LMFDB - Embedded newform 12.10.b.a.11.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [12,10,Mod(11,12)]

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, 1]))

N = Newforms(chi, 10, names="a")

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

chi := DirichletCharacter("12.11");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 12 = 2^{2} \cdot 3 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	12.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.18043003397$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 43 x^{14} - 1652 x^{12} - 2031680 x^{10} + 40456192 x^{8} - 33287045120 x^{6} + \cdots + 72\!\cdots\!36 $ x^16 + 43x^14 - 1652x^12 - 2031680x^10 + 40456192x^8 - 33287045120x^6 - 443455373312x^4 + 189115999977472*x^2 + 72057594037927936
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{68}\cdot 3^{24} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			11.12
Root			$-4.36842 + 10.4363i$ of defining polynomial
Character	$\chi$	$=$	12.11
Dual form			12.10.b.a.11.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(8.73683 + 20.8727i) q^{2} +(-132.615 + 45.7844i) q^{3} +(-359.336 + 364.722i) q^{4} -1832.33i q^{5} +(-2114.28 - 2368.02i) q^{6} +1303.88i q^{7} +(-10752.2 - 4313.78i) q^{8} +(15490.6 - 12143.4i) q^{9} +O(q^{10})$	\(q+(8.73683 + 20.8727i) q^{2} +(-132.615 + 45.7844i) q^{3} +(-359.336 + 364.722i) q^{4} -1832.33i q^{5} +(-2114.28 - 2368.02i) q^{6} +1303.88i q^{7} +(-10752.2 - 4313.78i) q^{8} +(15490.6 - 12143.4i) q^{9} +(38245.5 - 16008.7i) q^{10} -67089.2 q^{11} +(30954.8 - 64819.6i) q^{12} -128139. q^{13} +(-27215.5 + 11391.8i) q^{14} +(83891.9 + 242994. i) q^{15} +(-3899.91 - 262115. i) q^{16} +78730.3i q^{17} +(388804. + 217235. i) q^{18} +705525. i q^{19} +(668289. + 658420. i) q^{20} +(-59697.5 - 172915. i) q^{21} +(-586147. - 1.40033e6i) q^{22} -302728. q^{23} +(1.62340e6 + 79791.0i) q^{24} -1.40429e6 q^{25} +(-1.11953e6 - 2.67461e6i) q^{26} +(-1.49831e6 + 2.31963e6i) q^{27} +(-475555. - 468532. i) q^{28} -171214. i q^{29} +(-4.33899e6 + 3.87405e6i) q^{30} -8.57707e6i q^{31} +(5.43696e6 - 2.37146e6i) q^{32} +(8.89705e6 - 3.07164e6i) q^{33} +(-1.64331e6 + 687853. i) q^{34} +2.38914e6 q^{35} +(-1.13735e6 + 1.00133e7i) q^{36} -2.65453e6 q^{37} +(-1.47262e7 + 6.16405e6i) q^{38} +(1.69932e7 - 5.86678e6i) q^{39} +(-7.90424e6 + 1.97015e7i) q^{40} +3.10365e7i q^{41} +(3.08762e6 - 2.75677e6i) q^{42} -5.87204e6i q^{43} +(2.41075e7 - 2.44689e7i) q^{44} +(-2.22507e7 - 2.83838e7i) q^{45} +(-2.64489e6 - 6.31874e6i) q^{46} -3.06902e7 q^{47} +(1.25180e7 + 3.45819e7i) q^{48} +3.86535e7 q^{49} +(-1.22691e7 - 2.93113e7i) q^{50} +(-3.60462e6 - 1.04408e7i) q^{51} +(4.60450e7 - 4.67352e7i) q^{52} -66067.2i q^{53} +(-6.15072e7 - 1.10075e7i) q^{54} +1.22929e8i q^{55} +(5.62466e6 - 1.40196e7i) q^{56} +(-3.23020e7 - 9.35633e7i) q^{57} +(3.57370e6 - 1.49587e6i) q^{58} -3.52011e7 q^{59} +(-1.18771e8 - 5.67193e7i) q^{60} -8.17944e7 q^{61} +(1.79026e8 - 7.49364e7i) q^{62} +(1.58336e7 + 2.01979e7i) q^{63} +(9.70004e7 + 9.27649e7i) q^{64} +2.34793e8i q^{65} +(1.41845e8 + 1.58869e8i) q^{66} -4.25083e7i q^{67} +(-2.87146e7 - 2.82906e7i) q^{68} +(4.01464e7 - 1.38602e7i) q^{69} +(2.08735e7 + 4.98677e7i) q^{70} +7.59092e7 q^{71} +(-2.18941e8 + 6.37451e7i) q^{72} +1.16232e8 q^{73} +(-2.31922e7 - 5.54072e7i) q^{74} +(1.86231e8 - 6.42946e7i) q^{75} +(-2.57320e8 - 2.53520e8i) q^{76} -8.74766e7i q^{77} +(2.70922e8 + 3.03437e8i) q^{78} -4.69472e8i q^{79} +(-4.80280e8 + 7.14591e6i) q^{80} +(9.24958e7 - 3.76217e8i) q^{81} +(-6.47814e8 + 2.71161e8i) q^{82} -4.67905e8 q^{83} +(8.45172e7 + 4.03615e7i) q^{84} +1.44260e8 q^{85} +(1.22565e8 - 5.13031e7i) q^{86} +(7.83895e6 + 2.27056e7i) q^{87} +(7.21354e8 + 2.89408e8i) q^{88} +3.29105e7i q^{89} +(3.98045e8 - 7.12415e8i) q^{90} -1.67079e8i q^{91} +(1.08781e8 - 1.10412e8i) q^{92} +(3.92696e8 + 1.13745e9i) q^{93} +(-2.68135e8 - 6.40585e8i) q^{94} +1.29275e9 q^{95} +(-6.12448e8 + 5.63419e8i) q^{96} -1.39383e9 q^{97} +(3.37709e8 + 8.06801e8i) q^{98} +(-1.03925e9 + 8.14692e8i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 344 q^{4} - 1608 q^{6} - 13872 q^{9}+O(q^{10}) $ 16 * q - 344 * q^4 - 1608 * q^6 - 13872 * q^9	$ 16 q - 344 q^{4} - 1608 q^{6} - 13872 q^{9} - 15952 q^{10} + 42600 q^{12} - 97312 q^{13} + 164896 q^{16} + 256944 q^{18} + 356448 q^{21} + 322128 q^{22} + 166176 q^{24} - 2743728 q^{25} - 1447056 q^{28} + 3286128 q^{30} + 4715520 q^{33} - 13198144 q^{34} - 6827448 q^{36} + 10997600 q^{37} + 23411264 q^{40} + 23964432 q^{42} - 251904 q^{45} - 41256288 q^{46} - 87722976 q^{48} - 21356624 q^{49} + 132124208 q^{52} + 179732232 q^{54} - 88439904 q^{57} - 271309360 q^{58} - 414400704 q^{60} + 50685152 q^{61} + 742710400 q^{64} + 790585104 q^{66} + 63713280 q^{69} - 1188731232 q^{70} - 1250220480 q^{72} + 23382176 q^{73} + 1645242192 q^{76} + 2079579408 q^{78} + 349756560 q^{81} - 3274996000 q^{82} - 3734920464 q^{84} - 247261184 q^{85} + 4467199680 q^{88} + 5726283888 q^{90} - 262825248 q^{93} - 6146963136 q^{94} - 6944875392 q^{96} + 30926624 q^{97}+O(q^{100}) $ 16 * q - 344 * q^4 - 1608 * q^6 - 13872 * q^9 - 15952 * q^10 + 42600 * q^12 - 97312 * q^13 + 164896 * q^16 + 256944 * q^18 + 356448 * q^21 + 322128 * q^22 + 166176 * q^24 - 2743728 * q^25 - 1447056 * q^28 + 3286128 * q^30 + 4715520 * q^33 - 13198144 * q^34 - 6827448 * q^36 + 10997600 * q^37 + 23411264 * q^40 + 23964432 * q^42 - 251904 * q^45 - 41256288 * q^46 - 87722976 * q^48 - 21356624 * q^49 + 132124208 * q^52 + 179732232 * q^54 - 88439904 * q^57 - 271309360 * q^58 - 414400704 * q^60 + 50685152 * q^61 + 742710400 * q^64 + 790585104 * q^66 + 63713280 * q^69 - 1188731232 * q^70 - 1250220480 * q^72 + 23382176 * q^73 + 1645242192 * q^76 + 2079579408 * q^78 + 349756560 * q^81 - 3274996000 * q^82 - 3734920464 * q^84 - 247261184 * q^85 + 4467199680 * q^88 + 5726283888 * q^90 - 262825248 * q^93 - 6146963136 * q^94 - 6944875392 * q^96 + 30926624 * q^97

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 $

$2$	8.73683	+	20.8727i	0.386117	+	0.922450i
$2$	8.73683	+	20.8727i	0.386117	+	0.922450i
$3$	−132.615	+	45.7844i	−0.945252	+	0.326341i
$3$	−132.615	+	45.7844i	−0.945252	+	0.326341i
$4$	−359.336	+	364.722i	−0.701827	+	0.712347i
$5$		−	1832.33i		−	1.31111i	−0.755149	−	0.655553i	$-0.772436\pi$
$5$		−	1832.33i		−	1.31111i	0.755149	−	0.655553i	$-0.227564\pi$
$6$	−2114.28	−	2368.02i	−0.666011	−	0.745942i
$7$			1303.88i			0.205257i	0.994720	+	0.102628i	$0.0327253\pi$
$7$			1303.88i			0.205257i	−0.994720	+	0.102628i	$0.967275\pi$
$8$	−10752.2	−	4313.78i	−0.928092	−	0.372351i
$9$	15490.6	−	12143.4i	0.787003	−	0.616949i
$10$	38245.5	−	16008.7i	1.20943	−	0.506240i
$11$	−67089.2			−1.38161			−0.690805	−	0.723041i	$-0.742744\pi$
$11$	−67089.2			−1.38161			−0.690805	+	0.723041i	$0.742744\pi$
$12$	30954.8	−	64819.6i	0.430936	−	0.902383i
$13$	−128139.			−1.24434			−0.622168	−	0.782884i	$-0.713748\pi$
$13$	−128139.			−1.24434			−0.622168	+	0.782884i	$0.713748\pi$
$14$	−27215.5	+	11391.8i	−0.189339	+	0.0792532i
$15$	83891.9	+	242994.i	0.427867	+	1.23933i
$16$	−3899.91	−	262115.i	−0.0148770	−	0.999889i
$17$			78730.3i			0.228624i	0.993445	+	0.114312i	$0.0364663\pi$
$17$			78730.3i			0.228624i	−0.993445	+	0.114312i	$0.963534\pi$
$18$	388804.	+	217235.i	0.872980	+	0.487756i
$19$			705525.i			1.24200i	0.783811	+	0.620999i	$0.213273\pi$
$19$			705525.i			1.24200i	−0.783811	+	0.620999i	$0.786727\pi$
$20$	668289.	+	658420.i	0.933962	+	0.920170i
$21$	−59697.5	−	172915.i	−0.0669837	−	0.194020i
$22$	−586147.	−	1.40033e6i	−0.533463	−	1.27447i
$23$	−302728.			−0.225568			−0.112784	−	0.993620i	$-0.535977\pi$
$23$	−302728.			−0.225568			−0.112784	+	0.993620i	$0.535977\pi$
$24$	1.62340e6	+	79791.0i	0.998794	+	0.0490911i
$25$	−1.40429e6			−0.718998
$26$	−1.11953e6	−	2.67461e6i	−0.480459	−	1.14784i
$27$	−1.49831e6	+	2.31963e6i	−0.542581	+	0.840004i
$28$	−475555.	−	468532.i	−0.146214	−	0.144055i
$29$		−	171214.i		−	0.0449521i	−0.999747	−	0.0224760i	$-0.992845\pi$
$29$		−	171214.i		−	0.0449521i	0.999747	−	0.0224760i	$-0.00715494\pi$
$30$	−4.33899e6	+	3.87405e6i	−0.978008	+	0.873211i
$31$		−	8.57707e6i		−	1.66806i	−0.551720	−	0.834029i	$-0.686028\pi$
$31$		−	8.57707e6i		−	1.66806i	0.551720	−	0.834029i	$-0.313972\pi$
$32$	5.43696e6	−	2.37146e6i	0.916603	−	0.399798i
$33$	8.89705e6	−	3.07164e6i	1.30597	−	0.450876i
$34$	−1.64331e6	+	687853.i	−0.210894	+	0.0882756i
$35$	2.38914e6			0.269113
$36$	−1.13735e6	+	1.00133e7i	−0.112858	+	0.993611i
$37$	−2.65453e6			−0.232852			−0.116426	−	0.993199i	$-0.537144\pi$
$37$	−2.65453e6			−0.232852			−0.116426	+	0.993199i	$0.537144\pi$
$38$	−1.47262e7	+	6.16405e6i	−1.14568	+	0.479557i
$39$	1.69932e7	−	5.86678e6i	1.17621	−	0.406078i
$40$	−7.90424e6	+	1.97015e7i	−0.488191	+	1.21683i
$41$			3.10365e7i			1.71532i	0.514217	+	0.857660i	$0.328083\pi$
$41$			3.10365e7i			1.71532i	−0.514217	+	0.857660i	$0.671917\pi$
$42$	3.08762e6	−	2.75677e6i	0.153110	−	0.136703i
$43$		−	5.87204e6i		−	0.261928i	−0.991387	−	0.130964i	$-0.958193\pi$
$43$		−	5.87204e6i		−	0.261928i	0.991387	−	0.130964i	$-0.0418072\pi$
$44$	2.41075e7	−	2.44689e7i	0.969652	−	0.984186i
$45$	−2.22507e7	−	2.83838e7i	−0.808885	−	1.03184i
$46$	−2.64489e6	−	6.31874e6i	−0.0870957	−	0.208075i
$47$	−3.06902e7			−0.917400			−0.458700	−	0.888591i	$-0.651685\pi$
$47$	−3.06902e7			−0.917400			−0.458700	+	0.888591i	$0.651685\pi$
