LMFDB - Embedded newform 380.3.h.a.39.10

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			39.10
Character	$\chi$	$=$	380.39
Dual form			380.3.h.a.39.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.91201 + 0.586697i) q^{2} -5.34961 q^{3} +(3.31157 - 2.24354i) q^{4} +(-3.58581 - 3.48454i) q^{5} +(10.2285 - 3.13860i) q^{6} +0.878631 q^{7} +(-5.01548 + 6.23257i) q^{8} +19.6184 q^{9} +O(q^{10})$	\(q+(-1.91201 + 0.586697i) q^{2} -5.34961 q^{3} +(3.31157 - 2.24354i) q^{4} +(-3.58581 - 3.48454i) q^{5} +(10.2285 - 3.13860i) q^{6} +0.878631 q^{7} +(-5.01548 + 6.23257i) q^{8} +19.6184 q^{9} +(8.90047 + 4.55869i) q^{10} +9.57856i q^{11} +(-17.7156 + 12.0021i) q^{12} -6.75472i q^{13} +(-1.67995 + 0.515490i) q^{14} +(19.1827 + 18.6409i) q^{15} +(5.93303 - 14.8593i) q^{16} +24.8661i q^{17} +(-37.5105 + 11.5100i) q^{18} +4.35890i q^{19} +(-19.6924 - 3.49438i) q^{20} -4.70033 q^{21} +(-5.61972 - 18.3143i) q^{22} +19.9805 q^{23} +(26.8309 - 33.3418i) q^{24} +(0.716019 + 24.9897i) q^{25} +(3.96297 + 12.9151i) q^{26} -56.8042 q^{27} +(2.90965 - 1.97125i) q^{28} -13.7220 q^{29} +(-47.6141 - 24.3872i) q^{30} -37.3799i q^{31} +(-2.62610 + 31.8921i) q^{32} -51.2416i q^{33} +(-14.5889 - 47.5442i) q^{34} +(-3.15060 - 3.06162i) q^{35} +(64.9677 - 44.0147i) q^{36} -35.9721i q^{37} +(-2.55735 - 8.33426i) q^{38} +36.1351i q^{39} +(39.7022 - 4.87216i) q^{40} -7.57460 q^{41} +(8.98709 - 2.75767i) q^{42} +27.7577 q^{43} +(21.4899 + 31.7201i) q^{44} +(-70.3477 - 68.3609i) q^{45} +(-38.2029 + 11.7225i) q^{46} +62.6391 q^{47} +(-31.7394 + 79.4916i) q^{48} -48.2280 q^{49} +(-16.0304 - 47.3606i) q^{50} -133.024i q^{51} +(-15.1545 - 22.3687i) q^{52} -60.3963i q^{53} +(108.610 - 33.3269i) q^{54} +(33.3768 - 34.3469i) q^{55} +(-4.40676 + 5.47613i) q^{56} -23.3184i q^{57} +(26.2365 - 8.05063i) q^{58} +18.4875i q^{59} +(105.347 + 18.6936i) q^{60} -5.91165 q^{61} +(21.9307 + 71.4709i) q^{62} +17.2373 q^{63} +(-13.6898 - 62.5187i) q^{64} +(-23.5371 + 24.2211i) q^{65} +(30.0633 + 97.9745i) q^{66} -108.010 q^{67} +(55.7882 + 82.3459i) q^{68} -106.888 q^{69} +(7.82022 + 4.00540i) q^{70} -30.6097i q^{71} +(-98.3956 + 122.273i) q^{72} -90.3567i q^{73} +(21.1047 + 68.7790i) q^{74} +(-3.83043 - 133.685i) q^{75} +(9.77938 + 14.4348i) q^{76} +8.41602i q^{77} +(-21.2004 - 69.0908i) q^{78} +32.0898i q^{79} +(-73.0525 + 32.6088i) q^{80} +127.315 q^{81} +(14.4827 - 4.44400i) q^{82} -151.434 q^{83} +(-15.5655 + 10.5454i) q^{84} +(86.6468 - 89.1650i) q^{85} +(-53.0729 + 16.2853i) q^{86} +73.4072 q^{87} +(-59.6991 - 48.0411i) q^{88} -24.5129 q^{89} +(174.613 + 89.4341i) q^{90} -5.93490i q^{91} +(66.1668 - 44.8271i) q^{92} +199.968i q^{93} +(-119.767 + 36.7502i) q^{94} +(15.1887 - 15.6302i) q^{95} +(14.0486 - 170.610i) q^{96} +32.0221i q^{97} +(92.2125 - 28.2952i) q^{98} +187.916i 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 $

$2$	−1.91201	+	0.586697i	−0.956006	+	0.293349i
$2$	−1.91201	+	0.586697i	−0.956006	+	0.293349i
$3$	−5.34961			−1.78320			−0.891602	−	0.452819i	$-0.850418\pi$
$3$	−5.34961			−1.78320			−0.891602	+	0.452819i	$0.850418\pi$
$4$	3.31157	−	2.24354i	0.827893	−	0.560886i
$5$	−3.58581	−	3.48454i	−0.717161	−	0.696907i
$5$	−3.58581	−	3.48454i	−0.717161	−	0.696907i
$6$	10.2285	−	3.13860i	1.70475	−	0.523101i
$7$	0.878631			0.125519			0.0627593	−	0.998029i	$-0.480010\pi$
$7$	0.878631			0.125519			0.0627593	+	0.998029i	$0.480010\pi$
$8$	−5.01548	+	6.23257i	−0.626935	+	0.779071i
$9$	19.6184			2.17982
$10$	8.90047	+	4.55869i	0.890047	+	0.455869i
$11$			9.57856i			0.870779i	0.900242	+	0.435389i	$0.143389\pi$
$11$			9.57856i			0.870779i	−0.900242	+	0.435389i	$0.856611\pi$
$12$	−17.7156	+	12.0021i	−1.47630	+	1.00017i
$13$		−	6.75472i		−	0.519594i	−0.965663	−	0.259797i	$-0.916344\pi$
$13$		−	6.75472i		−	0.519594i	0.965663	−	0.259797i	$-0.0836556\pi$
$14$	−1.67995	+	0.515490i	−0.119997	+	0.0368207i
$15$	19.1827	+	18.6409i	1.27885	+	1.24273i
$16$	5.93303	−	14.8593i	0.370814	−	0.928707i
$17$			24.8661i			1.46271i	0.681996	+	0.731356i	$0.261112\pi$
$17$			24.8661i			1.46271i	−0.681996	+	0.731356i	$0.738888\pi$
$18$	−37.5105	+	11.5100i	−2.08392	+	0.639447i
$19$			4.35890i			0.229416i
$19$			4.35890i			0.229416i
$20$	−19.6924	−	3.49438i	−0.984618	−	0.174719i
$21$	−4.70033			−0.223825
$22$	−5.61972	−	18.3143i	−0.255442	−	0.832469i
$23$	19.9805			0.868716			0.434358	−	0.900740i	$-0.356975\pi$
$23$	19.9805			0.868716			0.434358	+	0.900740i	$0.356975\pi$
$24$	26.8309	−	33.3418i	1.11795	−	1.38924i
$25$	0.716019	+	24.9897i	0.0286408	+	0.999590i
$26$	3.96297	+	12.9151i	0.152422	+	0.496735i
$27$	−56.8042			−2.10386
$28$	2.90965	−	1.97125i	0.103916	−	0.0704016i
$29$	−13.7220			−0.473171			−0.236585	−	0.971611i	$-0.576028\pi$
$29$	−13.7220			−0.473171			−0.236585	+	0.971611i	$0.576028\pi$
$30$	−47.6141	−	24.3872i	−1.58714	−	0.812908i
$31$		−	37.3799i		−	1.20580i	−0.797815	−	0.602902i	$-0.794011\pi$
$31$		−	37.3799i		−	1.20580i	0.797815	−	0.602902i	$-0.205989\pi$
$32$	−2.62610	+	31.8921i	−0.0820657	+	0.996627i
$33$		−	51.2416i		−	1.55278i
$34$	−14.5889	−	47.5442i	−0.429084	−	1.39836i
$35$	−3.15060	−	3.06162i	−0.0900171	−	0.0874748i
$36$	64.9677	−	44.0147i	1.80466	−	1.22263i
$37$		−	35.9721i		−	0.972218i	−0.873898	−	0.486109i	$-0.838416\pi$
$37$		−	35.9721i		−	0.972218i	0.873898	−	0.486109i	$-0.161584\pi$
$38$	−2.55735	−	8.33426i	−0.0672988	−	0.219323i
$39$			36.1351i			0.926542i
$40$	39.7022	−	4.87216i	0.992554	−	0.121804i
$41$	−7.57460			−0.184746			−0.0923731	−	0.995724i	$-0.529445\pi$
$41$	−7.57460			−0.184746			−0.0923731	+	0.995724i	$0.529445\pi$
$42$	8.98709	−	2.75767i	0.213978	−	0.0656589i
$43$	27.7577			0.645527			0.322763	−	0.946480i	$-0.395388\pi$
$43$	27.7577			0.645527			0.322763	+	0.946480i	$0.395388\pi$
$44$	21.4899	+	31.7201i	0.488407	+	0.720912i
$45$	−70.3477	−	68.3609i	−1.56328	−	1.51913i
$46$	−38.2029	+	11.7225i	−0.830498	+	0.254837i
$47$	62.6391			1.33275			0.666373	−	0.745619i	$-0.267846\pi$
$47$	62.6391			1.33275			0.666373	+	0.745619i	$0.267846\pi$
$48$	−31.7394	+	79.4916i	−0.661238	+	1.65607i
$49$	−48.2280			−0.984245
$50$	−16.0304	−	47.3606i	−0.320609	−	0.947212i
$51$		−	133.024i		−	2.60831i
$52$	−15.1545	−	22.3687i	−0.291433	−	0.430168i
$53$		−	60.3963i		−	1.13955i	−0.821800	−	0.569777i	$-0.807030\pi$
$53$		−	60.3963i		−	1.13955i	0.821800	−	0.569777i	$-0.192970\pi$
$54$	108.610	−	33.3269i	2.01130	−	0.617164i
$55$	33.3768	−	34.3469i	0.606852	−	0.624489i
$56$	−4.40676	+	5.47613i	−0.0786921	+	0.0977880i
$57$		−	23.3184i		−	0.409095i
$58$	26.2365	−	8.05063i	0.452354	−	0.138804i
$59$			18.4875i			0.313348i	0.987650	+	0.156674i	$0.0500772\pi$
$59$			18.4875i			0.313348i	−0.987650	+	0.156674i	$0.949923\pi$
$60$	105.347	+	18.6936i	1.75578	+	0.311560i
$61$	−5.91165			−0.0969123			−0.0484562	−	0.998825i	$-0.515430\pi$
$61$	−5.91165			−0.0969123			−0.0484562	+	0.998825i	$0.515430\pi$
$62$	21.9307	+	71.4709i	0.353721	+	1.15276i
$63$	17.2373			0.273608
$64$	−13.6898	−	62.5187i	−0.213904	−	0.976855i
$65$	−23.5371	+	24.2211i	−0.362109	+	0.372633i
$66$	30.0633	+	97.9745i	0.455505	+	1.48446i
$67$	−108.010			−1.61208			−0.806042	−	0.591858i	$-0.798395\pi$
$67$	−108.010			−1.61208			−0.806042	+	0.591858i	$0.798395\pi$
$68$	55.7882	+	82.3459i	0.820414	+	1.21097i
$69$	−106.888			−1.54910
$70$	7.82022	+	4.00540i	0.111717	+	0.0572200i
$71$		−	30.6097i		−	0.431122i	−0.976490	−	0.215561i	$-0.930842\pi$
$71$		−	30.6097i		−	0.431122i	0.976490	−	0.215561i	$-0.0691581\pi$
$72$	−98.3956	+	122.273i	−1.36661	+	1.69823i
$73$		−	90.3567i		−	1.23776i	−0.785484	−	0.618881i	$-0.787586\pi$
$73$		−	90.3567i		−	1.23776i	0.785484	−	0.618881i	$-0.212414\pi$
$74$	21.1047	+	68.7790i	0.285199	+	0.929446i
$75$	−3.83043	−	133.685i	−0.0510724	−	1.78247i
$76$	9.77938	+	14.4348i	0.128676	+	0.189932i
$77$			8.41602i			0.109299i
$78$	−21.2004	−	69.0908i	−0.271800	−	0.885779i
