LMFDB - Embedded newform 33.9.b.a.23.1

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			23.1
Character	$\chi$	$=$	33.23
Dual form			33.9.b.a.23.26

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-30.7079i q^{2} +(79.3894 - 16.0724i) q^{3} -686.976 q^{4} -657.051i q^{5} +(-493.550 - 2437.88i) q^{6} -1255.62 q^{7} +13234.4i q^{8} +(6044.35 - 2551.96i) q^{9} +O(q^{10})$	\(q-30.7079i q^{2} +(79.3894 - 16.0724i) q^{3} -686.976 q^{4} -657.051i q^{5} +(-493.550 - 2437.88i) q^{6} -1255.62 q^{7} +13234.4i q^{8} +(6044.35 - 2551.96i) q^{9} -20176.7 q^{10} -4414.43i q^{11} +(-54538.6 + 11041.4i) q^{12} -40025.1 q^{13} +38557.5i q^{14} +(-10560.4 - 52162.9i) q^{15} +230534. q^{16} +48821.2i q^{17} +(-78365.3 - 185610. i) q^{18} +143900. q^{19} +451378. i q^{20} +(-99683.1 + 20180.9i) q^{21} -135558. q^{22} -127159. i q^{23} +(212708. + 1.05067e6i) q^{24} -41091.1 q^{25} +1.22909e6i q^{26} +(438842. - 299746. i) q^{27} +862582. q^{28} -1.23523e6i q^{29} +(-1.60181e6 + 324288. i) q^{30} -1.23031e6 q^{31} -3.69123e6i q^{32} +(-70950.5 - 350459. i) q^{33} +1.49920e6 q^{34} +825008. i q^{35} +(-4.15233e6 + 1.75313e6i) q^{36} +493626. q^{37} -4.41888e6i q^{38} +(-3.17757e6 + 643300. i) q^{39} +8.69566e6 q^{40} +2.58147e6i q^{41} +(619713. + 3.06106e6i) q^{42} -4.87980e6 q^{43} +3.03261e6i q^{44} +(-1.67677e6 - 3.97145e6i) q^{45} -3.90478e6 q^{46} -3.99550e6i q^{47} +(1.83020e7 - 3.70524e6i) q^{48} -4.18821e6 q^{49} +1.26182e6i q^{50} +(784675. + 3.87589e6i) q^{51} +2.74963e7 q^{52} -7.34753e6i q^{53} +(-9.20457e6 - 1.34759e7i) q^{54} -2.90050e6 q^{55} -1.66174e7i q^{56} +(1.14242e7 - 2.31282e6i) q^{57} -3.79314e7 q^{58} -1.78041e6i q^{59} +(7.25474e6 + 3.58347e7i) q^{60} +8.49193e6 q^{61} +3.77803e7i q^{62} +(-7.58942e6 + 3.20430e6i) q^{63} -5.43331e7 q^{64} +2.62985e7i q^{65} +(-1.07619e7 + 2.17874e6i) q^{66} +2.49283e6 q^{67} -3.35390e7i q^{68} +(-2.04375e6 - 1.00950e7i) q^{69} +2.53343e7 q^{70} -4.22862e7i q^{71} +(3.37736e7 + 7.99933e7i) q^{72} -9.54389e6 q^{73} -1.51582e7i q^{74} +(-3.26220e6 + 660433. i) q^{75} -9.88560e7 q^{76} +5.54285e6i q^{77} +(1.97544e7 + 9.75766e7i) q^{78} +5.39775e7 q^{79} -1.51473e8i q^{80} +(3.00217e7 - 3.08499e7i) q^{81} +7.92715e7 q^{82} -7.19238e6i q^{83} +(6.84799e7 - 1.38638e7i) q^{84} +3.20781e7 q^{85} +1.49848e8i q^{86} +(-1.98532e7 - 9.80644e7i) q^{87} +5.84222e7 q^{88} +4.49042e7i q^{89} +(-1.21955e8 + 5.14900e7i) q^{90} +5.02564e7 q^{91} +8.73549e7i q^{92} +(-9.76738e7 + 1.97741e7i) q^{93} -1.22693e8 q^{94} -9.45498e7i q^{95} +(-5.93269e7 - 2.93044e8i) q^{96} +1.04987e8 q^{97} +1.28611e8i q^{98} +(-1.12654e7 - 2.66824e7i) 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 $

$2$		−	30.7079i		−	1.91924i	−0.281292	−	0.959622i	$-0.590763\pi$
$2$		−	30.7079i		−	1.91924i	0.281292	−	0.959622i	$-0.409237\pi$
$3$	79.3894	−	16.0724i	0.980116	−	0.198425i
$3$	79.3894	−	16.0724i	0.980116	−	0.198425i
$4$	−686.976			−2.68350
$5$		−	657.051i		−	1.05128i	−0.850707	−	0.525641i	$-0.823826\pi$
$5$		−	657.051i		−	1.05128i	0.850707	−	0.525641i	$-0.176174\pi$
$6$	−493.550	−	2437.88i	−0.380826	−	1.88108i
$7$	−1255.62			−0.522958			−0.261479	−	0.965209i	$-0.584210\pi$
$7$	−1255.62			−0.522958			−0.261479	+	0.965209i	$0.584210\pi$
$8$			13234.4i			3.23105i
$9$	6044.35	−	2551.96i	0.921255	−	0.388959i
$10$	−20176.7			−2.01767
$11$		−	4414.43i		−	0.301511i
$11$		−	4414.43i		−	0.301511i
$12$	−54538.6	+	11041.4i	−2.63014	+	0.532473i
$13$	−40025.1			−1.40139			−0.700695	−	0.713461i	$-0.747127\pi$
$13$	−40025.1			−1.40139			−0.700695	+	0.713461i	$0.747127\pi$
$14$			38557.5i			1.00368i
$15$	−10560.4	−	52162.9i	−0.208600	−	1.03038i
$16$	230534.			3.51767
$17$			48821.2i			0.584539i	0.956336	+	0.292269i	$0.0944104\pi$
$17$			48821.2i			0.584539i	−0.956336	+	0.292269i	$0.905590\pi$
$18$	−78365.3	−	185610.i	−0.746507	−	1.76811i
$19$	143900.			1.10420			0.552099	−	0.833778i	$-0.313827\pi$
$19$	143900.			1.10420			0.552099	+	0.833778i	$0.313827\pi$
$20$			451378.i			2.82111i
$21$	−99683.1	+	20180.9i	−0.512559	+	0.103768i
$22$	−135558.			−0.578674
$23$		−	127159.i		−	0.454396i	−0.973849	−	0.227198i	$-0.927044\pi$
$23$		−	127159.i		−	0.454396i	0.973849	−	0.227198i	$-0.0729565\pi$
$24$	212708.	+	1.05067e6i	0.641121	+	3.16680i
$25$	−41091.1			−0.105193
$26$			1.22909e6i			2.68961i
$27$	438842.	−	299746.i	0.825758	−	0.564025i
$28$	862582.			1.40336
$29$		−	1.23523e6i		−	1.74645i	−0.487314	−	0.873227i	$-0.662023\pi$
$29$		−	1.23523e6i		−	1.74645i	0.487314	−	0.873227i	$-0.337977\pi$
$30$	−1.60181e6	+	324288.i	−1.97755	+	0.400355i
$31$	−1.23031e6			−1.33220			−0.666099	−	0.745863i	$-0.732037\pi$
$31$	−1.23031e6			−1.33220			−0.666099	+	0.745863i	$0.732037\pi$
$32$		−	3.69123e6i		−	3.52023i
$33$	−70950.5	−	350459.i	−0.0598274	−	0.295516i
$34$	1.49920e6			1.12187
$35$			825008.i			0.549776i
$36$	−4.15233e6	+	1.75313e6i	−2.47219	+	1.04377i
$37$	493626.			0.263385			0.131693	−	0.991291i	$-0.457959\pi$
$37$	493626.			0.263385			0.131693	+	0.991291i	$0.457959\pi$
$38$		−	4.41888e6i		−	2.11923i
$39$	−3.17757e6	+	643300.i	−1.37353	+	0.278071i
$40$	8.69566e6			3.39674
$41$			2.58147e6i			0.913548i	0.889583	+	0.456774i	$0.150995\pi$
$41$			2.58147e6i			0.913548i	−0.889583	+	0.456774i	$0.849005\pi$
$42$	619713.	+	3.06106e6i	0.199156	+	0.983727i
$43$	−4.87980e6			−1.42734			−0.713671	−	0.700481i	$-0.752969\pi$
$43$	−4.87980e6			−1.42734			−0.713671	+	0.700481i	$0.752969\pi$
$44$			3.03261e6i			0.809106i
$45$	−1.67677e6	−	3.97145e6i	−0.408905	−	0.968499i
$46$	−3.90478e6			−0.872097
$47$		−	3.99550e6i		−	0.818803i	−0.912354	−	0.409401i	$-0.865738\pi$
$47$		−	3.99550e6i		−	0.818803i	0.912354	−	0.409401i	$-0.134262\pi$
$48$	1.83020e7	−	3.70524e6i	3.44773	−	0.697994i
$49$	−4.18821e6			−0.726515
$50$			1.26182e6i			0.201891i
$51$	784675.	+	3.87589e6i	0.115987	+	0.572916i
$52$	2.74963e7			3.76063
$53$		−	7.34753e6i		−	0.931189i	−0.884998	−	0.465595i	$-0.845840\pi$
$53$		−	7.34753e6i		−	0.931189i	0.884998	−	0.465595i	$-0.154160\pi$
$54$	−9.20457e6	−	1.34759e7i	−1.08250	−	1.58483i
$55$	−2.90050e6			−0.316973
$56$		−	1.66174e7i		−	1.68970i
$57$	1.14242e7	−	2.31282e6i	1.08224	−	0.219100i
$58$	−3.79314e7			−3.35187
$59$		−	1.78041e6i		−	0.146931i	−0.997298	−	0.0734653i	$-0.976594\pi$
$59$		−	1.78041e6i		−	0.146931i	0.997298	−	0.0734653i	$-0.0234058\pi$
$60$	7.25474e6	+	3.58347e7i	0.559779	+	2.76502i
$61$	8.49193e6			0.613320			0.306660	−	0.951819i	$-0.400789\pi$
$61$	8.49193e6			0.613320			0.306660	+	0.951819i	$0.400789\pi$
$62$			3.77803e7i			2.55681i
$63$	−7.58942e6	+	3.20430e6i	−0.481778	+	0.203409i
$64$	−5.43331e7			−3.23850
$65$			2.62985e7i			1.47326i
$66$	−1.07619e7	+	2.17874e6i	−0.567168	+	0.114823i
$67$	2.49283e6			0.123707			0.0618533	−	0.998085i	$-0.480299\pi$
$67$	2.49283e6			0.123707			0.0618533	+	0.998085i	$0.480299\pi$
$68$		−	3.35390e7i		−	1.56861i
$69$	−2.04375e6	−	1.00950e7i	−0.0901635	−	0.445361i
$70$	2.53343e7			1.05515
$71$		−	4.22862e7i		−	1.66405i	−0.554741	−	0.832023i	$-0.687183\pi$
$71$		−	4.22862e7i		−	1.66405i	0.554741	−	0.832023i	$-0.312817\pi$
$72$	3.37736e7	+	7.99933e7i	1.25675	+	2.97662i
$73$	−9.54389e6			−0.336073			−0.168037	−	0.985781i	$-0.553743\pi$
$73$	−9.54389e6			−0.336073			−0.168037	+	0.985781i	$0.553743\pi$
$74$		−	1.51582e7i		−	0.505501i
$75$	−3.26220e6	+	660433.i	−0.103102	+	0.0208729i
$76$	−9.88560e7			−2.96312
$77$			5.54285e6i			0.157678i
$78$	1.97544e7	+	9.75766e7i	0.533686	+	2.63613i
$79$	5.39775e7			1.38581			0.692907	−	0.721027i	$-0.256330\pi$
$79$	5.39775e7			1.38581			0.692907	+	0.721027i	$0.256330\pi$
$80$		−	1.51473e8i		−	3.69807i
