LMFDB - Embedded newform 10.26.b.a.9.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [10,26,Mod(9,10)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(10, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 26, names="a")

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

chi := DirichletCharacter("10.9");

S:= CuspForms(chi, 26);

N := Newforms(S);

Level:	$ N $	$=$	$ 10 = 2 \cdot 5 $
Weight:	$ k $	$=$	$ 26 $
Character orbit:	$[\chi]$	$=$	10.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:	$39.5996779952$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 1406300109694 x^{10} + \cdots + 56\!\cdots\!01 $ x^12 + 1406300109694x^10 + 721371039010841274826815x^8 + 163583579306250445630287276512319780x^6 + 14727031184488621294308896513370084274619782815x^4 + 213559114414440049199738916498397853721503585895983619294*x^2 + 562442837480837791206109989109268286491448310078170789537309341601
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{90}\cdot 3^{8}\cdot 5^{29} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			9.10
Root			$116846. i$ of defining polynomial
Character	$\chi$	$=$	10.9
Dual form			10.26.b.a.9.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+4096.00i q^{2} +233693. i q^{3} -1.67772e7 q^{4} +(-3.44896e8 - 4.23166e8i) q^{5} -9.57206e8 q^{6} +6.39090e10i q^{7} -6.87195e10i q^{8} +7.92676e11 q^{9} +(1.73329e12 - 1.41270e12i) q^{10} +6.04007e12 q^{11} -3.92071e12i q^{12} +1.13809e14i q^{13} -2.61771e14 q^{14} +(9.88909e13 - 8.05998e13i) q^{15} +2.81475e14 q^{16} -9.52541e14i q^{17} +3.24680e15i q^{18} -8.44950e15 q^{19} +(5.78640e15 + 7.09955e15i) q^{20} -1.49351e16 q^{21} +2.47401e16i q^{22} -1.51928e16i q^{23} +1.60592e16 q^{24} +(-6.01162e16 + 2.91897e17i) q^{25} -4.66162e17 q^{26} +3.83248e17i q^{27} -1.07222e18i q^{28} +1.63360e18 q^{29} +(3.30137e17 + 4.05057e17i) q^{30} -7.82464e18 q^{31} +1.15292e18i q^{32} +1.41152e18i q^{33} +3.90161e18 q^{34} +(2.70441e19 - 2.20420e19i) q^{35} -1.32989e19 q^{36} -3.53342e19i q^{37} -3.46091e19i q^{38} -2.65964e19 q^{39} +(-2.90798e19 + 2.37011e19i) q^{40} -2.35937e20 q^{41} -6.11741e19i q^{42} +3.29832e19i q^{43} -1.01335e20 q^{44} +(-2.73391e20 - 3.35434e20i) q^{45} +6.22296e19 q^{46} -1.82685e20i q^{47} +6.57787e19i q^{48} -2.74329e21 q^{49} +(-1.19561e21 - 2.46236e20i) q^{50} +2.22602e20 q^{51} -1.90940e21i q^{52} -5.40172e21i q^{53} -1.56978e21 q^{54} +(-2.08320e21 - 2.55595e21i) q^{55} +4.39179e21 q^{56} -1.97459e21i q^{57} +6.69124e21i q^{58} +1.13226e22 q^{59} +(-1.65911e21 + 1.35224e21i) q^{60} -2.83642e22 q^{61} -3.20497e22i q^{62} +5.06592e22i q^{63} -4.72237e21 q^{64} +(4.81602e22 - 3.92523e22i) q^{65} -5.78158e21 q^{66} +1.16196e23i q^{67} +1.59810e22i q^{68} +3.55044e21 q^{69} +(9.02840e22 + 1.10773e23i) q^{70} +1.14601e23 q^{71} -5.44723e22i q^{72} -8.85118e21i q^{73} +1.44729e23 q^{74} +(-6.82142e22 - 1.40487e22i) q^{75} +1.41759e23 q^{76} +3.86015e23i q^{77} -1.08939e23i q^{78} -2.17397e23 q^{79} +(-9.70797e22 - 1.19111e23i) q^{80} +5.82063e23 q^{81} -9.66398e23i q^{82} +6.46451e22i q^{83} +2.50569e23 q^{84} +(-4.03083e23 + 3.28528e23i) q^{85} -1.35099e23 q^{86} +3.81761e23i q^{87} -4.15070e23i q^{88} -3.57337e24 q^{89} +(1.37394e24 - 1.11981e24i) q^{90} -7.27343e24 q^{91} +2.54893e23i q^{92} -1.82856e24i q^{93} +7.48277e23 q^{94} +(2.91420e24 + 3.57554e24i) q^{95} -2.69429e23 q^{96} -2.49389e24i q^{97} -1.12365e25i q^{98} +4.78782e24 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 201326592 q^{4} - 490295340 q^{5} - 6565199872 q^{6} - 1082937564236 q^{9} + 1636528619520 q^{10} + 19723089228624 q^{11} + 278591122243584 q^{14} - 449884766537680 q^{15} + 33\!\cdots\!72 q^{16}+ \cdots + 41\!\cdots\!28 q^{99}+O(q^{100}) $ 12 * q - 201326592 * q^4 - 490295340 * q^5 - 6565199872 * q^6 - 1082937564236 * q^9 + 1636528619520 * q^10 + 19723089228624 * q^11 + 278591122243584 * q^14 - 449884766537680 * q^15 + 3377699720527872 * q^16 - 4015312977833040 * q^19 + 8225790822973440 * q^20 - 56363420582029456 * q^21 + 110145776335716352 * q^24 - 1047554086248996900 * q^25 - 252210272532037632 * q^26 + 5852064063311009640 * q^29 - 3747916483574824960 * q^30 + 158585871554029824 * q^31 + 28121800210885115904 * q^34 - 42730948507221221040 * q^35 + 18168677429701246976 * q^36 - 249453273245123586912 * q^39 - 27456394139868856320 * q^40 + 206458603439752488024 * q^41 - 330898528175898230784 * q^44 + 957114913653485255020 * q^45 - 1111751773656740462592 * q^46 - 3432561496278055389084 * q^49 + 346631457781510963200 * q^50 - 3032451787323924027136 * q^51 + 6455741354411915345920 * q^54 - 7824754202169531625680 * q^55 - 4673983433563013382144 * q^56 + 24998150261761560337680 * q^59 + 7547813903312229498880 * q^60 + 7374571220622236593224 * q^61 - 56668397794435742564352 * q^64 + 20652620138653742557920 * q^65 + 56072959085731865952256 * q^66 - 370250651964757999709072 * q^69 + 157367128964587932549120 * q^70 + 149137752442507323299424 * q^71 + 27409492362780459270144 * q^74 + 1032897211530510645911200 * q^75 + 67365773136708124016640 * q^76 + 801700633747623249599040 * q^79 - 138005869407843165143040 * q^80 - 2864220237232227656687428 * q^81 + 945621281603553901674496 * q^84 + 2004099032091709203221760 * q^85 - 1363071174568488987328512 * q^86 - 5964345056120682049233480 * q^89 + 4840324611668628597309440 * q^90 - 14003423438242038482629536 * q^91 + 3325183945859356082110464 * q^94 + 18644670331946084490382800 * q^95 - 1847939481072001752236032 * q^96 + 4107440578564823447146928 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/10\mathbb{Z}\right)^\times$.

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

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 $

$2$			4096.00i			0.707107i
$2$			4096.00i			0.707107i
$3$			233693.i			0.253881i	0.991910	+	0.126940i	$0.0405157\pi$
$3$			233693.i			0.253881i	−0.991910	+	0.126940i	$0.959484\pi$
$4$	−1.67772e7			−0.500000
$5$	−3.44896e8	−	4.23166e8i	−0.631777	−	0.775150i
$5$	−3.44896e8	−	4.23166e8i	−0.631777	−	0.775150i
$6$	−9.57206e8			−0.179521
$7$			6.39090e10i			1.74517i	0.488466	+	0.872583i	$0.337557\pi$
$7$			6.39090e10i			1.74517i	−0.488466	+	0.872583i	$0.662443\pi$
$8$		−	6.87195e10i		−	0.353553i
$9$	7.92676e11			0.935545
$10$	1.73329e12	−	1.41270e12i	0.548114	−	0.446734i
$11$	6.04007e12			0.580274			0.290137	−	0.956985i	$-0.406299\pi$
$11$	6.04007e12			0.580274			0.290137	+	0.956985i	$0.406299\pi$
$12$		−	3.92071e12i		−	0.126940i
$13$			1.13809e14i			1.35483i	0.735601	+	0.677415i	$0.236900\pi$
$13$			1.13809e14i			1.35483i	−0.735601	+	0.677415i	$0.763100\pi$
$14$	−2.61771e14			−1.23402
$15$	9.88909e13	−	8.05998e13i	0.196796	−	0.160396i
$16$	2.81475e14			0.250000
$17$		−	9.52541e14i		−	0.396526i	−0.980149	−	0.198263i	$-0.936470\pi$
$17$		−	9.52541e14i		−	0.396526i	0.980149	−	0.198263i	$-0.0635301\pi$
$18$			3.24680e15i			0.661530i
$19$	−8.44950e15			−0.875812			−0.437906	−	0.899021i	$-0.644280\pi$
$19$	−8.44950e15			−0.875812			−0.437906	+	0.899021i	$0.644280\pi$
$20$	5.78640e15	+	7.09955e15i	0.315888	+	0.387575i
$21$	−1.49351e16			−0.443064
$22$			2.47401e16i			0.410316i
$23$		−	1.51928e16i		−	0.144557i	−0.997384	−	0.0722786i	$-0.976973\pi$
$23$		−	1.51928e16i		−	0.144557i	0.997384	−	0.0722786i	$-0.0230271\pi$
$24$	1.60592e16			0.0897604
$25$	−6.01162e16	+	2.91897e17i	−0.201717	+	0.979444i
$26$	−4.66162e17			−0.958010
$27$			3.83248e17i			0.491397i
$28$		−	1.07222e18i		−	0.872583i
$29$	1.63360e18			0.857376			0.428688	−	0.903452i	$-0.358976\pi$
$29$	1.63360e18			0.857376			0.428688	+	0.903452i	$0.358976\pi$
$30$	3.30137e17	+	4.05057e17i	0.113417	+	0.139156i
$31$	−7.82464e18			−1.78420			−0.892099	−	0.451840i	$-0.850768\pi$
$31$	−7.82464e18			−1.78420			−0.892099	+	0.451840i	$0.850768\pi$
$32$			1.15292e18i			0.176777i
$33$			1.41152e18i			0.147320i
$34$	3.90161e18			0.280386
$35$	2.70441e19	−	2.20420e19i	1.35277	−	1.10255i
$36$	−1.32989e19			−0.467772
$37$		−	3.53342e19i		−	0.882417i	−0.897405	−	0.441208i	$-0.854550\pi$
