LMFDB - Embedded newform 700.5.o.b.649.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [700,5,Mod(549,700)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(700, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 1]))

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

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

chi := DirichletCharacter("700.549");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$N$	$=$	$700 = 2^{2} \cdot 5^{2} \cdot 7$
Weight:	$k$	$=$	$5$
Character orbit:	$[\chi]$	$=$	700.o (of order $6$ , 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:	$72.3589741587$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 140)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			649.6
Character	$\chi$	$=$	700.649
Dual form			700.5.o.b.549.6

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.63369 - 8.02579i) q^{3} +(48.6896 + 5.50663i) q^{7} +(-2.44218 + 4.22998i) q^{9} +(-62.7346 - 108.660i) q^{11} -130.285 q^{13} +(-145.449 - 251.925i) q^{17} +(364.633 + 210.521i) q^{19} +(-181.417 - 416.288i) q^{21} +(723.350 + 417.626i) q^{23} -705.393 q^{27} -689.798 q^{29} +(155.091 - 89.5420i) q^{31} +(-581.386 + 1006.99i) q^{33} +(-2056.04 - 1187.06i) q^{37} +(603.701 + 1045.64i) q^{39} +8.95378i q^{41} -3416.97i q^{43} +(1039.22 - 1799.99i) q^{47} +(2340.35 + 536.232i) q^{49} +(-1347.93 + 2334.68i) q^{51} +(2060.70 - 1189.75i) q^{53} -3901.96i q^{57} +(1988.55 - 1148.09i) q^{59} +(2372.90 + 1369.99i) q^{61} +(-142.202 + 192.508i) q^{63} +(1638.05 - 945.729i) q^{67} -7740.60i q^{69} -8103.36 q^{71} +(480.080 + 831.523i) q^{73} +(-2456.18 - 5636.05i) q^{77} +(-4189.37 + 7256.20i) q^{79} +(3466.39 + 6003.96i) q^{81} -7331.34 q^{83} +(3196.31 + 5536.17i) q^{87} +(-1690.03 - 975.741i) q^{89} +(-6343.53 - 717.433i) q^{91} +(-1437.29 - 829.820i) q^{93} -4683.12 q^{97} +612.837 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$40 q - 468 q^{9} - 300 q^{11} - 1956 q^{19} - 5152 q^{21} + 624 q^{29} + 10392 q^{31} + 13440 q^{39} + 16384 q^{49} + 4264 q^{51} - 20016 q^{59} + 4416 q^{61} - 59664 q^{71} - 18664 q^{79} + 14132 q^{81}+ \cdots - 6120 q^{99}+O(q^{100})$ 40 * q - 468 * q^9 - 300 * q^11 - 1956 * q^19 - 5152 * q^21 + 624 * q^29 + 10392 * q^31 + 13440 * q^39 + 16384 * q^49 + 4264 * q^51 - 20016 * q^59 + 4416 * q^61 - 59664 * q^71 - 18664 * q^79 + 14132 * q^81 + 32112 * q^89 + 14512 * q^91 - 6120 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/700\mathbb{Z}\right)^\times$ .

