LMFDB - Embedded newform 380.3.h.a.39.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [380,3,Mod(39,380)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(380, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("380.39");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 380 = 2^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	380.h (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:	$10.3542500457$
Analytic rank:	$0$
Dimension:	$108$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			39.19
Character	$\chi$	$=$	380.39
Dual form			380.3.h.a.39.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.68898 - 1.07114i) q^{2} +5.94620 q^{3} +(1.70531 + 3.61828i) q^{4} +(1.71987 - 4.69490i) q^{5} +(-10.0430 - 6.36923i) q^{6} -9.59523 q^{7} +(0.995461 - 7.93782i) q^{8} +26.3573 q^{9} +O(q^{10})$	\(q+(-1.68898 - 1.07114i) q^{2} +5.94620 q^{3} +(1.70531 + 3.61828i) q^{4} +(1.71987 - 4.69490i) q^{5} +(-10.0430 - 6.36923i) q^{6} -9.59523 q^{7} +(0.995461 - 7.93782i) q^{8} +26.3573 q^{9} +(-7.93373 + 6.08736i) q^{10} -5.60839i q^{11} +(10.1401 + 21.5150i) q^{12} +1.46557i q^{13} +(16.2062 + 10.2779i) q^{14} +(10.2267 - 27.9168i) q^{15} +(-10.1839 + 12.3405i) q^{16} -30.4749i q^{17} +(-44.5169 - 28.2324i) q^{18} -4.35890i q^{19} +(19.9203 - 1.78326i) q^{20} -57.0551 q^{21} +(-6.00738 + 9.47246i) q^{22} +5.38208 q^{23} +(5.91921 - 47.1999i) q^{24} +(-19.0841 - 16.1492i) q^{25} +(1.56984 - 2.47533i) q^{26} +103.210 q^{27} +(-16.3628 - 34.7182i) q^{28} +25.0321 q^{29} +(-47.1755 + 36.1966i) q^{30} +26.0540i q^{31} +(30.4188 - 9.93458i) q^{32} -33.3486i q^{33} +(-32.6430 + 51.4716i) q^{34} +(-16.5026 + 45.0486i) q^{35} +(44.9473 + 95.3679i) q^{36} +35.8792i q^{37} +(-4.66900 + 7.36209i) q^{38} +8.71460i q^{39} +(-35.5552 - 18.3256i) q^{40} +3.18512 q^{41} +(96.3650 + 61.1142i) q^{42} +57.1393 q^{43} +(20.2927 - 9.56403i) q^{44} +(45.3311 - 123.745i) q^{45} +(-9.09023 - 5.76498i) q^{46} -30.6020 q^{47} +(-60.5552 + 73.3793i) q^{48} +43.0685 q^{49} +(14.9345 + 47.7175i) q^{50} -181.210i q^{51} +(-5.30285 + 2.49925i) q^{52} +61.6843i q^{53} +(-174.319 - 110.552i) q^{54} +(-26.3308 - 9.64571i) q^{55} +(-9.55168 + 76.1653i) q^{56} -25.9189i q^{57} +(-42.2788 - 26.8130i) q^{58} +50.5937i q^{59} +(118.450 - 10.6036i) q^{60} -31.5158 q^{61} +(27.9076 - 44.0047i) q^{62} -252.904 q^{63} +(-62.0181 - 15.8036i) q^{64} +(6.88072 + 2.52060i) q^{65} +(-35.7211 + 56.3251i) q^{66} -13.4084 q^{67} +(110.267 - 51.9691i) q^{68} +32.0029 q^{69} +(76.1260 - 58.4096i) q^{70} -23.8999i q^{71} +(26.2376 - 209.219i) q^{72} -63.7064i q^{73} +(38.4317 - 60.5992i) q^{74} +(-113.478 - 96.0266i) q^{75} +(15.7717 - 7.43326i) q^{76} +53.8138i q^{77} +(9.33458 - 14.7188i) q^{78} +57.1288i q^{79} +(40.4226 + 69.0363i) q^{80} +376.491 q^{81} +(-5.37961 - 3.41172i) q^{82} -71.3250 q^{83} +(-97.2965 - 206.441i) q^{84} +(-143.077 - 52.4130i) q^{85} +(-96.5072 - 61.2044i) q^{86} +148.846 q^{87} +(-44.5184 - 5.58293i) q^{88} -7.54874 q^{89} +(-209.112 + 160.446i) q^{90} -14.0625i q^{91} +(9.17811 + 19.4739i) q^{92} +154.922i q^{93} +(51.6861 + 32.7791i) q^{94} +(-20.4646 - 7.49675i) q^{95} +(180.876 - 59.0730i) q^{96} +118.660i q^{97} +(-72.7418 - 46.1325i) q^{98} -147.822i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 108 q + 4 q^{5} + 324 q^{9}+O(q^{10}) $ 108 * q + 4 * q^5 + 324 * q^9	$ 108 q + 4 q^{5} + 324 q^{9} - 8 q^{10} + 8 q^{14} - 104 q^{16} - 16 q^{21} - 8 q^{24} - 76 q^{25} + 80 q^{26} - 88 q^{29} - 140 q^{30} - 88 q^{34} - 256 q^{36} + 44 q^{40} - 200 q^{41} - 8 q^{44} + 108 q^{45} + 272 q^{46} + 916 q^{49} - 276 q^{50} - 320 q^{54} - 328 q^{56} + 172 q^{60} + 200 q^{61} - 216 q^{64} - 192 q^{65} + 152 q^{66} - 592 q^{69} + 200 q^{70} - 232 q^{74} + 340 q^{80} + 1052 q^{81} + 208 q^{84} + 248 q^{85} - 1048 q^{86} + 760 q^{89} + 268 q^{90} - 320 q^{94} + 720 q^{96}+O(q^{100}) $ 108 * q + 4 * q^5 + 324 * q^9 - 8 * q^10 + 8 * q^14 - 104 * q^16 - 16 * q^21 - 8 * q^24 - 76 * q^25 + 80 * q^26 - 88 * q^29 - 140 * q^30 - 88 * q^34 - 256 * q^36 + 44 * q^40 - 200 * q^41 - 8 * q^44 + 108 * q^45 + 272 * q^46 + 916 * q^49 - 276 * q^50 - 320 * q^54 - 328 * q^56 + 172 * q^60 + 200 * q^61 - 216 * q^64 - 192 * q^65 + 152 * q^66 - 592 * q^69 + 200 * q^70 - 232 * q^74 + 340 * q^80 + 1052 * q^81 + 208 * q^84 + 248 * q^85 - 1048 * q^86 + 760 * q^89 + 268 * q^90 - 320 * q^94 + 720 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/380\mathbb{Z}\right)^\times$.

$n$	$21$	$77$	$191$
$\chi(n)$	$1$	$-1$	$-1$

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 $

$2$	−1.68898	−	1.07114i	−0.844490	−	0.535571i
$2$	−1.68898	−	1.07114i	−0.844490	−	0.535571i
$3$	5.94620			1.98207			0.991033	−	0.133617i	$-0.0426591\pi$
$3$	5.94620			1.98207			0.991033	+	0.133617i	$0.0426591\pi$
$4$	1.70531	+	3.61828i	0.426327	+	0.904569i
$5$	1.71987	−	4.69490i	0.343974	−	0.938979i
$5$	1.71987	−	4.69490i	0.343974	−	0.938979i
$6$	−10.0430	−	6.36923i	−1.67384	−	1.06154i
$7$	−9.59523			−1.37075			−0.685374	−	0.728192i	$-0.740361\pi$
$7$	−9.59523			−1.37075			−0.685374	+	0.728192i	$0.740361\pi$
$8$	0.995461	−	7.93782i	0.124433	−	0.992228i
$9$	26.3573			2.92859
$10$	−7.93373	+	6.08736i	−0.793373	+	0.608736i
$11$		−	5.60839i		−	0.509854i	−0.966960	−	0.254927i	$-0.917949\pi$
$11$		−	5.60839i		−	0.509854i	0.966960	−	0.254927i	$-0.0820514\pi$
$12$	10.1401	+	21.5150i	0.845008	+	1.79292i
$13$			1.46557i			0.112736i	0.998410	+	0.0563682i	$0.0179521\pi$
$13$			1.46557i			0.112736i	−0.998410	+	0.0563682i	$0.982048\pi$
$14$	16.2062	+	10.2779i	1.15758	+	0.734133i
$15$	10.2267	−	27.9168i	0.681780	−	1.86112i
$16$	−10.1839	+	12.3405i	−0.636491	+	0.771284i
$17$		−	30.4749i		−	1.79264i	−0.443404	−	0.896322i	$-0.646229\pi$
$17$		−	30.4749i		−	1.79264i	0.443404	−	0.896322i	$-0.353771\pi$
$18$	−44.5169	−	28.2324i	−2.47316	−	1.56847i
$19$		−	4.35890i		−	0.229416i
$19$		−	4.35890i		−	0.229416i
$20$	19.9203	−	1.78326i	0.996017	−	0.0891632i
$21$	−57.0551			−2.71691
$22$	−6.00738	+	9.47246i	−0.273063	+	0.430566i
$23$	5.38208			0.234004			0.117002	−	0.993132i	$-0.462672\pi$
$23$	5.38208			0.234004			0.117002	+	0.993132i	$0.462672\pi$
$24$	5.91921	−	47.1999i	0.246634	−	1.96666i
$25$	−19.0841	−	16.1492i	−0.763363	−	0.645970i
$26$	1.56984	−	2.47533i	0.0603784	−	0.0952048i
$27$	103.210			3.82259
$28$	−16.3628	−	34.7182i	−0.584386	−	1.23994i
$29$	25.0321			0.863177			0.431589	−	0.902071i	$-0.357953\pi$
$29$	25.0321			0.863177			0.431589	+	0.902071i	$0.357953\pi$
$30$	−47.1755	+	36.1966i	−1.57252	+	1.20655i
$31$			26.0540i			0.840453i	0.907419	+	0.420226i	$0.138049\pi$
$31$			26.0540i			0.840453i	−0.907419	+	0.420226i	$0.861951\pi$
$32$	30.4188	−	9.93458i	0.950588	−	0.310456i
$33$		−	33.3486i		−	1.01056i
$34$	−32.6430	+	51.4716i	−0.960088	+	1.51387i
$35$	−16.5026	+	45.0486i	−0.471502	+	1.28710i
$36$	44.9473	+	95.3679i	1.24853	+	2.64911i
$37$			35.8792i			0.969708i	0.874595	+	0.484854i	$0.161127\pi$
$37$			35.8792i			0.969708i	−0.874595	+	0.484854i	$0.838873\pi$
$38$	−4.66900	+	7.36209i	−0.122868	+	0.193739i
$39$			8.71460i			0.223451i
$40$	−35.5552	−	18.3256i	−0.888880	−	0.458141i
$41$	3.18512			0.0776859			0.0388430	−	0.999245i	$-0.487633\pi$
$41$	3.18512			0.0776859			0.0388430	+	0.999245i	$0.487633\pi$
$42$	96.3650	+	61.1142i	2.29440	+	1.45510i
$43$	57.1393			1.32882			0.664411	−	0.747368i	$-0.268683\pi$
$43$	57.1393			1.32882			0.664411	+	0.747368i	$0.268683\pi$
$44$	20.2927	−	9.56403i	0.461198	−	0.217364i
$45$	45.3311	−	123.745i	1.00736	−	2.74988i
$46$	−9.09023	−	5.76498i	−0.197614	−	0.125326i
$47$	−30.6020			−0.651106			−0.325553	−	0.945524i	$-0.605550\pi$
$47$	−30.6020			−0.651106			−0.325553	+	0.945524i	$0.605550\pi$
$48$	−60.5552	+	73.3793i	−1.26157	+	1.52874i
$49$	43.0685			0.878948
$50$	14.9345	+	47.7175i	0.298690	+	0.954350i
$51$		−	181.210i		−	3.55314i
$52$	−5.30285	+	2.49925i	−0.101978	+	0.0480626i
$53$			61.6843i			1.16385i	0.813241	+	0.581927i	$0.197701\pi$
$53$			61.6843i			1.16385i	−0.813241	+	0.581927i	$0.802299\pi$
$54$	−174.319	−	110.552i	−3.22814	−	2.04727i
$55$	−26.3308	−	9.64571i	−0.478742	−	0.175377i
$56$	−9.55168	+	76.1653i	−0.170566	+	1.36009i
$57$		−	25.9189i		−	0.454717i
$58$	−42.2788	−	26.8130i	−0.728944	−	0.462293i
