LMFDB - Embedded newform 33.9.b.a.23.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [33,9,Mod(23,33)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(33, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 9, names="a")

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

chi := DirichletCharacter("33.23");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 33 = 3 \cdot 11 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	33.b (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:	$13.4434941320$
Analytic rank:	$0$
Dimension:	$26$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			23.11
Character	$\chi$	$=$	33.23
Dual form			33.9.b.a.23.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-8.17075i q^{2} +(-40.5699 + 70.1076i) q^{3} +189.239 q^{4} +920.235i q^{5} +(572.832 + 331.487i) q^{6} -1093.89 q^{7} -3637.93i q^{8} +(-3269.16 - 5688.52i) q^{9} +O(q^{10})$	\(q-8.17075i q^{2} +(-40.5699 + 70.1076i) q^{3} +189.239 q^{4} +920.235i q^{5} +(572.832 + 331.487i) q^{6} -1093.89 q^{7} -3637.93i q^{8} +(-3269.16 - 5688.52i) q^{9} +7519.00 q^{10} +4414.43i q^{11} +(-7677.41 + 13267.1i) q^{12} -25788.3 q^{13} +8937.88i q^{14} +(-64515.5 - 37333.8i) q^{15} +18720.5 q^{16} +37400.5i q^{17} +(-46479.5 + 26711.5i) q^{18} -191049. q^{19} +174144. i q^{20} +(44379.0 - 76689.9i) q^{21} +36069.2 q^{22} +257158. i q^{23} +(255047. + 147591. i) q^{24} -456207. q^{25} +210710. i q^{26} +(531439. + 1589.60i) q^{27} -207006. q^{28} -272338. i q^{29} +(-305045. + 527140. i) q^{30} -1.44072e6 q^{31} -1.08427e6i q^{32} +(-309485. - 179093. i) q^{33} +305590. q^{34} -1.00663e6i q^{35} +(-618653. - 1.07649e6i) q^{36} +240582. q^{37} +1.56101e6i q^{38} +(1.04623e6 - 1.80796e6i) q^{39} +3.34775e6 q^{40} +3.01500e6i q^{41} +(-626614. - 362609. i) q^{42} +6.24301e6 q^{43} +835381. i q^{44} +(5.23478e6 - 3.00840e6i) q^{45} +2.10118e6 q^{46} -3.04542e6i q^{47} +(-759490. + 1.31245e6i) q^{48} -4.56821e6 q^{49} +3.72755e6i q^{50} +(-2.62206e6 - 1.51733e6i) q^{51} -4.88015e6 q^{52} +680712. i q^{53} +(12988.2 - 4.34225e6i) q^{54} -4.06231e6 q^{55} +3.97949e6i q^{56} +(7.75085e6 - 1.33940e7i) q^{57} -2.22521e6 q^{58} +1.81032e7i q^{59} +(-1.22088e7 - 7.06502e6i) q^{60} +1.16867e7 q^{61} +1.17717e7i q^{62} +(3.57610e6 + 6.22261e6i) q^{63} -4.06686e6 q^{64} -2.37313e7i q^{65} +(-1.46332e6 + 2.52872e6i) q^{66} -1.58881e7 q^{67} +7.07763e6i q^{68} +(-1.80288e7 - 1.04329e7i) q^{69} -8.22495e6 q^{70} +4.27032e7i q^{71} +(-2.06945e7 + 1.18930e7i) q^{72} +1.96194e7 q^{73} -1.96573e6i q^{74} +(1.85083e7 - 3.19836e7i) q^{75} -3.61539e7 q^{76} -4.82889e6i q^{77} +(-1.47724e7 - 8.54847e6i) q^{78} +4.04857e7 q^{79} +1.72273e7i q^{80} +(-2.16719e7 + 3.71934e7i) q^{81} +2.46348e7 q^{82} +4.13228e7i q^{83} +(8.39823e6 - 1.45127e7i) q^{84} -3.44172e7 q^{85} -5.10101e7i q^{86} +(1.90930e7 + 1.10487e7i) q^{87} +1.60594e7 q^{88} +3.21055e7i q^{89} +(-2.45808e7 - 4.27720e7i) q^{90} +2.82095e7 q^{91} +4.86644e7i q^{92} +(5.84498e7 - 1.01005e8i) q^{93} -2.48834e7 q^{94} -1.75810e8i q^{95} +(7.60157e7 + 4.39888e7i) q^{96} +1.37061e8 q^{97} +3.73257e7i q^{98} +(2.51116e7 - 1.44315e7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 26 q - 35 q^{3} - 2596 q^{4} - 3746 q^{6} + 7156 q^{7} + 9011 q^{9}+O(q^{10}) $ 26 * q - 35 * q^3 - 2596 * q^4 - 3746 * q^6 + 7156 * q^7 + 9011 * q^9	\( 26 q - 35 q^{3} - 2596 q^{4} - 3746 q^{6} + 7156 q^{7} + 9011 q^{9} - 31836 q^{10} - 28900 q^{12} - 131624 q^{13} + 71041 q^{15} + 311972 q^{16} - 675394 q^{18} + 134608 q^{19} + 490306 q^{21} - 59088 q^{24} - 2324740 q^{25} + 2011426 q^{27} - 1996688 q^{28} - 324146 q^{30} + 964738 q^{31} - 512435 q^{33} + 9219648 q^{34} - 6887660 q^{36} - 5721542 q^{37} - 5782712 q^{39} + 8363496 q^{40} + 10350076 q^{42} + 4260820 q^{43} + 6595181 q^{45} - 39680292 q^{46} + 22674164 q^{48} + 20017254 q^{49} - 7985018 q^{51} + 48711952 q^{52} - 18774176 q^{54} - 4304454 q^{55} + 15476796 q^{57} - 16060008 q^{58} - 26730016 q^{60} + 58840 q^{61} - 42877282 q^{63} - 57365836 q^{64} - 10395110 q^{66} - 63186734 q^{67} + 100738079 q^{69} + 50969160 q^{70} + 48890880 q^{72} - 21879656 q^{73} - 122009926 q^{75} - 119289368 q^{76} - 123440744 q^{78} + 117211444 q^{79} + 138667019 q^{81} + 121755480 q^{82} - 28504816 q^{84} + 28880604 q^{85} + 14774868 q^{87} + 90481380 q^{88} + 189044834 q^{90} + 192183008 q^{91} - 113622071 q^{93} - 453996696 q^{94} + 11988416 q^{96} + 24314206 q^{97} - 57905155 q^{99}+O(q^{100}) \) 26 * q - 35 * q^3 - 2596 * q^4 - 3746 * q^6 + 7156 * q^7 + 9011 * q^9 - 31836 * q^10 - 28900 * q^12 - 131624 * q^13 + 71041 * q^15 + 311972 * q^16 - 675394 * q^18 + 134608 * q^19 + 490306 * q^21 - 59088 * q^24 - 2324740 * q^25 + 2011426 * q^27 - 1996688 * q^28 - 324146 * q^30 + 964738 * q^31 - 512435 * q^33 + 9219648 * q^34 - 6887660 * q^36 - 5721542 * q^37 - 5782712 * q^39 + 8363496 * q^40 + 10350076 * q^42 + 4260820 * q^43 + 6595181 * q^45 - 39680292 * q^46 + 22674164 * q^48 + 20017254 * q^49 - 7985018 * q^51 + 48711952 * q^52 - 18774176 * q^54 - 4304454 * q^55 + 15476796 * q^57 - 16060008 * q^58 - 26730016 * q^60 + 58840 * q^61 - 42877282 * q^63 - 57365836 * q^64 - 10395110 * q^66 - 63186734 * q^67 + 100738079 * q^69 + 50969160 * q^70 + 48890880 * q^72 - 21879656 * q^73 - 122009926 * q^75 - 119289368 * q^76 - 123440744 * q^78 + 117211444 * q^79 + 138667019 * q^81 + 121755480 * q^82 - 28504816 * q^84 + 28880604 * q^85 + 14774868 * q^87 + 90481380 * q^88 + 189044834 * q^90 + 192183008 * q^91 - 113622071 * q^93 - 453996696 * q^94 + 11988416 * q^96 + 24314206 * q^97 - 57905155 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/33\mathbb{Z}\right)^\times$.

$n$	$13$	$23$
$\chi(n)$	$1$	$-1$

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 $

$2$		−	8.17075i		−	0.510672i	−0.966852	−	0.255336i	$-0.917814\pi$
$2$		−	8.17075i		−	0.510672i	0.966852	−	0.255336i	$-0.0821860\pi$
$3$	−40.5699	+	70.1076i	−0.500863	+	0.865526i
$3$	−40.5699	+	70.1076i	−0.500863	+	0.865526i
$4$	189.239			0.739214
$5$			920.235i			1.47238i	0.676778	+	0.736188i	$0.263376\pi$
$5$			920.235i			1.47238i	−0.676778	+	0.736188i	$0.736624\pi$
$6$	572.832	+	331.487i	0.442000	+	0.255777i
$7$	−1093.89			−0.455597			−0.227798	−	0.973708i	$-0.573153\pi$
$7$	−1093.89			−0.455597			−0.227798	+	0.973708i	$0.573153\pi$
$8$		−	3637.93i		−	0.888168i
$9$	−3269.16	−	5688.52i	−0.498272	−	0.867021i
$10$	7519.00			0.751900
$11$			4414.43i			0.301511i
$11$			4414.43i			0.301511i
$12$	−7677.41	+	13267.1i	−0.370245	+	0.639810i
$13$	−25788.3			−0.902920			−0.451460	−	0.892291i	$-0.649097\pi$
$13$	−25788.3			−0.902920			−0.451460	+	0.892291i	$0.649097\pi$
$14$			8937.88i			0.232660i
$15$	−64515.5	−	37333.8i	−1.27438	−	0.737459i
$16$	18720.5			0.285652
$17$			37400.5i			0.447797i	0.974612	+	0.223899i	$0.0718785\pi$
$17$			37400.5i			0.447797i	−0.974612	+	0.223899i	$0.928122\pi$
$18$	−46479.5	+	26711.5i	−0.442763	+	0.254453i
$19$	−191049.			−1.46599			−0.732995	−	0.680235i	$-0.761878\pi$
$19$	−191049.			−1.46599			−0.732995	+	0.680235i	$0.761878\pi$
$20$			174144.i			1.08840i
$21$	44379.0	−	76689.9i	0.228192	−	0.394331i
$22$	36069.2			0.153973
$23$			257158.i			0.918944i	0.888192	+	0.459472i	$0.151961\pi$
$23$			257158.i			0.918944i	−0.888192	+	0.459472i	$0.848039\pi$
$24$	255047.	+	147591.i	0.768732	+	0.444850i
$25$	−456207.			−1.16789
$26$			210710.i			0.461095i
$27$	531439.	+	1589.60i	0.999996	+	0.00299112i
$28$	−207006.			−0.336784
$29$		−	272338.i		−	0.385050i	−0.981292	−	0.192525i	$-0.938332\pi$
$29$		−	272338.i		−	0.385050i	0.981292	−	0.192525i	$-0.0616676\pi$
$30$	−305045.	+	527140.i	−0.376599	+	0.650790i
$31$	−1.44072e6			−1.56003			−0.780014	−	0.625762i	$-0.784788\pi$
$31$	−1.44072e6			−1.56003			−0.780014	+	0.625762i	$0.784788\pi$
$32$		−	1.08427e6i		−	1.03404i
$33$	−309485.	−	179093.i	−0.260966	−	0.151016i
$34$	305590.			0.228677
$35$		−	1.00663e6i		−	0.670810i
$36$	−618653.	−	1.07649e6i	−0.368330	−	0.640914i
$37$	240582.			0.128368			0.0641839	−	0.997938i	$-0.479556\pi$
$37$	240582.			0.128368			0.0641839	+	0.997938i	$0.479556\pi$
$38$			1.56101e6i			0.748639i
$39$	1.04623e6	−	1.80796e6i	0.452239	−	0.781501i
$40$	3.34775e6			1.30772
$41$			3.01500e6i			1.06697i	0.845809	+	0.533485i	$0.179118\pi$
$41$			3.01500e6i			1.06697i	−0.845809	+	0.533485i	$0.820882\pi$
