LMFDB - Embedded newform 294.8.e.j.79.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [294,8,Mod(67,294)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(294, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("294.67");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 294 = 2 \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	294.e (of order $3$, degree $2$, not 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:	$91.8411974923$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 42)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			79.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	294.79
Dual form			294.8.e.j.67.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(4.00000 - 6.92820i) q^{2} +(-13.5000 - 23.3827i) q^{3} +(-32.0000 - 55.4256i) q^{4} +(61.0000 - 105.655i) q^{5} -216.000 q^{6} -512.000 q^{8} +(-364.500 + 631.333i) q^{9} +(-488.000 - 845.241i) q^{10} +(506.000 + 876.418i) q^{11} +(-864.000 + 1496.49i) q^{12} +3126.00 q^{13} -3294.00 q^{15} +(-2048.00 + 3547.24i) q^{16} +(14147.0 + 24503.3i) q^{17} +(2916.00 + 5050.66i) q^{18} +(11114.0 - 19250.0i) q^{19} -7808.00 q^{20} +8096.00 q^{22} +(54320.0 - 94085.0i) q^{23} +(6912.00 + 11971.9i) q^{24} +(31620.5 + 54768.3i) q^{25} +(12504.0 - 21657.6i) q^{26} +19683.0 q^{27} -41354.0 q^{29} +(-13176.0 + 22821.5i) q^{30} +(-23328.0 - 40405.3i) q^{31} +(16384.0 + 28377.9i) q^{32} +(13662.0 - 23663.3i) q^{33} +226352. q^{34} +46656.0 q^{36} +(42857.0 - 74230.5i) q^{37} +(-88912.0 - 154000. i) q^{38} +(-42201.0 - 73094.3i) q^{39} +(-31232.0 + 54095.4i) q^{40} -155694. q^{41} +926804. q^{43} +(32384.0 - 56090.7i) q^{44} +(44469.0 + 77022.6i) q^{45} +(-434560. - 752680. i) q^{46} +(264576. - 458259. i) q^{47} +110592. q^{48} +505928. q^{50} +(381969. - 661590. i) q^{51} +(-100032. - 173261. i) q^{52} +(147033. + 254669. i) q^{53} +(78732.0 - 136368. i) q^{54} +123464. q^{55} -600156. q^{57} +(-165416. + 286509. i) q^{58} +(333646. + 577892. i) q^{59} +(105408. + 182572. i) q^{60} +(-416715. + 721772. i) q^{61} -373248. q^{62} +262144. q^{64} +(190686. - 330278. i) q^{65} +(-109296. - 189306. i) q^{66} +(-576998. - 999390. i) q^{67} +(905408. - 1.56821e6i) q^{68} -2.93328e6 q^{69} +3.84234e6 q^{71} +(186624. - 323242. i) q^{72} +(-741845. - 1.28491e6i) q^{73} +(-342856. - 593844. i) q^{74} +(853754. - 1.47874e6i) q^{75} -1.42259e6 q^{76} -675216. q^{78} +(1.88191e6 - 3.25957e6i) q^{79} +(249856. + 432763. i) q^{80} +(-265720. - 460241. i) q^{81} +(-622776. + 1.07868e6i) q^{82} -5.39309e6 q^{83} +3.45187e6 q^{85} +(3.70722e6 - 6.42109e6i) q^{86} +(558279. + 966968. i) q^{87} +(-259072. - 448726. i) q^{88} +(-1.25134e6 + 2.16739e6i) q^{89} +711504. q^{90} -6.95296e6 q^{92} +(-629856. + 1.09094e6i) q^{93} +(-2.11661e6 - 3.66607e6i) q^{94} +(-1.35591e6 - 2.34850e6i) q^{95} +(442368. - 766204. i) q^{96} -4.59755e6 q^{97} -737748. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 8 q^{2} - 27 q^{3} - 64 q^{4} + 122 q^{5} - 432 q^{6} - 1024 q^{8} - 729 q^{9} - 976 q^{10} + 1012 q^{11} - 1728 q^{12} + 6252 q^{13} - 6588 q^{15} - 4096 q^{16} + 28294 q^{17} + 5832 q^{18} + 22228 q^{19}+ \cdots - 1475496 q^{99}+O(q^{100}) $ 2 * q + 8 * q^2 - 27 * q^3 - 64 * q^4 + 122 * q^5 - 432 * q^6 - 1024 * q^8 - 729 * q^9 - 976 * q^10 + 1012 * q^11 - 1728 * q^12 + 6252 * q^13 - 6588 * q^15 - 4096 * q^16 + 28294 * q^17 + 5832 * q^18 + 22228 * q^19 - 15616 * q^20 + 16192 * q^22 + 108640 * q^23 + 13824 * q^24 + 63241 * q^25 + 25008 * q^26 + 39366 * q^27 - 82708 * q^29 - 26352 * q^30 - 46656 * q^31 + 32768 * q^32 + 27324 * q^33 + 452704 * q^34 + 93312 * q^36 + 85714 * q^37 - 177824 * q^38 - 84402 * q^39 - 62464 * q^40 - 311388 * q^41 + 1853608 * q^43 + 64768 * q^44 + 88938 * q^45 - 869120 * q^46 + 529152 * q^47 + 221184 * q^48 + 1011856 * q^50 + 763938 * q^51 - 200064 * q^52 + 294066 * q^53 + 157464 * q^54 + 246928 * q^55 - 1200312 * q^57 - 330832 * q^58 + 667292 * q^59 + 210816 * q^60 - 833430 * q^61 - 746496 * q^62 + 524288 * q^64 + 381372 * q^65 - 218592 * q^66 - 1153996 * q^67 + 1810816 * q^68 - 5866560 * q^69 + 7684672 * q^71 + 373248 * q^72 - 1483690 * q^73 - 685712 * q^74 + 1707507 * q^75 - 2845184 * q^76 - 1350432 * q^78 + 3763824 * q^79 + 499712 * q^80 - 531441 * q^81 - 1245552 * q^82 - 10786184 * q^83 + 6903736 * q^85 + 7414432 * q^86 + 1116558 * q^87 - 518144 * q^88 - 2502690 * q^89 + 1423008 * q^90 - 13905920 * q^92 - 1259712 * q^93 - 4233216 * q^94 - 2711816 * q^95 + 884736 * q^96 - 9195100 * q^97 - 1475496 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/294\mathbb{Z}\right)^\times$.

$n$	$197$	$199$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	4.00000	−	6.92820i	0.353553	−	0.612372i
$2$	4.00000	−	6.92820i	0.353553	−	0.612372i
$3$	−13.5000	−	23.3827i	−0.288675	−	0.500000i
$3$	−13.5000	−	23.3827i	−0.288675	−	0.500000i
$4$	−32.0000	−	55.4256i	−0.250000	−	0.433013i
$5$	61.0000	−	105.655i	0.218240	−	0.378003i	−0.736030	−	0.676949i	$-0.763302\pi$
$5$	61.0000	−	105.655i	0.218240	−	0.378003i	0.954270	+	0.298946i	$0.0966350\pi$
$6$	−216.000			−0.408248
$7$		0			0
$7$		0			0
$8$	−512.000			−0.353553
$9$	−364.500	+	631.333i	−0.166667	+	0.288675i
$10$	−488.000	−	845.241i	−0.154319	−	0.267289i
$11$	506.000	+	876.418i	0.114624	+	0.198535i	0.917629	−	0.397437i	$-0.130100\pi$
$11$	506.000	+	876.418i	0.114624	+	0.198535i	−0.803005	+	0.595972i	$0.796767\pi$
$12$	−864.000	+	1496.49i	−0.144338	+	0.250000i
$13$	3126.00			0.394627			0.197314	−	0.980340i	$-0.436778\pi$
$13$	3126.00			0.394627			0.197314	+	0.980340i	$0.436778\pi$
$14$		0			0
$15$	−3294.00			−0.252002
$16$	−2048.00	+	3547.24i	−0.125000	+	0.216506i
$17$	14147.0	+	24503.3i	0.698382	+	1.20963i	0.969027	+	0.246954i	$0.0794297\pi$
$17$	14147.0	+	24503.3i	0.698382	+	1.20963i	−0.270645	+	0.962679i	$0.587237\pi$
$18$	2916.00	+	5050.66i	0.117851	+	0.204124i
$19$	11114.0	−	19250.0i	0.371734	−	0.643863i	−0.618098	−	0.786101i	$-0.712097\pi$
$19$	11114.0	−	19250.0i	0.371734	−	0.643863i	0.989832	+	0.142238i	$0.0454299\pi$
$20$	−7808.00			−0.218240
$21$		0			0
$22$	8096.00			0.162103
$23$	54320.0	−	94085.0i	0.930920	−	1.61240i	0.149167	−	0.988812i	$-0.452341\pi$
$23$	54320.0	−	94085.0i	0.930920	−	1.61240i	0.781753	−	0.623589i	$-0.214326\pi$
$24$	6912.00	+	11971.9i	0.102062	+	0.176777i
$25$	31620.5	+	54768.3i	0.404742	+	0.701034i
$26$	12504.0	−	21657.6i	0.139522	−	0.241659i
$27$	19683.0			0.192450
$28$		0			0
$29$	−41354.0			−0.314865			−0.157433	−	0.987530i	$-0.550322\pi$
$29$	−41354.0			−0.314865			−0.157433	+	0.987530i	$0.550322\pi$
$30$	−13176.0	+	22821.5i	−0.0890962	+	0.154319i
$31$	−23328.0	−	40405.3i	−0.140641	−	0.243597i	0.787097	−	0.616829i	$-0.211583\pi$
$31$	−23328.0	−	40405.3i	−0.140641	−	0.243597i	−0.927738	+	0.373232i	$0.878250\pi$
$32$	16384.0	+	28377.9i	0.0883883	+	0.153093i
$33$	13662.0	−	23663.3i	0.0661783	−	0.114624i
$34$	226352.			0.987662
$35$		0			0
$36$	46656.0			0.166667
$37$	42857.0	−	74230.5i	0.139096	−	0.240922i	−0.788058	−	0.615600i	$-0.788914\pi$
$37$	42857.0	−	74230.5i	0.139096	−	0.240922i	0.927155	+	0.374678i	$0.122247\pi$
$38$	−88912.0	−	154000.i	−0.262856	−	0.455280i
$39$	−42201.0	−	73094.3i	−0.113919	−	0.197314i
$40$	−31232.0	+	54095.4i	−0.0771596	+	0.133644i
$41$	−155694.			−0.352800			−0.176400	−	0.984319i	$-0.556445\pi$
$41$	−155694.			−0.352800			−0.176400	+	0.984319i	$0.556445\pi$
$42$		0			0
$43$	926804.			1.77766			0.888829	−	0.458239i	$-0.151519\pi$
$43$	926804.			1.77766			0.888829	+	0.458239i	$0.151519\pi$
$44$	32384.0	−	56090.7i	0.0573121	−	0.0992674i
$45$	44469.0	+	77022.6i	0.0727467	+	0.126001i
$46$	−434560.	−	752680.i	−0.658260	−	1.14014i
$47$	264576.	−	458259.i	0.371713	−	0.643826i	−0.618116	−	0.786087i	$-0.712104\pi$
$47$	264576.	−	458259.i	0.371713	−	0.643826i	0.989829	+	0.142261i	$0.0454372\pi$
$48$	110592.			0.144338
$49$		0			0
$50$	505928.			0.572392
$51$	381969.	−	661590.i	0.403211	−	0.698382i
$52$	−100032.	−	173261.i	−0.0986569	−	0.170879i
$53$	147033.	+	254669.i	0.135659	+	0.234969i	0.925849	−	0.377893i	$-0.123351\pi$
$53$	147033.	+	254669.i	0.135659	+	0.234969i	−0.790190	+	0.612862i	$0.790018\pi$
$54$	78732.0	−	136368.i	0.0680414	−	0.117851i
$55$	123464.			0.100062
$56$		0			0
$57$	−600156.			−0.429242
$58$	−165416.	+	286509.i	−0.111322	+	0.192815i
$59$	333646.	+	577892.i	0.211497	+	0.366323i	0.952183	−	0.305528i	$-0.0988329\pi$
$59$	333646.	+	577892.i	0.211497	+	0.366323i	−0.740686	+	0.671851i	$0.765500\pi$
$60$	105408.	+	182572.i	0.0630005	+	0.109120i
$61$	−416715.	+	721772.i	−0.235063	+	0.407141i	−0.959291	−	0.282419i	$-0.908863\pi$