$59$			50.5937i			0.857521i	0.903418	+	0.428761i	$0.141050\pi$
$59$			50.5937i			0.857521i	−0.903418	+	0.428761i	$0.858950\pi$
$60$	118.450	−	10.6036i	1.97417	−	0.176727i
$61$	−31.5158			−0.516652			−0.258326	−	0.966058i	$-0.583171\pi$
$61$	−31.5158			−0.516652			−0.258326	+	0.966058i	$0.583171\pi$
$62$	27.9076	−	44.0047i	0.450122	−	0.709754i
$63$	−252.904			−4.01435
$64$	−62.0181	−	15.8036i	−0.969033	−	0.246931i
$65$	6.88072	+	2.52060i	0.105857	+	0.0387785i
$66$	−35.7211	+	56.3251i	−0.541229	+	0.853411i
$67$	−13.4084			−0.200125			−0.100062	−	0.994981i	$-0.531904\pi$
$67$	−13.4084			−0.200125			−0.100062	+	0.994981i	$0.531904\pi$
$68$	110.267	−	51.9691i	1.62157	−	0.764252i
$69$	32.0029			0.463811
$70$	76.1260	−	58.4096i	1.08751	−	0.834423i
$71$		−	23.8999i		−	0.336618i	−0.985734	−	0.168309i	$-0.946169\pi$
$71$		−	23.8999i		−	0.336618i	0.985734	−	0.168309i	$-0.0538306\pi$
$72$	26.2376	−	209.219i	0.364412	−	2.90583i
$73$		−	63.7064i		−	0.872690i	−0.899779	−	0.436345i	$-0.856273\pi$
$73$		−	63.7064i		−	0.872690i	0.899779	−	0.436345i	$-0.143727\pi$
$74$	38.4317	−	60.5992i	0.519348	−	0.818908i
$75$	−113.478	−	96.0266i	−1.51304	−	1.28035i
$76$	15.7717	−	7.43326i	0.207522	−	0.0978061i
$77$			53.8138i			0.698880i
$78$	9.33458	−	14.7188i	0.119674	−	0.188702i
$79$			57.1288i			0.723149i	0.932343	+	0.361574i	$0.117761\pi$
$79$			57.1288i			0.723149i	−0.932343	+	0.361574i	$0.882239\pi$
$80$	40.4226	+	69.0363i	0.505283	+	0.862954i
$81$	376.491			4.64803
$82$	−5.37961	−	3.41172i	−0.0656050	−	0.0416063i
$83$	−71.3250			−0.859338			−0.429669	−	0.902987i	$-0.641370\pi$
$83$	−71.3250			−0.859338			−0.429669	+	0.902987i	$0.641370\pi$
$84$	−97.2965	−	206.441i	−1.15829	−	2.45763i
$85$	−143.077	−	52.4130i	−1.68325	−	0.616623i
$86$	−96.5072	−	61.2044i	−1.12218	−	0.711679i
$87$	148.846			1.71087
$88$	−44.5184	−	5.58293i	−0.505891	−	0.0634424i
$89$	−7.54874			−0.0848173			−0.0424086	−	0.999100i	$-0.513503\pi$
$89$	−7.54874			−0.0848173			−0.0424086	+	0.999100i	$0.513503\pi$
$90$	−209.112	+	160.446i	−2.32346	+	1.78273i
$91$		−	14.0625i		−	0.154533i
$92$	9.17811	+	19.4739i	0.0997620	+	0.211673i
$93$			154.922i			1.66583i
$94$	51.6861	+	32.7791i	0.549852	+	0.348714i
$95$	−20.4646	−	7.49675i	−0.215417	−	0.0789131i
$96$	180.876	−	59.0730i	1.88413	−	0.615343i
$97$			118.660i			1.22330i	0.791128	+	0.611650i	$0.209494\pi$
$97$			118.660i			1.22330i	−0.791128	+	0.611650i	$0.790506\pi$
$98$	−72.7418	−	46.1325i	−0.742263	−	0.470739i
$99$		−	147.822i		−	1.49315i
$100$	25.8882	−	96.5909i	0.258882	−	0.965909i
$101$	73.2975			0.725718			0.362859	−	0.931844i	$-0.381801\pi$
$101$	73.2975			0.725718			0.362859	+	0.931844i	$0.381801\pi$
$102$	−194.102	+	306.060i	−1.90296	+	3.00059i
$103$	23.4616			0.227782			0.113891	−	0.993493i	$-0.463669\pi$
$103$	23.4616			0.227782			0.113891	+	0.993493i	$0.463669\pi$
$104$	11.6335	+	1.45892i	0.111860	+	0.0140281i
$105$	−98.1276	+	267.868i	−0.934548	+	2.55112i
$106$	66.0727	−	104.184i	0.623327	−	0.982863i
$107$	−95.4606			−0.892155			−0.446077	−	0.894994i	$-0.647179\pi$
$107$	−95.4606			−0.892155			−0.446077	+	0.894994i	$0.647179\pi$
$108$	176.004	+	373.442i	1.62967	+	3.45779i
$109$	−79.3688			−0.728154			−0.364077	−	0.931369i	$-0.618616\pi$
$109$	−79.3688			−0.728154			−0.364077	+	0.931369i	$0.618616\pi$
$110$	34.1403	+	44.4955i	0.310366	+	0.404504i
$111$			213.345i			1.92202i
$112$	97.7164	−	118.410i	0.872468	−	1.05724i
$113$		−	63.7939i		−	0.564548i	−0.959334	−	0.282274i	$-0.908911\pi$
$113$		−	63.7939i		−	0.564548i	0.959334	−	0.282274i	$-0.0910887\pi$
$114$	−27.7628	+	43.7765i	−0.243533	+	0.384004i
$115$	9.25650	−	25.2683i	0.0804913	−	0.219725i
$116$	42.6875	+	90.5732i	0.367996	+	0.780803i
$117$			38.6286i			0.330159i
$118$	54.1931	−	85.4518i	0.459264	−	0.724168i
$119$			292.414i			2.45726i
$120$	−211.418	−	108.968i	−1.76182	−	0.908065i
$121$	89.5460			0.740049
$122$	53.2295	+	33.7579i	0.436308	+	0.276704i
$123$	18.9394			0.153979
$124$	−94.2707	+	44.4301i	−0.760248	+	0.358307i
$125$	−108.641	+	61.8231i	−0.869129	+	0.494585i
$126$	427.150	+	270.896i	3.39008	+	2.14997i
$127$	−24.0747			−0.189565			−0.0947823	−	0.995498i	$-0.530216\pi$
$127$	−24.0747			−0.189565			−0.0947823	+	0.995498i	$0.530216\pi$
$128$	87.8195	+	93.1222i	0.686090	+	0.727517i
$129$	339.762			2.63381
$130$	−8.92147	−	11.6275i	−0.0686267	−	0.0894421i
$131$			122.140i			0.932367i	0.884688	+	0.466184i	$0.154371\pi$
$131$			122.140i			0.932367i	−0.884688	+	0.466184i	$0.845629\pi$
$132$	120.664	−	56.8696i	0.914125	−	0.430830i
$133$			41.8246i			0.314471i
$134$	22.6464	+	14.3623i	0.169003	+	0.107181i
$135$	177.508	−	484.559i	1.31487	−	3.58933i
$136$	−241.905	−	30.3366i	−1.77871	−	0.223063i
$137$			83.0890i			0.606489i	0.952913	+	0.303245i	$0.0980699\pi$
$137$			83.0890i			0.606489i	−0.952913	+	0.303245i	$0.901930\pi$
$138$	−54.0523	−	34.2797i	−0.391684	−	0.248404i
$139$			81.3364i			0.585154i	0.956242	+	0.292577i	$0.0945128\pi$
$139$			81.3364i			0.585154i	−0.956242	+	0.292577i	$0.905487\pi$
$140$	−191.140	+	17.1108i	−1.36529	+	0.122220i
$141$	−181.965			−1.29053
$142$	−25.6002	+	40.3664i	−0.180283	+	0.284270i
$143$	8.21951			0.0574791
$144$	−268.419	+	325.263i	−1.86402	+	2.25877i
$145$	43.0521	−	117.523i	0.296911	−	0.810505i
$146$	−68.2386	+	107.599i	−0.467388	+	0.736978i
$147$	256.094			1.74213
$148$	−129.821	+	61.1850i	−0.877168	+	0.413412i
$149$	92.6290			0.621671			0.310836	−	0.950464i	$-0.399391\pi$
$149$	92.6290			0.621671			0.310836	+	0.950464i	$0.399391\pi$
$150$	88.8035	+	283.738i	0.592023	+	1.89159i
$151$		−	176.136i		−	1.16646i	−0.812307	−	0.583231i	$-0.801788\pi$
$151$		−	176.136i		−	1.16646i	0.812307	−	0.583231i	$-0.198212\pi$
$152$	−34.6002	−	4.33911i	−0.227633	−	0.0285468i
$153$		−	803.236i		−	5.24991i
$154$	57.6422	−	90.8904i	0.374300	−	0.590198i
$155$	122.321	+	44.8096i	0.789167	+	0.289094i
$156$	−31.5318	+	14.8611i	−0.202127	+	0.0952632i
$157$		−	139.701i		−	0.889814i	−0.895577	−	0.444907i	$-0.853237\pi$
$157$		−	139.701i		−	0.889814i	0.895577	−	0.444907i	$-0.146763\pi$
$158$	61.1930	−	96.4893i	0.387298	−	0.610692i
$159$			366.787i			2.30684i
$160$	5.67467	−	159.899i	0.0354667	−	0.999371i
$161$	−51.6423			−0.320760
$162$	−635.885	−	403.275i	−3.92522	−	2.48935i
$163$	−96.8205			−0.593991			−0.296995	−	0.954879i	$-0.595985\pi$
$163$	−96.8205			−0.593991			−0.296995	+	0.954879i	$0.595985\pi$
$164$	5.43161	+	11.5247i	0.0331196	+	0.0702723i
$165$	−156.568	−	57.3553i	−0.948898	−	0.347608i
$166$	120.467	+	76.3993i	0.725702	+	0.460237i
$167$	13.2832			0.0795399			0.0397700	−	0.999209i	$-0.487337\pi$
$167$	13.2832			0.0795399			0.0397700	+	0.999209i	$0.487337\pi$
$168$	−56.7962	+	452.894i	−0.338072	+	2.69580i
$169$	166.852			0.987290
$170$	185.512	+	241.780i	1.09125	+	1.42224i
$171$		−	114.889i		−	0.671864i
$172$	97.4401	+	206.746i	0.566512	+	1.20201i
$173$			113.836i			0.658014i	0.944327	+	0.329007i	$0.106714\pi$
$173$			113.836i			0.658014i	−0.944327	+	0.329007i	$0.893286\pi$
$174$	−251.398	−	159.435i	−1.44482	−	0.916295i
$175$	183.116	+	154.956i	1.04638	+	0.885461i
$176$	69.2106	+	57.1150i	0.393242	+	0.324517i
$177$			300.840i			1.69966i
$178$	12.7497	+	8.08577i	0.0716273	+	0.0454257i
$179$			156.693i			0.875380i	0.899126	+	0.437690i	$0.144203\pi$
$179$			156.693i			0.875380i	−0.899126	+	0.437690i	$0.855797\pi$
$180$	525.046	−	47.0020i	2.91692	−	0.261122i
$181$	−86.4748			−0.477761			−0.238881	−	0.971049i	$-0.576780\pi$
$181$	−86.4748			−0.477761			−0.238881	+	0.971049i	$0.576780\pi$
$182$	−15.0630	+	23.7513i	−0.0827636	+	0.130502i
$183$	−187.399			−1.02404
$184$	5.35765	−	42.7220i	0.0291177	−	0.232185i
$185$	168.449	+	61.7076i	0.910535	+	0.333555i
$186$	165.944	−	261.661i	0.892172	−	1.40678i
$187$	−170.915			−0.913986
$188$	−52.1858	−	110.726i	−0.277584	−	0.588970i
$189$	−990.322			−5.23980
$190$	26.5342	+	34.5823i	0.139654	+	0.182012i
$191$			174.191i			0.911993i	0.889982	+	0.455996i	$0.150717\pi$
$191$			174.191i			0.911993i	−0.889982	+	0.455996i	$0.849283\pi$
$192$	−368.772	−	93.9713i	−1.92069	−	0.489434i
$193$			361.081i			1.87088i	0.353480	+	0.935442i	$0.384998\pi$
$193$			361.081i			1.87088i	−0.353480	+	0.935442i	$0.615002\pi$