$42$	−626614.	−	362609.i	−0.201374	−	0.116531i
$43$	6.24301e6			1.82608			0.913041	−	0.407868i	$-0.133728\pi$
$43$	6.24301e6			1.82608			0.913041	+	0.407868i	$0.133728\pi$
$44$			835381.i			0.222882i
$45$	5.23478e6	−	3.00840e6i	1.27658	−	0.733643i
$46$	2.10118e6			0.469279
$47$		−	3.04542e6i		−	0.624103i	−0.950065	−	0.312051i	$-0.898984\pi$
$47$		−	3.04542e6i		−	0.624103i	0.950065	−	0.312051i	$-0.101016\pi$
$48$	−759490.	+	1.31245e6i	−0.143073	+	0.247240i
$49$	−4.56821e6			−0.792431
$50$			3.72755e6i			0.596408i
$51$	−2.62206e6	−	1.51733e6i	−0.387580	−	0.224285i
$52$	−4.88015e6			−0.667451
$53$			680712.i			0.0862701i	0.999069	+	0.0431350i	$0.0137346\pi$
$53$			680712.i			0.0862701i	−0.999069	+	0.0431350i	$0.986265\pi$
$54$	12988.2	−	4.34225e6i	0.00152748	−	0.510669i
$55$	−4.06231e6			−0.443938
$56$			3.97949e6i			0.404646i
$57$	7.75085e6	−	1.33940e7i	0.734260	−	1.26885i
$58$	−2.22521e6			−0.196634
$59$			1.81032e7i			1.49399i	0.664831	+	0.746994i	$0.268504\pi$
$59$			1.81032e7i			1.49399i	−0.664831	+	0.746994i	$0.731496\pi$
$60$	−1.22088e7	−	7.06502e6i	−0.942040	−	0.545140i
$61$	1.16867e7			0.844062			0.422031	−	0.906581i	$-0.361317\pi$
$61$	1.16867e7			0.844062			0.422031	+	0.906581i	$0.361317\pi$
$62$			1.17717e7i			0.796662i
$63$	3.57610e6	+	6.22261e6i	0.227011	+	0.395012i
$64$	−4.06686e6			−0.242404
$65$		−	2.37313e7i		−	1.32944i
$66$	−1.46332e6	+	2.52872e6i	−0.0771196	+	0.133268i
$67$	−1.58881e7			−0.788448			−0.394224	−	0.919014i	$-0.628987\pi$
$67$	−1.58881e7			−0.788448			−0.394224	+	0.919014i	$0.628987\pi$
$68$			7.07763e6i			0.331018i
$69$	−1.80288e7	−	1.04329e7i	−0.795371	−	0.460265i
$70$	−8.22495e6			−0.342563
$71$			4.27032e7i			1.68045i	0.542235	+	0.840227i	$0.317578\pi$
$71$			4.27032e7i			1.68045i	−0.542235	+	0.840227i	$0.682422\pi$
$72$	−2.06945e7	+	1.18930e7i	−0.770060	+	0.442549i
$73$	1.96194e7			0.690868			0.345434	−	0.938443i	$-0.387732\pi$
$73$	1.96194e7			0.690868			0.345434	+	0.938443i	$0.387732\pi$
$74$		−	1.96573e6i		−	0.0655538i
$75$	1.85083e7	−	3.19836e7i	0.584953	−	1.01084i
$76$	−3.61539e7			−1.08368
$77$		−	4.82889e6i		−	0.137368i
$78$	−1.47724e7	−	8.54847e6i	−0.399090	−	0.230946i
$79$	4.04857e7			1.03943			0.519713	−	0.854341i	$-0.326039\pi$
$79$	4.04857e7			1.03943			0.519713	+	0.854341i	$0.326039\pi$
$80$			1.72273e7i			0.420588i
$81$	−2.16719e7	+	3.71934e7i	−0.503450	+	0.864024i
$82$	2.46348e7			0.544871
$83$			4.13228e7i			0.870718i	0.900257	+	0.435359i	$0.143379\pi$
$83$			4.13228e7i			0.870718i	−0.900257	+	0.435359i	$0.856621\pi$
$84$	8.39823e6	−	1.45127e7i	0.168683	−	0.291495i
$85$	−3.44172e7			−0.659326
$86$		−	5.10101e7i		−	0.932528i
$87$	1.90930e7	+	1.10487e7i	0.333271	+	0.192857i
$88$	1.60594e7			0.267793
$89$			3.21055e7i			0.511704i	0.966716	+	0.255852i	$0.0823560\pi$
$89$			3.21055e7i			0.511704i	−0.966716	+	0.255852i	$0.917644\pi$
$90$	−2.45808e7	−	4.27720e7i	−0.374651	−	0.651913i
$91$	2.82095e7			0.411367
$92$			4.86644e7i			0.679297i
$93$	5.84498e7	−	1.01005e8i	0.781361	−	1.35025i
$94$	−2.48834e7			−0.318712
$95$		−	1.75810e8i		−	2.15849i
$96$	7.60157e7	+	4.39888e7i	0.894991	+	0.517914i
$97$	1.37061e8			1.54820			0.774100	−	0.633063i	$-0.218203\pi$
$97$	1.37061e8			1.54820			0.774100	+	0.633063i	$0.218203\pi$
$98$			3.73257e7i			0.404672i
$99$	2.51116e7	−	1.44315e7i	0.261417	−	0.150235i
$100$	−8.63320e7			−0.863320
$101$			5.54205e6i			0.0532580i	0.999645	+	0.0266290i	$0.00847728\pi$
$101$			5.54205e6i			0.0532580i	−0.999645	+	0.0266290i	$0.991523\pi$
$102$	−1.23978e7	+	2.14242e7i	−0.114536	+	0.197926i
$103$	−8.33499e7			−0.740553			−0.370276	−	0.928922i	$-0.620737\pi$
$103$	−8.33499e7			−0.740553			−0.370276	+	0.928922i	$0.620737\pi$
$104$			9.38161e7i			0.801944i
$105$	7.05727e7	+	4.08390e7i	0.580603	+	0.335984i
$106$	5.56193e6			0.0440557
$107$		−	1.30045e8i		−	0.992109i	−0.868292	−	0.496054i	$-0.834782\pi$
$107$		−	1.30045e8i		−	0.992109i	0.868292	−	0.496054i	$-0.165218\pi$
$108$	1.00569e8	+	300815.i	0.739211	+	0.00221108i
$109$	8.13552e7			0.576341			0.288170	−	0.957579i	$-0.406953\pi$
$109$	8.13552e7			0.576341			0.288170	+	0.957579i	$0.406953\pi$
$110$			3.31921e7i			0.226706i
$111$	−9.76039e6	+	1.68666e7i	−0.0642947	+	0.111106i
$112$	−2.04782e7			−0.130142
$113$		−	7.62161e7i		−	0.467447i	−0.972303	−	0.233724i	$-0.924909\pi$
$113$		−	7.62161e7i		−	0.467447i	0.972303	−	0.233724i	$-0.0750911\pi$
$114$	−1.09439e8	−	6.33302e7i	−0.647967	−	0.374966i
$115$	−2.36646e8			−1.35303
$116$		−	5.15370e7i		−	0.284634i
$117$	8.43061e7	+	1.46697e8i	0.449900	+	0.782850i
$118$	1.47917e8			0.762938
$119$		−	4.09119e7i		−	0.204015i
$120$	−1.35818e8	+	2.34703e8i	−0.654987	+	1.13186i
$121$	−1.94872e7			−0.0909091
$122$		−	9.54894e7i		−	0.431038i
$123$	−2.11375e8	−	1.22318e8i	−0.923491	−	0.534406i
$124$	−2.72640e8			−1.15320
$125$		−	6.03504e7i		−	0.247195i
$126$	5.08434e7	−	2.92194e7i	0.201721	−	0.115928i
$127$	3.70977e8			1.42604			0.713020	−	0.701144i	$-0.247327\pi$
$127$	3.70977e8			1.42604			0.713020	+	0.701144i	$0.247327\pi$
$128$		−	2.44344e8i		−	0.910254i
$129$	−2.53278e8	+	4.37683e8i	−0.914617	+	1.58052i
$130$	−1.93902e8			−0.678906
$131$			4.42637e7i			0.150301i	0.997172	+	0.0751505i	$0.0239437\pi$
$131$			4.42637e7i			0.150301i	−0.997172	+	0.0751505i	$0.976056\pi$
$132$	−5.85666e7	−	3.38914e7i	−0.192910	−	0.111633i
$133$	2.08986e8			0.667900
$134$			1.29818e8i			0.402638i
$135$	−1.46281e6	+	4.89048e8i	−0.00440405	+	1.47237i
$136$	1.36060e8			0.397719
$137$			5.28921e8i			1.50144i	0.660619	+	0.750721i	$0.270294\pi$
$137$			5.28921e8i			1.50144i	−0.660619	+	0.750721i	$0.729706\pi$
$138$	−8.52445e7	+	1.47308e8i	−0.235045	+	0.406173i
$139$	−5.99858e8			−1.60690			−0.803450	−	0.595372i	$-0.797005\pi$
$139$	−5.99858e8			−1.60690			−0.803450	+	0.595372i	$0.797005\pi$
$140$		−	1.90494e8i		−	0.495872i
$141$	2.13507e8	+	1.23553e8i	0.540177	+	0.312590i
$142$	3.48917e8			0.858160
$143$		−	1.13841e8i		−	0.272241i
$144$	−6.12004e7	−	1.06492e8i	−0.142333	−	0.247667i
$145$	2.50615e8			0.566938
$146$		−	1.60305e8i		−	0.352807i
$147$	1.85332e8	−	3.20266e8i	0.396900	−	0.685870i
$148$	4.55274e7			0.0948913
$149$		−	5.27609e8i		−	1.07045i	−0.844709	−	0.535226i	$-0.820226\pi$
$149$		−	5.27609e8i		−	1.07045i	0.844709	−	0.535226i	$-0.179774\pi$
$150$	−2.61330e8	−	1.51226e8i	−0.516207	−	0.298719i
$151$	−8.53669e8			−1.64203			−0.821016	−	0.570905i	$-0.806592\pi$
$151$	−8.53669e8			−1.64203			−0.821016	+	0.570905i	$0.806592\pi$
$152$			6.95024e8i			1.30204i
$153$	2.12754e8	−	1.22268e8i	0.388250	−	0.223125i
$154$	−3.94556e7			−0.0701498
$155$		−	1.32580e9i		−	2.29695i
$156$	1.97987e8	−	3.42136e8i	0.334302	−	0.577697i
$157$	3.17338e7			0.0522304			0.0261152	−	0.999659i	$-0.491686\pi$
$157$	3.17338e7			0.0522304			0.0261152	+	0.999659i	$0.491686\pi$
$158$		−	3.30798e8i		−	0.530805i
$159$	−4.77231e7	−	2.76164e7i	−0.0746690	−	0.0432095i
$160$	9.97784e8			1.52250
$161$		−	2.81302e8i		−	0.418668i
$162$	3.03898e8	+	1.77075e8i	0.441233	+	0.257098i
$163$	−8.59621e8			−1.21775			−0.608873	−	0.793268i	$-0.708378\pi$
$163$	−8.59621e8			−1.21775			−0.608873	+	0.793268i	$0.708378\pi$
$164$			5.70556e8i			0.788720i
$165$	1.64808e8	−	2.84799e8i	0.222352	−	0.384240i
$166$	3.37638e8			0.444651
$167$			9.95810e8i			1.28030i	0.768252	+	0.640148i	$0.221127\pi$
$167$			9.95810e8i			1.28030i	−0.768252	+	0.640148i	$0.778873\pi$
$168$	−2.78993e8	−	1.61448e8i	−0.350232	−	0.202672i
$169$	−1.50695e8			−0.184736
$170$			2.81214e8i			0.336699i
$171$	6.24571e8	+	1.08679e9i	0.730461	+	1.27104i
$172$	1.18142e9			1.34987
$173$			7.30357e8i			0.815363i	0.913124	+	0.407681i	$0.133663\pi$
$173$			7.30357e8i			0.815363i	−0.913124	+	0.407681i	$0.866337\pi$
$174$	9.02765e7	−	1.56004e8i	0.0984867	−	0.170192i
$175$	4.99039e8			0.532087
$176$			8.26404e7i			0.0861275i
$177$	−1.26917e9	−	7.34445e8i	−1.29309	−	0.748284i
$178$	2.62326e8			0.261313
$179$		−	1.42622e9i		−	1.38923i	−0.719383	−	0.694614i	$-0.755575\pi$
$179$		−	1.42622e9i		−	1.38923i	0.719383	−	0.694614i	$-0.244425\pi$
$180$	9.90623e8	−	5.69306e8i	0.943666	−	0.542320i
$181$	1.19424e9			1.11270			0.556350	−	0.830948i	$-0.312202\pi$
$181$	1.19424e9			1.11270			0.556350	+	0.830948i	$0.312202\pi$
$182$		−	2.30493e8i		−	0.210074i
$183$	−4.74130e8	+	8.19330e8i	−0.422759	+	0.730558i
$184$	9.35525e8			0.816177
$185$			2.21392e8i			0.189005i