$81$	3.00217e7	−	3.08499e7i	0.697422	−	0.716661i
$82$	7.92715e7			1.75332
$83$		−	7.19238e6i		−	0.151552i	−0.997125	−	0.0757758i	$-0.975857\pi$
$83$		−	7.19238e6i		−	0.151552i	0.997125	−	0.0757758i	$-0.0241433\pi$
$84$	6.84799e7	−	1.38638e7i	1.37545	−	0.278461i
$85$	3.20781e7			0.614515
$86$			1.49848e8i			2.73942i
$87$	−1.98532e7	−	9.80644e7i	−0.346540	−	1.71173i
$88$	5.84222e7			0.974198
$89$			4.49042e7i			0.715693i	0.933780	+	0.357846i	$0.116489\pi$
$89$			4.49042e7i			0.715693i	−0.933780	+	0.357846i	$0.883511\pi$
$90$	−1.21955e8	+	5.14900e7i	−1.85879	+	0.784789i
$91$	5.02564e7			0.732868
$92$			8.73549e7i			1.21937i
$93$	−9.76738e7	+	1.97741e7i	−1.30571	+	0.264341i
$94$	−1.22693e8			−1.57148
$95$		−	9.45498e7i		−	1.16082i
$96$	−5.93269e7	−	2.93044e8i	−0.698501	−	3.45023i
$97$	1.04987e8			1.18590			0.592949	−	0.805240i	$-0.297964\pi$
$97$	1.04987e8			1.18590			0.592949	+	0.805240i	$0.297964\pi$
$98$			1.28611e8i			1.39436i
$99$	−1.12654e7	−	2.66824e7i	−0.117276	−	0.277769i
$100$	2.82286e7			0.282286
$101$			3.34840e7i			0.321775i	0.986973	+	0.160887i	$0.0514356\pi$
$101$			3.34840e7i			0.321775i	−0.986973	+	0.160887i	$0.948564\pi$
$102$	1.19020e8	−	2.40957e7i	1.09957	−	0.222607i
$103$	9.57594e7			0.850810			0.425405	−	0.905003i	$-0.360132\pi$
$103$	9.57594e7			0.850810			0.425405	+	0.905003i	$0.360132\pi$
$104$		−	5.29708e8i		−	4.52796i
$105$	1.32599e7	+	6.54969e7i	0.109089	+	0.538844i
$106$	−2.25627e8			−1.78718
$107$			3.26803e7i			0.249316i	0.992200	+	0.124658i	$0.0397834\pi$
$107$			3.26803e7i			0.249316i	−0.992200	+	0.124658i	$0.960217\pi$
$108$	−3.01474e8	+	2.05918e8i	−2.21592	+	1.51356i
$109$	2.10901e8			1.49407			0.747037	−	0.664783i	$-0.231476\pi$
$109$	2.10901e8			1.49407			0.747037	+	0.664783i	$0.231476\pi$
$110$			8.90684e7i			0.608349i
$111$	3.91887e7	−	7.93377e6i	0.258148	−	0.0522622i
$112$	−2.89464e8			−1.83959
$113$		−	1.42874e8i		−	0.876275i	−0.898908	−	0.438138i	$-0.855638\pi$
$113$		−	1.42874e8i		−	0.876275i	0.898908	−	0.438138i	$-0.144362\pi$
$114$	−7.10220e7	−	3.50812e8i	−0.420507	−	2.07709i
$115$	−8.35497e7			−0.477698
$116$			8.48576e8i			4.68661i
$117$	−2.41926e8	+	1.02142e8i	−1.29104	+	0.545083i
$118$	−5.46727e7			−0.281996
$119$		−	6.13010e7i		−	0.305689i
$120$	6.90343e8	−	1.39760e8i	3.32920	−	0.673998i
$121$	−1.94872e7			−0.0909091
$122$		−	2.60769e8i		−	1.17711i
$123$	4.14904e7	+	2.04941e8i	0.181271	+	0.895383i
$124$	8.45195e8			3.57495
$125$		−	2.29662e8i		−	0.940694i
$126$	9.83972e7	+	2.33055e8i	0.390392	+	0.924649i
$127$	−4.70685e7			−0.180932			−0.0904659	−	0.995900i	$-0.528836\pi$
$127$	−4.70685e7			−0.180932			−0.0904659	+	0.995900i	$0.528836\pi$
$128$			7.23502e8i			2.69525i
$129$	−3.87404e8	+	7.84301e7i	−1.39896	+	0.283220i
$130$	8.07574e8			2.82754
$131$			1.98464e7i			0.0673901i	0.999432	+	0.0336950i	$0.0107275\pi$
$131$			1.98464e7i			0.0673901i	−0.999432	+	0.0336950i	$0.989273\pi$
$132$	4.87413e7	+	2.40757e8i	0.160547	+	0.793018i
$133$	−1.80684e8			−0.577449
$134$		−	7.65495e7i		−	0.237423i
$135$	−1.96948e8	−	2.88341e8i	−0.592949	−	0.868104i
$136$	−6.46119e8			−1.88867
$137$			1.38175e8i			0.392236i	0.980580	+	0.196118i	$0.0628336\pi$
$137$			1.38175e8i			0.392236i	−0.980580	+	0.196118i	$0.937166\pi$
$138$	−3.09998e8	+	6.27592e7i	−0.854757	+	0.173046i
$139$	1.28166e8			0.343330			0.171665	−	0.985155i	$-0.445085\pi$
$139$	1.28166e8			0.343330			0.171665	+	0.985155i	$0.445085\pi$
$140$		−	5.66760e8i		−	1.47532i
$141$	−6.42173e7	−	3.17200e8i	−0.162471	−	0.802522i
$142$	−1.29852e9			−3.19371
$143$			1.76688e8i			0.422535i
$144$	1.39343e9	−	5.88314e8i	3.24067	−	1.36823i
$145$	−8.11611e8			−1.83601
$146$			2.93073e8i			0.645007i
$147$	−3.32500e8	+	6.73147e7i	−0.712069	+	0.144159i
$148$	−3.39109e8			−0.706794
$149$			3.23333e6i			0.00656002i	0.999995	+	0.00328001i	$0.00104406\pi$
$149$			3.23333e6i			0.00656002i	−0.999995	+	0.00328001i	$0.998956\pi$
$150$	2.02805e7	+	1.00175e8i	0.0400603	+	0.197877i
$151$	3.43182e8			0.660110			0.330055	−	0.943962i	$-0.392933\pi$
$151$	3.43182e8			0.660110			0.330055	+	0.943962i	$0.392933\pi$
$152$			1.90443e9i			3.56772i
$153$	1.24590e8	+	2.95093e8i	0.227361	+	0.538509i
$154$	1.70209e8			0.302622
$155$			8.08378e8i			1.40052i
$156$	2.18291e9	−	4.41932e8i	3.68586	−	0.746203i
$157$	3.32574e8			0.547381			0.273691	−	0.961818i	$-0.411756\pi$
$157$	3.32574e8			0.547381			0.273691	+	0.961818i	$0.411756\pi$
$158$		−	1.65754e9i		−	2.65971i
$159$	−1.18093e8	−	5.83316e8i	−0.184771	−	0.912674i
$160$	−2.42532e9			−3.70075
$161$			1.59663e8i			0.237630i
$162$	−9.47336e8	−	9.21905e8i	−1.37545	−	1.33852i
$163$	−1.05929e8			−0.150060			−0.0750299	−	0.997181i	$-0.523905\pi$
$163$	−1.05929e8			−0.150060			−0.0750299	+	0.997181i	$0.523905\pi$
$164$		−	1.77341e9i		−	2.45150i
$165$	−2.30269e8	+	4.66181e7i	−0.310671	+	0.0628954i
$166$	−2.20863e8			−0.290865
$167$			5.54774e8i			0.713263i	0.934245	+	0.356632i	$0.116075\pi$
$167$			5.54774e8i			0.713263i	−0.934245	+	0.356632i	$0.883925\pi$
$168$	−2.67081e8	−	1.31924e9i	−0.335279	−	1.65610i
$169$	7.86280e8			0.963896
$170$		−	9.85050e8i		−	1.17940i
$171$	8.69784e8	−	3.67228e8i	1.01725	−	0.429488i
$172$	3.35230e9			3.83027
$173$			1.47626e9i			1.64809i	0.566527	+	0.824043i	$0.308287\pi$
$173$			1.47626e9i			1.64809i	−0.566527	+	0.824043i	$0.691713\pi$
$174$	−3.01135e9	+	6.09650e8i	−3.28522	+	0.665095i
$175$	5.15949e7			0.0550116
$176$		−	1.01768e9i		−	1.06062i
$177$	−2.86155e7	−	1.41346e8i	−0.0291547	−	0.144009i
$178$	1.37891e9			1.37359
$179$		−	8.98569e8i		−	0.875264i	−0.899154	−	0.437632i	$-0.855817\pi$
$179$		−	8.98569e8i		−	0.875264i	0.899154	−	0.437632i	$-0.144183\pi$
$180$	1.15190e9	+	2.72829e9i	1.09730	+	2.59897i
$181$	1.43400e9			1.33609			0.668043	−	0.744123i	$-0.267132\pi$
$181$	1.43400e9			1.33609			0.668043	+	0.744123i	$0.267132\pi$
$182$		−	1.54327e9i		−	1.40655i
$183$	6.74169e8	−	1.36486e8i	0.601125	−	0.121698i
$184$	1.68287e9			1.46818
$185$		−	3.24338e8i		−	0.276892i
$186$	6.07221e8	+	2.99936e9i	0.507335	+	2.50597i
$187$	2.15518e8			0.176245
$188$			2.74481e9i			2.19726i
$189$	−5.51019e8	+	3.76367e8i	−0.431837	+	0.294961i
$190$	−2.90343e9			−2.22790
$191$			1.26913e9i			0.953615i	0.879008	+	0.476808i	$0.158206\pi$
$191$			1.26913e9i			0.953615i	−0.879008	+	0.476808i	$0.841794\pi$
$192$	−4.31347e9	+	8.73264e8i	−3.17411	+	0.642600i
$193$	−7.17565e8			−0.517168			−0.258584	−	0.965989i	$-0.583256\pi$
$193$	−7.17565e8			−0.517168			−0.258584	+	0.965989i	$0.583256\pi$
$194$		−	3.22392e9i		−	2.27603i
$195$	4.22681e8	+	2.08783e9i	0.292331	+	1.44396i
$196$	2.87720e9			1.94960
$197$		−	1.82794e9i		−	1.21366i	−0.794833	−	0.606829i	$-0.792441\pi$
$197$		−	1.82794e9i		−	1.21366i	0.794833	−	0.606829i	$-0.207559\pi$
$198$	−8.19360e8	+	3.45938e8i	−0.533106	+	0.225080i
$199$	−2.33921e9			−1.49162			−0.745808	−	0.666161i	$-0.767936\pi$
$199$	−2.33921e9			−1.49162			−0.745808	+	0.666161i	$0.767936\pi$
$200$		−	5.43815e8i		−	0.339884i
$201$	1.97904e8	−	4.00658e7i	0.121247	−	0.0245465i
$202$	1.02822e9			0.617564
$203$			1.55099e9i			0.913321i
$204$	−5.39053e8	−	2.66264e9i	−0.311251	−	1.53742i
$205$	1.69616e9			0.960396
$206$		−	2.94057e9i		−	1.63291i
$207$	−3.24504e8	−	7.68592e8i	−0.176741	−	0.418615i
$208$	−9.22716e9			−4.92963
$209$		−	6.35237e8i		−	0.332928i
$210$	2.01127e9	−	4.07183e8i	1.03417	−	0.209369i
$211$	−2.17572e8			−0.109768			−0.0548838	−	0.998493i	$-0.517479\pi$
$211$	−2.17572e8			−0.109768			−0.0548838	+	0.998493i	$0.517479\pi$
$212$			5.04758e9i			2.49885i
$213$	−6.79641e8	−	3.35708e9i	−0.330188	−	1.63096i
$214$	1.00354e9			0.478499
$215$			3.20628e9i			1.50054i
