LMFDB - Embedded newform 84.12.k.b.5.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [84,12,Mod(5,84)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(84, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 5]))

N = Newforms(chi, 12, names="a")

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

chi := DirichletCharacter("84.5");

S:= CuspForms(chi, 12);

N := Newforms(S);

Level:	$ N $	$=$	$ 84 = 2^{2} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 12 $
Character orbit:	$[\chi]$	$=$	84.k (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$64.5408271670$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$28$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			5.7
Character	$\chi$	$=$	84.5
Dual form			84.12.k.b.17.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-293.330 + 301.836i) q^{3} +(2288.66 - 3964.07i) q^{5} +(14878.7 - 41904.1i) q^{7} +(-5062.60 - 177075. i) q^{9} +O(q^{10})$	\(q+(-293.330 + 301.836i) q^{3} +(2288.66 - 3964.07i) q^{5} +(14878.7 - 41904.1i) q^{7} +(-5062.60 - 177075. i) q^{9} +(602411. - 347802. i) q^{11} -801797. i q^{13} +(525167. + 1.85358e6i) q^{15} +(-1.69093e6 - 2.92878e6i) q^{17} +(3.34762e6 + 1.93275e6i) q^{19} +(8.28378e6 + 1.67826e7i) q^{21} +(-5.01711e7 - 2.89663e7i) q^{23} +(1.39382e7 + 2.41416e7i) q^{25} +(5.49325e7 + 5.04131e7i) q^{27} +1.26218e8i q^{29} +(-1.25812e7 + 7.26374e6i) q^{31} +(-7.17258e7 + 2.83850e8i) q^{33} +(-1.32058e8 - 1.54884e8i) q^{35} +(4.28757e7 - 7.42629e7i) q^{37} +(2.42011e8 + 2.35191e8i) q^{39} -6.77955e7 q^{41} -1.47763e8 q^{43} +(-7.13522e8 - 3.85194e8i) q^{45} +(-1.13191e8 + 1.96052e8i) q^{47} +(-1.53458e9 - 1.24696e9i) q^{49} +(1.38001e9 + 3.48714e8i) q^{51} +(4.20156e9 - 2.42577e9i) q^{53} -3.18400e9i q^{55} +(-1.56533e9 + 4.43499e8i) q^{57} +(-3.05171e9 - 5.28571e9i) q^{59} +(-5.23135e9 - 3.02032e9i) q^{61} +(-7.49547e9 - 2.42250e9i) q^{63} +(-3.17838e9 - 1.83504e9i) q^{65} +(-3.71415e9 - 6.43309e9i) q^{67} +(2.34597e10 - 6.64677e9i) q^{69} +1.70389e10i q^{71} +(-9.84429e9 + 5.68361e9i) q^{73} +(-1.13753e10 - 2.87441e9i) q^{75} +(-5.61123e9 - 3.04183e10i) q^{77} +(-1.28443e10 + 2.22470e10i) q^{79} +(-3.13298e10 + 1.79292e9i) q^{81} +6.44662e9 q^{83} -1.54798e10 q^{85} +(-3.80971e10 - 3.70234e10i) q^{87} +(1.05174e10 - 1.82167e10i) q^{89} +(-3.35986e10 - 1.19297e10i) q^{91} +(1.49797e9 - 5.92812e9i) q^{93} +(1.53231e10 - 8.84679e9i) q^{95} -1.27882e11i q^{97} +(-6.46367e10 - 1.04911e11i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 729 q^{3} - 27194 q^{7} - 172347 q^{9}+O(q^{10}) $ 56 * q - 729 * q^3 - 27194 * q^7 - 172347 * q^9	$ 56 q - 729 q^{3} - 27194 q^{7} - 172347 q^{9} - 4853058 q^{15} + 28700520 q^{19} - 11325429 q^{21} - 316601194 q^{25} - 1368416388 q^{31} + 40874949 q^{33} - 87435712 q^{37} + 1177474410 q^{39} - 3055078348 q^{43} + 4109921793 q^{45} - 742582522 q^{49} - 694793715 q^{51} + 14605100370 q^{57} + 72584834058 q^{61} - 7310837811 q^{63} + 6131679148 q^{67} - 74402605464 q^{73} - 161115157854 q^{75} + 52181713528 q^{79} + 44948282337 q^{81} + 4658488716 q^{85} + 243101263104 q^{87} - 85311757146 q^{91} - 256628211777 q^{93} + 157345775874 q^{99}+O(q^{100}) $ 56 * q - 729 * q^3 - 27194 * q^7 - 172347 * q^9 - 4853058 * q^15 + 28700520 * q^19 - 11325429 * q^21 - 316601194 * q^25 - 1368416388 * q^31 + 40874949 * q^33 - 87435712 * q^37 + 1177474410 * q^39 - 3055078348 * q^43 + 4109921793 * q^45 - 742582522 * q^49 - 694793715 * q^51 + 14605100370 * q^57 + 72584834058 * q^61 - 7310837811 * q^63 + 6131679148 * q^67 - 74402605464 * q^73 - 161115157854 * q^75 + 52181713528 * q^79 + 44948282337 * q^81 + 4658488716 * q^85 + 243101263104 * q^87 - 85311757146 * q^91 - 256628211777 * q^93 + 157345775874 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/84\mathbb{Z}\right)^\times$.

$n$	$29$	$43$	$73$
$\chi(n)$	$-1$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−293.330	+	301.836i	−0.696930	+	0.717140i
$3$	−293.330	+	301.836i	−0.696930	+	0.717140i
$4$		0			0
$5$	2288.66	−	3964.07i	0.327526	−	0.567291i	−0.654495	−	0.756067i	$-0.727119\pi$
$5$	2288.66	−	3964.07i	0.327526	−	0.567291i	0.982020	+	0.188776i	$0.0604519\pi$
$6$		0			0
$7$	14878.7	−	41904.1i	0.334600	−	0.942360i
$7$	14878.7	−	41904.1i	0.334600	−	0.942360i
$8$		0			0
$9$	−5062.60	−	177075.i	−0.0285785	−	0.999592i
$10$		0			0
$11$	602411.	−	347802.i	1.12780	−	0.651137i	0.184421	−	0.982847i	$-0.440959\pi$
$11$	602411.	−	347802.i	1.12780	−	0.651137i	0.943381	+	0.331710i	$0.107626\pi$
$12$		0			0
$13$		−	801797.i		−	0.598930i	−0.954107	−	0.299465i	$-0.903192\pi$
$13$		−	801797.i		−	0.598930i	0.954107	−	0.299465i	$-0.0968082\pi$
$14$		0			0
$15$	525167.	+	1.85358e6i	0.178565	+	0.630244i
$16$		0			0
$17$	−1.69093e6	−	2.92878e6i	−0.288840	−	0.500285i	0.684693	−	0.728831i	$-0.259936\pi$
$17$	−1.69093e6	−	2.92878e6i	−0.288840	−	0.500285i	−0.973533	+	0.228546i	$0.926603\pi$
$18$		0			0
$19$	3.34762e6	+	1.93275e6i	0.310164	+	0.179073i	0.647000	−	0.762490i	$-0.276023\pi$
$19$	3.34762e6	+	1.93275e6i	0.310164	+	0.179073i	−0.336836	+	0.941563i	$0.609357\pi$
$20$		0			0
$21$	8.28378e6	+	1.67826e7i	0.442611	+	0.896714i
$22$		0			0
$23$	−5.01711e7	−	2.89663e7i	−1.62536	−	0.938405i	−0.985451	−	0.169958i	$-0.945637\pi$
$23$	−5.01711e7	−	2.89663e7i	−1.62536	−	0.938405i	−0.639913	−	0.768447i	$-0.721030\pi$
$24$		0			0
$25$	1.39382e7	+	2.41416e7i	0.285454	+	0.494421i
$26$		0			0
$27$	5.49325e7	+	5.04131e7i	0.736764	+	0.676150i
$28$		0			0
$29$			1.26218e8i			1.14270i	0.820707	+	0.571350i	$0.193580\pi$
$29$			1.26218e8i			1.14270i	−0.820707	+	0.571350i	$0.806420\pi$
$30$		0			0
$31$	−1.25812e7	+	7.26374e6i	−0.0789281	+	0.0455692i	−0.538945	−	0.842341i	$-0.681177\pi$
$31$	−1.25812e7	+	7.26374e6i	−0.0789281	+	0.0455692i	0.460017	+	0.887910i	$0.347843\pi$
$32$		0			0
$33$	−7.17258e7	+	2.83850e8i	−0.319043	+	1.26259i
$34$		0			0
$35$	−1.32058e8	−	1.54884e8i	−0.425003	−	0.498463i
$36$		0			0
$37$	4.28757e7	−	7.42629e7i	0.101649	−	0.176061i	−0.810715	−	0.585441i	$-0.800922\pi$
$37$	4.28757e7	−	7.42629e7i	0.101649	−	0.176061i	0.912364	+	0.409380i	$0.134255\pi$
$38$		0			0
$39$	2.42011e8	+	2.35191e8i	0.429517	+	0.417412i
$40$		0			0
$41$	−6.77955e7			−0.0913882			−0.0456941	−	0.998955i	$-0.514550\pi$
$41$	−6.77955e7			−0.0913882			−0.0456941	+	0.998955i	$0.514550\pi$
$42$		0			0
$43$	−1.47763e8			−0.153281			−0.0766405	−	0.997059i	$-0.524419\pi$
$43$	−1.47763e8			−0.153281			−0.0766405	+	0.997059i	$0.524419\pi$
$44$		0			0
$45$	−7.13522e8	−	3.85194e8i	−0.576420	−	0.311180i
$46$		0			0
$47$	−1.13191e8	+	1.96052e8i	−0.0719901	+	0.124690i	−0.899773	−	0.436357i	$-0.856268\pi$
$47$	−1.13191e8	+	1.96052e8i	−0.0719901	+	0.124690i	0.827783	+	0.561048i	$0.189602\pi$
$48$		0			0
$49$	−1.53458e9	−	1.24696e9i	−0.776086	−	0.630627i
$50$		0			0
$51$	1.38001e9	+	3.48714e8i	0.560076	+	0.141525i
$52$		0			0
$53$	4.20156e9	−	2.42577e9i	1.38005	−	0.796770i	0.387881	−	0.921709i	$-0.373207\pi$
$53$	4.20156e9	−	2.42577e9i	1.38005	−	0.796770i	0.992164	+	0.124940i	$0.0398737\pi$
$54$		0			0
$55$		−	3.18400e9i		−	0.853056i
$56$		0			0
$57$	−1.56533e9	+	4.43499e8i	−0.344583	+	0.0976294i
$58$		0			0
$59$	−3.05171e9	−	5.28571e9i	−0.555721	−	0.962537i	−0.997847	−	0.0655841i	$-0.979109\pi$
$59$	−3.05171e9	−	5.28571e9i	−0.555721	−	0.962537i	0.442126	−	0.896953i	$-0.354224\pi$
