LMFDB - Embedded newform 117.3.u.a.68.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [117,3,Mod(68,117)]

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([5, 2]))

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

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

chi := DirichletCharacter("117.68");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 117 = 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	117.u (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			68.14
Character	$\chi$	$=$	117.68
Dual form			117.3.u.a.74.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.325651 - 0.188014i) q^{2} +(0.894719 - 2.86347i) q^{3} +(-1.92930 - 3.34165i) q^{4} +(0.994641 + 0.574256i) q^{5} +(-0.829740 + 0.764272i) q^{6} +5.14423 q^{7} +2.95506i q^{8} +(-7.39896 - 5.12401i) q^{9} +(-0.215937 - 0.374014i) q^{10} +(-13.0534 - 7.53640i) q^{11} +(-11.2949 + 2.53467i) q^{12} +(-7.81749 - 10.3869i) q^{13} +(-1.67522 - 0.967190i) q^{14} +(2.53429 - 2.33433i) q^{15} +(-7.16161 + 12.4043i) q^{16} +(24.4307 + 14.1051i) q^{17} +(1.44609 + 3.05975i) q^{18} +(10.6901 - 18.5158i) q^{19} -4.43165i q^{20} +(4.60264 - 14.7304i) q^{21} +(2.83390 + 4.90847i) q^{22} +14.5409i q^{23} +(8.46174 + 2.64395i) q^{24} +(-11.8405 - 20.5083i) q^{25} +(0.592890 + 4.85229i) q^{26} +(-21.2924 + 16.6022i) q^{27} +(-9.92477 - 17.1902i) q^{28} +(46.7423 + 26.9867i) q^{29} +(-1.26418 + 0.283692i) q^{30} +(20.6940 - 35.8431i) q^{31} +(14.9010 - 8.60310i) q^{32} +(-33.2594 + 30.6352i) q^{33} +(-5.30391 - 9.18664i) q^{34} +(5.11666 + 2.95411i) q^{35} +(-2.84781 + 34.6105i) q^{36} +(26.5470 + 45.9807i) q^{37} +(-6.96249 + 4.01980i) q^{38} +(-36.7370 + 13.0918i) q^{39} +(-1.69696 + 2.93923i) q^{40} -28.8607i q^{41} +(-4.26838 + 3.93159i) q^{42} +42.0583 q^{43} +58.1599i q^{44} +(-4.41681 - 9.34544i) q^{45} +(2.73390 - 4.73525i) q^{46} +(3.48340 - 2.01114i) q^{47} +(29.1117 + 31.6054i) q^{48} -22.5369 q^{49} +8.90471i q^{50} +(62.2480 - 57.3365i) q^{51} +(-19.6269 + 46.1627i) q^{52} +12.6540i q^{53} +(10.0553 - 1.40322i) q^{54} +(-8.65564 - 14.9920i) q^{55} +15.2015i q^{56} +(-43.4549 - 47.1774i) q^{57} +(-10.1478 - 17.5765i) q^{58} +(-19.0560 + 11.0020i) q^{59} +(-12.6899 - 3.96508i) q^{60} +10.3485 q^{61} +(-13.4780 + 7.78155i) q^{62} +(-38.0619 - 26.3591i) q^{63} +50.8229 q^{64} +(-1.81087 - 14.8204i) q^{65} +(16.5908 - 3.72311i) q^{66} +74.0229 q^{67} -108.852i q^{68} +(41.6375 + 13.0100i) q^{69} +(-1.11083 - 1.92401i) q^{70} +(-34.1908 - 19.7401i) q^{71} +(15.1418 - 21.8644i) q^{72} -65.2913 q^{73} -19.9649i q^{74} +(-69.3188 + 15.5557i) q^{75} -82.4979 q^{76} +(-67.1498 - 38.7690i) q^{77} +(14.4249 + 2.64371i) q^{78} +(-9.78025 - 16.9399i) q^{79} +(-14.2465 + 8.22520i) q^{80} +(28.4891 + 75.8246i) q^{81} +(-5.42622 + 9.39850i) q^{82} +(71.7112 - 41.4025i) q^{83} +(-58.1036 + 13.0389i) q^{84} +(16.1998 + 28.0589i) q^{85} +(-13.6963 - 7.90758i) q^{86} +(119.097 - 109.700i) q^{87} +(22.2705 - 38.5737i) q^{88} +(-134.830 + 77.8441i) q^{89} +(-0.318741 + 3.87377i) q^{90} +(-40.2150 - 53.4324i) q^{91} +(48.5905 - 28.0538i) q^{92} +(-84.1203 - 91.3262i) q^{93} -1.51249 q^{94} +(21.2657 - 12.2777i) q^{95} +(-11.3025 - 50.3660i) q^{96} +19.4397 q^{97} +(7.33915 + 4.23726i) q^{98} +(57.9651 + 122.647i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q - 3 q^{2} - q^{3} + 49 q^{4} - 6 q^{5} - 3 q^{6} + 2 q^{7} - 3 q^{9} - 6 q^{10} + 33 q^{11} - 39 q^{12} + 4 q^{13} - 6 q^{14} - 28 q^{15} - 83 q^{16} + 34 q^{18} + 5 q^{19} - 91 q^{21} - 15 q^{22}+ \cdots + 522 q^{99}+O(q^{100}) $ 52 * q - 3 * q^2 - q^3 + 49 * q^4 - 6 * q^5 - 3 * q^6 + 2 * q^7 - 3 * q^9 - 6 * q^10 + 33 * q^11 - 39 * q^12 + 4 * q^13 - 6 * q^14 - 28 * q^15 - 83 * q^16 + 34 * q^18 + 5 * q^19 - 91 * q^21 - 15 * q^22 + 36 * q^24 + 88 * q^25 + 132 * q^26 - 34 * q^27 - 22 * q^28 - 30 * q^29 + 31 * q^30 + 14 * q^31 - 63 * q^32 - 112 * q^33 - 6 * q^34 - 228 * q^35 + 47 * q^36 - 13 * q^37 - 192 * q^38 + 147 * q^39 + 72 * q^40 - 84 * q^42 + 62 * q^43 - 107 * q^45 + 6 * q^46 - 69 * q^47 - 58 * q^48 + 246 * q^49 + 235 * q^51 + 112 * q^52 + 444 * q^54 - 27 * q^55 + 189 * q^57 - 105 * q^58 - 435 * q^59 + 213 * q^60 - 16 * q^61 - 471 * q^62 - 170 * q^63 - 98 * q^64 - 435 * q^65 - 576 * q^66 + 68 * q^67 + 152 * q^69 - 57 * q^70 - 144 * q^71 + 513 * q^72 - 106 * q^73 + 98 * q^75 + 158 * q^76 + 282 * q^77 - 433 * q^78 - 25 * q^79 + 1050 * q^80 + 9 * q^81 + 81 * q^82 + 219 * q^83 - 172 * q^84 + 54 * q^85 - 24 * q^86 + 325 * q^87 - 15 * q^88 - 99 * q^89 + 183 * q^90 + 2 * q^91 + 888 * q^92 - 171 * q^93 - 606 * q^94 - 258 * q^95 - 439 * q^96 - 424 * q^97 + 405 * q^98 + 522 * q^99

Character values

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

$n$	$28$	$92$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.325651	−	0.188014i	−0.162825	−	0.0940072i	0.416373	−	0.909194i	$-0.363301\pi$
$2$	−0.325651	−	0.188014i	−0.162825	−	0.0940072i	−0.579198	+	0.815187i	$0.696634\pi$
$3$	0.894719	−	2.86347i	0.298240	−	0.954491i
$3$	0.894719	−	2.86347i	0.298240	−	0.954491i
$4$	−1.92930	−	3.34165i	−0.482325	−	0.835412i
$5$	0.994641	+	0.574256i	0.198928	+	0.114851i	0.596155	−	0.802869i	$-0.296694\pi$
$5$	0.994641	+	0.574256i	0.198928	+	0.114851i	−0.397227	+	0.917720i	$0.630028\pi$
$6$	−0.829740	+	0.764272i	−0.138290	+	0.127379i
$7$	5.14423			0.734890			0.367445	−	0.930045i	$-0.380233\pi$
$7$	5.14423			0.734890			0.367445	+	0.930045i	$0.380233\pi$
$8$			2.95506i			0.369383i
$9$	−7.39896	−	5.12401i	−0.822106	−	0.569334i
$10$	−0.215937	−	0.374014i	−0.0215937	−	0.0374014i
$11$	−13.0534	−	7.53640i	−1.18667	−	0.685127i	−0.229126	−	0.973397i	$-0.573587\pi$
$11$	−13.0534	−	7.53640i	−1.18667	−	0.685127i	−0.957549	+	0.288270i	$0.906920\pi$
$12$	−11.2949	+	2.53467i	−0.941242	+	0.211222i
$13$	−7.81749	−	10.3869i	−0.601345	−	0.798989i
$13$	−7.81749	−	10.3869i	−0.601345	−	0.798989i
$14$	−1.67522	−	0.967190i	−0.119659	−	0.0690850i
$15$	2.53429	−	2.33433i	0.168953	−	0.155622i
$16$	−7.16161	+	12.4043i	−0.447601	+	0.775267i
$17$	24.4307	+	14.1051i	1.43710	+	0.829709i	0.997647	−	0.0685572i	$-0.0218396\pi$
$17$	24.4307	+	14.1051i	1.43710	+	0.829709i	0.439451	+	0.898266i	$0.355173\pi$
$18$	1.44609	+	3.05975i	0.0803382	+	0.169986i
$19$	10.6901	−	18.5158i	0.562638	−	0.974518i	−0.434627	−	0.900611i	$-0.643120\pi$
$19$	10.6901	−	18.5158i	0.562638	−	0.974518i	0.997265	−	0.0739073i	$-0.0235469\pi$
$20$		−	4.43165i		−	0.221583i
$21$	4.60264	−	14.7304i	0.219173	−	0.701446i
$22$	2.83390	+	4.90847i	0.128814	+	0.223112i
$23$			14.5409i			0.632213i	0.948724	+	0.316106i	$0.102376\pi$
$23$			14.5409i			0.632213i	−0.948724	+	0.316106i	$0.897624\pi$
$24$	8.46174	+	2.64395i	0.352573	+	0.110165i
$25$	−11.8405	−	20.5083i	−0.473618	−	0.820331i
$26$	0.592890	+	4.85229i	0.0228035	+	0.186627i
$27$	−21.2924	+	16.6022i	−0.788609	+	0.614895i
$28$	−9.92477	−	17.1902i	−0.354456	−	0.613936i
$29$	46.7423	+	26.9867i	1.61180	+	0.930576i	0.988952	+	0.148236i	$0.0473596\pi$
$29$	46.7423	+	26.9867i	1.61180	+	0.930576i	0.622852	+	0.782339i	$0.285974\pi$
$30$	−1.26418	+	0.283692i	−0.0421394	+	0.00945641i
$31$	20.6940	−	35.8431i	0.667549	−	1.15623i	−0.311039	−	0.950397i	$-0.600677\pi$
$31$	20.6940	−	35.8431i	0.667549	−	1.15623i	0.978588	−	0.205831i	$-0.0659897\pi$
$32$	14.9010	−	8.60310i	0.465656	−	0.268847i
$33$	−33.2594	+	30.6352i	−1.00786	+	0.928338i
$34$	−5.30391	−	9.18664i	−0.155997	−	0.270195i
$35$	5.11666	+	2.95411i	0.146190	+	0.0844030i
$36$	−2.84781	+	34.6105i	−0.0791059	+	0.961402i
$37$	26.5470	+	45.9807i	0.717486	+	1.24272i	0.961993	+	0.273074i	$0.0880405\pi$
$37$	26.5470	+	45.9807i	0.717486	+	1.24272i	−0.244507	+	0.969647i	$0.578626\pi$
$38$	−6.96249	+	4.01980i	−0.183223	+	0.105784i
$39$	−36.7370	+	13.0918i	−0.941973	+	0.335688i
$40$	−1.69696	+	2.93923i	−0.0424241	+	0.0734806i
$41$		−	28.8607i		−	0.703919i	−0.936015	−	0.351959i	$-0.885516\pi$
$41$		−	28.8607i		−	0.703919i	0.936015	−	0.351959i	$-0.114484\pi$
$42$	−4.26838	+	3.93159i	−0.101628	+	0.0936093i
$43$	42.0583			0.978101			0.489050	−	0.872256i	$-0.337343\pi$
$43$	42.0583			0.978101			0.489050	+	0.872256i	$0.337343\pi$
$44$			58.1599i			1.32182i
$45$	−4.41681	−	9.34544i	−0.0981513	−	0.207676i
$46$	2.73390	−	4.73525i	0.0594326	−	0.102940i
$47$	3.48340	−	2.01114i	0.0741148	−	0.0427902i	−0.462485	−	0.886627i	$-0.653042\pi$
$47$	3.48340	−	2.01114i	0.0741148	−	0.0427902i	0.536599	+	0.843837i	$0.319709\pi$
$48$	29.1117	+	31.6054i	0.606493	+	0.658446i
$49$	−22.5369			−0.459937
$50$			8.90471i			0.178094i
$51$	62.2480	−	57.3365i	1.22055	−	1.12425i
$52$	−19.6269	+	46.1627i	−0.377441	+	0.887744i
$53$			12.6540i			0.238755i	0.992849	+	0.119378i	$0.0380899\pi$
$53$			12.6540i			0.238755i	−0.992849	+	0.119378i	$0.961910\pi$
$54$	10.0553	−	1.40322i	0.186210	−	0.0259855i
$55$	−8.65564	−	14.9920i	−0.157375	−	0.272582i
$56$			15.2015i			0.271456i
$57$	−43.4549	−	47.1774i	−0.762368	−	0.827673i
$58$	−10.1478	−	17.5765i	−0.174962	−	0.303043i
$59$	−19.0560	+	11.0020i	−0.322983	+	0.186474i	−0.652721	−	0.757598i	$-0.726373\pi$
$59$	−19.0560	+	11.0020i	−0.322983	+	0.186474i	0.329739	+	0.944072i	$0.393039\pi$
