LMFDB - Embedded newform 15.9.d.c.14.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [15,9,Mod(14,15)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(15, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("15.14");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 15 = 3 \cdot 5 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	15.d (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:	$6.11067915092$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 2096 x^{10} + 1966565 x^{8} + 942732880 x^{6} + 407378811520 x^{4} + 58185108489824 x^{2} + 32\!\cdots\!64 $ x^12 + 2096x^10 + 1966565x^8 + 942732880x^6 + 407378811520x^4 + 58185108489824*x^2 + 3250133486843364
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{13}\cdot 3^{18}\cdot 5^{7} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			14.2
Root			$14.6004 - 17.1593i$ of defining polynomial
Character	$\chi$	$=$	15.14
Dual form			15.9.d.c.14.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-29.2008 q^{2} +(-12.3596 + 80.0515i) q^{3} +596.686 q^{4} +(218.046 + 585.731i) q^{5} +(360.909 - 2337.57i) q^{6} +2074.09i q^{7} -9948.30 q^{8} +(-6255.48 - 1978.80i) q^{9} +O(q^{10})$	\(q-29.2008 q^{2} +(-12.3596 + 80.0515i) q^{3} +596.686 q^{4} +(218.046 + 585.731i) q^{5} +(360.909 - 2337.57i) q^{6} +2074.09i q^{7} -9948.30 q^{8} +(-6255.48 - 1978.80i) q^{9} +(-6367.13 - 17103.8i) q^{10} +11967.5i q^{11} +(-7374.78 + 47765.6i) q^{12} -27810.7i q^{13} -60565.0i q^{14} +(-49583.6 + 10215.6i) q^{15} +137746. q^{16} +32481.8 q^{17} +(182665. + 57782.6i) q^{18} -122980. q^{19} +(130105. + 349497. i) q^{20} +(-166034. - 25634.8i) q^{21} -349460. i q^{22} -266239. q^{23} +(122957. - 796376. i) q^{24} +(-295536. + 255433. i) q^{25} +812096. i q^{26} +(235721. - 476304. i) q^{27} +1.23758e6i q^{28} -793695. i q^{29} +(1.44788e6 - 298303. i) q^{30} +876091. q^{31} -1.47554e6 q^{32} +(-958016. - 147913. i) q^{33} -948494. q^{34} +(-1.21486e6 + 452247. i) q^{35} +(-3.73256e6 - 1.18072e6i) q^{36} +1.82354e6i q^{37} +3.59111e6 q^{38} +(2.22629e6 + 343729. i) q^{39} +(-2.16919e6 - 5.82702e6i) q^{40} +149999. i q^{41} +(4.84832e6 + 748556. i) q^{42} +1.65525e6i q^{43} +7.14084e6i q^{44} +(-204940. - 4.09550e6i) q^{45} +7.77439e6 q^{46} -3.35225e6 q^{47} +(-1.70249e6 + 1.10268e7i) q^{48} +1.46297e6 q^{49} +(8.62990e6 - 7.45885e6i) q^{50} +(-401461. + 2.60022e6i) q^{51} -1.65943e7i q^{52} -2.01969e6 q^{53} +(-6.88324e6 + 1.39084e7i) q^{54} +(-7.00973e6 + 2.60947e6i) q^{55} -2.06336e7i q^{56} +(1.51998e6 - 9.84472e6i) q^{57} +2.31765e7i q^{58} -2.16608e6i q^{59} +(-2.95858e7 + 6.09548e6i) q^{60} -1.66730e7 q^{61} -2.55825e7 q^{62} +(4.10421e6 - 1.29744e7i) q^{63} +7.82388e6 q^{64} +(1.62896e7 - 6.06403e6i) q^{65} +(2.79748e7 + 4.31918e6i) q^{66} +2.51124e7i q^{67} +1.93814e7 q^{68} +(3.29060e6 - 2.13128e7i) q^{69} +(3.54748e7 - 1.32060e7i) q^{70} +4.99704e7i q^{71} +(6.22314e7 + 1.96857e7i) q^{72} -4.82271e6i q^{73} -5.32488e7i q^{74} +(-1.67951e7 - 2.68152e7i) q^{75} -7.33803e7 q^{76} -2.48216e7 q^{77} +(-6.50095e7 - 1.00371e7i) q^{78} +2.56922e7 q^{79} +(3.00351e7 + 8.06824e7i) q^{80} +(3.52154e7 + 2.47567e7i) q^{81} -4.38010e6i q^{82} +4.83717e7 q^{83} +(-9.90700e7 - 1.52959e7i) q^{84} +(7.08254e6 + 1.90256e7i) q^{85} -4.83345e7i q^{86} +(6.35364e7 + 9.80972e6i) q^{87} -1.19056e8i q^{88} -3.21720e6i q^{89} +(5.98440e6 + 1.19592e8i) q^{90} +5.76819e7 q^{91} -1.58861e8 q^{92} +(-1.08281e7 + 7.01324e7i) q^{93} +9.78883e7 q^{94} +(-2.68153e7 - 7.20331e7i) q^{95} +(1.82370e7 - 1.18119e8i) q^{96} -5.09232e7i q^{97} -4.27198e7 q^{98} +(2.36813e7 - 7.48625e7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 1704 q^{4} - 3012 q^{6} - 22824 q^{9}+O(q^{10}) $ 12 * q + 1704 * q^4 - 3012 * q^6 - 22824 * q^9	$ 12 q + 1704 q^{4} - 3012 q^{6} - 22824 q^{9} - 35280 q^{10} - 95520 q^{15} + 413328 q^{16} + 276192 q^{19} - 604044 q^{21} + 1173336 q^{24} - 2036220 q^{25} + 3563460 q^{30} - 279216 q^{31} - 1225344 q^{34} - 10311840 q^{36} + 3780864 q^{39} - 3347040 q^{40} + 9523980 q^{45} + 37414536 q^{46} - 6222300 q^{49} + 3931248 q^{51} - 53281692 q^{54} - 16903440 q^{55} + 9900720 q^{60} - 91958256 q^{61} + 57497760 q^{64} + 111065040 q^{66} + 8138748 q^{69} + 3903480 q^{70} + 15031440 q^{75} - 232646880 q^{76} + 420402672 q^{79} + 98480772 q^{81} - 528357816 q^{84} - 117091440 q^{85} + 218602080 q^{90} - 100211328 q^{91} + 543022776 q^{94} + 333306864 q^{96} - 640360080 q^{99}+O(q^{100}) $ 12 * q + 1704 * q^4 - 3012 * q^6 - 22824 * q^9 - 35280 * q^10 - 95520 * q^15 + 413328 * q^16 + 276192 * q^19 - 604044 * q^21 + 1173336 * q^24 - 2036220 * q^25 + 3563460 * q^30 - 279216 * q^31 - 1225344 * q^34 - 10311840 * q^36 + 3780864 * q^39 - 3347040 * q^40 + 9523980 * q^45 + 37414536 * q^46 - 6222300 * q^49 + 3931248 * q^51 - 53281692 * q^54 - 16903440 * q^55 + 9900720 * q^60 - 91958256 * q^61 + 57497760 * q^64 + 111065040 * q^66 + 8138748 * q^69 + 3903480 * q^70 + 15031440 * q^75 - 232646880 * q^76 + 420402672 * q^79 + 98480772 * q^81 - 528357816 * q^84 - 117091440 * q^85 + 218602080 * q^90 - 100211328 * q^91 + 543022776 * q^94 + 333306864 * q^96 - 640360080 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/15\mathbb{Z}\right)^\times$.

$n$	$7$	$11$
$\chi(n)$	$-1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−29.2008			−1.82505			−0.912525	−	0.409022i	$-0.865870\pi$
$2$	−29.2008			−1.82505			−0.912525	+	0.409022i	$0.865870\pi$
$3$	−12.3596	+	80.0515i	−0.152587	+	0.988290i
$3$	−12.3596	+	80.0515i	−0.152587	+	0.988290i
$4$	596.686			2.33080
$5$	218.046	+	585.731i	0.348874	+	0.937170i
$5$	218.046	+	585.731i	0.348874	+	0.937170i
$6$	360.909	−	2337.57i	0.278479	−	1.80368i
$7$			2074.09i			0.863843i	0.901911	+	0.431921i	$0.142164\pi$
$7$			2074.09i			0.863843i	−0.901911	+	0.431921i	$0.857836\pi$
$8$	−9948.30			−2.42878
$9$	−6255.48	−	1978.80i	−0.953434	−	0.301601i
$10$	−6367.13	−	17103.8i	−0.636713	−	1.71038i
$11$			11967.5i			0.817396i	0.912670	+	0.408698i	$0.134017\pi$
$11$			11967.5i			0.817396i	−0.912670	+	0.408698i	$0.865983\pi$
$12$	−7374.78	+	47765.6i	−0.355651	+	2.30351i
$13$		−	27810.7i		−	0.973731i	−0.873477	−	0.486866i	$-0.838140\pi$
$13$		−	27810.7i		−	0.973731i	0.873477	−	0.486866i	$-0.161860\pi$
$14$		−	60565.0i		−	1.57656i
$15$	−49583.6	+	10215.6i	−0.979429	+	0.201789i
$16$	137746.			2.10184
$17$	32481.8			0.388906			0.194453	−	0.980912i	$-0.437707\pi$
$17$	32481.8			0.388906			0.194453	+	0.980912i	$0.437707\pi$
$18$	182665.	+	57782.6i	1.74006	+	0.550436i
$19$	−122980.			−0.943669			−0.471834	−	0.881687i	$-0.656408\pi$
$19$	−122980.			−0.943669			−0.471834	+	0.881687i	$0.656408\pi$
$20$	130105.	+	349497.i	0.813158	+	2.18436i
$21$	−166034.	−	25634.8i	−0.853727	−	0.131811i
$22$		−	349460.i		−	1.49179i
$23$	−266239.			−0.951394			−0.475697	−	0.879609i	$-0.657804\pi$
$23$	−266239.			−0.951394			−0.475697	+	0.879609i	$0.657804\pi$
$24$	122957.	−	796376.i	0.370601	−	2.40034i
$25$	−295536.	+	255433.i	−0.756573	+	0.653909i
$26$			812096.i			1.77711i
$27$	235721.	−	476304.i	0.443551	−	0.896249i
$28$			1.23758e6i			2.01345i
$29$		−	793695.i		−	1.12218i	−0.827756	−	0.561089i	$-0.810383\pi$
$29$		−	793695.i		−	1.12218i	0.827756	−	0.561089i	$-0.189617\pi$
$30$	1.44788e6	−	298303.i	1.78751	−	0.368275i
$31$	876091.			0.948642			0.474321	−	0.880352i	$-0.342694\pi$
$31$	876091.			0.948642			0.474321	+	0.880352i	$0.342694\pi$
$32$	−1.47554e6			−1.40719
$33$	−958016.	−	147913.i	−0.807824	−	0.124724i
$34$	−948494.			−0.709772
$35$	−1.21486e6	+	452247.i	−0.809567	+	0.301373i
$36$	−3.73256e6	−	1.18072e6i	−2.22227	−	0.702972i
$37$			1.82354e6i			0.972991i	0.873683	+	0.486495i	$0.161725\pi$
$37$			1.82354e6i			0.972991i	−0.873683	+	0.486495i	$0.838275\pi$
$38$	3.59111e6			1.72224
$39$	2.22629e6	+	343729.i	0.962329	+	0.148579i
$40$	−2.16919e6	−	5.82702e6i	−0.847340	−	2.27618i
$41$			149999.i			0.0530828i	0.999648	+	0.0265414i	$0.00844938\pi$
$41$			149999.i			0.0530828i	−0.999648	+	0.0265414i	$0.991551\pi$
$42$	4.84832e6	+	748556.i	1.55809	+	0.240562i
$43$			1.65525e6i			0.484160i	0.970256	+	0.242080i	$0.0778296\pi$
$43$			1.65525e6i			0.484160i	−0.970256	+	0.242080i	$0.922170\pi$
$44$			7.14084e6i			1.90519i
$45$	−204940.	−	4.09550e6i	−0.0499777	−	0.998750i
$46$	7.77439e6			1.73634
$47$	−3.35225e6			−0.686981			−0.343491	−	0.939156i	$-0.611609\pi$
$47$	−3.35225e6			−0.686981			−0.343491	+	0.939156i	$0.611609\pi$
$48$	−1.70249e6	+	1.10268e7i	−0.320715	+	2.07723i
$49$	1.46297e6			0.253776
$50$	8.62990e6	−	7.45885e6i	1.38078	−	1.19342i
$51$	−401461.	+	2.60022e6i	−0.0593420	+	0.384352i
$52$		−	1.65943e7i		−	2.26958i
