LMFDB - Embedded newform 7.17.b.b.6.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7,17,Mod(6,7)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7, base_ring=CyclotomicField(2))

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("7.6");

S:= CuspForms(chi, 17);

N := Newforms(S);

Level:	$ N $	$=$	$ 7 $
Weight:	$ k $	$=$	$ 17 $
Character orbit:	$[\chi]$	$=$	7.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:	$11.3627180700$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 5365384x^{6} + 10449491370210x^{4} + 8743024230718881600x^{2} + 2655236149032650377194000 $ x^8 + 5365384x^6 + 10449491370210x^4 + 8743024230718881600*x^2 + 2655236149032650377194000
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{17}\cdot 3^{5}\cdot 7^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			6.5
Root			$-1024.53i$ of defining polynomial
Character	$\chi$	$=$	7.6
Dual form			7.17.b.b.6.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+40.3121 q^{2} -6147.19i q^{3} -63910.9 q^{4} +623292. i q^{5} -247806. i q^{6} +(5.20719e6 - 2.47347e6i) q^{7} -5.21828e6 q^{8} +5.25876e6 q^{9} +O(q^{10})$	\(q+40.3121 q^{2} -6147.19i q^{3} -63910.9 q^{4} +623292. i q^{5} -247806. i q^{6} +(5.20719e6 - 2.47347e6i) q^{7} -5.21828e6 q^{8} +5.25876e6 q^{9} +2.51262e7i q^{10} +2.60168e8 q^{11} +3.92873e8i q^{12} +3.22901e7i q^{13} +(2.09913e8 - 9.97109e7i) q^{14} +3.83149e9 q^{15} +3.97811e9 q^{16} +4.55293e9i q^{17} +2.11992e8 q^{18} +3.21083e10i q^{19} -3.98352e10i q^{20} +(-1.52049e10 - 3.20096e10i) q^{21} +1.04879e10 q^{22} -2.53072e10 q^{23} +3.20778e10i q^{24} -2.35905e11 q^{25} +1.30168e9i q^{26} -2.96943e11i q^{27} +(-3.32797e11 + 1.58082e11i) q^{28} +6.07691e11 q^{29} +1.54456e11 q^{30} +6.88271e11i q^{31} +5.02351e11 q^{32} -1.59930e12i q^{33} +1.83538e11i q^{34} +(1.54170e12 + 3.24560e12i) q^{35} -3.36092e11 q^{36} +1.13142e12 q^{37} +1.29435e12i q^{38} +1.98493e11 q^{39} -3.25251e12i q^{40} -7.07970e12i q^{41} +(-6.12942e11 - 1.29038e12i) q^{42} -1.00123e13 q^{43} -1.66276e13 q^{44} +3.27774e12i q^{45} -1.02019e12 q^{46} +3.10807e13i q^{47} -2.44542e13i q^{48} +(2.09968e13 - 2.57597e13i) q^{49} -9.50982e12 q^{50} +2.79877e13 q^{51} -2.06369e12i q^{52} +2.29366e13 q^{53} -1.19704e13i q^{54} +1.62160e14i q^{55} +(-2.71726e13 + 1.29073e13i) q^{56} +1.97376e14 q^{57} +2.44973e13 q^{58} -1.29016e14i q^{59} -2.44874e14 q^{60} -8.46157e13i q^{61} +2.77457e13i q^{62} +(2.73834e13 - 1.30074e13i) q^{63} -2.40458e14 q^{64} -2.01261e13 q^{65} -6.44712e13i q^{66} -9.70344e13 q^{67} -2.90982e14i q^{68} +1.55568e14i q^{69} +(6.21490e13 + 1.30837e14i) q^{70} -2.60114e14 q^{71} -2.74417e13 q^{72} +2.61793e14i q^{73} +4.56098e13 q^{74} +1.45015e15i q^{75} -2.05207e15i q^{76} +(1.35474e15 - 6.43518e14i) q^{77} +8.00169e12 q^{78} +2.57747e15 q^{79} +2.47952e15i q^{80} -1.59899e15 q^{81} -2.85398e14i q^{82} +4.41804e14i q^{83} +(9.71760e14 + 2.04576e15i) q^{84} -2.83781e15 q^{85} -4.03618e14 q^{86} -3.73559e15i q^{87} -1.35763e15 q^{88} -4.20826e15i q^{89} +1.32133e14i q^{90} +(7.98686e13 + 1.68141e14i) q^{91} +1.61741e15 q^{92} +4.23093e15 q^{93} +1.25293e15i q^{94} -2.00128e16 q^{95} -3.08805e15i q^{96} +9.38572e15i q^{97} +(8.46425e14 - 1.03843e15i) q^{98} +1.36816e15 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 544 q^{2} + 18784 q^{4} - 3034472 q^{7} - 35863808 q^{8} - 41933880 q^{9}+O(q^{10}) $ 8 * q - 544 * q^2 + 18784 * q^4 - 3034472 * q^7 - 35863808 * q^8 - 41933880 * q^9	$ 8 q - 544 q^{2} + 18784 q^{4} - 3034472 q^{7} - 35863808 q^{8} - 41933880 q^{9} + 430398704 q^{11} - 2080234240 q^{14} + 83393280 q^{15} - 4357080832 q^{16} - 7232400864 q^{18} + 45847234944 q^{21} - 34275403968 q^{22} + 89765082416 q^{23} + 61966251080 q^{25} - 376785722656 q^{28} - 22437591664 q^{29} - 192018300480 q^{30} + 941689387008 q^{32} + 371925382080 q^{35} - 4527659399328 q^{36} + 5737866534416 q^{37} - 7975804007808 q^{39} - 13160568536640 q^{42} - 3976952110864 q^{43} + 45337613120448 q^{44} + 35817469755072 q^{46} - 27450534789496 q^{49} - 96564765668320 q^{50} + 58670380591488 q^{51} - 108679841507824 q^{53} - 15117119134208 q^{56} - 196163055495360 q^{57} + 650847682404672 q^{58} - 335782392744960 q^{60} + 223739049782808 q^{63} - 460533940742144 q^{64} + 573279455461440 q^{65} - 722120065643024 q^{67} + 12\!\cdots\!60 q^{70}+ \cdots - 15\!\cdots\!92 q^{99}+O(q^{100}) $ 8 * q - 544 * q^2 + 18784 * q^4 - 3034472 * q^7 - 35863808 * q^8 - 41933880 * q^9 + 430398704 * q^11 - 2080234240 * q^14 + 83393280 * q^15 - 4357080832 * q^16 - 7232400864 * q^18 + 45847234944 * q^21 - 34275403968 * q^22 + 89765082416 * q^23 + 61966251080 * q^25 - 376785722656 * q^28 - 22437591664 * q^29 - 192018300480 * q^30 + 941689387008 * q^32 + 371925382080 * q^35 - 4527659399328 * q^36 + 5737866534416 * q^37 - 7975804007808 * q^39 - 13160568536640 * q^42 - 3976952110864 * q^43 + 45337613120448 * q^44 + 35817469755072 * q^46 - 27450534789496 * q^49 - 96564765668320 * q^50 + 58670380591488 * q^51 - 108679841507824 * q^53 - 15117119134208 * q^56 - 196163055495360 * q^57 + 650847682404672 * q^58 - 335782392744960 * q^60 + 223739049782808 * q^63 - 460533940742144 * q^64 + 573279455461440 * q^65 - 722120065643024 * q^67 + 1268642086877760 * q^70 - 289095246669136 * q^71 + 1560006716205312 * q^72 - 5411665863643328 * q^74 + 4485628262682896 * q^77 + 192459573633600 * q^78 + 5832776866563376 * q^79 - 14617034931574584 * q^81 + 12924747561148416 * q^84 - 5815379514337920 * q^85 + 7508453217752512 * q^86 - 24665635192321536 * q^88 + 23929798963272384 * q^91 + 1197288221450688 * q^92 + 27012151562451840 * q^93 - 53204702857107840 * q^95 + 43278421367298656 * q^98 - 15738606124789392 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/7\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$-1$

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 $

$2$	40.3121			0.157469			0.0787346	−	0.996896i	$-0.474912\pi$
$2$	40.3121			0.157469			0.0787346	+	0.996896i	$0.474912\pi$
$3$		−	6147.19i		−	0.936929i	−0.883482	−	0.468465i	$-0.844807\pi$
$3$		−	6147.19i		−	0.936929i	0.883482	−	0.468465i	$-0.155193\pi$
$4$	−63910.9			−0.975203
$5$			623292.i			1.59563i	0.602904	+	0.797814i	$0.294010\pi$
$5$			623292.i			1.59563i	−0.602904	+	0.797814i	$0.705990\pi$
$6$		−	247806.i		−	0.147537i
$7$	5.20719e6	−	2.47347e6i	0.903274	−	0.429065i
$7$	5.20719e6	−	2.47347e6i	0.903274	−	0.429065i
$8$	−5.21828e6			−0.311034
$9$	5.25876e6			0.122164
$10$			2.51262e7i			0.251262i
$11$	2.60168e8			1.21370			0.606851	−	0.794816i	$-0.292433\pi$
$11$	2.60168e8			1.21370			0.606851	+	0.794816i	$0.292433\pi$
$12$			3.92873e8i			0.913696i
$13$			3.22901e7i			0.0395842i	0.999804	+	0.0197921i	$0.00630044\pi$
$13$			3.22901e7i			0.0395842i	−0.999804	+	0.0197921i	$0.993700\pi$
$14$	2.09913e8	−	9.97109e7i	0.142238	−	0.0675645i
$15$	3.83149e9			1.49499
$16$	3.97811e9			0.926225
$17$			4.55293e9i			0.652679i	0.945253	+	0.326340i	$0.105815\pi$
$17$			4.55293e9i			0.652679i	−0.945253	+	0.326340i	$0.894185\pi$
$18$	2.11992e8			0.0192371
$19$			3.21083e10i			1.89055i	0.326277	+	0.945274i	$0.394206\pi$
$19$			3.21083e10i			1.89055i	−0.326277	+	0.945274i	$0.605794\pi$
$20$		−	3.98352e10i		−	1.55606i
$21$	−1.52049e10	−	3.20096e10i	−0.402003	−	0.846303i
$22$	1.04879e10			0.191121
$23$	−2.53072e10			−0.323163			−0.161581	−	0.986859i	$-0.551659\pi$
$23$	−2.53072e10			−0.323163			−0.161581	+	0.986859i	$0.551659\pi$
$24$			3.20778e10i			0.291417i
$25$	−2.35905e11			−1.54603
$26$			1.30168e9i			0.00623330i
$27$		−	2.96943e11i		−	1.05139i
$28$	−3.32797e11	+	1.58082e11i	−0.880876	+	0.418425i
$29$	6.07691e11			1.21478			0.607392	−	0.794403i	$-0.292216\pi$
$29$	6.07691e11			1.21478			0.607392	+	0.794403i	$0.292216\pi$
$30$	1.54456e11			0.235415
$31$			6.88271e11i			0.806986i	0.914983	+	0.403493i	$0.132204\pi$
$31$			6.88271e11i			0.806986i	−0.914983	+	0.403493i	$0.867796\pi$
$32$	5.02351e11			0.456886
