LMFDB - Embedded newform 12.21.d.a.7.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [12,21,Mod(7,12)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(12, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 21, names="a")

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

chi := DirichletCharacter("12.7");

S:= CuspForms(chi, 21);

N := Newforms(S);

Level:	$ N $	$=$	$ 12 = 2^{2} \cdot 3 $
Weight:	$ k $	$=$	$ 21 $
Character orbit:	$[\chi]$	$=$	12.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:	$30.4216518123$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 8 x^{19} - 1800529 x^{18} + 10471600 x^{17} + 1401323871170 x^{16} - 8255926364216 x^{15} + \cdots + 17\!\cdots\!88 $ x^20 - 8x^19 - 1800529x^18 + 10471600x^17 + 1401323871170x^16 - 8255926364216x^15 - 618094244121155086x^14 + 4776792556997860420x^13 + 170108290172014159730219x^12 - 1822962046954348428067604x^11 - 30268361797163656482757584955x^10 + 429273525493411897272285527056x^9 + 3482282078039849041741632502870994x^8 - 60435809630459978311045044131417084x^7 - 250759366568586243949566404606021171194x^6 + 4820660604980619237148365440042241179296x^5 + 10477847059140453507669781324292395546888841x^4 - 190400851192787000531616700775511384585564956x^3 - 219026547432574645023476742933634147067753863733x^2 + 2495516610278349515190181419629668858430612303484*x + 1754305378275820584806685198344335887914554128464688
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{174}\cdot 3^{82}\cdot 5^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			7.10
Root			$374.026 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	12.7
Dual form			12.21.d.a.7.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-128.521 + 1015.90i) q^{2} +34092.0i q^{3} +(-1.01554e6 - 261130. i) q^{4} -1.38143e7 q^{5} +(-3.46341e7 - 4.38153e6i) q^{6} -4.88171e8i q^{7} +(3.95801e8 - 9.98130e8i) q^{8} -1.16226e9 q^{9} +O(q^{10})$	\(q+(-128.521 + 1015.90i) q^{2} +34092.0i q^{3} +(-1.01554e6 - 261130. i) q^{4} -1.38143e7 q^{5} +(-3.46341e7 - 4.38153e6i) q^{6} -4.88171e8i q^{7} +(3.95801e8 - 9.98130e8i) q^{8} -1.16226e9 q^{9} +(1.77543e9 - 1.40340e10i) q^{10} +4.21997e10i q^{11} +(8.90243e9 - 3.46218e10i) q^{12} +1.60787e10 q^{13} +(4.95934e11 + 6.27403e10i) q^{14} -4.70956e11i q^{15} +(9.63134e11 + 5.30376e11i) q^{16} -1.25482e12 q^{17} +(1.49375e11 - 1.18074e12i) q^{18} -4.07828e12i q^{19} +(1.40290e13 + 3.60732e12i) q^{20} +1.66427e13 q^{21} +(-4.28708e13 - 5.42356e12i) q^{22} +2.02090e12i q^{23} +(3.40282e13 + 1.34936e13i) q^{24} +9.54671e13 q^{25} +(-2.06645e12 + 1.63344e13i) q^{26} -3.96238e13i q^{27} +(-1.27476e14 + 4.95758e14i) q^{28} -4.84859e14 q^{29} +(4.78446e14 + 6.05278e13i) q^{30} -1.60488e13i q^{31} +(-6.62593e14 + 9.10286e14i) q^{32} -1.43867e15 q^{33} +(1.61271e14 - 1.27477e15i) q^{34} +6.74373e15i q^{35} +(1.18032e15 + 3.03501e14i) q^{36} +8.83129e15 q^{37} +(4.14314e15 + 5.24145e14i) q^{38} +5.48153e14i q^{39} +(-5.46771e15 + 1.37885e16i) q^{40} +9.52640e15 q^{41} +(-2.13894e15 + 1.69074e16i) q^{42} -2.56015e14i q^{43} +(1.10196e16 - 4.28556e16i) q^{44} +1.60558e16 q^{45} +(-2.05304e15 - 2.59728e14i) q^{46} +8.84804e16i q^{47} +(-1.80816e16 + 3.28351e16i) q^{48} -1.58519e17 q^{49} +(-1.22695e16 + 9.69853e16i) q^{50} -4.27792e16i q^{51} +(-1.63285e16 - 4.19862e15i) q^{52} +2.40767e17 q^{53} +(4.02539e16 + 5.09249e15i) q^{54} -5.82960e17i q^{55} +(-4.87258e17 - 1.93218e17i) q^{56} +1.39037e17 q^{57} +(6.23146e16 - 4.92569e17i) q^{58} -1.81913e17i q^{59} +(-1.22981e17 + 4.78275e17i) q^{60} +1.16472e18 q^{61} +(1.63040e16 + 2.06261e15i) q^{62} +5.67382e17i q^{63} +(-8.39605e17 - 7.90121e17i) q^{64} -2.22115e17 q^{65} +(1.84900e17 - 1.46155e18i) q^{66} -2.69149e17i q^{67} +(1.27432e18 + 3.27670e17i) q^{68} -6.88964e16 q^{69} +(-6.85098e18 - 8.66712e17i) q^{70} -1.97720e18i q^{71} +(-4.60024e17 + 1.16009e18i) q^{72} +2.82030e18 q^{73} +(-1.13501e18 + 8.97173e18i) q^{74} +3.25466e18i q^{75} +(-1.06496e18 + 4.14166e18i) q^{76} +2.06007e19 q^{77} +(-5.56870e17 - 7.04493e16i) q^{78} +1.10146e19i q^{79} +(-1.33050e19 - 7.32677e18i) q^{80} +1.35085e18 q^{81} +(-1.22434e18 + 9.67790e18i) q^{82} -8.89720e18i q^{83} +(-1.69013e19 - 4.34591e18i) q^{84} +1.73344e19 q^{85} +(2.60086e17 + 3.29033e16i) q^{86} -1.65298e19i q^{87} +(4.21208e19 + 1.67027e19i) q^{88} +8.01527e18 q^{89} +(-2.06351e18 + 1.63111e19i) q^{90} -7.84914e18i q^{91} +(5.27717e17 - 2.05230e18i) q^{92} +5.47135e17 q^{93} +(-8.98875e19 - 1.13716e19i) q^{94} +5.63385e19i q^{95} +(-3.10334e19 - 2.25891e19i) q^{96} -2.29774e19 q^{97} +(2.03730e19 - 1.61040e20i) q^{98} -4.90471e19i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 1254 q^{2} - 485524 q^{4} + 1476984 q^{5} - 36019890 q^{6} + 434160000 q^{8} - 23245229340 q^{9}+O(q^{10}) $ 20 * q + 1254 * q^2 - 485524 * q^4 + 1476984 * q^5 - 36019890 * q^6 + 434160000 * q^8 - 23245229340 * q^9	$ 20 q + 1254 q^{2} - 485524 q^{4} + 1476984 q^{5} - 36019890 q^{6} + 434160000 q^{8} - 23245229340 q^{9} + 3166779028 q^{10} + 35789598900 q^{12} - 197410187576 q^{13} + 1179712421976 q^{14} + 1592658749552 q^{16} + 4951946877000 q^{17} - 1457475879618 q^{18} - 20688414141528 q^{20} - 19078957703376 q^{21} + 54807260127768 q^{22} + 58196896476048 q^{24} + 513048947332092 q^{25} - 142319404376100 q^{26} - 10\!\cdots\!28 q^{28}+ \cdots + 30\!\cdots\!50 q^{98}+O(q^{100}) $ 20 * q + 1254 * q^2 - 485524 * q^4 + 1476984 * q^5 - 36019890 * q^6 + 434160000 * q^8 - 23245229340 * q^9 + 3166779028 * q^10 + 35789598900 * q^12 - 197410187576 * q^13 + 1179712421976 * q^14 + 1592658749552 * q^16 + 4951946877000 * q^17 - 1457475879618 * q^18 - 20688414141528 * q^20 - 19078957703376 * q^21 + 54807260127768 * q^22 + 58196896476048 * q^24 + 513048947332092 * q^25 - 142319404376100 * q^26 - 1064314324942128 * q^28 - 1120225678237608 * q^29 + 919562090032260 * q^30 + 926940361437984 * q^32 - 1250504741372400 * q^33 + 1615904447739868 * q^34 + 564305836503708 * q^36 + 13452822768639208 * q^37 + 30625874417040840 * q^38 - 42278345025251456 * q^40 + 26778887480335560 * q^41 + 34752013424992728 * q^42 - 160483087306778736 * q^44 - 1716641590575528 * q^45 + 312713467885194624 * q^46 - 170793646915261968 * q^48 - 198082137742572844 * q^49 + 575620844246091282 * q^50 - 896547684604982408 * q^52 + 241769380233802968 * q^53 + 41864530192578630 * q^54 - 2099928347597457216 * q^56 + 595468774322860464 * q^57 + 1656374273217670084 * q^58 + 94322711748139416 * q^60 + 430703667006221224 * q^61 + 1718273064332222664 * q^62 - 3197273374119743872 * q^64 - 1146808855391494992 * q^65 + 1921733716920631128 * q^66 + 4484111570418829944 * q^68 - 4519043719923504960 * q^69 - 12213680959006457904 * q^70 - 504607438512720000 * q^72 + 12562724768160620200 * q^73 - 22136012572796109780 * q^74 + 28495592855672115888 * q^76 + 19985445258493440192 * q^77 - 20625251537531633940 * q^78 + 49505459663687019552 * q^80 + 27017034353459841780 * q^81 - 50718250504081238180 * q^82 + 24536705912722373616 * q^84 - 15354475681609135696 * q^85 - 85391409389241086952 * q^86 + 66078172926918803520 * q^88 + 43679060294354361384 * q^89 - 3680625238748114076 * q^90 - 64869958570030809216 * q^92 - 50732545022865845424 * q^93 + 95503492747592513424 * q^94 - 89530085825201077920 * q^96 + 7230988441427384872 * q^97 + 304648861287114073350 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/12\mathbb{Z}\right)^\times$.

