LMFDB - Embedded newform 380.3.h.a.39.9

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

$q$-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	$-0.856611\pi$
$11$		−	9.57856i		−	0.870779i	0.900242	−	0.435389i	$-0.143389\pi$
$12$	−17.7156	−	12.0021i	−1.47630	−	1.00017i
$13$			6.75472i			0.519594i	0.965663	+	0.259797i	$0.0836556\pi$
$13$			6.75472i			0.519594i	−0.965663	+	0.259797i	$0.916344\pi$
$14$	−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	$-0.738888\pi$
$17$		−	24.8661i		−	1.46271i	0.681996	−	0.731356i	$-0.261112\pi$
$18$	−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	$0.205989\pi$
$31$			37.3799i			1.20580i	−0.797815	+	0.602902i	$0.794011\pi$
$32$	−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	$0.161584\pi$
$37$			35.9721i			0.972218i	−0.873898	+	0.486109i	$0.838416\pi$
$38$	−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	$0.192970\pi$
$53$			60.3963i			1.13955i	−0.821800	+	0.569777i	$0.807030\pi$
$54$	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	$-0.949923\pi$
$59$		−	18.4875i		−	0.313348i	0.987650	−	0.156674i	$-0.0500772\pi$
$60$	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	$0.0691581\pi$
$71$			30.6097i			0.431122i	−0.976490	+	0.215561i	$0.930842\pi$
$72$	−98.3956	−	122.273i	−1.36661	−	1.69823i
$73$			90.3567i			1.23776i	0.785484	+	0.618881i	$0.212414\pi$
$73$			90.3567i			1.23776i	−0.785484	+	0.618881i	$0.787586\pi$
$74$	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	$-0.934898\pi$
$79$		−	32.0898i		−	0.406200i	0.979158	−	0.203100i	$-0.0651017\pi$
$80$	−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	$-0.947217\pi$
$97$		−	32.0221i		−	0.330125i	0.986283	−	0.165062i	$-0.0527825\pi$
$98$	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	$-0.720528\pi$
$113$		−	173.897i		−	1.53891i	0.638700	−	0.769455i	$-0.279472\pi$
$114$	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	$0.450327\pi$
$131$			258.816i			1.97570i	−0.155418	+	0.987849i	$0.549673\pi$
$132$	−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	$0.181090\pi$
$137$			147.608i			1.07743i	−0.842488	+	0.538715i	$0.818910\pi$
$138$	204.371	+	62.7108i	1.48095	+	0.454426i
$139$		−	26.2682i		−	0.188980i	−0.995526	−	0.0944898i	$-0.969878\pi$
$139$		−	26.2682i		−	0.188980i	0.995526	−	0.0944898i	$-0.0301220\pi$
$140$	−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	$0.208264\pi$
$151$			183.794i			1.21718i	−0.793486	+	0.608588i	$0.791736\pi$
$152$	−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	$0.321167\pi$
$157$			265.734i			1.69257i	−0.532728	+	0.846287i	$0.678833\pi$
$158$	−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	$0.290229\pi$
$173$			273.546i			1.58119i	−0.612338	+	0.790596i	$0.709771\pi$
$174$	−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	$-0.785161\pi$
$179$		−	223.696i		−	1.24970i	0.780746	−	0.624849i	$-0.214839\pi$
$180$	−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	$0.148312\pi$
$191$			171.617i			0.898519i	−0.893401	+	0.449260i	$0.851688\pi$
$192$	73.2354	−	334.451i	0.381434	−	1.74193i
$193$			82.3208i			0.426533i	0.976994	+	0.213266i	$0.0684102\pi$
$193$			82.3208i			0.426533i	−0.976994	+	0.213266i	$0.931590\pi$
$194$	−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	$-0.881506\pi$
$197$		−	143.306i		−	0.727443i	0.931508	−	0.363721i	$-0.118494\pi$
$198$	−110.250	+	359.297i	−0.556817	+	1.81463i
$199$			263.248i			1.32285i	0.750010	+	0.661426i	$0.230049\pi$
$199$			263.248i			1.32285i	−0.750010	+	0.661426i	$0.769951\pi$
$200$	−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	$0.0184139\pi$
$211$			24.3986i			0.115633i	−0.998327	+	0.0578167i	$0.981586\pi$
$212$	−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	$-0.915231\pi$
$233$		−	122.639i		−	0.526349i	0.964748	−	0.263174i	$-0.0847694\pi$
$234$	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	$-0.988589\pi$
$239$		−	17.1320i		−	0.0716820i	0.999358	−	0.0358410i	$-0.0114110\pi$
$240$	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	$0.0351565\pi$
$251$			55.3319i			0.220446i	−0.993907	+	0.110223i	$0.964844\pi$
$252$	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	$0.362892\pi$
$257$			467.050i			1.81732i	−0.417540	+	0.908659i	$0.637108\pi$
$258$	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	$0.153656\pi$