$33$		−	1.59930e12i		−	1.13715i
$34$			1.83538e11i			0.102777i
$35$	1.54170e12	+	3.24560e12i	0.684627	+	1.44129i
$36$	−3.36092e11			−0.119135
$37$	1.13142e12			0.322114			0.161057	−	0.986945i	$-0.448510\pi$
$37$	1.13142e12			0.322114			0.161057	+	0.986945i	$0.448510\pi$
$38$			1.29435e12i			0.297703i
$39$	1.98493e11			0.0370876
$40$		−	3.25251e12i		−	0.496294i
$41$		−	7.07970e12i		−	0.886633i	−0.896365	−	0.443316i	$-0.853802\pi$
$41$		−	7.07970e12i		−	0.886633i	0.896365	−	0.443316i	$-0.146198\pi$
$42$	−6.12942e11	−	1.29038e12i	−0.0633031	−	0.133267i
$43$	−1.00123e13			−0.856618			−0.428309	−	0.903632i	$-0.640890\pi$
$43$	−1.00123e13			−0.856618			−0.428309	+	0.903632i	$0.640890\pi$
$44$	−1.66276e13			−1.18361
$45$			3.27774e12i			0.194928i
$46$	−1.02019e12			−0.0508882
$47$			3.10807e13i			1.30529i	0.757663	+	0.652646i	$0.226341\pi$
$47$			3.10807e13i			1.30529i	−0.757663	+	0.652646i	$0.773659\pi$
$48$		−	2.44542e13i		−	0.867807i
$49$	2.09968e13	−	2.57597e13i	0.631807	−	0.775126i
$50$	−9.50982e12			−0.243451
$51$	2.79877e13			0.611514
$52$		−	2.06369e12i		−	0.0386027i
$53$	2.29366e13			0.368402			0.184201	−	0.982889i	$-0.441030\pi$
$53$	2.29366e13			0.368402			0.184201	+	0.982889i	$0.441030\pi$
$54$		−	1.19704e13i		−	0.165561i
$55$			1.62160e14i			1.93662i
$56$	−2.71726e13	+	1.29073e13i	−0.280949	+	0.133454i
$57$	1.97376e14			1.77131
$58$	2.44973e13			0.191291
$59$		−	1.29016e14i		−	0.878674i	−0.898322	−	0.439337i	$-0.855213\pi$
$59$		−	1.29016e14i		−	0.878674i	0.898322	−	0.439337i	$-0.144787\pi$
$60$	−2.44874e14			−1.45792
$61$		−	8.46157e13i		−	0.441379i	−0.975344	−	0.220690i	$-0.929169\pi$
$61$		−	8.46157e13i		−	0.441379i	0.975344	−	0.220690i	$-0.0708308\pi$
$62$			2.77457e13i			0.127075i
$63$	2.73834e13	−	1.30074e13i	0.110348	−	0.0524163i
$64$	−2.40458e14			−0.854280
$65$	−2.01261e13			−0.0631617
$66$		−	6.44712e13i		−	0.179066i
$67$	−9.70344e13			−0.238961			−0.119481	−	0.992837i	$-0.538123\pi$
$67$	−9.70344e13			−0.238961			−0.119481	+	0.992837i	$0.538123\pi$
$68$		−	2.90982e14i		−	0.636495i
$69$			1.55568e14i			0.302781i
$70$	6.21490e13	+	1.30837e14i	0.107808	+	0.226958i
$71$	−2.60114e14			−0.402807			−0.201404	−	0.979508i	$-0.564550\pi$
$71$	−2.60114e14			−0.402807			−0.201404	+	0.979508i	$0.564550\pi$
$72$	−2.74417e13			−0.0379971
$73$			2.61793e14i			0.324620i	0.986740	+	0.162310i	$0.0518944\pi$
$73$			2.61793e14i			0.324620i	−0.986740	+	0.162310i	$0.948106\pi$
$74$	4.56098e13			0.0507230
$75$			1.45015e15i			1.44852i
$76$		−	2.05207e15i		−	1.84367i
$77$	1.35474e15	−	6.43518e14i	1.09630	−	0.520756i
$78$	8.00169e12			0.00584016
$79$	2.57747e15			1.69894			0.849468	−	0.527640i	$-0.176923\pi$
$79$	2.57747e15			1.69894			0.849468	+	0.527640i	$0.176923\pi$
$80$			2.47952e15i			1.47791i
$81$	−1.59899e15			−0.862912
$82$		−	2.85398e14i		−	0.139617i
$83$			4.41804e14i			0.196157i	0.995179	+	0.0980787i	$0.0312697\pi$
$83$			4.41804e14i			0.196157i	−0.995179	+	0.0980787i	$0.968730\pi$
$84$	9.71760e14	+	2.04576e15i	0.392035	+	0.825318i
$85$	−2.83781e15			−1.04143
$86$	−4.03618e14			−0.134891
$87$		−	3.73559e15i		−	1.13817i
$88$	−1.35763e15			−0.377502
$89$		−	4.20826e15i		−	1.06901i	−0.845165	−	0.534506i	$-0.820498\pi$
$89$		−	4.20826e15i		−	1.06901i	0.845165	−	0.534506i	$-0.179502\pi$
$90$			1.32133e14i			0.0306952i
$91$	7.98686e13	+	1.68141e14i	0.0169842	+	0.0357554i
$92$	1.61741e15			0.315149
$93$	4.23093e15			0.756089
$94$			1.25293e15i			0.205543i
$95$	−2.00128e16			−3.01661
$96$		−	3.08805e15i		−	0.428069i
$97$			9.38572e15i			1.19755i	0.800917	+	0.598775i	$0.204346\pi$
$97$			9.38572e15i			1.19755i	−0.800917	+	0.598775i	$0.795654\pi$
$98$	8.46425e14	−	1.03843e15i	0.0994901	−	0.122058i
$99$	1.36816e15			0.148271
$100$	1.50769e16			1.50769
$101$		−	1.07840e16i		−	0.995883i	−0.867211	−	0.497942i	$-0.834089\pi$
$101$		−	1.07840e16i		−	0.995883i	0.867211	−	0.497942i	$-0.165911\pi$
$102$	1.12825e15			0.0962946
$103$			1.59907e16i			1.26232i	0.775651	+	0.631162i	$0.217422\pi$
$103$			1.59907e16i			1.26232i	−0.775651	+	0.631162i	$0.782578\pi$
$104$		−	1.68499e14i		−	0.0123120i
$105$	1.99513e16	−	9.47710e15i	1.35038	−	0.641447i
$106$	9.24623e14			0.0580120
$107$	8.37293e15			0.487312			0.243656	−	0.969862i	$-0.421653\pi$
$107$	8.37293e15			0.487312			0.243656	+	0.969862i	$0.421653\pi$
$108$			1.89779e16i			1.02532i
$109$	−1.49661e16			−0.751099			−0.375550	−	0.926802i	$-0.622546\pi$
$109$	−1.49661e16			−0.751099			−0.375550	+	0.926802i	$0.622546\pi$
$110$			6.53703e15i			0.304957i
$111$		−	6.95504e15i		−	0.301798i
$112$	2.07148e16	−	9.83974e15i	0.836635	−	0.397411i
$113$	−3.36893e16			−1.26726			−0.633628	−	0.773638i	$-0.718435\pi$
$113$	−3.36893e16			−1.26726			−0.633628	+	0.773638i	$0.718435\pi$
$114$	7.95663e15			0.278927
$115$		−	1.57738e16i		−	0.515647i
$116$	−3.88381e16			−1.18466
$117$			1.69806e14i			0.00483577i
$118$		−	5.20091e15i		−	0.138364i
$119$	1.12616e16	+	2.37080e16i	0.280042	+	0.589548i
$120$	−1.99938e16			−0.464992
$121$	2.17375e16			0.473071
$122$		−	3.41104e15i		−	0.0695037i
$123$	−4.35202e16			−0.830712
$124$		−	4.39881e16i		−	0.786976i
$125$		−	5.19308e16i		−	0.871254i
$126$	1.10388e15	−	5.24356e14i	0.0173763	−	0.00825395i
$127$	3.07907e16			0.454978			0.227489	−	0.973781i	$-0.426948\pi$
$127$	3.07907e16			0.454978			0.227489	+	0.973781i	$0.426948\pi$
$128$	−4.26155e16			−0.591408
$129$			6.15476e16i			0.802590i
$130$	−8.11328e14			−0.00994602
$131$		−	6.81770e16i		−	0.786081i	−0.919521	−	0.393041i	$-0.871423\pi$
$131$		−	6.81770e16i		−	0.786081i	0.919521	−	0.393041i	$-0.128577\pi$
$132$			1.02213e17i			1.10895i
$133$	7.94189e16	+	1.67194e17i	0.811168	+	1.70768i
$134$	−3.91166e15			−0.0376290
$135$	1.85082e17			1.67762
$136$		−	2.37585e16i		−	0.203005i
$137$	−6.65605e16			−0.536354			−0.268177	−	0.963370i	$-0.586421\pi$
$137$	−6.65605e16			−0.536354			−0.268177	+	0.963370i	$0.586421\pi$
$138$			6.27128e15i			0.0476786i
$139$		−	1.09817e17i		−	0.788043i	−0.919101	−	0.394022i	$-0.871084\pi$
$139$		−	1.09817e17i		−	0.788043i	0.919101	−	0.394022i	$-0.128916\pi$
$140$	−9.85312e16	−	2.07429e17i	−0.667651	−	1.40555i
$141$	1.91059e17			1.22297
$142$	−1.04858e16			−0.0634297
$143$			8.40084e15i			0.0480435i
$144$	2.09199e16			0.113151
$145$			3.78769e17i			1.93834i
$146$			1.05534e16i			0.0511176i
$147$	−1.58350e17	−	1.29071e17i	−0.726238	−	0.591958i
$148$	−7.23100e16			−0.314126
$149$	−3.44994e17			−1.42011			−0.710055	−	0.704146i	$-0.751330\pi$
$149$	−3.44994e17			−1.42011			−0.710055	+	0.704146i	$0.751330\pi$
$150$			5.84587e16i			0.228097i
$151$	2.62854e17			0.972522			0.486261	−	0.873814i	$-0.338360\pi$
$151$	2.62854e17			0.972522			0.486261	+	0.873814i	$0.338360\pi$
$152$		−	1.67550e17i		−	0.588024i
$153$			2.39428e16i			0.0797339i
$154$	5.46126e16	−	2.59416e16i	0.172634	−	0.0820031i
$155$	−4.28994e17			−1.28765
$156$	−1.26859e16			−0.0361680
$157$		−	6.21380e17i		−	1.68329i	−0.540028	−	0.841647i	$-0.681586\pi$
$157$		−	6.21380e17i		−	1.68329i	0.540028	−	0.841647i	$-0.318414\pi$
$158$	1.03903e17			0.267530
$159$		−	1.40996e17i		−	0.345167i
$160$			3.13111e17i			0.729019i
$161$	−1.31779e17	+	6.25966e16i	−0.291904	+	0.138658i
$162$	−6.44588e16			−0.135882
$163$	−2.58361e17			−0.518473			−0.259236	−	0.965814i	$-0.583471\pi$
$163$	−2.58361e17			−0.518473			−0.259236	+	0.965814i	$0.583471\pi$
$164$			4.52470e17i			0.864647i
$165$	9.96831e17			1.81447
$166$			1.78100e16i			0.0308887i
$167$			3.06543e17i			0.506711i	0.967373	+	0.253355i	$0.0815342\pi$
$167$			3.06543e17i			0.506711i	−0.967373	+	0.253355i	$0.918466\pi$
$168$	7.93435e16	+	1.67035e17i	0.125037	+	0.263229i
$169$	6.64374e17			0.998433
$170$	−1.14398e17			−0.163994
$171$			1.68850e17i			0.230957i
$172$	6.39897e17			0.835377
$173$		−	5.05218e17i		−	0.629665i	−0.949147	−	0.314833i	$-0.898052\pi$
$173$		−	5.05218e17i		−	0.629665i	0.949147	−	0.314833i	$-0.101948\pi$
$174$		−	1.50590e17i		−	0.179226i
$175$	−1.22840e18	+	5.83504e17i	−1.39648	+	0.663345i
