LMFDB - Embedded newform 228.3.b.e.227.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [228,3,Mod(227,228)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(228, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("228.227");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 228 = 2^{2} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	228.b (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:	$6.21255002741$
Analytic rank:	$0$
Dimension:	$72$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			227.19
Character	$\chi$	$=$	228.227
Dual form			228.3.b.e.227.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.49065 + 1.33340i) q^{2} +(-2.57288 - 1.54282i) q^{3} +(0.444087 - 3.97527i) q^{4} -3.86301i q^{5} +(5.89246 - 1.13087i) q^{6} -8.43471i q^{7} +(4.63865 + 6.51789i) q^{8} +(4.23941 + 7.93898i) q^{9} +O(q^{10})$	\(q+(-1.49065 + 1.33340i) q^{2} +(-2.57288 - 1.54282i) q^{3} +(0.444087 - 3.97527i) q^{4} -3.86301i q^{5} +(5.89246 - 1.13087i) q^{6} -8.43471i q^{7} +(4.63865 + 6.51789i) q^{8} +(4.23941 + 7.93898i) q^{9} +(5.15095 + 5.75841i) q^{10} -4.89291 q^{11} +(-7.27571 + 9.54275i) q^{12} -7.90228i q^{13} +(11.2469 + 12.5732i) q^{14} +(-5.95994 + 9.93907i) q^{15} +(-15.6056 - 3.53073i) q^{16} +23.1691i q^{17} +(-16.9053 - 6.18142i) q^{18} +(-13.4532 - 13.4168i) q^{19} +(-15.3565 - 1.71551i) q^{20} +(-13.0132 + 21.7015i) q^{21} +(7.29363 - 6.52421i) q^{22} -4.04058 q^{23} +(-1.87875 - 23.9264i) q^{24} +10.0771 q^{25} +(10.5369 + 11.7796i) q^{26} +(1.34092 - 26.9667i) q^{27} +(-33.5303 - 3.74574i) q^{28} -36.6011 q^{29} +(-4.36857 - 22.7627i) q^{30} -40.7866 q^{31} +(27.9704 - 15.5454i) q^{32} +(12.5889 + 7.54888i) q^{33} +(-30.8937 - 34.5371i) q^{34} -32.5834 q^{35} +(33.4423 - 13.3272i) q^{36} +1.88569i q^{37} +(37.9441 + 2.06123i) q^{38} +(-12.1918 + 20.3316i) q^{39} +(25.1787 - 17.9192i) q^{40} +37.8215 q^{41} +(-9.53856 - 49.7012i) q^{42} +67.1721i q^{43} +(-2.17288 + 19.4507i) q^{44} +(30.6684 - 16.3769i) q^{45} +(6.02309 - 5.38771i) q^{46} -61.3292 q^{47} +(34.7040 + 33.1607i) q^{48} -22.1444 q^{49} +(-15.0215 + 13.4368i) q^{50} +(35.7458 - 59.6114i) q^{51} +(-31.4137 - 3.50930i) q^{52} -47.0866 q^{53} +(33.9585 + 41.9859i) q^{54} +18.9014i q^{55} +(54.9766 - 39.1257i) q^{56} +(13.9138 + 55.2757i) q^{57} +(54.5595 - 48.8039i) q^{58} +4.93250i q^{59} +(36.8638 + 28.1062i) q^{60} -78.7533 q^{61} +(60.7986 - 54.3848i) q^{62} +(66.9630 - 35.7582i) q^{63} +(-20.9658 + 60.4685i) q^{64} -30.5266 q^{65} +(-28.8313 + 5.53325i) q^{66} +127.213 q^{67} +(92.1036 + 10.2891i) q^{68} +(10.3959 + 6.23388i) q^{69} +(48.5705 - 43.4468i) q^{70} +18.1952i q^{71} +(-32.0803 + 64.4582i) q^{72} +6.94630 q^{73} +(-2.51438 - 2.81091i) q^{74} +(-25.9272 - 15.5472i) q^{75} +(-59.3098 + 47.5220i) q^{76} +41.2703i q^{77} +(-8.93645 - 46.5639i) q^{78} +12.5467 q^{79} +(-13.6393 + 60.2846i) q^{80} +(-45.0548 + 67.3132i) q^{81} +(-56.3787 + 50.4312i) q^{82} +65.7472 q^{83} +(80.4903 + 61.3685i) q^{84} +89.5027 q^{85} +(-89.5673 - 100.130i) q^{86} +(94.1702 + 56.4689i) q^{87} +(-22.6965 - 31.8915i) q^{88} -58.7091 q^{89} +(-23.8789 + 65.3055i) q^{90} -66.6535 q^{91} +(-1.79437 + 16.0624i) q^{92} +(104.939 + 62.9263i) q^{93} +(91.4205 - 81.7764i) q^{94} +(-51.8293 + 51.9700i) q^{95} +(-95.9481 - 3.15683i) q^{96} -24.5355i q^{97} +(33.0096 - 29.5274i) q^{98} +(-20.7431 - 38.8447i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - 16 q^{4} + 6 q^{6} - 48 q^{9}+O(q^{10}) $ 72 * q - 16 * q^4 + 6 * q^6 - 48 * q^9	$ 72 q - 16 q^{4} + 6 q^{6} - 48 q^{9} - 40 q^{16} + 94 q^{24} - 408 q^{25} + 60 q^{28} + 176 q^{30} - 214 q^{36} + 2 q^{42} + 96 q^{45} - 616 q^{49} + 72 q^{54} + 320 q^{57} + 564 q^{58} + 592 q^{61} - 424 q^{64} + 608 q^{66} + 128 q^{73} - 292 q^{76} - 208 q^{81} + 472 q^{82} - 160 q^{85} + 128 q^{93} + 166 q^{96}+O(q^{100}) $ 72 * q - 16 * q^4 + 6 * q^6 - 48 * q^9 - 40 * q^16 + 94 * q^24 - 408 * q^25 + 60 * q^28 + 176 * q^30 - 214 * q^36 + 2 * q^42 + 96 * q^45 - 616 * q^49 + 72 * q^54 + 320 * q^57 + 564 * q^58 + 592 * q^61 - 424 * q^64 + 608 * q^66 + 128 * q^73 - 292 * q^76 - 208 * q^81 + 472 * q^82 - 160 * q^85 + 128 * q^93 + 166 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/228\mathbb{Z}\right)^\times$.

$n$	$77$	$97$	$115$
$\chi(n)$	$-1$	$-1$	$-1$

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 $

$2$	−1.49065	+	1.33340i	−0.745326	+	0.666700i
$2$	−1.49065	+	1.33340i	−0.745326	+	0.666700i
$3$	−2.57288	−	1.54282i	−0.857626	−	0.514273i
$3$	−2.57288	−	1.54282i	−0.857626	−	0.514273i
$4$	0.444087	−	3.97527i	0.111022	−	0.993818i
$5$		−	3.86301i		−	0.772603i	−0.922373	−	0.386301i	$-0.873752\pi$
$5$		−	3.86301i		−	0.772603i	0.922373	−	0.386301i	$-0.126248\pi$
$6$	5.89246	−	1.13087i	0.982077	−	0.188478i
$7$		−	8.43471i		−	1.20496i	−0.798134	−	0.602480i	$-0.794179\pi$
$7$		−	8.43471i		−	1.20496i	0.798134	−	0.602480i	$-0.205821\pi$
$8$	4.63865	+	6.51789i	0.579831	+	0.814737i
$9$	4.23941	+	7.93898i	0.471046	+	0.882109i
$10$	5.15095	+	5.75841i	0.515095	+	0.575841i
$11$	−4.89291			−0.444810			−0.222405	−	0.974954i	$-0.571391\pi$
$11$	−4.89291			−0.444810			−0.222405	+	0.974954i	$0.571391\pi$
$12$	−7.27571	+	9.54275i	−0.606309	+	0.795229i
$13$		−	7.90228i		−	0.607868i	−0.952693	−	0.303934i	$-0.901700\pi$
$13$		−	7.90228i		−	0.607868i	0.952693	−	0.303934i	$-0.0983002\pi$
$14$	11.2469	+	12.5732i	0.803347	+	0.898087i
$15$	−5.95994	+	9.93907i	−0.397329	+	0.662605i
$16$	−15.6056	−	3.53073i	−0.975348	−	0.220671i
$17$			23.1691i			1.36289i	0.731869	+	0.681445i	$0.238648\pi$
$17$			23.1691i			1.36289i	−0.731869	+	0.681445i	$0.761352\pi$
$18$	−16.9053	−	6.18142i	−0.939185	−	0.343412i
$19$	−13.4532	−	13.4168i	−0.708065	−	0.706147i
$19$	−13.4532	−	13.4168i	−0.708065	−	0.706147i
$20$	−15.3565	−	1.71551i	−0.767827	−	0.0857757i
$21$	−13.0132	+	21.7015i	−0.619678	+	1.03340i
$22$	7.29363	−	6.52421i	0.331529	−	0.296555i
$23$	−4.04058			−0.175677			−0.0878386	−	0.996135i	$-0.527996\pi$
$23$	−4.04058			−0.175677			−0.0878386	+	0.996135i	$0.527996\pi$
$24$	−1.87875	−	23.9264i	−0.0782813	−	0.996931i
$25$	10.0771			0.403085
$26$	10.5369	+	11.7796i	0.405266	+	0.453060i
$27$	1.34092	−	26.9667i	0.0496639	−	0.998766i
$28$	−33.5303	−	3.74574i	−1.19751	−	0.133777i
$29$	−36.6011			−1.26211			−0.631053	−	0.775740i	$-0.717377\pi$
$29$	−36.6011			−1.26211			−0.631053	+	0.775740i	$0.717377\pi$
$30$	−4.36857	−	22.7627i	−0.145619	−	0.758756i
$31$	−40.7866			−1.31570			−0.657848	−	0.753151i	$-0.728533\pi$
$31$	−40.7866			−1.31570			−0.657848	+	0.753151i	$0.728533\pi$
$32$	27.9704	−	15.5454i	0.874074	−	0.485793i
$33$	12.5889	+	7.54888i	0.381481	+	0.228754i
$34$	−30.8937	−	34.5371i	−0.908639	−	1.01580i
$35$	−32.5834			−0.930955
$36$	33.4423	−	13.3272i	0.928952	−	0.370201i
$37$			1.88569i			0.0509646i	0.999675	+	0.0254823i	$0.00811214\pi$
$37$			1.88569i			0.0509646i	−0.999675	+	0.0254823i	$0.991888\pi$
$38$	37.9441	+	2.06123i	0.998528	+	0.0542429i
$39$	−12.1918	+	20.3316i	−0.312610	+	0.521323i
$40$	25.1787	−	17.9192i	0.629468	−	0.447979i
$41$	37.8215			0.922476			0.461238	−	0.887276i	$-0.347405\pi$
$41$	37.8215			0.922476			0.461238	+	0.887276i	$0.347405\pi$
$42$	−9.53856	−	49.7012i	−0.227109	−	1.18336i
$43$			67.1721i			1.56214i	0.624442	+	0.781071i	$0.285326\pi$
$43$			67.1721i			1.56214i	−0.624442	+	0.781071i	$0.714674\pi$
$44$	−2.17288	+	19.4507i	−0.0493836	+	0.442060i
$45$	30.6684	−	16.3769i	0.681520	−	0.363931i
$46$	6.02309	−	5.38771i	0.130937	−	0.117124i
$47$	−61.3292			−1.30488			−0.652439	−	0.757842i	$-0.726254\pi$
$47$	−61.3292			−1.30488			−0.652439	+	0.757842i	$0.726254\pi$
$48$	34.7040	+	33.1607i	0.722999	+	0.690849i
$49$	−22.1444			−0.451927
$50$	−15.0215	+	13.4368i	−0.300429	+	0.268737i
$51$	35.7458	−	59.6114i	0.700898	−	1.16885i
$52$	−31.4137	−	3.50930i	−0.604110	−	0.0674865i
$53$	−47.0866			−0.888427			−0.444213	−	0.895921i	$-0.646517\pi$
$53$	−47.0866			−0.888427			−0.444213	+	0.895921i	$0.646517\pi$
$54$	33.9585	+	41.9859i	0.628862	+	0.777517i
$55$			18.9014i			0.343662i
$56$	54.9766	−	39.1257i	0.981724	−	0.698673i
$57$	13.9138	+	55.2757i	0.244102	+	0.969749i
$58$	54.5595	−	48.8039i	0.940681	−	0.841447i
$59$			4.93250i			0.0836018i	0.999126	+	0.0418009i	$0.0133095\pi$
$59$			4.93250i			0.0836018i	−0.999126	+	0.0418009i	$0.986690\pi$
$60$	36.8638	+	28.1062i	0.614396	+	0.468436i
$61$	−78.7533			−1.29104			−0.645519	−	0.763744i	$-0.723359\pi$
$61$	−78.7533			−1.29104			−0.645519	+	0.763744i	$0.723359\pi$
