LMFDB - Embedded newform 11.13.b.b.10.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [11,13,Mod(10,11)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(11, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 13, names="a")

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

chi := DirichletCharacter("11.10");

S:= CuspForms(chi, 13);

N := Newforms(S);

Level:	$ N $	$=$	$ 11 $
Weight:	$ k $	$=$	$ 13 $
Character orbit:	$[\chi]$	$=$	11.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:	$10.0539319900$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + 30654x^{8} + 318945120x^{6} + 1305642637440x^{4} + 2049564619929600x^{2} + 957721368231936000 $ x^10 + 30654x^8 + 318945120x^6 + 1305642637440x^4 + 2049564619929600x^2 + 957721368231936000
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{16}\cdot 3^{3}\cdot 11^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			10.5
Root			$-28.3748i$ of defining polynomial
Character	$\chi$	$=$	11.10
Dual form			11.13.b.b.10.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-28.3748i q^{2} +796.959 q^{3} +3290.87 q^{4} +5720.10 q^{5} -22613.5i q^{6} +202583. i q^{7} -209601. i q^{8} +103703. q^{9} +O(q^{10})$	\(q-28.3748i q^{2} +796.959 q^{3} +3290.87 q^{4} +5720.10 q^{5} -22613.5i q^{6} +202583. i q^{7} -209601. i q^{8} +103703. q^{9} -162307. i q^{10} +(1.72001e6 + 424237. i) q^{11} +2.62269e6 q^{12} -6.56459e6i q^{13} +5.74825e6 q^{14} +4.55869e6 q^{15} +7.53204e6 q^{16} +2.59040e7i q^{17} -2.94254e6i q^{18} -7.15644e7i q^{19} +1.88241e7 q^{20} +1.61451e8i q^{21} +(1.20376e7 - 4.88050e7i) q^{22} -9.33277e7 q^{23} -1.67043e8i q^{24} -2.11421e8 q^{25} -1.86269e8 q^{26} -3.40890e8 q^{27} +6.66676e8i q^{28} -6.46246e7i q^{29} -1.29352e8i q^{30} +5.07265e8 q^{31} -1.07224e9i q^{32} +(1.37078e9 + 3.38100e8i) q^{33} +7.35021e8 q^{34} +1.15880e9i q^{35} +3.41272e8 q^{36} +5.29795e8 q^{37} -2.03062e9 q^{38} -5.23171e9i q^{39} -1.19894e9i q^{40} +4.97853e9i q^{41} +4.58112e9 q^{42} -1.97317e9i q^{43} +(5.66035e9 + 1.39611e9i) q^{44} +5.93190e8 q^{45} +2.64815e9i q^{46} -1.74890e10 q^{47} +6.00272e9 q^{48} -2.71987e10 q^{49} +5.99903e9i q^{50} +2.06445e10i q^{51} -2.16032e10i q^{52} -1.99556e10 q^{53} +9.67267e9i q^{54} +(9.83866e9 + 2.42668e9i) q^{55} +4.24616e10 q^{56} -5.70339e10i q^{57} -1.83371e9 q^{58} +2.01794e10 q^{59} +1.50021e10 q^{60} +5.39501e10i q^{61} -1.43935e10i q^{62} +2.10084e10i q^{63} +4.26511e8 q^{64} -3.75501e10i q^{65} +(9.59350e9 - 3.88956e10i) q^{66} +7.88695e10 q^{67} +8.52469e10i q^{68} -7.43784e10 q^{69} +3.28806e10 q^{70} +4.09323e10 q^{71} -2.17362e10i q^{72} -2.05886e10i q^{73} -1.50328e10i q^{74} -1.68494e11 q^{75} -2.35509e11i q^{76} +(-8.59434e10 + 3.48446e11i) q^{77} -1.48449e11 q^{78} -9.65135e10i q^{79} +4.30840e10 q^{80} -3.26787e11 q^{81} +1.41265e11 q^{82} -2.46796e11i q^{83} +5.31313e11i q^{84} +1.48174e11i q^{85} -5.59881e10 q^{86} -5.15032e10i q^{87} +(8.89205e10 - 3.60517e11i) q^{88} -1.49006e11 q^{89} -1.68316e10i q^{90} +1.32988e12 q^{91} -3.07130e11 q^{92} +4.04270e11 q^{93} +4.96247e11i q^{94} -4.09356e11i q^{95} -8.54535e11i q^{96} +5.12691e11 q^{97} +7.71757e11i q^{98} +(1.78370e11 + 4.39945e10i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 2436 q^{3} - 20348 q^{4} + 26492 q^{5} + 756294 q^{9}+O(q^{10}) $ 10 * q + 2436 * q^3 - 20348 * q^4 + 26492 * q^5 + 756294 * q^9	\( 10 q + 2436 q^{3} - 20348 q^{4} + 26492 q^{5} + 756294 q^{9} - 1716374 q^{11} - 8491644 q^{12} - 15139368 q^{14} + 9632184 q^{15} + 17974408 q^{16} - 125399668 q^{20} + 83533560 q^{22} + 330297476 q^{23} - 438477018 q^{25} - 372191832 q^{26} + 1665774072 q^{27} - 1921955548 q^{31} - 2301728484 q^{33} + 7677299352 q^{34} - 14333366928 q^{36} + 1788323996 q^{37} + 11254769640 q^{38} - 32091748680 q^{42} + 6124969708 q^{44} + 43304121996 q^{45} - 24975510124 q^{47} + 32578826856 q^{48} - 6325710998 q^{49} - 16325502124 q^{53} + 14298843812 q^{55} + 82892128176 q^{56} - 84518430720 q^{58} + 62339390564 q^{59} - 286034518116 q^{60} + 95192926864 q^{64} + 322939363560 q^{66} - 90035301244 q^{67} + 346118875824 q^{69} - 382808641560 q^{70} - 359910119740 q^{71} + 14209300764 q^{75} + 425991883680 q^{77} - 483427126680 q^{78} + 1147768798712 q^{80} - 515542099806 q^{81} + 625030365960 q^{82} - 1219447545552 q^{86} + 134692485840 q^{88} + 670996780412 q^{89} + 1356772643808 q^{91} - 3181666532764 q^{92} + 1928296959312 q^{93} - 6250704684964 q^{97} - 1402418596722 q^{99}+O(q^{100}) \) 10 * q + 2436 * q^3 - 20348 * q^4 + 26492 * q^5 + 756294 * q^9 - 1716374 * q^11 - 8491644 * q^12 - 15139368 * q^14 + 9632184 * q^15 + 17974408 * q^16 - 125399668 * q^20 + 83533560 * q^22 + 330297476 * q^23 - 438477018 * q^25 - 372191832 * q^26 + 1665774072 * q^27 - 1921955548 * q^31 - 2301728484 * q^33 + 7677299352 * q^34 - 14333366928 * q^36 + 1788323996 * q^37 + 11254769640 * q^38 - 32091748680 * q^42 + 6124969708 * q^44 + 43304121996 * q^45 - 24975510124 * q^47 + 32578826856 * q^48 - 6325710998 * q^49 - 16325502124 * q^53 + 14298843812 * q^55 + 82892128176 * q^56 - 84518430720 * q^58 + 62339390564 * q^59 - 286034518116 * q^60 + 95192926864 * q^64 + 322939363560 * q^66 - 90035301244 * q^67 + 346118875824 * q^69 - 382808641560 * q^70 - 359910119740 * q^71 + 14209300764 * q^75 + 425991883680 * q^77 - 483427126680 * q^78 + 1147768798712 * q^80 - 515542099806 * q^81 + 625030365960 * q^82 - 1219447545552 * q^86 + 134692485840 * q^88 + 670996780412 * q^89 + 1356772643808 * q^91 - 3181666532764 * q^92 + 1928296959312 * q^93 - 6250704684964 * q^97 - 1402418596722 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/11\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$-1$

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 $

$2$		−	28.3748i		−	0.443356i	−0.975120	−	0.221678i	$-0.928847\pi$
$2$		−	28.3748i		−	0.443356i	0.975120	−	0.221678i	$-0.0711534\pi$
$3$	796.959			1.09322			0.546611	−	0.837387i	$-0.315918\pi$
$3$	796.959			1.09322			0.546611	+	0.837387i	$0.315918\pi$
$4$	3290.87			0.803436
$5$	5720.10			0.366087			0.183043	−	0.983105i	$-0.441405\pi$
$5$	5720.10			0.366087			0.183043	+	0.983105i	$0.441405\pi$
$6$		−	22613.5i		−	0.484686i
$7$			202583.i			1.72193i	0.508665	+	0.860965i	$0.330139\pi$
$7$			202583.i			1.72193i	−0.508665	+	0.860965i	$0.669861\pi$
$8$		−	209601.i		−	0.799564i
$9$	103703.			0.195135
$10$		−	162307.i		−	0.162307i
$11$	1.72001e6	+	424237.i	0.970904	+	0.239471i
$11$	1.72001e6	+	424237.i	0.970904	+	0.239471i
$12$	2.62269e6			0.878334
$13$		−	6.56459e6i		−	1.36003i	−0.733200	−	0.680013i	$-0.761974\pi$
$13$		−	6.56459e6i		−	1.36003i	0.733200	−	0.680013i	$-0.238026\pi$
$14$	5.74825e6			0.763427
$15$	4.55869e6			0.400214
$16$	7.53204e6			0.448944
$17$			2.59040e7i			1.07318i	0.843842	+	0.536592i	$0.180288\pi$
$17$			2.59040e7i			1.07318i	−0.843842	+	0.536592i	$0.819712\pi$
$18$		−	2.94254e6i		−	0.0865142i
$19$		−	7.15644e7i		−	1.52116i	−0.649243	−	0.760581i	$-0.724914\pi$
$19$		−	7.15644e7i		−	1.52116i	0.649243	−	0.760581i	$-0.275086\pi$
$20$	1.88241e7			0.294127
$21$			1.61451e8i			1.88245i
$22$	1.20376e7	−	4.88050e7i	0.106171	−	0.430456i
$23$	−9.33277e7			−0.630440			−0.315220	−	0.949019i	$-0.602078\pi$
$23$	−9.33277e7			−0.630440			−0.315220	+	0.949019i	$0.602078\pi$
$24$		−	1.67043e8i		−	0.874101i
$25$	−2.11421e8			−0.865981
$26$	−1.86269e8			−0.602976
$27$	−3.40890e8			−0.879896
$28$			6.66676e8i			1.38346i
$29$		−	6.46246e7i		−	0.108645i	−0.998523	−	0.0543225i	$-0.982700\pi$
$29$		−	6.46246e7i		−	0.108645i	0.998523	−	0.0543225i	$-0.0172999\pi$
$30$		−	1.29352e8i		−	0.177437i
$31$	5.07265e8			0.571564			0.285782	−	0.958295i	$-0.407747\pi$
$31$	5.07265e8			0.571564			0.285782	+	0.958295i	$0.407747\pi$
$32$		−	1.07224e9i		−	0.998606i