$186$	−8.25289e8	−	4.77579e8i	−0.689532	−	0.399019i
$187$	−1.65102e8			−0.135016
$188$		−	5.76312e8i		−	0.461346i
$189$	−5.81334e8	−	1.73885e6i	−0.455595	−	0.00136274i
$190$	−1.43650e9			−1.10228
$191$			1.20776e9i			0.907499i	0.891129	+	0.453749i	$0.149914\pi$
$191$			1.20776e9i			0.907499i	−0.891129	+	0.453749i	$0.850086\pi$
$192$	1.64992e8	−	2.85118e8i	0.121411	−	0.209807i
$193$	−1.76867e7			−0.0127473			−0.00637363	−	0.999980i	$-0.502029\pi$
$193$	−1.76867e7			−0.0127473			−0.00637363	+	0.999980i	$0.502029\pi$
$194$		−	1.11989e9i		−	0.790622i
$195$	1.66374e9	+	9.62776e8i	1.15066	+	0.665866i
$196$	−8.64483e8			−0.585777
$197$			1.40718e9i			0.934296i	0.884179	+	0.467148i	$0.154719\pi$
$197$			1.40718e9i			0.934296i	−0.884179	+	0.467148i	$0.845281\pi$
$198$	−1.17916e8	−	2.05180e8i	−0.0767206	−	0.133498i
$199$	−2.40327e9			−1.53246			−0.766232	−	0.642564i	$-0.777871\pi$
$199$	−2.40327e9			−1.53246			−0.766232	+	0.642564i	$0.777871\pi$
$200$			1.65965e9i			1.03728i
$201$	6.44579e8	−	1.11388e9i	0.394905	−	0.682423i
$202$	4.52827e7			0.0271974
$203$			2.97908e8i			0.175427i
$204$	−4.96196e8	−	2.87139e8i	−0.286505	−	0.165795i
$205$	−2.77451e9			−1.57098
$206$			6.81031e8i			0.378179i
$207$	1.46285e9	−	8.40693e8i	0.796744	−	0.457884i
$208$	−4.82770e8			−0.257921
$209$		−	8.43373e8i		−	0.442012i
$210$	3.33686e8	−	5.76632e8i	0.171577	−	0.296498i
$211$	−2.14389e9			−1.08162			−0.540808	−	0.841146i	$-0.681881\pi$
$211$	−2.14389e9			−1.08162			−0.540808	+	0.841146i	$0.681881\pi$
$212$			1.28817e8i			0.0637721i
$213$	−2.99382e9	−	1.73246e9i	−1.45448	−	0.841678i
$214$	−1.06257e9			−0.506642
$215$			5.74503e9i			2.68868i
$216$	5.78287e6	−	1.93334e9i	0.00265661	−	0.888164i
$217$	1.57598e9			0.710744
$218$		−	6.64733e8i		−	0.294321i
$219$	−7.95959e8	+	1.37547e9i	−0.346030	+	0.597965i
$220$	−7.68747e8			−0.328165
$221$		−	9.64494e8i		−	0.404325i
$222$	1.37813e8	+	7.97496e7i	0.0567385	+	0.0328335i
$223$	1.55728e9			0.629719			0.314860	−	0.949138i	$-0.398043\pi$
$223$	1.55728e9			0.629719			0.314860	+	0.949138i	$0.398043\pi$
$224$			1.18607e9i			0.471106i
$225$	1.49141e9	+	2.59514e9i	0.581926	+	1.01258i
$226$	−6.22742e8			−0.238712
$227$		−	2.50798e9i		−	0.944542i	−0.881453	−	0.472271i	$-0.843434\pi$
$227$		−	2.50798e9i		−	0.944542i	0.881453	−	0.472271i	$-0.156566\pi$
$228$	1.46676e9	−	2.53467e9i	0.542776	−	0.937954i
$229$	3.79741e9			1.38085			0.690424	−	0.723405i	$-0.257424\pi$
$229$	3.79741e9			1.38085			0.690424	+	0.723405i	$0.257424\pi$
$230$			1.93357e9i			0.690955i
$231$	3.38542e8	+	1.95908e8i	0.118895	+	0.0688024i
$232$	−9.90749e8			−0.341989
$233$		−	4.66781e9i		−	1.58376i	−0.610677	−	0.791880i	$-0.709103\pi$
$233$		−	4.66781e9i		−	1.58376i	0.610677	−	0.791880i	$-0.290897\pi$
$234$	1.19863e9	−	6.88844e8i	0.399779	−	0.229751i
$235$	2.80250e9			0.918913
$236$			3.42583e9i			1.10438i
$237$	−1.64250e9	+	2.83836e9i	−0.520610	+	0.899650i
$238$	−3.34281e8			−0.104185
$239$			2.50261e9i			0.767011i	0.923539	+	0.383505i	$0.125283\pi$
$239$			2.50261e9i			0.767011i	−0.923539	+	0.383505i	$0.874717\pi$
$240$	−1.20776e9	−	6.98909e8i	−0.364030	−	0.210657i
$241$	3.78864e9			1.12309			0.561546	−	0.827445i	$-0.310207\pi$
$241$	3.78864e9			1.12309			0.561546	+	0.827445i	$0.310207\pi$
$242$			1.59225e8i			0.0464247i
$243$	−1.72832e9	−	3.02830e9i	−0.495676	−	0.868507i
$244$	2.21159e9			0.623943
$245$		−	4.20382e9i		−	1.16676i
$246$	−9.99433e8	+	1.72709e9i	−0.272906	+	0.471601i
$247$	4.92683e9			1.32367
$248$			5.24124e9i			1.38557i
$249$	−2.89705e9	−	1.67646e9i	−0.753630	−	0.436111i
$250$	−4.93108e8			−0.126236
$251$			1.50599e9i			0.379426i	0.981840	+	0.189713i	$0.0607558\pi$
$251$			1.50599e9i			0.379426i	−0.981840	+	0.189713i	$0.939244\pi$
$252$	6.76737e8	+	1.17756e9i	0.167810	+	0.291999i
$253$	−1.13521e9			−0.277072
$254$		−	3.03116e9i		−	0.728238i
$255$	1.39630e9	−	2.41291e9i	0.330232	−	0.570664i
$256$	−3.03759e9			−0.707244
$257$		−	3.29228e9i		−	0.754684i	−0.926074	−	0.377342i	$-0.876838\pi$
$257$		−	3.29228e9i		−	0.754684i	0.926074	−	0.377342i	$-0.123162\pi$
$258$	3.57619e9	+	2.06947e9i	0.807128	+	0.467069i
$259$	−2.63170e8			−0.0584840
$260$		−	4.49088e9i		−	0.982739i
$261$	−1.54920e9	+	8.90318e8i	−0.333846	+	0.191859i
$262$	3.61667e8			0.0767545
$263$		−	3.61862e9i		−	0.756345i	−0.925735	−	0.378173i	$-0.876553\pi$
$263$		−	3.61862e9i		−	0.756345i	0.925735	−	0.378173i	$-0.123447\pi$
$264$	−6.51528e8	+	1.12589e9i	−0.134127	+	0.231782i
$265$	−6.26415e8			−0.127022
$266$		−	1.70758e9i		−	0.341078i
$267$	−2.25084e9	−	1.30252e9i	−0.442893	−	0.256294i
$268$	−3.00665e9			−0.582832
$269$		−	9.83252e9i		−	1.87783i	−0.344152	−	0.938914i	$-0.611834\pi$
$269$		−	9.83252e9i		−	1.87783i	0.344152	−	0.938914i	$-0.388166\pi$
$270$	3.99589e9	+	1.19522e7i	0.751897	+	0.00224902i
$271$	−1.05247e9			−0.195135			−0.0975673	−	0.995229i	$-0.531106\pi$
$271$	−1.05247e9			−0.195135			−0.0975673	+	0.995229i	$0.531106\pi$
$272$			7.00156e8i			0.127914i
$273$	−1.14446e9	+	1.97770e9i	−0.206039	+	0.356049i
$274$	4.32168e9			0.766744
$275$		−	2.01389e9i		−	0.352132i
$276$	−3.41174e9	−	1.97431e9i	−0.587950	−	0.340235i
$277$	6.59739e9			1.12061			0.560303	−	0.828287i	$-0.310685\pi$
$277$	6.59739e9			1.12061			0.560303	+	0.828287i	$0.310685\pi$
$278$			4.90129e9i			0.820599i
$279$	4.70994e9	+	8.19556e9i	0.777318	+	1.35258i
$280$	−3.66207e9			−0.595791
$281$			4.93244e9i			0.791109i	0.918442	+	0.395555i	$0.129448\pi$
$281$			4.93244e9i			0.791109i	−0.918442	+	0.395555i	$0.870552\pi$
$282$	1.00952e9	−	1.74451e9i	0.159631	−	0.275853i
$283$	−1.22342e9			−0.190735			−0.0953675	−	0.995442i	$-0.530403\pi$
$283$	−1.22342e9			−0.190735			−0.0953675	+	0.995442i	$0.530403\pi$
$284$			8.08110e9i			1.24222i
$285$	1.23256e10	+	7.13260e9i	1.86823	+	1.08111i
$286$	−9.30162e8			−0.139026
$287$		−	3.29808e9i		−	0.486108i
$288$	−6.16790e9	+	3.54466e9i	−0.896536	+	0.515234i
$289$	5.57696e9			0.799478
$290$		−	2.04771e9i		−	0.289519i
$291$	−5.56056e9	+	9.60903e9i	−0.775437	+	1.34001i
$292$	3.71276e9			0.510700
$293$		−	1.13285e10i		−	1.53711i	−0.639786	−	0.768553i	$-0.720977\pi$
$293$		−	1.13285e10i		−	1.53711i	0.639786	−	0.768553i	$-0.279023\pi$
$294$	−2.61682e9	−	1.51430e9i	−0.350255	−	0.202685i
$295$	−1.66592e10			−2.19971
$296$		−	8.75221e8i		−	0.114012i
$297$	−7.01718e6	+	2.34600e9i	−0.000901856	+	0.301510i
$298$	−4.31096e9			−0.546650
$299$		−	6.63167e9i		−	0.829733i
$300$	3.50248e9	−	6.05254e9i	0.432405	−	0.747227i
$301$	−6.82916e9			−0.831957
$302$			6.97511e9i			0.838539i
$303$	−3.88540e8	−	2.24841e8i	−0.0460962	−	0.0266750i
$304$	−3.57654e9			−0.418763
$305$			1.07545e10i			1.24278i
$306$	−9.99023e8	−	1.73835e9i	−0.113944	−	0.198268i
$307$	−8.22300e9			−0.925714			−0.462857	−	0.886433i	$-0.653176\pi$
$307$	−8.22300e9			−0.925714			−0.462857	+	0.886433i	$0.653176\pi$
$308$		−	9.13814e8i		−	0.101544i
$309$	3.38150e9	−	5.84346e9i	0.370916	−	0.640968i
$310$	−1.08328e10			−1.17299
$311$			9.87907e9i			1.05603i	0.849236	+	0.528013i	$0.177063\pi$
$311$			9.87907e9i			1.05603i	−0.849236	+	0.528013i	$0.822937\pi$
$312$	−6.57723e9	−	3.80611e9i	−0.694104	−	0.401664i
$313$	3.01315e9			0.313937			0.156969	−	0.987604i	$-0.449828\pi$
$313$	3.01315e9			0.313937			0.156969	+	0.987604i	$0.449828\pi$
$314$		−	2.59289e8i		−	0.0266726i
$315$	−5.72626e9	+	3.29085e9i	−0.581606	+	0.334246i
$316$	7.66147e9			0.768358
$317$		−	5.50328e9i		−	0.544985i	−0.962158	−	0.272493i	$-0.912152\pi$
$317$		−	5.50328e9i		−	0.544985i	0.962158	−	0.272493i	$-0.0878480\pi$
$318$	−2.25647e8	+	3.89934e8i	−0.0220659	+	0.0381314i
$319$	1.20222e9			0.116097
$320$		−	3.74246e9i		−	0.356909i
$321$	9.11716e9	+	5.27592e9i	0.858696	+	0.496911i
$322$	−2.29845e9			−0.213802
$323$		−	7.14533e9i		−	0.656466i
$324$	−4.10116e9	+	7.03844e9i	−0.372157	+	0.638699i
$325$	1.17648e10			1.05451
$326$			7.02374e9i			0.621868i
$327$	−3.30057e9	+	5.70362e9i	−0.288668	+	0.498838i
$328$	1.09684e10			0.947648
$329$			3.33135e9i			0.284339i
$330$	−2.32702e9	−	1.34660e9i	−0.196220	−	0.113549i
$331$	−6.51916e9			−0.543099			−0.271550	−	0.962424i	$-0.587536\pi$
$331$	−6.51916e9			−0.543099			−0.271550	+	0.962424i	$0.587536\pi$
$332$			7.81989e9i			0.643648i
$333$	−7.86501e8	−	1.36856e9i	−0.0639621	−	0.111297i
$334$	8.13651e9			0.653811
$335$		−	1.46208e10i		−	1.16089i
$336$	8.30797e8	−	1.43568e9i	0.0651835	−	0.112642i