$79$			32.0898i			0.406200i	0.979158	+	0.203100i	$0.0651017\pi$
$79$			32.0898i			0.406200i	−0.979158	+	0.203100i	$0.934898\pi$
$80$	−73.0525	+	32.6088i	−0.913156	+	0.407610i
$81$	127.315			1.57179
$82$	14.4827	−	4.44400i	0.176618	−	0.0541951i
$83$	−151.434			−1.82450			−0.912251	−	0.409631i	$-0.865657\pi$
$83$	−151.434			−1.82450			−0.912251	+	0.409631i	$0.865657\pi$
$84$	−15.5655	+	10.5454i	−0.185304	+	0.125541i
$85$	86.6468	−	89.1650i	1.01937	−	1.04900i
$86$	−53.0729	+	16.2853i	−0.617127	+	0.189364i
$87$	73.4072			0.843760
$88$	−59.6991	−	48.0411i	−0.678398	−	0.545922i
$89$	−24.5129			−0.275426			−0.137713	−	0.990472i	$-0.543975\pi$
$89$	−24.5129			−0.275426			−0.137713	+	0.990472i	$0.543975\pi$
$90$	174.613	+	89.4341i	1.94014	+	0.993712i
$91$		−	5.93490i		−	0.0652187i
$92$	66.1668	−	44.8271i	0.719204	−	0.487251i
$93$			199.968i			2.15020i
$94$	−119.767	+	36.7502i	−1.27411	+	0.390959i
$95$	15.1887	−	15.6302i	0.159881	−	0.164528i
$96$	14.0486	−	170.610i	0.146340	−	1.77719i
$97$			32.0221i			0.330125i	0.986283	+	0.165062i	$0.0527825\pi$
$97$			32.0221i			0.330125i	−0.986283	+	0.165062i	$0.947217\pi$
$98$	92.2125	−	28.2952i	0.940944	−	0.288727i
$99$			187.916i			1.89814i
$100$	58.4367	+	81.1489i	0.584367	+	0.811489i
$101$	−42.4975			−0.420767			−0.210384	−	0.977619i	$-0.567471\pi$
$101$	−42.4975			−0.420767			−0.210384	+	0.977619i	$0.567471\pi$
$102$	78.0448	+	254.343i	0.765145	+	2.49356i
$103$	−178.697			−1.73492			−0.867460	−	0.497506i	$-0.834249\pi$
$103$	−178.697			−1.73492			−0.867460	+	0.497506i	$0.834249\pi$
$104$	42.0993	+	33.8782i	0.404801	+	0.325752i
$105$	16.8545	+	16.3785i	0.160519	+	0.155986i
$106$	35.4344	+	115.478i	0.334286	+	1.08942i
$107$	96.1517			0.898614			0.449307	−	0.893377i	$-0.351671\pi$
$107$	96.1517			0.898614			0.449307	+	0.893377i	$0.351671\pi$
$108$	−188.111	+	127.443i	−1.74177	+	1.18002i
$109$	139.022			1.27543			0.637717	−	0.770271i	$-0.279879\pi$
$109$	139.022			1.27543			0.637717	+	0.770271i	$0.279879\pi$
$110$	−43.6657	+	85.2537i	−0.396961	+	0.775034i
$111$			192.437i			1.73366i
$112$	5.21294	−	13.0558i	0.0465441	−	0.116570i
$113$			173.897i			1.53891i	0.638700	+	0.769455i	$0.279472\pi$
$113$			173.897i			1.53891i	−0.638700	+	0.769455i	$0.720528\pi$
$114$	13.6809	+	44.5851i	0.120008	+	0.391097i
$115$	−71.6461	−	69.6227i	−0.623010	−	0.605415i
$116$	−45.4412	+	30.7858i	−0.391735	+	0.265395i
$117$		−	132.517i		−	1.13262i
$118$	−10.8466	−	35.3484i	−0.0919202	−	0.299562i
$119$			21.8481i			0.183598i
$120$	−212.391	+	26.0642i	−1.76993	+	0.217201i
$121$	29.2511			0.241745
$122$	11.3031	−	3.46835i	0.0926487	−	0.0284291i
$123$	40.5212			0.329440
$124$	−83.8635	−	123.786i	−0.676319	−	0.998277i
$125$	84.5102	−	92.1034i	0.676081	−	0.736827i
$126$	−32.9579	+	10.1131i	−0.261571	+	0.0802625i
$127$	131.404			1.03468			0.517340	−	0.855780i	$-0.326922\pi$
$127$	131.404			1.03468			0.517340	+	0.855780i	$0.326922\pi$
$128$	62.8547	+	111.505i	0.491052	+	0.871130i
$129$	−148.493			−1.15111
$130$	30.7927	−	60.1202i	0.236867	−	0.462463i
$131$		−	258.816i		−	1.97570i	−0.155418	−	0.987849i	$-0.549673\pi$
$131$		−	258.816i		−	1.97570i	0.155418	−	0.987849i	$-0.450327\pi$
$132$	−114.963	−	169.690i	−0.870930	−	1.28553i
$133$			3.82986i			0.0287960i
$134$	206.516	−	63.3690i	1.54116	−	0.472903i
$135$	203.689	+	197.936i	1.50881	+	1.46619i
$136$	−154.980	−	124.715i	−1.13956	−	0.917026i
$137$		−	147.608i		−	1.07743i	−0.842488	−	0.538715i	$-0.818910\pi$
$137$		−	147.608i		−	1.07743i	0.842488	−	0.538715i	$-0.181090\pi$
$138$	204.371	−	62.7108i	1.48095	−	0.454426i
$139$			26.2682i			0.188980i	0.995526	+	0.0944898i	$0.0301220\pi$
$139$			26.2682i			0.188980i	−0.995526	+	0.0944898i	$0.969878\pi$
$140$	−17.3023	−	3.07027i	−0.123588	−	0.0219305i
$141$	−335.095			−2.37656
$142$	17.9586	+	58.5261i	0.126469	+	0.412155i
$143$	64.7005			0.452451
$144$	116.396	−	291.516i	0.808308	−	2.02441i
$145$	49.2043	+	47.8146i	0.339340	+	0.329756i
$146$	53.0120	+	172.763i	0.363096	+	1.18331i
$147$	258.001			1.75511
$148$	−80.7049	−	119.124i	−0.545303	−	0.804892i
$149$	−279.590			−1.87644			−0.938221	−	0.346037i	$-0.887527\pi$
$149$	−279.590			−1.87644			−0.938221	+	0.346037i	$0.887527\pi$
$150$	85.7567	+	253.361i	0.571711	+	1.68907i
$151$		−	183.794i		−	1.21718i	−0.793486	−	0.608588i	$-0.791736\pi$
$151$		−	183.794i		−	1.21718i	0.793486	−	0.608588i	$-0.208264\pi$
$152$	−27.1671	−	21.8620i	−0.178731	−	0.143829i
$153$			487.832i			3.18845i
$154$	−4.93765	−	16.0915i	−0.0320627	−	0.104490i
$155$	−130.252	+	134.037i	−0.840334	+	0.864756i
$156$	81.0707	+	119.664i	0.519684	+	0.767078i
$157$		−	265.734i		−	1.69257i	−0.532728	−	0.846287i	$-0.678833\pi$
$157$		−	265.734i		−	1.69257i	0.532728	−	0.846287i	$-0.321167\pi$
$158$	−18.8270	−	61.3561i	−0.119158	−	0.388330i
$159$			323.097i			2.03206i
$160$	120.546	−	105.208i	0.753411	−	0.657550i
$161$	17.5555			0.109040
$162$	−243.428	+	74.6955i	−1.50264	+	0.461083i
$163$	180.653			1.10830			0.554150	−	0.832417i	$-0.313043\pi$
$163$	180.653			1.10830			0.554150	+	0.832417i	$0.313043\pi$
$164$	−25.0838	+	16.9939i	−0.152950	+	0.103622i
$165$	−178.553	+	183.743i	−1.08214	+	1.11359i
$166$	289.543	−	88.8457i	1.74423	−	0.535215i
$167$	−184.016			−1.10189			−0.550946	−	0.834541i	$-0.685733\pi$
$167$	−184.016			−1.10189			−0.550946	+	0.834541i	$0.685733\pi$
$168$	23.5745	−	29.2952i	0.140324	−	0.174376i
$169$	123.374			0.730022
$170$	−113.357	+	221.320i	−0.666805	+	1.30188i
$171$			85.5145i			0.500085i
$172$	91.9215	−	62.2755i	0.534427	−	0.362067i
$173$		−	273.546i		−	1.58119i	−0.612338	−	0.790596i	$-0.709771\pi$
$173$		−	273.546i		−	1.58119i	0.612338	−	0.790596i	$-0.290229\pi$
$174$	−140.355	+	43.0678i	−0.806640	+	0.247516i
$175$	0.629116	+	21.9568i	0.00359495	+	0.125467i
$176$	142.331	+	56.8299i	0.808698	+	0.322897i
$177$		−	98.9011i		−	0.558764i
$178$	46.8689	−	14.3816i	0.263309	−	0.0807957i
$179$			223.696i			1.24970i	0.780746	+	0.624849i	$0.214839\pi$
$179$			223.696i			1.24970i	−0.780746	+	0.624849i	$0.785161\pi$
$180$	−386.332	−	68.5541i	−2.14629	−	0.380856i
$181$	249.613			1.37907			0.689537	−	0.724250i	$-0.257814\pi$
$181$	249.613			1.37907			0.689537	+	0.724250i	$0.257814\pi$
$182$	3.48199	+	11.3476i	0.0191318	+	0.0623494i
$183$	31.6251			0.172814
$184$	−100.212	+	124.530i	−0.544629	+	0.676792i
$185$	−125.346	+	128.989i	−0.677545	+	0.697237i
$186$	−117.321	−	382.342i	−0.630757	−	2.05560i
$187$	−238.181			−1.27370
$188$	207.434	−	140.533i	1.10337	−	0.747518i
$189$	−49.9099			−0.264074
$190$	−19.8709	+	38.7962i	−0.104583	+	0.204191i
$191$		−	171.617i		−	0.898519i	−0.893401	−	0.449260i	$-0.851688\pi$
$191$		−	171.617i		−	0.898519i	0.893401	−	0.449260i	$-0.148312\pi$
$192$	73.2354	+	334.451i	0.381434	+	1.74193i
$193$		−	82.3208i		−	0.426533i	−0.976994	−	0.213266i	$-0.931590\pi$
$193$		−	82.3208i		−	0.426533i	0.976994	−	0.213266i	$-0.0684102\pi$
$194$	−18.7873	−	61.2266i	−0.0968416	−	0.315601i
$195$	125.914	−	129.574i	0.645714	−	0.664480i
$196$	−159.711	+	108.202i	−0.814850	+	0.552049i
$197$			143.306i			0.727443i	0.931508	+	0.363721i	$0.118494\pi$
$197$			143.306i			0.727443i	−0.931508	+	0.363721i	$0.881506\pi$
$198$	−110.250	−	359.297i	−0.556817	−	1.81463i
$199$		−	263.248i		−	1.32285i	−0.750010	−	0.661426i	$-0.769951\pi$
$199$		−	263.248i		−	1.32285i	0.750010	−	0.661426i	$-0.230049\pi$
$200$	−159.342	−	120.873i	−0.796708	−	0.604365i
$201$	577.810			2.87468
$202$	81.2556	−	24.9331i	0.402256	−	0.123431i
$203$	−12.0565			−0.0593918
$204$	−298.445	−	440.519i	−1.46297	−	2.15941i
$205$	27.1610	+	26.3940i	0.132493	+	0.128751i
$206$	341.670	−	104.841i	1.65859	−	0.508937i
$207$	391.984			1.89364
$208$	−100.370	−	40.0759i	−0.482550	−	0.192673i
$209$	−41.7520			−0.199770
$210$	−41.8352	−	21.4274i	−0.199215	−	0.102035i
$211$		−	24.3986i		−	0.115633i	−0.998327	−	0.0578167i	$-0.981586\pi$
$211$		−	24.3986i		−	0.115633i	0.998327	−	0.0578167i	$-0.0184139\pi$