$33$	1.37078e9	+	3.38100e8i	1.06141	+	0.261795i
$34$	7.35021e8			0.475802
$35$			1.15880e9i			0.630375i
$36$	3.41272e8			0.156778
$37$	5.29795e8			0.206489			0.103245	−	0.994656i	$-0.467078\pi$
$37$	5.29795e8			0.206489			0.103245	+	0.994656i	$0.467078\pi$
$38$	−2.03062e9			−0.674416
$39$		−	5.23171e9i		−	1.48681i
$40$		−	1.19894e9i		−	0.292710i
$41$			4.97853e9i			1.04809i	0.851691	+	0.524044i	$0.175577\pi$
$41$			4.97853e9i			1.04809i	−0.851691	+	0.524044i	$0.824423\pi$
$42$	4.58112e9			0.834596
$43$		−	1.97317e9i		−	0.312142i	−0.987746	−	0.156071i	$-0.950117\pi$
$43$		−	1.97317e9i		−	0.312142i	0.987746	−	0.156071i	$-0.0498829\pi$
$44$	5.66035e9	+	1.39611e9i	0.780058	+	0.192399i
$45$	5.93190e8			0.0714362
$46$			2.64815e9i			0.279509i
$47$	−1.74890e10			−1.62248			−0.811239	−	0.584715i	$-0.801206\pi$
$47$	−1.74890e10			−1.62248			−0.811239	+	0.584715i	$0.801206\pi$
$48$	6.00272e9			0.490796
$49$	−2.71987e10			−1.96504
$50$			5.99903e9i			0.383938i
$51$			2.06445e10i			1.17323i
$52$		−	2.16032e10i		−	1.09269i
$53$	−1.99556e10			−0.900348			−0.450174	−	0.892941i	$-0.648638\pi$
$53$	−1.99556e10			−0.900348			−0.450174	+	0.892941i	$0.648638\pi$
$54$			9.67267e9i			0.390107i
$55$	9.83866e9	+	2.42668e9i	0.355435	+	0.0876670i
$56$	4.24616e10			1.37679
$57$		−	5.70339e10i		−	1.66297i
$58$	−1.83371e9			−0.0481684
$59$	2.01794e10			0.478407			0.239203	−	0.970970i	$-0.423114\pi$
$59$	2.01794e10			0.478407			0.239203	+	0.970970i	$0.423114\pi$
$60$	1.50021e10			0.321546
$61$			5.39501e10i			1.04716i	0.851976	+	0.523581i	$0.175404\pi$
$61$			5.39501e10i			1.04716i	−0.851976	+	0.523581i	$0.824596\pi$
$62$		−	1.43935e10i		−	0.253406i
$63$			2.10084e10i			0.336008i
$64$	4.26511e8			0.00620656
$65$		−	3.75501e10i		−	0.497887i
$66$	9.59350e9	−	3.88956e10i	0.116068	−	0.470584i
$67$	7.88695e10			0.871887			0.435944	−	0.899974i	$-0.356415\pi$
$67$	7.88695e10			0.871887			0.435944	+	0.899974i	$0.356415\pi$
$68$			8.52469e10i			0.862234i
$69$	−7.43784e10			−0.689211
$70$	3.28806e10			0.279480
$71$	4.09323e10			0.319533			0.159767	−	0.987155i	$-0.448926\pi$
$71$	4.09323e10			0.319533			0.159767	+	0.987155i	$0.448926\pi$
$72$		−	2.17362e10i		−	0.156023i
$73$		−	2.05886e10i		−	0.136047i	−0.997684	−	0.0680237i	$-0.978331\pi$
$73$		−	2.05886e10i		−	0.136047i	0.997684	−	0.0680237i	$-0.0216693\pi$
$74$		−	1.50328e10i		−	0.0915482i
$75$	−1.68494e11			−0.946709
$76$		−	2.35509e11i		−	1.22216i
$77$	−8.59434e10	+	3.48446e11i	−0.412352	+	1.67183i
$78$	−1.48449e11			−0.659187
$79$		−	9.65135e10i		−	0.397032i	−0.980098	−	0.198516i	$-0.936388\pi$
$79$		−	9.65135e10i		−	0.397032i	0.980098	−	0.198516i	$-0.0636122\pi$
$80$	4.30840e10			0.164352
$81$	−3.26787e11			−1.15706
$82$	1.41265e11			0.464676
$83$		−	2.46796e11i		−	0.754865i	−0.926037	−	0.377433i	$-0.876807\pi$
$83$		−	2.46796e11i		−	0.754865i	0.926037	−	0.377433i	$-0.123193\pi$
$84$			5.31313e11i			1.51243i
$85$			1.48174e11i			0.392878i
$86$	−5.59881e10			−0.138390
$87$		−	5.15032e10i		−	0.118773i
$88$	8.89205e10	−	3.60517e11i	0.191472	−	0.776299i
$89$	−1.49006e11			−0.299822			−0.149911	−	0.988700i	$-0.547899\pi$
$89$	−1.49006e11			−0.299822			−0.149911	+	0.988700i	$0.547899\pi$
$90$		−	1.68316e10i		−	0.0316717i
$91$	1.32988e12			2.34187
$92$	−3.07130e11			−0.506518
$93$	4.04270e11			0.624847
$94$			4.96247e11i			0.719335i
$95$		−	4.09356e11i		−	0.556877i
$96$		−	8.54535e11i		−	1.09170i
$97$	5.12691e11			0.615496			0.307748	−	0.951468i	$-0.400425\pi$
$97$	5.12691e11			0.615496			0.307748	+	0.951468i	$0.400425\pi$
$98$			7.71757e11i			0.871212i
$99$	1.78370e11	+	4.39945e10i	0.189457	+	0.0467291i
$100$	−6.95760e11			−0.695760
$101$		−	1.42552e12i		−	1.34290i	−0.741049	−	0.671451i	$-0.765671\pi$
$101$		−	1.42552e12i		−	1.34290i	0.741049	−	0.671451i	$-0.234329\pi$
$102$	5.85782e11			0.520157
$103$	−1.81395e11			−0.151916			−0.0759578	−	0.997111i	$-0.524201\pi$
$103$	−1.81395e11			−0.151916			−0.0759578	+	0.997111i	$0.524201\pi$
$104$	−1.37594e12			−1.08743
$105$			9.23514e11i			0.689140i
$106$			5.66237e11i			0.399175i
$107$			1.46510e12i			0.976261i	0.872771	+	0.488130i	$0.162321\pi$
$107$			1.46510e12i			0.976261i	−0.872771	+	0.488130i	$0.837679\pi$
$108$	−1.12183e12			−0.706940
$109$		−	1.45317e12i		−	0.866478i	−0.901279	−	0.433239i	$-0.857371\pi$
$109$		−	1.45317e12i		−	0.866478i	0.901279	−	0.433239i	$-0.142629\pi$
$110$	6.88565e10	−	2.79170e11i	0.0388677	−	0.157584i
$111$	4.22225e11			0.225739
$112$			1.52586e12i			0.773050i
$113$	1.39367e12			0.669406			0.334703	−	0.942324i	$-0.391364\pi$
$113$	1.39367e12			0.669406			0.334703	+	0.942324i	$0.391364\pi$
$114$	−1.61832e12			−0.737287
$115$	−5.33844e11			−0.230795
$116$		−	2.12671e11i		−	0.0872893i
$117$		−	6.80765e11i		−	0.265389i
$118$		−	5.72587e11i		−	0.212104i
$119$	−5.24772e12			−1.84795
$120$		−	9.55505e11i		−	0.319997i
$121$	2.77847e12	+	1.45939e12i	0.885307	+	0.465006i
$122$	1.53082e12			0.464265
$123$			3.96768e12i			1.14579i
$124$	1.66935e12			0.459215
$125$	−2.60586e12			−0.683110
$126$	5.96109e11			0.148971
$127$		−	6.83501e12i		−	1.62898i	−0.580175	−	0.814492i	$-0.697016\pi$
$127$		−	6.83501e12i		−	1.62898i	0.580175	−	0.814492i	$-0.302984\pi$
$128$		−	4.40402e12i		−	1.00136i
$129$		−	1.57253e12i		−	0.341241i
$130$	−1.06548e12			−0.220741
$131$			6.90567e12i			1.36640i	0.730231	+	0.683200i	$0.239412\pi$
$131$			6.90567e12i			1.36640i	−0.730231	+	0.683200i	$0.760588\pi$
$132$	4.51107e12	+	1.11264e12i	0.852777	+	0.210335i
$133$	1.44978e13			2.61933
$134$		−	2.23790e12i		−	0.386556i
$135$	−1.94993e12			−0.322118
$136$	5.42951e12			0.858078
$137$	−1.70381e12			−0.257690			−0.128845	−	0.991665i	$-0.541127\pi$
$137$	−1.70381e12			−0.257690			−0.128845	+	0.991665i	$0.541127\pi$
$138$			2.11047e12i			0.305566i
$139$			3.62462e12i			0.502544i	0.967917	+	0.251272i	$0.0808489\pi$
$139$			3.62462e12i			0.502544i	−0.967917	+	0.251272i	$0.919151\pi$
$140$			3.81345e12i			0.506466i
$141$	−1.39380e13			−1.77373
$142$		−	1.16145e12i		−	0.141667i
$143$	2.78494e12	−	1.12912e13i	0.325687	−	1.32045i
$144$	7.81092e11			0.0876047
$145$		−	3.69659e11i		−	0.0397735i
$146$	−5.84198e11			−0.0603174
$147$	−2.16762e13			−2.14823
$148$	1.74349e12			0.165901
$149$			1.25488e13i			1.14679i	0.819279	+	0.573395i	$0.194374\pi$
$149$			1.25488e13i			1.14679i	−0.819279	+	0.573395i	$0.805626\pi$
$150$			4.78098e12i			0.419729i
$151$		−	3.55541e12i		−	0.299935i	−0.988691	−	0.149968i	$-0.952083\pi$
$151$		−	3.55541e12i		−	0.299935i	0.988691	−	0.149968i	$-0.0479170\pi$
$152$	−1.50000e13			−1.21627
$153$			2.68632e12i			0.209415i
$154$	9.88708e12	+	2.43862e12i	0.741214	+	0.182819i
$155$	2.90161e12			0.209242
$156$		−	1.72169e13i		−	1.19456i
$157$	2.60390e13			1.73871			0.869354	−	0.494190i	$-0.164535\pi$
$157$	2.60390e13			1.73871			0.869354	+	0.494190i	$0.164535\pi$
$158$	−2.73855e12			−0.176026
$159$	−1.59038e13			−0.984281
$160$		−	6.13335e12i		−	0.365576i
$161$		−	1.89066e13i		−	1.08557i
$162$			9.27251e12i			0.512988i
$163$	−1.49507e13			−0.797142			−0.398571	−	0.917138i	$-0.630494\pi$
$163$	−1.49507e13			−0.797142			−0.398571	+	0.917138i	$0.630494\pi$
$164$			1.63837e13i			0.842071i
$165$	7.84101e12	+	1.93396e12i	0.388569	+	0.0958396i
$166$	−7.00278e12			−0.334674
$167$			4.23695e13i			1.95323i	0.214985	+	0.976617i	$0.431030\pi$
$167$			4.23695e13i			1.95323i	−0.214985	+	0.976617i	$0.568970\pi$
$168$	3.38402e13			1.50514
$169$	−1.97957e13			−0.849673
$170$	4.20440e12			0.174185
$171$		−	7.42142e12i		−	0.296832i
$172$		−	6.49344e12i		−	0.250786i
$173$		−	1.81846e13i		−	0.678309i	−0.940731	−	0.339154i	$-0.889859\pi$
$173$		−	1.81846e13i		−	0.678309i	0.940731	−	0.339154i	$-0.110141\pi$
$174$	−1.46139e12			−0.0526588
$175$		−	4.28304e13i		−	1.49116i