$61$	−416715.	+	721772.i	−0.235063	+	0.407141i	0.724228	+	0.689561i	$0.242196\pi$
$62$	−373248.			−0.198896
$63$		0			0
$64$	262144.			0.125000
$65$	190686.	−	330278.i	0.0861236	−	0.149170i
$66$	−109296.	−	189306.i	−0.0467951	−	0.0810515i
$67$	−576998.	−	999390.i	−0.234376	−	0.405951i	0.724715	−	0.689048i	$-0.241971\pi$
$67$	−576998.	−	999390.i	−0.234376	−	0.405951i	−0.959091	+	0.283098i	$0.908638\pi$
$68$	905408.	−	1.56821e6i	0.349191	−	0.604817i
$69$	−2.93328e6			−1.07493
$70$		0			0
$71$	3.84234e6			1.27406			0.637032	−	0.770838i	$-0.280162\pi$
$71$	3.84234e6			1.27406			0.637032	+	0.770838i	$0.280162\pi$
$72$	186624.	−	323242.i	0.0589256	−	0.102062i
$73$	−741845.	−	1.28491e6i	−0.223194	−	0.386584i	0.732582	−	0.680679i	$-0.238315\pi$
$73$	−741845.	−	1.28491e6i	−0.223194	−	0.386584i	−0.955776	+	0.294095i	$0.904982\pi$
$74$	−342856.	−	593844.i	−0.0983560	−	0.170358i
$75$	853754.	−	1.47874e6i	0.233678	−	0.404742i
$76$	−1.42259e6			−0.371734
$77$		0			0
$78$	−675216.			−0.161106
$79$	1.88191e6	−	3.25957e6i	0.429442	−	0.743815i	−0.567382	−	0.823455i	$-0.692044\pi$
$79$	1.88191e6	−	3.25957e6i	0.429442	−	0.743815i	0.996824	+	0.0796396i	$0.0253769\pi$
$80$	249856.	+	432763.i	0.0545601	+	0.0945008i
$81$	−265720.	−	460241.i	−0.0555556	−	0.0962250i
$82$	−622776.	+	1.07868e6i	−0.124734	+	0.216045i
$83$	−5.39309e6			−1.03530			−0.517648	−	0.855594i	$-0.673192\pi$
$83$	−5.39309e6			−1.03530			−0.517648	+	0.855594i	$0.673192\pi$
$84$		0			0
$85$	3.45187e6			0.609660
$86$	3.70722e6	−	6.42109e6i	0.628497	−	1.08859i
$87$	558279.	+	966968.i	0.0908937	+	0.157433i
$88$	−259072.	−	448726.i	−0.0405258	−	0.0701927i
$89$	−1.25134e6	+	2.16739e6i	−0.188153	+	0.325891i	−0.944635	−	0.328124i	$-0.893584\pi$
$89$	−1.25134e6	+	2.16739e6i	−0.188153	+	0.325891i	0.756481	+	0.654015i	$0.226917\pi$
$90$	711504.			0.102879
$91$		0			0
$92$	−6.95296e6			−0.930920
$93$	−629856.	+	1.09094e6i	−0.0811991	+	0.140641i
$94$	−2.11661e6	−	3.66607e6i	−0.262841	−	0.455254i
$95$	−1.35591e6	−	2.34850e6i	−0.162255	−	0.281034i
$96$	442368.	−	766204.i	0.0510310	−	0.0883883i
$97$	−4.59755e6			−0.511476			−0.255738	−	0.966746i	$-0.582318\pi$
$97$	−4.59755e6			−0.511476			−0.255738	+	0.966746i	$0.582318\pi$
$98$		0			0
$99$	−737748.			−0.0764161
$100$	2.02371e6	−	3.50517e6i	0.202371	−	0.350517i
$101$	−1.02642e7	−	1.77782e7i	−0.991292	−	1.71697i	−0.609684	−	0.792645i	$-0.708703\pi$
$101$	−1.02642e7	−	1.77782e7i	−0.991292	−	1.71697i	−0.381609	−	0.924324i	$-0.624630\pi$
$102$	−3.05575e6	−	5.29272e6i	−0.285113	−	0.493831i
$103$	−7.11670e6	+	1.23265e7i	−0.641724	+	1.11150i	0.343324	+	0.939217i	$0.388447\pi$
$103$	−7.11670e6	+	1.23265e7i	−0.641724	+	1.11150i	−0.985048	+	0.172282i	$0.944886\pi$
$104$	−1.60051e6			−0.139522
$105$		0			0
$106$	2.35253e6			0.191851
$107$	4.66012e6	−	8.07157e6i	0.367751	−	0.636964i	−0.621462	−	0.783444i	$-0.713461\pi$
$107$	4.66012e6	−	8.07157e6i	0.367751	−	0.636964i	0.989214	+	0.146480i	$0.0467945\pi$
$108$	−629856.	−	1.09094e6i	−0.0481125	−	0.0833333i
$109$	−2.15312e6	−	3.72932e6i	−0.159249	−	0.275827i	0.775349	−	0.631533i	$-0.217574\pi$
$109$	−2.15312e6	−	3.72932e6i	−0.159249	−	0.275827i	−0.934598	+	0.355706i	$0.884241\pi$
$110$	493856.	−	855384.i	0.0353774	−	0.0612755i
$111$	−2.31428e6			−0.160615
$112$		0			0
$113$	6.93570e6			0.452184			0.226092	−	0.974106i	$-0.427405\pi$
$113$	6.93570e6			0.452184			0.226092	+	0.974106i	$0.427405\pi$
$114$	−2.40062e6	+	4.15800e6i	−0.151760	+	0.262856i
$115$	−6.62704e6	−	1.14784e7i	−0.406328	−	0.703781i
$116$	1.32333e6	+	2.29207e6i	0.0787163	+	0.136341i
$117$	−1.13943e6	+	1.97355e6i	−0.0657712	+	0.113919i
$118$	5.33834e6			0.299102
$119$		0			0
$120$	1.68653e6			0.0890962
$121$	9.23151e6	−	1.59895e7i	0.473723	−	0.820512i
$122$	3.33372e6	+	5.77417e6i	0.166215	+	0.287892i
$123$	2.10187e6	+	3.64054e6i	0.101845	+	0.176400i
$124$	−1.49299e6	+	2.58594e6i	−0.0703204	+	0.121799i
$125$	1.72467e7			0.789805
$126$		0			0
$127$	−3.14502e7			−1.36242			−0.681209	−	0.732089i	$-0.738545\pi$
$127$	−3.14502e7			−1.36242			−0.681209	+	0.732089i	$0.738545\pi$
$128$	1.04858e6	−	1.81619e6i	0.0441942	−	0.0765466i
$129$	−1.25119e7	−	2.16712e7i	−0.513166	−	0.888829i
$130$	−1.52549e6	−	2.64222e6i	−0.0608986	−	0.105479i
$131$	2.24401e6	−	3.88674e6i	0.0872118	−	0.151055i	−0.819120	−	0.573623i	$-0.805538\pi$
$131$	2.24401e6	−	3.88674e6i	0.0872118	−	0.151055i	0.906332	+	0.422567i	$0.138871\pi$
$132$	−1.74874e6			−0.0661783
$133$		0			0
$134$	−9.23197e6			−0.331457
$135$	1.20066e6	−	2.07961e6i	0.0420004	−	0.0727467i
$136$	−7.24326e6	−	1.25457e7i	−0.246915	−	0.427670i
$137$	−7.81282e6	−	1.35322e7i	−0.259589	−	0.449621i	0.706543	−	0.707670i	$-0.250254\pi$
$137$	−7.81282e6	−	1.35322e7i	−0.259589	−	0.449621i	−0.966132	+	0.258049i	$0.916920\pi$
$138$	−1.17331e7	+	2.03224e7i	−0.380046	+	0.658260i
$139$	−5.42435e7			−1.71315			−0.856577	−	0.516020i	$-0.827413\pi$
$139$	−5.42435e7			−1.71315			−0.856577	+	0.516020i	$0.827413\pi$
$140$		0			0
$141$	−1.42871e7			−0.429217
$142$	1.53693e7	−	2.66205e7i	0.450450	−	0.780201i
$143$	1.58176e6	+	2.73968e6i	0.0452338	+	0.0783473i
$144$	−1.49299e6	−	2.58594e6i	−0.0416667	−	0.0721688i
$145$	−2.52259e6	+	4.36926e6i	−0.0687162	+	0.119020i
$146$	−1.18695e7			−0.315644
$147$		0			0
$148$	−5.48570e6			−0.139096
$149$	1.62475e7	−	2.81415e7i	0.402378	−	0.696939i	−0.591635	−	0.806206i	$-0.701517\pi$
$149$	1.62475e7	−	2.81415e7i	0.402378	−	0.696939i	0.994012	+	0.109267i	$0.0348505\pi$
$150$	−6.83003e6	−	1.18300e7i	−0.165235	−	0.286196i
$151$	3.81669e7	+	6.61070e7i	0.902127	+	1.56253i	0.824728	+	0.565530i	$0.191328\pi$
$151$	3.81669e7	+	6.61070e7i	0.902127	+	1.56253i	0.0773993	+	0.997000i	$0.475338\pi$
$152$	−5.69037e6	+	9.85601e6i	−0.131428	+	0.227640i
$153$	−2.06263e7			−0.465588
$154$		0			0
$155$	−5.69203e6			−0.122774
$156$	−2.70086e6	+	4.67803e6i	−0.0569596	+	0.0986569i
$157$	1.46210e7	+	2.53244e7i	0.301529	+	0.522264i	0.976483	−	0.215596i	$-0.0691695\pi$
$157$	1.46210e7	+	2.53244e7i	0.301529	+	0.522264i	−0.674953	+	0.737861i	$0.735836\pi$
$158$	−1.50553e7	−	2.60765e7i	−0.303661	−	0.525957i
$159$	3.96989e6	−	6.87605e6i	0.0783229	−	0.135659i
$160$	3.99770e6			0.0771596
$161$		0			0
$162$	−4.25153e6			−0.0785674
$163$	4.75449e7	−	8.23502e7i	0.859899	−	1.48939i	−0.0121263	−	0.999926i	$-0.503860\pi$
$163$	4.75449e7	−	8.23502e7i	0.859899	−	1.48939i	0.872025	−	0.489462i	$-0.162807\pi$
$164$	4.98221e6	+	8.62944e6i	0.0882000	+	0.152767i
$165$	−1.66676e6	−	2.88692e6i	−0.0288855	−	0.0500312i
$166$	−2.15724e7	+	3.73644e7i	−0.366032	+	0.633987i
$167$	−2.29949e7			−0.382054			−0.191027	−	0.981585i	$-0.561182\pi$
$167$	−2.29949e7			−0.382054			−0.191027	+	0.981585i	$0.561182\pi$
$168$		0			0
$169$	−5.29766e7			−0.844269
$170$	1.38075e7	−	2.39152e7i	0.215547	−	0.373339i
$171$	8.10211e6	+	1.40333e7i	0.123911	+	0.214621i
$172$	−2.96577e7	−	5.13687e7i	−0.444415	−	0.769749i
$173$	−5.97430e7	+	1.03478e8i	−0.877255	+	1.51945i	−0.0229141	+	0.999737i	$0.507294\pi$
$173$	−5.97430e7	+	1.03478e8i	−0.877255	+	1.51945i	−0.854341	+	0.519713i	$0.826039\pi$
$174$	8.93246e6			0.128543
$175$		0			0
$176$	−4.14515e6			−0.0573121
$177$	9.00844e6	−	1.56031e7i	0.122108	−	0.211497i
$178$	1.00108e7	+	1.73391e7i	0.133045	+	0.230440i
$179$	−4.69127e7	−	8.12553e7i	−0.611372	−	1.05893i	−0.991010	−	0.133791i	$-0.957285\pi$
$179$	−4.69127e7	−	8.12553e7i	−0.611372	−	1.05893i	0.379638	−	0.925135i	$-0.376049\pi$
$180$	2.84602e6	−	4.92944e6i	0.0363734	−	0.0630005i
$181$	1.48834e8			1.86564			0.932819	−	0.360346i	$-0.117341\pi$
$181$	1.48834e8			1.86564			0.932819	+	0.360346i	$0.117341\pi$
$182$		0			0
$183$	2.25026e7			0.271428
$184$	−2.78118e7	+	4.81715e7i	−0.329130	+	0.570070i
$185$	−5.22855e6	−	9.05612e6i	−0.0607128	−	0.105158i
$186$	5.03885e6	+	8.72754e6i	0.0574164	+	0.0994481i
$187$	−1.43168e7	+	2.47974e7i	−0.160103	+	0.277306i
$188$	−3.38657e7			−0.371713
$189$		0			0
$190$	−2.16945e7			−0.229463
$191$	5.07030e7	−	8.78202e7i	0.526522	−	0.911963i	−0.473000	−	0.881062i	$-0.656829\pi$
$191$	5.07030e7	−	8.78202e7i	0.526522	−	0.911963i	0.999522	−	0.0309010i	$-0.00983767\pi$
$192$	−3.53894e6	−	6.12963e6i	−0.0360844	−	0.0625000i
$193$	−3.52948e7	−	6.11324e7i	−0.353395	−	0.612097i	0.633447	−	0.773786i	$-0.281639\pi$
$193$	−3.52948e7	−	6.11324e7i	−0.353395	−	0.612097i	−0.986842	+	0.161688i	$0.948306\pi$
$194$	−1.83902e7	+	3.18528e7i	−0.180834	+	0.313214i
$195$	−1.02970e7			−0.0994469
$196$		0			0
$197$	5.02307e7			0.468099			0.234049	−	0.972225i	$-0.424802\pi$
$197$	5.02307e7			0.468099			0.234049	+	0.972225i	$0.424802\pi$