$62$	60.7986	−	54.3848i	0.980622	−	0.877175i
$63$	66.9630	−	35.7582i	1.06291	−	0.567591i
$64$	−20.9658	+	60.4685i	−0.327591	+	0.944820i
$65$	−30.5266			−0.469641
$66$	−28.8313	+	5.53325i	−0.436838	+	0.0838371i
$67$	127.213			1.89870			0.949350	−	0.314219i	$-0.101743\pi$
$67$	127.213			1.89870			0.949350	+	0.314219i	$0.101743\pi$
$68$	92.1036	+	10.2891i	1.35446	+	0.151310i
$69$	10.3959	+	6.23388i	0.150665	+	0.0903461i
$70$	48.5705	−	43.4468i	0.693865	−	0.620668i
$71$			18.1952i			0.256270i	0.991757	+	0.128135i	$0.0408991\pi$
$71$			18.1952i			0.256270i	−0.991757	+	0.128135i	$0.959101\pi$
$72$	−32.0803	+	64.4582i	−0.445559	+	0.895252i
$73$	6.94630			0.0951548			0.0475774	−	0.998868i	$-0.484850\pi$
$73$	6.94630			0.0951548			0.0475774	+	0.998868i	$0.484850\pi$
$74$	−2.51438	−	2.81091i	−0.0339781	−	0.0379852i
$75$	−25.9272	−	15.5472i	−0.345696	−	0.207296i
$76$	−59.3098	+	47.5220i	−0.780392	+	0.625290i
$77$			41.2703i			0.535978i
$78$	−8.93645	−	46.5639i	−0.114570	−	0.596973i
$79$	12.5467			0.158819			0.0794096	−	0.996842i	$-0.474696\pi$
$79$	12.5467			0.158819			0.0794096	+	0.996842i	$0.474696\pi$
$80$	−13.6393	+	60.2846i	−0.170491	+	0.753557i
$81$	−45.0548	+	67.3132i	−0.556232	+	0.831027i
$82$	−56.3787	+	50.4312i	−0.687546	+	0.615015i
$83$	65.7472			0.792135			0.396068	−	0.918221i	$-0.370375\pi$
$83$	65.7472			0.792135			0.396068	+	0.918221i	$0.370375\pi$
$84$	80.4903	+	61.3685i	0.958218	+	0.730578i
$85$	89.5027			1.05297
$86$	−89.5673	−	100.130i	−1.04148	−	1.16431i
$87$	94.1702	+	56.4689i	1.08242	+	0.649068i
$88$	−22.6965	−	31.8915i	−0.257915	−	0.362403i
$89$	−58.7091			−0.659652			−0.329826	−	0.944042i	$-0.606990\pi$
$89$	−58.7091			−0.659652			−0.329826	+	0.944042i	$0.606990\pi$
$90$	−23.8789	+	65.3055i	−0.265321	+	0.725617i
$91$	−66.6535			−0.732456
$92$	−1.79437	+	16.0624i	−0.0195040	+	0.174591i
$93$	104.939	+	62.9263i	1.12838	+	0.676627i
$94$	91.4205	−	81.7764i	0.972559	−	0.869962i
$95$	−51.8293	+	51.9700i	−0.545572	+	0.547053i
$96$	−95.9481	−	3.15683i	−0.999459	−	0.0328836i
$97$		−	24.5355i		−	0.252943i	−0.991970	−	0.126472i	$-0.959635\pi$
$97$		−	24.5355i		−	0.252943i	0.991970	−	0.126472i	$-0.0403653\pi$
$98$	33.0096	−	29.5274i	0.336833	−	0.301300i
$99$	−20.7431	−	38.8447i	−0.209526	−	0.392371i
$100$	4.47511	−	40.0593i	0.0447511	−	0.400593i
$101$		−	165.635i		−	1.63995i	−0.572399	−	0.819975i	$-0.693987\pi$
$101$		−	165.635i		−	1.63995i	0.572399	−	0.819975i	$-0.306013\pi$
$102$	26.2013	+	136.523i	0.256875	+	1.33846i
$103$	−10.5349			−0.102280			−0.0511402	−	0.998691i	$-0.516286\pi$
$103$	−10.5349			−0.102280			−0.0511402	+	0.998691i	$0.516286\pi$
$104$	51.5062	−	36.6559i	0.495252	−	0.352461i
$105$	83.8332	+	50.2704i	0.798412	+	0.478765i
$106$	70.1898	−	62.7853i	0.662168	−	0.592314i
$107$		−	30.1602i		−	0.281871i	−0.990019	−	0.140936i	$-0.954989\pi$
$107$		−	30.1602i		−	0.281871i	0.990019	−	0.140936i	$-0.0450111\pi$
$108$	−106.604	−	17.3061i	−0.987078	−	0.160241i
$109$		−	183.693i		−	1.68525i	−0.538498	−	0.842627i	$-0.681008\pi$
$109$		−	183.693i		−	1.68525i	0.538498	−	0.842627i	$-0.318992\pi$
$110$	−25.2031	−	28.1754i	−0.229119	−	0.256140i
$111$	2.90928	−	4.85165i	0.0262097	−	0.0437085i
$112$	−29.7807	+	131.629i	−0.265899	+	1.17525i
$113$	49.7735			0.440474			0.220237	−	0.975446i	$-0.429317\pi$
$113$	49.7735			0.440474			0.220237	+	0.975446i	$0.429317\pi$
$114$	−94.4454	−	63.8442i	−0.828468	−	0.560036i
$115$			15.6088i			0.135729i
$116$	−16.2541	+	145.499i	−0.140121	+	1.25430i
$117$	62.7361	−	33.5010i	0.536206	−	0.286334i
$118$	−6.57700	−	7.35265i	−0.0557373	−	0.0623106i
$119$	195.425			1.64223
$120$	−92.4279	+	7.25764i	−0.770232	+	0.0604804i
$121$	−97.0594			−0.802144
$122$	117.394	−	105.010i	0.962244	−	0.860735i
$123$	−97.3102	−	58.3518i	−0.791140	−	0.474405i
$124$	−18.1128	+	162.138i	−0.146071	+	1.30756i
$125$		−	135.503i		−	1.08403i
$126$	−52.1385	+	142.592i	−0.413798	+	1.13168i
$127$	−51.9861			−0.409339			−0.204670	−	0.978831i	$-0.565612\pi$
$127$	−51.9861			−0.409339			−0.204670	+	0.978831i	$0.565612\pi$
$128$	−49.3759	−	118.093i	−0.385749	−	0.922604i
$129$	103.634	−	172.826i	0.803368	−	1.33973i
$130$	45.5046	−	40.7042i	0.350035	−	0.313109i
$131$	−185.137			−1.41326			−0.706631	−	0.707582i	$-0.749786\pi$
$131$	−185.137			−1.41326			−0.706631	+	0.707582i	$0.749786\pi$
$132$	35.5994	−	46.6918i	0.269692	−	0.353726i
$133$	−113.167	+	113.474i	−0.850879	+	0.853189i
$134$	−189.630	+	169.626i	−1.41515	+	1.26586i
$135$	−104.173	−	5.18001i	−0.771650	−	0.0383704i
$136$	−151.014	+	107.473i	−1.11040	+	0.790246i
$137$		−	209.911i		−	1.53219i	−0.642724	−	0.766097i	$-0.722196\pi$
$137$		−	209.911i		−	1.53219i	0.642724	−	0.766097i	$-0.277804\pi$
$138$	−23.8090	+	4.56937i	−0.172529	+	0.0331114i
$139$		−	244.001i		−	1.75541i	−0.479205	−	0.877703i	$-0.659075\pi$
$139$		−	244.001i		−	1.75541i	0.479205	−	0.877703i	$-0.340925\pi$
$140$	−14.4699	+	129.528i	−0.103356	+	0.925200i
$141$	157.793	+	94.6200i	1.11910	+	0.671064i
$142$	−24.2614	−	27.1227i	−0.170855	−	0.191005i
$143$			38.6652i			0.270386i
$144$	−38.1281	−	138.861i	−0.264778	−	0.964309i
$145$			141.391i			0.975107i
$146$	−10.3545	+	9.26220i	−0.0709213	+	0.0634397i
$147$	56.9749	+	34.1648i	0.387584	+	0.232414i
$148$	7.49612	+	0.837409i	0.0506495	+	0.00565817i
$149$			48.8242i			0.327679i	0.986487	+	0.163840i	$0.0523879\pi$
$149$			48.8242i			0.327679i	−0.986487	+	0.163840i	$0.947612\pi$
$150$	59.3790	−	11.3959i	0.395860	−	0.0759727i
$151$	104.293			0.690685			0.345343	−	0.938477i	$-0.387763\pi$
$151$	104.293			0.690685			0.345343	+	0.938477i	$0.387763\pi$
$152$	25.0444	−	149.923i	0.164766	−	0.986333i
$153$	−183.939	+	98.2235i	−1.20222	+	0.641983i
$154$	−55.0298	−	61.5197i	−0.357337	−	0.399478i
$155$			157.559i			1.01651i
$156$	75.4095	+	57.4947i	0.483394	+	0.368556i
$157$	36.2218			0.230712			0.115356	−	0.993324i	$-0.463199\pi$
$157$	36.2218			0.230712			0.115356	+	0.993324i	$0.463199\pi$
$158$	−18.7028	+	16.7298i	−0.118372	+	0.105885i
$159$	121.148	+	72.6462i	0.761938	+	0.456894i
$160$	−60.0521	−	108.050i	−0.375325	−	0.675312i
$161$			34.0811i			0.211684i
$162$	−22.5945	−	160.417i	−0.139472	−	0.990226i
$163$			61.4979i			0.377288i	0.982046	+	0.188644i	$0.0604092\pi$
$163$			61.4979i			0.377288i	−0.982046	+	0.188644i	$0.939591\pi$
$164$	16.7960	−	150.351i	0.102415	−	0.916774i
$165$	29.1614	−	48.6310i	0.176736	−	0.294733i
$166$	−98.0062	+	87.6674i	−0.590399	+	0.528117i
$167$			132.309i			0.792271i	0.918192	+	0.396135i	$0.129649\pi$
$167$			132.309i			0.792271i	−0.918192	+	0.396135i	$0.870351\pi$
$168$	−201.812	+	15.8467i	−1.20126	+	0.0943258i
$169$	106.554			0.630497
$170$	−133.417	+	119.343i	−0.784808	+	0.702017i
$171$	49.4819	−	163.684i	0.289368	−	0.957218i
$172$	267.027	+	29.8302i	1.55249	+	0.173432i
$173$	−179.362			−1.03677			−0.518386	−	0.855147i	$-0.673467\pi$
$173$	−179.362			−1.03677			−0.518386	+	0.855147i	$0.673467\pi$
$174$	−215.671	+	41.3911i	−1.23949	+	0.237880i
$175$		−	84.9976i		−	0.485700i
$176$	76.3567	+	17.2755i	0.433845	+	0.0981565i
$177$	7.60997	−	12.6907i	0.0429942	−	0.0716991i
$178$	87.5148	−	78.2827i	0.491656	−	0.439790i
$179$			24.5295i			0.137036i	0.997650	+	0.0685180i	$0.0218271\pi$
$179$			24.5295i			0.137036i	−0.997650	+	0.0685180i	$0.978173\pi$
$180$	−51.4833	−	129.188i	−0.286018	−	0.717711i
$181$		−	316.659i		−	1.74949i	−0.484579	−	0.874747i	$-0.661027\pi$
$181$		−	316.659i		−	1.74949i	0.484579	−	0.874747i	$-0.338973\pi$
$182$	99.3572	−	88.8758i	0.545918	−	0.488329i
$183$	202.623	+	121.502i	1.10723	+	0.663947i
$184$	−18.7428	−	26.3360i	−0.101863	−	0.143131i
$185$	7.28444			0.0393754
$186$	−240.333	+	46.1243i	−1.29211	+	0.247980i
$187$		−	113.364i		−	0.606227i
$188$	−27.2355	+	243.800i	−0.144870	+	1.29681i
$189$	−227.456	−	11.3103i	−1.20347	−	0.0598429i
$190$	7.96257	−	146.578i	0.0419082	−	0.771466i
$191$	−265.749			−1.39136			−0.695678	−	0.718353i	$-0.744896\pi$
$191$	−265.749			−1.39136			−0.695678	+	0.718353i	$0.744896\pi$
$192$	147.235	−	123.231i	0.766846	−	0.641831i
$193$			226.768i			1.17496i	0.809238	+	0.587481i	$0.199880\pi$
$193$			226.768i			1.17496i	−0.809238	+	0.587481i	$0.800120\pi$
$194$	32.7157	+	36.5739i	0.168637	+	0.188525i
$195$	78.5413	+	47.0971i	0.402776	+	0.241524i
$196$	−9.83403	+	88.0300i	−0.0501736	+	0.449133i
$197$			18.1015i			0.0918860i	0.998944	+	0.0459430i	$0.0146293\pi$
$197$			18.1015i			0.0918860i	−0.998944	+	0.0459430i	$0.985371\pi$