$53$	−2.01969e6			−0.255965			−0.127982	−	0.991776i	$-0.540850\pi$
$53$	−2.01969e6			−0.255965			−0.127982	+	0.991776i	$0.540850\pi$
$54$	−6.88324e6	+	1.39084e7i	−0.809502	+	1.63570i
$55$	−7.00973e6	+	2.60947e6i	−0.766039	+	0.285169i
$56$		−	2.06336e7i		−	2.09809i
$57$	1.51998e6	−	9.84472e6i	0.143992	−	0.932618i
$58$			2.31765e7i			2.04803i
$59$		−	2.16608e6i		−	0.178758i	−0.995998	−	0.0893792i	$-0.971512\pi$
$59$		−	2.16608e6i		−	0.178758i	0.995998	−	0.0893792i	$-0.0284883\pi$
$60$	−2.95858e7	+	6.09548e6i	−2.28286	+	0.470331i
$61$	−1.66730e7			−1.20419			−0.602094	−	0.798425i	$-0.705667\pi$
$61$	−1.66730e7			−1.20419			−0.602094	+	0.798425i	$0.705667\pi$
$62$	−2.55825e7			−1.73132
$63$	4.10421e6	−	1.29744e7i	0.260536	−	0.823617i
$64$	7.82388e6			0.466339
$65$	1.62896e7	−	6.06403e6i	0.912551	−	0.339710i
$66$	2.79748e7	+	4.31918e6i	1.47432	+	0.227628i
$67$			2.51124e7i			1.24620i	0.782140	+	0.623102i	$0.214128\pi$
$67$			2.51124e7i			1.24620i	−0.782140	+	0.623102i	$0.785872\pi$
$68$	1.93814e7			0.906463
$69$	3.29060e6	−	2.13128e7i	0.145171	−	0.940253i
$70$	3.54748e7	−	1.32060e7i	1.47750	−	0.550020i
$71$			4.99704e7i			1.96643i	0.182441	+	0.983217i	$0.441600\pi$
$71$			4.99704e7i			1.96643i	−0.182441	+	0.983217i	$0.558400\pi$
$72$	6.22314e7	+	1.96857e7i	2.31569	+	0.732523i
$73$		−	4.82271e6i		−	0.169824i	−0.996388	−	0.0849122i	$-0.972939\pi$
$73$		−	4.82271e6i		−	0.169824i	0.996388	−	0.0849122i	$-0.0270610\pi$
$74$		−	5.32488e7i		−	1.77576i
$75$	−1.67951e7	−	2.68152e7i	−0.530808	−	0.847492i
$76$	−7.33803e7			−2.19951
$77$	−2.48216e7			−0.706102
$78$	−6.50095e7	−	1.00371e7i	−1.75630	−	0.271164i
$79$	2.56922e7			0.659618			0.329809	−	0.944048i	$-0.393016\pi$
$79$	2.56922e7			0.659618			0.329809	+	0.944048i	$0.393016\pi$
$80$	3.00351e7	+	8.06824e7i	0.733280	+	1.96978i
$81$	3.52154e7	+	2.47567e7i	0.818074	+	0.575113i
$82$		−	4.38010e6i		−	0.0968787i
$83$	4.83717e7			1.01925			0.509623	−	0.860398i	$-0.329785\pi$
$83$	4.83717e7			1.01925			0.509623	+	0.860398i	$0.329785\pi$
$84$	−9.90700e7	−	1.52959e7i	−1.98987	−	0.307226i
$85$	7.08254e6	+	1.90256e7i	0.135679	+	0.364471i
$86$		−	4.83345e7i		−	0.883615i
$87$	6.35364e7	+	9.80972e6i	1.10904	+	0.171230i
$88$		−	1.19056e8i		−	1.98528i
$89$		−	3.21720e6i		−	0.0512764i	−0.999671	−	0.0256382i	$-0.991838\pi$
$89$		−	3.21720e6i		−	0.0512764i	0.999671	−	0.0256382i	$-0.00816178\pi$
$90$	5.98440e6	+	1.19592e8i	0.0912117	+	1.82277i
$91$	5.76819e7			0.841151
$92$	−1.58861e8			−2.21751
$93$	−1.08281e7	+	7.01324e7i	−0.144751	+	0.937533i
$94$	9.78883e7			1.25377
$95$	−2.68153e7	−	7.20331e7i	−0.329222	−	0.884378i
$96$	1.82370e7	−	1.18119e8i	0.214719	−	1.39071i
$97$		−	5.09232e7i		−	0.575214i	−0.957749	−	0.287607i	$-0.907140\pi$
$97$		−	5.09232e7i		−	0.575214i	0.957749	−	0.287607i	$-0.0928596\pi$
$98$	−4.27198e7			−0.463153
$99$	2.36813e7	−	7.48625e7i	0.246527	−	0.779334i
$100$	−1.76342e8	+	1.52413e8i	−1.76342	+	1.52413i
$101$			1.75796e8i			1.68936i	0.535271	+	0.844680i	$0.320209\pi$
$101$			1.75796e8i			1.68936i	−0.535271	+	0.844680i	$0.679791\pi$
$102$	1.17230e7	−	7.59284e7i	0.108302	−	0.701461i
$103$		−	4.78629e7i		−	0.425256i	−0.977133	−	0.212628i	$-0.931798\pi$
$103$		−	4.78629e7i		−	0.425256i	0.977133	−	0.212628i	$-0.0682022\pi$
$104$			2.76669e8i			2.36498i
$105$	−2.11880e7	−	1.02841e8i	−0.174314	−	0.846073i
$106$	5.89764e7			0.467149
$107$	1.00866e8			0.769500			0.384750	−	0.923021i	$-0.374288\pi$
$107$	1.00866e8			0.769500			0.384750	+	0.923021i	$0.374288\pi$
$108$	1.40651e8	−	2.84204e8i	1.03383	−	2.08898i
$109$	−1.41159e8			−1.00001			−0.500004	−	0.866023i	$-0.666668\pi$
$109$	−1.41159e8			−1.00001			−0.500004	+	0.866023i	$0.666668\pi$
$110$	2.04690e8	−	7.61986e7i	1.39806	−	0.520447i
$111$	−1.45977e8	−	2.25382e7i	−0.961597	−	0.148466i
$112$			2.85698e8i			1.81566i
$113$	−2.03148e8			−1.24595			−0.622974	−	0.782243i	$-0.714076\pi$
$113$	−2.03148e8			−1.24595			−0.622974	+	0.782243i	$0.714076\pi$
$114$	−4.43845e7	+	2.87474e8i	−0.262792	+	1.70207i
$115$	−5.80525e7	−	1.55944e8i	−0.331917	−	0.891618i
$116$		−	4.73586e8i		−	2.61558i
$117$	−5.50320e7	+	1.73970e8i	−0.293678	+	0.928389i
$118$			6.32512e7i			0.326243i
$119$			6.73701e7i			0.335953i
$120$	4.93272e8	−	1.01627e8i	2.37882	−	0.490102i
$121$	7.11379e7			0.331864
$122$	4.86864e8			2.19770
$123$	−1.20077e7	−	1.85393e6i	−0.0524612	−	0.00809976i
$124$	5.22751e8			2.21110
$125$	−2.14056e8	−	1.17409e8i	−0.876772	−	0.480906i
$126$	−1.19846e8	+	3.78863e8i	−0.475490	+	1.50314i
$127$			1.01064e8i			0.388493i	0.980953	+	0.194247i	$0.0622262\pi$
$127$			1.01064e8i			0.388493i	−0.980953	+	0.194247i	$0.937774\pi$
$128$	1.49275e8			0.556094
$129$	−1.32505e8	−	2.04581e7i	−0.478490	−	0.0738765i
$130$	−4.75669e8	+	1.77075e8i	−1.66545	+	0.619987i
$131$			3.45932e8i			1.17464i	0.809354	+	0.587322i	$0.199818\pi$
$131$			3.45932e8i			1.17464i	−0.809354	+	0.587322i	$0.800182\pi$
$132$	−5.71635e8	−	8.82576e7i	−1.88288	−	0.290708i
$133$		−	2.55071e8i		−	0.815181i
$134$		−	7.33302e8i		−	2.27438i
$135$	3.30384e8	+	3.42129e7i	0.994681	+	0.103004i
$136$	−3.23139e8			−0.944568
$137$	−5.03253e8			−1.42858			−0.714290	−	0.699850i	$-0.753250\pi$
$137$	−5.03253e8			−1.42858			−0.714290	+	0.699850i	$0.753250\pi$
$138$	−9.60881e7	+	6.22352e8i	−0.264943	+	1.71601i
$139$	−3.10576e7			−0.0831973			−0.0415987	−	0.999134i	$-0.513245\pi$
$139$	−3.10576e7			−0.0831973			−0.0415987	+	0.999134i	$0.513245\pi$
$140$	−7.24888e8	+	2.69850e8i	−1.88694	+	0.702440i
$141$	4.14323e7	−	2.68353e8i	0.104825	−	0.678937i
$142$		−	1.45917e9i		−	3.58884i
$143$	3.32825e8			0.795924
$144$	−8.61671e8	−	2.72573e8i	−2.00397	−	0.633918i
$145$	4.64892e8	−	1.73062e8i	1.05167	−	0.391499i
$146$			1.40827e8i			0.309938i
$147$	−1.80816e7	+	1.17113e8i	−0.0387229	+	0.250804i
$148$			1.08808e9i			2.26785i
$149$		−	2.95589e8i		−	0.599712i	−0.953984	−	0.299856i	$-0.903061\pi$
$149$		−	2.95589e8i		−	0.599712i	0.953984	−	0.299856i	$-0.0969387\pi$
$150$	4.90430e8	+	7.83024e8i	0.968751	+	1.54671i
$151$	2.81094e8			0.540684			0.270342	−	0.962764i	$-0.412863\pi$
$151$	2.81094e8			0.540684			0.270342	+	0.962764i	$0.412863\pi$
$152$	1.22344e9			2.29197
$153$	−2.03189e8	−	6.42751e7i	−0.370796	−	0.117294i
$154$	7.24811e8			1.28867
$155$	1.91028e8	+	5.13153e8i	0.330957	+	0.889038i
$156$	1.32840e9	+	2.05098e8i	2.24300	+	0.346308i
$157$			9.80391e8i			1.61362i	0.590812	+	0.806809i	$0.298807\pi$
$157$			9.80391e8i			1.61362i	−0.590812	+	0.806809i	$0.701193\pi$
$158$	−7.50232e8			−1.20384
$159$	2.49624e7	−	1.61679e8i	0.0390570	−	0.252968i
$160$	−3.21737e8	−	8.64270e8i	−0.490931	−	1.31877i
$161$		−	5.52203e8i		−	0.821855i
$162$	−1.02832e9	−	7.22916e8i	−1.49303	−	1.04961i
$163$			1.47481e8i			0.208922i	0.994529	+	0.104461i	$0.0333118\pi$
$163$			1.47481e8i			0.208922i	−0.994529	+	0.104461i	$0.966688\pi$
$164$			8.95025e7i			0.123726i
$165$	−1.22255e8	−	5.93392e8i	−0.164941	−	0.800582i
$166$	−1.41249e9			−1.86017
$167$	1.01192e9			1.30101			0.650507	−	0.759500i	$-0.274556\pi$
$167$	1.01192e9			1.30101			0.650507	+	0.759500i	$0.274556\pi$
$168$	1.65175e9	+	2.55023e8i	2.07352	+	0.320141i
$169$	4.22934e7			0.0518472
$170$	−2.06816e8	−	5.55562e8i	−0.247621	−	0.665177i
$171$	7.69298e8	+	2.43353e8i	0.899726	+	0.284611i
$172$			9.87661e8i			1.12848i
$173$	1.60800e8			0.179516			0.0897578	−	0.995964i	$-0.471391\pi$
$173$	1.60800e8			0.179516			0.0897578	+	0.995964i	$0.471391\pi$
$174$	−1.85531e9	−	2.86452e8i	−2.02405	−	0.312503i
$175$	−5.29790e8	−	6.12968e8i	−0.564874	−	0.653561i
$176$			1.64848e9i			1.71804i
$177$	1.73398e8	+	2.67718e7i	0.176665	+	0.0272762i
$178$			9.39446e7i			0.0935819i
$179$			1.90240e9i			1.85306i	0.376218	+	0.926531i	$0.377224\pi$
$179$			1.90240e9i			1.85306i	−0.376218	+	0.926531i	$0.622776\pi$
$180$	−1.22285e8	−	2.44373e9i	−0.116488	−	2.32789i
$181$	−1.50229e9			−1.39971			−0.699857	−	0.714283i	$-0.746753\pi$
$181$	−1.50229e9			−1.39971			−0.699857	+	0.714283i	$0.746753\pi$
$182$	−1.68436e9			−1.53514
$183$	2.06071e8	−	1.33470e9i	0.183744	−	1.19009i
$184$	2.64863e9			2.31073
$185$	−1.06810e9	+	3.97617e8i	−0.911857	+	0.339451i
$186$	3.16189e8	−	2.04792e9i	0.264177	−	1.71104i
$187$			3.88726e8i			0.317890i
$188$	−2.00024e9			−1.60122
$189$	9.87895e8	+	4.88906e8i	0.774218	+	0.383158i
$190$	7.83028e8	+	2.10342e9i	0.600846	+	1.61403i
$191$		−	2.19783e9i		−	1.65143i	−0.564088	−	0.825714i	$-0.690772\pi$
$191$		−	2.19783e9i		−	1.65143i	0.564088	−	0.825714i	$-0.309228\pi$
$192$	−9.66997e7	+	6.26313e8i	−0.0711574	+	0.460878i
$193$			4.40358e8i			0.317378i	0.987329	+	0.158689i	$0.0507267\pi$
$193$			4.40358e8i			0.317378i	−0.987329	+	0.158689i	$0.949273\pi$
