LMFDB - Embedded newform 117.3.k.a.29.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("117.29");

S:= CuspForms(chi, 3);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.18801909302$
Analytic rank:	$0$
Dimension:	$52$
Relative dimension:	$26$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			29.14
Character	$\chi$	$=$	117.29
Dual form			117.3.k.a.113.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-0.376029i q^{2} +(-2.92720 - 0.656887i) q^{3} +3.85860 q^{4} +(0.994641 - 0.574256i) q^{5} +(-0.247009 + 1.10071i) q^{6} +(-2.57212 - 4.45503i) q^{7} -2.95506i q^{8} +(8.13700 + 3.84568i) q^{9} +(-0.215937 - 0.374014i) q^{10} -15.0728i q^{11} +(-11.2949 - 2.53467i) q^{12} +(12.9040 - 1.57671i) q^{13} +(-1.67522 + 0.967190i) q^{14} +(-3.28873 + 1.02760i) q^{15} +14.3232 q^{16} +(-24.4307 - 14.1051i) q^{17} +(1.44609 - 3.05975i) q^{18} +(10.6901 - 18.5158i) q^{19} +(3.83792 - 2.21583i) q^{20} +(4.60264 + 14.7304i) q^{21} -5.66781 q^{22} +(12.5928 + 7.27045i) q^{23} +(-1.94114 + 8.65006i) 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} +53.9734i q^{29} +(0.386406 + 1.23666i) q^{30} +(20.6940 + 35.8431i) q^{31} -17.2062i q^{32} +(-9.90113 + 44.1211i) q^{33} +(-5.30391 + 9.18664i) q^{34} +(-5.11666 - 2.95411i) q^{35} +(31.3974 + 14.8390i) q^{36} +(26.5470 + 45.9807i) q^{37} +(-6.96249 - 4.01980i) q^{38} +(-38.8084 - 3.86114i) q^{39} +(-1.69696 - 2.93923i) q^{40} +(-24.9941 - 14.4303i) q^{41} +(5.53904 - 1.73073i) q^{42} +(-21.0292 - 36.4236i) q^{43} -58.1599i q^{44} +(10.3018 - 0.847651i) q^{45} +(2.73390 - 4.73525i) q^{46} +(3.48340 + 2.01114i) q^{47} +(-41.9269 - 9.40874i) q^{48} +(11.2684 - 19.5175i) q^{49} +(7.71171 + 4.45236i) q^{50} +(62.2480 + 57.3365i) q^{51} +(49.7915 - 6.08391i) q^{52} -12.6540i q^{53} +(-6.24290 + 8.00658i) q^{54} +(-8.65564 - 14.9920i) q^{55} +(-13.1649 + 7.60076i) q^{56} +(-43.4549 + 47.1774i) q^{57} +20.2956 q^{58} +22.0040i q^{59} +(-12.6899 + 3.96508i) q^{60} +(-5.17426 - 8.96208i) q^{61} +(13.4780 - 7.78155i) q^{62} +(-3.79666 - 46.1421i) q^{63} +50.8229 q^{64} +(11.9294 - 8.97848i) q^{65} +(16.5908 + 3.72311i) q^{66} +(-37.0115 + 64.1058i) q^{67} +(-94.2683 - 54.4258i) q^{68} +(-32.0857 - 29.5541i) q^{69} +(-1.11083 + 1.92401i) q^{70} +(34.1908 + 19.7401i) q^{71} +(11.3642 - 24.0453i) q^{72} -65.2913 q^{73} +(17.2901 - 9.98243i) q^{74} +(48.1310 - 52.2540i) q^{75} +(41.2489 - 71.4453i) q^{76} +(-67.1498 + 38.7690i) q^{77} +(-1.45190 + 14.5931i) q^{78} +(-9.78025 + 16.9399i) q^{79} +(14.2465 - 8.22520i) q^{80} +(51.4215 + 62.5846i) q^{81} +(-5.42622 + 9.39850i) q^{82} +(71.7112 + 41.4025i) q^{83} +(17.7598 + 56.8386i) q^{84} -32.3997 q^{85} +(-13.6963 + 7.90758i) q^{86} +(35.4544 - 157.991i) q^{87} -44.5410 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} +(-37.0306 - 118.513i) q^{93} +(0.756247 - 1.30986i) q^{94} -24.5555i q^{95} +(-11.3025 + 50.3660i) q^{96} +(-9.71984 - 16.8353i) q^{97} +(-7.33915 - 4.23726i) q^{98} +(57.9651 - 122.647i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q - q^{3} - 98 q^{4} - 6 q^{5} + 12 q^{6} - q^{7} - 3 q^{9} - 6 q^{10} - 39 q^{12} + 4 q^{13} - 6 q^{14} - 25 q^{15} + 166 q^{16} + 34 q^{18} + 5 q^{19} + 21 q^{20} - 91 q^{21} + 30 q^{22} - 75 q^{23}+ \cdots + 522 q^{99}+O(q^{100}) $ 52 * q - q^3 - 98 * q^4 - 6 * q^5 + 12 * q^6 - q^7 - 3 * q^9 - 6 * q^10 - 39 * q^12 + 4 * q^13 - 6 * q^14 - 25 * q^15 + 166 * q^16 + 34 * q^18 + 5 * q^19 + 21 * q^20 - 91 * q^21 + 30 * q^22 - 75 * q^23 - 24 * q^24 + 88 * q^25 - 132 * q^26 - 34 * q^27 - 22 * q^28 + 70 * q^30 + 14 * q^31 + 95 * q^33 - 6 * q^34 + 228 * q^35 - 58 * q^36 - 13 * q^37 - 192 * q^38 - 111 * q^39 + 72 * q^40 + 33 * q^41 + 159 * q^42 - 31 * q^43 - 47 * q^45 + 6 * q^46 - 69 * q^47 + 293 * q^48 - 123 * q^49 - 168 * q^50 + 235 * q^51 - 92 * q^52 - 339 * q^54 - 27 * q^55 + 168 * q^56 + 189 * q^57 + 210 * q^58 + 213 * q^60 + 8 * q^61 + 471 * q^62 + 169 * q^63 - 98 * q^64 - 246 * q^65 - 576 * q^66 - 34 * q^67 + 18 * q^68 - 193 * q^69 - 57 * q^70 + 144 * q^71 + 36 * q^72 - 106 * q^73 - 465 * q^74 - 58 * q^75 - 79 * q^76 + 282 * q^77 - 76 * q^78 - 25 * q^79 - 1050 * q^80 - 279 * q^81 + 81 * q^82 + 219 * q^83 + 395 * q^84 - 108 * q^85 - 24 * q^86 - 518 * q^87 + 30 * q^88 + 99 * q^89 + 183 * q^90 + 2 * q^91 + 888 * q^92 + 582 * q^93 + 303 * q^94 - 439 * q^96 + 212 * q^97 - 405 * q^98 + 522 * q^99

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		−	0.376029i		−	0.188014i	−0.995572	−	0.0940072i	$-0.970032\pi$
$2$		−	0.376029i		−	0.188014i	0.995572	−	0.0940072i	$-0.0299677\pi$
$3$	−2.92720	−	0.656887i	−0.975733	−	0.218962i
$3$	−2.92720	−	0.656887i	−0.975733	−	0.218962i
$4$	3.85860			0.964651
$5$	0.994641	−	0.574256i	0.198928	−	0.114851i	−0.397227	−	0.917720i	$-0.630028\pi$
$5$	0.994641	−	0.574256i	0.198928	−	0.114851i	0.596155	+	0.802869i	$0.296694\pi$
$6$	−0.247009	+	1.10071i	−0.0411681	+	0.183452i
$7$	−2.57212	−	4.45503i	−0.367445	−	0.636434i	0.621720	−	0.783239i	$-0.286434\pi$
$7$	−2.57212	−	4.45503i	−0.367445	−	0.636434i	−0.989165	+	0.146806i	$0.953101\pi$
$8$		−	2.95506i		−	0.369383i
$9$	8.13700	+	3.84568i	0.904111	+	0.427298i
$10$	−0.215937	−	0.374014i	−0.0215937	−	0.0374014i
$11$		−	15.0728i		−	1.37025i	−0.728424	−	0.685127i	$-0.759747\pi$
$11$		−	15.0728i		−	1.37025i	0.728424	−	0.685127i	$-0.240253\pi$
$12$	−11.2949	−	2.53467i	−0.941242	−	0.211222i
$13$	12.9040	−	1.57671i	0.992618	−	0.121286i
$13$	12.9040	−	1.57671i	0.992618	−	0.121286i
$14$	−1.67522	+	0.967190i	−0.119659	+	0.0690850i
$15$	−3.28873	+	1.02760i	−0.219249	+	0.0685064i
$16$	14.3232			0.895201
$17$	−24.4307	−	14.1051i	−1.43710	−	0.829709i	−0.439451	−	0.898266i	$-0.644827\pi$
$17$	−24.4307	−	14.1051i	−1.43710	−	0.829709i	−0.997647	+	0.0685572i	$0.978160\pi$
$18$	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	$-0.0235469\pi$