$60$		0			0
$61$	−5.23135e9	−	3.02032e9i	−0.793048	−	0.457866i	0.0479866	−	0.998848i	$-0.484720\pi$
$61$	−5.23135e9	−	3.02032e9i	−0.793048	−	0.457866i	−0.841034	+	0.540982i	$0.818053\pi$
$62$		0			0
$63$	−7.49547e9	−	2.42250e9i	−0.951538	−	0.307532i
$64$		0			0
$65$	−3.17838e9	−	1.83504e9i	−0.339768	−	0.196165i
$66$		0			0
$67$	−3.71415e9	−	6.43309e9i	−0.336084	−	0.582114i	0.647609	−	0.761973i	$-0.275769\pi$
$67$	−3.71415e9	−	6.43309e9i	−0.336084	−	0.582114i	−0.983692	+	0.179859i	$0.942436\pi$
$68$		0			0
$69$	2.34597e10	−	6.64677e9i	1.80573	−	0.511612i
$70$		0			0
$71$			1.70389e10i			1.12078i	0.828230	+	0.560389i	$0.189348\pi$
$71$			1.70389e10i			1.12078i	−0.828230	+	0.560389i	$0.810652\pi$
$72$		0			0
$73$	−9.84429e9	+	5.68361e9i	−0.555788	+	0.320884i	−0.751453	−	0.659787i	$-0.770647\pi$
$73$	−9.84429e9	+	5.68361e9i	−0.555788	+	0.320884i	0.195665	+	0.980671i	$0.437313\pi$
$74$		0			0
$75$	−1.13753e10	−	2.87441e9i	−0.553510	−	0.139866i
$76$		0			0
$77$	−5.61123e9	−	3.04183e10i	−0.236243	−	1.28067i
$78$		0			0
$79$	−1.28443e10	+	2.22470e10i	−0.469636	+	0.813434i	−0.999397	−	0.0347131i	$-0.988948\pi$
$79$	−1.28443e10	+	2.22470e10i	−0.469636	+	0.813434i	0.529761	+	0.848147i	$0.322282\pi$
$80$		0			0
$81$	−3.13298e10	+	1.79292e9i	−0.998367	+	0.0571337i
$82$		0			0
$83$	6.44662e9			0.179640			0.0898199	−	0.995958i	$-0.471371\pi$
$83$	6.44662e9			0.179640			0.0898199	+	0.995958i	$0.471371\pi$
$84$		0			0
$85$	−1.54798e10			−0.378410
$86$		0			0
$87$	−3.80971e10	−	3.70234e10i	−0.819475	−	0.796381i
$88$		0			0
$89$	1.05174e10	−	1.82167e10i	0.199648	−	0.345801i	−0.748766	−	0.662834i	$-0.769353\pi$
$89$	1.05174e10	−	1.82167e10i	0.199648	−	0.345801i	0.948414	+	0.317034i	$0.102687\pi$
$90$		0			0
$91$	−3.35986e10	−	1.19297e10i	−0.564408	−	0.200402i
$92$		0			0
$93$	1.49797e9	−	5.92812e9i	0.0223279	−	0.0883610i
$94$		0			0
$95$	1.53231e10	−	8.84679e9i	0.203173	−	0.117302i
$96$		0			0
$97$		−	1.27882e11i		−	1.51205i	−0.654545	−	0.756023i	$-0.727140\pi$
$97$		−	1.27882e11i		−	1.51205i	0.654545	−	0.756023i	$-0.272860\pi$
$98$		0			0
$99$	−6.46367e10	−	1.04911e11i	−0.683102	−	1.10873i
$100$		0			0
$101$	1.01169e11	+	1.75230e11i	0.957813	+	1.65898i	0.727795	+	0.685795i	$0.240545\pi$
$101$	1.01169e11	+	1.75230e11i	0.957813	+	1.65898i	0.230019	+	0.973186i	$0.426121\pi$
$102$		0			0
$103$	−1.84386e11	−	1.06456e11i	−1.56720	−	0.904823i	−0.996494	−	0.0836673i	$-0.973337\pi$
$103$	−1.84386e11	−	1.06456e11i	−1.56720	−	0.904823i	−0.570705	−	0.821155i	$-0.693330\pi$
$104$		0			0
$105$	8.54862e10	+	5.57217e9i	0.653664	+	0.0426072i
$106$		0			0
$107$	−2.08969e10	−	1.20648e10i	−0.144036	−	0.0831594i	0.426250	−	0.904605i	$-0.359834\pi$
$107$	−2.08969e10	−	1.20648e10i	−0.144036	−	0.0831594i	−0.570286	+	0.821446i	$0.693168\pi$
$108$		0			0
$109$	−9.92153e10	−	1.71846e11i	−0.617636	−	1.06978i	−0.989916	−	0.141657i	$-0.954757\pi$
$109$	−9.92153e10	−	1.71846e11i	−0.617636	−	1.06978i	0.372279	−	0.928121i	$-0.378576\pi$
$110$		0			0
$111$	9.83849e9	+	3.47249e10i	0.0554182	+	0.195598i
$112$		0			0
$113$		−	3.09273e11i		−	1.57910i	−0.613683	−	0.789552i	$-0.710313\pi$
$113$		−	3.09273e11i		−	1.57910i	0.613683	−	0.789552i	$-0.289687\pi$
$114$		0			0
$115$	−2.29649e11	+	1.32588e11i	−1.06470	+	0.614703i
$116$		0			0
$117$	−1.41978e11	+	4.05918e9i	−0.598686	+	0.0171165i
$118$		0			0
$119$	−1.47887e11	+	2.72805e10i	−0.568095	+	0.104796i
$120$		0			0
$121$	9.92767e10	−	1.71952e11i	0.347959	−	0.602682i
$122$		0			0
$123$	1.98864e10	−	2.04631e10i	0.0636911	−	0.0655381i
$124$		0			0
$125$	3.51100e11			1.02903
$126$		0			0
$127$	−1.09811e11			−0.294936			−0.147468	−	0.989067i	$-0.547112\pi$
$127$	−1.09811e11			−0.294936			−0.147468	+	0.989067i	$0.547112\pi$
$128$		0			0
$129$	4.33431e10	−	4.46000e10i	0.106826	−	0.109924i
$130$		0			0
$131$	3.21561e10	−	5.56960e10i	0.0728234	−	0.126134i	−0.827314	−	0.561739i	$-0.810132\pi$
$131$	3.21561e10	−	5.56960e10i	0.0728234	−	0.126134i	0.900138	+	0.435605i	$0.143466\pi$
$132$		0			0
$133$	1.30798e11	−	1.11522e11i	0.272532	−	0.232368i
$134$		0			0
$135$	3.25563e11	−	1.02378e11i	0.624883	−	0.196503i
$136$		0			0
$137$	−5.16235e11	+	2.98048e11i	−0.913869	+	0.527623i	−0.881674	−	0.471859i	$-0.843583\pi$
$137$	−5.16235e11	+	2.98048e11i	−0.913869	+	0.527623i	−0.0321951	+	0.999482i	$0.510250\pi$
$138$		0			0
$139$			4.33055e11i			0.707884i	0.935267	+	0.353942i	$0.115159\pi$
$139$			4.33055e11i			0.707884i	−0.935267	+	0.353942i	$0.884841\pi$
$140$		0			0
$141$	−2.59733e10	−	9.16729e10i	−0.0392485	−	0.138527i
$142$		0			0
$143$	−2.78867e11	−	4.83011e11i	−0.389986	−	0.675475i
$144$		0			0
$145$	5.00336e11	+	2.88869e11i	0.648243	+	0.374264i
$146$		0			0
$147$	8.26512e11	−	9.74205e10i	0.993125	−	0.117059i
$148$		0			0
$149$	3.89454e11	+	2.24851e11i	0.434442	+	0.250825i	0.701237	−	0.712928i	$-0.252631\pi$
$149$	3.89454e11	+	2.24851e11i	0.434442	+	0.250825i	−0.266795	+	0.963753i	$0.585965\pi$
$150$		0			0
$151$	8.65731e11	+	1.49949e12i	0.897449	+	1.55443i	0.830745	+	0.556654i	$0.187915\pi$
$151$	8.65731e11	+	1.49949e12i	0.897449	+	1.55443i	0.0667041	+	0.997773i	$0.478752\pi$
$152$		0			0
$153$	−5.10052e11	+	3.14249e11i	−0.491827	+	0.303019i
$154$		0			0
$155$			6.64968e10i			0.0597003i
$156$		0			0
$157$	−3.75857e11	+	2.17001e11i	−0.314467	+	0.181557i	−0.648924	−	0.760854i	$-0.724780\pi$
$157$	−3.75857e11	+	2.17001e11i	−0.314467	+	0.181557i	0.334457	+	0.942411i	$0.391447\pi$
$158$		0			0
$159$	−5.00257e11	+	1.97973e12i	−0.390399	+	1.54498i
$160$		0			0
$161$	−1.96029e12	+	1.67139e12i	−1.42816	+	1.21769i
$162$		0			0
$163$	−4.62644e11	+	8.01323e11i	−0.314931	+	0.545476i	−0.979423	−	0.201819i	$-0.935315\pi$
$163$	−4.62644e11	+	8.01323e11i	−0.314931	+	0.545476i	0.664492	+	0.747295i	$0.268648\pi$
$164$		0			0
$165$	9.61044e11	+	9.33960e11i	0.611760	+	0.594520i
$166$		0			0
$167$	1.67140e12			0.995724			0.497862	−	0.867256i	$-0.334119\pi$
$167$	1.67140e12			0.995724			0.497862	+	0.867256i	$0.334119\pi$
$168$		0			0
$169$	1.14928e12			0.641283
$170$		0			0
$171$	3.25293e11	−	6.02563e11i	0.170136	−	0.315155i
$172$		0			0
$173$	1.09424e12	−	1.89528e12i	0.536859	−	0.929867i	−0.462212	−	0.886769i	$-0.652944\pi$
$173$	1.09424e12	−	1.89528e12i	0.536859	−	0.929867i	0.999071	−	0.0430975i	$-0.0137226\pi$
$174$		0			0
$175$	1.21901e12	−	2.24870e11i	0.561435	−	0.103567i
$176$		0			0
$177$	2.49057e12	+	6.29341e11i	1.07757	+	0.272291i
$178$		0			0
$179$	−4.44064e11	+	2.56380e11i	−0.180615	+	0.104278i	−0.587582	−	0.809165i	$-0.699920\pi$
$179$	−4.44064e11	+	2.56380e11i	−0.180615	+	0.104278i	0.406967	+	0.913443i	$0.366587\pi$
$180$		0			0
$181$		−	3.75396e12i		−	1.43634i	−0.695866	−	0.718171i	$-0.744979\pi$
$181$		−	3.75396e12i		−	1.43634i	0.695866	−	0.718171i	$-0.255021\pi$
$182$		0			0
$183$	2.44615e12	−	6.93058e11i	0.881053	−	0.249625i
$184$		0			0
$185$	−1.96255e11	−	3.39924e11i	−0.0665851	−	0.115329i
$186$		0			0
$187$	−2.03727e12	−	1.17622e12i	−0.651509	−	0.376149i
$188$		0			0
$189$	2.92984e12	−	1.55181e12i	0.883698	−	0.468057i
$190$		0			0
$191$	−4.52254e12	−	2.61109e12i	−1.28736	−	0.743256i	−0.309176	−	0.951005i	$-0.600053\pi$
$191$	−4.52254e12	−	2.61109e12i	−1.28736	−	0.743256i	−0.978182	+	0.207749i	$0.933386\pi$
$192$		0			0
$193$	1.68130e12	+	2.91209e12i	0.451939	+	0.782781i	0.998506	−	0.0546343i	$-0.0173993\pi$