$48$	1.25180e7	+	3.45819e7i	0.340367	+	0.940293i
$49$	3.86535e7			0.957870
$50$	−1.22691e7	−	2.93113e7i	−0.277617	−	0.663239i
$51$	−3.60462e6	−	1.04408e7i	−0.0746094	−	0.216107i
$52$	4.60450e7	−	4.67352e7i	0.873309	−	0.886399i
$53$		−	66067.2i		−	0.00115012i	−1.00000		0.000575062i	$-0.999817\pi$
$53$		−	66067.2i		−	0.00115012i	1.00000		0.000575062i	$-0.000183048\pi$
$54$	−6.15072e7	−	1.10075e7i	−0.984361	−	0.176164i
$55$			1.22929e8i			1.81144i
$56$	5.62466e6	−	1.40196e7i	0.0764276	−	0.190497i
$57$	−3.23020e7	−	9.35633e7i	−0.405315	−	1.17400i
$58$	3.57370e6	−	1.49587e6i	0.0414660	−	0.0173568i
$59$	−3.52011e7			−0.378200			−0.189100	−	0.981958i	$-0.560557\pi$
$59$	−3.52011e7			−0.378200			−0.189100	+	0.981958i	$0.560557\pi$
$60$	−1.18771e8	−	5.67193e7i	−1.18312	−	0.565002i
$61$	−8.17944e7			−0.756379			−0.378189	−	0.925728i	$-0.623453\pi$
$61$	−8.17944e7			−0.756379			−0.378189	+	0.925728i	$0.623453\pi$
$62$	1.79026e8	−	7.49364e7i	1.53870	−	0.644066i
$63$	1.58336e7	+	2.01979e7i	0.126633	+	0.161538i
$64$	9.70004e7	+	9.27649e7i	0.722709	+	0.691152i
$65$			2.34793e8i			1.63146i
$66$	1.41845e8	+	1.58869e8i	0.920168	+	1.03060i
$67$		−	4.25083e7i		−	0.257713i	−0.991663	−	0.128857i	$-0.958869\pi$
$67$		−	4.25083e7i		−	0.257713i	0.991663	−	0.128857i	$-0.0411307\pi$
$68$	−2.87146e7	−	2.82906e7i	−0.162860	−	0.160455i
$69$	4.01464e7	−	1.38602e7i	0.213219	−	0.0736121i
$70$	2.08735e7	+	4.98677e7i	0.103909	+	0.248244i
$71$	7.59092e7			0.354513			0.177256	−	0.984165i	$-0.443278\pi$
$71$	7.59092e7			0.354513			0.177256	+	0.984165i	$0.443278\pi$
$72$	−2.18941e8	+	6.37451e7i	−0.960133	+	0.279544i
$73$	1.16232e8			0.479041			0.239521	−	0.970891i	$-0.423010\pi$
$73$	1.16232e8			0.479041			0.239521	+	0.970891i	$0.423010\pi$
$74$	−2.31922e7	−	5.54072e7i	−0.0899083	−	0.214795i
$75$	1.86231e8	−	6.42946e7i	0.679634	−	0.234638i
$76$	−2.57320e8	−	2.53520e8i	−0.884734	−	0.871669i
$77$		−	8.74766e7i		−	0.283585i
$78$	2.70922e8	+	3.03437e8i	0.828741	+	0.928202i
$79$		−	4.69472e8i		−	1.35609i	−0.735022	−	0.678043i	$-0.762828\pi$
$79$		−	4.69472e8i		−	1.35609i	0.735022	−	0.678043i	$-0.237172\pi$
$80$	−4.80280e8	+	7.14591e6i	−1.31096	+	0.0195053i
$81$	9.24958e7	−	3.76217e8i	0.238748	−	0.971082i
$82$	−6.47814e8	+	2.71161e8i	−1.58230	+	0.662314i
$83$	−4.67905e8			−1.08220			−0.541099	−	0.840959i	$-0.681992\pi$
$83$	−4.67905e8			−1.08220			−0.541099	+	0.840959i	$0.681992\pi$
$84$	8.45172e7	+	4.03615e7i	0.185220	+	0.0884525i
$85$	1.44260e8			0.299750
$86$	1.22565e8	−	5.13031e7i	0.241615	−	0.101135i
$87$	7.83895e6	+	2.27056e7i	0.0146697	+	0.0424910i
$88$	7.21354e8	+	2.89408e8i	1.28226	+	0.514444i
$89$			3.29105e7i			0.0556005i	0.999613	+	0.0278003i	$0.00885024\pi$
$89$			3.29105e7i			0.0556005i	−0.999613	+	0.0278003i	$0.991150\pi$
$90$	3.98045e8	−	7.12415e8i	0.639500	−	1.14457i
$91$		−	1.67079e8i		−	0.255408i
$92$	1.08781e8	−	1.10412e8i	0.158310	−	0.160683i
$93$	3.92696e8	+	1.13745e9i	0.544356	+	1.57674i
$94$	−2.68135e8	−	6.40585e8i	−0.354224	−	0.846255i
$95$	1.29275e9			1.62839
$96$	−6.12448e8	+	5.63419e8i	−0.735951	+	0.677035i
$97$	−1.39383e9			−1.59859			−0.799296	−	0.600938i	$-0.794794\pi$
$97$	−1.39383e9			−1.59859			−0.799296	+	0.600938i	$0.794794\pi$
$98$	3.37709e8	+	8.06801e8i	0.369850	+	0.883587i
$99$	−1.03925e9	+	8.14692e8i	−1.08733	+	0.852383i
$100$	5.04612e8	−	5.12176e8i	0.504612	−	0.512176i
$101$		−	1.04432e9i		−	0.998589i	−0.866432	−	0.499294i	$-0.833593\pi$
$101$		−	1.04432e9i		−	0.998589i	0.866432	−	0.499294i	$-0.166407\pi$
$102$	1.86435e8	−	1.66458e8i	0.170540	−	0.152266i
$103$			1.46690e9i			1.28420i	0.766620	+	0.642101i	$0.221937\pi$
$103$			1.46690e9i			1.28420i	−0.766620	+	0.642101i	$0.778063\pi$
$104$	1.37778e9	+	5.52764e8i	1.15486	+	0.463330i
$105$	−3.16836e8	+	1.09385e8i	−0.254380	+	0.0878228i
$106$	1.37900e6	−	577218.i	0.00106093	−	0.000444082i
$107$	−6.47578e8			−0.477601			−0.238800	−	0.971069i	$-0.576754\pi$
$107$	−6.47578e8			−0.477601			−0.238800	+	0.971069i	$0.576754\pi$
$108$	−3.07623e8	−	1.37999e9i	−0.217576	−	0.976043i
$109$	1.23602e9			0.838697			0.419349	−	0.907825i	$-0.362259\pi$
$109$	1.23602e9			0.838697			0.419349	+	0.907825i	$0.362259\pi$
$110$	−2.56586e9	+	1.07401e9i	−1.67096	+	0.699427i
$111$	3.52032e8	−	1.21536e8i	0.220104	−	0.0759893i
$112$	3.41768e8	−	5.08504e6i	0.205234	−	0.00305361i
$113$		−	1.42157e9i		−	0.820194i	−0.912042	−	0.410097i	$-0.865495\pi$
$113$		−	1.42157e9i		−	0.820194i	0.912042	−	0.410097i	$-0.134505\pi$
$114$	1.67070e9	−	1.49168e9i	0.926459	−	0.827185i
$115$			5.54697e8i			0.295744i
$116$	6.24456e7	+	6.15235e7i	0.0320215	+	0.0315486i
$117$	−1.98495e9	+	1.55605e9i	−0.979296	+	0.767692i
$118$	−3.07546e8	−	7.34740e8i	−0.146030	−	0.348871i
$119$	−1.02655e8			−0.0469266
$120$	1.46203e8	−	2.97461e9i	0.0643637	−	1.30952i
$121$	2.14302e9			0.908848
$122$	−7.14624e8	−	1.70727e9i	−0.292051	−	0.697721i
$123$	−1.42099e9	−	4.11591e9i	−0.559779	−	1.62141i
$124$	3.12824e9	+	3.08205e9i	1.18824	+	1.17069i
$125$		−	1.00564e9i		−	0.368424i
$126$	−2.83249e8	+	5.06955e8i	−0.100115	+	0.179185i
$127$		−	1.50003e8i		−	0.0511663i	−0.999673	−	0.0255831i	$-0.991856\pi$
$127$		−	1.50003e8i		−	0.0511663i	0.999673	−	0.0255831i	$-0.00814425\pi$
$128$	−1.08877e9	+	2.83513e9i	−0.358503	+	0.933529i
$129$	2.68848e8	+	7.78722e8i	0.0854777	+	0.247588i
$130$	−4.90076e9	+	2.05135e9i	−1.50494	+	0.629933i
$131$	−7.07763e7			−0.0209975			−0.0104987	−	0.999945i	$-0.503342\pi$
$131$	−7.07763e7			−0.0209975			−0.0104987	+	0.999945i	$0.503342\pi$
$132$	−2.07673e9	+	4.34870e9i	−0.595385	+	1.24674i
$133$	−9.19923e8			−0.254929
$134$	8.87261e8	−	3.71388e8i	0.237728	−	0.0995075i
$135$	4.25031e9	+	2.74539e9i	1.10133	+	0.711380i
$136$	3.39625e8	−	8.46521e8i	0.0851284	−	0.212184i
$137$			2.80158e9i			0.679455i	0.940524	+	0.339728i	$0.110335\pi$
$137$			2.80158e9i			0.679455i	−0.940524	+	0.339728i	$0.889665\pi$
$138$	6.40052e8	+	7.16867e8i	0.150231	+	0.168261i
$139$		−	6.68332e9i		−	1.51854i	−0.650777	−	0.759269i	$-0.725557\pi$
$139$		−	6.68332e9i		−	1.51854i	0.650777	−	0.759269i	$-0.274443\pi$
$140$	−8.58503e8	+	8.71371e8i	−0.188871	+	0.191702i
$141$	4.06998e9	−	1.40513e9i	0.867174	−	0.299385i
$142$	6.63206e8	+	1.58443e9i	0.136883	+	0.327020i
$143$	8.59677e9			1.71919
$144$	−3.24338e9	−	4.01296e9i	−0.628589	−	0.777738i
$145$	−3.13721e8			−0.0589369
$146$	1.01550e9	+	2.42607e9i	0.184966	+	0.441891i
$147$	−5.12604e9	+	1.76973e9i	−0.905428	+	0.312592i
$148$	9.53869e8	−	9.68166e8i	0.163422	−	0.165872i
$149$			3.17930e8i			0.0528437i	0.999651	+	0.0264218i	$0.00841131\pi$
$149$			3.17930e8i			0.0528437i	−0.999651	+	0.0264218i	$0.991589\pi$
$150$	2.96906e9	+	3.32539e9i	0.478860	+	0.536330i
$151$			3.20370e9i			0.501482i	0.968054	+	0.250741i	$0.0806742\pi$
$151$			3.20370e9i			0.501482i	−0.968054	+	0.250741i	$0.919326\pi$
$152$	3.04348e9	−	7.58592e9i	0.462460	−	1.15269i
$153$	9.56054e8	+	1.21958e9i	0.141049	+	0.179928i
$154$	1.82587e9	−	7.64268e8i	0.261593	−	0.109497i
$155$	−1.57160e10			−2.18700
$156$	−3.96653e9	+	8.30594e9i	−0.536229	+	1.12287i
$157$	−8.89906e9			−1.16895			−0.584475	−	0.811412i	$-0.698699\pi$
$157$	−8.89906e9			−1.16895			−0.584475	+	0.811412i	$0.698699\pi$
$158$	9.79912e9	−	4.10169e9i	1.25092	−	0.523608i
$159$	3.02485e6	+	8.76152e6i	0.000375332	+	0.00108716i
$160$	−4.34528e9	−	9.96229e9i	−0.524177	−	1.20176i
$161$		−	3.94723e8i		−	0.0462994i
$162$	8.66077e9	−	1.35631e9i	0.987959	−	0.154718i
$163$			7.22072e9i			0.801192i	0.916255	+	0.400596i	$0.131197\pi$
$163$			7.22072e9i			0.801192i	−0.916255	+	0.400596i	$0.868803\pi$
$164$	−1.13197e10	−	1.11525e10i	−1.22190	−	1.20386i
$165$	−5.62824e9	−	1.63023e10i	−0.591146	−	1.71227i
$166$	−4.08801e9	−	9.76643e9i	−0.417855	−	0.998273i
$167$	4.15539e9			0.413417			0.206708	−	0.978403i	$-0.433725\pi$
$167$	4.15539e9			0.413417			0.206708	+	0.978403i	$0.433725\pi$
$168$	−1.04038e8	+	2.11673e9i	−0.0100763	+	0.205009i
$169$	5.81520e9			0.548371
$170$	1.26037e9	+	3.01108e9i	0.115739	+	0.276504i
$171$	8.56748e9	+	1.09290e10i	0.766250	+	0.977457i
$172$	2.14166e9	+	2.11003e9i	0.186583	+	0.183828i
$173$			1.53321e10i			1.30135i	0.759355	+	0.650677i	$0.225515\pi$
$173$			1.53321e10i			1.30135i	−0.759355	+	0.650677i	$0.774485\pi$
$174$	−4.05440e8	+	3.61995e8i	−0.0335316	+	0.0299386i
$175$		−	1.83103e9i		−	0.147579i
$176$	2.61642e8	+	1.75851e10i	0.0205542	+	1.38146i
$177$	4.66820e9	−	1.61166e9i	0.357495	−	0.123422i
$178$	−6.86929e8	+	2.87533e8i	−0.0512887	+	0.0214683i
$179$	−1.46369e10			−1.06564			−0.532819	−	0.846229i	$-0.678867\pi$
$179$	−1.46369e10			−1.06564			−0.532819	+	0.846229i	$0.678867\pi$
$180$	1.83476e10	+	2.08400e9i	1.30273	+	0.147969i
$181$	6.15663e9			0.426373			0.213186	−	0.977012i	$-0.431616\pi$
$181$	6.15663e9			0.426373			0.213186	+	0.977012i	$0.431616\pi$
$182$	3.48738e9	−	1.45974e9i	0.235602	−	0.0986176i
$183$	1.08472e10	−	3.74490e9i	0.714968	−	0.246837i
$184$	3.25498e9	+	1.30590e9i	0.209348	+	0.0839905i
$185$			4.86397e9i			0.305294i
$186$	−2.03107e10	+	1.81343e10i	−1.24427	+	1.11095i
$187$		−	5.28195e9i		−	0.315869i
$188$	1.10281e10	−	1.11934e10i	0.643856	−	0.653507i
$189$	−3.02452e9	−	1.95362e9i	−0.172417	−	0.111368i
$190$	1.12946e10	+	2.69832e10i	0.628750	+	1.50211i
$191$	1.97925e10			1.07610			0.538049	−	0.842914i	$-0.319162\pi$
$191$	1.97925e10			1.07610			0.538049	+	0.842914i	$0.319162\pi$
$192$	−1.71109e10	−	7.86093e9i	−0.908694	−	0.417463i