$216$	3.96695e9	+	5.80779e9i	1.82239	+	2.66806i
$217$	1.54481e9			0.696683
$218$		−	6.47632e9i		−	2.86749i
$219$	−7.57684e8	+	1.53393e8i	−0.329391	+	0.0666853i
$220$	1.99258e9			0.850598
$221$		−	1.95408e9i		−	0.819167i
$222$	−2.43629e8	−	1.20340e9i	−0.100304	−	0.495449i
$223$	−1.80202e7			−0.00728687			−0.00364344	−	0.999993i	$-0.501160\pi$
$223$	−1.80202e7			−0.00728687			−0.00364344	+	0.999993i	$0.501160\pi$
$224$			4.63478e9i			1.84093i
$225$	−2.48369e8	+	1.04863e8i	−0.0969097	+	0.0409158i
$226$	−4.38737e9			−1.68179
$227$			1.66517e9i			0.627126i	0.949567	+	0.313563i	$0.101523\pi$
$227$			1.66517e9i			0.627126i	−0.949567	+	0.313563i	$0.898477\pi$
$228$	−7.84812e9	+	1.58886e9i	−2.90420	+	0.587956i
$229$	7.51037e8			0.273099			0.136549	−	0.990633i	$-0.456399\pi$
$229$	7.51037e8			0.273099			0.136549	+	0.990633i	$0.456399\pi$
$230$			2.56564e9i			0.916820i
$231$	8.90870e7	+	4.40044e8i	0.0312872	+	0.154542i
$232$	1.63475e10			5.64288
$233$			1.07285e9i			0.364011i	0.983298	+	0.182006i	$0.0582589\pi$
$233$			1.07285e9i			0.364011i	−0.983298	+	0.182006i	$0.941741\pi$
$234$	3.13658e9	+	7.42904e9i	1.04615	+	2.47782i
$235$	−2.62524e9			−0.860792
$236$			1.22310e9i			0.394288i
$237$	4.28524e9	−	8.67549e8i	1.35826	−	0.274980i
$238$	−1.88243e9			−0.586692
$239$			3.50838e9i			1.07527i	0.843179	+	0.537633i	$0.180681\pi$
$239$			3.50838e9i			1.07527i	−0.843179	+	0.537633i	$0.819319\pi$
$240$	−2.43453e9	−	1.20253e10i	−0.733788	−	3.62453i
$241$	1.99770e9			0.592191			0.296096	−	0.955158i	$-0.404315\pi$
$241$	1.99770e9			0.592191			0.296096	+	0.955158i	$0.404315\pi$
$242$			5.98410e8i			0.174477i
$243$	1.88757e9	−	2.93168e9i	0.541351	−	0.840797i
$244$	−5.83375e9			−1.64584
$245$			2.75187e9i			0.763772i
$246$	6.29331e9	−	1.27408e9i	1.71846	−	0.347903i
$247$	−5.75963e9			−1.54741
$248$		−	1.62824e10i		−	4.30440i
$249$	−1.15599e8	−	5.70999e8i	−0.0300716	−	0.148538i
$250$	−7.05243e9			−1.80542
$251$		−	2.05652e9i		−	0.518130i	−0.965860	−	0.259065i	$-0.916586\pi$
$251$		−	2.05652e9i		−	0.518130i	0.965860	−	0.259065i	$-0.0834144\pi$
$252$	5.21375e9	−	2.20127e9i	1.29285	−	0.545848i
$253$	−5.61333e8			−0.137006
$254$			1.44537e9i			0.347252i
$255$	2.54666e9	−	5.15572e8i	0.602296	−	0.121935i
$256$	8.30796e9			1.93435
$257$			1.74299e9i			0.399542i	0.979843	+	0.199771i	$0.0640198\pi$
$257$			1.74299e9i			0.399542i	−0.979843	+	0.199771i	$0.935980\pi$
$258$	2.40843e9	+	1.18964e10i	0.543569	+	2.68495i
$259$	−6.19808e8			−0.137739
$260$		−	1.80665e10i		−	3.95348i
$261$	−3.15226e9	−	7.46619e9i	−0.679298	−	1.60893i
$262$	6.09441e8			0.129338
$263$		−	2.24656e9i		−	0.469564i	−0.972048	−	0.234782i	$-0.924562\pi$
$263$		−	2.24656e9i		−	0.469564i	0.972048	−	0.234782i	$-0.0754377\pi$
$264$	4.63810e9	−	9.38986e8i	0.954827	−	0.193305i
$265$	−4.82770e9			−0.978942
$266$			5.54844e9i			1.10827i
$267$	7.21718e8	+	3.56492e9i	0.142011	+	0.701462i
$268$	−1.71251e9			−0.331967
$269$		−	8.82525e9i		−	1.68546i	−0.538337	−	0.842729i	$-0.680947\pi$
$269$		−	8.82525e9i		−	1.68546i	0.538337	−	0.842729i	$-0.319053\pi$
$270$	−8.85436e9	+	6.04787e9i	−1.66610	+	1.13801i
$271$	−9.74083e9			−1.80601			−0.903003	−	0.429635i	$-0.858642\pi$
$271$	−9.74083e9			−1.80601			−0.903003	+	0.429635i	$0.858642\pi$
$272$			1.12550e10i			2.05622i
$273$	3.98983e9	−	8.07742e8i	0.718296	−	0.145419i
$274$	4.24307e9			0.752797
$275$			1.81394e8i			0.0317169i
$276$	1.40401e9	+	6.93506e9i	0.241954	+	1.19513i
$277$	−9.01116e9			−1.53060			−0.765300	−	0.643674i	$-0.777409\pi$
$277$	−9.01116e9			−1.53060			−0.765300	+	0.643674i	$0.777409\pi$
$278$		−	3.93570e9i		−	0.658935i
$279$	−7.43645e9	+	3.13971e9i	−1.22729	+	0.518170i
$280$	−1.09185e10			−1.77635
$281$		−	5.99854e9i		−	0.962100i	−0.876693	−	0.481050i	$-0.840256\pi$
$281$		−	5.99854e9i		−	0.962100i	0.876693	−	0.481050i	$-0.159744\pi$
$282$	−9.74055e9	+	1.97198e9i	−1.54024	+	0.311821i
$283$	8.53262e9			1.33026			0.665130	−	0.746727i	$-0.268376\pi$
$283$	8.53262e9			1.33026			0.665130	+	0.746727i	$0.268376\pi$
$284$			2.90496e10i			4.46547i
$285$	−1.51964e9	−	7.50625e9i	−0.230336	−	1.13774i
$286$	5.42572e9			0.810948
$287$		−	3.24135e9i		−	0.477747i
$288$	−9.41986e9	−	2.23111e10i	−1.36922	−	3.24303i
$289$	4.59224e9			0.658315
$290$			2.49229e10i			3.52376i
$291$	8.33483e9	−	1.68739e9i	1.16232	−	0.235312i
$292$	6.55642e9			0.901853
$293$		−	2.34707e9i		−	0.318460i	−0.987241	−	0.159230i	$-0.949099\pi$
$293$		−	2.34707e9i		−	0.318460i	0.987241	−	0.159230i	$-0.0509012\pi$
$294$	2.06710e9	+	1.02104e10i	0.276676	+	1.36663i
$295$	−1.16982e9			−0.154465
$296$			6.53284e9i			0.851011i
$297$	−1.32321e9	−	1.93723e9i	−0.170060	−	0.248975i
$298$	9.92889e7			0.0125903
$299$			5.08954e9i			0.636786i
$300$	2.24105e9	−	4.53702e8i	0.276673	−	0.0560125i
$301$	6.12718e9			0.746439
$302$		−	1.05384e10i		−	1.26691i
$303$	5.38169e8	+	2.65827e9i	0.0638481	+	0.315376i
$304$	3.31739e10			3.88421
$305$		−	5.57963e9i		−	0.644772i
$306$	9.06169e9	−	3.82589e9i	1.03353	−	0.436362i
$307$	6.53062e9			0.735192			0.367596	−	0.929986i	$-0.380181\pi$
$307$	6.53062e9			0.735192			0.367596	+	0.929986i	$0.380181\pi$
$308$		−	3.80781e9i		−	0.423128i
$309$	7.60228e9	−	1.53909e9i	0.833893	−	0.168822i
$310$	2.48236e10			2.68793
$311$			1.08360e10i			1.15831i	0.815216	+	0.579157i	$0.196618\pi$
$311$			1.08360e10i			1.15831i	−0.815216	+	0.579157i	$0.803382\pi$
$312$	−8.51368e9	−	4.20532e10i	−0.898460	−	4.43793i
$313$	−1.07685e10			−1.12197			−0.560983	−	0.827828i	$-0.689577\pi$
$313$	−1.07685e10			−1.12197			−0.560983	+	0.827828i	$0.689577\pi$
$314$		−	1.02127e10i		−	1.05056i
$315$	2.10539e9	+	4.98664e9i	0.213840	+	0.506484i
$316$	−3.70813e10			−3.71883
$317$			3.10898e9i			0.307879i	0.988080	+	0.153940i	$0.0491961\pi$
$317$			3.10898e9i			0.307879i	−0.988080	+	0.153940i	$0.950804\pi$
$318$	−1.79124e10	+	3.62638e9i	−1.75164	+	0.354621i
$319$	−5.45285e9			−0.526575
$320$			3.56996e10i			3.40458i
$321$	5.25251e8	+	2.59447e9i	0.0494705	+	0.244359i
$322$	4.90292e9			0.456070
$323$			7.02539e9i			0.645447i
$324$	−2.06242e10	+	2.11931e10i	−1.87153	+	1.92316i
$325$	1.64468e9			0.147417
$326$			3.25286e9i			0.288002i
$327$	1.67433e10	−	3.38968e9i	1.46437	−	0.296461i
$328$	−3.41641e10			−2.95172
$329$			5.01683e9i			0.428199i
$330$	1.43155e9	+	7.07109e9i	0.120712	+	0.596253i
$331$	2.17325e10			1.81049			0.905247	−	0.424886i	$-0.139686\pi$
$331$	2.17325e10			1.81049			0.905247	+	0.424886i	$0.139686\pi$
$332$			4.94099e9i			0.406689i
$333$	2.98365e9	−	1.25971e9i	0.242645	−	0.102446i
$334$	1.70359e10			1.36893
$335$		−	1.63792e9i		−	0.130051i
$336$	−2.29804e10	+	4.65238e9i	−1.80302	+	0.365021i
$337$	5.94373e9			0.460829			0.230414	−	0.973093i	$-0.425992\pi$
$337$	5.94373e9			0.460829			0.230414	+	0.973093i	$0.425992\pi$
$338$		−	2.41450e10i		−	1.84995i
$339$	−2.29634e9	−	1.13427e10i	−0.173875	−	0.858852i
$340$	−2.20369e10			−1.64905
$341$			5.43113e9i			0.401673i
$342$	−1.12768e10	−	2.67093e10i	−0.824292	−	1.95235i
$343$	1.24972e10			0.902895
$344$		−	6.45811e10i		−	4.61181i
$345$	−6.63296e9	+	1.34285e9i	−0.468200	+	0.0947872i
$346$	4.53330e10			3.16308
$347$			2.58679e10i			1.78420i	0.451838	+	0.892100i	$0.350768\pi$
$347$			2.58679e10i			1.78420i	−0.451838	+	0.892100i	$0.649232\pi$
$348$	1.36387e10	+	6.73679e10i	0.929940	+	4.59342i
$349$	−7.21209e9			−0.486138			−0.243069	−	0.970009i	$-0.578154\pi$
$349$	−7.21209e9			−0.486138			−0.243069	+	0.970009i	$0.578154\pi$
$350$		−	1.58437e9i		−	0.105581i
$351$	−1.75647e10	+	1.19974e10i	−1.15721	+	0.790419i
$352$	−1.62946e10			−1.06139
$353$		−	2.79580e10i		−	1.80056i	−0.435310	−	0.900281i	$-0.643361\pi$