$n$	$101$	$351$	$477$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$-1$

Coefficient data

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

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

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

$2$		0			0
$2$		0			0
$3$	−4.63369	−	8.02579i	−0.514855	−	0.891754i	−0.999851	−	0.0172383i	$-0.994513\pi$
$3$	−4.63369	−	8.02579i	−0.514855	−	0.891754i	0.484997	−	0.874516i	$-0.338821\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	48.6896	+	5.50663i	0.993665	+	0.112380i
$7$	48.6896	+	5.50663i	0.993665	+	0.112380i
$8$		0			0
$9$	−2.44218	+	4.22998i	−0.0301504	+	0.0522220i
$10$		0			0
$11$	−62.7346	−	108.660i	−0.518468	−	0.898013i	−0.999770	−	0.0214579i	$-0.993169\pi$
$11$	−62.7346	−	108.660i	−0.518468	−	0.898013i	0.481302	−	0.876555i	$-0.340164\pi$
$12$		0			0
$13$	−130.285			−0.770918			−0.385459	−	0.922725i	$-0.625957\pi$
$13$	−130.285			−0.770918			−0.385459	+	0.922725i	$0.625957\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−145.449	−	251.925i	−0.503284	−	0.871713i	−0.999993	−	0.00379573i	$-0.998792\pi$
$17$	−145.449	−	251.925i	−0.503284	−	0.871713i	0.496709	−	0.867917i	$-0.334542\pi$
$18$		0			0
$19$	364.633	+	210.521i	1.01006	+	0.583161i	0.911210	−	0.411941i	$-0.135149\pi$
$19$	364.633	+	210.521i	1.01006	+	0.583161i	0.0988538	+	0.995102i	$0.468482\pi$
$20$		0			0
$21$	−181.417	−	416.288i	−0.411377	−	0.943965i
$22$		0			0
$23$	723.350	+	417.626i	1.36739	+	0.789463i	0.990594	−	0.136833i	$-0.0436923\pi$
$23$	723.350	+	417.626i	1.36739	+	0.789463i	0.376796	+	0.926296i	$0.377026\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−705.393			−0.967617
$28$		0			0
$29$	−689.798			−0.820211			−0.410106	−	0.912038i	$-0.634508\pi$
$29$	−689.798			−0.820211			−0.410106	+	0.912038i	$0.634508\pi$
$30$		0			0
$31$	155.091	−	89.5420i	0.161385	−	0.0931758i	−0.417132	−	0.908846i	$-0.636965\pi$
$31$	155.091	−	89.5420i	0.161385	−	0.0931758i	0.578517	+	0.815670i	$0.303631\pi$
$32$		0			0
$33$	−581.386	+	1006.99i	−0.533871	+	0.924692i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−2056.04	−	1187.06i	−1.50186	−	0.867098i	−0.999998	−	0.00214865i	$-0.999316\pi$
$37$	−2056.04	−	1187.06i	−1.50186	−	0.867098i	−0.501860	−	0.864949i	$-0.667351\pi$
$38$		0			0
$39$	603.701	+	1045.64i	0.396911	+	0.687470i
$40$		0			0
$41$			8.95378i			0.00532646i	0.999996	+	0.00266323i	$0.000847733\pi$
$41$			8.95378i			0.00532646i	−0.999996	+	0.00266323i	$0.999152\pi$
$42$		0			0
$43$		−	3416.97i		−	1.84801i	−0.382384	−	0.924004i	$-0.624897\pi$
$43$		−	3416.97i		−	1.84801i	0.382384	−	0.924004i	$-0.375103\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	1039.22	−	1799.99i	0.470450	−	0.814844i	−0.528979	−	0.848635i	$-0.677425\pi$
$47$	1039.22	−	1799.99i	0.470450	−	0.814844i	0.999429	+	0.0337914i	$0.0107582\pi$
$48$		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
$53$	2060.70	−	1189.75i	0.733607	−	0.423548i	−0.0861333	−	0.996284i	$-0.527451\pi$
$53$	2060.70	−	1189.75i	0.733607	−	0.423548i	0.819740	+	0.572735i	$0.194118\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$		−	3901.96i		−	1.20097i
$58$		0			0
$59$	1988.55	−	1148.09i	0.571257	−	0.329815i	−0.186394	−	0.982475i	$-0.559680\pi$
$59$	1988.55	−	1148.09i	0.571257	−	0.329815i	0.757651	+	0.652660i	$0.226347\pi$
$60$		0			0
$61$	2372.90	+	1369.99i	0.637705	+	0.368179i	0.783730	−	0.621102i	$-0.213315\pi$
$61$	2372.90	+	1369.99i	0.637705	+	0.368179i	−0.146025	+	0.989281i	$0.546648\pi$
$62$		0			0
$63$	−142.202	+	192.508i	−0.0358281	+	0.0485029i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	1638.05	−	945.729i	0.364903	−	0.210677i	−0.306326	−	0.951927i	$-0.599100\pi$
$67$	1638.05	−	945.729i	0.364903	−	0.210677i	0.671229	+	0.741250i	$0.265767\pi$
$68$		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
$73$	480.080	+	831.523i	0.0900882	+	0.156037i	0.907548	−	0.419948i	$-0.137952\pi$
$73$	480.080	+	831.523i	0.0900882	+	0.156037i	−0.817460	+	0.575986i	$0.804618\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−2456.18	−	5636.05i	−0.414265	−	0.950590i
$78$		0			0
$79$	−4189.37	+	7256.20i	−0.671266	+	1.16267i	0.306280	+	0.951941i	$0.400916\pi$
$79$	−4189.37	+	7256.20i	−0.671266	+	1.16267i	−0.977545	+	0.210725i	$0.932418\pi$
$80$		0			0
$81$	3466.39	+	6003.96i	0.528332	+	0.915098i
$82$		0			0
$83$	−7331.34			−1.06421			−0.532105	−	0.846679i	$-0.678599\pi$
$83$	−7331.34			−1.06421			−0.532105	+	0.846679i	$0.678599\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	3196.31	+	5536.17i	0.422290	+	0.731427i
$88$		0			0
$89$	−1690.03	−	975.741i	−0.213361	−	0.123184i	0.389511	−	0.921022i	$-0.372644\pi$
$89$	−1690.03	−	975.741i	−0.213361	−	0.123184i	−0.602872	+	0.797838i	$0.705977\pi$
$90$		0			0
$91$	−6343.53	−	717.433i	−0.766035	−	0.0866360i
$92$		0			0
$93$	−1437.29	−	829.820i	−0.166180	−	0.0959440i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−4683.12			−0.497728			−0.248864	−	0.968538i	$-0.580057\pi$
$97$	−4683.12			−0.497728			−0.248864	+	0.968538i	$0.580057\pi$
$98$		0			0
$99$	612.837			0.0625280
$100$		0			0
$101$	−10839.9	+	6258.42i	−1.06263	+	0.613511i	−0.926159	−	0.377133i	$-0.876910\pi$
$101$	−10839.9	+	6258.42i	−1.06263	+	0.613511i	−0.136473	+	0.990644i	$0.543577\pi$
$102$		0			0
$103$	−2281.63	+	3951.90i	−0.215065	+	0.372504i	−0.953293	−	0.302048i	$-0.902330\pi$
$103$	−2281.63	+	3951.90i	−0.215065	+	0.372504i	0.738227	+	0.674552i	$0.235663\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−15067.1	−	8698.97i	−1.31602	−	0.759802i	−0.332930	−	0.942951i	$-0.608037\pi$
$107$	−15067.1	−	8698.97i	−1.31602	−	0.759802i	−0.983085	+	0.183150i	$0.941371\pi$
$108$		0			0
$109$	3865.44	+	6695.14i	0.325346	+	0.563516i	0.981582	−	0.191039i	$-0.0611858\pi$
$109$	3865.44	+	6695.14i	0.325346	+	0.563516i	−0.656236	+	0.754556i	$0.727852\pi$
$110$		0			0
$111$			22001.8i			1.78572i
$112$		0			0
$113$			3128.82i			0.245032i	0.992467	+	0.122516i	$0.0390963\pi$
$113$			3128.82i			0.245032i	−0.992467	+	0.122516i	$0.960904\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	318.180	−	551.104i	0.0232435	−	0.0402589i
