LMFDB - Embedded newform 5.17.c.a.2.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5,17,Mod(2,5)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5, base_ring=CyclotomicField(4))

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

N = Newforms(chi, 17, names="a")

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

chi := DirichletCharacter("5.2");

S:= CuspForms(chi, 17);

N := Newforms(S);

Level:	$ N $	$=$	$ 5 $
Weight:	$ k $	$=$	$ 17 $
Character orbit:	$[\chi]$	$=$	5.c (of order $4$, degree $2$, 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:	$8.11622719283$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(i)$
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} + 354217 x^{12} + 47647865256 x^{10} + \cdots + 84\!\cdots\!36 $ x^14 + 354217x^12 + 47647865256x^10 + 3062948254140560x^8 + 97982926395671183360x^6 + 1450505914836224854327296x^4 + 7749363027207208037244731392x^2 + 8484029084015876402584471207936
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{34}\cdot 3^{10}\cdot 5^{18} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			2.7
Root			$336.317i$ of defining polynomial
Character	$\chi$	$=$	5.2
Dual form			5.17.c.a.3.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(336.317 + 336.317i) q^{2} +(6051.53 - 6051.53i) q^{3} +160682. i q^{4} +(335305. - 200395. i) q^{5} +4.07046e6 q^{6} +(-371312. - 371312. i) q^{7} +(-3.19992e7 + 3.19992e7i) q^{8} -3.01954e7i q^{9} +O(q^{10})$	\(q+(336.317 + 336.317i) q^{2} +(6051.53 - 6051.53i) q^{3} +160682. i q^{4} +(335305. - 200395. i) q^{5} +4.07046e6 q^{6} +(-371312. - 371312. i) q^{7} +(-3.19992e7 + 3.19992e7i) q^{8} -3.01954e7i q^{9} +(1.80165e8 + 4.53727e7i) q^{10} -2.87674e8 q^{11} +(9.72372e8 + 9.72372e8i) q^{12} +(-9.55195e7 + 9.55195e7i) q^{13} -2.49757e8i q^{14} +(8.16416e8 - 3.24181e9i) q^{15} -1.09933e10 q^{16} +(-6.35046e8 - 6.35046e8i) q^{17} +(1.01552e10 - 1.01552e10i) q^{18} -1.35652e10i q^{19} +(3.21999e10 + 5.38776e10i) q^{20} -4.49401e9 q^{21} +(-9.67496e10 - 9.67496e10i) q^{22} +(5.40328e10 - 5.40328e10i) q^{23} +3.87288e11i q^{24} +(7.22717e10 - 1.34387e11i) q^{25} -6.42496e10 q^{26} +(7.77704e10 + 7.77704e10i) q^{27} +(5.96631e10 - 5.96631e10i) q^{28} +1.69248e11i q^{29} +(1.36485e12 - 8.15700e11i) q^{30} -1.28377e12 q^{31} +(-1.60013e12 - 1.60013e12i) q^{32} +(-1.74087e12 + 1.74087e12i) q^{33} -4.27153e11i q^{34} +(-1.98912e11 - 5.00939e10i) q^{35} +4.85185e12 q^{36} +(2.40048e12 + 2.40048e12i) q^{37} +(4.56221e12 - 4.56221e12i) q^{38} +1.15608e12i q^{39} +(-4.31703e12 + 1.71420e13i) q^{40} -5.05325e12 q^{41} +(-1.51141e12 - 1.51141e12i) q^{42} +(-8.53023e12 + 8.53023e12i) q^{43} -4.62240e13i q^{44} +(-6.05100e12 - 1.01247e13i) q^{45} +3.63443e13 q^{46} +(6.90127e12 + 6.90127e12i) q^{47} +(-6.65262e13 + 6.65262e13i) q^{48} -3.29572e13i q^{49} +(6.95028e13 - 2.08904e13i) q^{50} -7.68600e12 q^{51} +(-1.53483e13 - 1.53483e13i) q^{52} +(3.19201e13 - 3.19201e13i) q^{53} +5.23110e13i q^{54} +(-9.64587e13 + 5.76484e13i) q^{55} +2.37634e13 q^{56} +(-8.20903e13 - 8.20903e13i) q^{57} +(-5.69210e13 + 5.69210e13i) q^{58} +2.15375e14i q^{59} +(5.20900e14 + 1.31183e14i) q^{60} +2.85646e14 q^{61} +(-4.31753e14 - 4.31753e14i) q^{62} +(-1.12119e13 + 1.12119e13i) q^{63} -3.55844e14i q^{64} +(-1.28866e13 + 5.11698e13i) q^{65} -1.17097e15 q^{66} +(3.15528e14 + 3.15528e14i) q^{67} +(1.02041e14 - 1.02041e14i) q^{68} -6.53963e14i q^{69} +(-5.00500e13 - 8.37448e13i) q^{70} +3.15103e14 q^{71} +(9.66228e14 + 9.66228e14i) q^{72} +(-3.46889e14 + 3.46889e14i) q^{73} +1.61465e15i q^{74} +(-3.75893e14 - 1.25060e15i) q^{75} +2.17968e15 q^{76} +(1.06817e14 + 1.06817e14i) q^{77} +(-3.88809e14 + 3.88809e14i) q^{78} -1.88973e15i q^{79} +(-3.68611e15 + 2.20300e15i) q^{80} +2.24107e15 q^{81} +(-1.69949e15 - 1.69949e15i) q^{82} +(-2.43560e14 + 2.43560e14i) q^{83} -7.22106e14i q^{84} +(-3.40194e14 - 8.56745e13i) q^{85} -5.73772e15 q^{86} +(1.02421e15 + 1.02421e15i) q^{87} +(9.20534e15 - 9.20534e15i) q^{88} +4.86801e15i q^{89} +(1.37004e15 - 5.44015e15i) q^{90} +7.09350e13 q^{91} +(8.68211e15 + 8.68211e15i) q^{92} +(-7.76876e15 + 7.76876e15i) q^{93} +4.64203e15i q^{94} +(-2.71840e15 - 4.54849e15i) q^{95} -1.93664e16 q^{96} +(-5.87093e15 - 5.87093e15i) q^{97} +(1.10841e16 - 1.10841e16i) q^{98} +8.68642e15i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 2 q^{2} + 7908 q^{3} + 192880 q^{5} + 4417368 q^{6} - 386452 q^{7} - 10493340 q^{8}+O(q^{10}) $ 14 * q - 2 * q^2 + 7908 * q^3 + 192880 * q^5 + 4417368 * q^6 - 386452 * q^7 - 10493340 * q^8	\( 14 q - 2 q^{2} + 7908 q^{3} + 192880 q^{5} + 4417368 q^{6} - 386452 q^{7} - 10493340 q^{8} + 398727830 q^{10} - 539141632 q^{11} + 1973309928 q^{12} - 681358582 q^{13} + 3514452060 q^{15} - 22953579016 q^{16} + 13124182498 q^{17} - 11293583022 q^{18} - 20186820060 q^{20} + 133652286048 q^{21} - 244784660624 q^{22} + 236373052228 q^{23} + 13144083650 q^{25} + 223473840788 q^{26} + 608106053880 q^{27} - 1494176423768 q^{28} + 2252131613760 q^{30} - 1105223074952 q^{31} - 2024535639992 q^{32} - 6385551058704 q^{33} + 6956678093980 q^{35} + 12514339524924 q^{36} - 9027827087002 q^{37} - 7824802789560 q^{38} + 31912538913900 q^{40} + 39543901484288 q^{41} - 70814500818384 q^{42} - 63017457929452 q^{43} + 126481294123110 q^{45} + 44357914058008 q^{46} - 2826187575452 q^{47} - 405160526368272 q^{48} + 461109216233650 q^{50} + 208649050954008 q^{51} - 389623094881012 q^{52} - 275142037498442 q^{53} + 330504874256560 q^{55} + 865011118900080 q^{56} - 644237427525840 q^{57} - 991296507673440 q^{58} + 16\!\cdots\!80 q^{60}+ \cdots + 48\!\cdots\!02 q^{98}+O(q^{100}) \) 14 * q - 2 * q^2 + 7908 * q^3 + 192880 * q^5 + 4417368 * q^6 - 386452 * q^7 - 10493340 * q^8 + 398727830 * q^10 - 539141632 * q^11 + 1973309928 * q^12 - 681358582 * q^13 + 3514452060 * q^15 - 22953579016 * q^16 + 13124182498 * q^17 - 11293583022 * q^18 - 20186820060 * q^20 + 133652286048 * q^21 - 244784660624 * q^22 + 236373052228 * q^23 + 13144083650 * q^25 + 223473840788 * q^26 + 608106053880 * q^27 - 1494176423768 * q^28 + 2252131613760 * q^30 - 1105223074952 * q^31 - 2024535639992 * q^32 - 6385551058704 * q^33 + 6956678093980 * q^35 + 12514339524924 * q^36 - 9027827087002 * q^37 - 7824802789560 * q^38 + 31912538913900 * q^40 + 39543901484288 * q^41 - 70814500818384 * q^42 - 63017457929452 * q^43 + 126481294123110 * q^45 + 44357914058008 * q^46 - 2826187575452 * q^47 - 405160526368272 * q^48 + 461109216233650 * q^50 + 208649050954008 * q^51 - 389623094881012 * q^52 - 275142037498442 * q^53 + 330504874256560 * q^55 + 865011118900080 * q^56 - 644237427525840 * q^57 - 991296507673440 * q^58 + 1631207111049480 * q^60 + 683634528395968 * q^61 - 938995013191864 * q^62 - 1361911146729372 * q^63 + 517066464980110 * q^65 - 196778043917184 * q^66 - 181547742064252 * q^67 - 917821658187868 * q^68 + 1066699466039880 * q^70 - 1337544011098792 * q^71 + 2573199832214340 * q^72 + 778038215296478 * q^73 - 1442550824447700 * q^75 - 233750796900240 * q^76 + 1099376123524976 * q^77 + 8472064951325256 * q^78 - 14934736099860320 * q^80 + 809940307363794 * q^81 - 303814693723184 * q^82 + 13357181209550188 * q^83 - 16045734952112470 * q^85 - 20034048539985352 * q^86 + 17327533268211840 * q^87 + 22952328705949920 * q^88 - 21878453293909290 * q^90 - 24534035720748632 * q^91 + 40652972845631848 * q^92 + 15958372062212256 * q^93 - 22489885958711400 * q^95 - 27488119051061472 * q^96 - 3303551663290402 * q^97 + 48233459501789102 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/5\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	336.317	+	336.317i	1.31374	+	1.31374i	0.918638	+	0.395099i	$0.129290\pi$
$2$	336.317	+	336.317i	1.31374	+	1.31374i	0.395099	+	0.918638i	$0.370710\pi$
$3$	6051.53	−	6051.53i	0.922349	−	0.922349i	−0.0748461	−	0.997195i	$-0.523847\pi$
$3$	6051.53	−	6051.53i	0.922349	−	0.922349i	0.997195	+	0.0748461i	$0.0238465\pi$
$4$			160682.i			2.45181i
$5$	335305.	−	200395.i	0.858382	−	0.513011i
$5$	335305.	−	200395.i	0.858382	−	0.513011i
$6$	4.07046e6			2.42345
$7$	−371312.	−	371312.i	−0.0644101	−	0.0644101i	0.674168	−	0.738578i	$-0.264502\pi$
$7$	−371312.	−	371312.i	−0.0644101	−	0.0644101i	−0.738578	+	0.674168i	$0.764502\pi$
$8$	−3.19992e7	+	3.19992e7i	−1.90730	+	1.90730i
$9$		−	3.01954e7i		−	0.701456i
$10$	1.80165e8	+	4.53727e7i	1.80165	+	0.453727i
$11$	−2.87674e8			−1.34202			−0.671010	−	0.741448i	$-0.734139\pi$
$11$	−2.87674e8			−1.34202			−0.671010	+	0.741448i	$0.734139\pi$
$12$	9.72372e8	+	9.72372e8i	2.26143	+	2.26143i
$13$	−9.55195e7	+	9.55195e7i	−0.117097	+	0.117097i	−0.763227	−	0.646130i	$-0.776386\pi$
$13$	−9.55195e7	+	9.55195e7i	−0.117097	+	0.117097i	0.646130	+	0.763227i	$0.276386\pi$
$14$		−	2.49757e8i		−	0.169236i
$15$	8.16416e8	−	3.24181e9i	0.318553	−	1.26490i
$16$	−1.09933e10			−2.55957
$17$	−6.35046e8	−	6.35046e8i	−0.0910362	−	0.0910362i	0.660122	−	0.751158i	$-0.270505\pi$
$17$	−6.35046e8	−	6.35046e8i	−0.0910362	−	0.0910362i	−0.751158	+	0.660122i	$0.770505\pi$
$18$	1.01552e10	−	1.01552e10i	0.921528	−	0.921528i
$19$		−	1.35652e10i		−	0.798726i	−0.916793	−	0.399363i	$-0.869231\pi$
$19$		−	1.35652e10i		−	0.798726i	0.916793	−	0.399363i	$-0.130769\pi$
$20$	3.21999e10	+	5.38776e10i	1.25781	+	2.10459i
$21$	−4.49401e9			−0.118817
$22$	−9.67496e10	−	9.67496e10i	−1.76306	−	1.76306i
$23$	5.40328e10	−	5.40328e10i	0.689978	−	0.689978i	−0.272249	−	0.962227i	$-0.587767\pi$
$23$	5.40328e10	−	5.40328e10i	0.689978	−	0.689978i	0.962227	+	0.272249i	$0.0877675\pi$
$24$			3.87288e11i			3.51840i
$25$	7.22717e10	−	1.34387e11i	0.473640	−	0.880719i
$26$	−6.42496e10			−0.307669
$27$	7.77704e10	+	7.77704e10i	0.275362	+	0.275362i
$28$	5.96631e10	−	5.96631e10i	0.157922	−	0.157922i
$29$			1.69248e11i			0.338330i	0.985588	+	0.169165i	$0.0541070\pi$
