LMFDB - Embedded newform 8.16.b.a.5.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8,16,Mod(5,8)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 16, names="a")

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

chi := DirichletCharacter("8.5");

S:= CuspForms(chi, 16);

N := Newforms(S);

Level:	$ N $	$=$	$ 8 = 2^{3} $
Weight:	$ k $	$=$	$ 16 $
Character orbit:	$[\chi]$	$=$	8.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:	$11.4154804080$
Analytic rank:	$0$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 3 x^{13} - 6354 x^{12} + 136110 x^{11} + 41390651 x^{10} - 1368564777 x^{9} + \cdots + 24\!\cdots\!00 $ x^14 - 3x^13 - 6354x^12 + 136110x^11 + 41390651x^10 - 1368564777x^9 - 361745089708x^8 + 52039630950804x^7 - 1350212102075609x^6 - 202833046637545317x^5 + 15458794901317392766x^4 + 1792289418481984019550x^3 - 184645940533558790286339x^2 - 14754933471339430268597775*x + 2433324183085485312818967200
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{91}\cdot 3^{6}\cdot 5^{4}\cdot 31^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			5.8
Root			$11.1806 - 89.3919i$ of defining polynomial
Character	$\chi$	$=$	8.5
Dual form			8.16.b.a.5.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-28.3613 + 178.784i) q^{2} -2380.16i q^{3} +(-31159.3 - 10141.1i) q^{4} +9943.39i q^{5} +(425534. + 67504.4i) q^{6} +1.24365e6 q^{7} +(2.69677e6 - 5.28316e6i) q^{8} +8.68373e6 q^{9} +O(q^{10})$	\(q+(-28.3613 + 178.784i) q^{2} -2380.16i q^{3} +(-31159.3 - 10141.1i) q^{4} +9943.39i q^{5} +(425534. + 67504.4i) q^{6} +1.24365e6 q^{7} +(2.69677e6 - 5.28316e6i) q^{8} +8.68373e6 q^{9} +(-1.77772e6 - 282007. i) q^{10} +6.55864e7i q^{11} +(-2.41374e7 + 7.41641e7i) q^{12} +1.91929e8i q^{13} +(-3.52715e7 + 2.22344e8i) q^{14} +2.36669e7 q^{15} +(8.68059e8 + 6.31977e8i) q^{16} +1.98739e9 q^{17} +(-2.46282e8 + 1.55251e9i) q^{18} +8.13478e8i q^{19} +(1.00837e8 - 3.09829e8i) q^{20} -2.96009e9i q^{21} +(-1.17258e10 - 1.86011e9i) q^{22} +8.30671e8 q^{23} +(-1.25748e10 - 6.41876e9i) q^{24} +3.04187e10 q^{25} +(-3.43138e10 - 5.44335e9i) q^{26} -5.48214e10i q^{27} +(-3.87512e10 - 1.26119e10i) q^{28} -5.26318e10i q^{29} +(-6.71223e8 + 4.23125e9i) q^{30} +2.31580e11 q^{31} +(-1.37606e11 + 1.37271e11i) q^{32} +1.56106e11 q^{33} +(-5.63650e10 + 3.55314e11i) q^{34} +1.23661e10i q^{35} +(-2.70579e11 - 8.80623e10i) q^{36} +5.88641e11i q^{37} +(-1.45437e11 - 2.30713e10i) q^{38} +4.56822e11 q^{39} +(5.25325e10 + 2.68151e10i) q^{40} +2.88417e11 q^{41} +(5.29216e11 + 8.39518e10i) q^{42} -1.77551e12i q^{43} +(6.65116e11 - 2.04362e12i) q^{44} +8.63457e10i q^{45} +(-2.35589e10 + 1.48511e11i) q^{46} -6.45781e12 q^{47} +(1.50421e12 - 2.06612e12i) q^{48} -3.20090e12 q^{49} +(-8.62713e11 + 5.43837e12i) q^{50} -4.73032e12i q^{51} +(1.94637e12 - 5.98037e12i) q^{52} +1.55187e13i q^{53} +(9.80118e12 + 1.55480e12i) q^{54} -6.52151e11 q^{55} +(3.35384e12 - 6.57040e12i) q^{56} +1.93621e12 q^{57} +(9.40970e12 + 1.49270e12i) q^{58} -1.28387e13i q^{59} +(-7.37443e11 - 2.40007e11i) q^{60} +3.34293e13i q^{61} +(-6.56790e12 + 4.14027e13i) q^{62} +1.07995e13 q^{63} +(-2.06392e13 - 2.84950e13i) q^{64} -1.90843e12 q^{65} +(-4.42737e12 + 2.79093e13i) q^{66} -8.71055e13i q^{67} +(-6.19257e13 - 2.01543e13i) q^{68} -1.97713e12i q^{69} +(-2.21086e12 - 3.50718e11i) q^{70} +1.73139e13 q^{71} +(2.34181e13 - 4.58776e13i) q^{72} +1.25837e14 q^{73} +(-1.05239e14 - 1.66946e13i) q^{74} -7.24015e13i q^{75} +(8.24953e12 - 2.53474e13i) q^{76} +8.15665e13i q^{77} +(-1.29561e13 + 8.16724e13i) q^{78} -4.05635e12 q^{79} +(-6.28399e12 + 8.63145e12i) q^{80} -5.88183e12 q^{81} +(-8.17986e12 + 5.15642e13i) q^{82} +2.09495e14i q^{83} +(-3.00184e13 + 9.22342e13i) q^{84} +1.97614e13i q^{85} +(3.17432e14 + 5.03557e13i) q^{86} -1.25272e14 q^{87} +(3.46503e14 + 1.76872e14i) q^{88} -3.43643e14 q^{89} +(-1.54372e13 - 2.44887e12i) q^{90} +2.38693e14i q^{91} +(-2.58831e13 - 8.42390e12i) q^{92} -5.51198e14i q^{93} +(1.83152e14 - 1.15455e15i) q^{94} -8.08872e12 q^{95} +(3.26728e14 + 3.27526e14i) q^{96} -7.44295e14 q^{97} +(9.07815e13 - 5.72269e14i) q^{98} +5.69535e14i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 90 q^{2} + 51444 q^{4} - 189428 q^{6} - 1647088 q^{7} + 1889640 q^{8} - 57395630 q^{9}+O(q^{10}) $ 14 * q - 90 * q^2 + 51444 * q^4 - 189428 * q^6 - 1647088 * q^7 + 1889640 * q^8 - 57395630 * q^9	\( 14 q - 90 q^{2} + 51444 q^{4} - 189428 q^{6} - 1647088 q^{7} + 1889640 q^{8} - 57395630 q^{9} + 58467784 q^{10} + 399357832 q^{12} - 518960496 q^{14} + 712135312 q^{15} - 1435931120 q^{16} + 728554812 q^{17} + 526853306 q^{18} - 3449250768 q^{20} + 28367364252 q^{22} - 35548816080 q^{23} + 40155187088 q^{24} - 75899954794 q^{25} + 17666210712 q^{26} + 79863955680 q^{28} - 124878825712 q^{30} - 105758138816 q^{31} - 37651613280 q^{32} - 150458001384 q^{33} + 537472307308 q^{34} + 338679650892 q^{36} + 1649727781164 q^{38} - 2251546247120 q^{39} + 1251083710304 q^{40} - 53229185940 q^{41} - 2437011096800 q^{42} - 3416842360344 q^{44} - 3303531082064 q^{46} + 12527998446432 q^{47} - 6441543679584 q^{48} + 8427385380990 q^{49} + 1179755527374 q^{50} - 2436018627056 q^{52} + 3357642572216 q^{54} - 30557833792176 q^{55} + 7549064859072 q^{56} + 18277230892472 q^{57} - 8014960165320 q^{58} - 53574657402912 q^{60} + 77882578979904 q^{62} + 36142362113776 q^{63} + 76083381630528 q^{64} + 5437123965600 q^{65} - 134116957601160 q^{66} - 69772560247896 q^{68} + 133952399750848 q^{70} - 173249927708016 q^{71} + 163390222317848 q^{72} - 182057837882196 q^{73} + 2072780135688 q^{74} - 248503439494072 q^{76} + 636498768647600 q^{78} - 294370273271392 q^{79} + 766230078246336 q^{80} + 256903428263798 q^{81} - 10\!\cdots\!32 q^{82}+ \cdots - 51\!\cdots\!58 q^{98}+O(q^{100}) \) 14 * q - 90 * q^2 + 51444 * q^4 - 189428 * q^6 - 1647088 * q^7 + 1889640 * q^8 - 57395630 * q^9 + 58467784 * q^10 + 399357832 * q^12 - 518960496 * q^14 + 712135312 * q^15 - 1435931120 * q^16 + 728554812 * q^17 + 526853306 * q^18 - 3449250768 * q^20 + 28367364252 * q^22 - 35548816080 * q^23 + 40155187088 * q^24 - 75899954794 * q^25 + 17666210712 * q^26 + 79863955680 * q^28 - 124878825712 * q^30 - 105758138816 * q^31 - 37651613280 * q^32 - 150458001384 * q^33 + 537472307308 * q^34 + 338679650892 * q^36 + 1649727781164 * q^38 - 2251546247120 * q^39 + 1251083710304 * q^40 - 53229185940 * q^41 - 2437011096800 * q^42 - 3416842360344 * q^44 - 3303531082064 * q^46 + 12527998446432 * q^47 - 6441543679584 * q^48 + 8427385380990 * q^49 + 1179755527374 * q^50 - 2436018627056 * q^52 + 3357642572216 * q^54 - 30557833792176 * q^55 + 7549064859072 * q^56 + 18277230892472 * q^57 - 8014960165320 * q^58 - 53574657402912 * q^60 + 77882578979904 * q^62 + 36142362113776 * q^63 + 76083381630528 * q^64 + 5437123965600 * q^65 - 134116957601160 * q^66 - 69772560247896 * q^68 + 133952399750848 * q^70 - 173249927708016 * q^71 + 163390222317848 * q^72 - 182057837882196 * q^73 + 2072780135688 * q^74 - 248503439494072 * q^76 + 636498768647600 * q^78 - 294370273271392 * q^79 + 766230078246336 * q^80 + 256903428263798 * q^81 - 1021513680215332 * q^82 - 1701668269684544 * q^84 + 1418597672590812 * q^86 + 1493385390675312 * q^87 + 1948789255860816 * q^88 + 314213951649228 * q^89 - 3574690367103304 * q^90 - 3044080509008736 * q^92 + 3407319354561120 * q^94 - 851301047679984 * q^95 + 4705878559349312 * q^96 - 672574291859236 * q^97 - 5140373067292458 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/8\mathbb{Z}\right)^\times$.

