LMFDB - Embedded newform 81.6.e.a.19.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [81,6,Mod(10,81)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(81, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([8]))

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("81.10");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 81 = 3^{4} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	81.e (of order $9$, degree $6$, 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:	$12.9910894049$
Analytic rank:	$0$
Dimension:	$84$
Relative dimension:	$14$ over $\Q(\zeta_{9})$
Twist minimal:	no (minimal twist has level 27)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			19.11
Character	$\chi$	$=$	81.19
Dual form			81.6.e.a.64.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(5.55790 - 2.02291i) q^{2} +(2.28464 - 1.91704i) q^{4} +(3.90711 + 22.1583i) q^{5} +(69.5798 + 58.3844i) q^{7} +(-85.8137 + 148.634i) q^{8} +O(q^{10})$	\(q+(5.55790 - 2.02291i) q^{2} +(2.28464 - 1.91704i) q^{4} +(3.90711 + 22.1583i) q^{5} +(69.5798 + 58.3844i) q^{7} +(-85.8137 + 148.634i) q^{8} +(66.5396 + 115.250i) q^{10} +(-47.2935 + 268.215i) q^{11} +(263.041 + 95.7391i) q^{13} +(504.823 + 183.741i) q^{14} +(-192.844 + 1093.67i) q^{16} +(736.555 + 1275.75i) q^{17} +(121.121 - 209.787i) q^{19} +(51.4047 + 43.1337i) q^{20} +(279.722 + 1586.38i) q^{22} +(101.784 - 85.4070i) q^{23} +(2460.81 - 895.663i) q^{25} +1655.63 q^{26} +270.890 q^{28} +(-7780.54 + 2831.88i) q^{29} +(5831.61 - 4893.30i) q^{31} +(186.902 + 1059.97i) q^{32} +(6674.43 + 5600.51i) q^{34} +(-1021.84 + 1769.89i) q^{35} +(-5732.04 - 9928.18i) q^{37} +(248.796 - 1410.99i) q^{38} +(-3628.76 - 1320.76i) q^{40} +(5445.05 + 1981.84i) q^{41} +(-3076.71 + 17448.9i) q^{43} +(406.129 + 703.437i) q^{44} +(392.935 - 680.584i) q^{46} +(-9830.35 - 8248.65i) q^{47} +(-1485.89 - 8426.92i) q^{49} +(11865.1 - 9956.00i) q^{50} +(784.489 - 285.531i) q^{52} +19826.8 q^{53} -6127.97 q^{55} +(-14648.8 + 5331.72i) q^{56} +(-37514.8 + 31478.6i) q^{58} +(2930.29 + 16618.5i) q^{59} +(-4754.68 - 3989.65i) q^{61} +(22512.8 - 38993.3i) q^{62} +(-14585.7 - 25263.1i) q^{64} +(-1093.69 + 6202.61i) q^{65} +(-21549.3 - 7843.29i) q^{67} +(4128.43 + 1502.63i) q^{68} +(-2098.99 + 11903.9i) q^{70} +(-22448.7 - 38882.4i) q^{71} +(32058.0 - 55526.1i) q^{73} +(-51941.9 - 43584.4i) q^{74} +(-125.453 - 711.481i) q^{76} +(-18950.2 + 15901.1i) q^{77} +(95268.0 - 34674.7i) q^{79} -24987.4 q^{80} +34272.1 q^{82} +(9484.75 - 3452.17i) q^{83} +(-25390.7 + 21305.3i) q^{85} +(18197.5 + 103203. i) q^{86} +(-35807.3 - 30045.9i) q^{88} +(22900.3 - 39664.6i) q^{89} +(12712.7 + 22019.0i) q^{91} +(68.8113 - 390.248i) q^{92} +(-71322.4 - 25959.2i) q^{94} +(5121.77 + 1864.17i) q^{95} +(-24215.3 + 137332. i) q^{97} +(-25305.3 - 43830.1i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q + 6 q^{2} - 6 q^{4} + 93 q^{5} - 6 q^{7} - 573 q^{8}+O(q^{10}) $ 84 * q + 6 * q^2 - 6 * q^4 + 93 * q^5 - 6 * q^7 - 573 * q^8	$ 84 q + 6 q^{2} - 6 q^{4} + 93 q^{5} - 6 q^{7} - 573 q^{8} - 3 q^{10} - 111 q^{11} - 6 q^{13} + 1641 q^{14} + 90 q^{16} - 3465 q^{17} - 3 q^{19} - 9987 q^{20} - 2850 q^{22} + 7716 q^{23} + 4953 q^{25} + 7806 q^{26} - 12 q^{28} + 20418 q^{29} - 6657 q^{31} - 51192 q^{32} - 11394 q^{34} - 35868 q^{35} - 3 q^{37} + 44076 q^{38} + 12441 q^{40} + 79077 q^{41} - 9465 q^{43} - 110757 q^{44} - 3 q^{46} - 103557 q^{47} + 5484 q^{49} + 105513 q^{50} + 68625 q^{52} + 206406 q^{53} - 12 q^{55} + 147237 q^{56} - 9753 q^{58} - 116484 q^{59} - 70116 q^{61} - 246066 q^{62} - 86019 q^{64} + 19815 q^{65} + 48117 q^{67} + 48105 q^{68} + 270111 q^{70} - 279531 q^{71} - 27012 q^{73} - 233691 q^{74} - 125670 q^{76} + 345135 q^{77} - 216186 q^{79} + 924114 q^{80} - 12 q^{82} + 370401 q^{83} - 43731 q^{85} - 116682 q^{86} + 371418 q^{88} - 154827 q^{89} - 91002 q^{91} - 1279059 q^{92} + 11667 q^{94} - 1087671 q^{95} - 420621 q^{97} - 463410 q^{98}+O(q^{100}) $ 84 * q + 6 * q^2 - 6 * q^4 + 93 * q^5 - 6 * q^7 - 573 * q^8 - 3 * q^10 - 111 * q^11 - 6 * q^13 + 1641 * q^14 + 90 * q^16 - 3465 * q^17 - 3 * q^19 - 9987 * q^20 - 2850 * q^22 + 7716 * q^23 + 4953 * q^25 + 7806 * q^26 - 12 * q^28 + 20418 * q^29 - 6657 * q^31 - 51192 * q^32 - 11394 * q^34 - 35868 * q^35 - 3 * q^37 + 44076 * q^38 + 12441 * q^40 + 79077 * q^41 - 9465 * q^43 - 110757 * q^44 - 3 * q^46 - 103557 * q^47 + 5484 * q^49 + 105513 * q^50 + 68625 * q^52 + 206406 * q^53 - 12 * q^55 + 147237 * q^56 - 9753 * q^58 - 116484 * q^59 - 70116 * q^61 - 246066 * q^62 - 86019 * q^64 + 19815 * q^65 + 48117 * q^67 + 48105 * q^68 + 270111 * q^70 - 279531 * q^71 - 27012 * q^73 - 233691 * q^74 - 125670 * q^76 + 345135 * q^77 - 216186 * q^79 + 924114 * q^80 - 12 * q^82 + 370401 * q^83 - 43731 * q^85 - 116682 * q^86 + 371418 * q^88 - 154827 * q^89 - 91002 * q^91 - 1279059 * q^92 + 11667 * q^94 - 1087671 * q^95 - 420621 * q^97 - 463410 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/81\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{8}{9}\right)$

Coefficient data

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

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

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

$2$	5.55790	−	2.02291i	0.982507	−	0.357603i	0.199692	−	0.979859i	$-0.436006\pi$
$2$	5.55790	−	2.02291i	0.982507	−	0.357603i	0.782814	+	0.622255i	$0.213783\pi$
$3$		0			0
$3$		0			0
$4$	2.28464	−	1.91704i	0.0713950	−	0.0599075i
$5$	3.90711	+	22.1583i	0.0698925	+	0.396380i	0.999605	+	0.0280948i	$0.00894402\pi$
$5$	3.90711	+	22.1583i	0.0698925	+	0.396380i	−0.929713	+	0.368286i	$0.879945\pi$
$6$		0			0
$7$	69.5798	+	58.3844i	0.536708	+	0.450351i	0.870410	−	0.492327i	$-0.163854\pi$
$7$	69.5798	+	58.3844i	0.536708	+	0.450351i	−0.333702	+	0.942678i	$0.608298\pi$
$8$	−85.8137	+	148.634i	−0.474058	+	0.821093i
$9$		0			0
$10$	66.5396	+	115.250i	0.210417	+	0.364453i
$11$	−47.2935	+	268.215i	−0.117847	+	0.668345i	0.867454	+	0.497518i	$0.165755\pi$
$11$	−47.2935	+	268.215i	−0.117847	+	0.668345i	−0.985301	+	0.170827i	$0.945356\pi$
$12$		0			0
$13$	263.041	+	95.7391i	0.431683	+	0.157120i	0.548717	−	0.836008i	$-0.315116\pi$
$13$	263.041	+	95.7391i	0.431683	+	0.157120i	−0.117034	+	0.993128i	$0.537339\pi$
$14$	504.823	+	183.741i	0.688366	+	0.250545i
$15$		0			0
$16$	−192.844	+	1093.67i	−0.188324	+	1.06804i
$17$	736.555	+	1275.75i	0.618135	+	1.07064i	0.989826	+	0.142284i	$0.0454447\pi$
$17$	736.555	+	1275.75i	0.618135	+	1.07064i	−0.371691	+	0.928356i	$0.621222\pi$
$18$		0			0
$19$	121.121	−	209.787i	0.0769723	−	0.133320i	−0.824970	−	0.565177i	$-0.808808\pi$
$19$	121.121	−	209.787i	0.0769723	−	0.133320i	0.901942	+	0.431857i	$0.142141\pi$
$20$	51.4047	+	43.1337i	0.0287361	+	0.0241125i
$21$		0			0
$22$	279.722	+	1586.38i	0.123217	+	0.698796i
$23$	101.784	−	85.4070i	0.0401200	−	0.0336646i	−0.622507	−	0.782614i	$-0.713886\pi$
$23$	101.784	−	85.4070i	0.0401200	−	0.0336646i	0.662627	+	0.748949i	$0.269441\pi$
$24$		0			0
$25$	2460.81	−	895.663i	0.787460	−	0.286612i
$26$	1655.63			0.480318
$27$		0			0
$28$	270.890			0.0652976
$29$	−7780.54	+	2831.88i	−1.71797	+	0.625289i	−0.997660	−	0.0683681i	$-0.978221\pi$
$29$	−7780.54	+	2831.88i	−1.71797	+	0.625289i	−0.720306	+	0.693657i	$0.755999\pi$
$30$		0			0
$31$	5831.61	−	4893.30i	1.08989	−	0.914530i	0.0931898	−	0.995648i	$-0.470294\pi$
$31$	5831.61	−	4893.30i	1.08989	−	0.914530i	0.996704	+	0.0811185i	$0.0258492\pi$
$32$	186.902	+	1059.97i	0.0322655	+	0.182987i
$33$		0			0
$34$	6674.43	+	5600.51i	0.990186	+	0.830865i
$35$	−1021.84	+	1769.89i	−0.140999	+	0.244217i
$36$		0			0
$37$	−5732.04	−	9928.18i	−0.688343	−	1.19224i	−0.972374	−	0.233429i	$-0.925005\pi$
$37$	−5732.04	−	9928.18i	−0.688343	−	1.19224i	0.284031	−	0.958815i	$-0.408328\pi$
$38$	248.796	−	1410.99i	0.0279502	−	0.158513i
$39$		0			0
$40$	−3628.76	−	1320.76i	−0.358598	−	0.130519i
$41$	5445.05	+	1981.84i	0.505874	+	0.184123i	0.582334	−	0.812950i	$-0.302140\pi$
$41$	5445.05	+	1981.84i	0.505874	+	0.184123i	−0.0764603	+	0.997073i	$0.524362\pi$
$42$		0			0
$43$	−3076.71	+	17448.9i	−0.253755	+	1.43912i	0.545492	+	0.838116i	$0.316343\pi$
$43$	−3076.71	+	17448.9i	−0.253755	+	1.43912i	−0.799247	+	0.601003i	$0.794768\pi$
$44$	406.129	+	703.437i	0.0316252	+	0.0547764i
$45$		0			0