$60$	−12.6899	−	3.96508i	−0.211499	−	0.0660847i
$61$	10.3485			0.169648			0.0848239	−	0.996396i	$-0.472967\pi$
$61$	10.3485			0.169648			0.0848239	+	0.996396i	$0.472967\pi$
$62$	−13.4780	+	7.78155i	−0.217388	+	0.125509i
$63$	−38.0619	−	26.3591i	−0.604158	−	0.418398i
$64$	50.8229			0.794107
$65$	−1.81087	−	14.8204i	−0.0278596	−	0.228007i
$66$	16.5908	−	3.72311i	0.251376	−	0.0564108i
$67$	74.0229			1.10482			0.552410	−	0.833573i	$-0.313708\pi$
$67$	74.0229			1.10482			0.552410	+	0.833573i	$0.313708\pi$
$68$		−	108.852i		−	1.60076i
$69$	41.6375	+	13.0100i	0.603441	+	0.188551i
$70$	−1.11083	−	1.92401i	−0.0158690	−	0.0274859i
$71$	−34.1908	−	19.7401i	−0.481561	−	0.278029i	0.239506	−	0.970895i	$-0.423015\pi$
$71$	−34.1908	−	19.7401i	−0.481561	−	0.278029i	−0.721067	+	0.692865i	$0.756348\pi$
$72$	15.1418	−	21.8644i	0.210302	−	0.303672i
$73$	−65.2913			−0.894402			−0.447201	−	0.894434i	$-0.647579\pi$
$73$	−65.2913			−0.894402			−0.447201	+	0.894434i	$0.647579\pi$
$74$		−	19.9649i		−	0.269795i
$75$	−69.3188	+	15.5557i	−0.924250	+	0.207409i
$76$	−82.4979			−1.08550
$77$	−67.1498	−	38.7690i	−0.872076	−	0.503493i
$78$	14.4249	+	2.64371i	0.184934	+	0.0338937i
$79$	−9.78025	−	16.9399i	−0.123801	−	0.214429i	0.797463	−	0.603368i	$-0.206175\pi$
$79$	−9.78025	−	16.9399i	−0.123801	−	0.214429i	−0.921263	+	0.388939i	$0.872842\pi$
$80$	−14.2465	+	8.22520i	−0.178081	+	0.102815i
$81$	28.4891	+	75.8246i	0.351717	+	0.936106i
$82$	−5.42622	+	9.39850i	−0.0661735	+	0.114616i
$83$	71.7112	−	41.4025i	0.863991	−	0.498825i	−0.00135589	−	0.999999i	$-0.500432\pi$
$83$	71.7112	−	41.4025i	0.863991	−	0.498825i	0.865347	+	0.501174i	$0.167098\pi$
$84$	−58.1036	+	13.0389i	−0.691709	+	0.155225i
$85$	16.1998	+	28.0589i	0.190586	+	0.330105i
$86$	−13.6963	−	7.90758i	−0.159260	−	0.0919486i
$87$	119.097	−	109.700i	1.36893	−	1.26092i
$88$	22.2705	−	38.5737i	0.253074	−	0.438337i
$89$	−134.830	+	77.8441i	−1.51494	+	0.874653i	−0.515097	+	0.857132i	$0.672244\pi$
$89$	−134.830	+	77.8441i	−1.51494	+	0.874653i	−0.999846	+	0.0175212i	$0.994423\pi$
$90$	−0.318741	+	3.87377i	−0.00354157	+	0.0430419i
$91$	−40.2150	−	53.4324i	−0.441923	−	0.587169i
$92$	48.5905	−	28.0538i	0.528158	−	0.304932i
$93$	−84.1203	−	91.3262i	−0.904520	−	0.982002i
$94$	−1.51249			−0.0160904
$95$	21.2657	−	12.2777i	0.223849	−	0.129239i
$96$	−11.3025	−	50.3660i	−0.117735	−	0.524646i
$97$	19.4397			0.200409			0.100205	−	0.994967i	$-0.468050\pi$
$97$	19.4397			0.200409			0.100205	+	0.994967i	$0.468050\pi$
$98$	7.33915	+	4.23726i	0.0748893	+	0.0432374i
$99$	57.9651	+	122.647i	0.585507	+	1.23886i
$100$	−45.6876	+	79.1333i	−0.456876	+	0.791333i
$101$	71.7887	+	41.4472i	0.710779	+	0.410369i	0.811349	−	0.584561i	$-0.198733\pi$
$101$	71.7887	+	41.4472i	0.710779	+	0.410369i	−0.100570	+	0.994930i	$0.532067\pi$
$102$	−31.0512	+	6.96814i	−0.304424	+	0.0683151i
$103$	−38.2718	+	66.2886i	−0.371571	+	0.643579i	−0.989807	−	0.142413i	$-0.954514\pi$
$103$	−38.2718	+	66.2886i	−0.371571	+	0.643579i	0.618237	+	0.785992i	$0.287847\pi$
$104$	30.6938	−	23.1012i	0.295133	−	0.222127i
$105$	13.0370	−	12.0083i	0.124162	−	0.114365i
$106$	2.37914	−	4.12079i	0.0224447	−	0.0388754i
$107$	−20.6786	+	11.9388i	−0.193258	+	0.111578i	−0.593507	−	0.804829i	$-0.702257\pi$
$107$	−20.6786	+	11.9388i	−0.193258	+	0.111578i	0.400249	+	0.916407i	$0.368924\pi$
$108$	96.5581	+	39.1213i	0.894057	+	0.362234i
$109$	5.84222			0.0535983			0.0267992	−	0.999641i	$-0.491469\pi$
$109$	5.84222			0.0535983			0.0267992	+	0.999641i	$0.491469\pi$
$110$			6.50955i			0.0591777i
$111$	155.417	−	34.8767i	1.40015	−	0.314205i
$112$	−36.8410	+	63.8104i	−0.328937	+	0.569736i
$113$	−115.545	+	66.7097i	−1.02252	+	0.590351i	−0.914832	−	0.403834i	$-0.867678\pi$
$113$	−115.545	+	66.7097i	−1.02252	+	0.590351i	−0.107686	+	0.994185i	$0.534344\pi$
$114$	5.28111	+	23.5335i	0.0463255	+	0.206434i
$115$	−8.35020	+	14.4630i	−0.0726104	+	0.125765i
$116$		−	208.262i		−	1.79536i
$117$	4.61891	+	116.909i	0.0394778	+	0.999220i
$118$	8.27412			0.0701197
$119$	125.677	+	72.5597i	1.05611	+	0.609745i
$120$	6.89809	+	7.48899i	0.0574841	+	0.0624082i
$121$	53.0946	+	91.9625i	0.438798	+	0.760020i
$122$	−3.37000	−	1.94567i	−0.0276230	−	0.0159481i
$123$	−82.6417	−	25.8222i	−0.671884	−	0.209936i
$124$	−159.700			−1.28790
$125$		−	55.9106i		−	0.447285i
$126$	7.43901	+	15.7400i	0.0590397	+	0.124921i
$127$	5.22700	+	9.05343i	0.0411575	+	0.0712869i	0.885870	−	0.463933i	$-0.153562\pi$
$127$	5.22700	+	9.05343i	0.0411575	+	0.0712869i	−0.844713	+	0.535220i	$0.820229\pi$
$128$	−76.1545	−	43.9678i	−0.594957	−	0.343499i
$129$	37.6304	−	120.433i	0.291708	−	0.933588i
$130$	−2.19674	+	5.16676i	−0.0168980	+	0.0397443i
$131$	−74.2522	−	42.8695i	−0.566811	−	0.327248i	0.189064	−	0.981965i	$-0.439455\pi$
$131$	−74.2522	−	42.8695i	−0.566811	−	0.327248i	−0.755875	+	0.654716i	$0.772788\pi$
$132$	166.539	+	52.0368i	1.26166	+	0.394218i
$133$	54.9925	−	95.2497i	0.413477	−	0.716164i
$134$	−24.1056	−	13.9174i	−0.179893	−	0.103861i
$135$	−30.7122	+	4.28587i	−0.227498	+	0.0317472i
$136$	−41.6813	+	72.1942i	−0.306480	+	0.530839i
$137$		−	111.047i		−	0.810558i	−0.914193	−	0.405279i	$-0.867174\pi$
$137$		−	111.047i		−	0.810558i	0.914193	−	0.405279i	$-0.132826\pi$
$138$	−11.1132	−	12.0652i	−0.0805304	−	0.0874287i
$139$	101.422	+	175.667i	0.729652	+	1.26379i	0.957030	+	0.289988i	$0.0936514\pi$
$139$	101.422	+	175.667i	0.729652	+	1.26379i	−0.227378	+	0.973807i	$0.573015\pi$
$140$		−	22.7974i		−	0.162839i
$141$	−2.64218	−	11.7740i	−0.0187389	−	0.0835036i
$142$	7.42285	+	12.8567i	0.0522736	+	0.0905405i
$143$	23.7655	+	194.500i	0.166192	+	1.36014i
$144$	116.548	−	55.0825i	0.809361	−	0.382518i
$145$	30.9945	+	53.6841i	0.213755	+	0.370235i
$146$	21.2622	+	12.2757i	0.145631	+	0.0840803i
$147$	−20.1642	+	64.5338i	−0.137171	+	0.439005i
$148$	102.434	−	177.421i	0.692123	−	1.19879i
$149$	−203.709	+	117.612i	−1.36718	+	0.789340i	−0.990567	−	0.137032i	$-0.956244\pi$
$149$	−203.709	+	117.612i	−1.36718	+	0.789340i	−0.376610	+	0.926372i	$0.622910\pi$
$150$	25.4984	+	7.96721i	0.169989	+	0.0531148i
$151$	133.267	+	230.825i	0.882561	+	1.52864i	0.848483	+	0.529222i	$0.177516\pi$
$151$	133.267	+	230.825i	0.882561	+	1.52864i	0.0340779	+	0.999419i	$0.489151\pi$
$152$	54.7155	+	31.5900i	0.359970	+	0.207829i
$153$	−108.487	−	229.546i	−0.709066	−	1.50030i
$154$	14.5783	+	25.2503i	0.0946640	+	0.163963i
$155$	41.1662	−	23.7673i	0.265588	−	0.153338i
$156$	114.625	+	97.5038i	0.734775	+	0.625025i
$157$	29.0426	−	50.3033i	0.184985	−	0.320403i	−0.758587	−	0.651572i	$-0.774110\pi$
$157$	29.0426	−	50.3033i	0.184985	−	0.320403i	0.943571	+	0.331169i	$0.107443\pi$
$158$			7.35531i			0.0465526i
$159$	36.2344	+	11.3218i	0.227890	+	0.0712062i
$160$	19.7615			0.123510
$161$			74.8017i			0.464607i
$162$	4.97863	−	30.0487i	0.0307323	−	0.185486i
$163$	−8.10087	+	14.0311i	−0.0496986	+	0.0860805i	−0.889805	−	0.456342i	$-0.849159\pi$
$163$	−8.10087	+	14.0311i	−0.0496986	+	0.0860805i	0.840106	+	0.542422i	$0.182493\pi$
$164$	−96.4422	+	55.6809i	−0.588062	+	0.339518i
$165$	−50.6736	+	11.3716i	−0.307113	+	0.0689186i
$166$	−31.1371			−0.187573
$167$		−	31.2855i		−	0.187338i	−0.995603	−	0.0936691i	$-0.970140\pi$
$167$		−	31.2855i		−	0.187338i	0.995603	−	0.0936691i	$-0.0298596\pi$
$168$	43.5291	+	13.6011i	0.259102	+	0.0809589i
$169$	−46.7737	+	162.398i	−0.276768	+	0.960937i
$170$		−	12.1832i		−	0.0716659i
$171$	−173.971	+	82.2216i	−1.01737	+	0.480828i
$172$	−81.1432	−	140.544i	−0.471763	−	0.817117i
$173$		−	4.32233i		−	0.0249846i	−0.999922	−	0.0124923i	$-0.996023\pi$
$173$		−	4.32233i		−	0.0249846i	0.999922	−	0.0124923i	$-0.00397652\pi$
$174$	−59.4092	+	13.3319i	−0.341432	+	0.0766201i
$175$	−60.9101	−	105.499i	−0.348057	−	0.602853i
$176$	186.967	−	107.945i	1.06231	−	0.613327i
$177$	14.4541	+	64.4100i	0.0816617	+	0.363898i
$178$	58.5433			0.328895
$179$	1.59962	−	0.923541i	0.00893642	−	0.00515945i	−0.495525	−	0.868594i	$-0.665024\pi$
$179$	1.59962	−	0.923541i	0.00893642	−	0.00515945i	0.504462	+	0.863434i	$0.331691\pi$
$180$	−22.7078	+	32.7896i	−0.126155	+	0.182164i
$181$	−10.7339			−0.0593032			−0.0296516	−	0.999560i	$-0.509440\pi$
$181$	−10.7339			−0.0593032			−0.0296516	+	0.999560i	$0.509440\pi$
$182$	3.04996	+	24.9613i	0.0167580	+	0.137150i
$183$	9.25901	−	29.6327i	0.0505957	−	0.161927i
$184$	−42.9692			−0.233529
$185$			60.9790i			0.329616i
$186$	10.2232	+	45.5563i	0.0549634	+	0.244926i
$187$	−212.603	−	368.239i	−1.13691	−	1.96919i
$188$	−13.4410	−	7.76019i	−0.0714949	−	0.0412776i
$189$	−109.533	+	85.4054i	−0.579541	+	0.451880i
$190$	−9.23357			−0.0485977
$191$		−	65.9244i		−	0.345154i	−0.984996	−	0.172577i	$-0.944791\pi$
$191$		−	65.9244i		−	0.345154i	0.984996	−	0.172577i	$-0.0552094\pi$
$192$	45.4722	−	145.530i	0.236834	−	0.757968i
$193$	−111.858			−0.579578			−0.289789	−	0.957091i	$-0.593585\pi$
$193$	−111.858			−0.579578			−0.289789	+	0.957091i	$0.593585\pi$
$194$	−6.33055	−	3.65494i	−0.0326317	−	0.0188399i
$195$	−44.0581	−	8.07473i	−0.225939	−	0.0414089i
$196$	43.4804	+	75.3103i	0.221839	+	0.384236i
$197$	−10.1710	+	5.87226i	−0.0516297	+	0.0298084i	−0.525593	−	0.850736i	$-0.676156\pi$