$193$	1.68130e12	+	2.91209e12i	0.451939	+	0.782781i	−0.546568	+	0.837415i	$0.684066\pi$
$194$		0			0
$195$	1.48619e12	−	4.21078e11i	0.377472	−	0.106948i
$196$		0			0
$197$			5.07405e12i			1.21840i	0.793016	+	0.609201i	$0.208510\pi$
$197$			5.07405e12i			1.21840i	−0.793016	+	0.609201i	$0.791490\pi$
$198$		0			0
$199$	−4.58573e12	+	2.64757e12i	−1.04164	+	0.601389i	−0.920296	−	0.391222i	$-0.872053\pi$
$199$	−4.58573e12	+	2.64757e12i	−1.04164	+	0.601389i	−0.121340	+	0.992611i	$0.538719\pi$
$200$		0			0
$201$	3.03120e12	+	7.65953e11i	0.651684	+	0.164674i
$202$		0			0
$203$	5.28905e12	+	1.87796e12i	1.07683	+	0.382347i
$204$		0			0
$205$	−1.55161e11	+	2.68746e11i	−0.0299320	+	0.0518437i
$206$		0			0
$207$	−4.87520e12	+	9.03068e12i	−0.891571	+	1.65152i
$208$		0			0
$209$	2.68885e12			0.466405
$210$		0			0
$211$	−4.13706e12			−0.680986			−0.340493	−	0.940247i	$-0.610594\pi$
$211$	−4.13706e12			−0.680986			−0.340493	+	0.940247i	$0.610594\pi$
$212$		0			0
$213$	−5.14294e12	−	4.99800e12i	−0.803754	−	0.781103i
$214$		0			0
$215$	−3.38178e11	+	5.85741e11i	−0.0502034	+	0.0869549i
$216$		0			0
$217$	1.17189e11	+	6.35277e11i	0.0165332	+	0.0896262i
$218$		0			0
$219$	1.17211e12	−	4.63853e12i	0.157226	−	0.622211i
$220$		0			0
$221$	−2.34829e12	+	1.35579e12i	−0.299636	+	0.172995i
$222$		0			0
$223$		−	3.07771e12i		−	0.373724i	−0.982386	−	0.186862i	$-0.940168\pi$
$223$		−	3.07771e12i		−	0.373724i	0.982386	−	0.186862i	$-0.0598317\pi$
$224$		0			0
$225$	4.20431e12	−	2.59032e12i	0.486061	−	0.299467i
$226$		0			0
$227$	1.61808e12	+	2.80260e12i	0.178180	+	0.308616i	0.941257	−	0.337691i	$-0.109646\pi$
$227$	1.61808e12	+	2.80260e12i	0.178180	+	0.308616i	−0.763078	+	0.646307i	$0.776313\pi$
$228$		0			0
$229$	−1.11436e13	−	6.43374e12i	−1.16931	−	0.675101i	−0.215792	−	0.976439i	$-0.569233\pi$
$229$	−1.11436e13	−	6.43374e12i	−1.16931	−	0.675101i	−0.953517	+	0.301339i	$0.902567\pi$
$230$		0			0
$231$	1.08273e13	+	7.22892e12i	1.08306	+	0.723115i
$232$		0			0
$233$	1.66048e12	+	9.58680e11i	0.158408	+	0.0914569i	0.577108	−	0.816667i	$-0.304181\pi$
$233$	1.66048e12	+	9.58680e11i	0.158408	+	0.0914569i	−0.418701	+	0.908124i	$0.637514\pi$
$234$		0			0
$235$	5.18109e11	+	8.97391e11i	0.0471572	+	0.0816787i
$236$		0			0
$237$	−2.94732e12	−	1.04026e13i	−0.256042	−	0.903701i
$238$		0			0
$239$		−	1.04316e13i		−	0.865289i	−0.901565	−	0.432645i	$-0.857580\pi$
$239$		−	1.04316e13i		−	0.865289i	0.901565	−	0.432645i	$-0.142420\pi$
$240$		0			0
$241$	−1.93828e13	+	1.11906e13i	−1.53575	+	0.886668i	−0.536674	+	0.843790i	$0.680320\pi$
$241$	−1.93828e13	+	1.11906e13i	−1.53575	+	0.886668i	−0.999080	+	0.0428786i	$0.986347\pi$
$242$		0			0
$243$	8.64879e12	−	9.98237e12i	0.654818	−	0.755786i
$244$		0			0
$245$	−8.45513e12	+	3.22931e12i	−0.611937	+	0.233720i
$246$		0			0
$247$	1.54967e12	−	2.68411e12i	0.107252	−	0.185766i
$248$		0			0
$249$	−1.89098e12	+	1.94582e12i	−0.125196	+	0.128827i
$250$		0			0
$251$	−1.04993e13			−0.665201			−0.332601	−	0.943068i	$-0.607926\pi$
$251$	−1.04993e13			−0.665201			−0.332601	+	0.943068i	$0.607926\pi$
$252$		0			0
$253$	−4.02982e13			−2.44412
$254$		0			0
$255$	4.54070e12	−	4.67237e12i	0.263725	−	0.271373i
$256$		0			0
$257$	1.13288e13	−	1.96221e13i	0.630309	−	1.09173i	−0.357180	−	0.934036i	$-0.616262\pi$
$257$	1.13288e13	−	1.96221e13i	0.630309	−	1.09173i	0.987489	−	0.157691i	$-0.0504050\pi$
$258$		0			0
$259$	−2.47398e12	−	2.90160e12i	−0.131901	−	0.154700i
$260$		0			0
$261$	2.23500e13	−	6.38991e11i	1.14223	−	0.0326567i
$262$		0			0
$263$	1.74287e13	−	1.00625e13i	0.854102	−	0.493116i	−0.00793104	−	0.999969i	$-0.502525\pi$
$263$	1.74287e13	−	1.00625e13i	0.854102	−	0.493116i	0.862033	+	0.506853i	$0.169191\pi$
$264$		0			0
$265$		−	2.22070e13i		−	1.04385i
$266$		0			0
$267$	2.41339e12	+	8.51805e12i	0.108847	+	0.384174i
$268$		0			0
$269$	−1.75334e13	−	3.03688e13i	−0.758979	−	1.31459i	−0.943372	−	0.331737i	$-0.892365\pi$
$269$	−1.75334e13	−	3.03688e13i	−0.758979	−	1.31459i	0.184393	−	0.982853i	$-0.440968\pi$
$270$		0			0
$271$	−3.69535e13	−	2.13351e13i	−1.53576	−	0.886674i	−0.999080	−	0.0428905i	$-0.986343\pi$
$271$	−3.69535e13	−	2.13351e13i	−1.53576	−	0.886674i	−0.536684	−	0.843783i	$-0.680323\pi$
$272$		0			0
$273$	1.34563e13	−	6.64191e12i	0.537069	−	0.265093i
$274$		0			0
$275$	1.67930e13	+	9.69545e12i	0.643871	+	0.371739i
$276$		0			0
$277$	−1.91420e13	−	3.31549e13i	−0.705259	−	1.22154i	−0.966598	−	0.256298i	$-0.917497\pi$
$277$	−1.91420e13	−	3.31549e13i	−0.705259	−	1.22154i	0.261339	−	0.965247i	$-0.415836\pi$
$278$		0			0
$279$	1.34992e12	+	2.19103e12i	0.0478062	+	0.0775936i
$280$		0			0
$281$			2.61830e13i			0.891526i	0.895151	+	0.445763i	$0.147068\pi$
$281$			2.61830e13i			0.891526i	−0.895151	+	0.445763i	$0.852932\pi$
$282$		0			0
$283$	−2.27664e13	+	1.31442e13i	−0.745535	+	0.430435i	−0.824078	−	0.566476i	$-0.808307\pi$
$283$	−2.27664e13	+	1.31442e13i	−0.745535	+	0.430435i	0.0785431	+	0.996911i	$0.474973\pi$
$284$		0			0
$285$	−1.82444e12	+	7.22008e12i	−0.0574754	+	0.227455i
$286$		0			0
$287$	−1.00871e12	+	2.84091e12i	−0.0305785	+	0.0861206i
$288$		0			0
$289$	1.14174e13	−	1.97756e13i	0.333143	−	0.577021i
$290$		0			0
$291$	3.85994e13	+	3.75116e13i	1.08435	+	1.05379i
$292$		0			0
$293$	2.38647e13			0.645630			0.322815	−	0.946462i	$-0.395371\pi$
$293$	2.38647e13			0.645630			0.322815	+	0.946462i	$0.395371\pi$
$294$		0			0
$295$	−2.79372e13			−0.728052
$296$		0			0
$297$	5.06257e13	+	1.12638e13i	1.27119	+	0.282829i
$298$		0			0
$299$	−2.32251e13	+	4.02271e13i	−0.562039	+	0.973480i
$300$		0			0
$301$	−2.19852e12	+	6.19186e12i	−0.0512878	+	0.144446i
$302$		0			0
$303$	−8.25667e13	−	2.08637e13i	−1.85725	−	0.469307i
$304$		0			0
$305$	−2.39455e13	+	1.38249e13i	−0.519487	+	0.299926i
$306$		0			0
$307$			6.08703e13i			1.27393i	0.770894	+	0.636964i	$0.219810\pi$
$307$			6.08703e13i			1.27393i	−0.770894	+	0.636964i	$0.780190\pi$
$308$		0			0
$309$	8.62180e13	−	2.44278e13i	1.74111	−	0.493303i
$310$		0			0
$311$	−2.37633e13	−	4.11592e13i	−0.463153	−	0.802205i	0.535963	−	0.844241i	$-0.319949\pi$
$311$	−2.37633e13	−	4.11592e13i	−0.463153	−	0.802205i	−0.999116	+	0.0420369i	$0.986615\pi$
$312$		0			0
$313$	−1.37987e13	−	7.96666e12i	−0.259623	−	0.149893i	0.364540	−	0.931188i	$-0.381226\pi$
$313$	−1.37987e13	−	7.96666e12i	−0.259623	−	0.149893i	−0.624163	+	0.781295i	$0.714560\pi$
$314$		0			0
$315$	−2.67575e13	+	2.41683e13i	−0.486113	+	0.439074i
$316$		0			0
$317$	4.59916e13	+	2.65533e13i	0.806961	+	0.465899i	0.845899	−	0.533343i	$-0.179064\pi$
$317$	4.59916e13	+	2.65533e13i	0.806961	+	0.465899i	−0.0389385	+	0.999242i	$0.512398\pi$
$318$		0			0
$319$	4.38989e13	+	7.60351e13i	0.744054	+	1.28874i
$320$		0			0
$321$	9.77129e12	−	2.76846e12i	0.160020	−	0.0453379i
$322$		0			0
$323$		−	1.30726e13i		−	0.206894i
$324$		0			0
$325$	1.93567e13	−	1.11756e13i	0.296123	−	0.170967i
$326$		0			0
$327$	8.09720e13	+	2.04608e13i	1.19763	+	0.302628i
$328$		0			0
$329$	6.53125e12	+	7.66015e12i	0.0934155	+	0.109562i
$330$		0			0
$331$	−3.74753e13	+	6.49092e13i	−0.518432	+	0.897950i	0.481339	+	0.876535i	$0.340151\pi$
$331$	−3.74753e13	+	6.49092e13i	−0.518432	+	0.897950i	−0.999771	+	0.0214157i	$0.993183\pi$
$332$		0			0
$333$	−1.33671e13	−	7.21624e12i	−0.178894	−	0.0965757i
$334$		0			0