$212$	−135.502	−	200.007i	−0.639159	−	0.943428i
$213$			163.750i			0.768780i
$214$	−183.843	+	56.4119i	−0.859080	+	0.263607i
$215$	−99.5336	−	96.7225i	−0.462947	−	0.449872i
$216$	284.901	−	354.036i	1.31898	−	1.63906i
$217$		−	32.8432i		−	0.151351i
$218$	−265.812	+	81.5640i	−1.21932	+	0.374147i
$219$			483.373i			2.20718i
$220$	33.4712	−	188.625i	0.152142	−	0.857384i
$221$	167.963			0.760016
$222$	−112.902	−	367.941i	−0.508568	−	1.65739i
$223$	−123.139			−0.552194			−0.276097	−	0.961130i	$-0.589041\pi$
$223$	−123.139			−0.552194			−0.276097	+	0.961130i	$0.589041\pi$
$224$	−2.30737	+	28.0213i	−0.0103008	+	0.125095i
$225$	14.0471	+	490.258i	0.0624317	+	2.17893i
$226$	−102.025	−	332.493i	−0.451437	−	1.47121i
$227$	−118.791			−0.523307			−0.261653	−	0.965162i	$-0.584268\pi$
$227$	−118.791			−0.523307			−0.261653	+	0.965162i	$0.584268\pi$
$228$	−52.3159	−	77.2207i	−0.229456	−	0.338687i
$229$	−150.341			−0.656509			−0.328254	−	0.944589i	$-0.606460\pi$
$229$	−150.341			−0.656509			−0.328254	+	0.944589i	$0.606460\pi$
$230$	177.836	+	91.0848i	0.773198	+	0.396021i
$231$		−	45.0225i		−	0.194902i
$232$	68.8222	−	85.5230i	0.296648	−	0.368634i
$233$			122.639i			0.526349i	0.964748	+	0.263174i	$0.0847694\pi$
$233$			122.639i			0.526349i	−0.964748	+	0.263174i	$0.915231\pi$
$234$	77.7471	+	253.373i	0.332253	+	1.08279i
$235$	−224.612	−	218.268i	−0.955794	−	0.928800i
$236$	41.4776	+	61.2228i	0.175752	+	0.259419i
$237$		−	171.668i		−	0.724338i
$238$	−12.8182	−	41.7738i	−0.0538581	−	0.175520i
$239$			17.1320i			0.0716820i	0.999358	+	0.0358410i	$0.0114110\pi$
$239$			17.1320i			0.0716820i	−0.999358	+	0.0358410i	$0.988589\pi$
$240$	390.803	−	174.444i	1.62834	−	0.726851i
$241$	244.293			1.01366			0.506832	−	0.862045i	$-0.330816\pi$
$241$	244.293			1.01366			0.506832	+	0.862045i	$0.330816\pi$
$242$	−55.9285	+	17.1615i	−0.231109	+	0.0709155i
$243$	−169.850			−0.698969
$244$	−19.5769	+	13.2630i	−0.0802330	+	0.0543567i
$245$	172.936	+	168.052i	0.705863	+	0.685927i
$246$	−77.4769	+	23.7737i	−0.314947	+	0.0966409i
$247$	29.4431			0.119203
$248$	232.973	+	187.478i	0.939408	+	0.755962i
$249$	810.112			3.25346
$250$	−107.548	+	225.685i	−0.430190	+	0.902738i
$251$		−	55.3319i		−	0.220446i	−0.993907	−	0.110223i	$-0.964844\pi$
$251$		−	55.3319i		−	0.220446i	0.993907	−	0.110223i	$-0.0351565\pi$
$252$	57.0826	−	38.6726i	0.226518	−	0.153463i
$253$			191.384i			0.756460i
$254$	−251.247	+	77.0946i	−0.989160	+	0.303522i
$255$	−463.527	+	476.998i	−1.81775	+	1.87058i
$256$	−185.598	−	176.321i	−0.724993	−	0.688756i
$257$		−	467.050i		−	1.81732i	−0.417540	−	0.908659i	$-0.637108\pi$
$257$		−	467.050i		−	1.81732i	0.417540	−	0.908659i	$-0.362892\pi$
$258$	283.920	−	87.1203i	1.10046	−	0.337675i
$259$		−	31.6061i		−	0.122031i
$260$	−23.6036	+	133.016i	−0.0907830	+	0.511602i
$261$	−269.202			−1.03143
$262$	151.847	+	494.860i	0.579568	+	1.88878i
$263$	−32.2976			−0.122804			−0.0614022	−	0.998113i	$-0.519557\pi$
$263$	−32.2976			−0.122804			−0.0614022	+	0.998113i	$0.519557\pi$
$264$	319.367	+	257.002i	1.20972	+	0.973491i
$265$	−210.453	+	216.570i	−0.794163	+	0.817244i
$266$	−2.24697	−	7.32274i	−0.00844725	−	0.0275291i
$267$	131.135			0.491140
$268$	−357.682	+	242.324i	−1.33463	+	0.904195i
$269$	−328.476			−1.22110			−0.610551	−	0.791977i	$-0.709052\pi$
$269$	−328.476			−1.22110			−0.610551	+	0.791977i	$0.709052\pi$
$270$	−505.584	−	258.953i	−1.87253	−	0.959084i
$271$		−	251.593i		−	0.928386i	−0.885734	−	0.464193i	$-0.846344\pi$
$271$		−	251.593i		−	0.928386i	0.885734	−	0.464193i	$-0.153656\pi$
$272$	369.493	+	147.531i	1.35843	+	0.542394i
$273$			31.7494i			0.116298i
$274$	86.6011	+	282.228i	0.316062	+	1.03003i
$275$	−239.366	+	6.85844i	−0.870421	+	0.0249398i
$276$	−353.967	+	239.807i	−1.28249	+	0.868868i
$277$			227.583i			0.821598i	0.911726	+	0.410799i	$0.134750\pi$
$277$			227.583i			0.821598i	−0.911726	+	0.410799i	$0.865250\pi$
$278$	−15.4115	−	50.2250i	−0.0554369	−	0.180666i
$279$		−	733.334i		−	2.62844i
$280$	34.8835	−	4.28083i	0.124584	−	0.0152887i
$281$	360.756			1.28383			0.641914	−	0.766777i	$-0.278141\pi$
$281$	360.756			1.28383			0.641914	+	0.766777i	$0.278141\pi$
$282$	640.705	−	196.599i	2.27200	−	0.697160i
$283$	6.35466			0.0224546			0.0112273	−	0.999937i	$-0.496426\pi$
$283$	6.35466			0.0224546			0.0112273	+	0.999937i	$0.496426\pi$
$284$	−68.6742	−	101.366i	−0.241810	−	0.356923i
$285$	−81.2539	+	83.6154i	−0.285101	+	0.293387i
$286$	−123.708	+	37.9596i	−0.432546	+	0.132726i
$287$	−6.65527			−0.0231891
$288$	−51.5198	+	625.670i	−0.178888	+	2.17247i
$289$	−329.323			−1.13952
$290$	−122.132	−	62.5541i	−0.421144	−	0.215704i
$291$		−	171.306i		−	0.588680i
$292$	−202.719	−	299.223i	−0.694244	−	1.02474i
$293$		−	431.765i		−	1.47360i	−0.676110	−	0.736801i	$-0.736336\pi$
$293$		−	431.765i		−	1.47360i	0.676110	−	0.736801i	$-0.263664\pi$
$294$	−493.301	+	151.369i	−1.67790	+	0.514859i
$295$	64.4205	−	66.2927i	0.218374	−	0.224721i
$296$	224.198	+	180.417i	0.757427	+	0.609518i
$297$		−	544.103i		−	1.83200i
$298$	534.579	−	164.035i	1.79389	−	0.550451i
$299$		−	134.963i		−	0.451380i
$300$	−312.614	−	434.116i	−1.04205	−	1.44705i
$301$	24.3887			0.0810257
$302$	107.831	+	351.415i	0.357057	+	1.16363i
$303$	227.345			0.750314
$304$	64.7702	+	25.8615i	0.213060	+	0.0850706i
$305$	21.1980	+	20.5994i	0.0695018	+	0.0675389i
$306$	−286.210	−	932.741i	−0.935326	−	3.04817i
$307$	−30.6928			−0.0999765			−0.0499882	−	0.998750i	$-0.515918\pi$
$307$	−30.6928			−0.0999765			−0.0499882	+	0.998750i	$0.515918\pi$
$308$	18.8817	+	27.8703i	0.0613042	+	0.0904879i
$309$	955.959			3.09372
$310$	170.403	−	332.699i	0.549689	−	1.07322i
$311$			444.911i			1.43058i	0.698826	+	0.715292i	$0.253706\pi$
$311$			444.911i			1.43058i	−0.698826	+	0.715292i	$0.746294\pi$
$312$	−225.215	−	181.235i	−0.721842	−	0.580882i
$313$		−	175.621i		−	0.561091i	−0.959841	−	0.280545i	$-0.909485\pi$
$313$		−	175.621i		−	0.561091i	0.959841	−	0.280545i	$-0.0905153\pi$
$314$	155.905	+	508.086i	0.496514	+	1.61811i
$315$	−61.8096	−	60.0640i	−0.196221	−	0.190679i
$316$	71.9949	+	106.268i	0.227832	+	0.336290i
$317$		−	59.9791i		−	0.189209i	−0.995515	−	0.0946043i	$-0.969841\pi$
$317$		−	59.9791i		−	0.189209i	0.995515	−	0.0946043i	$-0.0301586\pi$
$318$	−189.560	−	617.765i	−0.596101	−	1.94266i
$319$		−	131.437i		−	0.412027i
$320$	−168.760	+	271.883i	−0.527373	+	0.849634i
$321$	−514.375			−1.60241
$322$	−33.5662	+	10.2997i	−0.104243	+	0.0319868i
$323$	−108.389			−0.335569
$324$	421.614	−	285.637i	1.30128	−	0.881596i
$325$	168.799	−	4.83651i	0.519381	−	0.0148816i
$326$	−345.410	+	105.989i	−1.05954	+	0.325118i
$327$	−743.716			−2.27436
$328$	37.9903	−	47.2092i	0.115824	−	0.143931i
$329$	55.0366			0.167284
$330$	233.595	−	456.074i	0.707862	−	1.38204i
$331$		−	292.191i		−	0.882753i	−0.897322	−	0.441377i	$-0.854490\pi$
$331$		−	292.191i		−	0.882753i	0.897322	−	0.441377i	$-0.145510\pi$
$332$	−501.484	+	339.748i	−1.51049	+	1.02334i
$333$		−	705.713i		−	2.11926i
$334$	351.840	−	107.962i	1.05341	−	0.323238i
$335$	387.302	+	376.363i	1.15612	+	1.12347i
$336$	−27.8872	+	69.8437i	−0.0829977	+	0.207868i
$337$			492.646i			1.46186i	0.682453	+	0.730929i	$0.260913\pi$
$337$			492.646i			1.46186i	−0.682453	+	0.730929i	$0.739087\pi$
$338$	−235.892	+	72.3830i	−0.697905	+	0.214151i
$339$		−	930.282i		−	2.74419i
$340$	86.8917	−	489.672i	0.255564	−	1.44021i
$341$	358.046			1.04999
$342$	−50.1711	−	163.505i	−0.146699	−	0.478084i
$343$	−85.4275			−0.249060
$344$	−139.218	+	173.002i	−0.404704	+	0.502911i
$345$	383.279	+	372.455i	1.11095	+	1.07958i
$346$	160.489	+	523.024i	0.463841	+	1.51163i
$347$	65.0958			0.187596			0.0937980	−	0.995591i	$-0.470099\pi$
$347$	65.0958			0.187596			0.0937980	+	0.995591i	$0.470099\pi$
$348$	243.093	−	164.692i	0.698544	−	0.473253i
$349$	32.4044			0.0928493			0.0464247	−	0.998922i	$-0.485217\pi$