$118$		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
$123$	71.8611	−	41.4890i	0.00474989	−	0.00274235i
$124$		0			0
$125$		0			0
$126$		0			0
$127$			22571.7i			1.39945i	0.714412	+	0.699725i	$0.246694\pi$
$127$			22571.7i			1.39945i	−0.714412	+	0.699725i	$0.753306\pi$
$128$		0			0
$129$	−27423.8	+	15833.2i	−1.64797	+	0.951455i
$130$		0			0
$131$	−15092.8	−	8713.81i	−0.879480	−	0.507768i	−0.00899336	−	0.999960i	$-0.502863\pi$
$131$	−15092.8	−	8713.81i	−0.879480	−	0.507768i	−0.870487	+	0.492191i	$0.836196\pi$
$132$		0			0
$133$	16594.6	+	12258.1i	0.938130	+	0.692978i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−4510.82	+	2604.32i	−0.240334	+	0.138757i	−0.615330	−	0.788270i	$-0.710977\pi$
$137$	−4510.82	+	2604.32i	−0.240334	+	0.138757i	0.374996	+	0.927026i	$0.377644\pi$
$138$		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
$143$	8173.39	+	14156.7i	0.399696	+	0.692295i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−6540.80	−	21267.9i	−0.302688	−	0.984216i
$148$		0			0
$149$	−12533.4	+	21708.4i	−0.564540	+	0.977812i	0.432552	+	0.901609i	$0.357613\pi$
$149$	−12533.4	+	21708.4i	−0.564540	+	0.977812i	−0.997092	+	0.0762034i	$0.975720\pi$
$150$		0			0
$151$	−13334.0	−	23095.2i	−0.584799	−	1.01290i	−0.994900	−	0.100862i	$-0.967840\pi$
$151$	−13334.0	−	23095.2i	−0.584799	−	1.01290i	0.410102	−	0.912040i	$-0.365493\pi$
$152$		0			0
$153$	1420.85			0.0606967
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−19581.8	−	33916.7i	−0.794426	−	1.37599i	−0.923203	−	0.384312i	$-0.874439\pi$
$157$	−19581.8	−	33916.7i	−0.794426	−	1.37599i	0.128777	−	0.991674i	$-0.458895\pi$
$158$		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
$163$	15056.6	+	8692.95i	0.566700	+	0.327184i	0.755830	−	0.654768i	$-0.227234\pi$
$163$	15056.6	+	8692.95i	0.566700	+	0.327184i	−0.189131	+	0.981952i	$0.560567\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	58.5044			0.00209776			0.00104888	−	0.999999i	$-0.499666\pi$
$167$	58.5044			0.00209776			0.00104888	+	0.999999i	$0.499666\pi$
$168$		0			0
$169$	−11586.8			−0.405685
$170$		0			0
$171$	−1781.00	+	1028.26i	−0.0609076	+	0.0351650i
$172$		0			0
$173$	17586.4	−	30460.5i	0.587603	−	1.01776i	−0.406942	−	0.913454i	$-0.633405\pi$
$173$	17586.4	−	30460.5i	0.587603	−	1.01776i	0.994545	−	0.104305i	$-0.0332617\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−18428.6	−	10639.8i	−0.588229	−	0.339614i
$178$		0			0
$179$	17397.5	+	30133.4i	0.542976	+	0.940462i	0.998731	+	0.0503571i	$0.0160359\pi$
$179$	17397.5	+	30133.4i	0.542976	+	0.940462i	−0.455755	+	0.890105i	$0.650631\pi$
$180$		0			0
$181$			49619.6i			1.51459i	0.653071	+	0.757296i	$0.273480\pi$
$181$			49619.6i			1.51459i	−0.653071	+	0.757296i	$0.726520\pi$
$182$		0			0
$183$		−	25392.5i		−	0.758234i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−18249.4	+	31608.8i	−0.521873	+	0.903910i
$188$		0			0
$189$	−34345.3	−	3884.34i	−0.961487	−	0.108741i
$190$		0			0
$191$	−17409.5	+	30154.1i	−0.477221	+	0.826571i	−0.999659	−	0.0261063i	$-0.991689\pi$
$191$	−17409.5	+	30154.1i	−0.477221	+	0.826571i	0.522438	+	0.852677i	$0.325022\pi$
$192$		0			0
$193$	−8926.21	+	5153.55i	−0.239636	+	0.138354i	−0.615010	−	0.788520i	$-0.710848\pi$
$193$	−8926.21	+	5153.55i	−0.239636	+	0.138354i	0.375373	+	0.926874i	$0.377515\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	19115.5i		−	0.492554i	−0.969200	−	0.246277i	$-0.920793\pi$
$197$		−	19115.5i		−	0.492554i	0.969200	−	0.246277i	$-0.0792072\pi$
$198$		0			0
$199$	25836.3	−	14916.6i	0.652415	−	0.376672i	−0.136966	−	0.990576i	$-0.543735\pi$
$199$	25836.3	−	14916.6i	0.652415	−	0.376672i	0.789381	+	0.613904i	$0.210402\pi$
$200$		0			0
$201$	−15180.4	−	8764.43i	−0.375744	−	0.216936i
$202$		0			0
$203$	−33586.0	−	3798.46i	−0.815016	−	0.0921756i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−3533.10	+	2039.84i	−0.0824547	+	0.0476052i
$208$		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
$213$	37548.5	+	65035.9i	0.827624	+	1.43349i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	8044.41	−	3505.73i	0.170834	−	0.0744491i
$218$		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
$223$	−45901.0			−0.923022			−0.461511	−	0.887135i	$-0.652692\pi$
$223$	−45901.0			−0.923022			−0.461511	+	0.887135i	$0.652692\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−43542.8	−	75418.4i	−0.845016	−	1.46361i	−0.885607	−	0.464435i	$-0.846257\pi$
$227$	−43542.8	−	75418.4i	−0.845016	−	1.46361i	0.0405908	−	0.999176i	$-0.487076\pi$
$228$		0			0
$229$	81318.7	+	46949.3i	1.55067	+	0.895279i	0.998087	+	0.0618210i	$0.0196908\pi$
$229$	81318.7	+	46949.3i	1.55067	+	0.895279i	0.552582	+	0.833458i	$0.313643\pi$
$230$		0			0
$231$	−33852.6	+	45828.4i	−0.634406	+	0.858838i
$232$		0			0
$233$	−28528.0	−	16470.7i	−0.525484	−	0.303388i	0.213691	−	0.976901i	$-0.431451\pi$
$233$	−28528.0	−	16470.7i	−0.525484	−	0.303388i	−0.739176	+	0.673513i	$0.764785\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	77648.9			1.38242
$238$		0			0
$239$	−4707.47			−0.0824122			−0.0412061	−	0.999151i	$-0.513120\pi$
$239$	−4707.47			−0.0824122			−0.0412061	+	0.999151i	$0.513120\pi$
$240$		0			0
$241$	2641.95	−	1525.33i	0.0454873	−	0.0262621i	−0.477084	−	0.878858i	$-0.658306\pi$
$241$	2641.95	−	1525.33i	0.0454873	−	0.0262621i	0.522571	+	0.852596i	$0.324973\pi$
$242$		0			0
$243$	3555.94	−	6159.06i	0.0602201	−	0.104304i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−47506.3	−	27427.8i	−0.778677	−	0.449569i
$248$		0			0
$249$	33971.1	+	58839.8i	0.547913	+	0.949013i
$250$		0			0
$251$		−	48062.2i		−	0.762879i	−0.924394	−	0.381440i	$-0.875428\pi$
$251$		−	48062.2i		−	0.762879i	0.924394	−	0.381440i	$-0.124572\pi$
$252$		0			0
$253$		−	104798.i		−	1.63725i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	49950.2	−	86516.2i	0.756259	−	1.30988i	−0.188487	−	0.982076i	$-0.560358\pi$
$257$	49950.2	−	86516.2i	0.756259	−	1.30988i	0.944746	−	0.327803i	$-0.106308\pi$
$258$		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