$176$	1.29552e13	+	3.19537e12i	0.435882	+	0.107509i
$177$	1.60822e13			0.523005
$178$			4.22801e12i			0.132928i
$179$	6.49766e13			1.97533			0.987663	−	0.156595i	$-0.0500516\pi$
$179$	6.49766e13			1.97533			0.987663	+	0.156595i	$0.0500516\pi$
$180$	1.95211e12			0.0573944
$181$	4.20118e12			0.119481			0.0597406	−	0.998214i	$-0.480973\pi$
$181$	4.20118e12			0.119481			0.0597406	+	0.998214i	$0.480973\pi$
$182$		−	3.77349e13i		−	1.03828i
$183$			4.29961e13i			1.14478i
$184$			1.95616e13i			0.504077i
$185$	3.03048e12			0.0755929
$186$		−	1.14711e13i		−	0.277029i
$187$	−1.09895e13	+	4.45553e13i	−0.256996	+	1.04196i
$188$	−5.75542e13			−1.30356
$189$		−	6.90586e13i		−	1.51512i
$190$	−1.16154e13			−0.246895
$191$	−6.83704e13			−1.40821			−0.704106	−	0.710095i	$-0.748652\pi$
$191$	−6.83704e13			−1.40821			−0.704106	+	0.710095i	$0.748652\pi$
$192$	3.39912e11			0.00678515
$193$			4.94523e13i			0.956847i	0.878129	+	0.478423i	$0.158792\pi$
$193$			4.94523e13i			0.956847i	−0.878129	+	0.478423i	$0.841208\pi$
$194$		−	1.45475e13i		−	0.272884i
$195$		−	2.99259e13i		−	0.544302i
$196$	−8.95074e13			−1.57878
$197$			4.92155e13i			0.841986i	0.907064	+	0.420993i	$0.138318\pi$
$197$			4.92155e13i			0.841986i	−0.907064	+	0.420993i	$0.861682\pi$
$198$	1.24833e12	−	5.06121e12i	0.0207176	−	0.0839969i
$199$	3.73073e13			0.600724			0.300362	−	0.953825i	$-0.402893\pi$
$199$	3.73073e13			0.600724			0.300362	+	0.953825i	$0.402893\pi$
$200$			4.43140e13i			0.692407i
$201$	6.28558e13			0.953167
$202$	−4.04488e13			−0.595384
$203$	1.30919e13			0.187079
$204$			6.79383e13i			0.942613i
$205$			2.84777e13i			0.383691i
$206$			5.14705e12i			0.0673527i
$207$	−9.67833e12			−0.123021
$208$		−	4.94447e13i		−	0.610576i
$209$	3.03603e13	−	1.23092e14i	0.364274	−	1.47690i
$210$	2.62045e13			0.305534
$211$		−	9.99441e13i		−	1.13256i	−0.824212	−	0.566282i	$-0.808381\pi$
$211$		−	9.99441e13i		−	1.13256i	0.824212	−	0.566282i	$-0.191619\pi$
$212$	−6.56715e13			−0.723372
$213$	3.26214e13			0.349321
$214$	4.15720e13			0.432831
$215$		−	1.12867e13i		−	0.114271i
$216$			7.14508e13i			0.703533i
$217$			1.02763e14i			0.984193i
$218$	−4.12334e13			−0.384158
$219$		−	1.64083e13i		−	0.148730i
$220$	3.23778e13	+	7.98589e12i	0.285569	+	0.0704348i
$221$	1.70049e14			1.45956
$222$		−	1.19805e13i		−	0.100083i
$223$	−1.90991e14			−1.55304			−0.776522	−	0.630090i	$-0.783018\pi$
$223$	−1.90991e14			−1.55304			−0.776522	+	0.630090i	$0.783018\pi$
$224$	2.17219e14			1.71953
$225$	−2.19249e13			−0.168983
$226$		−	3.95451e13i		−	0.296785i
$227$		−	1.33471e14i		−	0.975514i	−0.872980	−	0.487757i	$-0.837815\pi$
$227$		−	1.33471e14i		−	0.975514i	0.872980	−	0.487757i	$-0.162185\pi$
$228$		−	1.87691e14i		−	1.33609i
$229$	1.38292e14			0.958923			0.479461	−	0.877563i	$-0.340832\pi$
$229$	1.38292e14			0.958923			0.479461	+	0.877563i	$0.340832\pi$
$230$			1.51477e13i			0.102325i
$231$	−6.84933e13	+	2.77697e14i	−0.450792	+	1.82768i
$232$	−1.35454e13			−0.0868686
$233$			8.94554e13i			0.559076i	0.960135	+	0.279538i	$0.0901813\pi$
$233$			8.94554e13i			0.559076i	−0.960135	+	0.279538i	$0.909819\pi$
$234$	−1.93166e13			−0.117662
$235$	−1.00039e14			−0.593967
$236$	6.64080e13			0.384369
$237$		−	7.69173e13i		−	0.434044i
$238$			1.48903e14i			0.819298i
$239$			6.20606e13i			0.332988i	0.986042	+	0.166494i	$0.0532446\pi$
$239$			6.20606e13i			0.332988i	−0.986042	+	0.166494i	$0.946755\pi$
$240$	3.43362e13			0.179674
$241$		−	1.35796e14i		−	0.693080i	−0.938035	−	0.346540i	$-0.887356\pi$
$241$		−	1.35796e14i		−	0.693080i	0.938035	−	0.346540i	$-0.112644\pi$
$242$	4.14098e13	−	7.88386e13i	0.206163	−	0.392506i
$243$	−7.92731e13			−0.385024
$244$			1.77543e14i			0.841327i
$245$	−1.55579e14			−0.719375
$246$	1.12582e14			0.507994
$247$	−4.69791e14			−2.06882
$248$		−	1.06323e14i		−	0.457002i
$249$		−	1.96686e14i		−	0.825236i
$250$			7.39407e13i			0.302861i
$251$	1.05784e14			0.423037			0.211518	−	0.977374i	$-0.432159\pi$
$251$	1.05784e14			0.423037			0.211518	+	0.977374i	$0.432159\pi$
$252$			6.91360e13i			0.269961i
$253$	−1.60525e14	−	3.95931e13i	−0.612096	−	0.150972i
$254$	−1.93942e14			−0.722219
$255$			1.18088e14i			0.429503i
$256$	−1.23216e14			−0.437751
$257$	1.63502e14			0.567447			0.283724	−	0.958906i	$-0.408430\pi$
$257$	1.63502e14			0.567447			0.283724	+	0.958906i	$0.408430\pi$
$258$	−4.46203e13			−0.151291
$259$			1.07328e14i			0.355560i
$260$		−	1.23573e14i		−	0.400020i
$261$		−	6.70174e12i		−	0.0212004i
$262$	1.95947e14			0.605802
$263$			4.62791e14i			1.39846i	0.714896	+	0.699231i	$0.246474\pi$
$263$			4.62791e14i			1.39846i	−0.714896	+	0.699231i	$0.753526\pi$
$264$	7.08660e13	−	2.87317e14i	0.209322	−	0.848668i
$265$	−1.14148e14			−0.329605
$266$		−	4.11370e14i		−	1.16130i
$267$	−1.18751e14			−0.327772
$268$	2.59549e14			0.700505
$269$	5.11347e14			1.34959			0.674796	−	0.738005i	$-0.264232\pi$
$269$	5.11347e14			1.34959			0.674796	+	0.738005i	$0.264232\pi$
$270$			5.53287e13i			0.142813i
$271$		−	6.40456e13i		−	0.161687i	−0.996727	−	0.0808433i	$-0.974239\pi$
$271$		−	6.40456e13i		−	0.161687i	0.996727	−	0.0808433i	$-0.0257613\pi$
$272$			1.95110e14i			0.481800i
$273$	1.05986e15			2.56018
$274$			4.83451e13i			0.114248i
$275$	−3.63647e14	−	8.96927e13i	−0.840784	−	0.207377i
$276$	−2.44770e14			−0.553736
$277$			1.88209e13i			0.0416640i	0.999783	+	0.0208320i	$0.00663151\pi$
$277$			1.88209e13i			0.0416640i	−0.999783	+	0.0208320i	$0.993368\pi$
$278$	1.02848e14			0.222806
$279$	5.26048e13			0.111532
$280$	2.42885e14			0.504025
$281$			3.89257e14i			0.790676i	0.918536	+	0.395338i	$0.129372\pi$
$281$			3.89257e14i			0.790676i	−0.918536	+	0.395338i	$0.870628\pi$
$282$			3.95489e14i			0.786393i
$283$		−	6.47501e14i		−	1.26044i	−0.776417	−	0.630219i	$-0.782965\pi$
$283$		−	6.47501e14i		−	1.26044i	0.776417	−	0.630219i	$-0.217035\pi$
$284$	1.34703e14			0.256725
$285$		−	3.26240e14i		−	0.608790i
$286$	−3.20385e14	−	7.90221e13i	−0.585431	−	0.144395i
$287$	−1.00857e15			−1.80473
$288$		−	1.11195e14i		−	0.194863i
$289$	−8.83968e13			−0.151722
$290$	−1.04890e13			−0.0176338
$291$	4.08594e14			0.672874
$292$		−	6.77545e13i		−	0.109305i
$293$		−	1.33757e14i		−	0.211403i	−0.994398	−	0.105702i	$-0.966291\pi$
$293$		−	1.33757e14i		−	0.211403i	0.994398	−	0.105702i	$-0.0337088\pi$
$294$			6.15058e14i			0.952429i
$295$	1.15428e14			0.175138
$296$		−	1.11045e14i		−	0.165101i
$297$	−5.86336e14	−	1.44618e14i	−0.854295	−	0.210710i
$298$	3.56069e14			0.508436
$299$			6.12658e14i			0.857415i
$300$	−5.54492e14			−0.760620
$301$	3.99730e14			0.537487
$302$	−1.00884e14			−0.132978
$303$		−	1.13608e15i		−	1.46809i
$304$		−	5.39026e14i		−	0.682917i
$305$			3.08600e14i			0.383352i
$306$	7.62237e13			0.0928456
$307$			8.22723e14i			0.982706i	0.870961	+	0.491353i	$0.163497\pi$
$307$			8.22723e14i			0.982706i	−0.870961	+	0.491353i	$0.836503\pi$
$308$	−2.82829e14	+	1.14669e15i	−0.331298	+	1.34321i
$309$	−1.44565e14			−0.166077
$310$		−	8.23325e13i		−	0.0927686i
$311$	−4.75876e14			−0.525934			−0.262967	−	0.964805i	$-0.584701\pi$
$311$	−4.75876e14			−0.525934			−0.262967	+	0.964805i	$0.584701\pi$
$312$	−1.09657e15			−1.18880
$313$	9.18043e14			0.976330			0.488165	−	0.872751i	$-0.337666\pi$
$313$	9.18043e14			0.976330			0.488165	+	0.872751i	$0.337666\pi$
$314$		−	7.38851e14i		−	0.770867i
$315$			1.20170e14i			0.123008i
$316$		−	3.17613e14i		−	0.318990i
$317$	−8.76189e14			−0.863460			−0.431730	−	0.902003i	$-0.642097\pi$
$317$	−8.76189e14			−0.863460			−0.431730	+	0.902003i	$0.642097\pi$
$318$			4.51268e14i			0.436387i
$319$	2.74162e13	−	1.11155e14i	0.0260173	−	0.105484i
$320$	2.43969e12			0.00227214
$321$			1.16763e15i			1.06727i
$322$	−5.36471e14			−0.481295
$323$	1.85381e15			1.63249
$324$	−1.07541e15			−0.929621
