LMFDB - Embedded newform 13.5.d.a.5.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [13,5,Mod(5,13)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(13, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("13.5");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 13 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	13.d (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.34380952009$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(i)$
Coefficient field:	6.0.53039932416.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} + 2x^{4} - 12x^{3} + 529x^{2} - 1334x + 1682 $ x^6 - 2x^5 + 2x^4 - 12x^3 + 529x^2 - 1334*x + 1682
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			5.3
Root			$-3.48832 + 3.48832i$ of defining polynomial
Character	$\chi$	$=$	13.5
Dual form			13.5.d.a.8.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(3.48832 - 3.48832i) q^{2} -1.36015 q^{3} -8.33680i q^{4} +(-6.84848 + 6.84848i) q^{5} +(-4.74466 + 4.74466i) q^{6} +(15.2891 + 15.2891i) q^{7} +(26.7317 + 26.7317i) q^{8} -79.1500 q^{9} +47.7794i q^{10} +(-94.2642 - 94.2642i) q^{11} +11.3393i q^{12} +(149.045 - 79.6662i) q^{13} +106.667 q^{14} +(9.31499 - 9.31499i) q^{15} +319.887 q^{16} -349.910i q^{17} +(-276.101 + 276.101i) q^{18} +(-217.788 + 217.788i) q^{19} +(57.0944 + 57.0944i) q^{20} +(-20.7955 - 20.7955i) q^{21} -657.648 q^{22} +310.298i q^{23} +(-36.3593 - 36.3593i) q^{24} +531.197i q^{25} +(242.014 - 797.817i) q^{26} +217.829 q^{27} +(127.462 - 127.462i) q^{28} +1076.14 q^{29} -64.9874i q^{30} +(-334.152 + 334.152i) q^{31} +(688.160 - 688.160i) q^{32} +(128.214 + 128.214i) q^{33} +(-1220.60 - 1220.60i) q^{34} -209.414 q^{35} +659.858i q^{36} +(-458.644 - 458.644i) q^{37} +1519.43i q^{38} +(-202.724 + 108.358i) q^{39} -366.143 q^{40} +(1405.06 - 1405.06i) q^{41} -145.083 q^{42} +3179.23i q^{43} +(-785.862 + 785.862i) q^{44} +(542.057 - 542.057i) q^{45} +(1082.42 + 1082.42i) q^{46} +(-2450.75 - 2450.75i) q^{47} -435.095 q^{48} -1933.49i q^{49} +(1852.99 + 1852.99i) q^{50} +475.932i q^{51} +(-664.161 - 1242.56i) q^{52} -2638.17 q^{53} +(759.857 - 759.857i) q^{54} +1291.13 q^{55} +817.408i q^{56} +(296.226 - 296.226i) q^{57} +(3753.91 - 3753.91i) q^{58} +(-190.247 - 190.247i) q^{59} +(-77.6572 - 77.6572i) q^{60} +3511.79 q^{61} +2331.26i q^{62} +(-1210.13 - 1210.13i) q^{63} +317.133i q^{64} +(-475.137 + 1566.32i) q^{65} +894.503 q^{66} +(-2011.87 + 2011.87i) q^{67} -2917.13 q^{68} -422.053i q^{69} +(-730.504 + 730.504i) q^{70} +(-5580.77 + 5580.77i) q^{71} +(-2115.81 - 2115.81i) q^{72} +(328.685 + 328.685i) q^{73} -3199.79 q^{74} -722.510i q^{75} +(1815.66 + 1815.66i) q^{76} -2882.43i q^{77} +(-329.177 + 1085.16i) q^{78} +4040.07 q^{79} +(-2190.74 + 2190.74i) q^{80} +6114.87 q^{81} -9802.63i q^{82} +(5522.44 - 5522.44i) q^{83} +(-173.368 + 173.368i) q^{84} +(2396.35 + 2396.35i) q^{85} +(11090.2 + 11090.2i) q^{86} -1463.71 q^{87} -5039.69i q^{88} +(-5862.57 - 5862.57i) q^{89} -3781.74i q^{90} +(3496.78 + 1060.73i) q^{91} +2586.89 q^{92} +(454.499 - 454.499i) q^{93} -17098.0 q^{94} -2983.04i q^{95} +(-936.005 + 936.005i) q^{96} +(-10865.4 + 10865.4i) q^{97} +(-6744.63 - 6744.63i) q^{98} +(7461.01 + 7461.01i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 2 q^{2} - 4 q^{3} - 14 q^{5} + 32 q^{6} + 48 q^{7} - 96 q^{8} - 58 q^{9} - 32 q^{11} - 244 q^{14} + 404 q^{15} + 1044 q^{16} - 802 q^{18} + 732 q^{19} + 428 q^{20} - 2128 q^{21} - 1632 q^{22} - 24 q^{24}+ \cdots + 17492 q^{99}+O(q^{100}) $ 6 * q - 2 * q^2 - 4 * q^3 - 14 * q^5 + 32 * q^6 + 48 * q^7 - 96 * q^8 - 58 * q^9 - 32 * q^11 - 244 * q^14 + 404 * q^15 + 1044 * q^16 - 802 * q^18 + 732 * q^19 + 428 * q^20 - 2128 * q^21 - 1632 * q^22 - 24 * q^24 + 910 * q^26 + 236 * q^27 + 1884 * q^28 + 4184 * q^29 - 3468 * q^31 + 2092 * q^32 + 2324 * q^33 - 5304 * q^34 - 4204 * q^35 - 1758 * q^37 + 1196 * q^39 - 708 * q^40 + 4750 * q^41 + 9532 * q^42 - 3956 * q^44 + 830 * q^45 + 516 * q^46 - 6872 * q^47 - 9436 * q^48 - 322 * q^50 + 3900 * q^52 + 2108 * q^53 - 184 * q^54 + 6408 * q^55 - 5800 * q^57 + 6516 * q^58 + 4372 * q^59 + 1324 * q^60 + 5988 * q^61 - 652 * q^63 - 5018 * q^65 - 4592 * q^66 + 72 * q^67 - 10572 * q^68 + 7368 * q^70 - 14672 * q^71 - 7980 * q^72 + 5874 * q^73 + 1544 * q^74 + 3576 * q^76 + 5720 * q^78 + 2616 * q^79 - 12080 * q^80 - 19450 * q^81 + 19264 * q^83 + 6296 * q^84 + 4164 * q^85 + 29376 * q^86 + 35584 * q^87 - 986 * q^89 - 30888 * q^91 + 5304 * q^92 - 9520 * q^93 - 36156 * q^94 + 20720 * q^96 - 23154 * q^97 - 41426 * q^98 + 17492 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/13\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	3.48832	−	3.48832i	0.872081	−	0.872081i	−0.120618	−	0.992699i	$-0.538488\pi$
$2$	3.48832	−	3.48832i	0.872081	−	0.872081i	0.992699	+	0.120618i	$0.0384876\pi$
$3$	−1.36015			−0.151128			−0.0755642	−	0.997141i	$-0.524076\pi$
$3$	−1.36015			−0.151128			−0.0755642	+	0.997141i	$0.524076\pi$
$4$		−	8.33680i		−	0.521050i
$5$	−6.84848	+	6.84848i	−0.273939	+	0.273939i	−0.830684	−	0.556745i	$-0.812050\pi$
$5$	−6.84848	+	6.84848i	−0.273939	+	0.273939i	0.556745	+	0.830684i	$0.312050\pi$
$6$	−4.74466	+	4.74466i	−0.131796	+	0.131796i
$7$	15.2891	+	15.2891i	0.312022	+	0.312022i	0.845693	−	0.533670i	$-0.179188\pi$
$7$	15.2891	+	15.2891i	0.312022	+	0.312022i	−0.533670	+	0.845693i	$0.679188\pi$
$8$	26.7317	+	26.7317i	0.417683	+	0.417683i
$9$	−79.1500			−0.977160
$10$			47.7794i			0.477794i
$11$	−94.2642	−	94.2642i	−0.779043	−	0.779043i	0.200625	−	0.979668i	$-0.435703\pi$
$11$	−94.2642	−	94.2642i	−0.779043	−	0.779043i	−0.979668	+	0.200625i	$0.935703\pi$
$12$			11.3393i			0.0787454i
$13$	149.045	−	79.6662i	0.881921	−	0.471398i
$13$	149.045	−	79.6662i	0.881921	−	0.471398i
$14$	106.667			0.544218
$15$	9.31499	−	9.31499i	0.0414000	−	0.0414000i
$16$	319.887			1.24956
$17$		−	349.910i		−	1.21076i	−0.795936	−	0.605381i	$-0.793021\pi$
$17$		−	349.910i		−	1.21076i	0.795936	−	0.605381i	$-0.206979\pi$
$18$	−276.101	+	276.101i	−0.852163	+	0.852163i
$19$	−217.788	+	217.788i	−0.603291	+	0.603291i	−0.941184	−	0.337893i	$-0.890286\pi$
$19$	−217.788	+	217.788i	−0.603291	+	0.603291i	0.337893	+	0.941184i	$0.390286\pi$
$20$	57.0944	+	57.0944i	0.142736	+	0.142736i
$21$	−20.7955	−	20.7955i	−0.0471554	−	0.0471554i
$22$	−657.648			−1.35878
$23$			310.298i			0.586575i	0.956024	+	0.293287i	$0.0947492\pi$
$23$			310.298i			0.586575i	−0.956024	+	0.293287i	$0.905251\pi$
$24$	−36.3593	−	36.3593i	−0.0631237	−	0.0631237i
$25$			531.197i			0.849915i
$26$	242.014	−	797.817i	0.358009	−	1.18020i
$27$	217.829			0.298805
$28$	127.462	−	127.462i	0.162579	−	0.162579i
$29$	1076.14			1.27959			0.639796	−	0.768545i	$-0.279019\pi$
$29$	1076.14			1.27959			0.639796	+	0.768545i	$0.279019\pi$
$30$		−	64.9874i		−	0.0722082i
$31$	−334.152	+	334.152i	−0.347713	+	0.347713i	−0.859257	−	0.511544i	$-0.829074\pi$
$31$	−334.152	+	334.152i	−0.347713	+	0.347713i	0.511544	+	0.859257i	$0.329074\pi$
$32$	688.160	−	688.160i	0.672032	−	0.672032i
$33$	128.214	+	128.214i	0.117735	+	0.117735i
$34$	−1220.60	−	1220.60i	−1.05588	−	1.05588i
$35$	−209.414			−0.170950
$36$			659.858i			0.509149i
$37$	−458.644	−	458.644i	−0.335021	−	0.335021i	0.519469	−	0.854489i	$-0.326130\pi$
$37$	−458.644	−	458.644i	−0.335021	−	0.335021i	−0.854489	+	0.519469i	$0.826130\pi$
$38$			1519.43i			1.05224i
$39$	−202.724	+	108.358i	−0.133283	+	0.0712415i
$40$	−366.143			−0.228839
$41$	1405.06	−	1405.06i	0.835849	−	0.835849i	−0.152460	−	0.988310i	$-0.548720\pi$
$41$	1405.06	−	1405.06i	0.835849	−	0.835849i	0.988310	+	0.152460i	$0.0487196\pi$
$42$	−145.083			−0.0822467
$43$			3179.23i			1.71943i	0.510774	+	0.859715i	$0.329359\pi$
$43$			3179.23i			1.71943i	−0.510774	+	0.859715i	$0.670641\pi$
$44$	−785.862	+	785.862i	−0.405920	+	0.405920i
$45$	542.057	−	542.057i	0.267682	−	0.267682i
$46$	1082.42	+	1082.42i	0.511540	+	0.511540i
$47$	−2450.75	−	2450.75i	−1.10944	−	1.10944i	−0.993224	−	0.116214i	$-0.962924\pi$
$47$	−2450.75	−	2450.75i	−1.10944	−	1.10944i	−0.116214	−	0.993224i	$-0.537076\pi$
$48$	−435.095			−0.188843
$49$		−	1933.49i		−	0.805284i
$50$	1852.99	+	1852.99i	0.741194	+	0.741194i
$51$			475.932i			0.182980i
$52$	−664.161	−	1242.56i	−0.245622	−	0.459525i
$53$	−2638.17			−0.939185			−0.469593	−	0.882883i	$-0.655599\pi$
$53$	−2638.17			−0.939185			−0.469593	+	0.882883i	$0.655599\pi$
$54$	759.857	−	759.857i	0.260582	−	0.260582i
