i	$0.284356\pi$
$137$			1.09241e29i			1.55833i	−0.626819	+	0.779165i	$0.715644\pi$
$138$	8.59806e28	−	2.26956e27i	1.11182	−	0.0293477i
$139$		−	1.42628e29i		−	1.67303i	−0.547945	−	0.836515i	$-0.684590\pi$
$139$		−	1.42628e29i		−	1.67303i	0.547945	−	0.836515i	$-0.315410\pi$
$140$	−7.38156e28	+	5.74470e28i	−0.785995	+	0.611701i
$141$	−1.35864e29	+	3.58630e27i	−1.31416	+	0.0346887i
$142$	7.86852e28			0.691831
$143$	−2.44650e29			−1.95663
$144$	3.42948e28	−	1.81177e27i	0.249652	−	0.0131889i
$145$		−	1.71005e29i		−	1.13381i
$146$	−1.31891e29			−0.796988
$147$	−3.99068e28	+	1.77019e29i	−0.219919	+	0.975518i
$148$	7.71345e27			0.0387896
$149$			1.46346e29i			0.671997i	0.941863	+	0.335998i	$0.109074\pi$
$149$			1.46346e29i			0.671997i	−0.941863	+	0.335998i	$0.890926\pi$
$150$	1.31993e28	+	5.00046e29i	0.0553757	+	2.09787i
$151$	3.73590e29			1.43287			0.716435	−	0.697654i	$-0.245773\pi$
$151$	3.73590e29			1.43287			0.716435	+	0.697654i	$0.245773\pi$
$152$	5.27140e28			0.184943
$153$	2.65674e29	−	1.40353e28i	0.853130	−	0.0450701i
$154$	2.35436e29	−	1.83228e29i	0.692377	−	0.538842i
$155$		−	2.49636e29i		−	0.672713i
$156$	8.42100e27	+	3.19023e29i	0.0208057	+	0.788207i
$157$			8.87758e28i			0.201210i	0.994926	+	0.100605i	$0.0320778\pi$
$157$			8.87758e28i			0.201210i	−0.994926	+	0.100605i	$0.967922\pi$
$158$			1.60879e29i			0.334679i
$159$	9.71296e27	+	3.67968e29i	0.0185563	+	0.702990i
$160$		−	2.00596e29i		−	0.352130i
$161$	−5.98603e29	−	7.69165e29i	−0.966028	−	1.24128i
$162$	−5.01916e28	−	4.73711e29i	−0.0745038	−	0.703171i
$163$	−6.61052e29			−0.903031			−0.451516	−	0.892263i	$-0.649116\pi$
$163$	−6.61052e29			−0.903031			−0.451516	+	0.892263i	$0.649116\pi$
$164$	5.52262e28			0.0694630
$165$	−5.62844e28	−	2.13229e30i	−0.0652161	−	2.47066i
$166$		−	3.51072e28i		−	0.0374919i
$167$	5.88090e29			0.579124			0.289562	−	0.957159i	$-0.406490\pi$
$167$	5.88090e29			0.579124			0.289562	+	0.957159i	$0.406490\pi$
$168$	−2.47033e29	−	3.00702e29i	−0.224430	−	0.273187i
$169$	−1.77308e30			−1.48681
$170$		−	1.55398e30i		−	1.20333i
$171$	−3.85743e28	−	7.30171e29i	−0.0275963	−	0.522369i
$172$	4.53779e28			0.0300061
$173$	2.95263e29			0.180546			0.0902728	−	0.995917i	$-0.471226\pi$
$173$	2.95263e29			0.180546			0.0902728	+	0.995917i	$0.471226\pi$
$174$	7.11230e29	−	1.87738e28i	0.402342	−	0.0106203i
$175$	4.47332e30	−	3.48136e30i	2.34216	−	1.82278i
$176$			6.39804e29i			0.310189i
$177$	2.00822e30	−	5.30093e28i	0.901929	−	0.0238075i
$178$		−	1.89897e30i		−	0.790402i
$179$			3.05520e30i			1.17903i	0.807758	+	0.589514i	$0.200681\pi$
$179$			3.05520e30i			1.17903i	−0.807758	+	0.589514i	$0.799319\pi$
$180$	−2.77858e30	+	1.46790e29i	−0.994588	+	0.0525433i
$181$			9.99579e29i			0.332014i	0.986125	+	0.166007i	$0.0530875\pi$
$181$			9.99579e29i			0.332014i	−0.986125	+	0.166007i	$0.946913\pi$
$182$	2.85392e30	−	2.22106e30i	0.879991	−	0.684853i
$183$	−7.27223e27	−	2.75503e29i	−0.00208247	−	0.0788927i
$184$	2.09023e30			0.556101
$185$	−6.24946e29			−0.154534
$186$	1.03827e30	−	2.74063e28i	0.238718	−	0.00630124i
$187$			4.95642e30i			1.06000i
$188$	−3.30293e30			−0.657308
$189$	−3.98442e30	+	3.64184e30i	−0.738126	+	0.674663i
$190$	−4.27090e30			−0.736794
$191$		−	1.77931e30i		−	0.285957i	−0.989726	−	0.142979i	$-0.954332\pi$
$191$		−	1.77931e30i		−	0.285957i	0.989726	−	0.142979i	$-0.0456680\pi$
$192$	8.34306e29	−	2.20225e28i	0.124956	−	0.00329837i
$193$	4.61282e30			0.644084			0.322042	−	0.946725i	$-0.395631\pi$
$193$	4.61282e30			0.644084			0.322042	+	0.946725i	$0.395631\pi$
$194$	−7.04145e30			−0.916936
$195$	−6.82272e29	−	2.58474e31i	−0.0828877	−	3.14014i
$196$	−1.08299e30	+	4.27483e30i	−0.122792	+	0.484688i
$197$			1.04413e31i			1.10525i	0.833430	+	0.552625i	$0.186374\pi$
$197$			1.04413e31i			1.10525i	−0.833430	+	0.552625i	$0.813626\pi$
$198$	8.86229e30	−	4.68188e29i	0.876125	−	0.0462850i
$199$			3.80839e29i			0.0351742i	0.999845	+	0.0175871i	$0.00559844\pi$
$199$			3.80839e29i			0.0351742i	−0.999845	+	0.0175871i	$0.994402\pi$
$200$			1.21564e31i			1.04930i
$201$	9.13023e30	−	2.41003e29i	0.736775	−	0.0194481i
$202$		−	5.40001e30i		−	0.407522i
$203$	−4.95163e30	−	6.36252e30i	−0.349584	−	0.449193i
$204$	6.46318e30	−	1.70603e29i	0.427011	−	0.0112715i
$205$	−4.47444e30			−0.276734
$206$	1.93223e31			1.11905
$207$	−1.52956e30	−	2.89530e31i	−0.0829789	−	1.57070i
$208$			7.75562e30i			0.394241i
$209$	1.36221e31			0.649036
$210$	2.00147e31	+	2.43629e31i	0.894105	+	1.08835i
$211$	7.21806e30			0.302418			0.151209	−	0.988502i	$-0.451683\pi$
$211$	7.21806e30			0.302418			0.151209	+	0.988502i	$0.451683\pi$
$212$			8.94550e30i			0.351618i
$213$	−6.99890e29	−	2.65148e31i	−0.0258170	−	0.978057i
$214$	1.75465e31			0.607582
$215$	−3.67653e30			−0.119541
$216$	−9.15563e29	−	1.15403e31i	−0.0279616	−	0.352446i
$217$	−7.22850e30	−	9.28815e30i	−0.207416	−	0.266516i
$218$		−	4.84988e31i		−	1.30788i
$219$	1.17315e30	+	4.44438e31i	0.0297411	+	1.12672i
$220$		−	5.18371e31i		−	1.23576i
$221$			6.00811e31i			1.34723i
$222$	−6.86097e28	−	2.59923e30i	−0.00144751	−	0.0548377i
$223$			1.14085e30i			0.0226523i	0.999936	+	0.0113262i	$0.00360530\pi$
$223$			1.14085e30i			0.0226523i	−0.999936	+	0.0113262i	$0.996395\pi$
$224$	−5.80850e30	−	7.46354e30i	−0.108571	−	0.139507i
$225$	1.68385e32	−	8.89564e30i	2.96373	−	0.156572i
$226$	−1.86905e31			−0.309854
$227$	5.15038e31			0.804434			0.402217	−	0.915544i	$-0.368240\pi$
$227$	5.15038e31			0.804434			0.402217	+	0.915544i	$0.368240\pi$
$228$	−4.68881e29	−	1.77632e31i	−0.00690148	−	0.261457i
$229$		−	1.10267e32i		−	1.52991i	−0.644082	−	0.764956i	$-0.722761\pi$
$229$		−	1.10267e32i		−	1.52991i	0.644082	−	0.764956i	$-0.277239\pi$
$230$	−1.69351e32			−2.21545
$231$	−6.38371e31	−	7.77058e31i	−0.787610	−	0.958720i
$232$	1.72904e31			0.201241
$233$			5.86207e31i			0.643793i	0.946775	+	0.321896i	$0.104320\pi$
$233$			5.86207e31i			0.643793i	−0.946775	+	0.321896i	$0.895680\pi$
$234$	1.07428e32	−	5.67531e30i	1.11353	−	0.0588268i
$235$	2.67604e32			2.61865
$236$	4.88209e31			0.451122
$237$	5.42120e31	−	1.43099e30i	0.473143	−	0.0124892i
$238$	−4.49971e31	−	5.78183e31i	−0.371019	−	0.476735i
$239$			4.13192e31i			0.321944i	0.986959	+	0.160972i	$0.0514629\pi$
$239$			4.13192e31i			0.321944i	−0.986959	+	0.160972i	$0.948537\pi$
$240$	−6.75957e31	+	1.78427e30i	−0.497814	+	0.0131404i
$241$		−	3.09111e31i		−	0.215221i	−0.994193	−	0.107610i	$-0.965680\pi$
$241$		−	3.09111e31i		−	0.215221i	0.994193	−	0.107610i	$-0.0343199\pi$
$242$			5.79379e31i			0.381466i
$243$	−1.59182e32	+	2.11268e31i	−0.991307	+	0.131568i
$244$		−	6.69763e30i		−	0.0394601i
$245$	8.77445e31	−	3.46348e32i	0.489190	−	1.93095i
$246$	−4.91227e29	−	1.86098e31i	−0.00259214	−	0.0982013i
$247$	1.65125e32			0.824905
$248$	2.52408e31			0.119401
$249$	−1.18302e31	+	3.12272e29i	−0.0530031	+	0.00139908i