$29$			1.69248e11i			0.338330i	−0.985588	+	0.169165i	$0.945893\pi$
$30$	1.36485e12	−	8.15700e11i	2.08025	−	1.24326i
$31$	−1.28377e12			−1.50520			−0.752598	−	0.658480i	$-0.771200\pi$
$31$	−1.28377e12			−1.50520			−0.752598	+	0.658480i	$0.771200\pi$
$32$	−1.60013e12	−	1.60013e12i	−1.45531	−	1.45531i
$33$	−1.74087e12	+	1.74087e12i	−1.23781	+	1.23781i
$34$		−	4.27153e11i		−	0.239195i
$35$	−1.98912e11	−	5.00939e10i	−0.0883316	−	0.0222454i
$36$	4.85185e12			1.71984
$37$	2.40048e12	+	2.40048e12i	0.683415	+	0.683415i	0.960768	−	0.277353i	$-0.0894571\pi$
$37$	2.40048e12	+	2.40048e12i	0.683415	+	0.683415i	−0.277353	+	0.960768i	$0.589457\pi$
$38$	4.56221e12	−	4.56221e12i	1.04932	−	1.04932i
$39$			1.15608e12i			0.216008i
$40$	−4.31703e12	+	1.71420e13i	−0.658727	+	2.61566i
$41$	−5.05325e12			−0.632849			−0.316425	−	0.948618i	$-0.602482\pi$
$41$	−5.05325e12			−0.632849			−0.316425	+	0.948618i	$0.602482\pi$
$42$	−1.51141e12	−	1.51141e12i	−0.156095	−	0.156095i
$43$	−8.53023e12	+	8.53023e12i	−0.729815	+	0.729815i	−0.970583	−	0.240767i	$-0.922601\pi$
$43$	−8.53023e12	+	8.53023e12i	−0.729815	+	0.729815i	0.240767	+	0.970583i	$0.422601\pi$
$44$		−	4.62240e13i		−	3.29038i
$45$	−6.05100e12	−	1.01247e13i	−0.359854	−	0.602117i
$46$	3.63443e13			1.81290
$47$	6.90127e12	+	6.90127e12i	0.289832	+	0.289832i	0.837014	−	0.547182i	$-0.184299\pi$
$47$	6.90127e12	+	6.90127e12i	0.289832	+	0.289832i	−0.547182	+	0.837014i	$0.684299\pi$
$48$	−6.65262e13	+	6.65262e13i	−2.36082	+	2.36082i
$49$		−	3.29572e13i		−	0.991703i
$50$	6.95028e13	−	2.08904e13i	1.77927	−	0.534795i
$51$	−7.68600e12			−0.167934
$52$	−1.53483e13	−	1.53483e13i	−0.287100	−	0.287100i
$53$	3.19201e13	−	3.19201e13i	0.512694	−	0.512694i	−0.402657	−	0.915351i	$-0.631913\pi$
$53$	3.19201e13	−	3.19201e13i	0.512694	−	0.512694i	0.915351	+	0.402657i	$0.131913\pi$
$54$			5.23110e13i			0.723507i
$55$	−9.64587e13	+	5.76484e13i	−1.15197	+	0.688471i
$56$	2.37634e13			0.245699
$57$	−8.20903e13	−	8.20903e13i	−0.736704	−	0.736704i
$58$	−5.69210e13	+	5.69210e13i	−0.444476	+	0.444476i
$59$			2.15375e14i			1.46683i	0.679783	+	0.733413i	$0.262074\pi$
$59$			2.15375e14i			1.46683i	−0.679783	+	0.733413i	$0.737926\pi$
$60$	5.20900e14	+	1.31183e14i	3.10131	+	0.781032i
$61$	2.85646e14			1.49001			0.745005	−	0.667058i	$-0.232447\pi$
$61$	2.85646e14			1.49001			0.745005	+	0.667058i	$0.232447\pi$
$62$	−4.31753e14	−	4.31753e14i	−1.97743	−	1.97743i
$63$	−1.12119e13	+	1.12119e13i	−0.0451808	+	0.0451808i
$64$		−	3.55844e14i		−	1.26421i
$65$	−1.28866e13	+	5.11698e13i	−0.0404419	+	0.160586i
$66$	−1.17097e15			−3.25232
$67$	3.15528e14	+	3.15528e14i	0.777033	+	0.777033i	0.979325	−	0.202292i	$-0.0648390\pi$
$67$	3.15528e14	+	3.15528e14i	0.777033	+	0.777033i	−0.202292	+	0.979325i	$0.564839\pi$
$68$	1.02041e14	−	1.02041e14i	0.223204	−	0.223204i
$69$		−	6.53963e14i		−	1.27280i
$70$	−5.00500e13	−	8.37448e13i	−0.0868199	−	0.145269i
$71$	3.15103e14			0.487962			0.243981	−	0.969780i	$-0.421547\pi$
$71$	3.15103e14			0.487962			0.243981	+	0.969780i	$0.421547\pi$
$72$	9.66228e14	+	9.66228e14i	1.33789	+	1.33789i
$73$	−3.46889e14	+	3.46889e14i	−0.430137	+	0.430137i	−0.888675	−	0.458538i	$-0.848373\pi$
$73$	−3.46889e14	+	3.46889e14i	−0.430137	+	0.430137i	0.458538	+	0.888675i	$0.348373\pi$
$74$			1.61465e15i			1.79566i
$75$	−3.75893e14	−	1.25060e15i	−0.375469	−	1.24919i
$76$	2.17968e15			1.95833
$77$	1.06817e14	+	1.06817e14i	0.0864397	+	0.0864397i
$78$	−3.88809e14	+	3.88809e14i	−0.283778	+	0.283778i
$79$		−	1.88973e15i		−	1.24561i	−0.782377	−	0.622805i	$-0.785993\pi$
$79$		−	1.88973e15i		−	1.24561i	0.782377	−	0.622805i	$-0.214007\pi$
$80$	−3.68611e15	+	2.20300e15i	−2.19709	+	1.31309i
$81$	2.24107e15			1.20942
$82$	−1.69949e15	−	1.69949e15i	−0.831398	−	0.831398i
$83$	−2.43560e14	+	2.43560e14i	−0.108139	+	0.108139i	−0.759106	−	0.650967i	$-0.774364\pi$
$83$	−2.43560e14	+	2.43560e14i	−0.108139	+	0.108139i	0.650967	+	0.759106i	$0.274364\pi$
$84$		−	7.22106e14i		−	0.291318i
$85$	−3.40194e14	−	8.56745e13i	−0.124846	−	0.0314413i
$86$	−5.73772e15			−1.91757
$87$	1.02421e15	+	1.02421e15i	0.312058	+	0.312058i
$88$	9.20534e15	−	9.20534e15i	2.55964	−	2.55964i
$89$			4.86801e15i			1.23661i	0.785940	+	0.618303i	$0.212179\pi$
$89$			4.86801e15i			1.23661i	−0.785940	+	0.618303i	$0.787821\pi$
$90$	1.37004e15	−	5.44015e15i	0.318269	−	1.26378i
$91$	7.09350e13			0.0150844
$92$	8.68211e15	+	8.68211e15i	1.69170	+	1.69170i
$93$	−7.76876e15	+	7.76876e15i	−1.38832	+	1.38832i
$94$			4.64203e15i			0.761526i
$95$	−2.71840e15	−	4.54849e15i	−0.409755	−	0.685612i
$96$	−1.93664e16			−2.68460
$97$	−5.87093e15	−	5.87093e15i	−0.749089	−	0.749089i	0.225219	−	0.974308i	$-0.427690\pi$
$97$	−5.87093e15	−	5.87093e15i	−0.749089	−	0.749089i	−0.974308	+	0.225219i	$0.927690\pi$
$98$	1.10841e16	−	1.10841e16i	1.30284	−	1.30284i
$99$			8.68642e15i			0.941368i
$100$	2.15936e16	+	1.16128e16i	2.15936	+	1.16128i
$101$	6.45438e15			0.596051			0.298026	−	0.954558i	$-0.403672\pi$
$101$	6.45438e15			0.596051			0.298026	+	0.954558i	$0.403672\pi$
$102$	−2.58493e15	−	2.58493e15i	−0.220622	−	0.220622i
$103$	−2.00133e15	+	2.00133e15i	−0.157987	+	0.157987i	−0.781674	−	0.623687i	$-0.785634\pi$
$103$	−2.00133e15	+	2.00133e15i	−0.157987	+	0.157987i	0.623687	+	0.781674i	$0.285634\pi$
$104$		−	6.11310e15i		−	0.446678i
$105$	−1.50687e15	+	9.00576e14i	−0.101991	+	0.0609545i
$106$	2.14706e16			1.34709
$107$	−2.03930e16	−	2.03930e16i	−1.18689	−	1.18689i	−0.977922	−	0.208970i	$-0.932989\pi$
$107$	−2.03930e16	−	2.03930e16i	−1.18689	−	1.18689i	−0.208970	−	0.977922i	$-0.567011\pi$
$108$	−1.24963e16	+	1.24963e16i	−0.675137	+	0.675137i
$109$			1.82128e16i			0.914038i	0.889457	+	0.457019i	$0.151083\pi$
$109$			1.82128e16i			0.914038i	−0.889457	+	0.457019i	$0.848917\pi$
$110$	−5.18288e16	−	1.30525e16i	−2.41785	−	0.608911i
$111$	2.90532e16			1.26070
$112$	4.08193e15	+	4.08193e15i	0.164862	+	0.164862i
$113$	1.87445e16	−	1.87445e16i	0.705093	−	0.705093i	−0.260406	−	0.965499i	$-0.583856\pi$
$113$	1.87445e16	−	1.87445e16i	0.705093	−	0.705093i	0.965499	+	0.260406i	$0.0838564\pi$
$114$		−	5.52167e16i		−	1.93567i
$115$	7.28960e15	−	2.89454e16i	0.238298	−	0.946231i
$116$	−2.71951e16			−0.829521
$117$	2.88424e15	+	2.88424e15i	0.0821382	+	0.0821382i
$118$	−7.24341e16	+	7.24341e16i	−1.92702	+	1.92702i
$119$			4.71600e14i			0.0117273i
$120$	7.76106e16	+	1.29860e17i	1.80498	+	3.02013i
$121$	3.68066e16			0.801019
$122$	9.60676e16	+	9.60676e16i	1.95748	+	1.95748i
$123$	−3.05799e16	+	3.05799e16i	−0.583708	+	0.583708i
$124$		−	2.06278e17i		−	3.69046i
$125$	−2.69739e15	−	5.95436e16i	−0.0452547	−	0.998975i
$126$	−7.54149e15			−0.118712
$127$	5.06090e15	+	5.06090e15i	0.0747821	+	0.0747821i	0.743509	−	0.668726i	$-0.233160\pi$
$127$	5.06090e15	+	5.06090e15i	0.0747821	+	0.0747821i	−0.668726	+	0.743509i	$0.733160\pi$
$128$	1.48102e16	−	1.48102e16i	0.205533	−	0.205533i
$129$			1.03242e17i			1.34629i
$130$	−2.15432e16	+	1.28753e16i	−0.264098	+	0.157838i
$131$	−6.46825e16			−0.745790			−0.372895	−	0.927874i	$-0.621635\pi$
$131$	−6.46825e16			−0.745790			−0.372895	+	0.927874i	$0.621635\pi$
$132$	−2.79726e17	−	2.79726e17i	−3.03488	−	3.03488i
$133$	−5.03692e15	+	5.03692e15i	−0.0514460	+	0.0514460i
$134$			2.12235e17i			2.04164i
$135$	4.16616e16	+	1.04921e16i	0.377630	+	0.0951022i
$136$	4.06420e16			0.347267
$137$	3.44238e16	+	3.44238e16i	0.277392	+	0.277392i	0.832067	−	0.554675i	$-0.187157\pi$
$137$	3.44238e16	+	3.44238e16i	0.277392	+	0.277392i	−0.554675	+	0.832067i	$0.687157\pi$
$138$	2.19939e17	−	2.19939e17i	1.67213	−	1.67213i
$139$		−	6.24994e16i		−	0.448495i	−0.974532	−	0.224248i	$-0.928008\pi$
$139$		−	6.24994e16i		−	0.448495i	0.974532	−	0.224248i	$-0.0719924\pi$
$140$	8.04918e15	−	3.19615e16i	0.0545415	−	0.216573i
$141$	8.35265e16			0.534652
$142$	1.05975e17	+	1.05975e17i	0.641054	+	0.641054i
$143$	2.74785e16	−	2.74785e16i	0.157146	−	0.157146i
$144$			3.31946e17i			1.79543i
$145$	3.39165e16	+	5.67498e16i	0.173567	+	0.290416i
$146$	−2.33329e17			−1.13018
$147$	−1.99441e17	−	1.99441e17i	−0.914696	−	0.914696i
$148$	−3.85714e17	+	3.85714e17i	−1.67561	+	1.67561i
$149$		−	5.55029e16i		−	0.228468i	−0.993454	−	0.114234i	$-0.963559\pi$
$149$		−	5.55029e16i		−	0.228468i	0.993454	−	0.114234i	$-0.0364413\pi$
$150$	2.94179e17	−	5.47018e17i	1.14784	−	2.13438i
$151$	9.45707e16			0.349898			0.174949	−	0.984578i	$-0.444024\pi$
$151$	9.45707e16			0.349898			0.174949	+	0.984578i	$0.444024\pi$
$152$	4.34076e17	+	4.34076e17i	1.52341	+	1.52341i
$153$	−1.91754e16	+	1.91754e16i	−0.0638578	+	0.0638578i
$154$			7.18485e16i			0.227118i
$155$	−4.30454e17	+	2.57261e17i	−1.29203	+	0.772182i
$156$	−1.85761e17			−0.529612
$157$	8.78341e16	+	8.78341e16i	0.237939	+	0.237939i	0.815996	−	0.578057i	$-0.196189\pi$
$157$	8.78341e16	+	8.78341e16i	0.237939	+	0.237939i	−0.578057	+	0.815996i	$0.696189\pi$
$158$	6.35547e17	−	6.35547e17i	1.63641	−	1.63641i
$159$		−	3.86332e17i		−	0.945765i
$160$	−8.57189e17	−	2.15874e17i	−1.99580	−	0.502621i
$161$	−4.01260e16			−0.0888831
$162$	7.53710e17	+	7.53710e17i	1.58885	+	1.58885i
$163$	4.20586e17	−	4.20586e17i	0.844023	−	0.844023i	−0.145357	−	0.989379i	$-0.546433\pi$
$163$	4.20586e17	−	4.20586e17i	0.844023	−	0.844023i	0.989379	+	0.145357i	$0.0464330\pi$
$164$		−	8.11967e17i		−	1.55163i
$165$	−2.34862e17	+	9.32584e17i	−0.427504	+	1.69753i
$166$	−1.63827e17			−0.284132
$167$	−4.62254e17	−	4.62254e17i	−0.764097	−	0.764097i	0.212963	−	0.977060i	$-0.431689\pi$
$167$	−4.62254e17	−	4.62254e17i	−0.764097	−	0.764097i	−0.977060	+	0.212963i	$0.931689\pi$
$168$	1.43805e17	−	1.43805e17i	0.226620	−	0.226620i
$169$			6.47169e17i			0.972577i
$170$	−8.55994e16	−	1.43227e17i	−0.122710	−	0.205321i
$171$	−4.09606e17			−0.560270
$172$	−1.37065e18	−	1.37065e18i	−1.78937	−	1.78937i
$173$	−7.12705e17	+	7.12705e17i	−0.888261	+	0.888261i	−0.994356	−	0.106095i	$-0.966165\pi$
