LMFDB - Embedded newform 10.26.b.a.9.2

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			9.2
Root			$-540092. i$ of defining polynomial
Character	$\chi$	$=$	10.9
Dual form			10.26.b.a.9.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-4096.00i q^{2} -1.08018e6i q^{3} -1.67772e7 q^{4} +(3.02592e8 + 4.54380e8i) q^{5} -4.42443e9 q^{6} +5.43159e10i q^{7} +6.87195e10i q^{8} -3.19509e11 q^{9} +(1.86114e12 - 1.23942e12i) q^{10} -3.24375e12 q^{11} +1.81225e13i q^{12} -7.83357e13i q^{13} +2.22478e14 q^{14} +(4.90814e14 - 3.26855e14i) q^{15} +2.81475e14 q^{16} -4.33806e15i q^{17} +1.30871e15i q^{18} -8.87783e15 q^{19} +(-5.07665e15 - 7.62323e15i) q^{20} +5.86711e16 q^{21} +1.32864e16i q^{22} -7.05451e16i q^{23} +7.42297e16 q^{24} +(-1.14900e17 + 2.74984e17i) q^{25} -3.20863e17 q^{26} -5.70099e17i q^{27} -9.11269e17i q^{28} +1.11391e18 q^{29} +(-1.33880e18 - 2.01037e18i) q^{30} +6.30227e18 q^{31} -1.15292e18i q^{32} +3.50385e18i q^{33} -1.77687e19 q^{34} +(-2.46800e19 + 1.64355e19i) q^{35} +5.36047e18 q^{36} -1.55100e19i q^{37} +3.63636e19i q^{38} -8.46169e19 q^{39} +(-3.12248e19 + 2.07940e19i) q^{40} -3.82653e19 q^{41} -2.40317e20i q^{42} -3.32618e20i q^{43} +5.44211e19 q^{44} +(-9.66807e19 - 1.45178e20i) q^{45} -2.88953e20 q^{46} -1.01157e21i q^{47} -3.04045e20i q^{48} -1.60914e21 q^{49} +(1.12633e21 + 4.70628e20i) q^{50} -4.68591e21 q^{51} +1.31425e21i q^{52} -3.43480e21i q^{53} -2.33513e21 q^{54} +(-9.81532e20 - 1.47390e21i) q^{55} -3.73256e21 q^{56} +9.58969e21i q^{57} -4.56259e21i q^{58} -4.09753e21 q^{59} +(-8.23450e21 + 5.48371e21i) q^{60} +3.14378e22 q^{61} -2.58141e22i q^{62} -1.73544e22i q^{63} -4.72237e21 q^{64} +(3.55942e22 - 2.37037e22i) q^{65} +1.43518e22 q^{66} +1.01756e23i q^{67} +7.27806e22i q^{68} -7.62017e22 q^{69} +(6.73200e22 + 1.01089e23i) q^{70} +2.10284e23 q^{71} -2.19565e22i q^{72} -1.56829e23i q^{73} -6.35289e22 q^{74} +(2.97033e23 + 1.24113e23i) q^{75} +1.48945e23 q^{76} -1.76187e23i q^{77} +3.46591e23i q^{78} -6.00925e22 q^{79} +(8.51720e22 + 1.27897e23i) q^{80} -8.86528e23 q^{81} +1.56735e23i q^{82} +7.40331e23i q^{83} -9.84338e23 q^{84} +(1.97113e24 - 1.31266e24i) q^{85} -1.36240e24 q^{86} -1.20323e24i q^{87} -2.22909e23i q^{88} -3.21148e24 q^{89} +(-5.94651e23 + 3.96004e23i) q^{90} +4.25487e24 q^{91} +1.18355e24i q^{92} -6.80761e24i q^{93} -4.14341e24 q^{94} +(-2.68636e24 - 4.03391e24i) q^{95} -1.24537e24 q^{96} -5.32805e24i q^{97} +6.59105e24i q^{98} +1.03641e24 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
$3$		−	1.08018e6i		−	1.17350i	−0.809769	−	0.586749i	$-0.800408\pi$
$3$		−	1.08018e6i		−	1.17350i	0.809769	−	0.586749i	$-0.199592\pi$
$4$	−1.67772e7			−0.500000
$5$	3.02592e8	+	4.54380e8i	0.554284	+	0.832328i
$5$	3.02592e8	+	4.54380e8i	0.554284	+	0.832328i
$6$	−4.42443e9			−0.829788
$7$			5.43159e10i			1.48320i	0.670840	+	0.741602i	$0.265934\pi$
$7$			5.43159e10i			1.48320i	−0.670840	+	0.741602i	$0.734066\pi$
$8$			6.87195e10i			0.353553i
$9$	−3.19509e11			−0.377095
$10$	1.86114e12	−	1.23942e12i	0.588545	−	0.391938i
$11$	−3.24375e12			−0.311630			−0.155815	−	0.987786i	$-0.549800\pi$
$11$	−3.24375e12			−0.311630			−0.155815	+	0.987786i	$0.549800\pi$
$12$			1.81225e13i			0.586749i
$13$		−	7.83357e13i		−	0.932541i	−0.884642	−	0.466270i	$-0.845597\pi$
$13$		−	7.83357e13i		−	0.932541i	0.884642	−	0.466270i	$-0.154403\pi$
$14$	2.22478e14			1.04878
$15$	4.90814e14	−	3.26855e14i	0.976734	−	0.650450i
$16$	2.81475e14			0.250000
$17$		−	4.33806e15i		−	1.80586i	−0.429786	−	0.902931i	$-0.641411\pi$
$17$		−	4.33806e15i		−	1.80586i	0.429786	−	0.902931i	$-0.358589\pi$
$18$			1.30871e15i			0.266647i
$19$	−8.87783e15			−0.920210			−0.460105	−	0.887865i	$-0.652188\pi$
$19$	−8.87783e15			−0.920210			−0.460105	+	0.887865i	$0.652188\pi$
$20$	−5.07665e15	−	7.62323e15i	−0.277142	−	0.416164i
$21$	5.86711e16			1.74054
$22$			1.32864e16i			0.220355i
$23$		−	7.05451e16i		−	0.671227i	−0.942000	−	0.335613i	$-0.891056\pi$
$23$		−	7.05451e16i		−	0.671227i	0.942000	−	0.335613i	$-0.108944\pi$
$24$	7.42297e16			0.414894
$25$	−1.14900e17	+	2.74984e17i	−0.385539	+	0.922692i
$26$	−3.20863e17			−0.659406
$27$		−	5.70099e17i		−	0.730977i
$28$		−	9.11269e17i		−	0.741602i
$29$	1.11391e18			0.584624			0.292312	−	0.956323i	$-0.405575\pi$
$29$	1.11391e18			0.584624			0.292312	+	0.956323i	$0.405575\pi$
$30$	−1.33880e18	−	2.01037e18i	−0.459938	−	0.690655i
$31$	6.30227e18			1.43706			0.718532	−	0.695494i	$-0.244815\pi$
$31$	6.30227e18			1.43706			0.718532	+	0.695494i	$0.244815\pi$
$32$		−	1.15292e18i		−	0.176777i
$33$			3.50385e18i			0.365696i
$34$	−1.77687e19			−1.27694
$35$	−2.46800e19	+	1.64355e19i	−1.23451	+	0.822116i
$36$	5.36047e18			0.188548
$37$		−	1.55100e19i		−	0.387338i	−0.981067	−	0.193669i	$-0.937961\pi$
$37$		−	1.55100e19i		−	0.387338i	0.981067	−	0.193669i	$-0.0620387\pi$
$38$			3.63636e19i			0.650687i
$39$	−8.46169e19			−1.09433
$40$	−3.12248e19	+	2.07940e19i	−0.294272	+	0.195969i
$41$	−3.82653e19			−0.264854			−0.132427	−	0.991193i	$-0.542277\pi$
$41$	−3.82653e19			−0.264854			−0.132427	+	0.991193i	$0.542277\pi$
$42$		−	2.40317e20i		−	1.23075i
$43$		−	3.32618e20i		−	1.26937i	−0.772770	−	0.634687i	$-0.781129\pi$
$43$		−	3.32618e20i		−	1.26937i	0.772770	−	0.634687i	$-0.218871\pi$
$44$	5.44211e19			0.155815
$45$	−9.66807e19	−	1.45178e20i	−0.209018	−	0.313867i
$46$	−2.88953e20			−0.474629
$47$		−	1.01157e21i		−	1.26992i	−0.772547	−	0.634958i	$-0.781018\pi$
$47$		−	1.01157e21i		−	1.26992i	0.772547	−	0.634958i	$-0.218982\pi$
$48$		−	3.04045e20i		−	0.293374i
$49$	−1.60914e21			−1.19990
$50$	1.12633e21	+	4.70628e20i	0.652441	+	0.272617i
$51$	−4.68591e21			−2.11917
$52$			1.31425e21i			0.466270i
$53$		−	3.43480e21i		−	0.960401i	−0.877159	−	0.480201i	$-0.840564\pi$
$53$		−	3.43480e21i		−	0.960401i	0.877159	−	0.480201i	$-0.159436\pi$
$54$	−2.33513e21			−0.516879
$55$	−9.81532e20	−	1.47390e21i	−0.172731	−	0.259378i
$56$	−3.73256e21			−0.524392
$57$			9.58969e21i			1.07986i
$58$		−	4.56259e21i		−	0.413392i
$59$	−4.09753e21			−0.299828			−0.149914	−	0.988699i	$-0.547900\pi$
$59$	−4.09753e21			−0.299828			−0.149914	+	0.988699i	$0.547900\pi$
$60$	−8.23450e21	+	5.48371e21i	−0.488367	+	0.325225i
$61$	3.14378e22			1.51646			0.758228	−	0.651990i	$-0.226065\pi$
$61$	3.14378e22			1.51646			0.758228	+	0.651990i	$0.226065\pi$
$62$		−	2.58141e22i		−	1.01616i
$63$		−	1.73544e22i		−	0.559310i
$64$	−4.72237e21			−0.125000
$65$	3.55942e22	−	2.37037e22i	0.776179	−	0.516892i
$66$	1.43518e22			0.258586
$67$			1.01756e23i			1.51923i	0.650372	+	0.759616i	$0.274613\pi$
$67$			1.01756e23i			1.51923i	−0.650372	+	0.759616i	$0.725387\pi$
$68$			7.27806e22i			0.902931i
$69$	−7.62017e22			−0.787682
$70$	6.73200e22	+	1.01089e23i	0.581324	+	0.872932i
$71$	2.10284e23			1.52081			0.760407	−	0.649446i	$-0.224999\pi$
$71$	2.10284e23			1.52081			0.760407	+	0.649446i	$0.224999\pi$
$72$		−	2.19565e22i		−	0.133323i
$73$		−	1.56829e23i		−	0.801478i	−0.916192	−	0.400739i	$-0.868753\pi$
$73$		−	1.56829e23i		−	0.801478i	0.916192	−	0.400739i	$-0.131247\pi$
$74$	−6.35289e22			−0.273889
$75$	2.97033e23	+	1.24113e23i	1.08278	+	0.452429i
$76$	1.48945e23			0.460105
$77$		−	1.76187e23i		−	0.462211i
$78$			3.46591e23i			0.773811i
$79$	−6.00925e22			−0.114415			−0.0572073	−	0.998362i	$-0.518220\pi$
