LMFDB - Embedded newform 168.3.g.a.43.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [168,3,Mod(43,168)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(168, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("168.43");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 168 = 2^{3} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	168.g (of order $2$, degree $1$, 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:	$4.57766844125$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			43.19
Character	$\chi$	$=$	168.43
Dual form			168.3.g.a.43.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.81394 - 0.842398i) q^{2} +1.73205 q^{3} +(2.58073 - 3.05611i) q^{4} +5.94177i q^{5} +(3.14183 - 1.45908i) q^{6} +2.64575i q^{7} +(2.10682 - 7.71760i) q^{8} +3.00000 q^{9} +O(q^{10})$	\(q+(1.81394 - 0.842398i) q^{2} +1.73205 q^{3} +(2.58073 - 3.05611i) q^{4} +5.94177i q^{5} +(3.14183 - 1.45908i) q^{6} +2.64575i q^{7} +(2.10682 - 7.71760i) q^{8} +3.00000 q^{9} +(5.00533 + 10.7780i) q^{10} +15.0849 q^{11} +(4.46996 - 5.29334i) q^{12} -11.2148i q^{13} +(2.22877 + 4.79923i) q^{14} +10.2914i q^{15} +(-2.67964 - 15.7740i) q^{16} -22.8244 q^{17} +(5.44181 - 2.52719i) q^{18} -33.0704 q^{19} +(18.1587 + 15.3341i) q^{20} +4.58258i q^{21} +(27.3631 - 12.7075i) q^{22} +1.69029i q^{23} +(3.64913 - 13.3673i) q^{24} -10.3046 q^{25} +(-9.44732 - 20.3429i) q^{26} +5.19615 q^{27} +(8.08571 + 6.82798i) q^{28} -28.9719i q^{29} +(8.66949 + 18.6680i) q^{30} +24.7233i q^{31} +(-18.1487 - 26.3557i) q^{32} +26.1278 q^{33} +(-41.4021 + 19.2272i) q^{34} -15.7204 q^{35} +(7.74220 - 9.16834i) q^{36} +53.7870i q^{37} +(-59.9877 + 27.8584i) q^{38} -19.4246i q^{39} +(45.8562 + 12.5183i) q^{40} +30.8925 q^{41} +(3.86035 + 8.31250i) q^{42} -44.2731 q^{43} +(38.9301 - 46.1012i) q^{44} +17.8253i q^{45} +(1.42389 + 3.06608i) q^{46} +37.2829i q^{47} +(-4.64127 - 27.3214i) q^{48} -7.00000 q^{49} +(-18.6919 + 8.68058i) q^{50} -39.5331 q^{51} +(-34.2737 - 28.9424i) q^{52} -72.2354i q^{53} +(9.42549 - 4.37723i) q^{54} +89.6310i q^{55} +(20.4188 + 5.57413i) q^{56} -57.2797 q^{57} +(-24.4058 - 52.5532i) q^{58} +33.2212 q^{59} +(31.4518 + 26.5595i) q^{60} -96.8692i q^{61} +(20.8269 + 44.8466i) q^{62} +7.93725i q^{63} +(-55.1226 - 32.5192i) q^{64} +66.6357 q^{65} +(47.3942 - 22.0100i) q^{66} -86.0604 q^{67} +(-58.9038 + 69.7540i) q^{68} +2.92767i q^{69} +(-28.5159 + 13.2429i) q^{70} +40.4798i q^{71} +(6.32047 - 23.1528i) q^{72} +28.5905 q^{73} +(45.3100 + 97.5662i) q^{74} -17.8481 q^{75} +(-85.3459 + 101.067i) q^{76} +39.9109i q^{77} +(-16.3632 - 35.2350i) q^{78} +80.5457i q^{79} +(93.7255 - 15.9218i) q^{80} +9.00000 q^{81} +(56.0370 - 26.0238i) q^{82} +36.2653 q^{83} +(14.0049 + 11.8264i) q^{84} -135.618i q^{85} +(-80.3086 + 37.2955i) q^{86} -50.1808i q^{87} +(31.7813 - 116.419i) q^{88} +13.9430 q^{89} +(15.0160 + 32.3340i) q^{90} +29.6716 q^{91} +(5.16571 + 4.36218i) q^{92} +42.8221i q^{93} +(31.4070 + 67.6288i) q^{94} -196.497i q^{95} +(-31.4344 - 45.6495i) q^{96} -66.0297 q^{97} +(-12.6976 + 5.89678i) q^{98} +45.2547 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 2 q^{2} + 10 q^{4} + 12 q^{6} + 10 q^{8} + 72 q^{9}+O(q^{10}) $ 24 * q - 2 * q^2 + 10 * q^4 + 12 * q^6 + 10 * q^8 + 72 * q^9	$ 24 q - 2 q^{2} + 10 q^{4} + 12 q^{6} + 10 q^{8} + 72 q^{9} + 12 q^{10} + 32 q^{11} + 24 q^{12} - 14 q^{14} + 66 q^{16} + 16 q^{17} - 6 q^{18} - 64 q^{19} + 20 q^{20} + 12 q^{22} - 36 q^{24} - 72 q^{25} + 100 q^{26} - 14 q^{28} + 72 q^{30} + 98 q^{32} - 108 q^{34} + 30 q^{36} - 72 q^{38} - 332 q^{40} - 80 q^{41} + 32 q^{43} - 292 q^{44} - 48 q^{48} - 168 q^{49} + 46 q^{50} + 192 q^{51} - 4 q^{52} + 36 q^{54} + 98 q^{56} - 96 q^{58} - 24 q^{60} - 16 q^{62} - 182 q^{64} - 192 q^{65} - 24 q^{66} - 32 q^{67} + 188 q^{68} - 84 q^{70} + 30 q^{72} - 240 q^{73} + 208 q^{74} - 384 q^{75} + 8 q^{76} + 168 q^{78} + 484 q^{80} + 216 q^{81} - 372 q^{82} - 320 q^{83} - 604 q^{86} + 468 q^{88} + 400 q^{89} + 36 q^{90} + 352 q^{92} - 72 q^{94} - 252 q^{96} + 144 q^{97} + 14 q^{98} + 96 q^{99}+O(q^{100}) $ 24 * q - 2 * q^2 + 10 * q^4 + 12 * q^6 + 10 * q^8 + 72 * q^9 + 12 * q^10 + 32 * q^11 + 24 * q^12 - 14 * q^14 + 66 * q^16 + 16 * q^17 - 6 * q^18 - 64 * q^19 + 20 * q^20 + 12 * q^22 - 36 * q^24 - 72 * q^25 + 100 * q^26 - 14 * q^28 + 72 * q^30 + 98 * q^32 - 108 * q^34 + 30 * q^36 - 72 * q^38 - 332 * q^40 - 80 * q^41 + 32 * q^43 - 292 * q^44 - 48 * q^48 - 168 * q^49 + 46 * q^50 + 192 * q^51 - 4 * q^52 + 36 * q^54 + 98 * q^56 - 96 * q^58 - 24 * q^60 - 16 * q^62 - 182 * q^64 - 192 * q^65 - 24 * q^66 - 32 * q^67 + 188 * q^68 - 84 * q^70 + 30 * q^72 - 240 * q^73 + 208 * q^74 - 384 * q^75 + 8 * q^76 + 168 * q^78 + 484 * q^80 + 216 * q^81 - 372 * q^82 - 320 * q^83 - 604 * q^86 + 468 * q^88 + 400 * q^89 + 36 * q^90 + 352 * q^92 - 72 * q^94 - 252 * q^96 + 144 * q^97 + 14 * q^98 + 96 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/168\mathbb{Z}\right)^\times$.

$n$	$73$	$85$	$113$	$127$
$\chi(n)$	$1$	$-1$	$1$	$-1$

Coefficient data

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

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

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

$2$	1.81394	−	0.842398i	0.906968	−	0.421199i
$2$	1.81394	−	0.842398i	0.906968	−	0.421199i
$3$	1.73205			0.577350
$3$	1.73205			0.577350
$4$	2.58073	−	3.05611i	0.645183	−	0.764028i
$5$			5.94177i			1.18835i	0.804334	+	0.594177i	$0.202522\pi$
$5$			5.94177i			1.18835i	−0.804334	+	0.594177i	$0.797478\pi$
$6$	3.14183	−	1.45908i	0.523638	−	0.243179i
$7$			2.64575i			0.377964i
$7$			2.64575i			0.377964i
$8$	2.10682	−	7.71760i	0.263353	−	0.964700i
$9$	3.00000			0.333333
$10$	5.00533	+	10.7780i	0.500533	+	1.07780i
$11$	15.0849			1.37136			0.685678	−	0.727905i	$-0.259506\pi$
$11$	15.0849			1.37136			0.685678	+	0.727905i	$0.259506\pi$
$12$	4.46996	−	5.29334i	0.372497	−	0.441112i
$13$		−	11.2148i		−	0.862677i	−0.902190	−	0.431338i	$-0.858042\pi$
$13$		−	11.2148i		−	0.862677i	0.902190	−	0.431338i	$-0.141958\pi$
$14$	2.22877	+	4.79923i	0.159198	+	0.342802i
$15$			10.2914i			0.686096i
$16$	−2.67964	−	15.7740i	−0.167477	−	0.985876i
$17$	−22.8244			−1.34261			−0.671307	−	0.741180i	$-0.734267\pi$
$17$	−22.8244			−1.34261			−0.671307	+	0.741180i	$0.734267\pi$
$18$	5.44181	−	2.52719i	0.302323	−	0.140400i
$19$	−33.0704			−1.74055			−0.870274	−	0.492567i	$-0.836059\pi$
$19$	−33.0704			−1.74055			−0.870274	+	0.492567i	$0.836059\pi$
$20$	18.1587	+	15.3341i	0.907935	+	0.766706i
$21$			4.58258i			0.218218i
$22$	27.3631	−	12.7075i	1.24378	−	0.577613i
$23$			1.69029i			0.0734908i	0.999325	+	0.0367454i	$0.0116991\pi$
$23$			1.69029i			0.0734908i	−0.999325	+	0.0367454i	$0.988301\pi$
$24$	3.64913	−	13.3673i	0.152047	−	0.556970i
$25$	−10.3046			−0.412185
$26$	−9.44732	−	20.3429i	−0.363358	−	0.782420i
$27$	5.19615			0.192450
$28$	8.08571	+	6.82798i	0.288775	+	0.243856i
$29$		−	28.9719i		−	0.999030i	−0.866305	−	0.499515i	$-0.833512\pi$
$29$		−	28.9719i		−	0.999030i	0.866305	−	0.499515i	$-0.166488\pi$
$30$	8.66949	+	18.6680i	0.288983	+	0.622268i
$31$			24.7233i			0.797527i	0.917054	+	0.398764i	$0.130561\pi$
$31$			24.7233i			0.797527i	−0.917054	+	0.398764i	$0.869439\pi$
$32$	−18.1487	−	26.3557i	−0.567146	−	0.823617i
$33$	26.1278			0.791752
$34$	−41.4021	+	19.2272i	−1.21771	+	0.565507i
$35$	−15.7204			−0.449156
$36$	7.74220	−	9.16834i	0.215061	−	0.254676i
$37$			53.7870i			1.45370i	0.686795	+	0.726851i	$0.259017\pi$
$37$			53.7870i			1.45370i	−0.686795	+	0.726851i	$0.740983\pi$
$38$	−59.9877	+	27.8584i	−1.57862	+	0.733117i
$39$		−	19.4246i		−	0.498067i
$40$	45.8562	+	12.5183i	1.14640	+	0.312957i
$41$	30.8925			0.753476			0.376738	−	0.926320i	$-0.377046\pi$
$41$	30.8925			0.753476			0.376738	+	0.926320i	$0.377046\pi$
$42$	3.86035	+	8.31250i	0.0919131	+	0.197917i
$43$	−44.2731			−1.02961			−0.514803	−	0.857308i	$-0.672135\pi$
$43$	−44.2731			−1.02961			−0.514803	+	0.857308i	$0.672135\pi$
$44$	38.9301	−	46.1012i	0.884775	−	1.04775i
$45$			17.8253i			0.396118i
$46$	1.42389	+	3.06608i	0.0309542	+	0.0666538i
$47$			37.2829i			0.793253i	0.917980	+	0.396627i	$0.129819\pi$