$325$			1.38789e15i			1.17776i
$326$			4.24222e14i			0.353417i
$327$		−	1.15812e15i		−	0.947253i
$328$	1.04350e15			0.838013
$329$		−	3.54298e15i		−	2.79379i
$330$	5.48758e13	−	2.22487e14i	0.0424910	−	0.172274i
$331$	1.83282e15			1.39365			0.696824	−	0.717243i	$-0.254596\pi$
$331$	1.83282e15			1.39365			0.696824	+	0.717243i	$0.254596\pi$
$332$		−	8.12174e14i		−	0.606486i
$333$	5.49411e13			0.0402932
$334$	1.20222e15			0.865978
$335$	4.51142e14			0.319186
$336$			1.21605e15i			0.845116i
$337$			1.84655e13i			0.0126061i	0.999980	+	0.00630307i	$0.00200634\pi$
$337$			1.84655e13i			0.0126061i	−0.999980	+	0.00630307i	$0.997994\pi$
$338$			5.61700e14i			0.376707i
$339$	1.11070e15			0.731809
$340$			4.87621e14i			0.315652i
$341$	8.72504e14	+	2.15201e14i	0.554934	+	0.136873i
$342$	−2.10581e14			−0.131602
$343$		−	2.70599e15i		−	1.66173i
$344$	−4.13577e14			−0.249578
$345$	−4.25452e14			−0.252311
$346$	−5.15984e14			−0.300732
$347$			1.42233e15i			0.814746i	0.913262	+	0.407373i	$0.133555\pi$
$347$			1.42233e15i			0.814746i	−0.913262	+	0.407373i	$0.866445\pi$
$348$		−	1.69490e14i		−	0.0954266i
$349$			1.50201e15i			0.831229i	0.909541	+	0.415614i	$0.136433\pi$
$349$			1.50201e15i			0.831229i	−0.909541	+	0.415614i	$0.863567\pi$
$350$	−1.21530e15			−0.661113
$351$			2.23780e15i			1.19668i
$352$	4.54886e14	−	1.84428e15i	0.239137	−	0.969550i
$353$	−1.63623e15			−0.845660			−0.422830	−	0.906209i	$-0.638963\pi$
$353$	−1.63623e15			−0.845660			−0.422830	+	0.906209i	$0.638963\pi$
$354$		−	4.56329e14i		−	0.231877i
$355$	2.34137e14			0.116977
$356$	−4.90359e14			−0.240887
$357$	−4.18222e15			−2.02022
$358$		−	1.84370e15i		−	0.875772i
$359$			3.23735e15i			1.51225i	0.654430	+	0.756123i	$0.272909\pi$
$359$			3.23735e15i			1.51225i	−0.654430	+	0.756123i	$0.727091\pi$
$360$		−	1.24333e14i		−	0.0571178i
$361$	−2.90815e15			−1.31393
$362$		−	1.19208e14i		−	0.0529727i
$363$	2.21433e15	+	1.16307e15i	0.967838	+	0.508355i
$364$	4.37645e15			1.88154
$365$		−	1.17769e14i		−	0.0498051i
$366$	1.22000e15			0.507545
$367$	−2.91438e15			−1.19275			−0.596375	−	0.802706i	$-0.703393\pi$
$367$	−2.91438e15			−1.19275			−0.596375	+	0.802706i	$0.703393\pi$
$368$	−7.02948e14			−0.283032
$369$			5.16286e14i			0.204518i
$370$		−	8.59892e13i		−	0.0335146i
$371$		−	4.04268e15i		−	1.55034i
$372$	1.33040e15			0.502024
$373$			6.90783e14i			0.256501i	0.991742	+	0.128250i	$0.0409361\pi$
$373$			6.90783e14i			0.256501i	−0.991742	+	0.128250i	$0.959064\pi$
$374$	1.26425e15	+	3.11823e14i	0.461958	+	0.113941i
$375$	−2.07676e15			−0.746791
$376$			3.66572e15i			1.29727i
$377$	−4.24234e14			−0.147760
$378$	−1.95952e15			−0.671737
$379$	2.25759e15			0.761746			0.380873	−	0.924627i	$-0.375624\pi$
$379$	2.25759e15			0.761746			0.380873	+	0.924627i	$0.375624\pi$
$380$		−	1.34714e15i		−	0.447415i
$381$		−	5.44722e15i		−	1.78084i
$382$			1.94000e15i			0.624339i
$383$	−4.02168e15			−1.27413			−0.637067	−	0.770809i	$-0.719852\pi$
$383$	−4.02168e15			−1.27413			−0.637067	+	0.770809i	$0.719852\pi$
$384$		−	3.50982e15i		−	1.09471i
$385$	−4.91605e14	+	1.99315e15i	−0.150956	+	0.612033i
$386$	1.40320e15			0.424224
$387$		−	2.04623e14i		−	0.0609099i
$388$	1.68720e15			0.494512
$389$	−3.86255e14			−0.111475			−0.0557374	−	0.998445i	$-0.517751\pi$
$389$	−3.86255e14			−0.111475			−0.0557374	+	0.998445i	$0.517751\pi$
$390$	−8.49141e14			−0.241319
$391$		−	2.41756e15i		−	0.676577i
$392$			5.70087e15i			1.57118i
$393$			5.50354e15i			1.49378i
$394$	1.39648e15			0.373299
$395$		−	5.52067e14i		−	0.145348i
$396$	5.86993e14	+	1.44780e14i	0.152217	+	0.0375438i
$397$	−3.65312e15			−0.933085			−0.466542	−	0.884499i	$-0.654500\pi$
$397$	−3.65312e15			−0.933085			−0.466542	+	0.884499i	$0.654500\pi$
$398$		−	1.05858e15i		−	0.266334i
$399$	1.15541e16			2.86351
$400$	−1.59243e15			−0.388777
$401$	7.66763e15			1.84415			0.922073	−	0.387017i	$-0.126495\pi$
$401$	7.66763e15			1.84415			0.922073	+	0.387017i	$0.126495\pi$
$402$		−	1.78352e15i		−	0.422592i
$403$		−	3.32999e15i		−	0.777343i
$404$		−	4.69120e15i		−	1.07894i
$405$	−1.86926e15			−0.423583
$406$		−	3.71479e14i		−	0.0829426i
$407$	9.11255e14	+	2.24759e14i	0.200481	+	0.0494481i
$408$	4.32709e15			0.938070
$409$			1.18941e15i			0.254093i	0.991897	+	0.127046i	$0.0405497\pi$
$409$			1.18941e15i			0.254093i	−0.991897	+	0.127046i	$0.959450\pi$
$410$	8.08048e14			0.170112
$411$	−1.35786e15			−0.281712
$412$	−5.96948e14			−0.122054
$413$			4.08802e15i			0.823782i
$414$			2.74620e14i			0.0545420i
$415$		−	1.41170e15i		−	0.276346i
$416$	−7.03885e15			−1.35813
$417$			2.88868e15i			0.549392i
$418$	−3.49270e15	−	8.61466e14i	−0.654793	−	0.161503i
$419$	1.01905e15			0.188327			0.0941636	−	0.995557i	$-0.469982\pi$
$419$	1.01905e15			0.188327			0.0941636	+	0.995557i	$0.469982\pi$
$420$			3.03917e15i			0.553680i
$421$	2.26680e15			0.407118			0.203559	−	0.979063i	$-0.434749\pi$
$421$	2.26680e15			0.407118			0.203559	+	0.979063i	$0.434749\pi$
$422$	−2.83589e15			−0.502129
$423$	−1.81366e15			−0.316602
$424$			4.18272e15i			0.719886i
$425$		−	5.47666e15i		−	0.929356i
$426$		−	9.25624e14i		−	0.154874i
$427$	−1.09294e16			−1.80314
$428$			4.82147e15i			0.784363i
$429$	2.21949e15	−	8.99862e15i	0.356048	−	1.44355i
$430$	−3.20258e14			−0.0506628
$431$		−	1.06287e15i		−	0.165813i	−0.996557	−	0.0829063i	$-0.973580\pi$
$431$		−	1.06287e15i		−	0.165813i	0.996557	−	0.0829063i	$-0.0264202\pi$
$432$	−2.56760e15			−0.395025
$433$	−8.41693e15			−1.27710			−0.638552	−	0.769579i	$-0.720466\pi$
$433$	−8.41693e15			−1.27710			−0.638552	+	0.769579i	$0.720466\pi$
$434$	2.91589e15			0.436348
$435$		−	2.94603e14i		−	0.0434813i
$436$		−	4.78220e15i		−	0.696160i
$437$			6.67894e15i			0.959001i
$438$	−4.65582e14			−0.0659403
$439$			5.16125e15i			0.721053i	0.932749	+	0.360527i	$0.117403\pi$
$439$			5.16125e15i			0.721053i	−0.932749	+	0.360527i	$0.882597\pi$
$440$	5.08634e14	−	2.06219e15i	0.0700954	−	0.284193i
$441$	−2.82058e15			−0.383448
$442$		−	4.82511e15i		−	0.647104i
$443$	1.03533e16			1.36980			0.684900	−	0.728637i	$-0.259846\pi$
$443$	1.03533e16			1.36980			0.684900	+	0.728637i	$0.259846\pi$
$444$	1.38949e15			0.181366
$445$	−8.52328e14			−0.109761
$446$			5.41933e15i			0.688551i
$447$			1.00009e16i			1.25370i
$448$			8.64041e13i			0.0106873i
$449$	3.64271e15			0.444576			0.222288	−	0.974981i	$-0.428647\pi$
$449$	3.64271e15			0.444576			0.222288	+	0.974981i	$0.428647\pi$
$450$			6.22115e14i			0.0749196i
$451$	−2.11208e15	+	8.56314e15i	−0.250986	+	1.01759i
$452$	4.58639e15			0.537824
$453$		−	2.83351e15i		−	0.327896i
$454$	−3.78722e15			−0.432500
$455$	7.60703e15			0.857327
$456$	−1.19544e16			−1.32965
$457$		−	1.41776e16i		−	1.55634i	−0.628053	−	0.778171i	$-0.716148\pi$
$457$		−	1.41776e16i		−	1.55634i	0.628053	−	0.778171i	$-0.283852\pi$
$458$		−	3.92400e15i		−	0.425144i
$459$		−	8.83042e15i		−	0.944290i
$460$	−1.75681e15			−0.185429
$461$		−	2.67820e15i		−	0.279021i	−0.990221	−	0.139510i	$-0.955447\pi$
$461$		−	2.67820e15i		−	0.279021i	0.990221	−	0.139510i	$-0.0445529\pi$
$462$	7.87960e15	+	1.94348e15i	0.810312	+	0.199861i
$463$	4.55837e15			0.462726			0.231363	−	0.972867i	$-0.425681\pi$
$463$	4.55837e15			0.462726			0.231363	+	0.972867i	$0.425681\pi$
$464$		−	4.86755e14i		−	0.0487756i
$465$	2.31246e15			0.228748
$466$	2.53828e15			0.247870
$467$	3.37304e15			0.325177			0.162589	−	0.986694i	$-0.448016\pi$
$467$	3.37304e15			0.325177			0.162589	+	0.986694i	$0.448016\pi$
$468$		−	2.24031e15i		−	0.213223i
$469$			1.59776e16i			1.50133i
$470$			2.83859e15i			0.263339i
$471$	2.07520e16			1.90079
$472$		−	4.22963e15i		−	0.382517i
$473$	8.37090e14	−	3.39387e15i	0.0747490	−	0.303060i
$474$	−2.18251e15			−0.192436
$475$			1.51302e16i			1.31730i
$476$	−1.72696e16			−1.48471