$37$		−	3.53342e19i		−	0.882417i	0.897405	−	0.441208i	$-0.145450\pi$
$38$		−	3.46091e19i		−	0.619293i
$39$	−2.65964e19			−0.343965
$40$	−2.90798e19	+	2.37011e19i	−0.274057	+	0.223367i
$41$	−2.35937e20			−1.63304			−0.816522	−	0.577315i	$-0.804101\pi$
$41$	−2.35937e20			−1.63304			−0.816522	+	0.577315i	$0.804101\pi$
$42$		−	6.11741e19i		−	0.313293i
$43$			3.29832e19i			0.125874i	0.998017	+	0.0629372i	$0.0200468\pi$
$43$			3.29832e19i			0.125874i	−0.998017	+	0.0629372i	$0.979953\pi$
$44$	−1.01335e20			−0.290137
$45$	−2.73391e20	−	3.35434e20i	−0.591055	−	0.725188i
$46$	6.22296e19			0.102217
$47$		−	1.82685e20i		−	0.229340i	−0.993404	−	0.114670i	$-0.963419\pi$
$47$		−	1.82685e20i		−	0.229340i	0.993404	−	0.114670i	$-0.0365810\pi$
$48$			6.57787e19i			0.0634702i
$49$	−2.74329e21			−2.04560
$50$	−1.19561e21	−	2.46236e20i	−0.692571	−	0.142635i
$51$	2.22602e20			0.100670
$52$		−	1.90940e21i		−	0.677415i
$53$		−	5.40172e21i		−	1.51037i	−0.655511	−	0.755186i	$-0.727547\pi$
$53$		−	5.40172e21i		−	1.51037i	0.655511	−	0.755186i	$-0.272453\pi$
$54$	−1.56978e21			−0.347470
$55$	−2.08320e21	−	2.55595e21i	−0.366604	−	0.449800i
$56$	4.39179e21			0.617009
$57$		−	1.97459e21i		−	0.222352i
$58$			6.69124e21i			0.606257i
$59$	1.13226e22			0.828509			0.414254	−	0.910161i	$-0.364042\pi$
$59$	1.13226e22			0.828509			0.414254	+	0.910161i	$0.364042\pi$
$60$	−1.65911e21	+	1.35224e21i	−0.0983979	+	0.0801979i
$61$	−2.83642e22			−1.36820			−0.684098	−	0.729390i	$-0.739804\pi$
$61$	−2.83642e22			−1.36820			−0.684098	+	0.729390i	$0.739804\pi$
$62$		−	3.20497e22i		−	1.26162i
$63$			5.06592e22i			1.63268i
$64$	−4.72237e21			−0.125000
$65$	4.81602e22	−	3.92523e22i	1.05020	−	0.855950i
$66$	−5.78158e21			−0.104171
$67$			1.16196e23i			1.73483i	0.497586	+	0.867415i	$0.334220\pi$
$67$			1.16196e23i			1.73483i	−0.497586	+	0.867415i	$0.665780\pi$
$68$			1.59810e22i			0.198263i
$69$	3.55044e21			0.0367003
$70$	9.02840e22	+	1.10773e23i	0.779624	+	0.956550i
$71$	1.14601e23			0.828816			0.414408	−	0.910091i	$-0.363989\pi$
$71$	1.14601e23			0.828816			0.414408	+	0.910091i	$0.363989\pi$
$72$		−	5.44723e22i		−	0.330765i
$73$		−	8.85118e21i		−	0.0452340i	−0.999744	−	0.0226170i	$-0.992800\pi$
$73$		−	8.85118e21i		−	0.0452340i	0.999744	−	0.0226170i	$-0.00719983\pi$
$74$	1.44729e23			0.623963
$75$	−6.82142e22	−	1.40487e22i	−0.248662	−	0.0512119i
$76$	1.41759e23			0.437906
$77$			3.86015e23i			1.01267i
$78$		−	1.08939e23i		−	0.243220i
$79$	−2.17397e23			−0.413918			−0.206959	−	0.978350i	$-0.566357\pi$
$79$	−2.17397e23			−0.413918			−0.206959	+	0.978350i	$0.566357\pi$
$80$	−9.70797e22	−	1.19111e23i	−0.157944	−	0.193788i
$81$	5.82063e23			0.810788
$82$		−	9.66398e23i		−	1.15474i
$83$			6.46451e22i			0.0663834i	0.999449	+	0.0331917i	$0.0105672\pi$
$83$			6.46451e22i			0.0663834i	−0.999449	+	0.0331917i	$0.989433\pi$
$84$	2.50569e23			0.221532
$85$	−4.03083e23	+	3.28528e23i	−0.307368	+	0.250516i
$86$	−1.35099e23			−0.0890067
$87$			3.81761e23i			0.217671i
$88$		−	4.15070e23i		−	0.205158i
$89$	−3.57337e24			−1.53357			−0.766783	−	0.641906i	$-0.778144\pi$
$89$	−3.57337e24			−1.53357			−0.766783	+	0.641906i	$0.778144\pi$
$90$	1.37394e24	−	1.11981e24i	0.512785	−	0.417939i
$91$	−7.27343e24			−2.36440
$92$			2.54893e23i			0.0722786i
$93$		−	1.82856e24i		−	0.452973i
$94$	7.48277e23			0.162168
$95$	2.91420e24	+	3.57554e24i	0.553317	+	0.678886i
$96$	−2.69429e23			−0.0448802
$97$		−	2.49389e24i		−	0.364948i	−0.983211	−	0.182474i	$-0.941589\pi$
$97$		−	2.49389e24i		−	0.364948i	0.983211	−	0.182474i	$-0.0584105\pi$
$98$		−	1.12365e25i		−	1.44646i
$99$	4.78782e24			0.542872
$100$	1.00858e24	−	4.89722e24i	0.100858	−	0.489722i
$101$	−1.34804e25			−1.19038			−0.595192	−	0.803584i	$-0.702924\pi$
$101$	−1.34804e25			−1.19038			−0.595192	+	0.803584i	$0.702924\pi$
$102$			9.11777e23i			0.0711847i
$103$			1.98475e25i			1.37164i	0.727769	+	0.685822i	$0.240557\pi$
$103$			1.98475e25i			1.37164i	−0.727769	+	0.685822i	$0.759443\pi$
$104$	7.82090e24			0.479005
$105$	5.15105e24	+	6.32002e24i	0.279917	+	0.343441i
$106$	2.21255e25			1.06799
$107$		−	6.60004e24i		−	0.283302i	−0.989917	−	0.141651i	$-0.954759\pi$
$107$		−	6.60004e24i		−	0.283302i	0.989917	−	0.141651i	$-0.0452411\pi$
$108$		−	6.42983e24i		−	0.245699i
$109$	6.35443e24			0.216394			0.108197	−	0.994129i	$-0.465492\pi$
$109$	6.35443e24			0.216394			0.108197	+	0.994129i	$0.465492\pi$
$110$	1.04692e25	−	8.53277e24i	0.318056	−	0.259228i
$111$	8.25735e24			0.224029
$112$			1.79888e25i			0.436291i
$113$			5.12661e25i			1.11263i	0.830973	+	0.556313i	$0.187785\pi$
$113$			5.12661e25i			1.11263i	−0.830973	+	0.556313i	$0.812215\pi$
$114$	8.08791e24			0.157226
$115$	−6.42907e24	+	5.23994e24i	−0.112054	+	0.0913278i
$116$	−2.74073e25			−0.428688
$117$			9.02138e25i			1.26750i
$118$			4.63775e25i			0.585844i
$119$	6.08759e25			0.692004
$120$	−5.53878e24	−	6.79573e24i	−0.0567085	−	0.0695778i
$121$	−7.18647e25			−0.663282
$122$		−	1.16180e26i		−	0.967460i
$123$		−	5.51368e25i		−	0.414598i
$124$	1.31276e26			0.892099
$125$	1.44255e26	−	7.52351e25i	0.886656	−	0.462429i
$126$	−2.07500e26			−1.15448
$127$		−	1.52068e26i		−	0.766462i	−0.923653	−	0.383231i	$-0.874811\pi$
$127$		−	1.52068e26i		−	0.766462i	0.923653	−	0.383231i	$-0.125189\pi$
$128$		−	1.93428e25i		−	0.0883883i
$129$	−7.70794e24			−0.0319571
$130$	1.60778e26	+	1.97264e26i	0.605248	+	0.742602i
$131$	−4.54456e26			−1.55454			−0.777268	−	0.629170i	$-0.783395\pi$
$131$	−4.54456e26			−1.55454			−0.777268	+	0.629170i	$0.783395\pi$
$132$		−	2.36814e25i		−	0.0736602i
$133$		−	5.39999e26i		−	1.52844i
$134$	−4.75940e26			−1.22671
$135$	1.62178e26	−	1.32181e26i	0.380907	−	0.310453i
$136$	−6.54581e25			−0.140193
$137$		−	5.90117e25i		−	0.115327i	−0.998336	−	0.0576635i	$-0.981635\pi$
$137$		−	5.90117e25i		−	0.115327i	0.998336	−	0.0576635i	$-0.0183651\pi$
$138$			1.45426e25i			0.0259510i
$139$	1.48479e26			0.242091			0.121046	−	0.992647i	$-0.461375\pi$
$139$	1.48479e26			0.242091			0.121046	+	0.992647i	$0.461375\pi$
$140$	−4.53725e26	+	3.69803e26i	−0.676383	+	0.551277i
$141$	4.26921e25			0.0582249
$142$			4.69405e26i			0.586062i
$143$			6.87414e26i			0.786173i
$144$	2.23119e26			0.233886
$145$	−5.63424e26	−	6.91286e26i	−0.541670	−	0.664596i
$146$	3.62544e25			0.0319853
$147$		−	6.41088e26i		−	0.519339i
$148$			5.92809e26i			0.441208i
$149$	5.34888e26			0.365961			0.182981	−	0.983117i	$-0.441425\pi$
$149$	5.34888e26			0.365961			0.182981	+	0.983117i	$0.441425\pi$
$150$	5.75436e25	−	2.79406e26i	0.0362123	−	0.175831i
$151$	2.12275e27			1.22938			0.614691	−	0.788768i	$-0.289281\pi$
$151$	2.12275e27			1.22938			0.614691	+	0.788768i	$0.289281\pi$
$152$			5.80645e26i			0.309646i
$153$		−	7.55056e26i		−	0.370968i
$154$	−1.58112e27			−0.716069
$155$	2.69869e27	+	3.31112e27i	1.12721	+	1.38302i
$156$	4.46213e26			0.171983
$157$		−	1.66162e26i		−	0.0591271i	−0.999563	−	0.0295636i	$-0.990588\pi$
$157$		−	1.66162e26i		−	0.0591271i	0.999563	−	0.0295636i	$-0.00941174\pi$
$158$		−	8.90456e26i		−	0.292684i
$159$	1.26234e27			0.383454
$160$	4.87878e26	−	3.97638e26i	0.137029	−	0.111683i
$161$	9.70956e26			0.252276
$162$			2.38413e27i			0.573314i
$163$			2.97944e27i			0.663421i	0.943381	+	0.331710i	$0.107626\pi$
$163$			2.97944e27i			0.663421i	−0.943381	+	0.331710i	$0.892374\pi$
$164$	3.95837e27			0.816522
$165$	5.97308e26	−	4.86828e26i	0.114195	−	0.0930735i
$166$	−2.64786e26			−0.0469401
$167$		−	8.95870e27i		−	1.47329i	−0.676278	−	0.736647i	$-0.736408\pi$
$167$		−	8.95870e27i		−	1.47329i	0.676278	−	0.736647i	$-0.263592\pi$
$168$			1.02633e27i			0.156647i
$169$	−5.89610e27			−0.835567
$170$	−1.34565e27	−	1.65103e27i	−0.177142	−	0.217342i
$171$	−6.69772e27			−0.819361
$172$		−	5.53367e26i		−	0.0629372i
$173$			1.40879e28i			1.49028i	0.666905	+	0.745142i	$0.267619\pi$
$173$			1.40879e28i			1.49028i	−0.666905	+	0.745142i	$0.732381\pi$
$174$	−1.56369e27			−0.153917
$175$	−1.86549e28	−	3.84197e27i	−1.70929	−	0.352029i
$176$	1.70013e27			0.145068
$177$			2.64602e27i			0.210342i