$47$			37.2829i			0.793253i	−0.917980	+	0.396627i	$0.870181\pi$
$48$	−4.64127	−	27.3214i	−0.0966931	−	0.569196i
$49$	−7.00000			−0.142857
$50$	−18.6919	+	8.68058i	−0.373838	+	0.173612i
$51$	−39.5331			−0.775158
$52$	−34.2737	−	28.9424i	−0.659109	−	0.556584i
$53$		−	72.2354i		−	1.36293i	−0.731850	−	0.681466i	$-0.761343\pi$
$53$		−	72.2354i		−	1.36293i	0.731850	−	0.681466i	$-0.238657\pi$
$54$	9.42549	−	4.37723i	0.174546	−	0.0810597i
$55$			89.6310i			1.62966i
$56$	20.4188	+	5.57413i	0.364622	+	0.0995381i
$57$	−57.2797			−1.00491
$58$	−24.4058	−	52.5532i	−0.420790	−	0.906089i
$59$	33.2212			0.563072			0.281536	−	0.959551i	$-0.409156\pi$
$59$	33.2212			0.563072			0.281536	+	0.959551i	$0.409156\pi$
$60$	31.4518	+	26.5595i	0.524197	+	0.442658i
$61$		−	96.8692i		−	1.58802i	−0.607905	−	0.794010i	$-0.707990\pi$
$61$		−	96.8692i		−	1.58802i	0.607905	−	0.794010i	$-0.292010\pi$
$62$	20.8269	+	44.8466i	0.335917	+	0.723332i
$63$			7.93725i			0.125988i
$64$	−55.1226	−	32.5192i	−0.861290	−	0.508113i
$65$	66.6357			1.02517
$66$	47.3942	−	22.0100i	0.718094	−	0.333485i
$67$	−86.0604			−1.28448			−0.642242	−	0.766502i	$-0.721995\pi$
$67$	−86.0604			−1.28448			−0.642242	+	0.766502i	$0.721995\pi$
$68$	−58.9038	+	69.7540i	−0.866232	+	1.02579i
$69$			2.92767i			0.0424299i
$70$	−28.5159	+	13.2429i	−0.407370	+	0.189184i
$71$			40.4798i			0.570137i	0.958507	+	0.285069i	$0.0920164\pi$
$71$			40.4798i			0.570137i	−0.958507	+	0.285069i	$0.907984\pi$
$72$	6.32047	−	23.1528i	0.0877844	−	0.321567i
$73$	28.5905			0.391651			0.195826	−	0.980639i	$-0.437261\pi$
$73$	28.5905			0.391651			0.195826	+	0.980639i	$0.437261\pi$
$74$	45.3100	+	97.5662i	0.612297	+	1.31846i
$75$	−17.8481			−0.237975
$76$	−85.3459	+	101.067i	−1.12297	+	1.32983i
$77$			39.9109i			0.518324i
$78$	−16.3632	−	35.2350i	−0.209785	−	0.451731i
$79$			80.5457i			1.01957i	0.860303	+	0.509783i	$0.170274\pi$
$79$			80.5457i			1.01957i	−0.860303	+	0.509783i	$0.829726\pi$
$80$	93.7255	−	15.9218i	1.17157	−	0.199022i
$81$	9.00000			0.111111
$82$	56.0370	−	26.0238i	0.683378	−	0.317363i
$83$	36.2653			0.436931			0.218466	−	0.975845i	$-0.429895\pi$
$83$	36.2653			0.436931			0.218466	+	0.975845i	$0.429895\pi$
$84$	14.0049	+	11.8264i	0.166725	+	0.140791i
$85$		−	135.618i		−	1.59550i
$86$	−80.3086	+	37.2955i	−0.933821	+	0.433669i
$87$		−	50.1808i		−	0.576790i
$88$	31.7813	−	116.419i	0.361151	−	1.32295i
$89$	13.9430			0.156663			0.0783313	−	0.996927i	$-0.475041\pi$
$89$	13.9430			0.156663			0.0783313	+	0.996927i	$0.475041\pi$
$90$	15.0160	+	32.3340i	0.166844	+	0.359266i
$91$	29.6716			0.326061
$92$	5.16571	+	4.36218i	0.0561490	+	0.0474150i
$93$			42.8221i			0.460453i
$94$	31.4070	+	67.6288i	0.334117	+	0.719456i
$95$		−	196.497i		−	2.06839i
$96$	−31.4344	−	45.6495i	−0.327442	−	0.475516i
$97$	−66.0297			−0.680718			−0.340359	−	0.940295i	$-0.610549\pi$
$97$	−66.0297			−0.680718			−0.340359	+	0.940295i	$0.610549\pi$
$98$	−12.6976	+	5.89678i	−0.129567	+	0.0601713i
$99$	45.2547			0.457118
$100$	−26.5935	+	31.4921i	−0.265935	+	0.314921i
$101$		−	158.436i		−	1.56867i	−0.620336	−	0.784336i	$-0.713004\pi$
$101$		−	158.436i		−	1.56867i	0.620336	−	0.784336i	$-0.286996\pi$
$102$	−71.7105	+	33.3026i	−0.703044	+	0.326496i
$103$			136.221i			1.32253i	0.750151	+	0.661266i	$0.229981\pi$
$103$			136.221i			1.32253i	−0.750151	+	0.661266i	$0.770019\pi$
$104$	−86.5513	−	23.6276i	−0.832224	−	0.227189i
$105$	−27.2286			−0.259320
$106$	−60.8509	−	131.030i	−0.574065	−	1.23614i
$107$	164.556			1.53790			0.768951	−	0.639307i	$-0.220779\pi$
$107$	164.556			1.53790			0.768951	+	0.639307i	$0.220779\pi$
$108$	13.4099	−	15.8800i	0.124166	−	0.147037i
$109$			18.6167i			0.170796i	0.996347	+	0.0853978i	$0.0272161\pi$
$109$			18.6167i			0.170796i	−0.996347	+	0.0853978i	$0.972784\pi$
$110$	75.5050	+	162.585i	0.686409	+	1.47805i
$111$			93.1618i			0.839295i
$112$	41.7341	−	7.08965i	0.372626	−	0.0633005i
$113$	140.406			1.24253			0.621267	−	0.783599i	$-0.286618\pi$
$113$	140.406			1.24253			0.621267	+	0.783599i	$0.286618\pi$
$114$	−103.902	+	48.2522i	−0.911418	+	0.423265i
$115$	−10.0433			−0.0873331
$116$	−88.5413	−	74.7687i	−0.763287	−	0.644558i
$117$		−	33.6444i		−	0.287559i
$118$	60.2612	−	27.9855i	0.510688	−	0.237165i
$119$		−	60.3878i		−	0.507460i
$120$	79.4252	+	21.6823i	0.661877	+	0.180686i
$121$	106.554			0.880615
$122$	−81.6024	−	175.715i	−0.668872	−	1.44028i
$123$	53.5074			0.435019
$124$	75.5573	+	63.8043i	0.609333	+	0.514551i
$125$			87.3166i			0.698533i
$126$	6.68632	+	14.3977i	0.0530661	+	0.114267i
$127$		−	191.983i		−	1.51168i	−0.654756	−	0.755840i	$-0.727229\pi$
$127$		−	191.983i		−	1.51168i	0.654756	−	0.755840i	$-0.272771\pi$
$128$	−127.383	−	12.5527i	−0.995180	−	0.0980682i
$129$	−76.6832			−0.594444
$130$	120.873	−	56.1338i	0.929792	−	0.431798i
$131$	13.5685			0.103576			0.0517881	−	0.998658i	$-0.483508\pi$
$131$	13.5685			0.103576			0.0517881	+	0.998658i	$0.483508\pi$
$132$	67.4289	−	79.8496i	0.510825	−	0.604921i
$133$		−	87.4961i		−	0.657866i
$134$	−156.108	+	72.4971i	−1.16499	+	0.541023i
$135$			30.8743i			0.228699i
$136$	−48.0871	+	176.150i	−0.353581	+	1.29522i
$137$	75.2780			0.549475			0.274737	−	0.961519i	$-0.411409\pi$
$137$	75.2780			0.549475			0.274737	+	0.961519i	$0.411409\pi$
$138$	2.46626	+	5.31060i	0.0178714	+	0.0384826i
$139$	222.721			1.60231			0.801153	−	0.598460i	$-0.204220\pi$
$139$	222.721			1.60231			0.801153	+	0.598460i	$0.204220\pi$
$140$	−40.5703	+	48.0434i	−0.289788	+	0.343167i
$141$			64.5759i			0.457985i
$142$	34.1000	+	73.4277i	0.240141	+	0.517097i
$143$		−	169.174i		−	1.18304i
$144$	−8.03891	−	47.3220i	−0.0558258	−	0.328625i
$145$	172.144			1.18720
$146$	51.8614	−	24.0846i	0.355215	−	0.164963i
$147$	−12.1244			−0.0824786
$148$	164.379	+	138.810i	1.11067	+	0.937904i
$149$			173.387i			1.16367i	0.813307	+	0.581835i	$0.197665\pi$
$149$			173.387i			1.16367i	−0.813307	+	0.581835i	$0.802335\pi$
$150$	−32.3754	+	15.0352i	−0.215836	+	0.100235i
$151$			84.9375i			0.562500i	0.959635	+	0.281250i	$0.0907490\pi$
$151$			84.9375i			0.562500i	−0.959635	+	0.281250i	$0.909251\pi$
$152$	−69.6736	+	255.224i	−0.458379	+	1.67911i
$153$	−68.4733			−0.447538
$154$	33.6209	+	72.3959i	0.218317	+	0.470103i
$155$	−146.900			−0.947744
$156$	−59.3637	−	50.1297i	−0.380537	−	0.321344i
$157$		−	57.6685i		−	0.367316i	−0.982990	−	0.183658i	$-0.941206\pi$
$157$		−	57.6685i		−	0.367316i	0.982990	−	0.183658i	$-0.0587938\pi$
$158$	67.8515	+	146.105i	0.429440	+	0.924714i
$159$		−	125.115i		−	0.786889i
$160$	156.600	−	107.835i	0.978748	−	0.673971i
$161$	−4.47208			−0.0277769
$162$	16.3254	−	7.58158i	0.100774	−	0.0467999i
$163$	10.8347			0.0664708			0.0332354	−	0.999448i	$-0.489419\pi$
$163$	10.8347			0.0664708			0.0332354	+	0.999448i	$0.489419\pi$
$164$	79.7253	−	94.4109i	0.486130	−	0.575676i
$165$			155.245i			0.940882i
$166$	65.7829	−	30.5498i	0.396283	−	0.184035i
$167$			57.5843i			0.344816i	0.985026	+	0.172408i	$0.0551548\pi$
$167$			57.5843i			0.344816i	−0.985026	+	0.172408i	$0.944845\pi$
$168$	35.3665	+	9.65468i	0.210515	+	0.0574684i
$169$	43.2283			0.255789
$170$	−114.244	−	246.002i	−0.672023	−	1.44707i
$171$	−99.2113			−0.580183
$172$	−114.257	+	135.304i	−0.664285	+	0.786648i
$173$			209.285i			1.20974i	0.796323	+	0.604871i	$0.206775\pi$
$173$			209.285i			1.20974i	−0.796323	+	0.604871i	$0.793225\pi$
$174$	−42.2722	−	91.0247i	−0.242943	−	0.523131i
$175$		−	27.2635i		−	0.155791i
$176$	−40.4221	−	237.950i	−0.229671	−	1.35199i
$177$	57.5409			0.325090
$178$	25.2917	−	11.7455i	0.142088	−	0.0659861i
$179$	−228.951			−1.27905			−0.639527	−	0.768768i	$-0.720870\pi$
$179$	−228.951			−1.27905			−0.639527	+	0.768768i	$0.720870\pi$
$180$	54.4761	+	46.0024i	0.302645	+	0.255569i
$181$		−	130.515i		−	0.721076i	−0.932744	−	0.360538i	$-0.882593\pi$
$181$		−	130.515i		−	0.721076i	0.932744	−	0.360538i	$-0.117407\pi$
$182$	53.8223	−	24.9953i	0.295727	−	0.137337i
$183$		−	167.782i		−	0.916843i
$184$	13.0450	+	3.56114i	0.0708965	+	0.0193540i
$185$	−319.590			−1.72751
$186$	36.0732	+	77.6765i	0.193942	+	0.417616i
$187$	−344.304			−1.84120
$188$	113.941	+	96.2172i	0.606068	+	0.511794i
$189$			13.7477i			0.0727393i