$20$	3.83792	−	2.21583i	0.191896	−	0.110791i
$21$	4.60264	+	14.7304i	0.219173	+	0.701446i
$22$	−5.66781			−0.257628
$23$	12.5928	+	7.27045i	0.547512	+	0.316106i	0.748118	−	0.663566i	$-0.230958\pi$
$23$	12.5928	+	7.27045i	0.547512	+	0.316106i	−0.200606	+	0.979672i	$0.564291\pi$
$24$	−1.94114	+	8.65006i	−0.0808809	+	0.360419i
$25$	−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
$29$			53.9734i			1.86115i	0.366100	+	0.930576i	$0.380693\pi$
$29$			53.9734i			1.86115i	−0.366100	+	0.930576i	$0.619307\pi$
$30$	0.386406	+	1.23666i	0.0128802	+	0.0412220i
$31$	20.6940	+	35.8431i	0.667549	+	1.15623i	0.978588	+	0.205831i	$0.0659897\pi$
$31$	20.6940	+	35.8431i	0.667549	+	1.15623i	−0.311039	+	0.950397i	$0.600677\pi$
$32$		−	17.2062i		−	0.537694i
$33$	−9.90113	+	44.1211i	−0.300034	+	1.33700i
$34$	−5.30391	+	9.18664i	−0.155997	+	0.270195i
$35$	−5.11666	−	2.95411i	−0.146190	−	0.0844030i
$36$	31.3974	+	14.8390i	0.872151	+	0.412193i
$37$	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
$39$	−38.8084	−	3.86114i	−0.995087	−	0.0990035i
$40$	−1.69696	−	2.93923i	−0.0424241	−	0.0734806i
$41$	−24.9941	−	14.4303i	−0.609612	−	0.351959i	0.163202	−	0.986593i	$-0.447818\pi$
$41$	−24.9941	−	14.4303i	−0.609612	−	0.351959i	−0.772813	+	0.634633i	$0.781151\pi$
$42$	5.53904	−	1.73073i	0.131882	−	0.0412078i
$43$	−21.0292	−	36.4236i	−0.489050	−	0.847060i	0.510870	−	0.859658i	$-0.329323\pi$
$43$	−21.0292	−	36.4236i	−0.489050	−	0.847060i	−0.999921	+	0.0125977i	$0.995990\pi$
$44$		−	58.1599i		−	1.32182i
$45$	10.3018	−	0.847651i	0.228929	−	0.0188367i
$46$	2.73390	−	4.73525i	0.0594326	−	0.102940i
$47$	3.48340	+	2.01114i	0.0741148	+	0.0427902i	0.536599	−	0.843837i	$-0.319709\pi$
$47$	3.48340	+	2.01114i	0.0741148	+	0.0427902i	−0.462485	+	0.886627i	$0.653042\pi$
$48$	−41.9269	−	9.40874i	−0.873478	−	0.196015i
$49$	11.2684	−	19.5175i	0.229968	−	0.398317i
$50$	7.71171	+	4.45236i	0.154234	+	0.0890471i
$51$	62.2480	+	57.3365i	1.22055	+	1.12425i
$52$	49.7915	−	6.08391i	0.957529	−	0.116998i
$53$		−	12.6540i		−	0.238755i	−0.992849	−	0.119378i	$-0.961910\pi$
$53$		−	12.6540i		−	0.238755i	0.992849	−	0.119378i	$-0.0380899\pi$
$54$	−6.24290	+	8.00658i	−0.115609	+	0.148270i
$55$	−8.65564	−	14.9920i	−0.157375	−	0.272582i
$56$	−13.1649	+	7.60076i	−0.235088	+	0.135728i
$57$	−43.4549	+	47.1774i	−0.762368	+	0.827673i
$58$	20.2956			0.349923
$59$			22.0040i			0.372948i	0.982460	+	0.186474i	$0.0597061\pi$
$59$			22.0040i			0.372948i	−0.982460	+	0.186474i	$0.940294\pi$
$60$	−12.6899	+	3.96508i	−0.211499	+	0.0660847i
$61$	−5.17426	−	8.96208i	−0.0848239	−	0.146919i	0.820492	−	0.571658i	$-0.193699\pi$
$61$	−5.17426	−	8.96208i	−0.0848239	−	0.146919i	−0.905316	+	0.424738i	$0.860366\pi$
$62$	13.4780	−	7.78155i	0.217388	−	0.125509i
$63$	−3.79666	−	46.1421i	−0.0602644	−	0.732415i
$64$	50.8229			0.794107
$65$	11.9294	−	8.97848i	0.183530	−	0.138130i
$66$	16.5908	+	3.72311i	0.251376	+	0.0564108i
$67$	−37.0115	+	64.1058i	−0.552410	+	0.956802i	0.445690	+	0.895187i	$0.352958\pi$
$67$	−37.0115	+	64.1058i	−0.552410	+	0.956802i	−0.998100	+	0.0616149i	$0.980375\pi$
$68$	−94.2683	−	54.4258i	−1.38630	−	0.800379i
$69$	−32.0857	−	29.5541i	−0.465011	−	0.428320i
$70$	−1.11083	+	1.92401i	−0.0158690	+	0.0274859i
$71$	34.1908	+	19.7401i	0.481561	+	0.278029i	0.721067	−	0.692865i	$-0.243652\pi$
$71$	34.1908	+	19.7401i	0.481561	+	0.278029i	−0.239506	+	0.970895i	$0.576985\pi$
$72$	11.3642	−	24.0453i	0.157836	−	0.333963i
$73$	−65.2913			−0.894402			−0.447201	−	0.894434i	$-0.647579\pi$
$73$	−65.2913			−0.894402			−0.447201	+	0.894434i	$0.647579\pi$
$74$	17.2901	−	9.98243i	0.233650	−	0.134898i
$75$	48.1310	−	52.2540i	0.641747	−	0.696720i
$76$	41.2489	−	71.4453i	0.542749	−	0.940069i
$77$	−67.1498	+	38.7690i	−0.872076	+	0.503493i
$78$	−1.45190	+	14.5931i	−0.0186141	+	0.187091i
$79$	−9.78025	+	16.9399i	−0.123801	+	0.214429i	−0.921263	−	0.388939i	$-0.872842\pi$
$79$	−9.78025	+	16.9399i	−0.123801	+	0.214429i	0.797463	+	0.603368i	$0.206175\pi$
$80$	14.2465	−	8.22520i	0.178081	−	0.102815i
$81$	51.4215	+	62.5846i	0.634833	+	0.772649i
$82$	−5.42622	+	9.39850i	−0.0661735	+	0.114616i
$83$	71.7112	+	41.4025i	0.863991	+	0.498825i	0.865347	−	0.501174i	$-0.167098\pi$
$83$	71.7112	+	41.4025i	0.863991	+	0.498825i	−0.00135589	+	0.999999i	$0.500432\pi$
$84$	17.7598	+	56.8386i	0.211426	+	0.676650i
$85$	−32.3997			−0.381172
$86$	−13.6963	+	7.90758i	−0.159260	+	0.0919486i
$87$	35.4544	−	157.991i	0.407522	−	1.81599i
$88$	−44.5410			−0.506148
$89$	134.830	−	77.8441i	1.51494	−	0.874653i	0.515097	−	0.857132i	$-0.327756\pi$
$89$	134.830	−	77.8441i	1.51494	−	0.874653i	0.999846	−	0.0175212i	$-0.00557746\pi$
$90$	−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
$93$	−37.0306	−	118.513i	−0.398179	−	1.27434i
$94$	0.756247	−	1.30986i	0.00804518	−	0.0139347i
$95$		−	24.5555i		−	0.258479i
$96$	−11.3025	+	50.3660i	−0.117735	+	0.524646i
$97$	−9.71984	−	16.8353i	−0.100205	−	0.173559i	0.811564	−	0.584263i	$-0.198616\pi$
$97$	−9.71984	−	16.8353i	−0.100205	−	0.173559i	−0.911769	+	0.410704i	$0.865283\pi$
$98$	−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
$101$			82.8944i			0.820737i	0.911920	+	0.410369i	$0.134600\pi$
$101$			82.8944i			0.820737i	−0.911920	+	0.410369i	$0.865400\pi$
$102$	21.5602	−	23.4071i	0.211374	−	0.229481i
$103$	−38.2718	−	66.2886i	−0.371571	−	0.643579i	0.618237	−	0.785992i	$-0.287847\pi$
$103$	−38.2718	−	66.2886i	−0.371571	−	0.643579i	−0.989807	+	0.142413i	$0.954514\pi$
$104$	−4.65929	−	38.1322i	−0.0448008	−	0.366656i
$105$	13.0370	+	12.0083i	0.124162	+	0.114365i
$106$	−4.75828			−0.0448894
$107$	20.6786	−	11.9388i	0.193258	−	0.111578i	−0.400249	−	0.916407i	$-0.631076\pi$
$107$	20.6786	−	11.9388i	0.193258	−	0.111578i	0.593507	+	0.804829i	$0.297743\pi$
