LMFDB - Embedded newform 21.30.c.a.20.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [21,30,Mod(20,21)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(21, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 30, names="a")

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

chi := DirichletCharacter("21.20");

S:= CuspForms(chi, 30);

N := Newforms(S);

Level:	$ N $	$=$	$ 21 = 3 \cdot 7 $
Weight:	$ k $	$=$	$ 30 $
Character orbit:	$[\chi]$	$=$	21.c (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$111.883889004$
Analytic rank:	$0$
Dimension:	$76$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			20.6
Character	$\chi$	$=$	21.20
Dual form			21.30.c.a.20.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+38457.7i q^{2} +(8.27750e6 + 336727. i) q^{3} -9.42122e8 q^{4} -2.26488e10 q^{5} +(-1.29498e10 + 3.18333e11i) q^{6} +(6.92104e11 + 1.65557e12i) q^{7} -1.55850e13i q^{8} +(6.84036e13 + 5.57452e12i) q^{9} +O(q^{10})$	\(q+38457.7i q^{2} +(8.27750e6 + 336727. i) q^{3} -9.42122e8 q^{4} -2.26488e10 q^{5} +(-1.29498e10 + 3.18333e11i) q^{6} +(6.92104e11 + 1.65557e12i) q^{7} -1.55850e13i q^{8} +(6.84036e13 + 5.57452e12i) q^{9} -8.71020e14i q^{10} -2.70292e14i q^{11} +(-7.79842e15 - 3.17238e14i) q^{12} +4.56446e15i q^{13} +(-6.36692e16 + 2.66167e16i) q^{14} +(-1.87475e17 - 7.62647e15i) q^{15} +9.35660e16 q^{16} +1.12100e18 q^{17} +(-2.14383e17 + 2.63064e18i) q^{18} -5.21426e18i q^{19} +2.13379e19 q^{20} +(5.17141e18 + 1.39370e19i) q^{21} +1.03948e19 q^{22} -7.10335e19i q^{23} +(5.24791e18 - 1.29005e20i) q^{24} +3.26704e20 q^{25} -1.75539e20 q^{26} +(5.64334e20 + 6.91765e19i) q^{27} +(-6.52046e20 - 1.55975e21i) q^{28} +4.93987e20i q^{29} +(2.93296e20 - 7.20987e21i) q^{30} -4.68274e21i q^{31} -4.76882e21i q^{32} +(9.10148e19 - 2.23734e21i) q^{33} +4.31110e22i q^{34} +(-1.56753e22 - 3.74966e22i) q^{35} +(-6.44446e22 - 5.25188e21i) q^{36} +8.67228e22 q^{37} +2.00528e23 q^{38} +(-1.53698e21 + 3.77823e22i) q^{39} +3.52982e23i q^{40} +7.90557e22 q^{41} +(-5.35984e23 + 1.98881e23i) q^{42} -3.53714e23 q^{43} +2.54648e23i q^{44} +(-1.54926e24 - 1.26256e23i) q^{45} +2.73178e24 q^{46} -1.01420e24 q^{47} +(7.74492e23 + 3.15062e22i) q^{48} +(-2.26189e24 + 2.29165e24i) q^{49} +1.25643e25i q^{50} +(9.27906e24 + 3.77471e23i) q^{51} -4.30028e24i q^{52} -1.01570e25i q^{53} +(-2.66037e24 + 2.17030e25i) q^{54} +6.12180e24i q^{55} +(2.58020e25 - 1.07865e25i) q^{56} +(1.75578e24 - 4.31611e25i) q^{57} -1.89976e25 q^{58} -4.20416e25 q^{59} +(1.76625e26 + 7.18507e24i) q^{60} -1.70909e25i q^{61} +1.80087e26 q^{62} +(3.81134e25 + 1.17105e26i) q^{63} +2.33631e26 q^{64} -1.03380e26i q^{65} +(8.60431e25 + 3.50022e24i) q^{66} +3.45672e26 q^{67} -1.05612e27 q^{68} +(2.39189e25 - 5.87980e26i) q^{69} +(1.44203e27 - 6.02837e26i) q^{70} +5.62685e26i q^{71} +(8.68791e25 - 1.06607e27i) q^{72} +1.75673e27i q^{73} +3.33516e27i q^{74} +(2.70429e27 + 1.10010e26i) q^{75} +4.91247e27i q^{76} +(4.47487e26 - 1.87070e26i) q^{77} +(-1.45302e27 - 5.91086e25i) q^{78} +3.30282e27 q^{79} -2.11916e27 q^{80} +(4.64798e27 + 7.62635e26i) q^{81} +3.04030e27i q^{82} -1.10330e27 q^{83} +(-4.87211e27 - 1.31304e28i) q^{84} -2.53893e28 q^{85} -1.36030e28i q^{86} +(-1.66339e26 + 4.08898e27i) q^{87} -4.21251e27 q^{88} +1.29438e28 q^{89} +(4.85552e27 - 5.95809e28i) q^{90} +(-7.55676e27 + 3.15908e27i) q^{91} +6.69222e28i q^{92} +(1.57681e27 - 3.87614e28i) q^{93} -3.90039e28i q^{94} +1.18097e29i q^{95} +(1.60579e27 - 3.94739e28i) q^{96} +1.79904e28i q^{97} +(-8.81314e28 - 8.69871e28i) q^{98} +(1.50675e27 - 1.84890e28i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 76 q - 20401094660 q^{4} + 1962751543872 q^{7} - 89581451225964 q^{9}+O(q^{10}) $ 76 * q - 20401094660 * q^4 + 1962751543872 * q^7 - 89581451225964 * q^9	$ 76 q - 20401094660 q^{4} + 1962751543872 q^{7} - 89581451225964 q^{9} - 11\!\cdots\!48 q^{15}+ \cdots - 23\!\cdots\!24 q^{99}+O(q^{100}) $ 76 * q - 20401094660 * q^4 + 1962751543872 * q^7 - 89581451225964 * q^9 - 116668222909200048 * q^15 + 4964525139713333892 * q^16 + 1542346202347854996 * q^18 + 33840646982361357348 * q^21 - 9870996616978150672 * q^22 + 3225406746743103424612 * q^25 - 3181907581338093199564 * q^28 + 5113912044496410095244 * q^30 - 85758641407134848258352 * q^36 - 17812771227715200149976 * q^37 + 388095283792424641491696 * q^39 + 804036587819434104664956 * q^42 + 2391536152977907871782320 * q^43 - 1070985628070611677307000 * q^46 - 512656982878691867441540 * q^49 - 961431915936904000664400 * q^51 + 20345422731681279280765248 * q^57 - 40096240109469024574169272 * q^58 - 164991837955115951799442596 * q^60 - 360764839802574990409097184 * q^63 - 1608343949909674725081473028 * q^64 + 483978610969894046870693264 * q^67 - 656026306765550013508448520 * q^70 + 1937172856654554597960695124 * q^72 - 8054141680325499868559088636 * q^78 - 11740735193468750125742145952 * q^79 + 18477545939654446572971367132 * q^81 - 7249045143271847568431965452 * q^84 + 14576359553686844022629140848 * q^85 - 1685535263940707754634995584 * q^88 + 44135166284535829618726469040 * q^91 + 226499776928895503792863540632 * q^93 - 231093384978708762520959066624 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/21\mathbb{Z}\right)^\times$.

$n$	$8$	$10$
$\chi(n)$	$-1$	$-1$

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 $

$2$			38457.7i			1.65977i	0.557934	+	0.829885i	$0.311594\pi$
$2$			38457.7i			1.65977i	−0.557934	+	0.829885i	$0.688406\pi$
$3$	8.27750e6	+	336727.i	0.999174	+	0.0406462i
$3$	8.27750e6	+	336727.i	0.999174	+	0.0406462i
$4$	−9.42122e8			−1.75484
$5$	−2.26488e10			−1.65951			−0.829756	−	0.558127i	$-0.811520\pi$
$5$	−2.26488e10			−1.65951			−0.829756	+	0.558127i	$0.811520\pi$
$6$	−1.29498e10	+	3.18333e11i	−0.0674634	+	1.65840i
$7$	6.92104e11	+	1.65557e12i	0.385700	+	0.922624i
$7$	6.92104e11	+	1.65557e12i	0.385700	+	0.922624i
$8$		−	1.55850e13i		−	1.25286i
$9$	6.84036e13	+	5.57452e12i	0.996696	+	0.0812253i
$10$		−	8.71020e14i		−	2.75441i
$11$		−	2.70292e14i		−	0.214605i	−0.994226	−	0.107302i	$-0.965779\pi$
$11$		−	2.70292e14i		−	0.214605i	0.994226	−	0.107302i	$-0.0342213\pi$
$12$	−7.79842e15	−	3.17238e14i	−1.75339	−	0.0713276i
$13$			4.56446e15i			0.321522i	0.986993	+	0.160761i	$0.0513948\pi$
$13$			4.56446e15i			0.321522i	−0.986993	+	0.160761i	$0.948605\pi$
$14$	−6.36692e16	+	2.66167e16i	−1.53134	+	0.640174i
$15$	−1.87475e17	−	7.62647e15i	−1.65814	−	0.0674529i
$16$	9.35660e16			0.324622
$17$	1.12100e18			1.61471			0.807357	−	0.590063i	$-0.200897\pi$
$17$	1.12100e18			1.61471			0.807357	+	0.590063i	$0.200897\pi$
$18$	−2.14383e17	+	2.63064e18i	−0.134815	+	1.65429i
$19$		−	5.21426e18i		−	1.49715i	−0.663049	−	0.748576i	$-0.730738\pi$
$19$		−	5.21426e18i		−	1.49715i	0.663049	−	0.748576i	$-0.269262\pi$
$20$	2.13379e19			2.91218
$21$	5.17141e18	+	1.39370e19i	0.347880	+	0.937539i
$22$	1.03948e19			0.356195
$23$		−	7.10335e19i		−	1.27764i	−0.769355	−	0.638821i	$-0.779422\pi$
$23$		−	7.10335e19i		−	1.27764i	0.769355	−	0.638821i	$-0.220578\pi$
$24$	5.24791e18	−	1.29005e20i	0.0509241	−	1.25183i
$25$	3.26704e20			1.75398
$26$	−1.75539e20			−0.533653
$27$	5.64334e20	+	6.91765e19i	0.992571	+	0.121670i
$28$	−6.52046e20	−	1.55975e21i	−0.676842	−	1.61906i
$29$			4.93987e20i			0.308280i	0.988049	+	0.154140i	$0.0492606\pi$
$29$			4.93987e20i			0.308280i	−0.988049	+	0.154140i	$0.950739\pi$
$30$	2.93296e20	−	7.20987e21i	0.111956	−	2.75213i
$31$		−	4.68274e21i		−	1.11111i	−0.831481	−	0.555553i	$-0.812506\pi$
$31$		−	4.68274e21i		−	1.11111i	0.831481	−	0.555553i	$-0.187494\pi$
$32$		−	4.76882e21i		−	0.714062i
$33$	9.10148e19	−	2.23734e21i	0.00872288	−	0.214428i
$34$			4.31110e22i			2.68006i
$35$	−1.56753e22	−	3.74966e22i	−0.640074	−	1.53111i
$36$	−6.44446e22	−	5.25188e21i	−1.74904	−	0.142537i
$37$	8.67228e22			1.58201			0.791003	−	0.611812i	$-0.209559\pi$
$37$	8.67228e22			1.58201			0.791003	+	0.611812i	$0.209559\pi$
$38$	2.00528e23			2.48493
$39$	−1.53698e21	+	3.77823e22i	−0.0130687	+	0.321256i
$40$			3.52982e23i			2.07914i
$41$	7.90557e22			0.325512			0.162756	−	0.986666i	$-0.447962\pi$
$41$	7.90557e22			0.325512			0.162756	+	0.986666i	$0.447962\pi$
$42$	−5.35984e23	+	1.98881e23i	−1.55610	+	0.577401i
$43$	−3.53714e23			−0.730061			−0.365031	−	0.930995i	$-0.618942\pi$
$43$	−3.53714e23			−0.730061			−0.365031	+	0.930995i	$0.618942\pi$
$44$			2.54648e23i			0.376597i
$45$	−1.54926e24	−	1.26256e23i	−1.65403	−	0.134794i
$46$	2.73178e24			2.12059
$47$	−1.01420e24			−0.576375			−0.288188	−	0.957574i	$-0.593053\pi$
$47$	−1.01420e24			−0.576375			−0.288188	+	0.957574i	$0.593053\pi$