$263$	−71495.8	+	41278.1i	−1.03364	+	0.596772i	−0.918025	−	0.396522i	$-0.870217\pi$
$263$	−71495.8	+	41278.1i	−1.03364	+	0.596772i	−0.115614	+	0.993294i	$0.536884\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$			18085.1i			0.253688i
$268$		0			0
$269$	110358.	−	63715.1i	1.52510	−	0.880517i	0.525542	−	0.850768i	$-0.323863\pi$
$269$	110358.	−	63715.1i	1.52510	−	0.880517i	0.999557	−	0.0297491i	$-0.00947082\pi$
$270$		0			0
$271$	−6655.65	−	3842.64i	−0.0906258	−	0.0523228i	0.454002	−	0.891001i	$-0.349996\pi$
$271$	−6655.65	−	3842.64i	−0.0906258	−	0.0523228i	−0.544628	+	0.838678i	$0.683329\pi$
$272$		0			0
$273$	23636.0	+	54236.2i	0.317138	+	0.727720i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−65548.3	+	37844.3i	−0.854283	+	0.493221i	−0.862094	−	0.506749i	$-0.830847\pi$
$277$	−65548.3	+	37844.3i	−0.854283	+	0.493221i	0.00781064	+	0.999969i	$0.497514\pi$
$278$		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
$283$	−12069.9	−	20905.8i	−0.150707	−	0.261032i	0.780781	−	0.624805i	$-0.214822\pi$
$283$	−12069.9	−	20905.8i	−0.150707	−	0.261032i	−0.931487	+	0.363773i	$0.881488\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−49.3052	+	435.956i	−0.000598589	+	0.00529272i
$288$		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
$293$	−37778.7			−0.440060			−0.220030	−	0.975493i	$-0.570616\pi$
$293$	−37778.7			−0.440060			−0.220030	+	0.975493i	$0.570616\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	44252.5	+	76647.7i	0.501678	+	0.868932i
$298$		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
$303$	100458.	+	57999.2i	1.09420	+	0.631738i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	10595.0			0.112415			0.0562075	−	0.998419i	$-0.482099\pi$
$307$	10595.0			0.112415			0.0562075	+	0.998419i	$0.482099\pi$
$308$		0			0
$309$	42289.4			0.442910
$310$		0			0
$311$	79569.5	−	45939.5i	0.822670	−	0.474969i	−0.0286661	−	0.999589i	$-0.509126\pi$
$311$	79569.5	−	45939.5i	0.822670	−	0.474969i	0.851336	+	0.524620i	$0.175793\pi$
$312$		0			0
$313$	44654.7	−	77344.2i	0.455804	−	0.789476i	−0.542930	−	0.839778i	$-0.682685\pi$
$313$	44654.7	−	77344.2i	0.455804	−	0.789476i	0.998734	+	0.0503017i	$0.0160183\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−7811.08	−	4509.73i	−0.0777307	−	0.0448779i	0.460631	−	0.887592i	$-0.347623\pi$
$317$	−7811.08	−	4509.73i	−0.0777307	−	0.0448779i	−0.538362	+	0.842714i	$0.680957\pi$
$318$		0			0
$319$	43274.2	+	74953.1i	0.425253	+	0.736560i
$320$		0			0
$321$			161233.i			1.56475i
$322$		0			0
$323$		−	122480.i		−	1.17398i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	35822.5	−	62046.4i	0.335012	−	0.580258i
$328$		0			0
$329$	60511.3	−	81918.1i	0.559042	−	0.756813i
$330$		0			0
$331$	64303.7	−	111377.i	0.586922	−	1.01658i	−0.407711	−	0.913111i	$-0.633673\pi$
$331$	64303.7	−	111377.i	0.586922	−	1.01658i	0.994633	−	0.103467i	$-0.0329937\pi$
$332$		0			0
$333$	10042.5	−	5798.01i	0.0905631	−	0.0522866i
$334$		0			0
$335$		0			0
$336$		0			0
$337$			53861.9i			0.474266i	0.971477	+	0.237133i	$0.0762078\pi$
$337$			53861.9i			0.474266i	−0.971477	+	0.237133i	$0.923792\pi$
$338$		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
$343$	110998.	+	38996.4i	0.943468	+	0.331464i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	16366.2	−	9449.06i	0.135922	−	0.0784747i	−0.430497	−	0.902592i	$-0.641662\pi$
$347$	16366.2	−	9449.06i	0.135922	−	0.0784747i	0.566419	+	0.824117i	$0.308328\pi$
$348$		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
$353$	71584.3	+	123988.i	0.574471	+	0.995013i	0.996099	+	0.0882441i	$0.0281255\pi$
$353$	71584.3	+	123988.i	0.574471	+	0.995013i	−0.421628	+	0.906769i	$0.638541\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−78486.5	+	106252.i	−0.615827	+	0.833685i
$358$		0			0
$359$	−107830.	+	186767.i	−0.836663	+	1.44914i	0.0560070	+	0.998430i	$0.482163\pi$
$359$	−107830.	+	186767.i	−0.836663	+	1.44914i	−0.892670	+	0.450712i	$0.851170\pi$
$360$		0			0
$361$	23477.7	+	40664.7i	0.180153	+	0.312035i
$362$		0			0
$363$	10208.3			0.0774714
$364$		0			0
$365$		0			0
$366$		0			0
$367$	79526.3	+	137744.i	0.590444	+	1.02268i	0.994173	+	0.107800i	$0.0343806\pi$
$367$	79526.3	+	137744.i	0.590444	+	1.02268i	−0.403729	+	0.914879i	$0.632286\pi$
$368$		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
$373$	−137806.	−	79562.3i	−0.990490	−	0.571860i	−0.0850696	−	0.996375i	$-0.527111\pi$
$373$	−137806.	−	79562.3i	−0.990490	−	0.571860i	−0.905421	+	0.424515i	$0.860445\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	89870.4			0.632316
$378$		0			0
$379$	−217562.			−1.51462			−0.757311	−	0.653055i	$-0.773487\pi$
$379$	−217562.			−1.51462			−0.757311	+	0.653055i	$0.773487\pi$
$380$		0			0
$381$	181156.	−	104590.i	1.24797	−	0.720513i
$382$		0			0
$383$	−12753.6	+	22090.0i	−0.0869434	+	0.150590i	−0.906218	−	0.422811i	$-0.861043\pi$
$383$	−12753.6	+	22090.0i	−0.0869434	+	0.150590i	0.819274	+	0.573402i	$0.194377\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	14453.7	+	8344.84i	0.0965066	+	0.0557181i
$388$		0			0
$389$	−32008.0	−	55439.5i	−0.211524	−	0.366370i	0.740668	−	0.671872i	$-0.234509\pi$
$389$	−32008.0	−	55439.5i	−0.211524	−	0.366370i	−0.952192	+	0.305501i	$0.901176\pi$
$390$		0			0
$391$		−	242973.i		−	1.58930i
$392$		0			0
$393$			161508.i			1.04571i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−73037.2	+	126504.i	−0.463408	+	0.802646i	−0.999128	−	0.0417498i	$-0.986707\pi$
$397$	−73037.2	+	126504.i	−0.463408	+	0.802646i	0.535720	+	0.844395i	$0.320040\pi$
$398$		0			0
$399$	21486.7	−	189985.i	0.134966	−	1.19336i
$400$		0			0
$401$	81104.6	−	140477.i	0.504379	−	0.873609i	−0.495609	−	0.868546i	$-0.665055\pi$
$401$	81104.6	−	140477.i	0.504379	−	0.873609i	0.999987	−	0.00506331i	$-0.00161171\pi$
$402$		0			0
$403$	−20206.1	+	11666.0i	−0.124415	+	0.0718310i
$404$		0			0
$405$		0			0
$406$		0			0
$407$			297878.i			1.79825i
$408$		0			0
$409$	130323.	−	75242.3i	0.779069	−	0.449796i	−0.0570313	−	0.998372i	$-0.518163\pi$
$409$	130323.	−	75242.3i	0.779069	−	0.449796i	0.836100	+	0.548577i	$0.184830\pi$