$198$	−2.95099e6	+	5.11127e6i	−0.0270172	+	0.0467951i
$199$	−1.04449e8	−	1.80910e8i	−0.939544	−	1.62734i	−0.766324	−	0.642454i	$-0.777916\pi$
$199$	−1.04449e8	−	1.80910e8i	−0.939544	−	1.62734i	−0.173220	−	0.984883i	$-0.555417\pi$
$200$	−1.61897e7	−	2.80414e7i	−0.143098	−	0.247853i
$201$	−1.55789e7	+	2.69835e7i	−0.135317	+	0.234376i
$202$	−1.64228e8			−1.40190
$203$		0			0
$204$	−4.88920e7			−0.403211
$205$	−9.49733e6	+	1.64499e7i	−0.0769951	+	0.133359i
$206$	5.69336e7	+	9.86119e7i	0.453767	+	0.785948i
$207$	3.95993e7	+	6.85880e7i	0.310307	+	0.537467i
$208$	−6.40205e6	+	1.10887e7i	−0.0493284	+	0.0854393i
$209$	2.24947e7			0.170439
$210$		0			0
$211$	−8.44931e7			−0.619202			−0.309601	−	0.950866i	$-0.600196\pi$
$211$	−8.44931e7			−0.619202			−0.309601	+	0.950866i	$0.600196\pi$
$212$	9.41011e6	−	1.62988e7i	0.0678296	−	0.117484i
$213$	−5.18715e7	−	8.98441e7i	−0.367790	−	0.637032i
$214$	−3.72810e7	−	6.45725e7i	−0.260039	−	0.450401i
$215$	5.65350e7	−	9.79216e7i	0.387957	−	0.671961i
$216$	−1.00777e7			−0.0680414
$217$		0			0
$218$	−3.44500e7			−0.225212
$219$	−2.00298e7	+	3.46927e7i	−0.128861	+	0.223194i
$220$	−3.95085e6	−	6.84307e6i	−0.0250156	−	0.0433283i
$221$	4.42235e7	+	7.65974e7i	0.275601	+	0.477354i
$222$	−9.25711e6	+	1.60338e7i	−0.0567858	+	0.0983560i
$223$	1.50175e8			0.906837			0.453418	−	0.891298i	$-0.350204\pi$
$223$	1.50175e8			0.906837			0.453418	+	0.891298i	$0.350204\pi$
$224$		0			0
$225$	−4.61027e7			−0.269828
$226$	2.77428e7	−	4.80519e7i	0.159871	−	0.276905i
$227$	1.51437e8	+	2.62296e8i	0.859293	+	1.48834i	0.872604	+	0.488428i	$0.162429\pi$
$227$	1.51437e8	+	2.62296e8i	0.859293	+	1.48834i	−0.0133116	+	0.999911i	$0.504237\pi$
$228$	1.92050e7	+	3.32640e7i	0.107310	+	0.185867i
$229$	2.65687e7	−	4.60183e7i	0.146199	−	0.253225i	−0.783620	−	0.621240i	$-0.786629\pi$
$229$	2.65687e7	−	4.60183e7i	0.146199	−	0.253225i	0.929820	+	0.368015i	$0.119963\pi$
$230$	−1.06033e8			−0.574635
$231$		0			0
$232$	2.11732e7			0.111322
$233$	6.81754e7	−	1.18083e8i	0.353087	−	0.611565i	−0.633702	−	0.773578i	$-0.718465\pi$
$233$	6.81754e7	−	1.18083e8i	0.353087	−	0.611565i	0.986789	+	0.162013i	$0.0517986\pi$
$234$	9.11542e6	+	1.57884e7i	0.0465073	+	0.0805530i
$235$	−3.22783e7	−	5.59076e7i	−0.162246	−	0.281018i
$236$	2.13533e7	−	3.69851e7i	0.105748	−	0.183162i
$237$	−1.01623e8			−0.495877
$238$		0			0
$239$	2.26802e8			1.07462			0.537309	−	0.843385i	$-0.319441\pi$
$239$	2.26802e8			1.07462			0.537309	+	0.843385i	$0.319441\pi$
$240$	6.74611e6	−	1.16846e7i	0.0315003	−	0.0545601i
$241$	−2.02527e8	−	3.50786e8i	−0.932014	−	1.61430i	−0.779874	−	0.625936i	$-0.784717\pi$
$241$	−2.02527e8	−	3.50786e8i	−0.932014	−	1.61430i	−0.152139	−	0.988359i	$-0.548616\pi$
$242$	−7.38521e7	−	1.27916e8i	−0.334972	−	0.580189i
$243$	−7.17445e6	+	1.24265e7i	−0.0320750	+	0.0555556i
$244$	5.33395e7			0.235063
$245$		0			0
$246$	3.36299e7			0.144030
$247$	3.47424e7	−	6.01755e7i	0.146697	−	0.254086i
$248$	1.19439e7	+	2.06875e7i	0.0497241	+	0.0861246i
$249$	7.28067e7	+	1.26105e8i	0.298864	+	0.517648i
$250$	6.89866e7	−	1.19488e8i	0.279238	−	0.483655i
$251$	−3.08065e7			−0.122966			−0.0614828	−	0.998108i	$-0.519583\pi$
$251$	−3.08065e7			−0.122966			−0.0614828	+	0.998108i	$0.519583\pi$
$252$		0			0
$253$	1.09944e8			0.426824
$254$	−1.25801e8	+	2.17893e8i	−0.481687	+	0.834307i
$255$	−4.66002e7	−	8.07139e7i	−0.175994	−	0.304830i
$256$	−8.38861e6	−	1.45295e7i	−0.0312500	−	0.0541266i
$257$	1.37566e8	−	2.38271e8i	0.505527	−	0.875599i	−0.494452	−	0.869205i	$-0.664631\pi$
$257$	1.37566e8	−	2.38271e8i	0.505527	−	0.875599i	0.999980	−	0.00639407i	$-0.00203531\pi$
$258$	−2.00190e8			−0.725726
$259$		0			0
$260$	−2.44078e7			−0.0861236
$261$	1.50735e7	−	2.61081e7i	0.0524775	−	0.0908937i
$262$	−1.79521e7	−	3.10939e7i	−0.0616681	−	0.106812i
$263$	2.41998e8	+	4.19153e8i	0.820288	+	1.42078i	0.905467	+	0.424416i	$0.139520\pi$
$263$	2.41998e8	+	4.19153e8i	0.820288	+	1.42078i	−0.0851790	+	0.996366i	$0.527146\pi$
$264$	−6.99494e6	+	1.21156e7i	−0.0233976	+	0.0405258i
$265$	3.58761e7			0.118425
$266$		0			0
$267$	6.75726e7			0.217261
$268$	−3.69279e7	+	6.39610e7i	−0.117188	+	0.202975i
$269$	−1.23687e8	−	2.14233e8i	−0.387429	−	0.671047i	0.604674	−	0.796473i	$-0.293303\pi$
$269$	−1.23687e8	−	2.14233e8i	−0.387429	−	0.671047i	−0.992103	+	0.125427i	$0.959970\pi$
$270$	−9.60530e6	−	1.66369e7i	−0.0296987	−	0.0514397i
$271$	1.14143e8	−	1.97702e8i	0.348384	−	0.603418i	−0.637579	−	0.770385i	$-0.720064\pi$
$271$	1.14143e8	−	1.97702e8i	0.348384	−	0.603418i	0.985963	+	0.166967i	$0.0533973\pi$
$272$	−1.15892e8			−0.349191
$273$		0			0
$274$	−1.25005e8			−0.367114
$275$	−3.19999e7	+	5.54255e7i	−0.0927865	+	0.160711i
$276$	9.38650e7	+	1.62579e8i	0.268733	+	0.465460i
$277$	1.77558e8	+	3.07539e8i	0.501950	+	0.869403i	0.999997	+	0.00225351i	$0.000717315\pi$
$277$	1.77558e8	+	3.07539e8i	0.501950	+	0.869403i	−0.498047	+	0.867150i	$0.665949\pi$
$278$	−2.16974e8	+	3.75810e8i	−0.605691	+	1.04909i
$279$	3.40122e7			0.0937606
$280$		0			0
$281$	2.28167e8			0.613453			0.306726	−	0.951798i	$-0.400766\pi$
$281$	2.28167e8			0.613453			0.306726	+	0.951798i	$0.400766\pi$
$282$	−5.71484e7	+	9.89840e7i	−0.151751	+	0.262841i
$283$	1.06896e8	+	1.85149e8i	0.280354	+	0.485588i	0.971472	−	0.237154i	$-0.0762147\pi$
$283$	1.06896e8	+	1.85149e8i	0.280354	+	0.485588i	−0.691118	+	0.722742i	$0.742881\pi$
$284$	−1.22955e8	−	2.12964e8i	−0.318516	−	0.551686i
$285$	−3.66095e7	+	6.34095e7i	−0.0936779	+	0.162255i
$286$	2.53081e7			0.0639703
$287$		0			0
$288$	−2.38879e7			−0.0589256
$289$	−1.95106e8	+	3.37933e8i	−0.475475	+	0.823547i
$290$	2.01808e7	+	3.49541e7i	0.0485897	+	0.0841599i
$291$	6.20669e7	+	1.07503e8i	0.147650	+	0.255738i
$292$	−4.74781e7	+	8.22344e7i	−0.111597	+	0.193292i
$293$	3.78816e8			0.879816			0.439908	−	0.898043i	$-0.355011\pi$
$293$	3.78816e8			0.879816			0.439908	+	0.898043i	$0.355011\pi$
$294$		0			0
$295$	8.14096e7			0.184628
$296$	−2.19428e7	+	3.80060e7i	−0.0491780	+	0.0851788i
$297$	9.95960e6	+	1.72505e7i	0.0220594	+	0.0382080i
$298$	−1.29980e8	−	2.25132e8i	−0.284524	−	0.492810i
$299$	1.69804e8	−	2.94110e8i	0.367367	−	0.636297i
$300$	−1.09280e8			−0.233678
$301$		0			0
$302$	6.10671e8			1.27580
$303$	−2.77134e8	+	4.80011e8i	−0.572323	+	0.991292i
$304$	4.55229e7	+	7.88481e7i	0.0929336	+	0.160966i
$305$	5.08392e7	+	8.80561e7i	0.102601	+	0.177709i
$306$	−8.25053e7	+	1.42903e8i	−0.164610	+	0.285113i
$307$	6.33814e8			1.25019			0.625097	−	0.780547i	$-0.285059\pi$
$307$	6.33814e8			1.25019			0.625097	+	0.780547i	$0.285059\pi$
$308$		0			0
$309$	3.84302e8			0.740999
$310$	−2.27681e7	+	3.94356e7i	−0.0434072	+	0.0751834i
$311$	1.95098e8	+	3.37919e8i	0.367782	+	0.637018i	0.989218	−	0.146447i	$-0.0467838\pi$
$311$	1.95098e8	+	3.37919e8i	0.367782	+	0.637018i	−0.621436	+	0.783465i	$0.713451\pi$
$312$	2.16069e7	+	3.74243e7i	0.0402765	+	0.0697609i
$313$	5.02221e8	−	8.69872e8i	0.925741	−	1.60343i	0.135376	−	0.990794i	$-0.456776\pi$
$313$	5.02221e8	−	8.69872e8i	0.925741	−	1.60343i	0.790365	−	0.612636i	$-0.209891\pi$
$314$	2.33937e8			0.426427
$315$		0			0
$316$	−2.40885e8			−0.429442
$317$	−1.21487e8	+	2.10422e8i	−0.214202	+	0.371009i	−0.953025	−	0.302890i	$-0.902048\pi$
$317$	−1.21487e8	+	2.10422e8i	−0.214202	+	0.371009i	0.738823	+	0.673899i	$0.235382\pi$
$318$	−3.17591e7	−	5.50084e7i	−0.0553826	−	0.0959255i
$319$	−2.09251e7	−	3.62434e7i	−0.0360911	−	0.0625117i
$320$	1.59908e7	−	2.76969e7i	0.0272800	−	0.0472504i
$321$	−2.51647e8			−0.424642
$322$		0			0
$323$	6.28919e8			1.03845
$324$	−1.70061e7	+	2.94555e7i	−0.0277778	+	0.0481125i
$325$	9.88457e7	+	1.71206e8i	0.159722	+	0.276647i
$326$	−3.80359e8	−	6.58801e8i	−0.608040	−	1.05316i
$327$	−5.81343e7	+	1.00692e8i	−0.0919423	+	0.159249i
$328$	7.97153e7			0.124734
$329$		0			0
$330$	−2.66682e7			−0.0408503
$331$	1.41758e7	−	2.45533e7i	0.0214858	−	0.0372144i	−0.855083	−	0.518492i	$-0.826494\pi$
$331$	1.41758e7	−	2.45533e7i	0.0214858	−	0.0372144i	0.876568	+	0.481277i	$0.159827\pi$
$332$	1.72579e8	+	2.98915e8i	0.258824	+	0.448296i
$333$	3.12428e7	+	5.41140e7i	0.0463654	+	0.0803073i
$334$	−9.19797e7	+	1.59314e8i	−0.135076	+	0.233959i
$335$	−1.40788e8			−0.204601
$336$		0			0
$337$	−1.01675e9			−1.44714			−0.723572	−	0.690249i	$-0.757501\pi$
$337$	−1.01675e9			−1.44714			−0.723572	+	0.690249i	$0.757501\pi$
$338$	−2.11907e8	+	3.67033e8i	−0.298494	+	0.517007i
$339$	−9.36319e7	−	1.62175e8i	−0.130534	−	0.226092i
$340$	−1.10460e8	−	1.91322e8i	−0.152415	−	0.263991i
$341$	2.36079e7	−	4.08901e7i	0.0322417	−	0.0558442i
$342$	1.29634e8			0.175237