$190$	−165.528	−	356.433i	−0.871202	−	1.87596i
$191$		−	91.3000i		−	0.478010i	−0.971018	−	0.239005i	$-0.923179\pi$
$191$		−	91.3000i		−	0.478010i	0.971018	−	0.239005i	$-0.0768213\pi$
$192$	−95.4751	−	56.3250i	−0.497266	−	0.293359i
$193$	−125.665			−0.651115			−0.325557	−	0.945522i	$-0.605552\pi$
$193$	−125.665			−0.651115			−0.325557	+	0.945522i	$0.605552\pi$
$194$	−119.774	+	55.6232i	−0.617390	+	0.286718i
$195$	115.416			0.591879
$196$	−18.0651	+	21.3928i	−0.0921690	+	0.109147i
$197$			74.5133i			0.378240i	0.981954	+	0.189120i	$0.0605635\pi$
$197$			74.5133i			0.378240i	−0.981954	+	0.189120i	$0.939436\pi$
$198$	82.0892	−	38.1225i	0.414592	−	0.192538i
$199$			77.2741i			0.388312i	0.980971	+	0.194156i	$0.0621968\pi$
$199$			77.2741i			0.388312i	−0.980971	+	0.194156i	$0.937803\pi$
$200$	−21.7100	+	79.5269i	−0.108550	+	0.397634i
$201$	−149.061			−0.741597
$202$	−133.466	−	287.393i	−0.660723	−	1.42274i
$203$	76.6524			0.377598
$204$	−102.024	+	120.818i	−0.500119	+	0.592243i
$205$			183.556i			0.895395i
$206$	114.752	+	247.096i	0.557049	+	1.19950i
$207$			5.07086i			0.0244969i
$208$	−176.902	+	30.0516i	−0.850492	+	0.144479i
$209$	−498.864			−2.38691
$210$	−49.3910	+	22.9373i	−0.235195	+	0.109225i
$211$	283.994			1.34594			0.672971	−	0.739669i	$-0.265018\pi$
$211$	283.994			1.34594			0.672971	+	0.739669i	$0.265018\pi$
$212$	−220.759	−	186.420i	−1.04132	−	0.879341i
$213$			70.1130i			0.329169i
$214$	298.493	−	138.621i	1.39483	−	0.647763i
$215$		−	263.060i		−	1.22354i
$216$	10.9474	−	40.1018i	0.0506823	−	0.185657i
$217$	−65.4118			−0.301437
$218$	15.6827	+	33.7696i	0.0719389	+	0.154906i
$219$	49.5203			0.226120
$220$	273.922	+	231.314i	1.24510	+	1.05143i
$221$			255.971i			1.15824i
$222$	78.4792	+	168.990i	0.353510	+	0.761214i
$223$			115.772i			0.519155i	0.965722	+	0.259577i	$0.0835833\pi$
$223$			115.772i			0.519155i	−0.965722	+	0.259577i	$0.916417\pi$
$224$	69.7307	−	48.0169i	0.311298	−	0.214361i
$225$	−30.9138			−0.137395
$226$	254.688	−	118.278i	1.12694	−	0.523354i
$227$	6.83029			0.0300894			0.0150447	−	0.999887i	$-0.495211\pi$
$227$	6.83029			0.0300894			0.0150447	+	0.999887i	$0.495211\pi$
$228$	−147.823	+	175.053i	−0.648349	+	0.767776i
$229$			217.138i			0.948203i	0.880470	+	0.474101i	$0.157227\pi$
$229$			217.138i			0.948203i	−0.880470	+	0.474101i	$0.842773\pi$
$230$	−18.2179	+	8.46045i	−0.0792083	+	0.0367846i
$231$			69.1277i			0.299254i
$232$	−223.593	−	61.0387i	−0.963764	−	0.263098i
$233$	134.382			0.576746			0.288373	−	0.957518i	$-0.406886\pi$
$233$	134.382			0.576746			0.288373	+	0.957518i	$0.406886\pi$
$234$	−28.3420	−	61.0288i	−0.121119	−	0.260807i
$235$	−221.526			−0.942665
$236$	85.7352	−	101.528i	0.363285	−	0.430203i
$237$			139.509i			0.588647i
$238$	−50.8705	−	109.540i	−0.213742	−	0.460250i
$239$			408.424i			1.70889i	0.519545	+	0.854443i	$0.326101\pi$
$239$			408.424i			1.70889i	−0.519545	+	0.854443i	$0.673899\pi$
$240$	162.337	−	27.5773i	0.676406	−	0.114906i
$241$	−237.295			−0.984629			−0.492314	−	0.870418i	$-0.663849\pi$
$241$	−237.295			−0.984629			−0.492314	+	0.870418i	$0.663849\pi$
$242$	193.283	−	89.7612i	0.798690	−	0.370914i
$243$	15.5885			0.0641500
$244$	−296.043	−	249.993i	−1.21329	−	1.02456i
$245$		−	41.5924i		−	0.169765i
$246$	97.0590	−	45.0745i	0.394549	−	0.183230i
$247$			370.878i			1.50153i
$248$	190.805	+	52.0877i	0.769374	+	0.210031i
$249$	62.8133			0.252262
$250$	73.5553	+	158.387i	0.294221	+	0.633547i
$251$	305.519			1.21721			0.608604	−	0.793474i	$-0.291730\pi$
$251$	305.519			1.21721			0.608604	+	0.793474i	$0.291730\pi$
$252$	24.2571	+	20.4839i	0.0962585	+	0.0812854i
$253$			25.4978i			0.100782i
$254$	−161.726	−	348.246i	−0.636718	−	1.37105i
$255$		−	234.896i		−	0.921162i
$256$	−241.639	+	84.5373i	−0.943903	+	0.330224i
$257$	−212.323			−0.826158			−0.413079	−	0.910695i	$-0.635547\pi$
$257$	−212.323			−0.826158			−0.413079	+	0.910695i	$0.635547\pi$
$258$	−139.099	+	64.5978i	−0.539142	+	0.250379i
$259$	−142.307			−0.549448
$260$	171.969	−	203.646i	0.661419	−	0.783255i
$261$		−	86.9156i		−	0.333010i
$262$	24.6124	−	11.4301i	0.0939403	−	0.0436262i
$263$			55.8138i			0.212220i	0.994354	+	0.106110i	$0.0338396\pi$
$263$			55.8138i			0.212220i	−0.994354	+	0.106110i	$0.966160\pi$
$264$	55.0467	−	201.644i	0.208510	−	0.763803i
$265$	429.206			1.61965
$266$	−73.7065	−	158.712i	−0.277092	−	0.596663i
$267$	24.1499			0.0904492
$268$	−222.099	+	263.010i	−0.828727	+	0.981381i
$269$		−	392.637i		−	1.45962i	−0.683651	−	0.729809i	$-0.739609\pi$
$269$		−	392.637i		−	1.45962i	0.683651	−	0.729809i	$-0.260391\pi$
$270$	26.0085	+	56.0041i	0.0963277	+	0.207423i
$271$		−	505.999i		−	1.86715i	−0.358377	−	0.933577i	$-0.616670\pi$
$271$		−	505.999i		−	1.86715i	0.358377	−	0.933577i	$-0.383330\pi$
$272$	61.1612	+	360.033i	0.224857	+	1.32365i
$273$	51.3927			0.188251
$274$	136.550	−	63.4140i	0.498356	−	0.231438i
$275$	−155.444			−0.565252
$276$	8.94727	+	7.55552i	0.0324177	+	0.0273751i
$277$		−	234.703i		−	0.847304i	−0.905825	−	0.423652i	$-0.860748\pi$
$277$		−	234.703i		−	0.847304i	0.905825	−	0.423652i	$-0.139252\pi$
$278$	404.001	−	187.619i	1.45324	−	0.674889i
$279$			74.1700i			0.265842i
$280$	−33.1202	+	121.324i	−0.118286	+	0.433300i
$281$	−260.538			−0.927182			−0.463591	−	0.886049i	$-0.653439\pi$
$281$	−260.538			−0.927182			−0.463591	+	0.886049i	$0.653439\pi$
$282$	54.3986	+	117.137i	0.192903	+	0.415378i
$283$	314.398			1.11095			0.555474	−	0.831534i	$-0.312537\pi$
$283$	314.398			1.11095			0.555474	+	0.831534i	$0.312537\pi$
$284$	123.711	+	104.467i	0.435601	+	0.367843i
$285$		−	340.342i		−	1.19418i
$286$	−142.512	−	306.871i	−0.498293	−	1.07298i
$287$			81.7339i			0.284787i
$288$	−54.4461	−	79.0672i	−0.189049	−	0.274539i
$289$	231.955			0.802612
$290$	312.259	−	145.014i	1.07675	−	0.500048i
$291$	−114.367			−0.393013
$292$	73.7846	−	87.3759i	0.252687	−	0.299233i
$293$			54.0484i			0.184465i	0.995737	+	0.0922327i	$0.0294004\pi$
$293$			54.0484i			0.184465i	−0.995737	+	0.0922327i	$0.970600\pi$
$294$	−21.9928	+	10.2135i	−0.0748055	+	0.0347399i
$295$			197.393i			0.669129i
$296$	415.106	+	113.320i	1.40239	+	0.382837i
$297$	78.3835			0.263917
$298$	146.061	+	314.513i	0.490136	+	1.05541i
$299$	18.9562			0.0633988
$300$	−46.0612	+	54.5458i	−0.153537	+	0.181819i
$301$		−	117.136i		−	0.389155i
$302$	71.5511	+	154.071i	0.236924	+	0.510169i
$303$		−	274.419i		−	0.905673i
$304$	88.6168	+	521.653i	0.291502	+	1.71597i
$305$	575.574			1.88713
$306$	−124.206	+	57.6817i	−0.405903	+	0.188502i
$307$	−82.1306			−0.267526			−0.133763	−	0.991013i	$-0.542706\pi$
$307$	−82.1306			−0.267526			−0.133763	+	0.991013i	$0.542706\pi$
$308$	121.972	+	102.999i	0.396014	+	0.334414i
$309$			235.941i			0.763565i
$310$	−266.468	+	123.749i	−0.859574	+	0.399189i
$311$			83.2457i			0.267671i	0.991004	+	0.133835i	$0.0427294\pi$
$311$			83.2457i			0.267671i	−0.991004	+	0.133835i	$0.957271\pi$
$312$	−149.911	−	40.9242i	−0.480485	−	0.131167i
$313$	49.4110			0.157863			0.0789314	−	0.996880i	$-0.474849\pi$
$313$	49.4110			0.157863			0.0789314	+	0.996880i	$0.474849\pi$
$314$	−48.5798	−	104.607i	−0.154713	−	0.333144i
$315$	−47.1613			−0.149719
$316$	246.157	+	207.867i	0.778977	+	0.657807i
$317$			449.103i			1.41673i	0.705847	+	0.708364i	$0.250566\pi$
$317$			449.103i			1.41673i	−0.705847	+	0.708364i	$0.749434\pi$
$318$	−105.397	−	226.951i	−0.331437	−	0.713683i
$319$		−	437.038i		−	1.37003i
$320$	193.222	−	327.526i	0.603818	−	1.02352i
$321$	285.019			0.887908
$322$	−8.11207	+	3.76727i	−0.0251928	+	0.0116996i
$323$	754.814			2.33688
$324$	23.2266	−	27.5050i	0.0716870	−	0.0848920i
$325$			115.564i			0.355582i
$326$	19.6535	−	9.12716i	0.0602869	−	0.0279974i
$327$			32.2451i			0.0986089i
$328$	65.0851	−	238.416i	0.198430	−	0.726877i
$329$	−98.6413			−0.299822
$330$	130.778	+	281.606i	0.396298	+	0.853350i
$331$	−107.798			−0.325674			−0.162837	−	0.986653i	$-0.552064\pi$
$331$	−107.798			−0.325674			−0.162837	+	0.986653i	$0.552064\pi$
$332$	93.5910	−	110.831i	0.281901	−	0.333828i
$333$			161.361i			0.484567i
$334$	48.5089	+	104.454i	0.145236	+	0.312737i
$335$		−	511.351i		−	1.52642i
$336$	72.2856	−	12.2796i	0.215136	−	0.0365466i