$337$	6.02461e9			0.467100			0.233550	−	0.972345i	$-0.424966\pi$
$337$	6.02461e9			0.467100			0.233550	+	0.972345i	$0.424966\pi$
$338$			1.23129e9i			0.0943395i
$339$	5.34333e9	+	3.09208e9i	0.404588	+	0.234127i
$340$	−6.51308e9			−0.487383
$341$		−	6.35995e9i		−	0.470366i
$342$	8.87987e9	−	5.10321e9i	0.649086	−	0.373026i
$343$	1.13032e10			0.816626
$344$		−	2.27117e10i		−	1.62187i
$345$	9.60071e9	−	1.65907e10i	0.677683	−	1.17108i
$346$	5.96756e9			0.416383
$347$			3.22351e9i			0.222336i	0.993802	+	0.111168i	$0.0354592\pi$
$347$			3.22351e9i			0.222336i	−0.993802	+	0.111168i	$0.964541\pi$
$348$	3.61314e9	+	2.09085e9i	0.246358	+	0.142563i
$349$	1.61884e10			1.09119			0.545596	−	0.838048i	$-0.316303\pi$
$349$	1.61884e10			1.09119			0.545596	+	0.838048i	$0.316303\pi$
$350$		−	4.07752e9i		−	0.271722i
$351$	−1.37049e10	−	4.09931e7i	−0.902916	−	0.00270074i
$352$	4.78644e9			0.311775
$353$			9.37483e9i			0.603761i	0.953346	+	0.301880i	$0.0976143\pi$
$353$			9.37483e9i			0.603761i	−0.953346	+	0.301880i	$0.902386\pi$
$354$	−6.00097e9	+	1.03701e10i	−0.382127	+	0.660343i
$355$	−3.92969e10			−2.47426
$356$			6.07560e9i			0.378259i
$357$	2.86824e9	+	1.65979e9i	0.176580	+	0.102184i
$358$	−1.16533e10			−0.709439
$359$			2.20261e9i			0.132605i	0.997800	+	0.0663025i	$0.0211202\pi$
$359$			2.20261e9i			0.132605i	−0.997800	+	0.0663025i	$0.978880\pi$
$360$	−1.09443e10	−	1.90438e10i	−0.651598	−	1.13382i
$361$	1.95162e10			1.14912
$362$		−	9.75784e9i		−	0.568224i
$363$	7.90593e8	−	1.36620e9i	0.0455330	−	0.0786842i
$364$	5.33834e9			0.304089
$365$			1.80545e10i			1.01722i
$366$	6.69454e9	+	3.87400e9i	0.373075	+	0.215891i
$367$	1.46910e10			0.809820			0.404910	−	0.914357i	$-0.367303\pi$
$367$	1.46910e10			0.809820			0.404910	+	0.914357i	$0.367303\pi$
$368$			4.81414e9i			0.262499i
$369$	1.71509e10	−	9.85654e9i	0.925085	−	0.531642i
$370$	1.80894e9			0.0965198
$371$		−	7.44623e8i		−	0.0393044i
$372$	1.10610e10	−	1.91141e10i	0.577593	−	0.998121i
$373$	−2.60905e10			−1.34787			−0.673934	−	0.738791i	$-0.735397\pi$
$373$	−2.60905e10			−1.34787			−0.673934	+	0.738791i	$0.735397\pi$
$374$			1.34900e9i			0.0689488i
$375$	4.23103e9	+	2.44841e9i	0.213954	+	0.123811i
$376$	−1.10790e10			−0.554308
$377$			7.02314e9i			0.347669i
$378$	−1.42077e7	+	4.74994e9i	−0.000695914	+	0.232659i
$379$	3.91882e9			0.189932			0.0949661	−	0.995481i	$-0.469726\pi$
$379$	3.91882e9			0.189932			0.0949661	+	0.995481i	$0.469726\pi$
$380$		−	3.32701e10i		−	1.59558i
$381$	−1.50505e10	+	2.60083e10i	−0.714251	+	1.23427i
$382$	9.86828e9			0.463434
$383$			1.10943e10i			0.515588i	0.966200	+	0.257794i	$0.0829956\pi$
$383$			1.10943e10i			0.515588i	−0.966200	+	0.257794i	$0.917004\pi$
$384$	1.71304e10	+	9.91303e9i	0.787848	+	0.455913i
$385$	4.44371e9			0.202257
$386$			1.44513e8i			0.00650967i
$387$	−2.04094e10	−	3.55135e10i	−0.909886	−	1.58325i
$388$	2.59373e10			1.14445
$389$			2.11439e10i			0.923393i	0.887038	+	0.461696i	$0.152759\pi$
$389$			2.11439e10i			0.923393i	−0.887038	+	0.461696i	$0.847241\pi$
$390$	7.86660e9	−	1.35940e10i	0.340039	−	0.587611i
$391$	−9.61785e9			−0.411501
$392$			1.66188e10i			0.703812i
$393$	−3.10322e9	−	1.79577e9i	−0.130090	−	0.0752803i
$394$	1.14977e10			0.477119
$395$			3.72563e10i			1.53042i
$396$	4.75209e9	−	2.73100e9i	0.193243	−	0.111056i
$397$	−2.22140e10			−0.894263			−0.447131	−	0.894468i	$-0.647554\pi$
$397$	−2.22140e10			−0.894263			−0.447131	+	0.894468i	$0.647554\pi$
$398$			1.96365e10i			0.782586i
$399$	−8.47856e9	+	1.46515e10i	−0.334527	+	0.578085i
$400$	−8.54042e9			−0.333610
$401$		−	1.07941e10i		−	0.417455i	−0.977974	−	0.208727i	$-0.933068\pi$
$401$		−	1.07941e10i		−	0.417455i	0.977974	−	0.208727i	$-0.0669321\pi$
$402$	−9.10122e9	−	5.26670e9i	−0.348494	−	0.201667i
$403$	3.71537e10			1.40858
$404$			1.04877e9i			0.0393691i
$405$	−3.42267e10	−	1.99432e10i	−1.27217	−	0.741267i
$406$	2.43413e9			0.0895858
$407$			1.06203e9i			0.0387043i
$408$	−5.51996e9	+	9.53888e9i	−0.199203	+	0.344236i
$409$	−7.15964e9			−0.255857			−0.127929	−	0.991783i	$-0.540833\pi$
$409$	−7.15964e9			−0.255857			−0.127929	+	0.991783i	$0.540833\pi$
$410$			2.26698e10i			0.802255i
$411$	−3.70814e10	−	2.14583e10i	−1.29954	−	0.752017i
$412$	−1.57730e10			−0.547427
$413$		−	1.98029e10i		−	0.680657i
$414$	−6.86909e9	−	1.19526e10i	−0.233829	−	0.406875i
$415$	−3.80267e10			−1.28202
$416$			2.79615e10i			0.933657i
$417$	2.43362e10	−	4.20546e10i	0.804837	−	1.39082i
$418$	−6.89098e9			−0.225723
$419$			3.54994e10i			1.15177i	0.817531	+	0.575884i	$0.195342\pi$
$419$			3.54994e10i			1.15177i	−0.817531	+	0.575884i	$0.804658\pi$
$420$	1.33551e10	+	7.72834e9i	0.429190	+	0.248364i
$421$	−1.40507e10			−0.447269			−0.223635	−	0.974673i	$-0.571792\pi$
$421$	−1.40507e10			−0.447269			−0.223635	+	0.974673i	$0.571792\pi$
$422$			1.75172e10i			0.552351i
$423$	−1.73240e10	+	9.95598e9i	−0.541110	+	0.310973i
$424$	2.47639e9			0.0766223
$425$		−	1.70623e10i		−	0.522978i
$426$	−1.41555e10	+	2.44617e10i	−0.429821	+	0.742760i
$427$	−1.27840e10			−0.384552
$428$		−	2.46096e10i		−	0.733381i
$429$	7.98109e9	+	4.61850e9i	0.235631	+	0.136355i
$430$	4.69412e10			1.37303
$431$		−	6.81421e8i		−	0.0197473i	−0.999951	−	0.00987363i	$-0.996857\pi$
$431$		−	6.81421e8i		−	0.0197473i	0.999951	−	0.00987363i	$-0.00314292\pi$
$432$	9.94881e9	+	2.97582e7i	0.285651	+	0.000854420i
$433$	2.35362e10			0.669551			0.334776	−	0.942298i	$-0.391339\pi$
$433$	2.35362e10			0.669551			0.334776	+	0.942298i	$0.391339\pi$
$434$		−	1.28770e10i		−	0.362957i
$435$	−1.01674e10	+	1.75700e10i	−0.283958	+	0.490699i
$436$	1.53956e10			0.426039
$437$		−	4.91299e10i		−	1.34716i
$438$	1.12386e10	+	6.50358e9i	0.305364	+	0.176708i
$439$	−6.14507e10			−1.65451			−0.827254	−	0.561828i	$-0.810098\pi$
$439$	−6.14507e10			−1.65451			−0.827254	+	0.561828i	$0.810098\pi$
$440$			1.47784e10i			0.394291i
$441$	1.49342e10	+	2.59864e10i	0.394846	+	0.687054i
$442$	−7.88064e9			−0.206477
$443$		−	2.88521e9i		−	0.0749140i	−0.999298	−	0.0374570i	$-0.988074\pi$
$443$		−	2.88521e9i		−	0.0749140i	0.999298	−	0.0374570i	$-0.0119257\pi$
$444$	−1.84704e9	+	3.19182e9i	−0.0475276	+	0.0821309i
$445$	−2.95445e10			−0.753420
$446$		−	1.27241e10i		−	0.321580i
$447$	3.69894e10	+	2.14051e10i	0.926505	+	0.536150i
$448$	4.44869e9			0.110438
$449$			1.77041e9i			0.0435600i	0.999763	+	0.0217800i	$0.00693334\pi$
$449$			1.77041e9i			0.0435600i	−0.999763	+	0.0217800i	$0.993067\pi$
$450$	2.12042e10	−	1.21860e10i	0.517098	−	0.297173i
$451$	−1.33095e10			−0.321704
$452$		−	1.44230e10i		−	0.345544i
$453$	3.46333e10	−	5.98487e10i	0.822433	−	1.42122i
$454$	−2.04921e10			−0.482351
$455$			2.59594e10i			0.605687i
$456$	−4.87265e10	−	2.81971e10i	−1.12695	−	0.652146i
$457$	7.00044e9			0.160495			0.0802473	−	0.996775i	$-0.474429\pi$
$457$	7.00044e9			0.160495			0.0802473	+	0.996775i	$0.474429\pi$
$458$		−	3.10277e10i		−	0.705160i
$459$	−5.94519e7	+	1.98761e10i	−0.00133941	+	0.447795i
$460$	−4.47826e10			−1.00018
$461$		−	6.17069e10i		−	1.36625i	−0.730301	−	0.683125i	$-0.760620\pi$
$461$		−	6.17069e10i		−	1.36625i	0.730301	−	0.683125i	$-0.239380\pi$
$462$	1.60071e9	−	2.76614e9i	0.0351354	−	0.0607165i
$463$	4.27029e10			0.929253			0.464626	−	0.885507i	$-0.346189\pi$
$463$	4.27029e10			0.929253			0.464626	+	0.885507i	$0.346189\pi$
$464$		−	5.09831e9i		−	0.109990i
$465$	9.29486e10	+	5.37876e10i	1.98807	+	1.15046i
$466$	−3.81395e10			−0.808781
$467$			3.33302e10i			0.700762i	0.936607	+	0.350381i	$0.113948\pi$
$467$			3.33302e10i			0.700762i	−0.936607	+	0.350381i	$0.886052\pi$
$468$	1.59540e10	+	2.77608e10i	0.332572	+	0.578694i
$469$	1.73798e10			0.359215
$470$		−	2.28985e10i		−	0.469263i
$471$	−1.28744e9	+	2.22478e9i	−0.0261603	+	0.0452068i
$472$	6.58582e10			1.32691
$473$			2.75593e10i			0.550584i
$474$	2.31915e10	+	1.34205e10i	0.459426	+	0.265861i
$475$	8.71579e10			1.71211
$476$		−	7.74213e9i		−	0.150811i
$477$	3.87225e9	−	2.22536e9i	0.0747979	−	0.0429860i
$478$	2.04482e10			0.391691
$479$		−	4.99987e10i		−	0.949766i	−0.880049	−	0.474883i	$-0.842490\pi$
$479$		−	4.99987e10i		−	0.949766i	0.880049	−	0.474883i	$-0.157510\pi$
$480$	−4.04800e10	+	6.99523e10i	−0.762563	+	1.31776i
$481$	−6.20419e9			−0.115906
$482$		−	3.09560e10i		−	0.573531i
$483$	1.97215e10	+	1.14124e10i	0.362368	+	0.209696i
$484$	−3.68773e9			−0.0672013
$485$			1.26128e11i			2.27953i