$46$	392.935	−	680.584i	0.0273796	−	0.0474228i
$47$	−9830.35	−	8248.65i	−0.649119	−	0.544676i	0.257684	−	0.966229i	$-0.417041\pi$
$47$	−9830.35	−	8248.65i	−0.649119	−	0.544676i	−0.906804	+	0.421553i	$0.861485\pi$
$48$		0			0
$49$	−1485.89	−	8426.92i	−0.0884092	−	0.501394i
$50$	11865.1	−	9956.00i	0.671192	−	0.563197i
$51$		0			0
$52$	784.489	−	285.531i	0.0402327	−	0.0146435i
$53$	19826.8			0.969532			0.484766	−	0.874644i	$-0.338905\pi$
$53$	19826.8			0.969532			0.484766	+	0.874644i	$0.338905\pi$
$54$		0			0
$55$	−6127.97			−0.273155
$56$	−14648.8	+	5331.72i	−0.624211	+	0.227194i
$57$		0			0
$58$	−37514.8	+	31478.6i	−1.46431	+	1.22870i
$59$	2930.29	+	16618.5i	0.109592	+	0.621530i	0.989286	+	0.145989i	$0.0466364\pi$
$59$	2930.29	+	16618.5i	0.109592	+	0.621530i	−0.879694	+	0.475541i	$0.842252\pi$
$60$		0			0
$61$	−4754.68	−	3989.65i	−0.163605	−	0.137281i	0.557310	−	0.830305i	$-0.311834\pi$
$61$	−4754.68	−	3989.65i	−0.163605	−	0.137281i	−0.720915	+	0.693024i	$0.756278\pi$
$62$	22512.8	−	38993.3i	0.743790	−	1.28828i
$63$		0			0
$64$	−14585.7	−	25263.1i	−0.445119	−	0.770969i
$65$	−1093.69	+	6202.61i	−0.0321078	+	0.182092i
$66$		0			0
$67$	−21549.3	−	7843.29i	−0.586470	−	0.213457i	0.0317063	−	0.999497i	$-0.489906\pi$
$67$	−21549.3	−	7843.29i	−0.586470	−	0.213457i	−0.618176	+	0.786040i	$0.712128\pi$
$68$	4128.43	+	1502.63i	0.108271	+	0.0394075i
$69$		0			0
$70$	−2098.99	+	11903.9i	−0.0511994	+	0.290366i
$71$	−22448.7	−	38882.4i	−0.528502	−	0.915391i	−0.999448	−	0.0332295i	$-0.989421\pi$
$71$	−22448.7	−	38882.4i	−0.528502	−	0.915391i	0.470946	−	0.882162i	$-0.343913\pi$
$72$		0			0
$73$	32058.0	−	55526.1i	0.704092	−	1.21952i	−0.262926	−	0.964816i	$-0.584688\pi$
$73$	32058.0	−	55526.1i	0.704092	−	1.21952i	0.967018	−	0.254707i	$-0.0819791\pi$
$74$	−51941.9	−	43584.4i	−1.10265	−	0.925235i
$75$		0			0
$76$	−125.453	−	711.481i	−0.00249143	−	0.0141296i
$77$	−18950.2	+	15901.1i	−0.364240	+	0.305633i
$78$		0			0
$79$	95268.0	−	34674.7i	1.71743	−	0.625094i	0.719820	−	0.694161i	$-0.244224\pi$
$79$	95268.0	−	34674.7i	1.71743	−	0.625094i	0.997612	+	0.0690671i	$0.0220022\pi$
$80$	−24987.4			−0.436511
$81$		0			0
$82$	34272.1			0.562867
$83$	9484.75	−	3452.17i	0.151123	−	0.0550043i	−0.265351	−	0.964152i	$-0.585488\pi$
$83$	9484.75	−	3452.17i	0.151123	−	0.0550043i	0.416474	+	0.909148i	$0.363266\pi$
$84$		0			0
$85$	−25390.7	+	21305.3i	−0.381178	+	0.319846i
$86$	18197.5	+	103203.i	0.265317	+	1.50469i
$87$		0			0
$88$	−35807.3	−	30045.9i	−0.492907	−	0.413598i
$89$	22900.3	−	39664.6i	0.306455	−	0.530796i	−0.671129	−	0.741341i	$-0.734190\pi$
$89$	22900.3	−	39664.6i	0.306455	−	0.530796i	0.977584	+	0.210545i	$0.0675237\pi$
$90$		0			0
$91$	12712.7	+	22019.0i	0.160929	+	0.278736i
$92$	68.8113	−	390.248i	0.000847599	−	0.00480697i
$93$		0			0
$94$	−71322.4	−	25959.2i	−0.832542	−	0.303020i
$95$	5121.77	+	1864.17i	0.0582252	+	0.0211922i
$96$		0			0
$97$	−24215.3	+	137332.i	−0.261312	+	1.48198i	0.518022	+	0.855367i	$0.326669\pi$
$97$	−24215.3	+	137332.i	−0.261312	+	1.48198i	−0.779334	+	0.626608i	$0.784443\pi$
$98$	−25305.3	−	43830.1i	−0.266163	−	0.461007i
$99$		0			0
$100$	3905.05	−	6763.74i	0.0390505	−	0.0676374i
$101$	122748.	+	102998.i	1.19732	+	1.00467i	0.999702	+	0.0243922i	$0.00776506\pi$
$101$	122748.	+	102998.i	1.19732	+	1.00467i	0.197618	+	0.980279i	$0.436679\pi$
$102$		0			0
$103$	15331.6	+	86949.9i	0.142395	+	0.807562i	0.969422	+	0.245400i	$0.0789193\pi$
$103$	15331.6	+	86949.9i	0.142395	+	0.807562i	−0.827027	+	0.562162i	$0.809970\pi$
$104$	−36802.6	+	30881.0i	−0.333653	+	0.279968i
$105$		0			0
$106$	110195.	−	40107.7i	0.952572	−	0.346708i
$107$	88915.7			0.750791			0.375396	−	0.926865i	$-0.377507\pi$
$107$	88915.7			0.750791			0.375396	+	0.926865i	$0.377507\pi$
$108$		0			0
$109$	105032.			0.846748			0.423374	−	0.905955i	$-0.360846\pi$
$109$	105032.			0.846748			0.423374	+	0.905955i	$0.360846\pi$
$110$	−34058.6	+	12396.3i	−0.268377	+	0.0976813i
$111$		0			0
$112$	−77271.2	+	64838.3i	−0.582067	+	0.488412i
$113$	27098.5	+	153683.i	0.199641	+	1.13222i	0.905653	+	0.424019i	$0.139381\pi$
$113$	27098.5	+	153683.i	0.199641	+	1.13222i	−0.706013	+	0.708199i	$0.749508\pi$
$114$		0			0
$115$	2290.16	+	1921.67i	0.0161481	+	0.0135499i
$116$	−12346.9	+	21385.4i	−0.0851947	+	0.147561i
$117$		0			0
$118$	49904.0	+	86436.2i	0.329936	+	0.571467i
$119$	−23234.6	+	131770.i	−0.150407	+	0.852999i
$120$		0			0
$121$	81636.0	+	29713.1i	0.506896	+	0.184495i
$122$	−34496.7	−	12555.8i	−0.209835	−	0.0763737i
$123$		0			0
$124$	3942.47	−	22358.9i	0.0230258	−	0.130586i
$125$	64617.6	+	111921.i	0.369893	+	0.640673i
$126$		0			0
$127$	23223.5	−	40224.3i	0.127767	−	0.221299i	−0.795044	−	0.606551i	$-0.792552\pi$
$127$	23223.5	−	40224.3i	0.127767	−	0.221299i	0.922811	+	0.385253i	$0.125886\pi$
$128$	−158555.	−	133043.i	−0.855372	−	0.717742i
$129$		0			0
$130$	6468.72	+	36685.9i	0.0335707	+	0.190389i
$131$	189429.	−	158950.i	0.964427	−	0.809250i	−0.0172406	−	0.999851i	$-0.505488\pi$
$131$	189429.	−	158950.i	0.964427	−	0.809250i	0.981668	+	0.190601i	$0.0610437\pi$
$132$		0			0
$133$	20675.8	−	7525.39i	0.101352	−	0.0368893i
$134$	−135635.			−0.652543
$135$		0			0
$136$	−252826.			−1.17213
$137$	−37319.2	+	13583.1i	−0.169875	+	0.0618296i	−0.425558	−	0.904931i	$-0.639922\pi$
$137$	−37319.2	+	13583.1i	−0.169875	+	0.0618296i	0.255682	+	0.966761i	$0.417700\pi$
$138$		0			0
$139$	297276.	−	249445.i	1.30504	−	1.09506i	0.315788	−	0.948830i	$-0.397731\pi$
$139$	297276.	−	249445.i	1.30504	−	1.09506i	0.989251	−	0.146228i	$-0.0467134\pi$
$140$	1058.40	+	6002.47i	0.00456382	+	0.0258827i
$141$		0			0
$142$	−203423.	−	170692.i	−0.846603	−	0.710384i
$143$	−38118.7	+	66023.6i	−0.155883	+	0.269997i
$144$		0			0
$145$	−93149.3	−	161339.i	−0.367925	−	0.637265i
$146$	65850.9	−	373459.i	0.255670	−	1.44998i
$147$		0			0
$148$	−32128.3	−	11693.8i	−0.120569	−	0.0438834i
$149$	−469863.	−	171016.i	−1.73382	−	0.631061i	−0.734933	−	0.678139i	$-0.762787\pi$
$149$	−469863.	−	171016.i	−1.73382	−	0.631061i	−0.998891	+	0.0470788i	$0.985009\pi$
$150$		0			0
$151$	−54044.9	+	306504.i	−0.192891	+	1.09394i	0.722499	+	0.691372i	$0.242993\pi$
$151$	−54044.9	+	306504.i	−0.192891	+	1.09394i	−0.915390	+	0.402568i	$0.868118\pi$
$152$	20787.6	+	36005.2i	0.0729787	+	0.126403i
$153$		0			0
$154$	−73156.8	+	126711.i	−0.248572	+	0.430540i
$155$	131212.	+	110100.i	0.438677	+	0.368094i
$156$		0			0
$157$	−65481.3	−	371363.i	−0.212016	−	1.20240i	−0.886010	−	0.463665i	$-0.846534\pi$
$157$	−65481.3	−	371363.i	−0.212016	−	1.20240i	0.673995	−	0.738736i	$-0.264577\pi$
$158$	459346.	−	385437.i	1.46385	−	1.22832i
$159$		0			0
$160$	−22757.0	+	8282.87i	−0.0702773	+	0.0255788i
$161$	12068.6			0.0366936
$162$		0			0
$163$	−184937.			−0.545198			−0.272599	−	0.962128i	$-0.587883\pi$
$163$	−184937.			−0.545198			−0.272599	+	0.962128i	$0.587883\pi$
$164$	16239.2	−	5910.59i	0.0471472	−	0.0171602i
$165$		0			0
$166$	45731.8	−	38373.6i	0.128810	−	0.108084i
$167$	−86830.0	−	492437.i	−0.240923	−	1.36634i	−0.829773	−	0.558101i	$-0.811530\pi$
$167$	−86830.0	−	492437.i	−0.240923	−	1.36634i	0.588850	−	0.808242i	$-0.299581\pi$
$168$		0			0
$169$	−224402.	−	188296.i	−0.604381	−	0.507136i
$170$	−98020.3	+	169776.i	−0.260132	+	0.450562i
$171$		0			0
$172$	26421.0	+	45762.6i	0.0680971	+	0.117948i
$173$	−5824.77	+	33033.9i	−0.0147966	+	0.0839159i	−0.991312	−	0.131533i	$-0.958010\pi$
$173$	−5824.77	+	33033.9i	−0.0147966	+	0.0839159i	0.976515	+	0.215448i	$0.0691213\pi$
$174$		0			0
$175$	223516.	+	81353.0i	0.551712	+	0.200807i
$176$	−284218.	−	103447.i	−0.691624	−	0.251730i
$177$		0			0
$178$	47040.0	−	266777.i	0.111280	−	0.631100i
$179$	71868.4	+	124480.i	0.167651	+	0.290379i	0.937593	−	0.347734i	$-0.113049\pi$
$179$	71868.4	+	124480.i	0.167651	+	0.290379i	−0.769943	+	0.638113i	$0.779715\pi$
$180$		0			0
$181$	−267616.	+	463524.i	−0.607177	+	1.05166i	0.384526	+	0.923114i	$0.374365\pi$
$181$	−267616.	+	463524.i	−0.607177	+	1.05166i	−0.991703	+	0.128548i	$0.958968\pi$
$182$	115198.	+	96662.7i	0.257790	+	0.216312i
$183$		0			0
$184$	3959.89	+	22457.6i	0.00862260	+	0.0489012i
$185$	197596.	−	165803.i	0.424472	−	0.356175i
$186$		0			0
$187$	−377009.	+	137220.i	−0.788403	+	0.286955i
$188$	−38271.8			−0.0789740
$189$		0			0
$190$	32237.3			0.0647851
