LMFDB - Embedded newform 140.5.r.a.101.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [140,5,Mod(61,140)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(140, base_ring=CyclotomicField(6))

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

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("140.61");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 140 = 2^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	140.r (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$14.4717948317$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 10 x^{19} + 1081 x^{18} - 9444 x^{17} + 488519 x^{16} - 3695380 x^{15} + 120074862 x^{14} + \cdots + 26\!\cdots\!01 $ x^20 - 10x^19 + 1081x^18 - 9444x^17 + 488519x^16 - 3695380x^15 + 120074862x^14 - 776597648x^13 + 17497172561x^12 - 95052648094x^11 + 1546116840759x^10 - 6877344390232x^9 + 81379309536645x^8 - 285267800245564x^7 + 2400457460992622x^6 - 6230806839424644x^5 + 35079138416926579x^4 - 60093162894428002x^3 + 208325811485546965x^2 - 179272139696141576*x + 268019223966268201
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4}\cdot 5^{4}\cdot 7^{5} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.4
Root			$0.500000 - 8.40136i$ of defining polynomial
Character	$\chi$	$=$	140.101
Dual form			140.5.r.a.61.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-8.02579 - 4.63369i) q^{3} +(-9.68246 + 5.59017i) q^{5} +(-5.50663 - 48.6896i) q^{7} +(2.44218 + 4.22998i) q^{9} +(-62.7346 + 108.660i) q^{11} -130.285i q^{13} +103.612 q^{15} +(251.925 + 145.449i) q^{17} +(-364.633 + 210.521i) q^{19} +(-181.417 + 416.288i) q^{21} +(417.626 + 723.350i) q^{23} +(62.5000 - 108.253i) q^{25} +705.393i q^{27} +689.798 q^{29} +(155.091 + 89.5420i) q^{31} +(1006.99 - 581.386i) q^{33} +(325.501 + 440.652i) q^{35} +(1187.06 + 2056.04i) q^{37} +(-603.701 + 1045.64i) q^{39} -8.95378i q^{41} -3416.97 q^{43} +(-47.2926 - 27.3044i) q^{45} +(1799.99 - 1039.22i) q^{47} +(-2340.35 + 536.232i) q^{49} +(-1347.93 - 2334.68i) q^{51} +(-1189.75 + 2060.70i) q^{53} -1402.79i q^{55} +3901.96 q^{57} +(-1988.55 - 1148.09i) q^{59} +(2372.90 - 1369.99i) q^{61} +(192.508 - 142.202i) q^{63} +(728.316 + 1261.48i) q^{65} +(945.729 - 1638.05i) q^{67} -7740.60i q^{69} -8103.36 q^{71} +(831.523 + 480.080i) q^{73} +(-1003.22 + 579.211i) q^{75} +(5636.05 + 2456.18i) q^{77} +(4189.37 + 7256.20i) q^{79} +(3466.39 - 6003.96i) q^{81} -7331.34i q^{83} -3252.34 q^{85} +(-5536.17 - 3196.31i) q^{87} +(1690.03 - 975.741i) q^{89} +(-6343.53 + 717.433i) q^{91} +(-829.820 - 1437.29i) q^{93} +(2353.70 - 4076.72i) q^{95} +4683.12i q^{97} -612.837 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 18 q^{3} - 22 q^{7} + 234 q^{9} - 150 q^{11} + 100 q^{15} + 864 q^{17} + 978 q^{19} - 2576 q^{21} - 666 q^{23} + 1250 q^{25} - 312 q^{29} + 5196 q^{31} - 384 q^{33} - 1050 q^{35} - 2900 q^{37} - 6720 q^{39}+ \cdots + 3060 q^{99}+O(q^{100}) $ 20 * q - 18 * q^3 - 22 * q^7 + 234 * q^9 - 150 * q^11 + 100 * q^15 + 864 * q^17 + 978 * q^19 - 2576 * q^21 - 666 * q^23 + 1250 * q^25 - 312 * q^29 + 5196 * q^31 - 384 * q^33 - 1050 * q^35 - 2900 * q^37 - 6720 * q^39 + 8756 * q^43 + 600 * q^45 + 13644 * q^47 - 8192 * q^49 + 2132 * q^51 - 8412 * q^53 + 288 * q^57 + 10008 * q^59 + 2208 * q^61 - 8816 * q^63 - 2250 * q^65 + 3842 * q^67 - 29832 * q^71 + 696 * q^73 - 2250 * q^75 + 8040 * q^77 + 9332 * q^79 + 7066 * q^81 + 12000 * q^85 - 30258 * q^87 - 16056 * q^89 + 7256 * q^91 - 6748 * q^93 + 300 * q^95 + 3060 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/140\mathbb{Z}\right)^\times$.

$n$	$57$	$71$	$101$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−8.02579	−	4.63369i	−0.891754	−	0.514855i	−0.0172383	−	0.999851i	$-0.505487\pi$
$3$	−8.02579	−	4.63369i	−0.891754	−	0.514855i	−0.874516	+	0.484997i	$0.838821\pi$
$4$		0			0
$5$	−9.68246	+	5.59017i	−0.387298	+	0.223607i
$5$	−9.68246	+	5.59017i	−0.387298	+	0.223607i
$6$		0			0
$7$	−5.50663	−	48.6896i	−0.112380	−	0.993665i
$7$	−5.50663	−	48.6896i	−0.112380	−	0.993665i
$8$		0			0
$9$	2.44218	+	4.22998i	0.0301504	+	0.0522220i
$10$		0			0
$11$	−62.7346	+	108.660i	−0.518468	+	0.898013i	0.481302	+	0.876555i	$0.340164\pi$
$11$	−62.7346	+	108.660i	−0.518468	+	0.898013i	−0.999770	+	0.0214579i	$0.993169\pi$
$12$		0			0
$13$		−	130.285i		−	0.770918i	−0.922725	−	0.385459i	$-0.874043\pi$
$13$		−	130.285i		−	0.770918i	0.922725	−	0.385459i	$-0.125957\pi$
$14$		0			0
$15$	103.612			0.460500
$16$		0			0
$17$	251.925	+	145.449i	0.871713	+	0.503284i	0.867917	−	0.496709i	$-0.165458\pi$
$17$	251.925	+	145.449i	0.871713	+	0.503284i	0.00379573	+	0.999993i	$0.498792\pi$
$18$		0			0
$19$	−364.633	+	210.521i	−1.01006	+	0.583161i	−0.911210	−	0.411941i	$-0.864851\pi$
$19$	−364.633	+	210.521i	−1.01006	+	0.583161i	−0.0988538	+	0.995102i	$0.531518\pi$
$20$		0			0
$21$	−181.417	+	416.288i	−0.411377	+	0.943965i
$22$		0			0
$23$	417.626	+	723.350i	0.789463	+	1.36739i	0.926296	+	0.376796i	$0.122974\pi$
$23$	417.626	+	723.350i	0.789463	+	1.36739i	−0.136833	+	0.990594i	$0.543692\pi$
$24$		0			0
$25$	62.5000	−	108.253i	0.100000	−	0.173205i
$26$		0			0
$27$			705.393i			0.967617i
$28$		0			0
$29$	689.798			0.820211			0.410106	−	0.912038i	$-0.365492\pi$
$29$	689.798			0.820211			0.410106	+	0.912038i	$0.365492\pi$
$30$		0			0
$31$	155.091	+	89.5420i	0.161385	+	0.0931758i	0.578517	−	0.815670i	$-0.303631\pi$
$31$	155.091	+	89.5420i	0.161385	+	0.0931758i	−0.417132	+	0.908846i	$0.636965\pi$
$32$		0			0
$33$	1006.99	−	581.386i	0.924692	−	0.533871i
$34$		0			0
$35$	325.501	+	440.652i	0.265715	+	0.359716i
$36$		0			0
$37$	1187.06	+	2056.04i	0.867098	+	1.50186i	0.864949	+	0.501860i	$0.167351\pi$
$37$	1187.06	+	2056.04i	0.867098	+	1.50186i	0.00214865	+	0.999998i	$0.499316\pi$
$38$		0			0
$39$	−603.701	+	1045.64i	−0.396911	+	0.687470i
$40$		0			0
$41$		−	8.95378i		−	0.00532646i	−0.999996	−	0.00266323i	$-0.999152\pi$
$41$		−	8.95378i		−	0.00532646i	0.999996	−	0.00266323i	$-0.000847733\pi$
$42$		0			0
$43$	−3416.97			−1.84801			−0.924004	−	0.382384i	$-0.875103\pi$
$43$	−3416.97			−1.84801			−0.924004	+	0.382384i	$0.875103\pi$
$44$		0			0
$45$	−47.2926	−	27.3044i	−0.0233544	−	0.0134837i
$46$		0			0
$47$	1799.99	−	1039.22i	0.814844	−	0.470450i	−0.0337914	−	0.999429i	$-0.510758\pi$
$47$	1799.99	−	1039.22i	0.814844	−	0.470450i	0.848635	+	0.528979i	$0.177425\pi$
$48$		0			0
$49$	−2340.35	+	536.232i	−0.974741	+	0.223337i
$50$		0			0
$51$	−1347.93	−	2334.68i	−0.518236	−	0.897611i
$52$		0			0
$53$	−1189.75	+	2060.70i	−0.423548	+	0.733607i	−0.996284	−	0.0861333i	$-0.972549\pi$
$53$	−1189.75	+	2060.70i	−0.423548	+	0.733607i	0.572735	+	0.819740i	$0.305882\pi$
$54$		0			0
$55$		−	1402.79i		−	0.463732i
$56$		0			0
