LMFDB - Embedded newform 48.8.k.a.11.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [48,8,Mod(11,48)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(48, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 2]))

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("48.11");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 48 = 2^{4} \cdot 3 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	48.k (of order $4$, 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:	$14.9944812232$
Analytic rank:	$0$
Dimension:	$108$
Relative dimension:	$54$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			11.20
Character	$\chi$	$=$	48.11
Dual form			48.8.k.a.35.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-5.44512 + 9.91719i) q^{2} +(40.1781 - 23.9317i) q^{3} +(-68.7013 - 108.001i) q^{4} +(-101.752 + 101.752i) q^{5} +(18.5603 + 528.764i) q^{6} -33.7333 q^{7} +(1445.15 - 93.2472i) q^{8} +(1041.55 - 1923.05i) q^{9} +O(q^{10})$	\(q+(-5.44512 + 9.91719i) q^{2} +(40.1781 - 23.9317i) q^{3} +(-68.7013 - 108.001i) q^{4} +(-101.752 + 101.752i) q^{5} +(18.5603 + 528.764i) q^{6} -33.7333 q^{7} +(1445.15 - 93.2472i) q^{8} +(1041.55 - 1923.05i) q^{9} +(-455.042 - 1563.15i) q^{10} +(-2398.00 - 2398.00i) q^{11} +(-5344.92 - 2695.12i) q^{12} +(-10780.0 + 10780.0i) q^{13} +(183.682 - 334.540i) q^{14} +(-1653.11 + 6523.30i) q^{15} +(-6944.27 + 14839.6i) q^{16} -30783.2i q^{17} +(13399.9 + 20800.5i) q^{18} +(-33104.3 - 33104.3i) q^{19} +(17979.8 + 3998.79i) q^{20} +(-1355.34 + 807.294i) q^{21} +(36838.8 - 10724.0i) q^{22} -57808.0i q^{23} +(55831.7 - 38331.3i) q^{24} +57418.0i q^{25} +(-48208.7 - 165605. i) q^{26} +(-4174.32 - 102191. i) q^{27} +(2317.52 + 3643.22i) q^{28} +(24169.3 + 24169.3i) q^{29} +(-55691.4 - 51914.3i) q^{30} -180087. i q^{31} +(-109354. - 149671. i) q^{32} +(-153735. - 38958.8i) q^{33} +(305283. + 167618. i) q^{34} +(3432.44 - 3432.44i) q^{35} +(-279247. + 19628.0i) q^{36} +(-87688.8 - 87688.8i) q^{37} +(508559. - 148045. i) q^{38} +(-175136. + 691100. i) q^{39} +(-137559. + 156535. i) q^{40} +106630. q^{41} +(-626.100 - 17837.0i) q^{42} +(-229157. + 229157. i) q^{43} +(-94239.6 + 423731. i) q^{44} +(89694.7 + 301655. i) q^{45} +(573292. + 314771. i) q^{46} -179533. q^{47} +(76128.2 + 762413. i) q^{48} -822405. q^{49} +(-569425. - 312648. i) q^{50} +(-736692. - 1.23681e6i) q^{51} +(1.90484e6 + 423645. i) q^{52} +(-320801. + 320801. i) q^{53} +(1.03617e6 + 515043. i) q^{54} +488002. q^{55} +(-48749.7 + 3145.54i) q^{56} +(-2.12231e6 - 537826. i) q^{57} +(-371297. + 108087. i) q^{58} +(926251. + 926251. i) q^{59} +(818091. - 269622. i) q^{60} +(344255. - 344255. i) q^{61} +(1.78596e6 + 980596. i) q^{62} +(-35135.0 + 64871.0i) q^{63} +(2.07976e6 - 269512. i) q^{64} -2.19377e6i q^{65} +(1.22347e6 - 1.31248e6i) q^{66} +(133558. + 133558. i) q^{67} +(-3.32460e6 + 2.11484e6i) q^{68} +(-1.38344e6 - 2.32261e6i) q^{69} +(15350.1 + 52730.1i) q^{70} +4.17509e6i q^{71} +(1.32588e6 - 2.87622e6i) q^{72} +509562. i q^{73} +(1.34710e6 - 392150. i) q^{74} +(1.37411e6 + 2.30694e6i) q^{75} +(-1.30098e6 + 5.84960e6i) q^{76} +(80892.4 + 80892.4i) q^{77} +(-5.90013e6 - 5.49998e6i) q^{78} +2.25276e6i q^{79} +(-803363. - 2.21655e6i) q^{80} +(-2.61331e6 - 4.00592e6i) q^{81} +(-580611. + 1.05746e6i) q^{82} +(3.77684e6 - 3.77684e6i) q^{83} +(180302. + 90915.3i) q^{84} +(3.13225e6 + 3.13225e6i) q^{85} +(-1.02480e6 - 3.52037e6i) q^{86} +(1.54949e6 + 392665. i) q^{87} +(-3.68907e6 - 3.24186e6i) q^{88} -9.47841e6 q^{89} +(-3.47997e6 - 753029. i) q^{90} +(363644. - 363644. i) q^{91} +(-6.24329e6 + 3.97148e6i) q^{92} +(-4.30978e6 - 7.23555e6i) q^{93} +(977579. - 1.78046e6i) q^{94} +6.73687e6 q^{95} +(-7.97552e6 - 3.39645e6i) q^{96} +5.68054e6 q^{97} +(4.47810e6 - 8.15595e6i) q^{98} +(-7.10912e6 + 2.11384e6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 108 q - 2 q^{3} - 4 q^{4} + 172 q^{6} - 8 q^{7}+O(q^{10}) $ 108 * q - 2 * q^3 - 4 * q^4 + 172 * q^6 - 8 * q^7	$ 108 q - 2 q^{3} - 4 q^{4} + 172 q^{6} - 8 q^{7} - 6504 q^{10} + 12016 q^{12} - 4 q^{13} - 55280 q^{16} + 21172 q^{18} - 60588 q^{19} - 4376 q^{21} - 212744 q^{22} - 317304 q^{24} + 238042 q^{27} + 219736 q^{28} - 503852 q^{30} - 4 q^{33} - 364856 q^{34} + 867620 q^{36} - 4 q^{37} - 283948 q^{39} + 390392 q^{40} - 3022344 q^{42} + 752844 q^{43} - 156252 q^{45} - 1166824 q^{46} + 358320 q^{48} + 9882508 q^{49} + 1121592 q^{51} - 4458688 q^{52} + 203816 q^{54} + 4191000 q^{55} + 4975544 q^{58} - 4390240 q^{60} - 2279892 q^{61} + 4781432 q^{64} + 1457476 q^{66} + 1552540 q^{67} + 4372 q^{69} - 9366152 q^{70} - 1660280 q^{72} - 886066 q^{75} - 6569272 q^{76} - 13616772 q^{78} - 4 q^{81} + 11560256 q^{82} - 10944176 q^{84} + 7846496 q^{85} - 40789116 q^{87} + 24614816 q^{88} + 25746032 q^{90} - 1590680 q^{91} - 14495396 q^{93} - 6995856 q^{94} - 13927736 q^{96} - 8 q^{97} - 4701076 q^{99}+O(q^{100}) $ 108 * q - 2 * q^3 - 4 * q^4 + 172 * q^6 - 8 * q^7 - 6504 * q^10 + 12016 * q^12 - 4 * q^13 - 55280 * q^16 + 21172 * q^18 - 60588 * q^19 - 4376 * q^21 - 212744 * q^22 - 317304 * q^24 + 238042 * q^27 + 219736 * q^28 - 503852 * q^30 - 4 * q^33 - 364856 * q^34 + 867620 * q^36 - 4 * q^37 - 283948 * q^39 + 390392 * q^40 - 3022344 * q^42 + 752844 * q^43 - 156252 * q^45 - 1166824 * q^46 + 358320 * q^48 + 9882508 * q^49 + 1121592 * q^51 - 4458688 * q^52 + 203816 * q^54 + 4191000 * q^55 + 4975544 * q^58 - 4390240 * q^60 - 2279892 * q^61 + 4781432 * q^64 + 1457476 * q^66 + 1552540 * q^67 + 4372 * q^69 - 9366152 * q^70 - 1660280 * q^72 - 886066 * q^75 - 6569272 * q^76 - 13616772 * q^78 - 4 * q^81 + 11560256 * q^82 - 10944176 * q^84 + 7846496 * q^85 - 40789116 * q^87 + 24614816 * q^88 + 25746032 * q^90 - 1590680 * q^91 - 14495396 * q^93 - 6995856 * q^94 - 13927736 * q^96 - 8 * q^97 - 4701076 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/48\mathbb{Z}\right)^\times$.

$n$	$17$	$31$	$37$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−5.44512	+	9.91719i	−0.481285	+	0.876564i
$2$	−5.44512	+	9.91719i	−0.481285	+	0.876564i
$3$	40.1781	−	23.9317i	0.859141	−	0.511739i
$3$	40.1781	−	23.9317i	0.859141	−	0.511739i
$4$	−68.7013	−	108.001i	−0.536729	−	0.843755i
$5$	−101.752	+	101.752i	−0.364039	+	0.364039i	−0.865298	−	0.501258i	$-0.832871\pi$
$5$	−101.752	+	101.752i	−0.364039	+	0.364039i	0.501258	+	0.865298i	$0.332871\pi$
$6$	18.5603	+	528.764i	0.0350797	+	0.999385i
$7$	−33.7333			−0.0371720			−0.0185860	−	0.999827i	$-0.505916\pi$
$7$	−33.7333			−0.0371720			−0.0185860	+	0.999827i	$0.505916\pi$
$8$	1445.15	−	93.2472i	0.997925	−	0.0643903i
$9$	1041.55	−	1923.05i	0.476247	−	0.879312i
$10$	−455.042	−	1563.15i	−0.143897	−	0.494311i
$11$	−2398.00	−	2398.00i	−0.543218	−	0.543218i	0.381253	−	0.924471i	$-0.375493\pi$
$11$	−2398.00	−	2398.00i	−0.543218	−	0.543218i	−0.924471	+	0.381253i	$0.875493\pi$
$12$	−5344.92	−	2695.12i	−0.892908	−	0.450240i
$13$	−10780.0	+	10780.0i	−1.36087	+	1.36087i	−0.488051	+	0.872815i	$0.662292\pi$
$13$	−10780.0	+	10780.0i	−1.36087	+	1.36087i	−0.872815	+	0.488051i	$0.837708\pi$
$14$	183.682	−	334.540i	0.0178903	−	0.0325836i
$15$	−1653.11	+	6523.30i	−0.126468	+	0.499054i
$16$	−6944.27	+	14839.6i	−0.423844	+	0.905735i
$17$		−	30783.2i		−	1.51964i	−0.650131	−	0.759822i	$-0.725286\pi$
$17$		−	30783.2i		−	1.51964i	0.650131	−	0.759822i	$-0.274714\pi$
$18$	13399.9	+	20800.5i	0.541562	+	0.840661i
$19$	−33104.3	−	33104.3i	−1.10725	−	1.10725i	−0.993510	−	0.113743i	$-0.963716\pi$
$19$	−33104.3	−	33104.3i	−1.10725	−	1.10725i	−0.113743	−	0.993510i	$-0.536284\pi$
$20$	17979.8	+	3998.79i	0.502550	+	0.111770i
$21$	−1355.34	+	807.294i	−0.0319360	+	0.0190224i
$22$	36838.8	−	10724.0i	0.737608	−	0.214722i
$23$		−	57808.0i		−	0.990696i	−0.868695	−	0.495348i	$-0.835041\pi$
$23$		−	57808.0i		−	0.990696i	0.868695	−	0.495348i	$-0.164959\pi$
$24$	55831.7	−	38331.3i	0.824407	−	0.565997i
$25$			57418.0i			0.734951i
$26$	−48208.7	−	165605.i	−0.537921	−	1.84785i
$27$	−4174.32	−	102191.i	−0.0408143	−	0.999167i
$28$	2317.52	+	3643.22i	0.0199513	+	0.0313641i
$29$	24169.3	+	24169.3i	0.184023	+	0.184023i	0.793106	−	0.609083i	$-0.208463\pi$
$29$	24169.3	+	24169.3i	0.184023	+	0.184023i	−0.609083	+	0.793106i	$0.708463\pi$
$30$	−55691.4	−	51914.3i	−0.376586	−	0.351045i
$31$		−	180087.i		−	1.08572i	−0.839824	−	0.542858i	$-0.817342\pi$
$31$		−	180087.i		−	1.08572i	0.839824	−	0.542858i	$-0.182658\pi$
$32$	−109354.	−	149671.i	−0.589945	−	0.807444i
$33$	−153735.	−	38958.8i	−0.744687	−	0.188715i
$34$	305283.	+	167618.i	1.33207	+	0.731383i
$35$	3432.44	−	3432.44i	0.0135321	−	0.0135321i
$36$	−279247.	+	19628.0i	−0.997539	+	0.0701161i
$37$	−87688.8	−	87688.8i	−0.284602	−	0.284602i	0.550339	−	0.834941i	$-0.314498\pi$
$37$	−87688.8	−	87688.8i	−0.284602	−	0.284602i	−0.834941	+	0.550339i	$0.814498\pi$
$38$	508559.	−	148045.i	1.50348	−	0.437674i
$39$	−175136.	+	691100.i	−0.472768	+	1.86558i
$40$	−137559.	+	156535.i	−0.339843	+	0.386724i
$41$	106630.			0.241621			0.120810	−	0.992676i	$-0.461451\pi$
$41$	106630.			0.241621			0.120810	+	0.992676i	$0.461451\pi$
$42$	−626.100	−	17837.0i	−0.00130398	−	0.0371491i
$43$	−229157.	+	229157.i	−0.439534	+	0.439534i	−0.891855	−	0.452321i	$-0.850596\pi$
$43$	−229157.	+	229157.i	−0.439534	+	0.439534i	0.452321	+	0.891855i	$0.350596\pi$
$44$	−94239.6	+	423731.i	−0.166782	+	0.749904i
$45$	89694.7	+	301655.i	0.146731	+	0.493477i
$46$	573292.	+	314771.i	0.868408	+	0.476807i
$47$	−179533.			−0.252233			−0.126116	−	0.992015i	$-0.540251\pi$
$47$	−179533.			−0.252233			−0.126116	+	0.992015i	$0.540251\pi$
$48$	76128.2	+	762413.i	0.0993576	+	0.995052i
$49$	−822405.			−0.998618
$50$	−569425.	−	312648.i	−0.644231	−	0.353721i
$51$	−736692.	−	1.23681e6i	−0.777661	−	1.30559i
$52$	1.90484e6	+	423645.i	1.87865	+	0.417821i
$53$	−320801.	+	320801.i	−0.295986	+	0.295986i	−0.839439	−	0.543454i	$-0.817116\pi$
$53$	−320801.	+	320801.i	−0.295986	+	0.295986i	0.543454	+	0.839439i	$0.317116\pi$