$191$	400202.	−	145662.i	0.793773	−	0.288910i	0.0868692	−	0.996220i	$-0.472314\pi$
$191$	400202.	−	145662.i	0.793773	−	0.288910i	0.706903	+	0.707310i	$0.250092\pi$
$192$		0			0
$193$	73786.7	−	61914.4i	0.142589	−	0.119646i	−0.568703	−	0.822543i	$-0.692555\pi$
$193$	73786.7	−	61914.4i	0.142589	−	0.119646i	0.711292	+	0.702897i	$0.248110\pi$
$194$	143223.	+	812260.i	0.273218	+	1.54950i
$195$		0			0
$196$	−19549.5	−	16404.0i	−0.0363492	−	0.0305006i
$197$	−195151.	+	338011.i	−0.358265	+	0.620534i	−0.987671	−	0.156543i	$-0.949965\pi$
$197$	−195151.	+	338011.i	−0.358265	+	0.620534i	0.629406	+	0.777077i	$0.283298\pi$
$198$		0			0
$199$	21457.6	+	37165.6i	0.0384103	+	0.0665286i	0.884591	−	0.466367i	$-0.154437\pi$
$199$	21457.6	+	37165.6i	0.0384103	+	0.0665286i	−0.846181	+	0.532895i	$0.821104\pi$
$200$	−78045.8	+	442620.i	−0.137967	+	0.782448i
$201$		0			0
$202$	890575.	+	324143.i	1.53565	+	0.558931i
$203$	−706706.	−	257220.i	−1.20365	−	0.438091i
$204$		0			0
$205$	−22639.8	+	128396.i	−0.0376259	+	0.213387i
$206$	261103.	+	452244.i	0.428691	+	0.742515i
$207$		0			0
$208$	−155433.	+	269217.i	−0.249106	+	0.431464i
$209$	50539.8	+	42407.9i	0.0800327	+	0.0671554i
$210$		0			0
$211$	−13546.9	−	76828.6i	−0.0209476	−	0.118800i	0.972541	−	0.232732i	$-0.0747665\pi$
$211$	−13546.9	−	76828.6i	−0.0209476	−	0.118800i	−0.993489	+	0.113932i	$0.963655\pi$
$212$	45297.0	−	38008.7i	0.0692197	−	0.0580822i
$213$		0			0
$214$	494184.	−	179868.i	0.737657	−	0.268485i
$215$	−398659.			−0.588174
$216$		0			0
$217$	691455.			0.996814
$218$	583755.	−	212470.i	0.831936	−	0.302800i
$219$		0			0
$220$	−14000.2	+	11747.6i	−0.0195019	+	0.0163641i
$221$	71605.0	+	406092.i	0.0986195	+	0.559299i
$222$		0			0
$223$	64786.7	+	54362.5i	0.0872416	+	0.0732044i	0.685365	−	0.728199i	$-0.259642\pi$
$223$	64786.7	+	54362.5i	0.0872416	+	0.0732044i	−0.598124	+	0.801404i	$0.704087\pi$
$224$	−48881.3	+	84664.9i	−0.0650912	+	0.112741i
$225$		0			0
$226$	461498.	+	799337.i	0.601033	+	1.04102i
$227$	−23061.0	+	130786.i	−0.0297039	+	0.168459i	−0.996051	−	0.0887822i	$-0.971702\pi$
$227$	−23061.0	+	130786.i	−0.0297039	+	0.168459i	0.966347	+	0.257242i	$0.0828136\pi$
$228$		0			0
$229$	−831897.	−	302786.i	−1.04829	−	0.381546i	−0.240272	−	0.970706i	$-0.577237\pi$
$229$	−831897.	−	302786.i	−1.04829	−	0.381546i	−0.808017	+	0.589160i	$0.799459\pi$
$230$	16615.8	+	6047.67i	0.0207111	+	0.00753822i
$231$		0			0
$232$	246763.	−	1.39946e6i	0.300996	−	1.70703i
$233$	−573445.	−	993236.i	−0.691994	−	1.19857i	−0.971184	−	0.238332i	$-0.923399\pi$
$233$	−573445.	−	993236.i	−0.691994	−	1.19857i	0.279190	−	0.960236i	$-0.409934\pi$
$234$		0			0
$235$	144368.	−	250053.i	0.170530	−	0.295367i
$236$	38553.0	+	32349.8i	0.0450586	+	0.0378087i
$237$		0			0
$238$	137423.	+	779365.i	0.157260	+	0.891863i
$239$	449946.	−	377550.i	0.509526	−	0.427543i	−0.351437	−	0.936212i	$-0.614307\pi$
$239$	449946.	−	377550.i	0.509526	−	0.427543i	0.860962	+	0.508669i	$0.169862\pi$
$240$		0			0
$241$	−1.27476e6	+	463973.i	−1.41379	+	0.514577i	−0.932239	−	0.361843i	$-0.882148\pi$
$241$	−1.27476e6	+	463973.i	−1.41379	+	0.514577i	−0.481548	+	0.876419i	$0.659925\pi$
$242$	513832.			0.564004
$243$		0			0
$244$	−18511.0			−0.0199047
$245$	180921.	−	65849.9i	0.192563	−	0.0700874i
$246$		0			0
$247$	51944.6	−	43586.7i	0.0541748	−	0.0454581i
$248$	226877.	+	1.28669e6i	0.234241	+	1.32844i
$249$		0			0
$250$	585544.	+	491329.i	0.592529	+	0.497190i
$251$	−127627.	+	221056.i	−0.127867	+	0.221472i	−0.922850	−	0.385160i	$-0.874146\pi$
$251$	−127627.	+	221056.i	−0.127867	+	0.221472i	0.794983	+	0.606632i	$0.207480\pi$
$252$		0			0
$253$	18093.7	+	31339.2i	0.0177716	+	0.0307813i
$254$	47703.8	−	270541.i	0.0463947	−	0.263117i
$255$		0			0
$256$	−273181.	−	99429.6i	−0.260525	−	0.0948235i
$257$	−1.58074e6	−	575342.i	−1.49289	−	0.543367i	−0.538681	−	0.842510i	$-0.681077\pi$
$257$	−1.58074e6	−	575342.i	−1.49289	−	0.543367i	−0.954208	+	0.299143i	$0.903299\pi$
$258$		0			0
$259$	180817.	−	1.02546e6i	0.167490	−	0.949883i
$260$	9391.97	+	16267.4i	0.00861635	+	0.0149240i
$261$		0			0
$262$	731288.	−	1.26663e6i	0.658165	−	1.13998i
$263$	816243.	+	684909.i	0.727663	+	0.610582i	0.929493	−	0.368839i	$-0.120245\pi$
$263$	816243.	+	684909.i	0.727663	+	0.610582i	−0.201830	+	0.979420i	$0.564689\pi$
$264$		0			0
$265$	77465.4	+	439328.i	0.0677631	+	0.384303i
$266$	99691.0	−	83650.7i	0.0863877	−	0.0724879i
$267$		0			0
$268$	−64268.2	+	23391.7i	−0.0546587	+	0.0198941i
$269$	−1.19705e6			−1.00863			−0.504314	−	0.863520i	$-0.668255\pi$
$269$	−1.19705e6			−1.00863			−0.504314	+	0.863520i	$0.668255\pi$
$270$		0			0
$271$	904750.			0.748351			0.374176	−	0.927358i	$-0.377926\pi$
$271$	904750.			0.748351			0.374176	+	0.927358i	$0.377926\pi$
$272$	−1.53729e6	+	559528.i	−1.25989	+	0.458564i
$273$		0			0
$274$	−179939.	+	150987.i	−0.144793	+	0.121496i
$275$	123849.	+	702385.i	0.0987557	+	0.560072i
$276$		0			0
$277$	981954.	+	823957.i	0.768939	+	0.645216i	0.940437	−	0.339968i	$-0.110416\pi$
$277$	981954.	+	823957.i	0.768939	+	0.645216i	−0.171498	+	0.985184i	$0.554861\pi$
$278$	1.14763e6	−	1.98775e6i	0.890614	−	1.54259i
$279$		0			0
$280$	−175376.	−	303761.i	−0.133683	−	0.231546i
$281$	133056.	−	754596.i	0.100523	−	0.570097i	−0.892391	−	0.451263i	$-0.850974\pi$
$281$	133056.	−	754596.i	0.100523	−	0.570097i	0.992914	−	0.118833i	$-0.0379154\pi$
$282$		0			0
$283$	−1.56002e6	−	567801.i	−1.15788	−	0.421435i	−0.309542	−	0.950886i	$-0.600176\pi$
$283$	−1.56002e6	−	567801.i	−1.15788	−	0.421435i	−0.848340	+	0.529451i	$0.822398\pi$
$284$	−125826.	−	45797.0i	−0.0925711	−	0.0336931i
$285$		0			0
$286$	−78300.3	+	444063.i	−0.0566042	+	0.321018i
$287$	263157.	+	455801.i	0.188586	+	0.326641i
$288$		0			0
$289$	−375099.	+	649691.i	−0.264181	+	0.457575i
$290$	−844089.	−	708275.i	−0.589377	−	0.494546i
$291$		0			0
$292$	−33204.8	−	188314.i	−0.0227899	−	0.129248i
$293$	907811.	−	761744.i	0.617770	−	0.518370i	−0.279332	−	0.960195i	$-0.590113\pi$
$293$	907811.	−	761744.i	0.617770	−	0.518370i	0.897102	+	0.441824i	$0.145669\pi$
$294$		0			0
$295$	−356789.	+	129861.i	−0.238702	+	0.0868806i
$296$	1.96755e6			1.30526
$297$		0			0
$298$	−2.95740e6			−1.92916
$299$	34950.2	−	12720.8i	0.0226085	−	0.00822882i
$300$		0			0
$301$	−1.23282e6	+	1.03446e6i	−0.784302	+	0.658107i
$302$	319653.	+	1.81284e6i	0.201680	+	1.14378i
$303$		0			0
$304$	206081.	+	172922.i	0.127895	+	0.107317i
$305$	69826.9	−	120944.i	0.0429807	−	0.0744447i
$306$		0			0
$307$	−778035.	−	1.34760e6i	−0.471143	−	0.816044i	0.528312	−	0.849050i	$-0.322825\pi$
$307$	−778035.	−	1.34760e6i	−0.471143	−	0.816044i	−0.999455	+	0.0330064i	$0.989492\pi$
$308$	−12811.3	+	72656.6i	−0.00769515	+	0.0436413i
$309$		0			0
$310$	951987.	+	346495.i	0.562635	+	0.204782i
$311$	1.94895e6	+	709360.i	1.14261	+	0.415878i	0.842857	−	0.538138i	$-0.180872\pi$
$311$	1.94895e6	+	709360.i	1.14261	+	0.415878i	0.299758	+	0.954015i	$0.403094\pi$
$312$		0			0
$313$	−224941.	+	1.27570e6i	−0.129780	+	0.736018i	0.848574	+	0.529077i	$0.177462\pi$
$313$	−224941.	+	1.27570e6i	−0.129780	+	0.736018i	−0.978353	+	0.206941i	$0.933649\pi$
$314$	−1.11517e6	−	1.93154e6i	−0.638290	−	1.10555i
$315$		0			0
$316$	151180.	−	261852.i	0.0851682	−	0.147516i
$317$	−1.16834e6	−	980357.i	−0.653014	−	0.547944i	0.254970	−	0.966949i	$-0.417934\pi$
$317$	−1.16834e6	−	980357.i	−0.653014	−	0.547944i	−0.907984	+	0.419005i	$0.862379\pi$
$318$		0			0
$319$	−391584.	−	2.22078e6i	−0.215451	−	1.22188i
$320$	502800.	−	421900.i	0.274486	−	0.230321i
$321$		0			0
$322$	67075.8	−	24413.6i	0.0360517	−	0.0131218i
$323$	356849.			0.190317
$324$		0			0
$325$	733045.			0.384966
$326$	−1.02786e6	+	374110.i	−0.535661	+	0.194965i
$327$		0			0
$328$	−761827.	+	639249.i	−0.390995	+	0.328084i
$329$	−202402.	−	1.14788e6i	−0.103092	−	0.584663i
$330$		0			0
$331$	2.01166e6	+	1.68799e6i	1.00922	+	0.846835i	0.988235	−	0.152944i	$-0.0488756\pi$
$331$	2.01166e6	+	1.68799e6i	1.00922	+	0.846835i	0.0209843	+	0.999780i	$0.493320\pi$
$332$	15051.3	−	26069.6i	0.00749425	−	0.0129804i
$333$		0			0
$334$	−1.47875e6	−	2.56127e6i	−0.725317	−	1.25629i
$335$	89598.9	−	508141.i	0.0436205	−	0.247384i
$336$		0			0
$337$	42807.4	+	15580.6i	0.0205326	+	0.00747326i	0.352266	−	0.935900i	$-0.385411\pi$