$178$		−	1.46365e28i		−	1.08440i
$179$	−9.19738e27			−0.635333			−0.317667	−	0.948202i	$-0.602899\pi$
$179$	−9.19738e27			−0.635333			−0.317667	+	0.948202i	$0.602899\pi$
$180$	4.58674e27	+	5.62765e27i	0.295528	+	0.362594i
$181$	2.77373e28			1.66756			0.833782	−	0.552094i	$-0.186171\pi$
$181$	2.77373e28			1.66756			0.833782	+	0.552094i	$0.186171\pi$
$182$		−	2.97920e28i		−	1.67189i
$183$		−	6.62852e27i		−	0.347358i
$184$	−1.04404e27			−0.0511087
$185$	−1.49522e28	+	1.21866e28i	−0.684006	+	0.557490i
$186$	7.48979e27			0.320301
$187$		−	5.75341e27i		−	0.230094i
$188$			3.06494e27i			0.114670i
$189$	−2.44930e28			−0.857570
$190$	−1.46454e28	+	1.19366e28i	−0.480045	+	0.391255i
$191$	−1.68120e28			−0.516064			−0.258032	−	0.966136i	$-0.583074\pi$
$191$	−1.68120e28			−0.516064			−0.258032	+	0.966136i	$0.583074\pi$
$192$		−	1.10358e27i		−	0.0317351i
$193$		−	2.97967e28i		−	0.802975i	−0.915865	−	0.401487i	$-0.868493\pi$
$193$		−	2.97967e28i		−	0.802975i	0.915865	−	0.401487i	$-0.131507\pi$
$194$	1.02150e28			0.258057
$195$	9.17299e27	+	1.12547e28i	0.217309	+	0.266625i
$196$	4.60248e28			1.02280
$197$			8.93281e27i			0.186277i	0.995653	+	0.0931387i	$0.0296900\pi$
$197$			8.93281e27i			0.186277i	−0.995653	+	0.0931387i	$0.970310\pi$
$198$			1.96109e28i			0.383869i
$199$	9.58646e28			1.76196			0.880978	−	0.473157i	$-0.156886\pi$
$199$	9.58646e28			1.76196			0.880978	+	0.473157i	$0.156886\pi$
$200$	2.00590e28	+	4.13116e27i	0.346286	+	0.0713176i
$201$	−2.71542e28			−0.440440
$202$		−	5.52159e28i		−	0.841728i
$203$			1.04402e29i			1.49626i
$204$	−3.73464e27			−0.0503352
$205$	8.13738e28	+	9.98406e28i	1.03172	+	1.26585i
$206$	−8.12956e28			−0.969899
$207$		−	1.20430e28i		−	0.135240i
$208$			3.20344e28i			0.338708i
$209$	−5.10355e28			−0.508211
$210$	−2.58868e28	+	2.10987e28i	−0.242850	+	0.197931i
$211$	5.69613e27			0.0503558			0.0251779	−	0.999683i	$-0.491985\pi$
$211$	5.69613e27			0.0503558			0.0251779	+	0.999683i	$0.491985\pi$
$212$			9.06259e28i			0.755186i
$213$			2.67814e28i			0.210420i
$214$	2.70338e28			0.200325
$215$	1.39574e28	−	1.13758e28i	0.0975716	−	0.0795245i
$216$	2.63366e28			0.173735
$217$		−	5.00065e29i		−	3.11372i
$218$			2.60278e28i			0.153014i
$219$	2.06846e27			0.0114840
$220$	3.49502e28	+	4.28818e28i	0.183302	+	0.224900i
$221$	1.08408e29			0.537226
$222$			3.38221e28i			0.158412i
$223$			5.84548e28i			0.258827i	0.991591	+	0.129413i	$0.0413094\pi$
$223$			5.84548e28i			0.258827i	−0.991591	+	0.129413i	$0.958691\pi$
$224$	−7.36821e28			−0.308505
$225$	−4.76527e28	+	2.31380e29i	−0.188715	+	0.916313i
$226$	−2.09986e29			−0.786746
$227$		−	5.52270e29i		−	1.95807i	−0.203691	−	0.979035i	$-0.565294\pi$
$227$		−	5.52270e29i		−	1.95807i	0.203691	−	0.979035i	$-0.434706\pi$
$228$			3.31281e28i			0.111176i
$229$	5.80273e28			0.184369			0.0921847	−	0.995742i	$-0.470615\pi$
$229$	5.80273e28			0.184369			0.0921847	+	0.995742i	$0.470615\pi$
$230$	−2.14628e28	−	2.63335e28i	−0.0645785	−	0.0792338i
$231$	−9.02088e28			−0.257098
$232$		−	1.12260e29i		−	0.303128i
$233$		−	1.93762e29i		−	0.495816i	−0.968784	−	0.247908i	$-0.920257\pi$
$233$		−	1.93762e29i		−	0.495816i	0.968784	−	0.247908i	$-0.0797430\pi$
$234$	−3.69516e29			−0.896261
$235$	−7.73061e28	+	6.30073e28i	−0.177773	+	0.144892i
$236$	−1.89962e29			−0.414254
$237$		−	5.08040e28i		−	0.105086i
$238$			2.49348e29i			0.489321i
$239$	−7.15964e28			−0.133327			−0.0666634	−	0.997776i	$-0.521235\pi$
$239$	−7.15964e28			−0.133327			−0.0666634	+	0.997776i	$0.521235\pi$
$240$	2.78353e28	−	2.26868e28i	0.0491989	−	0.0400990i
$241$	−8.42045e29			−1.41293			−0.706467	−	0.707746i	$-0.749712\pi$
$241$	−8.42045e29			−1.41293			−0.706467	+	0.707746i	$0.749712\pi$
$242$		−	2.94358e29i		−	0.469011i
$243$			4.60746e29i			0.697241i
$244$	4.75873e29			0.684098
$245$	9.46152e29	+	1.16087e30i	1.29236	+	1.58565i
$246$	2.25840e29			0.293165
$247$		−	9.61630e29i		−	1.18658i
$248$			5.37705e29i			0.630809i
$249$	−1.51071e28			−0.0168535
$250$	3.08163e29	+	5.90868e29i	0.326987	+	0.626961i
$251$	−3.23321e28			−0.0326372			−0.0163186	−	0.999867i	$-0.505195\pi$
$251$	−3.23321e28			−0.0326372			−0.0163186	+	0.999867i	$0.505195\pi$
$252$		−	8.49920e29i		−	0.816340i
$253$		−	9.17654e28i		−	0.0838827i
$254$	6.22869e29			0.541970
$255$	−7.67746e28	−	9.41976e28i	−0.0636012	−	0.0780347i
$256$	7.92282e28			0.0625000
$257$			2.39756e29i			0.180138i	0.995936	+	0.0900689i	$0.0287087\pi$
$257$			2.39756e29i			0.180138i	−0.995936	+	0.0900689i	$0.971291\pi$
$258$		−	3.15717e28i		−	0.0225971i
$259$	2.25817e30			1.53996
$260$	−8.07994e29	+	6.58545e29i	−0.525099	+	0.427975i
$261$	1.29492e30			0.802114
$262$		−	1.86145e30i		−	1.09922i
$263$			2.50236e30i			1.40898i	0.709716	+	0.704488i	$0.248823\pi$
$263$			2.50236e30i			1.40898i	−0.709716	+	0.704488i	$0.751177\pi$
$264$	9.69989e28			0.0520856
$265$	−2.28583e30	+	1.86303e30i	−1.17077	+	0.954218i
$266$	2.21184e30			1.08077
$267$		−	8.35070e29i		−	0.389343i
$268$		−	1.94945e30i		−	0.867415i
$269$	−3.20998e30			−1.36332			−0.681662	−	0.731667i	$-0.738743\pi$
$269$	−3.20998e30			−1.36332			−0.681662	+	0.731667i	$0.738743\pi$
$270$	5.41413e29	+	6.64280e29i	0.219524	+	0.269342i
$271$	1.88885e30			0.731277			0.365638	−	0.930757i	$-0.380851\pi$
$271$	1.88885e30			0.731277			0.365638	+	0.930757i	$0.380851\pi$
$272$		−	2.68116e29i		−	0.0991316i
$273$		−	1.69975e30i		−	0.600277i
$274$	2.41712e29			0.0815485
$275$	−3.63106e29	+	1.76308e30i	−0.117051	+	0.568346i
$276$	−5.95666e28			−0.0183501
$277$		−	2.14925e29i		−	0.0632835i	−0.999499	−	0.0316417i	$-0.989926\pi$
$277$		−	2.14925e29i		−	0.0632835i	0.999499	−	0.0316417i	$-0.0100736\pi$
$278$			6.08169e29i			0.171184i
$279$	−6.20241e30			−1.66920
$280$	−1.51471e30	−	1.85846e30i	−0.389812	−	0.478275i
$281$	−1.34905e30			−0.332048			−0.166024	−	0.986122i	$-0.553093\pi$
$281$	−1.34905e30			−0.332048			−0.166024	+	0.986122i	$0.553093\pi$
$282$			1.74867e29i			0.0411712i
$283$			7.01801e30i			1.58082i	0.612576	+	0.790412i	$0.290133\pi$
$283$			7.01801e30i			1.58082i	−0.612576	+	0.790412i	$0.709867\pi$
$284$	−1.92268e30			−0.414408
$285$	−8.35578e29	+	6.81028e29i	−0.172356	+	0.140477i
$286$	−2.81565e30			−0.555908
$287$		−	1.50785e31i		−	2.84993i
$288$			9.13894e29i			0.165382i
$289$	4.86329e30			0.842767
$290$	2.83151e30	−	2.30778e30i	0.469940	−	0.383019i
$291$	5.82805e29			0.0926533
$292$			1.48498e29i			0.0226170i
$293$		−	4.23132e30i		−	0.617491i	−0.951145	−	0.308746i	$-0.900091\pi$
$293$		−	4.23132e30i		−	0.617491i	0.951145	−	0.308746i	$-0.0999092\pi$
$294$	2.62590e30			0.367228
$295$	−3.90513e30	−	4.79136e30i	−0.523433	−	0.642219i
$296$	−2.42815e30			−0.311981
$297$			2.31484e30i			0.285145i
$298$			2.19090e30i			0.258774i
$299$	1.72908e30			0.195850
$300$	1.14445e30	+	2.35699e29i	0.124331	+	0.0256060i
$301$	−2.10793e30			−0.219672
$302$			8.69478e30i			0.869304i
$303$		−	3.15028e30i		−	0.302215i
$304$	−2.37832e30			−0.218953
$305$	9.78272e30	+	1.20028e31i	0.864394	+	1.06056i
$306$	3.09271e30			0.262314
$307$			3.15394e30i			0.256817i	0.991721	+	0.128409i	$0.0409869\pi$
$307$			3.15394e30i			0.256817i	−0.991721	+	0.128409i	$0.959013\pi$
$308$		−	6.47625e30i		−	0.506337i
$309$	−4.63823e30			−0.348234
$310$	−1.35624e31	+	1.10538e31i	−0.977944	+	0.797061i
$311$	1.98559e31			1.37526			0.687628	−	0.726063i	$-0.258652\pi$
$311$	1.98559e31			1.37526			0.687628	+	0.726063i	$0.258652\pi$
$312$			1.82769e30i			0.121610i
$313$		−	5.47200e29i		−	0.0349818i	−0.999847	−	0.0174909i	$-0.994432\pi$
$313$		−	5.47200e29i		−	0.0349818i	0.999847	−	0.0174909i	$-0.00556781\pi$
$314$	6.80601e29			0.0418092
$315$	2.14373e31	−	1.74722e31i	1.26557	−	1.03149i
$316$	3.64731e30			0.206959
$317$			2.18550e31i			1.19209i	0.802950	+	0.596046i	$0.203263\pi$
$317$			2.18550e31i			1.19209i	−0.802950	+	0.596046i	$0.796737\pi$
$318$			5.17056e30i			0.271143i
$319$	9.86707e30			0.497513
$320$	1.62873e30	+	1.99835e30i	0.0789721	+	0.0968938i
$321$	1.54238e30			0.0719249
$322$			3.97704e30i			0.178386i
$323$			8.04849e30i			0.347282i