$198$	82.7163	+	30.2451i	0.417759	+	0.152753i
$199$			82.2624i			0.413379i	0.978407	+	0.206690i	$0.0662690\pi$
$199$			82.2624i			0.413379i	−0.978407	+	0.206690i	$0.933731\pi$
$200$	46.7442	+	65.6816i	0.233721	+	0.328408i
$201$	−327.304	−	196.267i	−1.62838	−	0.976451i
$202$	220.858	+	246.904i	1.09336	+	1.22230i
$203$			308.720i			1.52079i
$204$	−221.097	−	168.572i	−1.08381	−	0.826333i
$205$		−	146.105i		−	0.712708i
$206$	15.7038	−	14.0472i	0.0762322	−	0.0681903i
$207$	−17.1297	−	32.0781i	−0.0827520	−	0.154966i
$208$	−27.9008	+	123.320i	−0.134139	+	0.592883i
$209$	65.8255	+	65.6472i	0.314954	+	0.314101i
$210$	−191.997	+	36.8476i	−0.914270	+	0.175465i
$211$	−272.444			−1.29120			−0.645602	−	0.763674i	$-0.723393\pi$
$211$	−272.444			−1.29120			−0.645602	+	0.763674i	$0.723393\pi$
$212$	−20.9105	+	187.182i	−0.0986346	+	0.882935i
$213$	28.0719	−	46.8140i	0.131793	−	0.219784i
$214$	40.2157	+	44.9584i	0.187924	+	0.210086i
$215$	259.487			1.20692
$216$	181.986	−	116.349i	0.842528	−	0.538653i
$217$			344.023i			1.58536i
$218$	244.936	+	273.822i	1.12356	+	1.25606i
$219$	−17.8720	−	10.7169i	−0.0816072	−	0.0489356i
$220$	75.1382	+	8.39385i	0.341537	+	0.0381539i
$221$	183.089			0.828457
$222$	2.13247	+	11.1114i	0.00960571	+	0.0500511i
$223$	255.928			1.14766			0.573829	−	0.818975i	$-0.305458\pi$
$223$	255.928			1.14766			0.573829	+	0.818975i	$0.305458\pi$
$224$	−131.121	−	235.922i	−0.585361	−	1.05322i
$225$	42.7210	+	80.0020i	0.189871	+	0.355564i
$226$	−74.1950	+	66.3681i	−0.328297	+	0.293664i
$227$		−	351.832i		−	1.54992i	−0.632011	−	0.774960i	$-0.717770\pi$
$227$		−	351.832i		−	1.54992i	0.632011	−	0.774960i	$-0.282230\pi$
$228$	225.915	−	30.7641i	0.990855	−	0.134930i
$229$	350.301			1.52970			0.764849	−	0.644210i	$-0.222814\pi$
$229$	350.301			1.52970			0.764849	+	0.644210i	$0.222814\pi$
$230$	−20.8128	−	23.2673i	−0.0904904	−	0.101162i
$231$	63.6727	−	106.183i	0.275639	−	0.459669i
$232$	−169.780	−	238.562i	−0.731809	−	1.02828i
$233$			73.7965i			0.316723i	0.987381	+	0.158362i	$0.0506212\pi$
$233$			73.7965i			0.316723i	−0.987381	+	0.158362i	$0.949379\pi$
$234$	−48.8473	+	133.591i	−0.208749	+	0.570900i
$235$			236.916i			1.00815i
$236$	19.6080	+	2.19046i	0.0830849	+	0.00928161i
$237$	−32.2812	−	19.3573i	−0.136208	−	0.0816765i
$238$	−291.311	+	260.580i	−1.22399	+	1.09487i
$239$	−114.879			−0.480665			−0.240333	−	0.970691i	$-0.577257\pi$
$239$	−114.879			−0.480665			−0.240333	+	0.970691i	$0.577257\pi$
$240$	128.100	−	134.062i	0.533752	−	0.558591i
$241$			13.4562i			0.0558349i	0.999610	+	0.0279174i	$0.00888755\pi$
$241$			13.4562i			0.0558349i	−0.999610	+	0.0279174i	$0.991112\pi$
$242$	144.682	−	129.419i	0.597859	−	0.534790i
$243$	219.773	−	103.677i	0.904414	−	0.426656i
$244$	−34.9733	+	313.066i	−0.143333	+	1.28306i
$245$			85.5442i			0.349160i
$246$	222.862	−	42.7712i	0.905943	−	0.173867i
$247$	−106.023	+	106.311i	−0.429244	+	0.430410i
$248$	−189.195	−	265.842i	−0.762882	−	1.07195i
$249$	−169.160	−	101.436i	−0.679356	−	0.407374i
$250$	180.680	+	201.988i	0.722721	+	0.807954i
$251$	−39.0233			−0.155471			−0.0777356	−	0.996974i	$-0.524769\pi$
$251$	−39.0233			−0.155471			−0.0777356	+	0.996974i	$0.524769\pi$
$252$	−112.411	−	282.076i	−0.446077	−	1.11935i
$253$	19.7702			0.0781430
$254$	77.4932	−	69.3183i	0.305091	−	0.272907i
$255$	−230.280	−	138.087i	−0.903057	−	0.541516i
$256$	231.068	+	110.198i	0.902609	+	0.430461i
$257$	346.641			1.34880			0.674400	−	0.738366i	$-0.264402\pi$
$257$	346.641			1.34880			0.674400	+	0.738366i	$0.264402\pi$
$258$	75.9629	+	395.809i	0.294430	+	1.53414i
$259$	15.9052			0.0614102
$260$	−13.5565	+	121.352i	−0.0521403	+	0.466737i
$261$	−155.167	−	290.575i	−0.594510	−	1.11332i
$262$	275.975	−	246.862i	1.05334	−	0.942222i
$263$	94.4212			0.359016			0.179508	−	0.983757i	$-0.442549\pi$
$263$	94.4212			0.359016			0.179508	+	0.983757i	$0.442549\pi$
$264$	9.19256	+	117.070i	0.0348203	+	0.443445i
$265$			181.896i			0.686401i
$266$	17.3859	−	320.047i	0.0653605	−	1.20319i
$267$	151.051	+	90.5775i	0.565735	+	0.339242i
$268$	56.4936	−	505.706i	0.210797	−	1.88696i
$269$	259.031			0.962939			0.481469	−	0.876463i	$-0.340103\pi$
$269$	259.031			0.962939			0.481469	+	0.876463i	$0.340103\pi$
$270$	162.192	−	131.182i	0.600712	−	0.485860i
$271$		−	141.103i		−	0.520675i	−0.965518	−	0.260337i	$-0.916166\pi$
$271$		−	141.103i		−	0.520675i	0.965518	−	0.260337i	$-0.0838338\pi$
$272$	81.8039	−	361.568i	0.300750	−	1.32929i
$273$	171.491	+	102.834i	0.628174	+	0.376683i
$274$	279.895	+	312.904i	1.02151	+	1.14198i
$275$	−49.3064			−0.179296
$276$	29.3981	−	38.5582i	0.106515	−	0.139704i
$277$	209.599			0.756674			0.378337	−	0.925668i	$-0.376496\pi$
$277$	209.599			0.756674			0.378337	+	0.925668i	$0.376496\pi$
$278$	325.352	+	363.721i	1.17033	+	1.30835i
$279$	−172.911	−	323.804i	−0.619753	−	1.16059i
$280$	−151.143	−	212.375i	−0.539797	−	0.758483i
$281$	−291.297			−1.03664			−0.518322	−	0.855186i	$-0.673443\pi$
$281$	−291.297			−1.03664			−0.518322	+	0.855186i	$0.673443\pi$
$282$	−361.380	+	69.3554i	−1.28149	+	0.245941i
$283$			256.124i			0.905033i	0.891756	+	0.452516i	$0.149474\pi$
$283$			256.124i			0.905033i	−0.891756	+	0.452516i	$0.850526\pi$
$284$	72.3307	+	8.08023i	0.254686	+	0.0284515i
$285$	213.531	−	53.7493i	0.749231	−	0.188594i
$286$	−51.5561	−	57.6363i	−0.180266	−	0.201526i
$287$		−	319.014i		−	1.11155i
$288$	241.992	+	156.153i	0.840251	+	0.542197i
$289$	−247.808			−0.857468
$290$	−188.530	−	210.764i	−0.650104	−	0.726773i
$291$	−37.8539	+	63.1269i	−0.130082	+	0.216931i
$292$	3.08476	−	27.6134i	0.0105642	−	0.0945665i
$293$	−489.310			−1.67000			−0.835000	−	0.550250i	$-0.814532\pi$
$293$	−489.310			−1.67000			−0.835000	+	0.550250i	$0.814532\pi$
$294$	−130.485	+	25.0424i	−0.443827	+	0.0851784i
$295$	19.0543			0.0645910
$296$	−12.2907	+	8.74705i	−0.0415227	+	0.0295508i
$297$	−6.56102	+	131.946i	−0.0220910	+	0.444261i
$298$	−65.1022	−	72.7799i	−0.218464	−	0.244228i
$299$			31.9298i			0.106789i
$300$	−73.3182	+	96.1634i	−0.244394	+	0.320545i
$301$	566.578			1.88232
$302$	−155.465	+	139.065i	−0.514786	+	0.460480i
$303$	−255.545	+	426.159i	−0.843383	+	1.40646i
$304$	162.574	+	256.877i	0.534784	+	0.844989i
$305$			304.225i			0.997460i
$306$	143.218	−	391.682i	0.468033	−	1.28001i
$307$	245.233			0.798805			0.399402	−	0.916776i	$-0.369218\pi$
$307$	245.233			0.798805			0.399402	+	0.916776i	$0.369218\pi$
$308$	164.061	+	18.3276i	0.532665	+	0.0595052i
$309$	27.1050	+	16.2534i	0.0877183	+	0.0526001i
$310$	−210.089	−	234.866i	−0.677708	−	0.757632i
$311$	−536.846			−1.72619			−0.863097	−	0.505039i	$-0.831478\pi$
$311$	−536.846			−1.72619			−0.863097	+	0.505039i	$0.831478\pi$
$312$	−189.073	+	14.8464i	−0.606003	+	0.0475847i
$313$	−500.379			−1.59866			−0.799328	−	0.600895i	$-0.794811\pi$
$313$	−500.379			−1.59866			−0.799328	+	0.600895i	$0.794811\pi$
$314$	−53.9941	+	48.2982i	−0.171956	+	0.153816i
$315$	−138.135	−	258.679i	−0.438522	−	0.821204i
$316$	5.57183	−	49.8766i	0.0176324	−	0.157837i
$317$	−372.385			−1.17472			−0.587358	−	0.809327i	$-0.699832\pi$
$317$	−372.385			−1.17472			−0.587358	+	0.809327i	$0.699832\pi$
$318$	−277.456	+	53.2488i	−0.872504	+	0.167449i
$319$	179.086			0.561398
$320$	233.591	+	80.9913i	0.729970	+	0.253098i
$321$	−46.5318	+	77.5986i	−0.144959	+	0.241740i
$322$	−45.4438	−	50.8031i	−0.141130	−	0.157774i
$323$	310.856	−	311.700i	0.962401	−	0.965014i
$324$	247.580	+	208.998i	0.764136	+	0.645055i
$325$		−	79.6322i		−	0.245022i
$326$	−82.0014	−	91.6720i	−0.251538	−	0.281202i
$327$	−283.405	+	472.619i	−0.866681	+	1.44532i
$328$	175.441	+	246.517i	0.534881	+	0.751575i
$329$			517.294i			1.57232i
$330$	21.3750	+	111.376i	0.0647728	+	0.337502i
$331$	−150.822			−0.455656			−0.227828	−	0.973701i	$-0.573162\pi$
$331$	−150.822			−0.455656			−0.227828	+	0.973701i	$0.573162\pi$
$332$	29.1975	−	261.363i	0.0879441	−	0.787238i
$333$	−14.9704	+	7.99421i	−0.0449563	+	0.0240066i
$334$	−176.421	−	197.227i	−0.528207	−	0.590500i
$335$		−	491.426i		−	1.46694i
$336$	279.701	−	292.718i	0.832444	−	0.871185i
$337$		−	358.426i		−	1.06358i	−0.846877	−	0.531790i	$-0.821520\pi$
$337$		−	358.426i		−	1.06358i	0.846877	−	0.531790i	$-0.178480\pi$
$338$	−158.835	+	142.079i	−0.469926	+	0.420352i
$339$	−128.061	−	76.7916i	−0.377762	−	0.226524i
$340$	39.7469	−	355.797i	0.116903	−	1.04646i
$341$	199.565			0.585235
$342$	144.496	+	309.975i	0.422504	+	0.906361i
$343$		−	226.519i		−	0.660406i