$486$	−2.47435e10	+	1.41216e10i	−0.443522	+	0.253128i
$487$	3.86527e10			0.687169			0.343585	−	0.939122i	$-0.388359\pi$
$487$	3.86527e10			0.687169			0.343585	+	0.939122i	$0.388359\pi$
$488$		−	4.25156e10i		−	0.749668i
$489$	3.48748e10	−	6.02660e10i	0.609924	−	1.05399i
$490$	−3.43484e10			−0.595829
$491$			1.60287e10i			0.275785i	0.990447	+	0.137893i	$0.0440329\pi$
$491$			1.60287e10i			0.275785i	−0.990447	+	0.137893i	$0.955967\pi$
$492$	−4.00003e10	−	2.31474e10i	−0.682658	−	0.395041i
$493$	1.01856e10			0.172424
$494$		−	4.02559e10i		−	0.675961i
$495$	1.32803e10	+	2.31085e10i	0.221202	+	0.384903i
$496$	−2.69710e10			−0.445626
$497$		−	4.67125e10i		−	0.765610i
$498$	−1.36980e10	+	2.36710e10i	−0.222709	+	0.384857i
$499$	5.56768e10			0.897991			0.448996	−	0.893534i	$-0.351782\pi$
$499$	5.56768e10			0.897991			0.448996	+	0.893534i	$0.351782\pi$
$500$		−	1.14206e10i		−	0.182730i
$501$	−6.98139e10	−	4.03999e10i	−1.10813	−	0.641253i
$502$	1.23051e10			0.193762
$503$		−	7.45783e10i		−	1.16504i	−0.812817	−	0.582519i	$-0.802067\pi$
$503$		−	7.45783e10i		−	1.16504i	0.812817	−	0.582519i	$-0.197933\pi$
$504$	2.26374e10	−	1.30096e10i	0.350837	−	0.201624i
$505$	−5.09999e9			−0.0784158
$506$			9.27549e9i			0.141493i
$507$	6.11368e9	−	1.05649e10i	0.0925275	−	0.159894i
$508$	7.02032e10			1.05415
$509$			1.43747e10i			0.214154i	0.994251	+	0.107077i	$0.0341492\pi$
$509$			1.43747e10i			0.214154i	−0.994251	+	0.107077i	$0.965851\pi$
$510$	−1.97153e10	−	1.14088e10i	−0.291422	−	0.168640i
$511$	−2.14615e10			−0.314757
$512$		−	3.77328e10i		−	0.549084i
$513$	−1.01531e11	−	3.03692e8i	−1.46598	−	0.00438494i
$514$	−2.69004e10			−0.385395
$515$		−	7.67014e10i		−	1.09037i
$516$	−4.79301e10	+	8.28266e10i	−0.676098	+	1.16834i
$517$	1.34438e10			0.188174
$518$			2.15029e9i			0.0298661i
$519$	−5.12036e10	−	2.96305e10i	−0.705718	−	0.408385i
$520$	−8.63328e10			−1.18076
$521$			1.16395e11i			1.57973i	0.613283	+	0.789863i	$0.289848\pi$
$521$			1.16395e11i			1.57973i	−0.613283	+	0.789863i	$0.710152\pi$
$522$	7.27457e9	+	1.26581e10i	0.0979772	+	0.170486i
$523$	−1.29256e11			−1.72760			−0.863802	−	0.503831i	$-0.831923\pi$
$523$	−1.29256e11			−1.72760			−0.863802	+	0.503831i	$0.831923\pi$
$524$			8.37640e9i			0.111105i
$525$	−2.02460e10	+	3.49864e10i	−0.266503	+	0.460535i
$526$	−2.95668e10			−0.386244
$527$		−	5.38836e10i		−	0.698576i
$528$	−5.79372e9	−	3.35271e9i	−0.0745456	−	0.0431381i
$529$	1.21806e10			0.155541
$530$			5.11828e9i			0.0648665i
$531$	1.02980e11	−	5.91823e10i	1.29532	−	0.744413i
$532$	3.95484e10			0.493721
$533$		−	7.77518e10i		−	0.963388i
$534$	−1.06425e10	+	1.83910e10i	−0.130882	+	0.226173i
$535$	1.19672e11			1.46076
$536$			5.77999e10i			0.700274i
$537$	9.99887e10	+	5.78615e10i	1.20241	+	0.695813i
$538$	−8.03390e10			−0.958953
$539$		−	2.01660e10i		−	0.238927i
$540$	−2.76820e8	+	9.25469e10i	−0.00325553	+	1.08840i
$541$	−1.13727e11			−1.32762			−0.663812	−	0.747900i	$-0.731062\pi$
$541$	−1.13727e11			−1.32762			−0.663812	+	0.747900i	$0.731062\pi$
$542$			8.59950e9i			0.0996497i
$543$	−4.84503e10	+	8.37254e10i	−0.557310	+	0.963071i
$544$	4.05523e10			0.463041
$545$			7.48659e10i			0.848590i
$546$	1.61593e10	+	9.35107e9i	0.181824	+	0.105218i
$547$	1.48219e11			1.65559			0.827797	−	0.561027i	$-0.189594\pi$
$547$	1.48219e11			1.65559			0.827797	+	0.561027i	$0.189594\pi$
$548$			1.00092e11i			1.10989i
$549$	−3.82059e10	−	6.64803e10i	−0.420572	−	0.731819i
$550$	−1.64550e10			−0.179824
$551$			5.20300e10i			0.564479i
$552$	−3.79542e10	+	6.55875e10i	−0.408793	+	0.706422i
$553$	−4.42868e10			−0.473559
$554$		−	5.39056e10i		−	0.572262i
$555$	−1.55213e10	−	8.98184e9i	−0.163589	−	0.0946659i
$556$	−1.13516e11			−1.18784
$557$			1.29659e11i			1.34704i	0.739169	+	0.673520i	$0.235218\pi$
$557$			1.29659e11i			1.34704i	−0.739169	+	0.673520i	$0.764782\pi$
$558$	6.69638e10	−	3.84838e10i	0.690722	−	0.396954i
$559$	−1.60997e11			−1.64881
$560$		−	1.88447e10i		−	0.191618i
$561$	6.69816e9	−	1.15749e10i	0.0676245	−	0.116860i
$562$	4.03017e10			0.403997
$563$			1.50170e11i			1.49468i	0.664440	+	0.747342i	$0.268670\pi$
$563$			1.50170e11i			1.49468i	−0.664440	+	0.747342i	$0.731330\pi$
$564$	4.04039e10	+	2.33809e10i	0.399307	+	0.231071i
$565$	7.01367e10			0.688258
$566$			9.99627e9i			0.0974030i
$567$	2.37066e10	−	4.06854e10i	0.229370	−	0.393647i
$568$	1.55351e11			1.49252
$569$		−	1.52337e11i		−	1.45330i	−0.687007	−	0.726651i	$-0.741076\pi$
$569$		−	1.52337e11i		−	1.45330i	0.687007	−	0.726651i	$-0.258924\pi$
$570$	5.82787e10	−	1.00710e11i	0.552090	−	0.954050i
$571$	−9.62434e10			−0.905371			−0.452685	−	0.891670i	$-0.649534\pi$
$571$	−9.62434e10			−0.905371			−0.452685	+	0.891670i	$0.649534\pi$
$572$		−	2.15431e10i		−	0.201244i
$573$	−8.46730e10	−	4.89986e10i	−0.785464	−	0.454533i
$574$	−2.69477e10			−0.248242
$575$		−	1.17317e11i		−	1.07322i
$576$	1.32952e10	+	2.31344e10i	0.120783	+	0.210169i
$577$	2.73865e9			0.0247078			0.0123539	−	0.999924i	$-0.496068\pi$
$577$	2.73865e9			0.0247078			0.0123539	+	0.999924i	$0.496068\pi$
$578$		−	4.55679e10i		−	0.408271i
$579$	7.17547e8	−	1.23997e9i	0.00638464	−	0.0110331i
$580$	4.74261e10			0.419088
$581$		−	4.52026e10i		−	0.396697i
$582$	7.85130e10	+	4.54339e10i	0.684305	+	0.395994i
$583$	−3.00496e9			−0.0260114
$584$		−	7.13742e10i		−	0.613607i
$585$	−1.34996e11	+	7.75814e10i	−1.15265	+	0.662421i
$586$	−9.25627e10			−0.784956
$587$		−	1.39589e11i		−	1.17571i	−0.808966	−	0.587855i	$-0.799973\pi$
$587$		−	1.39589e11i		−	1.17571i	0.808966	−	0.587855i	$-0.200027\pi$
$588$	3.50720e10	−	6.06069e10i	0.293394	−	0.507005i
$589$	2.75248e11			2.28698
$590$			1.36118e11i			1.12333i
$591$	−9.86540e10	−	5.70892e10i	−0.808658	−	0.467955i
$592$	4.50382e9			0.0366686
$593$			1.31508e11i			1.06349i	0.846905	+	0.531744i	$0.178463\pi$
$593$			1.31508e11i			1.06349i	−0.846905	+	0.531744i	$0.821537\pi$
$594$	1.91685e10	+	5.73356e7i	0.153973	+	0.000460552i
$595$	3.76486e10			0.300387
$596$		−	9.98442e10i		−	0.791294i
$597$	9.75005e10	−	1.68488e11i	0.767555	−	1.32639i
$598$	−5.41857e10			−0.423721
$599$			1.21641e10i			0.0944871i	0.998883	+	0.0472436i	$0.0150437\pi$
$599$			1.21641e10i			0.0944871i	−0.998883	+	0.0472436i	$0.984956\pi$
$600$	−1.16354e11	−	6.73318e10i	−0.897794	−	0.519536i
$601$	−1.15120e11			−0.882375			−0.441188	−	0.897415i	$-0.645443\pi$
$601$	−1.15120e11			−0.882375			−0.441188	+	0.897415i	$0.645443\pi$
$602$			5.57993e10i			0.424857i
$603$	5.19408e10	+	9.03799e10i	0.392862	+	0.683601i
$604$	−1.61547e11			−1.21381
$605$		−	1.79328e10i		−	0.133852i
$606$	−1.83712e9	+	3.17466e9i	−0.0136222	+	0.0235400i
$607$	1.47186e11			1.08421			0.542103	−	0.840312i	$-0.317628\pi$
$607$	1.47186e11			1.08421			0.542103	+	0.840312i	$0.317628\pi$
$608$			2.07149e11i			1.51589i
$609$	−2.08856e10	−	1.20861e10i	−0.151837	−	0.0878651i
$610$	8.78727e10			0.634650
$611$			7.85362e10i			0.563515i
$612$	4.02612e10	−	2.31379e10i	0.287000	−	0.164937i
$613$	2.53485e10			0.179519			0.0897595	−	0.995963i	$-0.471390\pi$
$613$	2.53485e10			0.179519			0.0897595	+	0.995963i	$0.471390\pi$
$614$			6.71880e10i			0.472736i
$615$	1.12562e11	−	1.94514e11i	0.786846	−	1.35973i
$616$	−1.75672e10			−0.122005
$617$			7.33854e10i			0.506371i	0.967418	+	0.253186i	$0.0814783\pi$
$617$			7.33854e10i			0.506371i	−0.967418	+	0.253186i	$0.918522\pi$
$618$	−4.77455e10	−	2.76294e10i	−0.327324	−	0.189416i
$619$	7.06830e10			0.481451			0.240726	−	0.970593i	$-0.422615\pi$
$619$	7.06830e10			0.481451			0.240726	+	0.970593i	$0.422615\pi$
$620$		−	2.50893e11i		−	1.69794i
$621$	−4.08779e8	+	1.36664e11i	−0.00274867	+	0.918940i
$622$	8.07194e10			0.539282
$623$		−	3.51198e10i		−	0.233131i
$624$	1.95859e10	−	3.38459e10i	0.129183	−	0.223238i
$625$	−1.22669e11			−0.803924
$626$		−	2.46197e10i		−	0.160319i
$627$	5.91269e10	+	3.42156e10i	0.382573	+	0.221388i
$628$	6.00527e9			0.0386095
$629$			8.99788e9i			0.0574827i
$630$	2.68887e10	+	4.67878e10i	0.170690	+	0.297010i
$631$	1.98254e11			1.25056			0.625281	−	0.780400i	$-0.284984\pi$
$631$	1.98254e11			1.25056			0.625281	+	0.780400i	$0.284984\pi$
$632$		−	1.47284e11i		−	0.923184i
$633$	8.69775e10	−	1.50303e11i	0.541742	−	0.936167i
$634$	−4.49659e10			−0.278308
$635$			3.41385e11i			2.09967i
$636$	−9.03108e9	−	5.22611e9i	−0.0551964	−	0.0319411i
$637$	1.17806e11			0.715502
$638$		−	9.82302e9i		−	0.0592874i