$349$	32.4044			0.0928493			0.0464247	+	0.998922i	$0.485217\pi$
$350$	−14.0848	−	41.6125i	−0.0402424	−	0.118893i
$351$			383.696i			1.09315i
$352$	−305.480	−	25.1543i	−0.867841	−	0.0714610i
$353$		−	222.380i		−	0.629971i	−0.949097	−	0.314985i	$-0.898000\pi$
$353$		−	222.380i		−	0.629971i	0.949097	−	0.314985i	$-0.102000\pi$
$354$	58.0250	+	189.100i	0.163912	+	0.534181i
$355$	−106.661	+	109.760i	−0.300452	+	0.309184i
$356$	−81.1762	+	54.9957i	−0.228023	+	0.154482i
$357$		−	116.879i		−	0.327392i
$358$	−131.242	−	427.709i	−0.366597	−	1.19472i
$359$		−	403.164i		−	1.12302i	−0.827470	−	0.561510i	$-0.810221\pi$
$359$		−	403.164i		−	1.12302i	0.827470	−	0.561510i	$-0.189779\pi$
$360$	778.892	−	95.5838i	2.16359	−	0.265511i
$361$	−19.0000			−0.0526316
$362$	−477.262	+	146.447i	−1.31840	+	0.404550i
$363$	−156.482			−0.431080
$364$	−13.3152	−	19.6539i	−0.0365802	−	0.0539941i
$365$	−314.851	+	324.002i	−0.862606	+	0.887676i
$366$	−60.4675	+	18.5543i	−0.165212	+	0.0506949i
$367$	−647.056			−1.76310			−0.881548	−	0.472094i	$-0.843498\pi$
$367$	−647.056			−1.76310			−0.881548	+	0.472094i	$0.843498\pi$
$368$	118.545	−	296.896i	0.322133	−	0.806783i
$369$	−148.601			−0.402714
$370$	163.985	−	320.168i	0.443204	−	0.865319i
$371$		−	53.0661i		−	0.143035i
$372$	448.637	+	662.209i	1.20601	+	1.78013i
$373$		−	22.5179i		−	0.0603698i	−0.999544	−	0.0301849i	$-0.990390\pi$
$373$		−	22.5179i		−	0.0603698i	0.999544	−	0.0301849i	$-0.00960962\pi$
$374$	455.406	−	139.740i	1.21766	−	0.373637i
$375$	−452.097	+	492.718i	−1.20559	+	1.31391i
$376$	−314.165	+	390.402i	−0.835546	+	1.03830i
$377$			92.6879i			0.245857i
$378$	95.4283	−	29.2820i	0.252456	−	0.0774656i
$379$			309.538i			0.816724i	0.912820	+	0.408362i	$0.133900\pi$
$379$			309.538i			0.816724i	−0.912820	+	0.408362i	$0.866100\pi$
$380$	15.2317	−	85.8370i	0.0400833	−	0.225887i
$381$	−702.963			−1.84505
$382$	100.687	+	328.134i	0.263579	+	0.858990i
$383$	267.637			0.698792			0.349396	−	0.936975i	$-0.386387\pi$
$383$	267.637			0.698792			0.349396	+	0.936975i	$0.386387\pi$
$384$	−336.248	−	596.507i	−0.875647	−	1.55340i
$385$	29.3259	−	30.1782i	0.0761712	−	0.0783850i
$386$	48.2974	+	157.398i	0.125123	+	0.407768i
$387$	544.560			1.40713
$388$	71.8430	+	106.044i	0.185162	+	0.273308i
$389$	263.012			0.676122			0.338061	−	0.941124i	$-0.390229\pi$
$389$	263.012			0.676122			0.338061	+	0.941124i	$0.390229\pi$
$390$	−164.729	+	321.620i	−0.422382	+	0.824666i
$391$			496.836i			1.27068i
$392$	241.887	−	300.584i	0.617058	−	0.766797i
$393$			1384.57i			3.52307i
$394$	−84.0774	−	274.003i	−0.213394	−	0.695439i
$395$	111.818	−	115.068i	0.283084	−	0.291311i
$396$	421.597	+	622.297i	1.06464	+	1.57146i
$397$			707.405i			1.78188i	0.454125	+	0.890938i	$0.349952\pi$
$397$			707.405i			1.78188i	−0.454125	+	0.890938i	$0.650048\pi$
$398$	154.447	+	503.333i	0.388057	+	1.26465i
$399$		−	20.4883i		−	0.0513491i
$400$	375.579	+	137.625i	0.938946	+	0.344063i
$401$	−568.903			−1.41871			−0.709355	−	0.704851i	$-0.751014\pi$
$401$	−568.903			−1.41871			−0.709355	+	0.704851i	$0.751014\pi$
$402$	−1104.78	+	338.999i	−2.74821	+	0.843282i
$403$	−252.491			−0.626528
$404$	−140.733	+	95.3449i	−0.348350	+	0.236002i
$405$	−456.528	−	443.634i	−1.12723	−	1.09539i
$406$	23.0522	−	7.07353i	0.0567789	−	0.0174225i
$407$	344.561			0.846586
$408$	829.081	+	667.180i	2.03206	+	1.63524i
$409$	750.852			1.83583			0.917913	−	0.396783i	$-0.129873\pi$
$409$	750.852			1.83583			0.917913	+	0.396783i	$0.129873\pi$
$410$	−67.4175	−	34.5302i	−0.164433	−	0.0842201i
$411$			789.645i			1.92128i
$412$	−591.768	+	400.914i	−1.43633	+	0.973092i
$413$			16.2437i			0.0393310i
$414$	−749.479	+	229.976i	−1.81033	+	0.555498i
$415$	543.012	+	527.676i	1.30846	+	1.27151i
$416$	215.422	+	17.7386i	0.517841	+	0.0426408i
$417$		−	140.525i		−	0.336989i
$418$	79.8303	−	24.4958i	0.190982	−	0.0586023i
$419$			428.115i			1.02176i	0.859653	+	0.510878i	$0.170679\pi$
$419$			428.115i			1.02176i	−0.859653	+	0.510878i	$0.829321\pi$
$420$	92.5607	+	16.4248i	0.220383	+	0.0391066i
$421$	−152.750			−0.362828			−0.181414	−	0.983407i	$-0.558067\pi$
$421$	−152.750			−0.362828			−0.181414	+	0.983407i	$0.558067\pi$
$422$	14.3146	+	46.6505i	0.0339209	+	0.110546i
$423$	1228.88			2.90515
$424$	376.424	+	302.917i	0.887793	+	0.714426i
$425$	−621.397	+	17.8046i	−1.46211	+	0.0418932i
$426$	−96.0717	−	313.092i	−0.225520	−	0.734958i
$427$	−5.19416			−0.0121643
$428$	318.413	−	215.721i	0.743957	−	0.504020i
$429$	−346.123			−0.806813
$430$	247.056	+	126.539i	0.574549	+	0.294276i
$431$		−	63.8836i		−	0.148222i	−0.997250	−	0.0741109i	$-0.976388\pi$
$431$		−	63.8836i		−	0.148222i	0.997250	−	0.0741109i	$-0.0236119\pi$
$432$	−337.021	+	844.071i	−0.780141	+	1.95387i
$433$		−	707.397i		−	1.63371i	−0.576842	−	0.816856i	$-0.695715\pi$
$433$		−	707.397i		−	1.63371i	0.576842	−	0.816856i	$-0.304285\pi$
$434$	19.2690	+	62.7965i	0.0443986	+	0.144692i
$435$	−263.224	−	255.790i	−0.605112	−	0.588023i
$436$	460.383	−	311.903i	1.05592	−	0.715373i
$437$			87.0929i			0.199297i
$438$	−283.594	−	924.215i	−0.647474	−	2.11008i
$439$			599.605i			1.36584i	0.730492	+	0.682921i	$0.239291\pi$
$439$			599.605i			1.36584i	−0.730492	+	0.682921i	$0.760709\pi$
$440$	46.6683	+	380.290i	0.106064	+	0.864295i
$441$	−946.155			−2.14548
$442$	−321.148	+	98.5437i	−0.726579	+	0.222950i
$443$	301.235			0.679989			0.339994	−	0.940427i	$-0.389575\pi$
$443$	301.235			0.679989			0.339994	+	0.940427i	$0.389575\pi$
$444$	431.740	+	637.268i	0.972387	+	1.43529i
$445$	87.8985	+	85.4160i	0.197525	+	0.191946i
$446$	235.444	−	72.2455i	0.527901	−	0.161985i
$447$	1495.70			3.34608
$448$	−12.0283	−	54.9308i	−0.0268489	−	0.122613i
$449$	−300.227			−0.668657			−0.334328	−	0.942457i	$-0.608509\pi$
$449$	−300.227			−0.668657			−0.334328	+	0.942457i	$0.608509\pi$
$450$	−314.491	−	929.138i	−0.698870	−	2.06475i
$451$		−	72.5538i		−	0.160873i
$452$	390.145	+	575.872i	0.863153	+	1.27405i
$453$			983.225i			2.17047i
$454$	227.129	−	69.6941i	0.500284	−	0.153511i
$455$	−20.6804	+	21.2814i	−0.0454514	+	0.0467723i
$456$	145.334	+	116.953i	0.318714	+	0.256476i
$457$		−	490.755i		−	1.07386i	−0.843626	−	0.536931i	$-0.819584\pi$
$457$		−	490.755i		−	1.07386i	0.843626	−	0.536931i	$-0.180416\pi$
$458$	287.453	−	88.2044i	0.627626	−	0.192586i
$459$		−	1412.50i		−	3.07734i
$460$	−393.463	−	69.8194i	−0.855354	−	0.151781i
$461$	189.799			0.411711			0.205855	−	0.978582i	$-0.434002\pi$
$461$	189.799			0.411711			0.205855	+	0.978582i	$0.434002\pi$
$462$	26.4145	+	86.0834i	0.0571743	+	0.186328i
$463$	−100.765			−0.217635			−0.108818	−	0.994062i	$-0.534706\pi$
$463$	−100.765			−0.217635			−0.108818	+	0.994062i	$0.534706\pi$
$464$	−81.4128	+	203.899i	−0.175459	+	0.439437i
$465$	696.797	−	717.047i	1.49849	−	1.54204i
$466$	−71.9521	−	234.488i	−0.154404	−	0.503192i
$467$	215.942			0.462402			0.231201	−	0.972906i	$-0.425734\pi$
$467$	215.942			0.462402			0.231201	+	0.972906i	$0.425734\pi$
$468$	−297.307	−	438.838i	−0.635271	−	0.937689i
$469$	−94.9006			−0.202347
$470$	557.517	+	285.552i	1.18621	+	0.607557i
$471$			1421.57i			3.01820i
$472$	−115.225	−	92.7239i	−0.244120	−	0.196449i
$473$			265.878i			0.562111i
$474$	100.717	+	328.231i	0.212483	+	0.692471i
$475$	−108.928	+	3.12106i	−0.229322	+	0.00657064i
$476$	49.0172	+	72.3516i	0.102977	+	0.151999i
$477$		−	1184.88i		−	2.48402i
$478$	−10.0513	−	32.7566i	−0.0210278	−	0.0685284i
$479$		−	495.217i		−	1.03386i	−0.856029	−	0.516928i	$-0.827075\pi$
$479$		−	495.217i		−	1.03386i	0.856029	−	0.516928i	$-0.172925\pi$
$480$	−644.873	+	562.822i	−1.34349	+	1.17255i
$481$	−242.981			−0.505158
$482$	−467.091	+	143.326i	−0.969068	+	0.297357i
$483$	−93.9149			−0.194441
$484$	96.8672	−	65.6261i	0.200139	−	0.135591i
$485$	111.582	−	114.825i	0.230066	−	0.236753i
$486$	324.754	−	99.6502i	0.668218	−	0.205042i
$487$	−701.060			−1.43955			−0.719774	−	0.694208i	$-0.755755\pi$