$193$	−2.53398e10			−1.31461			−0.657303	−	0.753627i	$-0.728303\pi$
$193$	−2.53398e10			−1.31461			−0.657303	+	0.753627i	$0.728303\pi$
$194$	−1.21777e10	−	2.90930e10i	−0.617243	−	1.47462i
$195$	−1.07499e10	−	3.11371e10i	−0.532411	−	1.54214i
$196$	−1.38896e10	+	1.40978e10i	−0.672259	+	0.682336i
$197$			1.40527e10i			0.664754i	0.943147	+	0.332377i	$0.107851\pi$
$197$			1.40527e10i			0.664754i	−0.943147	+	0.332377i	$0.892149\pi$
$198$	−2.60845e10	−	1.45741e10i	−1.20612	−	0.673889i
$199$			4.84789e9i			0.219136i	0.993979	+	0.109568i	$0.0349467\pi$
$199$			4.84789e9i			0.219136i	−0.993979	+	0.109568i	$0.965053\pi$
$200$	1.50992e10	+	6.05780e9i	0.667296	+	0.267720i
$201$	1.94621e9	+	5.63724e9i	0.0841024	+	0.243604i
$202$	2.17977e10	−	9.12403e9i	0.921148	−	0.385572i
$203$	2.23244e8			0.00922672
$204$	5.10327e9	+	2.43708e9i	0.206306	+	0.0985222i
$205$	5.68689e10			2.24897
$206$	−3.06181e10	+	1.28161e10i	−1.18461	+	0.495852i
$207$	−4.68944e9	+	3.67615e9i	−0.177523	+	0.139164i
$208$	4.99733e8	+	3.35873e10i	0.0185120	+	1.24420i
$209$		−	4.73331e10i		−	1.71596i
$210$	−5.05131e9	−	5.65753e9i	−0.179233	−	0.200743i
$211$		−	3.33861e10i		−	1.15956i	−0.814772	−	0.579781i	$-0.803138\pi$
$211$		−	3.33861e10i		−	1.15956i	0.814772	−	0.579781i	$-0.196862\pi$
$212$	2.40961e7	+	2.37403e7i	0.000819287	+	0.000807188i
$213$	−1.00667e10	+	3.47545e9i	−0.335104	+	0.115692i
$214$	−5.65778e9	−	1.35167e10i	−0.184410	−	0.440563i
$215$	−1.07595e10			−0.343415
$216$	2.61164e10	−	1.84777e10i	0.816341	−	0.577570i
$217$	1.11835e10			0.342380
$218$	1.07989e10	+	2.57990e10i	0.323835	+	0.773656i
$219$	−1.54141e10	+	5.32161e9i	−0.452815	+	0.156331i
$220$	−4.48350e10	−	4.41729e10i	−1.29037	−	1.27132i
$221$		−	1.00885e10i		−	0.284485i
$222$	5.61242e9	+	6.28599e9i	0.155082	+	0.173694i
$223$			4.63862e10i			1.25608i	0.778181	+	0.628040i	$0.216142\pi$
$223$			4.63862e10i			1.25608i	−0.778181	+	0.628040i	$0.783858\pi$
$224$	3.09210e9	+	7.08917e9i	0.0820612	+	0.188139i
$225$	−2.17533e10	+	1.70529e10i	−0.565853	+	0.443585i
$226$	2.96720e10	−	1.24201e10i	0.756588	−	0.316691i
$227$	4.75860e10			1.18950			0.594748	−	0.803912i	$-0.297252\pi$
$227$	4.75860e10			1.18950			0.594748	+	0.803912i	$0.297252\pi$
$228$	4.57318e10	+	2.18394e10i	1.12076	+	0.535222i
$229$	−6.49841e10			−1.56152			−0.780760	−	0.624831i	$-0.785168\pi$
$229$	−6.49841e10			−1.56152			−0.780760	+	0.624831i	$0.785168\pi$
$230$	−1.15780e10	+	4.84629e9i	−0.272809	+	0.114192i
$231$	4.00506e9	+	1.16007e10i	0.0925455	+	0.268059i
$232$	−7.38581e8	+	1.84093e9i	−0.0167379	+	0.0417196i
$233$			2.97575e10i			0.661448i	0.943728	+	0.330724i	$0.107293\pi$
$233$			2.97575e10i			0.661448i	−0.943728	+	0.330724i	$0.892707\pi$
$234$	−4.98211e10	−	2.78363e10i	−1.08628	−	0.606933i
$235$			5.62344e10i			1.20281i
$236$	1.26490e10	−	1.28386e10i	0.265431	−	0.269410i
$237$	2.14945e10	+	6.22591e10i	0.442547	+	1.28184i
$238$	−8.96881e8	−	2.14269e9i	−0.0181192	−	0.0432875i
$239$	−4.88849e10			−0.969135			−0.484568	−	0.874754i	$-0.661023\pi$
$239$	−4.88849e10			−0.969135			−0.484568	+	0.874754i	$0.661023\pi$
$240$	6.33653e10	−	2.29370e10i	1.23282	−	0.446258i
$241$	−4.16634e10			−0.795570			−0.397785	−	0.917479i	$-0.630221\pi$
$241$	−4.16634e10			−0.795570			−0.397785	+	0.917479i	$0.630221\pi$
$242$	1.87232e10	+	4.47304e10i	0.350922	+	0.838367i
$243$	4.95851e9	+	5.41269e10i	0.0912269	+	0.995830i
$244$	2.93916e10	−	2.98322e10i	0.530847	−	0.538804i
$245$		−	7.08258e10i		−	1.25587i
$246$	7.34950e10	−	6.56198e10i	1.27953	−	1.14242i
$247$		−	9.04055e10i		−	1.54546i
$248$	−3.69995e10	+	9.22221e10i	−0.621103	+	1.54811i
$249$	6.20514e10	−	2.14228e10i	1.02295	−	0.353165i
$250$	2.09904e10	−	8.78611e9i	0.339852	−	0.142255i
$251$	−5.36684e9			−0.0853468			−0.0426734	−	0.999089i	$-0.513587\pi$
$251$	−5.36684e9			−0.0853468			−0.0426734	+	0.999089i	$0.513587\pi$
$252$	−1.30562e10	−	1.48297e9i	−0.203946	−	0.0231650i
$253$	2.03098e10			0.311647
$254$	3.13097e9	−	1.31055e9i	0.0471983	−	0.0197562i
$255$	−1.91310e10	+	6.60483e9i	−0.283339	+	0.0978208i
$256$	−6.86891e10	+	2.04445e9i	−0.999557	+	0.0297507i
$257$		−	2.63871e10i		−	0.377305i	−0.982044	−	0.188652i	$-0.939588\pi$
$257$		−	2.63871e10i		−	0.377305i	0.982044	−	0.188652i	$-0.0604119\pi$
$258$	−1.39051e10	+	1.24151e10i	−0.195383	+	0.174447i
$259$		−	3.46120e9i		−	0.0477946i
$260$	−8.56341e10	−	8.43695e10i	−1.16216	−	1.14500i
$261$	−2.07913e9	−	2.65221e9i	−0.0277331	−	0.0353774i
$262$	−6.18360e8	−	1.47729e9i	−0.00810748	−	0.0193691i
$263$	2.48483e10			0.320255			0.160127	−	0.987096i	$-0.448809\pi$
$263$	2.48483e10			0.320255			0.160127	+	0.987096i	$0.448809\pi$
$264$	−1.08913e11	−	5.35311e9i	−1.37994	−	0.0678248i
$265$	−1.21057e8			−0.00150793
$266$	−8.03721e9	−	1.92012e10i	−0.0984324	−	0.235159i
$267$	−1.50678e9	−	4.36443e9i	−0.0181447	−	0.0525565i
$268$	1.55037e10	+	1.52747e10i	0.183581	+	0.180870i
$269$		−	4.66916e10i		−	0.543692i	−0.962341	−	0.271846i	$-0.912366\pi$
$269$		−	4.66916e10i		−	0.543692i	0.962341	−	0.271846i	$-0.0876342\pi$
$270$	−2.01693e10	+	1.12701e11i	−0.230969	+	1.29060i
$271$		−	5.95732e10i		−	0.670948i	−0.942049	−	0.335474i	$-0.891103\pi$
$271$		−	5.95732e10i		−	0.670948i	0.942049	−	0.335474i	$-0.108897\pi$
$272$	2.06364e10	−	3.07041e8i	0.228599	−	0.00340124i
$273$	7.64960e9	+	2.21572e10i	0.0833503	+	0.241425i
$274$	−5.84765e10	+	2.44770e10i	−0.626763	+	0.262349i
$275$	9.42129e10			0.993375
$276$	−9.37089e9	+	1.96227e10i	−0.0972053	+	0.203549i
$277$	5.62370e10			0.573935			0.286968	−	0.957940i	$-0.407353\pi$
$277$	5.62370e10			0.573935			0.286968	+	0.957940i	$0.407353\pi$
$278$	1.39499e11	−	5.83910e10i	1.40077	−	0.586333i
$279$	−1.04155e11	−	1.32864e11i	−1.02911	−	1.31277i
$280$	−2.56884e10	−	1.03062e10i	−0.249762	−	0.100205i
$281$			1.29973e11i			1.24358i	0.783184	+	0.621790i	$0.213594\pi$
$281$			1.29973e11i			1.24358i	−0.783184	+	0.621790i	$0.786406\pi$
$282$	6.48875e10	+	7.26749e10i	0.610999	+	0.684327i
$283$		−	3.99058e9i		−	0.0369826i	−0.999829	−	0.0184913i	$-0.994114\pi$
$283$		−	3.99058e9i		−	0.0369826i	0.999829	−	0.0184913i	$-0.00588630\pi$
$284$	−2.72769e10	+	2.76857e10i	−0.248807	+	0.252536i
$285$	−1.71439e11	+	5.91878e10i	−1.53924	+	0.531411i
$286$	7.51085e10	+	1.79437e11i	0.663808	+	1.58586i
$287$	−4.04680e10			−0.352081
$288$	5.54242e10	−	1.02758e11i	0.474715	−	0.880140i
$289$	1.12389e11			0.947731
$290$	−2.74092e9	−	6.54818e9i	−0.0227565	−	0.0543663i
$291$	1.84843e11	−	6.38157e10i	1.51107	−	0.521686i
$292$	−4.17663e10	+	4.23923e10i	−0.336204	+	0.341244i
$293$			5.61932e10i			0.445430i	0.974884	+	0.222715i	$0.0714919\pi$
$293$			5.61932e10i			0.445430i	−0.974884	+	0.222715i	$0.928508\pi$
$294$	−8.17242e10	−	9.15323e10i	−0.637952	−	0.714515i
$295$			6.44999e10i			0.495861i
$296$	2.85420e10	+	1.14511e10i	0.216108	+	0.0867028i
$297$	1.00520e11	−	1.55622e11i	0.749635	−	1.16056i
$298$	−6.63604e9	+	2.77770e9i	−0.0487457	+	0.0204039i
$299$	3.87914e10			0.280682
$300$	−4.34696e10	+	9.10257e10i	−0.309842	+	0.648811i
$301$	7.65646e9			0.0537624
$302$	−6.68696e10	+	2.79901e10i	−0.462592	+	0.193631i
$303$	4.78135e10	+	1.38492e11i	0.325881	+	0.943918i
$304$	1.84929e11	−	2.75149e9i	1.24186	−	0.0184772i
$305$			1.49874e11i			0.991692i
$306$	−1.71029e10	+	3.06106e10i	−0.111513	+	0.199584i
$307$			1.83860e11i			1.18131i	0.806922	+	0.590657i	$0.201132\pi$
$307$			1.83860e11i			1.18131i	−0.806922	+	0.590657i	$0.798868\pi$
$308$	3.19046e10	+	3.14334e10i	0.202011	+	0.199028i
$309$	−6.71612e10	−	1.94533e11i	−0.419088	−	1.21389i
$310$	−1.37308e11	−	3.28034e11i	−0.844438	−	2.01740i
$311$	−3.03576e11			−1.84012			−0.920058	−	0.391782i	$-0.871859\pi$
$311$	−3.03576e11			−1.84012			−0.920058	+	0.391782i	$0.871859\pi$
$312$	−2.08022e11	−	1.02244e10i	−1.24284	−	0.0610858i
$313$	−2.67815e11			−1.57720			−0.788598	−	0.614909i	$-0.789193\pi$
$313$	−2.67815e11			−1.57720			−0.788598	+	0.614909i	$0.789193\pi$
$314$	−7.77496e10	−	1.85747e11i	−0.451351	−	1.07830i
$315$	3.70092e10	−	2.90123e10i	0.211793	−	0.166029i
$316$	1.71227e11	+	1.68698e11i	0.966004	+	0.951739i
$317$		−	1.33818e11i		−	0.744300i	−0.928173	−	0.372150i	$-0.878621\pi$
$317$		−	1.33818e11i		−	0.744300i	0.928173	−	0.372150i	$-0.121379\pi$
$318$	−1.56449e8	+	1.39684e8i	−0.000857925	+	0.000765995i
$319$			1.14866e10i			0.0621062i
$320$	1.69975e11	−	1.77736e11i	0.906173	−	0.947548i
$321$	8.58787e10	−	2.96490e10i	0.451453	−	0.155861i
$322$	8.23891e9	−	3.44862e9i	0.0427089	−	0.0178770i
$323$	−5.55462e10			−0.283951
$324$	1.03977e11	+	1.68923e11i	0.524188	+	0.851603i
$325$	1.79945e11			0.894674
$326$	−1.50716e11	+	6.30862e10i	−0.739059	+	0.309354i
$327$	−1.63915e11	+	5.65903e10i	−0.792780	+	0.273701i
$328$	1.33884e11	−	3.33709e11i	0.638701	−	1.59197i
$329$		−	4.00164e10i		−	0.188303i
$330$	2.91099e11	−	2.59907e11i	1.35123	−	1.20644i
$331$		−	1.10121e11i		−	0.504250i	−0.967695	−	0.252125i	$-0.918871\pi$
$331$		−	1.10121e11i		−	0.504250i	0.967695	−	0.252125i	$-0.0811293\pi$
$332$	1.68135e11	−	1.70655e11i	0.759516	−	0.770900i
$333$	−4.11203e10	+	3.22351e10i	−0.183256	+	0.143658i
$334$	3.63050e10	+	8.67341e10i	0.159627	+	0.381356i
$335$	−7.78890e10			−0.337889
$336$	−4.50908e10	+	1.63220e10i	−0.193002	+	0.0698628i
$337$	−1.93041e11			−0.815294			−0.407647	−	0.913140i	$-0.633651\pi$
$337$	−1.93041e11			−0.815294			−0.407647	+	0.913140i	$0.633651\pi$
$338$	5.08064e10	+	1.21379e11i	0.211735	+	0.505845i
$339$	6.50859e10	+	1.88522e11i	0.267663	+	0.775290i