$173$	−7.12705e17	+	7.12705e17i	−0.888261	+	0.888261i	0.106095	+	0.994356i	$0.466165\pi$
$174$			6.88919e17i			0.819925i
$175$	−7.67347e16	+	2.30642e16i	−0.0872344	+	0.0262200i
$176$	3.16248e18			3.43500
$177$	1.30335e18	+	1.30335e18i	1.35293	+	1.35293i
$178$	−1.63719e18	+	1.63719e18i	−1.62458	+	1.62458i
$179$		−	1.55328e18i		−	1.47376i	−0.676026	−	0.736878i	$-0.736299\pi$
$179$		−	1.55328e18i		−	1.47376i	0.676026	−	0.736878i	$-0.263701\pi$
$180$	1.62685e18	−	9.72286e17i	1.47628	−	0.882296i
$181$	3.83773e17			0.333155			0.166577	−	0.986028i	$-0.446728\pi$
$181$	3.83773e17			0.333155			0.166577	+	0.986028i	$0.446728\pi$
$182$	2.38566e16	+	2.38566e16i	0.0198170	+	0.0198170i
$183$	1.72860e18	−	1.72860e18i	1.37431	−	1.37431i
$184$			3.45802e18i			2.63199i
$185$	1.28594e18	+	3.23850e17i	0.937231	+	0.236032i
$186$	−5.22553e18			−3.64777
$187$	1.82686e17	+	1.82686e17i	0.122172	+	0.122172i
$188$	−1.10891e18	+	1.10891e18i	−0.710613	+	0.710613i
$189$		−	5.77541e16i		−	0.0354722i
$190$	6.15490e17	−	2.44398e18i	0.362403	−	1.43902i
$191$	−2.69832e18			−1.52344			−0.761721	−	0.647905i	$-0.775645\pi$
$191$	−2.69832e18			−1.52344			−0.761721	+	0.647905i	$0.775645\pi$
$192$	−2.15340e18	−	2.15340e18i	−1.16604	−	1.16604i
$193$	1.53099e18	−	1.53099e18i	0.795270	−	0.795270i	−0.187076	−	0.982345i	$-0.559901\pi$
$193$	1.53099e18	−	1.53099e18i	0.795270	−	0.795270i	0.982345	+	0.187076i	$0.0599010\pi$
$194$		−	3.94899e18i		−	1.96821i
$195$	2.31672e17	+	3.87639e17i	0.110815	+	0.185418i
$196$	5.29563e18			2.43147
$197$	−3.07411e18	−	3.07411e18i	−1.35516	−	1.35516i	−0.879785	−	0.475371i	$-0.842314\pi$
$197$	−3.07411e18	−	3.07411e18i	−1.35516	−	1.35516i	−0.475371	−	0.879785i	$-0.657686\pi$
$198$	−2.92139e18	+	2.92139e18i	−1.23671	+	1.23671i
$199$			7.37981e17i			0.300069i	0.988681	+	0.150034i	$0.0479384\pi$
$199$			7.37981e17i			0.300069i	−0.988681	+	0.150034i	$0.952062\pi$
$200$	1.98764e18	+	6.61291e18i	0.776423	+	2.58317i
$201$	3.81886e18			1.43339
$202$	2.17072e18	+	2.17072e18i	0.783055	+	0.783055i
$203$	6.28438e16	−	6.28438e16i	0.0217919	−	0.0217919i
$204$		−	1.23500e18i		−	0.411743i
$205$	−1.69438e18	+	1.01265e18i	−0.543226	+	0.324659i
$206$	−1.34616e18			−0.415107
$207$	−1.63154e18	−	1.63154e18i	−0.483989	−	0.483989i
$208$	1.05007e18	−	1.05007e18i	0.299718	−	0.299718i
$209$			3.90236e18i			1.07191i
$210$	−8.09663e17	−	2.03905e17i	−0.214067	−	0.0539106i
$211$	1.14883e18			0.292413			0.146207	−	0.989254i	$-0.453294\pi$
$211$	1.14883e18			0.292413			0.146207	+	0.989254i	$0.453294\pi$
$212$	5.12899e18	+	5.12899e18i	1.25703	+	1.25703i
$213$	1.90686e18	−	1.90686e18i	0.450072	−	0.450072i
$214$		−	1.37170e19i		−	3.11853i
$215$	−1.15082e18	+	4.56965e18i	−0.252057	+	1.00086i
$216$	−4.97718e18			−1.05040
$217$	4.76678e17	+	4.76678e17i	0.0969498	+	0.0969498i
$218$	−6.12526e18	+	6.12526e18i	−1.20081	+	1.20081i
$219$			4.19842e18i			0.793474i
$220$	−9.26306e18	−	1.54992e19i	−1.68800	−	2.82441i
$221$	1.21319e17			0.0213201
$222$	9.77108e18	+	9.77108e18i	1.65622	+	1.65622i
$223$	−3.90465e18	+	3.90465e18i	−0.638474	+	0.638474i	−0.950179	−	0.311705i	$-0.899100\pi$
$223$	−3.90465e18	+	3.90465e18i	−0.638474	+	0.638474i	0.311705	+	0.950179i	$0.399100\pi$
$224$			1.18829e18i			0.187473i
$225$	−4.05786e18	−	2.18227e18i	−0.617785	−	0.332237i
$226$	1.26082e19			1.85261
$227$	−5.53218e18	−	5.53218e18i	−0.784674	−	0.784674i	0.195941	−	0.980616i	$-0.437224\pi$
$227$	−5.53218e18	−	5.53218e18i	−0.784674	−	0.784674i	−0.980616	+	0.195941i	$0.937224\pi$
$228$	1.31904e19	−	1.31904e19i	1.80626	−	1.80626i
$229$			9.74806e18i			1.28895i	0.764627	+	0.644473i	$0.222923\pi$
$229$			9.74806e18i			1.28895i	−0.764627	+	0.644473i	$0.777077\pi$
$230$	1.21864e19	−	7.28321e18i	1.55616	−	0.930037i
$231$	1.29281e18			0.159455
$232$	−5.41581e18	−	5.41581e18i	−0.645297	−	0.645297i
$233$	−4.13927e18	+	4.13927e18i	−0.476515	+	0.476515i	−0.904015	−	0.427500i	$-0.859394\pi$
$233$	−4.13927e18	+	4.13927e18i	−0.476515	+	0.476515i	0.427500	+	0.904015i	$0.359394\pi$
$234$			1.94004e18i			0.215816i
$235$	3.69701e18	+	9.31054e17i	0.397473	+	0.100100i
$236$	−3.46068e19			−3.59638
$237$	−1.14357e19	−	1.14357e19i	−1.14889	−	1.14889i
$238$	−1.58607e17	+	1.58607e17i	−0.0154066	+	0.0154066i
$239$		−	1.16508e19i		−	1.09439i	−0.837006	−	0.547194i	$-0.815696\pi$
$239$		−	1.16508e19i		−	1.09439i	0.837006	−	0.547194i	$-0.184304\pi$
$240$	−8.97509e18	+	3.56381e19i	−0.815359	+	3.23761i
$241$	2.18771e19			1.92245			0.961223	−	0.275771i	$-0.0889333\pi$
$241$	2.18771e19			1.92245			0.961223	+	0.275771i	$0.0889333\pi$
$242$	1.23787e19	+	1.23787e19i	1.05233	+	1.05233i
$243$	1.02142e19	−	1.02142e19i	0.840141	−	0.840141i
$244$			4.58982e19i			3.65323i
$245$	−6.60445e18	−	1.10507e19i	−0.508754	−	0.851260i
$246$	−2.05691e19			−1.53368
$247$	1.29574e18	+	1.29574e18i	0.0935282	+	0.0935282i
$248$	4.10796e19	−	4.10796e19i	2.87086	−	2.87086i
$249$			2.94782e18i			0.199483i
$250$	1.91183e19	−	2.09327e19i	1.25294	−	1.37184i
$251$	7.95441e18			0.504915			0.252458	−	0.967608i	$-0.418761\pi$
$251$	7.95441e18			0.504915			0.252458	+	0.967608i	$0.418761\pi$
$252$	−1.80155e18	−	1.80155e18i	−0.110775	−	0.110775i
$253$	−1.55438e19	+	1.55438e19i	−0.925964	+	0.925964i
$254$			3.40413e18i			0.196488i
$255$	−2.57716e18	+	1.54024e18i	−0.144152	+	0.0861521i
$256$	−1.33587e19			−0.724177
$257$	9.16947e18	+	9.16947e18i	0.481814	+	0.481814i	0.905711	−	0.423897i	$-0.139338\pi$
$257$	9.16947e18	+	9.16947e18i	0.481814	+	0.481814i	−0.423897	+	0.905711i	$0.639338\pi$
$258$	−3.47220e19	+	3.47220e19i	−1.76867	+	1.76867i
$259$		−	1.78265e18i		−	0.0880377i
$260$	−8.22207e18	−	2.07064e18i	−0.393726	−	0.0991559i
$261$	5.11051e18			0.237323
$262$	−2.17538e19	−	2.17538e19i	−0.979772	−	0.979772i
$263$	4.10589e18	−	4.10589e18i	0.179375	−	0.179375i	−0.611709	−	0.791083i	$-0.709517\pi$
$263$	4.10589e18	−	4.10589e18i	0.179375	−	0.179375i	0.791083	+	0.611709i	$0.209517\pi$
$264$		−	1.11413e20i		−	4.72176i
$265$	4.30637e18	−	1.70996e19i	0.177070	−	0.703104i
$266$	−3.38800e18			−0.135173
$267$	2.94589e19	+	2.94589e19i	1.14058	+	1.14058i
$268$	−5.06997e19	+	5.06997e19i	−1.90514	+	1.90514i
$269$		−	8.31122e18i		−	0.303142i	−0.988446	−	0.151571i	$-0.951567\pi$
$269$		−	8.31122e18i		−	0.303142i	0.988446	−	0.151571i	$-0.0484333\pi$
$270$	1.04829e19	+	1.75402e19i	0.371167	+	0.621046i
$271$	9.25539e18			0.318156			0.159078	−	0.987266i	$-0.449148\pi$
$271$	9.25539e18			0.318156			0.159078	+	0.987266i	$0.449148\pi$
$272$	6.98125e18	+	6.98125e18i	0.233014	+	0.233014i
$273$	4.29265e17	−	4.29265e17i	0.0139131	−	0.0139131i
$274$			2.31546e19i			0.728841i
$275$	−2.07907e19	+	3.86597e19i	−0.635634	+	1.18194i
$276$	1.05080e20			3.12067
$277$	−4.75485e19	−	4.75485e19i	−1.37182	−	1.37182i	−0.857739	−	0.514086i	$-0.828131\pi$
$277$	−4.75485e19	−	4.75485e19i	−1.37182	−	1.37182i	−0.514086	−	0.857739i	$-0.671869\pi$
$278$	2.10196e19	−	2.10196e19i	0.589205	−	0.589205i
$279$			3.87638e19i			1.05583i
$280$	7.96798e18	−	4.76205e18i	0.210904	−	0.126046i
$281$	2.34503e19			0.603250			0.301625	−	0.953427i	$-0.402471\pi$
$281$	2.34503e19			0.603250			0.301625	+	0.953427i	$0.402471\pi$
$282$	2.80914e19	+	2.80914e19i	0.702393	+	0.702393i
$283$	8.97167e18	−	8.97167e18i	0.218063	−	0.218063i	−0.589619	−	0.807682i	$-0.700722\pi$
$283$	8.97167e18	−	8.97167e18i	0.218063	−	0.218063i	0.807682	+	0.589619i	$0.200722\pi$
$284$			5.06314e19i			1.19639i
$285$	−4.39758e19	−	1.10748e19i	−1.01031	−	0.254436i
$286$	1.84829e19			0.412898
$287$	1.87633e18	+	1.87633e18i	0.0407619	+	0.0407619i
$288$	−4.83164e19	+	4.83164e19i	−1.02083	+	1.02083i
$289$		−	4.78546e19i		−	0.983425i
$290$	−7.67925e18	+	3.04926e19i	−0.153509	+	0.609552i
$291$	−7.10563e19			−1.38184
$292$	−5.57388e19	−	5.57388e19i	−1.05462	−	1.05462i
$293$	3.01448e19	−	3.01448e19i	0.554973	−	0.554973i	−0.372899	−	0.927872i	$-0.621636\pi$
$293$	3.01448e19	−	3.01448e19i	0.554973	−	0.554973i	0.927872	+	0.372899i	$0.121636\pi$
$294$		−	1.34151e20i		−	2.40334i
$295$	4.31600e19	+	7.22163e19i	0.752498	+	1.25910i
$296$	−1.53627e20			−2.60696
$297$	−2.23725e19	−	2.23725e19i	−0.369542	−	0.369542i
$298$	1.86665e19	−	1.86665e19i	0.300147	−	0.300147i
$299$			1.03224e19i			0.161588i
$300$	2.00949e20	−	6.03993e19i	3.06278	−	0.920580i
$301$	6.33474e18			0.0940150
$302$	3.18057e19	+	3.18057e19i	0.459674	+	0.459674i
$303$	3.90589e19	−	3.90589e19i	0.549767	−	0.549767i
$304$			1.49126e20i			2.04440i
$305$	9.57787e19	−	5.72420e19i	1.27900	−	0.764392i
$306$	−1.28981e19			−0.167785
$307$	4.61714e19	+	4.61714e19i	0.585148	+	0.585148i	0.936313	−	0.351165i	$-0.114215\pi$
$307$	4.61714e19	+	4.61714e19i	0.585148	+	0.585148i	−0.351165	+	0.936313i	$0.614215\pi$
$308$	−1.71635e19	+	1.71635e19i	−0.211934	+	0.211934i
$309$			2.42223e19i			0.291439i
$310$	−2.31290e20	−	5.82480e19i	−2.71184	−	0.682948i
$311$	−1.05199e20			−1.20207			−0.601034	−	0.799224i	$-0.705244\pi$
$311$	−1.05199e20			−1.20207			−0.601034	+	0.799224i	$0.705244\pi$
$312$	−3.69936e19	−	3.69936e19i	−0.411993	−	0.411993i
$313$	−9.34620e19	+	9.34620e19i	−1.01457	+	1.01457i	−0.0146733	+	0.999892i	$0.504671\pi$
$313$	−9.34620e19	+	9.34620e19i	−1.01457	+	1.01457i	−0.999892	+	0.0146733i	$0.995329\pi$
$314$			5.90802e19i			0.625180i
$315$	−1.51260e18	+	6.00621e18i	−0.0156042	+	0.0619607i
$316$	3.03645e20			3.05400
$317$	1.12873e19	+	1.12873e19i	0.110692	+	0.110692i	0.760283	−	0.649591i	$-0.225060\pi$
$317$	1.12873e19	+	1.12873e19i	0.110692	+	0.110692i	−0.649591	+	0.760283i	$0.725060\pi$
$318$	1.29930e20	−	1.29930e20i	1.24249	−	1.24249i
$319$		−	4.86883e19i		−	0.454045i
$320$	−7.13093e19	−	1.19316e20i	−0.648554	−	1.08518i
$321$	−2.46818e20			−2.18946
$322$	−1.34951e19	−	1.34951e19i	−0.116769	−	0.116769i
$323$	−8.61453e18	+	8.61453e18i	−0.0727129	+	0.0727129i
$324$			3.60100e20i			2.96526i