$108$	−82.1591	−	64.0612i	−0.760732	−	0.593159i
$109$	5.84222			0.0535983			0.0267992	−	0.999641i	$-0.491469\pi$
$109$	5.84222			0.0535983			0.0267992	+	0.999641i	$0.491469\pi$
$110$	−5.63743	+	3.25477i	−0.0512494	+	0.0295888i
$111$	−47.5042	−	152.033i	−0.427965	−	1.36967i
$112$	−36.8410	−	63.8104i	−0.328937	−	0.569736i
$113$			133.419i			1.18070i	0.807146	+	0.590351i	$0.201011\pi$
$113$			133.419i			1.18070i	−0.807146	+	0.590351i	$0.798989\pi$
$114$	17.7401	+	16.3403i	0.155615	+	0.143336i
$115$	16.7004			0.145221
$116$			208.262i			1.79536i
$117$	111.064	+	36.7951i	0.949262	+	0.314488i
$118$	8.27412			0.0701197
$119$			145.119i			1.21949i
$120$	3.03661	+	9.71841i	0.0253051	+	0.0809868i
$121$	−106.189			−0.877596
$122$	−3.37000	+	1.94567i	−0.0276230	+	0.0159481i
$123$	63.6835	+	58.6588i	0.517752	+	0.476900i
$124$	79.8499	+	138.304i	0.643951	+	1.11536i
$125$			55.9106i			0.447285i
$126$	−17.3508	+	1.42765i	−0.137705	+	0.0113306i
$127$	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	$0.820229\pi$
$128$		−	87.9356i		−	0.686997i
$129$	37.6304	+	120.433i	0.291708	+	0.933588i
$130$	−3.37617	−	4.48581i	−0.0259705	−	0.0345063i
$131$	−74.2522	+	42.8695i	−0.566811	+	0.327248i	−0.755875	−	0.654716i	$-0.772788\pi$
$131$	−74.2522	+	42.8695i	−0.566811	+	0.327248i	0.189064	+	0.981965i	$0.439455\pi$
$132$	−38.2045	+	170.246i	−0.289428	+	1.28974i
$133$	−109.985			−0.826954
$134$	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
$137$	96.1691	−	55.5233i	0.701964	−	0.405279i	−0.106114	−	0.994354i	$-0.533841\pi$
$137$	96.1691	−	55.5233i	0.701964	−	0.405279i	0.808079	+	0.589075i	$0.200508\pi$
$138$	−11.1132	+	12.0652i	−0.0805304	+	0.0874287i
$139$	−202.843			−1.45930			−0.729652	−	0.683818i	$-0.760318\pi$
$139$	−202.843			−1.45930			−0.729652	+	0.683818i	$0.760318\pi$
$140$	−19.7432	−	11.3987i	−0.141023	−	0.0814194i
$141$	−8.87550	−	8.17520i	−0.0629468	−	0.0579802i
$142$	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
$146$			24.5514i			0.168161i
$147$	−45.8058	+	49.7296i	−0.311604	+	0.338296i
$148$	102.434	+	177.421i	0.692123	+	1.19879i
$149$			235.223i			1.57868i	0.613957	+	0.789340i	$0.289577\pi$
$149$			235.223i			1.57868i	−0.613957	+	0.789340i	$0.710423\pi$
$150$	−19.6490	−	18.0987i	−0.130993	−	0.120658i
$151$	133.267	−	230.825i	0.882561	−	1.52864i	0.0340779	−	0.999419i	$-0.489151\pi$
$151$	133.267	−	230.825i	0.882561	−	1.52864i	0.848483	−	0.529222i	$-0.177516\pi$
$152$	−54.7155	−	31.5900i	−0.359970	−	0.207829i
$153$	−144.549	−	208.725i	−0.944764	−	1.36422i
$154$	14.5783	+	25.2503i	0.0946640	+	0.163963i
$155$	41.1662	+	23.7673i	0.265588	+	0.153338i
$156$	−149.746	−	14.8986i	−0.959911	−	0.0955038i
$157$	29.0426	+	50.3033i	0.184985	+	0.320403i	0.943571	−	0.331169i	$-0.107443\pi$
$157$	29.0426	+	50.3033i	0.184985	+	0.320403i	−0.758587	+	0.651572i	$0.774110\pi$
$158$	6.36989	+	3.67766i	0.0403158	+	0.0232763i
$159$	−8.31226	+	37.0408i	−0.0522784	+	0.232961i
$160$	−9.88076	−	17.1140i	−0.0617548	−	0.106962i
$161$		−	74.8017i		−	0.464607i
$162$	23.5336	−	19.3360i	0.145269	−	0.119358i
$163$	−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
$165$	15.4887	+	49.5704i	0.0938711	+	0.300427i
$166$	15.5685	−	26.9655i	0.0937864	−	0.162443i
$167$	−27.0940	−	15.6427i	−0.162240	−	0.0936691i	0.416682	−	0.909052i	$-0.363193\pi$
$167$	−27.0940	−	15.6427i	−0.162240	−	0.0936691i	−0.578922	+	0.815383i	$0.696526\pi$
$168$	43.5291	−	13.6011i	0.259102	−	0.0809589i
$169$	164.028	−	40.6919i	0.970580	−	0.240781i
$170$			12.1832i			0.0716659i
$171$	158.192	−	109.553i	0.925097	−	0.640658i
$172$	−81.1432	−	140.544i	−0.471763	−	0.817117i
$173$	3.74325	−	2.16116i	0.0216373	−	0.0124923i	−0.489142	−	0.872204i	$-0.662690\pi$
$173$	3.74325	−	2.16116i	0.0216373	−	0.0124923i	0.510780	+	0.859712i	$0.329357\pi$
$174$	−59.4092	−	13.3319i	−0.341432	−	0.0766201i
$175$	121.820			0.696115
$176$		−	215.891i		−	1.22665i
$177$	14.4541	−	64.4100i	0.0816617	−	0.363898i
$178$	−29.2716	−	50.7000i	−0.164447	−	0.284831i
$179$	−1.59962	+	0.923541i	−0.00893642	+	0.00515945i	−0.504462	−	0.863434i	$-0.668309\pi$
$179$	−1.59962	+	0.923541i	−0.00893642	+	0.00515945i	0.495525	+	0.868594i	$0.334976\pi$
$180$	39.7505	−	3.27075i	0.220836	−	0.0181708i
$181$	−10.7339			−0.0593032			−0.0296516	−	0.999560i	$-0.509440\pi$
$181$	−10.7339			−0.0593032			−0.0296516	+	0.999560i	$0.509440\pi$
$182$	−20.0921	+	15.1220i	−0.110396	+	0.0830879i
$183$	9.25901	+	29.6327i	0.0505957	+	0.161927i
$184$	21.4846	−	37.2125i	0.116764	−	0.202242i
$185$	52.8094	+	30.4895i	0.285456	+	0.164808i
$186$	−44.5645	+	13.9246i	−0.239594	+	0.0748634i
$187$	−212.603	+	368.239i	−1.13691	+	1.96919i
$188$	13.4410	+	7.76019i	0.0714949	+	0.0412776i
$189$	−19.1966	+	137.561i	−0.101569	+	0.727837i
$190$	−9.23357			−0.0485977
$191$	57.0922	−	32.9622i	0.298912	−	0.172577i	−0.343042	−	0.939320i	$-0.611457\pi$
$191$	57.0922	−	32.9622i	0.298912	−	0.172577i	0.641954	+	0.766743i	$0.278124\pi$
$192$	−148.769	−	33.3849i	−0.774837	−	0.173880i
$193$	55.9292	−	96.8723i	0.289789	−	0.501929i	−0.683970	−	0.729510i	$-0.739748\pi$
$193$	55.9292	−	96.8723i	0.289789	−	0.501929i	0.973759	+	0.227581i	$0.0730816\pi$
$194$	−6.33055	+	3.65494i	−0.0326317	+	0.0188399i
$195$	−40.8177	+	18.4455i	−0.209322	+	0.0945924i
$196$	43.4804	−	75.3103i	0.221839	−	0.384236i
$197$	10.1710	−	5.87226i	0.0516297	−	0.0298084i	−0.473963	−	0.880545i	$-0.657177\pi$
$197$	10.1710	−	5.87226i	0.0516297	−	0.0298084i	0.525593	+	0.850736i	$0.323844\pi$
$198$	−46.1189	−	21.7966i	−0.232924	−	0.110084i
$199$	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
$201$	150.450	−	163.338i	0.748509	−	0.812627i
$202$	31.1707			0.154310
$203$	240.453	−	138.826i	1.18450	−	0.683871i
$204$	240.190	+	221.239i	1.17740	+	1.08450i
$205$	−33.1468			−0.161692
$206$	−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