$79$	−6.00925e22			−0.114415			−0.0572073	+	0.998362i	$0.518220\pi$
$80$	8.51720e22	+	1.27897e23i	0.138571	+	0.208082i
$81$	−8.86528e23			−1.23489
$82$			1.56735e23i			0.187280i
$83$			7.40331e23i			0.760238i	0.924938	+	0.380119i	$0.124117\pi$
$83$			7.40331e23i			0.760238i	−0.924938	+	0.380119i	$0.875883\pi$
$84$	−9.84338e23			−0.870268
$85$	1.97113e24	−	1.31266e24i	1.50307	−	1.00096i
$86$	−1.36240e24			−0.897583
$87$		−	1.20323e24i		−	0.686055i
$88$		−	2.22909e23i		−	0.110178i
$89$	−3.21148e24			−1.37826			−0.689128	−	0.724640i	$-0.742006\pi$
$89$	−3.21148e24			−1.37826			−0.689128	+	0.724640i	$0.742006\pi$
$90$	−5.94651e23	+	3.96004e23i	−0.221937	+	0.147798i
$91$	4.25487e24			1.38315
$92$			1.18355e24i			0.335613i
$93$		−	6.80761e24i		−	1.68639i
$94$	−4.14341e24			−0.897966
$95$	−2.68636e24	−	4.03391e24i	−0.510057	−	0.765916i
$96$	−1.24537e24			−0.207447
$97$		−	5.32805e24i		−	0.779689i	−0.920881	−	0.389844i	$-0.872529\pi$
$97$		−	5.32805e24i		−	0.779689i	0.920881	−	0.389844i	$-0.127471\pi$
$98$			6.59105e24i			0.848455i
$99$	1.03641e24			0.117514
$100$	1.92769e24	−	4.61346e24i	0.192769	−	0.461346i
$101$	−9.97515e24			−0.880851			−0.440425	−	0.897789i	$-0.645172\pi$
$101$	−9.97515e24			−0.880851			−0.440425	+	0.897789i	$0.645172\pi$
$102$			1.91935e25i			1.49848i
$103$			6.46906e24i			0.447070i	0.974696	+	0.223535i	$0.0717598\pi$
$103$			6.46906e24i			0.447070i	−0.974696	+	0.223535i	$0.928240\pi$
$104$	5.38319e24			0.329703
$105$	1.77534e25	+	2.66590e25i	0.964751	+	1.44870i
$106$	−1.40689e25			−0.679106
$107$		−	2.37528e25i		−	1.01957i	−0.860302	−	0.509786i	$-0.829725\pi$
$107$		−	2.37528e25i		−	1.01957i	0.860302	−	0.509786i	$-0.170275\pi$
$108$			9.56468e24i			0.365488i
$109$	4.56311e25			1.55393			0.776963	−	0.629547i	$-0.216759\pi$
$109$	4.56311e25			1.55393			0.776963	+	0.629547i	$0.216759\pi$
$110$	−6.03708e24	+	4.02036e24i	−0.183408	+	0.122139i
$111$	−1.67536e25			−0.454540
$112$			1.52886e25i			0.370801i
$113$		−	4.40956e25i		−	0.957005i	−0.878086	−	0.478503i	$-0.841180\pi$
$113$		−	4.40956e25i		−	0.957005i	0.878086	−	0.478503i	$-0.158820\pi$
$114$	3.92794e25			0.763579
$115$	3.20543e25	−	2.13464e25i	0.558680	−	0.372050i
$116$	−1.86884e25			−0.292312
$117$			2.50289e25i			0.351657i
$118$			1.67835e25i			0.212011i
$119$	2.35626e26			2.67846
$120$	2.24613e25	+	3.37285e25i	0.229969	+	0.345328i
$121$	−9.78251e25			−0.902887
$122$		−	1.28769e26i		−	1.07230i
$123$			4.13335e25i			0.310805i
$124$	−1.05735e26			−0.718532
$125$	−1.59715e26	+	3.09997e25i	−0.981680	+	0.190538i
$126$	−7.10836e25			−0.395492
$127$			3.54526e26i			1.78691i	0.449157	+	0.893453i	$0.351724\pi$
$127$			3.54526e26i			1.78691i	−0.449157	+	0.893453i	$0.648276\pi$
$128$			1.93428e25i			0.0883883i
$129$	−3.59288e26			−1.48961
$130$	−9.70905e25	−	1.45794e26i	−0.365498	−	0.548842i
$131$	−3.11451e26			−1.06537			−0.532683	−	0.846315i	$-0.678816\pi$
$131$	−3.11451e26			−1.06537			−0.532683	+	0.846315i	$0.678816\pi$
$132$		−	5.87848e25i		−	0.182848i
$133$		−	4.82207e26i		−	1.36486i
$134$	4.16792e26			1.07426
$135$	2.59042e26	−	1.72507e26i	0.608412	−	0.405169i
$136$	2.98110e26			0.638468
$137$		−	4.08877e26i		−	0.799072i	−0.916718	−	0.399536i	$-0.869171\pi$
$137$		−	4.08877e26i		−	0.799072i	0.916718	−	0.399536i	$-0.130829\pi$
$138$			3.12122e26i			0.556976i
$139$	−2.66018e26			−0.433737			−0.216869	−	0.976201i	$-0.569584\pi$
$139$	−2.66018e26			−0.433737			−0.216869	+	0.976201i	$0.569584\pi$
$140$	4.14063e26	−	2.75743e26i	0.617256	−	0.411058i
$141$	−1.09269e27			−1.49024
$142$		−	8.61322e26i		−	1.07538i
$143$			2.54101e26i			0.290607i
$144$	−8.99337e25			−0.0942739
$145$	3.37062e26	+	5.06141e26i	0.324048	+	0.486599i
$146$	−6.42373e26			−0.566730
$147$			1.73817e27i			1.40807i
$148$			2.60214e26i			0.193669i
$149$	1.37183e26			0.0938579			0.0469290	−	0.998898i	$-0.485057\pi$
$149$	1.37183e26			0.0938579			0.0469290	+	0.998898i	$0.485057\pi$
$150$	5.08365e26	−	1.21665e27i	0.319915	−	0.765638i
$151$	2.28415e27			1.32286			0.661428	−	0.750009i	$-0.269951\pi$
$151$	2.28415e27			1.32286			0.661428	+	0.750009i	$0.269951\pi$
$152$		−	6.10080e26i		−	0.325343i
$153$			1.38605e27i			0.680982i
$154$	−7.21662e26			−0.326832
$155$	1.90702e27	+	2.86363e27i	0.796541	+	1.19611i
$156$	1.41964e27			0.547167
$157$			5.56736e26i			0.198109i	0.995082	+	0.0990544i	$0.0315818\pi$
$157$			5.56736e26i			0.198109i	−0.995082	+	0.0990544i	$0.968418\pi$
$158$			2.46139e26i			0.0809034i
$159$	−3.71021e27			−1.12703
$160$	5.23865e26	−	3.48865e26i	0.147136	−	0.0979845i
$161$	3.83172e27			0.995566
$162$			3.63122e27i			0.873202i
$163$		−	6.45827e27i		−	1.43804i	−0.694990	−	0.719020i	$-0.744591\pi$
$163$		−	6.45827e27i		−	1.43804i	0.694990	−	0.719020i	$-0.255409\pi$
$164$	6.41985e26			0.132427
$165$	−1.59208e27	+	1.06024e27i	−0.304379	+	0.202700i
$166$	3.03239e27			0.537569
$167$			9.17351e26i			0.150862i	0.997151	+	0.0754310i	$0.0240332\pi$
$167$			9.17351e26i			0.150862i	−0.997151	+	0.0754310i	$0.975967\pi$
$168$			4.03185e27i			0.615373i
$169$	9.19932e26			0.130368
$170$	−5.37667e27	−	8.07375e27i	−0.707786	−	1.06283i
$171$	2.83654e27			0.347007
$172$			5.58040e27i			0.634687i
$173$		−	1.13072e28i		−	1.19614i	−0.801445	−	0.598068i	$-0.795935\pi$
$173$		−	1.13072e28i		−	1.19614i	0.801445	−	0.598068i	$-0.204065\pi$
$174$	−4.92844e27			−0.485114
$175$	−1.49360e28	−	6.24087e27i	−1.36854	−	0.571833i
$176$	−9.13034e26			−0.0779074
$177$			4.42609e27i			0.351847i
$178$			1.31542e28i			0.974574i
$179$	3.61567e27			0.249762			0.124881	−	0.992172i	$-0.460145\pi$
$179$	3.61567e27			0.249762			0.124881	+	0.992172i	$0.460145\pi$
$180$	1.62203e27	+	2.43569e27i	0.104509	+	0.156933i
$181$	−1.10646e28			−0.665201			−0.332601	−	0.943068i	$-0.607926\pi$
$181$	−1.10646e28			−0.665201			−0.332601	+	0.943068i	$0.607926\pi$
$182$		−	1.74279e28i		−	0.978034i
$183$		−	3.39587e28i		−	1.77956i
$184$	4.84782e27			0.237314
$185$	7.04743e27	−	4.69320e27i	0.322392	−	0.214695i
$186$	−2.78840e28			−1.19246
$187$			1.40716e28i			0.562760i
$188$			1.69714e28i			0.634958i
$189$	3.09654e28			1.08419
$190$	−1.65229e28	+	1.10033e28i	−0.541585	+	0.360665i
$191$	5.84877e27			0.179534			0.0897671	−	0.995963i	$-0.471388\pi$
$191$	5.84877e27			0.179534			0.0897671	+	0.995963i	$0.471388\pi$
$192$			5.10102e27i			0.146687i
$193$			1.61649e28i			0.435620i	0.975991	+	0.217810i	$0.0698913\pi$
$193$			1.61649e28i			0.435620i	−0.975991	+	0.217810i	$0.930109\pi$
$194$	−2.18237e28			−0.551323
$195$	−2.56044e28	−	3.84483e28i	−0.606571	−	0.910844i
$196$	2.69969e28			0.599948
$197$			5.33679e28i			1.11289i	0.830885	+	0.556445i	$0.187835\pi$
$197$			5.33679e28i			1.11289i	−0.830885	+	0.556445i	$0.812165\pi$
$198$		−	4.24512e27i		−	0.0830950i
$199$	−7.95288e27			−0.146171			−0.0730855	−	0.997326i	$-0.523285\pi$
$199$	−7.95288e27			−0.146171			−0.0730855	+	0.997326i	$0.523285\pi$
$200$	−1.88967e28	−	7.89584e27i	−0.326221	−	0.136309i
$201$	1.09915e29			1.78281
$202$			4.08582e28i			0.622855i
$203$			6.05032e28i			0.867118i
$204$	7.86165e28			1.05959
$205$	−1.15788e28	−	1.73870e28i	−0.146804	−	0.220445i
$206$	2.64973e28			0.316127
$207$			2.25398e28i			0.253116i
$208$		−	2.20495e28i		−	0.233135i
$209$	2.87975e28			0.286765
$210$	1.09195e29	−	7.27179e28i	1.02438	−	0.682182i
$211$	−6.17913e28			−0.546257			−0.273128	−	0.961978i	$-0.588058\pi$