$194$	127.102	−	200.415i	0.655165	−	1.03307i
$195$	40.9141	+	14.9880i	0.209816	+	0.0768615i
$196$	73.4449	+	155.834i	0.374719	+	0.795069i
$197$			97.7118i			0.495999i	0.968760	+	0.248000i	$0.0797732\pi$
$197$			97.7118i			0.495999i	−0.968760	+	0.248000i	$0.920227\pi$
$198$	−158.338	+	249.668i	−0.799688	+	1.26095i
$199$		−	305.860i		−	1.53698i	−0.639860	−	0.768492i	$-0.721008\pi$
$199$		−	305.860i		−	1.53698i	0.639860	−	0.768492i	$-0.278992\pi$
$200$	−147.187	+	135.410i	−0.735936	+	0.677051i
$201$	−79.7288			−0.396660
$202$	−123.798	−	78.5121i	−0.612862	−	0.388674i
$203$	−240.189			−1.18320
$204$	655.668	−	309.019i	3.21406	−	1.51480i
$205$	5.47800	−	14.9538i	0.0267220	−	0.0729454i
$206$	−39.6261	−	25.1307i	−0.192360	−	0.121994i
$207$	141.857			0.685300
$208$	−18.0860	−	14.9252i	−0.0869519	−	0.0717558i
$209$	−24.4464			−0.116968
$210$	452.660	−	347.315i	2.15552	−	1.65388i
$211$			138.674i			0.657221i	0.944466	+	0.328611i	$0.106580\pi$
$211$			138.674i			0.657221i	−0.944466	+	0.328611i	$0.893420\pi$
$212$	−223.191	+	105.191i	−1.05279	+	0.496182i
$213$		−	142.113i		−	0.667199i
$214$	161.231	+	102.252i	0.753416	+	0.477813i
$215$	98.2723	−	268.263i	0.457081	−	1.24774i
$216$	102.741	−	819.261i	0.475654	−	3.79288i
$217$		−	249.994i		−	1.15205i
$218$	134.052	+	85.0153i	0.614919	+	0.389979i
$219$		−	378.811i		−	1.72973i
$220$	−10.0012	−	111.721i	−0.0454602	−	0.507823i
$221$	44.6633			0.202096
$222$	228.523	−	360.335i	1.02938	−	1.62313i
$223$	106.512			0.477631			0.238815	−	0.971065i	$-0.423241\pi$
$223$	106.512			0.477631			0.238815	+	0.971065i	$0.423241\pi$
$224$	−291.876	+	95.3246i	−1.30302	+	0.425556i
$225$	−503.004	−	425.650i	−2.23558	−	1.89178i
$226$	−68.3324	+	107.747i	−0.302356	+	0.476755i
$227$	−214.157			−0.943421			−0.471710	−	0.881754i	$-0.656363\pi$
$227$	−214.157			−0.943421			−0.471710	+	0.881754i	$0.656363\pi$
$228$	93.7817	−	44.1996i	0.411323	−	0.193858i
$229$	362.385			1.58247			0.791234	−	0.611513i	$-0.209439\pi$
$229$	362.385			1.58247			0.791234	+	0.611513i	$0.209439\pi$
$230$	−42.7000	+	32.7627i	−0.185652	+	0.142446i
$231$			319.987i			1.38523i
$232$	24.9185	−	198.701i	0.107407	−	0.856469i
$233$			313.374i			1.34495i	0.740119	+	0.672476i	$0.234769\pi$
$233$			313.374i			1.34495i	−0.740119	+	0.672476i	$0.765231\pi$
$234$	41.3767	−	65.2429i	0.176823	−	0.278816i
$235$	−52.6315	+	143.673i	−0.223964	+	0.611375i
$236$	−183.062	+	86.2779i	−0.775687	+	0.365584i
$237$			339.699i			1.43333i
$238$	313.217	−	493.882i	1.31604	−	2.07513i
$239$		−	234.305i		−	0.980357i	−0.871622	−	0.490179i	$-0.836932\pi$
$239$		−	234.305i		−	0.980357i	0.871622	−	0.490179i	$-0.163068\pi$
$240$	240.361	+	410.504i	1.00150	+	1.71043i
$241$	−33.4260			−0.138697			−0.0693485	−	0.997592i	$-0.522092\pi$
$241$	−33.4260			−0.138697			−0.0693485	+	0.997592i	$0.522092\pi$
$242$	−151.241	−	95.9165i	−0.624964	−	0.396349i
$243$	1309.80			5.39012
$244$	−53.7441	−	114.033i	−0.220263	−	0.467348i
$245$	74.0722	−	202.202i	0.302336	−	0.825314i
$246$	−31.9882	−	20.2868i	−0.130033	−	0.0824665i
$247$	6.38829			0.0258635
$248$	206.812	+	25.9358i	0.833921	+	0.104580i
$249$	−424.113			−1.70326
$250$	249.714	+	11.9521i	0.998857	+	0.0478085i
$251$		−	243.661i		−	0.970762i	−0.874303	−	0.485381i	$-0.838681\pi$
$251$		−	243.661i		−	0.970762i	0.874303	−	0.485381i	$-0.161319\pi$
$252$	−431.279	−	915.077i	−1.71143	−	3.63126i
$253$		−	30.1848i		−	0.119308i
$254$	40.6617	+	25.7875i	0.160085	+	0.101525i
$255$	−850.762	−	311.658i	−3.33632	−	1.22219i
$256$	−48.5782	−	251.349i	−0.189759	−	0.981831i
$257$			25.5522i			0.0994249i	0.998764	+	0.0497124i	$0.0158305\pi$
$257$			25.5522i			0.0994249i	−0.998764	+	0.0497124i	$0.984170\pi$
$258$	−573.851	−	363.933i	−2.22423	−	1.41059i
$259$		−	344.269i		−	1.32922i
$260$	2.61351	+	29.1947i	0.0100520	+	0.112287i
$261$	659.779			2.52789
$262$	130.829	−	206.292i	0.499349	−	0.787375i
$263$	70.2136			0.266972			0.133486	−	0.991051i	$-0.457383\pi$
$263$	70.2136			0.266972			0.133486	+	0.991051i	$0.457383\pi$
$264$	−264.715	−	33.1972i	−1.00271	−	0.125747i
$265$	289.601	+	106.089i	1.09283	+	0.400336i
$266$	44.8002	−	70.6410i	0.168422	−	0.265568i
$267$	−44.8863			−0.168113
$268$	−22.8654	−	48.5152i	−0.0853185	−	0.181027i
$269$	266.100			0.989219			0.494609	−	0.869115i	$-0.335311\pi$
$269$	266.100			0.989219			0.494609	+	0.869115i	$0.335311\pi$
$270$	−818.839	+	628.275i	−3.03274	+	2.32694i
$271$			38.6132i			0.142484i	0.997459	+	0.0712421i	$0.0226963\pi$
$271$			38.6132i			0.142484i	−0.997459	+	0.0712421i	$0.977304\pi$
$272$	376.077	+	310.352i	1.38264	+	1.14100i
$273$		−	83.6186i		−	0.306295i
$274$	89.0002	−	140.336i	0.324818	−	0.512174i
$275$	−90.5712	+	107.031i	−0.329350	+	0.389203i
$276$	54.5748	+	115.796i	0.197735	+	0.419549i
$277$			358.921i			1.29574i	0.761750	+	0.647872i	$0.224341\pi$
$277$			358.921i			1.29574i	−0.761750	+	0.647872i	$0.775659\pi$
$278$	87.1229	−	137.376i	0.313392	−	0.494157i
$279$			686.713i			2.46134i
$280$	341.160	+	175.839i	1.21843	+	0.627995i
$281$	268.327			0.954901			0.477450	−	0.878659i	$-0.341561\pi$
$281$	268.327			0.954901			0.477450	+	0.878659i	$0.341561\pi$
$282$	307.336	+	194.911i	1.08984	+	0.691173i
$283$	−421.545			−1.48956			−0.744779	−	0.667311i	$-0.767445\pi$
$283$	−421.545			−1.48956			−0.744779	+	0.667311i	$0.767445\pi$
$284$	86.4763	−	40.7566i	0.304494	−	0.143509i
$285$	−121.686	−	44.5772i	−0.426970	−	0.156411i
$286$	−13.8826	−	8.80427i	−0.0485405	−	0.0307842i
$287$	−30.5620			−0.106488
$288$	801.757	−	261.848i	2.78388	−	0.909196i
$289$	−639.722			−2.21357
$290$	−198.598	+	152.380i	−0.684822	+	0.525447i
$291$			705.577i			2.42466i
$292$	230.507	−	108.639i	0.789409	−	0.372051i
$293$		−	291.588i		−	0.995181i	−0.867412	−	0.497591i	$-0.834218\pi$
$293$		−	291.588i		−	0.995181i	0.867412	−	0.497591i	$-0.165782\pi$
$294$	−432.537	−	274.313i	−1.47121	−	0.933037i
$295$	237.532	+	87.0148i	0.805194	+	0.294965i
$296$	284.803	+	35.7163i	0.962171	+	0.120663i
$297$		−	578.841i		−	1.94896i
$298$	−156.449	−	99.2189i	−0.524995	−	0.332949i
$299$			7.88784i			0.0263808i
$300$	153.936	−	574.349i	0.513121	−	1.91450i
$301$	−548.265			−1.82148
$302$	−188.666	+	297.490i	−0.624723	+	0.985065i
$303$	435.842			1.43842
$304$	53.7912	+	44.3904i	0.176945	+	0.146021i
$305$	−54.2031	+	147.963i	−0.177715	+	0.485126i
$306$	−860.381	+	1356.65i	−2.81170	+	4.43350i
$307$	320.420			1.04371			0.521856	−	0.853033i	$-0.325240\pi$
$307$	320.420			1.04371			0.521856	+	0.853033i	$0.325240\pi$
$308$	−194.713	+	91.7690i	−0.632186	+	0.297951i
$309$	139.507			0.451479
$310$	−158.600	−	206.706i	−0.511613	−	0.666793i
$311$		−	539.671i		−	1.73528i	−0.497195	−	0.867639i	$-0.665637\pi$
$311$		−	539.671i		−	1.73528i	0.497195	−	0.867639i	$-0.334363\pi$
$312$	69.1749	+	8.67504i	0.221715	+	0.0278046i
$313$			340.685i			1.08845i	0.838940	+	0.544225i	$0.183176\pi$
$313$			340.685i			1.08845i	−0.838940	+	0.544225i	$0.816824\pi$
$314$	−149.640	+	235.952i	−0.476559	+	0.751439i
$315$	−434.963	+	1187.36i	−1.38083	+	3.76939i
$316$	−206.708	+	97.4221i	−0.654138	+	0.308298i
$317$		−	459.485i		−	1.44948i	−0.689022	−	0.724740i	$-0.741960\pi$
$317$		−	459.485i		−	1.44948i	0.689022	−	0.724740i	$-0.258040\pi$
$318$	392.881	−	619.496i	1.23548	−	1.94810i
$319$		−	140.390i		−	0.440094i
$320$	−180.859	+	263.988i	−0.565186	+	0.824964i
$321$	−567.628			−1.76831
$322$	87.2229	+	55.3163i	0.270879	+	0.171790i
$323$	−132.837			−0.411261
$324$	642.032	+	1362.25i	1.98158	+	4.20447i
$325$	23.6679	−	27.9691i	0.0728243	−	0.0860589i
$326$	163.528	+	103.709i	0.501619	+	0.318124i
$327$	−471.943			−1.44325
$328$	3.17066	−	25.2829i	0.00966666	−	0.0770821i
$329$	293.633			0.892501
$330$	203.005	+	264.579i	0.615166	+	0.801754i
$331$			389.319i			1.17619i	0.808792	+	0.588095i	$0.200122\pi$
$331$			389.319i			1.17619i	−0.808792	+	0.588095i	$0.799878\pi$
$332$	−121.631	−	258.074i	−0.366359	−	0.777330i
$333$			945.678i			2.83987i
$334$	−22.4350	−	14.2282i	−0.0671707	−	0.0425993i
$335$	−23.0607	+	62.9508i	−0.0688378	+	0.187913i
$336$	581.041	−	704.092i	1.72929	−	2.09551i
$337$		−	81.0640i		−	0.240546i	−0.992741	−	0.120273i	$-0.961623\pi$
$337$		−	81.0640i		−	0.240546i	0.992741	−	0.120273i	$-0.0383770\pi$
$338$	−281.810	−	178.722i	−0.833757	−	0.528764i