$48$	7.74492e23	+	3.15062e22i	0.324354	+	0.0131947i
$49$	−2.26189e24	+	2.29165e24i	−0.702471	+	0.711712i
$50$			1.25643e25i			2.91120i
$51$	9.27906e24	+	3.77471e23i	1.61338	+	0.0656320i
$52$		−	4.30028e24i		−	0.564220i
$53$		−	1.01570e25i		−	1.01103i	−0.862818	−	0.505514i	$-0.831303\pi$
$53$		−	1.01570e25i		−	1.01103i	0.862818	−	0.505514i	$-0.168697\pi$
$54$	−2.66037e24	+	2.17030e25i	−0.201944	+	1.64744i
$55$			6.12180e24i			0.356139i
$56$	2.58020e25	−	1.07865e25i	1.15592	−	0.483228i
$57$	1.75578e24	−	4.31611e25i	0.0608535	−	1.49591i
$58$	−1.89976e25			−0.511674
$59$	−4.20416e25			−0.883741			−0.441870	−	0.897079i	$-0.645685\pi$
$59$	−4.20416e25			−0.883741			−0.441870	+	0.897079i	$0.645685\pi$
$60$	1.76625e26	+	7.18507e24i	2.90977	+	0.118369i
$61$		−	1.70909e25i		−	0.221556i	−0.993845	−	0.110778i	$-0.964666\pi$
$61$		−	1.70909e25i		−	0.221556i	0.993845	−	0.110778i	$-0.0353342\pi$
$62$	1.80087e26			1.84418
$63$	3.81134e25	+	1.17105e26i	0.309485	+	0.950904i
$64$	2.33631e26			1.50980
$65$		−	1.03380e26i		−	0.533569i
$66$	8.60431e25	+	3.50022e24i	0.355901	+	0.0144780i
$67$	3.45672e26			1.14969			0.574843	−	0.818264i	$-0.305063\pi$
$67$	3.45672e26			1.14969			0.574843	+	0.818264i	$0.305063\pi$
$68$	−1.05612e27			−2.83356
$69$	2.39189e25	−	5.87980e26i	0.0519314	−	1.27659i
$70$	1.44203e27	−	6.02837e26i	2.54128	−	1.06238i
$71$			5.62685e26i			0.807270i	0.914920	+	0.403635i	$0.132254\pi$
$71$			5.62685e26i			0.807270i	−0.914920	+	0.403635i	$0.867746\pi$
$72$	8.68791e25	−	1.06607e27i	0.101764	−	1.24872i
$73$			1.75673e27i			1.68470i	0.538931	+	0.842350i	$0.318828\pi$
$73$			1.75673e27i			1.68470i	−0.538931	+	0.842350i	$0.681172\pi$
$74$			3.33516e27i			2.62577i
$75$	2.70429e27	+	1.10010e26i	1.75253	+	0.0712926i
$76$			4.91247e27i			2.62726i
$77$	4.47487e26	−	1.87070e26i	0.198000	−	0.0827731i
$78$	−1.45302e27	−	5.91086e25i	−0.533212	−	0.0216910i
$79$	3.30282e27			1.00761			0.503804	−	0.863818i	$-0.331933\pi$
$79$	3.30282e27			1.00761			0.503804	+	0.863818i	$0.331933\pi$
$80$	−2.11916e27			−0.538714
$81$	4.64798e27	+	7.62635e26i	0.986805	+	0.161914i
$82$			3.04030e27i			0.540276i
$83$	−1.10330e27			−0.164460			−0.0822300	−	0.996613i	$-0.526204\pi$
$83$	−1.10330e27			−0.164460			−0.0822300	+	0.996613i	$0.526204\pi$
$84$	−4.87211e27	−	1.31304e28i	−0.610474	−	1.64523i
$85$	−2.53893e28			−2.67964
$86$		−	1.36030e28i		−	1.21173i
$87$	−1.66339e26	+	4.08898e27i	−0.0125304	+	0.308025i
$88$	−4.21251e27			−0.268870
$89$	1.29438e28			0.701304			0.350652	−	0.936506i	$-0.385960\pi$
$89$	1.29438e28			0.701304			0.350652	+	0.936506i	$0.385960\pi$
$90$	4.85552e27	−	5.95809e28i	0.223728	−	2.74531i
$91$	−7.55676e27	+	3.15908e27i	−0.296644	+	0.124011i
$92$			6.69222e28i			2.24206i
$93$	1.57681e27	−	3.87614e28i	0.0451623	−	1.11019i
$94$		−	3.90039e28i		−	0.956651i
$95$			1.18097e29i			2.48454i
$96$	1.60579e27	−	3.94739e28i	0.0290239	−	0.713472i
$97$			1.79904e28i			0.279802i	0.990165	+	0.139901i	$0.0446785\pi$
$97$			1.79904e28i			0.279802i	−0.990165	+	0.139901i	$0.955322\pi$
$98$	−8.81314e28	−	8.69871e28i	−1.18128	−	1.16594i
$99$	1.50675e27	−	1.84890e28i	0.0174313	−	0.213896i
$100$	−3.07795e29			−3.07795
$101$	−2.73147e28			−0.236449			−0.118224	−	0.992987i	$-0.537720\pi$
$101$	−2.73147e28			−0.236449			−0.118224	+	0.992987i	$0.537720\pi$
$102$	−1.45167e28	+	3.56851e29i	−0.108934	+	2.67784i
$103$			2.71089e29i			1.76592i	0.469445	+	0.882961i	$0.344454\pi$
$103$			2.71089e29i			1.76592i	−0.469445	+	0.882961i	$0.655546\pi$
$104$	7.11372e28			0.402822
$105$	−1.17126e29	−	3.15656e29i	−0.577311	−	1.55586i
$106$	3.90613e29			1.67808
$107$		−	2.14216e29i		−	0.803131i	−0.915830	−	0.401565i	$-0.868466\pi$
$107$		−	2.14216e29i		−	0.803131i	0.915830	−	0.401565i	$-0.131534\pi$
$108$	−5.31671e29	−	6.51727e28i	−1.74180	−	0.213511i
$109$	−2.60574e29			−0.746872			−0.373436	−	0.927656i	$-0.621820\pi$
$109$	−2.60574e29			−0.746872			−0.373436	+	0.927656i	$0.621820\pi$
$110$	−2.35430e29			−0.591110
$111$	7.17848e29	+	2.92019e28i	1.58070	+	0.0643026i
$112$	6.47574e28	+	1.54905e29i	0.125207	+	0.299504i
$113$		−	8.14445e28i		−	0.138428i	−0.997602	−	0.0692141i	$-0.977951\pi$
$113$		−	8.14445e28i		−	0.138428i	0.997602	−	0.0692141i	$-0.0220492\pi$
$114$	1.65987e30	+	6.75234e28i	2.48287	+	0.101003i
$115$			1.60882e30i			2.12026i
$116$		−	4.65396e29i		−	0.540981i
$117$	−2.54447e28	+	3.12225e29i	−0.0261157	+	0.320460i
$118$		−	1.61682e30i		−	1.46681i
$119$	7.75847e29	+	1.85589e30i	0.622795	+	1.48977i
$120$	−1.18859e29	+	2.92181e30i	−0.0845090	+	2.07742i
$121$	1.51325e30			0.953945
$122$	6.57277e29			0.367732
$123$	6.54384e29	+	2.66202e28i	0.325243	+	0.0132308i
$124$			4.41172e30i			1.94981i
$125$	−3.18078e30			−1.25123
$126$	−4.50358e30	+	1.46575e30i	−1.57828	+	0.513675i
$127$	3.70027e29			0.115632			0.0578161	−	0.998327i	$-0.481586\pi$
$127$	3.70027e29			0.115632			0.0578161	+	0.998327i	$0.481586\pi$
$128$			6.42465e30i			1.79186i
$129$	−2.92787e30	−	1.19105e29i	−0.729458	−	0.0296742i
$130$	3.97574e30			0.885603
$131$	−7.07561e30			−1.41036			−0.705180	−	0.709028i	$-0.749134\pi$
$131$	−7.07561e30			−1.41036			−0.705180	+	0.709028i	$0.749134\pi$
$132$	−8.57471e28	+	2.10785e30i	−0.0153073	+	0.376286i
$133$	8.63255e30	−	3.60881e30i	1.38131	−	0.577451i
$134$			1.32937e31i			1.90821i
$135$	−1.27815e31	−	1.56676e30i	−1.64718	−	0.201913i
$136$		−	1.74708e31i		−	2.02301i
$137$		−	1.49881e31i		−	1.56062i	−0.625390	−	0.780312i	$-0.715060\pi$
$137$		−	1.49881e31i		−	1.56062i	0.625390	−	0.780312i	$-0.284940\pi$
$138$	2.26123e31	+	9.19866e29i	2.11884	+	0.0861942i
$139$		−	9.27965e30i		−	0.783100i	−0.920157	−	0.391550i	$-0.871939\pi$
$139$		−	9.27965e30i		−	0.783100i	0.920157	−	0.391550i	$-0.128061\pi$
$140$	1.47681e31	+	3.53264e31i	1.12323	+	2.68684i
$141$	−8.39506e30	−	3.41510e29i	−0.575899	−	0.0234275i
$142$	−2.16395e31			−1.33988
$143$	1.23374e30			0.0690002
$144$	6.40025e30	+	5.21585e29i	0.323550	+	0.0263675i
$145$		−	1.11882e31i		−	0.511593i
$146$	−6.75596e31			−2.79622
$147$	−1.94945e31	+	1.82075e31i	−0.730819	+	0.682571i
$148$	−8.17035e31			−2.77617
$149$		−	1.95223e31i		−	0.601632i	−0.953682	−	0.300816i	$-0.902741\pi$
$149$		−	1.95223e31i		−	0.601632i	0.953682	−	0.300816i	$-0.0972590\pi$
$150$	−4.23073e30	+	1.04001e32i	−0.118329	+	2.90879i
$151$	1.81054e31			0.459878			0.229939	−	0.973205i	$-0.426147\pi$
$151$	1.81054e31			0.459878			0.229939	+	0.973205i	$0.426147\pi$
$152$	−8.12644e31			−1.87572
$153$	7.66803e31	+	6.24903e30i	1.60938	+	0.131156i
$154$	7.19429e30	+	1.72093e31i	0.137384	+	0.328634i
$155$			1.06059e32i			1.84389i
$156$	1.44802e30	−	3.55956e31i	0.0229334	−	0.563753i
$157$		−	9.75167e31i		−	1.40778i	−0.710310	−	0.703889i	$-0.751445\pi$
$157$		−	9.75167e31i		−	1.40778i	0.710310	−	0.703889i	$-0.248555\pi$
$158$			1.27019e32i			1.67240i
$159$	3.42013e30	−	8.40742e31i	0.0410945	−	1.01019i
$160$			1.08008e32i			1.18499i
$161$	1.17601e32	−	4.91625e31i	1.17878	−	0.492787i
$162$	−2.93292e31	+	1.78750e32i	−0.268740	+	1.63787i
$163$	1.73117e32			1.45084			0.725418	−	0.688309i	$-0.241647\pi$
$163$	1.73117e32			1.45084			0.725418	+	0.688309i	$0.241647\pi$
$164$	−7.44802e31			−0.571222
$165$	−2.06138e30	+	5.06732e31i	−0.0144757	+	0.355845i
$166$		−	4.24303e31i		−	0.272966i
$167$	−7.62933e30			−0.0449881			−0.0224941	−	0.999747i	$-0.507161\pi$
$167$	−7.62933e30			−0.0449881			−0.0224941	+	0.999747i	$0.507161\pi$
$168$	2.17208e32	−	8.05966e31i	1.17461	−	0.435845i
$169$	1.80704e32			0.896624
$170$		−	9.76413e32i		−	4.44758i
$171$	2.90670e31	−	3.56674e32i	0.121607	−	1.49220i
$172$	3.33242e32			1.28114
$173$	−2.34259e31			−0.0827997			−0.0413998	−	0.999143i	$-0.513182\pi$
$173$	−2.34259e31			−0.0827997			−0.0413998	+	0.999143i	$0.513182\pi$
$174$	−1.57253e32	−	6.39701e30i	−0.511251	−	0.0207976i
$175$	2.26113e32	+	5.40879e32i	0.676509	+	1.61826i
$176$		−	2.52902e31i		−	0.0696655i
$177$	−3.47999e32	−	1.41565e31i	−0.883010	−	0.0359207i
$178$			4.97788e32i			1.16400i
$179$		−	3.98140e32i		−	0.858356i	−0.903220	−	0.429178i	$-0.858803\pi$
$179$		−	3.98140e32i		−	0.858356i	0.903220	−	0.429178i	$-0.141197\pi$
$180$	1.45959e33	+	1.18949e32i	2.90255	+	0.236542i
$181$			2.29515e32i			0.421183i	0.977574	+	0.210592i	$0.0675390\pi$
$181$			2.29515e32i			0.421183i	−0.977574	+	0.210592i	$0.932461\pi$
$182$	−1.21491e32	−	2.90616e32i	−0.205830	−	0.492361i
$183$	5.75498e30	−	1.41470e32i	0.00900541	−	0.221373i
$184$	−1.10706e33			−1.60071
$185$	−1.96417e33			−2.62536
$186$	1.49067e33	+	6.06404e31i	1.84266	+	0.0749591i
$187$		−	3.02997e32i		−	0.346526i
$188$	9.55502e32			1.01145
