LMFDB - Embedded newform 14.13.b.a.13.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [14,13,Mod(13,14)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(14, 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("14.13");

S:= CuspForms(chi, 13);

N := Newforms(S);

Level:	$ N $	$=$	$ 14 = 2 \cdot 7 $
Weight:	$ k $	$=$	$ 13 $
Character orbit:	$[\chi]$	$=$	14.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:	$12.7959134419$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 154710x^{6} + 8245426887x^{4} + 174724076278260x^{2} + 1264170035276291934 $ x^8 + 154710x^6 + 8245426887x^4 + 174724076278260*x^2 + 1264170035276291934
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{26}\cdot 3^{2}\cdot 7^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			13.8
Root			$237.947i$ of defining polynomial
Character	$\chi$	$=$	14.13
Dual form			14.13.b.a.13.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+45.2548 q^{2} +1072.00i q^{3} +2048.00 q^{4} +1140.63i q^{5} +48513.4i q^{6} +(74038.7 + 91430.6i) q^{7} +92681.9 q^{8} -617752. q^{9} +O(q^{10})$	\(q+45.2548 q^{2} +1072.00i q^{3} +2048.00 q^{4} +1140.63i q^{5} +48513.4i q^{6} +(74038.7 + 91430.6i) q^{7} +92681.9 q^{8} -617752. q^{9} +51619.1i q^{10} -2.90614e6 q^{11} +2.19546e6i q^{12} -491015. i q^{13} +(3.35061e6 + 4.13768e6i) q^{14} -1.22276e6 q^{15} +4.19430e6 q^{16} +3.15108e7i q^{17} -2.79563e7 q^{18} -1.15553e7i q^{19} +2.33601e6i q^{20} +(-9.80140e7 + 7.93698e7i) q^{21} -1.31517e8 q^{22} +6.83364e6 q^{23} +9.93554e7i q^{24} +2.42840e8 q^{25} -2.22208e7i q^{26} -9.25255e7i q^{27} +(1.51631e8 + 1.87250e8i) q^{28} +5.16944e8 q^{29} -5.53359e7 q^{30} -1.26298e9i q^{31} +1.89813e8 q^{32} -3.11539e9i q^{33} +1.42602e9i q^{34} +(-1.04289e8 + 8.44508e7i) q^{35} -1.26516e9 q^{36} +3.49935e9 q^{37} -5.22931e8i q^{38} +5.26370e8 q^{39} +1.05716e8i q^{40} +8.38090e9i q^{41} +(-4.43561e9 + 3.59187e9i) q^{42} -6.25311e8 q^{43} -5.95176e9 q^{44} -7.04627e8i q^{45} +3.09255e8 q^{46} -1.58996e10i q^{47} +4.49631e9i q^{48} +(-2.87784e9 + 1.35388e10i) q^{49} +1.09897e10 q^{50} -3.37797e10 q^{51} -1.00560e9i q^{52} +2.53616e10 q^{53} -4.18723e9i q^{54} -3.31483e9i q^{55} +(6.86204e9 + 8.47397e9i) q^{56} +1.23873e10 q^{57} +2.33942e10 q^{58} +4.34071e10i q^{59} -2.50422e9 q^{60} -7.58019e9i q^{61} -5.71561e10i q^{62} +(-4.57375e10 - 5.64814e10i) q^{63} +8.58993e9 q^{64} +5.60067e8 q^{65} -1.40986e11i q^{66} +2.50602e10 q^{67} +6.45341e10i q^{68} +7.32569e9i q^{69} +(-4.71956e9 + 3.82181e9i) q^{70} +1.41685e11 q^{71} -5.72544e10 q^{72} +1.37008e11i q^{73} +1.58363e11 q^{74} +2.60325e11i q^{75} -2.36652e10i q^{76} +(-2.15166e11 - 2.65710e11i) q^{77} +2.38208e10 q^{78} -1.68456e11 q^{79} +4.78415e9i q^{80} -2.29111e11 q^{81} +3.79276e11i q^{82} -7.26397e10i q^{83} +(-2.00733e11 + 1.62549e11i) q^{84} -3.59422e10 q^{85} -2.82983e10 q^{86} +5.54166e11i q^{87} -2.69346e11 q^{88} -5.99527e11i q^{89} -3.18878e10i q^{90} +(4.48938e10 - 3.63541e10i) q^{91} +1.39953e10 q^{92} +1.35392e12 q^{93} -7.19532e11i q^{94} +1.31803e10 q^{95} +2.03480e11i q^{96} -5.96235e11i q^{97} +(-1.30236e11 + 6.12696e11i) q^{98} +1.79527e12 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 16384 q^{4} + 195160 q^{7} - 1478904 q^{9}+O(q^{10}) $ 8 * q + 16384 * q^4 + 195160 * q^7 - 1478904 * q^9	\( 8 q + 16384 q^{4} + 195160 q^{7} - 1478904 q^{9} - 213840 q^{11} - 8418816 q^{14} + 65882304 q^{15} + 33554432 q^{16} + 32547840 q^{18} - 4449984 q^{21} - 221337600 q^{22} + 156731760 q^{23} + 191237000 q^{25} + 399687680 q^{28} + 308853648 q^{29} - 2203567104 q^{30} - 3764734848 q^{35} - 3028795392 q^{36} - 3243600880 q^{37} + 13521315264 q^{39} - 12108579840 q^{42} + 21006302000 q^{43} - 437944320 q^{44} + 9664610304 q^{46} - 19258758904 q^{49} + 26259489792 q^{50} - 80965832832 q^{51} + 180445637520 q^{53} - 17241735168 q^{56} - 63145962240 q^{57} - 94193264640 q^{58} + 134926958592 q^{60} - 402706514280 q^{63} + 68719476736 q^{64} - 424890168192 q^{65} + 369211259440 q^{67} - 137936354304 q^{70} + 574058144304 q^{71} + 66657976320 q^{72} + 450517137408 q^{74} - 73915435440 q^{77} - 251000847360 q^{78} - 607826610128 q^{79} + 919051941384 q^{81} - 9113567232 q^{84} - 247202260608 q^{85} - 413092638720 q^{86} - 453299404800 q^{88} + 144527421696 q^{91} + 320986644480 q^{92} + 2292312458880 q^{93} - 1053641981376 q^{95} - 290797516800 q^{98} - 1800954256464 q^{99}+O(q^{100}) \) 8 * q + 16384 * q^4 + 195160 * q^7 - 1478904 * q^9 - 213840 * q^11 - 8418816 * q^14 + 65882304 * q^15 + 33554432 * q^16 + 32547840 * q^18 - 4449984 * q^21 - 221337600 * q^22 + 156731760 * q^23 + 191237000 * q^25 + 399687680 * q^28 + 308853648 * q^29 - 2203567104 * q^30 - 3764734848 * q^35 - 3028795392 * q^36 - 3243600880 * q^37 + 13521315264 * q^39 - 12108579840 * q^42 + 21006302000 * q^43 - 437944320 * q^44 + 9664610304 * q^46 - 19258758904 * q^49 + 26259489792 * q^50 - 80965832832 * q^51 + 180445637520 * q^53 - 17241735168 * q^56 - 63145962240 * q^57 - 94193264640 * q^58 + 134926958592 * q^60 - 402706514280 * q^63 + 68719476736 * q^64 - 424890168192 * q^65 + 369211259440 * q^67 - 137936354304 * q^70 + 574058144304 * q^71 + 66657976320 * q^72 + 450517137408 * q^74 - 73915435440 * q^77 - 251000847360 * q^78 - 607826610128 * q^79 + 919051941384 * q^81 - 9113567232 * q^84 - 247202260608 * q^85 - 413092638720 * q^86 - 453299404800 * q^88 + 144527421696 * q^91 + 320986644480 * q^92 + 2292312458880 * q^93 - 1053641981376 * q^95 - 290797516800 * q^98 - 1800954256464 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/14\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$-1$

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 $

$2$	45.2548			0.707107
$2$	45.2548			0.707107
$3$			1072.00i			1.47051i	0.677789	+	0.735257i	$0.262938\pi$
$3$			1072.00i			1.47051i	−0.677789	+	0.735257i	$0.737062\pi$
$4$	2048.00			0.500000
$5$			1140.63i			0.0730004i	0.999334	+	0.0365002i	$0.0116210\pi$
$5$			1140.63i			0.0730004i	−0.999334	+	0.0365002i	$0.988379\pi$
$6$			48513.4i			1.03981i
$7$	74038.7	+	91430.6i	0.629318	+	0.777148i
$7$	74038.7	+	91430.6i	0.629318	+	0.777148i
$8$	92681.9			0.353553
$9$	−617752.			−1.16241
$10$			51619.1i			0.0516191i
$11$	−2.90614e6			−1.64044			−0.820219	−	0.572050i	$-0.806148\pi$
$11$	−2.90614e6			−1.64044			−0.820219	+	0.572050i	$0.806148\pi$
$12$			2.19546e6i			0.735257i
$13$		−	491015.i		−	0.101727i	−0.998706	−	0.0508633i	$-0.983803\pi$
$13$		−	491015.i		−	0.101727i	0.998706	−	0.0508633i	$-0.0161973\pi$
$14$	3.35061e6	+	4.13768e6i	0.444995	+	0.549526i
$15$	−1.22276e6			−0.107348
$16$	4.19430e6			0.250000
$17$			3.15108e7i			1.30547i	0.757588	+	0.652733i	$0.226378\pi$
$17$			3.15108e7i			1.30547i	−0.757588	+	0.652733i	$0.773622\pi$
$18$	−2.79563e7			−0.821947
$19$		−	1.15553e7i		−	0.245617i	−0.992430	−	0.122808i	$-0.960810\pi$
$19$		−	1.15553e7i		−	0.245617i	0.992430	−	0.122808i	$-0.0391901\pi$
$20$			2.33601e6i			0.0365002i
$21$	−9.80140e7	+	7.93698e7i	−1.14281	+	0.925421i
$22$	−1.31517e8			−1.15996
$23$	6.83364e6			0.0461621			0.0230810	−	0.999734i	$-0.492652\pi$
$23$	6.83364e6			0.0461621			0.0230810	+	0.999734i	$0.492652\pi$
$24$			9.93554e7i			0.519905i
$25$	2.42840e8			0.994671
$26$		−	2.22208e7i		−	0.0719316i
$27$		−	9.25255e7i		−	0.238825i
$28$	1.51631e8	+	1.87250e8i	0.314659	+	0.388574i
$29$	5.16944e8			0.869071			0.434536	−	0.900655i	$-0.356913\pi$
$29$	5.16944e8			0.869071			0.434536	+	0.900655i	$0.356913\pi$
$30$	−5.53359e7			−0.0759065
$31$		−	1.26298e9i		−	1.42307i	−0.702649	−	0.711537i	$-0.748000\pi$
$31$		−	1.26298e9i		−	1.42307i	0.702649	−	0.711537i	$-0.252000\pi$
$32$	1.89813e8			0.176777
$33$		−	3.11539e9i		−	2.41228i
$34$			1.42602e9i			0.923104i
$35$	−1.04289e8	+	8.44508e7i	−0.0567321	+	0.0459405i
$36$	−1.26516e9			−0.581204
$37$	3.49935e9			1.36388			0.681942	−	0.731406i	$-0.261136\pi$
$37$	3.49935e9			1.36388			0.681942	+	0.731406i	$0.261136\pi$