$477$	−2.06945e15			−0.175689
$478$	1.76096e15			0.147632
$479$		−	1.36085e16i		−	1.12667i	−0.826229	−	0.563335i	$-0.809518\pi$
$479$		−	1.36085e16i		−	1.12667i	0.826229	−	0.563335i	$-0.190482\pi$
$480$		−	4.88803e15i		−	0.399656i
$481$		−	3.47789e15i		−	0.280831i
$482$	−3.85317e15			−0.307281
$483$		−	1.50678e16i		−	1.18677i
$484$	9.14360e15	+	4.80266e15i	0.711287	+	0.373603i
$485$	2.93265e15			0.225325
$486$			2.24936e15i			0.170703i
$487$	−7.70378e15			−0.577471			−0.288735	−	0.957409i	$-0.593235\pi$
$487$	−7.70378e15			−0.577471			−0.288735	+	0.957409i	$0.593235\pi$
$488$	1.13080e16			0.837272
$489$	−1.19151e16			−0.871453
$490$			4.41453e15i			0.318939i
$491$		−	2.61085e16i		−	1.86334i	−0.363302	−	0.931671i	$-0.618351\pi$
$491$		−	2.61085e16i		−	1.86334i	0.363302	−	0.931671i	$-0.381649\pi$
$492$			1.30571e16i			0.920571i
$493$	1.67404e15			0.116596
$494$			1.33302e16i			0.917224i
$495$	1.02030e15	+	2.51653e14i	0.0693577	+	0.0171069i
$496$	3.82074e15			0.256601
$497$			8.29220e15i			0.550214i
$498$	−5.58093e15			−0.365873
$499$	−4.78679e15			−0.310056			−0.155028	−	0.987910i	$-0.549547\pi$
$499$	−4.78679e15			−0.310056			−0.155028	+	0.987910i	$0.549547\pi$
$500$	−8.57555e15			−0.548835
$501$			3.37667e16i			2.13532i
$502$		−	3.00160e15i		−	0.187556i
$503$			9.41542e15i			0.581342i	0.956823	+	0.290671i	$0.0938785\pi$
$503$			9.41542e15i			0.581342i	−0.956823	+	0.290671i	$0.906122\pi$
$504$	4.40338e15			0.268660
$505$		−	8.15411e15i		−	0.491618i
$506$	−1.12344e15	+	4.55486e15i	−0.0669343	+	0.271376i
$507$	−1.57764e16			−0.928881
$508$		−	2.24931e16i		−	1.30878i
$509$	−1.83516e16			−1.05528			−0.527638	−	0.849469i	$-0.676922\pi$
$509$	−1.83516e16			−1.05528			−0.527638	+	0.849469i	$0.676922\pi$
$510$	3.35073e15			0.190423
$511$	4.17091e15			0.234264
$512$		−	1.45426e16i		−	0.807278i
$513$			2.43956e16i			1.33847i
$514$		−	4.63935e15i		−	0.251581i
$515$	−1.03760e15			−0.0556142
$516$		−	5.17500e15i		−	0.274165i
$517$	−3.00814e16	−	7.41950e15i	−1.57527	−	0.388536i
$518$	3.04540e15			0.157640
$519$		−	1.44924e16i		−	0.741542i
$520$	−7.87054e15			−0.398093
$521$	−6.55952e15			−0.327979			−0.163989	−	0.986462i	$-0.552436\pi$
$521$	−6.55952e15			−0.327979			−0.163989	+	0.986462i	$0.552436\pi$
$522$	−1.90160e14			−0.00939934
$523$			1.98340e16i			0.969171i	0.874744	+	0.484585i	$0.161030\pi$
$523$			1.98340e16i			0.969171i	−0.874744	+	0.484585i	$0.838970\pi$
$524$			2.27257e16i			1.09781i
$525$		−	3.41340e16i		−	1.63017i
$526$	1.31316e16			0.620016
$527$			1.31402e16i			0.613393i
$528$	1.03248e16	+	2.54658e15i	0.476515	+	0.117531i
$529$	−1.32046e16			−0.602546
$530$			3.23893e15i			0.146132i
$531$	2.09266e15			0.0933538
$532$	4.77102e16			2.10447
$533$	3.26820e16			1.42543
$534$			3.36955e15i			0.145320i
$535$			8.38055e15i			0.357396i
$536$		−	1.65311e16i		−	0.697129i
$537$	5.17837e16			2.15947
$538$		−	1.45094e16i		−	0.598349i
$539$	−4.67822e16	−	1.15387e16i	−1.90786	−	0.470570i
$540$	−6.41695e15			−0.258801
$541$		−	3.20068e16i		−	1.27661i	−0.769784	−	0.638305i	$-0.779636\pi$
$541$		−	3.20068e16i		−	1.27661i	0.769784	−	0.638305i	$-0.220364\pi$
$542$	−1.81728e15			−0.0716847
$543$	3.34817e15			0.130620
$544$	2.77755e16			1.07169
$545$		−	8.31229e15i		−	0.317206i
$546$		−	3.00732e16i		−	1.13507i
$547$			4.37412e16i			1.63293i	0.577397	+	0.816463i	$0.304068\pi$
$547$			4.37412e16i			1.63293i	−0.577397	+	0.816463i	$0.695932\pi$
$548$	−5.60701e15			−0.207037
$549$			5.59477e15i			0.204338i
$550$	−2.54501e15	+	1.03184e16i	−0.0919419	+	0.372766i
$551$	−4.62482e15			−0.165267
$552$			1.55898e16i			0.551068i
$553$	1.95520e16			0.683661
$554$	5.34038e14			0.0184720
$555$	2.41517e15			0.0826399
$556$			1.19282e16i			0.403762i
$557$			3.56124e15i			0.119253i	0.998221	+	0.0596266i	$0.0189910\pi$
$557$			3.56124e15i			0.119253i	−0.998221	+	0.0596266i	$0.981009\pi$
$558$		−	1.49265e15i		−	0.0494484i
$559$	−1.29530e16			−0.424522
$560$			8.72810e15i			0.283003i
$561$	−8.75815e15	+	3.55088e16i	−0.280954	+	1.13909i
$562$	1.10451e16			0.350551
$563$			2.63784e16i			0.828321i	0.910204	+	0.414161i	$0.135925\pi$
$563$			2.63784e16i			0.828321i	−0.910204	+	0.414161i	$0.864075\pi$
$564$	−4.58683e16			−1.42508
$565$	7.97194e15			0.245060
$566$	−1.83727e16			−0.558823
$567$		−	6.62016e16i		−	1.99237i
$568$		−	8.57945e15i		−	0.255487i
$569$		−	7.10988e15i		−	0.209502i	−0.994498	−	0.104751i	$-0.966595\pi$
$569$		−	7.10988e15i		−	0.209502i	0.994498	−	0.104751i	$-0.0334046\pi$
$570$	−9.25698e15			−0.269911
$571$		−	8.51825e15i		−	0.245773i	−0.992421	−	0.122886i	$-0.960785\pi$
$571$		−	8.51825e15i		−	0.245773i	0.992421	−	0.122886i	$-0.0392151\pi$
$572$	9.16489e15	−	3.71579e16i	0.261668	−	1.06090i
$573$	−5.44884e16			−1.53949
$574$			2.86178e16i			0.800139i
$575$	1.97314e16			0.545949
$576$	4.42304e13			0.00121112
$577$	6.21541e16			1.68428			0.842142	−	0.539256i	$-0.181294\pi$
$577$	6.21541e16			1.68428			0.842142	+	0.539256i	$0.181294\pi$
$578$			2.50824e15i			0.0672670i
$579$			3.94114e16i			1.04605i
$580$		−	1.21650e15i		−	0.0319554i
$581$	4.99967e16			1.29982
$582$		−	1.15938e16i		−	0.298323i
$583$	−3.43240e16	−	8.46593e15i	−0.874151	−	0.215607i
$584$	−4.31539e15			−0.108779
$585$		−	3.89405e15i		−	0.0971552i
$586$	−3.79533e15			−0.0937269
$587$	−3.89652e16			−0.952464			−0.476232	−	0.879320i	$-0.657998\pi$
$587$	−3.89652e16			−0.952464			−0.476232	+	0.879320i	$0.657998\pi$
$588$	−7.13337e16			−1.72596
$589$		−	3.63021e16i		−	0.869442i
$590$		−	3.27526e15i		−	0.0776486i
$591$			3.92228e16i			0.920478i
$592$	3.99043e15			0.0927022
$593$			1.98094e15i			0.0455557i	0.999741	+	0.0227778i	$0.00725104\pi$
$593$			1.98094e15i			0.0455557i	−0.999741	+	0.0227778i	$0.992749\pi$
$594$	−4.10351e15	+	1.66371e16i	−0.0934193	+	0.378757i
$595$	−3.00175e16			−0.676508
$596$			4.12964e16i			0.921372i
$597$	2.97324e16			0.656725
$598$	1.73840e16			0.380140
$599$	−2.50941e16			−0.543264			−0.271632	−	0.962401i	$-0.587563\pi$
$599$	−2.50941e16			−0.543264			−0.271632	+	0.962401i	$0.587563\pi$
$600$			3.53165e16i			0.756954i
$601$		−	7.51896e16i		−	1.59555i	−0.602954	−	0.797776i	$-0.706010\pi$
$601$		−	7.51896e16i		−	1.59555i	0.602954	−	0.797776i	$-0.293990\pi$
$602$		−	1.13423e16i		−	0.238298i
$603$	8.17898e15			0.170136
$604$		−	1.17004e16i		−	0.240979i
$605$	1.58932e16	+	8.34785e15i	0.324099	+	0.170232i
$606$	−3.22360e16			−0.650887
$607$		−	8.16600e16i		−	1.63259i	−0.577635	−	0.816295i	$-0.696024\pi$
$607$		−	8.16600e16i		−	1.63259i	0.577635	−	0.816295i	$-0.303976\pi$
$608$	−7.67346e16			−1.51904
$609$	1.04337e16			0.204519
$610$	8.75646e15			0.169961
$611$			1.14808e17i			2.20661i
$612$			8.84033e15i			0.168252i
$613$			1.27903e16i			0.241055i	0.992710	+	0.120528i	$0.0384586\pi$
$613$			1.27903e16i			0.241055i	−0.992710	+	0.120528i	$0.961541\pi$
$614$	2.33446e16			0.435688
$615$			2.26955e16i			0.419459i
$616$	7.30346e16	+	1.80138e16i	1.33673	+	0.329702i
$617$	8.45198e16			1.53196			0.765980	−	0.642865i	$-0.222254\pi$
$617$	8.45198e16			1.53196			0.765980	+	0.642865i	$0.222254\pi$
$618$			4.10199e15i			0.0736314i
$619$	7.76197e15			0.137984			0.0689919	−	0.997617i	$-0.478022\pi$
$619$	7.76197e15			0.137984			0.0689919	+	0.997617i	$0.478022\pi$
$620$	9.54883e15			0.168112
$621$	3.18145e16			0.554722
$622$			1.35029e16i			0.233176i
$623$		−	3.01861e16i		−	0.516272i
$624$		−	3.94054e16i		−	0.667496i
$625$	3.67107e16			0.615903
$626$		−	2.60493e16i		−	0.432862i
$627$	2.41959e16	−	9.80992e16i	0.398232	−	1.61458i
$628$	8.56911e16			1.39694
$629$			1.37238e16i			0.221601i
$630$	3.40981e15			0.0545364
$631$	3.38172e15			0.0535749			0.0267875	−	0.999641i	$-0.491472\pi$
$631$	3.38172e15			0.0535749			0.0267875	+	0.999641i	$0.491472\pi$