$n$	$5$	$7$
$\chi(n)$	$1$	$-1$

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 $

$2$	−128.521	+	1015.90i	−0.125509	+	0.992092i
$2$	−128.521	+	1015.90i	−0.125509	+	0.992092i
$3$			34092.0i			0.577350i
$3$			34092.0i			0.577350i
$4$	−1.01554e6	−	261130.i	−0.968495	−	0.249033i
$5$	−1.38143e7			−1.41458			−0.707292	−	0.706922i	$-0.750083\pi$
$5$	−1.38143e7			−1.41458			−0.707292	+	0.706922i	$0.750083\pi$
$6$	−3.46341e7	−	4.38153e6i	−0.572785	−	0.0724626i
$7$		−	4.88171e8i		−	1.72819i	−0.503328	−	0.864095i	$-0.667891\pi$
$7$		−	4.88171e8i		−	1.72819i	0.503328	−	0.864095i	$-0.332109\pi$
$8$	3.95801e8	−	9.98130e8i	0.368618	−	0.929581i
$9$	−1.16226e9			−0.333333
$10$	1.77543e9	−	1.40340e10i	0.177543	−	1.40340i
$11$			4.21997e10i			1.62698i	0.581577	+	0.813492i	$0.302436\pi$
$11$			4.21997e10i			1.62698i	−0.581577	+	0.813492i	$0.697564\pi$
$12$	8.90243e9	−	3.46218e10i	0.143779	−	0.559161i
$13$	1.60787e10			0.116632			0.0583159	−	0.998298i	$-0.481427\pi$
$13$	1.60787e10			0.116632			0.0583159	+	0.998298i	$0.481427\pi$
$14$	4.95934e11	+	6.27403e10i	1.71452	+	0.216903i
$15$		−	4.70956e11i		−	0.816710i
$16$	9.63134e11	+	5.30376e11i	0.875965	+	0.482374i
$17$	−1.25482e12			−0.622432			−0.311216	−	0.950339i	$-0.600736\pi$
$17$	−1.25482e12			−0.622432			−0.311216	+	0.950339i	$0.600736\pi$
$18$	1.49375e11	−	1.18074e12i	0.0418363	−	0.330697i
$19$		−	4.07828e12i		−	0.665183i	−0.943071	−	0.332591i	$-0.892077\pi$
$19$		−	4.07828e12i		−	0.665183i	0.943071	−	0.332591i	$-0.107923\pi$
$20$	1.40290e13	+	3.60732e12i	1.37002	+	0.352278i
$21$	1.66427e13			0.997771
$22$	−4.28708e13	−	5.42356e12i	−1.61412	−	0.204201i
$23$			2.02090e12i			0.0487827i	0.999702	+	0.0243914i	$0.00776478\pi$
$23$			2.02090e12i			0.0487827i	−0.999702	+	0.0243914i	$0.992235\pi$
$24$	3.40282e13	+	1.34936e13i	0.536694	+	0.212822i
$25$	9.54671e13			1.00105
$26$	−2.06645e12	+	1.63344e13i	−0.0146383	+	0.115709i
$27$		−	3.96238e13i		−	0.192450i
$28$	−1.27476e14	+	4.95758e14i	−0.430376	+	1.67374i
$29$	−4.84859e14			−1.15248			−0.576242	−	0.817279i	$-0.695482\pi$
$29$	−4.84859e14			−1.15248			−0.576242	+	0.817279i	$0.695482\pi$
$30$	4.78446e14	+	6.05278e13i	0.810252	+	0.102504i
$31$		−	1.60488e13i		−	0.0195806i	−0.999952	−	0.00979029i	$-0.996884\pi$
$31$		−	1.60488e13i		−	0.0195806i	0.999952	−	0.00979029i	$-0.00311639\pi$
$32$	−6.62593e14	+	9.10286e14i	−0.588501	+	0.808496i
$33$	−1.43867e15			−0.939339
$34$	1.61271e14	−	1.27477e15i	0.0781207	−	0.617510i
$35$			6.74373e15i			2.44467i
$36$	1.18032e15	+	3.03501e14i	0.322832	+	0.0830109i
$37$	8.83129e15			1.83657			0.918283	−	0.395924i	$-0.129575\pi$
$37$	8.83129e15			1.83657			0.918283	+	0.395924i	$0.129575\pi$
$38$	4.14314e15	+	5.24145e14i	0.659923	+	0.0834863i
$39$			5.48153e14i			0.0673373i
$40$	−5.46771e15	+	1.37885e16i	−0.521441	+	1.31497i
$41$	9.52640e15			0.709725			0.354863	−	0.934918i	$-0.384528\pi$
$41$	9.52640e15			0.709725			0.354863	+	0.934918i	$0.384528\pi$
$42$	−2.13894e15	+	1.69074e16i	−0.125229	+	0.989881i
$43$		−	2.56015e14i		−	0.0118462i	−0.999982	−	0.00592312i	$-0.998115\pi$
$43$		−	2.56015e14i		−	0.0118462i	0.999982	−	0.00592312i	$-0.00188540\pi$
$44$	1.10196e16	−	4.28556e16i	0.405172	−	1.57572i
$45$	1.60558e16			0.471528
$46$	−2.05304e15	−	2.59728e14i	−0.0483970	−	0.00612266i
$47$			8.84804e16i			1.68217i	0.540907	+	0.841083i	$0.318081\pi$
$47$			8.84804e16i			1.68217i	−0.540907	+	0.841083i	$0.681919\pi$
$48$	−1.80816e16	+	3.28351e16i	−0.278499	+	0.505739i
$49$	−1.58519e17			−1.98664
$50$	−1.22695e16	+	9.69853e16i	−0.125640	+	0.993130i
$51$		−	4.27792e16i		−	0.359361i
$52$	−1.63285e16	−	4.19862e15i	−0.112957	−	0.0290451i
$53$	2.40767e17			1.37670			0.688349	−	0.725380i	$-0.258336\pi$
$53$	2.40767e17			1.37670			0.688349	+	0.725380i	$0.258336\pi$
$54$	4.02539e16	+	5.09249e15i	0.190928	+	0.0241542i
$55$		−	5.82960e17i		−	2.30150i
$56$	−4.87258e17	−	1.93218e17i	−1.60649	−	0.637043i
$57$	1.39037e17			0.384043
$58$	6.23146e16	−	4.92569e17i	0.144647	−	1.14337i
$59$		−	1.81913e17i		−	0.355913i	−0.984038	−	0.177956i	$-0.943051\pi$
$59$		−	1.81913e17i		−	0.355913i	0.984038	−	0.177956i	$-0.0569486\pi$
$60$	−1.22981e17	+	4.78275e17i	−0.203388	+	0.790980i
$61$	1.16472e18			1.63276			0.816382	−	0.577512i	$-0.195976\pi$
$61$	1.16472e18			1.63276			0.816382	+	0.577512i	$0.195976\pi$
$62$	1.63040e16	+	2.06261e15i	0.0194257	+	0.00245753i
$63$			5.67382e17i			0.576063i
$64$	−8.39605e17	−	7.90121e17i	−0.728241	−	0.685321i
$65$	−2.22115e17			−0.164985
$66$	1.84900e17	−	1.46155e18i	0.117895	−	0.931911i
$67$		−	2.69149e17i		−	0.147654i	−0.997271	−	0.0738270i	$-0.976479\pi$
$67$		−	2.69149e17i		−	0.147654i	0.997271	−	0.0738270i	$-0.0235213\pi$
$68$	1.27432e18	+	3.27670e17i	0.602822	+	0.155006i
$69$	−6.88964e16			−0.0281647
$70$	−6.85098e18	−	8.66712e17i	−2.42534	−	0.306828i
$71$		−	1.97720e18i		−	0.607388i	−0.952770	−	0.303694i	$-0.901780\pi$
$71$		−	1.97720e18i		−	0.607388i	0.952770	−	0.303694i	$-0.0982201\pi$
$72$	−4.60024e17	+	1.16009e18i	−0.122873	+	0.309860i
$73$	2.82030e18			0.656247			0.328123	−	0.944635i	$-0.393584\pi$
$73$	2.82030e18			0.656247			0.328123	+	0.944635i	$0.393584\pi$
$74$	−1.13501e18	+	8.97173e18i	−0.230505	+	1.82204i
$75$			3.25466e18i			0.577954i
$76$	−1.06496e18	+	4.14166e18i	−0.165652	+	0.644226i
$77$	2.06007e19			2.81174
$78$	−5.56870e17	−	7.04493e16i	−0.0668049	−	0.00845143i
$79$			1.10146e19i			1.16332i	0.813432	+	0.581660i	$0.197597\pi$
$79$			1.10146e19i			1.16332i	−0.813432	+	0.581660i	$0.802403\pi$
$80$	−1.33050e19	−	7.32677e18i	−1.23913	−	0.682358i
$81$	1.35085e18			0.111111
$82$	−1.22434e18	+	9.67790e18i	−0.0890768	+	0.704113i
$83$		−	8.89720e18i		−	0.573420i	−0.958017	−	0.286710i	$-0.907438\pi$
$83$		−	8.89720e18i		−	0.573420i	0.958017	−	0.286710i	$-0.0925616\pi$
$84$	−1.69013e19	−	4.34591e18i	−0.966336	−	0.248478i
$85$	1.73344e19			0.880481
$86$	2.60086e17	+	3.29033e16i	0.0117526	+	0.00148681i
$87$		−	1.65298e19i		−	0.665387i
$88$	4.21208e19	+	1.67027e19i	1.51241	+	0.599736i
$89$	8.01527e18			0.257050			0.128525	−	0.991706i	$-0.458976\pi$
$89$	8.01527e18			0.257050			0.128525	+	0.991706i	$0.458976\pi$
$90$	−2.06351e18	+	1.63111e19i	−0.0591809	+	0.467799i
$91$		−	7.84914e18i		−	0.201562i
$92$	5.27717e17	−	2.05230e18i	0.0121485	−	0.0472458i
$93$	5.47135e17			0.0113048
$94$	−8.98875e19	−	1.13716e19i	−1.66886	−	0.211127i
$95$			5.63385e19i			0.940956i
$96$	−3.10334e19	−	2.25891e19i	−0.466786	−	0.339771i
$97$	−2.29774e19			−0.311590			−0.155795	−	0.987789i	$-0.549794\pi$
$97$	−2.29774e19			−0.311590			−0.155795	+	0.987789i	$0.549794\pi$
$98$	2.03730e19	−	1.61040e20i	0.249341	−	1.97093i
$99$		−	4.90471e19i		−	0.542328i
$100$	−9.69508e19	−	2.49293e19i	−0.969508	−	0.249293i
$101$	1.18317e20			1.07111			0.535555	−	0.844501i	$-0.320103\pi$
$101$	1.18317e20			1.07111			0.535555	+	0.844501i	$0.320103\pi$
$102$	4.34595e19	+	5.49803e18i	0.356519	+	0.0451030i
$103$		−	3.03864e19i		−	0.226103i	−0.993589	−	0.113052i	$-0.963937\pi$
$103$		−	3.03864e19i		−	0.226103i	0.993589	−	0.113052i	$-0.0360626\pi$
$104$	6.36395e18	−	1.60486e19i	0.0429926	−	0.108419i
$105$	−2.29907e20			−1.41143
$106$	−3.09436e19	+	2.44596e20i	−0.172788	+	1.36581i
$107$		−	3.17762e20i		−	1.61534i	−0.589636	−	0.807669i	$-0.700729\pi$
$107$		−	3.17762e20i		−	1.61534i	0.589636	−	0.807669i	$-0.299271\pi$
$108$	−1.03469e19	+	4.02395e19i	−0.0479264	+	0.186387i
$109$	−2.23101e20			−0.942404			−0.471202	−	0.882025i	$-0.656180\pi$
$109$	−2.23101e20			−0.942404			−0.471202	+	0.882025i	$0.656180\pi$
$110$	5.92230e20	+	7.49226e19i	2.28330	+	0.288859i
$111$			3.01076e20i			1.06034i
$112$	2.58914e20	−	4.70174e20i	0.833634	−	1.51383i
$113$	6.38357e19			0.188053			0.0940263	−	0.995570i	$-0.470026\pi$
$113$	6.38357e19			0.188053			0.0940263	+	0.995570i	$0.470026\pi$
$114$	−1.78691e19	+	1.41248e20i	−0.0482009	+	0.381007i
$115$		−	2.79173e19i		−	0.0690072i
$116$	4.92394e20	+	1.26611e20i	1.11618	+	0.287007i
$117$	−1.86876e19			−0.0388772
$118$	1.84806e20	+	2.33797e19i	0.353098	+	0.0446702i
$119$			6.12566e20i			1.07568i
$120$	−4.70075e20	−	1.86405e20i	−0.759198	−	0.301054i
$121$	−1.10807e21			−1.64707
$122$	−1.49691e20	+	1.18324e21i	−0.204926	+	1.61985i
$123$			3.24774e20i			0.409760i
$124$	−4.19082e18	+	1.62982e19i	−0.00487620	+	0.0189637i
$125$	−1.37730e18			−0.00147887
$126$	−5.76405e20	−	7.29206e19i	−0.571508	−	0.0723011i
$127$			8.67231e20i			0.794507i	0.917709	+	0.397254i	$0.130037\pi$
$127$			8.67231e20i			0.794507i	−0.917709	+	0.397254i	$0.869963\pi$
$128$	9.10593e20	−	7.51410e20i	0.771302	−	0.636469i
$129$	8.72804e18			0.00683943
$130$	2.85465e19	−	2.25648e20i	0.0207071	−	0.163681i
$131$		−	8.84809e20i		−	0.594479i	−0.954803	−	0.297240i	$-0.903934\pi$
$131$		−	8.84809e20i		−	0.594479i	0.954803	−	0.297240i	$-0.0960660\pi$
$132$	1.46103e21	+	3.75680e20i	0.909745	+	0.233926i
$133$	−1.99090e21			−1.14956
$134$	2.73429e20	+	3.45914e19i	0.146486	+	0.0185319i
$135$			5.47374e20i			0.272237i
$136$	−4.96658e20	+	1.25247e21i	−0.229440	+	0.578601i
$137$	2.46304e21			1.05747			0.528733	−	0.848788i	$-0.322667\pi$
$137$	2.46304e21			1.05747			0.528733	+	0.848788i	$0.322667\pi$
$138$	8.85463e18	−	6.99920e19i	0.00353492	−	0.0279420i
$139$		−	2.25148e21i		−	0.836218i	−0.908397	−	0.418109i	$-0.862693\pi$
$139$		−	2.25148e21i		−	0.836218i	0.908397	−	0.418109i	$-0.137307\pi$
$140$	1.76099e21	−	6.84854e21i	0.608803	−	2.36765i
$141$	−3.01647e21			−0.971199
$142$	2.00864e21	+	2.54111e20i	0.602585	+	0.0762326i
$143$			6.78516e20i			0.189758i
$144$	−1.11941e21	−	6.16435e20i	−0.291988	−	0.160791i
