LMFDB - Embedded newform 117.3.n.a.38.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [117,3,Mod(38,117)]

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, 3]))

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

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

chi := DirichletCharacter("117.38");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 117 = 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	117.n (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			38.11
Character	$\chi$	$=$	117.38
Dual form			117.3.n.a.77.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.433498 + 0.750840i) q^{2} +(-0.162662 - 2.99559i) q^{3} +(1.62416 + 2.81313i) q^{4} +(-4.23652 - 7.33786i) q^{5} +(2.31972 + 1.17645i) q^{6} +(-3.54375 - 2.04598i) q^{7} -6.28426 q^{8} +(-8.94708 + 0.974539i) q^{9} +7.34608 q^{10} +(-2.60673 + 4.51499i) q^{11} +(8.16278 - 5.32290i) q^{12} +(5.26488 - 11.8862i) q^{13} +(3.07241 - 1.77386i) q^{14} +(-21.2921 + 13.8844i) q^{15} +(-3.77243 + 6.53403i) q^{16} -29.9878i q^{17} +(3.14682 - 7.14029i) q^{18} +3.71422i q^{19} +(13.7616 - 23.8357i) q^{20} +(-5.55248 + 10.9484i) q^{21} +(-2.26002 - 3.91448i) q^{22} +(15.2009 - 8.77627i) q^{23} +(1.02221 + 18.8250i) q^{24} +(-23.3961 + 40.5233i) q^{25} +(6.64230 + 9.10571i) q^{26} +(4.37467 + 26.6432i) q^{27} -13.2920i q^{28} +(7.85403 + 4.53453i) q^{29} +(-1.19493 - 22.0058i) q^{30} +(35.3345 - 20.4004i) q^{31} +(-15.8392 - 27.4343i) q^{32} +(13.9491 + 7.07427i) q^{33} +(22.5161 + 12.9997i) q^{34} +34.6714i q^{35} +(-17.2730 - 23.5865i) q^{36} +36.3463i q^{37} +(-2.78878 - 1.61011i) q^{38} +(-36.4625 - 13.8380i) q^{39} +(26.6234 + 46.1130i) q^{40} +(22.3968 + 38.7924i) q^{41} +(-5.81351 - 8.91514i) q^{42} +(7.68187 - 13.3054i) q^{43} -16.9350 q^{44} +(45.0555 + 61.5238i) q^{45} +15.2180i q^{46} +(-16.4364 + 28.4687i) q^{47} +(20.1869 + 10.2378i) q^{48} +(-16.1279 - 27.9344i) q^{49} +(-20.2844 - 35.1335i) q^{50} +(-89.8312 + 4.87789i) q^{51} +(41.9883 - 4.49427i) q^{52} +0.397357i q^{53} +(-21.9012 - 8.26511i) q^{54} +44.1738 q^{55} +(22.2698 + 12.8575i) q^{56} +(11.1263 - 0.604164i) q^{57} +(-6.80941 + 3.93141i) q^{58} +(-50.1902 - 86.9320i) q^{59} +(-73.6405 - 37.3468i) q^{60} +(-10.8878 + 18.8583i) q^{61} +35.3741i q^{62} +(33.7001 + 14.8521i) q^{63} -2.71439 q^{64} +(-109.524 + 11.7230i) q^{65} +(-11.3585 + 7.40683i) q^{66} +(70.7519 - 40.8486i) q^{67} +(84.3596 - 48.7050i) q^{68} +(-28.7627 - 44.1082i) q^{69} +(-26.0326 - 15.0300i) q^{70} +50.0834 q^{71} +(56.2258 - 6.12426i) q^{72} -135.863i q^{73} +(-27.2902 - 15.7560i) q^{74} +(125.197 + 63.4936i) q^{75} +(-10.4486 + 6.03249i) q^{76} +(18.4752 - 10.6667i) q^{77} +(26.1965 - 21.3787i) q^{78} +(39.5882 - 68.5688i) q^{79} +63.9278 q^{80} +(79.1005 - 17.4386i) q^{81} -38.8358 q^{82} +(-35.2829 + 61.1118i) q^{83} +(-39.8174 + 2.16211i) q^{84} +(-220.047 + 127.044i) q^{85} +(6.66015 + 11.5357i) q^{86} +(12.3060 - 24.2650i) q^{87} +(16.3814 - 28.3734i) q^{88} +46.8117 q^{89} +(-65.7260 + 7.15904i) q^{90} +(-42.9763 + 31.3497i) q^{91} +(49.3775 + 28.5081i) q^{92} +(-66.8587 - 102.529i) q^{93} +(-14.2503 - 24.6823i) q^{94} +(27.2544 - 15.7354i) q^{95} +(-79.6054 + 51.9102i) q^{96} +(-72.9925 - 42.1423i) q^{97} +27.9656 q^{98} +(18.9226 - 42.9363i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q - 4 q^{3} - 50 q^{4} + 4 q^{9} + 8 q^{10} - 38 q^{12} - 6 q^{13} - 6 q^{14} - 90 q^{16} + 14 q^{22} + 138 q^{23} - 92 q^{25} - 76 q^{27} + 48 q^{29} + 186 q^{30} - 154 q^{36} + 324 q^{38} - 2 q^{39}+ \cdots + 504 q^{95}+O(q^{100}) $ 52 * q - 4 * q^3 - 50 * q^4 + 4 * q^9 + 8 * q^10 - 38 * q^12 - 6 * q^13 - 6 * q^14 - 90 * q^16 + 14 * q^22 + 138 * q^23 - 92 * q^25 - 76 * q^27 + 48 * q^29 + 186 * q^30 - 154 * q^36 + 324 * q^38 - 2 * q^39 - 68 * q^40 - 216 * q^42 + 62 * q^43 + 230 * q^48 + 70 * q^49 + 90 * q^51 - 4 * q^52 + 92 * q^55 - 276 * q^56 + 12 * q^61 + 12 * q^64 - 588 * q^65 + 762 * q^66 - 144 * q^68 - 414 * q^69 + 342 * q^74 - 620 * q^75 - 510 * q^77 - 162 * q^78 - 24 * q^79 + 532 * q^81 - 292 * q^82 - 330 * q^87 - 62 * q^88 + 258 * q^90 + 264 * q^91 - 396 * q^92 - 160 * q^94 + 504 * q^95

Character values

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

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

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 $

$2$	−0.433498	+	0.750840i	−0.216749	+	0.375420i	−0.953812	−	0.300404i	$-0.902879\pi$
$2$	−0.433498	+	0.750840i	−0.216749	+	0.375420i	0.737063	+	0.675824i	$0.236212\pi$
$3$	−0.162662	−	2.99559i	−0.0542208	−	0.998529i
$3$	−0.162662	−	2.99559i	−0.0542208	−	0.998529i
$4$	1.62416	+	2.81313i	0.406040	+	0.703282i
$5$	−4.23652	−	7.33786i	−0.847303	−	1.46757i	−0.883606	−	0.468232i	$-0.844891\pi$
$5$	−4.23652	−	7.33786i	−0.847303	−	1.46757i	0.0363024	−	0.999341i	$-0.488442\pi$
$6$	2.31972	+	1.17645i	0.386620	+	0.196074i
$7$	−3.54375	−	2.04598i	−0.506249	−	0.292283i	0.225041	−	0.974349i	$-0.427748\pi$
$7$	−3.54375	−	2.04598i	−0.506249	−	0.292283i	−0.731291	+	0.682066i	$0.761082\pi$
$8$	−6.28426			−0.785532
$9$	−8.94708	+	0.974539i	−0.994120	+	0.108282i
$10$	7.34608			0.734608
$11$	−2.60673	+	4.51499i	−0.236975	+	0.410454i	−0.959845	−	0.280531i	$-0.909489\pi$
$11$	−2.60673	+	4.51499i	−0.236975	+	0.410454i	0.722869	+	0.690985i	$0.242823\pi$
$12$	8.16278	−	5.32290i	0.680231	−	0.443575i
$13$	5.26488	−	11.8862i	0.404991	−	0.914321i
$13$	5.26488	−	11.8862i	0.404991	−	0.914321i
$14$	3.07241	−	1.77386i	0.219458	−	0.126704i
$15$	−21.2921	+	13.8844i	−1.41947	+	0.925630i
$16$	−3.77243	+	6.53403i	−0.235777	+	0.408377i
$17$		−	29.9878i		−	1.76399i	−0.471259	−	0.881995i	$-0.656200\pi$
$17$		−	29.9878i		−	1.76399i	0.471259	−	0.881995i	$-0.343800\pi$
$18$	3.14682	−	7.14029i	0.174823	−	0.396683i
$19$			3.71422i			0.195485i	0.995212	+	0.0977426i	$0.0311622\pi$
$19$			3.71422i			0.195485i	−0.995212	+	0.0977426i	$0.968838\pi$
$20$	13.7616	−	23.8357i	0.688078	−	1.19179i
$21$	−5.55248	+	10.9484i	−0.264404	+	0.521353i
$22$	−2.26002	−	3.91448i	−0.102728	−	0.177931i
$23$	15.2009	−	8.77627i	0.660911	−	0.381577i	−0.131713	−	0.991288i	$-0.542048\pi$
$23$	15.2009	−	8.77627i	0.660911	−	0.381577i	0.792624	+	0.609711i	$0.208714\pi$
$24$	1.02221	+	18.8250i	0.0425922	+	0.784377i
$25$	−23.3961	+	40.5233i	−0.935846	+	1.62093i
$26$	6.64230	+	9.10571i	0.255473	+	0.350220i
$27$	4.37467	+	26.6432i	0.162025	+	0.986787i
$28$		−	13.2920i		−	0.474715i
$29$	7.85403	+	4.53453i	0.270829	+	0.156363i	0.629264	−	0.777192i	$-0.283356\pi$
$29$	7.85403	+	4.53453i	0.270829	+	0.156363i	−0.358436	+	0.933554i	$0.616690\pi$
$30$	−1.19493	−	22.0058i	−0.0398311	−	0.733528i
$31$	35.3345	−	20.4004i	1.13982	−	0.658077i	0.193436	−	0.981113i	$-0.438037\pi$
$31$	35.3345	−	20.4004i	1.13982	−	0.658077i	0.946387	+	0.323036i	$0.104703\pi$
$32$	−15.8392	−	27.4343i	−0.494975	−	0.857322i
$33$	13.9491	+	7.07427i	0.422699	+	0.214372i
$34$	22.5161	+	12.9997i	0.662237	+	0.382343i
$35$			34.6714i			0.990610i
$36$	−17.2730	−	23.5865i	−0.479805	−	0.655180i
$37$			36.3463i			0.982332i	0.871066	+	0.491166i	$0.163429\pi$
$37$			36.3463i			0.982332i	−0.871066	+	0.491166i	$0.836571\pi$
$38$	−2.78878	−	1.61011i	−0.0733891	−	0.0423712i