$410$		0			0
$411$	41803.5	+	24135.3i	0.247474	+	0.142879i
$412$		0			0
$413$	103144.	−	44949.7i	0.604703	−	0.263528i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	168594.	−	97338.0i	0.969551	−	0.559771i
$418$		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
$423$	5075.95	+	8791.80i	0.0283685	+	0.0491357i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	107991.	+	79771.1i	0.592289	+	0.437512i
$428$		0			0
$429$	75746.0	−	131196.i	0.411571	−	0.712862i
$430$		0			0
$431$	−82455.3	−	142817.i	−0.443878	−	0.768820i	0.554095	−	0.832454i	$-0.313064\pi$
$431$	−82455.3	−	142817.i	−0.443878	−	0.768820i	−0.997973	+	0.0636334i	$0.979731\pi$
$432$		0			0
$433$	−137151.			−0.731513			−0.365756	−	0.930711i	$-0.619190\pi$
$433$	−137151.			−0.731513			−0.365756	+	0.930711i	$0.619190\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	175838.	+	304561.i	0.920768	+	1.59482i
$438$		0			0
$439$	13345.3	+	7704.93i	0.0692469	+	0.0399797i	0.534224	−	0.845343i	$-0.320604\pi$
$439$	13345.3	+	7704.93i	0.0692469	+	0.0399797i	−0.464977	+	0.885323i	$0.653937\pi$
$440$		0			0
$441$	−7983.81	+	8590.08i	−0.0410519	+	0.0441692i
$442$		0			0
$443$	−194639.	−	112375.i	−0.991794	−	0.572612i	−0.0859837	−	0.996297i	$-0.527403\pi$
$443$	−194639.	−	112375.i	−0.991794	−	0.572612i	−0.905810	+	0.423684i	$0.860737\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	232303.			1.16262
$448$		0			0
$449$	−94012.1			−0.466328			−0.233164	−	0.972437i	$-0.574908\pi$
$449$	−94012.1			−0.466328			−0.233164	+	0.972437i	$0.574908\pi$
$450$		0			0
$451$	972.914	−	561.712i	0.00478323	−	0.00276160i
$452$		0			0
$453$	−123571.	+	214032.i	−0.602173	+	1.04299i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	116215.	+	67096.9i	0.556455	+	0.321270i	0.751722	−	0.659481i	$-0.229224\pi$
$457$	116215.	+	67096.9i	0.556455	+	0.321270i	−0.195266	+	0.980750i	$0.562557\pi$
$458$		0			0
$459$	102599.	+	177706.i	0.486986	+	0.843484i
$460$		0			0
$461$		−	159256.i		−	0.749365i	−0.927153	−	0.374683i	$-0.877752\pi$
$461$		−	159256.i		−	0.749365i	0.927153	−	0.374683i	$-0.122248\pi$
$462$		0			0
$463$		−	70003.7i		−	0.326557i	−0.986580	−	0.163279i	$-0.947793\pi$
$463$		−	70003.7i		−	0.326557i	0.986580	−	0.163279i	$-0.0522069\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	13070.1	−	22638.0i	0.0599300	−	0.103802i	−0.834504	−	0.551002i	$-0.814246\pi$
$467$	13070.1	−	22638.0i	0.0599300	−	0.103802i	0.894434	+	0.447200i	$0.147579\pi$
$468$		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
$473$	−371286.	+	214362.i	−1.65953	+	0.958133i
$474$		0			0
$475$		0			0
$476$		0			0
$477$			11622.3i			0.0510805i
$478$		0			0
$479$	−177431.	+	102440.i	−0.773321	+	0.446477i	−0.834058	−	0.551677i	$-0.813988\pi$
$479$	−177431.	+	102440.i	−0.773321	+	0.446477i	0.0607373	+	0.998154i	$0.480655\pi$
$480$		0			0
$481$	267872.	+	154656.i	1.15781	+	0.668462i
$482$		0			0
$483$	42624.7	−	376887.i	0.182712	−	1.61554i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	130653.	−	75432.7i	0.550887	−	0.318055i	−0.198593	−	0.980082i	$-0.563637\pi$
$487$	130653.	−	75432.7i	0.550887	−	0.318055i	0.749480	+	0.662027i	$0.230304\pi$
$488$		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
$493$	100330.	+	173777.i	0.412799	+	0.714989i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−394549.	−	44622.3i	−1.59731	−	0.180650i
$498$		0			0
$499$	233347.	−	404168.i	0.937131	−	1.62316i	0.166341	−	0.986068i	$-0.446805\pi$
$499$	233347.	−	404168.i	0.937131	−	1.62316i	0.770789	−	0.637090i	$-0.219862\pi$
$500$		0			0
$501$	−271.091	−	469.544i	−0.00108004	−	0.00187069i
$502$		0			0
$503$	476574.			1.88362			0.941812	−	0.336140i	$-0.109122\pi$
$503$	476574.			1.88362			0.941812	+	0.336140i	$0.109122\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	53689.5	+	92992.9i	0.208869	+	0.361771i
$508$		0			0
$509$	375715.	+	216919.i	1.45018	+	0.837264i	0.998491	−	0.0549101i	$-0.0174872\pi$
$509$	375715.	+	216919.i	1.45018	+	0.837264i	0.451692	+	0.892174i	$0.350821\pi$
$510$		0			0
$511$	18796.0	+	43130.1i	0.0719820	+	0.165173i
$512$		0			0
$513$	−257210.	−	148500.i	−0.977355	−	0.564276i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−260781.			−0.975654
$518$		0			0
$519$	−325959.			−1.21012
$520$		0			0
$521$	163547.	−	94423.9i	0.602514	−	0.347862i	−0.167516	−	0.985869i	$-0.553575\pi$
$521$	163547.	−	94423.9i	0.602514	−	0.347862i	0.770030	+	0.638008i	$0.220241\pi$
$522$		0			0
$523$	191634.	−	331920.i	0.700598	−	1.21347i	−0.267659	−	0.963514i	$-0.586250\pi$
$523$	191634.	−	331920.i	0.700598	−	1.21347i	0.968257	−	0.249957i	$-0.0804166\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−45115.7	−	26047.6i	−0.162445	−	0.0937877i
$528$		0			0
$529$	208903.	+	361830.i	0.746504	+	1.29298i
$530$		0			0
$531$			11215.3i			0.0397762i
$532$		0			0
$533$		−	1166.54i		−	0.00410627i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	161229.	−	279257.i	0.559107	−	0.968403i
$538$		0			0
$539$	−88554.5	−	287942.i	−0.304813	−	0.991123i
$540$		0			0
$541$	122882.	−	212838.i	0.419850	−	0.727202i	−0.576074	−	0.817398i	$-0.695416\pi$
$541$	122882.	−	212838.i	0.419850	−	0.727202i	0.995924	+	0.0901957i	$0.0287492\pi$
$542$		0			0
$543$	398236.	−	229922.i	1.35064	−	0.779795i
$544$		0			0
$545$		0			0
$546$		0			0
$547$		−	426220.i		−	1.42449i	−0.701931	−	0.712245i	$-0.747678\pi$
$547$		−	426220.i		−	1.42449i	0.701931	−	0.712245i	$-0.252322\pi$
$548$		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
$553$	−243936.	+	330232.i	−0.797674	+	1.07986i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	394342.	−	227674.i	1.27105	−	0.733841i	0.295865	−	0.955230i	$-0.404392\pi$
$557$	394342.	−	227674.i	1.27105	−	0.733841i	0.975186	+	0.221389i	$0.0710589\pi$
$558$		0			0
$559$			445180.i			1.42466i
$560$		0			0
$561$	338248.			1.07475
$562$		0			0
$563$	−2570.04	−	4451.44i	−0.00810817	−	0.0140438i	0.861943	−	0.507005i	$-0.169248\pi$
$563$	−2570.04	−	4451.44i	−0.00810817	−	0.0140438i	−0.870051	+	0.492962i	$0.835914\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	135715.	+	311419.i	0.422146	+	0.968676i