$487$	−701.060			−1.43955			−0.719774	+	0.694208i	$0.755755\pi$
$488$	29.6498	−	36.8448i	0.0607578	−	0.0755016i
$489$	−966.424			−1.97633
$490$	−429.252	−	219.856i	−0.876024	−	0.448687i
$491$		−	436.977i		−	0.889973i	−0.895537	−	0.444986i	$-0.853209\pi$
$491$		−	436.977i		−	0.889973i	0.895537	−	0.444986i	$-0.146791\pi$
$492$	134.189	−	90.9110i	0.272742	−	0.184778i
$493$		−	341.211i		−	0.692112i
$494$	−56.2956	+	17.2742i	−0.113959	+	0.0349680i
$495$	654.799	−	673.830i	1.32283	−	1.36127i
$496$	−555.440	−	221.776i	−1.11984	−	0.447130i
$497$		−	26.8946i		−	0.0541139i
$498$	−1548.94	+	475.290i	−3.11033	+	0.954398i
$499$		−	437.151i		−	0.876053i	−0.898962	−	0.438027i	$-0.855678\pi$
$499$		−	437.151i		−	0.876053i	0.898962	−	0.438027i	$-0.144322\pi$
$500$	73.2236	−	494.609i	0.146447	−	0.989218i
$501$	984.414			1.96490
$502$	32.4631	+	105.795i	0.0646675	+	0.210747i
$503$	371.547			0.738662			0.369331	−	0.929298i	$-0.379587\pi$
$503$	371.547			0.738662			0.369331	+	0.929298i	$0.379587\pi$
$504$	−86.4534	+	107.433i	−0.171535	+	0.213160i
$505$	152.388	+	148.084i	0.301758	+	0.293236i
$506$	−112.285	−	365.929i	−0.221906	−	0.723180i
$507$	−660.002			−1.30178
$508$	435.155	−	294.811i	0.856604	−	0.580337i
$509$	−139.802			−0.274660			−0.137330	−	0.990525i	$-0.543852\pi$
$509$	−139.802			−0.274660			−0.137330	+	0.990525i	$0.543852\pi$
$510$	606.415	−	1183.98i	1.18905	−	2.32152i
$511$		−	79.3901i		−	0.155362i
$512$	458.313	+	228.239i	0.895143	+	0.445779i
$513$		−	247.604i		−	0.482658i
$514$	274.017	+	893.006i	0.533107	+	1.73737i
$515$	640.772	+	622.676i	1.24422	+	1.20908i
$516$	−491.745	+	333.150i	−0.952993	+	0.645639i
$517$			599.992i			1.16053i
$518$	18.5432	+	60.4313i	0.0357978	+	0.116663i
$519$			1463.37i			2.81959i
$520$	−32.9101	−	268.177i	−0.0632886	−	0.515725i
$521$	−976.326			−1.87395			−0.936973	−	0.349402i	$-0.886385\pi$
$521$	−976.326			−1.87395			−0.936973	+	0.349402i	$0.886385\pi$
$522$	514.718	−	157.940i	0.986050	−	0.302568i
$523$	203.747			0.389573			0.194787	−	0.980846i	$-0.437599\pi$
$523$	203.747			0.389573			0.194787	+	0.980846i	$0.437599\pi$
$524$	−580.666	−	857.089i	−1.10814	−	1.63567i
$525$	−3.36553	−	117.460i	−0.00641053	−	0.223734i
$526$	61.7533	−	18.9489i	0.117402	−	0.0360245i
$527$	929.493			1.76374
$528$	−761.415	−	304.018i	−1.44207	−	0.575792i
$529$	−129.780			−0.245332
$530$	275.328	−	537.556i	0.519487	−	1.01426i
$531$			362.695i			0.683042i
$532$	8.59246	+	12.6829i	0.0161512	+	0.0238400i
$533$			51.1643i			0.0959930i
$534$	−250.731	+	76.9362i	−0.469533	+	0.144075i
$535$	−344.782	−	335.044i	−0.644451	−	0.626251i
$536$	541.721	−	673.178i	1.01067	−	1.25593i
$537$		−	1196.69i		−	2.22847i
$538$	628.050	−	192.716i	1.16738	−	0.358208i
$539$		−	461.955i		−	0.857059i
$540$	1118.61	+	198.496i	2.07150	+	0.367585i
$541$	246.917			0.456408			0.228204	−	0.973613i	$-0.426715\pi$
$541$	246.917			0.456408			0.228204	+	0.973613i	$0.426715\pi$
$542$	147.609	+	481.048i	0.272341	+	0.887542i
$543$	−1335.33			−2.45917
$544$	−793.031	−	65.3009i	−1.45778	−	0.120038i
$545$	−498.507	−	484.428i	−0.914692	−	0.888860i
$546$	−18.6273	−	60.7053i	−0.0341159	−	0.111182i
$547$	−416.599			−0.761606			−0.380803	−	0.924656i	$-0.624352\pi$
$547$	−416.599			−0.761606			−0.380803	+	0.924656i	$0.624352\pi$
$548$	−331.165	−	488.814i	−0.604315	−	0.891997i
$549$	−115.977			−0.211251
$550$	453.646	−	153.549i	0.824812	−	0.279179i
$551$		−	59.8126i		−	0.108553i
$552$	536.094	−	666.186i	0.971185	−	1.20686i
$553$			28.1951i			0.0509857i
$554$	−133.522	−	435.141i	−0.241015	−	0.785452i
$555$	670.552	−	690.041i	1.20820	−	1.24332i
$556$	58.9338	+	86.9889i	0.105996	+	0.156455i
$557$		−	483.169i		−	0.867448i	−0.901046	−	0.433724i	$-0.857199\pi$
$557$		−	483.169i		−	0.867448i	0.901046	−	0.433724i	$-0.142801\pi$
$558$	430.245	+	1402.14i	0.771048	+	2.51280i
$559$		−	187.495i		−	0.335412i
$560$	−64.1862	+	28.6511i	−0.114618	+	0.0511626i
$561$	1274.18			2.27126
$562$	−689.769	+	211.654i	−1.22735	+	0.376609i
$563$	−433.127			−0.769319			−0.384659	−	0.923059i	$-0.625681\pi$
$563$	−433.127			−0.769319			−0.384659	+	0.923059i	$0.625681\pi$
$564$	−1109.69	+	751.800i	−1.96754	+	1.33298i
$565$	605.950	−	623.561i	1.07248	−	1.10365i
$566$	−12.1502	+	3.72826i	−0.0214668	+	0.00658703i
$567$	111.863			0.197289
$568$	190.777	+	153.522i	0.335875	+	0.270286i
$569$	−642.028			−1.12834			−0.564172	−	0.825657i	$-0.690805\pi$
$569$	−642.028			−1.12834			−0.564172	+	0.825657i	$0.690805\pi$
$570$	106.301	−	207.545i	0.186494	−	0.364114i
$571$		−	466.041i		−	0.816183i	−0.912941	−	0.408092i	$-0.866194\pi$
$571$		−	466.041i		−	0.816183i	0.912941	−	0.408092i	$-0.133806\pi$
$572$	214.260	−	145.158i	0.374581	−	0.253773i
$573$			918.086i			1.60224i
$574$	12.7250	−	3.90463i	0.0221689	−	0.00680249i
$575$	14.3064	+	499.307i	0.0248807	+	0.868360i
$576$	−268.573	−	1226.52i	−0.466272	−	2.12937i
$577$		−	351.831i		−	0.609758i	−0.952391	−	0.304879i	$-0.901384\pi$
$577$		−	351.831i		−	0.609758i	0.952391	−	0.304879i	$-0.0986161\pi$
$578$	629.668	−	193.213i	1.08939	−	0.334278i
$579$			440.385i			0.760595i
$580$	270.218	+	47.9498i	0.465893	+	0.0826720i
$581$	−133.054			−0.229009
$582$	100.505	+	327.539i	0.172688	+	0.562781i
$583$	578.510			0.992299
$584$	563.154	+	453.182i	0.964305	+	0.775997i
$585$	−461.759	+	475.179i	−0.789331	+	0.812272i
$586$	253.315	+	825.540i	0.432279	+	1.40877i
$587$	−460.426			−0.784371			−0.392186	−	0.919886i	$-0.628281\pi$
$587$	−460.426			−0.784371			−0.392186	+	0.919886i	$0.628281\pi$
$588$	854.390	−	578.837i	1.45304	−	0.984416i
$589$	162.935			0.276631
$590$	−84.2789	+	164.548i	−0.142846	+	0.278894i
$591$		−	766.633i		−	1.29718i
$592$	−534.520	−	213.423i	−0.902905	−	0.360512i
$593$		−	355.866i		−	0.600111i	−0.953922	−	0.300056i	$-0.902995\pi$
$593$		−	355.866i		−	0.600111i	0.953922	−	0.300056i	$-0.0970052\pi$
$594$	319.224	+	1040.33i	0.537413	+	1.75140i
$595$	76.1305	−	78.3431i	0.127950	−	0.131669i
$596$	−925.882	+	627.272i	−1.55349	+	1.05247i
$597$			1408.27i			2.35892i
$598$	79.1821	+	258.050i	0.132412	+	0.431521i
$599$		−	439.952i		−	0.734478i	−0.930127	−	0.367239i	$-0.880303\pi$
$599$		−	439.952i		−	0.734478i	0.930127	−	0.367239i	$-0.119697\pi$
$600$	852.416	+	646.624i	1.42069	+	1.07771i
$601$	350.989			0.584008			0.292004	−	0.956417i	$-0.405678\pi$
$601$	350.989			0.584008			0.292004	+	0.956417i	$0.405678\pi$
$602$	−46.6315	+	14.3088i	−0.0774610	+	0.0237688i
$603$	−2118.97			−3.51405
$604$	−412.349	−	608.646i	−0.682697	−	1.00769i
$605$	−104.889	−	101.927i	−0.173370	−	0.168474i
$606$	−434.686	+	133.383i	−0.717304	+	0.220104i
$607$	51.0652			0.0841271			0.0420636	−	0.999115i	$-0.486607\pi$
$607$	51.0652			0.0841271			0.0420636	+	0.999115i	$0.486607\pi$
$608$	−139.014	−	11.4469i	−0.228642	−	0.0188272i
$609$	64.4978			0.105908
$610$	−52.6165	−	26.9494i	−0.0862565	−	0.0441793i
$611$		−	423.109i		−	0.692486i
$612$	1094.47	+	1615.49i	1.78835	+	2.63969i
$613$		−	37.2376i		−	0.0607465i	−0.999539	−	0.0303733i	$-0.990330\pi$
$613$		−	37.2376i		−	0.0607465i	0.999539	−	0.0303733i	$-0.00966960\pi$
$614$	58.6849	−	18.0074i	0.0955781	−	0.0293280i
$615$	−145.301	−	141.197i	−0.236262	−	0.229589i
$616$	−52.4534	−	42.2104i	−0.0851517	−	0.0685234i
$617$		−	593.626i		−	0.962116i	−0.876689	−	0.481058i	$-0.840253\pi$
$617$		−	593.626i		−	0.962116i	0.876689	−	0.481058i	$-0.159747\pi$
$618$	−1827.80	+	560.859i	−2.95761	+	0.907538i
$619$			28.8028i			0.0465312i	0.999729	+	0.0232656i	$0.00740633\pi$
$619$			28.8028i			0.0465312i	−0.999729	+	0.0232656i	$0.992594\pi$
$620$	−130.620	+	736.099i	−0.210677	+	1.18726i
$621$	−1134.98			−1.82766
$622$	−261.028	−	850.676i	−0.419660	−	1.36765i
$623$	−21.5378			−0.0345711
$624$	536.943	+	214.391i	0.860486	+	0.343575i
$625$	−623.975	+	35.7863i	−0.998359	+	0.0572580i
$626$	103.037	+	335.790i	0.164595	+	0.536406i
$627$	223.357			0.356231