$210$	4.51548	−	4.90228i	0.0215023	−	0.0233442i
$211$	−13.0910	+	22.6743i	−0.0620426	+	0.107461i	−0.895378	−	0.445306i	$-0.853095\pi$
$211$	−13.0910	+	22.6743i	−0.0620426	+	0.107461i	0.833336	+	0.552767i	$0.186428\pi$
$212$		−	48.8268i		−	0.230315i
$213$	−87.1164	−	80.2427i	−0.408997	−	0.376726i
$214$	−4.48934	−	7.77577i	−0.0209782	−	0.0363354i
$215$	−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
$218$		−	2.19684i		−	0.0100773i
$219$	191.121	+	42.8890i	0.872698	+	0.195840i
$220$	−33.3987	−	57.8482i	−0.151812	−	0.262946i
$221$	−337.494	−	143.492i	−1.52712	−	0.649285i
$222$	−57.1688	+	17.8629i	−0.257517	+	0.0804637i
$223$	−322.919			−1.44807			−0.724033	−	0.689765i	$-0.757714\pi$
$223$	−322.919			−1.44807			−0.724033	+	0.689765i	$0.757714\pi$
$224$	−76.6542	+	44.2563i	−0.342206	+	0.197573i
$225$	−175.214	+	121.341i	−0.778729	+	0.539294i
$226$	50.1696			0.221989
$227$	219.554	−	126.760i	0.967200	−	0.558413i	0.0688188	−	0.997629i	$-0.478077\pi$
$227$	219.554	−	126.760i	0.967200	−	0.558413i	0.898382	+	0.439216i	$0.144744\pi$
$228$	−167.675	+	182.039i	−0.735418	+	0.798415i
$229$	119.446	+	206.887i	0.521600	+	0.903437i	0.999684	+	0.0251232i	$0.00799781\pi$
$229$	119.446	+	206.887i	0.521600	+	0.903437i	−0.478085	+	0.878314i	$0.658669\pi$
$230$		−	6.27983i		−	0.0273036i
$231$	222.028	−	69.3747i	0.961159	−	0.300323i
$232$	159.495			0.687477
$233$			42.9145i			0.184182i	0.995751	+	0.0920912i	$0.0293551\pi$
$233$			42.9145i			0.184182i	−0.995751	+	0.0920912i	$0.970645\pi$
$234$	13.8360	−	41.7631i	0.0591282	−	0.178475i
$235$	4.61964			0.0196580
$236$			84.9045i			0.359765i
$237$	39.7563	−	43.1619i	0.167748	−	0.182118i
$238$	54.5691			0.229282
$239$	67.0524	−	38.7127i	0.280554	−	0.161978i	−0.353120	−	0.935578i	$-0.614879\pi$
$239$	67.0524	−	38.7127i	0.280554	−	0.161978i	0.633674	+	0.773600i	$0.281546\pi$
$240$	−47.1053	+	14.7185i	−0.196272	+	0.0613270i
$241$	47.8848	+	82.9389i	0.198692	+	0.344145i	0.948105	−	0.317959i	$-0.102997\pi$
$241$	47.8848	+	82.9389i	0.198692	+	0.344145i	−0.749412	+	0.662103i	$0.769664\pi$
$242$			39.9302i			0.165001i
$243$	−109.410	−	216.976i	−0.450247	−	0.892904i
$244$	−19.9654	−	34.5811i	−0.0818254	−	0.141726i
$245$		−	25.8839i		−	0.105649i
$246$	22.0574	−	23.9469i	0.0896642	−	0.0973450i
$247$	108.752	−	255.784i	0.440290	−	1.03556i
$248$	105.919	−	61.1521i	0.427091	−	0.246581i
$249$	−182.716	−	168.300i	−0.733801	−	0.675902i
$250$	21.0240			0.0840961
$251$	−365.360	−	210.940i	−1.45562	−	0.840400i	−0.456825	−	0.889557i	$-0.651013\pi$
$251$	−365.360	−	210.940i	−1.45562	−	0.840400i	−0.998791	+	0.0491566i	$0.984347\pi$
$252$	−14.6498	−	178.044i	−0.0581341	−	0.706524i
$253$	109.586	−	189.808i	0.433146	−	0.750231i
$254$	3.40435	−	1.96550i	0.0134030	−	0.00773820i
$255$	94.8403	+	21.2829i	0.371923	+	0.0834624i
$256$	170.225			0.664942
$257$	336.324	+	194.177i	1.30865	+	0.755552i	0.981872	−	0.189548i	$-0.0607022\pi$
$257$	336.324	+	194.177i	1.30865	+	0.755552i	0.326783	+	0.945100i	$0.394035\pi$
$258$	45.2863	−	14.1501i	0.175528	−	0.0548454i
$259$	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
$263$			159.385i			0.606027i	0.952986	+	0.303014i	$0.0979928\pi$
$263$			159.385i			0.606027i	−0.952986	+	0.303014i	$0.902007\pi$
$264$	130.381	+	29.2584i	0.493866	+	0.110827i
$265$	−7.26665	−	12.5862i	−0.0274213	−	0.0474951i
$266$			41.3575i			0.155479i
$267$	−445.809	+	139.297i	−1.66970	+	0.521712i
$268$	−142.813	+	247.359i	−0.532883	+	0.922980i
$269$	−138.125	−	79.7468i	−0.513478	−	0.296456i	0.220784	−	0.975323i	$-0.429138\pi$
$269$	−138.125	−	79.7468i	−0.513478	−	0.296456i	−0.734262	+	0.678866i	$0.762472\pi$
$270$	−1.61161	+	11.5487i	−0.00596894	+	0.0427729i
$271$	−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
$273$	82.6182	+	182.824i	0.302631	+	0.669685i
$274$	−20.8784	−	36.1624i	−0.0761984	−	0.131979i
$275$	309.117	+	178.469i	1.12406	+	0.648977i
$276$	−123.806	−	114.037i	−0.448573	−	0.413179i
$277$	160.981	+	278.828i	0.581159	+	1.00660i	0.995342	+	0.0964039i	$0.0307340\pi$
$277$	160.981	+	278.828i	0.581159	+	1.00660i	−0.414183	+	0.910194i	$0.635933\pi$
$278$			76.2750i			0.274370i
$279$	30.5461	+	371.238i	0.109484	+	1.33060i
$280$	−8.72957	+	15.1201i	−0.0311770	+	0.0540002i
$281$	−357.552	−	206.433i	−1.27243	−	0.734637i	−0.296984	−	0.954883i	$-0.595981\pi$
$281$	−357.552	−	206.433i	−1.27243	−	0.734637i	−0.975444	+	0.220246i	$0.929314\pi$
$282$	−3.07411	+	3.33745i	−0.0109011	+	0.0118349i
$283$	−243.879	+	422.411i	−0.861764	+	1.49262i	0.00846154	+	0.999964i	$0.497307\pi$
$283$	−243.879	+	422.411i	−0.861764	+	1.49262i	−0.870225	+	0.492654i	$0.836027\pi$
$284$	131.929	+	76.1692i	0.464538	+	0.268201i
$285$	−16.1302	+	71.8788i	−0.0565971	+	0.252206i
$286$	−73.1376	+	8.93651i	−0.255726	+	0.0312465i
$287$			148.466i			0.517303i
$288$	66.1695	−	140.007i	0.229755	−	0.486135i
$289$	253.405	+	438.911i	0.876835	+	1.51872i
$290$	20.1868	−	11.6548i	0.0696096	−	0.0401891i
$291$	17.3931	+	55.6650i	0.0597700	+	0.191289i
$292$	−251.933			−0.862785
$293$		−	548.637i		−	1.87248i	−0.351360	−	0.936240i	$-0.614281\pi$
$293$		−	548.637i		−	1.87248i	0.351360	−	0.936240i	$-0.385719\pi$
$294$	18.6998	+	17.2243i	0.0636046	+	0.0585861i
$295$	12.6359	+	21.8860i	0.0428336	+	0.0741899i
$296$	135.876	−	78.4479i	0.459040	−	0.265027i
$297$	−250.241	+	320.937i	−0.842562	+	1.08059i
$298$	88.4508			0.296815
$299$	173.961	+	73.9629i	0.581810	+	0.247367i
$300$	185.718	−	201.627i	0.619062	−	0.672091i
$301$	−108.179	+	187.371i	−0.359398	+	0.622496i
$302$	−86.7968	−	50.1122i	−0.287407	−	0.165934i
$303$	54.4523	−	242.649i	0.179711	−	0.800821i
$304$	153.117	−	265.206i	0.503674	−	0.872390i
$305$	−10.2931	−	5.94270i	−0.0337477	−	0.0194843i
$306$	−78.4868	+	54.3545i	−0.256493	+	0.177629i