$337$	−565.146			−1.67699			−0.838495	−	0.544909i	$-0.816564\pi$
$337$	−565.146			−1.67699			−0.838495	+	0.544909i	$0.816564\pi$
$338$	78.4135	−	36.4154i	0.231993	−	0.107738i
$339$	243.191			0.717378
$340$	−414.462	−	349.993i	−1.21901	−	1.02939i
$341$			372.949i			1.09369i
$342$	−179.963	+	83.5753i	−0.526208	+	0.244372i
$343$		−	18.5203i		−	0.0539949i
$344$	−93.2756	+	341.682i	−0.271150	+	0.993261i
$345$	−17.3955			−0.0504218
$346$	176.302	+	379.630i	0.509542	+	1.09720i
$347$	−617.119			−1.77844			−0.889221	−	0.457478i	$-0.848753\pi$
$347$	−617.119			−1.77844			−0.889221	+	0.457478i	$0.848753\pi$
$348$	−153.358	−	129.503i	−0.440684	−	0.372135i
$349$		−	208.548i		−	0.597557i	−0.954322	−	0.298779i	$-0.903421\pi$
$349$		−	208.548i		−	0.597557i	0.954322	−	0.298779i	$-0.0965792\pi$
$350$	−22.9667	−	49.4542i	−0.0656190	−	0.141298i
$351$		−	58.2738i		−	0.166022i
$352$	−273.771	−	397.574i	−0.777759	−	1.12947i
$353$	93.3007			0.264308			0.132154	−	0.991229i	$-0.457811\pi$
$353$	93.3007			0.264308			0.132154	+	0.991229i	$0.457811\pi$
$354$	104.376	−	48.4723i	0.294846	−	0.136927i
$355$	−240.521			−0.677525
$356$	35.9831	−	42.6113i	0.101076	−	0.119695i
$357$		−	104.595i		−	0.292982i
$358$	−415.302	+	192.868i	−1.16006	+	0.538736i
$359$			319.598i			0.890246i	0.895469	+	0.445123i	$0.146840\pi$
$359$			319.598i			0.890246i	−0.895469	+	0.445123i	$0.853160\pi$
$360$	137.569	+	37.5548i	0.382135	+	0.104319i
$361$	732.653			2.02951
$362$	−109.945	−	236.746i	−0.303716	−	0.653993i
$363$	184.558			0.508423
$364$	76.5744	−	90.6796i	0.210369	−	0.249120i
$365$			169.878i			0.465420i
$366$	−141.339	−	304.347i	−0.386173	−	0.831548i
$367$			489.607i			1.33408i	0.745022	+	0.667040i	$0.232439\pi$
$367$			489.607i			1.33408i	−0.745022	+	0.667040i	$0.767561\pi$
$368$	26.6626	−	4.52936i	0.0724528	−	0.0123080i
$369$	92.6775			0.251159
$370$	−579.716	+	269.222i	−1.56680	+	0.727626i
$371$	191.117			0.515140
$372$	130.869	+	110.512i	0.351799	+	0.297076i
$373$		−	427.590i		−	1.14635i	−0.819432	−	0.573177i	$-0.805711\pi$
$373$		−	427.590i		−	1.14635i	0.819432	−	0.573177i	$-0.194289\pi$
$374$	−624.547	+	290.041i	−1.66991	+	0.775511i
$375$			151.237i			0.403298i
$376$	287.734	+	78.5485i	0.765251	+	0.208906i
$377$	−324.914			−0.861840
$378$	11.5811	+	24.9375i	0.0306377	+	0.0659722i
$379$	−441.475			−1.16484			−0.582421	−	0.812887i	$-0.697894\pi$
$379$	−441.475			−1.16484			−0.582421	+	0.812887i	$0.697894\pi$
$380$	−600.516	−	507.106i	−1.58031	−	1.33449i
$381$		−	332.525i		−	0.872769i
$382$	−76.9109	−	165.612i	−0.201337	−	0.433540i
$383$		−	392.842i		−	1.02570i	−0.858479	−	0.512849i	$-0.828590\pi$
$383$		−	392.842i		−	1.02570i	0.858479	−	0.512849i	$-0.171410\pi$
$384$	−220.634	−	21.7420i	−0.574567	−	0.0566197i
$385$	−237.141			−0.615952
$386$	−227.949	+	105.860i	−0.590540	+	0.274249i
$387$	−132.819			−0.343202
$388$	−170.405	+	201.794i	−0.439188	+	0.520088i
$389$		−	539.166i		−	1.38603i	−0.720923	−	0.693015i	$-0.756282\pi$
$389$		−	539.166i		−	1.38603i	0.720923	−	0.693015i	$-0.243718\pi$
$390$	209.358	−	97.2266i	0.536816	−	0.249299i
$391$		−	38.5799i		−	0.0986698i
$392$	−14.7478	+	54.0232i	−0.0376219	+	0.137814i
$393$	23.5013			0.0597997
$394$	62.7698	+	135.162i	0.159314	+	0.343052i
$395$	−478.584			−1.21161
$396$	116.790	−	138.303i	0.294925	−	0.349251i
$397$		−	439.822i		−	1.10786i	−0.832562	−	0.553932i	$-0.813127\pi$
$397$		−	439.822i		−	1.10786i	0.832562	−	0.553932i	$-0.186873\pi$
$398$	65.0955	+	140.170i	0.163557	+	0.352187i
$399$		−	151.548i		−	0.379819i
$400$	27.6126	+	162.545i	0.0690316	+	0.406363i
$401$	256.316			0.639191			0.319596	−	0.947554i	$-0.396453\pi$
$401$	256.316			0.639191			0.319596	+	0.947554i	$0.396453\pi$
$402$	−270.387	+	125.569i	−0.672605	+	0.312360i
$403$	277.267			0.688008
$404$	−484.198	−	408.881i	−1.19851	−	1.01208i
$405$			53.4759i			0.132039i
$406$	139.043	−	64.5718i	0.342469	−	0.159044i
$407$			811.371i			1.99354i
$408$	−83.2893	+	305.100i	−0.204140	+	0.747795i
$409$	−401.361			−0.981322			−0.490661	−	0.871351i	$-0.663245\pi$
$409$	−401.361			−0.981322			−0.490661	+	0.871351i	$0.663245\pi$
$410$	154.627	+	332.959i	0.377139	+	0.812095i
$411$	130.385			0.317239
$412$	416.306	+	351.550i	1.01045	+	0.853276i
$413$			87.8951i			0.212821i
$414$	4.27168	+	9.19823i	0.0103181	+	0.0222179i
$415$			215.480i			0.519229i
$416$	−295.574	+	203.534i	−0.710515	+	0.489264i
$417$	385.763			0.925092
$418$	−904.908	+	420.242i	−2.16485	+	1.00536i
$419$	−185.720			−0.443247			−0.221623	−	0.975132i	$-0.571136\pi$
$419$	−185.720			−0.443247			−0.221623	+	0.975132i	$0.571136\pi$
$420$	−70.2698	+	83.2137i	−0.167309	+	0.198128i
$421$			361.664i			0.859060i	0.903053	+	0.429530i	$0.141321\pi$
$421$			361.664i			0.859060i	−0.903053	+	0.429530i	$0.858679\pi$
$422$	515.147	−	239.236i	1.22073	−	0.566909i
$423$			111.849i			0.264418i
$424$	−557.484	−	152.187i	−1.31482	−	0.358932i
$425$	235.197			0.553405
$426$	59.0630	+	127.181i	0.138646	+	0.298546i
$427$	256.292			0.600215
$428$	424.674	−	502.900i	0.992229	−	1.17500i
$429$		−	293.018i		−	0.683026i
$430$	−221.601	−	477.175i	−0.515352	−	1.10971i
$431$		−	130.748i		−	0.303359i	−0.988430	−	0.151679i	$-0.951532\pi$
$431$		−	130.748i		−	0.303359i	0.988430	−	0.151679i	$-0.0484681\pi$
$432$	−13.9238	−	81.9642i	−0.0322310	−	0.189732i
$433$	−450.084			−1.03945			−0.519727	−	0.854332i	$-0.673966\pi$
$433$	−450.084			−1.03945			−0.519727	+	0.854332i	$0.673966\pi$
$434$	−118.653	+	55.1028i	−0.273394	+	0.126965i
$435$	298.163			0.685431
$436$	56.8948	+	48.0448i	0.130493	+	0.110194i
$437$		−	55.8986i		−	0.127914i
$438$	89.8266	−	41.7158i	0.205084	−	0.0952415i
$439$		−	107.851i		−	0.245674i	−0.992427	−	0.122837i	$-0.960801\pi$
$439$		−	107.851i		−	0.245674i	0.992427	−	0.122837i	$-0.0391992\pi$
$440$	691.736	+	188.837i	1.57213	+	0.429175i
$441$	−21.0000			−0.0476190
$442$	215.630	+	464.316i	0.487850	+	1.05049i
$443$	−79.9983			−0.180583			−0.0902915	−	0.995915i	$-0.528780\pi$
$443$	−79.9983			−0.180583			−0.0902915	+	0.995915i	$0.528780\pi$
$444$	284.713	+	240.426i	0.641245	+	0.541499i
$445$			82.8459i			0.186171i
$446$	97.5256	+	210.002i	0.218667	+	0.470857i
$447$			300.315i			0.671845i
$448$	86.0378	−	145.841i	0.192049	−	0.325537i
$449$	498.405			1.11003			0.555017	−	0.831839i	$-0.312712\pi$
$449$	498.405			1.11003			0.555017	+	0.831839i	$0.312712\pi$
$450$	−56.0758	+	26.0418i	−0.124613	+	0.0578706i
$451$	466.010			1.03328
$452$	362.352	−	429.098i	0.801663	−	0.949331i
$453$			147.116i			0.324759i
$454$	12.3897	−	5.75382i	0.0272901	−	0.0126736i
$455$			176.302i			0.387476i
$456$	−120.678	+	442.061i	−0.264645	+	0.969433i
$457$	−469.124			−1.02653			−0.513264	−	0.858231i	$-0.671564\pi$
$457$	−469.124			−1.02653			−0.513264	+	0.858231i	$0.671564\pi$
$458$	182.917	+	393.875i	0.399382	+	0.859990i
$459$	−118.599			−0.258386
$460$	−25.9191	+	30.6935i	−0.0563458	+	0.0667249i
$461$		−	729.055i		−	1.58146i	−0.612162	−	0.790732i	$-0.709700\pi$
$461$		−	729.055i		−	1.58146i	0.612162	−	0.790732i	$-0.290300\pi$
$462$	58.2330	+	125.393i	0.126046	+	0.271414i
$463$		−	602.290i		−	1.30084i	−0.759574	−	0.650421i	$-0.774593\pi$
$463$		−	602.290i		−	1.30084i	0.759574	−	0.650421i	$-0.225407\pi$
$464$	−457.003	+	77.6341i	−0.984920	+	0.167315i
$465$	−254.439			−0.547180
$466$	243.760	−	113.203i	0.523090	−	0.242925i
$467$	−356.045			−0.762409			−0.381204	−	0.924491i	$-0.624491\pi$
$467$	−356.045			−0.762409			−0.381204	+	0.924491i	$0.624491\pi$
$468$	−102.821	−	86.8272i	−0.219703	−	0.185528i
$469$		−	227.694i		−	0.485489i
$470$	−401.835	+	186.613i	−0.854968	+	0.397050i
$471$		−	99.8848i		−	0.212070i
$472$	69.9913	−	256.388i	0.148287	−	0.543195i
$473$	−667.855			−1.41196
$474$	117.522	+	253.061i	0.247937	+	0.533884i
$475$	340.778			0.717427
$476$	−184.552	−	155.845i	−0.387714	−	0.327405i
$477$		−	216.706i		−	0.454311i
$478$	344.055	+	740.855i	0.719781	+	1.54991i
$479$			201.862i			0.421424i	0.977548	+	0.210712i	$0.0675782\pi$
$479$			201.862i			0.421424i	−0.977548	+	0.210712i	$0.932422\pi$
$480$	271.239	−	186.776i	0.565081	−	0.389117i
$481$	603.210			1.25407
$482$	−430.439	+	199.897i	−0.893027	+	0.414724i