$55$	1291.13			0.426821
$56$			817.408i			0.260653i
$57$	296.226	−	296.226i	0.0911744	−	0.0911744i
$58$	3753.91	−	3753.91i	1.11591	−	1.11591i
$59$	−190.247	−	190.247i	−0.0546529	−	0.0546529i	0.679252	−	0.733905i	$-0.262304\pi$
$59$	−190.247	−	190.247i	−0.0546529	−	0.0546529i	−0.733905	+	0.679252i	$0.762304\pi$
$60$	−77.6572	−	77.6572i	−0.0215715	−	0.0215715i
$61$	3511.79			0.943777			0.471888	−	0.881658i	$-0.343573\pi$
$61$	3511.79			0.943777			0.471888	+	0.881658i	$0.343573\pi$
$62$			2331.26i			0.606468i
$63$	−1210.13	−	1210.13i	−0.304896	−	0.304896i
$64$			317.133i			0.0774250i
$65$	−475.137	+	1566.32i	−0.112458	+	0.370727i
$66$	894.503			0.205350
$67$	−2011.87	+	2011.87i	−0.448177	+	0.448177i	−0.894748	−	0.446571i	$-0.852645\pi$
$67$	−2011.87	+	2011.87i	−0.448177	+	0.448177i	0.446571	+	0.894748i	$0.352645\pi$
$68$	−2917.13			−0.630868
$69$		−	422.053i		−	0.0886480i
$70$	−730.504	+	730.504i	−0.149082	+	0.149082i
$71$	−5580.77	+	5580.77i	−1.10708	+	1.10708i	−0.113544	+	0.993533i	$0.536220\pi$
$71$	−5580.77	+	5580.77i	−1.10708	+	1.10708i	−0.993533	+	0.113544i	$0.963780\pi$
$72$	−2115.81	−	2115.81i	−0.408143	−	0.408143i
$73$	328.685	+	328.685i	0.0616785	+	0.0616785i	0.737273	−	0.675595i	$-0.236113\pi$
$73$	328.685	+	328.685i	0.0616785	+	0.0616785i	−0.675595	+	0.737273i	$0.736113\pi$
$74$	−3199.79			−0.584331
$75$		−	722.510i		−	0.128446i
$76$	1815.66	+	1815.66i	0.314345	+	0.314345i
$77$		−	2882.43i		−	0.486158i
$78$	−329.177	+	1085.16i	−0.0541054	+	0.178362i
$79$	4040.07			0.647344			0.323672	−	0.946169i	$-0.395083\pi$
$79$	4040.07			0.647344			0.323672	+	0.946169i	$0.395083\pi$
$80$	−2190.74	+	2190.74i	−0.342303	+	0.342303i
$81$	6114.87			0.932002
$82$		−	9802.63i		−	1.45786i
$83$	5522.44	−	5522.44i	0.801631	−	0.801631i	−0.181719	−	0.983350i	$-0.558166\pi$
$83$	5522.44	−	5522.44i	0.801631	−	0.801631i	0.983350	+	0.181719i	$0.0581663\pi$
$84$	−173.368	+	173.368i	−0.0245703	+	0.0245703i
$85$	2396.35	+	2396.35i	0.331675	+	0.331675i
$86$	11090.2	+	11090.2i	1.49948	+	1.49948i
$87$	−1463.71			−0.193382
$88$		−	5039.69i		−	0.650786i
$89$	−5862.57	−	5862.57i	−0.740130	−	0.740130i	0.232473	−	0.972603i	$-0.425318\pi$
$89$	−5862.57	−	5862.57i	−0.740130	−	0.740130i	−0.972603	+	0.232473i	$0.925318\pi$
$90$		−	3781.74i		−	0.466881i
$91$	3496.78	+	1060.73i	0.422266	+	0.128092i
$92$	2586.89			0.305635
$93$	454.499	−	454.499i	0.0525493	−	0.0525493i
$94$	−17098.0			−1.93504
$95$		−	2983.04i		−	0.330530i
$96$	−936.005	+	936.005i	−0.101563	+	0.101563i
$97$	−10865.4	+	10865.4i	−1.15479	+	1.15479i	−0.169209	+	0.985580i	$0.554121\pi$
$97$	−10865.4	+	10865.4i	−1.15479	+	1.15479i	−0.985580	+	0.169209i	$0.945879\pi$
$98$	−6744.63	−	6744.63i	−0.702273	−	0.702273i
$99$	7461.01	+	7461.01i	0.761250	+	0.761250i
$100$	4428.48			0.442848
$101$			8361.44i			0.819669i	0.912160	+	0.409834i	$0.134414\pi$
$101$			8361.44i			0.819669i	−0.912160	+	0.409834i	$0.865586\pi$
$102$	1660.21	+	1660.21i	0.159574	+	0.159574i
$103$		−	8831.26i		−	0.832431i	−0.909266	−	0.416215i	$-0.863356\pi$
$103$		−	8831.26i		−	0.832431i	0.909266	−	0.416215i	$-0.136644\pi$
$104$	6113.83	+	1854.60i	0.565258	+	0.171469i
$105$	284.836			0.0258354
$106$	−9202.79	+	9202.79i	−0.819045	+	0.819045i
$107$	−392.728			−0.0343024			−0.0171512	−	0.999853i	$-0.505460\pi$
$107$	−392.728			−0.0343024			−0.0171512	+	0.999853i	$0.505460\pi$
$108$		−	1816.00i		−	0.155692i
$109$	−1174.35	+	1174.35i	−0.0988426	+	0.0988426i	−0.754799	−	0.655956i	$-0.772266\pi$
$109$	−1174.35	+	1174.35i	−0.0988426	+	0.0988426i	0.655956	+	0.754799i	$0.272266\pi$
$110$	4503.89	−	4503.89i	0.372222	−	0.372222i
$111$	623.826	+	623.826i	0.0506311	+	0.0506311i
$112$	4890.78	+	4890.78i	0.389890	+	0.389890i
$113$	5877.47			0.460292			0.230146	−	0.973156i	$-0.426080\pi$
$113$	5877.47			0.460292			0.230146	+	0.973156i	$0.426080\pi$
$114$		−	2066.66i		−	0.159023i
$115$	−2125.07	−	2125.07i	−0.160686	−	0.160686i
$116$		−	8971.53i		−	0.666731i
$117$	−11796.9	+	6305.58i	−0.861778	+	0.460631i
$118$	−1327.28			−0.0953235
$119$	5349.81	−	5349.81i	0.377785	−	0.377785i
$120$	498.011			0.0345841
$121$			3130.48i			0.213816i
$122$	12250.3	−	12250.3i	0.823049	−	0.823049i
$123$	−1911.10	+	1911.10i	−0.126321	+	0.126321i
$124$	2785.76	+	2785.76i	0.181176	+	0.181176i
$125$	−7918.19	−	7918.19i	−0.506764	−	0.506764i
$126$	−8442.66			−0.531788
$127$		−	18967.7i		−	1.17600i	−0.808862	−	0.587998i	$-0.799916\pi$
$127$		−	18967.7i		−	1.17600i	0.808862	−	0.587998i	$-0.200084\pi$
$128$	12116.8	+	12116.8i	0.739553	+	0.739553i
$129$		−	4324.24i		−	0.259855i
$130$	3806.40	+	7121.26i	0.225231	+	0.421377i
$131$	−166.709			−0.00971443			−0.00485722	−	0.999988i	$-0.501546\pi$
$131$	−166.709			−0.00971443			−0.00485722	+	0.999988i	$0.501546\pi$
$132$	1068.89	−	1068.89i	0.0613461	−	0.0613461i
$133$	−6659.57			−0.376481
$134$			14036.1i			0.781693i
$135$	−1491.80	+	1491.80i	−0.0818544	+	0.0818544i
$136$	9353.70	−	9353.70i	0.505715	−	0.505715i
$137$	−5287.93	−	5287.93i	−0.281737	−	0.281737i	0.552064	−	0.833802i	$-0.313840\pi$
$137$	−5287.93	−	5287.93i	−0.281737	−	0.281737i	−0.833802	+	0.552064i	$0.813840\pi$
$138$	−1472.26	−	1472.26i	−0.0773083	−	0.0773083i
$139$	33096.3			1.71297			0.856486	−	0.516170i	$-0.172643\pi$
$139$	33096.3			1.71297			0.856486	+	0.516170i	$0.172643\pi$
$140$			1745.84i			0.0890737i
$141$	3333.40	+	3333.40i	0.167667	+	0.167667i
$142$			38935.1i			1.93092i
$143$	−21559.2	−	6539.90i	−1.05429	−	0.319815i
$144$	−25319.0			−1.22102
$145$	−7369.90	+	7369.90i	−0.350530	+	0.350530i
$146$	2293.12			0.107577
$147$			2629.84i			0.121701i
$148$	−3823.62	+	3823.62i	−0.174563	+	0.174563i
$149$	6201.70	−	6201.70i	0.279343	−	0.279343i	−0.553503	−	0.832847i	$-0.686709\pi$
$149$	6201.70	−	6201.70i	0.279343	−	0.279343i	0.832847	+	0.553503i	$0.186709\pi$
$150$	−2520.35	−	2520.35i	−0.112015	−	0.112015i
$151$	−25174.0	−	25174.0i	−1.10408	−	1.10408i	−0.993914	−	0.110163i	$-0.964863\pi$
$151$	−25174.0	−	25174.0i	−1.10408	−	1.10408i	−0.110163	−	0.993914i	$-0.535137\pi$
$152$	−11643.7			−0.503969
$153$			27695.4i			1.18311i
$154$	−10054.8	−	10054.8i	−0.423969	−	0.423969i
$155$		−	4576.87i		−	0.190504i
$156$	903.362	+	1690.07i	0.0371204	+	0.0694472i
$157$	7614.82			0.308930			0.154465	−	0.987998i	$-0.450635\pi$
$157$	7614.82			0.308930			0.154465	+	0.987998i	$0.450635\pi$
$158$	14093.1	−	14093.1i	0.564536	−	0.564536i
$159$	3588.32			0.141937
$160$			9425.70i			0.368192i
$161$	−4744.18	+	4744.18i	−0.183024	+	0.183024i
$162$	21330.6	−	21330.6i	0.812781	−	0.812781i
$163$	36056.4	+	36056.4i	1.35709	+	1.35709i	0.877488	+	0.479598i	$0.159217\pi$
$163$	36056.4	+	36056.4i	1.35709	+	1.35709i	0.479598	+	0.877488i	$0.340783\pi$
$164$	−11713.7	−	11713.7i	−0.435519	−	0.435519i
$165$	−1756.14			−0.0645047
$166$		−	38528.1i		−	1.39817i
$167$	11597.5	+	11597.5i	0.415843	+	0.415843i	0.883768	−	0.467925i	$-0.154998\pi$
$167$	11597.5	+	11597.5i	0.415843	+	0.415843i	−0.467925	+	0.883768i	$0.654998\pi$
$168$		−	1111.80i		−	0.0393920i
$169$	15867.6	−	23747.6i	0.555569	−	0.831471i
$170$	16718.5			0.578495
$171$	17237.9	−	17237.9i	0.589512	−	0.589512i
$172$	26504.6			0.895909
$173$			20327.3i			0.679185i	0.940573	+	0.339592i	$0.110289\pi$
$173$			20327.3i			0.679185i	−0.940573	+	0.339592i	$0.889711\pi$
$174$	−5105.90	+	5105.90i	−0.168645	+	0.168645i
$175$	−8121.52	+	8121.52i	−0.265192	+	0.265192i
$176$	−30153.9	−	30153.9i	−0.973459	−	0.973459i
$177$	258.765	+	258.765i	0.00825960	+	0.00825960i
$178$	−40901.1			−1.29091
$179$			42116.9i			1.31447i	0.753687	+	0.657234i	$0.228274\pi$
$179$			42116.9i			1.31447i	−0.753687	+	0.657234i	$0.771726\pi$
$180$	−4519.02	−	4519.02i	−0.139476	−	0.139476i
$181$		−	11460.6i		−	0.349823i	−0.984584	−	0.174912i	$-0.944036\pi$
$181$		−	11460.6i		−	0.349823i	0.984584	−	0.174912i	$-0.0559640\pi$
$182$	15898.1	−	8497.73i	0.479957	−	0.256543i
$183$	−4776.58			−0.142631
$184$	−8294.80	+	8294.80i	−0.245002	+	0.245002i
$185$	6282.02			0.183551
$186$		−	3170.88i		−	0.0916545i
$187$	−32984.0	+	32984.0i	−0.943236	+	0.943236i
$188$	−20431.4	+	20431.4i	−0.578073	+	0.578073i
$189$	3330.41	+	3330.41i	0.0932338	+	0.0932338i
$190$	−10405.8	−	10405.8i	−0.288249	−	0.288249i
$191$	−29746.6			−0.815400			−0.407700	−	0.913116i	$-0.633669\pi$
$191$	−29746.6			−0.815400			−0.407700	+	0.913116i	$0.633669\pi$
$192$		−	431.350i		−	0.0117011i
