LMFDB - Embedded newform 13.5.d.a.8.3

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			8.3
Root			$-3.48832 - 3.48832i$ of defining polynomial
Character	$\chi$	$=$	13.8
Dual form			13.5.d.a.5.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.48832 + 3.48832i) q^{2} -1.36015 q^{3} +8.33680i q^{4} +(-6.84848 - 6.84848i) q^{5} +(-4.74466 - 4.74466i) q^{6} +(15.2891 - 15.2891i) q^{7} +(26.7317 - 26.7317i) q^{8} -79.1500 q^{9} +O(q^{10})$	\(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}+O(q^{10}) $ 6 * q - 2 * q^2 - 4 * q^3 - 14 * q^5 + 32 * q^6 + 48 * q^7 - 96 * q^8 - 58 * q^9	\( 6 q - 2 q^{2} - 4 q^{3} - 14 q^{5} + 32 q^{6} + 48 q^{7} - 96 q^{8} - 58 q^{9} - 32 q^{11} - 244 q^{14} + 404 q^{15} + 1044 q^{16} - 802 q^{18} + 732 q^{19} + 428 q^{20} - 2128 q^{21} - 1632 q^{22} - 24 q^{24} + 910 q^{26} + 236 q^{27} + 1884 q^{28} + 4184 q^{29} - 3468 q^{31} + 2092 q^{32} + 2324 q^{33} - 5304 q^{34} - 4204 q^{35} - 1758 q^{37} + 1196 q^{39} - 708 q^{40} + 4750 q^{41} + 9532 q^{42} - 3956 q^{44} + 830 q^{45} + 516 q^{46} - 6872 q^{47} - 9436 q^{48} - 322 q^{50} + 3900 q^{52} + 2108 q^{53} - 184 q^{54} + 6408 q^{55} - 5800 q^{57} + 6516 q^{58} + 4372 q^{59} + 1324 q^{60} + 5988 q^{61} - 652 q^{63} - 5018 q^{65} - 4592 q^{66} + 72 q^{67} - 10572 q^{68} + 7368 q^{70} - 14672 q^{71} - 7980 q^{72} + 5874 q^{73} + 1544 q^{74} + 3576 q^{76} + 5720 q^{78} + 2616 q^{79} - 12080 q^{80} - 19450 q^{81} + 19264 q^{83} + 6296 q^{84} + 4164 q^{85} + 29376 q^{86} + 35584 q^{87} - 986 q^{89} - 30888 q^{91} + 5304 q^{92} - 9520 q^{93} - 36156 q^{94} + 20720 q^{96} - 23154 q^{97} - 41426 q^{98} + 17492 q^{99}+O(q^{100}) \) 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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{4}\right)$

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	0.992699	−	0.120618i	$-0.0384876\pi$
$2$	3.48832	+	3.48832i	0.872081	+	0.872081i	−0.120618	+	0.992699i	$0.538488\pi$
$3$	−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	0.556745	−	0.830684i	$-0.312050\pi$
$5$	−6.84848	−	6.84848i	−0.273939	−	0.273939i	−0.830684	+	0.556745i	$0.812050\pi$
$6$	−4.74466	−	4.74466i	−0.131796	−	0.131796i
$7$	15.2891	−	15.2891i	0.312022	−	0.312022i	−0.533670	−	0.845693i	$-0.679188\pi$
$7$	15.2891	−	15.2891i	0.312022	−	0.312022i	0.845693	+	0.533670i	$0.179188\pi$
$8$	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	−0.979668	−	0.200625i	$-0.935703\pi$
$11$	−94.2642	+	94.2642i	−0.779043	+	0.779043i	0.200625	+	0.979668i	$0.435703\pi$
$12$		−	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	$0.206979\pi$
$17$			349.910i			1.21076i	−0.795936	+	0.605381i	$0.793021\pi$
$18$	−276.101	−	276.101i	−0.852163	−	0.852163i
$19$	−217.788	−	217.788i	−0.603291	−	0.603291i	0.337893	−	0.941184i	$-0.390286\pi$
$19$	−217.788	−	217.788i	−0.603291	−	0.603291i	−0.941184	+	0.337893i	$0.890286\pi$
$20$	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	$-0.905251\pi$
$23$		−	310.298i		−	0.586575i	0.956024	−	0.293287i	$-0.0947492\pi$
$24$	−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	0.511544	−	0.859257i	$-0.329074\pi$
$31$	−334.152	−	334.152i	−0.347713	−	0.347713i	−0.859257	+	0.511544i	$0.829074\pi$
$32$	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	−0.854489	−	0.519469i	$-0.826130\pi$