$54$	1.03617e6	+	515043.i	0.895477	+	0.445108i
$55$	488002.			0.395505
$56$	−48749.7	+	3145.54i	−0.0370949	+	0.00239352i
$57$	−2.12231e6	−	537826.i	−1.51791	−	0.384663i
$58$	−371297.	+	108087.i	−0.249875	+	0.0727402i
$59$	926251.	+	926251.i	0.587147	+	0.587147i	0.936858	−	0.349711i	$-0.113720\pi$
$59$	926251.	+	926251.i	0.587147	+	0.587147i	−0.349711	+	0.936858i	$0.613720\pi$
$60$	818091.	−	269622.i	0.488958	−	0.161149i
$61$	344255.	−	344255.i	0.194190	−	0.194190i	−0.603314	−	0.797504i	$-0.706153\pi$
$61$	344255.	−	344255.i	0.194190	−	0.194190i	0.797504	+	0.603314i	$0.206153\pi$
$62$	1.78596e6	+	980596.i	0.951700	+	0.522540i
$63$	−35135.0	+	64871.0i	−0.0177031	+	0.0326858i
$64$	2.07976e6	−	269512.i	0.991708	−	0.128513i
$65$		−	2.19377e6i		−	0.990817i
$66$	1.22347e6	−	1.31248e6i	0.523828	−	0.561940i
$67$	133558.	+	133558.i	0.0542511	+	0.0542511i	0.733712	−	0.679461i	$-0.237786\pi$
$67$	133558.	+	133558.i	0.0542511	+	0.0542511i	−0.679461	+	0.733712i	$0.737786\pi$
$68$	−3.32460e6	+	2.11484e6i	−1.28221	+	0.815637i
$69$	−1.38344e6	−	2.32261e6i	−0.506977	−	0.851147i
$70$	15350.1	+	52730.1i	0.00534894	+	0.0183745i
$71$			4.17509e6i			1.38440i	0.721706	+	0.692200i	$0.243358\pi$
$71$			4.17509e6i			1.38440i	−0.721706	+	0.692200i	$0.756642\pi$
$72$	1.32588e6	−	2.87622e6i	0.418640	−	0.908152i
$73$			509562.i			0.153309i	0.997058	+	0.0766543i	$0.0244238\pi$
$73$			509562.i			0.153309i	−0.997058	+	0.0766543i	$0.975576\pi$
$74$	1.34710e6	−	392150.i	0.386447	−	0.112497i
$75$	1.37411e6	+	2.30694e6i	0.376103	+	0.631426i
$76$	−1.30098e6	+	5.84960e6i	−0.339956	+	1.52855i
$77$	80892.4	+	80892.4i	0.0201925	+	0.0201925i
$78$	−5.90013e6	−	5.49998e6i	−1.40777	−	1.31229i
$79$			2.25276e6i			0.514067i	0.966402	+	0.257034i	$0.0827451\pi$
$79$			2.25276e6i			0.514067i	−0.966402	+	0.257034i	$0.917255\pi$
$80$	−803363.	−	2.21655e6i	−0.175427	−	0.484019i
$81$	−2.61331e6	−	4.00592e6i	−0.546378	−	0.837539i
$82$	−580611.	+	1.05746e6i	−0.116288	+	0.211796i
$83$	3.77684e6	−	3.77684e6i	0.725030	−	0.725030i	−0.244596	−	0.969625i	$-0.578655\pi$
$83$	3.77684e6	−	3.77684e6i	0.725030	−	0.725030i	0.969625	+	0.244596i	$0.0786552\pi$
$84$	180302.	+	90915.3i	0.0331912	+	0.0167363i
$85$	3.13225e6	+	3.13225e6i	0.553211	+	0.553211i
$86$	−1.02480e6	−	3.52037e6i	−0.173739	−	0.596821i
$87$	1.54949e6	+	392665.i	0.252273	+	0.0639299i
$88$	−3.68907e6	−	3.24186e6i	−0.577069	−	0.507113i
$89$	−9.47841e6			−1.42518			−0.712591	−	0.701580i	$-0.752478\pi$
$89$	−9.47841e6			−1.42518			−0.712591	+	0.701580i	$0.752478\pi$
$90$	−3.47997e6	−	753029.i	−0.503183	−	0.108884i
$91$	363644.	−	363644.i	0.0505861	−	0.0505861i
$92$	−6.24329e6	+	3.97148e6i	−0.835904	+	0.531735i
$93$	−4.30978e6	−	7.23555e6i	−0.555603	−	0.932784i
$94$	977579.	−	1.78046e6i	0.121396	−	0.221098i
$95$	6.73687e6			0.806168
$96$	−7.97552e6	−	3.39645e6i	−0.920046	−	0.391811i
$97$	5.68054e6			0.631958			0.315979	−	0.948766i	$-0.397667\pi$
$97$	5.68054e6			0.631958			0.315979	+	0.948766i	$0.397667\pi$
$98$	4.47810e6	−	8.15595e6i	0.480620	−	0.875353i
$99$	−7.10912e6	+	2.11384e6i	−0.736364	+	0.218952i
$100$	6.20118e6	−	3.94469e6i	0.620118	−	0.394469i
$101$	1.19084e7	−	1.19084e7i	1.15008	−	1.15008i	0.163546	−	0.986536i	$-0.447707\pi$
$101$	1.19084e7	−	1.19084e7i	1.15008	−	1.15008i	0.986536	−	0.163546i	$-0.0522933\pi$
$102$	1.62770e7	−	571345.i	1.51871	−	0.0533086i
$103$	1.92945e7			1.73982			0.869909	−	0.493212i	$-0.164177\pi$
$103$	1.92945e7			1.73982			0.869909	+	0.493212i	$0.164177\pi$
$104$	−1.45734e7	+	1.65839e7i	−1.27042	+	1.44567i
$105$	55764.7	−	220052.i	0.00470107	−	0.0185508i
$106$	−1.43464e6	−	4.92825e6i	−0.116997	−	0.401904i
$107$	1.17811e7	+	1.17811e7i	0.929697	+	0.929697i	0.997686	−	0.0679891i	$-0.0216583\pi$
$107$	1.17811e7	+	1.17811e7i	0.929697	+	0.929697i	−0.0679891	+	0.997686i	$0.521658\pi$
$108$	−1.07499e7	+	7.47146e6i	−0.821146	+	0.570719i
$109$	−1.24088e7	+	1.24088e7i	−0.917774	+	0.917774i	−0.996867	−	0.0790936i	$-0.974797\pi$
$109$	−1.24088e7	+	1.24088e7i	−0.917774	+	0.917774i	0.0790936	+	0.996867i	$0.474797\pi$
$110$	−2.65723e6	+	4.83961e6i	−0.190351	+	0.346686i
$111$	−5.62171e6	−	1.42463e6i	−0.390155	−	0.0988715i
$112$	234253.	−	500588.i	0.0157551	−	0.0336680i
$113$		−	1.43955e7i		−	0.938540i	−0.883055	−	0.469270i	$-0.844517\pi$
$113$		−	1.43955e7i		−	0.938540i	0.883055	−	0.469270i	$-0.155483\pi$
$114$	1.68899e7	−	1.81188e7i	1.06773	−	1.14541i
$115$	5.88208e6	+	5.88208e6i	0.360652	+	0.360652i
$116$	949838.	−	4.27076e6i	0.0564998	−	0.254040i
$117$	9.50256e6	+	3.19583e7i	0.548517	+	1.84473i
$118$	−1.42294e7	+	4.14226e6i	−0.797257	+	0.232087i
$119$			1.03842e6i			0.0564882i
$120$	−1.78071e6	+	9.58129e6i	−0.0940714	+	0.506162i
$121$		−	7.98640e6i		−	0.409828i
$122$	1.53953e6	+	5.28856e6i	0.0767590	+	0.263680i
$123$	4.28417e6	−	2.55182e6i	0.207586	−	0.123647i
$124$	−1.94495e7	+	1.23722e7i	−0.916079	+	0.582735i
$125$	−1.37918e7	−	1.37918e7i	−0.631590	−	0.631590i
$126$	−452024.	−	701671.i	−0.0201309	−	0.0312490i
$127$		−	2.25912e7i		−	0.978649i	−0.872102	−	0.489324i	$-0.837243\pi$
$127$		−	2.25912e7i		−	0.978649i	0.872102	−	0.489324i	$-0.162757\pi$
$128$	−8.65175e6	+	2.20929e7i	−0.364644	+	0.931147i
$129$	−3.72297e6	+	1.46912e7i	−0.152695	+	0.602549i
$130$	2.17560e7	+	1.19453e7i	0.868515	+	0.476866i
$131$	−1.06181e7	+	1.06181e7i	−0.412664	+	0.412664i	−0.882665	−	0.470002i	$-0.844253\pi$
$131$	−1.06181e7	+	1.06181e7i	−0.412664	+	0.412664i	0.470002	+	0.882665i	$0.344253\pi$
$132$	6.35421e6	+	1.92800e7i	0.240465	+	0.729622i
$133$	1.11672e6	+	1.11672e6i	0.0411588	+	0.0411588i
$134$	−2.05176e6	+	597281.i	−0.0736649	+	0.0214443i
$135$	1.08229e7	+	9.97337e6i	0.378594	+	0.348878i
$136$	−2.87044e6	−	4.44863e7i	−0.0978504	−	1.51649i
$137$	3.99430e7			1.32715			0.663574	−	0.748111i	$-0.269039\pi$
$137$	3.99430e7			1.32715			0.663574	+	0.748111i	$0.269039\pi$
$138$	3.05668e7	−	1.07293e6i	0.990086	−	0.0347533i
$139$	−1.58180e7	+	1.58180e7i	−0.499573	+	0.499573i	−0.911305	−	0.411732i	$-0.864924\pi$
$139$	−1.58180e7	+	1.58180e7i	−0.499573	+	0.499573i	0.411732	+	0.911305i	$0.364924\pi$
$140$	−606518.	−	134892.i	−0.0186808	−	0.00415470i
$141$	−7.21328e6	+	4.29652e6i	−0.216704	+	0.129077i
$142$	−4.14052e7	−	2.27339e7i	−1.21352	−	0.666292i
$143$	5.17006e7			1.47849
$144$	2.13045e7	+	2.88104e7i	0.594569	+	0.804045i
$145$	−4.91856e6			−0.133983
$146$	−5.05342e6	−	2.77462e6i	−0.134385	−	0.0737852i
$147$	−3.30426e7	+	1.96815e7i	−0.857954	+	0.511032i
$148$	−3.44611e6	+	1.54948e7i	−0.0873803	+	0.392889i
$149$	−5.85906e6	+	5.85906e6i	−0.145103	+	0.145103i	−0.775926	−	0.630823i	$-0.782717\pi$
$149$	−5.85906e6	+	5.85906e6i	−0.145103	+	0.145103i	0.630823	+	0.775926i	$0.282717\pi$
$150$	−3.03606e7	+	1.06570e6i	−0.734498	+	0.0257818i
$151$	1.91033e7			0.451532			0.225766	−	0.974182i	$-0.427511\pi$
$151$	1.91033e7			0.451532			0.225766	+	0.974182i	$0.427511\pi$
$152$	−5.09276e7	−	4.47538e7i	−1.17625	−	1.03366i
$153$	−5.91977e7	−	3.20623e7i	−1.33624	−	0.723726i
$154$	−1.24269e6	+	361756.i	−0.0274184	+	0.00798166i
$155$	1.83242e7	+	1.83242e7i	0.395244	+	0.395244i
$156$	8.66713e7	−	2.85647e7i	1.82784	−	0.602412i
$157$	−4.45436e7	+	4.45436e7i	−0.918620	+	0.918620i	−0.996929	−	0.0783087i	$-0.975048\pi$
$157$	−4.45436e7	+	4.45436e7i	−0.918620	+	0.918620i	0.0783087	+	0.996929i	$0.475048\pi$
$158$	−2.23410e7	−	1.22666e7i	−0.450613	−	0.247413i
$159$	−5.21187e6	+	2.05665e7i	−0.102826	+	0.405761i
$160$	2.63564e7	+	4.10228e6i	0.508704	+	0.0791782i
$161$			1.95005e6i			0.0368261i
$162$	5.39573e7	−	4.10392e6i	0.997120	−	0.0758396i
$163$	−4.40397e7	−	4.40397e7i	−0.796503	−	0.796503i	0.186039	−	0.982542i	$-0.440435\pi$
$163$	−4.40397e7	−	4.40397e7i	−0.796503	−	0.796503i	−0.982542	+	0.186039i	$0.940435\pi$
$164$	−7.32558e6	−	1.15161e7i	−0.129685	−	0.203869i
$165$	1.96070e7	−	1.16787e7i	0.339795	−	0.202395i
$166$	1.68903e7	+	5.80211e7i	0.286589	+	0.984481i
$167$		−	8.70074e7i		−	1.44560i	−0.691056	−	0.722801i	$-0.742854\pi$
$167$		−	8.70074e7i		−	1.44560i	0.691056	−	0.722801i	$-0.257146\pi$
$168$	−1.88339e6	+	1.29304e6i	−0.0306449	+	0.0210392i
$169$		−	1.69666e8i		−	2.70391i
$170$	−4.81186e7	+	1.40076e7i	−0.751177	+	0.218672i
$171$	−9.81413e7	+	2.91815e7i	−1.50095	+	0.446295i
$172$	4.04924e7	+	9.00570e6i	0.606770	+	0.134948i
$173$	7.65373e6	+	7.65373e6i	0.112386	+	0.112386i	0.761063	−	0.648678i	$-0.224678\pi$
$173$	7.65373e6	+	7.65373e6i	0.112386	+	0.112386i	−0.648678	+	0.761063i	$0.724678\pi$
$174$	−1.23313e7	+	1.32285e7i	−0.177454	+	0.190365i
$175$		−	1.93690e6i		−	0.0273196i
$176$	5.22375e7	−	1.89329e7i	0.722251	−	0.261772i
$177$	5.93817e7	+	1.50483e7i	0.804908	+	0.203976i
$178$	5.16111e7	−	9.39992e7i	0.685919	−	1.24926i
$179$	1.58365e7	−	1.58365e7i	0.206383	−	0.206383i	−0.596345	−	0.802728i	$-0.703381\pi$
$179$	1.58365e7	−	1.58365e7i	0.206383	−	0.206383i	0.802728	+	0.596345i	$0.203381\pi$
$180$	2.64168e7	−	3.04112e7i	0.337618	−	0.388668i
$181$	2.19962e6	+	2.19962e6i	0.0275723	+	0.0275723i	0.720759	−	0.693186i	$-0.243794\pi$
$181$	2.19962e6	+	2.19962e6i	0.0275723	+	0.0275723i	−0.693186	+	0.720759i	$0.743794\pi$
$182$	1.62624e6	+	5.58641e6i	0.0199956	+	0.0686883i
$183$	5.59291e6	−	2.20701e7i	0.0674620	−	0.266211i
$184$	−5.39043e6	−	8.35411e7i	−0.0637912	−	0.988640i
$185$	1.78450e7			0.207213
$186$	9.52236e7	−	3.34247e6i	1.08505	−	0.0380866i
$187$	−7.38179e7	+	7.38179e7i	−0.825498	+	0.825498i
$188$	1.23341e7	+	1.93897e7i	0.135381	+	0.212823i
$189$	140814.	+	3.44723e6i	0.00151715	+	0.0371410i
$190$	−3.66831e7	+	6.68108e7i	−0.387997	+	0.706657i
$191$	−9.39716e7			−0.975843			−0.487921	−	0.872888i	$-0.662245\pi$
$191$	−9.39716e7			−0.975843			−0.487921	+	0.872888i	$0.662245\pi$
$192$	7.71109e7	−	6.06006e7i	0.786252	−	0.617906i
$193$	−1.92329e8			−1.92573			−0.962863	−	0.269989i	$-0.912980\pi$
$193$	−1.92329e8			−1.92573			−0.962863	+	0.269989i	$0.912980\pi$