$197$	−10.1710	+	5.87226i	−0.0516297	+	0.0298084i	0.473963	+	0.880545i	$0.342823\pi$
$198$	4.18308	−	50.8385i	0.0211267	−	0.256760i
$199$	9.23826	−	16.0011i	0.0464234	−	0.0804077i	−0.841880	−	0.539665i	$-0.818551\pi$
$199$	9.23826	−	16.0011i	0.0464234	−	0.0804077i	0.888303	+	0.459257i	$0.151884\pi$
$200$	60.6032	−	34.9893i	0.303016	−	0.174946i
$201$	66.2297	−	211.963i	0.329501	−	1.05454i
$202$	−15.5854	−	26.9946i	−0.0771552	−	0.133637i
$203$	240.453	+	138.826i	1.18450	+	0.683871i
$204$	−311.694	−	97.3916i	−1.52791	−	0.477410i
$205$	16.5734	−	28.7060i	0.0808459	−	0.140029i
$206$	24.9265	−	14.3913i	0.121002	−	0.0698607i
$207$	74.5076	−	107.587i	0.359940	−	0.519746i
$208$	184.827	−	22.5836i	0.888593	−	0.108575i
$209$	−279.085	+	161.130i	−1.33534	+	0.770957i
$210$	−6.50324	+	1.45938i	−0.0309678	+	0.00694943i
$211$	26.1820			0.124085			0.0620426	−	0.998074i	$-0.480239\pi$
$211$	26.1820			0.124085			0.0620426	+	0.998074i	$0.480239\pi$
$212$	42.2853	−	24.4134i	0.199459	−	0.115158i
$213$	−87.1164	+	80.2427i	−0.408997	+	0.376726i
$214$	8.97868			0.0419565
$215$	41.8329	+	24.1523i	0.194572	+	0.112336i
$216$	−49.0604	−	62.9205i	−0.227132	−	0.291299i
$217$	106.455	−	184.385i	0.490575	−	0.849701i
$218$	−1.90252	−	1.09842i	−0.00872717	−	0.00503863i
$219$	−58.4174	+	186.960i	−0.266746	+	0.853698i
$220$	−33.3987	+	57.8482i	−0.151812	+	0.262946i
$221$	−44.4793	−	364.024i	−0.201264	−	1.64717i
$222$	−57.1688	−	17.8629i	−0.257517	−	0.0804637i
$223$	161.459	−	279.656i	0.724033	−	1.25406i	−0.235338	−	0.971914i	$-0.575620\pi$
$223$	161.459	−	279.656i	0.724033	−	1.25406i	0.959371	−	0.282149i	$-0.0910471\pi$
$224$	76.6542	−	44.2563i	0.342206	−	0.197573i
$225$	−17.4775	+	212.410i	−0.0776779	+	0.944046i
$226$	50.1696			0.221989
$227$		−	253.520i		−	1.11683i	−0.829563	−	0.558413i	$-0.811410\pi$
$227$		−	253.520i		−	1.11683i	0.829563	−	0.558413i	$-0.188590\pi$
$228$	−73.8124	+	236.230i	−0.323739	+	1.03610i
$229$	119.446	−	206.887i	0.521600	−	0.903437i	−0.478085	−	0.878314i	$-0.658669\pi$
$229$	119.446	−	206.887i	0.521600	−	0.903437i	0.999684	−	0.0251232i	$-0.00799781\pi$
$230$	5.43849	−	3.13992i	0.0236456	−	0.0136518i
$231$	−171.094	+	157.594i	−0.740667	+	0.682227i
$232$	−79.7474	+	138.126i	−0.343739	+	0.595373i
$233$		−	42.9145i		−	0.184182i	−0.995751	−	0.0920912i	$-0.970645\pi$
$233$		−	42.9145i		−	0.184182i	0.995751	−	0.0920912i	$-0.0293551\pi$
$234$	20.4764	−	38.9398i	0.0875060	−	0.166410i
$235$	4.61964			0.0196580
$236$	73.5294	+	42.4522i	0.311565	+	0.179882i
$237$	−57.2575	+	12.8490i	−0.241593	+	0.0542154i
$238$	−27.2845	−	47.2582i	−0.114641	−	0.198564i
$239$	67.0524	+	38.7127i	0.280554	+	0.161978i	0.633674	−	0.773600i	$-0.281546\pi$
$239$	67.0524	+	38.7127i	0.280554	+	0.161978i	−0.353120	+	0.935578i	$0.614879\pi$
$240$	10.8061	+	48.1536i	0.0450252	+	0.200640i
$241$	−95.7696			−0.397384			−0.198692	−	0.980062i	$-0.563669\pi$
$241$	−95.7696			−0.397384			−0.198692	+	0.980062i	$0.563669\pi$
$242$		−	39.9302i		−	0.165001i
$243$	242.611	−	13.7361i	0.998401	−	0.0565270i
$244$	−19.9654	−	34.5811i	−0.0818254	−	0.141726i
$245$	−22.4161	−	12.9419i	−0.0914943	−	0.0528243i
$246$	22.0574	+	23.9469i	0.0896642	+	0.0973450i
$247$	−275.891	+	33.7105i	−1.11697	+	0.136480i
$248$	105.919	+	61.1521i	0.427091	+	0.246581i
$249$	−54.3935	−	242.387i	−0.218448	−	0.973441i
$250$	−10.5120	+	18.2073i	−0.0420480	+	0.0728293i
$251$	365.360	+	210.940i	1.45562	+	0.840400i	0.998791	−	0.0491566i	$-0.0156533\pi$
$251$	365.360	+	210.940i	1.45562	+	0.840400i	0.456825	+	0.889557i	$0.348987\pi$
$252$	−14.6498	+	178.044i	−0.0581341	+	0.706524i
$253$	109.586	−	189.808i	0.433146	−	0.750231i
$254$		−	3.93101i		−	0.0154764i
$255$	94.8403	−	21.2829i	0.371923	−	0.0834624i
$256$	−85.1125	−	147.419i	−0.332471	−	0.575856i
$257$			388.354i			1.51110i	0.655089	+	0.755552i	$0.272631\pi$
$257$			388.354i			1.51110i	−0.655089	+	0.755552i	$0.727369\pi$
$258$	−34.8975	+	32.1440i	−0.135262	+	0.124589i
$259$	136.564	+	236.535i	0.527273	+	0.913264i
$260$	−46.0309	+	34.6444i	−0.177042	+	0.133248i
$261$	−207.564	−	439.181i	−0.795266	−	1.68269i
$262$	16.1202	+	27.9210i	0.0615275	+	0.106569i
$263$	138.032	+	79.6926i	0.524835	+	0.303014i	0.738911	−	0.673803i	$-0.235341\pi$
$263$	138.032	+	79.6926i	0.524835	+	0.303014i	−0.214076	+	0.976817i	$0.568674\pi$
$264$	−90.5288	−	98.2836i	−0.342912	−	0.372286i
$265$	−7.26665	+	12.5862i	−0.0274213	+	0.0474951i
$266$	−35.8167	+	20.6788i	−0.134649	+	0.0777397i
$267$	102.270	+	455.731i	0.383032	+	1.70686i
$268$	−142.813	−	247.359i	−0.532883	−	0.922980i
$269$	138.125	+	79.7468i	0.513478	+	0.296456i	0.734262	−	0.678866i	$-0.237528\pi$
$269$	138.125	+	79.7468i	0.513478	+	0.296456i	−0.220784	+	0.975323i	$0.570862\pi$
$270$	10.8073	+	4.37865i	0.0400269	+	0.0162172i
$271$	−96.7532	−	167.581i	−0.357023	−	0.618382i	0.630439	−	0.776239i	$-0.282875\pi$
$271$	−96.7532	−	167.581i	−0.357023	−	0.618382i	−0.987462	+	0.157857i	$0.949542\pi$
$272$	−349.926	+	202.030i	−1.28649	+	0.742757i
$273$	−188.983	+	67.3475i	−0.692247	+	0.246694i
$274$	−20.8784	+	36.1624i	−0.0761984	+	0.131979i
$275$			356.938i			1.29795i
$276$	−36.8563	−	164.238i	−0.133537	−	0.595065i
$277$	−321.962			−1.16232			−0.581159	−	0.813790i	$-0.697401\pi$
$277$	−321.962			−1.16232			−0.581159	+	0.813790i	$0.697401\pi$
$278$		−	76.2750i		−	0.274370i
$279$	−336.774	+	159.165i	−1.20708	+	0.570484i
$280$	−8.72957	+	15.1201i	−0.0311770	+	0.0540002i
$281$	−357.552	+	206.433i	−1.27243	+	0.734637i	−0.975444	−	0.220246i	$-0.929314\pi$
$281$	−357.552	+	206.433i	−1.27243	+	0.734637i	−0.296984	+	0.954883i	$0.595981\pi$
$282$	−1.35326	+	4.33098i	−0.00479878	+	0.0153581i
$283$	487.758			1.72353			0.861764	−	0.507310i	$-0.169360\pi$
$283$	487.758			1.72353			0.861764	+	0.507310i	$0.169360\pi$
$284$			152.338i			0.536403i
$285$	−16.1302	−	71.8788i	−0.0565971	−	0.252206i
$286$	28.8295	−	67.8072i	0.100803	−	0.237088i
$287$		−	148.466i		−	0.517303i
$288$	−154.334	−	12.6989i	−0.535883	−	0.0440934i
$289$	253.405	+	438.911i	0.876835	+	1.51872i
$290$		−	23.3097i		−	0.0803783i
$291$	17.3931	−	55.6650i	0.0597700	−	0.191289i
$292$	125.967	+	218.181i	0.431393	+	0.747194i
$293$	475.133	−	274.318i	1.62162	−	0.936240i	0.635128	−	0.772407i	$-0.280947\pi$
$293$	475.133	−	274.318i	1.62162	−	0.936240i	0.986488	−	0.163833i	$-0.0523859\pi$
$294$	18.6998	−	17.2243i	0.0636046	−	0.0585861i
$295$	−25.2718			−0.0856671
$296$	−135.876	+	78.4479i	−0.459040	+	0.265027i
$297$	403.060	−	56.2468i	1.35710	−	0.189383i
$298$	88.4508			0.296815
$299$	151.034	−	113.673i	0.505131	−	0.380178i
$300$	185.718	+	201.627i	0.619062	+	0.672091i
$301$	216.358			0.718797
$302$		−	100.224i		−	0.331869i
$303$	182.914	−	168.481i	0.603676	−	0.556044i
$304$	153.117	+	265.206i	0.503674	+	0.872390i
$305$	10.2931	+	5.94270i	0.0337477	+	0.0194843i
$306$	−7.82902	+	95.1488i	−0.0255850	+	0.310944i
$307$	78.3446			0.255194			0.127597	−	0.991826i	$-0.459274\pi$
$307$	78.3446			0.255194			0.127597	+	0.991826i	$0.459274\pi$
$308$			299.188i			0.971390i
$309$	155.573	+	168.900i	0.503473	+	0.546602i
$310$	−17.8744			−0.0576594
$311$	−390.829	−	225.645i	−1.25668	−	0.725547i	−0.284255	−	0.958749i	$-0.591746\pi$
$311$	−390.829	−	225.645i	−1.25668	−	0.725547i	−0.972428	+	0.233202i	$0.925080\pi$
$312$	−38.6872	−	108.560i	−0.123998	−	0.347949i
$313$	117.824	+	204.077i	0.376435	+	0.652004i	0.990541	−	0.137220i	$-0.0438166\pi$
$313$	117.824	+	204.077i	0.376435	+	0.652004i	−0.614106	+	0.789224i	$0.710483\pi$
$314$	−18.9155	+	10.9209i	−0.0602404	+	0.0347798i
$315$	−22.7211	−	48.0751i	−0.0721305	−	0.152619i
$316$	−37.7381	+	65.3643i	−0.119424	+	0.206849i
$317$	107.908	−	62.3008i	0.340404	−	0.196532i	−0.320047	−	0.947402i	$-0.603699\pi$
$317$	107.908	−	62.3008i	0.340404	−	0.196532i	0.660451	+	0.750869i	$0.270365\pi$
$318$	−9.67111	−	10.4995i	−0.0304123	−	0.0330174i
$319$	−406.765	−	704.537i	−1.27512	−	2.20858i
$320$	50.5505	+	29.1853i	0.157970	+	0.0912042i
$321$	15.6849	+	69.8946i	0.0488627	+	0.217740i
$322$	14.0638	−	24.3592i	0.0436764	−	0.0756498i
$323$	522.334	−	301.570i	1.61713	−	0.933652i
$324$	198.415	−	241.489i	0.612392	−	0.745337i
$325$	−120.454	+	283.308i	−0.370628	+	0.871718i
$326$	5.27611	−	3.04616i	0.0161844	−	0.00934406i
$327$	5.22714	−	16.7290i	0.0159851	−	0.0511591i
$328$	85.2851			0.260015
$329$	17.9194	−	10.3458i	0.0544662	−	0.0314461i
$330$	18.6399	+	5.82421i	0.0564846	+	0.0176491i
$331$	334.583			1.01083			0.505413	−	0.862878i	$-0.331340\pi$
$331$	334.583			1.01083			0.505413	+	0.862878i	$0.331340\pi$
$332$	−276.705	−	159.756i	−0.833449	−	0.481192i
$333$	39.1856	−	476.236i	0.117674	−	1.43014i
$334$	−5.88212	+	10.1881i	−0.0176111	+	0.0305034i
$335$	73.6262	+	42.5081i	0.219780	+	0.126890i
$336$	149.757	+	162.586i	0.445706	+	0.483886i
$337$	−185.957	+	322.088i	−0.551802	+	0.955750i	0.446342	+	0.894862i	$0.352726\pi$
$337$	−185.957	+	322.088i	−0.551802	+	0.955750i	−0.998145	+	0.0608873i	$0.980607\pi$
$338$	45.7651	−	44.0910i	0.135400	−	0.130447i
$339$	87.6415	+	390.545i	0.258530	+	1.15205i
$340$	62.5087	−	108.268i	0.183849	−	0.318436i
$341$	−540.255	+	311.916i	−1.58433	+	0.914711i