$176$	1.03497e18			1.12416
$177$	−7.93086e17			−0.823255
$178$		−	1.69644e17i		−	0.168336i
$179$	1.03994e17			0.0986693			0.0493347	−	0.998782i	$-0.484290\pi$
$179$	1.03994e17			0.0986693			0.0493347	+	0.998782i	$0.484290\pi$
$180$		−	2.09484e17i		−	0.190095i
$181$		−	7.74762e17i		−	0.672573i	−0.941760	−	0.336287i	$-0.890829\pi$
$181$		−	7.74762e17i		−	0.672573i	0.941760	−	0.336287i	$-0.109171\pi$
$182$	3.21967e15	+	6.77811e15i	0.00267449	+	0.00563038i
$183$	−5.20149e17			−0.413541
$184$	1.32060e17			0.100514
$185$			7.05203e17i			0.513973i
$186$	1.70558e17			0.119061
$187$			1.18453e18i			0.792158i
$188$		−	1.98639e18i		−	1.27292i
$189$	−7.34480e17	−	1.54624e18i	−0.451113	−	0.949691i
$190$	−8.06759e17			−0.475023
$191$	−2.72567e18			−1.53889			−0.769443	−	0.638716i	$-0.779466\pi$
$191$	−2.72567e18			−1.53889			−0.769443	+	0.638716i	$0.779466\pi$
$192$			1.47814e18i			0.800400i
$193$	−5.68442e16			−0.0295276			−0.0147638	−	0.999891i	$-0.504700\pi$
$193$	−5.68442e16			−0.0295276			−0.0147638	+	0.999891i	$0.504700\pi$
$194$			3.78358e17i			0.188577i
$195$			1.23719e17i			0.0591780i
$196$	−1.34193e18	+	1.64633e18i	−0.616140	+	0.755905i
$197$	3.43448e18			1.51402			0.757009	−	0.653404i	$-0.226660\pi$
$197$	3.43448e18			1.51402			0.757009	+	0.653404i	$0.226660\pi$
$198$	5.51534e16			0.0233481
$199$		−	3.08101e18i		−	1.25276i	−0.779517	−	0.626381i	$-0.784536\pi$
$199$		−	3.08101e18i		−	1.25276i	0.779517	−	0.626381i	$-0.215464\pi$
$200$	1.23102e18			0.480866
$201$			5.96489e17i			0.223890i
$202$		−	4.34725e17i		−	0.156821i
$203$	3.16436e18	−	1.50311e18i	1.09728	−	0.521221i
$204$	−1.78872e18			−0.596351
$205$	4.41272e18			1.41474
$206$			6.44621e17i			0.198777i
$207$	−1.33084e17			−0.0394788
$208$			1.28453e17i			0.0366639i
$209$			8.35353e18i			2.29456i
$210$	8.04280e17	−	3.82042e17i	0.212644	−	0.101008i
$211$	−3.66576e18			−0.933049			−0.466525	−	0.884508i	$-0.654494\pi$
$211$	−3.66576e18			−0.933049			−0.466525	+	0.884508i	$0.654494\pi$
$212$	−1.46590e18			−0.359267
$213$			1.59897e18i			0.377402i
$214$	3.37531e17			0.0767367
$215$		−	6.24060e18i		−	1.36684i
$216$			1.54953e18i			0.327017i
$217$	1.70242e18	+	3.58396e18i	0.346249	+	0.728929i
$218$	−6.03316e17			−0.118275
$219$	1.60929e18			0.304146
$220$		−	1.03638e19i		−	1.88859i
$221$	−1.47015e17			−0.0258358
$222$		−	2.80372e17i		−	0.0475238i
$223$		−	3.19020e18i		−	0.521649i	−0.965386	−	0.260824i	$-0.916006\pi$
$223$		−	3.19020e18i		−	0.521649i	0.965386	−	0.260824i	$-0.0839944\pi$
$224$	2.61584e18	−	1.24255e18i	0.412693	−	0.196033i
$225$	−1.24057e18			−0.188869
$226$	−1.35809e18			−0.199554
$227$			8.95087e18i			1.26958i	0.772686	+	0.634788i	$0.218913\pi$
$227$			8.95087e18i			1.26958i	−0.772686	+	0.634788i	$0.781087\pi$
$228$	−1.26145e19			−1.72739
$229$			5.64814e18i			0.746830i	0.927664	+	0.373415i	$0.121813\pi$
$229$			5.64814e18i			0.746830i	−0.927664	+	0.373415i	$0.878187\pi$
$230$		−	6.35874e17i		−	0.0811985i
$231$	−3.95583e18	−	8.32787e18i	−0.487912	−	1.02716i
$232$	−3.17110e18			−0.377839
$233$	9.79004e18			1.12703			0.563517	−	0.826104i	$-0.309448\pi$
$233$	9.79004e18			1.12703			0.563517	+	0.826104i	$0.309448\pi$
$234$			6.84523e15i			0.000761485i
$235$	−1.93723e19			−2.08276
$236$			8.24554e18i			0.856886i
$237$		−	1.58442e19i		−	1.59178i
$238$	4.53977e17	+	9.55720e17i	0.0440979	+	0.0928357i
$239$	1.06665e19			1.00194			0.500968	−	0.865466i	$-0.332977\pi$
$239$	1.06665e19			1.00194			0.500968	+	0.865466i	$0.332977\pi$
$240$	1.52421e19			1.38470
$241$			5.61508e18i			0.493423i	0.969089	+	0.246712i	$0.0793501\pi$
$241$			5.61508e18i			0.493423i	−0.969089	+	0.246712i	$0.920650\pi$
$242$	8.76285e17			0.0744942
$243$		−	2.95311e18i		−	0.242901i
$244$			5.40787e18i			0.430435i
$245$	1.60558e19	+	1.30871e19i	1.23681	+	1.00813i
$246$	−1.75439e18			−0.130812
$247$	−1.03678e18			−0.0748359
$248$		−	3.59159e18i		−	0.251000i
$249$	2.71585e18			0.183786
$250$		−	2.09344e18i		−	0.137196i
$251$		−	6.76431e18i		−	0.429372i	−0.976683	−	0.214686i	$-0.931127\pi$
$251$		−	6.76431e18i		−	0.429372i	0.976683	−	0.214686i	$-0.0688728\pi$
$252$	−1.75010e18	+	8.31315e17i	−0.107611	+	0.0511165i
$253$	−6.58411e18			−0.392223
$254$	1.24124e18			0.0716450
$255$			1.74445e19i			0.975749i
$256$	1.40408e19			0.761151
$257$		−	1.02920e19i		−	0.540800i	−0.962748	−	0.270400i	$-0.912844\pi$
$257$		−	1.02920e19i		−	0.540800i	0.962748	−	0.270400i	$-0.0871559\pi$
$258$			2.48112e18i			0.126383i
$259$	5.89151e18	−	2.79853e18i	0.290957	−	0.138208i
$260$	1.28628e18			0.0615955
$261$	3.19570e18			0.148403
$262$		−	2.74836e18i		−	0.123784i
$263$	−4.04989e19			−1.76928			−0.884641	−	0.466274i	$-0.845596\pi$
$263$	−4.04989e19			−1.76928			−0.884641	+	0.466274i	$0.845596\pi$
$264$			8.34560e18i			0.353693i
$265$			1.42962e19i			0.587833i
$266$	3.20154e18	+	6.73994e18i	0.127734	+	0.268907i
$267$	−2.58690e19			−1.00159
$268$	6.20156e18			0.233036
$269$		−	3.86108e19i		−	1.40828i	−0.710059	−	0.704142i	$-0.751332\pi$
$269$		−	3.86108e19i		−	1.40828i	0.710059	−	0.704142i	$-0.248668\pi$
$270$	7.46105e18			0.264174
$271$		−	4.75912e19i		−	1.63596i	−0.575248	−	0.817979i	$-0.695095\pi$
$271$		−	4.75912e19i		−	1.63596i	0.575248	−	0.817979i	$-0.304905\pi$
$272$			1.81121e19i			0.604528i
$273$	1.03359e18	−	4.90968e17i	0.0335003	−	0.0159130i
$274$	−2.68319e18			−0.0844593
$275$	−6.13748e19			−1.87641
$276$		−	9.94250e18i		−	0.295273i
$277$	2.78601e19			0.803792			0.401896	−	0.915685i	$-0.368351\pi$
$277$	2.78601e19			0.803792			0.401896	+	0.915685i	$0.368351\pi$
$278$		−	4.42694e18i		−	0.124093i
$279$			3.61945e18i			0.0985846i
$280$	−8.04500e18	−	1.69365e19i	−0.212942	−	0.448289i
$281$	1.70399e19			0.438346			0.219173	−	0.975686i	$-0.429664\pi$
$281$	1.70399e19			0.438346			0.219173	+	0.975686i	$0.429664\pi$
$282$	7.70198e18			0.192579
$283$			2.73203e19i			0.664040i	0.943272	+	0.332020i	$0.107730\pi$
$283$			2.73203e19i			0.664040i	−0.943272	+	0.332020i	$0.892270\pi$
$284$	1.66241e19			0.392819
$285$			1.23023e20i			2.82635i
$286$			3.38656e17i			0.00756537i
$287$	−1.75114e19	−	3.68653e19i	−0.380423	−	0.800872i
$288$	2.64174e18			0.0558150
$289$	2.79320e19			0.574010
$290$			1.52690e19i			0.305229i
$291$	5.76958e19			1.12202
$292$		−	1.67314e19i		−	0.316570i
$293$			5.02318e18i			0.0924779i	0.998930	+	0.0462389i	$0.0147236\pi$
$293$			5.02318e18i			0.0924779i	−0.998930	+	0.0462389i	$0.985276\pi$
$294$	−6.38342e18	−	5.20314e18i	−0.114360	−	0.0932152i
$295$	8.04147e19			1.40204
$296$	−5.90405e18			−0.100188
$297$		−	7.72550e19i		−	1.27607i
$298$	−1.39075e19			−0.223624
$299$		−	8.17171e17i		−	0.0127922i
$300$		−	9.26806e19i		−	1.41260i
$301$	−5.21361e19	+	2.47652e19i	−0.773760	+	0.367544i
$302$	1.05962e19			0.153142
$303$	−6.62912e19			−0.933072
$304$			1.27730e20i			1.75107i
$305$	5.27403e19			0.704277
$306$			9.65184e17i			0.0125556i
$307$			8.32589e19i			1.05517i	0.849501	+	0.527586i	$0.176903\pi$
$307$			8.32589e19i			1.05517i	−0.849501	+	0.527586i	$0.823097\pi$
$308$	−8.65829e19	+	4.11278e19i	−1.06912	+	0.507843i
$309$	9.82982e19			1.18271
$310$	−1.72936e19			−0.202765
$311$		−	4.39748e19i		−	0.502483i	−0.967924	−	0.251241i	$-0.919161\pi$
$311$		−	4.39748e19i		−	0.502483i	0.967924	−	0.251241i	$-0.0808388\pi$
$312$	−1.03579e18			−0.0115355
$313$		−	1.08020e20i		−	1.17260i	−0.810093	−	0.586301i	$-0.800583\pi$
$313$		−	1.08020e20i		−	1.17260i	0.810093	−	0.586301i	$-0.199417\pi$
$314$		−	2.50491e19i		−	0.265067i
$315$	8.10740e18	+	1.70678e19i	0.0836368	+	0.176074i
$316$	−1.64729e20			−1.65681
$317$	−1.58848e20			−1.55778			−0.778892	−	0.627158i	$-0.784218\pi$
$317$	−1.58848e20			−1.55778			−0.778892	+	0.627158i	$0.784218\pi$
$318$		−	5.68384e18i		−	0.0543531i
$319$	1.58102e20			1.47438
$320$		−	1.49876e20i		−	1.36311i
$321$		−	5.14700e19i		−	0.456577i
$322$	−5.31231e18	+	2.52340e18i	−0.0459659	+	0.0218343i
$323$	−1.46187e20			−1.23392
$324$	1.02193e20			0.841515