$193$	−15738.8	−	15738.8i	−0.422529	−	0.422529i	0.463545	−	0.886073i	$-0.346577\pi$
$193$	−15738.8	−	15738.8i	−0.422529	−	0.422529i	−0.886073	+	0.463545i	$0.846577\pi$
$194$			75804.2i			2.01414i
$195$	646.259	−	2130.44i	0.0169956	−	0.0560273i
$196$	−16119.1			−0.419593
$197$	22079.8	−	22079.8i	0.568934	−	0.568934i	−0.362896	−	0.931830i	$-0.618212\pi$
$197$	22079.8	−	22079.8i	0.568934	−	0.568934i	0.931830	+	0.362896i	$0.118212\pi$
$198$	52052.8			1.32774
$199$		−	63536.7i		−	1.60442i	−0.597041	−	0.802211i	$-0.703657\pi$
$199$		−	63536.7i		−	1.60442i	0.597041	−	0.802211i	$-0.296343\pi$
$200$	−14199.8	+	14199.8i	−0.354995	+	0.354995i
$201$	2736.45	−	2736.45i	0.0677323	−	0.0677323i
$202$	29167.4	+	29167.4i	0.714817	+	0.714817i
$203$	16453.2	+	16453.2i	0.399261	+	0.399261i
$204$	3967.75			0.0953420
$205$			19245.1i			0.457944i
$206$	−30806.3	−	30806.3i	−0.725947	−	0.725947i
$207$		−	24560.1i		−	0.573177i
$208$	47677.4	−	25484.1i	1.10201	−	0.589038i
$209$	41059.3			0.939980
$210$	993.599	−	993.599i	0.0225306	−	0.0225306i
$211$	−9438.33			−0.211997			−0.105999	−	0.994366i	$-0.533804\pi$
$211$	−9438.33			−0.211997			−0.105999	+	0.994366i	$0.533804\pi$
$212$			21993.9i			0.489363i
$213$	7590.72	−	7590.72i	0.167311	−	0.167311i
$214$	−1369.96	+	1369.96i	−0.0299145	+	0.0299145i
$215$	−21772.9	−	21772.9i	−0.471019	−	0.471019i
$216$	5822.94	+	5822.94i	0.124806	+	0.124806i
$217$	−10217.8			−0.216989
$218$			8193.02i			0.172397i
$219$	−447.062	−	447.062i	−0.00932137	−	0.00932137i
$220$		−	10763.9i		−	0.222395i
$221$	−27876.0	−	52152.2i	−0.570750	−	1.06780i
$222$	4352.22			0.0883089
$223$	−36897.6	+	36897.6i	−0.741974	+	0.741974i	−0.972958	−	0.230984i	$-0.925806\pi$
$223$	−36897.6	+	36897.6i	−0.741974	+	0.741974i	0.230984	+	0.972958i	$0.425806\pi$
$224$	21042.7			0.419378
$225$		−	42044.2i		−	0.830503i
$226$	20502.5	−	20502.5i	0.401412	−	0.401412i
$227$	−16881.0	+	16881.0i	−0.327601	+	0.327601i	−0.851674	−	0.524073i	$-0.824412\pi$
$227$	−16881.0	+	16881.0i	−0.327601	+	0.327601i	0.524073	+	0.851674i	$0.324412\pi$
$228$	−2469.57	−	2469.57i	−0.0475064	−	0.0475064i
$229$	−5795.38	−	5795.38i	−0.110512	−	0.110512i	0.649688	−	0.760201i	$-0.274899\pi$
$229$	−5795.38	−	5795.38i	−0.110512	−	0.110512i	−0.760201	+	0.649688i	$0.774899\pi$
$230$	−14825.9			−0.280262
$231$			3920.55i			0.0734722i
$232$	28767.0	+	28767.0i	0.534464	+	0.534464i
$233$		−	4361.29i		−	0.0803346i	−0.999193	−	0.0401673i	$-0.987211\pi$
$233$		−	4361.29i		−	0.0803346i	0.999193	−	0.0401673i	$-0.0127891\pi$
$234$	−19155.4	+	63147.2i	−0.349833	+	1.15325i
$235$	33567.8			0.607837
$236$	−1586.05	+	1586.05i	−0.0284769	+	0.0284769i
$237$	−5495.12			−0.0978320
$238$		−	37323.8i		−	0.658918i
$239$	−6740.89	+	6740.89i	−0.118011	+	0.118011i	−0.763646	−	0.645635i	$-0.776593\pi$
$239$	−6740.89	+	6740.89i	−0.118011	+	0.118011i	0.645635	+	0.763646i	$0.276593\pi$
$240$	2979.74	−	2979.74i	0.0517316	−	0.0517316i
$241$	41872.5	+	41872.5i	0.720932	+	0.720932i	0.968795	−	0.247863i	$-0.0797282\pi$
$241$	41872.5	+	41872.5i	0.720932	+	0.720932i	−0.247863	+	0.968795i	$0.579728\pi$
$242$	10920.1	+	10920.1i	0.186465	+	0.186465i
$243$	−25961.3			−0.439657
$244$		−	29277.1i		−	0.491755i
$245$	13241.4	+	13241.4i	0.220599	+	0.220599i
$246$			13333.1i			0.220323i
$247$	−15109.8	+	49810.5i	−0.247665	+	0.816445i
$248$	−17864.9			−0.290468
$249$	−7511.37	+	7511.37i	−0.121149	+	0.121149i
$250$	−55242.4			−0.883878
$251$			75079.1i			1.19171i	0.803091	+	0.595857i	$0.203187\pi$
$251$			75079.1i			1.19171i	−0.803091	+	0.595857i	$0.796813\pi$
$252$	−10088.6	+	10088.6i	−0.158866	+	0.158866i
$253$	29250.0	−	29250.0i	0.456967	−	0.456967i
$254$	−66165.3	−	66165.3i	−1.02556	−	1.02556i
$255$	−3259.41	−	3259.41i	−0.0501255	−	0.0501255i
$256$	79460.7			1.21247
$257$		−	32844.1i		−	0.497268i	−0.968597	−	0.248634i	$-0.920018\pi$
$257$		−	32844.1i		−	0.497268i	0.968597	−	0.248634i	$-0.0799817\pi$
$258$	−15084.3	−	15084.3i	−0.226614	−	0.226614i
$259$		−	14024.5i		−	0.209068i
$260$	13058.1	+	3961.12i	0.193167	+	0.0585965i
$261$	−85176.2			−1.25037
$262$	−581.536	+	581.536i	−0.00847177	+	0.00847177i
$263$	−61227.8			−0.885192			−0.442596	−	0.896721i	$-0.645942\pi$
$263$	−61227.8			−0.885192			−0.442596	+	0.896721i	$0.645942\pi$
$264$			6854.76i			0.0983522i
$265$	18067.5	−	18067.5i	0.257280	−	0.257280i
$266$	−23230.7	+	23230.7i	−0.328322	+	0.328322i
$267$	7974.00	+	7974.00i	0.111855	+	0.111855i
$268$	16772.5	+	16772.5i	0.233523	+	0.233523i
$269$	127164.			1.75736			0.878679	−	0.477413i	$-0.158425\pi$
$269$	127164.			1.75736			0.878679	+	0.477413i	$0.158425\pi$
$270$			10407.7i			0.142767i
$271$	21722.8	+	21722.8i	0.295786	+	0.295786i	0.839361	−	0.543575i	$-0.182930\pi$
$271$	21722.8	+	21722.8i	0.295786	+	0.295786i	−0.543575	+	0.839361i	$0.682930\pi$
$272$		−	111932.i		−	1.51292i
$273$	−4756.17	−	1442.76i	−0.0638163	−	0.0193584i
$274$	−36892.0			−0.491396
$275$	50072.8	−	50072.8i	0.662120	−	0.662120i
$276$	−3518.57			−0.0461901
$277$			70284.0i			0.916003i	0.888951	+	0.458002i	$0.151435\pi$
$277$			70284.0i			0.916003i	−0.888951	+	0.458002i	$0.848565\pi$
$278$	115451.	−	115451.i	1.49385	−	1.49385i
$279$	26448.1	−	26448.1i	0.339771	−	0.339771i
$280$	−5598.00	−	5598.00i	−0.0714030	−	0.0714030i
$281$	32616.5	+	32616.5i	0.413071	+	0.413071i	0.882807	−	0.469736i	$-0.155651\pi$
$281$	32616.5	+	32616.5i	0.413071	+	0.413071i	−0.469736	+	0.882807i	$0.655651\pi$
$282$	23255.9			0.292439
$283$		−	61904.1i		−	0.772941i	−0.922302	−	0.386470i	$-0.873694\pi$
$283$		−	61904.1i		−	0.772941i	0.922302	−	0.386470i	$-0.126306\pi$
$284$	46525.8	+	46525.8i	0.576842	+	0.576842i
$285$			4057.39i			0.0499525i
$286$	−98018.9	+	52392.3i	−1.19833	+	0.640524i
$287$	42964.3			0.521607
$288$	−54467.9	+	54467.9i	−0.656683	+	0.656683i
$289$	−38916.2			−0.465945
$290$			51417.2i			0.611381i
$291$	14778.6	−	14778.6i	0.174521	−	0.174521i
$292$	2740.18	−	2740.18i	0.0321376	−	0.0321376i
$293$	−31482.7	−	31482.7i	−0.366721	−	0.366721i	0.499559	−	0.866280i	$-0.333496\pi$
$293$	−31482.7	−	31482.7i	−0.366721	−	0.366721i	−0.866280	+	0.499559i	$0.833496\pi$
$294$	9173.74	+	9173.74i	0.106133	+	0.106133i
$295$	2605.80			0.0299431
$296$		−	24520.7i		−	0.279865i
$297$	−20533.5	−	20533.5i	−0.232782	−	0.232782i
$298$		−	43267.1i		−	0.487220i
$299$	24720.3	+	46248.2i	0.276510	+	0.517312i
$300$	−6023.42			−0.0669269
$301$	−48607.5	+	48607.5i	−0.536501	+	0.536501i
$302$	−175630.			−1.92569
$303$		−	11372.9i		−	0.123875i
$304$	−69667.5	+	69667.5i	−0.753847	+	0.753847i
$305$	−24050.4	+	24050.4i	−0.258537	+	0.258537i
$306$	96610.5	+	96610.5i	1.03177	+	1.03177i
$307$	−1138.57	−	1138.57i	−0.0120805	−	0.0120805i	0.701041	−	0.713121i	$-0.252719\pi$
$307$	−1138.57	−	1138.57i	−0.0120805	−	0.0120805i	−0.713121	+	0.701041i	$0.752719\pi$
$308$	−24030.2			−0.253313
$309$			12011.9i			0.125804i
$310$	−15965.6	−	15965.6i	−0.166135	−	0.166135i
$311$			30282.7i			0.313093i	0.987671	+	0.156547i	$0.0500361\pi$
$311$			30282.7i			0.313093i	−0.987671	+	0.156547i	$0.949964\pi$
$312$	−8315.76	−	2522.55i	−0.0854265	−	0.0259138i
$313$	−91111.3			−0.930001			−0.465001	−	0.885310i	$-0.653946\pi$
$313$	−91111.3			−0.930001			−0.465001	+	0.885310i	$0.653946\pi$
$314$	26563.0	−	26563.0i	0.269412	−	0.269412i
$315$	16575.1			0.167046
$316$		−	33681.3i		−	0.337299i
$317$	47317.6	−	47317.6i	0.470873	−	0.470873i	−0.431324	−	0.902197i	$-0.641953\pi$
$317$	47317.6	−	47317.6i	0.470873	−	0.470873i	0.902197	+	0.431324i	$0.141953\pi$
$318$	12517.2	−	12517.2i	0.123781	−	0.123781i
$319$	−101441.	−	101441.i	−0.996857	−	0.996857i
$320$	−2171.88	−	2171.88i	−0.0212097	−	0.0212097i
$321$	534.171			0.00518407
$322$			33098.4i			0.319224i
$323$	76206.3	+	76206.3i	0.730442	+	0.730442i
$324$		−	50978.4i		−	0.485620i
$325$	42318.4	+	79172.0i	0.400648	+	0.749557i
$326$	251553.			2.36698
$327$	1597.30	−	1597.30i	0.0149379	−	0.0149379i
$328$	75119.5			0.698240
$329$		−	74939.5i		−	0.692339i
$330$	−6125.99	+	6125.99i	−0.0562533	+	0.0562533i
$331$	−11598.3	+	11598.3i	−0.105861	+	0.105861i	−0.758054	−	0.652192i	$-0.773849\pi$
$331$	−11598.3	+	11598.3i	−0.105861	+	0.105861i	0.652192	+	0.758054i	$0.273849\pi$
$332$	−46039.5	−	46039.5i	−0.417690	−	0.417690i
$333$	36301.6	+	36301.6i	0.327369	+	0.327369i
$334$	80911.4			0.725298
$335$		−	27556.5i		−	0.245547i
$336$	−6652.21	−	6652.21i	−0.0589234	−	0.0589234i