$335$	−3.40016e13			−0.440304
$336$		0			0
$337$	1.01593e14			1.27321			0.636605	−	0.771190i	$-0.280338\pi$
$337$	1.01593e14			1.27321			0.636605	+	0.771190i	$0.280338\pi$
$338$		0			0
$339$	9.33497e13	+	9.07189e13i	1.13244	+	1.10052i
$340$		0			0
$341$	−5.05269e12	+	8.75151e12i	−0.0593435	+	0.102786i
$342$		0			0
$343$	−7.50850e13	+	4.57518e13i	−0.853956	+	0.520344i
$344$		0			0
$345$	2.73430e13	−	1.08208e14i	0.301191	−	1.19194i
$346$		0			0
$347$	−7.79188e13	+	4.49864e13i	−0.831438	+	0.480031i	−0.854345	−	0.519707i	$-0.826041\pi$
$347$	−7.79188e13	+	4.49864e13i	−0.831438	+	0.480031i	0.0229067	+	0.999738i	$0.492708\pi$
$348$		0			0
$349$		−	1.42008e13i		−	0.146816i	−0.997302	−	0.0734078i	$-0.976613\pi$
$349$		−	1.42008e13i		−	0.146816i	0.997302	−	0.0734078i	$-0.0233875\pi$
$350$		0			0
$351$	4.04211e13	−	4.40447e13i	0.404967	−	0.441270i
$352$		0			0
$353$	2.61013e13	+	4.52087e13i	0.253455	+	0.438997i	0.964475	−	0.264175i	$-0.0850997\pi$
$353$	2.61013e13	+	4.52087e13i	0.253455	+	0.438997i	−0.711020	+	0.703172i	$0.751766\pi$
$354$		0			0
$355$	6.75432e13	+	3.89961e13i	0.635807	+	0.367084i
$356$		0			0
$357$	3.51453e13	−	5.26397e13i	0.320769	−	0.480439i
$358$		0			0
$359$	3.72756e13	+	2.15211e13i	0.329918	+	0.190478i	0.655805	−	0.754931i	$-0.272330\pi$
$359$	3.72756e13	+	2.15211e13i	0.329918	+	0.190478i	−0.325887	+	0.945409i	$0.605663\pi$
$360$		0			0
$361$	−5.07741e13	−	8.79433e13i	−0.435866	−	0.754941i
$362$		0			0
$363$	2.27805e13	+	8.04039e13i	0.189705	+	0.669562i
$364$		0			0
$365$			5.20313e13i			0.420391i
$366$		0			0
$367$	2.57969e11	−	1.48938e11i	0.00202257	−	0.00116773i	−0.498988	−	0.866609i	$-0.666295\pi$
$367$	2.57969e11	−	1.48938e11i	0.00202257	−	0.00116773i	0.501011	+	0.865441i	$0.332962\pi$
$368$		0			0
$369$	3.43222e11	+	1.20049e13i	0.00261174	+	0.0913508i
$370$		0			0
$371$	−3.91360e13	−	2.12155e14i	−0.289081	−	1.56710i
$372$		0			0
$373$	3.58739e13	−	6.21354e13i	0.257265	−	0.445596i	−0.708243	−	0.705968i	$-0.750512\pi$
$373$	3.58739e13	−	6.21354e13i	0.257265	−	0.445596i	0.965508	+	0.260373i	$0.0838454\pi$
$374$		0			0
$375$	−1.02988e14	+	1.05975e14i	−0.717158	+	0.737955i
$376$		0			0
$377$	1.01201e14			0.684397
$378$		0			0
$379$	3.42666e13			0.225090			0.112545	−	0.993647i	$-0.464100\pi$
$379$	3.42666e13			0.225090			0.112545	+	0.993647i	$0.464100\pi$
$380$		0			0
$381$	3.22110e13	−	3.31450e13i	0.205549	−	0.211510i
$382$		0			0
$383$	−9.79381e13	+	1.69634e14i	−0.607237	+	1.05177i	0.384457	+	0.923143i	$0.374389\pi$
$383$	−9.79381e13	+	1.69634e14i	−0.607237	+	1.05177i	−0.991694	+	0.128622i	$0.958945\pi$
$384$		0			0
$385$	−1.33422e14	−	4.73737e13i	−0.803886	−	0.285433i
$386$		0			0
$387$	7.48063e11	+	2.61650e13i	0.00438054	+	0.153218i
$388$		0			0
$389$	2.94244e14	−	1.69882e14i	1.67489	−	0.966996i	0.710048	−	0.704153i	$-0.248673\pi$
$389$	2.94244e14	−	1.69882e14i	1.67489	−	0.966996i	0.964839	−	0.262843i	$-0.0846602\pi$
$390$		0			0
$391$			1.95920e14i			1.08420i
$392$		0			0
$393$	7.37871e12	+	2.60431e13i	0.0397028	+	0.140131i
$394$		0			0
$395$	5.87924e13	+	1.01831e14i	0.307636	+	0.532841i
$396$		0			0
$397$	−2.05168e14	−	1.18454e14i	−1.04415	−	0.602840i	−0.123144	−	0.992389i	$-0.539298\pi$
$397$	−2.05168e14	−	1.18454e14i	−1.04415	−	0.602840i	−0.921006	+	0.389549i	$0.872631\pi$
$398$		0			0
$399$	−4.70565e12	+	7.21923e13i	−0.0232953	+	0.357388i
$400$		0			0
$401$	−1.22273e14	−	7.05942e13i	−0.588892	−	0.339997i	0.175767	−	0.984432i	$-0.443759\pi$
$401$	−1.22273e14	−	7.05942e13i	−0.588892	−	0.339997i	−0.764659	+	0.644435i	$0.777093\pi$
$402$		0			0
$403$	5.82405e12	+	1.00876e13i	0.0272928	+	0.0472724i
$404$		0			0
$405$	−6.45959e13	+	1.28297e14i	−0.294579	+	0.585077i
$406$		0			0
$407$		−	5.96490e13i		−	0.264749i
$408$		0			0
$409$	3.24831e14	−	1.87541e14i	1.40339	−	0.810249i	0.408654	−	0.912690i	$-0.365998\pi$
$409$	3.24831e14	−	1.87541e14i	1.40339	−	0.810249i	0.994739	+	0.102440i	$0.0326651\pi$
$410$		0			0
$411$	6.14653e13	−	2.43244e14i	0.258523	−	1.02309i
$412$		0			0
$413$	−2.66898e14	+	4.92344e13i	−1.09300	+	0.201625i
$414$		0			0
$415$	1.47541e13	−	2.55548e13i	0.0588366	−	0.101908i
$416$		0			0
$417$	−1.30712e14	−	1.27028e14i	−0.507652	−	0.493345i
$418$		0			0
$419$	−4.27845e14			−1.61849			−0.809244	−	0.587473i	$-0.800123\pi$
$419$	−4.27845e14			−1.61849			−0.809244	+	0.587473i	$0.800123\pi$
$420$		0			0
$421$	−5.73543e13			−0.211356			−0.105678	−	0.994400i	$-0.533701\pi$
$421$	−5.73543e13			−0.211356			−0.105678	+	0.994400i	$0.533701\pi$
$422$		0			0
$423$	3.52889e13	+	1.90507e13i	0.126697	+	0.0683972i
$424$		0			0
$425$	4.71370e13	−	8.16437e13i	0.164901	−	0.285617i
$426$		0			0
$427$	−2.04399e14	+	1.74276e14i	−0.696829	+	0.594135i
$428$		0			0
$429$	2.27590e14	+	5.75095e13i	0.756202	+	0.191084i
$430$		0			0
$431$	3.55755e14	−	2.05395e14i	1.15219	−	0.665219i	0.202773	−	0.979226i	$-0.435005\pi$
$431$	3.55755e14	−	2.05395e14i	1.15219	−	0.665219i	0.949421	+	0.314006i	$0.101671\pi$
$432$		0			0
$433$		−	4.42845e13i		−	0.139820i	−0.997553	−	0.0699098i	$-0.977729\pi$
$433$		−	4.42845e13i		−	0.139820i	0.997553	−	0.0699098i	$-0.0222711\pi$
$434$		0			0
$435$	−2.33955e14	+	6.62855e13i	−0.720179	+	0.204046i
$436$		0			0
$437$	−1.11969e14	−	1.93936e14i	−0.336086	−	0.582118i
$438$		0			0
$439$	−2.01170e14	−	1.16146e14i	−0.588856	−	0.339976i	0.175789	−	0.984428i	$-0.443752\pi$
$439$	−2.01170e14	−	1.16146e14i	−0.588856	−	0.339976i	−0.764645	+	0.644452i	$0.777086\pi$
$440$		0			0
$441$	−2.13035e14	+	2.78047e14i	−0.608190	+	0.793791i
$442$		0			0
$443$	3.14033e14	+	1.81307e14i	0.874491	+	0.504887i	0.868838	−	0.495097i	$-0.164867\pi$
$443$	3.14033e14	+	1.81307e14i	0.874491	+	0.504887i	0.00565271	+	0.999984i	$0.498201\pi$
$444$		0			0
$445$	−4.81416e13	−	8.33837e13i	−0.130780	−	0.226517i
$446$		0			0
$447$	−1.82107e14	+	5.15956e13i	−0.482652	+	0.136748i
$448$		0			0
$449$			2.13315e14i			0.551653i	0.961207	+	0.275827i	$0.0889516\pi$
$449$			2.13315e14i			0.551653i	−0.961207	+	0.275827i	$0.911048\pi$
$450$		0			0
$451$	−4.08408e13	+	2.35794e13i	−0.103068	+	0.0595062i
$452$		0			0
$453$	−7.06544e14	−	1.78536e14i	−1.74020	−	0.439730i
$454$		0			0
$455$	−1.24186e14	+	1.05884e14i	−0.298544	+	0.254547i
$456$		0			0
$457$	2.32103e14	−	4.02015e14i	0.544681	−	0.943415i	−0.453946	−	0.891029i	$-0.649984\pi$
$457$	2.32103e14	−	4.02015e14i	0.544681	−	0.943415i	0.998627	−	0.0523856i	$-0.0166825\pi$
$458$		0			0
$459$	5.47620e13	−	2.46130e14i	0.125461	−	0.563891i
$460$		0			0
$461$	2.21439e14			0.495334			0.247667	−	0.968845i	$-0.420336\pi$
$461$	2.21439e14			0.495334			0.247667	+	0.968845i	$0.420336\pi$
$462$		0			0
$463$	2.15591e14			0.470906			0.235453	−	0.971886i	$-0.424343\pi$
$463$	2.15591e14			0.470906			0.235453	+	0.971886i	$0.424343\pi$
$464$		0			0
$465$	−2.00711e13	−	1.95055e13i	−0.0428134	−	0.0416069i
$466$		0			0
$467$	2.54765e14	−	4.41266e14i	0.530758	−	0.919301i	−0.468597	−	0.883412i	$-0.655240\pi$
$467$	2.54765e14	−	4.41266e14i	0.530758	−	0.919301i	0.999356	−	0.0358887i	$-0.0114262\pi$
$468$		0			0
$469$	−3.24834e14	+	5.99218e13i	−0.661015	+	0.121937i
$470$		0			0
$471$	4.47513e13	−	1.77100e14i	0.0889591	−	0.352049i
$472$		0			0
$473$	−8.90138e13	+	5.13922e13i	−0.172871	+	0.0998069i
$474$		0			0
$475$			1.07756e14i			0.204468i
$476$		0			0
$477$	−4.50814e14	−	7.31709e14i	−0.835884	−	1.35671i