$325$		−	7.61739e18i		−	0.0611983i
$326$	−1.04151e19			−0.0816435
$327$			9.19996e19i			0.703727i
$328$			3.69438e19i			0.275773i
$329$	7.68772e19	+	1.61843e20i	0.560054	+	1.17904i
$330$	4.01844e19			0.285723
$331$	−9.29554e18			−0.0645135			−0.0322567	−	0.999480i	$-0.510269\pi$
$331$	−9.29554e18			−0.0645135			−0.0322567	+	0.999480i	$0.510269\pi$
$332$		−	2.82361e19i		−	0.191293i
$333$	5.94985e18			0.0393507
$334$			1.23574e19i			0.0797913i
$335$		−	6.04808e19i		−	0.381293i
$336$	−6.04868e19	−	1.27338e20i	−0.372345	−	0.783868i
$337$	1.42306e20			0.855428			0.427714	−	0.903914i	$-0.359319\pi$
$337$	1.42306e20			0.855428			0.427714	+	0.903914i	$0.359319\pi$
$338$	2.67823e19			0.157222
$339$			2.07095e20i			1.18733i
$340$	1.81367e20			1.01561
$341$			1.79066e20i			0.979440i
$342$			6.80668e18i			0.0363686i
$343$	4.56185e19	−	1.86071e20i	0.238116	−	0.971237i
$344$	5.22471e19			0.266437
$345$	−9.69644e19			−0.483125
$346$		−	2.03664e19i		−	0.0991529i
$347$	−7.44967e19			−0.354406			−0.177203	−	0.984174i	$-0.556705\pi$
$347$	−7.44967e19			−0.354406			−0.177203	+	0.984174i	$0.556705\pi$
$348$			2.38745e20i			1.10994i
$349$			2.06622e19i			0.0938799i	0.998898	+	0.0469399i	$0.0149469\pi$
$349$			2.06622e19i			0.0938799i	−0.998898	+	0.0469399i	$0.985053\pi$
$350$	−4.95195e19	+	2.35223e19i	−0.219903	+	0.104456i
$351$	9.58832e18			0.0416184
$352$	1.30696e20			0.554523
$353$		−	3.98913e20i		−	1.65455i	−0.561795	−	0.827277i	$-0.689889\pi$
$353$		−	3.98913e20i		−	1.65455i	0.561795	−	0.827277i	$-0.310111\pi$
$354$	−3.19710e19			−0.129637
$355$		−	1.62127e20i		−	0.642730i
$356$			2.68954e20i			1.04250i
$357$	1.45738e20	−	6.92269e19i	0.552365	−	0.262379i
$358$	4.19220e18			0.0155374
$359$	3.17191e20			1.14965			0.574824	−	0.818277i	$-0.305071\pi$
$359$	3.17191e20			1.14965			0.574824	+	0.818277i	$0.305071\pi$
$360$		−	1.71042e19i		−	0.0606292i
$361$	−7.42498e20			−2.57417
$362$		−	3.12323e19i		−	0.105910i
$363$		−	1.33625e20i		−	0.443234i
$364$	−5.10448e18	−	1.07460e19i	−0.0165631	−	0.0348688i
$365$	−1.63173e20			−0.517972
$366$	−2.09683e19			−0.0651200
$367$			2.19641e20i			0.667399i	0.942680	+	0.333699i	$0.108297\pi$
$367$			2.19641e20i			0.667399i	−0.942680	+	0.333699i	$0.891703\pi$
$368$	−1.00675e20			−0.299321
$369$		−	3.72304e19i		−	0.108315i
$370$			2.84282e19i			0.0809350i
$371$	1.19435e20	−	5.67331e19i	0.332768	−	0.158068i
$372$	−2.70403e20			−0.737340
$373$	−7.19817e20			−1.92111			−0.960553	−	0.278096i	$-0.910297\pi$
$373$	−7.19817e20			−1.92111			−0.960553	+	0.278096i	$0.910297\pi$
$374$			4.77507e19i			0.124740i
$375$	−3.19228e20			−0.816303
$376$		−	1.62188e20i		−	0.405990i
$377$			1.96224e19i			0.0480863i
$378$	−2.96085e19	−	6.23322e19i	−0.0710365	−	0.149547i
$379$	6.23181e20			1.46386			0.731932	−	0.681378i	$-0.238619\pi$
$379$	6.23181e20			1.46386			0.731932	+	0.681378i	$0.238619\pi$
$380$	1.27904e21			2.94181
$381$		−	1.89276e20i		−	0.426282i
$382$	−1.09878e20			−0.242327
$383$		−	4.94572e20i		−	1.06817i	−0.845432	−	0.534083i	$-0.820657\pi$
$383$		−	4.94572e20i		−	1.06817i	0.845432	−	0.534083i	$-0.179343\pi$
$384$			2.61965e20i			0.554108i
$385$	4.01099e20	+	8.44401e20i	0.830933	+	1.74929i
$386$	−2.29151e18			−0.00464968
$387$	−5.26524e19			−0.104648
$388$		−	5.99850e20i		−	1.16786i
$389$	1.41308e20			0.269508			0.134754	−	0.990879i	$-0.456976\pi$
$389$	1.41308e20			0.269508			0.134754	+	0.990879i	$0.456976\pi$
$390$			4.98739e18i			0.00931872i
$391$		−	1.15222e20i		−	0.210922i
$392$	−1.09567e20	+	1.34421e20i	−0.196513	+	0.241090i
$393$	−4.19097e20			−0.736502
$394$	1.38451e20			0.238411
$395$			1.60652e21i			2.71087i
$396$	−8.74403e19			−0.144594
$397$			2.38112e20i			0.385884i	0.981210	+	0.192942i	$0.0618030\pi$
$397$			2.38112e20i			0.385884i	−0.981210	+	0.192942i	$0.938197\pi$
$398$		−	1.24202e20i		−	0.197271i
$399$	1.02777e21	−	4.88203e20i	1.59998	−	0.760007i
$400$	−9.38455e20			−1.43197
$401$	2.31372e20			0.346064			0.173032	−	0.984916i	$-0.444644\pi$
$401$	2.31372e20			0.346064			0.173032	+	0.984916i	$0.444644\pi$
$402$			2.40457e19i			0.0352557i
$403$	−2.22243e19			−0.0319439
$404$			6.89215e20i			0.971189i
$405$		−	9.96639e20i		−	1.37689i
$406$	1.27562e20	−	6.05934e19i	0.172788	−	0.0820762i
$407$	2.94358e20			0.390950
$408$	−1.46048e20			−0.190202
$409$		−	6.87825e20i		−	0.878399i	−0.898390	−	0.439199i	$-0.855262\pi$
$409$		−	6.87825e20i		−	0.878399i	0.898390	−	0.439199i	$-0.144738\pi$
$410$	1.77886e20			0.222777
$411$			4.09160e20i			0.502526i
$412$		−	1.02198e21i		−	1.23102i
$413$	−3.19118e20	−	6.71812e20i	−0.377008	−	0.793683i
$414$	−5.36491e18			−0.00621670
$415$	−2.75373e20			−0.312994
$416$			1.62210e19i			0.0180855i
$417$	−6.75064e20			−0.738340
$418$			3.36748e20i			0.361323i
$419$			9.94085e20i			1.04643i	0.852200	+	0.523216i	$0.175268\pi$
$419$			9.94085e20i			1.04643i	−0.852200	+	0.523216i	$0.824732\pi$
$420$	−1.27511e21	+	6.05690e20i	−1.31690	+	0.625541i
$421$	3.94678e19			0.0399932			0.0199966	−	0.999800i	$-0.493634\pi$
$421$	3.94678e19			0.0399932			0.0199966	+	0.999800i	$0.493634\pi$
$422$	−1.47775e20			−0.146927
$423$			1.63446e20i			0.159460i
$424$	−1.19690e20			−0.114586
$425$		−	1.07406e21i		−	1.00906i
$426$			6.44579e19i			0.0594291i
$427$	−2.09295e20	−	4.40610e20i	−0.189380	−	0.398687i
$428$	−5.35122e20			−0.475229
$429$	5.16416e19			0.0450133
$430$		−	2.51572e20i		−	0.215236i
$431$	−1.49811e20			−0.125813			−0.0629063	−	0.998019i	$-0.520037\pi$
$431$	−1.49811e20			−0.125813			−0.0629063	+	0.998019i	$0.520037\pi$
$432$		−	1.18127e21i		−	0.973822i
$433$			2.13528e21i			1.72803i	0.503466	+	0.864015i	$0.332058\pi$
$433$			2.13528e21i			1.72803i	−0.503466	+	0.864015i	$0.667942\pi$
$434$	6.86281e19	+	1.44477e20i	0.0545236	+	0.114784i
$435$	2.32836e21			1.81609
$436$	9.56499e20			0.732474
$437$		−	8.12570e20i		−	0.610955i
$438$	6.48739e19			0.0478936
$439$			1.28195e21i			0.929299i	0.885495	+	0.464650i	$0.153820\pi$
$439$			1.28195e21i			0.929299i	−0.885495	+	0.464650i	$0.846180\pi$
$440$		−	8.46198e20i		−	0.602353i
$441$	1.10417e20	−	1.35464e20i	0.0771841	−	0.0946925i
$442$	−5.92647e18			−0.00406835
$443$	−1.82700e21			−1.23171			−0.615857	−	0.787858i	$-0.711190\pi$
$443$	−1.82700e21			−1.23171			−0.615857	+	0.787858i	$0.711190\pi$
$444$			4.44503e20i			0.294314i
$445$	2.62297e21			1.70574
$446$		−	1.28604e20i		−	0.0821436i
$447$			2.12075e21i			1.33054i
$448$	−1.25211e21	+	5.94767e20i	−0.771649	+	0.366541i
$449$	9.58151e20			0.580047			0.290023	−	0.957020i	$-0.406337\pi$
$449$	9.58151e20			0.580047			0.290023	+	0.957020i	$0.406337\pi$
$450$	−5.00099e19			−0.0297410
$451$		−	1.84191e21i		−	1.07611i
$452$	2.15312e21			1.23583
$453$		−	1.61582e21i		−	0.911184i
$454$			3.60829e20i			0.199919i
$455$	−1.04801e20	+	4.97815e19i	−0.0570523	+	0.0271005i
$456$	−1.02996e21			−0.550937
$457$	−2.36275e21			−1.24190			−0.620952	−	0.783849i	$-0.713254\pi$
$457$	−2.36275e21			−1.24190			−0.620952	+	0.783849i	$0.713254\pi$
$458$			2.27689e20i			0.117603i
$459$	1.35196e21			0.686219
$460$			1.00812e21i			0.502861i
$461$		−	6.39726e20i		−	0.313608i	−0.987630	−	0.156804i	$-0.949881\pi$
$461$		−	6.39726e20i		−	0.313608i	0.987630	−	0.156804i	$-0.0501191\pi$
$462$	−1.59468e20	−	3.35714e20i	−0.0768311	−	0.161746i
$463$	9.10392e19			0.0431102			0.0215551	−	0.999768i	$-0.493138\pi$
$463$	9.10392e19			0.0431102			0.0215551	+	0.999768i	$0.493138\pi$
$464$	2.41746e21			1.12516
$465$			2.63711e21i			1.20644i
$466$	3.94657e20			0.177473
$467$			1.83619e21i			0.811676i	0.913945	+	0.405838i	$0.133020\pi$
$467$			1.83619e21i			0.811676i	−0.913945	+	0.405838i	$0.866980\pi$
$468$		−	1.08524e19i		−	0.00471586i
$469$	−5.05277e20	+	2.40012e20i	−0.215847	+	0.102530i
$470$	−7.80939e20			−0.327970
$471$	−3.81974e21			−1.57713
$472$			6.73242e20i			0.273297i
$473$	−2.60488e21			−1.03968
$474$		−	6.38713e20i		−	0.250657i
$475$		−	7.57449e21i		−	2.92284i
$476$	−7.19736e20	−	1.51520e21i	−0.273098	−	0.574929i