$340$	−5.18376e10	+	5.26146e10i	−0.210373	+	0.213526i
$341$			5.75429e11i			2.30461i
$342$	−1.53265e11	+	2.74311e11i	−0.605793	+	1.08424i
$343$			1.03016e11i			0.401866i
$344$	−2.53307e10	+	6.31372e10i	−0.0975290	+	0.243093i
$345$	−2.53964e10	−	7.35612e10i	−0.0965133	−	0.279552i
$346$	−3.20022e11	+	1.33954e11i	−1.20043	+	0.502475i
$347$	4.48226e11			1.65964			0.829821	−	0.558029i	$-0.188442\pi$
$347$	4.48226e11			1.65964			0.829821	+	0.558029i	$0.188442\pi$
$348$	−1.10981e10	−	5.29991e9i	−0.0405640	−	0.0193714i
$349$	2.02958e11			0.732305			0.366153	−	0.930555i	$-0.380675\pi$
$349$	2.02958e11			0.732305			0.366153	+	0.930555i	$0.380675\pi$
$350$	3.82186e10	−	1.59974e10i	0.136134	−	0.0569829i
$351$	1.91992e11	−	2.97236e11i	0.675152	−	1.04525i
$352$	−3.64762e11	+	1.59099e11i	−1.26639	+	0.552365i
$353$		−	3.98396e11i		−	1.36562i	−0.730597	−	0.682809i	$-0.760758\pi$
$353$		−	3.98396e11i		−	1.36562i	0.730597	−	0.682809i	$-0.239242\pi$
$354$	7.44249e10	+	8.33569e10i	0.251886	+	0.282116i
$355$		−	1.39090e11i		−	0.464803i
$356$	−1.20032e10	−	1.18259e10i	−0.0396069	−	0.0390220i
$357$	1.36136e10	−	4.70000e9i	0.0443575	−	0.0153141i
$358$	−1.27880e11	−	3.05511e11i	−0.411461	−	0.982998i
$359$	2.72944e10			0.0867260			0.0433630	−	0.999059i	$-0.486193\pi$
$359$	2.72944e10			0.0867260			0.0433630	+	0.999059i	$0.486193\pi$
$360$	1.16802e11	+	4.01172e11i	0.366512	+	1.25884i
$361$	−1.75078e11			−0.542561
$362$	5.37894e10	+	1.28505e11i	0.164630	+	0.393307i
$363$	−2.84197e11	+	9.81167e10i	−0.859091	+	0.296594i
$364$	6.09373e10	+	6.00374e10i	0.181940	+	0.179253i
$365$		−	2.12975e11i		−	0.628073i
$366$	1.72936e11	+	1.93691e11i	0.503757	+	0.564214i
$367$		−	4.74247e11i		−	1.36461i	−0.731070	−	0.682303i	$-0.760979\pi$
$367$		−	4.74247e11i		−	1.36461i	0.731070	−	0.682303i	$-0.239021\pi$
$368$	1.18061e9	+	7.93496e10i	0.00335578	+	0.225543i
$369$	3.76889e11	+	4.80773e11i	1.05827	+	1.34996i
$370$	−1.01524e11	+	4.24957e10i	−0.281618	+	0.117879i
$371$	8.61440e7			0.000236071
$372$	−5.55962e11	−	2.65501e11i	−1.50523	−	0.718826i
$373$	1.92852e11			0.515863			0.257931	−	0.966163i	$-0.416959\pi$
$373$	1.92852e11			0.515863			0.257931	+	0.966163i	$0.416959\pi$
$374$	1.10248e11	−	4.61475e10i	0.291374	−	0.121963i
$375$	4.60426e10	+	1.33363e11i	0.120232	+	0.348253i
$376$	3.29986e11	+	1.32390e11i	0.851432	+	0.341595i
$377$			2.19393e10i			0.0559354i
$378$	1.43525e10	−	8.01983e10i	0.0361588	−	0.202047i
$379$		−	2.74043e11i		−	0.682247i	−0.940018	−	0.341124i	$-0.889192\pi$
$379$		−	2.74043e11i		−	0.682247i	0.940018	−	0.341124i	$-0.110808\pi$
$380$	−4.64532e11	+	4.71495e11i	−1.14285	+	1.15998i
$381$	6.86780e9	+	1.98927e10i	0.0166977	+	0.0483650i
$382$	1.72924e11	+	4.13123e11i	0.415499	+	0.992646i
$383$	2.42929e11			0.576880			0.288440	−	0.957498i	$-0.406863\pi$
$383$	2.42929e11			0.576880			0.288440	+	0.957498i	$0.406863\pi$
$384$	1.45833e10	−	4.25830e11i	0.0342266	−	0.999414i
$385$	−1.60286e11			−0.371810
$386$	−2.21390e11	−	5.28909e11i	−0.507592	−	1.21266i
$387$	−7.13066e10	−	9.09614e10i	−0.161596	−	0.206138i
$388$	5.00853e11	−	5.08361e11i	1.12194	−	1.13875i
$389$		−	2.01059e10i		−	0.0445194i	−0.999752	−	0.0222597i	$-0.992914\pi$
$389$		−	2.01059e10i		−	0.0445194i	0.999752	−	0.0222597i	$-0.00708608\pi$
$390$	5.55995e11	−	4.96418e11i	1.21697	−	1.08657i
$391$		−	2.38339e10i		−	0.0515703i
$392$	−4.15609e11	−	1.66742e11i	−0.888991	−	0.356664i
$393$	9.38601e9	−	3.24045e9i	0.0198479	−	0.00685233i
$394$	−2.93317e11	+	1.22776e11i	−0.613203	+	0.256673i
$395$	−8.60225e11			−1.77797
$396$	7.63041e10	−	6.71785e11i	0.155926	−	1.37278i
$397$	−1.17213e11			−0.236821			−0.118410	−	0.992965i	$-0.537780\pi$
$397$	−1.17213e11			−0.236821			−0.118410	+	0.992965i	$0.537780\pi$
$398$	−1.01188e11	+	4.23552e10i	−0.202142	+	0.0846121i
$399$	1.21996e11	−	4.21181e10i	0.240972	−	0.0831937i
$400$	5.47662e9	+	3.68086e11i	0.0106965	+	0.718918i
$401$		−	6.80336e11i		−	1.31394i	−0.753919	−	0.656968i	$-0.771839\pi$
$401$		−	6.80336e11i		−	1.31394i	0.753919	−	0.656968i	$-0.228161\pi$
$402$	−1.00660e11	+	8.98743e10i	−0.192239	+	0.171640i
$403$			1.09906e12i			2.07562i
$404$	3.80886e11	+	3.75261e11i	0.711342	+	0.700837i
$405$	−6.89352e11	−	1.69482e11i	−1.27319	−	0.313024i
$406$	1.95044e9	+	4.65969e9i	0.00356259	+	0.00851119i
$407$	1.78091e11			0.321711
$408$	−6.28196e9	+	1.27811e11i	−0.0112234	+	0.228348i
$409$	−7.91215e10			−0.139810			−0.0699052	−	0.997554i	$-0.522270\pi$
$409$	−7.91215e10			−0.139810			−0.0699052	+	0.997554i	$0.522270\pi$
$410$	4.96854e11	+	1.18701e12i	0.868364	+	2.07456i
$411$	−1.28269e11	−	3.71532e11i	−0.221734	−	0.642256i
$412$	−5.35011e11	−	5.27110e11i	−0.914798	−	0.901288i
$413$		−	4.58981e10i		−	0.0776283i
$414$	−1.17702e11	−	6.57631e10i	−0.196916	−	0.110022i
$415$			8.57355e11i			1.41888i
$416$	−6.96689e11	+	3.03877e11i	−1.14056	+	0.497482i
$417$	3.05991e11	+	8.86309e11i	0.495561	+	1.43540i
$418$	9.87968e11	−	4.13542e11i	1.58289	−	0.662561i
$419$	6.07739e11			0.963284			0.481642	−	0.876368i	$-0.340041\pi$
$419$	6.07739e11			0.963284			0.481642	+	0.876368i	$0.340041\pi$
$420$	7.39554e10	−	1.54863e11i	0.115971	−	0.242843i
$421$	1.08935e12			1.69004			0.845019	−	0.534737i	$-0.179589\pi$
$421$	1.08935e12			1.69004			0.845019	+	0.534737i	$0.179589\pi$
$422$	6.96856e11	−	2.91688e11i	1.06964	−	0.447727i
$423$	−4.75408e11	+	3.72683e11i	−0.721997	+	0.565989i
$424$	−2.84999e8	+	7.10366e8i	−0.000428250	+	0.00106742i
$425$		−	1.10560e11i		−	0.164380i
$426$	−1.60493e11	−	1.79755e11i	−0.236109	−	0.264446i
$427$		−	1.06650e11i		−	0.155252i
$428$	2.32698e11	−	2.36186e11i	0.335193	−	0.340218i
$429$	−1.14006e12	+	3.93598e11i	−1.62507	+	0.561041i
$430$	−9.40039e10	−	2.24579e11i	−0.132598	−	0.316783i
$431$	1.10485e12			1.54225			0.771127	−	0.636682i	$-0.219693\pi$
$431$	1.10485e12			1.54225			0.771127	+	0.636682i	$0.219693\pi$
$432$	6.13852e11	+	3.83683e11i	0.847983	+	0.530024i
$433$	−5.88361e11			−0.804357			−0.402178	−	0.915561i	$-0.631747\pi$
$433$	−5.88361e11			−0.804357			−0.402178	+	0.915561i	$0.631747\pi$
$434$	9.77084e10	+	2.33429e11i	0.132199	+	0.315829i
$435$	4.16041e10	−	1.43635e10i	0.0557102	−	0.0192335i
$436$	−4.44145e11	+	4.50802e11i	−0.588620	+	0.597444i
$437$		−	2.13582e11i		−	0.280155i
$438$	−2.45747e11	−	2.75240e11i	−0.319047	−	0.357337i
$439$			3.00529e10i			0.0386185i	0.999814	+	0.0193093i	$0.00614672\pi$
$439$			3.00529e10i			0.0386185i	−0.999814	+	0.0193093i	$0.993853\pi$
$440$	5.30289e11	−	1.32176e12i	0.674491	−	1.68118i
$441$	5.98765e11	−	4.69385e11i	0.753846	−	0.590957i
$442$	2.10573e11	−	8.81411e10i	0.262423	−	0.109844i
$443$	−1.31509e12			−1.62232			−0.811162	−	0.584821i	$-0.801165\pi$
$443$	−1.31509e12			−1.62232			−0.811162	+	0.584821i	$0.801165\pi$
$444$	−8.21706e10	+	1.72066e11i	−0.100344	+	0.210122i
$445$	6.03027e10			0.0728981
$446$	−9.68203e11	+	4.05268e11i	−1.15867	+	0.484994i
$447$	−1.45562e10	−	4.21623e10i	−0.0172451	−	0.0499506i
$448$	−1.20955e11	+	1.26477e11i	−0.141864	+	0.148341i
$449$			1.39402e12i			1.61867i	0.587345	+	0.809337i	$0.300173\pi$
$449$			1.39402e12i			1.61867i	−0.587345	+	0.809337i	$0.699827\pi$
$450$	−5.45994e11	−	3.05061e11i	−0.627670	−	0.350696i
$451$		−	2.08221e12i		−	2.36990i
$452$	5.18479e11	+	5.10822e11i	0.584263	+	0.575634i
$453$	−1.46679e11	−	4.24859e11i	−0.163654	−	0.474026i
$454$	4.15751e11	+	9.93247e11i	0.459285	+	1.09725i
$455$	−3.06143e11			−0.334867
$456$	−5.62945e10	+	1.14535e12i	−0.0609711	+	1.24050i
$457$	−5.38367e11			−0.577372			−0.288686	−	0.957424i	$-0.593218\pi$
$457$	−5.38367e11			−0.577372			−0.288686	+	0.957424i	$0.593218\pi$
$458$	−5.67755e11	−	1.35639e12i	−0.602930	−	1.44042i
$459$	−1.82625e11	−	1.17962e11i	−0.192045	−	0.124047i
$460$	−2.02310e11	−	1.99322e11i	−0.210672	−	0.207561i
$461$		−	1.43244e12i		−	1.47714i	−0.674175	−	0.738571i	$-0.735501\pi$
$461$		−	1.43244e12i		−	1.47714i	0.674175	−	0.738571i	$-0.264499\pi$
$462$	−2.07146e11	+	1.84950e11i	−0.211538	+	0.188871i
$463$			1.01990e12i			1.03144i	0.856758	+	0.515719i	$0.172475\pi$
$463$			1.01990e12i			1.03144i	−0.856758	+	0.515719i	$0.827525\pi$
$464$	−4.48779e10	+	6.67722e8i	−0.0449471	+	0.000668751i
$465$	2.08418e12	−	7.19546e11i	2.06727	−	0.713708i
$466$	−6.21119e11	+	2.59987e11i	−0.610152	+	0.255396i
$467$	−4.66634e11			−0.453994			−0.226997	−	0.973895i	$-0.572891\pi$
$467$	−4.66634e11			−0.453994			−0.226997	+	0.973895i	$0.572891\pi$
$468$	1.45740e11	−	1.28310e12i	0.140434	−	1.23639i
$469$	5.54259e10			0.0528974
$470$	−1.17376e12	+	4.91310e11i	−1.10953	+	0.464425i
$471$	1.18015e12	−	4.07438e11i	1.10495	−	0.381476i
$472$	3.78488e11	+	1.51850e11i	0.351005	+	0.140823i
$473$			3.93951e11i			0.361882i
$474$	−1.11172e12	+	9.92594e11i	−1.01156	+	0.903169i
$475$		−	9.90763e11i		−	0.892994i
$476$	3.68877e10	−	3.74406e10i	0.0329344	−	0.0334281i
$477$	−8.02281e8	−	1.02342e9i	−0.000709568	−	0.000905151i
$478$	−4.27099e11	−	1.02036e12i	−0.374200	−	0.893979i
$479$	2.14286e12			1.85988			0.929939	−	0.367715i	$-0.119860\pi$
$479$	2.14286e12			1.85988			0.929939	+	0.367715i	$0.119860\pi$
$480$	1.03237e12	+	1.12220e12i	0.887664	+	0.964909i
$481$	3.40150e11			0.289746
$482$	−3.64006e11	−	8.69626e11i	−0.307183	−	0.733873i
$483$	1.80721e10	+	5.23462e10i	0.0151094	+	0.0437646i
$484$	−7.70062e11	+	7.81605e11i	−0.637854	+	0.647415i
$485$			2.55395e12i			2.09592i
$486$	−1.08645e12	+	5.76395e11i	−0.883379	+	0.468659i