$38$		−	5.22931e8i		−	0.173677i
$39$	5.26370e8			0.149590
$40$			1.05716e8i			0.0258095i
$41$			8.38090e9i			1.76436i	0.470911	+	0.882181i	$0.343925\pi$
$41$			8.38090e9i			1.76436i	−0.470911	+	0.882181i	$0.656075\pi$
$42$	−4.43561e9	+	3.59187e9i	−0.808086	+	0.654371i
$43$	−6.25311e8			−0.0989203			−0.0494601	−	0.998776i	$-0.515750\pi$
$43$	−6.25311e8			−0.0989203			−0.0494601	+	0.998776i	$0.515750\pi$
$44$	−5.95176e9			−0.820219
$45$		−	7.04627e8i		−	0.0848563i
$46$	3.09255e8			0.0326415
$47$		−	1.58996e10i		−	1.47502i	−0.675336	−	0.737510i	$-0.736001\pi$
$47$		−	1.58996e10i		−	1.47502i	0.675336	−	0.737510i	$-0.263999\pi$
$48$			4.49631e9i			0.367628i
$49$	−2.87784e9	+	1.35388e10i	−0.207917	+	0.978146i
$50$	1.09897e10			0.703339
$51$	−3.37797e10			−1.91971
$52$		−	1.00560e9i		−	0.0508633i
$53$	2.53616e10			1.14425			0.572126	−	0.820166i	$-0.306119\pi$
$53$	2.53616e10			1.14425			0.572126	+	0.820166i	$0.306119\pi$
$54$		−	4.18723e9i		−	0.168874i
$55$		−	3.31483e9i		−	0.119753i
$56$	6.86204e9	+	8.47397e9i	0.222498	+	0.274763i
$57$	1.23873e10			0.361183
$58$	2.33942e10			0.614526
$59$			4.34071e10i			1.02908i	0.857467	+	0.514539i	$0.172037\pi$
$59$			4.34071e10i			1.02908i	−0.857467	+	0.514539i	$0.827963\pi$
$60$	−2.50422e9			−0.0536740
$61$		−	7.58019e9i		−	0.147130i	−0.997290	−	0.0735649i	$-0.976562\pi$
$61$		−	7.58019e9i		−	0.147130i	0.997290	−	0.0735649i	$-0.0234376\pi$
$62$		−	5.71561e10i		−	1.00626i
$63$	−4.57375e10	−	5.64814e10i	−0.731525	−	0.903363i
$64$	8.58993e9			0.125000
$65$	5.60067e8			0.00742609
$66$		−	1.40986e11i		−	1.70574i
$67$	2.50602e10			0.277036			0.138518	−	0.990360i	$-0.455766\pi$
$67$	2.50602e10			0.277036			0.138518	+	0.990360i	$0.455766\pi$
$68$			6.45341e10i			0.652733i
$69$			7.32569e9i			0.0678819i
$70$	−4.71956e9	+	3.82181e9i	−0.0401156	+	0.0324848i
$71$	1.41685e11			1.10604			0.553022	−	0.833167i	$-0.313474\pi$
$71$	1.41685e11			1.10604			0.553022	+	0.833167i	$0.313474\pi$
$72$	−5.72544e10			−0.410974
$73$			1.37008e11i			0.905332i	0.891680	+	0.452666i	$0.149527\pi$
$73$			1.37008e11i			0.905332i	−0.891680	+	0.452666i	$0.850473\pi$
$74$	1.58363e11			0.964412
$75$			2.60325e11i			1.46268i
$76$		−	2.36652e10i		−	0.122808i
$77$	−2.15166e11	−	2.65710e11i	−1.03236	−	1.27486i
$78$	2.38208e10			0.105776
$79$	−1.68456e11			−0.692984			−0.346492	−	0.938053i	$-0.612627\pi$
$79$	−1.68456e11			−0.692984			−0.346492	+	0.938053i	$0.612627\pi$
$80$			4.78415e9i			0.0182501i
$81$	−2.29111e11			−0.811214
$82$			3.79276e11i			1.24759i
$83$		−	7.26397e10i		−	0.222180i	−0.993810	−	0.111090i	$-0.964566\pi$
$83$		−	7.26397e10i		−	0.222180i	0.993810	−	0.111090i	$-0.0354342\pi$
$84$	−2.00733e11	+	1.62549e11i	−0.571403	+	0.462710i
$85$	−3.59422e10			−0.0952996
$86$	−2.82983e10			−0.0699472
$87$			5.54166e11i			1.27798i
$88$	−2.69346e11			−0.579982
$89$		−	5.99527e11i		−	1.20634i	−0.797614	−	0.603169i	$-0.793905\pi$
$89$		−	5.99527e11i		−	1.20634i	0.797614	−	0.603169i	$-0.206095\pi$
$90$		−	3.18878e10i		−	0.0600025i
$91$	4.48938e10	−	3.63541e10i	0.0790567	−	0.0640185i
$92$	1.39953e10			0.0230810
$93$	1.35392e12			2.09265
$94$		−	7.19532e11i		−	1.04300i
$95$	1.31803e10			0.0179301
$96$			2.03480e11i			0.259952i
$97$		−	5.96235e11i		−	0.715792i	−0.933761	−	0.357896i	$-0.883494\pi$
$97$		−	5.96235e11i		−	0.715792i	0.933761	−	0.357896i	$-0.116506\pi$
$98$	−1.30236e11	+	6.12696e11i	−0.147019	+	0.691654i
$99$	1.79527e12			1.90686
$100$	4.97335e11			0.497335
$101$		−	3.03224e11i		−	0.285650i	−0.989748	−	0.142825i	$-0.954381\pi$
$101$		−	3.03224e11i		−	0.285650i	0.989748	−	0.142825i	$-0.0456187\pi$
$102$	−1.52869e12			−1.35744
$103$		−	2.19350e12i		−	1.83703i	−0.395391	−	0.918513i	$-0.629391\pi$
$103$		−	2.19350e12i		−	1.83703i	0.395391	−	0.918513i	$-0.370609\pi$
$104$		−	4.55082e10i		−	0.0359658i
$105$	−9.05316e10	−	1.11798e11i	−0.0675561	−	0.0834253i
$106$	1.14774e12			0.809109
$107$	−2.23020e12			−1.48608			−0.743038	−	0.669249i	$-0.766616\pi$
$107$	−2.23020e12			−1.48608			−0.743038	+	0.669249i	$0.766616\pi$
$108$		−	1.89492e11i		−	0.119412i
$109$	−2.47238e12			−1.47420			−0.737100	−	0.675783i	$-0.763805\pi$
$109$	−2.47238e12			−1.47420			−0.737100	+	0.675783i	$0.763805\pi$
$110$		−	1.50012e11i		−	0.0846779i
$111$			3.75132e12i			2.00561i
$112$	3.10541e11	+	3.83488e11i	0.157330	+	0.194287i
$113$	2.28940e12			1.09964			0.549820	−	0.835283i	$-0.314696\pi$
$113$	2.28940e12			1.09964			0.549820	+	0.835283i	$0.314696\pi$
$114$	5.60584e11			0.255395
$115$			7.79467e9i			0.00336985i
$116$	1.05870e12			0.434536
$117$			3.03326e11i			0.118248i
$118$			1.96438e12i			0.727669i
$119$	−2.88105e12	+	2.33302e12i	−1.01454	+	0.821554i
$120$	−1.13328e11			−0.0379533
$121$	5.30719e12			1.69104
$122$		−	3.43040e11i		−	0.104037i
$123$	−8.98436e12			−2.59452
$124$		−	2.58659e12i		−	0.711537i
$125$			5.55465e11i			0.145612i
$126$	−2.06984e12	−	2.55606e12i	−0.517266	−	0.638774i
$127$	2.34183e12			0.558127			0.279064	−	0.960273i	$-0.409976\pi$
$127$	2.34183e12			0.558127			0.279064	+	0.960273i	$0.409976\pi$
$128$	3.88736e11			0.0883883
$129$		−	6.70336e11i		−	0.145464i
$130$	2.53458e10			0.00525104
$131$			7.08702e12i			1.40228i	0.713021	+	0.701142i	$0.247326\pi$
$131$			7.08702e12i			1.40228i	−0.713021	+	0.701142i	$0.752674\pi$
$132$		−	6.38032e12i		−	1.20614i
$133$	1.05650e12	−	8.55536e11i	0.190880	−	0.154571i
$134$	1.13410e12			0.195894
$135$	1.05537e11			0.0174343
$136$			2.92048e12i			0.461552i
$137$	−4.08596e12			−0.617975			−0.308988	−	0.951066i	$-0.599990\pi$
$137$	−4.08596e12			−0.617975			−0.308988	+	0.951066i	$0.599990\pi$
$138$			3.31523e11i			0.0479998i
$139$		−	9.72215e12i		−	1.34795i	−0.738754	−	0.673975i	$-0.764586\pi$
$139$		−	9.72215e12i		−	1.34795i	0.738754	−	0.673975i	$-0.235414\pi$
$140$	−2.13583e11	+	1.72955e11i	−0.0283660	+	0.0229702i
$141$	1.70444e13			2.16904
$142$	6.41191e12			0.782091
$143$			1.42696e12i			0.166876i
$144$	−2.59104e12			−0.290602
$145$			5.89642e11i			0.0634425i
$146$			6.20026e12i			0.640166i
$147$	−1.45137e13	−	3.08505e12i	−1.43838	−	0.305745i
$148$	7.16668e12			0.681942
$149$	−6.54133e12			−0.597789			−0.298895	−	0.954286i	$-0.596618\pi$
$149$	−6.54133e12			−0.597789			−0.298895	+	0.954286i	$0.596618\pi$
$150$			1.17810e13i			1.03427i
$151$	1.44620e13			1.22002			0.610008	−	0.792395i	$-0.291166\pi$
$151$	1.44620e13			1.22002			0.610008	+	0.792395i	$0.291166\pi$
$152$		−	1.07096e12i		−	0.0868386i
$153$		−	1.94658e13i		−	1.51749i
$154$	−9.73732e12	−	1.20247e13i	−0.729987	−	0.901464i
$155$	1.44060e12			0.103885
$156$	1.07801e12			0.0747952
$157$		−	2.68217e13i		−	1.79097i	−0.445088	−	0.895487i	$-0.646828\pi$
$157$		−	2.68217e13i		−	1.79097i	0.445088	−	0.895487i	$-0.353172\pi$
$158$	−7.62344e12			−0.490014
$159$			2.71878e13i			1.68264i
$160$			2.16506e11i			0.0129048i
$161$	5.05954e11	+	6.24804e11i	0.0290506	+	0.0358747i
$162$	−1.03684e13			−0.573615
$163$	−2.66320e12			−0.141997			−0.0709984	−	0.997476i	$-0.522619\pi$
$163$	−2.66320e12			−0.141997			−0.0709984	+	0.997476i	$0.522619\pi$
$164$			1.71641e13i			0.882181i
$165$	3.55351e12			0.176098
$166$		−	3.28730e12i		−	0.157105i
$167$			3.67875e13i			1.69591i	0.530071	+	0.847953i	$0.322165\pi$
$167$			3.67875e13i			1.69591i	−0.530071	+	0.847953i	$0.677835\pi$
$168$	−9.08413e12	+	7.35614e12i	−0.404043	+	0.327186i
$169$	2.30570e13			0.989652
$170$	−1.62656e12			−0.0673870
$171$			7.13828e12i			0.285507i
$172$	−1.28064e12			−0.0494601
$173$		−	1.50745e13i		−	0.562298i	−0.959664	−	0.281149i	$-0.909284\pi$
$173$		−	1.50745e13i		−	0.562298i	0.959664	−	0.281149i	$-0.0907156\pi$
$174$			2.50787e13i			0.903669i
$175$	1.79795e13	+	2.22030e13i	0.625965	+	0.773006i
$176$	−1.21892e13			−0.410109
$177$	−4.65326e13			−1.51327
$178$		−	2.71315e13i		−	0.853009i
$179$	−4.06701e13			−1.23639			−0.618197	−	0.786023i	$-0.712137\pi$
$179$	−4.06701e13			−1.23639			−0.618197	+	0.786023i	$0.712137\pi$
$180$		−	1.44308e12i		−	0.0424282i