$477$	1.20618e20			0.0450055
$478$	4.29991e20			0.157774
$479$		−	1.65360e21i		−	0.596686i	−0.954459	−	0.298343i	$-0.903566\pi$
$479$		−	1.65360e21i		−	0.596686i	0.954459	−	0.298343i	$-0.0964339\pi$
$480$	1.92476e21			0.683039
$481$			3.65336e19i			0.0127506i
$482$			2.26356e20i			0.0776990i
$483$	3.84793e20	+	8.10073e20i	0.129912	+	0.273494i
$484$	−1.38926e21			−0.461341
$485$	−5.85004e21			−1.91084
$486$		−	1.19046e20i		−	0.0382494i
$487$	3.75298e21			1.18616			0.593082	−	0.805142i	$-0.297911\pi$
$487$	3.75298e21			1.18616			0.593082	+	0.805142i	$0.297911\pi$
$488$			4.41548e20i			0.137284i
$489$			1.58819e21i			0.485772i
$490$	6.47244e20	+	5.27570e20i	0.194760	+	0.158749i
$491$	−7.63709e20			−0.226087			−0.113044	−	0.993590i	$-0.536060\pi$
$491$	−7.63709e20			−0.226087			−0.113044	+	0.993590i	$0.536060\pi$
$492$	2.78142e21			0.810113
$493$			2.76678e21i			0.792864i
$494$	−4.17947e19			−0.0117844
$495$			8.52763e20i			0.236585i
$496$			2.73802e21i			0.747451i
$497$	−1.35446e21	+	6.43385e20i	−0.363845	+	0.172830i
$498$	1.09482e20			0.0289406
$499$	1.69383e21			0.440622			0.220311	−	0.975430i	$-0.429293\pi$
$499$	1.69383e21			0.440622			0.220311	+	0.975430i	$0.429293\pi$
$500$			3.31894e21i			0.849650i
$501$	1.88438e21			0.474752
$502$		−	2.72684e20i		−	0.0676129i
$503$		−	3.54421e21i		−	0.864919i	−0.901653	−	0.432459i	$-0.857646\pi$
$503$		−	3.54421e21i		−	0.864919i	0.901653	−	0.432459i	$-0.142354\pi$
$504$	−1.42894e20	+	6.78762e19i	−0.0343218	+	0.0163032i
$505$	6.72157e21			1.58906
$506$	−2.65420e20			−0.0617630
$507$		−	4.08403e21i		−	0.935461i
$508$	−1.96786e21			−0.443696
$509$		−	3.64033e21i		−	0.807976i	−0.914764	−	0.403988i	$-0.867624\pi$
$509$		−	3.64033e21i		−	0.807976i	0.914764	−	0.403988i	$-0.132376\pi$
$510$			7.03226e20i			0.153650i
$511$	6.47537e20	+	1.36321e21i	0.139283	+	0.293220i
$512$	3.35886e21			0.711266
$513$	9.53432e21			1.98770
$514$		−	4.14894e20i		−	0.0851593i
$515$	−9.96690e21			−2.01420
$516$		−	3.93357e21i		−	0.782689i
$517$			8.08618e21i			1.58423i
$518$	2.37499e20	−	1.12815e20i	0.0458167	−	0.0217634i
$519$	−3.10567e21			−0.589951
$520$	1.05024e20			0.0196454
$521$		−	2.82487e21i		−	0.520351i	−0.965561	−	0.260176i	$-0.916220\pi$
$521$		−	2.82487e21i		−	0.520351i	0.965561	−	0.260176i	$-0.0837805\pi$
$522$	1.28825e20			0.0233689
$523$			2.39390e21i			0.427654i	0.976872	+	0.213827i	$0.0685929\pi$
$523$			2.39390e21i			0.427654i	−0.976872	+	0.213827i	$0.931407\pi$
$524$			4.35726e21i			0.766589i
$525$	3.58691e21	+	7.55122e21i	0.621507	+	1.30841i
$526$	−1.63259e21			−0.278607
$527$	−3.13365e21			−0.526703
$528$		−	6.36219e21i		−	1.05326i
$529$	−5.49216e21			−0.895566
$530$			5.76310e20i			0.0925655i
$531$		−	6.78464e20i		−	0.107342i
$532$	−5.07573e21	−	1.06855e22i	−0.791053	−	1.66534i
$533$	2.28604e20			0.0350967
$534$	−1.04283e21			−0.157719
$535$			5.21878e21i			0.777569i
$536$	5.06353e20			0.0743250
$537$		−	6.39268e20i		−	0.0924462i
$538$		−	1.55648e21i		−	0.221761i
$539$	5.46269e21	−	6.70184e21i	0.766825	−	0.940771i
$540$	−1.18288e22			−1.63602
$541$	4.22852e21			0.576250			0.288125	−	0.957593i	$-0.406968\pi$
$541$	4.22852e21			0.576250			0.288125	+	0.957593i	$0.406968\pi$
$542$		−	1.91850e21i		−	0.257613i
$543$	−4.76261e21			−0.630153
$544$			2.28717e21i			0.298200i
$545$		−	9.32826e21i		−	1.19847i
$546$	4.16663e19	−	1.97920e19i	0.00527526	−	0.00250581i
$547$	−8.08807e21			−1.00913			−0.504564	−	0.863374i	$-0.668347\pi$
$547$	−8.08807e21			−1.00913			−0.504564	+	0.863374i	$0.668347\pi$
$548$	4.25394e21			0.523055
$549$		−	4.44973e20i		−	0.0539207i
$550$	−2.47415e21			−0.295477
$551$			1.95119e22i			2.29661i
$552$		−	8.11798e20i		−	0.0941749i
$553$	1.34214e22	−	6.37530e21i	1.53460	−	0.728953i
$554$	1.12310e21			0.126573
$555$	4.33502e21			0.481557
$556$			7.01849e21i			0.768502i
$557$	5.00350e21			0.540048			0.270024	−	0.962854i	$-0.412968\pi$
$557$	5.00350e21			0.540048			0.270024	+	0.962854i	$0.412968\pi$
$558$			1.45908e20i			0.0155240i
$559$		−	3.23299e20i		−	0.0339086i
$560$	6.13303e21	+	1.29113e22i	0.634119	+	1.33496i
$561$	7.28151e21			0.742196
$562$	6.86915e20			0.0690260
$563$		−	5.03732e21i		−	0.499036i	−0.968370	−	0.249518i	$-0.919728\pi$
$563$		−	5.03732e21i		−	0.499036i	0.968370	−	0.249518i	$-0.0802722\pi$
$564$	−1.22107e22			−1.19264
$565$		−	2.09983e22i		−	2.02207i
$566$			1.10134e21i			0.104566i
$567$	−8.32627e21	+	3.95507e21i	−0.779446	+	0.370245i
$568$	1.35735e21			0.125287
$569$	5.62710e21			0.512137			0.256069	−	0.966659i	$-0.417573\pi$
$569$	5.62710e21			0.512137			0.256069	+	0.966659i	$0.417573\pi$
$570$			4.95930e21i			0.445063i
$571$	2.57678e21			0.228028			0.114014	−	0.993479i	$-0.463629\pi$
$571$	2.57678e21			0.228028			0.114014	+	0.993479i	$0.463629\pi$
$572$		−	5.36905e20i		−	0.0468521i
$573$			1.67552e22i			1.44183i
$574$	−7.05923e20	−	1.48612e21i	−0.0599049	−	0.126113i
$575$	5.97009e21			0.499618
$576$	−1.26451e21			−0.104362
$577$			1.42797e22i			1.16228i	0.813803	+	0.581141i	$0.197393\pi$
$577$			1.42797e22i			1.16228i	−0.813803	+	0.581141i	$0.802607\pi$
$578$	1.12600e21			0.0903889
$579$			3.49432e20i			0.0276652i
$580$		−	2.42075e22i		−	1.89028i
$581$	1.09279e21	+	2.30056e21i	0.0841642	+	0.177184i
$582$	2.32584e21			0.176684
$583$	5.96736e21			0.447130
$584$		−	1.36611e21i		−	0.100968i
$585$	−1.05839e20			−0.00771609
$586$			2.02495e20i			0.0145624i
$587$		−	3.46757e21i		−	0.245992i	−0.992407	−	0.122996i	$-0.960750\pi$
$587$		−	3.46757e21i		−	0.245992i	0.992407	−	0.122996i	$-0.0392502\pi$
$588$	1.01203e22	+	8.24907e21i	0.708230	+	0.577280i
$589$	−2.20992e22			−1.52565
$590$	3.24168e21			0.220777
$591$		−	2.11124e22i		−	1.41853i
$592$	4.50090e21			0.298350
$593$		−	8.80651e21i		−	0.575926i	−0.957642	−	0.287963i	$-0.907022\pi$
$593$		−	8.80651e21i		−	0.575926i	0.957642	−	0.287963i	$-0.0929780\pi$
$594$		−	3.11431e21i		−	0.200942i
$595$	−1.47770e22	+	7.01923e21i	−0.940699	+	0.446842i
$596$	2.20489e22			1.38490
$597$	−1.89396e22			−1.17375
$598$		−	3.29419e19i		−	0.00201437i
$599$	−2.68657e22			−1.62100			−0.810501	−	0.585738i	$-0.800805\pi$
$599$	−2.68657e22			−1.62100			−0.810501	+	0.585738i	$0.800805\pi$
$600$		−	7.56730e21i		−	0.450537i
$601$			1.85567e22i			1.09019i	0.838373	+	0.545097i	$0.183507\pi$
$601$			1.85567e22i			1.09019i	−0.838373	+	0.545097i	$0.816493\pi$
$602$	−2.10172e21	+	9.98337e20i	−0.121843	+	0.0578769i
$603$	−5.10281e20			−0.0291925
$604$	−1.67993e22			−0.948407
$605$			1.35488e22i			0.754845i
$606$	−2.67234e21			−0.146930
$607$			5.06354e20i			0.0274755i	0.999906	+	0.0137377i	$0.00437299\pi$
$607$			5.06354e20i			0.0274755i	−0.999906	+	0.0137377i	$0.995627\pi$
$608$			1.61296e22i			0.863765i
$609$	−9.23989e21	−	1.94520e22i	−0.488347	−	1.02808i
$610$	2.12607e21			0.110902
$611$	−1.00360e21			−0.0516690
$612$		−	1.53021e21i		−	0.0777568i
$613$	1.57036e22			0.787616			0.393808	−	0.919193i	$-0.371157\pi$
$613$	1.57036e22			0.787616			0.393808	+	0.919193i	$0.371157\pi$
$614$			3.35634e21i			0.166157i
$615$		−	2.71258e22i		−	1.32551i
$616$	−7.06943e21	+	3.35805e21i	−0.340988	+	0.161973i
$617$	1.64387e22			0.782685			0.391343	−	0.920245i	$-0.372011\pi$
$617$	1.64387e22			0.782685			0.391343	+	0.920245i	$0.372011\pi$
$618$	3.96261e21			0.186240
$619$		−	1.26727e22i		−	0.587954i	−0.955812	−	0.293977i	$-0.905021\pi$
$619$		−	1.26727e22i		−	0.587954i	0.955812	−	0.293977i	$-0.0949790\pi$
$620$	2.74174e22			1.25572
$621$			7.51479e21i			0.339769i
$622$		−	1.77272e21i		−	0.0791255i
$623$	−1.04090e22	−	2.19132e22i	−0.458675	−	0.965610i
$624$	7.89628e20			0.0343515
$625$	−3.62819e21			−0.155830
$626$		−	4.35453e21i		−	0.184649i
$627$	5.13507e22			2.14984
$628$			3.97130e22i			1.64155i
$629$			5.15127e21i			0.210237i
$630$	3.26827e20	+	6.88041e20i	0.0131702	+	0.0277262i
$631$	−7.39318e21			−0.294169			−0.147084	−	0.989124i	$-0.546989\pi$
$631$	−7.39318e21			−0.294169			−0.147084	+	0.989124i	$0.546989\pi$
$632$	−1.34500e22			−0.528426