$337$	42807.4	+	15580.6i	0.0205326	+	0.00747326i	−0.331733	+	0.943373i	$0.607633\pi$
$338$	−1.62811e6	−	592584.i	−0.775161	−	0.282136i
$339$		0			0
$340$	−17165.4	+	97350.0i	−0.00805300	+	0.0456708i
$341$	1.03666e6	+	1.79554e6i	0.482780	+	0.836200i
$342$		0			0
$343$	1.15190e6	−	1.99515e6i	0.528664	−	0.915674i
$344$	−2.32947e6	−	1.95466e6i	−1.06135	−	0.890583i
$345$		0			0
$346$	34451.1	+	195382.i	0.0154708	+	0.0877393i
$347$	1.55980e6	−	1.30883e6i	0.695417	−	0.583524i	−0.225049	−	0.974348i	$-0.572254\pi$
$347$	1.55980e6	−	1.30883e6i	0.695417	−	0.583524i	0.920466	+	0.390823i	$0.127810\pi$
$348$		0			0
$349$	−1.04233e6	+	379375.i	−0.458078	+	0.166727i	−0.560744	−	0.827989i	$-0.689485\pi$
$349$	−1.04233e6	+	379375.i	−0.458078	+	0.166727i	0.102666	+	0.994716i	$0.467263\pi$
$350$	1.40685e6			0.613870
$351$		0			0
$352$	−293140.			−0.126101
$353$	−2.45555e6	+	893746.i	−1.04884	+	0.381748i	−0.808227	−	0.588872i	$-0.799572\pi$
$353$	−2.45555e6	+	893746.i	−1.04884	+	0.381748i	−0.240618	+	0.970620i	$0.577350\pi$
$354$		0			0
$355$	773859.	−	649345.i	0.325905	−	0.273467i
$356$	−23719.5	−	134520.i	−0.00991929	−	0.0562551i
$357$		0			0
$358$	651248.	+	546462.i	0.268558	+	0.225347i
$359$	−231841.	+	401561.i	−0.0949412	+	0.164443i	−0.909584	−	0.415520i	$-0.863600\pi$
$359$	−231841.	+	401561.i	−0.0949412	+	0.164443i	0.814643	+	0.579963i	$0.196933\pi$
$360$		0			0
$361$	1.20871e6	+	2.09355e6i	0.488151	+	0.845502i
$362$	−549714.	+	3.11758e6i	−0.220478	+	1.25039i
$363$		0			0
$364$	71255.1	+	25934.7i	0.0281879	+	0.0102596i
$365$	1.35562e6	+	493405.i	0.532606	+	0.193853i
$366$		0			0
$367$	65028.1	−	368792.i	0.0252020	−	0.142928i	−0.969610	−	0.244654i	$-0.921326\pi$
$367$	65028.1	−	368792.i	0.0252020	−	0.142928i	0.994812	+	0.101726i	$0.0324366\pi$
$368$	73778.7	+	127788.i	0.0283996	+	0.0491895i
$369$		0			0
$370$	762815.	−	1.32123e6i	0.289678	−	0.501736i
$371$	1.37954e6	+	1.15757e6i	0.520355	+	0.436630i
$372$		0			0
$373$	79569.7	+	451262.i	0.0296125	+	0.167941i	0.996028	−	0.0890453i	$-0.0283816\pi$
$373$	79569.7	+	451262.i	0.0296125	+	0.167941i	−0.966415	+	0.256986i	$0.917270\pi$
$374$	−1.81780e6	+	1.52531e6i	−0.671995	+	0.563871i
$375$		0			0
$376$	2.06960e6	−	753275.i	0.754949	−	0.274779i
$377$	−2.31772e6			−0.839862
$378$		0			0
$379$	3.96988e6			1.41964			0.709821	−	0.704382i	$-0.248776\pi$
$379$	3.96988e6			1.41964			0.709821	+	0.704382i	$0.248776\pi$
$380$	15275.1	−	5559.67i	0.00542656	−	0.00197511i
$381$		0			0
$382$	1.92962e6	−	1.61915e6i	0.676572	−	0.567711i
$383$	160732.	+	911554.i	0.0559892	+	0.317531i	0.999920	−	0.0126115i	$-0.00401446\pi$
$383$	160732.	+	911554.i	0.0559892	+	0.317531i	−0.943931	+	0.330142i	$0.892903\pi$
$384$		0			0
$385$	−426383.	−	357778.i	−0.146605	−	0.123016i
$386$	284852.	−	493378.i	0.0973085	−	0.168543i
$387$		0			0
$388$	207947.	+	360175.i	0.0701251	+	0.121460i
$389$	73740.7	−	418205.i	0.0247078	−	0.140125i	−0.969958	−	0.243271i	$-0.921780\pi$
$389$	73740.7	−	418205.i	0.0247078	−	0.140125i	0.994666	+	0.103146i	$0.0328908\pi$
$390$		0			0
$391$	183928.	+	66944.3i	0.0608423	+	0.0221448i
$392$	1.38003e6	+	502291.i	0.453602	+	0.165098i
$393$		0			0
$394$	−400863.	+	2.27340e6i	−0.130093	+	0.737796i
$395$	1.14056e6	+	1.97550e6i	0.367811	+	0.637067i
$396$		0			0
$397$	−1.64686e6	+	2.85245e6i	−0.524422	+	0.908325i	0.475174	+	0.879892i	$0.342385\pi$
$397$	−1.64686e6	+	2.85245e6i	−0.524422	+	0.908325i	−0.999596	+	0.0284333i	$0.990948\pi$
$398$	194442.	+	163156.i	0.0615292	+	0.0516291i
$399$		0			0
$400$	505008.	+	2.86404e6i	0.157815	+	0.895013i
$401$	−2.24282e6	+	1.88195e6i	−0.696521	+	0.584451i	−0.920782	−	0.390079i	$-0.872448\pi$
$401$	−2.24282e6	+	1.88195e6i	−0.696521	+	0.584451i	0.224260	+	0.974529i	$0.428003\pi$
$402$		0			0
$403$	2.00243e6	−	728826.i	0.614180	−	0.223543i
$404$	477885.			0.145670
$405$		0			0
$406$	−4.44813e6			−1.33925
$407$	2.93397e6	−	1.06788e6i	0.877950	−	0.319548i
$408$		0			0
$409$	−1.79186e6	+	1.50355e6i	−0.529659	+	0.444437i	−0.867984	−	0.496593i	$-0.834584\pi$
$409$	−1.79186e6	+	1.50355e6i	−0.529659	+	0.444437i	0.338324	+	0.941030i	$0.390140\pi$
$410$	133905.	+	759412.i	0.0393402	+	0.223109i
$411$		0			0
$412$	201714.	+	169258.i	0.0585453	+	0.0491254i
$413$	−766372.	+	1.32739e6i	−0.221088	+	0.382935i
$414$		0			0
$415$	113552.	+	196678.i	0.0323650	+	0.0560578i
$416$	−52318.0	+	296710.i	−0.0148224	+	0.0840619i
$417$		0			0
$418$	366682.	+	133461.i	0.102648	+	0.0373607i
$419$	176455.	+	64224.3i	0.0491019	+	0.0178716i	0.366454	−	0.930436i	$-0.380572\pi$
$419$	176455.	+	64224.3i	0.0491019	+	0.0178716i	−0.317352	+	0.948308i	$0.602794\pi$
$420$		0			0
$421$	−68615.9	+	389140.i	−0.0188677	+	0.107004i	−0.992787	−	0.119890i	$-0.961746\pi$
$421$	−68615.9	+	389140.i	−0.0188677	+	0.107004i	0.973920	+	0.226894i	$0.0728570\pi$
$422$	−230710.	−	399601.i	−0.0630645	−	0.109231i
$423$		0			0
$424$	−1.70141e6	+	2.94692e6i	−0.459614	+	0.796075i
$425$	2.95517e6	+	2.47968e6i	0.793615	+	0.665922i
$426$		0			0
$427$	−97896.3	−	555198.i	−0.0259834	−	0.147359i
$428$	203140.	−	170455.i	0.0536027	−	0.0449780i
$429$		0			0
$430$	−2.21571e6	+	806452.i	−0.577885	+	0.210333i
$431$	1.09070e6			0.282820			0.141410	−	0.989951i	$-0.454836\pi$
$431$	1.09070e6			0.282820			0.141410	+	0.989951i	$0.454836\pi$
$432$		0			0
$433$	3.50848e6			0.899288			0.449644	−	0.893208i	$-0.351551\pi$
$433$	3.50848e6			0.899288			0.449644	+	0.893208i	$0.351551\pi$
$434$	3.84303e6	−	1.39875e6i	0.979377	−	0.356464i
$435$		0			0
$436$	239959.	−	201350.i	0.0604535	−	0.0507265i
$437$	−5589.14	−	31697.6i	−0.00140004	−	0.00794004i
$438$		0			0
$439$	−5.26819e6	−	4.42054e6i	−1.30467	−	1.09475i	−0.989318	−	0.145773i	$-0.953433\pi$
$439$	−5.26819e6	−	4.42054e6i	−1.30467	−	1.09475i	−0.315351	−	0.948975i	$-0.602122\pi$
$440$	525863.	−	910822.i	0.129492	−	0.224286i
$441$		0			0
$442$	1.21946e6	+	2.11217e6i	0.296901	+	0.514248i
$443$	204086.	−	1.15743e6i	0.0494088	−	0.280211i	−0.950086	−	0.311987i	$-0.899005\pi$
$443$	204086.	−	1.15743e6i	0.0494088	−	0.280211i	0.999495	+	0.0317764i	$0.0101164\pi$
$444$		0			0
$445$	968375.	+	352460.i	0.231816	+	0.0843741i
$446$	470048.	+	171083.i	0.111894	+	0.0407259i
$447$		0			0
$448$	460103.	−	2.60937e6i	0.108308	−	0.614245i
$449$	−2.50234e6	−	4.33418e6i	−0.585774	−	1.01459i	−0.994778	−	0.102058i	$-0.967457\pi$
$449$	−2.50234e6	−	4.33418e6i	−0.585774	−	1.01459i	0.409005	−	0.912532i	$-0.365876\pi$
$450$		0			0
$451$	−789072.	+	1.36671e6i	−0.182673	+	0.316400i
$452$	356527.	+	299162.i	0.0820817	+	0.0688747i
$453$		0			0
$454$	136397.	+	773543.i	0.0310573	+	0.176135i
$455$	−438234.	+	367722.i	−0.0992380	+	0.0832705i
$456$		0			0
$457$	3.41544e6	−	1.24312e6i	0.764991	−	0.278434i	0.0700913	−	0.997541i	$-0.477671\pi$
$457$	3.41544e6	−	1.24312e6i	0.764991	−	0.278434i	0.694900	+	0.719107i	$0.255449\pi$
$458$	−5.23611e6			−1.16639
$459$		0			0
$460$	8916.11			0.00196463
$461$	2.03452e6	−	740506.i	0.445872	−	0.162284i	−0.109319	−	0.994007i	$-0.534867\pi$
$461$	2.03452e6	−	740506.i	0.445872	−	0.162284i	0.555192	+	0.831722i	$0.312645\pi$
$462$		0			0
$463$	1.25618e6	−	1.05406e6i	0.272332	−	0.228513i	−0.496386	−	0.868102i	$-0.665340\pi$
$463$	1.25618e6	−	1.05406e6i	0.272332	−	0.228513i	0.768717	+	0.639589i	$0.220895\pi$
$464$	−1.59672e6	−	9.05545e6i	−0.344298	−	1.95261i
$465$		0			0
$466$	−5.19638e6	−	4.36028e6i	−1.10850	−	0.930142i
$467$	−1.51425e6	+	2.62275e6i	−0.321295	+	0.556500i	−0.980756	−	0.195240i	$-0.937452\pi$
$467$	−1.51425e6	+	2.62275e6i	−0.321295	+	0.556500i	0.659460	+	0.751739i	$0.270785\pi$
$468$		0			0
$469$	−1.04147e6	−	1.80387e6i	−0.218632	−	0.378682i
$470$	296549.	−	1.68181e6i	0.0619229	−	0.351182i
$471$		0			0
$472$	−2.72153e6	−	990555.i	−0.562287	−	0.204656i
$473$	−4.53454e6	−	1.65044e6i	−0.931923	−	0.339192i
$474$		0			0
$475$	110157.	−	624731.i	0.0224015	−	0.127045i
$476$	199525.	+	345588.i	0.0403627	+	0.0699103i
$477$		0			0
$478$	1.73701e6	−	3.00858e6i	0.347722	−	0.602272i
$479$	1.87616e6	+	1.57428e6i	0.373621	+	0.313505i	0.810192	−	0.586165i	$-0.199363\pi$
$479$	1.87616e6	+	1.57428e6i	0.373621	+	0.313505i	−0.436571	+	0.899670i	$0.643807\pi$
$480$		0			0
$481$	−557246.	−	3.16030e6i	−0.109821	−	0.622824i
$482$	−6.14638e6	+	5.15743e6i	−1.20504	+	1.01115i
$483$		0			0
$484$	243470.	−	88615.8i	0.0472424	−	0.0171948i