$353$		−	2.79580e10i		−	1.80056i	0.435310	−	0.900281i	$-0.356639\pi$
$354$	−4.34043e9	+	8.78722e8i	−0.276388	+	0.0559550i
$355$	−2.77842e10			−1.74938
$356$		−	3.08481e10i		−	1.92056i
$357$	−9.85256e8	−	4.86665e9i	−0.0606563	−	0.299611i
$358$	−2.75932e10			−1.67985
$359$		−	6.52206e9i		−	0.392651i	−0.980539	−	0.196326i	$-0.937099\pi$
$359$		−	6.52206e9i		−	0.392651i	0.980539	−	0.196326i	$-0.0629010\pi$
$360$	5.25597e10	−	2.21910e10i	3.12927	−	1.32119i
$361$	3.72372e9			0.219254
$362$		−	4.40351e10i		−	2.56428i
$363$	−1.54707e9	+	3.13206e8i	−0.0891015	+	0.0180386i
$364$	−3.45250e10			−1.96665
$365$			6.27082e9i			0.353308i
$366$	−4.19120e9	−	2.07023e10i	−0.233568	−	1.15371i
$367$	4.82324e9			0.265873			0.132937	−	0.991125i	$-0.457559\pi$
$367$	4.82324e9			0.265873			0.132937	+	0.991125i	$0.457559\pi$
$368$		−	2.93144e10i		−	1.59842i
$369$	6.58780e9	+	1.56033e10i	0.355332	+	0.841610i
$370$	−9.95973e9			−0.531424
$371$			9.22572e9i			0.486973i
$372$	6.70996e10	−	1.35843e10i	3.50387	−	0.709360i
$373$	1.95591e10			1.01045			0.505224	−	0.862988i	$-0.331410\pi$
$373$	1.95591e10			1.01045			0.505224	+	0.862988i	$0.331410\pi$
$374$		−	6.61810e9i		−	0.338257i
$375$	−3.69122e9	−	1.82327e10i	−0.186657	−	0.921989i
$376$	5.28779e10			2.64559
$377$			4.94404e10i			2.44746i
$378$	1.15575e10	+	1.69206e10i	0.566103	+	0.828800i
$379$	−1.60175e10			−0.776317			−0.388159	−	0.921593i	$-0.626889\pi$
$379$	−1.60175e10			−0.776317			−0.388159	+	0.921593i	$0.626889\pi$
$380$			6.49535e10i			3.11507i
$381$	−3.73674e9	+	7.56504e8i	−0.177334	+	0.0359014i
$382$	3.89724e10			1.83022
$383$			2.36763e10i			1.10032i	0.835060	+	0.550159i	$0.185433\pi$
$383$			2.36763e10i			1.10032i	−0.835060	+	0.550159i	$0.814567\pi$
$384$	1.16284e10	+	5.74384e10i	0.534805	+	2.64166i
$385$	3.64194e9			0.165764
$386$			2.20349e10i			0.992573i
$387$	−2.94952e10	+	1.24530e10i	−1.31495	+	0.555177i
$388$	−7.21233e10			−3.18236
$389$		−	2.11361e10i		−	0.923051i	−0.887127	−	0.461525i	$-0.847302\pi$
$389$		−	2.11361e10i		−	0.923051i	0.887127	−	0.461525i	$-0.152698\pi$
$390$	6.41128e10	−	1.29797e10i	2.77132	−	0.561054i
$391$	6.20804e9			0.265612
$392$		−	5.54284e10i		−	2.34741i
$393$	3.18979e8	+	1.57559e9i	0.0133719	+	0.0660501i
$394$	−5.61321e10			−2.32931
$395$		−	3.54660e10i		−	1.45688i
$396$	7.73909e9	+	1.83301e10i	0.314709	+	0.745393i
$397$	−1.06918e10			−0.430418			−0.215209	−	0.976568i	$-0.569043\pi$
$397$	−1.06918e10			−0.430418			−0.215209	+	0.976568i	$0.569043\pi$
$398$			7.18323e10i			2.86278i
$399$	−1.43444e10	+	2.90403e9i	−0.565967	+	0.114580i
$400$	−9.47290e9			−0.370035
$401$		−	2.97887e10i		−	1.15206i	−0.817429	−	0.576029i	$-0.804601\pi$
$401$		−	2.97887e10i		−	1.15206i	0.817429	−	0.576029i	$-0.195399\pi$
$402$	−1.23034e9	−	6.07722e9i	−0.0471107	−	0.232702i
$403$	4.92434e10			1.86693
$404$		−	2.30027e10i		−	0.863482i
$405$	−2.02700e10	−	1.97258e10i	−0.753412	−	0.733187i
$406$	4.76275e10			1.75289
$407$		−	2.17908e9i		−	0.0794136i
$408$	−5.12950e10	+	1.03847e10i	−1.85112	+	0.374760i
$409$	−2.27393e10			−0.812614			−0.406307	−	0.913737i	$-0.633184\pi$
$409$	−2.27393e10			−0.812614			−0.406307	+	0.913737i	$0.633184\pi$
$410$		−	5.20854e10i		−	1.84323i
$411$	2.22081e9	+	1.09696e10i	0.0778294	+	0.384437i
$412$	−6.57844e10			−2.28315
$413$			2.23552e9i			0.0768385i
$414$	−2.36019e10	+	9.96483e9i	−0.803424	+	0.339210i
$415$	−4.72576e9			−0.159323
$416$			1.47742e11i			4.93321i
$417$	1.01750e10	−	2.05993e9i	0.336503	−	0.0681253i
$418$	−1.95068e10			−0.638971
$419$		−	1.19230e8i		−	0.00386838i	−0.999998	−	0.00193419i	$-0.999384\pi$
$419$		−	1.19230e8i		−	0.00386838i	0.999998	−	0.00193419i	$-0.000615671\pi$
$420$	−9.10921e9	−	4.49948e10i	−0.292741	−	1.44599i
$421$	4.48257e10			1.42692			0.713458	−	0.700698i	$-0.247128\pi$
$421$	4.48257e10			1.42692			0.713458	+	0.700698i	$0.247128\pi$
$422$			6.68119e9i			0.210671i
$423$	−1.01963e10	−	2.41502e10i	−0.318481	−	0.754326i
$424$	9.72400e10			3.00872
$425$		−	2.00612e9i		−	0.0614895i
$426$	−1.03089e11	+	2.08704e10i	−3.13021	+	0.633712i
$427$	−1.06627e10			−0.320740
$428$		−	2.24506e10i		−	0.669040i
$429$	2.83980e9	+	1.40272e10i	0.0838415	+	0.414134i
$430$	9.84580e10			2.87990
$431$			6.10032e10i			1.76784i	0.467636	+	0.883921i	$0.345106\pi$
$431$			6.10032e10i			1.76784i	−0.467636	+	0.883921i	$0.654894\pi$
$432$	1.01168e11	−	6.91017e10i	2.90475	−	1.98405i
$433$	−3.92339e10			−1.11612			−0.558059	−	0.829801i	$-0.688454\pi$
$433$	−3.92339e10			−1.11612			−0.558059	+	0.829801i	$0.688454\pi$
$434$		−	4.74378e10i		−	1.33711i
$435$	−6.44333e10	+	1.30446e10i	−1.79951	+	0.364311i
$436$	−1.44884e11			−4.00935
$437$		−	1.82982e10i		−	0.501743i
$438$	4.71039e9	+	2.32669e10i	0.127985	+	0.632182i
$439$	1.45558e9			0.0391903			0.0195952	−	0.999808i	$-0.493762\pi$
$439$	1.45558e9			0.0391903			0.0195952	+	0.999808i	$0.493762\pi$
$440$		−	3.83864e10i		−	1.02416i
$441$	−2.53151e10	+	1.06882e10i	−0.669306	+	0.282584i
$442$	−6.00056e10			−1.57218
$443$			4.06812e10i			1.05628i	0.849157	+	0.528140i	$0.177110\pi$
$443$			4.06812e10i			1.05628i	−0.849157	+	0.528140i	$0.822890\pi$
$444$	−2.69217e10	+	5.45031e9i	−0.692741	+	0.140246i
$445$	2.95043e10			0.752395
$446$			5.53364e8i			0.0139853i
$447$	5.19675e7	+	2.56692e8i	0.00130167	+	0.00642958i
$448$	6.82218e10			1.69360
$449$		−	5.36920e10i		−	1.32106i	−0.750798	−	0.660532i	$-0.770331\pi$
$449$		−	5.36920e10i		−	1.32106i	0.750798	−	0.660532i	$-0.229669\pi$
$450$	3.22012e9	+	7.62690e9i	0.0785275	+	0.185994i
$451$	1.13957e10			0.275445
$452$			9.81513e10i			2.35149i
$453$	2.72450e10	−	5.51576e9i	0.646985	−	0.130982i
$454$	5.11338e10			1.20361
$455$		−	3.30210e10i		−	0.770451i
$456$	3.06088e10	+	1.51192e11i	0.707924	+	3.49678i
$457$	−1.27274e10			−0.291793			−0.145897	−	0.989300i	$-0.546607\pi$
$457$	−1.27274e10			−0.291793			−0.145897	+	0.989300i	$0.546607\pi$
$458$		−	2.30628e10i		−	0.524143i
$459$	1.46340e10	+	2.14248e10i	0.329694	+	0.482687i
$460$	5.73967e10			1.28190
$461$		−	2.52036e10i		−	0.558031i	−0.960287	−	0.279016i	$-0.909992\pi$
$461$		−	2.52036e10i		−	0.558031i	0.960287	−	0.279016i	$-0.0900081\pi$
$462$	1.35128e10	−	2.73568e9i	0.296605	−	0.0600478i
$463$	−2.72712e10			−0.593444			−0.296722	−	0.954964i	$-0.595893\pi$
$463$	−2.72712e10			−0.593444			−0.296722	+	0.954964i	$0.595893\pi$
$464$		−	2.84764e11i		−	6.14345i
$465$	1.29926e10	+	6.41767e10i	0.277897	+	1.37267i
$466$	3.29449e10			0.698626
$467$			1.39838e10i			0.294007i	0.989136	+	0.147004i	$0.0469629\pi$
$467$			1.39838e10i			0.294007i	−0.989136	+	0.147004i	$0.953037\pi$
$468$	1.66197e11	−	7.01694e10i	3.46450	−	1.46273i
$469$	−3.13005e9			−0.0646934
$470$			8.06158e10i			1.65207i
$471$	2.64029e10	−	5.34527e9i	0.536497	−	0.108614i
$472$	2.35626e10			0.474740
$473$			2.15415e10i			0.430360i
$474$	−2.66406e10	−	1.31591e11i	−0.527754	−	2.60683i
$475$	−5.91302e9			−0.116154
$476$			4.21123e10i			0.820317i
$477$	−1.87506e10	−	4.44111e10i	−0.362194	−	0.857863i
$478$	1.07735e11			2.06370
$479$		−	3.10789e10i		−	0.590369i	−0.955440	−	0.295185i	$-0.904619\pi$
$479$		−	3.10789e10i		−	0.590369i	0.955440	−	0.295185i	$-0.0953812\pi$
$480$	−1.92545e11	+	3.89808e10i	−3.62716	+	0.734321i
$481$	−1.97575e10			−0.369106
$482$		−	6.13452e10i		−	1.13656i
$483$	2.56617e9	+	1.26756e10i	0.0471517	+	0.232905i
$484$	1.33872e10			0.243955
$485$		−	6.89816e10i		−	1.24671i
$486$	−9.00257e10	−	5.79635e10i	−1.61369	−	1.03899i
$487$	2.33956e10			0.415928			0.207964	−	0.978136i	$-0.433316\pi$
$487$	2.33956e10			0.415928			0.207964	+	0.978136i	$0.433316\pi$
$488$			1.12385e11i			1.98167i
$489$	−8.40964e9	+	1.70254e9i	−0.147076	+	0.0297756i