$37$	−458.644	+	458.644i	−0.335021	+	0.335021i	0.519469	+	0.854489i	$0.326130\pi$
$38$		−	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	0.988310	−	0.152460i	$-0.0487196\pi$
$41$	1405.06	+	1405.06i	0.835849	+	0.835849i	−0.152460	+	0.988310i	$0.548720\pi$
$42$	−145.083			−0.0822467
$43$		−	3179.23i		−	1.71943i	−0.510774	−	0.859715i	$-0.670641\pi$
$43$		−	3179.23i		−	1.71943i	0.510774	−	0.859715i	$-0.329359\pi$
$44$	−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	−0.116214	+	0.993224i	$0.537076\pi$
$47$	−2450.75	+	2450.75i	−1.10944	+	1.10944i	−0.993224	+	0.116214i	$0.962924\pi$
$48$	−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	−0.733905	−	0.679252i	$-0.762304\pi$
$59$	−190.247	+	190.247i	−0.0546529	+	0.0546529i	0.679252	+	0.733905i	$0.262304\pi$
$60$	−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	0.446571	−	0.894748i	$-0.352645\pi$
$67$	−2011.87	−	2011.87i	−0.448177	−	0.448177i	−0.894748	+	0.446571i	$0.852645\pi$
$68$	−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	−0.993533	−	0.113544i	$-0.963780\pi$
$71$	−5580.77	−	5580.77i	−1.10708	−	1.10708i	−0.113544	−	0.993533i	$-0.536220\pi$
$72$	−2115.81	+	2115.81i	−0.408143	+	0.408143i
$73$	328.685	−	328.685i	0.0616785	−	0.0616785i	−0.675595	−	0.737273i	$-0.736113\pi$
$73$	328.685	−	328.685i	0.0616785	−	0.0616785i	0.737273	+	0.675595i	$0.236113\pi$
$74$	−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	0.983350	−	0.181719i	$-0.0581663\pi$
$83$	5522.44	+	5522.44i	0.801631	+	0.801631i	−0.181719	+	0.983350i	$0.558166\pi$
$84$	−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	−0.972603	−	0.232473i	$-0.925318\pi$
$89$	−5862.57	+	5862.57i	−0.740130	+	0.740130i	0.232473	+	0.972603i	$0.425318\pi$
$90$			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	−0.985580	−	0.169209i	$-0.945879\pi$
$97$	−10865.4	−	10865.4i	−1.15479	−	1.15479i	−0.169209	−	0.985580i	$-0.554121\pi$
$98$	−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	$-0.865586\pi$
$101$		−	8361.44i		−	0.819669i	0.912160	−	0.409834i	$-0.134414\pi$
$102$	1660.21	−	1660.21i	0.159574	−	0.159574i
$103$			8831.26i			0.832431i	0.909266	+	0.416215i	$0.136644\pi$
$103$			8831.26i			0.832431i	−0.909266	+	0.416215i	$0.863356\pi$
$104$	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	0.655956	−	0.754799i	$-0.272266\pi$
$109$	−1174.35	−	1174.35i	−0.0988426	−	0.0988426i	−0.754799	+	0.655956i	$0.772266\pi$
$110$	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	$0.200084\pi$
$127$			18967.7i			1.17600i	−0.808862	+	0.587998i	$0.799916\pi$
$128$	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	−0.833802	−	0.552064i	$-0.813840\pi$
$137$	−5287.93	+	5287.93i	−0.281737	+	0.281737i	0.552064	+	0.833802i	$0.313840\pi$
$138$	−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	0.832847	−	0.553503i	$-0.186709\pi$
$149$	6201.70	+	6201.70i	0.279343	+	0.279343i	−0.553503	+	0.832847i	$0.686709\pi$
$150$	−2520.35	+	2520.35i	−0.112015	+	0.112015i
$151$	−25174.0	+	25174.0i	−1.10408	+	1.10408i	−0.110163	+	0.993914i	$0.535137\pi$
$151$	−25174.0	+	25174.0i	−1.10408	+	1.10408i	−0.993914	+	0.110163i	$0.964863\pi$
$152$	−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	0.479598	−	0.877488i	$-0.340783\pi$
$163$	36056.4	−	36056.4i	1.35709	−	1.35709i	0.877488	−	0.479598i	$-0.159217\pi$