$57$	3901.96			1.20097
$58$		0			0
$59$	−1988.55	−	1148.09i	−0.571257	−	0.329815i	0.186394	−	0.982475i	$-0.440320\pi$
$59$	−1988.55	−	1148.09i	−0.571257	−	0.329815i	−0.757651	+	0.652660i	$0.773653\pi$
$60$		0			0
$61$	2372.90	−	1369.99i	0.637705	−	0.368179i	−0.146025	−	0.989281i	$-0.546648\pi$
$61$	2372.90	−	1369.99i	0.637705	−	0.368179i	0.783730	+	0.621102i	$0.213315\pi$
$62$		0			0
$63$	192.508	−	142.202i	0.0485029	−	0.0358281i
$64$		0			0
$65$	728.316	+	1261.48i	0.172383	+	0.298575i
$66$		0			0
$67$	945.729	−	1638.05i	0.210677	−	0.364903i	−0.741250	−	0.671229i	$-0.765767\pi$
$67$	945.729	−	1638.05i	0.210677	−	0.364903i	0.951927	+	0.306326i	$0.0990998\pi$
$68$		0			0
$69$		−	7740.60i		−	1.62583i
$70$		0			0
$71$	−8103.36			−1.60749			−0.803746	−	0.594973i	$-0.797163\pi$
$71$	−8103.36			−1.60749			−0.803746	+	0.594973i	$0.797163\pi$
$72$		0			0
$73$	831.523	+	480.080i	0.156037	+	0.0900882i	0.575986	−	0.817460i	$-0.304618\pi$
$73$	831.523	+	480.080i	0.156037	+	0.0900882i	−0.419948	+	0.907548i	$0.637952\pi$
$74$		0			0
$75$	−1003.22	+	579.211i	−0.178351	+	0.102971i
$76$		0			0
$77$	5636.05	+	2456.18i	0.950590	+	0.414265i
$78$		0			0
$79$	4189.37	+	7256.20i	0.671266	+	1.16267i	0.977545	+	0.210725i	$0.0675823\pi$
$79$	4189.37	+	7256.20i	0.671266	+	1.16267i	−0.306280	+	0.951941i	$0.599084\pi$
$80$		0			0
$81$	3466.39	−	6003.96i	0.528332	−	0.915098i
$82$		0			0
$83$		−	7331.34i		−	1.06421i	−0.846679	−	0.532105i	$-0.821401\pi$
$83$		−	7331.34i		−	1.06421i	0.846679	−	0.532105i	$-0.178599\pi$
$84$		0			0
$85$	−3252.34			−0.450151
$86$		0			0
$87$	−5536.17	−	3196.31i	−0.731427	−	0.422290i
$88$		0			0
$89$	1690.03	−	975.741i	0.213361	−	0.123184i	−0.389511	−	0.921022i	$-0.627356\pi$
$89$	1690.03	−	975.741i	0.213361	−	0.123184i	0.602872	+	0.797838i	$0.294023\pi$
$90$		0			0
$91$	−6343.53	+	717.433i	−0.766035	+	0.0866360i
$92$		0			0
$93$	−829.820	−	1437.29i	−0.0959440	−	0.166180i
$94$		0			0
$95$	2353.70	−	4076.72i	0.260797	−	0.451714i
$96$		0			0
$97$			4683.12i			0.497728i	0.968538	+	0.248864i	$0.0800572\pi$
$97$			4683.12i			0.497728i	−0.968538	+	0.248864i	$0.919943\pi$
$98$		0			0
$99$	−612.837			−0.0625280
$100$		0			0
$101$	−10839.9	−	6258.42i	−1.06263	−	0.613511i	−0.136473	−	0.990644i	$-0.543577\pi$
$101$	−10839.9	−	6258.42i	−1.06263	−	0.613511i	−0.926159	+	0.377133i	$0.876910\pi$
$102$		0			0
$103$	3951.90	−	2281.63i	0.372504	−	0.215065i	−0.302048	−	0.953293i	$-0.597670\pi$
$103$	3951.90	−	2281.63i	0.372504	−	0.215065i	0.674552	+	0.738227i	$0.264337\pi$
$104$		0			0
$105$	−570.556	−	5044.85i	−0.0517511	−	0.457583i
$106$		0			0
$107$	8698.97	+	15067.1i	0.759802	+	1.31602i	0.942951	+	0.332930i	$0.108037\pi$
$107$	8698.97	+	15067.1i	0.759802	+	1.31602i	−0.183150	+	0.983085i	$0.558629\pi$
$108$		0			0
$109$	−3865.44	+	6695.14i	−0.325346	+	0.563516i	−0.981582	−	0.191039i	$-0.938814\pi$
$109$	−3865.44	+	6695.14i	−0.325346	+	0.563516i	0.656236	+	0.754556i	$0.272148\pi$
$110$		0			0
$111$		−	22001.8i		−	1.78572i
$112$		0			0
$113$	3128.82			0.245032			0.122516	−	0.992467i	$-0.460904\pi$
$113$	3128.82			0.245032			0.122516	+	0.992467i	$0.460904\pi$
$114$		0			0
$115$	−8087.29	−	4669.20i	−0.611516	−	0.353059i
$116$		0			0
$117$	551.104	−	318.180i	0.0402589	−	0.0232435i
$118$		0			0
$119$	5694.59	−	13067.1i	0.402132	−	0.922750i
$120$		0			0
$121$	−550.767	−	953.956i	−0.0376181	−	0.0651564i
$122$		0			0
$123$	−41.4890	+	71.8611i	−0.00274235	+	0.00474989i
$124$		0			0
$125$			1397.54i			0.0894427i
$126$		0			0
$127$	−22571.7			−1.39945			−0.699725	−	0.714412i	$-0.746694\pi$
$127$	−22571.7			−1.39945			−0.699725	+	0.714412i	$0.746694\pi$
$128$		0			0
$129$	27423.8	+	15833.2i	1.64797	+	0.951455i
$130$		0			0
$131$	−15092.8	+	8713.81i	−0.879480	+	0.507768i	−0.870487	−	0.492191i	$-0.836196\pi$
$131$	−15092.8	+	8713.81i	−0.879480	+	0.507768i	−0.00899336	+	0.999960i	$0.502863\pi$
$132$		0			0
$133$	12258.1	+	16594.6i	0.692978	+	0.938130i
$134$		0			0
$135$	−3943.26	−	6829.94i	−0.216366	−	0.374756i
$136$		0			0
$137$	−2604.32	+	4510.82i	−0.138757	+	0.240334i	−0.927026	−	0.374996i	$-0.877644\pi$
$137$	−2604.32	+	4510.82i	−0.138757	+	0.240334i	0.788270	+	0.615330i	$0.210977\pi$
$138$		0			0
$139$			21006.6i			1.08724i	0.839331	+	0.543620i	$0.182947\pi$
$139$			21006.6i			1.08724i	−0.839331	+	0.543620i	$0.817053\pi$
$140$		0			0
$141$	−19261.8			−0.968854
$142$		0			0
$143$	14156.7	+	8173.39i	0.692295	+	0.399696i
$144$		0			0
$145$	−6678.94	+	3856.09i	−0.317666	+	0.183405i
$146$		0			0
$147$	21267.9	+	6540.80i	0.984216	+	0.302688i
$148$		0			0
$149$	12533.4	+	21708.4i	0.564540	+	0.977812i	0.997092	+	0.0762034i	$0.0242798\pi$
$149$	12533.4	+	21708.4i	0.564540	+	0.977812i	−0.432552	+	0.901609i	$0.642387\pi$
$150$		0			0
$151$	−13334.0	+	23095.2i	−0.584799	+	1.01290i	0.410102	+	0.912040i	$0.365493\pi$
$151$	−13334.0	+	23095.2i	−0.584799	+	1.01290i	−0.994900	+	0.100862i	$0.967840\pi$
$152$		0			0
$153$			1420.85i			0.0606967i
$154$		0			0
$155$	−2002.22			−0.0833390
$156$		0			0
$157$	33916.7	+	19581.8i	1.37599	+	0.794426i	0.991674	−	0.128777i	$-0.0411052\pi$
$157$	33916.7	+	19581.8i	1.37599	+	0.794426i	0.384312	+	0.923203i	$0.374439\pi$
$158$		0			0
$159$	19097.3	−	11025.8i	0.755402	−	0.436131i
$160$		0			0
$161$	32919.9	−	24317.3i	1.27001	−	0.938130i
$162$		0			0
$163$	8692.95	+	15056.6i	0.327184	+	0.566700i	0.981952	−	0.189131i	$-0.0605669\pi$
$163$	8692.95	+	15056.6i	0.327184	+	0.566700i	−0.654768	+	0.755830i	$0.727234\pi$
$164$		0			0
$165$	−6500.09	+	11258.5i	−0.238754	+	0.413535i
$166$		0			0
$167$		−	58.5044i		−	0.00209776i	−0.999999	−	0.00104888i	$-0.999666\pi$
$167$		−	58.5044i		−	0.00209776i	0.999999	−	0.00104888i	$-0.000333869\pi$
$168$		0			0
$169$	11586.8			0.405685
$170$		0			0
$171$	−1781.00	−	1028.26i	−0.0609076	−	0.0351650i
$172$		0			0
$173$	−30460.5	+	17586.4i	−1.01776	+	0.587603i	−0.913454	−	0.406942i	$-0.866595\pi$
$173$	−30460.5	+	17586.4i	−1.01776	+	0.587603i	−0.104305	+	0.994545i	$0.533262\pi$
$174$		0			0
$175$	−5614.97	−	2446.99i	−0.183346	−	0.0799017i
$176$		0			0
$177$	10639.8	+	18428.6i	0.339614	+	0.588229i
$178$		0			0
$179$	−17397.5	+	30133.4i	−0.542976	+	0.940462i	0.455755	+	0.890105i	$0.349369\pi$
$179$	−17397.5	+	30133.4i	−0.542976	+	0.940462i	−0.998731	+	0.0503571i	$0.983964\pi$
$180$		0			0
$181$		−	49619.6i		−	1.51459i	−0.653071	−	0.757296i	$-0.726520\pi$
$181$		−	49619.6i		−	1.51459i	0.653071	−	0.757296i	$-0.273480\pi$
$182$		0			0
$183$	−25392.5			−0.758234
$184$		0			0
$185$	−22987.3	−	13271.7i	−0.671651	−	0.387778i
$186$		0			0
$187$	−31608.8	+	18249.4i	−0.903910	+	0.521873i
$188$		0			0
$189$	34345.3	−	3884.34i	0.961487	−	0.108741i
$190$		0			0