$339$		−	379.331i		−	1.11897i
$340$	−54.3449	−	607.071i	−0.159838	−	1.78550i
$341$	146.121			0.428508
$342$	−123.062	+	194.045i	−0.359831	+	0.567382i
$343$	56.9146			0.165932
$344$	56.8800	−	453.562i	0.165349	−	1.31849i
$345$	55.0410	−	150.250i	0.159539	−	0.435509i
$346$	121.935	−	192.268i	0.352414	−	0.555687i
$347$	−387.114			−1.11560			−0.557801	−	0.829975i	$-0.688355\pi$
$347$	−387.114			−1.11560			−0.557801	+	0.829975i	$0.688355\pi$
$348$	253.828	+	538.566i	0.729391	+	1.54760i
$349$	−529.262			−1.51651			−0.758255	−	0.651959i	$-0.773948\pi$
$349$	−529.262			−1.51651			−0.758255	+	0.651959i	$0.773948\pi$
$350$	−143.300	−	457.861i	−0.409428	−	1.30817i
$351$			151.262i			0.430945i
$352$	−55.7170	−	170.601i	−0.158287	−	0.484661i
$353$		−	95.5466i		−	0.270670i	−0.990800	−	0.135335i	$-0.956789\pi$
$353$		−	95.5466i		−	0.270670i	0.990800	−	0.135335i	$-0.0432111\pi$
$354$	322.243	−	508.113i	0.910291	−	1.43535i
$355$	−112.207	−	41.1047i	−0.316077	−	0.115788i
$356$	−12.8729	−	27.3134i	−0.0361599	−	0.0767231i
$357$			1738.75i			4.87045i
$358$	167.841	−	264.651i	0.468828	−	0.739249i
$359$			180.861i			0.503790i	0.967755	+	0.251895i	$0.0810538\pi$
$359$			180.861i			0.503790i	−0.967755	+	0.251895i	$0.918946\pi$
$360$	−937.138	−	483.014i	−2.60316	−	1.34170i
$361$	−19.0000			−0.0526316
$362$	146.054	+	92.6268i	0.403465	+	0.255875i
$363$	532.458			1.46683
$364$	50.8821	−	23.9809i	0.139786	−	0.0658817i
$365$	−299.095	−	109.567i	−0.819438	−	0.300183i
$366$	316.513	+	200.731i	0.864791	+	0.548446i
$367$	−300.710			−0.819373			−0.409686	−	0.912226i	$-0.634362\pi$
$367$	−300.710			−0.819373			−0.409686	+	0.912226i	$0.634362\pi$
$368$	−54.8104	+	66.4179i	−0.148941	+	0.180483i
$369$	83.9512			0.227510
$370$	−218.409	−	284.656i	−0.590296	−	0.769340i
$371$		−	591.875i		−	1.59535i
$372$	−560.552	+	264.190i	−1.50686	+	0.710189i
$373$		−	612.828i		−	1.64297i	−0.570229	−	0.821486i	$-0.693146\pi$
$373$		−	612.828i		−	1.64297i	0.570229	−	0.821486i	$-0.306854\pi$
$374$	288.673	+	183.075i	0.771852	+	0.489505i
$375$	−646.002	+	367.613i	−1.72267	+	0.980300i
$376$	−30.4631	+	242.913i	−0.0810188	+	0.646045i
$377$			36.6865i			0.0973116i
$378$	1672.63	+	1060.78i	4.42496	+	2.80629i
$379$		−	45.3764i		−	0.119727i	−0.998207	−	0.0598633i	$-0.980934\pi$
$379$		−	45.3764i		−	0.119727i	0.998207	−	0.0598633i	$-0.0190665\pi$
$380$	−7.77307	−	86.8308i	−0.0204555	−	0.228502i
$381$	−143.153			−0.375730
$382$	186.583	−	294.205i	0.488437	−	0.770169i
$383$	−454.950			−1.18786			−0.593930	−	0.804517i	$-0.702424\pi$
$383$	−454.950			−1.18786			−0.593930	+	0.804517i	$0.702424\pi$
$384$	522.192	+	553.723i	1.35987	+	1.44199i
$385$	252.650	+	92.5528i	0.656234	+	0.240397i
$386$	386.769	−	609.858i	1.00199	−	1.57994i
$387$	1506.04			3.89157
$388$	−429.345	+	202.352i	−1.10656	+	0.521526i
$389$	375.923			0.966382			0.483191	−	0.875515i	$-0.339478\pi$
$389$	375.923			0.966382			0.483191	+	0.875515i	$0.339478\pi$
$390$	−53.0489	−	69.1393i	−0.136023	−	0.177280i
$391$		−	164.019i		−	0.419485i
$392$	42.8730	−	341.870i	0.109370	−	0.872117i
$393$			726.269i			1.84801i
$394$	104.663	−	165.033i	0.265643	−	0.418866i
$395$	268.214	+	98.2542i	0.679022	+	0.248745i
$396$	534.860	−	252.082i	1.35066	−	0.636570i
$397$		−	234.640i		−	0.591033i	−0.955338	−	0.295516i	$-0.904508\pi$
$397$		−	234.640i		−	0.591033i	0.955338	−	0.295516i	$-0.0954917\pi$
$398$	−327.619	+	516.591i	−0.823164	+	1.29797i
$399$			248.698i			0.623302i
$400$	393.640	−	71.0465i	0.984100	−	0.177616i
$401$	370.607			0.924207			0.462103	−	0.886826i	$-0.347095\pi$
$401$	370.607			0.924207			0.462103	+	0.886826i	$0.347095\pi$
$402$	134.660	+	85.4009i	0.334976	+	0.212440i
$403$	−38.1841			−0.0947497
$404$	124.995	+	265.211i	0.309393	+	0.656462i
$405$	647.516	−	1767.58i	1.59880	−	4.36440i
$406$	405.675	+	257.277i	0.999199	+	0.633687i
$407$	201.224			0.494409
$408$	−1438.41	−	180.387i	−3.52552	−	0.442126i
$409$	47.8575			0.117011			0.0585055	−	0.998287i	$-0.481366\pi$
$409$	47.8575			0.117011			0.0585055	+	0.998287i	$0.481366\pi$
$410$	−25.2699	+	19.3890i	−0.0616339	+	0.0472902i
$411$			494.064i			1.20210i
$412$	40.0092	+	84.8904i	0.0971096	+	0.206045i
$413$		−	485.459i		−	1.17544i
$414$	−239.594	−	151.949i	−0.578729	−	0.367027i
$415$	−122.670	+	334.864i	−0.295590	+	0.806900i
$416$	14.5599	+	44.5810i	0.0349997	+	0.107166i
$417$			483.642i			1.15981i
$418$	41.2895	+	26.1856i	0.0987787	+	0.0626449i
$419$		−	27.2392i		−	0.0650101i	−0.999472	−	0.0325050i	$-0.989652\pi$
$419$		−	27.2392i		−	0.0650101i	0.999472	−	0.0325050i	$-0.0103485\pi$
$420$	−1136.56	+	101.744i	−2.70609	+	0.242249i
$421$	−478.944			−1.13763			−0.568817	−	0.822464i	$-0.692599\pi$
$421$	−478.944			−1.13763			−0.568817	+	0.822464i	$0.692599\pi$
$422$	148.539	−	234.217i	0.351989	−	0.555017i
$423$	−806.585			−1.90682
$424$	489.639	+	61.4043i	1.15481	+	0.144821i
$425$	−492.147	+	581.586i	−1.15799	+	1.36844i
$426$	−152.224	+	240.027i	−0.357333	+	0.563443i
$427$	302.401			0.708200
$428$	−162.790	−	345.403i	−0.380350	−	0.807016i
$429$	48.8749			0.113927
$430$	−453.328	+	347.827i	−1.05425	+	0.808901i
$431$		−	637.923i		−	1.48010i	−0.672552	−	0.740050i	$-0.734802\pi$
$431$		−	637.923i		−	1.48010i	0.672552	−	0.740050i	$-0.265198\pi$
$432$	−1051.07	+	1273.67i	−2.43304	+	2.94830i
$433$		−	616.138i		−	1.42295i	−0.702711	−	0.711476i	$-0.748027\pi$
$433$		−	616.138i		−	1.42295i	0.702711	−	0.711476i	$-0.251973\pi$
$434$	−267.780	+	422.236i	−0.617004	+	0.972893i
$435$	255.996	−	698.817i	0.588497	−	1.60647i
$436$	−135.348	−	287.178i	−0.310432	−	0.658666i
$437$		−	23.4600i		−	0.0536841i
$438$	−405.760	+	639.804i	−0.926394	+	1.46074i
$439$			329.983i			0.751669i	0.926687	+	0.375834i	$0.122644\pi$
$439$			329.983i			0.751669i	−0.926687	+	0.375834i	$0.877356\pi$
$440$	−102.777	+	199.407i	−0.233585	+	0.453199i
$441$	1135.17			2.57408
$442$	−75.4354	−	47.8408i	−0.170668	−	0.108237i
$443$	−253.518			−0.572274			−0.286137	−	0.958189i	$-0.592371\pi$
$443$	−253.518			−0.572274			−0.286137	+	0.958189i	$0.592371\pi$
$444$	−771.940	+	363.818i	−1.73860	+	0.819411i
$445$	−12.9829	+	35.4405i	−0.0291750	+	0.0796416i
$446$	−179.896	−	114.089i	−0.403354	−	0.255805i
$447$	550.791			1.23219
$448$	595.078	+	151.639i	1.32830	+	0.338480i
$449$	377.768			0.841354			0.420677	−	0.907210i	$-0.361793\pi$
$449$	377.768			0.841354			0.420677	+	0.907210i	$0.361793\pi$
$450$	393.633	+	1257.70i	0.874739	+	2.79490i
$451$		−	17.8634i		−	0.0396084i
$452$	230.824	−	108.788i	0.510673	−	0.240682i
$453$		−	1047.34i		−	2.31200i
$454$	361.706	+	229.392i	0.796709	+	0.505269i
$455$	−66.0221	−	24.1857i	−0.145103	−	0.0531555i
$456$	−205.740	−	25.8012i	−0.451183	−	0.0565816i
$457$		−	439.338i		−	0.961353i	−0.876898	−	0.480677i	$-0.840391\pi$
$457$		−	439.338i		−	0.961353i	0.876898	−	0.480677i	$-0.159609\pi$
$458$	−612.061	−	388.166i	−1.33638	−	0.847525i
$459$		−	3145.31i		−	6.85253i
$460$	107.213	−	9.59768i	0.233072	−	0.0208645i
$461$	−384.916			−0.834958			−0.417479	−	0.908687i	$-0.637086\pi$
$461$	−384.916			−0.834958			−0.417479	+	0.908687i	$0.637086\pi$
$462$	342.752	−	540.452i	0.741888	−	1.16981i
$463$	−684.264			−1.47789			−0.738946	−	0.673764i	$-0.764676\pi$
$463$	−684.264			−1.47789			−0.738946	+	0.673764i	$0.764676\pi$
$464$	−254.924	+	308.910i	−0.549404	+	0.665755i
$465$	727.345	+	266.447i	1.56418	+	0.573004i
$466$	335.668	−	529.282i	0.720318	−	1.13580i
$467$	871.751			1.86670			0.933352	−	0.358963i	$-0.116869\pi$
$467$	871.751			1.86670			0.933352	+	0.358963i	$0.116869\pi$
$468$	−139.769	+	65.8735i	−0.298651	+	0.140755i
$469$	128.656			0.274320
$470$	242.788	−	186.285i	0.516570	−	0.396351i
$471$		−	830.689i		−	1.76367i
$472$	401.604	+	50.3641i	0.850856	+	0.106704i
$473$		−	320.460i		−	0.677505i
$474$	363.866	−	573.745i	0.767650	−	1.21043i
$475$	−70.3929	+	83.1856i	−0.148196	+	0.175128i
$476$	−1058.04	+	498.656i	−2.22276	+	1.04760i
$477$			1625.83i			3.40845i
$478$	−250.974	+	395.737i	−0.525051	+	0.827902i
$479$		−	320.952i		−	0.670047i	−0.942210	−	0.335023i	$-0.891256\pi$
$479$		−	320.952i		−	0.670047i	0.942210	−	0.335023i	$-0.108744\pi$
$480$	33.7427	−	950.793i	0.0702974	−	1.98082i
$481$	−52.5836			−0.109321
$482$	56.4558	+	35.8040i	0.117128	+	0.0742822i