$478$		0			0
$479$	1.36720e13	+	2.36806e13i	0.0247735	+	0.0429090i	0.878146	−	0.478392i	$-0.158780\pi$
$479$	1.36720e13	+	2.36806e13i	0.0247735	+	0.0429090i	−0.853373	+	0.521301i	$0.825447\pi$
$480$		0			0
$481$	−5.95438e13	−	3.43776e13i	−0.105448	−	0.0608805i
$482$		0			0
$483$	7.05241e13	−	1.08195e15i	0.122075	−	1.87284i
$484$		0			0
$485$	−5.06933e14	−	2.92678e14i	−0.857770	−	0.495234i
$486$		0			0
$487$	2.15564e14	+	3.73367e14i	0.356588	+	0.617628i	0.987388	−	0.158317i	$-0.0506068\pi$
$487$	2.15564e14	+	3.73367e14i	0.356588	+	0.617628i	−0.630801	+	0.775945i	$0.717273\pi$
$488$		0			0
$489$	−1.06161e14	−	3.74694e14i	−0.171698	−	0.606008i
$490$		0			0
$491$			9.08798e14i			1.43721i	0.695420	+	0.718604i	$0.255218\pi$
$491$			9.08798e14i			1.43721i	−0.695420	+	0.718604i	$0.744782\pi$
$492$		0			0
$493$	3.69665e14	−	2.13426e14i	0.571676	−	0.330057i
$494$		0			0
$495$	−5.63805e14	+	1.61193e13i	−0.852708	+	0.0243791i
$496$		0			0
$497$	7.13997e14	+	2.53516e14i	1.05618	+	0.375012i
$498$		0			0
$499$	5.65604e14	−	9.79654e14i	0.818388	−	1.41749i	−0.0884818	−	0.996078i	$-0.528202\pi$
$499$	5.65604e14	−	9.79654e14i	0.818388	−	1.41749i	0.906870	−	0.421411i	$-0.138465\pi$
$500$		0			0
$501$	−4.90270e14	+	5.04487e14i	−0.693949	+	0.714073i
$502$		0			0
$503$	4.46529e14			0.618338			0.309169	−	0.951007i	$-0.399949\pi$
$503$	4.46529e14			0.618338			0.309169	+	0.951007i	$0.399949\pi$
$504$		0			0
$505$	9.26166e14			1.25483
$506$		0			0
$507$	−3.37118e14	+	3.46894e14i	−0.446929	+	0.459889i
$508$		0			0
$509$	5.83062e14	−	1.00989e15i	0.756427	−	1.31017i	−0.188235	−	0.982124i	$-0.560277\pi$
$509$	5.83062e14	−	1.00989e15i	0.756427	−	1.31017i	0.944662	−	0.328046i	$-0.106390\pi$
$510$		0			0
$511$	9.16959e13	+	4.97081e14i	0.116422	+	0.631120i
$512$		0			0
$513$	8.64570e13	+	2.74935e14i	0.107437	+	0.341652i
$514$		0			0
$515$	−8.43994e14	+	4.87280e14i	−1.02660	+	0.592705i
$516$		0			0
$517$			1.57472e14i			0.187502i
$518$		0			0
$519$	2.51091e14	+	8.86224e14i	0.292692	+	1.03305i
$520$		0			0
$521$	1.78296e14	+	3.08818e14i	0.203486	+	0.352448i	0.949649	−	0.313315i	$-0.101440\pi$
$521$	1.78296e14	+	3.08818e14i	0.203486	+	0.352448i	−0.746163	+	0.665763i	$0.768106\pi$
$522$		0			0
$523$	3.58466e14	+	2.06960e14i	0.400579	+	0.231274i	0.686734	−	0.726909i	$-0.259044\pi$
$523$	3.58466e14	+	2.06960e14i	0.400579	+	0.231274i	−0.286155	+	0.958183i	$0.592377\pi$
$524$		0			0
$525$	−2.89699e14	+	4.33903e14i	−0.317009	+	0.474806i
$526$		0			0
$527$	4.25478e13	+	2.45650e13i	0.0455952	+	0.0263244i
$528$		0			0
$529$	1.20169e15	+	2.08139e15i	1.26121	+	2.18447i
$530$		0			0
$531$	−9.20516e14	+	5.67139e14i	−0.946262	+	0.583002i
$532$		0			0
$533$			5.43583e13i			0.0547351i
$534$		0			0
$535$	−9.56517e13	+	5.52246e13i	−0.0943511	+	0.0544737i
$536$		0			0
$537$	5.28723e13	−	2.09238e14i	0.0510939	−	0.202201i
$538$		0			0
$539$	−1.35814e15	−	2.17452e14i	−1.28590	−	0.205885i
$540$		0			0
$541$	2.58141e14	−	4.47113e14i	0.239482	−	0.414794i	−0.721084	−	0.692848i	$-0.756356\pi$
$541$	2.58141e14	−	4.47113e14i	0.239482	−	0.414794i	0.960566	+	0.278053i	$0.0896892\pi$
$542$		0			0
$543$	1.13308e15	+	1.10115e15i	1.03006	+	1.00103i
$544$		0			0
$545$	−9.08278e14			−0.809167
$546$		0			0
$547$	1.96104e15			1.71221			0.856103	−	0.516805i	$-0.172879\pi$
$547$	1.96104e15			1.71221			0.856103	+	0.516805i	$0.172879\pi$
$548$		0			0
$549$	−5.08338e14	+	9.41629e14i	−0.435015	+	0.805809i
$550$		0			0
$551$	−2.43947e14	+	4.22529e14i	−0.204627	+	0.354424i
$552$		0			0
$553$	7.41133e14	+	8.69235e14i	0.609407	+	0.714741i
$554$		0			0
$555$	1.60169e14	+	4.04730e13i	0.129112	+	0.0326252i
$556$		0			0
$557$	−1.64381e15	+	9.49057e14i	−1.29912	+	0.750047i	−0.980252	−	0.197752i	$-0.936636\pi$
$557$	−1.64381e15	+	9.49057e14i	−1.29912	+	0.750047i	−0.318868	+	0.947799i	$0.603303\pi$
$558$		0			0
$559$			1.18476e14i			0.0918046i
$560$		0			0
$561$	9.52617e14	−	2.69902e14i	0.723807	−	0.205074i
$562$		0			0
$563$	−4.88117e14	−	8.45443e14i	−0.363687	−	0.629924i	0.624878	−	0.780723i	$-0.285149\pi$
$563$	−4.88117e14	−	8.45443e14i	−0.363687	−	0.629924i	−0.988565	+	0.150799i	$0.951815\pi$
$564$		0			0
$565$	−1.22598e15	−	7.07820e14i	−0.895812	−	0.517197i
$566$		0			0
$567$	−3.91016e14	+	1.33952e15i	−0.280213	+	0.959938i
$568$		0			0
$569$	1.68583e15	+	9.73314e14i	1.18494	+	0.684125i	0.957152	−	0.289586i	$-0.0935175\pi$
$569$	1.68583e15	+	9.73314e14i	1.18494	+	0.684125i	0.227787	+	0.973711i	$0.426851\pi$
$570$		0			0
$571$	1.01533e15	+	1.75861e15i	0.700018	+	1.21247i	0.968459	+	0.249171i	$0.0801582\pi$
$571$	1.01533e15	+	1.75861e15i	0.700018	+	1.21247i	−0.268441	+	0.963296i	$0.586508\pi$
$572$		0			0
$573$	2.11472e15	−	5.99155e14i	1.43022	−	0.405218i
$574$		0			0
$575$		−	1.61495e15i		−	1.07149i
$576$		0			0
$577$	1.75093e15	−	1.01090e15i	1.13973	−	0.658022i	0.193364	−	0.981127i	$-0.438060\pi$
$577$	1.75093e15	−	1.01090e15i	1.13973	−	0.658022i	0.946363	+	0.323105i	$0.104727\pi$
$578$		0			0
$579$	−1.37215e15	−	3.46727e14i	−0.876332	−	0.221440i
$580$		0			0
$581$	9.59173e13	−	2.70140e14i	0.0601075	−	0.169285i
$582$		0			0
$583$	1.68738e15	−	2.92262e15i	1.03761	−	1.79720i
$584$		0			0
$585$	−3.08848e14	+	5.72100e14i	−0.186375	+	0.345235i
$586$		0			0
$587$	1.86653e15			1.10541			0.552707	−	0.833376i	$-0.313595\pi$
$587$	1.86653e15			1.10541			0.552707	+	0.833376i	$0.313595\pi$
$588$		0			0
$589$	−5.61559e13			−0.0326409
$590$		0			0
$591$	−1.53153e15	−	1.48837e15i	−0.873764	−	0.849140i
$592$		0			0
$593$	−2.19279e14	+	3.79802e14i	−0.122799	+	0.212695i	−0.920871	−	0.389869i	$-0.872520\pi$
$593$	−2.19279e14	+	3.79802e14i	−0.122799	+	0.212695i	0.798071	+	0.602563i	$0.205854\pi$
$594$		0			0
$595$	−2.30320e14	+	6.48669e14i	−0.126616	+	0.356599i
$596$		0			0
$597$	5.45998e14	−	2.16075e15i	0.294667	−	1.16612i
$598$		0			0
$599$	2.13916e15	−	1.23505e15i	1.13343	−	0.654389i	0.188638	−	0.982047i	$-0.439593\pi$
$599$	2.13916e15	−	1.23505e15i	1.13343	−	0.654389i	0.944796	+	0.327658i	$0.106259\pi$
$600$		0			0
$601$			1.50056e15i			0.780627i	0.920682	+	0.390313i	$0.127633\pi$
$601$			1.50056e15i			0.780627i	−0.920682	+	0.390313i	$0.872367\pi$
$602$		0			0
$603$	−1.12033e15	+	6.90249e14i	−0.572272	+	0.352582i
$604$		0			0
$605$	−4.54420e14	−	7.87079e14i	−0.227931	−	0.394788i
$606$		0			0
$607$	−3.00707e15	−	1.73613e15i	−1.48117	−	0.855155i	−0.481400	−	0.876501i	$-0.659872\pi$
$607$	−3.00707e15	−	1.73613e15i	−1.48117	−	0.855155i	−0.999772	+	0.0213457i	$0.993205\pi$
$608$		0			0
$609$	−2.11827e15	+	1.04556e15i	−1.02467	+	0.505772i
$610$		0			0
$611$	1.57194e14	+	9.07560e13i	0.0746809	+	0.0431170i
$612$		0			0
$613$	1.64528e15	+	2.84972e15i	0.767729	+	1.32975i	0.938791	+	0.344486i	$0.111947\pi$
$613$	1.64528e15	+	2.84972e15i	0.767729	+	1.32975i	−0.171062	+	0.985260i	$0.554720\pi$
$614$		0			0
$615$	−3.56040e13	−	1.25664e14i	−0.0163187	−	0.0575968i
$616$		0			0
$617$			1.69767e15i			0.764336i	0.924093	+	0.382168i	$0.124822\pi$
$617$			1.69767e15i			0.764336i	−0.924093	+	0.382168i	$0.875178\pi$
$618$		0			0
$619$	−1.28861e15	+	7.43979e14i	−0.569932	+	0.329050i	−0.757122	−	0.653273i	$-0.773395\pi$
$619$	−1.28861e15	+	7.43979e14i	−0.569932	+	0.329050i	0.187190	+	0.982324i	$0.440062\pi$
$620$		0			0
$621$	−1.29574e15	−	4.12048e15i	−0.563008	−	1.79037i