$490$	8.45042e10			1.46587
$491$		−	2.30972e10i		−	0.397406i	−0.980060	−	0.198703i	$-0.936327\pi$
$491$		−	2.30972e10i		−	0.397406i	0.980060	−	0.198703i	$-0.0636729\pi$
$492$	−2.85029e10	−	1.40790e11i	−0.486440	−	2.40276i
$493$	6.03056e10			1.02087
$494$			1.76866e11i			2.96987i
$495$	−1.75317e10	+	7.40197e9i	−0.292013	+	0.123290i
$496$	−2.83629e11			−4.68624
$497$			5.30955e10i			0.870226i
$498$	−1.75342e10	+	3.54980e9i	−0.285081	+	0.0577148i
$499$	1.40446e10			0.226520			0.113260	−	0.993565i	$-0.463871\pi$
$499$	1.40446e10			0.226520			0.113260	+	0.993565i	$0.463871\pi$
$500$			1.57772e11i			2.52435i
$501$	8.91655e9	+	4.40432e10i	0.141529	+	0.699081i
$502$	−6.31515e10			−0.994418
$503$			1.11437e11i			1.74083i	0.492318	+	0.870416i	$0.336150\pi$
$503$			1.11437e11i			1.74083i	−0.492318	+	0.870416i	$0.663850\pi$
$504$	−4.24069e10	−	1.00441e11i	−0.657225	−	1.55665i
$505$	2.20007e10			0.338276
$506$			1.72374e10i			0.262947i
$507$	6.24223e10	−	1.26374e10i	0.944730	−	0.191261i
$508$	3.23349e10			0.485531
$509$		−	7.40975e10i		−	1.10391i	−0.833875	−	0.551953i	$-0.813883\pi$
$509$		−	7.40975e10i		−	1.10391i	0.833875	−	0.551953i	$-0.186117\pi$
$510$	−1.58321e10	−	7.82025e10i	−0.234023	−	1.15595i
$511$	1.19835e10			0.175752
$512$		−	6.99038e10i		−	1.01723i
$513$	6.31494e10	−	4.31335e10i	0.911801	−	0.622795i
$514$	5.35235e10			0.766818
$515$		−	6.29188e10i		−	0.894441i
$516$	2.66137e11	−	5.38796e10i	3.75411	−	0.760021i
$517$	−1.76378e10			−0.246878
$518$			1.90330e10i			0.264356i
$519$	2.37271e10	+	1.17200e11i	0.327021	+	1.61532i
$520$	−3.48045e11			−4.76016
$521$			7.05338e10i			0.957296i	0.878007	+	0.478648i	$0.158873\pi$
$521$			7.05338e10i			0.957296i	−0.878007	+	0.478648i	$0.841127\pi$
$522$	−2.29271e11	+	9.67995e10i	−3.08793	+	1.30374i
$523$	−1.91850e9			−0.0256421			−0.0128211	−	0.999918i	$-0.504081\pi$
$523$	−1.91850e9			−0.0256421			−0.0128211	+	0.999918i	$0.504081\pi$
$524$		−	1.36340e10i		−	0.180841i
$525$	4.09609e9	−	8.29254e8i	0.0539177	−	0.0109157i
$526$	−6.89872e10			−0.901209
$527$		−	6.00654e10i		−	0.778721i
$528$	−1.63565e10	−	8.07927e10i	−0.210453	−	1.03953i
$529$	6.21417e10			0.793524
$530$			1.48249e11i			1.87883i
$531$	−4.54353e9	−	1.07614e10i	−0.0571499	−	0.135361i
$532$	1.24126e11			1.54959
$533$		−	1.03324e11i		−	1.28024i
$534$	1.09471e11	−	2.21625e10i	1.34628	−	0.272554i
$535$	2.14726e10			0.262101
$536$			3.29910e10i			0.399702i
$537$	−1.44422e10	−	7.13368e10i	−0.173674	−	0.857861i
$538$	−2.71005e11			−3.23481
$539$			1.84886e10i			0.219053i
$540$	1.35299e11	+	1.98084e11i	1.59118	+	2.32956i
$541$	−6.65503e9			−0.0776892			−0.0388446	−	0.999245i	$-0.512368\pi$
$541$	−6.65503e9			−0.0776892			−0.0388446	+	0.999245i	$0.512368\pi$
$542$			2.99121e11i			3.46617i
$543$	1.13844e11	−	2.30478e10i	1.30952	−	0.265113i
$544$	1.80210e11			2.05771
$545$		−	1.38573e11i		−	1.57069i
$546$	−2.48041e10	−	1.22519e11i	−0.279095	−	1.37859i
$547$	−1.13789e11			−1.27102			−0.635509	−	0.772094i	$-0.719210\pi$
$547$	−1.13789e11			−1.27102			−0.635509	+	0.772094i	$0.719210\pi$
$548$		−	9.49230e10i		−	1.05257i
$549$	5.13282e10	−	2.16711e10i	0.565024	−	0.238556i
$550$	5.57022e9			0.0608726
$551$		−	1.77750e11i		−	1.92843i
$552$	1.33602e11	−	2.70477e10i	1.43898	−	0.291323i
$553$	−6.77754e10			−0.724722
$554$			2.76714e11i			2.93760i
$555$	−5.21289e9	−	2.57490e10i	−0.0549423	−	0.271386i
$556$	−8.80467e10			−0.921327
$557$		−	4.04207e10i		−	0.419936i	−0.977708	−	0.209968i	$-0.932664\pi$
$557$		−	4.04207e10i		−	0.419936i	0.977708	−	0.209968i	$-0.0673360\pi$
$558$	9.64139e10	+	2.28358e11i	0.994495	+	2.35548i
$559$	1.95314e11			2.00026
$560$			1.90192e11i			1.93393i
$561$	1.71098e10	−	3.46389e9i	0.172741	−	0.0349714i
$562$	−1.84203e11			−1.84651
$563$			6.39708e10i			0.636719i	0.947970	+	0.318360i	$0.103132\pi$
$563$			6.39708e10i			0.636719i	−0.947970	+	0.318360i	$0.896868\pi$
$564$	4.41157e10	+	2.17909e11i	0.435991	+	2.15357i
$565$	−9.38758e10			−0.921212
$566$		−	2.62019e11i		−	2.55310i
$567$	−3.76959e10	+	3.87358e10i	−0.364722	+	0.374783i
$568$	5.59631e11			5.37661
$569$			8.53346e10i			0.814097i	0.913407	+	0.407048i	$0.133442\pi$
$569$			8.53346e10i			0.814097i	−0.913407	+	0.407048i	$0.866558\pi$
$570$	−2.30501e11	+	4.66651e10i	−2.18361	+	0.442072i
$571$	−2.00855e11			−1.88947			−0.944733	−	0.327840i	$-0.893679\pi$
$571$	−2.00855e11			−1.88947			−0.944733	+	0.327840i	$0.893679\pi$
$572$		−	1.21380e11i		−	1.13387i
$573$	2.03980e10	+	1.00756e11i	0.189221	+	0.934654i
$574$	−9.95350e10			−0.916913
$575$			5.22509e9i			0.0477994i
$576$	−3.28408e11	+	1.38656e11i	−2.98349	+	1.25964i
$577$	5.01587e10			0.452525			0.226263	−	0.974066i	$-0.427349\pi$
$577$	5.01587e10			0.452525			0.226263	+	0.974066i	$0.427349\pi$
$578$		−	1.41018e11i		−	1.26347i
$579$	−5.69670e10	+	1.15330e10i	−0.506885	+	0.102619i
$580$	5.57557e11			4.92694
$581$			9.03091e9i			0.0792551i
$582$	−5.18162e10	−	2.55945e11i	−0.451621	−	2.23077i
$583$	−3.24352e10			−0.280764
$584$		−	1.26307e11i		−	1.08587i
$585$	6.71128e10	+	1.58958e11i	0.573036	+	1.35725i
$586$	−7.20736e10			−0.611203
$587$		−	8.07369e10i		−	0.680017i	−0.940422	−	0.340008i	$-0.889570\pi$
$587$		−	8.07369e10i		−	0.680017i	0.940422	−	0.340008i	$-0.110430\pi$
$588$	2.28419e11	−	4.62436e10i	1.91084	−	0.386850i
$589$	−1.77042e11			−1.47101
$590$			3.59228e10i			0.296457i
$591$	−2.93794e10	−	1.45119e11i	−0.240820	−	1.18953i
$592$	1.13798e11			0.926503
$593$		−	1.90426e11i		−	1.53995i	−0.638074	−	0.769975i	$-0.720269\pi$
$593$		−	1.90426e11i		−	1.53995i	0.638074	−	0.769975i	$-0.279731\pi$
$594$	−5.94884e10	+	4.06329e10i	−0.477845	+	0.326387i
$595$	−4.02779e10			−0.321365
$596$		−	2.22122e9i		−	0.0176038i
$597$	−1.85708e11	+	3.75968e10i	−1.46196	+	0.295974i
$598$	1.56289e11			1.22215
$599$			1.31302e11i			1.01991i	0.860201	+	0.509956i	$0.170338\pi$
$599$			1.31302e11i			1.01991i	−0.860201	+	0.509956i	$0.829662\pi$
$600$	−8.74042e9	−	4.31731e10i	−0.0674415	−	0.333126i
$601$	−9.72221e10			−0.745190			−0.372595	−	0.927994i	$-0.621532\pi$
$601$	−9.72221e10			−0.745190			−0.372595	+	0.927994i	$0.621532\pi$
$602$		−	1.88153e11i		−	1.43260i
$603$	1.50675e10	−	6.36159e9i	0.113965	−	0.0481168i
$604$	−2.35758e11			−1.77141
$605$			1.28041e10i			0.0955711i
$606$	8.16300e10	−	1.65260e10i	0.605284	−	0.122540i
$607$	4.28602e10			0.315718			0.157859	−	0.987462i	$-0.449541\pi$
$607$	4.28602e10			0.315718			0.157859	+	0.987462i	$0.449541\pi$
$608$		−	5.31168e11i		−	3.88703i
$609$	2.49281e10	+	1.23132e11i	0.181226	+	0.895161i
$610$	−1.71339e11			−1.23748
$611$			1.59920e11i			1.14746i
$612$	−8.55902e10	−	2.02722e11i	−0.610125	−	1.44509i
$613$	9.45121e9			0.0669338			0.0334669	−	0.999440i	$-0.489345\pi$
$613$	9.45121e9			0.0669338			0.0334669	+	0.999440i	$0.489345\pi$
$614$		−	2.00542e11i		−	1.41101i
$615$	1.34657e11	−	2.72613e10i	0.941299	−	0.190566i
$616$	−7.33562e10			−0.509464
$617$			1.85733e11i			1.28159i	0.767712	+	0.640795i	$0.221395\pi$
$617$			1.85733e11i			1.28159i	−0.767712	+	0.640795i	$0.778605\pi$
$618$	−4.72621e10	−	2.33450e11i	−0.324011	−	1.60044i
$619$	8.00935e10			0.545550			0.272775	−	0.962078i	$-0.412059\pi$
$619$	8.00935e10			0.545550			0.272775	+	0.962078i	$0.412059\pi$
$620$		−	5.55336e11i		−	3.75828i
$621$	−3.81153e10	−	5.58025e10i	−0.256291	−	0.375221i
$622$	3.32750e11			2.22309
$623$		−	5.63827e10i		−	0.374277i
$624$	−7.32539e11	+	1.48303e11i	−4.83161	+	0.978162i
$625$	−1.66951e11			−1.09413
$626$			3.30679e11i			2.15333i
$627$	−1.02098e10	−	5.04311e10i	−0.0660613	−	0.326308i
$628$	−2.28471e11			−1.46890
$629$			2.40995e10i			0.153959i