$194$			1.48700e9i			1.04979i
$195$	2.84102e8	+	1.37896e9i	0.196488	+	0.953701i
$196$	8.72931e8			0.591501
$197$	3.14912e8			0.209085			0.104543	−	0.994520i	$-0.466662\pi$
$197$	3.14912e8			0.209085			0.104543	+	0.994520i	$0.466662\pi$
$198$	−6.91513e8	+	2.18604e9i	−0.449924	+	1.42232i
$199$	−9.45118e8			−0.602662			−0.301331	−	0.953520i	$-0.597431\pi$
$199$	−9.45118e8			−0.602662			−0.301331	+	0.953520i	$0.597431\pi$
$200$	2.94008e9	−	2.54112e9i	1.83755	−	1.58820i
$201$	−2.01029e9	−	3.10379e8i	−1.23161	−	0.190155i
$202$		−	5.13337e9i		−	3.08317i
$203$	1.64619e9			0.969385
$204$	−2.39546e8	+	1.55151e9i	−0.138315	+	0.895849i
$205$	−8.78592e7	+	3.27068e7i	−0.0497476	+	0.0185192i
$206$			1.39763e9i			0.776112i
$207$	1.66545e9	+	5.26835e8i	0.907092	+	0.286941i
$208$		−	3.83083e9i		−	2.04663i
$209$		−	1.47176e9i		−	0.771351i
$210$	6.18705e8	+	3.00303e9i	0.318131	+	1.54412i
$211$	1.48716e9			0.750286			0.375143	−	0.926967i	$-0.377594\pi$
$211$	1.48716e9			0.750286			0.375143	+	0.926967i	$0.377594\pi$
$212$	−1.20512e9			−0.596604
$213$	−4.00020e9	−	6.17612e8i	−1.94341	−	0.300053i
$214$	−2.94536e9			−1.40438
$215$	−9.69528e8	+	3.60920e8i	−0.453740	+	0.168911i
$216$	−2.34502e9	+	4.73841e9i	−1.07729	+	2.17679i
$217$			1.81709e9i			0.819477i
$218$	4.12196e9			1.82506
$219$	3.86065e8	+	5.96066e7i	0.167836	+	0.0259130i
$220$	−4.18261e9	+	1.55703e9i	−1.78549	+	0.664672i
$221$		−	9.03343e8i		−	0.378690i
$222$	4.26265e9	+	6.58132e8i	1.75496	+	0.270958i
$223$		−	1.30153e8i		−	0.0526301i	−0.999654	−	0.0263150i	$-0.991623\pi$
$223$		−	1.30153e8i		−	0.0526301i	0.999654	−	0.0263150i	$-0.00837730\pi$
$224$		−	3.06040e9i		−	1.21559i
$225$	2.35418e9	−	1.01305e9i	0.918562	−	0.395276i
$226$	5.93209e9			2.27391
$227$	−3.06375e9			−1.15385			−0.576926	−	0.816797i	$-0.695748\pi$
$227$	−3.06375e9			−1.15385			−0.576926	+	0.816797i	$0.695748\pi$
$228$	9.06949e8	−	5.87421e9i	0.335617	−	2.17375i
$229$	4.48632e9			1.63135			0.815677	−	0.578508i	$-0.196365\pi$
$229$	4.48632e9			1.63135			0.815677	+	0.578508i	$0.196365\pi$
$230$	1.69518e9	+	4.55370e9i	0.605765	+	1.62725i
$231$	3.06784e8	−	1.98701e9i	0.107742	−	0.697833i
$232$			7.89591e9i			2.72553i
$233$	2.04765e9			0.694756			0.347378	−	0.937725i	$-0.387072\pi$
$233$	2.04765e9			0.694756			0.347378	+	0.937725i	$0.387072\pi$
$234$	1.60698e9	−	5.08005e9i	0.535977	−	1.69436i
$235$	−7.30946e8	−	1.96352e9i	−0.239670	−	0.643818i
$236$		−	1.29247e9i		−	0.416651i
$237$	−3.17544e8	+	2.05670e9i	−0.100649	+	0.651894i
$238$		−	1.96726e9i		−	0.613131i
$239$		−	2.57439e9i		−	0.789011i	−0.918893	−	0.394506i	$-0.870916\pi$
$239$		−	2.57439e9i		−	0.789011i	0.918893	−	0.394506i	$-0.129084\pi$
$240$	−6.82997e9	+	1.40716e9i	−2.05861	+	0.424129i
$241$	−2.53228e8			−0.0750662			−0.0375331	−	0.999295i	$-0.511950\pi$
$241$	−2.53228e8			−0.0750662			−0.0375331	+	0.999295i	$0.511950\pi$
$242$	−2.07728e9			−0.605667
$243$	−2.41706e9	+	2.51306e9i	−0.693206	+	0.720739i
$244$	−9.94854e9			−2.80673
$245$	3.18995e8	+	8.56905e8i	0.0885358	+	0.237831i
$246$	3.50633e8	+	5.41361e7i	0.0957443	+	0.0147825i
$247$			3.42016e9i			0.918880i
$248$	−8.71561e9			−2.30405
$249$	−5.97853e8	+	3.87222e9i	−0.155524	+	1.00731i
$250$	6.25060e9	+	3.42842e9i	1.60015	+	0.877676i
$251$		−	3.88618e8i		−	0.0979101i	−0.998801	−	0.0489551i	$-0.984411\pi$
$251$		−	3.88618e8i		−	0.0979101i	0.998801	−	0.0489551i	$-0.0155891\pi$
$252$	2.44892e9	−	7.74165e9i	0.607258	−	1.91969i
$253$		−	3.18622e9i		−	0.777666i
$254$		−	2.95116e9i		−	0.709019i
$255$	−1.61056e9	+	3.31820e8i	−0.380906	+	0.0784769i
$256$	−6.36187e9			−1.48124
$257$	−2.95713e9			−0.677857			−0.338928	−	0.940812i	$-0.610064\pi$
$257$	−2.95713e9			−0.677857			−0.338928	+	0.940812i	$0.610064\pi$
$258$	3.86925e9	+	5.97393e8i	0.873268	+	0.134828i
$259$	−3.78218e9			−0.840511
$260$	9.71978e9	−	3.61832e9i	2.12698	−	0.791797i
$261$	−1.57057e9	+	4.96494e9i	−0.338450	+	1.06992i
$262$		−	1.01015e10i		−	2.14378i
$263$	2.13881e9			0.447042			0.223521	−	0.974699i	$-0.428245\pi$
$263$	2.13881e9			0.447042			0.223521	+	0.974699i	$0.428245\pi$
$264$	9.53063e9	+	1.47148e9i	1.96203	+	0.302928i
$265$	−4.40385e8	−	1.18299e9i	−0.0892996	−	0.239883i
$266$			7.44827e9i			1.48775i
$267$	2.57541e8	+	3.97631e7i	0.0506759	+	0.00782412i
$268$			1.49842e10i			2.90466i
$269$		−	2.43278e9i		−	0.464616i	−0.972642	−	0.232308i	$-0.925372\pi$
$269$		−	2.43278e9i		−	0.464616i	0.972642	−	0.232308i	$-0.0746277\pi$
$270$	−9.64747e9	−	9.99043e8i	−1.81534	−	0.187988i
$271$	3.00867e9			0.557825			0.278913	−	0.960317i	$-0.410026\pi$
$271$	3.00867e9			0.557825			0.278913	+	0.960317i	$0.410026\pi$
$272$	4.47425e9			0.817419
$273$	−7.12923e8	+	4.61752e9i	−0.128349	+	0.831301i
$274$	1.46954e10			2.60723
$275$	−3.05689e9	−	3.53683e9i	−0.534502	−	0.618420i
$276$	1.96345e9	−	1.27171e10i	0.338364	−	2.19155i
$277$		−	7.84116e9i		−	1.33187i	−0.746011	−	0.665934i	$-0.768033\pi$
$277$		−	7.84116e9i		−	1.33187i	0.746011	−	0.665934i	$-0.231967\pi$
$278$	9.06908e8			0.151839
$279$	−5.48037e9	−	1.73361e9i	−0.904468	−	0.286111i
$280$	1.20858e10	−	4.49909e9i	1.96626	−	0.731969i
$281$			1.64823e9i			0.264358i	0.991226	+	0.132179i	$0.0421973\pi$
$281$			1.64823e9i			0.264358i	−0.991226	+	0.132179i	$0.957803\pi$
$282$	−1.20986e9	+	7.83611e9i	−0.191310	+	1.23909i
$283$		−	9.15379e9i		−	1.42710i	−0.700603	−	0.713551i	$-0.747086\pi$
$283$		−	9.15379e9i		−	1.42710i	0.700603	−	0.713551i	$-0.252914\pi$
$284$			2.98166e10i			4.58337i
$285$	6.09778e9	−	1.25631e9i	0.924257	−	0.190422i
$286$	−9.71875e9			−1.45260
$287$	−3.11112e8			−0.0458552
$288$	9.23022e9	+	2.91981e9i	1.34166	+	0.424408i
$289$	−5.92069e9			−0.848752
$290$	−1.35752e10	+	5.05356e9i	−1.91935	+	0.714505i
$291$	4.07648e9	+	6.29389e8i	0.568478	+	0.0877702i
$292$		−	2.87765e9i		−	0.395827i
$293$	1.35840e10			1.84313			0.921565	−	0.388224i	$-0.126911\pi$
$293$	1.35840e10			1.84313			0.921565	+	0.388224i	$0.126911\pi$
$294$	5.27998e8	−	3.41978e9i	0.0706712	−	0.457729i
$295$	1.26874e9	−	4.72306e8i	0.167527	−	0.0623642i
$296$		−	1.81411e10i		−	2.36318i
$297$	5.70016e9	+	2.82099e9i	0.732591	+	0.362557i
$298$			8.63142e9i			1.09450i
$299$			7.40431e9i			0.926402i
$300$	−1.00214e10	−	1.60002e10i	−1.23721	−	1.97534i
$301$	−3.43312e9			−0.418238
$302$	−8.20816e9			−0.986775
$303$	−1.40727e10	−	2.17276e9i	−1.66958	−	0.257775i
$304$	−1.69400e10			−1.98344
$305$	−3.63549e9	−	9.76589e9i	−0.420110	−	1.12853i
$306$	5.93329e9	+	1.87688e9i	0.676721	+	0.214068i
$307$			1.01834e10i			1.14640i	0.819414	+	0.573202i	$0.194299\pi$
$307$			1.01834e10i			1.14640i	−0.819414	+	0.573202i	$0.805701\pi$
$308$	−1.48107e10			−1.64579
$309$	3.83150e9	+	5.91564e8i	0.420276	+	0.0648886i
$310$	−5.57818e9	−	1.49845e10i	−0.604012	−	1.62254i
$311$			1.21888e10i			1.30292i	0.758682	+	0.651462i	$0.225844\pi$
$311$			1.21888e10i			1.30292i	−0.758682	+	0.651462i	$0.774156\pi$
$312$	−2.21478e10	−	3.41951e9i	−2.33729	−	0.360866i
$313$			9.39665e9i			0.979029i	0.871995	+	0.489515i	$0.162826\pi$
$313$			9.39665e9i			0.979029i	−0.871995	+	0.489515i	$0.837174\pi$
$314$		−	2.86282e10i		−	2.94493i
$315$	8.49442e9	−	4.25063e8i	0.862763	−	0.0431728i
$316$	1.53302e10			1.53744
$317$	1.70423e10			1.68768			0.843841	−	0.536593i	$-0.180289\pi$
$317$	1.70423e10			1.68768			0.843841	+	0.536593i	$0.180289\pi$
$318$	−7.28923e8	+	4.72115e9i	−0.0712809	+	0.461678i
$319$	9.49854e9			0.917263
$320$	1.70597e9	+	4.58269e9i	0.162694	+	0.437039i
$321$	−1.24666e9	+	8.07446e9i	−0.117416	+	0.760489i
$322$			1.61248e10i			1.49993i
$323$	−3.99461e9			−0.366998
$324$	2.10125e10	+	1.47720e10i	1.90677	+	1.34048i
$325$	7.10378e9	+	8.21909e9i	0.636731	+	0.736699i
$326$		−	4.30656e9i		−	0.381294i
$327$	1.74467e9	−	1.13000e10i	0.152588	−	0.988297i
$328$		−	1.49224e9i		−	0.128927i
$329$		−	6.95286e9i		−	0.593444i
$330$	3.56993e9	+	1.73275e10i	0.301026	+	1.46110i
$331$	1.59236e10			1.32657			0.663284	−	0.748368i	$-0.269162\pi$
$331$	1.59236e10			1.32657			0.663284	+	0.748368i	$0.269162\pi$
$332$	2.88627e10			2.37566
$333$	3.60843e9	−	1.14071e10i	0.293455	−	0.927683i
$334$	−2.95490e10			−2.37442
$335$	−1.47091e10	+	5.47567e9i	−1.16791	+	0.434769i
$336$	−2.28706e10	−	3.53110e9i	−1.79440	−	0.277047i
$337$		−	1.48149e10i		−	1.14863i	−0.818634	−	0.574315i	$-0.805268\pi$
$337$		−	1.48149e10i		−	1.14863i	0.818634	−	0.574315i	$-0.194732\pi$
$338$	−1.23500e9			−0.0946238
$339$	2.51083e9	−	1.62623e10i	0.190116	−	1.23136i
$340$	4.22605e9	+	1.13523e10i	0.316242	+	0.849510i
$341$			1.04846e10i			0.775416i
$342$	−2.24641e10	−	7.10610e9i	−1.64204	−	0.519430i
$343$			1.49910e10i			1.08307i
$344$		−	1.64669e10i		−	1.17592i