$191$	−17409.5	−	30154.1i	−0.477221	−	0.826571i	0.522438	−	0.852677i	$-0.325022\pi$
$191$	−17409.5	−	30154.1i	−0.477221	−	0.826571i	−0.999659	+	0.0261063i	$0.991689\pi$
$192$		0			0
$193$	5153.55	−	8926.21i	0.138354	−	0.239636i	−0.788520	−	0.615010i	$-0.789152\pi$
$193$	5153.55	−	8926.21i	0.138354	−	0.239636i	0.926874	+	0.375373i	$0.122485\pi$
$194$		0			0
$195$		−	13499.2i		−	0.355008i
$196$		0			0
$197$	19115.5			0.492554			0.246277	−	0.969200i	$-0.420793\pi$
$197$	19115.5			0.492554			0.246277	+	0.969200i	$0.420793\pi$
$198$		0			0
$199$	−25836.3	−	14916.6i	−0.652415	−	0.376672i	0.136966	−	0.990576i	$-0.456265\pi$
$199$	−25836.3	−	14916.6i	−0.652415	−	0.376672i	−0.789381	+	0.613904i	$0.789598\pi$
$200$		0			0
$201$	−15180.4	+	8764.43i	−0.375744	+	0.216936i
$202$		0			0
$203$	−3798.46	−	33586.0i	−0.0921756	−	0.815016i
$204$		0			0
$205$	50.0531	+	86.6946i	0.00119103	+	0.00206293i
$206$		0			0
$207$	−2039.84	+	3533.10i	−0.0476052	+	0.0824547i
$208$		0			0
$209$		−	52827.8i		−	1.20940i
$210$		0			0
$211$	−77248.3			−1.73510			−0.867549	−	0.497352i	$-0.834306\pi$
$211$	−77248.3			−1.73510			−0.867549	+	0.497352i	$0.834306\pi$
$212$		0			0
$213$	65035.9	+	37548.5i	1.43349	+	0.827624i
$214$		0			0
$215$	33084.6	−	19101.4i	0.715730	−	0.413227i
$216$		0			0
$217$	3505.73	−	8044.41i	0.0744491	−	0.170834i
$218$		0			0
$219$	−4449.08	−	7706.04i	−0.0927646	−	0.160673i
$220$		0			0
$221$	18949.8	−	32822.1i	0.387991	−	0.672019i
$222$		0			0
$223$		−	45901.0i		−	0.923022i	−0.887135	−	0.461511i	$-0.847308\pi$
$223$		−	45901.0i		−	0.923022i	0.887135	−	0.461511i	$-0.152692\pi$
$224$		0			0
$225$	610.545			0.0120601
$226$		0			0
$227$	75418.4	+	43542.8i	1.46361	+	0.845016i	0.999176	−	0.0405908i	$-0.0129240\pi$
$227$	75418.4	+	43542.8i	1.46361	+	0.845016i	0.464435	+	0.885607i	$0.346257\pi$
$228$		0			0
$229$	−81318.7	+	46949.3i	−1.55067	+	0.895279i	−0.552582	+	0.833458i	$0.686357\pi$
$229$	−81318.7	+	46949.3i	−1.55067	+	0.895279i	−0.998087	+	0.0618210i	$0.980309\pi$
$230$		0			0
$231$	−33852.6	−	45828.4i	−0.634406	−	0.858838i
$232$		0			0
$233$	−16470.7	−	28528.0i	−0.303388	−	0.525484i	0.673513	−	0.739176i	$-0.264785\pi$
$233$	−16470.7	−	28528.0i	−0.303388	−	0.525484i	−0.976901	+	0.213691i	$0.931451\pi$
$234$		0			0
$235$	−11618.9	+	20124.5i	−0.210392	+	0.364409i
$236$		0			0
$237$		−	77648.9i		−	1.38242i
$238$		0			0
$239$	4707.47			0.0824122			0.0412061	−	0.999151i	$-0.486880\pi$
$239$	4707.47			0.0824122			0.0412061	+	0.999151i	$0.486880\pi$
$240$		0			0
$241$	2641.95	+	1525.33i	0.0454873	+	0.0262621i	0.522571	−	0.852596i	$-0.324973\pi$
$241$	2641.95	+	1525.33i	0.0454873	+	0.0262621i	−0.477084	+	0.878858i	$0.658306\pi$
$242$		0			0
$243$	−6159.06	+	3555.94i	−0.104304	+	0.0602201i
$244$		0			0
$245$	19662.8	−	18275.0i	0.327576	−	0.304457i
$246$		0			0
$247$	27427.8	+	47506.3i	0.449569	+	0.778677i
$248$		0			0
$249$	−33971.1	+	58839.8i	−0.547913	+	0.949013i
$250$		0			0
$251$			48062.2i			0.762879i	0.924394	+	0.381440i	$0.124572\pi$
$251$			48062.2i			0.762879i	−0.924394	+	0.381440i	$0.875428\pi$
$252$		0			0
$253$	−104798.			−1.63725
$254$		0			0
$255$	26102.6	+	15070.3i	0.401424	+	0.231762i
$256$		0			0
$257$	86516.2	−	49950.2i	1.30988	−	0.756259i	0.327803	−	0.944746i	$-0.393692\pi$
$257$	86516.2	−	49950.2i	1.30988	−	0.756259i	0.982076	+	0.188487i	$0.0603583\pi$
$258$		0			0
$259$	93571.2	−	69119.2i	1.39490	−	1.03038i
$260$		0			0
$261$	1684.61	+	2917.83i	0.0247297	+	0.0428331i
$262$		0			0
$263$	41278.1	−	71495.8i	0.596772	−	1.03364i	−0.396522	−	0.918025i	$-0.629783\pi$
$263$	41278.1	−	71495.8i	0.596772	−	1.03364i	0.993294	−	0.115614i	$-0.0368836\pi$
$264$		0			0
$265$		−	26603.5i		−	0.378833i
$266$		0			0
$267$	−18085.1			−0.253688
$268$		0			0
$269$	−110358.	−	63715.1i	−1.52510	−	0.880517i	−0.999557	−	0.0297491i	$-0.990529\pi$
$269$	−110358.	−	63715.1i	−1.52510	−	0.880517i	−0.525542	−	0.850768i	$-0.676137\pi$
$270$		0			0
$271$	−6655.65	+	3842.64i	−0.0906258	+	0.0523228i	−0.544628	−	0.838678i	$-0.683329\pi$
$271$	−6655.65	+	3842.64i	−0.0906258	+	0.0523228i	0.454002	+	0.891001i	$0.349996\pi$
$272$		0			0
$273$	54236.2	+	23636.0i	0.727720	+	0.317138i
$274$		0			0
$275$	7841.83	+	13582.4i	0.103694	+	0.179603i
$276$		0			0
$277$	−37844.3	+	65548.3i	−0.493221	+	0.854283i	−0.999969	−	0.00781064i	$-0.997514\pi$
$277$	−37844.3	+	65548.3i	−0.493221	+	0.854283i	0.506749	+	0.862094i	$0.330847\pi$
$278$		0			0
$279$			874.711i			0.0112371i
$280$		0			0
$281$	−6610.49			−0.0837184			−0.0418592	−	0.999124i	$-0.513328\pi$
$281$	−6610.49			−0.0837184			−0.0418592	+	0.999124i	$0.513328\pi$
$282$		0			0
$283$	−20905.8	−	12069.9i	−0.261032	−	0.150707i	0.363773	−	0.931487i	$-0.381488\pi$
$283$	−20905.8	−	12069.9i	−0.261032	−	0.150707i	−0.624805	+	0.780781i	$0.714822\pi$
$284$		0			0
$285$	−37780.5	+	21812.6i	−0.465134	+	0.268546i
$286$		0			0
$287$	−435.956	+	49.3052i	−0.00529272	+	0.000598589i
$288$		0			0
$289$	550.299	+	953.146i	0.00658875	+	0.0114120i
$290$		0			0
$291$	21700.1	−	37585.7i	0.256257	−	0.443851i
$292$		0			0
$293$		−	37778.7i		−	0.440060i	−0.975493	−	0.220030i	$-0.929384\pi$
$293$		−	37778.7i		−	0.440060i	0.975493	−	0.220030i	$-0.0706155\pi$
$294$		0			0
$295$	25672.0			0.294996
$296$		0			0
$297$	−76647.7	−	44252.5i	−0.868932	−	0.501678i
$298$		0			0
$299$	94241.7	−	54410.5i	1.05415	−	0.608612i
$300$		0			0
$301$	18816.0	+	166371.i	0.207680	+	1.83630i
$302$		0			0
$303$	57999.2	+	100458.i	0.631738	+	1.09420i
$304$		0			0
$305$	−15317.0	+	26529.8i	−0.164655	+	0.285190i
$306$		0			0
$307$		−	10595.0i		−	0.112415i	−0.998419	−	0.0562075i	$-0.982099\pi$
$307$		−	10595.0i		−	0.112415i	0.998419	−	0.0562075i	$-0.0179008\pi$
$308$		0			0
$309$	−42289.4			−0.442910
$310$		0			0
$311$	79569.5	+	45939.5i	0.822670	+	0.474969i	0.851336	−	0.524620i	$-0.175793\pi$
$311$	79569.5	+	45939.5i	0.822670	+	0.474969i	−0.0286661	+	0.999589i	$0.509126\pi$
$312$		0			0
$313$	−77344.2	+	44654.7i	−0.789476	+	0.455804i	−0.839778	−	0.542930i	$-0.817315\pi$
$313$	−77344.2	+	44654.7i	−0.789476	+	0.455804i	0.0503017	+	0.998734i	$0.483982\pi$
$314$		0			0
$315$	−1069.02	+	2453.01i	−0.0107737	+	0.0247217i
$316$		0			0
$317$	4509.73	+	7811.08i	0.0448779	+	0.0777307i	0.887592	−	0.460631i	$-0.152377\pi$
$317$	4509.73	+	7811.08i	0.0448779	+	0.0777307i	−0.842714	+	0.538362i	$0.819043\pi$
$318$		0			0
$319$	−43274.2	+	74953.1i	−0.425253	+	0.736560i
$320$		0			0
$321$		−	161233.i		−	1.56475i
$322$		0			0
$323$	−122480.			−1.17398
$324$		0			0
$325$	−14103.8	−	8142.82i	−0.133527	−	0.0770918i
$326$		0			0
$327$	62046.4	−	35822.5i	0.580258	−	0.335012i
$328$		0			0
$329$	−60511.3	−	81918.1i	−0.559042	−	0.756813i
$330$		0			0