$342$	72.1126	+	5.93356i	0.210856	+	0.0173496i
$343$	−368.002			−1.07289
$344$			124.285i			0.361294i
$345$	33.9432	+	36.8509i	0.0983862	+	0.106814i
$346$	−0.812660	+	1.40757i	−0.00234873	+	0.00406812i
$347$	−147.917	+	85.4000i	−0.426274	+	0.246110i	−0.697758	−	0.716333i	$-0.745819\pi$
$347$	−147.917	+	85.4000i	−0.426274	+	0.246110i	0.271484	+	0.962443i	$0.412486\pi$
$348$	−596.352	−	186.336i	−1.71366	−	0.535448i
$349$	−67.3588	+	116.669i	−0.193005	+	0.334295i	−0.946245	−	0.323452i	$-0.895157\pi$
$349$	−67.3588	+	116.669i	−0.193005	+	0.334295i	0.753240	+	0.657746i	$0.228490\pi$
$350$			45.8079i			0.130880i
$351$	338.898	+	91.3744i	0.965521	+	0.260326i
$352$	−259.345			−0.736777
$353$	−109.964	−	63.4880i	−0.311514	−	0.179853i	0.336090	−	0.941830i	$-0.390895\pi$
$353$	−109.964	−	63.4880i	−0.311514	−	0.179853i	−0.647604	+	0.761977i	$0.724229\pi$
$354$	7.40301	−	23.6927i	0.0209125	−	0.0669286i
$355$	−22.6717	−	39.2686i	−0.0638640	−	0.110616i
$356$	520.255	+	300.370i	1.46139	+	0.843735i
$357$	320.218	−	294.952i	0.896970	−	0.826197i
$358$	−0.694556			−0.00194010
$359$		−	443.856i		−	1.23637i	−0.786034	−	0.618184i	$-0.787869\pi$
$359$		−	443.856i		−	1.23637i	0.786034	−	0.618184i	$-0.212131\pi$
$360$	27.6164	−	13.0520i	0.0767121	−	0.0362554i
$361$	−48.0575	−	83.2381i	−0.133123	−	0.230576i
$362$	3.49550	+	2.01813i	0.00965606	+	0.00557493i
$363$	310.837	−	69.7543i	0.856300	−	0.192161i
$364$	−100.965	+	237.471i	−0.277378	+	0.652394i
$365$	−64.9414	−	37.4939i	−0.177922	−	0.102723i
$366$	−8.58658	+	7.90908i	−0.0234606	+	0.0216095i
$367$	58.0864	−	100.609i	0.158274	−	0.274138i	−0.775973	−	0.630767i	$-0.782741\pi$
$367$	58.0864	−	100.609i	0.158274	−	0.274138i	0.934246	+	0.356629i	$0.116074\pi$
$368$	−180.369	−	104.136i	−0.490134	−	0.282979i
$369$	−147.882	+	213.539i	−0.400765	+	0.578696i
$370$	11.4649	−	19.8579i	0.0309863	−	0.0536699i
$371$			65.0952i			0.175459i
$372$	−142.887	+	457.296i	−0.384104	+	1.22929i
$373$	−105.494	−	182.720i	−0.282825	−	0.489866i	0.689255	−	0.724519i	$-0.257938\pi$
$373$	−105.494	−	182.720i	−0.282825	−	0.489866i	−0.972079	+	0.234653i	$0.924605\pi$
$374$			159.889i			0.427512i
$375$	−160.099	−	50.0243i	−0.426930	−	0.133398i
$376$	5.94304	+	10.2936i	0.0158060	+	0.0273767i
$377$	−85.1006	−	696.474i	−0.225731	−	1.84741i
$378$	51.7270	−	7.21848i	0.136844	−	0.0190965i
$379$	−190.883	−	330.619i	−0.503650	−	0.872347i	−0.999991	−	0.00421947i	$-0.998657\pi$
$379$	−190.883	−	330.619i	−0.503650	−	0.872347i	0.496341	−	0.868127i	$-0.334676\pi$
$380$	−82.0557	−	47.3749i	−0.215936	−	0.124671i
$381$	30.6010	−	6.86710i	0.0803175	−	0.0180239i
$382$	−12.3947	+	21.4683i	−0.0324470	+	0.0561998i
$383$	−219.929	+	126.976i	−0.574227	+	0.331530i	−0.758836	−	0.651282i	$-0.774232\pi$
$383$	−219.929	+	126.976i	−0.574227	+	0.331530i	0.184609	+	0.982812i	$0.440898\pi$
$384$	−194.038	+	178.728i	−0.505306	+	0.465436i
$385$	−44.5266	−	77.1224i	−0.115654	−	0.200318i
$386$	36.4268	+	21.0310i	0.0943699	+	0.0544845i
$387$	−311.188	−	215.507i	−0.804103	−	0.556866i
$388$	−37.5050	−	64.9606i	−0.0966624	−	0.167424i
$389$	−291.388	+	168.233i	−0.749070	+	0.432476i	−0.825358	−	0.564610i	$-0.809027\pi$
$389$	−291.388	+	168.233i	−0.749070	+	0.432476i	0.0762879	+	0.997086i	$0.475693\pi$
$390$	12.8294	+	10.9131i	0.0328959	+	0.0279823i
$391$	−205.100	+	355.244i	−0.524553	+	0.908552i
$392$		−	66.5979i		−	0.169893i
$393$	−189.191	+	174.263i	−0.481401	+	0.443418i
$394$	4.41628			0.0112088
$395$		−	22.4655i		−	0.0568746i
$396$	298.012	−	430.323i	0.752555	−	1.08667i
$397$	−124.854	+	216.254i	−0.314494	+	0.544720i	−0.979330	−	0.202269i	$-0.935168\pi$
$397$	−124.854	+	216.254i	−0.314494	+	0.544720i	0.664835	+	0.746990i	$0.268502\pi$
$398$	−6.01689	+	3.47385i	−0.0151178	+	0.00872828i
$399$	−223.542	−	242.691i	−0.560256	−	0.608249i
$400$	339.187			0.847968
$401$		−	562.927i		−	1.40381i	−0.712271	−	0.701904i	$-0.752333\pi$
$401$		−	562.927i		−	1.40381i	0.712271	−	0.701904i	$-0.247667\pi$
$402$	−61.4198	+	56.5736i	−0.152786	+	0.140730i
$403$	−534.072	+	65.2570i	−1.32524	+	0.161928i
$404$		−	319.857i		−	0.791724i
$405$	−15.2063	+	91.7783i	−0.0375465	+	0.226613i
$406$	−52.2025	−	90.4174i	−0.128578	−	0.222703i
$407$		−	800.274i		−	1.96628i
$408$	169.433	+	183.947i	0.415277	+	0.450850i
$409$	370.218	+	641.237i	0.905179	+	1.56782i	0.820676	+	0.571393i	$0.193597\pi$
$409$	370.218	+	641.237i	0.905179	+	1.56782i	0.0845027	+	0.996423i	$0.473070\pi$
$410$	−10.7943	+	6.23208i	−0.0263275	+	0.0152002i
$411$	−317.979	−	99.3554i	−0.773671	−	0.241741i
$412$	295.351			0.716872
$413$	−98.0284	+	56.5967i	−0.237357	+	0.137038i
$414$	−44.4915	+	21.0274i	−0.107467	+	0.0507908i
$415$	95.1026			0.229163
$416$	−205.848	−	87.5200i	−0.494826	−	0.210385i
$417$	593.763	−	133.245i	1.42389	−	0.319533i
$418$	121.179			0.289902
$419$			447.245i			1.06741i	0.845670	+	0.533705i	$0.179201\pi$
$419$			447.245i			1.06741i	−0.845670	+	0.533705i	$0.820799\pi$
$420$	−65.2799	−	20.3973i	−0.155428	−	0.0485650i
$421$	−159.450	−	276.175i	−0.378741	−	0.655999i	0.612138	−	0.790751i	$-0.290310\pi$
$421$	−159.450	−	276.175i	−0.378741	−	0.655999i	−0.990879	+	0.134752i	$0.956976\pi$
$422$	−8.52618	−	4.92259i	−0.0202042	−	0.0116649i
$423$	−36.0786	−	2.96861i	−0.0852922	−	0.00701799i
$424$	−37.3934			−0.0881920
$425$		−	668.041i		−	1.57186i
$426$	43.4563	−	9.75195i	0.102010	−	0.0228919i
$427$	53.2351			0.124672
$428$	79.7906	+	46.0671i	0.186427	+	0.107634i
$429$	578.208	+	105.971i	1.34780	+	0.247018i
$430$	−9.08195	−	15.7304i	−0.0211208	−	0.0365823i
$431$	−101.578	+	58.6459i	−0.235679	+	0.136069i	−0.613189	−	0.789936i	$-0.710114\pi$
$431$	−101.578	+	58.6459i	−0.235679	+	0.136069i	0.377510	+	0.926005i	$0.376780\pi$
$432$	−53.4496	−	383.015i	−0.123726	−	0.886610i
$433$	211.520	−	366.363i	0.488498	−	0.846104i	−0.511414	−	0.859334i	$-0.670878\pi$
$433$	211.520	−	366.363i	0.488498	−	0.846104i	0.999912	+	0.0132303i	$0.00421145\pi$
$434$	−69.3341	+	40.0301i	−0.159756	+	0.0922352i
$435$	181.454	−	40.7198i	0.417137	−	0.0936088i
$436$	−11.2714	−	19.5226i	−0.0258518	−	0.0447767i
$437$	269.237	+	155.444i	0.616103	+	0.355707i
$438$	54.1748	−	49.9003i	0.123687	−	0.113928i
$439$	134.308	−	232.629i	0.305941	−	0.529906i	−0.671529	−	0.740978i	$-0.734362\pi$
$439$	134.308	−	232.629i	0.305941	−	0.529906i	0.977470	+	0.211072i	$0.0676956\pi$
$440$	44.3023	−	25.5780i	0.100687	−	0.0581317i
$441$	166.749	+	115.479i	0.378117	+	0.261858i
$442$	−53.9571	+	126.907i	−0.122075	+	0.287121i
$443$	33.2832	−	19.2161i	0.0751314	−	0.0433771i	−0.461964	−	0.886899i	$-0.652855\pi$
$443$	33.2832	−	19.2161i	0.0751314	−	0.0433771i	0.537095	+	0.843522i	$0.319522\pi$
$444$	−416.391	−	452.060i	−0.937818	−	1.01815i
$445$	−178.810			−0.401820
$446$	−105.159	+	60.7134i	−0.235782	+	0.136129i
$447$	154.515	+	688.546i	0.345672	+	1.54037i
$448$	261.444			0.583581
$449$	521.983	+	301.367i	1.16254	+	0.671196i	0.951913	−	0.306370i	$-0.0991144\pi$
$449$	521.983	+	301.367i	1.16254	+	0.671196i	0.210632	+	0.977565i	$0.432448\pi$
$450$	45.6278	−	65.8856i	0.101395	−	0.146412i
$451$	−217.505	+	376.730i	−0.482274	+	0.835323i
$452$	445.841	+	257.406i	0.986373	+	0.569483i
$453$	780.197	−	175.082i	1.72229	−	0.386496i
$454$	−47.6654	+	82.5589i	−0.104990	+	0.181848i
$455$	−9.31556	−	76.2397i	−0.0204738	−	0.167560i
$456$	139.412	−	128.412i	0.305728	−	0.281605i
$457$	−129.801	+	224.822i	−0.284029	+	0.491952i	−0.972373	−	0.233432i	$-0.925004\pi$
$457$	−129.801	+	224.822i	−0.284029	+	0.491952i	0.688344	+	0.725384i	$0.258338\pi$
$458$	−77.7955	+	44.9153i	−0.169859	+	0.0980683i
$459$	−754.363	+	105.271i	−1.64349	+	0.229349i
$460$	64.4402			0.140087
$461$			534.455i			1.15934i	0.814852	+	0.579669i	$0.196818\pi$
$461$			534.455i			1.15934i	−0.814852	+	0.579669i	$0.803182\pi$
$462$	85.3469	−	19.1525i	0.184734	−	0.0414557i
$463$	−307.484	+	532.579i	−0.664113	+	1.15028i	0.315412	+	0.948955i	$0.397857\pi$
$463$	−307.484	+	532.579i	−0.664113	+	1.15028i	−0.979525	+	0.201323i	$0.935476\pi$
$464$	−669.501	+	386.536i	−1.44289	+	0.833052i
$465$	−31.2249	−	139.143i	−0.0671503	−	0.299233i
$466$	−8.06855	+	13.9751i	−0.0173145	+	0.0299896i
$467$		−	247.090i		−	0.529100i	−0.964372	−	0.264550i	$-0.914777\pi$
$467$		−	247.090i		−	0.529100i	0.964372	−	0.264550i	$-0.0852234\pi$
$468$	381.757	−	240.987i	0.815719	−	0.514930i
$469$	380.791			0.811921
$470$	−1.50439	−	0.868558i	−0.00320082	−	0.00184800i
$471$	−118.057	−	128.170i	−0.250652	−	0.272123i
$472$	−32.5115	−	56.3116i	−0.0688803	−	0.119304i
$473$	−549.005	−	316.968i	−1.16069	−	0.670123i
$474$	21.0617	+	6.58094i	0.0444341	+	0.0138838i
$475$	−506.304			−1.06590
$476$		−	559.958i		−	1.17638i
$477$	64.8393	−	93.6265i	0.135931	−	0.196282i
$478$	−14.5571	−	25.2136i	−0.0304542	−	0.0527482i
$479$	−710.396	−	410.147i	−1.48308	−	0.856257i	−0.483266	−	0.875474i	$-0.660549\pi$
$479$	−710.396	−	410.147i	−1.48308	−	0.856257i	−0.999815	+	0.0192166i	$0.993883\pi$
$480$	17.6810	−	56.5866i	0.0368354	−	0.117889i
$481$	270.065	−	635.193i	0.561465	−	1.32057i
$482$	31.1874	+	18.0061i	0.0647042	+	0.0373570i
$483$	214.193	+	66.9265i	0.443463	+	0.138564i