$325$	5.93323e18	+	1.97399e19i	0.0476677	+	0.158591i
$326$	2.82900e20			2.21765
$327$	1.10215e20	+	1.10215e20i	0.843062	+	0.843062i
$328$	1.61700e20	−	1.61700e20i	1.20703	−	1.20703i
$329$		−	5.12504e18i		−	0.0373362i
$330$	−3.92632e20	+	2.34656e20i	−2.79173	+	1.66848i
$331$	−1.15661e20			−0.802717			−0.401358	−	0.915921i	$-0.631462\pi$
$331$	−1.15661e20			−0.802717			−0.401358	+	0.915921i	$0.631462\pi$
$332$	−3.91357e19	−	3.91357e19i	−0.265136	−	0.265136i
$333$	7.24834e19	−	7.24834e19i	0.479385	−	0.479385i
$334$		−	3.10927e20i		−	2.00765i
$335$	1.69029e20	+	4.25681e19i	1.06562	+	0.268365i
$336$	4.94039e19			0.304122
$337$	1.20713e20	+	1.20713e20i	0.725628	+	0.725628i	0.969746	−	0.244118i	$-0.0784983\pi$
$337$	1.20713e20	+	1.20713e20i	0.725628	+	0.725628i	−0.244118	+	0.969746i	$0.578498\pi$
$338$	−2.17654e20	+	2.17654e20i	−1.27771	+	1.27771i
$339$		−	2.26866e20i		−	1.30068i
$340$	1.37663e19	−	5.46631e19i	0.0770881	−	0.306100i
$341$	3.69307e20			2.02000
$342$	−1.37757e20	−	1.37757e20i	−0.736048	−	0.736048i
$343$	−2.45772e19	+	2.45772e19i	−0.128286	+	0.128286i
$344$		−	5.45921e20i		−	2.78396i
$345$	−1.31051e20	−	2.19277e20i	−0.652961	−	1.09255i
$346$	−4.79389e20			−2.33389
$347$	−6.19151e19	−	6.19151e19i	−0.294551	−	0.294551i	0.544324	−	0.838875i	$-0.316786\pi$
$347$	−6.19151e19	−	6.19151e19i	−0.294551	−	0.294551i	−0.838875	+	0.544324i	$0.816786\pi$
$348$	−1.64572e20	+	1.64572e20i	−0.765108	+	0.765108i
$349$			1.80830e20i			0.821610i	0.911723	+	0.410805i	$0.134752\pi$
$349$			1.80830e20i			0.821610i	−0.911723	+	0.410805i	$0.865248\pi$
$350$	−3.35641e19	−	1.80503e19i	−0.149049	−	0.0801569i
$351$	−1.48572e19			−0.0644881
$352$	4.60315e20	+	4.60315e20i	1.95305	+	1.95305i
$353$	−5.63816e19	+	5.63816e19i	−0.233851	+	0.233851i	−0.814298	−	0.580447i	$-0.802878\pi$
$353$	−5.63816e19	+	5.63816e19i	−0.233851	+	0.233851i	0.580447	+	0.814298i	$0.302878\pi$
$354$			8.76675e20i			3.55478i
$355$	1.05656e20	−	6.31451e19i	0.418858	−	0.250330i
$356$	−7.82201e20			−3.03193
$357$	2.85390e18	+	2.85390e18i	0.0108167	+	0.0108167i
$358$	5.22394e20	−	5.22394e20i	1.93613	−	1.93613i
$359$		−	3.98348e20i		−	1.44380i	−0.691997	−	0.721901i	$-0.743269\pi$
$359$		−	3.98348e20i		−	1.44380i	0.691997	−	0.721901i	$-0.256731\pi$
$360$	5.17609e20	+	1.30354e20i	1.83477	+	0.462068i
$361$	1.04427e20			0.362037
$362$	1.29069e20	+	1.29069e20i	0.437678	+	0.437678i
$363$	2.22736e20	−	2.22736e20i	0.738819	−	0.738819i
$364$			1.13980e19i			0.0369842i
$365$	−4.67990e19	+	1.85828e20i	−0.148557	+	0.589888i
$366$	1.16271e21			3.61097
$367$	−1.02197e20	−	1.02197e20i	−0.310535	−	0.310535i	0.534581	−	0.845117i	$-0.320469\pi$
$367$	−1.02197e20	−	1.02197e20i	−0.310535	−	0.310535i	−0.845117	+	0.534581i	$0.820469\pi$
$368$	−5.93999e20	+	5.93999e20i	−1.76605	+	1.76605i
$369$			1.52585e20i			0.443915i
$370$	3.23567e20	+	5.41399e20i	0.921192	+	1.54136i
$371$	−2.37046e19			−0.0660453
$372$	−1.24830e21	−	1.24830e21i	−3.40389	−	3.40389i
$373$	−2.35792e20	+	2.35792e20i	−0.629301	+	0.629301i	−0.947892	−	0.318591i	$-0.896790\pi$
$373$	−2.35792e20	+	2.35792e20i	−0.629301	+	0.629301i	0.318591	+	0.947892i	$0.396790\pi$
$374$			1.22881e20i			0.321005i
$375$	−3.76653e20	−	3.44007e20i	−0.963145	−	0.879663i
$376$	−4.41670e20			−1.10559
$377$	−1.61665e19	−	1.61665e19i	−0.0396173	−	0.0396173i
$378$	1.94237e19	−	1.94237e19i	0.0466012	−	0.0466012i
$379$			4.41886e20i			1.03800i	0.854775	+	0.518999i	$0.173695\pi$
$379$			4.41886e20i			1.03800i	−0.854775	+	0.518999i	$0.826305\pi$
$380$	7.30860e20	−	4.36798e20i	1.68099	−	1.00464i
$381$	6.12524e19			0.137950
$382$	−9.07489e20	−	9.07489e20i	−2.00140	−	2.00140i
$383$	−6.14078e20	+	6.14078e20i	−1.32627	+	1.32627i	−0.417680	+	0.908594i	$0.637157\pi$
$383$	−6.14078e20	+	6.14078e20i	−1.32627	+	1.32627i	−0.908594	+	0.417680i	$0.862843\pi$
$384$		−	1.79249e20i		−	0.379147i
$385$	5.72217e19	+	1.44107e19i	0.118543	+	0.0298538i
$386$	1.02980e21			2.08955
$387$	2.57573e20	+	2.57573e20i	0.511933	+	0.511933i
$388$	9.43353e20	−	9.43353e20i	1.83663	−	1.83663i
$389$			9.46296e19i			0.180480i	0.995920	+	0.0902402i	$0.0287635\pi$
$389$			9.46296e19i			0.180480i	−0.995920	+	0.0902402i	$0.971237\pi$
$390$	−5.24544e19	+	2.08285e20i	−0.0980088	+	0.389171i
$391$	−6.86267e19			−0.125626
$392$	1.05460e21	+	1.05460e21i	1.89148	+	1.89148i
$393$	−3.91428e20	+	3.91428e20i	−0.687878	+	0.687878i
$394$		−	2.06775e21i		−	3.56064i
$395$	−3.78692e20	−	6.33636e20i	−0.639012	−	1.06921i
$396$	−1.39575e21			−2.30806
$397$	7.84672e20	+	7.84672e20i	1.27164	+	1.27164i	0.945228	+	0.326412i	$0.105840\pi$
$397$	7.84672e20	+	7.84672e20i	1.27164	+	1.27164i	0.326412	+	0.945228i	$0.394160\pi$
$398$	−2.48195e20	+	2.48195e20i	−0.394211	+	0.394211i
$399$			6.09621e19i			0.0949024i
$400$	−7.94503e20	+	1.47736e21i	−1.21232	+	2.25427i
$401$	−2.00662e20			−0.300130			−0.150065	−	0.988676i	$-0.547948\pi$
$401$	−2.00662e20			−0.300130			−0.150065	+	0.988676i	$0.547948\pi$
$402$	1.28435e21	+	1.28435e21i	1.88310	+	1.88310i
$403$	1.22625e20	−	1.22625e20i	0.176254	−	0.176254i
$404$			1.03710e21i			1.46141i
$405$	7.51444e20	−	4.49099e20i	1.03814	−	0.620444i
$406$	4.22709e19			0.0572576
$407$	−6.90556e20	−	6.90556e20i	−0.917157	−	0.917157i
$408$	2.45946e20	−	2.45946e20i	0.320301	−	0.320301i
$409$		−	4.86410e20i		−	0.621177i	−0.950544	−	0.310589i	$-0.899474\pi$
$409$		−	4.86410e20i		−	0.621177i	0.950544	−	0.310589i	$-0.100526\pi$
$410$	−9.10420e20	−	2.29280e20i	−1.14017	−	0.287141i
$411$	4.16634e20			0.511705
$412$	−3.21578e20	−	3.21578e20i	−0.387355	−	0.387355i
$413$	7.99711e19	−	7.99711e19i	0.0944784	−	0.0944784i
$414$		−	1.09743e21i		−	1.27167i
$415$	−3.28588e19	+	1.30475e20i	−0.0373480	+	0.148301i
$416$	3.05687e20			0.340824
$417$	−3.78217e20	−	3.78217e20i	−0.413669	−	0.413669i
$418$	−1.31243e21	+	1.31243e21i	−1.40820	+	1.40820i
$419$			6.85131e19i			0.0721210i	0.999350	+	0.0360605i	$0.0114809\pi$
$419$			6.85131e19i			0.0721210i	−0.999350	+	0.0360605i	$0.988519\pi$
$420$	−1.44706e20	−	2.42126e20i	−0.149449	−	0.250062i
$421$	6.59559e20			0.668339			0.334169	−	0.942513i	$-0.391544\pi$
$421$	6.59559e20			0.668339			0.334169	+	0.942513i	$0.391544\pi$
$422$	3.86372e20	+	3.86372e20i	0.384154	+	0.384154i
$423$	2.08386e20	−	2.08386e20i	0.203304	−	0.203304i
$424$			2.04284e21i			1.95572i
$425$	−1.31238e20	+	3.94461e19i	−0.123296	+	0.0370589i
$426$	1.28262e21			1.18255
$427$	−1.06064e20	−	1.06064e20i	−0.0959718	−	0.0959718i
$428$	3.27679e21	−	3.27679e21i	2.91004	−	2.91004i
$429$		−	3.32574e20i		−	0.289888i
$430$	−1.92389e21	+	1.14981e21i	−1.64601	+	0.983736i
$431$	−8.29007e19			−0.0696210			−0.0348105	−	0.999394i	$-0.511083\pi$
$431$	−8.29007e19			−0.0696210			−0.0348105	+	0.999394i	$0.511083\pi$
$432$	−8.54953e20	−	8.54953e20i	−0.704810	−	0.704810i
$433$	5.64309e20	−	5.64309e20i	0.456682	−	0.456682i	−0.440883	−	0.897565i	$-0.645335\pi$
$433$	5.64309e20	−	5.64309e20i	0.456682	−	0.456682i	0.897565	+	0.440883i	$0.145335\pi$
$434$			3.20630e20i			0.254733i
$435$	5.48670e20	+	1.38177e20i	0.427954	+	0.107776i
$436$	−2.92646e21			−2.24105
$437$	−7.32967e20	−	7.32967e20i	−0.551103	−	0.551103i
$438$	−1.41200e21	+	1.41200e21i	−1.04242	+	1.04242i
$439$			1.12569e21i			0.816024i	0.912976	+	0.408012i	$0.133778\pi$
$439$			1.12569e21i			0.816024i	−0.912976	+	0.408012i	$0.866222\pi$
$440$	1.24190e21	−	4.93131e21i	0.884025	−	3.51027i
$441$	−9.95154e20			−0.695635
$442$	4.08015e19	+	4.08015e19i	0.0280090	+	0.0280090i
$443$	8.58659e20	−	8.58659e20i	0.578883	−	0.578883i	−0.355712	−	0.934596i	$-0.615762\pi$
$443$	8.58659e20	−	8.58659e20i	0.578883	−	0.578883i	0.934596	+	0.355712i	$0.115762\pi$
$444$			4.66833e21i			3.09099i
$445$	9.75524e20	+	1.63227e21i	0.634392	+	1.06148i
$446$	−2.62640e21			−1.67757
$447$	−3.35877e20	−	3.35877e20i	−0.210727	−	0.210727i
$448$	−1.32129e20	+	1.32129e20i	−0.0814280	+	0.0814280i
$449$			1.05049e21i			0.635948i	0.948099	+	0.317974i	$0.103003\pi$
$449$			1.05049e21i			0.635948i	−0.948099	+	0.317974i	$0.896997\pi$
$450$	−6.30794e20	−	2.09866e21i	−0.375135	−	1.24808i
$451$	1.45369e21			0.849297
$452$	3.01191e21	+	3.01191e21i	1.72876	+	1.72876i
$453$	5.72298e20	−	5.72298e20i	0.322728	−	0.322728i
$454$		−	3.72113e21i		−	2.06171i
$455$	2.37849e19	−	1.42150e19i	0.0129482	−	0.00773848i
$456$	5.25365e21			2.81023
$457$	9.80238e20	+	9.80238e20i	0.515231	+	0.515231i	0.916125	−	0.400894i	$-0.131300\pi$
$457$	9.80238e20	+	9.80238e20i	0.515231	+	0.515231i	−0.400894	+	0.916125i	$0.631300\pi$
$458$	−3.27844e21	+	3.27844e21i	−1.69334	+	1.69334i
$459$		−	9.87756e19i		−	0.0501358i
$460$	4.65101e21	+	1.17131e21i	2.31998	+	0.584263i
$461$	−2.84661e21			−1.39547			−0.697735	−	0.716356i	$-0.745809\pi$
$461$	−2.84661e21			−1.39547			−0.697735	+	0.716356i	$0.745809\pi$
$462$	4.34793e20	+	4.34793e20i	0.209482	+	0.209482i
$463$	−5.66373e20	+	5.66373e20i	−0.268198	+	0.268198i	−0.828374	−	0.560176i	$-0.810734\pi$
$463$	−5.66373e20	+	5.66373e20i	−0.268198	+	0.268198i	0.560176	+	0.828374i	$0.310734\pi$
$464$		−	1.86059e21i		−	0.865980i
$465$	−1.04809e21	+	4.16173e21i	−0.479484	+	1.90393i
$466$	−2.78421e21			−1.25203
$467$	−8.71716e20	−	8.71716e20i	−0.385337	−	0.385337i	0.487684	−	0.873020i	$-0.337842\pi$
$467$	−8.71716e20	−	8.71716e20i	−0.385337	−	0.385337i	−0.873020	+	0.487684i	$0.837842\pi$
$468$	−4.63446e20	+	4.63446e20i	−0.201388	+	0.201388i
$469$		−	2.34318e20i		−	0.100098i
$470$	9.30238e20	+	1.55650e21i	0.390671	+	0.653680i
$471$	1.06306e21			0.438926
$472$	−6.89182e21	−	6.89182e21i	−2.79768	−	2.79768i
$473$	2.45393e21	−	2.45393e21i	0.979427	−	0.979427i
$474$		−	7.69206e21i		−	3.01867i
$475$	−1.82299e21	−	9.80380e20i	−0.703453	−	0.378308i
$476$	−7.57776e19			−0.0287531
$477$	−9.63840e20	−	9.63840e20i	−0.359632	−	0.359632i
$478$	3.91835e21	−	3.91835e21i	1.43774	−	1.43774i
$479$		−	4.50080e20i		−	0.162407i	−0.996698	−	0.0812036i	$-0.974124\pi$
