LMFDB - Embedded newform 228.3.b.e.227.20

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			227.20
Character	$\chi$	$=$	228.227
Dual form			228.3.b.e.227.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.49065 + 1.33340i) q^{2} +(2.57288 - 1.54282i) q^{3} +(0.444087 - 3.97527i) q^{4} +3.86301i q^{5} +(-1.77807 + 5.73049i) q^{6} -8.43471i q^{7} +(4.63865 + 6.51789i) q^{8} +(4.23941 - 7.93898i) q^{9} +O(q^{10})$	\(q+(-1.49065 + 1.33340i) q^{2} +(2.57288 - 1.54282i) q^{3} +(0.444087 - 3.97527i) q^{4} +3.86301i q^{5} +(-1.77807 + 5.73049i) 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} +(-4.99055 - 10.9130i) 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} +(4.26635 + 17.4871i) 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} +(21.9906 + 9.61314i) 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} +(-22.1370 - 6.86871i) 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} +(-29.6769 - 20.3784i) q^{36} -1.88569i q^{37} +(-2.16412 + 37.9383i) q^{38} +(12.1918 + 20.3316i) q^{39} +(-25.1787 + 17.9192i) q^{40} +37.8215 q^{41} +(48.3350 + 14.9975i) 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} +(-45.5985 + 14.9925i) 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} +(37.9562 + 38.4099i) 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} +(42.1572 - 19.2786i) 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} +(-8.69994 + 28.0388i) 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} +(71.4106 - 9.19412i) q^{72} +6.94630 q^{73} +(2.51438 + 2.81091i) q^{74} +(25.9272 - 15.5472i) q^{75} +(-47.3610 - 59.4385i) q^{76} -41.2703i q^{77} +(-45.2839 - 14.0508i) 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} +(-92.0484 + 42.0939i) 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} +(-67.5529 + 16.4810i) 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} +(47.9806 - 83.1496i) 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	$0.126248\pi$
$5$			3.86301i			0.772603i	−0.922373	+	0.386301i	$0.873752\pi$
$6$	−1.77807	+	5.73049i	−0.296345	+	0.955081i
$7$		−	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	$-0.428609\pi$
$11$	4.89291			0.444810			0.222405	+	0.974954i	$0.428609\pi$
$12$	−4.99055	−	10.9130i	−0.415879	−	0.909420i
$13$			7.90228i			0.607868i	0.952693	+	0.303934i	$0.0983002\pi$
$13$			7.90228i			0.607868i	−0.952693	+	0.303934i	$0.901700\pi$
$14$	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	$-0.761352\pi$
$17$		−	23.1691i		−	1.36289i	0.731869	−	0.681445i	$-0.238648\pi$
$18$	4.26635	+	17.4871i	0.237019	+	0.971505i
$19$	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	$-0.472004\pi$
$23$	4.04058			0.175677			0.0878386	+	0.996135i	$0.472004\pi$
$24$	21.9906	+	9.61314i	0.916276	+	0.400548i
$25$	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	$0.717377\pi$
$30$	−22.1370	−	6.86871i	−0.737898	−	0.228957i
$31$	40.7866			1.31570			0.657848	−	0.753151i	$-0.271467\pi$
$31$	40.7866			1.31570			0.657848	+	0.753151i	$0.271467\pi$
$32$	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
$36$	−29.6769	−	20.3784i	−0.824359	−	0.566067i
$37$		−	1.88569i		−	0.0509646i	−0.999675	−	0.0254823i	$-0.991888\pi$
$37$		−	1.88569i		−	0.0509646i	0.999675	−	0.0254823i	$-0.00811214\pi$
$38$	−2.16412	+	37.9383i	−0.0569506	+	0.998377i
$39$	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	$0.347405\pi$
$42$	48.3350	+	14.9975i	1.15083	+	0.357084i
$43$			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	$-0.273746\pi$
$47$	61.3292			1.30488			0.652439	+	0.757842i	$0.273746\pi$
$48$	−45.5985	+	14.9925i	−0.949969	+	0.312343i
$49$	−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	$0.646517\pi$
$54$	37.9562	+	38.4099i	0.702893	+	0.711295i
$55$			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	$0.986690\pi$
$60$	42.1572	−	19.2786i	0.702621	−	0.321309i
$61$	−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
$66$	−8.69994	+	28.0388i	−0.131817	+	0.424830i
$67$	−127.213			−1.89870			−0.949350	−	0.314219i	$-0.898257\pi$
$67$	−127.213			−1.89870			−0.949350	+	0.314219i	$0.898257\pi$
$68$	−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	$0.959101\pi$