$194$	−3.09312e7	+	5.63350e7i	−0.304152	+	0.553952i
$195$	−5.25005e7	−	8.81413e7i	−0.507040	−	0.851252i
$196$	5.65003e7	+	8.88203e7i	0.535987	+	0.842589i
$197$	3.43521e7	−	3.43521e7i	0.320126	−	0.320126i	−0.528689	−	0.848816i	$-0.677316\pi$
$197$	3.43521e7	−	3.43521e7i	0.320126	−	0.320126i	0.848816	+	0.528689i	$0.177316\pi$
$198$	1.77467e7	−	8.20126e7i	0.162476	−	0.750848i
$199$	1.22367e8			1.10073			0.550363	−	0.834926i	$-0.314489\pi$
$199$	1.22367e8			1.10073			0.550363	+	0.834926i	$0.314489\pi$
$200$	5.35407e6	+	8.29776e7i	0.0473237	+	0.733426i
$201$	8.56238e6	+	2.16984e6i	0.0743718	+	0.0188470i
$202$	5.32552e7	+	1.82941e8i	0.454603	+	1.56164i
$203$	−815311.	−	815311.i	−0.00684049	−	0.00684049i
$204$	−8.29643e7	+	1.64533e8i	−0.684204	+	1.35690i
$205$	−1.08498e7	+	1.08498e7i	−0.0879594	+	0.0879594i
$206$	−1.05061e8	+	1.91347e8i	−0.837349	+	1.52506i
$207$	−1.11168e8	−	6.02100e7i	−0.871130	−	0.471816i
$208$	−8.51110e7	−	2.34829e8i	−0.655789	−	1.80938i
$209$			1.58768e8i			1.20296i
$210$	1.87866e6	+	1.75124e6i	0.0139984	+	0.0130490i
$211$	−1.37896e7	−	1.37896e7i	−0.101056	−	0.101056i	0.654771	−	0.755827i	$-0.272765\pi$
$211$	−1.37896e7	−	1.37896e7i	−0.101056	−	0.101056i	−0.755827	+	0.654771i	$0.772765\pi$
$212$	5.66862e7	+	1.26073e7i	0.408603	+	0.0908753i
$213$	9.99168e7	+	1.67747e8i	0.708451	+	1.18940i
$214$	−1.80984e8	+	5.26857e7i	−1.26239	+	0.367489i
$215$		−	4.66343e7i		−	0.320016i
$216$	−1.55615e7	−	1.47292e8i	−0.105066	−	0.994465i
$217$			6.07493e6i			0.0403583i
$218$	−5.54928e7	−	1.90627e8i	−0.362776	−	1.24620i
$219$	1.21946e7	+	2.04732e7i	0.0784540	+	0.131714i
$220$	−3.35264e7	−	5.27045e7i	−0.212279	−	0.333710i
$221$	3.31841e8	+	3.31841e8i	2.06803	+	2.06803i
$222$	4.47392e7	−	4.79942e7i	0.274443	−	0.294411i
$223$			5.91422e6i			0.0357134i	0.999841	+	0.0178567i	$0.00568426\pi$
$223$			5.91422e6i			0.0357134i	−0.999841	+	0.0178567i	$0.994316\pi$
$224$	3.68889e6	+	5.04889e6i	0.0219294	+	0.0300143i
$225$	1.10418e8	+	5.98039e7i	0.646251	+	0.350018i
$226$	1.42763e8	+	7.83854e7i	0.822691	+	0.451706i
$227$	5.02517e7	−	5.02517e7i	0.285141	−	0.285141i	−0.550014	−	0.835155i	$-0.685378\pi$
$227$	5.02517e7	−	5.02517e7i	0.285141	−	0.285141i	0.835155	+	0.550014i	$0.185378\pi$
$228$	8.77197e7	+	2.66160e8i	0.490146	+	1.48720i
$229$	1.34270e8	+	1.34270e8i	0.738845	+	0.738845i	0.972355	−	0.233509i	$-0.0750209\pi$
$229$	1.34270e8	+	1.34270e8i	0.738845	+	0.738845i	−0.233509	+	0.972355i	$0.575021\pi$
$230$	−9.03623e7	+	2.63051e7i	−0.489711	+	0.142558i
$231$	5.18599e6	+	1.31421e6i	0.0276815	+	0.00701492i
$232$	3.71820e7	+	3.26746e7i	0.195490	+	0.171792i
$233$	−1.20798e8			−0.625624			−0.312812	−	0.949815i	$-0.601271\pi$
$233$	−1.20798e8			−0.625624			−0.312812	+	0.949815i	$0.601271\pi$
$234$	−3.68679e8	−	7.97784e7i	−1.88102	−	0.407033i
$235$	1.82679e7	−	1.82679e7i	0.0918227	−	0.0918227i
$236$	3.64011e7	−	1.63670e8i	0.180269	−	0.810547i
$237$	5.39123e7	+	9.05115e7i	0.263068	+	0.441656i
$238$	−1.02982e7	−	5.65432e6i	−0.0495156	−	0.0271870i
$239$	−1.51779e8			−0.719150			−0.359575	−	0.933116i	$-0.617078\pi$
$239$	−1.51779e8			−0.719150			−0.359575	+	0.933116i	$0.617078\pi$
$240$	−8.53233e7	−	6.98309e7i	−0.398408	−	0.326068i
$241$	2.09287e8			0.963123			0.481562	−	0.876412i	$-0.340070\pi$
$241$	2.09287e8			0.963123			0.481562	+	0.876412i	$0.340070\pi$
$242$	7.92026e7	+	4.34869e7i	0.359241	+	0.197244i
$243$	−2.00866e8	−	9.84095e7i	−0.898017	−	0.439962i
$244$	−6.08306e7	−	1.35290e7i	−0.268076	−	0.0596213i
$245$	8.36814e7	−	8.36814e7i	0.363536	−	0.363536i
$246$	1.97907e6	+	5.63819e7i	0.00847597	+	0.241472i
$247$	7.13726e8			3.01365
$248$	−1.67926e7	−	2.60253e8i	−0.0699097	−	1.08346i
$249$	6.13601e7	−	2.42132e8i	0.251877	−	0.993929i
$250$	2.11874e8	−	6.16778e7i	0.857604	−	0.249654i
$251$	−2.48754e8	−	2.48754e8i	−0.992914	−	0.992914i	0.00706061	−	0.999975i	$-0.497753\pi$
$251$	−2.48754e8	−	2.48754e8i	−0.992914	−	0.992914i	−0.999975	+	0.00706061i	$0.997753\pi$
$252$	9.41993e6	−	662119.i	0.0370805	−	0.00260636i
$253$	−1.38623e8	+	1.38623e8i	−0.538164	+	0.538164i
$254$	2.24042e8	+	1.23012e8i	0.857848	+	0.471009i
$255$	2.00808e8	+	5.08878e7i	0.758385	+	0.192187i
$256$	−1.71990e8	−	2.06100e8i	−0.640712	−	0.767781i
$257$		−	3.56475e8i		−	1.30997i	−0.755640	−	0.654987i	$-0.772674\pi$
$257$		−	3.56475e8i		−	1.30997i	0.755640	−	0.654987i	$-0.227326\pi$
$258$	−1.25423e8	−	1.16917e8i	−0.454682	−	0.423845i
$259$	2.95804e6	+	2.95804e6i	0.0105792	+	0.0105792i
$260$	−2.36928e8	+	1.50715e8i	−0.836007	+	0.531800i
$261$	7.16525e7	−	2.13053e7i	0.249454	−	0.0741730i
$262$	−4.74847e7	−	1.63118e8i	−0.163117	−	0.560335i
$263$		−	3.10734e7i		−	0.105328i	−0.998612	−	0.0526640i	$-0.983229\pi$
$263$		−	3.10734e7i		−	0.105328i	0.998612	−	0.0526640i	$-0.0167712\pi$
$264$	−2.25803e8	−	4.19660e7i	−0.755293	−	0.140373i
$265$		−	6.52844e7i		−	0.215501i
$266$	−1.71554e7	+	4.99404e6i	−0.0558875	+	0.0162692i
$267$	−3.80824e8	+	2.26834e8i	−1.22443	+	0.729321i
$268$	5.24875e6	−	2.36000e7i	0.0166565	−	0.0748928i
$269$	−2.67645e8	−	2.67645e8i	−0.838351	−	0.838351i	0.150291	−	0.988642i	$-0.451979\pi$
$269$	−2.67645e8	−	2.67645e8i	−0.838351	−	0.838351i	−0.988642	+	0.150291i	$0.951979\pi$
$270$	−1.57840e8	+	5.30261e7i	−0.488026	+	0.163952i
$271$			4.18957e8i			1.27873i	0.768905	+	0.639363i	$0.220802\pi$
$271$			4.18957e8i			1.27873i	−0.768905	+	0.639363i	$0.779198\pi$
$272$	4.56809e8	+	2.13766e8i	1.37640	+	0.644093i
$273$	5.90790e6	−	2.33131e7i	0.0175737	−	0.0693475i
$274$	−2.17495e8	+	3.96123e8i	−0.638736	+	1.16333i
$275$	1.37688e8	−	1.37688e8i	0.399238	−	0.399238i
$276$	−1.55799e8	+	3.08979e8i	−0.446050	+	0.884600i
$277$	5.76868e7	+	5.76868e7i	0.163079	+	0.163079i	0.783929	−	0.620850i	$-0.213213\pi$
$277$	5.76868e7	+	5.76868e7i	0.163079	+	0.163079i	−0.620850	+	0.783929i	$0.713213\pi$
$278$	−7.07391e7	−	2.43001e8i	−0.197471	−	0.678345i
$279$	−3.46317e8	−	1.87570e8i	−0.954683	−	0.517069i
$280$	4.64032e6	−	5.28045e6i	0.0126327	−	0.0143753i
$281$	7.53427e7			0.202567			0.101284	−	0.994858i	$-0.467705\pi$
$281$	7.53427e7			0.202567			0.101284	+	0.994858i	$0.467705\pi$
$282$	−3.33218e6	−	9.49306e7i	−0.00884824	−	0.252078i
$283$	−9.48009e6	+	9.48009e6i	−0.0248634	+	0.0248634i	−0.719429	−	0.694566i	$-0.755597\pi$
$283$	−9.48009e6	+	9.48009e6i	−0.0248634	+	0.0248634i	0.694566	+	0.719429i	$0.255597\pi$
$284$	4.50912e8	−	2.86834e8i	1.16809	−	0.743048i
$285$	2.70674e8	−	1.61224e8i	0.692612	−	0.412547i
$286$	−2.81516e8	+	5.12725e8i	−0.711577	+	1.29599i
$287$	−3.59697e6			−0.00898152
$288$	−4.01723e8	+	5.44044e7i	−0.990954	+	0.134202i
$289$	−5.37265e8			−1.30932
$290$	2.67821e7	−	4.87783e7i	0.0644841	−	0.117445i
$291$	2.28233e8	−	1.35945e8i	0.542941	−	0.323397i
$292$	5.50330e7	−	3.50075e7i	0.129355	−	0.0822852i
$293$	−4.92229e8	+	4.92229e8i	−1.14322	+	1.14322i	−0.155366	+	0.987857i	$0.549656\pi$
$293$	−4.92229e8	+	4.92229e8i	−1.14322	+	1.14322i	−0.987857	+	0.155366i	$0.950344\pi$
$294$	−1.52641e7	−	4.34858e8i	−0.0350312	−	0.998004i
$295$	−1.88496e8			−0.427489
$296$	−1.34900e8	−	1.18547e8i	−0.302337	−	0.265686i
$297$	−2.35043e8	+	2.55063e8i	−0.520594	+	0.564936i
$298$	−2.62021e7	−	9.00088e7i	−0.0573561	−	0.197028i
$299$	6.23167e8	+	6.23167e8i	1.34820	+	1.34820i
$300$	1.54748e8	−	3.06895e8i	0.330904	−	0.656243i
$301$	7.73021e6	−	7.73021e6i	0.0163384	−	0.0163384i
$302$	−1.04020e8	+	1.89451e8i	−0.217316	+	0.395797i
$303$	1.93469e8	−	7.63444e8i	0.399541	−	1.57662i
$304$	7.21139e8	−	2.61368e8i	1.47218	−	0.533575i
$305$			7.00574e7i			0.141385i
$306$	6.40306e8	−	4.12492e8i	1.27751	−	0.822982i
$307$	4.68197e8	+	4.68197e8i	0.923517	+	0.923517i	0.997276	−	0.0737593i	$-0.0234997\pi$
$307$	4.68197e8	+	4.68197e8i	0.923517	+	0.923517i	−0.0737593	+	0.997276i	$0.523500\pi$
$308$	3.17902e6	−	1.42938e7i	0.00619962	−	0.0278754i
$309$	7.75217e8	−	4.61750e8i	1.49475	−	0.890332i
$310$	−2.81503e8	+	8.19472e7i	−0.536681	+	0.156231i
$311$			158766.i			0.000299293i	1.00000		0.000149647i	$4.76340e-5\pi$
$311$			158766.i			0.000299293i	−1.00000		0.000149647i	$0.999952\pi$
$312$	−1.88654e8	+	1.01507e9i	−0.351662	+	1.89215i
$313$		−	6.37434e8i		−	1.17498i	−0.809232	−	0.587490i	$-0.800116\pi$
$313$		−	6.37434e8i		−	1.17498i	0.809232	−	0.587490i	$-0.199884\pi$
$314$	−1.99202e8	−	6.84292e8i	−0.363111	−	1.24735i
$315$	−3.02570e6	−	1.01758e7i	−0.00545430	−	0.0183435i
$316$	2.43299e8	−	1.54767e8i	0.433747	−	0.275915i
$317$	−5.98731e8	−	5.98731e8i	−1.05566	−	1.05566i	−0.998357	−	0.0573047i	$-0.981749\pi$
$317$	−5.98731e8	−	5.98731e8i	−1.05566	−	1.05566i	−0.0573047	−	0.998357i	$-0.518251\pi$
$318$	−1.75582e8	−	1.63674e8i	−0.306186	−	0.285420i
$319$		−	1.15916e8i		−	0.199929i
$320$	−1.84197e8	+	2.39044e8i	−0.314237	+	0.407805i
$321$	7.55281e8	+	1.91400e8i	1.27450	+	0.322979i
$322$	−1.93391e7	−	1.06183e7i	−0.0322805	−	0.0177239i
$323$	−1.01906e9	+	1.01906e9i	−1.68263	+	1.68263i
$324$	−2.53105e8	+	5.57451e8i	−0.413421	+	0.910540i
$325$	−6.18964e8	−	6.18964e8i	−1.00017	−	1.00017i
$326$	6.76551e8	−	1.96948e8i	1.08153	−	0.314841i
$327$	−2.01598e8	+	7.95522e8i	−0.318837	+	1.25816i
$328$	1.54096e8	−	9.94290e6i	0.241119	−	0.0155580i
$329$	6.05624e6			0.00937600
$330$	9.05746e6	+	2.58038e8i	0.0138742	+	0.395262i
$331$	5.18640e8	−	5.18640e8i	0.786082	−	0.786082i	−0.194768	−	0.980849i	$-0.562395\pi$
$331$	5.18640e8	−	5.18640e8i	0.786082	−	0.786082i	0.980849	+	0.194768i	$0.0623953\pi$
$332$	−6.67376e8	−	1.48427e8i	−1.00089	−	0.222603i
$333$	−2.59963e8	+	7.72979e7i	−0.385795	+	0.114713i
$334$	8.62869e8	+	4.73766e8i	1.26716	+	0.695747i
$335$	−2.71797e7			−0.0394991
$336$	−2.56806e6	−	2.57187e7i	−0.00369332	−	0.0369881i
$337$	−6.96903e8			−0.991900			−0.495950	−	0.868351i	$-0.665180\pi$
$337$	−6.96903e8			−0.991900			−0.495950	+	0.868351i	$0.665180\pi$
$338$	1.68261e9	+	9.23855e8i	2.37015	+	1.30135i
$339$	−3.44509e8	−	5.78384e8i	−0.480287	−	0.806339i
$340$	1.23095e8	−	5.53475e8i	0.169850	−	0.763698i