$479$		−	4.50080e20i		−	0.162407i	0.996698	−	0.0812036i	$-0.0258764\pi$
$480$	−6.49368e21	+	3.88094e21i	−2.30442	+	1.37723i
$481$	−4.58586e20			−0.160052
$482$	7.35765e21	+	7.35765e21i	2.52559	+	2.52559i
$483$	−2.42824e20	+	2.42824e20i	−0.0819812	+	0.0819812i
$484$			5.91416e21i			1.96395i
$485$	−3.14506e21	−	7.92051e20i	−1.02730	−	0.258714i
$486$	6.87038e21			2.20745
$487$	9.70460e20	+	9.70460e20i	0.306723	+	0.306723i	0.843637	−	0.536914i	$-0.180410\pi$
$487$	9.70460e20	+	9.70460e20i	0.306723	+	0.306723i	−0.536914	+	0.843637i	$0.680410\pi$
$488$	−9.14045e21	+	9.14045e21i	−2.84190	+	2.84190i
$489$		−	5.09038e21i		−	1.55697i
$490$	1.49536e21	−	5.93773e21i	0.449962	−	1.78670i
$491$	6.05872e20			0.179361			0.0896807	−	0.995971i	$-0.471415\pi$
$491$	6.05872e20			0.179361			0.0896807	+	0.995971i	$0.471415\pi$
$492$	−4.91364e21	−	4.91364e21i	−1.43114	−	1.43114i
$493$	1.07480e20	−	1.07480e20i	0.0308002	−	0.0308002i
$494$			8.71559e20i			0.245743i
$495$	1.74071e21	+	2.91260e21i	0.482932	+	0.808053i
$496$	1.41128e22			3.85266
$497$	−1.17002e20	−	1.17002e20i	−0.0314297	−	0.0314297i
$498$	−9.91402e20	+	9.91402e20i	−0.262069	+	0.262069i
$499$			8.34117e20i			0.216981i	0.994097	+	0.108491i	$0.0346018\pi$
$499$			8.34117e20i			0.216981i	−0.994097	+	0.108491i	$0.965398\pi$
$500$	9.56758e21	−	4.33423e20i	2.44930	−	0.110956i
$501$	−5.59469e21			−1.40953
$502$	2.67520e21	+	2.67520e21i	0.663326	+	0.663326i
$503$	−2.58150e21	+	2.58150e21i	−0.629982	+	0.629982i	−0.948063	−	0.318081i	$-0.896961\pi$
$503$	−2.58150e21	+	2.58150e21i	−0.629982	+	0.629982i	0.318081	+	0.948063i	$0.396961\pi$
$504$		−	7.17543e20i		−	0.172347i
$505$	2.16419e21	−	1.29343e21i	0.511640	−	0.305781i
$506$	−1.04553e22			−2.43295
$507$	3.91636e21	+	3.91636e21i	0.897055	+	0.897055i
$508$	−8.13195e20	+	8.13195e20i	−0.183352	+	0.183352i
$509$		−	4.00742e21i		−	0.889453i	−0.895667	−	0.444726i	$-0.853301\pi$
$509$		−	4.00742e21i		−	0.889453i	0.895667	−	0.444726i	$-0.146699\pi$
$510$	−1.38475e21	−	3.48735e20i	−0.302559	−	0.0761963i
$511$	2.57608e20			0.0554104
$512$	−5.46336e21	−	5.46336e21i	−1.15691	−	1.15691i
$513$	1.05497e21	−	1.05497e21i	0.219939	−	0.219939i
$514$			6.16770e21i			1.26595i
$515$	−2.70001e20	+	1.07212e21i	−0.0545642	+	0.216662i
$516$	−1.65891e22			−3.30085
$517$	−1.98532e21	−	1.98532e21i	−0.388960	−	0.388960i
$518$	5.99536e20	−	5.99536e20i	0.115658	−	0.115658i
$519$			8.62591e21i			1.63857i
$520$	−1.22503e21	−	2.04975e21i	−0.229151	−	0.383420i
$521$	1.01590e22			1.87133			0.935665	−	0.352889i	$-0.114801\pi$
$521$	1.01590e22			1.87133			0.935665	+	0.352889i	$0.114801\pi$
$522$	1.71875e21	+	1.71875e21i	0.311780	+	0.311780i
$523$	−4.88787e20	+	4.88787e20i	−0.0873185	+	0.0873185i	−0.749417	−	0.662098i	$-0.769666\pi$
$523$	−4.88787e20	+	4.88787e20i	−0.0873185	+	0.0873185i	0.662098	+	0.749417i	$0.269666\pi$
$524$		−	1.03933e22i		−	1.82854i
$525$	−3.24789e20	+	6.03936e20i	−0.0562765	+	0.104645i
$526$	2.76176e21			0.471303
$527$	8.15252e20	+	8.15252e20i	0.137027	+	0.137027i
$528$	1.91379e22	−	1.91379e22i	3.16827	−	3.16827i
$529$			2.93515e20i			0.0478613i
$530$	7.19920e21	−	4.30259e21i	1.15632	−	0.691072i
$531$	6.50332e21			1.02891
$532$	−8.09342e20	−	8.09342e20i	−0.126136	−	0.126136i
$533$	4.82684e20	−	4.82684e20i	0.0741046	−	0.0741046i
$534$			1.98150e22i			2.99685i
$535$	−1.09245e22	−	2.75123e21i	−1.62770	−	0.409918i
$536$	−2.01933e22			−2.96407
$537$	−9.39973e21	−	9.39973e21i	−1.35932	−	1.35932i
$538$	2.79520e21	−	2.79520e21i	0.398250	−	0.398250i
$539$			9.48093e21i			1.33089i
$540$	−1.68588e21	+	6.69428e21i	−0.233173	+	0.925878i
$541$	1.27581e21			0.173863			0.0869314	−	0.996214i	$-0.472294\pi$
$541$	1.27581e21			0.173863			0.0869314	+	0.996214i	$0.472294\pi$
$542$	3.11274e21	+	3.11274e21i	0.417974	+	0.417974i
$543$	2.32241e21	−	2.32241e21i	0.307285	−	0.307285i
$544$			2.03231e21i			0.264971i
$545$	3.64975e21	+	6.10684e21i	0.468911	+	0.784593i
$546$	2.88738e20			0.0365564
$547$	−5.75598e21	−	5.75598e21i	−0.718159	−	0.718159i	0.250069	−	0.968228i	$-0.419547\pi$
$547$	−5.75598e21	−	5.75598e21i	−0.718159	−	0.718159i	−0.968228	+	0.250069i	$0.919547\pi$
$548$	−5.53129e21	+	5.53129e21i	−0.680114	+	0.680114i
$549$		−	8.62518e21i		−	1.04518i
$550$	−1.99941e22	+	6.00964e21i	−2.38782	+	0.717706i
$551$	2.29589e21			0.270233
$552$	2.09263e22	+	2.09263e22i	2.42761	+	2.42761i
$553$	−7.01677e20	+	7.01677e20i	−0.0802299	+	0.0802299i
$554$		−	3.19827e22i		−	3.60444i
$555$	9.74170e21	−	5.82211e21i	1.08216	−	0.646750i
$556$	1.00425e22			1.09963
$557$	2.85063e21	+	2.85063e21i	0.307680	+	0.307680i	0.844009	−	0.536329i	$-0.180189\pi$
$557$	2.85063e21	+	2.85063e21i	0.307680	+	0.307680i	−0.536329	+	0.844009i	$0.680189\pi$
$558$	−1.30369e22	+	1.30369e22i	−1.38708	+	1.38708i
$559$		−	1.62961e21i		−	0.170918i
$560$	2.18669e21	+	5.50696e20i	0.226091	+	0.0569387i
$561$	2.21106e21			0.225371
$562$	7.88672e21	+	7.88672e21i	0.792512	+	0.792512i
$563$	1.00638e22	−	1.00638e22i	0.997000	−	0.997000i	−0.00299588	−	0.999996i	$-0.500954\pi$
$563$	1.00638e22	−	1.00638e22i	0.997000	−	0.997000i	0.999996	+	0.00299588i	$0.000953621\pi$
$564$			1.34212e22i			1.31087i
$565$	2.52883e21	−	1.00414e22i	0.243519	−	0.966960i
$566$	6.03465e21			0.572955
$567$	−8.32136e20	−	8.32136e20i	−0.0778986	−	0.0778986i
$568$	−1.00831e22	+	1.00831e22i	−0.930691	+	0.930691i
$569$			1.48136e22i			1.34822i	0.738629	+	0.674112i	$0.235474\pi$
$569$			1.48136e22i			1.34822i	−0.738629	+	0.674112i	$0.764526\pi$
$570$	−1.10651e22	−	1.85145e22i	−0.993020	−	1.66155i
$571$	5.94204e21			0.525831			0.262916	−	0.964819i	$-0.415316\pi$
$571$	5.94204e21			0.525831			0.262916	+	0.964819i	$0.415316\pi$
$572$	4.41530e21	+	4.41530e21i	0.385293	+	0.385293i
$573$	−1.63290e22	+	1.63290e22i	−1.40515	+	1.40515i
$574$			1.26208e21i			0.107101i
$575$	−3.35627e21	−	1.11664e22i	−0.280876	−	0.934477i
$576$	−1.07448e22			−0.886787
$577$	6.79999e21	+	6.79999e21i	0.553480	+	0.553480i	0.927443	−	0.373963i	$-0.122001\pi$
$577$	6.79999e21	+	6.79999e21i	0.553480	+	0.553480i	−0.373963	+	0.927443i	$0.622001\pi$
$578$	1.60943e22	−	1.60943e22i	1.29196	−	1.29196i
$579$		−	1.85297e22i		−	1.46703i
$580$	−9.11868e21	+	5.44977e21i	−0.712046	+	0.425553i
$581$	1.80873e20			0.0139305
$582$	−2.38974e22	−	2.38974e22i	−1.81538	−	1.81538i
$583$	−9.18260e21	+	9.18260e21i	−0.688045	+	0.688045i
$584$		−	2.22003e22i		−	1.64080i
$585$	1.54509e21	+	3.89115e20i	0.112644	+	0.0283682i
$586$	2.02764e22			1.45818
$587$	4.60252e21	+	4.60252e21i	0.326505	+	0.326505i	0.851256	−	0.524751i	$-0.175841\pi$
$587$	4.60252e21	+	4.60252e21i	0.326505	+	0.326505i	−0.524751	+	0.851256i	$0.675841\pi$
$588$	3.20467e22	−	3.20467e22i	2.24266	−	2.24266i
$589$			1.74146e22i			1.20224i
$590$	−9.77213e21	+	3.88030e22i	−0.665539	+	2.64271i
$591$	−3.72061e22			−2.49985
$592$	−2.63892e22	−	2.63892e22i	−1.74925	−	1.74925i
$593$	−1.38310e22	+	1.38310e22i	−0.904518	+	0.904518i	−0.995823	−	0.0913053i	$-0.970896\pi$
$593$	−1.38310e22	+	1.38310e22i	−0.904518	+	0.904518i	0.0913053	+	0.995823i	$0.470896\pi$
$594$		−	1.50485e22i		−	0.970962i
$595$	9.45062e19	+	1.58130e20i	0.00601623	+	0.0100665i
$596$	8.91831e21			0.560161
$597$	4.46591e21	+	4.46591e21i	0.276768	+	0.276768i
$598$	−3.47159e21	+	3.47159e21i	−0.212285	+	0.212285i
$599$			1.39652e22i			0.842624i	0.906916	+	0.421312i	$0.138430\pi$
$599$			1.39652e22i			0.842624i	−0.906916	+	0.421312i	$0.861570\pi$
$600$	5.20465e22	+	2.79900e22i	3.09872	+	1.66645i
$601$	−4.28172e21			−0.251549			−0.125774	−	0.992059i	$-0.540142\pi$
$601$	−4.28172e21			−0.251549			−0.125774	+	0.992059i	$0.540142\pi$
$602$	2.13048e21	+	2.13048e21i	0.123511	+	0.123511i
$603$	9.52748e21	−	9.52748e21i	0.545054	−	0.545054i
$604$			1.51958e22i			0.857884i
$605$	1.23415e22	−	7.37586e21i	0.687581	−	0.410932i
$606$	2.62723e22			1.44450
$607$	−8.39700e21	−	8.39700e21i	−0.455632	−	0.455632i	0.441586	−	0.897219i	$-0.354416\pi$
$607$	−8.39700e21	−	8.39700e21i	−0.455632	−	0.455632i	−0.897219	+	0.441586i	$0.854416\pi$
$608$	−2.17061e22	+	2.17061e22i	−1.16239	+	1.16239i
$609$		−	7.60603e20i		−	0.0401994i
$610$	5.14634e22	+	1.29605e22i	2.68448	+	0.676058i
$611$	−1.31841e21			−0.0678768
$612$	−3.08115e21	−	3.08115e21i	−0.156567	−	0.156567i
$613$	3.28621e20	−	3.28621e20i	0.0164820	−	0.0164820i	−0.698818	−	0.715300i	$-0.746290\pi$
$613$	3.28621e20	−	3.28621e20i	0.0164820	−	0.0164820i	0.715300	+	0.698818i	$0.246290\pi$
$614$			3.10564e22i			1.53746i
$615$	−4.12556e21	+	1.63817e22i	−0.201596	+	0.800493i
$616$	−6.83610e21			−0.329733
$617$	4.84147e21	+	4.84147e21i	0.230513	+	0.230513i	0.812907	−	0.582394i	$-0.197884\pi$
$617$	4.84147e21	+	4.84147e21i	0.230513	+	0.230513i	−0.582394	+	0.812907i	$0.697884\pi$
$618$	−8.14636e21	+	8.14636e21i	−0.382874	+	0.382874i
$619$		−	2.47483e22i		−	1.14821i	−0.818783	−	0.574104i	$-0.805351\pi$
$619$		−	2.47483e22i		−	1.14821i	0.818783	−	0.574104i	$-0.194649\pi$
$620$	−4.13372e22	−	6.91663e22i	−1.89325	−	3.16782i
$621$	8.40431e21			0.379988
$622$	−3.53802e22	−	3.53802e22i	−1.57920	−	1.57920i
$623$	1.80755e21	−	1.80755e21i	0.0796499	−	0.0796499i
$624$		−	1.27091e22i		−	0.552889i
$625$	−1.28367e22	−	1.94247e22i	−0.551331	−	0.834286i
$626$	−6.28657e22			−2.66575
$627$	2.36152e22	+	2.36152e22i	0.988672	+	0.988672i
$628$	−1.41134e22	+	1.41134e22i	−0.583383	+	0.583383i
$629$		−	3.04883e21i		−	0.124431i
$630$	−2.52870e21	+	1.51128e21i	−0.101900	+	0.0609003i
$631$	−2.87349e22			−1.14334			−0.571670	−	0.820484i	$-0.693704\pi$
$631$	−2.87349e22			−1.14334			−0.571670	+	0.820484i	$0.693704\pi$
$632$	6.04698e22	+	6.04698e22i	2.37575	+	2.37575i
$633$	6.95220e21	−	6.95220e21i	0.269707	−	0.269707i
$634$			7.59222e21i			0.290840i
$635$	2.71112e21	+	6.82769e20i	0.102556	+	0.0258276i
$636$	6.20765e22			2.31884
$637$	3.14805e21	+	3.14805e21i	0.116125	+	0.116125i