$331$	64303.7	+	111377.i	0.586922	+	1.01658i	0.994633	+	0.103467i	$0.0329937\pi$
$331$	64303.7	+	111377.i	0.586922	+	1.01658i	−0.407711	+	0.913111i	$0.633673\pi$
$332$		0			0
$333$	−5798.01	+	10042.5i	−0.0522866	+	0.0905631i
$334$		0			0
$335$			21147.1i			0.188435i
$336$		0			0
$337$	−53861.9			−0.474266			−0.237133	−	0.971477i	$-0.576208\pi$
$337$	−53861.9			−0.474266			−0.237133	+	0.971477i	$0.576208\pi$
$338$		0			0
$339$	−25111.2	−	14498.0i	−0.218509	−	0.126156i
$340$		0			0
$341$	−19459.2	+	11234.8i	−0.167346	+	0.0966174i
$342$		0			0
$343$	38996.4	+	110998.i	0.331464	+	0.943468i
$344$		0			0
$345$	43271.3	+	74948.0i	0.363548	+	0.629683i
$346$		0			0
$347$	9449.06	−	16366.2i	0.0784747	−	0.135922i	−0.824117	−	0.566419i	$-0.808328\pi$
$347$	9449.06	−	16366.2i	0.0784747	−	0.135922i	0.902592	+	0.430497i	$0.141662\pi$
$348$		0			0
$349$			195493.i			1.60502i	0.596639	+	0.802510i	$0.296502\pi$
$349$			195493.i			1.60502i	−0.596639	+	0.802510i	$0.703498\pi$
$350$		0			0
$351$	91902.2			0.745954
$352$		0			0
$353$	123988.	+	71584.3i	0.995013	+	0.574471i	0.906769	−	0.421628i	$-0.138541\pi$
$353$	123988.	+	71584.3i	0.995013	+	0.574471i	0.0882441	+	0.996099i	$0.471874\pi$
$354$		0			0
$355$	78460.5	−	45299.2i	0.622579	−	0.359446i
$356$		0			0
$357$	−106252.	+	78486.5i	−0.833685	+	0.615827i
$358$		0			0
$359$	107830.	+	186767.i	0.836663	+	1.44914i	0.892670	+	0.450712i	$0.148830\pi$
$359$	107830.	+	186767.i	0.836663	+	1.44914i	−0.0560070	+	0.998430i	$0.517837\pi$
$360$		0			0
$361$	23477.7	−	40664.7i	0.180153	−	0.312035i
$362$		0			0
$363$			10208.3i			0.0774714i
$364$		0			0
$365$	−10734.9			−0.0805773
$366$		0			0
$367$	−137744.	−	79526.3i	−1.02268	−	0.590444i	−0.107800	−	0.994173i	$-0.534381\pi$
$367$	−137744.	−	79526.3i	−1.02268	−	0.590444i	−0.914879	+	0.403729i	$0.867714\pi$
$368$		0			0
$369$	37.8743	−	21.8667i	0.000278158	−	0.000160595i
$370$		0			0
$371$	106886.	+	46580.8i	0.776558	+	0.338422i
$372$		0			0
$373$	−79562.3	−	137806.i	−0.571860	−	0.990490i	−0.996375	−	0.0850696i	$-0.972889\pi$
$373$	−79562.3	−	137806.i	−0.571860	−	0.990490i	0.424515	−	0.905421i	$-0.360445\pi$
$374$		0			0
$375$	6475.78	−	11216.4i	0.0460500	−	0.0797609i
$376$		0			0
$377$		−	89870.4i		−	0.632316i
$378$		0			0
$379$	217562.			1.51462			0.757311	−	0.653055i	$-0.226513\pi$
$379$	217562.			1.51462			0.757311	+	0.653055i	$0.226513\pi$
$380$		0			0
$381$	181156.	+	104590.i	1.24797	+	0.720513i
$382$		0			0
$383$	22090.0	−	12753.6i	0.150590	−	0.0869434i	−0.422811	−	0.906218i	$-0.638957\pi$
$383$	22090.0	−	12753.6i	0.150590	−	0.0869434i	0.573402	+	0.819274i	$0.305623\pi$
$384$		0			0
$385$	−68301.2	+	7724.65i	−0.460794	+	0.0521143i
$386$		0			0
$387$	−8344.84	−	14453.7i	−0.0557181	−	0.0965066i
$388$		0			0
$389$	32008.0	−	55439.5i	0.211524	−	0.366370i	−0.740668	−	0.671872i	$-0.765491\pi$
$389$	32008.0	−	55439.5i	0.211524	−	0.366370i	0.952192	+	0.305501i	$0.0988240\pi$
$390$		0			0
$391$			242973.i			1.58930i
$392$		0			0
$393$	161508.			1.04571
$394$		0			0
$395$	−81126.8	−	46838.6i	−0.519960	−	0.300199i
$396$		0			0
$397$	−126504.	+	73037.2i	−0.802646	+	0.463408i	−0.844395	−	0.535720i	$-0.820040\pi$
$397$	−126504.	+	73037.2i	−0.802646	+	0.463408i	0.0417498	+	0.999128i	$0.486707\pi$
$398$		0			0
$399$	−21486.7	−	189985.i	−0.134966	−	1.19336i
$400$		0			0
$401$	81104.6	+	140477.i	0.504379	+	0.873609i	0.999987	+	0.00506331i	$0.00161171\pi$
$401$	81104.6	+	140477.i	0.504379	+	0.873609i	−0.495609	+	0.868546i	$0.665055\pi$
$402$		0			0
$403$	11666.0	−	20206.1i	0.0718310	−	0.124415i
$404$		0			0
$405$			77510.8i			0.472555i
$406$		0			0
$407$	−297878.			−1.79825
$408$		0			0
$409$	−130323.	−	75242.3i	−0.779069	−	0.449796i	0.0570313	−	0.998372i	$-0.481837\pi$
$409$	−130323.	−	75242.3i	−0.779069	−	0.449796i	−0.836100	+	0.548577i	$0.815170\pi$
$410$		0			0
$411$	41803.5	−	24135.3i	0.247474	−	0.142879i
$412$		0			0
$413$	−44949.7	+	103144.i	−0.263528	+	0.604703i
$414$		0			0
$415$	40983.4	+	70985.4i	0.237964	+	0.412166i
$416$		0			0
$417$	97338.0	−	168594.i	0.559771	−	0.969551i
$418$		0			0
$419$		−	179241.i		−	1.02096i	−0.859889	−	0.510482i	$-0.829467\pi$
$419$		−	179241.i		−	1.02096i	0.859889	−	0.510482i	$-0.170533\pi$
$420$		0			0
$421$	−124884.			−0.704600			−0.352300	−	0.935887i	$-0.614600\pi$
$421$	−124884.			−0.704600			−0.352300	+	0.935887i	$0.614600\pi$
$422$		0			0
$423$	8791.80	+	5075.95i	0.0491357	+	0.0283685i
$424$		0			0
$425$	31490.6	−	18181.1i	0.174343	−	0.100657i
$426$		0			0
$427$	−79771.1	−	107991.i	−0.437512	−	0.592289i
$428$		0			0
$429$	−75746.0	−	131196.i	−0.411571	−	0.712862i
$430$		0			0
$431$	−82455.3	+	142817.i	−0.443878	+	0.768820i	−0.997973	−	0.0636334i	$-0.979731\pi$
$431$	−82455.3	+	142817.i	−0.443878	+	0.768820i	0.554095	+	0.832454i	$0.313064\pi$
$432$		0			0
$433$		−	137151.i		−	0.731513i	−0.930711	−	0.365756i	$-0.880810\pi$
$433$		−	137151.i		−	0.731513i	0.930711	−	0.365756i	$-0.119190\pi$
$434$		0			0
$435$	71471.7			0.377707
$436$		0			0
$437$	−304561.	−	175838.i	−1.59482	−	0.920768i
$438$		0			0
$439$	−13345.3	+	7704.93i	−0.0692469	+	0.0399797i	−0.534224	−	0.845343i	$-0.679396\pi$
$439$	−13345.3	+	7704.93i	−0.0692469	+	0.0399797i	0.464977	+	0.885323i	$0.346063\pi$
$440$		0			0
$441$	−7983.81	−	8590.08i	−0.0410519	−	0.0441692i
$442$		0			0
$443$	−112375.	−	194639.i	−0.572612	−	0.991794i	−0.996297	−	0.0859837i	$-0.972597\pi$
$443$	−112375.	−	194639.i	−0.572612	−	0.991794i	0.423684	−	0.905810i	$-0.360737\pi$
$444$		0			0
$445$	−10909.1	+	18895.1i	−0.0550896	+	0.0954180i
$446$		0			0
$447$		−	232303.i		−	1.16262i
$448$		0			0
$449$	94012.1			0.466328			0.233164	−	0.972437i	$-0.425092\pi$
$449$	94012.1			0.466328			0.233164	+	0.972437i	$0.425092\pi$
$450$		0			0
$451$	972.914	+	561.712i	0.00478323	+	0.00276160i
$452$		0			0
$453$	214032.	−	123571.i	1.04299	−	0.602173i
$454$		0			0
$455$	57410.4	−	42407.9i	0.277312	−	0.204845i
$456$		0			0
$457$	−67096.9	−	116215.i	−0.321270	−	0.556455i	0.659481	−	0.751722i	$-0.270776\pi$
$457$	−67096.9	−	116215.i	−0.321270	−	0.556455i	−0.980750	+	0.195266i	$0.937443\pi$
$458$		0			0
$459$	−102599.	+	177706.i	−0.486986	+	0.843484i
$460$		0			0
$461$			159256.i			0.749365i	0.927153	+	0.374683i	$0.122248\pi$
$461$			159256.i			0.749365i	−0.927153	+	0.374683i	$0.877752\pi$
$462$		0			0
$463$	−70003.7			−0.326557			−0.163279	−	0.986580i	$-0.552207\pi$
$463$	−70003.7			−0.326557			−0.163279	+	0.986580i	$0.552207\pi$
$464$		0			0
$465$	16069.4	+	9277.67i	0.0743179	+	0.0429075i
$466$		0			0
$467$	22638.0	−	13070.1i	0.103802	−	0.0599300i	−0.447200	−	0.894434i	$-0.647579\pi$
$467$	22638.0	−	13070.1i	0.103802	−	0.0599300i	0.551002	+	0.834504i	$0.314246\pi$
$468$		0			0
$469$	−84963.8	−	37027.0i	−0.386268	−	0.168334i
