LMFDB - Embedded newform 117.3.k.a.29.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [117,3,Mod(29,117)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(117, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 2]))

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

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

chi := DirichletCharacter("117.29");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 117 = 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	117.k (of order $6$, degree $2$, 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:	$3.18801909302$
Analytic rank:	$0$
Dimension:	$52$
Relative dimension:	$26$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			29.1
Character	$\chi$	$=$	117.29
Dual form			117.3.k.a.113.26

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-3.86461i q^{2} +(1.97875 - 2.25490i) q^{3} -10.9352 q^{4} +(0.468040 - 0.270223i) q^{5} +(-8.71431 - 7.64708i) q^{6} +(-0.276958 - 0.479705i) q^{7} +26.8020i q^{8} +(-1.16913 - 8.92374i) q^{9} +(-1.04431 - 1.80879i) q^{10} +1.70674i q^{11} +(-21.6380 + 24.6578i) q^{12} +(-3.85396 - 12.4156i) q^{13} +(-1.85387 + 1.07033i) q^{14} +(0.316807 - 1.59009i) q^{15} +59.8383 q^{16} +(20.3230 + 11.7335i) q^{17} +(-34.4868 + 4.51825i) q^{18} +(15.3969 - 26.6681i) q^{19} +(-5.11813 + 2.95495i) q^{20} +(-1.62971 - 0.324702i) q^{21} +6.59589 q^{22} +(-8.17133 - 4.71772i) q^{23} +(60.4357 + 53.0343i) q^{24} +(-12.3540 + 21.3977i) q^{25} +(-47.9815 + 14.8941i) q^{26} +(-22.4355 - 15.0215i) q^{27} +(3.02860 + 5.24568i) q^{28} -11.5393i q^{29} +(-6.14507 - 1.22433i) q^{30} +(22.4177 + 38.8286i) q^{31} -124.044i q^{32} +(3.84853 + 3.37721i) q^{33} +(45.3453 - 78.5403i) q^{34} +(-0.259255 - 0.149681i) q^{35} +(12.7848 + 97.5831i) q^{36} +(-20.2057 - 34.9973i) q^{37} +(-103.062 - 59.5029i) q^{38} +(-35.6219 - 15.8770i) q^{39} +(7.24252 + 12.5444i) q^{40} +(14.3692 + 8.29606i) q^{41} +(-1.25485 + 6.29821i) q^{42} +(-15.5125 - 26.8685i) q^{43} -18.6636i q^{44} +(-2.95860 - 3.86074i) q^{45} +(-18.2322 + 31.5790i) q^{46} +(47.9945 + 27.7096i) q^{47} +(118.405 - 134.929i) q^{48} +(24.3466 - 42.1695i) q^{49} +(82.6938 + 47.7433i) q^{50} +(66.6717 - 22.6087i) q^{51} +(42.1439 + 135.767i) q^{52} +20.2665i q^{53} +(-58.0524 + 86.7047i) q^{54} +(0.461201 + 0.798824i) q^{55} +(12.8570 - 7.42301i) q^{56} +(-29.6675 - 87.4878i) q^{57} -44.5947 q^{58} +101.998i q^{59} +(-3.46435 + 17.3880i) q^{60} +(-6.58519 - 11.4059i) q^{61} +(150.058 - 86.6358i) q^{62} +(-3.95696 + 3.03234i) q^{63} -240.029 q^{64} +(-5.15879 - 4.76957i) q^{65} +(13.0516 - 14.8731i) q^{66} +(-5.01287 + 8.68254i) q^{67} +(-222.236 - 128.308i) q^{68} +(-26.8070 + 9.09036i) q^{69} +(-0.578458 + 1.00192i) q^{70} +(30.2162 + 17.4453i) q^{71} +(239.174 - 31.3351i) q^{72} +93.7942 q^{73} +(-135.251 + 78.0871i) q^{74} +(23.8043 + 70.1975i) q^{75} +(-168.368 + 291.622i) q^{76} +(0.818732 - 0.472695i) q^{77} +(-61.3585 + 137.665i) q^{78} +(-37.3274 + 64.6530i) q^{79} +(28.0067 - 16.1697i) q^{80} +(-78.2662 + 20.8661i) q^{81} +(32.0610 - 55.5313i) q^{82} +(74.9652 + 43.2812i) q^{83} +(17.8213 + 3.55069i) q^{84} +12.6826 q^{85} +(-103.836 + 59.9500i) q^{86} +(-26.0198 - 22.8332i) q^{87} -45.7440 q^{88} +(70.2790 - 40.5756i) q^{89} +(-14.9203 + 11.4339i) q^{90} +(-4.88844 + 5.28736i) q^{91} +(89.3554 + 51.5894i) q^{92} +(131.914 + 26.2823i) q^{93} +(107.087 - 185.480i) q^{94} -16.6424i q^{95} +(-279.707 - 245.451i) q^{96} +(37.2466 + 64.5130i) q^{97} +(-162.969 - 94.0901i) q^{98} +(15.2305 - 1.99541i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q - q^{3} - 98 q^{4} - 6 q^{5} + 12 q^{6} - q^{7} - 3 q^{9} - 6 q^{10} - 39 q^{12} + 4 q^{13} - 6 q^{14} - 25 q^{15} + 166 q^{16} + 34 q^{18} + 5 q^{19} + 21 q^{20} - 91 q^{21} + 30 q^{22} - 75 q^{23}+ \cdots + 522 q^{99}+O(q^{100}) $ 52 * q - q^3 - 98 * q^4 - 6 * q^5 + 12 * q^6 - q^7 - 3 * q^9 - 6 * q^10 - 39 * q^12 + 4 * q^13 - 6 * q^14 - 25 * q^15 + 166 * q^16 + 34 * q^18 + 5 * q^19 + 21 * q^20 - 91 * q^21 + 30 * q^22 - 75 * q^23 - 24 * q^24 + 88 * q^25 - 132 * q^26 - 34 * q^27 - 22 * q^28 + 70 * q^30 + 14 * q^31 + 95 * q^33 - 6 * q^34 + 228 * q^35 - 58 * q^36 - 13 * q^37 - 192 * q^38 - 111 * q^39 + 72 * q^40 + 33 * q^41 + 159 * q^42 - 31 * q^43 - 47 * q^45 + 6 * q^46 - 69 * q^47 + 293 * q^48 - 123 * q^49 - 168 * q^50 + 235 * q^51 - 92 * q^52 - 339 * q^54 - 27 * q^55 + 168 * q^56 + 189 * q^57 + 210 * q^58 + 213 * q^60 + 8 * q^61 + 471 * q^62 + 169 * q^63 - 98 * q^64 - 246 * q^65 - 576 * q^66 - 34 * q^67 + 18 * q^68 - 193 * q^69 - 57 * q^70 + 144 * q^71 + 36 * q^72 - 106 * q^73 - 465 * q^74 - 58 * q^75 - 79 * q^76 + 282 * q^77 - 76 * q^78 - 25 * q^79 - 1050 * q^80 - 279 * q^81 + 81 * q^82 + 219 * q^83 + 395 * q^84 - 108 * q^85 - 24 * q^86 - 518 * q^87 + 30 * q^88 + 99 * q^89 + 183 * q^90 + 2 * q^91 + 888 * q^92 + 582 * q^93 + 303 * q^94 - 439 * q^96 + 212 * q^97 - 405 * q^98 + 522 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/117\mathbb{Z}\right)^\times$.

$n$	$28$	$92$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$		−	3.86461i		−	1.93231i	−0.257969	−	0.966153i	$-0.583053\pi$
$2$		−	3.86461i		−	1.93231i	0.257969	−	0.966153i	$-0.416947\pi$
$3$	1.97875	−	2.25490i	0.659582	−	0.751633i
$3$	1.97875	−	2.25490i	0.659582	−	0.751633i
$4$	−10.9352			−2.73381
$5$	0.468040	−	0.270223i	0.0936081	−	0.0540446i	−0.452465	−	0.891782i	$-0.649455\pi$
$5$	0.468040	−	0.270223i	0.0936081	−	0.0540446i	0.546073	+	0.837737i	$0.316122\pi$
$6$	−8.71431	−	7.64708i	−1.45238	−	1.27451i
$7$	−0.276958	−	0.479705i	−0.0395654	−	0.0685293i	0.845565	−	0.533873i	$-0.179264\pi$
$7$	−0.276958	−	0.479705i	−0.0395654	−	0.0685293i	−0.885130	+	0.465344i	$0.845931\pi$
$8$			26.8020i			3.35025i
$9$	−1.16913	−	8.92374i	−0.129904	−	0.991527i
$10$	−1.04431	−	1.80879i	−0.104431	−	0.180879i
$11$			1.70674i			0.155158i	0.996986	+	0.0775791i	$0.0247190\pi$
$11$			1.70674i			0.155158i	−0.996986	+	0.0775791i	$0.975281\pi$
$12$	−21.6380	+	24.6578i	−1.80317	+	2.05482i
$13$	−3.85396	−	12.4156i	−0.296458	−	0.955046i
$13$	−3.85396	−	12.4156i	−0.296458	−	0.955046i
$14$	−1.85387	+	1.07033i	−0.132420	+	0.0764524i
$15$	0.316807	−	1.59009i	0.0211204	−	0.106006i
$16$	59.8383			3.73989
$17$	20.3230	+	11.7335i	1.19547	+	0.690204i	0.959542	−	0.281567i	$-0.0908542\pi$
$17$	20.3230	+	11.7335i	1.19547	+	0.690204i	0.235926	+	0.971771i	$0.424188\pi$
$18$	−34.4868	+	4.51825i	−1.91593	+	0.251014i
$19$	15.3969	−	26.6681i	0.810361	−	1.40359i	−0.102250	−	0.994759i	$-0.532604\pi$
$19$	15.3969	−	26.6681i	0.810361	−	1.40359i	0.912611	−	0.408828i	$-0.134062\pi$
$20$	−5.11813	+	2.95495i	−0.255906	+	0.147748i
$21$	−1.62971	−	0.324702i	−0.0776054	−	0.0154620i
$22$	6.59589			0.299813
$23$	−8.17133	−	4.71772i	−0.355275	−	0.205118i	0.311731	−	0.950170i	$-0.399091\pi$
$23$	−8.17133	−	4.71772i	−0.355275	−	0.205118i	−0.667006	+	0.745052i	$0.732425\pi$
$24$	60.4357	+	53.0343i	2.51816	+	2.20976i
$25$	−12.3540	+	21.3977i	−0.494158	+	0.855907i
$26$	−47.9815	+	14.8941i	−1.84544	+	0.572848i
$27$	−22.4355	−	15.0215i	−0.830946	−	0.556353i
$28$	3.02860	+	5.24568i	0.108164	+	0.187346i
$29$		−	11.5393i		−	0.397905i	−0.980009	−	0.198953i	$-0.936246\pi$
$29$		−	11.5393i		−	0.397905i	0.980009	−	0.198953i	$-0.0637540\pi$
$30$	−6.14507	−	1.22433i	−0.204836	−	0.0408112i