$39$	−36.4625	−	13.8380i	−0.934935	−	0.354820i
$40$	26.6234	+	46.1130i	0.665584	+	1.15283i
$41$	22.3968	+	38.7924i	0.546263	+	0.946156i	0.998526	+	0.0542713i	$0.0172836\pi$
$41$	22.3968	+	38.7924i	0.546263	+	0.946156i	−0.452263	+	0.891885i	$0.649383\pi$
$42$	−5.81351	−	8.91514i	−0.138417	−	0.212265i
$43$	7.68187	−	13.3054i	0.178648	−	0.309428i	−0.762770	−	0.646670i	$-0.776161\pi$
$43$	7.68187	−	13.3054i	0.178648	−	0.309428i	0.941418	+	0.337243i	$0.109494\pi$
$44$	−16.9350			−0.384886
$45$	45.0555	+	61.5238i	1.00123	+	1.36720i
$46$			15.2180i			0.330826i
$47$	−16.4364	+	28.4687i	−0.349711	+	0.605718i	−0.986198	−	0.165570i	$-0.947054\pi$
$47$	−16.4364	+	28.4687i	−0.349711	+	0.605718i	0.636487	+	0.771288i	$0.280387\pi$
$48$	20.1869	+	10.2378i	0.420560	+	0.213287i
$49$	−16.1279	−	27.9344i	−0.329141	−	0.570089i
$50$	−20.2844	−	35.1335i	−0.405687	−	0.702671i
$51$	−89.8312	+	4.87789i	−1.76140	+	0.0956450i
$52$	41.9883	−	4.49427i	0.807467	−	0.0864283i
$53$			0.397357i			0.00749731i	0.999993	+	0.00374865i	$0.00119324\pi$
$53$			0.397357i			0.00749731i	−0.999993	+	0.00374865i	$0.998807\pi$
$54$	−21.9012	−	8.26511i	−0.405578	−	0.153058i
$55$	44.1738			0.803161
$56$	22.2698	+	12.8575i	0.397675	+	0.229598i
$57$	11.1263	−	0.604164i	0.195198	−	0.0105994i
$58$	−6.80941	+	3.93141i	−0.117404	+	0.0677830i
$59$	−50.1902	−	86.9320i	−0.850682	−	1.47342i	−0.880594	−	0.473872i	$-0.842856\pi$
$59$	−50.1902	−	86.9320i	−0.850682	−	1.47342i	0.0299122	−	0.999553i	$-0.490477\pi$
$60$	−73.6405	−	37.3468i	−1.22734	−	0.622446i
$61$	−10.8878	+	18.8583i	−0.178489	+	0.309152i	−0.941363	−	0.337395i	$-0.890454\pi$
$61$	−10.8878	+	18.8583i	−0.178489	+	0.309152i	0.762874	+	0.646547i	$0.223788\pi$
$62$			35.3741i			0.570550i
$63$	33.7001	+	14.8521i	0.534922	+	0.235747i
$64$	−2.71439			−0.0424123
$65$	−109.524	+	11.7230i	−1.68498	+	0.180354i
$66$	−11.3585	+	7.40683i	−0.172099	+	0.112225i
$67$	70.7519	−	40.8486i	1.05600	−	0.609681i	0.131676	−	0.991293i	$-0.457964\pi$
$67$	70.7519	−	40.8486i	1.05600	−	0.609681i	0.924323	+	0.381612i	$0.124631\pi$
$68$	84.3596	−	48.7050i	1.24058	−	0.716250i
$69$	−28.7627	−	44.1082i	−0.416851	−	0.639249i
$70$	−26.0326	−	15.0300i	−0.371895	−	0.214714i
$71$	50.0834			0.705400			0.352700	−	0.935736i	$-0.385264\pi$
$71$	50.0834			0.705400			0.352700	+	0.935736i	$0.385264\pi$
$72$	56.2258	−	6.12426i	0.780914	−	0.0850591i
$73$		−	135.863i		−	1.86114i	−0.366118	−	0.930568i	$-0.619313\pi$
$73$		−	135.863i		−	1.86114i	0.366118	−	0.930568i	$-0.380687\pi$
$74$	−27.2902	−	15.7560i	−0.368787	−	0.212919i
$75$	125.197	+	63.4936i	1.66929	+	0.846581i
$76$	−10.4486	+	6.03249i	−0.137481	+	0.0793748i
$77$	18.4752	−	10.6667i	0.239937	−	0.138528i
$78$	26.1965	−	21.3787i	0.335852	−	0.274087i
$79$	39.5882	−	68.5688i	0.501117	−	0.867960i	−0.498882	−	0.866670i	$-0.666256\pi$
$79$	39.5882	−	68.5688i	0.501117	−	0.867960i	0.999999	−	0.00129016i	$-0.000410670\pi$
$80$	63.9278			0.799097
$81$	79.1005	−	17.4386i	0.976550	−	0.215291i
$82$	−38.8358			−0.473608
$83$	−35.2829	+	61.1118i	−0.425095	+	0.736287i	−0.996429	−	0.0844309i	$-0.973093\pi$
$83$	−35.2829	+	61.1118i	−0.425095	+	0.736287i	0.571334	+	0.820718i	$0.306426\pi$
$84$	−39.8174	+	2.16211i	−0.474016	+	0.0257394i
$85$	−220.047	+	127.044i	−2.58878	+	1.49463i
$86$	6.66015	+	11.5357i	0.0774436	+	0.134136i
$87$	12.3060	−	24.2650i	0.141448	−	0.278908i
$88$	16.3814	−	28.3734i	0.186152	−	0.322425i
$89$	46.8117			0.525974			0.262987	−	0.964799i	$-0.415292\pi$
$89$	46.8117			0.525974			0.262987	+	0.964799i	$0.415292\pi$
$90$	−65.7260	+	7.15904i	−0.730289	+	0.0795449i
$91$	−42.9763	+	31.3497i	−0.472267	+	0.344502i
$92$	49.3775	+	28.5081i	0.536712	+	0.309871i
$93$	−66.8587	−	102.529i	−0.718911	−	1.10246i
$94$	−14.2503	−	24.6823i	−0.151599	−	0.262577i
$95$	27.2544	−	15.7354i	0.286889	−	0.165635i
$96$	−79.6054	+	51.9102i	−0.829222	+	0.540731i
$97$	−72.9925	−	42.1423i	−0.752500	−	0.434456i	0.0740964	−	0.997251i	$-0.476393\pi$
$97$	−72.9925	−	42.1423i	−0.752500	−	0.434456i	−0.826597	+	0.562795i	$0.809726\pi$
$98$	27.9656			0.285364
$99$	18.9226	−	42.9363i	0.191137	−	0.433700i
$100$	−151.996			−1.51996
$101$	−108.398	−	62.5836i	−1.07325	−	0.619640i	−0.144181	−	0.989551i	$-0.546055\pi$
$101$	−108.398	−	62.5836i	−1.07325	−	0.619640i	−0.929067	+	0.369911i	$0.879388\pi$
$102$	35.2791	−	69.5634i	0.345873	−	0.681994i
$103$	−16.0190	−	27.7457i	−0.155524	−	0.269376i	0.777726	−	0.628604i	$-0.216373\pi$
$103$	−16.0190	−	27.7457i	−0.155524	−	0.269376i	−0.933250	+	0.359228i	$0.883040\pi$
$104$	−33.0859	+	74.6958i	−0.318133	+	0.718229i
$105$	103.861	−	5.63973i	0.989153	−	0.0537117i
$106$	−0.298352	−	0.172253i	−0.00281464	−	0.00162503i
$107$			102.573i			0.958628i	0.877643	+	0.479314i	$0.159115\pi$
$107$			102.573i			0.958628i	−0.877643	+	0.479314i	$0.840885\pi$
$108$	−67.8456	+	55.5794i	−0.628200	+	0.514624i
$109$			93.0071i			0.853276i	0.904422	+	0.426638i	$0.140302\pi$
$109$			93.0071i			0.853276i	−0.904422	+	0.426638i	$0.859698\pi$
$110$	−19.1493	+	33.1675i	−0.174084	+	0.301523i
$111$	108.878	−	5.91217i	0.980887	−	0.0532628i
$112$	26.7370	−	15.4366i	0.238724	−	0.137827i
$113$	−110.583	+	63.8450i	−0.978608	+	0.565000i	−0.901850	−	0.432050i	$-0.857790\pi$
$113$	−110.583	+	63.8450i	−0.978608	+	0.565000i	−0.0767586	+	0.997050i	$0.524457\pi$
$114$	−4.36958	+	8.61595i	−0.0383297	+	0.0755785i
$115$	−128.798	−	74.3616i	−1.11998	−	0.646623i
$116$			29.4592i			0.253958i
$117$	−35.5218	+	111.477i	−0.303605	+	0.952798i
$118$	87.0294			0.737537
$119$	−61.3546	+	106.269i	−0.515585	+	0.893019i
$120$	133.805	−	87.2535i	1.11504	−	0.727112i
$121$	46.9099	+	81.2504i	0.387685	+	0.671491i
$122$	−9.43969	−	16.3500i	−0.0773745	−	0.134017i
$123$	112.563	−	73.4016i	0.915145	−	0.596761i
$124$	114.778	+	66.2670i	0.925627	+	0.534411i
$125$	184.647			1.47718
$126$	−25.7604	+	18.8650i	−0.204448	+	0.149722i
$127$	203.258			1.60045			0.800227	−	0.599697i	$-0.204712\pi$
$127$	203.258			1.60045			0.800227	+	0.599697i	$0.204712\pi$
$128$	64.5335	−	111.775i	0.504168	−	0.873244i
$129$	−41.1070	−	20.8474i	−0.318659	−	0.161608i
$130$	38.6762	−	87.3168i	0.297509	−	0.671668i
$131$	59.4628	−	34.3308i	0.453914	−	0.262067i	−0.255568	−	0.966791i	$-0.582262\pi$
$131$	59.4628	−	34.3308i	0.453914	−	0.262067i	0.709482	+	0.704724i	$0.248929\pi$
$132$	2.75469	+	50.7302i	0.0208688	+	0.384320i
$133$	7.59923	−	13.1623i	0.0571371	−	0.0989643i
$134$			70.8312i			0.528591i
$135$	176.971	−	144.975i	1.31090	−	1.07389i
$136$			188.451i			1.38567i
$137$	−10.1226	+	17.5329i	−0.0738876	+	0.127977i	−0.900602	−	0.434645i	$-0.856874\pi$
$137$	−10.1226	+	17.5329i	−0.0738876	+	0.127977i	0.826714	+	0.562622i	$0.190207\pi$
$138$	45.5868	−	2.47539i	0.330339	−	0.0179376i
$139$	−53.3805	−	92.4577i	−0.384032	−	0.665163i	0.607602	−	0.794242i	$-0.292132\pi$
$139$	−53.3805	−	92.4577i	−0.384032	−	0.665163i	−0.991634	+	0.129078i	$0.958798\pi$
$140$	−97.5349	+	56.3118i	−0.696678	+	0.402227i
$141$	87.9542	+	44.6060i	0.623788	+	0.316354i
$142$	−21.7111	+	37.6046i	−0.152895	+	0.264821i
$143$	39.9418	+	54.7549i	0.279313	+	0.382901i
$144$	27.3845	−	62.1369i	0.190170	−	0.431506i
$145$		−	76.8424i		−	0.529947i
