LMFDB - Embedded newform 10.26.b.a.9.11

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

$q$-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	$0.199592\pi$
$3$			1.08018e6i			1.17350i	−0.809769	+	0.586749i	$0.800408\pi$
$4$	−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	$-0.734066\pi$
$7$		−	5.43159e10i		−	1.48320i	0.670840	−	0.741602i	$-0.265934\pi$
$8$		−	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	$0.154403\pi$
$13$			7.83357e13i			0.932541i	−0.884642	+	0.466270i	$0.845597\pi$
$14$	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	$0.358589\pi$
$17$			4.33806e15i			1.80586i	−0.429786	+	0.902931i	$0.641411\pi$
$18$		−	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	$0.108944\pi$
$23$			7.05451e16i			0.671227i	−0.942000	+	0.335613i	$0.891056\pi$
$24$	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	$0.0620387\pi$
$37$			1.55100e19i			0.387338i	−0.981067	+	0.193669i	$0.937961\pi$
$38$		−	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	$0.218871\pi$
$43$			3.32618e20i			1.26937i	−0.772770	+	0.634687i	$0.781129\pi$
$44$	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	$0.218982\pi$
$47$			1.01157e21i			1.26992i	−0.772547	+	0.634958i	$0.781018\pi$
$48$			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	$0.159436\pi$
$53$			3.43480e21i			0.960401i	−0.877159	+	0.480201i	$0.840564\pi$
$54$	−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	$-0.725387\pi$
$67$		−	1.01756e23i		−	1.51923i	0.650372	−	0.759616i	$-0.274613\pi$
$68$		−	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	$0.131247\pi$
$73$			1.56829e23i			0.801478i	−0.916192	+	0.400739i	$0.868753\pi$
$74$	−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	$-0.875883\pi$
$83$		−	7.40331e23i		−	0.760238i	0.924938	−	0.380119i	$-0.124117\pi$
$84$	−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	$0.127471\pi$
$97$			5.32805e24i			0.779689i	−0.920881	+	0.389844i	$0.872529\pi$
$98$		−	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	$-0.928240\pi$
$103$		−	6.46906e24i		−	0.447070i	0.974696	−	0.223535i	$-0.0717598\pi$
$104$	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	$0.170275\pi$
$107$			2.37528e25i			1.01957i	−0.860302	+	0.509786i	$0.829725\pi$
$108$		−	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	$0.158820\pi$
$113$			4.40956e25i			0.957005i	−0.878086	+	0.478503i	$0.841180\pi$
$114$	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	$-0.648276\pi$
$127$		−	3.54526e26i		−	1.78691i	0.449157	−	0.893453i	$-0.351724\pi$
$128$		−	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	$0.130829\pi$
$137$			4.08877e26i			0.799072i	−0.916718	+	0.399536i	$0.869171\pi$
$138$		−	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	$-0.968418\pi$
$157$		−	5.56736e26i		−	0.198109i	0.995082	−	0.0990544i	$-0.0315818\pi$
$158$		−	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	$0.255409\pi$
$163$			6.45827e27i			1.43804i	−0.694990	+	0.719020i	$0.744591\pi$
$164$	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	$-0.975967\pi$
$167$		−	9.17351e26i		−	0.150862i	0.997151	−	0.0754310i	$-0.0240332\pi$
$168$		−	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	$0.204065\pi$
$173$			1.13072e28i			1.19614i	−0.801445	+	0.598068i	$0.795935\pi$
$174$	−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	$-0.930109\pi$
$193$		−	1.61649e28i		−	0.435620i	0.975991	−	0.217810i	$-0.0698913\pi$
$194$	−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	$-0.812165\pi$
$197$		−	5.33679e28i		−	1.11289i	0.830885	−	0.556445i	$-0.187835\pi$
$198$			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	$-0.662413\pi$
$223$		−	3.94158e29i		−	1.74526i	0.488382	−	0.872630i	$-0.337587\pi$
$224$	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	$-0.918087\pi$
$227$		−	1.43566e29i		−	0.509012i	0.967071	−	0.254506i	$-0.0819129\pi$
$228$			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	$0.195999\pi$
$233$			4.51422e29i			1.15514i	−0.816342	+	0.577569i	$0.804001\pi$
$234$	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	$-0.551877\pi$
$257$		−	2.62664e30i		−	1.97350i	0.162254	−	0.986749i	$-0.448123\pi$
$258$		−	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	$0.117815\pi$
$263$			1.28488e30i			0.723465i	−0.932282	+	0.361732i	$0.882185\pi$
$264$	−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	$0.164729\pi$