$622$		0			0
$623$	−6.06870e14	−	7.11765e14i	−0.259067	−	0.303845i
$624$		0			0
$625$	1.22972e14	−	2.12994e14i	0.0515783	−	0.0893363i
$626$		0			0
$627$	−7.88720e14	+	8.11592e14i	−0.325051	+	0.334477i
$628$		0			0
$629$	−2.90000e14			−0.117441
$630$		0			0
$631$	−8.10684e14			−0.322619			−0.161309	−	0.986904i	$-0.551572\pi$
$631$	−8.10684e14			−0.322619			−0.161309	+	0.986904i	$0.551572\pi$
$632$		0			0
$633$	1.21352e15	−	1.24871e15i	0.474599	−	0.488362i
$634$		0			0
$635$	−2.51321e14	+	4.35300e14i	−0.0965990	+	0.167314i
$636$		0			0
$637$	−9.99806e14	+	1.23042e15i	−0.377702	+	0.464821i
$638$		0			0
$639$	3.01715e15	−	8.62609e13i	1.12032	−	0.0320302i
$640$		0			0
$641$	−2.44689e15	+	1.41272e15i	−0.893092	+	0.515627i	−0.874953	−	0.484209i	$-0.839108\pi$
$641$	−2.44689e15	+	1.41272e15i	−0.893092	+	0.515627i	−0.0181392	+	0.999835i	$0.505774\pi$
$642$		0			0
$643$		−	2.02025e15i		−	0.724846i	−0.932014	−	0.362423i	$-0.881950\pi$
$643$		−	2.02025e15i		−	0.724846i	0.932014	−	0.362423i	$-0.118050\pi$
$644$		0			0
$645$	−7.76001e13	−	2.73889e14i	−0.0273706	−	0.0966043i
$646$		0			0
$647$	2.25398e15	+	3.90401e15i	0.781586	+	1.35375i	0.931018	+	0.364974i	$0.118922\pi$
$647$	2.25398e15	+	3.90401e15i	0.781586	+	1.35375i	−0.149432	+	0.988772i	$0.547744\pi$
$648$		0			0
$649$	−3.67676e15	−	2.12278e15i	−1.25349	−	0.723701i
$650$		0			0
$651$	−2.26124e14	−	1.50974e14i	−0.0757970	−	0.0506065i
$652$		0			0
$653$	2.22746e15	+	1.28602e15i	0.734153	+	0.423864i	0.819940	−	0.572450i	$-0.194007\pi$
$653$	2.22746e15	+	1.28602e15i	0.734153	+	0.423864i	−0.0857864	+	0.996314i	$0.527340\pi$
$654$		0			0
$655$	−1.47188e14	−	2.54938e14i	−0.0477031	−	0.0826242i
$656$		0			0
$657$	1.05626e15	+	1.71440e15i	0.336637	+	0.546390i
$658$		0			0
$659$		−	4.82477e15i		−	1.51219i	−0.654462	−	0.756095i	$-0.727105\pi$
$659$		−	4.82477e15i		−	1.51219i	0.654462	−	0.756095i	$-0.272895\pi$
$660$		0			0
$661$	−3.09492e15	+	1.78685e15i	−0.953985	+	0.550783i	−0.894317	−	0.447435i	$-0.852338\pi$
$661$	−3.09492e15	+	1.78685e15i	−0.953985	+	0.550783i	−0.0596683	+	0.998218i	$0.519004\pi$
$662$		0			0
$663$	2.79598e14	−	1.10649e15i	0.0847637	−	0.335446i
$664$		0			0
$665$	−1.42729e14	−	7.73728e14i	−0.0425591	−	0.230712i
$666$		0			0
$667$	3.65607e15	−	6.33250e15i	1.07231	−	1.85730i
$668$		0			0
$669$	9.28962e14	+	9.02782e14i	0.268012	+	0.260459i
$670$		0			0
$671$	−4.20189e15			−1.19253
$672$		0			0
$673$	4.71010e13			0.0131506			0.00657532	−	0.999978i	$-0.497907\pi$
$673$	4.71010e13			0.0131506			0.00657532	+	0.999978i	$0.497907\pi$
$674$		0			0
$675$	−4.51397e14	+	2.02883e15i	−0.123990	+	0.557281i
$676$		0			0
$677$	1.18334e15	−	2.04961e15i	0.319796	−	0.553903i	−0.660649	−	0.750695i	$-0.729719\pi$
$677$	1.18334e15	−	2.04961e15i	0.319796	−	0.553903i	0.980445	+	0.196792i	$0.0630523\pi$
$678$		0			0
$679$	−5.35878e15	−	1.90272e15i	−1.42489	−	0.505931i
$680$		0			0
$681$	−1.32055e15	−	3.33690e14i	−0.345499	−	0.0873040i
$682$		0			0
$683$	−2.20706e15	+	1.27425e15i	−0.568198	+	0.328049i	−0.756429	−	0.654075i	$-0.773058\pi$
$683$	−2.20706e15	+	1.27425e15i	−0.568198	+	0.328049i	0.188231	+	0.982125i	$0.439725\pi$
$684$		0			0
$685$			2.72852e15i			0.691240i
$686$		0			0
$687$	5.21067e15	−	1.47632e15i	1.29907	−	0.368060i
$688$		0			0
$689$	−1.94498e15	−	3.36880e15i	−0.477209	−	0.826551i
$690$		0			0
$691$	−5.05921e15	−	2.92094e15i	−1.22167	−	0.705331i	−0.256395	−	0.966572i	$-0.582535\pi$
$691$	−5.05921e15	−	2.92094e15i	−1.22167	−	0.705331i	−0.965274	+	0.261241i	$0.915868\pi$
$692$		0			0
$693$	−5.35790e15	+	1.14760e15i	−1.27339	+	0.272746i
$694$		0			0
$695$	1.71666e15	+	9.91115e14i	0.401576	+	0.231850i
$696$		0			0
$697$	1.14638e14	+	1.98558e14i	0.0263966	+	0.0457202i
$698$		0			0
$699$	−7.76433e14	+	2.19984e14i	−0.175986	+	0.0498616i
$700$		0			0
$701$			2.09264e13i			0.00466923i	0.999997	+	0.00233462i	$0.000743132\pi$
$701$			2.09264e13i			0.00466923i	−0.999997	+	0.00233462i	$0.999257\pi$
$702$		0			0
$703$	2.87063e14	−	1.65736e14i	0.0630555	−	0.0364051i
$704$		0			0
$705$	−4.22841e14	−	1.06848e14i	−0.0914403	−	0.0231060i
$706$		0			0
$707$	8.84813e15	−	1.63220e15i	1.88384	−	0.347510i
$708$		0			0
$709$	−9.49666e14	+	1.64487e15i	−0.199075	+	0.344808i	−0.948229	−	0.317588i	$-0.897127\pi$
$709$	−9.49666e14	+	1.64487e15i	−0.199075	+	0.344808i	0.749154	+	0.662396i	$0.230460\pi$
$710$		0			0
$711$	4.00440e15	+	2.16177e15i	0.826523	+	0.446198i
$712$		0			0
$713$	8.41616e14			0.171049
$714$		0			0
$715$	−2.55292e15			−0.510921
$716$		0			0
$717$	3.14862e15	+	3.05989e15i	0.620533	+	0.603046i
$718$		0			0
$719$	−3.94778e14	+	6.83776e14i	−0.0766204	+	0.132710i	−0.901790	−	0.432175i	$-0.857746\pi$
$719$	−3.94778e14	+	6.83776e14i	−0.0766204	+	0.132710i	0.825169	+	0.564885i	$0.191080\pi$
$720$		0			0
$721$	−7.20435e15	+	6.14262e15i	−1.37705	+	1.17411i
$722$		0			0
$723$	2.30780e15	−	9.13295e15i	0.434448	−	1.71930i
$724$		0			0
$725$	−3.04711e15	+	1.75925e15i	−0.564974	+	0.326188i
$726$		0			0
$727$		−	5.66468e15i		−	1.03451i	−0.855830	−	0.517256i	$-0.826953\pi$
$727$		−	5.66468e15i		−	1.03451i	0.855830	−	0.517256i	$-0.173047\pi$
$728$		0			0
$729$	4.76090e14	+	5.53864e15i	0.0856422	+	0.996326i
$730$		0			0
$731$	2.49857e14	+	4.32765e14i	0.0442737	+	0.0766842i
$732$		0			0
$733$	−5.90786e15	−	3.41091e15i	−1.03124	−	0.595385i	−0.113898	−	0.993492i	$-0.536334\pi$
$733$	−5.90786e15	−	3.41091e15i	−1.03124	−	0.595385i	−0.917339	+	0.398107i	$0.869667\pi$
$734$		0			0
$735$	1.50542e15	−	3.49931e15i	0.258867	−	0.601731i
$736$		0			0
$737$	−4.47488e15	−	2.58357e15i	−0.758072	−	0.437673i
$738$		0			0
$739$	−1.27003e15	−	2.19975e15i	−0.211967	−	0.367138i	0.740363	−	0.672208i	$-0.234654\pi$
$739$	−1.27003e15	−	2.19975e15i	−0.211967	−	0.367138i	−0.952330	+	0.305069i	$0.901320\pi$
$740$		0			0
$741$	3.55596e14	+	1.25508e15i	0.0584732	+	0.206381i
$742$		0			0
$743$			5.78015e15i			0.936485i	0.883600	+	0.468242i	$0.155113\pi$
$743$			5.78015e15i			0.936485i	−0.883600	+	0.468242i	$0.844887\pi$
$744$		0			0
$745$	1.78265e15	−	1.02922e15i	0.284582	−	0.164303i
$746$		0			0
$747$	−3.26367e13	−	1.14153e15i	−0.00513384	−	0.179566i
$748$		0			0
$749$	−8.16486e14	+	6.96157e14i	−0.126561	+	0.107909i
$750$		0			0
$751$	1.98569e15	−	3.43932e15i	0.303314	−	0.525355i	−0.673571	−	0.739123i	$-0.735240\pi$
$751$	1.98569e15	−	3.43932e15i	0.303314	−	0.525355i	0.976884	+	0.213768i	$0.0685737\pi$
$752$		0			0
$753$	3.07974e15	−	3.16905e15i	0.463598	−	0.477042i
$754$		0			0
$755$	7.92544e15			1.17575
$756$		0			0
$757$	8.33721e15			1.21897			0.609486	−	0.792797i	$-0.291376\pi$
$757$	8.33721e15			1.21897			0.609486	+	0.792797i	$0.291376\pi$
$758$		0			0
$759$	1.18206e16	−	1.21634e16i	1.70338	−	1.75278i
$760$		0			0
$761$	5.46301e15	−	9.46221e15i	0.775919	−	1.34393i	−0.158357	−	0.987382i	$-0.550620\pi$
$761$	5.46301e15	−	9.46221e15i	0.775919	−	1.34393i	0.934276	−	0.356550i	$-0.116047\pi$
$762$		0			0
$763$	−8.67724e15	+	1.60068e15i	−1.21478	+	0.224088i
$764$		0			0
$765$	7.83683e13	+	2.74109e15i	0.0108144	+	0.378255i
$766$		0			0
$767$	−4.23807e15	+	2.44685e15i	−0.576493	+	0.332838i
$768$		0			0
$769$			6.91791e15i			0.927641i	0.885929	+	0.463821i	$0.153522\pi$
$769$			6.91791e15i			0.927641i	−0.885929	+	0.463821i	$0.846478\pi$
$770$		0			0
$771$	2.59958e15	+	9.17520e15i	0.343640	+	1.21288i