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

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 $

$2$	−28.3613	+	178.784i	−0.156675	+	0.987650i
$2$	−28.3613	+	178.784i	−0.156675	+	0.987650i
$3$		−	2380.16i		−	0.628344i	−0.949366	−	0.314172i	$-0.898273\pi$
$3$		−	2380.16i		−	0.628344i	0.949366	−	0.314172i	$-0.101727\pi$
$4$	−31159.3	−	10141.1i	−0.950906	−	0.309481i
$5$			9943.39i			0.0569193i	0.999595	+	0.0284596i	$0.00906021\pi$
$5$			9943.39i			0.0569193i	−0.999595	+	0.0284596i	$0.990940\pi$
$6$	425534.	+	67504.4i	0.620584	+	0.0984459i
$7$	1.24365e6			0.570772			0.285386	−	0.958413i	$-0.407878\pi$
$7$	1.24365e6			0.570772			0.285386	+	0.958413i	$0.407878\pi$
$8$	2.69677e6	−	5.28316e6i	0.454642	−	0.890674i
$9$	8.68373e6			0.605184
$10$	−1.77772e6	−	282007.i	−0.0562163	−	0.00891784i
$11$			6.55864e7i			1.01477i	0.861719	+	0.507386i	$0.169388\pi$
$11$			6.55864e7i			1.01477i	−0.861719	+	0.507386i	$0.830612\pi$
$12$	−2.41374e7	+	7.41641e7i	−0.194460	+	0.597496i
$13$			1.91929e8i			0.848332i	0.905585	+	0.424166i	$0.139433\pi$
$13$			1.91929e8i			0.848332i	−0.905585	+	0.424166i	$0.860567\pi$
$14$	−3.52715e7	+	2.22344e8i	−0.0894259	+	0.563723i
$15$	2.36669e7			0.0357649
$16$	8.68059e8	+	6.31977e8i	0.808443	+	0.588574i
$17$	1.98739e9			1.17467			0.587336	−	0.809343i	$-0.300177\pi$
$17$	1.98739e9			1.17467			0.587336	+	0.809343i	$0.300177\pi$
$18$	−2.46282e8	+	1.55251e9i	−0.0948174	+	0.597710i
$19$			8.13478e8i			0.208782i	0.994536	+	0.104391i	$0.0332894\pi$
$19$			8.13478e8i			0.208782i	−0.994536	+	0.104391i	$0.966711\pi$
$20$	1.00837e8	−	3.09829e8i	0.0176154	−	0.0541249i
$21$		−	2.96009e9i		−	0.358641i
$22$	−1.17258e10	−	1.86011e9i	−1.00224	−	0.158990i
$23$	8.30671e8			0.0508710			0.0254355	−	0.999676i	$-0.491903\pi$
$23$	8.30671e8			0.0508710			0.0254355	+	0.999676i	$0.491903\pi$
$24$	−1.25748e10	−	6.41876e9i	−0.559649	−	0.285672i
$25$	3.04187e10			0.996760
$26$	−3.43138e10	−	5.44335e9i	−0.837855	−	0.132913i
$27$		−	5.48214e10i		−	1.00861i
$28$	−3.87512e10	−	1.26119e10i	−0.542750	−	0.176643i
$29$		−	5.26318e10i		−	0.566582i	−0.959034	−	0.283291i	$-0.908574\pi$
$29$		−	5.26318e10i		−	0.566582i	0.959034	−	0.283291i	$-0.0914262\pi$
$30$	−6.71223e8	+	4.23125e9i	−0.00560347	+	0.0353232i
$31$	2.31580e11			1.51178			0.755889	−	0.654700i	$-0.227205\pi$
$31$	2.31580e11			1.51178			0.755889	+	0.654700i	$0.227205\pi$
$32$	−1.37606e11	+	1.37271e11i	−0.707968	+	0.706244i
$33$	1.56106e11			0.637626
$34$	−5.63650e10	+	3.55314e11i	−0.184042	+	1.16017i
$35$			1.23661e10i			0.0324879i
$36$	−2.70579e11	−	8.80623e10i	−0.575473	−	0.187293i
$37$			5.88641e11i			1.01938i	0.860357	+	0.509691i	$0.170240\pi$
$37$			5.88641e11i			1.01938i	−0.860357	+	0.509691i	$0.829760\pi$
$38$	−1.45437e11	−	2.30713e10i	−0.206204	−	0.0327110i
$39$	4.56822e11			0.533044
$40$	5.25325e10	+	2.68151e10i	0.0506965	+	0.0258779i
$41$	2.88417e11			0.231282			0.115641	−	0.993291i	$-0.463108\pi$
$41$	2.88417e11			0.231282			0.115641	+	0.993291i	$0.463108\pi$
$42$	5.29216e11	+	8.39518e10i	0.354212	+	0.0561902i
$43$		−	1.77551e12i		−	0.996115i	−0.867144	−	0.498057i	$-0.834047\pi$
$43$		−	1.77551e12i		−	0.996115i	0.867144	−	0.498057i	$-0.165953\pi$
$44$	6.65116e11	−	2.04362e12i	0.314053	−	0.964953i
$45$			8.63457e10i			0.0344466i
$46$	−2.35589e10	+	1.48511e11i	−0.00797023	+	0.0502428i
$47$	−6.45781e12			−1.85931			−0.929654	−	0.368434i	$-0.879894\pi$
$47$	−6.45781e12			−1.85931			−0.929654	+	0.368434i	$0.879894\pi$
$48$	1.50421e12	−	2.06612e12i	0.369827	−	0.507980i
$49$	−3.20090e12			−0.674219
$50$	−8.62713e11	+	5.43837e12i	−0.156168	+	0.984450i
$51$		−	4.73032e12i		−	0.738098i
$52$	1.94637e12	−	5.98037e12i	0.262542	−	0.806683i
$53$			1.55187e13i			1.81463i	0.420454	+	0.907314i	$0.361871\pi$
$53$			1.55187e13i			1.81463i	−0.420454	+	0.907314i	$0.638129\pi$
$54$	9.80118e12	+	1.55480e12i	0.996151	+	0.158024i
$55$	−6.52151e11			−0.0577601
$56$	3.35384e12	−	6.57040e12i	0.259497	−	0.508372i
$57$	1.93621e12			0.131187
$58$	9.40970e12	+	1.49270e12i	0.559585	+	0.0887694i
$59$		−	1.28387e13i		−	0.671633i	−0.941927	−	0.335816i	$-0.890988\pi$
$59$		−	1.28387e13i		−	0.671633i	0.941927	−	0.335816i	$-0.109012\pi$
$60$	−7.37443e11	−	2.40007e11i	−0.0340090	−	0.0110685i
$61$			3.34293e13i			1.36193i	0.732317	+	0.680963i	$0.238439\pi$
$61$			3.34293e13i			1.36193i	−0.732317	+	0.680963i	$0.761561\pi$
$62$	−6.56790e12	+	4.14027e13i	−0.236858	+	1.49311i
$63$	1.07995e13			0.345422
$64$	−2.06392e13	−	2.84950e13i	−0.586601	−	0.809876i
$65$	−1.90843e12			−0.0482864
$66$	−4.42737e12	+	2.79093e13i	−0.0999002	+	0.629751i
$67$		−	8.71055e13i		−	1.75584i	−0.478808	−	0.877920i	$-0.658931\pi$
$67$		−	8.71055e13i		−	1.75584i	0.478808	−	0.877920i	$-0.341069\pi$
$68$	−6.19257e13	−	2.01543e13i	−1.11700	−	0.363539i
$69$		−	1.97713e12i		−	0.0319645i
$70$	−2.21086e12	−	3.50718e11i	−0.0320867	−	0.00509006i
$71$	1.73139e13			0.225922			0.112961	−	0.993599i	$-0.463966\pi$
$71$	1.73139e13			0.225922			0.112961	+	0.993599i	$0.463966\pi$
$72$	2.34181e13	−	4.58776e13i	0.275142	−	0.539022i
$73$	1.25837e14			1.33318			0.666589	−	0.745425i	$-0.267753\pi$
$73$	1.25837e14			1.33318			0.666589	+	0.745425i	$0.267753\pi$
$74$	−1.05239e14	−	1.66946e13i	−1.00679	−	0.159712i
$75$		−	7.24015e13i		−	0.626308i
$76$	8.24953e12	−	2.53474e13i	0.0646141	−	0.198532i
$77$			8.15665e13i			0.579204i
$78$	−1.29561e13	+	8.16724e13i	−0.0835148	+	0.526461i
$79$	−4.05635e12			−0.0237647			−0.0118824	−	0.999929i	$-0.503782\pi$
$79$	−4.05635e12			−0.0237647			−0.0118824	+	0.999929i	$0.503782\pi$
$80$	−6.28399e12	+	8.63145e12i	−0.0335012	+	0.0460160i
$81$	−5.88183e12			−0.0285677
$82$	−8.17986e12	+	5.15642e13i	−0.0362361	+	0.228425i
$83$			2.09495e14i			0.847400i	0.905803	+	0.423700i	$0.139269\pi$
$83$			2.09495e14i			0.847400i	−0.905803	+	0.423700i	$0.860731\pi$
$84$	−3.00184e13	+	9.22342e13i	−0.110992	+	0.341034i
$85$			1.97614e13i			0.0668615i
$86$	3.17432e14	+	5.03557e13i	0.983813	+	0.156067i
$87$	−1.25272e14			−0.356008
$88$	3.46503e14	+	1.76872e14i	0.903831	+	0.461358i
$89$	−3.43643e14			−0.823536			−0.411768	−	0.911289i	$-0.635089\pi$
$89$	−3.43643e14			−0.823536			−0.411768	+	0.911289i	$0.635089\pi$
$90$	−1.54372e13	−	2.44887e12i	−0.0340212	−	0.00539694i
$91$			2.38693e14i			0.484204i
$92$	−2.58831e13	−	8.42390e12i	−0.0483735	−	0.0157436i
$93$		−	5.51198e14i		−	0.949916i
$94$	1.83152e14	−	1.15455e15i	0.291308	−	1.83635i
$95$	−8.08872e12			−0.0118837
$96$	3.26728e14	+	3.27526e14i	0.443764	+	0.444847i
$97$	−7.44295e14			−0.935313			−0.467657	−	0.883910i	$-0.654902\pi$
$97$	−7.44295e14			−0.935313			−0.467657	+	0.883910i	$0.654902\pi$
$98$	9.07815e13	−	5.72269e14i	0.105634	−	0.665893i
$99$			5.69535e14i			0.614124i
$100$	−9.47825e14	−	3.08478e14i	−0.947825	−	0.308478i
$101$		−	5.21858e14i		−	0.484331i	−0.970235	−	0.242165i	$-0.922142\pi$
$101$		−	5.21858e14i		−	0.484331i	0.970235	−	0.242165i	$-0.0778576\pi$
$102$	8.45704e14	+	1.34158e14i	0.728983	+	0.115642i
$103$	−3.05095e14			−0.244431			−0.122215	−	0.992504i	$-0.539000\pi$
$103$	−3.05095e14			−0.244431			−0.122215	+	0.992504i	$0.539000\pi$
$104$	1.01399e15	+	5.17590e14i	0.755587	+	0.385687i
$105$	2.94333e13			0.0204136
$106$	−2.77450e15	−	4.40131e14i	−1.79222	−	0.284307i
$107$			1.74238e15i			1.04898i	0.851418	+	0.524488i	$0.175743\pi$
$107$			1.74238e15i			1.04898i	−0.851418	+	0.524488i	$0.824257\pi$
$108$	−5.55948e14	+	1.70820e15i	−0.312145	+	0.959090i
$109$		−	2.64214e15i		−	1.38439i	−0.721712	−	0.692194i	$-0.756644\pi$
$109$		−	2.64214e15i		−	1.38439i	0.721712	−	0.692194i	$-0.243356\pi$
$110$	1.84958e13	−	1.16594e14i	0.00904958	−	0.0570468i
$111$	1.40106e15			0.640523
$112$	1.07956e15	+	7.85957e14i	0.461437	+	0.335942i
$113$	3.80929e15			1.52320			0.761598	−	0.648050i	$-0.224415\pi$
$113$	3.80929e15			1.52320			0.761598	+	0.648050i	$0.224415\pi$
$114$	−5.49133e13	+	3.46163e14i	−0.0205538	+	0.129567i
$115$			8.25969e12i			0.00289554i
$116$	−5.33742e14	+	1.63997e15i	−0.175346	+	0.538766i
$117$			1.66666e15i			0.513397i
$118$	2.29536e15	+	3.64122e14i	0.663338	+	0.105228i
$119$	2.47162e15			0.670470
$120$	6.38242e13	−	1.25036e14i	0.0162602	−	0.0318548i
$121$	−1.24325e14			−0.0297625
$122$	−5.97662e15	−	9.48098e14i	−1.34511	−	0.213380i
$123$		−	6.86478e14i		−	0.145324i
$124$	−7.21586e15	−	2.34847e15i	−1.43756	−	0.467866i
$125$			6.05913e14i			0.113654i
$126$	−3.06288e14	+	1.93078e15i	−0.0541191	+	0.341156i
$127$	−3.11928e15			−0.519430			−0.259715	−	0.965685i	$-0.583629\pi$
$127$	−3.11928e15			−0.519430			−0.259715	+	0.965685i	$0.583629\pi$
$128$	5.67979e15	−	2.88180e15i	0.891780	−	0.452469i
$129$	−4.22600e15			−0.625902
$130$	5.41253e13	−	3.41195e14i	0.00756529	−	0.0476901i
$131$		−	5.48452e15i		−	0.723775i	−0.932222	−	0.361887i	$-0.882132\pi$
$131$		−	5.48452e15i		−	0.723775i	0.932222	−	0.361887i	$-0.117868\pi$
$132$	−4.86416e15	−	1.58308e15i	−0.606322	−	0.197333i
$133$			1.01168e15i			0.119167i
$134$	1.55731e16	+	2.47042e15i	1.73416	+	0.275097i
$135$	5.45111e14			0.0574092
$136$	5.35955e15	−	1.04997e16i	0.534056	−	1.04625i
$137$	−5.52159e15			−0.520786			−0.260393	−	0.965503i	$-0.583852\pi$
$137$	−5.52159e15			−0.520786			−0.260393	+	0.965503i	$0.583852\pi$
$138$	3.53479e14	+	5.60740e13i	0.0315697	+	0.00500805i
$139$		−	1.40813e16i		−	1.19133i	−0.803233	−	0.595665i	$-0.796889\pi$
$139$		−	1.40813e16i		−	1.19133i	0.803233	−	0.595665i	$-0.203111\pi$
$140$	1.25405e14	−	3.85318e14i	0.0100544	−	0.0308930i
$141$			1.53706e16i			1.16828i
$142$	−4.91045e14	+	3.09545e15i	−0.0353964	+	0.223132i
$143$	−1.25879e16			−0.860863
$144$	7.53800e15	+	5.48792e15i	0.489257	+	0.356196i
$145$	5.23338e14			0.0322494