$145$	6.69798e21			1.63029
$146$	−3.62468e20	+	2.86515e21i	−0.0823648	+	0.651057i
$147$		−	5.40421e21i		−	1.14699i
$148$	−8.96853e21	−	2.30611e21i	−1.77871	−	0.457365i
$149$	−1.00674e21			−0.186661			−0.0933305	−	0.995635i	$-0.529751\pi$
$149$	−1.00674e21			−0.186661			−0.0933305	+	0.995635i	$0.529751\pi$
$150$	−3.30642e21	−	4.18293e20i	−0.573384	−	0.0725383i
$151$		−	5.98485e21i		−	0.971145i	−0.874196	−	0.485573i	$-0.838611\pi$
$151$		−	5.98485e21i		−	0.971145i	0.874196	−	0.485573i	$-0.161389\pi$
$152$	−4.07065e21	−	1.61419e21i	−0.618341	−	0.245199i
$153$	1.45843e21			0.207477
$154$	−2.64762e21	+	2.09283e22i	−0.352898	+	2.78950i
$155$			2.21703e20i			0.0276983i
$156$	1.43139e20	−	5.56672e20i	0.0167692	−	0.0652159i
$157$	8.77069e21			0.963911			0.481956	−	0.876196i	$-0.339927\pi$
$157$	8.77069e21			0.963911			0.481956	+	0.876196i	$0.339927\pi$
$158$	−1.11898e22	−	1.41561e21i	−1.15412	−	0.146007i
$159$			8.20822e21i			0.794836i
$160$	9.15325e21	−	1.25750e22i	0.832484	−	1.14369i
$161$	9.86544e20			0.0843058
$162$	−1.73613e20	+	1.37233e21i	−0.0139454	+	0.110232i
$163$			1.79135e22i			1.35302i	0.736434	+	0.676509i	$0.236508\pi$
$163$			1.79135e22i			1.35302i	−0.736434	+	0.676509i	$0.763492\pi$
$164$	−9.67445e21	−	2.48763e21i	−0.687365	−	0.176745i
$165$	1.98742e22			1.32877
$166$	9.03869e21	+	1.14348e21i	0.568885	+	0.0719692i
$167$			8.30784e21i			0.492406i	0.969218	+	0.246203i	$0.0791830\pi$
$167$			8.30784e21i			0.492406i	−0.969218	+	0.246203i	$0.920817\pi$
$168$	6.58720e21	−	1.66116e22i	0.367797	−	0.927509i
$169$	−1.87464e22			−0.986397
$170$	−2.22784e21	+	1.76101e22i	−0.110508	+	0.873519i
$171$			4.74003e21i			0.221728i
$172$	−6.68531e19	+	2.59993e20i	−0.00295010	+	0.0114730i
$173$	2.18162e22			0.908485			0.454243	−	0.890878i	$-0.349910\pi$
$173$	2.18162e22			0.908485			0.454243	+	0.890878i	$0.349910\pi$
$174$	1.67927e22	+	2.12443e21i	0.660126	+	0.0835120i
$175$		−	4.66043e22i		−	1.73000i
$176$	−2.23817e22	+	4.06440e22i	−0.784814	+	1.42518i
$177$	6.20177e21			0.205486
$178$	−1.03013e21	+	8.14274e21i	−0.0322621	+	0.255018i
$179$			1.88177e22i			0.557232i	0.960403	+	0.278616i	$0.0898757\pi$
$179$			1.88177e22i			0.557232i	−0.960403	+	0.278616i	$0.910124\pi$
$180$	−1.63053e22	−	4.19265e21i	−0.456672	−	0.117426i
$181$	6.20643e22			1.64458			0.822292	−	0.569065i	$-0.192695\pi$
$181$	6.20643e22			1.64458			0.822292	+	0.569065i	$0.192695\pi$
$182$	7.97396e21	+	1.00878e21i	0.199968	+	0.0252978i
$183$			3.97076e22i			0.942677i
$184$	2.01712e21	+	7.99873e20i	0.0453475	+	0.0179822i
$185$	−1.21998e23			−2.59798
$186$	−7.03183e19	+	5.55836e20i	−0.00141886	+	0.0112155i
$187$		−	5.29530e22i		−	1.01269i
$188$	2.31049e22	−	8.98555e22i	0.418914	−	1.62917i
$189$	−1.93432e22			−0.332590
$190$	−5.72345e22	−	7.24069e21i	−0.933516	−	0.118098i
$191$		−	1.43387e22i		−	0.221910i	−0.993825	−	0.110955i	$-0.964609\pi$
$191$		−	1.43387e22i		−	0.221910i	0.993825	−	0.110955i	$-0.0353909\pi$
$192$	2.69368e22	−	2.86238e22i	0.395670	−	0.420450i
$193$	−8.48344e22			−1.18304			−0.591519	−	0.806291i	$-0.701472\pi$
$193$	−8.48344e22			−1.18304			−0.591519	+	0.806291i	$0.701472\pi$
$194$	2.95308e21	−	2.33428e22i	0.0391073	−	0.309126i
$195$		−	7.57235e21i		−	0.0952543i
$196$	1.60982e23	+	4.13939e22i	1.92405	+	0.494739i
$197$	−7.22551e22			−0.820741			−0.410370	−	0.911919i	$-0.634601\pi$
$197$	−7.22551e22			−0.820741			−0.410370	+	0.911919i	$0.634601\pi$
$198$	4.98271e22	+	6.30359e21i	0.538039	+	0.0680669i
$199$		−	1.78963e23i		−	1.83752i	−0.394816	−	0.918760i	$-0.629192\pi$
$199$		−	1.78963e23i		−	1.83752i	0.394816	−	0.918760i	$-0.370808\pi$
$200$	3.77860e22	−	9.52886e22i	0.369004	−	0.930553i
$201$	9.17583e21			0.0852481
$202$	−1.52062e22	+	1.20199e23i	−0.134434	+	1.06264i
$203$			2.36694e23i			1.99171i
$204$	−1.11709e22	+	4.34440e22i	−0.0894927	+	0.348039i
$205$	−1.31600e23			−1.00397
$206$	3.08696e22	+	3.90529e21i	0.224315	+	0.0283780i
$207$		−	2.34881e21i		−	0.0162609i
$208$	1.54859e22	+	8.52774e21i	0.102165	+	0.0562601i
$209$	1.72102e23			1.08224
$210$	2.95479e22	−	2.33563e23i	0.177147	−	1.40027i
$211$			3.54272e22i			0.202541i	0.994859	+	0.101270i	$0.0322907\pi$
$211$			3.54272e22i			0.202541i	−0.994859	+	0.101270i	$0.967709\pi$
$212$	−2.44509e23	−	6.28715e22i	−1.33332	−	0.342843i
$213$	6.74065e22			0.350676
$214$	3.22815e23	+	4.08391e22i	1.60257	+	0.202739i
$215$			3.53666e21i			0.0167575i
$216$	−3.95497e22	−	1.56831e22i	−0.178898	−	0.0709406i
$217$	−7.83455e21			−0.0338390
$218$	2.86732e22	−	2.26649e23i	0.118280	−	0.934952i
$219$			9.61496e22i			0.378884i
$220$	−1.52228e23	+	5.92019e23i	−0.573150	+	2.22899i
$221$	−2.01758e22			−0.0725953
$222$	−3.05864e23	−	3.86946e22i	−1.05196	−	0.133082i
$223$			1.12677e23i			0.370498i	0.982692	+	0.185249i	$0.0593092\pi$
$223$			1.12677e23i			0.370498i	−0.982692	+	0.185249i	$0.940691\pi$
$224$	4.44375e23	+	3.23459e23i	1.39724	+	1.01704i
$225$	−1.10958e23			−0.333682
$226$	−8.20423e21	+	6.48509e22i	−0.0236023	+	0.186566i
$227$			3.53214e22i			0.0972254i	0.998818	+	0.0486127i	$0.0154800\pi$
$227$			3.53214e22i			0.0972254i	−0.998818	+	0.0486127i	$0.984520\pi$
$228$	−1.41197e23	−	3.63066e22i	−0.371944	−	0.0956394i
$229$	7.70158e22			0.194189			0.0970946	−	0.995275i	$-0.469045\pi$
$229$	7.70158e22			0.194189			0.0970946	+	0.995275i	$0.469045\pi$
$230$	2.83612e22	+	3.58796e21i	0.0684615	+	0.00866102i
$231$			7.02318e23i			1.62336i
$232$	−1.91907e23	+	4.83952e23i	−0.424827	+	1.07133i
$233$	2.20145e23			0.466820			0.233410	−	0.972378i	$-0.425012\pi$
$233$	2.20145e23			0.466820			0.233410	+	0.972378i	$0.425012\pi$
$234$	2.40175e21	−	1.89848e22i	0.00487944	−	0.0385698i
$235$		−	1.22229e24i		−	2.37956i
$236$	−4.75029e22	+	1.84740e23i	−0.0886340	+	0.344700i
$237$	−3.75511e23			−0.671644
$238$	−6.22307e23	−	7.87276e22i	−1.06717	−	0.135007i
$239$		−	6.45954e23i		−	1.06224i	−0.847296	−	0.531120i	$-0.821771\pi$
$239$		−	6.45954e23i		−	1.06224i	0.847296	−	0.531120i	$-0.178229\pi$
$240$	2.49784e23	−	4.53594e23i	0.393960	−	0.715410i
$241$	3.98715e23			0.603243			0.301622	−	0.953428i	$-0.402472\pi$
$241$	3.98715e23			0.603243			0.301622	+	0.953428i	$0.402472\pi$
$242$	1.42410e23	−	1.12569e24i	0.206722	−	1.63405i
$243$			4.60532e22i			0.0641500i
$244$	−1.18282e24	−	3.04143e23i	−1.58132	−	0.406612i
$245$	2.18982e24			2.81027
$246$	−3.29938e23	−	4.17403e22i	−0.406520	−	0.0514285i
$247$		−	6.55733e22i		−	0.0775814i
$248$	−1.60188e22	−	6.35212e21i	−0.0182017	−	0.00721776i
$249$	3.03323e23			0.331064
$250$	1.77013e20	−	1.39921e21i	0.000185611	−	0.00146718i
$251$			1.54318e24i			1.55482i	0.628996	+	0.777408i	$0.283466\pi$
$251$			1.54318e24i			1.55482i	−0.628996	+	0.777408i	$0.716534\pi$
$252$	1.48160e23	−	5.76200e23i	0.143459	−	0.557915i
$253$	−8.52814e22			−0.0793687
$254$	−8.81023e23	−	1.11458e23i	−0.788225	−	0.0997177i
$255$			5.90964e23i			0.508346i
$256$	6.46329e23	+	1.02165e24i	0.534631	+	0.845086i
$257$	−2.08063e23			−0.165525			−0.0827624	−	0.996569i	$-0.526374\pi$
$257$	−2.08063e23			−0.165525			−0.0827624	+	0.996569i	$0.526374\pi$
$258$	−1.12174e21	+	8.86684e21i	−0.000858409	+	0.00678535i
$259$		−	4.31118e24i		−	3.17394i
$260$	2.25567e23	+	5.80010e22i	0.159787	+	0.0410867i
$261$	5.63533e23			0.384162
$262$	8.98880e23	+	1.13717e23i	0.589778	+	0.0746124i
$263$			4.86758e23i			0.307437i	0.988115	+	0.153718i	$0.0491248\pi$
$263$			4.86758e23i			0.307437i	−0.988115	+	0.153718i	$0.950875\pi$
$264$	−5.69428e23	+	1.43598e24i	−0.346258	+	0.873192i
$265$	−3.32603e24			−1.94745
$266$	2.55872e23	−	2.02256e24i	0.144280	−	1.14047i
$267$			2.73256e23i			0.148408i
$268$	−7.02829e22	+	2.73332e23i	−0.0367707	+	0.143002i
$269$	−3.60025e24			−1.81472			−0.907360	−	0.420355i	$-0.861906\pi$
$269$	−3.60025e24			−1.81472			−0.907360	+	0.420355i	$0.861906\pi$
$270$	−5.56079e23	−	7.03491e22i	−0.270084	−	0.0341681i
$271$			2.66421e24i			1.24703i	0.781813	+	0.623513i	$0.214295\pi$
$271$			2.66421e24i			1.24703i	−0.781813	+	0.623513i	$0.785705\pi$
$272$	−1.20856e24	−	6.65525e23i	−0.545229	−	0.300245i
$273$	2.67593e23			0.116372
$274$	−3.16553e23	+	2.50221e24i	−0.132721	+	1.04910i
$275$			4.02869e24i			1.62868i
$276$	6.99671e22	+	1.79909e22i	0.0272774	+	0.00701394i
$277$	3.82769e24			1.43926			0.719631	−	0.694357i	$-0.244311\pi$
$277$	3.82769e24			1.43926			0.719631	+	0.694357i	$0.244311\pi$
$278$	2.28728e24	+	2.89362e23i	0.829606	+	0.104953i
$279$			1.86529e22i			0.00652686i
$280$	6.73112e24	+	2.66918e24i	2.27252	+	0.901150i
$281$	3.49351e24			1.13815			0.569075	−	0.822286i	$-0.307302\pi$
$281$	3.49351e24			1.13815			0.569075	+	0.822286i	$0.307302\pi$
$282$	3.87680e23	−	3.06444e24i	0.121894	−	0.963519i
$283$		−	8.75068e23i		−	0.265569i	−0.991145	−	0.132785i	$-0.957608\pi$
$283$		−	8.75068e23i		−	0.265569i	0.991145	−	0.132785i	$-0.0423918\pi$
$284$	−5.16305e23	+	2.00792e24i	−0.151260	+	0.588252i
$285$	−1.92069e24			−0.543261
$286$	−6.89306e23	−	8.72036e22i	−0.188257	−	0.0238163i
$287$		−	4.65051e24i		−	1.22654i
$288$	7.70107e23	−	1.05799e24i	0.196167	−	0.269499i
$289$	−2.48966e24			−0.612579
$290$	−8.60831e23	+	6.80449e24i	−0.204615	+	1.61739i
$291$		−	7.83345e23i		−	0.179897i
$292$	−2.86413e24	−	7.36465e23i	−0.635572	−	0.163427i
$293$	−6.80633e24			−1.45961			−0.729805	−	0.683655i	$-0.760389\pi$
$293$	−6.80633e24			−1.45961			−0.729805	+	0.683655i	$0.760389\pi$
$294$	5.49015e24	+	6.94555e23i	1.13792	+	0.143957i
$295$			2.51300e24i			0.503468i
$296$	3.49543e24	−	8.81477e24i	0.676992	−	1.70724i
$297$	1.67211e24			0.313113