$211$	−6.17913e28			−0.546257			−0.273128	+	0.961978i	$0.588058\pi$
$212$			5.76263e28i			0.480201i
$213$		−	2.27145e29i		−	1.78467i
$214$	−9.72914e28			−0.720946
$215$	1.51135e29	−	1.00647e29i	1.05653	−	0.703593i
$216$	3.91769e28			0.258439
$217$			3.42313e29i			2.13146i
$218$		−	1.86905e29i		−	1.09879i
$219$	−1.69404e29			−0.940532
$220$	1.64674e28	+	2.47279e28i	0.0863656	+	0.129689i
$221$	−3.39825e29			−1.68404
$222$			6.86229e28i			0.321408i
$223$			3.94158e29i			1.74526i	0.488382	+	0.872630i	$0.337587\pi$
$223$			3.94158e29i			1.74526i	−0.488382	+	0.872630i	$0.662413\pi$
$224$	6.26219e28			0.262196
$225$	3.67114e28	−	8.78596e28i	0.145385	−	0.347943i
$226$	−1.80615e29			−0.676705
$227$			1.43566e29i			0.509012i	0.967071	+	0.254506i	$0.0819129\pi$
$227$			1.43566e29i			0.509012i	−0.967071	+	0.254506i	$0.918087\pi$
$228$		−	1.60888e29i		−	0.539932i
$229$	−3.75130e29			−1.19189			−0.595947	−	0.803023i	$-0.703223\pi$
$229$	−3.75130e29			−1.19189			−0.595947	+	0.803023i	$0.703223\pi$
$230$	−8.74348e28	−	1.31294e29i	−0.263079	−	0.395047i
$231$	−1.90314e29			−0.542403
$232$			7.65476e28i			0.206696i
$233$		−	4.51422e29i		−	1.15514i	−0.816342	−	0.577569i	$-0.804001\pi$
$233$		−	4.51422e29i		−	1.15514i	0.816342	−	0.577569i	$-0.195999\pi$
$234$	1.02518e29			0.248659
$235$	4.59639e29	−	3.06094e29i	1.05699	−	0.703893i
$236$	6.87452e28			0.149914
$237$			6.49109e28i			0.134265i
$238$		−	9.65123e29i		−	1.89396i
$239$	1.77838e29			0.331169			0.165585	−	0.986196i	$-0.447049\pi$
$239$	1.77838e29			0.331169			0.165585	+	0.986196i	$0.447049\pi$
$240$	1.38152e29	−	9.20015e28i	0.244184	−	0.162613i
$241$	−5.18328e28			−0.0869745			−0.0434872	−	0.999054i	$-0.513847\pi$
$241$	−5.18328e28			−0.0869745			−0.0434872	+	0.999054i	$0.513847\pi$
$242$			4.00692e29i			0.638438i
$243$			4.74575e29i			0.718168i
$244$	−5.27439e29			−0.758228
$245$	−4.86914e29	−	7.31163e29i	−0.665083	−	0.998707i
$246$	1.69302e29			0.219773
$247$			6.95451e29i			0.858133i
$248$			4.33089e29i			0.508079i
$249$	7.99693e29			0.892137
$250$	1.26975e29	+	6.54192e29i	0.134731	+	0.694152i
$251$	9.22037e29			0.930737			0.465368	−	0.885117i	$-0.345922\pi$
$251$	9.22037e29			0.930737			0.465368	+	0.885117i	$0.345922\pi$
$252$			2.91158e29i			0.279655i
$253$			2.28831e29i			0.209174i
$254$	1.45214e30			1.26353
$255$	−1.41792e30	−	2.12918e30i	−1.17462	−	1.76385i
$256$	7.92282e28			0.0625000
$257$			2.62664e30i			1.97350i	0.162254	+	0.986749i	$0.448123\pi$
$257$			2.62664e30i			1.97350i	−0.162254	+	0.986749i	$0.551877\pi$
$258$			1.47164e30i			1.05331i
$259$	8.42438e29			0.574501
$260$	−5.97171e29	+	3.97683e29i	−0.388090	+	0.258446i
$261$	−3.55905e29			−0.220459
$262$			1.27570e30i			0.753328i
$263$		−	1.28488e30i		−	0.723465i	−0.932282	−	0.361732i	$-0.882185\pi$
$263$		−	1.28488e30i		−	0.723465i	0.932282	−	0.361732i	$-0.117815\pi$
$264$	−2.40782e29			−0.129293
$265$	1.56070e30	−	1.03934e30i	0.799369	−	0.532335i
$266$	−1.97512e30			−0.965102
$267$			3.46899e30i			1.61738i
$268$		−	1.70718e30i		−	0.759616i
$269$	2.87870e30			1.22262			0.611312	−	0.791390i	$-0.290642\pi$
$269$	2.87870e30			1.22262			0.611312	+	0.791390i	$0.290642\pi$
$270$	−7.06591e29	−	1.06104e30i	−0.286497	−	0.430212i
$271$	6.47478e29			0.250674			0.125337	−	0.992114i	$-0.459999\pi$
$271$	6.47478e29			0.250674			0.125337	+	0.992114i	$0.459999\pi$
$272$		−	1.22106e30i		−	0.451465i
$273$		−	4.59604e30i		−	1.62312i
$274$	−1.67476e30			−0.565029
$275$	3.72705e29	−	8.91978e29i	0.120145	−	0.287538i
$276$	1.27845e30			0.393841
$277$		−	3.36035e30i		−	0.989436i	−0.869054	−	0.494718i	$-0.835271\pi$
$277$		−	3.36035e30i		−	0.989436i	0.869054	−	0.494718i	$-0.164729\pi$
$278$			1.08961e30i			0.306699i
$279$	−2.01363e30			−0.541910
$280$	−1.12944e30	−	1.69600e30i	−0.290662	−	0.436466i
$281$	3.79608e30			0.934343			0.467172	−	0.884167i	$-0.345273\pi$
$281$	3.79608e30			0.934343			0.467172	+	0.884167i	$0.345273\pi$
$282$			4.47564e30i			1.05376i
$283$			2.26117e30i			0.509334i	0.967029	+	0.254667i	$0.0819658\pi$
$283$			2.26117e30i			0.509334i	−0.967029	+	0.254667i	$0.918034\pi$
$284$	−3.52798e30			−0.760407
$285$	−4.35737e30	+	2.90176e30i	−0.898800	+	0.598551i
$286$	1.04080e30			0.205490
$287$		−	2.07841e30i		−	0.392833i
$288$			3.68368e29i			0.0666617i
$289$	−1.30482e31			−2.26114
$290$	2.07315e30	−	1.38060e30i	0.344077	−	0.229136i
$291$	−5.75527e30			−0.914962
$292$			2.63116e30i			0.400739i
$293$		−	8.20237e30i		−	1.19700i	−0.801123	−	0.598500i	$-0.795764\pi$
$293$		−	8.20237e30i		−	1.19700i	0.801123	−	0.598500i	$-0.204236\pi$
$294$	7.11955e30			0.995659
$295$	−1.23988e30	−	1.86184e30i	−0.166190	−	0.249555i
$296$	1.06584e30			0.136945
$297$			1.84926e30i			0.227794i
$298$		−	5.61900e29i		−	0.0663676i
$299$	−5.52620e30			−0.625946
$300$	−4.98338e30	−	2.08226e30i	−0.541388	−	0.226214i
$301$	1.80664e31			1.88274
$302$		−	9.35588e30i		−	0.935401i
$303$			1.07750e31i			1.03368i
$304$	−2.49889e30			−0.230052
$305$	9.51284e30	+	1.42847e31i	0.840547	+	1.26219i
$306$	5.67726e30			0.481527
$307$			1.16923e31i			0.952072i	0.879426	+	0.476036i	$0.157927\pi$
$307$			1.16923e31i			0.952072i	−0.879426	+	0.476036i	$0.842073\pi$
$308$			2.95593e30i			0.231105i
$309$	6.98778e30			0.524636
$310$	1.17294e31	−	7.81114e30i	0.845776	−	0.563240i
$311$	−9.75410e30			−0.675588			−0.337794	−	0.941220i	$-0.609681\pi$
$311$	−9.75410e30			−0.675588			−0.337794	+	0.941220i	$0.609681\pi$
$312$		−	5.81483e30i		−	0.386905i
$313$		−	2.13999e31i		−	1.36807i	−0.729449	−	0.684035i	$-0.760224\pi$
$313$		−	2.13999e31i		−	1.36807i	0.729449	−	0.684035i	$-0.239776\pi$
$314$	2.28039e30			0.140084
$315$	7.88549e30	−	5.25130e30i	0.465529	−	0.310016i
$316$	1.00818e30			0.0572073
$317$			2.87837e31i			1.57002i	0.619482	+	0.785011i	$0.287343\pi$
$317$			2.87837e31i			1.57002i	−0.619482	+	0.785011i	$0.712657\pi$
$318$			1.51970e31i			0.796929i
$319$	−3.61326e30			−0.182186
$320$	−1.42895e30	−	2.14575e30i	−0.0692855	−	0.104041i
$321$	−2.56574e31			−1.19646
$322$		−	1.56947e31i		−	0.703972i
$323$			3.85126e31i			1.66177i
$324$	1.48735e31			0.617447
$325$	2.15410e31	+	9.00073e30i	0.860447	+	0.359531i
$326$	−2.64531e31			−1.01685
$327$		−	4.92900e31i		−	1.82353i
$328$		−	2.62957e30i		−	0.0936400i
$329$	5.49445e31			1.88354
$330$	4.34272e30	+	6.52115e30i	0.143330	+	0.215229i
$331$	7.95904e30			0.252936			0.126468	−	0.991971i	$-0.459636\pi$
$331$	7.95904e30			0.252936			0.126468	+	0.991971i	$0.459636\pi$
$332$		−	1.24207e31i		−	0.380119i
$333$			4.95557e30i			0.146063i
$334$	3.75747e30			0.106675
$335$	−4.62358e31	+	3.07905e31i	−1.26450	+	0.842085i
$336$	1.65144e31			0.435134
$337$		−	5.91626e31i		−	1.50201i	−0.660295	−	0.751006i	$-0.729569\pi$
$337$		−	5.91626e31i		−	1.50201i	0.660295	−	0.751006i	$-0.270431\pi$
$338$		−	3.76804e30i		−	0.0921842i
$339$	−4.76313e31			−1.12304
$340$	−3.30701e31	+	2.20228e31i	−0.751534	+	0.500480i
$341$	−2.04430e31			−0.447832
$342$		−	1.16185e31i		−	0.245371i
$343$		−	1.45607e31i		−	0.296487i
$344$	2.28573e31			0.448791
$345$	−2.30580e31	−	3.46246e31i	−0.436600	−	0.655610i
$346$	−4.63145e31			−0.845796
$347$			2.62292e31i			0.462026i	0.972951	+	0.231013i	$0.0742039\pi$
$347$			2.62292e31i			0.462026i	−0.972951	+	0.231013i	$0.925796\pi$
$348$			2.01869e31i			0.343028i