$343$		0			0
$344$	−4.74524e8			−0.628497
$345$	−1.78930e8	+	3.09916e8i	−0.234594	+	0.406328i
$346$	4.77944e8	+	8.27824e8i	0.620313	+	1.07441i
$347$	4.85247e8	+	8.40472e8i	0.623461	+	1.07987i	0.988836	+	0.149006i	$0.0476075\pi$
$347$	4.85247e8	+	8.40472e8i	0.623461	+	1.07987i	−0.365375	+	0.930860i	$0.619059\pi$
$348$	3.57299e7	−	6.18859e7i	0.0454469	−	0.0787163i
$349$	8.84145e8			1.11336			0.556678	−	0.830728i	$-0.312076\pi$
$349$	8.84145e8			1.11336			0.556678	+	0.830728i	$0.312076\pi$
$350$		0			0
$351$	6.15291e7			0.0759461
$352$	−1.65806e7	+	2.87185e7i	−0.0202629	+	0.0350963i
$353$	5.45231e8	+	9.44367e8i	0.659734	+	1.14269i	0.980684	+	0.195597i	$0.0626643\pi$
$353$	5.45231e8	+	9.44367e8i	0.659734	+	1.14269i	−0.320951	+	0.947096i	$0.604002\pi$
$354$	−7.20675e7	−	1.24825e8i	−0.0863432	−	0.149551i
$355$	2.34382e8	−	4.05962e8i	0.278052	−	0.481600i
$356$	1.60172e8			0.188153
$357$		0			0
$358$	−7.50604e8			−0.864610
$359$	−5.16865e8	+	8.95236e8i	−0.589585	+	1.02119i	0.404702	+	0.914449i	$0.367375\pi$
$359$	−5.16865e8	+	8.95236e8i	−0.589585	+	1.02119i	−0.994287	+	0.106742i	$0.965958\pi$
$360$	−2.27681e7	−	3.94356e7i	−0.0257199	−	0.0445481i
$361$	1.99894e8	+	3.46226e8i	0.223627	+	0.387333i
$362$	5.95336e8	−	1.03115e9i	0.659603	−	1.14247i
$363$	−4.98502e8			−0.547008
$364$		0			0
$365$	−1.81010e8			−0.194840
$366$	9.00104e7	−	1.55903e8i	0.0959642	−	0.166215i
$367$	1.21092e8	+	2.09737e8i	0.127874	+	0.221484i	0.922853	−	0.385153i	$-0.125851\pi$
$367$	1.21092e8	+	2.09737e8i	0.127874	+	0.221484i	−0.794979	+	0.606637i	$0.792518\pi$
$368$	2.22495e8	+	3.85372e8i	0.232730	+	0.403100i
$369$	5.67505e7	−	9.82947e7i	0.0588000	−	0.101845i
$370$	−8.36569e7			−0.0858609
$371$		0			0
$372$	8.06216e7			0.0811991
$373$	7.18844e8	−	1.24507e9i	0.717222	−	1.24226i	−0.244874	−	0.969555i	$-0.578747\pi$
$373$	7.18844e8	−	1.24507e9i	0.717222	−	1.24226i	0.962096	−	0.272710i	$-0.0879199\pi$
$374$	1.14534e8	+	1.98379e8i	0.113210	+	0.196085i
$375$	−2.32830e8	−	4.03273e8i	−0.227997	−	0.394902i
$376$	−1.35463e8	+	2.34629e8i	−0.131420	+	0.227627i
$377$	−1.29273e8			−0.124254
$378$		0			0
$379$	1.20169e9			1.13385			0.566924	−	0.823770i	$-0.308133\pi$
$379$	1.20169e9			1.13385			0.566924	+	0.823770i	$0.308133\pi$
$380$	−8.67781e7	+	1.50304e8i	−0.0811274	+	0.140517i
$381$	4.24577e8	+	7.35390e8i	0.393296	+	0.681209i
$382$	−4.05624e8	−	7.02561e8i	−0.372307	−	0.644855i
$383$	−3.15429e8	+	5.46340e8i	−0.286884	+	0.496898i	−0.973064	−	0.230534i	$-0.925953\pi$
$383$	−3.15429e8	+	5.46340e8i	−0.286884	+	0.496898i	0.686180	+	0.727431i	$0.259286\pi$
$384$	−5.66231e7			−0.0510310
$385$		0			0
$386$	−5.64717e8			−0.499775
$387$	−3.37820e8	+	5.85122e8i	−0.296276	+	0.513166i
$388$	1.47122e8	+	2.54822e8i	0.127869	+	0.221476i
$389$	7.10929e8	+	1.23137e9i	0.612354	+	1.06063i	0.990843	+	0.135022i	$0.0431106\pi$
$389$	7.10929e8	+	1.23137e9i	0.612354	+	1.06063i	−0.378488	+	0.925606i	$0.623556\pi$
$390$	−4.11882e7	+	7.13400e7i	−0.0351598	+	0.0608986i
$391$	3.07386e9			2.60055
$392$		0			0
$393$	−1.21177e8			−0.100704
$394$	2.00923e8	−	3.48009e8i	0.165498	−	0.286651i
$395$	−2.29593e8	−	3.97667e8i	−0.187443	−	0.324661i
$396$	2.36079e7	+	4.08901e7i	0.0191040	+	0.0330891i
$397$	−3.52485e7	+	6.10521e7i	−0.0282731	+	0.0489704i	−0.879816	−	0.475315i	$-0.842334\pi$
$397$	−3.52485e7	+	6.10521e7i	−0.0282731	+	0.0489704i	0.851543	+	0.524285i	$0.175667\pi$
$398$	−1.67118e9			−1.32872
$399$		0			0
$400$	−2.59035e8			−0.202371
$401$	−1.01161e9	+	1.75216e9i	−0.783444	+	1.35697i	0.146480	+	0.989214i	$0.453206\pi$
$401$	−1.01161e9	+	1.75216e9i	−0.783444	+	1.35697i	−0.929924	+	0.367752i	$0.880128\pi$
$402$	1.24632e8	+	2.15868e8i	0.0956835	+	0.165729i
$403$	−7.29233e7	−	1.26307e8i	−0.0555007	−	0.0961301i
$404$	−6.56911e8	+	1.13780e9i	−0.495646	+	0.858484i
$405$	−6.48358e7			−0.0484978
$406$		0			0
$407$	8.67426e7			0.0637752
$408$	−1.95568e8	+	3.38734e8i	−0.142557	+	0.246915i
$409$	−7.18632e8	−	1.24471e9i	−0.519368	−	0.899571i	−0.999747	−	0.0225102i	$-0.992834\pi$
$409$	−7.18632e8	−	1.24471e9i	−0.519368	−	0.899571i	0.480379	−	0.877061i	$-0.340499\pi$
$410$	7.59787e7	+	1.31599e8i	0.0544438	+	0.0942994i
$411$	−2.10946e8	+	3.65369e8i	−0.149874	+	0.259589i
$412$	9.10938e8			0.641724
$413$		0			0
$414$	6.33588e8			0.438840
$415$	−3.28979e8	+	5.69808e8i	−0.225943	+	0.391345i
$416$	5.12164e7	+	8.87094e7i	0.0348805	+	0.0604147i
$417$	7.32288e8	+	1.26836e9i	0.494545	+	0.856577i
$418$	8.99789e7	−	1.55848e8i	0.0602593	−	0.104372i
$419$	8.62098e7			0.0572542			0.0286271	−	0.999590i	$-0.490886\pi$
$419$	8.62098e7			0.0572542			0.0286271	+	0.999590i	$0.490886\pi$
$420$		0			0
$421$	−1.18254e9			−0.772378			−0.386189	−	0.922420i	$-0.626209\pi$
$421$	−1.18254e9			−0.772378			−0.386189	+	0.922420i	$0.626209\pi$
$422$	−3.37972e8	+	5.85385e8i	−0.218921	+	0.379183i
$423$	1.92876e8	+	3.34071e8i	0.123904	+	0.214609i
$424$	−7.52809e7	−	1.30390e8i	−0.0479628	−	0.0830740i
$425$	−8.94670e8	+	1.54961e9i	−0.565330	+	0.979180i
$426$	−8.29945e8			−0.520134
$427$		0			0
$428$	−5.96496e8			−0.367751
$429$	4.27074e7	−	7.39714e7i	0.0261158	−	0.0452338i
$430$	−4.52280e8	−	7.83373e8i	−0.274327	−	0.475148i
$431$	−3.02329e8	−	5.23649e8i	−0.181890	−	0.315043i	0.760634	−	0.649181i	$-0.224888\pi$
$431$	−3.02329e8	−	5.23649e8i	−0.181890	−	0.315043i	−0.942524	+	0.334138i	$0.891555\pi$
$432$	−4.03108e7	+	6.98203e7i	−0.0240563	+	0.0416667i
$433$	7.16394e7			0.0424076			0.0212038	−	0.999775i	$-0.493250\pi$
$433$	7.16394e7			0.0424076			0.0212038	+	0.999775i	$0.493250\pi$
$434$		0			0
$435$	1.36220e8			0.0793467
$436$	−1.37800e8	+	2.38676e8i	−0.0796244	+	0.137913i
$437$	−1.20742e9	−	2.09132e9i	−0.692110	−	1.19877i
$438$	1.60239e8	+	2.77541e8i	0.0911187	+	0.157822i
$439$	−9.74587e7	+	1.68803e8i	−0.0549788	+	0.0952260i	−0.892205	−	0.451631i	$-0.850842\pi$
$439$	−9.74587e7	+	1.68803e8i	−0.0549788	+	0.0952260i	0.837226	+	0.546857i	$0.184176\pi$
$440$	−6.32136e7			−0.0353774
$441$		0			0
$442$	7.07576e8			0.389758
$443$	1.04009e9	−	1.80149e9i	0.568405	−	0.984507i	−0.428319	−	0.903628i	$-0.640894\pi$
$443$	1.04009e9	−	1.80149e9i	0.568405	−	0.984507i	0.996724	−	0.0808791i	$-0.0257728\pi$
$444$	7.40569e7	+	1.28270e8i	0.0401537	+	0.0695482i
$445$	1.52664e8	+	2.64422e8i	0.0821253	+	0.142245i
$446$	6.00698e8	−	1.04044e9i	0.320615	−	0.555322i
$447$	−8.77364e8			−0.464626
$448$		0			0
$449$	1.78606e9			0.931180			0.465590	−	0.885000i	$-0.345842\pi$
$449$	1.78606e9			0.931180			0.465590	+	0.885000i	$0.345842\pi$
$450$	−1.84411e8	+	3.19409e8i	−0.0953987	+	0.165235i
$451$	−7.87812e7	−	1.36453e8i	−0.0404394	−	0.0700431i
$452$	−2.21942e8	−	3.84415e8i	−0.113046	−	0.195802i
$453$	1.03051e9	−	1.78489e9i	0.520843	−	0.902127i
$454$	2.42299e9			1.21522
$455$		0			0
$456$	3.07280e8			0.151760
$457$	1.12154e9	−	1.94256e9i	0.549678	−	0.952069i	−0.448619	−	0.893723i	$-0.648084\pi$
$457$	1.12154e9	−	1.94256e9i	0.549678	−	0.952069i	0.998296	−	0.0583463i	$-0.0185827\pi$
$458$	−2.12549e8	−	3.68146e8i	−0.103379	−	0.179057i
$459$	2.78455e8	+	4.82299e8i	0.134404	+	0.232794i
$460$	−4.24131e8	+	7.34616e8i	−0.203164	+	0.351891i
$461$	−2.60254e9			−1.23721			−0.618607	−	0.785701i	$-0.712303\pi$
$461$	−2.60254e9			−1.23721			−0.618607	+	0.785701i	$0.712303\pi$
$462$		0			0
$463$	−7.12557e8			−0.333646			−0.166823	−	0.985987i	$-0.553351\pi$
$463$	−7.12557e8			−0.333646			−0.166823	+	0.985987i	$0.553351\pi$
$464$	8.46930e7	−	1.46693e8i	0.0393581	−	0.0681703i
$465$	7.68424e7	+	1.33095e8i	0.0354418	+	0.0613870i
$466$	−5.45403e8	−	9.44666e8i	−0.249670	−	0.432442i
$467$	3.16734e8	−	5.48600e8i	0.143908	−	0.249257i	−0.785057	−	0.619424i	$-0.787366\pi$
$467$	3.16734e8	−	5.48600e8i	0.143908	−	0.249257i	0.928965	+	0.370167i	$0.120700\pi$
$468$	1.45847e8			0.0657712
$469$		0			0
$470$	−5.16452e8			−0.229450
$471$	3.94768e8	−	6.83759e8i	0.174088	−	0.301529i
$472$	−1.70827e8	−	2.95881e8i	−0.0747754	−	0.129515i
$473$	4.68963e8	+	8.12267e8i	0.203763	+	0.352927i
$474$	−4.06493e8	+	7.04067e8i	−0.175319	+	0.303661i
$475$	1.40572e9			0.601827
$476$		0			0
$477$	−2.14374e8			−0.0904395
$478$	9.07208e8	−	1.57133e9i	0.379935	−	0.658067i
$479$	1.10276e8	+	1.91004e8i	0.0458466	+	0.0794086i	0.888038	−	0.459770i	$-0.152068\pi$
$479$	1.10276e8	+	1.91004e8i	0.0458466	+	0.0794086i	−0.842191	+	0.539179i	$0.818735\pi$
$480$	−5.39689e7	−	9.34769e7i	−0.0222741	−	0.0385798i
$481$	1.33971e8	−	2.32045e8i	0.0548912	−	0.0950744i
$482$	−3.24042e9			−1.31807
$483$		0			0
$484$	−1.18163e9			−0.473723
$485$	−2.80451e8	+	4.85755e8i	−0.111625	+	0.193340i
$486$	5.73956e7	+	9.94121e7i	0.0226805	+	0.0392837i