$298$	1.29387e23	−	1.02275e24i	0.0234276	−	0.185185i
$299$			3.24934e22i			0.00568961i
$300$	8.49889e23	−	3.30524e24i	0.143929	−	0.559745i
$301$	−1.24979e23			−0.0204726
$302$	6.08003e24	+	7.69180e23i	0.963466	+	0.121887i
$303$			4.03366e24i			0.618405i
$304$	2.16302e24	−	3.92793e24i	0.320867	−	0.582677i
$305$	−1.60898e25			−2.30968
$306$	−1.87439e23	+	1.48162e24i	−0.0260402	+	0.205837i
$307$			8.65196e24i			1.16340i	0.813402	+	0.581702i	$0.197613\pi$
$307$			8.65196e24i			1.16340i	−0.813402	+	0.581702i	$0.802387\pi$
$308$	−2.09208e25	−	5.37945e24i	−2.72315	−	0.700215i
$309$	1.03593e24			0.130541
$310$	−2.25228e23	−	2.84935e22i	−0.0274793	−	0.00347639i
$311$		−	6.25520e24i		−	0.738988i	−0.929233	−	0.369494i	$-0.879531\pi$
$311$		−	6.25520e24i		−	0.738988i	0.929233	−	0.369494i	$-0.120469\pi$
$312$	5.47128e23	+	2.16960e23i	0.0625955	+	0.0248218i
$313$	8.20211e24			0.908829			0.454415	−	0.890790i	$-0.349848\pi$
$313$	8.20211e24			0.908829			0.454415	+	0.890790i	$0.349848\pi$
$314$	−1.12722e24	+	8.91016e24i	−0.120979	+	0.956289i
$315$		−	7.83798e24i		−	0.814890i
$316$	2.87625e24	−	1.11858e25i	0.289705	−	1.12667i
$317$	6.07532e23			0.0592893			0.0296447	−	0.999561i	$-0.490562\pi$
$317$	6.07532e23			0.0592893			0.0296447	+	0.999561i	$0.490562\pi$
$318$	−8.33875e24	−	1.05493e24i	−0.788551	−	0.0997590i
$319$		−	2.04609e25i		−	1.87507i
$320$	1.15985e25	+	1.09150e25i	1.03016	+	0.969443i
$321$	1.08331e25			0.932616
$322$	−1.26792e23	+	1.00223e24i	−0.0105811	+	0.0836392i
$323$			5.11750e24i			0.414031i
$324$	−1.37184e24	−	3.52748e23i	−0.107611	−	0.0276703i
$325$	1.53498e24			0.116754
$326$	−1.81984e25	−	2.30226e24i	−1.34232	−	0.169816i
$327$		−	7.60596e24i		−	0.544097i
$328$	3.77056e24	−	9.50858e24i	0.261618	−	0.659747i
$329$	4.31936e25			2.90710
$330$	−2.55426e24	+	2.01903e25i	−0.166773	+	1.31827i
$331$			7.86243e24i			0.498055i	0.968496	+	0.249027i	$0.0801109\pi$
$331$			7.86243e24i			0.498055i	−0.968496	+	0.249027i	$0.919889\pi$
$332$	−2.32332e24	+	9.03547e24i	−0.142800	+	0.555354i
$333$	−1.02643e25			−0.612189
$334$	−8.43996e24	−	1.06773e24i	−0.488513	−	0.0618014i
$335$			3.71811e24i			0.208869i
$336$	1.60292e25	+	8.82689e24i	0.874013	+	0.481299i
$337$	−1.12317e25			−0.594494			−0.297247	−	0.954801i	$-0.596068\pi$
$337$	−1.12317e25			−0.594494			−0.297247	+	0.954801i	$0.596068\pi$
$338$	2.40931e24	−	1.90446e25i	0.123802	−	0.978597i
$339$			2.17628e24i			0.108572i
$340$	−1.76038e25	−	4.52653e24i	−0.852742	−	0.219269i
$341$	6.77255e23			0.0318573
$342$	−4.81541e24	−	6.09193e23i	−0.219974	−	0.0278288i
$343$			3.84319e25i			1.70510i
$344$	−2.55536e23	−	1.01331e23i	−0.0110120	−	0.00436674i
$345$	9.51754e23			0.0398413
$346$	−2.80384e24	+	2.21631e25i	−0.114023	+	0.901301i
$347$		−	4.77799e24i		−	0.188778i	−0.995535	−	0.0943889i	$-0.969910\pi$
$347$		−	4.77799e24i		−	0.188778i	0.995535	−	0.0943889i	$-0.0300897\pi$
$348$	−4.31642e24	+	1.67867e25i	−0.165703	+	0.644424i
$349$	1.65853e25			0.618684			0.309342	−	0.950951i	$-0.399891\pi$
$349$	1.65853e25			0.618684			0.309342	+	0.950951i	$0.399891\pi$
$350$	4.73454e25	+	5.98963e24i	1.71632	+	0.217130i
$351$		−	6.37098e23i		−	0.0224458i
$352$	−3.84138e25	−	2.79613e25i	−1.31541	−	0.957481i
$353$	1.72320e25			0.573573			0.286787	−	0.957994i	$-0.407413\pi$
$353$	1.72320e25			0.573573			0.286787	+	0.957994i	$0.407413\pi$
$354$	−7.97058e23	+	6.30039e24i	−0.0257904	+	0.203861i
$355$			2.73136e25i			0.859201i
$356$	−8.13984e24	−	2.09303e24i	−0.248952	−	0.0640140i
$357$	−2.08836e25			−0.621044
$358$	−1.91170e25	−	2.41847e24i	−0.552826	−	0.0699376i
$359$		−	2.76453e24i		−	0.0777457i	−0.999244	−	0.0388728i	$-0.987623\pi$
$359$		−	2.76453e24i		−	0.0777457i	0.999244	−	0.0388728i	$-0.0123767\pi$
$360$	6.35491e24	−	1.60258e25i	0.173814	−	0.438323i
$361$	2.09576e25			0.557532
$362$	−7.97657e24	+	6.30513e25i	−0.206410	+	1.63158i
$363$		−	3.77762e25i		−	0.950938i
$364$	−2.04964e24	+	7.97112e24i	−0.0501955	+	0.195212i
$365$	−3.89605e25			−0.928315
$366$	−4.03391e25	−	5.10326e24i	−0.935223	−	0.118314i
$367$			2.50050e25i			0.564113i	0.959398	+	0.282056i	$0.0910166\pi$
$367$			2.50050e25i			0.564113i	−0.959398	+	0.282056i	$0.908983\pi$
$368$	−1.07184e24	+	1.94640e24i	−0.0235315	+	0.0427320i
$369$	−1.10722e25			−0.236575
$370$	1.56793e25	−	1.23938e26i	0.326069	−	2.57743i
$371$		−	1.17536e26i		−	2.37919i
$372$	−5.55637e23	−	1.42873e23i	−0.0109487	−	0.00281528i
$373$	5.66300e25			1.08632			0.543160	−	0.839629i	$-0.317228\pi$
$373$	5.66300e25			1.08632			0.543160	+	0.839629i	$0.317228\pi$
$374$	5.37951e25	+	6.80558e24i	1.00468	+	0.127101i
$375$		−	4.69550e22i		−	0.000853826i
$376$	8.83150e25	+	3.50206e25i	1.56371	+	0.620077i
$377$	−7.79588e24			−0.134416
$378$	2.48601e24	−	1.96508e25i	0.0417430	−	0.329960i
$379$			8.12157e25i			1.32815i	0.747665	+	0.664076i	$0.231175\pi$
$379$			8.12157e25i			1.32815i	−0.747665	+	0.664076i	$0.768825\pi$
$380$	1.47117e25	−	5.72141e25i	0.234329	−	0.911312i
$381$	−2.95656e25			−0.458709
$382$	1.45667e25	+	1.84283e24i	0.220155	+	0.0278516i
$383$		−	4.89940e24i		−	0.0721366i	−0.999349	−	0.0360683i	$-0.988517\pi$
$383$		−	4.89940e24i		−	0.0721366i	0.999349	−	0.0360683i	$-0.0114834\pi$
$384$	2.56170e25	+	3.10439e25i	0.367465	+	0.445312i
$385$	−2.84584e26			−3.97743
$386$	1.09030e25	−	8.61835e25i	0.148482	−	1.17368i
$387$			2.97556e23i			0.00394875i
$388$	2.33345e25	+	6.00009e24i	0.301773	+	0.0775962i
$389$	4.99493e25			0.629554			0.314777	−	0.949166i	$-0.398070\pi$
$389$	4.99493e25			0.629554			0.314777	+	0.949166i	$0.398070\pi$
$390$	7.69277e24	+	9.73206e23i	0.0945011	+	0.0119553i
$391$		−	2.53586e24i		−	0.0303639i
$392$	−6.27418e25	+	1.58222e26i	−0.732312	+	1.84674i
$393$	3.01649e25			0.343223
$394$	9.28630e24	−	7.34041e25i	0.103010	−	0.814251i
$395$		−	1.52159e26i		−	1.64561i
$396$	−1.28077e25	+	4.98094e25i	−0.135057	+	0.525242i
$397$	3.67145e25			0.377513			0.188757	−	0.982024i	$-0.439554\pi$
$397$	3.67145e25			0.377513			0.188757	+	0.982024i	$0.439554\pi$
$398$	1.81809e26	+	2.30005e25i	1.82299	+	0.230625i
$399$		−	6.78736e25i		−	0.663700i
$400$	9.19476e25	+	5.06335e25i	0.876881	+	0.482878i
$401$	−5.37320e25			−0.499792			−0.249896	−	0.968273i	$-0.580396\pi$
$401$	−5.37320e25			−0.499792			−0.249896	+	0.968273i	$0.580396\pi$
$402$	−1.17929e24	+	9.32175e24i	−0.0106994	+	0.0845740i
$403$		−	2.58043e23i		−	0.00228372i
$404$	−1.20156e26	−	3.08961e25i	−1.03736	−	0.266741i
$405$	−1.86611e25			−0.157176
$406$	−2.40458e26	−	3.04202e25i	−1.97596	−	0.249978i
$407$			3.72678e26i			2.98806i
$408$	−4.26992e25	−	1.69320e25i	−0.334055	−	0.132467i
$409$	8.32590e25			0.635621			0.317810	−	0.948154i	$-0.397052\pi$
$409$	8.32590e25			0.635621			0.317810	+	0.948154i	$0.397052\pi$
$410$	1.69134e25	−	1.33693e26i	0.126007	−	0.996027i
$411$			8.39700e25i			0.610529i
$412$	−7.93480e24	+	3.08586e25i	−0.0563072	+	0.218980i
$413$	−8.88046e25			−0.615085
$414$	2.38616e24	+	3.01872e23i	0.0161323	+	0.00204089i
$415$			1.22909e26i			0.811150i
$416$	−1.06536e25	+	1.46362e25i	−0.0686379	+	0.0942963i
$417$	7.67573e25			0.482791
$418$	−2.21188e25	+	1.74839e26i	−0.135831	+	1.07368i
$419$			2.55512e26i			1.53204i	0.642815	+	0.766021i	$0.277766\pi$
$419$			2.55512e26i			1.53204i	−0.642815	+	0.766021i	$0.722234\pi$
$420$	2.33480e26	+	6.00356e25i	1.36696	+	0.351492i
$421$	3.02418e26			1.72897			0.864483	−	0.502662i	$-0.167646\pi$
$421$	3.02418e26			1.72897			0.864483	+	0.502662i	$0.167646\pi$
$422$	−3.59906e25	−	4.55314e24i	−0.200939	−	0.0254207i
$423$		−	1.02837e26i		−	0.560722i
$424$	9.52958e25	−	2.40317e26i	0.507476	−	1.27975i
$425$	−1.19794e26			−0.623082
$426$	−8.66315e24	+	6.84784e25i	−0.0440129	+	0.347903i
$427$		−	5.68583e26i		−	2.82173i
$428$	−8.29770e25	+	3.22700e26i	−0.402272	+	1.56445i
$429$	−2.31319e25			−0.109557
$430$	−3.59290e24	−	4.54536e23i	−0.0166250	−	0.00210321i
$431$		−	1.70352e26i		−	0.770148i	−0.922886	−	0.385074i	$-0.874176\pi$
$431$		−	1.70352e26i		−	0.770148i	0.922886	−	0.385074i	$-0.125824\pi$
$432$	2.10155e25	−	3.81630e25i	0.0928329	−	0.168580i
$433$	1.14844e26			0.495714			0.247857	−	0.968797i	$-0.420274\pi$
$433$	1.14844e26			0.495714			0.247857	+	0.968797i	$0.420274\pi$
$434$	1.00691e24	−	7.95914e24i	0.00424709	−	0.0335714i
$435$			2.28347e26i			0.941246i
$436$	2.26568e26	+	5.82584e25i	0.912713	+	0.234689i
$437$	8.24179e24			0.0324494
$438$	−9.76787e25	−	1.23573e25i	−0.375888	−	0.0475533i
$439$		−	8.33201e25i		−	0.313404i	−0.987646	−	0.156702i	$-0.949914\pi$
$439$		−	8.33201e25i		−	0.313404i	0.987646	−	0.156702i	$-0.0500862\pi$
$440$	−5.81869e26	−	2.30736e26i	−2.13943	−	0.848376i
$441$	1.84240e26			0.662214
$442$	2.59302e24	−	2.04967e25i	0.00911135	−	0.0720212i
$443$		−	3.79460e26i		−	1.30355i	−0.758412	−	0.651776i	$-0.774024\pi$
$443$		−	3.79460e26i		−	1.30355i	0.758412	−	0.651776i	$-0.225976\pi$
$444$	7.86199e25	−	3.05755e26i	0.264060	−	1.02694i
$445$	−1.10725e26			−0.363619
$446$	−1.14469e26	−	1.44814e25i	−0.367569	−	0.0465008i
$447$		−	3.43216e25i		−	0.107769i
$448$	−3.85714e26	+	4.09871e26i	−1.18437	+	1.25854i
$449$	5.43311e26			1.63149			0.815747	−	0.578409i	$-0.196326\pi$
$449$	5.43311e26			1.63149			0.815747	+	0.578409i	$0.196326\pi$
$450$	1.42604e25	−	1.12722e26i	0.0418800	−	0.331043i
$451$			4.02012e26i			1.15471i
$452$	−6.48278e25	−	1.66694e25i	−0.182128	−	0.0468312i
$453$	2.04035e26			0.560691
$454$	−3.58831e25	−	4.53955e24i	−0.0964566	−	0.0122026i
$455$			1.08430e26i			0.285126i
$456$	5.50308e25	−	1.38777e26i	0.141565	−	0.356999i
$457$	−1.46062e26			−0.367599			−0.183799	−	0.982964i	$-0.558840\pi$