$164$	−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	−0.467925	−	0.883768i	$-0.654998\pi$
$167$	11597.5	−	11597.5i	0.415843	−	0.415843i	0.883768	+	0.467925i	$0.154998\pi$
$168$			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	$-0.889711\pi$
$173$		−	20327.3i		−	0.679185i	0.940573	−	0.339592i	$-0.110289\pi$
$174$	−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	$-0.771726\pi$
$179$		−	42116.9i		−	1.31447i	0.753687	−	0.657234i	$-0.228274\pi$
$180$	−4519.02	+	4519.02i	−0.139476	+	0.139476i
$181$			11460.6i			0.349823i	0.984584	+	0.174912i	$0.0559640\pi$
$181$			11460.6i			0.349823i	−0.984584	+	0.174912i	$0.944036\pi$
$182$	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	−0.886073	−	0.463545i	$-0.846577\pi$
$193$	−15738.8	+	15738.8i	−0.422529	+	0.422529i	0.463545	+	0.886073i	$0.346577\pi$
$194$		−	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	0.931830	−	0.362896i	$-0.118212\pi$
$197$	22079.8	+	22079.8i	0.568934	+	0.568934i	−0.362896	+	0.931830i	$0.618212\pi$
$198$	52052.8			1.32774
$199$			63536.7i			1.60442i	0.597041	+	0.802211i	$0.296343\pi$
$199$			63536.7i			1.60442i	−0.597041	+	0.802211i	$0.703657\pi$
$200$	−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	0.230984	−	0.972958i	$-0.425806\pi$
$223$	−36897.6	−	36897.6i	−0.741974	−	0.741974i	−0.972958	+	0.230984i	$0.925806\pi$
$224$	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	0.524073	−	0.851674i	$-0.324412\pi$
$227$	−16881.0	−	16881.0i	−0.327601	−	0.327601i	−0.851674	+	0.524073i	$0.824412\pi$
$228$	−2469.57	+	2469.57i	−0.0475064	+	0.0475064i
$229$	−5795.38	+	5795.38i	−0.110512	+	0.110512i	−0.760201	−	0.649688i	$-0.774899\pi$
$229$	−5795.38	+	5795.38i	−0.110512	+	0.110512i	0.649688	+	0.760201i	$0.274899\pi$
$230$	−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	$0.0127891\pi$
$233$			4361.29i			0.0803346i	−0.999193	+	0.0401673i	$0.987211\pi$
$234$	−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	0.645635	−	0.763646i	$-0.276593\pi$
$239$	−6740.89	−	6740.89i	−0.118011	−	0.118011i	−0.763646	+	0.645635i	$0.776593\pi$
$240$	2979.74	+	2979.74i	0.0517316	+	0.0517316i
$241$	41872.5	−	41872.5i	0.720932	−	0.720932i	−0.247863	−	0.968795i	$-0.579728\pi$
$241$	41872.5	−	41872.5i	0.720932	−	0.720932i	0.968795	+	0.247863i	$0.0797282\pi$
$242$	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	$-0.796813\pi$
$251$		−	75079.1i		−	1.19171i	0.803091	−	0.595857i	$-0.203187\pi$
$252$	−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	$0.0799817\pi$
$257$			32844.1i			0.497268i	−0.968597	+	0.248634i	$0.920018\pi$
$258$	−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	−0.543575	−	0.839361i	$-0.682930\pi$
$271$	21722.8	−	21722.8i	0.295786	−	0.295786i	0.839361	+	0.543575i	$0.182930\pi$
$272$			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	$-0.848565\pi$
$277$		−	70284.0i		−	0.916003i	0.888951	−	0.458002i	$-0.151435\pi$
$278$	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	−0.469736	−	0.882807i	$-0.655651\pi$
$281$	32616.5	−	32616.5i	0.413071	−	0.413071i	0.882807	+	0.469736i	$0.155651\pi$
$282$	23255.9			0.292439
$283$			61904.1i			0.772941i	0.922302	+	0.386470i	$0.126306\pi$
$283$			61904.1i			0.772941i	−0.922302	+	0.386470i	$0.873694\pi$