$337$			50574.4i			0.445319i	0.974896	+	0.222659i	$0.0714738\pi$
$337$			50574.4i			0.445319i	−0.974896	+	0.222659i	$0.928526\pi$
$338$	−27488.1	−	138191.i	−0.240609	−	1.20961i
$339$	−7994.27			−0.0695632
$340$	19977.9	−	19977.9i	0.172819	−	0.172819i
$341$	62997.2			0.541767
$342$		−	120263.i		−	1.02820i
$343$	66270.4	−	66270.4i	0.563289	−	0.563289i
$344$	−84986.1	+	84986.1i	−0.718177	+	0.718177i
$345$	2890.42	+	2890.42i	0.0242842	+	0.0242842i
$346$	70908.3	+	70908.3i	0.592304	+	0.592304i
$347$	−151929.			−1.26177			−0.630885	−	0.775876i	$-0.717308\pi$
$347$	−151929.			−1.26177			−0.630885	+	0.775876i	$0.717308\pi$
$348$			12202.7i			0.100762i
$349$	−141017.	−	141017.i	−1.15776	−	1.15776i	−0.984955	−	0.172810i	$-0.944715\pi$
$349$	−141017.	−	141017.i	−1.15776	−	1.15776i	−0.172810	−	0.984955i	$-0.555285\pi$
$350$			56661.0i			0.462539i
$351$	32466.2	−	17353.6i	0.263522	−	0.140856i
$352$	−129738.			−1.04708
$353$	−111821.	+	111821.i	−0.897375	+	0.897375i	−0.995203	−	0.0978279i	$-0.968811\pi$
$353$	−111821.	+	111821.i	−0.897375	+	0.897375i	0.0978279	+	0.995203i	$0.468811\pi$
$354$	1805.31			0.0144061
$355$		−	76439.6i		−	0.606543i
$356$	−48875.1	+	48875.1i	−0.385645	+	0.385645i
$357$	−7276.57	+	7276.57i	−0.0570940	+	0.0570940i
$358$	146917.	+	146917.i	1.14632	+	1.14632i
$359$	−16698.6	−	16698.6i	−0.129566	−	0.129566i	0.639350	−	0.768916i	$-0.279204\pi$
$359$	−16698.6	−	16698.6i	−0.129566	−	0.129566i	−0.768916	+	0.639350i	$0.779204\pi$
$360$	28980.2			0.223613
$361$			35457.6i			0.272079i
$362$	−39978.2	−	39978.2i	−0.305074	−	0.305074i
$363$		−	4257.94i		−	0.0323137i
$364$	8843.13	−	29152.0i	0.0667426	−	0.220022i
$365$	−4501.98			−0.0337923
$366$	−16662.3	+	16662.3i	−0.124386	+	0.124386i
$367$	237835.			1.76581			0.882905	−	0.469551i	$-0.155584\pi$
$367$	237835.			1.76581			0.882905	+	0.469551i	$0.155584\pi$
$368$			99260.1i			0.732958i
$369$	−111211.	+	111211.i	−0.816759	+	0.816759i
$370$	21913.7	−	21913.7i	0.160071	−	0.160071i
$371$	−40335.3	−	40335.3i	−0.293047	−	0.293047i
$372$	−3789.07	−	3789.07i	−0.0273808	−	0.0273808i
$373$	−176379.			−1.26773			−0.633867	−	0.773442i	$-0.718533\pi$
$373$	−176379.			−1.26773			−0.633867	+	0.773442i	$0.718533\pi$
$374$			230118.i			1.64516i
$375$	10770.0	+	10770.0i	0.0765864	+	0.0765864i
$376$		−	131025.i		−	0.926787i
$377$	160392.	−	85731.7i	1.12850	−	0.603196i
$378$	23235.1			0.162615
$379$	145770.	−	145770.i	1.01482	−	1.01482i	0.0149312	−	0.999889i	$-0.495247\pi$
$379$	145770.	−	145770.i	1.01482	−	1.01482i	0.999889	−	0.0149312i	$-0.00475293\pi$
$380$	−24869.0			−0.172223
$381$			25798.9i			0.177726i
$382$	−103766.	+	103766.i	−0.711095	+	0.711095i
$383$	−93481.5	+	93481.5i	−0.637277	+	0.637277i	−0.949883	−	0.312606i	$-0.898798\pi$
$383$	−93481.5	+	93481.5i	−0.637277	+	0.637277i	0.312606	+	0.949883i	$0.398798\pi$
$384$	−16480.8	−	16480.8i	−0.111767	−	0.111767i
$385$	19740.3	+	19740.3i	0.133178	+	0.133178i
$386$	−109804.			−0.736958
$387$		−	251636.i		−	1.68016i
$388$	90582.8	+	90582.8i	0.601703	+	0.601703i
$389$			230862.i			1.52565i	0.646607	+	0.762824i	$0.276187\pi$
$389$			230862.i			1.52565i	−0.646607	+	0.762824i	$0.723813\pi$
$390$	−5177.30	−	9686.02i	−0.0340388	−	0.0636819i
$391$	108576.			0.710202
$392$	51685.4	−	51685.4i	0.336353	−	0.336353i
$393$	226.751			0.00146813
$394$		−	154043.i		−	0.992313i
$395$	−27668.3	+	27668.3i	−0.177333	+	0.177333i
$396$	62201.0	−	62201.0i	0.396649	−	0.396649i
$397$	−52860.3	−	52860.3i	−0.335389	−	0.335389i	0.519240	−	0.854629i	$-0.326215\pi$
$397$	−52860.3	−	52860.3i	−0.335389	−	0.335389i	−0.854629	+	0.519240i	$0.826215\pi$
$398$	−221637.	−	221637.i	−1.39919	−	1.39919i
$399$	9058.05			0.0568969
$400$			169923.i			1.06202i
$401$	−55481.9	−	55481.9i	−0.345034	−	0.345034i	0.513222	−	0.858256i	$-0.328452\pi$
$401$	−55481.9	−	55481.9i	−0.345034	−	0.345034i	−0.858256	+	0.513222i	$0.828452\pi$
$402$		−	19091.3i		−	0.118136i
$403$	−23183.0	+	76424.2i	−0.142744	+	0.470567i
$404$	69707.7			0.427089
$405$	−41877.5	+	41877.5i	−0.255312	+	0.255312i
$406$	114788.			0.696376
$407$			86467.3i			0.521991i
$408$	−12722.5	+	12722.5i	−0.0764278	+	0.0764278i
$409$	222055.	−	222055.i	1.32743	−	1.32743i	0.419834	−	0.907601i	$-0.362088\pi$
$409$	222055.	−	222055.i	1.32743	−	1.32743i	0.907601	−	0.419834i	$-0.137912\pi$
$410$	67133.1	+	67133.1i	0.399364	+	0.399364i
$411$	7192.40	+	7192.40i	0.0425785	+	0.0425785i
$412$	−73624.5			−0.433738
$413$		−	5817.40i		−	0.0341058i
$414$	−85673.5	−	85673.5i	−0.499857	−	0.499857i
$415$			75640.6i			0.439196i
$416$	47743.5	−	157390.i	0.275885	−	0.909473i
$417$	−45016.2			−0.258879
$418$	143228.	−	143228.i	0.819738	−	0.819738i
$419$	−106881.			−0.608797			−0.304399	−	0.952545i	$-0.598455\pi$
$419$	−106881.			−0.608797			−0.304399	+	0.952545i	$0.598455\pi$
$420$		−	2374.62i		−	0.0134616i
$421$	32008.8	−	32008.8i	0.180595	−	0.180595i	−0.611020	−	0.791615i	$-0.709241\pi$
$421$	32008.8	−	32008.8i	0.180595	−	0.180595i	0.791615	+	0.611020i	$0.209241\pi$
$422$	−32924.0	+	32924.0i	−0.184879	+	0.184879i
$423$	193977.	+	193977.i	1.08410	+	1.08410i
$424$	−70522.8	−	70522.8i	−0.392282	−	0.392282i
$425$	185871.			1.02904
$426$		−	52957.8i		−	0.291817i
$427$	53692.1	+	53692.1i	0.294479	+	0.294479i
$428$			3274.10i			0.0178733i
$429$	29323.9	+	8895.28i	0.159334	+	0.0483331i
$430$	−151902.			−0.821534
$431$	−4372.31	+	4372.31i	−0.0235373	+	0.0235373i	−0.718777	−	0.695240i	$-0.755298\pi$
$431$	−4372.31	+	4372.31i	−0.0235373	+	0.0235373i	0.695240	+	0.718777i	$0.255298\pi$
$432$	69680.5			0.373374
$433$			299051.i			1.59503i	0.603298	+	0.797516i	$0.293853\pi$
$433$			299051.i			1.59503i	−0.603298	+	0.797516i	$0.706147\pi$
$434$	−35642.9	+	35642.9i	−0.189232	+	0.189232i
$435$	10024.2	−	10024.2i	0.0529750	−	0.0529750i
$436$	9790.31	+	9790.31i	0.0515019	+	0.0515019i
$437$	−67579.2	−	67579.2i	−0.353875	−	0.353875i
$438$	−3118.99			−0.0162580
$439$			52613.5i			0.273003i	0.990640	+	0.136502i	$0.0435859\pi$
$439$			52613.5i			0.273003i	−0.990640	+	0.136502i	$0.956414\pi$
$440$	34514.2	+	34514.2i	0.178276	+	0.178276i
$441$			153035.i			0.786892i
$442$	−279164.	−	84683.3i	−1.42895	−	0.433464i
$443$	−157260.			−0.801329			−0.400664	−	0.916225i	$-0.631221\pi$
$443$	−157260.			−0.801329			−0.400664	+	0.916225i	$0.631221\pi$
$444$	5200.72	−	5200.72i	0.0263814	−	0.0263814i
$445$	80299.4			0.405501
$446$			257422.i			1.29412i
$447$	−8435.28	+	8435.28i	−0.0422167	+	0.0422167i
$448$	−4848.67	+	4848.67i	−0.0241583	+	0.0241583i
$449$	−156794.	−	156794.i	−0.777743	−	0.777743i	0.201704	−	0.979447i	$-0.435352\pi$
$449$	−156794.	−	156794.i	−0.777743	−	0.777743i	−0.979447	+	0.201704i	$0.935352\pi$
$450$	−146664.	−	146664.i	−0.724266	−	0.724266i
$451$	−264894.			−1.30233
$452$		−	48999.3i		−	0.239835i
$453$	34240.6	+	34240.6i	0.166857	+	0.166857i
$454$			117772.i			0.571389i
$455$	−31212.0	+	16683.2i	−0.150765	+	0.0805856i
$456$	15837.2			0.0761640
$457$	−69443.0	+	69443.0i	−0.332503	+	0.332503i	−0.853537	−	0.521033i	$-0.825547\pi$
$457$	−69443.0	+	69443.0i	−0.332503	+	0.332503i	0.521033	+	0.853537i	$0.325547\pi$
$458$	−40432.3			−0.192751
$459$		−	76220.5i		−	0.361782i
$460$	−17716.3	+	17716.3i	−0.0837253	+	0.0837253i
$461$	110039.	−	110039.i	0.517779	−	0.517779i	−0.399120	−	0.916899i	$-0.630684\pi$
$461$	110039.	−	110039.i	0.517779	−	0.517779i	0.916899	+	0.399120i	$0.130684\pi$
$462$	13676.1	+	13676.1i	0.0640737	+	0.0640737i
$463$	−55855.2	−	55855.2i	−0.260556	−	0.260556i	0.564724	−	0.825280i	$-0.308983\pi$
$463$	−55855.2	−	55855.2i	−0.260556	−	0.260556i	−0.825280	+	0.564724i	$0.808983\pi$
$464$	344242.			1.59892
$465$			6225.25i			0.0287906i
$466$	−15213.6	−	15213.6i	−0.0700583	−	0.0700583i
$467$			122121.i			0.559960i	0.960006	+	0.279980i	$0.0903279\pi$
$467$			122121.i			0.559960i	−0.960006	+	0.279980i	$0.909672\pi$
$468$	52568.3	+	98348.2i	0.240012	+	0.449030i
$469$	−61519.3			−0.279683
$470$	117095.	−	117095.i	0.530083	−	0.530083i
$471$	−10357.3			−0.0466881
$472$		−	10171.2i		−	0.0456552i
$473$	299687.	−	299687.i	1.33951	−	1.33951i
$474$	−19168.8	+	19168.8i	−0.0853174	+	0.0853174i
$475$	−115688.	−	115688.i	−0.512746	−	0.512746i
$476$	−44600.3	−	44600.3i	−0.196845	−	0.196845i
$477$	208811.			0.917734
$478$			47028.8i			0.205830i
$479$	228045.	+	228045.i	0.993915	+	0.993915i	0.999982	−	0.00606704i	$-0.00193121\pi$
$479$	228045.	+	228045.i	0.993915	+	0.993915i	−0.00606704	+	0.999982i	$0.501931\pi$