$470$		0			0
$471$	−181472.	−	314319.i	−0.818028	−	1.41687i
$472$		0			0
$473$	214362.	−	371286.i	0.958133	−	1.65953i
$474$		0			0
$475$			52630.3i			0.233264i
$476$		0			0
$477$	−11622.3			−0.0510805
$478$		0			0
$479$	177431.	+	102440.i	0.773321	+	0.446477i	0.834058	−	0.551677i	$-0.186012\pi$
$479$	177431.	+	102440.i	0.773321	+	0.446477i	−0.0607373	+	0.998154i	$0.519345\pi$
$480$		0			0
$481$	267872.	−	154656.i	1.15781	−	0.668462i
$482$		0			0
$483$	−376887.	+	42624.7i	−1.61554	+	0.182712i
$484$		0			0
$485$	−26179.4	−	45344.1i	−0.111295	−	0.192769i
$486$		0			0
$487$	75432.7	−	130653.i	0.318055	−	0.550887i	−0.662027	−	0.749480i	$-0.730304\pi$
$487$	75432.7	−	130653.i	0.318055	−	0.550887i	0.980082	+	0.198593i	$0.0636371\pi$
$488$		0			0
$489$		−	161122.i		−	0.673809i
$490$		0			0
$491$	302409.			1.25439			0.627194	−	0.778863i	$-0.284203\pi$
$491$	302409.			1.25439			0.627194	+	0.778863i	$0.284203\pi$
$492$		0			0
$493$	173777.	+	100330.i	0.714989	+	0.412799i
$494$		0			0
$495$	5933.77	−	3425.86i	0.0242170	−	0.0139817i
$496$		0			0
$497$	44622.3	+	394549.i	0.180650	+	1.59731i
$498$		0			0
$499$	−233347.	−	404168.i	−0.937131	−	1.62316i	−0.770789	−	0.637090i	$-0.780138\pi$
$499$	−233347.	−	404168.i	−0.937131	−	1.62316i	−0.166341	−	0.986068i	$-0.553195\pi$
$500$		0			0
$501$	−271.091	+	469.544i	−0.00108004	+	0.00187069i
$502$		0			0
$503$			476574.i			1.88362i	0.336140	+	0.941812i	$0.390878\pi$
$503$			476574.i			1.88362i	−0.336140	+	0.941812i	$0.609122\pi$
$504$		0			0
$505$	139943.			0.548741
$506$		0			0
$507$	−92992.9	−	53689.5i	−0.361771	−	0.208869i
$508$		0			0
$509$	−375715.	+	216919.i	−1.45018	+	0.837264i	−0.998491	−	0.0549101i	$-0.982513\pi$
$509$	−375715.	+	216919.i	−1.45018	+	0.837264i	−0.451692	+	0.892174i	$0.649179\pi$
$510$		0			0
$511$	18796.0	−	43130.1i	0.0719820	−	0.165173i
$512$		0			0
$513$	−148500.	−	257210.i	−0.564276	−	0.977355i
$514$		0			0
$515$	−25509.4	+	44183.5i	−0.0961802	+	0.166589i
$516$		0			0
$517$			260781.i			0.975654i
$518$		0			0
$519$	325959.			1.21012
$520$		0			0
$521$	163547.	+	94423.9i	0.602514	+	0.347862i	0.770030	−	0.638008i	$-0.220241\pi$
$521$	163547.	+	94423.9i	0.602514	+	0.347862i	−0.167516	+	0.985869i	$0.553575\pi$
$522$		0			0
$523$	−331920.	+	191634.i	−1.21347	+	0.700598i	−0.963514	−	0.267659i	$-0.913750\pi$
$523$	−331920.	+	191634.i	−1.21347	+	0.700598i	−0.249957	+	0.968257i	$0.580417\pi$
$524$		0			0
$525$	33726.0	+	45657.0i	0.122362	+	0.165649i
$526$		0			0
$527$	26047.6	+	45115.7i	0.0937877	+	0.162445i
$528$		0			0
$529$	−208903.	+	361830.i	−0.746504	+	1.29298i
$530$		0			0
$531$		−	11215.3i		−	0.0397762i
$532$		0			0
$533$	−1166.54			−0.00410627
$534$		0			0
$535$	−168455.	−	97257.4i	−0.588540	−	0.339794i
$536$		0			0
$537$	279257.	−	161229.i	0.968403	−	0.559107i
$538$		0			0
$539$	88554.5	−	287942.i	0.304813	−	0.991123i
$540$		0			0
$541$	122882.	+	212838.i	0.419850	+	0.727202i	0.995924	−	0.0901957i	$-0.0287492\pi$
$541$	122882.	+	212838.i	0.419850	+	0.727202i	−0.576074	+	0.817398i	$0.695416\pi$
$542$		0			0
$543$	−229922.	+	398236.i	−0.779795	+	1.35064i
$544$		0			0
$545$		−	86433.9i		−	0.290999i
$546$		0			0
$547$	426220.			1.42449			0.712245	−	0.701931i	$-0.247678\pi$
$547$	426220.			1.42449			0.712245	+	0.701931i	$0.247678\pi$
$548$		0			0
$549$	11590.1	+	6691.54i	0.0384541	+	0.0222015i
$550$		0			0
$551$	−251523.	+	145217.i	−0.828466	+	0.478315i
$552$		0			0
$553$	330232.	−	243936.i	1.07986	−	0.797674i
$554$		0			0
$555$	122994.	+	213032.i	0.399298	+	0.691605i
$556$		0			0
$557$	227674.	−	394342.i	0.733841	−	1.27105i	−0.221389	−	0.975186i	$-0.571059\pi$
$557$	227674.	−	394342.i	0.733841	−	1.27105i	0.955230	−	0.295865i	$-0.0956078\pi$
$558$		0			0
$559$			445180.i			1.42466i
$560$		0			0
$561$	338248.			1.07475
$562$		0			0
$563$	−4451.44	−	2570.04i	−0.0140438	−	0.00810817i	0.492962	−	0.870051i	$-0.335914\pi$
$563$	−4451.44	−	2570.04i	−0.0140438	−	0.00810817i	−0.507005	+	0.861943i	$0.669248\pi$
$564$		0			0
$565$	−30294.7	+	17490.6i	−0.0949007	+	0.0547909i
$566$		0			0
$567$	−311419.	−	135715.i	−0.968676	−	0.422146i
$568$		0			0
$569$	−229289.	−	397141.i	−0.708206	−	1.22665i	−0.965522	−	0.260321i	$-0.916172\pi$
$569$	−229289.	−	397141.i	−0.708206	−	1.22665i	0.257317	−	0.966327i	$-0.417162\pi$
$570$		0			0
$571$	99846.4	−	172939.i	0.306239	−	0.530421i	−0.671298	−	0.741188i	$-0.734263\pi$
$571$	99846.4	−	172939.i	0.306239	−	0.530421i	0.977536	+	0.210767i	$0.0675961\pi$
$572$		0			0
$573$			322681.i			0.982797i
$574$		0			0
$575$	104407.			0.315785
$576$		0			0
$577$	363358.	+	209785.i	1.09140	+	0.630119i	0.933948	−	0.357408i	$-0.116339\pi$
$577$	363358.	+	209785.i	1.09140	+	0.630119i	0.157450	+	0.987527i	$0.449673\pi$
$578$		0			0
$579$	−82722.6	+	47759.9i	−0.246756	+	0.142464i
$580$		0			0
$581$	−356960.	+	40371.0i	−1.05747	+	0.119596i
$582$		0			0
$583$	−149277.	−	258555.i	−0.439192	−	0.760703i
$584$		0			0
$585$	−3557.36	+	6161.53i	−0.0103948	+	0.0180043i
$586$		0			0
$587$			536841.i			1.55801i	0.627019	+	0.779004i	$0.284275\pi$
$587$			536841.i			1.55801i	−0.627019	+	0.779004i	$0.715725\pi$
$588$		0			0
$589$	−75401.9			−0.217346
$590$		0			0
$591$	−153417.	−	88575.4i	−0.439237	−	0.253593i
$592$		0			0
$593$	−296791.	+	171352.i	−0.843998	+	0.487282i	−0.858621	−	0.512611i	$-0.828678\pi$
$593$	−296791.	+	171352.i	−0.843998	+	0.487282i	0.0146235	+	0.999893i	$0.495345\pi$
$594$		0			0
$595$	17909.4	+	158355.i	0.0505880	+	0.447299i
$596$		0			0
$597$	138238.	+	239435.i	0.387862	+	0.671797i
$598$		0			0
$599$	234677.	−	406472.i	0.654059	−	1.13286i	−0.328070	−	0.944653i	$-0.606398\pi$
$599$	234677.	−	406472.i	0.654059	−	1.13286i	0.982129	−	0.188210i	$-0.0602685\pi$
$600$		0			0
$601$			239086.i			0.661919i	0.943645	+	0.330959i	$0.107372\pi$
$601$			239086.i			0.661919i	−0.943645	+	0.330959i	$0.892628\pi$
$602$		0			0
$603$	9238.56			0.0254080
$604$		0			0
$605$	10665.5	+	6157.76i	0.0291388	+	0.0168233i
$606$		0			0
$607$	345589.	−	199526.i	0.937955	−	0.541529i	0.0486365	−	0.998817i	$-0.484512\pi$
$607$	345589.	−	199526.i	0.937955	−	0.541529i	0.889319	+	0.457288i	$0.151179\pi$
$608$		0			0
$609$	−125141.	+	287155.i	−0.337416	+	0.774251i
$610$		0			0
$611$	−135396.	−	234512.i	−0.362679	−	0.628178i
$612$		0			0
$613$	222797.	−	385895.i	0.592909	−	1.02695i	−0.400930	−	0.916109i	$-0.631313\pi$
$613$	222797.	−	385895.i	0.592909	−	1.02695i	0.993838	−	0.110839i	$-0.0353538\pi$
$614$		0			0
$615$		−	927.723i		−	0.00245283i
$616$		0			0
$617$	−211730.			−0.556176			−0.278088	−	0.960556i	$-0.589701\pi$
$617$	−211730.			−0.556176			−0.278088	+	0.960556i	$0.589701\pi$
$618$		0			0
$619$	−140215.	−	80953.0i	−0.365942	−	0.211277i	0.305742	−	0.952114i	$-0.401095\pi$