$284$	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	−0.866280	−	0.499559i	$-0.833496\pi$
$293$	−31482.7	+	31482.7i	−0.366721	+	0.366721i	0.499559	+	0.866280i	$0.333496\pi$
$294$	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	−0.713121	−	0.701041i	$-0.752719\pi$
$307$	−1138.57	+	1138.57i	−0.0120805	+	0.0120805i	0.701041	+	0.713121i	$0.252719\pi$
$308$	−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	$-0.949964\pi$
$311$		−	30282.7i		−	0.313093i	0.987671	−	0.156547i	$-0.0500361\pi$
$312$	−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	0.902197	−	0.431324i	$-0.141953\pi$
$317$	47317.6	+	47317.6i	0.470873	+	0.470873i	−0.431324	+	0.902197i	$0.641953\pi$
$318$	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	0.652192	−	0.758054i	$-0.273849\pi$
$331$	−11598.3	−	11598.3i	−0.105861	−	0.105861i	−0.758054	+	0.652192i	$0.773849\pi$
$332$	−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	$-0.928526\pi$
$337$		−	50574.4i		−	0.445319i	0.974896	−	0.222659i	$-0.0714738\pi$
$338$	−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	−0.172810	+	0.984955i	$0.555285\pi$
$349$	−141017.	+	141017.i	−1.15776	+	1.15776i	−0.984955	+	0.172810i	$0.944715\pi$
$350$		−	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	0.0978279	−	0.995203i	$-0.468811\pi$
$353$	−111821.	−	111821.i	−0.897375	−	0.897375i	−0.995203	+	0.0978279i	$0.968811\pi$
$354$	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	−0.768916	−	0.639350i	$-0.779204\pi$
$359$	−16698.6	+	16698.6i	−0.129566	+	0.129566i	0.639350	+	0.768916i	$0.279204\pi$
$360$	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	0.999889	+	0.0149312i	$0.00475293\pi$
$379$	145770.	+	145770.i	1.01482	+	1.01482i	0.0149312	+	0.999889i	$0.495247\pi$
$380$	−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	0.312606	−	0.949883i	$-0.398798\pi$
$383$	−93481.5	−	93481.5i	−0.637277	−	0.637277i	−0.949883	+	0.312606i	$0.898798\pi$
$384$	−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	$-0.723813\pi$
$389$		−	230862.i		−	1.52565i	0.646607	−	0.762824i	$-0.276187\pi$
$390$	−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	−0.854629	−	0.519240i	$-0.826215\pi$
$397$	−52860.3	+	52860.3i	−0.335389	+	0.335389i	0.519240	+	0.854629i	$0.326215\pi$
$398$	−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	−0.858256	−	0.513222i	$-0.828452\pi$
$401$	−55481.9	+	55481.9i	−0.345034	+	0.345034i	0.513222	+	0.858256i	$0.328452\pi$
$402$			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	0.907601	+	0.419834i	$0.137912\pi$
$409$	222055.	+	222055.i	1.32743	+	1.32743i	0.419834	+	0.907601i	$0.362088\pi$
$410$	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	0.791615	−	0.611020i	$-0.209241\pi$
$421$	32008.8	+	32008.8i	0.180595	+	0.180595i	−0.611020	+	0.791615i	$0.709241\pi$
$422$	−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	0.695240	−	0.718777i	$-0.255298\pi$
$431$	−4372.31	−	4372.31i	−0.0235373	−	0.0235373i	−0.718777	+	0.695240i	$0.755298\pi$
$432$	69680.5			0.373374
$433$		−	299051.i		−	1.59503i	−0.603298	−	0.797516i	$-0.706147\pi$
$433$		−	299051.i		−	1.59503i	0.603298	−	0.797516i	$-0.293853\pi$
$434$	−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	$-0.956414\pi$
$439$		−	52613.5i		−	0.273003i	0.990640	−	0.136502i	$-0.0435859\pi$