$483$	−7.74587			−0.0160370
$484$	274.988	−	325.642i	0.568158	−	0.672815i
$485$		−	392.333i		−	0.808934i
$486$	28.2765	−	13.1317i	0.0581820	−	0.0270199i
$487$		−	343.994i		−	0.706353i	−0.935557	−	0.353177i	$-0.885102\pi$
$487$		−	343.994i		−	0.706353i	0.935557	−	0.353177i	$-0.114898\pi$
$488$	−747.597	−	204.086i	−1.53196	−	0.418210i
$489$	18.7663			0.0383770
$490$	−35.0373	−	75.4459i	−0.0715047	−	0.153971i
$491$	178.510			0.363564			0.181782	−	0.983339i	$-0.441813\pi$
$491$	178.510			0.363564			0.181782	+	0.983339i	$0.441813\pi$
$492$	138.088	−	163.525i	0.280667	−	0.332367i
$493$			661.267i			1.34131i
$494$	312.427	+	672.749i	0.632443	+	1.36184i
$495$			268.893i			0.543218i
$496$	389.986	−	66.2496i	0.786263	−	0.133568i
$497$	−107.099			−0.215492
$498$	113.939	−	52.9138i	0.228794	−	0.106253i
$499$	548.499			1.09920			0.549598	−	0.835429i	$-0.314781\pi$
$499$	548.499			1.09920			0.549598	+	0.835429i	$0.314781\pi$
$500$	266.849	+	225.341i	0.533698	+	0.450681i
$501$			99.7390i			0.199080i
$502$	554.193	−	257.369i	1.10397	−	0.512687i
$503$			394.287i			0.783872i	0.919993	+	0.391936i	$0.128194\pi$
$503$			394.287i			0.783872i	−0.919993	+	0.391936i	$0.871806\pi$
$504$	61.2565	+	16.7224i	0.121541	+	0.0331794i
$505$	941.389			1.86414
$506$	21.4793	+	46.2515i	0.0424492	+	0.0914061i
$507$	74.8737			0.147680
$508$	−586.723	−	495.458i	−1.15497	−	0.975310i
$509$		−	863.631i		−	1.69672i	−0.529419	−	0.848360i	$-0.677590\pi$
$509$		−	863.631i		−	1.69672i	0.529419	−	0.848360i	$-0.322410\pi$
$510$	−197.876	−	426.087i	−0.387992	−	0.835465i
$511$			75.6435i			0.148030i
$512$	−367.104	+	356.901i	−0.717000	+	0.697073i
$513$	−171.839			−0.334969
$514$	−385.140	+	178.860i	−0.749299	+	0.347977i
$515$	−809.393			−1.57164
$516$	−197.899	+	234.353i	−0.383525	+	0.454172i
$517$			562.409i			1.08783i
$518$	−258.136	+	119.879i	−0.498332	+	0.231427i
$519$			362.493i			0.698445i
$520$	140.390	−	514.268i	0.269980	−	0.988976i
$521$	499.986			0.959666			0.479833	−	0.877360i	$-0.340697\pi$
$521$	499.986			0.959666			0.479833	+	0.877360i	$0.340697\pi$
$522$	−73.2175	−	157.659i	−0.140263	−	0.302030i
$523$	−80.9144			−0.154712			−0.0773561	−	0.997004i	$-0.524648\pi$
$523$	−80.9144			−0.154712			−0.0773561	+	0.997004i	$0.524648\pi$
$524$	35.0166	−	41.4668i	0.0668256	−	0.0791351i
$525$		−	47.2217i		−	0.0899461i
$526$	47.0174	+	101.243i	0.0893868	+	0.192477i
$527$		−	564.296i		−	1.07077i
$528$	−70.0131	−	412.141i	−0.132601	−	0.780570i
$529$	526.143			0.994599
$530$	778.552	−	361.562i	1.46897	−	0.682193i
$531$	99.6637			0.187691
$532$	−267.398	−	225.804i	−0.502628	−	0.424444i
$533$		−	346.453i		−	0.650006i
$534$	43.8065	−	20.3439i	0.0820346	−	0.0380971i
$535$			977.751i			1.82757i
$536$	−181.314	+	664.179i	−0.338273	+	1.23914i
$537$	−396.554			−0.738462
$538$	−330.757	−	712.219i	−0.614789	−	1.32383i
$539$	−105.594			−0.195908
$540$	94.3554	+	79.6784i	0.174732	+	0.147553i
$541$		−	552.750i		−	1.02172i	−0.859664	−	0.510860i	$-0.829327\pi$
$541$		−	552.750i		−	1.02172i	0.859664	−	0.510860i	$-0.170673\pi$
$542$	−426.252	−	917.850i	−0.786443	−	1.69345i
$543$		−	226.058i		−	0.416314i
$544$	414.233	+	601.555i	0.761459	+	1.10580i
$545$	−110.616			−0.202966
$546$	93.2230	−	43.2930i	0.170738	−	0.0792913i
$547$	−570.865			−1.04363			−0.521814	−	0.853059i	$-0.674745\pi$
$547$	−570.865			−1.04363			−0.521814	+	0.853059i	$0.674745\pi$
$548$	194.272	−	230.058i	0.354512	−	0.419814i
$549$		−	290.608i		−	0.529340i
$550$	−281.966	+	130.946i	−0.512665	+	0.238083i
$551$			958.112i			1.73886i
$552$	22.5945	+	6.16808i	0.0409321	+	0.0111741i
$553$	−213.104			−0.385360
$554$	−197.713	−	425.737i	−0.356883	−	0.768478i
$555$	−553.546			−0.997380
$556$	574.782	−	680.659i	1.03378	−	1.22421i
$557$			1107.30i			1.98797i	0.109496	+	0.993987i	$0.465076\pi$
$557$			1107.30i			1.98797i	−0.109496	+	0.993987i	$0.534924\pi$
$558$	62.4806	+	134.540i	0.111972	+	0.241111i
$559$			496.514i			0.888218i
$560$	42.1251	+	247.974i	0.0752234	+	0.442812i
$561$	−596.353			−1.06302
$562$	−472.600	+	219.477i	−0.840924	+	0.390528i
$563$	32.2930			0.0573587			0.0286794	−	0.999589i	$-0.490870\pi$
$563$	32.2930			0.0573587			0.0286794	+	0.999589i	$0.490870\pi$
$564$	197.351	+	166.653i	0.349913	+	0.295484i
$565$			834.263i			1.47657i
$566$	570.298	−	264.848i	1.00759	−	0.467930i
$567$			23.8118i			0.0419961i
$568$	312.406	+	85.2837i	0.550011	+	0.150147i
$569$	838.069			1.47288			0.736440	−	0.676503i	$-0.236505\pi$
$569$	838.069			1.47288			0.736440	+	0.676503i	$0.236505\pi$
$570$	−286.704	−	617.360i	−0.502989	−	1.08309i
$571$	−590.149			−1.03354			−0.516768	−	0.856126i	$-0.672865\pi$
$571$	−590.149			−1.03354			−0.516768	+	0.856126i	$0.672865\pi$
$572$	−517.015	−	436.593i	−0.903873	−	0.763275i
$573$		−	158.136i		−	0.275979i
$574$	68.8524	+	148.260i	0.119952	+	0.258293i
$575$		−	17.4178i		−	0.0302918i
$576$	−165.368	−	97.5577i	−0.287097	−	0.169371i
$577$	376.385			0.652314			0.326157	−	0.945316i	$-0.394246\pi$
$577$	376.385			0.652314			0.326157	+	0.945316i	$0.394246\pi$
$578$	420.751	−	195.398i	0.727943	−	0.338059i
$579$	−217.658			−0.375921
$580$	444.258	−	526.092i	0.765962	−	0.907055i
$581$			95.9489i			0.165144i
$582$	−207.454	+	96.3423i	−0.356450	+	0.165537i
$583$		−	1089.66i		−	1.86906i
$584$	60.2353	−	220.650i	0.103143	−	0.377826i
$585$	199.907			0.341722
$586$	45.5302	+	98.0404i	0.0776966	+	0.167304i
$587$	−489.154			−0.833311			−0.416656	−	0.909064i	$-0.636798\pi$
$587$	−489.154			−0.833311			−0.416656	+	0.909064i	$0.636798\pi$
$588$	−31.2897	+	37.0534i	−0.0532138	+	0.0630160i
$589$		−	817.611i		−	1.38813i
$590$	166.283	+	358.058i	0.281836	+	0.606879i
$591$			129.061i			0.218377i
$592$	848.436	−	144.130i	1.43317	−	0.243462i
$593$	180.522			0.304421			0.152211	−	0.988348i	$-0.451361\pi$
$593$	180.522			0.304421			0.152211	+	0.988348i	$0.451361\pi$
$594$	142.183	−	66.0301i	0.239365	−	0.111162i
$595$	358.810			0.603042
$596$	529.889	+	447.465i	0.889076	+	0.750780i
$597$			133.843i			0.224192i
$598$	34.3854	−	15.9687i	0.0575007	−	0.0267035i
$599$			16.6365i			0.0277738i	0.999904	+	0.0138869i	$0.00442048\pi$
$599$			16.6365i			0.0277738i	−0.999904	+	0.0138869i	$0.995580\pi$
$600$	−37.6029	+	137.745i	−0.0626714	+	0.229574i
$601$	−763.074			−1.26967			−0.634837	−	0.772646i	$-0.718933\pi$
$601$	−763.074			−1.26967			−0.634837	+	0.772646i	$0.718933\pi$
$602$	−98.6747	−	212.477i	−0.163912	−	0.352951i
$603$	−258.181			−0.428161
$604$	259.578	+	219.201i	0.429765	+	0.362915i
$605$			633.122i			1.04648i
$606$	−231.170	−	497.779i	−0.381468	−	0.821417i
$607$			82.3314i			0.135637i	0.997698	+	0.0678183i	$0.0216038\pi$
$607$			82.3314i			0.135637i	−0.997698	+	0.0678183i	$0.978396\pi$
$608$	600.185	+	871.596i	0.987146	+	1.43355i
$609$	132.766			0.218006
$610$	1044.06	−	484.862i	1.71157	−	0.794856i
$611$	418.120			0.684321
$612$	−176.711	+	209.262i	−0.288744	+	0.341931i
$613$			522.712i			0.852712i	0.904556	+	0.426356i	$0.140203\pi$
$613$			522.712i			0.852712i	−0.904556	+	0.426356i	$0.859797\pi$
$614$	−148.980	+	69.1866i	−0.242638	+	0.112682i
$615$			317.928i			0.516957i
$616$	308.016	+	84.0853i	0.500026	+	0.136502i
$617$	−1005.31			−1.62935			−0.814674	−	0.579920i	$-0.803084\pi$
$617$	−1005.31			−1.62935			−0.814674	+	0.579920i	$0.803084\pi$
$618$	198.757	+	427.983i	0.321612	+	0.692529i
$619$	519.176			0.838734			0.419367	−	0.907817i	$-0.362252\pi$
$619$	519.176			0.838734			0.419367	+	0.907817i	$0.362252\pi$
$620$	−379.111	+	448.944i	−0.611469	+	0.724103i
$621$			8.78300i			0.0141433i
$622$	70.1259	+	151.002i	0.112743	+	0.242769i
$623$			36.8896i			0.0592129i
$624$	−306.404	+	52.0509i	−0.491032	+	0.0834149i
$625$	−776.430			−1.24229
$626$	89.6285	−	41.6237i	0.143177	−	0.0664916i
$627$	−864.058			−1.37808
$628$	−176.241	−	148.827i	−0.280639	−	0.236986i
$629$		−	1227.66i		−	1.95176i
$630$	−85.5477	+	39.7286i	−0.135790	+	0.0630612i
$631$			62.6700i			0.0993185i	0.998766	+	0.0496592i	$0.0158135\pi$
$631$			62.6700i			0.0993185i	−0.998766	+	0.0496592i	$0.984186\pi$
$632$	621.619	+	169.696i	0.983575	+	0.268506i
$633$	491.892			0.777080
$634$	378.323	+	814.644i	0.596724	+	1.28493i
$635$	1140.72			1.79641