$341$	−4.31848e8	+	4.31848e8i	−0.589781	+	0.589781i
$342$	2.44993e8	−	1.13218e9i	0.331178	−	1.53047i
$343$	5.55233e7			0.0742926
$344$	−3.09797e8	+	3.52534e8i	−0.410320	+	0.466924i
$345$	3.77098e8	+	9.55627e7i	0.494411	+	0.125291i
$346$	−1.17579e8	+	3.42280e7i	−0.152603	+	0.0444237i
$347$	5.59993e8	+	5.59993e8i	0.719497	+	0.719497i	0.968502	−	0.249005i	$-0.0801035\pi$
$347$	5.59993e8	+	5.59993e8i	0.719497	+	0.719497i	−0.249005	+	0.968502i	$0.580104\pi$
$348$	−6.40438e7	−	1.94322e8i	−0.0814610	−	0.247170i
$349$	−6.92192e8	+	6.92192e8i	−0.871640	+	0.871640i	−0.992651	−	0.121011i	$-0.961386\pi$
$349$	−6.92192e8	+	6.92192e8i	−0.871640	+	0.871640i	0.121011	+	0.992651i	$0.461386\pi$
$350$	1.92086e7	+	1.05467e7i	0.0239474	+	0.0131485i
$351$	1.14661e9	+	1.05661e9i	1.41527	+	1.30419i
$352$	−9.66787e7	+	6.21142e8i	−0.118149	+	0.759086i
$353$			2.04914e8i			0.247948i	0.992285	+	0.123974i	$0.0395640\pi$
$353$			2.04914e8i			0.247948i	−0.992285	+	0.123974i	$0.960436\pi$
$354$	−4.72577e8	+	5.06960e8i	−0.566189	+	0.607383i
$355$	−4.24824e8	−	4.24824e8i	−0.503976	−	0.503976i
$356$	6.51179e8	+	1.02367e9i	0.764936	+	1.20250i
$357$	2.48511e7	+	4.17216e7i	0.0289072	+	0.0485314i
$358$	7.08220e7	+	2.43286e8i	0.0815789	+	0.280237i
$359$			1.04370e8i			0.119054i	0.998227	+	0.0595272i	$0.0189593\pi$
$359$			1.04370e8i			0.119054i	−0.998227	+	0.0595272i	$0.981041\pi$
$360$	1.57751e8	+	4.27573e8i	0.178202	+	0.483004i
$361$			1.29792e9i			1.45202i
$362$	−3.37913e7	+	9.83687e6i	−0.0374391	+	0.0108988i
$363$	−1.91128e8	−	3.20878e8i	−0.209725	−	0.352100i
$364$	−6.42565e7	−	1.42910e7i	−0.0698333	−	0.0155312i
$365$	−5.18490e7	−	5.18490e7i	−0.0558104	−	0.0558104i
$366$	1.88419e8	+	1.75640e8i	0.200882	+	0.187258i
$367$		−	1.41842e9i		−	1.49787i	−0.662642	−	0.748936i	$-0.730565\pi$
$367$		−	1.41842e9i		−	1.49787i	0.662642	−	0.748936i	$-0.269435\pi$
$368$	8.57845e8	+	4.01434e8i	0.897308	+	0.419901i
$369$	1.11060e8	−	2.05054e8i	0.115071	−	0.212460i
$370$	−9.71684e7	+	1.76973e8i	−0.0997285	+	0.181635i
$371$	1.08217e7	−	1.08217e7i	0.0110024	−	0.0110024i
$372$	−4.85356e8	+	9.62550e8i	−0.488833	+	0.969445i
$373$	−8.55701e8	−	8.55701e8i	−0.853770	−	0.853770i	0.136825	−	0.990595i	$-0.456310\pi$
$373$	−8.55701e8	−	8.55701e8i	−0.853770	−	0.853770i	−0.990595	+	0.136825i	$0.956310\pi$
$374$	−3.30119e8	−	1.13401e9i	−0.326302	−	1.12090i
$375$	−8.84187e8	−	2.24067e8i	−0.865834	−	0.219416i
$376$	−2.59452e8	+	1.67409e7i	−0.251709	+	0.0162414i
$377$	−5.21088e8			−0.500860
$378$	−3.49536e7	−	1.73741e7i	−0.0332867	−	0.0165456i
$379$	4.58551e8	−	4.58551e8i	0.432664	−	0.432664i	−0.456870	−	0.889534i	$-0.651030\pi$
$379$	4.58551e8	−	4.58551e8i	0.432664	−	0.432664i	0.889534	+	0.456870i	$0.151030\pi$
$380$	−4.62831e8	−	7.27586e8i	−0.432693	−	0.680208i
$381$	−5.40645e8	−	9.07672e8i	−0.500813	−	0.840798i
$382$	5.11687e8	−	9.31934e8i	0.469659	−	0.855388i
$383$	−8.63968e8			−0.785782			−0.392891	−	0.919585i	$-0.628525\pi$
$383$	−8.63968e8			−0.785782			−0.392891	+	0.919585i	$0.628525\pi$
$384$	1.81109e8	+	1.09470e9i	0.163223	+	0.986589i
$385$	−1.64619e7			−0.0147017
$386$	1.04726e9	−	1.90737e9i	0.926824	−	1.68802i
$387$	2.02002e8	+	6.79359e8i	0.177161	+	0.595814i
$388$	−3.90260e8	−	6.13501e8i	−0.339190	−	0.533218i
$389$	5.07486e8	−	5.07486e8i	0.437120	−	0.437120i	−0.453922	−	0.891042i	$-0.649975\pi$
$389$	5.07486e8	−	5.07486e8i	0.437120	−	0.437120i	0.891042	+	0.453922i	$0.149975\pi$
$390$	1.15999e9	−	4.07169e7i	0.990208	−	0.0347575i
$391$	−1.77951e9			−1.50551
$392$	−1.18850e9	+	7.66869e7i	−0.996546	+	0.0643014i
$393$	−1.72506e8	+	6.80722e8i	−0.143360	+	0.565712i
$394$	1.53625e8	+	5.27728e8i	0.126539	+	0.434683i
$395$	−2.29223e8	−	2.29223e8i	−0.187141	−	0.187141i
$396$	7.16701e8	+	6.22565e8i	0.579969	+	0.503793i
$397$	8.39799e8	−	8.39799e8i	0.673610	−	0.673610i	−0.284936	−	0.958546i	$-0.591973\pi$
$397$	8.39799e8	−	8.39799e8i	0.673610	−	0.673610i	0.958546	+	0.284936i	$0.0919725\pi$
$398$	−6.66304e8	+	1.21354e9i	−0.529763	+	0.964856i
$399$	7.15925e7	+	1.81427e7i	0.0564238	+	0.0142987i
$400$	−8.52058e8	−	3.98726e8i	−0.665671	−	0.311505i
$401$		−	2.36274e9i		−	1.82983i	−0.403651	−	0.914913i	$-0.632259\pi$
$401$		−	2.36274e9i		−	1.82983i	0.403651	−	0.914913i	$-0.367741\pi$
$402$	−6.81419e7	+	7.30997e7i	−0.0523146	+	0.0561209i
$403$	1.94133e9	+	1.94133e9i	1.47751	+	1.47751i
$404$	−2.10424e9	−	4.67992e8i	−1.58767	−	0.353105i
$405$	6.73520e8	+	1.41702e8i	0.503800	+	0.105994i
$406$	1.25251e7	−	3.64613e6i	0.00928836	−	0.00270390i
$407$			4.20555e8i			0.309202i
$408$	−1.17996e9	−	1.71868e9i	−0.860115	−	1.25281i
$409$			9.19716e8i			0.664695i	0.943157	+	0.332347i	$0.107841\pi$
$409$			9.19716e8i			0.664695i	−0.943157	+	0.332347i	$0.892159\pi$
$410$	−4.85209e7	−	1.66678e8i	−0.0347685	−	0.119436i
$411$	1.60483e9	−	9.55903e8i	1.14021	−	0.679153i
$412$	−1.32556e9	−	2.08382e9i	−0.933811	−	1.46798i
$413$	−3.12455e7	−	3.12455e7i	−0.0218254	−	0.0218254i
$414$	1.20244e9	−	7.74622e8i	0.832839	−	0.536523i
$415$			7.68604e8i			0.527879i
$416$	2.79228e9	+	4.34610e8i	1.90166	+	0.295987i
$417$	−2.56985e8	+	1.01409e9i	−0.173553	+	0.684855i
$418$	−1.57453e9	−	8.64512e8i	−1.05447	−	0.578967i
$419$	2.04336e9	−	2.04336e9i	1.35705	−	1.35705i	0.479510	−	0.877536i	$-0.340814\pi$
$419$	2.04336e9	−	2.04336e9i	1.35705	−	1.35705i	0.877536	−	0.479510i	$-0.159186\pi$
$420$	−2.75969e7	+	9.09526e6i	−0.0181756	+	0.00599022i
$421$	−7.03457e8	−	7.03457e8i	−0.459463	−	0.459463i	0.439016	−	0.898479i	$-0.355327\pi$
$421$	−7.03457e8	−	7.03457e8i	−0.459463	−	0.459463i	−0.898479	+	0.439016i	$0.855327\pi$
$422$	2.11840e8	−	6.16681e7i	0.137219	−	0.0399454i
$423$	−1.86993e8	+	3.45252e8i	−0.120125	+	0.221791i
$424$	−4.33692e8	+	4.93520e8i	−0.276313	+	0.314430i
$425$	1.76751e9			1.11686
$426$	−2.20764e9	+	7.74909e7i	−1.38355	+	0.0485643i
$427$	−1.16129e7	+	1.16129e7i	−0.00721842	+	0.00721842i
$428$	4.62988e8	−	2.08174e9i	0.285441	−	1.28343i
$429$	2.07723e9	−	1.23728e9i	1.27023	−	0.756602i
$430$	4.62481e8	+	2.53930e8i	0.280514	+	0.154019i
$431$	−3.18008e8			−0.191323			−0.0956616	−	0.995414i	$-0.530497\pi$
$431$	−3.18008e8			−0.191323			−0.0956616	+	0.995414i	$0.530497\pi$
$432$	1.54545e9	+	6.47694e8i	0.922279	+	0.386524i
$433$	5.06398e8			0.299767			0.149884	−	0.988704i	$-0.452110\pi$
$433$	5.06398e8			0.299767			0.149884	+	0.988704i	$0.452110\pi$
$434$	−6.02463e7	−	3.30788e7i	−0.0353766	−	0.0194238i
$435$	−1.97618e8	+	1.17709e8i	−0.115110	+	0.0685643i
$436$	2.19265e9	+	4.87656e8i	1.26697	+	0.281780i
$437$	−1.91369e9	+	1.91369e9i	−1.09695	+	1.09695i
$438$	−2.69438e8	+	9.45761e6i	−0.153214	+	0.00537802i
$439$	2.34568e9			1.32325			0.661627	−	0.749833i	$-0.269866\pi$
$439$	2.34568e9			1.32325			0.661627	+	0.749833i	$0.269866\pi$
$440$	7.05236e8	−	4.55048e7i	0.394685	−	0.0254667i
$441$	−8.56578e8	+	1.58153e9i	−0.475589	+	0.878097i
$442$	−5.09785e9	+	1.48402e9i	−2.80808	+	0.817449i
$443$	−9.69946e8	−	9.69946e8i	−0.530072	−	0.530072i	0.390522	−	0.920594i	$-0.372295\pi$
$443$	−9.69946e8	−	9.69946e8i	−0.530072	−	0.530072i	−0.920594	+	0.390522i	$0.872295\pi$
$444$	2.32358e8	+	7.05021e8i	0.125984	+	0.382263i
$445$	9.64448e8	−	9.64448e8i	0.518822	−	0.518822i
$446$	−5.86525e7	−	3.22037e7i	−0.0313051	−	0.0171883i
$447$	−9.51887e7	+	3.75623e8i	−0.0504091	+	0.198919i
$448$	−7.01573e7	+	9.09154e6i	−0.0368638	+	0.00477710i
$449$			2.78656e8i			0.145280i	0.997358	+	0.0726400i	$0.0231424\pi$
$449$			2.78656e8i			0.145280i	−0.997358	+	0.0726400i	$0.976858\pi$
$450$	−1.19433e9	+	7.69397e8i	−0.617844	+	0.398021i
$451$	−2.55697e8	−	2.55697e8i	−0.131253	−	0.131253i
$452$	−1.55473e9	+	9.88991e8i	−0.791898	+	0.503742i
$453$	7.67533e8	−	4.57173e8i	0.387930	−	0.231067i
$454$	2.24729e8	+	7.71982e8i	0.112710	+	0.387179i
$455$			7.40030e7i			0.0368307i
$456$	−3.11720e9	−	5.79340e8i	−1.53953	−	0.286125i
$457$			7.41681e8i			0.363505i	0.983344	+	0.181752i	$0.0581769\pi$
$457$			7.41681e8i			0.363505i	−0.983344	+	0.181752i	$0.941823\pi$
$458$	−2.06269e9	+	6.00463e8i	−1.00324	+	0.292050i
$459$	−3.14575e9	+	1.28499e8i	−1.51838	+	0.0620233i
$460$	2.31162e8	−	1.03937e9i	0.110730	−	0.497874i
$461$	1.65263e9	+	1.65263e9i	0.785636	+	0.785636i	0.980776	−	0.195139i	$-0.0625158\pi$
$461$	1.65263e9	+	1.65263e9i	0.785636	+	0.785636i	−0.195139	+	0.980776i	$0.562516\pi$
$462$	−4.12716e7	+	4.42744e7i	−0.0194717	+	0.0208884i
$463$			2.70194e9i			1.26515i	0.774498	+	0.632576i	$0.218002\pi$
$463$			2.70194e9i			1.26515i	−0.774498	+	0.632576i	$0.781998\pi$
$464$	−5.26500e8	+	1.90824e8i	−0.244673	+	0.0886788i
$465$	1.17476e9	+	2.97703e8i	0.541831	+	0.137309i
$466$	6.57759e8	−	1.19797e9i	0.301103	−	0.548399i
$467$	9.33540e8	−	9.33540e8i	0.424154	−	0.424154i	−0.462477	−	0.886631i	$-0.653039\pi$
$467$	9.33540e8	−	9.33540e8i	0.424154	−	0.424154i	0.886631	+	0.462477i	$0.153039\pi$
$468$	2.79868e9	−	3.22186e9i	1.26210	−	1.45294i
$469$	−4.50536e6	−	4.50536e6i	−0.00201662	−	0.00201662i
$470$	8.16951e7	+	2.80636e8i	0.0362955	+	0.124681i
$471$	−7.23673e8	+	2.85567e9i	−0.319131	+	1.25932i
$472$	1.42494e9	+	1.25220e9i	0.623735	+	0.548122i
$473$	1.09903e9			0.477526
$474$	−1.19118e9	+	4.18119e7i	−0.513751	+	0.0180333i
$475$	1.90078e9	−	1.90078e9i	0.813777	−	0.813777i
$476$	1.12150e8	−	7.13407e7i	0.0476622	−	0.0303189i
$477$	2.82787e8	+	9.51050e8i	0.119301	+	0.401226i
$478$	8.26456e8	−	1.50522e9i	0.346117	−	0.630381i
$479$	−2.35263e8			−0.0978092			−0.0489046	−	0.998803i	$-0.515573\pi$
$479$	−2.35263e8			−0.0978092			−0.0489046	+	0.998803i	$0.515573\pi$
$480$	1.15712e9	−	4.65929e8i	0.477567	−	0.192298i
$481$	1.89056e9			0.774611
$482$	−1.13959e9	+	2.07554e9i	−0.463537	+	0.844239i
$483$	4.66680e7	+	7.83494e7i	0.0188454	+	0.0316388i
$484$	−8.62536e8	+	5.48676e8i	−0.345795	+	0.219967i
$485$	−5.78006e8	+	5.78006e8i	−0.230058	+	0.230058i
$486$	2.06968e9	−	1.45617e9i	0.817857	−	0.575422i
$487$	−4.34096e9			−1.70308			−0.851539	−	0.524292i	$-0.824330\pi$