$345$	1.32011e10	−	2.71978e9i	0.931823	−	0.191981i
$346$	−4.69549e9			−0.327625
$347$	−1.98893e10			−1.37183			−0.685916	−	0.727681i	$-0.740598\pi$
$347$	−1.98893e10			−1.37183			−0.685916	+	0.727681i	$0.740598\pi$
$348$	3.79113e10	+	5.85332e9i	2.58495	+	0.399103i
$349$	−8.03757e9			−0.541780			−0.270890	−	0.962610i	$-0.587318\pi$
$349$	−8.03757e9			−0.541780			−0.270890	+	0.962610i	$0.587318\pi$
$350$	1.54703e10	+	1.78992e10i	1.03092	+	1.19278i
$351$	−1.32464e10	−	6.55558e9i	−0.872706	−	0.431899i
$352$		−	1.76585e10i		−	1.15023i
$353$	1.08598e10			0.699398			0.349699	−	0.936862i	$-0.386284\pi$
$353$	1.08598e10			0.699398			0.349699	+	0.936862i	$0.386284\pi$
$354$	−5.06335e9	−	7.81757e8i	−0.322422	−	0.0497805i
$355$	−2.92692e10	+	1.08959e10i	−1.84288	+	0.686038i
$356$		−	1.91966e9i		−	0.119515i
$357$	−5.39307e9	−	8.32664e8i	−0.332019	−	0.0512622i
$358$		−	5.55516e10i		−	3.38193i
$359$			1.46792e9i			0.0883741i	0.999023	+	0.0441870i	$0.0140698\pi$
$359$			1.46792e9i			0.0883741i	−0.999023	+	0.0441870i	$0.985930\pi$
$360$	2.03880e9	+	4.07433e10i	0.121385	+	2.42575i
$361$	−1.85952e9			−0.109489
$362$	4.38680e10			2.55455
$363$	−8.79233e8	+	5.69469e9i	−0.0506381	+	0.327977i
$364$	3.44180e10			1.96056
$365$	2.82481e9	−	1.05158e9i	0.159154	−	0.0592474i
$366$	−6.01743e9	+	3.89742e10i	−0.335341	+	2.17197i
$367$		−	9.23259e9i		−	0.508931i	−0.967082	−	0.254466i	$-0.918100\pi$
$367$		−	9.23259e9i		−	0.508931i	0.967082	−	0.254466i	$-0.0818996\pi$
$368$	−3.66735e10			−1.99968
$369$	2.96819e8	−	9.38318e8i	0.0160098	−	0.0506110i
$370$	3.11895e10	−	1.16107e10i	1.66418	−	0.619516i
$371$		−	4.18900e9i		−	0.221113i
$372$	−6.46097e9	+	4.18470e10i	−0.337385	+	2.18521i
$373$			1.35736e10i			0.701230i	0.936520	+	0.350615i	$0.114027\pi$
$373$			1.35736e10i			0.701230i	−0.936520	+	0.350615i	$0.885973\pi$
$374$		−	1.13511e10i		−	0.580165i
$375$	1.20444e10	−	1.56844e10i	0.609058	−	0.793125i
$376$	3.33492e10			1.66853
$377$	−2.20732e10			−1.09270
$378$	−2.88473e10	−	1.42764e10i	−1.41299	−	0.699283i
$379$	−1.72701e10			−0.837024			−0.418512	−	0.908211i	$-0.637448\pi$
$379$	−1.72701e10			−0.837024			−0.418512	+	0.908211i	$0.637448\pi$
$380$	−1.60003e10	−	4.29811e10i	−0.767352	−	2.06131i
$381$	−8.09035e9	−	1.24911e9i	−0.383944	−	0.0592791i
$382$			6.41782e10i			3.01394i
$383$	−1.59940e9			−0.0743294			−0.0371647	−	0.999309i	$-0.511833\pi$
$383$	−1.59940e9			−0.0743294			−0.0371647	+	0.999309i	$0.511833\pi$
$384$	−1.84498e9	+	1.19497e10i	−0.0848528	+	0.549582i
$385$	−5.41227e9	−	1.45388e10i	−0.246341	−	0.661737i
$386$		−	1.28588e10i		−	0.579231i
$387$	3.27540e9	−	1.03544e10i	0.146023	−	0.461614i
$388$		−	3.03852e10i		−	1.34071i
$389$			1.30946e10i			0.571864i	0.958250	+	0.285932i	$0.0923031\pi$
$389$			1.30946e10i			0.571864i	−0.958250	+	0.285932i	$0.907697\pi$
$390$	−8.29601e9	−	4.02666e10i	−0.358601	−	1.74055i
$391$	−8.64792e9			−0.370003
$392$	−1.45540e10			−0.616366
$393$	−2.76924e10	−	4.27557e9i	−1.16089	−	0.179236i
$394$	−9.19567e9			−0.381591
$395$	5.60209e9	+	1.50487e10i	0.230124	+	0.618174i
$396$	1.41303e10	−	4.46694e10i	0.574607	−	1.81647i
$397$			6.76571e9i			0.272365i	0.990684	+	0.136183i	$0.0434834\pi$
$397$			6.76571e9i			0.272365i	−0.990684	+	0.136183i	$0.956517\pi$
$398$	2.75982e10			1.09989
$399$	2.04188e10	+	3.15256e9i	0.805636	+	0.124386i
$400$	−4.07091e10	+	3.51850e10i	−1.59020	+	1.37441i
$401$		−	1.74684e10i		−	0.675577i	−0.941222	−	0.337788i	$-0.890321\pi$
$401$		−	1.74684e10i		−	0.675577i	0.941222	−	0.337788i	$-0.109679\pi$
$402$	5.87020e10	+	9.06330e9i	2.24775	+	0.347042i
$403$		−	2.43647e10i		−	0.923722i
$404$			1.04895e11i			3.93757i
$405$	−6.82219e9	+	2.60249e10i	−0.253573	+	0.967316i
$406$	−4.80701e10			−1.76917
$407$	−2.18232e10			−0.795319
$408$	3.99385e9	−	2.58677e10i	0.144129	−	0.933507i
$409$	3.04268e10			1.08733			0.543667	−	0.839301i	$-0.317036\pi$
$409$	3.04268e10			1.08733			0.543667	+	0.839301i	$0.317036\pi$
$410$	2.56556e9	−	9.55065e8i	0.0907918	−	0.0337985i
$411$	6.21999e9	−	4.02862e10i	0.217983	−	1.41185i
$412$		−	2.85591e10i		−	0.991188i
$413$	4.49264e9			0.154419
$414$	−4.86326e10	−	1.53840e10i	−1.65549	−	0.523682i
$415$	1.05473e10	+	2.83328e10i	0.355588	+	0.955205i
$416$			4.10359e10i			1.37022i
$417$	3.83859e8	−	2.48621e9i	0.0126948	−	0.0822231i
$418$			4.29766e10i			1.40775i
$419$			6.79143e8i			0.0220346i	0.999939	+	0.0110173i	$0.00350698\pi$
$419$			6.79143e8i			0.0220346i	−0.999939	+	0.0110173i	$0.996493\pi$
$420$	−1.26426e10	−	6.13636e10i	−0.406292	−	1.97203i
$421$	2.29924e10			0.731905			0.365953	−	0.930633i	$-0.380743\pi$
$421$	2.29924e10			0.731905			0.365953	+	0.930633i	$0.380743\pi$
$422$	−4.34262e10			−1.36931
$423$	2.09699e10	+	6.63344e9i	0.654992	+	0.207194i
$424$	2.00924e10			0.621683
$425$	−9.59956e9	+	8.29693e9i	−0.294236	+	0.254309i
$426$	1.16809e11	+	1.80348e10i	3.54681	+	0.547611i
$427$		−	3.45812e10i		−	1.04023i
$428$	6.01852e10			1.79355
$429$	−4.11357e9	+	2.66431e10i	−0.121448	+	0.786604i
$430$	2.83110e10	−	1.05392e10i	0.828097	−	0.308271i
$431$			2.00633e10i			0.581426i	0.956810	+	0.290713i	$0.0938925\pi$
$431$			2.00633e10i			0.581426i	−0.956810	+	0.290713i	$0.906108\pi$
$432$	3.24698e10	−	6.56091e10i	0.932275	−	1.88378i
$433$			5.21365e10i			1.48317i	0.670861	+	0.741583i	$0.265925\pi$
$433$			5.21365e10i			1.48317i	−0.670861	+	0.741583i	$0.734075\pi$
$434$		−	5.30604e10i		−	1.49559i
$435$	8.10804e9	+	3.93542e10i	0.226443	+	1.09909i
$436$	−8.42277e10			−2.33082
$437$	3.27420e10			0.897801
$438$	−1.12734e10	−	1.74056e9i	−0.306308	−	0.0472925i
$439$	2.32256e10			0.625330			0.312665	−	0.949864i	$-0.398778\pi$
$439$	2.32256e10			0.625330			0.312665	+	0.949864i	$0.398778\pi$
$440$	6.97349e10	−	2.59598e10i	1.86054	−	0.692613i
$441$	−9.15156e9	−	2.89492e9i	−0.241958	−	0.0765389i
$442$			2.63783e10i			0.691127i
$443$	1.55300e10			0.403234			0.201617	−	0.979464i	$-0.435380\pi$
$443$	1.55300e10			0.403234			0.201617	+	0.979464i	$0.435380\pi$
$444$	−8.71025e10	−	1.34482e10i	−2.24129	−	0.346045i
$445$	1.88441e9	−	7.01498e8i	0.0480547	−	0.0178890i
$446$			3.80056e9i			0.0960524i
$447$	2.36623e10	+	3.65335e9i	0.592689	+	0.0915084i
$448$			1.62274e10i			0.402844i
$449$		−	1.61490e10i		−	0.397338i	−0.980067	−	0.198669i	$-0.936338\pi$
$449$		−	1.61490e10i		−	0.397338i	0.980067	−	0.198669i	$-0.0636619\pi$
$450$	−6.87438e10	+	2.95818e10i	−1.67642	+	0.721398i
$451$	−1.79512e9			−0.0433897
$452$	−1.21216e11			−2.90406
$453$	−3.47420e9	+	2.25020e10i	−0.0825015	+	0.534353i
$454$	8.94639e10			2.10584
$455$	1.25773e10	+	3.37861e10i	0.293456	+	0.788301i
$456$	−1.51212e10	+	9.79382e10i	−0.349725	+	2.26513i
$457$		−	5.74255e10i		−	1.31656i	−0.752774	−	0.658279i	$-0.771285\pi$
$457$		−	5.74255e10i		−	1.31656i	0.752774	−	0.658279i	$-0.228715\pi$
$458$	−1.31004e11			−2.97730
$459$	7.65665e9	−	1.54712e10i	0.172499	−	0.348556i
$460$	−3.46391e10	−	9.30499e10i	−0.773634	−	2.07819i
$461$		−	8.72792e10i		−	1.93245i	−0.257709	−	0.966223i	$-0.582968\pi$
$461$		−	8.72792e10i		−	1.93245i	0.257709	−	0.966223i	$-0.417032\pi$
$462$	−8.95835e9	+	5.80222e10i	−0.196635	+	1.27358i
$463$		−	6.70739e10i		−	1.45958i	−0.683669	−	0.729792i	$-0.739617\pi$
$463$		−	6.70739e10i		−	1.45958i	0.683669	−	0.729792i	$-0.260383\pi$
$464$		−	1.09329e11i		−	2.35864i
$465$	−4.34397e10	+	8.94976e9i	−0.929127	+	0.191425i
$466$	−5.97931e10			−1.26796
$467$	6.93467e10			1.45800			0.729001	−	0.684512i	$-0.239985\pi$
$467$	6.93467e10			1.45800			0.729001	+	0.684512i	$0.239985\pi$
$468$	−3.28368e10	+	1.03805e11i	−0.684506	+	2.16389i
$469$	−5.20853e10			−1.07652
$470$	2.13442e10	+	5.73362e10i	0.437410	+	1.17500i
$471$	−7.84818e10	−	1.21172e10i	−1.59472	−	0.246217i
$472$			2.15488e10i			0.434165i
$473$	−1.98091e10			−0.395750
$474$	9.27253e9	−	6.00572e10i	0.183690	−	1.18974i
$475$	3.63450e10	−	3.14131e10i	0.713955	−	0.617073i
$476$			4.01988e10i			0.783042i
$477$	1.26341e10	+	3.99656e9i	0.244046	+	0.0771992i
$478$			7.51743e10i			1.43998i
$479$			6.78536e10i			1.28893i	0.764632	+	0.644467i	$0.222921\pi$
$479$			6.78536e10i			1.28893i	−0.764632	+	0.644467i	$0.777079\pi$
$480$	7.31627e10	−	1.50735e10i	1.37824	−	0.283955i
$481$	5.07140e10			0.947432
$482$	7.39447e9			0.136999
$483$	4.42047e10	+	6.82499e9i	0.812231	+	0.125405i
$484$	4.24470e10			0.773509
$485$	2.98273e10	−	1.11036e10i	0.539073	−	0.200677i
$486$	7.05801e10	−	7.33834e10i	1.26514	−	1.31538i
$487$			5.60442e10i			0.996357i	0.867074	+	0.498179i	$0.165998\pi$
$487$			5.60442e10i			0.996357i	−0.867074	+	0.498179i	$0.834002\pi$
$488$	1.65868e11			2.92471
$489$	−1.18061e10	−	1.82280e9i	−0.206476	−	0.0318789i