$487$	−1.96466e9	−	3.40289e9i	−0.770791	−	1.33505i	−0.937130	−	0.348980i	$-0.886528\pi$
$487$	−1.96466e9	−	3.40289e9i	−0.770791	−	1.33505i	0.166339	−	0.986069i	$-0.446805\pi$
$488$	2.13358e8	−	3.69547e8i	0.0831074	−	0.143946i
$489$	−2.56742e9			−0.992925
$490$		0			0
$491$	−3.28904e9			−1.25396			−0.626980	−	0.779036i	$-0.715709\pi$
$491$	−3.28904e9			−1.25396			−0.626980	+	0.779036i	$0.715709\pi$
$492$	1.34520e8	−	2.32995e8i	0.0509223	−	0.0882000i
$493$	−5.85035e8	−	1.01331e9i	−0.219896	−	0.380871i
$494$	−2.77939e8	−	4.81404e8i	−0.103730	−	0.179666i
$495$	−4.50026e7	+	7.79468e7i	−0.0166771	+	0.0288855i
$496$	1.91103e8			0.0703204
$497$		0			0
$498$	1.16491e9			0.422658
$499$	2.15315e9	−	3.72937e9i	0.775752	−	1.34364i	−0.158619	−	0.987340i	$-0.550704\pi$
$499$	2.15315e9	−	3.72937e9i	0.775752	−	1.34364i	0.934371	−	0.356302i	$-0.115962\pi$
$500$	−5.51893e8	−	9.55906e8i	−0.197451	−	0.341995i
$501$	3.10432e8	+	5.37683e8i	0.110289	+	0.191027i
$502$	−1.23226e8	+	2.13433e8i	−0.0434749	+	0.0753008i
$503$	−2.56392e9			−0.898291			−0.449145	−	0.893459i	$-0.648271\pi$
$503$	−2.56392e9			−0.898291			−0.449145	+	0.893459i	$0.648271\pi$
$504$		0			0
$505$	−2.50447e9			−0.865360
$506$	4.39775e8	−	7.61712e8i	0.150905	−	0.261375i
$507$	7.15185e8	+	1.23874e9i	0.243720	+	0.422135i
$508$	1.00641e9	+	1.74315e9i	0.340604	+	0.589944i
$509$	−2.10193e9	+	3.64065e9i	−0.706490	+	1.22368i	0.259661	+	0.965700i	$0.416389\pi$
$509$	−2.10193e9	+	3.64065e9i	−0.706490	+	1.22368i	−0.966151	+	0.257977i	$0.916944\pi$
$510$	−7.45603e8			−0.248893
$511$		0			0
$512$	−1.34218e8			−0.0441942
$513$	2.18757e8	−	3.78898e8i	0.0715403	−	0.123911i
$514$	−1.10053e9	−	1.90617e9i	−0.357462	−	0.619142i
$515$	8.68237e8	+	1.50383e9i	0.280100	+	0.485148i
$516$	−8.00759e8	+	1.38695e9i	−0.256583	+	0.444415i
$517$	5.35502e8			0.170429
$518$		0			0
$519$	3.22612e9			1.01297
$520$	−9.76312e7	+	1.69102e8i	−0.0304493	+	0.0527397i
$521$	−2.25385e9	−	3.90378e9i	−0.698220	−	1.20935i	−0.969083	−	0.246735i	$-0.920642\pi$
$521$	−2.25385e9	−	3.90378e9i	−0.698220	−	1.20935i	0.270862	−	0.962618i	$-0.412691\pi$
$522$	−1.20588e8	−	2.08865e8i	−0.0371072	−	0.0642716i
$523$	2.73176e9	−	4.73154e9i	0.835000	−	1.44626i	−0.0590308	−	0.998256i	$-0.518801\pi$
$523$	2.73176e9	−	4.73154e9i	0.835000	−	1.44626i	0.894031	−	0.448006i	$-0.147866\pi$
$524$	−2.87233e8			−0.0872118
$525$		0			0
$526$	3.87197e9			1.16006
$527$	6.60042e8	−	1.14323e9i	0.196442	−	0.340248i
$528$	5.59596e7	+	9.69248e7i	0.0165446	+	0.0286560i
$529$	−4.19891e9	−	7.27273e9i	−1.23322	−	2.13601i
$530$	1.43504e8	−	2.48557e8i	0.0418696	−	0.0725203i
$531$	−4.86456e8			−0.140998
$532$		0			0
$533$	−4.86699e8			−0.139224
$534$	2.70291e8	−	4.68157e8i	0.0768133	−	0.133045i
$535$	−5.68535e8	−	9.84731e8i	−0.160516	−	0.278022i
$536$	2.95423e8	+	5.11688e8i	0.0828643	+	0.143525i
$537$	−1.26664e9	+	2.19389e9i	−0.352976	+	0.611372i
$538$	−1.97900e9			−0.547907
$539$		0			0
$540$	−1.53685e8			−0.0420004
$541$	3.29315e9	−	5.70390e9i	0.894171	−	1.54875i	0.0593443	−	0.998238i	$-0.481099\pi$
$541$	3.29315e9	−	5.70390e9i	0.894171	−	1.54875i	0.834827	−	0.550512i	$-0.185568\pi$
$542$	−9.13146e8	−	1.58162e9i	−0.246345	−	0.426681i
$543$	−2.00926e9	−	3.48014e9i	−0.538563	−	0.932819i
$544$	−4.63569e8	+	8.02925e8i	−0.123458	+	0.213835i
$545$	−5.25362e8			−0.139018
$546$		0			0
$547$	−1.71749e9			−0.448681			−0.224340	−	0.974511i	$-0.572023\pi$
$547$	−1.71749e9			−0.448681			−0.224340	+	0.974511i	$0.572023\pi$
$548$	−5.00021e8	+	8.66061e8i	−0.129794	+	0.224810i
$549$	−3.03785e8	−	5.26171e8i	−0.0783544	−	0.135714i
$550$	2.56000e8	+	4.43404e8i	0.0656100	+	0.113640i
$551$	−4.59608e8	+	7.96065e8i	−0.117046	+	0.202730i
$552$	1.50184e9			0.380046
$553$		0			0
$554$	2.84093e9			0.709865
$555$	−1.41171e8	+	2.44515e8i	−0.0350526	+	0.0607128i
$556$	1.73579e9	+	3.00648e9i	0.428288	+	0.741817i
$557$	−2.47132e9	−	4.28045e9i	−0.605949	−	1.04953i	−0.991901	−	0.127015i	$-0.959460\pi$
$557$	−2.47132e9	−	4.28045e9i	−0.605949	−	1.04953i	0.385952	−	0.922519i	$-0.373873\pi$
$558$	1.36049e8	−	2.35644e8i	0.0331494	−	0.0574164i
$559$	2.89719e9			0.701513
$560$		0			0
$561$	7.73105e8			0.184871
$562$	9.12669e8	−	1.58079e9i	0.216888	−	0.375661i
$563$	1.69154e9	+	2.92983e9i	0.399487	+	0.691932i	0.993663	−	0.112404i	$-0.0358549\pi$
$563$	1.69154e9	+	2.92983e9i	0.399487	+	0.691932i	−0.594176	+	0.804335i	$0.702522\pi$
$564$	4.57187e8	+	7.91872e8i	0.107304	+	0.185857i
$565$	4.23078e8	−	7.32792e8i	0.0986848	−	0.170927i
$566$	1.71033e9			0.396481
$567$		0			0
$568$	−1.96728e9			−0.450450
$569$	1.12318e9	−	1.94540e9i	0.255596	−	0.442706i	−0.709461	−	0.704745i	$-0.751062\pi$
$569$	1.12318e9	−	1.94540e9i	0.255596	−	0.442706i	0.965057	+	0.262039i	$0.0843949\pi$
$570$	2.92876e8	+	5.07276e8i	0.0662403	+	0.114731i
$571$	3.40547e8	+	5.89845e8i	0.0765509	+	0.132590i	0.901760	−	0.432238i	$-0.142276\pi$
$571$	3.40547e8	+	5.89845e8i	0.0765509	+	0.132590i	−0.825209	+	0.564828i	$0.808943\pi$
$572$	1.01232e8	−	1.75340e8i	0.0226169	−	0.0391736i
$573$	−2.73796e9			−0.607976
$574$		0			0
$575$	6.87050e9			1.50713
$576$	−9.55515e7	+	1.65500e8i	−0.0208333	+	0.0360844i
$577$	3.74148e8	+	6.48043e8i	0.0810827	+	0.140439i	0.903715	−	0.428134i	$-0.140829\pi$
$577$	3.74148e8	+	6.48043e8i	0.0810827	+	0.140439i	−0.822633	+	0.568573i	$0.807496\pi$
$578$	1.56085e9	+	2.70347e9i	0.336212	+	0.582336i
$579$	−9.52959e8	+	1.65057e9i	−0.204032	+	0.353395i
$580$	3.22892e8			0.0687162
$581$		0			0
$582$	9.93071e8			0.208809
$583$	−1.48797e8	+	2.57725e8i	−0.0310996	+	0.0538662i
$584$	3.79825e8	+	6.57876e8i	0.0789111	+	0.136678i
$585$	1.39010e8	+	2.40773e8i	0.0287079	+	0.0497235i
$586$	1.51527e9	−	2.62452e9i	0.311062	−	0.538775i
$587$	−6.17294e9			−1.25968			−0.629838	−	0.776727i	$-0.716879\pi$
$587$	−6.17294e9			−1.25968			−0.629838	+	0.776727i	$0.716879\pi$
$588$		0			0
$589$	−1.03707e9			−0.209124
$590$	3.25638e8	−	5.64022e8i	0.0652760	−	0.113061i
$591$	−6.78115e8	−	1.17453e9i	−0.135129	−	0.234049i
$592$	1.75542e8	+	3.04048e8i	0.0347741	+	0.0602305i
$593$	−5.02125e9	+	8.69705e9i	−0.988826	+	1.71270i	−0.365314	+	0.930885i	$0.619038\pi$
$593$	−5.02125e9	+	8.69705e9i	−0.988826	+	1.71270i	−0.623513	+	0.781813i	$0.714295\pi$
$594$	1.59354e8			0.0311967
$595$		0			0
$596$	−2.07968e9			−0.402378
$597$	−2.82011e9	+	4.88458e9i	−0.542446	+	0.939544i
$598$	−1.35843e9	−	2.35288e9i	−0.259767	−	0.449930i
$599$	6.61221e8	+	1.14527e9i	0.125705	+	0.217728i	0.922008	−	0.387170i	$-0.126547\pi$
$599$	6.61221e8	+	1.14527e9i	0.125705	+	0.217728i	−0.796303	+	0.604898i	$0.793214\pi$
$600$	−4.37122e8	+	7.57117e8i	−0.0826177	+	0.143098i
$601$	−4.48600e8			−0.0842944			−0.0421472	−	0.999111i	$-0.513420\pi$
$601$	−4.48600e8			−0.0842944			−0.0421472	+	0.999111i	$0.513420\pi$
$602$		0			0
$603$	8.41263e8			0.156250
$604$	2.44268e9	−	4.23085e9i	0.451064	−	0.781265i
$605$	−1.12624e9	−	1.95071e9i	−0.206771	−	0.358137i
$606$	2.21707e9	+	3.84009e9i	0.404693	+	0.700950i
$607$	−4.45750e8	+	7.72061e8i	−0.0808967	+	0.140117i	−0.903635	−	0.428303i	$-0.859112\pi$
$607$	−4.45750e8	+	7.72061e8i	−0.0808967	+	0.140117i	0.822739	+	0.568420i	$0.192445\pi$
$608$	7.28367e8			0.131428
$609$		0			0
$610$	8.13428e8			0.145099
$611$	8.27065e8	−	1.43252e9i	0.146688	−	0.254071i
$612$	6.60042e8	+	1.14323e9i	0.116397	+	0.201606i
$613$	−1.75709e9	−	3.04336e9i	−0.308092	−	0.533632i	0.669853	−	0.742494i	$-0.266357\pi$
$613$	−1.75709e9	−	3.04336e9i	−0.308092	−	0.533632i	−0.977945	+	0.208862i	$0.933024\pi$
$614$	2.53525e9	−	4.39119e9i	0.442010	−	0.765584i
$615$	5.12856e8			0.0889063
$616$		0			0
$617$	3.78067e9			0.647993			0.323996	−	0.946058i	$-0.394973\pi$
$617$	3.78067e9			0.647993			0.323996	+	0.946058i	$0.394973\pi$
$618$	1.53721e9	−	2.66252e9i	0.261983	−	0.453767i
$619$	−1.34483e9	−	2.32932e9i	−0.227903	−	0.394740i	0.729283	−	0.684212i	$-0.239854\pi$
$619$	−1.34483e9	−	2.32932e9i	−0.227903	−	0.394740i	−0.957187	+	0.289472i	$0.906520\pi$
$620$	1.82145e8	+	3.15484e8i	0.0306935	+	0.0531627i
$621$	1.06918e9	−	1.85188e9i	0.179156	−	0.310307i
$622$	3.12156e9			0.520123
$623$		0			0
$624$	3.45711e8			0.0569596
$625$	−1.41831e9	+	2.45658e9i	−0.232375	+	0.402486i
$626$	−4.01777e9	−	6.95898e9i	−0.654598	−	1.13380i
$627$	−3.03679e8	−	5.25987e8i	−0.0492015	−	0.0852195i
$628$	9.35747e8	−	1.62076e9i	0.150765	−	0.261132i
$629$	2.42519e9			0.388570
$630$		0			0
$631$	−6.91824e9			−1.09621			−0.548104	−	0.836410i	$-0.684650\pi$
$631$	−6.91824e9			−1.09621			−0.548104	+	0.836410i	$0.684650\pi$
$632$	−9.63539e8	+	1.66890e9i	−0.151831	+	0.262978i