$72$	71.4106	−	9.19412i	0.991813	−	0.127696i
$73$	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
$76$	−47.3610	−	59.4385i	−0.623171	−	0.782085i
$77$		−	41.2703i		−	0.535978i
$78$	−45.2839	−	14.0508i	−0.580563	−	0.180139i
$79$	−12.5467			−0.158819			−0.0794096	−	0.996842i	$-0.525304\pi$
$79$	−12.5467			−0.158819			−0.0794096	+	0.996842i	$0.525304\pi$
$80$	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	$-0.629625\pi$
$83$	−65.7472			−0.792135			−0.396068	+	0.918221i	$0.629625\pi$
$84$	−92.0484	+	42.0939i	−1.09581	+	0.501117i
$85$	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	$0.606990\pi$
$90$	−67.5529	+	16.4810i	−0.750588	+	0.183122i
$91$	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
$96$	47.9806	−	83.1496i	0.499798	−	0.866142i
$97$			24.5355i			0.252943i	0.991970	+	0.126472i	$0.0403653\pi$
$97$			24.5355i			0.252943i	−0.991970	+	0.126472i	$0.959635\pi$
$98$	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	$0.306013\pi$
$101$			165.635i			1.63995i	−0.572399	+	0.819975i	$0.693987\pi$
$102$	132.770	+	41.1963i	1.30167	+	0.403886i
$103$	10.5349			0.102280			0.0511402	−	0.998691i	$-0.483714\pi$
$103$	10.5349			0.102280			0.0511402	+	0.998691i	$0.483714\pi$
$104$	−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	$-0.0450111\pi$
$108$	−107.795	−	6.64500i	−0.998105	−	0.0615278i
$109$			183.693i			1.68525i	0.538498	+	0.842627i	$0.318992\pi$
$109$			183.693i			1.68525i	−0.538498	+	0.842627i	$0.681008\pi$
$110$	−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	$0.429317\pi$
$114$	52.9640	+	100.950i	0.464596	+	0.885523i
$115$			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
$120$	−37.1357	+	84.9501i	−0.309464	+	0.707918i
$121$	−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
$126$	147.499	−	35.9854i	1.17062	−	0.285599i
$127$	51.9861			0.409339			0.204670	−	0.978831i	$-0.434388\pi$
$127$	51.9861			0.409339			0.204670	+	0.978831i	$0.434388\pi$
$128$	−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	$-0.250214\pi$
$131$	185.137			1.41326			0.706631	+	0.707582i	$0.250214\pi$
$132$	−24.4183	−	53.3965i	−0.184987	−	0.404519i
$133$	−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	$0.277804\pi$
$137$			209.911i			1.53219i	−0.642724	+	0.766097i	$0.722196\pi$
$138$	−7.18443	+	23.1545i	−0.0520611	+	0.167786i
$139$		−	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
$144$	−94.1888	+	108.924i	−0.654089	+	0.756417i
$145$		−	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	$-0.947612\pi$
$149$		−	48.8242i		−	0.327679i	0.986487	−	0.163840i	$-0.0523879\pi$
$150$	−17.9178	+	57.7468i	−0.119452	+	0.384978i
$151$	−104.293			−0.690685			−0.345343	−	0.938477i	$-0.612237\pi$
$151$	−104.293			−0.690685			−0.345343	+	0.938477i	$0.612237\pi$
$152$	149.854	+	25.4509i	0.985882	+	0.167440i
$153$	−183.939	−	98.2235i	−1.20222	−	0.641983i
$154$	55.0298	+	61.5197i	0.357337	+	0.399478i
$155$			157.559i			1.01651i
$156$	86.2379	−	39.4367i	0.552807	−	0.252800i
$157$	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
$162$	156.916	+	40.2645i	0.968620	+	0.248546i
$163$			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	$0.870351\pi$
$168$	81.0841	−	185.485i	0.482644	−	1.10408i
$169$	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	$0.673467\pi$
$174$	65.0793	−	209.742i	0.374019	−	1.20541i
$175$		−	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	$0.978173\pi$
$180$	78.7221	−	114.642i	0.437345	−	0.636902i
$181$			316.659i			1.74949i	0.484579	+	0.874747i	$0.338973\pi$
$181$			316.659i			1.74949i	−0.484579	+	0.874747i	$0.661027\pi$
$182$	−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
$186$	−72.5214	+	233.727i	−0.389900	+	1.25660i
$187$		−	113.364i		−	0.606227i
$188$	27.2355	−	243.800i	0.144870	−	1.29681i
$189$	−227.456	+	11.3103i	−1.20347	+	0.0598429i
$190$	−146.556	−	8.36004i	−0.771349	−	0.0440002i
$191$	265.749			1.39136			0.695678	−	0.718353i	$-0.255104\pi$
$191$	265.749			1.39136			0.695678	+	0.718353i	$0.255104\pi$
$192$	39.3494	+	187.925i	0.204945	+	0.978774i
$193$		−	226.768i		−	1.17496i	−0.809238	−	0.587481i	$-0.800120\pi$
$193$		−	226.768i		−	1.17496i	0.809238	−	0.587481i	$-0.199880\pi$