$638$	1.63747e22	−	1.63747e22i	0.596496	−	0.596496i
$639$		−	9.51466e21i		−	0.342284i
$640$	1.99806e21	−	7.93385e21i	0.0709853	−	0.281867i
$641$	2.21002e22			0.775412			0.387706	−	0.921783i	$-0.373268\pi$
$641$	2.21002e22			0.775412			0.387706	+	0.921783i	$0.373268\pi$
$642$	−8.30090e22	−	8.30090e22i	−2.87637	−	2.87637i
$643$	2.95279e22	−	2.95279e22i	1.01052	−	1.01052i	0.0105744	−	0.999944i	$-0.496634\pi$
$643$	2.95279e22	−	2.95279e22i	1.01052	−	1.01052i	0.999944	−	0.0105744i	$-0.00336601\pi$
$644$		−	6.44753e21i		−	0.217925i
$645$	2.06892e22	+	3.46176e22i	0.690661	+	1.15563i
$646$	−5.79442e21			−0.191051
$647$	1.86305e21	+	1.86305e21i	0.0606723	+	0.0606723i	0.736792	−	0.676120i	$-0.236340\pi$
$647$	1.86305e21	+	1.86305e21i	0.0606723	+	0.0606723i	−0.676120	+	0.736792i	$0.736340\pi$
$648$	−7.17125e22	+	7.17125e22i	−2.30672	+	2.30672i
$649$		−	6.19577e22i		−	1.96851i
$650$	−4.64343e21	+	8.63431e21i	−0.145724	+	0.270970i
$651$	5.76926e21			0.178843
$652$	6.75806e22	+	6.75806e22i	2.06939	+	2.06939i
$653$	8.24522e21	−	8.24522e21i	0.249400	−	0.249400i	−0.571324	−	0.820724i	$-0.693570\pi$
$653$	8.24522e21	−	8.24522e21i	0.249400	−	0.249400i	0.820724	+	0.571324i	$0.193570\pi$
$654$			7.41344e22i			2.21512i
$655$	−2.16884e22	+	1.29620e22i	−0.640172	+	0.382598i
$656$	5.55519e22			1.61982
$657$	1.04744e22	+	1.04744e22i	0.301722	+	0.301722i
$658$	1.72364e21	−	1.72364e21i	0.0490500	−	0.0490500i
$659$		−	4.75532e22i		−	1.33689i	−0.743761	−	0.668446i	$-0.766960\pi$
$659$		−	4.75532e22i		−	1.33689i	0.743761	−	0.668446i	$-0.233040\pi$
$660$	−1.49849e23	−	3.77380e22i	−4.16202	−	1.04816i
$661$	4.67704e22			1.28339			0.641697	−	0.766958i	$-0.278231\pi$
$661$	4.67704e22			1.28339			0.641697	+	0.766958i	$0.278231\pi$
$662$	−3.88987e22	−	3.88987e22i	−1.05456	−	1.05456i
$663$	7.34163e20	−	7.34163e20i	0.0196646	−	0.0196646i
$664$		−	1.55875e22i		−	0.412506i
$665$	−6.79533e20	+	2.69828e21i	−0.0177680	+	0.0705527i
$666$	4.87548e22			1.25957
$667$	9.14496e21	+	9.14496e21i	0.233440	+	0.233440i
$668$	7.42759e22	−	7.42759e22i	1.87342	−	1.87342i
$669$			4.72582e22i			1.17779i
$670$	4.25308e22	+	7.11635e22i	1.04738	+	1.75250i
$671$	−8.21729e22			−1.99963
$672$	7.19099e21	+	7.19099e21i	0.172916	+	0.172916i
$673$	−5.30419e22	+	5.30419e22i	−1.26037	+	1.26037i	−0.309460	+	0.950913i	$0.600148\pi$
$673$	−5.30419e22	+	5.30419e22i	−1.26037	+	1.26037i	−0.950913	+	0.309460i	$0.899852\pi$
$674$			8.11955e22i			1.90657i
$675$	1.60719e22	−	4.83074e21i	0.372939	−	0.112094i
$676$	−1.03988e23			−2.38458
$677$	−2.71174e22	−	2.71174e22i	−0.614523	−	0.614523i	0.329598	−	0.944121i	$-0.393087\pi$
$677$	−2.71174e22	−	2.71174e22i	−0.614523	−	0.614523i	−0.944121	+	0.329598i	$0.893087\pi$
$678$	7.62989e22	−	7.62989e22i	1.70876	−	1.70876i
$679$			4.35989e21i			0.0964978i
$680$	1.36275e22	−	8.14444e21i	0.298088	−	0.178152i
$681$	−6.69563e22			−1.44749
$682$	1.24204e23	+	1.24204e23i	2.65376	+	2.65376i
$683$	−1.17516e22	+	1.17516e22i	−0.248160	+	0.248160i	−0.820215	−	0.572055i	$-0.806146\pi$
$683$	−1.17516e22	+	1.17516e22i	−0.248160	+	0.248160i	0.572055	+	0.820215i	$0.306146\pi$
$684$		−	6.58164e22i		−	1.37368i
$685$	1.84408e22	+	4.64414e21i	0.380414	+	0.0958033i
$686$	−1.65314e22			−0.337068
$687$	5.89907e22	+	5.89907e22i	1.18886	+	1.18886i
$688$	9.37753e22	−	9.37753e22i	1.86802	−	1.86802i
$689$			6.09799e21i			0.120070i
$690$	2.96721e22	−	1.17821e23i	0.577504	−	2.29314i
$691$	9.87813e21			0.190042			0.0950212	−	0.995475i	$-0.469708\pi$
$691$	9.87813e21			0.190042			0.0950212	+	0.995475i	$0.469708\pi$
$692$	−1.14519e23	−	1.14519e23i	−2.17785	−	2.17785i
$693$	3.22537e21	−	3.22537e21i	0.0606336	−	0.0606336i
$694$		−	4.16462e22i		−	0.773926i
$695$	−1.25246e22	−	2.09564e22i	−0.230083	−	0.384980i
$696$	−6.55479e22			−1.19038
$697$	3.20905e21	+	3.20905e21i	0.0576122	+	0.0576122i
$698$	−6.08160e22	+	6.08160e22i	−1.07938	+	1.07938i
$699$			5.00979e22i			0.879026i
$700$	−3.70599e21	−	1.23299e22i	−0.0642866	−	0.213882i
$701$	6.05029e22			1.03760			0.518802	−	0.854894i	$-0.326378\pi$
$701$	6.05029e22			1.03760			0.518802	+	0.854894i	$0.326378\pi$
$702$	−4.99672e21	−	4.99672e21i	−0.0847204	−	0.0847204i
$703$	3.25630e22	−	3.25630e22i	0.545861	−	0.545861i
$704$			1.02367e23i			1.69660i
$705$	2.80069e22	−	1.67383e22i	0.458936	−	0.274282i
$706$	−3.79241e22			−0.614438
$707$	−2.39659e21	−	2.39659e21i	−0.0383917	−	0.0383917i
$708$	−2.09424e23	+	2.09424e23i	−3.31712	+	3.31712i
$709$		−	4.31217e22i		−	0.675345i	−0.941264	−	0.337672i	$-0.890360\pi$
$709$		−	4.31217e22i		−	0.675345i	0.941264	−	0.337672i	$-0.109640\pi$
$710$	5.67706e22	+	1.42971e22i	0.879138	+	0.221402i
$711$	−5.70610e22			−0.873740
$712$	−1.55772e23	−	1.55772e23i	−2.35858	−	2.35858i
$713$	−6.93656e22	+	6.93656e22i	−1.03855	+	1.03855i
$714$			1.91963e21i			0.0284205i
$715$	3.70714e21	−	1.47202e22i	0.0542738	−	0.215509i
$716$	2.49584e23			3.61337
$717$	−7.05050e22	−	7.05050e22i	−1.00941	−	1.00941i
$718$	1.33971e23	−	1.33971e23i	1.89678	−	1.89678i
$719$			8.16788e22i			1.14361i	0.820389	+	0.571805i	$0.193757\pi$
$719$			8.16788e22i			1.14361i	−0.820389	+	0.571805i	$0.806243\pi$
$720$	6.65203e22	+	1.11303e23i	0.921074	+	1.54116i
$721$	1.48624e21			0.0203519
$722$	3.51204e22	+	3.51204e22i	0.475622	+	0.475622i
$723$	1.32390e23	−	1.32390e23i	1.77317	−	1.77317i
$724$			6.16654e22i			0.816833i
$725$	2.27448e22	+	1.22318e22i	0.297973	+	0.160246i
$726$	1.49820e23			1.94123
$727$	−2.07289e22	−	2.07289e22i	−0.265645	−	0.265645i	0.561698	−	0.827343i	$-0.310148\pi$
$727$	−2.07289e22	−	2.07289e22i	−0.265645	−	0.265645i	−0.827343	+	0.561698i	$0.810148\pi$
$728$	−2.26986e21	+	2.26986e21i	−0.0287706	+	0.0287706i
$729$		−	2.71518e22i		−	0.340391i
$730$	−7.82365e22	+	4.67579e22i	−0.970122	+	0.579792i
$731$	1.08342e22			0.132879
$732$	2.77754e23	+	2.77754e23i	3.36955	+	3.36955i
$733$	−5.17301e22	+	5.17301e22i	−0.620743	+	0.620743i	−0.945721	−	0.324978i	$-0.894643\pi$
$733$	−5.17301e22	+	5.17301e22i	−0.620743	+	0.620743i	0.324978	+	0.945721i	$0.394643\pi$
$734$		−	6.87414e22i		−	0.815924i
$735$	−1.06841e23	−	2.69068e22i	−1.25441	−	0.315910i
$736$	−1.72919e23			−2.00826
$737$	−9.07692e22	−	9.07692e22i	−1.04279	−	1.04279i
$738$	−5.13168e22	+	5.13168e22i	−0.583188	+	0.583188i
$739$			6.59756e22i			0.741699i	0.928693	+	0.370850i	$0.120933\pi$
$739$			6.59756e22i			0.741699i	−0.928693	+	0.370850i	$0.879067\pi$
$740$	−5.20370e22	+	2.06627e23i	−0.578706	+	2.29792i
$741$	1.56824e22			0.172531
$742$	−7.97227e21	−	7.97227e21i	−0.0867662	−	0.0867662i
$743$	−6.68400e22	+	6.68400e22i	−0.719658	+	0.719658i	−0.968535	−	0.248877i	$-0.919939\pi$
$743$	−6.68400e22	+	6.68400e22i	−0.719658	+	0.719658i	0.248877	+	0.968535i	$0.419939\pi$
$744$		−	4.97189e23i		−	5.29587i
$745$	−1.11225e22	−	1.86104e22i	−0.117207	−	0.196113i
$746$	−1.58602e23			−1.65347
$747$	7.35438e21	+	7.35438e21i	0.0758545	+	0.0758545i
$748$	−2.93544e22	+	2.93544e22i	−0.299544	+	0.299544i
$749$			1.51443e22i			0.152896i
$750$	−1.09796e22	−	2.42370e23i	−0.109673	−	2.42097i
$751$	1.99115e23			1.96782			0.983910	−	0.178666i	$-0.0571782\pi$
$751$	1.99115e23			1.96782			0.983910	+	0.178666i	$0.0571782\pi$
$752$	−7.58676e22	−	7.58676e22i	−0.741846	−	0.741846i
$753$	4.81364e22	−	4.81364e22i	0.465708	−	0.465708i
$754$		−	1.08741e22i		−	0.104094i
$755$	3.17101e22	−	1.89515e22i	0.300346	−	0.179501i
$756$	9.28005e21			0.0869713
$757$	−4.99979e21	−	4.99979e21i	−0.0463644	−	0.0463644i	0.683544	−	0.729909i	$-0.260438\pi$
$757$	−4.99979e21	−	4.99979e21i	−0.0463644	−	0.0463644i	−0.729909	+	0.683544i	$0.760438\pi$
$758$	−1.48614e23	+	1.48614e23i	−1.36366	+	1.36366i
$759$			1.88128e23i			1.70812i
$760$	2.32535e23	+	5.85614e22i	2.08919	+	0.526142i
$761$	1.23073e23			1.09417			0.547084	−	0.837078i	$-0.315738\pi$
$761$	1.23073e23			1.09417			0.547084	+	0.837078i	$0.315738\pi$
$762$	2.06002e22	+	2.06002e22i	0.181231	+	0.181231i
$763$	6.76261e21	−	6.76261e21i	0.0588733	−	0.0588733i
$764$		−	4.33571e23i		−	3.73520i
$765$	−2.58697e21	+	1.02723e22i	−0.0220546	+	0.0875742i
$766$	−4.13050e23			−3.48475
$767$	−2.05725e22	−	2.05725e22i	−0.171761	−	0.171761i
$768$	−8.08406e22	+	8.08406e22i	−0.667944	+	0.667944i
$769$		−	9.70633e22i		−	0.793678i	−0.917888	−	0.396839i	$-0.870107\pi$
$769$		−	9.70633e22i		−	0.793678i	0.917888	−	0.396839i	$-0.129893\pi$
$770$	1.43981e22	+	2.40912e22i	0.116514	+	0.194954i
$771$	1.10979e23			0.888801
$772$	2.46003e23	+	2.46003e23i	1.94985	+	1.94985i
$773$	3.65226e22	−	3.65226e22i	0.286500	−	0.286500i	−0.549194	−	0.835695i	$-0.685065\pi$
$773$	3.65226e22	−	3.65226e22i	0.286500	−	0.286500i	0.835695	+	0.549194i	$0.185065\pi$
$774$			1.73253e23i			1.34509i
$775$	−9.27800e22	+	1.72522e23i	−0.712920	+	1.32565i
$776$	3.75730e23			2.85748
$777$	−1.07878e22	−	1.07878e22i	−0.0812015	−	0.0812015i
$778$	−3.18255e22	+	3.18255e22i	−0.237104	+	0.237104i
$779$			6.85484e22i			0.505473i
$780$	−6.22867e22	+	3.72256e22i	−0.454609	+	0.271697i
$781$	−9.06471e22			−0.654855
$782$	−2.30803e22	−	2.30803e22i	−0.165039	−	0.165039i
$783$	−1.31625e22	+	1.31625e22i	−0.0931632	+	0.0931632i
$784$			3.62308e23i			2.53834i
$785$	4.70528e22	+	1.18498e22i	0.326308	+	0.0821773i
$786$	−2.63288e23			−1.80738
$787$	2.68452e22	+	2.68452e22i	0.182419	+	0.182419i	0.792409	−	0.609990i	$-0.208827\pi$
$787$	2.68452e22	+	2.68452e22i	0.182419	+	0.182419i	−0.609990	+	0.792409i	$0.708827\pi$
$788$	4.93954e23	−	4.93954e23i	3.32259	−	3.32259i
$789$		−	4.96938e22i		−	0.330892i
$790$	8.57420e22	−	3.40463e23i	0.565167	−	2.24415i
$791$	−1.39201e22			−0.0908303
$792$	−2.77959e23	−	2.77959e23i	−1.79547	−	1.79547i
$793$	−2.72848e22	+	2.72848e22i	−0.174476	+	0.174476i
$794$			5.27797e23i			3.34120i
$795$	−7.74189e22	−	1.29539e23i	−0.485188	−	0.811828i
$796$	−1.18580e23			−0.735712
$797$	−1.17771e23	−	1.17771e23i	−0.723389	−	0.723389i	0.245905	−	0.969294i	$-0.420915\pi$