$344$	−437.821	+	311.588i	−1.27273	+	0.905779i
$345$	24.0816	−	40.1596i	0.0698017	−	0.116405i
$346$	267.366	−	239.161i	0.772733	−	0.691216i
$347$	286.724			0.826293			0.413146	−	0.910665i	$-0.364430\pi$
$347$	286.724			0.826293			0.413146	+	0.910665i	$0.364430\pi$
$348$	266.299	−	349.275i	0.765227	−	1.00366i
$349$	−243.384			−0.697376			−0.348688	−	0.937239i	$-0.613373\pi$
$349$	−243.384			−0.697376			−0.348688	+	0.937239i	$0.613373\pi$
$350$	113.336	+	126.702i	0.323817	+	0.362005i
$351$	−213.098	−	10.5964i	−0.607118	−	0.0301891i
$352$	−136.856	+	76.0622i	−0.388797	+	0.216086i
$353$		−	283.425i		−	0.802902i	−0.915880	−	0.401451i	$-0.868506\pi$
$353$		−	283.425i		−	0.802902i	0.915880	−	0.401451i	$-0.131494\pi$
$354$	5.57802	+	29.0646i	0.0157571	+	0.0821034i
$355$	70.2882			0.197995
$356$	−26.0719	+	233.384i	−0.0732357	+	0.655574i
$357$	−502.805	−	301.506i	−1.40842	−	0.844553i
$358$	−32.7076	−	36.5649i	−0.0913620	−	0.102137i
$359$	85.1673			0.237235			0.118617	−	0.992940i	$-0.462154\pi$
$359$	85.1673			0.237235			0.118617	+	0.992940i	$0.462154\pi$
$360$	249.003	+	123.927i	0.691675	+	0.344240i
$361$	0.978992	+	360.999i	0.00271189	+	0.999996i
$362$	422.233	+	472.028i	1.16639	+	1.30394i
$363$	249.722	+	149.745i	0.687940	+	0.412521i
$364$	−29.5999	+	264.966i	−0.0813185	+	0.727928i
$365$		−	26.8337i		−	0.0735169i
$366$	−464.051	+	89.0598i	−1.26790	+	0.243333i
$367$			13.7873i			0.0375677i	0.999824	+	0.0187838i	$0.00597944\pi$
$367$			13.7873i			0.0375677i	−0.999824	+	0.0187838i	$0.994021\pi$
$368$	63.0555	+	14.2662i	0.171347	+	0.0387668i
$369$	160.341	+	300.264i	0.434529	+	0.813725i
$370$	−10.8586	+	9.71308i	−0.0293475	+	0.0262516i
$371$			397.162i			1.07052i
$372$	296.751	−	389.216i	0.797718	−	1.04628i
$373$			318.887i			0.854926i	0.904033	+	0.427463i	$0.140593\pi$
$373$			318.887i			0.854926i	−0.904033	+	0.427463i	$0.859407\pi$
$374$	151.160	+	168.987i	0.404172	+	0.451837i
$375$	−209.057	+	348.634i	−0.557486	+	0.929690i
$376$	−284.485	−	399.737i	−0.756609	−	1.06313i
$377$			289.232i			0.767194i
$378$	354.139	−	286.431i	0.936876	−	0.757753i
$379$	−547.694			−1.44510			−0.722552	−	0.691317i	$-0.757031\pi$
$379$	−547.694			−1.44510			−0.722552	+	0.691317i	$0.757031\pi$
$380$	183.578	+	229.115i	0.483101	+	0.602934i
$381$	133.754	+	80.2052i	0.351060	+	0.210512i
$382$	396.139	−	354.350i	1.03701	−	0.927618i
$383$		−	180.836i		−	0.472157i	−0.971734	−	0.236079i	$-0.924138\pi$
$383$		−	180.836i		−	0.472157i	0.971734	−	0.236079i	$-0.0758623\pi$
$384$	−55.1585	+	380.018i	−0.143642	+	0.989630i
$385$	159.428			0.414098
$386$	−302.372	−	338.032i	−0.783348	−	0.875730i
$387$	−533.278	+	284.770i	−1.37798	+	0.735840i
$388$	−97.5353	−	10.8959i	−0.251380	−	0.0280822i
$389$		−	676.754i		−	1.73973i	−0.493291	−	0.869864i	$-0.664206\pi$
$389$		−	676.754i		−	1.73973i	0.493291	−	0.869864i	$-0.335794\pi$
$390$	−179.877	+	34.5217i	−0.461223	+	0.0885171i
$391$		−	93.6166i		−	0.239429i
$392$	−102.720	−	144.335i	−0.262041	−	0.368201i
$393$	476.336	+	285.634i	1.21205	+	0.726803i
$394$	−24.1366	−	26.9831i	−0.0612604	−	0.0684850i
$395$		−	48.4682i		−	0.122704i
$396$	−163.630	+	65.2089i	−0.413207	+	0.164669i
$397$	−254.968			−0.642237			−0.321119	−	0.947039i	$-0.604059\pi$
$397$	−254.968			−0.642237			−0.321119	+	0.947039i	$0.604059\pi$
$398$	−109.689	−	122.625i	−0.275600	−	0.308102i
$399$	466.235	−	117.359i	1.16851	−	0.294133i
$400$	−157.259	−	35.5796i	−0.393148	−	0.0889489i
$401$	−226.176			−0.564031			−0.282015	−	0.959410i	$-0.591003\pi$
$401$	−226.176			−0.564031			−0.282015	+	0.959410i	$0.591003\pi$
$402$	749.598	−	143.861i	1.86467	−	0.357864i
$403$			322.307i			0.799769i
$404$	−658.444	−	73.5563i	−1.62981	−	0.182070i
$405$	260.032	+	174.047i	0.642054	+	0.429746i
$406$	−411.647	−	460.194i	−1.01391	−	1.13348i
$407$		−	9.22651i		−	0.0226695i
$408$	554.353	−	43.5290i	1.35871	−	0.106689i
$409$			146.135i			0.357299i	0.983913	+	0.178649i	$0.0571728\pi$
$409$			146.135i			0.357299i	−0.983913	+	0.178649i	$0.942827\pi$
$410$	194.817	+	217.792i	0.475163	+	0.531200i
$411$	−323.854	+	540.075i	−0.787967	+	1.31405i
$412$	−4.67840	+	41.8790i	−0.0113553	+	0.101648i
$413$	41.6043			0.100737
$414$	68.3073	+	24.9765i	0.164993	+	0.0603297i
$415$		−	253.982i		−	0.612006i
$416$	−122.844	−	221.030i	−0.295298	−	0.531321i
$417$	−376.450	+	627.786i	−0.902758	+	1.50548i
$418$	−185.657	−	10.0854i	−0.444155	−	0.0241278i
$419$	531.918			1.26949			0.634747	−	0.772720i	$-0.281104\pi$
$419$	531.918			1.26949			0.634747	+	0.772720i	$0.281104\pi$
$420$	237.068	−	310.935i	0.564447	−	0.740322i
$421$			477.779i			1.13487i	0.823419	+	0.567433i	$0.192063\pi$
$421$			477.779i			1.13487i	−0.823419	+	0.567433i	$0.807937\pi$
$422$	406.119	−	363.277i	0.962367	−	0.860845i
$423$	−260.000	−	486.891i	−0.614657	−	1.15104i
$424$	−218.418	−	306.906i	−0.515138	−	0.723834i
$425$			233.478i			0.549360i
$426$	20.5764	+	107.214i	0.0483013	+	0.251677i
$427$			664.262i			1.55565i
$428$	−119.895	−	13.3938i	−0.280129	−	0.0312938i
$429$	59.6534	−	99.4808i	0.139052	−	0.231890i
$430$	−386.805	+	346.000i	−0.899546	+	0.804651i
$431$			72.3916i			0.167962i	0.996467	+	0.0839810i	$0.0267635\pi$
$431$			72.3916i			0.167962i	−0.996467	+	0.0839810i	$0.973237\pi$
$432$	−116.138	+	416.096i	−0.268838	+	0.963185i
$433$		−	829.253i		−	1.91513i	−0.288210	−	0.957567i	$-0.593060\pi$
$433$		−	829.253i		−	1.91513i	0.288210	−	0.957567i	$-0.406940\pi$
$434$	−458.720	−	512.819i	−1.05696	−	1.18161i
$435$	218.140	−	363.781i	0.501472	−	0.836278i
$436$	−730.228	−	81.5755i	−1.67484	−	0.187100i
$437$	54.3588	+	54.2116i	0.124391	+	0.124054i
$438$	40.9308	−	7.85536i	0.0934494	−	0.0179346i
$439$	−129.412			−0.294787			−0.147394	−	0.989078i	$-0.547088\pi$
$439$	−129.412			−0.294787			−0.147394	+	0.989078i	$0.547088\pi$
$440$	−123.197	+	87.6769i	−0.279994	+	0.199266i
$441$	−93.8792	−	175.804i	−0.212878	−	0.398648i
$442$	−272.922	+	244.131i	−0.617470	+	0.552332i
$443$	201.558			0.454984			0.227492	−	0.973780i	$-0.426947\pi$
$443$	201.558			0.454984			0.227492	+	0.973780i	$0.426947\pi$
$444$	−17.9947	−	13.7197i	−0.0405285	−	0.0309003i
$445$			226.794i			0.509649i
$446$	−381.499	+	341.254i	−0.855379	+	0.765143i
$447$	75.3269	−	125.619i	0.168517	−	0.281026i
$448$	510.034	+	176.841i	1.13847	+	0.394734i
$449$	698.201			1.55501			0.777507	−	0.628874i	$-0.216484\pi$
$449$	698.201			1.55501			0.777507	+	0.628874i	$0.216484\pi$
$450$	−170.357	−	62.2909i	−0.378571	−	0.138424i
$451$	−185.057			−0.410327
$452$	22.1038	−	197.863i	0.0489021	−	0.437751i
$453$	−268.334	−	160.906i	−0.592350	−	0.355201i
$454$	469.133	+	524.459i	1.03333	+	1.15520i
$455$			257.483i			0.565898i
$456$	−295.740	+	347.094i	−0.648552	+	0.761170i
$457$	−16.4642			−0.0360267			−0.0180133	−	0.999838i	$-0.505734\pi$
$457$	−16.4642			−0.0360267			−0.0180133	+	0.999838i	$0.505734\pi$
$458$	−522.176	+	467.091i	−1.14012	+	1.01985i
$459$	624.794	+	31.0680i	1.36121	+	0.0676864i
$460$	62.0493	+	6.93166i	0.134890	+	0.0150688i
$461$			388.330i			0.842364i	0.906976	+	0.421182i	$0.138385\pi$
$461$			388.330i			0.842364i	−0.906976	+	0.421182i	$0.861615\pi$
$462$	46.6713	+	243.184i	0.101020	+	0.526372i
$463$		−	602.607i		−	1.30153i	−0.759280	−	0.650764i	$-0.774449\pi$
$463$		−	602.607i		−	1.30153i	0.759280	−	0.650764i	$-0.225551\pi$
$464$	571.181	+	129.229i	1.23099	+	0.278510i
$465$	243.085	−	405.380i	0.522764	−	0.871786i
$466$	−98.4003	−	110.005i	−0.211159	−	0.236062i
$467$	−704.360			−1.50827			−0.754133	−	0.656722i	$-0.771943\pi$
$467$	−704.360			−1.50827			−0.754133	+	0.656722i	$0.771943\pi$
$468$	−105.315	−	264.270i	−0.225033	−	0.564680i
$469$		−	1073.00i		−	2.28786i
$470$	−315.904	−	353.159i	−0.672135	−	0.751402i
$471$	−93.1944	−	55.8838i	−0.197865	−	0.118649i
$472$	−32.1495	+	22.8802i	−0.0681134	+	0.0484749i
$473$		−	328.667i		−	0.694857i
$474$	73.9311	−	14.1887i	0.155973	−	0.0299340i
$475$	−135.570	−	135.203i	−0.285410	−	0.284637i
$476$	86.7856	−	776.867i	0.182323	−	1.63207i
$477$	−199.620	−	373.820i	−0.418490	−	0.783689i
$478$	171.245	−	153.180i	0.358252	−	0.320460i
$479$	−327.028			−0.682731			−0.341366	−	0.939931i	$-0.610889\pi$
$479$	−327.028			−0.682731			−0.341366	+	0.939931i	$0.610889\pi$
$480$	−12.1949	+	370.649i	−0.0254060	+	0.772185i
$481$	14.9012			0.0309797
$482$	−17.9425	−	20.0585i	−0.0372251	−	0.0416152i
$483$	52.5810	−	87.6866i	0.108863	−	0.181546i
$484$	−43.1028	+	385.838i	−0.0890553	+	0.797185i
$485$	−94.7810			−0.195425