$146$	−3.56891e15	+	2.24977e16i	−0.208876	+	1.31671i
$147$			7.61866e15i			0.423641i
$148$	5.96945e15	−	1.83416e16i	0.315479	−	0.969337i
$149$			3.53835e16i			1.77789i	0.458018	+	0.888943i	$0.348560\pi$
$149$			3.53835e16i			1.77789i	−0.458018	+	0.888943i	$0.651440\pi$
$150$	1.29442e16	+	2.05340e15i	0.618573	+	0.0981270i
$151$	−1.54452e16			−0.702208			−0.351104	−	0.936336i	$-0.614194\pi$
$151$	−1.54452e16			−0.702208			−0.351104	+	0.936336i	$0.614194\pi$
$152$	4.29773e15	+	2.19377e15i	0.185957	+	0.0949212i
$153$	1.72580e16			0.710893
$154$	−1.45828e16	−	2.31333e15i	−0.572050	−	0.0907469i
$155$			2.30269e15i			0.0860493i
$156$	−1.42343e16	−	4.63267e15i	−0.506874	−	0.164967i
$157$		−	3.86897e16i		−	1.31325i	−0.754216	−	0.656627i	$-0.771983\pi$
$157$		−	3.86897e16i		−	1.31325i	0.754216	−	0.656627i	$-0.228017\pi$
$158$	1.15043e14	−	7.25210e14i	0.00372334	−	0.0234712i
$159$	3.69371e16			1.14021
$160$	−1.36494e15	−	1.36827e15i	−0.0401989	−	0.0402970i
$161$	1.03306e15			0.0290358
$162$	1.66816e14	−	1.05158e15i	0.00447585	−	0.0282149i
$163$		−	4.32097e16i		−	1.10707i	−0.832827	−	0.553534i	$-0.813279\pi$
$163$		−	4.32097e16i		−	1.10707i	0.832827	−	0.553534i	$-0.186721\pi$
$164$	−8.98685e15	−	2.92485e15i	−0.219927	−	0.0715772i
$165$			1.55222e15i			0.0362932i
$166$	−3.74543e16	−	5.94155e15i	−0.836934	−	0.132767i
$167$	−3.46562e15			−0.0740299			−0.0370149	−	0.999315i	$-0.511785\pi$
$167$	−3.46562e15			−0.0740299			−0.0370149	+	0.999315i	$0.511785\pi$
$168$	−1.56386e16	−	7.98269e15i	−0.319432	−	0.163053i
$169$	1.43491e16			0.280333
$170$	−3.53302e15	−	5.60459e14i	−0.0660358	−	0.0104755i
$171$			7.06402e15i			0.126352i
$172$	−1.80056e16	+	5.53236e16i	−0.308278	+	0.947211i
$173$		−	7.03681e16i		−	1.15353i	−0.816909	−	0.576766i	$-0.804314\pi$
$173$		−	7.03681e16i		−	1.15353i	0.816909	−	0.576766i	$-0.195686\pi$
$174$	3.55288e15	−	2.23966e16i	0.0557777	−	0.351612i
$175$	3.78302e16			0.568923
$176$	−4.14491e16	+	5.69329e16i	−0.597269	+	0.820386i
$177$	−3.05583e16			−0.422016
$178$	9.74616e15	−	6.14378e16i	0.129028	−	0.813366i
$179$			1.11332e17i			1.41326i	0.707584	+	0.706629i	$0.249785\pi$
$179$			1.11332e17i			1.41326i	−0.707584	+	0.706629i	$0.750215\pi$
$180$	8.75638e14	−	2.69047e15i	0.0106606	−	0.0327555i
$181$			1.29611e16i			0.151374i	0.997132	+	0.0756871i	$0.0241150\pi$
$181$			1.29611e16i			0.151374i	−0.997132	+	0.0756871i	$0.975885\pi$
$182$	−4.26743e16	−	6.76962e15i	−0.478224	−	0.0758628i
$183$	7.95672e16			0.855758
$184$	2.24013e15	−	4.38857e15i	0.0231281	−	0.0453095i
$185$	−5.85308e15			−0.0580225
$186$	9.85452e16	+	1.56327e16i	0.938185	+	0.148828i
$187$			1.30346e17i			1.19202i
$188$	2.01221e17	+	6.54891e16i	1.76803	+	0.575420i
$189$		−	6.81786e16i		−	0.575685i
$190$	2.29406e14	−	1.44613e15i	0.00186189	−	0.0117370i
$191$	−1.61349e17			−1.25897			−0.629485	−	0.777013i	$-0.716734\pi$
$191$	−1.61349e17			−1.25897			−0.629485	+	0.777013i	$0.716734\pi$
$192$	−6.78227e16	+	4.91246e16i	−0.508881	+	0.368587i
$193$	3.53401e16			0.255028			0.127514	−	0.991837i	$-0.459300\pi$
$193$	3.53401e16			0.255028			0.127514	+	0.991837i	$0.459300\pi$
$194$	2.11091e16	−	1.33068e17i	0.146540	−	0.923762i
$195$			4.54236e15i			0.0303405i
$196$	9.97377e16	+	3.24605e16i	0.641119	+	0.208658i
$197$		−	5.78781e16i		−	0.358111i	−0.983839	−	0.179056i	$-0.942696\pi$
$197$		−	5.78781e16i		−	0.358111i	0.983839	−	0.179056i	$-0.0573042\pi$
$198$	−1.01824e17	−	1.61527e16i	−0.606540	−	0.0962181i
$199$	−1.30039e17			−0.745894			−0.372947	−	0.927853i	$-0.621653\pi$
$199$	−1.30039e17			−0.745894			−0.372947	+	0.927853i	$0.621653\pi$
$200$	8.20324e16	−	1.60707e17i	0.453169	−	0.887789i
$201$	−2.07325e17			−1.10327
$202$	9.32997e16	+	1.48005e16i	0.478349	+	0.0758827i
$203$		−	6.54554e16i		−	0.323389i
$204$	−4.79705e16	+	1.47393e17i	−0.228427	+	0.701862i
$205$			2.86784e15i			0.0131644i
$206$	8.65288e15	−	5.45461e16i	0.0382963	−	0.241412i
$207$	7.21333e15			0.0307863
$208$	−1.21295e17	+	1.66606e17i	−0.499306	+	0.685828i
$209$	−5.33530e16			−0.211866
$210$	−8.34765e14	+	5.26220e15i	−0.00319830	+	0.0201615i
$211$			4.82411e16i			0.178361i	0.996016	+	0.0891803i	$0.0284247\pi$
$211$			4.82411e16i			0.178361i	−0.996016	+	0.0891803i	$0.971575\pi$
$212$	1.57377e17	−	4.83553e17i	0.561592	−	1.72554i
$213$		−	4.12100e16i		−	0.141957i
$214$	−3.11510e17	−	4.94162e16i	−1.03602	−	0.164349i
$215$	1.76546e16			0.0566981
$216$	−2.89630e17	−	1.47841e17i	−0.898340	−	0.458555i
$217$	2.88004e17			0.862881
$218$	4.72372e17	+	7.49345e16i	1.36729	+	0.216899i
$219$		−	2.99514e17i		−	0.837694i
$220$	2.03205e16	+	6.61350e15i	0.0549244	+	0.0178756i
$221$			3.81438e17i			0.996512i
$222$	−3.97358e16	+	2.50487e17i	−0.100354	+	0.632612i
$223$	5.47989e17			1.33809			0.669045	−	0.743222i	$-0.266703\pi$
$223$	5.47989e17			1.33809			0.669045	+	0.743222i	$0.266703\pi$
$224$	−1.71134e17	+	1.70717e17i	−0.404089	+	0.403104i
$225$	2.64148e17			0.603224
$226$	−1.08036e17	+	6.81039e17i	−0.238647	+	1.50438i
$227$		−	3.57860e17i		−	0.764750i	−0.924007	−	0.382375i	$-0.875106\pi$
$227$		−	3.57860e17i		−	0.764750i	0.924007	−	0.382375i	$-0.124894\pi$
$228$	−6.03309e16	−	1.96352e16i	−0.124746	−	0.0405999i
$229$			5.19138e17i			1.03876i	0.854542	+	0.519381i	$0.173838\pi$
$229$			5.19138e17i			1.03876i	−0.854542	+	0.519381i	$0.826162\pi$
$230$	−1.47670e15	−	2.34255e14i	−0.00285978	−	0.000453660i
$231$	1.94141e17			0.363939
$232$	−2.78062e17	−	1.41936e17i	−0.504640	−	0.257592i
$233$	−2.40828e17			−0.423192			−0.211596	−	0.977357i	$-0.567866\pi$
$233$	−2.40828e17			−0.423192			−0.211596	+	0.977357i	$0.567866\pi$
$234$	−2.97972e17	−	4.72686e16i	−0.507057	−	0.0804366i
$235$		−	6.42125e16i		−	0.105830i
$236$	−1.30198e17	+	4.00045e17i	−0.207857	+	0.638659i
$237$			9.65478e15i			0.0149324i
$238$	−7.00983e16	+	4.41886e17i	−0.105046	+	0.662190i
$239$	−6.71814e17			−0.975584			−0.487792	−	0.872960i	$-0.662198\pi$
$239$	−6.71814e17			−0.975584			−0.487792	+	0.872960i	$0.662198\pi$
$240$	2.05443e16	+	1.49569e16i	0.0289139	+	0.0210503i
$241$	5.56278e17			0.758864			0.379432	−	0.925220i	$-0.376119\pi$
$241$	5.56278e17			0.758864			0.379432	+	0.925220i	$0.376119\pi$
$242$	3.52602e15	−	2.22273e16i	0.00466304	−	0.0293949i
$243$		−	7.72628e17i		−	0.990657i
$244$	3.39009e17	−	1.04163e18i	0.421490	−	1.29506i
$245$		−	3.18278e16i		−	0.0383761i
$246$	1.22731e17	+	1.94694e16i	0.143530	+	0.0227687i
$247$	−1.56130e17			−0.177117
$248$	6.24519e17	−	1.22347e18i	0.687318	−	1.34650i
$249$	4.98633e17			0.532458
$250$	−1.08327e17	−	1.71845e16i	−0.112251	−	0.0178068i
$251$			1.15081e17i			0.115731i	0.998324	+	0.0578654i	$0.0184294\pi$
$251$			1.15081e17i			0.115731i	−0.998324	+	0.0578654i	$0.981571\pi$
$252$	−3.36505e17	−	1.09519e17i	−0.328464	−	0.106902i
$253$			5.44807e16i			0.0516225i
$254$	8.84668e16	−	5.57677e17i	0.0813818	−	0.513015i
$255$	4.70354e16			0.0420120
$256$	3.54132e17	+	1.09719e18i	0.307161	+	0.951658i
$257$	−2.14601e18			−1.80773			−0.903864	−	0.427819i	$-0.859282\pi$
$257$	−2.14601e18			−1.80773			−0.903864	+	0.427819i	$0.859282\pi$
$258$	1.19855e17	−	7.55540e17i	0.0980635	−	0.618173i
$259$			7.32063e17i			0.581835i
$260$	5.94651e16	+	1.93535e16i	0.0459158	+	0.0149437i
$261$		−	4.57040e17i		−	0.342887i
$262$	9.80542e17	+	1.55548e17i	0.714836	+	0.113398i
$263$	−2.26162e18			−1.60233			−0.801164	−	0.598444i	$-0.795786\pi$
$263$	−2.26162e18			−1.60233			−0.801164	+	0.598444i	$0.795786\pi$
$264$	4.20983e17	−	8.24734e17i	0.289892	−	0.567917i
$265$	−1.54309e17			−0.103287
$266$	−1.80872e17	−	2.86925e16i	−0.117695	−	0.0186705i
$267$			8.17927e17i			0.517464i
$268$	−8.83343e17	+	2.71415e18i	−0.543399	+	1.66964i
$269$			9.71587e17i			0.581218i	0.956842	+	0.290609i	$0.0938580\pi$
$269$			9.71587e17i			0.581218i	−0.956842	+	0.290609i	$0.906142\pi$
$270$	−1.54600e16	+	9.74569e16i	−0.00899460	+	0.0567002i
$271$	1.94678e18			1.10166			0.550828	−	0.834619i	$-0.314312\pi$
$271$	1.94678e18			1.10166			0.550828	+	0.834619i	$0.314312\pi$
$272$	1.72517e18	+	1.25599e18i	0.949656	+	0.691382i
$273$	5.68127e17			0.304246
$274$	1.56599e17	−	9.87170e17i	0.0815944	−	0.514355i
$275$			1.99505e18i			1.01148i
$276$	−2.00502e16	+	6.16060e16i	−0.00989240	+	0.0303952i
$277$		−	3.11603e18i		−	1.49625i	−0.663560	−	0.748123i	$-0.730955\pi$
$277$		−	3.11603e18i		−	1.49625i	0.663560	−	0.748123i	$-0.269045\pi$
$278$	2.51751e18	+	3.99364e17i	1.17662	+	0.186652i
$279$	2.01098e18			0.914905
$280$	6.53320e16	+	3.33486e16i	0.0289362	+	0.0147704i
$281$	−1.24836e18			−0.538323			−0.269161	−	0.963095i	$-0.586747\pi$
$281$	−1.24836e18			−0.538323			−0.269161	+	0.963095i	$0.586747\pi$
$282$	−2.74802e18	−	4.35931e17i	−1.15386	−	0.183041i
$283$			1.29236e16i			0.00528429i	0.999997	+	0.00264215i	$0.000841022\pi$
$283$			1.29236e16i			0.00528429i	−0.999997	+	0.00264215i	$0.999159\pi$
$284$	−5.39490e17	−	1.75582e17i	−0.214831	−	0.0699185i
$285$			1.92525e16i			0.00746707i
$286$	3.57010e17	−	2.25052e18i	0.134876	−	0.850232i
$287$	3.58689e17			0.132009
$288$	−1.19494e18	+	1.19203e18i	−0.428451	+	0.427408i
$289$	1.08731e18			0.379855
$290$	−1.48425e16	+	9.35643e16i	−0.00505269	+	0.0318512i
$291$			1.77154e18i			0.587698i
$292$	−3.92100e18	−	1.27613e18i	−1.26773	−	0.412593i
$293$		−	2.74547e18i		−	0.865186i	−0.901589	−	0.432593i	$-0.857599\pi$
$293$		−	2.74547e18i		−	0.865186i	0.901589	−	0.432593i	$-0.142401\pi$
$294$	−1.36209e18	−	2.16075e17i	−0.418410	−	0.0663742i
$295$	1.27660e17			0.0382288
$296$	3.10988e18	+	1.58743e18i	0.907938	+	0.463455i
$297$	3.59554e18			1.02351
$298$	−6.32600e18	−	1.00352e18i	−1.75593	−	0.278551i
$299$			1.59430e17i			0.0431555i
$300$	−7.34228e17	+	2.25598e18i	−0.193830	+	0.595560i