$349$	−6.42126e31			−1.05269			−0.526347	−	0.850270i	$-0.676439\pi$
$349$	−6.42126e31			−1.05269			−0.526347	+	0.850270i	$0.676439\pi$
$350$	−2.55626e31	+	6.11777e31i	−0.404347	+	0.967704i
$351$	−4.46591e31			−0.681665
$352$			3.73979e30i			0.0550889i
$353$		−	3.67958e31i		−	0.523136i	−0.965185	−	0.261568i	$-0.915760\pi$
$353$		−	3.67958e31i		−	0.523136i	0.965185	−	0.261568i	$-0.0842396\pi$
$354$	1.81293e31			0.248794
$355$	6.36302e31	+	9.55488e31i	0.842963	+	1.26582i
$356$	5.38797e31			0.689128
$357$		−	2.54519e32i		−	3.14317i
$358$		−	1.48098e31i		−	0.176608i
$359$	1.54521e32			1.77953			0.889766	−	0.456418i	$-0.150868\pi$
$359$	1.54521e32			1.77953			0.889766	+	0.456418i	$0.150868\pi$
$360$	9.97658e30	−	6.64385e30i	0.110969	−	0.0738990i
$361$	−1.42606e31			−0.153214
$362$			4.53205e31i			0.470368i
$363$			1.05669e32i			1.05954i
$364$	−7.13849e31			−0.691574
$365$	7.12601e31	−	4.74553e31i	0.667092	−	0.444246i
$366$	−1.39095e32			−1.25834
$367$		−	3.45113e31i		−	0.301742i	−0.988553	−	0.150871i	$-0.951792\pi$
$367$		−	3.45113e31i		−	0.301742i	0.988553	−	0.150871i	$-0.0482078\pi$
$368$		−	1.98567e31i		−	0.167807i
$369$	1.22261e31			0.0998752
$370$	−1.92233e31	−	2.88663e31i	−0.151812	−	0.227966i
$371$	1.86564e32			1.42447
$372$			1.14213e32i			0.843195i
$373$			5.25010e31i			0.374807i	0.982283	+	0.187403i	$0.0600072\pi$
$373$			5.25010e31i			0.374807i	−0.982283	+	0.187403i	$0.939993\pi$
$374$	5.76372e31			0.397931
$375$	3.34854e31	+	1.72521e32i	0.223596	+	1.15200i
$376$	6.95149e31			0.448983
$377$		−	8.72593e31i		−	0.545186i
$378$		−	1.26834e32i		−	0.766637i
$379$	−3.14351e32			−1.83834			−0.919169	−	0.393864i	$-0.871138\pi$
$379$	−3.14351e32			−1.83834			−0.919169	+	0.393864i	$0.871138\pi$
$380$	4.50696e31	+	6.76778e31i	0.255029	+	0.382958i
$381$	3.82953e32			2.09693
$382$		−	2.39566e31i		−	0.126950i
$383$			2.45971e32i			1.26154i	0.775972	+	0.630768i	$0.217260\pi$
$383$			2.45971e32i			1.26154i	−0.775972	+	0.630768i	$0.782740\pi$
$384$	2.08938e31			0.103723
$385$	8.00559e31	−	5.33128e31i	0.384711	−	0.256196i
$386$	6.62116e31			0.308030
$387$			1.06274e32i			0.478675i
$388$			8.93898e31i			0.389844i
$389$	−2.32919e32			−0.983638			−0.491819	−	0.870698i	$-0.663668\pi$
$389$	−2.32919e32			−0.983638			−0.491819	+	0.870698i	$0.663668\pi$
$390$	−1.57484e32	+	1.04876e32i	−0.644064	+	0.428911i
$391$	−3.06029e32			−1.21214
$392$		−	1.10579e32i		−	0.424227i
$393$			3.36425e32i			1.25020i
$394$	2.18595e32			0.786932
$395$	−1.81835e31	−	2.73048e31i	−0.0634182	−	0.0952305i
$396$	−1.73880e31			−0.0587571
$397$		−	2.38017e32i		−	0.779338i	−0.920955	−	0.389669i	$-0.872589\pi$
$397$		−	2.38017e32i		−	0.779338i	0.920955	−	0.389669i	$-0.127411\pi$
$398$			3.25750e31i			0.103358i
$399$	−5.20872e32			−1.60166
$400$	−3.23413e31	+	7.74010e31i	−0.0963847	+	0.230673i
$401$	5.61815e32			1.62289			0.811444	−	0.584430i	$-0.198682\pi$
$401$	5.61815e32			1.62289			0.811444	+	0.584430i	$0.198682\pi$
$402$		−	4.50212e32i		−	1.26064i
$403$		−	4.93693e32i		−	1.34012i
$404$	1.67355e32			0.440425
$405$	−2.68256e32	−	4.02821e32i	−0.684482	−	1.02784i
$406$	2.47821e32			0.613145
$407$			5.03105e31i			0.120706i
$408$		−	3.22013e32i		−	0.749241i
$409$	3.90144e32			0.880408			0.440204	−	0.897898i	$-0.354906\pi$
$409$	3.90144e32			0.880408			0.440204	+	0.897898i	$0.354906\pi$
$410$	−7.12171e31	+	4.74266e31i	−0.155878	+	0.103806i
$411$	−4.41662e32			−0.937708
$412$		−	1.08533e32i		−	0.223535i
$413$		−	2.22561e32i		−	0.444707i
$414$	9.23229e31			0.178980
$415$	−3.36392e32	+	2.24018e32i	−0.632767	+	0.421388i
$416$	−9.03149e31			−0.164851
$417$			2.87349e32i			0.508989i
$418$		−	1.17954e32i		−	0.202773i
$419$	−5.77394e32			−0.963378			−0.481689	−	0.876342i	$-0.659977\pi$
$419$	−5.77394e32			−0.963378			−0.481689	+	0.876342i	$0.659977\pi$
$420$	−2.97853e32	−	4.47264e32i	−0.482376	−	0.724348i
$421$	−9.43709e32			−1.48358			−0.741792	−	0.670630i	$-0.766024\pi$
$421$	−9.43709e32			−1.48358			−0.741792	+	0.670630i	$0.766024\pi$
$422$			2.53097e32i			0.386262i
$423$			3.23207e32i			0.478879i
$424$	2.36037e32			0.339553
$425$	1.19290e33	+	4.98442e32i	1.66625	+	0.696230i
$426$	−9.30386e32			−1.26195
$427$			1.70757e33i			2.24921i
$428$			3.98506e32i			0.509786i
$429$	2.74476e32			0.341027
$430$	−4.12252e32	−	6.19048e32i	−0.497516	−	0.747083i
$431$	3.90741e32			0.458061			0.229030	−	0.973419i	$-0.426444\pi$
$431$	3.90741e32			0.458061			0.229030	+	0.973419i	$0.426444\pi$
$432$		−	1.60469e32i		−	0.182744i
$433$		−	7.17692e32i		−	0.794034i	−0.917811	−	0.397017i	$-0.870045\pi$
$433$		−	7.17692e32i		−	0.794034i	0.917811	−	0.397017i	$-0.129955\pi$
$434$	1.40211e33			1.50717
$435$	5.46725e32	−	3.64088e32i	0.571023	−	0.380269i
$436$	−7.65564e32			−0.776963
$437$			6.26288e32i			0.617669i
$438$			6.93881e32i			0.665056i
$439$	4.73065e32			0.440671			0.220336	−	0.975424i	$-0.429285\pi$
$439$	4.73065e32			0.440671			0.220336	+	0.975424i	$0.429285\pi$
$440$	1.01285e32	−	6.74504e31i	0.0917040	−	0.0610697i
$441$	5.14135e32			0.452475
$442$			1.39192e33i			1.19080i
$443$		−	1.16496e33i		−	0.968871i	−0.874827	−	0.484436i	$-0.839025\pi$
$443$		−	1.16496e33i		−	0.968871i	0.874827	−	0.484436i	$-0.160975\pi$
$444$	2.81079e32			0.227270
$445$	−9.71767e32	−	1.45923e33i	−0.763945	−	1.14716i
$446$	1.61447e33			1.23408
$447$		−	1.48183e32i		−	0.110142i
$448$		−	2.56499e32i		−	0.185401i
$449$	1.31459e33			0.924082			0.462041	−	0.886859i	$-0.347117\pi$
$449$	1.31459e33			0.924082			0.462041	+	0.886859i	$0.347117\pi$
$450$	−3.59873e32	−	1.50370e32i	−0.246033	−	0.102803i
$451$	1.24123e32			0.0825363
$452$			7.39801e32i			0.478503i
$453$		−	2.46730e33i		−	1.55237i
$454$	5.88046e32			0.359926
$455$	1.28749e33	+	1.93333e33i	0.766657	+	1.15123i
$456$	−6.58999e32			−0.381789
$457$		−	4.66527e32i		−	0.262981i	−0.991317	−	0.131490i	$-0.958024\pi$
$457$		−	4.66527e32i		−	0.262981i	0.991317	−	0.131490i	$-0.0419763\pi$
$458$			1.53653e33i			0.842797i
$459$	−2.47313e33			−1.32004
$460$	−5.37782e32	+	3.58133e32i	−0.279340	+	0.186025i
$461$	1.54013e33			0.778566			0.389283	−	0.921118i	$-0.372723\pi$
$461$	1.54013e33			0.778566			0.389283	+	0.921118i	$0.372723\pi$
$462$			7.79528e32i			0.383537i
$463$			2.04979e33i			0.981628i	0.871264	+	0.490814i	$0.163301\pi$
$463$			2.04979e33i			0.981628i	−0.871264	+	0.490814i	$0.836699\pi$
$464$	3.13539e32			0.146156
$465$	3.09324e33	−	2.05993e33i	1.40363	−	0.934739i
$466$	−1.84903e33			−0.816806
$467$			1.89201e33i			0.813699i	0.913495	+	0.406849i	$0.133373\pi$
$467$			1.89201e33i			0.813699i	−0.913495	+	0.406849i	$0.866627\pi$
$468$		−	4.19916e32i		−	0.175828i
$469$	−5.52695e33			−2.25333
$470$	−1.25376e33	−	1.88268e33i	−0.497728	−	0.747402i
$471$	6.01378e32			0.232480
$472$		−	2.81580e32i		−	0.106005i
$473$			1.07893e33i			0.395574i
$474$	2.65875e32			0.0949399
$475$	1.02006e33	−	2.44126e33i	0.354777	−	0.849070i
$476$	−3.95314e33			−1.33923
$477$			1.09745e33i			0.362163i
$478$		−	7.28423e32i		−	0.234172i
$479$	−9.31244e32			−0.291655			−0.145828	−	0.989310i	$-0.546584\pi$
$479$	−9.31244e32			−0.291655			−0.145828	+	0.989310i	$0.546584\pi$
$480$	−3.76838e32	−	5.65870e32i	−0.114984	−	0.172664i
$481$	−1.21499e33			−0.361208
$482$			2.12307e32i			0.0615003i
$483$		−	4.13896e33i		−	1.16829i
$484$	1.64123e33			0.451443
$485$	2.42096e33	−	1.61222e33i	0.648957	−	0.432169i