$486$	−189.361	+	447.592i	−0.389632	+	0.920971i
$487$	182.891			0.375546			0.187773	−	0.982212i	$-0.439873\pi$
$487$	182.891			0.375546			0.187773	+	0.982212i	$0.439873\pi$
$488$	−365.309	−	513.306i	−0.748584	−	1.05186i
$489$	94.8802	−	158.227i	0.194029	−	0.323572i
$490$	−114.065	−	127.517i	−0.232785	−	0.260238i
$491$	674.288			1.37330			0.686648	−	0.726990i	$-0.259081\pi$
$491$	674.288			1.37330			0.686648	+	0.726990i	$0.259081\pi$
$492$	−275.179	+	360.921i	−0.559306	+	0.733580i
$493$		−	848.015i		−	1.72011i
$494$	16.2884	−	299.845i	0.0329725	−	0.606973i
$495$	−150.058	+	80.1308i	−0.303147	+	0.161880i
$496$	636.498	+	144.006i	1.28326	+	0.290335i
$497$	153.471			0.308795
$498$	387.413	−	74.3515i	0.777938	−	0.149300i
$499$		−	431.909i		−	0.865550i	−0.901502	−	0.432775i	$-0.857534\pi$
$499$		−	431.909i		−	0.865550i	0.901502	−	0.432775i	$-0.142466\pi$
$500$	−538.663	−	60.1753i	−1.07733	−	0.120351i
$501$	204.129	−	340.416i	0.407444	−	0.679472i
$502$	58.1701	−	52.0337i	0.115877	−	0.103653i
$503$	392.419			0.780157			0.390078	−	0.920782i	$-0.372448\pi$
$503$	392.419			0.780157			0.390078	+	0.920782i	$0.372448\pi$
$504$	543.686	+	270.588i	1.07874	+	0.536881i
$505$	−639.850			−1.26703
$506$	−29.4705	+	26.3616i	−0.0582420	+	0.0520980i
$507$	−274.150	−	164.394i	−0.540730	−	0.324248i
$508$	−23.0863	+	206.659i	−0.0454455	+	0.406809i
$509$	606.450			1.19145			0.595727	−	0.803187i	$-0.296864\pi$
$509$	606.450			1.19145			0.595727	+	0.803187i	$0.296864\pi$
$510$	527.391	−	101.216i	1.03410	−	0.198463i
$511$		−	58.5900i		−	0.114658i
$512$	−491.380	+	143.839i	−0.959727	+	0.280935i
$513$	−379.846	+	344.798i	−0.740441	+	0.672121i
$514$	−516.722	+	462.212i	−1.00530	+	0.899245i
$515$			40.6964i			0.0790221i
$516$	−641.007	−	488.725i	−1.24226	−	0.947141i
$517$	300.078			0.580423
$518$	−23.7092	+	21.2081i	−0.0457706	+	0.0409422i
$519$	461.476	+	276.723i	0.889163	+	0.533184i
$520$	−141.602	−	198.969i	−0.272312	−	0.382633i
$521$	893.422			1.71482			0.857411	−	0.514633i	$-0.172072\pi$
$521$	893.422			1.71482			0.857411	+	0.514633i	$0.172072\pi$
$522$	618.753	+	226.247i	1.18535	+	0.433423i
$523$	388.270			0.742390			0.371195	−	0.928555i	$-0.378948\pi$
$523$	388.270			0.742390			0.371195	+	0.928555i	$0.378948\pi$
$524$	−82.2170	+	735.971i	−0.156903	+	1.40453i
$525$	−131.136	+	218.688i	−0.249783	+	0.416550i
$526$	−140.749	+	125.901i	−0.267584	+	0.239356i
$527$		−	944.989i		−	1.79315i
$528$	−169.803	−	162.253i	−0.321597	−	0.307296i
$529$	−512.674			−0.969138
$530$	−242.541	−	271.144i	−0.457624	−	0.511593i
$531$	−39.1590	+	20.9109i	−0.0737459	+	0.0393803i
$532$	400.835	+	500.261i	0.753449	+	0.940341i
$533$		−	298.876i		−	0.560744i
$534$	−345.941	+	66.3923i	−0.647830	+	0.124330i
$535$	−116.509			−0.217775
$536$	590.096	+	829.160i	1.10093	+	1.54694i
$537$	37.8445	−	63.1113i	0.0704740	−	0.117526i
$538$	−386.124	+	345.391i	−0.717703	+	0.641992i
$539$	108.351			0.201021
$540$	−66.8536	+	411.814i	−0.123803	+	0.762619i
$541$	−442.329			−0.817614			−0.408807	−	0.912621i	$-0.634055\pi$
$541$	−442.329			−0.817614			−0.408807	+	0.912621i	$0.634055\pi$
$542$	188.147	+	210.335i	0.347134	+	0.388072i
$543$	−488.547	+	814.724i	−0.899719	+	1.50041i
$544$	360.173	+	648.049i	0.662083	+	1.19127i
$545$	−709.608			−1.30203
$546$	−392.753	+	75.3764i	−0.719328	+	0.138052i
$547$	−486.853			−0.890042			−0.445021	−	0.895520i	$-0.646804\pi$
$547$	−486.853			−0.890042			−0.445021	+	0.895520i	$0.646804\pi$
$548$	−834.452	−	93.2185i	−1.52272	−	0.170107i
$549$	−333.868	−	625.221i	−0.608138	−	1.13884i
$550$	73.4987	−	65.7452i	0.133634	−	0.119537i
$551$	492.403	+	491.069i	0.893653	+	0.891233i
$552$	7.59124	+	96.6763i	0.0137522	+	0.175138i
$553$		−	105.828i		−	0.191371i
$554$	−312.439	+	279.479i	−0.563969	+	0.504475i
$555$	−18.7420	−	11.2386i	−0.0337694	−	0.0202497i
$556$	−969.972	−	108.358i	−1.74455	−	0.194888i
$557$			1069.06i			1.91933i	0.281153	+	0.959663i	$0.409283\pi$
$557$			1069.06i			1.91933i	−0.281153	+	0.959663i	$0.590717\pi$
$558$	689.510	+	252.119i	1.23568	+	0.451826i
$559$	530.813			0.949576
$560$	508.483	+	115.043i	0.908005	+	0.205434i
$561$	−174.901	+	291.673i	−0.311766	+	0.519916i
$562$	434.222	−	388.415i	0.772638	−	0.691131i
$563$		−	318.004i		−	0.564838i	−0.959291	−	0.282419i	$-0.908863\pi$
$563$		−	318.004i		−	0.564838i	0.959291	−	0.282419i	$-0.0911369\pi$
$564$	446.214	−	585.249i	0.791159	−	1.03768i
$565$		−	192.276i		−	0.340311i
$566$	−341.516	−	381.792i	−0.603386	−	0.674545i
$567$	567.768	+	380.024i	1.00135	+	0.670237i
$568$	−118.594	+	84.4010i	−0.208793	+	0.148593i
$569$	904.414			1.58948			0.794740	−	0.606950i	$-0.207607\pi$
$569$	904.414			1.58948			0.794740	+	0.606950i	$0.207607\pi$
$570$	−246.631	+	364.844i	−0.432686	+	0.640077i
$571$			112.212i			0.196519i	0.995161	+	0.0982596i	$0.0313275\pi$
$571$			112.212i			0.196519i	−0.995161	+	0.0982596i	$0.968672\pi$
$572$	153.705	+	17.1707i	0.268714	+	0.0300187i
$573$	683.740	+	410.003i	1.19326	+	0.715538i
$574$	425.373	+	475.539i	0.741068	+	0.828464i
$575$	−40.7174			−0.0708128
$576$	−568.941	+	89.9033i	−0.987744	+	0.156082i
$577$	12.3318			0.0213723			0.0106862	−	0.999943i	$-0.496598\pi$
$577$	12.3318			0.0213723			0.0106862	+	0.999943i	$0.496598\pi$
$578$	369.396	−	330.428i	0.639094	−	0.571674i
$579$	349.862	−	583.446i	0.604252	−	1.00768i
$580$	562.066	+	62.7897i	0.969079	+	0.108258i
$581$		−	554.559i		−	0.954490i
$582$	−27.7465	−	144.575i	−0.0476743	−	0.248410i
$583$	230.391			0.395181
$584$	32.2215	+	45.2752i	0.0551737	+	0.0775261i
$585$	−129.415	−	242.350i	−0.221222	−	0.414274i
$586$	729.391	−	652.446i	1.24469	−	1.11339i
$587$	183.598			0.312774			0.156387	−	0.987696i	$-0.450015\pi$
$587$	183.598			0.312774			0.156387	+	0.987696i	$0.450015\pi$
$588$	161.116	−	211.318i	0.274007	−	0.359385i
$589$	548.711	+	547.225i	0.931598	+	0.929075i
$590$	−28.4034	+	25.4071i	−0.0481413	+	0.0430628i
$591$	27.9274	−	46.5731i	0.0472545	−	0.0788038i
$592$	6.65786	−	29.4273i	0.0112464	−	0.0497082i
$593$		−	488.731i		−	0.824167i	−0.911146	−	0.412083i	$-0.864801\pi$
$593$		−	488.731i		−	0.824167i	0.911146	−	0.412083i	$-0.135199\pi$
$594$	−166.156	−	205.433i	−0.279724	−	0.345847i
$595$		−	754.930i		−	1.26879i
$596$	194.089	+	21.6822i	0.325653	+	0.0363795i
$597$	126.916	−	211.651i	0.212590	−	0.354525i
$598$	−42.5752	−	47.5962i	−0.0711960	−	0.0795923i
$599$			47.6552i			0.0795580i	0.999209	+	0.0397790i	$0.0126654\pi$
$599$			47.6552i			0.0795580i	−0.999209	+	0.0397790i	$0.987335\pi$
$600$	−18.9324	−	241.109i	−0.0315540	−	0.401848i
$601$		−	6.98813i		−	0.0116275i	−0.999983	−	0.00581375i	$-0.998149\pi$
$601$		−	6.98813i		−	0.0116275i	0.999983	−	0.00581375i	$-0.00185058\pi$
$602$	−844.570	+	755.475i	−1.40294	+	1.25494i
$603$	539.308	+	1009.94i	0.894375	+	1.67486i
$604$	46.3153	−	414.595i	0.0766810	−	0.686415i
$605$			374.942i			0.619739i
$606$	−187.312	−	975.998i	−0.309095	−	1.61056i
$607$	1166.33			1.92146			0.960732	−	0.277479i	$-0.0894988\pi$
$607$	1166.33			1.92146			0.960732	+	0.277479i	$0.0894988\pi$
$608$	−584.861	−	166.137i	−0.961943	−	0.273251i
$609$	476.299	−	794.298i	0.782100	−	1.30427i
$610$	−405.654	−	453.494i	−0.665007	−	0.743433i
$611$			484.641i			0.793193i
$612$	308.780	+	774.828i	0.504543	+	1.26606i
$613$	729.842			1.19061			0.595303	−	0.803501i	$-0.297032\pi$
$613$	729.842			1.19061			0.595303	+	0.803501i	$0.297032\pi$
$614$	−365.557	+	326.994i	−0.595370	+	0.532563i
$615$	−225.414	+	375.911i	−0.366527	+	0.611237i
$616$	−268.995	+	191.439i	−0.436681	+	0.310777i
$617$			211.316i			0.342490i	0.985229	+	0.171245i	$0.0547789\pi$
$617$			211.316i			0.342490i	−0.985229	+	0.171245i	$0.945221\pi$
$618$	−62.0764	+	11.9136i	−0.100447	+	0.0192776i
$619$			1160.53i			1.87484i	0.348201	+	0.937420i	$0.386793\pi$
$619$			1160.53i			1.87484i	−0.348201	+	0.937420i	$0.613207\pi$
$620$	626.340	+	69.9699i	1.01023	+	0.112855i
$621$	−5.41811	+	108.961i	−0.00872481	+	0.175460i
$622$	800.251	−	715.831i	1.28658	−	1.15085i
$623$			495.194i			0.794854i
$624$	262.046	−	274.241i	0.419945	−	0.439488i
$625$	−271.524			−0.434438
$626$	745.891	−	667.206i	1.19152	−	1.06582i
$627$	−68.0791	−	270.459i	−0.108579	−	0.431354i
$628$	16.0856	−	143.992i	0.0256141	−	0.229286i
$629$	−43.6898			−0.0694591
$630$	550.833	+	201.412i	0.874339	+	0.319701i
$631$		−	153.464i		−	0.243208i	−0.992579	−	0.121604i	$-0.961196\pi$
$631$		−	153.464i		−	0.243208i	0.992579	−	0.121604i	$-0.0388037\pi$
$632$	58.1998	+	81.7781i	0.0920883	+	0.129396i