$189$	2.76051e32	+	9.82169e32i	0.270579	+	0.962698i
$190$	−4.54173e33			−4.12377
$191$			2.83099e32i			0.238207i	0.992882	+	0.119103i	$0.0380020\pi$
$191$			2.83099e32i			0.238207i	−0.992882	+	0.119103i	$0.961998\pi$
$192$	1.93388e33	+	7.86698e31i	1.50855	+	0.0613677i
$193$	4.55989e32			0.329893			0.164947	−	0.986303i	$-0.447255\pi$
$193$	4.55989e32			0.329893			0.164947	+	0.986303i	$0.447255\pi$
$194$	−6.91870e32			−0.464408
$195$	3.48107e31	−	8.55724e32i	0.0216876	−	0.533128i
$196$	2.13098e33	−	2.15901e33i	1.23272	−	1.24894i
$197$		−	2.52192e33i		−	1.35510i	−0.735476	−	0.677551i	$-0.763041\pi$
$197$		−	2.52192e33i		−	1.35510i	0.735476	−	0.677551i	$-0.236959\pi$
$198$	7.11043e32	+	5.79461e31i	0.355018	+	0.0289320i
$199$		−	2.83707e32i		−	0.131674i	−0.997830	−	0.0658370i	$-0.979028\pi$
$199$		−	2.83707e32i		−	0.131674i	0.997830	−	0.0658370i	$-0.0209717\pi$
$200$		−	5.09169e33i		−	2.19749i
$201$	2.86130e33	+	1.16397e32i	1.14874	+	0.0467304i
$202$		−	1.05046e33i		−	0.392451i
$203$	−8.17828e32	+	3.41891e32i	−0.284426	+	0.118903i
$204$	−8.74201e33	−	3.55624e32i	−2.83122	−	0.115174i
$205$	−1.79052e33			−0.540191
$206$	−1.04254e34			−2.93103
$207$	3.95978e32	−	4.85895e33i	0.103777	−	1.27342i
$208$			4.27078e32i			0.104373i
$209$	−1.40937e33			−0.321296
$210$	1.21394e34	−	4.50441e33i	2.58237	−	0.958204i
$211$	3.05740e33			0.607095			0.303547	−	0.952816i	$-0.401829\pi$
$211$	3.05740e33			0.607095			0.303547	+	0.952816i	$0.401829\pi$
$212$			9.56910e33i			1.77419i
$213$	−1.89471e32	+	4.65762e33i	−0.0328125	+	0.806603i
$214$	8.23823e33			1.33301
$215$	8.01119e33			1.21155
$216$	1.07812e33	−	8.79516e33i	0.152436	−	1.24355i
$217$	7.75259e33	−	3.24094e33i	1.02513	−	0.428554i
$218$		−	1.00211e34i		−	1.23964i
$219$	−5.91538e32	+	1.45413e34i	−0.0684767	+	1.68331i
$220$		−	5.76748e33i		−	0.624967i
$221$			5.11675e33i			0.519166i
$222$	−1.12304e33	+	2.76068e34i	−0.106728	+	2.62360i
$223$			1.40921e34i			1.25475i	0.778719	+	0.627373i	$0.215870\pi$
$223$			1.40921e34i			1.25475i	−0.778719	+	0.627373i	$0.784130\pi$
$224$	7.89509e33	−	3.30052e33i	0.658811	−	0.275414i
$225$	2.23477e34	+	1.82122e33i	1.74818	+	0.142467i
$226$	3.13217e33			0.229759
$227$	−2.52431e34			−1.73687			−0.868435	−	0.495803i	$-0.834874\pi$
$227$	−2.52431e34			−1.73687			−0.868435	+	0.495803i	$0.834874\pi$
$228$	−1.65416e33	+	4.06630e34i	−0.106788	+	2.62509i
$229$		−	2.67628e34i		−	1.62150i	−0.585391	−	0.810751i	$-0.699059\pi$
$229$		−	2.67628e34i		−	1.62150i	0.585391	−	0.810751i	$-0.300941\pi$
$230$	−6.18716e34			−3.51915
$231$	3.76706e33	−	1.39779e33i	0.201200	−	0.0746568i
$232$	7.69881e33			0.386231
$233$		−	6.46876e33i		−	0.304902i	−0.988311	−	0.152451i	$-0.951283\pi$
$233$		−	6.46876e33i		−	0.304902i	0.988311	−	0.152451i	$-0.0487166\pi$
$234$	−1.20075e34	−	9.78543e32i	−0.531890	−	0.0433461i
$235$	2.29705e34			0.956501
$236$	3.96083e34			1.55082
$237$	2.73390e34	+	1.11215e33i	1.00677	+	0.0409554i
$238$	−7.13731e34	+	2.98373e34i	−2.47268	+	1.03370i
$239$			9.92111e33i			0.323438i	0.986837	+	0.161719i	$0.0517038\pi$
$239$			9.92111e33i			0.323438i	−0.986837	+	0.161719i	$0.948296\pi$
$240$	−1.75413e34	−	7.13578e32i	−0.538269	−	0.0218967i
$241$			3.90029e34i			1.12681i	0.826181	+	0.563404i	$0.190509\pi$
$241$			3.90029e34i			1.12681i	−0.826181	+	0.563404i	$0.809491\pi$
$242$			5.81961e34i			1.58333i
$243$	3.82168e34	+	7.87781e33i	0.979408	+	0.201890i
$244$			1.61017e34i			0.388795i
$245$	5.12291e34	−	5.19031e34i	1.16576	−	1.18109i
$246$	−1.02375e33	+	2.51661e34i	−0.0219602	+	0.539829i
$247$	2.38003e34			0.481367
$248$	−7.29807e34			−1.39206
$249$	−9.13254e33	−	3.71510e32i	−0.164324	−	0.00668468i
$250$		−	1.22325e35i		−	2.07676i
$251$	−7.00461e33			−0.112232			−0.0561158	−	0.998424i	$-0.517872\pi$
$251$	−7.00461e33			−0.112232			−0.0561158	+	0.998424i	$0.517872\pi$
$252$	−3.59075e34	−	1.10327e35i	−0.543097	−	1.66868i
$253$	−1.91998e34			−0.274188
$254$			1.42304e34i			0.191923i
$255$	−2.10160e35	−	8.54926e33i	−2.67742	−	0.108917i
$256$	−1.21648e35			−1.46428
$257$	3.49331e34			0.397380			0.198690	−	0.980062i	$-0.436331\pi$
$257$	3.49331e34			0.397380			0.198690	+	0.980062i	$0.436331\pi$
$258$	4.58051e33	−	1.12599e35i	0.0492524	−	1.21073i
$259$	6.00212e34	+	1.43575e35i	0.610180	+	1.45960i
$260$			9.73962e34i			0.936329i
$261$	−2.75374e33	+	3.37905e34i	−0.0250401	+	0.307261i
$262$		−	2.72112e35i		−	2.34088i
$263$			1.42561e34i			0.116049i	0.998315	+	0.0580245i	$0.0184802\pi$
$263$			1.42561e34i			0.116049i	−0.998315	+	0.0580245i	$0.981520\pi$
$264$	−3.48691e34	−	1.41847e33i	−0.268648	−	0.0109286i
$265$			2.30043e35i			1.67781i
$266$	1.38787e35	+	3.31988e35i	0.958437	+	2.29265i
$267$	1.07142e35	+	4.35853e33i	0.700725	+	0.0285054i
$268$	−3.25665e35			−2.01751
$269$	−4.00535e34			−0.235089			−0.117545	−	0.993068i	$-0.537502\pi$
$269$	−4.00535e34			−0.235089			−0.117545	+	0.993068i	$0.537502\pi$
$270$	6.02541e34	−	4.91546e35i	0.335129	−	2.73394i
$271$			7.49708e34i			0.395219i	0.980281	+	0.197609i	$0.0633178\pi$
$271$			7.49708e34i			0.395219i	−0.980281	+	0.197609i	$0.936682\pi$
$272$	1.04887e35			0.524172
$273$	−6.36148e34	+	2.36047e34i	−0.301439	+	0.111851i
$274$	5.76408e35			2.59028
$275$		−	8.83055e34i		−	0.376412i
$276$	−2.25345e34	+	5.53949e35i	−0.0911312	+	2.24021i
$277$	3.47843e35			1.33483			0.667416	−	0.744685i	$-0.267400\pi$
$277$	3.47843e35			1.33483			0.667416	+	0.744685i	$0.267400\pi$
$278$	3.56874e35			1.29977
$279$	2.61041e34	−	3.20317e35i	0.0902500	−	1.10744i
$280$	−5.84385e35	+	2.44300e35i	−1.91826	+	0.801923i
$281$		−	3.09052e35i		−	0.963363i	−0.876346	−	0.481682i	$-0.840026\pi$
$281$		−	3.09052e35i		−	0.963363i	0.876346	−	0.481682i	$-0.159974\pi$
$282$	1.31337e34	−	3.22854e35i	0.0388843	−	0.955861i
$283$			1.61227e35i			0.453455i	0.973958	+	0.226727i	$0.0728026\pi$
$283$			1.61227e35i			0.453455i	−0.973958	+	0.226727i	$0.927197\pi$
$284$		−	5.30118e35i		−	1.41663i
$285$	−3.97664e34	+	9.77546e35i	−0.100987	+	2.48249i
$286$			4.74467e34i			0.114525i
$287$	5.47148e34	+	1.30882e35i	0.125550	+	0.300326i
$288$	2.65839e34	−	3.26204e35i	0.0579999	−	0.711703i
$289$	7.74669e35			1.60730
$290$	4.30273e35			0.849128
$291$	−6.05787e33	+	1.48916e35i	−0.0113729	+	0.279571i
$292$		−	1.65505e36i		−	2.95638i
$293$	6.93789e35			1.17936			0.589681	−	0.807636i	$-0.299254\pi$
$293$	6.93789e35			1.17936			0.589681	+	0.807636i	$0.299254\pi$
$294$	−7.00217e35	−	7.49711e35i	−1.13291	−	1.21299i
$295$	9.52191e35			1.46658
$296$		−	1.35158e36i		−	1.98203i
$297$	1.86979e34	−	1.52535e35i	0.0261110	−	0.213011i
$298$	7.50784e35			0.998571
$299$	3.24229e35			0.410790
$300$	−2.54777e36	−	1.03643e35i	−3.07540	−	0.125107i
$301$	−2.44807e35	−	5.85596e35i	−0.281585	−	0.673572i
$302$			6.96293e35i			0.763293i
$303$	−2.26098e35	−	9.19762e33i	−0.236253	−	0.00961075i
$304$		−	4.87877e35i		−	0.486008i
$305$			3.87089e35i			0.367674i
$306$	−2.40323e35	+	2.94895e36i	−0.217688	+	2.67120i
$307$		−	7.37793e35i		−	0.637424i	−0.947852	−	0.318712i	$-0.896750\pi$
$307$		−	7.37793e35i		−	0.637424i	0.947852	−	0.318712i	$-0.103250\pi$
$308$	−4.21587e35	+	1.76243e35i	−0.347458	+	0.145254i
$309$	−9.12830e34	+	2.24394e36i	−0.0717781	+	1.76446i
$310$	−4.07876e36			−3.06044
$311$	1.68006e36			1.20309			0.601545	−	0.798839i	$-0.294552\pi$
$311$	1.68006e36			1.20309			0.601545	+	0.798839i	$0.294552\pi$
$312$	5.88838e35	+	2.39539e34i	0.402489	+	0.0163732i
$313$		−	1.99981e36i		−	1.30496i	−0.757807	−	0.652479i	$-0.773729\pi$
$313$		−	1.99981e36i		−	1.30496i	0.757807	−	0.652479i	$-0.226271\pi$
$314$	3.75027e36			2.33659
$315$	−8.63223e35	−	2.65228e36i	−0.513594	−	1.57804i
$316$	−3.11166e36			−1.76819
$317$			1.51211e36i			0.820776i	0.911911	+	0.410388i	$0.134607\pi$
$317$			1.51211e36i			0.820776i	−0.911911	+	0.410388i	$0.865393\pi$
$318$	3.23330e36	+	1.31530e35i	1.67669	+	0.0682075i
$319$	1.33521e35			0.0661583
$320$	−5.29145e36			−2.50553
$321$	7.21323e34	−	1.77317e36i	0.0326442	−	0.802467i
$322$	1.89068e36	+	4.52265e36i	0.817913	+	1.95651i
$323$		−	5.84518e36i		−	2.41747i
$324$	−4.37896e36	−	7.18495e35i	−1.73168	−	0.284133i
$325$			1.49123e36i			0.563942i
$326$			6.65766e36i			2.40805i
$327$	−2.15690e36	−	8.77422e34i	−0.746255	−	0.0303575i
$328$		−	1.23209e36i		−	0.407822i
$329$	−7.01933e35	−	1.67908e36i	−0.222308	−	0.531778i
$330$	−1.94877e36	−	7.92757e34i	−0.590621	−	0.0240264i
$331$	3.80003e36			1.10225			0.551126	−	0.834422i	$-0.314198\pi$
$331$	3.80003e36			1.10225			0.551126	+	0.834422i	$0.314198\pi$
$332$	1.03944e36			0.288601
$333$	5.93215e36	+	4.83438e35i	1.57678	+	0.128499i
$334$		−	2.93406e35i		−	0.0746700i
$335$	−7.82905e36			−1.90792