$568$		0			0
$569$	229289.	−	397141.i	0.708206	−	1.22665i	−0.257317	−	0.966327i	$-0.582838\pi$
$569$	229289.	−	397141.i	0.708206	−	1.22665i	0.965522	−	0.260321i	$-0.0838284\pi$
$570$		0			0
$571$	99846.4	+	172939.i	0.306239	+	0.530421i	0.977536	−	0.210767i	$-0.0675961\pi$
$571$	99846.4	+	172939.i	0.306239	+	0.530421i	−0.671298	+	0.741188i	$0.734263\pi$
$572$		0			0
$573$	322681.			0.982797
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−209785.	−	363358.i	−0.630119	−	1.09140i	−0.987527	−	0.157450i	$-0.949673\pi$
$577$	−209785.	−	363358.i	−0.630119	−	1.09140i	0.357408	−	0.933948i	$-0.383661\pi$
$578$		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
$583$	−258555.	−	149277.i	−0.760703	−	0.439192i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−536841.			−1.55801			−0.779004	−	0.627019i	$-0.784275\pi$
$587$	−536841.			−1.55801			−0.779004	+	0.627019i	$0.784275\pi$
$588$		0			0
$589$	75401.9			0.217346
$590$		0			0
$591$	−153417.	+	88575.4i	−0.439237	+	0.253593i
$592$		0			0
$593$	171352.	−	296791.i	0.487282	−	0.843998i	−0.512611	−	0.858621i	$-0.671322\pi$
$593$	171352.	−	296791.i	0.487282	−	0.843998i	0.999893	+	0.0146235i	$0.00465498\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−239435.	−	138238.i	−0.671797	−	0.387862i
$598$		0			0
$599$	−234677.	−	406472.i	−0.654059	−	1.13286i	−0.982129	−	0.188210i	$-0.939731\pi$
$599$	−234677.	−	406472.i	−0.654059	−	1.13286i	0.328070	−	0.944653i	$-0.393602\pi$
$600$		0			0
$601$		−	239086.i		−	0.661919i	−0.943645	−	0.330959i	$-0.892628\pi$
$601$		−	239086.i		−	0.661919i	0.943645	−	0.330959i	$-0.107372\pi$
$602$		0			0
$603$			9238.56i			0.0254080i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	199526.	−	345589.i	0.541529	−	0.937955i	−0.457288	−	0.889319i	$-0.651179\pi$
$607$	199526.	−	345589.i	0.541529	−	0.937955i	0.998817	−	0.0486365i	$-0.0154876\pi$
$608$		0			0
$609$	125141.	+	287155.i	0.337416	+	0.774251i
$610$		0			0
$611$	−135396.	+	234512.i	−0.362679	+	0.628178i
$612$		0			0
$613$	−385895.	+	222797.i	−1.02695	+	0.592909i	−0.916109	−	0.400930i	$-0.868687\pi$
$613$	−385895.	+	222797.i	−1.02695	+	0.592909i	−0.110839	+	0.993838i	$0.535354\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$			211730.i			0.556176i	0.960556	+	0.278088i	$0.0897007\pi$
$617$			211730.i			0.556176i	−0.960556	+	0.278088i	$0.910299\pi$
$618$		0			0
$619$	140215.	−	80953.0i	0.365942	−	0.211277i	−0.305742	−	0.952114i	$-0.598905\pi$
$619$	140215.	−	80953.0i	0.365942	−	0.211277i	0.671684	+	0.740838i	$0.265571\pi$
$620$		0			0
$621$	−510245.	−	294590.i	−1.32311	−	0.763898i
$622$		0			0
$623$	−76914.0	−	56814.8i	−0.198166	−	0.146381i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−423985.	+	244788.i	−1.07849	+	0.622666i
$628$		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
$633$	357945.	+	619978.i	0.893323	+	1.54728i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−304913.	−	69863.0i	−0.751446	−	0.172174i
$638$		0			0
$639$	19789.9	−	34277.1i	0.0484665	−	0.0839464i
$640$		0			0
$641$	138209.	+	239386.i	0.336373	+	0.582615i	0.983748	−	0.179557i	$-0.0574664\pi$
$641$	138209.	+	239386.i	0.336373	+	0.582615i	−0.647375	+	0.762172i	$0.724133\pi$
$642$		0			0
$643$	−585755.			−1.41675			−0.708376	−	0.705835i	$-0.750572\pi$
$643$	−585755.			−1.41675			−0.708376	+	0.705835i	$0.750572\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	290520.	+	503195.i	0.694012	+	1.20206i	0.970513	+	0.241051i	$0.0774920\pi$
$647$	290520.	+	503195.i	0.694012	+	1.20206i	−0.276500	+	0.961014i	$0.589175\pi$
$648$		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
$653$	394196.	+	227589.i	0.924456	+	0.533735i	0.885054	−	0.465489i	$-0.154121\pi$
$653$	394196.	+	227589.i	0.924456	+	0.533735i	0.0394018	+	0.999223i	$0.487455\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−4689.77			−0.0108648
$658$		0			0
$659$	−516645.			−1.18965			−0.594827	−	0.803853i	$-0.702780\pi$
$659$	−516645.			−1.18965			−0.594827	+	0.803853i	$0.702780\pi$
$660$		0			0
$661$	26623.2	−	15370.9i	0.0609338	−	0.0351801i	−0.469224	−	0.883079i	$-0.655466\pi$
$661$	26623.2	−	15370.9i	0.0609338	−	0.0351801i	0.530157	+	0.847899i	$0.322133\pi$
$662$		0			0
$663$	175615.	−	304175.i	0.399517	−	0.691984i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−498965.	−	288078.i	−1.12155	−	0.647527i
$668$		0			0
$669$	212691.	+	368391.i	0.475222	+	0.823109i
$670$		0			0
$671$		−	343784.i		−	0.763556i
$672$		0			0
$673$			652774.i			1.44123i	0.693336	+	0.720614i	$0.256140\pi$
$673$			652774.i			1.44123i	−0.693336	+	0.720614i	$0.743860\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	212401.	−	367890.i	0.463425	−	0.802676i	−0.535703	−	0.844406i	$-0.679954\pi$
$677$	212401.	−	367890.i	0.463425	−	0.802676i	0.999129	+	0.0417297i	$0.0132868\pi$
$678$		0			0
$679$	−228019.	−	25788.2i	−0.494575	−	0.0559348i
$680$		0			0
$681$	−403528.	+	698931.i	−0.870121	+	1.50709i
$682$		0			0
$683$	381847.	−	220459.i	0.818555	−	0.472593i	−0.0313629	−	0.999508i	$-0.509985\pi$
$683$	381847.	−	220459.i	0.818555	−	0.472593i	0.849918	+	0.526915i	$0.176651\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$		−	870195.i		−	1.84375i
$688$		0			0
$689$	−268479.	+	155006.i	−0.565551	+	0.326521i
$690$		0			0
$691$	307462.	+	177513.i	0.643925	+	0.371770i	0.786125	−	0.618068i	$-0.212084\pi$
$691$	307462.	+	177513.i	0.643925	+	0.371770i	−0.142200	+	0.989838i	$0.545418\pi$
$692$		0			0
$693$	29838.8	+	3374.67i	0.0621319	+	0.00702692i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	2255.68	−	1302.32i	0.00464314	−	0.00268072i
$698$		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
$703$	−499801.	−	865681.i	−1.01131	−	1.75165i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−562254.	+	245029.i	−1.12485	+	0.490206i
$708$		0			0
$709$	258615.	−	447935.i	0.514472	−	0.891092i	−0.485387	−	0.874300i	$-0.661321\pi$
$709$	258615.	−	447935.i	0.514472	−	0.891092i	0.999859	−	0.0167927i	$-0.00534553\pi$
$710$		0			0