$639$	2.42918e11	−	1.39604e11i	1.45699	−	0.837323i
$640$	2.24854e11			1.34023
$641$			5.71415e10i			0.338469i	0.985576	+	0.169235i	$0.0541296\pi$
$641$			5.71415e10i			0.338469i	−0.985576	+	0.169235i	$0.945870\pi$
$642$	4.31082e10	−	7.44940e10i	0.253758	−	0.438512i
$643$	−1.99569e11			−1.16748			−0.583740	−	0.811941i	$-0.698411\pi$
$643$	−1.99569e11			−1.16748			−0.583740	+	0.811941i	$0.698411\pi$
$644$		−	5.32334e10i		−	0.309486i
$645$	−4.02771e11	−	2.33076e11i	−2.32712	−	1.34666i
$646$	−5.83827e10			−0.335239
$647$		−	6.68944e10i		−	0.381745i	−0.981615	−	0.190872i	$-0.938868\pi$
$647$		−	6.68944e10i		−	0.381745i	0.981615	−	0.190872i	$-0.0611316\pi$
$648$	1.35307e11	+	7.88408e10i	0.767398	+	0.447148i
$649$	−7.99153e10			−0.450454
$650$		−	9.61271e10i		−	0.538508i
$651$	−6.39376e10	+	1.10489e11i	−0.355985	+	0.615168i
$652$	−1.62674e11			−0.900175
$653$			2.66264e11i			1.46440i	0.681089	+	0.732201i	$0.261507\pi$
$653$			2.66264e11i			1.46440i	−0.681089	+	0.732201i	$0.738493\pi$
$654$	4.66028e10	+	2.69682e10i	0.254743	+	0.147415i
$655$	−4.07329e10			−0.221300
$656$			5.64424e10i			0.304783i
$657$	−6.41391e10	−	1.11606e11i	−0.344240	−	0.598997i
$658$	2.72196e10			0.145204
$659$			1.57740e11i			0.836374i	0.908361	+	0.418187i	$0.137334\pi$
$659$			1.57740e11i			0.836374i	−0.908361	+	0.418187i	$0.862666\pi$
$660$	3.11880e10	−	5.38950e10i	0.164366	−	0.284036i
$661$	−2.32168e11			−1.21618			−0.608088	−	0.793870i	$-0.708063\pi$
$661$	−2.32168e11			−1.21618			−0.608088	+	0.793870i	$0.708063\pi$
$662$			5.32664e10i			0.277346i
$663$	6.76184e10	+	3.91295e10i	0.349954	+	0.202512i
$664$	1.50330e11			0.773344
$665$			1.92317e11i			0.983400i
$666$	−1.11821e10	+	6.42630e9i	−0.0568365	+	0.0326636i
$667$	7.00341e10			0.353839
$668$			1.88446e11i			0.946413i
$669$	−6.31787e10	+	1.09177e11i	−0.315403	+	0.545039i
$670$	−1.19463e11			−0.592834
$671$			5.15903e10i			0.254494i
$672$	−8.31527e10	−	4.81189e10i	−0.407755	−	0.235960i
$673$	8.20276e10			0.399853			0.199926	−	0.979811i	$-0.435930\pi$
$673$	8.20276e10			0.399853			0.199926	+	0.979811i	$0.435930\pi$
$674$		−	4.92256e10i		−	0.238535i
$675$	−2.42446e11	−	7.25187e8i	−1.16788	−	0.00349329i
$676$	−2.85173e10			−0.136560
$677$			2.60571e10i			0.124043i	0.998075	+	0.0620214i	$0.0197547\pi$
$677$			2.60571e10i			0.124043i	−0.998075	+	0.0620214i	$0.980245\pi$
$678$	2.52646e10	−	4.36590e10i	0.119562	−	0.206612i
$679$	−1.49930e11			−0.705356
$680$			1.25208e11i			0.585592i
$681$	1.75829e11	+	1.01749e11i	0.817526	+	0.473087i
$682$	−5.19655e10			−0.240203
$683$		−	3.79773e11i		−	1.74519i	−0.488448	−	0.872593i	$-0.662437\pi$
$683$		−	3.79773e11i		−	1.74519i	0.488448	−	0.872593i	$-0.337563\pi$
$684$	1.18193e11	+	2.05662e11i	0.539968	+	0.939573i
$685$	−4.86732e11			−2.21069
$686$		−	9.23552e10i		−	0.417028i
$687$	−1.54061e11	+	2.66228e11i	−0.691616	+	1.19516i
$688$	1.16872e11			0.521625
$689$		−	1.75544e10i		−	0.0778950i
$690$	−1.35558e11	−	7.84450e10i	−0.598040	−	0.346074i
$691$	−1.74075e11			−0.763527			−0.381764	−	0.924260i	$-0.624683\pi$
$691$	−1.74075e11			−0.763527			−0.381764	+	0.924260i	$0.624683\pi$
$692$			1.38212e11i			0.602728i
$693$	−2.74693e10	+	1.57864e10i	−0.119101	+	0.0684465i
$694$	2.63385e10			0.113541
$695$		−	5.52010e11i		−	2.36596i
$696$	4.01946e10	−	6.94591e10i	0.171290	−	0.296000i
$697$	−1.12763e11			−0.477786
$698$		−	1.32271e11i		−	0.557241i
$699$	3.27249e11	+	1.89373e11i	1.37079	+	0.793247i
$700$	9.44376e10			0.393326
$701$			8.01503e10i			0.331920i	0.986133	+	0.165960i	$0.0530722\pi$
$701$			8.01503e10i			0.331920i	−0.986133	+	0.165960i	$0.946928\pi$
$702$	−3.34944e8	+	1.11979e11i	−0.00137919	+	0.461093i
$703$	−4.59630e10			−0.188186
$704$		−	1.79528e10i		−	0.0730874i
$705$	−1.13697e11	+	1.96477e11i	−0.460250	+	0.795344i
$706$	7.65994e10			0.308323
$707$		−	6.06239e9i		−	0.0242642i
$708$	−2.40177e11	−	1.38986e11i	−0.955868	−	0.553142i
$709$	1.09642e11			0.433903			0.216951	−	0.976182i	$-0.430389\pi$
$709$	1.09642e11			0.433903			0.216951	+	0.976182i	$0.430389\pi$
$710$			3.21085e11i			1.26353i
$711$	−1.32354e11	−	2.30304e11i	−0.517917	−	0.901203i
$712$	1.16798e11			0.454479
$713$		−	3.70493e11i		−	1.43358i
$714$	1.35618e10	−	2.34357e10i	0.0521823	−	0.0901746i
$715$	1.04760e11			0.400840
$716$		−	2.69896e11i		−	1.02694i
$717$	−1.75452e11	−	1.01531e11i	−0.663868	−	0.384167i
$718$	1.79970e10			0.0677176
$719$			8.42211e10i			0.315141i	0.987508	+	0.157571i	$0.0503662\pi$
$719$			8.42211e10i			0.315141i	−0.987508	+	0.157571i	$0.949634\pi$
$720$	9.79977e10	−	5.63188e10i	0.364658	−	0.209567i
$721$	9.11755e10			0.337394
$722$		−	1.59462e11i		−	0.586825i
$723$	−1.53705e11	+	2.65613e11i	−0.562516	+	0.972066i
$724$	2.25997e11			0.822523
$725$			1.24243e11i			0.449695i
$726$	−1.11629e10	−	6.45973e9i	−0.0401818	−	0.0232524i
$727$	4.46692e10			0.159908			0.0799540	−	0.996799i	$-0.474523\pi$
$727$	4.46692e10			0.159908			0.0799540	+	0.996799i	$0.474523\pi$
$728$		−	1.02624e11i		−	0.365363i
$729$	2.82424e11	+	1.68955e9i	0.999982	+	0.00598221i
$730$	1.47519e11			0.519464
$731$			2.33492e11i			0.817715i
$732$	−8.97239e10	+	1.55049e11i	−0.312510	+	0.540039i
$733$	4.31283e11			1.49399			0.746993	−	0.664832i	$-0.231497\pi$
$733$	4.31283e11			1.49399			0.746993	+	0.664832i	$0.231497\pi$
$734$		−	1.20037e11i		−	0.413552i
$735$	2.94720e11	+	1.70549e11i	1.00986	+	0.584385i
$736$	2.78830e11			0.950227
$737$		−	7.01369e10i		−	0.237726i
$738$	−8.05353e10	−	1.40136e11i	−0.271494	−	0.472415i
$739$	−4.05825e11			−1.36069			−0.680347	−	0.732890i	$-0.738171\pi$
$739$	−4.05825e11			−1.36069			−0.680347	+	0.732890i	$0.738171\pi$
$740$			4.18959e10i			0.139716i
$741$	−1.99881e11	+	3.45408e11i	−0.662978	+	1.14567i
$742$	−6.08413e9			−0.0200716
$743$			3.33131e11i			1.09310i	0.837427	+	0.546549i	$0.184059\pi$
$743$			3.33131e11i			1.09310i	−0.837427	+	0.546549i	$0.815941\pi$
$744$	−3.67451e11	−	2.12637e11i	−1.19924	−	0.693979i
$745$	4.85524e11			1.57611
$746$			2.13179e11i			0.688318i
$747$	2.35066e11	−	1.35091e11i	0.754931	−	0.433855i
$748$	−3.12437e10			−0.0998058
$749$			1.42255e11i			0.452002i
$750$	2.00054e10	−	3.45706e10i	0.0632268	−	0.109260i
$751$	−1.22019e11			−0.383592			−0.191796	−	0.981435i	$-0.561431\pi$
$751$	−1.22019e11			−0.383592			−0.191796	+	0.981435i	$0.561431\pi$
$752$		−	5.70119e10i		−	0.178276i
$753$	−1.05581e11	−	6.10979e10i	−0.328404	−	0.190041i
$754$	5.73843e10			0.177545
$755$		−	7.85576e11i		−	2.41769i
$756$	−1.10011e11	−	3.29057e8i	−0.336782	−	0.00100736i
$757$	2.45108e11			0.746406			0.373203	−	0.927750i	$-0.378260\pi$
$757$	2.45108e11			0.746406			0.373203	+	0.927750i	$0.378260\pi$
$758$		−	3.20197e10i		−	0.0969930i
$759$	4.60553e10	−	7.95867e10i	0.138775	−	0.239813i
$760$	−6.39585e11			−1.91710
$761$			1.19967e11i			0.357704i	0.983876	+	0.178852i	$0.0572384\pi$
$761$			1.19967e11i			0.357704i	−0.983876	+	0.178852i	$0.942762\pi$
$762$	2.12507e11	+	1.22974e11i	0.630309	+	0.364748i
$763$	−8.89935e10			−0.262579
$764$			2.28555e11i			0.670836i
$765$	1.12515e11	+	1.95783e11i	0.328524	+	0.571649i
$766$	9.06484e10			0.263296
$767$		−	4.66850e11i		−	1.34895i
$768$	1.23235e11	−	2.12958e11i	0.354233	−	0.612139i
$769$	−5.47917e11			−1.56679			−0.783393	−	0.621527i	$-0.786513\pi$
$769$	−5.47917e11			−1.56679			−0.783393	+	0.621527i	$0.786513\pi$
$770$		−	3.63084e10i		−	0.103287i
$771$	2.30814e11	+	1.33568e11i	0.653199	+	0.377993i
$772$	−3.34701e9			−0.00942296
$773$		−	2.82645e11i		−	0.791633i	−0.918330	−	0.395817i	$-0.870462\pi$
$773$		−	2.82645e11i		−	0.791633i	0.918330	−	0.395817i	$-0.129538\pi$
$774$	−2.90172e11	+	1.66760e11i	−0.808521	+	0.464653i
$775$	6.57265e11			1.82194
$776$		−	4.98619e11i		−	1.37506i
$777$	1.06768e10	−	1.84502e10i	0.0292925	−	0.0506194i
$778$	1.72761e11			0.471551
$779$		−	5.76014e11i		−	1.56417i
$780$	3.14845e11	+	1.82195e11i	0.850586	+	0.492218i
$781$	−1.88510e11			−0.506676
$782$			7.85850e10i			0.210142i
$783$	4.32909e8	−	1.44731e11i	0.00115173	−	0.385048i
$784$	−8.55193e10			−0.226360
$785$			2.92025e10i			0.0769028i
$786$	−1.46728e10	+	2.53556e10i	−0.0384435	+	0.0664330i
$787$	1.85536e10			0.0483647			0.0241823	−	0.999708i	$-0.492302\pi$
$787$	1.85536e10			0.0483647			0.0241823	+	0.999708i	$0.492302\pi$
$788$			2.66293e11i			0.690645i
$789$	2.53693e11	+	1.46807e11i	0.654637	+	0.378826i
$790$	3.04412e11			0.781544