$181$		−	7.64135e11i		−	0.0217319i	−0.999941	−	0.0108660i	$-0.996541\pi$
$181$		−	7.64135e11i		−	0.0217319i	0.999941	−	0.0108660i	$-0.00345881\pi$
$182$	2.03166e12	−	1.64520e12i	0.0559015	−	0.0452679i
$183$	8.12599e12			0.216356
$184$	6.33355e11			0.0163208
$185$			3.99147e12i			0.0995641i
$186$	6.12715e13			1.47973
$187$		−	9.15746e13i		−	2.14154i
$188$		−	3.25623e13i		−	0.737510i
$189$	8.45967e12	−	6.85047e12i	0.185602	−	0.150297i
$190$	5.96472e11			0.0126785
$191$	3.10154e12			0.0638817			0.0319409	−	0.999490i	$-0.489831\pi$
$191$	3.10154e12			0.0638817			0.0319409	+	0.999490i	$0.489831\pi$
$192$			9.20845e12i			0.183814i
$193$	5.22452e13			1.01089			0.505444	−	0.862860i	$-0.331329\pi$
$193$	5.22452e13			1.01089			0.505444	+	0.862860i	$0.331329\pi$
$194$		−	2.69825e13i		−	0.506141i
$195$			6.00394e11i			0.0109202i
$196$	−5.89381e12	+	2.77275e13i	−0.103958	+	0.489073i
$197$	−1.29468e13			−0.221496			−0.110748	−	0.993849i	$-0.535325\pi$
$197$	−1.29468e13			−0.221496			−0.110748	+	0.993849i	$0.535325\pi$
$198$	8.12447e13			1.34835
$199$			5.00931e11i			0.00806603i	0.999992	+	0.00403302i	$0.00128375\pi$
$199$			5.00931e11i			0.00806603i	−0.999992	+	0.00403302i	$0.998716\pi$
$200$	2.25068e13			0.351669
$201$			2.68646e13i			0.407385i
$202$		−	1.37223e13i		−	0.201985i
$203$	3.82738e13	+	4.72645e13i	0.546922	+	0.675397i
$204$	−6.91808e13			−0.959853
$205$	−9.55952e12			−0.128799
$206$		−	9.92667e13i		−	1.29897i
$207$	−4.22150e12			−0.0536592
$208$		−	2.05947e12i		−	0.0254317i
$209$			3.35811e13i			0.402919i
$210$	−4.09699e12	−	5.05939e12i	−0.0477694	−	0.0589906i
$211$	−1.26806e14			−1.43696			−0.718480	−	0.695548i	$-0.755162\pi$
$211$	−1.26806e14			−1.43696			−0.718480	+	0.695548i	$0.755162\pi$
$212$	5.19406e13			0.572126
$213$			1.51886e14i			1.62645i
$214$	−1.00927e14			−1.05081
$215$		−	7.13249e11i		−	0.00722122i
$216$		−	8.57544e12i		−	0.0844372i
$217$	1.15475e14	−	9.35096e13i	1.10594	−	0.895566i
$218$	−1.11887e14			−1.04242
$219$	−1.46873e14			−1.33130
$220$		−	6.78877e12i		−	0.0598763i
$221$	1.54723e13			0.132801
$222$			1.69765e14i			1.41818i
$223$			4.73295e13i			0.384860i	0.981311	+	0.192430i	$0.0616369\pi$
$223$			4.73295e13i			0.384860i	−0.981311	+	0.192430i	$0.938363\pi$
$224$	1.40535e13	+	1.73547e13i	0.111249	+	0.137382i
$225$	−1.50015e14			−1.15621
$226$	1.03606e14			0.777562
$227$		−	2.17390e12i		−	0.0158886i	−0.999968	−	0.00794429i	$-0.997471\pi$
$227$		−	2.17390e12i		−	0.0158886i	0.999968	−	0.00794429i	$-0.00252877\pi$
$228$	2.53692e13			0.180591
$229$			2.05092e14i			1.42212i	0.703133	+	0.711058i	$0.251784\pi$
$229$			2.05092e14i			1.42212i	−0.703133	+	0.711058i	$0.748216\pi$
$230$			3.52746e11i			0.00238284i
$231$	2.84842e14	−	2.30659e14i	1.87470	−	1.51810i
$232$	4.79113e13			0.307263
$233$	−6.80772e13			−0.425467			−0.212734	−	0.977110i	$-0.568237\pi$
$233$	−6.80772e13			−0.425467			−0.212734	+	0.977110i	$0.568237\pi$
$234$			1.37269e13i			0.0836140i
$235$	1.81355e13			0.107677
$236$			8.88977e13i			0.514539i
$237$		−	1.80585e14i		−	1.01904i
$238$	−1.30382e14	+	1.05580e14i	−0.717388	+	0.580926i
$239$	1.26369e14			0.678036			0.339018	−	0.940780i	$-0.389905\pi$
$239$	1.26369e14			0.678036			0.339018	+	0.940780i	$0.389905\pi$
$240$	−5.12863e12			−0.0268370
$241$		−	3.02064e13i		−	0.154169i	−0.997025	−	0.0770844i	$-0.975439\pi$
$241$		−	3.02064e13i		−	0.154169i	0.997025	−	0.0770844i	$-0.0245611\pi$
$242$	2.40176e14			1.19574
$243$		−	2.94780e14i		−	1.43173i
$244$		−	1.55242e13i		−	0.0735649i
$245$	−1.54428e13	−	3.28255e12i	−0.0714051	−	0.0151780i
$246$	−4.06586e14			−1.83460
$247$	−5.67381e12			−0.0249858
$248$		−	1.17056e14i		−	0.503132i
$249$	7.78700e13			0.326719
$250$			2.51375e13i			0.102963i
$251$		−	2.03645e14i		−	0.814390i	−0.913341	−	0.407195i	$-0.866507\pi$
$251$		−	2.03645e14i		−	0.814390i	0.913341	−	0.407195i	$-0.133493\pi$
$252$	−9.36704e13	−	1.15674e14i	−0.365763	−	0.451682i
$253$	−1.98595e13			−0.0757260
$254$	1.05979e14			0.394655
$255$		−	3.85302e13i		−	0.140139i
$256$	1.75922e13			0.0625000
$257$			2.29316e14i			0.795858i	0.917416	+	0.397929i	$0.130271\pi$
$257$			2.29316e14i			0.795858i	−0.917416	+	0.397929i	$0.869729\pi$
$258$		−	3.03359e13i		−	0.102858i
$259$	2.59088e14	+	3.19948e14i	0.858317	+	1.05994i
$260$	1.14702e12			0.00371304
$261$	−3.19343e14			−1.01022
$262$			3.20722e14i			0.991565i
$263$	3.02864e14			0.915193			0.457596	−	0.889160i	$-0.348710\pi$
$263$	3.02864e14			0.915193			0.457596	+	0.889160i	$0.348710\pi$
$264$		−	2.88740e14i		−	0.852872i
$265$			2.89283e13i			0.0835309i
$266$	4.78119e13	−	3.87171e13i	0.134973	−	0.109298i
$267$	6.42695e14			1.77393
$268$	5.13233e13			0.138518
$269$			3.63942e13i			0.0960547i	0.998846	+	0.0480274i	$0.0152935\pi$
$269$			3.63942e13i			0.0960547i	−0.998846	+	0.0480274i	$0.984707\pi$
$270$	4.77608e12			0.0123279
$271$		−	2.97191e14i		−	0.750274i	−0.926969	−	0.375137i	$-0.877596\pi$
$271$		−	2.97191e14i		−	0.750274i	0.926969	−	0.375137i	$-0.122404\pi$
$272$			1.32166e14i			0.326367i
$273$	3.89718e13	+	4.81264e13i	0.0941400	+	0.116254i
$274$	−1.84910e14			−0.436974
$275$	−7.05725e14			−1.63170
$276$			1.50030e13i			0.0339410i
$277$	−6.62941e14			−1.46756			−0.733781	−	0.679386i	$-0.762246\pi$
$277$	−6.62941e14			−1.46756			−0.733781	+	0.679386i	$0.762246\pi$
$278$		−	4.39974e14i		−	0.953144i
$279$			7.80210e14i			1.65419i
$280$	−9.66567e12	+	7.82706e12i	−0.0200578	+	0.0162424i
$281$	−4.31286e14			−0.876046			−0.438023	−	0.898964i	$-0.644321\pi$
$281$	−4.31286e14			−0.876046			−0.438023	+	0.898964i	$0.644321\pi$
$282$	7.71341e14			1.53374
$283$		−	5.58480e14i		−	1.08715i	−0.839361	−	0.543574i	$-0.817071\pi$
$283$		−	5.58480e14i		−	1.08715i	0.839361	−	0.543574i	$-0.182929\pi$
$284$	2.90170e14			0.553022
$285$			1.41293e13i			0.0263665i
$286$			6.45767e13i			0.117999i
$287$	−7.66271e14	+	6.20511e14i	−1.37117	+	1.11034i
$288$	−1.17257e14			−0.205487
$289$	−4.10307e14			−0.704243
$290$			2.66842e13i			0.0448606i
$291$	6.39166e14			1.05258
$292$			2.80592e14i			0.452666i
$293$			3.66225e14i			0.578818i	0.957205	+	0.289409i	$0.0934588\pi$
$293$			3.66225e14i			0.578818i	−0.957205	+	0.289409i	$0.906541\pi$
$294$	−6.56813e14	−	1.39614e14i	−1.01709	−	0.216194i
$295$	−4.95115e13			−0.0751232
$296$	3.24327e14			0.482206
$297$			2.68892e14i			0.391777i
$298$	−2.96027e14			−0.422701
$299$		−	3.35542e12i		−	0.00469591i
$300$			5.33146e14i			0.731338i
$301$	−4.62972e13	−	5.71726e13i	−0.0622523	−	0.0768757i
$302$	6.54474e14			0.862682
$303$	3.25057e14			0.420053
$304$		−	4.84663e13i		−	0.0614042i
$305$	8.64620e12			0.0107405
$306$		−	8.80924e14i		−	1.07302i
$307$		−	1.45983e14i		−	0.174370i	−0.996192	−	0.0871851i	$-0.972213\pi$
$307$		−	1.45983e14i		−	0.174370i	0.996192	−	0.0871851i	$-0.0277872\pi$
$308$	−4.40661e14	−	5.44174e14i	−0.516179	−	0.637431i
$309$	2.35145e15			2.70137
$310$	6.51940e13			0.0734577
$311$		−	1.23106e15i		−	1.36055i	−0.732955	−	0.680277i	$-0.761859\pi$
$311$		−	1.23106e15i		−	1.36055i	0.732955	−	0.680277i	$-0.238141\pi$
$312$	4.87850e13			0.0528882
$313$			1.82094e15i			1.93656i	0.249875	+	0.968278i	$0.419611\pi$
$313$			1.82094e15i			1.93656i	−0.249875	+	0.968278i	$0.580389\pi$
$314$		−	1.21381e15i		−	1.26641i
$315$	6.44245e13	−	5.21696e13i	0.0659459	−	0.0534016i
$316$	−3.44998e14			−0.346492
$317$	1.29361e14			0.127482			0.0637410	−	0.997966i	$-0.479697\pi$
$317$	1.29361e14			0.127482			0.0637410	+	0.997966i	$0.479697\pi$
$318$			1.23038e15i			1.18981i
$319$	−1.50231e15			−1.42566
$320$			9.79795e12i			0.00912505i
$321$		−	2.39078e15i		−	2.18530i
$322$	2.28969e13	+	2.82754e13i	0.0205419	+	0.0253673i
$323$	3.64115e14			0.320644
$324$	−4.69219e14			−0.405607
$325$		−	1.19238e14i		−	0.101185i
$326$	−1.20523e14			−0.100407
$327$		−	2.65040e15i		−	2.16783i
$328$			7.76758e14i			0.623796i
$329$	1.45371e15	−	1.17718e15i	1.14631	−	0.928257i
$330$	1.60813e14			0.124520