$250$		−	6.53054e32i		−	2.77178i
$251$	2.98626e32			1.20097			0.600486	−	0.799635i	$-0.294974\pi$
$251$	2.98626e32			1.20097			0.600486	+	0.799635i	$0.294974\pi$
$252$	−9.91312e31	+	8.59184e31i	−0.377836	+	0.327475i
$253$	5.40147e32			1.95157
$254$		−	1.90966e31i		−	0.0654185i
$255$	−5.23649e32	+	1.38223e31i	−1.70117	+	0.0449044i
$256$	2.02824e31			0.0625000
$257$	1.34092e32			0.392018			0.196009	−	0.980602i	$-0.437202\pi$
$257$	1.34092e32			0.392018			0.196009	+	0.980602i	$0.437202\pi$
$258$	−4.03628e29	−	1.52911e31i	−0.00111973	−	0.0424203i
$259$	−2.32522e31	+	1.80960e31i	−0.0612233	+	0.0476471i
$260$		−	6.28363e32i		−	1.57062i
$261$	−1.26525e31	−	2.39499e32i	−0.0300282	−	0.568403i
$262$			4.37950e32i			0.987091i
$263$		−	5.63766e32i		−	1.20697i	−0.797375	−	0.603484i	$-0.793779\pi$
$263$		−	5.63766e32i		−	1.20697i	0.797375	−	0.603484i	$-0.206221\pi$
$264$	2.15597e32	−	5.69094e30i	0.438521	−	0.0115753i
$265$		−	7.24767e32i		−	1.40081i
$266$	−1.58906e32	+	1.23669e32i	−0.291903	+	0.227174i
$267$	−6.39902e32	+	1.68910e31i	−1.11741	+	0.0294953i
$268$	2.21961e32			0.368516
$269$	−2.68962e32			−0.424654			−0.212327	−	0.977199i	$-0.568104\pi$
$269$	−2.68962e32			−0.424654			−0.212327	+	0.977199i	$0.568104\pi$
$270$	7.41792e31	+	9.35001e32i	0.111396	+	1.40411i
$271$		−	8.66247e32i		−	1.23753i	−0.785576	−	0.618766i	$-0.787633\pi$
$271$		−	8.66247e32i		−	1.23753i	0.785576	−	0.618766i	$-0.212367\pi$
$272$	1.57123e32			0.213580
$273$	−7.73825e32	−	9.41940e32i	−1.00103	−	1.21850i
$274$	8.94905e32			1.10191
$275$			3.14139e33i			3.68240i
$276$	−1.85922e31	−	7.04353e32i	−0.0207519	−	0.786172i
$277$	6.47333e32			0.688099			0.344050	−	0.938951i	$-0.388201\pi$
$277$	6.47333e32			0.688099			0.344050	+	0.938951i	$0.388201\pi$
$278$	−1.16840e33			−1.18301
$279$	−1.84704e31	−	3.49625e32i	−0.0178164	−	0.337245i
$280$	4.70606e32	+	6.04698e32i	0.432538	+	0.555783i
$281$		−	8.33284e32i		−	0.729890i	−0.931029	−	0.364945i	$-0.881088\pi$
$281$		−	8.33284e32i		−	0.729890i	0.931029	−	0.364945i	$-0.118912\pi$
$282$	2.93790e31	+	1.11300e33i	0.0245286	+	0.929250i
$283$		−	1.54622e33i		−	1.23071i	−0.788251	−	0.615354i	$-0.789013\pi$
$283$		−	1.54622e33i		−	1.23071i	0.788251	−	0.615354i	$-0.210987\pi$
$284$		−	6.44589e32i		−	0.489199i
$285$	3.79889e31	+	1.43918e33i	0.0274948	+	1.04162i
$286$			2.00417e33i			1.38354i
$287$	−1.66479e32	+	1.29563e32i	−0.109636	+	0.0853246i
$288$	−1.48420e31	−	2.80943e32i	−0.00932596	−	0.176531i
$289$	−4.50513e32			−0.270139
$290$	−1.40087e33			−0.801724
$291$	6.26324e31	+	2.37278e33i	0.0342172	+	1.29629i
$292$			1.08045e33i			0.563556i
$293$	−1.91803e33			−0.955305			−0.477653	−	0.878549i	$-0.658512\pi$
$293$	−1.91803e33			−0.955305			−0.477653	+	0.878549i	$0.658512\pi$
$294$	1.45014e33	+	3.26916e32i	0.689795	+	0.155506i
$295$	−3.95548e33			−1.79722
$296$		−	6.31886e31i		−	0.0274284i
$297$	−2.36595e32	−	2.98219e33i	−0.0981282	−	1.23687i
$298$	1.19887e33			0.475173
$299$	6.54759e33			2.48039
$300$	4.09638e33	−	1.08129e32i	1.48342	−	0.0391565i
$301$	−1.36791e32	+	1.06458e32i	−0.0473600	+	0.0368579i
$302$		−	3.06045e33i		−	1.01319i
$303$	−1.81966e33	+	4.80321e31i	−0.576122	+	0.0152074i
$304$		−	4.31833e32i		−	0.130774i
$305$			5.42644e32i			0.157205i
$306$	−1.14978e32	−	2.17640e33i	−0.0318694	−	0.603254i
$307$		−	2.67651e31i		−	0.00709907i	−0.999994	−	0.00354953i	$-0.998870\pi$
$307$		−	2.67651e31i		−	0.00709907i	0.999994	−	0.00354953i	$-0.00112985\pi$
$308$	−1.50100e33	−	1.92869e33i	−0.381019	−	0.489584i
$309$	−1.71868e32	−	6.51109e33i	−0.0417595	−	1.58203i
$310$	−2.04502e33			−0.475680
$311$	4.42190e33			0.984790			0.492395	−	0.870372i	$-0.336122\pi$
$311$	4.42190e33			0.984790			0.492395	+	0.870372i	$0.336122\pi$
$312$	2.61344e33	−	6.89848e31i	0.557347	−	0.0147118i
$313$			6.94665e33i			1.41882i	0.704796	+	0.709410i	$0.251038\pi$
$313$			6.94665e33i			1.41882i	−0.704796	+	0.709410i	$0.748962\pi$
$314$	7.27252e32			0.142277
$315$	8.03164e33	−	6.96113e33i	1.50526	−	1.30463i
$316$	1.31792e33			0.236654
$317$			1.13535e34i			1.95357i	0.214232	+	0.976783i	$0.431275\pi$
$317$			1.13535e34i			1.95357i	−0.214232	+	0.976783i	$0.568725\pi$
$318$	3.01440e33	−	7.95686e31i	0.497089	−	0.0131213i
$319$	4.46809e33			0.706232
$320$	−1.64329e33			−0.248994
$321$	−1.56073e32	−	5.91271e33i	−0.0226730	−	0.858951i
$322$	−6.30100e33	+	4.90376e33i	−0.877719	+	0.683085i
$323$		−	3.34531e33i		−	0.446892i
$324$	−3.88064e33	+	4.11170e32i	−0.497217	+	0.0526821i
$325$			3.80795e34i			4.68022i
$326$			5.41534e33i			0.638540i
$327$	−1.63428e34	+	4.31388e32i	−1.84898	+	0.0488060i
$328$		−	4.52413e32i		−	0.0491177i
$329$	9.95668e33	−	7.74879e33i	1.03746	−	0.807401i
$330$	−1.74677e34	+	4.61082e32i	−1.74702	+	0.0461147i
$331$	−1.54827e34			−1.48651			−0.743255	−	0.669008i	$-0.766719\pi$
$331$	−1.54827e34			−1.48651			−0.743255	+	0.669008i	$0.766719\pi$
$332$	−2.87598e32			−0.0265108
$333$	−8.75261e32	+	4.62393e31i	−0.0774712	+	0.00409274i
$334$		−	4.81763e33i		−	0.409502i
$335$	−1.79833e34			−1.46813
$336$	−2.46335e33	+	2.02370e33i	−0.193173	+	0.158696i
$337$	1.59751e34			1.20348			0.601742	−	0.798690i	$-0.294473\pi$
$337$	1.59751e34			1.20348			0.601742	+	0.798690i	$0.294473\pi$
$338$			1.45250e34i			1.05134i
$339$	1.66249e32	+	6.29821e33i	0.0115628	+	0.438047i
$340$	−1.27302e34			−0.850881
$341$	6.52261e33			0.419023
$342$	−5.98156e33	+	3.16001e32i	−0.369370	+	0.0195135i
$343$	−6.76422e33	−	1.54272e34i	−0.401557	−	0.915834i
$344$		−	3.71735e32i		−	0.0212175i
$345$	1.50635e33	+	5.70669e34i	0.0826737	+	3.13203i
$346$		−	2.41880e33i		−	0.127665i
$347$			3.02576e34i			1.53598i	0.640461	+	0.767991i	$0.278744\pi$
$347$			3.02576e34i			1.53598i	−0.640461	+	0.767991i	$0.721256\pi$
$348$	−1.53795e32	−	5.82639e33i	−0.00750968	−	0.284499i
$349$			1.16860e34i			0.548936i	0.961596	+	0.274468i	$0.0885018\pi$
$349$			1.16860e34i			0.548936i	−0.961596	+	0.274468i	$0.911498\pi$
$350$	−2.85193e34	−	3.66454e34i	−1.28890	−	1.65615i
$351$	−2.86798e33	−	3.61497e34i	−0.124718	−	1.57202i
$352$	5.24128e33			0.219337
$353$	−1.68269e34			−0.677712			−0.338856	−	0.940838i	$-0.610040\pi$
$353$	−1.68269e34			−0.677712			−0.338856	+	0.940838i	$0.610040\pi$
$354$	−4.34253e32	−	1.64513e34i	−0.0168344	−	0.637760i
$355$			5.22248e34i			1.94892i
$356$	−1.55564e34			−0.558899
$357$	−1.90830e34	+	1.56771e34i	−0.660124	+	0.542307i
$358$	2.50282e34			0.833699
$359$			1.48213e34i			0.475455i	0.971332	+	0.237728i	$0.0764026\pi$
$359$			1.48213e34i			0.475455i	−0.971332	+	0.237728i	$0.923597\pi$
$360$	1.20250e33	+	2.27621e34i	0.0371537	+	0.703280i
$361$	2.44065e34			0.726369
$362$	8.18855e33			0.234769
$363$	1.95236e34	−	5.15347e32i	0.539286	−	0.0142351i
$364$	−1.81950e34	−	2.33793e34i	−0.484264	−	0.622247i
$365$		−	8.75385e34i		−	2.24515i
$366$	−2.25692e33	+	5.95741e31i	−0.0557856	+	0.00147253i