$487$		−	2.14691e12i		−	1.72955i	−0.502157	−	0.864777i	$-0.667460\pi$
$487$		−	2.14691e12i		−	1.72955i	0.502157	−	0.864777i	$-0.332540\pi$
$488$	8.79467e11	+	3.52843e11i	0.701989	+	0.281638i
$489$	−3.30596e11	−	9.57577e11i	−0.261462	−	0.757328i
$490$	1.47832e12	−	6.18793e11i	1.15848	−	0.484912i
$491$	−1.65999e12			−1.28896			−0.644478	−	0.764622i	$-0.722925\pi$
$491$	−1.65999e12			−1.28896			−0.644478	+	0.764622i	$0.722925\pi$
$492$	2.01177e12	+	9.60728e11i	1.54788	+	0.739192i
$493$	1.34798e10			0.0102771
$494$	1.88700e12	−	7.89858e11i	1.42561	−	0.596730i
$495$	1.49278e12	+	1.90425e12i	1.11756	+	1.42561i
$496$	−2.24818e12	+	3.34498e10i	−1.66787	+	0.0248157i
$497$			9.89768e10i			0.0727662i
$498$	9.89282e11	+	1.10801e12i	0.720756	+	0.807257i
$499$			2.16275e12i			1.56154i	0.624819	+	0.780770i	$0.285173\pi$
$499$			2.16275e12i			1.56154i	−0.624819	+	0.780770i	$0.714827\pi$
$500$	3.66779e11	+	3.61362e11i	0.262446	+	0.258570i
$501$	−5.51068e11	+	1.90252e11i	−0.390783	+	0.134915i
$502$	−4.68892e10	−	1.12020e11i	−0.0329538	−	0.0787281i
$503$	−2.65354e12			−1.84829			−0.924145	−	0.382042i	$-0.875221\pi$
$503$	−2.65354e12			−1.84829			−0.924145	+	0.382042i	$0.875221\pi$
$504$	−8.31162e10	−	2.85474e11i	−0.0573783	−	0.197074i
$505$	−1.91353e12			−1.30926
$506$	1.77443e11	+	4.23920e11i	0.120332	+	0.287479i
$507$	−7.71184e11	+	2.66245e11i	−0.518349	+	0.178956i
$508$	5.47094e10	+	5.39015e10i	0.0364482	+	0.0359099i
$509$			3.74403e11i			0.247235i	0.992330	+	0.123617i	$0.0394496\pi$
$509$			3.74403e11i			0.247235i	−0.992330	+	0.123617i	$0.960550\pi$
$510$	−3.05005e11	−	3.41610e11i	−0.199637	−	0.223596i
$511$			1.51553e11i			0.0983265i
$512$	−6.42798e11	−	1.41586e12i	−0.413390	−	0.910554i
$513$	−1.63655e12	−	1.05709e12i	−1.04328	−	0.673884i
$514$	5.50768e11	−	2.30539e11i	0.348045	−	0.145684i
$515$	2.68784e12			1.68372
$516$	−3.80624e11	−	1.81768e11i	−0.236359	−	0.112874i
$517$	2.05898e12			1.26749
$518$	7.22445e10	−	3.02400e10i	0.0440881	−	0.0184543i
$519$	−7.01972e11	−	2.03327e12i	−0.424685	−	1.23011i
$520$	1.01284e12	−	2.52453e12i	0.607474	−	1.51414i
$521$			1.67662e12i			0.996929i	0.866910	+	0.498465i	$0.166103\pi$
$521$			1.67662e12i			0.996929i	−0.866910	+	0.498465i	$0.833897\pi$
$522$	3.71937e10	−	6.65688e10i	0.0219256	−	0.0392422i
$523$			3.04037e12i			1.77692i	0.458951	+	0.888461i	$0.348225\pi$
$523$			3.04037e12i			1.77692i	−0.458951	+	0.888461i	$0.651775\pi$
$524$	2.54324e10	−	2.58136e10i	0.0147366	−	0.0149575i
$525$	8.38328e10	+	2.42823e11i	0.0481612	+	0.139500i
$526$	2.17095e11	+	5.18650e11i	0.123656	+	0.295419i
$527$	6.75275e11			0.381358
$528$	−8.39820e11	−	2.32007e12i	−0.470255	−	1.29912i
$529$	−1.70951e12			−0.949119
$530$	−1.05765e9	−	2.52677e9i	−0.000582239	−	0.00139099i
$531$	−5.45285e11	+	4.27461e11i	−0.297645	+	0.233330i
$532$	3.30561e11	−	3.35516e11i	0.178916	−	0.181598i
$533$		−	3.97700e12i		−	2.13443i
$534$	7.79326e10	−	6.95819e10i	0.0414748	−	0.0370306i
$535$			1.18657e12i			0.626185i
$536$	−1.83371e11	+	4.57056e11i	−0.0959598	+	0.239182i
$537$	1.94107e12	−	6.70140e11i	1.00730	−	0.347761i
$538$	9.74577e11	−	4.07936e11i	0.501529	−	0.209929i
$539$	−2.59323e12			−1.32340
$540$	−2.52859e12	+	5.63666e11i	−1.27970	+	0.285266i
$541$	2.50937e12			1.25944			0.629720	−	0.776822i	$-0.283170\pi$
$541$	2.50937e12			1.25944			0.629720	+	0.776822i	$0.283170\pi$
$542$	1.24345e12	−	5.20481e11i	0.618916	−	0.259065i
$543$	−8.16463e11	+	2.81877e11i	−0.403030	+	0.139143i
$544$	1.86705e11	+	4.28054e11i	0.0914033	+	0.209557i
$545$		−	2.26479e12i		−	1.09962i
$546$	−3.95646e11	+	3.53251e11i	−0.190520	+	0.170105i
$547$		−	2.47135e12i		−	1.18030i	−0.807295	−	0.590148i	$-0.799069\pi$
$547$		−	2.47135e12i		−	1.18030i	0.807295	−	0.590148i	$-0.200931\pi$
$548$	−1.02180e12	−	1.00671e12i	−0.484008	−	0.476860i
$549$	−1.26704e12	+	9.93263e11i	−0.595272	+	0.466647i
$550$	8.23122e11	+	1.96647e12i	0.383559	+	0.916338i
$551$	1.20796e11			0.0558304
$552$	−4.91450e11	−	2.41550e10i	−0.225296	−	0.0110734i
$553$	6.12137e11			0.278346
$554$	4.91333e11	+	1.17382e12i	0.221606	+	0.529427i
$555$	−2.22694e11	−	6.45037e11i	−0.0996299	−	0.288580i
$556$	2.43755e12	+	2.40155e12i	1.08173	+	1.06575i
$557$			3.78554e12i			1.66640i	0.552972	+	0.833200i	$0.313494\pi$
$557$			3.78554e12i			1.66640i	−0.552972	+	0.833200i	$0.686506\pi$
$558$	1.86324e12	−	3.33480e12i	0.813606	−	1.45618i
$559$			7.52440e11i			0.325926i
$560$	−9.31744e9	−	6.26229e11i	−0.00400360	−	0.269084i
$561$	2.41831e11	+	7.00467e11i	0.103081	+	0.298576i
$562$	−2.71288e12	+	1.13555e12i	−1.14714	+	0.480168i
$563$	2.44811e12			1.02694			0.513468	−	0.858109i	$-0.328361\pi$
$563$	2.44811e12			1.02694			0.513468	+	0.858109i	$0.328361\pi$
$564$	−9.50008e11	+	1.98932e12i	−0.395340	+	0.827846i
$565$	−2.60479e12			−1.07536
$566$	8.32940e10	−	3.48650e10i	0.0341146	−	0.0142796i
$567$	4.90543e11	+	1.20604e11i	0.199321	+	0.0490046i
$568$	−8.16188e11	−	3.27455e11i	−0.329020	−	0.132003i
$569$		−	3.08511e11i		−	0.123386i	−0.998095	−	0.0616930i	$-0.980350\pi$
$569$		−	3.08511e11i		−	0.123386i	0.998095	−	0.0616930i	$-0.0196500\pi$
$570$	−2.73324e12	−	3.06126e12i	−1.08453	−	1.21469i
$571$		−	2.85732e12i		−	1.12485i	−0.826847	−	0.562427i	$-0.809868\pi$
$571$		−	2.85732e12i		−	1.12485i	0.826847	−	0.562427i	$-0.190132\pi$
$572$	−3.08913e12	+	3.13543e12i	−1.20657	+	1.22466i
$573$	−2.62479e12	+	9.06189e11i	−1.01718	+	0.351175i
$574$	−3.53562e11	−	8.44674e11i	−0.135945	−	0.324777i
$575$	4.25119e11			0.162183
$576$	2.62907e12	+	2.59066e11i	0.995180	+	0.0980639i
$577$	−1.25262e12			−0.470465			−0.235233	−	0.971939i	$-0.575585\pi$
$577$	−1.25262e12			−0.470465			−0.235233	+	0.971939i	$0.575585\pi$
$578$	9.81927e11	+	2.34587e12i	0.365935	+	0.874234i
$579$	3.36044e12	−	1.16017e12i	1.24263	−	0.429010i
$580$	1.12731e11	−	1.14421e11i	0.0413635	−	0.0419835i
$581$		−	6.10094e11i		−	0.222129i
$582$	2.94695e12	+	3.30062e12i	1.06468	+	1.19246i
$583$			4.43240e9i			0.00158902i
$584$	−1.24975e12	−	5.01399e11i	−0.444594	−	0.178371i
$585$	2.85119e12	+	3.63708e12i	1.00652	+	1.28396i
$586$	−1.17290e12	+	4.90951e11i	−0.410887	+	0.171988i
$587$	1.21795e12			0.423406			0.211703	−	0.977334i	$-0.432099\pi$
$587$	1.21795e12			0.423406			0.211703	+	0.977334i	$0.432099\pi$
$588$	1.19651e12	−	2.50550e12i	0.412780	−	0.864365i
$589$	6.05134e12			2.07173
$590$	−1.34628e12	+	5.63524e11i	−0.457407	+	0.191460i
$591$	−6.43393e11	−	1.86360e12i	−0.216937	−	0.628360i
$592$	1.03525e10	+	6.95793e11i	0.00346414	+	0.232827i
$593$			1.50764e11i			0.0500670i	0.999687	+	0.0250335i	$0.00796925\pi$
$593$			1.50764e11i			0.0500670i	−0.999687	+	0.0250335i	$0.992031\pi$
$594$	4.12647e12	+	7.38483e11i	1.36000	+	0.243389i
$595$			1.88098e11i			0.0615258i
$596$	−1.15956e11	−	1.14244e11i	−0.0376431	−	0.0370871i
$597$	−2.21958e11	−	6.42904e11i	−0.0715131	−	0.207139i
$598$	3.38914e11	+	8.09680e11i	0.108376	+	0.258915i
$599$	−2.79246e12			−0.886271			−0.443136	−	0.896455i	$-0.646134\pi$
$599$	−2.79246e12			−0.886271			−0.443136	+	0.896455i	$0.646134\pi$
$600$	−2.27973e12	−	1.12050e11i	−0.718131	−	0.0352964i
$601$	1.18581e12			0.370750			0.185375	−	0.982668i	$-0.440650\pi$
$601$	1.18581e12			0.370750			0.185375	+	0.982668i	$0.440650\pi$
$602$	6.68932e10	+	1.59811e11i	0.0207586	+	0.0495932i
$603$	−5.16195e11	−	6.58478e11i	−0.158996	−	0.202821i
$604$	−1.16846e12	−	1.15120e12i	−0.357229	−	0.351953i
$605$		−	3.92670e12i		−	1.19160i
$606$	−2.47297e12	+	2.20798e12i	−0.744889	+	0.665071i
$607$		−	7.75431e11i		−	0.231843i	−0.993258	−	0.115922i	$-0.963018\pi$
$607$		−	7.75431e11i		−	0.231843i	0.993258	−	0.115922i	$-0.0369821\pi$
$608$	1.67312e12	+	3.83591e12i	0.496548	+	1.13842i
$609$	−2.96055e10	+	1.02211e10i	−0.00872158	+	0.00301106i
$610$	−3.12827e12	+	1.30942e12i	−0.914786	+	0.382909i
$611$	3.93262e12			1.14155
$612$	−7.88351e11	−	8.95440e10i	−0.227163	−	0.0258021i
$613$	−2.37652e12			−0.679780			−0.339890	−	0.940465i	$-0.610390\pi$
$613$	−2.37652e12			−0.679780			−0.339890	+	0.940465i	$0.610390\pi$
$614$	−3.83766e12	+	1.60636e12i	−1.08970	+	0.456126i
$615$	−7.54169e12	+	2.60371e12i	−2.12584	+	0.733930i
$616$	−3.77354e11	+	9.40563e11i	−0.105593	+	0.263193i
$617$		−	4.81693e12i		−	1.33810i	−0.743219	−	0.669048i	$-0.766702\pi$
$617$		−	4.81693e12i		−	1.33810i	0.743219	−	0.669048i	$-0.233298\pi$
$618$	3.47365e12	−	3.10144e12i	0.957940	−	0.855293i
$619$			3.31276e11i			0.0906948i	0.998971	+	0.0453474i	$0.0144395\pi$
$619$			3.31276e11i			0.0906948i	−0.998971	+	0.0453474i	$0.985561\pi$
$620$	5.64731e12	−	5.73196e12i	1.53490	−	1.55790i
$621$	4.53580e11	−	7.02217e11i	0.122389	−	0.189478i
$622$	−2.65229e12	−	6.33643e12i	−0.710500	−	1.69741i
$623$	−4.29114e10			−0.0114124
$624$	−1.60404e12	−	4.43130e12i	−0.423531	−	1.17004i
$625$	−4.58542e12			−1.20204
$626$	−2.33986e12	−	5.59002e12i	−0.608982	−	1.45488i
$627$	2.16712e12	+	6.27709e12i	0.559988	+	1.62201i
$628$	3.19775e12	−	3.24568e12i	0.820401	−	0.832698i
$629$		−	2.08992e11i		−	0.0532356i
$630$	9.28907e11	+	5.19004e11i	0.234931	+	0.131262i
$631$		−	3.71482e12i		−	0.932836i	−0.884564	−	0.466418i	$-0.845544\pi$
$631$		−	3.71482e12i		−	0.932836i	0.884564	−	0.466418i	$-0.154456\pi$
$632$	−2.02519e12	+	5.04784e12i	−0.504940	+	1.25857i
$633$	1.52856e12	+	4.42750e12i	0.378413	+	1.09608i
$634$	2.79314e12	−	1.16915e12i	0.686579	−	0.287387i
$635$	−2.74855e11			−0.0670844
$636$	−4.28245e9	−	2.04510e9i	−0.00103785	−	0.000495629i