$480$		−	12820.4i		−	0.0556442i
$481$	−104897.	−	31820.0i	−0.453390	−	0.137534i
$482$	292129.			1.25742
$483$	6452.81	−	6452.81i	0.0276602	−	0.0276602i
$484$	26098.2			0.111409
$485$		−	148823.i		−	0.632684i
$486$	−90561.4	+	90561.4i	−0.383416	+	0.383416i
$487$	139290.	−	139290.i	0.587304	−	0.587304i	−0.349597	−	0.936900i	$-0.613681\pi$
$487$	139290.	−	139290.i	0.587304	−	0.587304i	0.936900	+	0.349597i	$0.113681\pi$
$488$	93876.2	+	93876.2i	0.394199	+	0.394199i
$489$	−49042.3	−	49042.3i	−0.205094	−	0.205094i
$490$	92380.9			0.384760
$491$		−	321820.i		−	1.33490i	−0.744653	−	0.667451i	$-0.767385\pi$
$491$		−	321820.i		−	1.33490i	0.744653	−	0.667451i	$-0.232615\pi$
$492$	15932.5	+	15932.5i	0.0658193	+	0.0658193i
$493$		−	376551.i		−	1.54928i
$494$	121047.	+	226463.i	0.496022	+	0.927990i
$495$	−102193.			−0.417072
$496$	−106891.	+	106891.i	−0.434487	+	0.434487i
$497$	−170650.			−0.690865
$498$			52404.2i			0.211304i
$499$	−228774.	+	228774.i	−0.918767	+	0.918767i	−0.996940	−	0.0781727i	$-0.975091\pi$
$499$	−228774.	+	228774.i	−0.918767	+	0.918767i	0.0781727	+	0.996940i	$0.475091\pi$
$500$	−66012.4	+	66012.4i	−0.264049	+	0.264049i
$501$	−15774.3	−	15774.3i	−0.0628457	−	0.0628457i
$502$	261900.	+	261900.i	1.03927	+	1.03927i
$503$	−353111.			−1.39565			−0.697823	−	0.716271i	$-0.745848\pi$
$503$	−353111.			−1.39565			−0.697823	+	0.716271i	$0.745848\pi$
$504$		−	64697.8i		−	0.254700i
$505$	−57263.1	−	57263.1i	−0.224539	−	0.224539i
$506$		−	204067.i		−	0.797024i
$507$	−21582.4	+	32300.5i	−0.0839622	+	0.125659i
$508$	−158130.			−0.612753
$509$	56162.6	−	56162.6i	0.216776	−	0.216776i	−0.590362	−	0.807138i	$-0.701015\pi$
$509$	56162.6	−	56162.6i	0.216776	−	0.216776i	0.807138	+	0.590362i	$0.201015\pi$
$510$	−22739.8			−0.0874270
$511$			10050.6i			0.0384901i
$512$	83315.4	−	83315.4i	0.317823	−	0.317823i
$513$	−47440.5	+	47440.5i	−0.180266	+	0.180266i
$514$	−114571.	−	114571.i	−0.433658	−	0.433658i
$515$	60480.7	+	60480.7i	0.228035	+	0.228035i
$516$	−36050.3			−0.135397
$517$			462036.i			1.72860i
$518$	−48922.0	−	48922.0i	−0.182324	−	0.182324i
$519$		−	27648.3i		−	0.102644i
$520$	−54571.7	+	29169.2i	−0.201818	+	0.107874i
$521$	−653.559			−0.00240774			−0.00120387	−	0.999999i	$-0.500383\pi$
$521$	−653.559			−0.00240774			−0.00120387	+	0.999999i	$0.500383\pi$
$522$	−297122.	+	297122.i	−1.09042	+	1.09042i
$523$	−90474.5			−0.330768			−0.165384	−	0.986229i	$-0.552886\pi$
$523$	−90474.5			−0.330768			−0.165384	+	0.986229i	$0.552886\pi$
$524$			1389.82i			0.00506171i
$525$	11046.5	−	11046.5i	0.0400781	−	0.0400781i
$526$	−213582.	+	213582.i	−0.771959	+	0.771959i
$527$	116923.	+	116923.i	0.420998	+	0.420998i
$528$	41013.9	+	41013.9i	0.147117	+	0.147117i
$529$	183556.			0.655930
$530$		−	126050.i		−	0.448737i
$531$	15058.0	+	15058.0i	0.0534046	+	0.0534046i
$532$			55519.5i			0.196165i
$533$	97481.0	−	321353.i	0.343136	−	1.13117i
$534$	55631.8			0.195093
$535$	2689.59	−	2689.59i	0.00939677	−	0.00939677i
$536$	−107561.			−0.374392
$537$		−	57285.5i		−	0.198653i
$538$	443590.	−	443590.i	1.53256	−	1.53256i
$539$	−182259.	+	182259.i	−0.627351	+	0.627351i
$540$	12436.8	+	12436.8i	0.0426502	+	0.0426502i
$541$	406174.	+	406174.i	1.38777	+	1.38777i	0.829987	+	0.557782i	$0.188348\pi$
$541$	406174.	+	406174.i	1.38777	+	1.38777i	0.557782	+	0.829987i	$0.311652\pi$
$542$	151552.			0.515898
$543$			15588.1i			0.0528682i
$544$	−240794.	−	240794.i	−0.813671	−	0.813671i
$545$		−	16085.0i		−	0.0541537i
$546$	−21623.9	+	11558.2i	−0.0725351	+	0.0387709i
$547$	315859.			1.05565			0.527823	−	0.849354i	$-0.323008\pi$
$547$	315859.			1.05565			0.527823	+	0.849354i	$0.323008\pi$
$548$	−44084.4	+	44084.4i	−0.146799	+	0.146799i
$549$	−277958.			−0.922221
$550$		−	349340.i		−	1.15484i
$551$	−234370.	+	234370.i	−0.771966	+	0.771966i
$552$	11282.2	−	11282.2i	0.0370268	−	0.0370268i
$553$	61769.1	+	61769.1i	0.201986	+	0.201986i
$554$	245173.	+	245173.i	0.798829	+	0.798829i
$555$	−8544.52			−0.0277397
$556$		−	275918.i		−	0.892545i
$557$	−203963.	−	203963.i	−0.657416	−	0.657416i	0.297352	−	0.954768i	$-0.403896\pi$
$557$	−203963.	−	203963.i	−0.657416	−	0.657416i	−0.954768	+	0.297352i	$0.903896\pi$
$558$		−	184519.i		−	0.592616i
$559$	253277.	+	473846.i	0.810535	+	1.51640i
$560$	−66988.8			−0.213612
$561$	44863.4	−	44863.4i	0.142550	−	0.142550i
$562$	227554.			0.720462
$563$		−	454782.i		−	1.43478i	−0.696669	−	0.717392i	$-0.745336\pi$
$563$		−	454782.i		−	1.43478i	0.696669	−	0.717392i	$-0.254664\pi$
$564$	27789.9	−	27789.9i	0.0873632	−	0.0873632i
$565$	−40251.7	+	40251.7i	−0.126092	+	0.126092i
$566$	−215941.	−	215941.i	−0.674067	−	0.674067i
$567$	93490.8	+	93490.8i	0.290806	+	0.290806i
$568$	−298367.			−0.924814
$569$			61243.8i			0.189164i	0.995517	+	0.0945818i	$0.0301514\pi$
$569$			61243.8i			0.189164i	−0.995517	+	0.0945818i	$0.969849\pi$
$570$	14153.5	+	14153.5i	0.0435626	+	0.0435626i
$571$		−	385360.i		−	1.18194i	−0.806694	−	0.590969i	$-0.798745\pi$
$571$		−	385360.i		−	1.18194i	0.806694	−	0.590969i	$-0.201255\pi$
$572$	−54521.9	+	179735.i	−0.166640	+	0.549340i
$573$	40460.0			0.123230
$574$	149873.	−	149873.i	0.454884	−	0.454884i
$575$	−164829.			−0.498538
$576$		−	25101.1i		−	0.0756566i
$577$	17322.8	−	17322.8i	0.0520316	−	0.0520316i	−0.680612	−	0.732644i	$-0.738286\pi$
$577$	17322.8	−	17322.8i	0.0520316	−	0.0520316i	0.732644	+	0.680612i	$0.238286\pi$
$578$	−135752.	+	135752.i	−0.406342	+	0.406342i
$579$	21407.2	+	21407.2i	0.0638561	+	0.0638561i
$580$	61441.4	+	61441.4i	0.182644	+	0.182644i
$581$	168866.			0.500254
$582$		−	103105.i		−	0.304394i
$583$	248685.	+	248685.i	0.731666	+	0.731666i
$584$			17572.6i			0.0515241i
$585$	37607.1	−	123974.i	0.109890	−	0.362260i
$586$	−219643.			−0.639622
$587$	−195267.	+	195267.i	−0.566698	+	0.566698i	−0.931202	−	0.364504i	$-0.881239\pi$
$587$	−195267.	+	195267.i	−0.566698	+	0.566698i	0.364504	+	0.931202i	$0.381239\pi$
$588$	21924.5			0.0634124
$589$		−	145549.i		−	0.419545i
$590$	9089.88	−	9089.88i	0.0261128	−	0.0261128i
$591$	−30031.9	+	30031.9i	−0.0859820	+	0.0859820i
$592$	−146714.	−	146714.i	−0.418628	−	0.418628i
$593$	194446.	+	194446.i	0.552956	+	0.552956i	0.927293	−	0.374337i	$-0.122130\pi$
$593$	194446.	+	194446.i	0.552956	+	0.552956i	−0.374337	+	0.927293i	$0.622130\pi$
$594$	−143255.			−0.406009
$595$			73276.2i			0.206980i
$596$	−51702.4	−	51702.4i	−0.145552	−	0.145552i
$597$			86419.8i			0.242474i
$598$	247561.	+	75096.6i	0.692277	+	0.209999i
$599$	547193.			1.52506			0.762531	−	0.646952i	$-0.223957\pi$
$599$	547193.			1.52506			0.762531	+	0.646952i	$0.223957\pi$
$600$	19313.9	−	19313.9i	0.0536498	−	0.0536498i
$601$	−4486.27			−0.0124204			−0.00621021	−	0.999981i	$-0.501977\pi$
$601$	−4486.27			−0.0124204			−0.00621021	+	0.999981i	$0.501977\pi$
$602$			339117.i			0.935744i
$603$	159239.	−	159239.i	0.437941	−	0.437941i
$604$	−209871.	+	209871.i	−0.575279	+	0.575279i
$605$	−21439.0	−	21439.0i	−0.0585726	−	0.0585726i
$606$	−39672.2	−	39672.2i	−0.108029	−	0.108029i
$607$	17313.3			0.0469898			0.0234949	−	0.999724i	$-0.492521\pi$
$607$	17313.3			0.0469898			0.0234949	+	0.999724i	$0.492521\pi$
$608$			299746.i			0.810862i
$609$	−22378.8	−	22378.8i	−0.0603397	−	0.0603397i
$610$			167791.i			0.450931i
$611$	−560513.	−	170029.i	−1.50142	−	0.455450i
$612$	230891.			0.616459
$613$	−338843.	+	338843.i	−0.901732	+	0.901732i	−0.995586	−	0.0938541i	$-0.970081\pi$
$613$	−338843.	+	338843.i	−0.901732	+	0.901732i	0.0938541	+	0.995586i	$0.470081\pi$
$614$	−7943.41			−0.0210703
$615$		−	26176.3i		−	0.0692083i
$616$	77052.3	−	77052.3i	0.203060	−	0.203060i
$617$	130914.	−	130914.i	0.343888	−	0.343888i	−0.513939	−	0.857827i	$-0.671814\pi$
$617$	130914.	−	130914.i	0.343888	−	0.343888i	0.857827	+	0.513939i	$0.171814\pi$
$618$	41901.3	+	41901.3i	0.109711	+	0.109711i
$619$	−408183.	−	408183.i	−1.06530	−	1.06530i	−0.997713	−	0.0675916i	$-0.978469\pi$
$619$	−408183.	−	408183.i	−1.06530	−	1.06530i	−0.0675916	−	0.997713i	$-0.521531\pi$
$620$	−38156.5			−0.0992624
$621$			67591.8i			0.175271i
$622$	105636.	+	105636.i	0.273043	+	0.273043i
$623$		−	179267.i		−	0.461874i
$624$	−64848.6	+	34662.4i	−0.166545	+	0.0890203i
$625$	−223543.			−0.572270
$626$	−317826.	+	317826.i	−0.811036	+	0.811036i
$627$	−55847.0			−0.142058
$628$		−	63483.3i		−	0.160968i
$629$	−160484.	+	160484.i	−0.405631	+	0.405631i