$487$	−4.34096e9			−1.70308			−0.851539	+	0.524292i	$0.824330\pi$
$488$	4.65400e8	−	5.29601e8i	0.181283	−	0.206291i
$489$	−2.82337e9	−	7.15487e8i	−1.09191	−	0.276707i
$490$	3.74229e8	+	1.28554e9i	0.143698	+	0.493628i
$491$	2.59768e9	+	2.59768e9i	0.990378	+	0.990378i	0.999954	−	0.00957582i	$-0.00304813\pi$
$491$	2.59768e9	+	2.59768e9i	0.990378	+	0.990378i	−0.00957582	+	0.999954i	$0.503048\pi$
$492$	−5.69926e8	−	2.87379e8i	−0.215745	−	0.108787i
$493$	7.44008e8	−	7.44008e8i	0.279649	−	0.279649i
$494$	−3.88633e9	+	7.07816e9i	−1.45042	+	2.64165i
$495$	5.08280e8	−	9.38455e8i	0.188358	−	0.347772i
$496$	2.67241e9	+	1.25057e9i	0.983372	+	0.460175i
$497$		−	1.40840e8i		−	0.0514609i
$498$	2.06716e9	+	1.92696e9i	0.750017	+	0.699150i
$499$	1.48945e9	+	1.48945e9i	0.536628	+	0.536628i	0.922537	−	0.385909i	$-0.126112\pi$
$499$	1.48945e9	+	1.48945e9i	0.536628	+	0.536628i	−0.385909	+	0.922537i	$0.626112\pi$
$500$	−5.42008e8	+	2.43703e9i	−0.193915	+	0.871900i
$501$	−2.08223e9	−	3.49579e9i	−0.739770	−	1.24198i
$502$	3.82143e9	−	1.11244e9i	1.34823	−	0.392478i
$503$		−	5.14782e9i		−	1.80358i	−0.432175	−	0.901790i	$-0.642254\pi$
$503$		−	5.14782e9i		−	1.80358i	0.432175	−	0.901790i	$-0.357746\pi$
$504$	−4.47263e7	+	9.70245e7i	−0.0155617	+	0.0337578i
$505$			2.42341e9i			0.837350i
$506$	−6.19933e8	−	2.12957e9i	−0.212725	−	0.730745i
$507$	−4.06040e9	−	6.81687e9i	−1.38370	−	2.32304i
$508$	−2.43987e9	+	1.55205e9i	−0.825740	+	0.525269i
$509$	2.16871e9	+	2.16871e9i	0.728935	+	0.728935i	0.970408	−	0.241473i	$-0.0776304\pi$
$509$	2.16871e9	+	2.16871e9i	0.728935	+	0.728935i	−0.241473	+	0.970408i	$0.577630\pi$
$510$	−1.59809e9	+	1.71436e9i	−0.533464	+	0.572276i
$511$		−	1.71892e7i		−	0.00569879i
$512$	2.98044e9	−	5.83417e8i	0.981375	−	0.192103i
$513$	−3.24476e9	+	3.52114e9i	−1.06114	+	1.15152i
$514$	3.53523e9	+	1.94105e9i	1.14828	+	0.630472i
$515$	−1.96326e9	+	1.96326e9i	−0.633362	+	0.633362i
$516$	1.84243e9	−	6.07219e8i	0.590359	−	0.194568i
$517$	4.30519e8	+	4.30519e8i	0.137017	+	0.137017i
$518$	−4.54423e7	+	1.32285e7i	−0.0143650	+	0.00418174i
$519$	4.90678e8	+	1.24346e8i	0.154068	+	0.0390431i
$520$	−2.04563e8	−	3.17032e9i	−0.0637991	−	0.988761i
$521$	4.79698e9			1.48606			0.743029	−	0.669260i	$-0.233389\pi$
$521$	4.79698e9			1.48606			0.743029	+	0.669260i	$0.233389\pi$
$522$	−1.78868e8	+	8.26602e8i	−0.0550409	+	0.254360i
$523$	−1.02602e9	+	1.02602e9i	−0.313619	+	0.313619i	−0.846310	−	0.532691i	$-0.821181\pi$
$523$	−1.02602e9	+	1.02602e9i	−0.313619	+	0.313619i	0.532691	+	0.846310i	$0.321181\pi$
$524$	1.87623e9	+	4.17283e8i	0.569675	+	0.126698i
$525$	−4.63532e7	−	7.78209e7i	−0.0139805	−	0.0234714i
$526$	3.08161e8	+	1.69199e8i	0.0923267	+	0.0506928i
$527$	−5.54365e9			−1.64990
$528$	1.64571e9	−	2.01082e9i	0.486557	−	0.594503i
$529$	6.30656e7			0.0185224
$530$	6.47438e8	+	3.55482e8i	0.188900	+	0.103717i
$531$	2.74597e9	−	8.16493e8i	0.795912	−	0.236658i
$532$	4.38863e7	−	1.97326e8i	0.0126368	−	0.0568191i
$533$	−1.14946e9	+	1.14946e9i	−0.328813	+	0.328813i
$534$	−1.75922e8	−	5.01184e9i	−0.0499949	−	1.42431i
$535$	−2.39750e9			−0.676893
$536$	2.05466e8	+	1.80558e8i	0.0576318	+	0.0506453i
$537$	2.57287e8	−	1.01527e9i	0.0716980	−	0.282927i
$538$	4.11164e9	−	1.19693e9i	1.13835	−	0.331382i
$539$	1.97212e9	+	1.97212e9i	0.542467	+	0.542467i
$540$	3.33585e8	−	1.85406e9i	0.0911651	−	0.506693i
$541$	1.30423e9	−	1.30423e9i	0.354130	−	0.354130i	−0.507514	−	0.861644i	$-0.669435\pi$
$541$	1.30423e9	−	1.30423e9i	0.354130	−	0.354130i	0.861644	+	0.507514i	$0.169435\pi$
$542$	−4.15488e9	−	2.28127e9i	−1.12089	−	0.615432i
$543$	1.41017e8	+	3.57360e7i	0.0377984	+	0.00957869i
$544$	−4.60734e9	+	3.36627e9i	−1.22703	+	0.896506i
$545$		−	2.52523e9i		−	0.668211i
$546$	1.99031e8	+	1.85532e8i	0.0523295	+	0.0487804i
$547$	−4.31478e9	−	4.31478e9i	−1.12721	−	1.12721i	−0.990630	−	0.136576i	$-0.956390\pi$
$547$	−4.31478e9	−	4.31478e9i	−1.12721	−	1.12721i	−0.136576	−	0.990630i	$-0.543610\pi$
$548$	−2.74414e9	−	4.31387e9i	−0.712318	−	1.11979i
$549$	−3.03462e8	−	1.02058e9i	−0.0782710	−	0.263236i
$550$	6.15751e8	+	2.11521e9i	0.157810	+	0.542106i
$551$		−	1.60022e9i		−	0.407520i
$552$	−2.21585e9	−	3.22752e9i	−0.560731	−	0.816737i
$553$		−	7.59931e7i		−	0.0191089i
$554$	−8.86202e8	+	2.57979e8i	−0.221436	+	0.0644615i
$555$	7.16979e8	−	4.27061e8i	0.178025	−	0.106039i
$556$	2.79507e9	+	6.21636e8i	0.689653	+	0.153382i
$557$	−2.56744e9	−	2.56744e9i	−0.629515	−	0.629515i	0.318431	−	0.947946i	$-0.396844\pi$
$557$	−2.56744e9	−	2.56744e9i	−0.629515	−	0.629515i	−0.947946	+	0.318431i	$0.896844\pi$
$558$	3.74591e9	−	2.41315e9i	0.912719	−	0.587983i
$559$		−	4.94060e9i		−	1.19629i
$560$	2.71001e7	+	7.47716e7i	0.00652098	+	0.0179920i
$561$	−1.19928e9	+	4.73245e9i	−0.286780	+	1.13166i
$562$	−4.10250e8	+	7.47188e8i	−0.0974926	+	0.177563i
$563$	1.29413e9	−	1.29413e9i	0.305633	−	0.305633i	−0.537580	−	0.843213i	$-0.680661\pi$
$563$	1.29413e9	−	1.29413e9i	0.305633	−	0.305633i	0.843213	+	0.537580i	$0.180661\pi$
$564$	9.59589e8	+	4.83863e8i	0.225221	+	0.113565i
$565$	1.46477e9	+	1.46477e9i	0.341666	+	0.341666i
$566$	−4.23956e7	−	1.45636e8i	−0.00982795	−	0.0337607i
$567$	8.81555e7	+	1.35133e8i	0.0203099	+	0.0311330i
$568$	3.89315e8	+	6.03363e9i	0.0891420	+	1.38153i
$569$	4.67384e9			1.06361			0.531803	−	0.846868i	$-0.321515\pi$
$569$	4.67384e9			1.06361			0.531803	+	0.846868i	$0.321515\pi$
$570$	1.25038e8	+	3.56221e9i	0.0282801	+	0.805671i
$571$	−1.73063e9	+	1.73063e9i	−0.389026	+	0.389026i	−0.874340	−	0.485314i	$-0.838705\pi$
$571$	−1.73063e9	+	1.73063e9i	−0.389026	+	0.389026i	0.485314	+	0.874340i	$0.338705\pi$
$572$	−3.55190e9	−	5.58370e9i	−0.793550	−	1.24749i
$573$	−3.77560e9	+	2.24890e9i	−0.838387	+	0.499376i
$574$	1.95859e7	−	3.56718e7i	0.00432267	−	0.00787288i
$575$	3.31922e9			0.728112
$576$	1.64789e9	−	4.28021e9i	0.359295	−	0.933224i
$577$	1.19928e9			0.259899			0.129950	−	0.991521i	$-0.458518\pi$
$577$	1.19928e9			0.259899			0.129950	+	0.991521i	$0.458518\pi$
$578$	2.92547e9	−	5.32816e9i	0.630157	−	1.14770i
$579$	−7.72741e9	+	4.60276e9i	−1.65447	+	0.985469i
$580$	3.37911e8	+	5.31207e8i	0.0719125	+	0.113049i
$581$	−1.27406e8	+	1.27406e8i	−0.0269508	+	0.0269508i
$582$	1.05432e8	+	3.00366e9i	0.0221689	+	0.631569i
$583$	1.53856e9			0.321569
$584$	4.75152e7	+	7.36393e8i	0.00987160	+	0.152990i
$585$	−4.21873e9	−	2.28492e9i	−0.871237	−	0.471874i
$586$	−2.20128e9	−	7.56178e9i	−0.451892	−	1.55232i
$587$	7.52696e8	+	7.52696e8i	0.153598	+	0.153598i	0.779723	−	0.626125i	$-0.215360\pi$
$587$	7.52696e8	+	7.52696e8i	0.153598	+	0.153598i	−0.626125	+	0.779723i	$0.715360\pi$
$588$	4.39569e9	+	2.21648e9i	0.891674	+	0.449617i
$589$	−5.96166e9	+	5.96166e9i	−1.20216	+	1.20216i
$590$	1.02638e9	−	1.86935e9i	0.205744	−	0.374722i
$591$	5.58098e8	−	2.20230e9i	0.111213	−	0.438855i
$592$	1.91020e9	−	6.92329e8i	0.378401	−	0.137147i
$593$			2.58913e9i			0.509873i	0.966958	+	0.254937i	$0.0820546\pi$
$593$			2.58913e9i			0.509873i	−0.966958	+	0.254937i	$0.917945\pi$
$594$	−1.24967e9	−	3.71981e9i	−0.244649	−	0.728230i
$595$	−1.05661e8	−	1.05661e8i	−0.0205639	−	0.0205639i
$596$	1.03531e9	+	2.30257e8i	0.200312	+	0.0445504i
$597$	4.91647e9	−	2.92845e9i	0.945679	−	0.563284i
$598$	−9.57329e9	+	2.78685e9i	−1.83066	+	0.532916i
$599$		−	5.91912e9i		−	1.12529i	−0.826699	−	0.562644i	$-0.809784\pi$
$599$		−	5.91912e9i		−	1.12529i	0.826699	−	0.562644i	$-0.190216\pi$
$600$	2.20091e9	+	3.20575e9i	0.415980	+	0.605899i
$601$		−	6.15564e9i		−	1.15668i	−0.815796	−	0.578339i	$-0.803701\pi$
$601$		−	6.15564e9i		−	1.15668i	0.815796	−	0.578339i	$-0.196299\pi$
$602$	3.45700e7	+	1.18754e8i	0.00645821	+	0.0221850i
$603$	3.95948e8	−	1.17732e8i	0.0735406	−	0.0218667i
$604$	−1.31242e9	−	2.06317e9i	−0.242350	−	0.380983i
$605$	8.12633e8	+	8.12633e8i	0.149194	+	0.149194i
$606$	6.51776e9	+	6.07571e9i	1.18972	+	1.10903i
$607$			2.26335e9i			0.410764i	0.978682	+	0.205382i	$0.0658436\pi$
$607$			2.26335e9i			0.410764i	−0.978682	+	0.205382i	$0.934156\pi$
$608$	−1.33465e9	+	8.57485e9i	−0.240827	+	1.54726i
$609$	−5.22694e7	−	1.32459e7i	−0.00937749	−	0.00237640i
$610$	−6.94772e8	−	3.81471e8i	−0.123933	−	0.0680467i
$611$	1.93536e9	−	1.93536e9i	0.343255	−	0.343255i
$612$	6.04213e8	+	8.59611e9i	0.106552	+	1.51590i
$613$	7.63220e8	+	7.63220e8i	0.133825	+	0.133825i	0.770846	−	0.637021i	$-0.219834\pi$
$613$	7.63220e8	+	7.63220e8i	0.133825	+	0.133825i	−0.637021	+	0.770846i	$0.719834\pi$
$614$	−7.19260e9	+	2.09381e9i	−1.25400	+	0.365046i
$615$	−1.76270e8	+	6.95576e8i	−0.0305573	+	0.120582i
$616$	1.24445e8	+	1.09359e8i	0.0214508	+	0.0188504i
$617$	−3.81668e9			−0.654166			−0.327083	−	0.944996i	$-0.606066\pi$
$617$	−3.81668e9			−0.654166			−0.327083	+	0.944996i	$0.606066\pi$
$618$	3.58112e8	+	1.02023e10i	0.0610322	+	1.73875i
$619$	−4.81315e9	+	4.81315e9i	−0.815666	+	0.815666i	−0.985477	−	0.169810i	$-0.945684\pi$
$619$	−4.81315e9	+	4.81315e9i	−0.815666	+	0.815666i	0.169810	+	0.985477i	$0.445684\pi$
$620$	7.20130e8	−	3.23793e9i	0.121350	−	0.545627i
$621$	−5.90743e9	+	2.41309e8i	−0.989870	+	0.0404346i
$622$	−1.57452e6	−	864502.i	−0.000262350	−	0.000144045i
$623$	3.19738e8			0.0529769
$624$	−9.03943e9	−	7.39812e9i	−1.48934	−	1.21892i
$625$	−1.67910e9			−0.275103
$626$	6.32156e9	+	3.47091e9i	1.02994	+	0.565500i
$627$	3.79958e9	+	6.37899e9i	0.615601	+	1.03351i
$628$	7.87093e9	+	1.75053e9i	1.26814	+	0.282040i
$629$	−2.69934e9	+	2.69934e9i	−0.432494	+	0.432494i
$630$	1.17391e8	+	2.54022e7i	0.0187043	+	0.00404742i
$631$	1.23940e9			0.196386			0.0981929	−	0.995167i	$-0.468694\pi$
$631$	1.23940e9			0.196386			0.0981929	+	0.995167i	$0.468694\pi$
$632$	2.10063e8	+	3.25557e9i	0.0331010	+	0.513001i
$633$	−8.84048e8	−	2.24032e8i	−0.138536	−	0.0351072i
$634$	9.19790e9	−	2.67757e9i	1.43343	−	0.417280i
$635$	2.29871e9	+	2.29871e9i	0.356267	+	0.356267i
$636$	2.57925e9	−	8.50058e8i	0.397552	−	0.131023i
$637$	8.86549e9	−	8.86549e9i	1.35899	−	1.35899i
$638$	1.14956e9	+	6.31176e8i	0.175250	+	0.0962228i