$630$	1.53129e11	−	6.46520e10i	0.972067	−	0.410412i
$631$	−1.42159e11			−0.896718			−0.448359	−	0.893854i	$-0.647991\pi$
$631$	−1.42159e11			−0.896718			−0.448359	+	0.893854i	$0.647991\pi$
$632$			7.14359e11i			4.47763i
$633$	−1.72729e10	+	3.49691e9i	−0.107585	+	0.0217806i
$634$	9.54702e10			0.590895
$635$			3.09264e10i			0.190210i
$636$	8.11268e10	+	4.00724e11i	0.495833	+	2.44916i
$637$	1.67634e11			1.01813
$638$			1.67446e11i			1.01063i
$639$	−1.07913e11	−	2.55593e11i	−0.647245	−	1.53301i
$640$	4.75378e11			2.83347
$641$			2.94947e11i			1.74707i	0.486757	+	0.873537i	$0.338180\pi$
$641$			2.94947e11i			1.74707i	−0.486757	+	0.873537i	$0.661820\pi$
$642$	7.96707e10	−	1.61294e10i	0.468984	−	0.0949461i
$643$	−2.57916e10			−0.150881			−0.0754406	−	0.997150i	$-0.524036\pi$
$643$	−2.57916e10			−0.150881			−0.0754406	+	0.997150i	$0.524036\pi$
$644$		−	1.09685e11i		−	0.637680i
$645$	5.15326e10	+	2.54544e11i	0.297744	+	1.47070i
$646$	2.15735e11			1.23877
$647$		−	1.06263e11i		−	0.606409i	−0.952926	−	0.303204i	$-0.901944\pi$
$647$		−	1.06263e11i		−	0.606409i	0.952926	−	0.303204i	$-0.0980565\pi$
$648$	4.08279e11	+	3.97319e11i	2.31557	+	2.25340i
$649$	−7.85949e9			−0.0443012
$650$		−	5.05046e10i		−	0.282929i
$651$	1.22641e11	−	2.48288e10i	0.682831	−	0.138239i
$652$	7.27707e10			0.402686
$653$		−	1.76356e10i		−	0.0969922i	−0.998823	−	0.0484961i	$-0.984557\pi$
$653$		−	1.76356e10i		−	0.0969922i	0.998823	−	0.0484961i	$-0.0154429\pi$
$654$	−1.04090e11	−	5.14151e11i	−0.568982	−	2.81048i
$655$	1.30401e10			0.0708459
$656$			5.95117e11i			3.21356i
$657$	−5.76867e10	+	2.43556e10i	−0.309609	+	0.130719i
$658$	1.54056e11			0.821819
$659$			7.85572e10i			0.416528i	0.978073	+	0.208264i	$0.0667813\pi$
$659$			7.85572e10i			0.416528i	−0.978073	+	0.208264i	$0.933219\pi$
$660$	1.58189e11	−	3.20255e10i	0.833685	−	0.168780i
$661$	1.98836e11			1.04157			0.520786	−	0.853687i	$-0.325639\pi$
$661$	1.98836e11			1.04157			0.520786	+	0.853687i	$0.325639\pi$
$662$		−	6.67359e11i		−	3.47478i
$663$	−3.14067e10	−	1.55133e11i	−0.162543	−	0.802879i
$664$	9.51867e10			0.489670
$665$			1.18719e11i			0.607062i
$666$	−3.86832e10	−	9.16218e10i	−0.196619	−	0.465695i
$667$	−1.57071e11			−0.793581
$668$		−	3.81116e11i		−	1.91404i
$669$	−1.43062e9	+	2.89629e8i	−0.00714198	+	0.00144590i
$670$	−5.02970e10			−0.249599
$671$		−	3.74870e10i		−	0.184923i
$672$	7.44922e10	+	3.67953e11i	0.365286	+	1.80433i
$673$	1.13188e11			0.551748			0.275874	−	0.961194i	$-0.411033\pi$
$673$	1.13188e11			0.551748			0.275874	+	0.961194i	$0.411033\pi$
$674$		−	1.82520e11i		−	0.884443i
$675$	−1.80325e10	+	1.23169e10i	−0.0868641	+	0.0593316i
$676$	−5.40155e11			−2.58662
$677$			1.74851e11i			0.832363i	0.909282	+	0.416181i	$0.136632\pi$
$677$			1.74851e11i			0.832363i	−0.909282	+	0.416181i	$0.863368\pi$
$678$	−3.48311e11	+	7.05157e10i	−1.64835	+	0.333708i
$679$	−1.31824e11			−0.620174
$680$			4.24533e11i			1.98553i
$681$	2.67633e10	+	1.32197e11i	0.124437	+	0.614656i
$682$	1.66779e11			0.770908
$683$		−	3.29031e11i		−	1.51201i	−0.654568	−	0.756003i	$-0.727149\pi$
$683$		−	3.29031e11i		−	1.51201i	0.654568	−	0.756003i	$-0.272851\pi$
$684$	−5.97521e11	+	2.52277e11i	−2.72979	+	1.15253i
$685$	9.07881e10			0.412351
$686$		−	3.83764e11i		−	1.73288i
$687$	5.96244e10	−	1.20710e10i	0.267668	−	0.0541896i
$688$	−1.12496e12			−5.02092
$689$			2.94086e11i			1.30496i
$690$	4.12360e10	+	2.03684e11i	0.181920	+	0.898590i
$691$	7.71021e10			0.338185			0.169092	−	0.985600i	$-0.445916\pi$
$691$	7.71021e10			0.338185			0.169092	+	0.985600i	$0.445916\pi$
$692$		−	1.01416e12i		−	4.42264i
$693$	1.41451e10	+	3.35030e10i	0.0613301	+	0.145261i
$694$	7.94350e11			3.42432
$695$		−	8.42113e10i		−	0.360937i
$696$	1.29782e12	−	2.62744e11i	5.53067	−	1.11969i
$697$	−1.26030e11			−0.534004
$698$			2.21468e11i			0.933018i
$699$	1.72433e10	+	8.51728e10i	0.0722289	+	0.356773i
$700$	−3.54444e10			−0.147624
$701$		−	3.45206e11i		−	1.42957i	−0.699342	−	0.714787i	$-0.746524\pi$
$701$		−	3.45206e11i		−	1.42957i	0.699342	−	0.714787i	$-0.253476\pi$
$702$	3.68414e11	+	5.39375e11i	1.51701	+	2.22097i
$703$	7.10330e10			0.290830
$704$			2.39849e11i			0.976446i
$705$	−2.08417e11	+	4.21940e10i	−0.843676	+	0.170803i
$706$	−8.58533e11			−3.45572
$707$		−	4.20432e10i		−	0.168275i
$708$	1.96582e10	+	9.71011e10i	0.0782366	+	0.386448i
$709$	4.72067e11			1.86818			0.934091	−	0.357035i	$-0.116212\pi$
$709$	4.72067e11			1.86818			0.934091	+	0.357035i	$0.116212\pi$
$710$			8.53195e11i			3.35749i
$711$	3.26259e11	−	1.37748e11i	1.27669	−	0.539024i
$712$	−5.94279e11			−2.31244
$713$			1.56445e11i			0.605345i
$714$	−1.49445e11	+	3.02551e10i	−0.575026	+	0.116414i
$715$	1.16093e11			0.444204
$716$			6.17295e11i			2.34877i
$717$	5.63882e10	+	2.78529e11i	0.213359	+	1.05388i
$718$	−2.00279e11			−0.753594
$719$			4.29879e11i			1.60853i	0.594268	+	0.804267i	$0.297442\pi$
$719$			4.29879e11i			1.60853i	−0.594268	+	0.804267i	$0.702558\pi$
$720$	−3.86552e11	−	9.15555e11i	−1.43840	−	3.40686i
$721$	−1.20238e11			−0.444938
$722$		−	1.14348e11i		−	0.420803i
$723$	1.58596e11	−	3.21079e10i	0.580416	−	0.117506i
$724$	−9.85123e11			−3.58539
$725$			5.07571e10i			0.183715i
$726$	9.61790e9	+	4.75074e10i	0.0346205	+	0.171008i
$727$	−3.07420e11			−1.10051			−0.550255	−	0.834996i	$-0.685470\pi$
$727$	−3.07420e11			−1.10051			−0.550255	+	0.834996i	$0.685470\pi$
$728$			6.65112e11i			2.36793i
$729$	1.02734e11	−	2.63082e11i	0.363752	−	0.931496i
$730$	1.92564e11			0.678084
$731$		−	2.38238e11i		−	0.834336i
$732$	−4.63138e11	+	9.37625e10i	−1.61312	+	0.326576i
$733$	−7.80423e10			−0.270342			−0.135171	−	0.990822i	$-0.543158\pi$
$733$	−7.80423e10			−0.270342			−0.135171	+	0.990822i	$0.543158\pi$
$734$		−	1.48112e11i		−	0.510276i
$735$	4.42292e10	+	2.18469e11i	0.151551	+	0.748585i
$736$	−4.69371e11			−1.59958
$737$		−	1.10044e10i		−	0.0372990i
$738$	4.79145e11	−	2.02298e11i	1.61526	−	0.681970i
$739$	5.26326e11			1.76472			0.882362	−	0.470571i	$-0.155952\pi$
$739$	5.26326e11			1.76472			0.882362	+	0.470571i	$0.155952\pi$
$740$			2.22812e11i			0.743040i
$741$	−4.57253e11	+	9.25711e10i	−1.51665	+	0.307045i
$742$	2.83303e11			0.934620
$743$		−	3.23028e11i		−	1.05995i	−0.848013	−	0.529975i	$-0.822201\pi$
$743$		−	3.23028e11i		−	1.05995i	0.848013	−	0.529975i	$-0.177799\pi$
$744$	−2.61698e11	−	1.29265e12i	−0.854099	−	4.21881i
$745$	2.12446e9			0.00689643
$746$		−	6.00620e11i		−	1.93930i
$747$	−1.83547e10	−	4.34733e10i	−0.0589473	−	0.139618i
$748$	−1.48056e11			−0.472954
$749$		−	4.10340e10i		−	0.130382i
$750$	−5.59888e11	+	1.13350e11i	−1.76952	+	0.358241i
$751$	3.11096e11			0.977989			0.488995	−	0.872287i	$-0.337364\pi$
$751$	3.11096e11			0.977989			0.488995	+	0.872287i	$0.337364\pi$
$752$		−	9.21099e11i		−	2.88028i
$753$	−3.30533e10	−	1.63266e11i	−0.102810	−	0.507828i
$754$	1.51821e12			4.69728
$755$		−	2.25488e11i		−	0.693962i
$756$	3.78537e11	−	2.58555e11i	1.15883	−	0.791528i
$757$	−9.82160e10			−0.299088			−0.149544	−	0.988755i	$-0.547781\pi$
$757$	−9.82160e10			−0.299088			−0.149544	+	0.988755i	$0.547781\pi$
$758$			4.91866e11i			1.48994i
$759$	−4.45639e10	+	9.02197e9i	−0.134281	+	0.0271853i
$760$	1.25131e12			3.75068
$761$		−	6.07470e10i		−	0.181128i	−0.995891	−	0.0905641i	$-0.971133\pi$
$761$		−	6.07470e10i		−	0.181128i	0.995891	−	0.0905641i	$-0.0288670\pi$
$762$	2.32307e10	+	1.14747e11i	0.0689035	+	0.340348i
$763$	−2.64812e11			−0.781338
$764$		−	8.71863e11i		−	2.55903i
$765$	1.93891e11	−	8.18619e10i	0.566125	−	0.239021i
$766$	7.27050e11			2.11178
$767$			7.12611e10i			0.205907i
$768$	6.59564e11	−	1.33529e11i	1.89589	−	0.383823i