$619$	−140215.	−	80953.0i	−0.365942	−	0.211277i	−0.671684	+	0.740838i	$0.734429\pi$
$620$		0			0
$621$	−510245.	+	294590.i	−1.32311	+	0.763898i
$622$		0			0
$623$	−56814.8	−	76914.0i	−0.146381	−	0.198166i
$624$		0			0
$625$	−7812.50	−	13531.6i	−0.0200000	−	0.0346410i
$626$		0			0
$627$	−244788.	+	423985.i	−0.622666	+	1.07849i
$628$		0			0
$629$			690625.i			1.74558i
$630$		0			0
$631$	−169560.			−0.425858			−0.212929	−	0.977068i	$-0.568300\pi$
$631$	−169560.			−0.425858			−0.212929	+	0.977068i	$0.568300\pi$
$632$		0			0
$633$	619978.	+	357945.i	1.54728	+	0.893323i
$634$		0			0
$635$	218550.	−	126180.i	0.542005	−	0.312927i
$636$		0			0
$637$	69863.0	+	304913.i	0.172174	+	0.751446i
$638$		0			0
$639$	−19789.9	−	34277.1i	−0.0484665	−	0.0839464i
$640$		0			0
$641$	138209.	−	239386.i	0.336373	−	0.582615i	−0.647375	−	0.762172i	$-0.724133\pi$
$641$	138209.	−	239386.i	0.336373	−	0.582615i	0.983748	+	0.179557i	$0.0574664\pi$
$642$		0			0
$643$		−	585755.i		−	1.41675i	−0.705835	−	0.708376i	$-0.749428\pi$
$643$		−	585755.i		−	1.41675i	0.705835	−	0.708376i	$-0.250572\pi$
$644$		0			0
$645$	−354040.			−0.851007
$646$		0			0
$647$	−503195.	−	290520.i	−1.20206	−	0.694012i	−0.241051	−	0.970513i	$-0.577492\pi$
$647$	−503195.	−	290520.i	−1.20206	−	0.694012i	−0.961014	+	0.276500i	$0.910825\pi$
$648$		0			0
$649$	249501.	−	144050.i	0.592357	−	0.341997i
$650$		0			0
$651$	−65411.6	+	48318.2i	−0.154345	+	0.114012i
$652$		0			0
$653$	227589.	+	394196.i	0.533735	+	0.924456i	0.999223	+	0.0394018i	$0.0125452\pi$
$653$	227589.	+	394196.i	0.533735	+	0.924456i	−0.465489	+	0.885054i	$0.654121\pi$
$654$		0			0
$655$	97423.4	−	168742.i	0.227081	−	0.393316i
$656$		0			0
$657$			4689.77i			0.0108648i
$658$		0			0
$659$	516645.			1.18965			0.594827	−	0.803853i	$-0.297220\pi$
$659$	516645.			1.18965			0.594827	+	0.803853i	$0.297220\pi$
$660$		0			0
$661$	26623.2	+	15370.9i	0.0609338	+	0.0351801i	0.530157	−	0.847899i	$-0.322133\pi$
$661$	26623.2	+	15370.9i	0.0609338	+	0.0351801i	−0.469224	+	0.883079i	$0.655466\pi$
$662$		0			0
$663$	−304175.	+	175615.i	−0.691984	+	0.399517i
$664$		0			0
$665$	−211455.	−	92151.5i	−0.478161	−	0.208382i
$666$		0			0
$667$	288078.	+	498965.i	0.647527	+	1.12155i
$668$		0			0
$669$	−212691.	+	368391.i	−0.475222	+	0.823109i
$670$		0			0
$671$			343784.i			0.763556i
$672$		0			0
$673$	652774.			1.44123			0.720614	−	0.693336i	$-0.243860\pi$
$673$	652774.			1.44123			0.720614	+	0.693336i	$0.243860\pi$
$674$		0			0
$675$	76361.0	+	44087.0i	0.167596	+	0.0967617i
$676$		0			0
$677$	367890.	−	212401.i	0.802676	−	0.463425i	−0.0417297	−	0.999129i	$-0.513287\pi$
$677$	367890.	−	212401.i	0.802676	−	0.463425i	0.844406	+	0.535703i	$0.179954\pi$
$678$		0			0
$679$	228019.	−	25788.2i	0.494575	−	0.0559348i
$680$		0			0
$681$	−403528.	−	698931.i	−0.870121	−	1.50709i
$682$		0			0
$683$	−220459.	+	381847.i	−0.472593	+	0.818555i	−0.999508	−	0.0313629i	$-0.990015\pi$
$683$	−220459.	+	381847.i	−0.472593	+	0.818555i	0.526915	+	0.849918i	$0.323349\pi$
$684$		0			0
$685$		−	58234.5i		−	0.124108i
$686$		0			0
$687$	870195.			1.84375
$688$		0			0
$689$	268479.	+	155006.i	0.565551	+	0.326521i
$690$		0			0
$691$	307462.	−	177513.i	0.643925	−	0.371770i	−0.142200	−	0.989838i	$-0.545418\pi$
$691$	307462.	−	177513.i	0.643925	−	0.371770i	0.786125	+	0.618068i	$0.212084\pi$
$692$		0			0
$693$	3374.67	+	29838.8i	0.00702692	+	0.0621319i
$694$		0			0
$695$	−117430.	−	203395.i	−0.243114	−	0.421086i
$696$		0			0
$697$	1302.32	−	2255.68i	0.00268072	−	0.00464314i
$698$		0			0
$699$			305280.i			0.624804i
$700$		0			0
$701$	124187.			0.252720			0.126360	−	0.991984i	$-0.459671\pi$
$701$	124187.			0.252720			0.126360	+	0.991984i	$0.459671\pi$
$702$		0			0
$703$	−865681.	−	499801.i	−1.75165	−	1.01131i
$704$		0			0
$705$	186501.	−	107677.i	0.375235	−	0.216642i
$706$		0			0
$707$	−245029.	+	562254.i	−0.490206	+	1.12485i
$708$		0			0
$709$	−258615.	−	447935.i	−0.514472	−	0.891092i	−0.999859	−	0.0167927i	$-0.994654\pi$
$709$	−258615.	−	447935.i	−0.514472	−	0.891092i	0.485387	−	0.874300i	$-0.338679\pi$
$710$		0			0
$711$	−20462.4	+	35441.9i	−0.0404778	+	0.0701096i
$712$		0			0
$713$			149580.i			0.294236i
$714$		0			0
$715$	−182763.			−0.357499
$716$		0			0
$717$	−37781.1	−	21813.0i	−0.0734914	−	0.0424303i
$718$		0			0
$719$	−191605.	+	110623.i	−0.370637	+	0.213987i	−0.673737	−	0.738971i	$-0.735312\pi$
$719$	−191605.	+	110623.i	−0.370637	+	0.213987i	0.303100	+	0.952959i	$0.401978\pi$
$720$		0			0
$721$	−132853.	−	179852.i	−0.255565	−	0.345975i
$722$		0			0
$723$	−14135.8	−	24483.9i	−0.0270423	−	0.0468387i
$724$		0			0
$725$	43112.4	−	74672.8i	0.0820211	−	0.142065i
$726$		0			0
$727$		−	689793.i		−	1.30512i	−0.757738	−	0.652559i	$-0.773695\pi$
$727$		−	689793.i		−	1.30512i	0.757738	−	0.652559i	$-0.226305\pi$
$728$		0			0
$729$	−495646.			−0.932646
$730$		0			0
$731$	−860819.	−	496994.i	−1.61093	−	0.930072i
$732$		0			0
$733$	601579.	−	347322.i	1.11966	−	0.646434i	0.178344	−	0.983968i	$-0.442926\pi$
$733$	601579.	−	347322.i	1.11966	−	0.646434i	0.941313	+	0.337534i	$0.109593\pi$
$734$		0			0
$735$	−242490.	+	55560.3i	−0.448868	+	0.102847i
$736$		0			0
$737$	118660.	+	205525.i	0.218459	+	0.378381i
$738$		0			0
$739$	298417.	−	516873.i	0.546430	−	0.946445i	−0.452085	−	0.891975i	$-0.649320\pi$
$739$	298417.	−	516873.i	0.546430	−	0.946445i	0.998515	−	0.0544702i	$-0.0173470\pi$
$740$		0			0
$741$		−	508367.i		−	0.925851i
$742$		0			0
$743$	246075.			0.445749			0.222874	−	0.974847i	$-0.428456\pi$
$743$	246075.			0.445749			0.222874	+	0.974847i	$0.428456\pi$
$744$		0			0
$745$	−242707.	−	140127.i	−0.437291	−	0.252470i
$746$		0			0
$747$	31011.4	−	17904.4i	0.0555751	−	0.0320863i
$748$		0			0
$749$	685707.	−	506518.i	1.22229	−	0.902883i
$750$		0			0
$751$	−300133.	−	519845.i	−0.532149	−	0.921709i	−0.999296	−	0.0375292i	$-0.988051\pi$
$751$	−300133.	−	519845.i	−0.532149	−	0.921709i	0.467147	−	0.884180i	$-0.345282\pi$
$752$		0			0
$753$	222705.	−	385737.i	0.392772	−	0.680301i
$754$		0			0
$755$		−	298157.i		−	0.523060i
$756$		0			0
$757$	−526244.			−0.918323			−0.459161	−	0.888353i	$-0.651850\pi$
$757$	−526244.			−0.918323			−0.459161	+	0.888353i	$0.651850\pi$
$758$		0			0
$759$	841090.	+	485604.i	1.46002	+	0.842943i
$760$		0			0
$761$	−49134.9	+	28368.1i	−0.0848440	+	0.0489847i	−0.541822	−	0.840493i	$-0.682265\pi$
$761$	−49134.9	+	28368.1i	−0.0848440	+	0.0489847i	0.456978	+	0.889478i	$0.348932\pi$
$762$		0			0
$763$	347269.	+	151339.i	0.596509	+	0.259957i
$764$		0			0
$765$	−7942.79	−	13757.3i	−0.0135722	−	0.0235077i
$766$		0			0
$767$	−149579.	+	259078.i	−0.254261	+	0.440392i
$768$		0			0
$769$			490999.i			0.830286i	0.909756	+	0.415143i	$0.136268\pi$