$485$	−3.13765e6			−0.605690
$486$		0			0
$487$	5.79768e6			1.10772			0.553862	−	0.832608i	$-0.313153\pi$
$487$	5.79768e6			1.10772			0.553862	+	0.832608i	$0.313153\pi$
$488$	1.00101e6	−	364339.i	0.190279	−	0.0692557i
$489$		0			0
$490$	872332.	−	731974.i	0.164131	−	0.137723i
$491$	−1.39338e6	−	7.90227e6i	−0.260836	−	1.47927i	−0.780637	−	0.624985i	$-0.785105\pi$
$491$	−1.39338e6	−	7.90227e6i	−0.260836	−	1.47927i	0.519801	−	0.854287i	$-0.326006\pi$
$492$		0			0
$493$	−9.34358e6	−	7.84019e6i	−1.73139	−	1.45281i
$494$	200531.	−	347329.i	0.0369712	−	0.0640360i
$495$		0			0
$496$	4.22707e6	+	7.32150e6i	0.771499	+	1.33628i
$497$	708144.	−	4.01608e6i	0.128597	−	0.729309i
$498$		0			0
$499$	−1.77935e6	−	647632.i	−0.319898	−	0.116433i	0.177080	−	0.984196i	$-0.443335\pi$
$499$	−1.77935e6	−	647632.i	−0.319898	−	0.116433i	−0.496978	+	0.867763i	$0.665557\pi$
$500$	362185.	+	131824.i	0.0647896	+	0.0235815i
$501$		0			0
$502$	−262161.	+	1.48679e6i	−0.0464310	+	0.263323i
$503$	−395461.	−	684959.i	−0.0696922	−	0.120710i	0.829074	−	0.559139i	$-0.188868\pi$
$503$	−395461.	−	684959.i	−0.0696922	−	0.120710i	−0.898766	+	0.438429i	$0.855535\pi$
$504$		0			0
$505$	−1.80267e6	+	3.12231e6i	−0.314548	+	0.544813i
$506$	163959.	+	137578.i	0.0284682	+	0.0238876i
$507$		0			0
$508$	−24054.2	−	136418.i	−0.00413554	−	0.0234538i
$509$	441409.	−	370386.i	0.0755174	−	0.0633666i	−0.604248	−	0.796797i	$-0.706526\pi$
$509$	441409.	−	370386.i	0.0755174	−	0.0633666i	0.679765	+	0.733430i	$0.262082\pi$
$510$		0			0
$511$	5.47245e6	−	1.99181e6i	0.927106	−	0.337439i
$512$	4.90387e6			0.826731
$513$		0			0
$514$	−9.94945e6			−1.66108
$515$	−1.86676e6	+	679446.i	−0.310150	+	0.112885i
$516$		0			0
$517$	2.67732e6	−	2.24654e6i	0.440528	−	0.369647i
$518$	−1.06946e6	−	6.06519e6i	−0.175121	−	0.993161i
$519$		0			0
$520$	−828064.	−	694828.i	−0.134294	−	0.112686i
$521$	−2.21807e6	+	3.84180e6i	−0.357998	+	0.620070i	−0.987626	−	0.156826i	$-0.949874\pi$
$521$	−2.21807e6	+	3.84180e6i	−0.357998	+	0.620070i	0.629628	+	0.776896i	$0.283207\pi$
$522$		0			0
$523$	−2.80297e6	−	4.85488e6i	−0.448088	−	0.776112i	0.550173	−	0.835050i	$-0.314562\pi$
$523$	−2.80297e6	−	4.85488e6i	−0.448088	−	0.776112i	−0.998262	+	0.0589388i	$0.981228\pi$
$524$	128064.	−	726288.i	0.0203751	−	0.115553i
$525$		0			0
$526$	5.92211e6	+	2.15547e6i	0.933280	+	0.339686i
$527$	1.05379e7	+	3.83550e6i	1.65283	+	0.601583i
$528$		0			0
$529$	−1.11459e6	+	6.32117e6i	−0.173172	+	0.982107i
$530$	1.31927e6	+	2.28503e6i	0.204006	+	0.353348i
$531$		0			0
$532$	32810.4	−	56829.2i	0.00502611	−	0.00870548i
$533$	1.24253e6	+	1.04261e6i	0.189448	+	0.158966i
$534$		0			0
$535$	347404.	+	1.97022e6i	0.0524747	+	0.297599i
$536$	3.01500e6	−	2.52988e6i	0.453289	−	0.380355i
$537$		0			0
$538$	−6.65307e6	+	2.42152e6i	−0.990984	+	0.360689i
$539$	2.33050e6			0.345523
$540$		0			0
$541$	−9.23300e6			−1.35628			−0.678141	−	0.734932i	$-0.737214\pi$
$541$	−9.23300e6			−1.35628			−0.678141	+	0.734932i	$0.737214\pi$
$542$	5.02851e6	−	1.83023e6i	0.735260	−	0.267613i
$543$		0			0
$544$	−1.21460e6	+	1.01917e6i	−0.175969	+	0.147655i
$545$	410371.	+	2.32733e6i	0.0591814	+	0.335634i
$546$		0			0
$547$	8.97053e6	+	7.52717e6i	1.28189	+	1.07563i	0.992981	+	0.118274i	$0.0377360\pi$
$547$	8.97053e6	+	7.52717e6i	1.28189	+	1.07563i	0.288906	+	0.957357i	$0.406708\pi$
$548$	−59221.6	+	102575.i	−0.00842420	+	0.0145911i
$549$		0			0
$550$	2.10920e6	+	3.65325e6i	0.297312	+	0.514959i
$551$	−348291.	+	1.97526e6i	−0.0488724	+	0.277169i
$552$		0			0
$553$	8.65319e6	+	3.14950e6i	1.20327	+	0.437955i
$554$	7.12439e6	+	2.59307e6i	0.986219	+	0.358954i
$555$		0			0
$556$	200974.	−	1.13978e6i	0.0275711	−	0.156363i
$557$	2.45391e6	+	4.25030e6i	0.335136	+	0.580472i	0.983511	−	0.180849i	$-0.0578845\pi$
$557$	2.45391e6	+	4.25030e6i	0.335136	+	0.580472i	−0.648375	+	0.761321i	$0.724551\pi$
$558$		0			0
$559$	−2.47984e6	+	4.29521e6i	−0.335656	+	0.581373i
$560$	−1.73862e6	−	1.45887e6i	−0.234279	−	0.196583i
$561$		0			0
$562$	−786969.	−	4.46312e6i	−0.105103	−	0.596071i
$563$	−8.81692e6	+	7.39827e6i	−1.17232	+	0.983693i	−0.999999	−	0.00134852i	$-0.999571\pi$
$563$	−8.81692e6	+	7.39827e6i	−1.17232	+	0.983693i	−0.172320	+	0.985041i	$0.555126\pi$
$564$		0			0
$565$	−3.29949e6	+	1.20091e6i	−0.434836	+	0.158267i
$566$	−9.81905e6			−1.28833
$567$		0			0
$568$	7.70564e6			1.00216
$569$	−1.24676e7	+	4.53784e6i	−1.61437	+	0.587582i	−0.982298	−	0.187327i	$-0.940017\pi$
$569$	−1.24676e7	+	4.53784e6i	−1.61437	+	0.587582i	−0.632072	+	0.774910i	$0.717795\pi$
$570$		0			0
$571$	39210.6	−	32901.6i	0.00503284	−	0.00422306i	−0.640268	−	0.768152i	$-0.721177\pi$
$571$	39210.6	−	32901.6i	0.00503284	−	0.00422306i	0.645301	+	0.763929i	$0.276732\pi$
$572$	39482.3	+	223915.i	0.00504559	+	0.0286150i
$573$		0			0
$574$	2.38464e6	+	2.00095e6i	0.302095	+	0.253488i
$575$	173976.	−	301335.i	0.0219442	−	0.0380084i
$576$		0			0
$577$	−190195.	−	329427.i	−0.0237826	−	0.0411927i	0.853889	−	0.520455i	$-0.174238\pi$
$577$	−190195.	−	329427.i	−0.0237826	−	0.0411927i	−0.877672	+	0.479262i	$0.840904\pi$
$578$	−770498.	+	4.36971e6i	−0.0959294	+	0.544043i
$579$		0			0
$580$	−522106.	−	190031.i	−0.0644449	−	0.0234560i
$581$	861499.	+	313560.i	0.105880	+	0.0385372i
$582$		0			0
$583$	−937676.	+	5.31783e6i	−0.114257	+	0.647982i
$584$	5.50203e6	+	9.52980e6i	0.667561	+	1.15625i
$585$		0			0
$586$	3.50458e6	−	6.07011e6i	0.421592	−	0.730219i
$587$	4.66461e6	+	3.91407e6i	0.558753	+	0.468850i	0.877892	−	0.478858i	$-0.158949\pi$
$587$	4.66461e6	+	3.91407e6i	0.558753	+	0.468850i	−0.319139	+	0.947708i	$0.603394\pi$
$588$		0			0
$589$	−320224.	−	1.81608e6i	−0.0380334	−	0.215698i
$590$	−1.72030e6	+	1.44351e6i	−0.203458	+	0.170722i
$591$		0			0
$592$	1.19635e7	−	4.35437e6i	1.40299	−	0.510648i
$593$	1.43821e7			1.67953			0.839763	−	0.542953i	$-0.182694\pi$
$593$	1.43821e7			1.67953			0.839763	+	0.542953i	$0.182694\pi$
$594$		0			0
$595$	−3.01058e6			−0.348624
$596$	−1.40131e6	+	510035.i	−0.161592	+	0.0588145i
$597$		0			0
$598$	168517.	−	141402.i	0.0192703	−	0.0161697i
$599$	−2.54779e6	−	1.44492e7i	−0.290132	−	1.64542i	−0.686354	−	0.727267i	$-0.740790\pi$
$599$	−2.54779e6	−	1.44492e7i	−0.290132	−	1.64542i	0.396222	−	0.918155i	$-0.370321\pi$
$600$		0			0
$601$	6.89234e6	+	5.78336e6i	0.778360	+	0.653122i	0.942835	−	0.333260i	$-0.108149\pi$
$601$	6.89234e6	+	5.78336e6i	0.778360	+	0.653122i	−0.164475	+	0.986381i	$0.552593\pi$
$602$	−4.75927e6	+	8.24329e6i	−0.535240	+	0.927063i
$603$		0			0
$604$	464107.	+	803856.i	0.0517637	+	0.0896574i
$605$	−339431.	+	1.92501e6i	−0.0377019	+	0.213818i
$606$		0			0
$607$	1.77972e6	+	647766.i	0.196056	+	0.0713586i	0.438182	−	0.898886i	$-0.355623\pi$
$607$	1.77972e6	+	647766.i	0.196056	+	0.0713586i	−0.242126	+	0.970245i	$0.577845\pi$
$608$	245007.	+	89175.1i	0.0268794	+	0.00978328i
$609$		0			0
$610$	143433.	−	813447.i	0.0156071	−	0.0885125i
$611$	−1.79607e6	−	3.11088e6i	−0.194634	−	0.337117i
$612$		0			0
$613$	868390.	−	1.50410e6i	0.0933391	−	0.161668i	−0.815575	−	0.578651i	$-0.803579\pi$
$613$	868390.	−	1.50410e6i	0.0933391	−	0.161668i	0.908914	+	0.416983i	$0.136913\pi$
$614$	−7.05030e6	−	5.91590e6i	−0.754721	−	0.633286i
$615$		0			0
$616$	−737253.	−	4.18117e6i	−0.0782825	−	0.443962i
$617$	−1.04114e6	+	873621.i	−0.110102	+	0.0923868i	−0.696177	−	0.717870i	$-0.745117\pi$
$617$	−1.04114e6	+	873621.i	−0.110102	+	0.0923868i	0.586074	+	0.810257i	$0.300673\pi$
$618$		0			0
$619$	−5.45920e6	+	1.98698e6i	−0.572667	+	0.208434i	−0.612089	−	0.790789i	$-0.709671\pi$
$619$	−5.45920e6	+	1.98698e6i	−0.572667	+	0.208434i	0.0394221	+	0.999223i	$0.487448\pi$
$620$	510839.			0.0533709
$621$		0			0
$622$	1.22670e7			1.27135
$623$	3.90919e6	−	1.42283e6i	0.403522	−	0.146870i
$624$		0			0
$625$	4.04147e6	−	3.39119e6i	0.413846	−	0.347258i
$626$	1.33043e6	+	7.54526e6i	0.135693	+	0.769552i
$627$		0			0
$628$	−861519.	−	722900.i	−0.0871697	−	0.0731441i
$629$	8.44393e6	−	1.46253e7i	0.850977	−	1.47394i
$630$		0			0
$631$	−6.69017e6	−	1.15877e7i	−0.668904	−	1.15858i	−0.978211	−	0.207613i	$-0.933430\pi$
$631$	−6.69017e6	−	1.15877e7i	−0.668904	−	1.15858i	0.309307	−	0.950962i	$-0.399903\pi$
$632$	−3.02147e6	+	1.71356e7i	−0.300902	+	1.70650i
$633$		0			0
$634$	−8.47671e6	−	3.08527e6i	−0.837537	−	0.304839i