$486$	1.94386e33			0.507822
$487$		−	1.90079e33i		−	0.483973i	−0.970280	−	0.241987i	$-0.922201\pi$
$487$		−	1.90079e33i		−	0.483973i	0.970280	−	0.241987i	$-0.0777990\pi$
$488$			2.16039e33i			0.536148i
$489$	−6.97611e33			−1.68754
$490$	−2.99484e33	+	1.99440e33i	−0.706192	+	0.470285i
$491$	−1.53089e32			−0.0351905			−0.0175953	−	0.999845i	$-0.505601\pi$
$491$	−1.53089e32			−0.0351905			−0.0175953	+	0.999845i	$0.505601\pi$
$492$		−	6.93461e32i		−	0.155403i
$493$		−	4.83223e33i		−	1.05575i
$494$	2.84857e33			0.606792
$495$	3.13608e32	+	4.70922e32i	0.0651362	+	0.0978103i
$496$	1.77393e33			0.359266
$497$			1.14217e34i			2.25568i
$498$		−	3.27554e33i		−	0.630836i
$499$	3.99567e33			0.750469			0.375234	−	0.926930i	$-0.377562\pi$
$499$	3.99567e33			0.750469			0.375234	+	0.926930i	$0.377562\pi$
$500$	2.67957e33	−	5.20089e32i	0.490840	−	0.0952692i
$501$	9.90908e32			0.177036
$502$		−	3.77666e33i		−	0.658130i
$503$			7.03745e33i			1.19623i	0.801410	+	0.598116i	$0.204084\pi$
$503$			7.03745e33i			1.19623i	−0.801410	+	0.598116i	$0.795916\pi$
$504$	1.19258e33			0.197746
$505$	−3.01840e33	−	4.53251e33i	−0.488241	−	0.733156i
$506$	9.37291e32			0.147908
$507$		−	9.93695e32i		−	0.152987i
$508$		−	5.94796e33i		−	0.893453i
$509$	−5.62123e32			−0.0823870			−0.0411935	−	0.999151i	$-0.513116\pi$
$509$	−5.62123e32			−0.0823870			−0.0411935	+	0.999151i	$0.513116\pi$
$510$	−8.72114e33	+	5.80779e33i	−1.24723	+	0.830584i
$511$	8.51832e33			1.18876
$512$		−	3.24519e32i		−	0.0441942i
$513$			5.06125e33i			0.672652i
$514$	1.07587e34			1.39547
$515$	−2.93941e33	+	1.95749e33i	−0.372109	+	0.247804i
$516$	6.02785e33			0.744803
$517$			3.28129e33i			0.395743i
$518$		−	3.45063e33i		−	0.406234i
$519$	−1.22139e34			−1.40366
$520$	1.62891e33	+	2.44601e33i	0.182749	+	0.274421i
$521$	1.15250e34			1.26232			0.631162	−	0.775651i	$-0.282578\pi$
$521$	1.15250e34			1.26232			0.631162	+	0.775651i	$0.282578\pi$
$522$			1.45779e33i			0.155888i
$523$			1.37858e34i			1.43933i	0.694323	+	0.719663i	$0.255704\pi$
$523$			1.37858e34i			1.43933i	−0.694323	+	0.719663i	$0.744296\pi$
$524$	5.22529e33			0.532683
$525$	−6.74128e33	+	1.61336e34i	−0.671044	+	1.60598i
$526$	−5.26289e33			−0.511567
$527$		−	2.73397e34i		−	2.59514i
$528$			9.86245e32i			0.0914241i
$529$	6.06915e33			0.549455
$530$	−4.25714e33	−	6.39264e33i	−0.376418	−	0.565239i
$531$	1.30920e33			0.113064
$532$			8.09009e33i			0.682430i
$533$			2.99754e33i			0.246987i
$534$	1.42090e34			1.14366
$535$	1.07928e34	−	7.18740e33i	0.848617	−	0.565132i
$536$	−6.99260e33			−0.537129
$537$		−	3.90559e33i		−	0.293095i
$538$		−	1.17911e34i		−	0.864525i
$539$	5.21966e33			0.373923
$540$	−4.34600e33	+	2.89419e33i	−0.304206	+	0.202584i
$541$	−2.20638e34			−1.50909			−0.754543	−	0.656251i	$-0.772141\pi$
$541$	−2.20638e34			−1.50909			−0.754543	+	0.656251i	$0.772141\pi$
$542$		−	2.65207e33i		−	0.177253i
$543$			1.19518e34i			0.780612i
$544$	−5.00145e33			−0.319234
$545$	1.38076e34	+	2.07339e34i	0.861316	+	1.29338i
$546$	−1.88254e34			−1.14772
$547$		−	1.59179e34i		−	0.948514i	−0.880387	−	0.474257i	$-0.842717\pi$
$547$		−	1.59179e34i		−	0.948514i	0.880387	−	0.474257i	$-0.157283\pi$
$548$			6.85982e33i			0.399536i
$549$	−1.00447e34			−0.571849
$550$	−3.65354e33	−	1.52660e33i	−0.203320	−	0.0849556i
$551$	−9.88915e33			−0.537977
$552$		−	5.23654e33i		−	0.278488i
$553$		−	3.26398e33i		−	0.169700i
$554$	−1.37640e34			−0.699637
$555$	−5.06951e33	−	7.61252e33i	−0.251944	−	0.378326i
$556$	4.46305e33			0.216869
$557$		−	1.37117e34i		−	0.651479i	−0.945460	−	0.325739i	$-0.894387\pi$
$557$		−	1.37117e34i		−	0.651479i	0.945460	−	0.325739i	$-0.105613\pi$
$558$			8.24783e33i			0.383188i
$559$	−2.60558e34			−1.18374
$560$	−6.94682e33	+	4.62619e33i	−0.308628	+	0.205529i
$561$	1.51999e34			0.660397
$562$		−	1.55488e34i		−	0.660681i
$563$		−	3.01185e34i		−	1.25164i	−0.779969	−	0.625818i	$-0.784765\pi$
$563$		−	3.01185e34i		−	1.25164i	0.779969	−	0.625818i	$-0.215235\pi$
$564$	1.83322e34			0.745121
$565$	2.00361e34	−	1.33430e34i	0.796542	−	0.530452i
$566$	9.26175e33			0.360153
$567$		−	4.81525e34i		−	1.83160i
$568$			1.44506e34i			0.537689i
$569$	−1.37959e34			−0.502166			−0.251083	−	0.967966i	$-0.580787\pi$
$569$	−1.37959e34			−0.502166			−0.251083	+	0.967966i	$0.580787\pi$
$570$	1.18856e34	+	1.78478e34i	0.423239	+	0.635548i
$571$	1.46730e34			0.511173			0.255587	−	0.966786i	$-0.417731\pi$
$571$	1.46730e34			0.511173			0.255587	+	0.966786i	$0.417731\pi$
$572$		−	4.26311e33i		−	0.145304i
$573$		−	6.31775e33i		−	0.210683i
$574$	−8.51317e33			−0.277775
$575$	1.93987e34	+	8.10560e33i	0.619335	+	0.258784i
$576$	1.50884e33			0.0471369
$577$			5.61780e34i			1.71739i	0.512488	+	0.858694i	$0.328724\pi$
$577$			5.61780e34i			1.71739i	−0.512488	+	0.858694i	$0.671276\pi$
$578$			5.34453e34i			1.59886i
$579$	1.74611e34			0.511199
$580$	−5.65495e33	−	8.49163e33i	−0.162024	−	0.243300i
$581$	−4.02117e34			−1.12759
$582$			2.35736e34i			0.646976i
$583$			1.11416e34i			0.299290i
$584$	1.07772e34			0.283365
$585$	−1.13726e34	+	7.57355e33i	−0.292694	+	0.194918i
$586$	−3.35969e34			−0.846407
$587$		−	3.79085e34i		−	0.934889i	−0.884022	−	0.467444i	$-0.845175\pi$
$587$		−	3.79085e34i		−	0.934889i	0.884022	−	0.467444i	$-0.154825\pi$
$588$		−	2.91617e34i		−	0.704037i
$589$	−5.59505e34			−1.32240
$590$	−7.62609e33	+	5.07855e33i	−0.176462	+	0.117514i
$591$	5.76471e34			1.30597
$592$		−	4.36567e33i		−	0.0968344i
$593$			1.87221e34i			0.406604i	0.979116	+	0.203302i	$0.0651673\pi$
$593$			1.87221e34i			0.406604i	−0.979116	+	0.203302i	$0.934833\pi$
$594$	7.57457e33			0.161075
$595$	7.12984e34	+	1.07064e35i	1.48463	+	2.22936i
$596$	−2.30154e33			−0.0469290
$597$			8.59057e33i			0.171531i
$598$			2.26353e34i			0.442611i
$599$	5.76089e34			1.10320			0.551601	−	0.834108i	$-0.314017\pi$
$599$	5.76089e34			1.10320			0.551601	+	0.834108i	$0.314017\pi$
$600$	−8.52895e33	+	2.04119e34i	−0.159958	+	0.382819i
$601$	4.67680e34			0.859049			0.429525	−	0.903055i	$-0.358681\pi$
$601$	4.67680e34			0.859049			0.429525	+	0.903055i	$0.358681\pi$
$602$		−	7.40000e34i		−	1.33130i
$603$		−	3.25118e34i		−	0.572895i
$604$	−3.83217e34			−0.661428
$605$	−2.96011e34	−	4.44498e34i	−0.500456	−	0.751498i
$606$	4.41344e34			0.730919
$607$		−	3.27875e33i		−	0.0531924i	−0.999646	−	0.0265962i	$-0.991533\pi$
$607$		−	3.27875e33i		−	0.0531924i	0.999646	−	0.0265962i	$-0.00846684\pi$
$608$			1.02354e34i			0.162672i
$609$	6.53546e34			1.01756
$610$	5.85103e34	−	3.89646e34i	0.892502	−	0.594356i
$611$	−7.92424e34			−1.18425
$612$		−	2.32540e34i		−	0.340491i
$613$			3.82074e34i			0.548140i	0.961710	+	0.274070i	$0.0883701\pi$
$613$			3.82074e34i			0.548140i	−0.961710	+	0.274070i	$0.911630\pi$
$614$	4.78916e34			0.673216
$615$	−1.87811e34	+	1.25072e34i	−0.258692	+	0.172274i
$616$	1.21075e34			0.163416
$617$			8.69280e34i			1.14973i	0.818249	+	0.574864i	$0.194945\pi$
$617$			8.69280e34i			1.14973i	−0.818249	+	0.574864i	$0.805055\pi$
$618$		−	2.86219e34i		−	0.370974i
$619$	3.61889e34			0.459666			0.229833	−	0.973230i	$-0.426182\pi$
$619$	3.61889e34			0.459666			0.229833	+	0.973230i	$0.426182\pi$
$620$	−3.19944e34	−	4.80437e34i	−0.398270	−	0.598054i
$621$	−4.02177e34			−0.490651
$622$			3.99528e34i			0.477713i
$623$		−	1.74434e35i		−	2.04424i
$624$	−2.38176e34			−0.273583