$194$	−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	$-0.985371\pi$
$197$		−	18.1015i		−	0.0918860i	0.998944	−	0.0459430i	$-0.0146293\pi$
$198$	20.8749	+	85.5628i	0.105429	+	0.432135i
$199$			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
$204$	−252.846	+	115.627i	−1.23944	+	0.566797i
$205$			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
$210$	−57.9356	+	186.719i	−0.275884	+	0.889137i
$211$	272.444			1.29120			0.645602	−	0.763674i	$-0.276607\pi$
$211$	272.444			1.29120			0.645602	+	0.763674i	$0.276607\pi$
$212$	−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
$216$	169.546	−	133.829i	0.784934	−	0.619579i
$217$		−	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
$222$	10.8059	+	3.35289i	0.0486753	+	0.0151031i
$223$	−255.928			−1.14766			−0.573829	−	0.818975i	$-0.694542\pi$
$223$	−255.928			−1.14766			−0.573829	+	0.818975i	$0.694542\pi$
$224$	−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	$-0.282230\pi$
$228$	−213.557	−	79.8585i	−0.936654	−	0.350256i
$229$	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	$-0.949379\pi$
$233$		−	73.7965i		−	0.316723i	0.987381	−	0.158362i	$-0.0506212\pi$
$234$	−138.188	+	33.7139i	−0.590547	+	0.144077i
$235$			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	$-0.422743\pi$
$239$	114.879			0.480665			0.240333	+	0.970691i	$0.422743\pi$
$240$	−57.9161	−	176.148i	−0.241317	−	0.733949i
$241$		−	13.4562i		−	0.0558349i	−0.999610	−	0.0279174i	$-0.991112\pi$
$241$		−	13.4562i		−	0.0558349i	0.999610	−	0.0279174i	$-0.00888755\pi$
$242$	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
$246$	−67.2493	+	216.736i	−0.273371	+	0.881040i
$247$	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	$-0.475231\pi$
$251$	39.0233			0.155471			0.0777356	+	0.996974i	$0.475231\pi$
$252$	−171.886	+	250.316i	−0.682088	+	0.993319i
$253$	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	$0.264402\pi$
$258$	−384.929	−	119.437i	−1.49197	−	0.462933i
$259$	−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	$-0.557451\pi$
$263$	−94.4212			−0.359016			−0.179508	+	0.983757i	$0.557451\pi$
$264$	107.598	+	47.0363i	0.407569	+	0.178168i
$265$		−	181.896i		−	0.686401i
$266$	319.999	+	18.2538i	1.20300	+	0.0686232i
$267$	−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	$0.340103\pi$
$270$	−148.378	+	146.626i	−0.549549	+	0.543057i
$271$		−	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
$276$	−20.1647	−	44.0950i	−0.0730605	−	0.159764i
$277$	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	$0.673443\pi$
$282$	−109.048	+	351.446i	−0.386694	+	1.24626i
$283$			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
$288$	−4.83666	−	287.959i	−0.0167940	−	0.999859i
$289$	−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	$0.814532\pi$
$294$	39.3743	−	126.898i	0.133926	−	0.431626i
$295$	−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
$300$	−50.2903	−	109.972i	−0.167634	−	0.366573i
$301$	566.578			1.88232
$302$	155.465	−	139.065i	0.514786	−	0.460480i
$303$	255.545	+	426.159i	0.843383	+	1.40646i
$304$	−257.317	+	161.877i	−0.846436	+	0.532491i
$305$		−	304.225i		−	0.997460i
$306$	405.161	−	98.8476i	1.32405	−	0.323031i
$307$	−245.233			−0.798805			−0.399402	−	0.916776i	$-0.630782\pi$
$307$	−245.233			−0.798805			−0.399402	+	0.916776i	$0.630782\pi$
$308$	−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	$-0.168522\pi$
$311$	536.846			1.72619			0.863097	+	0.505039i	$0.168522\pi$
$312$	−75.9658	+	173.776i	−0.243480	+	0.556975i
$313$	−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	$0.699832\pi$
$318$	83.7233	−	269.829i	0.263281	−	0.848520i
$319$	−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
$324$	−287.597	+	149.212i	−0.887644	+	0.460531i
$325$			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
$330$	−108.314	−	33.6080i	−0.328225	−	0.101842i
$331$	150.822			0.455656			0.227828	−	0.973701i	$-0.426838\pi$
$331$	150.822			0.455656			0.227828	+	0.973701i	$0.426838\pi$
$332$	−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
$336$	126.457	+	384.611i	0.376360	+	1.14467i
$337$			358.426i			1.06358i	0.846877	+	0.531790i	$0.178480\pi$