$484$	204.871	−	354.847i	0.423287	−	0.733154i
$485$	19.3355	+	11.1634i	0.0398670	+	0.0230172i
$486$	−81.5892	−	41.1413i	−0.167879	−	0.0846529i
$487$	−367.489	+	636.510i	−0.754598	+	1.30700i	0.190976	+	0.981595i	$0.438835\pi$
$487$	−367.489	+	636.510i	−0.754598	+	1.30700i	−0.945574	+	0.325407i	$0.894499\pi$
$488$			30.5805i			0.0626650i
$489$	32.9297	+	35.7505i	0.0673410	+	0.0731095i
$490$	4.86655	+	8.42911i	0.00993173	+	0.0172023i
$491$			130.593i			0.265974i	0.991118	+	0.132987i	$0.0424569\pi$
$491$			130.593i			0.265974i	−0.991118	+	0.132987i	$0.957543\pi$
$492$	73.1522	+	325.978i	0.148683	+	0.662558i
$493$	761.298	+	1318.61i	1.54421	+	2.67466i
$494$	96.1823	+	40.8937i	0.194701	+	0.0827808i
$495$	−12.7765	+	155.277i	−0.0258110	+	0.313691i
$496$	296.405	+	513.388i	0.597590	+	1.03506i
$497$	−175.886	−	101.548i	−0.353895	−	0.204321i
$498$	−27.8589	+	89.1602i	−0.0559416	+	0.179037i
$499$	−14.4740	+	25.0696i	−0.0290059	+	0.0502397i	−0.880164	−	0.474670i	$-0.842568\pi$
$499$	−14.4740	+	25.0696i	−0.0290059	+	0.0502397i	0.851158	+	0.524909i	$0.175901\pi$
$500$	−186.834	+	107.868i	−0.373667	+	0.215737i
$501$	−89.5851	−	27.9917i	−0.178813	−	0.0558717i
$502$	−79.3197	−	137.386i	−0.158007	−	0.273677i
$503$	255.144	+	147.308i	0.507245	+	0.292858i	0.731701	−	0.681626i	$-0.238727\pi$
$503$	255.144	+	147.308i	0.507245	+	0.292858i	−0.224455	+	0.974484i	$0.572060\pi$
$504$	77.8927	−	112.475i	0.154549	−	0.223165i
$505$	47.6026	+	82.4502i	0.0942627	+	0.163268i
$506$	−71.3735	+	41.2075i	−0.141054	+	0.0814377i
$507$	423.174	+	279.236i	0.834662	+	0.550762i
$508$	20.1689	−	34.9336i	0.0397026	−	0.0687669i
$509$			621.265i			1.22056i	0.792186	+	0.610280i	$0.208943\pi$
$509$			621.265i			1.22056i	−0.792186	+	0.610280i	$0.791057\pi$
$510$	−34.8863	−	10.9005i	−0.0684045	−	0.0213736i
$511$	−335.874			−0.657287
$512$			415.752i			0.812016i
$513$	79.7841	+	571.727i	0.155525	+	1.11448i
$514$	73.0161	−	126.468i	0.142055	−	0.246046i
$515$	−76.1333	+	43.9556i	−0.147832	+	0.0853507i
$516$	−475.045	+	106.604i	−0.920629	+	0.206597i
$517$	−60.6270			−0.117267
$518$		−	102.704i		−	0.198270i
$519$	−12.3769	−	3.86727i	−0.0238475	−	0.00745138i
$520$	43.7953	−	5.35125i	0.0842217	−	0.0102909i
$521$			166.583i			0.319738i	0.987138	+	0.159869i	$0.0511071\pi$
$521$			166.583i			0.319738i	−0.987138	+	0.159869i	$0.948893\pi$
$522$	−14.9790	+	182.045i	−0.0286954	+	0.348745i
$523$	−51.1561	−	88.6049i	−0.0978127	−	0.169417i	0.812966	−	0.582311i	$-0.197851\pi$
$523$	−51.1561	−	88.6049i	−0.0978127	−	0.169417i	−0.910779	+	0.412894i	$0.864518\pi$
$524$			330.833i			0.631361i
$525$	−356.592	+	80.0221i	−0.679223	+	0.152423i
$526$	−29.9667	−	51.9039i	−0.0569709	−	0.0986766i
$527$	1011.14	−	583.780i	1.91867	−	1.10774i
$528$	−141.816	−	631.956i	−0.268591	−	1.19689i
$529$	317.562			0.600307
$530$	4.73278	−	2.73247i	0.00892977	−	0.00515560i
$531$	197.369	+	16.2398i	0.371692	+	0.0305835i
$532$	−424.388			−0.797722
$533$	−299.772	+	225.618i	−0.562424	+	0.423298i
$534$	52.3798	−	167.637i	0.0980895	−	0.313927i
$535$	−27.4238			−0.0512594
$536$			218.742i			0.408102i
$537$	−1.21332	−	5.40678i	−0.00225945	−	0.0100685i
$538$	−29.9871	−	51.9392i	−0.0557381	−	0.0965412i
$539$	294.184	+	169.847i	0.545795	+	0.315115i
$540$	73.5750	+	94.3607i	0.136250	+	0.174742i
$541$	638.732			1.18065			0.590325	−	0.807166i	$-0.299000\pi$
$541$	638.732			1.18065			0.590325	+	0.807166i	$0.299000\pi$
$542$			72.7640i			0.134251i
$543$	−9.60381	+	30.7362i	−0.0176866	+	0.0566044i
$544$	485.389			0.892259
$545$	5.81091	+	3.35493i	0.0106622	+	0.00615583i
$546$	74.2049	+	13.5999i	0.135906	+	0.0249082i
$547$	−250.228	−	433.408i	−0.457456	−	0.792337i	0.541370	−	0.840785i	$-0.317906\pi$
$547$	−250.228	−	433.408i	−0.457456	−	0.792337i	−0.998826	+	0.0484477i	$0.984573\pi$
$548$	−371.078	+	214.242i	−0.677150	+	0.390953i
$549$	−76.5682	−	53.0259i	−0.139468	−	0.0965863i
$550$	67.1094	−	116.237i	0.122017	−	0.211340i
$551$	999.363	−	576.982i	1.81373	−	1.04715i
$552$	−38.4454	+	123.041i	−0.0696475	+	0.222901i
$553$	−50.3119	−	87.1427i	−0.0909798	−	0.157582i
$554$	104.847	+	60.5336i	0.189255	+	0.109266i
$555$	174.612	+	54.5591i	0.314616	+	0.0983047i
$556$	391.346	−	677.831i	0.703859	−	1.21912i
$557$	217.719	−	125.700i	0.390877	−	0.225673i	−0.291663	−	0.956521i	$-0.594209\pi$
$557$	217.719	−	125.700i	0.390877	−	0.225673i	0.682540	+	0.730848i	$0.260875\pi$
$558$	139.596	+	11.4862i	0.250172	+	0.0205846i
$559$	−328.791	−	436.854i	−0.588176	−	0.781492i
$560$	−73.2871	+	42.3123i	−0.130870	+	0.0755577i
$561$	−1244.66	+	279.312i	−2.21865	+	0.497882i
$562$	155.249			0.276245
$563$	−651.090	+	375.907i	−1.15647	+	0.667685i	−0.950454	−	0.310864i	$-0.899382\pi$
$563$	−651.090	+	375.907i	−1.15647	+	0.667685i	−0.206011	+	0.978550i	$0.566048\pi$
$564$	−34.2470	+	31.5449i	−0.0607217	+	0.0559306i
$565$	−153.234			−0.271210
$566$	−158.839	−	91.7056i	−0.280634	−	0.162024i
$567$	146.555	+	390.059i	0.258474	+	0.687935i
$568$	58.3332	−	101.036i	0.102699	−	0.177880i
$569$	464.413	+	268.129i	0.816191	+	0.471228i	0.849101	−	0.528230i	$-0.177144\pi$
$569$	464.413	+	268.129i	0.816191	+	0.471228i	−0.0329102	+	0.999458i	$0.510478\pi$
$570$	−8.26145	+	26.4401i	−0.0144938	+	0.0463861i
$571$	−50.9656	+	88.2750i	−0.0892567	+	0.154597i	−0.907197	−	0.420706i	$-0.861782\pi$
$571$	−50.9656	+	88.2750i	−0.0892567	+	0.154597i	0.817940	+	0.575303i	$0.195116\pi$
$572$	604.099	−	454.664i	1.05612	−	0.794868i
$573$	−188.773	−	58.9838i	−0.329447	−	0.102939i
$574$	−27.9137	+	48.3480i	−0.0486302	+	0.0842300i
$575$	298.209	−	172.171i	0.518624	−	0.299428i
$576$	−376.036	−	260.417i	−0.652840	−	0.452112i
$577$	−6.86778			−0.0119026			−0.00595128	−	0.999982i	$-0.501894\pi$
$577$	−6.86778			−0.0119026			−0.00595128	+	0.999982i	$0.501894\pi$
$578$		−	190.575i		−	0.329715i
$579$	−100.082	+	320.304i	−0.172853	+	0.553202i
$580$	119.596	−	207.146i	0.206199	−	0.357148i
$581$	368.899	−	212.984i	0.634938	−	0.366582i
$582$	−16.1299	+	14.8572i	−0.0277146	+	0.0255278i
$583$	95.3657	−	165.178i	0.163578	−	0.283325i
$584$		−	192.940i		−	0.330377i
$585$	−62.5414	+	118.935i	−0.106908	+	0.203307i
$586$	−206.303			−0.352054
$587$	452.291	+	261.130i	0.770512	+	0.444855i	0.833057	−	0.553187i	$-0.186588\pi$
$587$	452.291	+	261.130i	0.770512	+	0.444855i	−0.0625452	+	0.998042i	$0.519922\pi$
$588$	254.552	−	57.1235i	0.432911	−	0.0971488i
$589$	−442.443	−	766.334i	−0.751177	−	1.30108i
$590$	8.22978	+	4.75147i	0.0139488	+	0.00805333i
$591$	7.71482	+	34.3785i	0.0130538	+	0.0581701i
$592$	−760.476			−1.28459
$593$			624.635i			1.05335i	0.850068	+	0.526674i	$0.176561\pi$
$593$			624.635i			1.05335i	−0.850068	+	0.526674i	$0.823439\pi$
$594$	−141.832	−	57.4643i	−0.238774	−	0.0967412i
$595$	83.3357	+	144.342i	0.140060	+	0.242591i
$596$	786.033	+	453.817i	1.31885	+	0.761437i
$597$	−37.5532	−	40.7700i	−0.0629032	−	0.0682915i
$598$	−70.5566	+	8.62115i	−0.117988	+	0.0144166i
$599$	−472.937	−	273.050i	−0.789544	−	0.455843i	0.0502581	−	0.998736i	$-0.483996\pi$
$599$	−472.937	−	273.050i	−0.789544	−	0.455843i	−0.839802	+	0.542893i	$0.817329\pi$
$600$	−45.9680	−	204.841i	−0.0766134	−	0.341402i
$601$	−281.855	+	488.187i	−0.468977	+	0.812291i	−0.999371	−	0.0354598i	$-0.988710\pi$
$601$	−281.855	+	488.187i	−0.468977	+	0.812291i	0.530395	+	0.847751i	$0.322044\pi$
$602$	−70.4571	−	40.6784i	−0.117038	−	0.0675721i
$603$	−547.693	−	379.294i	−0.908279	−	0.629012i
$604$	514.223	−	890.661i	0.851363	−	1.47460i
$605$			121.959i			0.201586i
$606$	−91.2429	+	20.4756i	−0.150566	+	0.0337882i
$607$	−100.683	−	174.388i	−0.165869	−	0.287294i	0.771094	−	0.636721i	$-0.219710\pi$
$607$	−100.683	−	174.388i	−0.165869	−	0.287294i	−0.936964	+	0.349427i	$0.886376\pi$
$608$		−	367.873i		−	0.605054i
$609$	612.662	−	564.322i	1.00601	−	0.926636i
$610$	−2.23463	−	3.87049i	−0.00366332	−	0.00634506i
$611$	−48.1208	−	20.4595i	−0.0787575	−	0.0334852i
$612$	−557.756	+	805.388i	−0.911367	+	1.31599i
$613$	−317.568	−	550.044i	−0.518055	−	0.897298i	−0.999780	−	0.0209752i	$-0.993323\pi$
$613$	−317.568	−	550.044i	−0.518055	−	0.897298i	0.481725	−	0.876322i	$-0.340010\pi$
$614$	−25.5130	−	14.7299i	−0.0415521	−	0.0239901i
$615$	−67.3703	−	73.1413i	−0.109545	−	0.118929i
$616$	114.565	−	198.432i	0.185982	−	0.322130i
$617$	55.5849	−	32.0919i	0.0900889	−	0.0520129i	−0.454279	−	0.890860i	$-0.650103\pi$
$617$	55.5849	−	32.0919i	0.0900889	−	0.0520129i	0.544368	+	0.838847i	$0.316770\pi$
$618$	−18.9069	−	84.2524i	−0.0305937	−	0.136331i
$619$	3.79581	+	6.57454i	0.00613217	+	0.0106212i	0.869075	−	0.494680i	$-0.164715\pi$
$619$	3.79581	+	6.57454i	0.00613217	+	0.0106212i	−0.862943	+	0.505301i	$0.831381\pi$
$620$	−158.844	−	91.7086i	−0.256200	−	0.147917i
$621$	−241.410	−	309.611i	−0.388745	−	0.498569i
$622$	84.8491	+	146.963i	0.136413	+	0.236275i
$623$	−693.597	+	400.448i	−1.11332	+	0.642774i
$624$	100.701	−	549.454i	0.161380	−	0.880535i
$625$	−263.904	+	457.096i	−0.422247	+	0.731354i
$626$		−	88.6105i		−	0.141550i
$627$	211.689	+	943.320i	0.337621	+	1.50450i
$628$	−224.128			−0.356891
$629$			1497.79i			2.38122i
$630$	−1.63968	+	19.9276i	−0.00260266	+	0.0316311i