$367$		−	6.69869e34i		−	1.59587i	−0.602742	−	0.797936i	$-0.705925\pi$
$367$		−	6.69869e34i		−	1.59587i	0.602742	−	0.797936i	$-0.294075\pi$
$368$		−	1.71232e34i		−	0.393223i
$369$	−6.26663e33	+	3.31061e32i	−0.138733	+	0.00732912i
$370$			5.11956e33i			0.109272i
$371$	−2.09864e34	−	2.69662e34i	−0.431908	−	0.554973i
$372$	−2.24513e32	−	8.50550e33i	−0.00445565	−	0.168799i
$373$	4.97246e34			0.951705			0.475853	−	0.879525i	$-0.342140\pi$
$373$	4.97246e34			0.951705			0.475853	+	0.879525i	$0.342140\pi$
$374$	4.06030e34			0.749534
$375$	−2.20062e35	+	5.80880e33i	−3.91853	+	0.103434i
$376$			2.70576e34i			0.464787i
$377$	5.41616e34			0.897600
$378$	2.98340e34	+	3.26404e34i	0.477059	+	0.521934i
$379$	−6.95093e34			−1.07254			−0.536270	−	0.844046i	$-0.680167\pi$
$379$	−6.95093e34			−1.07254			−0.536270	+	0.844046i	$0.680167\pi$
$380$			3.49872e34i			0.520992i
$381$	−6.43504e33	+	1.69860e32i	−0.0924834	+	0.00244121i
$382$	−1.45761e34			−0.202202
$383$	1.17378e35			1.57182			0.785911	−	0.618339i	$-0.212194\pi$
$383$	1.17378e35			1.57182			0.785911	+	0.618339i	$0.212194\pi$
$384$	−1.80408e32	−	6.83463e33i	−0.00233230	−	0.0883576i
$385$	1.21612e35	+	1.56263e35i	1.51794	+	1.95046i
$386$		−	3.77882e34i		−	0.455436i
$387$	−5.14912e33	+	2.72024e32i	−0.0599287	+	0.00316598i
$388$			5.76836e34i			0.648372i
$389$			1.10794e35i			1.20281i	0.798944	+	0.601405i	$0.205392\pi$
$389$			1.10794e35i			1.20281i	−0.798944	+	0.601405i	$0.794608\pi$
$390$	−2.11742e35	+	5.58917e33i	−2.22041	+	0.0586105i
$391$		−	1.32649e35i		−	1.34375i
$392$	3.50194e34	+	8.87189e33i	0.342726	+	0.0868268i
$393$	1.47578e35	−	3.89548e33i	1.39547	−	0.0368351i
$394$	8.55351e34			0.781530
$395$	−1.06778e35			−0.942806
$396$	−3.83539e33	−	7.25999e34i	−0.0327284	−	0.619514i
$397$		−	1.34212e35i		−	1.10692i	−0.832874	−	0.553462i	$-0.813306\pi$
$397$		−	1.34212e35i		−	1.10692i	0.832874	−	0.553462i	$-0.186694\pi$
$398$	3.11983e33			0.0248719
$399$	4.30865e34	+	5.24472e34i	0.332053	+	0.404192i
$400$	9.95851e34			0.741967
$401$			4.35619e34i			0.313803i	0.987614	+	0.156902i	$0.0501506\pi$
$401$			4.35619e34i			0.313803i	−0.987614	+	0.156902i	$0.949849\pi$
$402$	−1.97430e33	−	7.47949e34i	−0.0137519	−	0.520979i
$403$	7.90662e34			0.532565
$404$	−4.42369e34			−0.288161
$405$	3.14411e35	−	3.33131e34i	1.98086	−	0.209880i
$406$	−5.21218e34	+	4.05638e34i	−0.317627	+	0.247193i
$407$		−	1.63289e34i		−	0.0962569i
$408$	−1.39758e33	−	5.29464e34i	−0.00797012	−	0.301942i
$409$			7.22875e34i			0.398840i	0.979914	+	0.199420i	$0.0639057\pi$
$409$			7.22875e34i			0.398840i	−0.979914	+	0.199420i	$0.936094\pi$
$410$			3.66546e34i			0.195680i
$411$	−7.96001e33	−	3.01559e35i	−0.0411196	−	1.55779i
$412$		−	1.58288e35i		−	0.791290i
$413$	−1.47170e35	+	1.14535e35i	−0.712024	+	0.554133i
$414$	−2.37183e35	+	1.25302e34i	−1.11065	+	0.0586749i
$415$	2.33013e34			0.105616
$416$	6.35341e34			0.278770
$417$	1.03927e34	+	3.93721e35i	0.0441462	+	1.67245i
$418$		−	1.11592e35i		−	0.458937i
$419$	−1.84174e35			−0.733397			−0.366698	−	0.930340i	$-0.619512\pi$
$419$	−1.84174e35			−0.733397			−0.366698	+	0.930340i	$0.619512\pi$
$420$	1.99581e35	−	1.63960e35i	0.769581	−	0.632228i
$421$	−2.98325e35			−1.11399			−0.556995	−	0.830516i	$-0.688046\pi$
$421$	−2.98325e35			−1.11399			−0.556995	+	0.830516i	$0.688046\pi$
$422$		−	5.91303e34i		−	0.213842i
$423$	3.74790e35	−	1.97999e34i	1.31278	−	0.0693533i
$424$	7.32815e34			0.248631
$425$	7.71463e35			2.53551
$426$	−2.17209e35	+	5.73350e33i	−0.691590	+	0.0182553i
$427$	1.57129e34	+	2.01900e34i	0.0484707	+	0.0622816i
$428$		−	1.43741e35i		−	0.429625i
$429$	6.75352e35	−	1.78267e34i	1.95595	−	0.0516295i
$430$			3.01181e34i			0.0845286i
$431$		−	4.63199e35i		−	1.25987i	−0.776649	−	0.629933i	$-0.783082\pi$
$431$		−	4.63199e35i		−	1.25987i	0.776649	−	0.629933i	$-0.216918\pi$
$432$	−9.45384e34	+	7.50029e33i	−0.249217	+	0.0197719i
$433$			2.89951e35i			0.740862i	0.928860	+	0.370431i	$0.120790\pi$
$433$			2.89951e35i			0.740862i	−0.928860	+	0.370431i	$0.879210\pi$
$434$	−7.60885e34	+	5.92159e34i	−0.188455	+	0.146665i
$435$	1.24605e34	+	4.72056e35i	0.0299178	+	1.13341i
$436$	−3.97302e35			−0.924812
$437$	−3.64570e35			−0.822775
$438$	3.64083e35	−	9.61041e33i	0.796710	−	0.0210301i
$439$		−	7.83504e35i		−	1.66253i	−0.555875	−	0.831266i	$-0.687617\pi$
$439$		−	7.83504e35i		−	1.66253i	0.555875	−	0.831266i	$-0.312383\pi$
$440$	−4.24650e35			−0.873816
$441$	9.72635e34	−	4.91566e35i	0.194101	−	0.980981i
$442$	4.92184e35			0.952636
$443$		−	5.80000e35i		−	1.08887i	−0.838802	−	0.544437i	$-0.816743\pi$
$443$		−	5.80000e35i		−	1.08887i	0.838802	−	0.544437i	$-0.183257\pi$
$444$	−2.12929e34	+	5.62051e32i	−0.0387761	+	0.00102354i
$445$	1.26038e36			2.22660
$446$	9.34584e33			0.0160176
$447$	−1.06637e34	−	4.03987e35i	−0.0177320	−	0.671763i
$448$	−6.11413e34	+	4.75832e34i	−0.0986464	+	0.0767716i
$449$			7.38374e35i			1.15598i	0.816043	+	0.577991i	$0.196163\pi$
$449$			7.38374e35i			1.15598i	−0.816043	+	0.577991i	$0.803837\pi$
$450$	−7.28731e34	−	1.37941e36i	−0.110713	−	2.09568i
$451$		−	1.16910e35i		−	0.172373i
$452$			1.53113e35i			0.219100i
$453$	−1.03129e36	+	2.72221e34i	−1.43237	+	0.0378091i
$454$		−	4.21919e35i		−	0.568821i
$455$	1.47416e36	+	1.89420e36i	1.92926	+	2.47897i
$456$	−1.45516e35	+	3.84107e33i	−0.184878	+	0.00488008i
$457$	−9.77025e35			−1.20514			−0.602569	−	0.798067i	$-0.705856\pi$
$457$	−9.77025e35			−1.20514			−0.602569	+	0.798067i	$0.705856\pi$
$458$	−9.03307e35			−1.08181
$459$	−7.32367e35	+	5.81031e34i	−0.851643	+	0.0675660i
$460$			1.38733e36i			1.56656i
$461$	1.17440e35			0.128782			0.0643908	−	0.997925i	$-0.479490\pi$
$461$	1.17440e35			0.128782			0.0643908	+	0.997925i	$0.479490\pi$
$462$	−6.36566e35	+	5.22953e35i	−0.677917	+	0.556925i
$463$	1.63735e35			0.169355			0.0846777	−	0.996408i	$-0.473014\pi$
$463$	1.63735e35			0.169355			0.0846777	+	0.996408i	$0.473014\pi$
$464$		−	1.41643e35i		−	0.142299i
$465$	1.81901e34	+	6.89118e35i	0.0177509	+	0.672479i
$466$	4.80221e35			0.455230
$467$	−5.47417e35			−0.504128			−0.252064	−	0.967711i	$-0.581109\pi$
$467$	−5.47417e35			−0.504128			−0.252064	+	0.967711i	$0.581109\pi$
$468$	−4.64921e34	−	8.80046e35i	−0.0415968	−	0.787384i
$469$	−6.69100e35	+	5.20727e35i	−0.581645	+	0.452665i
$470$		−	2.19222e36i		−	1.85166i
$471$	−6.46877e33	−	2.45065e35i	−0.00530932	−	0.201140i
$472$		−	3.99941e35i		−	0.318991i
$473$		−	9.60620e34i		−	0.0744605i
$474$	−1.17227e34	−	4.44105e35i	−0.00883118	−	0.334563i
$475$		−	2.12027e36i		−	1.55248i
$476$	−4.73648e35	+	3.68616e35i	−0.337102	+	0.262350i
$477$	−5.36250e34	−	1.01506e36i	−0.0370996	−	0.702256i
$478$	3.38487e35			0.227649
$479$	2.23121e36			1.45885			0.729427	−	0.684059i	$-0.239787\pi$
$479$	2.23121e36			1.45885			0.729427	+	0.684059i	$0.239787\pi$
$480$	1.46167e34	+	5.53744e35i	0.00929166	+	0.352008i
$481$		−	1.97936e35i		−	0.122340i