$633$	1.14066e9	+	1.97568e9i	0.178748	+	0.309601i
$634$	9.71898e8	+	1.68338e9i	0.151464	+	0.262343i
$635$	−1.91846e9	+	3.32287e9i	−0.297334	+	0.514998i
$636$	−5.08146e8			−0.0783229
$637$		0			0
$638$	−3.34802e8			−0.0510406
$639$	−1.40053e9	+	2.42579e9i	−0.212344	+	0.367790i
$640$	−1.27926e8	−	2.21575e8i	−0.0192899	−	0.0334111i
$641$	2.74979e9	+	4.76278e9i	0.412379	+	0.714262i	0.995149	−	0.0983750i	$-0.0313645\pi$
$641$	2.74979e9	+	4.76278e9i	0.412379	+	0.714262i	−0.582770	+	0.812637i	$0.698031\pi$
$642$	−1.00659e9	+	1.74346e9i	−0.150134	+	0.260039i
$643$	−1.35931e9			−0.201641			−0.100821	−	0.994905i	$-0.532147\pi$
$643$	−1.35931e9			−0.201641			−0.100821	+	0.994905i	$0.532147\pi$
$644$		0			0
$645$	−3.05289e9			−0.447974
$646$	2.51568e9	−	4.35728e9i	0.367148	−	0.635919i
$647$	3.64592e9	+	6.31492e9i	0.529228	+	0.916649i	0.999419	+	0.0340847i	$0.0108516\pi$
$647$	3.64592e9	+	6.31492e9i	0.529228	+	0.916649i	−0.470191	+	0.882565i	$0.655815\pi$
$648$	1.36049e8	+	2.35644e8i	0.0196419	+	0.0340207i
$649$	−3.37650e8	+	5.84827e8i	−0.0484853	+	0.0839790i
$650$	1.58153e9			0.225882
$651$		0			0
$652$	−6.08575e9			−0.859899
$653$	4.98442e8	−	8.63327e8i	0.0700517	−	0.121333i	−0.828872	−	0.559438i	$-0.811017\pi$
$653$	4.98442e8	−	8.63327e8i	0.0700517	−	0.121333i	0.898924	+	0.438105i	$0.144350\pi$
$654$	4.65075e8	+	8.05533e8i	0.0650130	+	0.112606i
$655$	−2.73769e8	−	4.74182e8i	−0.0380662	−	0.0659327i
$656$	3.18861e8	−	5.52284e8i	0.0441000	−	0.0763834i
$657$	1.08161e9			0.148796
$658$		0			0
$659$	−1.35118e10			−1.83914			−0.919568	−	0.392932i	$-0.871461\pi$
$659$	−1.35118e10			−1.83914			−0.919568	+	0.392932i	$0.871461\pi$
$660$	−1.06673e8	+	1.84763e8i	−0.0144428	+	0.0250156i
$661$	3.89968e9	+	6.75444e9i	0.525199	+	0.909671i	0.999569	+	0.0293460i	$0.00934245\pi$
$661$	3.89968e9	+	6.75444e9i	0.525199	+	0.909671i	−0.474370	+	0.880325i	$0.657324\pi$
$662$	−1.13407e8	−	1.96426e8i	−0.0151927	−	0.0263146i
$663$	1.19404e9	−	2.06813e9i	0.159118	−	0.275601i
$664$	2.76126e9			0.366032
$665$		0			0
$666$	4.99884e8			0.0655706
$667$	−2.24635e9	+	3.89079e9i	−0.293114	+	0.507689i
$668$	7.35838e8	+	1.27451e9i	0.0955135	+	0.165434i
$669$	−2.02736e9	−	3.51148e9i	−0.261781	−	0.453418i
$670$	−5.63150e8	+	9.75404e8i	−0.0723373	+	0.125292i
$671$	−8.43431e8			−0.107776
$672$		0			0
$673$	−6.85231e9			−0.866531			−0.433265	−	0.901266i	$-0.642639\pi$
$673$	−6.85231e9			−0.866531			−0.433265	+	0.901266i	$0.642639\pi$
$674$	−4.06702e9	+	7.04428e9i	−0.511642	+	0.886191i
$675$	6.22386e8	+	1.07800e9i	0.0778927	+	0.134914i
$676$	1.69525e9	+	2.93626e9i	0.211067	+	0.365579i
$677$	3.82852e9	−	6.63119e9i	0.474210	−	0.821355i	−0.525354	−	0.850884i	$-0.676067\pi$
$677$	3.82852e9	−	6.63119e9i	0.474210	−	0.821355i	0.999564	+	0.0295283i	$0.00940051\pi$
$678$	−1.49811e9			−0.184604
$679$		0			0
$680$	−1.76736e9			−0.215547
$681$	4.08880e9	−	7.08200e9i	0.496113	−	0.859293i
$682$	−1.88863e8	−	3.27121e8i	−0.0227983	−	0.0394878i
$683$	2.76338e9	+	4.78631e9i	0.331870	+	0.574815i	0.982878	−	0.184255i	$-0.0589873\pi$
$683$	2.76338e9	+	4.78631e9i	0.331870	+	0.574815i	−0.651009	+	0.759070i	$0.725654\pi$
$684$	5.18535e8	−	8.98129e8i	0.0619557	−	0.107310i
$685$	−1.90633e9			−0.226611
$686$		0			0
$687$	−1.43471e9			−0.168817
$688$	−1.89809e9	+	3.28760e9i	−0.222207	+	0.384874i
$689$	4.59625e8	+	7.96094e8i	0.0535348	+	0.0927251i
$690$	1.43144e9	+	2.47933e9i	0.165883	+	0.287318i
$691$	−7.59635e8	+	1.31573e9i	−0.0875854	+	0.151702i	−0.906490	−	0.422227i	$-0.861248\pi$
$691$	−7.59635e8	+	1.31573e9i	−0.0875854	+	0.151702i	0.818905	+	0.573930i	$0.194582\pi$
$692$	7.64711e9			0.877255
$693$		0			0
$694$	7.76395e9			0.881708
$695$	−3.30886e9	+	5.73111e9i	−0.373879	+	0.647577i
$696$	−2.85839e8	−	4.95087e8i	−0.0321358	−	0.0556608i
$697$	−2.20260e9	−	3.81502e9i	−0.246389	−	0.426758i
$698$	3.53658e9	−	6.12553e9i	0.393631	−	0.681789i
$699$	−3.68147e9			−0.407710
$700$		0			0
$701$	6.81967e9			0.747739			0.373869	−	0.927481i	$-0.378031\pi$
$701$	6.81967e9			0.747739			0.373869	+	0.927481i	$0.378031\pi$
$702$	2.46116e8	−	4.26286e8i	0.0268510	−	0.0465073i
$703$	−9.52625e8	−	1.65000e9i	−0.103414	−	0.179118i
$704$	1.32645e8	+	2.29748e8i	0.0143280	+	0.0248169i
$705$	−8.71513e8	+	1.50951e9i	−0.0936725	+	0.162246i
$706$	8.72369e9			0.933005
$707$		0			0
$708$	−1.15308e9			−0.122108
$709$	−6.08497e9	+	1.05395e10i	−0.641205	+	1.11060i	0.343959	+	0.938984i	$0.388232\pi$
$709$	−6.08497e9	+	1.05395e10i	−0.641205	+	1.11060i	−0.985164	+	0.171615i	$0.945102\pi$
$710$	−1.87506e9	−	3.24770e9i	−0.196612	−	0.340543i
$711$	1.37191e9	+	2.37622e9i	0.143147	+	0.247938i
$712$	6.40689e8	−	1.10971e9i	0.0665223	−	0.115220i
$713$	−5.06871e9			−0.523702
$714$		0			0
$715$	3.85948e8			0.0394874
$716$	−3.00242e9	+	5.20034e9i	−0.305686	+	0.529463i
$717$	−3.06183e9	−	5.30324e9i	−0.310216	−	0.537309i
$718$	4.13492e9	+	7.16189e9i	0.416899	+	0.722091i
$719$	−1.00013e9	+	1.73227e9i	−0.100347	+	0.173806i	−0.911828	−	0.410573i	$-0.865329\pi$
$719$	−1.00013e9	+	1.73227e9i	−0.100347	+	0.173806i	0.811481	+	0.584379i	$0.198662\pi$
$720$	−3.64290e8			−0.0363734
$721$		0			0
$722$	3.19830e9			0.316256
$723$	−5.46822e9	+	9.47123e9i	−0.538098	+	0.932014i
$724$	−4.76269e9	−	8.24922e9i	−0.466409	−	0.807845i
$725$	−1.30763e9	−	2.26489e9i	−0.127439	−	0.220731i
$726$	−1.99401e9	+	3.45372e9i	−0.193396	+	0.334972i
$727$	1.21193e10			1.16979			0.584895	−	0.811109i	$-0.301136\pi$
$727$	1.21193e10			1.16979			0.584895	+	0.811109i	$0.301136\pi$
$728$		0			0
$729$	3.87420e8			0.0370370
$730$	−7.24041e8	+	1.25408e9i	−0.0688863	+	0.119315i
$731$	1.31115e10	+	2.27098e10i	1.24148	+	2.15031i
$732$	−7.20084e8	−	1.24722e9i	−0.0678569	−	0.117532i
$733$	−6.52266e9	+	1.12976e10i	−0.611732	+	1.05955i	0.379217	+	0.925308i	$0.376193\pi$
$733$	−6.52266e9	+	1.12976e10i	−0.611732	+	1.05955i	−0.990948	+	0.134243i	$0.957140\pi$
$734$	1.93746e9			0.180841
$735$		0			0
$736$	3.55992e9			0.329130
$737$	5.83922e8	−	1.01138e9i	0.0537302	−	0.0930635i
$738$	−4.54004e8	−	7.86357e8i	−0.0415779	−	0.0720150i
$739$	−1.13794e9	−	1.97096e9i	−0.103720	−	0.179648i	0.809495	−	0.587127i	$-0.199741\pi$
$739$	−1.13794e9	−	1.97096e9i	−0.103720	−	0.179648i	−0.913214	+	0.407479i	$0.866408\pi$
$740$	−3.34627e8	+	5.79592e8i	−0.0303564	+	0.0525789i
$741$	−1.87609e9			−0.169391
$742$		0			0
$743$	2.13411e9			0.190878			0.0954390	−	0.995435i	$-0.469575\pi$
$743$	2.13411e9			0.190878			0.0954390	+	0.995435i	$0.469575\pi$
$744$	3.22486e8	−	5.58563e8i	0.0287082	−	0.0497241i
$745$	−1.98219e9	−	3.43326e9i	−0.175630	−	0.304200i
$746$	−5.75075e9	−	9.96059e9i	−0.507152	−	0.878414i
$747$	1.96578e9	−	3.40483e9i	0.172549	−	0.298864i
$748$	1.83255e9			0.160103
$749$		0			0
$750$	−3.72528e9			−0.322436
$751$	−1.02089e10	+	1.76823e10i	−0.879503	+	1.52334i	−0.0276155	+	0.999619i	$0.508791\pi$
$751$	−1.02089e10	+	1.76823e10i	−0.879503	+	1.52334i	−0.851887	+	0.523725i	$0.824542\pi$
$752$	1.08370e9	+	1.87703e9i	0.0929283	+	0.160957i
$753$	4.15887e8	+	7.20338e8i	0.0354971	+	0.0614828i
$754$	−5.17090e8	+	8.95627e8i	−0.0439306	+	0.0760900i
$755$	9.31273e9			0.787522
$756$		0			0
$757$	8.04759e9			0.674265			0.337132	−	0.941457i	$-0.390543\pi$
$757$	8.04759e9			0.674265			0.337132	+	0.941457i	$0.390543\pi$
$758$	4.80676e9	−	8.32555e9i	0.400876	−	0.694337i
$759$	−1.48424e9	−	2.57078e9i	−0.123213	−	0.213412i
$760$	6.94225e8	+	1.20243e9i	0.0573657	+	0.0993604i
$761$	−2.80867e9	+	4.86476e9i	−0.231023	+	0.400143i	−0.958109	−	0.286403i	$-0.907541\pi$
$761$	−2.80867e9	+	4.86476e9i	−0.231023	+	0.400143i	0.727087	+	0.686546i	$0.240874\pi$
$762$	6.79324e9			0.556204
$763$		0			0
$764$	−6.48998e9			−0.526522
$765$	−1.25821e9	+	2.17928e9i	−0.101610	+	0.175994i
$766$	2.52343e9	+	4.37072e9i	0.202858	+	0.351360i
$767$	1.04298e9	+	1.80649e9i	0.0834624	+	0.144561i
$768$	−2.26492e8	+	3.92296e8i	−0.0180422	+	0.0312500i
$769$	−8.92653e9			−0.707849			−0.353924	−	0.935274i	$-0.615153\pi$
$769$	−8.92653e9			−0.707849			−0.353924	+	0.935274i	$0.615153\pi$
$770$		0			0
$771$	−7.42855e9			−0.583733
$772$	−2.25887e9	+	3.91247e9i	−0.176697	+	0.306049i
$773$	8.99328e9	+	1.55768e10i	0.700310	+	1.21297i	0.968358	+	0.249566i	$0.0802880\pi$
$773$	8.99328e9	+	1.55768e10i	0.700310	+	1.21297i	−0.268048	+	0.963406i	$0.586379\pi$
$774$	2.70256e9	+	4.68097e9i	0.209499	+	0.362863i
$775$	1.47529e9	−	2.55527e9i	0.113847	−	0.197188i
$776$	2.35395e9			0.180834
$777$		0			0
$778$	1.13749e10			0.866000
$779$	−1.73038e9	+	2.99711e9i	−0.131148	+	0.227155i
$780$	3.29505e8	+	5.70720e8i	0.0248617	+	0.0430618i
$781$	1.94422e9	+	3.36749e9i	0.146038	+	0.252946i