$628$	−596.186	−	879.997i	−0.949340	−	1.40127i
$629$	894.484			1.42207
$630$	153.420	+	78.5795i	0.243524	+	0.124729i
$631$		−	130.361i		−	0.206594i	−0.994651	−	0.103297i	$-0.967061\pi$
$631$		−	130.361i		−	0.206594i	0.994651	−	0.103297i	$-0.0329392\pi$
$632$	−200.002	−	160.946i	−0.316459	−	0.254661i
$633$			130.523i			0.206198i
$634$	35.1896	+	114.681i	0.0555041	+	0.180884i
$635$	−471.191	−	457.883i	−0.742032	−	0.721076i
$636$	724.882	+	1069.96i	1.13975	+	1.68233i
$637$			325.767i			0.511408i
$638$	77.1135	+	251.308i	0.120868	+	0.393900i
$639$		−	600.512i		−	0.939769i
$640$	163.157	−	618.854i	0.254933	−	0.966959i
$641$	−43.8092			−0.0683451			−0.0341725	−	0.999416i	$-0.510880\pi$
$641$	−43.8092			−0.0683451			−0.0341725	+	0.999416i	$0.510880\pi$
$642$	983.490	−	301.782i	1.53192	−	0.470066i
$643$	1234.51			1.91992			0.959958	−	0.280144i	$-0.0903823\pi$
$643$	1234.51			1.91992			0.959958	+	0.280144i	$0.0903823\pi$
$644$	58.1362	−	39.3864i	0.0902736	−	0.0611590i
$645$	532.466	+	517.428i	0.825529	+	0.802214i
$646$	207.241	−	63.5914i	0.320806	−	0.0984387i
$647$	118.953			0.183853			0.0919263	−	0.995766i	$-0.470698\pi$
$647$	118.953			0.183853			0.0919263	+	0.995766i	$0.470698\pi$
$648$	−638.547	+	793.501i	−0.985413	+	1.22454i
$649$	−177.084			−0.272857
$650$	−319.907	+	108.281i	−0.492165	+	0.166586i
$651$			175.698i			0.269890i
$652$	598.245	−	405.303i	0.917554	−	0.621630i
$653$		−	427.567i		−	0.654774i	−0.944890	−	0.327387i	$-0.893832\pi$
$653$		−	427.567i		−	0.654774i	0.944890	−	0.327387i	$-0.106168\pi$
$654$	1421.99	−	436.336i	2.17430	−	0.667181i
$655$	−901.855	+	928.065i	−1.37688	+	1.41689i
$656$	−44.9403	+	112.553i	−0.0685066	+	0.171575i
$657$		−	1772.65i		−	2.69810i
$658$	−105.231	+	32.2898i	−0.159925	+	0.0490727i
$659$			227.831i			0.345722i	0.984946	+	0.172861i	$0.0553012\pi$
$659$			227.831i			0.345722i	−0.984946	+	0.172861i	$0.944699\pi$
$660$	−179.058	+	1009.07i	−0.271300	+	1.52889i
$661$	−146.365			−0.221429			−0.110715	−	0.993852i	$-0.535314\pi$
$661$	−146.365			−0.221429			−0.110715	+	0.993852i	$0.535314\pi$
$662$	171.428	+	558.673i	0.258954	+	0.843917i
$663$	−898.540			−1.35526
$664$	759.513	−	943.821i	1.14385	−	1.42142i
$665$	13.3453	−	13.7331i	0.0200681	−	0.0206513i
$666$	414.040	+	1349.33i	0.621682	+	2.02602i
$667$	−274.171			−0.411051
$668$	−609.382	+	412.848i	−0.912249	+	0.618035i
$669$	658.748			0.984676
$670$	−961.337	−	492.382i	−1.43483	−	0.734899i
$671$		−	56.6251i		−	0.0843892i
$672$	12.3436	−	149.903i	0.0183684	−	0.223070i
$673$			330.405i			0.490943i	0.969404	+	0.245472i	$0.0789428\pi$
$673$			330.405i			0.490943i	−0.969404	+	0.245472i	$0.921057\pi$
$674$	−289.034	−	941.945i	−0.428834	−	1.39755i
$675$	−40.6729	−	1419.52i	−0.0602562	−	2.10300i
$676$	408.561	−	276.794i	0.604381	−	0.409459i
$677$			369.084i			0.545176i	0.962131	+	0.272588i	$0.0878796\pi$
$677$			369.084i			0.545176i	−0.962131	+	0.272588i	$0.912120\pi$
$678$	545.794	+	1778.71i	0.805005	+	2.62346i
$679$			28.1356i			0.0414368i
$680$	121.152	+	987.238i	0.178164	+	1.45182i
$681$	635.484			0.933163
$682$	−684.588	+	210.065i	−1.00379	+	0.308013i
$683$	288.174			0.421924			0.210962	−	0.977494i	$-0.432340\pi$
$683$	288.174			0.421924			0.210962	+	0.977494i	$0.432340\pi$
$684$	191.855	+	283.188i	0.280490	+	0.414017i
$685$	−514.345	+	529.293i	−0.750868	+	0.772691i
$686$	163.338	−	50.1201i	0.238103	−	0.0730613i
$687$	804.264			1.17069
$688$	164.687	−	412.460i	0.239371	−	0.599505i
$689$	−407.960			−0.592105
$690$	−951.352	−	487.268i	−1.37877	−	0.706186i
$691$		−	355.074i		−	0.513856i	−0.966431	−	0.256928i	$-0.917290\pi$
$691$		−	355.074i		−	0.513856i	0.966431	−	0.256928i	$-0.0827103\pi$
$692$	−613.713	−	905.869i	−0.886868	−	1.30906i
$693$			165.109i			0.238252i
$694$	−124.464	+	38.1915i	−0.179343	+	0.0550310i
$695$	91.5324	−	94.1926i	0.131701	−	0.135529i
$696$	−368.172	+	457.515i	−0.528983	+	0.657349i
$697$		−	188.351i		−	0.270230i
$698$	−61.9576	+	19.0116i	−0.0887645	+	0.0272372i
$699$		−	656.073i		−	0.938587i
$700$	51.3443	+	71.2999i	0.0733490	+	0.101857i
$701$	−600.600			−0.856776			−0.428388	−	0.903595i	$-0.640918\pi$
$701$	−600.600			−0.856776			−0.428388	+	0.903595i	$0.640918\pi$
$702$	−225.114	−	733.632i	−0.320675	−	1.04506i
$703$	156.799			0.223042
$704$	598.839	−	131.129i	0.850624	−	0.186263i
$705$	1201.59	+	1167.65i	1.70438	+	1.65624i
$706$	130.470	+	425.192i	0.184801	+	0.602256i
$707$	−37.3396			−0.0528141
$708$	−221.889	−	327.518i	−0.313403	−	0.462597i
$709$	89.7244			0.126551			0.0632753	−	0.997996i	$-0.479845\pi$
$709$	89.7244			0.126551			0.0632753	+	0.997996i	$0.479845\pi$
$710$	139.540	−	272.441i	0.196535	−	0.383719i
$711$			629.550i			0.885443i
$712$	122.944	−	152.778i	0.172674	−	0.214576i
$713$		−	746.869i		−	1.04750i
$714$	68.5726	+	223.474i	0.0960400	+	0.312989i
$715$	−232.004	−	225.451i	−0.324480	−	0.315316i
$716$	501.871	+	740.785i	0.700938	+	1.03462i
$717$		−	91.6496i		−	0.127824i
$718$	236.535	+	770.854i	0.329436	+	1.07361i
$719$			67.3848i			0.0937201i	0.998901	+	0.0468601i	$0.0149215\pi$
$719$			67.3848i			0.0937201i	−0.998901	+	0.0468601i	$0.985079\pi$
$720$	−1433.17	+	639.731i	−1.99052	+	0.888515i
$721$	−157.009			−0.217765
$722$	36.3282	−	11.1472i	0.0503161	−	0.0154394i
$723$	−1306.87			−1.80757
$724$	826.610	−	560.017i	1.14173	−	0.773503i
$725$	−9.82518	−	342.908i	−0.0135520	−	0.472977i
$726$	299.196	−	91.8077i	0.412115	−	0.126457i
$727$	−309.592			−0.425848			−0.212924	−	0.977069i	$-0.568299\pi$
$727$	−309.592			−0.425848			−0.212924	+	0.977069i	$0.568299\pi$
$728$	36.9897	+	29.7664i	0.0508100	+	0.0408879i
$729$	−237.208			−0.325388
$730$	411.908	−	804.217i	0.564258	−	1.10167i
$731$			690.224i			0.944219i
$732$	104.729	−	70.9522i	0.143072	−	0.0969292i
$733$		−	696.629i		−	0.950380i	−0.879883	−	0.475190i	$-0.842379\pi$
$733$		−	696.629i		−	0.950380i	0.879883	−	0.475190i	$-0.157621\pi$
$734$	1237.18	−	379.626i	1.68553	−	0.517202i
$735$	−925.143	−	899.015i	−1.25870	−	1.22315i
$736$	−52.4708	+	637.219i	−0.0712918	+	0.865786i
$737$		−	1034.58i		−	1.40377i
$738$	284.127	−	87.1840i	0.384996	−	0.118135i
$739$			730.320i			0.988254i	0.869390	+	0.494127i	$0.164512\pi$
$739$			730.320i			0.988254i	−0.869390	+	0.494127i	$0.835488\pi$
$740$	−125.700	+	708.375i	−0.169865	+	0.957263i
$741$	−157.509			−0.212563
$742$	31.1337	+	101.463i	0.0419592	+	0.136742i
$743$	−443.701			−0.597175			−0.298588	−	0.954382i	$-0.596516\pi$
$743$	−443.701			−0.597175			−0.298588	+	0.954382i	$0.596516\pi$
$744$	−1246.32	−	1002.94i	−1.67516	−	1.34803i
$745$	1002.55	+	974.241i	1.34571	+	1.30771i
$746$	13.2112	+	43.0546i	0.0177094	+	0.0577139i
$747$	−2970.88			−3.97709
$748$	−788.755	+	534.370i	−1.05449	+	0.714399i
$749$	84.4818			0.112793
$750$	575.338	−	1207.33i	0.767117	−	1.60977i
$751$		−	524.319i		−	0.698161i	−0.937093	−	0.349081i	$-0.886494\pi$
$751$		−	524.319i		−	0.698161i	0.937093	−	0.349081i	$-0.113506\pi$
$752$	371.639	−	930.773i	0.494201	−	1.23773i
$753$			296.004i			0.393100i
$754$	−54.3798	−	177.220i	−0.0721217	−	0.235040i
$755$	−640.435	+	659.048i	−0.848259	+	0.872912i
$756$	−165.280	+	111.975i	−0.218625	+	0.148115i
$757$			682.519i			0.901611i	0.892622	+	0.450805i	$0.148863\pi$
$757$			682.519i			0.901611i	−0.892622	+	0.450805i	$0.851137\pi$
$758$	−181.605	−	591.841i	−0.239585	−	0.780793i
$759$		−	1023.83i		−	1.34892i
$760$	21.2372	+	173.058i	0.0279437	+	0.227708i
$761$	122.801			0.161368			0.0806840	−	0.996740i	$-0.474290\pi$
$761$	122.801			0.161368			0.0806840	+	0.996740i	$0.474290\pi$
$762$	1344.07	−	412.426i	1.76387	−	0.541242i
$763$	122.149			0.160091
$764$	−385.031	−	568.323i	−0.503967	−	0.743878i
$765$	1699.87	−	1749.27i	2.22205	−	2.28663i
$766$	−511.726	+	157.022i	−0.668049	+	0.204990i
$767$	124.878			0.162814
$768$	992.879	+	943.252i	1.29281	+	1.22819i
$769$	662.384			0.861357			0.430679	−	0.902505i	$-0.358274\pi$