$711$	−20462.4	−	35441.9i	−0.0404778	−	0.0701096i
$712$		0			0
$713$	149580.			0.294236
$714$		0			0
$715$		0			0
$716$		0			0
$717$	21813.0	+	37781.1i	0.0424303	+	0.0734914i
$718$		0			0
$719$	191605.	+	110623.i	0.370637	+	0.213987i	0.673737	−	0.738971i	$-0.264688\pi$
$719$	191605.	+	110623.i	0.370637	+	0.213987i	−0.303100	+	0.952959i	$0.598022\pi$
$720$		0			0
$721$	−132853.	+	179852.i	−0.255565	+	0.345975i
$722$		0			0
$723$	−24483.9	−	14135.8i	−0.0468387	−	0.0270423i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	689793.			1.30512			0.652559	−	0.757738i	$-0.273695\pi$
$727$	689793.			1.30512			0.652559	+	0.757738i	$0.273695\pi$
$728$		0			0
$729$	495646.			0.932646
$730$		0			0
$731$	−860819.	+	496994.i	−1.61093	+	0.930072i
$732$		0			0
$733$	−347322.	+	601579.i	−0.646434	+	1.11966i	0.337534	+	0.941313i	$0.390407\pi$
$733$	−347322.	+	601579.i	−0.646434	+	1.11966i	−0.983968	+	0.178344i	$0.942926\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−205525.	−	118660.i	−0.378381	−	0.218459i
$738$		0			0
$739$	−298417.	−	516873.i	−0.546430	−	0.946445i	−0.998515	−	0.0544702i	$-0.982653\pi$
$739$	−298417.	−	516873.i	−0.546430	−	0.946445i	0.452085	−	0.891975i	$-0.350680\pi$
$740$		0			0
$741$			508367.i			0.925851i
$742$		0			0
$743$			246075.i			0.445749i	0.974847	+	0.222874i	$0.0715440\pi$
$743$			246075.i			0.445749i	−0.974847	+	0.222874i	$0.928456\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	17904.4	−	31011.4i	0.0320863	−	0.0555751i
$748$		0			0
$749$	−685707.	−	506518.i	−1.22229	−	0.902883i
$750$		0			0
$751$	−300133.	+	519845.i	−0.532149	+	0.921709i	0.467147	+	0.884180i	$0.345282\pi$
$751$	−300133.	+	519845.i	−0.532149	+	0.921709i	−0.999296	+	0.0375292i	$0.988051\pi$
$752$		0			0
$753$	−385737.	+	222705.i	−0.680301	+	0.392772i
$754$		0			0
$755$		0			0
$756$		0			0
$757$			526244.i			0.918323i	0.888353	+	0.459161i	$0.151850\pi$
$757$			526244.i			0.918323i	−0.888353	+	0.459161i	$0.848150\pi$
$758$		0			0
$759$	−841090.	+	485604.i	−1.46002	+	0.842943i
$760$		0			0
$761$	−49134.9	−	28368.1i	−0.0848440	−	0.0489847i	0.456978	−	0.889478i	$-0.348932\pi$
$761$	−49134.9	−	28368.1i	−0.0848440	−	0.0489847i	−0.541822	+	0.840493i	$0.682265\pi$
$762$		0			0
$763$	151339.	+	347269.i	0.259957	+	0.596509i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−259078.	+	149579.i	−0.440392	+	0.254261i
$768$		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
$773$	−226678.	−	392618.i	−0.379359	−	0.657070i	0.611610	−	0.791160i	$-0.290522\pi$
$773$	−226678.	−	392618.i	−0.379359	−	0.657070i	−0.990969	+	0.134090i	$0.957189\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−121156.	+	1.07126e6i	−0.200679	+	1.77440i
$778$		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.			0.793650
$784$		0			0
$785$		0			0
$786$		0			0
$787$	504381.	+	873614.i	0.814347	+	1.41049i	0.909796	+	0.415056i	$0.136238\pi$
$787$	504381.	+	873614.i	0.814347	+	1.41049i	−0.0954489	+	0.995434i	$0.530429\pi$
$788$		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
$793$	−309154.	−	178490.i	−0.491618	−	0.283836i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	594164.			0.935384			0.467692	−	0.883892i	$-0.345086\pi$
$797$	594164.			0.935384			0.467692	+	0.883892i	$0.345086\pi$
$798$		0			0
$799$	−604617.			−0.947080
$800$		0			0
$801$	8254.73	−	4765.87i	0.0128658	−	0.00742809i
$802$		0			0
$803$	60235.3	−	104331.i	0.0934157	−	0.161801i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−1.02273e6	−	590472.i	−1.57041	−	0.906676i
$808$		0			0
$809$	−474663.	−	822141.i	−0.725251	−	1.25617i	−0.958870	−	0.283844i	$-0.908390\pi$
$809$	−474663.	−	822141.i	−0.725251	−	1.25617i	0.233619	−	0.972328i	$-0.424943\pi$
$810$		0			0
$811$			920610.i			1.39970i	0.714291	+	0.699849i	$0.246749\pi$
$811$			920610.i			1.39970i	−0.714291	+	0.699849i	$0.753251\pi$
$812$		0			0
$813$			71222.4i			0.107755i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	719343.	−	1.24594e6i	1.07769	−	1.86661i
$818$		0			0
$819$	18526.8	−	25080.9i	0.0276205	−	0.0373917i
$820$		0			0
$821$	267658.	−	463597.i	0.397094	−	0.687787i	−0.596272	−	0.802783i	$-0.703352\pi$
$821$	267658.	−	463597.i	0.397094	−	0.687787i	0.993366	+	0.114995i	$0.0366853\pi$
$822$		0			0
$823$	389535.	−	224898.i	0.575105	−	0.332037i	−0.184081	−	0.982911i	$-0.558931\pi$
$823$	389535.	−	224898.i	0.575105	−	0.332037i	0.759186	+	0.650874i	$0.225597\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	166361.i		−	0.243243i	−0.992577	−	0.121622i	$-0.961191\pi$
$827$		−	166361.i		−	0.243243i	0.992577	−	0.121622i	$-0.0388095\pi$
$828$		0			0
$829$	−905482.	+	522780.i	−1.31756	+	0.760694i	−0.983336	−	0.181799i	$-0.941808\pi$
$829$	−905482.	+	522780.i	−1.31756	+	0.760694i	−0.334225	+	0.942493i	$0.608475\pi$
$830$		0			0
$831$	607461.	+	350718.i	0.879663	+	0.507874i
$832$		0			0
$833$	−205312.	−	667588.i	−0.295886	−	0.962096i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−109400.	+	63162.3i	−0.156159	+	0.0901585i
$838$		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
$843$	30631.0	+	53054.4i	0.0431028	+	0.0746563i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−32069.7	+	43414.8i	−0.0447021	+	0.0605162i
$848$		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.			0.647773			0.323886	−	0.946096i	$-0.395010\pi$
$853$	471325.			0.647773			0.323886	+	0.946096i	$0.395010\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−516160.	−	894015.i	−0.702785	−	1.21726i	−0.967485	−	0.252929i	$-0.918606\pi$
$857$	−516160.	−	894015.i	−0.702785	−	1.21726i	0.264700	−	0.964331i	$-0.414727\pi$
$858$		0			0
$859$	166917.	+	96369.5i	0.226211	+	0.130603i	0.608823	−	0.793306i	$-0.291642\pi$
$859$	166917.	+	96369.5i	0.226211	+	0.130603i	−0.382612	+	0.923909i	$0.624975\pi$
$860$		0			0
$861$	3727.35	−	1624.37i	0.00502799	−	0.00219119i
$862$		0			0
$863$	455079.	+	262740.i	0.611034	+	0.352781i	0.773370	−	0.633955i	$-0.218569\pi$
$863$	455079.	+	262740.i	0.611034	+	0.352781i	−0.162336	+	0.986736i	$0.551903\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	10199.7			0.0135690