$630$	57819.4	−	57819.4i	0.145677	−	0.145677i
$631$	39255.5	+	39255.5i	0.0985921	+	0.0985921i	0.754682	−	0.656090i	$-0.227791\pi$
$631$	39255.5	+	39255.5i	0.0985921	+	0.0985921i	−0.656090	+	0.754682i	$0.727791\pi$
$632$	107998.	+	107998.i	0.270384	+	0.270384i
$633$	12837.6			0.0320388
$634$		−	330118.i		−	0.821279i
$635$	129900.	+	129900.i	0.322152	+	0.322152i
$636$		−	29915.1i		−	0.0739565i
$637$	−154034.	−	288176.i	−0.379609	−	0.710197i
$638$	−707719.			−1.73868
$639$	441718.	−	441718.i	1.08179	−	1.08179i
$640$	−165964.			−0.405185
$641$			359360.i			0.874608i	0.899314	+	0.437304i	$0.144067\pi$
$641$			359360.i			0.874608i	−0.899314	+	0.437304i	$0.855933\pi$
$642$	1863.36	−	1863.36i	0.00452092	−	0.00452092i
$643$	75424.7	−	75424.7i	0.182428	−	0.182428i	−0.609985	−	0.792413i	$-0.708825\pi$
$643$	75424.7	−	75424.7i	0.182428	−	0.182428i	0.792413	+	0.609985i	$0.208825\pi$
$644$	39551.3	+	39551.3i	0.0953649	+	0.0953649i
$645$	29614.5	+	29614.5i	0.0711843	+	0.0711843i
$646$	531665.			1.27401
$647$		−	124143.i		−	0.296561i	−0.988945	−	0.148280i	$-0.952626\pi$
$647$		−	124143.i		−	0.296561i	0.988945	−	0.148280i	$-0.0473738\pi$
$648$	163461.	+	163461.i	0.389282	+	0.389282i
$649$			35866.9i			0.0851539i
$650$	423798.	+	128557.i	1.00307	+	0.304278i
$651$	13897.8			0.0327931
$652$	300595.	−	300595.i	0.707110	−	0.707110i
$653$	281319.			0.659741			0.329870	−	0.944026i	$-0.392995\pi$
$653$	281319.			0.659741			0.329870	+	0.944026i	$0.392995\pi$
$654$		−	11143.8i		−	0.0260541i
$655$	1141.71	−	1141.71i	0.00266116	−	0.00266116i
$656$	449461.	−	449461.i	1.04444	−	1.04444i
$657$	−26015.4	−	26015.4i	−0.0602698	−	0.0602698i
$658$	−261413.	−	261413.i	−0.603776	−	0.603776i
$659$	380522.			0.876211			0.438105	−	0.898924i	$-0.355650\pi$
$659$	380522.			0.876211			0.438105	+	0.898924i	$0.355650\pi$
$660$			14640.6i			0.0336102i
$661$	−228096.	−	228096.i	−0.522053	−	0.522053i	0.396138	−	0.918191i	$-0.370350\pi$
$661$	−228096.	−	228096.i	−0.522053	−	0.522053i	−0.918191	+	0.396138i	$0.870350\pi$
$662$			80917.1i			0.184639i
$663$	37915.7	+	70935.1i	0.0862566	+	0.161374i
$664$	295248.			0.669655
$665$	45607.9	−	45607.9i	0.103133	−	0.103133i
$666$	253264.			0.570985
$667$			333923.i			0.750576i
$668$	96685.7	−	96685.7i	0.216675	−	0.216675i
$669$	50186.5	−	50186.5i	0.112133	−	0.112133i
$670$	−96125.8	−	96125.8i	−0.214136	−	0.214136i
$671$	−331036.	−	331036.i	−0.735242	−	0.735242i
$672$	−28621.3			−0.0633799
$673$			344055.i			0.759623i	0.925064	+	0.379812i	$0.124011\pi$
$673$			344055.i			0.759623i	−0.925064	+	0.379812i	$0.875989\pi$
$674$	176420.	+	176420.i	0.388354	+	0.388354i
$675$			115710.i			0.253959i
$676$	−197979.	−	132285.i	−0.433238	−	0.289479i
$677$	−587949.			−1.28281			−0.641405	−	0.767203i	$-0.721648\pi$
$677$	−587949.			−1.28281			−0.641405	+	0.767203i	$0.721648\pi$
$678$	−27886.6	+	27886.6i	−0.0606647	+	0.0606647i
$679$	−332245.			−0.720640
$680$			128117.i			0.277070i
$681$	22960.7	−	22960.7i	0.0495098	−	0.0495098i
$682$	219755.	−	219755.i	0.472465	−	0.472465i
$683$	196194.	+	196194.i	0.420577	+	0.420577i	0.885402	−	0.464826i	$-0.153883\pi$
$683$	196194.	+	196194.i	0.420577	+	0.420577i	−0.464826	+	0.885402i	$0.653883\pi$
$684$	−143709.	−	143709.i	−0.307165	−	0.307165i
$685$	72428.5			0.154358
$686$		−	462345.i		−	0.982467i
$687$	7882.61	+	7882.61i	0.0167015	+	0.0167015i
$688$			1.01699e6i			2.14853i
$689$	−393205.	+	210173.i	−0.828287	+	0.442730i
$690$	20165.5			0.0423555
$691$	365985.	−	365985.i	0.766491	−	0.766491i	−0.210996	−	0.977487i	$-0.567671\pi$
$691$	365985.	−	365985.i	0.766491	−	0.766491i	0.977487	+	0.210996i	$0.0676708\pi$
$692$	169465.			0.353889
$693$			228144.i			0.475054i
$694$	−529976.	+	529976.i	−1.10037	+	1.10037i
$695$	−226660.	+	226660.i	−0.469250	+	0.469250i
$696$	−39127.5	−	39127.5i	−0.0807726	−	0.0807726i
$697$	−491646.	−	491646.i	−1.01201	−	1.01201i
$698$	−983825.			−2.01933
$699$			5932.02i			0.0121408i
$700$	67707.5	+	67707.5i	0.138179	+	0.138179i
$701$			98155.0i			0.199745i	0.995000	+	0.0998727i	$0.0318435\pi$
$701$			98155.0i			0.199745i	−0.995000	+	0.0998727i	$0.968156\pi$
$702$	52717.7	−	173788.i	0.106975	−	0.352650i
$703$	199774.			0.404230
$704$	29894.3	−	29894.3i	0.0603174	−	0.0603174i
$705$	−45657.4			−0.0918614
$706$			780136.i			1.56517i
$707$	−127839.	+	127839.i	−0.255755	+	0.255755i
$708$	2157.27	−	2157.27i	0.00430367	−	0.00430367i
$709$	355920.	+	355920.i	0.708044	+	0.708044i	0.966124	−	0.258080i	$-0.0830898\pi$
$709$	355920.	+	355920.i	0.708044	+	0.708044i	−0.258080	+	0.966124i	$0.583090\pi$
$710$	−266646.	−	266646.i	−0.528955	−	0.528955i
$711$	−319772.			−0.632559
$712$		−	313433.i		−	0.618279i
$713$	−103687.	−	103687.i	−0.203960	−	0.203960i
$714$			50766.1i			0.0995812i
$715$	192436.	−	102860.i	0.376422	−	0.201202i
$716$	351120.			0.684904
$717$	9168.65	−	9168.65i	0.0178348	−	0.0178348i
$718$	−116500.			−0.225984
$719$		−	210007.i		−	0.406234i	−0.979154	−	0.203117i	$-0.934893\pi$
$719$		−	210007.i		−	0.406234i	0.979154	−	0.203117i	$-0.0651072\pi$
$720$	173397.	−	173397.i	0.334484	−	0.334484i
$721$	135022.	−	135022.i	0.259737	−	0.259737i
$722$	123688.	+	123688.i	0.237275	+	0.237275i
$723$	−56953.0	−	56953.0i	−0.108953	−	0.108953i
$724$	−95544.5			−0.182276
$725$			571640.i			1.08754i
$726$	−14853.1	−	14853.1i	−0.0281801	−	0.0281801i
$727$		−	577302.i		−	1.09228i	−0.837694	−	0.546140i	$-0.816097\pi$
$727$		−	577302.i		−	1.09228i	0.837694	−	0.546140i	$-0.183903\pi$
$728$	65119.8	+	121830.i	0.122871	+	0.229875i
$729$	−459993.			−0.865558
$730$	−15704.4	+	15704.4i	−0.0294696	+	0.0294696i
$731$	1.11244e6			2.08182
$732$			39821.4i			0.0743181i
$733$	275772.	−	275772.i	0.513267	−	0.513267i	−0.402259	−	0.915526i	$-0.631775\pi$
$733$	275772.	−	275772.i	0.513267	−	0.513267i	0.915526	+	0.402259i	$0.131775\pi$
$734$	829646.	−	829646.i	1.53993	−	1.53993i
$735$	−18010.4	−	18010.4i	−0.0333387	−	0.0333387i
$736$	213535.	+	213535.i	0.394197	+	0.394197i
$737$	379294.			0.698298
$738$			775878.i			1.42456i
$739$	85132.1	+	85132.1i	0.155885	+	0.155885i	0.780740	−	0.624855i	$-0.214842\pi$
$739$	85132.1	+	85132.1i	0.155885	+	0.155885i	−0.624855	+	0.780740i	$0.714842\pi$
$740$		−	52372.0i		−	0.0956391i
$741$	20551.7	−	67750.0i	0.0374292	−	0.123388i
$742$	−281405.			−0.511121
$743$	424331.	−	424331.i	0.768648	−	0.768648i	−0.209221	−	0.977868i	$-0.567093\pi$
$743$	424331.	−	424331.i	0.768648	−	0.768648i	0.977868	+	0.209221i	$0.0670927\pi$
$744$	24299.1			0.0438979
$745$			84944.5i			0.153046i
$746$	−615265.	+	615265.i	−1.10557	+	1.10557i
$747$	−437101.	+	437101.i	−0.783322	+	0.783322i
$748$	274981.	+	274981.i	0.491473	+	0.491473i
$749$	−6004.46	−	6004.46i	−0.0107031	−	0.0107031i
$750$	75138.2			0.133579
$751$		−	503003.i		−	0.891847i	−0.895071	−	0.445924i	$-0.852875\pi$
$751$		−	503003.i		−	0.891847i	0.895071	−	0.445924i	$-0.147125\pi$
$752$	−783961.	−	783961.i	−1.38631	−	1.38631i
$753$		−	102119.i		−	0.180102i
$754$	260440.	−	858560.i	0.458106	−	1.51018i
$755$	344808.			0.604899
$756$	27764.9	−	27764.9i	0.0485795	−	0.0485795i
$757$	−57856.7			−0.100963			−0.0504815	−	0.998725i	$-0.516076\pi$
$757$	−57856.7			−0.100963			−0.0504815	+	0.998725i	$0.516076\pi$
$758$		−	1.01698e6i		−	1.77001i
$759$	−39784.5	+	39784.5i	−0.0690606	+	0.0690606i
$760$	79741.6	−	79741.6i	0.138057	−	0.138057i
$761$	104906.	+	104906.i	0.181147	+	0.181147i	0.791855	−	0.610709i	$-0.209115\pi$
$761$	104906.	+	104906.i	0.181147	+	0.181147i	−0.610709	+	0.791855i	$0.709115\pi$
$762$	89995.1	+	89995.1i	0.154992	+	0.154992i
$763$	−35909.5			−0.0616822
$764$			247992.i			0.424864i
$765$	−189671.	−	189671.i	−0.324100	−	0.324100i
$766$			652188.i			1.11151i
$767$	−43511.5	−	13199.0i	−0.0739628	−	0.0224363i
$768$	−108079.			−0.183239
$769$	−708587.	+	708587.i	−1.19823	+	1.19823i	−0.223535	+	0.974696i	$0.571760\pi$
$769$	−708587.	+	708587.i	−1.19823	+	1.19823i	−0.974696	+	0.223535i	$0.928240\pi$
$770$	137721.			0.232283
$771$			44673.0i			0.0751513i
$772$	−131211.	+	131211.i	−0.220159	+	0.220159i
$773$	−316939.	+	316939.i	−0.530417	+	0.530417i	−0.920696	−	0.390280i	$-0.872378\pi$
$773$	−316939.	+	316939.i	−0.530417	+	0.530417i	0.390280	+	0.920696i	$0.372378\pi$
$774$	−877787.	−	877787.i	−1.46523	−	1.46523i
$775$	−177501.	−	177501.i	−0.295526	−	0.295526i
$776$	−580902.			−0.964672
$777$			19075.5i			0.0315961i
$778$	805323.	+	805323.i	1.33049	+	1.33049i