$633$			2.25341e22i			0.874201i
$634$	−6.40350e21			−0.245303
$635$			1.91916e22i			0.725975i
$636$			9.01117e21i			0.336608i
$637$	8.31783e20	+	6.77988e20i	0.0306828	+	0.0250096i
$638$	6.37341e21			0.232170
$639$	−1.36788e21			−0.0492085
$640$		−	2.65619e22i		−	0.943667i
$641$	1.31859e22			0.462644			0.231322	−	0.972877i	$-0.425695\pi$
$641$	1.31859e22			0.462644			0.231322	+	0.972877i	$0.425695\pi$
$642$		−	2.07487e21i		−	0.0718968i
$643$			2.22778e22i			0.762404i	0.924492	+	0.381202i	$0.124490\pi$
$643$			2.22778e22i			0.762404i	−0.924492	+	0.381202i	$0.875510\pi$
$644$	8.42215e21	−	4.00061e21i	0.284666	−	0.135219i
$645$	−3.83621e22			−1.28063
$646$	−5.89309e21			−0.194305
$647$			2.36756e22i			0.771021i	0.922704	+	0.385510i	$0.125975\pi$
$647$			2.36756e22i			0.771021i	−0.922704	+	0.385510i	$0.874025\pi$
$648$	8.34399e21			0.268395
$649$		−	3.35658e22i		−	1.06645i
$650$		−	3.07073e20i		−	0.00963684i
$651$	2.20313e22	−	1.04651e22i	0.682955	−	0.324411i
$652$	1.65121e22			0.505617
$653$	1.78219e22			0.539074			0.269537	−	0.962990i	$-0.413129\pi$
$653$	1.78219e22			0.539074			0.269537	+	0.962990i	$0.413129\pi$
$654$			3.70870e21i			0.110815i
$655$	4.24942e22			1.25429
$656$		−	2.81638e22i		−	0.821222i
$657$			1.37671e21i			0.0396568i
$658$	3.09908e21	+	6.52423e21i	0.0881913	+	0.185662i
$659$	−1.48752e22			−0.418196			−0.209098	−	0.977895i	$-0.567053\pi$
$659$	−1.48752e22			−0.418196			−0.209098	+	0.977895i	$0.567053\pi$
$660$	−6.37084e22			−1.76948
$661$		−	5.43526e22i		−	1.49145i	−0.666254	−	0.745725i	$-0.732103\pi$
$661$		−	5.43526e22i		−	1.49145i	0.666254	−	0.745725i	$-0.267897\pi$
$662$	−3.74723e20			−0.0101589
$663$			9.03727e20i			0.0242063i
$664$		−	2.30546e21i		−	0.0610116i
$665$	−1.04211e23	+	4.95011e22i	−2.72483	+	1.29432i
$666$	2.39851e20			0.00619652
$667$	−1.53790e22			−0.392573
$668$		−	1.95915e22i		−	0.494146i
$669$	−1.96107e22			−0.488748
$670$		−	2.43811e21i		−	0.0600419i
$671$		−	2.20143e22i		−	0.535703i
$672$	−7.63820e21	−	1.60801e22i	−0.183669	−	0.386664i
$673$	2.42636e22			0.576548			0.288274	−	0.957548i	$-0.406919\pi$
$673$	2.42636e22			0.576548			0.288274	+	0.957548i	$0.406919\pi$
$674$	5.73665e21			0.134704
$675$			7.00503e22i			1.62547i
$676$	−4.24608e22			−0.973675
$677$		−	5.94850e22i		−	1.34803i	−0.738720	−	0.674013i	$-0.764569\pi$
$677$		−	5.94850e22i		−	1.34803i	0.738720	−	0.674013i	$-0.235431\pi$
$678$			8.34842e21i			0.186968i
$679$	2.32153e22	+	4.88733e22i	0.513827	+	1.08172i
$680$	1.48085e22			0.323921
$681$	5.50227e22			1.18950
$682$			7.21853e21i			0.154232i
$683$	−2.83284e21			−0.0598214			−0.0299107	−	0.999553i	$-0.509522\pi$
$683$	−2.83284e21			−0.0598214			−0.0299107	+	0.999553i	$0.509522\pi$
$684$		−	1.07913e22i		−	0.225230i
$685$		−	4.14866e22i		−	0.855822i
$686$	1.83898e21	−	7.50091e21i	0.0374959	−	0.152940i
$687$	3.47202e22			0.699727
$688$	−3.98301e22			−0.793421
$689$			7.40625e20i			0.0145829i
$690$	−3.90884e21			−0.0760773
$691$			5.24183e22i			1.00846i	0.863570	+	0.504229i	$0.168223\pi$
$691$			5.24183e22i			1.00846i	−0.863570	+	0.504229i	$0.831777\pi$
$692$			3.22889e22i			0.614052i
$693$	7.12427e21	−	3.38410e21i	0.133929	−	0.0636177i
$694$	−3.00312e21			−0.0558081
$695$	6.84479e22			1.25742
$696$			1.94934e22i			0.354008i
$697$	3.22334e22			0.578687
$698$			8.32936e20i			0.0147832i
$699$		−	6.01813e22i		−	1.05595i
$700$	7.85083e22	−	3.72923e22i	1.36186	−	0.646896i
$701$	−4.26586e22			−0.731581			−0.365791	−	0.930697i	$-0.619201\pi$
$701$	−4.26586e22			−0.731581			−0.365791	+	0.930697i	$0.619201\pi$
$702$	3.86525e20			0.00655362
$703$			3.63278e22i			0.608972i
$704$	−6.25595e22			−1.03684
$705$			1.19085e23i			1.95140i
$706$		−	1.60810e22i		−	0.260541i
$707$	−2.66739e22	−	5.61543e22i	−0.427298	−	0.899555i
$708$	5.06869e22			0.802841
$709$	3.55885e22			0.557365			0.278683	−	0.960383i	$-0.410102\pi$
$709$	3.55885e22			0.557365			0.278683	+	0.960383i	$0.410102\pi$
$710$		−	6.53568e21i		−	0.101210i
$711$	1.35543e22			0.207549
$712$			2.19599e22i			0.332499i
$713$		−	1.74182e22i		−	0.260788i
$714$	5.87499e21	−	2.79068e21i	0.0869804	−	0.0413166i
$715$	−5.23617e21			−0.0766594
$716$	−6.64633e21			−0.0962227
$717$		−	6.55693e22i		−	0.938744i
$718$	1.27866e22			0.181034
$719$		−	5.27920e22i		−	0.739157i	−0.929199	−	0.369579i	$-0.879502\pi$
$719$		−	5.27920e22i		−	0.739157i	0.929199	−	0.369579i	$-0.120498\pi$
$720$			1.30392e22i			0.180547i
$721$	3.95527e22	+	8.32669e22i	0.541619	+	1.14022i
$722$	−2.99317e22			−0.405353
$723$	3.45170e22			0.462303
$724$			4.95158e22i			0.655896i
$725$	−1.43357e23			−1.87809
$726$		−	5.38669e21i		−	0.0697957i
$727$			1.22585e23i			1.57095i	0.618893	+	0.785475i	$0.287581\pi$
$727$			1.22585e23i			1.57095i	−0.618893	+	0.785475i	$0.712419\pi$
$728$	−4.16777e20	−	8.77405e20i	−0.00528266	−	0.0111211i
$729$	−8.69847e22			−1.09049
$730$	−6.57786e21			−0.0815646
$731$		−	4.55854e22i		−	0.559097i
$732$	3.32432e22			0.403287
$733$		−	5.29761e22i		−	0.635694i	−0.948142	−	0.317847i	$-0.897040\pi$
$733$		−	5.29761e22i		−	0.635694i	0.948142	−	0.317847i	$-0.102960\pi$
$734$			8.85420e21i			0.105095i
$735$	8.04491e22	−	9.86981e22i	0.944545	−	1.15880i
$736$	−1.27131e22			−0.147648
$737$	−2.52452e22			−0.290028
$738$		−	1.50084e21i		−	0.0170562i
$739$	−1.22811e23			−1.38064			−0.690322	−	0.723502i	$-0.742531\pi$
$739$	−1.22811e23			−1.38064			−0.690322	+	0.723502i	$0.742531\pi$
$740$		−	4.50702e22i		−	0.501229i
$741$			6.37327e21i			0.0701160i
$742$	4.81469e21	−	2.28703e21i	0.0524007	−	0.0248909i
$743$	−2.97211e22			−0.320003			−0.160002	−	0.987117i	$-0.551150\pi$
$743$	−2.97211e22			−0.320003			−0.160002	+	0.987117i	$0.551150\pi$
$744$	−2.20782e22			−0.235169
$745$		−	2.15032e23i		−	2.26597i
$746$	−2.90173e22			−0.302515
$747$			2.32334e21i			0.0239634i
$748$		−	7.57042e22i		−	0.772515i
$749$	4.35995e22	−	2.07102e22i	0.440176	−	0.209088i
$750$	−1.28688e22			−0.128543
$751$	9.64033e22			0.952736			0.476368	−	0.879246i	$-0.341953\pi$
$751$	9.64033e22			0.952736			0.476368	+	0.879246i	$0.341953\pi$
$752$			1.23642e23i			1.20899i
$753$	−4.15815e22			−0.402291
$754$			7.91020e20i			0.00757211i
$755$			1.63835e23i			1.55178i
$756$	4.69413e22	+	9.88216e22i	0.439927	+	0.926142i
$757$	−1.19827e23			−1.11119			−0.555595	−	0.831453i	$-0.687509\pi$
$757$	−1.19827e23			−1.11119			−0.555595	+	0.831453i	$0.687509\pi$
$758$	2.51217e22			0.230513
$759$			4.04738e22i			0.367485i
$760$	1.04432e23			0.938268
$761$			9.49459e22i			0.844109i	0.906570	+	0.422055i	$0.138691\pi$
$761$			9.49459e22i			0.844109i	−0.906570	+	0.422055i	$0.861309\pi$
$762$		−	7.63013e21i		−	0.0671262i
$763$	−7.79315e22	+	3.70183e22i	−0.678448	+	0.322270i
$764$	1.74200e23			1.50073
$765$	−1.49233e22			−0.127226
$766$		−	1.99372e22i		−	0.168203i
$767$	4.16594e21			0.0347816
$768$		−	8.63112e22i		−	0.713145i
$769$			7.13568e22i			0.583479i	0.956498	+	0.291739i	$0.0942340\pi$
$769$			7.13568e22i			0.583479i	−0.956498	+	0.291739i	$0.905766\pi$
$770$	1.61692e22	+	3.40396e22i	0.130846	+	0.275460i
$771$	−6.32672e22			−0.506691
$772$	3.63297e21			0.0287954
$773$			9.03893e21i			0.0709057i	0.999371	+	0.0354529i	$0.0112874\pi$
$773$			9.03893e21i			0.0709057i	−0.999371	+	0.0354529i	$0.988713\pi$
$774$	−2.12253e21			−0.0164788
$775$		−	1.62366e23i		−	1.24762i
$776$		−	4.89773e22i		−	0.372479i
$777$	−1.72031e22	−	3.62162e22i	−0.129491	−	0.272606i
$778$	5.69644e21			0.0424392
$779$	2.27317e23			1.67622
$780$		−	7.90701e21i		−	0.0577106i
$781$	−6.76733e22			−0.488888
$782$		−	4.64484e21i		−	0.0332137i
$783$		−	1.80450e23i		−	1.27721i
$784$	8.35275e22	−	1.02475e23i	0.585196	−	0.717941i
$785$	3.87301e23			2.68591
$786$	−1.68947e22			−0.115976
$787$			2.12355e23i			1.44300i	0.692417	+	0.721498i	$0.256546\pi$
$787$			2.12355e23i			1.44300i	−0.692417	+	0.721498i	$0.743454\pi$
$788$	−2.19501e23			−1.47648
$789$			2.48954e23i			1.65769i
$790$			6.47621e22i			0.426878i
$791$	−1.75427e23	+	8.33296e22i	−1.14468	+	0.543735i