$482$	−2.53224e35			−0.152184
$483$	1.70848e36	+	2.07965e36i	0.998445	+	1.21536i
$484$	4.74628e35			0.269737
$485$		−	4.67354e36i		−	2.58305i
$486$	1.73071e35	+	1.30402e36i	0.0930324	+	0.700960i
$487$	−1.67179e36			−0.874057			−0.437029	−	0.899448i	$-0.643969\pi$
$487$	−1.67179e36			−0.874057			−0.437029	+	0.899448i	$0.643969\pi$
$488$	−5.48670e34			−0.0279025
$489$	1.82482e36	−	4.81684e34i	0.902717	−	0.0238283i
$490$	−2.83728e36	−	7.18803e35i	−1.36539	−	0.345910i
$491$			1.53458e36i			0.718438i	0.933253	+	0.359219i	$0.116957\pi$
$491$			1.53458e36i			0.718438i	−0.933253	+	0.359219i	$0.883043\pi$
$492$	−1.52451e35	+	4.02413e33i	−0.0694388	+	0.00183292i
$493$		−	1.09727e36i		−	0.486275i
$494$		−	1.35270e36i		−	0.583296i
$495$	3.10745e35	+	5.88206e36i	0.130387	+	2.46808i
$496$		−	2.06773e35i		−	0.0844289i
$497$	1.51223e36	+	1.94311e36i	0.600905	+	0.772123i
$498$	2.55813e33	+	9.69131e34i	0.000989298	+	0.0374788i
$499$	2.64421e36			0.995263			0.497632	−	0.867389i	$-0.334203\pi$
$499$	2.64421e36			0.995263			0.497632	+	0.867389i	$0.334203\pi$
$500$	−5.34982e36			−1.95995
$501$	−1.62341e36	+	4.28519e34i	−0.578922	+	0.0152813i
$502$		−	2.44635e36i		−	0.849216i
$503$	−2.81570e36			−0.951520			−0.475760	−	0.879575i	$-0.657827\pi$
$503$	−2.81570e36			−0.951520			−0.475760	+	0.879575i	$0.657827\pi$
$504$	7.03843e35	+	8.12083e35i	0.231560	+	0.267170i
$505$	3.58408e36			1.14801
$506$		−	4.42489e36i		−	1.37997i
$507$	4.89455e36	−	1.29197e35i	1.48630	−	0.0392326i
$508$	−1.56439e35			−0.0462578
$509$	4.37859e36			1.26079			0.630397	−	0.776273i	$-0.282892\pi$
$509$	4.37859e36			1.26079			0.630397	+	0.776273i	$0.282892\pi$
$510$	1.13232e35	+	4.28973e36i	0.0317522	+	1.20291i
$511$	−2.53478e36	−	3.25702e36i	−0.692241	−	0.889484i
$512$		−	1.66153e35i		−	0.0441942i
$513$	1.59689e35	+	2.01282e36i	0.0413704	+	0.521459i
$514$		−	1.09848e36i		−	0.277198i
$515$			1.28245e37i			3.15242i
$516$	−1.25265e35	+	3.30652e33i	−0.0299957	+	0.000791771i
$517$			6.99209e36i			1.63112i
$518$	1.48243e35	+	1.90482e35i	0.0336916	+	0.0432914i
$519$	−8.15070e35	+	2.15147e34i	−0.180483	+	0.00476406i
$520$	−5.14755e36			−1.11059
$521$	−1.10927e36			−0.233200			−0.116600	−	0.993179i	$-0.537200\pi$
$521$	−1.10927e36			−0.233200			−0.116600	+	0.993179i	$0.537200\pi$
$522$	−1.96197e36	+	1.03649e35i	−0.401921	+	0.0212332i
$523$			6.07243e36i			1.21224i	0.795372	+	0.606121i	$0.207275\pi$
$523$			6.07243e36i			1.21224i	−0.795372	+	0.606121i	$0.792725\pi$
$524$	3.58769e36			0.697978
$525$	−1.20949e37	+	9.93620e36i	−2.29324	+	1.88395i
$526$	−4.61837e36			−0.853456
$527$		−	1.60182e36i		−	0.288517i
$528$	−4.66202e34	−	1.76617e36i	−0.00818495	−	0.310081i
$529$	−8.61284e36			−1.47399
$530$	−5.93729e36			−0.990522
$531$	−5.53980e36	+	2.92663e35i	−0.900987	+	0.0475984i
$532$	1.01309e36	+	1.30176e36i	0.160636	+	0.206407i
$533$		−	1.41717e36i		−	0.219081i
$534$	1.38371e35	+	5.24208e36i	0.0208563	+	0.790127i
$535$			1.16459e37i			1.71158i
$536$		−	1.81830e36i		−	0.260580i
$537$	−2.22621e35	−	8.43385e36i	−0.0311110	−	1.17862i
$538$			2.20334e36i			0.300276i
$539$	9.04954e36	+	2.29263e36i	1.20276	+	0.304709i
$540$	7.65952e36	−	6.07676e35i	0.992856	−	0.0787692i
$541$	−7.61743e36			−0.963042			−0.481521	−	0.876434i	$-0.659916\pi$
$541$	−7.61743e36			−0.963042			−0.481521	+	0.876434i	$0.659916\pi$
$542$	−7.09629e36			−0.875067
$543$	−7.28357e34	−	2.75933e36i	−0.00876085	−	0.331899i
$544$		−	1.28715e36i		−	0.151024i
$545$	3.21895e37			3.68436
$546$	−7.71637e36	+	6.33917e36i	−0.861613	+	0.707835i
$547$	−1.39357e37			−1.51809			−0.759047	−	0.651035i	$-0.774335\pi$
$547$	−1.39357e37			−1.51809			−0.759047	+	0.651035i	$0.774335\pi$
$548$		−	7.33106e36i		−	0.779165i
$549$	4.01498e34	+	7.59993e35i	0.00416348	+	0.0788103i
$550$	2.57343e37			2.60385
$551$	−3.01571e36			−0.297744
$552$	−5.77006e36	+	1.52308e35i	−0.555908	+	0.0146738i
$553$	−3.97287e36	+	3.09189e36i	−0.373521	+	0.290693i
$554$		−	5.30295e36i		−	0.486560i
$555$	1.72516e36	−	4.55375e34i	0.154480	−	0.00407769i
$556$			9.57157e36i			0.836515i
$557$		−	5.21238e36i		−	0.444622i	−0.974976	−	0.222311i	$-0.928640\pi$
$557$		−	5.21238e36i		−	0.444622i	0.974976	−	0.222311i	$-0.0713600\pi$
$558$	−2.86413e36	+	1.51310e35i	−0.238469	+	0.0125981i
$559$		−	1.16445e36i		−	0.0946372i
$560$	4.95368e36	−	3.85521e36i	0.392998	−	0.305850i
$561$	−3.61156e35	−	1.36821e37i	−0.0279702	−	1.05963i
$562$	−6.82626e36			−0.516110
$563$	5.28177e36			0.389866			0.194933	−	0.980817i	$-0.437551\pi$
$563$	5.28177e36			0.389866			0.194933	+	0.980817i	$0.437551\pi$
$564$	9.11770e36	−	2.40672e35i	0.657079	−	0.0173444i
$565$		−	1.24052e37i		−	0.872872i
$566$	−1.26666e37			−0.870241
$567$	1.07336e37	−	1.03436e37i	0.720067	−	0.693905i
$568$	−5.28047e36			−0.345916
$569$			9.44383e36i			0.604133i	0.953287	+	0.302066i	$0.0976764\pi$
$569$			9.44383e36i			0.604133i	−0.953287	+	0.302066i	$0.902324\pi$
$570$	1.17898e37	−	3.11205e35i	0.736537	−	0.0194418i
$571$	−9.84334e36			−0.600558			−0.300279	−	0.953851i	$-0.597080\pi$
$571$	−9.84334e36			−0.600558			−0.300279	+	0.953851i	$0.597080\pi$
$572$	1.64182e37			0.978313
$573$	1.29652e35	+	4.91176e36i	0.00754555	+	0.285858i
$574$	1.06138e36	+	1.36380e36i	0.0603336	+	0.0775247i
$575$		−	8.40735e37i		−	4.66813i
$576$	−2.30149e36	+	1.21586e35i	−0.124826	+	0.00659445i
$577$		−	1.14890e37i		−	0.608707i	−0.952559	−	0.304353i	$-0.901560\pi$
$577$		−	1.14890e37i		−	0.608707i	0.952559	−	0.304353i	$-0.0984403\pi$
$578$			3.69060e36i			0.191017i
$579$	−1.27336e37	+	3.36119e35i	−0.643860	+	0.0169954i
$580$			1.14759e37i			0.566904i
$581$	8.66965e35	−	6.74716e35i	0.0418431	−	0.0325644i
$582$	1.94378e37	−	5.13085e35i	0.916617	−	0.0241952i
$583$	1.89370e37			0.872543
$584$	8.85106e36			0.398494
$585$	3.76680e36	+	7.13016e37i	0.165718	+	3.13686i
$586$			1.57125e37i			0.675503i
$587$	−2.69706e37			−1.13312			−0.566560	−	0.824021i	$-0.691726\pi$
$587$	−2.69706e37			−1.13312			−0.566560	+	0.824021i	$0.691726\pi$
$588$	2.67810e36	−	1.18795e37i	0.109959	−	0.487759i
$589$	−4.40241e36			−0.176658
$590$			3.24033e37i			1.27083i
$591$	−7.60819e35	−	2.88231e37i	−0.0291642	−	1.10487i
$592$	−5.17641e35			−0.0193948
$593$	−3.10052e37			−1.13552			−0.567761	−	0.823193i	$-0.692190\pi$
$593$	−3.10052e37			−1.13552			−0.567761	+	0.823193i	$0.692190\pi$
$594$	−2.44301e37	+	1.93819e36i	−0.874598	+	0.0693871i
$595$	3.83751e37	−	2.98654e37i	1.34298	−	1.04518i
$596$		−	9.82113e36i		−	0.335998i
$597$	−2.77503e34	−	1.05130e36i	−0.000928142	−	0.0351620i
$598$		−	5.36379e37i		−	1.75390i
$599$			1.90330e37i			0.608478i	0.952596	+	0.304239i	$0.0984021\pi$
$599$			1.90330e37i			0.608478i	−0.952596	+	0.304239i	$0.901598\pi$
$600$	−8.85791e35	−	3.35575e37i	−0.0276879	−	1.04893i
$601$			1.12056e37i			0.342477i	0.985230	+	0.171239i	$0.0547769\pi$