$639$	8.02893e9	+	4.34858e9i	1.21732	+	0.659317i
$640$	−1.36767e9	−	3.12833e9i	−0.206229	−	0.471719i
$641$		−	1.07188e10i		−	1.60747i	−0.594988	−	0.803734i	$-0.702843\pi$
$641$		−	1.07188e10i		−	1.60747i	0.594988	−	0.803734i	$-0.297157\pi$
$642$	−6.01075e9	+	6.44807e9i	−0.896511	+	0.961738i
$643$	−6.25737e8	−	6.25737e8i	−0.0928225	−	0.0928225i	0.659171	−	0.751993i	$-0.270907\pi$
$643$	−6.25737e8	−	6.25737e8i	−0.0928225	−	0.0928225i	−0.751993	+	0.659171i	$0.770907\pi$
$644$	2.10607e8	−	1.33971e8i	0.0310722	−	0.0197656i
$645$	−1.11604e9	−	1.87368e9i	−0.163764	−	0.274939i
$646$	−4.55729e9	−	1.56551e10i	−0.665108	−	2.28476i
$647$			9.33595e9i			1.35517i	0.735445	+	0.677585i	$0.236973\pi$
$647$			9.33595e9i			1.35517i	−0.735445	+	0.677585i	$0.763027\pi$
$648$	−4.15016e9	−	5.54547e9i	−0.599173	−	0.800619i
$649$		−	4.44230e9i		−	0.637898i
$650$	9.50872e9	−	2.76805e9i	1.35808	−	0.395346i
$651$	1.45383e8	+	2.44079e8i	0.0206529	+	0.0346734i
$652$	−1.73073e9	+	7.78190e9i	−0.244547	+	1.09956i
$653$	−5.55587e9	−	5.55587e9i	−0.780829	−	0.780829i	0.199142	−	0.979971i	$-0.436185\pi$
$653$	−5.55587e9	−	5.55587e9i	−0.780829	−	0.780829i	−0.979971	+	0.199142i	$0.936185\pi$
$654$	−6.79162e9	−	6.33100e9i	−0.949404	−	0.885014i
$655$		−	2.16082e9i		−	0.300452i
$656$	−7.40464e8	+	1.58234e9i	−0.102410	+	0.218844i
$657$	9.79915e8	+	5.30735e8i	0.134806	+	0.0730128i
$658$	−3.29770e7	+	6.00609e7i	−0.00451253	+	0.00821866i
$659$	−4.20225e9	+	4.20225e9i	−0.571983	+	0.571983i	−0.932682	−	0.360699i	$-0.882538\pi$
$659$	−4.20225e9	+	4.20225e9i	−0.571983	+	0.571983i	0.360699	+	0.932682i	$0.382538\pi$
$660$	−2.60833e9	−	1.31522e9i	−0.353150	−	0.178072i
$661$	8.84549e9	+	8.84549e9i	1.19129	+	1.19129i	0.976706	+	0.214581i	$0.0688388\pi$
$661$	8.84549e9	+	8.84549e9i	1.19129	+	1.19129i	0.214581	+	0.976706i	$0.431161\pi$
$662$	2.31939e9	+	7.96750e9i	0.310721	+	1.06738i
$663$	2.12742e10	+	5.39123e9i	2.83502	+	0.718440i
$664$	5.10592e9	−	5.81029e9i	0.676840	−	0.770210i
$665$	−2.27257e8			−0.0299669
$666$	6.48952e8	−	2.99900e9i	0.0851241	−	0.393384i
$667$	1.39718e9	−	1.39718e9i	0.182310	−	0.182310i
$668$	−9.39685e9	+	5.97752e9i	−1.21973	+	0.775896i
$669$	1.41537e8	+	2.37622e8i	0.0182759	+	0.0306828i
$670$	1.47997e8	−	2.69546e8i	0.0190103	−	0.0346235i
$671$	−1.65105e9			−0.210975
$672$	2.69041e8	+	1.14574e8i	0.0341999	+	0.0145644i
$673$	5.31868e9			0.672591			0.336296	−	0.941756i	$-0.390826\pi$
$673$	5.31868e9			0.672591			0.336296	+	0.941756i	$0.390826\pi$
$674$	3.79472e9	−	6.91132e9i	0.477387	−	0.869464i
$675$	5.86759e9	−	2.39681e8i	0.734338	−	0.0299965i
$676$	−1.83241e10	+	1.16563e10i	−2.28144	+	1.45127i
$677$	−3.73883e9	+	3.73883e9i	−0.463100	+	0.463100i	−0.899670	−	0.436570i	$-0.856193\pi$
$677$	−3.73883e9	+	3.73883e9i	−0.463100	+	0.463100i	0.436570	+	0.899670i	$0.356193\pi$
$678$	7.61184e9	−	2.67185e8i	0.937963	−	0.0329237i
$679$	−1.91623e8			−0.0234911
$680$	4.81865e9	+	4.23450e9i	0.587684	+	0.516441i
$681$	8.16409e8	−	3.22162e9i	0.0990588	−	0.390894i
$682$	−1.93125e9	−	6.63418e9i	−0.233128	−	0.800834i
$683$	9.17424e9	+	9.17424e9i	1.10179	+	1.10179i	0.994195	+	0.107592i	$0.0343140\pi$
$683$	9.17424e9	+	9.17424e9i	1.10179	+	1.10179i	0.107592	+	0.994195i	$0.465686\pi$
$684$	9.89405e9	+	8.59451e9i	1.18216	+	1.02689i
$685$	−4.06429e9	+	4.06429e9i	−0.483134	+	0.483134i
$686$	−3.02331e8	+	5.50635e8i	−0.0357560	+	0.0651222i
$687$	8.60798e9	+	2.18140e9i	1.01287	+	0.256677i
$688$	−1.80926e9	−	4.99191e9i	−0.211808	−	0.584396i
$689$		−	6.91645e9i		−	0.805593i
$690$	−3.00106e9	+	3.21941e9i	−0.347779	+	0.373082i
$691$	−1.11923e10	−	1.11923e10i	−1.29047	−	1.29047i	−0.934499	−	0.355967i	$-0.884152\pi$
$691$	−1.11923e10	−	1.11923e10i	−1.29047	−	1.29047i	−0.355967	−	0.934499i	$-0.615848\pi$
$692$	3.00786e8	−	1.35243e9i	0.0345054	−	0.155147i
$693$	2.39814e8	−	7.13068e7i	0.0273721	−	0.00813888i
$694$	−8.60278e9	+	2.50432e9i	−0.976969	+	0.284402i
$695$		−	3.21902e9i		−	0.363729i
$696$	2.27586e9	+	4.22974e8i	0.255866	+	0.0475533i
$697$		−	3.28239e9i		−	0.367177i
$698$	−3.09553e9	−	1.06337e10i	−0.344541	−	1.18356i
$699$	−4.85342e9	+	2.89089e9i	−0.537499	+	0.320156i
$700$	−2.09186e8	+	1.33068e8i	−0.0230510	+	0.0146632i
$701$	7.38480e9	+	7.38480e9i	0.809703	+	0.809703i	0.984589	−	0.174886i	$-0.0559557\pi$
$701$	7.38480e9	+	7.38480e9i	0.809703	+	0.809703i	−0.174886	+	0.984589i	$0.555956\pi$
$702$	−1.67221e10	+	5.61777e9i	−1.82436	+	0.612892i
$703$			5.80576e9i			0.630254i
$704$	−5.63355e9	−	4.34097e9i	−0.608524	−	0.468903i
$705$	2.96787e8	−	1.17115e9i	0.0318994	−	0.125878i
$706$	−2.03217e9	−	1.11578e9i	−0.217342	−	0.119334i
$707$	−4.01710e8	+	4.01710e8i	−0.0427508	+	0.0427508i
$708$	−2.45438e9	−	7.44710e9i	−0.259911	−	0.788625i
$709$	6.99621e9	+	6.99621e9i	0.737227	+	0.737227i	0.972040	−	0.234813i	$-0.0754479\pi$
$709$	6.99621e9	+	6.99621e9i	0.737227	+	0.737227i	−0.234813	+	0.972040i	$0.575448\pi$
$710$	6.52628e9	−	1.89984e9i	0.684324	−	0.199211i
$711$	4.33218e9	+	2.34637e9i	0.452025	+	0.244823i
$712$	−1.36977e10	+	8.83835e8i	−1.42222	+	0.0917680i
$713$	−1.04105e10			−1.07561
$714$	−5.49078e8	+	1.92733e7i	−0.0564535	+	0.00198159i
$715$	−5.26064e9	+	5.26064e9i	−0.538230	+	0.538230i
$716$	−2.79834e9	−	6.22365e8i	−0.284909	−	0.0633650i
$717$	−6.09819e9	+	3.63233e9i	−0.617852	+	0.368017i
$718$	−1.03506e9	−	5.68308e8i	−0.104359	−	0.0572991i
$719$	−1.14243e10			−1.14625			−0.573125	−	0.819468i	$-0.694269\pi$
$719$	−1.14243e10			−1.14625			−0.573125	+	0.819468i	$0.694269\pi$
$720$	−5.09929e9	−	7.63742e8i	−0.509150	−	0.0762576i
$721$	−6.50868e8			−0.0646725
$722$	−1.28717e10	−	7.06733e9i	−1.27279	−	0.698836i
$723$	8.40873e9	−	5.00857e9i	0.827459	−	0.492867i
$724$	8.64437e7	−	3.88678e8i	0.00846542	−	0.0380631i
$725$	−1.38775e9	+	1.38775e9i	−0.135248	+	0.135248i
$726$	4.22292e9	−	1.48230e8i	0.409576	−	0.0143766i
$727$	1.11370e10			1.07497			0.537487	−	0.843272i	$-0.319374\pi$
$727$	1.11370e10			1.07497			0.537487	+	0.843272i	$0.319374\pi$
$728$	4.91611e8	−	5.59428e8i	0.0472239	−	0.0537384i
$729$	−1.04255e10	+	8.53153e8i	−0.996668	+	0.0815606i
$730$	7.96520e8	−	2.31872e8i	0.0757821	−	0.0220606i
$731$	7.05417e9	+	7.05417e9i	0.667936	+	0.667936i
$732$	−2.76783e9	+	9.12207e8i	−0.260825	+	0.0859616i
$733$	−1.13009e10	+	1.13009e10i	−1.05986	+	1.05986i	−0.0617721	+	0.998090i	$0.519675\pi$
$733$	−1.13009e10	+	1.13009e10i	−1.05986	+	1.05986i	−0.998090	+	0.0617721i	$0.980325\pi$
$734$	1.40668e10	+	7.72349e9i	1.31298	+	0.720904i
$735$	1.35952e9	−	5.36479e9i	0.126293	−	0.498365i
$736$	−8.65216e9	+	6.32155e9i	−0.799931	+	0.584456i
$737$		−	6.40544e8i		−	0.0589404i
$738$	1.42883e9	+	2.21795e9i	0.130853	+	0.203121i
$739$	−2.70861e9	−	2.70861e9i	−0.246883	−	0.246883i	0.572807	−	0.819690i	$-0.305854\pi$
$739$	−2.70861e9	−	2.70861e9i	−0.246883	−	0.246883i	−0.819690	+	0.572807i	$0.805854\pi$
$740$	−1.22598e9	−	1.92728e9i	−0.111217	−	0.174837i
$741$	2.86761e10	−	1.70806e10i	2.58915	−	1.54220i
$742$	4.83953e7	+	1.66246e8i	0.00434900	+	0.0149396i
$743$		−	9.11771e9i		−	0.815502i	−0.913093	−	0.407751i	$-0.866313\pi$
$743$		−	9.11771e9i		−	0.815502i	0.913093	−	0.407751i	$-0.133687\pi$
$744$	−6.90297e9	−	1.00546e10i	−0.614513	−	0.895073i
$745$		−	1.19234e9i		−	0.105646i
$746$	1.31455e10	−	3.82675e9i	1.15929	−	0.337477i
$747$	−3.32930e9	−	1.11969e10i	−0.292234	−	0.982820i
$748$	1.30438e10	+	2.90099e9i	1.13959	+	0.253449i
$749$	−3.97414e8	−	3.97414e8i	−0.0345587	−	0.0345587i
$750$	7.03662e9	−	7.54858e9i	0.609046	−	0.653358i
$751$		−	1.26234e10i		−	1.08752i	−0.839242	−	0.543759i	$-0.817001\pi$
$751$		−	1.26234e10i		−	1.08752i	0.839242	−	0.543759i	$-0.182999\pi$
$752$	1.24672e9	−	2.66419e9i	0.106907	−	0.228456i
$753$	−1.59475e10	−	4.04136e9i	−1.36117	−	0.344941i
$754$	2.83739e9	−	5.16773e9i	0.241057	−	0.439036i
$755$	−1.94380e9	+	1.94380e9i	−0.164376	+	0.164376i
$756$	3.62629e8	−	2.52037e8i	0.0305236	−	0.0212148i
$757$	−4.08387e9	−	4.08387e9i	−0.342166	−	0.342166i	0.515015	−	0.857181i	$-0.327786\pi$
$757$	−4.08387e9	−	4.08387e9i	−0.342166	−	0.342166i	−0.857181	+	0.515015i	$0.827786\pi$
$758$	2.05067e9	+	7.04440e9i	0.171023	+	0.587492i
$759$	−2.25213e9	+	8.88710e9i	−0.186959	+	0.737758i
$760$	9.73578e9	−	6.28194e8i	0.804495	−	0.0519094i
$761$	2.79891e9			0.230219			0.115110	−	0.993353i	$-0.463278\pi$
$761$	2.79891e9			0.230219			0.115110	+	0.993353i	$0.463278\pi$
$762$	1.19454e10	−	4.19300e8i	0.978047	−	0.0343307i
$763$	4.18589e8	−	4.18589e8i	0.0341155	−	0.0341155i
$764$	6.45597e9	+	1.01490e10i	0.523763	+	0.823372i
$765$	9.28589e9	−	2.76109e9i	0.749909	−	0.222980i
$766$	4.70441e9	−	8.56814e9i	0.378185	−	0.688788i
$767$	−1.99699e10			−1.59806
$768$	−1.18425e10	−	4.16469e9i	−0.943365	−	0.331755i
$769$	−1.74308e9			−0.138221			−0.0691105	−	0.997609i	$-0.522016\pi$
$769$	−1.74308e9			−0.138221			−0.0691105	+	0.997609i	$0.522016\pi$
$770$	8.96373e7	−	1.63256e8i	0.00707573	−	0.0128870i
$771$	−8.53103e9	−	1.43225e10i	−0.670365	−	1.12545i
$772$	1.32133e10	+	2.07717e10i	1.03359	+	1.62484i
$773$	−3.04188e9	+	3.04188e9i	−0.236872	+	0.236872i	−0.815554	−	0.578682i	$-0.803567\pi$
$773$	−3.04188e9	+	3.04188e9i	−0.236872	+	0.236872i	0.578682	+	0.815554i	$0.303567\pi$
$774$	−7.83726e9	−	1.69590e9i	−0.607534	−	0.131464i
$775$	1.03402e10			0.797948
$776$	8.20922e9	−	5.29694e8i	0.630647	−	0.0406920i
$777$	1.89639e8	+	4.80574e7i	0.0145029	+	0.00367525i
$778$	2.26951e9	+	7.79616e9i	0.172784	+	0.593543i
$779$	−3.52990e9	−	3.52990e9i	−0.267535	−	0.267535i
$780$	−5.91246e9	+	1.17255e10i	−0.446105	+	0.884709i
$781$	1.00119e10	−	1.00119e10i	0.752031	−	0.752031i
$782$	9.68966e9	−	1.76478e10i	0.724578	−	1.31967i
$783$	2.36899e9	−	2.57077e9i	0.176359	−	0.191380i
$784$	5.71100e9	−	1.22041e10i	0.423259	−	0.904484i
$785$		−	9.06480e9i		−	0.668828i
$786$	−5.81153e9	−	5.41738e9i	−0.426886	−	0.397934i
$787$	−2.53769e9	−	2.53769e9i	−0.185578	−	0.185578i	0.608203	−	0.793781i	$-0.291891\pi$