$632$	−2.02293e16			−0.317452
$633$		−	7.96514e16i		−	1.23814i
$634$			2.48617e16i			0.382820i
$635$		−	3.90969e16i		−	0.596349i
$636$	−5.23375e16			−0.790806
$637$			1.78548e17i			2.67251i
$638$	−3.15401e15	−	7.77927e14i	−0.0467669	−	0.0115349i
$639$	4.24479e15			0.0623521
$640$		−	2.51914e16i		−	0.366583i
$641$	2.36873e16			0.341482			0.170741	−	0.985316i	$-0.445384\pi$
$641$	2.36873e16			0.341482			0.170741	+	0.985316i	$0.445384\pi$
$642$	3.31312e16			0.473180
$643$	−1.13535e17			−1.60644			−0.803222	−	0.595680i	$-0.796883\pi$
$643$	−1.13535e17			−1.60644			−0.803222	+	0.595680i	$0.796883\pi$
$644$		−	6.22193e16i		−	0.872188i
$645$		−	8.99505e15i		−	0.124924i
$646$		−	5.26014e16i		−	0.723772i
$647$	−6.65637e16			−0.907427			−0.453714	−	0.891148i	$-0.649901\pi$
$647$	−6.65637e16			−0.907427			−0.453714	+	0.891148i	$0.649901\pi$
$648$			6.84949e16i			0.925141i
$649$	3.47089e16	+	8.56087e15i	0.464487	+	0.114564i
$650$	3.93811e16			0.522165
$651$			8.18983e16i			1.07594i
$652$	−4.92008e16			−0.640452
$653$	−9.02146e16			−1.16358			−0.581792	−	0.813338i	$-0.697648\pi$
$653$	−9.02146e16			−1.16358			−0.581792	+	0.813338i	$0.697648\pi$
$654$	−3.28613e16			−0.419970
$655$			3.95011e16i			0.500221i
$656$			3.74984e16i			0.470533i
$657$		−	2.13510e15i		−	0.0265476i
$658$	−1.00531e17			−1.23864
$659$		−	1.60575e17i		−	1.96050i	−0.197765	−	0.980249i	$-0.563368\pi$
$659$		−	1.60575e17i		−	1.96050i	0.197765	−	0.980249i	$-0.436632\pi$
$660$	2.58038e16	+	6.36443e15i	0.312190	+	0.0770009i
$661$	−8.80832e16			−1.05605			−0.528025	−	0.849229i	$-0.677067\pi$
$661$	−8.80832e16			−1.05605			−0.528025	+	0.849229i	$0.677067\pi$
$662$		−	5.20060e16i		−	0.617882i
$663$	1.35522e17			1.59562
$664$	−5.17286e16			−0.603563
$665$	8.29286e16			0.958903
$666$		−	1.55894e15i		−	0.0178642i
$667$			6.03127e15i			0.0684942i
$668$			1.39433e17i			1.56930i
$669$	−1.52212e17			−1.69782
$670$		−	1.28010e16i		−	0.141513i
$671$	−2.28877e16	+	9.27951e16i	−0.250765	+	1.01669i
$672$	1.73115e17			1.87983
$673$			3.87433e16i			0.416971i	0.978025	+	0.208486i	$0.0668534\pi$
$673$			3.87433e16i			0.416971i	−0.978025	+	0.208486i	$0.933147\pi$
$674$	5.23955e14			0.00558901
$675$	7.20713e16			0.761973
$676$	−6.51453e16			−0.682657
$677$		−	7.15891e16i		−	0.743558i	−0.928321	−	0.371779i	$-0.878748\pi$
$677$		−	7.15891e16i		−	0.743558i	0.928321	−	0.371779i	$-0.121252\pi$
$678$		−	3.15158e16i		−	0.324452i
$679$			1.03863e17i			1.05984i
$680$	3.10573e16			0.314131
$681$		−	1.06371e17i		−	1.06645i
$682$	6.10628e15	−	2.47571e16i	0.0606834	−	0.246033i
$683$	−5.49164e16			−0.540975			−0.270488	−	0.962723i	$-0.587185\pi$
$683$	−5.49164e16			−0.540975			−0.270488	+	0.962723i	$0.587185\pi$
$684$		−	2.44229e16i		−	0.238485i
$685$	−9.74595e15			−0.0943367
$686$	−7.67818e16			−0.736738
$687$	1.10213e17			1.04832
$688$		−	1.48620e16i		−	0.140135i
$689$			1.31001e17i			1.22450i
$690$			1.20721e16i			0.111863i
$691$	−1.32837e17			−1.22026			−0.610130	−	0.792302i	$-0.708883\pi$
$691$	−1.32837e17			−1.22026			−0.610130	+	0.792302i	$0.708883\pi$
$692$		−	5.98432e16i		−	0.544977i
$693$	−8.91256e15	+	3.61348e16i	−0.0804642	+	0.326232i
$694$	4.03582e16			0.361222
$695$			2.07332e16i			0.183975i
$696$	−1.07951e16			−0.0949667
$697$	−1.28964e17			−1.12479
$698$	4.26192e16			0.368530
$699$			7.12923e16i			0.611195i
$700$		−	1.40949e17i		−	1.19805i
$701$		−	1.77394e17i		−	1.49497i	−0.664280	−	0.747484i	$-0.731262\pi$
$701$		−	1.77394e17i		−	1.49497i	0.664280	−	0.747484i	$-0.268738\pi$
$702$	6.34971e16			0.530556
$703$		−	3.79145e16i		−	0.314104i
$704$	7.33606e14	+	1.80942e14i	0.00602597	+	0.00148629i
$705$	−7.97270e16			−0.649338
$706$			4.64276e16i			0.374928i
$707$	2.88786e17			2.31238
$708$	5.29244e16			0.420201
$709$	4.68731e16			0.369017			0.184509	−	0.982831i	$-0.440931\pi$
$709$	4.68731e16			0.369017			0.184509	+	0.982831i	$0.440931\pi$
$710$		−	6.64359e15i		−	0.0518624i
$711$		−	1.00087e16i		−	0.0774748i
$712$			3.12317e16i			0.239727i
$713$	−4.73419e16			−0.360337
$714$			1.18670e17i			0.895674i
$715$	1.59302e16	−	6.45868e16i	0.119230	−	0.483401i
$716$	2.13830e17			1.58705
$717$			4.94598e16i			0.364030i
$718$	9.18590e16			0.670463
$719$	−2.60451e16			−0.188518			−0.0942590	−	0.995548i	$-0.530048\pi$
$719$	−2.60451e16			−0.188518			−0.0942590	+	0.995548i	$0.530048\pi$
$720$	4.46793e15			0.0320709
$721$		−	3.67476e16i		−	0.261588i
$722$			8.25181e16i			0.582540i
$723$		−	1.08224e17i		−	0.757690i
$724$	1.38255e16			0.0959955
$725$			1.36630e16i			0.0940845i
$726$	3.30019e16	−	6.28311e16i	0.225382	−	0.429097i
$727$	−1.63356e17			−1.10644			−0.553221	−	0.833034i	$-0.686602\pi$
$727$	−1.63356e17			−1.10644			−0.553221	+	0.833034i	$0.686602\pi$
$728$		−	2.78743e17i		−	1.87247i
$729$	1.10491e17			0.736140
$730$	−3.34167e15			−0.0220814
$731$	5.11130e16			0.334986
$732$			1.41495e17i			0.919757i
$733$			9.00313e16i			0.580457i	0.956957	+	0.290228i	$0.0937313\pi$
$733$			9.00313e16i			0.580457i	−0.956957	+	0.290228i	$0.906269\pi$
$734$			8.26949e16i			0.528813i
$735$	−1.23990e17			−0.786437
$736$			1.00070e17i			0.629561i
$737$	1.35657e17	+	3.34594e16i	0.846518	+	0.208792i
$738$	1.46495e16			0.0906745
$739$		−	1.01482e17i		−	0.623049i	−0.950238	−	0.311525i	$-0.899160\pi$
$739$		−	1.01482e17i		−	0.623049i	0.950238	−	0.311525i	$-0.100840\pi$
$740$	9.97292e15			0.0607340
$741$	−3.74404e17			−2.26168
$742$	−1.14710e17			−0.687350
$743$			1.91065e17i			1.13566i	0.823146	+	0.567830i	$0.192217\pi$
$743$			1.91065e17i			1.13566i	−0.823146	+	0.567830i	$0.807783\pi$
$744$		−	8.47353e16i		−	0.499605i
$745$			7.17803e16i			0.419824i
$746$	1.96008e16			0.113721
$747$		−	2.55934e16i		−	0.147301i
$748$	−3.61649e16	+	1.46626e17i	−0.206480	+	0.837146i
$749$	−2.96806e17			−1.68105
$750$			5.89277e16i			0.331094i
$751$	1.85503e17			1.03398			0.516988	−	0.855993i	$-0.327053\pi$
$751$	1.85503e17			1.03398			0.516988	+	0.855993i	$0.327053\pi$
$752$	−1.31728e17			−0.728402
$753$	8.43056e16			0.462473
$754$			1.20375e16i			0.0655103i
$755$		−	2.03373e16i		−	0.109802i
$756$		−	2.27263e17i		−	1.21730i
$757$	6.08839e16			0.323539			0.161770	−	0.986829i	$-0.448280\pi$
$757$	6.08839e16			0.323539			0.161770	+	0.986829i	$0.448280\pi$
$758$		−	6.40586e16i		−	0.337724i
$759$	−1.27932e17	−	3.15541e16i	−0.669157	−	0.165046i
$760$	−8.58013e16			−0.445259
$761$		−	2.10303e16i		−	0.108277i	−0.998533	−	0.0541387i	$-0.982759\pi$
$761$		−	2.10303e16i		−	0.108277i	0.998533	−	0.0541387i	$-0.0172413\pi$
$762$	−1.54564e17			−0.789546
$763$	2.94388e17			1.49201
$764$	−2.24998e17			−1.13141
$765$			1.53660e16i			0.0766642i
$766$			1.14114e17i			0.564894i
$767$		−	1.32470e17i		−	0.650646i
$768$	−9.81981e16			−0.478559
$769$		−	1.06082e17i		−	0.512959i	−0.966550	−	0.256479i	$-0.917437\pi$
$769$		−	1.06082e17i		−	0.512959i	0.966550	−	0.256479i	$-0.0825626\pi$
$770$	5.65551e16	+	1.39492e16i	0.271349	+	0.0669274i
$771$	1.30305e17			0.620346
$772$			1.62741e17i			0.768765i
$773$	−1.20551e17			−0.565060			−0.282530	−	0.959258i	$-0.591174\pi$
$773$	−1.20551e17			−0.565060			−0.282530	+	0.959258i	$0.591174\pi$
$774$	−5.80612e15			−0.0270048
$775$	−1.07247e17			−0.494964
$776$		−	1.07461e17i		−	0.492129i
$777$			8.55357e16i			0.388706i
$778$			1.09599e16i			0.0494230i
$779$	3.56285e17			1.59431
$780$		−	9.84823e16i		−	0.437311i
$781$	7.04042e16	+	1.73650e16i	0.310236	+	0.0765189i
$782$	−6.85978e16			−0.299965
$783$			2.20299e16i			0.0955964i
$784$	−2.04862e17			−0.882194
$785$	1.48946e17			0.636518
$786$	1.56162e17			0.662276
$787$		−	4.09082e17i		−	1.72172i	−0.508845	−	0.860858i	$-0.669927\pi$
$787$		−	4.09082e17i		−	1.72172i	0.508845	−	0.860858i	$-0.330073\pi$
$788$			1.61962e17i			0.676481i
$789$			3.68826e17i			1.52883i