$772$		0			0
$773$	1.86294e15	+	3.22671e15i	0.242780	+	0.420507i	0.961505	−	0.274787i	$-0.0886075\pi$
$773$	1.86294e15	+	3.22671e15i	0.242780	+	0.420507i	−0.718725	+	0.695294i	$0.755274\pi$
$774$		0			0
$775$	−3.50717e14	−	2.02487e14i	−0.0450607	−	0.0260158i
$776$		0			0
$777$	1.60150e15	+	1.04389e14i	0.202867	+	0.0132233i
$778$		0			0
$779$	−2.26954e14	−	1.31032e14i	−0.0283453	−	0.0163652i
$780$		0			0
$781$	5.92615e15	+	1.02644e16i	0.729780	+	1.26402i
$782$		0			0
$783$	−6.36304e15	+	6.93346e15i	−0.772636	+	0.841900i
$784$		0			0
$785$			1.98656e15i			0.237859i
$786$		0			0
$787$	3.89375e15	−	2.24806e15i	0.459734	−	0.265428i	−0.252198	−	0.967676i	$-0.581154\pi$
$787$	3.89375e15	−	2.24806e15i	0.459734	−	0.265428i	0.711932	+	0.702248i	$0.247820\pi$
$788$		0			0
$789$	−2.07515e15	+	8.21224e15i	−0.241616	+	0.956177i
$790$		0			0
$791$	−1.29598e16	−	4.60158e15i	−1.48809	−	0.528368i
$792$		0			0
$793$	−2.42168e15	+	4.19448e15i	−0.274230	+	0.474980i
$794$		0			0
$795$	6.70287e15	+	6.51398e15i	0.748586	+	0.727490i
$796$		0			0
$797$	−1.61510e16			−1.77901			−0.889503	−	0.456929i	$-0.848949\pi$
$797$	−1.61510e16			−1.77901			−0.889503	+	0.456929i	$0.848949\pi$
$798$		0			0
$799$	7.65592e14			0.0831745
$800$		0			0
$801$	−3.27897e15	−	1.77015e15i	−0.351365	−	0.189684i
$802$		0			0
$803$	−3.95354e15	+	6.84773e15i	−0.417879	+	0.723788i
$804$		0			0
$805$	2.13909e15	+	1.15960e16i	0.223024	+	1.20901i
$806$		0			0
$807$	1.43095e16	+	3.61585e15i	1.47170	+	0.371883i
$808$		0			0
$809$	1.54933e16	−	8.94505e15i	1.57191	−	0.907541i	0.575971	−	0.817470i	$-0.304624\pi$
$809$	1.54933e16	−	8.94505e15i	1.57191	−	0.907541i	0.995935	−	0.0900709i	$-0.0287094\pi$
$810$		0			0
$811$			1.53671e16i			1.53808i	0.639202	+	0.769039i	$0.279265\pi$
$811$			1.53671e16i			1.53808i	−0.639202	+	0.769039i	$0.720735\pi$
$812$		0			0
$813$	1.72793e16	−	4.89567e15i	1.70619	−	0.483408i
$814$		0			0
$815$	2.11767e15	+	3.66791e15i	0.206296	+	0.357315i
$816$		0			0
$817$	−4.94653e14	−	2.85588e14i	−0.0475422	−	0.0274485i
$818$		0			0
$819$	−1.94235e15	+	6.00985e15i	−0.184190	+	0.569905i
$820$		0			0
$821$	−3.39421e15	−	1.95965e15i	−0.317578	−	0.183354i	0.332734	−	0.943021i	$-0.392029\pi$
$821$	−3.39421e15	−	1.95965e15i	−0.317578	−	0.183354i	−0.650313	+	0.759667i	$0.725362\pi$
$822$		0			0
$823$	−5.25023e14	−	9.09366e14i	−0.0484707	−	0.0839537i	0.840772	−	0.541389i	$-0.182101\pi$
$823$	−5.25023e14	−	9.09366e14i	−0.0484707	−	0.0839537i	−0.889243	+	0.457435i	$0.848768\pi$
$824$		0			0
$825$	−7.85232e15	+	2.22477e15i	−0.715322	+	0.202669i
$826$		0			0
$827$		−	1.47529e15i		−	0.132616i	−0.997799	−	0.0663080i	$-0.978878\pi$
$827$		−	1.47529e15i		−	0.132616i	0.997799	−	0.0663080i	$-0.0211220\pi$
$828$		0			0
$829$	1.14702e16	−	6.62231e15i	1.01747	−	0.587435i	0.104098	−	0.994567i	$-0.466804\pi$
$829$	1.14702e16	−	6.62231e15i	1.01747	−	0.587435i	0.913369	+	0.407132i	$0.133471\pi$
$830$		0			0
$831$	1.56223e16	+	3.94758e15i	1.36753	+	0.345561i
$832$		0			0
$833$	−1.05720e15	+	6.60295e15i	−0.0913292	+	0.570415i
$834$		0			0
$835$	3.82525e15	−	6.62553e15i	0.326125	−	0.564865i
$836$		0			0
$837$	−1.05730e15	−	2.35241e14i	−0.0889630	−	0.0197935i
$838$		0			0
$839$	−9.48206e15			−0.787430			−0.393715	−	0.919233i	$-0.628810\pi$
$839$	−9.48206e15			−0.787430			−0.393715	+	0.919233i	$0.628810\pi$
$840$		0			0
$841$	−3.73046e15			−0.305763
$842$		0			0
$843$	−7.90295e15	−	7.68024e15i	−0.639349	−	0.621331i
$844$		0			0
$845$	2.63031e15	−	4.55583e15i	0.210037	−	0.363794i
$846$		0			0
$847$	−5.72839e15	−	6.71852e15i	−0.451517	−	0.529560i
$848$		0			0
$849$	2.71067e15	−	1.07273e16i	0.210904	−	0.834636i
$850$		0			0
$851$	−4.30225e15	+	2.48390e15i	−0.330433	+	0.190775i
$852$		0			0
$853$		−	1.98483e14i		−	0.0150489i	−0.999972	−	0.00752445i	$-0.997605\pi$
$853$		−	1.98483e14i		−	0.0150489i	0.999972	−	0.00752445i	$-0.00239513\pi$
$854$		0			0
$855$	−1.64412e15	−	2.66854e15i	−0.123061	−	0.199738i
$856$		0			0
$857$	1.31968e16	+	2.28575e16i	0.975157	+	1.68902i	0.679416	+	0.733753i	$0.262233\pi$
$857$	1.31968e16	+	2.28575e16i	0.975157	+	1.68902i	0.295741	+	0.955268i	$0.404434\pi$
$858$		0			0
$859$	2.60131e15	+	1.50186e15i	0.189771	+	0.109564i	0.591875	−	0.806030i	$-0.298388\pi$
$859$	2.60131e15	+	1.50186e15i	0.189771	+	0.109564i	−0.402105	+	0.915594i	$0.631721\pi$
$860$		0			0
$861$	−5.61603e14	−	1.13779e15i	−0.0404494	−	0.0819490i
$862$		0			0
$863$	1.41267e16	+	8.15604e15i	1.00457	+	0.579989i	0.909597	−	0.415491i	$-0.136390\pi$
$863$	1.41267e16	+	8.15604e15i	1.00457	+	0.579989i	0.0949730	+	0.995480i	$0.469724\pi$
$864$		0			0
$865$	−5.00869e15	−	8.67531e15i	−0.351670	−	0.609111i
$866$		0			0
$867$	2.61991e15	+	9.24695e15i	0.181627	+	0.641053i
$868$		0			0
$869$			1.78691e16i			1.22319i
$870$		0			0
$871$	−5.15803e15	+	2.97799e15i	−0.348646	+	0.201291i
$872$		0			0
$873$	−2.26447e16	+	6.47416e14i	−1.51143	+	0.0432121i
$874$		0			0
$875$	5.22392e15	−	1.47125e16i	0.344312	−	0.969712i
$876$		0			0
$877$	5.69508e15	−	9.86417e15i	0.370683	−	0.642041i	−0.618988	−	0.785400i	$-0.712457\pi$
$877$	5.69508e15	−	9.86417e15i	0.370683	−	0.642041i	0.989671	+	0.143359i	$0.0457904\pi$
$878$		0			0
$879$	−7.00021e15	+	7.20321e15i	−0.449958	+	0.463007i
$880$		0			0
$881$	6.01407e15			0.381769			0.190885	−	0.981612i	$-0.438864\pi$
$881$	6.01407e15			0.381769			0.190885	+	0.981612i	$0.438864\pi$
$882$		0			0
$883$	−1.77508e16			−1.11285			−0.556423	−	0.830899i	$-0.687826\pi$
$883$	−1.77508e16			−1.11285			−0.556423	+	0.830899i	$0.687826\pi$
$884$		0			0
$885$	8.19481e15	−	8.43245e15i	0.507401	−	0.522115i
$886$		0			0
$887$	6.35987e15	−	1.10156e16i	0.388927	−	0.673642i	−0.603378	−	0.797455i	$-0.706179\pi$
$887$	6.35987e15	−	1.10156e16i	0.388927	−	0.673642i	0.992306	+	0.123813i	$0.0395124\pi$
$888$		0			0
$889$	−1.63385e15	+	4.60155e15i	−0.0986855	+	0.277936i
$890$		0			0
$891$	−1.82498e16	+	1.19766e16i	−1.08876	+	0.714509i
$892$		0			0
$893$	−7.57839e14	+	4.37538e14i	−0.0446574	+	0.0257830i
$894$		0			0
$895$			2.34707e15i			0.136615i
$896$		0			0
$897$	−5.32936e15	−	1.88100e16i	−0.306420	−	1.08151i
$898$		0			0
$899$	−9.16815e14	−	1.58797e15i	−0.0520719	−	0.0901911i
$900$		0			0
$901$	−1.42091e16	−	8.20364e15i	−0.797225	−	0.460278i
$902$		0			0
$903$	−1.22403e15	−	2.47985e15i	−0.0678439	−	0.137449i
$904$		0			0
$905$	−1.48810e16	−	8.59153e15i	−0.814824	−	0.470439i
$906$		0			0
$907$	−3.38697e15	−	5.86641e15i	−0.183219	−	0.317345i	0.759756	−	0.650209i	$-0.225319\pi$
$907$	−3.38697e15	−	5.86641e15i	−0.183219	−	0.317345i	−0.942975	+	0.332863i	$0.891985\pi$
$908$		0			0
$909$	3.05167e16	−	1.88016e16i	1.63093	−	1.00483i
$910$		0			0
$911$		−	2.62025e16i		−	1.38354i	−0.722119	−	0.691769i	$-0.756832\pi$
$911$		−	2.62025e16i		−	1.38354i	0.722119	−	0.691769i	$-0.243168\pi$
$912$		0			0
$913$	3.88351e15	−	2.24215e15i	0.202598	−	0.116970i
$914$		0			0
$915$	2.85106e15	−	1.12829e16i	0.146957	−	0.581572i
$916$		0			0
$917$	−1.85545e15	−	2.17615e15i	−0.0944968	−	0.110830i
$918$		0			0
$919$	7.89457e15	−	1.36738e16i	0.397277	−	0.688104i	−0.596112	−	0.802901i	$-0.703289\pi$
$919$	7.89457e15	−	1.36738e16i	0.397277	−	0.688104i	0.993389	+	0.114798i	$0.0366219\pi$
$920$		0			0
$921$	−1.83728e16	−	1.78551e16i	−0.913584	−	0.887837i
$922$		0			0
$923$	1.36617e16			0.671268