$782$	1.22954e10	−	2.12963e10i	0.919434	−	1.59251i
$783$	−8.13971e8			−0.0605958
$784$		0			0
$785$	3.56753e9			0.263223
$786$	−4.84706e8	+	8.39536e8i	−0.0356041	+	0.0616681i
$787$	6.57941e9	+	1.13959e10i	0.481144	+	0.833366i	0.999766	−	0.0216375i	$-0.00688797\pi$
$787$	6.57941e9	+	1.13959e10i	0.481144	+	0.833366i	−0.518622	+	0.855004i	$0.673555\pi$
$788$	−1.60738e9	−	2.78407e9i	−0.117025	−	0.202693i
$789$	6.53395e9	−	1.13171e10i	0.473594	−	0.820288i
$790$	−3.67349e9			−0.265084
$791$		0			0
$792$	3.77727e8			0.0270172
$793$	−1.30265e9	+	2.25626e9i	−0.0927624	+	0.160669i
$794$	2.81988e8	+	4.88417e8i	0.0199921	+	0.0346273i
$795$	−4.84327e8	−	8.38878e8i	−0.0341864	−	0.0592126i
$796$	−6.68471e9	+	1.15783e10i	−0.469772	+	0.813669i
$797$	2.50099e9			0.174988			0.0874939	−	0.996165i	$-0.472114\pi$
$797$	2.50099e9			0.174988			0.0874939	+	0.996165i	$0.472114\pi$
$798$		0			0
$799$	1.49718e10			1.03839
$800$	−1.03614e9	+	1.79465e9i	−0.0715490	+	0.123927i
$801$	−9.12231e8	−	1.58003e9i	−0.0627178	−	0.108630i
$802$	8.09289e9	+	1.40173e10i	0.553979	+	0.959519i
$803$	7.50747e8	−	1.30033e9i	0.0511669	−	0.0886237i
$804$	1.99411e9			0.135317
$805$		0			0
$806$	−1.16677e9			−0.0784899
$807$	−3.33956e9	+	5.78428e9i	−0.223682	+	0.387429i
$808$	5.25529e9	+	9.10243e9i	0.350475	+	0.607040i
$809$	−5.60593e9	−	9.70975e9i	−0.372244	−	0.644746i	0.617666	−	0.786440i	$-0.288078\pi$
$809$	−5.60593e9	−	9.70975e9i	−0.372244	−	0.644746i	−0.989910	+	0.141695i	$0.954745\pi$
$810$	−2.59343e8	+	4.49196e8i	−0.0171466	+	0.0296987i
$811$	−2.38194e10			−1.56804			−0.784020	−	0.620736i	$-0.786834\pi$
$811$	−2.38194e10			−1.56804			−0.784020	+	0.620736i	$0.786834\pi$
$812$		0			0
$813$	−6.16374e9			−0.402279
$814$	3.46970e8	−	6.00970e8i	0.0225479	−	0.0390542i
$815$	−5.80048e9	−	1.00467e10i	−0.375329	−	0.650089i
$816$	1.56455e9	+	2.70987e9i	0.100803	+	0.174596i
$817$	1.03005e10	−	1.78410e10i	0.660817	−	1.14457i
$818$	−1.14981e10			−0.734497
$819$		0			0
$820$	1.21566e9			0.0769951
$821$	1.01461e10	−	1.75735e10i	0.639877	−	1.10830i	−0.345582	−	0.938389i	$-0.612318\pi$
$821$	1.01461e10	−	1.75735e10i	0.639877	−	1.10830i	0.985459	−	0.169912i	$-0.0543483\pi$
$822$	1.68757e9	+	2.92296e9i	0.105977	+	0.183557i
$823$	2.77965e9	+	4.81449e9i	0.173816	+	0.301059i	0.939751	−	0.341860i	$-0.111057\pi$
$823$	2.77965e9	+	4.81449e9i	0.173816	+	0.301059i	−0.765935	+	0.642918i	$0.777723\pi$
$824$	3.64375e9	−	6.31116e9i	0.226884	−	0.392974i
$825$	1.72800e9			0.107141
$826$		0			0
$827$	2.02195e10			1.24308			0.621542	−	0.783381i	$-0.286507\pi$
$827$	2.02195e10			1.24308			0.621542	+	0.783381i	$0.286507\pi$
$828$	2.53435e9	−	4.38963e9i	0.155153	−	0.268733i
$829$	−1.87400e9	−	3.24586e9i	−0.114243	−	0.197874i	0.803234	−	0.595663i	$-0.203111\pi$
$829$	−1.87400e9	−	3.24586e9i	−0.114243	−	0.197874i	−0.917477	+	0.397789i	$0.869777\pi$
$830$	2.63183e9	+	4.55846e9i	0.159766	+	0.276723i
$831$	4.79406e9	−	8.30356e9i	0.289801	−	0.501950i
$832$	8.19462e8			0.0493284
$833$		0			0
$834$	1.17166e10			0.699392
$835$	−1.40269e9	+	2.42953e9i	−0.0833795	+	0.144418i
$836$	−7.19832e8	−	1.24678e9i	−0.0426097	−	0.0738022i
$837$	−4.59165e8	−	7.95297e8i	−0.0270664	−	0.0468803i
$838$	3.44839e8	−	5.97279e8i	0.0202424	−	0.0350609i
$839$	2.03224e10			1.18798			0.593988	−	0.804474i	$-0.297553\pi$
$839$	2.03224e10			1.18798			0.593988	+	0.804474i	$0.297553\pi$
$840$		0			0
$841$	−1.55397e10			−0.900860
$842$	−4.73017e9	+	8.19290e9i	−0.273077	+	0.472983i
$843$	−3.08026e9	−	5.33516e9i	−0.177089	−	0.306726i
$844$	2.70378e9	+	4.68308e9i	0.154801	+	0.268123i
$845$	−3.23158e9	+	5.59725e9i	−0.184254	+	0.319136i
$846$	3.08601e9			0.175227
$847$		0			0
$848$	−1.20449e9			−0.0678296
$849$	2.88618e9	−	4.99901e9i	0.161863	−	0.280354i
$850$	7.15736e9	+	1.23969e10i	0.399748	+	0.692385i
$851$	−4.65598e9	−	8.06440e9i	−0.258975	−	0.448558i
$852$	−3.31978e9	+	5.75002e9i	−0.183895	+	0.318516i
$853$	3.86410e8			0.0213170			0.0106585	−	0.999943i	$-0.496607\pi$
$853$	3.86410e8			0.0213170			0.0106585	+	0.999943i	$0.496607\pi$
$854$		0			0
$855$	1.97691e9			0.108170
$856$	−2.38598e9	+	4.13264e9i	−0.130020	+	0.225201i
$857$	2.32122e9	+	4.02047e9i	0.125975	+	0.218195i	0.922114	−	0.386919i	$-0.126461\pi$
$857$	2.32122e9	+	4.02047e9i	0.125975	+	0.218195i	−0.796139	+	0.605114i	$0.793127\pi$
$858$	−3.41659e8	−	5.91771e8i	−0.0184666	−	0.0319851i
$859$	1.36654e10	−	2.36691e10i	0.735606	−	1.27411i	−0.218851	−	0.975758i	$-0.570231\pi$
$859$	1.36654e10	−	2.36691e10i	0.735606	−	1.27411i	0.954457	−	0.298349i	$-0.0964358\pi$
$860$	−7.23649e9			−0.387957
$861$		0			0
$862$	−4.83726e9			−0.257231
$863$	−9.21669e9	+	1.59638e10i	−0.488132	+	0.845469i	−0.999907	−	0.0136503i	$-0.995655\pi$
$863$	−9.21669e9	+	1.59638e10i	−0.488132	+	0.845469i	0.511775	+	0.859120i	$0.328988\pi$
$864$	3.22486e8	+	5.58563e8i	0.0170103	+	0.0294628i
$865$	7.28865e9	+	1.26243e10i	0.382905	+	0.663210i
$866$	2.86558e8	−	4.96332e8i	0.0149934	−	0.0259693i
$867$	1.05357e10			0.549032
$868$		0			0
$869$	3.80899e9			0.196898
$870$	5.44880e8	−	9.43760e8i	0.0280533	−	0.0485897i
$871$	−1.80370e9	−	3.12409e9i	−0.0924911	−	0.160199i
$872$	1.10240e9	+	1.90941e9i	0.0563029	+	0.0975196i
$873$	1.67581e9	−	2.90258e9i	0.0852460	−	0.147650i
$874$	−1.93188e10			−0.978791
$875$		0			0
$876$	2.56382e9			0.128861
$877$	6.51437e9	−	1.12832e10i	0.326117	−	0.564852i	−0.655620	−	0.755091i	$-0.727593\pi$
$877$	6.51437e9	−	1.12832e10i	0.326117	−	0.564852i	0.981738	+	0.190239i	$0.0609262\pi$
$878$	7.79670e8	+	1.35043e9i	0.0388759	+	0.0673350i
$879$	−5.11402e9	−	8.85774e9i	−0.253981	−	0.439908i
$880$	−2.52854e8	+	4.37956e8i	−0.0125078	+	0.0216641i
$881$	3.46348e10			1.70646			0.853232	−	0.521531i	$-0.174639\pi$
$881$	3.46348e10			1.70646			0.853232	+	0.521531i	$0.174639\pi$
$882$		0			0
$883$	3.40346e10			1.66363			0.831817	−	0.555049i	$-0.187301\pi$
$883$	3.40346e10			1.66363			0.831817	+	0.555049i	$0.187301\pi$
$884$	2.83031e9	−	4.90223e9i	0.137800	−	0.238677i
$885$	−1.09903e9	−	1.90358e9i	−0.0532977	−	0.0923142i
$886$	−8.32073e9	−	1.44119e10i	−0.401923	−	0.696152i
$887$	2.39074e9	−	4.14089e9i	0.115027	−	0.199233i	−0.802764	−	0.596298i	$-0.796638\pi$
$887$	2.39074e9	−	4.14089e9i	0.115027	−	0.199233i	0.917791	+	0.397065i	$0.129971\pi$
$888$	1.18491e9			0.0567858
$889$		0			0
$890$	2.44263e9			0.116143
$891$	2.68909e8	−	4.65764e8i	0.0127360	−	0.0220594i
$892$	−4.80558e9	−	8.32352e9i	−0.226709	−	0.392672i
$893$	−5.88100e9	−	1.01862e10i	−0.276357	−	0.478665i
$894$	−3.50946e9	+	6.07856e9i	−0.164270	+	0.284524i
$895$	−1.14467e10			−0.533704
$896$		0			0
$897$	−9.16943e9			−0.424198
$898$	7.14424e9	−	1.23742e10i	0.329222	−	0.570229i
$899$	9.64706e8	+	1.67092e9i	0.0442829	+	0.0767002i
$900$	1.47529e9	+	2.55527e9i	0.0674571	+	0.116839i
$901$	−4.16015e9	+	7.20559e9i	−0.189484	+	0.328196i
$902$	−1.26050e9			−0.0571899
$903$		0			0
$904$	−3.55108e9			−0.159871
$905$	9.07888e9	−	1.57251e10i	0.407157	−	0.705217i
$906$	−8.24405e9	−	1.42791e10i	−0.368292	−	0.637900i
$907$	1.39320e10	+	2.41309e10i	0.619993	+	1.07386i	0.989486	+	0.144626i	$0.0461978\pi$
$907$	1.39320e10	+	2.41309e10i	0.619993	+	1.07386i	−0.369494	+	0.929233i	$0.620469\pi$
$908$	9.69196e9	−	1.67870e10i	0.429646	−	0.744169i
$909$	1.49653e10			0.660862
$910$		0			0
$911$	3.21050e10			1.40689			0.703443	−	0.710752i	$-0.251645\pi$
$911$	3.21050e10			1.40689			0.703443	+	0.710752i	$0.251645\pi$
$912$	1.22912e9	−	2.12890e9i	0.0536552	−	0.0929336i
$913$	−2.72890e9	−	4.72660e9i	−0.118670	−	0.205542i
$914$	−8.97232e9	−	1.55405e10i	−0.388681	−	0.673215i
$915$	1.37266e9	−	2.37752e9i	0.0592364	−	0.102601i
$916$	−3.40079e9			−0.146199
$917$		0			0
$918$	4.45529e9			0.190076
$919$	−1.41227e10	+	2.44612e10i	−0.600224	+	1.03962i	0.392563	+	0.919725i	$0.371588\pi$
$919$	−1.41227e10	+	2.44612e10i	−0.600224	+	1.03962i	−0.992787	+	0.119893i	$0.961745\pi$
$920$	3.39304e9	+	5.87693e9i	0.143659	+	0.248824i
$921$	−8.55648e9	−	1.48203e10i	−0.360900	−	0.625097i
$922$	−1.04102e10	+	1.80309e10i	−0.437421	+	0.757636i
$923$	1.20111e10			0.502780
$924$		0			0
$925$	5.42064e9			0.225193
$926$	−2.85023e9	+	4.93674e9i	−0.117962	+	0.204316i
$927$	−5.18807e9	−	8.98601e9i	−0.213908	−	0.370500i
$928$	−6.77544e8	−	1.17354e9i	−0.0278304	−	0.0482037i
$929$	−5.14871e9	+	8.91783e9i	−0.210690	+	0.364925i	−0.951931	−	0.306314i	$-0.900904\pi$
$929$	−5.14871e9	+	8.91783e9i	−0.210690	+	0.364925i	0.741241	+	0.671239i	$0.234238\pi$
$930$	1.22948e9			0.0501223
$931$		0			0
$932$	−8.72645e9			−0.353087
$933$	5.26764e9	−	9.12382e9i	0.212339	−	0.367782i