$483$	−307.076			−0.635767
$484$	152.703	+	324.002i	0.315503	+	0.669426i
$485$	557.097	+	204.080i	1.14865	+	0.420784i
$486$	−2212.22	−	1402.98i	−4.55190	−	2.88679i
$487$	515.213			1.05793			0.528966	−	0.848643i	$-0.322580\pi$
$487$	515.213			1.05793			0.528966	+	0.848643i	$0.322580\pi$
$488$	−31.3727	+	250.167i	−0.0642884	+	0.512637i
$489$	−575.714			−1.17733
$490$	−341.694	+	262.173i	−0.697334	+	0.535047i
$491$		−	494.567i		−	1.00726i	−0.863918	−	0.503632i	$-0.831997\pi$
$491$		−	494.567i		−	1.00726i	0.863918	−	0.503632i	$-0.168003\pi$
$492$	32.2974	+	68.5279i	0.0656452	+	0.139284i
$493$		−	762.853i		−	1.54737i
$494$	−10.7897	−	6.84277i	−0.0218415	−	0.0138518i
$495$	−694.008	−	254.235i	−1.40204	−	0.513606i
$496$	−321.521	−	265.330i	−0.648228	−	0.534940i
$497$			229.325i			0.461418i
$498$	716.318	+	454.285i	1.43839	+	0.912219i
$499$		−	443.284i		−	0.888345i	−0.895941	−	0.444172i	$-0.853498\pi$
$499$		−	443.284i		−	0.888345i	0.895941	−	0.444172i	$-0.146502\pi$
$500$	−408.960	−	287.666i	−0.817919	−	0.575333i
$501$	78.9844			0.157653
$502$	−260.996	+	411.539i	−0.519912	+	0.819799i
$503$	−636.079			−1.26457			−0.632285	−	0.774736i	$-0.717883\pi$
$503$	−636.079			−1.26457			−0.632285	+	0.774736i	$0.717883\pi$
$504$	−251.756	+	2007.51i	−0.499516	+	3.98315i
$505$	126.062	−	344.124i	0.249628	−	0.681434i
$506$	−32.3323	+	50.9816i	−0.0638977	+	0.100754i
$507$	992.136			1.95688
$508$	−41.0548	−	87.1090i	−0.0808165	−	0.171474i
$509$	364.309			0.715735			0.357868	−	0.933772i	$-0.383504\pi$
$509$	364.309			0.715735			0.357868	+	0.933772i	$0.383504\pi$
$510$	1103.09	+	1437.67i	2.16292	+	2.81896i
$511$			611.277i			1.19624i
$512$	−187.183	+	476.557i	−0.365591	+	0.930776i
$513$		−	449.881i		−	0.876961i
$514$	27.3700	−	43.1572i	0.0532491	−	0.0839633i
$515$	40.3509	−	110.150i	0.0783512	−	0.213883i
$516$	579.398	+	1229.35i	1.12286	+	2.38247i
$517$			171.628i			0.331969i
$518$	−368.761	+	581.464i	−0.711894	+	1.12252i
$519$			676.894i			1.30423i
$520$	26.8576	−	52.1088i	0.0516492	−	0.100209i
$521$	25.4568			0.0488615			0.0244308	−	0.999702i	$-0.492223\pi$
$521$	25.4568			0.0488615			0.0244308	+	0.999702i	$0.492223\pi$
$522$	−1114.35	−	706.717i	−2.13478	−	1.35386i
$523$	1006.89			1.92522			0.962610	−	0.270890i	$-0.0873179\pi$
$523$	1006.89			1.92522			0.962610	+	0.270890i	$0.0873179\pi$
$524$	−441.937	+	208.286i	−0.843391	+	0.397493i
$525$	1088.85	+	921.397i	2.07399	+	1.75504i
$526$	−118.589	−	75.2088i	−0.225455	−	0.142983i
$527$	793.995			1.50663
$528$	411.540	+	339.617i	0.779432	+	0.643215i
$529$	−500.033			−0.945242
$530$	−375.494	−	489.387i	−0.708480	−	0.923371i
$531$			1333.51i			2.51132i
$532$	−151.333	+	71.3239i	−0.284461	+	0.134067i
$533$			4.66803i			0.00875804i
$534$	75.8120	+	48.0796i	0.141970	+	0.0900367i
$535$	−164.180	+	448.177i	−0.306878	+	0.837715i
$536$	−13.3475	+	106.433i	−0.0249020	+	0.198569i
$537$			931.728i			1.73506i
$538$	−449.437	−	285.031i	−0.835385	−	0.529797i
$539$		−	241.545i		−	0.448135i
$540$	2055.97	−	184.050i	3.80736	−	0.340834i
$541$	473.253			0.874774			0.437387	−	0.899273i	$-0.355904\pi$
$541$	473.253			0.874774			0.437387	+	0.899273i	$0.355904\pi$
$542$	41.3603	−	65.2170i	0.0763105	−	0.120326i
$543$	−514.196			−0.946955
$544$	−302.756	−	927.011i	−0.556536	−	1.70407i
$545$	−136.504	+	372.628i	−0.250466	+	0.683722i
$546$	−89.5674	+	141.230i	−0.164043	+	0.258663i
$547$	−470.952			−0.860972			−0.430486	−	0.902597i	$-0.641658\pi$
$547$	−470.952			−0.860972			−0.430486	+	0.902597i	$0.641658\pi$
$548$	−300.639	+	141.692i	−0.548611	+	0.258563i
$549$	−830.671			−1.51306
$550$	267.618	−	83.7585i	0.486579	−	0.152288i
$551$		−	109.113i		−	0.198026i
$552$	31.8577	−	254.034i	0.0577132	−	0.460206i
$553$		−	548.164i		−	0.991254i
$554$	384.455	−	606.210i	0.693963	−	1.09424i
$555$	1001.63	+	366.926i	1.80474	+	0.661127i
$556$	−294.298	+	138.704i	−0.529312	+	0.249467i
$557$		−	51.0296i		−	0.0916152i	−0.998950	−	0.0458076i	$-0.985414\pi$
$557$		−	51.0296i		−	0.0916152i	0.998950	−	0.0458076i	$-0.0145861\pi$
$558$	735.568	−	1159.84i	1.31822	−	2.07858i
$559$			83.7419i			0.149807i
$560$	−387.865	−	662.419i	−0.692615	−	1.18289i
$561$	−1016.30			−1.81158
$562$	−453.199	−	287.417i	−0.806404	−	0.511418i
$563$	−107.822			−0.191514			−0.0957570	−	0.995405i	$-0.530527\pi$
$563$	−107.822			−0.191514			−0.0957570	+	0.995405i	$0.530527\pi$
$564$	−310.307	−	658.401i	−0.550190	−	1.16738i
$565$	−299.506	−	109.717i	−0.530099	−	0.194190i
$566$	711.981	+	451.535i	1.25792	+	0.797765i
$567$	−3612.51			−6.37128
$568$	−189.713	−	23.7914i	−0.334002	−	0.0418862i
$569$	567.877			0.998026			0.499013	−	0.866595i	$-0.333696\pi$
$569$	567.877			0.998026			0.499013	+	0.866595i	$0.333696\pi$
$570$	157.777	+	205.633i	0.276803	+	0.360760i
$571$		−	342.894i		−	0.600515i	−0.953858	−	0.300258i	$-0.902927\pi$
$571$		−	342.894i		−	0.600515i	0.953858	−	0.300258i	$-0.0970726\pi$
$572$	14.0168	+	29.7405i	0.0245049	+	0.0519938i
$573$			1035.77i			1.80763i
$574$	51.6186	+	32.7362i	0.0899278	+	0.0570318i
$575$	−102.712	−	86.9166i	−0.178630	−	0.151159i
$576$	−1634.63	−	416.539i	−2.83790	−	0.723159i
$577$			14.6235i			0.0253440i	0.999920	+	0.0126720i	$0.00403373\pi$
$577$			14.6235i			0.0253440i	−0.999920	+	0.0126720i	$0.995966\pi$
$578$	1080.48	+	685.233i	1.86934	+	1.18552i
$579$			2147.06i			3.70822i
$580$	498.649	−	44.6389i	0.859739	−	0.0769637i
$581$	684.380			1.17793
$582$	755.774	−	1191.71i	1.29858	−	2.04760i
$583$	345.949			0.593395
$584$	−505.690	−	63.4172i	−0.865908	−	0.108591i
$585$	181.357	+	66.4362i	0.310012	+	0.113566i
$586$	−312.332	+	492.486i	−0.532990	+	0.840421i
$587$	633.620			1.07942			0.539711	−	0.841851i	$-0.318534\pi$
$587$	633.620			1.07942			0.539711	+	0.841851i	$0.318534\pi$
$588$	436.718	+	926.617i	0.742718	+	1.57588i
$589$	113.567			0.192813
$590$	−307.982	−	401.397i	−0.522004	−	0.680334i
$591$			581.014i			0.983103i
$592$	−442.769	−	365.388i	−0.747920	−	0.617210i
$593$			284.861i			0.480373i	0.970727	+	0.240186i	$0.0772085\pi$
$593$			284.861i			0.480373i	−0.970727	+	0.240186i	$0.922791\pi$
$594$	−620.021	+	977.651i	−1.04381	+	1.64588i
$595$	1372.85	+	502.915i	2.30732	+	0.845235i
$596$	157.961	+	335.157i	0.265035	+	0.562345i
$597$		−	1818.70i		−	3.04640i
$598$	8.44901	−	13.3224i	0.0141288	−	0.0222783i
$599$			222.749i			0.371868i	0.982562	+	0.185934i	$0.0595310\pi$
$599$			222.749i			0.371868i	−0.982562	+	0.185934i	$0.940469\pi$
$600$	−875.205	+	805.176i	−1.45867	+	1.34196i
$601$	−908.522			−1.51168			−0.755842	−	0.654755i	$-0.772772\pi$
$601$	−908.522			−1.51168			−0.755842	+	0.654755i	$0.772772\pi$
$602$	926.009	+	587.270i	1.53822	+	0.975532i
$603$	−353.408			−0.586083
$604$	637.308	−	300.365i	1.05515	−	0.497294i
$605$	154.008	−	420.409i	0.254558	−	0.694891i
$606$	−736.128	−	466.848i	−1.21473	−	0.770377i
$607$	−853.291			−1.40575			−0.702876	−	0.711313i	$-0.748101\pi$
$607$	−853.291			−1.40575			−0.702876	+	0.711313i	$0.748101\pi$
$608$	−43.3038	−	132.593i	−0.0712234	−	0.218080i
$609$	−1428.21			−2.34518
$610$	250.038	−	191.848i	0.409898	−	0.314505i
$611$		−	44.8495i		−	0.0734034i
$612$	2906.33	−	1369.76i	4.74891	−	2.23818i
$613$		−	34.7413i		−	0.0566742i	−0.999598	−	0.0283371i	$-0.990979\pi$
$613$		−	34.7413i		−	0.0566742i	0.999598	−	0.0283371i	$-0.00902118\pi$
$614$	−541.183	−	343.215i	−0.881405	−	0.558982i
$615$	32.5733	−	88.9184i	0.0529647	−	0.144583i
$616$	427.164	+	53.5695i	0.693449	+	0.0869635i
$617$		−	622.522i		−	1.00895i	−0.863427	−	0.504475i	$-0.831686\pi$
$617$		−	622.522i		−	1.00895i	0.863427	−	0.504475i	$-0.168314\pi$
$618$	−235.625	−	149.432i	−0.381270	−	0.241799i
$619$			173.004i			0.279490i	0.990188	+	0.139745i	$0.0446283\pi$
$619$			173.004i			0.279490i	−0.990188	+	0.139745i	$0.955372\pi$
$620$	46.4612	+	519.005i	0.0749375	+	0.837105i
$621$	555.484			0.894499
$622$	−578.065	+	911.494i	−0.929365	+	1.46542i
$623$	72.4319			0.116263
$624$	−107.543	−	88.7482i	−0.172344	−	0.142225i
$625$	103.404	+	616.387i	0.165447	+	0.986219i
$626$	364.922	−	575.409i	0.582942	−	0.919184i
$627$	−145.363			−0.231839
$628$	505.476	−	238.233i	0.804899	−	0.379352i
$629$	1093.42			1.73834
$630$	2006.47	−	1539.52i	3.18488	−	2.44368i