$31$	22.4177	+	38.8286i	0.723152	+	1.25254i	0.959730	+	0.280924i	$0.0906407\pi$
$31$	22.4177	+	38.8286i	0.723152	+	1.25254i	−0.236578	+	0.971612i	$0.576026\pi$
$32$		−	124.044i		−	3.87638i
$33$	3.84853	+	3.37721i	0.116622	+	0.102340i
$34$	45.3453	−	78.5403i	1.33368	−	2.31001i
$35$	−0.259255	−	0.149681i	−0.00740728	−	0.00427659i
$36$	12.7848	+	97.5831i	0.355132	+	2.71064i
$37$	−20.2057	−	34.9973i	−0.546099	−	0.945872i	−0.998537	−	0.0540758i	$-0.982779\pi$
$37$	−20.2057	−	34.9973i	−0.546099	−	0.945872i	0.452437	−	0.891796i	$-0.350555\pi$
$38$	−103.062	−	59.5029i	−2.71216	−	1.56587i
$39$	−35.6219	−	15.8770i	−0.913382	−	0.407103i
$40$	7.24252	+	12.5444i	0.181063	+	0.313610i
$41$	14.3692	+	8.29606i	0.350468	+	0.202343i	0.664891	−	0.746940i	$-0.268478\pi$
$41$	14.3692	+	8.29606i	0.350468	+	0.202343i	−0.314423	+	0.949283i	$0.601811\pi$
$42$	−1.25485	+	6.29821i	−0.0298773	+	0.149957i
$43$	−15.5125	−	26.8685i	−0.360757	−	0.624849i	0.627329	−	0.778755i	$-0.284148\pi$
$43$	−15.5125	−	26.8685i	−0.360757	−	0.624849i	−0.988086	+	0.153905i	$0.950815\pi$
$44$		−	18.6636i		−	0.424173i
$45$	−2.95860	−	3.86074i	−0.0657468	−	0.0857943i
$46$	−18.2322	+	31.5790i	−0.396351	+	0.686501i
$47$	47.9945	+	27.7096i	1.02116	+	0.589566i	0.914439	−	0.404723i	$-0.132632\pi$
$47$	47.9945	+	27.7096i	1.02116	+	0.589566i	0.106719	+	0.994289i	$0.465965\pi$
$48$	118.405	−	134.929i	2.46677	−	2.81103i
$49$	24.3466	−	42.1695i	0.496869	−	0.860603i
$50$	82.6938	+	47.7433i	1.65388	+	0.954865i
$51$	66.6717	−	22.6087i	1.30729	−	0.443307i
$52$	42.1439	+	135.767i	0.810460	+	2.61091i
$53$			20.2665i			0.382387i	0.981552	+	0.191194i	$0.0612358\pi$
$53$			20.2665i			0.382387i	−0.981552	+	0.191194i	$0.938764\pi$
$54$	−58.0524	+	86.7047i	−1.07504	+	1.60564i
$55$	0.461201	+	0.798824i	0.00838547	+	0.0145241i
$56$	12.8570	−	7.42301i	0.229590	−	0.132554i
$57$	−29.6675	−	87.4878i	−0.520482	−	1.53487i
$58$	−44.5947			−0.768875
$59$			101.998i			1.72878i	0.502826	+	0.864388i	$0.332294\pi$
$59$			101.998i			1.72878i	−0.502826	+	0.864388i	$0.667706\pi$
$60$	−3.46435	+	17.3880i	−0.0577392	+	0.289799i
$61$	−6.58519	−	11.4059i	−0.107954	−	0.186982i	0.806987	−	0.590569i	$-0.201097\pi$
$61$	−6.58519	−	11.4059i	−0.107954	−	0.186982i	−0.914941	+	0.403587i	$0.867763\pi$
$62$	150.058	−	86.6358i	2.42028	−	1.39735i
$63$	−3.95696	+	3.03234i	−0.0628089	+	0.0481323i
$64$	−240.029			−3.75045
$65$	−5.15879	−	4.76957i	−0.0793660	−	0.0733780i
$66$	13.0516	−	14.8731i	0.197751	−	0.225350i
$67$	−5.01287	+	8.68254i	−0.0748189	+	0.129590i	−0.901008	−	0.433803i	$-0.857171\pi$
$67$	−5.01287	+	8.68254i	−0.0748189	+	0.129590i	0.826189	+	0.563394i	$0.190505\pi$
$68$	−222.236	−	128.308i	−3.26818	−	1.88688i
$69$	−26.8070	+	9.09036i	−0.388507	+	0.131744i
$70$	−0.578458	+	1.00192i	−0.00826369	+	0.0143131i
$71$	30.2162	+	17.4453i	0.425580	+	0.245709i	0.697462	−	0.716622i	$-0.254313\pi$
$71$	30.2162	+	17.4453i	0.425580	+	0.245709i	−0.271882	+	0.962331i	$0.587646\pi$
$72$	239.174	−	31.3351i	3.32186	−	0.435210i
$73$	93.7942			1.28485			0.642426	−	0.766348i	$-0.277928\pi$
$73$	93.7942			1.28485			0.642426	+	0.766348i	$0.277928\pi$
$74$	−135.251	+	78.0871i	−1.82771	+	1.05523i
$75$	23.8043	+	70.1975i	0.317390	+	0.935967i
$76$	−168.368	+	291.622i	−2.21537	+	3.83714i
$77$	0.818732	−	0.472695i	0.0106329	−	0.00613890i
$78$	−61.3585	+	137.665i	−0.786647	+	1.76493i
$79$	−37.3274	+	64.6530i	−0.472499	+	0.818393i	−0.999505	−	0.0314692i	$-0.989981\pi$
$79$	−37.3274	+	64.6530i	−0.472499	+	0.818393i	0.527005	+	0.849862i	$0.323315\pi$
$80$	28.0067	−	16.1697i	0.350084	−	0.202121i
$81$	−78.2662	+	20.8661i	−0.966250	+	0.257606i
$82$	32.0610	−	55.5313i	0.390988	−	0.677212i
$83$	74.9652	+	43.2812i	0.903196	+	0.521460i	0.878236	−	0.478228i	$-0.158721\pi$
$83$	74.9652	+	43.2812i	0.903196	+	0.521460i	0.0249601	+	0.999688i	$0.492054\pi$
$84$	17.8213	+	3.55069i	0.212158	+	0.0422701i
$85$	12.6826			0.149207
$86$	−103.836	+	59.9500i	−1.20740	+	0.697093i
$87$	−26.0198	−	22.8332i	−0.299079	−	0.262451i
$88$	−45.7440			−0.519818
$89$	70.2790	−	40.5756i	0.789651	−	0.455905i	−0.0501884	−	0.998740i	$-0.515982\pi$
$89$	70.2790	−	40.5756i	0.789651	−	0.455905i	0.839840	+	0.542834i	$0.182649\pi$
$90$	−14.9203	+	11.4339i	−0.165781	+	0.127043i
$91$	−4.88844	+	5.28736i	−0.0537191	+	0.0581028i
$92$	89.3554	+	51.5894i	0.971254	+	0.560754i
$93$	131.914	+	26.2823i	1.41843	+	0.282605i
$94$	107.087	−	185.480i	1.13922	−	1.97319i
$95$		−	16.6424i		−	0.175183i
$96$	−279.707	−	245.451i	−2.91361	−	2.55679i
$97$	37.2466	+	64.5130i	0.383985	+	0.665082i	0.991628	−	0.129129i	$-0.0412180\pi$
$97$	37.2466	+	64.5130i	0.383985	+	0.665082i	−0.607643	+	0.794211i	$0.707885\pi$
$98$	−162.969	−	94.0901i	−1.66295	−	0.960103i
$99$	15.2305	−	1.99541i	0.153844	−	0.0201557i
$100$	135.093	−	233.989i	1.35093	−	2.33989i
$101$			54.3528i			0.538147i	0.963120	+	0.269073i	$0.0867174\pi$
$101$			54.3528i			0.538147i	−0.963120	+	0.269073i	$0.913283\pi$
$102$	−87.3737	−	257.660i	−0.856605	−	2.52608i
$103$	−58.9763	−	102.150i	−0.572586	−	0.991747i	−0.996299	−	0.0859511i	$-0.972607\pi$
$103$	−58.9763	−	102.150i	−0.572586	−	0.991747i	0.423714	−	0.905796i	$-0.360726\pi$
$104$	332.762	−	103.294i	3.19964	−	0.993209i
$105$	−0.850514	+	0.288413i	−0.00810013	+	0.00274679i
$106$	78.3223			0.738889
$107$	−103.584	+	59.8043i	−0.968075	+	0.558919i	−0.898649	−	0.438668i	$-0.855450\pi$
$107$	−103.584	+	59.8043i	−0.968075	+	0.558919i	−0.0694265	+	0.997587i	$0.522117\pi$
$108$	245.338	+	164.264i	2.27165	+	1.52096i
$109$	−13.8158			−0.126750			−0.0633750	−	0.997990i	$-0.520186\pi$
$109$	−13.8158			−0.126750			−0.0633750	+	0.997990i	$0.520186\pi$
$110$	3.08714	−	1.78236i	0.0280649	−	0.0162033i
$111$	−118.897	−	23.6889i	−1.07115	−	0.213414i
$112$	−16.5727	−	28.7047i	−0.147970	−	0.256292i
$113$			74.9047i			0.662873i	0.943477	+	0.331437i	$0.107533\pi$
$113$			74.9047i			0.662873i	−0.943477	+	0.331437i	$0.892467\pi$
$114$	−338.107	+	114.653i	−2.96585	+	1.00573i
$115$	−5.09935			−0.0443422
$116$			126.184i			1.08780i
$117$	−106.288	+	48.9072i	−0.908442	+	0.418011i
$118$	394.182			3.34052
$119$		−	12.9987i		−	0.109233i
$120$	42.6175	+	8.49104i	0.355145	+	0.0707587i
$121$	118.087			0.975926
$122$	−44.0793	+	25.4492i	−0.361306	+	0.208600i
$123$	47.1397	−	15.9853i	0.383250	−	0.129962i
$124$	−245.143	−	424.600i	−1.97696	−	3.42419i
$125$			26.8645i			0.214916i
$126$	11.7188	+	15.2921i	0.0930064	+	0.121366i
$127$	−22.5361	−	39.0336i	−0.177449	−	0.307351i	0.763557	−	0.645741i	$-0.223451\pi$
$127$	−22.5361	−	39.0336i	−0.177449	−	0.307351i	−0.941006	+	0.338389i	$0.890118\pi$
$128$			431.442i			3.37064i
$129$	−91.2812	−	18.1867i	−0.707606	−	0.140982i
$130$	−18.4325	+	19.9367i	−0.141789	+	0.153359i
$131$	18.7361	−	10.8173i	0.143024	−	0.0825748i	−0.426781	−	0.904355i	$-0.640352\pi$
$131$	18.7361	−	10.8173i	0.143024	−	0.0825748i	0.569804	+	0.821780i	$0.307019\pi$
$132$	−42.0845	−	36.9305i	−0.318822	−	0.279777i
$133$	−17.0571			−0.128249
$134$	33.5547	+	19.3728i	0.250408	+	0.144573i
$135$	−14.5599	−	0.968075i	−0.107851	−	0.00717092i
$136$	−314.480	+	544.695i	−2.31235	+	4.00511i
$137$	17.5630	−	10.1400i	0.128197	−	0.0740145i	−0.434530	−	0.900657i	$-0.643086\pi$
$137$	17.5630	−	10.1400i	0.128197	−	0.0740145i	0.562727	+	0.826643i	$0.309752\pi$
$138$	35.1307	+	103.599i	0.254570	+	0.750714i