$331$	9.24861e14			0.703248			0.351624	−	0.936141i	$-0.385630\pi$
$331$	9.24861e14			0.703248			0.351624	+	0.936141i	$0.385630\pi$
$332$		−	1.48766e14i		−	0.111090i
$333$	−2.16173e15			−1.58539
$334$			1.66481e15i			1.19919i
$335$			2.85844e13i			0.0202237i
$336$	−4.11101e14	+	3.32901e14i	−0.285701	+	0.231355i
$337$	1.90391e15			1.29977			0.649884	−	0.760033i	$-0.274817\pi$
$337$	1.90391e15			1.29977			0.649884	+	0.760033i	$0.274817\pi$
$338$	1.04344e15			0.699789
$339$			2.45424e15i			1.61703i
$340$	−7.36096e13			−0.0476498
$341$			3.67040e15i			2.33446i
$342$			3.23042e14i			0.201884i
$343$	−1.45093e15	+	7.39273e14i	−0.891010	+	0.453983i
$344$	−5.79550e13			−0.0349736
$345$	−8.35591e12			−0.00495541
$346$		−	6.82195e14i		−	0.397605i
$347$	−1.72203e15			−0.986425			−0.493212	−	0.869909i	$-0.664177\pi$
$347$	−1.72203e15			−0.986425			−0.493212	+	0.869909i	$0.664177\pi$
$348$			1.13493e15i			0.638990i
$349$		−	1.49883e15i		−	0.829467i	−0.909943	−	0.414733i	$-0.863875\pi$
$349$		−	1.49883e15i		−	0.829467i	0.909943	−	0.414733i	$-0.136125\pi$
$350$	8.13660e14	+	1.00479e15i	0.442624	+	0.546598i
$351$	−4.54314e13			−0.0242948
$352$	−5.51621e14			−0.289991
$353$			1.79110e14i			0.0925702i	0.998928	+	0.0462851i	$0.0147383\pi$
$353$			1.79110e14i			0.0925702i	−0.998928	+	0.0462851i	$0.985262\pi$
$354$	−2.10582e15			−1.07005
$355$			1.61610e14i			0.0807417i
$356$		−	1.22783e15i		−	0.603169i
$357$	−2.50100e15	−	3.08850e15i	−1.20811	−	1.49189i
$358$	−1.84052e15			−0.874263
$359$	−5.28786e14			−0.247009			−0.123505	−	0.992344i	$-0.539413\pi$
$359$	−5.28786e14			−0.247009			−0.123505	+	0.992344i	$0.539413\pi$
$360$		−	6.53062e13i		−	0.0300012i
$361$	2.07979e15			0.939672
$362$		−	3.45808e13i		−	0.0153668i
$363$			5.68933e15i			2.48669i
$364$	9.19426e13	−	7.44532e13i	0.0395283	−	0.0320092i
$365$	−1.56275e14			−0.0660896
$366$	3.67740e14			0.152987
$367$		−	6.75196e14i		−	0.276333i	−0.990409	−	0.138167i	$-0.955879\pi$
$367$		−	6.75196e14i		−	0.276333i	0.990409	−	0.138167i	$-0.0441210\pi$
$368$	2.86624e13			0.0115405
$369$		−	5.17732e15i		−	2.05091i
$370$			1.80633e14i			0.0704024i
$371$	1.87774e15	+	2.31883e15i	0.720099	+	0.889253i
$372$	2.77283e15			1.04632
$373$	1.84851e15			0.686388			0.343194	−	0.939265i	$-0.388491\pi$
$373$	1.84851e15			0.686388			0.343194	+	0.939265i	$0.388491\pi$
$374$		−	4.14419e15i		−	1.51429i
$375$	−5.95461e14			−0.214124
$376$		−	1.47360e15i		−	0.521498i
$377$		−	2.53827e14i		−	0.0884077i
$378$	3.82841e14	−	3.10017e14i	0.131240	−	0.106276i
$379$	2.24253e15			0.756663			0.378332	−	0.925670i	$-0.376498\pi$
$379$	2.24253e15			0.756663			0.378332	+	0.925670i	$0.376498\pi$
$380$	2.69932e13			0.00896506
$381$			2.51045e15i			0.820733i
$382$	1.40360e14			0.0451712
$383$		−	8.89625e14i		−	0.281847i	−0.990020	−	0.140924i	$-0.954993\pi$
$383$		−	8.89625e14i		−	0.281847i	0.990020	−	0.140924i	$-0.0450072\pi$
$384$			4.16727e14i			0.129976i
$385$	3.03077e14	−	2.45425e14i	0.0930654	−	0.0753625i
$386$	2.36435e15			0.714805
$387$	3.86287e14			0.114986
$388$		−	1.22109e15i		−	0.357896i
$389$	7.42639e14			0.214329			0.107164	−	0.994241i	$-0.465823\pi$
$389$	7.42639e14			0.214329			0.107164	+	0.994241i	$0.465823\pi$
$390$			2.71708e13i			0.00772172i
$391$			2.15333e14i			0.0602630i
$392$	−2.66723e14	+	1.25480e15i	−0.0735097	+	0.345827i
$393$	−7.59732e15			−2.06208
$394$	−5.85906e14			−0.156621
$395$		−	1.92146e14i		−	0.0505881i
$396$	3.67671e15			0.953430
$397$		−	1.99583e15i		−	0.509776i	−0.966971	−	0.254888i	$-0.917961\pi$
$397$		−	1.99583e15i		−	0.509776i	0.966971	−	0.254888i	$-0.0820386\pi$
$398$			2.26696e13i			0.00570354i
$399$	9.17138e14	+	1.13258e15i	0.227299	+	0.280692i
$400$	1.01854e15			0.248668
$401$	2.28427e15			0.549390			0.274695	−	0.961531i	$-0.411423\pi$
$401$	2.28427e15			0.549390			0.274695	+	0.961531i	$0.411423\pi$
$402$			1.21575e15i			0.288064i
$403$	−6.20144e14			−0.144765
$404$		−	6.21002e14i		−	0.142825i
$405$		−	2.61331e14i		−	0.0592190i
$406$	1.73208e15	+	2.13895e15i	0.386733	+	0.477577i
$407$	−1.01696e16			−2.23737
$408$	−3.13077e15			−0.678718
$409$		−	3.53443e15i		−	0.755056i	−0.925998	−	0.377528i	$-0.876774\pi$
$409$		−	3.53443e15i		−	0.755056i	0.925998	−	0.377528i	$-0.123226\pi$
$410$	−4.32614e14			−0.0910747
$411$		−	4.38017e15i		−	0.908741i
$412$		−	4.49230e15i		−	0.918513i
$413$	−3.96874e15	+	3.21380e15i	−0.799746	+	0.647618i
$414$	−1.91043e14			−0.0379428
$415$	8.28551e13			0.0162192
$416$		−	9.32009e13i		−	0.0179829i
$417$	1.04222e16			1.98218
$418$			1.51971e15i			0.284907i
$419$			2.73391e15i			0.505243i	0.967565	+	0.252621i	$0.0812927\pi$
$419$			2.73391e15i			0.505243i	−0.967565	+	0.252621i	$0.918707\pi$
$420$	−1.85409e14	−	2.28962e14i	−0.0337780	−	0.0417126i
$421$	3.49107e15			0.626998			0.313499	−	0.949589i	$-0.398499\pi$
$421$	3.49107e15			0.626998			0.313499	+	0.949589i	$0.398499\pi$
$422$	−5.73858e15			−1.01608
$423$			9.82198e15i			1.71458i
$424$	2.35056e15			0.404554
$425$			7.65207e15i			1.29851i
$426$			6.87360e15i			1.15008i
$427$	6.93061e14	−	5.61227e14i	0.114342	−	0.0925915i
$428$	−4.56745e15			−0.743038
$429$	−1.52970e15			−0.245394
$430$		−	3.22780e13i		−	0.00510617i
$431$	8.84090e15			1.37922			0.689609	−	0.724182i	$-0.257782\pi$
$431$	8.84090e15			1.37922			0.689609	+	0.724182i	$0.257782\pi$
$432$		−	3.88080e14i		−	0.0597061i
$433$		−	4.47537e15i		−	0.679049i	−0.940597	−	0.339525i	$-0.889734\pi$
$433$		−	4.47537e15i		−	0.679049i	0.940597	−	0.339525i	$-0.110266\pi$
$434$	5.22582e15	−	4.23176e15i	0.782016	−	0.633261i
$435$	−6.32099e14			−0.0932931
$436$	−5.06344e15			−0.737100
$437$		−	7.89645e13i		−	0.0113382i
$438$	−6.64671e15			−0.941373
$439$			2.76499e15i			0.386283i	0.981171	+	0.193142i	$0.0618677\pi$
$439$			2.76499e15i			0.386283i	−0.981171	+	0.193142i	$0.938132\pi$
$440$		−	3.07225e14i		−	0.0423389i
$441$	1.77779e15	−	8.36362e15i	0.241684	−	1.13701i
$442$	7.00195e14			0.0939043
$443$	−1.06887e16			−1.41418			−0.707089	−	0.707125i	$-0.749992\pi$
$443$	−1.06887e16			−1.41418			−0.707089	+	0.707125i	$0.749992\pi$
$444$			7.68271e15i			1.00280i
$445$	6.83839e14			0.0880631
$446$			2.14189e15i			0.272137i
$447$		−	7.01233e15i		−	0.879057i
$448$	6.35987e14	+	7.85383e14i	0.0786648	+	0.0971435i
$449$	−5.18103e15			−0.632321			−0.316161	−	0.948706i	$-0.602394\pi$
$449$	−5.18103e15			−0.632321			−0.316161	+	0.948706i	$0.602394\pi$
$450$	−6.78889e15			−0.817567
$451$		−	2.43560e16i		−	2.89432i
$452$	4.68868e15			0.549820
$453$			1.55033e16i			1.79405i
$454$		−	9.83796e13i		−	0.0112349i
$455$	4.14666e13	+	5.12073e13i	0.00467337	+	0.00577117i
$456$	1.14808e15			0.127697
$457$	8.48271e15			0.931188			0.465594	−	0.884998i	$-0.345841\pi$
$457$	8.48271e15			0.931188			0.465594	+	0.884998i	$0.345841\pi$
$458$			9.28139e15i			1.00559i
$459$	2.91555e15			0.311777
$460$			1.59635e13i			0.00168492i
$461$		−	2.25369e15i		−	0.234795i	−0.993085	−	0.117397i	$-0.962545\pi$
$461$		−	2.25369e15i		−	0.234795i	0.993085	−	0.117397i	$-0.0374551\pi$
$462$	1.28905e16	−	1.04384e16i	1.32561	−	1.07346i
$463$	−8.71667e15			−0.884840			−0.442420	−	0.896808i	$-0.645880\pi$
$463$	−8.71667e15			−0.884840			−0.442420	+	0.896808i	$0.645880\pi$
$464$	2.16822e15			0.217268
$465$			1.54433e15i			0.152764i
$466$	−3.08082e15			−0.300851
$467$		−	3.59681e15i		−	0.346750i	−0.984856	−	0.173375i	$-0.944533\pi$
$467$		−	3.59681e15i		−	0.346750i	0.984856	−	0.173375i	$-0.0554673\pi$
$468$			6.21211e14i			0.0591240i
$469$	1.85542e15	+	2.29127e15i	0.174344	+	0.215298i
$470$	8.20720e14			0.0761392
$471$	2.87530e16			2.63365
$472$			4.02305e15i			0.363834i
$473$	1.81724e15			0.162273
$474$		−	8.17236e15i		−	0.720572i
$475$		−	2.80607e15i		−	0.244308i
$476$	−5.90039e15	+	4.77802e15i	−0.507270	+	0.410777i
$477$	−1.56672e16			−1.33009
$478$	5.71880e15			0.479444
$479$		−	6.00535e15i		−	0.497194i	−0.968607	−	0.248597i	$-0.920031\pi$
$479$		−	6.00535e15i		−	0.497194i	0.968607	−	0.248597i	$-0.0799694\pi$