$791$			8.33719e10i			0.212968i
$792$	−5.25008e10	−	9.13543e10i	−0.133434	−	0.232182i
$793$	−3.01381e11			−0.762120
$794$			1.81505e11i			0.456675i
$795$	2.54136e10	−	4.39165e10i	0.0636206	−	0.109941i
$796$	−4.54792e11			−1.13282
$797$			1.34073e11i			0.332283i	0.986102	+	0.166142i	$0.0531309\pi$
$797$			1.34073e11i			0.332283i	−0.986102	+	0.166142i	$0.946869\pi$
$798$	1.19714e11	+	6.92762e10i	0.295212	+	0.170833i
$799$	1.13900e11			0.279472
$800$			4.94652e11i			1.20765i
$801$	1.82633e11	−	1.04958e11i	0.443658	−	0.254968i
$802$	−8.81959e10			−0.213182
$803$			8.66086e10i			0.208305i
$804$	1.21980e11	−	2.10789e11i	0.291919	−	0.504457i
$805$	2.58864e11			0.616437
$806$		−	3.03573e11i		−	0.719322i
$807$	6.89335e11	+	3.98905e11i	1.62531	+	0.940535i
$808$	2.01616e10			0.0473021
$809$			7.63886e11i			1.78334i	0.452684	+	0.891671i	$0.350466\pi$
$809$			7.63886e11i			1.78334i	−0.452684	+	0.891671i	$0.649534\pi$
$810$	−1.62951e11	+	2.79657e11i	−0.378544	+	0.649660i
$811$	7.45480e11			1.72327			0.861634	−	0.507531i	$-0.169442\pi$
$811$	7.45480e11			1.72327			0.861634	+	0.507531i	$0.169442\pi$
$812$			5.63757e10i			0.129678i
$813$	4.26988e10	−	7.37865e10i	0.0977357	−	0.168894i
$814$	8.67759e9			0.0197652
$815$		−	7.91053e11i		−	1.79298i
$816$	−4.90863e10	−	2.84053e10i	−0.110713	−	0.0640676i
$817$	−1.19272e12			−2.67702
$818$			5.84996e10i			0.130659i
$819$	−9.22215e10	−	1.60470e11i	−0.204973	−	0.356664i
$820$	−5.25045e11			−1.16129
$821$			4.36200e10i			0.0960092i	0.998847	+	0.0480046i	$0.0152862\pi$
$821$			4.36200e10i			0.0960092i	−0.998847	+	0.0480046i	$0.984714\pi$
$822$	−1.75330e11	+	3.02983e11i	−0.384034	+	0.663637i
$823$	−4.99565e10			−0.108891			−0.0544456	−	0.998517i	$-0.517339\pi$
$823$	−4.99565e10			−0.108891			−0.0544456	+	0.998517i	$0.517339\pi$
$824$			3.03221e11i			0.657735i
$825$	1.41189e11	+	8.17034e10i	0.304779	+	0.176370i
$826$	−1.61804e11			−0.347592
$827$		−	4.13623e11i		−	0.884266i	−0.896950	−	0.442133i	$-0.854222\pi$
$827$		−	4.13623e11i		−	0.884266i	0.896950	−	0.442133i	$-0.145778\pi$
$828$	2.76828e11	−	1.59092e11i	0.588965	−	0.338475i
$829$	2.98092e11			0.631150			0.315575	−	0.948901i	$-0.397803\pi$
$829$	2.98092e11			0.631150			0.315575	+	0.948901i	$0.397803\pi$
$830$			3.10707e11i			0.654693i
$831$	−2.67656e11	+	4.62528e11i	−0.561271	+	0.969915i
$832$	1.04877e11			0.218871
$833$		−	1.70853e11i		−	0.354849i
$834$	−3.43618e11	−	1.98845e11i	−0.710250	−	0.411008i
$835$	−9.16378e11			−1.88508
$836$		−	1.59599e11i		−	0.326742i
$837$	−7.65653e11	−	2.29017e9i	−1.56002	−	0.00466622i
$838$	2.90057e11			0.588175
$839$		−	5.22634e11i		−	1.05475i	−0.849632	−	0.527375i	$-0.823176\pi$
$839$		−	5.22634e11i		−	1.05475i	0.849632	−	0.527375i	$-0.176824\pi$
$840$	1.48570e11	−	2.56739e11i	0.298410	−	0.515673i
$841$	4.26078e11			0.851737
$842$			1.14805e11i			0.228408i
$843$	−3.45802e11	−	2.00109e11i	−0.684726	−	0.396238i
$844$	−4.05708e11			−0.799546
$845$		−	1.38675e11i		−	0.272001i
$846$	8.13478e10	+	1.41550e11i	0.158805	+	0.276330i
$847$	2.13168e10			0.0414179
$848$			1.27433e10i			0.0246433i
$849$	4.96341e10	−	8.57712e10i	0.0955322	−	0.165086i
$850$	−1.39412e11			−0.267070
$851$			6.18676e10i			0.117963i
$852$	−5.66547e11	−	3.27850e11i	−1.07517	−	0.622180i
$853$	2.14498e11			0.405160			0.202580	−	0.979266i	$-0.435067\pi$
$853$	2.14498e11			0.405160			0.202580	+	0.979266i	$0.435067\pi$
$854$			1.04455e11i			0.196380i
$855$	−1.00010e12	+	5.74752e11i	−1.87145	+	1.07551i
$856$	−4.73096e11			−0.881159
$857$		−	4.73529e11i		−	0.877855i	−0.898522	−	0.438928i	$-0.855358\pi$
$857$		−	4.73529e11i		−	0.877855i	0.898522	−	0.438928i	$-0.144642\pi$
$858$	3.77366e10	−	6.52115e10i	0.0696328	−	0.120330i
$859$	6.18410e11			1.13581			0.567903	−	0.823096i	$-0.307755\pi$
$859$	6.18410e11			1.13581			0.567903	+	0.823096i	$0.307755\pi$
$860$			1.08718e12i			1.98751i
$861$	2.31220e11	+	1.33803e11i	0.420740	+	0.243474i
$862$	−5.56772e9			−0.0100844
$863$			9.65446e11i			1.74054i	0.492573	+	0.870271i	$0.336057\pi$
$863$			9.65446e11i			1.74054i	−0.492573	+	0.870271i	$0.663943\pi$
$864$	1.72356e9	−	5.76224e11i	0.00309294	−	1.03404i
$865$	−6.72100e11			−1.20052
$866$		−	1.92308e11i		−	0.341921i
$867$	−2.26257e11	+	3.90988e11i	−0.400429	+	0.691969i
$868$	2.98238e11			0.525392
$869$			1.78721e11i			0.313399i
$870$	1.43560e11	+	8.30755e10i	0.250586	+	0.145009i
$871$	4.09727e11			0.711905
$872$		−	2.95965e11i		−	0.511887i
$873$	−4.48075e11	−	7.79675e11i	−0.771425	−	1.34232i
$874$	−4.01428e11			−0.687958
$875$			6.60166e10i			0.112621i
$876$	−1.50626e11	+	2.60293e11i	−0.255791	+	0.442024i
$877$	6.22057e11			1.05155			0.525777	−	0.850622i	$-0.323775\pi$
$877$	6.22057e11			1.05155			0.525777	+	0.850622i	$0.323775\pi$
$878$			5.02098e11i			0.844910i
$879$	7.94218e11	+	4.59598e11i	1.33041	+	0.769880i
$880$	−7.60485e10			−0.126812
$881$		−	6.19419e10i		−	0.102821i	−0.998678	−	0.0514104i	$-0.983628\pi$
$881$		−	6.19419e10i		−	0.102821i	0.998678	−	0.0514104i	$-0.0163716\pi$
$882$	2.12328e11	−	1.22024e11i	0.350859	−	0.201637i
$883$	4.38356e11			0.721081			0.360541	−	0.932743i	$-0.382592\pi$
$883$	4.38356e11			0.721081			0.360541	+	0.932743i	$0.382592\pi$
$884$		−	1.82520e11i		−	0.298883i
$885$	6.75862e11	−	1.16794e12i	1.10175	−	1.90391i
$886$	−2.35743e10			−0.0382565
$887$		−	4.48509e11i		−	0.724564i	−0.932069	−	0.362282i	$-0.881998\pi$
$887$		−	4.48509e11i		−	0.724564i	0.932069	−	0.362282i	$-0.118002\pi$
$888$	6.13597e10	+	3.55076e10i	0.0986805	+	0.0571045i
$889$	−4.05807e11			−0.649699
$890$			2.41401e11i			0.384750i
$891$	−1.64188e11	−	9.56689e10i	−0.260513	−	0.151796i
$892$	2.94698e11			0.465498
$893$			5.81825e11i			0.914928i
$894$	1.74895e11	−	3.02231e11i	0.273797	−	0.473140i
$895$	1.31245e12			2.04546
$896$			2.67285e11i			0.414709i
$897$	4.64931e11	+	2.69046e11i	0.718156	+	0.415583i
$898$	1.44656e10			0.0222449
$899$			3.92363e11i			0.600688i
$900$	2.82233e11	+	4.91102e11i	0.430168	+	0.748517i
$901$	−2.54590e10			−0.0386315
$902$			1.08749e11i			0.164285i
$903$	2.77058e11	−	4.78776e11i	0.416697	−	0.720081i
$904$	−2.77269e11			−0.415172
$905$			1.09898e12i			1.63831i
$906$	−4.89009e11	−	2.82980e11i	−0.725778	−	0.419993i
$907$	−9.27260e11			−1.37016			−0.685081	−	0.728466i	$-0.740233\pi$
$907$	−9.27260e11			−1.37016			−0.685081	+	0.728466i	$0.740233\pi$
$908$		−	4.74608e11i		−	0.698219i
$909$	3.15261e10	−	1.81179e10i	0.0461758	−	0.0265370i
$910$	2.12107e11			0.309307
$911$			8.03623e11i			1.16675i	0.812202	+	0.583377i	$0.198269\pi$
$911$			8.03623e11i			1.16675i	−0.812202	+	0.583377i	$0.801731\pi$
$912$	1.45100e11	−	2.50743e11i	0.209743	−	0.362451i
$913$	−1.82417e11			−0.262531
$914$		−	5.71988e10i		−	0.0819601i
$915$	−7.53976e11	−	4.36311e11i	−1.07566	−	0.622461i
$916$	7.18618e11			1.02074
$917$		−	4.84195e10i		−	0.0684767i
$918$	1.62402e11	+	4.85766e8i	0.228676	+	0.000684001i
$919$	6.48981e11			0.909850			0.454925	−	0.890530i	$-0.349666\pi$
$919$	6.48981e11			0.909850			0.454925	+	0.890530i	$0.349666\pi$
$920$			8.60903e11i			1.20172i
$921$	3.33606e11	−	5.76495e11i	0.463656	−	0.801230i
$922$	−5.04192e11			−0.697705
$923$		−	1.10124e12i		−	1.51731i
$924$	6.40653e10	+	3.70734e10i	0.0878891	+	0.0508597i
$925$	−1.09755e11			−0.149919
$926$		−	3.48915e11i		−	0.474543i
$927$	2.72484e11	+	4.74138e11i	0.368997	+	0.642075i
$928$	−2.95289e11			−0.398158
$929$		−	4.36496e11i		−	0.586027i	−0.956108	−	0.293014i	$-0.905342\pi$
$929$		−	4.36496e11i		−	0.586027i	0.956108	−	0.293014i	$-0.0946581\pi$
$930$	4.39484e11	−	7.59460e11i	0.587505	−	1.01525i
$931$	8.72753e11			1.16170
$932$		−	8.83331e11i		−	1.17074i
$933$	−6.92598e11	−	4.00793e11i	−0.914018	−	0.528924i
$934$	2.72333e11			0.357859
$935$		−	1.51932e11i		−	0.198794i
$936$	5.33675e11	−	3.06700e11i	0.695302	−	0.399586i
$937$	−5.45023e11			−0.707061			−0.353530	−	0.935423i	$-0.615019\pi$
$937$	−5.45023e11			−0.707061			−0.353530	+	0.935423i	$0.615019\pi$
$938$		−	1.42006e11i		−	0.183441i
$939$	−1.22243e11	+	2.11245e11i	−0.157240	+	0.271721i
$940$	5.30342e11			0.679274
$941$		−	9.05430e11i		−	1.15477i	−0.816471	−	0.577386i	$-0.804073\pi$
$941$		−	9.05430e11i		−	1.15477i	0.816471	−	0.577386i	$-0.195927\pi$
$942$	1.81781e10	+	1.05193e10i	0.0230858	+	0.0133593i
$943$	−7.75333e11			−0.980486
$944$			3.38901e11i			0.426761i
$945$	1.60015e9	−	5.34964e11i	0.00200647	−	0.670807i