$139$	−181.018			−1.30228			−0.651142	−	0.758956i	$-0.725710\pi$
$139$	−181.018			−1.30228			−0.651142	+	0.758956i	$0.725710\pi$
$140$	2.83501	+	1.63679i	0.0202501	+	0.0116914i
$141$	157.451	−	53.3924i	1.11668	−	0.378669i
$142$	67.4194	−	116.774i	0.474785	−	0.822351i
$143$	21.1902	−	6.57771i	0.148183	−	0.0459980i
$144$	−69.9591	−	533.982i	−0.485827	−	3.70820i
$145$	−3.11817	−	5.40084i	−0.0215047	−	0.0372471i
$146$		−	362.478i		−	2.48273i
$147$	−46.9123	−	138.342i	−0.319131	−	0.941101i
$148$	220.954	+	382.703i	1.49293	+	2.58583i
$149$		−	179.535i		−	1.20493i	−0.798145	−	0.602466i	$-0.794185\pi$
$149$		−	179.535i		−	1.20493i	0.798145	−	0.602466i	$-0.205815\pi$
$150$	271.286	−	91.9943i	1.80857	−	0.613295i
$151$	−95.7200	+	165.792i	−0.633907	+	1.09796i	0.352838	+	0.935684i	$0.385217\pi$
$151$	−95.7200	+	165.792i	−0.633907	+	1.09796i	−0.986746	+	0.162275i	$0.948117\pi$
$152$	714.759	+	412.666i	4.70236	+	2.71491i
$153$	80.9461	−	195.075i	0.529059	−	1.27500i
$154$	−1.82678	−	3.16408i	−0.0118622	−	0.0205460i
$155$	20.9848	+	12.1156i	0.135386	+	0.0781650i
$156$	389.534	+	173.619i	2.49701	+	1.11294i
$157$	−132.762	−	229.951i	−0.845618	−	1.46465i	−0.885083	−	0.465433i	$-0.845899\pi$
$157$	−132.762	−	229.951i	−0.845618	−	1.46465i	0.0394645	−	0.999221i	$-0.487435\pi$
$158$	249.859	+	144.256i	1.58139	+	0.913013i
$159$	45.6990	+	40.1023i	0.287415	+	0.252216i
$160$	−33.5196	−	58.0576i	−0.209497	−	0.362860i
$161$			5.22644i			0.0324623i
$162$	80.6394	+	302.469i	0.497774	+	1.86709i
$163$	−85.3519	+	147.834i	−0.523632	+	0.906956i	0.475990	+	0.879451i	$0.342090\pi$
$163$	−85.3519	+	147.834i	−0.523632	+	0.906956i	−0.999622	+	0.0275058i	$0.991244\pi$
$164$	−157.130	−	90.7193i	−0.958112	−	0.553166i
$165$	2.71387	+	0.540707i	0.0164477	+	0.00327701i
$166$	167.265	−	289.712i	1.00762	−	1.74525i
$167$	−162.448	−	93.7895i	−0.972744	−	0.561614i	−0.0726720	−	0.997356i	$-0.523153\pi$
$167$	−162.448	−	93.7895i	−0.972744	−	0.561614i	−0.900072	+	0.435742i	$0.856486\pi$
$168$	8.70266	−	43.6796i	0.0518015	−	0.259997i
$169$	−139.294	+	95.6984i	−0.824225	+	0.566263i
$170$		−	49.0134i		−	0.288314i
$171$	−255.981	−	106.219i	−1.49696	−	0.621163i
$172$	169.633	+	293.813i	0.986240	+	1.70822i
$173$	−94.6178	+	54.6276i	−0.546923	+	0.315766i	−0.747880	−	0.663834i	$-0.768928\pi$
$173$	−94.6178	+	54.6276i	−0.546923	+	0.315766i	0.200957	+	0.979600i	$0.435595\pi$
$174$	−88.2416	+	100.557i	−0.507136	+	0.577912i
$175$	13.6861			0.0782063
$176$			102.129i			0.580276i
$177$	229.995	+	201.828i	1.29940	+	1.14027i
$178$	−156.809	−	271.601i	−0.880949	−	1.52585i
$179$	−0.514219	+	0.296885i	−0.00287273	+	0.00165857i	−0.501436	−	0.865195i	$-0.667195\pi$
$179$	−0.514219	+	0.296885i	−0.00287273	+	0.00165857i	0.498563	+	0.866853i	$0.333861\pi$
$180$	32.3530	+	42.2181i	0.179739	+	0.234545i
$181$	33.4332			0.184714			0.0923570	−	0.995726i	$-0.470560\pi$
$181$	33.4332			0.184714			0.0923570	+	0.995726i	$0.470560\pi$
$182$	20.4336	+	18.8919i	0.112272	+	0.103802i
$183$	−38.7495	−	7.72040i	−0.211746	−	0.0421880i
$184$	126.444	−	219.008i	0.687197	−	1.19026i
$185$	−18.9141	−	10.9201i	−0.102239	−	0.0590275i
$186$	101.571	−	509.795i	0.546080	−	2.74083i
$187$	−20.0260	+	34.6860i	−0.107091	+	0.185487i
$188$	−524.830	−	303.011i	−2.79165	−	1.61176i
$189$	−0.992201	+	14.9228i	−0.00524974	+	0.0789564i
$190$	−64.3163			−0.338507
$191$	−48.5590	+	28.0355i	−0.254235	+	0.146783i	−0.621702	−	0.783254i	$-0.713559\pi$
$191$	−48.5590	+	28.0355i	−0.254235	+	0.146783i	0.367467	+	0.930037i	$0.380225\pi$
$192$	−474.956	+	541.240i	−2.47373	+	2.81896i
$193$	46.7215	−	80.9240i	0.242080	−	0.419295i	−0.719226	−	0.694776i	$-0.755504\pi$
$193$	46.7215	−	80.9240i	0.242080	−	0.419295i	0.961307	+	0.275480i	$0.0888369\pi$
$194$	249.318	−	143.944i	1.28514	−	0.741977i
$195$	−20.9628	+	2.19478i	−0.107502	+	0.0112553i
$196$	−266.236	+	461.133i	−1.35834	+	2.35272i
$197$	−58.7451	+	33.9165i	−0.298199	+	0.172165i	−0.641633	−	0.767012i	$-0.721743\pi$
$197$	−58.7451	+	33.9165i	−0.298199	+	0.172165i	0.343435	+	0.939177i	$0.388410\pi$
$198$	−7.71149	−	58.8600i	−0.0389469	−	0.297273i
$199$	−63.5358	+	110.047i	−0.319276	+	0.553001i	−0.980337	−	0.197330i	$-0.936773\pi$
$199$	−63.5358	+	110.047i	−0.319276	+	0.553001i	0.661062	+	0.750332i	$0.270106\pi$
$200$	−573.500	−	331.110i	−2.86750	−	1.65555i
$201$	9.65906	+	28.4841i	0.0480550	+	0.141712i
$202$	210.053			1.03986
$203$	−5.53544	+	3.19589i	−0.0272682	+	0.0157433i
$204$	−729.071	+	247.231i	−3.57388	+	1.21192i
$205$	8.96715			0.0437422
$206$	−394.770	+	227.921i	−1.91636	+	1.10641i
$207$	−32.5463	+	78.4345i	−0.157229	+	0.378911i
$208$	−230.614	−	742.928i	−1.10872	−	3.57177i
$209$	45.5156	+	26.2785i	0.217778	+	0.125734i
$210$	1.11460	+	3.28691i	0.00530764	+	0.0156519i
$211$	−99.6893	+	172.667i	−0.472461	+	0.818327i	−0.999503	−	0.0315121i	$-0.989968\pi$
$211$	−99.6893	+	172.667i	−0.472461	+	0.818327i	0.527042	+	0.849839i	$0.323301\pi$
$212$		−	221.619i		−	1.04537i
$213$	99.1276	−	33.6146i	0.465388	−	0.157815i
$214$	231.120	+	400.312i	1.08000	+	1.87062i
$215$	−14.5210	−	8.38370i	−0.0675395	−	0.0389940i
$216$	402.607	−	601.317i	1.86392	−	2.78387i
$217$	12.4175	−	21.5078i	0.0572236	−	0.0991141i
$218$			53.3925i			0.244920i
$219$	185.595	−	211.496i	0.847465	−	0.965737i
$220$	−5.04334	−	8.73532i	−0.0229243	−	0.0397060i
$221$	67.3541	−	297.542i	0.304770	−	1.34634i
$222$	−91.5484	+	459.491i	−0.412380	+	2.06978i
$223$	−111.973			−0.502122			−0.251061	−	0.967971i	$-0.580779\pi$
$223$	−111.973			−0.502122			−0.251061	+	0.967971i	$0.580779\pi$
$224$	−59.5045	+	34.3549i	−0.265645	+	0.153370i
$225$	205.391	+	85.2267i	0.912848	+	0.378785i
$226$	289.478			1.28087
$227$	43.9655	−	25.3835i	0.193681	−	0.111822i	−0.400024	−	0.916505i	$-0.630998\pi$
$227$	43.9655	−	25.3835i	0.193681	−	0.111822i	0.593704	+	0.804683i	$0.297665\pi$
$228$	324.421	+	956.699i	1.42290	+	4.19605i
$229$	12.7484	+	22.0810i	0.0556701	+	0.0964234i	0.892517	−	0.451013i	$-0.148937\pi$
$229$	12.7484	+	22.0810i	0.0556701	+	0.0964234i	−0.836847	+	0.547436i	$0.815604\pi$
$230$			19.7070i			0.0856827i
$231$	0.554182	−	2.78150i	0.00239906	−	0.0120411i
$232$	309.275			1.33308
$233$		−	350.274i		−	1.50332i	−0.659549	−	0.751661i	$-0.729253\pi$
$233$		−	350.274i		−	1.50332i	0.659549	−	0.751661i	$-0.270747\pi$
$234$	189.007	+	410.761i	0.807724	+	1.75539i
$235$	29.9511			0.127452
$236$		−	1115.37i		−	4.72614i
$237$	71.9245	+	212.101i	0.303479	+	0.894943i
$238$	−50.2349			−0.211071
$239$	37.1471	−	21.4469i	0.155427	−	0.0897359i	−0.420269	−	0.907399i	$-0.638064\pi$
$239$	37.1471	−	21.4469i	0.155427	−	0.0897359i	0.575696	+	0.817664i	$0.304731\pi$
$240$	18.9572	−	95.1481i	0.0789882	−	0.396450i
$241$	80.0937	+	138.726i	0.332339	+	0.575628i	0.982970	−	0.183766i	$-0.0588288\pi$
$241$	80.0937	+	138.726i	0.332339	+	0.575628i	−0.650631	+	0.759394i	$0.725495\pi$
$242$		−	456.361i		−	1.88579i
$243$	−107.818	+	217.771i	−0.443696	+	0.896178i
$244$	72.0106	+	124.726i	0.295125	+	0.511172i
$245$		−	26.3161i		−	0.107412i
$246$	−61.7769	−	182.177i	−0.251126	−	0.740556i
$247$	−390.440	−	88.3833i	−1.58073	−	0.357827i
$248$	−1040.68	+	600.839i	−4.19630	+	2.42274i
$249$	245.932	−	83.3965i	0.987678	−	0.334926i
$250$	103.821			0.415283
$251$	118.743	+	68.5561i	0.473078	+	0.273132i	0.717527	−	0.696530i	$-0.245274\pi$