$337$			358.426i			1.06358i	−0.846877	+	0.531790i	$0.821520\pi$
$338$	−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
$342$	292.017	+	178.017i	0.853851	+	0.520518i
$343$		−	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	$-0.635570\pi$
$347$	−286.724			−0.826293			−0.413146	+	0.910665i	$0.635570\pi$
$348$	182.660	+	399.429i	0.524884	+	1.14778i
$349$	−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	$0.131494\pi$
$353$			283.425i			0.802902i	−0.915880	+	0.401451i	$0.868506\pi$
$354$	−28.2656	−	8.77034i	−0.0798465	−	0.0247750i
$355$	−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	$-0.537846\pi$
$359$	−85.1673			−0.237235			−0.118617	+	0.992940i	$0.537846\pi$
$360$	35.5170	+	275.860i	0.0986584	+	0.766278i
$361$	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
$366$	140.029	−	451.295i	0.382593	−	1.23305i
$367$			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
$372$	−203.547	−	445.105i	−0.547170	−	1.19652i
$373$		−	318.887i		−	0.854926i	−0.904033	−	0.427463i	$-0.859407\pi$
$373$		−	318.887i		−	0.854926i	0.904033	−	0.427463i	$-0.140593\pi$
$374$	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
$378$	323.977	−	320.150i	0.857082	−	0.846958i
$379$	547.694			1.44510			0.722552	−	0.691317i	$-0.242969\pi$
$379$	547.694			1.44510			0.722552	+	0.691317i	$0.242969\pi$
$380$	229.612	−	182.956i	0.604241	−	0.481464i
$381$	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	$-0.0758623\pi$
$384$	−309.235	−	227.662i	−0.805299	−	0.592869i
$385$	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	$0.335794\pi$
$389$			676.754i			1.73973i	−0.493291	+	0.869864i	$0.664206\pi$
$390$	54.2785	−	174.932i	0.139176	−	0.448545i
$391$		−	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
$396$	−145.207	−	99.7097i	−0.366683	−	0.251792i
$397$	−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	$0.591003\pi$
$402$	226.194	−	728.992i	0.562670	−	1.81341i
$403$			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
$408$	222.728	−	509.503i	0.545902	−	1.24878i
$409$		−	146.135i		−	0.357299i	−0.983913	−	0.178649i	$-0.942827\pi$
$409$		−	146.135i		−	0.357299i	0.983913	−	0.178649i	$-0.0571728\pi$
$410$	−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
$414$	17.2385	+	70.6579i	0.0416389	+	0.170671i
$415$		−	253.982i		−	0.612006i
$416$	122.844	+	221.030i	0.295298	+	0.531321i
$417$	−376.450	−	627.786i	−0.902758	−	1.50548i
$418$	−10.5889	+	185.629i	−0.0253322	+	0.444088i
$419$	−531.918			−1.26949			−0.634747	−	0.772720i	$-0.718896\pi$
$419$	−531.918			−1.26949			−0.634747	+	0.772720i	$0.718896\pi$
$420$	−162.609	−	355.584i	−0.387165	−	0.846629i
$421$		−	477.779i		−	1.13487i	−0.823419	−	0.567433i	$-0.807937\pi$
$421$		−	477.779i		−	1.13487i	0.823419	−	0.567433i	$-0.192063\pi$
$422$	−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
$426$	−104.267	−	32.3523i	−0.244759	−	0.0759443i
$427$			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	$0.973237\pi$
$432$	−74.2862	+	425.565i	−0.171959	+	0.985104i
$433$			829.253i			1.91513i	0.288210	+	0.957567i	$0.406940\pi$
$433$			829.253i			1.91513i	−0.288210	+	0.957567i	$0.593060\pi$
$434$	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
$438$	−12.3510	+	39.8057i	−0.0281986	+	0.0908805i
$439$	129.412			0.294787			0.147394	−	0.989078i	$-0.452912\pi$
$439$	129.412			0.294787			0.147394	+	0.989078i	$0.452912\pi$
$440$	−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	$-0.573053\pi$
$443$	−201.558			−0.454984			−0.227492	+	0.973780i	$0.573053\pi$
$444$	−20.5786	+	9.41062i	−0.0463482	+	0.0211951i
$445$		−	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	$0.216484\pi$
$450$	42.9925	+	176.219i	0.0955389	+	0.391599i
$451$	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
$456$	424.823	−	165.716i	0.931629	−	0.363412i
$457$	−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	$-0.861615\pi$
$461$		−	388.330i		−	0.842364i	0.906976	−	0.421182i	$-0.138385\pi$
$462$	236.499	+	73.3815i	0.511902	+	0.158834i
$463$		−	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	$-0.228057\pi$
$467$	704.360			1.50827			0.754133	+	0.656722i	$0.228057\pi$