$790$	−1.56648e16			−0.0644409
$791$			2.82334e17i			1.15267i
$792$	9.22129e15	−	3.73865e16i	0.0373629	−	0.151483i
$793$	3.54161e17			1.42417
$794$			1.03656e17i			0.413689i
$795$	−9.09715e16			−0.360332
$796$	1.22773e17			0.482643
$797$	1.62848e16			0.0635378			0.0317689	−	0.999495i	$-0.489886\pi$
$797$	1.62848e16			0.0635378			0.0317689	+	0.999495i	$0.489886\pi$
$798$		−	3.27845e17i		−	1.26956i
$799$		−	4.53036e17i		−	1.74122i
$800$			2.26695e17i			0.864773i
$801$	−1.54523e16			−0.0585057
$802$		−	2.17567e17i		−	0.817613i
$803$	8.73446e15	−	3.54127e16i	0.0325794	−	0.132089i
$804$	2.06850e17			0.765808
$805$		−	1.08148e17i		−	0.397413i
$806$	−9.44877e16			−0.344639
$807$	4.07523e17			1.47540
$808$	−2.98790e17			−1.07374
$809$			3.40224e17i			1.21360i	0.794856	+	0.606798i	$0.207546\pi$
$809$			3.40224e17i			1.21360i	−0.794856	+	0.606798i	$0.792454\pi$
$810$			5.30397e16i			0.187798i
$811$			2.44360e17i			0.858826i	0.903108	+	0.429413i	$0.141279\pi$
$811$			2.44360e17i			0.858826i	−0.903108	+	0.429413i	$0.858721\pi$
$812$	4.30836e16			0.150306
$813$		−	5.10418e16i		−	0.176759i
$814$	6.37748e15	−	2.58567e16i	0.0219231	−	0.0888845i
$815$	−8.55194e16			−0.291823
$816$			1.55495e17i			0.526714i
$817$	−1.41208e17			−0.474819
$818$	3.37493e16			0.112653
$819$	1.37912e17			0.456980
$820$			9.37164e16i			0.308271i
$821$		−	3.71539e17i		−	1.21324i	−0.794993	−	0.606618i	$-0.792526\pi$
$821$		−	3.71539e17i		−	1.21324i	0.794993	−	0.606618i	$-0.207474\pi$
$822$			3.85291e16i			0.124899i
$823$	1.26922e17			0.408448			0.204224	−	0.978924i	$-0.434533\pi$
$823$	1.26922e17			0.408448			0.204224	+	0.978924i	$0.434533\pi$
$824$			3.80206e16i			0.121466i
$825$	−2.89812e17	−	7.14814e16i	−0.919163	−	0.226709i
$826$	1.15997e17			0.365229
$827$			3.43242e17i			1.07292i	0.843926	+	0.536460i	$0.180239\pi$
$827$			3.43242e17i			1.07292i	−0.843926	+	0.536460i	$0.819761\pi$
$828$	−3.18502e16			−0.0988393
$829$	−4.21187e16			−0.129762			−0.0648810	−	0.997893i	$-0.520667\pi$
$829$	−4.21187e16			−0.129762			−0.0648810	+	0.997893i	$0.520667\pi$
$830$	−4.00566e16			−0.122520
$831$			1.49995e16i			0.0455480i
$832$		−	2.79987e15i		−	0.00844108i
$833$		−	7.04556e17i		−	2.10885i
$834$	8.19655e16			0.243576
$835$			2.42358e17i			0.715053i
$836$	9.99118e16	−	4.05080e17i	0.292671	−	1.18660i
$837$	−1.72922e17			−0.502917
$838$		−	2.89154e16i		−	0.0834960i
$839$	−5.14030e17			−1.47373			−0.736863	−	0.676042i	$-0.763694\pi$
$839$	−5.14030e17			−1.47373			−0.736863	+	0.676042i	$0.763694\pi$
$840$	1.93569e17			0.551011
$841$	3.49638e17			0.988196
$842$		−	6.43198e16i		−	0.180498i
$843$			3.10222e17i			0.864384i
$844$		−	3.28903e17i		−	0.909942i
$845$	−1.13234e17			−0.311054
$846$			5.14622e16i			0.140367i
$847$	−2.95648e17	+	5.62872e17i	−0.800708	+	1.52444i
$848$	−1.50307e17			−0.404206
$849$		−	5.16032e17i		−	1.37794i
$850$	−1.55399e17			−0.412035
$851$	−4.94445e16			−0.130179
$852$	1.07353e17			0.280657
$853$			4.35001e17i			1.12926i	0.825343	+	0.564632i	$0.190982\pi$
$853$			4.35001e17i			1.12926i	−0.825343	+	0.564632i	$0.809018\pi$
$854$			3.10119e17i			0.799432i
$855$		−	4.24513e16i		−	0.108666i
$856$	3.07087e17			0.780583
$857$			3.40343e17i			0.859076i	0.903049	+	0.429538i	$0.141324\pi$
$857$			3.40343e17i			0.859076i	−0.903049	+	0.429538i	$0.858676\pi$
$858$	−2.55334e17	−	6.29774e16i	−0.640007	−	0.157856i
$859$	8.42820e16			0.209786			0.104893	−	0.994484i	$-0.466550\pi$
$859$	8.42820e16			0.209786			0.104893	+	0.994484i	$0.466550\pi$
$860$		−	3.71431e16i		−	0.0918095i
$861$	−8.03786e17			−1.97297
$862$	−3.01587e16			−0.0735139
$863$	−2.91261e17			−0.705046			−0.352523	−	0.935803i	$-0.614676\pi$
$863$	−2.91261e17			−0.705046			−0.352523	+	0.935803i	$0.614676\pi$
$864$			3.65517e17i			0.878670i
$865$		−	1.04018e17i		−	0.248320i
$866$			2.38829e17i			0.566212i
$867$	−7.04486e16			−0.165866
$868$			3.38181e17i			0.790736i
$869$	4.09446e16	−	1.66005e17i	0.0950776	−	0.385480i
$870$	−8.35930e15			−0.0192777
$871$		−	5.17746e17i		−	1.18579i
$872$	−3.04586e17			−0.692805
$873$	5.31675e16			0.120105
$874$	1.89513e17			0.425179
$875$		−	5.27903e17i		−	1.17627i
$876$		−	5.39976e16i		−	0.119495i
$877$			3.33377e17i			0.732721i	0.930473	+	0.366360i	$0.119396\pi$
$877$			3.33377e17i			0.732721i	−0.930473	+	0.366360i	$0.880604\pi$
$878$	1.46449e17			0.319683
$879$		−	1.06599e17i		−	0.231111i
$880$	7.41051e16	+	1.82778e16i	0.159570	+	0.0393576i
$881$	−5.75035e17			−1.22981			−0.614906	−	0.788600i	$-0.710806\pi$
$881$	−5.75035e17			−1.22981			−0.614906	+	0.788600i	$0.710806\pi$
$882$			8.00332e16i			0.170004i
$883$	8.43666e17			1.77994			0.889972	−	0.456016i	$-0.150724\pi$
$883$	8.43666e17			1.77994			0.889972	+	0.456016i	$0.150724\pi$
$884$	5.59611e17			1.17266
$885$	9.19918e16			0.191465
$886$		−	2.93773e17i		−	0.607309i
$887$		−	6.37579e17i		−	1.30916i	−0.755994	−	0.654579i	$-0.772846\pi$
$887$		−	6.37579e17i		−	1.30916i	0.755994	−	0.654579i	$-0.227154\pi$
$888$		−	8.84987e16i		−	0.180492i
$889$	1.38466e18			2.80499
$890$			2.41846e16i			0.0486630i
$891$	−5.62079e17	−	1.38635e17i	−1.12339	−	0.277081i
$892$	−6.28527e17			−1.24777
$893$			1.25159e18i			2.46805i
$894$	2.83772e17			0.555834
$895$	3.71673e17			0.723140
$896$	8.92180e17			1.72427
$897$			4.88263e17i			0.937345i
$898$		−	1.03361e17i		−	0.197105i
$899$		−	3.27818e16i		−	0.0620976i
$900$	−7.21521e16			−0.135767
$901$		−	5.16932e17i		−	0.966239i
$902$	2.42977e17	+	5.99297e16i	0.451155	+	0.111276i
$903$	3.18569e17			0.587593
$904$		−	2.92114e17i		−	0.535233i
$905$	2.40312e16			0.0437405
$906$	−8.04003e16			−0.145375
$907$	−6.23413e17			−1.11978			−0.559889	−	0.828567i	$-0.689156\pi$
$907$	−6.23413e17			−1.11978			−0.559889	+	0.828567i	$0.689156\pi$
$908$		−	4.39238e17i		−	0.783762i
$909$		−	1.47830e17i		−	0.262047i
$910$		−	2.15848e17i		−	0.380101i
$911$	3.31218e17			0.579434			0.289717	−	0.957112i	$-0.406439\pi$
$911$	3.31218e17			0.579434			0.289717	+	0.957112i	$0.406439\pi$
$912$		−	4.29581e17i		−	0.746580i
$913$	1.04700e17	−	4.24493e17i	0.180768	−	0.732901i
$914$	−4.02286e17			−0.690013
$915$			2.45942e17i			0.419089i
$916$	4.55101e17			0.770433
$917$	−1.39897e18			−2.35285
$918$	−2.50561e17			−0.418657
$919$		−	4.57969e17i		−	0.760226i	−0.924940	−	0.380113i	$-0.875885\pi$
$919$		−	4.57969e17i		−	0.760226i	0.924940	−	0.380113i	$-0.124115\pi$
$920$			1.11894e17i			0.184536i
$921$			6.55677e17i			1.07432i
$922$	−7.59932e16			−0.123706
$923$		−	2.68704e17i		−	0.434574i
$924$	−2.25403e17	+	9.13867e17i	−0.362183	+	1.46842i
$925$	−1.12010e17			−0.178816
$926$		−	1.29343e17i		−	0.205152i
$927$	−1.88112e16			−0.0296440
$928$	−6.92934e16			−0.108494
$929$	6.45211e17			1.00371			0.501854	−	0.864952i	$-0.332651\pi$
$929$	6.45211e17			1.00371			0.501854	+	0.864952i	$0.332651\pi$
$930$		−	6.56156e16i		−	0.101417i
$931$			1.94646e18i			2.98914i
$932$			2.94386e17i			0.449182i
$933$	−3.79253e17			−0.574962
$934$		−	9.57093e16i		−	0.144169i
$935$	−6.28608e16	+	2.54861e17i	−0.0940828	+	0.381447i
$936$	−1.42689e17			−0.212195
$937$		−	3.58414e17i		−	0.529599i	−0.964303	−	0.264799i	$-0.914694\pi$
$937$		−	3.58414e17i		−	0.529599i	0.964303	−	0.264799i	$-0.0853058\pi$
$938$	4.53362e17			0.665623
$939$	7.31642e17			1.06735
$940$	−3.29216e17			−0.477214
$941$		−	2.96405e17i		−	0.426921i	−0.976952	−	0.213461i	$-0.931527\pi$
$941$		−	2.96405e17i		−	0.426921i	0.976952	−	0.213461i	$-0.0684735\pi$
$942$		−	5.88834e17i		−	0.842728i
$943$		−	4.64634e17i		−	0.660756i
$944$	1.51992e17			0.214778
$945$		−	3.95022e17i		−	0.554665i
$946$	−9.63004e16	−	2.37523e16i	−0.134364	−	0.0331404i
$947$	−3.19466e17			−0.442919			−0.221460	−	0.975170i	$-0.571082\pi$
$947$	−3.19466e17			−0.442919			−0.221460	+	0.975170i	$0.571082\pi$