$336$	4.83868e35	+	1.30403e36i	0.112930	+	0.304346i
$337$	−7.28308e36			−1.62810			−0.814051	−	0.580793i	$-0.802743\pi$
$337$	−7.28308e36			−1.62810			−0.814051	+	0.580793i	$0.802743\pi$
$338$			6.94945e36i			1.48819i
$339$	2.74246e34	−	6.74157e35i	0.00562658	−	0.138314i
$340$	2.39198e37			4.70233
$341$	−1.26571e36			−0.238449
$342$	1.37169e37	+	1.11785e36i	2.47672	+	0.201839i
$343$	−5.35944e36	−	2.15865e36i	−0.927586	−	0.373609i
$344$			5.51264e36i			0.914665i
$345$	−5.41735e35	+	1.33170e37i	−0.0861807	+	2.11851i
$346$		−	9.00908e35i		−	0.137428i
$347$		−	4.70220e36i		−	0.687898i	−0.938988	−	0.343949i	$-0.888235\pi$
$347$		−	4.70220e36i		−	0.687898i	0.938988	−	0.343949i	$-0.111765\pi$
$348$	1.56712e35	−	3.85232e36i	0.0219888	−	0.540534i
$349$			8.47899e36i			1.14124i	0.821216	+	0.570618i	$0.193296\pi$
$349$			8.47899e36i			1.14124i	−0.821216	+	0.570618i	$0.806704\pi$
$350$	−2.08010e37	+	8.69578e36i	−2.68594	+	1.12285i
$351$	−3.15753e35	+	2.57588e36i	−0.0391196	+	0.319133i
$352$	−1.28897e36			−0.153241
$353$	1.15005e37			1.31215			0.656076	−	0.754695i	$-0.272215\pi$
$353$	1.15005e37			1.31215			0.656076	+	0.754695i	$0.272215\pi$
$354$	5.44428e35	−	1.33832e37i	0.0596202	−	1.46559i
$355$		−	1.27441e37i		−	1.33967i
$356$	−1.21946e37			−1.23068
$357$	5.79715e36	+	1.56234e37i	0.561727	+	1.51386i
$358$	1.53116e37			1.42467
$359$			1.99530e37i			1.78295i	0.453068	+	0.891476i	$0.350329\pi$
$359$			1.99530e37i			1.78295i	−0.453068	+	0.891476i	$0.649671\pi$
$360$	−1.96771e36	+	2.41453e37i	−0.168878	+	2.07227i
$361$	−1.50587e37			−1.24146
$362$	−8.82660e36			−0.699068
$363$	1.25259e37	+	5.09553e35i	0.953156	+	0.0387743i
$364$	7.11939e36	−	2.97624e36i	0.520563	−	0.217620i
$365$		−	3.97877e37i		−	2.79578i
$366$	5.44061e36	+	2.21323e35i	0.367428	+	0.0149469i
$367$		−	3.61576e35i		−	0.0234716i	−0.999931	−	0.0117358i	$-0.996264\pi$
$367$		−	3.61576e35i		−	0.0234716i	0.999931	−	0.0117358i	$-0.00373570\pi$
$368$		−	6.64632e36i		−	0.414751i
$369$	5.40770e36	+	4.40698e35i	0.324437	+	0.0264398i
$370$		−	7.55373e37i		−	4.35749i
$371$	1.68155e37	−	7.02967e36i	0.932800	−	0.389954i
$372$	−1.48555e36	+	3.65180e37i	−0.0792526	+	1.94820i
$373$	−3.55697e37			−1.82516			−0.912582	−	0.408894i	$-0.865915\pi$
$373$	−3.55697e37			−1.82516			−0.912582	+	0.408894i	$0.865915\pi$
$374$	1.16526e37			0.575153
$375$	−2.63289e37	−	1.07106e36i	−1.25020	−	0.0508579i
$376$			1.58064e37i			0.722118i
$377$	−2.25478e36			−0.0991187
$378$	−3.77719e37	+	1.06163e37i	−1.59786	+	0.449099i
$379$	2.05886e37			0.838219			0.419110	−	0.907936i	$-0.362342\pi$
$379$	2.05886e37			0.838219			0.419110	+	0.907936i	$0.362342\pi$
$380$		−	1.11262e38i		−	4.35997i
$381$	3.06290e36	+	1.24598e35i	0.115537	+	0.00470002i
$382$	−1.08873e37			−0.395369
$383$	−1.21324e37			−0.424193			−0.212096	−	0.977249i	$-0.568029\pi$
$383$	−1.21324e37			−0.424193			−0.212096	+	0.977249i	$0.568029\pi$
$384$	−2.16336e36	+	5.31800e37i	−0.0728325	+	1.79038i
$385$	−1.01350e37	+	4.23692e36i	−0.328583	+	0.137363i
$386$			1.75363e37i			0.547547i
$387$	−2.41953e37	−	1.97179e36i	−0.727649	−	0.0592994i
$388$		−	1.69492e37i		−	0.491008i
$389$			5.01531e37i			1.39968i	0.714300	+	0.699840i	$0.246745\pi$
$389$			5.01531e37i			1.39968i	−0.714300	+	0.699840i	$0.753255\pi$
$390$	3.29092e37	+	1.33874e36i	0.884871	+	0.0359964i
$391$		−	7.96284e37i		−	2.06303i
$392$	3.57154e37	+	3.52516e37i	0.891676	+	0.880098i
$393$	−5.85684e37	−	2.38255e36i	−1.40920	−	0.0573258i
$394$	9.69874e37			2.24916
$395$	−7.48048e37			−1.67214
$396$	−1.41954e36	+	1.74189e37i	−0.0305892	+	0.375353i
$397$			4.76288e37i			0.989481i	0.869041	+	0.494741i	$0.164737\pi$
$397$			4.76288e37i			0.989481i	−0.869041	+	0.494741i	$0.835263\pi$
$398$	1.09107e37			0.218549
$399$	7.26711e37	−	2.69651e37i	1.40364	−	0.520829i
$400$	3.05683e37			0.569380
$401$		−	1.04863e37i		−	0.188377i	−0.995554	−	0.0941885i	$-0.969974\pi$
$401$		−	1.04863e37i		−	0.188377i	0.995554	−	0.0941885i	$-0.0300256\pi$
$402$	−4.47636e36	+	1.10039e38i	−0.0775617	+	1.90664i
$403$	2.13742e37			0.357245
$404$	2.57338e37			0.414930
$405$	−1.05271e38	−	1.72728e37i	−1.63761	−	0.268698i
$406$	−1.31483e37	−	3.14518e37i	−0.197353	−	0.472082i
$407$		−	2.34405e37i		−	0.339506i
$408$	5.88289e36	−	1.44614e38i	0.0822278	−	2.02134i
$409$			9.82064e37i			1.32480i	0.749148	+	0.662402i	$0.230463\pi$
$409$			9.82064e37i			1.32480i	−0.749148	+	0.662402i	$0.769537\pi$
$410$		−	6.88591e37i		−	0.896594i
$411$	5.04691e36	−	1.24064e38i	0.0634335	−	1.55934i
$412$		−	2.55399e38i		−	3.09891i
$413$	−2.90971e37	−	6.96026e37i	−0.340859	−	0.815360i
$414$	1.86864e38	+	1.52284e37i	2.11359	+	0.172246i
$415$	2.49884e37			0.272923
$416$	2.17671e37			0.229587
$417$	3.12471e36	−	7.68123e37i	0.0318301	−	0.782453i
$418$		−	5.42013e37i		−	0.533278i
$419$	1.19025e38			1.13119			0.565593	−	0.824685i	$-0.308647\pi$
$419$	1.19025e38			1.13119			0.565593	+	0.824685i	$0.308647\pi$
$420$	1.10347e38	+	2.97387e38i	1.01309	+	2.73028i
$421$	8.78733e37			0.779411			0.389706	−	0.920939i	$-0.372577\pi$
$421$	8.78733e37			0.779411			0.389706	+	0.920939i	$0.372577\pi$
$422$			1.17580e38i			1.00764i
$423$	−6.93751e37	−	5.65369e36i	−0.574471	−	0.0468163i
$424$	−1.58296e38			−1.26668
$425$	3.66234e38			2.83217
$426$	−1.79121e38	−	7.28663e36i	−1.33878	−	0.0544612i
$427$	2.82952e37	−	1.18287e37i	0.204413	−	0.0854541i
$428$			2.01817e38i			1.40937i
$429$	1.02123e37	+	4.15433e35i	0.0689432	+	0.00280460i
$430$			3.08092e38i			2.01089i
$431$			7.39165e37i			0.466467i	0.972421	+	0.233234i	$0.0749307\pi$
$431$			7.39165e37i			0.466467i	−0.972421	+	0.233234i	$0.925069\pi$
$432$	5.28024e37	+	6.47256e36i	0.322210	+	0.0394968i
$433$		−	4.84871e37i		−	0.286122i	−0.989714	−	0.143061i	$-0.954305\pi$
$433$		−	4.84871e37i		−	0.286122i	0.989714	−	0.143061i	$-0.0456946\pi$
$434$	1.24639e38	+	2.98147e38i	0.711301	+	1.70149i
$435$	3.76738e36	−	9.26105e37i	0.0207943	−	0.511171i
$436$	2.45492e38			1.31064
$437$	−3.70387e38			−1.91282
$438$	−5.59225e38	−	2.27492e37i	−2.79390	−	0.113656i
$439$		−	1.46341e37i		−	0.0707342i	−0.999374	−	0.0353671i	$-0.988740\pi$
$439$		−	1.46341e37i		−	0.0707342i	0.999374	−	0.0353671i	$-0.0112601\pi$
$440$	9.54084e37			0.446193
$441$	−1.67496e38	+	1.44148e38i	−0.757959	+	0.652302i
$442$	−1.96778e38			−0.861697
$443$			3.47079e38i			1.47087i	0.677596	+	0.735434i	$0.263022\pi$
$443$			3.47079e38i			1.47087i	−0.677596	+	0.735434i	$0.736978\pi$
$444$	−6.76301e38	−	2.75118e37i	−2.77387	−	0.112841i
$445$	−2.93161e38			−1.16382
$446$	−5.41950e38			−2.08259
$447$	6.57371e36	−	1.61596e38i	0.0244541	−	0.601135i
$448$	1.61697e38	+	3.86791e38i	0.582331	+	1.39298i
$449$		−	4.82451e38i		−	1.68221i	−0.540868	−	0.841107i	$-0.681904\pi$
$449$		−	4.82451e38i		−	1.68221i	0.540868	−	0.841107i	$-0.318096\pi$
$450$	−7.00398e37	+	8.59441e38i	−0.236463	+	2.90158i
$451$		−	2.13681e37i		−	0.0698565i
$452$			7.67307e37i			0.242919i
$453$	1.49868e38	+	6.09659e36i	0.459498	+	0.0186923i
$454$		−	9.70790e38i		−	2.88281i
$455$	1.71152e38	−	7.15494e37i	0.492284	−	0.205798i
$456$	−6.72666e38	−	2.73640e37i	−1.87417	−	0.0762410i
$457$	2.40631e38			0.649482			0.324741	−	0.945803i	$-0.394723\pi$
$457$	2.40631e38			0.649482			0.324741	+	0.945803i	$0.394723\pi$
$458$	1.02924e39			2.69132
$459$	6.32617e38	+	7.75467e37i	1.60272	+	0.196462i
$460$		−	1.51571e39i		−	3.72072i
$461$	6.18821e37			0.147198			0.0735989	−	0.997288i	$-0.476552\pi$
$461$	6.18821e37			0.147198			0.0735989	+	0.997288i	$0.476552\pi$
$462$	5.37559e37	+	1.44872e38i	0.123913	+	0.333947i
$463$	−1.28888e38			−0.287932			−0.143966	−	0.989583i	$-0.545986\pi$
$463$	−1.28888e38			−0.287932			−0.143966	+	0.989583i	$0.545986\pi$
$464$			4.62204e37i			0.100074i
$465$	−3.57128e37	+	8.77899e38i	−0.0749473	+	1.84237i
$466$	2.48774e38			0.506068
$467$	−1.69432e38			−0.334118			−0.167059	−	0.985947i	$-0.553427\pi$
$467$	−1.69432e38			−0.334118			−0.167059	+	0.985947i	$0.553427\pi$
$468$	2.39720e37	−	2.94155e38i	0.0458289	−	0.562355i
$469$	2.39241e38	+	5.72282e38i	0.443434	+	1.06073i
$470$			8.83391e38i			1.58757i
$471$	3.28365e37	−	8.07194e38i	0.0572209	−	1.40661i
$472$			6.55219e38i			1.10720i
$473$			9.56061e37i			0.156675i
$474$	−4.27706e37	+	1.05140e39i	−0.0679767	+	1.67102i
$475$		−	1.70352e39i		−	2.62597i
$476$	−7.30943e38	−	1.74847e39i	−1.09291	−	2.61432i
$477$	5.66202e37	−	6.94773e38i	0.0821211	−	1.00769i
$478$	−3.81543e38			−0.536833
$479$	8.24390e38			1.12530			0.562649	−	0.826696i	$-0.309782\pi$
$479$	8.24390e38			1.12530			0.562649	+	0.826696i	$0.309782\pi$
$480$	−3.63693e37	+	8.94036e38i	−0.0481655	+	1.18401i