$769$			490999.i			0.830286i	−0.909756	+	0.415143i	$0.863732\pi$
$770$		0			0
$771$	−925814.			−1.55745
$772$		0			0
$773$	−392618.	−	226678.i	−0.657070	−	0.379359i	0.134090	−	0.990969i	$-0.457189\pi$
$773$	−392618.	−	226678.i	−0.657070	−	0.379359i	−0.791160	+	0.611610i	$0.790522\pi$
$774$		0			0
$775$	19386.4	−	11192.7i	0.0322771	−	0.0186352i
$776$		0			0
$777$	−1.07126e6	+	121156.i	−1.77440	+	0.200679i
$778$		0			0
$779$	1884.96	+	3264.84i	0.00310618	+	0.00538007i
$780$		0			0
$781$	508361.	−	880508.i	0.833433	−	1.44355i
$782$		0			0
$783$			486578.i			0.793650i
$784$		0			0
$785$	−437862.			−0.710556
$786$		0			0
$787$	−873614.	−	504381.i	−1.41049	−	0.814347i	−0.415056	−	0.909796i	$-0.636238\pi$
$787$	−873614.	−	504381.i	−1.41049	−	0.814347i	−0.995434	+	0.0954489i	$0.969571\pi$
$788$		0			0
$789$	−662579.	+	382540.i	−1.06435	+	0.614501i
$790$		0			0
$791$	−17229.3	−	152341.i	−0.0275368	−	0.243480i
$792$		0			0
$793$	−178490.	−	309154.i	−0.283836	−	0.491618i
$794$		0			0
$795$	−123273.	+	213514.i	−0.195044	+	0.337826i
$796$		0			0
$797$		−	594164.i		−	0.935384i	−0.883892	−	0.467692i	$-0.845086\pi$
$797$		−	594164.i		−	0.935384i	0.883892	−	0.467692i	$-0.154914\pi$
$798$		0			0
$799$	604617.			0.947080
$800$		0			0
$801$	8254.73	+	4765.87i	0.0128658	+	0.00742809i
$802$		0			0
$803$	−104331.	+	60235.3i	−0.161801	+	0.0934157i
$804$		0			0
$805$	−182808.	+	419479.i	−0.282100	+	0.647319i
$806$		0			0
$807$	590472.	+	1.02273e6i	0.906676	+	1.57041i
$808$		0			0
$809$	474663.	−	822141.i	0.725251	−	1.25617i	−0.233619	−	0.972328i	$-0.575057\pi$
$809$	474663.	−	822141.i	0.725251	−	1.25617i	0.958870	−	0.283844i	$-0.0916098\pi$
$810$		0			0
$811$		−	920610.i		−	1.39970i	−0.714291	−	0.699849i	$-0.753251\pi$
$811$		−	920610.i		−	1.39970i	0.714291	−	0.699849i	$-0.246749\pi$
$812$		0			0
$813$	71222.4			0.107755
$814$		0			0
$815$	−168338.	−	97190.2i	−0.253436	−	0.146321i
$816$		0			0
$817$	1.24594e6	−	719343.i	1.86661	−	1.07769i
$818$		0			0
$819$	−18526.8	−	25080.9i	−0.0276205	−	0.0373917i
$820$		0			0
$821$	267658.	+	463597.i	0.397094	+	0.687787i	0.993366	−	0.114995i	$-0.0366853\pi$
$821$	267658.	+	463597.i	0.397094	+	0.687787i	−0.596272	+	0.802783i	$0.703352\pi$
$822$		0			0
$823$	−224898.	+	389535.i	−0.332037	+	0.575105i	−0.982911	−	0.184081i	$-0.941069\pi$
$823$	−224898.	+	389535.i	−0.332037	+	0.575105i	0.650874	+	0.759186i	$0.274403\pi$
$824$		0			0
$825$		−	145346.i		−	0.213548i
$826$		0			0
$827$	166361.			0.243243			0.121622	−	0.992577i	$-0.461191\pi$
$827$	166361.			0.243243			0.121622	+	0.992577i	$0.461191\pi$
$828$		0			0
$829$	905482.	+	522780.i	1.31756	+	0.760694i	0.983336	−	0.181799i	$-0.0581920\pi$
$829$	905482.	+	522780.i	1.31756	+	0.760694i	0.334225	+	0.942493i	$0.391525\pi$
$830$		0			0
$831$	607461.	−	350718.i	0.879663	−	0.507874i
$832$		0			0
$833$	−667588.	−	205312.i	−0.962096	−	0.295886i
$834$		0			0
$835$	327.050	+	566.467i	0.000469073	+	0.000812459i
$836$		0			0
$837$	−63162.3	+	109400.i	−0.0901585	+	0.156159i
$838$		0			0
$839$		−	933965.i		−	1.32680i	−0.748263	−	0.663402i	$-0.769112\pi$
$839$		−	933965.i		−	1.32680i	0.748263	−	0.663402i	$-0.230888\pi$
$840$		0			0
$841$	−231460.			−0.327253
$842$		0			0
$843$	53054.4	+	30631.0i	0.0746563	+	0.0431028i
$844$		0			0
$845$	−112188.	+	64772.0i	−0.157121	+	0.0907139i
$846$		0			0
$847$	−43414.8	+	32069.7i	−0.0605162	+	0.0447021i
$848$		0			0
$849$	111857.	+	193742.i	0.155184	+	0.268787i
$850$		0			0
$851$	−991492.	+	1.71731e6i	−1.36908	+	2.37132i
$852$		0			0
$853$			471325.i			0.647773i	0.946096	+	0.323886i	$0.104990\pi$
$853$			471325.i			0.647773i	−0.946096	+	0.323886i	$0.895010\pi$
$854$		0			0
$855$	22992.6			0.0314526
$856$		0			0
$857$	894015.	+	516160.i	1.21726	+	0.702785i	0.964331	−	0.264700i	$-0.0852728\pi$
$857$	894015.	+	516160.i	1.21726	+	0.702785i	0.252929	+	0.967485i	$0.418606\pi$
$858$		0			0
$859$	−166917.	+	96369.5i	−0.226211	+	0.130603i	−0.608823	−	0.793306i	$-0.708358\pi$
$859$	−166917.	+	96369.5i	−0.226211	+	0.130603i	0.382612	+	0.923909i	$0.375025\pi$
$860$		0			0
$861$	3727.35	+	1624.37i	0.00502799	+	0.00219119i
$862$		0			0
$863$	262740.	+	455079.i	0.352781	+	0.611034i	0.986736	−	0.162336i	$-0.0519028\pi$
$863$	262740.	+	455079.i	0.352781	+	0.611034i	−0.633955	+	0.773370i	$0.718569\pi$
$864$		0			0
$865$	196622.	−	340559.i	0.262784	−	0.455156i
$866$		0			0
$867$		−	10199.7i		−	0.0135690i
$868$		0			0
$869$	−1.05127e6			−1.39212
$870$		0			0
$871$	−213414.	−	123214.i	−0.281311	−	0.162415i
$872$		0			0
$873$	−19809.5	+	11437.0i	−0.0259923	+	0.0150067i
$874$		0			0
$875$	68045.8	−	7695.76i	0.0888761	−	0.0100516i
$876$		0			0
$877$	459691.	+	796209.i	0.597678	+	1.03521i	0.993163	+	0.116736i	$0.0372432\pi$
$877$	459691.	+	796209.i	0.597678	+	1.03521i	−0.395485	+	0.918472i	$0.629423\pi$
$878$		0			0
$879$	−175055.	+	303204.i	−0.226567	+	0.392425i
$880$		0			0
$881$		−	307096.i		−	0.395660i	−0.980236	−	0.197830i	$-0.936611\pi$
$881$		−	307096.i		−	0.395660i	0.980236	−	0.197830i	$-0.0633894\pi$
$882$		0			0
$883$	747006.			0.958082			0.479041	−	0.877792i	$-0.340984\pi$
$883$	747006.			0.958082			0.479041	+	0.877792i	$0.340984\pi$
$884$		0			0
$885$	−206038.	−	118956.i	−0.263064	−	0.151880i
$886$		0			0
$887$	352945.	−	203773.i	0.448600	−	0.259000i	−0.258639	−	0.965974i	$-0.583274\pi$
$887$	352945.	−	203773.i	0.448600	−	0.259000i	0.707239	+	0.706975i	$0.249941\pi$
$888$		0			0
$889$	124294.	+	1.09901e6i	0.157271	+	1.39059i
$890$		0			0
$891$	434925.	+	753312.i	0.547847	+	0.948898i
$892$		0			0
$893$	−437557.	+	757872.i	−0.548696	+	0.950370i
$894$		0			0
$895$		−	389020.i		−	0.485653i
$896$		0			0
$897$	−1.00849e6			−1.25339
$898$		0			0
$899$	106982.	+	61765.9i	0.132370	+	0.0764239i
$900$		0			0
$901$	−599454.	+	346095.i	−0.738425	+	0.426330i
$902$		0			0
$903$	619897.	−	1.42244e6i	0.760228	−	1.74445i
$904$		0			0
$905$	277382.	+	480439.i	0.338673	+	0.586599i
$906$		0			0
$907$	198239.	−	343360.i	0.240976	−	0.417383i	−0.720016	−	0.693957i	$-0.755866\pi$
$907$	198239.	−	343360.i	0.240976	−	0.417383i	0.960993	+	0.276574i	$0.0891991\pi$
$908$		0			0
$909$		−	61136.8i		−	0.0739903i
$910$		0			0
$911$	682934.			0.822890			0.411445	−	0.911434i	$-0.365024\pi$
$911$	682934.			0.822890			0.411445	+	0.911434i	$0.365024\pi$
$912$		0			0
$913$	796620.	+	459929.i	0.955673	+	0.551758i
$914$		0			0
$915$	245862.	−	141948.i	0.293663	−	0.169546i
$916$		0			0
$917$	507382.	+	686877.i	0.603388	+	0.816846i
$918$		0			0
$919$	175122.	+	303321.i	0.207353	+	0.359146i	0.950880	−	0.309560i	$-0.100182\pi$
$919$	175122.	+	303321.i	0.207353	+	0.359146i	−0.743527	+	0.668706i	$0.766848\pi$
$920$		0			0