$457$	−1.46062e26			−0.367599			−0.183799	+	0.982964i	$0.558840\pi$
$458$	−9.89815e24	+	7.82406e25i	−0.0243725	+	0.192654i
$459$			4.97206e25i			0.119787i
$460$	−7.29003e24	+	2.83511e25i	−0.0171851	+	0.0668332i
$461$	−4.35585e26			−1.00476			−0.502381	−	0.864646i	$-0.667543\pi$
$461$	−4.35585e26			−1.00476			−0.502381	+	0.864646i	$0.667543\pi$
$462$	−7.13487e26	−	9.02626e25i	−1.61052	−	0.203746i
$463$		−	6.33456e26i		−	1.39929i	−0.714492	−	0.699644i	$-0.753342\pi$
$463$		−	6.33456e26i		−	1.39929i	0.714492	−	0.699644i	$-0.246658\pi$
$464$	−4.66984e26	−	2.57157e26i	−1.00954	−	0.555929i
$465$	−7.55828e24			−0.0159916
$466$	−2.82932e25	+	2.23646e26i	−0.0585900	+	0.463128i
$467$		−	8.06286e25i		−	0.163426i	−0.996656	−	0.0817128i	$-0.973961\pi$
$467$		−	8.06286e25i		−	0.163426i	0.996656	−	0.0817128i	$-0.0260390\pi$
$468$	1.89780e25	+	4.87989e24i	0.0376524	+	0.00968171i
$469$	−1.31391e26			−0.255174
$470$	1.24173e27	+	1.57091e26i	2.36075	+	0.298656i
$471$			2.99010e26i			0.556514i
$472$	−1.81573e26	−	7.20013e25i	−0.330850	−	0.131196i
$473$	1.08038e25			0.0192736
$474$	4.82610e25	−	3.81482e26i	0.0842972	−	0.666333i
$475$		−	3.89342e26i		−	0.665878i
$476$	1.59959e26	−	6.22086e26i	0.267880	−	1.04179i
$477$	−2.79834e26			−0.458899
$478$	6.56227e26	+	8.30187e25i	1.05384	+	0.133321i
$479$			4.38364e26i			0.689414i	0.938710	+	0.344707i	$0.112022\pi$
$479$			4.38364e26i			0.689414i	−0.938710	+	0.344707i	$0.887978\pi$
$480$	4.28705e26	+	3.12052e26i	0.660307	+	0.480635i
$481$	1.41995e26			0.214202
$482$	−5.12433e25	+	4.05056e26i	−0.0757124	+	0.598473i
$483$			3.36332e25i			0.0486740i
$484$	1.12529e27	+	2.89350e26i	1.59518	+	0.410175i
$485$	3.17417e26			0.440770
$486$	−4.67855e25	−	5.91880e24i	−0.0636428	−	0.00805140i
$487$			8.52895e26i			1.13660i	0.822823	+	0.568298i	$0.192398\pi$
$487$			8.52895e26i			1.13660i	−0.822823	+	0.568298i	$0.807602\pi$
$488$	4.60997e26	−	1.16254e27i	0.601867	−	1.51779i
$489$	−6.10706e26			−0.781166
$490$	−2.81438e26	+	2.22465e27i	−0.352714	+	2.78805i
$491$			1.10954e27i			1.36247i	0.732065	+	0.681234i	$0.238557\pi$
$491$			1.10954e27i			1.36247i	−0.732065	+	0.681234i	$0.761443\pi$
$492$	8.48081e25	−	3.29821e26i	0.102044	−	0.396851i
$493$	6.08410e26			0.717343
$494$	6.66161e25	+	8.42755e24i	0.0769679	+	0.00973715i
$495$			6.77551e26i			0.767168i
$496$	8.51189e24	−	1.54571e25i	0.00944516	−	0.0171519i
$497$	−9.65210e26			−1.04968
$498$	−3.89834e25	+	3.08147e26i	−0.0415515	+	0.328446i
$499$		−	1.49376e27i		−	1.56054i	−0.625440	−	0.780272i	$-0.715081\pi$
$499$		−	1.49376e27i		−	1.56054i	0.625440	−	0.780272i	$-0.284919\pi$
$500$	1.39871e24	+	3.59655e23i	0.00143228	+	0.000368287i
$501$	−2.83231e26			−0.284291
$502$	−1.56772e27	−	1.98331e26i	−1.54252	−	0.195143i
$503$			4.20233e26i			0.405332i	0.979248	+	0.202666i	$0.0649605\pi$
$503$			4.20233e26i			0.405332i	−0.979248	+	0.202666i	$0.935039\pi$
$504$	5.66321e26	+	2.24570e26i	0.535498	+	0.212348i
$505$	−1.63447e27			−1.51517
$506$	1.09605e25	−	8.66376e25i	0.00996147	−	0.0787411i
$507$		−	6.39103e26i		−	0.569497i
$508$	2.26460e26	−	8.80709e26i	0.197858	−	0.769476i
$509$	1.80757e27			1.54852			0.774260	−	0.632868i	$-0.218122\pi$
$509$	1.80757e27			1.54852			0.774260	+	0.632868i	$0.218122\pi$
$510$	−6.00362e26	−	7.59514e25i	−0.504326	−	0.0638019i
$511$		−	1.37679e27i		−	1.13412i
$512$	−1.12096e27	+	5.25304e26i	−0.905504	+	0.424337i
$513$	−1.61597e26			−0.128014
$514$	2.67405e25	−	2.11372e26i	0.0207748	−	0.164216i
$515$			4.19767e26i			0.319842i
$516$	−8.86368e24	−	2.27915e24i	−0.00662395	−	0.00170324i
$517$	−3.73385e27			−2.73685
$518$	4.37974e27	+	5.54077e26i	3.14884	+	0.398357i
$519$			7.43757e26i			0.524514i
$520$	−8.79135e25	+	2.21700e26i	−0.0608166	+	0.153367i
$521$	−5.01338e26			−0.340215			−0.170107	−	0.985426i	$-0.554411\pi$
$521$	−5.01338e26			−0.340215			−0.170107	+	0.985426i	$0.554411\pi$
$522$	−7.24258e25	+	5.72494e26i	−0.0482157	+	0.381124i
$523$		−	1.38908e27i		−	0.907217i	−0.891201	−	0.453608i	$-0.850137\pi$
$523$		−	1.38908e27i		−	0.907217i	0.891201	−	0.453608i	$-0.149863\pi$
$524$	−2.31050e26	+	8.98560e26i	−0.148045	+	0.575750i
$525$	1.58883e27			0.998814
$526$	−4.94499e26	−	6.25586e25i	−0.305006	−	0.0385860i
$527$			2.01383e25i			0.0121876i
$528$	−1.38563e27	−	7.63037e26i	−0.822828	−	0.453113i
$529$	1.71207e27			0.997620
$530$	4.27464e26	−	3.37892e27i	0.244423	−	1.93205i
$531$			2.11430e26i			0.118638i
$532$	2.02184e27	+	5.19883e26i	1.11335	+	0.286279i
$533$	1.53172e26			0.0827765
$534$	−2.77602e26	−	3.51192e25i	−0.147235	−	0.0186265i
$535$			4.38965e27i			2.28503i
$536$	−2.68646e26	−	1.06530e26i	−0.137256	−	0.0544280i
$537$	−6.41532e26			−0.321718
$538$	4.62708e26	−	3.65750e27i	0.227763	−	1.80037i
$539$		−	6.68945e27i		−	3.23223i
$540$	1.42936e26	−	5.55881e26i	0.0677959	−	0.263660i
$541$	1.41612e27			0.659367			0.329683	−	0.944092i	$-0.393058\pi$
$541$	1.41612e27			0.659367			0.329683	+	0.944092i	$0.393058\pi$
$542$	−2.70658e27	−	3.42407e26i	−1.23716	−	0.156513i
$543$			2.11589e27i			0.949502i
$544$	8.31434e26	−	1.14224e27i	0.366302	−	0.503234i
$545$	3.08198e27			1.33311
$546$	−3.43913e25	+	2.71848e26i	−0.0146057	+	0.115452i
$547$		−	1.11079e27i		−	0.463188i	−0.972812	−	0.231594i	$-0.925606\pi$
$547$		−	1.11079e27i		−	0.463188i	0.972812	−	0.231594i	$-0.0743941\pi$
$548$	−2.50132e27	−	6.43174e26i	−1.02415	−	0.263344i
$549$	−1.35371e27			−0.544255
$550$	−4.09276e27	−	5.17771e26i	−1.61581	−	0.204414i
$551$			1.97739e27i			0.766613i
$552$	−2.72692e25	+	6.87675e25i	−0.0103820	+	0.0261814i
$553$	5.37703e27			2.01044
$554$	−4.91939e26	+	3.88857e27i	−0.180640	+	1.42788i
$555$		−	4.15915e27i		−	1.49994i
$556$	−5.87928e26	+	2.28647e27i	−0.208246	+	0.809873i
$557$	−3.04701e27			−1.06004			−0.530019	−	0.847986i	$-0.677815\pi$
$557$	−3.04701e27			−1.06004			−0.530019	+	0.847986i	$0.677815\pi$
$558$	−1.89495e25	−	2.39729e24i	−0.00647525	−	0.000819178i
$559$		−	4.11638e24i		−	0.00138165i
$560$	−3.57671e27	+	6.49512e27i	−1.17924	+	2.14145i
$561$	1.80527e27			0.584674
$562$	−4.48990e26	+	3.54907e27i	−0.142848	+	1.12915i
$563$			3.35088e27i			1.04731i	0.851931	+	0.523655i	$0.175432\pi$
$563$			3.35088e27i			1.04731i	−0.851931	+	0.523655i	$0.824568\pi$
$564$	3.06335e27	+	7.87691e26i	0.940601	+	0.241860i
$565$	−8.81845e26			−0.266016
$566$	8.88984e26	+	1.12465e26i	0.263469	+	0.0333313i
$567$		−	6.59447e26i		−	0.192021i
$568$	−1.97350e27	−	7.82576e26i	−0.564616	−	0.223894i
$569$	4.04414e26			0.113685			0.0568425	−	0.998383i	$-0.481897\pi$
$569$	4.04414e26			0.113685			0.0568425	+	0.998383i	$0.481897\pi$
$570$	2.46849e26	−	1.95124e27i	0.0681841	−	0.538966i
$571$			4.09993e27i			1.11279i	0.830916	+	0.556397i	$0.187817\pi$
$571$			4.09993e27i			1.11279i	−0.830916	+	0.556397i	$0.812183\pi$
$572$	1.77181e26	−	6.89061e26i	0.0472559	−	0.183780i
$573$	4.88834e26			0.128120
$574$	4.72447e27	+	5.97689e26i	1.21684	+	0.153942i
$575$			1.92929e26i			0.0488337i
$576$	9.75840e26	+	9.18328e26i	0.242747	+	0.228440i
$577$	5.22204e27			1.27668			0.638340	−	0.769755i	$-0.279621\pi$
$577$	5.22204e27			1.27668			0.638340	+	0.769755i	$0.279621\pi$
$578$	3.19974e26	−	2.52925e27i	0.0768841	−	0.607735i
$579$		−	2.89217e27i		−	0.683028i
$580$	−6.80207e27	−	1.74904e27i	−1.57892	−	0.405995i
$581$	−4.34336e27			−0.990978
$582$	7.95802e26	+	1.00676e26i	0.178474	+	0.0225786i
$583$			1.01603e28i			2.23986i
$584$	1.11628e27	−	2.81503e27i	0.241904	−	0.610034i
$585$	2.58156e26			0.0549951
$586$	8.74757e26	−	6.91457e27i	0.183194	−	1.44807i
$587$		−	2.77051e27i		−	0.570398i	−0.958468	−	0.285199i	$-0.907940\pi$
$587$		−	2.77051e27i		−	0.570398i	0.958468	−	0.285199i	$-0.0920597\pi$
$588$	−1.41120e27	+	5.48820e27i	−0.285638	+	1.11085i
$589$	−6.54515e25			−0.0130247
$590$	−2.55296e27	−	3.22973e26i	−0.499487	−	0.0631897i
$591$		−	2.46332e27i		−	0.473855i
$592$	8.50571e27	+	4.68390e27i	1.60877	+	0.885912i
$593$	−7.95285e27			−1.47903			−0.739513	−	0.673143i	$-0.764944\pi$
$593$	−7.95285e27			−1.47903			−0.739513	+	0.673143i	$0.764944\pi$
$594$	−2.14902e26	+	1.69870e27i	−0.0392985	+	0.310637i
$595$		−	8.46216e27i		−	1.52164i
$596$	1.02238e27	+	2.62889e26i	0.180780	+	0.0464847i
$597$	6.10120e27			1.06089
$598$	−3.30101e25	−	4.17608e24i	−0.00564462	−	0.000714097i
$599$		−	8.24440e24i		−	0.00138641i	−1.00000		0.000693204i	$-0.999779\pi$
$599$		−	8.24440e24i		−	0.00138641i	1.00000		0.000693204i	$-0.000220654\pi$
$600$	3.24857e27	+	1.28820e27i	0.537255	+	0.213044i
$601$	−2.61629e27			−0.425541			−0.212770	−	0.977102i	$-0.568249\pi$
$601$	−2.61629e27			−0.425541			−0.212770	+	0.977102i	$0.568249\pi$
$602$	1.60624e25	−	1.26967e26i	0.00256949	−	0.0203107i
$603$			3.12822e26i			0.0492180i
$604$	−1.56282e27	+	6.07786e27i	−0.241847	+	0.940549i
$605$	1.53072e28			2.32992
$606$	−4.09781e27	−	5.18411e26i	−0.613515	−	0.0776153i
$607$			4.09452e27i			0.602998i	0.953467	+	0.301499i	$0.0974870\pi$
$607$			4.09452e27i			0.602998i	−0.953467	+	0.301499i	$0.902513\pi$
$608$	3.71240e27	+	2.70224e27i	0.537798	+	0.391461i
$609$	−8.06936e27			−1.14992
$610$	2.06788e27	−	1.63457e28i	0.289885	−	2.29142i
$611$			1.42265e27i			0.196194i
$612$	−1.48109e27	−	3.80839e26i	−0.200941	−	0.0516686i
$613$	−8.57060e27			−1.14395			−0.571974	−	0.820272i	$-0.693822\pi$
$613$	−8.57060e27			−1.14395			−0.571974	+	0.820272i	$0.693822\pi$
$614$	−8.78955e27	−	1.11196e27i	−1.15420	−	0.146017i
$615$		−	4.48652e27i		−	0.579640i
$616$	8.15377e27	−	2.05622e28i	1.03646	−	2.61374i
$617$	−7.58913e27			−0.949162			−0.474581	−	0.880212i	$-0.657400\pi$