$769$	662.384			0.861357			0.430679	+	0.902505i	$0.358274\pi$
$770$	−38.3660	+	74.9065i	−0.0498260	+	0.0972812i
$771$			2498.54i			3.24065i
$772$	−184.690	−	272.611i	−0.239236	−	0.353124i
$773$		−	133.167i		−	0.172273i	−0.996283	−	0.0861367i	$-0.972548\pi$
$773$		−	133.167i		−	0.172273i	0.996283	−	0.0861367i	$-0.0274522\pi$
$774$	−1041.20	+	319.492i	−1.34523	+	0.412780i
$775$	934.115	−	26.7648i	1.20531	−	0.0345352i
$776$	−199.580	−	160.606i	−0.257191	−	0.206967i
$777$			169.081i			0.217607i
$778$	−502.881	+	154.308i	−0.646377	+	0.198340i
$779$		−	33.0169i		−	0.0423837i
$780$	126.270	−	711.586i	0.161885	−	0.912290i
$781$	293.197			0.375412
$782$	−291.493	−	949.957i	−0.372753	−	1.21478i
$783$	779.465			0.995485
$784$	−286.138	+	716.635i	−0.364972	+	0.914075i
$785$	−925.960	+	952.871i	−1.17957	+	1.21385i
$786$	−812.322	−	2647.31i	−1.03349	−	3.36808i
$787$	701.877			0.891839			0.445919	−	0.895073i	$-0.352877\pi$
$787$	701.877			0.891839			0.445919	+	0.895073i	$0.352877\pi$
$788$	321.514	+	474.569i	0.408012	+	0.602245i
$789$	172.780			0.218986
$790$	−146.287	+	285.614i	−0.185174	+	0.361537i
$791$			152.791i			0.193162i
$792$	−1171.20	−	942.489i	−1.47879	−	1.19001i
$793$			39.9315i			0.0503550i
$794$	−415.032	−	1352.57i	−0.522711	−	1.70348i
$795$	1125.84	−	1158.56i	1.41616	−	1.45731i
$796$	−590.608	−	871.764i	−0.741969	−	1.09518i
$797$			153.942i			0.193152i	0.995326	+	0.0965759i	$0.0307891\pi$
$797$			153.942i			0.193152i	−0.995326	+	0.0965759i	$0.969211\pi$
$798$	12.0204	+	39.1738i	0.0150632	+	0.0490900i
$799$			1557.59i			1.94942i
$800$	−798.855	−	42.7903i	−0.998569	−	0.0534878i
$801$	−480.903			−0.600378
$802$	1087.75	−	333.774i	1.35629	−	0.416177i
$803$	865.487			1.07782
$804$	1913.46	−	1296.34i	2.37993	−	1.61237i
$805$	−62.9505	−	61.1726i	−0.0781994	−	0.0759908i
$806$	482.766	−	148.136i	0.598965	−	0.183791i
$807$	1757.22			2.17747
$808$	213.145	−	264.868i	0.263794	−	0.327808i
$809$	1362.01			1.68357			0.841785	−	0.539813i	$-0.181505\pi$
$809$	1362.01			1.68357			0.841785	+	0.539813i	$0.181505\pi$
$810$	1133.17	+	580.390i	1.39897	+	0.716531i
$811$			361.178i			0.445349i	0.974893	+	0.222674i	$0.0714787\pi$
$811$			361.178i			0.445349i	−0.974893	+	0.222674i	$0.928521\pi$
$812$	−39.9261	+	27.0493i	−0.0491700	+	0.0333120i
$813$			1345.92i			1.65550i
$814$	−658.804	+	202.153i	−0.809341	+	0.248345i
$815$	−647.787	−	629.492i	−0.794830	−	0.772382i
$816$	−1976.65	−	789.235i	−2.42236	−	0.967200i
$817$			120.993i			0.148094i
$818$	−1435.64	+	440.523i	−1.75506	+	0.538537i
$819$		−	116.433i		−	0.142165i
$820$	149.162	+	26.4685i	0.181905	+	0.0322787i
$821$	−531.089			−0.646881			−0.323440	−	0.946249i	$-0.604840\pi$
$821$	−531.089			−0.646881			−0.323440	+	0.946249i	$0.604840\pi$
$822$	−463.283	−	1509.81i	−0.563604	−	1.83675i
$823$	1300.29			1.57994			0.789970	−	0.613146i	$-0.210096\pi$
$823$	1300.29			1.57994			0.789970	+	0.613146i	$0.210096\pi$
$824$	896.251	−	1113.74i	1.08768	−	1.35163i
$825$	1280.52	−	36.6900i	1.55214	−	0.0444727i
$826$	−9.53014	−	31.0581i	−0.0115377	−	0.0376007i
$827$	1386.03			1.67597			0.837984	−	0.545694i	$-0.183734\pi$
$827$	1386.03			1.67597			0.837984	+	0.545694i	$0.183734\pi$
$828$	1298.09	−	879.434i	1.56774	−	1.06212i
$829$	−291.379			−0.351483			−0.175741	−	0.984436i	$-0.556232\pi$
$829$	−291.379			−0.351483			−0.175741	+	0.984436i	$0.556232\pi$
$830$	−1347.83	−	690.339i	−1.62389	−	0.831734i
$831$		−	1217.48i		−	1.46508i
$832$	−422.296	+	92.4711i	−0.507568	+	0.111143i
$833$		−	1199.24i		−	1.43967i
$834$	82.4454	+	268.684i	0.0988553	+	0.322164i
$835$	659.845	+	641.210i	0.790234	+	0.767916i
$836$	−138.265	+	93.6724i	−0.165388	+	0.112048i
$837$			2123.34i			2.53684i
$838$	−251.174	−	818.561i	−0.299730	−	0.976804i
$839$			893.428i			1.06487i	0.846470	+	0.532436i	$0.178723\pi$
$839$			893.428i			1.06487i	−0.846470	+	0.532436i	$0.821277\pi$
$840$	−186.613	+	22.9008i	−0.222159	+	0.0272628i
$841$	−652.708			−0.776109
$842$	292.060	−	89.6182i	0.346865	−	0.106435i
$843$	−1929.90			−2.28933
$844$	−54.7394	−	80.7979i	−0.0648571	−	0.0957321i
$845$	−442.394	−	429.900i	−0.523544	−	0.508758i
$846$	−2349.63	+	720.978i	−2.77733	+	0.852220i
$847$	25.7009			0.0303435
$848$	−897.448	−	358.333i	−1.05831	−	0.422563i
$849$	−33.9950			−0.0400412
$850$	1177.67	−	398.615i	1.38550	−	0.468958i
$851$		−	718.739i		−	0.844582i
$852$	367.380	+	542.270i	0.431198	+	0.636467i
$853$			868.956i			1.01871i	0.860558	+	0.509353i	$0.170115\pi$
$853$			868.956i			1.01871i	−0.860558	+	0.509353i	$0.829885\pi$
$854$	9.93129	−	3.04740i	0.0116291	−	0.00356838i
$855$	297.978	−	306.638i	0.348513	−	0.358642i
$856$	−482.247	+	599.272i	−0.563373	+	0.700085i
$857$			193.271i			0.225521i	0.993622	+	0.112760i	$0.0359693\pi$
$857$			193.271i			0.225521i	−0.993622	+	0.112760i	$0.964031\pi$
$858$	661.791	−	203.069i	0.771318	−	0.236677i
$859$			149.653i			0.174217i	0.996199	+	0.0871087i	$0.0277627\pi$
$859$			149.653i			0.174217i	−0.996199	+	0.0871087i	$0.972237\pi$
$860$	−546.614	−	96.9959i	−0.635598	−	0.112786i
$861$	35.6031			0.0413509
$862$	37.4803	+	122.146i	0.0434806	+	0.141701i
$863$	721.476			0.836009			0.418005	−	0.908445i	$-0.362730\pi$
$863$	721.476			0.836009			0.418005	+	0.908445i	$0.362730\pi$
$864$	149.174	−	1811.60i	0.172655	−	2.09676i
$865$	−953.182	+	980.884i	−1.10194	+	1.13397i
$866$	415.028	+	1352.55i	0.479247	+	1.56184i
$867$	1761.75			2.03201
$868$	−73.6850	−	108.763i	−0.0848906	−	0.125302i
$869$	−307.374			−0.353710
$870$	653.358	+	334.640i	0.750986	+	0.384644i
$871$			729.575i			0.837629i
$872$	−697.264	+	866.467i	−0.799615	+	0.993654i
$873$			628.222i			0.719612i
$874$	−51.0971	−	166.523i	−0.0584636	−	0.190529i
$875$	74.2532	−	80.9249i	0.0848608	−	0.0924855i
$876$	1084.47	+	1600.73i	1.23798	+	1.82731i
$877$			1021.54i			1.16482i	0.812897	+	0.582408i	$0.197889\pi$
$877$			1021.54i			1.16482i	−0.812897	+	0.582408i	$0.802111\pi$
$878$	−351.786	−	1146.45i	−0.400668	−	1.30575i
$879$			2309.78i			2.62773i
$880$	−312.345	−	699.738i	−0.354938	−	0.795157i
$881$	−1194.62			−1.35598			−0.677990	−	0.735071i	$-0.737149\pi$
$881$	−1194.62			−1.35598			−0.677990	+	0.735071i	$0.737149\pi$
$882$	1809.06	−	555.107i	2.05109	−	0.629372i
$883$	767.899			0.869648			0.434824	−	0.900515i	$-0.356811\pi$
$883$	767.899			0.869648			0.434824	+	0.900515i	$0.356811\pi$
$884$	556.223	−	376.833i	0.629212	−	0.426282i
$885$	−344.625	+	354.640i	−0.389406	+	0.400724i
$886$	−575.965	+	176.734i	−0.650073	+	0.199474i
$887$	737.554			0.831515			0.415757	−	0.909476i	$-0.363517\pi$
$887$	737.554			0.831515			0.415757	+	0.909476i	$0.363517\pi$
$888$	−1199.37	−	965.163i	−1.35065	−	1.08689i
$889$	115.456			0.129872
$890$	−218.176	−	111.747i	−0.245142	−	0.125558i
$891$			1219.50i			1.36868i
$892$	−407.785	+	276.268i	−0.457158	+	0.309718i
$893$			273.037i			0.305753i
$894$	−2859.79	+	877.522i	−3.19887	+	0.981568i
$895$	779.476	−	802.130i	0.870923	−	0.896235i
$896$	55.2260	+	97.9714i	0.0616362	+	0.109343i
$897$			721.997i			0.804902i
$898$	574.037	−	176.142i	0.639239	−	0.196149i
$899$			512.926i			0.570551i
$900$	1146.43	+	1592.01i	1.27381	+	1.76890i
$901$	1501.82			1.66684
$902$	42.5671	+	138.724i	0.0471919	+	0.153796i
$903$	−130.470			−0.144485
$904$	−1083.82	−	872.177i	−1.19892	−	0.964798i
$905$	−895.062	−	869.784i	−0.989019	−	0.961087i
$906$	−576.855	−	1879.94i	−0.636706	−	2.07499i
$907$	833.893			0.919397			0.459699	−	0.888075i	$-0.347957\pi$
$907$	833.893			0.919397			0.459699	+	0.888075i	$0.347957\pi$
$908$	−393.384	+	266.512i	−0.433242	+	0.293515i
$909$	−833.731			−0.917196
$910$	27.0554	−	52.8234i	0.0297312	−	0.0580477i
$911$		−	1322.21i		−	1.45138i	−0.688023	−	0.725689i	$-0.741521\pi$
$911$		−	1322.21i		−	1.45138i	0.688023	−	0.725689i	$-0.258479\pi$
$912$	−346.496	−	138.349i	−0.379930	−	0.151698i
$913$		−	1450.52i		−	1.58874i
$914$	287.924	+	938.328i	0.315016	+	1.02662i