$480$	−2.32095e14			−0.0189766
$481$		−	1.71824e15i		−	0.138743i
$482$		−	1.36698e15i		−	0.109014i
$483$	−6.69793e14	+	5.42385e14i	−0.0527543	+	0.0427193i
$484$	1.08691e16			0.845518
$485$	6.80084e14			0.0522531
$486$		−	1.33402e16i		−	1.01238i
$487$	1.14520e16			0.858434			0.429217	−	0.903201i	$-0.358790\pi$
$487$	1.14520e16			0.858434			0.429217	+	0.903201i	$0.358790\pi$
$488$		−	7.02546e14i		−	0.0520183i
$489$		−	2.85497e15i		−	0.208808i
$490$	−6.98861e14	−	1.48551e14i	−0.0504910	−	0.0107325i
$491$	−1.14179e16			−0.814883			−0.407442	−	0.913231i	$-0.633579\pi$
$491$	−1.14179e16			−0.814883			−0.407442	+	0.913231i	$0.633579\pi$
$492$	−1.84000e16			−1.29726
$493$			1.62893e16i			1.13454i
$494$	−2.56767e14			−0.0176676
$495$			2.04774e15i			0.139201i
$496$		−	5.29733e15i		−	0.355768i
$497$	1.04901e16	+	1.29543e16i	0.696054	+	0.859560i
$498$	3.52400e15			0.231025
$499$	−1.13206e16			−0.733272			−0.366636	−	0.930365i	$-0.619490\pi$
$499$	−1.13206e16			−0.733272			−0.366636	+	0.930365i	$0.619490\pi$
$500$			1.13759e15i			0.0728059i
$501$	−3.94364e16			−2.49385
$502$		−	9.21594e15i		−	0.575860i
$503$			9.12462e15i			0.563387i	0.959504	+	0.281694i	$0.0908962\pi$
$503$			9.12462e15i			0.563387i	−0.959504	+	0.281694i	$0.909104\pi$
$504$	−4.23904e15	−	5.23481e15i	−0.258633	−	0.319387i
$505$	3.45866e14			0.0208526
$506$	−8.98738e14			−0.0535464
$507$			2.47172e16i			1.45530i
$508$	4.79607e15			0.279064
$509$		−	9.35116e15i		−	0.537723i	−0.963179	−	0.268862i	$-0.913353\pi$
$509$		−	9.35116e15i		−	0.537723i	0.963179	−	0.268862i	$-0.0866475\pi$
$510$		−	1.74368e15i		−	0.0990934i
$511$	−1.25267e16	+	1.01439e16i	−0.703577	+	0.569742i
$512$	7.96131e14			0.0441942
$513$	−1.06916e15			−0.0586593
$514$			1.03777e16i			0.562756i
$515$	2.50198e15			0.134104
$516$		−	1.37285e15i		−	0.0727318i
$517$			4.62063e16i			2.41968i
$518$	1.17250e16	+	1.44792e16i	0.606922	+	0.749490i
$519$	1.61599e16			0.826867
$520$	5.19081e13			0.00262552
$521$		−	3.53242e16i		−	1.76623i	−0.469160	−	0.883113i	$-0.655443\pi$
$521$		−	3.53242e16i		−	1.76623i	0.469160	−	0.883113i	$-0.344557\pi$
$522$	−1.44518e16			−0.714331
$523$			2.35177e15i			0.114917i	0.998348	+	0.0574587i	$0.0182997\pi$
$523$			2.35177e15i			0.114917i	−0.998348	+	0.0574587i	$0.981700\pi$
$524$			1.45142e16i			0.701142i
$525$	−2.38017e16	+	1.92741e16i	−1.13672	+	0.920489i
$526$	1.37060e16			0.647139
$527$	3.97976e16			1.85777
$528$		−	1.30669e16i		−	0.603071i
$529$	−2.18679e16			−0.997869
$530$			1.30914e15i			0.0590653i
$531$		−	2.68148e16i		−	1.19621i
$532$	2.16372e15	−	1.75214e15i	0.0954402	−	0.0772856i
$533$	4.11515e15			0.179483
$534$	2.90851e16			1.25436
$535$		−	2.54384e15i		−	0.108484i
$536$	2.32263e15			0.0979469
$537$		−	4.35985e16i		−	1.81813i
$538$			1.64701e15i			0.0679209i
$539$	8.36338e15	−	3.93456e16i	0.341075	−	1.60459i
$540$	2.16141e14			0.00871714
$541$	−1.86470e16			−0.743748			−0.371874	−	0.928283i	$-0.621285\pi$
$541$	−1.86470e16			−0.743748			−0.371874	+	0.928283i	$0.621285\pi$
$542$		−	1.34493e16i		−	0.530524i
$543$	8.19156e14			0.0319571
$544$			5.98114e15i			0.230776i
$545$		−	2.82008e15i		−	0.107617i
$546$	1.76366e15	+	2.17795e15i	0.0665670	+	0.0822039i
$547$	2.59639e16			0.969273			0.484636	−	0.874716i	$-0.338952\pi$
$547$	2.59639e16			0.969273			0.484636	+	0.874716i	$0.338952\pi$
$548$	−8.36805e15			−0.308988
$549$			4.68267e15i			0.171025i
$550$	−3.19375e16			−1.15378
$551$		−	5.97342e15i		−	0.213458i
$552$			6.78959e14i			0.0239999i
$553$	−1.24722e16	−	1.54020e16i	−0.436108	−	0.538551i
$554$	−3.00013e16			−1.03772
$555$	−4.27887e15			−0.146410
$556$		−	1.99110e16i		−	0.673975i
$557$	2.00221e16			0.670468			0.335234	−	0.942135i	$-0.391185\pi$
$557$	2.00221e16			0.670468			0.335234	+	0.942135i	$0.391185\pi$
$558$			3.53083e16i			1.16969i
$559$			3.07037e14i			0.0100628i
$560$	−4.37418e14	+	3.54212e14i	−0.0141830	+	0.0114851i
$561$	9.81683e16			3.14916
$562$	−1.95178e16			−0.619458
$563$			1.70380e16i			0.535018i	0.963555	+	0.267509i	$0.0862005\pi$
$563$			1.70380e16i			0.535018i	−0.963555	+	0.267509i	$0.913799\pi$
$564$	3.49069e16			1.08452
$565$			2.61136e15i			0.0802741i
$566$		−	2.52739e16i		−	0.768730i
$567$	−1.69631e16	−	2.09478e16i	−0.510512	−	0.630433i
$568$	1.31316e16			0.391046
$569$	2.03057e16			0.598334			0.299167	−	0.954201i	$-0.403291\pi$
$569$	2.03057e16			0.598334			0.299167	+	0.954201i	$0.403291\pi$
$570$			6.39420e14i			0.0186439i
$571$	−9.05567e15			−0.261279			−0.130639	−	0.991430i	$-0.541703\pi$
$571$	−9.05567e15			−0.261279			−0.130639	+	0.991430i	$0.541703\pi$
$572$			2.92241e15i			0.0834381i
$573$			3.32486e15i			0.0939389i
$574$	−3.46775e16	+	2.80811e16i	−0.969563	+	0.785132i
$575$	1.65948e15			0.0459161
$576$	−5.30645e15			−0.145301
$577$			5.78906e16i			1.56875i	0.620288	+	0.784374i	$0.287016\pi$
$577$			5.78906e16i			1.56875i	−0.620288	+	0.784374i	$0.712984\pi$
$578$	−1.85684e16			−0.497975
$579$			5.60071e16i			1.48652i
$580$			1.20759e15i			0.0317213i
$581$	6.64149e15	−	5.37815e15i	0.172667	−	0.139822i
$582$	2.89254e16			0.744288
$583$	−7.37043e16			−1.87707
$584$			1.26981e16i			0.320083i
$585$	−3.45983e14			−0.00863215
$586$			1.65735e16i			0.409286i
$587$		−	5.59880e16i		−	1.36857i	−0.729215	−	0.684284i	$-0.760115\pi$
$587$		−	5.59880e16i		−	1.36857i	0.729215	−	0.684284i	$-0.239885\pi$
$588$	−2.97240e16	−	6.31819e15i	−0.719189	−	0.152872i
$589$	−1.45941e16			−0.349531
$590$	−2.24063e15			−0.0531201
$591$		−	1.38790e16i		−	0.325713i
$592$	1.46774e16			0.340971
$593$		−	3.11797e16i		−	0.717041i	−0.933522	−	0.358520i	$-0.883281\pi$
$593$		−	3.11797e16i		−	0.717041i	0.933522	−	0.358520i	$-0.116719\pi$
$594$			1.21686e16i			0.277028i
$595$	−2.66111e15	−	3.28622e15i	−0.0599738	−	0.0740618i
$596$	−1.33966e16			−0.298895
$597$	−5.37001e14			−0.0118612
$598$		−	1.51849e14i		−	0.00332051i
$599$	−3.49414e16			−0.756449			−0.378224	−	0.925714i	$-0.623465\pi$
$599$	−3.49414e16			−0.756449			−0.378224	+	0.925714i	$0.623465\pi$
$600$			2.41274e16i			0.517134i
$601$		−	2.44503e16i		−	0.518844i	−0.965764	−	0.259422i	$-0.916468\pi$
$601$		−	2.44503e16i		−	0.518844i	0.965764	−	0.259422i	$-0.0835320\pi$
$602$	−2.09517e15	−	2.58734e15i	−0.0440191	−	0.0543593i
$603$	−1.54810e16			−0.322029
$604$	2.96181e16			0.610008
$605$			6.05355e15i			0.123446i
$606$	1.47104e16			0.297022
$607$			6.93176e16i			1.38583i	0.721017	+	0.692917i	$0.243675\pi$
$607$			6.93176e16i			1.38583i	−0.721017	+	0.692917i	$0.756325\pi$
$608$		−	2.19333e15i		−	0.0434193i
$609$	−5.06677e16	+	4.10297e16i	−0.993180	+	0.804257i
$610$	3.91282e14			0.00759471
$611$	−7.80693e15			−0.150049
$612$		−	3.98660e16i		−	0.758743i
$613$	5.03889e15			0.0949668			0.0474834	−	0.998872i	$-0.484880\pi$
$613$	5.03889e15			0.0949668			0.0474834	+	0.998872i	$0.484880\pi$
$614$		−	6.60644e15i		−	0.123298i
$615$		−	1.02478e16i		−	0.189401i
$616$	−1.99420e16	−	2.46265e16i	−0.364993	−	0.450732i
$617$	1.01129e16			0.183301			0.0916505	−	0.995791i	$-0.470786\pi$
$617$	1.01129e16			0.183301			0.0916505	+	0.995791i	$0.470786\pi$
$618$	1.06414e17			1.91016
$619$			4.17757e16i			0.742643i	0.928504	+	0.371322i	$0.121095\pi$
$619$			4.17757e16i			0.742643i	−0.928504	+	0.371322i	$0.878905\pi$
$620$	2.95034e15			0.0519425
$621$		−	6.32286e14i		−	0.0110246i
$622$		−	5.57113e16i		−	0.962057i
$623$	5.48151e16	−	4.43882e16i	0.937502	−	0.759170i
$624$	2.20776e15			0.0373976
$625$	5.86534e16			0.984041
$626$			8.24064e16i			1.36935i
$627$	−3.59991e16			−0.592498
$628$		−	5.49309e16i		−	0.895487i
$629$			1.10267e17i			1.78051i
$630$	2.91552e15	−	2.36093e15i	0.0466308	−	0.0377607i
$631$	1.76249e16			0.279222			0.139611	−	0.990206i	$-0.455415\pi$
$631$	1.76249e16			0.279222			0.139611	+	0.990206i	$0.455415\pi$
$632$	−1.56128e16			−0.245007
$633$		−	1.35936e17i		−	2.11307i
$634$	5.85422e15			0.0901434
$635$			2.67116e15i			0.0407435i
$636$			5.56805e16i			0.841319i
$637$	6.64776e15	+	1.41306e15i	0.0995036	+	0.0211507i