$946$	2.25180e11			0.281168
$947$			1.29258e12i			1.60716i	0.595197	+	0.803580i	$0.297074\pi$
$947$			1.29258e12i			1.60716i	−0.595197	+	0.803580i	$0.702926\pi$
$948$	−3.10825e11	+	5.37128e11i	−0.384842	+	0.665035i
$949$	−5.05952e11			−0.623798
$950$		−	7.12145e11i		−	0.874327i
$951$	3.85822e11	+	2.23268e11i	0.471699	+	0.272963i
$952$	−1.48835e11			−0.181200
$953$		−	1.91757e11i		−	0.232477i	−0.993221	−	0.116238i	$-0.962916\pi$
$953$		−	1.91757e11i		−	0.232477i	0.993221	−	0.116238i	$-0.0370836\pi$
$954$	−1.81829e10	−	3.16392e10i	−0.0219517	−	0.0381972i
$955$	−1.11142e12			−1.33618
$956$			4.73591e11i			0.566985i
$957$	−4.87739e10	+	8.42846e10i	−0.0581486	+	0.100485i
$958$	−4.08527e11			−0.485019
$959$		−	5.78581e11i		−	0.684053i
$960$	2.62375e11	+	1.51831e11i	0.308914	+	0.178763i
$961$	1.22278e12			1.43369
$962$			5.06929e10i			0.0591898i
$963$	−7.39765e11	+	4.25139e11i	−0.860179	+	0.494340i
$964$	7.16959e11			0.830206
$965$		−	1.62759e10i		−	0.0187688i
$966$	9.32480e10	−	1.61139e11i	0.107086	−	0.185051i
$967$	9.05553e10			0.103564			0.0517819	−	0.998658i	$-0.483510\pi$
$967$	9.05553e10			0.103564			0.0517819	+	0.998658i	$0.483510\pi$
$968$			7.08930e10i			0.0807425i
$969$	5.00942e11	+	2.89885e11i	0.568189	+	0.328800i
$970$	1.03056e12			1.16409
$971$			3.31035e11i			0.372389i	0.982513	+	0.186195i	$0.0596155\pi$
$971$			3.31035e11i			0.372389i	−0.982513	+	0.186195i	$0.940384\pi$
$972$	−3.27065e11	−	5.73072e11i	−0.366411	−	0.642013i
$973$	6.56177e11			0.732099
$974$		−	3.15821e11i		−	0.350918i
$975$	−4.77296e11	+	8.24801e11i	−0.528165	+	0.912706i
$976$	2.18782e11			0.241108
$977$		−	2.52515e11i		−	0.277146i	−0.990352	−	0.138573i	$-0.955748\pi$
$977$		−	2.52515e11i		−	0.277146i	0.990352	−	0.138573i	$-0.0442516\pi$
$978$	−4.92418e11	−	2.84953e11i	−0.538243	−	0.311471i
$979$	−1.41727e11			−0.154285
$980$		−	7.95527e11i		−	0.862483i
$981$	−2.65963e11	−	4.62791e11i	−0.287174	−	0.499699i
$982$	1.30966e11			0.140836
$983$			8.65547e11i			0.926993i	0.886099	+	0.463497i	$0.153405\pi$
$983$			8.65547e11i			0.926993i	−0.886099	+	0.463497i	$0.846595\pi$
$984$	−4.44986e11	+	7.68967e11i	−0.474642	+	0.820215i
$985$	−1.29494e12			−1.37563
$986$		−	8.32238e10i		−	0.0880522i
$987$	−2.33553e11	−	1.35153e11i	−0.246103	−	0.142415i
$988$	9.32348e11			0.978476
$989$			1.60544e12i			1.67807i
$990$	1.88814e11	−	1.08510e11i	0.196559	−	0.112962i
$991$	9.20244e11			0.954132			0.477066	−	0.878868i	$-0.341700\pi$
$991$	9.20244e11			0.954132			0.477066	+	0.878868i	$0.341700\pi$
$992$			1.56213e12i			1.61313i
$993$	2.64482e11	−	4.57043e11i	0.272019	−	0.470067i
$994$	−3.81676e11			−0.390975
$995$		−	2.21157e12i		−	2.25636i
$996$	−5.48234e11	−	3.17252e11i	−0.557094	−	0.322379i
$997$	−3.36123e11			−0.340186			−0.170093	−	0.985428i	$-0.554407\pi$
$997$	−3.36123e11			−0.340186			−0.170093	+	0.985428i	$0.554407\pi$
$998$		−	4.54921e11i		−	0.458579i
$999$	1.27854e11	+	3.82429e8i	0.128367	+	0.000383963i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	33.9.b.a.23.11	✓	26
3.2	odd	2	inner	33.9.b.a.23.16	yes	26

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.9.b.a.23.11	✓	26	1.1	even	1	trivial
33.9.b.a.23.16	yes	26	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 33 = 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	33.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-8.17075i q^{2} +(-40.5699 + 70.1076i) q^{3} +189.239 q^{4} +920.235i q^{5} +(572.832 + 331.487i) q^{6} -1093.89 q^{7} -3637.93i q^{8} +(-3269.16 - 5688.52i) q^{9} +O(q^{10})\)	\(q-8.17075i q^{2} +(-40.5699 + 70.1076i) q^{3} +189.239 q^{4} +920.235i q^{5} +(572.832 + 331.487i) q^{6} -1093.89 q^{7} -3637.93i q^{8} +(-3269.16 - 5688.52i) q^{9} +7519.00 q^{10} +4414.43i q^{11} +(-7677.41 + 13267.1i) q^{12} -25788.3 q^{13} +8937.88i q^{14} +(-64515.5 - 37333.8i) q^{15} +18720.5 q^{16} +37400.5i q^{17} +(-46479.5 + 26711.5i) q^{18} -191049. q^{19} +174144. i q^{20} +(44379.0 - 76689.9i) q^{21} +36069.2 q^{22} +257158. i q^{23} +(255047. + 147591. i) q^{24} -456207. q^{25} +210710. i q^{26} +(531439. + 1589.60i) q^{27} -207006. q^{28} -272338. i q^{29} +(-305045. + 527140. i) q^{30} -1.44072e6 q^{31} -1.08427e6i q^{32} +(-309485. - 179093. i) q^{33} +305590. q^{34} -1.00663e6i q^{35} +(-618653. - 1.07649e6i) q^{36} +240582. q^{37} +1.56101e6i q^{38} +(1.04623e6 - 1.80796e6i) q^{39} +3.34775e6 q^{40} +3.01500e6i q^{41} +(-626614. - 362609. i) q^{42} +6.24301e6 q^{43} +835381. i q^{44} +(5.23478e6 - 3.00840e6i) q^{45} +2.10118e6 q^{46} -3.04542e6i q^{47} +(-759490. + 1.31245e6i) q^{48} -4.56821e6 q^{49} +3.72755e6i q^{50} +(-2.62206e6 - 1.51733e6i) q^{51} -4.88015e6 q^{52} +680712. i q^{53} +(12988.2 - 4.34225e6i) q^{54} -4.06231e6 q^{55} +3.97949e6i q^{56} +(7.75085e6 - 1.33940e7i) q^{57} -2.22521e6 q^{58} +1.81032e7i q^{59} +(-1.22088e7 - 7.06502e6i) q^{60} +1.16867e7 q^{61} +1.17717e7i q^{62} +(3.57610e6 + 6.22261e6i) q^{63} -4.06686e6 q^{64} -2.37313e7i q^{65} +(-1.46332e6 + 2.52872e6i) q^{66} -1.58881e7 q^{67} +7.07763e6i q^{68} +(-1.80288e7 - 1.04329e7i) q^{69} -8.22495e6 q^{70} +4.27032e7i q^{71} +(-2.06945e7 + 1.18930e7i) q^{72} +1.96194e7 q^{73} -1.96573e6i q^{74} +(1.85083e7 - 3.19836e7i) q^{75} -3.61539e7 q^{76} -4.82889e6i q^{77} +(-1.47724e7 - 8.54847e6i) q^{78} +4.04857e7 q^{79} +1.72273e7i q^{80} +(-2.16719e7 + 3.71934e7i) q^{81} +2.46348e7 q^{82} +4.13228e7i q^{83} +(8.39823e6 - 1.45127e7i) q^{84} -3.44172e7 q^{85} -5.10101e7i q^{86} +(1.90930e7 + 1.10487e7i) q^{87} +1.60594e7 q^{88} +3.21055e7i q^{89} +(-2.45808e7 - 4.27720e7i) q^{90} +2.82095e7 q^{91} +4.86644e7i q^{92} +(5.84498e7 - 1.01005e8i) q^{93} -2.48834e7 q^{94} -1.75810e8i q^{95} +(7.60157e7 + 4.39888e7i) q^{96} +1.37061e8 q^{97} +3.73257e7i q^{98} +(2.51116e7 - 1.44315e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 26 q - 35 q^{3} - 2596 q^{4} - 3746 q^{6} + 7156 q^{7} + 9011 q^{9}+O(q^{10}) \) 26 * q - 35 * q^3 - 2596 * q^4 - 3746 * q^6 + 7156 * q^7 + 9011 * q^9	\( 26 q - 35 q^{3} - 2596 q^{4} - 3746 q^{6} + 7156 q^{7} + 9011 q^{9} - 31836 q^{10} - 28900 q^{12} - 131624 q^{13} + 71041 q^{15} + 311972 q^{16} - 675394 q^{18} + 134608 q^{19} + 490306 q^{21} - 59088 q^{24} - 2324740 q^{25} + 2011426 q^{27} - 1996688 q^{28} - 324146 q^{30} + 964738 q^{31} - 512435 q^{33} + 9219648 q^{34} - 6887660 q^{36} - 5721542 q^{37} - 5782712 q^{39} + 8363496 q^{40} + 10350076 q^{42} + 4260820 q^{43} + 6595181 q^{45} - 39680292 q^{46} + 22674164 q^{48} + 20017254 q^{49} - 7985018 q^{51} + 48711952 q^{52} - 18774176 q^{54} - 4304454 q^{55} + 15476796 q^{57} - 16060008 q^{58} - 26730016 q^{60} + 58840 q^{61} - 42877282 q^{63} - 57365836 q^{64} - 10395110 q^{66} - 63186734 q^{67} + 100738079 q^{69} + 50969160 q^{70} + 48890880 q^{72} - 21879656 q^{73} - 122009926 q^{75} - 119289368 q^{76} - 123440744 q^{78} + 117211444 q^{79} + 138667019 q^{81} + 121755480 q^{82} - 28504816 q^{84} + 28880604 q^{85} + 14774868 q^{87} + 90481380 q^{88} + 189044834 q^{90} + 192183008 q^{91} - 113622071 q^{93} - 453996696 q^{94} + 11988416 q^{96} + 24314206 q^{97} - 57905155 q^{99}+O(q^{100}) \) 26 * q - 35 * q^3 - 2596 * q^4 - 3746 * q^6 + 7156 * q^7 + 9011 * q^9 - 31836 * q^10 - 28900 * q^12 - 131624 * q^13 + 71041 * q^15 + 311972 * q^16 - 675394 * q^18 + 134608 * q^19 + 490306 * q^21 - 59088 * q^24 - 2324740 * q^25 + 2011426 * q^27 - 1996688 * q^28 - 324146 * q^30 + 964738 * q^31 - 512435 * q^33 + 9219648 * q^34 - 6887660 * q^36 - 5721542 * q^37 - 5782712 * q^39 + 8363496 * q^40 + 10350076 * q^42 + 4260820 * q^43 + 6595181 * q^45 - 39680292 * q^46 + 22674164 * q^48 + 20017254 * q^49 - 7985018 * q^51 + 48711952 * q^52 - 18774176 * q^54 - 4304454 * q^55 + 15476796 * q^57 - 16060008 * q^58 - 26730016 * q^60 + 58840 * q^61 - 42877282 * q^63 - 57365836 * q^64 - 10395110 * q^66 - 63186734 * q^67 + 100738079 * q^69 + 50969160 * q^70 + 48890880 * q^72 - 21879656 * q^73 - 122009926 * q^75 - 119289368 * q^76 - 123440744 * q^78 + 117211444 * q^79 + 138667019 * q^81 + 121755480 * q^82 - 28504816 * q^84 + 28880604 * q^85 + 14774868 * q^87 + 90481380 * q^88 + 189044834 * q^90 + 192183008 * q^91 - 113622071 * q^93 - 453996696 * q^94 + 11988416 * q^96 + 24314206 * q^97 - 57905155 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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