$631$		−	715.897i		−	1.13454i	−0.823530	−	0.567272i	$-0.807999\pi$
$631$		−	715.897i		−	1.13454i	0.823530	−	0.567272i	$-0.192001\pi$
$632$	453.478	+	56.8694i	0.717529	+	0.0899833i
$633$			824.581i			1.30266i
$634$	−492.174	+	776.061i	−0.776300	+	1.22407i
$635$	−41.4054	+	113.028i	−0.0652054	+	0.177997i
$636$	−1327.14	+	625.484i	−2.08669	+	0.983466i
$637$			63.1200i			0.0990895i
$638$	−150.378	+	237.116i	−0.235702	+	0.371655i
$639$		−	629.935i		−	0.985814i
$640$	588.237	−	252.145i	0.919121	−	0.393976i
$641$	194.821			0.303933			0.151967	−	0.988386i	$-0.451439\pi$
$641$	194.821			0.303933			0.151967	+	0.988386i	$0.451439\pi$
$642$	958.712	+	608.010i	1.49332	+	0.947056i
$643$	−700.497			−1.08942			−0.544710	−	0.838624i	$-0.683360\pi$
$643$	−700.497			−1.08942			−0.544710	+	0.838624i	$0.683360\pi$
$644$	−88.0661	−	186.856i	−0.136749	−	0.290150i
$645$	584.347	−	1595.15i	0.905964	−	2.47309i
$646$	224.359	+	142.288i	0.347305	+	0.220259i
$647$	−377.524			−0.583499			−0.291750	−	0.956495i	$-0.594237\pi$
$647$	−377.524			−0.583499			−0.291750	+	0.956495i	$0.594237\pi$
$648$	374.782	−	2988.52i	0.578367	−	4.61191i
$649$	283.749			0.437210
$650$	−69.9336	+	21.8876i	−0.107590	+	0.0336732i
$651$		−	1486.52i		−	2.28344i
$652$	−165.109	−	350.323i	−0.253234	−	0.537306i
$653$		−	212.287i		−	0.325095i	−0.986701	−	0.162548i	$-0.948029\pi$
$653$		−	212.287i		−	0.325095i	0.986701	−	0.162548i	$-0.0519711\pi$
$654$	797.102	+	505.518i	1.21881	+	0.772963i
$655$	573.435	+	210.065i	0.875473	+	0.320710i
$656$	−32.4368	+	39.3062i	−0.0494464	+	0.0599179i
$657$		−	1679.13i		−	2.55575i
$658$	−495.940	−	314.523i	−0.753709	−	0.477998i
$659$			301.196i			0.457051i	0.973538	+	0.228525i	$0.0733904\pi$
$659$			301.196i			0.457051i	−0.973538	+	0.228525i	$0.926610\pi$
$660$	−59.4694	−	664.315i	−0.0901051	−	1.00654i
$661$	162.779			0.246261			0.123130	−	0.992390i	$-0.460707\pi$
$661$	162.779			0.246261			0.123130	+	0.992390i	$0.460707\pi$
$662$	417.016	−	657.552i	0.629934	−	0.993281i
$663$	265.577			0.400568
$664$	−71.0013	+	566.166i	−0.106930	+	0.852659i
$665$	196.362	+	71.9330i	0.295282	+	0.108170i
$666$	1012.96	−	1597.23i	1.52095	−	2.39824i
$667$	134.725			0.201987
$668$	22.6519	+	48.0622i	0.0339100	+	0.0719494i
$669$	633.339			0.946695
$670$	106.378	−	81.6214i	0.158774	−	0.121823i
$671$			176.753i			0.263417i
$672$	−1735.55	+	566.819i	−2.58266	+	0.843480i
$673$			398.525i			0.592162i	0.955163	+	0.296081i	$0.0956799\pi$
$673$			398.525i			0.592162i	−0.955163	+	0.296081i	$0.904320\pi$
$674$	−86.8311	+	136.916i	−0.128830	+	0.203139i
$675$	−1969.66	−	1666.76i	−2.91802	−	2.46927i
$676$	284.534	+	603.717i	0.420908	+	0.893073i
$677$			1257.14i			1.85693i	0.371422	+	0.928464i	$0.378870\pi$
$677$			1257.14i			1.85693i	−0.371422	+	0.928464i	$0.621130\pi$
$678$	−406.318	+	640.683i	−0.599289	+	0.944960i
$679$		−	1138.57i		−	1.67684i
$680$	−558.472	+	1083.54i	−0.821283	+	1.59344i
$681$	−1273.42			−1.86992
$682$	−246.796	−	156.517i	−0.361871	−	0.229496i
$683$	−856.254			−1.25367			−0.626833	−	0.779154i	$-0.715649\pi$
$683$	−856.254			−1.25367			−0.626833	+	0.779154i	$0.715649\pi$
$684$	415.699	−	195.921i	0.607747	−	0.286434i
$685$	390.094	+	142.902i	0.569481	+	0.208617i
$686$	−96.1276	−	60.9636i	−0.140128	−	0.0888682i
$687$	2154.81			3.13656
$688$	−581.899	+	705.131i	−0.845783	+	1.02490i
$689$	−90.4029			−0.131209
$690$	−253.903	+	194.813i	−0.367975	+	0.282338i
$691$			228.113i			0.330120i	0.986284	+	0.165060i	$0.0527818\pi$
$691$			228.113i			0.330120i	−0.986284	+	0.165060i	$0.947218\pi$
$692$	−411.892	+	194.126i	−0.595219	+	0.280529i
$693$			1418.39i			2.04673i
$694$	653.828	+	414.654i	0.942115	+	0.597484i
$695$	381.866	+	139.888i	0.549447	+	0.201278i
$696$	148.170	−	1181.51i	0.212888	−	1.69758i
$697$		−	97.0664i		−	0.139263i
$698$	893.912	+	566.915i	1.28068	+	0.812199i
$699$			1863.38i			2.66578i
$700$	−248.403	+	926.812i	−0.354862	+	1.32402i
$701$	−427.683			−0.610104			−0.305052	−	0.952336i	$-0.598674\pi$
$701$	−427.683			−0.610104			−0.305052	+	0.952336i	$0.598674\pi$
$702$	162.023	−	255.478i	0.230802	−	0.363929i
$703$	156.394			0.222466
$704$	−88.6327	+	347.822i	−0.125899	+	0.494065i
$705$	−312.957	+	854.308i	−0.443911	+	1.21179i
$706$	−102.344	+	161.376i	−0.144963	+	0.228578i
$707$	−703.306			−0.994776
$708$	−1088.52	+	513.025i	−1.53746	+	0.724612i
$709$	−482.104			−0.679977			−0.339989	−	0.940430i	$-0.610423\pi$
$709$	−482.104			−0.679977			−0.339989	+	0.940430i	$0.610423\pi$
$710$	145.487	+	189.615i	0.204911	+	0.267064i
$711$			1505.76i			2.11780i
$712$	−7.51447	+	59.9205i	−0.0105540	+	0.0841581i
$713$			140.225i			0.196669i
$714$	1862.45	−	2936.72i	2.60848	−	4.11305i
$715$	14.1365	−	38.5897i	0.0197713	−	0.0539717i
$716$	−566.959	+	267.210i	−0.791842	+	0.373198i
$717$		−	1393.23i		−	1.94313i
$718$	193.728	−	305.470i	0.269816	−	0.425446i
$719$		−	621.374i		−	0.864219i	−0.901821	−	0.432110i	$-0.857769\pi$
$719$		−	621.374i		−	0.864219i	0.901821	−	0.432110i	$-0.142231\pi$
$720$	1065.43	+	1819.61i	1.47977	+	2.52723i
$721$	−225.119			−0.312232
$722$	32.0906	+	20.3517i	0.0444468	+	0.0281880i
$723$	−198.758			−0.274907
$724$	−147.466	−	312.890i	−0.203682	−	0.432168i
$725$	−477.715	−	404.250i	−0.658918	−	0.557586i
$726$	−899.311	−	570.339i	−1.23872	−	0.785590i
$727$	−500.188			−0.688017			−0.344009	−	0.938967i	$-0.611785\pi$
$727$	−500.188			−0.688017			−0.344009	+	0.938967i	$0.611785\pi$
$728$	−111.626	−	13.9987i	−0.153332	−	0.0192290i
$729$	4399.91			6.03554
$730$	387.803	+	505.429i	0.531238	+	0.692369i
$731$		−	1741.32i		−	2.38210i
$732$	−319.573	−	678.062i	−0.436575	−	0.926314i
$733$			1128.57i			1.53966i	0.638251	+	0.769828i	$0.279658\pi$
$733$			1128.57i			1.53966i	−0.638251	+	0.769828i	$0.720342\pi$
$734$	507.893	+	322.103i	0.691952	+	0.438833i
$735$	440.448	−	1202.33i	0.599249	−	1.63583i
$736$	163.717	−	53.4687i	0.222441	−	0.0726477i
$737$			75.1993i			0.102034i
$738$	−141.792	−	89.9237i	−0.192130	−	0.121848i
$739$			859.823i			1.16349i	0.813370	+	0.581747i	$0.197631\pi$
$739$			859.823i			1.16349i	−0.813370	+	0.581747i	$0.802369\pi$
$740$	63.9821	+	714.726i	0.0864623	+	0.965845i
$741$	37.9860			0.0512632
$742$	−633.982	+	999.665i	−0.854424	+	1.34726i
$743$	546.879			0.736042			0.368021	−	0.929817i	$-0.380035\pi$
$743$	546.879			0.736042			0.368021	+	0.929817i	$0.380035\pi$
$744$	1229.75	+	154.219i	1.65289	+	0.207284i
$745$	159.310	−	434.884i	0.213839	−	0.583736i
$746$	−656.427	+	1035.05i	−0.879928	+	1.38747i
$747$	−1879.93			−2.51664
$748$	−291.463	−	618.419i	−0.389657	−	0.826763i
$749$	915.966			1.22292
$750$	1484.85	+	71.0698i	1.97980	+	0.0947597i
$751$			470.979i			0.627135i	0.949566	+	0.313568i	$0.101524\pi$
$751$			470.979i			0.627135i	−0.949566	+	0.313568i	$0.898476\pi$
$752$	311.646	−	377.645i	0.414423	−	0.502188i
$753$		−	1448.86i		−	1.92411i
$754$	39.2964	−	61.9627i	0.0521173	−	0.0821786i
$755$	−826.938	−	302.931i	−1.09528	−	0.401233i
$756$	−1688.80	−	3583.26i	−2.23387	−	4.73976i
$757$			1011.74i			1.33651i	0.743932	+	0.668255i	$0.232959\pi$
$757$			1011.74i			1.33651i	−0.743932	+	0.668255i	$0.767041\pi$
$758$	−48.6046	+	76.6399i	−0.0641222	+	0.101108i
$759$		−	179.485i		−	0.236476i
$760$	−79.8796	+	154.981i	−0.105105	+	0.203923i
$761$	−1071.31			−1.40776			−0.703881	−	0.710318i	$-0.748551\pi$
$761$	−1071.31			−1.40776			−0.703881	+	0.710318i	$0.748551\pi$
$762$	241.783	+	153.337i	0.317300	+	0.201230i
$763$	761.562			0.998116
$764$	−630.270	+	297.049i	−0.824961	+	0.388807i
$765$	−3771.11	−	1381.46i	−4.92956	−	1.80584i
$766$	768.402	+	487.317i	1.00314	+	0.636184i
$767$	−74.1489			−0.0966739
$768$	−288.856	−	1494.57i	−0.376114	−	1.94605i
$769$	−1361.48			−1.77045			−0.885227	−	0.465160i	$-0.845997\pi$
$769$	−1361.48			−1.77045			−0.885227	+	0.465160i	$0.845997\pi$
$770$	−327.584	−	426.944i	−0.425433	−	0.554473i
$771$			151.938i			0.197067i
$772$	−1306.49	+	615.753i	−1.69234	+	0.797608i
$773$		−	85.6518i		−	0.110804i	−0.998464	−	0.0554022i	$-0.982356\pi$
$773$		−	85.6518i		−	0.110804i	0.998464	−	0.0554022i	$-0.0176441\pi$
$774$	−2543.67	−	1613.18i	−3.28639	−	2.08421i
$775$	420.753	−	497.217i	0.542907	−	0.641571i
$776$	941.904	+	118.122i	1.21379	+	0.152218i
$777$		−	2047.09i		−	2.63461i