$251$	118.743	+	68.5561i	0.473078	+	0.273132i	−0.244449	+	0.969662i	$0.578607\pi$
$252$	43.2703	−	33.1593i	0.171707	−	0.131585i
$253$	8.05193	−	13.9463i	0.0318258	−	0.0551239i
$254$	−150.850	+	87.0931i	−0.593896	+	0.342886i
$255$	25.0957	−	28.5980i	0.0984144	−	0.112149i
$256$	707.241			2.76266
$257$	180.620	+	104.281i	0.702800	+	0.405762i	0.808390	−	0.588648i	$-0.200340\pi$
$257$	180.620	+	104.281i	0.702800	+	0.405762i	−0.105589	+	0.994410i	$0.533673\pi$
$258$	−70.2847	+	352.766i	−0.272421	+	1.36731i
$259$	−11.1922	+	19.3855i	−0.0432133	+	0.0748476i
$260$	56.4126	+	52.1563i	0.216971	+	0.200601i
$261$	−102.973	+	13.4909i	−0.394534	+	0.0516894i
$262$	−41.8047	−	72.4078i	−0.159560	−	0.276366i
$263$			351.373i			1.33602i	0.744153	+	0.668009i	$0.232853\pi$
$263$			351.373i			1.33602i	−0.744153	+	0.668009i	$0.767147\pi$
$264$	−90.5158	+	103.148i	−0.342863	+	0.390713i
$265$	5.47649	+	9.48555i	0.0206660	+	0.0357945i
$266$			65.9192i			0.247816i
$267$	47.5704	−	238.761i	0.178166	−	0.894235i
$268$	54.8169	−	94.9456i	0.204541	−	0.354275i
$269$	−119.383	−	68.9255i	−0.443801	−	0.256229i	0.261407	−	0.965229i	$-0.415813\pi$
$269$	−119.383	−	68.9255i	−0.443801	−	0.256229i	−0.705209	+	0.709000i	$0.749147\pi$
$270$	−3.74123	+	56.2684i	−0.0138564	+	0.208401i
$271$	125.296	+	217.020i	0.462348	+	0.800811i	0.999077	−	0.0429439i	$-0.0136737\pi$
$271$	125.296	+	217.020i	0.462348	+	0.800811i	−0.536729	+	0.843755i	$0.680340\pi$
$272$	1216.09	+	702.111i	4.47092	+	2.58129i
$273$	2.24948	+	21.4853i	0.00823986	+	0.0787006i
$274$	−39.1871	−	67.8741i	−0.143019	−	0.247716i
$275$	−36.5203	−	21.0850i	−0.132801	−	0.0766728i
$276$	293.140	−	99.4051i	1.06210	−	0.360164i
$277$	157.907	+	273.503i	0.570061	+	0.987375i	0.996559	+	0.0828864i	$0.0264139\pi$
$277$	157.907	+	273.503i	0.570061	+	0.987375i	−0.426498	+	0.904489i	$0.640253\pi$
$278$			699.563i			2.51641i
$279$	320.287	−	245.446i	1.14798	−	0.879734i
$280$	4.01174	−	6.94854i	0.0143276	−	0.0248162i
$281$	383.848	+	221.615i	1.36601	+	0.788664i	0.990415	−	0.138122i	$-0.0441065\pi$
$281$	383.848	+	221.615i	1.36601	+	0.788664i	0.375591	+	0.926786i	$0.377440\pi$
$282$	−206.341	−	608.488i	−0.731705	−	2.15776i
$283$	121.823	−	211.004i	0.430470	−	0.745596i	−0.566444	−	0.824100i	$-0.691681\pi$
$283$	121.823	−	211.004i	0.430470	−	0.745596i	0.996914	+	0.0785045i	$0.0250145\pi$
$284$	−330.421	−	190.769i	−1.16345	−	0.671721i
$285$	−37.5268	−	32.9310i	−0.131673	−	0.115547i
$286$	−25.4203	−	81.8919i	−0.0888822	−	0.286335i
$287$		−	9.19063i		−	0.0320231i
$288$	−1106.94	+	145.024i	−3.84353	+	0.503556i
$289$	130.848	+	226.636i	0.452762	+	0.784208i
$290$	−20.8721	+	12.0505i	−0.0719729	+	0.0415536i
$291$	219.172	+	43.6675i	0.753167	+	0.150060i
$292$	−1025.66			−3.51254
$293$		−	122.772i		−	0.419017i	−0.977807	−	0.209509i	$-0.932814\pi$
$293$		−	122.772i		−	0.419017i	0.977807	−	0.209509i	$-0.0671864\pi$
$294$	−534.638	+	181.298i	−1.81850	+	0.616660i
$295$	27.5622	+	47.7391i	0.0934310	+	0.161827i
$296$	937.996	−	541.552i	3.16890	−	1.82957i
$297$	25.6379	−	38.2917i	0.0863227	−	0.128928i
$298$	−693.833			−2.32830
$299$	−27.0813	+	119.634i	−0.0905730	+	0.400113i
$300$	−260.305	−	767.626i	−0.867684	−	2.55875i
$301$	−8.59264	+	14.8829i	−0.0285470	+	0.0494448i
$302$	640.721	+	369.921i	2.12159	+	1.22490i
$303$	122.560	+	107.550i	0.404489	+	0.354952i
$304$	921.322	−	1595.78i	3.03067	−	5.24927i
$305$	−6.16427	−	3.55894i	−0.0202107	−	0.0116687i
$306$	−753.888	−	312.825i	−2.46369	−	1.02230i
$307$	76.1769			0.248133			0.124067	−	0.992274i	$-0.460406\pi$
$307$	76.1769			0.248133			0.124067	+	0.992274i	$0.460406\pi$
$308$	−8.95302	+	5.16903i	−0.0290682	+	0.0167826i
$309$	−347.037	−	69.1432i	−1.12310	−	0.223764i
$310$	46.8220	−	81.0981i	0.151039	−	0.261607i
$311$	−477.528	+	275.701i	−1.53546	+	0.886498i	−0.536364	+	0.843986i	$0.680203\pi$
$311$	−477.528	+	275.701i	−1.53546	+	0.886498i	−0.999096	+	0.0425120i	$0.986464\pi$
$312$	425.535	−	954.737i	1.36389	−	3.06006i
$313$	114.005	−	197.462i	0.364233	−	0.630870i	−0.624420	−	0.781089i	$-0.714664\pi$
$313$	114.005	−	197.462i	0.364233	−	0.630870i	0.988653	+	0.150219i	$0.0479978\pi$
$314$	−888.670	+	513.074i	−2.83016	+	1.63399i
$315$	−1.03261	+	2.48852i	−0.00327812	+	0.00790006i
$316$	408.184	−	706.996i	1.29172	−	2.23733i
$317$	−235.372	−	135.892i	−0.742499	−	0.428682i	0.0804783	−	0.996756i	$-0.474355\pi$
$317$	−235.372	−	135.892i	−0.742499	−	0.428682i	−0.822977	+	0.568074i	$0.807689\pi$
$318$	154.980	−	176.609i	0.487358	−	0.555373i
$319$	19.6945			0.0617383
$320$	−112.343	+	64.8613i	−0.351072	+	0.202692i
$321$	−70.1139	+	351.909i	−0.218423	+	1.09629i
$322$	20.1982			0.0627272
$323$	625.820	−	361.317i	1.93752	−	1.11863i
$324$	855.859	−	228.176i	2.64154	−	0.704246i
$325$	313.277	+	70.9159i	0.963928	+	0.218203i
$326$	571.321	+	329.852i	1.75252	+	1.01182i
$327$	−27.3379	+	31.1531i	−0.0836020	+	0.0952695i
$328$	−222.351	+	385.123i	−0.677898	+	1.17415i
$329$		−	30.6976i		−	0.0933057i
$330$	2.08962	−	10.4880i	0.00633219	−	0.0317819i
$331$	−162.417	−	281.314i	−0.490685	−	0.849892i	0.509257	−	0.860614i	$-0.329920\pi$
$331$	−162.417	−	281.314i	−0.490685	−	0.849892i	−0.999943	+	0.0107226i	$0.996587\pi$
$332$	−819.762	−	473.290i	−2.46916	−	1.42557i
$333$	−288.683	+	221.227i	−0.866917	+	0.664344i
$334$	−362.460	+	627.799i	−1.08521	+	1.87964i
$335$			5.41837i			0.0161743i
$336$	−97.5194	−	19.4296i	−0.290236	−	0.0578263i
$337$	103.575	+	179.397i	0.307344	+	0.532336i	0.977780	−	0.209631i	$-0.0672264\pi$
$337$	103.575	+	179.397i	0.307344	+	0.532336i	−0.670436	+	0.741967i	$0.733893\pi$
$338$	369.837	+	538.317i	1.09419	+	1.59265i
$339$	168.902	+	148.217i	0.498237	+	0.437219i
$340$	−138.687			−0.407904
$341$	−66.2704	+	38.2612i	−0.194341	+	0.112203i
$342$	−410.495	+	989.266i	−1.20028	+	2.89259i
$343$	−54.1138			−0.157766
$344$	720.129	−	415.767i	2.09340	−	1.20862i
$345$	−10.0903	+	11.4985i	−0.0292473	+	0.0333290i
$346$	211.114	+	365.661i	0.610157	+	1.05682i
$347$		−	640.856i		−	1.84685i	−0.383781	−	0.923424i	$-0.625378\pi$
$347$		−	640.856i		−	1.84685i	0.383781	−	0.923424i	$-0.374622\pi$
$348$	284.533	+	249.687i	0.817623	+	0.717491i
$349$	57.7210			0.165390			0.0826949	−	0.996575i	$-0.473647\pi$
$349$	57.7210			0.165390			0.0826949	+	0.996575i	$0.473647\pi$
$350$		−	52.8915i		−	0.151118i
$351$	−100.036	+	336.443i	−0.285001	+	0.958527i
$352$	211.711			0.601452
$353$		−	336.066i		−	0.952027i	−0.879438	−	0.476014i	$-0.842081\pi$
$353$		−	336.066i		−	0.952027i	0.879438	−	0.476014i	$-0.157919\pi$
$354$	779.985	−	888.840i	2.20335	−	2.51085i
$355$	18.8565			0.0531170
$356$	−768.517	+	443.703i	−2.15875	+	1.24636i
$357$	−29.3107	−	25.7211i	−0.0821029	−	0.0720479i
$358$	1.14734	+	1.98726i	0.00320487	+	0.00555100i
$359$			445.683i			1.24146i	0.784026	+	0.620728i	$0.213163\pi$
$359$			445.683i			1.24146i	−0.784026	+	0.620728i	$0.786837\pi$
$360$	103.476	−	79.2964i	0.287432	−	0.220268i
$361$	−293.627	−	508.576i	−0.813371	−	1.40880i
$362$		−	129.207i		−	0.356924i
$363$	233.664	−	266.274i	0.643703	−	0.733538i
$364$	53.4562	−	57.8185i	0.146858	−	0.158842i
$365$	43.8995	−	25.3454i	0.120273	−	0.0694394i
$366$	−29.8364	+	149.752i	−0.0815201	+	0.409158i
$367$	−407.772			−1.11110			−0.555548	−	0.831484i	$-0.687492\pi$
$367$	−407.772			−1.11110			−0.555548	+	0.831484i	$0.687492\pi$
$368$	−488.959	−	282.300i	−1.32869	−	0.767121i