$301$		−	2.20811e18i		−	0.568555i
$302$	4.38045e17	−	2.76135e18i	0.110019	−	0.693536i
$303$	−1.24211e18			−0.304326
$304$	−5.14099e17	+	7.06147e17i	−0.122884	+	0.168789i
$305$	−3.32401e17			−0.0775199
$306$	−4.89458e17	+	3.08545e18i	−0.111379	+	0.702114i
$307$		−	4.87988e18i		−	1.08361i	−0.840506	−	0.541803i	$-0.817742\pi$
$307$		−	4.87988e18i		−	1.08361i	0.840506	−	0.541803i	$-0.182258\pi$
$308$	8.27171e17	−	2.54155e18i	0.179252	−	0.550768i
$309$			7.26176e17i			0.153587i
$310$	−4.11683e17	−	6.53071e16i	−0.0849866	−	0.0134818i
$311$	−5.97100e17			−0.120322			−0.0601609	−	0.998189i	$-0.519161\pi$
$311$	−5.97100e17			−0.120322			−0.0601609	+	0.998189i	$0.519161\pi$
$312$	1.23195e18	−	2.41347e18i	0.242344	−	0.474768i
$313$	−1.48478e18			−0.285153			−0.142577	−	0.989784i	$-0.545539\pi$
$313$	−1.48478e18			−0.285153			−0.142577	+	0.989784i	$0.545539\pi$
$314$	6.91710e18	+	1.09729e18i	1.29703	+	0.205754i
$315$			1.07384e17i			0.0196612i
$316$	1.26393e17	+	4.11357e16i	0.0225980	+	0.00735472i
$317$			4.83677e18i			0.844521i	0.906474	+	0.422261i	$0.138763\pi$
$317$			4.83677e18i			0.844521i	−0.906474	+	0.422261i	$0.861237\pi$
$318$	−1.04758e18	+	6.60376e18i	−0.178643	+	1.12613i
$319$	3.45193e18			0.574952
$320$	2.83337e17	−	2.05223e17i	0.0460976	−	0.0333889i
$321$	4.14716e18			0.659118
$322$	−2.92990e16	+	1.84695e17i	−0.00454919	+	0.0286772i
$323$			1.61670e18i			0.245251i
$324$	1.83274e17	+	5.96480e16i	0.0271652	+	0.00884115i
$325$			5.83823e18i			0.845583i
$326$	7.72519e18	+	1.22548e18i	1.09339	+	0.173450i
$327$	−6.28873e18			−0.869871
$328$	7.77794e17	−	1.52375e18i	0.105150	−	0.205997i
$329$	−8.03125e18			−1.06124
$330$	−2.77513e17	−	4.40231e16i	−0.0358450	−	0.00568625i
$331$			1.17425e18i			0.148270i	0.997248	+	0.0741348i	$0.0236195\pi$
$331$			1.17425e18i			0.148270i	−0.997248	+	0.0741348i	$0.976380\pi$
$332$	2.12450e18	−	6.52772e18i	0.262254	−	0.805797i
$333$			5.11160e18i			0.616915i
$334$	9.82893e16	−	6.19596e17i	0.0115987	−	0.0731156i
$335$	8.66124e17			0.0999411
$336$	1.87071e18	−	2.56953e18i	0.211087	−	0.289941i
$337$	−6.61936e18			−0.730452			−0.365226	−	0.930919i	$-0.619008\pi$
$337$	−6.61936e18			−0.730452			−0.365226	+	0.930919i	$0.619008\pi$
$338$	−4.06959e17	+	2.56539e18i	−0.0439213	+	0.276871i
$339$		−	9.06673e18i		−	0.957090i
$340$	2.00402e17	−	6.15751e17i	0.0206924	−	0.0635790i
$341$			1.51885e19i			1.53411i
$342$	−1.26293e18	−	2.00345e17i	−0.124791	−	0.0197962i
$343$	−9.88510e18			−0.955598
$344$	−9.38030e18	−	4.78815e18i	−0.887214	−	0.452876i
$345$	1.96594e16			0.00181939
$346$	1.25807e19	+	1.99573e18i	1.13929	+	0.180730i
$347$		−	1.48938e19i		−	1.31988i	−0.751318	−	0.659941i	$-0.770581\pi$
$347$		−	1.48938e19i		−	1.31988i	0.751318	−	0.659941i	$-0.229419\pi$
$348$	3.90339e18	+	1.27039e18i	0.338530	+	0.110178i
$349$		−	1.42663e19i		−	1.21093i	−0.795871	−	0.605466i	$-0.792987\pi$
$349$		−	1.42663e19i		−	1.21093i	0.795871	−	0.605466i	$-0.207013\pi$
$350$	−1.07291e18	+	6.76343e18i	−0.0891362	+	0.561897i
$351$	1.05218e19			0.855634
$352$	−9.00313e18	−	9.02511e18i	−0.716677	−	0.718427i
$353$	4.56762e18			0.355942			0.177971	−	0.984036i	$-0.443047\pi$
$353$	4.56762e18			0.355942			0.177971	+	0.984036i	$0.443047\pi$
$354$	8.66671e17	−	5.46332e18i	0.0661195	−	0.416804i
$355$			1.72159e17i			0.0128593i
$356$	1.07077e19	+	3.48491e18i	0.783105	+	0.254869i
$357$		−	5.88286e18i		−	0.421286i
$358$	−1.99043e19	−	3.15751e18i	−1.39580	−	0.221423i
$359$	−1.36834e19			−0.939692			−0.469846	−	0.882749i	$-0.655690\pi$
$359$	−1.36834e19			−0.939692			−0.469846	+	0.882749i	$0.655690\pi$
$360$	4.56178e17	+	2.32855e17i	0.0306807	+	0.0156609i
$361$	1.45194e19			0.956410
$362$	−2.31723e18	−	3.67593e17i	−0.149505	−	0.0237166i
$363$			2.95914e17i			0.0187011i
$364$	2.42060e18	−	7.43749e18i	0.149852	−	0.460432i
$365$			1.25125e18i			0.0758836i
$366$	−2.25663e18	+	1.42253e19i	−0.134076	+	0.845189i
$367$	1.90250e19			1.10747			0.553733	−	0.832694i	$-0.313203\pi$
$367$	1.90250e19			1.10747			0.553733	+	0.832694i	$0.313203\pi$
$368$	7.21072e17	+	5.24965e17i	0.0411263	+	0.0299414i
$369$	2.50453e18			0.139968
$370$	1.66001e17	−	1.04644e18i	0.00909070	−	0.0573060i
$371$			1.92999e19i			1.03574i
$372$	−5.58973e18	+	1.71749e19i	−0.293981	+	0.903281i
$373$		−	2.25771e18i		−	0.116373i	−0.998306	−	0.0581865i	$-0.981468\pi$
$373$		−	2.25771e18i		−	0.116373i	0.998306	−	0.0581865i	$-0.0185318\pi$
$374$	−2.33037e19	−	3.69677e18i	−1.17730	−	0.186761i
$375$	1.44217e18			0.0714138
$376$	−1.74153e19	+	3.41176e19i	−0.845320	+	1.65604i
$377$	1.01016e19			0.480650
$378$	1.21892e19	+	1.93363e18i	0.568575	+	0.0901956i
$379$			2.46190e19i			1.12584i	0.826511	+	0.562920i	$0.190322\pi$
$379$			2.46190e19i			1.12584i	−0.826511	+	0.562920i	$0.809678\pi$
$380$	2.52039e17	+	8.20283e16i	0.0113003	+	0.00367779i
$381$			7.42440e18i			0.326380i
$382$	4.57605e18	−	2.88465e19i	0.197250	−	1.24342i
$383$	1.64962e19			0.697257			0.348629	−	0.937261i	$-0.386647\pi$
$383$	1.64962e19			0.697257			0.348629	+	0.937261i	$0.386647\pi$
$384$	−6.85915e18	−	1.35188e19i	−0.284306	−	0.560344i
$385$	−8.11047e17			−0.0329678
$386$	−1.00229e18	+	6.31824e18i	−0.0399566	+	0.251879i
$387$		−	1.54180e19i		−	0.602833i
$388$	2.31917e19	+	7.54794e18i	0.889394	+	0.289461i
$389$		−	2.02343e19i		−	0.761143i	−0.924751	−	0.380572i	$-0.875727\pi$
$389$		−	2.02343e19i		−	0.761143i	0.924751	−	0.380572i	$-0.124273\pi$
$390$	−8.12101e17	−	1.28827e17i	−0.0299658	−	0.00475360i
$391$	1.65087e18			0.0597568
$392$	−8.63210e18	+	1.69109e19i	−0.306529	+	0.600510i
$393$	−1.30540e19			−0.454779
$394$	1.03477e19	+	1.64150e18i	0.353689	+	0.0561072i
$395$		−	4.03339e16i		−	0.00135267i
$396$	5.77569e18	−	1.77463e19i	0.190060	−	0.583974i
$397$		−	4.94869e19i		−	1.59795i	−0.601367	−	0.798973i	$-0.705377\pi$
$397$		−	4.94869e19i		−	1.59795i	0.601367	−	0.798973i	$-0.294623\pi$
$398$	3.68808e18	−	2.32490e19i	0.116863	−	0.736682i
$399$	2.40796e18			0.0748779
$400$	2.64052e19	+	1.92239e19i	0.805824	+	0.586667i
$401$	−2.17764e19			−0.652234			−0.326117	−	0.945329i	$-0.605740\pi$
$401$	−2.17764e19			−0.652234			−0.326117	+	0.945329i	$0.605740\pi$
$402$	5.88001e18	−	3.70664e19i	0.172855	−	1.08965i
$403$			4.44469e19i			1.28249i
$404$	−5.29220e18	+	1.62607e19i	−0.149891	+	0.460553i
$405$		−	5.84853e16i		−	0.00162605i
$406$	1.17024e19	+	1.85640e18i	0.319395	+	0.0506671i
$407$	−3.86068e19			−1.03444
$408$	−2.49910e19	−	1.27566e19i	−0.657405	−	0.335571i
$409$	−3.84378e19			−0.992735			−0.496368	−	0.868112i	$-0.665333\pi$
$409$	−3.84378e19			−0.992735			−0.496368	+	0.868112i	$0.665333\pi$
$410$	−5.12723e17	−	8.13355e16i	−0.0130018	−	0.00206253i
$411$			1.31423e19i			0.327233i
$412$	9.50655e18	+	3.09399e18i	0.232431	+	0.0756467i
$413$		−	1.59669e19i		−	0.383349i
$414$	−2.04579e17	+	1.28963e18i	−0.00482346	+	0.0304061i
$415$	−2.08309e18			−0.0482334
$416$	−2.63463e19	−	2.64107e19i	−0.599129	−	0.600592i
$417$	−3.35158e19			−0.748565
$418$	1.51316e18	−	9.53866e18i	0.0331942	−	0.209250i
$419$		−	4.27455e19i		−	0.921053i	−0.887646	−	0.460527i	$-0.847661\pi$
$419$		−	4.27455e19i		−	0.921053i	0.887646	−	0.460527i	$-0.152339\pi$
$420$	−9.17120e17	−	2.98485e17i	−0.0194114	−	0.00631761i
$421$			5.62283e19i			1.16907i	0.811370	+	0.584533i	$0.198722\pi$
$421$			5.62283e19i			1.16907i	−0.811370	+	0.584533i	$0.801278\pi$
$422$	−8.62473e18	−	1.36818e18i	−0.176158	−	0.0279447i
$423$	−5.60779e19			−1.12522
$424$	8.19880e19	+	4.18505e19i	1.61624	+	0.825006i
$425$	6.04539e19			1.17087
$426$	7.36768e18	+	1.16877e18i	0.140204	+	0.0222411i
$427$			4.15743e19i			0.777350i
$428$	1.76696e19	−	5.42915e19i	0.324638	−	0.997478i
$429$			2.99613e19i			0.540918i
$430$	−5.00706e17	+	3.15635e18i	−0.00888320	+	0.0559979i
$431$	9.82364e19			1.71275			0.856373	−	0.516358i	$-0.172712\pi$
$431$	9.82364e19			1.71275			0.856373	+	0.516358i	$0.172712\pi$
$432$	3.46459e19	−	4.75883e19i	0.593640	−	0.815402i
$433$	6.33031e19			1.06602			0.533010	−	0.846109i	$-0.321061\pi$
$433$	6.33031e19			1.06602			0.533010	+	0.846109i	$0.321061\pi$
$434$	−8.16816e18	+	5.14905e19i	−0.135192	+	0.852224i
$435$		−	1.24563e18i		−	0.0202637i
$436$	−2.67942e19	+	8.23273e19i	−0.428441	+	1.31642i
$437$			6.75733e17i			0.0106210i
$438$	5.35482e19	+	8.49458e18i	0.827349	+	0.131246i
$439$	−9.36988e19			−1.42315			−0.711574	−	0.702611i	$-0.752018\pi$
$439$	−9.36988e19			−1.42315			−0.711574	+	0.702611i	$0.752018\pi$
$440$	−1.75870e18	+	3.44542e18i	−0.0262602	+	0.0514454i
$441$	−2.77957e19			−0.408027
$442$	−6.81950e19	−	1.08181e19i	−0.984205	−	0.156129i
$443$		−	9.95376e19i		−	1.41241i	−0.708010	−	0.706203i	$-0.750407\pi$
$443$		−	9.95376e19i		−	1.41241i	0.708010	−	0.706203i	$-0.249593\pi$
$444$	−4.36560e19	−	1.42083e19i	−0.609077	−	0.198230i
$445$		−	3.41698e18i		−	0.0468751i
$446$	−1.55417e19	+	9.79716e19i	−0.209646	+	1.32157i
$447$	8.42185e19			1.11712
$448$	−2.56679e19	−	3.54378e19i	−0.334815	−	0.462255i
$449$	6.08712e19			0.780844			0.390422	−	0.920636i	$-0.372329\pi$
$449$	6.08712e19			0.780844			0.390422	+	0.920636i	$0.372329\pi$
$450$	−7.49157e18	+	4.72254e19i	−0.0945103	+	0.595774i
$451$			1.89162e19i			0.234698i
$452$	−1.18695e20	−	3.86303e19i	−1.44842	−	0.471400i
$453$			3.67620e19i			0.441228i
$454$	6.39796e19	+	1.01494e19i	0.755306	+	0.119817i
$455$	−2.37341e18			−0.0275605
$456$	5.22152e18	−	1.02293e19i	0.0596431	−	0.116845i
$457$	−5.20069e19			−0.584372			−0.292186	−	0.956362i	$-0.594383\pi$
$457$	−5.20069e19			−0.584372			−0.292186	+	0.956362i	$0.594383\pi$
$458$	−9.28134e19	−	1.47234e19i	−1.02593	−	0.162749i
$459$		−	1.08952e20i		−	1.18478i
$460$	8.37620e16	−	2.57366e17i	0.000896115	−	0.00275339i