$277$			3.36035e30i			0.989436i	−0.869054	+	0.494718i	$0.835271\pi$
$278$		−	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	$-0.918034\pi$
$283$		−	2.26117e30i		−	0.509334i	0.967029	−	0.254667i	$-0.0819658\pi$
$284$	−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	$0.204236\pi$
$293$			8.20237e30i			1.19700i	−0.801123	+	0.598500i	$0.795764\pi$
$294$	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	$-0.842073\pi$
$307$		−	1.16923e31i		−	0.952072i	0.879426	−	0.476036i	$-0.157927\pi$
$308$		−	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	$0.239776\pi$
$313$			2.13999e31i			1.36807i	−0.729449	+	0.684035i	$0.760224\pi$
$314$	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	$-0.712657\pi$
$317$		−	2.87837e31i		−	1.57002i	0.619482	−	0.785011i	$-0.287343\pi$
$318$		−	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	$0.270431\pi$
$337$			5.91626e31i			1.50201i	−0.660295	+	0.751006i	$0.729569\pi$
$338$			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	$-0.925796\pi$
$347$		−	2.62292e31i		−	0.462026i	0.972951	−	0.231013i	$-0.0742039\pi$
$348$		−	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	$0.0842396\pi$
$353$			3.67958e31i			0.523136i	−0.965185	+	0.261568i	$0.915760\pi$
$354$	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	$0.0482078\pi$
$367$			3.45113e31i			0.301742i	−0.988553	+	0.150871i	$0.951792\pi$
$368$			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	$-0.939993\pi$
$373$		−	5.25010e31i		−	0.374807i	0.982283	−	0.187403i	$-0.0600072\pi$
$374$	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	$-0.782740\pi$
$383$		−	2.45971e32i		−	1.26154i	0.775972	−	0.630768i	$-0.217260\pi$
$384$	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	$0.127411\pi$
$397$			2.38017e32i			0.779338i	−0.920955	+	0.389669i	$0.872589\pi$
$398$		−	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	$0.129955\pi$
$433$			7.17692e32i			0.794034i	−0.917811	+	0.397017i	$0.870045\pi$
$434$	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	$0.160975\pi$
$443$			1.16496e33i			0.968871i	−0.874827	+	0.484436i	$0.839025\pi$
$444$	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	$0.0419763\pi$
$457$			4.66527e32i			0.262981i	−0.991317	+	0.131490i	$0.958024\pi$
$458$		−	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	$-0.836699\pi$
$463$		−	2.04979e33i		−	0.981628i	0.871264	−	0.490814i	$-0.163301\pi$
$464$	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	$-0.866627\pi$
$467$		−	1.89201e33i		−	0.813699i	0.913495	−	0.406849i	$-0.133373\pi$
$468$			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	$0.0777990\pi$
$487$			1.90079e33i			0.483973i	−0.970280	+	0.241987i	$0.922201\pi$
$488$		−	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	$-0.795916\pi$
$503$		−	7.03745e33i		−	1.19623i	0.801410	−	0.598116i	$-0.204084\pi$
$504$	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	$-0.744296\pi$
$523$		−	1.37858e34i		−	1.43933i	0.694323	−	0.719663i	$-0.255704\pi$
$524$	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	$0.157283\pi$
$547$			1.59179e34i			0.948514i	−0.880387	+	0.474257i	$0.842717\pi$
$548$		−	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	$0.105613\pi$
$557$			1.37117e34i			0.651479i	−0.945460	+	0.325739i	$0.894387\pi$
$558$		−	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	$0.215235\pi$
$563$			3.01185e34i			1.25164i	−0.779969	+	0.625818i	$0.784765\pi$
$564$	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	$-0.671276\pi$
$577$		−	5.61780e34i		−	1.71739i	0.512488	−	0.858694i	$-0.328724\pi$
$578$		−	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	$0.154825\pi$
$587$			3.79085e34i			0.934889i	−0.884022	+	0.467444i	$0.845175\pi$
$588$			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	$-0.934833\pi$
$593$		−	1.87221e34i		−	0.406604i	0.979116	−	0.203302i	$-0.0651673\pi$
$594$	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	$0.00846684\pi$
$607$			3.27875e33i			0.0531924i	−0.999646	+	0.0265962i	$0.991533\pi$
$608$		−	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	$-0.911630\pi$
$613$		−	3.82074e34i		−	0.548140i	0.961710	−	0.274070i	$-0.0883701\pi$
$614$	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	$-0.805055\pi$
$617$		−	8.69280e34i		−	1.14973i	0.818249	−	0.574864i	$-0.194945\pi$
$618$			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	$-0.829930\pi$