$490$	−9.31489e9	−	2.50223e10i	−0.161582	−	0.434053i
$491$			2.96652e10i			0.510412i	0.966887	+	0.255206i	$0.0821433\pi$
$491$			2.96652e10i			0.510412i	−0.966887	+	0.255206i	$0.917857\pi$
$492$	−7.16481e9	−	1.10621e9i	−0.122277	−	0.0188789i
$493$		−	2.57806e10i		−	0.436421i
$494$		−	9.98714e10i		−	1.67700i
$495$	4.90129e10	−	2.45261e9i	0.816375	−	0.0408515i
$496$	1.20678e11			1.99390
$497$	−1.03643e11			−1.69869
$498$	1.74578e10	−	1.13072e11i	0.283838	−	1.83839i
$499$	−7.38741e10			−1.19149			−0.595744	−	0.803174i	$-0.703143\pi$
$499$	−7.38741e10			−1.19149			−0.595744	+	0.803174i	$0.703143\pi$
$500$	−1.27724e11	−	7.00561e10i	−2.04358	−	1.12090i
$501$	−1.25069e10	+	8.10061e10i	−0.198518	+	1.28578i
$502$			1.13479e10i			0.178691i
$503$	−2.33952e10			−0.365472			−0.182736	−	0.983162i	$-0.558495\pi$
$503$	−2.33952e10			−0.365472			−0.182736	+	0.983162i	$0.558495\pi$
$504$	−4.08299e10	+	1.29073e11i	−0.632785	+	2.00039i
$505$	−1.02969e11	+	3.83316e10i	−1.58322	+	0.589374i
$506$			9.30400e10i			1.41928i
$507$	−5.22728e8	+	3.38565e9i	−0.00791122	+	0.0512401i
$508$			6.03037e10i			0.905501i
$509$		−	3.61802e10i		−	0.539014i	−0.962998	−	0.269507i	$-0.913139\pi$
$509$		−	3.61802e10i		−	0.539014i	0.962998	−	0.269507i	$-0.0868608\pi$
$510$	4.70297e10	−	9.68940e9i	0.695171	−	0.143224i
$511$	1.00027e10			0.146702
$512$	1.47557e11			2.14724
$513$	−2.89890e10	+	5.85757e10i	−0.418565	+	0.845762i
$514$	8.63505e10			1.23712
$515$	2.80348e10	−	1.04363e10i	0.398537	−	0.148361i
$516$	−7.90638e10	−	1.22071e10i	−1.11527	−	0.172192i
$517$		−	4.01180e10i		−	0.561536i
$518$	1.10443e11			1.53397
$519$	−1.98742e9	+	1.28723e10i	−0.0273918	+	0.177413i
$520$	−1.62054e11	+	6.03268e10i	−2.21639	+	0.825082i
$521$		−	1.09399e11i		−	1.48478i	−0.669966	−	0.742392i	$-0.733691\pi$
$521$		−	1.09399e11i		−	1.48478i	0.669966	−	0.742392i	$-0.266309\pi$
$522$	4.58617e10	−	1.44980e11i	0.617687	−	1.95266i
$523$			1.03949e10i			0.138936i	0.997584	+	0.0694679i	$0.0221301\pi$
$523$			1.03949e10i			0.138936i	−0.997584	+	0.0694679i	$0.977870\pi$
$524$			2.06413e11i			2.73786i
$525$	5.56170e10	−	3.48345e10i	0.732100	−	0.458535i
$526$	−6.24548e10			−0.815874
$527$	2.84570e10			0.368932
$528$	−1.31963e11	−	2.03745e10i	−1.69792	−	0.262151i
$529$	−7.42772e9			−0.0948491
$530$	1.28596e10	+	3.45443e10i	0.162976	+	0.437797i
$531$	−4.28624e9	+	1.35499e10i	−0.0539137	+	0.170434i
$532$		−	1.52197e11i		−	1.90003i
$533$	4.17159e9			0.0516884
$534$	−7.52041e9	−	1.16111e9i	−0.0924861	−	0.0142794i
$535$	2.19934e10	+	5.90802e10i	0.268459	+	0.721152i
$536$		−	2.49826e11i		−	3.02676i
$537$	−1.52290e11	−	2.35128e10i	−1.83136	−	0.282754i
$538$			7.10392e10i			0.847947i
$539$			1.75080e10i			0.207435i
$540$	1.97135e11	+	2.04143e10i	2.31841	+	0.240082i
$541$	1.14995e11			1.34243			0.671215	−	0.741263i	$-0.265773\pi$
$541$	1.14995e11			1.34243			0.671215	+	0.741263i	$0.265773\pi$
$542$	−8.78557e10			−1.01806
$543$	1.85676e10	−	1.20260e11i	0.213578	−	1.38332i
$544$	−4.79282e10			−0.547263
$545$	−3.07793e10	−	8.26813e10i	−0.348877	−	0.937176i
$546$	2.08179e10	−	1.34835e11i	0.234243	−	1.51717i
$547$			9.64858e10i			1.07774i	0.842389	+	0.538870i	$0.181149\pi$
$547$			9.64858e10i			1.07774i	−0.842389	+	0.538870i	$0.818851\pi$
$548$	−3.00284e11			−3.32974
$549$	1.04298e11	+	3.29926e10i	1.14811	+	0.363184i
$550$	8.92637e10	+	1.03278e11i	0.975493	+	1.12865i
$551$			9.76085e10i			1.05896i
$552$	−3.27359e10	+	2.12026e11i	−0.352588	+	2.28367i
$553$			5.32878e10i			0.569806i
$554$			2.28968e11i			2.43072i
$555$	−1.86285e10	−	9.04177e10i	−0.196339	−	0.952975i
$556$	−1.85317e10			−0.193917
$557$	7.55411e10			0.784806			0.392403	−	0.919793i	$-0.371644\pi$
$557$	7.55411e10			0.784806			0.392403	+	0.919793i	$0.371644\pi$
$558$	1.60031e11	+	5.06228e10i	1.65070	+	0.522167i
$559$	4.60336e10			0.471441
$560$	−1.67342e11	+	6.22955e10i	−1.70158	+	0.633438i
$561$	−3.11181e10	−	4.80448e9i	−0.314168	−	0.0485060i
$562$		−	4.81296e10i		−	0.482466i
$563$	−1.11903e11			−1.11381			−0.556903	−	0.830578i	$-0.688010\pi$
$563$	−1.11903e11			−1.11381			−0.556903	+	0.830578i	$0.688010\pi$
$564$	2.47221e10	−	1.60122e11i	0.244326	−	1.58247i
$565$	−4.42958e10	−	1.18990e11i	−0.434679	−	1.16766i
$566$			2.67298e11i			2.60453i
$567$	−5.13476e10	+	7.30398e10i	−0.496807	+	0.706687i
$568$		−	4.97120e11i		−	4.77604i
$569$		−	1.49452e11i		−	1.42578i	−0.701275	−	0.712891i	$-0.747385\pi$
$569$		−	1.49452e11i		−	1.42578i	0.701275	−	0.712891i	$-0.252615\pi$
$570$	−1.78060e11	+	3.66852e10i	−1.68681	+	0.347529i
$571$	5.21898e10			0.490954			0.245477	−	0.969402i	$-0.421055\pi$
$571$	5.21898e10			0.490954			0.245477	+	0.969402i	$0.421055\pi$
$572$	1.98592e11			1.85514
$573$	1.75939e11	+	2.71642e10i	1.63209	+	0.251987i
$574$	9.08470e9			0.0836880
$575$	7.86834e10	−	6.80063e10i	0.719800	−	0.622125i
$576$	−4.89421e10	−	1.54819e10i	−0.444624	−	0.140648i
$577$			2.00263e11i			1.80674i	0.428859	+	0.903372i	$0.358916\pi$
$577$			2.00263e11i			1.80674i	−0.428859	+	0.903372i	$0.641084\pi$
$578$	1.72889e11			1.54901
$579$	−3.52513e10	−	5.44264e9i	−0.313662	−	0.0484278i
$580$	2.77394e11	−	1.03264e11i	2.45124	−	0.912507i
$581$			1.00327e11i			0.880468i
$582$	−1.19036e11	−	1.83787e10i	−1.03750	−	0.160185i
$583$		−	2.41706e10i		−	0.209225i
$584$			4.79778e10i			0.412467i
$585$	−1.13899e11	+	5.69952e9i	−0.972515	+	0.0486648i
$586$	−3.96662e11			−3.36380
$587$	4.86434e10			0.409705			0.204852	−	0.978793i	$-0.434329\pi$
$587$	4.86434e10			0.409705			0.204852	+	0.978793i	$0.434329\pi$
$588$	−1.07890e10	+	6.98794e10i	−0.0902555	+	0.584575i
$589$	−1.07742e11			−0.895204
$590$	−3.70482e10	+	1.37917e10i	−0.305745	+	0.113818i
$591$	−3.89217e9	+	2.52092e10i	−0.0319038	+	0.206637i
$592$			2.51186e11i			2.04507i
$593$	−2.19946e11			−1.77868			−0.889340	−	0.457247i	$-0.848835\pi$
$593$	−2.19946e11			−1.77868			−0.889340	+	0.457247i	$0.848835\pi$
$594$	−1.66449e11	−	8.23752e10i	−1.33701	−	0.661684i
$595$	−3.94607e10	+	1.46898e10i	−0.314845	+	0.117206i
$596$		−	1.76374e11i		−	1.39781i
$597$	1.16812e10	−	7.56581e10i	0.0919585	−	0.595605i
$598$		−	2.16212e11i		−	1.69073i
$599$		−	1.45254e11i		−	1.12829i	−0.825675	−	0.564145i	$-0.809206\pi$
$599$		−	1.45254e11i		−	1.12829i	0.825675	−	0.564145i	$-0.190794\pi$
$600$	1.67083e11	+	2.66765e11i	1.28922	+	2.05837i
$601$	−3.38288e10			−0.259292			−0.129646	−	0.991560i	$-0.541384\pi$
$601$	−3.38288e10			−0.259292			−0.129646	+	0.991560i	$0.541384\pi$
$602$	1.00250e11			0.763304
$603$	4.96925e10	−	1.57090e11i	0.375856	−	1.18817i
$604$	1.67725e11			1.26023
$605$	1.55114e10	+	4.16677e10i	0.115779	+	0.311012i
$606$	4.10934e11	+	6.34462e10i	3.04706	+	0.470452i
$607$		−	8.61846e10i		−	0.634856i	−0.948282	−	0.317428i	$-0.897181\pi$
$607$		−	8.61846e10i		−	0.634856i	0.948282	−	0.317428i	$-0.102819\pi$
$608$	1.81462e11			1.32792
$609$	−2.03462e10	+	1.31780e11i	−0.147916	+	0.958033i
$610$	1.06159e11	+	2.85172e11i	0.766722	+	2.05962i
$611$			9.32286e10i			0.668935i
$612$	−1.21240e11	−	3.83520e10i	−0.864253	−	0.273390i
$613$			1.61967e11i			1.14706i	0.819186	+	0.573528i	$0.194426\pi$
$613$			1.61967e11i			1.14706i	−0.819186	+	0.573528i	$0.805574\pi$
$614$		−	2.97362e11i		−	2.09224i
$615$	−1.53233e9	−	7.43750e9i	−0.0107115	−	0.0519908i
$616$	2.46933e11			1.71497
$617$	1.33433e11			0.920711			0.460356	−	0.887735i	$-0.347722\pi$
$617$	1.33433e11			0.920711			0.460356	+	0.887735i	$0.347722\pi$
$618$	−1.11883e11	−	1.72741e10i	−0.767024	−	0.118425i
$619$	8.29100e10			0.564735			0.282367	−	0.959306i	$-0.408880\pi$
$619$	8.29100e10			0.564735			0.282367	+	0.959306i	$0.408880\pi$
$620$	1.13984e11	+	3.06191e11i	0.771395	+	2.07217i
$621$	−6.27582e10	+	1.26811e11i	−0.421992	+	0.852686i
$622$		−	3.55922e11i		−	2.37790i
$623$	6.67274e9			0.0442947
$624$	3.06664e11	+	4.73474e10i	2.02267	+	0.312290i
$625$	2.20958e10	−	1.50980e11i	0.144807	−	0.989460i
$626$		−	2.74390e11i		−	1.78678i
$627$	1.17817e11	+	1.81903e10i	0.762319	+	0.117698i
$628$			5.84986e11i			3.76103i
$629$			5.92319e10i			0.378402i
$630$	−2.48044e11	+	1.24122e10i	−1.57459	+	0.0787926i
$631$	−1.87684e11			−1.18389			−0.591944	−	0.805979i	$-0.701639\pi$
$631$	−1.87684e11			−1.18389			−0.591944	+	0.805979i	$0.701639\pi$
$632$	−2.55593e11			−1.60207
$633$	−1.83806e10	+	1.19049e11i	−0.114484	+	0.741501i
$634$	−4.97648e11			−3.08010
$635$	−5.91965e10	+	2.20367e10i	−0.364084	+	0.135535i
$636$	1.48947e10	−	9.64715e10i	0.0910342	−	0.589618i
$637$		−	4.06862e10i		−	0.247109i
$638$	−2.77365e11			−1.67405
$639$	9.88815e10	−	3.12589e11i	0.593078	−	1.87487i
$640$	3.25490e10	+	8.74352e10i	0.194007	+	0.521154i