$461$			9.63171e19i			1.01379i	0.862009	+	0.506893i	$0.169206\pi$
$461$			9.63171e19i			1.01379i	−0.862009	+	0.506893i	$0.830794\pi$
$462$	−5.50610e18	+	3.47093e19i	−0.0570202	+	0.359444i
$463$	7.66416e19			0.780921			0.390460	−	0.920620i	$-0.372316\pi$
$463$	7.66416e19			0.780921			0.390460	+	0.920620i	$0.372316\pi$
$464$	3.32620e19	−	4.56875e19i	0.333476	−	0.458049i
$465$	5.48077e18			0.0540685
$466$	6.83018e18	−	4.30561e19i	0.0663037	−	0.417965i
$467$		−	1.17176e20i		−	1.11934i	−0.828714	−	0.559672i	$-0.810927\pi$
$467$		−	1.17176e20i		−	1.11934i	0.828714	−	0.559672i	$-0.189073\pi$
$468$	1.69017e19	−	5.19320e19i	0.158887	−	0.488192i
$469$		−	1.08329e20i		−	1.00218i
$470$	1.14802e19	+	1.82115e18i	0.104523	+	0.0165810i
$471$	−9.20879e19			−0.825174
$472$	−6.78290e19	−	3.46232e19i	−0.598206	−	0.305353i
$473$	1.16449e20			1.01083
$474$	−1.72612e18	−	2.73822e17i	−0.0147480	−	0.00233954i
$475$			2.47449e19i			0.208106i
$476$	−7.70139e19	−	2.50649e19i	−0.637554	−	0.207498i
$477$			1.34761e20i			1.09818i
$478$	1.90535e19	−	1.20109e20i	0.152850	−	0.963536i
$479$	1.22565e20			0.967944			0.483972	−	0.875084i	$-0.339194\pi$
$479$	1.22565e20			0.967944			0.483972	+	0.875084i	$0.339194\pi$
$480$	−3.25671e18	+	3.24878e18i	−0.0253204	+	0.0252587i
$481$	−1.12977e20			−0.864775
$482$	−1.57767e19	+	9.94535e19i	−0.118895	+	0.749492i
$483$		−	2.45886e18i		−	0.0182444i
$484$	3.87388e18	+	1.26079e18i	0.0283013	+	0.00921091i
$485$		−	7.40081e18i		−	0.0532373i
$486$	1.38133e20	+	2.19127e19i	0.978423	+	0.155212i
$487$	−1.18086e20			−0.823628			−0.411814	−	0.911268i	$-0.635105\pi$
$487$	−1.18086e20			−0.823628			−0.411814	+	0.911268i	$0.635105\pi$
$488$	1.76612e20	+	9.01513e19i	1.21303	+	0.619189i
$489$	−1.02846e20			−0.695619
$490$	5.69029e18	+	9.02676e17i	0.0379021	+	0.00601258i
$491$			1.58783e20i			1.04158i	0.853685	+	0.520789i	$0.174362\pi$
$491$			1.58783e20i			1.04158i	−0.853685	+	0.520789i	$0.825638\pi$
$492$	−6.96162e18	+	2.13902e19i	−0.0449751	+	0.138190i
$493$		−	1.04600e20i		−	0.665548i
$494$	4.42804e18	−	2.79135e19i	0.0277498	−	0.174929i
$495$	−5.66310e18			−0.0349555
$496$	2.01025e20	+	1.46353e20i	1.22219	+	0.889794i
$497$	2.15325e19			0.128950
$498$	−1.41418e19	+	8.91474e19i	−0.0834231	+	0.525882i
$499$			2.07261e20i			1.20438i	0.798353	+	0.602190i	$0.205705\pi$
$499$			2.07261e20i			1.20438i	−0.798353	+	0.602190i	$0.794295\pi$
$500$	6.14461e18	−	1.88798e19i	0.0351738	−	0.108074i
$501$			8.24873e18i			0.0465162i
$502$	−2.05745e19	−	3.26383e18i	−0.114302	−	0.0181322i
$503$	−2.98541e20			−1.63397			−0.816984	−	0.576661i	$-0.804356\pi$
$503$	−2.98541e20			−1.63397			−0.816984	+	0.576661i	$0.804356\pi$
$504$	2.91239e19	−	5.70556e19i	0.157044	−	0.307659i
$505$	5.18903e18			0.0275677
$506$	−9.74027e18	−	1.54514e18i	−0.0509850	−	0.00808797i
$507$		−	3.41532e19i		−	0.176146i
$508$	9.71946e19	+	3.16329e19i	0.493929	+	0.160754i
$509$			1.35908e20i			0.680552i	0.940326	+	0.340276i	$0.110521\pi$
$509$			1.35908e20i			0.680552i	−0.940326	+	0.340276i	$0.889479\pi$
$510$	−1.33398e18	+	8.40916e18i	−0.00658224	+	0.0414932i
$511$	1.56498e20			0.760941
$512$	−2.06203e20	+	3.21955e19i	−0.988029	+	0.154266i
$513$	4.45960e19			0.210579
$514$	6.08635e19	−	3.83672e20i	0.283226	−	1.78540i
$515$		−	3.03368e18i		−	0.0139128i
$516$	1.31679e20	+	4.28562e19i	0.595174	+	0.193705i
$517$		−	4.23544e20i		−	1.88677i
$518$	−1.30881e20	−	2.07622e19i	−0.574650	−	0.0911592i
$519$	−1.67487e20			−0.724815
$520$	−5.14659e18	+	1.00825e19i	−0.0219530	+	0.0430075i
$521$	−4.87015e19			−0.204767			−0.102383	−	0.994745i	$-0.532647\pi$
$521$	−4.87015e19			−0.204767			−0.102383	+	0.994745i	$0.532647\pi$
$522$	8.17114e19	+	1.29622e19i	0.338652	+	0.0537219i
$523$			3.31732e20i			1.35527i	0.735400	+	0.677633i	$0.236994\pi$
$523$			3.31732e20i			1.35527i	−0.735400	+	0.677633i	$0.763006\pi$
$524$	−5.56188e19	+	1.70894e20i	−0.223994	+	0.688242i
$525$		−	9.00420e19i		−	0.357479i
$526$	6.41424e19	−	4.04341e20i	0.251045	−	1.58254i
$527$	4.60240e20			1.77584
$528$	1.35509e20	+	9.86555e19i	0.515484	+	0.375290i
$529$	−2.65945e20			−0.997412
$530$	4.37639e18	−	2.75879e19i	0.0161826	−	0.102012i
$531$		−	1.11488e20i		−	0.406462i
$532$	1.02595e19	−	3.15232e19i	0.0368799	−	0.113317i
$533$			5.53555e19i			0.196204i
$534$	−1.46232e20	−	2.31974e19i	−0.511073	−	0.0810738i
$535$	−1.73252e19			−0.0597070
$536$	−4.60193e20	−	2.34904e20i	−1.56388	−	0.798279i
$537$	2.64988e20			0.888012
$538$	−1.73704e20	−	2.75554e19i	−0.574041	−	0.0910626i
$539$		−	2.09935e20i		−	0.684179i
$540$	−1.69853e19	−	5.52800e18i	−0.0545907	−	0.0177670i
$541$		−	5.67118e20i		−	1.79760i	−0.438356	−	0.898801i	$-0.644439\pi$
$541$		−	5.67118e20i		−	1.79760i	0.438356	−	0.898801i	$-0.355561\pi$
$542$	−5.52130e19	+	3.48052e20i	−0.172602	+	1.08805i
$543$	3.08495e19			0.0951150
$544$	−2.73478e20	+	2.72812e20i	−0.831631	+	0.829605i
$545$	2.62719e19			0.0787983
$546$	−1.61128e19	+	1.01572e20i	−0.0476679	+	0.300489i
$547$			2.33879e20i			0.682475i	0.939977	+	0.341238i	$0.110846\pi$
$547$			2.33879e20i			0.682475i	−0.939977	+	0.341238i	$0.889154\pi$
$548$	1.72049e20	+	5.59948e19i	0.495219	+	0.161173i
$549$			2.90291e20i			0.824217i
$550$	−3.56683e20	−	5.65822e19i	−0.998993	−	0.158475i
$551$	4.28147e19			0.118292
$552$	−1.04455e19	−	5.33188e18i	−0.0284699	−	0.0145324i
$553$	−5.04468e18			−0.0135642
$554$	5.57095e20	+	8.83745e19i	1.47777	+	0.234425i
$555$			1.39313e19i			0.0364581i
$556$	−1.42800e20	+	4.38763e20i	−0.368694	+	1.13284i
$557$			2.53453e20i			0.645630i	0.946462	+	0.322815i	$0.104629\pi$
$557$			2.53453e20i			0.645630i	−0.946462	+	0.322815i	$0.895371\pi$
$558$	−5.70339e19	+	3.59530e20i	−0.143343	+	0.903606i
$559$	3.40772e20			0.845036
$560$	−7.81508e18	+	1.07345e19i	−0.0191216	+	0.0262646i
$561$	3.10244e20			0.749001
$562$	3.54051e19	−	2.23187e20i	0.0843419	−	0.531675i
$563$		−	1.13398e20i		−	0.266558i	−0.991079	−	0.133279i	$-0.957449\pi$
$563$		−	1.13398e20i		−	0.266558i	0.991079	−	0.133279i	$-0.0425507\pi$
$564$	1.55875e20	−	4.78938e20i	0.361562	−	1.11093i
$565$			3.78772e19i			0.0866992i
$566$	−2.31054e18	−	3.66531e17i	−0.00521903	−	0.000827918i
$567$	−7.31493e18			−0.0163056
$568$	4.66918e19	−	9.14724e19i	0.102714	−	0.201223i
$569$	−8.17119e19			−0.177396			−0.0886979	−	0.996059i	$-0.528271\pi$
$569$	−8.17119e19			−0.177396			−0.0886979	+	0.996059i	$0.528271\pi$
$570$	−3.44203e18	−	5.46024e17i	−0.00737485	−	0.00116991i
$571$		−	2.75197e20i		−	0.581933i	−0.956733	−	0.290967i	$-0.906023\pi$
$571$		−	2.75197e20i		−	0.581933i	0.956733	−	0.290967i	$-0.0939768\pi$
$572$	3.92231e20	+	1.27655e20i	0.818600	+	0.266421i
$573$			3.84036e20i			0.791066i
$574$	−1.01729e19	+	6.41278e19i	−0.0206826	+	0.130379i
$575$	2.52680e19			0.0507062
$576$	−1.79225e20	−	2.47443e20i	−0.355002	−	0.490124i
$577$	3.55434e20			0.694929			0.347465	−	0.937693i	$-0.387043\pi$
$577$	3.55434e20			0.694929			0.347465	+	0.937693i	$0.387043\pi$
$578$	−3.08374e19	+	1.94393e20i	−0.0595140	+	0.375164i
$579$		−	8.41153e19i		−	0.160245i
$580$	−1.63068e19	−	5.30720e18i	−0.0306662	−	0.00998058i
$581$			2.60539e20i			0.483672i
$582$	−3.16723e20	−	5.02432e19i	−0.580440	−	0.0920778i
$583$	−1.01782e21			−1.84143
$584$	3.39355e20	−	6.64819e20i	0.606119	−	1.18743i
$585$	−1.65723e19			−0.0292222
$586$	4.90845e20	+	7.78649e19i	0.854501	+	0.135553i
$587$		−	1.74771e20i		−	0.300388i	−0.988657	−	0.150194i	$-0.952010\pi$
$587$		−	1.74771e20i		−	0.300388i	0.988657	−	0.150194i	$-0.0479899\pi$
$588$	7.72613e19	−	2.37392e20i	0.131109	−	0.402843i
$589$			1.88385e20i			0.315632i
$590$	−3.62061e18	+	2.28236e19i	−0.00598952	+	0.0377567i
$591$	−1.37759e20			−0.225017
$592$	−3.72007e20	+	5.10975e20i	−0.599982	+	0.824113i
$593$	−5.71741e20			−0.910519			−0.455260	−	0.890359i	$-0.650454\pi$
$593$	−5.71741e20			−0.910519			−0.455260	+	0.890359i	$0.650454\pi$
$594$	−1.01974e20	+	6.42824e20i	−0.160358	+	1.01087i
$595$			2.45763e19i			0.0381627i
$596$	3.58827e20	−	1.10252e21i	0.550222	−	1.69060i
$597$			3.09515e20i			0.468678i
$598$	−2.85035e19	−	4.52164e18i	−0.0426225	−	0.00676140i
$599$	−1.14459e21			−1.69024			−0.845119	−	0.534578i	$-0.820471\pi$
$599$	−1.14459e21			−1.69024			−0.845119	+	0.534578i	$0.820471\pi$
$600$	−3.82509e20	−	1.95250e20i	−0.557836	−	0.284746i
$601$	−7.89436e20			−1.13699			−0.568497	−	0.822685i	$-0.692475\pi$
$601$	−7.89436e20			−1.13699			−0.568497	+	0.822685i	$0.692475\pi$
$602$	3.94774e20	+	6.26248e19i	0.561533	+	0.0890785i
$603$		−	7.56401e20i		−	1.06261i
$604$	4.81261e20	+	1.56631e20i	0.667734	+	0.217320i
$605$		−	1.23621e18i		−	0.00169406i
$606$	3.52277e19	−	2.22069e20i	0.0476804	−	0.300568i
$607$	1.43171e21			1.91399			0.956994	−	0.290108i	$-0.0936912\pi$
$607$	1.43171e21			1.91399			0.956994	+	0.290108i	$0.0936912\pi$
$608$	−1.11667e20	−	1.11940e20i	−0.147451	−	0.147811i
$609$	−1.55795e20			−0.203200
$610$	9.42730e18	−	5.94278e19i	0.0121455	−	0.0765625i
$611$		−	1.23944e21i		−	1.57731i
$612$	−5.37746e20	−	1.75014e20i	−0.675993	−	0.220008i
$613$		−	2.16151e20i		−	0.268413i	−0.990953	−	0.134207i	$-0.957151\pi$
$613$		−	2.16151e20i		−	0.268413i	0.990953	−	0.134207i	$-0.0428486\pi$
$614$	8.72443e20	+	1.38400e20i	1.07022	+	0.169774i
$615$	6.82592e18			0.00827176
$616$	4.30929e20	+	2.19966e20i	0.515882	+	0.263330i
$617$	4.00200e20			0.473302			0.236651	−	0.971595i	$-0.423950\pi$
$617$	4.00200e20			0.473302			0.236651	+	0.971595i	$0.423950\pi$
$618$	−1.29829e20	−	2.05953e19i	−0.151690	−	0.0240632i
$619$			1.50880e21i			1.74162i	0.491623	+	0.870808i	$0.336404\pi$
$619$			1.50880e21i			1.74162i	−0.491623	+	0.870808i	$0.663596\pi$
$620$	2.33517e19	−	7.17501e19i	0.0266306	−	0.0818248i
$621$		−	4.55386e19i		−	0.0513089i