$868$		0			0
$869$	1.05127e6			1.39212
$870$		0			0
$871$	−213414.	+	123214.i	−0.281311	+	0.162415i
$872$		0			0
$873$	11437.0	−	19809.5i	0.0150067	−	0.0259923i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−796209.	−	459691.i	−1.03521	−	0.597678i	−0.116736	−	0.993163i	$-0.537243\pi$
$877$	−796209.	−	459691.i	−1.03521	−	0.597678i	−0.918472	+	0.395485i	$0.870577\pi$
$878$		0			0
$879$	175055.	+	303204.i	0.226567	+	0.392425i
$880$		0			0
$881$			307096.i			0.395660i	0.980236	+	0.197830i	$0.0633894\pi$
$881$			307096.i			0.395660i	−0.980236	+	0.197830i	$0.936611\pi$
$882$		0			0
$883$			747006.i			0.958082i	0.877792	+	0.479041i	$0.159016\pi$
$883$			747006.i			0.958082i	−0.877792	+	0.479041i	$0.840984\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	203773.	−	352945.i	0.259000	−	0.448600i	−0.706975	−	0.707239i	$-0.749941\pi$
$887$	203773.	−	352945.i	0.259000	−	0.448600i	0.965974	+	0.258639i	$0.0832739\pi$
$888$		0			0
$889$	−124294.	+	1.09901e6i	−0.157271	+	1.39059i
$890$		0			0
$891$	434925.	−	753312.i	0.547847	−	0.948898i
$892$		0			0
$893$	757872.	−	437557.i	0.950370	−	0.548696i
$894$		0			0
$895$		0			0
$896$		0			0
$897$			1.00849e6i			1.25339i
$898$		0			0
$899$	−106982.	+	61765.9i	−0.132370	+	0.0764239i
$900$		0			0
$901$	−599454.	−	346095.i	−0.738425	−	0.426330i
$902$		0			0
$903$	−1.42244e6	+	619897.i	−1.74445	+	0.760228i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	343360.	−	198239.i	0.417383	−	0.240976i	−0.276574	−	0.960993i	$-0.589199\pi$
$907$	343360.	−	198239.i	0.417383	−	0.240976i	0.693957	+	0.720016i	$0.255866\pi$
$908$		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
$913$	459929.	+	796620.i	0.551758	+	0.955673i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−686877.	−	507382.i	−0.816846	−	0.603388i
$918$		0			0
$919$	−175122.	+	303321.i	−0.207353	+	0.359146i	−0.950880	−	0.309560i	$-0.899818\pi$
$919$	−175122.	+	303321.i	−0.207353	+	0.359146i	0.743527	+	0.668706i	$0.233152\pi$
$920$		0			0
$921$	−49094.0	−	85033.2i	−0.0578774	−	0.100247i
$922$		0			0
$923$	1.05575e6			1.23924
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−11144.3	−	19302.5i	−0.0129686	−	0.0224623i
$928$		0			0
$929$	1.34168e6	+	774617.i	1.55459	+	0.897544i	0.997758	+	0.0669199i	$0.0213172\pi$
$929$	1.34168e6	+	774617.i	1.55459	+	0.897544i	0.556833	+	0.830624i	$0.312016\pi$
$930$		0			0
$931$	740483.	+	688222.i	0.854310	+	0.794016i
$932$		0			0
$933$	−737401.	−	425739.i	−0.847111	−	0.489080i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−431939.			−0.491975			−0.245988	−	0.969273i	$-0.579112\pi$
$937$	−431939.			−0.491975			−0.245988	+	0.969273i	$0.579112\pi$
$938$		0			0
$939$	−827664.			−0.938692
$940$		0			0
$941$	−560859.	+	323812.i	−0.633395	+	0.365691i	−0.782066	−	0.623196i	$-0.785834\pi$
$941$	−560859.	+	323812.i	−0.633395	+	0.365691i	0.148671	+	0.988887i	$0.452501\pi$
$942$		0			0
$943$	−3739.33	+	6476.71i	−0.00420504	+	0.00728335i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−1.51615e6	−	875350.i	−1.69061	−	0.976071i	−0.954028	−	0.299718i	$-0.903107\pi$
$947$	−1.51615e6	−	875350.i	−1.69061	−	0.976071i	−0.736577	−	0.676353i	$-0.763559\pi$
$948$		0			0
$949$	−62547.3	−	108335.i	−0.0694506	−	0.120292i
$950$		0			0
$951$			83586.8i			0.0924223i
$952$		0			0
$953$		−	1.11747e6i		−	1.23041i	−0.788367	−	0.615206i	$-0.789073\pi$
$953$		−	1.11747e6i		−	1.23041i	0.788367	−	0.615206i	$-0.210927\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	401039.	−	694619.i	0.437887	−	0.758443i
$958$		0			0
$959$	−233971.	+	101964.i	−0.254405	+	0.110869i
$960$		0			0
$961$	−445725.	+	772018.i	−0.482637	+	0.835951i
$962$		0			0
$963$	73592.9	−	42488.9i	0.0793567	−	0.0458166i
$964$		0			0
$965$		0			0
$966$		0			0
$967$			1.24016e6i			1.32625i	0.748508	+	0.663126i	$0.230771\pi$
$967$			1.24016e6i			1.32625i	−0.748508	+	0.663126i	$0.769229\pi$
$968$		0			0
$969$	−983001.	+	567536.i	−1.04690	+	0.604430i
$970$		0			0
$971$	−429350.	−	247885.i	−0.455379	−	0.262913i	0.254720	−	0.967015i	$-0.418017\pi$
$971$	−429350.	−	247885.i	−0.455379	−	0.262913i	−0.710099	+	0.704101i	$0.751350\pi$
$972$		0			0
$973$	−115676.	+	1.02280e6i	−0.122184	+	1.08035i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−545099.	+	314713.i	−0.571066	+	0.329705i	−0.757575	−	0.652748i	$-0.773616\pi$
$977$	−545099.	+	314713.i	−0.571066	+	0.329705i	0.186509	+	0.982453i	$0.440283\pi$
$978$		0			0
$979$			244851.i			0.255468i
$980$		0			0
$981$	−37760.4			−0.0392373
$982$		0			0
$983$	117853.	+	204127.i	0.121964	+	0.211248i	0.920542	−	0.390643i	$-0.127747\pi$
$983$	117853.	+	204127.i	0.121964	+	0.211248i	−0.798578	+	0.601891i	$0.794414\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−937848.	−	106068.i	−0.962716	−	0.108880i
$988$		0			0
$989$	1.42701e6	−	2.47166e6i	1.45893	−	2.52695i
$990$		0			0
$991$	−651369.	−	1.12820e6i	−0.663254	−	1.14879i	−0.979756	−	0.200198i	$-0.935842\pi$
$991$	−651369.	−	1.12820e6i	−0.663254	−	1.14879i	0.316502	−	0.948592i	$-0.397492\pi$
$992$		0			0
$993$	−1.19185e6			−1.20872
$994$		0			0
$995$		0			0
$996$		0			0
$997$	881908.	+	1.52751e6i	0.887224	+	1.53672i	0.843143	+	0.537689i	$0.180702\pi$
$997$	881908.	+	1.52751e6i	0.887224	+	1.53672i	0.0440803	+	0.999028i	$0.485964\pi$
$998$		0			0
$999$	1.45032e6	+	837341.i	1.45322	+	0.839018i

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

)

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.5.r.a.61.4	✓	20	5.2	odd	4
140.5.r.a.101.4	yes	20	35.17	even	12
700.5.o.b.549.6		40	35.24	odd	6	inner
700.5.o.b.549.15		40	7.3	odd	6	inner
700.5.o.b.649.6		40	1.1	even	1	trivial
700.5.o.b.649.15		40	5.4	even	2	inner
700.5.s.b.101.7		20	35.3	even	12
700.5.s.b.201.7		20	5.3	odd	4
980.5.d.a.881.6		20	35.2	odd	12
980.5.d.a.881.15		20	35.12	even	12

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Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	700.5.o.b.649.6

Level	$700$
Weight	$5$
Character	700.649
Analytic conductor	$72.359$
Analytic rank	$0$
Dimension	$40$
Inner twists	$4$