$641$			2.47743e11i			1.46747i	0.679436	+	0.733735i	$0.262225\pi$
$641$			2.47743e11i			1.46747i	−0.679436	+	0.733735i	$0.737775\pi$
$642$	3.64034e10	−	2.35780e11i	0.214290	−	1.38793i
$643$		−	1.96282e11i		−	1.14825i	−0.818767	−	0.574125i	$-0.805342\pi$
$643$		−	1.96282e11i		−	1.14825i	0.818767	−	0.574125i	$-0.194658\pi$
$644$		−	3.29492e11i		−	1.91558i
$645$	−1.69093e10	−	8.20730e10i	−0.0976980	−	0.474200i
$646$	1.16646e11			0.669790
$647$	−5.06782e10			−0.289204			−0.144602	−	0.989490i	$-0.546190\pi$
$647$	−5.06782e10			−0.289204			−0.144602	+	0.989490i	$0.546190\pi$
$648$	−3.50333e11	−	2.46287e11i	−1.98692	−	1.39682i
$649$	2.59225e10			0.146116
$650$	−2.07436e11	−	2.40004e11i	−1.16207	−	1.34451i
$651$	−1.45461e11	−	2.24584e10i	−0.809881	−	0.125042i
$652$			8.79997e10i			0.486957i
$653$	2.96579e11			1.63113			0.815563	−	0.578668i	$-0.196427\pi$
$653$	2.96579e11			1.63113			0.815563	+	0.578668i	$0.196427\pi$
$654$	−5.09456e10	+	3.29969e11i	−0.278481	+	1.80369i
$655$	−2.02623e11	+	7.54293e10i	−1.10084	+	0.409803i
$656$			2.06619e10i			0.111572i
$657$	−9.54320e9	+	3.01684e10i	−0.0512192	+	0.161916i
$658$			2.03029e11i			1.08306i
$659$			2.16427e11i			1.14754i	0.819015	+	0.573772i	$0.194521\pi$
$659$			2.16427e11i			1.14754i	−0.819015	+	0.573772i	$0.805479\pi$
$660$	−7.29477e10	−	3.54068e11i	−0.384446	−	1.86600i
$661$	2.43348e11			1.27474			0.637370	−	0.770558i	$-0.280022\pi$
$661$	2.43348e11			1.27474			0.637370	+	0.770558i	$0.280022\pi$
$662$	−4.64982e11			−2.42105
$663$	7.23139e10	+	1.11649e10i	0.374255	+	0.0577832i
$664$	−4.81216e11			−2.47553
$665$	1.49403e11	−	5.56173e10i	0.763963	−	0.284396i
$666$	−1.05369e11	+	3.33097e11i	−0.535569	+	1.69307i
$667$			2.11313e11i			1.06763i
$668$	6.03801e11			3.03241
$669$	1.04189e10	+	1.60863e9i	0.0520138	+	0.00803067i
$670$	4.29518e11	−	1.59894e11i	2.13148	−	0.793474i
$671$		−	1.99534e11i		−	0.984298i
$672$	2.44990e11	+	3.78252e10i	1.20135	+	0.185483i
$673$		−	1.94434e11i		−	0.947790i	−0.880581	−	0.473895i	$-0.842848\pi$
$673$		−	1.94434e11i		−	0.947790i	0.880581	−	0.473895i	$-0.157152\pi$
$674$			4.32608e11i			2.09631i
$675$	5.19995e10	+	2.00976e11i	0.250486	+	0.968120i
$676$	2.52359e10			0.120846
$677$	2.37969e11			1.13283			0.566417	−	0.824119i	$-0.308329\pi$
$677$	2.37969e11			1.13283			0.566417	+	0.824119i	$0.308329\pi$
$678$	−7.33181e10	+	4.74873e11i	−0.346970	+	2.24729i
$679$	1.05619e11			0.496894
$680$	−7.04592e10	−	1.89272e11i	−0.329535	−	0.885220i
$681$	3.78666e10	−	2.45258e11i	0.176063	−	1.14034i
$682$		−	3.06159e11i		−	1.41517i
$683$	−3.02984e11			−1.39231			−0.696156	−	0.717891i	$-0.745108\pi$
$683$	−3.02984e11			−1.39231			−0.696156	+	0.717891i	$0.745108\pi$
$684$	4.59029e11	+	1.45205e11i	2.09709	+	0.663373i
$685$	−1.09733e11	−	2.94771e11i	−0.498395	−	1.33882i
$686$		−	4.37749e11i		−	1.97665i
$687$	−5.54489e10	+	3.59136e11i	−0.248924	+	1.61225i
$688$			2.28004e11i			1.01763i
$689$			5.61690e10i			0.249241i
$690$	−3.85482e11	+	7.94198e10i	−1.70062	+	0.350374i
$691$	3.45611e11			1.51592			0.757959	−	0.652303i	$-0.226197\pi$
$691$	3.45611e11			1.51592			0.757959	+	0.652303i	$0.226197\pi$
$692$	9.59472e10			0.418416
$693$	1.55271e11	+	4.91171e10i	0.673222	+	0.212961i
$694$	5.80782e11			2.50366
$695$	−6.77201e9	−	1.81914e10i	−0.0290254	−	0.0779700i
$696$	−6.32079e11	−	9.75900e10i	−2.69361	−	0.415880i
$697$			4.87225e9i			0.0206442i
$698$	2.34703e11			0.988775
$699$	−2.53081e10	+	1.63918e11i	−0.106011	+	0.686621i
$700$	−3.16118e11	−	3.65750e11i	−1.31661	−	1.52332i
$701$		−	1.76735e11i		−	0.731896i	−0.930635	−	0.365948i	$-0.880745\pi$
$701$		−	1.76735e11i		−	0.731896i	0.930635	−	0.365948i	$-0.119255\pi$
$702$	3.86804e11	+	1.91428e11i	1.59273	+	0.788238i
$703$		−	2.24259e11i		−	0.918181i
$704$			9.36322e10i			0.381184i
$705$	1.66217e11	−	3.42451e10i	0.672850	−	0.138625i
$706$	−3.17116e11			−1.27644
$707$	−3.64615e11			−1.45934
$708$	1.03464e11	+	1.59744e10i	0.411772	+	0.0635756i
$709$	6.57734e10			0.260295			0.130147	−	0.991495i	$-0.458455\pi$
$709$	6.57734e10			0.260295			0.130147	+	0.991495i	$0.458455\pi$
$710$	8.54684e11	−	3.18168e11i	3.36335	−	1.25205i
$711$	−1.60717e11	−	5.08397e10i	−0.628902	−	0.198941i
$712$			3.20056e10i			0.124539i
$713$	−2.33250e11			−0.902532
$714$	1.57482e11	+	2.43145e10i	0.605952	+	0.0935560i
$715$	7.25713e10	+	1.94946e11i	0.277678	+	0.745916i
$716$			1.13514e12i			4.31912i
$717$	2.06084e11	+	3.18184e10i	0.779772	+	0.120393i
$718$		−	4.28645e10i		−	0.161287i
$719$			7.88079e10i			0.294886i	0.989071	+	0.147443i	$0.0471043\pi$
$719$			7.88079e10i			0.294886i	−0.989071	+	0.147443i	$0.952896\pi$
$720$	−2.82297e10	−	5.64141e11i	−0.105045	−	2.09922i
$721$	9.92718e10			0.367354
$722$	5.42994e10			0.199823
$723$	3.12979e9	−	2.02713e10i	0.0114541	−	0.0741871i
$724$	−8.96395e11			−3.26246
$725$	2.02736e11	+	2.34566e11i	0.733802	+	0.849010i
$726$	2.56743e10	−	1.66290e11i	0.0924171	−	0.598575i
$727$		−	1.84656e11i		−	0.661036i	−0.943800	−	0.330518i	$-0.892777\pi$
$727$		−	1.84656e11i		−	0.661036i	0.943800	−	0.330518i	$-0.107223\pi$
$728$	−5.73836e11			−2.04297
$729$	−1.71301e11	−	2.24550e11i	−0.606525	−	0.795064i
$730$	−8.24868e10	+	3.07068e10i	−0.290464	+	0.108129i
$731$			5.37653e10i			0.188292i
$732$	1.22960e11	−	7.96395e11i	0.428270	−	2.77386i
$733$			5.18772e11i			1.79705i	0.438921	+	0.898526i	$0.355361\pi$
$733$			5.18772e11i			1.79705i	−0.438921	+	0.898526i	$0.644639\pi$
$734$			2.69599e11i			0.928825i
$735$	−7.25391e10	+	1.49450e10i	−0.248555	+	0.0512091i
$736$	3.92847e11			1.33879
$737$	−3.00533e11			−1.01864
$738$	−8.66735e9	+	2.73996e10i	−0.0292187	+	0.0923675i
$739$	−3.63264e11			−1.21799			−0.608997	−	0.793173i	$-0.708428\pi$
$739$	−3.63264e11			−1.21799			−0.608997	+	0.793173i	$0.708428\pi$
$740$	−6.37323e11	+	2.37252e11i	−2.12536	+	0.791195i
$741$	−2.73789e11	−	4.22717e10i	−0.908120	−	0.140209i
$742$			1.22322e11i			0.403543i
$743$	−1.03812e11			−0.340637			−0.170318	−	0.985389i	$-0.554480\pi$
$743$	−1.03812e11			−0.340637			−0.170318	+	0.985389i	$0.554480\pi$
$744$	1.07721e11	−	6.97698e11i	0.351568	−	2.27707i
$745$	1.73135e11	−	6.44521e10i	0.562032	−	0.209224i
$746$		−	3.96360e11i		−	1.27978i
$747$	−3.02588e11	−	9.57180e10i	−0.971783	−	0.307405i
$748$			2.31947e11i			0.740940i
$749$			2.09204e11i			0.664727i
$750$	−3.51705e11	+	4.57996e11i	−1.11156	+	1.44749i
$751$	8.69686e10			0.273403			0.136701	−	0.990612i	$-0.456350\pi$
$751$	8.69686e10			0.273403			0.136701	+	0.990612i	$0.456350\pi$
$752$	−4.61761e11			−1.44393
$753$	3.11094e10	+	4.80314e9i	0.0967636	+	0.0149398i
$754$	6.44556e11			1.99423
$755$	6.12915e10	+	1.64645e11i	0.188631	+	0.506713i
$756$	5.89463e11	+	2.91723e11i	1.80455	+	0.893067i
$757$		−	9.42170e10i		−	0.286910i	−0.989657	−	0.143455i	$-0.954179\pi$
$757$		−	9.42170e10i		−	0.286910i	0.989657	−	0.143455i	$-0.0458212\pi$
$758$	5.04300e11			1.52761
$759$	2.55061e11	+	3.93802e10i	0.768560	+	0.118662i
$760$	2.66767e11	+	7.16607e11i	0.799608	+	2.14796i
$761$		−	3.69015e11i		−	1.10029i	−0.835071	−	0.550143i	$-0.814573\pi$
$761$		−	3.69015e11i		−	1.10029i	0.835071	−	0.550143i	$-0.185427\pi$
$762$	2.36245e11	+	3.64750e10i	0.700716	+	0.108187i
$763$		−	2.92776e11i		−	0.863849i
$764$		−	1.31141e12i		−	3.84916i
$765$	−6.65681e9	−	1.33029e11i	−0.0194366	−	0.388420i
$766$	4.67036e10			0.135655
$767$	−6.02403e10			−0.174063
$768$	7.86299e10	−	5.09277e11i	0.226018	−	1.46389i
$769$	−2.57584e11			−0.736569			−0.368284	−	0.929713i	$-0.620055\pi$
$769$	−2.57584e11			−0.736569			−0.368284	+	0.929713i	$0.620055\pi$
$770$	1.58042e11	+	4.24544e11i	0.449584	+	1.20770i
$771$	3.65488e10	−	2.36723e11i	0.103432	−	0.669919i
$772$			2.62756e11i			0.739746i
$773$	4.50174e11			1.26085			0.630424	−	0.776251i	$-0.282881\pi$
$773$	4.50174e11			1.26085			0.630424	+	0.776251i	$0.282881\pi$
$774$	−9.56444e10	+	3.02355e11i	−0.266499	+	0.842469i
$775$	−2.58917e11	+	2.23783e11i	−0.717717	+	0.620325i
$776$			5.06600e11i			1.39707i
$777$	4.67461e10	−	3.02769e11i	0.128251	−	0.830669i
$778$		−	3.82371e11i		−	1.04368i
$779$		−	1.84469e10i		−	0.0500926i
$780$	1.69520e11	+	8.22804e11i	0.457976	+	2.22289i
$781$	−5.98020e11			−1.60736
$782$	2.52526e11			0.675273
$783$	−3.78040e11	−	1.87091e11i	−1.00575	−	0.497743i
$784$	2.01518e11			0.533397
$785$	−5.74245e11	+	2.13771e11i	−1.51223	+	0.562950i
$786$	8.08640e11	+	1.24850e11i	2.11868	+	0.327114i
$787$			1.63448e11i			0.426070i	0.977045	+	0.213035i	$0.0683348\pi$
$787$			1.63448e11i			0.426070i	−0.977045	+	0.213035i	$0.931665\pi$
$788$	1.87903e11			0.487337
$789$	−2.64347e10	+	1.71215e11i	−0.0682129	+	0.441807i
$790$	−1.63585e11	−	4.39434e11i	−0.419987	−	1.12820i