$601$			1.12056e37i			0.342477i	−0.985230	+	0.171239i	$0.945223\pi$
$602$	8.72104e35	+	1.12060e36i	0.0260625	+	0.0334886i
$603$	−2.51863e37	+	1.33057e36i	−0.736006	+	0.0388826i
$604$	−2.50712e37			−0.716435
$605$	−3.84545e37			−1.07461
$606$	3.93479e35	+	1.49066e37i	0.0107533	+	0.407380i
$607$			1.01791e37i			0.272057i	0.990705	+	0.136029i	$0.0434339\pi$
$607$			1.01791e37i			0.272057i	−0.990705	+	0.136029i	$0.956566\pi$
$608$	−3.53757e36			−0.0924714
$609$	1.41325e37	+	1.72028e37i	0.361315	+	0.439812i
$610$	4.44534e36			0.111161
$611$			8.47572e37i			2.07310i
$612$	−1.78291e37	+	9.41896e35i	−0.426565	+	0.0225351i
$613$	−5.49378e37			−1.28574			−0.642872	−	0.765974i	$-0.722257\pi$
$613$	−5.49378e37			−1.28574			−0.642872	+	0.765974i	$0.722257\pi$
$614$	−2.19260e35			−0.00501980
$615$	1.23516e37	−	3.26036e35i	0.276637	−	0.00730217i
$616$	−1.57998e37	+	1.22962e37i	−0.346188	+	0.269421i
$617$		−	5.16609e37i		−	1.10742i	−0.832710	−	0.553710i	$-0.813212\pi$
$617$		−	5.16609e37i		−	1.10742i	0.832710	−	0.553710i	$-0.186788\pi$
$618$	−5.33389e37	+	1.40794e36i	−1.11866	+	0.0295284i
$619$		−	5.10239e37i		−	1.04701i	−0.852023	−	0.523504i	$-0.824625\pi$
$619$		−	5.10239e37i		−	1.04701i	0.852023	−	0.523504i	$-0.175375\pi$
$620$			1.67528e37i			0.336356i
$621$	6.33204e36	+	7.98129e37i	0.124396	+	1.56797i
$622$		−	3.62242e37i		−	0.696352i
$623$	4.68946e37	−	3.64957e37i	0.882134	−	0.686521i
$624$	−5.65124e35	−	2.14093e37i	−0.0104028	−	0.394104i
$625$	2.68694e38			4.84037
$626$	5.69070e37			1.00326
$627$	−3.76036e37	+	9.92591e35i	−0.648810	+	0.0171261i
$628$		−	5.95765e36i		−	0.100605i
$629$	−4.01005e36			−0.0662774
$630$	−5.70256e37	−	6.57952e37i	−0.922512	−	1.06438i
$631$	5.75937e37			0.911966			0.455983	−	0.889988i	$-0.349288\pi$
$631$	5.75937e37			0.911966			0.455983	+	0.889988i	$0.349288\pi$
$632$		−	1.07964e37i		−	0.167340i
$633$	−1.99254e37	+	5.25953e35i	−0.302312	+	0.00797989i
$634$	9.30075e37			1.38138
$635$	1.26747e37			0.184287
$636$	−6.51826e35	−	2.46939e37i	−0.00927813	−	0.351495i
$637$	1.09697e38	+	2.77909e37i	1.52867	+	0.387276i
$638$		−	3.66026e37i		−	0.499382i
$639$	3.86407e36	+	7.31428e37i	0.0516159	+	0.977035i
$640$			1.34618e37i			0.176065i
$641$		−	1.23168e38i		−	1.57730i	−0.614842	−	0.788651i	$-0.710780\pi$
$641$		−	1.23168e38i		−	1.57730i	0.614842	−	0.788651i	$-0.289220\pi$
$642$	−4.84369e37	+	1.27855e36i	−0.607370	+	0.0160323i
$643$		−	4.88694e37i		−	0.600052i	−0.953931	−	0.300026i	$-0.903005\pi$
$643$		−	4.88694e37i		−	0.600052i	0.953931	−	0.300026i	$-0.0969954\pi$
$644$	4.01716e37	+	5.16178e37i	0.483014	+	0.620641i
$645$	1.01490e37	−	2.67895e35i	0.119500	−	0.00315434i
$646$	−2.74048e37			−0.316000
$647$	5.23125e37			0.590742			0.295371	−	0.955383i	$-0.404557\pi$
$647$	5.23125e37			0.590742			0.295371	+	0.955383i	$0.404557\pi$
$648$	3.36830e36	+	3.17902e37i	0.0372519	+	0.351585i
$649$		−	1.03351e38i		−	1.11946i
$650$	3.11947e38			3.30941
$651$	2.06310e37	+	2.51131e37i	0.214376	+	0.260950i
$652$	4.43624e37			0.451516
$653$		−	4.08011e37i		−	0.406765i	−0.979099	−	0.203382i	$-0.934807\pi$
$653$		−	4.08011e37i		−	0.406765i	0.979099	−	0.203382i	$-0.0651935\pi$
$654$	3.53393e36	+	1.33880e38i	0.0345111	+	1.30743i
$655$	−2.90675e38			−2.78068
$656$	−3.70617e36			−0.0347315
$657$	−6.47691e36	−	1.22601e38i	−0.0594614	−	1.12554i
$658$	−6.34781e37	−	8.15651e37i	−0.570919	−	0.733593i
$659$		−	1.43342e38i		−	1.26305i	−0.775356	−	0.631524i	$-0.782430\pi$
$659$		−	1.43342e38i		−	1.26305i	0.775356	−	0.631524i	$-0.217570\pi$
$660$	3.77718e36	+	1.43096e38i	0.0326080	+	1.23533i
$661$			6.68264e37i			0.565234i	0.959233	+	0.282617i	$0.0912026\pi$
$661$			6.68264e37i			0.565234i	−0.959233	+	0.282617i	$0.908797\pi$
$662$			1.26834e38i			1.05112i
$663$	−4.37789e36	−	1.65853e38i	−0.0355494	−	1.34676i
$664$			2.35601e36i			0.0187459i
$665$	−8.20812e37	−	1.05469e38i	−0.639958	−	0.822304i
$666$	3.78792e35	+	7.17014e36i	0.00289400	+	0.0547804i
$667$	−1.19580e38			−0.895283
$668$	−3.94660e37			−0.289562
$669$	−8.31295e34	−	3.14930e36i	−0.000597726	−	0.0226444i
$670$			1.47319e38i			1.03813i
$671$	−1.41784e37			−0.0979207
$672$	1.65781e37	+	2.01798e37i	0.112215	+	0.136594i
$673$	1.25255e38			0.830983			0.415491	−	0.909597i	$-0.363610\pi$
$673$	1.25255e38			0.830983			0.415491	+	0.909597i	$0.363610\pi$
$674$		−	1.30868e38i		−	0.850992i
$675$	−4.64176e38	+	3.68259e37i	−2.95857	+	0.234721i
$676$	1.18989e38			0.743407
$677$	3.82128e37			0.234025			0.117012	−	0.993130i	$-0.462668\pi$
$677$	3.82128e37			0.234025			0.117012	+	0.993130i	$0.462668\pi$
$678$	5.15949e37	−	1.36191e36i	0.309746	−	0.00817612i
$679$	−1.35328e38	−	1.73887e38i	−0.796425	−	1.02335i
$680$			1.04286e38i			0.601664i
$681$	−1.42176e38	+	3.75289e36i	−0.804154	+	0.0212266i
$682$		−	5.34332e37i		−	0.296294i
$683$			1.45565e37i			0.0791368i	0.999217	+	0.0395684i	$0.0125983\pi$
$683$			1.45565e37i			0.0791368i	−0.999217	+	0.0395684i	$0.987402\pi$
$684$	2.58868e36	+	4.90009e37i	0.0137982	+	0.261184i
$685$			5.93965e38i			3.10412i
$686$	−1.26380e38	+	5.54125e37i	−0.647593	+	0.283943i
$687$	8.03475e36	+	3.04391e38i	0.0403698	+	1.52938i
$688$	−3.04526e36			−0.0150031
$689$	2.29552e38			1.10898
$690$	4.67492e38	−	1.23400e37i	2.21468	−	0.0584591i
$691$			9.64470e37i			0.448059i	0.974582	+	0.224029i	$0.0719212\pi$
$691$			9.64470e37i			0.448059i	−0.974582	+	0.224029i	$0.928079\pi$
$692$	−1.98148e37			−0.0902728
$693$	1.81884e38	+	2.09854e38i	0.812634	+	0.937604i
$694$	2.47870e38			1.08610
$695$		−	7.75491e38i		−	3.33259i
$696$	−4.77298e37	+	1.25989e36i	−0.201171	+	0.00531014i
$697$	−2.87109e37			−0.118687
$698$	9.57316e37			0.388157
$699$	−4.27147e36	−	1.61822e38i	−0.0169878	−	0.643569i
$700$	−3.00199e38	+	2.33630e38i	−1.17108	+	0.911392i
$701$			2.73678e38i			1.04724i	0.851951	+	0.523621i	$0.175419\pi$
$701$			2.73678e38i			1.04724i	−0.851951	+	0.523621i	$0.824581\pi$
$702$	−2.96139e38	+	2.34945e37i	−1.11159	+	0.0881890i
$703$			1.10211e37i			0.0405815i
$704$		−	4.29365e37i		−	0.155094i
$705$	−7.38719e38	+	1.94993e37i	−2.61774	+	0.0690982i
$706$			1.37846e38i			0.479214i
$707$	1.33352e38	−	1.03781e38i	0.454818	−	0.353962i
$708$	−1.34769e38	+	3.55740e36i	−0.450964	+	0.0119037i
$709$	1.91128e38			0.627481			0.313741	−	0.949509i	$-0.398418\pi$
$709$	1.91128e38			0.627481			0.313741	+	0.949509i	$0.398418\pi$
$710$	4.27825e38			1.37809
$711$	−1.49547e38	+	7.90046e36i	−0.472649	+	0.0249697i
$712$			1.27438e38i			0.395201i
$713$	−1.74566e38			−0.531190
$714$	1.28427e38	+	1.56328e38i	0.383469	+	0.466778i
$715$	−1.33020e39			−3.89750
$716$		−	2.05031e38i		−	0.589514i
$717$	−3.01078e36	−	1.14061e38i	−0.00849513	−	0.321832i
$718$	1.21416e38			0.336198
$719$	−3.12749e38			−0.849877			−0.424938	−	0.905222i	$-0.639704\pi$
$719$	−3.12749e38			−0.849877			−0.424938	+	0.905222i	$0.639704\pi$
$720$	1.86467e38	−	9.85090e36i	0.497294	−	0.0262716i