$637$	−4.95303e12			−1.19191
$638$	−2.39757e11	+	1.00357e11i	−0.0572899	+	0.0239803i
$639$	1.17588e12	−	9.21796e11i	0.279003	−	0.218716i
$640$	5.19488e12	+	1.99499e12i	1.22395	+	0.470035i
$641$			1.37939e12i			0.322720i	0.986896	+	0.161360i	$0.0515881\pi$
$641$			1.37939e12i			0.322720i	−0.986896	+	0.161360i	$0.948412\pi$
$642$	1.36916e12	+	1.53348e12i	0.318087	+	0.356262i
$643$			7.02703e12i			1.62115i	0.585637	+	0.810573i	$0.300844\pi$
$643$			7.02703e12i			1.62115i	−0.585637	+	0.810573i	$0.699156\pi$
$644$	1.43964e11	+	1.41838e11i	0.0329813	+	0.0324942i
$645$	1.42687e12	−	4.92617e11i	0.324613	−	0.112070i
$646$	−4.85298e11	−	1.15940e12i	−0.109638	−	0.261930i
$647$	−5.71078e12			−1.28123			−0.640613	−	0.767864i	$-0.721320\pi$
$647$	−5.71078e12			−1.28123			−0.640613	+	0.767864i	$0.721320\pi$
$648$	−2.61745e12	+	3.64614e12i	−0.583163	+	0.812355i
$649$	2.36161e12			0.522526
$650$	1.57215e12	+	3.75593e12i	0.345449	+	0.825292i
$651$	−1.48310e12	+	5.12030e11i	−0.323636	+	0.111733i
$652$	−2.63355e12	−	2.59466e12i	−0.570727	−	0.562298i
$653$			5.18880e12i			1.11675i	0.829587	+	0.558377i	$0.188576\pi$
$653$			5.18880e12i			1.11675i	−0.829587	+	0.558377i	$0.811424\pi$
$654$	−2.61328e12	−	2.92691e12i	−0.558582	−	0.625619i
$655$			1.29685e11i			0.0275299i
$656$	8.13513e12	−	1.21040e11i	1.71513	−	0.0255188i
$657$	1.80050e12	−	1.41145e12i	0.377007	−	0.295544i
$658$	8.35249e11	−	3.49617e11i	0.173700	−	0.0727069i
$659$	1.90586e12			0.393646			0.196823	−	0.980439i	$-0.436938\pi$
$659$	1.90586e12			0.393646			0.196823	+	0.980439i	$0.436938\pi$
$660$	7.96823e12	+	3.80525e12i	1.63461	+	0.780613i
$661$	−5.07877e12			−1.03479			−0.517395	−	0.855747i	$-0.673098\pi$
$661$	−5.07877e12			−1.03479			−0.517395	+	0.855747i	$0.673098\pi$
$662$	2.29853e12	−	9.62112e11i	0.465145	−	0.194699i
$663$	4.61893e11	+	1.33788e12i	0.0928391	+	0.268910i
$664$	5.03100e12	+	2.01844e12i	1.00438	+	0.402957i
$665$			1.68560e12i			0.334239i
$666$	−1.03209e12	−	5.76657e11i	−0.203275	−	0.113575i
$667$			5.18315e10i			0.0101397i
$668$	−1.49318e12	+	1.51556e12i	−0.290147	+	0.294496i
$669$	−2.12376e12	−	6.15152e12i	−0.409910	−	1.18731i
$670$	−6.80503e11	−	1.62575e12i	−0.130465	−	0.311686i
$671$	5.48752e12			1.04502
$672$	−7.34633e11	−	7.98562e11i	−0.138966	−	0.151059i
$673$	8.09293e12			1.52068			0.760340	−	0.649525i	$-0.225032\pi$
$673$	8.09293e12			1.52068			0.760340	+	0.649525i	$0.225032\pi$
$674$	−1.68656e12	−	4.02927e12i	−0.314799	−	0.752068i
$675$	2.10406e12	−	3.25743e12i	0.390114	−	0.603961i
$676$	−2.08961e12	+	2.12093e12i	−0.384862	+	0.390631i
$677$		−	1.26729e12i		−	0.231861i	−0.993257	−	0.115931i	$-0.963015\pi$
$677$		−	1.26729e12i		−	0.231861i	0.993257	−	0.115931i	$-0.0369850\pi$
$678$	−3.36632e12	+	3.00560e12i	−0.611817	+	0.546258i
$679$		−	1.81739e12i		−	0.328122i
$680$	−1.55110e12	−	6.22303e11i	−0.278196	−	0.111612i
$681$	−6.31063e12	+	2.17870e12i	−1.12437	+	0.388181i
$682$	−1.20107e13	+	5.02742e12i	−2.12588	+	0.889848i
$683$	1.13577e12			0.199710			0.0998548	−	0.995002i	$-0.468162\pi$
$683$	1.13577e12			0.199710			0.0998548	+	0.995002i	$0.468162\pi$
$684$	−7.06464e12	−	8.02430e11i	−1.23406	−	0.140170i
$685$	5.13341e12			0.890837
$686$	−2.15022e12	+	9.00034e11i	−0.370701	+	0.155167i
$687$	8.61788e12	−	2.97526e12i	1.47603	−	0.509588i
$688$	−1.53915e12	+	2.29005e10i	−0.261899	+	0.00389669i
$689$			8.46581e9i			0.00143114i
$690$	1.31353e12	−	1.17278e12i	0.220608	−	0.196969i
$691$			6.93411e12i			1.15702i	0.815677	+	0.578508i	$0.196365\pi$
$691$			6.93411e12i			1.15702i	−0.815677	+	0.578508i	$0.803635\pi$
$692$	−5.59196e12	−	5.50938e12i	−0.927015	−	0.913325i
$693$	−1.06226e12	−	1.35506e12i	−0.174958	−	0.223182i
$694$	3.91608e12	+	9.35567e12i	0.640816	+	1.53094i
$695$	−1.22460e13			−1.99096
$696$	1.36614e10	−	2.77950e11i	0.00220675	−	0.0448979i
$697$	−2.44351e12			−0.392163
$698$	1.77321e12	+	4.23628e12i	0.282756	+	0.675515i
$699$	−1.36243e12	−	3.94630e12i	−0.215858	−	0.625235i
$700$	6.67818e11	+	6.57956e11i	0.105128	+	0.103575i
$701$			8.24498e12i			1.28961i	0.764347	+	0.644805i	$0.223062\pi$
$701$			8.24498e12i			1.28961i	−0.764347	+	0.644805i	$0.776938\pi$
$702$	7.88150e12	+	1.41049e12i	1.22488	+	0.219207i
$703$		−	1.87284e12i		−	0.289202i
$704$	−6.50768e12	−	6.22352e12i	−0.998503	−	0.954903i
$705$	−2.57465e12	−	7.45753e12i	−0.392526	−	1.13696i
$706$	8.31559e12	−	3.48072e12i	1.25971	−	0.527288i
$707$	1.36167e12			0.204967
$708$	−1.08964e12	+	2.28172e12i	−0.162980	+	0.341282i
$709$	1.18757e13			1.76503			0.882514	−	0.470287i	$-0.155850\pi$
$709$	1.18757e13			1.76503			0.882514	+	0.470287i	$0.155850\pi$
$710$	2.90318e12	−	1.21521e12i	0.428758	−	0.179469i
$711$	−5.70099e12	−	7.27239e12i	−0.836636	−	1.06724i
$712$	1.41968e11	−	3.53859e11i	0.0207029	−	0.0516024i
$713$			2.59652e12i			0.376261i
$714$	2.17042e11	+	2.43090e11i	0.0312537	+	0.0350045i
$715$		−	1.57521e13i		−	2.25404i
$716$	5.25955e12	−	5.33839e12i	0.747894	−	0.759104i
$717$	6.48288e12	−	2.23817e12i	0.916077	−	0.316269i
$718$	2.38467e11	+	5.69708e11i	0.0334864	+	0.0800004i
$719$	−3.48403e12			−0.486185			−0.243092	−	0.970003i	$-0.578162\pi$
$719$	−3.48403e12			−0.486185			−0.243092	+	0.970003i	$0.578162\pi$
$720$	−7.35304e12	+	5.94293e12i	−1.01970	+	0.824147i
$721$	−1.91267e12			−0.263591
$722$	−1.52963e12	−	3.65434e12i	−0.209492	−	0.500485i
$723$	5.52520e12	−	1.90753e12i	0.752014	−	0.259627i
$724$	−2.21230e12	+	2.24546e12i	−0.299240	+	0.303725i
$725$			2.40435e11i			0.0323204i
$726$	−4.53093e12	−	5.07471e12i	−0.605303	−	0.677948i
$727$			1.90029e12i			0.252299i	0.992011	+	0.126149i	$0.0402619\pi$
$727$			1.90029e12i			0.252299i	−0.992011	+	0.126149i	$0.959738\pi$
$728$	−7.20741e11	+	1.79646e12i	−0.0951016	+	0.237043i
$729$	−3.13574e12	−	6.95103e12i	−0.411213	−	0.911539i
$730$	4.44535e12	−	1.86072e12i	0.579366	−	0.242510i
$731$	4.62308e11			0.0598829
$732$	−2.53193e12	+	5.30188e12i	−0.325950	+	0.682543i
$733$	−8.41372e12			−1.07651			−0.538257	−	0.842780i	$-0.680917\pi$
$733$	−8.41372e12			−1.07651			−0.538257	+	0.842780i	$0.680917\pi$
$734$	9.89879e12	−	4.14341e12i	1.25878	−	0.526897i
$735$	3.24271e12	+	9.39258e12i	0.409841	+	1.18711i
$736$	−1.64592e12	+	7.17907e11i	−0.206757	+	0.0901816i
$737$			2.85185e12i			0.356059i
$738$	−6.74220e12	+	1.20671e13i	−0.836658	+	1.49744i
$739$			4.63915e12i			0.572188i	0.958202	+	0.286094i	$0.0923569\pi$
$739$			4.63915e12i			0.572188i	−0.958202	+	0.286094i	$0.907643\pi$
$740$	−1.77400e12	−	1.74780e12i	−0.217475	−	0.214264i
$741$	4.13916e12	+	1.19891e13i	0.504348	+	1.46085i
$742$	7.52625e8	+	1.79805e9i	9.11510e−5	+	0.000217763i
$743$	9.43638e12			1.13594			0.567970	−	0.823049i	$-0.307729\pi$
$743$	9.43638e12			1.13594			0.567970	+	0.823049i	$0.307729\pi$
$744$	6.84372e11	−	1.39240e13i	0.0818869	−	1.66605i
$745$	5.82551e11			0.0692837
$746$	1.68491e12	+	4.02533e12i	0.199183	+	0.475858i
$747$	−7.24813e12	+	5.68197e12i	−0.851693	+	0.667661i
$748$	1.92644e12	+	1.89799e12i	0.225009	+	0.221686i
$749$		−	8.44367e11i		−	0.0980309i
$750$	−2.38138e12	+	2.12620e12i	−0.274823	+	0.245374i
$751$			5.79470e12i			0.664739i	0.943149	+	0.332369i	$0.107848\pi$
$751$			5.79470e12i			0.664739i	−0.943149	+	0.332369i	$0.892152\pi$
$752$	1.19689e11	+	8.04435e12i	0.0136482	+	0.917298i
$753$	7.11725e11	−	2.45718e11i	0.0806742	−	0.0278521i
$754$	−4.57932e11	+	1.91680e11i	−0.0515976	+	0.0215976i
$755$	5.87021e12			0.657495
$756$	1.79935e12	−	4.01105e11i	0.200340	−	0.0446591i
$757$	−4.94427e12			−0.547231			−0.273615	−	0.961839i	$-0.588220\pi$
$757$	−4.94427e12			−0.547231			−0.273615	+	0.961839i	$0.588220\pi$
$758$	5.72000e12	−	2.39427e12i	0.629339	−	0.263427i
$759$	−2.69339e12	+	9.29872e11i	−0.294585	+	0.101703i
$760$	−1.38999e13	−	5.57664e12i	−1.51130	−	0.606333i
$761$		−	8.08769e12i		−	0.874165i	−0.899421	−	0.437082i	$-0.856012\pi$
$761$		−	8.08769e12i		−	0.874165i	0.899421	−	0.437082i	$-0.143988\pi$
$762$	−3.55211e11	+	3.17149e11i	−0.0381671	+	0.0340773i
$763$			1.61162e12i			0.172148i
$764$	−7.11216e12	+	7.21877e12i	−0.755234	+	0.766555i
$765$	2.23466e12	−	1.75180e12i	0.235904	−	0.184931i
$766$	2.12243e12	+	5.07058e12i	0.222743	+	0.532143i
$767$	4.51065e12			0.470608
$768$	9.01561e12	−	3.41601e12i	0.935125	−	0.354318i
$769$	−8.10783e12			−0.836058			−0.418029	−	0.908434i	$-0.637279\pi$
$769$	−8.10783e12			−0.836058			−0.418029	+	0.908434i	$0.637279\pi$
$770$	−1.40039e12	−	3.34559e12i	−0.143562	−	0.342976i
$771$	1.20812e12	+	3.49933e12i	0.123130	+	0.356648i
$772$	9.10549e12	−	9.24198e12i	0.922626	−	0.936455i
$773$		−	4.98799e12i		−	0.502478i	−0.967925	−	0.251239i	$-0.919162\pi$
$773$		−	4.98799e12i		−	0.502478i	0.967925	−	0.251239i	$-0.0808381\pi$
$774$	1.27561e12	−	2.28307e12i	0.127757	−	0.228657i
$775$			1.20447e13i			1.19933i
$776$	1.49867e13	+	6.01268e12i	1.48364	+	0.595237i
$777$	1.58469e11	+	4.59008e11i	0.0155973	+	0.0451779i
$778$	4.19663e11	−	1.75662e11i	0.0410670	−	0.0171897i
$779$	−2.18970e13			−2.13043
$780$	1.52192e13	+	7.26797e12i	1.47220	+	0.703052i
$781$	−5.09269e12			−0.489798
$782$	4.97476e11	−	2.08233e11i	0.0475710	−	0.0199122i
$783$	3.97154e11	+	2.56532e11i	0.0377599	+	0.0243901i
$784$	−1.50745e11	−	1.01317e13i	−0.0142502	−	0.957764i
$785$			1.63060e13i			1.53262i
$786$	1.49641e11	+	1.67600e11i	0.0139845	+	0.0156629i
$787$		−	1.39424e13i		−	1.29554i	−0.761837	−	0.647769i	$-0.775702\pi$
$787$		−	1.39424e13i		−	1.29554i	0.761837	−	0.647769i	$-0.224298\pi$