$369$	57.2323	−	137.926i	0.155101	−	0.373783i
$370$	−42.2019	+	73.0958i	−0.114059	+	0.197556i
$371$	9.72195	−	5.61297i	0.0262047	−	0.0151293i
$372$	−1442.50	−	287.403i	−3.87770	−	0.772588i
$373$	426.685			1.14393			0.571964	−	0.820279i	$-0.306182\pi$
$373$	426.685			1.14393			0.571964	+	0.820279i	$0.306182\pi$
$374$	134.048	+	77.3927i	0.358417	+	0.206932i
$375$	60.5766	+	53.1579i	0.161538	+	0.141754i
$376$	−742.672	+	1286.35i	−1.97519	+	3.42113i
$377$	−143.267	+	44.4718i	−0.380018	+	0.117962i
$378$	57.6707	+	3.83447i	0.152568	+	0.0101441i
$379$	18.8743	+	32.6913i	0.0498004	+	0.0862568i	0.889851	−	0.456251i	$-0.150808\pi$
$379$	18.8743	+	32.6913i	0.0498004	+	0.0862568i	−0.840051	+	0.542508i	$0.817475\pi$
$380$			181.988i			0.478916i
$381$	−132.610	−	26.4210i	−0.348057	−	0.0693465i
$382$	108.346	+	187.662i	0.283630	+	0.491261i
$383$			388.387i			1.01406i	0.861927	+	0.507032i	$0.169258\pi$
$383$			388.387i			1.01406i	−0.861927	+	0.507032i	$0.830742\pi$
$384$	972.858	+	853.714i	2.53348	+	2.22321i
$385$	0.255466	−	0.442481i	0.000663549	−	0.00114930i
$386$	−312.740	−	180.560i	−0.810207	−	0.467773i
$387$	−221.631	+	169.843i	−0.572691	+	0.438870i
$388$	−407.300	−	705.464i	−1.04974	−	1.81821i
$389$	−441.326	−	254.800i	−1.13452	−	0.655013i	−0.189449	−	0.981891i	$-0.560670\pi$
$389$	−441.326	−	254.800i	−1.13452	−	0.655013i	−0.945067	+	0.326878i	$0.894003\pi$
$390$	8.48199	+	81.0132i	0.0217487	+	0.207726i
$391$	−110.710	−	191.756i	−0.283147	−	0.490425i
$392$	1130.23	+	652.537i	2.88323	+	1.66463i
$393$	12.6821	−	63.6527i	0.0322699	−	0.161966i
$394$	131.074	+	227.027i	0.332676	+	0.576211i
$395$			40.3470i			0.102144i
$396$	−166.549	+	21.8203i	−0.420579	+	0.0551017i
$397$	242.327	−	419.722i	0.610395	−	1.05724i	−0.380779	−	0.924666i	$-0.624344\pi$
$397$	242.327	−	419.722i	0.610395	−	1.05724i	0.991174	−	0.132569i	$-0.0423226\pi$
$398$	425.290	+	245.541i	1.06857	+	0.616938i
$399$	−33.7517	+	38.4621i	−0.0845907	+	0.0963962i
$400$	−739.240	+	1280.40i	−1.84810	+	3.20100i
$401$	−448.786	−	259.107i	−1.11917	−	0.646151i	−0.177978	−	0.984034i	$-0.556956\pi$
$401$	−448.786	−	259.107i	−1.11917	−	0.646151i	−0.941188	+	0.337883i	$0.890289\pi$
$402$	110.080	−	37.3285i	0.273830	−	0.0928571i
$403$	395.683	−	427.973i	0.981845	−	1.06197i
$404$		−	594.361i		−	1.47119i
$405$	−30.9933	+	30.9155i	−0.0765266	+	0.0763347i
$406$	12.3509	+	21.3923i	0.0304208	+	0.0526904i
$407$	59.7313	−	34.4859i	0.146760	−	0.0847318i
$408$	605.957	+	1786.93i	1.48519	+	4.37974i
$409$	280.634			0.686148			0.343074	−	0.939308i	$-0.388532\pi$
$409$	280.634			0.686148			0.343074	+	0.939308i	$0.388532\pi$
$410$		−	34.6545i		−	0.0845233i
$411$	11.8880	−	59.6672i	0.0289246	−	0.145176i
$412$	644.919	+	1117.03i	1.56534	+	2.71125i
$413$	48.9288	−	28.2491i	0.118472	−	0.0683997i
$414$	303.119	+	125.779i	0.732171	+	0.303814i
$415$	46.7823			0.112729
$416$	−1540.08	+	478.061i	−3.70212	+	1.14918i
$417$	−358.188	+	408.176i	−0.858963	+	0.978840i
$418$	101.556	−	175.900i	0.242957	−	0.420814i
$419$	31.9900	+	18.4694i	0.0763484	+	0.0440798i	0.537688	−	0.843144i	$-0.319298\pi$
$419$	31.9900	+	18.4694i	0.0763484	+	0.0440798i	−0.461340	+	0.887224i	$0.652631\pi$
$420$	9.30057	−	3.15386i	0.0221442	−	0.00750920i
$421$	129.038	−	223.501i	0.306504	−	0.530880i	−0.671091	−	0.741375i	$-0.734174\pi$
$421$	129.038	−	223.501i	0.306504	−	0.530880i	0.977595	+	0.210495i	$0.0675074\pi$
$422$	667.291	+	385.261i	1.58126	+	0.912940i
$423$	191.161	−	460.686i	0.451918	−	1.08909i
$424$	−543.183			−1.28109
$425$	−502.138	+	289.909i	−1.18150	+	0.682140i
$426$	−129.907	−	383.090i	−0.304947	−	0.899272i
$427$	−3.64764	+	6.31790i	−0.00854248	+	0.0147960i
$428$	1132.72	−	653.974i	2.64653	−	1.52798i
$429$	27.0979	−	60.7974i	0.0631654	−	0.141719i
$430$	−32.3998	+	56.1180i	−0.0753483	+	0.130507i
$431$	528.929	−	305.377i	1.22721	−	0.708532i	0.260768	−	0.965402i	$-0.416024\pi$
$431$	528.929	−	305.377i	1.22721	−	0.708532i	0.966446	+	0.256869i	$0.0826910\pi$
$432$	−1342.51	−	898.863i	−3.10765	−	2.08070i
$433$	263.137	−	455.767i	0.607707	−	1.05258i	−0.383911	−	0.923370i	$-0.625423\pi$
$433$	263.137	−	455.767i	0.607707	−	1.05258i	0.991617	−	0.129209i	$-0.0412437\pi$
$434$	−83.1192	−	47.9889i	−0.191519	−	0.110573i
$435$	−18.3484	−	3.65571i	−0.0421803	−	0.00840394i
$436$	151.078			0.346510
$437$	−251.626	+	145.276i	−0.575803	+	0.332440i
$438$	−817.352	−	717.252i	−1.86610	−	1.63756i
$439$	194.833			0.443811			0.221905	−	0.975068i	$-0.428772\pi$
$439$	194.833			0.443811			0.221905	+	0.975068i	$0.428772\pi$
$440$	−21.4101	+	12.3611i	−0.0486592	+	0.0280934i
$441$	−404.774	−	167.961i	−0.917856	−	0.380863i
$442$	−1149.88	−	260.297i	−2.60155	−	0.588908i
$443$	363.417	+	209.819i	0.820355	+	0.473632i	0.850539	−	0.525912i	$-0.176276\pi$
$443$	363.417	+	209.819i	0.820355	+	0.473632i	−0.0301838	+	0.999544i	$0.509609\pi$
$444$	1300.17	+	259.044i	2.92831	+	0.583432i
$445$	21.9289	−	37.9820i	0.0492785	−	0.0853529i
$446$			432.733i			0.970253i
$447$	−404.833	−	355.254i	−0.905666	−	0.794751i
$448$	66.4778	+	115.143i	0.148388	+	0.257015i
$449$	−18.0050	−	10.3952i	−0.0401002	−	0.0231518i	0.479816	−	0.877369i	$-0.340703\pi$
$449$	−18.0050	−	10.3952i	−0.0401002	−	0.0231518i	−0.519916	+	0.854217i	$0.674037\pi$
$450$	329.368	−	793.756i	0.731930	−	1.76390i
$451$	−14.1592	+	24.5245i	−0.0313952	+	0.0543780i
$452$		−	819.100i		−	1.81217i
$453$	184.438	+	543.899i	0.407149	+	1.20066i
$454$	−98.0974	−	169.910i	−0.216073	−	0.374250i
$455$	−0.859219	+	3.79567i	−0.00188839	+	0.00834212i
$456$	2344.85	−	795.147i	5.14221	−	1.74374i
$457$	−299.179			−0.654658			−0.327329	−	0.944910i	$-0.606149\pi$
$457$	−299.179			−0.654658			−0.327329	+	0.944910i	$0.606149\pi$
$458$	85.3344	−	49.2678i	0.186320	−	0.107572i
$459$	−279.702	−	568.528i	−0.609373	−	1.23862i
$460$	55.7626			0.121223
$461$	−536.782	+	309.911i	−1.16439	+	0.672258i	−0.952351	−	0.305004i	$-0.901342\pi$
$461$	−536.782	+	309.911i	−1.16439	+	0.672258i	−0.212034	+	0.977262i	$0.568009\pi$
$462$	−10.7494	−	2.14170i	−0.0232671	−	0.00463571i
$463$	80.9569	+	140.221i	0.174853	+	0.302854i	0.940110	−	0.340870i	$-0.110722\pi$
$463$	80.9569	+	140.221i	0.174853	+	0.302854i	−0.765257	+	0.643724i	$0.777388\pi$
$464$		−	690.489i		−	1.48812i
$465$	68.8429	−	23.3449i	0.148049	−	0.0502042i
$466$	−1353.67			−2.90488
$467$		−	150.782i		−	0.322873i	−0.986883	−	0.161437i	$-0.948387\pi$
$467$		−	150.782i		−	0.322873i	0.986883	−	0.161437i	$-0.0516128\pi$
$468$	1162.28	−	534.812i	2.48351	−	1.14276i
$469$	5.55341			0.0118410
$470$		−	115.749i		−	0.246276i
$471$	−781.218	−	155.649i	−1.65864	−	0.330465i
$472$	−2733.74			−5.79182
$473$	45.8576	−	26.4759i	0.0969505	−	0.0559744i
$474$	819.690	−	277.960i	1.72930	−	0.586414i
$475$	380.424	+	658.914i	0.800894	+	1.38719i
$476$			142.144i			0.298621i
$477$	180.853	−	23.6943i	0.379147	−	0.0496736i
$478$	−82.8839	−	143.559i	−0.173397	−	0.300333i
$479$		−	851.339i		−	1.77733i	−0.458561	−	0.888663i	$-0.651635\pi$
$479$		−	851.339i		−	1.77733i	0.458561	−	0.888663i	$-0.348365\pi$
$480$	−197.241	−	39.2980i	−0.410918	−	0.0818708i
$481$	−356.640	+	385.744i	−0.741455	+	0.801962i
$482$	536.124	−	309.531i	1.11229	−	0.642181i
$483$	11.7851	+	10.3418i	0.0243998	+	0.0214116i
$484$	−1291.31			−2.66799
$485$	34.8658	+	20.1298i	0.0718882	+	0.0415047i