$787$	−2.53769e9	−	2.53769e9i	−0.185578	−	0.185578i	−0.793781	+	0.608203i	$0.791891\pi$
$788$	−6.07008e9	−	1.35001e9i	−0.441929	−	0.0982871i
$789$	−7.43638e8	−	1.24847e9i	−0.0539004	−	0.0904916i
$790$	3.52139e9	−	1.02510e9i	0.254109	−	0.0739727i
$791$			4.85609e8i			0.0348874i
$792$	−1.00766e10	+	3.71772e9i	−0.720737	+	0.265912i
$793$			7.42212e9i			0.528532i
$794$	3.75564e9	+	1.29013e10i	0.266264	+	0.914661i
$795$	−1.56236e9	−	2.62300e9i	−0.110280	−	0.185146i
$796$	−8.40678e9	−	1.32157e10i	−0.590791	−	0.928742i
$797$	−1.20480e10	−	1.20480e10i	−0.842971	−	0.842971i	0.146273	−	0.989244i	$-0.453272\pi$
$797$	−1.20480e10	−	1.20480e10i	−0.842971	−	0.842971i	−0.989244	+	0.146273i	$0.953272\pi$
$798$	−5.69754e8	+	6.11207e8i	−0.0396897	+	0.0425773i
$799$			5.52659e9i			0.383304i
$800$	8.59380e9	−	6.27891e9i	0.593431	−	0.433580i
$801$	−9.87226e9	+	1.82275e10i	−0.678739	+	1.25318i
$802$	2.34317e10	+	1.28654e10i	1.60396	+	0.880669i
$803$	1.22193e9	−	1.22193e9i	0.0832800	−	0.0832800i
$804$	−3.53902e8	−	1.07381e9i	−0.0240153	−	0.0728673i
$805$	−1.98422e8	−	1.98422e8i	−0.0134062	−	0.0134062i
$806$	−2.98233e10	+	8.68176e9i	−2.00624	+	0.584030i
$807$	−1.71586e10	−	4.34827e9i	−1.14928	−	0.291245i
$808$	1.60990e10	−	1.83198e10i	1.07364	−	1.22175i
$809$	7.83175e8			0.0520042			0.0260021	−	0.999662i	$-0.491722\pi$
$809$	7.83175e8			0.0520042			0.0260021	+	0.999662i	$0.491722\pi$
$810$	−5.07268e9	+	5.90785e9i	−0.335382	+	0.390600i
$811$	−1.25095e10	+	1.25095e10i	−0.823509	+	0.823509i	−0.986609	−	0.163100i	$-0.947851\pi$
$811$	−1.25095e10	+	1.25095e10i	−0.823509	+	0.823509i	0.163100	+	0.986609i	$0.447851\pi$
$812$	−3.20412e7	+	1.44067e8i	−0.00210021	+	0.00944319i
$813$	1.00263e10	+	1.68329e10i	0.654373	+	1.09861i
$814$	−4.17072e9	−	2.28997e9i	−0.271035	−	0.148814i
$815$	8.96226e9			0.579917
$816$	2.34695e10	−	2.34347e9i	1.51213	−	0.150988i
$817$	1.51721e10			0.973352
$818$	−9.12100e9	−	5.00797e9i	−0.582647	−	0.319908i
$819$	−3.20553e8	−	1.07806e9i	−0.0203895	−	0.0685724i
$820$	1.91718e9	+	4.26389e8i	0.121426	+	0.0270058i
$821$	−1.49695e10	+	1.49695e10i	−0.944073	+	0.944073i	−0.998517	−	0.0544443i	$-0.982661\pi$
$821$	−1.49695e10	+	1.49695e10i	−0.944073	+	0.944073i	0.0544443	+	0.998517i	$0.482661\pi$
$822$	7.41354e8	+	2.11204e10i	0.0465559	+	1.32633i
$823$	−1.78105e10			−1.11372			−0.556860	−	0.830606i	$-0.687994\pi$
$823$	−1.78105e10			−1.11372			−0.556860	+	0.830606i	$0.687994\pi$
$824$	2.78835e10	−	1.79916e9i	1.73621	−	0.112027i
$825$	2.23694e9	−	8.82715e9i	0.138696	−	0.547308i
$826$	4.80004e8	−	1.39732e8i	0.0296356	−	0.00862713i
$827$	7.15296e8	+	7.15296e8i	0.0439761	+	0.0439761i	0.728753	−	0.684777i	$-0.240100\pi$
$827$	7.15296e8	+	7.15296e8i	0.0439761	+	0.0439761i	−0.684777	+	0.728753i	$0.740100\pi$
$828$	1.13466e9	+	1.61427e10i	0.0694637	+	0.988257i
$829$	−8.77466e9	+	8.77466e9i	−0.534921	+	0.534921i	−0.922033	−	0.387112i	$-0.873473\pi$
$829$	−8.77466e9	+	8.77466e9i	−0.534921	+	0.534921i	0.387112	+	0.922033i	$0.373473\pi$
$830$	−7.62239e9	−	4.18514e9i	−0.462719	−	0.254060i
$831$	3.69828e9	+	9.37203e8i	0.223561	+	0.0566539i
$832$	−1.95144e10	+	2.53251e10i	−1.17469	+	1.52447i
$833$			2.53162e10i			1.51755i
$834$	−8.65756e9	−	8.07039e9i	−0.516791	−	0.481741i
$835$	8.85319e9	+	8.85319e9i	0.526256	+	0.526256i
$836$	1.71470e10	−	1.09076e10i	1.01500	−	0.645663i
$837$	−1.84032e10	+	7.51741e8i	−1.08481	+	0.0443128i
$838$	9.13802e9	+	3.13907e10i	0.536412	+	1.84266i
$839$			4.42767e9i			0.258826i	0.991591	+	0.129413i	$0.0413093\pi$
$839$			4.42767e9i			0.258826i	−0.991591	+	0.129413i	$0.958691\pi$
$840$	6.00691e7	−	3.23209e8i	0.00349682	−	0.0188150i
$841$		−	1.60816e10i		−	0.932271i
$842$	1.08067e10	−	3.14591e9i	0.623881	−	0.181616i
$843$	3.02712e9	−	1.80307e9i	0.174034	−	0.103661i
$844$	−5.41923e8	+	2.43665e9i	−0.0310269	+	0.139507i
$845$	1.72639e10	+	1.72639e10i	0.984330	+	0.984330i
$846$	−2.40573e9	−	3.73438e9i	−0.136600	−	0.212042i
$847$			2.69408e8i			0.0152341i
$848$	−2.53282e9	−	6.98828e9i	−0.142633	−	0.393536i
$849$	−1.54017e8	+	6.07765e8i	−0.00863759	+	0.0340847i
$850$	−9.62430e9	+	1.75287e10i	−0.537530	+	0.979003i
$851$	−5.06911e9	+	5.06911e9i	−0.281954	+	0.281954i
$852$	1.12524e10	−	2.23155e10i	0.623312	−	1.23614i
$853$	−1.04844e10	−	1.04844e10i	−0.578393	−	0.578393i	0.356068	−	0.934460i	$-0.384117\pi$
$853$	−1.04844e10	−	1.04844e10i	−0.578393	−	0.578393i	−0.934460	+	0.356068i	$0.884117\pi$
$854$	−5.19336e7	−	1.78401e8i	−0.00285329	−	0.00980153i
$855$	7.01680e9	−	1.29554e10i	0.383935	−	0.708872i
$856$	1.81240e10	+	1.59269e10i	0.987631	+	0.867904i
$857$	1.24532e10			0.675844			0.337922	−	0.941174i	$-0.390276\pi$
$857$	1.24532e10			0.675844			0.337922	+	0.941174i	$0.390276\pi$
$858$	9.59578e8	+	2.73374e10i	0.0518651	+	1.47758i
$859$	1.32446e9	−	1.32446e9i	0.0712956	−	0.0712956i	−0.670560	−	0.741855i	$-0.733946\pi$
$859$	1.32446e9	−	1.32446e9i	0.0712956	−	0.0712956i	0.741855	+	0.670560i	$0.233946\pi$
$860$	−5.03654e9	+	3.20384e9i	−0.270015	+	0.171762i
$861$	−1.44519e8	+	8.60814e7i	−0.00771639	+	0.00459619i
$862$	1.73159e9	−	3.15374e9i	0.0920810	−	0.167707i
$863$	1.32148e9			0.0699881			0.0349941	−	0.999388i	$-0.488859\pi$
$863$	1.32148e9			0.0699881			0.0349941	+	0.999388i	$0.488859\pi$
$864$	−1.48385e10	+	1.17998e10i	−0.782693	+	0.622408i
$865$	−1.55757e9			−0.0818258
$866$	−2.75740e9	+	5.02204e9i	−0.144274	+	0.262765i
$867$	−2.15863e10	+	1.28576e10i	−1.12489	+	0.670030i
$868$	6.56097e8	−	4.17356e8i	0.0340525	−	0.0216614i
$869$	5.40211e9	−	5.40211e9i	0.279251	−	0.279251i
$870$	−9.12898e7	−	2.60076e9i	−0.00470008	−	0.133901i
$871$	−2.87950e9			−0.147657
$872$	−1.67754e10	+	1.90896e10i	−0.856773	+	0.974965i
$873$	5.91658e9	−	1.09240e10i	0.300968	−	0.555688i
$874$	−8.55816e9	−	2.93987e10i	−0.433601	−	1.48949i
$875$	4.65243e8	+	4.65243e8i	0.0234775	+	0.0234775i
$876$	1.37333e9	−	2.72356e9i	0.0690256	−	0.136890i
$877$	7.93721e9	−	7.93721e9i	0.397346	−	0.397346i	−0.479950	−	0.877296i	$-0.659345\pi$
$877$	7.93721e9	−	7.93721e9i	0.397346	−	0.397346i	0.877296	+	0.479950i	$0.159345\pi$
$878$	−1.27725e10	+	2.32626e10i	−0.636862	+	1.15992i
$879$	−7.99696e9	+	3.15567e10i	−0.397158	+	1.56722i
$880$	−3.38882e9	+	7.24174e9i	−0.167633	+	0.358223i
$881$		−	1.99826e10i		−	0.984547i	−0.870440	−	0.492274i	$-0.836166\pi$
$881$		−	1.99826e10i		−	0.984547i	0.870440	−	0.492274i	$-0.163834\pi$
$882$	−1.10202e10	−	1.71065e10i	−0.540814	−	0.839499i
$883$	4.38253e9	+	4.38253e9i	0.214221	+	0.214221i	0.806058	−	0.591837i	$-0.201597\pi$
$883$	4.38253e9	+	4.38253e9i	0.214221	+	0.214221i	−0.591837	+	0.806058i	$0.701597\pi$
$884$	1.30411e10	−	5.86370e10i	0.634940	−	2.85489i
$885$	−7.57340e9	+	4.51102e9i	−0.367274	+	0.218763i
$886$	1.49006e10	−	4.33767e9i	0.719758	−	0.209526i
$887$		−	1.36903e10i		−	0.658688i	−0.944210	−	0.329344i	$-0.893172\pi$
$887$		−	1.36903e10i		−	0.658688i	0.944210	−	0.329344i	$-0.106828\pi$
$888$	−8.25705e9	−	1.53459e9i	−0.395712	−	0.0735441i
$889$			7.62077e8i			0.0363783i
$890$	4.31308e9	+	1.48161e10i	0.205079	+	0.704483i
$891$	−3.33949e9	+	1.58729e10i	−0.158164	+	0.751768i
$892$	6.38740e8	−	4.06315e8i	0.0301333	−	0.0191684i
$893$	5.94332e9	+	5.94332e9i	0.279286	+	0.279286i
$894$	−3.20681e9	−	2.98932e9i	−0.150104	−	0.139923i
$895$			3.22280e9i			0.150263i
$896$	2.91852e8	−	7.45267e8i	0.0135546	−	0.0346126i
$897$	3.99511e10	+	1.01242e10i	1.84823	+	0.468369i
$898$	−2.76348e9	−	1.51732e9i	−0.127347	−	0.0699212i
$899$	4.35258e9	−	4.35258e9i	0.199797	−	0.199797i
$900$	−1.12700e9	−	1.60338e10i	−0.0515319	−	0.733142i
$901$	9.87528e9	+	9.87528e9i	0.449793	+	0.449793i
$902$	3.92810e9	−	1.14349e9i	0.178221	−	0.0518814i
$903$	1.25588e8	−	4.95582e8i	0.00567599	−	0.0223979i
$904$	−1.34234e9	−	2.08037e10i	−0.0604329	−	0.936593i
$905$	−4.47633e8			−0.0200748
$906$	3.54563e8	+	1.01011e10i	0.0158396	+	0.451254i
$907$	1.67847e10	−	1.67847e10i	0.746943	−	0.746943i	−0.226961	−	0.973904i	$-0.572879\pi$
$907$	1.67847e10	−	1.67847e10i	0.746943	−	0.746943i	0.973904	+	0.226961i	$0.0728790\pi$
$908$	−8.87957e9	−	1.97486e9i	−0.393633	−	0.0875458i
$909$	−1.04973e10	−	3.53037e10i	−0.463557	−	1.55900i
$910$	−7.33902e8	−	4.02955e8i	−0.0322844	−	0.0177261i
$911$	2.74822e9			0.120431			0.0602154	−	0.998185i	$-0.480821\pi$
$911$	2.74822e9			0.120431			0.0602154	+	0.998185i	$0.480821\pi$
$912$	2.27190e10	−	2.77593e10i	0.991760	−	1.21179i
$913$	−1.81137e10			−0.787698
$914$	−7.35539e9	−	4.03854e9i	−0.318635	−	0.174950i
$915$	1.67659e9	+	2.81477e9i	0.0723524	+	0.121470i
$916$	5.27670e9	−	2.37257e10i	0.226845	−	1.01996i
$917$	3.58183e8	−	3.58183e8i	0.0153395	−	0.0153395i
$918$	1.58547e10	−	3.18967e10i	0.676406	−	1.36081i
$919$	−1.77094e10			−0.752662			−0.376331	−	0.926485i	$-0.622814\pi$
$919$	−1.77094e10			−0.752662			−0.376331	+	0.926485i	$0.622814\pi$
$920$	9.04897e9	+	7.95200e9i	0.383126	+	0.336681i
$921$	3.00160e10	+	7.60653e9i	1.26603	+	0.320832i
$922$	−2.53882e10	+	7.39066e9i	−1.06678	+	0.310545i
$923$	−4.50073e10	−	4.50073e10i	−1.88398	−	1.88398i
$924$	−2.14348e8	−	6.50378e8i	−0.00893858	−	0.0271215i
$925$	5.03492e9	−	5.03492e9i	0.209169	−	0.209169i
$926$	−2.67957e10	−	1.47124e10i	−1.10899	−	0.608899i
$927$	2.00963e10	−	3.71044e10i	0.828583	−	1.52984i
$928$	9.74421e8	−	6.26046e9i	0.0400248	−	0.257151i
$929$			3.79470e10i			1.55282i	0.630226	+	0.776412i	$0.282962\pi$
$929$			3.79470e10i			1.55282i	−0.630226	+	0.776412i	$0.717038\pi$
$930$	−9.34909e9	+	1.00293e10i	−0.381135	+	0.408865i
$931$	2.72252e10	+	2.72252e10i	1.10572	+	1.10572i
$932$	8.29896e9	+	1.30462e10i	0.335790	+	0.527873i
$933$	3.79954e6	+	6.37892e6i	0.000153160	+	0.000257135i
$934$	4.17485e9	+	1.43413e10i	0.167659	+	0.575937i
$935$		−	1.50223e10i		−	0.601028i
$936$	1.67126e10	+	4.52985e10i	0.666161	+	1.80559i
$937$			3.14155e10i			1.24754i	0.781606	+	0.623772i	$0.214401\pi$
$937$			3.14155e10i			1.24754i	−0.781606	+	0.623772i	$0.785599\pi$