$778$	−634.926	−	402.667i	−0.816100	−	0.517566i
$779$		−	13.8836i		−	0.0178224i
$780$	15.5404	+	173.598i	0.0199236	+	0.222561i
$781$	−134.040			−0.171626
$782$	−175.687	+	277.024i	−0.224664	+	0.354251i
$783$	2583.56			3.29957
$784$	−438.603	+	531.488i	−0.559442	+	0.677919i
$785$	−655.881	−	240.268i	−0.835517	−	0.306073i
$786$	777.938	−	1226.65i	0.989743	−	1.56063i
$787$	242.404			0.308010			0.154005	−	0.988070i	$-0.450783\pi$
$787$	242.404			0.308010			0.154005	+	0.988070i	$0.450783\pi$
$788$	−353.549	+	166.629i	−0.448666	+	0.211458i
$789$	417.504			0.529156
$790$	−347.763	−	453.244i	−0.440206	−	0.573727i
$791$			612.117i			0.773853i
$792$	−1173.38	−	147.151i	−1.48155	−	0.185797i
$793$		−	46.1887i		−	0.0582456i
$794$	−251.333	+	396.302i	−0.316540	+	0.499121i
$795$	1722.03	+	630.827i	2.16607	+	0.793493i
$796$	1106.68	−	521.585i	1.39031	−	0.655257i
$797$		−	763.446i		−	0.957899i	−0.877842	−	0.478950i	$-0.841018\pi$
$797$		−	763.446i		−	0.957899i	0.877842	−	0.478950i	$-0.158982\pi$
$798$	266.391	−	420.045i	0.333823	−	0.526373i
$799$			932.593i			1.16720i
$800$	−740.951	−	301.648i	−0.926189	−	0.377060i
$801$	−198.964			−0.248395
$802$	−625.948	−	396.973i	−0.780483	−	0.494978i
$803$	−357.290			−0.444944
$804$	−135.962	−	288.481i	−0.169107	−	0.358807i
$805$	−88.8182	+	242.455i	−0.110333	+	0.301187i
$806$	64.4922	+	40.9006i	0.0800152	+	0.0507452i
$807$	1582.28			1.96070
$808$	72.9648	−	581.823i	0.0903030	−	0.720078i
$809$	−994.007			−1.22869			−0.614343	−	0.789039i	$-0.710579\pi$
$809$	−994.007			−1.22869			−0.614343	+	0.789039i	$0.710579\pi$
$810$	−2986.98	+	2291.83i	−3.68762	+	2.82942i
$811$		−	722.784i		−	0.891226i	−0.895226	−	0.445613i	$-0.852986\pi$
$811$		−	722.784i		−	0.891226i	0.895226	−	0.445613i	$-0.147014\pi$
$812$	−409.596	−	869.071i	−0.504429	−	1.07028i
$813$			229.602i			0.282413i
$814$	−339.864	−	215.540i	−0.417523	−	0.264791i
$815$	−166.519	+	454.562i	−0.204318	+	0.557745i
$816$	2236.23	+	1845.42i	2.74048	+	2.26154i
$817$		−	249.065i		−	0.304853i
$818$	−80.8303	−	51.2622i	−0.0988146	−	0.0626677i
$819$		−	370.650i		−	0.452564i
$820$	63.4487	−	5.67992i	0.0773765	−	0.00692673i
$821$	347.379			0.423117			0.211559	−	0.977365i	$-0.432146\pi$
$821$	347.379			0.423117			0.211559	+	0.977365i	$0.432146\pi$
$822$	529.213	−	834.464i	0.643811	−	1.01516i
$823$	1156.27			1.40495			0.702473	−	0.711710i	$-0.252079\pi$
$823$	1156.27			1.40495			0.702473	+	0.711710i	$0.252079\pi$
$824$	23.3551	−	186.234i	0.0283435	−	0.226012i
$825$	−538.554	+	636.427i	−0.652793	+	0.771427i
$826$	−519.995	+	819.930i	−0.629534	+	0.992651i
$827$	279.759			0.338282			0.169141	−	0.985592i	$-0.445901\pi$
$827$	279.759			0.338282			0.169141	+	0.985592i	$0.445901\pi$
$828$	241.910	+	513.278i	0.292162	+	0.619901i
$829$	−1494.76			−1.80309			−0.901546	−	0.432684i	$-0.857567\pi$
$829$	−1494.76			−1.80309			−0.901546	+	0.432684i	$0.857567\pi$
$830$	565.874	−	434.181i	0.681775	−	0.523109i
$831$			2134.21i			2.56825i
$832$	23.1613	−	90.8922i	0.0278381	−	0.109245i
$833$		−	1312.51i		−	1.57564i
$834$	518.050	−	816.862i	0.621163	−	0.979451i
$835$	22.8454	−	62.3631i	0.0273597	−	0.0746863i
$836$	−41.6886	−	88.4539i	−0.0498668	−	0.105806i
$837$			2689.03i			3.21270i
$838$	−29.1771	+	46.0065i	−0.0348175	+	0.0549004i
$839$			947.342i			1.12913i	0.825388	+	0.564566i	$0.190957\pi$
$839$			947.342i			1.12913i	−0.825388	+	0.564566i	$0.809043\pi$
$840$	2028.61	+	1045.57i	2.41501	+	1.24473i
$841$	−214.392			−0.254925
$842$	808.926	+	513.017i	0.960720	+	0.609284i
$843$	1595.53			1.89268
$844$	−501.760	+	236.481i	−0.594502	+	0.280191i
$845$	286.964	−	783.353i	0.339603	−	0.927045i
$846$	1362.31	+	863.967i	1.61029	+	1.02124i
$847$	−859.214			−1.01442
$848$	−761.218	−	628.184i	−0.897662	−	0.740783i
$849$	−2506.59			−2.95240
$850$	1454.19	−	455.128i	1.71081	−	0.535444i
$851$			193.105i			0.226915i
$852$	514.205	−	242.347i	0.603527	−	0.284445i
$853$			1113.72i			1.30565i	0.757508	+	0.652826i	$0.226417\pi$
$853$			1113.72i			1.30565i	−0.757508	+	0.652826i	$0.773583\pi$
$854$	−510.750	−	323.915i	−0.598068	−	0.379291i
$855$	−539.390	−	197.594i	−0.630866	−	0.231104i
$856$	−95.0273	+	757.749i	−0.111013	+	0.885221i
$857$			1294.60i			1.51062i	0.655367	+	0.755311i	$0.272514\pi$
$857$			1294.60i			1.51062i	−0.655367	+	0.755311i	$0.727486\pi$
$858$	−82.5487	−	52.3519i	−0.0962105	−	0.0610162i
$859$			790.141i			0.919839i	0.887961	+	0.459919i	$0.152122\pi$
$859$			790.141i			0.919839i	−0.887961	+	0.459919i	$0.847878\pi$
$860$	1138.24	−	101.895i	1.32353	−	0.118482i
$861$	−181.728			−0.211066
$862$	−683.306	+	1077.44i	−0.792699	+	1.24993i
$863$	−274.774			−0.318394			−0.159197	−	0.987247i	$-0.550891\pi$
$863$	−274.774			−0.318394			−0.159197	+	0.987247i	$0.550891\pi$
$864$	3139.52	−	1025.35i	3.63370	−	1.18674i
$865$	534.450	+	195.784i	0.617862	+	0.226340i
$866$	−659.972	+	1040.64i	−0.762092	+	1.20167i
$867$	−3803.91			−4.38744
$868$	904.549	−	426.317i	1.04211	−	0.491149i
$869$	320.400			0.368700
$870$	−1180.90	+	906.079i	−1.35736	+	1.04147i
$871$		−	19.6509i		−	0.0225614i
$872$	−79.0086	+	630.016i	−0.0906061	+	0.722495i
$873$			3127.56i			3.58254i
$874$	−25.1290	+	39.6234i	−0.0287517	+	0.0453357i
$875$	1042.44	−	593.207i	1.19136	−	0.677951i
$876$	1370.64	−	645.989i	1.56466	−	0.737430i
$877$			713.727i			0.813828i	0.913467	+	0.406914i	$0.133395\pi$
$877$			713.727i			0.813828i	−0.913467	+	0.406914i	$0.866605\pi$
$878$	353.458	−	557.334i	0.402572	−	0.634777i
$879$		−	1733.84i		−	1.97251i
$880$	387.182	−	226.706i	0.439980	−	0.257620i
$881$	−1530.65			−1.73740			−0.868698	−	0.495342i	$-0.835043\pi$
$881$	−1530.65			−1.73740			−0.868698	+	0.495342i	$0.835043\pi$
$882$	−1917.27	−	1215.93i	−2.17378	−	1.37860i
$883$	768.156			0.869938			0.434969	−	0.900445i	$-0.356759\pi$
$883$	768.156			0.869938			0.434969	+	0.900445i	$0.356759\pi$
$884$	76.1646	+	161.604i	0.0861591	+	0.182810i
$885$	1412.41	+	517.407i	1.59595	+	0.584641i
$886$	428.186	+	271.553i	0.483280	+	0.306494i
$887$	959.350			1.08157			0.540784	−	0.841162i	$-0.318128\pi$
$887$	959.350			1.08157			0.540784	+	0.841162i	$0.318128\pi$
$888$	1693.49	+	212.376i	1.90709	+	0.239163i
$889$	231.002			0.259845
$890$	59.8897	−	45.9518i	0.0672917	−	0.0516313i
$891$		−	2111.51i		−	2.36982i
$892$	181.635	+	385.388i	0.203627	+	0.432050i
$893$			133.391i			0.149374i
$894$	−930.274	−	589.975i	−1.04058	−	0.659928i
$895$	735.657	+	269.492i	0.821963	+	0.301108i
$896$	−842.648	−	893.529i	−0.940455	−	0.997242i
$897$			46.9027i			0.0522884i
$898$	−638.043	−	404.643i	−0.710515	−	0.450605i
$899$			652.188i			0.725459i
$900$	682.342	−	2545.87i	0.758158	−	2.82875i
$901$	1879.82			2.08638
$902$	−19.1343	+	30.1709i	−0.0212131	+	0.0334489i
$903$	−3260.09			−3.61029
$904$	−506.385	−	63.5043i	−0.560160	−	0.0702482i
$905$	−148.726	+	405.990i	−0.164338	+	0.448608i
$906$	−1121.85	+	1768.93i	−1.23824	+	1.95246i
$907$	1051.70			1.15954			0.579769	−	0.814781i	$-0.303143\pi$
$907$	1051.70			1.15954			0.579769	+	0.814781i	$0.303143\pi$
$908$	−365.203	−	774.878i	−0.402206	−	0.853389i
$909$	1931.92			2.12533
$910$	85.6036	+	111.568i	0.0940699	+	0.122603i
$911$		−	877.343i		−	0.963055i	−0.876431	−	0.481528i	$-0.840082\pi$
$911$		−	877.343i		−	0.963055i	0.876431	−	0.481528i	$-0.159918\pi$
$912$	319.853	+	263.954i	0.350716	+	0.289423i
$913$			400.019i			0.438136i
$914$	−470.594	+	742.034i	−0.514873	+	0.811853i
$915$	−322.303	+	879.819i	−0.352243	+	0.961551i
$916$	617.978	+	1311.21i	0.674649	+	1.43145i
$917$		−	1171.96i		−	1.27804i
$918$	−3369.08	+	5312.37i	−3.67002	+	5.78690i
$919$			650.090i			0.707389i	0.935361	+	0.353694i	$0.115075\pi$
$919$			650.090i			0.707389i	−0.935361	+	0.353694i	$0.884925\pi$
$920$	−191.361	−	98.6301i	−0.208001	−	0.107207i
$921$	1905.28			2.06871
$922$	650.115	+	412.300i	0.705114	+	0.447180i
$923$	35.0270			0.0379491
$924$	−1157.80	+	545.677i	−1.25303	+	0.590559i
$925$	579.422	−	684.721i	0.626402	−	0.740239i
$926$	1155.71	+	732.945i	1.24807	+	0.791517i
$927$	618.383			0.667080
$928$	761.448	−	248.684i	0.820526	−	0.267978i
$929$	559.216			0.601955			0.300977	−	0.953631i	$-0.402687\pi$
$929$	559.216			0.601955			0.300977	+	0.953631i	$0.402687\pi$
$930$	−943.068	−	1229.11i	−1.01405	−	1.32163i