$271$			251.593i			0.928386i	−0.885734	+	0.464193i	$0.846344\pi$
$272$	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	$-0.865250\pi$
$277$		−	227.583i		−	0.821598i	0.911726	−	0.410799i	$-0.134750\pi$
$278$	−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	$0.263664\pi$
$293$			431.765i			1.47360i	−0.676110	+	0.736801i	$0.736336\pi$
$294$	−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	$-0.746294\pi$
$311$		−	444.911i		−	1.43058i	0.698826	−	0.715292i	$-0.253706\pi$
$312$	−225.215	+	181.235i	−0.721842	+	0.580882i
$313$			175.621i			0.561091i	0.959841	+	0.280545i	$0.0905153\pi$
$313$			175.621i			0.561091i	−0.959841	+	0.280545i	$0.909485\pi$
$314$	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	$0.0301586\pi$
$317$			59.9791i			0.189209i	−0.995515	+	0.0946043i	$0.969841\pi$
$318$	−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	$0.145510\pi$
$331$			292.191i			0.882753i	−0.897322	+	0.441377i	$0.854490\pi$
$332$	−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	$-0.739087\pi$
$337$		−	492.646i		−	1.46186i	0.682453	−	0.730929i	$-0.260913\pi$
$338$	−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	$0.102000\pi$
$353$			222.380i			0.629971i	−0.949097	+	0.314985i	$0.898000\pi$
$354$	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	$0.189779\pi$
$359$			403.164i			1.12302i	−0.827470	+	0.561510i	$0.810221\pi$
$360$	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	$0.00960962\pi$
$373$			22.5179i			0.0603698i	−0.999544	+	0.0301849i	$0.990390\pi$
$374$	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	$-0.866100\pi$
$379$		−	309.538i		−	0.816724i	0.912820	−	0.408362i	$-0.133900\pi$
$380$	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	$-0.650048\pi$
$397$		−	707.405i		−	1.78188i	0.454125	−	0.890938i	$-0.349952\pi$
$398$	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	$-0.829321\pi$
$419$		−	428.115i		−	1.02176i	0.859653	−	0.510878i	$-0.170679\pi$
$420$	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	$0.0236119\pi$
$431$			63.8836i			0.148222i	−0.997250	+	0.0741109i	$0.976388\pi$
$432$	−337.021	−	844.071i	−0.780141	−	1.95387i
$433$			707.397i			1.63371i	0.576842	+	0.816856i	$0.304285\pi$
$433$			707.397i			1.63371i	−0.576842	+	0.816856i	$0.695715\pi$
$434$	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	$-0.760709\pi$
$439$		−	599.605i		−	1.36584i	0.730492	−	0.682921i	$-0.239291\pi$
$440$	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	$0.180416\pi$
$457$			490.755i			1.07386i	−0.843626	+	0.536931i	$0.819584\pi$
$458$	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	$0.172925\pi$
$479$			495.217i			1.03386i	−0.856029	+	0.516928i	$0.827075\pi$
$480$	−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	$0.146791\pi$
$491$			436.977i			0.889973i	−0.895537	+	0.444986i	$0.853209\pi$
$492$	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	$0.144322\pi$
$499$			437.151i			0.876053i	−0.898962	+	0.438027i	$0.855678\pi$
$500$	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	$0.142801\pi$
$557$			483.169i			0.867448i	−0.901046	+	0.433724i	$0.857199\pi$
$558$	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	$0.133806\pi$
$571$			466.041i			0.816183i	−0.912941	+	0.408092i	$0.866194\pi$
$572$	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	$0.0986161\pi$
$577$			351.831i			0.609758i	−0.952391	+	0.304879i	$0.901384\pi$
$578$	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	$0.0970052\pi$
$593$			355.866i			0.600111i	−0.953922	+	0.300056i	$0.902995\pi$
$594$	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	$0.119697\pi$
$599$			439.952i			0.734478i	−0.930127	+	0.367239i	$0.880303\pi$
$600$	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	$0.00966960\pi$
$613$			37.2376i			0.0607465i	−0.999539	+	0.0303733i	$0.990330\pi$
$614$	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	$0.159747\pi$
$617$			593.626i			0.962116i	−0.876689	+	0.481058i	$0.840253\pi$
$618$	−1827.80	−	560.859i	−2.95761	−	0.907538i
$619$		−	28.8028i		−	0.0465312i	−0.999729	−	0.0232656i	$-0.992594\pi$
$619$		−	28.8028i		−	0.0465312i	0.999729	−	0.0232656i	$-0.00740633\pi$
$620$	−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	$0.0329392\pi$
$631$			130.361i			0.206594i	−0.994651	+	0.103297i	$0.967061\pi$