$625$	−6.24140e34	−	6.31910e34i	−0.702720	−	0.711467i
$626$	−8.76542e34			−0.967372
$627$		−	3.11066e34i		−	0.336517i
$628$		−	9.34049e33i		−	0.0990544i
$629$	−6.72833e34			−0.699478
$630$	−2.15093e34	−	3.22990e34i	−0.219215	−	0.329179i
$631$	−6.79781e34			−0.679207			−0.339604	−	0.940569i	$-0.610293\pi$
$631$	−6.79781e34			−0.679207			−0.339604	+	0.940569i	$0.610293\pi$
$632$		−	4.12953e33i		−	0.0404517i
$633$			6.67460e34i			0.641030i
$634$	1.17898e35			1.11017
$635$	−1.61090e35	+	1.07277e35i	−1.48729	+	0.990453i
$636$	6.22470e34			0.563514
$637$			1.26053e35i			1.11895i
$638$			1.47999e34i			0.128825i
$639$	−6.71875e34			−0.573492
$640$	−8.78899e33	+	5.85298e33i	−0.0735681	+	0.0489922i
$641$	−8.90435e34			−0.730932			−0.365466	−	0.930825i	$-0.619090\pi$
$641$	−8.90435e34			−0.730932			−0.365466	+	0.930825i	$0.619090\pi$
$642$			1.05093e35i			0.846028i
$643$			1.28997e35i			1.01846i	0.860630	+	0.509230i	$0.170070\pi$
$643$			1.28997e35i			1.01846i	−0.860630	+	0.509230i	$0.829930\pi$
$644$	−6.42856e34			−0.497783
$645$	−1.08718e35	−	1.63253e35i	−0.825665	−	1.23984i
$646$	1.57748e35			1.17505
$647$		−	1.39383e34i		−	0.101837i	−0.998703	−	0.0509186i	$-0.983785\pi$
$647$		−	1.39383e34i		−	0.101837i	0.998703	−	0.0509186i	$-0.0162149\pi$
$648$		−	6.09218e34i		−	0.436601i
$649$	1.32914e34			0.0934353
$650$	3.68670e34	−	8.82320e34i	0.254227	−	0.608428i
$651$	3.69761e35			2.50126
$652$			1.08352e35i			0.719020i
$653$		−	1.27030e35i		−	0.826970i	−0.910511	−	0.413485i	$-0.864311\pi$
$653$		−	1.27030e35i		−	0.826970i	0.910511	−	0.413485i	$-0.135689\pi$
$654$	−2.01892e35			−1.28943
$655$	−9.42427e34	−	1.41517e35i	−0.590516	−	0.886734i
$656$	−1.07707e34			−0.0662135
$657$			5.01083e34i			0.302234i
$658$		−	2.25053e35i		−	1.33187i
$659$	−4.18479e34			−0.243000			−0.121500	−	0.992591i	$-0.538770\pi$
$659$	−4.18479e34			−0.243000			−0.121500	+	0.992591i	$0.538770\pi$
$660$	2.67106e34	−	1.77878e34i	0.152190	−	0.101350i
$661$	−2.05843e34			−0.115085			−0.0575424	−	0.998343i	$-0.518326\pi$
$661$	−2.05843e34			−0.115085			−0.0575424	+	0.998343i	$0.518326\pi$
$662$		−	3.26002e34i		−	0.178853i
$663$			3.67074e35i			1.97621i
$664$	−5.08751e34			−0.268785
$665$	2.19105e35	−	1.45912e35i	1.13601	−	0.756520i
$666$	2.02980e34			0.103282
$667$		−	7.85813e34i		−	0.392415i
$668$		−	1.53906e34i		−	0.0754310i
$669$	4.25764e35			2.04806
$670$	1.26118e35	+	1.89382e35i	0.595444	+	0.894135i
$671$	−1.01976e35			−0.472573
$672$		−	6.76432e34i		−	0.307686i
$673$		−	1.99051e35i		−	0.888741i	−0.895843	−	0.444370i	$-0.853427\pi$
$673$		−	1.99051e35i		−	0.888741i	0.895843	−	0.444370i	$-0.146573\pi$
$674$	−2.42330e35			−1.06208
$675$	1.56768e35	+	6.55042e34i	0.674466	+	0.281820i
$676$	−1.54339e34			−0.0651841
$677$			3.44905e35i			1.43002i	0.699116	+	0.715008i	$0.253577\pi$
$677$			3.44905e35i			1.43002i	−0.699116	+	0.715008i	$0.746423\pi$
$678$			1.95098e35i			0.794111i
$679$	2.89397e35			1.15644
$680$	9.02055e34	+	1.35455e35i	0.353893	+	0.531415i
$681$	1.55078e35			0.597324
$682$			8.37345e34i			0.316665i
$683$		−	3.76388e35i		−	1.39758i	−0.715326	−	0.698791i	$-0.753722\pi$
$683$		−	3.76388e35i		−	1.39758i	0.715326	−	0.698791i	$-0.246278\pi$
$684$	−4.75893e34			−0.173503
$685$	1.85786e35	−	1.23723e35i	0.665089	−	0.442912i
$686$	−5.96407e34			−0.209648
$687$			4.05209e35i			1.39869i
$688$		−	9.36235e34i		−	0.317343i
$689$	−2.69067e35			−0.895613
$690$	−1.41822e35	+	9.44457e34i	−0.463586	+	0.308723i
$691$	−5.21059e35			−1.67268			−0.836338	−	0.548215i	$-0.815308\pi$
$691$	−5.21059e35			−1.67268			−0.836338	+	0.548215i	$0.815308\pi$
$692$			1.89704e35i			0.598068i
$693$			5.62933e34i			0.174297i
$694$	1.07435e35			0.326702
$695$	−8.04950e34	−	1.20873e35i	−0.240414	−	0.361011i
$696$	8.26855e34			0.242557
$697$			1.65997e35i			0.478290i
$698$			2.63015e35i			0.744368i
$699$	−4.87619e35			−1.35555
$700$	2.50584e35	+	1.04704e35i	0.684270	+	0.285917i
$701$	2.95057e35			0.791462			0.395731	−	0.918366i	$-0.370491\pi$
$701$	2.95057e35			0.791462			0.395731	+	0.918366i	$0.370491\pi$
$702$			1.82924e35i			0.482010i
$703$			1.37695e35i			0.356432i
$704$	1.53182e34			0.0389537
$705$	−3.30638e35	−	4.96495e35i	−0.826017	−	1.24037i
$706$	−1.50716e35			−0.369913
$707$		−	5.41809e35i		−	1.30648i
$708$		−	7.42575e34i		−	0.175924i
$709$	6.60823e35			1.53818			0.769090	−	0.639141i	$-0.220710\pi$
$709$	6.60823e35			1.53818			0.769090	+	0.639141i	$0.220710\pi$
$710$	3.91368e35	−	2.60629e35i	0.895067	−	0.596065i
$711$	1.92001e34			0.0431452
$712$		−	2.20691e35i		−	0.487287i
$713$		−	4.44595e35i		−	0.964595i
$714$	−1.04251e36			−2.22256
$715$	−1.15459e35	+	7.68890e34i	−0.241880	+	0.161079i
$716$	−6.06609e34			−0.124881
$717$		−	1.92097e35i		−	0.388626i
$718$		−	6.32916e35i		−	1.25832i
$719$	5.66102e35			1.10607			0.553036	−	0.833157i	$-0.313469\pi$
$719$	5.66102e35			1.10607			0.553036	+	0.833157i	$0.313469\pi$
$720$	−2.72132e34	−	4.08641e34i	−0.0522545	−	0.0784667i
$721$	−3.51373e35			−0.663097
$722$			5.84114e34i			0.108339i
$723$			5.59890e34i			0.102064i
$724$	1.85633e35			0.332601
$725$	−1.27988e35	+	3.06308e35i	−0.225395	+	0.539428i
$726$	4.32821e35			0.749205
$727$		−	1.18938e35i		−	0.202368i	−0.994868	−	0.101184i	$-0.967737\pi$
$727$		−	1.18938e35i		−	0.202368i	0.994868	−	0.101184i	$-0.0322631\pi$
$728$			2.92392e35i			0.489017i
$729$	−2.38517e35			−0.392126
$730$	−1.94377e35	−	2.91881e35i	−0.314129	−	0.471705i
$731$	−1.44292e36			−2.29231
$732$			5.69732e35i			0.889778i
$733$			2.75860e35i			0.423534i	0.977320	+	0.211767i	$0.0679219\pi$
$733$			2.75860e35i			0.423534i	−0.977320	+	0.211767i	$0.932078\pi$
$734$	−1.41358e35			−0.213364
$735$	−7.89790e35	+	5.25956e35i	−1.17198	+	0.780473i
$736$	−8.13330e34			−0.118657
$737$		−	3.30070e35i		−	0.473438i
$738$		−	5.00780e34i		−	0.0706224i
$739$	7.44302e35			1.03203			0.516017	−	0.856579i	$-0.327414\pi$
$739$	7.44302e35			1.03203			0.516017	+	0.856579i	$0.327414\pi$
$740$	−1.18236e35	+	7.87388e34i	−0.161196	+	0.107348i
$741$	7.51215e35			1.00702
$742$		−	7.64166e35i		−	1.00725i
$743$			9.71605e35i			1.25930i	0.776878	+	0.629651i	$0.216802\pi$
$743$			9.71605e35i			1.25930i	−0.776878	+	0.629651i	$0.783198\pi$
$744$	4.67816e35			0.596229
$745$	4.15104e34	+	6.23331e34i	0.0520239	+	0.0781206i
$746$	2.15044e35			0.265028
$747$		−	2.36542e35i		−	0.286682i
$748$		−	2.36082e35i		−	0.281380i
$749$	1.29015e36			1.51223
$750$	7.06647e35	−	1.37156e35i	0.814586	−	0.158106i
$751$	−3.81212e35			−0.432183			−0.216091	−	0.976373i	$-0.569331\pi$
$751$	−3.81212e35			−0.432183			−0.216091	+	0.976373i	$0.569331\pi$
$752$		−	2.84733e35i		−	0.317479i
$753$		−	9.95969e35i		−	1.09222i
$754$	−3.57414e35			−0.385505
$755$	6.91165e35	+	1.03787e36i	0.733238	+	1.10105i
$756$	−5.19514e35			−0.542094
$757$		−	1.20614e35i		−	0.123794i	−0.998083	−	0.0618968i	$-0.980285\pi$
$757$		−	1.20614e35i		−	0.123794i	0.998083	−	0.0618968i	$-0.0197150\pi$
$758$			1.28758e36i			1.29990i
$759$	2.47179e35			0.245465
$760$	2.77208e35	−	1.84605e35i	0.270792	−	0.180333i
$761$	−1.39110e36			−1.33675			−0.668374	−	0.743825i	$-0.733010\pi$
$761$	−1.39110e36			−1.33675			−0.668374	+	0.743825i	$0.733010\pi$
$762$		−	1.56858e36i		−	1.48275i
$763$			2.47849e36i			2.30479i
$764$	−9.81260e34			−0.0897671
$765$	−6.29793e35	+	4.19407e35i	−0.566800	+	0.377457i