$934$	−2.53388e9	−	4.38880e9i	−0.101759	−	0.176251i
$935$	1.74665e9	+	3.02528e9i	0.0698818	+	0.121039i
$936$	5.83387e8	−	1.01046e9i	0.0232536	−	0.0402765i
$937$	−3.96648e10			−1.57513			−0.787565	−	0.616231i	$-0.788659\pi$
$937$	−3.96648e10			−1.57513			−0.787565	+	0.616231i	$0.788659\pi$
$938$		0			0
$939$	−2.71199e10			−1.06895
$940$	−2.06581e9	+	3.57809e9i	−0.0811228	+	0.140509i
$941$	−1.43147e9	−	2.47938e9i	−0.0560040	−	0.0970017i	0.836664	−	0.547716i	$-0.184503\pi$
$941$	−1.43147e9	−	2.47938e9i	−0.0560040	−	0.0970017i	−0.892668	+	0.450714i	$0.851169\pi$
$942$	−3.15815e9	−	5.47007e9i	−0.123099	−	0.213213i
$943$	−8.45730e9	+	1.46485e10i	−0.328428	+	0.568855i
$944$	−2.73323e9			−0.105748
$945$		0			0
$946$	7.50341e9			0.288164
$947$	−3.42124e9	+	5.92575e9i	−0.130906	+	0.226735i	−0.924026	−	0.382330i	$-0.875122\pi$
$947$	−3.42124e9	+	5.92575e9i	−0.130906	+	0.226735i	0.793120	+	0.609065i	$0.208455\pi$
$948$	3.25194e9	+	5.63253e9i	0.123969	+	0.214721i
$949$	−2.31901e9	−	4.01664e9i	−0.0880786	−	0.152557i
$950$	5.62288e9	−	9.73912e9i	0.212778	−	0.368542i
$951$	6.56031e9			0.247339
$952$		0			0
$953$	−2.50283e10			−0.936711			−0.468356	−	0.883540i	$-0.655153\pi$
$953$	−2.50283e10			−0.936711			−0.468356	+	0.883540i	$0.655153\pi$
$954$	−8.57496e8	+	1.48523e9i	−0.0319752	+	0.0553826i
$955$	−6.18576e9	−	1.07141e10i	−0.229817	−	0.398054i
$956$	−7.25766e9	−	1.25706e10i	−0.268655	−	0.465323i
$957$	−5.64978e8	+	9.78571e8i	−0.0208372	+	0.0360911i
$958$	1.76442e9			0.0648368
$959$		0			0
$960$	−8.63502e8			−0.0315003
$961$	1.26679e10	−	2.19415e10i	0.460440	−	0.797506i
$962$	−1.07177e9	−	1.85636e9i	−0.0388140	−	0.0672278i
$963$	3.39723e9	+	5.88417e9i	0.122584	+	0.212321i
$964$	−1.29617e10	+	2.24503e10i	−0.466007	+	0.807148i
$965$	−8.61193e9			−0.308500
$966$		0			0
$967$	−5.13292e10			−1.82546			−0.912730	−	0.408564i	$-0.866030\pi$
$967$	−5.13292e10			−1.82546			−0.912730	+	0.408564i	$0.866030\pi$
$968$	−4.72653e9	+	8.18660e9i	−0.167486	+	0.290095i
$969$	−8.49041e9	−	1.47058e10i	−0.299775	−	0.519225i
$970$	2.24360e9	+	3.88604e9i	0.0789306	+	0.136712i
$971$	−1.81266e10	+	3.13962e10i	−0.635403	+	1.10055i	0.351027	+	0.936365i	$0.385833\pi$
$971$	−1.81266e10	+	3.13962e10i	−0.635403	+	1.10055i	−0.986430	+	0.164184i	$0.947501\pi$
$972$	9.18330e8			0.0320750
$973$		0			0
$974$	−3.14346e10			−1.09006
$975$	2.66883e9	−	4.62256e9i	0.0922158	−	0.159722i
$976$	−1.70686e9	−	2.95638e9i	−0.0587658	−	0.101785i
$977$	1.78987e10	+	3.10014e10i	0.614031	+	1.06353i	0.990554	+	0.137125i	$0.0437863\pi$
$977$	1.78987e10	+	3.10014e10i	0.614031	+	1.06353i	−0.376523	+	0.926407i	$0.622880\pi$
$978$	−1.02697e10	+	1.77876e10i	−0.351052	+	0.608040i
$979$	−2.53272e9			−0.0862677
$980$		0			0
$981$	3.13925e9			0.106166
$982$	−1.31561e10	+	2.27871e10i	−0.443342	+	0.767890i
$983$	−2.44510e10	−	4.23504e10i	−0.821030	−	1.42207i	−0.904916	−	0.425591i	$-0.860066\pi$
$983$	−2.44510e10	−	4.23504e10i	−0.821030	−	1.42207i	0.0838854	−	0.996475i	$-0.473267\pi$
$984$	−1.07616e9	−	1.86396e9i	−0.0360075	−	0.0623668i
$985$	3.06407e9	−	5.30713e9i	0.102158	−	0.176943i
$986$	−9.36056e9			−0.310980
$987$		0			0
$988$	−4.44702e9			−0.146697
$989$	5.03440e10	−	8.71984e10i	1.65486	−	2.86630i
$990$	3.60021e8	+	6.23575e8i	0.0117925	+	0.0204252i
$991$	3.44941e9	+	5.97455e9i	0.112587	+	0.195006i	0.916812	−	0.399318i	$-0.130753\pi$
$991$	3.44941e9	+	5.97455e9i	0.112587	+	0.195006i	−0.804226	+	0.594324i	$0.797420\pi$
$992$	7.64412e8	−	1.32400e9i	0.0248620	−	0.0430623i
$993$	−7.65495e8			−0.0248096
$994$		0			0
$995$	−2.54855e10			−0.820185
$996$	4.65963e9	−	8.07072e9i	0.149432	−	0.258824i
$997$	2.76515e9	+	4.78939e9i	0.0883662	+	0.153055i	0.906821	−	0.421517i	$-0.138502\pi$
$997$	2.76515e9	+	4.78939e9i	0.0883662	+	0.153055i	−0.818454	+	0.574571i	$0.805169\pi$
$998$	−1.72252e10	−	2.98349e10i	−0.548539	−	0.950098i
$999$	8.43554e8	−	1.46108e9i	0.0267691	−	0.0463654i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	294.8.e.j.79.1		2
7.2	even	3		42.8.a.c.1.1	✓	1
7.3	odd	6		294.8.e.n.67.1		2
7.4	even	3	inner	294.8.e.j.67.1		2
7.5	odd	6		294.8.a.c.1.1		1
7.6	odd	2		294.8.e.n.79.1		2
21.2	odd	6		126.8.a.g.1.1		1
28.23	odd	6		336.8.a.d.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.8.a.c.1.1	✓	1	7.2	even	3
126.8.a.g.1.1		1	21.2	odd	6
294.8.a.c.1.1		1	7.5	odd	6
294.8.e.j.67.1		2	7.4	even	3	inner
294.8.e.j.79.1		2	1.1	even	1	trivial
294.8.e.n.67.1		2	7.3	odd	6
294.8.e.n.79.1		2	7.6	odd	2
336.8.a.d.1.1		1	28.23	odd	6

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:	\( N \)	\(=\)	\( 294 = 2 \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	294.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(4.00000 - 6.92820i) q^{2} +(-13.5000 - 23.3827i) q^{3} +(-32.0000 - 55.4256i) q^{4} +(61.0000 - 105.655i) q^{5} -216.000 q^{6} -512.000 q^{8} +(-364.500 + 631.333i) q^{9} +(-488.000 - 845.241i) q^{10} +(506.000 + 876.418i) q^{11} +(-864.000 + 1496.49i) q^{12} +3126.00 q^{13} -3294.00 q^{15} +(-2048.00 + 3547.24i) q^{16} +(14147.0 + 24503.3i) q^{17} +(2916.00 + 5050.66i) q^{18} +(11114.0 - 19250.0i) q^{19} -7808.00 q^{20} +8096.00 q^{22} +(54320.0 - 94085.0i) q^{23} +(6912.00 + 11971.9i) q^{24} +(31620.5 + 54768.3i) q^{25} +(12504.0 - 21657.6i) q^{26} +19683.0 q^{27} -41354.0 q^{29} +(-13176.0 + 22821.5i) q^{30} +(-23328.0 - 40405.3i) q^{31} +(16384.0 + 28377.9i) q^{32} +(13662.0 - 23663.3i) q^{33} +226352. q^{34} +46656.0 q^{36} +(42857.0 - 74230.5i) q^{37} +(-88912.0 - 154000. i) q^{38} +(-42201.0 - 73094.3i) q^{39} +(-31232.0 + 54095.4i) q^{40} -155694. q^{41} +926804. q^{43} +(32384.0 - 56090.7i) q^{44} +(44469.0 + 77022.6i) q^{45} +(-434560. - 752680. i) q^{46} +(264576. - 458259. i) q^{47} +110592. q^{48} +505928. q^{50} +(381969. - 661590. i) q^{51} +(-100032. - 173261. i) q^{52} +(147033. + 254669. i) q^{53} +(78732.0 - 136368. i) q^{54} +123464. q^{55} -600156. q^{57} +(-165416. + 286509. i) q^{58} +(333646. + 577892. i) q^{59} +(105408. + 182572. i) q^{60} +(-416715. + 721772. i) q^{61} -373248. q^{62} +262144. q^{64} +(190686. - 330278. i) q^{65} +(-109296. - 189306. i) q^{66} +(-576998. - 999390. i) q^{67} +(905408. - 1.56821e6i) q^{68} -2.93328e6 q^{69} +3.84234e6 q^{71} +(186624. - 323242. i) q^{72} +(-741845. - 1.28491e6i) q^{73} +(-342856. - 593844. i) q^{74} +(853754. - 1.47874e6i) q^{75} -1.42259e6 q^{76} -675216. q^{78} +(1.88191e6 - 3.25957e6i) q^{79} +(249856. + 432763. i) q^{80} +(-265720. - 460241. i) q^{81} +(-622776. + 1.07868e6i) q^{82} -5.39309e6 q^{83} +3.45187e6 q^{85} +(3.70722e6 - 6.42109e6i) q^{86} +(558279. + 966968. i) q^{87} +(-259072. - 448726. i) q^{88} +(-1.25134e6 + 2.16739e6i) q^{89} +711504. q^{90} -6.95296e6 q^{92} +(-629856. + 1.09094e6i) q^{93} +(-2.11661e6 - 3.66607e6i) q^{94} +(-1.35591e6 - 2.34850e6i) q^{95} +(442368. - 766204. i) q^{96} -4.59755e6 q^{97} -737748. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 8 q^{2} - 27 q^{3} - 64 q^{4} + 122 q^{5} - 432 q^{6} - 1024 q^{8} - 729 q^{9} - 976 q^{10} + 1012 q^{11} - 1728 q^{12} + 6252 q^{13} - 6588 q^{15} - 4096 q^{16} + 28294 q^{17} + 5832 q^{18} + 22228 q^{19}+ \cdots - 1475496 q^{99}+O(q^{100}) \) 2 * q + 8 * q^2 - 27 * q^3 - 64 * q^4 + 122 * q^5 - 432 * q^6 - 1024 * q^8 - 729 * q^9 - 976 * q^10 + 1012 * q^11 - 1728 * q^12 + 6252 * q^13 - 6588 * q^15 - 4096 * q^16 + 28294 * q^17 + 5832 * q^18 + 22228 * q^19 - 15616 * q^20 + 16192 * q^22 + 108640 * q^23 + 13824 * q^24 + 63241 * q^25 + 25008 * q^26 + 39366 * q^27 - 82708 * q^29 - 26352 * q^30 - 46656 * q^31 + 32768 * q^32 + 27324 * q^33 + 452704 * q^34 + 93312 * q^36 + 85714 * q^37 - 177824 * q^38 - 84402 * q^39 - 62464 * q^40 - 311388 * q^41 + 1853608 * q^43 + 64768 * q^44 + 88938 * q^45 - 869120 * q^46 + 529152 * q^47 + 221184 * q^48 + 1011856 * q^50 + 763938 * q^51 - 200064 * q^52 + 294066 * q^53 + 157464 * q^54 + 246928 * q^55 - 1200312 * q^57 - 330832 * q^58 + 667292 * q^59 + 210816 * q^60 - 833430 * q^61 - 746496 * q^62 + 524288 * q^64 + 381372 * q^65 - 218592 * q^66 - 1153996 * q^67 + 1810816 * q^68 - 5866560 * q^69 + 7684672 * q^71 + 373248 * q^72 - 1483690 * q^73 - 685712 * q^74 + 1707507 * q^75 - 2845184 * q^76 - 1350432 * q^78 + 3763824 * q^79 + 499712 * q^80 - 531441 * q^81 - 1245552 * q^82 - 10786184 * q^83 + 6903736 * q^85 + 7414432 * q^86 + 1116558 * q^87 - 518144 * q^88 - 2502690 * q^89 + 1423008 * q^90 - 13905920 * q^92 - 1259712 * q^93 - 4233216 * q^94 - 2711816 * q^95 + 884736 * q^96 - 9195100 * q^97 - 1475496 * q^99

Introduction

L-functions

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