$636$	−382.367	−	322.889i	−0.601205	−	0.507688i
$637$			78.5036i			0.123240i
$638$	−368.160	−	792.759i	−0.577053	−	1.24257i
$639$			121.439i			0.190046i
$640$	74.5854	−	756.880i	0.116540	−	1.18263i
$641$	800.473			1.24879			0.624394	−	0.781110i	$-0.285346\pi$
$641$	800.473			1.24879			0.624394	+	0.781110i	$0.285346\pi$
$642$	517.006	−	240.099i	0.805305	−	0.373986i
$643$	−818.686			−1.27323			−0.636614	−	0.771183i	$-0.719666\pi$
$643$	−818.686			−1.27323			−0.636614	+	0.771183i	$0.719666\pi$
$644$	−11.5412	+	13.6672i	−0.0179212	+	0.0212223i
$645$		−	455.634i		−	0.706409i
$646$	1369.18	−	635.853i	2.11948	−	0.984293i
$647$		−	509.102i		−	0.786866i	−0.919353	−	0.393433i	$-0.871287\pi$
$647$		−	509.102i		−	0.786866i	0.919353	−	0.393433i	$-0.128713\pi$
$648$	18.9614	−	69.4584i	0.0292615	−	0.107189i
$649$	501.139			0.772172
$650$	97.3510	+	209.626i	0.149771	+	0.322502i
$651$	−113.297			−0.174035
$652$	27.9616	−	33.1122i	0.0428859	−	0.0507856i
$653$			997.554i			1.52765i	0.645424	+	0.763824i	$0.276681\pi$
$653$			997.554i			1.52765i	−0.645424	+	0.763824i	$0.723319\pi$
$654$	27.1632	+	58.4906i	0.0415339	+	0.0894351i
$655$			80.6208i			0.123085i
$656$	−82.7807	−	487.299i	−0.126190	−	0.742833i
$657$	85.7716			0.130550
$658$	−178.929	+	83.0952i	−0.271929	+	0.126284i
$659$	179.635			0.272588			0.136294	−	0.990668i	$-0.456481\pi$
$659$	179.635			0.272588			0.136294	+	0.990668i	$0.456481\pi$
$660$	474.448	+	400.647i	0.718860	+	0.607041i
$661$			155.299i			0.234946i	0.993076	+	0.117473i	$0.0374793\pi$
$661$			155.299i			0.234946i	−0.993076	+	0.117473i	$0.962521\pi$
$662$	−195.539	+	90.8088i	−0.295376	+	0.137173i
$663$			443.355i			0.668711i
$664$	76.4046	−	279.881i	0.115067	−	0.421507i
$665$	519.882			0.781777
$666$	135.930	+	292.698i	0.204099	+	0.439487i
$667$	48.9708			0.0734195
$668$	175.984	+	148.610i	0.263449	+	0.222470i
$669$			200.522i			0.299734i
$670$	−430.761	−	927.558i	−0.642927	−	1.38442i
$671$		−	1461.26i		−	2.17774i
$672$	120.777	−	83.1677i	0.179728	−	0.123761i
$673$	−1066.49			−1.58469			−0.792343	−	0.610076i	$-0.791139\pi$
$673$	−1066.49			−1.58469			−0.792343	+	0.610076i	$0.791139\pi$
$674$	−1025.14	+	476.077i	−1.52098	+	0.706346i
$675$	−53.5444			−0.0793250
$676$	111.561	−	132.111i	0.165031	−	0.195430i
$677$		−	248.880i		−	0.367622i	−0.982962	−	0.183811i	$-0.941157\pi$
$677$		−	248.880i		−	0.367622i	0.982962	−	0.183811i	$-0.0588434\pi$
$678$	441.133	−	204.864i	0.650639	−	0.302159i
$679$		−	174.698i		−	0.257287i
$680$	−1046.64	−	285.722i	−1.53918	−	0.420180i
$681$	11.8304			0.0173721
$682$	314.172	+	676.506i	0.460662	+	0.991945i
$683$	465.842			0.682053			0.341026	−	0.940054i	$-0.389225\pi$
$683$	465.842			0.682053			0.341026	+	0.940054i	$0.389225\pi$
$684$	−256.038	+	303.201i	−0.374324	+	0.443276i
$685$			447.285i			0.652970i
$686$	−15.6014	−	33.5946i	−0.0227426	−	0.0489717i
$687$			376.095i			0.547445i
$688$	118.636	+	698.364i	0.172436	+	1.01506i
$689$	−810.105			−1.17577
$690$	−31.5544	+	14.6539i	−0.0457309	+	0.0212376i
$691$	−854.073			−1.23600			−0.617998	−	0.786180i	$-0.712056\pi$
$691$	−854.073			−1.23600			−0.617998	+	0.786180i	$0.712056\pi$
$692$	639.600	+	540.110i	0.924277	+	0.780505i
$693$			119.733i			0.172775i
$694$	−1119.42	+	519.860i	−1.61299	+	0.749077i
$695$			1323.35i			1.90411i
$696$	−387.275	−	105.722i	−0.556429	−	0.151900i
$697$	−705.104			−1.01163
$698$	−175.680	−	378.292i	−0.251690	−	0.541966i
$699$	232.756			0.332985
$700$	−83.3202	−	70.3597i	−0.119029	−	0.100514i
$701$		−	746.975i		−	1.06559i	−0.846246	−	0.532793i	$-0.821143\pi$
$701$		−	746.975i		−	1.06559i	0.846246	−	0.532793i	$-0.178857\pi$
$702$	−49.0897	−	105.705i	−0.0699283	−	0.150577i
$703$		−	1778.76i		−	2.53024i
$704$	−831.519	−	490.550i	−1.18113	−	0.696804i
$705$	−383.695			−0.544248
$706$	169.241	−	78.5962i	0.239719	−	0.111326i
$707$	419.182			0.592902
$708$	148.498	−	175.851i	0.209742	−	0.248378i
$709$			939.270i			1.32478i	0.749158	+	0.662391i	$0.230458\pi$
$709$			939.270i			1.32478i	−0.749158	+	0.662391i	$0.769542\pi$
$710$	−436.290	+	202.615i	−0.614494	+	0.285373i
$711$			241.637i			0.339855i
$712$	29.3754	−	107.606i	0.0412576	−	0.151132i
$713$	−41.7896			−0.0586109
$714$	−88.1103	−	189.728i	−0.123404	−	0.265726i
$715$	1005.19			1.40587
$716$	−590.861	+	699.699i	−0.825224	+	0.977233i
$717$			707.411i			0.986626i
$718$	269.229	+	579.731i	0.374971	+	0.807425i
$719$			683.284i			0.950325i	0.879898	+	0.475163i	$0.157611\pi$
$719$			683.284i			0.950325i	−0.879898	+	0.475163i	$0.842389\pi$
$720$	281.177	−	47.7654i	0.390523	−	0.0663408i
$721$	−360.407			−0.499870
$722$	1328.99	−	617.185i	1.84070	−	0.854827i
$723$	−411.008			−0.568476
$724$	−398.868	−	336.824i	−0.550922	−	0.465226i
$725$			298.544i			0.411785i
$726$	334.776	−	155.471i	0.461124	−	0.214147i
$727$		−	77.6493i		−	0.106808i	−0.998573	−	0.0534039i	$-0.982993\pi$
$727$		−	77.6493i		−	0.106808i	0.998573	−	0.0534039i	$-0.0170071\pi$
$728$	62.5128	−	228.993i	0.0858692	−	0.314551i
$729$	27.0000			0.0370370
$730$	143.105	+	308.149i	0.196034	+	0.422121i
$731$	1010.51			1.38236
$732$	−512.762	−	433.001i	−0.700494	−	0.591532i
$733$			829.362i			1.13146i	0.824590	+	0.565731i	$0.191406\pi$
$733$			829.362i			1.13146i	−0.824590	+	0.565731i	$0.808594\pi$
$734$	412.444	+	888.116i	0.561913	+	1.20997i
$735$		−	72.0401i		−	0.0980138i
$736$	44.5488	−	30.6765i	0.0605283	−	0.0416800i
$737$	−1298.21			−1.76148
$738$	168.111	−	78.0713i	0.227793	−	0.105788i
$739$	961.998			1.30176			0.650878	−	0.759182i	$-0.274401\pi$
$739$	961.998			1.30176			0.650878	+	0.759182i	$0.274401\pi$
$740$	−824.776	+	976.702i	−1.11456	+	1.31987i
$741$			642.380i			0.866909i
$742$	346.674	−	160.996i	0.467216	−	0.216976i
$743$		−	1037.64i		−	1.39656i	−0.715826	−	0.698279i	$-0.753949\pi$
$743$		−	1037.64i		−	1.39656i	0.715826	−	0.698279i	$-0.246051\pi$
$744$	330.484	+	90.2186i	0.444198	+	0.121262i
$745$	−1030.22			−1.38285
$746$	−360.201	−	775.621i	−0.482843	−	1.03971i
$747$	108.796			0.145644
$748$	−888.558	+	1052.23i	−1.18791	+	1.40673i
$749$			435.373i			0.581273i
$750$	127.401	+	274.334i	0.169869	+	0.365778i
$751$		−	988.651i		−	1.31645i	−0.752823	−	0.658223i	$-0.771308\pi$
$751$		−	988.651i		−	1.31645i	0.752823	−	0.658223i	$-0.228692\pi$
$752$	588.101	−	99.9047i	0.782049	−	0.132852i
$753$	529.175			0.702756
$754$	−589.373	+	273.707i	−0.781662	+	0.363006i
$755$	−504.679			−0.668449
$756$	42.0146	+	35.4792i	0.0555749	+	0.0469302i
$757$			398.170i			0.525984i	0.964798	+	0.262992i	$0.0847093\pi$
$757$			398.170i			0.525984i	−0.964798	+	0.262992i	$0.915291\pi$
$758$	−800.808	+	371.898i	−1.05647	+	0.490630i
$759$			44.1636i			0.0581865i
$760$	−1516.48	−	413.984i	−1.99537	−	0.544716i
$761$	573.007			0.752966			0.376483	−	0.926424i	$-0.377133\pi$
$761$	573.007			0.752966			0.376483	+	0.926424i	$0.377133\pi$
$762$	−280.118	−	603.179i	−0.367609	−	0.791574i
$763$	−49.2552			−0.0645547
$764$	−279.023	−	235.621i	−0.365213	−	0.308404i
$765$		−	406.853i		−	0.531833i
$766$	−330.929	−	712.591i	−0.432023	−	0.930275i
$767$		−	372.569i		−	0.485749i
$768$	−418.531	+	146.423i	−0.544962	+	0.190655i
$769$	1317.67			1.71349			0.856743	−	0.515743i	$-0.172484\pi$
$769$	1317.67			1.71349			0.856743	+	0.515743i	$0.172484\pi$
$770$	−430.160	+	199.767i	−0.558649	+	0.259438i
$771$	−367.753			−0.476982
$772$	−324.308	+	384.047i	−0.420088	+	0.497470i
$773$		−	753.284i		−	0.974495i	−0.873264	−	0.487247i	$-0.838001\pi$
$773$		−	753.284i		−	0.974495i	0.873264	−	0.487247i	$-0.161999\pi$
$774$	−240.926	+	111.887i	−0.311274	+	0.144556i
$775$		−	254.765i		−	0.328728i
$776$	−139.113	+	509.590i	−0.179269	+	0.656689i
$777$	−246.483			−0.317224
$778$	−454.192	−	978.013i	−0.583794	−	1.25709i
$779$	−1021.63			−1.31146
$780$	297.859	−	352.726i	0.381871	−	0.452212i
$781$			610.633i			0.781861i
$782$	−32.4996	−	69.9814i	−0.0415596	−	0.0894903i
$783$		−	150.542i		−	0.192263i
$784$	18.7575	+	110.418i	0.0239253	+	0.140839i
$785$	342.653			0.436501
$786$	42.6299	−	19.7974i	0.0542365	−	0.0251876i
$787$	−77.2279			−0.0981295			−0.0490648	−	0.998796i	$-0.515624\pi$
$787$	−77.2279			−0.0981295			−0.0490648	+	0.998796i	$0.515624\pi$