$638$	−6.79867e16			−1.00809
$639$	−8.75259e16			−1.28568
$640$			4.43404e14i			0.00645238i
$641$	9.19775e16			1.32597			0.662985	−	0.748633i	$-0.269289\pi$
$641$	9.19775e16			1.32597			0.662985	+	0.748633i	$0.269289\pi$
$642$		−	1.08195e17i		−	1.54524i
$643$			8.41252e16i			1.19031i	0.803611	+	0.595155i	$0.202909\pi$
$643$			8.41252e16i			1.19031i	−0.803611	+	0.595155i	$0.797091\pi$
$644$	1.03619e15	+	1.27960e15i	0.0145253	+	0.0179374i
$645$	7.64606e14			0.0106189
$646$	1.64780e16			0.226730
$647$			2.78573e16i			0.379763i	0.981807	+	0.189882i	$0.0608104\pi$
$647$			2.78573e16i			0.379763i	−0.981807	+	0.189882i	$0.939190\pi$
$648$	−2.12344e16			−0.286808
$649$		−	1.26147e17i		−	1.68814i
$650$		−	5.39609e15i		−	0.0715483i
$651$	1.00243e17	+	1.23790e17i	1.31694	+	1.62630i
$652$	−5.45424e15			−0.0709984
$653$	−1.21824e17			−1.57129			−0.785643	−	0.618680i	$-0.787668\pi$
$653$	−1.21824e17			−1.57129			−0.785643	+	0.618680i	$0.787668\pi$
$654$		−	1.19944e17i		−	1.53289i
$655$	−8.08368e15			−0.102367
$656$			3.51520e16i			0.441090i
$657$		−	8.46368e16i		−	1.05237i
$658$	6.57873e16	−	5.32732e16i	0.810562	−	0.656377i
$659$	−3.66111e16			−0.446993			−0.223496	−	0.974705i	$-0.571747\pi$
$659$	−3.66111e16			−0.446993			−0.223496	+	0.974705i	$0.571747\pi$
$660$	7.27759e15			0.0880489
$661$		−	7.72872e16i		−	0.926614i	−0.886198	−	0.463307i	$-0.846663\pi$
$661$		−	7.72872e16i		−	0.926614i	0.886198	−	0.463307i	$-0.153337\pi$
$662$	4.18544e16			0.497272
$663$			1.65863e16i			0.195285i
$664$		−	6.73238e15i		−	0.0785526i
$665$	9.75851e14	+	1.20508e15i	0.0112838	+	0.0139344i
$666$	−9.78288e16			−1.12104
$667$	3.53261e15			0.0401181
$668$			7.53409e16i			0.847953i
$669$	−5.07375e16			−0.565942
$670$			1.29358e15i			0.0143003i
$671$			2.20290e16i			0.241357i
$672$	−1.86043e16	+	1.50654e16i	−0.202021	+	0.163593i
$673$	1.52714e17			1.64357			0.821787	−	0.569795i	$-0.192977\pi$
$673$	1.52714e17			1.64357			0.821787	+	0.569795i	$0.192977\pi$
$674$	8.61609e16			0.919075
$675$		−	2.24689e16i		−	0.237552i
$676$	4.72207e16			0.494826
$677$		−	1.07425e16i		−	0.111577i	−0.998443	−	0.0557883i	$-0.982233\pi$
$677$		−	1.07425e16i		−	0.111577i	0.998443	−	0.0557883i	$-0.0177672\pi$
$678$			1.11066e17i			1.14342i
$679$	5.45141e16	−	4.41444e16i	0.556276	−	0.450461i
$680$	−3.33119e15			−0.0336935
$681$	2.33043e15			0.0233644
$682$			1.66103e17i			1.65071i
$683$	1.03035e17			1.01498			0.507491	−	0.861657i	$-0.330573\pi$
$683$	1.03035e17			1.01498			0.507491	+	0.861657i	$0.330573\pi$
$684$			1.46192e16i			0.142754i
$685$		−	4.66058e15i		−	0.0451124i
$686$	−6.56617e16	+	3.34557e16i	−0.630039	+	0.321015i
$687$	−2.19859e17			−2.09124
$688$	−2.62274e15			−0.0247301
$689$		−	1.24529e16i		−	0.116401i
$690$	−3.78145e14			−0.00350400
$691$			5.70743e16i			0.524291i	0.965028	+	0.262145i	$0.0844300\pi$
$691$			5.70743e16i			0.524291i	−0.965028	+	0.262145i	$0.915570\pi$
$692$		−	3.08726e16i		−	0.281149i
$693$	1.32919e17	+	1.64143e17i	1.20002	+	1.48191i
$694$	−7.79302e16			−0.697508
$695$	1.10894e16			0.0984009
$696$			5.13611e16i			0.451834i
$697$	−2.64089e17			−2.30331
$698$		−	6.78292e16i		−	0.586521i
$699$		−	7.29790e16i		−	0.625655i
$700$	3.68221e16	+	4.54717e16i	0.312982	+	0.386503i
$701$	−1.95015e17			−1.64347			−0.821733	−	0.569873i	$-0.806992\pi$
$701$	−1.95015e17			−1.64347			−0.821733	+	0.569873i	$0.806992\pi$
$702$	−2.05599e15			−0.0171790
$703$		−	4.04359e16i		−	0.334993i
$704$	−2.49635e16			−0.205055
$705$			1.94414e16i			0.158340i
$706$			8.10559e15i			0.0654570i
$707$	2.77239e16	−	2.24503e16i	0.221993	−	0.179765i
$708$	−9.52987e16			−0.756637
$709$	−1.08301e16			−0.0852617			−0.0426309	−	0.999091i	$-0.513574\pi$
$709$	−1.08301e16			−0.0852617			−0.0426309	+	0.999091i	$0.513574\pi$
$710$			7.31363e15i			0.0570930i
$711$	1.04064e17			0.805531
$712$		−	5.55653e16i		−	0.426505i
$713$		−	8.63077e15i		−	0.0656920i
$714$	−1.13182e17	−	1.39770e17i	−0.854260	−	1.05493i
$715$	−1.62763e15			−0.0121820
$716$	−8.32923e16			−0.618197
$717$			1.35468e17i			0.997061i
$718$	−2.39301e16			−0.174662
$719$			1.00540e17i			0.727723i	0.931453	+	0.363861i	$0.118542\pi$
$719$			1.00540e17i			0.727723i	−0.931453	+	0.363861i	$0.881458\pi$
$720$		−	2.95542e15i		−	0.0212141i
$721$	2.00554e17	−	1.62404e17i	1.42764	−	1.15607i
$722$	9.41206e16			0.664449
$723$	3.23813e16			0.226707
$724$		−	1.56495e15i		−	0.0108660i
$725$	1.25534e17			0.864440
$726$			2.57470e17i			1.75836i
$727$		−	1.63046e17i		−	1.10434i	−0.833731	−	0.552171i	$-0.813799\pi$
$727$		−	1.63046e17i		−	1.10434i	0.833731	−	0.552171i	$-0.186201\pi$
$728$	4.16085e15	−	3.36937e15i	0.0279507	−	0.0226339i
$729$	1.94246e17			1.29416
$730$	−7.07221e15			−0.0467324
$731$		−	1.97040e16i		−	0.129137i
$732$	1.66420e16			0.108178
$733$			1.65426e16i			0.106655i	0.998577	+	0.0533274i	$0.0169827\pi$
$733$			1.65426e16i			0.106655i	−0.998577	+	0.0533274i	$0.983017\pi$
$734$		−	3.05559e16i		−	0.195397i
$735$	3.51891e15	−	1.65547e16i	0.0223195	−	0.105002i
$736$	1.29711e15			0.00816038
$737$	−7.28283e16			−0.454460
$738$		−	2.34299e17i		−	1.45021i
$739$	2.54256e17			1.56101			0.780503	−	0.625152i	$-0.214963\pi$
$739$	2.54256e17			1.56101			0.780503	+	0.625152i	$0.214963\pi$
$740$			8.17453e15i			0.0497820i
$741$		−	6.08235e15i		−	0.0367419i
$742$	8.49769e16	+	1.04938e17i	0.509187	+	0.628797i
$743$	−1.70698e17			−1.01460			−0.507300	−	0.861770i	$-0.669356\pi$
$743$	−1.70698e17			−1.01460			−0.507300	+	0.861770i	$0.669356\pi$
$744$	1.25484e17			0.739863
$745$		−	7.46124e15i		−	0.0436389i
$746$	8.36542e16			0.485350
$747$			4.48733e16i			0.258264i
$748$		−	1.87545e17i		−	1.07077i
$749$	−1.65121e17	−	2.03909e17i	−0.935215	−	1.15490i
$750$	−2.69475e16			−0.151409
$751$	−1.89343e17			−1.05538			−0.527692	−	0.849436i	$-0.676942\pi$
$751$	−1.89343e17			−1.05538			−0.527692	+	0.849436i	$0.676942\pi$
$752$		−	6.66876e16i		−	0.368755i
$753$	2.18309e17			1.19757
$754$		−	1.14869e16i		−	0.0625137i
$755$			1.64958e16i			0.0890617i
$756$	1.73254e16	−	1.40298e16i	0.0928010	−	0.0751483i
$757$	8.85304e16			0.470454			0.235227	−	0.971940i	$-0.424417\pi$
$757$	8.85304e16			0.470454			0.235227	+	0.971940i	$0.424417\pi$
$758$	1.01485e17			0.535042
$759$		−	2.12895e16i		−	0.111356i
$760$	1.22157e15			0.00633926
$761$			4.28372e16i			0.220553i	0.993901	+	0.110277i	$0.0351736\pi$
$761$			4.28372e16i			0.220553i	−0.993901	+	0.110277i	$0.964826\pi$
$762$			1.13610e17i			0.580346i
$763$	−1.83052e17	−	2.26051e17i	−0.927741	−	1.14567i
$764$	6.35195e15			0.0319409
$765$	2.22033e16			0.110777
$766$		−	4.02598e16i		−	0.199296i
$767$	2.13135e16			0.104685
$768$			1.88589e16i			0.0919071i
$769$			2.46242e17i			1.19071i	0.803464	+	0.595353i	$0.202988\pi$
$769$			2.46242e17i			1.19071i	−0.803464	+	0.595353i	$0.797012\pi$
$770$	1.37157e16	−	1.11067e16i	0.0658072	−	0.0532893i
$771$	−2.45828e17			−1.17032
$772$	1.06998e17			0.505444
$773$			1.94663e17i			0.912446i	0.889865	+	0.456223i	$0.150798\pi$
$773$			1.94663e17i			0.912446i	−0.889865	+	0.456223i	$0.849202\pi$
$774$	1.74814e16			0.0813072
$775$		−	3.06702e17i		−	1.41549i
$776$		−	5.52602e16i		−	0.253071i
$777$	−3.42986e17	+	2.77743e17i	−1.55865	+	1.26217i
$778$	3.36080e16			0.151553
$779$	9.68435e16			0.433357
$780$			1.22961e15i			0.00546008i
$781$	−4.11755e17			−1.81440
$782$			9.74488e15i			0.0426124i
$783$		−	4.78305e16i		−	0.207556i
$784$	−1.20705e16	+	5.67859e16i	−0.0519792	+	0.244537i
$785$	3.05937e16			0.130742
$786$	−3.43815e17			−1.45811
$787$			1.48111e17i			0.623359i	0.950187	+	0.311679i	$0.100892\pi$
$787$			1.48111e17i			0.623359i	−0.950187	+	0.311679i	$0.899108\pi$
$788$	−2.65151e16			−0.110748
$789$			3.24671e17i			1.34580i
$790$		−	8.69553e15i		−	0.0357712i
$791$	1.69504e17	+	2.09321e17i	0.692023	+	0.854582i
$792$	1.66389e17			0.674177
$793$	−3.72199e15			−0.0149670
$794$		−	9.03208e16i		−	0.360466i
$795$	−3.10112e16			−0.122833
$796$			1.02591e15i			0.00403302i