$481$			3.95843e38i			0.508650i
$482$	−1.49996e39			−1.87024
$483$	9.89993e38	−	3.67344e38i	1.19784	−	0.444467i
$484$	−1.42567e39			−1.67402
$485$		−	4.07462e38i		−	0.464335i
$486$	−3.02962e38	+	1.46973e39i	−0.335091	+	1.62559i
$487$	1.14817e39			1.23264			0.616321	−	0.787495i	$-0.288622\pi$
$487$	1.14817e39			1.23264			0.616321	+	0.787495i	$0.288622\pi$
$488$	−2.66363e38			−0.277578
$489$	1.43297e39	+	5.82931e37i	1.44964	+	0.0589710i
$490$	1.99607e39	+	1.97015e39i	1.96035	+	1.93489i
$491$			6.04572e38i			0.576456i	0.957562	+	0.288228i	$0.0930661\pi$
$491$			6.04572e38i			0.576456i	−0.957562	+	0.288228i	$0.906934\pi$
$492$	−6.16509e38	−	2.50795e37i	−0.570750	−	0.0232180i
$493$			5.53759e38i			0.497783i
$494$			9.15304e38i			0.798959i
$495$	−3.41261e37	+	4.18753e38i	−0.0289275	+	0.354962i
$496$		−	4.38145e38i		−	0.360690i
$497$	−9.31562e38	+	3.89436e38i	−0.744807	+	0.311364i
$498$	1.42874e37	−	3.51216e38i	0.0110950	−	0.272740i
$499$	1.45576e39			1.09807			0.549037	−	0.835798i	$-0.314995\pi$
$499$	1.45576e39			1.09807			0.549037	+	0.835798i	$0.314995\pi$
$500$	2.99668e39			2.19571
$501$	−6.31518e37	−	2.56901e36i	−0.0449509	−	0.00182860i
$502$		−	2.69381e38i		−	0.186279i
$503$	−1.23391e39			−0.828985			−0.414493	−	0.910053i	$-0.636041\pi$
$503$	−1.23391e39			−0.828985			−0.414493	+	0.910053i	$0.636041\pi$
$504$	1.82508e39	−	5.93999e38i	1.19135	−	0.387742i
$505$	6.18646e38			0.392390
$506$		−	7.38380e38i		−	0.455090i
$507$	1.49578e39	+	6.08479e37i	0.895883	+	0.0364444i
$508$	−3.48610e38			−0.202916
$509$	−2.01483e39			−1.13981			−0.569903	−	0.821712i	$-0.693019\pi$
$509$	−2.01483e39			−1.13981			−0.569903	+	0.821712i	$0.693019\pi$
$510$	3.28785e38	−	8.08225e39i	0.180777	−	4.44391i
$511$	−2.90838e39	+	1.21584e39i	−1.55434	+	0.649789i
$512$		−	1.22908e39i		−	0.638507i
$513$	3.60704e38	−	2.94258e39i	0.182158	−	1.48603i
$514$			1.34344e39i			0.659560i
$515$		−	6.13984e39i		−	2.93057i
$516$	2.75841e39	+	1.12212e38i	1.28008	+	0.0520735i
$517$			2.74131e38i			0.123693i
$518$	−5.52157e39	+	2.30828e39i	−2.42260	+	1.01276i
$519$	−1.93908e38	−	7.88816e36i	−0.0827312	−	0.00336549i
$520$	−1.61117e39			−0.668488
$521$	1.92698e39			0.777555			0.388777	−	0.921332i	$-0.372898\pi$
$521$	1.92698e39			0.777555			0.388777	+	0.921332i	$0.372898\pi$
$522$	−1.29950e39	−	1.05903e38i	−0.509983	−	0.0415608i
$523$		−	2.09948e39i		−	0.801378i	−0.916214	−	0.400689i	$-0.868771\pi$
$523$		−	2.09948e39i		−	0.801378i	0.916214	−	0.400689i	$-0.131229\pi$
$524$	6.66609e39			2.47496
$525$	1.68952e39	+	4.55327e39i	0.610174	+	1.64442i
$526$	−5.48255e38			−0.192615
$527$		−	5.24935e39i		−	1.79412i
$528$	8.51589e36	−	2.09339e38i	0.00283164	−	0.0696079i
$529$	−1.95470e39			−0.632371
$530$	−8.84692e39			−2.78479
$531$	−2.87580e39	−	2.34362e38i	−0.880820	−	0.0717821i
$532$	−8.13292e39	+	3.39994e39i	−2.42397	+	1.01333i
$533$			3.60847e38i			0.104659i
$534$	−1.67619e38	+	4.12044e39i	−0.0473124	+	1.16304i
$535$			4.85173e39i			1.33280i
$536$		−	5.38730e39i		−	1.44040i
$537$	1.34065e38	−	3.29561e39i	0.0348889	−	0.857646i
$538$		−	1.54037e39i		−	0.390194i
$539$	6.19414e38	+	6.11371e38i	0.152737	+	0.150754i
$540$	1.20417e40	+	1.47608e39i	2.89054	+	0.354325i
$541$	−2.26614e39			−0.529574			−0.264787	−	0.964307i	$-0.585302\pi$
$541$	−2.26614e39			−0.529574			−0.264787	+	0.964307i	$0.585302\pi$
$542$	−2.88320e39			−0.655973
$543$	−7.72839e37	+	1.89981e39i	−0.0171195	+	0.420835i
$544$		−	5.34584e39i		−	1.15301i
$545$	5.90168e39			1.23944
$546$	−9.07782e38	−	2.44648e39i	−0.185647	−	0.500320i
$547$	2.35298e39			0.468600			0.234300	−	0.972164i	$-0.424720\pi$
$547$	2.35298e39			0.468600			0.234300	+	0.972164i	$0.424720\pi$
$548$			1.41206e40i			2.73865i
$549$	9.52737e37	−	1.16908e39i	0.0179959	−	0.220824i
$550$	3.39602e39			0.624758
$551$	2.57578e39			0.461541
$552$	−9.16368e39	−	3.72777e38i	−1.59939	−	0.0650628i
$553$	2.28589e39	+	5.46803e39i	0.388634	+	0.929643i
$554$			1.33772e40i			2.21551i
$555$	−1.62584e40	−	6.61389e38i	−2.62319	−	0.106711i
$556$			8.74257e39i			1.37421i
$557$			7.49881e39i			1.14840i	0.818716	+	0.574198i	$0.194686\pi$
$557$			7.49881e39i			1.14840i	−0.818716	+	0.574198i	$0.805314\pi$
$558$	1.23186e40	+	1.00390e39i	1.83809	+	0.149794i
$559$		−	1.61451e39i		−	0.234731i
$560$	−1.46668e39	−	3.50840e39i	−0.207782	−	0.497031i
$561$	1.02027e38	−	2.50806e39i	0.0140850	−	0.346239i
$562$	1.18854e40			1.59896
$563$	8.01663e39			1.05104			0.525521	−	0.850781i	$-0.323870\pi$
$563$	8.01663e39			1.05104			0.525521	+	0.850781i	$0.323870\pi$
$564$	7.90917e39	+	3.21744e38i	1.01061	+	0.0411115i
$565$			1.84462e39i			0.229723i
$566$	−6.20041e39			−0.752631
$567$	1.95429e39	+	8.22286e39i	0.231225	+	0.972900i
$568$	8.76946e39			1.01140
$569$		−	1.59640e40i		−	1.79480i	−0.441223	−	0.897398i	$-0.645455\pi$
$569$		−	1.59640e40i		−	1.79480i	0.441223	−	0.897398i	$-0.354545\pi$
$570$	−3.75942e40	−	1.52932e39i	−4.12036	−	0.167616i
$571$	4.55261e39			0.486449			0.243224	−	0.969970i	$-0.421795\pi$
$571$	4.55261e39			0.486449			0.243224	+	0.969970i	$0.421795\pi$
$572$	−1.16233e39			−0.121084
$573$	−9.53271e37	+	2.34335e39i	−0.00968221	+	0.238010i
$574$	−5.03342e39	+	2.10420e39i	−0.498472	+	0.208384i
$575$		−	2.32069e40i		−	2.24096i
$576$	1.59812e40	+	1.30238e39i	1.50481	+	0.122634i
$577$		−	9.87344e39i		−	0.906608i	−0.891356	−	0.453304i	$-0.850245\pi$
$577$		−	9.87344e39i		−	0.906608i	0.891356	−	0.453304i	$-0.149755\pi$
$578$			2.97920e40i			2.66775i
$579$	3.77445e39	+	1.53544e38i	0.329620	+	0.0134089i
$580$			1.05407e40i			0.897764i
$581$	−7.63596e38	−	1.82658e39i	−0.0634322	−	0.151735i
$582$	−5.72695e39	−	2.32972e38i	−0.464024	−	0.0188764i
$583$	−2.74535e39			−0.216972
$584$	2.73786e40			2.11069
$585$	5.76291e38	−	7.07153e39i	0.0433393	−	0.531806i
$586$			2.66815e40i			1.95747i
$587$	−1.31675e40			−0.942431			−0.471216	−	0.882018i	$-0.656185\pi$
$587$	−1.31675e40			−0.942431			−0.471216	+	0.882018i	$0.656185\pi$
$588$	1.83662e40	−	1.71537e40i	1.28247	−	1.19780i
$589$	−2.44171e40			−1.66349
$590$			3.66191e40i			2.43418i
$591$	8.49201e38	−	2.08752e40i	0.0550798	−	1.35398i
$592$	8.11430e39			0.513554
$593$	8.54716e39			0.527872			0.263936	−	0.964540i	$-0.414979\pi$
$593$	8.54716e39			0.527872			0.263936	+	0.964540i	$0.414979\pi$
$594$	5.86614e39	+	7.19076e38i	0.353549	+	0.0433383i
$595$	−1.75720e40	−	4.20336e40i	−1.03354	−	2.47230i
$596$			1.83924e40i			1.05577i
$597$	9.55318e37	−	2.34838e39i	0.00535205	−	0.131565i
$598$			1.24691e40i			0.681818i
$599$			2.56471e40i			1.36883i	0.729093	+	0.684414i	$0.239942\pi$
$599$			2.56471e40i			1.36883i	−0.729093	+	0.684414i	$0.760058\pi$
$600$	1.71451e39	−	4.21464e40i	0.0893196	−	2.19567i
$601$		−	2.37314e40i		−	1.20682i	−0.797430	−	0.603411i	$-0.793808\pi$
$601$		−	2.37314e40i		−	1.20682i	0.797430	−	0.603411i	$-0.206192\pi$
$602$	2.25207e40	−	9.41470e39i	1.11798	−	0.467366i
$603$	2.36452e40	+	1.92695e39i	1.14589	+	0.0933835i
$604$	−1.70575e40			−0.807013
$605$	−3.42733e40			−1.58308
$606$	3.53719e38	−	8.69520e39i	0.0159517	−	0.392127i
$607$			3.00569e40i			1.32345i	0.749745	+	0.661727i	$0.230176\pi$
$607$			3.00569e40i			1.32345i	−0.749745	+	0.661727i	$0.769824\pi$
$608$	−2.48659e40			−1.06906
$609$	−6.88470e39	+	2.55461e39i	−0.289024	+	0.107244i
$610$	−1.48865e40			−0.610255
$611$		−	4.62928e39i		−	0.185317i
$612$	−7.22423e40	−	5.88735e39i	−2.82420	−	0.230157i
$613$	1.43309e40			0.547137			0.273568	−	0.961853i	$-0.411796\pi$
$613$	1.43309e40			0.547137			0.273568	+	0.961853i	$0.411796\pi$
$614$	2.83738e40			1.05798
$615$	−1.48210e40	−	6.02916e38i	−0.539745	−	0.0219567i
$616$	−2.91550e39	−	6.97409e39i	−0.103703	−	0.248066i
$617$		−	5.04374e40i		−	1.75234i	−0.482004	−	0.876169i	$-0.660091\pi$
$617$		−	5.04374e40i		−	1.75234i	0.482004	−	0.876169i	$-0.339909\pi$
$618$	−8.62966e40	−	3.51053e39i	−2.92861	−	0.119135i
$619$			2.74656e40i			0.910489i	0.890367	+	0.455244i	$0.150448\pi$
$619$			2.74656e40i			0.910489i	−0.890367	+	0.455244i	$0.849552\pi$
$620$		−	9.99201e40i		−	3.23574i
$621$	4.91384e39	−	4.00866e40i	0.155451	−	1.26815i
$622$			6.46111e40i			1.99685i
$623$	8.95845e39	+	2.14293e40i	0.270493	+	0.647040i
$624$	−1.43809e38	+	3.53514e39i	−0.00424238	+	0.104287i
$625$	1.11875e40			0.322459
$626$	7.69082e40			2.16593
$627$	−1.16661e40	−	4.74575e38i	−0.321030	−	0.0130595i
$628$			9.18727e40i			2.47042i
$629$	9.72161e40			2.55449
$630$	1.02001e41	−	3.31976e40i	2.61918	−	0.852449i
$631$	−5.69393e40			−1.42885			−0.714424	−	0.699713i	$-0.753311\pi$
$631$	−5.69393e40			−1.42885			−0.714424	+	0.699713i	$0.753311\pi$
$632$		−	5.14745e40i		−	1.26239i