$788$	−5.12532e12	−	5.04963e12i	−0.473536	−	0.466543i
$789$	−3.29526e12	+	1.13766e12i	−0.302722	+	0.104512i
$790$	−7.51564e12	−	1.79552e13i	−0.686506	−	1.64009i
$791$	1.85357e12			0.168350
$792$	1.46886e13	−	4.27661e12i	1.32653	−	0.386221i
$793$	1.04811e13			0.941189
$794$	−1.02407e12	−	2.44656e12i	−0.0914406	−	0.218455i
$795$	1.60539e10	−	5.54250e9i	0.00142538	−	0.000492100i
$796$	−1.76813e12	−	1.74202e12i	−0.156101	−	0.153796i
$797$		−	3.83269e12i		−	0.336466i	−0.985747	−	0.168233i	$-0.946194\pi$
$797$		−	3.83269e12i		−	0.336466i	0.985747	−	0.168233i	$-0.0538061\pi$
$798$	1.94497e12	+	2.17840e12i	0.169785	+	0.190162i
$799$		−	2.41624e12i		−	0.209740i
$800$	−7.63509e12	+	3.33022e12i	−0.659036	+	0.287454i
$801$	3.99645e11	+	5.09802e11i	0.0343027	+	0.0437578i
$802$	1.42004e13	−	5.94398e12i	1.21204	−	0.507333i
$803$	−7.79791e12			−0.661848
$804$	−2.75537e12	−	1.31584e12i	−0.232556	−	0.111058i
$805$	−7.23260e11			−0.0607034
$806$	−2.29403e13	+	9.60230e12i	−1.91466	+	0.801434i
$807$	2.13774e12	+	6.19201e12i	0.177429	+	0.513926i
$808$	−4.50495e12	+	1.12287e13i	−0.371826	+	0.926782i
$809$		−	1.38580e13i		−	1.13745i	−0.822528	−	0.568725i	$-0.807437\pi$
$809$		−	1.38580e13i		−	1.13745i	0.822528	−	0.568725i	$-0.192563\pi$
$810$	−2.48520e12	−	1.58693e13i	−0.202852	−	1.29532i
$811$			1.21585e13i			0.986926i	0.869767	+	0.493463i	$0.164269\pi$
$811$			1.21585e13i			0.986926i	−0.869767	+	0.493463i	$0.835731\pi$
$812$	−8.02195e10	+	8.14219e10i	−0.00647556	+	0.00657263i
$813$	2.72752e12	+	7.90031e12i	0.218958	+	0.634215i
$814$	1.55595e12	+	3.71722e12i	0.124218	+	0.296762i
$815$	1.32307e13			1.05045
$816$	−2.72264e12	+	9.85543e11i	−0.214973	+	0.0778161i
$817$	4.14287e12			0.325314
$818$	−6.91271e11	−	1.65148e12i	−0.0539832	−	0.128968i
$819$	−2.02891e12	−	2.58815e12i	−0.157574	−	0.201007i
$820$	−2.04350e13	+	2.07413e13i	−1.57839	+	1.60204i
$821$		−	2.21983e13i		−	1.70520i	−0.522565	−	0.852599i	$-0.675025\pi$
$821$		−	2.21983e13i		−	1.70520i	0.522565	−	0.852599i	$-0.324975\pi$
$822$	6.63421e12	−	5.92332e12i	0.506834	−	0.452525i
$823$		−	2.31916e13i		−	1.76210i	−0.473022	−	0.881050i	$-0.656837\pi$
$823$		−	2.31916e13i		−	1.76210i	0.473022	−	0.881050i	$-0.343163\pi$
$824$	6.32788e12	−	1.57724e13i	0.478174	−	1.19186i
$825$	−1.24941e13	+	4.31348e12i	−0.938990	+	0.324179i
$826$	9.58016e11	−	4.01004e11i	0.0716082	−	0.0299736i
$827$	−4.95365e12			−0.368257			−0.184128	−	0.982902i	$-0.558946\pi$
$827$	−4.95365e12			−0.368257			−0.184128	+	0.982902i	$0.558946\pi$
$828$	3.44309e11	−	3.03131e12i	0.0254572	−	0.224127i
$829$	−5.19375e12			−0.381932			−0.190966	−	0.981597i	$-0.561162\pi$
$829$	−5.19375e12			−0.381932			−0.190966	+	0.981597i	$0.561162\pi$
$830$	−1.78953e13	+	7.49057e12i	−1.30884	+	0.547852i
$831$	−7.45788e12	+	2.57478e12i	−0.542514	+	0.187299i
$832$	−1.24296e13	−	1.18868e13i	−0.899293	−	0.860025i
$833$			3.04320e12i			0.218992i
$834$	−1.58262e13	+	1.41304e13i	−1.13274	+	1.01136i
$835$		−	7.61403e12i		−	0.542033i
$836$	1.72634e13	+	1.70085e13i	1.22236	+	1.20431i
$837$	1.98956e13	+	1.28511e13i	1.40118	+	0.905056i
$838$	5.30972e12	+	1.26851e13i	0.371940	+	0.888581i
$839$	1.92640e13			1.34220			0.671100	−	0.741367i	$-0.265822\pi$
$839$	1.92640e13			1.34220			0.671100	+	0.741367i	$0.265822\pi$
$840$	3.87854e12	+	1.90632e11i	0.268789	+	0.0132111i
$841$	1.44778e13			0.997979
$842$	9.51743e12	+	2.27375e13i	0.652552	+	1.55897i
$843$	−5.95072e12	−	1.72364e13i	−0.405831	−	1.17550i
$844$	1.21766e13	+	1.19968e13i	0.826011	+	0.813812i
$845$		−	1.06553e13i		−	0.718973i
$846$	−1.19324e13	−	6.66697e12i	−0.800872	−	0.447468i
$847$			2.79424e12i			0.186547i
$848$	−1.73172e10	+	2.57656e8i	−0.00115000	+	1.71104e-5i
$849$	1.82706e11	+	5.29212e11i	0.0120689	+	0.0349579i
$850$	2.30769e12	−	9.65947e11i	0.151632	−	0.0634699i
$851$	8.03603e11			0.0525241
$852$	2.34975e12	−	4.92040e12i	0.152772	−	0.319906i
$853$	−1.58841e13			−1.02729			−0.513644	−	0.858003i	$-0.671705\pi$
$853$	−1.58841e13			−1.02729			−0.513644	+	0.858003i	$0.671705\pi$
$854$	2.22608e12	−	9.31787e11i	0.143212	−	0.0599454i
$855$	2.00255e13	−	1.56984e13i	1.28155	−	1.00463i
$856$	6.96287e12	+	2.79351e12i	0.443257	+	0.177835i
$857$			1.76716e13i			1.11908i	0.828803	+	0.559541i	$0.189023\pi$
$857$			1.76716e13i			1.11908i	−0.828803	+	0.559541i	$0.810977\pi$
$858$	−1.81760e13	−	2.03573e13i	−1.14500	−	1.28241i
$859$			1.60684e13i			1.00694i	0.864013	+	0.503470i	$0.167944\pi$
$859$			1.60684e13i			1.00694i	−0.864013	+	0.503470i	$0.832056\pi$
$860$	3.86627e12	−	3.92422e12i	0.241018	−	0.244630i
$861$	5.36667e12	−	1.85280e12i	0.332806	−	0.114899i
$862$	9.65289e12	+	2.30612e13i	0.595490	+	1.42265i
$863$	2.11583e13			1.29847			0.649234	−	0.760589i	$-0.275089\pi$
$863$	2.11583e13			1.29847			0.649234	+	0.760589i	$0.275089\pi$
$864$	−2.64535e12	+	1.61649e13i	−0.161500	+	0.986873i
$865$	2.80935e13			1.70621
$866$	−5.14041e12	−	1.22807e13i	−0.310576	−	0.741979i
$867$	−1.49045e13	+	5.14568e12i	−0.895845	+	0.309284i
$868$	−4.01863e12	+	4.07887e12i	−0.240292	+	0.243894i
$869$			3.14965e13i			1.87358i
$870$	6.63293e11	+	7.42897e11i	0.0392526	+	0.0439635i
$871$			5.44698e12i			0.320682i
$872$	−1.32899e13	−	5.33190e12i	−0.778388	−	0.312290i
$873$	−2.15913e13	+	1.69259e13i	−1.25810	+	0.986250i
$874$	4.45803e12	−	1.86603e12i	0.258429	−	0.108173i
$875$	1.31124e12			0.0756215
$876$	3.59794e12	−	7.53411e12i	0.206436	−	0.432278i
$877$	−2.08743e13			−1.19156			−0.595778	−	0.803149i	$-0.703156\pi$
$877$	−2.08743e13			−1.19156			−0.595778	+	0.803149i	$0.703156\pi$
$878$	−6.27284e11	+	2.62567e11i	−0.0356237	+	0.0149113i
$879$	−2.57277e12	−	7.45207e12i	−0.145362	−	0.421044i
$880$	3.22216e13	−	4.79414e11i	1.81124	−	0.0269487i
$881$		−	2.43138e13i		−	1.35976i	−0.733325	−	0.679878i	$-0.762033\pi$
$881$		−	2.43138e13i		−	1.35976i	0.733325	−	0.679878i	$-0.237967\pi$
$882$	1.50286e13	+	8.39688e12i	0.836201	+	0.467207i
$883$		−	2.57502e13i		−	1.42547i	−0.701436	−	0.712733i	$-0.747457\pi$
$883$		−	2.57502e13i		−	1.42547i	0.701436	−	0.712733i	$-0.252543\pi$
$884$	3.67948e12	+	3.62514e12i	0.202652	+	0.199659i
$885$	−2.95309e12	−	8.55366e12i	−0.161820	−	0.468713i
$886$	−1.14897e13	−	2.74494e13i	−0.626407	−	1.49651i
$887$	−2.12882e13			−1.15473			−0.577367	−	0.816485i	$-0.695920\pi$
$887$	−2.12882e13			−1.15473			−0.577367	+	0.816485i	$0.695920\pi$
$888$	−4.30938e12	−	2.11808e11i	−0.232572	−	0.0114310i
$889$	1.95587e11			0.0105022
$890$	5.26854e11	+	1.25868e12i	0.0281472	+	0.0672449i
$891$	−6.20547e12	+	2.52401e13i	−0.329856	+	1.34166i
$892$	−1.69181e13	−	1.66682e13i	−0.894764	−	0.881551i
$893$		−	2.16527e13i		−	1.13941i
$894$	7.52865e11	−	6.72192e11i	0.0394183	−	0.0351945i
$895$			2.68195e13i			1.39716i
$896$	−3.69668e12	−	1.41963e12i	−0.191613	−	0.0735851i
$897$	−5.14433e12	+	1.77604e12i	−0.265316	+	0.0915982i
$898$	−2.90968e13	+	1.21793e13i	−1.49315	+	0.624998i
$899$	−1.46852e12			−0.0749826
$900$	1.59717e12	−	1.40616e13i	0.0811449	−	0.714404i
$901$	5.20149e9			0.000262946
$902$	4.34613e13	−	1.81919e13i	2.18612	−	0.915061i
$903$	−1.01536e12	+	3.50546e11i	−0.0508191	+	0.0175449i
$904$	−6.13235e12	+	1.52850e13i	−0.305400	+	0.761215i
$905$		−	1.12810e13i		−	0.559020i
$906$	7.58642e12	−	6.77350e12i	0.374076	−	0.333992i
$907$			3.26042e11i			0.0159971i	0.999968	+	0.00799854i	$0.00254604\pi$
$907$			3.26042e11i			0.0159971i	−0.999968	+	0.00799854i	$0.997454\pi$
$908$	−1.70993e13	+	1.73557e13i	−0.834821	+	0.847334i
$909$	−1.26816e13	−	1.61771e13i	−0.616079	−	0.785893i
$910$	−2.67472e12	−	6.39002e12i	−0.129298	−	0.308898i
$911$	−1.96607e13			−0.945730			−0.472865	−	0.881135i	$-0.656780\pi$
$911$	−1.96607e13			−0.945730			−0.472865	+	0.881135i	$0.656780\pi$
$912$	−2.43984e13	+	8.83173e12i	−1.16784	+	0.422736i
$913$	3.13914e13			1.49518
$914$	−4.70363e12	−	1.12372e13i	−0.222933	−	0.532597i
$915$	−6.86189e12	−	1.98756e13i	−0.323630	−	0.937399i
$916$	2.33511e13	−	2.37011e13i	1.09592	−	1.11234i
$917$		−	9.22840e10i		−	0.00430987i
$918$	8.66622e11	−	4.84248e12i	0.0402752	−	0.225048i
$919$			2.06713e13i			0.955979i	0.878366	+	0.477989i	$0.158634\pi$
$919$			2.06713e13i			0.955979i	−0.878366	+	0.477989i	$0.841366\pi$
$920$	2.39284e12	−	5.96419e12i	0.110120	−	0.274477i
$921$	−8.41794e12	−	2.43827e13i	−0.385511	−	1.11664i
$922$	2.98988e13	−	1.25150e13i	1.36259	−	0.570350i
$923$	−9.72695e12			−0.441133
$924$	−5.67020e12	−	2.70782e12i	−0.255902	−	0.122207i
$925$	3.72774e12			0.167420
$926$	−2.12880e13	+	8.91069e12i	−0.951449	+	0.398255i
$927$	1.78132e13	+	2.27232e13i	0.792287	+	1.01067i
$928$	−4.06028e11	−	9.30887e11i	−0.0179717	−	0.0412032i
$929$			3.58981e13i			1.58125i	0.612301	+	0.790625i	$0.290244\pi$
$929$			3.58981e13i			1.58125i	−0.612301	+	0.790625i	$0.709756\pi$
$930$	3.32280e13	+	3.72158e13i	1.45657	+	1.63137i
$931$			2.72710e13i			1.18967i
$932$	−1.08532e13	−	1.06929e13i	−0.471180	−	0.464222i
$933$	4.02587e13	−	1.38990e13i	1.73937	−	0.600505i
$934$	−4.07690e12	−	9.73989e12i	−0.175295	−	0.418787i
$935$	−9.67826e12			−0.414138
$936$	2.80550e13	−	8.16825e12i	1.19473	−	0.347847i
$937$	−3.11338e13			−1.31948			−0.659741	−	0.751493i	$-0.729334\pi$
$937$	−3.11338e13			−1.31948			−0.659741	+	0.751493i	$0.729334\pi$
$938$	4.84246e11	+	1.15688e12i	0.0204246	+	0.0487952i
$939$	3.55164e13	−	1.22618e13i	1.49085	−	0.514704i
$940$	−2.05099e13	−	2.02070e13i	−0.856817	−	0.844164i
$941$			3.86024e13i			1.60495i	0.596686	+	0.802475i	$0.296484\pi$