$307$	78.3446			0.255194			0.127597	−	0.991826i	$-0.459274\pi$
$307$	78.3446			0.255194			0.127597	+	0.991826i	$0.459274\pi$
$308$	−259.104	+	149.594i	−0.841248	+	0.485695i
$309$	68.4850	+	219.180i	0.221634	+	0.709322i
$310$	8.93720	−	15.4797i	0.0288297	−	0.0499345i
$311$	−390.829	+	225.645i	−1.25668	+	0.725547i	−0.972428	−	0.233202i	$-0.925080\pi$
$311$	−390.829	+	225.645i	−1.25668	+	0.725547i	−0.284255	+	0.958749i	$0.591746\pi$
$312$	−11.4099	+	114.681i	−0.0365702	+	0.367568i
$313$	117.824	−	204.077i	0.376435	−	0.652004i	−0.614106	−	0.789224i	$-0.710483\pi$
$313$	117.824	−	204.077i	0.376435	−	0.652004i	0.990541	+	0.137220i	$0.0438166\pi$
$314$	18.9155	−	10.9209i	0.0602404	−	0.0347798i
$315$	−30.2737	−	43.7146i	−0.0961070	−	0.138777i
$316$	−37.7381	+	65.3643i	−0.119424	+	0.206849i
$317$	107.908	+	62.3008i	0.340404	+	0.196532i	0.660451	−	0.750869i	$-0.270365\pi$
$317$	107.908	+	62.3008i	0.340404	+	0.196532i	−0.320047	+	0.947402i	$0.603699\pi$
$318$	13.9284	+	3.12565i	0.0438001	+	0.00982909i
$319$	813.530			2.55025
$320$	50.5505	−	29.1853i	0.157970	−	0.0912042i
$321$	−68.3730	+	21.3638i	−0.213000	+	0.0665538i
$322$	−28.1276			−0.0873528
$323$	−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
$327$	−17.1013	−	3.83768i	−0.0522977	−	0.0117360i
$328$	−42.6425	+	73.8590i	−0.130008	+	0.225180i
$329$		−	20.6915i		−	0.0628922i
$330$	18.6399	−	5.82421i	0.0564846	−	0.0176491i
$331$	−167.292	−	289.758i	−0.505413	−	0.875401i	−0.999980	−	0.00626172i	$-0.998007\pi$
$331$	−167.292	−	289.758i	−0.505413	−	0.875401i	0.494567	−	0.869139i	$-0.335327\pi$
$332$	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
$335$			85.0163i			0.253780i
$336$	65.9246	+	210.986i	0.196204	+	0.627935i
$337$	−185.957	−	322.088i	−0.551802	−	0.955750i	−0.998145	−	0.0608873i	$-0.980607\pi$
$337$	−185.957	−	322.088i	−0.551802	−	0.955750i	0.446342	−	0.894862i	$-0.352726\pi$
$338$	−15.3013	−	61.6793i	−0.0452702	−	0.182483i
$339$	87.6415	−	390.545i	0.258530	−	1.15205i
$340$	−125.017			−0.367698
$341$	540.255	−	311.916i	1.58433	−	0.914711i
$342$	−41.1949	−	59.4846i	−0.120453	−	0.173932i
$343$	−368.002			−1.07289
$344$	−107.634	+	62.1425i	−0.312889	+	0.180647i
$345$	−48.8854	−	10.9703i	−0.141697	−	0.0317979i
$346$	−0.812660	−	1.40757i	−0.00234873	−	0.00406812i
$347$			170.800i			0.492219i	0.969242	+	0.246110i	$0.0791523\pi$
$347$			170.800i			0.492219i	−0.969242	+	0.246110i	$0.920848\pi$
$348$	136.805	−	609.624i	0.393116	−	1.75179i
$349$	134.718			0.386010			0.193005	−	0.981198i	$-0.438177\pi$
$349$	134.718			0.386010			0.193005	+	0.981198i	$0.438177\pi$
$350$		−	45.8079i		−	0.130880i
$351$	−300.935	−	180.663i	−0.857365	−	0.514709i
$352$	−259.345			−0.736777
$353$		−	126.976i		−	0.359705i	−0.983694	−	0.179853i	$-0.942438\pi$
$353$		−	126.976i		−	0.359705i	0.983694	−	0.179853i	$-0.0575621\pi$
$354$	−24.2200	−	5.43517i	−0.0684181	−	0.0153536i
$355$	45.3435			0.127728
$356$	520.255	−	300.370i	1.46139	−	0.843735i
$357$	95.3270	−	424.793i	0.267023	−	1.18990i
$358$	0.347278	+	0.601503i	0.000970051	+	0.00168018i
$359$			443.856i			1.23637i	0.786034	+	0.618184i	$0.212131\pi$
$359$			443.856i			1.23637i	−0.786034	+	0.618184i	$0.787869\pi$
$360$	−2.50486	−	30.4424i	−0.00695795	−	0.0845624i
$361$	−48.0575	−	83.2381i	−0.133123	−	0.230576i
$362$			4.03625i			0.0111499i
$363$	310.837	+	69.7543i	0.856300	+	0.192161i
$364$	−155.174	−	206.174i	−0.426301	−	0.566413i
$365$	−64.9414	+	37.4939i	−0.177922	+	0.102723i
$366$	11.1428	−	3.48166i	0.0304447	−	0.00951272i
$367$	−116.173			−0.316547			−0.158274	−	0.987395i	$-0.550593\pi$
$367$	−116.173			−0.316547			−0.158274	+	0.987395i	$0.550593\pi$
$368$	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
$371$	−56.3741	+	32.5476i	−0.151952	+	0.0877294i
$372$	−142.887	−	457.296i	−0.384104	−	1.22929i
$373$	210.987			0.565649			0.282825	−	0.959172i	$-0.408729\pi$
$373$	210.987			0.565649			0.282825	+	0.959172i	$0.408729\pi$
$374$	138.468	+	79.9447i	0.370236	+	0.213756i
$375$	36.7270	−	163.662i	0.0979386	−	0.436431i
$376$	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	$-0.334676\pi$
$380$		−	94.7498i		−	0.249342i
$381$	−9.35339	−	29.9348i	−0.0245496	−	0.0785689i
$382$	−12.3947	−	21.4683i	−0.0324470	−	0.0561998i
$383$			253.952i			0.663061i	0.943445	+	0.331530i	$0.107565\pi$
$383$			253.952i			0.663061i	−0.943445	+	0.331530i	$0.892435\pi$
$384$	−57.7638	+	257.405i	−0.150427	+	0.670326i
$385$	−44.5266	+	77.1224i	−0.115654	+	0.200318i
$386$	−36.4268	−	21.0310i	−0.0943699	−	0.0544845i
$387$	−31.0408	−	377.250i	−0.0802089	−	0.974806i
$388$	−37.5050	−	64.9606i	−0.0966624	−	0.167424i
$389$	−291.388	−	168.233i	−0.749070	−	0.432476i	0.0762879	−	0.997086i	$-0.475693\pi$
$389$	−291.388	−	168.233i	−0.749070	−	0.432476i	−0.825358	+	0.564610i	$0.809027\pi$
$390$	6.93605	+	15.3486i	0.0177847	+	0.0393555i
$391$	−205.100	−	355.244i	−0.524553	−	0.908552i
$392$	−57.6755	−	33.2990i	−0.147131	−	0.0849463i
$393$	245.512	−	76.7124i	0.624711	−	0.195197i
$394$	−2.20814	−	3.82461i	−0.00560441	−	0.00970713i
$395$			22.4655i			0.0568746i
$396$	223.664	−	473.247i	0.564809	−	1.19507i
$397$	−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
$399$	321.948	+	72.2477i	0.806887	+	0.181072i
$400$	−169.594	+	293.745i	−0.423984	+	0.734361i
$401$	−487.509	−	281.464i	−1.21573	−	0.701904i	−0.251731	−	0.967797i	$-0.581000\pi$
$401$	−487.509	−	281.464i	−1.21573	−	0.701904i	−0.964003	+	0.265893i	$0.914333\pi$
$402$	−61.4198	−	56.5736i	−0.152786	−	0.140730i
$403$	323.550	+	429.892i	0.802854	+	1.06673i
$404$			319.857i			0.791724i
$405$	87.0855	+	32.7201i	0.215026	+	0.0807903i
$406$	−52.2025	−	90.4174i	−0.128578	−	0.222703i
$407$	693.058	−	400.137i	1.70284	−	0.983138i
$408$	169.433	−	183.947i	0.415277	−	0.450850i
$409$	−740.437			−1.81036			−0.905179	−	0.425030i	$-0.860264\pi$