$631$	423.578	−	733.658i	0.671280	−	1.16269i	−0.306262	−	0.951947i	$-0.599078\pi$
$631$	423.578	−	733.658i	0.671280	−	1.16269i	0.977541	−	0.210743i	$-0.0675884\pi$
$632$	50.0584	−	28.9012i	0.0792064	−	0.0457298i
$633$	23.4255	−	74.9714i	0.0370071	−	0.118438i
$634$	−46.8538			−0.0739019
$635$			12.0065i			0.0189080i
$636$	−32.0737	−	142.926i	−0.0504304	−	0.224726i
$637$	176.182	+	234.088i	0.276581	+	0.367484i
$638$			305.911i			0.479484i
$639$	151.828	+	321.250i	0.237603	+	0.502739i
$640$	−50.4976	−	87.4644i	−0.0789025	−	0.136663i
$641$		−	1071.90i		−	1.67222i	−0.548559	−	0.836112i	$-0.684823\pi$
$641$		−	1071.90i		−	1.67222i	0.548559	−	0.836112i	$-0.315177\pi$
$642$	8.03340	−	25.7102i	0.0125131	−	0.0400471i
$643$	−205.775	−	356.413i	−0.320023	−	0.554297i	0.660469	−	0.750853i	$-0.270357\pi$
$643$	−205.775	−	356.413i	−0.320023	−	0.554297i	−0.980492	+	0.196557i	$0.937024\pi$
$644$	249.961	−	144.315i	0.388138	−	0.224092i
$645$	106.588	−	98.1780i	0.165253	−	0.152214i
$646$	−226.798			−0.351080
$647$	−872.018	+	503.460i	−1.34779	+	0.778145i	−0.987936	−	0.154865i	$-0.950506\pi$
$647$	−872.018	+	503.460i	−1.34779	+	0.778145i	−0.359851	+	0.933010i	$0.617172\pi$
$648$	−224.066	+	84.1871i	−0.345782	+	0.129918i
$649$	331.661			0.511034
$650$	92.4920	−	69.6125i	0.142295	−	0.107096i
$651$	−432.734	−	469.803i	−0.664723	−	0.721664i
$652$	62.5161			0.0958836
$653$		−	1153.60i		−	1.76662i	−0.468791	−	0.883309i	$-0.655310\pi$
$653$		−	1153.60i		−	1.76662i	0.468791	−	0.883309i	$-0.344690\pi$
$654$	−4.84752	+	4.46504i	−0.00741212	+	0.00682728i
$655$	−49.2362	−	85.2796i	−0.0751698	−	0.130198i
$656$	357.996	+	206.689i	0.545725	+	0.315074i
$657$	483.088	+	334.553i	0.735293	+	0.509213i
$658$	−7.78061			−0.0118246
$659$			310.724i			0.471509i	0.971813	+	0.235754i	$0.0757561\pi$
$659$			310.724i			0.471509i	−0.971813	+	0.235754i	$0.924244\pi$
$660$	135.764	+	147.394i	0.205704	+	0.223324i
$661$	−515.710			−0.780197			−0.390099	−	0.920773i	$-0.627559\pi$
$661$	−515.710			−0.780197			−0.390099	+	0.920773i	$0.627559\pi$
$662$	−108.957	−	62.9065i	−0.164588	−	0.0950250i
$663$	−1082.17	−	198.334i	−1.63223	−	0.299146i
$664$	122.347	+	211.911i	0.184257	+	0.319143i
$665$	109.395	−	63.1595i	0.164505	−	0.0949767i
$666$	−102.300	+	147.719i	−0.153604	+	0.221800i
$667$	−392.411	+	679.675i	−0.588322	+	1.01900i
$668$	−104.545	+	60.3591i	−0.156505	+	0.0903580i
$669$	−656.326	−	712.548i	−0.981056	−	1.06509i
$670$	−15.9843	−	27.6856i	−0.0238571	−	0.0413218i
$671$	−135.084	−	77.9905i	−0.201317	−	0.116230i
$672$	−58.1428	−	259.094i	−0.0865221	−	0.385557i
$673$	104.909	−	181.708i	0.155883	−	0.269997i	−0.777497	−	0.628886i	$-0.783511\pi$
$673$	104.909	−	181.708i	0.155883	−	0.269997i	0.933380	+	0.358889i	$0.116844\pi$
$674$	121.114	−	69.9254i	0.179695	−	0.103747i
$675$	592.594	+	240.094i	0.877917	+	0.355695i
$676$	632.919	−	157.014i	0.936270	−	0.232269i
$677$	11.9220	−	6.88315i	0.0176100	−	0.0101671i	−0.491169	−	0.871064i	$-0.663430\pi$
$677$	11.9220	−	6.88315i	0.0176100	−	0.0101671i	0.508779	+	0.860897i	$0.330097\pi$
$678$	44.8877	−	143.659i	0.0662060	−	0.211887i
$679$	100.002			0.147279
$680$	−82.9159	+	47.8715i	−0.121935	+	0.0703993i
$681$	−725.947	−	226.829i	−1.06600	−	0.333082i
$682$	234.579			0.343958
$683$	−402.924	−	232.628i	−0.589933	−	0.340598i	0.175138	−	0.984544i	$-0.443963\pi$
$683$	−402.924	−	232.628i	−0.589933	−	0.340598i	−0.765071	+	0.643946i	$0.777296\pi$
$684$	610.398	+	422.720i	0.892395	+	0.618011i
$685$	63.7691	−	110.451i	0.0930936	−	0.161243i
$686$	119.840	+	69.1898i	0.174694	+	0.100860i
$687$	−485.545	−	527.137i	−0.706761	−	0.767303i
$688$	−301.205	+	521.703i	−0.437799	+	0.758289i
$689$	131.436	−	98.9226i	0.190763	−	0.143574i
$690$	−4.12514	−	18.3823i	−0.00597847	−	0.0266411i
$691$	259.190	−	448.930i	0.375094	−	0.649681i	−0.615247	−	0.788334i	$-0.710944\pi$
$691$	259.190	−	448.930i	0.375094	−	0.649681i	0.990341	+	0.138653i	$0.0442772\pi$
$692$	−14.4437	+	8.33907i	−0.0208724	+	0.0120507i
$693$	298.186	+	630.926i	0.430283	+	0.910427i
$694$	64.2258			0.0925443
$695$			232.968i			0.335206i
$696$	324.170	+	351.939i	0.465761	+	0.505659i
$697$	407.081	−	705.086i	0.584048	−	1.01160i
$698$	43.8709	−	25.3289i	0.0628522	−	0.0362878i
$699$	−122.885	−	38.3964i	−0.175800	−	0.0549305i
$700$	−235.028	+	407.080i	−0.335754	+	0.581543i
$701$			775.035i			1.10561i	0.833310	+	0.552806i	$0.186443\pi$
$701$			775.035i			1.10561i	−0.833310	+	0.552806i	$0.813557\pi$
$702$	−93.1826	−	93.4738i	−0.132739	−	0.133154i
$703$	1135.16			1.61474
$704$	−663.412	−	383.021i	−0.942347	−	0.544064i
$705$	4.13328	−	13.2282i	0.00586280	−	0.0187634i
$706$	23.8733	+	41.3498i	0.0338149	+	0.0585691i
$707$	369.298	+	213.214i	0.522345	+	0.301576i
$708$	187.349	−	172.567i	0.264617	−	0.243738i
$709$	617.138			0.870435			0.435217	−	0.900325i	$-0.356671\pi$
$709$	617.138			0.870435			0.435217	+	0.900325i	$0.356671\pi$
$710$			17.0505i			0.0240147i
$711$	−14.4365	+	175.452i	−0.0203045	+	0.246767i
$712$	−230.034	−	398.431i	−0.323082	−	0.559594i
$713$	521.190	+	300.909i	0.730982	+	0.422033i
$714$	−159.735	+	35.8457i	−0.223718	+	0.0502041i
$715$	−88.0546	+	207.105i	−0.123153	+	0.289657i
$716$	−6.17230	−	3.56358i	−0.00862052	−	0.00497706i
$717$	170.846	−	157.366i	0.238279	−	0.219478i
$718$	−83.4513	+	144.542i	−0.116227	+	0.201312i
$719$	534.714	+	308.717i	0.743692	+	0.429371i	0.823410	−	0.567447i	$-0.192069\pi$
$719$	534.714	+	308.717i	0.743692	+	0.429371i	−0.0797184	+	0.996817i	$0.525402\pi$
$720$	147.555	+	12.1411i	0.204937	+	0.0168626i
$721$	−196.879	+	341.004i	−0.273064	+	0.472960i
$722$			36.1420i			0.0500582i
$723$	−85.6869	+	274.234i	−0.118516	+	0.379300i
$724$	20.7089	+	35.8688i	0.0286034	+	0.0495426i
$725$		−	1278.14i		−	1.76295i
$726$	−114.339	−	35.7263i	−0.157492	−	0.0492098i
$727$	−527.853	−	914.268i	−0.726070	−	1.25759i	−0.958532	−	0.284984i	$-0.908012\pi$
$727$	−527.853	−	914.268i	−0.726070	−	1.25759i	0.232462	−	0.972605i	$-0.425322\pi$
$728$	157.896	−	118.838i	0.216890	−	0.163239i
$729$	177.736	−	707.001i	0.243808	−	0.969823i
$730$	14.0988	+	24.4199i	0.0193134	+	0.0334519i
$731$	1027.51	+	593.235i	1.40563	+	0.811539i
$732$	−116.885	+	26.2300i	−0.159680	+	0.0358334i
$733$	435.712	−	754.675i	0.594422	−	1.02957i	−0.399206	−	0.916861i	$-0.630714\pi$
$733$	435.712	−	754.675i	0.594422	−	1.02957i	0.993628	−	0.112708i	$-0.0359526\pi$
$734$	−37.8318	+	21.8422i	−0.0515419	+	0.0297577i
$735$	−57.1150	+	52.6085i	−0.0777075	+	0.0715762i
$736$	125.097	+	216.674i	0.169968	+	0.294394i
$737$	−966.253	−	557.866i	−1.31106	−	0.756942i
$738$	88.3064	−	41.7350i	0.119656	−	0.0565516i
$739$	38.1201	+	66.0259i	0.0515833	+	0.0893449i	0.890664	−	0.454662i	$-0.150240\pi$
$739$	38.1201	+	66.0259i	0.0515833	+	0.0893449i	−0.839081	+	0.544007i	$0.816907\pi$
$740$	203.770	−	117.647i	0.275365	−	0.158982i
$741$	−150.316	+	820.169i	−0.202856	+	1.10684i
$742$	12.2388	−	21.1983i	0.0164944	−	0.0285691i
$743$			492.520i			0.662880i	0.943476	+	0.331440i	$0.107534\pi$
$743$			492.520i			0.662880i	−0.943476	+	0.331440i	$0.892466\pi$
$744$	269.875	−	248.581i	0.362735	−	0.334114i
$745$	−270.157			−0.362627
$746$			79.3373i			0.106350i
$747$	−742.735	−	61.1136i	−0.994290	−	0.0818120i
$748$	−820.349	+	1420.89i	−1.09672	+	1.89958i
$749$	−106.376	+	61.4160i	−0.142024	+	0.0819974i
$750$	42.7309	+	46.3913i	0.0569746	+	0.0618551i
$751$	394.887			0.525815			0.262907	−	0.964821i	$-0.415319\pi$
$751$	394.887			0.525815			0.262907	+	0.964821i	$0.415319\pi$
$752$			57.6120i			0.0766117i
$753$	930.916	−	857.465i	1.23628	−	1.13873i
$754$	−103.234	+	242.807i	−0.136915	+	0.322026i
$755$			306.117i			0.405453i
$756$	496.717	+	201.249i	0.657033	+	0.266202i
$757$	45.1326	+	78.1720i	0.0596204	+	0.103266i	0.894295	−	0.447478i	$-0.147678\pi$
$757$	45.1326	+	78.1720i	0.0596204	+	0.103266i	−0.834675	+	0.550743i	$0.814344\pi$
$758$			143.555i			0.189387i
$759$	−445.463	−	483.622i	−0.586907	−	0.637183i
$760$	36.2815	+	62.8414i	0.0477388	+	0.0826860i
$761$	−649.252	+	374.846i	−0.853156	+	0.492570i	−0.861715	−	0.507393i	$-0.830609\pi$
$761$	−649.252	+	374.846i	−0.853156	+	0.492570i	0.00855819	+	0.999963i	$0.497276\pi$
$762$	−11.2563	−	3.51715i	−0.0147721	−	0.00461568i
$763$	30.0537			0.0393889
$764$	−220.296	+	127.188i	−0.288346	+	0.166477i
$765$	23.9123	−	290.615i	0.0312579	−	0.379889i
$766$	95.4934			0.124665
$767$	263.246	+	111.924i	0.343215	+	0.145924i
$768$	−498.283	+	111.819i	−0.648806	+	0.145597i
$769$	−13.5920			−0.0176749			−0.00883743	−	0.999961i	$-0.502813\pi$
$769$	−13.5920			−0.0176749			−0.00883743	+	0.999961i	$0.502813\pi$
$770$			33.4866i			0.0434891i
$771$	1112.04	+	347.467i	1.44233	+	0.450671i
$772$	215.809	+	373.792i	0.279545	+	0.484186i
$773$	20.8183	+	12.0195i	0.0269318	+	0.0155491i	0.513405	−	0.858146i	$-0.328384\pi$
$773$	20.8183	+	12.0195i	0.0269318	+	0.0155491i	−0.486474	+	0.873695i	$0.661717\pi$
$774$	60.8200	+	128.688i	0.0785788	+	0.166263i
$775$	−980.106			−1.26465
$776$			57.4455i			0.0740277i
$777$	799.499	−	179.414i	1.02896	−	0.230906i
$778$	126.521			0.162623
$779$	−534.379	−	308.524i	−0.685981	−	0.396052i