$721$	3.71349e38	+	4.77159e38i	0.971978	+	1.24893i
$722$		−	1.99938e38i		−	0.513621i
$723$	2.25238e36	+	8.53297e37i	0.00567903	+	0.215146i
$724$		−	6.70806e37i		−	0.166007i
$725$		−	6.95455e38i		−	1.68930i
$726$	−4.22172e36	−	1.59937e38i	−0.0100657	−	0.381333i
$727$		−	3.62384e38i		−	0.848115i	−0.905635	−	0.424058i	$-0.860605\pi$
$727$		−	3.62384e38i		−	0.848115i	0.905635	−	0.424058i	$-0.139395\pi$
$728$	−1.91523e38	+	1.49053e38i	−0.439995	+	0.342426i
$729$	4.37879e38	−	6.99193e37i	0.987490	−	0.157680i
$730$	−7.17115e38			−1.58756
$731$	−2.35909e37			−0.0512696
$732$	4.88031e35	+	1.84887e37i	0.00104123	+	0.0394464i
$733$			2.33242e38i			0.488543i	0.969707	+	0.244272i	$0.0785488\pi$
$733$			2.33242e38i			0.488543i	−0.969707	+	0.244272i	$0.921451\pi$
$734$	−5.48757e38			−1.12845
$735$	−2.16980e38	+	9.62483e38i	−0.438068	+	1.94318i
$736$	−1.40273e38			−0.278051
$737$		−	4.69876e38i		−	0.914476i
$738$	2.71205e36	+	5.13362e37i	0.00518247	+	0.0980987i
$739$	6.05659e38			1.13639			0.568196	−	0.822893i	$-0.307641\pi$
$739$	6.05659e38			1.13639			0.568196	+	0.822893i	$0.307641\pi$
$740$	4.19394e37			0.0772670
$741$	−4.55825e38	+	1.20321e37i	−0.824618	+	0.0217668i
$742$	−2.20907e38	+	1.71921e38i	−0.392425	+	0.305405i
$743$			9.76725e38i			1.70382i	0.523689	+	0.851910i	$0.324555\pi$
$743$			9.76725e38i			1.70382i	−0.523689	+	0.851910i	$0.675445\pi$
$744$	−6.96770e37	+	1.83921e36i	−0.119359	+	0.00315062i
$745$			7.95711e38i			1.33858i
$746$		−	4.07344e38i		−	0.672957i
$747$	3.26344e37	−	1.72405e36i	0.0529477	−	0.00279718i
$748$		−	3.32620e38i		−	0.530001i
$749$	3.37221e38	+	4.33307e38i	0.527728	+	0.678096i
$750$	4.75857e37	+	1.80275e39i	0.0731390	+	2.77082i
$751$	5.00509e37			0.0755566			0.0377783	−	0.999286i	$-0.487972\pi$
$751$	5.00509e37			0.0755566			0.0377783	+	0.999286i	$0.487972\pi$
$752$	2.21656e38			0.328654
$753$	−8.24354e38	+	2.17598e37i	−1.20055	+	0.0316900i
$754$		−	4.43692e38i		−	0.634699i
$755$	2.03128e39			2.85421
$756$	2.67390e38	−	2.44400e38i	0.369063	−	0.337331i
$757$	−2.43010e38			−0.329480			−0.164740	−	0.986337i	$-0.552679\pi$
$757$	−2.43010e38			−0.329480			−0.164740	+	0.986337i	$0.552679\pi$
$758$			5.69421e38i			0.758401i
$759$	−1.49107e39	+	3.93585e37i	−1.95090	+	0.0514962i
$760$	2.86615e38			0.368397
$761$	−1.08477e39			−1.36977			−0.684884	−	0.728653i	$-0.740147\pi$
$761$	−1.08477e39			−1.36977			−0.684884	+	0.728653i	$0.740147\pi$
$762$	1.39150e36	+	5.27158e37i	0.00172620	+	0.0653957i
$763$	1.19767e39	−	9.32084e38i	1.45967	−	1.13599i
$764$			1.19407e38i			0.142979i
$765$	1.44452e39	−	7.63127e37i	1.69939	−	0.0897775i
$766$		−	9.61561e38i		−	1.11145i
$767$		−	1.25280e39i		−	1.42280i
$768$	−5.59893e37	+	1.47790e36i	−0.0624782	+	0.00164919i
$769$		−	2.43762e38i		−	0.267276i	−0.991030	−	0.133638i	$-0.957334\pi$
$769$		−	2.43762e38i		−	0.267276i	0.991030	−	0.133638i	$-0.0426660\pi$
$770$	1.28011e39	−	9.96243e38i	1.37918	−	1.07335i
$771$	−3.70159e38	+	9.77079e36i	−0.391881	+	0.0103442i
$772$	−3.09561e38			−0.322042
$773$	1.67567e39			1.71303			0.856517	−	0.516118i	$-0.172623\pi$
$773$	1.67567e39			1.71303			0.856517	+	0.516118i	$0.172623\pi$
$774$	2.22842e36	+	4.21816e37i	0.00223869	+	0.0423760i
$775$		−	1.01524e39i		−	1.00230i
$776$	4.72544e38			0.458468
$777$	6.28688e37	−	5.16481e37i	0.0599448	−	0.0492460i
$778$	9.07626e38			0.850516
$779$			7.89081e37i			0.0726718i
$780$	4.57865e37	+	1.73459e39i	0.0414439	+	1.57007i
$781$	−1.36455e39			−1.21395
$782$	−1.08666e39			−0.950176
$783$	5.23785e37	+	6.60211e38i	0.0450162	+	0.567412i
$784$	7.26785e37	−	2.86879e38i	0.0613959	−	0.242344i
$785$			4.82690e38i			0.400800i
$786$	−3.19118e37	−	1.20895e39i	−0.0260463	−	0.986747i
$787$			2.22245e38i			0.178309i	0.996018	+	0.0891546i	$0.0284165\pi$
$787$			2.22245e38i			0.178309i	−0.996018	+	0.0891546i	$0.971583\pi$
$788$		−	7.00704e38i		−	0.552625i
$789$	4.10795e37	+	1.55627e39i	0.0318483	+	1.20655i
$790$			8.74729e38i			0.666665i
$791$	−3.59207e38	−	4.61558e38i	−0.269130	−	0.345815i
$792$	−5.94738e38	+	3.14195e37i	−0.438062	+	0.0231425i
$793$	−1.71869e38			−0.124454
$794$	−1.09946e39			−0.782714
$795$	5.28111e37	+	2.00071e39i	0.0369631	+	1.40032i
$796$		−	2.55577e37i		−	0.0175871i
$797$	1.95746e39			1.32436			0.662180	−	0.749345i	$-0.269632\pi$
$797$	1.95746e39			1.32436			0.662180	+	0.749345i	$0.269632\pi$
$798$	4.29647e38	−	3.52965e38i	0.285807	−	0.234797i
$799$	1.71712e39			1.12310
$800$		−	8.15801e38i		−	0.524650i
$801$	1.76521e39	−	9.32547e37i	1.11624	−	0.0589701i
$802$	3.56859e38			0.221893
$803$	2.28725e39			1.39847
$804$	−6.12720e38	+	1.61735e37i	−0.368388	+	0.00972403i
$805$	−3.25471e39	−	4.18209e39i	−1.92428	−	2.47257i
$806$		−	6.47711e38i		−	0.376581i
$807$	7.42466e38	−	1.95983e37i	0.424506	−	0.0112053i
$808$			3.62388e38i			0.203761i
$809$		−	1.71978e39i		−	0.950972i	−0.879723	−	0.475486i	$-0.842272\pi$
$809$		−	1.71978e39i		−	0.950972i	0.879723	−	0.475486i	$-0.157728\pi$
$810$	−2.72901e38	−	2.57565e39i	−0.148408	−	1.40068i
$811$		−	2.56554e38i		−	0.137214i	−0.997644	−	0.0686069i	$-0.978145\pi$
$811$		−	2.56554e38i		−	0.137214i	0.997644	−	0.0686069i	$-0.0218554\pi$
$812$	3.32298e38	+	4.26982e38i	0.174792	+	0.224596i
$813$	6.31202e37	+	2.39126e39i	0.0326547	+	1.23710i
$814$	−1.33766e38			−0.0680639
$815$	−3.59426e39			−1.79879
$816$	−4.33737e38	+	1.14490e37i	−0.213505	+	0.00563573i
$817$			6.48366e37i			0.0313922i
$818$	5.92179e38			0.282022
$819$	2.20477e39	+	2.54383e39i	1.03283	+	1.19167i
$820$	3.00275e38			0.138367
$821$			2.63868e39i			1.19606i	0.801472	+	0.598032i	$0.204050\pi$
$821$			2.63868e39i			1.19606i	−0.801472	+	0.598032i	$0.795950\pi$
$822$	−2.47037e39	+	6.52084e37i	−1.10152	+	0.0290760i
$823$	1.61360e39			0.707779			0.353890	−	0.935287i	$-0.384859\pi$
$823$	1.61360e39			0.707779			0.353890	+	0.935287i	$0.384859\pi$
$824$	−1.29670e39			−0.559527
$825$	−2.28902e38	−	8.67177e39i	−0.0971674	−	3.68111i
$826$	9.38274e38	+	1.20562e39i	0.391831	+	0.503477i
$827$			1.31706e39i			0.541106i	0.962705	+	0.270553i	$0.0872066\pi$
$827$			1.31706e39i			0.541106i	−0.962705	+	0.270553i	$0.912793\pi$
$828$	1.02647e38	+	1.94300e39i	0.0414894	+	0.785351i
$829$		−	2.62096e39i		−	1.04225i	−0.853479	−	0.521127i	$-0.825512\pi$
$829$		−	2.62096e39i		−	1.04225i	0.853479	−	0.521127i	$-0.174488\pi$
$830$		−	1.90884e38i		−	0.0746820i
$831$	−1.78696e39	+	4.71688e37i	−0.687860	+	0.0181569i
$832$		−	5.20471e38i		−	0.197120i
$833$	5.63024e38	−	2.22239e39i	0.209807	−	0.828156i
$834$	3.22537e39	−	8.51373e37i	1.18260	−	0.0312161i
$835$	3.19755e39			1.15359
$836$	−9.14162e38			−0.324518
$837$	7.64632e37	+	9.63790e38i	0.0267091	+	0.336658i
$838$			1.50875e39i			0.518590i
$839$	2.23910e39			0.757334			0.378667	−	0.925533i	$-0.376382\pi$
$839$	2.23910e39			0.757334			0.378667	+	0.925533i	$0.376382\pi$
$840$	−1.34316e39	−	1.63497e39i	−0.447053	−	0.544176i