$779$			612012.i			1.00852i
$780$	−17761.1	−	5387.74i	−0.0291930	−	0.00885558i
$781$	1.05213e6			1.72492
$782$	378750.	−	378750.i	0.619354	−	0.619354i
$783$	234413.			0.382348
$784$		−	618496.i		−	1.00625i
$785$	−52150.0	+	52150.0i	−0.0846281	+	0.0846281i
$786$	790.979	−	790.979i	0.00128032	−	0.00128032i
$787$	1612.16	+	1612.16i	0.00260291	+	0.00260291i	0.708407	−	0.705804i	$-0.249414\pi$
$787$	1612.16	+	1612.16i	0.00260291	+	0.00260291i	−0.705804	+	0.708407i	$0.749414\pi$
$788$	−184075.	−	184075.i	−0.296443	−	0.296443i
$789$	83279.3			0.133778
$790$			193032.i			0.309297i
$791$	89861.2	+	89861.2i	0.143621	+	0.143621i
$792$			398891.i			0.635922i
$793$	523414.	−	279771.i	0.832336	−	0.444894i
$794$	−368788.			−0.584972
$795$	−24574.5	+	24574.5i	−0.0388822	+	0.0388822i
$796$	−529693.			−0.835984
$797$		−	271788.i		−	0.427872i	−0.976848	−	0.213936i	$-0.931372\pi$
$797$		−	271788.i		−	0.427872i	0.976848	−	0.213936i	$-0.0686284\pi$
$798$	31597.4	−	31597.4i	0.0496187	−	0.0496187i
$799$	−857542.	+	857542.i	−1.34327	+	1.34327i
$800$	365549.	+	365549.i	0.571170	+	0.571170i
$801$	464022.	+	464022.i	0.723225	+	0.723225i
$802$	−387077.			−0.601796
$803$		−	61966.4i		−	0.0961004i
$804$	−22813.2	−	22813.2i	−0.0352919	−	0.0352919i
$805$		−	64980.8i		−	0.100275i
$806$	185723.	+	347462.i	0.285887	+	0.534857i
$807$	−172963.			−0.265587
$808$	−223516.	+	223516.i	−0.342362	+	0.342362i
$809$	1.21512e6			1.85661			0.928307	−	0.371816i	$-0.121265\pi$
$809$	1.21512e6			1.85661			0.928307	+	0.371816i	$0.121265\pi$
$810$			292165.i			0.445305i
$811$	−412152.	+	412152.i	−0.626637	+	0.626637i	−0.947220	−	0.320583i	$-0.896121\pi$
$811$	−412152.	+	412152.i	−0.626637	+	0.626637i	0.320583	+	0.947220i	$0.396121\pi$
$812$	137167.	−	137167.i	0.208035	−	0.208035i
$813$	−29546.4	−	29546.4i	−0.0447016	−	0.0447016i
$814$	301626.	+	301626.i	0.455219	+	0.455219i
$815$	−493863.			−0.743518
$816$			152244.i			0.228645i
$817$	−692398.	−	692398.i	−1.03732	−	1.03732i
$818$		−	1.54920e6i		−	2.31526i
$819$	−276770.	−	83957.0i	−0.412621	−	0.125167i
$820$	160442.			0.238612
$821$	−179399.	+	179399.i	−0.266155	+	0.266155i	−0.827549	−	0.561394i	$-0.810265\pi$
$821$	−179399.	+	179399.i	−0.266155	+	0.266155i	0.561394	+	0.827549i	$0.310265\pi$
$822$	50178.9			0.0742638
$823$		−	184011.i		−	0.271672i	−0.990731	−	0.135836i	$-0.956628\pi$
$823$		−	184011.i		−	0.271672i	0.990731	−	0.135836i	$-0.0433720\pi$
$824$	236075.	−	236075.i	0.347692	−	0.347692i
$825$	−68106.8	+	68106.8i	−0.100065	+	0.100065i
$826$	−20293.0	−	20293.0i	−0.0297431	−	0.0297431i
$827$	576070.	+	576070.i	0.842295	+	0.842295i	0.989157	−	0.146862i	$-0.0469173\pi$
$827$	576070.	+	576070.i	0.842295	+	0.842295i	−0.146862	+	0.989157i	$0.546917\pi$
$828$	−204752.			−0.298654
$829$		−	563450.i		−	0.819872i	−0.912114	−	0.409936i	$-0.865551\pi$
$829$		−	563450.i		−	0.819872i	0.912114	−	0.409936i	$-0.134449\pi$
$830$	263859.	+	263859.i	0.383015	+	0.383015i
$831$		−	95597.2i		−	0.138434i
$832$	25264.8	+	47266.9i	0.0364980	+	0.0682827i
$833$	−676547.			−0.975007
$834$	−157031.	+	157031.i	−0.225763	+	0.225763i
$835$	−158850.			−0.227832
$836$		−	342303.i		−	0.489777i
$837$	−72788.0	+	72788.0i	−0.103898	+	0.103898i
$838$	−372836.	+	372836.i	−0.530921	+	0.530921i
$839$	−48831.3	−	48831.3i	−0.0693705	−	0.0693705i	0.671570	−	0.740941i	$-0.265620\pi$
$839$	−48831.3	−	48831.3i	−0.0693705	−	0.0693705i	−0.740941	+	0.671570i	$0.765620\pi$
$840$	7614.15	+	7614.15i	0.0107910	+	0.0107910i
$841$	450788.			0.637354
$842$		−	223314.i		−	0.314987i
$843$	−44363.5	−	44363.5i	−0.0624267	−	0.0624267i
$844$			78685.5i			0.110461i
$845$	53966.3	+	271304.i	0.0755804	+	0.379964i
$846$	1.35331e6			1.89084
$847$	−47862.2	+	47862.2i	−0.0667154	+	0.0667154i
$848$	−843915.			−1.17357
$849$			84199.1i			0.116813i
$850$	648379.	−	648379.i	0.897410	−	0.897410i
$851$	142316.	−	142316.i	0.196515	−	0.196515i
$852$	−63282.3	−	63282.3i	−0.0871772	−	0.0871772i
$853$	−848662.	−	848662.i	−1.16637	−	1.16637i	−0.983054	−	0.183317i	$-0.941316\pi$
$853$	−848662.	−	848662.i	−1.16637	−	1.16637i	−0.183317	−	0.983054i	$-0.558684\pi$
$854$	374591.			0.513620
$855$			236107.i			0.322981i
$856$	−10498.3	−	10498.3i	−0.0143275	−	0.0143275i
$857$		−	279281.i		−	0.380259i	−0.981759	−	0.190129i	$-0.939109\pi$
$857$		−	279281.i		−	0.380259i	0.981759	−	0.190129i	$-0.0608908\pi$
$858$	133321.	−	71261.7i	0.181102	−	0.0968014i
$859$	428907.			0.581268			0.290634	−	0.956834i	$-0.406134\pi$
$859$	428907.			0.581268			0.290634	+	0.956834i	$0.406134\pi$
$860$	−181516.	+	181516.i	−0.245425	+	0.245425i
$861$	−58438.1			−0.0788297
$862$			30504.1i			0.0410528i
$863$	649915.	−	649915.i	0.872640	−	0.872640i	−0.120120	−	0.992759i	$-0.538328\pi$
$863$	649915.	−	649915.i	0.872640	−	0.872640i	0.992759	+	0.120120i	$0.0383278\pi$
$864$	149901.	−	149901.i	0.200806	−	0.200806i
$865$	−139211.	−	139211.i	−0.186055	−	0.186055i
$866$	1.04319e6	+	1.04319e6i	1.39100	+	1.39100i
$867$	52932.1			0.0704175
$868$			85183.6i			0.113062i
$869$	−380834.	−	380834.i	−0.504309	−	0.504309i
$870$		−	69935.3i		−	0.0923970i
$871$	−139580.	+	460136.i	−0.183987	+	0.606526i
$872$	−62784.7			−0.0825697
$873$	859997.	−	859997.i	1.12841	−	1.12841i
$874$	−471476.			−0.617216
$875$		−	242124.i		−	0.316243i
$876$	−3727.07	+	3727.07i	−0.00485690	+	0.00485690i
$877$	−19817.7	+	19817.7i	−0.0257665	+	0.0257665i	−0.719873	−	0.694106i	$-0.755800\pi$
$877$	−19817.7	+	19817.7i	−0.0257665	+	0.0257665i	0.694106	+	0.719873i	$0.255800\pi$
$878$	183533.	+	183533.i	0.238081	+	0.238081i
$879$	42821.3	+	42821.3i	0.0554220	+	0.0554220i
$880$	413016.			0.533337
$881$			415393.i			0.535190i	0.963532	+	0.267595i	$0.0862288\pi$
$881$			415393.i			0.535190i	−0.963532	+	0.267595i	$0.913771\pi$
$882$	533837.	+	533837.i	0.686233	+	0.686233i
$883$			107872.i			0.138353i	0.997604	+	0.0691763i	$0.0220371\pi$
$883$			107872.i			0.138353i	−0.997604	+	0.0691763i	$0.977963\pi$
$884$	−434783.	+	232397.i	−0.556375	+	0.297390i
$885$	−3544.29			−0.00452525
$886$	−548574.	+	548574.i	−0.698824	+	0.698824i
$887$	−745391.			−0.947408			−0.473704	−	0.880684i	$-0.657083\pi$
$887$	−745391.			−0.947408			−0.473704	+	0.880684i	$0.657083\pi$
$888$			33351.9i			0.0422955i
$889$	289998.	−	289998.i	0.366937	−	0.366937i
$890$	280110.	−	280110.i	0.353630	−	0.353630i
$891$	−576413.	−	576413.i	−0.726070	−	0.726070i
$892$	307608.	+	307608.i	0.386606	+	0.386606i
$893$	1.06749e6			1.33863
$894$			58850.0i			0.0736328i
$895$	−288436.	−	288436.i	−0.360084	−	0.360084i
$896$			370511.i			0.461514i
$897$	−33623.4	−	62904.8i	−0.0417885	−	0.0781806i
$898$	−1.09389e6			−1.35651
$899$	−359593.	+	359593.i	−0.444931	+	0.444931i
$900$	−350514.			−0.432734
$901$			923123.i			1.13713i
$902$	−924037.	+	924037.i	−1.13573	+	1.13573i
$903$	66113.7	−	66113.7i	0.0810804	−	0.0810804i
$904$	157115.	+	157115.i	0.192256	+	0.192256i
$905$	78487.4	+	78487.4i	0.0958303	+	0.0958303i
$906$	238885.			0.291026
$907$		−	639615.i		−	0.777507i	−0.921342	−	0.388753i	$-0.872906\pi$
$907$		−	639615.i		−	0.777507i	0.921342	−	0.388753i	$-0.127094\pi$
$908$	140733.	+	140733.i	0.170697	+	0.170697i
$909$		−	661808.i		−	0.800948i
$910$	−50681.2	+	167074.i	−0.0612018	+	0.201756i
$911$	−1.62099e6			−1.95319			−0.976593	−	0.215096i	$-0.930994\pi$
$911$	−1.62099e6			−1.95319			−0.976593	+	0.215096i	$0.930994\pi$
$912$	94758.6	−	94758.6i	0.113928	−	0.113928i
$913$	−1.04114e6			−1.24901
$914$			484479.i			0.579940i
$915$	32712.3	−	32712.3i	0.0390723	−	0.0390723i
$916$	−48314.9	+	48314.9i	−0.0575825	+	0.0575825i
$917$	−2548.84	−	2548.84i	−0.00303112	−	0.00303112i
$918$	−265882.	−	265882.i	−0.315503	−	0.315503i
$919$	−235731.			−0.279116			−0.139558	−	0.990214i	$-0.544568\pi$
$919$	−235731.			−0.279116			−0.139558	+	0.990214i	$0.544568\pi$
$920$		−	113613.i		−	0.134231i
$921$	1548.63	+	1548.63i	0.00182570	+	0.00182570i
$922$		−	767703.i		−	0.903091i
$923$	−387185.	+	1.27638e6i	−0.454481	+	1.49823i
$924$	32684.9			0.0382827
$925$	243630.	−	243630.i	0.284739	−	0.284739i
$926$	−389682.			−0.454452
$927$			698994.i			0.813418i
$928$	740554.	−	740554.i	0.859926	−	0.859926i
$929$	144574.	−	144574.i	0.167517	−	0.167517i	−0.618370	−	0.785887i	$-0.712207\pi$
$929$	144574.	−	144574.i	0.167517	−	0.167517i	0.785887	+	0.618370i	$0.212207\pi$
$930$	21715.7	+	21715.7i	0.0251077	+	0.0251077i
$931$	421091.	+	421091.i	0.485821	+	0.485821i