$924$		0			0
$925$	2.39044e15			0.116064
$926$		0			0
$927$	−1.79171e16	+	3.31891e16i	−0.859665	+	1.59242i
$928$		0			0
$929$	4.27524e14	−	7.40493e14i	0.0202709	−	0.0351103i	−0.855712	−	0.517452i	$-0.826880\pi$
$929$	4.27524e14	−	7.40493e14i	0.0202709	−	0.0351103i	0.875983	+	0.482342i	$0.160214\pi$
$930$		0			0
$931$	−2.72712e15	−	7.14028e15i	−0.127785	−	0.334574i
$932$		0			0
$933$	1.93938e16	+	4.90061e15i	0.898078	+	0.226935i
$934$		0			0
$935$	−9.32523e15	+	5.38392e15i	−0.426772	+	0.246397i
$936$		0			0
$937$		−	2.08188e16i		−	0.941647i	−0.882227	−	0.470823i	$-0.843957\pi$
$937$		−	2.08188e16i		−	0.941647i	0.882227	−	0.470823i	$-0.156043\pi$
$938$		0			0
$939$	6.45218e15	−	1.82807e15i	0.288433	−	0.0817208i
$940$		0			0
$941$	−5.81954e15	−	1.00797e16i	−0.257126	−	0.445355i	0.708345	−	0.705866i	$-0.249442\pi$
$941$	−5.81954e15	−	1.00797e16i	−0.257126	−	0.445355i	−0.965471	+	0.260511i	$0.916109\pi$
$942$		0			0
$943$	3.40138e15	+	1.96379e15i	0.148539	+	0.0857591i
$944$		0			0
$945$	5.53908e14	−	1.51656e16i	0.0239091	−	0.654615i
$946$		0			0
$947$	−1.37448e16	−	7.93557e15i	−0.586427	−	0.338574i	0.177257	−	0.984165i	$-0.443278\pi$
$947$	−1.37448e16	−	7.93557e15i	−0.586427	−	0.338574i	−0.763683	+	0.645591i	$0.776611\pi$
$948$		0			0
$949$	4.55710e15	+	7.89313e15i	0.192187	+	0.332878i
$950$		0			0
$951$	−2.15054e16	+	6.09305e15i	−0.896510	+	0.254005i
$952$		0			0
$953$		−	2.14296e16i		−	0.883085i	−0.897240	−	0.441542i	$-0.854431\pi$
$953$		−	2.14296e16i		−	0.883085i	0.897240	−	0.441542i	$-0.145569\pi$
$954$		0			0
$955$	−2.07011e16	+	1.19518e16i	−0.843285	+	0.486871i
$956$		0			0
$957$	−3.58269e16	−	9.05308e15i	−1.44276	−	0.364570i
$958$		0			0
$959$	4.80853e15	+	2.60669e16i	0.191430	+	1.03774i
$960$		0			0
$961$	−1.25987e16	+	2.18216e16i	−0.495847	+	0.858832i
$962$		0			0
$963$	−2.03059e15	+	3.76140e15i	−0.0790090	+	0.146354i
$964$		0			0
$965$	1.53916e16			0.592086
$966$		0			0
$967$	1.67370e16			0.636549			0.318274	−	0.947999i	$-0.396897\pi$
$967$	1.67370e16			0.636549			0.318274	+	0.947999i	$0.396897\pi$
$968$		0			0
$969$	3.94577e15	+	3.83458e15i	0.148372	+	0.144190i
$970$		0			0
$971$	−1.91722e16	+	3.32072e16i	−0.712798	+	1.23460i	0.251005	+	0.967986i	$0.419239\pi$
$971$	−1.91722e16	+	3.32072e16i	−0.712798	+	1.23460i	−0.963803	+	0.266616i	$0.914094\pi$
$972$		0			0
$973$	1.81468e16	+	6.44330e15i	0.667082	+	0.236858i
$974$		0			0
$975$	−2.30470e15	+	9.12067e15i	−0.0837700	+	0.331514i
$976$		0			0
$977$	2.12401e16	−	1.22630e16i	0.763374	−	0.440734i	−0.0671319	−	0.997744i	$-0.521385\pi$
$977$	2.12401e16	−	1.22630e16i	0.763374	−	0.440734i	0.830506	+	0.557010i	$0.188051\pi$
$978$		0			0
$979$		−	1.46320e16i		−	0.519993i
$980$		0			0
$981$	−2.99273e16	+	1.84385e16i	−1.05169	+	0.647957i
$982$		0			0
$983$	−2.72140e16	−	4.71360e16i	−0.945688	−	1.63798i	−0.754367	−	0.656453i	$-0.772056\pi$
$983$	−2.72140e16	−	4.71360e16i	−0.945688	−	1.63798i	−0.191322	−	0.981527i	$-0.561277\pi$
$984$		0			0
$985$	2.01139e16	+	1.16128e16i	0.691189	+	0.399058i
$986$		0			0
$987$	−4.22792e15	−	2.75585e14i	−0.143675	−	0.00936506i
$988$		0			0
$989$	7.41342e15	+	4.28014e15i	0.249137	+	0.143840i
$990$		0			0
$991$	1.12113e16	+	1.94186e16i	0.372607	+	0.645375i	0.989966	−	0.141307i	$-0.0451306\pi$
$991$	1.12113e16	+	1.94186e16i	0.372607	+	0.645375i	−0.617359	+	0.786682i	$0.711797\pi$
$992$		0			0
$993$	−8.59929e15	−	3.03512e16i	−0.282645	−	0.997596i
$994$		0			0
$995$			2.42375e16i			0.787882i
$996$		0			0
$997$	7.68788e15	−	4.43860e15i	0.247163	−	0.142700i	−0.371302	−	0.928512i	$-0.621088\pi$
$997$	7.68788e15	−	4.43860e15i	0.247163	−	0.142700i	0.618465	+	0.785813i	$0.287755\pi$
$998$		0			0
$999$	6.09910e15	−	1.91795e15i	0.193935	−	0.0609854i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	84.12.k.b.5.7	yes	56
3.2	odd	2	inner	84.12.k.b.5.4	✓	56
7.3	odd	6	inner	84.12.k.b.17.4	yes	56
21.17	even	6	inner	84.12.k.b.17.7	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.12.k.b.5.4	✓	56	3.2	odd	2	inner
84.12.k.b.5.7	yes	56	1.1	even	1	trivial
84.12.k.b.17.4	yes	56	7.3	odd	6	inner
84.12.k.b.17.7	yes	56	21.17	even	6	inner

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:	\( N \)	\(=\)	\( 84 = 2^{2} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	84.k (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-293.330 + 301.836i) q^{3} +(2288.66 - 3964.07i) q^{5} +(14878.7 - 41904.1i) q^{7} +(-5062.60 - 177075. i) q^{9} +O(q^{10})\)	\(q+(-293.330 + 301.836i) q^{3} +(2288.66 - 3964.07i) q^{5} +(14878.7 - 41904.1i) q^{7} +(-5062.60 - 177075. i) q^{9} +(602411. - 347802. i) q^{11} -801797. i q^{13} +(525167. + 1.85358e6i) q^{15} +(-1.69093e6 - 2.92878e6i) q^{17} +(3.34762e6 + 1.93275e6i) q^{19} +(8.28378e6 + 1.67826e7i) q^{21} +(-5.01711e7 - 2.89663e7i) q^{23} +(1.39382e7 + 2.41416e7i) q^{25} +(5.49325e7 + 5.04131e7i) q^{27} +1.26218e8i q^{29} +(-1.25812e7 + 7.26374e6i) q^{31} +(-7.17258e7 + 2.83850e8i) q^{33} +(-1.32058e8 - 1.54884e8i) q^{35} +(4.28757e7 - 7.42629e7i) q^{37} +(2.42011e8 + 2.35191e8i) q^{39} -6.77955e7 q^{41} -1.47763e8 q^{43} +(-7.13522e8 - 3.85194e8i) q^{45} +(-1.13191e8 + 1.96052e8i) q^{47} +(-1.53458e9 - 1.24696e9i) q^{49} +(1.38001e9 + 3.48714e8i) q^{51} +(4.20156e9 - 2.42577e9i) q^{53} -3.18400e9i q^{55} +(-1.56533e9 + 4.43499e8i) q^{57} +(-3.05171e9 - 5.28571e9i) q^{59} +(-5.23135e9 - 3.02032e9i) q^{61} +(-7.49547e9 - 2.42250e9i) q^{63} +(-3.17838e9 - 1.83504e9i) q^{65} +(-3.71415e9 - 6.43309e9i) q^{67} +(2.34597e10 - 6.64677e9i) q^{69} +1.70389e10i q^{71} +(-9.84429e9 + 5.68361e9i) q^{73} +(-1.13753e10 - 2.87441e9i) q^{75} +(-5.61123e9 - 3.04183e10i) q^{77} +(-1.28443e10 + 2.22470e10i) q^{79} +(-3.13298e10 + 1.79292e9i) q^{81} +6.44662e9 q^{83} -1.54798e10 q^{85} +(-3.80971e10 - 3.70234e10i) q^{87} +(1.05174e10 - 1.82167e10i) q^{89} +(-3.35986e10 - 1.19297e10i) q^{91} +(1.49797e9 - 5.92812e9i) q^{93} +(1.53231e10 - 8.84679e9i) q^{95} -1.27882e11i q^{97} +(-6.46367e10 - 1.04911e11i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 729 q^{3} - 27194 q^{7} - 172347 q^{9}+O(q^{10}) \) 56 * q - 729 * q^3 - 27194 * q^7 - 172347 * q^9	\( 56 q - 729 q^{3} - 27194 q^{7} - 172347 q^{9} - 4853058 q^{15} + 28700520 q^{19} - 11325429 q^{21} - 316601194 q^{25} - 1368416388 q^{31} + 40874949 q^{33} - 87435712 q^{37} + 1177474410 q^{39} - 3055078348 q^{43} + 4109921793 q^{45} - 742582522 q^{49} - 694793715 q^{51} + 14605100370 q^{57} + 72584834058 q^{61} - 7310837811 q^{63} + 6131679148 q^{67} - 74402605464 q^{73} - 161115157854 q^{75} + 52181713528 q^{79} + 44948282337 q^{81} + 4658488716 q^{85} + 243101263104 q^{87} - 85311757146 q^{91} - 256628211777 q^{93} + 157345775874 q^{99}+O(q^{100}) \) 56 * q - 729 * q^3 - 27194 * q^7 - 172347 * q^9 - 4853058 * q^15 + 28700520 * q^19 - 11325429 * q^21 - 316601194 * q^25 - 1368416388 * q^31 + 40874949 * q^33 - 87435712 * q^37 + 1177474410 * q^39 - 3055078348 * q^43 + 4109921793 * q^45 - 742582522 * q^49 - 694793715 * q^51 + 14605100370 * q^57 + 72584834058 * q^61 - 7310837811 * q^63 + 6131679148 * q^67 - 74402605464 * q^73 - 161115157854 * q^75 + 52181713528 * q^79 + 44948282337 * q^81 + 4658488716 * q^85 + 243101263104 * q^87 - 85311757146 * q^91 - 256628211777 * q^93 + 157345775874 * q^99

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