$440$	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	−0.979447	−	0.201704i	$-0.935352\pi$
$449$	−156794.	+	156794.i	−0.777743	+	0.777743i	0.201704	+	0.979447i	$0.435352\pi$
$450$	−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	0.521033	−	0.853537i	$-0.325547\pi$
$457$	−69443.0	−	69443.0i	−0.332503	−	0.332503i	−0.853537	+	0.521033i	$0.825547\pi$
$458$	−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	0.916899	−	0.399120i	$-0.130684\pi$
$461$	110039.	+	110039.i	0.517779	+	0.517779i	−0.399120	+	0.916899i	$0.630684\pi$
$462$	13676.1	−	13676.1i	0.0640737	−	0.0640737i
$463$	−55855.2	+	55855.2i	−0.260556	+	0.260556i	−0.825280	−	0.564724i	$-0.808983\pi$
$463$	−55855.2	+	55855.2i	−0.260556	+	0.260556i	0.564724	+	0.825280i	$0.308983\pi$
$464$	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	$-0.909672\pi$
$467$		−	122121.i		−	0.559960i	0.960006	−	0.279980i	$-0.0903279\pi$
$468$	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	−0.00606704	−	0.999982i	$-0.501931\pi$
$479$	228045.	−	228045.i	0.993915	−	0.993915i	0.999982	+	0.00606704i	$0.00193121\pi$
$480$			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	0.936900	−	0.349597i	$-0.113681\pi$
$487$	139290.	+	139290.i	0.587304	+	0.587304i	−0.349597	+	0.936900i	$0.613681\pi$
$488$	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	$0.232615\pi$
$491$			321820.i			1.33490i	−0.744653	+	0.667451i	$0.767385\pi$
$492$	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	0.0781727	−	0.996940i	$-0.475091\pi$
$499$	−228774.	−	228774.i	−0.918767	−	0.918767i	−0.996940	+	0.0781727i	$0.975091\pi$
$500$	−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	0.807138	−	0.590362i	$-0.201015\pi$
$509$	56162.6	+	56162.6i	0.216776	+	0.216776i	−0.590362	+	0.807138i	$0.701015\pi$
$510$	−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	0.557782	−	0.829987i	$-0.311652\pi$
$541$	406174.	−	406174.i	1.38777	−	1.38777i	0.829987	−	0.557782i	$-0.188348\pi$
$542$	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	−0.954768	−	0.297352i	$-0.903896\pi$
$557$	−203963.	+	203963.i	−0.657416	+	0.657416i	0.297352	+	0.954768i	$0.403896\pi$
$558$			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	$0.254664\pi$
$563$			454782.i			1.43478i	−0.696669	+	0.717392i	$0.745336\pi$
$564$	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	$-0.969849\pi$
$569$		−	61243.8i		−	0.189164i	0.995517	−	0.0945818i	$-0.0301514\pi$
$570$	14153.5	−	14153.5i	0.0435626	−	0.0435626i
$571$			385360.i			1.18194i	0.806694	+	0.590969i	$0.201255\pi$
$571$			385360.i			1.18194i	−0.806694	+	0.590969i	$0.798745\pi$
$572$	−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	0.732644	−	0.680612i	$-0.238286\pi$
$577$	17322.8	+	17322.8i	0.0520316	+	0.0520316i	−0.680612	+	0.732644i	$0.738286\pi$
$578$	−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	0.364504	−	0.931202i	$-0.381239\pi$
$587$	−195267.	−	195267.i	−0.566698	−	0.566698i	−0.931202	+	0.364504i	$0.881239\pi$
$588$	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	−0.374337	−	0.927293i	$-0.622130\pi$
$593$	194446.	−	194446.i	0.552956	−	0.552956i	0.927293	+	0.374337i	$0.122130\pi$
$594$	−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	0.0938541	−	0.995586i	$-0.470081\pi$
$613$	−338843.	−	338843.i	−0.901732	−	0.901732i	−0.995586	+	0.0938541i	$0.970081\pi$