$941$			3.86024e13i			1.60495i	−0.596686	+	0.802475i	$0.703516\pi$
$942$	1.88151e13	+	2.10732e13i	0.778533	+	0.871968i
$943$		−	9.39562e12i		−	0.386922i
$944$	1.37281e11	+	9.22673e12i	0.00562649	+	0.378159i
$945$	−3.57967e12	+	5.54191e12i	−0.146016	+	0.226056i
$946$	−8.22280e12	+	3.44188e12i	−0.333818	+	0.139729i
$947$	2.51469e12			0.101604			0.0508019	−	0.998709i	$-0.483822\pi$
$947$	2.51469e12			0.101604			0.0508019	+	0.998709i	$0.483822\pi$
$948$	−3.04310e13	−	1.45324e13i	−1.22371	−	0.584386i
$949$	−1.48939e13			−0.596088
$950$	2.06799e13	−	8.65613e12i	0.823742	−	0.344800i
$951$	6.12678e12	+	1.77463e13i	0.242896	+	0.703551i
$952$	1.10377e12	+	4.42831e11i	0.0435522	+	0.0174732i
$953$		−	1.44824e13i		−	0.568753i	−0.958713	−	0.284377i	$-0.908213\pi$
$953$		−	1.44824e13i		−	0.568753i	0.958713	−	0.284377i	$-0.0917866\pi$
$954$	1.43521e10	−	2.56872e10i	0.000560980	−	0.00100403i
$955$		−	3.62664e13i		−	1.41088i
$956$	1.75661e13	−	1.78294e13i	0.680166	−	0.690361i
$957$	−5.25909e11	−	1.52330e12i	−0.0202678	−	0.0587061i
$958$	1.87218e13	+	4.47272e13i	0.718130	+	1.71564i
$959$	−3.65294e12			−0.139463
$960$	−1.44038e13	+	3.13528e13i	−0.547338	+	1.19139i
$961$	−4.71265e13			−1.78242
$962$	2.97184e12	+	7.09984e12i	0.111876	+	0.267277i
$963$	−1.00314e13	+	7.86380e12i	−0.375873	+	0.294655i
$964$	1.49712e13	−	1.51956e13i	0.558353	−	0.566722i
$965$			4.64308e13i			1.72359i
$966$	−9.34711e11	+	8.34553e11i	−0.0345367	+	0.0308359i
$967$		−	2.84274e13i		−	1.04549i	−0.852490	−	0.522744i	$-0.824909\pi$
$967$		−	2.84274e13i		−	1.04549i	0.852490	−	0.522744i	$-0.175091\pi$
$968$	−2.30421e13	−	9.24449e12i	−0.843495	−	0.338411i
$969$	7.36627e12	−	2.54315e12i	0.268405	−	0.0926647i
$970$	−5.33078e13	+	2.23135e13i	−1.93338	+	0.809271i
$971$	1.01920e13			0.367938			0.183969	−	0.982932i	$-0.441105\pi$
$971$	1.01920e13			0.367938			0.183969	+	0.982932i	$0.441105\pi$
$972$	−2.15230e13	−	1.76413e13i	−0.773402	−	0.633915i
$973$	8.71427e12			0.311690
$974$	4.48118e13	−	1.87572e13i	1.59543	−	0.667810i
$975$	−2.38635e13	+	8.23868e12i	−0.845693	+	0.291969i
$976$	3.18991e11	+	2.14395e13i	0.0112526	+	0.756295i
$977$		−	2.67930e13i		−	0.940795i	−0.882455	−	0.470398i	$-0.844110\pi$
$977$		−	2.67930e13i		−	0.940795i	0.882455	−	0.470398i	$-0.155890\pi$
$978$	1.70988e13	−	1.52666e13i	0.597642	−	0.533603i
$979$		−	2.20794e12i		−	0.0768183i
$980$	2.58317e13	+	2.54502e13i	0.894614	+	0.881402i
$981$	1.91466e13	−	1.50095e13i	0.660057	−	0.517433i
$982$	−1.45030e13	−	3.46484e13i	−0.497688	−	1.18900i
$983$	2.49705e13			0.852976			0.426488	−	0.904493i	$-0.359751\pi$
$983$	2.49705e13			0.852976			0.426488	+	0.904493i	$0.359751\pi$
$984$	−2.47643e12	+	5.03848e13i	−0.0842070	+	1.71325i
$985$	2.57491e13			0.871563
$986$	1.17770e11	+	2.81359e11i	0.00396817	+	0.00948012i
$987$	1.83213e12	+	5.30678e12i	0.0614509	+	0.177994i
$988$	3.29729e13	+	3.24859e13i	1.10091	+	1.08465i
$989$			1.77763e12i			0.0590825i
$990$	−2.67045e13	+	4.77954e13i	−0.883540	+	1.58135i
$991$		−	4.10234e13i		−	1.35114i	−0.737296	−	0.675569i	$-0.763898\pi$
$991$		−	4.10234e13i		−	1.35114i	0.737296	−	0.675569i	$-0.236102\pi$
$992$	−2.03401e13	−	4.66332e13i	−0.666886	−	1.52895i
$993$	5.04184e12	+	1.46038e13i	0.164557	+	0.476643i
$994$	−2.06591e12	+	8.64743e11i	−0.0671231	+	0.0280963i
$995$	8.88291e12			0.287310
$996$	−1.44839e13	+	3.03294e13i	−0.466358	+	0.976556i
$997$	1.48516e13			0.476043			0.238022	−	0.971260i	$-0.423501\pi$
$997$	1.48516e13			0.476043			0.238022	+	0.971260i	$0.423501\pi$
$998$	−4.51422e13	+	1.88955e13i	−1.44044	+	0.602937i
$999$	3.97731e12	−	6.15753e12i	0.126341	−	0.195597i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	12.10.b.a.11.12	yes	16
3.2	odd	2	inner	12.10.b.a.11.5	✓	16
4.3	odd	2	inner	12.10.b.a.11.6	yes	16
8.3	odd	2		192.10.c.d.191.2		16
8.5	even	2		192.10.c.d.191.15		16
12.11	even	2	inner	12.10.b.a.11.11	yes	16
24.5	odd	2		192.10.c.d.191.1		16
24.11	even	2		192.10.c.d.191.16		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
12.10.b.a.11.5	✓	16	3.2	odd	2	inner
12.10.b.a.11.6	yes	16	4.3	odd	2	inner
12.10.b.a.11.11	yes	16	12.11	even	2	inner
12.10.b.a.11.12	yes	16	1.1	even	1	trivial
192.10.c.d.191.1		16	24.5	odd	2
192.10.c.d.191.2		16	8.3	odd	2
192.10.c.d.191.15		16	8.5	even	2
192.10.c.d.191.16		16	24.11	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:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	12.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(8.73683 + 20.8727i) q^{2} +(-132.615 + 45.7844i) q^{3} +(-359.336 + 364.722i) q^{4} -1832.33i q^{5} +(-2114.28 - 2368.02i) q^{6} +1303.88i q^{7} +(-10752.2 - 4313.78i) q^{8} +(15490.6 - 12143.4i) q^{9} +O(q^{10})\)	\(q+(8.73683 + 20.8727i) q^{2} +(-132.615 + 45.7844i) q^{3} +(-359.336 + 364.722i) q^{4} -1832.33i q^{5} +(-2114.28 - 2368.02i) q^{6} +1303.88i q^{7} +(-10752.2 - 4313.78i) q^{8} +(15490.6 - 12143.4i) q^{9} +(38245.5 - 16008.7i) q^{10} -67089.2 q^{11} +(30954.8 - 64819.6i) q^{12} -128139. q^{13} +(-27215.5 + 11391.8i) q^{14} +(83891.9 + 242994. i) q^{15} +(-3899.91 - 262115. i) q^{16} +78730.3i q^{17} +(388804. + 217235. i) q^{18} +705525. i q^{19} +(668289. + 658420. i) q^{20} +(-59697.5 - 172915. i) q^{21} +(-586147. - 1.40033e6i) q^{22} -302728. q^{23} +(1.62340e6 + 79791.0i) q^{24} -1.40429e6 q^{25} +(-1.11953e6 - 2.67461e6i) q^{26} +(-1.49831e6 + 2.31963e6i) q^{27} +(-475555. - 468532. i) q^{28} -171214. i q^{29} +(-4.33899e6 + 3.87405e6i) q^{30} -8.57707e6i q^{31} +(5.43696e6 - 2.37146e6i) q^{32} +(8.89705e6 - 3.07164e6i) q^{33} +(-1.64331e6 + 687853. i) q^{34} +2.38914e6 q^{35} +(-1.13735e6 + 1.00133e7i) q^{36} -2.65453e6 q^{37} +(-1.47262e7 + 6.16405e6i) q^{38} +(1.69932e7 - 5.86678e6i) q^{39} +(-7.90424e6 + 1.97015e7i) q^{40} +3.10365e7i q^{41} +(3.08762e6 - 2.75677e6i) q^{42} -5.87204e6i q^{43} +(2.41075e7 - 2.44689e7i) q^{44} +(-2.22507e7 - 2.83838e7i) q^{45} +(-2.64489e6 - 6.31874e6i) q^{46} -3.06902e7 q^{47} +(1.25180e7 + 3.45819e7i) q^{48} +3.86535e7 q^{49} +(-1.22691e7 - 2.93113e7i) q^{50} +(-3.60462e6 - 1.04408e7i) q^{51} +(4.60450e7 - 4.67352e7i) q^{52} -66067.2i q^{53} +(-6.15072e7 - 1.10075e7i) q^{54} +1.22929e8i q^{55} +(5.62466e6 - 1.40196e7i) q^{56} +(-3.23020e7 - 9.35633e7i) q^{57} +(3.57370e6 - 1.49587e6i) q^{58} -3.52011e7 q^{59} +(-1.18771e8 - 5.67193e7i) q^{60} -8.17944e7 q^{61} +(1.79026e8 - 7.49364e7i) q^{62} +(1.58336e7 + 2.01979e7i) q^{63} +(9.70004e7 + 9.27649e7i) q^{64} +2.34793e8i q^{65} +(1.41845e8 + 1.58869e8i) q^{66} -4.25083e7i q^{67} +(-2.87146e7 - 2.82906e7i) q^{68} +(4.01464e7 - 1.38602e7i) q^{69} +(2.08735e7 + 4.98677e7i) q^{70} +7.59092e7 q^{71} +(-2.18941e8 + 6.37451e7i) q^{72} +1.16232e8 q^{73} +(-2.31922e7 - 5.54072e7i) q^{74} +(1.86231e8 - 6.42946e7i) q^{75} +(-2.57320e8 - 2.53520e8i) q^{76} -8.74766e7i q^{77} +(2.70922e8 + 3.03437e8i) q^{78} -4.69472e8i q^{79} +(-4.80280e8 + 7.14591e6i) q^{80} +(9.24958e7 - 3.76217e8i) q^{81} +(-6.47814e8 + 2.71161e8i) q^{82} -4.67905e8 q^{83} +(8.45172e7 + 4.03615e7i) q^{84} +1.44260e8 q^{85} +(1.22565e8 - 5.13031e7i) q^{86} +(7.83895e6 + 2.27056e7i) q^{87} +(7.21354e8 + 2.89408e8i) q^{88} +3.29105e7i q^{89} +(3.98045e8 - 7.12415e8i) q^{90} -1.67079e8i q^{91} +(1.08781e8 - 1.10412e8i) q^{92} +(3.92696e8 + 1.13745e9i) q^{93} +(-2.68135e8 - 6.40585e8i) q^{94} +1.29275e9 q^{95} +(-6.12448e8 + 5.63419e8i) q^{96} -1.39383e9 q^{97} +(3.37709e8 + 8.06801e8i) q^{98} +(-1.03925e9 + 8.14692e8i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 344 q^{4} - 1608 q^{6} - 13872 q^{9}+O(q^{10}) \) 16 * q - 344 * q^4 - 1608 * q^6 - 13872 * q^9	\( 16 q - 344 q^{4} - 1608 q^{6} - 13872 q^{9} - 15952 q^{10} + 42600 q^{12} - 97312 q^{13} + 164896 q^{16} + 256944 q^{18} + 356448 q^{21} + 322128 q^{22} + 166176 q^{24} - 2743728 q^{25} - 1447056 q^{28} + 3286128 q^{30} + 4715520 q^{33} - 13198144 q^{34} - 6827448 q^{36} + 10997600 q^{37} + 23411264 q^{40} + 23964432 q^{42} - 251904 q^{45} - 41256288 q^{46} - 87722976 q^{48} - 21356624 q^{49} + 132124208 q^{52} + 179732232 q^{54} - 88439904 q^{57} - 271309360 q^{58} - 414400704 q^{60} + 50685152 q^{61} + 742710400 q^{64} + 790585104 q^{66} + 63713280 q^{69} - 1188731232 q^{70} - 1250220480 q^{72} + 23382176 q^{73} + 1645242192 q^{76} + 2079579408 q^{78} + 349756560 q^{81} - 3274996000 q^{82} - 3734920464 q^{84} - 247261184 q^{85} + 4467199680 q^{88} + 5726283888 q^{90} - 262825248 q^{93} - 6146963136 q^{94} - 6944875392 q^{96} + 30926624 q^{97}+O(q^{100}) \) 16 * q - 344 * q^4 - 1608 * q^6 - 13872 * q^9 - 15952 * q^10 + 42600 * q^12 - 97312 * q^13 + 164896 * q^16 + 256944 * q^18 + 356448 * q^21 + 322128 * q^22 + 166176 * q^24 - 2743728 * q^25 - 1447056 * q^28 + 3286128 * q^30 + 4715520 * q^33 - 13198144 * q^34 - 6827448 * q^36 + 10997600 * q^37 + 23411264 * q^40 + 23964432 * q^42 - 251904 * q^45 - 41256288 * q^46 - 87722976 * q^48 - 21356624 * q^49 + 132124208 * q^52 + 179732232 * q^54 - 88439904 * q^57 - 271309360 * q^58 - 414400704 * q^60 + 50685152 * q^61 + 742710400 * q^64 + 790585104 * q^66 + 63713280 * q^69 - 1188731232 * q^70 - 1250220480 * q^72 + 23382176 * q^73 + 1645242192 * q^76 + 2079579408 * q^78 + 349756560 * q^81 - 3274996000 * q^82 - 3734920464 * q^84 - 247261184 * q^85 + 4467199680 * q^88 + 5726283888 * q^90 - 262825248 * q^93 - 6146963136 * q^94 - 6944875392 * q^96 + 30926624 * q^97

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