$769$	6.47898e11			1.85268			0.926342	−	0.376682i	$-0.122935\pi$
$769$	6.47898e11			1.85268			0.926342	+	0.376682i	$0.122935\pi$
$770$		−	1.11836e11i		−	0.318141i
$771$	2.80140e10	+	1.38375e11i	0.0792790	+	0.391597i
$772$	4.92950e11			1.38782
$773$			3.86423e11i			1.08229i	0.840928	+	0.541147i	$0.182010\pi$
$773$			3.86423e11i			1.08229i	−0.840928	+	0.541147i	$0.817990\pi$
$774$	3.82407e11	+	9.05737e11i	1.06552	+	2.52370i
$775$	5.05549e10			0.140138
$776$			1.38943e12i			3.83169i
$777$	−4.92062e10	+	9.96181e9i	−0.135001	+	0.0273309i
$778$	−6.49044e11			−1.77156
$779$			3.71474e11i			1.00874i
$780$	−2.90372e11	−	1.43429e12i	−0.784470	−	3.87487i
$781$	−1.86669e11			−0.501729
$782$		−	1.90636e11i		−	0.509775i
$783$	−3.70256e11	−	5.42072e11i	−0.985043	−	1.44215i
$784$	−9.65527e11			−2.55564
$785$		−	2.18518e11i		−	0.575452i
$786$	4.83831e10	−	9.79518e9i	0.126766	−	0.0256639i
$787$	−5.08444e11			−1.32539			−0.662696	−	0.748889i	$-0.730588\pi$
$787$	−5.08444e11			−1.32539			−0.662696	+	0.748889i	$0.730588\pi$
$788$			1.25575e12i			3.25685i
$789$	−3.61077e10	−	1.78353e11i	−0.0931733	−	0.460228i
$790$	−1.08909e12			−2.79611
$791$			1.79396e11i			0.458255i
$792$	3.53124e11	−	1.49091e11i	0.897485	−	0.378923i
$793$	−3.39891e11			−0.859501
$794$			3.28324e11i			0.826078i
$795$	−3.83269e11	+	7.75929e10i	−0.959477	+	0.194247i
$796$	1.60698e12			4.00275
$797$			6.37379e11i			1.57966i	0.613324	+	0.789832i	$0.289832\pi$
$797$			6.37379e11i			1.57966i	−0.613324	+	0.789832i	$0.710168\pi$
$798$	8.91768e10	+	4.40487e11i	0.219908	+	1.08623i
$799$	1.95065e11			0.478622
$800$			1.51676e11i			0.370304i
$801$	1.14594e11	+	2.71417e11i	0.278375	+	0.659336i
$802$	−9.14750e11			−2.21108
$803$			4.21308e10i			0.101330i
$804$	−1.35955e11	+	2.75242e10i	−0.325366	+	0.0658705i
$805$	1.04907e11			0.249816
$806$		−	1.51216e12i		−	3.58309i
$807$	−1.41843e11	−	7.00632e11i	−0.334437	−	1.65195i
$808$	−4.43140e11			−1.03967
$809$		−	8.44207e11i		−	1.97086i	−0.170093	−	0.985428i	$-0.554407\pi$
$809$		−	8.44207e11i		−	1.97086i	0.170093	−	0.985428i	$-0.445593\pi$
$810$	−6.05738e11	+	6.22448e11i	−1.40717	+	1.44598i
$811$	7.47304e11			1.72748			0.863742	−	0.503934i	$-0.168115\pi$
$811$	7.47304e11			1.72748			0.863742	+	0.503934i	$0.168115\pi$
$812$		−	1.06549e12i		−	2.45090i
$813$	−7.73319e11	+	1.56559e11i	−1.77009	+	0.358356i
$814$	−6.69149e10			−0.152414
$815$			6.96008e10i			0.157755i
$816$	1.80895e11	+	8.93525e11i	0.408004	+	2.01533i
$817$	−7.02204e11			−1.57607
$818$			6.98278e11i			1.55961i
$819$	3.03768e11	−	1.28252e11i	0.675159	−	0.285056i
$820$	−1.16522e12			−2.57722
$821$			6.62273e11i			1.45769i	0.684681	+	0.728843i	$0.259942\pi$
$821$			6.62273e11i			1.45769i	−0.684681	+	0.728843i	$0.740058\pi$
$822$	3.36855e11	−	6.81964e10i	0.737829	−	0.149374i
$823$	3.33964e11			0.727948			0.363974	−	0.931409i	$-0.381420\pi$
$823$	3.33964e11			0.727948			0.363974	+	0.931409i	$0.381420\pi$
$824$			1.26732e12i			2.74901i
$825$	2.91543e9	+	1.44007e10i	0.00629343	+	0.0310863i
$826$	6.86482e10			0.147472
$827$		−	3.17589e11i		−	0.678959i	−0.940613	−	0.339480i	$-0.889749\pi$
$827$		−	3.17589e11i		−	0.678959i	0.940613	−	0.339480i	$-0.110251\pi$
$828$	2.22926e11	+	5.28004e11i	0.474286	+	1.12335i
$829$	−2.23031e9			−0.00472223			−0.00236112	−	0.999997i	$-0.500752\pi$
$829$	−2.23031e9			−0.00472223			−0.00236112	+	0.999997i	$0.500752\pi$
$830$			1.45118e11i			0.305781i
$831$	−7.15391e11	+	1.44831e11i	−1.50017	+	0.303709i
$832$	2.17469e12			4.53841
$833$		−	2.04474e11i		−	0.424676i
$834$	−6.32562e10	−	3.12453e11i	−0.130749	−	0.645833i
$835$	3.64515e11			0.749841
$836$			4.36393e11i			0.893413i
$837$	−5.39912e11	+	3.68781e11i	−1.10007	+	0.751393i
$838$	−3.66130e9			−0.00742436
$839$		−	3.98606e11i		−	0.804445i	−0.915542	−	0.402222i	$-0.868238\pi$
$839$		−	3.98606e11i		−	0.804445i	0.915542	−	0.402222i	$-0.131762\pi$
$840$	−8.66810e11	+	1.75486e11i	−1.74103	+	0.352473i
$841$	−1.02555e12			−2.05010
$842$		−	1.37650e12i		−	2.73860i
$843$	−9.64110e10	−	4.76220e11i	−0.190905	−	0.942970i
$844$	1.49467e11			0.294561
$845$		−	5.16626e11i		−	1.01333i
$846$	−7.41602e11	+	3.13108e11i	−1.44774	+	0.611242i
$847$	2.44685e10			0.0475416
$848$		−	1.69386e12i		−	3.27562i
$849$	6.77400e11	−	1.37140e11i	1.30381	−	0.263957i
$850$	−6.16037e10			−0.118013
$851$		−	6.27689e10i		−	0.119681i
$852$	4.66897e11	+	2.30623e12i	0.886060	+	4.37668i
$853$	4.41972e11			0.834832			0.417416	−	0.908716i	$-0.362936\pi$
$853$	4.41972e11			0.834832			0.417416	+	0.908716i	$0.362936\pi$
$854$			3.27428e11i			0.615579i
$855$	−2.41287e11	−	5.71493e11i	−0.451513	−	1.06941i
$856$	−4.32503e11			−0.805553
$857$		−	3.16970e10i		−	0.0587617i	−0.999568	−	0.0293809i	$-0.990646\pi$
$857$		−	3.16970e10i		−	0.0587617i	0.999568	−	0.0293809i	$-0.00935357\pi$
$858$	4.30745e11	−	8.72044e10i	0.794824	−	0.160912i
$859$	4.38651e10			0.0805651			0.0402825	−	0.999188i	$-0.487174\pi$
$859$	4.38651e10			0.0805651			0.0402825	+	0.999188i	$0.487174\pi$
$860$		−	2.20263e12i		−	4.02669i
$861$	−5.20963e10	−	2.57329e11i	−0.0947969	−	0.468247i
$862$	1.87328e12			3.39292
$863$			8.48354e11i			1.52945i	0.644359	+	0.764723i	$0.277124\pi$
$863$			8.48354e11i			1.52945i	−0.644359	+	0.764723i	$0.722876\pi$
$864$	−1.10643e12	−	1.61986e12i	−1.98550	−	2.90685i
$865$	9.69981e11			1.73260
$866$			1.20479e12i			2.14210i
$867$	3.64575e11	−	7.38084e10i	0.645225	−	0.130626i
$868$	−1.06125e12			−1.86955
$869$		−	2.38280e11i		−	0.417838i
$870$	4.00571e11	+	1.97861e12i	0.699202	+	3.45369i
$871$	−9.97757e10			−0.173361
$872$			2.79114e12i			4.82743i
$873$	6.34577e11	−	2.67922e11i	1.09251	−	0.461265i
$874$	−5.61898e11			−0.962969
$875$			2.88368e11i			0.491943i
$876$	5.20511e11	−	1.05378e11i	0.883921	−	0.178950i
$877$	−5.14999e11			−0.870579			−0.435290	−	0.900290i	$-0.643354\pi$
$877$	−5.14999e11			−0.870579			−0.435290	+	0.900290i	$0.643354\pi$
$878$		−	4.46979e10i		−	0.0752158i
$879$	−3.77231e10	−	1.86332e11i	−0.0631905	−	0.312128i
$880$	−6.68666e11			−1.11501
$881$			4.41505e11i			0.732878i	0.930442	+	0.366439i	$0.119423\pi$
$881$			4.41505e11i			0.732878i	−0.930442	+	0.366439i	$0.880577\pi$
$882$	3.28211e11	+	7.77373e11i	0.542349	+	1.28456i
$883$	3.57059e11			0.587351			0.293675	−	0.955905i	$-0.405122\pi$
$883$	3.57059e11			0.587351			0.293675	+	0.955905i	$0.405122\pi$
$884$			1.34240e12i			2.19823i
$885$	−9.28714e10	+	1.88018e10i	−0.151394	+	0.0306498i
$886$	1.24924e12			2.02726
$887$		−	7.38204e11i		−	1.19256i	−0.802775	−	0.596282i	$-0.796644\pi$
$887$		−	7.38204e11i		−	1.19256i	0.802775	−	0.596282i	$-0.203356\pi$
$888$	1.04998e11	+	5.18638e11i	0.168862	+	0.834089i
$889$	5.91002e10			0.0946197
$890$		−	9.06016e11i		−	1.44403i
$891$	−1.36185e11	−	1.32529e11i	−0.216081	−	0.210281i
$892$	1.23795e10			0.0195543
$893$		−	5.74953e11i		−	0.904121i
$894$	7.88249e9	−	1.59581e9i	0.0123399	−	0.00249823i
$895$	−5.90406e11			−0.920149
$896$		−	9.08444e11i		−	1.40950i
$897$	8.18012e10	+	4.04056e11i	0.126354	+	0.624125i
$898$	−1.64877e12			−2.53545
$899$			1.51972e12i			2.32662i
$900$	1.70624e11	−	7.20382e10i	0.260057	−	0.109798i
$901$	3.58716e11			0.544316
$902$		−	3.49938e11i		−	0.528646i
$903$	4.86433e11	−	9.84786e10i	0.731597	−	0.148112i
$904$	1.89085e12			2.83129
$905$		−	9.42210e11i		−	1.40460i
$906$	−1.69377e11	−	8.36637e11i	−0.251387	−	1.24172i
$907$	−5.61984e11			−0.830415			−0.415207	−	0.909727i	$-0.636291\pi$
$907$	−5.61984e11			−0.830415			−0.415207	+	0.909727i	$0.636291\pi$
$908$		−	1.14393e12i		−	1.68289i
$909$	8.54498e10	+	2.02389e11i	0.125157	+	0.296436i
$910$	−1.01401e12			−1.47868
$911$			6.15219e11i			0.893215i	0.894730	+	0.446607i	$0.147368\pi$