$633$	700.965	+	420.332i	1.10737	+	0.664031i
$634$	555.096	−	496.538i	0.875546	−	0.783183i
$635$			200.823i			0.316257i
$636$	342.589	−	449.336i	0.538661	−	0.706503i
$637$			174.991i			0.274712i
$638$	−266.955	+	238.793i	−0.418424	+	0.374284i
$639$	−144.451	+	77.1368i	−0.226058	+	0.120715i
$640$	−456.196	+	190.740i	−0.712806	+	0.298031i
$641$	−870.299			−1.35772			−0.678860	−	0.734268i	$-0.737526\pi$
$641$	−870.299			−1.35772			−0.678860	+	0.734268i	$0.737526\pi$
$642$	−34.1073	−	177.718i	−0.0531266	−	0.276819i
$643$			511.034i			0.794765i	0.917653	+	0.397382i	$0.130081\pi$
$643$			511.034i			0.794765i	−0.917653	+	0.397382i	$0.869919\pi$
$644$	135.482	+	15.1350i	0.210375	+	0.0235015i
$645$	−667.628	−	400.342i	−1.03508	−	0.620685i
$646$	−47.7569	+	879.131i	−0.0739271	+	1.36088i
$647$	940.178			1.45314			0.726568	−	0.687095i	$-0.241114\pi$
$647$	940.178			1.45314			0.726568	+	0.687095i	$0.241114\pi$
$648$	−647.734	+	18.5803i	−0.999589	+	0.0286732i
$649$		−	24.1343i		−	0.0371869i
$650$	106.182	+	118.704i	0.163356	+	0.182621i
$651$	530.766	−	885.130i	0.815308	−	1.35965i
$652$	244.471	+	27.3104i	0.374955	+	0.0418871i
$653$		−	1230.75i		−	1.88477i	−0.334536	−	0.942383i	$-0.608580\pi$
$653$		−	1230.75i		−	1.88477i	0.334536	−	0.942383i	$-0.391420\pi$
$654$	−207.733	−	1082.40i	−0.317634	−	1.65505i
$655$			715.189i			1.09189i
$656$	−590.227	−	133.538i	−0.899736	−	0.203563i
$657$	29.4482	+	55.1465i	0.0448223	+	0.0839369i
$658$	−689.761	−	771.106i	−1.04827	−	1.17189i
$659$			444.737i			0.674866i	0.941350	+	0.337433i	$0.109559\pi$
$659$			444.737i			0.674866i	−0.941350	+	0.337433i	$0.890441\pi$
$660$	−180.371	−	137.521i	−0.273290	−	0.208365i
$661$			711.531i			1.07645i	0.842802	+	0.538223i	$0.180904\pi$
$661$			711.531i			1.07645i	−0.842802	+	0.538223i	$0.819096\pi$
$662$	224.823	−	201.106i	0.339612	−	0.303786i
$663$	−471.066	−	282.473i	−0.710506	−	0.426053i
$664$	304.978	+	428.533i	0.459305	+	0.645381i
$665$	438.352	+	437.165i	0.659177	+	0.657391i
$666$	11.6562	−	31.8782i	0.0175019	−	0.0478651i
$667$	147.890			0.221723
$668$	525.965	+	58.7568i	0.787373	+	0.0879592i
$669$	−658.471	−	394.850i	−0.984261	−	0.590210i
$670$	655.267	+	732.544i	0.978011	+	1.09335i
$671$	385.333			0.574267
$672$	−26.6269	+	809.295i	−0.0396234	+	1.20431i
$673$		−	277.546i		−	0.412401i	−0.978510	−	0.206201i	$-0.933890\pi$
$673$		−	277.546i		−	0.412401i	0.978510	−	0.206201i	$-0.0661100\pi$
$674$	477.926	+	534.289i	0.709088	+	0.792713i
$675$	13.5126	−	271.746i	0.0200187	−	0.402587i
$676$	47.3192	−	423.581i	0.0699988	−	0.626599i
$677$	−615.395			−0.909003			−0.454502	−	0.890746i	$-0.650183\pi$
$677$	−615.395			−0.909003			−0.454502	+	0.890746i	$0.650183\pi$
$678$	293.289	−	56.2874i	0.432579	−	0.0830198i
$679$	−206.950			−0.304786
$680$	415.172	+	583.369i	0.610547	+	0.857895i
$681$	−542.813	+	905.220i	−0.797082	+	1.32925i
$682$	−297.482	+	266.100i	−0.436191	+	0.390176i
$683$		−	1190.05i		−	1.74238i	−0.490944	−	0.871191i	$-0.663348\pi$
$683$		−	1190.05i		−	1.74238i	0.490944	−	0.871191i	$-0.336652\pi$
$684$	−628.715	−	269.394i	−0.919174	−	0.393851i
$685$	−810.888			−1.18378
$686$	302.041	+	337.661i	0.440293	+	0.492218i
$687$	−901.281	−	540.451i	−1.31191	−	0.786682i
$688$	237.167	−	1048.26i	0.344719	−	1.52363i
$689$			372.092i			0.540046i
$690$	17.6515	+	91.9743i	0.0255819	+	0.133296i
$691$		−	1023.91i		−	1.48177i	−0.671630	−	0.740887i	$-0.734405\pi$
$691$		−	1023.91i		−	1.48177i	0.671630	−	0.740887i	$-0.265595\pi$
$692$	−79.6521	+	713.011i	−0.115104	+	1.03036i
$693$	−327.644	+	174.962i	−0.472791	+	0.252470i
$694$	−427.405	+	382.317i	−0.615857	+	0.550890i
$695$	−942.581			−1.35623
$696$	68.7643	+	875.731i	0.0987993	+	1.25823i
$697$			876.292i			1.25723i
$698$	362.801	−	324.528i	0.519772	−	0.464941i
$699$	113.855	−	189.869i	0.162882	−	0.271630i
$700$	−337.889	−	37.7463i	−0.482698	−	0.0539233i
$701$			417.674i			0.595826i	0.954593	+	0.297913i	$0.0962906\pi$
$701$			417.674i			0.595826i	−0.954593	+	0.297913i	$0.903709\pi$
$702$	331.785	−	268.350i	0.472628	−	0.382265i
$703$	25.2999	−	25.3686i	0.0359885	−	0.0360862i
$704$	102.584	−	295.867i	0.145716	−	0.420265i
$705$	365.518	−	609.555i	0.518466	−	0.864618i
$706$	377.918	+	422.487i	0.535295	+	0.598424i
$707$	−1397.08			−1.97607
$708$	−47.0696	−	35.8875i	−0.0664825	−	0.0506885i
$709$	217.152			0.306279			0.153139	−	0.988205i	$-0.451062\pi$
$709$	217.152			0.306279			0.153139	+	0.988205i	$0.451062\pi$
$710$	−104.775	+	93.7223i	−0.147571	+	0.132003i
$711$	53.1907	+	99.6081i	0.0748111	+	0.140096i
$712$	−272.331	−	382.659i	−0.382487	−	0.537443i
$713$	164.801			0.231138
$714$	1151.53	−	221.000i	1.61279	−	0.309524i
$715$	149.364			0.208901
$716$	97.5113	+	10.8932i	0.136189	+	0.0152140i
$717$	295.570	+	177.238i	0.412231	+	0.247193i
$718$	−126.955	+	113.562i	−0.176817	+	0.158164i
$719$	485.984			0.675916			0.337958	−	0.941161i	$-0.390264\pi$
$719$	485.984			0.675916			0.337958	+	0.941161i	$0.390264\pi$
$720$	−536.420	+	147.289i	−0.745028	+	0.204568i
$721$			88.8586i			0.123244i
$722$	−482.815	−	536.818i	−0.668719	−	0.743515i
$723$	20.7605	−	34.6212i	0.0287144	−	0.0478855i
$724$	−1258.80	−	140.624i	−1.73868	−	0.194232i
$725$	−368.833			−0.508736
$726$	−571.919	+	109.762i	−0.787767	+	0.151187i
$727$			373.971i			0.514404i	0.966358	+	0.257202i	$0.0828005\pi$
$727$			373.971i			0.514404i	−0.966358	+	0.257202i	$0.917199\pi$
$728$	−309.182	−	434.440i	−0.424701	−	0.596759i
$729$	−725.404	−	72.3205i	−0.995067	−	0.0992051i
$730$	35.7800	+	39.9996i	0.0490137	+	0.0547940i
$731$	−1556.32			−2.12903
$732$	572.986	−	751.523i	0.782768	−	1.02667i
$733$	−542.295			−0.739830			−0.369915	−	0.929066i	$-0.620613\pi$
$733$	−542.295			−0.739830			−0.369915	+	0.929066i	$0.620613\pi$
$734$	−18.3840	−	20.5521i	−0.0250464	−	0.0280002i
$735$	131.979	−	220.095i	0.179564	−	0.299449i
$736$	−113.016	+	62.8123i	−0.153555	+	0.0853429i
$737$	−622.442			−0.844561
$738$	−639.385	−	233.791i	−0.866376	−	0.316790i
$739$			777.352i			1.05190i	0.850516	+	0.525949i	$0.176290\pi$
$739$			777.352i			1.05190i	−0.850516	+	0.525949i	$0.823710\pi$
$740$	3.23492	−	28.9576i	0.00437152	−	0.0391319i
$741$	436.804	−	109.951i	0.589480	−	0.148382i
$742$	−529.576	−	592.031i	−0.713715	−	0.797885i
$743$			1103.92i			1.48576i	0.669426	+	0.742879i	$0.266540\pi$
$743$			1103.92i			1.48576i	−0.669426	+	0.742879i	$0.733460\pi$
$744$	76.6278	+	975.874i	0.102994	+	1.31166i
$745$	188.609			0.253166
$746$	−425.204	−	475.350i	−0.569979	−	0.637198i
$747$	278.730	+	521.966i	0.373132	+	0.698749i
$748$	−450.655	−	50.3436i	−0.602479	−	0.0673043i
$749$	−254.393			−0.339643
$750$	−153.237	−	798.449i	−0.204316	−	1.06460i
$751$	−575.467			−0.766267			−0.383134	−	0.923693i	$-0.625155\pi$
$751$	−575.467			−0.766267			−0.383134	+	0.923693i	$0.625155\pi$
$752$	957.078	+	216.537i	1.27271	+	0.287948i
$753$	100.402	+	60.2059i	0.133336	+	0.0799547i
$754$	−385.662	−	431.144i	−0.511488	−	0.571810i
$755$		−	402.887i		−	0.533625i
$756$	−145.972	+	899.178i	−0.193084	+	1.18939i
$757$	412.166			0.544474			0.272237	−	0.962230i	$-0.412237\pi$
$757$	412.166			0.544474			0.272237	+	0.962230i	$0.412237\pi$
$758$	816.422	−	730.296i	1.07707	−	0.963451i
$759$	−50.8663	−	30.5018i	−0.0670175	−	0.0401869i
$760$	−579.153	−	96.7469i	−0.762044	−	0.127299i
$761$		−	345.595i		−	0.454132i	−0.973879	−	0.227066i	$-0.927087\pi$
$761$		−	345.595i		−	0.454132i	0.973879	−	0.227066i	$-0.0729133\pi$
$762$	−306.326	+	58.7895i	−0.402003	+	0.0771516i
$763$	−1549.40			−2.03066
$764$	−118.016	+	1056.42i	−0.154471	+	1.38276i
$765$	379.439	+	710.560i	0.495998	+	0.928836i
$766$	241.127	+	269.564i	0.314787	+	0.351911i
$767$	38.9780			0.0508188
$768$	−424.494	−	640.023i	−0.552726	−	0.833363i
$769$	875.630			1.13866			0.569331	−	0.822109i	$-0.307202\pi$
$769$	875.630			1.13866			0.569331	+	0.822109i	$0.307202\pi$
$770$	−237.651	+	212.581i	−0.308638	+	0.276079i
$771$	−891.866	−	534.805i	−1.15677	−	0.693652i
$772$	901.463	+	100.705i	1.16770	+	0.130446i
$773$	297.068			0.384306			0.192153	−	0.981365i	$-0.438453\pi$
$773$	297.068			0.384306			0.192153	+	0.981365i	$0.438453\pi$
$774$	415.219	−	1135.57i	0.536459	−	1.46714i
$775$	−411.011			−0.530337
$776$	159.920	−	113.812i	0.206082	−	0.146665i
$777$	−40.9223	−	24.5389i	−0.0526670	−	0.0315816i
$778$	902.385	+	1008.81i	1.15988	+	1.29667i
$779$	−508.822	−	507.444i	−0.653173	−	0.651404i
$780$	222.103	−	291.308i	0.284747	−	0.373472i
$781$		−	89.0273i		−	0.113991i