$780$	58.0185	+	162.805i	0.0743827	+	0.208725i
$781$	297.538	+	515.351i	0.380971	+	0.659861i
$782$	133.582	−	77.1236i	0.170821	−	0.0986235i
$783$	−1443.30	+	201.411i	−1.84329	+	0.257230i
$784$	161.400	−	279.554i	0.205868	−	0.356574i
$785$	57.7739	−	33.3558i	0.0735974	−	0.0424915i
$786$	94.3741	−	21.1783i	0.120069	−	0.0269444i
$787$	282.354	+	489.052i	0.358773	+	0.621413i	0.987756	−	0.156006i	$-0.0498619\pi$
$787$	282.354	+	489.052i	0.358773	+	0.621413i	−0.628983	+	0.777419i	$0.716529\pi$
$788$	39.2460	+	22.6587i	0.0498046	+	0.0287547i
$789$	351.697	−	323.947i	0.445750	−	0.410580i
$790$	−4.22383	+	7.31589i	−0.00534663	+	0.00926063i
$791$	−594.388	+	343.170i	−0.751439	+	0.433843i
$792$	−362.430	+	171.291i	−0.457614	+	0.216276i
$793$	−80.8994	−	107.489i	−0.102017	−	0.135547i
$794$	81.3178	−	46.9488i	0.102415	−	0.0591295i
$795$	29.5386	+	32.0690i	0.0371555	+	0.0403383i
$796$	−71.2936			−0.0895648
$797$	−355.367	+	205.171i	−0.445880	+	0.257429i	−0.706089	−	0.708123i	$-0.749542\pi$
$797$	−355.367	+	205.171i	−0.445880	+	0.257429i	0.260208	+	0.965552i	$0.416209\pi$
$798$	27.1672	+	121.062i	0.0340441	+	0.151706i
$799$	113.469			0.142014
$800$	−352.869	−	203.729i	−0.441087	−	0.254662i
$801$	1396.47	+	114.905i	1.74341	+	0.143451i
$802$	−105.838	+	183.318i	−0.131968	+	0.228576i
$803$	852.275	+	492.061i	1.06136	+	0.612779i
$804$	−836.082	+	187.623i	−1.03990	+	0.233363i
$805$	−42.9553	+	74.4008i	−0.0533607	+	0.0924234i
$806$	186.190	+	79.1623i	0.231005	+	0.0982163i
$807$	351.936	−	324.168i	0.436104	−	0.401695i
$808$	−122.479	+	212.140i	−0.151583	+	0.262550i
$809$	518.289	−	299.234i	0.640654	−	0.369882i	−0.144212	−	0.989547i	$-0.546065\pi$
$809$	518.289	−	299.234i	0.640654	−	0.369882i	0.784867	+	0.619665i	$0.212731\pi$
$810$	22.2076	−	27.0286i	0.0274168	−	0.0333687i
$811$	−427.373			−0.526971			−0.263485	−	0.964663i	$-0.584872\pi$
$811$	−427.373			−0.526971			−0.263485	+	0.964663i	$0.584872\pi$
$812$		−	1071.35i		−	1.31939i
$813$	−566.432	+	127.112i	−0.696718	+	0.156349i
$814$	−150.463	+	260.610i	−0.184844	+	0.320159i
$815$	−16.1149	+	9.30395i	−0.0197729	+	0.0114159i
$816$	265.422	+	1182.76i	0.325272	+	1.44946i
$817$	449.609	−	778.745i	0.550317	−	0.953177i
$818$		−	278.426i		−	0.340374i
$819$	23.7607	+	601.406i	0.0290119	+	0.734317i
$820$	−127.900			−0.155976
$821$	−446.131	−	257.574i	−0.543399	−	0.313732i	0.203056	−	0.979167i	$-0.434913\pi$
$821$	−446.131	−	257.574i	−0.543399	−	0.313732i	−0.746455	+	0.665435i	$0.768246\pi$
$822$	84.8697	+	92.1398i	0.103248	+	0.112092i
$823$	496.291	+	859.601i	0.603026	+	1.04447i	0.992360	+	0.123376i	$0.0393720\pi$
$823$	496.291	+	859.601i	0.603026	+	1.04447i	−0.389334	+	0.921097i	$0.627295\pi$
$824$	−195.887	−	113.095i	−0.237727	−	0.137252i
$825$	1022.08	+	319.359i	1.23889	+	0.387102i
$826$	42.5640			0.0515303
$827$		−	943.762i		−	1.14119i	−0.821233	−	0.570594i	$-0.806713\pi$
$827$		−	943.762i		−	1.14119i	0.821233	−	0.570594i	$-0.193287\pi$
$828$	−503.267	−	41.4097i	−0.607810	−	0.0500118i
$829$	133.486	+	231.205i	0.161021	+	0.278896i	0.935235	−	0.354027i	$-0.115188\pi$
$829$	133.486	+	231.205i	0.161021	+	0.278896i	−0.774214	+	0.632924i	$0.781855\pi$
$830$	−30.9702	−	17.8807i	−0.0373135	−	0.0215430i
$831$	−288.066	+	921.930i	−0.346650	+	1.10942i
$832$	−397.307	−	527.890i	−0.477533	−	0.634483i
$833$	−550.591	−	317.884i	−0.660974	−	0.381614i
$834$	−218.411	−	68.2447i	−0.261884	−	0.0818281i
$835$	17.9659	−	31.1178i	0.0215160	−	0.0372668i
$836$	1076.88	+	621.737i	1.28813	+	0.743704i
$837$	154.447	+	1106.75i	0.184524	+	1.32228i
$838$	84.0886	−	145.646i	0.100344	−	0.173802i
$839$		−	811.237i		−	0.966909i	−0.875369	−	0.483455i	$-0.839382\pi$
$839$		−	811.237i		−	0.966909i	0.875369	−	0.483455i	$-0.160618\pi$
$840$	35.4854	+	38.5251i	0.0422445	+	0.0458632i
$841$	1036.06	+	1794.51i	1.23194	+	2.13379i
$842$			119.916i			0.142418i
$843$	271.206	+	1208.54i	0.321716	+	1.43362i
$844$	−50.5129	−	87.4909i	−0.0598494	−	0.103662i
$845$	−139.781	+	134.668i	−0.165422	+	0.159370i
$846$	11.1909	+	7.75003i	0.0132280	+	0.00916079i
$847$	273.131	+	473.076i	0.322468	+	0.558531i
$848$	−156.964	−	90.6231i	−0.185099	−	0.106867i
$849$	436.407	−	1396.68i	0.514024	−	1.64509i
$850$	−125.601	+	217.548i	−0.147766	+	0.255939i
$851$	−668.601	+	386.017i	−0.785665	+	0.453604i
$852$	436.217	+	136.300i	0.511991	+	0.159977i
$853$	294.569	+	510.209i	0.345333	+	0.598135i	0.985414	−	0.170173i	$-0.0544326\pi$
$853$	294.569	+	510.209i	0.345333	+	0.598135i	−0.640081	+	0.768307i	$0.721099\pi$
$854$	−17.3361	−	10.0090i	−0.0202998	−	0.0117201i
$855$	−220.255	−	18.1230i	−0.257608	−	0.0211965i
$856$	−35.2799	−	61.1067i	−0.0412149	−	0.0713863i
$857$	1354.80	−	782.195i	1.58086	−	0.912713i	0.586131	−	0.810216i	$-0.300650\pi$
$857$	1354.80	−	782.195i	1.58086	−	0.912713i	0.994733	−	0.102496i	$-0.0326830\pi$
$858$	−168.370	−	143.221i	−0.196235	−	0.166924i
$859$	219.269	−	379.785i	0.255261	−	0.442124i	−0.709706	−	0.704498i	$-0.751172\pi$
$859$	219.269	−	379.785i	0.255261	−	0.442124i	0.964966	+	0.262374i	$0.0845054\pi$
$860$		−	186.388i		−	0.216730i
$861$	−425.128	−	132.835i	−0.493761	−	0.154280i
$862$	44.1051			0.0511660
$863$		−	1057.49i		−	1.22536i	−0.790331	−	0.612680i	$-0.790091\pi$
$863$		−	1057.49i		−	1.22536i	0.790331	−	0.612680i	$-0.209909\pi$
$864$	−174.449	+	430.570i	−0.201908	+	0.498345i
$865$	2.48212	−	4.29916i	0.00286951	−	0.00497013i
$866$	−137.763	+	79.5376i	−0.159080	+	0.0918448i
$867$	1483.54	−	332.917i	1.71111	−	0.383988i
$868$	−821.533			−0.946467
$869$			294.831i			0.339277i
$870$	−66.7467	−	20.8556i	−0.0767203	−	0.0239720i
$871$	−578.674	−	768.866i	−0.664378	−	0.882739i
$872$			17.2641i			0.0197983i
$873$	−143.833	−	99.6091i	−0.164758	−	0.114100i
$874$	−58.4514	−	101.241i	−0.0668781	−	0.115836i
$875$		−	287.617i		−	0.328705i
$876$	737.459	−	165.492i	0.841848	−	0.188918i
$877$	−76.3797	−	132.293i	−0.0870920	−	0.150848i	0.819189	−	0.573524i	$-0.194424\pi$
$877$	−76.3797	−	132.293i	−0.0870920	−	0.150848i	−0.906281	+	0.422676i	$0.861091\pi$
$878$	−87.4751	+	50.5038i	−0.0996299	+	0.0575214i
$879$	−360.393	−	1605.97i	−0.410003	−	1.82704i
$880$	247.953			0.281765
$881$	−1343.46	+	775.645i	−1.52492	+	0.880414i	−0.525358	+	0.850882i	$0.676068\pi$
$881$	−1343.46	+	775.645i	−1.52492	+	0.880414i	−0.999564	+	0.0295323i	$0.990598\pi$
$882$	−32.5903	−	68.9572i	−0.0369505	−	0.0781828i
$883$	−613.125			−0.694366			−0.347183	−	0.937797i	$-0.612862\pi$
$883$	−613.125			−0.694366			−0.347183	+	0.937797i	$0.612862\pi$
$884$	−1130.63	+	850.946i	−1.27899	+	0.962609i
$885$	−22.6112	+	72.3651i	−0.0255493	+	0.0817685i
$886$	−14.4516			−0.0163110
$887$			935.026i			1.05414i	0.849821	+	0.527072i	$0.176710\pi$
$887$			935.026i			1.05414i	−0.849821	+	0.527072i	$0.823290\pi$
$888$	103.063	+	459.266i	0.116062	+	0.517191i
$889$	26.8889	+	46.5729i	0.0302462	+	0.0523880i
$890$	58.2295	+	33.6188i	0.0654265	+	0.0377740i
$891$	199.564	−	1204.48i	0.223978	−	1.35182i
$892$	−1246.02			−1.39688
$893$		−	85.9973i		−	0.0963016i
$894$	79.1386	−	253.276i	0.0885219	−	0.283307i
$895$	2.12140			0.00237027
$896$	−391.756	−	226.181i	−0.437228	−	0.252434i
$897$	−190.367	−	534.188i	−0.212226	−	0.595527i
$898$	−113.323	−	196.281i	−0.126195	−	0.218575i
$899$	1934.57	−	1116.93i	2.15192	−	1.24241i
$900$	743.520	−	351.400i	0.826134	−	0.390444i
$901$	−178.486	+	309.146i	−0.198097	+	0.343115i
$902$	141.662	−	81.7884i	0.157053	−	0.0906745i
$903$	193.579	−	619.535i	0.214374	−	0.686085i
$904$	−197.131	−	341.442i	−0.218066	−	0.377701i
$905$	−10.6764	−	6.16400i	−0.0117971	−	0.00681105i
$906$	−286.990	−	89.6726i	−0.316766	−	0.0989764i
$907$	−574.524	+	995.104i	−0.633433	+	1.09714i	0.353412	+	0.935468i	$0.385021\pi$
$907$	−574.524	+	995.104i	−0.633433	+	1.09714i	−0.986845	+	0.161670i	$0.948312\pi$
$908$	−847.173	+	489.116i	−0.933010	+	0.538674i
$909$	−318.786	−	674.512i	−0.350699	−	0.742037i
$910$	−11.3006	+	26.5790i	−0.0124182	+	0.0292077i
$911$	443.854	−	256.259i	0.487216	−	0.281294i	−0.236203	−	0.971704i	$-0.575903\pi$
$911$	443.854	−	256.259i	0.487216	−	0.281294i	0.723419	+	0.690410i	$0.242570\pi$
$912$	896.408	−	201.161i	0.982904	−	0.220571i
$913$	−1248.10			−1.36703
$914$	84.5397	−	48.8090i	0.0924942	−	0.0534015i
$915$	26.2261	−	24.1568i	0.0286625	−	0.0264009i
$916$	−921.791			−1.00632
$917$	−381.971	−	220.531i	−0.416544	−	0.240492i
$918$	265.451	+	107.550i	0.289163	+	0.117156i
$919$	314.275	−	544.341i	0.341975	−	0.592318i	−0.642824	−	0.766014i	$-0.722237\pi$
$919$	314.275	−	544.341i	0.341975	−	0.592318i	0.984799	+	0.173695i	$0.0555708\pi$
$920$	−42.7390	−	24.6754i	−0.0464554	−	0.0268210i
$921$	70.0964	−	224.338i	0.0761090	−	0.243580i
$922$	100.485	−	174.046i	0.108986	−	0.188770i
$923$	62.2489	+	509.453i	0.0674420	+	0.551954i
$924$	856.717	+	267.689i	0.927183	+	0.289707i
$925$	628.657	−	1088.87i	0.679629	−	1.17715i
$926$	200.265	−	115.623i	0.216269	−	0.124863i
$927$	622.835	−	294.362i	0.671882	−	0.317543i
$928$	928.677			1.00073
$929$		−	234.522i		−	0.252446i	−0.992002	−	0.126223i	$-0.959714\pi$
$929$		−	234.522i		−	0.252446i	0.992002	−	0.126223i	$-0.0402855\pi$
$930$	−15.9926	+	51.1829i	−0.0171963	+	0.0550353i