$632$	−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	$0.106168\pi$
$653$			427.567i			0.654774i	−0.944890	+	0.327387i	$0.893832\pi$
$654$	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	$-0.944699\pi$
$659$		−	227.831i		−	0.345722i	0.984946	−	0.172861i	$-0.0553012\pi$
$660$	−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	$-0.921057\pi$
$673$		−	330.405i		−	0.490943i	0.969404	−	0.245472i	$-0.0789428\pi$
$674$	−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	$-0.912120\pi$
$677$		−	369.084i		−	0.545176i	0.962131	−	0.272588i	$-0.0878796\pi$
$678$	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	$0.0827103\pi$
$691$			355.074i			0.513856i	−0.966431	+	0.256928i	$0.917290\pi$
$692$	−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	$-0.985079\pi$
$719$		−	67.3848i		−	0.0937201i	0.998901	−	0.0468601i	$-0.0149215\pi$
$720$	−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	$0.157621\pi$
$733$			696.629i			0.950380i	−0.879883	+	0.475190i	$0.842379\pi$
$734$	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	$-0.835488\pi$
$739$		−	730.320i		−	0.988254i	0.869390	−	0.494127i	$-0.164512\pi$
$740$	−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	$0.113506\pi$
$751$			524.319i			0.698161i	−0.937093	+	0.349081i	$0.886494\pi$
$752$	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	$-0.851137\pi$
$757$		−	682.519i		−	0.901611i	0.892622	−	0.450805i	$-0.148863\pi$
$758$	−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	$0.0274522\pi$
$773$			133.167i			0.172273i	−0.996283	+	0.0861367i	$0.972548\pi$
$774$	−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	$-0.969211\pi$
$797$		−	153.942i		−	0.193152i	0.995326	−	0.0965759i	$-0.0307891\pi$
$798$	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	$-0.928521\pi$
$811$		−	361.178i		−	0.445349i	0.974893	−	0.222674i	$-0.0714787\pi$
$812$	−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	$-0.821277\pi$
$839$		−	893.428i		−	1.06487i	0.846470	−	0.532436i	$-0.178723\pi$
$840$	−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	$-0.829885\pi$
$853$		−	868.956i		−	1.01871i	0.860558	−	0.509353i	$-0.170115\pi$
$854$	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	$-0.964031\pi$
$857$		−	193.271i		−	0.225521i	0.993622	−	0.112760i	$-0.0359693\pi$
$858$	661.791	+	203.069i	0.771318	+	0.236677i
$859$		−	149.653i		−	0.174217i	−0.996199	−	0.0871087i	$-0.972237\pi$
$859$		−	149.653i		−	0.174217i	0.996199	−	0.0871087i	$-0.0277627\pi$
$860$	−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	$-0.802111\pi$
$877$		−	1021.54i		−	1.16482i	0.812897	−	0.582408i	$-0.197889\pi$
$878$	−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	$0.258479\pi$
$911$			1322.21i			1.45138i	−0.688023	+	0.725689i	$0.741521\pi$
$912$	−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	$-0.891306\pi$
$919$		−	615.500i		−	0.669750i	0.942263	−	0.334875i	$-0.108694\pi$
$920$	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	$0.0914210\pi$
$937$			530.858i			0.566550i	−0.959039	+	0.283275i	$0.908579\pi$
$938$	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	$-0.748069\pi$
$953$		−	1355.89i		−	1.42276i	0.702805	−	0.711382i	$-0.251931\pi$
$954$	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	$0.170033\pi$
$971$			988.730i			1.01826i	−0.860690	+	0.509130i	$0.829967\pi$
$972$	−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	$0.352999\pi$
$977$			1749.31i			1.79049i	−0.445577	+	0.895244i	$0.647001\pi$
$978$	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	$0.131553\pi$
$991$			796.012i			0.803241i	−0.915806	+	0.401620i	$0.868447\pi$
$992$	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	$-0.792164\pi$
$997$		−	1211.40i		−	1.21504i	0.794303	−	0.607522i	$-0.207836\pi$
$998$	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.39.9	✓	108
4.3	odd	2	inner	380.3.h.a.39.99	yes	108
5.4	even	2	inner	380.3.h.a.39.100	yes	108
20.19	odd	2	inner	380.3.h.a.39.10	yes	108

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

\(f(q)\)	\(=\)	\(q+(-1.91201 - 0.586697i) q^{2} -5.34961 q^{3} +(3.31157 + 2.24354i) q^{4} +(-3.58581 + 3.48454i) q^{5} +(10.2285 + 3.13860i) q^{6} +0.878631 q^{7} +(-5.01548 - 6.23257i) q^{8} +19.6184 q^{9} +O(q^{10})\)	\(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

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