$791$		−	4.21347e11i		−	1.07630i
$792$	−2.35589e11	+	7.44754e11i	−0.598761	+	1.89283i
$793$			4.63688e11i			1.17256i
$794$		−	1.97564e11i		−	0.497080i
$795$	1.00143e11	−	2.06322e10i	0.250699	−	0.0516509i
$796$	−5.63939e11			−1.40469
$797$	9.45344e10			0.234292			0.117146	−	0.993115i	$-0.462626\pi$
$797$	9.45344e10			0.234292			0.117146	+	0.993115i	$0.462626\pi$
$798$	−5.96245e11	−	9.20574e10i	−1.47032	−	0.227011i
$799$	−1.08887e11			−0.267171
$800$	4.36076e11	−	3.76902e11i	1.06464	−	0.920171i
$801$	−6.36619e9	+	2.01251e10i	−0.0154650	+	0.0488887i
$802$			5.10090e11i			1.23296i
$803$	5.77158e10			0.138814
$804$	−1.19951e12	−	1.85198e11i	−2.87065	−	0.443214i
$805$	3.23442e11	−	1.20406e11i	0.770217	−	0.286724i
$806$			7.11469e11i			1.68584i
$807$	1.94748e11	+	3.00681e10i	0.459175	+	0.0708944i
$808$		−	1.74887e12i		−	4.10309i
$809$		−	1.27394e11i		−	0.297409i	−0.988882	−	0.148704i	$-0.952490\pi$
$809$		−	1.27394e11i		−	0.297409i	0.988882	−	0.148704i	$-0.0475102\pi$
$810$	1.99213e11	−	7.59947e11i	0.462784	−	1.76540i
$811$	8.64282e10			0.199789			0.0998946	−	0.994998i	$-0.468149\pi$
$811$	8.64282e10			0.199789			0.0998946	+	0.994998i	$0.468149\pi$
$812$	9.82259e11			2.25945
$813$	−3.71859e10	+	2.40849e11i	−0.0851170	+	0.551293i
$814$	6.37255e11			1.45150
$815$	−8.63841e10	+	3.21577e10i	−0.195796	+	0.0728877i
$816$	−5.52998e10	+	3.58171e11i	−0.124728	+	0.807847i
$817$		−	2.03562e11i		−	0.456886i
$818$	−8.88486e11			−1.98444
$819$	−3.60828e11	−	1.14141e11i	−0.801982	−	0.253692i
$820$	−5.24244e10	+	1.95157e10i	−0.115952	+	0.0431647i
$821$			4.69914e11i			1.03430i	0.855895	+	0.517149i	$0.173007\pi$
$821$			4.69914e11i			1.03430i	−0.855895	+	0.517149i	$0.826993\pi$
$822$	−1.81629e11	+	1.17639e12i	−0.397830	+	2.57670i
$823$		−	2.66887e11i		−	0.581739i	−0.956763	−	0.290869i	$-0.906056\pi$
$823$		−	2.66887e11i		−	0.581739i	0.956763	−	0.290869i	$-0.0939445\pi$
$824$			4.76154e11i			1.03285i
$825$	3.20911e11	−	2.00995e11i	0.692737	−	0.433880i
$826$	−1.31189e11			−0.281822
$827$	7.66086e11			1.63778			0.818889	−	0.573951i	$-0.194590\pi$
$827$	7.66086e11			1.63778			0.818889	+	0.573951i	$0.194590\pi$
$828$	9.93753e11	+	3.14355e11i	2.11425	+	0.668804i
$829$	5.72793e11			1.21277			0.606386	−	0.795170i	$-0.292619\pi$
$829$	5.72793e11			1.21277			0.606386	+	0.795170i	$0.292619\pi$
$830$	−3.07989e11	−	8.27339e11i	−0.648966	−	1.74330i
$831$	6.27696e11	+	9.69133e10i	1.31627	+	0.203226i
$832$		−	2.17588e11i		−	0.454089i
$833$	4.75198e10			0.0986948
$834$	−1.12090e10	+	7.25993e10i	−0.0231687	+	0.150061i
$835$	2.20647e11	+	5.92715e11i	0.453891	+	1.21927i
$836$		−	8.78179e11i		−	1.79787i
$837$	2.06513e11	−	4.17285e11i	0.420771	−	0.850219i
$838$		−	1.98315e10i		−	0.0402142i
$839$		−	1.37426e11i		−	0.277346i	−0.990338	−	0.138673i	$-0.955716\pi$
$839$		−	1.37426e11i		−	0.277346i	0.990338	−	0.138673i	$-0.0442836\pi$
$840$	2.10784e11	+	1.02309e12i	0.423371	+	2.05493i
$841$	−1.29705e11			−0.259282
$842$	−6.71395e11			−1.33576
$843$	−1.31943e11	−	2.03714e10i	−0.261262	−	0.0403376i
$844$	8.87366e11			1.74877
$845$	9.22192e9	+	2.47725e10i	0.0180882	+	0.0485897i
$846$	−6.12339e11	−	1.93702e11i	−1.19539	−	0.378139i
$847$			1.47546e11i			0.286678i
$848$	−2.78205e11			−0.537998
$849$	7.32774e11	+	1.13137e11i	1.41039	+	0.217758i
$850$	2.80315e11	−	2.42277e11i	0.536995	−	0.464126i
$851$		−	4.85498e11i		−	0.925698i
$852$	−2.38687e12	−	3.68520e11i	−4.52970	−	0.699364i
$853$			5.59514e11i			1.05685i	0.848979	+	0.528426i	$0.177218\pi$
$853$			5.59514e11i			1.05685i	−0.848979	+	0.528426i	$0.822782\pi$
$854$			1.00980e12i			1.89847i
$855$	2.52034e10	+	5.03664e11i	0.0471624	+	0.942490i
$856$	−1.00344e12			−1.86895
$857$	−4.92440e11			−0.912914			−0.456457	−	0.889745i	$-0.650882\pi$
$857$	−4.92440e11			−0.912914			−0.456457	+	0.889745i	$0.650882\pi$
$858$	1.20120e11	−	7.78000e11i	0.221648	−	1.43559i
$859$	−2.33490e11			−0.428840			−0.214420	−	0.976742i	$-0.568786\pi$
$859$	−2.33490e11			−0.428840			−0.214420	+	0.976742i	$0.568786\pi$
$860$	−5.78504e11	+	2.15356e11i	−1.05758	+	0.393698i
$861$	3.84520e9	−	2.49049e10i	0.00699692	−	0.0453182i
$862$		−	5.85866e11i		−	1.06113i
$863$	1.43714e11			0.259093			0.129546	−	0.991573i	$-0.458648\pi$
$863$	1.43714e11			0.259093			0.129546	+	0.991573i	$0.458648\pi$
$864$	−3.47816e11	+	7.02806e11i	−0.624159	+	1.26119i
$865$	3.50619e10	+	9.41856e10i	0.0626284	+	0.168237i
$866$		−	1.52243e12i		−	2.70685i
$867$	7.31771e10	−	4.73960e11i	0.129509	−	0.838813i
$868$			1.08423e12i			1.91004i
$869$			3.07471e11i			0.539169i
$870$	−2.36761e11	−	1.14917e12i	−0.413270	−	2.00590i
$871$	6.98395e11			1.21347
$872$	1.40429e12			2.42880
$873$	−1.00767e11	+	3.18549e11i	−0.173485	+	0.548428i
$874$	−9.56094e11			−1.63853
$875$	2.43516e11	−	4.43970e11i	0.415427	−	0.757393i
$876$	2.30360e11	+	3.55664e10i	0.391192	+	0.0603982i
$877$		−	6.46204e11i		−	1.09237i	−0.837663	−	0.546187i	$-0.816079\pi$
$877$		−	6.46204e11i		−	1.09237i	0.837663	−	0.546187i	$-0.183921\pi$
$878$	−6.78206e11			−1.14126
$879$	−1.67892e11	+	1.08742e12i	−0.281238	+	1.82155i
$880$	−9.65566e11	+	3.59445e11i	−1.61009	+	0.599380i
$881$			8.24361e11i			1.36840i	0.729294	+	0.684201i	$0.239849\pi$
$881$			8.24361e11i			1.36840i	−0.729294	+	0.684201i	$0.760151\pi$
$882$	2.67233e11	+	8.45340e10i	0.441586	+	0.139687i
$883$		−	7.15195e11i		−	1.17647i	−0.808689	−	0.588236i	$-0.799822\pi$
$883$		−	7.15195e11i		−	1.17647i	0.808689	−	0.588236i	$-0.200178\pi$
$884$		−	5.39012e11i		−	0.882652i
$885$	2.21277e10	+	1.07402e11i	0.0360715	+	0.175081i
$886$	−4.53489e11			−0.735922
$887$	6.02155e11			0.972779			0.486389	−	0.873742i	$-0.338314\pi$
$887$	6.02155e11			0.972779			0.486389	+	0.873742i	$0.338314\pi$
$888$	1.45222e12	+	2.24216e11i	2.33551	+	0.360592i
$889$	−2.09616e11			−0.335597
$890$	−5.50263e10	+	2.04843e10i	−0.0877021	+	0.0326483i
$891$	−2.96276e11	+	4.21440e11i	−0.470095	+	0.668690i
$892$		−	7.76603e10i		−	0.122670i
$893$	4.12259e11			0.648283
$894$	−6.90958e11	−	1.06681e11i	−1.08169	−	0.167007i
$895$	−1.11430e12	+	4.14812e11i	−1.73663	+	0.646486i
$896$			3.09610e11i			0.480378i
$897$	−5.92726e11	−	9.15140e10i	−0.915554	−	0.141357i
$898$			4.71563e11i			0.725162i
$899$		−	6.95349e11i		−	1.06454i
$900$	1.40470e12	−	6.04472e11i	2.14099	−	0.921311i
$901$	−6.56030e10			−0.0995462
$902$	5.24188e10			0.0791883
$903$	4.24319e10	−	2.74827e11i	0.0638177	−	0.413340i
$904$	2.02098e12			3.02614
$905$	−3.27569e11	−	8.79937e11i	−0.488324	−	1.31177i
$906$	1.01449e11	−	6.57076e11i	0.150569	−	0.975220i
$907$			5.73238e11i			0.847044i	0.905886	+	0.423522i	$0.139206\pi$
$907$			5.73238e11i			0.847044i	−0.905886	+	0.423522i	$0.860794\pi$
$908$	−1.82810e12			−2.68940
$909$	3.47865e11	−	1.09969e12i	0.509512	−	1.61069i
$910$	−3.67268e11	−	9.86580e11i	−0.535571	−	1.43869i
$911$			5.47261e11i			0.794550i	0.917700	+	0.397275i	$0.130044\pi$
$911$			5.47261e11i			0.794550i	−0.917700	+	0.397275i	$0.869956\pi$
$912$	2.09372e11	−	1.35608e12i	0.302648	−	1.96022i
$913$			5.78888e11i			0.833127i
$914$			1.67687e12i			2.40278i
$915$	8.26707e11	−	1.70324e11i	1.17942	−	0.242992i
$916$	2.67692e12			3.80236
$917$	−7.17494e11			−1.01471
$918$	−2.23580e11	+	4.51771e11i	−0.314820	+	0.636133i
$919$	5.41675e11			0.759410			0.379705	−	0.925108i	$-0.376025\pi$
$919$	5.41675e11			0.759410			0.379705	+	0.925108i	$0.376025\pi$
$920$	5.77523e11	+	1.55138e12i	0.806154	+	2.16555i
$921$	−8.15193e11	−	1.25862e11i	−1.13298	−	0.174927i
$922$			2.54862e12i			3.52681i
$923$	1.38971e12			1.91478
$924$	1.83054e11	−	1.18562e12i	0.251126	−	1.62651i
$925$	−4.65793e11	−	5.38923e11i	−0.636247	−	0.736139i
$926$			1.95861e12i			2.66381i
$927$	−9.47112e10	+	2.99406e11i	−0.128257	+	0.405453i
$928$			1.17113e12i			1.57911i
$929$			3.66914e10i			0.0492608i	0.999697	+	0.0246304i	$0.00784090\pi$
$929$			3.66914e10i			0.0492608i	−0.999697	+	0.0246304i	$0.992159\pi$
$930$	1.26847e12	−	2.61340e11i	1.69570	−	0.349361i
$931$	−1.79915e11			−0.239480
$932$	1.22181e12			1.61934
$933$	−9.75730e11	−	1.50648e11i	−1.28767	−	0.198809i
$934$	−2.02498e12			−2.66093
$935$	−2.27689e11	+	8.47603e10i	−0.297917	+	0.110904i
$936$	5.47474e11	−	1.73070e12i	0.713281	−	2.25486i
$937$		−	1.06583e12i		−	1.38271i	−0.722515	−	0.691355i	$-0.757014\pi$
$937$		−	1.06583e12i		−	1.38271i	0.722515	−	0.691355i	$-0.242986\pi$
$938$	1.52093e12			1.96471
$939$	−7.52216e11	−	1.16138e11i	−0.967565	−	0.149387i
$940$	−4.36145e11	−	1.17160e12i	−0.558624	−	1.50061i
$941$		−	3.16869e11i		−	0.404130i	−0.979372	−	0.202065i	$-0.935235\pi$
$941$		−	3.16869e11i		−	0.404130i	0.979372	−	0.202065i	$-0.0647652\pi$
$942$	2.29173e12	+	3.53832e11i	2.91045	+	0.449359i