$948$		−	2.53125e17i		−	0.348726i
$949$	−1.35156e17			−0.185028
$950$	4.29317e17			0.584031
$951$	−6.98286e17			−0.943953
$952$			1.09993e18i			1.47755i
$953$		−	2.25984e17i		−	0.301662i	−0.988560	−	0.150831i	$-0.951805\pi$
$953$		−	2.25984e17i		−	0.301662i	0.988560	−	0.150831i	$-0.0481950\pi$
$954$			5.87203e16i			0.0778929i
$955$	−3.91086e17			−0.515527
$956$			2.04234e17i			0.267534i
$957$	2.18496e16	−	8.85862e16i	0.0284427	−	0.115317i
$958$	−3.86137e17			−0.499515
$959$		−	3.45163e17i		−	0.443723i
$960$	1.94433e15			0.00248395
$961$	−5.30345e17			−0.673314
$962$	−9.86842e16			−0.124508
$963$			1.51935e17i			0.190503i
$964$		−	4.46886e17i		−	0.556845i
$965$			2.82872e17i			0.350289i
$966$	−4.27546e17			−0.526162
$967$			4.09931e17i			0.501363i	0.968070	+	0.250681i	$0.0806547\pi$
$967$			4.09931e17i			0.501363i	−0.968070	+	0.250681i	$0.919345\pi$
$968$	3.05889e17	−	5.82370e17i	0.371802	−	0.707860i
$969$	1.47741e18			1.78467
$970$		−	8.32132e16i		−	0.0998991i
$971$	−8.57537e17			−1.02315			−0.511573	−	0.859240i	$-0.670937\pi$
$971$	−8.57537e17			−1.02315			−0.511573	+	0.859240i	$0.670937\pi$
$972$	−2.60878e17			−0.309342
$973$	−7.34288e17			−0.865345
$974$			2.18593e17i			0.256025i
$975$			1.10609e18i			1.28755i
$976$			4.06354e17i			0.470117i
$977$	3.22710e17			0.371061			0.185530	−	0.982639i	$-0.440600\pi$
$977$	3.22710e17			0.371061			0.185530	+	0.982639i	$0.440600\pi$
$978$			3.38088e17i			0.386364i
$979$	−2.56292e17	−	6.32138e16i	−0.291098	−	0.0717986i
$980$	−5.11992e17			−0.577971
$981$		−	1.50698e17i		−	0.169080i
$982$	−7.40822e17			−0.826124
$983$	3.07462e17			0.340777			0.170388	−	0.985377i	$-0.445498\pi$
$983$	3.07462e17			0.340777			0.170388	+	0.985377i	$0.445498\pi$
$984$	8.31629e17			0.916134
$985$			2.81518e17i			0.308240i
$986$		−	4.75005e16i		−	0.0516935i
$987$		−	2.82361e18i		−	3.05423i
$988$	−1.54602e18			−1.66216
$989$			1.84151e17i			0.196787i
$990$	7.14060e15	−	2.89507e16i	0.00758444	−	0.0307501i
$991$	1.22016e18			1.28818			0.644089	−	0.764951i	$-0.277237\pi$
$991$	1.22016e18			1.28818			0.644089	+	0.764951i	$0.277237\pi$
$992$		−	5.43913e17i		−	0.570767i
$993$	1.46069e18			1.52357
$994$	2.35289e17			0.243941
$995$	2.13401e17			0.219917
$996$		−	6.47269e17i		−	0.663024i
$997$		−	8.87685e17i		−	0.903832i	−0.892060	−	0.451916i	$-0.850741\pi$
$997$		−	8.87685e17i		−	0.903832i	0.892060	−	0.451916i	$-0.149259\pi$
$998$			1.35824e17i			0.137465i
$999$	−1.80602e17			−0.181689

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	11.13.b.b.10.5	✓	10
3.2	odd	2		99.13.c.b.10.6		10
4.3	odd	2		176.13.h.c.65.3		10
11.10	odd	2	inner	11.13.b.b.10.6	yes	10
33.32	even	2		99.13.c.b.10.5		10
44.43	even	2		176.13.h.c.65.4		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
11.13.b.b.10.5	✓	10	1.1	even	1	trivial
11.13.b.b.10.6	yes	10	11.10	odd	2	inner
99.13.c.b.10.5		10	33.32	even	2
99.13.c.b.10.6		10	3.2	odd	2
176.13.h.c.65.3		10	4.3	odd	2
176.13.h.c.65.4		10	44.43	even	2

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:	\( N \)	\(=\)	\( 11 \)
Weight:	\( k \)	\(=\)	\( 13 \)
Character orbit:	\([\chi]\)	\(=\)	11.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-28.3748i q^{2} +796.959 q^{3} +3290.87 q^{4} +5720.10 q^{5} -22613.5i q^{6} +202583. i q^{7} -209601. i q^{8} +103703. q^{9} +O(q^{10})\)	\(q-28.3748i q^{2} +796.959 q^{3} +3290.87 q^{4} +5720.10 q^{5} -22613.5i q^{6} +202583. i q^{7} -209601. i q^{8} +103703. q^{9} -162307. i q^{10} +(1.72001e6 + 424237. i) q^{11} +2.62269e6 q^{12} -6.56459e6i q^{13} +5.74825e6 q^{14} +4.55869e6 q^{15} +7.53204e6 q^{16} +2.59040e7i q^{17} -2.94254e6i q^{18} -7.15644e7i q^{19} +1.88241e7 q^{20} +1.61451e8i q^{21} +(1.20376e7 - 4.88050e7i) q^{22} -9.33277e7 q^{23} -1.67043e8i q^{24} -2.11421e8 q^{25} -1.86269e8 q^{26} -3.40890e8 q^{27} +6.66676e8i q^{28} -6.46246e7i q^{29} -1.29352e8i q^{30} +5.07265e8 q^{31} -1.07224e9i q^{32} +(1.37078e9 + 3.38100e8i) q^{33} +7.35021e8 q^{34} +1.15880e9i q^{35} +3.41272e8 q^{36} +5.29795e8 q^{37} -2.03062e9 q^{38} -5.23171e9i q^{39} -1.19894e9i q^{40} +4.97853e9i q^{41} +4.58112e9 q^{42} -1.97317e9i q^{43} +(5.66035e9 + 1.39611e9i) q^{44} +5.93190e8 q^{45} +2.64815e9i q^{46} -1.74890e10 q^{47} +6.00272e9 q^{48} -2.71987e10 q^{49} +5.99903e9i q^{50} +2.06445e10i q^{51} -2.16032e10i q^{52} -1.99556e10 q^{53} +9.67267e9i q^{54} +(9.83866e9 + 2.42668e9i) q^{55} +4.24616e10 q^{56} -5.70339e10i q^{57} -1.83371e9 q^{58} +2.01794e10 q^{59} +1.50021e10 q^{60} +5.39501e10i q^{61} -1.43935e10i q^{62} +2.10084e10i q^{63} +4.26511e8 q^{64} -3.75501e10i q^{65} +(9.59350e9 - 3.88956e10i) q^{66} +7.88695e10 q^{67} +8.52469e10i q^{68} -7.43784e10 q^{69} +3.28806e10 q^{70} +4.09323e10 q^{71} -2.17362e10i q^{72} -2.05886e10i q^{73} -1.50328e10i q^{74} -1.68494e11 q^{75} -2.35509e11i q^{76} +(-8.59434e10 + 3.48446e11i) q^{77} -1.48449e11 q^{78} -9.65135e10i q^{79} +4.30840e10 q^{80} -3.26787e11 q^{81} +1.41265e11 q^{82} -2.46796e11i q^{83} +5.31313e11i q^{84} +1.48174e11i q^{85} -5.59881e10 q^{86} -5.15032e10i q^{87} +(8.89205e10 - 3.60517e11i) q^{88} -1.49006e11 q^{89} -1.68316e10i q^{90} +1.32988e12 q^{91} -3.07130e11 q^{92} +4.04270e11 q^{93} +4.96247e11i q^{94} -4.09356e11i q^{95} -8.54535e11i q^{96} +5.12691e11 q^{97} +7.71757e11i q^{98} +(1.78370e11 + 4.39945e10i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 2436 q^{3} - 20348 q^{4} + 26492 q^{5} + 756294 q^{9}+O(q^{10}) \) 10 * q + 2436 * q^3 - 20348 * q^4 + 26492 * q^5 + 756294 * q^9	\( 10 q + 2436 q^{3} - 20348 q^{4} + 26492 q^{5} + 756294 q^{9} - 1716374 q^{11} - 8491644 q^{12} - 15139368 q^{14} + 9632184 q^{15} + 17974408 q^{16} - 125399668 q^{20} + 83533560 q^{22} + 330297476 q^{23} - 438477018 q^{25} - 372191832 q^{26} + 1665774072 q^{27} - 1921955548 q^{31} - 2301728484 q^{33} + 7677299352 q^{34} - 14333366928 q^{36} + 1788323996 q^{37} + 11254769640 q^{38} - 32091748680 q^{42} + 6124969708 q^{44} + 43304121996 q^{45} - 24975510124 q^{47} + 32578826856 q^{48} - 6325710998 q^{49} - 16325502124 q^{53} + 14298843812 q^{55} + 82892128176 q^{56} - 84518430720 q^{58} + 62339390564 q^{59} - 286034518116 q^{60} + 95192926864 q^{64} + 322939363560 q^{66} - 90035301244 q^{67} + 346118875824 q^{69} - 382808641560 q^{70} - 359910119740 q^{71} + 14209300764 q^{75} + 425991883680 q^{77} - 483427126680 q^{78} + 1147768798712 q^{80} - 515542099806 q^{81} + 625030365960 q^{82} - 1219447545552 q^{86} + 134692485840 q^{88} + 670996780412 q^{89} + 1356772643808 q^{91} - 3181666532764 q^{92} + 1928296959312 q^{93} - 6250704684964 q^{97} - 1402418596722 q^{99}+O(q^{100}) \) 10 * q + 2436 * q^3 - 20348 * q^4 + 26492 * q^5 + 756294 * q^9 - 1716374 * q^11 - 8491644 * q^12 - 15139368 * q^14 + 9632184 * q^15 + 17974408 * q^16 - 125399668 * q^20 + 83533560 * q^22 + 330297476 * q^23 - 438477018 * q^25 - 372191832 * q^26 + 1665774072 * q^27 - 1921955548 * q^31 - 2301728484 * q^33 + 7677299352 * q^34 - 14333366928 * q^36 + 1788323996 * q^37 + 11254769640 * q^38 - 32091748680 * q^42 + 6124969708 * q^44 + 43304121996 * q^45 - 24975510124 * q^47 + 32578826856 * q^48 - 6325710998 * q^49 - 16325502124 * q^53 + 14298843812 * q^55 + 82892128176 * q^56 - 84518430720 * q^58 + 62339390564 * q^59 - 286034518116 * q^60 + 95192926864 * q^64 + 322939363560 * q^66 - 90035301244 * q^67 + 346118875824 * q^69 - 382808641560 * q^70 - 359910119740 * q^71 + 14209300764 * q^75 + 425991883680 * q^77 - 483427126680 * q^78 + 1147768798712 * q^80 - 515542099806 * q^81 + 625030365960 * q^82 - 1219447545552 * q^86 + 134692485840 * q^88 + 670996780412 * q^89 + 1356772643808 * q^91 - 3181666532764 * q^92 + 1928296959312 * q^93 - 6250704684964 * q^97 - 1402418596722 * q^99

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