$409$	−740.437			−1.81036			−0.905179	+	0.425030i	$0.860264\pi$
$410$			12.4642i			0.0304004i
$411$	−317.979	+	99.3554i	−0.773671	+	0.241741i
$412$	−147.676	−	255.782i	−0.358436	−	0.620829i
$413$	98.0284	−	56.5967i	0.237357	−	0.137038i
$414$	40.4560	−	28.0170i	0.0977198	−	0.0676740i
$415$	95.1026			0.229163
$416$	−27.1292	−	222.029i	−0.0652145	−	0.533724i
$417$	593.763	+	133.245i	1.42389	+	0.319533i
$418$	−60.5896	+	104.944i	−0.144951	+	0.251063i
$419$	387.326	+	223.623i	0.924405	+	0.533705i	0.885038	−	0.465519i	$-0.154132\pi$
$419$	387.326	+	223.623i	0.924405	+	0.533705i	0.0393673	+	0.999225i	$0.487466\pi$
$420$	50.3045	+	46.3354i	0.119773	+	0.110322i
$421$	−159.450	+	276.175i	−0.378741	+	0.655999i	−0.990879	−	0.134752i	$-0.956976\pi$
$421$	−159.450	+	276.175i	−0.378741	+	0.655999i	0.612138	+	0.790751i	$0.290310\pi$
$422$	8.52618	+	4.92259i	0.0202042	+	0.0116649i
$423$	20.6102	+	29.7607i	0.0487238	+	0.0703562i
$424$	−37.3934			−0.0881920
$425$	578.541	−	334.021i	1.36127	−	0.785931i
$426$	−30.1736	+	32.7583i	−0.0708300	+	0.0768974i
$427$	−26.6176	+	46.1030i	−0.0623362	+	0.107970i
$428$	79.7906	−	46.0671i	0.186427	−	0.107634i
$429$	−58.1981	+	584.951i	−0.135660	+	1.36352i
$430$	−9.08195	+	15.7304i	−0.0211208	+	0.0365823i
$431$	101.578	−	58.6459i	0.235679	−	0.136069i	−0.377510	−	0.926005i	$-0.623220\pi$
$431$	101.578	−	58.6459i	0.235679	−	0.136069i	0.613189	+	0.789936i	$0.289886\pi$
$432$	−304.976	−	237.796i	−0.705964	−	0.550455i
$433$	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
$435$	−55.4628	−	177.504i	−0.127501	−	0.408055i
$436$	22.5428			0.0517037
$437$	269.237	−	155.444i	0.616103	−	0.355707i
$438$	16.1275	−	71.8670i	0.0368208	−	0.164080i
$439$	−268.616			−0.611882			−0.305941	−	0.952050i	$-0.598971\pi$
$439$	−268.616			−0.611882			−0.305941	+	0.952050i	$0.598971\pi$
$440$	−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	0.537095	−	0.843522i	$-0.319522\pi$
$443$	33.2832	+	19.2161i	0.0751314	+	0.0433771i	−0.461964	+	0.886899i	$0.652855\pi$
$444$	−183.300	−	586.635i	−0.412837	−	1.32125i
$445$	89.4049	−	154.854i	0.200910	−	0.347986i
$446$			121.427i			0.272257i
$447$	154.515	−	688.546i	0.345672	−	1.54037i
$448$	−130.722	−	226.418i	−0.291791	−	0.505396i
$449$	−521.983	−	301.367i	−1.16254	−	0.671196i	−0.210632	−	0.977565i	$-0.567552\pi$
$449$	−521.983	−	301.367i	−1.16254	−	0.671196i	−0.951913	+	0.306370i	$0.900886\pi$
$450$	45.6278	+	65.8856i	0.101395	+	0.146412i
$451$	−217.505	+	376.730i	−0.482274	+	0.835323i
$452$			514.812i			1.13897i
$453$	−541.724	+	588.129i	−1.19586	+	1.29830i
$454$	−47.6654	−	82.5589i	−0.104990	−	0.181848i
$455$	−70.6833	−	30.0524i	−0.155348	−	0.0660491i
$456$	139.412	+	128.412i	0.305728	+	0.281605i
$457$	259.602			0.568058			0.284029	−	0.958816i	$-0.408329\pi$
$457$	259.602			0.568058			0.284029	+	0.958816i	$0.408329\pi$
$458$	77.7955	−	44.9153i	0.169859	−	0.0980683i
$459$	286.014	+	705.933i	0.623125	+	1.53798i
$460$	64.4402			0.140087
$461$	−462.851	+	267.227i	−1.00402	+	0.579669i	−0.909434	−	0.415848i	$-0.863485\pi$
$461$	−462.851	+	267.227i	−1.00402	+	0.579669i	−0.0945820	+	0.995517i	$0.530151\pi$
$462$	−26.0869	−	83.4889i	−0.0564651	−	0.180712i
$463$	−307.484	−	532.579i	−0.664113	−	1.15028i	−0.979525	−	0.201323i	$-0.935476\pi$
$463$	−307.484	−	532.579i	−0.664113	−	1.15028i	0.315412	−	0.948955i	$-0.397857\pi$
$464$			773.073i			1.66610i
$465$	−104.889	−	96.6132i	−0.225568	−	0.207770i
$466$	16.1371			0.0346290
$467$			247.090i			0.529100i	0.964372	+	0.264550i	$0.0852234\pi$
$467$			247.090i			0.529100i	−0.964372	+	0.264550i	$0.914777\pi$
$468$	428.550	+	141.977i	0.915706	+	0.303371i
$469$	380.791			0.811921
$470$		−	1.73712i		−	0.00369599i
$471$	−51.9700	−	166.325i	−0.110340	−	0.353133i
$472$	65.0230			0.137761
$473$	−549.005	+	316.968i	−1.16069	+	0.670123i
$474$	−16.2301	−	14.9495i	−0.0342408	−	0.0315391i
$475$	253.152	+	438.472i	0.532952	+	0.923099i
$476$			559.958i			1.17638i
$477$	48.6633	−	102.966i	0.102020	−	0.215861i
$478$	−14.5571	−	25.2136i	−0.0304542	−	0.0527482i
$479$		−	820.294i		−	1.71251i	−0.516550	−	0.856257i	$-0.672784\pi$
$479$		−	820.294i		−	1.71251i	0.516550	−	0.856257i	$-0.327216\pi$
$480$	17.6810	+	56.5866i	0.0368354	+	0.117889i
$481$	415.061	+	551.479i	0.862913	+	1.14653i
$482$	31.1874	−	18.0061i	0.0647042	−	0.0373570i
$483$	−49.1363	+	218.960i	−0.101731	+	0.453332i
$484$	−409.742			−0.846573
$485$	−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	$0.894499\pi$
$488$	−26.4835	+	15.2903i	−0.0542695	+	0.0313325i
$489$	32.9297	−	35.7505i	0.0673410	−	0.0731095i
$490$	−9.73309			−0.0198635
$491$	113.097	+	65.2966i	0.230340	+	0.132987i	0.610729	−	0.791840i	$-0.290876\pi$
$491$	113.097	+	65.2966i	0.230340	+	0.132987i	−0.380389	+	0.924827i	$0.624210\pi$
$492$	245.729	+	226.341i	0.499450	+	0.460042i
$493$	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
$497$		−	203.095i		−	0.408642i
$498$	−63.2855	+	68.7066i	−0.127079	+	0.137965i
$499$	−14.4740	−	25.0696i	−0.0290059	−	0.0502397i	0.851158	−	0.524909i	$-0.175901\pi$
$499$	−14.4740	−	25.0696i	−0.0290059	−	0.0502397i	−0.880164	+	0.474670i	$0.842568\pi$
$500$			215.737i			0.431474i
$501$	69.0341	+	63.5871i	0.137793	+	0.126920i
$502$	−79.3197	+	137.386i	−0.158007	+	0.273677i
$503$	−255.144	−	147.308i	−0.507245	−	0.292858i	0.224455	−	0.974484i	$-0.427940\pi$
$503$	−255.144	−	147.308i	−0.507245	−	0.292858i	−0.731701	+	0.681626i	$0.761273\pi$
$504$	−136.353	+	11.2194i	−0.270541	+	0.0222606i
$505$	47.6026	+	82.4502i	0.0942627	+	0.163268i
$506$	−71.3735	−	41.2075i	−0.141054	−	0.0814377i
$507$	−506.873	+	11.3655i	−0.999749	+	0.0224172i
$508$	20.1689	+	34.9336i	0.0397026	+	0.0687669i
$509$	538.032	+	310.633i	1.05704	+	0.610280i	0.924611	−	0.380913i	$-0.124390\pi$
$509$	538.032	+	310.633i	1.05704	+	0.610280i	0.132425	+	0.991193i	$0.457724\pi$