$792$	−7.13944e21			−0.0461172
$793$	2.73225e21			0.0174717
$794$			9.59879e21i			0.0607649i
$795$	8.78815e22			0.550757
$796$			1.96910e23i			1.22170i
$797$		−	3.08940e23i		−	1.89761i	−0.315855	−	0.948807i	$-0.602291\pi$
$797$		−	3.08940e23i		−	1.89761i	0.315855	−	0.948807i	$-0.397709\pi$
$798$	4.14317e22	−	1.96805e22i	0.251947	−	0.119678i
$799$	−1.41508e23			−0.851936
$800$	−1.18507e23			−0.706357
$801$		−	2.21302e22i		−	0.130595i
$802$	9.32710e21			0.0544944
$803$			6.81100e22i			0.393991i
$804$		−	3.81222e22i		−	0.218338i
$805$	−3.90160e22	−	8.21370e22i	−0.221246	−	0.465771i
$806$	−8.95910e20			−0.00503019
$807$	−2.37348e23			−1.31946
$808$			5.62739e22i			0.309753i
$809$	3.05192e23			1.66335			0.831677	−	0.555260i	$-0.187381\pi$
$809$	3.05192e23			1.66335			0.831677	+	0.555260i	$0.187381\pi$
$810$		−	4.01766e22i		−	0.216817i
$811$		−	1.27032e23i		−	0.678810i	−0.940640	−	0.339405i	$-0.889774\pi$
$811$		−	1.27032e23i		−	0.678810i	0.940640	−	0.339405i	$-0.110226\pi$
$812$	−2.02237e23	+	9.60650e22i	−1.07007	+	0.508296i
$813$	−2.92552e23			−1.53278
$814$	1.18662e22			0.0615626
$815$		−	1.61034e23i		−	0.827289i
$816$	1.11338e23			0.566400
$817$		−	3.21478e23i		−	1.61948i
$818$		−	2.77277e22i		−	0.138321i
$819$	4.20010e20	+	8.84212e20i	0.00207486	+	0.00436802i
$820$	−2.82021e23			−1.37965
$821$	−1.58546e23			−0.768085			−0.384042	−	0.923315i	$-0.625468\pi$
$821$	−1.58546e23			−0.768085			−0.384042	+	0.923315i	$0.625468\pi$
$822$			1.64941e22i			0.0791324i
$823$	1.45503e23			0.691310			0.345655	−	0.938362i	$-0.387657\pi$
$823$	1.45503e23			0.691310			0.345655	+	0.938362i	$0.387657\pi$
$824$		−	8.34442e22i		−	0.392625i
$825$			3.77283e23i			1.75807i
$826$	−1.28643e22	−	2.70821e22i	−0.0593671	−	0.124981i
$827$	3.85565e23			1.76219			0.881097	−	0.472936i	$-0.156806\pi$
$827$	3.85565e23			1.76219			0.881097	+	0.472936i	$0.156806\pi$
$828$	8.50555e21			0.0384999
$829$			3.00079e23i			1.34524i	0.739990	+	0.672618i	$0.234830\pi$
$829$			3.00079e23i			1.34524i	−0.739990	+	0.672618i	$0.765170\pi$
$830$	−1.11009e22			−0.0492869
$831$		−	1.71261e23i		−	0.753097i
$832$		−	7.76442e21i		−	0.0338160i
$833$	1.17282e23	+	9.55970e22i	0.505908	+	0.412367i
$834$	−2.72133e22			−0.116266
$835$	−1.91066e23			−0.808521
$836$		−	5.33882e23i		−	2.23766i
$837$	2.04377e23			0.848455
$838$			4.00737e22i			0.164781i
$839$			3.55587e23i			1.44827i	0.689656	+	0.724137i	$0.257762\pi$
$839$			3.55587e23i			1.44827i	−0.689656	+	0.724137i	$0.742238\pi$
$840$	−1.04112e23	+	4.94541e22i	−0.420015	+	0.199512i
$841$	1.19042e23			0.475698
$842$	1.59103e21			0.00629770
$843$		−	1.04748e23i		−	0.410699i
$844$	2.34282e23			0.909913
$845$			4.14099e23i			1.59313i
$846$			6.58884e21i			0.0251100i
$847$	1.13191e23	−	5.37671e22i	0.427313	−	0.202978i
$848$	9.12443e22			0.341223
$849$	1.67943e23			0.622159
$850$		−	4.32976e22i		−	0.158896i
$851$	−2.86330e22			−0.104095
$852$		−	1.02192e23i		−	0.368043i
$853$		−	1.46929e22i		−	0.0524222i	−0.999656	−	0.0262111i	$-0.991656\pi$
$853$		−	1.46929e22i		−	0.0524222i	0.999656	−	0.0262111i	$-0.00834421\pi$
$854$	−8.43711e21	−	1.77619e22i	−0.0298216	−	0.0627808i
$855$	−1.05243e23			−0.368521
$856$	−4.36923e22			−0.151571
$857$			4.48681e23i			1.54203i	0.636820	+	0.771013i	$0.280250\pi$
$857$			4.48681e23i			1.54203i	−0.636820	+	0.771013i	$0.719750\pi$
$858$	2.08178e21			0.00708821
$859$		−	3.88939e23i		−	1.31201i	−0.754758	−	0.656003i	$-0.772246\pi$
$859$		−	3.88939e23i		−	1.31201i	0.754758	−	0.656003i	$-0.227754\pi$
$860$			3.98842e23i			1.33295i
$861$	−2.26618e23	+	1.07646e23i	−0.750360	+	0.356429i
$862$	−6.03918e21			−0.0198116
$863$	−2.45782e23			−0.798846			−0.399423	−	0.916767i	$-0.630790\pi$
$863$	−2.45782e23			−0.798846			−0.399423	+	0.916767i	$0.630790\pi$
$864$		−	1.49170e23i		−	0.480364i
$865$	3.14898e23			1.00471
$866$			8.60776e22i			0.272112i
$867$		−	1.71703e23i		−	0.537806i
$868$	−1.08803e23	−	2.29054e23i	−0.337663	−	0.710854i
$869$	6.70575e23			2.06200
$870$	9.38613e22			0.285978
$871$		−	3.13325e21i		−	0.00945910i
$872$	7.80974e22			0.233617
$873$			4.93573e22i			0.146298i
$874$		−	3.27564e22i		−	0.0962066i
$875$	−1.28449e23	−	2.70414e23i	−0.373824	−	0.786981i
$876$	−1.02851e23			−0.296604
$877$	−2.27621e23			−0.650453			−0.325226	−	0.945636i	$-0.605440\pi$
$877$	−2.27621e23			−0.650453			−0.325226	+	0.945636i	$0.605440\pi$
$878$			5.16782e22i			0.146336i
$879$	3.08785e22			0.0866452
$880$			6.45091e23i			1.79374i
$881$		−	6.76796e23i		−	1.86488i	−0.361327	−	0.932439i	$-0.617676\pi$
$881$		−	6.76796e23i		−	1.86488i	0.361327	−	0.932439i	$-0.382324\pi$
$882$	4.45115e21	−	5.46084e21i	0.0121541	−	0.0149111i
$883$	−5.59922e23			−1.51510			−0.757550	−	0.652777i	$-0.773604\pi$
$883$	−5.59922e23			−1.51510			−0.757550	+	0.652777i	$0.773604\pi$
$884$	9.39584e21			0.0251952
$885$		−	4.94324e23i		−	1.31361i
$886$	−7.36504e22			−0.193957
$887$		−	2.31146e22i		−	0.0603250i	−0.999545	−	0.0301625i	$-0.990398\pi$
$887$		−	2.31146e22i		−	0.0603250i	0.999545	−	0.0301625i	$-0.00960248\pi$
$888$			3.62934e22i			0.0938693i
$889$	1.60333e23	−	7.61600e22i	0.410969	−	0.195215i
$890$	1.05738e23			0.268602
$891$	−4.16006e23			−1.04732
$892$			2.03888e23i			0.508714i
$893$	−9.97946e23			−2.46772
$894$			8.54918e22i			0.209519i
$895$			6.48183e22i			0.157439i
$896$	−2.21907e23	+	1.05408e23i	−0.534204	+	0.253752i
$897$	−5.02331e21			−0.0119853
$898$	3.86251e22			0.0913395
$899$			4.18256e23i			0.980313i
$900$	7.92858e22			0.184185
$901$			1.04429e23i			0.240448i
$902$		−	7.42512e22i		−	0.169454i
$903$	1.52236e23	+	3.20490e23i	0.344363	+	0.724959i
$904$	1.75800e23			0.394160
$905$	4.82903e23			1.07318
$906$		−	6.51369e22i		−	0.143483i
$907$	−1.90740e23			−0.416471			−0.208235	−	0.978079i	$-0.566772\pi$
$907$	−1.90740e23			−0.416471			−0.208235	+	0.978079i	$0.566772\pi$
$908$		−	5.72059e23i		−	1.23809i
$909$		−	5.67104e22i		−	0.121661i
$910$	−4.22474e21	+	2.00680e21i	−0.00898398	+	0.00426749i
$911$	3.53113e23			0.744332			0.372166	−	0.928166i	$-0.378615\pi$
$911$	3.53113e23			0.744332			0.372166	+	0.928166i	$0.378615\pi$
$912$	7.85181e23			1.64063
$913$			1.14943e23i			0.238077i
$914$	−9.52474e22			−0.195562
$915$		−	3.24204e23i		−	0.659858i
$916$		−	3.60978e23i		−	0.728312i
$917$	−1.68634e23	−	3.55011e23i	−0.337280	−	0.710047i
$918$	5.45004e22			0.108058
$919$	−2.68223e23			−0.527195			−0.263598	−	0.964633i	$-0.584909\pi$
$919$	−2.68223e23			−0.527195			−0.263598	+	0.964633i	$0.584909\pi$
$920$			8.23119e22i			0.160384i
$921$	5.11808e23			0.988622
$922$		−	2.57887e22i		−	0.0493836i
$923$		−	8.39911e21i		−	0.0159448i
$924$	2.52821e23	+	5.32242e23i	0.475813	+	1.00169i
$925$	−2.66907e23			−0.497996
$926$	3.66998e21			0.00678853
$927$			8.40915e22i			0.154211i
$928$	3.05274e23			0.555017
$929$			1.77060e23i			0.319150i	0.987186	+	0.159575i	$0.0510124\pi$
$929$			1.77060e23i			0.319150i	−0.987186	+	0.159575i	$0.948988\pi$
$930$			1.06307e23i			0.189976i
$931$	8.27099e23	+	6.74171e23i	1.46541	+	1.19446i
$932$	−6.25691e23			−1.09909
$933$	−2.70322e23			−0.470791
$934$			7.40207e22i			0.127814i
$935$	−7.38305e23			−1.26399
$936$		−	8.86094e20i		−	0.00150409i
$937$			6.25391e23i			1.05253i	0.850321	+	0.526265i	$0.176408\pi$
$937$			6.25391e23i			1.05253i	−0.850321	+	0.526265i	$0.823592\pi$
$938$	−2.03688e22	+	9.67539e21i	−0.0339893	+	0.0161453i
$939$	−6.64022e23			−1.09865
$940$	1.23810e24			2.03111
$941$		−	2.87180e23i		−	0.467129i	−0.972341	−	0.233564i	$-0.924961\pi$
$941$		−	2.87180e23i		−	0.467129i	0.972341	−	0.233564i	$-0.0750389\pi$
$942$	−1.53982e23			−0.248349
$943$			1.79167e23i			0.286527i
$944$		−	5.13240e23i		−	0.813850i
$945$	9.63759e23	−	4.57796e23i	1.51535	−	0.719809i
$946$	−1.05008e23			−0.163717
$947$	−2.59809e22			−0.0401656			−0.0200828	−	0.999798i	$-0.506393\pi$
$947$	−2.59809e22			−0.0401656			−0.0200828	+	0.999798i	$0.506393\pi$
$948$			1.01262e24i			1.55231i
$949$	−8.45331e21			−0.0128498