$633$	2.53076e40	+	1.02951e39i	0.606593	+	0.0246761i
$634$	−5.81523e40			−1.36230
$635$	−8.38066e39			−0.191893
$636$	−3.22218e39	+	7.92082e40i	−0.0721143	+	1.77273i
$637$	−1.04601e40	−	1.03243e40i	−0.228831	−	0.225860i
$638$			5.13491e39i			0.109808i
$639$	−3.13670e39	+	3.84897e40i	−0.0655708	+	0.804603i
$640$		−	1.45511e41i		−	2.97362i
$641$		−	5.17757e40i		−	1.03439i	−0.855867	−	0.517195i	$-0.826976\pi$
$641$		−	5.17757e40i		−	1.03439i	0.855867	−	0.517195i	$-0.173024\pi$
$642$	6.81920e40	+	2.77404e39i	1.33191	+	0.0541820i
$643$			3.73349e40i			0.712946i	0.934306	+	0.356473i	$0.116021\pi$
$643$			3.73349e40i			0.712946i	−0.934306	+	0.356473i	$0.883979\pi$
$644$	−1.10794e41	+	4.63171e40i	−2.06858	+	0.864762i
$645$	6.63127e40	+	2.69759e39i	1.21054	+	0.0492447i
$646$	2.24792e41			4.01245
$647$	−3.84820e40			−0.671654			−0.335827	−	0.941924i	$-0.609016\pi$
$647$	−3.84820e40			−0.671654			−0.335827	+	0.941924i	$0.609016\pi$
$648$	1.18857e40	−	7.24389e40i	0.202855	−	1.23633i
$649$			1.13635e40i			0.189655i
$650$	−5.73491e40			−0.936015
$651$	6.52634e40	−	2.42164e40i	1.04171	−	0.386532i
$652$	−1.63097e41			−2.54598
$653$			1.14977e40i			0.175538i	0.996141	+	0.0877688i	$0.0279737\pi$
$653$			1.14977e40i			0.175538i	−0.996141	+	0.0877688i	$0.972026\pi$
$654$	3.37436e39	−	8.29493e40i	0.0503865	−	1.23861i
$655$	1.60254e41			2.34051
$656$	7.39692e39			0.105668
$657$	−9.79291e39	+	1.20166e41i	−0.136840	+	1.67913i
$658$	6.45734e40	−	2.69947e40i	0.882630	−	0.368980i
$659$		−	1.40806e41i		−	1.88271i	−0.337417	−	0.941355i	$-0.609553\pi$
$659$		−	1.40806e41i		−	1.88271i	0.337417	−	0.941355i	$-0.390447\pi$
$660$	1.94207e39	−	4.77403e40i	0.0254026	−	0.624451i
$661$		−	2.80928e40i		−	0.359479i	−0.983714	−	0.179739i	$-0.942475\pi$
$661$		−	2.80928e40i		−	0.359479i	0.983714	−	0.179739i	$-0.0575254\pi$
$662$			1.46140e41i			1.82949i
$663$	−1.72295e39	+	4.23539e40i	−0.0211021	+	0.518737i
$664$			1.71949e40i			0.206045i
$665$	−1.95517e41	+	8.17352e40i	−2.29230	+	0.958287i
$666$	−1.85919e40	+	2.28137e41i	−0.213279	+	2.61709i
$667$	3.50896e40			0.393871
$668$	7.18777e39			0.0789469
$669$	−4.74520e39	+	1.16648e41i	−0.0510007	+	1.25371i
$670$		−	3.01087e41i		−	3.16670i
$671$	−4.61955e39			−0.0475470
$672$	6.64630e40	−	2.46615e40i	0.669461	−	0.248408i
$673$	5.75574e40			0.567391			0.283696	−	0.958914i	$-0.408439\pi$
$673$	5.75574e40			0.567391			0.283696	+	0.958914i	$0.408439\pi$
$674$		−	2.80090e41i		−	2.70228i
$675$	1.84370e41	+	2.26002e40i	1.74095	+	0.213407i
$676$	−1.70245e41			−1.57343
$677$	−1.35604e41			−1.22669			−0.613346	−	0.789814i	$-0.710177\pi$
$677$	−1.35604e41			−1.22669			−0.613346	+	0.789814i	$0.710177\pi$
$678$	2.59265e40	+	1.05469e39i	0.229569	+	0.00933884i
$679$	−2.97843e40	+	1.24512e40i	−0.258152	+	0.107920i
$680$			3.95693e41i			3.35721i
$681$	−2.08950e41	−	8.50004e39i	−1.73543	−	0.0705972i
$682$		−	4.86762e40i		−	0.395771i
$683$			1.77966e41i			1.41657i	0.705927	+	0.708285i	$0.250531\pi$
$683$			1.77966e41i			1.41657i	−0.705927	+	0.708285i	$0.749469\pi$
$684$	−2.73847e40	+	3.36031e41i	−0.213400	+	2.61858i
$685$			3.39463e41i			2.58987i
$686$	8.30167e40	−	2.06111e41i	0.620106	−	1.53958i
$687$	9.01178e39	−	2.21529e41i	0.0659079	−	1.62016i
$688$	−3.30956e40			−0.236994
$689$	4.63610e40			0.325068
$690$	−5.12142e41	−	2.08339e40i	−3.51624	−	0.143040i
$691$			3.43405e40i			0.230874i	0.993315	+	0.115437i	$0.0368269\pi$
$691$			3.43405e40i			0.230874i	−0.993315	+	0.115437i	$0.963173\pi$
$692$	2.20701e40			0.145300
$693$	3.16525e40	−	1.03018e40i	0.204069	−	0.0664170i
$694$	1.80836e41			1.14175
$695$			2.10173e41i			1.29956i
$696$	6.37269e40	+	2.59240e39i	0.385912	+	0.0156988i
$697$	8.86214e40			0.525609
$698$	−3.26082e41			−1.89419
$699$	2.17821e39	−	5.35452e40i	0.0123931	−	0.304650i
$700$	−2.13026e41	−	5.09575e41i	−1.18716	−	2.83979i
$701$			1.75246e40i			0.0956615i	0.998855	+	0.0478307i	$0.0152308\pi$
$701$			1.75246e40i			0.0956615i	−0.998855	+	0.0478307i	$0.984769\pi$
$702$	−9.90623e40	−	1.21431e40i	−0.529688	−	0.0649296i
$703$		−	4.52195e41i		−	2.36850i
$704$		−	6.31485e40i		−	0.324011i
$705$	1.90138e41	+	7.73478e39i	0.955711	+	0.0388782i
$706$			4.42283e41i			2.17787i
$707$	−1.89046e40	−	4.52214e40i	−0.0911983	−	0.218153i
$708$	3.27858e41	+	1.33372e40i	1.54954	+	0.0630351i
$709$	2.33578e41			1.08159			0.540793	−	0.841156i	$-0.318124\pi$
$709$	2.33578e41			1.08159			0.540793	+	0.841156i	$0.318124\pi$
$710$	4.90110e41			2.22355
$711$	2.25924e41	+	1.84116e40i	1.00428	+	0.0818432i
$712$		−	2.01729e41i		−	0.878637i
$713$	−3.32632e41			−1.41960
$714$	−6.00838e41	+	2.22945e41i	−2.51266	+	0.932338i
$715$	−2.79427e40			−0.114507
$716$			3.75097e41i			1.50628i
$717$	−3.34071e39	+	8.21220e40i	−0.0131465	+	0.323170i
$718$	−7.67348e41			−2.95929
$719$	−8.57988e40			−0.324274			−0.162137	−	0.986768i	$-0.551839\pi$
$719$	−8.57988e40			−0.324274			−0.162137	+	0.986768i	$0.551839\pi$
$720$	−1.44958e41	−	1.18133e40i	−0.536934	−	0.0437572i
$721$	−4.48805e41	+	1.87622e41i	−1.62928	+	0.681117i
$722$		−	5.79123e41i		−	2.06054i
$723$	−1.31334e40	+	3.22847e41i	−0.0458005	+	1.12588i
$724$		−	2.16231e41i		−	0.739109i
$725$			1.61387e41i			0.540715i
$726$	−1.95962e40	+	4.81718e41i	−0.0643564	+	1.58202i
$727$		−	5.74080e41i		−	1.84809i	−0.382283	−	0.924045i	$-0.624862\pi$
$727$		−	5.74080e41i		−	1.84809i	0.382283	−	0.924045i	$-0.375138\pi$
$728$	4.92343e40	+	1.17772e41i	0.155369	+	0.371654i
$729$	3.13687e41	+	7.80772e40i	0.970393	+	0.241532i
$730$	1.53014e42			4.64035
$731$	−3.96513e41			−1.17884
$732$	−5.42190e39	+	1.33282e41i	−0.0158030	+	0.388474i
$733$			2.25888e41i			0.645484i	0.946487	+	0.322742i	$0.104605\pi$
$733$			2.25888e41i			0.645484i	−0.946487	+	0.322742i	$0.895395\pi$
$734$	1.39054e40			0.0389574
$735$	4.41526e41	−	4.12377e41i	1.21280	−	1.13273i
$736$	−3.38746e41			−0.912316
$737$		−	9.34324e40i		−	0.246728i
$738$	−1.69482e40	+	2.07967e41i	−0.0438841	+	0.538491i
$739$	4.92269e41			1.24985			0.624925	−	0.780685i	$-0.285129\pi$
$739$	4.92269e41			1.24985			0.624925	+	0.780685i	$0.285129\pi$
$740$	1.85049e42			4.60708
$741$	1.97007e41	+	8.01421e39i	0.480969	+	0.0195658i
$742$	2.70345e41	+	6.46686e41i	0.647234	+	1.54823i
$743$			1.40196e41i			0.329152i	0.986364	+	0.164576i	$0.0526256\pi$
$743$			1.40196e41i			0.329152i	−0.986364	+	0.164576i	$0.947374\pi$
$744$	−6.04098e41	−	2.45746e40i	−1.39091	−	0.0565821i
$745$			4.42158e41i			0.998415i
$746$		−	1.36793e42i		−	3.02935i
$747$	−7.54695e40	−	6.15035e39i	−0.163917	−	0.0133583i
$748$			2.85460e41i			0.608097i
$749$	3.54648e41	−	1.48259e41i	0.740988	−	0.309768i
$750$	4.11903e40	−	1.01255e42i	0.0844125	−	2.07504i
$751$	−5.68191e41			−1.14213			−0.571064	−	0.820905i	$-0.693469\pi$
$751$	−5.68191e41			−1.14213			−0.571064	+	0.820905i	$0.693469\pi$
$752$	−9.48948e40			−0.187104
$753$	−5.79807e40	−	2.35865e39i	−0.112139	−	0.00456179i
$754$		−	8.67138e40i		−	0.164514i
$755$	−4.10066e41			−0.763173
$756$	−2.60074e41	−	9.25323e41i	−0.474822	−	1.68938i
$757$	−4.08823e40			−0.0732227			−0.0366113	−	0.999330i	$-0.511656\pi$
$757$	−4.08823e40			−0.0732227			−0.0366113	+	0.999330i	$0.511656\pi$
$758$			7.91789e41i			1.39125i
$759$	−1.58926e41	−	6.46510e39i	−0.273962	−	0.0111447i
$760$	1.84054e42			3.11278
$761$	3.35427e41			0.556571			0.278285	−	0.960498i	$-0.410234\pi$
$761$	3.35427e41			0.556571			0.278285	+	0.960498i	$0.410234\pi$
$762$	−4.79175e39	+	1.17792e41i	−0.00780095	+	0.191764i
$763$	−1.80344e41	−	4.31397e41i	−0.288068	−	0.689082i
$764$		−	2.66714e41i		−	0.418015i
$765$	−1.73672e42	−	1.41533e41i	−2.67078	−	0.217654i
$766$		−	4.66583e41i		−	0.704063i
$767$		−	1.91897e41i		−	0.284142i
$768$	−1.00694e42	−	4.09621e40i	−1.46307	−	0.0595175i
$769$			4.90939e41i			0.699996i	0.936750	+	0.349998i	$0.113818\pi$
$769$			4.90939e41i			0.699996i	−0.936750	+	0.349998i	$0.886182\pi$
$770$	−1.62942e41	−	3.89770e41i	−0.227991	−	0.545372i
$771$	2.89158e41	+	1.17629e40i	0.397052	+	0.0161520i
$772$	−4.29597e41			−0.578909
$773$	−5.27038e41			−0.697010			−0.348505	−	0.937307i	$-0.613311\pi$
$773$	−5.27038e41			−0.697010			−0.348505	+	0.937307i	$0.613311\pi$
$774$	7.58303e40	−	9.30495e41i	0.0984235	−	1.20773i
$775$		−	1.52987e42i		−	1.94886i
$776$	2.80381e41			0.350553
$777$	4.48480e41	+	1.20866e42i	0.550349	+	1.48319i
$778$	−1.92877e42			−2.32315
$779$		−	4.12217e41i		−	0.487341i
$780$	−3.27960e40	+	8.06197e41i	−0.0380582	+	0.935555i
$781$	1.52089e41			0.173244
$782$	3.06232e42			3.42415
$783$	−3.41723e40	+	2.78774e41i	−0.0375084	+	0.305989i
$784$	−2.11636e41	+	2.14420e41i	−0.228038	+	0.231038i
$785$			2.20864e42i			2.33622i