$324$	−9.76540e30			−0.405394
$325$	−3.32205e31	−	6.84177e30i	−1.32698	−	0.273292i
$326$	−1.22038e31			−0.469109
$327$			1.48499e30i			0.0549383i
$328$			1.62135e31i			0.577368i
$329$	1.16752e31			0.400236
$330$	1.99405e30	+	2.44657e30i	0.0658129	+	0.0807484i
$331$	−2.93057e31			−0.931325			−0.465663	−	0.884962i	$-0.654184\pi$
$331$	−2.93057e31			−0.931325			−0.465663	+	0.884962i	$0.654184\pi$
$332$		−	1.08456e30i		−	0.0331917i
$333$		−	2.80086e31i		−	0.825540i
$334$	3.66949e31			1.04178
$335$	4.91703e31	−	4.00756e31i	1.34475	−	1.09602i
$336$	−4.20385e30			−0.110766
$337$			4.60143e31i			1.16821i	0.811680	+	0.584103i	$0.198553\pi$
$337$			4.60143e31i			1.16821i	−0.811680	+	0.584103i	$0.801447\pi$
$338$		−	2.41504e31i		−	0.590835i
$339$	−1.19805e31			−0.282474
$340$	6.76261e30	−	5.51178e30i	0.153684	−	0.125258i
$341$	−4.72613e31			−1.03532
$342$		−	2.74338e31i		−	0.579376i
$343$		−	8.96148e31i		−	1.82475i
$344$	2.26659e30			0.0445033
$345$	−1.22454e30	−	1.50243e30i	−0.0231864	−	0.0284482i
$346$	−5.77039e31			−1.05379
$347$			7.38077e31i			1.30012i	0.759883	+	0.650060i	$0.225256\pi$
$347$			7.38077e31i			1.30012i	−0.759883	+	0.650060i	$0.774744\pi$
$348$		−	6.40489e30i		−	0.108836i
$349$	−3.56553e31			−0.584530			−0.292265	−	0.956337i	$-0.594409\pi$
$349$	−3.56553e31			−0.584530			−0.292265	+	0.956337i	$0.594409\pi$
$350$	1.57367e31	−	7.64103e31i	0.248922	−	1.20865i
$351$	−4.36171e31			−0.665760
$352$			6.96372e30i			0.102579i
$353$			8.69355e31i			1.23599i	0.786184	+	0.617993i	$0.212054\pi$
$353$			8.69355e31i			1.23599i	−0.786184	+	0.617993i	$0.787946\pi$
$354$	−1.08381e31			−0.148735
$355$	−3.95254e31	−	4.84952e31i	−0.523627	−	0.642457i
$356$	5.99512e31			0.766783
$357$			1.42263e31i			0.175686i
$358$		−	3.76725e31i		−	0.449248i
$359$	−2.26294e30			−0.0260611			−0.0130305	−	0.999915i	$-0.504148\pi$
$359$	−2.26294e30			−0.0260611			−0.0130305	+	0.999915i	$0.504148\pi$
$360$	−2.30508e31	+	1.87873e31i	−0.256393	+	0.208970i
$361$	−2.16825e31			−0.232954
$362$			1.13612e32i			1.17915i
$363$		−	1.67943e31i		−	0.168395i
$364$	1.22028e32			1.18220
$365$	−3.74552e30	+	3.05274e30i	−0.0350632	+	0.0285778i
$366$	2.71504e31			0.245619
$367$			3.34192e31i			0.292193i	0.989270	+	0.146096i	$0.0466710\pi$
$367$			3.34192e31i			0.292193i	−0.989270	+	0.146096i	$0.953329\pi$
$368$		−	4.27639e30i		−	0.0361393i
$369$	−1.87022e32			−1.52779
$370$	−4.99165e31	−	6.12444e31i	−0.394205	−	0.483665i
$371$	3.45219e32			2.63585
$372$			3.06782e31i			0.226487i
$373$			1.79027e32i			1.27808i	0.769172	+	0.639041i	$0.220669\pi$
$373$			1.79027e32i			1.27808i	−0.769172	+	0.639041i	$0.779331\pi$
$374$	2.35660e31			0.162701
$375$	1.75819e31	+	3.37113e31i	0.117402	+	0.225105i
$376$	−1.25540e31			−0.0810839
$377$			1.85919e32i			1.16160i
$378$		−	1.00323e32i		−	0.606393i
$379$	9.45760e31			0.553084			0.276542	−	0.961002i	$-0.410812\pi$
$379$	9.45760e31			0.553084			0.276542	+	0.961002i	$0.410812\pi$
$380$	−4.88922e31	−	5.99876e31i	−0.276659	−	0.339443i
$381$	3.55371e31			0.194590
$382$		−	6.88621e31i		−	0.364912i
$383$		−	2.01782e32i		−	1.03490i	−0.855714	−	0.517449i	$-0.826882\pi$
$383$		−	2.01782e32i		−	1.03490i	0.855714	−	0.517449i	$-0.173118\pi$
$384$	4.52028e30			0.0224401
$385$	1.63348e32	−	1.33135e32i	0.784975	−	0.639784i
$386$	1.22047e32			0.567789
$387$			2.61450e31i			0.117761i
$388$			4.18406e31i			0.182474i
$389$	−1.16247e32			−0.490921			−0.245460	−	0.969407i	$-0.578939\pi$
$389$	−1.16247e32			−0.490921			−0.245460	+	0.969407i	$0.578939\pi$
$390$	−4.60992e31	+	3.75726e31i	−0.188532	+	0.153661i
$391$	−1.44717e31			−0.0573207
$392$			1.88518e32i			0.723230i
$393$		−	1.06203e32i		−	0.394667i
$394$	−3.65888e31			−0.131718
$395$	7.49793e31	+	9.19949e31i	0.261504	+	0.320849i
$396$	−8.03262e31			−0.271436
$397$			2.03760e32i			0.667172i	0.942720	+	0.333586i	$0.108259\pi$
$397$			2.03760e32i			0.667172i	−0.942720	+	0.333586i	$0.891741\pi$
$398$			3.92662e32i			1.24589i
$399$	1.26194e32			0.388041
$400$	−1.69212e31	+	8.21617e31i	−0.0504291	+	0.244861i
$401$	−1.67418e32			−0.483613			−0.241806	−	0.970324i	$-0.577740\pi$
$401$	−1.67418e32			−0.483613			−0.241806	+	0.970324i	$0.577740\pi$
$402$		−	1.11224e32i		−	0.311438i
$403$		−	8.90515e32i		−	2.41729i
$404$	2.26164e32			0.595192
$405$	−2.00752e32	−	2.46310e32i	−0.512237	−	0.628483i
$406$	−4.27630e32			−1.05802
$407$		−	2.13421e32i		−	0.512043i
$408$		−	1.52971e31i		−	0.0355924i
$409$	−7.52295e32			−1.69765			−0.848823	−	0.528678i	$-0.822688\pi$
$409$	−7.52295e32			−1.69765			−0.848823	+	0.528678i	$0.822688\pi$
$410$	−4.08947e32	+	3.33307e32i	−0.895094	+	0.729535i
$411$	1.37906e31			0.0292793
$412$		−	3.32987e32i		−	0.685822i
$413$			7.23618e32i			1.44589i
$414$	4.93280e31			0.0956288
$415$	2.73556e31	−	2.22959e31i	0.0514571	−	0.0419395i
$416$	−1.31213e32			−0.239503
$417$			3.46984e31i			0.0614623i
$418$		−	2.09041e32i		−	0.359359i
$419$	6.25496e31			0.104364			0.0521818	−	0.998638i	$-0.483382\pi$
$419$	6.25496e31			0.104364			0.0521818	+	0.998638i	$0.483382\pi$
$420$	−8.64203e31	−	1.06032e32i	−0.139959	−	0.171721i
$421$	8.02159e32			1.26106			0.630528	−	0.776167i	$-0.282838\pi$
$421$	8.02159e32			1.26106			0.630528	+	0.776167i	$0.282838\pi$
$422$			2.33314e31i			0.0356069i
$423$		−	1.44810e32i		−	0.214558i
$424$	−3.71204e32			−0.533997
$425$	2.78044e32	+	5.72631e31i	0.388375	+	0.0799859i
$426$	−1.09697e32			−0.148790
$427$		−	1.81273e33i		−	2.38773i
$428$			1.10730e32i			0.141651i
$429$	−1.60644e32			−0.199594
$430$	4.65953e31	+	5.71695e31i	0.0562323	+	0.0689936i
$431$	1.32299e33			1.55092			0.775460	−	0.631397i	$-0.217518\pi$
$431$	1.32299e33			1.55092			0.775460	+	0.631397i	$0.217518\pi$
$432$			1.07875e32i			0.122849i
$433$			1.44206e33i			1.59546i	0.603015	+	0.797730i	$0.293966\pi$
$433$			1.44206e33i			1.59546i	−0.603015	+	0.797730i	$0.706034\pi$
$434$	2.04827e33			2.20173
$435$	1.61549e32	−	1.31668e32i	0.168728	−	0.137520i
$436$	−1.06610e32			−0.108197
$437$			1.28371e32i			0.126605i
$438$			8.47240e30i			0.00812045i
$439$	−9.88019e32			−0.920362			−0.460181	−	0.887825i	$-0.652215\pi$
$439$	−9.88019e32			−0.920362			−0.460181	+	0.887825i	$0.652215\pi$
$440$	−1.75644e32	+	1.43156e32i	−0.159028	+	0.129614i
$441$	−2.17454e33			−1.91375
$442$			4.44038e32i			0.379876i
$443$			6.78172e32i			0.564018i	0.959412	+	0.282009i	$0.0910008\pi$
$443$			6.78172e32i			0.564018i	−0.959412	+	0.282009i	$0.908999\pi$
$444$	−1.38535e32			−0.112014
$445$	1.23244e33	+	1.51213e33i	0.968872	+	1.18874i
$446$	−2.39431e32			−0.183018
$447$			1.25000e32i			0.0929104i
$448$		−	3.01802e32i		−	0.218146i
$449$	1.40094e33			0.984784			0.492392	−	0.870374i	$-0.336123\pi$
$449$	1.40094e33			0.984784			0.492392	+	0.870374i	$0.336123\pi$
$450$	−9.47732e32	−	1.95185e32i	−0.647931	−	0.133442i
$451$	−1.42507e33			−0.947613
$452$		−	8.60102e32i		−	0.556313i
$453$			4.96071e32i			0.312116i
$454$	2.26210e33			1.38456
$455$	2.50858e33	+	3.07787e33i	1.49378	+	1.83277i
$456$	−1.35693e32			−0.0786132
$457$		−	2.87797e33i		−	1.62231i	−0.584830	−	0.811156i	$-0.698839\pi$
$457$		−	2.87797e33i		−	1.62231i	0.584830	−	0.811156i	$-0.301161\pi$
$458$			2.37680e32i			0.130369i
$459$	3.65059e32			0.194852
$460$	1.07862e32	−	8.79115e31i	0.0560268	−	0.0456639i
$461$	−4.62750e32			−0.233930			−0.116965	−	0.993136i	$-0.537316\pi$
$461$	−4.62750e32			−0.233930			−0.116965	+	0.993136i	$0.537316\pi$
$462$		−	3.69495e32i		−	0.181796i
$463$			2.53220e32i			0.121265i	0.998160	+	0.0606325i	$0.0193118\pi$
$463$			2.53220e32i			0.121265i	−0.998160	+	0.0606325i	$0.980688\pi$
$464$	4.59818e32			0.214344
$465$	−7.73786e32	+	6.30664e32i	−0.351123	+	0.286178i
$466$	7.93650e32			0.350595
$467$			1.56052e33i			0.671134i	0.942016	+	0.335567i	$0.108928\pi$
$467$			1.56052e33i			0.671134i	−0.942016	+	0.335567i	$0.891072\pi$
$468$		−	1.51354e33i		−	0.633752i
$469$	−7.42598e33			−3.02757
$470$	−2.58078e32	−	3.16646e32i	−0.102454	−	0.125704i
$471$	3.88309e31			0.0150112
$472$		−	7.78085e32i		−	0.292922i
$473$			1.99221e32i			0.0730416i