$943$		−	3.99357e10i		−	0.0505027i
$944$		−	2.98370e11i		−	0.375722i
$945$	−7.09605e10	+	6.85245e11i	−0.0889793	+	0.859248i
$946$	5.78443e11			0.722264
$947$	−1.13510e12			−1.41135			−0.705676	−	0.708535i	$-0.749356\pi$
$947$	−1.13510e12			−1.41135			−0.705676	+	0.708535i	$0.749356\pi$
$948$	−1.89474e11	+	1.22720e12i	−0.234594	+	1.51944i
$949$	−1.34123e11			−0.165363
$950$	−1.06130e12	+	9.17288e11i	−1.30300	+	1.12619i
$951$	−2.10635e11	+	1.36426e12i	−0.257519	+	1.66792i
$952$		−	6.70217e11i		−	0.815958i
$953$	−6.52210e10			−0.0790707			−0.0395354	−	0.999218i	$-0.512588\pi$
$953$	−6.52210e10			−0.0790707			−0.0395354	+	0.999218i	$0.512588\pi$
$954$	−3.68926e11	−	1.16703e11i	−0.445395	−	0.140892i
$955$	1.28733e12	−	4.79228e11i	1.54767	−	0.576141i
$956$		−	1.53610e12i		−	1.83903i
$957$	−1.17398e11	+	7.60372e11i	−0.139963	+	0.906522i
$958$		−	1.98138e12i		−	2.35237i
$959$		−	1.04379e12i		−	1.23407i
$960$	−3.87936e11	+	7.99253e10i	−0.456746	+	0.0941021i
$961$	−8.53562e10			−0.100079
$962$	−1.48089e12			−1.72911
$963$	−6.30964e11	−	1.99593e11i	−0.733668	−	0.232082i
$964$	−1.51098e11			−0.174965
$965$	−2.57931e11	+	9.60186e10i	−0.297437	+	0.110725i
$966$	−1.29081e12	−	1.99295e11i	−1.48236	−	0.228869i
$967$		−	1.04679e12i		−	1.19716i	−0.801063	−	0.598580i	$-0.795732\pi$
$967$		−	1.04679e12i		−	1.19716i	0.801063	−	0.598580i	$-0.204268\pi$
$968$	−7.07701e11			−0.806025
$969$	4.93716e10	−	3.19774e11i	0.0559992	−	0.362701i
$970$	−8.70981e11	+	3.24235e11i	−0.983834	+	0.366246i
$971$		−	1.75655e10i		−	0.0197598i	−0.999951	−	0.00987992i	$-0.996855\pi$
$971$		−	1.75655e10i		−	0.0197598i	0.999951	−	0.00987992i	$-0.00314493\pi$
$972$	−1.44223e12	+	1.49951e12i	−1.61573	+	1.67990i
$973$		−	6.44162e10i		−	0.0718694i
$974$		−	1.63654e12i		−	1.81840i
$975$	−7.45750e11	+	4.67084e11i	−0.825230	+	0.516864i
$976$	−2.29665e12			−2.53101
$977$	6.94557e10			0.0762307			0.0381153	−	0.999273i	$-0.487865\pi$
$977$	6.94557e10			0.0762307			0.0381153	+	0.999273i	$0.487865\pi$
$978$	3.44746e11	+	5.32271e10i	0.376829	+	0.0581805i
$979$	3.85018e10			0.0419131
$980$	1.90340e11	+	5.11303e11i	0.206360	+	0.554337i
$981$	8.83019e11	+	2.79326e11i	0.953441	+	0.301603i
$982$		−	8.66246e11i		−	0.931527i
$983$	4.48002e11			0.479806			0.239903	−	0.970797i	$-0.422884\pi$
$983$	4.48002e11			0.479806			0.239903	+	0.970797i	$0.422884\pi$
$984$	1.19456e11	+	1.84434e10i	0.127417	+	0.0196725i
$985$	6.86654e10	+	1.84454e11i	0.0729446	+	0.195949i
$986$			7.52815e11i			0.796490i
$987$	5.56587e11	+	8.59343e10i	0.586495	+	0.0905519i
$988$			2.04076e12i			2.14173i
$989$		−	4.40691e11i		−	0.460627i
$990$	−1.43121e12	+	7.16183e10i	−1.48992	+	0.0745561i
$991$	−1.56270e11			−0.162025			−0.0810123	−	0.996713i	$-0.525815\pi$
$991$	−1.56270e11			−0.162025			−0.0810123	+	0.996713i	$0.525815\pi$
$992$	−1.29271e12			−1.33492
$993$	−1.96809e11	+	1.27471e12i	−0.202417	+	1.31103i
$994$	3.02645e12			3.10019
$995$	−2.06080e11	−	5.53585e11i	−0.210253	−	0.564797i
$996$	−3.56730e11	+	2.31050e12i	−0.362495	+	2.34784i
$997$			4.60730e11i			0.466300i	0.972441	+	0.233150i	$0.0749033\pi$
$997$			4.60730e11i			0.466300i	−0.972441	+	0.233150i	$0.925097\pi$
$998$	2.15718e12			2.17452
$999$	8.68559e11	+	4.29847e11i	0.872042	+	0.431571i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	15.9.d.c.14.2	yes	12
3.2	odd	2	inner	15.9.d.c.14.12	yes	12
4.3	odd	2		240.9.c.c.209.7		12
5.2	odd	4		75.9.c.h.26.2		12
5.3	odd	4		75.9.c.h.26.11		12
5.4	even	2	inner	15.9.d.c.14.11	yes	12
12.11	even	2		240.9.c.c.209.5		12
15.2	even	4		75.9.c.h.26.12		12
15.8	even	4		75.9.c.h.26.1		12
15.14	odd	2	inner	15.9.d.c.14.1	✓	12
20.19	odd	2		240.9.c.c.209.6		12
60.59	even	2		240.9.c.c.209.8		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
15.9.d.c.14.1	✓	12	15.14	odd	2	inner
15.9.d.c.14.2	yes	12	1.1	even	1	trivial
15.9.d.c.14.11	yes	12	5.4	even	2	inner
15.9.d.c.14.12	yes	12	3.2	odd	2	inner
75.9.c.h.26.1		12	15.8	even	4
75.9.c.h.26.2		12	5.2	odd	4
75.9.c.h.26.11		12	5.3	odd	4
75.9.c.h.26.12		12	15.2	even	4
240.9.c.c.209.5		12	12.11	even	2
240.9.c.c.209.6		12	20.19	odd	2
240.9.c.c.209.7		12	4.3	odd	2
240.9.c.c.209.8		12	60.59	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:	\( N \)	\(=\)	\( 15 = 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	15.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-29.2008 q^{2} +(-12.3596 + 80.0515i) q^{3} +596.686 q^{4} +(218.046 + 585.731i) q^{5} +(360.909 - 2337.57i) q^{6} +2074.09i q^{7} -9948.30 q^{8} +(-6255.48 - 1978.80i) q^{9} +O(q^{10})\)	\(q-29.2008 q^{2} +(-12.3596 + 80.0515i) q^{3} +596.686 q^{4} +(218.046 + 585.731i) q^{5} +(360.909 - 2337.57i) q^{6} +2074.09i q^{7} -9948.30 q^{8} +(-6255.48 - 1978.80i) q^{9} +(-6367.13 - 17103.8i) q^{10} +11967.5i q^{11} +(-7374.78 + 47765.6i) q^{12} -27810.7i q^{13} -60565.0i q^{14} +(-49583.6 + 10215.6i) q^{15} +137746. q^{16} +32481.8 q^{17} +(182665. + 57782.6i) q^{18} -122980. q^{19} +(130105. + 349497. i) q^{20} +(-166034. - 25634.8i) q^{21} -349460. i q^{22} -266239. q^{23} +(122957. - 796376. i) q^{24} +(-295536. + 255433. i) q^{25} +812096. i q^{26} +(235721. - 476304. i) q^{27} +1.23758e6i q^{28} -793695. i q^{29} +(1.44788e6 - 298303. i) q^{30} +876091. q^{31} -1.47554e6 q^{32} +(-958016. - 147913. i) q^{33} -948494. q^{34} +(-1.21486e6 + 452247. i) q^{35} +(-3.73256e6 - 1.18072e6i) q^{36} +1.82354e6i q^{37} +3.59111e6 q^{38} +(2.22629e6 + 343729. i) q^{39} +(-2.16919e6 - 5.82702e6i) q^{40} +149999. i q^{41} +(4.84832e6 + 748556. i) q^{42} +1.65525e6i q^{43} +7.14084e6i q^{44} +(-204940. - 4.09550e6i) q^{45} +7.77439e6 q^{46} -3.35225e6 q^{47} +(-1.70249e6 + 1.10268e7i) q^{48} +1.46297e6 q^{49} +(8.62990e6 - 7.45885e6i) q^{50} +(-401461. + 2.60022e6i) q^{51} -1.65943e7i q^{52} -2.01969e6 q^{53} +(-6.88324e6 + 1.39084e7i) q^{54} +(-7.00973e6 + 2.60947e6i) q^{55} -2.06336e7i q^{56} +(1.51998e6 - 9.84472e6i) q^{57} +2.31765e7i q^{58} -2.16608e6i q^{59} +(-2.95858e7 + 6.09548e6i) q^{60} -1.66730e7 q^{61} -2.55825e7 q^{62} +(4.10421e6 - 1.29744e7i) q^{63} +7.82388e6 q^{64} +(1.62896e7 - 6.06403e6i) q^{65} +(2.79748e7 + 4.31918e6i) q^{66} +2.51124e7i q^{67} +1.93814e7 q^{68} +(3.29060e6 - 2.13128e7i) q^{69} +(3.54748e7 - 1.32060e7i) q^{70} +4.99704e7i q^{71} +(6.22314e7 + 1.96857e7i) q^{72} -4.82271e6i q^{73} -5.32488e7i q^{74} +(-1.67951e7 - 2.68152e7i) q^{75} -7.33803e7 q^{76} -2.48216e7 q^{77} +(-6.50095e7 - 1.00371e7i) q^{78} +2.56922e7 q^{79} +(3.00351e7 + 8.06824e7i) q^{80} +(3.52154e7 + 2.47567e7i) q^{81} -4.38010e6i q^{82} +4.83717e7 q^{83} +(-9.90700e7 - 1.52959e7i) q^{84} +(7.08254e6 + 1.90256e7i) q^{85} -4.83345e7i q^{86} +(6.35364e7 + 9.80972e6i) q^{87} -1.19056e8i q^{88} -3.21720e6i q^{89} +(5.98440e6 + 1.19592e8i) q^{90} +5.76819e7 q^{91} -1.58861e8 q^{92} +(-1.08281e7 + 7.01324e7i) q^{93} +9.78883e7 q^{94} +(-2.68153e7 - 7.20331e7i) q^{95} +(1.82370e7 - 1.18119e8i) q^{96} -5.09232e7i q^{97} -4.27198e7 q^{98} +(2.36813e7 - 7.48625e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 1704 q^{4} - 3012 q^{6} - 22824 q^{9}+O(q^{10}) \) 12 * q + 1704 * q^4 - 3012 * q^6 - 22824 * q^9	\( 12 q + 1704 q^{4} - 3012 q^{6} - 22824 q^{9} - 35280 q^{10} - 95520 q^{15} + 413328 q^{16} + 276192 q^{19} - 604044 q^{21} + 1173336 q^{24} - 2036220 q^{25} + 3563460 q^{30} - 279216 q^{31} - 1225344 q^{34} - 10311840 q^{36} + 3780864 q^{39} - 3347040 q^{40} + 9523980 q^{45} + 37414536 q^{46} - 6222300 q^{49} + 3931248 q^{51} - 53281692 q^{54} - 16903440 q^{55} + 9900720 q^{60} - 91958256 q^{61} + 57497760 q^{64} + 111065040 q^{66} + 8138748 q^{69} + 3903480 q^{70} + 15031440 q^{75} - 232646880 q^{76} + 420402672 q^{79} + 98480772 q^{81} - 528357816 q^{84} - 117091440 q^{85} + 218602080 q^{90} - 100211328 q^{91} + 543022776 q^{94} + 333306864 q^{96} - 640360080 q^{99}+O(q^{100}) \) 12 * q + 1704 * q^4 - 3012 * q^6 - 22824 * q^9 - 35280 * q^10 - 95520 * q^15 + 413328 * q^16 + 276192 * q^19 - 604044 * q^21 + 1173336 * q^24 - 2036220 * q^25 + 3563460 * q^30 - 279216 * q^31 - 1225344 * q^34 - 10311840 * q^36 + 3780864 * q^39 - 3347040 * q^40 + 9523980 * q^45 + 37414536 * q^46 - 6222300 * q^49 + 3931248 * q^51 - 53281692 * q^54 - 16903440 * q^55 + 9900720 * q^60 - 91958256 * q^61 + 57497760 * q^64 + 111065040 * q^66 + 8138748 * q^69 + 3903480 * q^70 + 15031440 * q^75 - 232646880 * q^76 + 420402672 * q^79 + 98480772 * q^81 - 528357816 * q^84 - 117091440 * q^85 + 218602080 * q^90 - 100211328 * q^91 + 543022776 * q^94 + 333306864 * q^96 - 640360080 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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