$468$	161.036	−	234.516i	0.344094	−	0.501102i
$469$			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
$474$	22.3089	−	71.8988i	0.0470653	−	0.151685i
$475$	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	$-0.389111\pi$
$479$	327.028			0.682731			0.341366	+	0.939931i	$0.389111\pi$
$480$	321.208	+	185.350i	0.669184	+	0.386145i
$481$	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
$486$	465.848	−	138.498i	0.958535	−	0.284976i
$487$	−182.891			−0.375546			−0.187773	−	0.982212i	$-0.560127\pi$
$487$	−182.891			−0.375546			−0.187773	+	0.982212i	$0.560127\pi$
$488$	−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	$-0.740919\pi$
$491$	−674.288			−1.37330			−0.686648	+	0.726990i	$0.740919\pi$
$492$	−188.750	−	412.748i	−0.383639	−	0.838918i
$493$			848.015i			1.72011i
$494$	−299.799	−	17.1015i	−0.606881	−	0.0346185i
$495$	150.058	+	80.1308i	0.303147	+	0.161880i
$496$	−636.498	−	144.006i	−1.28326	−	0.290335i
$497$	153.471			0.308795
$498$	116.903	−	376.763i	0.234745	−	0.756553i
$499$		−	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	$-0.627552\pi$
$503$	−392.419			−0.780157			−0.390078	+	0.920782i	$0.627552\pi$
$504$	−77.5498	−	602.328i	−0.153869	−	1.19509i
$505$	−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	$0.296864\pi$
$510$	−159.142	+	512.894i	−0.312043	+	1.00567i
$511$		−	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
$516$	733.052	−	335.226i	1.42064	−	0.649662i
$517$	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	$0.172072\pi$
$522$	−156.153	−	640.046i	−0.299144	−	1.22614i
$523$	−388.270			−0.742390			−0.371195	−	0.928555i	$-0.621052\pi$
$523$	−388.270			−0.742390			−0.371195	+	0.928555i	$0.621052\pi$
$524$	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
$528$	−223.110	+	73.3567i	−0.422556	+	0.138933i
$529$	−512.674			−0.969138
$530$	242.541	+	271.144i	0.457624	+	0.511593i
$531$	39.1590	+	20.9109i	0.0737459	+	0.0393803i
$532$	−501.347	+	399.477i	−0.942381	+	0.750896i
$533$			298.876i			0.560744i
$534$	104.389	−	336.431i	0.195485	−	0.630021i
$535$	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
$540$	25.6698	−	416.415i	0.0475366	−	0.771139i
$541$	−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
$546$	−118.515	+	381.957i	−0.217060	+	0.699555i
$547$	486.853			0.890042			0.445021	−	0.895520i	$-0.353196\pi$
$547$	486.853			0.890042			0.445021	+	0.895520i	$0.353196\pi$
$548$	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
$552$	88.8548	+	38.8426i	0.160969	+	0.0703671i
$553$			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	$-0.590717\pi$
$557$		−	1069.06i		−	1.91933i	0.281153	−	0.959663i	$-0.409283\pi$
$558$	174.010	+	713.238i	0.311845	+	1.27820i
$559$	−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	$-0.0911369\pi$
$564$	−306.066	−	669.288i	−0.542671	−	1.18668i
$565$			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	$0.207607\pi$
$570$	−389.970	+	204.601i	−0.684157	+	0.358949i
$571$			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
$576$	391.175	+	422.798i	0.679123	+	0.734024i
$577$	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
$582$	−140.600	−	43.6259i	−0.241581	−	0.0749585i
$583$	−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	$-0.549985\pi$
$587$	−183.598			−0.312774			−0.156387	+	0.987696i	$0.549985\pi$
$588$	110.513	+	241.663i	0.187947	+	0.410991i
$589$	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	$0.135199\pi$
$593$			488.731i			0.824167i	−0.911146	+	0.412083i	$0.864801\pi$
$594$	185.716	+	187.936i	0.312654	+	0.316391i
$595$		−	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	$0.987335\pi$
$600$	221.602	+	96.8728i	0.369337	+	0.161455i
$601$			6.98813i			0.0116275i	0.999983	+	0.00581375i	$0.00185058\pi$
$601$			6.98813i			0.0116275i	−0.999983	+	0.00581375i	$0.998149\pi$
$602$	−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
$606$	−949.169	−	294.511i	−1.56629	−	0.485991i
$607$	−1166.33			−1.92146			−0.960732	−	0.277479i	$-0.910501\pi$
$607$	−1166.33			−1.92146			−0.960732	+	0.277479i	$0.910501\pi$
$608$	167.722	−	584.408i	0.275859	−	0.961198i
$609$	476.299	+	794.298i	0.782100	+	1.30427i
$610$	405.654	+	453.494i	0.665007	+	0.743433i