$766$	1.00750e36			0.892040
$767$			3.20983e35i			0.279602i
$768$		−	8.55810e34i		−	0.0733436i
$769$	−5.62814e35			−0.474554			−0.237277	−	0.971442i	$-0.576255\pi$
$769$	−5.62814e35			−0.474554			−0.237277	+	0.971442i	$0.576255\pi$
$770$	−2.18369e35	−	3.27909e35i	−0.181158	−	0.272032i
$771$	2.83726e36			2.31589
$772$		−	2.71203e35i		−	0.217810i
$773$		−	1.08729e36i		−	0.859211i	−0.903017	−	0.429605i	$-0.858653\pi$
$773$		−	1.08729e36i		−	0.859211i	0.903017	−	0.429605i	$-0.141347\pi$
$774$	4.35299e35			0.338474
$775$	−7.24128e35	+	1.73302e36i	−0.554044	+	1.32597i
$776$	3.66141e35			0.275662
$777$		−	9.09988e35i		−	0.674175i
$778$			9.54037e35i			0.695537i
$779$	3.39713e35			0.243721
$780$	4.29571e35	+	6.45055e35i	0.303286	+	0.455422i
$781$	−6.82108e35			−0.473931
$782$			1.25350e36i			0.857114i
$783$		−	6.35042e35i		−	0.427347i
$784$	−4.52934e35			−0.299974
$785$	−2.52970e35	+	1.68464e35i	−0.164892	+	0.109809i
$786$	1.37800e36			0.884028
$787$		−	5.64847e35i		−	0.356654i	−0.983971	−	0.178327i	$-0.942932\pi$
$787$		−	5.64847e35i		−	0.356654i	0.983971	−	0.178327i	$-0.0570684\pi$
$788$		−	8.95364e35i		−	0.556445i
$789$	−1.38791e36			−0.848984
$790$	−1.11841e35	+	7.44796e34i	−0.0673381	+	0.0448434i
$791$	2.39509e36			1.41943
$792$			7.12213e34i			0.0415475i
$793$		−	2.46270e36i		−	1.41416i
$794$	−9.74916e35			−0.551075
$795$	−1.12268e36	−	1.68585e36i	−0.624694	−	0.938057i
$796$	1.33427e35			0.0730855
$797$		−	2.16083e34i		−	0.0116517i	−0.999983	−	0.00582587i	$-0.998146\pi$
$797$		−	2.16083e34i		−	0.0116517i	0.999983	−	0.00582587i	$-0.00185444\pi$
$798$			2.13349e36i			1.13254i
$799$	−4.38828e36			−2.29329
$800$	3.17034e35	+	1.32470e35i	0.163110	+	0.0681543i
$801$	1.02610e36			0.519734
$802$		−	2.30119e36i		−	1.14756i
$803$			5.08715e35i			0.249764i
$804$	−1.84407e36			−0.891407
$805$	1.15945e36	+	1.74106e36i	0.551826	+	0.828638i
$806$	−2.02217e36			−0.947608
$807$		−	3.10952e36i		−	1.43474i
$808$		−	6.85487e35i		−	0.311428i
$809$	3.34498e36			1.49637			0.748183	−	0.663493i	$-0.230927\pi$
$809$	3.34498e36			1.49637			0.748183	+	0.663493i	$0.230927\pi$
$810$	−1.64995e36	+	1.09878e36i	−0.726790	+	0.484002i
$811$	−3.06093e36			−1.32768			−0.663838	−	0.747876i	$-0.731074\pi$
$811$	−3.06093e36			−1.32768			−0.663838	+	0.747876i	$0.731074\pi$
$812$		−	1.01508e36i		−	0.433559i
$813$		−	6.99395e35i		−	0.294165i
$814$	2.06072e35			0.0853520
$815$	2.93451e36	−	1.95422e36i	1.19692	−	0.797082i
$816$	−1.31897e36			−0.529793
$817$			2.95292e36i			1.16809i
$818$		−	1.59803e36i		−	0.622542i
$819$	−1.35947e36			−0.521579
$820$	1.94259e35	+	2.91705e35i	0.0734021	+	0.110223i
$821$	4.35079e36			1.61912			0.809559	−	0.587039i	$-0.199706\pi$
$821$	4.35079e36			1.61912			0.809559	+	0.587039i	$0.199706\pi$
$822$			1.80905e36i			0.663060i
$823$			2.15419e35i			0.0777655i	0.999244	+	0.0388827i	$0.0123799\pi$
$823$			2.15419e35i			0.0777655i	−0.999244	+	0.0388827i	$0.987620\pi$
$824$	−4.44550e35			−0.158063
$825$	−9.63500e35	−	4.02590e35i	−0.337425	−	0.140990i
$826$	−9.11610e35			−0.314455
$827$		−	1.29774e36i		−	0.440929i	−0.975395	−	0.220465i	$-0.929243\pi$
$827$		−	1.29774e36i		−	0.440929i	0.975395	−	0.220465i	$-0.0707574\pi$
$828$		−	3.78155e35i		−	0.126558i
$829$	−2.45539e36			−0.809447			−0.404723	−	0.914439i	$-0.632632\pi$
$829$	−2.45539e36			−0.809447			−0.404723	+	0.914439i	$0.632632\pi$
$830$	9.17578e35	+	1.37786e36i	0.297966	+	0.447434i
$831$	−3.62980e36			−1.16110
$832$			3.69930e35i			0.116568i
$833$			6.98057e36i			2.16685i
$834$	1.17698e36			0.359910
$835$	−4.16826e35	+	2.77583e35i	−0.125567	+	0.0836203i
$836$	−4.83141e35			−0.143382
$837$		−	3.59292e36i		−	1.05046i
$838$			2.36500e36i			0.681211i
$839$	4.28477e36			1.21591			0.607957	−	0.793970i	$-0.291989\pi$
$839$	4.28477e36			1.21591			0.607957	+	0.793970i	$0.291989\pi$
$840$	−1.83199e36	+	1.22000e36i	−0.512192	+	0.341091i
$841$	−2.38956e36			−0.658214
$842$			3.86543e36i			1.04905i
$843$		−	4.10047e36i		−	1.09645i
$844$	1.03669e36			0.273128
$845$	2.78364e35	+	4.17999e35i	0.0722610	+	0.108509i
$846$	1.32386e36			0.338619
$847$		−	5.31346e36i		−	1.33917i
$848$		−	9.66810e35i		−	0.240100i
$849$	2.44248e36			0.597702
$850$	2.04162e36	−	4.88610e36i	0.492309	−	1.17822i
$851$	−1.09415e36			−0.259991
$852$			3.81086e36i			0.892336i
$853$			5.04634e36i			1.16443i	0.813035	+	0.582215i	$0.197814\pi$
$853$			5.04634e36i			1.16443i	−0.813035	+	0.582215i	$0.802186\pi$
$854$	6.99422e36			1.59043
$855$	8.58315e35	+	1.28887e36i	0.192340	+	0.288823i
$856$	1.63228e36			0.360473
$857$		−	1.55987e35i		−	0.0339491i	−0.999856	−	0.0169745i	$-0.994597\pi$
$857$		−	1.55987e35i		−	0.0339491i	0.999856	−	0.0169745i	$-0.00540342\pi$
$858$		−	1.12425e36i		−	0.241142i
$859$	6.31632e36			1.33521			0.667605	−	0.744516i	$-0.267320\pi$
$859$	6.31632e36			1.33521			0.667605	+	0.744516i	$0.267320\pi$
$860$	−2.53562e36	+	1.68858e36i	−0.528267	+	0.351797i
$861$	−2.24507e36			−0.460988
$862$		−	1.60048e36i		−	0.323898i
$863$		−	3.19641e36i		−	0.637569i	−0.947827	−	0.318785i	$-0.896725\pi$
$863$		−	3.19641e36i		−	0.637569i	0.947827	−	0.318785i	$-0.103275\pi$
$864$	−6.57280e35			−0.129220
$865$	5.13779e36	−	3.42148e36i	0.995577	−	0.662999i
$866$	−2.93967e36			−0.561467
$867$			1.40944e37i			2.65344i
$868$		−	5.74306e36i		−	1.06573i
$869$	1.94925e35			0.0356550
$870$	−1.49131e36	−	2.23939e36i	−0.268891	−	0.403774i
$871$	7.97111e36			1.41674
$872$			3.13575e36i			0.549396i
$873$			1.70236e36i			0.294017i
$874$	2.56527e36			0.436758
$875$	−1.68378e36	−	8.67504e36i	−0.282607	−	1.45603i
$876$	2.84214e36			0.470266
$877$			1.75514e36i			0.286297i	0.989701	+	0.143148i	$0.0457226\pi$
$877$			1.75514e36i			0.286297i	−0.989701	+	0.143148i	$0.954277\pi$
$878$		−	1.93768e36i		−	0.311602i
$879$	−8.86007e36			−1.40468
$880$	−2.76277e35	−	4.14865e35i	−0.0431828	−	0.0648445i
$881$	−1.15533e36			−0.178035			−0.0890177	−	0.996030i	$-0.528373\pi$
$881$	−1.15533e36			−0.178035			−0.0890177	+	0.996030i	$0.528373\pi$
$882$		−	2.10590e36i		−	0.319948i
$883$			2.62306e35i			0.0392916i	0.999807	+	0.0196458i	$0.00625386\pi$
$883$			2.62306e35i			0.0392916i	−0.999807	+	0.0196458i	$0.993746\pi$
$884$	5.70132e36			0.842020
$885$	−2.01113e36	+	1.33930e36i	−0.292852	+	0.195023i
$886$	−4.77170e36			−0.685096
$887$			1.26656e37i			1.79299i	0.443049	+	0.896497i	$0.353897\pi$
$887$			1.26656e37i			1.79299i	−0.443049	+	0.896497i	$0.646103\pi$
$888$		−	1.15130e36i		−	0.160704i
$889$	−1.92564e37			−2.65035
$890$	−5.97701e36	+	3.98036e36i	−0.811165	+	0.540191i
$891$	2.87568e36			0.384830
$892$		−	6.61288e36i		−	0.872630i
$893$			8.98059e36i			1.16859i
$894$	−6.06956e35			−0.0778822
$895$	1.09407e36	+	1.64289e36i	0.138439	+	0.207884i
$896$	−1.05062e36			−0.131098
$897$			5.96931e36i			0.734546i
$898$		−	5.38455e36i		−	0.653424i
$899$	7.02019e36			0.840142
$900$	−6.15915e35	+	1.47404e36i	−0.0726925	+	0.173971i
$901$	−1.49004e37			−1.73435
$902$		−	5.08408e35i		−	0.0583620i
$903$		−	1.95150e37i		−	2.20939i
$904$	3.03022e36			0.338352
$905$	−3.34805e36	−	5.02753e36i	−0.368710	−	0.553665i
$906$	−1.01061e37			−1.09769
$907$			1.10945e37i			1.18855i	0.804262	+	0.594275i	$0.202561\pi$
$907$			1.10945e37i			1.18855i	−0.804262	+	0.594275i	$0.797439\pi$
$908$		−	2.40864e36i		−	0.254506i
$909$	3.18715e36			0.332165