$622$	1.69345e19	−	1.06752e20i	0.0188514	−	0.118836i
$623$	−4.27372e20			−0.470052
$624$	3.96549e20	+	2.88701e20i	0.430936	+	0.313736i
$625$	9.22280e20			0.990291
$626$	4.21101e19	−	2.65454e20i	0.0446765	−	0.281632i
$627$			1.26989e20i			0.133125i
$628$	−3.92355e20	+	1.20554e21i	−0.406427	+	1.24878i
$629$			1.16986e21i			1.19744i
$630$	−1.91985e19	−	3.04554e18i	−0.0194184	−	0.00308042i
$631$	1.14570e21			1.14512			0.572558	−	0.819864i	$-0.305951\pi$
$631$	1.14570e21			1.14512			0.572558	+	0.819864i	$0.305951\pi$
$632$	−1.09391e19	+	2.14304e19i	−0.0108044	+	0.0211666i
$633$	1.14822e20			0.112072
$634$	−8.64735e20	−	1.37177e20i	−0.834092	−	0.132316i
$635$		−	3.10162e19i		−	0.0295656i
$636$	−1.15093e21	−	3.74582e20i	−1.08423	−	0.352873i
$637$		−	6.14345e20i		−	0.571962i
$638$	−9.79010e19	+	6.17148e20i	−0.0900807	+	0.567851i
$639$	1.50350e20			0.136724
$640$	2.86548e19	+	5.64764e19i	0.0257542	+	0.0507595i
$641$	−9.28279e20			−0.824600			−0.412300	−	0.911048i	$-0.635274\pi$
$641$	−9.28279e20			−0.824600			−0.412300	+	0.911048i	$0.635274\pi$
$642$	−1.17619e20	+	7.41445e20i	−0.103267	+	0.650978i
$643$			1.38224e21i			1.19950i	0.800188	+	0.599749i	$0.204733\pi$
$643$			1.38224e21i			1.19950i	−0.800188	+	0.599749i	$0.795267\pi$
$644$	−3.21895e19	−	1.04764e19i	−0.0276103	−	0.00898601i
$645$		−	4.20208e19i		−	0.0356259i
$646$	−2.89040e20	−	4.58516e19i	−0.242222	−	0.0384247i
$647$	4.33047e20			0.358718			0.179359	−	0.983784i	$-0.442598\pi$
$647$	4.33047e20			0.358718			0.179359	+	0.983784i	$0.442598\pi$
$648$	−1.58620e19	+	3.10747e19i	−0.0129881	+	0.0254445i
$649$	8.42046e20			0.681554
$650$	−1.04378e21	−	1.65580e20i	−0.835140	−	0.132482i
$651$		−	6.85497e20i		−	0.542186i
$652$	−4.38192e20	+	1.34638e21i	−0.342616	+	1.05272i
$653$		−	1.49679e21i		−	1.15694i	−0.815702	−	0.578472i	$-0.803649\pi$
$653$		−	1.49679e21i		−	1.15694i	0.815702	−	0.578472i	$-0.196351\pi$
$654$	1.78356e20	−	1.12432e21i	0.136287	−	0.859128i
$655$	5.45347e19			0.0411967
$656$	2.50363e20	+	1.82273e20i	0.186978	+	0.136126i
$657$	1.09274e21			0.806819
$658$	2.27776e20	−	1.43586e21i	0.166270	−	1.04813i
$659$			1.32459e21i			0.955961i	0.878370	+	0.477981i	$0.158631\pi$
$659$			1.32459e21i			0.955961i	−0.878370	+	0.477981i	$0.841369\pi$
$660$	1.57412e19	−	4.83662e19i	0.0112320	−	0.0345114i
$661$		−	2.40747e21i		−	1.69844i	−0.528042	−	0.849218i	$-0.677074\pi$
$661$		−	2.40747e21i		−	1.69844i	0.528042	−	0.849218i	$-0.322926\pi$
$662$	−2.09938e20	−	3.33033e19i	−0.146438	−	0.0232302i
$663$	9.07886e20			0.626152
$664$	1.10680e21	+	5.64961e20i	0.754757	+	0.385264i
$665$	−1.00595e19			−0.00678290
$666$	−9.13871e20	−	1.44971e20i	−0.609296	−	0.0966553i
$667$		−	4.37197e19i		−	0.0288226i
$668$	1.07986e20	+	3.51450e19i	0.0703954	+	0.0229108i
$669$		−	1.30430e21i		−	0.840780i
$670$	−2.45644e19	+	1.54849e20i	−0.0156583	+	0.0987068i
$671$	−2.19251e21			−1.38205
$672$	4.06335e20	+	4.07327e20i	0.253288	+	0.253906i
$673$	2.34745e19			0.0144705			0.00723524	−	0.999974i	$-0.497697\pi$
$673$	2.34745e19			0.0144705			0.00723524	+	0.999974i	$0.497697\pi$
$674$	1.87733e20	−	1.18343e21i	0.114444	−	0.721431i
$675$		−	1.66760e21i		−	1.00534i
$676$	−4.47108e20	−	1.45515e20i	−0.266571	−	0.0867578i
$677$			1.10436e21i			0.651171i	0.945513	+	0.325586i	$0.105561\pi$
$677$			1.10436e21i			0.651171i	−0.945513	+	0.325586i	$0.894439\pi$
$678$	1.62098e21	+	2.57144e20i	0.945270	+	0.149952i
$679$	−9.25642e20			−0.533850
$680$	1.04403e20	+	5.32921e19i	0.0595518	+	0.0303981i
$681$	−8.51766e20			−0.480526
$682$	−2.71545e21	−	4.30765e20i	−1.51516	−	0.240357i
$683$			1.38917e21i			0.766658i	0.923612	+	0.383329i	$0.125222\pi$
$683$			1.38917e21i			0.766658i	−0.923612	+	0.383329i	$0.874778\pi$
$684$	7.16367e19	−	2.20110e20i	0.0391034	−	0.120149i
$685$		−	5.49033e19i		−	0.0296428i
$686$	2.80354e20	−	1.76729e21i	0.149719	−	0.943796i
$687$	1.23563e21			0.652700
$688$	1.12208e21	−	1.54125e21i	0.586288	−	0.805302i
$689$	−2.97850e21			−1.53941
$690$	−5.57565e17	+	3.51478e18i	−0.000285054	+	0.00179693i
$691$			2.53593e21i			1.28248i	0.767338	+	0.641242i	$0.221581\pi$
$691$			2.53593e21i			1.28248i	−0.767338	+	0.641242i	$0.778419\pi$
$692$	−7.13607e20	+	2.19262e21i	−0.356996	+	1.09690i
$693$			7.08301e20i			0.350525i
$694$	2.66277e21	+	4.22407e20i	1.30358	+	0.206793i
$695$	1.40016e20			0.0678096
$696$	−3.37831e20	+	6.61833e20i	−0.161856	+	0.317087i
$697$	5.73197e20			0.271680
$698$	2.55058e21	+	4.04610e20i	1.19598	+	0.189723i
$699$			5.73209e20i			0.265910i
$700$	−1.17876e21	−	3.83639e20i	−0.540992	−	0.176071i
$701$			2.17192e21i			0.986185i	0.869977	+	0.493093i	$0.164134\pi$
$701$			2.17192e21i			0.986185i	−0.869977	+	0.493093i	$0.835866\pi$
$702$	−2.98412e20	+	1.88113e21i	−0.134057	+	0.845067i
$703$	−4.78846e20			−0.212829
$704$	1.86888e21	−	1.35365e21i	0.821840	−	0.595266i
$705$	−1.52836e20			−0.0664979
$706$	−1.29543e20	+	8.16616e20i	−0.0557674	+	0.351546i
$707$		−	6.49008e20i		−	0.276442i
$708$	9.52173e20	+	3.09893e20i	0.401298	+	0.130606i
$709$		−	5.09501e20i		−	0.212470i	−0.994341	−	0.106235i	$-0.966120\pi$
$709$		−	5.09501e20i		−	0.212470i	0.994341	−	0.106235i	$-0.0338797\pi$
$710$	−3.07793e19	−	4.88266e18i	−0.0127005	−	0.00201474i
$711$	−3.52243e19			−0.0143820
$712$	−9.26729e20	+	1.81552e21i	−0.374414	+	0.733503i
$713$	1.92367e20			0.0769057
$714$	1.05176e21	+	1.66845e20i	0.416083	+	0.0660051i
$715$		−	1.25167e20i		−	0.0489997i
$716$	1.12902e21	−	3.46902e21i	0.437376	−	1.34388i
$717$			1.59903e21i			0.613002i
$718$	3.88078e20	−	2.44637e21i	0.147226	−	0.928087i
$719$	−1.66156e21			−0.623804			−0.311902	−	0.950114i	$-0.600966\pi$
$719$	−1.66156e21			−0.623804			−0.311902	+	0.950114i	$0.600966\pi$
$720$	−5.45685e19	+	7.49532e19i	−0.0202744	+	0.0278482i
$721$	−3.79431e20			−0.139514
$722$	−4.11788e20	+	2.59583e21i	−0.149846	+	0.944598i
$723$		−	1.32403e21i		−	0.476828i
$724$	1.31439e20	−	4.03858e20i	0.0468474	−	0.143943i
$725$		−	1.60099e21i		−	0.564746i
$726$	−5.29047e19	−	8.39250e18i	−0.0184701	−	0.00292999i
$727$	1.87981e21			0.649539			0.324769	−	0.945793i	$-0.394713\pi$
$727$	1.87981e21			0.649539			0.324769	+	0.945793i	$0.394713\pi$
$728$	1.26105e21	+	6.43700e20i	0.431268	+	0.220140i
$729$	−1.92338e21			−0.651041
$730$	−2.23703e20	−	3.54870e19i	−0.0749464	−	0.0118891i
$731$		−	3.52863e21i		−	1.17011i
$732$	−2.47926e21	−	8.06896e20i	−0.813745	−	0.264841i
$733$			2.94480e21i			0.956701i	0.878169	+	0.478351i	$0.158765\pi$
$733$			2.94480e21i			0.956701i	−0.878169	+	0.478351i	$0.841235\pi$
$734$	−5.39574e20	+	3.40137e21i	−0.173513	+	1.09379i
$735$	−7.57552e19			−0.0241134
$736$	−1.14306e20	+	1.14027e20i	−0.0360151	+	0.0359274i
$737$	5.71294e21			1.78178
$738$	−7.10317e19	+	4.47770e20i	−0.0219295	+	0.138239i
$739$		−	5.74402e21i		−	1.75543i	−0.479187	−	0.877713i	$-0.659068\pi$
$739$		−	5.74402e21i		−	1.75543i	0.479187	−	0.877713i	$-0.340932\pi$
$740$	1.82378e20	+	5.93565e19i	0.0551740	+	0.0179569i
$741$			3.71615e20i			0.111290i
$742$	−3.45050e21	−	5.47369e20i	−1.02295	−	0.162275i
$743$	2.12554e21			0.623810			0.311905	−	0.950113i	$-0.399033\pi$
$743$	2.12554e21			0.623810			0.311905	+	0.950113i	$0.399033\pi$
$744$	−2.91207e21	−	1.48646e21i	−0.846066	−	0.431872i
$745$	−3.51832e20			−0.101196
$746$	4.03642e20	+	6.40316e19i	0.114936	+	0.0182328i
$747$			1.81920e21i			0.512833i
$748$	1.32185e21	−	4.06148e21i	0.368909	−	1.13350i
$749$			2.16692e21i			0.598726i
$750$	−4.09018e19	+	2.57837e20i	−0.0111888	+	0.0705319i
$751$	−5.41638e21			−1.46693			−0.733465	−	0.679727i	$-0.762098\pi$
$751$	−5.41638e21			−1.46693			−0.733465	+	0.679727i	$0.762098\pi$
$752$	−5.60576e21	−	4.08119e21i	−1.50315	−	1.09434i
$753$	2.73910e20			0.0727187
$754$	−2.86493e20	+	1.80600e21i	−0.0753059	+	0.474714i
$755$		−	1.53577e20i		−	0.0399692i
$756$	−6.91404e20	+	2.12440e21i	−0.178163	+	0.547422i
$757$		−	1.53010e21i		−	0.390392i	−0.980764	−	0.195196i	$-0.937466\pi$
$757$		−	1.53010e21i		−	0.390392i	0.980764	−	0.195196i	$-0.0625342\pi$
$758$	−4.40148e21	−	6.98227e20i	−1.11194	−	0.176391i
$759$	1.29673e20			0.0324367
$760$	−2.18135e19	+	4.27340e19i	−0.00540285	+	0.0105845i
$761$	4.57526e21			1.12210			0.561049	−	0.827782i	$-0.310398\pi$
$761$	4.57526e21			1.12210			0.561049	+	0.827782i	$0.310398\pi$
$762$	−1.32736e21	−	2.10565e20i	−0.322350	−	0.0511357i
$763$		−	3.28590e21i		−	0.790170i
$764$	5.02751e21	+	1.63625e21i	1.19716	+	0.389627i
$765$			1.71603e20i			0.0404635i
$766$	−4.67853e20	+	2.94925e21i	−0.109243	+	0.688646i
$767$	2.46412e21			0.569767
$768$	2.61148e21	−	8.42893e20i	0.597968	−	0.193003i
$769$	−1.36697e21			−0.309965			−0.154983	−	0.987917i	$-0.549532\pi$
$769$	−1.36697e21			−0.309965			−0.154983	+	0.987917i	$0.549532\pi$
$770$	2.30023e19	−	1.45002e20i	0.00516525	−	0.0325607i
$771$			5.10785e21i			1.13587i
$772$	−1.10117e21	−	3.58387e20i	−0.242508	−	0.0789264i
$773$		−	7.87361e20i		−	0.171723i	−0.996307	−	0.0858614i	$-0.972636\pi$
$773$		−	7.87361e20i		−	0.171723i	0.996307	−	0.0858614i	$-0.0273642\pi$
$774$	2.75650e21	+	4.37275e20i	0.595388	+	0.0944491i
$775$	7.04436e21			1.50688
$776$	−2.00720e21	+	3.93223e21i	−0.425233	+	0.833059i
$777$	1.74243e21			0.365592
$778$	3.61757e21	+	5.73871e20i	0.751743	+	0.119252i
$779$			2.34620e20i			0.0482875i
$780$	4.60644e19	−	1.41537e20i	0.00938979	−	0.0288509i
$781$			1.13556e21i			0.229259i
$782$	−4.68208e19	+	2.95149e20i	−0.00936242	+	0.0590188i
$783$	−2.88535e21			−0.571459
$784$	−2.77857e21	−	2.02289e21i	−0.545068	−	0.396828i
$785$	3.84707e20			0.0747494
$786$	3.70229e20	−	2.33385e21i	0.0712527	−	0.449163i
$787$		−	3.99883e21i		−	0.762294i	−0.924514	−	0.381147i	$-0.875529\pi$