$786$	9.16274e40	−	2.25240e42i	0.0951478	−	2.33894i
$787$			3.80835e41i			0.388243i	0.980978	+	0.194121i	$0.0621856\pi$
$787$			3.80835e41i			0.388243i	−0.980978	+	0.194121i	$0.937814\pi$
$788$			2.37596e42i			2.37799i
$789$	−4.80041e39	+	1.18005e41i	−0.00471695	+	0.115953i
$790$		−	2.87682e42i		−	2.77536i
$791$	1.34837e41	−	5.63681e40i	0.127717	−	0.0533917i
$792$	−2.88151e41	−	2.34827e40i	−0.267982	−	0.0218390i
$793$	7.80108e40			0.0712351
$794$	−1.83169e42			−1.64231
$795$	−7.74618e40	+	1.90418e42i	−0.0681968	+	1.67643i
$796$			2.67286e41i			0.231067i
$797$	−5.31179e41			−0.450916			−0.225458	−	0.974253i	$-0.572388\pi$
$797$	−5.31179e41			−0.450916			−0.225458	+	0.974253i	$0.572388\pi$
$798$	1.03702e42	+	2.79476e42i	0.864457	+	2.32972i
$799$	−1.13692e42			−0.930682
$800$		−	1.55799e42i		−	1.25245i
$801$	8.85402e41	+	7.21555e40i	0.698987	+	0.0569636i
$802$	4.03278e41			0.312663
$803$	4.74829e41			0.361545
$804$	−2.69569e42	−	1.09660e41i	−2.01585	−	0.0820043i
$805$	−2.66351e42	+	1.11347e42i	−1.95621	+	0.817785i
$806$			8.22002e41i			0.592945i
$807$	−3.31543e41	−	1.34871e40i	−0.234895	−	0.00955549i
$808$			4.25701e41i			0.296237i
$809$		−	6.30880e41i		−	0.431214i	−0.976480	−	0.215607i	$-0.930827\pi$
$809$		−	6.30880e41i		−	0.431214i	0.976480	−	0.215607i	$-0.0691730\pi$
$810$	6.64270e41	−	4.04848e42i	0.445977	−	2.71806i
$811$		−	2.89004e42i		−	1.90591i	−0.303114	−	0.952954i	$-0.598026\pi$
$811$		−	2.89004e42i		−	1.90591i	0.303114	−	0.952954i	$-0.401974\pi$
$812$	7.70494e41	−	3.22103e41i	0.499122	−	0.208656i
$813$	−2.52447e40	+	6.20571e41i	−0.0160642	+	0.394892i
$814$	9.01467e41			0.563503
$815$	−3.92088e42			−2.40768
$816$	8.68205e41	+	3.53184e40i	0.523739	+	0.0213056i
$817$			1.84436e42i			1.09301i
$818$	−3.77679e42			−2.19887
$819$	−5.34520e41	+	1.73967e41i	−0.305737	+	0.0995063i
$820$	1.68689e42			0.947949
$821$		−	3.07163e42i		−	1.69587i	−0.530098	−	0.847936i	$-0.677845\pi$
$821$		−	3.07163e42i		−	1.69587i	0.530098	−	0.847936i	$-0.322155\pi$
$822$	4.77121e42	+	1.94092e41i	2.58814	+	0.105285i
$823$	2.54479e42			1.35629			0.678147	−	0.734926i	$-0.262783\pi$
$823$	2.54479e42			1.35629			0.678147	+	0.734926i	$0.262783\pi$
$824$	4.22493e42			2.21246
$825$	2.97349e40	−	7.30949e41i	0.0152997	−	0.376101i
$826$	2.67675e42	−	1.11901e42i	1.35331	−	0.565747i
$827$		−	1.05955e42i		−	0.526370i	−0.964745	−	0.263185i	$-0.915227\pi$
$827$		−	1.05955e42i		−	0.526370i	0.964745	−	0.263185i	$-0.0847729\pi$
$828$	−3.73059e41	+	4.57772e42i	−0.182112	+	2.23465i
$829$			2.36511e42i			1.13452i	0.823539	+	0.567259i	$0.191996\pi$
$829$			2.36511e42i			1.13452i	−0.823539	+	0.567259i	$0.808004\pi$
$830$			9.60995e41i			0.452990i
$831$	2.87927e42	+	1.17128e41i	1.33373	+	0.0542559i
$832$			1.06640e42i			0.485435i
$833$	−2.53558e42	+	2.56893e42i	−1.13429	+	1.14921i
$834$	2.95402e42	+	1.20169e41i	1.29869	+	0.0528306i
$835$	1.72795e41			0.0746583
$836$	1.32780e42			0.563823
$837$	3.23936e41	−	2.64263e42i	0.135188	−	1.10285i
$838$			4.57741e42i			1.87751i
$839$	−6.56103e41			−0.264499			−0.132249	−	0.991216i	$-0.542220\pi$
$839$	−6.56103e41			−0.264499			−0.132249	+	0.991216i	$0.542220\pi$
$840$	−4.91951e42	+	1.82542e42i	−1.94927	+	0.723290i
$841$	2.32366e42			0.904964
$842$			3.37940e42i			1.29364i
$843$	1.04066e41	−	2.55818e42i	0.0391571	−	0.962567i
$844$	−2.88044e42			−1.06535
$845$	−4.09273e42			−1.48796
$846$	2.17428e41	−	2.66800e42i	0.0777043	−	0.953490i
$847$	1.04733e42	+	2.50529e42i	0.367937	+	0.880133i
$848$		−	9.50346e41i		−	0.328202i
$849$	−5.42895e40	+	1.33455e42i	−0.0184312	+	0.453080i
$850$			1.40845e43i			4.70076i
$851$		−	6.16022e42i		−	2.02124i
$852$	1.78505e41	−	4.38805e42i	0.0575807	−	1.41546i
$853$		−	3.33238e42i		−	1.05680i	−0.848995	−	0.528400i	$-0.822792\pi$
$853$		−	3.33238e42i		−	1.05680i	0.848995	−	0.528400i	$-0.177208\pi$
$854$	4.54904e41	+	1.08817e42i	0.141834	+	0.339278i
$855$	−6.58333e41	+	8.07825e42i	−0.201807	+	2.47633i
$856$	−3.33856e42			−1.00621
$857$	4.96398e42			1.47098			0.735492	−	0.677533i	$-0.236951\pi$
$857$	4.96398e42			1.47098			0.735492	+	0.677533i	$0.236951\pi$
$858$	−1.59766e40	+	3.92740e41i	−0.00465499	+	0.114430i
$859$		−	4.33630e41i		−	0.124228i	−0.998069	−	0.0621139i	$-0.980216\pi$
$859$		−	4.33630e41i		−	0.124228i	0.998069	−	0.0621139i	$-0.0197842\pi$
$860$	−7.54752e42			−2.12607
$861$	4.08830e41	+	1.10180e42i	0.113239	+	0.305180i
$862$	−2.84266e42			−0.774228
$863$			6.25098e42i			1.67414i	0.547096	+	0.837070i	$0.315733\pi$
$863$			6.25098e42i			1.67414i	−0.547096	+	0.837070i	$0.684267\pi$
$864$	3.29890e41	−	2.69120e42i	0.0868800	−	0.708757i
$865$	5.30570e41			0.137407
$866$	1.86470e42			0.474898
$867$	6.41232e42	+	2.60852e41i	1.60597	+	0.0653308i
$868$	−7.30389e42	+	3.05337e42i	−1.79895	+	0.752043i
$869$		−	8.92725e41i		−	0.216238i
$870$	3.56158e42	+	1.44885e41i	0.848426	+	0.0345138i
$871$			1.57780e42i			0.369649i
$872$			4.06105e42i			0.935726i
$873$	−1.00288e41	+	1.23061e42i	−0.0227270	+	0.278878i
$874$		−	1.42442e43i		−	3.17485i
$875$	−2.20143e42	−	5.26599e42i	−0.482601	−	1.15442i
$876$	5.57301e41	−	1.36997e43i	0.120166	−	2.95393i
$877$	−1.32291e42			−0.280567			−0.140284	−	0.990111i	$-0.544801\pi$
$877$	−1.32291e42			−0.280567			−0.140284	+	0.990111i	$0.544801\pi$
$878$	5.62792e41			0.117403
$879$	5.74284e42	+	2.33618e41i	1.17839	+	0.0479366i
$880$			5.72792e41i			0.115611i
$881$	−1.48118e42			−0.294075			−0.147037	−	0.989131i	$-0.546974\pi$
$881$	−1.48118e42			−0.294075			−0.147037	+	0.989131i	$0.546974\pi$
$882$	−5.54360e42	−	6.44152e42i	−1.08267	−	1.25804i
$883$	−1.51901e42			−0.291831			−0.145915	−	0.989297i	$-0.546613\pi$
$883$	−1.51901e42			−0.291831			−0.145915	+	0.989297i	$0.546613\pi$
$884$		−	4.82061e42i		−	0.911053i
$885$	7.88176e42	+	3.20629e41i	1.46537	+	0.0596108i
$886$	−1.33478e43			−2.44130
$887$	1.42680e42			0.256727			0.128363	−	0.991727i	$-0.459028\pi$
$887$	1.42680e42			0.256727			0.128363	+	0.991727i	$0.459028\pi$
$888$	4.55113e41	−	1.11877e43i	0.0805622	−	1.98040i
$889$	2.56097e41	+	6.12603e41i	0.0445994	+	0.106685i
$890$		−	1.12743e43i		−	1.93168i
$891$	2.06134e41	−	1.25631e42i	0.0347475	−	0.211773i
$892$		−	1.32765e43i		−	2.20188i
$893$			5.28831e42i			0.862921i
$894$	6.21461e42	+	2.52809e41i	0.997746	+	0.0405882i
$895$			9.01740e42i			1.42445i
$896$	−1.06364e43	+	4.44652e42i	−1.65322	+	0.691122i
$897$	2.68381e42	+	1.09177e41i	0.410451	+	0.0166971i
$898$	1.85540e43			2.79209
$899$	2.31322e42			0.342532
$900$	−2.10543e43	−	1.71581e42i	−3.06778	−	0.250007i
$901$		−	1.13859e43i		−	1.63252i
$902$	8.21769e41			0.115946
$903$	−1.82920e42	−	4.92971e42i	−0.253974	−	0.684461i
$904$	−1.26932e42			−0.173431
$905$		−	5.19823e42i		−	0.698958i
$906$	−2.34461e41	+	5.76356e42i	−0.0310250	+	0.762662i
$907$	−5.06614e42			−0.659738			−0.329869	−	0.944027i	$-0.607005\pi$
$907$	−5.06614e42			−0.659738			−0.329869	+	0.944027i	$0.607005\pi$
$908$	2.37821e43			3.04793
$909$	−1.86843e42	−	1.52267e41i	−0.235668	−	0.0192056i
$910$	2.75162e42	+	6.58209e42i	0.341577	+	0.817079i
$911$		−	3.12175e42i		−	0.381401i	−0.981648	−	0.190701i	$-0.938924\pi$
$911$		−	3.12175e42i		−	0.381401i	0.981648	−	0.190701i	$-0.0610760\pi$
$912$	1.64282e41	−	4.03841e42i	0.0197544	−	0.485607i
$913$			2.98213e41i			0.0352939i
$914$			9.25412e42i			1.07799i
$915$	−1.30343e41	+	3.20413e42i	−0.0149446	+	0.367370i
$916$			2.52139e43i			2.84548i
$917$	−4.89706e42	−	1.17141e43i	−0.543976	−	1.30123i
$918$	−2.98227e42	+	2.43290e43i	−0.326083	+	2.66014i
$919$	−9.11913e42			−0.981474			−0.490737	−	0.871308i	$-0.663272\pi$
$919$	−9.11913e42			−0.981474			−0.490737	+	0.871308i	$0.663272\pi$
$920$	2.50736e43			2.65639
$921$	2.48435e41	−	6.10709e42i	0.0259089	−	0.636897i
$922$			2.37984e42i			0.244315i
$923$	−2.56835e42			−0.259555
$924$	−3.54903e42	+	1.31689e42i	−0.353075	+	0.131011i
$925$	2.83327e43			2.77480
$926$		−	4.95675e42i		−	0.477901i
$927$	−1.51119e42	+	1.85434e43i	−0.143438	+	1.76009i
$928$	2.35574e42			0.220131
$929$	−1.78770e43			−1.64463			−0.822313	−	0.569036i	$-0.807317\pi$
$929$	−1.78770e43			−1.64463			−0.822313	+	0.569036i	$0.807317\pi$
$930$	−3.37620e43	−	1.37343e42i	−3.05791	−	0.124395i
$931$	1.19492e43	+	1.17941e43i	1.06554	+	1.05171i
$932$			6.09437e42i			0.535054i
$933$	1.39067e43	+	5.65721e41i	1.20210	+	0.0489011i
$934$		−	6.51594e42i		−	0.554559i
$935$			6.86252e42i			0.575063i
$936$	4.86604e42	+	3.96556e41i	0.401491	+	0.0327193i
$937$		−	1.15690e43i		−	0.939878i	−0.882699	−	0.469939i	$-0.844276\pi$
$937$		−	1.15690e43i		−	0.939878i	0.882699	−	0.469939i	$-0.155724\pi$
$938$	−2.20086e43	+	9.20064e42i	−1.76057	+	0.735999i