$797$	−1.17771e23	−	1.17771e23i	−0.723389	−	0.723389i	−0.969294	+	0.245905i	$0.920915\pi$
$798$	−2.05026e22	+	2.05026e22i	−0.124677	+	0.124677i
$799$		−	8.76525e21i		−	0.0527703i
$800$	−3.30680e23	+	9.93925e22i	−1.97101	+	0.592426i
$801$	1.46991e23			0.867424
$802$	−6.74859e22	−	6.74859e22i	−0.394292	−	0.394292i
$803$	9.97909e22	−	9.97909e22i	0.577253	−	0.577253i
$804$			6.13622e23i			3.51441i
$805$	−1.34545e22	+	8.04105e21i	−0.0762957	+	0.0455980i
$806$	8.24816e22			0.463102
$807$	−5.02956e22	−	5.02956e22i	−0.279603	−	0.279603i
$808$	−2.06535e23	+	2.06535e23i	−1.13685	+	1.13685i
$809$		−	1.88036e23i		−	1.02483i	−0.858738	−	0.512415i	$-0.828751\pi$
$809$		−	1.88036e23i		−	1.02483i	0.858738	−	0.512415i	$-0.171249\pi$
$810$	4.03763e23	+	1.01683e23i	2.17894	+	0.548745i
$811$	2.08734e23			1.11539			0.557696	−	0.830045i	$-0.311686\pi$
$811$	2.08734e23			1.11539			0.557696	+	0.830045i	$0.311686\pi$
$812$	1.00979e22	+	1.00979e22i	0.0534295	+	0.0534295i
$813$	5.60093e22	−	5.60093e22i	0.293451	−	0.293451i
$814$		−	4.64492e23i		−	2.40981i
$815$	5.67415e22	−	2.25308e23i	0.291501	−	1.15749i
$816$	8.44945e22			0.429840
$817$	1.15714e23	+	1.15714e23i	0.582922	+	0.582922i
$818$	1.63588e23	−	1.63588e23i	0.816064	−	0.816064i
$819$		−	2.14191e21i		−	0.0105811i
$820$	−1.62714e23	−	2.72257e23i	−0.796002	−	1.33189i
$821$	−3.99301e23			−1.93444			−0.967219	−	0.253943i	$-0.918272\pi$
$821$	−3.99301e23			−1.93444			−0.967219	+	0.253943i	$0.918272\pi$
$822$	1.40121e23	+	1.40121e23i	0.672246	+	0.672246i
$823$	−2.36061e23	+	2.36061e23i	−1.12157	+	1.12157i	−0.130063	+	0.991506i	$0.541518\pi$
$823$	−2.36061e23	+	2.36061e23i	−1.12157	+	1.12157i	−0.991506	+	0.130063i	$0.958482\pi$
$824$		−	1.28082e23i		−	0.602658i
$825$	1.08135e23	+	3.59766e23i	0.503887	+	1.67644i
$826$	5.37913e22			0.248240
$827$	2.74602e23	+	2.74602e23i	1.25505	+	1.25505i	0.953429	+	0.301618i	$0.0975268\pi$
$827$	2.74602e23	+	2.74602e23i	1.25505	+	1.25505i	0.301618	+	0.953429i	$0.402473\pi$
$828$	2.62159e23	−	2.62159e23i	1.18665	−	1.18665i
$829$		−	3.35172e23i		−	1.50256i	−0.659984	−	0.751280i	$-0.729437\pi$
$829$		−	3.35172e23i		−	1.50256i	0.659984	−	0.751280i	$-0.270563\pi$
$830$	−5.49320e22	+	3.28300e22i	−0.243894	+	0.145763i
$831$	−5.75482e23			−2.53060
$832$	3.39900e22	+	3.39900e22i	0.148035	+	0.148035i
$833$	−2.09293e22	+	2.09293e22i	−0.0902808	+	0.0902808i
$834$		−	2.54402e23i		−	1.08691i
$835$	−2.47630e23	−	6.23629e22i	−1.04788	−	0.263897i
$836$	−6.27039e23			−2.62811
$837$	−9.98392e22	−	9.98392e22i	−0.414474	−	0.414474i
$838$	−2.30421e22	+	2.30421e22i	−0.0947480	+	0.0947480i
$839$			2.05076e23i			0.835253i	0.908619	+	0.417627i	$0.137138\pi$
$839$			2.05076e23i			0.835253i	−0.908619	+	0.417627i	$0.862862\pi$
$840$	1.94008e22	−	7.70362e22i	0.0782681	−	0.310785i
$841$	2.21602e23			0.885533
$842$	2.21821e23	+	2.21821e23i	0.878022	+	0.878022i
$843$	1.41910e23	−	1.41910e23i	0.556407	−	0.556407i
$844$			1.84597e23i			0.716943i
$845$	1.29689e23	+	2.16999e23i	0.498942	+	0.834842i
$846$	1.40168e23			0.534177
$847$	−1.36667e22	−	1.36667e22i	−0.0515937	−	0.0515937i
$848$	−3.50907e23	+	3.50907e23i	−1.31228	+	1.31228i
$849$		−	1.08585e23i		−	0.402260i
$850$	−5.74039e22	−	3.08711e22i	−0.210664	−	0.113292i
$851$	2.59410e23			0.943083
$852$	3.06398e23	+	3.06398e23i	1.10349	+	1.10349i
$853$	−2.20341e23	+	2.20341e23i	−0.786146	+	0.786146i	−0.980860	−	0.194714i	$-0.937622\pi$
$853$	−2.20341e23	+	2.20341e23i	−0.786146	+	0.786146i	0.194714	+	0.980860i	$0.437622\pi$
$854$		−	7.13420e22i		−	0.252163i
$855$	−1.37343e23	+	8.20830e22i	−0.480926	+	0.287425i
$856$	1.30512e24			4.52752
$857$	7.34874e22	+	7.34874e22i	0.252561	+	0.252561i	0.822020	−	0.569459i	$-0.192847\pi$
$857$	7.34874e22	+	7.34874e22i	0.252561	+	0.252561i	−0.569459	+	0.822020i	$0.692847\pi$
$858$	1.11850e23	−	1.11850e23i	0.380836	−	0.380836i
$859$			1.24022e23i			0.418363i	0.977877	+	0.209182i	$0.0670800\pi$
$859$			1.24022e23i			0.418363i	−0.977877	+	0.209182i	$0.932920\pi$
$860$	−7.34260e23	−	1.84916e23i	−2.45393	−	0.617997i
$861$	2.27094e22			0.0751934
$862$	−2.78809e22	−	2.78809e22i	−0.0914637	−	0.0914637i
$863$	3.75851e23	−	3.75851e23i	1.22160	−	1.22160i	0.254539	−	0.967062i	$-0.418076\pi$
$863$	3.75851e23	−	3.75851e23i	1.22160	−	1.22160i	0.967062	−	0.254539i	$-0.0819237\pi$
$864$		−	2.48885e23i		−	0.801474i
$865$	−9.61514e22	+	3.81796e23i	−0.306780	+	1.21816i
$866$	3.79573e23			1.19992
$867$	−2.89594e23	−	2.89594e23i	−0.907061	−	0.907061i
$868$	−7.65936e22	+	7.65936e22i	−0.237703	+	0.237703i
$869$			5.43625e23i			1.67163i
$870$	1.38056e23	+	2.30998e23i	0.420630	+	0.703809i
$871$	−6.02782e22			−0.181976
$872$	−5.82794e23	−	5.82794e23i	−1.74335	−	1.74335i
$873$	−1.77275e23	+	1.77275e23i	−0.525452	+	0.525452i
$874$		−	4.93018e23i		−	1.44801i
$875$	−2.11076e22	+	2.31108e22i	−0.0614293	+	0.0672590i
$876$	−6.74610e23			−1.94545
$877$	2.20730e21	+	2.20730e21i	0.00630761	+	0.00630761i	0.710254	−	0.703946i	$-0.248580\pi$
$877$	2.20730e21	+	2.20730e21i	0.00630761	+	0.00630761i	−0.703946	+	0.710254i	$0.748580\pi$
$878$	−3.78589e23	+	3.78589e23i	−1.07204	+	1.07204i
$879$		−	3.64845e23i		−	1.02376i
$880$	1.06040e24	−	6.33746e23i	2.94854	−	1.76219i
$881$	−2.85602e23			−0.786962			−0.393481	−	0.919333i	$-0.628729\pi$
$881$	−2.85602e23			−0.786962			−0.393481	+	0.919333i	$0.628729\pi$
$882$	−3.34687e23	−	3.34687e23i	−0.913882	−	0.913882i
$883$	4.71788e23	−	4.71788e23i	1.27662	−	1.27662i	0.334071	−	0.942548i	$-0.391577\pi$
$883$	4.71788e23	−	4.71788e23i	1.27662	−	1.27662i	0.942548	−	0.334071i	$-0.108423\pi$
$884$			1.94937e22i			0.0522729i
$885$	6.98203e23	+	1.75835e23i	1.85539	+	0.467261i
$886$	5.77563e23			1.52100
$887$	−6.85087e22	−	6.85087e22i	−0.178796	−	0.178796i	0.612035	−	0.790831i	$-0.290351\pi$
$887$	−6.85087e22	−	6.85087e22i	−0.178796	−	0.178796i	−0.790831	+	0.612035i	$0.790351\pi$
$888$	−9.29679e23	+	9.29679e23i	−2.40453	+	2.40453i
$889$		−	3.75834e21i		−	0.00963345i
$890$	−2.20875e23	+	8.77045e23i	−0.561081	+	2.22793i
$891$	−6.44698e23			−1.62306
$892$	−6.27407e23	−	6.27407e23i	−1.56542	−	1.56542i
$893$	9.36171e22	−	9.36171e22i	0.231496	−	0.231496i
$894$		−	2.25922e23i		−	0.553680i
$895$	−3.11270e23	−	5.20823e23i	−0.756053	−	1.26505i
$896$	−1.09984e22			−0.0264769
$897$	6.24662e22	+	6.24662e22i	0.149041	+	0.149041i
$898$	−3.53298e23	+	3.53298e23i	−0.835469	+	0.835469i
$899$		−	2.17275e23i		−	0.509252i
$900$	3.50651e23	−	6.52026e23i	0.814583	−	1.51469i
$901$	−4.05415e22			−0.0933473
$902$	4.88900e23	+	4.88900e23i	1.11575	+	1.11575i
$903$	3.83349e22	−	3.83349e22i	0.0867146	−	0.0867146i
$904$			1.19962e24i			2.68965i
$905$	1.28681e23	−	7.69062e22i	0.285974	−	0.170912i
$906$	3.84947e23			0.847960
$907$	4.67817e23	+	4.67817e23i	1.02145	+	1.02145i	0.999765	+	0.0216864i	$0.00690355\pi$
$907$	4.67817e23	+	4.67817e23i	1.02145	+	1.02145i	0.0216864	+	0.999765i	$0.493096\pi$
$908$	8.88922e23	−	8.88922e23i	1.92387	−	1.92387i
$909$		−	1.94892e23i		−	0.418103i
$910$	1.27800e22	+	3.21851e21i	0.0271769	+	0.00684422i
$911$	3.34094e23			0.704242			0.352121	−	0.935954i	$-0.385461\pi$
$911$	3.34094e23			0.704242			0.352121	+	0.935954i	$0.385461\pi$
$912$	9.02442e23	+	9.02442e23i	1.88565	+	1.88565i
$913$	7.00659e22	−	7.00659e22i	0.145124	−	0.145124i
$914$			6.59341e23i			1.35376i
$915$	2.33206e23	−	9.26010e23i	0.474647	−	1.88472i
$916$	−1.56634e24			−3.16025
$917$	2.40174e22	+	2.40174e22i	0.0480364	+	0.0480364i
$918$	3.32199e22	−	3.32199e22i	0.0658653	−	0.0658653i
$919$			3.79151e23i			0.745226i	0.927987	+	0.372613i	$0.121538\pi$
$919$			3.79151e23i			0.745226i	−0.927987	+	0.372613i	$0.878462\pi$
$920$	6.92969e23	+	1.15949e24i	1.35024	+	2.25925i
$921$	5.58815e23			1.07942
$922$	−9.57363e23	−	9.57363e23i	−1.83328	−	1.83328i
$923$	−3.00985e22	+	3.00985e22i	−0.0571388	+	0.0571388i
$924$			2.07731e23i			0.390954i
$925$	4.96081e23	−	1.49107e23i	0.925589	−	0.278204i
$926$	−3.80962e23			−0.704683
$927$	6.04310e22	+	6.04310e22i	0.110821	+	0.110821i
$928$	2.70819e23	−	2.70819e23i	0.492374	−	0.492374i
$929$		−	8.70089e23i		−	1.56833i	−0.620551	−	0.784166i	$-0.713091\pi$
$929$		−	8.70089e23i		−	1.56833i	0.620551	−	0.784166i	$-0.286909\pi$
$930$	−1.75215e24	+	1.04717e24i	−3.13118	+	1.87134i
$931$	−4.47071e23			−0.792098
$932$	−6.65106e23	−	6.65106e23i	−1.16833	−	1.16833i
$933$	−6.36616e23	+	6.36616e23i	−1.10873	+	1.10873i
$934$		−	5.86346e23i		−	1.01246i
$935$	9.78651e22	+	2.46463e22i	0.167546	+	0.0421948i
$936$	−1.84587e23			−0.313325
$937$	3.54678e23	+	3.54678e23i	0.596922	+	0.596922i	0.939492	−	0.342571i	$-0.111298\pi$
$937$	3.54678e23	+	3.54678e23i	0.596922	+	0.596922i	−0.342571	+	0.939492i	$0.611298\pi$
$938$	7.88052e22	−	7.88052e22i	0.131502	−	0.131502i
$939$			1.13118e24i			1.87157i
$940$	−1.49604e23	+	5.94043e23i	−0.245425	+	0.974530i
$941$	−3.88142e23			−0.631356			−0.315678	−	0.948866i	$-0.602232\pi$
$941$	−3.88142e23			−0.631356			−0.315678	+	0.948866i	$0.602232\pi$
$942$	3.57526e23	+	3.57526e23i	0.576634	+	0.576634i
$943$	−2.73042e23	+	2.73042e23i	−0.436652	+	0.436652i
$944$		−	2.36768e24i		−	3.75445i
$945$	−1.15736e22	−	1.93653e22i	−0.0181976	−	0.0304487i
$946$	1.65059e24			2.57342
$947$	−2.47270e23	−	2.47270e23i	−0.382271	−	0.382271i	0.489648	−	0.871920i	$-0.337125\pi$
$947$	−2.47270e23	−	2.47270e23i	−0.382271	−	0.382271i	−0.871920	+	0.489648i	$0.837125\pi$
$948$	1.83752e24	−	1.83752e24i	2.81686	−	2.81686i
$949$		−	6.62693e22i		−	0.100735i
$950$	−2.83383e23	−	9.42820e23i	−0.427155	−	1.42115i
$951$	1.36611e23			0.204193
$952$	−1.50908e22	−	1.50908e22i	−0.0223675	−	0.0223675i
$953$	−5.42046e23	+	5.42046e23i	−0.796697	+	0.796697i	−0.982573	−	0.185876i	$-0.940488\pi$
$953$	−5.42046e23	+	5.42046e23i	−0.796697	+	0.796697i	0.185876	+	0.982573i	$0.440488\pi$
$954$		−	6.48311e23i		−	0.944923i