$938$	6.92128e7	−	2.01483e7i	0.00273827	−	0.000797128i
$939$	−1.52549e10	−	2.56109e10i	−0.601282	−	1.00947i
$940$	−3.22796e9	−	7.17914e8i	−0.126760	−	0.0281919i
$941$	−1.37341e10	−	1.37341e10i	−0.537324	−	0.537324i	0.385418	−	0.922742i	$-0.374057\pi$
$941$	−1.37341e10	−	1.37341e10i	−0.537324	−	0.537324i	−0.922742	+	0.385418i	$0.874057\pi$
$942$	−2.43798e10	−	2.27263e10i	−0.950280	−	0.885830i
$943$		−	6.16403e9i		−	0.239372i
$944$	−2.01773e10	+	7.31303e9i	−0.780659	+	0.282941i
$945$	−3.65091e8	−	3.36435e8i	−0.0140731	−	0.0129685i
$946$	−5.98437e9	+	1.08993e10i	−0.229826	+	0.418582i
$947$	1.43920e10	−	1.43920e10i	0.550675	−	0.550675i	−0.375960	−	0.926636i	$-0.622687\pi$
$947$	1.43920e10	−	1.43920e10i	0.550675	−	0.550675i	0.926636	+	0.375960i	$0.122687\pi$
$948$	6.07146e9	−	1.20408e10i	0.231453	−	0.459015i
$949$	−5.49305e9	−	5.49305e9i	−0.208633	−	0.208633i
$950$	8.50044e9	+	2.92004e10i	0.321669	+	1.10499i
$951$	−3.83845e10	−	9.72723e9i	−1.44718	−	0.366739i
$952$	9.68296e7	+	1.50067e9i	0.00363730	+	0.0563710i
$953$	3.13684e10			1.17400			0.586998	−	0.809588i	$-0.300310\pi$
$953$	3.13684e10			1.17400			0.586998	+	0.809588i	$0.300310\pi$
$954$	−1.09715e10	−	2.37413e9i	−0.409118	−	0.0885289i
$955$	9.56181e9	−	9.56181e9i	0.355245	−	0.355245i
$956$	1.04274e10	+	1.63923e10i	0.385989	+	0.606787i
$957$	−2.77406e9	−	4.65727e9i	−0.102311	−	0.171767i
$958$	1.28104e9	−	2.33315e9i	0.0470742	−	0.0857361i
$959$	−1.34741e9			−0.0493327
$960$	−1.67996e9	+	1.40124e10i	−0.0612843	+	0.511169i
$961$	−4.91873e9			−0.178781
$962$	−1.02944e10	+	1.87491e10i	−0.372809	+	0.678996i
$963$	3.49262e10	−	1.03850e10i	1.26026	−	0.374728i
$964$	−1.43783e10	−	2.26031e10i	−0.516936	−	0.812640i
$965$	1.95699e10	−	1.95699e10i	0.701040	−	0.701040i
$966$	−1.03112e9	+	3.61936e7i	−0.0368035	+	0.00129185i
$967$	7.61996e9			0.270994			0.135497	−	0.990778i	$-0.456737\pi$
$967$	7.61996e9			0.270994			0.135497	+	0.990778i	$0.456737\pi$
$968$	−7.44709e8	−	1.15415e10i	−0.0263890	−	0.408978i
$969$	−1.65560e10	+	6.53314e10i	−0.584550	+	2.30669i
$970$	−2.58488e9	−	8.87951e9i	−0.0909369	−	0.312384i
$971$	2.05325e10	+	2.05325e10i	0.719737	+	0.719737i	0.968551	−	0.248814i	$-0.0800408\pi$
$971$	2.05325e10	+	2.05325e10i	0.719737	+	0.719737i	−0.248814	+	0.968551i	$0.580041\pi$
$972$	3.17147e9	+	2.84545e10i	0.110772	+	0.993846i
$973$	5.33593e8	−	5.33593e8i	0.0185701	−	0.0185701i
$974$	2.36371e10	−	4.30501e10i	0.819666	−	1.49286i
$975$	−3.96816e10	−	1.00559e10i	−1.37111	−	0.347461i
$976$	2.71800e9	+	7.49920e9i	0.0935782	+	0.258191i
$977$		−	1.85036e10i		−	0.634782i	−0.948295	−	0.317391i	$-0.897193\pi$
$977$		−	1.85036e10i		−	0.634782i	0.948295	−	0.317391i	$-0.102807\pi$
$978$	2.24692e10	−	2.41040e10i	0.768072	−	0.823954i
$979$	2.27292e10	+	2.27292e10i	0.774185	+	0.774185i
$980$	−1.47867e10	−	3.28862e9i	−0.501856	−	0.111615i
$981$	1.09383e10	+	3.67871e10i	0.369922	+	1.24410i
$982$	−3.99064e10	+	1.16170e10i	−1.34478	+	0.391475i
$983$			8.57421e9i			0.287910i	0.989584	+	0.143955i	$0.0459821\pi$
$983$			8.57421e9i			0.287910i	−0.989584	+	0.143955i	$0.954018\pi$
$984$	5.95331e9	−	4.08725e9i	0.199194	−	0.136757i
$985$			6.99080e9i			0.233077i
$986$	3.32725e9	+	1.14297e10i	0.110539	+	0.379721i
$987$	2.43328e8	−	1.44936e8i	0.00805531	−	0.00479806i
$988$	−4.90339e10	−	7.70829e10i	−1.61751	−	2.54278i
$989$	1.32471e10	+	1.32471e10i	0.435445	+	0.435445i
$990$	6.53919e9	+	1.01507e10i	0.214191	+	0.332486i
$991$		−	2.57686e9i		−	0.0841071i	−0.999115	−	0.0420536i	$-0.986610\pi$
$991$		−	2.57686e9i		−	0.0841071i	0.999115	−	0.0420536i	$-0.0133900\pi$
$992$	−2.69538e10	+	1.96933e10i	−0.876655	+	0.640513i
$993$	8.42603e9	−	3.32498e10i	0.273087	−	1.07762i
$994$	1.39673e9	+	7.66889e8i	0.0451088	+	0.0247674i
$995$	−1.24511e10	+	1.24511e10i	−0.400707	+	0.400707i
$996$	−3.03660e10	+	1.00079e10i	−0.973822	+	0.320948i
$997$	−3.71242e10	−	3.71242e10i	−1.18638	−	1.18638i	−0.978061	−	0.208321i	$-0.933200\pi$
$997$	−3.71242e10	−	3.71242e10i	−1.18638	−	1.18638i	−0.208321	−	0.978061i	$-0.566800\pi$
$998$	−2.28814e10	+	6.66091e9i	−0.728660	+	0.212118i
$999$	−8.59494e9	+	9.32702e9i	−0.272749	+	0.295981i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	48.8.k.a.11.20	✓	108
3.2	odd	2	inner	48.8.k.a.11.35	yes	108
16.3	odd	4	inner	48.8.k.a.35.35	yes	108
48.35	even	4	inner	48.8.k.a.35.20	yes	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.8.k.a.11.20	✓	108	1.1	even	1	trivial
48.8.k.a.11.35	yes	108	3.2	odd	2	inner
48.8.k.a.35.20	yes	108	48.35	even	4	inner
48.8.k.a.35.35	yes	108	16.3	odd	4	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:	\( N \)	\(=\)	\( 48 = 2^{4} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	48.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-5.44512 + 9.91719i) q^{2} +(40.1781 - 23.9317i) q^{3} +(-68.7013 - 108.001i) q^{4} +(-101.752 + 101.752i) q^{5} +(18.5603 + 528.764i) q^{6} -33.7333 q^{7} +(1445.15 - 93.2472i) q^{8} +(1041.55 - 1923.05i) q^{9} +O(q^{10})\)	\(q+(-5.44512 + 9.91719i) q^{2} +(40.1781 - 23.9317i) q^{3} +(-68.7013 - 108.001i) q^{4} +(-101.752 + 101.752i) q^{5} +(18.5603 + 528.764i) q^{6} -33.7333 q^{7} +(1445.15 - 93.2472i) q^{8} +(1041.55 - 1923.05i) q^{9} +(-455.042 - 1563.15i) q^{10} +(-2398.00 - 2398.00i) q^{11} +(-5344.92 - 2695.12i) q^{12} +(-10780.0 + 10780.0i) q^{13} +(183.682 - 334.540i) q^{14} +(-1653.11 + 6523.30i) q^{15} +(-6944.27 + 14839.6i) q^{16} -30783.2i q^{17} +(13399.9 + 20800.5i) q^{18} +(-33104.3 - 33104.3i) q^{19} +(17979.8 + 3998.79i) q^{20} +(-1355.34 + 807.294i) q^{21} +(36838.8 - 10724.0i) q^{22} -57808.0i q^{23} +(55831.7 - 38331.3i) q^{24} +57418.0i q^{25} +(-48208.7 - 165605. i) q^{26} +(-4174.32 - 102191. i) q^{27} +(2317.52 + 3643.22i) q^{28} +(24169.3 + 24169.3i) q^{29} +(-55691.4 - 51914.3i) q^{30} -180087. i q^{31} +(-109354. - 149671. i) q^{32} +(-153735. - 38958.8i) q^{33} +(305283. + 167618. i) q^{34} +(3432.44 - 3432.44i) q^{35} +(-279247. + 19628.0i) q^{36} +(-87688.8 - 87688.8i) q^{37} +(508559. - 148045. i) q^{38} +(-175136. + 691100. i) q^{39} +(-137559. + 156535. i) q^{40} +106630. q^{41} +(-626.100 - 17837.0i) q^{42} +(-229157. + 229157. i) q^{43} +(-94239.6 + 423731. i) q^{44} +(89694.7 + 301655. i) q^{45} +(573292. + 314771. i) q^{46} -179533. q^{47} +(76128.2 + 762413. i) q^{48} -822405. q^{49} +(-569425. - 312648. i) q^{50} +(-736692. - 1.23681e6i) q^{51} +(1.90484e6 + 423645. i) q^{52} +(-320801. + 320801. i) q^{53} +(1.03617e6 + 515043. i) q^{54} +488002. q^{55} +(-48749.7 + 3145.54i) q^{56} +(-2.12231e6 - 537826. i) q^{57} +(-371297. + 108087. i) q^{58} +(926251. + 926251. i) q^{59} +(818091. - 269622. i) q^{60} +(344255. - 344255. i) q^{61} +(1.78596e6 + 980596. i) q^{62} +(-35135.0 + 64871.0i) q^{63} +(2.07976e6 - 269512. i) q^{64} -2.19377e6i q^{65} +(1.22347e6 - 1.31248e6i) q^{66} +(133558. + 133558. i) q^{67} +(-3.32460e6 + 2.11484e6i) q^{68} +(-1.38344e6 - 2.32261e6i) q^{69} +(15350.1 + 52730.1i) q^{70} +4.17509e6i q^{71} +(1.32588e6 - 2.87622e6i) q^{72} +509562. i q^{73} +(1.34710e6 - 392150. i) q^{74} +(1.37411e6 + 2.30694e6i) q^{75} +(-1.30098e6 + 5.84960e6i) q^{76} +(80892.4 + 80892.4i) q^{77} +(-5.90013e6 - 5.49998e6i) q^{78} +2.25276e6i q^{79} +(-803363. - 2.21655e6i) q^{80} +(-2.61331e6 - 4.00592e6i) q^{81} +(-580611. + 1.05746e6i) q^{82} +(3.77684e6 - 3.77684e6i) q^{83} +(180302. + 90915.3i) q^{84} +(3.13225e6 + 3.13225e6i) q^{85} +(-1.02480e6 - 3.52037e6i) q^{86} +(1.54949e6 + 392665. i) q^{87} +(-3.68907e6 - 3.24186e6i) q^{88} -9.47841e6 q^{89} +(-3.47997e6 - 753029. i) q^{90} +(363644. - 363644. i) q^{91} +(-6.24329e6 + 3.97148e6i) q^{92} +(-4.30978e6 - 7.23555e6i) q^{93} +(977579. - 1.78046e6i) q^{94} +6.73687e6 q^{95} +(-7.97552e6 - 3.39645e6i) q^{96} +5.68054e6 q^{97} +(4.47810e6 - 8.15595e6i) q^{98} +(-7.10912e6 + 2.11384e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q - 2 q^{3} - 4 q^{4} + 172 q^{6} - 8 q^{7}+O(q^{10}) \) 108 * q - 2 * q^3 - 4 * q^4 + 172 * q^6 - 8 * q^7	\( 108 q - 2 q^{3} - 4 q^{4} + 172 q^{6} - 8 q^{7} - 6504 q^{10} + 12016 q^{12} - 4 q^{13} - 55280 q^{16} + 21172 q^{18} - 60588 q^{19} - 4376 q^{21} - 212744 q^{22} - 317304 q^{24} + 238042 q^{27} + 219736 q^{28} - 503852 q^{30} - 4 q^{33} - 364856 q^{34} + 867620 q^{36} - 4 q^{37} - 283948 q^{39} + 390392 q^{40} - 3022344 q^{42} + 752844 q^{43} - 156252 q^{45} - 1166824 q^{46} + 358320 q^{48} + 9882508 q^{49} + 1121592 q^{51} - 4458688 q^{52} + 203816 q^{54} + 4191000 q^{55} + 4975544 q^{58} - 4390240 q^{60} - 2279892 q^{61} + 4781432 q^{64} + 1457476 q^{66} + 1552540 q^{67} + 4372 q^{69} - 9366152 q^{70} - 1660280 q^{72} - 886066 q^{75} - 6569272 q^{76} - 13616772 q^{78} - 4 q^{81} + 11560256 q^{82} - 10944176 q^{84} + 7846496 q^{85} - 40789116 q^{87} + 24614816 q^{88} + 25746032 q^{90} - 1590680 q^{91} - 14495396 q^{93} - 6995856 q^{94} - 13927736 q^{96} - 8 q^{97} - 4701076 q^{99}+O(q^{100}) \) 108 * q - 2 * q^3 - 4 * q^4 + 172 * q^6 - 8 * q^7 - 6504 * q^10 + 12016 * q^12 - 4 * q^13 - 55280 * q^16 + 21172 * q^18 - 60588 * q^19 - 4376 * q^21 - 212744 * q^22 - 317304 * q^24 + 238042 * q^27 + 219736 * q^28 - 503852 * q^30 - 4 * q^33 - 364856 * q^34 + 867620 * q^36 - 4 * q^37 - 283948 * q^39 + 390392 * q^40 - 3022344 * q^42 + 752844 * q^43 - 156252 * q^45 - 1166824 * q^46 + 358320 * q^48 + 9882508 * q^49 + 1121592 * q^51 - 4458688 * q^52 + 203816 * q^54 + 4191000 * q^55 + 4975544 * q^58 - 4390240 * q^60 - 2279892 * q^61 + 4781432 * q^64 + 1457476 * q^66 + 1552540 * q^67 + 4372 * q^69 - 9366152 * q^70 - 1660280 * q^72 - 886066 * q^75 - 6569272 * q^76 - 13616772 * q^78 - 4 * q^81 + 11560256 * q^82 - 10944176 * q^84 + 7846496 * q^85 - 40789116 * q^87 + 24614816 * q^88 + 25746032 * q^90 - 1590680 * q^91 - 14495396 * q^93 - 6995856 * q^94 - 13927736 * q^96 - 8 * q^97 - 4701076 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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