$915$	−113.401	−	110.199i	−0.123936	−	0.120436i
$916$	−497.864	+	337.295i	−0.543519	+	0.368226i
$917$		−	227.404i		−	0.247987i
$918$	828.709	+	2700.71i	0.902733	+	2.94195i
$919$			615.500i			0.669750i	0.942263	+	0.334875i	$0.108694\pi$
$919$			615.500i			0.669750i	−0.942263	+	0.334875i	$0.891306\pi$
$920$	793.268	−	97.3480i	0.862248	−	0.105813i
$921$	164.195			0.178279
$922$	−362.897	+	111.354i	−0.393598	+	0.120775i
$923$	−206.760			−0.224009
$924$	−101.010	−	149.095i	−0.109318	−	0.161358i
$925$	898.932	−	25.7567i	0.971819	−	0.0278451i
$926$	192.664	−	59.1186i	0.208061	−	0.0638430i
$927$	−3505.74			−3.78181
$928$	36.0352	−	437.621i	0.0388311	−	0.471575i
$929$	−192.270			−0.206965			−0.103482	−	0.994631i	$-0.532999\pi$
$929$	−192.270			−0.206965			−0.103482	+	0.994631i	$0.532999\pi$
$930$	−911.593	+	1779.81i	−0.980208	+	1.91378i
$931$		−	210.221i		−	0.225801i
$932$	275.146	+	406.129i	0.295221	+	0.435760i
$933$		−	2380.10i		−	2.55102i
$934$	−412.883	+	126.692i	−0.442059	+	0.135645i
$935$	854.073	+	829.952i	0.913447	+	0.887649i
$936$	825.919	+	664.635i	0.882392	+	0.710080i
$937$		−	530.858i		−	0.566550i	−0.959039	−	0.283275i	$-0.908579\pi$
$937$		−	530.858i		−	0.566550i	0.959039	−	0.283275i	$-0.0914210\pi$
$938$	181.451	−	55.6779i	0.193445	−	0.0593581i
$939$			939.507i			1.00054i
$940$	−1233.51	−	218.885i	−1.31225	−	0.232856i
$941$	1088.17			1.15639			0.578197	−	0.815897i	$-0.303756\pi$
$941$	1088.17			1.15639			0.578197	+	0.815897i	$0.303756\pi$
$942$	−834.034	−	2718.07i	−0.885386	−	2.88542i
$943$	−151.344			−0.160492
$944$	274.712	+	109.687i	0.291008	+	0.116194i
$945$	178.967	+	173.913i	0.189383	+	0.184035i
$946$	−155.990	−	508.363i	−0.164894	−	0.537381i
$947$	−1636.17			−1.72774			−0.863871	−	0.503714i	$-0.831967\pi$
$947$	−1636.17			−1.72774			−0.863871	+	0.503714i	$0.831967\pi$
$948$	−385.145	−	568.491i	−0.406271	−	0.599674i
$949$	−610.334			−0.643134
$950$	206.440	−	69.8751i	0.217305	−	0.0735527i
$951$			320.865i			0.337398i
$952$	−136.170	−	109.579i	−0.143036	−	0.115104i
$953$			1355.89i			1.42276i	0.702805	+	0.711382i	$0.251931\pi$
$953$			1355.89i			1.42276i	−0.702805	+	0.711382i	$0.748069\pi$
$954$	695.164	+	2265.50i	0.728684	+	2.37474i
$955$	−598.006	+	615.386i	−0.626185	+	0.644383i
$956$	38.4364	+	56.7339i	0.0402054	+	0.0593450i
$957$			703.135i			0.734728i
$958$	290.542	+	946.860i	0.303280	+	0.988372i
$959$		−	129.693i		−	0.135238i
$960$	902.798	−	1454.47i	0.940415	−	1.51507i
$961$	−436.260			−0.453964
$962$	464.583	−	142.556i	0.482934	−	0.148187i
$963$	1886.34			1.95882
$964$	808.994	−	548.082i	0.839206	−	0.568550i
$965$	−286.850	+	295.187i	−0.297254	+	0.305893i
$966$	179.566	−	55.0996i	0.185887	−	0.0570389i
$967$	668.242			0.691047			0.345523	−	0.938410i	$-0.387701\pi$
$967$	668.242			0.691047			0.345523	+	0.938410i	$0.387701\pi$
$968$	−146.709	+	182.310i	−0.151558	+	0.188336i
$969$	579.838			0.598388
$970$	−145.979	+	285.012i	−0.150494	+	0.293827i
$971$		−	988.730i		−	1.01826i	−0.860690	−	0.509130i	$-0.829967\pi$
$971$		−	988.730i		−	1.01826i	0.860690	−	0.509130i	$-0.170033\pi$
$972$	−562.469	+	381.065i	−0.578672	+	0.392042i
$973$			23.0800i			0.0237205i
$974$	1340.43	−	411.310i	1.37622	−	0.422289i
$975$	−903.008	+	25.8735i	−0.926162	+	0.0265369i
$976$	−35.0740	+	87.8431i	−0.0359365	+	0.0900031i
$977$		−	1749.31i		−	1.79049i	−0.445577	−	0.895244i	$-0.647001\pi$
$977$		−	1749.31i		−	1.79049i	0.445577	−	0.895244i	$-0.352999\pi$
$978$	1847.81	−	566.998i	1.88938	−	0.579753i
$979$		−	234.798i		−	0.239835i
$980$	949.724	+	168.527i	0.969106	+	0.171966i
$981$	2727.39			2.78022
$982$	256.373	+	835.504i	0.261072	+	0.850819i
$983$	344.576			0.350535			0.175268	−	0.984521i	$-0.443921\pi$
$983$	344.576			0.350535			0.175268	+	0.984521i	$0.443921\pi$
$984$	−203.233	+	252.551i	−0.206538	+	0.256658i
$985$	499.356	−	513.868i	0.506960	−	0.521694i
$986$	200.188	+	652.400i	0.203030	+	0.661663i
$987$	−294.425			−0.298302
$988$	97.5031	−	66.0569i	0.0986873	−	0.0668593i
$989$	554.611			0.560780
$990$	−856.650	+	1672.54i	−0.865303	+	1.68943i
$991$		−	796.012i		−	0.803241i	−0.915806	−	0.401620i	$-0.868447\pi$
$991$		−	796.012i		−	0.803241i	0.915806	−	0.401620i	$-0.131553\pi$
$992$	1192.12	+	98.1635i	1.20174	+	0.0989552i
$993$			1563.11i			1.57413i
$994$	15.7790	+	51.4228i	0.0158742	+	0.0517332i
$995$	−917.296	+	943.955i	−0.921906	+	0.948699i
$996$	2682.74	−	1817.52i	2.69352	−	1.82482i
$997$			1211.40i			1.21504i	0.794303	+	0.607522i	$0.207836\pi$
$997$			1211.40i			1.21504i	−0.794303	+	0.607522i	$0.792164\pi$
$998$	256.475	+	835.837i	0.256989	+	0.837512i
$999$			2043.36i			2.04541i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.3.h.a.39.10	yes	108
4.3	odd	2	inner	380.3.h.a.39.100	yes	108
5.4	even	2	inner	380.3.h.a.39.99	yes	108
20.19	odd	2	inner	380.3.h.a.39.9	✓	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.3.h.a.39.9	✓	108	20.19	odd	2	inner
380.3.h.a.39.10	yes	108	1.1	even	1	trivial
380.3.h.a.39.99	yes	108	5.4	even	2	inner
380.3.h.a.39.100	yes	108	4.3	odd	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)

\(f(q)\)	\(=\)	\(q+(-1.91201 + 0.586697i) q^{2} -5.34961 q^{3} +(3.31157 - 2.24354i) q^{4} +(-3.58581 - 3.48454i) q^{5} +(10.2285 - 3.13860i) q^{6} +0.878631 q^{7} +(-5.01548 + 6.23257i) q^{8} +19.6184 q^{9} +O(q^{10})\)	\(q+(-1.91201 + 0.586697i) q^{2} -5.34961 q^{3} +(3.31157 - 2.24354i) q^{4} +(-3.58581 - 3.48454i) q^{5} +(10.2285 - 3.13860i) q^{6} +0.878631 q^{7} +(-5.01548 + 6.23257i) q^{8} +19.6184 q^{9} +(8.90047 + 4.55869i) q^{10} +9.57856i q^{11} +(-17.7156 + 12.0021i) q^{12} -6.75472i q^{13} +(-1.67995 + 0.515490i) q^{14} +(19.1827 + 18.6409i) q^{15} +(5.93303 - 14.8593i) q^{16} +24.8661i q^{17} +(-37.5105 + 11.5100i) q^{18} +4.35890i q^{19} +(-19.6924 - 3.49438i) q^{20} -4.70033 q^{21} +(-5.61972 - 18.3143i) q^{22} +19.9805 q^{23} +(26.8309 - 33.3418i) q^{24} +(0.716019 + 24.9897i) q^{25} +(3.96297 + 12.9151i) q^{26} -56.8042 q^{27} +(2.90965 - 1.97125i) q^{28} -13.7220 q^{29} +(-47.6141 - 24.3872i) q^{30} -37.3799i q^{31} +(-2.62610 + 31.8921i) q^{32} -51.2416i q^{33} +(-14.5889 - 47.5442i) q^{34} +(-3.15060 - 3.06162i) q^{35} +(64.9677 - 44.0147i) q^{36} -35.9721i q^{37} +(-2.55735 - 8.33426i) q^{38} +36.1351i q^{39} +(39.7022 - 4.87216i) q^{40} -7.57460 q^{41} +(8.98709 - 2.75767i) q^{42} +27.7577 q^{43} +(21.4899 + 31.7201i) q^{44} +(-70.3477 - 68.3609i) q^{45} +(-38.2029 + 11.7225i) q^{46} +62.6391 q^{47} +(-31.7394 + 79.4916i) q^{48} -48.2280 q^{49} +(-16.0304 - 47.3606i) q^{50} -133.024i q^{51} +(-15.1545 - 22.3687i) q^{52} -60.3963i q^{53} +(108.610 - 33.3269i) q^{54} +(33.3768 - 34.3469i) q^{55} +(-4.40676 + 5.47613i) q^{56} -23.3184i q^{57} +(26.2365 - 8.05063i) q^{58} +18.4875i q^{59} +(105.347 + 18.6936i) q^{60} -5.91165 q^{61} +(21.9307 + 71.4709i) q^{62} +17.2373 q^{63} +(-13.6898 - 62.5187i) q^{64} +(-23.5371 + 24.2211i) q^{65} +(30.0633 + 97.9745i) q^{66} -108.010 q^{67} +(55.7882 + 82.3459i) q^{68} -106.888 q^{69} +(7.82022 + 4.00540i) q^{70} -30.6097i q^{71} +(-98.3956 + 122.273i) q^{72} -90.3567i q^{73} +(21.1047 + 68.7790i) q^{74} +(-3.83043 - 133.685i) q^{75} +(9.77938 + 14.4348i) q^{76} +8.41602i q^{77} +(-21.2004 - 69.0908i) q^{78} +32.0898i q^{79} +(-73.0525 + 32.6088i) q^{80} +127.315 q^{81} +(14.4827 - 4.44400i) q^{82} -151.434 q^{83} +(-15.5655 + 10.5454i) q^{84} +(86.6468 - 89.1650i) q^{85} +(-53.0729 + 16.2853i) q^{86} +73.4072 q^{87} +(-59.6991 - 48.0411i) q^{88} -24.5129 q^{89} +(174.613 + 89.4341i) q^{90} -5.93490i q^{91} +(66.1668 - 44.8271i) q^{92} +199.968i q^{93} +(-119.767 + 36.7502i) q^{94} +(15.1887 - 15.6302i) q^{95} +(14.0486 - 170.610i) q^{96} +32.0221i q^{97} +(92.2125 - 28.2952i) q^{98} +187.916i 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

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Database

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