$910$	7.91891e36	−	5.27355e36i	0.814045	−	0.542108i
$911$	−6.00569e36			−0.608952			−0.304476	−	0.952520i	$-0.598481\pi$
$911$	−6.00569e36			−0.608952			−0.304476	+	0.952520i	$0.598481\pi$
$912$			2.69926e36i			0.269966i
$913$		−	2.40145e36i		−	0.236913i
$914$	−1.91089e36			−0.185956
$915$	1.54301e37	−	1.02756e37i	1.48117	−	0.986379i
$916$	6.29363e36			0.595947
$917$		−	1.69167e37i		−	1.58016i
$918$			1.01299e37i			0.933411i
$919$	−8.07538e36			−0.734039			−0.367020	−	0.930213i	$-0.619622\pi$
$919$	−8.07538e36			−0.734039			−0.367020	+	0.930213i	$0.619622\pi$
$920$	1.46691e36	+	2.20276e36i	0.131540	+	0.197523i
$921$	1.26298e37			1.11725
$922$		−	6.30837e36i		−	0.550529i
$923$		−	1.64727e37i		−	1.41822i
$924$	3.19295e36			0.271201
$925$	4.26499e36	+	1.78209e36i	0.357393	+	0.149334i
$926$	8.39594e36			0.694116
$927$		−	2.06692e36i		−	0.168588i
$928$		−	1.28426e36i		−	0.103348i
$929$	−1.77412e37			−1.40860			−0.704299	−	0.709903i	$-0.748739\pi$
$929$	−1.77412e37			−1.40860			−0.704299	+	0.709903i	$0.748739\pi$
$930$	−8.43747e36	−	1.26699e37i	−0.660960	−	0.992515i
$931$	1.42857e37			1.10416
$932$			7.57361e36i			0.577569i
$933$			1.05362e37i			0.792801i
$934$	7.74969e36			0.575372
$935$	−6.39385e36	+	4.25795e36i	−0.468401	+	0.311929i
$936$	−1.71997e36			−0.124329
$937$			1.54851e37i			1.10451i	0.833676	+	0.552254i	$0.186232\pi$
$937$			1.54851e37i			1.10451i	−0.833676	+	0.552254i	$0.813768\pi$
$938$			2.26384e37i			1.59335i
$939$	−2.31159e37			−1.60543
$940$	−7.71147e36	+	5.13541e36i	−0.528493	+	0.351947i
$941$	6.87286e36			0.464801			0.232400	−	0.972620i	$-0.425342\pi$
$941$	6.87286e36			0.464801			0.232400	+	0.972620i	$0.425342\pi$
$942$		−	2.46324e36i		−	0.164388i
$943$			2.69943e36i			0.177777i
$944$	−1.15335e36			−0.0749570
$945$	9.36989e36	+	1.40701e37i	0.600948	+	0.902400i
$946$	4.41929e36			0.279713
$947$		−	6.52055e36i		−	0.407295i	−0.979044	−	0.203648i	$-0.934720\pi$
$947$		−	6.52055e36i		−	0.407295i	0.979044	−	0.203648i	$-0.0652797\pi$
$948$		−	1.08903e36i		−	0.0671326i
$949$	−1.22853e37			−0.747410
$950$	−9.99939e36	−	4.17816e36i	−0.600383	−	0.250865i
$951$	3.10917e37			1.84242
$952$			1.61921e37i			0.946979i
$953$		−	8.60992e36i		−	0.496979i	−0.968635	−	0.248489i	$-0.920066\pi$
$953$		−	8.60992e36i		−	0.496979i	0.968635	−	0.248489i	$-0.0799341\pi$
$954$	4.49515e36			0.256088
$955$	1.76979e36	+	2.65756e36i	0.0995129	+	0.149431i
$956$	−2.98362e36			−0.165585
$957$			3.90299e36i			0.213795i
$958$			3.81438e36i			0.206231i
$959$	2.22085e37			1.18519
$960$	−2.31780e36	+	1.54353e36i	−0.122092	+	0.0813063i
$961$	2.04858e37			1.06515
$962$			4.97658e36i			0.255413i
$963$			7.58922e36i			0.384476i
$964$	8.69611e35			0.0434872
$965$	−7.34503e36	+	4.89138e36i	−0.362579	+	0.241457i
$966$	−1.69532e37			−0.826109
$967$			1.52261e37i			0.732415i	0.930533	+	0.366208i	$0.119344\pi$
$967$			1.52261e37i			0.732415i	−0.930533	+	0.366208i	$0.880656\pi$
$968$		−	6.72249e36i		−	0.319219i
$969$	4.16007e37			1.95008
$970$	−6.60367e36	−	9.91625e36i	−0.305590	−	0.458882i
$971$	−1.36186e37			−0.622145			−0.311072	−	0.950386i	$-0.600688\pi$
$971$	−1.36186e37			−0.622145			−0.311072	+	0.950386i	$0.600688\pi$
$972$		−	7.96204e36i		−	0.359084i
$973$		−	1.44490e37i		−	0.643321i
$974$	−7.78562e36			−0.342221
$975$	9.72245e36	−	2.32683e37i	0.421908	−	1.00973i
$976$	8.84897e36			0.379114
$977$		−	1.77242e37i		−	0.749696i	−0.927086	−	0.374848i	$-0.877695\pi$
$977$		−	1.77242e37i		−	0.749696i	0.927086	−	0.374848i	$-0.122305\pi$
$978$			2.85742e37i			1.19327i
$979$	1.04172e37			0.429505
$980$	8.16906e36	+	1.22669e37i	0.332542	+	0.499354i
$981$	−1.45795e37			−0.585978
$982$			6.27053e35i			0.0248835i
$983$			1.62613e37i			0.637140i	0.947899	+	0.318570i	$0.103203\pi$
$983$			1.62613e37i			0.637140i	−0.947899	+	0.318570i	$0.896797\pi$
$984$	−2.84042e36			−0.109886
$985$	−2.42493e37	+	1.61487e37i	−0.926289	+	0.616857i
$986$	−1.97928e37			−0.746528
$987$		−	5.93502e37i		−	2.21033i
$988$		−	1.16677e37i		−	0.429066i
$989$	−2.34645e37			−0.852037
$990$	1.92890e36	−	1.28454e36i	0.0691623	−	0.0460582i
$991$	−2.62346e37			−0.928869			−0.464434	−	0.885608i	$-0.653742\pi$
$991$	−2.62346e37			−0.928869			−0.464434	+	0.885608i	$0.653742\pi$
$992$		−	7.26602e36i		−	0.254039i
$993$		−	8.59723e36i		−	0.296820i
$994$	4.67835e37			1.59501
$995$	−2.40648e36	−	3.61363e36i	−0.0810202	−	0.121662i
$996$	−1.34166e37			−0.446069
$997$		−	4.75249e37i		−	1.56038i	−0.625540	−	0.780192i	$-0.715121\pi$
$997$		−	4.75249e37i		−	1.56038i	0.625540	−	0.780192i	$-0.284879\pi$
$998$		−	1.63663e37i		−	0.530662i
$999$	−8.84223e36			−0.283135

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	10.26.b.a.9.2	✓	12
5.2	odd	4		50.26.a.l.1.2		6
5.3	odd	4		50.26.a.k.1.5		6
5.4	even	2	inner	10.26.b.a.9.11	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.26.b.a.9.2	✓	12	1.1	even	1	trivial
10.26.b.a.9.11	yes	12	5.4	even	2	inner
50.26.a.k.1.5		6	5.3	odd	4
50.26.a.l.1.2		6	5.2	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} -1.08018e6i q^{3} -1.67772e7 q^{4} +(3.02592e8 + 4.54380e8i) q^{5} -4.42443e9 q^{6} +5.43159e10i q^{7} +6.87195e10i q^{8} -3.19509e11 q^{9} +(1.86114e12 - 1.23942e12i) q^{10} -3.24375e12 q^{11} +1.81225e13i q^{12} -7.83357e13i q^{13} +2.22478e14 q^{14} +(4.90814e14 - 3.26855e14i) q^{15} +2.81475e14 q^{16} -4.33806e15i q^{17} +1.30871e15i q^{18} -8.87783e15 q^{19} +(-5.07665e15 - 7.62323e15i) q^{20} +5.86711e16 q^{21} +1.32864e16i q^{22} -7.05451e16i q^{23} +7.42297e16 q^{24} +(-1.14900e17 + 2.74984e17i) q^{25} -3.20863e17 q^{26} -5.70099e17i q^{27} -9.11269e17i q^{28} +1.11391e18 q^{29} +(-1.33880e18 - 2.01037e18i) q^{30} +6.30227e18 q^{31} -1.15292e18i q^{32} +3.50385e18i q^{33} -1.77687e19 q^{34} +(-2.46800e19 + 1.64355e19i) q^{35} +5.36047e18 q^{36} -1.55100e19i q^{37} +3.63636e19i q^{38} -8.46169e19 q^{39} +(-3.12248e19 + 2.07940e19i) q^{40} -3.82653e19 q^{41} -2.40317e20i q^{42} -3.32618e20i q^{43} +5.44211e19 q^{44} +(-9.66807e19 - 1.45178e20i) q^{45} -2.88953e20 q^{46} -1.01157e21i q^{47} -3.04045e20i q^{48} -1.60914e21 q^{49} +(1.12633e21 + 4.70628e20i) q^{50} -4.68591e21 q^{51} +1.31425e21i q^{52} -3.43480e21i q^{53} -2.33513e21 q^{54} +(-9.81532e20 - 1.47390e21i) q^{55} -3.73256e21 q^{56} +9.58969e21i q^{57} -4.56259e21i q^{58} -4.09753e21 q^{59} +(-8.23450e21 + 5.48371e21i) q^{60} +3.14378e22 q^{61} -2.58141e22i q^{62} -1.73544e22i q^{63} -4.72237e21 q^{64} +(3.55942e22 - 2.37037e22i) q^{65} +1.43518e22 q^{66} +1.01756e23i q^{67} +7.27806e22i q^{68} -7.62017e22 q^{69} +(6.73200e22 + 1.01089e23i) q^{70} +2.10284e23 q^{71} -2.19565e22i q^{72} -1.56829e23i q^{73} -6.35289e22 q^{74} +(2.97033e23 + 1.24113e23i) q^{75} +1.48945e23 q^{76} -1.76187e23i q^{77} +3.46591e23i q^{78} -6.00925e22 q^{79} +(8.51720e22 + 1.27897e23i) q^{80} -8.86528e23 q^{81} +1.56735e23i q^{82} +7.40331e23i q^{83} -9.84338e23 q^{84} +(1.97113e24 - 1.31266e24i) q^{85} -1.36240e24 q^{86} -1.20323e24i q^{87} -2.22909e23i q^{88} -3.21148e24 q^{89} +(-5.94651e23 + 3.96004e23i) q^{90} +4.25487e24 q^{91} +1.18355e24i q^{92} -6.80761e24i q^{93} -4.14341e24 q^{94} +(-2.68636e24 - 4.03391e24i) q^{95} -1.24537e24 q^{96} -5.32805e24i q^{97} +6.59105e24i q^{98} +1.03641e24 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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