$486$	841.601	+	416.675i	1.73169	+	0.857356i
$487$	123.900	−	214.601i	0.254415	−	0.440660i	−0.710322	−	0.703877i	$-0.751450\pi$
$487$	123.900	−	214.601i	0.254415	−	0.440660i	0.964736	+	0.263218i	$0.0847838\pi$
$488$	305.700	−	176.496i	0.626435	−	0.361672i
$489$	164.461	+	484.986i	0.336320	+	0.991791i
$490$	−101.701			−0.207554
$491$	−5.01170	−	2.89351i	−0.0102071	−	0.00589309i	0.494888	−	0.868957i	$-0.335209\pi$
$491$	−5.01170	−	2.89351i	−0.0102071	−	0.00589309i	−0.505095	+	0.863064i	$0.668543\pi$
$492$	−515.484	+	174.803i	−1.04773	+	0.355290i
$493$	135.395	−	234.512i	0.274636	−	0.475683i
$494$	−341.567	+	1508.90i	−0.691431	+	3.05445i
$495$	6.58929	−	5.04957i	0.0133117	−	0.0102012i
$496$	1341.44	+	2323.44i	2.70451	+	4.68435i
$497$		−	19.3265i		−	0.0388863i
$498$	−322.295	−	950.431i	−0.647179	−	1.90850i
$499$	15.3764	+	26.6327i	0.0308144	+	0.0533722i	0.881021	−	0.473076i	$-0.156857\pi$
$499$	15.3764	+	26.6327i	0.0308144	+	0.0533722i	−0.850207	+	0.526449i	$0.823523\pi$
$500$		−	293.769i		−	0.587538i
$501$	−532.929	+	180.719i	−1.06373	+	0.360716i
$502$	264.943	−	458.894i	0.527774	−	0.914132i
$503$	548.629	+	316.751i	1.09071	+	0.629724i	0.933766	−	0.357883i	$-0.116501\pi$
$503$	548.629	+	316.751i	1.09071	+	0.629724i	0.156948	+	0.987607i	$0.449835\pi$
$504$	−81.2726	−	106.054i	−0.161255	−	0.210425i
$505$	14.6874	+	25.4393i	0.0290840	+	0.0503749i
$506$	−53.8972	−	31.1176i	−0.106516	−	0.0614972i
$507$	−59.8372	+	503.457i	−0.118022	+	0.993011i
$508$	246.437	+	426.841i	0.485112	+	0.840239i
$509$	83.2041	+	48.0379i	0.163466	+	0.0943770i	0.579501	−	0.814971i	$-0.303247\pi$
$509$	83.2041	+	48.0379i	0.163466	+	0.0943770i	−0.416035	+	0.909348i	$0.636581\pi$
$510$	−110.520	−	96.9850i	−0.216706	−	0.190167i
$511$	−25.9770	−	44.9935i	−0.0508357	−	0.0880500i
$512$		−	1007.45i		−	1.96767i
$513$	−746.033	+	367.030i	−1.45426	+	0.715458i
$514$	403.005	−	698.025i	0.784056	−	1.35803i
$515$	−55.2066	−	31.8735i	−0.107197	−	0.0618904i
$516$	998.180	+	198.876i	1.93446	+	0.385419i
$517$	−47.2931	+	81.9141i	−0.0914761	+	0.158441i
$518$	74.9175	+	43.2537i	0.144628	+	0.0835013i
$519$	−64.0448	+	321.448i	−0.123400	+	0.619359i
$520$	127.834	−	138.266i	0.245834	−	0.265896i
$521$			4.52094i			0.00867743i	0.999991	+	0.00433872i	$0.00138106\pi$
$521$			4.52094i			0.00867743i	−0.999991	+	0.00433872i	$0.998619\pi$
$522$	52.1373	+	397.952i	0.0998798	+	0.762360i
$523$	133.527	+	231.275i	0.255309	+	0.442208i	0.964979	−	0.262326i	$-0.0844895\pi$
$523$	133.527	+	231.275i	0.255309	+	0.442208i	−0.709671	+	0.704534i	$0.751156\pi$
$524$	−204.884	+	118.290i	−0.390999	+	0.225744i
$525$	27.0813	−	30.8608i	0.0515834	−	0.0587824i
$526$	1357.92			2.58160
$527$			1052.15i			1.99649i
$528$	230.289	+	202.086i	0.436154	+	0.382739i
$529$	−219.986	−	381.027i	−0.415853	−	0.720278i
$530$	36.6580	−	21.1645i	0.0691660	−	0.0399330i
$531$	910.201	−	119.249i	1.71413	−	0.224575i
$532$	186.523			0.350608
$533$	47.6222	−	210.375i	0.0893475	−	0.394699i
$534$	−922.718	−	183.841i	−1.72794	−	0.344272i
$535$	−32.3210	+	55.9816i	−0.0604131	+	0.104639i
$536$	−232.709	−	134.355i	−0.434159	−	0.250662i
$537$	−0.348064	+	1.74697i	−0.000648164	+	0.00325321i
$538$	−266.371	+	461.367i	−0.495112	+	0.857560i
$539$	71.9725	+	41.5533i	0.133530	+	0.0770934i
$540$	159.216	+	10.5861i	0.294844	+	0.0196039i
$541$	−392.541			−0.725584			−0.362792	−	0.931870i	$-0.618176\pi$
$541$	−392.541			−0.725584			−0.362792	+	0.931870i	$0.618176\pi$
$542$	838.697	−	484.222i	1.54741	−	0.893398i
$543$	66.1559	−	75.3886i	0.121834	−	0.138837i
$544$	1455.47	−	2520.94i	2.67549	−	4.63408i
$545$	−6.46633	+	3.73334i	−0.0118648	+	0.00685016i
$546$	83.0322	−	8.69338i	0.152074	−	0.0159219i
$547$	468.922	−	812.196i	0.857261	−	1.48482i	−0.0172707	−	0.999851i	$-0.505498\pi$
$547$	468.922	−	812.196i	0.857261	−	1.48482i	0.874532	−	0.484969i	$-0.161169\pi$
$548$	−192.055	+	110.883i	−0.350465	+	0.202341i
$549$	−94.0842	+	72.0995i	−0.171374	+	0.131329i
$550$	−81.4854	+	141.137i	−0.148155	+	0.256612i
$551$	−307.731	−	177.668i	−0.558495	−	0.322447i
$552$	−243.640	−	718.480i	−0.441376	−	1.30159i
$553$	41.3525			0.0747785
$554$	1056.98	−	610.249i	1.90791	−	1.10153i
$555$	−62.0500	+	21.0414i	−0.111802	+	0.0379124i
$556$	1979.47			3.56019
$557$	−553.510	+	319.569i	−0.993734	+	0.573733i	−0.906388	−	0.422445i	$-0.861172\pi$
$557$	−553.510	+	319.569i	−0.993734	+	0.573733i	−0.0873459	+	0.996178i	$0.527839\pi$
$558$	−948.552	−	1237.79i	−1.69991	−	2.21825i
$559$	−273.804	+	296.148i	−0.489810	+	0.529781i
$560$	−15.5134	−	8.95665i	−0.0277024	−	0.0159940i
$561$	38.5871	+	113.791i	0.0687828	+	0.202837i
$562$	856.454	−	1483.42i	1.52394	−	2.63954i
$563$			889.448i			1.57984i	0.613212	+	0.789918i	$0.289877\pi$
$563$			889.448i			1.57984i	−0.613212	+	0.789918i	$0.710123\pi$
$564$	−1721.76	+	583.858i	−3.05277	+	1.03521i
$565$	20.2410	+	35.0584i	0.0358248	+	0.0620503i
$566$	−815.447	−	470.799i	−1.44072	−	0.831800i
$567$	31.6860	+	31.7657i	0.0558836	+	0.0560241i
$568$	−467.569	+	809.854i	−0.823185	+	1.42580i
$569$			1050.87i			1.84687i	0.383758	+	0.923434i	$0.374630\pi$
$569$			1050.87i			1.84687i	−0.383758	+	0.923434i	$0.625370\pi$
$570$	−127.266	+	145.027i	−0.223273	+	0.254433i
$571$	353.632	+	612.508i	0.619320	+	1.07269i	0.989610	+	0.143777i	$0.0459248\pi$
$571$	353.632	+	612.508i	0.619320	+	1.07269i	−0.370290	+	0.928916i	$0.620742\pi$
$572$	−231.720	+	71.9288i	−0.405104	+	0.125750i
$573$	−32.8685	+	164.971i	−0.0573622	+	0.287907i
$574$	−35.5182			−0.0618784
$575$	201.897	−	116.565i	0.351125	−	0.202722i
$576$	280.626	+	2141.95i	0.487198	+	3.71867i
$577$	231.351			0.400956			0.200478	−	0.979698i	$-0.435751\pi$
$577$	231.351			0.400956			0.200478	+	0.979698i	$0.435751\pi$
$578$	875.860	−	505.678i	1.51533	−	0.874876i
$579$	−90.0255	−	265.480i	−0.155484	−	0.458515i
$580$	34.0980	+	59.0594i	0.0587896	+	0.101827i
$581$		−	47.9483i		−	0.0825271i
$582$	168.758	−	847.013i	0.289962	−	1.45535i
$583$	−34.5897			−0.0593305
$584$			2513.87i			4.30457i
$585$	−36.5311	+	51.6120i	−0.0624463	+	0.0882256i
$586$	−474.466			−0.809669
$587$			905.686i			1.54291i	0.636286	+	0.771453i	$0.280470\pi$
$587$			905.686i			1.54291i	−0.636286	+	0.771453i	$0.719530\pi$
$588$	512.997	+	1512.80i	0.872444	+	2.57279i
$589$	1380.65			2.34406
$590$	184.493	−	106.517i	0.312700	−	0.180537i
$591$	−39.7633	+	199.576i	−0.0672814	+	0.337693i
$592$	−1209.07	−	2094.18i	−2.04235	−	3.53746i
$593$		−	399.311i		−	0.673374i	−0.941617	−	0.336687i	$-0.890694\pi$
$593$		−	399.311i		−	0.673374i	0.941617	−	0.336687i	$-0.109306\pi$
$594$	−147.982	−	99.0804i	−0.249129	−	0.166802i
$595$	−3.51255	−	6.08391i	−0.00590344	−	0.0102251i
$596$			1963.25i			3.29405i
$597$	122.424	+	361.022i	0.205066	+	0.604728i
$598$	462.338	+	104.659i	0.773141	+	0.175015i
$599$	87.1739	−	50.3299i	0.145532	−	0.0840231i	−0.425466	−	0.904975i	$-0.639890\pi$
$599$	87.1739	−	50.3299i	0.145532	−	0.0840231i	0.570998	+	0.820951i	$0.306556\pi$
$600$	−1881.43	+	638.001i	−3.13572	+	1.06334i
$601$	−356.765			−0.593619			−0.296809	−	0.954937i	$-0.595923\pi$
$601$	−356.765			−0.593619			−0.296809	+	0.954937i	$0.595923\pi$
$602$	57.5166	+	33.2072i	0.0955425	+	0.0551615i
$603$	83.3415	+	34.5825i	0.138211	+	0.0573507i
$604$	1046.72	−	1812.97i	1.73298	−	3.00161i
$605$	55.2695	−	31.9099i	0.0913545	−	0.0527436i