$146$	102.011	+	58.8963i	0.698708	+	0.403399i
$147$	−81.0564	+	52.8564i	−0.551404	+	0.359568i
$148$	−102.247	+	59.0322i	−0.690856	+	0.398866i
$149$	−9.36666	−	16.2235i	−0.0628635	−	0.108883i	0.832881	−	0.553452i	$-0.186690\pi$
$149$	−9.36666	−	16.2235i	−0.0628635	−	0.108883i	−0.895744	+	0.444570i	$0.853357\pi$
$150$	−101.946	+	66.4785i	−0.679640	+	0.443190i
$151$	0.176520	+	0.101914i	0.00116901	+	0.000674927i	0.500584	−	0.865688i	$-0.333118\pi$
$151$	0.176520	+	0.101914i	0.00116901	+	0.000674927i	−0.499415	+	0.866363i	$0.666452\pi$
$152$		−	23.3411i		−	0.153560i
$153$	29.2243	+	268.304i	0.191009	+	1.75362i
$154$			18.4959i			0.120103i
$155$	−299.391	−	172.853i	−1.93155	−	1.11518i
$156$	−20.2929	−	125.049i	−0.130083	−	0.801593i
$157$	−14.9419	−	25.8802i	−0.0951714	−	0.164842i	0.814509	−	0.580151i	$-0.197007\pi$
$157$	−14.9419	−	25.8802i	−0.0951714	−	0.164842i	−0.909680	+	0.415310i	$0.863673\pi$
$158$	34.3228	+	59.4489i	0.217233	+	0.376259i
$159$	1.19032	−	0.0646351i	0.00748628	−	0.000406510i
$160$	−134.206	+	232.452i	−0.838788	+	1.45282i
$161$	−71.8244			−0.446114
$162$	−21.1963	+	66.9514i	−0.130842	+	0.413280i
$163$		−	224.330i		−	1.37626i	−0.725588	−	0.688130i	$-0.758432\pi$
$163$		−	224.330i		−	1.37626i	0.725588	−	0.688130i	$-0.241568\pi$
$164$	−72.7520	+	126.010i	−0.443609	+	0.768354i
$165$	−7.18542	−	132.327i	−0.0435480	−	0.801979i
$166$	−30.5901	−	52.9837i	−0.184278	−	0.319179i
$167$	55.4010	+	95.9573i	0.331742	+	0.574595i	0.982854	−	0.184388i	$-0.0590302\pi$
$167$	55.4010	+	95.9573i	0.331742	+	0.574595i	−0.651111	+	0.758982i	$0.725697\pi$
$168$	34.8933	−	68.8026i	0.207698	−	0.409539i
$169$	−113.562	−	125.158i	−0.671965	−	0.740583i
$170$		−	220.293i		−	1.29584i
$171$	−3.61965	−	33.2314i	−0.0211676	−	0.194336i
$172$	49.9063			0.290153
$173$	81.0760	+	46.8092i	0.468647	+	0.270574i	0.715673	−	0.698435i	$-0.246120\pi$
$173$	81.0760	+	46.8092i	0.468647	+	0.270574i	−0.247026	+	0.969009i	$0.579453\pi$
$174$	12.8845	+	19.7587i	0.0740490	+	0.113556i
$175$	165.820	−	95.7362i	0.947543	−	0.547064i
$176$	−19.6674	−	34.0649i	−0.111747	−	0.193551i
$177$	−252.248	+	164.490i	−1.42513	+	0.929321i
$178$	−20.2928	+	35.1481i	−0.114004	+	0.197461i
$179$		−	19.1155i		−	0.106790i	−0.998573	−	0.0533951i	$-0.982996\pi$
$179$		−	19.1155i		−	0.106790i	0.998573	−	0.0533951i	$-0.0170043\pi$
$180$	−99.8969	+	226.671i	−0.554983	+	1.25928i
$181$	−183.331			−1.01288			−0.506440	−	0.862275i	$-0.669039\pi$
$181$	−183.331			−1.01288			−0.506440	+	0.862275i	$0.669039\pi$
$182$	−4.90851	−	45.8584i	−0.0269698	−	0.251969i
$183$	58.2626	+	29.5479i	0.318375	+	0.161464i
$184$	−95.5267	+	55.1524i	−0.519167	+	0.299741i
$185$	266.704	−	153.982i	1.44164	−	0.832333i
$186$	105.966	−	5.75404i	0.569711	−	0.0309357i
$187$	135.395	+	78.1702i	0.724036	+	0.418022i
$188$	−106.782			−0.567987
$189$	39.0089	−	103.367i	0.206396	−	0.546917i
$190$			27.2850i			0.143605i
$191$	326.200	+	188.332i	1.70785	+	0.986030i	0.937212	+	0.348761i	$0.113398\pi$
$191$	326.200	+	188.332i	1.70785	+	0.986030i	0.770642	+	0.637269i	$0.219936\pi$
$192$	0.441529	+	8.13119i	0.00229963	+	0.0423499i
$193$	111.317	−	64.2686i	0.576770	−	0.332998i	−0.183079	−	0.983098i	$-0.558606\pi$
$193$	111.317	−	64.2686i	0.576770	−	0.332998i	0.759849	+	0.650100i	$0.225273\pi$
$194$	63.2842	−	36.5371i	0.326207	−	0.188336i
$195$	52.9327	+	326.181i	0.271450	+	1.67272i
$196$	52.3886	−	90.7397i	0.267289	−	0.462958i
$197$	−207.729			−1.05446			−0.527232	−	0.849721i	$-0.676770\pi$
$197$	−207.729			−1.05446			−0.527232	+	0.849721i	$0.676770\pi$
$198$	24.0354	+	32.8206i	0.121391	+	0.165761i
$199$	−71.8150			−0.360879			−0.180440	−	0.983586i	$-0.557752\pi$
$199$	−71.8150			−0.360879			−0.180440	+	0.983586i	$0.557752\pi$
$200$	147.027	−	254.659i	0.735137	−	1.27330i
$201$	−133.874	−	205.299i	−0.666042	−	1.02139i
$202$	93.9806	−	54.2597i	0.465251	−	0.268613i
$203$	−18.5551	−	32.1384i	−0.0914045	−	0.158317i
$204$	−159.622	−	244.784i	−0.782462	−	1.19992i
$205$	189.769	−	328.689i	0.925702	−	1.60336i
$206$	27.7768			0.134839
$207$	−127.451	+	93.3359i	−0.615707	+	0.450898i
$208$	57.8033	+	79.2406i	0.277900	+	0.380964i
$209$	−16.7697	−	9.68197i	−0.0802376	−	0.0463252i
$210$	−40.7890	+	80.4279i	−0.194233	+	0.382990i
$211$	171.628	+	297.268i	0.813402	+	1.40885i	0.910470	+	0.413575i	$0.135720\pi$
$211$	171.628	+	297.268i	0.813402	+	1.40885i	−0.0970681	+	0.995278i	$0.530946\pi$
$212$	−1.11782	+	0.645371i	−0.00527272	+	0.00304420i
$213$	−8.14669	−	150.029i	−0.0382474	−	0.704363i
$214$	−77.0161	−	44.4652i	−0.359888	−	0.207782i
$215$	−130.177			−0.605477
$216$	−27.4916	−	167.433i	−0.127276	−	0.775153i
$217$	−166.955			−0.769380
$218$	−69.8334	−	40.3184i	−0.320337	−	0.184947i
$219$	−406.989	+	22.0998i	−1.85840	+	0.100912i
$220$	71.7453	+	124.267i	0.326115	+	0.564848i
$221$	−356.441	−	157.882i	−1.61285	−	0.714399i
$222$	−42.7595	+	84.3132i	−0.192610	+	0.379789i
$223$	162.357	+	93.7369i	0.728058	+	0.420345i	0.817711	−	0.575628i	$-0.195242\pi$
$223$	162.357	+	93.7369i	0.728058	+	0.420345i	−0.0896531	+	0.995973i	$0.528576\pi$
$224$			129.627i			0.578691i
$225$	169.836	−	385.366i	0.754825	−	1.71274i
$226$		−	110.707i		−	0.489852i
$227$	6.75796	−	11.7051i	0.0297707	−	0.0515644i	−0.850756	−	0.525561i	$-0.823856\pi$
$227$	6.75796	−	11.7051i	0.0297707	−	0.0515644i	0.880527	+	0.473996i	$0.157189\pi$
$228$	19.7704	+	30.3183i	0.0867124	+	0.132975i
$229$	−276.011	+	159.355i	−1.20529	+	0.695874i	−0.961726	−	0.274011i	$-0.911649\pi$
$229$	−276.011	+	159.355i	−1.20529	+	0.695874i	−0.243563	+	0.969885i	$0.578316\pi$
$230$	111.667	−	64.4712i	0.485510	−	0.280310i
$231$	−34.9581	−	53.6089i	−0.151334	−	0.232073i
$232$	−49.3567	−	28.4961i	−0.212745	−	0.122828i
$233$			64.6139i			0.277313i	0.990341	+	0.138656i	$0.0442784\pi$
$233$			64.6139i			0.277313i	−0.990341	+	0.138656i	$0.955722\pi$
$234$	−68.3031	−	74.9963i	−0.291894	−	0.320497i
$235$	278.533			1.18525
$236$	163.034	−	282.383i	0.690821	−	1.19654i
$237$	−211.843	−	107.436i	−0.893854	−	0.453318i
$238$	−53.1941	−	92.1350i	−0.223505	−	0.387122i
$239$	−20.1969	−	34.9820i	−0.0845058	−	0.146368i	0.820675	−	0.571396i	$-0.193598\pi$
$239$	−20.1969	−	34.9820i	−0.0845058	−	0.146368i	−0.905181	+	0.425027i	$0.860264\pi$
$240$	−10.3986	−	191.501i	−0.0433277	−	0.797922i
$241$	407.067	+	235.020i	1.68908	+	0.975188i	0.955226	+	0.295876i	$0.0956116\pi$
$241$	407.067	+	235.020i	1.68908	+	0.975188i	0.733849	+	0.679312i	$0.237722\pi$
$242$	−81.3414			−0.336121
$243$	−65.1054	−	234.116i	−0.267924	−	0.963440i
$244$	−70.7342			−0.289894
$245$	−136.652	+	236.689i	−0.557765	+	0.966077i
$246$	6.31713	+	116.336i	0.0256794	+	0.472911i
$247$	44.1479	+	19.5549i	0.178736	+	0.0791697i
$248$	−222.051	+	128.201i	−0.895368	+	0.516941i
$249$	188.805	+	95.7524i	0.758253	+	0.384548i
$250$	−80.0440	+	138.640i	−0.320176	+	0.554561i
$251$		−	78.9093i		−	0.314380i	−0.987568	−	0.157190i	$-0.949757\pi$
$251$		−	78.9093i		−	0.314380i	0.987568	−	0.157190i	$-0.0502434\pi$
$252$	12.9536	+	118.925i	0.0514031	+	0.471923i
$253$			91.5095i			0.361698i
$254$	−88.1117	+	152.614i	−0.346897	+	0.600843i
$255$	416.365	+	638.503i	1.63280	+	2.50394i
$256$	50.5214	+	87.5057i	0.197349	+	0.341819i