$474$	2.08093e32			0.0743068
$475$	5.07952e32	−	2.46638e33i	0.176666	−	0.857809i
$476$	−1.02133e33			−0.346002
$477$		−	4.28182e33i		−	1.41302i
$478$		−	2.93259e32i		−	0.0942763i
$479$	−7.23567e32			−0.226613			−0.113306	−	0.993560i	$-0.536144\pi$
$479$	−7.23567e32			−0.226613			−0.113306	+	0.993560i	$0.536144\pi$
$480$	9.29252e31	+	1.14013e32i	0.0283543	+	0.0347889i
$481$	4.02135e33			1.19553
$482$		−	3.44901e33i		−	0.999096i
$483$			2.26905e32i			0.0640480i
$484$	1.20569e33			0.331641
$485$	−1.05533e33	+	8.60134e32i	−0.282890	+	0.230566i
$486$	−1.88721e33			−0.493024
$487$		−	3.11091e33i		−	0.792091i	−0.918231	−	0.396046i	$-0.870382\pi$
$487$		−	3.11091e33i		−	0.792091i	0.918231	−	0.396046i	$-0.129618\pi$
$488$			1.94918e33i			0.483730i
$489$	−6.96273e32			−0.168430
$490$	−4.75492e33	+	3.87544e33i	−1.12122	+	0.913839i
$491$	3.51132e33			0.807146			0.403573	−	0.914948i	$-0.367768\pi$
$491$	3.51132e33			0.807146			0.403573	+	0.914948i	$0.367768\pi$
$492$			9.25042e32i			0.207299i
$493$		−	1.55607e33i		−	0.339972i
$494$	3.93883e33			0.839037
$495$	−1.65130e33	−	2.02604e33i	−0.342974	−	0.420808i
$496$	−2.20244e33			−0.446050
$497$			7.32402e33i			1.44642i
$498$		−	6.18787e31i		−	0.0119172i
$499$	−8.78119e33			−1.64929			−0.824644	−	0.565652i	$-0.808624\pi$
$499$	−8.78119e33			−1.64929			−0.824644	+	0.565652i	$0.808624\pi$
$500$	−2.42019e33	+	1.26224e33i	−0.443328	+	0.231215i
$501$	2.09358e33			0.374041
$502$		−	1.32432e32i		−	0.0230780i
$503$		−	1.68186e33i		−	0.285883i	−0.989731	−	0.142942i	$-0.954344\pi$
$503$		−	1.68186e33i		−	0.285883i	0.989731	−	0.142942i	$-0.0456562\pi$
$504$	3.48127e33			0.577240
$505$	4.64936e33	+	5.70447e33i	0.752057	+	0.922727i
$506$	3.75871e32			0.0593140
$507$		−	1.37788e33i		−	0.212134i
$508$			2.55127e33i			0.383231i
$509$	5.67785e33			0.832169			0.416084	−	0.909326i	$-0.363402\pi$
$509$	5.67785e33			0.832169			0.416084	+	0.909326i	$0.363402\pi$
$510$	3.85833e32	−	3.14469e32i	0.0551789	−	0.0449728i
$511$	5.65670e32			0.0789409
$512$			3.24519e32i			0.0441942i
$513$		−	3.23825e33i		−	0.430372i
$514$	−9.82039e32			−0.127377
$515$	8.39881e33	−	6.84535e33i	1.06323	−	0.866573i
$516$	1.29318e32			0.0159785
$517$		−	1.10343e33i		−	0.133080i
$518$			9.24948e33i			1.08892i
$519$	−3.29224e33			−0.378355
$520$	−2.69740e33	−	3.30954e33i	−0.302624	−	0.371301i
$521$	8.57848e33			0.939591			0.469796	−	0.882775i	$-0.344328\pi$
$521$	8.57848e33			0.939591			0.469796	+	0.882775i	$0.344328\pi$
$522$			5.30399e33i			0.567180i
$523$			1.65708e34i			1.73010i	0.501683	+	0.865052i	$0.332714\pi$
$523$			1.65708e34i			1.73010i	−0.501683	+	0.865052i	$0.667286\pi$
$524$	7.62451e33			0.777268
$525$	8.97840e32	−	4.35950e33i	0.0893733	−	0.433956i
$526$	−1.02497e34			−0.996296
$527$			7.45329e33i			0.707482i
$528$			3.97307e32i			0.0368301i
$529$	1.08149e34			0.979103
$530$	−7.63099e33	−	9.36275e33i	−0.674734	−	0.827856i
$531$	8.97518e33			0.775107
$532$			9.05968e33i			0.764218i
$533$		−	2.68518e34i		−	2.21250i
$534$	3.42045e33			0.275307
$535$	−2.79292e33	+	2.27633e33i	−0.219602	+	0.178984i
$536$	7.98494e33			0.613355
$537$		−	2.14936e33i		−	0.161299i
$538$		−	1.31481e34i		−	0.964016i
$539$	−1.65697e34			−1.18701
$540$	−2.72089e33	+	2.21763e33i	−0.190453	+	0.155227i
$541$	−4.23198e33			−0.289453			−0.144727	−	0.989472i	$-0.546230\pi$
$541$	−4.23198e33			−0.289453			−0.144727	+	0.989472i	$0.546230\pi$
$542$			7.73674e33i			0.517091i
$543$			6.48202e33i			0.423362i
$544$	1.09820e33			0.0700966
$545$	−2.19162e33	−	2.68898e33i	−0.136713	−	0.167738i
$546$	6.96217e33			0.424460
$547$			5.57179e33i			0.332011i	0.986125	+	0.166006i	$0.0530870\pi$
$547$			5.57179e33i			0.332011i	−0.986125	+	0.166006i	$0.946913\pi$
$548$			9.90052e32i			0.0576635i
$549$	−2.24837e34			−1.28001
$550$	−7.22156e33	−	1.48728e33i	−0.401881	−	0.0827675i
$551$	−1.38031e34			−0.750900
$552$		−	2.43985e32i		−	0.0129755i
$553$		−	1.38936e34i		−	0.722355i
$554$	8.80334e32			0.0447482
$555$	−2.84793e33	−	3.49423e33i	−0.141536	−	0.173656i
$556$	−2.49106e33			−0.121046
$557$			1.51207e34i			0.718427i	0.933255	+	0.359213i	$0.116955\pi$
$557$			1.51207e34i			0.718427i	−0.933255	+	0.359213i	$0.883045\pi$
$558$		−	2.54051e34i		−	1.18030i
$559$	−3.75379e33			−0.170539
$560$	7.61225e33	−	6.20427e33i	0.338191	−	0.275639i
$561$	1.34453e33			0.0584164
$562$		−	5.52573e33i		−	0.234793i
$563$			1.21471e34i			0.504799i	0.967623	+	0.252400i	$0.0812198\pi$
$563$			1.21471e34i			0.504799i	−0.967623	+	0.252400i	$0.918780\pi$
$564$	−7.16255e32			−0.0291125
$565$	2.16941e34	−	1.76815e34i	0.862453	−	0.702932i
$566$	−2.87458e34			−1.11781
$567$			3.71991e34i			1.41496i
$568$		−	7.87531e33i		−	0.293031i
$569$	−2.58692e34			−0.941628			−0.470814	−	0.882232i	$-0.656040\pi$
$569$	−2.58692e34			−0.941628			−0.470814	+	0.882232i	$0.656040\pi$
$570$	−2.78949e33	−	3.42253e33i	−0.0993320	−	0.121874i
$571$	−3.34607e34			−1.16569			−0.582846	−	0.812583i	$-0.698061\pi$
$571$	−3.34607e34			−1.16569			−0.582846	+	0.812583i	$0.698061\pi$
$572$		−	1.15329e34i		−	0.393086i
$573$		−	3.92885e33i		−	0.131019i
$574$	6.17615e34			2.01521
$575$	4.43473e33	+	9.13333e32i	0.141586	+	0.0291596i
$576$	−3.74331e33			−0.116943
$577$			1.34968e34i			0.412603i	0.978488	+	0.206302i	$0.0661428\pi$
$577$			1.34968e34i			0.412603i	−0.978488	+	0.206302i	$0.933857\pi$
$578$			1.99201e34i			0.595926i
$579$	6.96328e33			0.203860
$580$	9.45268e33	+	1.15978e34i	0.270835	+	0.332298i
$581$	−4.13140e33			−0.115850
$582$			2.38717e33i			0.0655158i
$583$		−	3.26268e34i		−	0.876429i
$584$	−6.08248e32			−0.0159926
$585$	3.81754e34	−	3.11144e34i	0.982507	−	0.800780i
$586$	1.73315e34			0.436632
$587$			4.17737e34i			1.03021i	0.857126	+	0.515107i	$0.172248\pi$
$587$			4.17737e34i			1.03021i	−0.857126	+	0.515107i	$0.827752\pi$
$588$			1.07557e34i			0.259670i
$589$	6.61143e34			1.56262
$590$	1.96254e34	−	1.59954e34i	0.454117	−	0.370123i
$591$	−2.08753e33			−0.0472923
$592$		−	9.94569e33i		−	0.220604i
$593$		−	2.55607e33i		−	0.0555123i	−0.999615	−	0.0277562i	$-0.991164\pi$
$593$		−	2.55607e33i		−	0.0555123i	0.999615	−	0.0277562i	$-0.00883620\pi$
$594$	−9.48160e33			−0.201628
$595$	−2.09959e34	−	2.57606e34i	−0.437192	−	0.536407i
$596$	−8.97394e33			−0.182981
$597$			2.24029e34i			0.447327i
$598$			7.08230e33i			0.138487i
$599$	−4.70324e34			−0.900662			−0.450331	−	0.892862i	$-0.648694\pi$
$599$	−4.70324e34			−0.900662			−0.450331	+	0.892862i	$0.648694\pi$
$600$	−9.65421e32	+	4.68765e33i	−0.0181062	+	0.0879153i
$601$	5.96787e34			1.09620			0.548099	−	0.836414i	$-0.315352\pi$
$601$	5.96787e34			1.09620			0.548099	+	0.836414i	$0.315352\pi$
$602$		−	8.63406e33i		−	0.155331i
$603$			9.21060e34i			1.62301i
$604$	−3.56138e34			−0.614691
$605$	2.47859e34	+	3.04107e34i	0.419046	+	0.514143i
$606$	1.29036e34			0.213699
$607$			2.92667e34i			0.474804i	0.971411	+	0.237402i	$0.0762959\pi$
$607$			2.92667e34i			0.474804i	−0.971411	+	0.237402i	$0.923704\pi$
$608$		−	9.74161e33i		−	0.154823i
$609$	−2.43980e34			−0.379872
$610$	−4.91634e34	+	4.00700e34i	−0.749927	+	0.611219i
$611$	2.07912e34			0.310717
$612$			1.26677e34i			0.185484i
$613$			8.48844e34i			1.21779i	0.793251	+	0.608895i	$0.208387\pi$
$613$			8.48844e34i			1.21779i	−0.793251	+	0.608895i	$0.791613\pi$
$614$	−1.29186e34			−0.181597
$615$	−2.33320e34	+	1.90165e34i	−0.321376	+	0.261933i
$616$	2.65267e34			0.358034
$617$		−	1.30414e35i		−	1.72488i	−0.506156	−	0.862442i	$-0.668934\pi$
$617$		−	1.30414e35i		−	1.72488i	0.506156	−	0.862442i	$-0.331066\pi$
$618$		−	1.89982e34i		−	0.246239i
$619$	8.02670e34			1.01954			0.509770	−	0.860311i	$-0.329731\pi$
$619$	8.02670e34			1.01954			0.509770	+	0.860311i	$0.329731\pi$
$620$	−4.52765e34	−	5.55514e34i	−0.563607	−	0.691511i
$621$	5.82260e33			0.0710350
$622$			8.13296e34i			0.972453i
$623$		−	2.28370e35i		−	2.67633i
$624$	−7.48621e33			−0.0859913
$625$	−8.15899e34	−	3.50955e34i	−0.918621	−	0.395140i
$626$	2.24133e33			0.0247359
$627$		−	1.19266e34i		−	0.129025i
$628$			2.78774e33i			0.0295636i