$939$	6.73392e41	−	1.65534e43i	0.0530416	−	1.30388i
$940$	−2.16410e43			−1.67851
$941$	1.10791e43			0.846167			0.423083	−	0.906091i	$-0.360948\pi$
$941$	1.10791e43			0.846167			0.423083	+	0.906091i	$0.360948\pi$
$942$	3.10428e43	+	1.26282e42i	2.33466	+	0.0949735i
$943$		−	5.61560e42i		−	0.415888i
$944$	−3.93366e42			−0.286882
$945$	−6.25223e42	−	2.22449e43i	−0.449028	−	1.59761i
$946$	−3.67679e42			−0.260044
$947$			7.27568e42i			0.506756i	0.967367	+	0.253378i	$0.0815417\pi$
$947$			7.27568e42i			0.506756i	−0.967367	+	0.253378i	$0.918458\pi$
$948$	−2.57567e43	−	1.04778e42i	−1.76673	−	0.0718702i
$949$	−8.01850e42			−0.541668
$950$	6.55134e43			4.35851
$951$	−5.09170e41	+	1.25165e43i	−0.0333615	+	0.820098i
$952$	2.89240e43	−	1.20916e43i	1.86648	−	0.780276i
$953$			3.23993e42i			0.205915i	0.994686	+	0.102958i	$0.0328306\pi$
$953$			3.23993e42i			0.205915i	−0.994686	+	0.102958i	$0.967169\pi$
$954$	2.67193e43	+	2.17748e42i	1.67253	+	0.136302i
$955$		−	6.41185e42i		−	0.395307i
$956$		−	9.34690e42i		−	0.567581i
$957$	1.10522e42	+	4.49602e40i	0.0661036	+	0.00268909i
$958$			3.17041e43i			1.86774i
$959$	2.48138e43	−	1.03733e43i	1.43987	−	0.601933i
$960$	−4.38000e43	−	1.78178e42i	−2.50346	−	0.101840i
$961$	−4.16620e42			−0.234558
$962$	−1.52232e43			−0.844242
$963$	1.19415e42	−	1.46531e43i	0.0652345	−	0.800477i
$964$		−	3.67455e43i		−	1.97737i
$965$	−1.03276e43			−0.547461
$966$	1.41272e43	+	3.80728e43i	0.737713	+	1.98814i
$967$	−3.54910e43			−1.82572			−0.912859	−	0.408274i	$-0.866131\pi$
$967$	−3.54910e43			−1.82572			−0.912859	+	0.408274i	$0.866131\pi$
$968$		−	2.35841e43i		−	1.19516i
$969$	1.96823e42	−	4.83835e43i	0.0982611	−	2.41547i
$970$	1.56700e43			0.770690
$971$	2.64784e43			1.28296			0.641480	−	0.767139i	$-0.278321\pi$
$971$	2.64784e43			1.28296			0.641480	+	0.767139i	$0.278321\pi$
$972$	−3.60049e43	−	7.42186e42i	−1.71870	−	0.354284i
$973$	1.53631e43	−	6.42248e42i	0.722507	−	0.302042i
$974$			4.41560e43i			2.04590i
$975$	−5.02137e41	+	1.23436e43i	−0.0229221	+	0.563476i
$976$		−	1.59913e42i		−	0.0719219i
$977$		−	2.47276e43i		−	1.09575i	−0.836560	−	0.547875i	$-0.815437\pi$
$977$		−	2.47276e43i		−	1.09575i	0.836560	−	0.547875i	$-0.184563\pi$
$978$	−2.24182e42	+	5.51088e43i	−0.0978783	+	2.40606i
$979$		−	3.49861e42i		−	0.150503i
$980$	−4.82641e43	+	4.88990e43i	−2.04572	+	2.07263i
$981$	−1.78242e43	−	1.45257e42i	−0.744404	−	0.0606649i
$982$	−2.32504e43			−0.956785
$983$	−2.10568e43			−0.853819			−0.426909	−	0.904294i	$-0.640398\pi$
$983$	−2.10568e43			−0.853819			−0.426909	+	0.904294i	$0.640398\pi$
$984$	4.14877e41	−	1.01986e43i	0.0165764	−	0.407485i
$985$			5.71186e43i			2.24881i
$986$	−2.12963e43			−0.826207
$987$	−5.24486e42	−	1.41349e43i	−0.200510	−	0.540374i
$988$	−2.24228e43			−0.844722
$989$			2.51255e43i			0.932758i
$990$	−1.61043e43	−	1.31241e42i	−0.589156	−	0.0480130i
$991$	1.24714e43			0.449621			0.224810	−	0.974403i	$-0.427824\pi$
$991$	1.24714e43			0.449621			0.224810	+	0.974403i	$0.427824\pi$
$992$	−2.23312e43			−0.793399
$993$	3.14547e43	+	1.27957e42i	1.10134	+	0.0448024i
$994$	−1.49768e43	−	3.58257e43i	−0.516793	−	1.23621i
$995$			6.42561e42i			0.218514i
$996$	8.60397e42	+	3.50008e41i	0.288362	+	0.0117305i
$997$		−	1.44247e43i		−	0.476461i	−0.971209	−	0.238230i	$-0.923433\pi$
$997$		−	1.44247e43i		−	0.476461i	0.971209	−	0.238230i	$-0.0765673\pi$
$998$			5.59851e43i			1.82255i
$999$	4.89406e43	+	5.99918e42i	1.57025	+	0.192483i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	21.30.c.a.20.6	yes	76
3.2	odd	2	inner	21.30.c.a.20.71	yes	76
7.6	odd	2	inner	21.30.c.a.20.72	yes	76
21.20	even	2	inner	21.30.c.a.20.5	✓	76

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.30.c.a.20.5	✓	76	21.20	even	2	inner
21.30.c.a.20.6	yes	76	1.1	even	1	trivial
21.30.c.a.20.71	yes	76	3.2	odd	2	inner
21.30.c.a.20.72	yes	76	7.6	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 21 = 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 30 \)
Character orbit:	\([\chi]\)	\(=\)	21.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+38457.7i q^{2} +(8.27750e6 + 336727. i) q^{3} -9.42122e8 q^{4} -2.26488e10 q^{5} +(-1.29498e10 + 3.18333e11i) q^{6} +(6.92104e11 + 1.65557e12i) q^{7} -1.55850e13i q^{8} +(6.84036e13 + 5.57452e12i) q^{9} +O(q^{10})\)	\(q+38457.7i q^{2} +(8.27750e6 + 336727. i) q^{3} -9.42122e8 q^{4} -2.26488e10 q^{5} +(-1.29498e10 + 3.18333e11i) q^{6} +(6.92104e11 + 1.65557e12i) q^{7} -1.55850e13i q^{8} +(6.84036e13 + 5.57452e12i) q^{9} -8.71020e14i q^{10} -2.70292e14i q^{11} +(-7.79842e15 - 3.17238e14i) q^{12} +4.56446e15i q^{13} +(-6.36692e16 + 2.66167e16i) q^{14} +(-1.87475e17 - 7.62647e15i) q^{15} +9.35660e16 q^{16} +1.12100e18 q^{17} +(-2.14383e17 + 2.63064e18i) q^{18} -5.21426e18i q^{19} +2.13379e19 q^{20} +(5.17141e18 + 1.39370e19i) q^{21} +1.03948e19 q^{22} -7.10335e19i q^{23} +(5.24791e18 - 1.29005e20i) q^{24} +3.26704e20 q^{25} -1.75539e20 q^{26} +(5.64334e20 + 6.91765e19i) q^{27} +(-6.52046e20 - 1.55975e21i) q^{28} +4.93987e20i q^{29} +(2.93296e20 - 7.20987e21i) q^{30} -4.68274e21i q^{31} -4.76882e21i q^{32} +(9.10148e19 - 2.23734e21i) q^{33} +4.31110e22i q^{34} +(-1.56753e22 - 3.74966e22i) q^{35} +(-6.44446e22 - 5.25188e21i) q^{36} +8.67228e22 q^{37} +2.00528e23 q^{38} +(-1.53698e21 + 3.77823e22i) q^{39} +3.52982e23i q^{40} +7.90557e22 q^{41} +(-5.35984e23 + 1.98881e23i) q^{42} -3.53714e23 q^{43} +2.54648e23i q^{44} +(-1.54926e24 - 1.26256e23i) q^{45} +2.73178e24 q^{46} -1.01420e24 q^{47} +(7.74492e23 + 3.15062e22i) q^{48} +(-2.26189e24 + 2.29165e24i) q^{49} +1.25643e25i q^{50} +(9.27906e24 + 3.77471e23i) q^{51} -4.30028e24i q^{52} -1.01570e25i q^{53} +(-2.66037e24 + 2.17030e25i) q^{54} +6.12180e24i q^{55} +(2.58020e25 - 1.07865e25i) q^{56} +(1.75578e24 - 4.31611e25i) q^{57} -1.89976e25 q^{58} -4.20416e25 q^{59} +(1.76625e26 + 7.18507e24i) q^{60} -1.70909e25i q^{61} +1.80087e26 q^{62} +(3.81134e25 + 1.17105e26i) q^{63} +2.33631e26 q^{64} -1.03380e26i q^{65} +(8.60431e25 + 3.50022e24i) q^{66} +3.45672e26 q^{67} -1.05612e27 q^{68} +(2.39189e25 - 5.87980e26i) q^{69} +(1.44203e27 - 6.02837e26i) q^{70} +5.62685e26i q^{71} +(8.68791e25 - 1.06607e27i) q^{72} +1.75673e27i q^{73} +3.33516e27i q^{74} +(2.70429e27 + 1.10010e26i) q^{75} +4.91247e27i q^{76} +(4.47487e26 - 1.87070e26i) q^{77} +(-1.45302e27 - 5.91086e25i) q^{78} +3.30282e27 q^{79} -2.11916e27 q^{80} +(4.64798e27 + 7.62635e26i) q^{81} +3.04030e27i q^{82} -1.10330e27 q^{83} +(-4.87211e27 - 1.31304e28i) q^{84} -2.53893e28 q^{85} -1.36030e28i q^{86} +(-1.66339e26 + 4.08898e27i) q^{87} -4.21251e27 q^{88} +1.29438e28 q^{89} +(4.85552e27 - 5.95809e28i) q^{90} +(-7.55676e27 + 3.15908e27i) q^{91} +6.69222e28i q^{92} +(1.57681e27 - 3.87614e28i) q^{93} -3.90039e28i q^{94} +1.18097e29i q^{95} +(1.60579e27 - 3.94739e28i) q^{96} +1.79904e28i q^{97} +(-8.81314e28 - 8.69871e28i) q^{98} +(1.50675e27 - 1.84890e28i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 76 q - 20401094660 q^{4} + 1962751543872 q^{7} - 89581451225964 q^{9}+O(q^{10}) \) 76 * q - 20401094660 * q^4 + 1962751543872 * q^7 - 89581451225964 * q^9	\( 76 q - 20401094660 q^{4} + 1962751543872 q^{7} - 89581451225964 q^{9} - 11\!\cdots\!48 q^{15}+ \cdots - 23\!\cdots\!24 q^{99}+O(q^{100}) \) 76 * q - 20401094660 * q^4 + 1962751543872 * q^7 - 89581451225964 * q^9 - 116668222909200048 * q^15 + 4964525139713333892 * q^16 + 1542346202347854996 * q^18 + 33840646982361357348 * q^21 - 9870996616978150672 * q^22 + 3225406746743103424612 * q^25 - 3181907581338093199564 * q^28 + 5113912044496410095244 * q^30 - 85758641407134848258352 * q^36 - 17812771227715200149976 * q^37 + 388095283792424641491696 * q^39 + 804036587819434104664956 * q^42 + 2391536152977907871782320 * q^43 - 1070985628070611677307000 * q^46 - 512656982878691867441540 * q^49 - 961431915936904000664400 * q^51 + 20345422731681279280765248 * q^57 - 40096240109469024574169272 * q^58 - 164991837955115951799442596 * q^60 - 360764839802574990409097184 * q^63 - 1608343949909674725081473028 * q^64 + 483978610969894046870693264 * q^67 - 656026306765550013508448520 * q^70 + 1937172856654554597960695124 * q^72 - 8054141680325499868559088636 * q^78 - 11740735193468750125742145952 * q^79 + 18477545939654446572971367132 * q^81 - 7249045143271847568431965452 * q^84 + 14576359553686844022629140848 * q^85 - 1685535263940707754634995584 * q^88 + 44135166284535829618726469040 * q^91 + 226499776928895503792863540632 * q^93 - 231093384978708762520959066624 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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