$788$	227.721	+	192.299i	0.288986	+	0.244034i
$789$			96.6724i			0.122525i
$790$	−868.121	+	403.158i	−1.09889	+	0.510327i
$791$			371.481i			0.469634i
$792$	95.3438	−	349.258i	0.120384	−	0.440982i
$793$	−1086.37			−1.36995
$794$	−370.505	−	797.809i	−0.466631	−	1.00480i
$795$	743.407			0.935103
$796$	236.158	+	199.424i	0.296681	+	0.250532i
$797$		−	509.008i		−	0.638655i	−0.947644	−	0.319327i	$-0.896543\pi$
$797$		−	509.008i		−	0.638655i	0.947644	−	0.319327i	$-0.103457\pi$
$798$	−127.663	−	274.898i	−0.159979	−	0.344484i
$799$		−	850.961i		−	1.06503i
$800$	187.015	+	271.586i	0.233769	+	0.339482i
$801$	41.8289			0.0522209
$802$	464.940	−	215.920i	0.579726	−	0.269227i
$803$	431.286			0.537093
$804$	−384.687	+	455.547i	−0.478466	+	0.566601i
$805$		−	26.5721i		−	0.0330088i
$806$	502.945	−	233.569i	0.624002	−	0.289788i
$807$		−	680.068i		−	0.842711i
$808$	−1222.74	−	333.797i	−1.51330	−	0.413115i
$809$	692.461			0.855946			0.427973	−	0.903791i	$-0.359228\pi$
$809$	692.461			0.855946			0.427973	+	0.903791i	$0.359228\pi$
$810$	45.0480	+	97.0019i	0.0556148	+	0.119755i
$811$	1496.99			1.84585			0.922926	−	0.384978i	$-0.125791\pi$
$811$	1496.99			1.84585			0.922926	+	0.384978i	$0.125791\pi$
$812$	197.819	−	234.258i	0.243620	−	0.288495i
$813$		−	876.415i		−	1.07800i
$814$	683.497	+	1471.78i	0.839677	+	1.80808i
$815$			64.3775i			0.0789909i
$816$	105.934	+	623.595i	0.129821	+	0.764210i
$817$	1464.13			1.79208
$818$	−728.043	+	338.105i	−0.890028	+	0.413332i
$819$	89.0147			0.108687
$820$	560.968	+	473.709i	0.684107	+	0.577694i
$821$		−	1081.65i		−	1.31748i	−0.752371	−	0.658740i	$-0.771090\pi$
$821$		−	1081.65i		−	1.31748i	0.752371	−	0.658740i	$-0.228910\pi$
$822$	236.511	−	109.836i	0.287726	−	0.133621i
$823$			684.571i			0.831799i	0.909410	+	0.415900i	$0.136533\pi$
$823$			684.571i			0.831799i	−0.909410	+	0.415900i	$0.863467\pi$
$824$	1051.30	+	286.993i	1.27585	+	0.348293i
$825$	−269.237			−0.326348
$826$	74.0427	+	159.436i	0.0896400	+	0.193022i
$827$	526.172			0.636242			0.318121	−	0.948050i	$-0.396948\pi$
$827$	526.172			0.636242			0.318121	+	0.948050i	$0.396948\pi$
$828$	15.4971	+	13.0865i	0.0187163	+	0.0158050i
$829$		−	1255.76i		−	1.51479i	−0.652959	−	0.757393i	$-0.726473\pi$
$829$		−	1255.76i		−	1.51479i	0.652959	−	0.757393i	$-0.273527\pi$
$830$	181.520	+	390.867i	0.218699	+	0.470924i
$831$		−	406.518i		−	0.489191i
$832$	−364.697	+	618.189i	−0.438337	+	0.743015i
$833$	159.771			0.191802
$834$	699.750	−	324.966i	0.839029	−	0.389648i
$835$	−342.153			−0.409764
$836$	−1287.44	+	1524.59i	−1.53999	+	1.82367i
$837$			128.466i			0.153484i
$838$	−336.885	+	156.450i	−0.402011	+	0.186695i
$839$		−	93.1019i		−	0.110968i	−0.998460	−	0.0554839i	$-0.982330\pi$
$839$		−	93.1019i		−	0.110968i	0.998460	−	0.0554839i	$-0.0176701\pi$
$840$	−57.3659	+	210.139i	−0.0682927	+	0.250166i
$841$	1.63019			0.00193840
$842$	304.665	+	656.036i	0.361835	+	0.779141i
$843$	−451.265			−0.535309
$844$	732.912	−	867.917i	0.868379	−	1.02834i
$845$			256.853i			0.303968i
$846$	94.2211	+	202.886i	0.111372	+	0.239819i
$847$			281.917i			0.332841i
$848$	−1139.44	+	193.565i	−1.34368	+	0.228260i
$849$	544.553			0.641406
$850$	426.633	−	198.129i	0.501921	−	0.233093i
$851$	−90.9155			−0.106834
$852$	214.273	+	180.943i	0.251494	+	0.212374i
$853$			1226.85i			1.43828i	0.694867	+	0.719138i	$0.255463\pi$
$853$			1226.85i			1.43828i	−0.694867	+	0.719138i	$0.744537\pi$
$854$	464.897	−	215.900i	0.544376	−	0.252810i
$855$		−	589.490i		−	0.689463i
$856$	346.690	−	1269.97i	0.405011	−	1.48361i
$857$	201.847			0.235528			0.117764	−	0.993042i	$-0.462427\pi$
$857$	201.847			0.235528			0.117764	+	0.993042i	$0.462427\pi$
$858$	−246.838	−	531.517i	−0.287690	−	0.619483i
$859$	−1493.93			−1.73915			−0.869574	−	0.493802i	$-0.835607\pi$
$859$	−1493.93			−1.73915			−0.869574	+	0.493802i	$0.835607\pi$
$860$	−803.942	−	678.889i	−0.934816	−	0.789405i
$861$			141.567i			0.164422i
$862$	−110.141	−	237.168i	−0.127774	−	0.275137i
$863$		−	453.506i		−	0.525499i	−0.964864	−	0.262750i	$-0.915371\pi$
$863$		−	453.506i		−	0.525499i	0.964864	−	0.262750i	$-0.0846294\pi$
$864$	−94.3033	−	136.948i	−0.109147	−	0.158505i
$865$	−1243.53			−1.43760
$866$	−816.424	+	379.150i	−0.942753	+	0.437817i
$867$	401.757			0.463388
$868$	−168.810	+	199.906i	−0.194482	+	0.230306i
$869$			1215.02i			1.39819i
$870$	540.848	−	251.171i	0.621664	−	0.288703i
$871$			965.150i			1.10809i
$872$	143.676	+	39.2222i	0.164766	+	0.0449796i
$873$	−198.089			−0.226906
$874$	−47.0888	−	101.396i	−0.0538774	−	0.116014i
$875$	−231.018			−0.264020
$876$	127.799	−	151.340i	0.145889	−	0.172762i
$877$			75.4930i			0.0860809i	0.999073	+	0.0430405i	$0.0137044\pi$
$877$			75.4930i			0.0860809i	−0.999073	+	0.0430405i	$0.986296\pi$
$878$	−90.8533	−	195.635i	−0.103478	−	0.222819i
$879$			93.6146i			0.106501i
$880$	1413.84	−	240.179i	1.60664	−	0.272930i
$881$	−1065.89			−1.20986			−0.604931	−	0.796278i	$-0.706799\pi$
$881$	−1065.89			−1.20986			−0.604931	+	0.796278i	$0.706799\pi$
$882$	−38.0927	+	17.6903i	−0.0431890	+	0.0200571i
$883$	−956.369			−1.08309			−0.541545	−	0.840672i	$-0.682161\pi$
$883$	−956.369			−1.08309			−0.541545	+	0.840672i	$0.682161\pi$
$884$	782.277	+	660.594i	0.884929	+	0.747278i
$885$			341.895i			0.386322i
$886$	−145.112	+	67.3904i	−0.163783	+	0.0760614i
$887$		−	158.851i		−	0.179088i	−0.995983	−	0.0895440i	$-0.971459\pi$
$887$		−	158.851i		−	0.179088i	0.995983	−	0.0895440i	$-0.0285410\pi$
$888$	718.985	+	196.276i	0.809668	+	0.221031i
$889$	507.940			0.571361
$890$	69.7892	+	150.277i	0.0784148	+	0.168851i
$891$	135.764			0.152373
$892$	353.811	+	298.775i	0.396649	+	0.334950i
$893$		−	1232.96i		−	1.38070i
$894$	252.984	+	544.752i	0.282980	+	0.609342i
$895$		−	1360.37i		−	1.51997i
$896$	33.2114	−	337.024i	0.0370663	−	0.376143i
$897$	32.8332			0.0366033
$898$	904.075	−	419.855i	1.00676	−	0.467545i
$899$	716.282			0.796754
$900$	−79.7804	+	94.4762i	−0.0886449	+	0.104974i
$901$			1648.73i			1.82989i
$902$	845.313	−	392.566i	0.937155	−	0.435217i
$903$		−	202.885i		−	0.224679i
$904$	295.812	−	1083.60i	0.327225	−	1.19867i
$905$	775.489			0.856894
$906$	123.930	+	266.859i	0.136788	+	0.294546i
$907$	1106.62			1.22008			0.610042	−	0.792369i	$-0.291152\pi$
$907$	1106.62			1.22008			0.610042	+	0.792369i	$0.291152\pi$
$908$	17.6271	−	20.8741i	0.0194132	−	0.0229891i
$909$		−	475.308i		−	0.522891i
$910$	148.516	+	319.800i	0.163204	+	0.351428i
$911$		−	950.439i		−	1.04329i	−0.853162	−	0.521646i	$-0.825318\pi$
$911$		−	950.439i		−	1.04329i	0.853162	−	0.521646i	$-0.174682\pi$
$912$	153.489	+	903.530i	0.168299	+	0.990713i
$913$	547.059			0.599188
$914$	−850.961	+	395.189i	−0.931029	+	0.432373i
$915$	996.924			1.08953
$916$	663.599	+	560.376i	0.724453	+	0.611764i
$917$			35.8988i			0.0391481i
$918$	−215.132	+	99.9077i	−0.234348	+	0.108832i
$919$		−	609.662i		−	0.663397i	−0.943385	−	0.331698i	$-0.892378\pi$
$919$		−	609.662i		−	0.663397i	0.943385	−	0.331698i	$-0.107622\pi$
$920$	−21.1595	+	77.5101i	−0.0229994	+	0.0842502i
$921$	−142.254			−0.154456
$922$	−614.154	−	1322.46i	−0.666111	−	1.43434i
$923$	453.972			0.491844
$924$	211.262	+	178.400i	0.228639	+	0.193074i
$925$		−	554.254i		−	0.599194i
$926$	−507.367	−	1092.52i	−0.547913	−	1.17982i
$927$			408.663i			0.440844i
$928$	−763.575	+	525.801i	−0.822818	+	0.566596i
$929$	−306.485			−0.329909			−0.164954	−	0.986301i	$-0.552748\pi$
$929$	−306.485			−0.329909			−0.164954	+	0.986301i	$0.552748\pi$
$930$	−461.536	+	214.339i	−0.496275	+	0.230472i
$931$	231.493			0.248650
$932$	346.804	−	410.686i	0.372107	−	0.440650i
$933$			144.186i			0.154540i
$934$	−645.843	+	299.931i	−0.691481	+	0.321126i
$935$		−	2045.78i		−	2.18800i
$936$	−259.654	−	70.8828i	−0.277408	−	0.0757295i
$937$	885.867			0.945429			0.472715	−	0.881216i	$-0.343274\pi$
$937$	885.867			0.945429			0.472715	+	0.881216i	$0.343274\pi$
$938$	−191.809	−	413.023i	−0.204487	−	0.440323i
$939$	85.5824			0.0911421
$940$	−571.700	+	677.009i	−0.608192	+	0.720223i
$941$			1527.11i			1.62285i	0.584454	+	0.811427i	$0.301309\pi$
$941$			1527.11i			1.62285i	−0.584454	+	0.811427i	$0.698691\pi$