$629$	−3.36573e34			−0.349901
$630$	7.15660e34	+	8.78070e34i	0.729373	+	0.894895i
$631$	−3.51125e34			−0.350828			−0.175414	−	0.984495i	$-0.556126\pi$
$631$	−3.51125e34			−0.350828			−0.175414	+	0.984495i	$0.556126\pi$
$632$			1.49394e34i			0.146342i
$633$			1.33115e33i			0.0127844i
$634$	−8.95181e34			−0.842937
$635$	−6.43499e34	+	5.24476e34i	−0.594123	+	0.484233i
$636$	−2.11786e34			−0.191727
$637$		−	3.12212e35i		−	2.77145i
$638$			4.04155e34i			0.351795i
$639$	9.08413e34			0.775394
$640$	−8.18523e33	+	6.67127e33i	−0.0685143	+	0.0558417i
$641$	−1.10476e35			−0.906862			−0.453431	−	0.891291i	$-0.649800\pi$
$641$	−1.10476e35			−0.906862			−0.453431	+	0.891291i	$0.649800\pi$
$642$			6.31760e33i			0.0508586i
$643$			5.33371e34i			0.421107i	0.977582	+	0.210553i	$0.0675266\pi$
$643$			5.33371e34i			0.421107i	−0.977582	+	0.210553i	$0.932473\pi$
$644$	−1.62899e34			−0.126138
$645$	2.65844e33	+	3.26174e33i	0.0201897	+	0.0247715i
$646$	−3.29666e34			−0.245566
$647$		−	2.39579e34i		−	0.175043i	−0.996163	−	0.0875216i	$-0.972105\pi$
$647$		−	2.39579e34i		−	0.175043i	0.996163	−	0.0875216i	$-0.0278947\pi$
$648$		−	3.99991e34i		−	0.286657i
$649$	6.83894e34			0.480762
$650$	2.80239e34	−	1.36071e35i	0.193246	−	0.938317i
$651$	1.16862e35			0.790514
$652$		−	4.99866e34i		−	0.331710i
$653$			6.46858e34i			0.421109i	0.977582	+	0.210554i	$0.0675269\pi$
$653$			6.46858e34i			0.421109i	−0.977582	+	0.210554i	$0.932473\pi$
$654$	−6.08250e33			−0.0388472
$655$	1.56740e35	+	1.92310e35i	0.982119	+	1.20500i
$656$	−6.64104e34			−0.408261
$657$		−	7.01612e33i		−	0.0423185i
$658$			4.78217e34i			0.283010i
$659$	−1.74748e35			−1.01471			−0.507357	−	0.861736i	$-0.669377\pi$
$659$	−1.74748e35			−1.01471			−0.507357	+	0.861736i	$0.669377\pi$
$660$	−1.00212e34	+	8.16762e33i	−0.0570977	+	0.0465368i
$661$	2.05707e35			1.15009			0.575044	−	0.818123i	$-0.304985\pi$
$661$	2.05707e35			1.15009			0.575044	+	0.818123i	$0.304985\pi$
$662$		−	1.20036e35i		−	0.658547i
$663$			2.53341e34i			0.136391i
$664$	4.44238e33			0.0234701
$665$	−2.28509e35	+	1.86244e35i	−1.18477	+	0.965631i
$666$	1.14723e35			0.583745
$667$		−	2.48190e34i		−	0.123940i
$668$			1.50302e35i			0.736647i
$669$	−1.36605e34			−0.0657112
$670$	1.64150e35	+	2.01402e35i	0.775007	+	0.950885i
$671$	−1.71322e35			−0.793928
$672$		−	1.72190e34i		−	0.0783234i
$673$			1.94000e35i			0.866190i	0.901348	+	0.433095i	$0.142579\pi$
$673$			1.94000e35i			0.866190i	−0.901348	+	0.433095i	$0.857421\pi$
$674$	−1.88475e35			−0.826046
$675$	−1.11869e35	−	2.30394e34i	−0.481296	−	0.0991230i
$676$	9.89201e34			0.417783
$677$			1.50061e35i			0.622172i	0.950382	+	0.311086i	$0.100693\pi$
$677$			1.50061e35i			0.622172i	−0.950382	+	0.311086i	$0.899307\pi$
$678$		−	4.90722e34i		−	0.199740i
$679$	1.59382e35			0.636895
$680$	2.25763e34	+	2.76997e34i	0.0885708	+	0.108671i
$681$	1.29062e35			0.497116
$682$		−	1.93582e35i		−	0.732084i
$683$		−	2.23175e35i		−	0.828679i	−0.910122	−	0.414339i	$-0.864013\pi$
$683$		−	2.23175e35i		−	0.828679i	0.910122	−	0.414339i	$-0.135987\pi$
$684$	1.12369e35			0.409681
$685$	−2.49718e34	+	2.03529e34i	−0.0893958	+	0.0728609i
$686$	3.67062e35			1.29029
$687$			1.35606e34i			0.0468078i
$688$			9.28395e33i			0.0314686i
$689$	6.14765e35			2.04630
$690$	6.15395e33	−	5.01570e33i	0.0201159	−	0.0163952i
$691$	4.24403e34			0.136240			0.0681198	−	0.997677i	$-0.478300\pi$
$691$	4.24403e34			0.136240			0.0681198	+	0.997677i	$0.478300\pi$
$692$		−	2.36355e35i		−	0.745142i
$693$			3.05985e35i			0.947402i
$694$	−3.02316e35			−0.919324
$695$	−5.12098e34	−	6.28312e34i	−0.152948	−	0.187657i
$696$	2.62344e34			0.0769584
$697$			2.24740e35i			0.647545i
$698$		−	1.46044e35i		−	0.413325i
$699$	4.52808e34			0.125878
$700$	3.12977e35	+	6.44575e34i	0.854646	+	0.176014i
$701$	−6.67347e35			−1.79010			−0.895048	−	0.445969i	$-0.852859\pi$
$701$	−6.67347e35			−1.79010			−0.895048	+	0.445969i	$0.852859\pi$
$702$		−	1.78656e35i		−	0.470764i
$703$			2.98556e35i			0.772831i
$704$	−2.85234e34			−0.0725342
$705$	−1.47244e34	−	1.80659e34i	−0.0367852	−	0.0451331i
$706$	−3.56088e35			−0.873974
$707$		−	8.61522e35i		−	2.07742i
$708$		−	4.43928e34i		−	0.105171i
$709$	−5.82085e35			−1.35490			−0.677452	−	0.735567i	$-0.736916\pi$
$709$	−5.82085e35			−1.35490			−0.677452	+	0.735567i	$0.736916\pi$
$710$	1.98636e35	−	1.61896e35i	0.454286	−	0.370260i
$711$	−1.72325e35			−0.387238
$712$			2.45560e35i			0.542198i
$713$			1.18878e35i			0.257919i
$714$	−5.82708e34			−0.124229
$715$	2.90891e35	−	2.37087e35i	0.609402	−	0.496686i
$716$	1.54307e35			0.317667
$717$		−	1.67316e34i		−	0.0338491i
$718$		−	9.26900e33i		−	0.0184280i
$719$	4.08106e35			0.797374			0.398687	−	0.917087i	$-0.369466\pi$
$719$	4.08106e35			0.797374			0.398687	+	0.917087i	$0.369466\pi$
$720$	−7.69528e34	−	9.44162e34i	−0.147764	−	0.181297i
$721$	−1.26844e36			−2.39375
$722$		−	8.88115e34i		−	0.164723i
$723$		−	1.96780e35i		−	0.358717i
$724$	−4.65355e35			−0.833782
$725$	−9.82060e34	+	4.76844e35i	−0.172947	+	0.839752i
$726$	6.87893e34			0.119073
$727$		−	7.44759e34i		−	0.126717i	−0.997991	−	0.0633586i	$-0.979819\pi$
$727$		−	7.44759e34i		−	0.126717i	0.997991	−	0.0633586i	$-0.0201812\pi$
$728$			4.99826e35i			0.835943i
$729$	3.85503e35			0.633772
$730$	−1.25040e34	−	1.53417e34i	−0.0202076	−	0.0247934i
$731$	3.14179e34			0.0499125
$732$			1.11208e35i			0.173679i
$733$		−	1.00546e36i		−	1.54371i	−0.635802	−	0.771853i	$-0.719330\pi$
$733$		−	1.00546e36i		−	1.54371i	0.635802	−	0.771853i	$-0.280670\pi$
$734$	−1.36885e35			−0.206612
$735$	−2.71287e35	+	2.21109e35i	−0.402566	+	0.328106i
$736$	1.75161e34			0.0255543
$737$			7.01833e35i			1.00668i
$738$		−	7.66041e35i		−	1.08031i
$739$	7.42029e35			1.02888			0.514441	−	0.857526i	$-0.327999\pi$
$739$	7.42029e35			1.02888			0.514441	+	0.857526i	$0.327999\pi$
$740$	2.50857e35	−	2.04458e35i	0.342003	−	0.278745i
$741$	2.24726e35			0.301249
$742$			1.41402e36i			1.86383i
$743$		−	4.93877e35i		−	0.640115i	−0.947398	−	0.320058i	$-0.896298\pi$
$743$		−	4.93877e35i		−	0.640115i	0.947398	−	0.320058i	$-0.103702\pi$
$744$	−1.25658e35			−0.160150
$745$	−1.84481e35	−	2.26347e35i	−0.231206	−	0.283675i
$746$	−7.33296e35			−0.903741
$747$			5.12426e34i			0.0621046i
$748$			9.65262e34i			0.115047i
$749$	4.21802e35			0.494409
$750$	−1.38082e35	+	7.20154e34i	−0.159173	+	0.0830156i
$751$	1.60017e36			1.81413			0.907063	−	0.420995i	$-0.138319\pi$
$751$	1.60017e36			1.81413			0.907063	+	0.420995i	$0.138319\pi$
$752$		−	5.14212e34i		−	0.0573349i
$753$		−	7.55579e33i		−	0.00828595i
$754$	−7.61524e35			−0.821375
$755$	−7.32128e35	−	8.98276e35i	−0.776695	−	0.952956i
$756$	4.10924e35			0.428785
$757$		−	9.77978e34i		−	0.100376i	−0.998740	−	0.0501881i	$-0.984018\pi$
$757$		−	9.77978e34i		−	0.100376i	0.998740	−	0.0501881i	$-0.0159821\pi$
$758$			3.87383e35i			0.391089i
$759$	2.14449e34			0.0212962
$760$	2.45709e35	−	2.00262e35i	0.240022	−	0.195627i
$761$	1.42035e36			1.36485			0.682427	−	0.730954i	$-0.260924\pi$
$761$	1.42035e36			1.36485			0.682427	+	0.730954i	$0.260924\pi$
$762$			1.45560e35i			0.137596i
$763$			4.06106e35i			0.377644i
$764$	2.82059e35			0.258032
$765$	−3.19514e35	+	2.60416e35i	−0.287556	+	0.234369i
$766$	8.26499e35			0.731784
$767$			1.28862e36i			1.12249i
$768$			1.85151e34i			0.0158675i
$769$	−4.43106e35			−0.373619			−0.186809	−	0.982396i	$-0.559815\pi$
$769$	−4.43106e35			−0.373619			−0.186809	+	0.982396i	$0.559815\pi$
$770$	5.45321e35	+	6.69075e35i	0.452395	+	0.555061i
$771$	−5.60292e34			−0.0457335
$772$			4.99906e35i			0.401487i
$773$			1.04683e36i			0.827241i	0.910449	+	0.413621i	$0.135736\pi$
$773$			1.04683e36i			0.827241i	−0.910449	+	0.413621i	$0.864264\pi$
$774$	−1.07090e35			−0.0832697
$775$	4.70388e35	−	2.28399e36i	0.359902	−	1.74752i
$776$	−1.71379e35			−0.129029
$777$			5.27719e35i			0.390967i
$778$		−	4.76147e35i		−	0.347133i
$779$	1.99355e36			1.43024
$780$	−1.53897e35	−	1.88822e35i	−0.108655	−	0.133312i
$781$	6.92196e35			0.480940
$782$		−	5.92763e34i		−	0.0405319i