$617$	−7.58913e27			−0.949162			−0.474581	+	0.880212i	$0.657400\pi$
$618$	−1.33139e26	+	1.05241e27i	−0.0163840	+	0.129509i
$619$		−	1.03786e27i		−	0.125670i	−0.998024	−	0.0628349i	$-0.979986\pi$
$619$		−	1.03786e27i		−	0.125670i	0.998024	−	0.0628349i	$-0.0200142\pi$
$620$	5.78932e25	−	2.25148e26i	0.00689780	−	0.0268257i
$621$	8.00756e25			0.00938824
$622$	6.35467e27	+	8.03925e26i	0.733144	+	0.0927495i
$623$		−	3.91282e27i		−	0.444232i
$624$	−2.90727e26	+	5.27945e26i	−0.0324818	+	0.0589852i
$625$	−9.08543e27			−0.998953
$626$	−1.05414e27	+	8.33255e27i	−0.114066	+	0.901643i
$627$			5.86731e27i			0.624832i
$628$	−8.90699e27	−	2.29029e27i	−0.933543	−	0.240045i
$629$	−1.10817e28			−1.14314
$630$	7.96263e27	+	1.00735e27i	0.808446	+	0.102276i
$631$			6.71215e27i			0.670761i	0.942083	+	0.335381i	$0.108865\pi$
$631$			6.71215e27i			0.670761i	−0.942083	+	0.335381i	$0.891135\pi$
$632$	1.09940e28	+	4.35961e27i	1.08140	+	0.428821i
$633$	−1.20778e27			−0.116937
$634$	−7.80806e25	+	6.17193e26i	−0.00744133	+	0.0588205i
$635$		−	1.19802e28i		−	1.12390i
$636$	2.14341e27	−	8.33578e27i	0.197940	−	0.769795i
$637$	−2.54877e27			−0.231705
$638$	2.07863e28	+	2.62966e27i	1.86025	+	0.235338i
$639$			2.29802e27i			0.202463i
$640$	−1.25792e28	+	1.03802e28i	−1.09107	+	0.900338i
$641$	−6.58592e27			−0.562388			−0.281194	−	0.959651i	$-0.590731\pi$
$641$	−6.58592e27			−0.562388			−0.281194	+	0.959651i	$0.590731\pi$
$642$	−1.39228e27	+	1.10054e28i	−0.117052	+	0.925242i
$643$		−	1.15954e27i		−	0.0959791i	−0.998848	−	0.0479896i	$-0.984719\pi$
$643$		−	1.15954e27i		−	0.0959791i	0.998848	−	0.0479896i	$-0.0152814\pi$
$644$	−1.00188e27	−	2.57616e26i	−0.0816498	−	0.0209949i
$645$	−1.20572e26			−0.00967494
$646$	−5.19888e27	−	6.57707e26i	−0.410757	−	0.0519645i
$647$		−	1.04472e27i		−	0.0812748i	−0.999174	−	0.0406374i	$-0.987061\pi$
$647$		−	1.04472e27i		−	0.0812748i	0.999174	−	0.0406374i	$-0.0129388\pi$
$648$	5.34668e26	−	1.34833e27i	0.0409576	−	0.103287i
$649$	7.67668e27			0.579064
$650$	−1.97278e26	+	1.55940e27i	−0.0146536	+	0.115830i
$651$		−	2.67095e26i		−	0.0195369i
$652$	4.67774e27	−	1.81919e28i	0.336946	−	1.31039i
$653$	7.31912e27			0.519191			0.259596	−	0.965717i	$-0.416411\pi$
$653$	7.31912e27			0.519191			0.259596	+	0.965717i	$0.416411\pi$
$654$	7.72691e27	+	9.77526e26i	0.539795	+	0.0682890i
$655$			1.22230e28i			0.840940i
$656$	9.17520e27	+	5.05257e27i	0.621695	+	0.342353i
$657$	−3.27793e27			−0.218749
$658$	−5.55129e27	+	4.38805e28i	−0.364867	+	2.88411i
$659$		−	1.24899e28i		−	0.808548i	−0.914638	−	0.404274i	$-0.867524\pi$
$659$		−	1.24899e28i		−	0.808548i	0.914638	−	0.404274i	$-0.132476\pi$
$660$	−2.01831e28	−	5.18975e27i	−1.28691	−	0.330908i
$661$	2.62247e28			1.64701			0.823504	−	0.567310i	$-0.192016\pi$
$661$	2.62247e28			1.64701			0.823504	+	0.567310i	$0.192016\pi$
$662$	−7.98747e27	−	1.01049e27i	−0.494116	−	0.0625103i
$663$		−	6.87833e26i		−	0.0419129i
$664$	−8.88056e27	−	3.52152e27i	−0.533040	−	0.211373i
$665$	2.75028e28			1.62615
$666$	1.31917e27	−	1.04275e28i	0.0768351	−	0.607348i
$667$		−	9.79850e26i		−	0.0562214i
$668$	2.16943e27	−	8.43695e27i	0.122625	−	0.476893i
$669$	−3.84138e27			−0.213907
$670$	−3.77723e27	−	4.77855e26i	−0.207217	−	0.0262149i
$671$			4.91509e28i			2.65648i
$672$	−1.10273e28	+	1.51496e28i	−0.587189	+	0.806694i
$673$	−2.22993e27			−0.116988			−0.0584940	−	0.998288i	$-0.518630\pi$
$673$	−2.22993e27			−0.116988			−0.0584940	+	0.998288i	$0.518630\pi$
$674$	1.44351e27	−	1.14103e28i	0.0746142	−	0.589793i
$675$		−	3.78277e27i		−	0.192651i
$676$	1.90378e28	+	4.89525e27i	0.955321	+	0.245645i
$677$	3.33367e28			1.64830			0.824150	−	0.566372i	$-0.191653\pi$
$677$	3.33367e28			1.64830			0.824150	+	0.566372i	$0.191653\pi$
$678$	−2.21089e27	−	2.79698e26i	−0.107714	−	0.0136268i
$679$			1.12169e28i			0.538487i
$680$	6.86098e27	−	1.73020e28i	0.324561	−	0.818479i
$681$	−1.20418e27			−0.0561331
$682$	−8.70415e25	+	6.88025e26i	−0.00399837	+	0.0316053i
$683$		−	2.55767e28i		−	1.15781i	−0.815395	−	0.578904i	$-0.803480\pi$
$683$		−	2.55767e28i		−	1.15781i	0.815395	−	0.578904i	$-0.196520\pi$
$684$	1.23776e27	−	4.81369e27i	0.0552174	−	0.214742i
$685$	−3.40252e28			−1.49587
$686$	−3.90431e28	−	4.93931e27i	−1.69162	−	0.214006i
$687$			2.62562e27i			0.112115i
$688$	1.35784e26	−	2.46577e26i	0.00571432	−	0.0103769i
$689$	3.87121e27			0.160567
$690$	−1.22320e26	+	9.66890e26i	−0.00500044	+	0.0395263i
$691$		−	3.32551e28i		−	1.33992i	−0.742398	−	0.669959i	$-0.766312\pi$
$691$		−	3.32551e28i		−	1.33992i	0.742398	−	0.669959i	$-0.233688\pi$
$692$	−2.21552e28	−	5.69686e27i	−0.879864	−	0.226243i
$693$	−2.39434e28			−0.937245
$694$	4.85398e27	+	6.14073e26i	0.187285	+	0.0236933i
$695$			3.11026e28i			1.18290i
$696$	−1.64989e28	−	6.54250e27i	−0.618531	−	0.245274i
$697$	−1.19539e28			−0.441755
$698$	−2.13156e27	+	1.68491e28i	−0.0776503	+	0.613792i
$699$			7.50517e27i			0.269518i
$700$	−1.21698e28	+	4.73285e28i	−0.430826	+	1.67549i
$701$	−8.44624e27			−0.294770			−0.147385	−	0.989079i	$-0.547086\pi$
$701$	−8.44624e27			−0.294770			−0.147385	+	0.989079i	$0.547086\pi$
$702$	6.47229e26	+	8.18805e25i	0.0222683	+	0.00281714i
$703$		−	3.60165e28i		−	1.22165i
$704$	3.33429e28	−	3.54311e28i	1.11501	−	1.18484i
$705$	4.16704e28			1.37384
$706$	−2.21468e27	+	1.75060e28i	−0.0719885	+	0.569038i
$707$		−	5.77590e28i		−	1.85108i
$708$	−6.29815e27	−	1.61947e27i	−0.199013	−	0.0511728i
$709$	5.00855e28			1.56045			0.780225	−	0.625499i	$-0.215105\pi$
$709$	5.00855e28			1.56045			0.780225	+	0.625499i	$0.215105\pi$
$710$	−2.77479e28	−	3.51037e27i	−0.852407	−	0.107837i
$711$		−	1.28019e28i		−	0.387774i
$712$	3.17245e27	−	8.00028e27i	0.0947535	−	0.238949i
$713$	3.24330e25			0.000955194
$714$	2.68398e27	−	2.12157e28i	0.0779466	−	0.616133i
$715$		−	9.37321e27i		−	0.268428i
$716$	4.91386e27	−	1.91101e28i	0.138769	−	0.539677i
$717$	2.20218e28			0.613285
$718$	2.80849e27	+	3.55300e26i	0.0771309	+	0.00975777i
$719$			5.37119e28i			1.45473i	0.686252	+	0.727364i	$0.259255\pi$
$719$			5.37119e28i			1.45473i	−0.686252	+	0.727364i	$0.740745\pi$
$720$	1.54639e28	+	8.51562e27i	0.413042	+	0.227453i
$721$	−1.48338e28			−0.390750
$722$	−2.69349e27	+	2.12909e28i	−0.0699752	+	0.553123i
$723$			1.35930e28i			0.348283i
$724$	−6.30288e28	−	1.62068e28i	−1.59277	−	0.409556i
$725$	−4.62881e28			−1.15369
$726$	3.83770e28	+	4.85504e27i	0.943419	+	0.119351i
$727$		−	4.55647e28i		−	1.10480i	−0.833579	−	0.552401i	$-0.813712\pi$
$727$		−	4.55647e28i		−	1.10480i	0.833579	−	0.552401i	$-0.186288\pi$
$728$	−7.83446e27	−	3.10670e27i	−0.187368	−	0.0742994i
$729$	−1.57004e27			−0.0370370
$730$	5.00724e27	−	3.95800e28i	0.116512	−	0.920975i
$731$			3.21252e26i			0.00737347i
$732$	1.03688e28	−	4.03247e28i	0.234757	−	0.912978i
$733$	2.52622e28			0.564198			0.282099	−	0.959385i	$-0.408969\pi$
$733$	2.52622e28			0.564198			0.282099	+	0.959385i	$0.408969\pi$
$734$	−2.54026e28	−	3.21367e27i	−0.559652	−	0.0708012i
$735$			7.46553e28i			1.62251i
$736$	−1.83960e27	−	1.33903e27i	−0.0394407	−	0.0287087i
$737$	1.13580e28			0.240231
$738$	1.42301e27	−	1.12482e28i	0.0296923	−	0.234704i
$739$		−	7.55939e28i		−	1.55612i	−0.628191	−	0.778059i	$-0.716204\pi$
$739$		−	7.55939e28i		−	1.55612i	0.628191	−	0.778059i	$-0.283796\pi$
$740$	1.23894e29	+	3.18573e28i	2.51613	+	0.646981i
$741$	2.23552e27			0.0447916
$742$	1.19405e29	+	1.51058e28i	2.36038	+	0.298610i
$743$			1.49557e28i			0.291687i	0.989308	+	0.145844i	$0.0465896\pi$
$743$			1.49557e28i			0.291687i	−0.989308	+	0.145844i	$0.953410\pi$
$744$	2.16556e26	−	5.46111e26i	0.00416717	−	0.0105088i
$745$	1.39074e28			0.264047
$746$	−7.27815e27	+	5.75306e28i	−0.136343	+	1.07773i
$747$			1.03409e28i			0.191140i
$748$	−1.38276e28	+	5.37759e28i	−0.252192	+	0.980781i
$749$	−1.55122e29			−2.79161
$750$	4.77017e25	+	6.03471e24i	0.000847074	+	0.000107163i
$751$			3.56497e28i			0.624679i	0.949971	+	0.312340i	$0.101113\pi$
$751$			3.56497e28i			0.624679i	−0.949971	+	0.312340i	$0.898887\pi$
$752$	−4.69279e28	+	8.52185e28i	−0.811433	+	1.47352i
$753$	−5.26100e28			−0.897674
$754$	1.00194e27	−	7.91986e27i	0.0168704	−	0.133353i
$755$			8.26765e28i			1.37377i
$756$	1.96438e28	+	5.05108e27i	0.322112	+	0.0828259i
$757$	−8.09135e28			−1.30937			−0.654685	−	0.755902i	$-0.727199\pi$
$757$	−8.09135e28			−1.30937			−0.654685	+	0.755902i	$0.727199\pi$
$758$	−8.25073e28	−	1.04379e28i	−1.31765	−	0.166695i
$759$		−	2.90741e27i		−	0.0458235i
$760$	5.62332e28	+	2.22988e28i	0.874695	+	0.346854i
$761$	3.34261e28			0.513145			0.256572	−	0.966525i	$-0.417407\pi$
$761$	3.34261e28			0.513145			0.256572	+	0.966525i	$0.417407\pi$
$762$	3.79980e27	−	3.00358e28i	0.0575720	−	0.455082i
$763$			1.08912e29i			1.62865i
$764$	−3.74426e27	+	1.45615e28i	−0.0552628	+	0.214918i
$765$	−2.01471e28			−0.293494
$766$	4.97732e27	+	6.29676e26i	0.0715661	+	0.00905378i
$767$		−	2.92492e27i		−	0.0415107i
$768$	−3.48299e28	+	2.20346e28i	−0.487911	+	0.308669i
$769$	−9.35739e28			−1.29387			−0.646936	−	0.762544i	$-0.723950\pi$
$769$	−9.35739e28			−1.29387			−0.646936	+	0.762544i	$0.723950\pi$
$770$	3.65750e28	−	2.89110e29i	0.499203	−	3.94598i
$771$		−	7.09327e27i		−	0.0955658i
$772$	8.61528e28	+	2.21528e28i	1.14577	+	0.294615i
$773$	9.57882e28			1.25753			0.628763	−	0.777597i	$-0.283561\pi$
$773$	9.57882e28			1.25753			0.628763	+	0.777597i	$0.283561\pi$
$774$	−3.02288e26	−	3.82422e25i	−0.00391752	−	0.000495603i
$775$		−	1.53213e27i		−	0.0196010i
$776$	−9.09448e27	+	2.29344e28i	−0.114858	+	0.289648i
$777$	1.46977e29			1.83247