$257$	145.387	−	83.9391i	0.565707	−	0.326611i	−0.189726	−	0.981837i	$-0.560760\pi$
$257$	145.387	−	83.9391i	0.565707	−	0.326611i	0.755433	+	0.655226i	$0.227427\pi$
$258$	33.4729	−	21.8275i	0.129740	−	0.0846026i
$259$	74.3639	−	128.802i	0.287119	−	0.497305i
$260$	−210.863	−	289.064i	−0.811010	−	1.11179i
$261$	−74.6897	−	32.9167i	−0.286167	−	0.126118i
$262$			59.5294i			0.227211i
$263$	148.389	+	85.6723i	0.564216	+	0.325750i	0.754836	−	0.655914i	$-0.227716\pi$
$263$	148.389	+	85.6723i	0.564216	+	0.325750i	−0.190620	+	0.981664i	$0.561050\pi$
$264$	−87.6595	−	44.4565i	−0.332044	−	0.168396i
$265$	2.91575	−	1.68341i	0.0110028	−	0.00635249i
$266$	6.58850	+	11.4116i	0.0247688	+	0.0429008i
$267$	−7.61451	−	140.229i	−0.0285188	−	0.525200i
$268$	229.825	+	132.689i	0.857555	+	0.495110i
$269$		−	18.7954i		−	0.0698715i	−0.999390	−	0.0349357i	$-0.988877\pi$
$269$		−	18.7954i		−	0.0698715i	0.999390	−	0.0349357i	$-0.0111227\pi$
$270$	32.1367	+	195.723i	0.119025	+	0.724902i
$271$		−	268.245i		−	0.989835i	−0.868940	−	0.494917i	$-0.835198\pi$
$271$		−	268.245i		−	0.989835i	0.868940	−	0.494917i	$-0.164802\pi$
$272$	195.942	+	113.127i	0.720373	+	0.415908i
$273$	100.901	+	123.640i	0.369602	+	0.452893i
$274$	−8.77625	−	15.2009i	−0.0320301	−	0.0554778i
$275$	−121.975	−	211.267i	−0.443545	−	0.768243i
$276$	77.3667	−	152.552i	0.280314	−	0.552724i
$277$	83.6899	−	144.955i	0.302130	−	0.523304i	−0.674488	−	0.738285i	$-0.735636\pi$
$277$	83.6899	−	144.955i	0.302130	−	0.523304i	0.976618	+	0.214981i	$0.0689691\pi$
$278$	92.5613			0.332954
$279$	−296.260	+	216.959i	−1.06186	+	0.777630i
$280$		−	217.884i		−	0.778156i
$281$	196.532	−	340.403i	0.699401	−	1.21140i	−0.269274	−	0.963064i	$-0.586784\pi$
$281$	196.532	−	340.403i	0.699401	−	1.21140i	0.968675	−	0.248334i	$-0.0798830\pi$
$282$	−71.6199	+	46.7029i	−0.253971	+	0.165613i
$283$	189.678	+	328.532i	0.670240	+	1.16089i	0.977836	+	0.209372i	$0.0671420\pi$
$283$	189.678	+	328.532i	0.670240	+	1.16089i	−0.307596	+	0.951517i	$0.599525\pi$
$284$	81.3435	+	140.891i	0.286421	+	0.496095i
$285$	−51.5699	−	79.0835i	−0.180947	−	0.277486i
$286$	−58.4269	+	6.25379i	−0.204290	+	0.0218664i
$287$		−	183.294i		−	0.638655i
$288$	168.450	+	230.021i	0.584897	+	0.798684i
$289$	−610.270			−2.11166
$290$	57.6963	+	33.3110i	0.198953	+	0.114865i
$291$	−114.368	+	225.510i	−0.393016	+	0.774950i
$292$	382.200	−	220.663i	1.30890	−	0.755696i
$293$	220.439	+	381.812i	0.752352	+	1.30311i	0.946680	+	0.322175i	$0.104414\pi$
$293$	220.439	+	381.812i	0.752352	+	1.30311i	−0.194328	+	0.980937i	$0.562253\pi$
$294$	−4.54896	−	83.7735i	−0.0154727	−	0.284944i
$295$	−425.263	+	736.578i	−1.44157	+	2.49687i
$296$		−	228.409i		−	0.771654i
$297$	−131.698	−	49.7002i	−0.443426	−	0.167341i
$298$	16.2417			0.0545023
$299$	−24.2851	−	226.887i	−0.0812212	−	0.758820i
$300$	24.7241	+	455.318i	0.0824136	+	1.51773i
$301$	−54.4452	+	31.4339i	−0.180881	+	0.104432i
$302$	−0.153042	+	0.0883590i	−0.000506763	+	0.000292580i
$303$	−169.842	+	334.896i	−0.560536	+	1.10527i
$304$	−24.2688	−	14.0116i	−0.0798317	−	0.0460908i
$305$	184.506			0.604937
$306$	−214.122	−	94.3662i	−0.699744	−	0.308386i
$307$		−	218.522i		−	0.711797i	−0.934525	−	0.355898i	$-0.884175\pi$
$307$		−	218.522i		−	0.711797i	0.934525	−	0.355898i	$-0.115825\pi$
$308$	60.0133	+	34.6487i	0.194848	+	0.112496i
$309$	−80.5090	+	52.4995i	−0.260547	+	0.169901i
$310$	259.570	−	149.863i	0.837323	−	0.483429i
$311$	−243.743	+	140.725i	−0.783740	+	0.452493i	−0.837754	−	0.546048i	$-0.816132\pi$
$311$	−243.743	+	140.725i	−0.783740	+	0.452493i	0.0540140	+	0.998540i	$0.482798\pi$
$312$	229.140	+	86.9614i	0.734422	+	0.278722i
$313$	18.0768	−	31.3099i	0.0577533	−	0.100032i	−0.835703	−	0.549181i	$-0.814940\pi$
$313$	18.0768	−	31.3099i	0.0577533	−	0.100032i	0.893457	+	0.449150i	$0.148273\pi$
$314$	25.9091			0.0825132
$315$	−33.7886	−	310.207i	−0.107265	−	0.984786i
$316$	257.190			0.813894
$317$	−141.041	+	244.290i	−0.444924	+	0.770631i	−0.998047	−	0.0624684i	$-0.980103\pi$
$317$	−141.041	+	244.290i	−0.444924	+	0.770631i	0.553123	+	0.833100i	$0.313436\pi$
$318$	−0.467469	+	0.921758i	−0.00147003	+	0.00289861i
$319$	−40.9467	+	23.6406i	−0.128359	+	0.0741084i
$320$	11.4996	+	19.9178i	0.0359361	+	0.0622431i
$321$	307.267	−	16.6848i	0.957218	−	0.0519776i
$322$	31.1357	−	53.9286i	0.0966948	−	0.167480i
$323$	111.381			0.344834
$324$	177.529	+	194.197i	0.547928	+	0.599373i
$325$	358.489	+	491.441i	1.10304	+	1.51213i
$326$	168.436	+	97.2467i	0.516675	+	0.298303i
$327$	278.611	−	15.1288i	0.852021	−	0.0462653i
$328$	−140.747	−	243.781i	−0.429108	−	0.743236i
$329$	116.493	−	67.2573i	0.354082	−	0.204430i
$330$	102.471	+	51.9682i	0.310518	+	0.157479i
$331$	−318.178	−	183.700i	−0.961262	−	0.554985i	−0.0647006	−	0.997905i	$-0.520609\pi$
$331$	−318.178	−	183.700i	−0.961262	−	0.554985i	−0.896561	+	0.442920i	$0.853943\pi$
$332$	−229.220			−0.690423
$333$	−35.4209	−	325.193i	−0.106369	−	0.976556i
$334$	−96.0648			−0.287619
$335$	−599.483	−	346.112i	−1.78950	−	1.03317i
$336$	−50.5909	−	77.5822i	−0.150568	−	0.230899i
$337$	−145.856	−	252.630i	−0.432807	−	0.749644i	0.564307	−	0.825565i	$-0.309144\pi$
$337$	−145.856	−	252.630i	−0.432807	−	0.749644i	−0.997114	+	0.0759215i	$0.975810\pi$
$338$	143.203	−	31.0111i	0.423677	−	0.0917488i
$339$	209.241	+	320.875i	0.617230	+	0.946534i
$340$	−714.782	−	412.679i	−2.10230	−	1.21376i
$341$			212.713i			0.623793i
$342$	26.5206	+	11.6880i	0.0775456	+	0.0341753i
$343$			332.496i			0.969376i
$344$	−48.2749	+	83.6145i	−0.140334	+	0.243065i
$345$	−201.806	+	397.922i	−0.584945	+	1.15340i
$346$	−70.2925	+	40.5834i	−0.203158	+	0.117293i
$347$	449.891	−	259.745i	1.29652	−	0.748543i	0.316715	−	0.948521i	$-0.397420\pi$
$347$	449.891	−	259.745i	1.29652	−	0.748543i	0.979800	+	0.199978i	$0.0640869\pi$
$348$	88.2475	−	4.79190i	0.253585	−	0.0137698i
$349$	208.012	+	120.096i	0.596022	+	0.344113i	0.767475	−	0.641079i	$-0.221513\pi$
$349$	208.012	+	120.096i	0.596022	+	0.344113i	−0.171453	+	0.985192i	$0.554846\pi$
$350$			166.006i			0.474302i
$351$	339.718	+	88.2753i	0.967858	+	0.251497i
$352$	165.154			0.469188
$353$	163.692	−	283.523i	0.463716	−	0.803180i	−0.535426	−	0.844582i	$-0.679849\pi$
$353$	163.692	−	283.523i	0.463716	−	0.803180i	0.999143	+	0.0414019i	$0.0131824\pi$
$354$	−14.1564	−	260.704i	−0.0399899	−	0.736452i
$355$	−212.179	−	367.505i	−0.597688	−	1.03523i
$356$	76.0297	+	131.687i	0.213566	+	0.369908i
$357$	328.319	+	166.507i	0.919661	+	0.466406i
$358$	14.3526	+	8.28651i	0.0400912	+	0.0231467i
$359$	34.2625			0.0954387			0.0477194	−	0.998861i	$-0.484805\pi$
$359$	34.2625			0.0954387			0.0477194	+	0.998861i	$0.484805\pi$
$360$	−283.140	−	386.632i	−0.786501	−	1.07398i
$361$	347.205			0.961786
$362$	79.4736	−	137.652i	0.219540	−	0.380255i
$363$	235.762	−	153.739i	0.649482	−	0.423524i
$364$	−157.991	−	69.9808i	−0.434041	−	0.192255i
$365$	−996.944	+	575.586i	−2.73135	+	1.57695i
$366$	−47.4424	+	30.9369i	−0.129624	+	0.0845272i
$367$	−231.833	+	401.546i	−0.631696	+	1.09413i	0.355509	+	0.934673i	$0.384308\pi$
$367$	−231.833	+	401.546i	−0.631696	+	1.09413i	−0.987205	+	0.159457i	$0.949026\pi$
$368$			132.431i			0.359868i
$369$	−238.191	−	325.252i	−0.645503	−	0.881442i