$635$	982040.	+	357433.i	0.0966484	+	0.0351772i
$636$		0			0
$637$	415935.	−	2.35888e6i	0.0406141	−	0.230334i
$638$	−6.66883e6	−	1.15507e7i	−0.648631	−	1.12346i
$639$		0			0
$640$	2.32853e6	−	4.03313e6i	0.224715	−	0.389217i
$641$	−1.55200e7	−	1.30229e7i	−1.49193	−	1.25188i	−0.892173	−	0.451693i	$-0.850820\pi$
$641$	−1.55200e7	−	1.30229e7i	−1.49193	−	1.25188i	−0.599755	−	0.800184i	$-0.704735\pi$
$642$		0			0
$643$	2.81281e6	+	1.59522e7i	0.268295	+	1.52158i	0.759486	+	0.650524i	$0.225451\pi$
$643$	2.81281e6	+	1.59522e7i	0.268295	+	1.52158i	−0.491191	+	0.871052i	$0.663438\pi$
$644$	27572.3	−	23135.9i	0.00261974	−	0.00219822i
$645$		0			0
$646$	1.98333e6	−	721872.i	0.186988	−	0.0680580i
$647$	−6.91898e6			−0.649802			−0.324901	−	0.945748i	$-0.605331\pi$
$647$	−6.91898e6			−0.649802			−0.324901	+	0.945748i	$0.605331\pi$
$648$		0			0
$649$	−4.59591e6			−0.428311
$650$	4.07419e6	−	1.48288e6i	0.378231	−	0.137665i
$651$		0			0
$652$	−422514.	+	354531.i	−0.0389244	+	0.0326615i
$653$	1.17014e6	+	6.63621e6i	0.107388	+	0.609028i	0.990240	+	0.139376i	$0.0445096\pi$
$653$	1.17014e6	+	6.63621e6i	0.107388	+	0.609028i	−0.882852	+	0.469652i	$0.844379\pi$
$654$		0			0
$655$	4.26219e6	+	3.57641e6i	0.388177	+	0.325719i
$656$	−3.21752e6	+	5.57290e6i	−0.291918	+	0.505617i
$657$		0			0
$658$	−3.44698e6	−	5.97035e6i	−0.310366	−	0.537570i
$659$	2.39200e6	−	1.35657e7i	0.214560	−	1.21683i	−0.667110	−	0.744960i	$-0.732469\pi$
$659$	2.39200e6	−	1.35657e7i	0.214560	−	1.21683i	0.881669	−	0.471868i	$-0.156420\pi$
$660$		0			0
$661$	−9.38711e6	−	3.41663e6i	−0.835658	−	0.304155i	−0.111479	−	0.993767i	$-0.535559\pi$
$661$	−9.38711e6	−	3.41663e6i	−0.835658	−	0.304155i	−0.724179	+	0.689612i	$0.757781\pi$
$662$	1.45953e7	+	5.31224e6i	1.29440	+	0.471121i
$663$		0			0
$664$	−300813.	+	1.70600e6i	−0.0264775	+	0.150161i
$665$	247533.	+	428740.i	0.0217060	+	0.0375958i
$666$		0			0
$667$	−550073.	+	952754.i	−0.0478746	+	0.0829213i
$668$	−1.14240e6	−	958585.i	−0.0990549	−	0.0831169i
$669$		0			0
$670$	−529941.	−	3.00544e6i	−0.0456079	−	0.258655i
$671$	1.29495e6	−	1.08659e6i	0.111031	−	0.0931664i
$672$		0			0
$673$	−1.08774e7	+	3.95905e6i	−0.925737	+	0.336941i	−0.760519	−	0.649316i	$-0.775055\pi$
$673$	−1.08774e7	+	3.95905e6i	−0.925737	+	0.336941i	−0.165219	+	0.986257i	$0.552833\pi$
$674$	269437.			0.0228459
$675$		0			0
$676$	−873649.			−0.0735310
$677$	−1.25492e7	+	4.56755e6i	−1.05231	+	0.383011i	−0.809536	−	0.587071i	$-0.800281\pi$
$677$	−1.25492e7	+	4.56755e6i	−1.05231	+	0.383011i	−0.242779	+	0.970082i	$0.578059\pi$
$678$		0			0
$679$	−9.70291e6	+	8.14171e6i	−0.807658	+	0.677705i
$680$	−987820.	−	5.60221e6i	−0.0819229	−	0.464608i
$681$		0			0
$682$	9.39386e6	+	7.88239e6i	0.773363	+	0.648928i
$683$	1.02501e7	−	1.77536e7i	0.840765	−	1.45625i	−0.0484836	−	0.998824i	$-0.515439\pi$
$683$	1.02501e7	−	1.77536e7i	0.840765	−	1.45625i	0.889249	−	0.457424i	$-0.151228\pi$
$684$		0			0
$685$	−446788.	−	773860.i	−0.0363811	−	0.0630139i
$686$	2.36614e6	−	1.34190e7i	0.191969	−	1.08871i
$687$		0			0
$688$	−1.84900e7	−	6.72981e6i	−1.48924	−	0.542041i
$689$	5.21525e6	+	1.89820e6i	0.418531	+	0.152333i
$690$		0			0
$691$	3.25289e6	−	1.84480e7i	0.259163	−	1.46979i	−0.525991	−	0.850490i	$-0.676306\pi$
$691$	3.25289e6	−	1.84480e7i	0.259163	−	1.46979i	0.785155	−	0.619299i	$-0.212583\pi$
$692$	50019.8	+	86636.8i	0.00397079	+	0.00687761i
$693$		0			0
$694$	6.02157e6	−	1.04297e7i	0.474582	−	0.822000i
$695$	6.68877e6	+	5.61254e6i	0.525272	+	0.440755i
$696$		0			0
$697$	1.48225e6	+	8.40626e6i	0.115569	+	0.655422i
$698$	−5.02569e6	+	4.21706e6i	−0.390443	+	0.327621i
$699$		0			0
$700$	666609.	−	242626.i	0.0514193	−	0.0187151i
$701$	1.35917e7			1.04467			0.522333	−	0.852741i	$-0.325062\pi$
$701$	1.35917e7			1.04467			0.522333	+	0.852741i	$0.325062\pi$
$702$		0			0
$703$	−2.77707e6			−0.211933
$704$	7.46574e6	−	2.71731e6i	0.567729	−	0.206636i
$705$		0			0
$706$	−1.18397e7	+	9.93469e6i	−0.893983	+	0.750141i
$707$	2.52731e6	+	1.43331e7i	0.190156	+	1.07843i
$708$		0			0
$709$	−4.19159e6	−	3.51716e6i	−0.313158	−	0.262771i	0.472638	−	0.881257i	$-0.343302\pi$
$709$	−4.19159e6	−	3.51716e6i	−0.313158	−	0.262771i	−0.785796	+	0.618486i	$0.787746\pi$
$710$	2.98746e6	−	5.17444e6i	0.222411	−	0.385227i
$711$		0			0
$712$	3.93032e6	+	6.80752e6i	0.290555	+	0.503256i
$713$	175643.	−	996121.i	0.0129392	−	0.0733818i
$714$		0			0
$715$	−1.61191e6	−	586686.i	−0.117917	−	0.0429181i
$716$	402826.	+	146617.i	0.0293653	+	0.0106881i
$717$		0			0
$718$	−476229.	+	2.70083e6i	−0.0344750	+	0.195518i
$719$	−1.05477e7	−	1.82692e7i	−0.760914	−	1.31794i	−0.942380	−	0.334545i	$-0.891418\pi$
$719$	−1.05477e7	−	1.82692e7i	−0.760914	−	1.31794i	0.181466	−	0.983397i	$-0.441916\pi$
$720$		0			0
$721$	−4.00974e6	+	6.94508e6i	−0.287262	+	0.497553i
$722$	1.09529e7	+	9.19060e6i	0.781965	+	0.656147i
$723$		0			0
$724$	277189.	+	1.57202e6i	0.0196530	+	0.111458i
$725$	−1.66100e7	+	1.39375e7i	−1.17361	+	0.984780i
$726$		0			0
$727$	−1.63466e6	+	594967.i	−0.114707	+	0.0417501i	−0.398736	−	0.917066i	$-0.630551\pi$
$727$	−1.63466e6	+	594967.i	−0.114707	+	0.0417501i	0.284029	+	0.958816i	$0.408329\pi$
$728$	−4.36368e6			−0.305158
$729$		0			0
$730$	8.53251e6			0.592611
$731$	−2.45266e7	+	8.92696e6i	−1.69763	+	0.617888i
$732$		0			0
$733$	−2.32665e6	+	1.95229e6i	−0.159945	+	0.134210i	−0.719248	−	0.694753i	$-0.755513\pi$
$733$	−2.32665e6	+	1.95229e6i	−0.159945	+	0.134210i	0.559303	+	0.828964i	$0.311069\pi$
$734$	−384614.	−	2.18126e6i	−0.0263503	−	0.149440i
$735$		0			0
$736$	109553.	+	91925.8i	0.00745468	+	0.00625522i
$737$	3.12283e6	−	5.40889e6i	0.211777	−	0.366809i
$738$		0			0
$739$	−1.93674e6	−	3.35453e6i	−0.130455	−	0.225954i	0.793397	−	0.608704i	$-0.208310\pi$
$739$	−1.93674e6	−	3.35453e6i	−0.130455	−	0.225954i	−0.923852	+	0.382750i	$0.874977\pi$
$740$	133585.	−	757600.i	0.00896766	−	0.0508581i
$741$		0			0
$742$	1.00090e7	+	3.64298e6i	0.667393	+	0.242911i
$743$	−1.34259e7	−	4.88663e6i	−0.892220	−	0.324741i	−0.145089	−	0.989419i	$-0.546347\pi$
$743$	−1.34259e7	−	4.88663e6i	−0.892220	−	0.324741i	−0.747131	+	0.664677i	$0.768569\pi$
$744$		0			0
$745$	1.95362e6	−	1.10795e7i	0.128959	−	0.731360i
$746$	1.35510e6	+	2.34711e6i	0.0891507	+	0.154414i
$747$		0			0
$748$	−598274.	+	1.03624e6i	−0.0390972	+	0.0677184i
$749$	6.18674e6	+	5.19129e6i	0.402955	+	0.338120i
$750$		0			0
$751$	−2.89119e6	−	1.63967e7i	−0.187058	−	1.06086i	−0.923282	−	0.384122i	$-0.874504\pi$
$751$	−2.89119e6	−	1.63967e7i	−0.187058	−	1.06086i	0.736224	−	0.676738i	$-0.236607\pi$
$752$	1.09170e7	−	9.16046e6i	0.703978	−	0.590708i
$753$		0			0
$754$	−1.28817e7	+	4.68854e6i	−0.825170	+	0.300337i
$755$	−7.00277e6			−0.447098
$756$		0			0
$757$	1.05939e7			0.671921			0.335960	−	0.941876i	$-0.390939\pi$
$757$	1.05939e7			0.671921			0.335960	+	0.941876i	$0.390939\pi$
$758$	2.20642e7	−	8.03070e6i	1.39481	−	0.507669i
$759$		0			0
$760$	−716596.	+	601296.i	−0.0450029	+	0.0377619i
$761$	1.68852e6	+	9.57607e6i	0.105693	+	0.599412i	0.990941	+	0.134295i	$0.0428769\pi$
$761$	1.68852e6	+	9.57607e6i	0.105693	+	0.599412i	−0.885249	+	0.465118i	$0.846012\pi$
$762$		0			0
$763$	7.30808e6	+	6.13221e6i	0.454456	+	0.381334i
$764$	635078.	−	1.09999e6i	0.0393635	−	0.0681796i
$765$		0			0
$766$	2.73732e6	+	4.74118e6i	0.168560	+	0.291954i
$767$	−820254.	+	4.65189e6i	−0.0503454	+	0.285523i
$768$		0			0
$769$	1.56285e6	+	568831.i	0.0953019	+	0.0346870i	0.389231	−	0.921140i	$-0.372741\pi$
$769$	1.56285e6	+	568831.i	0.0953019	+	0.0346870i	−0.293929	+	0.955827i	$0.594963\pi$
$770$	−3.09354e6	−	1.12596e6i	−0.188031	−	0.0684377i
$771$		0			0
$772$	49883.6	−	282904.i	0.00301242	−	0.0170843i
$773$	−937345.	−	1.62353e6i	−0.0564223	−	0.0977262i	0.836435	−	0.548067i	$-0.184636\pi$
$773$	−937345.	−	1.62353e6i	−0.0564223	−	0.0977262i	−0.892857	+	0.450340i	$0.851303\pi$
$774$		0			0
$775$	9.96776e6	−	1.72647e7i	0.596133	−	1.03253i
$776$	−1.83341e7	−	1.53841e7i	−1.09296	−	0.917104i
$777$		0			0
$778$	−436146.	−	2.47351e6i	−0.0258335	−	0.146509i
$779$	1.07527e6	−	902260.i	0.0634855	−	0.0532707i
$780$		0			0
$781$	1.14905e7	−	4.18220e6i	0.674080	−	0.245345i
$782$	1.15767e6			0.0676970
$783$		0			0
$784$	9.50282e6			0.552157
$785$	7.97294e6	−	2.90191e6i	0.461790	−	0.168078i
$786$		0			0