$950$		−	3.05344e23i		−	0.460257i
$951$			9.76468e23i			1.45953i
$952$	−5.87659e22	−	1.23715e23i	−0.0871024	−	0.183369i
$953$	8.21128e23			1.20689			0.603445	−	0.797405i	$-0.293794\pi$
$953$	8.21128e23			1.20689			0.603445	+	0.797405i	$0.293794\pi$
$954$	4.86237e21			0.00708698
$955$		−	1.69889e24i		−	2.45549i
$956$	−6.81709e23			−0.977092
$957$		−	9.71881e23i		−	1.38139i
$958$		−	6.66600e22i		−	0.0939596i
$959$	−3.46593e23	+	1.64635e23i	−0.484475	+	0.230131i
$960$	−9.21315e23			−1.27714
$961$	2.53706e23			0.348774
$962$			1.47275e21i			0.00200783i
$963$	4.40312e22			0.0595320
$964$		−	3.58865e23i		−	0.481188i
$965$		−	3.54305e22i		−	0.0471150i
$966$	1.55118e22	+	3.26558e22i	0.0204572	+	0.0430668i
$967$	−1.19319e23			−0.156063			−0.0780314	−	0.996951i	$-0.524863\pi$
$967$	−1.19319e23			−0.156063			−0.0780314	+	0.996951i	$0.524863\pi$
$968$	−1.13432e23			−0.147141
$969$			8.98638e23i			1.15610i
$970$	−2.35828e23			−0.300899
$971$			1.25449e24i			1.58750i	0.608243	+	0.793751i	$0.291875\pi$
$971$			1.25449e24i			1.58750i	−0.608243	+	0.793751i	$0.708125\pi$
$972$			1.88736e23i			0.236878i
$973$	−2.71629e23	−	5.71837e23i	−0.338121	−	0.711819i
$974$	1.51291e23			0.186784
$975$	−4.68255e22			−0.0573384
$976$		−	3.36610e23i		−	0.408817i
$977$	−1.57158e24			−1.89312			−0.946562	−	0.322522i	$-0.895469\pi$
$977$	−1.57158e24			−1.89312			−0.946562	+	0.322522i	$0.895469\pi$
$978$			6.40235e22i			0.0764942i
$979$		−	1.09485e24i		−	1.29746i
$980$	−1.02614e24	−	8.36411e23i	−1.20614	−	0.983130i
$981$	−7.87032e22			−0.0917573
$982$	−3.07867e22			−0.0356018
$983$		−	1.08958e24i		−	1.24977i	−0.780718	−	0.624884i	$-0.785146\pi$
$983$		−	1.08958e24i		−	1.24977i	0.780718	−	0.624884i	$-0.214854\pi$
$984$	2.27101e23			0.258379
$985$			2.14068e24i			2.41581i
$986$			1.11535e23i			0.124852i
$987$	9.94880e23	−	4.72579e23i	1.10467	−	0.524731i
$988$	6.62615e22			0.0729803
$989$	2.53384e23			0.276827
$990$			3.43767e22i			0.0372548i
$991$	−1.13774e23			−0.122307			−0.0611537	−	0.998128i	$-0.519478\pi$
$991$	−1.13774e23			−0.122307			−0.0611537	+	0.998128i	$0.519478\pi$
$992$			3.45754e23i			0.368700i
$993$			5.71414e22i			0.0604446i
$994$	−5.46013e22	+	2.59362e22i	−0.0572944	+	0.0272154i
$995$	1.92037e24			1.99894
$996$	−1.73573e23			−0.179228
$997$			8.17061e23i			0.836938i	0.908231	+	0.418469i	$0.137433\pi$
$997$			8.17061e23i			0.836938i	−0.908231	+	0.418469i	$0.862567\pi$
$998$	6.82820e22			0.0693844
$999$		−	3.35967e23i		−	0.338666i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7.17.b.b.6.5	✓	8
3.2	odd	2		63.17.d.c.55.3		8
4.3	odd	2		112.17.c.b.97.6		8
7.6	odd	2	inner	7.17.b.b.6.6	yes	8
21.20	even	2		63.17.d.c.55.4		8
28.27	even	2		112.17.c.b.97.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7.17.b.b.6.5	✓	8	1.1	even	1	trivial
7.17.b.b.6.6	yes	8	7.6	odd	2	inner
63.17.d.c.55.3		8	3.2	odd	2
63.17.d.c.55.4		8	21.20	even	2
112.17.c.b.97.3		8	28.27	even	2
112.17.c.b.97.6		8	4.3	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:	\( N \)	\(=\)	\( 7 \)
Weight:	\( k \)	\(=\)	\( 17 \)
Character orbit:	\([\chi]\)	\(=\)	7.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+40.3121 q^{2} -6147.19i q^{3} -63910.9 q^{4} +623292. i q^{5} -247806. i q^{6} +(5.20719e6 - 2.47347e6i) q^{7} -5.21828e6 q^{8} +5.25876e6 q^{9} +O(q^{10})\)	\(q+40.3121 q^{2} -6147.19i q^{3} -63910.9 q^{4} +623292. i q^{5} -247806. i q^{6} +(5.20719e6 - 2.47347e6i) q^{7} -5.21828e6 q^{8} +5.25876e6 q^{9} +2.51262e7i q^{10} +2.60168e8 q^{11} +3.92873e8i q^{12} +3.22901e7i q^{13} +(2.09913e8 - 9.97109e7i) q^{14} +3.83149e9 q^{15} +3.97811e9 q^{16} +4.55293e9i q^{17} +2.11992e8 q^{18} +3.21083e10i q^{19} -3.98352e10i q^{20} +(-1.52049e10 - 3.20096e10i) q^{21} +1.04879e10 q^{22} -2.53072e10 q^{23} +3.20778e10i q^{24} -2.35905e11 q^{25} +1.30168e9i q^{26} -2.96943e11i q^{27} +(-3.32797e11 + 1.58082e11i) q^{28} +6.07691e11 q^{29} +1.54456e11 q^{30} +6.88271e11i q^{31} +5.02351e11 q^{32} -1.59930e12i q^{33} +1.83538e11i q^{34} +(1.54170e12 + 3.24560e12i) q^{35} -3.36092e11 q^{36} +1.13142e12 q^{37} +1.29435e12i q^{38} +1.98493e11 q^{39} -3.25251e12i q^{40} -7.07970e12i q^{41} +(-6.12942e11 - 1.29038e12i) q^{42} -1.00123e13 q^{43} -1.66276e13 q^{44} +3.27774e12i q^{45} -1.02019e12 q^{46} +3.10807e13i q^{47} -2.44542e13i q^{48} +(2.09968e13 - 2.57597e13i) q^{49} -9.50982e12 q^{50} +2.79877e13 q^{51} -2.06369e12i q^{52} +2.29366e13 q^{53} -1.19704e13i q^{54} +1.62160e14i q^{55} +(-2.71726e13 + 1.29073e13i) q^{56} +1.97376e14 q^{57} +2.44973e13 q^{58} -1.29016e14i q^{59} -2.44874e14 q^{60} -8.46157e13i q^{61} +2.77457e13i q^{62} +(2.73834e13 - 1.30074e13i) q^{63} -2.40458e14 q^{64} -2.01261e13 q^{65} -6.44712e13i q^{66} -9.70344e13 q^{67} -2.90982e14i q^{68} +1.55568e14i q^{69} +(6.21490e13 + 1.30837e14i) q^{70} -2.60114e14 q^{71} -2.74417e13 q^{72} +2.61793e14i q^{73} +4.56098e13 q^{74} +1.45015e15i q^{75} -2.05207e15i q^{76} +(1.35474e15 - 6.43518e14i) q^{77} +8.00169e12 q^{78} +2.57747e15 q^{79} +2.47952e15i q^{80} -1.59899e15 q^{81} -2.85398e14i q^{82} +4.41804e14i q^{83} +(9.71760e14 + 2.04576e15i) q^{84} -2.83781e15 q^{85} -4.03618e14 q^{86} -3.73559e15i q^{87} -1.35763e15 q^{88} -4.20826e15i q^{89} +1.32133e14i q^{90} +(7.98686e13 + 1.68141e14i) q^{91} +1.61741e15 q^{92} +4.23093e15 q^{93} +1.25293e15i q^{94} -2.00128e16 q^{95} -3.08805e15i q^{96} +9.38572e15i q^{97} +(8.46425e14 - 1.03843e15i) q^{98} +1.36816e15 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 544 q^{2} + 18784 q^{4} - 3034472 q^{7} - 35863808 q^{8} - 41933880 q^{9}+O(q^{10}) \) 8 * q - 544 * q^2 + 18784 * q^4 - 3034472 * q^7 - 35863808 * q^8 - 41933880 * q^9	\( 8 q - 544 q^{2} + 18784 q^{4} - 3034472 q^{7} - 35863808 q^{8} - 41933880 q^{9} + 430398704 q^{11} - 2080234240 q^{14} + 83393280 q^{15} - 4357080832 q^{16} - 7232400864 q^{18} + 45847234944 q^{21} - 34275403968 q^{22} + 89765082416 q^{23} + 61966251080 q^{25} - 376785722656 q^{28} - 22437591664 q^{29} - 192018300480 q^{30} + 941689387008 q^{32} + 371925382080 q^{35} - 4527659399328 q^{36} + 5737866534416 q^{37} - 7975804007808 q^{39} - 13160568536640 q^{42} - 3976952110864 q^{43} + 45337613120448 q^{44} + 35817469755072 q^{46} - 27450534789496 q^{49} - 96564765668320 q^{50} + 58670380591488 q^{51} - 108679841507824 q^{53} - 15117119134208 q^{56} - 196163055495360 q^{57} + 650847682404672 q^{58} - 335782392744960 q^{60} + 223739049782808 q^{63} - 460533940742144 q^{64} + 573279455461440 q^{65} - 722120065643024 q^{67} + 12\!\cdots\!60 q^{70}+ \cdots - 15\!\cdots\!92 q^{99}+O(q^{100}) \) 8 * q - 544 * q^2 + 18784 * q^4 - 3034472 * q^7 - 35863808 * q^8 - 41933880 * q^9 + 430398704 * q^11 - 2080234240 * q^14 + 83393280 * q^15 - 4357080832 * q^16 - 7232400864 * q^18 + 45847234944 * q^21 - 34275403968 * q^22 + 89765082416 * q^23 + 61966251080 * q^25 - 376785722656 * q^28 - 22437591664 * q^29 - 192018300480 * q^30 + 941689387008 * q^32 + 371925382080 * q^35 - 4527659399328 * q^36 + 5737866534416 * q^37 - 7975804007808 * q^39 - 13160568536640 * q^42 - 3976952110864 * q^43 + 45337613120448 * q^44 + 35817469755072 * q^46 - 27450534789496 * q^49 - 96564765668320 * q^50 + 58670380591488 * q^51 - 108679841507824 * q^53 - 15117119134208 * q^56 - 196163055495360 * q^57 + 650847682404672 * q^58 - 335782392744960 * q^60 + 223739049782808 * q^63 - 460533940742144 * q^64 + 573279455461440 * q^65 - 722120065643024 * q^67 + 1268642086877760 * q^70 - 289095246669136 * q^71 + 1560006716205312 * q^72 - 5411665863643328 * q^74 + 4485628262682896 * q^77 + 192459573633600 * q^78 + 5832776866563376 * q^79 - 14617034931574584 * q^81 + 12924747561148416 * q^84 - 5815379514337920 * q^85 + 7508453217752512 * q^86 - 24665635192321536 * q^88 + 23929798963272384 * q^91 + 1197288221450688 * q^92 + 27012151562451840 * q^93 - 53204702857107840 * q^95 + 43278421367298656 * q^98 - 15738606124789392 * q^99

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