$370$			267.003i			0.721629i
$371$	0.812986	−	1.40813i	0.00219134	−	0.00379551i
$372$	179.838	−	354.606i	0.483437	−	0.953242i
$373$	220.601	+	382.092i	0.591424	+	1.02438i	0.994041	+	0.109008i	$0.0347674\pi$
$373$	220.601	+	382.092i	0.591424	+	1.02438i	−0.402617	+	0.915369i	$0.631899\pi$
$374$	−117.387	+	67.7732i	−0.313868	+	0.181212i
$375$	−30.0351	−	553.126i	−0.0800936	−	1.47500i
$376$	103.291	−	178.905i	0.274710	−	0.475811i
$377$	95.2486	−	69.4806i	0.252649	−	0.184299i
$378$	60.7021	+	74.0990i	0.160588	+	0.196029i
$379$			450.703i			1.18919i	0.804026	+	0.594594i	$0.202687\pi$
$379$			450.703i			1.18919i	−0.804026	+	0.594594i	$0.797313\pi$
$380$	88.5311	+	51.1134i	0.232977	+	0.134509i
$381$	−33.0624	−	608.876i	−0.0867779	−	1.59810i
$382$	−282.814	+	163.283i	−0.740351	+	0.427442i
$383$	12.1335	+	21.0158i	0.0316801	+	0.0548716i	0.881431	−	0.472313i	$-0.156581\pi$
$383$	12.1335	+	21.0158i	0.0316801	+	0.0548716i	−0.849751	+	0.527185i	$0.823248\pi$
$384$	−345.330	−	175.134i	−0.899296	−	0.456078i
$385$	−156.541	−	90.3789i	−0.406600	−	0.234750i
$386$			111.441i			0.288708i
$387$	−55.7637	+	126.531i	−0.144092	+	0.326953i
$388$		−	273.783i		−	0.705626i
$389$	225.254	+	130.050i	0.579058	+	0.334320i	0.760759	−	0.649034i	$-0.224827\pi$
$389$	225.254	+	130.050i	0.579058	+	0.334320i	−0.181701	+	0.983354i	$0.558160\pi$
$390$	−267.856	−	101.655i	−0.686811	−	0.260653i
$391$	−263.181	−	455.844i	−0.673098	−	1.16584i
$392$	101.352	+	175.547i	0.258551	+	0.447823i
$393$	−112.513	−	172.542i	−0.286294	−	0.439037i
$394$	90.0502	−	155.972i	0.228554	−	0.395867i
$395$	−670.865			−1.69839
$396$	151.519	−	16.5038i	0.382623	−	0.0416763i
$397$		−	167.017i		−	0.420698i	−0.977626	−	0.210349i	$-0.932540\pi$
$397$		−	167.017i		−	0.420698i	0.977626	−	0.210349i	$-0.0674600\pi$
$398$	31.1316	−	53.9216i	0.0782202	−	0.135481i
$399$	−40.6648	−	20.6231i	−0.101917	−	0.0516871i
$400$	−176.520	−	305.742i	−0.441301	−	0.764356i
$401$	112.408	+	194.696i	0.280319	+	0.485526i	0.971463	−	0.237190i	$-0.0762265\pi$
$401$	112.408	+	194.696i	0.280319	+	0.485526i	−0.691144	+	0.722717i	$0.742893\pi$
$402$	212.181	−	11.5216i	0.527813	−	0.0286606i
$403$	−56.4507	−	527.398i	−0.140076	−	1.30868i
$404$		−	406.583i		−	1.00639i
$405$	−463.073	−	506.550i	−1.14339	−	1.25074i
$406$	32.1744			0.0792473
$407$	−164.103	−	94.7450i	−0.403202	−	0.232789i
$408$	564.522	−	30.6540i	1.38363	−	0.0751322i
$409$	−327.809	+	189.261i	−0.801490	+	0.462740i	−0.843992	−	0.536356i	$-0.819800\pi$
$409$	−327.809	+	189.261i	−0.801490	+	0.462740i	0.0425020	+	0.999096i	$0.486467\pi$
$410$	164.529	+	284.972i	0.401290	+	0.695054i
$411$	54.1678	+	27.4712i	0.131795	+	0.0668399i
$412$	52.0348	−	90.1269i	0.126298	−	0.218755i
$413$			410.753i			0.994560i
$414$	−14.8305	−	136.156i	−0.0358225	−	0.328880i
$415$	597.907			1.44074
$416$	−409.480	+	43.8292i	−0.984327	+	0.105359i
$417$	−268.282	+	174.945i	−0.643362	+	0.419533i
$418$	14.5392	−	8.39422i	0.0347828	−	0.0200819i
$419$	231.060	−	133.402i	0.551455	−	0.318383i	−0.198254	−	0.980151i	$-0.563527\pi$
$419$	231.060	−	133.402i	0.551455	−	0.318383i	0.749709	+	0.661768i	$0.230194\pi$
$420$	184.552	+	283.015i	0.439410	+	0.673844i
$421$	181.446	+	104.758i	0.430987	+	0.248831i	0.699767	−	0.714371i	$-0.253287\pi$
$421$	181.446	+	104.758i	0.430987	+	0.248831i	−0.268780	+	0.963202i	$0.586620\pi$
$422$	−297.601			−0.705216
$423$	119.314	−	270.730i	0.282067	−	0.640024i
$424$		−	2.49710i		−	0.00588938i
$425$	1215.21	+	701.600i	2.85931	+	1.65082i
$426$	116.180	+	58.9205i	0.272722	+	0.138311i
$427$	77.1673	−	44.5526i	0.180720	−	0.104339i
$428$	−288.551	+	166.595i	−0.674186	+	0.389241i
$429$	157.526	−	128.556i	0.367194	−	0.299664i
$430$	56.4316	−	97.7425i	0.131236	−	0.227308i
$431$	260.189			0.603686			0.301843	−	0.953358i	$-0.402398\pi$
$431$	260.189			0.603686			0.301843	+	0.953358i	$0.402398\pi$
$432$	−190.591	−	71.9254i	−0.441183	−	0.166494i
$433$	−843.669			−1.94843			−0.974214	−	0.225627i	$-0.927557\pi$
$433$	−843.669			−1.94843			−0.974214	+	0.225627i	$0.927557\pi$
$434$	72.3748	−	125.357i	0.166762	−	0.288841i
$435$	−230.188	+	12.4994i	−0.529168	+	0.0287342i
$436$	−261.641	+	151.058i	−0.600093	+	0.346464i
$437$	32.5970	+	56.4597i	0.0745927	+	0.129198i
$438$	159.836	−	315.164i	0.364921	−	0.719553i
$439$	98.7471	−	171.035i	0.224936	−	0.389601i	−0.731364	−	0.681987i	$-0.761116\pi$
$439$	98.7471	−	171.035i	0.224936	−	0.389601i	0.956300	+	0.292386i	$0.0944492\pi$
$440$	−277.600			−0.630909
$441$	171.521	+	234.214i	0.388936	+	0.531097i
$442$	273.060	−	199.188i	0.617784	−	0.450652i
$443$	−139.549	−	80.5687i	−0.315009	−	0.181871i	0.334157	−	0.942518i	$-0.391549\pi$
$443$	−139.549	−	80.5687i	−0.315009	−	0.181871i	−0.649166	+	0.760647i	$0.724882\pi$
$444$	193.468	+	296.687i	0.435738	+	0.668213i
$445$	−198.319	−	343.498i	−0.445660	−	0.771905i
$446$	−140.763	+	81.2694i	−0.315612	+	0.182218i
$447$	−47.0754	+	30.6976i	−0.105314	+	0.0686747i
$448$	9.61910	+	5.55359i	0.0214712	+	0.0123964i
$449$	752.642			1.67626			0.838131	−	0.545469i	$-0.183648\pi$
$449$	752.642			1.67626			0.838131	+	0.545469i	$0.183648\pi$
$450$	215.725	+	294.575i	0.479388	+	0.654610i
$451$	−233.530			−0.517804
$452$	−359.208	−	207.389i	−0.794708	−	0.458825i
$453$	0.276579	−	0.545360i	0.000610550	−	0.00120388i
$454$	5.85912	+	10.1483i	0.0129055	+	0.0223531i
$455$	412.110	+	182.540i	0.905736	+	0.401188i
$456$	−69.9204	+	3.79672i	−0.153334	+	0.00832615i
$457$	26.9151	+	15.5394i	0.0588952	+	0.0340031i	0.529158	−	0.848523i	$-0.322508\pi$
$457$	26.9151	+	15.5394i	0.0588952	+	0.0340031i	−0.470263	+	0.882526i	$0.655841\pi$
$458$		−	276.320i		−	0.603320i
$459$	798.973	−	131.187i	1.74068	−	0.285810i
$460$		−	483.101i		−	1.05022i
$461$	89.1379	−	154.391i	0.193358	−	0.334905i	−0.753003	−	0.658017i	$-0.771396\pi$
$461$	89.1379	−	154.391i	0.193358	−	0.334905i	0.946361	+	0.323112i	$0.104729\pi$
$462$	55.4060	−	3.00858i	0.119926	−	0.00651209i
$463$	−102.557	+	59.2113i	−0.221505	+	0.127886i	−0.606647	−	0.794971i	$-0.707486\pi$
$463$	−102.557	+	59.2113i	−0.221505	+	0.127886i	0.385142	+	0.922857i	$0.374153\pi$
$464$	−59.2575	+	34.2123i	−0.127710	+	0.0737334i
$465$	−469.097	+	924.967i	−1.00881	+	1.98918i
$466$	−48.5147	−	28.0100i	−0.104109	−	0.0601073i
$467$		−	832.894i		−	1.78350i	−0.452529	−	0.891750i	$-0.649478\pi$
$467$		−	832.894i		−	1.78350i	0.452529	−	0.891750i	$-0.350522\pi$
$468$	−371.293	+	81.1298i	−0.793361	+	0.173354i
$469$	−334.302			−0.712798
$470$	−120.743	+	209.134i	−0.256901	+	0.444965i
$471$	−75.0958	+	48.9695i	−0.159439	+	0.103969i
$472$	315.408	+	546.303i	0.668238	+	1.15742i
$473$	40.0491	+	69.3671i	0.0846705	+	0.146654i
$474$	172.501	−	112.487i	0.363927	−	0.237315i
$475$	−150.513	−	86.8984i	−0.316868	−	0.182944i
$476$	−398.599			−0.837392
$477$	−0.387240	−	3.55519i	−0.000811824	−	0.00745322i
$478$	35.0212			0.0732661
$479$	−29.1233	+	50.4430i	−0.0608002	+	0.105309i	−0.894823	−	0.446420i	$-0.852699\pi$
$479$	−29.1233	+	50.4430i	−0.0608002	+	0.105309i	0.834023	+	0.551729i	$0.186032\pi$
$480$	718.159	+	364.215i	1.49617	+	0.758781i
$481$	432.018	+	191.359i	0.898167	+	0.397835i
$482$	−352.925	+	203.762i	−0.732210	+	0.422742i