$911$			6.15219e11i			0.893215i	−0.894730	+	0.446607i	$0.852632\pi$
$912$	2.63366e12	−	5.33185e11i	3.80698	−	0.770724i
$913$	−3.17503e10			−0.0456945
$914$			3.90832e11i			0.560022i
$915$	−8.96782e10	−	4.42964e11i	−0.127939	−	0.631951i
$916$	−5.15945e11			−0.732860
$917$		−	2.49195e10i		−	0.0352422i
$918$	6.57911e11	−	4.49379e11i	0.926395	−	0.632764i
$919$	−1.82507e11			−0.255868			−0.127934	−	0.991783i	$-0.540835\pi$
$919$	−1.82507e11			−0.255868			−0.127934	+	0.991783i	$0.540835\pi$
$920$		−	1.10573e12i		−	1.54347i
$921$	5.18462e11	−	1.04963e11i	0.720574	−	0.145880i
$922$	−7.73949e11			−1.07100
$923$			1.69251e12i			2.33198i
$924$	−6.12006e10	−	3.02299e11i	−0.0839592	−	0.414715i
$925$	−2.02836e10			−0.0277063
$926$			8.37440e11i			1.13896i
$927$	5.78804e11	−	2.44374e11i	0.783813	−	0.330930i
$928$	−4.55952e12			−6.14791
$929$		−	1.24677e12i		−	1.67388i	−0.547296	−	0.836939i	$-0.684343\pi$
$929$		−	1.24677e12i		−	1.67388i	0.547296	−	0.836939i	$-0.315657\pi$
$930$	1.97073e12	−	3.98975e11i	2.63448	−	0.533352i
$931$	−6.02685e11			−0.802217
$932$		−	7.37021e11i		−	0.976824i
$933$	1.74160e11	+	8.60261e11i	0.229838	+	1.13528i
$934$	4.29413e11			0.564271
$935$		−	1.41606e11i		−	0.185283i
$936$	−1.35179e12	−	3.20174e12i	−1.76119	−	4.17141i
$937$	4.52083e11			0.586489			0.293244	−	0.956037i	$-0.405265\pi$
$937$	4.52083e11			0.586489			0.293244	+	0.956037i	$0.405265\pi$
$938$			9.61173e10i			0.124162i
$939$	−8.54908e11	+	1.73076e11i	−1.09966	+	0.222626i
$940$	1.80348e12			2.30994
$941$		−	1.05326e12i		−	1.34331i	−0.740863	−	0.671656i	$-0.765583\pi$
$941$		−	1.05326e12i		−	1.34331i	0.740863	−	0.671656i	$-0.234417\pi$
$942$	−1.64142e11	−	8.10777e11i	−0.208457	−	1.02967i
$943$	3.28256e11			0.415112
$944$		−	4.10446e11i		−	0.516854i
$945$	2.47293e11	+	3.62048e11i	0.310087	+	0.453982i
$946$	6.61495e11			0.825966
$947$			1.18082e12i			1.46820i	0.679041	+	0.734100i	$0.262396\pi$
$947$			1.18082e12i			1.46820i	−0.679041	+	0.734100i	$0.737604\pi$
$948$	−2.94386e12	+	5.95986e11i	−3.64488	+	0.737908i
$949$	3.81995e11			0.470970
$950$			1.81576e11i			0.222928i
$951$	4.99688e10	+	2.46820e11i	0.0610909	+	0.301757i
$952$	8.11281e11			0.987696
$953$		−	1.23786e12i		−	1.50072i	−0.661030	−	0.750360i	$-0.729880\pi$
$953$		−	1.23786e12i		−	1.50072i	0.661030	−	0.750360i	$-0.270120\pi$
$954$	−1.36377e12	+	5.75792e11i	−1.64645	+	0.695140i
$955$	8.33884e11			1.00252
$956$		−	2.41018e12i		−	2.88547i
$957$	−4.32898e11	+	8.76404e10i	−0.516105	+	0.104486i
$958$	−9.54368e11			−1.13306
$959$		−	1.73496e11i		−	0.205123i
$960$	5.73779e11	+	2.83417e12i	0.675553	+	3.33688i
$961$	6.60778e11			0.774751
$962$			6.06710e11i			0.708404i
$963$	8.33987e10	+	1.97531e11i	0.0969737	+	0.229684i
$964$	−1.37237e12			−1.58915
$965$			4.71477e11i			0.543690i
$966$	3.89240e11	−	7.88018e10i	0.447002	−	0.0904957i
$967$	−7.22994e11			−0.826854			−0.413427	−	0.910537i	$-0.635668\pi$
$967$	−7.22994e11			−0.826854			−0.413427	+	0.910537i	$0.635668\pi$
$968$		−	2.57901e11i		−	0.293732i
$969$	1.12915e11	+	5.57742e11i	0.128073	+	0.632613i
$970$	−2.11828e12			−2.39275
$971$			1.08875e12i			1.22476i	0.790565	+	0.612378i	$0.209787\pi$
$971$			1.08875e12i			1.22476i	−0.790565	+	0.612378i	$0.790213\pi$
$972$	−1.29672e12	+	2.01399e12i	−1.45272	+	2.25628i
$973$	−1.60927e11			−0.179547
$974$		−	7.18430e11i		−	0.798268i
$975$	1.30570e11	−	2.64339e10i	0.144486	−	0.0292512i
$976$	1.95768e12			2.15746
$977$		−	3.30165e11i		−	0.362370i	−0.983449	−	0.181185i	$-0.942007\pi$
$977$		−	3.30165e11i		−	0.362370i	0.983449	−	0.181185i	$-0.0579933\pi$
$978$	5.22813e10	+	2.58243e11i	0.0571467	+	0.282275i
$979$	1.98226e11			0.215789
$980$		−	1.89047e12i		−	2.04958i
$981$	1.27476e12	−	5.38210e11i	1.37642	−	0.581133i
$982$	−7.09268e11			−0.762719
$983$		−	1.00744e12i		−	1.07896i	−0.841999	−	0.539479i	$-0.818621\pi$
$983$		−	1.00744e12i		−	1.07896i	0.841999	−	0.539479i	$-0.181379\pi$
$984$	−2.71227e12	+	5.49100e11i	−2.89303	+	0.585694i
$985$	−1.20105e12			−1.27590
$986$		−	1.85186e12i		−	1.95930i
$987$	8.06326e10	+	3.98283e11i	0.0849654	+	0.419685i
$988$	3.95672e12			4.15249
$989$			6.20508e11i			0.648578i
$990$	2.27299e11	+	5.38361e11i	0.236623	+	0.560445i
$991$	−6.00590e11			−0.622707			−0.311353	−	0.950294i	$-0.600782\pi$
$991$	−6.00590e11			−0.622707			−0.311353	+	0.950294i	$0.600782\pi$
$992$			4.54136e12i			4.68964i
$993$	1.72533e12	−	3.49293e11i	1.77449	−	0.359247i
$994$	1.63045e12			1.67018
$995$			1.53698e12i			1.56811i
$996$	7.94137e10	+	3.92263e11i	0.0806971	+	0.398602i
$997$	−5.65908e10			−0.0572750			−0.0286375	−	0.999590i	$-0.509117\pi$
$997$	−5.65908e10			−0.0572750			−0.0286375	+	0.999590i	$0.509117\pi$
$998$		−	4.31280e11i		−	0.434748i
$999$	2.16624e11	−	1.47962e11i	0.217492	−	0.148556i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	33.9.b.a.23.1	✓	26
3.2	odd	2	inner	33.9.b.a.23.26	yes	26

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.9.b.a.23.1	✓	26	1.1	even	1	trivial
33.9.b.a.23.26	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)

\(f(q)\)	\(=\)	\(q-30.7079i q^{2} +(79.3894 - 16.0724i) q^{3} -686.976 q^{4} -657.051i q^{5} +(-493.550 - 2437.88i) q^{6} -1255.62 q^{7} +13234.4i q^{8} +(6044.35 - 2551.96i) q^{9} +O(q^{10})\)	\(q-30.7079i q^{2} +(79.3894 - 16.0724i) q^{3} -686.976 q^{4} -657.051i q^{5} +(-493.550 - 2437.88i) q^{6} -1255.62 q^{7} +13234.4i q^{8} +(6044.35 - 2551.96i) q^{9} -20176.7 q^{10} -4414.43i q^{11} +(-54538.6 + 11041.4i) q^{12} -40025.1 q^{13} +38557.5i q^{14} +(-10560.4 - 52162.9i) q^{15} +230534. q^{16} +48821.2i q^{17} +(-78365.3 - 185610. i) q^{18} +143900. q^{19} +451378. i q^{20} +(-99683.1 + 20180.9i) q^{21} -135558. q^{22} -127159. i q^{23} +(212708. + 1.05067e6i) q^{24} -41091.1 q^{25} +1.22909e6i q^{26} +(438842. - 299746. i) q^{27} +862582. q^{28} -1.23523e6i q^{29} +(-1.60181e6 + 324288. i) q^{30} -1.23031e6 q^{31} -3.69123e6i q^{32} +(-70950.5 - 350459. i) q^{33} +1.49920e6 q^{34} +825008. i q^{35} +(-4.15233e6 + 1.75313e6i) q^{36} +493626. q^{37} -4.41888e6i q^{38} +(-3.17757e6 + 643300. i) q^{39} +8.69566e6 q^{40} +2.58147e6i q^{41} +(619713. + 3.06106e6i) q^{42} -4.87980e6 q^{43} +3.03261e6i q^{44} +(-1.67677e6 - 3.97145e6i) q^{45} -3.90478e6 q^{46} -3.99550e6i q^{47} +(1.83020e7 - 3.70524e6i) q^{48} -4.18821e6 q^{49} +1.26182e6i q^{50} +(784675. + 3.87589e6i) q^{51} +2.74963e7 q^{52} -7.34753e6i q^{53} +(-9.20457e6 - 1.34759e7i) q^{54} -2.90050e6 q^{55} -1.66174e7i q^{56} +(1.14242e7 - 2.31282e6i) q^{57} -3.79314e7 q^{58} -1.78041e6i q^{59} +(7.25474e6 + 3.58347e7i) q^{60} +8.49193e6 q^{61} +3.77803e7i q^{62} +(-7.58942e6 + 3.20430e6i) q^{63} -5.43331e7 q^{64} +2.62985e7i q^{65} +(-1.07619e7 + 2.17874e6i) q^{66} +2.49283e6 q^{67} -3.35390e7i q^{68} +(-2.04375e6 - 1.00950e7i) q^{69} +2.53343e7 q^{70} -4.22862e7i q^{71} +(3.37736e7 + 7.99933e7i) q^{72} -9.54389e6 q^{73} -1.51582e7i q^{74} +(-3.26220e6 + 660433. i) q^{75} -9.88560e7 q^{76} +5.54285e6i q^{77} +(1.97544e7 + 9.75766e7i) q^{78} +5.39775e7 q^{79} -1.51473e8i q^{80} +(3.00217e7 - 3.08499e7i) q^{81} +7.92715e7 q^{82} -7.19238e6i q^{83} +(6.84799e7 - 1.38638e7i) q^{84} +3.20781e7 q^{85} +1.49848e8i q^{86} +(-1.98532e7 - 9.80644e7i) q^{87} +5.84222e7 q^{88} +4.49042e7i q^{89} +(-1.21955e8 + 5.14900e7i) q^{90} +5.02564e7 q^{91} +8.73549e7i q^{92} +(-9.76738e7 + 1.97741e7i) q^{93} -1.22693e8 q^{94} -9.45498e7i q^{95} +(-5.93269e7 - 2.93044e8i) q^{96} +1.04987e8 q^{97} +1.28611e8i q^{98} +(-1.12654e7 - 2.66824e7i) 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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