$931$		−	187.731i		−	0.201645i
$932$	−1133.87	+	534.399i	−1.21660	+	0.573389i
$933$		−	3208.99i		−	3.43943i
$934$	−1472.37	−	933.769i	−1.57641	−	0.999753i
$935$	−293.953	+	802.430i	−0.314388	+	0.858213i
$936$	306.627	+	38.4532i	0.327593	+	0.0410825i
$937$		−	1082.01i		−	1.15476i	−0.816476	−	0.577380i	$-0.804075\pi$
$937$		−	1082.01i		−	1.15476i	0.816476	−	0.577380i	$-0.195925\pi$
$938$	−217.298	−	137.809i	−0.231661	−	0.146918i
$939$			2025.78i			2.15738i
$940$	−609.602	+	54.5714i	−0.648512	+	0.0580547i
$941$	−1259.52			−1.33849			−0.669244	−	0.743042i	$-0.733382\pi$
$941$	−1259.52			−1.33849			−0.669244	+	0.743042i	$0.733382\pi$
$942$	−889.787	+	1403.02i	−0.944572	+	1.48940i
$943$	17.1426			0.0181788
$944$	−624.354	−	515.239i	−0.661392	−	0.545804i
$945$	−1703.23	+	4649.46i	−1.80236	+	4.92006i
$946$	−343.258	+	541.250i	−0.362852	+	0.572146i
$947$	1810.83			1.91217			0.956085	−	0.293089i	$-0.0946833\pi$
$947$	1810.83			1.91217			0.956085	+	0.293089i	$0.0946833\pi$
$948$	−1229.12	+	579.291i	−1.29655	+	0.611067i
$949$	93.3664			0.0983840
$950$	207.996	−	65.0980i	0.218943	−	0.0685242i
$951$		−	2732.19i		−	2.87297i
$952$	2321.13	+	291.087i	2.43816	+	0.305763i
$953$		−	837.455i		−	0.878757i	−0.898302	−	0.439378i	$-0.855199\pi$
$953$		−	837.455i		−	0.878757i	0.898302	−	0.439378i	$-0.144801\pi$
$954$	1741.50	−	2745.99i	1.82547	−	2.87840i
$955$	817.807	+	299.586i	0.856342	+	0.313702i
$956$	847.782	−	399.563i	0.886801	−	0.417952i
$957$		−	834.787i		−	0.872295i
$958$	−343.786	+	542.082i	−0.358858	+	0.565848i
$959$		−	797.258i		−	0.831343i
$960$	−1075.43	+	1569.73i	−1.12024	+	1.63513i
$961$	282.188			0.293640
$962$	88.8127	+	56.3246i	0.0923209	+	0.0585494i
$963$	−2516.08			−2.61275
$964$	−57.0016	−	120.944i	−0.0591303	−	0.125461i
$965$	1695.24	+	621.012i	1.75672	+	0.643536i
$966$	518.645	+	328.922i	0.536899	+	0.340499i
$967$	−876.040			−0.905936			−0.452968	−	0.891527i	$-0.649635\pi$
$967$	−876.040			−0.905936			−0.452968	+	0.891527i	$0.649635\pi$
$968$	89.1395	−	710.800i	0.0920863	−	0.734298i
$969$	−789.876			−0.815146
$970$	−722.327	−	941.418i	−0.744667	−	0.970534i
$971$		−	544.201i		−	0.560454i	−0.959934	−	0.280227i	$-0.909590\pi$
$971$		−	544.201i		−	0.560454i	0.959934	−	0.280227i	$-0.0904098\pi$
$972$	2233.61	+	4739.22i	2.29795	+	4.87574i
$973$		−	780.442i		−	0.802098i
$974$	−870.184	−	551.866i	−0.893412	−	0.566598i
$975$	140.734	−	166.310i	0.144343	−	0.170574i
$976$	320.952	−	388.922i	0.328845	−	0.398486i
$977$		−	1823.45i		−	1.86637i	−0.359394	−	0.933186i	$-0.617017\pi$
$977$		−	1823.45i		−	1.86637i	0.359394	−	0.933186i	$-0.382983\pi$
$978$	972.369	+	616.672i	0.994243	+	0.630544i
$979$			42.3363i			0.0432444i
$980$	857.938	−	76.8025i	0.875447	−	0.0783699i
$981$	−2091.95			−2.13246
$982$	−529.752	+	835.314i	−0.539462	+	0.850625i
$983$	521.962			0.530989			0.265495	−	0.964112i	$-0.414465\pi$
$983$	521.962			0.530989			0.265495	+	0.964112i	$0.414465\pi$
$984$	18.8534	−	150.337i	0.0191600	−	0.152782i
$985$	458.747	+	168.052i	0.465733	+	0.170611i
$986$	−817.124	+	1288.44i	−0.828726	+	1.30674i
$987$	1746.00			1.76900
$988$	10.8940	+	23.1146i	0.0110263	+	0.0233953i
$989$	307.529			0.310949
$990$	899.844	+	1172.78i	0.908934	+	1.18463i
$991$		−	978.158i		−	0.987041i	−0.869734	−	0.493521i	$-0.835710\pi$
$991$		−	978.158i		−	0.987041i	0.869734	−	0.493521i	$-0.164290\pi$
$992$	258.836	+	792.533i	0.260923	+	0.798924i
$993$			2314.97i			2.33129i
$994$	245.639	−	387.325i	0.247122	−	0.389663i
$995$	−1435.98	−	526.039i	−1.44319	−	0.528683i
$996$	−723.243	−	1534.56i	−0.726147	−	1.54072i
$997$		−	41.2743i		−	0.0413985i	−0.999786	−	0.0206993i	$-0.993411\pi$
$997$		−	41.2743i		−	0.0413985i	0.999786	−	0.0206993i	$-0.00658925\pi$
$998$	−474.820	+	748.698i	−0.475772	+	0.750198i
$999$			3703.08i			3.70679i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.3.h.a.39.19	✓	108
4.3	odd	2	inner	380.3.h.a.39.89	yes	108
5.4	even	2	inner	380.3.h.a.39.90	yes	108
20.19	odd	2	inner	380.3.h.a.39.20	yes	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.3.h.a.39.19	✓	108	1.1	even	1	trivial
380.3.h.a.39.20	yes	108	20.19	odd	2	inner
380.3.h.a.39.89	yes	108	4.3	odd	2	inner
380.3.h.a.39.90	yes	108	5.4	even	2	inner

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:	\( N \)	\(=\)	\( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	380.h (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.68898 - 1.07114i) q^{2} +5.94620 q^{3} +(1.70531 + 3.61828i) q^{4} +(1.71987 - 4.69490i) q^{5} +(-10.0430 - 6.36923i) q^{6} -9.59523 q^{7} +(0.995461 - 7.93782i) q^{8} +26.3573 q^{9} +O(q^{10})\)	\(q+(-1.68898 - 1.07114i) q^{2} +5.94620 q^{3} +(1.70531 + 3.61828i) q^{4} +(1.71987 - 4.69490i) q^{5} +(-10.0430 - 6.36923i) q^{6} -9.59523 q^{7} +(0.995461 - 7.93782i) q^{8} +26.3573 q^{9} +(-7.93373 + 6.08736i) q^{10} -5.60839i q^{11} +(10.1401 + 21.5150i) q^{12} +1.46557i q^{13} +(16.2062 + 10.2779i) q^{14} +(10.2267 - 27.9168i) q^{15} +(-10.1839 + 12.3405i) q^{16} -30.4749i q^{17} +(-44.5169 - 28.2324i) q^{18} -4.35890i q^{19} +(19.9203 - 1.78326i) q^{20} -57.0551 q^{21} +(-6.00738 + 9.47246i) q^{22} +5.38208 q^{23} +(5.91921 - 47.1999i) q^{24} +(-19.0841 - 16.1492i) q^{25} +(1.56984 - 2.47533i) q^{26} +103.210 q^{27} +(-16.3628 - 34.7182i) q^{28} +25.0321 q^{29} +(-47.1755 + 36.1966i) q^{30} +26.0540i q^{31} +(30.4188 - 9.93458i) q^{32} -33.3486i q^{33} +(-32.6430 + 51.4716i) q^{34} +(-16.5026 + 45.0486i) q^{35} +(44.9473 + 95.3679i) q^{36} +35.8792i q^{37} +(-4.66900 + 7.36209i) q^{38} +8.71460i q^{39} +(-35.5552 - 18.3256i) q^{40} +3.18512 q^{41} +(96.3650 + 61.1142i) q^{42} +57.1393 q^{43} +(20.2927 - 9.56403i) q^{44} +(45.3311 - 123.745i) q^{45} +(-9.09023 - 5.76498i) q^{46} -30.6020 q^{47} +(-60.5552 + 73.3793i) q^{48} +43.0685 q^{49} +(14.9345 + 47.7175i) q^{50} -181.210i q^{51} +(-5.30285 + 2.49925i) q^{52} +61.6843i q^{53} +(-174.319 - 110.552i) q^{54} +(-26.3308 - 9.64571i) q^{55} +(-9.55168 + 76.1653i) q^{56} -25.9189i q^{57} +(-42.2788 - 26.8130i) q^{58} +50.5937i q^{59} +(118.450 - 10.6036i) q^{60} -31.5158 q^{61} +(27.9076 - 44.0047i) q^{62} -252.904 q^{63} +(-62.0181 - 15.8036i) q^{64} +(6.88072 + 2.52060i) q^{65} +(-35.7211 + 56.3251i) q^{66} -13.4084 q^{67} +(110.267 - 51.9691i) q^{68} +32.0029 q^{69} +(76.1260 - 58.4096i) q^{70} -23.8999i q^{71} +(26.2376 - 209.219i) q^{72} -63.7064i q^{73} +(38.4317 - 60.5992i) q^{74} +(-113.478 - 96.0266i) q^{75} +(15.7717 - 7.43326i) q^{76} +53.8138i q^{77} +(9.33458 - 14.7188i) q^{78} +57.1288i q^{79} +(40.4226 + 69.0363i) q^{80} +376.491 q^{81} +(-5.37961 - 3.41172i) q^{82} -71.3250 q^{83} +(-97.2965 - 206.441i) q^{84} +(-143.077 - 52.4130i) q^{85} +(-96.5072 - 61.2044i) q^{86} +148.846 q^{87} +(-44.5184 - 5.58293i) q^{88} -7.54874 q^{89} +(-209.112 + 160.446i) q^{90} -14.0625i q^{91} +(9.17811 + 19.4739i) q^{92} +154.922i q^{93} +(51.6861 + 32.7791i) q^{94} +(-20.4646 - 7.49675i) q^{95} +(180.876 - 59.0730i) q^{96} +118.660i q^{97} +(-72.7418 - 46.1325i) q^{98} -147.822i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q + 4 q^{5} + 324 q^{9}+O(q^{10}) \) 108 * q + 4 * q^5 + 324 * q^9	\( 108 q + 4 q^{5} + 324 q^{9} - 8 q^{10} + 8 q^{14} - 104 q^{16} - 16 q^{21} - 8 q^{24} - 76 q^{25} + 80 q^{26} - 88 q^{29} - 140 q^{30} - 88 q^{34} - 256 q^{36} + 44 q^{40} - 200 q^{41} - 8 q^{44} + 108 q^{45} + 272 q^{46} + 916 q^{49} - 276 q^{50} - 320 q^{54} - 328 q^{56} + 172 q^{60} + 200 q^{61} - 216 q^{64} - 192 q^{65} + 152 q^{66} - 592 q^{69} + 200 q^{70} - 232 q^{74} + 340 q^{80} + 1052 q^{81} + 208 q^{84} + 248 q^{85} - 1048 q^{86} + 760 q^{89} + 268 q^{90} - 320 q^{94} + 720 q^{96}+O(q^{100}) \) 108 * q + 4 * q^5 + 324 * q^9 - 8 * q^10 + 8 * q^14 - 104 * q^16 - 16 * q^21 - 8 * q^24 - 76 * q^25 + 80 * q^26 - 88 * q^29 - 140 * q^30 - 88 * q^34 - 256 * q^36 + 44 * q^40 - 200 * q^41 - 8 * q^44 + 108 * q^45 + 272 * q^46 + 916 * q^49 - 276 * q^50 - 320 * q^54 - 328 * q^56 + 172 * q^60 + 200 * q^61 - 216 * q^64 - 192 * q^65 + 152 * q^66 - 592 * q^69 + 200 * q^70 - 232 * q^74 + 340 * q^80 + 1052 * q^81 + 208 * q^84 + 248 * q^85 - 1048 * q^86 + 760 * q^89 + 268 * q^90 - 320 * q^94 + 720 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more