$483$	11.6831	+	215.156i	0.0241887	+	0.445458i
$484$	−152.378	+	263.927i	−0.314831	+	0.545304i
$485$			714.145i			1.47246i
$486$	204.007	+	52.6050i	0.419767	+	0.108241i
$487$		−	753.906i		−	1.54806i	−0.633148	−	0.774031i	$-0.718238\pi$
$487$		−	753.906i		−	1.54806i	0.633148	−	0.774031i	$-0.281762\pi$
$488$	68.4219	−	118.510i	0.140209	−	0.242849i
$489$	−672.001	+	36.4901i	−1.37423	+	0.0746219i
$490$	−118.477	−	205.208i	−0.241790	−	0.418792i
$491$	−211.650	+	122.196i	−0.431058	+	0.248872i	−0.699797	−	0.714341i	$-0.746726\pi$
$491$	−211.650	+	122.196i	−0.431058	+	0.248872i	0.268739	+	0.963213i	$0.413393\pi$
$492$	389.308	+	197.438i	0.791277	+	0.401296i
$493$	135.981	−	235.525i	0.275823	−	0.477739i
$494$	−33.8206	+	24.6710i	−0.0684628	+	0.0499412i
$495$	−395.227	+	43.0491i	−0.798438	+	0.0869679i
$496$			307.836i			0.620637i
$497$	−177.483	−	102.470i	−0.357109	−	0.206177i
$498$	−153.741	+	100.254i	−0.308717	+	0.201313i
$499$	394.606	−	227.826i	0.790793	−	0.456565i	−0.0494486	−	0.998777i	$-0.515746\pi$
$499$	394.606	−	227.826i	0.790793	−	0.456565i	0.840242	+	0.542212i	$0.182413\pi$
$500$	299.896	+	519.435i	0.599792	+	1.03887i
$501$	278.437	−	181.567i	0.555762	−	0.362409i
$502$	59.2483	+	34.2070i	0.118024	+	0.0681414i
$503$			107.616i			0.213948i	0.994262	+	0.106974i	$0.0341162\pi$
$503$			107.616i			0.213948i	−0.994262	+	0.106974i	$0.965884\pi$
$504$	−211.780	−	93.3342i	−0.420198	−	0.185187i
$505$			1060.55i			2.10009i
$506$	−68.7090	−	39.6692i	−0.135789	−	0.0783975i
$507$	−356.451	+	360.544i	−0.703059	+	0.711132i
$508$	330.123	+	571.790i	0.649848	+	1.12557i
$509$	−20.8864	−	36.1762i	−0.0410341	−	0.0710732i	0.844779	−	0.535115i	$-0.179732\pi$
$509$	−20.8864	−	36.1762i	−0.0410341	−	0.0710732i	−0.885813	+	0.464042i	$0.846399\pi$
$510$	−659.907	+	35.8334i	−1.29394	+	0.0702616i
$511$	−277.973	+	481.464i	−0.543979	+	0.942199i
$512$	428.664			0.837234
$513$	−98.9588	+	16.2485i	−0.192902	+	0.0316735i
$514$			145.550i			0.283171i
$515$	−135.729	+	235.090i	−0.263552	+	0.456486i
$516$	−8.11789	−	149.499i	−0.0157323	−	0.289726i
$517$	−85.6907	−	148.421i	−0.165746	−	0.287081i
$518$	64.4731	+	111.671i	0.124465	+	0.215581i
$519$	127.033	−	250.484i	0.244765	−	0.482629i
$520$	688.276	−	73.6705i	1.32361	−	0.141674i
$521$		−	551.285i		−	1.05813i	−0.848582	−	0.529065i	$-0.822543\pi$
$521$		−	551.285i		−	1.05813i	0.848582	−	0.529065i	$-0.177457\pi$
$522$	57.0930	−	41.8107i	0.109374	−	0.0800971i
$523$	−405.935			−0.776167			−0.388083	−	0.921624i	$-0.626863\pi$
$523$	−405.935			−0.776167			−0.388083	+	0.921624i	$0.626863\pi$
$524$	193.154	+	111.518i	0.368615	+	0.212820i
$525$	−313.759	−	481.156i	−0.597636	−	0.916487i
$526$	−128.652	+	74.2775i	−0.244586	+	0.141212i
$527$	−611.764	−	1059.61i	−1.16084	−	2.01064i
$528$	−98.8453	+	64.4565i	−0.187207	+	0.122077i
$529$	−110.454	+	191.312i	−0.208798	+	0.361649i
$530$			2.91902i			0.00550758i
$531$	533.775	+	728.876i	1.00523	+	1.37265i
$532$	49.3694			0.0927997
$533$	579.010	−	61.9750i	1.08632	−	0.116276i
$534$	108.590	+	55.0715i	0.203352	+	0.103130i
$535$	752.668	−	434.553i	1.40686	−	0.812249i
$536$	−444.623	+	256.703i	−0.829521	+	0.478924i
$537$	−57.2620	+	3.10937i	−0.106633	+	0.00579025i
$538$	14.1124	+	8.14777i	0.0262311	+	0.0151446i
$539$	168.164			0.311993
$540$	695.263	+	262.379i	1.28752	+	0.485887i
$541$		−	214.662i		−	0.396788i	−0.980122	−	0.198394i	$-0.936428\pi$
$541$		−	214.662i		−	0.396788i	0.980122	−	0.198394i	$-0.0635725\pi$
$542$	201.409	+	116.284i	0.371604	+	0.214546i
$543$	29.8211	+	549.184i	0.0549191	+	1.01139i
$544$	−822.695	+	474.983i	−1.51231	+	0.873131i
$545$	682.473	−	394.026i	1.25224	−	0.722984i
$546$	−136.574	+	22.1633i	−0.250136	+	0.0405921i
$547$	178.594	−	309.334i	0.326497	−	0.565509i	−0.655317	−	0.755354i	$-0.727465\pi$
$547$	178.594	−	309.334i	0.326497	−	0.565509i	0.981814	+	0.189844i	$0.0607984\pi$
$548$	−65.7629			−0.120005
$549$	79.0361	−	179.337i	0.143964	−	0.326661i
$550$	211.503			0.384552
$551$	−16.8422	+	29.1716i	−0.0305666	+	0.0529430i
$552$	180.752	+	277.187i	0.327450	+	0.502151i
$553$	−280.581	+	161.994i	−0.507380	+	0.292936i
$554$	72.5588	+	125.675i	0.130973	+	0.226851i
$555$	−504.648	−	773.888i	−0.909276	−	1.39439i
$556$	173.397	−	300.332i	0.311865	−	0.540166i
$557$	−207.167			−0.371934			−0.185967	−	0.982556i	$-0.559542\pi$
$557$	−207.167			−0.371934			−0.185967	+	0.982556i	$0.559542\pi$
$558$	−34.4734	−	316.495i	−0.0617803	−	0.567195i
$559$	−117.706	−	161.359i	−0.210565	−	0.288657i
$560$	−226.544	−	130.795i	−0.404543	−	0.233563i
$561$	212.142	−	418.302i	0.378150	−	0.745637i
$562$	170.392	+	295.128i	0.303189	+	0.525138i
$563$	524.862	−	303.029i	0.932259	−	0.538240i	0.0447336	−	0.998999i	$-0.485756\pi$
$563$	524.862	−	303.029i	0.932259	−	0.538240i	0.887525	+	0.460759i	$0.152423\pi$
$564$	17.3693	+	319.873i	0.0307967	+	0.567151i
$565$	936.971	+	540.961i	1.65836	+	0.957452i
$566$	−328.900			−0.581095
$567$	−315.991	−	100.041i	−0.557304	−	0.176438i
$568$	−314.737			−0.554115
$569$	−601.199	−	347.102i	−1.05659	−	0.610021i	−0.132102	−	0.991236i	$-0.542172\pi$
$569$	−601.199	−	347.102i	−1.05659	−	0.610021i	−0.924486	+	0.381215i	$0.875506\pi$
$570$	81.7345	−	4.43824i	0.143394	−	0.00778638i
$571$	39.3922	+	68.2293i	0.0689881	+	0.119491i	0.898456	−	0.439063i	$-0.144690\pi$
$571$	39.3922	+	68.2293i	0.0689881	+	0.119491i	−0.829468	+	0.558554i	$0.811356\pi$
$572$	−89.1606	+	201.292i	−0.155875	+	0.351909i
$573$	511.103	−	1007.79i	0.891978	−	1.75880i
$574$	137.624	+	79.4575i	0.239764	+	0.138428i
$575$			821.324i			1.42839i
$576$	24.2859	−	2.64528i	0.0421629	−	0.00459249i
$577$		−	688.316i		−	1.19292i	−0.802642	−	0.596461i	$-0.796573\pi$
$577$		−	688.316i		−	1.19292i	0.802642	−	0.596461i	$-0.203427\pi$
$578$	264.551	−	458.215i	0.457700	−	0.792760i
$579$	−210.629	−	323.004i	−0.363781	−	0.557866i
$580$	216.167	−	124.804i	0.372702	−	0.215180i
$581$	250.067	−	144.376i	0.430409	−	0.248497i
$582$	−119.744	−	183.630i	−0.205746	−	0.315516i
$583$	−1.79406	−	1.03580i	−0.00307730	−	0.00177668i
$584$			853.798i			1.46198i
$585$	968.494	−	211.622i	1.65555	−	0.361747i
$586$	−382.239			−0.652286
$587$	−527.268	+	913.256i	−0.898242	+	1.55580i	−0.0685028	+	0.997651i	$0.521822\pi$
$587$	−527.268	+	913.256i	−0.898242	+	1.55580i	−0.829740	+	0.558151i	$0.811511\pi$
$588$	−280.340	−	142.175i	−0.476769	−	0.241794i
$589$	75.7715	+	131.240i	0.128644	+	0.222819i
$590$	−368.701	−	638.610i	−0.624918	−	1.08239i
$591$	33.7898	+	622.272i	0.0571739	+	1.05291i
$592$	−237.488	−	137.114i	−0.401162	−	0.231611i
$593$	93.4687			0.157620			0.0788100	−	0.996890i	$-0.474888\pi$
$593$	93.4687			0.157620			0.0788100	+	0.996890i	$0.474888\pi$
$594$	94.4074	−	77.3389i	0.158935	−	0.130200i
$595$	1039.72			1.74743
$596$	30.4259	−	52.6992i	0.0510501	−	0.0884214i
$597$	11.6816	+	215.128i	0.0195672	+	0.360348i
$598$	180.883	+	80.1208i	0.302481	+	0.133981i
$599$	211.509	−	122.115i	0.353103	−	0.203864i	−0.312948	−	0.949770i	$-0.601317\pi$
$599$	211.509	−	122.115i	0.353103	−	0.203864i	0.666051	+	0.745906i	$0.267983\pi$
$600$	−786.769	−	399.010i	−1.31128	−	0.665017i
$601$	−341.955	+	592.283i	−0.568976	+	0.985496i	0.427691	+	0.903925i	$0.359327\pi$