$841$	2.06397e39			0.676017
$842$			2.44388e39i			0.787709i
$843$	6.07183e37	+	2.30027e39i	0.0192596	+	0.729636i
$844$	−4.84396e38			−0.151209
$845$	−9.64053e39			−2.96166
$846$	−1.62200e38	−	3.07028e39i	−0.0490402	−	0.928279i
$847$	−1.43076e39	+	1.11349e39i	−0.425738	+	0.331330i
$848$		−	6.00322e38i		−	0.175809i
$849$	1.12667e38	+	4.26832e39i	0.0324747	+	1.23028i
$850$		−	6.31983e39i		−	1.79287i
$851$			4.37012e38i			0.122024i
$852$	4.69688e37	+	1.77938e39i	0.0129085	+	0.489028i
$853$			6.33396e39i			1.71342i	0.515799	+	0.856710i	$0.327495\pi$
$853$			6.33396e39i			1.71342i	−0.515799	+	0.856710i	$0.672505\pi$
$854$	1.65396e38	−	1.28720e38i	0.0440397	−	0.0342739i
$855$	−2.09736e38	−	3.97007e39i	−0.0549705	−	1.04053i
$856$	−1.17753e39			−0.303791
$857$	1.52158e39			0.386414			0.193207	−	0.981158i	$-0.438111\pi$
$857$	1.52158e39			0.386414			0.193207	+	0.981158i	$0.438111\pi$
$858$	−1.46036e38	−	5.53248e39i	−0.0365076	−	1.38306i
$859$			1.82784e39i			0.449812i	0.974380	+	0.224906i	$0.0722075\pi$
$859$			1.82784e39i			0.449812i	−0.974380	+	0.224906i	$0.927792\pi$
$860$	2.46728e38			0.0597707
$861$	4.50123e38	−	3.69787e38i	0.107347	−	0.0881878i
$862$	−3.79453e39			−0.890860
$863$			3.53482e39i			0.816999i	0.912759	+	0.408499i	$0.133948\pi$
$863$			3.53482e39i			0.816999i	−0.912759	+	0.408499i	$0.866052\pi$
$864$	6.14424e37	+	7.74458e38i	0.0139808	+	0.176223i
$865$	1.60540e39			0.359638
$866$	2.37527e39			0.523868
$867$	1.24364e39	−	3.28272e37i	0.270044	−	0.00712814i
$868$	4.85097e38	+	6.23317e38i	0.103708	+	0.133258i
$869$		−	2.78995e39i		−	0.587260i
$870$	3.86708e39	−	1.02076e38i	0.801445	−	0.0211551i
$871$		−	5.69578e39i		−	1.16227i
$872$			3.25470e39i			0.653941i
$873$	−3.45792e38	−	6.54547e39i	−0.0684105	−	1.29494i
$874$			2.98656e39i			0.581790i
$875$	1.61270e40	−	1.25509e40i	3.09347	−	2.40749i
$876$	−7.87285e37	−	2.98257e39i	−0.0148705	−	0.563359i
$877$	−8.60012e39			−1.59959			−0.799797	−	0.600270i	$-0.795060\pi$
$877$	−8.60012e39			−1.59959			−0.799797	+	0.600270i	$0.795060\pi$
$878$	−6.41846e39			−1.17559
$879$	5.29469e39	−	1.39760e38i	0.954973	−	0.0252076i
$880$			3.47873e39i			0.617881i
$881$	6.06470e39			1.06080			0.530401	−	0.847747i	$-0.322041\pi$
$881$	6.06470e39			1.06080			0.530401	+	0.847747i	$0.322041\pi$
$882$	−4.02691e39	−	7.96782e38i	−0.693659	−	0.137250i
$883$	1.42607e39			0.241920			0.120960	−	0.992657i	$-0.461403\pi$
$883$	1.42607e39			0.241920			0.120960	+	0.992657i	$0.461403\pi$
$884$		−	4.03197e39i		−	0.673615i
$885$	1.09191e40	−	2.88221e38i	1.79660	−	0.0474233i
$886$	−4.75136e39			−0.769950
$887$	−1.80416e39			−0.287943			−0.143972	−	0.989582i	$-0.545987\pi$
$887$	−1.80416e39			−0.287943			−0.143972	+	0.989582i	$0.545987\pi$
$888$	4.60432e36	+	1.74431e38i	0.000723753	+	0.0274189i
$889$	4.71586e38	−	3.67011e38i	0.0730107	−	0.0568206i
$890$		−	1.03250e40i		−	1.57444i
$891$	8.70419e38	+	8.21507e39i	0.130731	+	1.23385i
$892$		−	7.65611e37i		−	0.0113262i
$893$		−	4.71928e39i		−	0.687671i
$894$	−3.30946e39	+	8.73572e37i	−0.475008	+	0.0125384i
$895$			1.66117e40i			2.34857i
$896$	3.89802e38	+	5.00869e38i	0.0542857	+	0.0697536i
$897$	−1.80745e40	+	4.77099e38i	−2.47953	+	0.0654501i
$898$	6.04876e39			0.817402
$899$	−1.44400e39			−0.192226
$900$	−1.13001e40	+	5.96976e38i	−1.48187	+	0.0782858i
$901$		−	4.65056e39i		−	0.600787i
$902$	−9.57730e38			−0.121886
$903$	3.69854e38	−	3.03843e38i	0.0463709	−	0.0380948i
$904$	1.25430e39			0.154927
$905$			5.43489e39i			0.661356i
$906$	2.23004e38	+	8.44834e39i	0.0267351	+	1.01284i
$907$	7.61805e38			0.0899799			0.0449900	−	0.998987i	$-0.485674\pi$
$907$	7.61805e38			0.0899799			0.0449900	+	0.998987i	$0.485674\pi$
$908$	−3.45636e39			−0.402217
$909$	5.01965e39	−	2.65184e38i	0.575520	−	0.0304043i
$910$	1.55173e40	−	1.20763e40i	1.75290	−	1.36419i
$911$			1.61145e40i			1.79357i	0.442466	+	0.896786i	$0.354104\pi$
$911$			1.61145e40i			1.79357i	−0.442466	+	0.896786i	$0.645896\pi$
$912$	3.14661e37	+	1.19207e39i	0.00345074	+	0.130729i
$913$			6.08827e38i			0.0657868i
$914$			8.00379e39i			0.852161i
$915$	−3.95404e37	−	1.49796e39i	−0.00414817	−	0.157150i
$916$			7.39989e39i			0.764956i
$917$	−1.08151e40	+	8.41683e39i	−1.10165	+	0.857359i
$918$	4.75980e38	+	5.99955e39i	0.0477763	+	0.602203i
$919$	1.52888e39			0.151221			0.0756107	−	0.997137i	$-0.475909\pi$
$919$	1.52888e39			0.151221			0.0756107	+	0.997137i	$0.475909\pi$
$920$	1.13650e40			1.10773
$921$	1.95028e36	+	7.38848e37i	0.000187323	+	0.00709660i
$922$		−	9.62069e38i		−	0.0910623i
$923$	−1.65409e40			−1.54290
$924$	4.28404e39	+	5.21475e39i	0.393805	+	0.479360i
$925$	−2.54158e39			−0.230245
$926$		−	1.34132e39i		−	0.119752i
$927$	9.48879e38	+	1.79613e40i	0.0834900	+	1.58038i
$928$	−1.16034e39			−0.100620
$929$	8.52250e39			0.728375			0.364187	−	0.931326i	$-0.381347\pi$
$929$	8.52250e39			0.728375			0.364187	+	0.931326i	$0.381347\pi$
$930$	5.64525e39	−	1.49013e38i	0.475514	−	0.0125518i
$931$	−6.10794e39	−	1.54740e39i	−0.507077	−	0.128464i
$932$		−	3.93397e39i		−	0.321896i
$933$	−1.22066e40	+	3.22208e38i	−0.984447	+	0.0259856i
$934$			4.48444e39i			0.356472i
$935$			2.69489e40i			2.11147i
$936$	−7.20934e39	+	3.80863e38i	−0.556764	+	0.0294134i
$937$			2.33753e40i			1.77940i	0.456547	+	0.889699i	$0.349086\pi$
$937$			2.33753e40i			1.77940i	−0.456547	+	0.889699i	$0.650914\pi$
$938$	4.26580e39	+	5.48127e39i	0.320083	+	0.411285i
$939$	−5.06177e38	−	1.91761e40i	−0.0374384	−	1.41833i
$940$	−1.79586e40			−1.30932
$941$	−1.29975e40			−0.934112			−0.467056	−	0.884228i	$-0.654685\pi$
$941$	−1.29975e40			−0.934112			−0.467056	+	0.884228i	$0.654685\pi$
$942$	−2.00757e39	+	5.29921e37i	−0.142227	+	0.00375426i
$943$			3.12889e39i			0.218516i
$944$	−3.27631e39			−0.225561
$945$	−2.16640e40	+	1.98013e40i	−1.47031	+	1.34389i
$946$	−7.86940e38			−0.0526516
$947$			1.14758e40i			0.756934i	0.925615	+	0.378467i	$0.123549\pi$
$947$			1.14758e40i			0.756934i	−0.925615	+	0.378467i	$0.876451\pi$
$948$	−3.63811e39	+	9.60321e37i	−0.236572	+	0.00624459i
$949$	2.77257e40			1.77741
$950$	−1.73692e40			−1.09777
$951$	−8.27284e38	−	3.13411e40i	−0.0515487	−	1.95289i
$952$	3.01971e39	+	3.88012e39i	0.185509	+	0.238367i
$953$		−	1.88401e40i		−	1.14112i	−0.821257	−	0.570558i	$-0.806727\pi$
$953$		−	1.88401e40i		−	1.14112i	0.821257	−	0.570558i	$-0.193273\pi$
$954$	−8.31540e39	+	4.39296e38i	−0.496570	+	0.0262334i
$955$		−	9.67443e39i		−	0.569613i
$956$		−	2.77288e39i		−	0.160972i
$957$	−1.23341e40	+	3.25573e38i	−0.705986	+	0.0186353i
$958$		−	1.82781e40i		−	1.03156i
$959$	1.71989e40	+	2.20995e40i	0.957084	+	1.22979i
$960$	4.53627e39	−	1.19740e38i	0.248907	−	0.00657020i
$961$	1.63747e40			0.885948
$962$	−1.62150e39			−0.0865072
$963$	8.61675e38	+	1.63106e40i	0.0453303	+	0.858054i
$964$			2.07441e39i			0.107610i
$965$	2.50807e40			1.28298