$787$	−1.57265e7	+	1.31961e7i	−0.905099	+	0.759468i	−0.971180	−	0.238346i	$-0.923395\pi$
$787$	−1.57265e7	+	1.31961e7i	−0.905099	+	0.759468i	0.0660813	+	0.997814i	$0.478950\pi$
$788$	202132.	+	1.14635e6i	0.0115963	+	0.0657658i
$789$		0			0
$790$	1.03354e7	+	8.67240e6i	0.589194	+	0.494392i
$791$	−7.08719e6	+	1.22754e7i	−0.402747	+	0.697579i
$792$		0			0
$793$	−868710.	−	1.50465e6i	−0.0490560	−	0.0849674i
$794$	−3.38284e6	+	1.91851e7i	−0.190428	+	1.07997i
$795$		0			0
$796$	120271.	+	43774.9i	0.00672786	+	0.00244874i
$797$	3.77532e6	+	1.37410e6i	0.210527	+	0.0766256i	0.445131	−	0.895465i	$-0.353157\pi$
$797$	3.77532e6	+	1.37410e6i	0.210527	+	0.0766256i	−0.234604	+	0.972091i	$0.575379\pi$
$798$		0			0
$799$	3.28262e6	−	1.86167e7i	0.181909	−	1.03166i
$800$	1.40931e6	+	2.44100e6i	0.0778541	+	0.134847i
$801$		0			0
$802$	−8.65837e6	+	1.49967e7i	−0.475335	+	0.823305i
$803$	1.33768e7	+	1.12244e7i	0.732087	+	0.614294i
$804$		0			0
$805$	47153.2	+	267419.i	0.00256461	+	0.0145446i
$806$	9.65497e6	−	8.10148e6i	0.523496	−	0.439265i
$807$		0			0
$808$	−2.58424e7	+	9.40585e6i	−1.39253	+	0.506839i
$809$	−9.10494e6			−0.489109			−0.244554	−	0.969636i	$-0.578642\pi$
$809$	−9.10494e6			−0.489109			−0.244554	+	0.969636i	$0.578642\pi$
$810$		0			0
$811$	−2.55204e7			−1.36249			−0.681247	−	0.732054i	$-0.738562\pi$
$811$	−2.55204e7			−1.36249			−0.681247	+	0.732054i	$0.738562\pi$
$812$	−2.10767e6	+	767128.i	−0.112179	+	0.0408299i
$813$		0			0
$814$	1.41465e7	−	1.18703e7i	0.748320	−	0.627915i
$815$	−722569.	−	4.09789e6i	−0.0381053	−	0.216106i
$816$		0			0
$817$	3.28790e6	+	2.75888e6i	0.172331	+	0.144603i
$818$	−6.91744e6	+	1.19814e7i	−0.361462	+	0.626070i
$819$		0			0
$820$	194417.	+	336741.i	0.0100972	+	0.0174888i
$821$	5.96745e6	−	3.38431e7i	0.308980	−	1.75231i	−0.295170	−	0.955445i	$-0.595376\pi$
$821$	5.96745e6	−	3.38431e7i	0.308980	−	1.75231i	0.604151	−	0.796870i	$-0.293513\pi$
$822$		0			0
$823$	1.81341e7	+	6.60026e6i	0.933245	+	0.339673i	0.763495	−	0.645814i	$-0.223482\pi$
$823$	1.81341e7	+	6.60026e6i	0.933245	+	0.339673i	0.169750	+	0.985487i	$0.445704\pi$
$824$	−1.42393e7	−	5.18270e6i	−0.730587	−	0.265912i
$825$		0			0
$826$	−1.57422e6	+	8.92783e6i	−0.0802813	+	0.455298i
$827$	1.42703e7	+	2.47169e7i	0.725553	+	1.25670i	0.958746	+	0.284265i	$0.0917495\pi$
$827$	1.42703e7	+	2.47169e7i	0.725553	+	1.25670i	−0.233192	+	0.972431i	$0.574917\pi$
$828$		0			0
$829$	−2.90175e6	+	5.02597e6i	−0.146647	+	0.254000i	−0.929986	−	0.367594i	$-0.880181\pi$
$829$	−2.90175e6	+	5.02597e6i	−0.146647	+	0.254000i	0.783339	+	0.621595i	$0.213515\pi$
$830$	1.02897e6	+	863412.i	0.0518453	+	0.0435033i
$831$		0			0
$832$	−1.41796e6	−	8.04165e6i	−0.0710159	−	0.402751i
$833$	9.65622e6	−	8.10253e6i	0.482164	−	0.404583i
$834$		0			0
$835$	1.05723e7	−	3.84801e6i	0.524753	−	0.190994i
$836$	196763.			0.00973705
$837$		0			0
$838$	1.11064e6			0.0546339
$839$	−1.87894e7	+	6.83879e6i	−0.921528	+	0.335409i	−0.758846	−	0.651270i	$-0.774237\pi$
$839$	−1.87894e7	+	6.83879e6i	−0.921528	+	0.335409i	−0.162682	+	0.986679i	$0.552014\pi$
$840$		0			0
$841$	3.68047e7	−	3.08828e7i	1.79438	−	1.50566i
$842$	405835.	+	2.30160e6i	0.0197274	+	0.111879i
$843$		0			0
$844$	−178233.	−	149555.i	−0.00861257	−	0.00722680i
$845$	3.29556e6	−	5.70808e6i	0.158777	−	0.275010i
$846$		0			0
$847$	3.94544e6	+	6.83370e6i	0.188967	+	0.327301i
$848$	−3.82346e6	+	2.16839e7i	−0.182586	+	1.03550i
$849$		0			0
$850$	2.14407e7	+	7.80377e6i	1.01787	+	0.370474i
$851$	−1.43137e6	−	520975.i	−0.0677528	−	0.0246600i
$852$		0			0
$853$	−624757.	+	3.54317e6i	−0.0293994	+	0.166732i	−0.995973	−	0.0896588i	$-0.971422\pi$
$853$	−624757.	+	3.54317e6i	−0.0293994	+	0.166732i	0.966573	+	0.256391i	$0.0825335\pi$
$854$	−1.66721e6	−	2.88770e6i	−0.0782251	−	0.135490i
$855$		0			0
$856$	−7.63018e6	+	1.32159e7i	−0.355919	+	0.616469i
$857$	−7.30628e6	−	6.13070e6i	−0.339816	−	0.285140i	0.456869	−	0.889534i	$-0.348971\pi$
$857$	−7.30628e6	−	6.13070e6i	−0.339816	−	0.285140i	−0.796685	+	0.604394i	$0.793415\pi$
$858$		0			0
$859$	4.24731e6	+	2.40877e7i	0.196395	+	1.11381i	0.910418	+	0.413690i	$0.135760\pi$
$859$	4.24731e6	+	2.40877e7i	0.196395	+	1.11381i	−0.714023	+	0.700123i	$0.753129\pi$
$860$	−910793.	+	764246.i	−0.0419927	+	0.0352360i
$861$		0			0
$862$	6.06198e6	−	2.20638e6i	0.277873	−	0.101137i
$863$	4.56914e6			0.208837			0.104419	−	0.994533i	$-0.466702\pi$
$863$	4.56914e6			0.208837			0.104419	+	0.994533i	$0.466702\pi$
$864$		0			0
$865$	−754734.			−0.0342968
$866$	1.94998e7	−	7.09733e6i	0.883557	−	0.321588i
$867$		0			0
$868$	1.57972e6	−	1.32555e6i	0.0711675	−	0.0597166i
$869$	4.79471e6	+	2.71922e7i	0.215384	+	1.22150i
$870$		0			0
$871$	−4.91743e6	−	4.12622e6i	−0.219631	−	0.184292i
$872$	−9.01315e6	+	1.56112e7i	−0.401408	+	0.695258i
$873$		0			0
$874$	−95185.2	−	164866.i	−0.00421493	−	0.00730048i
$875$	−2.03836e6	+	1.15601e7i	−0.0900036	+	0.510436i
$876$		0			0
$877$	1.09013e7	+	3.96774e6i	0.478606	+	0.174198i	0.570047	−	0.821612i	$-0.306925\pi$
$877$	1.09013e7	+	3.96774e6i	0.478606	+	0.174198i	−0.0914409	+	0.995811i	$0.529147\pi$
$878$	−3.82224e7	−	1.39118e7i	−1.67333	−	0.609043i
$879$		0			0
$880$	1.18174e6	−	6.70198e6i	0.0514417	−	0.291740i
$881$	1.36913e7	+	2.37139e7i	0.594297	+	1.02935i	0.993646	+	0.112553i	$0.0359029\pi$
$881$	1.36913e7	+	2.37139e7i	0.594297	+	1.02935i	−0.399349	+	0.916799i	$0.630764\pi$
$882$		0			0
$883$	2.77132e6	−	4.80007e6i	0.119615	−	0.207179i	−0.800000	−	0.600000i	$-0.795167\pi$
$883$	2.77132e6	−	4.80007e6i	0.119615	−	0.207179i	0.919615	+	0.392821i	$0.128501\pi$
$884$	942086.	+	790504.i	0.0405471	+	0.0340231i
$885$		0			0
$886$	−1.20709e6	−	6.84572e6i	−0.0516599	−	0.292978i
$887$	3.12874e7	−	2.62533e7i	1.33524	−	1.12040i	0.352424	−	0.935841i	$-0.385358\pi$
$887$	3.12874e7	−	2.62533e7i	1.33524	−	1.12040i	0.982821	−	0.184562i	$-0.0590868\pi$
$888$		0			0
$889$	3.96435e6	−	1.44291e6i	0.168236	−	0.0612328i
$890$	6.09512e6			0.257933
$891$		0			0
$892$	252229.			0.0106141
$893$	−2.92112e6	+	1.06320e6i	−0.122580	+	0.0446156i
$894$		0			0
$895$	−2.47746e6	+	2.07884e6i	−0.103383	+	0.0867488i
$896$	−3.26456e6	−	1.85143e7i	−0.135849	−	0.770435i
$897$		0			0
$898$	−2.26754e7	−	1.90269e7i	−0.938347	−	0.787367i
$899$	−3.15158e7	+	5.45870e7i	−1.30056	+	2.25263i
$900$		0			0
$901$	1.46035e7	+	2.52940e7i	0.599301	+	1.03802i
$902$	−1.62085e6	+	9.19227e6i	−0.0663323	+	0.376189i
$903$		0			0
$904$	−2.51679e7	−	9.16037e6i	−1.02430	−	0.372814i
$905$	−1.13165e7	−	4.11888e6i	−0.459295	−	0.167170i
$906$		0			0
$907$	−7.88892e6	+	4.47403e7i	−0.318419	+	1.80584i	0.233954	+	0.972248i	$0.424833\pi$
$907$	−7.88892e6	+	4.47403e7i	−0.318419	+	1.80584i	−0.552373	+	0.833597i	$0.686278\pi$
$908$	198035.	+	343007.i	0.00797127	+	0.0138066i
$909$		0			0
$910$	−1.69179e6	+	2.93027e6i	−0.0677241	+	0.117302i
$911$	1.62935e7	+	1.36718e7i	0.650455	+	0.545797i	0.907209	−	0.420680i	$-0.138209\pi$
$911$	1.62935e7	+	1.36718e7i	0.650455	+	0.545797i	−0.256754	+	0.966477i	$0.582653\pi$
$912$		0			0
$913$	477355.	+	2.70721e6i	0.0189524	+	0.107484i
$914$	1.64680e7	−	1.38183e7i	0.652040	−	0.547126i
$915$		0			0
$916$	−2.48104e6	+	903024.i	−0.0977000	+	0.0355599i
$917$	2.24607e7			0.882062
$918$		0			0
$919$	−2.95674e7			−1.15485			−0.577423	−	0.816445i	$-0.695942\pi$
$919$	−2.95674e7			−1.15485			−0.577423	+	0.816445i	$0.695942\pi$
$920$	−482152.	+	175489.i	−0.0187808	+	0.00683566i
$921$		0			0
$922$	9.80970e6	−	8.23131e6i	0.380039	−	0.318891i
$923$	−2.18238e6	−	1.23769e7i	−0.0843191	−	0.478197i
$924$		0			0
$925$	−2.29978e7	−	1.92974e7i	−0.883754	−	0.741558i
$926$	4.84944e6	−	8.39947e6i	0.185851	−	0.321903i
$927$		0			0
$928$	−4.45592e6	−	7.71788e6i	−0.169851	−	0.294190i
$929$	3.49906e6	−	1.98442e7i	0.133019	−	0.754386i	−0.843200	−	0.537599i	$-0.819331\pi$
$929$	3.49906e6	−	1.98442e7i	0.133019	−	0.754386i	0.976219	−	0.216787i	$-0.0695576\pi$
$930$		0			0
$931$	−1.94783e6	−	708953.i	−0.0736508	−	0.0268067i
$932$	−3.21419e6	−	1.16987e6i	−0.121208	−	0.0441161i
$933$		0			0
$934$	−3.11044e6	+	1.76402e7i	−0.116669	+	0.661661i
$935$	−4.51359e6	−	7.81777e6i	−0.168847	−	0.292451i
$936$		0			0
$937$	−4.99124e6	+	8.64509e6i	−0.185720	+	0.321677i	−0.943819	−	0.330463i	$-0.892795\pi$
$937$	−4.99124e6	+	8.64509e6i	−0.185720	+	0.321677i	0.758099	+	0.652140i	$0.226129\pi$