$601$	−341.955	+	592.283i	−0.568976	+	0.985496i	−0.996668	+	0.0815711i	$0.974006\pi$
$602$		−	54.5062i		−	0.0905418i
$603$	−593.215	+	434.427i	−0.983772	+	0.720442i
$604$			0.662099i			0.00109619i
$605$	397.469	−	688.437i	0.656974	−	1.13791i
$606$	−177.827	−	272.701i	−0.293444	−	0.450002i
$607$	262.238	+	454.210i	0.432024	+	0.748287i	0.997047	−	0.0767876i	$-0.0244663\pi$
$607$	262.238	+	454.210i	0.432024	+	0.748287i	−0.565024	+	0.825075i	$0.691133\pi$
$608$	101.897	−	58.8302i	0.167594	−	0.0967603i
$609$	−93.2552	+	60.8112i	−0.153128	+	0.0998542i
$610$	−79.9828	+	138.534i	−0.131119	+	0.227105i
$611$	251.848	+	345.251i	0.412191	+	0.565058i
$612$	−707.307	+	517.980i	−1.15573	+	0.846372i
$613$			51.1328i			0.0834140i	0.999130	+	0.0417070i	$0.0132796\pi$
$613$			51.1328i			0.0834140i	−0.999130	+	0.0417070i	$0.986720\pi$
$614$	164.075	+	94.7286i	0.267223	+	0.154281i
$615$	−1015.49	−	515.004i	−1.65120	−	0.837404i
$616$	−116.103	+	67.0320i	−0.188479	+	0.108818i
$617$	−374.413	−	648.502i	−0.606828	−	1.05106i	−0.991760	−	0.128112i	$-0.959108\pi$
$617$	−374.413	−	648.502i	−0.606828	−	1.05106i	0.384932	−	0.922945i	$-0.374225\pi$
$618$	−4.51824	−	83.2078i	−0.00731107	−	0.134640i
$619$	185.367	+	107.022i	0.299462	+	0.172894i	0.642201	−	0.766536i	$-0.278021\pi$
$619$	185.367	+	107.022i	0.299462	+	0.172894i	−0.342739	+	0.939431i	$0.611355\pi$
$620$		−	1122.96i		−	1.81123i
$621$	300.327	+	366.609i	0.483619	+	0.590353i
$622$		−	244.016i		−	0.392309i
$623$	−165.889	−	95.7759i	−0.266274	−	0.153733i
$624$	227.970	−	186.044i	0.365336	−	0.298148i
$625$	−197.356	−	341.830i	−0.315769	−	0.546929i
$626$	15.6725	+	27.1455i	0.0250359	+	0.0433635i
$627$	−26.2754	+	51.8099i	−0.0419065	+	0.0826314i
$628$	48.5361	−	84.0670i	0.0772868	−	0.133865i
$629$	1089.95			1.73282
$630$	247.563	+	109.104i	0.392958	+	0.173182i
$631$			448.257i			0.710392i	0.934792	+	0.355196i	$0.115586\pi$
$631$			448.257i			0.710392i	−0.934792	+	0.355196i	$0.884414\pi$
$632$	−248.783	+	430.904i	−0.393644	+	0.681811i
$633$	862.575	−	562.480i	1.36268	−	0.888594i
$634$	−122.282	−	211.798i	−0.192874	−	0.334067i
$635$	−861.105	−	1491.48i	−1.35607	−	2.34878i
$636$	2.11509	+	3.24354i	0.00332562	+	0.00509990i
$637$	−416.944	+	44.6281i	−0.654543	+	0.0700599i
$638$		−	40.9925i		−	0.0642516i
$639$	−448.101	+	48.8083i	−0.701253	+	0.0763822i
$640$	−1093.59			−1.70873
$641$	−400.143	−	231.023i	−0.624249	−	0.360410i	0.154273	−	0.988028i	$-0.450697\pi$
$641$	−400.143	−	231.023i	−0.624249	−	0.360410i	−0.778521	+	0.627618i	$0.784030\pi$
$642$	−120.672	+	237.941i	−0.187962	+	0.370625i
$643$	−477.862	+	275.894i	−0.743176	+	0.429073i	−0.823223	−	0.567718i	$-0.807826\pi$
$643$	−477.862	+	275.894i	−0.743176	+	0.429073i	0.0800471	+	0.996791i	$0.474493\pi$
$644$	−116.654	−	202.051i	−0.181140	−	0.313744i
$645$	21.1750	+	389.958i	0.0328294	+	0.604586i
$646$	−48.2836	+	83.6296i	−0.0747424	+	0.129458i
$647$		−	901.778i		−	1.39378i	−0.717176	−	0.696892i	$-0.754566\pi$
$647$		−	901.778i		−	1.39378i	0.717176	−	0.696892i	$-0.245434\pi$
$648$	−497.088	+	109.588i	−0.767112	+	0.169118i
$649$	523.330			0.806363
$650$	−524.398	+	56.1296i	−0.806766	+	0.0863532i
$651$	27.1574	+	500.129i	0.0417164	+	0.768248i
$652$	631.069	−	364.348i	0.967898	−	0.558816i
$653$	519.216	−	299.770i	0.795124	−	0.459065i	−0.0466391	−	0.998912i	$-0.514851\pi$
$653$	519.216	−	299.770i	0.795124	−	0.459065i	0.841763	+	0.539847i	$0.181518\pi$
$654$	−109.418	+	215.750i	−0.167306	+	0.329894i
$655$	−503.830	−	290.886i	−0.769206	−	0.444101i
$656$	−337.961			−0.515185
$657$	132.404	+	1215.58i	0.201528	+	1.85019i
$658$			116.624i			0.177239i
$659$	147.756	+	85.3071i	0.224213	+	0.129449i	0.607899	−	0.794014i	$-0.292012\pi$
$659$	147.756	+	85.3071i	0.224213	+	0.129449i	−0.383687	+	0.923463i	$0.625346\pi$
$660$	360.581	−	235.133i	0.546335	−	0.356262i
$661$	−529.951	+	305.967i	−0.801741	+	0.462885i	−0.844079	−	0.536218i	$-0.819852\pi$
$661$	−529.951	+	305.967i	−0.801741	+	0.462885i	0.0423387	+	0.999103i	$0.486519\pi$
$662$	275.859	−	159.267i	0.416705	−	0.240585i
$663$	−414.971	+	1093.43i	−0.625898	+	1.64922i
$664$	221.727	−	384.042i	0.333926	−	0.578377i
$665$	−128.777			−0.193650
$666$	259.523	+	114.375i	0.389674	+	0.171734i
$667$	159.185			0.238658
$668$	−179.960	+	311.700i	−0.269401	+	0.466617i
$669$	254.388	−	501.602i	0.380250	−	0.749779i
$670$	519.749	−	300.077i	0.775745	−	0.447877i
$671$	−56.7632	−	98.3168i	−0.0845950	−	0.146523i
$672$	388.309	−	21.0854i	0.577840	−	0.0313771i
$673$	−272.015	+	471.143i	−0.404182	+	0.700064i	−0.994226	−	0.107307i	$-0.965777\pi$
$673$	−272.015	+	471.143i	−0.404182	+	0.700064i	0.590044	+	0.807371i	$0.299111\pi$
$674$	252.913			0.375242
$675$	−1182.02	−	446.073i	−1.75115	−	0.660849i
$676$	167.644	−	522.742i	0.247994	−	0.773287i
$677$	56.2001	+	32.4471i	0.0830134	+	0.0479278i	0.540932	−	0.841066i	$-0.318072\pi$
$677$	56.2001	+	32.4471i	0.0830134	+	0.0479278i	−0.457919	+	0.888994i	$0.651405\pi$
$678$	−331.631	+	18.0078i	−0.489132	+	0.0265602i
$679$	172.445	+	298.683i	0.253969	+	0.439886i
$680$	1382.83	−	798.377i	2.03357	−	1.17408i
$681$	−36.1630	−	18.3401i	−0.0531028	−	0.0269311i
$682$	−159.714	−	92.2107i	−0.234184	−	0.135206i
$683$	−923.328			−1.35187			−0.675936	−	0.736961i	$-0.736260\pi$
$683$	−923.328			−1.35187			−0.675936	+	0.736961i	$0.736260\pi$
$684$	87.6053	−	64.1557i	0.128078	−	0.0937948i
$685$	171.538			0.250421
$686$	−249.651	−	144.136i	−0.363923	−	0.210111i
$687$	522.259	+	800.894i	0.760202	+	1.16579i
$688$	57.9586	+	100.387i	0.0842421	+	0.145912i
$689$	4.72306	+	2.09204i	0.00685494	+	0.00303634i
$690$	−211.293	−	324.022i	−0.306222	−	0.469598i
$691$	308.875	+	178.329i	0.446997	+	0.258074i	0.706561	−	0.707652i	$-0.250246\pi$
$691$	308.875	+	178.329i	0.446997	+	0.258074i	−0.259564	+	0.965726i	$0.583579\pi$
$692$			304.103i			0.439455i
$693$	−154.904	+	113.440i	−0.223527	+	0.163694i
$694$			450.395i			0.648984i
$695$	−452.295	+	783.397i	−0.650784	+	1.12719i
$696$	−77.3341	+	152.488i	−0.111112	+	0.219091i
$697$	1163.30	−	671.632i	1.66901	−	0.963603i
$698$	−180.345	+	104.122i	−0.258374	+	0.149172i
$699$	193.557	−	10.5103i	0.276905	−	0.0150361i
$700$	538.636	+	310.982i	0.769480	+	0.444260i
$701$		−	433.680i		−	0.618660i	−0.950955	−	0.309330i	$-0.899895\pi$
$701$		−	433.680i		−	0.618660i	0.950955	−	0.309330i	$-0.100105\pi$
$702$	−213.548	+	216.807i	−0.304199	+	0.308842i
$703$	−134.998			−0.192031
$704$	7.07568	−	12.2554i	0.0100507	−	0.0174083i
$705$	−45.3068	−	834.370i	−0.0642650	−	1.18350i
$706$	141.920	+	245.813i	0.201020	+	0.348177i
$707$	256.090	+	443.561i	0.362221	+	0.627385i
$708$	−872.422	−	442.449i	−1.23223	−	0.624928i
$709$	−446.829	−	257.977i	−0.630224	−	0.363860i	0.150615	−	0.988593i	$-0.451875\pi$
$709$	−446.829	−	257.977i	−0.630224	−	0.363860i	−0.780839	+	0.624732i	$0.785208\pi$
$710$	367.917			0.518193
$711$	−287.376	+	652.071i	−0.404186	+	0.917118i
$712$	−294.177			−0.413170
$713$	358.079	−	620.211i	0.502214	−	0.869861i
$714$	−267.346	+	174.335i	−0.374434	+	0.244166i
$715$	232.570	−	525.058i	0.325272	−	0.734346i
$716$	53.7742	−	31.0465i	0.0751036	−	0.0433611i
$717$	−101.506	+	66.1918i	−0.141571	+	0.0923177i