$797$			1.70921e17i			0.666877i	0.942772	+	0.333438i	$0.108209\pi$
$797$			1.70921e17i			0.666877i	−0.942772	+	0.333438i	$0.891791\pi$
$798$	4.15049e16	+	5.12546e16i	0.160725	+	0.198479i
$799$	5.01008e17			1.92559
$800$	4.60940e16			0.175835
$801$			3.70359e17i			1.40226i
$802$	1.03374e17			0.388477
$803$		−	3.98163e17i		−	1.48514i
$804$			5.50188e16i			0.203692i
$805$	−7.12671e14	+	5.77107e14i	−0.00261887	+	0.00212071i
$806$	−2.80645e16			−0.102364
$807$	−3.90147e16			−0.141250
$808$		−	2.81034e16i		−	0.100993i
$809$	−4.96156e17			−1.76981			−0.884907	−	0.465769i	$-0.845778\pi$
$809$	−4.96156e17			−1.76981			−0.884907	+	0.465769i	$0.845778\pi$
$810$		−	1.18265e16i		−	0.0418741i
$811$			3.70989e17i			1.30388i	0.758272	+	0.651938i	$0.226044\pi$
$811$			3.70989e17i			1.30388i	−0.758272	+	0.651938i	$0.773956\pi$
$812$	7.83848e16	+	9.67977e16i	0.273461	+	0.337698i
$813$	3.18590e17			1.10329
$814$	−4.60223e17			−1.58206
$815$		−	3.03773e15i		−	0.0103658i
$816$	−1.41682e17			−0.479926
$817$			7.22563e15i			0.0242965i
$818$		−	1.59950e17i		−	0.533905i
$819$	−2.77333e16	+	2.24578e16i	−0.0918962	+	0.0744156i
$820$	−1.95779e16			−0.0643995
$821$	2.64103e17			0.862410			0.431205	−	0.902254i	$-0.358089\pi$
$821$	2.64103e17			0.862410			0.431205	+	0.902254i	$0.358089\pi$
$822$		−	1.98224e17i		−	0.642577i
$823$	3.77684e17			1.21543			0.607714	−	0.794156i	$-0.292087\pi$
$823$	3.77684e17			1.21543			0.607714	+	0.794156i	$0.292087\pi$
$824$		−	2.03298e17i		−	0.649487i
$825$		−	7.56540e17i		−	2.39943i
$826$	−1.79605e17	+	1.45440e17i	−0.565506	+	0.457935i
$827$	−9.11557e16			−0.284938			−0.142469	−	0.989799i	$-0.545504\pi$
$827$	−9.11557e16			−0.284938			−0.142469	+	0.989799i	$0.545504\pi$
$828$	−8.64562e15			−0.0268296
$829$		−	4.69921e17i		−	1.44776i	−0.689924	−	0.723882i	$-0.742356\pi$
$829$		−	4.69921e17i		−	1.44776i	0.689924	−	0.723882i	$-0.257644\pi$
$830$	3.74959e15			0.0114687
$831$		−	7.10676e17i		−	2.15807i
$832$		−	4.21779e15i		−	0.0127158i
$833$	−4.26618e17	−	9.06829e16i	−1.27694	−	0.271429i
$834$	4.71654e17			1.40161
$835$	−4.19610e16			−0.123802
$836$			6.87742e16i			0.201459i
$837$	−1.16858e17			−0.339865
$838$			1.23723e17i			0.357261i
$839$			5.97909e17i			1.71421i	0.515145	+	0.857103i	$0.327738\pi$
$839$			5.97909e17i			1.71421i	−0.515145	+	0.857103i	$0.672262\pi$
$840$	−8.39064e15	−	1.03616e16i	−0.0238847	−	0.0294953i
$841$	−8.65839e16			−0.244715
$842$	1.57988e17			0.443354
$843$		−	4.62340e17i		−	1.28824i
$844$	−2.59698e17			−0.718480
$845$			2.62995e16i			0.0722450i
$846$			4.44492e17i			1.21239i
$847$	3.92938e17	+	4.85240e17i	1.06420	+	1.31418i
$848$	1.06374e17			0.286063
$849$	5.98693e17			1.59867
$850$			3.46293e17i			0.918185i
$851$	2.39133e16			0.0629597
$852$			3.11063e17i			0.813226i
$853$		−	2.66720e16i		−	0.0692406i	−0.999401	−	0.0346203i	$-0.988978\pi$
$853$		−	2.66720e16i		−	0.0692406i	0.999401	−	0.0346203i	$-0.0110222\pi$
$854$	3.13644e16	−	2.53982e16i	0.0808517	−	0.0654721i
$855$	−8.14215e15			−0.0208421
$856$	−2.06699e17			−0.525407
$857$			1.73795e17i			0.438685i	0.975648	+	0.219342i	$0.0703911\pi$
$857$			1.73795e17i			0.438685i	−0.975648	+	0.219342i	$0.929609\pi$
$858$	−6.92265e16			−0.173520
$859$			6.29015e16i			0.156568i	0.996931	+	0.0782839i	$0.0249441\pi$
$859$			6.29015e16i			0.156568i	−0.996931	+	0.0782839i	$0.975056\pi$
$860$		−	1.46073e15i		−	0.00361061i
$861$	−6.65190e17	−	8.21446e17i	−1.63278	−	2.01632i
$862$	4.00094e17			0.975255
$863$	6.35808e17			1.53908			0.769540	−	0.638599i	$-0.220486\pi$
$863$	6.35808e17			1.53908			0.769540	+	0.638599i	$0.220486\pi$
$864$		−	1.75625e16i		−	0.0422186i
$865$	1.71945e16			0.0410480
$866$		−	2.02532e17i		−	0.480160i
$867$		−	4.39851e17i		−	1.03560i
$868$	2.36493e17	−	1.91508e17i	0.552969	−	0.447783i
$869$	4.89555e17			1.13680
$870$	−2.86055e16			−0.0659682
$871$		−	1.23049e16i		−	0.0281819i
$872$	−2.29145e17			−0.521209
$873$			3.68325e17i			0.832043i
$874$		−	3.57353e15i		−	0.00801730i
$875$	−5.07865e16	+	4.11259e16i	−0.113162	+	0.0916362i
$876$	−3.00796e17			−0.665651
$877$	−8.85746e16			−0.194676			−0.0973378	−	0.995251i	$-0.531033\pi$
$877$	−8.85746e16			−0.194676			−0.0973378	+	0.995251i	$0.531033\pi$
$878$			1.25129e17i			0.273143i
$879$	−3.92595e17			−0.851160
$880$		−	1.39034e16i		−	0.0299381i
$881$		−	1.56026e17i		−	0.333689i	−0.985983	−	0.166844i	$-0.946642\pi$
$881$		−	1.56026e17i		−	0.333689i	0.985983	−	0.166844i	$-0.0533577\pi$
$882$	8.04536e16	−	3.78494e17i	0.170897	−	0.803985i
$883$	−6.56199e17			−1.38443			−0.692215	−	0.721691i	$-0.743365\pi$
$883$	−6.56199e17			−1.38443			−0.692215	+	0.721691i	$0.743365\pi$
$884$	3.16872e16			0.0664004
$885$		−	5.30765e16i		−	0.110470i
$886$	−4.83717e17			−0.999975
$887$			7.09153e17i			1.45612i	0.685511	+	0.728062i	$0.259579\pi$
$887$			7.09153e17i			1.45612i	−0.685511	+	0.728062i	$0.740421\pi$
$888$			3.47680e17i			0.709090i
$889$	1.73386e17	+	2.14115e17i	0.351240	+	0.433747i
$890$	3.09470e16			0.0622700
$891$	6.65827e17			1.33075
$892$			9.69309e16i			0.192430i
$893$	−1.83723e17			−0.362290
$894$		−	3.17342e17i		−	0.621587i
$895$		−	4.63896e16i		−	0.0902573i
$896$	2.87815e16	+	3.55424e16i	0.0556244	+	0.0686908i
$897$	3.59703e15			0.00690540
$898$	−2.34467e17			−0.447119
$899$		−	6.52891e17i		−	1.23675i
$900$	−3.07230e17			−0.578107
$901$			7.99165e17i			1.49378i
$902$		−	1.10223e18i		−	2.04660i
$903$	6.12892e16	−	4.96308e16i	0.113047	−	0.0915429i
$904$	2.12186e17			0.388781
$905$	8.71596e14			0.00158644
$906$			7.01599e17i			1.26859i
$907$	−4.73361e17			−0.850254			−0.425127	−	0.905134i	$-0.639771\pi$
$907$	−4.73361e17			−0.850254			−0.425127	+	0.905134i	$0.639771\pi$
$908$		−	4.45215e15i		−	0.00794429i
$909$			1.87317e17i			0.332043i
$910$	1.87657e15	+	2.31738e15i	0.00330457	+	0.00408083i
$911$	−5.76025e16			−0.100770			−0.0503850	−	0.998730i	$-0.516045\pi$
$911$	−5.76025e16			−0.100770			−0.0503850	+	0.998730i	$0.516045\pi$
$912$	5.19560e16			0.0902957
$913$			2.11101e17i			0.364473i
$914$	3.83884e17			0.658450
$915$			9.26876e15i			0.0157941i
$916$			4.20028e17i			0.711058i
$917$	−6.47971e17	+	5.24714e17i	−1.08978	+	0.882483i
$918$	1.31943e17			0.220460
$919$	−1.13104e18			−1.87752			−0.938762	−	0.344565i	$-0.888026\pi$
$919$	−1.13104e18			−1.87752			−0.938762	+	0.344565i	$0.888026\pi$
$920$			7.22424e14i			0.00119142i
$921$	1.56494e17			0.256414
$922$		−	1.01990e17i		−	0.166025i
$923$		−	6.95693e16i		−	0.112514i
$924$	5.83356e17	−	4.72390e17i	0.937351	−	0.759048i
$925$	8.49782e17			1.35662
$926$	−3.94471e17			−0.625676
$927$			1.35504e18i			2.13538i
$928$	9.81224e16			0.153632
$929$			7.95751e17i			1.23789i	0.785433	+	0.618947i	$0.212440\pi$
$929$			7.95751e17i			1.23789i	−0.785433	+	0.618947i	$0.787560\pi$
$930$			6.98882e16i			0.108021i
$931$	1.56444e17	+	3.32542e16i	0.240249	+	0.0510679i
$932$	−1.39422e17			−0.212734
$933$	1.31970e18			2.00071
$934$		−	1.62773e17i		−	0.245189i
$935$	1.04453e17			0.156333
$936$			2.81128e16i			0.0418070i
$937$		−	1.07138e18i		−	1.58309i	−0.611108	−	0.791547i	$-0.709276\pi$
$937$		−	1.07138e18i		−	1.58309i	0.611108	−	0.791547i	$-0.290724\pi$
$938$	8.39669e16	+	1.03691e17i	0.123280	+	0.152238i
$939$	−1.95206e18			−2.84773
$940$	3.71416e16			0.0538385
$941$		−	8.32860e17i		−	1.19959i	−0.800152	−	0.599797i	$-0.795248\pi$
$941$		−	8.32860e17i		−	1.19959i	0.800152	−	0.599797i	$-0.204752\pi$
$942$	1.30121e18			1.86227
$943$			5.72721e16i			0.0814466i
$944$			1.82063e17i			0.257270i
$945$	7.81386e15	+	9.64936e15i	0.0109717	+	0.0135490i
$946$	8.22388e16			0.114744
$947$	−1.32682e17			−0.183956			−0.0919779	−	0.995761i	$-0.529319\pi$
$947$	−1.32682e17			−0.183956			−0.0919779	+	0.995761i	$0.529319\pi$
$948$		−	3.69839e17i		−	0.509521i
$949$	6.72729e16			0.0920964
$950$		−	1.26988e17i		−	0.172752i
$951$			1.38676e17i			0.187464i
$952$	−2.67021e17	+	2.16228e17i	−0.358694	+	0.290463i
$953$	−2.25730e17			−0.301323			−0.150662	−	0.988585i	$-0.548140\pi$