$611$			484.641i			0.793193i
$612$	−472.150	+	687.589i	−0.771487	+	1.12351i
$613$	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	$-0.945221\pi$
$617$		−	211.316i		−	0.342490i	0.985229	−	0.171245i	$-0.0547789\pi$
$618$	−18.7317	+	60.3699i	−0.0303103	+	0.0976860i
$619$			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
$624$	−118.475	−	360.333i	−0.189863	−	0.577456i
$625$	−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
$630$	139.012	+	569.789i	0.220654	+	0.904427i
$631$		−	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
$636$	234.988	+	513.858i	0.369478	+	0.807953i
$637$		−	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	$0.737526\pi$
$642$	172.833	+	53.6270i	0.269210	+	0.0835311i
$643$			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
$646$	878.998	+	50.1408i	1.36068	+	0.0776174i
$647$	−940.178			−1.45314			−0.726568	−	0.687095i	$-0.758886\pi$
$647$	−940.178			−1.45314			−0.726568	+	0.687095i	$0.758886\pi$
$648$	229.747	−	605.905i	0.354548	−	0.935038i
$649$			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	$0.391420\pi$
$653$			1230.75i			1.88477i	−0.334536	+	0.942383i	$0.608580\pi$
$654$	−1052.65	−	326.618i	−1.60955	−	0.499417i
$655$			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	$0.890441\pi$
$660$	206.272	−	94.3283i	0.312533	−	0.142922i
$661$		−	711.531i		−	1.07645i	−0.842802	−	0.538223i	$-0.819096\pi$
$661$		−	711.531i		−	1.07645i	0.842802	−	0.538223i	$-0.180904\pi$
$662$	−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
$666$	32.9752	−	8.04501i	0.0495123	−	0.0120796i
$667$	−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
$672$	−701.343	−	404.703i	−1.04367	−	0.602236i
$673$			277.546i			0.412401i	0.978510	+	0.206201i	$0.0661100\pi$
$673$			277.546i			0.412401i	−0.978510	+	0.206201i	$0.933890\pi$
$674$	−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	$0.650183\pi$
$678$	−88.5008	+	285.227i	−0.130532	+	0.420688i
$679$	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	$-0.336652\pi$
$684$	−672.664	+	124.014i	−0.983427	+	0.181307i
$685$	−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
$690$	−89.4461	−	27.7536i	−0.129632	−	0.0402225i
$691$		−	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
$696$	−804.881	−	351.852i	−1.15644	−	0.505534i
$697$		−	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	$-0.903709\pi$
$701$		−	417.674i		−	0.595826i	0.954593	−	0.297913i	$-0.0962906\pi$
$702$	−303.526	+	299.941i	−0.432374	+	0.427266i
$703$	−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
$708$	53.8286	−	24.6159i	0.0760291	−	0.0347682i
$709$	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
$714$	347.479	−	1119.88i	0.486666	−	1.56846i
$715$	−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	$-0.609736\pi$
$719$	−485.984			−0.675916			−0.337958	+	0.941161i	$0.609736\pi$
$720$	−420.775	−	363.853i	−0.584410	−	0.505351i
$721$		−	88.8586i		−	0.123244i
$722$	479.896	+	539.429i	0.664677	+	0.747131i
$723$	−20.7605	−	34.6212i	−0.0287144	−	0.0478855i
$724$	1258.80	+	140.624i	1.73868	+	0.194232i
$725$	−368.833			−0.508736
$726$	172.578	−	556.198i	0.237711	−	0.766112i
$727$			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
$732$	393.022	+	859.438i	0.536916	+	1.17410i
$733$	−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
$738$	161.360	+	661.388i	0.218645	+	0.896190i
$739$			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	$0.733460\pi$
$744$	896.922	+	392.087i	1.20554	+	0.526999i
$745$	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
$750$	−776.500	−	240.935i	−1.03533	−	0.321246i
$751$	575.467			0.766267			0.383134	−	0.923693i	$-0.374845\pi$
$751$	575.467			0.766267			0.383134	+	0.923693i	$0.374845\pi$
$752$	−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
$756$	−56.0487	+	909.223i	−0.0741385	+	1.20268i
$757$	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
$760$	−98.3171	+	578.889i	−0.129365	+	0.761696i
$761$			345.595i			0.454132i	0.973879	+	0.227066i	$0.0729133\pi$
$761$			345.595i			0.454132i	−0.973879	+	0.227066i	$0.927087\pi$
$762$	−92.4349	+	297.906i	−0.121306	+	0.390952i