$938$	−9.43744e6	−	7.91896e6i	−0.350225	−	0.293874i
$939$		0			0
$940$	−149532.	−	848039.i	−0.00551969	−	0.0313037i
$941$	2.18332e7	−	1.83202e7i	0.803791	−	0.674460i	−0.145326	−	0.989384i	$-0.546423\pi$
$941$	2.18332e7	−	1.83202e7i	0.803791	−	0.674460i	0.949117	+	0.314923i	$0.101979\pi$
$942$		0			0
$943$	723482.	−	263326.i	0.0264941	−	0.00964305i
$944$	−1.87402e7			−0.684456
$945$		0			0
$946$	−2.85412e7			−1.03692
$947$	1.86328e7	−	6.78179e6i	0.675155	−	0.245736i	0.0183892	−	0.999831i	$-0.494146\pi$
$947$	1.86328e7	−	6.78179e6i	0.675155	−	0.245736i	0.656766	+	0.754095i	$0.271924\pi$
$948$		0			0
$949$	1.37486e7	−	1.15364e7i	0.495556	−	0.415821i
$950$	−651533.	−	3.69503e6i	−0.0234222	−	0.132834i
$951$		0			0
$952$	−1.75916e7	−	1.47611e7i	−0.629090	−	0.527869i
$953$	2.48702e7	−	4.30765e7i	0.887048	−	1.53641i	0.0437005	−	0.999045i	$-0.486085\pi$
$953$	2.48702e7	−	4.30765e7i	0.887048	−	1.53641i	0.843348	−	0.537368i	$-0.180581\pi$
$954$		0			0
$955$	4.79126e6	+	8.29870e6i	0.169997	+	0.294443i
$956$	304187.	−	1.72513e6i	0.0107645	−	0.0610488i
$957$		0			0
$958$	1.36121e7	+	4.95441e6i	0.479195	+	0.174413i
$959$	−3.38970e6	−	1.23375e6i	−0.119019	−	0.0433192i
$960$		0			0
$961$	5.09188e6	−	2.88775e7i	0.177856	−	1.00867i
$962$	−9.49011e6	−	1.64374e7i	−0.330623	−	0.572657i
$963$		0			0
$964$	−2.02290e6	+	3.50377e6i	−0.0701103	+	0.121435i
$965$	1.66021e6	+	1.39308e6i	0.0573913	+	0.0481570i
$966$		0			0
$967$	−3.55112e6	−	2.01394e7i	−0.122124	−	0.692597i	−0.982975	−	0.183740i	$-0.941179\pi$
$967$	−3.55112e6	−	2.01394e7i	−0.122124	−	0.692597i	0.860851	−	0.508857i	$-0.169932\pi$
$968$	−1.14219e7	+	9.58407e6i	−0.391785	+	0.328747i
$969$		0			0
$970$	−1.74387e7	+	6.34718e6i	−0.595094	+	0.216597i
$971$	−3.91500e7			−1.33255			−0.666275	−	0.745707i	$-0.732112\pi$
$971$	−3.91500e7			−1.33255			−0.666275	+	0.745707i	$0.732112\pi$
$972$		0			0
$973$	3.52481e7			1.19359
$974$	3.22229e7	−	1.17282e7i	1.08835	−	0.396126i
$975$		0			0
$976$	5.28027e6	−	4.43067e6i	0.177432	−	0.148883i
$977$	2.18527e6	+	1.23933e7i	0.0732433	+	0.415383i	0.999280	+	0.0379490i	$0.0120825\pi$
$977$	2.18527e6	+	1.23933e7i	0.0732433	+	0.415383i	−0.926036	+	0.377434i	$0.876806\pi$
$978$		0			0
$979$	9.55558e6	+	8.01808e6i	0.318640	+	0.267371i
$980$	287102.	−	497276.i	0.00954930	−	0.0165399i
$981$		0			0
$982$	−2.37299e7	−	4.11013e7i	−0.785265	−	1.36012i
$983$	5.42580e6	−	3.07713e7i	0.179094	−	1.01569i	−0.754218	−	0.656624i	$-0.771984\pi$
$983$	5.42580e6	−	3.07713e7i	0.179094	−	1.01569i	0.933312	−	0.359067i	$-0.116905\pi$
$984$		0			0
$985$	−8.25224e6	−	3.00357e6i	−0.271008	−	0.0986387i
$986$	−6.77906e7	−	2.46738e7i	−2.22064	−	0.808246i
$987$		0			0
$988$	35117.2	−	199160.i	0.00114453	−	0.00649096i
$989$	1.17710e6	+	2.03879e6i	0.0382668	+	0.0662800i
$990$		0			0
$991$	−6.26173e6	+	1.08456e7i	−0.202540	+	0.350809i	−0.949346	−	0.314232i	$-0.898253\pi$
$991$	−6.26173e6	+	1.08456e7i	−0.202540	+	0.350809i	0.746806	+	0.665042i	$0.231586\pi$
$992$	6.27671e6	+	5.26679e6i	0.202513	+	0.169929i
$993$		0			0
$994$	−4.18838e6	−	2.37535e7i	−0.134456	−	0.762538i
$995$	−739690.	+	620674.i	−0.0236860	+	0.0198749i
$996$		0			0
$997$	1.89449e7	−	6.89539e6i	0.603608	−	0.219695i	−0.0220959	−	0.999756i	$-0.507034\pi$
$997$	1.89449e7	−	6.89539e6i	0.603608	−	0.219695i	0.625704	+	0.780060i	$0.284812\pi$
$998$	−1.11996e7			−0.355938
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	81.6.e.a.19.11		84
3.2	odd	2		27.6.e.a.7.4	yes	84
27.2	odd	18		729.6.a.c.1.32		42
27.4	even	9	inner	81.6.e.a.64.11		84
27.23	odd	18		27.6.e.a.4.4	✓	84
27.25	even	9		729.6.a.e.1.11		42

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.6.e.a.4.4	✓	84	27.23	odd	18
27.6.e.a.7.4	yes	84	3.2	odd	2
81.6.e.a.19.11		84	1.1	even	1	trivial
81.6.e.a.64.11		84	27.4	even	9	inner
729.6.a.c.1.32		42	27.2	odd	18
729.6.a.e.1.11		42	27.25	even	9

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:	\( N \)	\(=\)	\( 81 = 3^{4} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	81.e (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(5.55790 - 2.02291i) q^{2} +(2.28464 - 1.91704i) q^{4} +(3.90711 + 22.1583i) q^{5} +(69.5798 + 58.3844i) q^{7} +(-85.8137 + 148.634i) q^{8} +O(q^{10})\)	\(q+(5.55790 - 2.02291i) q^{2} +(2.28464 - 1.91704i) q^{4} +(3.90711 + 22.1583i) q^{5} +(69.5798 + 58.3844i) q^{7} +(-85.8137 + 148.634i) q^{8} +(66.5396 + 115.250i) q^{10} +(-47.2935 + 268.215i) q^{11} +(263.041 + 95.7391i) q^{13} +(504.823 + 183.741i) q^{14} +(-192.844 + 1093.67i) q^{16} +(736.555 + 1275.75i) q^{17} +(121.121 - 209.787i) q^{19} +(51.4047 + 43.1337i) q^{20} +(279.722 + 1586.38i) q^{22} +(101.784 - 85.4070i) q^{23} +(2460.81 - 895.663i) q^{25} +1655.63 q^{26} +270.890 q^{28} +(-7780.54 + 2831.88i) q^{29} +(5831.61 - 4893.30i) q^{31} +(186.902 + 1059.97i) q^{32} +(6674.43 + 5600.51i) q^{34} +(-1021.84 + 1769.89i) q^{35} +(-5732.04 - 9928.18i) q^{37} +(248.796 - 1410.99i) q^{38} +(-3628.76 - 1320.76i) q^{40} +(5445.05 + 1981.84i) q^{41} +(-3076.71 + 17448.9i) q^{43} +(406.129 + 703.437i) q^{44} +(392.935 - 680.584i) q^{46} +(-9830.35 - 8248.65i) q^{47} +(-1485.89 - 8426.92i) q^{49} +(11865.1 - 9956.00i) q^{50} +(784.489 - 285.531i) q^{52} +19826.8 q^{53} -6127.97 q^{55} +(-14648.8 + 5331.72i) q^{56} +(-37514.8 + 31478.6i) q^{58} +(2930.29 + 16618.5i) q^{59} +(-4754.68 - 3989.65i) q^{61} +(22512.8 - 38993.3i) q^{62} +(-14585.7 - 25263.1i) q^{64} +(-1093.69 + 6202.61i) q^{65} +(-21549.3 - 7843.29i) q^{67} +(4128.43 + 1502.63i) q^{68} +(-2098.99 + 11903.9i) q^{70} +(-22448.7 - 38882.4i) q^{71} +(32058.0 - 55526.1i) q^{73} +(-51941.9 - 43584.4i) q^{74} +(-125.453 - 711.481i) q^{76} +(-18950.2 + 15901.1i) q^{77} +(95268.0 - 34674.7i) q^{79} -24987.4 q^{80} +34272.1 q^{82} +(9484.75 - 3452.17i) q^{83} +(-25390.7 + 21305.3i) q^{85} +(18197.5 + 103203. i) q^{86} +(-35807.3 - 30045.9i) q^{88} +(22900.3 - 39664.6i) q^{89} +(12712.7 + 22019.0i) q^{91} +(68.8113 - 390.248i) q^{92} +(-71322.4 - 25959.2i) q^{94} +(5121.77 + 1864.17i) q^{95} +(-24215.3 + 137332. i) q^{97} +(-25305.3 - 43830.1i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q + 6 q^{2} - 6 q^{4} + 93 q^{5} - 6 q^{7} - 573 q^{8}+O(q^{10}) \) 84 * q + 6 * q^2 - 6 * q^4 + 93 * q^5 - 6 * q^7 - 573 * q^8	\( 84 q + 6 q^{2} - 6 q^{4} + 93 q^{5} - 6 q^{7} - 573 q^{8} - 3 q^{10} - 111 q^{11} - 6 q^{13} + 1641 q^{14} + 90 q^{16} - 3465 q^{17} - 3 q^{19} - 9987 q^{20} - 2850 q^{22} + 7716 q^{23} + 4953 q^{25} + 7806 q^{26} - 12 q^{28} + 20418 q^{29} - 6657 q^{31} - 51192 q^{32} - 11394 q^{34} - 35868 q^{35} - 3 q^{37} + 44076 q^{38} + 12441 q^{40} + 79077 q^{41} - 9465 q^{43} - 110757 q^{44} - 3 q^{46} - 103557 q^{47} + 5484 q^{49} + 105513 q^{50} + 68625 q^{52} + 206406 q^{53} - 12 q^{55} + 147237 q^{56} - 9753 q^{58} - 116484 q^{59} - 70116 q^{61} - 246066 q^{62} - 86019 q^{64} + 19815 q^{65} + 48117 q^{67} + 48105 q^{68} + 270111 q^{70} - 279531 q^{71} - 27012 q^{73} - 233691 q^{74} - 125670 q^{76} + 345135 q^{77} - 216186 q^{79} + 924114 q^{80} - 12 q^{82} + 370401 q^{83} - 43731 q^{85} - 116682 q^{86} + 371418 q^{88} - 154827 q^{89} - 91002 q^{91} - 1279059 q^{92} + 11667 q^{94} - 1087671 q^{95} - 420621 q^{97} - 463410 q^{98}+O(q^{100}) \) 84 * q + 6 * q^2 - 6 * q^4 + 93 * q^5 - 6 * q^7 - 573 * q^8 - 3 * q^10 - 111 * q^11 - 6 * q^13 + 1641 * q^14 + 90 * q^16 - 3465 * q^17 - 3 * q^19 - 9987 * q^20 - 2850 * q^22 + 7716 * q^23 + 4953 * q^25 + 7806 * q^26 - 12 * q^28 + 20418 * q^29 - 6657 * q^31 - 51192 * q^32 - 11394 * q^34 - 35868 * q^35 - 3 * q^37 + 44076 * q^38 + 12441 * q^40 + 79077 * q^41 - 9465 * q^43 - 110757 * q^44 - 3 * q^46 - 103557 * q^47 + 5484 * q^49 + 105513 * q^50 + 68625 * q^52 + 206406 * q^53 - 12 * q^55 + 147237 * q^56 - 9753 * q^58 - 116484 * q^59 - 70116 * q^61 - 246066 * q^62 - 86019 * q^64 + 19815 * q^65 + 48117 * q^67 + 48105 * q^68 + 270111 * q^70 - 279531 * q^71 - 27012 * q^73 - 233691 * q^74 - 125670 * q^76 + 345135 * q^77 - 216186 * q^79 + 924114 * q^80 - 12 * q^82 + 370401 * q^83 - 43731 * q^85 - 116682 * q^86 + 371418 * q^88 - 154827 * q^89 - 91002 * q^91 - 1279059 * q^92 + 11667 * q^94 - 1087671 * q^95 - 420621 * q^97 - 463410 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

Properties

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