$614$	−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	0.857827	−	0.513939i	$-0.171814\pi$
$617$	130914.	+	130914.i	0.343888	+	0.343888i	−0.513939	+	0.857827i	$0.671814\pi$
$618$	41901.3	−	41901.3i	0.109711	−	0.109711i
$619$	−408183.	+	408183.i	−1.06530	+	1.06530i	−0.0675916	+	0.997713i	$0.521531\pi$
$619$	−408183.	+	408183.i	−1.06530	+	1.06530i	−0.997713	+	0.0675916i	$0.978469\pi$
$620$	−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	−0.656090	−	0.754682i	$-0.727791\pi$
$631$	39255.5	−	39255.5i	0.0985921	−	0.0985921i	0.754682	+	0.656090i	$0.227791\pi$
$632$	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	$-0.855933\pi$
$641$		−	359360.i		−	0.874608i	0.899314	−	0.437304i	$-0.144067\pi$
$642$	1863.36	+	1863.36i	0.00452092	+	0.00452092i
$643$	75424.7	+	75424.7i	0.182428	+	0.182428i	0.792413	−	0.609985i	$-0.208825\pi$
$643$	75424.7	+	75424.7i	0.182428	+	0.182428i	−0.609985	+	0.792413i	$0.708825\pi$
$644$	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	$0.0473738\pi$
$647$			124143.i			0.296561i	−0.988945	+	0.148280i	$0.952626\pi$
$648$	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	−0.918191	−	0.396138i	$-0.870350\pi$
$661$	−228096.	+	228096.i	−0.522053	+	0.522053i	0.396138	+	0.918191i	$0.370350\pi$
$662$		−	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	$-0.875989\pi$
$673$		−	344055.i		−	0.759623i	0.925064	−	0.379812i	$-0.124011\pi$
$674$	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	−0.464826	−	0.885402i	$-0.653883\pi$
$683$	196194.	−	196194.i	0.420577	−	0.420577i	0.885402	+	0.464826i	$0.153883\pi$
$684$	−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	0.977487	−	0.210996i	$-0.0676708\pi$
$691$	365985.	+	365985.i	0.766491	+	0.766491i	−0.210996	+	0.977487i	$0.567671\pi$
$692$	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	$-0.968156\pi$
$701$		−	98155.0i		−	0.199745i	0.995000	−	0.0998727i	$-0.0318435\pi$
$702$	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	−0.258080	−	0.966124i	$-0.583090\pi$
$709$	355920.	−	355920.i	0.708044	−	0.708044i	0.966124	+	0.258080i	$0.0830898\pi$
$710$	−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	$0.0651072\pi$
$719$			210007.i			0.406234i	−0.979154	+	0.203117i	$0.934893\pi$
$720$	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	$0.183903\pi$
$727$			577302.i			1.09228i	−0.837694	+	0.546140i	$0.816097\pi$
$728$	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	0.915526	−	0.402259i	$-0.131775\pi$
$733$	275772.	+	275772.i	0.513267	+	0.513267i	−0.402259	+	0.915526i	$0.631775\pi$
$734$	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	−0.624855	−	0.780740i	$-0.714842\pi$
$739$	85132.1	−	85132.1i	0.155885	−	0.155885i	0.780740	+	0.624855i	$0.214842\pi$
$740$			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	0.977868	−	0.209221i	$-0.0670927\pi$
$743$	424331.	+	424331.i	0.768648	+	0.768648i	−0.209221	+	0.977868i	$0.567093\pi$
$744$	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	$0.147125\pi$
$751$			503003.i			0.891847i	−0.895071	+	0.445924i	$0.852875\pi$
$752$	−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	−0.610709	−	0.791855i	$-0.709115\pi$
$761$	104906.	−	104906.i	0.181147	−	0.181147i	0.791855	+	0.610709i	$0.209115\pi$