$783$			6.26075e35i			0.421313i
$784$	−7.72169e35			−0.511401
$785$	−7.03143e34	+	5.73088e34i	−0.0458324	+	0.0373551i
$786$	4.35008e35			0.279071
$787$			1.02940e36i			0.649977i	0.945718	+	0.324989i	$0.105360\pi$
$787$			1.02940e36i			0.649977i	−0.945718	+	0.324989i	$0.894640\pi$
$788$		−	1.49868e35i		−	0.0931387i
$789$	−5.84784e35			−0.357712
$790$	−3.76811e35	+	3.07115e35i	−0.226874	+	0.184911i
$791$	−3.27636e36			−1.94172
$792$		−	3.29016e35i		−	0.191934i
$793$		−	3.22811e36i		−	1.85367i
$794$	−8.34601e35			−0.471762
$795$	−4.35378e35	−	5.34181e35i	−0.242257	−	0.297235i
$796$	−1.60834e36			−0.880978
$797$			2.74499e36i			1.48017i	0.672512	+	0.740086i	$0.265215\pi$
$797$			2.74499e36i			1.48017i	−0.672512	+	0.740086i	$0.734785\pi$
$798$			5.16890e35i			0.274386i
$799$	−1.74015e35			−0.0909393
$800$	−3.36534e35	−	6.93093e34i	−0.173143	−	0.0356588i
$801$	−2.83252e36			−1.43472
$802$		−	6.85745e35i		−	0.341966i
$803$		−	5.34617e34i		−	0.0262481i
$804$	4.55572e35			0.220220
$805$	−3.34879e35	−	4.10876e35i	−0.159382	−	0.195552i
$806$	3.64755e36			1.70928
$807$		−	7.50150e35i		−	0.346122i
$808$			9.26369e35i			0.420864i
$809$	−2.35511e36			−1.05355			−0.526776	−	0.850004i	$-0.676599\pi$
$809$	−2.35511e36			−1.05355			−0.526776	+	0.850004i	$0.676599\pi$
$810$	1.00888e36	−	8.22278e35i	0.444405	−	0.362206i
$811$	3.33343e36			1.44587			0.722936	−	0.690915i	$-0.242792\pi$
$811$	3.33343e36			1.44587			0.722936	+	0.690915i	$0.242792\pi$
$812$		−	1.75157e36i		−	0.748132i
$813$			4.41411e35i			0.185657i
$814$	8.74172e35			0.362069
$815$	1.26080e36	−	1.02760e36i	0.514251	−	0.419134i
$816$	6.26569e34			0.0251676
$817$		−	2.78692e35i		−	0.110242i
$818$		−	3.08140e36i		−	1.20042i
$819$	−5.76547e36			−2.21201
$820$	−1.36523e36	−	1.67505e36i	−0.515859	−	0.632927i
$821$	1.82523e36			0.679249			0.339625	−	0.940561i	$-0.389700\pi$
$821$	1.82523e36			0.679249			0.339625	+	0.940561i	$0.389700\pi$
$822$			5.64864e34i			0.0207036i
$823$		−	1.63571e36i		−	0.590483i	−0.955423	−	0.295241i	$-0.904600\pi$
$823$		−	1.63571e36i		−	0.590483i	0.955423	−	0.295241i	$-0.0954001\pi$
$824$	1.36391e36			0.484950
$825$	−4.12018e35	−	8.48552e34i	−0.144292	−	0.0297170i
$826$	−2.96394e36			−1.02240
$827$			3.73907e36i			1.27041i	0.772342	+	0.635206i	$0.219085\pi$
$827$			3.73907e36i			1.27041i	−0.772342	+	0.635206i	$0.780915\pi$
$828$			2.02047e35i			0.0676198i
$829$	3.08664e36			1.01755			0.508773	−	0.860901i	$-0.330099\pi$
$829$	3.08664e36			1.01755			0.508773	+	0.860901i	$0.330099\pi$
$830$	9.13238e34	+	1.12049e35i	0.0296557	+	0.0363857i
$831$	5.02265e34			0.0160665
$832$		−	5.37448e35i		−	0.169354i
$833$			2.61310e36i			0.811135i
$834$	−1.42125e35			−0.0434604
$835$	−3.79102e36	+	3.08982e36i	−1.14202	+	0.930792i
$836$	8.56234e35			0.254105
$837$		−	2.99878e36i		−	0.876750i
$838$			2.56203e35i			0.0737963i
$839$	3.69450e36			1.04841			0.524205	−	0.851592i	$-0.324363\pi$
$839$	3.69450e36			1.04841			0.524205	+	0.851592i	$0.324363\pi$
$840$	4.34309e35	−	3.53978e35i	0.121425	−	0.0989657i
$841$	−9.61704e35			−0.264906
$842$			3.28564e36i			0.891701i
$843$		−	3.15264e35i		−	0.0843005i
$844$	−9.55652e34			−0.0251779
$845$	2.03354e36	+	2.49503e36i	0.527891	+	0.647690i
$846$	5.93142e35			0.151715
$847$		−	4.59280e36i		−	1.15754i
$848$		−	1.52045e36i		−	0.377593i
$849$	−1.64006e36			−0.401341
$850$	−2.34550e35	+	1.13887e36i	−0.0565586	+	0.274623i
$851$	−5.36825e35			−0.127560
$852$		−	4.49317e35i		−	0.105210i
$853$			7.36060e35i			0.169844i	0.996388	+	0.0849220i	$0.0270641\pi$
$853$			7.36060e35i			0.169844i	−0.996388	+	0.0849220i	$0.972936\pi$
$854$	7.42494e36			1.68838
$855$	2.31002e36	+	2.83425e36i	0.517653	+	0.635128i
$856$	−4.53551e35			−0.100162
$857$			5.06811e35i			0.110303i	0.998478	+	0.0551513i	$0.0175641\pi$
$857$			5.06811e35i			0.110303i	−0.998478	+	0.0551513i	$0.982436\pi$
$858$		−	6.57997e35i		−	0.141134i
$859$	−7.80778e33			−0.00165049			−0.000825245	−	1.00000i	$-0.500263\pi$
$859$	−7.80778e33			−0.00165049			−0.000825245		1.00000i	$0.500263\pi$
$860$	−2.34166e35	+	1.90854e35i	−0.0487858	+	0.0397623i
$861$	3.52374e36			0.723543
$862$			5.41895e36i			1.09667i
$863$			8.60176e36i			1.71574i	0.513864	+	0.857871i	$0.328213\pi$
$863$			8.60176e36i			1.71574i	−0.513864	+	0.857871i	$0.671787\pi$
$864$	−4.41855e35			−0.0868676
$865$	5.96152e36	−	4.85886e36i	1.15520	−	0.941527i
$866$	−5.90669e36			−1.12816
$867$			1.13652e36i			0.213962i
$868$			8.38970e36i			1.55686i
$869$	−1.31309e36			−0.240186
$870$	5.39312e35	+	6.61703e35i	0.0972411	+	0.119309i
$871$	−1.32242e37			−2.35040
$872$		−	4.36673e35i		−	0.0765069i
$873$		−	1.97685e36i		−	0.341425i
$874$	−5.25809e35			−0.0895231
$875$	4.80820e36	+	9.21919e36i	0.807015	+	1.54736i
$876$	−3.47029e34			−0.00574202
$877$		−	7.33903e36i		−	1.19714i	−0.801072	−	0.598568i	$-0.795737\pi$
$877$		−	7.33903e36i		−	1.19714i	0.801072	−	0.598568i	$-0.204263\pi$
$878$		−	4.04692e36i		−	0.650794i
$879$	9.88829e35			0.156769
$880$	−5.86368e35	−	7.19437e35i	−0.0916509	−	0.112450i
$881$	7.73442e36			1.19187			0.595935	−	0.803032i	$-0.296781\pi$
$881$	7.73442e36			1.19187			0.595935	+	0.803032i	$0.296781\pi$
$882$		−	8.90693e36i		−	1.35323i
$883$		−	1.11931e37i		−	1.67664i	−0.545178	−	0.838320i	$-0.683538\pi$
$883$		−	1.11931e37i		−	1.67664i	0.545178	−	0.838320i	$-0.316462\pi$
$884$	−1.81878e36			−0.268613
$885$	1.11971e36	−	9.12602e35i	0.163047	−	0.132889i
$886$	−2.77779e36			−0.398821
$887$		−	9.94167e36i		−	1.40739i	−0.710502	−	0.703695i	$-0.751532\pi$
$887$		−	9.94167e36i		−	1.40739i	0.710502	−	0.703695i	$-0.248468\pi$
$888$		−	5.67441e35i		−	0.0792060i
$889$	9.71850e36			1.33760
$890$	−6.19368e36	+	5.04808e36i	−0.840570	+	0.685096i
$891$	3.51570e36			0.470479
$892$		−	9.80709e35i		−	0.129413i
$893$			1.54360e36i			0.200858i
$894$	−5.11998e35			−0.0656976
$895$	3.17214e36	+	3.89202e36i	0.401389	+	0.492479i
$896$	1.23618e36			0.154252
$897$			4.04073e35i			0.0497226i
$898$			5.73826e36i			0.696347i
$899$	−1.27824e37			−1.52973
$900$	7.99480e35	−	3.88191e36i	0.0943574	−	0.458157i
$901$	−5.14536e36			−0.598902
$902$		−	5.83711e36i		−	0.670063i
$903$		−	4.92607e35i		−	0.0557704i
$904$	3.52298e36			0.393373
$905$	−9.56651e36	−	1.17375e37i	−1.05353	−	1.29261i
$906$	−2.03191e36			−0.220700
$907$			2.49643e36i			0.267441i	0.991019	+	0.133721i	$0.0426924\pi$
$907$			2.49643e36i			0.267441i	−0.991019	+	0.133721i	$0.957308\pi$
$908$			9.26555e36i			0.979035i
$909$	−1.06856e37			−1.11366
$910$	−1.26070e37	+	1.02751e37i	−1.29596	+	1.05626i
$911$	9.34594e36			0.947640			0.473820	−	0.880622i	$-0.342875\pi$
$911$	9.34594e36			0.947640			0.473820	+	0.880622i	$0.342875\pi$
$912$		−	5.55797e35i		−	0.0555879i
$913$			3.90461e35i			0.0385205i
$914$	1.17882e37			1.14715
$915$	−2.80497e36	+	2.28615e36i	−0.269255	+	0.219453i
$916$	−9.73537e35			−0.0921847
$917$		−	2.90438e37i		−	2.71292i
$918$			1.49528e36i			0.137781i
$919$	−2.08298e37			−1.89340			−0.946698	−	0.322122i	$-0.895604\pi$
$919$	−2.08298e37			−1.89340			−0.946698	+	0.322122i	$0.895604\pi$
$920$	3.60086e35	+	4.41803e35i	0.0322893	+	0.0396169i
$921$	−7.37054e35			−0.0652010
$922$		−	1.89543e36i		−	0.165413i
$923$			1.30426e37i			1.12291i
$924$	1.51345e36			0.128549
$925$	1.03139e37	+	2.12416e36i	0.864278	+	0.177998i
$926$	−1.03719e36			−0.0857474
$927$			1.57327e37i			1.28323i
$928$			1.88342e36i			0.151564i
$929$	2.93833e36			0.233294			0.116647	−	0.993173i	$-0.462785\pi$
$929$	2.93833e36			0.233294			0.116647	+	0.993173i	$0.462785\pi$
$930$	−2.58320e36	−	3.16943e36i	−0.202358	−	0.248281i
$931$	2.31795e37			1.79156
$932$			3.25079e36i			0.247908i
$933$			4.64017e36i			0.349151i
$934$	−6.39190e36			−0.474563
$935$	−2.43465e36	+	1.98433e36i	−0.178357	+	0.145368i
$936$	6.19944e36			0.448131
$937$			1.33465e37i			0.951968i	0.879454	+	0.475984i	$0.157908\pi$
$937$			1.33465e37i			0.951968i	−0.879454	+	0.475984i	$0.842092\pi$
$938$		−	3.04168e37i		−	2.14081i
$939$	1.27877e35			0.00888120
$940$	1.29698e36	−	1.05709e36i	0.0888864	−	0.0724458i