$782$	124.828	+	139.550i	0.159627	+	0.178452i
$783$	−49.0793	+	987.010i	−0.0626811	+	1.26055i
$784$	345.576	+	78.1859i	0.440786	+	0.0997269i
$785$		−	139.925i		−	0.178249i
$786$	−1090.92	+	209.366i	−1.38793	+	0.266369i
$787$	−619.217			−0.786807			−0.393403	−	0.919366i	$-0.628702\pi$
$787$	−619.217			−0.786807			−0.393403	+	0.919366i	$0.628702\pi$
$788$	71.9585	+	8.03865i	0.0913179	+	0.0102013i
$789$	−242.934	−	145.675i	−0.307901	−	0.184632i
$790$	64.6275	+	72.2491i	0.0818069	+	0.0914546i
$791$		−	419.826i		−	0.530753i
$792$	156.966	−	315.388i	0.198189	−	0.398217i
$793$			622.331i			0.784781i
$794$	380.069	−	339.975i	0.478676	−	0.428180i
$795$	280.633	−	467.997i	0.352998	−	0.588676i
$796$	327.016	+	36.5316i	0.410824	+	0.0458940i
$797$	−52.8332			−0.0662901			−0.0331450	−	0.999451i	$-0.510552\pi$
$797$	−52.8332			−0.0662901			−0.0331450	+	0.999451i	$0.510552\pi$
$798$	−538.507	+	796.620i	−0.674821	+	0.998270i
$799$		−	1420.94i		−	1.77840i
$800$	281.861	−	156.653i	0.352326	−	0.195816i
$801$	−248.892	−	466.090i	−0.310726	−	0.581885i
$802$	337.150	−	301.584i	0.420387	−	0.376039i
$803$	−33.9876			−0.0423258
$804$	−925.565	+	1213.96i	−1.15120	+	1.50990i
$805$	131.656			0.163548
$806$	−429.764	−	480.447i	−0.533206	−	0.596089i
$807$	−666.454	−	399.638i	−0.825842	−	0.495214i
$808$	1079.59	−	768.323i	1.33613	−	0.950894i
$809$			654.048i			0.808465i	0.914656	+	0.404232i	$0.132461\pi$
$809$			654.048i			0.808465i	−0.914656	+	0.404232i	$0.867539\pi$
$810$	−619.692	+	87.2827i	−0.765052	+	0.107756i
$811$	141.919			0.174993			0.0874966	−	0.996165i	$-0.472113\pi$
$811$	141.919			0.174993			0.0874966	+	0.996165i	$0.472113\pi$
$812$	1227.24	+	137.098i	1.51139	+	0.168840i
$813$	−217.696	+	363.040i	−0.267769	+	0.446544i
$814$	12.3026	+	13.7535i	0.0151138	+	0.0168962i
$815$	237.567			0.291494
$816$	−768.305	+	804.061i	−0.941551	+	0.985368i
$817$	901.235	−	903.682i	1.10310	−	1.10610i
$818$	−194.857	−	217.837i	−0.238211	−	0.266304i
$819$	−282.572	−	529.161i	−0.345020	−	0.646106i
$820$	−580.808	−	64.8833i	−0.708302	−	0.0791260i
$821$			90.7138i			0.110492i	0.998473	+	0.0552459i	$0.0175943\pi$
$821$			90.7138i			0.110492i	−0.998473	+	0.0552459i	$0.982406\pi$
$822$	−237.382	−	1236.89i	−0.288786	−	1.50473i
$823$		−	1103.90i		−	1.34131i	−0.741771	−	0.670653i	$-0.766014\pi$
$823$		−	1103.90i		−	1.34131i	0.741771	−	0.670653i	$-0.233986\pi$
$824$	−48.8676	−	68.6652i	−0.0593053	−	0.0833315i
$825$	126.859	+	76.0710i	0.153769	+	0.0922072i
$826$	−62.0175	+	55.4751i	−0.0750817	+	0.0671612i
$827$		−	650.029i		−	0.786009i	−0.919537	−	0.393004i	$-0.871436\pi$
$827$		−	650.029i		−	0.786009i	0.919537	−	0.393004i	$-0.128564\pi$
$828$	−135.126	+	53.8497i	−0.163196	+	0.0650358i
$829$			697.415i			0.841272i	0.907229	+	0.420636i	$0.138193\pi$
$829$			697.415i			0.841272i	−0.907229	+	0.420636i	$0.861807\pi$
$830$	338.660	+	378.599i	0.408024	+	0.456144i
$831$	−539.272	−	323.373i	−0.648943	−	0.389137i
$832$	477.839	+	165.678i	0.574325	+	0.199132i
$833$		−	513.066i		−	0.615926i
$834$	−275.934	−	1437.77i	−0.330856	−	1.72394i
$835$	511.112			0.612111
$836$	290.198	−	232.521i	0.347126	−	0.278135i
$837$	−54.6917	+	1099.88i	−0.0653425	+	1.31407i
$838$	−792.904	+	709.259i	−0.946187	+	0.846372i
$839$			664.815i			0.792390i	0.918166	+	0.396195i	$0.129670\pi$
$839$			664.815i			0.792390i	−0.918166	+	0.396195i	$0.870330\pi$
$840$	61.2161	+	779.603i	0.0728764	+	0.928098i
$841$	498.640			0.592913
$842$	−637.070	−	712.202i	−0.756616	−	0.845845i
$843$	749.472	+	449.419i	0.889053	+	0.533118i
$844$	−120.989	+	1083.04i	−0.143352	+	1.28322i
$845$		−	411.619i		−	0.487124i
$846$	1036.79	+	379.102i	1.22552	+	0.448111i
$847$			818.668i			0.966551i
$848$	734.814	+	166.250i	0.866526	+	0.196050i
$849$	395.154	−	658.977i	0.465434	−	0.776180i
$850$	−311.320	−	348.034i	−0.366258	−	0.409452i
$851$		−	7.61927i		−	0.00895331i
$852$	−173.632	−	132.383i	−0.203793	−	0.155379i
$853$	745.353			0.873802			0.436901	−	0.899510i	$-0.356076\pi$
$853$	745.353			0.873802			0.436901	+	0.899510i	$0.356076\pi$
$854$	−885.727	−	990.183i	−1.03715	−	1.15947i
$855$	−632.315	−	191.149i	−0.739549	−	0.223566i
$856$	196.581	−	139.903i	0.229651	−	0.163438i
$857$	−964.664			−1.12563			−0.562814	−	0.826583i	$-0.690281\pi$
$857$	−964.664			−1.12563			−0.562814	+	0.826583i	$0.690281\pi$
$858$	43.7253	+	227.833i	0.0509619	+	0.265540i
$859$		−	66.9326i		−	0.0779193i	−0.999241	−	0.0389596i	$-0.987596\pi$
$859$		−	66.9326i		−	0.0779193i	0.999241	−	0.0389596i	$-0.0124044\pi$
$860$	115.235	−	1031.53i	0.133994	−	1.19945i
$861$	−492.181	+	820.784i	−0.571639	+	0.953291i
$862$	−96.5270	−	107.911i	−0.111980	−	0.125186i
$863$		−	263.380i		−	0.305191i	−0.988289	−	0.152596i	$-0.951237\pi$
$863$		−	263.380i		−	0.305191i	0.988289	−	0.152596i	$-0.0487632\pi$
$864$	−381.701	−	775.113i	−0.441784	−	0.897121i
$865$			692.877i			0.801013i
$866$	1105.73	+	1236.13i	1.27682	+	1.42740i
$867$	637.581	+	382.324i	0.735388	+	0.440973i
$868$	1367.58	+	152.776i	1.57556	+	0.176009i
$869$	−61.3900			−0.0706444
$870$	159.894	+	833.139i	0.183787	+	0.957631i
$871$		−	1005.27i		−	1.15416i
$872$	1197.29	−	852.086i	1.37304	−	0.977163i
$873$	194.787	−	104.016i	0.223124	−	0.119148i
$874$	−153.316	−	8.32856i	−0.175419	−	0.00952925i
$875$	−1142.93			−1.30621
$876$	−50.5393	+	66.2868i	−0.0576932	+	0.0756698i
$877$			930.455i			1.06095i	0.847700	+	0.530476i	$0.177987\pi$
$877$			930.455i			1.06095i	−0.847700	+	0.530476i	$0.822013\pi$
$878$	192.908	−	172.557i	0.219713	−	0.196535i
$879$	1258.94	+	754.917i	1.43224	+	0.858837i
$880$	66.7357	−	294.967i	0.0758360	−	0.335190i
$881$		−	757.292i		−	0.859583i	−0.902928	−	0.429791i	$-0.858587\pi$
$881$		−	757.292i		−	0.859583i	0.902928	−	0.429791i	$-0.141413\pi$
$882$	374.358	+	136.884i	0.424443	+	0.155197i
$883$			812.387i			0.920031i	0.887911	+	0.460015i	$0.152156\pi$
$883$			812.387i			0.920031i	−0.887911	+	0.460015i	$0.847844\pi$
$884$	81.3074	−	727.828i	0.0919767	−	0.823335i
$885$	−49.0245	−	29.3974i	−0.0553949	−	0.0332174i
$886$	−300.453	+	268.758i	−0.339112	+	0.303338i
$887$			298.123i			0.336102i	0.985778	+	0.168051i	$0.0537474\pi$
$887$			298.123i			0.336102i	−0.985778	+	0.168051i	$0.946253\pi$
$888$	45.1176	−	3.54274i	0.0508082	−	0.00398957i
$889$			438.488i			0.493237i
$890$	−302.407	−	338.071i	−0.339783	−	0.379855i
$891$	220.449	−	329.358i	0.247418	−	0.369649i
$892$	113.654	−	1017.38i	0.127415	−	1.14056i
$893$	825.076	+	822.842i	0.923938	+	0.921436i
$894$	55.2138	+	287.695i	0.0617604	+	0.321806i
$895$	94.7577			0.105874
$896$	−996.083	+	416.472i	−1.11170	+	0.464812i
$897$	49.2619	−	82.1515i	0.0549185	−	0.0915847i
$898$	−1040.78	+	930.982i	−1.15899	+	1.03673i
$899$	1492.83			1.66055
$900$	337.002	−	134.300i	0.374446	−	0.149222i
$901$		−	1090.96i		−	1.21083i
$902$	275.856	−	246.756i	0.305827	−	0.273565i
$903$	−1457.74	−	874.127i	−1.61433	−	0.968026i
$904$	230.882	+	324.419i	0.255401	+	0.358870i
$905$	−1223.26			−1.35167
$906$	614.545	−	117.942i	0.678306	−	0.130179i
$907$	−239.471			−0.264025			−0.132013	−	0.991248i	$-0.542144\pi$
$907$	−239.471			−0.264025			−0.132013	+	0.991248i	$0.542144\pi$
$908$	−1398.63	−	156.244i	−1.54034	−	0.172075i
$909$	1314.97	−	702.195i	1.44661	−	0.772491i
$910$	−343.329	−	383.818i	−0.377284	−	0.421778i
$911$			1630.15i			1.78941i	0.446658	+	0.894705i	$0.352614\pi$
$911$			1630.15i			1.78941i	−0.446658	+	0.894705i	$0.647386\pi$
$912$	−21.9697	−	911.735i	−0.0240896	−	0.999710i
$913$	−321.695			−0.352350
$914$	24.5424	−	21.9533i	0.0268516	−	0.0240190i
$915$	469.365	−	782.735i	0.512967	−	0.855448i
$916$	155.564	−	1392.54i	0.169829	−	1.52024i
$917$			1561.58i			1.70292i
$918$	−972.777	+	786.790i	−1.05967	+	0.857069i
$919$			7.42057i			0.00807461i	0.999992	+	0.00403731i	$0.00128512\pi$
$919$			7.42057i			0.00807461i	−0.999992	+	0.00403731i	$0.998715\pi$
$920$	−101.737	+	72.4038i	−0.110583	+	0.0786998i
$921$	−630.955	−	378.350i	−0.685076	−	0.410804i
$922$	−517.799	−	578.865i	−0.561605	−	0.627836i
$923$	143.783			0.155778
$924$	−393.832	−	300.271i	−0.426225	−	0.324968i
$925$			19.0023i			0.0205430i
$926$	803.517	+	898.278i	0.867729	+	0.970063i
$927$	−44.6617	−	83.6361i	−0.0481787	−	0.0902224i
$928$	−1023.75	+	568.978i	−1.10317	+	0.613123i
$929$		−	1109.77i		−	1.19459i	−0.802023	−	0.597293i	$-0.796243\pi$
$929$		−	1109.77i		−	1.19459i	0.802023	−	0.597293i	$-0.203757\pi$
$930$	178.179	+	928.411i	0.191590	+	0.998292i
$931$	297.914	+	297.107i	0.319993	+	0.319127i