$762$	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	−0.974696	−	0.223535i	$-0.928240\pi$
$769$	−708587.	−	708587.i	−1.19823	−	1.19823i	−0.223535	−	0.974696i	$-0.571760\pi$
$770$	137721.			0.232283
$771$		−	44673.0i		−	0.0751513i
$772$	−131211.	−	131211.i	−0.220159	−	0.220159i
$773$	−316939.	−	316939.i	−0.530417	−	0.530417i	0.390280	−	0.920696i	$-0.372378\pi$
$773$	−316939.	−	316939.i	−0.530417	−	0.530417i	−0.920696	+	0.390280i	$0.872378\pi$
$774$	−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	−0.705804	−	0.708407i	$-0.749414\pi$
$787$	1612.16	−	1612.16i	0.00260291	−	0.00260291i	0.708407	+	0.705804i	$0.249414\pi$
$788$	−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	$0.0686284\pi$
$797$			271788.i			0.427872i	−0.976848	+	0.213936i	$0.931372\pi$
$798$	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	0.320583	−	0.947220i	$-0.396121\pi$
$811$	−412152.	−	412152.i	−0.626637	−	0.626637i	−0.947220	+	0.320583i	$0.896121\pi$
$812$	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	0.561394	−	0.827549i	$-0.310265\pi$
$821$	−179399.	−	179399.i	−0.266155	−	0.266155i	−0.827549	+	0.561394i	$0.810265\pi$
$822$	50178.9			0.0742638
$823$			184011.i			0.271672i	0.990731	+	0.135836i	$0.0433720\pi$
$823$			184011.i			0.271672i	−0.990731	+	0.135836i	$0.956628\pi$
$824$	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	−0.146862	−	0.989157i	$-0.546917\pi$
$827$	576070.	−	576070.i	0.842295	−	0.842295i	0.989157	+	0.146862i	$0.0469173\pi$
$828$	−204752.			−0.298654
$829$			563450.i			0.819872i	0.912114	+	0.409936i	$0.134449\pi$
$829$			563450.i			0.819872i	−0.912114	+	0.409936i	$0.865551\pi$
$830$	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	−0.740941	−	0.671570i	$-0.765620\pi$
$839$	−48831.3	+	48831.3i	−0.0693705	+	0.0693705i	0.671570	+	0.740941i	$0.265620\pi$
$840$	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	−0.183317	+	0.983054i	$0.558684\pi$
$853$	−848662.	+	848662.i	−1.16637	+	1.16637i	−0.983054	+	0.183317i	$0.941316\pi$
$854$	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	$0.0608908\pi$
$857$			279281.i			0.380259i	−0.981759	+	0.190129i	$0.939109\pi$
$858$	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	0.992759	−	0.120120i	$-0.0383278\pi$
$863$	649915.	+	649915.i	0.872640	+	0.872640i	−0.120120	+	0.992759i	$0.538328\pi$
$864$	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	0.694106	−	0.719873i	$-0.255800\pi$
$877$	−19817.7	−	19817.7i	−0.0257665	−	0.0257665i	−0.719873	+	0.694106i	$0.755800\pi$
$878$	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	$-0.913771\pi$
$881$		−	415393.i		−	0.535190i	0.963532	−	0.267595i	$-0.0862288\pi$
$882$	533837.	−	533837.i	0.686233	−	0.686233i
$883$		−	107872.i		−	0.138353i	−0.997604	−	0.0691763i	$-0.977963\pi$
$883$		−	107872.i		−	0.138353i	0.997604	−	0.0691763i	$-0.0220371\pi$
$884$	−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	$0.127094\pi$
$907$			639615.i			0.777507i	−0.921342	+	0.388753i	$0.872906\pi$
$908$	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	0.785887	−	0.618370i	$-0.212207\pi$
$929$	144574.	+	144574.i	0.167517	+	0.167517i	−0.618370	+	0.785887i	$0.712207\pi$
$930$	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	0.880994	−	0.473128i	$-0.156875\pi$
$941$	361157.	+	361157.i	0.407866	+	0.407866i	−0.473128	+	0.880994i	$0.656875\pi$