$787$		−	3.99883e21i		−	0.762294i	0.924514	−	0.381147i	$-0.124471\pi$
$788$	−5.86946e20	+	1.80344e21i	−0.110829	+	0.340530i
$789$			5.38302e21i			1.00681i
$790$	7.21104e18	+	1.14392e18i	0.00133596	+	0.000211930i
$791$	4.73742e21			0.869397
$792$	3.00894e21	+	1.53591e21i	0.546985	+	0.279207i
$793$	−6.41606e21			−1.15537
$794$	8.84746e21	+	1.40351e21i	1.57821	+	0.250359i
$795$			3.67280e20i			0.0648999i
$796$	4.05194e21	+	1.31874e21i	0.709275	+	0.230840i
$797$		−	5.29831e21i		−	0.918756i	−0.888241	−	0.459378i	$-0.848072\pi$
$797$		−	5.29831e21i		−	0.918756i	0.888241	−	0.459378i	$-0.151928\pi$
$798$	−6.82929e19	+	4.30505e20i	−0.0117315	+	0.0739531i
$799$	−1.28342e22			−2.18408
$800$	−4.18581e21	+	4.17561e21i	−0.705675	+	0.703956i
$801$	−2.98411e21			−0.498391
$802$	6.17607e20	−	3.89327e21i	0.102189	−	0.644180i
$803$			8.25322e21i			1.35287i
$804$	6.46011e21	+	2.10250e21i	1.04911	+	0.341441i
$805$			1.02722e19i			0.00165269i
$806$	−7.94639e21	−	1.26057e21i	−1.26665	−	0.200934i
$807$	2.31253e21			0.365205
$808$	−2.75706e21	−	1.40733e21i	−0.431381	−	0.220197i
$809$	−8.17463e21			−1.26723			−0.633613	−	0.773650i	$-0.718429\pi$
$809$	−8.17463e21			−1.26723			−0.633613	+	0.773650i	$0.718429\pi$
$810$	1.04562e19	+	1.65872e18i	0.00160597	+	0.000254762i
$811$			6.50807e21i			0.990367i	0.868788	+	0.495183i	$0.164899\pi$
$811$			6.50807e21i			0.990367i	−0.868788	+	0.495183i	$0.835101\pi$
$812$	−6.63788e20	+	2.03954e21i	−0.100083	+	0.307513i
$813$		−	4.63364e21i		−	0.692219i
$814$	1.09494e21	−	6.90227e21i	0.162071	−	1.02167i
$815$	4.29650e20			0.0630134
$816$	2.98945e21	−	4.10620e21i	0.434425	−	0.596710i
$817$	1.44434e21			0.207971
$818$	1.09014e21	−	6.87205e21i	0.155537	−	0.980475i
$819$			2.07274e21i			0.293033i
$820$	2.90829e19	−	8.93597e19i	0.00407412	−	0.0125181i
$821$		−	5.84596e21i		−	0.811488i	−0.913987	−	0.405744i	$-0.867012\pi$
$821$		−	5.84596e21i		−	0.811488i	0.913987	−	0.405744i	$-0.132988\pi$
$822$	−2.34963e21	−	3.72731e20i	−0.323192	−	0.0512693i
$823$	1.50787e21			0.205525			0.102762	−	0.994706i	$-0.467232\pi$
$823$	1.50787e21			0.205525			0.102762	+	0.994706i	$0.467232\pi$
$824$	−8.22773e20	+	1.61187e21i	−0.111129	+	0.217708i
$825$	4.74855e21			0.635560
$826$	2.85462e21	+	4.52841e20i	0.378615	+	0.0600613i
$827$		−	8.62150e20i		−	0.113316i	−0.998394	−	0.0566580i	$-0.981956\pi$
$827$		−	8.62150e20i		−	0.113316i	0.998394	−	0.0566580i	$-0.0180445\pi$
$828$	−2.24762e20	−	7.31509e19i	−0.0292749	−	0.00952778i
$829$		−	4.85501e20i		−	0.0626658i	−0.999509	−	0.0313329i	$-0.990025\pi$
$829$		−	4.85501e20i		−	0.0626658i	0.999509	−	0.0313329i	$-0.00997521\pi$
$830$	5.90791e19	−	3.72423e20i	0.00755698	−	0.0476377i
$831$	−7.41665e21			−0.940157
$832$	5.46902e21	−	3.96126e21i	0.687044	−	0.497632i
$833$	−6.36144e21			−0.791987
$834$	9.50551e20	−	5.99208e21i	0.117282	−	0.739320i
$835$		−	3.44600e19i		−	0.00421373i
$836$	1.66244e21	+	5.41057e20i	0.201465	+	0.0655686i
$837$		−	1.26955e22i		−	1.52479i
$838$	7.64220e21	+	1.21232e21i	0.909679	+	0.144306i
$839$	4.54768e21			0.536507			0.268254	−	0.963348i	$-0.413554\pi$
$839$	4.54768e21			0.536507			0.268254	+	0.963348i	$0.413554\pi$
$840$	7.93750e19	−	1.55501e20i	0.00928088	−	0.0181818i
$841$	5.85909e21			0.678985
$842$	−1.00527e22	−	1.59470e21i	−1.15463	−	0.183164i
$843$			2.97130e21i			0.338252i
$844$	4.89216e20	−	1.50316e21i	0.0551992	−	0.169604i
$845$			1.42679e20i			0.0159564i
$846$	1.59044e21	−	1.00258e22i	0.176295	−	1.11133i
$847$	−1.54617e20			−0.0169876
$848$	−9.80748e21	+	1.34712e22i	−1.06804	+	1.46702i
$849$	3.07604e19			0.00332035
$850$	−1.71455e21	+	1.08082e22i	−0.183446	+	1.15641i
$851$			4.88967e20i			0.0518571i
$852$	−4.17914e20	+	1.28407e21i	−0.0439329	+	0.134987i
$853$			1.10589e22i			1.15238i	0.817317	+	0.576188i	$0.195460\pi$
$853$			1.10589e22i			1.15238i	−0.817317	+	0.576188i	$0.804540\pi$
$854$	−7.43282e21	−	1.17910e21i	−0.767749	−	0.121792i
$855$	−7.02403e19			−0.00719185
$856$	9.20530e21	+	4.69882e21i	0.934296	+	0.476909i
$857$	1.25141e22			1.25905			0.629526	−	0.776979i	$-0.283249\pi$
$857$	1.25141e22			1.25905			0.629526	+	0.776979i	$0.283249\pi$
$858$	−5.35660e21	−	8.49741e20i	−0.534238	−	0.0847485i
$859$			8.74633e20i			0.0864723i	0.999065	+	0.0432362i	$0.0137668\pi$
$859$			8.74633e20i			0.0864723i	−0.999065	+	0.0432362i	$0.986233\pi$
$860$	−5.50104e20	−	1.79036e20i	−0.0539146	−	0.0175470i
$861$		−	8.53738e20i		−	0.0829471i
$862$	−2.78611e21	+	1.75631e22i	−0.268345	+	1.69159i
$863$	−7.93718e20			−0.0757854			−0.0378927	−	0.999282i	$-0.512065\pi$
$863$	−7.93718e20			−0.0757854			−0.0378927	+	0.999282i	$0.512065\pi$
$864$	7.52541e21	+	7.54378e21i	0.712323	+	0.714062i
$865$	6.99697e20			0.0656582
$866$	−1.79536e21	+	1.13176e22i	−0.167019	+	1.05286i
$867$		−	2.58797e21i		−	0.238680i
$868$	−8.97400e21	−	2.92067e21i	−0.820518	−	0.267045i
$869$		−	2.66042e20i		−	0.0241158i
$870$	2.22698e20	+	3.53276e19i	0.0200135	+	0.00317483i
$871$	1.67181e22			1.48953
$872$	−1.39589e22	−	7.12527e21i	−1.23304	−	0.629401i
$873$	−6.46326e21			−0.566037
$874$	−1.20810e20	−	1.91646e19i	−0.0104898	−	0.00166404i
$875$			7.53543e20i			0.0648706i
$876$	−3.03739e21	+	9.33263e21i	−0.259250	+	0.796568i
$877$			4.20486e21i			0.355840i	0.984045	+	0.177920i	$0.0569368\pi$
$877$			4.20486e21i			0.355840i	−0.984045	+	0.177920i	$0.943063\pi$
$878$	2.65742e21	−	1.67518e22i	0.222972	−	1.40557i
$879$	−6.53466e21			−0.543634
$880$	−5.66106e20	−	4.12144e20i	−0.0466957	−	0.0339961i
$881$	1.10473e22			0.903519			0.451760	−	0.892140i	$-0.350797\pi$
$881$	1.10473e22			0.903519			0.451760	+	0.892140i	$0.350797\pi$
$882$	7.88322e20	−	4.96943e21i	0.0639278	−	0.402988i
$883$		−	4.28634e21i		−	0.344653i	−0.985040	−	0.172326i	$-0.944872\pi$
$883$		−	4.28634e21i		−	0.344653i	0.985040	−	0.172326i	$-0.0551284\pi$
$884$	3.86819e21	−	1.18853e22i	0.308401	−	0.947589i
$885$		−	3.03853e20i		−	0.0240208i
$886$	1.77957e22	+	2.82301e21i	1.39496	+	0.221289i
$887$	1.74633e22			1.35737			0.678686	−	0.734428i	$-0.262550\pi$
$887$	1.74633e22			1.35737			0.678686	+	0.734428i	$0.262550\pi$
$888$	3.77835e21	−	7.40203e21i	0.291209	−	0.570497i
$889$	−3.87929e21			−0.296476
$890$	6.10900e20	+	9.69098e19i	0.0462962	+	0.00734417i
$891$		−	3.85768e20i		−	0.0289897i
$892$	−1.70749e22	−	5.55719e21i	−1.27240	−	0.414113i
$893$		−	5.25328e21i		−	0.388191i
$894$	−2.38854e21	+	1.50569e22i	−0.175026	+	1.10333i
$895$	−1.10702e21			−0.0804416
$896$	7.06367e21	−	3.58395e21i	0.509003	−	0.258257i
$897$	3.79469e20			0.0271165
$898$	−1.72638e21	+	1.08828e22i	−0.122339	+	0.771200i
$899$		−	1.21885e22i		−	0.856546i
$900$	−8.23066e21	−	2.67874e21i	−0.573609	−	0.186686i
$901$			3.08418e22i			2.13159i
$902$	−3.38191e21	−	5.36487e20i	−0.231800	−	0.0367714i
$903$	−5.25566e21			−0.357248
$904$	1.02728e22	−	2.01251e22i	0.692509	−	1.35667i
$905$	−1.28877e20			−0.00861611
$906$	−6.57246e21	−	1.04262e21i	−0.435779	−	0.0691296i
$907$		−	2.71139e22i		−	1.78294i	−0.453077	−	0.891471i	$-0.649674\pi$
$907$		−	2.71139e22i		−	1.78294i	0.453077	−	0.891471i	$-0.350326\pi$
$908$	−3.62909e21	+	1.11507e22i	−0.236675	+	0.727205i
$909$		−	4.53167e21i		−	0.293109i
$910$	6.73130e19	−	4.24328e20i	0.00431806	−	0.0272202i
$911$	−1.30962e22			−0.833217			−0.416609	−	0.909086i	$-0.636781\pi$
$911$	−1.30962e22			−0.833217			−0.416609	+	0.909086i	$0.636781\pi$
$912$	1.68074e21	+	1.22364e21i	0.106057	+	0.0772133i
$913$	−1.37400e22			−0.859918
$914$	1.47498e21	−	9.29799e21i	0.0915567	−	0.577155i
$915$			7.91168e20i			0.0487091i
$916$	5.26461e21	−	1.61760e22i	0.321477	−	0.987766i
$917$		−	6.82081e21i		−	0.413110i
$918$	1.94788e22	+	3.09001e21i	1.17015	+	0.185626i
$919$	−2.44676e22			−1.45789			−0.728946	−	0.684571i	$-0.759990\pi$
$919$	−2.44676e22			−1.45789			−0.728946	+	0.684571i	$0.759990\pi$
$920$	4.36372e19	+	2.22745e19i	0.00257898	+	0.00131644i
$921$	−1.16149e22			−0.680877
$922$	−1.72199e22	−	2.73167e21i	−1.00127	−	0.158835i
$923$			3.32305e21i			0.191657i
$924$	−6.04931e21	−	1.96880e21i	−0.346072	−	0.112632i
$925$			1.79057e22i			1.01608i
$926$	−2.17365e21	+	1.37023e22i	−0.122351	+	0.771277i
$927$	−2.64937e21			−0.147926
$928$	7.22483e21	+	7.24247e21i	0.400145	+	0.401122i
$929$	1.99321e21			0.109506			0.0547528	−	0.998500i	$-0.482563\pi$
$929$	1.99321e21			0.109506			0.0547528	+	0.998500i	$0.482563\pi$
$930$	−1.55442e20	+	9.79873e20i	−0.00847121	+	0.0534008i
$931$		−	2.60386e21i		−	0.140765i
$932$	7.50402e21	+	2.44225e21i	0.402415	+	0.130970i
$933$			1.42119e21i			0.0756034i
$934$	2.09493e22	+	3.32327e21i	1.10552	+	0.175374i
$935$	−1.29608e21			−0.0678492
$936$	8.80524e21	+	4.49461e21i	0.457269	+	0.233412i
$937$	1.03535e22			0.533386			0.266693	−	0.963782i	$-0.414069\pi$
$937$	1.03535e22			0.533386			0.266693	+	0.963782i	$0.414069\pi$
$938$	1.93674e22	+	3.07234e21i	0.989807	+	0.157018i
$939$			3.53401e21i			0.179174i
$940$	−6.51183e20	+	2.00082e21i	−0.0327525	+	0.100635i
$941$		−	8.05907e21i		−	0.402127i	−0.979578	−	0.201063i	$-0.935560\pi$
$941$		−	8.05907e21i		−	0.402127i	0.979578	−	0.201063i	$-0.0644397\pi$
$942$	2.61173e21	−	1.64638e22i	0.129284	−	0.814984i
$943$	2.39579e20			0.0117655
$944$	8.11377e21	−	1.11448e22i	0.395306	−	0.542977i
$945$	6.77927e20			0.0327676
$946$	−3.30265e21	+	2.08192e22i	−0.158372	+	0.998346i
$947$			1.49168e22i			0.709663i	0.934930	+	0.354832i	$0.115462\pi$
$947$			1.49168e22i			0.709663i	−0.934930	+	0.354832i	$0.884538\pi$
$948$	9.79098e19	−	3.00836e20i	0.00462129	−	0.0141993i
$949$			2.41519e22i			1.13098i
$950$	−4.42399e21	−	7.01798e20i	−0.205536	−	0.0326050i
$951$	1.15123e22			0.530650
$952$	6.66540e21	−	1.30580e22i	0.304824	−	0.597170i
$953$	−1.13867e22			−0.516654			−0.258327	−	0.966058i	$-0.583171\pi$