$778$	−6.41953e27	+	5.07436e28i	−0.0790146	+	0.624576i
$779$		−	3.88513e28i		−	0.472097i
$780$	−1.97737e27	+	7.69003e27i	−0.0237214	+	0.0922533i
$781$	8.34372e28			0.988210
$782$	2.57619e27	+	3.25911e26i	0.0301238	+	0.00381094i
$783$			1.92119e28i			0.221796i
$784$	−1.52675e29	−	8.40745e28i	−1.74023	−	0.958304i
$785$	−1.21161e29			−1.36353
$786$	−3.87682e27	+	3.06446e28i	−0.0430775	+	0.340509i
$787$		−	1.36569e29i		−	1.49832i	−0.662388	−	0.749161i	$-0.730457\pi$
$787$		−	1.36569e29i		−	1.49832i	0.662388	−	0.749161i	$-0.269543\pi$
$788$	7.33780e28	+	1.88680e28i	0.794884	+	0.204391i
$789$	−1.65945e28			−0.177499
$790$	1.54579e29	+	1.95557e28i	1.63260	+	0.206539i
$791$		−	3.11627e28i		−	0.324991i
$792$	−4.89554e28	−	1.94129e28i	−0.504137	−	0.199912i
$793$	1.87272e28			0.190432
$794$	−4.71858e27	+	3.72983e28i	−0.0473813	+	0.374528i
$795$		−	1.13391e29i		−	1.12436i
$796$	−4.67325e28	+	1.81744e29i	−0.457603	+	1.77963i
$797$	9.91266e28			0.958532			0.479266	−	0.877670i	$-0.340903\pi$
$797$	9.91266e28			0.958532			0.479266	+	0.877670i	$0.340903\pi$
$798$	6.89530e28	+	8.72319e27i	0.658452	+	0.0833003i
$799$		−	1.11027e29i		−	1.04703i
$800$	−6.32559e28	+	8.69024e28i	−0.589116	+	0.809342i
$801$	−9.31584e27			−0.0856835
$802$	6.90570e27	−	5.45865e28i	0.0627284	−	0.495840i
$803$			1.19016e29i			1.06770i
$804$	−9.31842e27	−	2.39608e27i	−0.0825623	−	0.0212296i
$805$	−1.36284e28			−0.119258
$806$	2.62147e26	+	3.31640e25i	0.00226566	+	0.000286627i
$807$		−	1.22739e29i		−	1.04773i
$808$	4.68300e28	−	1.18096e29i	0.394830	−	0.995683i
$809$	2.49996e28			0.208185			0.104092	−	0.994568i	$-0.466806\pi$
$809$	2.49996e28			0.208185			0.104092	+	0.994568i	$0.466806\pi$
$810$	2.39834e27	−	1.89578e28i	0.0197270	−	0.155933i
$811$			2.25994e29i			1.83607i	0.396499	+	0.918035i	$0.370225\pi$
$811$			2.25994e29i			1.83607i	−0.396499	+	0.918035i	$0.629775\pi$
$812$	6.18079e28	−	2.40372e29i	0.496002	−	1.92896i
$813$	−9.08281e28			−0.719970
$814$	−3.78605e29	−	4.78970e28i	−2.96444	−	0.375028i
$815$		−	2.47462e29i		−	1.91396i
$816$	2.26891e28	−	4.12021e28i	0.173346	−	0.314788i
$817$	−1.04410e27			−0.00787991
$818$	−1.07005e28	+	8.45830e28i	−0.0797760	+	0.630594i
$819$			9.12275e27i			0.0671873i
$820$	1.33646e29	+	3.43648e28i	0.972336	+	0.250020i
$821$	−6.70423e28			−0.481856			−0.240928	−	0.970543i	$-0.577452\pi$
$821$	−6.70423e28			−0.481856			−0.240928	+	0.970543i	$0.577452\pi$
$822$	−8.53054e28	−	1.07919e28i	−0.605701	−	0.0766267i
$823$			1.00762e29i			0.706805i	0.935471	+	0.353402i	$0.114975\pi$
$823$			1.00762e29i			0.706805i	−0.935471	+	0.353402i	$0.885025\pi$
$824$	−3.03296e28	−	1.20270e28i	−0.210181	−	0.0833458i
$825$	−1.37346e29			−0.940321
$826$	1.14133e28	−	9.02169e28i	0.0771986	−	0.610221i
$827$			1.34357e29i			0.897853i	0.893569	+	0.448927i	$0.148194\pi$
$827$			1.34357e29i			0.897853i	−0.893569	+	0.448927i	$0.851806\pi$
$828$	−6.13345e26	+	2.38531e27i	−0.00404950	+	0.0157486i
$829$	2.73744e29			1.78566			0.892830	−	0.450393i	$-0.148716\pi$
$829$	2.73744e29			1.78566			0.892830	+	0.450393i	$0.148716\pi$
$830$	−1.24863e29	−	1.57963e28i	−0.804736	−	0.101806i
$831$			1.30494e29i			0.830958i
$832$	−1.34997e28	−	1.27041e28i	−0.0849360	−	0.0799302i
$833$	1.98912e29			1.23655
$834$	−9.86493e27	+	7.79779e28i	−0.0605945	+	0.478973i
$835$		−	1.14767e29i		−	0.696550i
$836$	−1.74777e29	−	4.49411e28i	−1.04815	−	0.269514i
$837$	−6.35914e26			−0.00376828
$838$	−2.59575e29	−	3.28387e28i	−1.51993	−	0.192285i
$839$		−	2.99143e29i		−	1.73085i	−0.501041	−	0.865423i	$-0.667049\pi$
$839$		−	2.99143e29i		−	1.73085i	0.501041	−	0.865423i	$-0.332951\pi$
$840$	−9.09974e28	+	2.29477e29i	−0.520279	+	1.31204i
$841$	5.80934e28			0.328221
$842$	−3.88671e28	+	3.07227e29i	−0.217001	+	1.71529i
$843$			1.19101e29i			0.657111i
$844$	9.25110e27	−	3.59778e28i	0.0504393	−	0.196160i
$845$	2.58969e29			1.39534
$846$	1.04473e29	+	1.32168e28i	0.556288	+	0.0703755i
$847$			5.40927e29i			2.84646i
$848$	2.31891e29	+	1.27697e29i	1.20594	+	0.664083i
$849$	2.98328e28			0.153326
$850$	1.53960e28	−	1.21699e29i	0.0782024	−	0.618155i
$851$			1.78471e28i			0.0895927i
$852$	−6.84540e28	−	1.76018e28i	−0.339628	−	0.0873297i
$853$	−4.54788e28			−0.223007			−0.111504	−	0.993764i	$-0.535567\pi$
$853$	−4.54788e28			−0.223007			−0.111504	+	0.993764i	$0.535567\pi$
$854$	5.77625e29	+	7.30749e28i	2.79941	+	0.354152i
$855$		−	6.54801e28i		−	0.313652i
$856$	−3.17167e29	−	1.25770e29i	−1.50159	−	0.595443i
$857$	3.70615e29			1.73426			0.867132	−	0.498079i	$-0.165961\pi$
$857$	3.70615e29			1.73426			0.867132	+	0.498079i	$0.165961\pi$
$858$	2.97294e27	−	2.34998e28i	0.0137503	−	0.108690i
$859$		−	1.62839e29i		−	0.744437i	−0.928145	−	0.372218i	$-0.878597\pi$
$859$		−	1.62839e29i		−	0.744437i	0.928145	−	0.372218i	$-0.121403\pi$
$860$	9.23528e26	−	3.59162e27i	0.00417316	−	0.0162295i
$861$	1.58545e29			0.708143
$862$	1.73061e29	+	2.18938e28i	0.764058	+	0.0966604i
$863$		−	7.53346e28i		−	0.328766i	−0.986397	−	0.164383i	$-0.947437\pi$
$863$		−	7.53346e28i		−	0.328766i	0.986397	−	0.164383i	$-0.0525632\pi$
$864$	3.60690e28	+	2.62544e28i	0.155595	+	0.113257i
$865$	−3.01375e29			−1.28513
$866$	−1.47599e28	+	1.16671e29i	−0.0622165	+	0.491794i
$867$		−	8.48775e28i		−	0.353673i
$868$	7.95631e27	+	2.04584e27i	0.0327729	+	0.00842701i
$869$	−4.64815e29			−1.89270
$870$	−2.31979e29	−	2.93474e28i	−0.933803	−	0.118135i
$871$		−	4.32756e27i		−	0.0172211i
$872$	−8.83037e28	+	2.22684e29i	−0.347387	+	0.876040i
$873$	2.67058e28			0.103863
$874$	−1.05924e27	+	8.37286e27i	−0.00407269	+	0.0321928i
$875$			6.72360e26i			0.00255577i
$876$	2.51075e28	−	9.76438e28i	0.0943546	−	0.366947i
$877$	−5.06360e29			−1.88132			−0.940662	−	0.339346i	$-0.889794\pi$
$877$	−5.06360e29			−1.88132			−0.940662	+	0.339346i	$0.889794\pi$
$878$	8.46451e28	+	1.07084e28i	0.310926	+	0.0393350i
$879$		−	2.32041e29i		−	0.842707i
$880$	3.09188e29	−	5.61468e29i	1.11019	−	2.01604i
$881$	−2.51016e29			−0.891133			−0.445567	−	0.895249i	$-0.646998\pi$
$881$	−2.51016e29			−0.891133			−0.445567	+	0.895249i	$0.646998\pi$
$882$	−2.36787e28	+	1.87170e29i	−0.0831137	+	0.656977i
$883$			4.01033e29i			1.39179i	0.718144	+	0.695895i	$0.244992\pi$
$883$			4.01033e29i			1.39179i	−0.718144	+	0.695895i	$0.755008\pi$
$884$	2.04894e28	+	5.26851e27i	0.0703082	+	0.0180786i
$885$	−8.56730e28			−0.290678
$886$	3.85494e29	+	4.87685e28i	1.29324	+	0.163607i
$887$			1.80439e29i			0.598541i	0.954168	+	0.299270i	$0.0967432\pi$
$887$			1.80439e29i			0.598541i	−0.954168	+	0.299270i	$0.903257\pi$
$888$	3.00513e29	+	1.19166e29i	0.985674	+	0.390862i
$889$	4.23357e29			1.37306
$890$	1.42305e28	−	1.12486e29i	0.0456374	−	0.360744i
$891$			5.70056e28i			0.180776i
$892$	2.94233e28	−	1.14428e29i	0.0922662	−	0.358826i
$893$	3.60848e29			1.11895
$894$	3.48674e28	+	4.41105e27i	0.106917	+	0.0135259i
$895$		−	2.59953e29i		−	0.788251i
$896$	−3.66816e29	−	4.44525e29i	−1.09994	−	1.33296i
$897$	−1.10776e27			−0.00328490
$898$	−6.98270e28	+	5.51951e29i	−0.204767	+	1.61859i
$899$			7.78140e27i			0.0225663i
$900$	1.12682e29	+	2.89744e28i	0.323169	+	0.0830977i
$901$	−3.02119e29			−0.856900
$902$	−4.08405e29	−	5.16670e28i	−1.14558	−	0.144926i
$903$		−	4.26078e27i		−	0.0118198i
$904$	2.52662e28	−	6.37163e28i	0.0693196	−	0.174810i
$905$	−8.57375e29			−2.32640
$906$	−2.62228e28	+	2.07280e29i	−0.0703717	+	0.556257i
$907$			1.19967e29i			0.318411i	0.987245	+	0.159205i	$0.0508932\pi$
$907$			1.19967e29i			0.318411i	−0.987245	+	0.159205i	$0.949107\pi$
$908$	9.22348e27	−	3.58703e28i	0.0242123	−	0.0941623i
$909$	−1.37515e29			−0.357036
$910$	−1.10155e29	−	1.39356e28i	−0.282871	−	0.0357858i
$911$		−	3.49060e29i		−	0.886576i	−0.896379	−	0.443288i	$-0.853812\pi$
$911$		−	3.49060e29i		−	0.886576i	0.896379	−	0.443288i	$-0.146188\pi$
$912$	1.33911e29	+	7.37416e28i	0.336409	+	0.185253i
$913$	3.75460e29			0.932944
$914$	1.87720e28	−	1.48384e29i	0.0461369	−	0.364692i
$915$		−	5.48532e29i		−	1.33349i
$916$	−7.82127e28	−	2.01111e28i	−0.188071	−	0.0483595i
$917$	−4.31938e29			−1.02737
$918$	−5.05113e28	−	6.39015e27i	−0.118840	−	0.0150343i
$919$		−	4.42357e29i		−	1.02948i	−0.857346	−	0.514740i	$-0.827888\pi$
$919$		−	4.42357e29i		−	1.02948i	0.857346	−	0.514740i	$-0.172112\pi$
$920$	−2.78651e28	−	1.10497e28i	−0.0641478	−	0.0254373i
$921$	−2.94962e29			−0.671692
$922$	5.59818e28	−	4.42512e29i	0.126107	−	0.996818i
$923$		−	3.17907e28i		−	0.0708407i
$924$	1.83396e29	−	7.13232e29i	0.404269	−	1.57221i
$925$	8.43098e29			1.83849
$926$	6.43530e29	+	8.14125e28i	1.38822	+	0.175623i
$927$			3.53169e28i			0.0753678i
$928$	3.21264e29	−	4.41360e29i	0.678239	−	0.931780i
$929$	−1.63255e29			−0.340965			−0.170482	−	0.985361i	$-0.554533\pi$
$929$	−1.63255e29			−0.340965			−0.170482	+	0.985361i	$0.554533\pi$
$930$	9.71398e26	−	7.67847e27i	0.00200709	−	0.0158652i
$931$			6.46483e29i			1.32148i
$932$	−2.23566e29	−	5.74864e28i	−0.452113	−	0.116253i
$933$	2.13252e29			0.426655
$934$	8.19108e28	+	1.03625e28i	0.162133	+	0.0205114i
$935$			7.31508e29i			1.43253i
$936$	−7.39658e27	+	1.86527e28i	−0.0143309	+	0.0361395i
$937$	−7.59741e29			−1.45636			−0.728181	−	0.685385i	$-0.759634\pi$
$937$	−7.59741e29			−1.45636			−0.728181	+	0.685385i	$0.759634\pi$
$938$	1.68865e28	−	1.33480e29i	0.0320266	−	0.253156i
$939$			2.79626e29i			0.524713i
$940$	−3.19177e29	+	1.24129e30i	−0.592589	+	2.30459i
$941$	4.31905e29			0.793400			0.396700	−	0.917948i	$-0.370155\pi$
$941$	4.31905e29			0.793400			0.396700	+	0.917948i	$0.370155\pi$
$942$	−3.03765e29	−	3.84291e28i	−0.552114	−	0.0698475i
$943$			1.92519e28i			0.0346223i