$953$	−2.25730e17			−0.301323			−0.150662	+	0.988585i	$0.548140\pi$
$954$	−7.09016e17			−0.940515
$955$			3.53771e15i			0.00466339i
$956$	2.58804e17			0.339018
$957$		−	1.61048e18i		−	2.09645i
$958$		−	2.71771e17i		−	0.351569i
$959$	−3.02519e17	−	3.73582e17i	−0.388903	−	0.480258i
$960$	−1.05034e16			−0.0134185
$961$	−8.07463e17			−1.02514
$962$		−	7.77585e16i		−	0.0981064i
$963$	1.37771e18			1.72743
$964$		−	6.18626e16i		−	0.0770844i
$965$			5.95925e16i			0.0737952i
$966$	−3.03114e16	+	2.45455e16i	−0.0373029	+	0.0302071i
$967$	−8.43823e17			−1.03203			−0.516015	−	0.856580i	$-0.672585\pi$
$967$	−8.43823e17			−1.03203			−0.516015	+	0.856580i	$0.672585\pi$
$968$	4.91881e17			0.597871
$969$			3.90333e17i			0.471512i
$970$	3.07771e16			0.0369485
$971$		−	9.09833e17i		−	1.08554i	−0.839881	−	0.542770i	$-0.817375\pi$
$971$		−	9.09833e17i		−	1.08554i	0.839881	−	0.542770i	$-0.182625\pi$
$972$		−	6.03709e17i		−	0.715863i
$973$	8.88903e17	−	7.19815e17i	1.04756	−	0.848289i
$974$	5.18258e17			0.607005
$975$	1.27824e17			0.148793
$976$		−	3.17936e16i		−	0.0367825i
$977$	1.42216e17			0.163524			0.0817621	−	0.996652i	$-0.473945\pi$
$977$	1.42216e17			0.163524			0.0817621	+	0.996652i	$0.473945\pi$
$978$		−	1.29201e17i		−	0.147650i
$979$			1.74231e18i			1.97892i
$980$	−3.16268e16	−	6.72266e15i	−0.0357025	−	0.00758901i
$981$	1.52732e18			1.71362
$982$	−5.16713e17			−0.576210
$983$		−	1.66871e18i		−	1.84953i	−0.380544	−	0.924763i	$-0.624263\pi$
$983$		−	1.66871e18i		−	1.84953i	0.380544	−	0.924763i	$-0.375737\pi$
$984$	−8.32688e17			−0.917300
$985$		−	1.47675e16i		−	0.0161693i
$986$			7.37170e17i			0.802243i
$987$	1.26194e18	+	1.55838e18i	1.36501	+	1.68566i
$988$	−1.16200e16			−0.0124929
$989$	−4.27315e15			−0.00456636
$990$			9.26702e16i			0.0984303i
$991$	1.52777e18			1.61293			0.806465	−	0.591282i	$-0.201378\pi$
$991$	1.52777e18			1.61293			0.806465	+	0.591282i	$0.201378\pi$
$992$		−	2.39730e17i		−	0.251566i
$993$			9.91455e17i			1.03414i
$994$	4.74729e17	+	5.86245e17i	0.492184	+	0.607801i
$995$	−5.71378e14			−0.000588823
$996$	1.59478e17			0.163359
$997$		−	1.22406e18i		−	1.24632i	−0.782093	−	0.623162i	$-0.785848\pi$
$997$		−	1.22406e18i		−	1.24632i	0.782093	−	0.623162i	$-0.214152\pi$
$998$	−5.12310e17			−0.518501
$999$		−	3.23780e17i		−	0.325729i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	14.13.b.a.13.8	yes	8
3.2	odd	2		126.13.c.a.55.2		8
4.3	odd	2		112.13.c.c.97.2		8
7.2	even	3		98.13.d.b.31.1		16
7.3	odd	6		98.13.d.b.19.1		16
7.4	even	3		98.13.d.b.19.4		16
7.5	odd	6		98.13.d.b.31.4		16
7.6	odd	2	inner	14.13.b.a.13.5	✓	8
21.20	even	2		126.13.c.a.55.3		8
28.27	even	2		112.13.c.c.97.7		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.13.b.a.13.5	✓	8	7.6	odd	2	inner
14.13.b.a.13.8	yes	8	1.1	even	1	trivial
98.13.d.b.19.1		16	7.3	odd	6
98.13.d.b.19.4		16	7.4	even	3
98.13.d.b.31.1		16	7.2	even	3
98.13.d.b.31.4		16	7.5	odd	6
112.13.c.c.97.2		8	4.3	odd	2
112.13.c.c.97.7		8	28.27	even	2
126.13.c.a.55.2		8	3.2	odd	2
126.13.c.a.55.3		8	21.20	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:	\( N \)	\(=\)	\( 14 = 2 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 13 \)
Character orbit:	\([\chi]\)	\(=\)	14.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+45.2548 q^{2} +1072.00i q^{3} +2048.00 q^{4} +1140.63i q^{5} +48513.4i q^{6} +(74038.7 + 91430.6i) q^{7} +92681.9 q^{8} -617752. q^{9} +O(q^{10})\)	\(q+45.2548 q^{2} +1072.00i q^{3} +2048.00 q^{4} +1140.63i q^{5} +48513.4i q^{6} +(74038.7 + 91430.6i) q^{7} +92681.9 q^{8} -617752. q^{9} +51619.1i q^{10} -2.90614e6 q^{11} +2.19546e6i q^{12} -491015. i q^{13} +(3.35061e6 + 4.13768e6i) q^{14} -1.22276e6 q^{15} +4.19430e6 q^{16} +3.15108e7i q^{17} -2.79563e7 q^{18} -1.15553e7i q^{19} +2.33601e6i q^{20} +(-9.80140e7 + 7.93698e7i) q^{21} -1.31517e8 q^{22} +6.83364e6 q^{23} +9.93554e7i q^{24} +2.42840e8 q^{25} -2.22208e7i q^{26} -9.25255e7i q^{27} +(1.51631e8 + 1.87250e8i) q^{28} +5.16944e8 q^{29} -5.53359e7 q^{30} -1.26298e9i q^{31} +1.89813e8 q^{32} -3.11539e9i q^{33} +1.42602e9i q^{34} +(-1.04289e8 + 8.44508e7i) q^{35} -1.26516e9 q^{36} +3.49935e9 q^{37} -5.22931e8i q^{38} +5.26370e8 q^{39} +1.05716e8i q^{40} +8.38090e9i q^{41} +(-4.43561e9 + 3.59187e9i) q^{42} -6.25311e8 q^{43} -5.95176e9 q^{44} -7.04627e8i q^{45} +3.09255e8 q^{46} -1.58996e10i q^{47} +4.49631e9i q^{48} +(-2.87784e9 + 1.35388e10i) q^{49} +1.09897e10 q^{50} -3.37797e10 q^{51} -1.00560e9i q^{52} +2.53616e10 q^{53} -4.18723e9i q^{54} -3.31483e9i q^{55} +(6.86204e9 + 8.47397e9i) q^{56} +1.23873e10 q^{57} +2.33942e10 q^{58} +4.34071e10i q^{59} -2.50422e9 q^{60} -7.58019e9i q^{61} -5.71561e10i q^{62} +(-4.57375e10 - 5.64814e10i) q^{63} +8.58993e9 q^{64} +5.60067e8 q^{65} -1.40986e11i q^{66} +2.50602e10 q^{67} +6.45341e10i q^{68} +7.32569e9i q^{69} +(-4.71956e9 + 3.82181e9i) q^{70} +1.41685e11 q^{71} -5.72544e10 q^{72} +1.37008e11i q^{73} +1.58363e11 q^{74} +2.60325e11i q^{75} -2.36652e10i q^{76} +(-2.15166e11 - 2.65710e11i) q^{77} +2.38208e10 q^{78} -1.68456e11 q^{79} +4.78415e9i q^{80} -2.29111e11 q^{81} +3.79276e11i q^{82} -7.26397e10i q^{83} +(-2.00733e11 + 1.62549e11i) q^{84} -3.59422e10 q^{85} -2.82983e10 q^{86} +5.54166e11i q^{87} -2.69346e11 q^{88} -5.99527e11i q^{89} -3.18878e10i q^{90} +(4.48938e10 - 3.63541e10i) q^{91} +1.39953e10 q^{92} +1.35392e12 q^{93} -7.19532e11i q^{94} +1.31803e10 q^{95} +2.03480e11i q^{96} -5.96235e11i q^{97} +(-1.30236e11 + 6.12696e11i) q^{98} +1.79527e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 16384 q^{4} + 195160 q^{7} - 1478904 q^{9}+O(q^{10}) \) 8 * q + 16384 * q^4 + 195160 * q^7 - 1478904 * q^9	\( 8 q + 16384 q^{4} + 195160 q^{7} - 1478904 q^{9} - 213840 q^{11} - 8418816 q^{14} + 65882304 q^{15} + 33554432 q^{16} + 32547840 q^{18} - 4449984 q^{21} - 221337600 q^{22} + 156731760 q^{23} + 191237000 q^{25} + 399687680 q^{28} + 308853648 q^{29} - 2203567104 q^{30} - 3764734848 q^{35} - 3028795392 q^{36} - 3243600880 q^{37} + 13521315264 q^{39} - 12108579840 q^{42} + 21006302000 q^{43} - 437944320 q^{44} + 9664610304 q^{46} - 19258758904 q^{49} + 26259489792 q^{50} - 80965832832 q^{51} + 180445637520 q^{53} - 17241735168 q^{56} - 63145962240 q^{57} - 94193264640 q^{58} + 134926958592 q^{60} - 402706514280 q^{63} + 68719476736 q^{64} - 424890168192 q^{65} + 369211259440 q^{67} - 137936354304 q^{70} + 574058144304 q^{71} + 66657976320 q^{72} + 450517137408 q^{74} - 73915435440 q^{77} - 251000847360 q^{78} - 607826610128 q^{79} + 919051941384 q^{81} - 9113567232 q^{84} - 247202260608 q^{85} - 413092638720 q^{86} - 453299404800 q^{88} + 144527421696 q^{91} + 320986644480 q^{92} + 2292312458880 q^{93} - 1053641981376 q^{95} - 290797516800 q^{98} - 1800954256464 q^{99}+O(q^{100}) \) 8 * q + 16384 * q^4 + 195160 * q^7 - 1478904 * q^9 - 213840 * q^11 - 8418816 * q^14 + 65882304 * q^15 + 33554432 * q^16 + 32547840 * q^18 - 4449984 * q^21 - 221337600 * q^22 + 156731760 * q^23 + 191237000 * q^25 + 399687680 * q^28 + 308853648 * q^29 - 2203567104 * q^30 - 3764734848 * q^35 - 3028795392 * q^36 - 3243600880 * q^37 + 13521315264 * q^39 - 12108579840 * q^42 + 21006302000 * q^43 - 437944320 * q^44 + 9664610304 * q^46 - 19258758904 * q^49 + 26259489792 * q^50 - 80965832832 * q^51 + 180445637520 * q^53 - 17241735168 * q^56 - 63145962240 * q^57 - 94193264640 * q^58 + 134926958592 * q^60 - 402706514280 * q^63 + 68719476736 * q^64 - 424890168192 * q^65 + 369211259440 * q^67 - 137936354304 * q^70 + 574058144304 * q^71 + 66657976320 * q^72 + 450517137408 * q^74 - 73915435440 * q^77 - 251000847360 * q^78 - 607826610128 * q^79 + 919051941384 * q^81 - 9113567232 * q^84 - 247202260608 * q^85 - 413092638720 * q^86 - 453299404800 * q^88 + 144527421696 * q^91 + 320986644480 * q^92 + 2292312458880 * q^93 - 1053641981376 * q^95 - 290797516800 * q^98 - 1800954256464 * q^99

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