$966$	1.70365e40	−	1.39959e40i	0.859389	−	0.706007i
$967$	−3.86290e39			−0.192157			−0.0960784	−	0.995374i	$-0.530630\pi$
$967$	−3.86290e39			−0.192157			−0.0960784	+	0.995374i	$0.530630\pi$
$968$		−	3.88815e39i		−	0.190733i
$969$	2.43761e38	+	9.23469e39i	0.0117921	+	0.446736i
$970$	−3.82856e40			−1.82649
$971$	2.97153e39			0.139804			0.0699022	−	0.997554i	$-0.477731\pi$
$971$	2.97153e39			0.139804			0.0699022	+	0.997554i	$0.477731\pi$
$972$	1.06825e40	−	1.41780e39i	0.495654	−	0.0657839i
$973$	−2.24552e40	−	2.88535e40i	−1.02753	−	1.32031i
$974$			1.36953e40i			0.618052i
$975$	−2.77471e39	−	1.05118e41i	−0.123497	−	4.67859i
$976$			4.49470e38i			0.0197301i
$977$		−	4.37499e40i		−	1.89409i	−0.321099	−	0.947045i	$-0.604052\pi$
$977$		−	4.37499e40i		−	1.89409i	0.321099	−	0.947045i	$-0.395948\pi$
$978$	−3.94596e38	−	1.49490e40i	−0.0168491	−	0.638317i
$979$			3.29318e40i			1.38691i
$980$	−5.88843e39	+	2.32430e40i	−0.244595	+	0.965474i
$981$	4.50827e40	−	2.38168e39i	1.84705	−	0.0975780i
$982$	1.25713e40			0.508012
$983$	−3.57552e40			−1.42517			−0.712584	−	0.701586i	$-0.752475\pi$
$983$	−3.57552e40			−1.42517			−0.712584	+	0.701586i	$0.752475\pi$
$984$	3.29657e37	+	1.24888e39i	0.00129607	+	0.0491006i
$985$			5.67712e40i			2.20160i
$986$	−8.98887e39			−0.343848
$987$	−2.69207e40	+	2.21159e40i	−1.01579	+	0.834495i
$988$	−1.10814e40			−0.412453
$989$			2.57092e39i			0.0943928i
$990$	4.81859e40	−	2.54562e39i	1.74520	−	0.0921973i
$991$	3.99114e40			1.42594			0.712972	−	0.701193i	$-0.247349\pi$
$991$	3.99114e40			1.42594			0.712972	+	0.701193i	$0.247349\pi$
$992$	−1.69388e39			−0.0597003
$993$	4.27397e40	−	1.12817e39i	1.48599	−	0.0392245i
$994$	1.59180e40	−	1.23882e40i	0.545974	−	0.424904i
$995$			2.07069e39i			0.0700653i
$996$	7.93912e38	−	2.09562e37i	0.0265015	−	0.000699540i
$997$		−	4.54216e40i		−	1.49582i	−0.663803	−	0.747908i	$-0.731059\pi$
$997$		−	4.54216e40i		−	1.49582i	0.663803	−	0.747908i	$-0.268941\pi$
$998$		−	2.16613e40i		−	0.703757i
$999$	2.41278e39	−	1.91420e38i	0.0773362	−	0.00613555i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	42.28.d.a.41.11	✓	72
3.2	odd	2	inner	42.28.d.a.41.62	yes	72
7.6	odd	2	inner	42.28.d.a.41.61	yes	72
21.20	even	2	inner	42.28.d.a.41.12	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.28.d.a.41.11	✓	72	1.1	even	1	trivial
42.28.d.a.41.12	yes	72	21.20	even	2	inner
42.28.d.a.41.61	yes	72	7.6	odd	2	inner
42.28.d.a.41.62	yes	72	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 42 = 2 \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 28 \)
Character orbit:	\([\chi]\)	\(=\)	42.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-8192.00i q^{2} +(-2.76049e6 + 72866.3i) q^{3} -6.71089e7 q^{4} +5.43718e9 q^{5} +(5.96921e8 + 2.26139e10i) q^{6} +(2.02300e11 - 1.57440e11i) q^{7} +5.49756e11i q^{8} +(7.61498e12 - 4.02293e11i) q^{9} -4.45414e13i q^{10} +1.42065e14i q^{11} +(1.85253e14 - 4.88998e12i) q^{12} +1.72209e15i q^{13} +(-1.28975e15 - 1.65724e15i) q^{14} +(-1.50093e16 + 3.96187e14i) q^{15} +4.50360e15 q^{16} +3.48884e16 q^{17} +(-3.29558e15 - 6.23819e16i) q^{18} -9.58862e16i q^{19} -3.64883e17 q^{20} +(-5.46973e17 + 4.49351e17i) q^{21} +1.16380e18 q^{22} -3.80211e18i q^{23} +(-4.00587e16 - 1.51759e18i) q^{24} +2.21123e19 q^{25} +1.41074e19 q^{26} +(-2.09917e19 + 1.66540e18i) q^{27} +(-1.35761e19 + 1.05656e19i) q^{28} -3.14510e19i q^{29} +(3.24557e18 + 1.22956e20i) q^{30} -4.59128e19i q^{31} -3.68935e19i q^{32} +(-1.03518e19 - 3.92169e20i) q^{33} -2.85806e20i q^{34} +(1.09994e21 - 8.56028e20i) q^{35} +(-5.11033e20 + 2.69974e19i) q^{36} -1.14939e20 q^{37} -7.85499e20 q^{38} +(-1.25483e20 - 4.75382e21i) q^{39} +2.98912e21i q^{40} -8.22935e20 q^{41} +(3.68108e21 + 4.48080e21i) q^{42} -6.76183e20 q^{43} -9.53383e21i q^{44} +(4.14040e22 - 2.18734e21i) q^{45} -3.11469e22 q^{46} +4.92175e22 q^{47} +(-1.24321e22 + 3.28161e20i) q^{48} +(1.61379e22 - 6.37000e22i) q^{49} -1.81144e23i q^{50} +(-9.63089e22 + 2.54219e21i) q^{51} -1.15568e23i q^{52} -1.33298e23i q^{53} +(1.36430e22 + 1.71964e23i) q^{54} +7.72433e23i q^{55} +(8.65534e22 + 1.11215e23i) q^{56} +(6.98687e21 + 2.64692e23i) q^{57} -2.57647e23 q^{58} -7.27488e23 q^{59} +(1.00725e24 - 2.65877e22i) q^{60} +9.98024e22i q^{61} -3.76118e23 q^{62} +(1.47717e24 - 1.28028e24i) q^{63} -3.02231e23 q^{64} +9.36333e24i q^{65} +(-3.21265e24 + 8.48016e22i) q^{66} -3.30747e24 q^{67} -2.34132e24 q^{68} +(2.77046e23 + 1.04957e25i) q^{69} +(-7.01258e24 - 9.01070e24i) q^{70} +9.60512e24i q^{71} +(2.21163e23 + 4.18638e24i) q^{72} -1.61000e25i q^{73} +9.41583e23i q^{74} +(-6.10408e25 + 1.61124e24i) q^{75} +6.43481e24i q^{76} +(2.23667e25 + 2.87397e25i) q^{77} +(-3.89433e25 + 1.02795e24i) q^{78} -1.96386e25 q^{79} +2.44869e25 q^{80} +(5.78261e25 - 6.12691e24i) q^{81} +6.74148e24i q^{82} +4.28555e24 q^{83} +(3.67068e25 - 3.01554e25i) q^{84} +1.89694e26 q^{85} +5.53929e24i q^{86} +(2.29172e24 + 8.68200e25i) q^{87} -7.81011e25 q^{88} +2.31808e26 q^{89} +(-1.79187e25 - 3.39182e26i) q^{90} +(2.71126e26 + 3.48379e26i) q^{91} +2.55155e26i q^{92} +(3.34550e24 + 1.26742e26i) q^{93} -4.03190e26i q^{94} -5.21350e26i q^{95} +(2.68829e24 + 1.01844e26i) q^{96} -8.59553e26i q^{97} +(-5.21830e26 - 1.32201e26i) q^{98} +(5.71518e25 + 1.08182e27i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 4831838208 q^{4} + 173098572084 q^{7} + 10931690833860 q^{9} - 26\!\cdots\!68 q^{15} + 32\!\cdots\!12 q^{16} - 24\!\cdots\!00 q^{18} + 10\!\cdots\!36 q^{21} - 26\!\cdots\!80 q^{22} + 11\!\cdots\!60 q^{25}+ \cdots - 59\!\cdots\!40 q^{99}+O(q^{100}) \) 72 * q - 4831838208 * q^4 + 173098572084 * q^7 + 10931690833860 * q^9 - 26442633448919268 * q^15 + 324259173170675712 * q^16 - 242698684300492800 * q^18 + 1081562836793204136 * q^21 - 2684750441896673280 * q^22 + 112067860522999462560 * q^25 - 11616448532579352576 * q^28 - 400382102997890531328 * q^30 - 733613353459557335040 * q^36 + 2987518151389179781008 * q^37 + 5509242802593360042396 * q^39 + 7342334144630240477184 * q^42 + 38276543559094928933184 * q^43 - 47129436388964590682112 * q^46 - 246837558232318243206960 * q^49 + 180152926647992184062232 * q^51 + 2549537180400127603920132 * q^57 - 463456938429255032045568 * q^58 + 1774535091925374103191552 * q^60 + 1839194856473813675870064 * q^63 - 21760664753063325144711168 * q^64 - 5521386041924492099769264 * q^67 - 899114292517766427574272 * q^70 + 16287232997700706448179200 * q^72 - 127774240517705488068280320 * q^78 + 91626681768773661319484520 * q^79 + 25422207502947578014228992 * q^81 - 72582453321809332487061504 * q^84 - 112192359350687429664946176 * q^85 + 180170552279183749199953920 * q^88 + 1190684031659173062666572472 * q^91 + 1605040757349523360531558488 * q^93 - 5985962449271479573968162240 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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