$955$	−9.04761e23	+	5.40729e23i	−1.30770	+	0.781543i
$956$	1.87207e24			2.68323
$957$	−2.94639e23	−	2.94639e23i	−0.418788	−	0.418788i
$958$	1.51369e23	−	1.51369e23i	0.213360	−	0.213360i
$959$		−	2.55639e22i		−	0.0357337i
$960$	−1.15358e24	−	2.90516e23i	−1.59910	−	0.402718i
$961$	9.20637e23			1.26561
$962$	−1.54230e23	−	1.54230e23i	−0.210266	−	0.210266i
$963$	−6.15774e23	+	6.15774e23i	−0.832552	+	0.832552i
$964$			3.51526e24i			4.71348i
$965$	2.06547e23	−	8.20153e23i	0.274663	−	1.09063i
$966$	−1.63332e23			−0.215404
$967$	9.52108e23	+	9.52108e23i	1.24530	+	1.24530i	0.957772	+	0.287530i	$0.0928342\pi$
$967$	9.52108e23	+	9.52108e23i	1.24530	+	1.24530i	0.287530	+	0.957772i	$0.407166\pi$
$968$	−1.17778e24	+	1.17778e24i	−1.52779	+	1.52779i
$969$			1.04262e23i			0.134133i
$970$	−7.91357e23	−	1.32412e24i	−1.00971	−	1.68948i
$971$	−1.03461e24			−1.30925			−0.654624	−	0.755955i	$-0.727173\pi$
$971$	−1.03461e24			−1.30925			−0.654624	+	0.755955i	$0.727173\pi$
$972$	1.64123e24	+	1.64123e24i	2.05987	+	2.05987i
$973$	−2.32068e22	+	2.32068e22i	−0.0288876	+	0.0288876i
$974$			6.52764e23i			0.805907i
$975$	1.55362e23	+	8.35517e22i	0.190243	+	0.102310i
$976$	−3.14019e24			−3.81379
$977$	−7.39187e23	−	7.39187e23i	−0.890426	−	0.890426i	0.104137	−	0.994563i	$-0.466792\pi$
$977$	−7.39187e23	−	7.39187e23i	−0.890426	−	0.890426i	−0.994563	+	0.104137i	$0.966792\pi$
$978$	1.71198e24	−	1.71198e24i	2.04545	−	2.04545i
$979$		−	1.40040e24i		−	1.65955i
$980$	1.77565e24	−	1.06122e24i	2.08713	−	1.24737i
$981$	5.49941e23			0.641157
$982$	2.03765e23	+	2.03765e23i	0.235634	+	0.235634i
$983$	3.16506e23	−	3.16506e23i	0.363039	−	0.363039i	−0.501892	−	0.864931i	$-0.667362\pi$
$983$	3.16506e23	−	3.16506e23i	0.363039	−	0.363039i	0.864931	+	0.501892i	$0.167362\pi$
$984$		−	1.95707e24i		−	2.22661i
$985$	−1.64680e24	−	4.14730e23i	−1.85845	−	0.468032i
$986$	7.22949e22			0.0809268
$987$	−3.10143e22	−	3.10143e22i	−0.0344370	−	0.0344370i
$988$	−2.08202e23	+	2.08202e23i	−0.229314	+	0.229314i
$989$			9.21825e23i			1.00711i
$990$	−3.94126e23	+	1.56499e24i	−0.427124	+	1.69602i
$991$	7.48684e23			0.804840			0.402420	−	0.915455i	$-0.368169\pi$
$991$	7.48684e23			0.804840			0.402420	+	0.915455i	$0.368169\pi$
$992$	2.05419e24	+	2.05419e24i	2.19052	+	2.19052i
$993$	−6.99925e23	+	6.99925e23i	−0.740385	+	0.740385i
$994$		−	7.86992e22i		−	0.0825808i
$995$	1.47888e23	+	2.47449e23i	0.153938	+	0.257573i
$996$	−4.73662e23			−0.489096
$997$	3.73374e23	+	3.73374e23i	0.382457	+	0.382457i	0.871987	−	0.489529i	$-0.162831\pi$
$997$	3.73374e23	+	3.73374e23i	0.382457	+	0.382457i	−0.489529	+	0.871987i	$0.662831\pi$
$998$	−2.80527e23	+	2.80527e23i	−0.285057	+	0.285057i
$999$			3.73373e23i			0.376374i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5.17.c.a.2.7	✓	14
3.2	odd	2		45.17.g.a.37.1		14
4.3	odd	2		80.17.p.c.17.2		14
5.2	odd	4		25.17.c.b.18.1		14
5.3	odd	4	inner	5.17.c.a.3.7	yes	14
5.4	even	2		25.17.c.b.7.1		14
15.8	even	4		45.17.g.a.28.1		14
20.3	even	4		80.17.p.c.33.2		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.17.c.a.2.7	✓	14	1.1	even	1	trivial
5.17.c.a.3.7	yes	14	5.3	odd	4	inner
25.17.c.b.7.1		14	5.4	even	2
25.17.c.b.18.1		14	5.2	odd	4
45.17.g.a.28.1		14	15.8	even	4
45.17.g.a.37.1		14	3.2	odd	2
80.17.p.c.17.2		14	4.3	odd	2
80.17.p.c.33.2		14	20.3	even	4

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:	\( N \)	\(=\)	\( 5 \)
Weight:	\( k \)	\(=\)	\( 17 \)
Character orbit:	\([\chi]\)	\(=\)	5.c (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(336.317 + 336.317i) q^{2} +(6051.53 - 6051.53i) q^{3} +160682. i q^{4} +(335305. - 200395. i) q^{5} +4.07046e6 q^{6} +(-371312. - 371312. i) q^{7} +(-3.19992e7 + 3.19992e7i) q^{8} -3.01954e7i q^{9} +O(q^{10})\)	\(q+(336.317 + 336.317i) q^{2} +(6051.53 - 6051.53i) q^{3} +160682. i q^{4} +(335305. - 200395. i) q^{5} +4.07046e6 q^{6} +(-371312. - 371312. i) q^{7} +(-3.19992e7 + 3.19992e7i) q^{8} -3.01954e7i q^{9} +(1.80165e8 + 4.53727e7i) q^{10} -2.87674e8 q^{11} +(9.72372e8 + 9.72372e8i) q^{12} +(-9.55195e7 + 9.55195e7i) q^{13} -2.49757e8i q^{14} +(8.16416e8 - 3.24181e9i) q^{15} -1.09933e10 q^{16} +(-6.35046e8 - 6.35046e8i) q^{17} +(1.01552e10 - 1.01552e10i) q^{18} -1.35652e10i q^{19} +(3.21999e10 + 5.38776e10i) q^{20} -4.49401e9 q^{21} +(-9.67496e10 - 9.67496e10i) q^{22} +(5.40328e10 - 5.40328e10i) q^{23} +3.87288e11i q^{24} +(7.22717e10 - 1.34387e11i) q^{25} -6.42496e10 q^{26} +(7.77704e10 + 7.77704e10i) q^{27} +(5.96631e10 - 5.96631e10i) q^{28} +1.69248e11i q^{29} +(1.36485e12 - 8.15700e11i) q^{30} -1.28377e12 q^{31} +(-1.60013e12 - 1.60013e12i) q^{32} +(-1.74087e12 + 1.74087e12i) q^{33} -4.27153e11i q^{34} +(-1.98912e11 - 5.00939e10i) q^{35} +4.85185e12 q^{36} +(2.40048e12 + 2.40048e12i) q^{37} +(4.56221e12 - 4.56221e12i) q^{38} +1.15608e12i q^{39} +(-4.31703e12 + 1.71420e13i) q^{40} -5.05325e12 q^{41} +(-1.51141e12 - 1.51141e12i) q^{42} +(-8.53023e12 + 8.53023e12i) q^{43} -4.62240e13i q^{44} +(-6.05100e12 - 1.01247e13i) q^{45} +3.63443e13 q^{46} +(6.90127e12 + 6.90127e12i) q^{47} +(-6.65262e13 + 6.65262e13i) q^{48} -3.29572e13i q^{49} +(6.95028e13 - 2.08904e13i) q^{50} -7.68600e12 q^{51} +(-1.53483e13 - 1.53483e13i) q^{52} +(3.19201e13 - 3.19201e13i) q^{53} +5.23110e13i q^{54} +(-9.64587e13 + 5.76484e13i) q^{55} +2.37634e13 q^{56} +(-8.20903e13 - 8.20903e13i) q^{57} +(-5.69210e13 + 5.69210e13i) q^{58} +2.15375e14i q^{59} +(5.20900e14 + 1.31183e14i) q^{60} +2.85646e14 q^{61} +(-4.31753e14 - 4.31753e14i) q^{62} +(-1.12119e13 + 1.12119e13i) q^{63} -3.55844e14i q^{64} +(-1.28866e13 + 5.11698e13i) q^{65} -1.17097e15 q^{66} +(3.15528e14 + 3.15528e14i) q^{67} +(1.02041e14 - 1.02041e14i) q^{68} -6.53963e14i q^{69} +(-5.00500e13 - 8.37448e13i) q^{70} +3.15103e14 q^{71} +(9.66228e14 + 9.66228e14i) q^{72} +(-3.46889e14 + 3.46889e14i) q^{73} +1.61465e15i q^{74} +(-3.75893e14 - 1.25060e15i) q^{75} +2.17968e15 q^{76} +(1.06817e14 + 1.06817e14i) q^{77} +(-3.88809e14 + 3.88809e14i) q^{78} -1.88973e15i q^{79} +(-3.68611e15 + 2.20300e15i) q^{80} +2.24107e15 q^{81} +(-1.69949e15 - 1.69949e15i) q^{82} +(-2.43560e14 + 2.43560e14i) q^{83} -7.22106e14i q^{84} +(-3.40194e14 - 8.56745e13i) q^{85} -5.73772e15 q^{86} +(1.02421e15 + 1.02421e15i) q^{87} +(9.20534e15 - 9.20534e15i) q^{88} +4.86801e15i q^{89} +(1.37004e15 - 5.44015e15i) q^{90} +7.09350e13 q^{91} +(8.68211e15 + 8.68211e15i) q^{92} +(-7.76876e15 + 7.76876e15i) q^{93} +4.64203e15i q^{94} +(-2.71840e15 - 4.54849e15i) q^{95} -1.93664e16 q^{96} +(-5.87093e15 - 5.87093e15i) q^{97} +(1.10841e16 - 1.10841e16i) q^{98} +8.68642e15i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 2 q^{2} + 7908 q^{3} + 192880 q^{5} + 4417368 q^{6} - 386452 q^{7} - 10493340 q^{8}+O(q^{10}) \) 14 * q - 2 * q^2 + 7908 * q^3 + 192880 * q^5 + 4417368 * q^6 - 386452 * q^7 - 10493340 * q^8	\( 14 q - 2 q^{2} + 7908 q^{3} + 192880 q^{5} + 4417368 q^{6} - 386452 q^{7} - 10493340 q^{8} + 398727830 q^{10} - 539141632 q^{11} + 1973309928 q^{12} - 681358582 q^{13} + 3514452060 q^{15} - 22953579016 q^{16} + 13124182498 q^{17} - 11293583022 q^{18} - 20186820060 q^{20} + 133652286048 q^{21} - 244784660624 q^{22} + 236373052228 q^{23} + 13144083650 q^{25} + 223473840788 q^{26} + 608106053880 q^{27} - 1494176423768 q^{28} + 2252131613760 q^{30} - 1105223074952 q^{31} - 2024535639992 q^{32} - 6385551058704 q^{33} + 6956678093980 q^{35} + 12514339524924 q^{36} - 9027827087002 q^{37} - 7824802789560 q^{38} + 31912538913900 q^{40} + 39543901484288 q^{41} - 70814500818384 q^{42} - 63017457929452 q^{43} + 126481294123110 q^{45} + 44357914058008 q^{46} - 2826187575452 q^{47} - 405160526368272 q^{48} + 461109216233650 q^{50} + 208649050954008 q^{51} - 389623094881012 q^{52} - 275142037498442 q^{53} + 330504874256560 q^{55} + 865011118900080 q^{56} - 644237427525840 q^{57} - 991296507673440 q^{58} + 16\!\cdots\!80 q^{60}+ \cdots + 48\!\cdots\!02 q^{98}+O(q^{100}) \) 14 * q - 2 * q^2 + 7908 * q^3 + 192880 * q^5 + 4417368 * q^6 - 386452 * q^7 - 10493340 * q^8 + 398727830 * q^10 - 539141632 * q^11 + 1973309928 * q^12 - 681358582 * q^13 + 3514452060 * q^15 - 22953579016 * q^16 + 13124182498 * q^17 - 11293583022 * q^18 - 20186820060 * q^20 + 133652286048 * q^21 - 244784660624 * q^22 + 236373052228 * q^23 + 13144083650 * q^25 + 223473840788 * q^26 + 608106053880 * q^27 - 1494176423768 * q^28 + 2252131613760 * q^30 - 1105223074952 * q^31 - 2024535639992 * q^32 - 6385551058704 * q^33 + 6956678093980 * q^35 + 12514339524924 * q^36 - 9027827087002 * q^37 - 7824802789560 * q^38 + 31912538913900 * q^40 + 39543901484288 * q^41 - 70814500818384 * q^42 - 63017457929452 * q^43 + 126481294123110 * q^45 + 44357914058008 * q^46 - 2826187575452 * q^47 - 405160526368272 * q^48 + 461109216233650 * q^50 + 208649050954008 * q^51 - 389623094881012 * q^52 - 275142037498442 * q^53 + 330504874256560 * q^55 + 865011118900080 * q^56 - 644237427525840 * q^57 - 991296507673440 * q^58 + 1631207111049480 * q^60 + 683634528395968 * q^61 - 938995013191864 * q^62 - 1361911146729372 * q^63 + 517066464980110 * q^65 - 196778043917184 * q^66 - 181547742064252 * q^67 - 917821658187868 * q^68 + 1066699466039880 * q^70 - 1337544011098792 * q^71 + 2573199832214340 * q^72 + 778038215296478 * q^73 - 1442550824447700 * q^75 - 233750796900240 * q^76 + 1099376123524976 * q^77 + 8472064951325256 * q^78 - 14934736099860320 * q^80 + 809940307363794 * q^81 - 303814693723184 * q^82 + 13357181209550188 * q^83 - 16045734952112470 * q^85 - 20034048539985352 * q^86 + 17327533268211840 * q^87 + 22952328705949920 * q^88 - 21878453293909290 * q^90 - 24534035720748632 * q^91 + 40652972845631848 * q^92 + 15958372062212256 * q^93 - 22489885958711400 * q^95 - 27488119051061472 * q^96 - 3303551663290402 * q^97 + 48233459501789102 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more