$932$	293.361	+	32.7720i	0.314765	+	0.0351631i
$933$	1381.24	+	828.257i	1.48043	+	0.887735i
$934$	1049.96	−	939.194i	1.12415	−	1.00556i
$935$	−437.929			−0.468373
$936$	509.367	+	253.507i	0.544195	+	0.270841i
$937$	1004.92			1.07249			0.536243	−	0.844064i	$-0.319843\pi$
$937$	1004.92			1.07249			0.536243	+	0.844064i	$0.319843\pi$
$938$	1430.75	+	1599.48i	1.52531	+	1.70520i
$939$	1287.41	+	771.995i	1.37105	+	0.822146i
$940$	941.804	+	105.211i	1.00192	+	0.111927i
$941$	−1057.73			−1.12405			−0.562026	−	0.827120i	$-0.689978\pi$
$941$	−1057.73			−1.12405			−0.562026	+	0.827120i	$0.689978\pi$
$942$	213.436	−	40.9622i	0.226577	−	0.0434843i
$943$	−152.821			−0.162058
$944$	17.4153	−	76.9746i	0.0184485	−	0.0815408i
$945$	−43.6919	+	878.667i	−0.0462348	+	0.929806i
$946$	438.245	+	489.928i	0.463261	+	0.517895i
$947$	−381.180			−0.402513			−0.201257	−	0.979539i	$-0.564503\pi$
$947$	−381.180			−0.402513			−0.201257	+	0.979539i	$0.564503\pi$
$948$	−91.2863	+	119.730i	−0.0962935	+	0.126298i
$949$		−	54.8916i		−	0.0578415i
$950$	382.367	+	20.7713i	0.402491	+	0.0218645i
$951$	958.101	+	574.523i	1.00747	+	0.604125i
$952$	906.508	+	1273.76i	0.952214	+	1.33798i
$953$	−822.129			−0.862674			−0.431337	−	0.902191i	$-0.641958\pi$
$953$	−822.129			−0.862674			−0.431337	+	0.902191i	$0.641958\pi$
$954$	796.015	+	291.062i	0.834397	+	0.305097i
$955$			1026.59i			1.07497i
$956$	−51.0162	+	456.675i	−0.0533643	+	0.477694i
$957$	−460.766	−	276.297i	−0.481469	−	0.288712i
$958$	487.485	−	436.060i	0.508857	−	0.455177i
$959$	−1770.54			−1.84623
$960$	−476.045	−	568.769i	−0.495880	−	0.592468i
$961$	702.544			0.731055
$962$	−22.2126	+	19.8693i	−0.0230900	+	0.0206542i
$963$	239.441	−	127.862i	0.248641	−	0.132774i
$964$	53.4921	+	5.97572i	0.0554897	+	0.00619888i
$965$	876.007			0.907779
$966$	38.5413	+	200.822i	0.0398978	+	0.207890i
$967$			664.783i			0.687470i	0.939067	+	0.343735i	$0.111692\pi$
$967$			664.783i			0.687470i	−0.939067	+	0.343735i	$0.888308\pi$
$968$	−450.225	−	632.623i	−0.465108	−	0.653536i
$969$	−1280.69	+	322.371i	−1.32166	+	0.332685i
$970$	141.286	−	126.381i	0.145655	−	0.130290i
$971$		−	301.705i		−	0.310715i	−0.987858	−	0.155358i	$-0.950347\pi$
$971$		−	301.705i		−	0.310715i	0.987858	−	0.155358i	$-0.0496530\pi$
$972$	−314.547	−	919.698i	−0.323608	−	0.946191i
$973$	−2058.08			−2.11519
$974$	−272.626	+	243.867i	−0.279904	+	0.250376i
$975$	−122.858	+	204.884i	−0.126008	+	0.210137i
$976$	1228.99	+	278.057i	1.25921	+	0.284894i
$977$	−1463.58			−1.49803			−0.749017	−	0.662550i	$-0.769474\pi$
$977$	−1463.58			−1.49803			−0.749017	+	0.662550i	$0.769474\pi$
$978$	69.5461	+	362.374i	0.0711106	+	0.370526i
$979$	287.258			0.293420
$980$	340.061	+	37.9890i	0.347001	+	0.0387643i
$981$	1458.33	−	778.749i	1.48658	−	0.793832i
$982$	−1005.13	+	899.096i	−1.02355	+	0.915577i
$983$		−	1450.72i		−	1.47581i	−0.674907	−	0.737903i	$-0.735816\pi$
$983$		−	1450.72i		−	1.47581i	0.674907	−	0.737903i	$-0.264184\pi$
$984$	−71.0572	−	904.931i	−0.0722126	−	0.919646i
$985$	69.9265			0.0709914
$986$	1130.74	+	1264.10i	1.14680	+	1.28204i
$987$	798.092	−	1330.94i	0.808604	−	1.34847i
$988$	375.533	+	468.683i	0.380094	+	0.474376i
$989$		−	271.414i		−	0.274433i
$990$	116.837	−	319.534i	0.118018	−	0.322762i
$991$	1083.39			1.09323			0.546615	−	0.837384i	$-0.315916\pi$
$991$	1083.39			1.09323			0.546615	+	0.837384i	$0.315916\pi$
$992$	−1140.81	+	634.043i	−1.15001	+	0.639156i
$993$	388.047	+	232.691i	0.390782	+	0.234332i
$994$	−228.772	+	204.638i	−0.230153	+	0.205874i
$995$	317.781			0.319378
$996$	−478.358	+	627.409i	−0.480279	+	0.629929i
$997$	−379.701			−0.380844			−0.190422	−	0.981702i	$-0.560986\pi$
$997$	−379.701			−0.380844			−0.190422	+	0.981702i	$0.560986\pi$
$998$	575.908	+	643.827i	0.577062	+	0.645117i
$999$	50.8508	+	2.52857i	0.0509017	+	0.00253110i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	228.3.b.e.227.19	yes	72
3.2	odd	2	inner	228.3.b.e.227.53	yes	72
4.3	odd	2	inner	228.3.b.e.227.18	yes	72
12.11	even	2	inner	228.3.b.e.227.56	yes	72
19.18	odd	2	inner	228.3.b.e.227.54	yes	72
57.56	even	2	inner	228.3.b.e.227.20	yes	72
76.75	even	2	inner	228.3.b.e.227.55	yes	72
228.227	odd	2	inner	228.3.b.e.227.17	✓	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
228.3.b.e.227.17	✓	72	228.227	odd	2	inner
228.3.b.e.227.18	yes	72	4.3	odd	2	inner
228.3.b.e.227.19	yes	72	1.1	even	1	trivial
228.3.b.e.227.20	yes	72	57.56	even	2	inner
228.3.b.e.227.53	yes	72	3.2	odd	2	inner
228.3.b.e.227.54	yes	72	19.18	odd	2	inner
228.3.b.e.227.55	yes	72	76.75	even	2	inner
228.3.b.e.227.56	yes	72	12.11	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:	\( N \)	\(=\)	\( 228 = 2^{2} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	228.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.49065 + 1.33340i) q^{2} +(-2.57288 - 1.54282i) q^{3} +(0.444087 - 3.97527i) q^{4} -3.86301i q^{5} +(5.89246 - 1.13087i) q^{6} -8.43471i q^{7} +(4.63865 + 6.51789i) q^{8} +(4.23941 + 7.93898i) q^{9} +O(q^{10})\)	\(q+(-1.49065 + 1.33340i) q^{2} +(-2.57288 - 1.54282i) q^{3} +(0.444087 - 3.97527i) q^{4} -3.86301i q^{5} +(5.89246 - 1.13087i) q^{6} -8.43471i q^{7} +(4.63865 + 6.51789i) q^{8} +(4.23941 + 7.93898i) q^{9} +(5.15095 + 5.75841i) q^{10} -4.89291 q^{11} +(-7.27571 + 9.54275i) q^{12} -7.90228i q^{13} +(11.2469 + 12.5732i) q^{14} +(-5.95994 + 9.93907i) q^{15} +(-15.6056 - 3.53073i) q^{16} +23.1691i q^{17} +(-16.9053 - 6.18142i) q^{18} +(-13.4532 - 13.4168i) q^{19} +(-15.3565 - 1.71551i) q^{20} +(-13.0132 + 21.7015i) q^{21} +(7.29363 - 6.52421i) q^{22} -4.04058 q^{23} +(-1.87875 - 23.9264i) q^{24} +10.0771 q^{25} +(10.5369 + 11.7796i) q^{26} +(1.34092 - 26.9667i) q^{27} +(-33.5303 - 3.74574i) q^{28} -36.6011 q^{29} +(-4.36857 - 22.7627i) q^{30} -40.7866 q^{31} +(27.9704 - 15.5454i) q^{32} +(12.5889 + 7.54888i) q^{33} +(-30.8937 - 34.5371i) q^{34} -32.5834 q^{35} +(33.4423 - 13.3272i) q^{36} +1.88569i q^{37} +(37.9441 + 2.06123i) q^{38} +(-12.1918 + 20.3316i) q^{39} +(25.1787 - 17.9192i) q^{40} +37.8215 q^{41} +(-9.53856 - 49.7012i) q^{42} +67.1721i q^{43} +(-2.17288 + 19.4507i) q^{44} +(30.6684 - 16.3769i) q^{45} +(6.02309 - 5.38771i) q^{46} -61.3292 q^{47} +(34.7040 + 33.1607i) q^{48} -22.1444 q^{49} +(-15.0215 + 13.4368i) q^{50} +(35.7458 - 59.6114i) q^{51} +(-31.4137 - 3.50930i) q^{52} -47.0866 q^{53} +(33.9585 + 41.9859i) q^{54} +18.9014i q^{55} +(54.9766 - 39.1257i) q^{56} +(13.9138 + 55.2757i) q^{57} +(54.5595 - 48.8039i) q^{58} +4.93250i q^{59} +(36.8638 + 28.1062i) q^{60} -78.7533 q^{61} +(60.7986 - 54.3848i) q^{62} +(66.9630 - 35.7582i) q^{63} +(-20.9658 + 60.4685i) q^{64} -30.5266 q^{65} +(-28.8313 + 5.53325i) q^{66} +127.213 q^{67} +(92.1036 + 10.2891i) q^{68} +(10.3959 + 6.23388i) q^{69} +(48.5705 - 43.4468i) q^{70} +18.1952i q^{71} +(-32.0803 + 64.4582i) q^{72} +6.94630 q^{73} +(-2.51438 - 2.81091i) q^{74} +(-25.9272 - 15.5472i) q^{75} +(-59.3098 + 47.5220i) q^{76} +41.2703i q^{77} +(-8.93645 - 46.5639i) q^{78} +12.5467 q^{79} +(-13.6393 + 60.2846i) q^{80} +(-45.0548 + 67.3132i) q^{81} +(-56.3787 + 50.4312i) q^{82} +65.7472 q^{83} +(80.4903 + 61.3685i) q^{84} +89.5027 q^{85} +(-89.5673 - 100.130i) q^{86} +(94.1702 + 56.4689i) q^{87} +(-22.6965 - 31.8915i) q^{88} -58.7091 q^{89} +(-23.8789 + 65.3055i) q^{90} -66.6535 q^{91} +(-1.79437 + 16.0624i) q^{92} +(104.939 + 62.9263i) q^{93} +(91.4205 - 81.7764i) q^{94} +(-51.8293 + 51.9700i) q^{95} +(-95.9481 - 3.15683i) q^{96} -24.5355i q^{97} +(33.0096 - 29.5274i) q^{98} +(-20.7431 - 38.8447i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 16 q^{4} + 6 q^{6} - 48 q^{9}+O(q^{10}) \) 72 * q - 16 * q^4 + 6 * q^6 - 48 * q^9	\( 72 q - 16 q^{4} + 6 q^{6} - 48 q^{9} - 40 q^{16} + 94 q^{24} - 408 q^{25} + 60 q^{28} + 176 q^{30} - 214 q^{36} + 2 q^{42} + 96 q^{45} - 616 q^{49} + 72 q^{54} + 320 q^{57} + 564 q^{58} + 592 q^{61} - 424 q^{64} + 608 q^{66} + 128 q^{73} - 292 q^{76} - 208 q^{81} + 472 q^{82} - 160 q^{85} + 128 q^{93} + 166 q^{96}+O(q^{100}) \) 72 * q - 16 * q^4 + 6 * q^6 - 48 * q^9 - 40 * q^16 + 94 * q^24 - 408 * q^25 + 60 * q^28 + 176 * q^30 - 214 * q^36 + 2 * q^42 + 96 * q^45 - 616 * q^49 + 72 * q^54 + 320 * q^57 + 564 * q^58 + 592 * q^61 - 424 * q^64 + 608 * q^66 + 128 * q^73 - 292 * q^76 - 208 * q^81 + 472 * q^82 - 160 * q^85 + 128 * q^93 + 166 * q^96

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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