$931$	−240.922	+	417.289i	−0.258778	+	0.448216i
$932$	−143.405	+	82.7950i	−0.153868	+	0.0888358i
$933$	−995.810	+	917.238i	−1.06732	+	0.983106i
$934$	−46.4564	+	80.4649i	−0.0497392	+	0.0861508i
$935$		−	488.353i		−	0.522303i
$936$	−345.473	+	13.6492i	−0.369095	+	0.0145824i
$937$	−598.868			−0.639133			−0.319567	−	0.947564i	$-0.603537\pi$
$937$	−598.868			−0.639133			−0.319567	+	0.947564i	$0.603537\pi$
$938$	−124.005	−	71.5943i	−0.132201	−	0.0763265i
$939$	689.789	−	154.794i	0.734599	−	0.164850i
$940$	−8.91267	−	15.4372i	−0.00948156	−	0.0164225i
$941$	−219.420	−	126.682i	−0.233178	−	0.134625i	0.378859	−	0.925454i	$-0.376316\pi$
$941$	−219.420	−	126.682i	−0.233178	−	0.134625i	−0.612037	+	0.790829i	$0.709650\pi$
$942$	14.3476	+	63.9351i	0.0152309	+	0.0678717i
$943$	419.660			0.445026
$944$		−	315.167i		−	0.333864i
$945$	−157.991	+	22.0475i	−0.167186	+	0.0233307i
$946$	119.189	+	206.442i	0.125993	+	0.218226i
$947$	−1345.27	−	776.694i	−1.42056	−	0.820163i	−0.424217	−	0.905561i	$-0.639451\pi$
$947$	−1345.27	−	776.694i	−1.42056	−	0.820163i	−0.996347	+	0.0853978i	$0.972784\pi$
$948$	153.404	+	166.545i	0.161818	+	0.175680i
$949$	510.414	+	678.172i	0.537844	+	0.714617i
$950$	164.878	+	95.1925i	0.173556	+	0.100203i
$951$	−81.8492	−	364.734i	−0.0860664	−	0.383526i
$952$	−214.418	+	371.383i	−0.225229	+	0.390109i
$953$	−373.494	−	215.637i	−0.391914	−	0.226272i	0.291075	−	0.956700i	$-0.405987\pi$
$953$	−373.494	−	215.637i	−0.391914	−	0.226272i	−0.682989	+	0.730429i	$0.739320\pi$
$954$	−38.7181	+	18.2988i	−0.0405850	+	0.0191811i
$955$	37.8575	−	65.5711i	0.0396414	−	0.0686609i
$956$		−	298.754i		−	0.312504i
$957$	−2381.36	+	534.397i	−2.48836	+	0.558409i
$958$	154.227	+	267.129i	0.160989	+	0.278841i
$959$		−	571.249i		−	0.595671i
$960$	128.800	−	118.637i	0.134167	−	0.123580i
$961$	−375.984	−	651.223i	−0.391242	−	0.677651i
$962$	−207.372	+	156.075i	−0.215564	+	0.162240i
$963$	214.175	+	17.6227i	0.222404	+	0.0182998i
$964$	184.768	+	320.028i	0.191668	+	0.331980i
$965$	−111.259	−	64.2354i	−0.115294	−	0.0665652i
$966$	−57.1688	−	62.0660i	−0.0591810	−	0.0642505i
$967$	548.133	−	949.394i	0.566839	−	0.981794i	−0.430037	−	0.902811i	$-0.641500\pi$
$967$	548.133	−	949.394i	0.566839	−	0.981794i	0.996876	−	0.0789825i	$-0.0251671\pi$
$968$	−271.755	+	156.898i	−0.280738	+	0.162084i
$969$	−396.194	−	1765.51i	−0.408869	−	1.82199i
$970$	−4.19775	−	7.27071i	−0.00432757	−	0.00749558i
$971$	−88.2684	−	50.9618i	−0.0909046	−	0.0524838i	0.453859	−	0.891074i	$-0.350047\pi$
$971$	−88.2684	−	50.9618i	−0.0909046	−	0.0524838i	−0.544763	+	0.838590i	$0.683380\pi$
$972$	−513.972	−	784.221i	−0.528777	−	0.806812i
$973$	521.736	+	903.674i	0.536214	+	0.928750i
$974$	239.346	−	138.187i	0.245735	−	0.141875i
$975$	703.474	+	598.398i	0.721511	+	0.613742i
$976$	−74.1120	+	128.366i	−0.0759345	+	0.131522i
$977$			1009.99i			1.03377i	0.856054	+	0.516886i	$0.172909\pi$
$977$			1009.99i			1.03377i	−0.856054	+	0.516886i	$0.827091\pi$
$978$	−4.00197	−	17.8335i	−0.00409199	−	0.0182346i
$979$	2346.66			2.39699
$980$			99.8756i			0.101914i
$981$	−43.2263	−	29.9356i	−0.0440635	−	0.0305154i
$982$	24.5534	−	42.5278i	0.0250035	−	0.0433073i
$983$	−1248.07	+	720.573i	−1.26965	+	0.733035i	−0.974922	−	0.222546i	$-0.928563\pi$
$983$	−1248.07	+	720.573i	−1.26965	+	0.733035i	−0.294731	+	0.955580i	$0.595230\pi$
$984$	76.3062	−	244.212i	0.0775469	−	0.248182i
$985$	−13.4887			−0.0136941
$986$		−	572.540i		−	0.580669i
$987$	−13.5920	−	60.5682i	−0.0137710	−	0.0613660i
$988$	644.926	+	856.894i	0.652759	+	0.867302i
$989$			611.566i			0.618368i
$990$	33.3550	−	48.1638i	0.0336919	−	0.0486503i
$991$	−698.522	−	1209.87i	−0.704865	−	1.22086i	−0.966740	−	0.255761i	$-0.917674\pi$
$991$	−698.522	−	1209.87i	−0.704865	−	1.22086i	0.261875	−	0.965102i	$-0.415659\pi$
$992$		−	712.130i		−	0.717873i
$993$	299.358	−	958.071i	0.301468	−	0.964824i
$994$	38.1848	+	66.1381i	0.0384153	+	0.0665373i
$995$	18.3775	−	10.6103i	0.0184699	−	0.0106636i
$996$	−705.030	+	649.401i	−0.707861	+	0.652009i
$997$	−1364.39			−1.36849			−0.684247	−	0.729250i	$-0.739869\pi$
$997$	−1364.39			−1.36849			−0.684247	+	0.729250i	$0.739869\pi$
$998$	9.42691	−	5.44263i	0.00944580	−	0.00545354i
$999$	−1328.63	−	538.304i	−1.32996	−	0.538843i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	117.3.u.a.68.14	yes	52
3.2	odd	2		351.3.u.a.341.13		52
9.2	odd	6		117.3.k.a.29.14	✓	52
9.7	even	3		351.3.k.a.224.13		52
13.9	even	3		117.3.k.a.113.13	yes	52
39.35	odd	6		351.3.k.a.152.14		52
117.61	even	3		351.3.u.a.35.13		52
117.74	odd	6	inner	117.3.u.a.74.14	yes	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.3.k.a.29.14	✓	52	9.2	odd	6
117.3.k.a.113.13	yes	52	13.9	even	3
117.3.u.a.68.14	yes	52	1.1	even	1	trivial
117.3.u.a.74.14	yes	52	117.74	odd	6	inner
351.3.k.a.152.14		52	39.35	odd	6
351.3.k.a.224.13		52	9.7	even	3
351.3.u.a.35.13		52	117.61	even	3
351.3.u.a.341.13		52	3.2	odd	2

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

\(f(q)\)	\(=\)	\(q+(-0.325651 - 0.188014i) q^{2} +(0.894719 - 2.86347i) q^{3} +(-1.92930 - 3.34165i) q^{4} +(0.994641 + 0.574256i) q^{5} +(-0.829740 + 0.764272i) q^{6} +5.14423 q^{7} +2.95506i q^{8} +(-7.39896 - 5.12401i) q^{9} +(-0.215937 - 0.374014i) q^{10} +(-13.0534 - 7.53640i) q^{11} +(-11.2949 + 2.53467i) q^{12} +(-7.81749 - 10.3869i) q^{13} +(-1.67522 - 0.967190i) q^{14} +(2.53429 - 2.33433i) q^{15} +(-7.16161 + 12.4043i) q^{16} +(24.4307 + 14.1051i) q^{17} +(1.44609 + 3.05975i) q^{18} +(10.6901 - 18.5158i) q^{19} -4.43165i q^{20} +(4.60264 - 14.7304i) q^{21} +(2.83390 + 4.90847i) q^{22} +14.5409i q^{23} +(8.46174 + 2.64395i) q^{24} +(-11.8405 - 20.5083i) q^{25} +(0.592890 + 4.85229i) q^{26} +(-21.2924 + 16.6022i) q^{27} +(-9.92477 - 17.1902i) q^{28} +(46.7423 + 26.9867i) q^{29} +(-1.26418 + 0.283692i) q^{30} +(20.6940 - 35.8431i) q^{31} +(14.9010 - 8.60310i) q^{32} +(-33.2594 + 30.6352i) q^{33} +(-5.30391 - 9.18664i) q^{34} +(5.11666 + 2.95411i) q^{35} +(-2.84781 + 34.6105i) q^{36} +(26.5470 + 45.9807i) q^{37} +(-6.96249 + 4.01980i) q^{38} +(-36.7370 + 13.0918i) q^{39} +(-1.69696 + 2.93923i) q^{40} -28.8607i q^{41} +(-4.26838 + 3.93159i) q^{42} +42.0583 q^{43} +58.1599i q^{44} +(-4.41681 - 9.34544i) q^{45} +(2.73390 - 4.73525i) q^{46} +(3.48340 - 2.01114i) q^{47} +(29.1117 + 31.6054i) q^{48} -22.5369 q^{49} +8.90471i q^{50} +(62.2480 - 57.3365i) q^{51} +(-19.6269 + 46.1627i) q^{52} +12.6540i q^{53} +(10.0553 - 1.40322i) q^{54} +(-8.65564 - 14.9920i) q^{55} +15.2015i q^{56} +(-43.4549 - 47.1774i) q^{57} +(-10.1478 - 17.5765i) q^{58} +(-19.0560 + 11.0020i) q^{59} +(-12.6899 - 3.96508i) q^{60} +10.3485 q^{61} +(-13.4780 + 7.78155i) q^{62} +(-38.0619 - 26.3591i) q^{63} +50.8229 q^{64} +(-1.81087 - 14.8204i) q^{65} +(16.5908 - 3.72311i) q^{66} +74.0229 q^{67} -108.852i q^{68} +(41.6375 + 13.0100i) q^{69} +(-1.11083 - 1.92401i) q^{70} +(-34.1908 - 19.7401i) q^{71} +(15.1418 - 21.8644i) q^{72} -65.2913 q^{73} -19.9649i q^{74} +(-69.3188 + 15.5557i) q^{75} -82.4979 q^{76} +(-67.1498 - 38.7690i) q^{77} +(14.4249 + 2.64371i) q^{78} +(-9.78025 - 16.9399i) q^{79} +(-14.2465 + 8.22520i) q^{80} +(28.4891 + 75.8246i) q^{81} +(-5.42622 + 9.39850i) q^{82} +(71.7112 - 41.4025i) q^{83} +(-58.1036 + 13.0389i) q^{84} +(16.1998 + 28.0589i) q^{85} +(-13.6963 - 7.90758i) q^{86} +(119.097 - 109.700i) q^{87} +(22.2705 - 38.5737i) q^{88} +(-134.830 + 77.8441i) q^{89} +(-0.318741 + 3.87377i) q^{90} +(-40.2150 - 53.4324i) q^{91} +(48.5905 - 28.0538i) q^{92} +(-84.1203 - 91.3262i) q^{93} -1.51249 q^{94} +(21.2657 - 12.2777i) q^{95} +(-11.3025 - 50.3660i) q^{96} +19.4397 q^{97} +(7.33915 + 4.23726i) q^{98} +(57.9651 + 122.647i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q - 3 q^{2} - q^{3} + 49 q^{4} - 6 q^{5} - 3 q^{6} + 2 q^{7} - 3 q^{9} - 6 q^{10} + 33 q^{11} - 39 q^{12} + 4 q^{13} - 6 q^{14} - 28 q^{15} - 83 q^{16} + 34 q^{18} + 5 q^{19} - 91 q^{21} - 15 q^{22}+ \cdots + 522 q^{99}+O(q^{100}) \) 52 * q - 3 * q^2 - q^3 + 49 * q^4 - 6 * q^5 - 3 * q^6 + 2 * q^7 - 3 * q^9 - 6 * q^10 + 33 * q^11 - 39 * q^12 + 4 * q^13 - 6 * q^14 - 28 * q^15 - 83 * q^16 + 34 * q^18 + 5 * q^19 - 91 * q^21 - 15 * q^22 + 36 * q^24 + 88 * q^25 + 132 * q^26 - 34 * q^27 - 22 * q^28 - 30 * q^29 + 31 * q^30 + 14 * q^31 - 63 * q^32 - 112 * q^33 - 6 * q^34 - 228 * q^35 + 47 * q^36 - 13 * q^37 - 192 * q^38 + 147 * q^39 + 72 * q^40 - 84 * q^42 + 62 * q^43 - 107 * q^45 + 6 * q^46 - 69 * q^47 - 58 * q^48 + 246 * q^49 + 235 * q^51 + 112 * q^52 + 444 * q^54 - 27 * q^55 + 189 * q^57 - 105 * q^58 - 435 * q^59 + 213 * q^60 - 16 * q^61 - 471 * q^62 - 170 * q^63 - 98 * q^64 - 435 * q^65 - 576 * q^66 + 68 * q^67 + 152 * q^69 - 57 * q^70 - 144 * q^71 + 513 * q^72 - 106 * q^73 + 98 * q^75 + 158 * q^76 + 282 * q^77 - 433 * q^78 - 25 * q^79 + 1050 * q^80 + 9 * q^81 + 81 * q^82 + 219 * q^83 - 172 * q^84 + 54 * q^85 - 24 * q^86 + 325 * q^87 - 15 * q^88 - 99 * q^89 + 183 * q^90 + 2 * q^91 + 888 * q^92 - 171 * q^93 - 606 * q^94 - 258 * q^95 - 439 * q^96 - 424 * q^97 + 405 * q^98 + 522 * q^99

Introduction

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