$953$	−1.13867e22			−0.516654			−0.258327	+	0.966058i	$0.583171\pi$
$954$	−2.40930e22	−	3.82198e21i	−1.08462	−	0.172058i
$955$		−	1.60435e21i		−	0.0716596i
$956$	2.09332e22	+	6.81291e21i	0.927688	+	0.301925i
$957$		−	8.21615e21i		−	0.361267i
$958$	−3.47610e21	+	2.19126e22i	−0.151653	+	0.955990i
$959$	−6.86692e21			−0.297250
$960$	−4.88465e20	−	6.74387e20i	−0.0209797	−	0.0289651i
$961$	3.01640e22			1.28547
$962$	3.20418e21	−	2.01985e22i	0.135489	−	0.854095i
$963$			1.51304e22i			0.634824i
$964$	−1.73332e22	−	5.64125e21i	−0.721608	−	0.234854i
$965$			3.51401e20i			0.0145160i
$966$	4.39604e20	+	6.97364e19i	0.0180191	+	0.00285845i
$967$	−1.30131e21			−0.0529274			−0.0264637	−	0.999650i	$-0.508425\pi$
$967$	−1.30131e21			−0.0529274			−0.0264637	+	0.999650i	$0.508425\pi$
$968$	−3.35277e20	+	6.56830e20i	−0.0135313	+	0.0265087i
$969$	3.84801e21			0.154102
$970$	1.32314e21	+	2.09896e20i	0.0525799	+	0.00834098i
$971$			1.76428e22i			0.695703i	0.937550	+	0.347851i	$0.113089\pi$
$971$			1.76428e22i			0.695703i	−0.937550	+	0.347851i	$0.886911\pi$
$972$	−7.83527e21	+	2.40745e22i	−0.306589	+	0.942021i
$973$		−	1.75122e22i		−	0.679978i
$974$	3.34907e21	−	2.11119e22i	0.129042	−	0.813456i
$975$	1.38959e22			0.531317
$976$	−2.11265e22	+	2.90186e22i	−0.801595	+	1.10104i
$977$	−2.07355e22			−0.780740			−0.390370	−	0.920658i	$-0.627653\pi$
$977$	−2.07355e22			−0.780740			−0.390370	+	0.920658i	$0.627653\pi$
$978$	2.91684e21	−	1.83872e22i	0.108986	−	0.687028i
$979$		−	2.25383e22i		−	0.835702i
$980$	−3.22767e20	+	9.91730e20i	−0.0118767	+	0.0364920i
$981$		−	2.29437e22i		−	0.837810i
$982$	−2.83878e22	−	4.50328e21i	−1.02872	−	0.163190i
$983$	1.68619e22			0.606393			0.303196	−	0.952928i	$-0.401946\pi$
$983$	1.68619e22			0.606393			0.303196	+	0.952928i	$0.401946\pi$
$984$	−3.62677e21	−	1.85128e21i	−0.129437	−	0.0660706i
$985$	5.75505e20			0.0203834
$986$	1.87008e22	+	2.96659e21i	0.657329	+	0.104275i
$987$			1.91157e22i			0.666824i
$988$	4.86490e21	+	1.58332e21i	0.168421	+	0.0548142i
$989$		−	1.47486e21i		−	0.0506734i
$990$	1.60613e20	−	1.01247e21i	0.00547666	−	0.0345238i
$991$	4.56273e21			0.154409			0.0772045	−	0.997015i	$-0.475401\pi$
$991$	4.56273e21			0.154409			0.0772045	+	0.997015i	$0.475401\pi$
$992$	−3.18669e22	+	3.17893e22i	−1.07029	+	1.06768i
$993$	2.79492e21			0.0931643
$994$	−6.10688e20	+	3.84966e21i	−0.0202033	+	0.127357i
$995$		−	1.29303e21i		−	0.0424557i
$996$	−1.55370e22	−	5.05667e21i	−0.506317	−	0.164786i
$997$		−	4.32033e22i		−	1.39734i	−0.715442	−	0.698672i	$-0.753775\pi$
$997$		−	4.32033e22i		−	1.39734i	0.715442	−	0.698672i	$-0.246225\pi$
$998$	−3.70549e22	−	5.87818e21i	−1.18951	−	0.188697i
$999$	3.22701e22			1.02816

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8.16.b.a.5.8	yes	14
3.2	odd	2		72.16.d.b.37.7		14
4.3	odd	2		32.16.b.a.17.10		14
8.3	odd	2		32.16.b.a.17.5		14
8.5	even	2	inner	8.16.b.a.5.7	✓	14
24.5	odd	2		72.16.d.b.37.8		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8.16.b.a.5.7	✓	14	8.5	even	2	inner
8.16.b.a.5.8	yes	14	1.1	even	1	trivial
32.16.b.a.17.5		14	8.3	odd	2
32.16.b.a.17.10		14	4.3	odd	2
72.16.d.b.37.7		14	3.2	odd	2
72.16.d.b.37.8		14	24.5	odd	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:	\( N \)	\(=\)	\( 8 = 2^{3} \)
Weight:	\( k \)	\(=\)	\( 16 \)
Character orbit:	\([\chi]\)	\(=\)	8.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-28.3613 + 178.784i) q^{2} -2380.16i q^{3} +(-31159.3 - 10141.1i) q^{4} +9943.39i q^{5} +(425534. + 67504.4i) q^{6} +1.24365e6 q^{7} +(2.69677e6 - 5.28316e6i) q^{8} +8.68373e6 q^{9} +O(q^{10})\)	\(q+(-28.3613 + 178.784i) q^{2} -2380.16i q^{3} +(-31159.3 - 10141.1i) q^{4} +9943.39i q^{5} +(425534. + 67504.4i) q^{6} +1.24365e6 q^{7} +(2.69677e6 - 5.28316e6i) q^{8} +8.68373e6 q^{9} +(-1.77772e6 - 282007. i) q^{10} +6.55864e7i q^{11} +(-2.41374e7 + 7.41641e7i) q^{12} +1.91929e8i q^{13} +(-3.52715e7 + 2.22344e8i) q^{14} +2.36669e7 q^{15} +(8.68059e8 + 6.31977e8i) q^{16} +1.98739e9 q^{17} +(-2.46282e8 + 1.55251e9i) q^{18} +8.13478e8i q^{19} +(1.00837e8 - 3.09829e8i) q^{20} -2.96009e9i q^{21} +(-1.17258e10 - 1.86011e9i) q^{22} +8.30671e8 q^{23} +(-1.25748e10 - 6.41876e9i) q^{24} +3.04187e10 q^{25} +(-3.43138e10 - 5.44335e9i) q^{26} -5.48214e10i q^{27} +(-3.87512e10 - 1.26119e10i) q^{28} -5.26318e10i q^{29} +(-6.71223e8 + 4.23125e9i) q^{30} +2.31580e11 q^{31} +(-1.37606e11 + 1.37271e11i) q^{32} +1.56106e11 q^{33} +(-5.63650e10 + 3.55314e11i) q^{34} +1.23661e10i q^{35} +(-2.70579e11 - 8.80623e10i) q^{36} +5.88641e11i q^{37} +(-1.45437e11 - 2.30713e10i) q^{38} +4.56822e11 q^{39} +(5.25325e10 + 2.68151e10i) q^{40} +2.88417e11 q^{41} +(5.29216e11 + 8.39518e10i) q^{42} -1.77551e12i q^{43} +(6.65116e11 - 2.04362e12i) q^{44} +8.63457e10i q^{45} +(-2.35589e10 + 1.48511e11i) q^{46} -6.45781e12 q^{47} +(1.50421e12 - 2.06612e12i) q^{48} -3.20090e12 q^{49} +(-8.62713e11 + 5.43837e12i) q^{50} -4.73032e12i q^{51} +(1.94637e12 - 5.98037e12i) q^{52} +1.55187e13i q^{53} +(9.80118e12 + 1.55480e12i) q^{54} -6.52151e11 q^{55} +(3.35384e12 - 6.57040e12i) q^{56} +1.93621e12 q^{57} +(9.40970e12 + 1.49270e12i) q^{58} -1.28387e13i q^{59} +(-7.37443e11 - 2.40007e11i) q^{60} +3.34293e13i q^{61} +(-6.56790e12 + 4.14027e13i) q^{62} +1.07995e13 q^{63} +(-2.06392e13 - 2.84950e13i) q^{64} -1.90843e12 q^{65} +(-4.42737e12 + 2.79093e13i) q^{66} -8.71055e13i q^{67} +(-6.19257e13 - 2.01543e13i) q^{68} -1.97713e12i q^{69} +(-2.21086e12 - 3.50718e11i) q^{70} +1.73139e13 q^{71} +(2.34181e13 - 4.58776e13i) q^{72} +1.25837e14 q^{73} +(-1.05239e14 - 1.66946e13i) q^{74} -7.24015e13i q^{75} +(8.24953e12 - 2.53474e13i) q^{76} +8.15665e13i q^{77} +(-1.29561e13 + 8.16724e13i) q^{78} -4.05635e12 q^{79} +(-6.28399e12 + 8.63145e12i) q^{80} -5.88183e12 q^{81} +(-8.17986e12 + 5.15642e13i) q^{82} +2.09495e14i q^{83} +(-3.00184e13 + 9.22342e13i) q^{84} +1.97614e13i q^{85} +(3.17432e14 + 5.03557e13i) q^{86} -1.25272e14 q^{87} +(3.46503e14 + 1.76872e14i) q^{88} -3.43643e14 q^{89} +(-1.54372e13 - 2.44887e12i) q^{90} +2.38693e14i q^{91} +(-2.58831e13 - 8.42390e12i) q^{92} -5.51198e14i q^{93} +(1.83152e14 - 1.15455e15i) q^{94} -8.08872e12 q^{95} +(3.26728e14 + 3.27526e14i) q^{96} -7.44295e14 q^{97} +(9.07815e13 - 5.72269e14i) q^{98} +5.69535e14i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 90 q^{2} + 51444 q^{4} - 189428 q^{6} - 1647088 q^{7} + 1889640 q^{8} - 57395630 q^{9}+O(q^{10}) \) 14 * q - 90 * q^2 + 51444 * q^4 - 189428 * q^6 - 1647088 * q^7 + 1889640 * q^8 - 57395630 * q^9	\( 14 q - 90 q^{2} + 51444 q^{4} - 189428 q^{6} - 1647088 q^{7} + 1889640 q^{8} - 57395630 q^{9} + 58467784 q^{10} + 399357832 q^{12} - 518960496 q^{14} + 712135312 q^{15} - 1435931120 q^{16} + 728554812 q^{17} + 526853306 q^{18} - 3449250768 q^{20} + 28367364252 q^{22} - 35548816080 q^{23} + 40155187088 q^{24} - 75899954794 q^{25} + 17666210712 q^{26} + 79863955680 q^{28} - 124878825712 q^{30} - 105758138816 q^{31} - 37651613280 q^{32} - 150458001384 q^{33} + 537472307308 q^{34} + 338679650892 q^{36} + 1649727781164 q^{38} - 2251546247120 q^{39} + 1251083710304 q^{40} - 53229185940 q^{41} - 2437011096800 q^{42} - 3416842360344 q^{44} - 3303531082064 q^{46} + 12527998446432 q^{47} - 6441543679584 q^{48} + 8427385380990 q^{49} + 1179755527374 q^{50} - 2436018627056 q^{52} + 3357642572216 q^{54} - 30557833792176 q^{55} + 7549064859072 q^{56} + 18277230892472 q^{57} - 8014960165320 q^{58} - 53574657402912 q^{60} + 77882578979904 q^{62} + 36142362113776 q^{63} + 76083381630528 q^{64} + 5437123965600 q^{65} - 134116957601160 q^{66} - 69772560247896 q^{68} + 133952399750848 q^{70} - 173249927708016 q^{71} + 163390222317848 q^{72} - 182057837882196 q^{73} + 2072780135688 q^{74} - 248503439494072 q^{76} + 636498768647600 q^{78} - 294370273271392 q^{79} + 766230078246336 q^{80} + 256903428263798 q^{81} - 10\!\cdots\!32 q^{82}+ \cdots - 51\!\cdots\!58 q^{98}+O(q^{100}) \) 14 * q - 90 * q^2 + 51444 * q^4 - 189428 * q^6 - 1647088 * q^7 + 1889640 * q^8 - 57395630 * q^9 + 58467784 * q^10 + 399357832 * q^12 - 518960496 * q^14 + 712135312 * q^15 - 1435931120 * q^16 + 728554812 * q^17 + 526853306 * q^18 - 3449250768 * q^20 + 28367364252 * q^22 - 35548816080 * q^23 + 40155187088 * q^24 - 75899954794 * q^25 + 17666210712 * q^26 + 79863955680 * q^28 - 124878825712 * q^30 - 105758138816 * q^31 - 37651613280 * q^32 - 150458001384 * q^33 + 537472307308 * q^34 + 338679650892 * q^36 + 1649727781164 * q^38 - 2251546247120 * q^39 + 1251083710304 * q^40 - 53229185940 * q^41 - 2437011096800 * q^42 - 3416842360344 * q^44 - 3303531082064 * q^46 + 12527998446432 * q^47 - 6441543679584 * q^48 + 8427385380990 * q^49 + 1179755527374 * q^50 - 2436018627056 * q^52 + 3357642572216 * q^54 - 30557833792176 * q^55 + 7549064859072 * q^56 + 18277230892472 * q^57 - 8014960165320 * q^58 - 53574657402912 * q^60 + 77882578979904 * q^62 + 36142362113776 * q^63 + 76083381630528 * q^64 + 5437123965600 * q^65 - 134116957601160 * q^66 - 69772560247896 * q^68 + 133952399750848 * q^70 - 173249927708016 * q^71 + 163390222317848 * q^72 - 182057837882196 * q^73 + 2072780135688 * q^74 - 248503439494072 * q^76 + 636498768647600 * q^78 - 294370273271392 * q^79 + 766230078246336 * q^80 + 256903428263798 * q^81 - 1021513680215332 * q^82 - 1701668269684544 * q^84 + 1418597672590812 * q^86 + 1493385390675312 * q^87 + 1948789255860816 * q^88 + 314213951649228 * q^89 - 3574690367103304 * q^90 - 3044080509008736 * q^92 + 3407319354561120 * q^94 - 851301047679984 * q^95 + 4705878559349312 * q^96 - 672574291859236 * q^97 - 5140373067292458 * q^98

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