$944$	9.64823e28	−	1.75207e29i	0.171683	−	0.311767i
$945$	2.67212e29			0.470477
$946$	−1.38851e27	+	1.09756e28i	−0.00241901	+	0.0191212i
$947$			4.71698e29i			0.813138i	0.913620	+	0.406569i	$0.133275\pi$
$947$			4.71698e29i			0.813138i	−0.913620	+	0.406569i	$0.866725\pi$
$948$	3.81346e29	+	9.80570e28i	0.650484	+	0.167261i
$949$	4.53467e28			0.0765392
$950$	3.95533e29	+	5.00386e28i	0.660613	+	0.0835736i
$951$			2.07119e28i			0.0342307i
$952$	6.11420e29	+	2.42454e29i	0.999932	+	0.396515i
$953$	−7.64887e29			−1.23785			−0.618925	−	0.785450i	$-0.712432\pi$
$953$	−7.64887e29			−1.23785			−0.618925	+	0.785450i	$0.712432\pi$
$954$	3.59646e28	−	2.84284e29i	0.0575959	−	0.455270i
$955$			1.98079e29i			0.313910i
$956$	−1.68678e29	+	6.55993e29i	−0.264533	+	1.02877i
$957$	6.97553e29			1.08257
$958$	−4.45335e29	−	5.63390e28i	−0.683962	−	0.0865275i
$959$		−	1.20239e30i		−	1.82750i
$960$	−3.72112e29	+	3.95417e29i	−0.559708	+	0.594762i
$961$	6.71533e29			0.999617
$962$	−1.82494e28	+	1.44253e29i	−0.0268842	+	0.212508i
$963$			3.69322e29i			0.538446i
$964$	−4.04912e29	−	1.04116e29i	−0.584238	−	0.150227i
$965$	1.17193e30			1.67351
$966$	−3.41681e28	−	4.32258e27i	−0.0482891	−	0.00610902i
$967$		−	9.30714e29i		−	1.30182i	−0.759154	−	0.650911i	$-0.774387\pi$
$967$		−	9.30714e29i		−	1.30182i	0.759154	−	0.650911i	$-0.225613\pi$
$968$	−4.38575e29	+	1.10600e30i	−0.607141	+	1.53109i
$969$	−1.74466e29			−0.239041
$970$	−4.07947e28	+	3.22464e29i	−0.0553206	+	0.437285i
$971$		−	9.49355e29i		−	1.27420i	−0.770783	−	0.637098i	$-0.780135\pi$
$971$		−	9.49355e29i		−	1.27420i	0.770783	−	0.637098i	$-0.219865\pi$
$972$	1.20259e28	−	4.67689e28i	0.0159755	−	0.0621290i
$973$	−1.09911e30			−1.44514
$974$	−8.66458e29	−	1.09615e29i	−1.12761	−	0.142653i
$975$			5.23306e28i			0.0674077i
$976$	1.12178e30	+	6.17740e29i	1.43024	+	0.787603i
$977$	7.95458e29			1.00386			0.501928	−	0.864909i	$-0.332624\pi$
$977$	7.95458e29			1.00386			0.501928	+	0.864909i	$0.332624\pi$
$978$	7.84885e28	−	6.20417e29i	0.0980432	−	0.774989i
$979$			3.38243e29i			0.418217i
$980$	−2.22385e30	−	5.71828e29i	−2.72173	−	0.699849i
$981$	2.59302e29			0.314135
$982$	−1.12718e30	−	1.42599e29i	−1.35170	−	0.171002i
$983$			1.21639e30i			1.44390i	0.691943	+	0.721952i	$0.256755\pi$
$983$			1.21639e30i			1.44390i	−0.691943	+	0.721952i	$0.743245\pi$
$984$	3.24166e29	+	1.28546e29i	0.380905	+	0.151045i
$985$	9.98152e29			1.16101
$986$	−7.81935e28	+	6.18085e29i	−0.0900329	+	0.711671i
$987$			1.47255e30i			1.67842i
$988$	−1.71231e28	+	6.65924e28i	−0.0193203	+	0.0751372i
$989$	5.17380e26			0.000577892
$990$	−6.88326e29	−	8.70796e28i	−0.761101	−	0.0962863i
$991$		−	1.68906e30i		−	1.84888i	−0.381326	−	0.924441i	$-0.624532\pi$
$991$		−	1.68906e30i		−	1.84888i	0.381326	−	0.924441i	$-0.375468\pi$
$992$	1.46090e28	+	1.06338e28i	0.0158308	+	0.0115232i
$993$	−2.68046e29			−0.287552
$994$	1.24050e29	−	9.80559e29i	0.131744	−	1.04138i
$995$			2.47225e30i			2.59933i
$996$	−3.08037e29	−	7.92067e28i	−0.320634	−	0.0824458i
$997$	1.25826e29			0.129664			0.0648318	−	0.997896i	$-0.479349\pi$
$997$	1.25826e29			0.129664			0.0648318	+	0.997896i	$0.479349\pi$
$998$	1.51752e30	+	1.91980e29i	1.54820	+	0.195862i
$999$		−	3.49929e29i		−	0.353447i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	12.21.d.a.7.10	yes	20
3.2	odd	2		36.21.d.c.19.11		20
4.3	odd	2	inner	12.21.d.a.7.9	✓	20
12.11	even	2		36.21.d.c.19.12		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
12.21.d.a.7.9	✓	20	4.3	odd	2	inner
12.21.d.a.7.10	yes	20	1.1	even	1	trivial
36.21.d.c.19.11		20	3.2	odd	2
36.21.d.c.19.12		20	12.11	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:	\( N \)	\(=\)	\( 12 = 2^{2} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 21 \)
Character orbit:	\([\chi]\)	\(=\)	12.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-128.521 + 1015.90i) q^{2} +34092.0i q^{3} +(-1.01554e6 - 261130. i) q^{4} -1.38143e7 q^{5} +(-3.46341e7 - 4.38153e6i) q^{6} -4.88171e8i q^{7} +(3.95801e8 - 9.98130e8i) q^{8} -1.16226e9 q^{9} +O(q^{10})\)	\(q+(-128.521 + 1015.90i) q^{2} +34092.0i q^{3} +(-1.01554e6 - 261130. i) q^{4} -1.38143e7 q^{5} +(-3.46341e7 - 4.38153e6i) q^{6} -4.88171e8i q^{7} +(3.95801e8 - 9.98130e8i) q^{8} -1.16226e9 q^{9} +(1.77543e9 - 1.40340e10i) q^{10} +4.21997e10i q^{11} +(8.90243e9 - 3.46218e10i) q^{12} +1.60787e10 q^{13} +(4.95934e11 + 6.27403e10i) q^{14} -4.70956e11i q^{15} +(9.63134e11 + 5.30376e11i) q^{16} -1.25482e12 q^{17} +(1.49375e11 - 1.18074e12i) q^{18} -4.07828e12i q^{19} +(1.40290e13 + 3.60732e12i) q^{20} +1.66427e13 q^{21} +(-4.28708e13 - 5.42356e12i) q^{22} +2.02090e12i q^{23} +(3.40282e13 + 1.34936e13i) q^{24} +9.54671e13 q^{25} +(-2.06645e12 + 1.63344e13i) q^{26} -3.96238e13i q^{27} +(-1.27476e14 + 4.95758e14i) q^{28} -4.84859e14 q^{29} +(4.78446e14 + 6.05278e13i) q^{30} -1.60488e13i q^{31} +(-6.62593e14 + 9.10286e14i) q^{32} -1.43867e15 q^{33} +(1.61271e14 - 1.27477e15i) q^{34} +6.74373e15i q^{35} +(1.18032e15 + 3.03501e14i) q^{36} +8.83129e15 q^{37} +(4.14314e15 + 5.24145e14i) q^{38} +5.48153e14i q^{39} +(-5.46771e15 + 1.37885e16i) q^{40} +9.52640e15 q^{41} +(-2.13894e15 + 1.69074e16i) q^{42} -2.56015e14i q^{43} +(1.10196e16 - 4.28556e16i) q^{44} +1.60558e16 q^{45} +(-2.05304e15 - 2.59728e14i) q^{46} +8.84804e16i q^{47} +(-1.80816e16 + 3.28351e16i) q^{48} -1.58519e17 q^{49} +(-1.22695e16 + 9.69853e16i) q^{50} -4.27792e16i q^{51} +(-1.63285e16 - 4.19862e15i) q^{52} +2.40767e17 q^{53} +(4.02539e16 + 5.09249e15i) q^{54} -5.82960e17i q^{55} +(-4.87258e17 - 1.93218e17i) q^{56} +1.39037e17 q^{57} +(6.23146e16 - 4.92569e17i) q^{58} -1.81913e17i q^{59} +(-1.22981e17 + 4.78275e17i) q^{60} +1.16472e18 q^{61} +(1.63040e16 + 2.06261e15i) q^{62} +5.67382e17i q^{63} +(-8.39605e17 - 7.90121e17i) q^{64} -2.22115e17 q^{65} +(1.84900e17 - 1.46155e18i) q^{66} -2.69149e17i q^{67} +(1.27432e18 + 3.27670e17i) q^{68} -6.88964e16 q^{69} +(-6.85098e18 - 8.66712e17i) q^{70} -1.97720e18i q^{71} +(-4.60024e17 + 1.16009e18i) q^{72} +2.82030e18 q^{73} +(-1.13501e18 + 8.97173e18i) q^{74} +3.25466e18i q^{75} +(-1.06496e18 + 4.14166e18i) q^{76} +2.06007e19 q^{77} +(-5.56870e17 - 7.04493e16i) q^{78} +1.10146e19i q^{79} +(-1.33050e19 - 7.32677e18i) q^{80} +1.35085e18 q^{81} +(-1.22434e18 + 9.67790e18i) q^{82} -8.89720e18i q^{83} +(-1.69013e19 - 4.34591e18i) q^{84} +1.73344e19 q^{85} +(2.60086e17 + 3.29033e16i) q^{86} -1.65298e19i q^{87} +(4.21208e19 + 1.67027e19i) q^{88} +8.01527e18 q^{89} +(-2.06351e18 + 1.63111e19i) q^{90} -7.84914e18i q^{91} +(5.27717e17 - 2.05230e18i) q^{92} +5.47135e17 q^{93} +(-8.98875e19 - 1.13716e19i) q^{94} +5.63385e19i q^{95} +(-3.10334e19 - 2.25891e19i) q^{96} -2.29774e19 q^{97} +(2.03730e19 - 1.61040e20i) q^{98} -4.90471e19i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 1254 q^{2} - 485524 q^{4} + 1476984 q^{5} - 36019890 q^{6} + 434160000 q^{8} - 23245229340 q^{9}+O(q^{10}) \) 20 * q + 1254 * q^2 - 485524 * q^4 + 1476984 * q^5 - 36019890 * q^6 + 434160000 * q^8 - 23245229340 * q^9	\( 20 q + 1254 q^{2} - 485524 q^{4} + 1476984 q^{5} - 36019890 q^{6} + 434160000 q^{8} - 23245229340 q^{9} + 3166779028 q^{10} + 35789598900 q^{12} - 197410187576 q^{13} + 1179712421976 q^{14} + 1592658749552 q^{16} + 4951946877000 q^{17} - 1457475879618 q^{18} - 20688414141528 q^{20} - 19078957703376 q^{21} + 54807260127768 q^{22} + 58196896476048 q^{24} + 513048947332092 q^{25} - 142319404376100 q^{26} - 10\!\cdots\!28 q^{28}+ \cdots + 30\!\cdots\!50 q^{98}+O(q^{100}) \) 20 * q + 1254 * q^2 - 485524 * q^4 + 1476984 * q^5 - 36019890 * q^6 + 434160000 * q^8 - 23245229340 * q^9 + 3166779028 * q^10 + 35789598900 * q^12 - 197410187576 * q^13 + 1179712421976 * q^14 + 1592658749552 * q^16 + 4951946877000 * q^17 - 1457475879618 * q^18 - 20688414141528 * q^20 - 19078957703376 * q^21 + 54807260127768 * q^22 + 58196896476048 * q^24 + 513048947332092 * q^25 - 142319404376100 * q^26 - 1064314324942128 * q^28 - 1120225678237608 * q^29 + 919562090032260 * q^30 + 926940361437984 * q^32 - 1250504741372400 * q^33 + 1615904447739868 * q^34 + 564305836503708 * q^36 + 13452822768639208 * q^37 + 30625874417040840 * q^38 - 42278345025251456 * q^40 + 26778887480335560 * q^41 + 34752013424992728 * q^42 - 160483087306778736 * q^44 - 1716641590575528 * q^45 + 312713467885194624 * q^46 - 170793646915261968 * q^48 - 198082137742572844 * q^49 + 575620844246091282 * q^50 - 896547684604982408 * q^52 + 241769380233802968 * q^53 + 41864530192578630 * q^54 - 2099928347597457216 * q^56 + 595468774322860464 * q^57 + 1656374273217670084 * q^58 + 94322711748139416 * q^60 + 430703667006221224 * q^61 + 1718273064332222664 * q^62 - 3197273374119743872 * q^64 - 1146808855391494992 * q^65 + 1921733716920631128 * q^66 + 4484111570418829944 * q^68 - 4519043719923504960 * q^69 - 12213680959006457904 * q^70 - 504607438512720000 * q^72 + 12562724768160620200 * q^73 - 22136012572796109780 * q^74 + 28495592855672115888 * q^76 + 19985445258493440192 * q^77 - 20625251537531633940 * q^78 + 49505459663687019552 * q^80 + 27017034353459841780 * q^81 - 50718250504081238180 * q^82 + 24536705912722373616 * q^84 - 15354475681609135696 * q^85 - 85391409389241086952 * q^86 + 66078172926918803520 * q^88 + 43679060294354361384 * q^89 - 3680625238748114076 * q^90 - 64869958570030809216 * q^92 - 50732545022865845424 * q^93 + 95503492747592513424 * q^94 - 89530085825201077920 * q^96 + 7230988441427384872 * q^97 + 304648861287114073350 * q^98

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