$941$	−1.37070e37			−0.926983			−0.463492	−	0.886101i	$-0.653404\pi$
$941$	−1.37070e37			−0.926983			−0.463492	+	0.886101i	$0.653404\pi$
$942$			1.59051e35i			0.0106145i
$943$			3.58454e36i			0.236068i
$944$	3.18704e36			0.207127
$945$	8.44755e36	+	1.03646e37i	0.541793	+	0.664746i
$946$	−8.16009e35			−0.0516482
$947$		−	3.73876e36i		−	0.233535i	−0.993159	−	0.116768i	$-0.962747\pi$
$947$		−	3.73876e36i		−	0.233535i	0.993159	−	0.116768i	$-0.0372533\pi$
$948$			8.52350e35i			0.0525429i
$949$	1.00734e36			0.0612845
$950$	1.01023e37	+	2.08057e36i	0.606562	+	0.124922i
$951$	−5.10736e36			−0.302649
$952$		−	4.18336e36i		−	0.244660i
$953$		−	4.80715e36i		−	0.277477i	−0.990329	−	0.138738i	$-0.955695\pi$
$953$		−	4.80715e36i		−	0.277477i	0.990329	−	0.138738i	$-0.0443047\pi$
$954$	1.75383e37			0.999156
$955$	5.79841e36	+	7.11429e36i	0.326037	+	0.400027i
$956$	1.20119e36			0.0666634
$957$			2.30586e36i			0.126309i
$958$		−	2.96373e36i		−	0.160240i
$959$	3.77138e36			0.201265
$960$	−4.66999e35	+	3.80622e35i	−0.0245995	+	0.0200495i
$961$	4.19922e37			2.18336
$962$			1.64715e37i			0.845364i
$963$		−	5.23170e36i		−	0.265042i
$964$	1.41272e37			0.706467
$965$	−1.26090e37	+	1.02768e37i	−0.622426	+	0.507301i
$966$	−9.29405e35			−0.0452888
$967$		−	1.46042e37i		−	0.702498i	−0.936282	−	0.351249i	$-0.885757\pi$
$967$		−	1.46042e37i		−	0.702498i	0.936282	−	0.351249i	$-0.114243\pi$
$968$			4.93850e36i			0.234506i
$969$	−1.88087e36			−0.0881683
$970$	−3.52311e36	−	4.32264e36i	−0.163035	−	0.200033i
$971$	−3.16381e37			−1.44534			−0.722670	−	0.691193i	$-0.757085\pi$
$971$	−3.16381e37			−1.44534			−0.722670	+	0.691193i	$0.757085\pi$
$972$		−	7.73003e36i		−	0.348620i
$973$			9.48913e36i			0.422490i
$974$	1.27423e37			0.560093
$975$	1.59887e36	−	7.76340e36i	0.0693835	−	0.336895i
$976$	−7.98382e36			−0.342049
$977$			3.15815e37i			1.33583i	0.744239	+	0.667914i	$0.232812\pi$
$977$			3.15815e37i			1.33583i	−0.744239	+	0.667914i	$0.767188\pi$
$978$		−	2.85193e36i		−	0.119098i
$979$	−2.15834e37			−0.889889
$980$	−1.58738e37	−	1.94762e37i	−0.646182	−	0.792825i
$981$	5.03701e36			0.202446
$982$			1.43824e37i			0.570738i
$983$			1.30026e37i			0.509461i	0.967012	+	0.254731i	$0.0819868\pi$
$983$			1.30026e37i			0.509461i	−0.967012	+	0.254731i	$0.918013\pi$
$984$	−3.78897e36			−0.146583
$985$	3.78006e36	−	3.08089e36i	0.144393	−	0.117686i
$986$	6.37368e36			0.240397
$987$			2.72841e36i			0.101612i
$988$			1.61335e37i			0.593288i
$989$	5.01107e35			0.0181960
$990$	8.29867e36	−	6.76373e36i	0.297556	−	0.242519i
$991$	1.69845e37			0.601355			0.300677	−	0.953726i	$-0.402787\pi$
$991$	1.69845e37			0.601355			0.300677	+	0.953726i	$0.402787\pi$
$992$		−	9.02119e36i		−	0.315405i
$993$		−	6.84852e36i		−	0.236446i
$994$	−2.99992e37			−1.02277
$995$	−3.30634e37	−	4.05667e37i	−1.11316	−	1.36578i
$996$	2.53455e35			0.00842673
$997$		−	1.43944e37i		−	0.472612i	−0.971679	−	0.236306i	$-0.924063\pi$
$997$		−	1.43944e37i		−	0.472612i	0.971679	−	0.236306i	$-0.0759368\pi$
$998$		−	3.59677e37i		−	1.16622i
$999$	1.35418e37			0.433617

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	10.26.b.a.9.10	yes	12
5.2	odd	4		50.26.a.k.1.4		6
5.3	odd	4		50.26.a.l.1.3		6
5.4	even	2	inner	10.26.b.a.9.3	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.26.b.a.9.3	✓	12	5.4	even	2	inner
10.26.b.a.9.10	yes	12	1.1	even	1	trivial
50.26.a.k.1.4		6	5.2	odd	4
50.26.a.l.1.3		6	5.3	odd	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:	\( N \)	\(=\)	\( 10 = 2 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 26 \)
Character orbit:	\([\chi]\)	\(=\)	10.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+4096.00i q^{2} +233693. i q^{3} -1.67772e7 q^{4} +(-3.44896e8 - 4.23166e8i) q^{5} -9.57206e8 q^{6} +6.39090e10i q^{7} -6.87195e10i q^{8} +7.92676e11 q^{9} +(1.73329e12 - 1.41270e12i) q^{10} +6.04007e12 q^{11} -3.92071e12i q^{12} +1.13809e14i q^{13} -2.61771e14 q^{14} +(9.88909e13 - 8.05998e13i) q^{15} +2.81475e14 q^{16} -9.52541e14i q^{17} +3.24680e15i q^{18} -8.44950e15 q^{19} +(5.78640e15 + 7.09955e15i) q^{20} -1.49351e16 q^{21} +2.47401e16i q^{22} -1.51928e16i q^{23} +1.60592e16 q^{24} +(-6.01162e16 + 2.91897e17i) q^{25} -4.66162e17 q^{26} +3.83248e17i q^{27} -1.07222e18i q^{28} +1.63360e18 q^{29} +(3.30137e17 + 4.05057e17i) q^{30} -7.82464e18 q^{31} +1.15292e18i q^{32} +1.41152e18i q^{33} +3.90161e18 q^{34} +(2.70441e19 - 2.20420e19i) q^{35} -1.32989e19 q^{36} -3.53342e19i q^{37} -3.46091e19i q^{38} -2.65964e19 q^{39} +(-2.90798e19 + 2.37011e19i) q^{40} -2.35937e20 q^{41} -6.11741e19i q^{42} +3.29832e19i q^{43} -1.01335e20 q^{44} +(-2.73391e20 - 3.35434e20i) q^{45} +6.22296e19 q^{46} -1.82685e20i q^{47} +6.57787e19i q^{48} -2.74329e21 q^{49} +(-1.19561e21 - 2.46236e20i) q^{50} +2.22602e20 q^{51} -1.90940e21i q^{52} -5.40172e21i q^{53} -1.56978e21 q^{54} +(-2.08320e21 - 2.55595e21i) q^{55} +4.39179e21 q^{56} -1.97459e21i q^{57} +6.69124e21i q^{58} +1.13226e22 q^{59} +(-1.65911e21 + 1.35224e21i) q^{60} -2.83642e22 q^{61} -3.20497e22i q^{62} +5.06592e22i q^{63} -4.72237e21 q^{64} +(4.81602e22 - 3.92523e22i) q^{65} -5.78158e21 q^{66} +1.16196e23i q^{67} +1.59810e22i q^{68} +3.55044e21 q^{69} +(9.02840e22 + 1.10773e23i) q^{70} +1.14601e23 q^{71} -5.44723e22i q^{72} -8.85118e21i q^{73} +1.44729e23 q^{74} +(-6.82142e22 - 1.40487e22i) q^{75} +1.41759e23 q^{76} +3.86015e23i q^{77} -1.08939e23i q^{78} -2.17397e23 q^{79} +(-9.70797e22 - 1.19111e23i) q^{80} +5.82063e23 q^{81} -9.66398e23i q^{82} +6.46451e22i q^{83} +2.50569e23 q^{84} +(-4.03083e23 + 3.28528e23i) q^{85} -1.35099e23 q^{86} +3.81761e23i q^{87} -4.15070e23i q^{88} -3.57337e24 q^{89} +(1.37394e24 - 1.11981e24i) q^{90} -7.27343e24 q^{91} +2.54893e23i q^{92} -1.82856e24i q^{93} +7.48277e23 q^{94} +(2.91420e24 + 3.57554e24i) q^{95} -2.69429e23 q^{96} -2.49389e24i q^{97} -1.12365e25i q^{98} +4.78782e24 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 201326592 q^{4} - 490295340 q^{5} - 6565199872 q^{6} - 1082937564236 q^{9} + 1636528619520 q^{10} + 19723089228624 q^{11} + 278591122243584 q^{14} - 449884766537680 q^{15} + 33\!\cdots\!72 q^{16}+ \cdots + 41\!\cdots\!28 q^{99}+O(q^{100}) \) 12 * q - 201326592 * q^4 - 490295340 * q^5 - 6565199872 * q^6 - 1082937564236 * q^9 + 1636528619520 * q^10 + 19723089228624 * q^11 + 278591122243584 * q^14 - 449884766537680 * q^15 + 3377699720527872 * q^16 - 4015312977833040 * q^19 + 8225790822973440 * q^20 - 56363420582029456 * q^21 + 110145776335716352 * q^24 - 1047554086248996900 * q^25 - 252210272532037632 * q^26 + 5852064063311009640 * q^29 - 3747916483574824960 * q^30 + 158585871554029824 * q^31 + 28121800210885115904 * q^34 - 42730948507221221040 * q^35 + 18168677429701246976 * q^36 - 249453273245123586912 * q^39 - 27456394139868856320 * q^40 + 206458603439752488024 * q^41 - 330898528175898230784 * q^44 + 957114913653485255020 * q^45 - 1111751773656740462592 * q^46 - 3432561496278055389084 * q^49 + 346631457781510963200 * q^50 - 3032451787323924027136 * q^51 + 6455741354411915345920 * q^54 - 7824754202169531625680 * q^55 - 4673983433563013382144 * q^56 + 24998150261761560337680 * q^59 + 7547813903312229498880 * q^60 + 7374571220622236593224 * q^61 - 56668397794435742564352 * q^64 + 20652620138653742557920 * q^65 + 56072959085731865952256 * q^66 - 370250651964757999709072 * q^69 + 157367128964587932549120 * q^70 + 149137752442507323299424 * q^71 + 27409492362780459270144 * q^74 + 1032897211530510645911200 * q^75 + 67365773136708124016640 * q^76 + 801700633747623249599040 * q^79 - 138005869407843165143040 * q^80 - 2864220237232227656687428 * q^81 + 945621281603553901674496 * q^84 + 2004099032091709203221760 * q^85 - 1363071174568488987328512 * q^86 - 5964345056120682049233480 * q^89 + 4840324611668628597309440 * q^90 - 14003423438242038482629536 * q^91 + 3325183945859356082110464 * q^94 + 18644670331946084490382800 * q^95 - 1847939481072001752236032 * q^96 + 4107440578564823447146928 * q^99

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