$718$	−14.8527	+	25.7257i	−0.0206862	+	0.0358296i
$719$			1091.62i			1.51825i	0.650943	+	0.759127i	$0.274374\pi$
$719$			1091.62i			1.51825i	−0.650943	+	0.759127i	$0.725626\pi$
$720$	−571.967	+	62.3001i	−0.794399	+	0.0865279i
$721$			131.098i			0.181828i
$722$	−150.512	+	260.695i	−0.208466	+	0.361074i
$723$	637.809	−	1257.63i	0.882171	−	1.73947i
$724$	−297.759	−	515.734i	−0.411269	−	0.712339i
$725$	−367.508	+	212.181i	−0.506908	+	0.292663i
$726$	13.2312	+	243.665i	0.0182248	+	0.335627i
$727$	−31.8859	+	55.2279i	−0.0438595	+	0.0759669i	−0.887122	−	0.461535i	$-0.847299\pi$
$727$	−31.8859	+	55.2279i	−0.0438595	+	0.0759669i	0.843262	+	0.537502i	$0.180632\pi$
$728$	270.074	−	197.010i	0.370981	−	0.270618i
$729$	−690.725	+	233.111i	−0.947496	+	0.319768i
$730$		−	998.060i		−	1.36721i
$731$	−399.000	−	230.363i	−0.545827	−	0.315134i
$732$	11.5058	+	211.891i	0.0157183	+	0.289468i
$733$	323.537	−	186.794i	0.441387	−	0.254835i	−0.262799	−	0.964851i	$-0.584646\pi$
$733$	323.537	−	186.794i	0.441387	−	0.254835i	0.704186	+	0.710016i	$0.251312\pi$
$734$	−200.998	−	348.138i	−0.273839	−	0.474303i
$735$	731.250	+	370.854i	0.994898	+	0.504563i
$736$	−481.542	−	278.018i	−0.654268	−	0.377742i
$737$			425.926i			0.577918i
$738$	347.468	−	37.8470i	0.470823	−	0.0512833i
$739$		−	713.612i		−	0.965646i	−0.875718	−	0.482823i	$-0.839611\pi$
$739$		−	713.612i		−	0.965646i	0.875718	−	0.482823i	$-0.160389\pi$
$740$	866.340	+	500.181i	1.17073	+	0.675921i
$741$	51.3972	−	135.430i	0.0693620	−	0.182766i
$742$	0.704855	+	1.22084i	0.000949939	+	0.00164534i
$743$	96.9877	+	167.988i	0.130535	+	0.226094i	0.923883	−	0.382675i	$-0.124997\pi$
$743$	96.9877	+	167.988i	0.130535	+	0.226094i	−0.793348	+	0.608769i	$0.791664\pi$
$744$	420.158	+	644.320i	0.564728	+	0.866022i
$745$	−79.3640	+	137.462i	−0.106529	+	0.184513i
$746$	−382.520			−0.512762
$747$	256.123	−	581.157i	0.342869	−	0.777988i
$748$			507.843i			0.678935i
$749$	209.863	−	363.493i	0.280191	−	0.485305i
$750$	428.329	+	217.227i	0.571106	+	0.289636i
$751$	16.7860	+	29.0742i	0.0223516	+	0.0387140i	0.876985	−	0.480518i	$-0.159551\pi$
$751$	16.7860	+	29.0742i	0.0223516	+	0.0387140i	−0.854633	+	0.519232i	$0.826218\pi$
$752$	−124.010	−	214.792i	−0.164908	−	0.285628i
$753$	−236.380	+	12.8356i	−0.313917	+	0.0170459i
$754$	10.8788	+	101.636i	0.0144281	+	0.134796i
$755$		−	1.72704i		−	0.00228747i
$756$	354.142	−	58.1482i	0.468442	−	0.0769155i
$757$	940.856			1.24287			0.621437	−	0.783464i	$-0.286549\pi$
$757$	940.856			1.24287			0.621437	+	0.783464i	$0.286549\pi$
$758$	−338.406	−	195.379i	−0.446445	−	0.257755i
$759$	274.125	−	14.8852i	0.361166	−	0.0196115i
$760$	−171.274	+	98.8850i	−0.225360	+	0.130112i
$761$	310.037	+	536.999i	0.407407	+	0.705649i	0.994598	−	0.103799i	$-0.0330998\pi$
$761$	310.037	+	536.999i	0.407407	+	0.705649i	−0.587192	+	0.809448i	$0.699766\pi$
$762$	471.501	+	239.122i	0.618768	+	0.313808i
$763$	190.291	−	329.593i	0.249398	−	0.431970i
$764$			1223.52i			1.60147i
$765$	1844.97	−	1351.12i	2.41172	−	1.76617i
$766$	−21.0394			−0.0274665
$767$	−1297.53	+	138.883i	−1.69170	+	0.181073i
$768$	253.913	−	165.575i	0.330616	−	0.215593i
$769$	−485.507	+	280.307i	−0.631348	+	0.364509i	−0.781274	−	0.624188i	$-0.785430\pi$
$769$	−485.507	+	280.307i	−0.631348	+	0.364509i	0.149926	+	0.988697i	$0.452097\pi$
$770$	135.720	−	78.3581i	0.176260	−	0.101764i
$771$	−275.096	−	421.865i	−0.356804	−	0.547166i

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.n (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.433498 + 0.750840i) q^{2} +(-0.162662 - 2.99559i) q^{3} +(1.62416 + 2.81313i) q^{4} +(-4.23652 - 7.33786i) q^{5} +(2.31972 + 1.17645i) q^{6} +(-3.54375 - 2.04598i) q^{7} -6.28426 q^{8} +(-8.94708 + 0.974539i) q^{9} +7.34608 q^{10} +(-2.60673 + 4.51499i) q^{11} +(8.16278 - 5.32290i) q^{12} +(5.26488 - 11.8862i) q^{13} +(3.07241 - 1.77386i) q^{14} +(-21.2921 + 13.8844i) q^{15} +(-3.77243 + 6.53403i) q^{16} -29.9878i q^{17} +(3.14682 - 7.14029i) q^{18} +3.71422i q^{19} +(13.7616 - 23.8357i) q^{20} +(-5.55248 + 10.9484i) q^{21} +(-2.26002 - 3.91448i) q^{22} +(15.2009 - 8.77627i) q^{23} +(1.02221 + 18.8250i) q^{24} +(-23.3961 + 40.5233i) q^{25} +(6.64230 + 9.10571i) q^{26} +(4.37467 + 26.6432i) q^{27} -13.2920i q^{28} +(7.85403 + 4.53453i) q^{29} +(-1.19493 - 22.0058i) q^{30} +(35.3345 - 20.4004i) q^{31} +(-15.8392 - 27.4343i) q^{32} +(13.9491 + 7.07427i) q^{33} +(22.5161 + 12.9997i) q^{34} +34.6714i q^{35} +(-17.2730 - 23.5865i) q^{36} +36.3463i q^{37} +(-2.78878 - 1.61011i) q^{38} +(-36.4625 - 13.8380i) q^{39} +(26.6234 + 46.1130i) q^{40} +(22.3968 + 38.7924i) q^{41} +(-5.81351 - 8.91514i) q^{42} +(7.68187 - 13.3054i) q^{43} -16.9350 q^{44} +(45.0555 + 61.5238i) q^{45} +15.2180i q^{46} +(-16.4364 + 28.4687i) q^{47} +(20.1869 + 10.2378i) q^{48} +(-16.1279 - 27.9344i) q^{49} +(-20.2844 - 35.1335i) q^{50} +(-89.8312 + 4.87789i) q^{51} +(41.9883 - 4.49427i) q^{52} +0.397357i q^{53} +(-21.9012 - 8.26511i) q^{54} +44.1738 q^{55} +(22.2698 + 12.8575i) q^{56} +(11.1263 - 0.604164i) q^{57} +(-6.80941 + 3.93141i) q^{58} +(-50.1902 - 86.9320i) q^{59} +(-73.6405 - 37.3468i) q^{60} +(-10.8878 + 18.8583i) q^{61} +35.3741i q^{62} +(33.7001 + 14.8521i) q^{63} -2.71439 q^{64} +(-109.524 + 11.7230i) q^{65} +(-11.3585 + 7.40683i) q^{66} +(70.7519 - 40.8486i) q^{67} +(84.3596 - 48.7050i) q^{68} +(-28.7627 - 44.1082i) q^{69} +(-26.0326 - 15.0300i) q^{70} +50.0834 q^{71} +(56.2258 - 6.12426i) q^{72} -135.863i q^{73} +(-27.2902 - 15.7560i) q^{74} +(125.197 + 63.4936i) q^{75} +(-10.4486 + 6.03249i) q^{76} +(18.4752 - 10.6667i) q^{77} +(26.1965 - 21.3787i) q^{78} +(39.5882 - 68.5688i) q^{79} +63.9278 q^{80} +(79.1005 - 17.4386i) q^{81} -38.8358 q^{82} +(-35.2829 + 61.1118i) q^{83} +(-39.8174 + 2.16211i) q^{84} +(-220.047 + 127.044i) q^{85} +(6.66015 + 11.5357i) q^{86} +(12.3060 - 24.2650i) q^{87} +(16.3814 - 28.3734i) q^{88} +46.8117 q^{89} +(-65.7260 + 7.15904i) q^{90} +(-42.9763 + 31.3497i) q^{91} +(49.3775 + 28.5081i) q^{92} +(-66.8587 - 102.529i) q^{93} +(-14.2503 - 24.6823i) q^{94} +(27.2544 - 15.7354i) q^{95} +(-79.6054 + 51.9102i) q^{96} +(-72.9925 - 42.1423i) q^{97} +27.9656 q^{98} +(18.9226 - 42.9363i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q - 4 q^{3} - 50 q^{4} + 4 q^{9} + 8 q^{10} - 38 q^{12} - 6 q^{13} - 6 q^{14} - 90 q^{16} + 14 q^{22} + 138 q^{23} - 92 q^{25} - 76 q^{27} + 48 q^{29} + 186 q^{30} - 154 q^{36} + 324 q^{38} - 2 q^{39}+ \cdots + 504 q^{95}+O(q^{100}) \) 52 * q - 4 * q^3 - 50 * q^4 + 4 * q^9 + 8 * q^10 - 38 * q^12 - 6 * q^13 - 6 * q^14 - 90 * q^16 + 14 * q^22 + 138 * q^23 - 92 * q^25 - 76 * q^27 + 48 * q^29 + 186 * q^30 - 154 * q^36 + 324 * q^38 - 2 * q^39 - 68 * q^40 - 216 * q^42 + 62 * q^43 + 230 * q^48 + 70 * q^49 + 90 * q^51 - 4 * q^52 + 92 * q^55 - 276 * q^56 + 12 * q^61 + 12 * q^64 - 588 * q^65 + 762 * q^66 - 144 * q^68 - 414 * q^69 + 342 * q^74 - 620 * q^75 - 510 * q^77 - 162 * q^78 - 24 * q^79 + 532 * q^81 - 292 * q^82 - 330 * q^87 - 62 * q^88 + 258 * q^90 + 264 * q^91 - 396 * q^92 - 160 * q^94 + 504 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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