$942$	−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	0.354077	−	0.935216i	$-0.384795\pi$
$947$	1.15625e6	−	1.15625e6i	1.28929	−	1.28929i	0.935216	−	0.354077i	$-0.115205\pi$
$948$		−	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	$0.160997\pi$
$953$			880049.i			0.968994i	−0.874793	+	0.484497i	$0.839003\pi$
$954$	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	0.729082	−	0.684427i	$-0.239947\pi$
$967$	41756.2	+	41756.2i	0.0446548	+	0.0446548i	−0.684427	+	0.729082i	$0.739947\pi$
$968$	−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	0.197117	−	0.980380i	$-0.436842\pi$
$977$	−747647.	−	747647.i	−0.783263	−	0.783263i	−0.980380	+	0.197117i	$0.936842\pi$
$978$	−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	−0.999986	−	0.00522282i	$-0.998338\pi$
$983$	−961229.	+	961229.i	−0.994764	+	0.994764i	0.00522282	+	0.999986i	$0.498338\pi$
$984$	−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.8.3	yes	6
3.2	odd	2		117.5.j.a.73.1		6
4.3	odd	2		208.5.t.c.177.2		6
13.5	odd	4	inner	13.5.d.a.5.3	✓	6
13.8	odd	4		169.5.d.a.70.1		6
13.12	even	2		169.5.d.a.99.1		6
39.5	even	4		117.5.j.a.109.1		6
52.31	even	4		208.5.t.c.161.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.5.d.a.5.3	✓	6	13.5	odd	4	inner
13.5.d.a.8.3	yes	6	1.1	even	1	trivial
117.5.j.a.73.1		6	3.2	odd	2
117.5.j.a.109.1		6	39.5	even	4
169.5.d.a.70.1		6	13.8	odd	4
169.5.d.a.99.1		6	13.12	even	2
208.5.t.c.161.2		6	52.31	even	4
208.5.t.c.177.2		6	4.3	odd	2

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)

\(f(q)\)	\(=\)	\(q+(3.48832 + 3.48832i) q^{2} -1.36015 q^{3} +8.33680i q^{4} +(-6.84848 - 6.84848i) q^{5} +(-4.74466 - 4.74466i) q^{6} +(15.2891 - 15.2891i) q^{7} +(26.7317 - 26.7317i) q^{8} -79.1500 q^{9} +O(q^{10})\)	\(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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 2 q^{2} - 4 q^{3} - 14 q^{5} + 32 q^{6} + 48 q^{7} - 96 q^{8} - 58 q^{9}+O(q^{10}) \) 6 * q - 2 * q^2 - 4 * q^3 - 14 * q^5 + 32 * q^6 + 48 * q^7 - 96 * q^8 - 58 * q^9	\( 6 q - 2 q^{2} - 4 q^{3} - 14 q^{5} + 32 q^{6} + 48 q^{7} - 96 q^{8} - 58 q^{9} - 32 q^{11} - 244 q^{14} + 404 q^{15} + 1044 q^{16} - 802 q^{18} + 732 q^{19} + 428 q^{20} - 2128 q^{21} - 1632 q^{22} - 24 q^{24} + 910 q^{26} + 236 q^{27} + 1884 q^{28} + 4184 q^{29} - 3468 q^{31} + 2092 q^{32} + 2324 q^{33} - 5304 q^{34} - 4204 q^{35} - 1758 q^{37} + 1196 q^{39} - 708 q^{40} + 4750 q^{41} + 9532 q^{42} - 3956 q^{44} + 830 q^{45} + 516 q^{46} - 6872 q^{47} - 9436 q^{48} - 322 q^{50} + 3900 q^{52} + 2108 q^{53} - 184 q^{54} + 6408 q^{55} - 5800 q^{57} + 6516 q^{58} + 4372 q^{59} + 1324 q^{60} + 5988 q^{61} - 652 q^{63} - 5018 q^{65} - 4592 q^{66} + 72 q^{67} - 10572 q^{68} + 7368 q^{70} - 14672 q^{71} - 7980 q^{72} + 5874 q^{73} + 1544 q^{74} + 3576 q^{76} + 5720 q^{78} + 2616 q^{79} - 12080 q^{80} - 19450 q^{81} + 19264 q^{83} + 6296 q^{84} + 4164 q^{85} + 29376 q^{86} + 35584 q^{87} - 986 q^{89} - 30888 q^{91} + 5304 q^{92} - 9520 q^{93} - 36156 q^{94} + 20720 q^{96} - 23154 q^{97} - 41426 q^{98} + 17492 q^{99}+O(q^{100}) \) 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

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Database

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