$510$	8.00300	−	35.6627i	0.0156921	−	0.0699269i
$511$	167.937	+	290.875i	0.328644	+	0.569227i
$512$		−	415.752i		−	0.812016i
$513$	−535.022	+	216.768i	−1.04293	+	0.422550i
$514$	73.0161	−	126.468i	0.142055	−	0.246046i
$515$	−76.1333	−	43.9556i	−0.147832	−	0.0853507i
$516$	145.201	+	464.703i	0.281397	+	0.900587i
$517$	30.3135	−	52.5045i	0.0586334	−	0.101556i
$518$	−88.9441	−	51.3519i	−0.171707	−	0.0991350i
$519$	−12.3769	+	3.86727i	−0.0238475	+	0.00745138i
$520$	−26.5320	−	35.2522i	−0.0510230	−	0.0677927i
$521$		−	166.583i		−	0.319738i	−0.987138	−	0.159869i	$-0.948893\pi$
$521$		−	166.583i		−	0.319738i	0.987138	−	0.159869i	$-0.0511071\pi$
$522$	165.145	+	78.0502i	0.316370	+	0.149522i
$523$	−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	$0.864518\pi$
$524$	−286.510	+	165.417i	−0.546775	+	0.315680i
$525$	−356.592	−	80.0221i	−0.679223	−	0.152423i
$526$	59.9334			0.113942
$527$		−	1167.56i		−	2.21548i
$528$	−141.816	+	631.956i	−0.268591	+	1.19689i
$529$	−158.781	−	275.017i	−0.300153	−	0.519881i
$530$	−4.73278	+	2.73247i	−0.00892977	+	0.00515560i
$531$	−84.6202	+	179.046i	−0.159360	+	0.337187i
$532$	−424.388			−0.797722
$533$	−345.277	−	146.801i	−0.647799	−	0.275424i
$534$	52.3798	+	167.637i	0.0980895	+	0.313927i
$535$	13.7119	−	23.7497i	0.0256297	−	0.0443919i
$536$	189.436	+	109.371i	0.353426	+	0.204051i
$537$	5.28907	−	1.65262i	0.00984929	−	0.00307750i
$538$	−29.9871	+	51.9392i	−0.0557381	+	0.0965412i
$539$	−294.184	−	169.847i	−0.545795	−	0.315115i
$540$	−118.506	−	16.5375i	−0.219456	−	0.0306250i
$541$	638.732			1.18065			0.590325	−	0.807166i	$-0.299000\pi$
$541$	638.732			1.18065			0.590325	+	0.807166i	$0.299000\pi$
$542$	−63.0155	+	36.3820i	−0.116265	+	0.0671255i
$543$	31.4202	+	7.05095i	0.0578641	+	0.0129852i
$544$	−242.694	+	420.359i	−0.446129	+	0.772719i
$545$	5.81091	−	3.35493i	0.0106622	−	0.00615583i
$546$	68.7471	−	31.0668i	0.125911	−	0.0568990i
$547$	−250.228	+	433.408i	−0.457456	+	0.792337i	−0.998826	−	0.0484477i	$-0.984573\pi$
$547$	−250.228	+	433.408i	−0.457456	+	0.792337i	0.541370	+	0.840785i	$0.317906\pi$
$548$	371.078	−	214.242i	0.677150	−	0.390953i
$549$	−7.63764	−	92.8229i	−0.0139119	−	0.169076i
$550$	67.1094	−	116.237i	0.122017	−	0.211340i
$551$	999.363	+	576.982i	1.81373	+	1.04715i
$552$	−87.3342	+	94.8153i	−0.158214	+	0.171767i
$553$	100.624			0.181960
$554$	104.847	−	60.5336i	0.189255	−	0.109266i
$555$	−134.555	−	123.939i	−0.242442	−	0.223313i
$556$	−782.692			−1.40772
$557$	−217.719	+	125.700i	−0.390877	+	0.225673i	−0.682540	−	0.730848i	$-0.739125\pi$
$557$	−217.719	+	125.700i	−0.390877	+	0.225673i	0.291663	+	0.956521i	$0.405791\pi$
$558$	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
$561$	864.221	−	938.252i	1.54050	−	1.67246i
$562$	−77.6247	+	134.450i	−0.138122	+	0.239235i
$563$			751.814i			1.33537i	0.744443	+	0.667685i	$0.232715\pi$
$563$			751.814i			1.33537i	−0.744443	+	0.667685i	$0.767285\pi$
$564$	−34.2470	−	31.5449i	−0.0607217	−	0.0559306i
$565$	76.6169	+	132.704i	0.135605	+	0.234875i
$566$	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
$569$			536.258i			0.942456i	0.882011	+	0.471228i	$0.156189\pi$
$569$			536.258i			0.942456i	−0.882011	+	0.471228i	$0.843811\pi$
$570$	27.0285	+	6.06541i	0.0474184	+	0.0106411i
$571$	−50.9656	−	88.2750i	−0.0892567	−	0.154597i	0.817940	−	0.575303i	$-0.195116\pi$
$571$	−50.9656	−	88.2750i	−0.0892567	−	0.154597i	−0.907197	+	0.420706i	$0.861782\pi$
$572$	−91.7015	−	750.497i	−0.160317	−	1.31206i
$573$	−188.773	+	58.9838i	−0.329447	+	0.102939i
$574$	55.8275			0.0972605
$575$	−298.209	+	172.171i	−0.518624	+	0.299428i
$576$	413.545	+	195.448i	0.717961	+	0.339320i
$577$	−6.86778			−0.0119026			−0.00595128	−	0.999982i	$-0.501894\pi$
$577$	−6.86778			−0.0119026			−0.00595128	+	0.999982i	$0.501894\pi$
$578$	165.043	−	95.2877i	0.285542	−	0.164858i
$579$	−227.350	+	246.825i	−0.392660	+	0.426296i
$580$	119.596	+	207.146i	0.206199	+	0.357148i
$581$		−	425.968i		−	0.733164i
$582$	20.9317	−	6.54029i	0.0359651	−	0.0112376i
$583$	−190.731			−0.327155
$584$			192.940i			0.330377i
$585$	131.598	−	27.1811i	0.224954	−	0.0464634i
$586$	−206.303			−0.352054
$587$			522.260i			0.889711i	0.895602	+	0.444855i	$0.146745\pi$
$587$			522.260i			0.889711i	−0.895602	+	0.444855i	$0.853255\pi$
$588$	−176.746	+	191.887i	−0.300589	+	0.326338i
$589$	884.886			1.50235
$590$	8.22978	−	4.75147i	0.0139488	−	0.00805333i
$591$	−33.6301	+	10.5080i	−0.0569037	+	0.0177801i
$592$	380.238	+	658.592i	0.642294	+	1.11249i
$593$		−	624.635i		−	1.05335i	−0.850068	−	0.526674i	$-0.823439\pi$
$593$		−	624.635i		−	1.05335i	0.850068	−	0.526674i	$-0.176561\pi$
$594$	120.681	+	94.0979i	0.203167	+	0.158414i
$595$	83.3357	+	144.342i	0.140060	+	0.242591i
$596$			907.633i			1.52287i
$597$	−37.5532	+	40.7700i	−0.0629032	+	0.0682915i
$598$	27.8122	−	65.4144i	0.0465087	−	0.109389i
$599$	−472.937	+	273.050i	−0.789544	+	0.455843i	−0.839802	−	0.542893i	$-0.817329\pi$
$599$	−472.937	+	273.050i	−0.789544	+	0.455843i	0.0502581	+	0.998736i	$0.483996\pi$
$600$	−154.414	−	142.230i	−0.257356	−	0.237050i
$601$	563.710			0.937953			0.468977	−	0.883211i	$-0.344623\pi$
$601$	563.710			0.937953			0.468977	+	0.883211i	$0.344623\pi$
$602$	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
$605$	−105.620	+	60.9797i	−0.174579	+	0.100793i
$606$	−91.2429	−	20.4756i	−0.150566	−	0.0337882i
$607$	201.365			0.331739			0.165869	−	0.986148i	$-0.446957\pi$
$607$	201.365			0.331739			0.165869	+	0.986148i	$0.446957\pi$
$608$	−318.587	−	183.936i	−0.523992	−	0.302527i
$609$	−795.048	+	248.420i	−1.30550	+	0.407915i
$610$	−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	$-0.340010\pi$
$614$		−	29.4598i		−	0.0479802i
$615$	97.0274	+	21.7737i	0.157768	+	0.0354044i
$616$	114.565	+	198.432i	0.185982	+	0.322130i