$763$	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
$768$	764.526	−	72.9697i	0.995476	−	0.0950127i
$769$	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	$0.438453\pi$
$774$	−1174.64	+	286.580i	−1.51763	+	0.370258i
$775$	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
$780$	152.345	+	333.138i	0.195314	+	0.427100i
$781$			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
$786$	−329.187	+	1060.93i	−0.418813	+	1.34978i
$787$	619.217			0.786807			0.393403	−	0.919366i	$-0.371298\pi$
$787$	619.217			0.786807			0.393403	+	0.919366i	$0.371298\pi$
$788$	−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
$792$	349.406	−	44.9860i	0.441169	−	0.0568005i
$793$		−	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	$0.510552\pi$
$798$	851.481	−	446.736i	1.06702	−	0.559820i
$799$		−	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
$804$	634.862	+	1388.28i	0.789630	+	1.72672i
$805$	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	$-0.867539\pi$
$809$		−	654.048i		−	0.808465i	0.914656	−	0.404232i	$-0.132461\pi$
$810$	−155.542	+	606.171i	−0.192028	+	0.748359i
$811$	−141.919			−0.174993			−0.0874966	−	0.996165i	$-0.527887\pi$
$811$	−141.919			−0.174993			−0.0874966	+	0.996165i	$0.527887\pi$
$812$	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
$816$	347.362	+	1056.48i	0.425689	+	1.29470i
$817$	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	$-0.982406\pi$
$821$		−	90.7138i		−	0.110492i	0.998473	−	0.0552459i	$-0.0175943\pi$
$822$	−1202.89	−	373.236i	−1.46337	−	0.454058i
$823$		−	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	$-0.128564\pi$
$828$	−119.912	−	82.3405i	−0.144821	−	0.0994451i
$829$		−	697.415i		−	0.841272i	−0.907229	−	0.420636i	$-0.861807\pi$
$829$		−	697.415i		−	0.841272i	0.907229	−	0.420636i	$-0.138193\pi$
$830$	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
$834$	1398.25	+	433.851i	1.67655	+	0.520206i
$835$	−511.112			−0.612111
$836$	−231.733	−	290.827i	−0.277193	−	0.347879i
$837$	−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	$0.870330\pi$
$840$	716.530	+	313.229i	0.853012	+	0.372892i
$841$	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
$846$	261.652	+	1072.47i	0.309281	+	1.26769i
$847$			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
$852$	198.565	−	90.8039i	0.233057	−	0.106577i
$853$	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	$0.690281\pi$
$858$	−221.570	−	68.7494i	−0.258240	−	0.0801275i
$859$		−	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	$-0.0487632\pi$
$864$	−456.714	−	733.423i	−0.528604	−	0.848869i
$865$		−	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
$870$	810.237	+	251.402i	0.931306	+	0.288968i
$871$		−	1005.27i		−	1.15416i
$872$	−1197.29	+	852.086i	−1.37304	+	0.977163i
$873$	194.787	+	104.016i	0.223124	+	0.119148i
$874$	−8.74431	+	153.293i	−0.0100049	+	0.175392i
$875$	1142.93			1.30621
$876$	−34.6658	−	75.8052i	−0.0395729	−	0.0865357i
$877$		−	930.455i		−	1.06095i	−0.847700	−	0.530476i	$-0.822013\pi$
$877$		−	930.455i		−	1.06095i	0.847700	−	0.530476i	$-0.177987\pi$
$878$	−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	$0.141413\pi$
$881$			757.292i			0.859583i	−0.902928	+	0.429791i	$0.858587\pi$
$882$	−94.4758	−	387.241i	−0.107115	−	0.439049i
$883$			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	$0.946253\pi$
$888$	18.1274	−	41.4675i	0.0204137	−	0.0466976i
$889$		−	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
$894$	279.786	+	86.8128i	0.312960	+	0.0971060i
$895$	−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
$900$	−299.058	−	205.356i	−0.332287	−	0.228173i
$901$			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
$906$	185.441	−	597.652i	0.204681	−	0.659660i
$907$	239.471			0.264025			0.132013	−	0.991248i	$-0.457856\pi$
$907$	239.471			0.264025			0.132013	+	0.991248i	$0.457856\pi$
$908$	−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	$0.647386\pi$
$912$	−412.297	+	813.483i	−0.452080	+	0.891977i
$913$	−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
$918$	889.925	−	879.413i	0.969417	−	0.957966i
$919$			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