$932$	−36359.2			−0.0418584
$933$		−	41189.1i		−	0.0473172i
$934$	425998.	+	425998.i	0.488331	+	0.488331i
$935$		−	451781.i		−	0.516778i
$936$	−483910.	−	146792.i	−0.552348	−	0.167552i
$937$	1.44059e6			1.64082			0.820412	−	0.571772i	$-0.193744\pi$
$937$	1.44059e6			1.64082			0.820412	+	0.571772i	$0.193744\pi$
$938$	−214599.	+	214599.i	−0.243906	+	0.243906i
$939$	123925.			0.140550
$940$		−	279848.i		−	0.316713i
$941$	361157.	−	361157.i	0.407866	−	0.407866i	−0.473128	−	0.880994i	$-0.656875\pi$
$941$	361157.	−	361157.i	0.407866	−	0.407866i	0.880994	+	0.473128i	$0.156875\pi$
$942$	−36129.8	+	36129.8i	−0.0407158	+	0.0407158i
$943$	435988.	+	435988.i	0.490288	+	0.490288i
$944$	−60857.4	−	60857.4i	−0.0682919	−	0.0682919i
$945$	−45616.4			−0.0510808
$946$		−	2.09081e6i		−	2.33632i
$947$	1.15625e6	+	1.15625e6i	1.28929	+	1.28929i	0.935216	+	0.354077i	$0.115205\pi$
$947$	1.15625e6	+	1.15625e6i	1.28929	+	1.28929i	0.354077	+	0.935216i	$0.384795\pi$
$948$			45811.8i			0.0509754i
$949$	75173.7	+	22803.6i	0.0834706	+	0.0253204i
$950$	−807117.			−0.894312
$951$	−64359.2	+	64359.2i	−0.0711623	+	0.0711623i
$952$	286019.			0.315589
$953$		−	880049.i		−	0.968994i	−0.874793	−	0.484497i	$-0.839003\pi$
$953$		−	880049.i		−	0.968994i	0.874793	−	0.484497i	$-0.160997\pi$
$954$	728401.	−	728401.i	0.800339	−	0.800339i
$955$	203719.	−	203719.i	0.223370	−	0.223370i
$956$	56197.4	+	56197.4i	0.0614895	+	0.0614895i
$957$	137976.	+	137976.i	0.150653	+	0.150653i
$958$	1.59099e6			1.73355
$959$		−	161695.i		−	0.175817i
$960$	2954.09	+	2954.09i	0.00320539	+	0.00320539i
$961$			700206.i			0.758191i
$962$	−476912.	+	254915.i	−0.515333	+	0.275452i
$963$	31084.4			0.0335189
$964$	349082.	−	349082.i	0.375642	−	0.375642i
$965$	215573.			0.231494
$966$		−	45019.0i		−	0.0482438i
$967$	41756.2	−	41756.2i	0.0446548	−	0.0446548i	−0.684427	−	0.729082i	$-0.739947\pi$
$967$	41756.2	−	41756.2i	0.0446548	−	0.0446548i	0.729082	+	0.684427i	$0.239947\pi$
$968$	−83683.1	+	83683.1i	−0.0893073	+	0.0893073i
$969$	−103652.	−	103652.i	−0.110391	−	0.110391i
$970$	−519143.	−	519143.i	−0.551752	−	0.551752i
$971$	360542.			0.382399			0.191200	−	0.981551i	$-0.438762\pi$
$971$	360542.			0.382399			0.191200	+	0.981551i	$0.438762\pi$
$972$			216434.i			0.229083i
$973$	506013.	+	506013.i	0.534486	+	0.534486i
$974$		−	971779.i		−	1.02435i
$975$	−57559.6	−	107686.i	−0.0605492	−	0.113279i
$976$	1.12338e6			1.17930
$977$	−747647.	+	747647.i	−0.783263	+	0.783263i	−0.980380	−	0.197117i	$-0.936842\pi$
$977$	−747647.	+	747647.i	−0.783263	+	0.783263i	0.197117	+	0.980380i	$0.436842\pi$
$978$	−342151.			−0.357717
$979$			1.10526e6i			1.15319i
$980$	110391.	−	110391.i	0.114943	−	0.114943i
$981$	92949.7	−	92949.7i	0.0965850	−	0.0965850i
$982$	−1.12261e6	−	1.12261e6i	−1.16414	−	1.16414i
$983$	−961229.	−	961229.i	−0.994764	−	0.994764i	0.00522282	−	0.999986i	$-0.498338\pi$
$983$	−961229.	−	961229.i	−0.994764	−	0.994764i	−0.999986	+	0.00522282i	$0.998338\pi$
$984$	−102174.			−0.105524
$985$			302425.i			0.311707i
$986$	−1.31353e6	−	1.31353e6i	−1.35110	−	1.35110i
$987$			101929.i			0.104632i
$988$	415260.	+	125967.i	0.425409	+	0.129046i
$989$	−986507.			−1.00857
$990$	−356483.	+	356483.i	−0.363721	+	0.363721i
$991$	116023.			0.118140			0.0590700	−	0.998254i	$-0.481186\pi$
$991$	116023.			0.118140			0.0590700	+	0.998254i	$0.481186\pi$
$992$			459901.i			0.467348i
$993$	15775.5	−	15775.5i	0.0159986	−	0.0159986i
$994$	−595282.	+	595282.i	−0.602491	+	0.602491i
$995$	435130.	+	435130.i	0.439514	+	0.439514i
$996$	62620.8	+	62620.8i	0.0631248	+	0.0631248i
$997$	206164.			0.207407			0.103704	−	0.994608i	$-0.466931\pi$
$997$	206164.			0.207407			0.103704	+	0.994608i	$0.466931\pi$
$998$			1.59607e6i			1.60248i
$999$	−99905.8	−	99905.8i	−0.100106	−	0.100106i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	13.5.d.a.5.3	✓	6
3.2	odd	2		117.5.j.a.109.1		6
4.3	odd	2		208.5.t.c.161.2		6
13.5	odd	4		169.5.d.a.99.1		6
13.8	odd	4	inner	13.5.d.a.8.3	yes	6
13.12	even	2		169.5.d.a.70.1		6
39.8	even	4		117.5.j.a.73.1		6
52.47	even	4		208.5.t.c.177.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.5.d.a.5.3	✓	6	1.1	even	1	trivial
13.5.d.a.8.3	yes	6	13.8	odd	4	inner
117.5.j.a.73.1		6	39.8	even	4
117.5.j.a.109.1		6	3.2	odd	2
169.5.d.a.70.1		6	13.12	even	2
169.5.d.a.99.1		6	13.5	odd	4
208.5.t.c.161.2		6	4.3	odd	2
208.5.t.c.177.2		6	52.47	even	4

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:	\( N \)	\(=\)	\( 13 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	13.d (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(3.48832 - 3.48832i) q^{2} -1.36015 q^{3} -8.33680i q^{4} +(-6.84848 + 6.84848i) q^{5} +(-4.74466 + 4.74466i) q^{6} +(15.2891 + 15.2891i) q^{7} +(26.7317 + 26.7317i) q^{8} -79.1500 q^{9} +47.7794i q^{10} +(-94.2642 - 94.2642i) q^{11} +11.3393i q^{12} +(149.045 - 79.6662i) q^{13} +106.667 q^{14} +(9.31499 - 9.31499i) q^{15} +319.887 q^{16} -349.910i q^{17} +(-276.101 + 276.101i) q^{18} +(-217.788 + 217.788i) q^{19} +(57.0944 + 57.0944i) q^{20} +(-20.7955 - 20.7955i) q^{21} -657.648 q^{22} +310.298i q^{23} +(-36.3593 - 36.3593i) q^{24} +531.197i q^{25} +(242.014 - 797.817i) q^{26} +217.829 q^{27} +(127.462 - 127.462i) q^{28} +1076.14 q^{29} -64.9874i q^{30} +(-334.152 + 334.152i) q^{31} +(688.160 - 688.160i) q^{32} +(128.214 + 128.214i) q^{33} +(-1220.60 - 1220.60i) q^{34} -209.414 q^{35} +659.858i q^{36} +(-458.644 - 458.644i) q^{37} +1519.43i q^{38} +(-202.724 + 108.358i) q^{39} -366.143 q^{40} +(1405.06 - 1405.06i) q^{41} -145.083 q^{42} +3179.23i q^{43} +(-785.862 + 785.862i) q^{44} +(542.057 - 542.057i) q^{45} +(1082.42 + 1082.42i) q^{46} +(-2450.75 - 2450.75i) q^{47} -435.095 q^{48} -1933.49i q^{49} +(1852.99 + 1852.99i) q^{50} +475.932i q^{51} +(-664.161 - 1242.56i) q^{52} -2638.17 q^{53} +(759.857 - 759.857i) q^{54} +1291.13 q^{55} +817.408i q^{56} +(296.226 - 296.226i) q^{57} +(3753.91 - 3753.91i) q^{58} +(-190.247 - 190.247i) q^{59} +(-77.6572 - 77.6572i) q^{60} +3511.79 q^{61} +2331.26i q^{62} +(-1210.13 - 1210.13i) q^{63} +317.133i q^{64} +(-475.137 + 1566.32i) q^{65} +894.503 q^{66} +(-2011.87 + 2011.87i) q^{67} -2917.13 q^{68} -422.053i q^{69} +(-730.504 + 730.504i) q^{70} +(-5580.77 + 5580.77i) q^{71} +(-2115.81 - 2115.81i) q^{72} +(328.685 + 328.685i) q^{73} -3199.79 q^{74} -722.510i q^{75} +(1815.66 + 1815.66i) q^{76} -2882.43i q^{77} +(-329.177 + 1085.16i) q^{78} +4040.07 q^{79} +(-2190.74 + 2190.74i) q^{80} +6114.87 q^{81} -9802.63i q^{82} +(5522.44 - 5522.44i) q^{83} +(-173.368 + 173.368i) q^{84} +(2396.35 + 2396.35i) q^{85} +(11090.2 + 11090.2i) q^{86} -1463.71 q^{87} -5039.69i q^{88} +(-5862.57 - 5862.57i) q^{89} -3781.74i q^{90} +(3496.78 + 1060.73i) q^{91} +2586.89 q^{92} +(454.499 - 454.499i) q^{93} -17098.0 q^{94} -2983.04i q^{95} +(-936.005 + 936.005i) q^{96} +(-10865.4 + 10865.4i) q^{97} +(-6744.63 - 6744.63i) q^{98} +(7461.01 + 7461.01i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 2 q^{2} - 4 q^{3} - 14 q^{5} + 32 q^{6} + 48 q^{7} - 96 q^{8} - 58 q^{9} - 32 q^{11} - 244 q^{14} + 404 q^{15} + 1044 q^{16} - 802 q^{18} + 732 q^{19} + 428 q^{20} - 2128 q^{21} - 1632 q^{22} - 24 q^{24}+ \cdots + 17492 q^{99}+O(q^{100}) \) 6 * q - 2 * q^2 - 4 * q^3 - 14 * q^5 + 32 * q^6 + 48 * q^7 - 96 * q^8 - 58 * q^9 - 32 * q^11 - 244 * q^14 + 404 * q^15 + 1044 * q^16 - 802 * q^18 + 732 * q^19 + 428 * q^20 - 2128 * q^21 - 1632 * q^22 - 24 * q^24 + 910 * q^26 + 236 * q^27 + 1884 * q^28 + 4184 * q^29 - 3468 * q^31 + 2092 * q^32 + 2324 * q^33 - 5304 * q^34 - 4204 * q^35 - 1758 * q^37 + 1196 * q^39 - 708 * q^40 + 4750 * q^41 + 9532 * q^42 - 3956 * q^44 + 830 * q^45 + 516 * q^46 - 6872 * q^47 - 9436 * q^48 - 322 * q^50 + 3900 * q^52 + 2108 * q^53 - 184 * q^54 + 6408 * q^55 - 5800 * q^57 + 6516 * q^58 + 4372 * q^59 + 1324 * q^60 + 5988 * q^61 - 652 * q^63 - 5018 * q^65 - 4592 * q^66 + 72 * q^67 - 10572 * q^68 + 7368 * q^70 - 14672 * q^71 - 7980 * q^72 + 5874 * q^73 + 1544 * q^74 + 3576 * q^76 + 5720 * q^78 + 2616 * q^79 - 12080 * q^80 - 19450 * q^81 + 19264 * q^83 + 6296 * q^84 + 4164 * q^85 + 29376 * q^86 + 35584 * q^87 - 986 * q^89 - 30888 * q^91 + 5304 * q^92 - 9520 * q^93 - 36156 * q^94 + 20720 * q^96 - 23154 * q^97 - 41426 * q^98 + 17492 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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