$942$	−84.1427	−	181.185i	−0.0893235	−	0.192341i
$943$			52.2172i			0.0553735i
$944$	−89.0209	−	524.032i	−0.0943018	−	0.555119i
$945$	−81.6858			−0.0864400
$946$	−1211.45	+	562.600i	−1.28060	+	0.594714i
$947$	−43.0382			−0.0454468			−0.0227234	−	0.999742i	$-0.507234\pi$
$947$	−43.0382			−0.0454468			−0.0227234	+	0.999742i	$0.507234\pi$
$948$	426.356	+	360.036i	0.449742	+	0.379785i
$949$		−	320.637i		−	0.337868i
$950$	618.150	−	287.071i	0.650684	−	0.302180i
$951$			777.869i			0.817948i
$952$	−466.048	−	127.226i	−0.489547	−	0.133641i
$953$	701.454			0.736048			0.368024	−	0.929816i	$-0.380034\pi$
$953$	701.454			0.736048			0.368024	+	0.929816i	$0.380034\pi$
$954$	−182.553	−	393.091i	−0.191355	−	0.412045i
$955$	542.483			0.568045
$956$	1248.19	+	1054.03i	1.30564	+	1.10254i
$957$		−	756.972i		−	0.790985i
$958$	170.048	+	366.165i	0.177503	+	0.382218i
$959$			199.167i			0.207682i
$960$	334.670	−	567.291i	0.348615	−	0.590928i
$961$	349.756			0.363950
$962$	1094.18	−	508.143i	1.13741	−	0.528215i
$963$	493.667			0.512634
$964$	−612.396	+	725.202i	−0.635266	+	0.752284i
$965$		−	746.673i		−	0.773755i
$966$	−14.0505	+	6.52511i	−0.0145451	+	0.00675477i
$967$			1078.20i			1.11500i	0.830178	+	0.557499i	$0.188239\pi$
$967$			1078.20i			1.11500i	−0.830178	+	0.557499i	$0.811761\pi$
$968$	224.491	−	822.344i	0.231913	−	0.849529i
$969$	1307.38			1.34920
$970$	−330.500	−	711.668i	−0.340722	−	0.733678i
$971$	68.6986			0.0707504			0.0353752	−	0.999374i	$-0.488737\pi$
$971$	68.6986			0.0707504			0.0353752	+	0.999374i	$0.488737\pi$
$972$	40.2296	−	47.6401i	0.0413885	−	0.0490124i
$973$			589.263i			0.605615i
$974$	−289.780	−	623.983i	−0.297515	−	0.640640i
$975$			200.163i			0.205295i
$976$	−1528.02	+	259.574i	−1.56559	+	0.265957i
$977$	785.845			0.804345			0.402172	−	0.915564i	$-0.368255\pi$
$977$	785.845			0.804345			0.402172	+	0.915564i	$0.368255\pi$
$978$	34.0409	−	15.8087i	0.0348067	−	0.0161643i
$979$	210.328			0.214840
$980$	−127.111	−	107.339i	−0.129705	−	0.109529i
$981$			55.8502i			0.0569319i
$982$	323.806	−	150.376i	0.329741	−	0.153133i
$983$			14.8697i			0.0151269i	0.999971	+	0.00756345i	$0.00240754\pi$
$983$			14.8697i			0.0151269i	−0.999971	+	0.00756345i	$0.997592\pi$
$984$	112.731	−	412.948i	0.114564	−	0.419663i
$985$	−442.741			−0.449483
$986$	557.049	+	1199.50i	0.564959	+	1.21653i
$987$	−170.852			−0.173102
$988$	1133.44	+	957.137i	1.14721	+	0.968762i
$989$		−	74.8343i		−	0.0756666i
$990$	226.515	+	487.755i	0.228803	+	0.492682i
$991$			1163.67i			1.17424i	0.809499	+	0.587121i	$0.199739\pi$
$991$			1163.67i			1.17424i	−0.809499	+	0.587121i	$0.800261\pi$
$992$	651.602	−	448.696i	0.656857	−	0.452315i
$993$	−186.712			−0.188028
$994$	−194.271	+	90.2202i	−0.195444	+	0.0907648i
$995$	−459.145			−0.461452
$996$	162.104	−	191.965i	0.162755	−	0.192735i
$997$		−	1235.53i		−	1.23925i	−0.784898	−	0.619625i	$-0.787285\pi$
$997$		−	1235.53i		−	1.23925i	0.784898	−	0.619625i	$-0.212715\pi$
$998$	994.942	−	462.054i	0.996936	−	0.462980i
$999$			279.485i			0.279765i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	168.3.g.a.43.19	✓	24
3.2	odd	2		504.3.g.d.379.6		24
4.3	odd	2		672.3.g.a.463.9		24
8.3	odd	2	inner	168.3.g.a.43.20	yes	24
8.5	even	2		672.3.g.a.463.4		24
12.11	even	2		2016.3.g.d.1135.5		24
24.5	odd	2		2016.3.g.d.1135.20		24
24.11	even	2		504.3.g.d.379.5		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.3.g.a.43.19	✓	24	1.1	even	1	trivial
168.3.g.a.43.20	yes	24	8.3	odd	2	inner
504.3.g.d.379.5		24	24.11	even	2
504.3.g.d.379.6		24	3.2	odd	2
672.3.g.a.463.4		24	8.5	even	2
672.3.g.a.463.9		24	4.3	odd	2
2016.3.g.d.1135.5		24	12.11	even	2
2016.3.g.d.1135.20		24	24.5	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:	\( N \)	\(=\)	\( 168 = 2^{3} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	168.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.81394 - 0.842398i) q^{2} +1.73205 q^{3} +(2.58073 - 3.05611i) q^{4} +5.94177i q^{5} +(3.14183 - 1.45908i) q^{6} +2.64575i q^{7} +(2.10682 - 7.71760i) q^{8} +3.00000 q^{9} +O(q^{10})\)	\(q+(1.81394 - 0.842398i) q^{2} +1.73205 q^{3} +(2.58073 - 3.05611i) q^{4} +5.94177i q^{5} +(3.14183 - 1.45908i) q^{6} +2.64575i q^{7} +(2.10682 - 7.71760i) q^{8} +3.00000 q^{9} +(5.00533 + 10.7780i) q^{10} +15.0849 q^{11} +(4.46996 - 5.29334i) q^{12} -11.2148i q^{13} +(2.22877 + 4.79923i) q^{14} +10.2914i q^{15} +(-2.67964 - 15.7740i) q^{16} -22.8244 q^{17} +(5.44181 - 2.52719i) q^{18} -33.0704 q^{19} +(18.1587 + 15.3341i) q^{20} +4.58258i q^{21} +(27.3631 - 12.7075i) q^{22} +1.69029i q^{23} +(3.64913 - 13.3673i) q^{24} -10.3046 q^{25} +(-9.44732 - 20.3429i) q^{26} +5.19615 q^{27} +(8.08571 + 6.82798i) q^{28} -28.9719i q^{29} +(8.66949 + 18.6680i) q^{30} +24.7233i q^{31} +(-18.1487 - 26.3557i) q^{32} +26.1278 q^{33} +(-41.4021 + 19.2272i) q^{34} -15.7204 q^{35} +(7.74220 - 9.16834i) q^{36} +53.7870i q^{37} +(-59.9877 + 27.8584i) q^{38} -19.4246i q^{39} +(45.8562 + 12.5183i) q^{40} +30.8925 q^{41} +(3.86035 + 8.31250i) q^{42} -44.2731 q^{43} +(38.9301 - 46.1012i) q^{44} +17.8253i q^{45} +(1.42389 + 3.06608i) q^{46} +37.2829i q^{47} +(-4.64127 - 27.3214i) q^{48} -7.00000 q^{49} +(-18.6919 + 8.68058i) q^{50} -39.5331 q^{51} +(-34.2737 - 28.9424i) q^{52} -72.2354i q^{53} +(9.42549 - 4.37723i) q^{54} +89.6310i q^{55} +(20.4188 + 5.57413i) q^{56} -57.2797 q^{57} +(-24.4058 - 52.5532i) q^{58} +33.2212 q^{59} +(31.4518 + 26.5595i) q^{60} -96.8692i q^{61} +(20.8269 + 44.8466i) q^{62} +7.93725i q^{63} +(-55.1226 - 32.5192i) q^{64} +66.6357 q^{65} +(47.3942 - 22.0100i) q^{66} -86.0604 q^{67} +(-58.9038 + 69.7540i) q^{68} +2.92767i q^{69} +(-28.5159 + 13.2429i) q^{70} +40.4798i q^{71} +(6.32047 - 23.1528i) q^{72} +28.5905 q^{73} +(45.3100 + 97.5662i) q^{74} -17.8481 q^{75} +(-85.3459 + 101.067i) q^{76} +39.9109i q^{77} +(-16.3632 - 35.2350i) q^{78} +80.5457i q^{79} +(93.7255 - 15.9218i) q^{80} +9.00000 q^{81} +(56.0370 - 26.0238i) q^{82} +36.2653 q^{83} +(14.0049 + 11.8264i) q^{84} -135.618i q^{85} +(-80.3086 + 37.2955i) q^{86} -50.1808i q^{87} +(31.7813 - 116.419i) q^{88} +13.9430 q^{89} +(15.0160 + 32.3340i) q^{90} +29.6716 q^{91} +(5.16571 + 4.36218i) q^{92} +42.8221i q^{93} +(31.4070 + 67.6288i) q^{94} -196.497i q^{95} +(-31.4344 - 45.6495i) q^{96} -66.0297 q^{97} +(-12.6976 + 5.89678i) q^{98} +45.2547 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 2 q^{2} + 10 q^{4} + 12 q^{6} + 10 q^{8} + 72 q^{9}+O(q^{10}) \) 24 * q - 2 * q^2 + 10 * q^4 + 12 * q^6 + 10 * q^8 + 72 * q^9	\( 24 q - 2 q^{2} + 10 q^{4} + 12 q^{6} + 10 q^{8} + 72 q^{9} + 12 q^{10} + 32 q^{11} + 24 q^{12} - 14 q^{14} + 66 q^{16} + 16 q^{17} - 6 q^{18} - 64 q^{19} + 20 q^{20} + 12 q^{22} - 36 q^{24} - 72 q^{25} + 100 q^{26} - 14 q^{28} + 72 q^{30} + 98 q^{32} - 108 q^{34} + 30 q^{36} - 72 q^{38} - 332 q^{40} - 80 q^{41} + 32 q^{43} - 292 q^{44} - 48 q^{48} - 168 q^{49} + 46 q^{50} + 192 q^{51} - 4 q^{52} + 36 q^{54} + 98 q^{56} - 96 q^{58} - 24 q^{60} - 16 q^{62} - 182 q^{64} - 192 q^{65} - 24 q^{66} - 32 q^{67} + 188 q^{68} - 84 q^{70} + 30 q^{72} - 240 q^{73} + 208 q^{74} - 384 q^{75} + 8 q^{76} + 168 q^{78} + 484 q^{80} + 216 q^{81} - 372 q^{82} - 320 q^{83} - 604 q^{86} + 468 q^{88} + 400 q^{89} + 36 q^{90} + 352 q^{92} - 72 q^{94} - 252 q^{96} + 144 q^{97} + 14 q^{98} + 96 q^{99}+O(q^{100}) \) 24 * q - 2 * q^2 + 10 * q^4 + 12 * q^6 + 10 * q^8 + 72 * q^9 + 12 * q^10 + 32 * q^11 + 24 * q^12 - 14 * q^14 + 66 * q^16 + 16 * q^17 - 6 * q^18 - 64 * q^19 + 20 * q^20 + 12 * q^22 - 36 * q^24 - 72 * q^25 + 100 * q^26 - 14 * q^28 + 72 * q^30 + 98 * q^32 - 108 * q^34 + 30 * q^36 - 72 * q^38 - 332 * q^40 - 80 * q^41 + 32 * q^43 - 292 * q^44 - 48 * q^48 - 168 * q^49 + 46 * q^50 + 192 * q^51 - 4 * q^52 + 36 * q^54 + 98 * q^56 - 96 * q^58 - 24 * q^60 - 16 * q^62 - 182 * q^64 - 192 * q^65 - 24 * q^66 - 32 * q^67 + 188 * q^68 - 84 * q^70 + 30 * q^72 - 240 * q^73 + 208 * q^74 - 384 * q^75 + 8 * q^76 + 168 * q^78 + 484 * q^80 + 216 * q^81 - 372 * q^82 - 320 * q^83 - 604 * q^86 + 468 * q^88 + 400 * q^89 + 36 * q^90 + 352 * q^92 - 72 * q^94 - 252 * q^96 + 144 * q^97 + 14 * q^98 + 96 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more