$924$	−450.384	+	205.961i	−0.487429	+	0.222902i
$925$		−	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	$0.203757\pi$
$929$			1109.77i			1.19459i	−0.802023	+	0.597293i	$0.796243\pi$
$930$	−902.890	−	280.151i	−0.970850	−	0.301238i
$931$	−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
$936$	72.6546	+	564.306i	0.0776224	+	0.602891i
$937$	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	$0.689978\pi$
$942$	−64.4049	+	207.569i	−0.0683704	+	0.220349i
$943$	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	$-0.435497\pi$
$947$	381.180			0.402513			0.201257	+	0.979539i	$0.435497\pi$
$948$	62.6150	+	136.923i	0.0660496	+	0.144433i
$949$			54.8916i			0.0578415i
$950$	−21.8081	+	382.309i	−0.0229559	+	0.402430i
$951$	−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	$0.641958\pi$
$954$	−200.888	−	823.408i	−0.210574	−	0.863111i
$955$			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
$960$	−725.955	+	152.007i	−0.756203	+	0.158341i
$961$	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
$966$	195.301	+	60.5986i	0.202175	+	0.0627315i
$967$			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	$-0.0496530\pi$
$972$	−509.744	+	827.614i	−0.524428	+	0.851455i
$973$	−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	$0.769474\pi$
$978$	−352.413	−	109.348i	−0.360340	−	0.111807i
$979$	−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	$-0.264184\pi$
$984$	831.719	+	363.584i	0.845243	+	0.369496i
$985$	69.9265			0.0709914
$986$	−1130.74	−	1264.10i	−1.14680	−	1.28204i
$987$	−798.092	−	1330.94i	−0.808604	−	1.34847i
$988$	469.700	−	374.260i	0.475405	−	0.378806i
$989$			271.414i			0.274433i
$990$	−330.530	+	80.6400i	−0.333869	+	0.0814545i
$991$	−1083.39			−1.09323			−0.546615	−	0.837384i	$-0.684084\pi$
$991$	−1083.39			−1.09323			−0.546615	+	0.837384i	$0.684084\pi$
$992$	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
$996$	328.115	+	717.502i	0.329432	+	0.720383i
$997$	−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.227.20	yes	72
3.2	odd	2	inner	228.3.b.e.227.54	yes	72
4.3	odd	2	inner	228.3.b.e.227.17	✓	72
12.11	even	2	inner	228.3.b.e.227.55	yes	72
19.18	odd	2	inner	228.3.b.e.227.53	yes	72
57.56	even	2	inner	228.3.b.e.227.19	yes	72
76.75	even	2	inner	228.3.b.e.227.56	yes	72
228.227	odd	2	inner	228.3.b.e.227.18	yes	72

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

\(f(q)\)	\(=\)	\(q+(-1.49065 + 1.33340i) q^{2} +(2.57288 - 1.54282i) q^{3} +(0.444087 - 3.97527i) q^{4} +3.86301i q^{5} +(-1.77807 + 5.73049i) q^{6} -8.43471i q^{7} +(4.63865 + 6.51789i) q^{8} +(4.23941 - 7.93898i) q^{9} +O(q^{10})\)	\(q+(-1.49065 + 1.33340i) q^{2} +(2.57288 - 1.54282i) q^{3} +(0.444087 - 3.97527i) q^{4} +3.86301i q^{5} +(-1.77807 + 5.73049i) 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} +(-4.99055 - 10.9130i) 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} +(4.26635 + 17.4871i) 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} +(21.9906 + 9.61314i) 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} +(-22.1370 - 6.86871i) 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} +(-29.6769 - 20.3784i) q^{36} -1.88569i q^{37} +(-2.16412 + 37.9383i) q^{38} +(12.1918 + 20.3316i) q^{39} +(-25.1787 + 17.9192i) q^{40} +37.8215 q^{41} +(48.3350 + 14.9975i) 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} +(-45.5985 + 14.9925i) 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} +(37.9562 + 38.4099i) 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} +(42.1572 - 19.2786i) 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} +(-8.69994 + 28.0388i) 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} +(71.4106 - 9.19412i) q^{72} +6.94630 q^{73} +(2.51438 + 2.81091i) q^{74} +(25.9272 - 15.5472i) q^{75} +(-47.3610 - 59.4385i) q^{76} -41.2703i q^{77} +(-45.2839 - 14.0508i) 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} +(-92.0484 + 42.0939i) 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} +(-67.5529 + 16.4810i) 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} +(47.9806 - 83.1496i) 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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