$606$	415.641	−	473.647i	0.685876	−	0.781596i
$607$	−295.176			−0.486287			−0.243143	−	0.969990i	$-0.578179\pi$
$607$	−295.176			−0.486287			−0.243143	+	0.969990i	$0.578179\pi$
$608$	−3308.02	−	1909.89i	−5.44083	−	3.14126i
$609$	−3.74682	+	18.8057i	−0.00615241	+	0.0308796i
$610$	−13.7539	+	23.8225i	−0.0225474	+	0.0390533i
$611$	159.063	−	702.672i	0.260332	−	1.15004i
$612$	−885.164	+	2133.19i	−1.44635	+	3.48560i
$613$	364.492	+	631.318i	0.594603	+	1.02988i	0.993603	+	0.112931i	$0.0360240\pi$
$613$	364.492	+	631.318i	0.594603	+	1.02988i	−0.399000	+	0.916951i	$0.630643\pi$
$614$		−	294.394i		−	0.479470i
$615$	17.7437	−	20.2200i	0.0288515	−	0.0328781i
$616$	12.6692	+	21.9436i	0.0205668	+	0.0356228i
$617$		−	648.128i		−	1.05045i	−0.850963	−	0.525225i	$-0.823981\pi$
$617$		−	648.128i		−	1.05045i	0.850963	−	0.525225i	$-0.176019\pi$
$618$	−267.212	+	1341.16i	−0.432381	+	2.17017i
$619$	351.842	−	609.409i	0.568404	−	0.984505i	−0.428320	−	0.903627i	$-0.640894\pi$
$619$	351.842	−	609.409i	0.568404	−	0.984505i	0.996724	−	0.0808778i	$-0.0257724\pi$
$620$	−229.473	−	132.487i	−0.370118	−	0.213688i
$621$	112.461	+	228.591i	0.181097	+	0.368101i
$622$	1065.48	+	1845.46i	1.71299	+	2.96698i
$623$	−38.9286	−	22.4754i	−0.0624857	−	0.0360762i
$624$	−2131.56	−	950.054i	−3.41595	−	1.52252i
$625$	−301.590	−	522.368i	−0.482543	−	0.835790i
$626$	−763.116	−	440.585i	−1.21903	−	0.703810i
$627$	149.319	−	50.6347i	0.238148	−	0.0807572i
$628$	1451.78	+	2514.56i	2.31176	+	4.00408i
$629$		−	948.330i		−	1.50768i
$630$	9.61716	+	3.99063i	0.0152653	+	0.00633434i
$631$	−0.945257	+	1.63723i	−0.00149803	+	0.00259466i	−0.866773	−	0.498702i	$-0.833810\pi$
$631$	−0.945257	+	1.63723i	−0.00149803	+	0.00259466i	0.865275	+	0.501297i	$0.167144\pi$
$632$	−1732.83	−	1000.45i	−2.74182	−	1.58299i
$633$	192.087	+	566.453i	0.303455	+	0.894871i
$634$	−525.171	+	909.622i	−0.828345	+	1.43474i
$635$	−21.0956	−	12.1795i	−0.0332214	−	0.0191804i
$636$	−499.729	−	438.528i	−0.785737	−	0.689509i
$637$	−617.391	−	139.758i	−0.969216	−	0.219400i
$638$		−	76.1117i		−	0.119297i
$639$	120.351	−	290.037i	0.188342	−	0.453893i
$640$	116.586	+	201.932i	0.182165	+	0.315519i
$641$	−450.667	+	260.193i	−0.703069	+	0.405917i	−0.808490	−	0.588511i	$-0.799715\pi$
$641$	−450.667	+	260.193i	−0.703069	+	0.405917i	0.105420	+	0.994428i	$0.466381\pi$
$642$	1359.99	+	270.963i	2.11837	+	0.422061i
$643$	−817.953			−1.27209			−0.636045	−	0.771652i	$-0.719431\pi$
$643$	−817.953			−1.27209			−0.636045	+	0.771652i	$0.719431\pi$
$644$		−	57.1523i		−	0.0887458i
$645$	−47.6377	+	16.1542i	−0.0738570	+	0.0250452i
$646$	−1396.35	−	2418.55i	−2.16153	−	3.74389i
$647$	−345.890	+	199.700i	−0.534606	+	0.308655i	−0.742890	−	0.669414i	$-0.766545\pi$
$647$	−345.890	+	199.700i	−0.534606	+	0.308655i	0.208284	+	0.978068i	$0.433212\pi$
$648$	−559.253	−	2097.69i	−0.863044	−	3.23718i
$649$	−174.084			−0.268234
$650$	274.063	−	1210.69i	0.421635	−	1.86260i
$651$	−23.9267	−	70.5586i	−0.0367538	−	0.108385i
$652$	933.343	−	1616.60i	1.43151	−	2.47944i
$653$	−444.374	−	256.560i	−0.680512	−	0.392894i	0.119536	−	0.992830i	$-0.461859\pi$
$653$	−444.374	−	256.560i	−0.680512	−	0.392894i	−0.800048	+	0.599936i	$0.795193\pi$
$654$	120.395	+	105.650i	0.184090	+	0.161545i
$655$	5.84617	−	10.1259i	0.00892545	−	0.0154593i
$656$	859.828	+	496.422i	1.31071	+	0.756741i
$657$	−109.658	−	836.995i	−0.166907	−	1.27396i
$658$	−118.634			−0.180295
$659$	420.060	−	242.522i	0.637421	−	0.368015i	−0.146200	−	0.989255i	$-0.546704\pi$
$659$	420.060	−	242.522i	0.637421	−	0.368015i	0.783620	+	0.621240i	$0.213371\pi$
$660$	−29.6767	−	5.91275i	−0.0449648	−	0.00895872i
$661$	−276.604	+	479.092i	−0.418463	+	0.724798i	−0.995785	−	0.0917178i	$-0.970764\pi$
$661$	−276.604	+	479.092i	−0.418463	+	0.724798i	0.577322	+	0.816516i	$0.304098\pi$
$662$	−1087.17	+	627.678i	−1.64225	+	0.948154i
$663$	−537.650	−	740.636i	−0.810935	−	1.11710i
$664$	−1160.02	+	2009.22i	−1.74702	+	3.02593i
$665$	−7.98342	+	4.60923i	−0.0120051	+	0.00693117i
$666$	854.955	+	1115.65i	1.28372	+	1.67515i
$667$	−54.4390	+	94.2911i	−0.0816177	+	0.141366i
$668$	1776.41	+	1025.61i	2.65929	+	1.53534i
$669$	−221.566	+	252.488i	−0.331190	+	0.377411i
$670$	20.9399			0.0312536
$671$	19.4669	−	11.2392i	0.0290118	−	0.0167499i
$672$	−40.2773	+	202.156i	−0.0599365	+	0.300828i
$673$	732.210			1.08798			0.543990	−	0.839092i	$-0.316913\pi$
$673$	732.210			1.08798			0.543990	+	0.839092i	$0.316913\pi$
$674$	693.300	−	400.277i	1.02864	−	0.593883i
$675$	598.594	−	294.493i	0.886805	−	0.436287i
$676$	1523.21	−	1046.48i	2.25327	−	1.54805i
$677$	688.003	+	397.219i	1.01625	+	0.586734i	0.913016	−	0.407923i	$-0.133747\pi$
$677$	688.003	+	397.219i	1.01625	+	0.586734i	0.103236	+	0.994657i	$0.467080\pi$
$678$	572.802	−	652.743i	0.844841	−	0.962747i
$679$	20.6314	−	35.7347i	0.0303851	−	0.0526285i
$680$			339.919i			0.499881i
$681$	29.7593	−	149.365i	0.0436994	−	0.219332i
$682$	147.865	+	256.109i	0.216811	+	0.375527i
$683$	906.498	+	523.367i	1.32723	+	0.766277i	0.984870	−	0.173292i	$-0.0554405\pi$
$683$	906.498	+	523.367i	1.32723	+	0.766277i	0.342360	+	0.939569i	$0.388774\pi$
$684$	2799.21	+	1161.53i	4.09241	+	1.69814i
$685$	5.48012	−	9.49184i	0.00800017	−	0.0138567i
$686$			209.129i			0.304852i
$687$	75.0163	+	14.9461i	0.109194	+	0.0217557i
$688$	−928.245	−	1607.77i	−1.34919	−	2.33687i
$689$	251.621	−	78.1064i	0.365197	−	0.113362i
$690$	44.4373	+	38.9952i	0.0644019	+	0.0565147i
$691$	−292.944			−0.423942			−0.211971	−	0.977276i	$-0.567988\pi$
$691$	−292.944			−0.423942			−0.211971	+	0.977276i	$0.567988\pi$
$692$	1034.67	−	597.365i	1.49518	−	0.863244i
$693$	−5.17542	−	6.75351i	−0.00746813	−	0.00974532i
$694$	−2476.66			−3.56868
$695$	−84.7235	+	48.9151i	−0.121904	+	0.0703815i
$696$	611.976	−	697.383i	0.879276	−	1.00199i
$697$	194.683	+	337.201i	0.279316	+	0.483789i
$698$		−	223.069i		−	0.319584i
$699$	−789.833	−	693.103i	−1.12995	−	0.991564i
$700$	−149.661			−0.213801
$701$			1014.32i			1.44697i	0.690342	+	0.723484i	$0.257460\pi$
$701$			1014.32i			1.44697i	−0.690342	+	0.723484i	$0.742540\pi$
$702$	1300.22	+	386.598i	1.85217	+	0.550710i
$703$	−1244.42			−1.77015
$704$		−	409.667i		−	0.581913i
$705$	59.2656	−	67.5367i	0.0840647	−	0.0957968i
$706$	−1298.76			−1.83961
$707$	26.0733	−	15.0534i	0.0368788	−	0.0212920i
$708$	−2515.04	−	2207.03i	−3.55232	−	3.11727i
$709$	271.431	+	470.132i	0.382836	+	0.663092i	0.991466	−	0.130362i	$-0.0416140\pi$
$709$	271.431	+	470.132i	0.382836	+	0.663092i	−0.608630	+	0.793454i	$0.708281\pi$
$710$		−	72.8732i		−	0.102638i
$711$	620.588	+	257.512i	0.872838	+	0.362183i
$712$	1087.51	+	1883.62i	1.52740	+	2.64553i
$713$		−	423.042i		−	0.593327i
$714$	−99.4021	+	113.275i	−0.139219	+	0.158648i
$715$	8.14042	−	8.80472i	0.0113852	−	0.0123143i
$716$	5.62311	−	3.24650i	0.00785350	−	0.00453422i
$717$	25.1441	−	126.201i	0.0350685	−	0.176012i
$718$	1722.39			2.39887
$719$	−1002.72	−	578.919i	−1.39460	−	0.805173i	−0.400780	−	0.916174i	$-0.631261\pi$
$719$	−1002.72	−	578.919i	−1.39460	−	0.805173i	−0.993820	+	0.111001i	$0.964594\pi$
$720$	−177.038	−	231.020i	−0.245886	−	0.320862i
$721$	−32.6679	+	56.5824i	−0.0453091	+	0.0784777i
$722$	−1965.45	+	1134.75i	−2.72223	+	1.57168i
$723$	471.299	+	93.9010i	0.651866	+	0.129877i
$724$	−365.600			−0.504973
$725$	246.913	+	142.555i	0.340570	+	0.196628i