$643$		−	1.28997e35i		−	1.01846i	0.860630	−	0.509230i	$-0.170070\pi$
$644$	−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	$0.0162149\pi$
$647$			1.39383e34i			0.101837i	−0.998703	+	0.0509186i	$0.983785\pi$
$648$			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	$0.135689\pi$
$653$			1.27030e35i			0.826970i	−0.910511	+	0.413485i	$0.864311\pi$
$654$	−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	$0.146573\pi$
$673$			1.99051e35i			0.888741i	−0.895843	+	0.444370i	$0.853427\pi$
$674$	−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	$-0.746423\pi$
$677$		−	3.44905e35i		−	1.43002i	0.699116	−	0.715008i	$-0.253577\pi$
$678$		−	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	$0.246278\pi$
$683$			3.76388e35i			1.39758i	−0.715326	+	0.698791i	$0.753722\pi$
$684$	−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	$0.0322631\pi$
$727$			1.18938e35i			0.202368i	−0.994868	+	0.101184i	$0.967737\pi$
$728$		−	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	$-0.932078\pi$
$733$		−	2.75860e35i		−	0.423534i	0.977320	−	0.211767i	$-0.0679219\pi$
$734$	−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	$-0.783198\pi$
$743$		−	9.71605e35i		−	1.25930i	0.776878	−	0.629651i	$-0.216802\pi$
$744$	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	$0.0197150\pi$
$757$			1.20614e35i			0.123794i	−0.998083	+	0.0618968i	$0.980285\pi$
$758$		−	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	$0.141347\pi$
$773$			1.08729e36i			0.859211i	−0.903017	+	0.429605i	$0.858653\pi$
$774$	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	$0.0570684\pi$
$787$			5.64847e35i			0.356654i	−0.983971	+	0.178327i	$0.942932\pi$
$788$			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	$0.00185444\pi$
$797$			2.16083e34i			0.0116517i	−0.999983	+	0.00582587i	$0.998146\pi$
$798$		−	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	$-0.987620\pi$
$823$		−	2.15419e35i		−	0.0777655i	0.999244	−	0.0388827i	$-0.0123799\pi$
$824$	−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	$0.0707574\pi$
$827$			1.29774e36i			0.440929i	−0.975395	+	0.220465i	$0.929243\pi$
$828$			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	$-0.802186\pi$
$853$		−	5.04634e36i		−	1.16443i	0.813035	−	0.582215i	$-0.197814\pi$
$854$	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	$0.00540342\pi$
$857$			1.55987e35i			0.0339491i	−0.999856	+	0.0169745i	$0.994597\pi$
$858$			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	$0.103275\pi$
$863$			3.19641e36i			0.637569i	−0.947827	+	0.318785i	$0.896725\pi$
$864$	−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	$-0.954277\pi$
$877$		−	1.75514e36i		−	0.286297i	0.989701	−	0.143148i	$-0.0457226\pi$
$878$			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	$-0.993746\pi$
$883$		−	2.62306e35i		−	0.0392916i	0.999807	−	0.0196458i	$-0.00625386\pi$
$884$	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	$-0.646103\pi$
$887$		−	1.26656e37i		−	1.79299i	0.443049	−	0.896497i	$-0.353897\pi$
$888$			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	$-0.797439\pi$
$907$		−	1.10945e37i		−	1.18855i	0.804262	−	0.594275i	$-0.202561\pi$
$908$			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	$-0.813768\pi$
$937$		−	1.54851e37i		−	1.10451i	0.833676	−	0.552254i	$-0.186232\pi$
$938$		−	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	$0.0652797\pi$
$947$			6.52055e36i			0.407295i	−0.979044	+	0.203648i	$0.934720\pi$
$948$			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	$0.0799341\pi$
$953$			8.60992e36i			0.496979i	−0.968635	+	0.248489i	$0.920066\pi$
$954$	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	$-0.880656\pi$
$967$		−	1.52261e37i		−	0.732415i	0.930533	−	0.366208i	$-0.119344\pi$
$968$			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	$0.122305\pi$
$977$			1.77242e37i			0.749696i	−0.927086	+	0.374848i	$0.877695\pi$
$978$		−	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	$-0.896797\pi$
$983$		−	1.62613e37i		−	0.637140i	0.947899	−	0.318570i	$-0.103203\pi$
$984$	−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	$0.284879\pi$
$997$			4.75249e37i			1.56038i	−0.625540	+	0.780192i	$0.715121\pi$
$998$			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.9.11	yes	12
5.2	odd	4		50.26.a.k.1.5		6
5.3	odd	4		50.26.a.l.1.2		6
5.4	even	2	inner	10.26.b.a.9.2	✓	12

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