$921$	−49094.0	+	85033.2i	−0.0578774	+	0.100247i
$922$		0			0
$923$			1.05575e6i			1.23924i
$924$		0			0
$925$	296764.			0.346839
$926$		0			0
$927$	19302.5	+	11144.3i	0.0224623	+	0.0129686i
$928$		0			0
$929$	−1.34168e6	+	774617.i	−1.55459	+	0.897544i	−0.556833	+	0.830624i	$0.687984\pi$
$929$	−1.34168e6	+	774617.i	−1.55459	+	0.897544i	−0.997758	+	0.0669199i	$0.978683\pi$
$930$		0			0
$931$	740483.	−	688222.i	0.854310	−	0.794016i
$932$		0			0
$933$	−425739.	−	737401.i	−0.489080	−	0.847111i
$934$		0			0
$935$	204034.	−	353398.i	0.233389	−	0.404241i
$936$		0			0
$937$			431939.i			0.491975i	0.969273	+	0.245988i	$0.0791122\pi$
$937$			431939.i			0.491975i	−0.969273	+	0.245988i	$0.920888\pi$
$938$		0			0
$939$	827664.			0.938692
$940$		0			0
$941$	−560859.	−	323812.i	−0.633395	−	0.365691i	0.148671	−	0.988887i	$-0.452501\pi$
$941$	−560859.	−	323812.i	−0.633395	−	0.365691i	−0.782066	+	0.623196i	$0.785834\pi$
$942$		0			0
$943$	6476.71	−	3739.33i	0.00728335	−	0.00420504i
$944$		0			0
$945$	−310833.	+	229606.i	−0.348067	+	0.257110i
$946$		0			0
$947$	875350.	+	1.51615e6i	0.976071	+	1.69061i	0.676353	+	0.736577i	$0.263559\pi$
$947$	875350.	+	1.51615e6i	0.976071	+	1.69061i	0.299718	+	0.954028i	$0.403107\pi$
$948$		0			0
$949$	62547.3	−	108335.i	0.0694506	−	0.120292i
$950$		0			0
$951$		−	83586.8i		−	0.0924223i
$952$		0			0
$953$	−1.11747e6			−1.23041			−0.615206	−	0.788367i	$-0.710927\pi$
$953$	−1.11747e6			−1.23041			−0.615206	+	0.788367i	$0.710927\pi$
$954$		0			0
$955$	337133.	+	194644.i	0.369654	+	0.213420i
$956$		0			0
$957$	694619.	−	401039.i	0.758443	−	0.437887i
$958$		0			0
$959$	233971.	+	101964.i	0.254405	+	0.110869i
$960$		0			0
$961$	−445725.	−	772018.i	−0.482637	−	0.835951i
$962$		0			0
$963$	−42488.9	+	73592.9i	−0.0458166	+	0.0793567i
$964$		0			0
$965$			115237.i			0.123748i
$966$		0			0
$967$	−1.24016e6			−1.32625			−0.663126	−	0.748508i	$-0.730771\pi$
$967$	−1.24016e6			−1.32625			−0.663126	+	0.748508i	$0.730771\pi$
$968$		0			0
$969$	983001.	+	567536.i	1.04690	+	0.604430i
$970$		0			0
$971$	−429350.	+	247885.i	−0.455379	+	0.262913i	−0.710099	−	0.704101i	$-0.751350\pi$
$971$	−429350.	+	247885.i	−0.455379	+	0.262913i	0.254720	+	0.967015i	$0.418017\pi$
$972$		0			0
$973$	1.02280e6	−	115676.i	1.08035	−	0.122184i
$974$		0			0
$975$	75462.7	+	130705.i	0.0793822	+	0.137494i
$976$		0			0
$977$	−314713.	+	545099.i	−0.329705	+	0.571066i	−0.982453	−	0.186509i	$-0.940283\pi$
$977$	−314713.	+	545099.i	−0.329705	+	0.571066i	0.652748	+	0.757575i	$0.273616\pi$
$978$		0			0
$979$			244851.i			0.255468i
$980$		0			0
$981$	−37760.4			−0.0392373
$982$		0			0
$983$	204127.	+	117853.i	0.211248	+	0.121964i	0.601891	−	0.798578i	$-0.294414\pi$
$983$	204127.	+	117853.i	0.211248	+	0.121964i	−0.390643	+	0.920542i	$0.627747\pi$
$984$		0			0
$985$	−185085.	+	106859.i	−0.190765	+	0.110138i
$986$		0			0
$987$	106068.	+	937848.i	0.108880	+	0.962716i
$988$		0			0
$989$	−1.42701e6	−	2.47166e6i	−1.45893	−	2.52695i
$990$		0			0
$991$	−651369.	+	1.12820e6i	−0.663254	+	1.14879i	0.316502	+	0.948592i	$0.397492\pi$
$991$	−651369.	+	1.12820e6i	−0.663254	+	1.14879i	−0.979756	+	0.200198i	$0.935842\pi$
$992$		0			0
$993$		−	1.19185e6i		−	1.20872i
$994$		0			0
$995$	333545.			0.336906
$996$		0			0
$997$	−1.52751e6	−	881908.i	−1.53672	−	0.887224i	−0.999028	−	0.0440803i	$-0.985964\pi$
$997$	−1.52751e6	−	881908.i	−1.53672	−	0.887224i	−0.537689	−	0.843143i	$-0.680702\pi$
$998$		0			0
$999$	−1.45032e6	+	837341.i	−1.45322	+	0.839018i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	140.5.r.a.101.4	yes	20
5.2	odd	4		700.5.o.b.549.6		40
5.3	odd	4		700.5.o.b.549.15		40
5.4	even	2		700.5.s.b.101.7		20
7.3	odd	6		980.5.d.a.881.6		20
7.4	even	3		980.5.d.a.881.15		20
7.5	odd	6	inner	140.5.r.a.61.4	✓	20
35.12	even	12		700.5.o.b.649.15		40
35.19	odd	6		700.5.s.b.201.7		20
35.33	even	12		700.5.o.b.649.6		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.5.r.a.61.4	✓	20	7.5	odd	6	inner
140.5.r.a.101.4	yes	20	1.1	even	1	trivial
700.5.o.b.549.6		40	5.2	odd	4
700.5.o.b.549.15		40	5.3	odd	4
700.5.o.b.649.6		40	35.33	even	12
700.5.o.b.649.15		40	35.12	even	12
700.5.s.b.101.7		20	5.4	even	2
700.5.s.b.201.7		20	35.19	odd	6
980.5.d.a.881.6		20	7.3	odd	6
980.5.d.a.881.15		20	7.4	even	3

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:	\( N \)	\(=\)	\( 140 = 2^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	140.r (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-8.02579 - 4.63369i) q^{3} +(-9.68246 + 5.59017i) q^{5} +(-5.50663 - 48.6896i) q^{7} +(2.44218 + 4.22998i) q^{9} +(-62.7346 + 108.660i) q^{11} -130.285i q^{13} +103.612 q^{15} +(251.925 + 145.449i) q^{17} +(-364.633 + 210.521i) q^{19} +(-181.417 + 416.288i) q^{21} +(417.626 + 723.350i) q^{23} +(62.5000 - 108.253i) q^{25} +705.393i q^{27} +689.798 q^{29} +(155.091 + 89.5420i) q^{31} +(1006.99 - 581.386i) q^{33} +(325.501 + 440.652i) q^{35} +(1187.06 + 2056.04i) q^{37} +(-603.701 + 1045.64i) q^{39} -8.95378i q^{41} -3416.97 q^{43} +(-47.2926 - 27.3044i) q^{45} +(1799.99 - 1039.22i) q^{47} +(-2340.35 + 536.232i) q^{49} +(-1347.93 - 2334.68i) q^{51} +(-1189.75 + 2060.70i) q^{53} -1402.79i q^{55} +3901.96 q^{57} +(-1988.55 - 1148.09i) q^{59} +(2372.90 - 1369.99i) q^{61} +(192.508 - 142.202i) q^{63} +(728.316 + 1261.48i) q^{65} +(945.729 - 1638.05i) q^{67} -7740.60i q^{69} -8103.36 q^{71} +(831.523 + 480.080i) q^{73} +(-1003.22 + 579.211i) q^{75} +(5636.05 + 2456.18i) q^{77} +(4189.37 + 7256.20i) q^{79} +(3466.39 - 6003.96i) q^{81} -7331.34i q^{83} -3252.34 q^{85} +(-5536.17 - 3196.31i) q^{87} +(1690.03 - 975.741i) q^{89} +(-6343.53 + 717.433i) q^{91} +(-829.820 - 1437.29i) q^{93} +(2353.70 - 4076.72i) q^{95} +4683.12i q^{97} -612.837 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 18 q^{3} - 22 q^{7} + 234 q^{9} - 150 q^{11} + 100 q^{15} + 864 q^{17} + 978 q^{19} - 2576 q^{21} - 666 q^{23} + 1250 q^{25} - 312 q^{29} + 5196 q^{31} - 384 q^{33} - 1050 q^{35} - 2900 q^{37} - 6720 q^{39}+ \cdots + 3060 q^{99}+O(q^{100}) \) 20 * q - 18 * q^3 - 22 * q^7 + 234 * q^9 - 150 * q^11 + 100 * q^15 + 864 * q^17 + 978 * q^19 - 2576 * q^21 - 666 * q^23 + 1250 * q^25 - 312 * q^29 + 5196 * q^31 - 384 * q^33 - 1050 * q^35 - 2900 * q^37 - 6720 * q^39 + 8756 * q^43 + 600 * q^45 + 13644 * q^47 - 8192 * q^49 + 2132 * q^51 - 8412 * q^53 + 288 * q^57 + 10008 * q^59 + 2208 * q^61 - 8816 * q^63 - 2250 * q^65 + 3842 * q^67 - 29832 * q^71 + 696 * q^73 - 2250 * q^75 + 8040 * q^77 + 9332 * q^79 + 7066 * q^81 + 12000 * q^85 - 30258 * q^87 - 16056 * q^89 + 7256 * q^91 - 6748 * q^93 + 300 * q^95 + 3060 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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