$726$	−1029.05	−	903.021i	−1.41742	−	1.24383i
$727$	33.2872	−	57.6552i	0.0457871	−	0.0793056i	−0.842224	−	0.539128i	$-0.818754\pi$
$727$	33.2872	−	57.6552i	0.0457871	−	0.0793056i	0.888011	+	0.459823i	$0.152087\pi$
$728$	−141.712	−	131.020i	−0.194659	−	0.179972i
$729$	277.707	+	674.032i	0.380943	+	0.924598i
$730$	−97.9500	−	169.654i	−0.134178	−	0.232403i
$731$		−	728.064i		−	0.995983i
$732$	423.735	+	84.4244i	0.578873	+	0.115334i
$733$	224.677	+	389.152i	0.306517	+	0.530903i	0.977598	−	0.210481i	$-0.0675030\pi$
$733$	224.677	+	389.152i	0.306517	+	0.530903i	−0.671081	+	0.741384i	$0.734170\pi$
$734$			1575.88i			2.14698i
$735$	−59.3400	−	52.0728i	−0.0807347	−	0.0708473i
$736$	−585.205	+	1013.60i	−0.795115	+	1.37718i
$737$	−14.8189	−	8.55567i	−0.0201070	−	0.0116088i
$738$	−533.031	−	221.181i	−0.722264	−	0.299703i
$739$	−32.6253	−	56.5087i	−0.0441480	−	0.0764665i	0.843107	−	0.537746i	$-0.180724\pi$
$739$	−32.6253	−	56.5087i	−0.0441480	−	0.0764665i	−0.887255	+	0.461279i	$0.847391\pi$
$740$	206.831	+	119.414i	0.279501	+	0.161370i
$741$	−971.876	+	705.514i	−1.31157	+	0.952111i
$742$	−21.6920	−	37.5716i	−0.0292344	−	0.0506355i
$743$	−961.902	−	555.355i	−1.29462	−	0.747449i	−0.315150	−	0.949042i	$-0.602055\pi$
$743$	−961.902	−	555.355i	−1.29462	−	0.747449i	−0.979469	+	0.201593i	$0.935388\pi$
$744$	−704.417	+	3535.54i	−0.946797	+	4.75207i
$745$	−48.5145	−	84.0296i	−0.0651201	−	0.112791i
$746$		−	1648.97i		−	2.21042i
$747$	298.586	−	719.572i	0.399713	−	0.963282i
$748$	218.989	−	379.300i	0.292766	−	0.507085i
$749$	57.3768	+	33.1265i	0.0766046	+	0.0442277i
$750$	205.435	−	234.105i	0.273913	−	0.312140i
$751$	222.453	−	385.301i	0.296210	−	0.513050i	−0.679056	−	0.734087i	$-0.737611\pi$
$751$	222.453	−	385.301i	0.296210	−	0.513050i	0.975266	+	0.221036i	$0.0709440\pi$
$752$	2871.91	+	1658.10i	3.81903	+	2.20492i
$753$	389.548	−	132.098i	0.517329	−	0.175428i
$754$	171.866	+	553.670i	0.227939	+	0.734311i
$755$			103.463i			0.137037i
$756$	10.8499	−	163.184i	0.0143518	−	0.215852i
$757$	−482.015	−	834.875i	−0.636744	−	1.10287i	−0.986143	−	0.165899i	$-0.946947\pi$
$757$	−482.015	−	834.875i	−0.636744	−	1.10287i	0.349399	−	0.936974i	$-0.386386\pi$
$758$	126.339	−	72.9420i	0.166674	−	0.0962296i
$759$	−15.5149	−	45.7526i	−0.0204412	−	0.0602800i
$760$	446.048			0.586905
$761$			408.347i			0.536593i	0.963336	+	0.268296i	$0.0864606\pi$
$761$			408.347i			0.536593i	−0.963336	+	0.268296i	$0.913539\pi$
$762$	−102.107	+	512.486i	−0.133999	+	0.672554i
$763$	3.82638	+	6.62748i	0.00501492	+	0.00868609i
$764$	531.003	−	306.575i	0.695031	−	0.401276i
$765$	−14.8277	−	113.176i	−0.0193826	−	0.147943i
$766$	1500.96			1.95948
$767$	1266.36	−	393.095i	1.65106	−	0.512510i
$768$	1399.45	−	1594.76i	1.82220	−	2.07651i
$769$	−474.569	+	821.977i	−0.617125	+	1.06889i	0.372883	+	0.927878i	$0.378369\pi$
$769$	−474.569	+	821.977i	−0.617125	+	1.06889i	−0.990008	+	0.141013i	$0.954964\pi$

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:	\( N \)	\(=\)	\( 117 = 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	117.k (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-3.86461i q^{2} +(1.97875 - 2.25490i) q^{3} -10.9352 q^{4} +(0.468040 - 0.270223i) q^{5} +(-8.71431 - 7.64708i) q^{6} +(-0.276958 - 0.479705i) q^{7} +26.8020i q^{8} +(-1.16913 - 8.92374i) q^{9} +(-1.04431 - 1.80879i) q^{10} +1.70674i q^{11} +(-21.6380 + 24.6578i) q^{12} +(-3.85396 - 12.4156i) q^{13} +(-1.85387 + 1.07033i) q^{14} +(0.316807 - 1.59009i) q^{15} +59.8383 q^{16} +(20.3230 + 11.7335i) q^{17} +(-34.4868 + 4.51825i) q^{18} +(15.3969 - 26.6681i) q^{19} +(-5.11813 + 2.95495i) q^{20} +(-1.62971 - 0.324702i) q^{21} +6.59589 q^{22} +(-8.17133 - 4.71772i) q^{23} +(60.4357 + 53.0343i) q^{24} +(-12.3540 + 21.3977i) q^{25} +(-47.9815 + 14.8941i) q^{26} +(-22.4355 - 15.0215i) q^{27} +(3.02860 + 5.24568i) q^{28} -11.5393i q^{29} +(-6.14507 - 1.22433i) q^{30} +(22.4177 + 38.8286i) q^{31} -124.044i q^{32} +(3.84853 + 3.37721i) q^{33} +(45.3453 - 78.5403i) q^{34} +(-0.259255 - 0.149681i) q^{35} +(12.7848 + 97.5831i) q^{36} +(-20.2057 - 34.9973i) q^{37} +(-103.062 - 59.5029i) q^{38} +(-35.6219 - 15.8770i) q^{39} +(7.24252 + 12.5444i) q^{40} +(14.3692 + 8.29606i) q^{41} +(-1.25485 + 6.29821i) q^{42} +(-15.5125 - 26.8685i) q^{43} -18.6636i q^{44} +(-2.95860 - 3.86074i) q^{45} +(-18.2322 + 31.5790i) q^{46} +(47.9945 + 27.7096i) q^{47} +(118.405 - 134.929i) q^{48} +(24.3466 - 42.1695i) q^{49} +(82.6938 + 47.7433i) q^{50} +(66.6717 - 22.6087i) q^{51} +(42.1439 + 135.767i) q^{52} +20.2665i q^{53} +(-58.0524 + 86.7047i) q^{54} +(0.461201 + 0.798824i) q^{55} +(12.8570 - 7.42301i) q^{56} +(-29.6675 - 87.4878i) q^{57} -44.5947 q^{58} +101.998i q^{59} +(-3.46435 + 17.3880i) q^{60} +(-6.58519 - 11.4059i) q^{61} +(150.058 - 86.6358i) q^{62} +(-3.95696 + 3.03234i) q^{63} -240.029 q^{64} +(-5.15879 - 4.76957i) q^{65} +(13.0516 - 14.8731i) q^{66} +(-5.01287 + 8.68254i) q^{67} +(-222.236 - 128.308i) q^{68} +(-26.8070 + 9.09036i) q^{69} +(-0.578458 + 1.00192i) q^{70} +(30.2162 + 17.4453i) q^{71} +(239.174 - 31.3351i) q^{72} +93.7942 q^{73} +(-135.251 + 78.0871i) q^{74} +(23.8043 + 70.1975i) q^{75} +(-168.368 + 291.622i) q^{76} +(0.818732 - 0.472695i) q^{77} +(-61.3585 + 137.665i) q^{78} +(-37.3274 + 64.6530i) q^{79} +(28.0067 - 16.1697i) q^{80} +(-78.2662 + 20.8661i) q^{81} +(32.0610 - 55.5313i) q^{82} +(74.9652 + 43.2812i) q^{83} +(17.8213 + 3.55069i) q^{84} +12.6826 q^{85} +(-103.836 + 59.9500i) q^{86} +(-26.0198 - 22.8332i) q^{87} -45.7440 q^{88} +(70.2790 - 40.5756i) q^{89} +(-14.9203 + 11.4339i) q^{90} +(-4.88844 + 5.28736i) q^{91} +(89.3554 + 51.5894i) q^{92} +(131.914 + 26.2823i) q^{93} +(107.087 - 185.480i) q^{94} -16.6424i q^{95} +(-279.707 - 245.451i) q^{96} +(37.2466 + 64.5130i) q^{97} +(-162.969 - 94.0901i) q^{98} +(15.2305 - 1.99541i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q - q^{3} - 98 q^{4} - 6 q^{5} + 12 q^{6} - q^{7} - 3 q^{9} - 6 q^{10} - 39 q^{12} + 4 q^{13} - 6 q^{14} - 25 q^{15} + 166 q^{16} + 34 q^{18} + 5 q^{19} + 21 q^{20} - 91 q^{21} + 30 q^{22} - 75 q^{23}+ \cdots + 522 q^{99}+O(q^{100}) \) 52 * q - q^3 - 98 * q^4 - 6 * q^5 + 12 * q^6 - q^7 - 3 * q^9 - 6 * q^10 - 39 * q^12 + 4 * q^13 - 6 * q^14 - 25 * q^15 + 166 * q^16 + 34 * q^18 + 5 * q^19 + 21 * q^20 - 91 * q^21 + 30 * q^22 - 75 * q^23 - 24 * q^24 + 88 * q^25 - 132 * q^26 - 34 * q^27 - 22 * q^28 + 70 * q^30 + 14 * q^31 + 95 * q^33 - 6 * q^34 + 228 * q^35 - 58 * q^36 - 13 * q^37 - 192 * q^38 - 111 * q^39 + 72 * q^40 + 33 * q^41 + 159 * q^42 - 31 * q^43 - 47 * q^45 + 6 * q^46 - 69 * q^47 + 293 * q^48 - 123 * q^49 - 168 * q^50 + 235 * q^51 - 92 * q^52 - 339 * q^54 - 27 * q^55 + 168 * q^56 + 189 * q^57 + 210 * q^58 + 213 * q^60 + 8 * q^61 + 471 * q^62 + 169 * q^63 - 98 * q^64 - 246 * q^65 - 576 * q^66 - 34 * q^67 + 18 * q^68 - 193 * q^69 - 57 * q^70 + 144 * q^71 + 36 * q^72 - 106 * q^73 - 465 * q^74 - 58 * q^75 - 79 * q^76 + 282 * q^77 - 76 * q^78 - 25 * q^79 - 1050 * q^80 - 279 * q^81 + 81 * q^82 + 219 * q^83 + 395 * q^84 - 108 * q^85 - 24 * q^86 - 518 * q^87 + 30 * q^88 + 99 * q^89 + 183 * q^90 + 2 * q^91 + 888 * q^92 + 582 * q^93 + 303 * q^94 - 439 * q^96 + 212 * q^97 - 405 * q^98 + 522 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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