$617$		−	64.1839i		−	0.104026i	−0.998646	−	0.0520129i	$-0.983436\pi$
$617$		−	64.1839i		−	0.104026i	0.998646	−	0.0520129i	$-0.0165637\pi$
$618$	82.4182	−	25.7523i	0.133363	−	0.0416704i
$619$	3.79581	−	6.57454i	0.00613217	−	0.0106212i	−0.862943	−	0.505301i	$-0.831381\pi$
$619$	3.79581	−	6.57454i	0.00613217	−	0.0106212i	0.869075	+	0.494680i	$0.164715\pi$
$620$	158.844	+	91.7086i	0.256200	+	0.147917i
$621$	−147.426	−	363.873i	−0.237401	−	0.585947i
$622$	84.8491	+	146.963i	0.136413	+	0.236275i
$623$	−693.597	−	400.448i	−1.11332	−	0.642774i
$624$	−555.861	−	55.3039i	−0.890803	−	0.0886281i
$625$	−263.904	−	457.096i	−0.422247	−	0.731354i
$626$	−76.7389	−	44.3052i	−0.122586	−	0.0707752i
$627$	711.095	+	654.987i	1.13412	+	1.04464i
$628$	112.064	+	194.100i	0.178446	+	0.309077i
$629$		−	1497.79i		−	2.38122i
$630$	−16.4380	+	11.3838i	−0.0260920	+	0.0180695i
$631$	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
$633$	53.2144	−	57.7728i	0.0840669	−	0.0912682i
$634$	23.4269	−	40.5766i	0.0369509	−	0.0640009i
$635$	10.3980	+	6.00327i	0.0163748	+	0.00945398i
$636$	−32.0737	+	142.926i	−0.0504304	+	0.224726i
$637$	114.635	−	269.622i	0.179960	−	0.423268i
$638$		−	305.911i		−	0.479484i
$639$	202.297	+	292.112i	0.316583	+	0.457139i
$640$	−50.4976	−	87.4644i	−0.0789025	−	0.136663i
$641$	928.289	−	535.948i	1.44819	−	0.836112i	0.449815	−	0.893122i	$-0.351490\pi$
$641$	928.289	−	535.948i	1.44819	−	0.836112i	0.998374	+	0.0570099i	$0.0181567\pi$
$642$	8.03340	+	25.7102i	0.0125131	+	0.0400471i
$643$	411.550			0.640047			0.320023	−	0.947410i	$-0.396309\pi$
$643$	411.550			0.640047			0.320023	+	0.947410i	$0.396309\pi$
$644$		−	288.630i		−	0.448183i
$645$	106.588	+	98.1780i	0.165253	+	0.152214i
$646$	113.399	+	196.413i	0.175540	+	0.304044i
$647$	872.018	−	503.460i	1.34779	−	0.778145i	0.359851	−	0.933010i	$-0.382828\pi$
$647$	872.018	−	503.460i	1.34779	−	0.778145i	0.987936	+	0.154865i	$0.0494943\pi$
$648$	184.941	−	151.954i	0.285403	−	0.234496i
$649$	331.661			0.511034
$650$	106.532	+	45.2942i	0.163896	+	0.0696834i
$651$	−432.734	+	469.803i	−0.664723	+	0.721664i
$652$	−31.2580	+	54.1405i	−0.0479418	+	0.0830376i
$653$	−999.048	−	576.801i	−1.52994	−	0.883309i	−0.999364	−	0.0356698i	$-0.988644\pi$
$653$	−999.048	−	576.801i	−1.52994	−	0.883309i	−0.530573	−	0.847639i	$-0.678023\pi$
$654$	−1.44308	+	6.43060i	−0.00220654	+	0.00983272i
$655$	−49.2362	+	85.2796i	−0.0751698	+	0.130198i
$656$	−357.996	−	206.689i	−0.545725	−	0.315074i
$657$	−531.275	−	251.090i	−0.808638	−	0.382176i
$658$	−7.78061			−0.0118246
$659$	−269.095	+	155.362i	−0.408338	+	0.235754i	−0.690076	−	0.723737i	$-0.742423\pi$
$659$	−269.095	+	155.362i	−0.408338	+	0.235754i	0.281737	+	0.959492i	$0.409089\pi$
$660$	59.7649	+	191.272i	0.0905528	+	0.289807i
$661$	257.855	−	446.618i	0.390099	−	0.675670i	−0.602364	−	0.798222i	$-0.705774\pi$
$661$	257.855	−	446.618i	0.390099	−	0.675670i	0.992462	+	0.122551i	$0.0391076\pi$
$662$	−108.957	+	62.9065i	−0.164588	+	0.0950250i
$663$	893.654	+	641.725i	1.34789	+	0.967911i
$664$	122.347	−	211.911i	0.184257	−	0.319143i
$665$	−109.395	+	63.1595i	−0.164505	+	0.0949767i
$666$	179.079	−	14.7349i	0.268887	−	0.0221245i
$667$	−392.411	+	679.675i	−0.588322	+	1.01900i
$668$	−104.545	−	60.3591i	−0.156505	−	0.0903580i
$669$	945.248	+	212.121i	1.41293	+	0.317072i
$670$	31.9686			0.0477143
$671$	−135.084	+	77.9905i	−0.201317	+	0.116230i
$672$	253.454	−	79.1939i	0.377163	−	0.117848i
$673$	−209.818			−0.311765			−0.155883	−	0.987776i	$-0.549822\pi$
$673$	−209.818			−0.311765			−0.155883	+	0.987776i	$0.549822\pi$
$674$	−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	0.508779	−	0.860897i	$-0.330097\pi$
$677$	11.9220	+	6.88315i	0.0176100	+	0.0101671i	−0.491169	+	0.871064i	$0.663430\pi$
$678$	−146.856	−	32.9557i	−0.216602	−	0.0486073i
$679$	−50.0011	+	86.6045i	−0.0736394	+	0.127547i
$680$			95.7430i			0.140799i
$681$	−725.947	+	226.829i	−1.06600	+	0.333082i
$682$	−117.290	−	203.152i	−0.171979	−	0.297876i
$683$	402.924	+	232.628i	0.589933	+	0.340598i	0.765071	−	0.643946i	$-0.222704\pi$
$683$	402.924	+	232.628i	0.589933	+	0.340598i	−0.175138	+	0.984544i	$0.556037\pi$
$684$	610.398	−	422.720i	0.892395	−	0.618011i
$685$	63.7691	−	110.451i	0.0930936	−	0.161243i
$686$			138.380i			0.201719i
$687$	−213.742	−	684.062i	−0.311123	−	0.995724i
$688$	−301.205	−	521.703i	−0.437799	−	0.758289i
$689$	−19.9518	−	163.288i	−0.0289576	−	0.236992i
$690$	−4.12514	+	18.3823i	−0.00597847	+	0.0266411i
$691$	−518.379			−0.750187			−0.375094	−	0.926987i	$-0.622389\pi$
$691$	−518.379			−0.750187			−0.375094	+	0.926987i	$0.622389\pi$
$692$	14.4437	−	8.33907i	0.0208724	−	0.0120507i
$693$	−695.491	+	57.2263i	−1.00359	+	0.0825776i
$694$	64.2258			0.0925443
$695$	−201.756	+	116.484i	−0.290297	+	0.167603i
$696$	−466.873	−	104.770i	−0.670794	−	0.150532i
$697$	407.081	+	705.086i	0.584048	+	1.01160i
$698$		−	50.6577i		−	0.0725755i
$699$	28.1900	−	125.619i	0.0403290	−	0.179713i
$700$	470.055			0.671508
$701$		−	775.035i		−	1.10561i	−0.833310	−	0.552806i	$-0.813557\pi$
$701$		−	775.035i		−	1.10561i	0.833310	−	0.552806i	$-0.186443\pi$
$702$	−67.9344	+	113.160i	−0.0967727	+	0.161197i
$703$	1135.16			1.61474
$704$		−	766.042i		−	1.08813i
$705$	−13.5226	−	3.03458i	−0.0191810	−	0.00430437i
$706$	−47.7466			−0.0676298
$707$	369.298	−	213.214i	0.522345	−	0.301576i
$708$	55.7727	−	248.532i	0.0787750	−	0.351034i
$709$	−308.569	−	534.457i	−0.435217	−	0.753819i	0.562096	−	0.827072i	$-0.309995\pi$
$709$	−308.569	−	534.457i	−0.435217	−	0.753819i	−0.997313	+	0.0732533i	$0.976662\pi$
$710$		−	17.0505i		−	0.0240147i
$711$	−144.727	+	100.228i	−0.203555	+	0.140968i
$712$	−230.034	−	398.431i	−0.323082	−	0.559594i
$713$			601.819i			0.844066i
$714$	−159.735	−	35.8457i	−0.223718	−	0.0502041i
$715$	−135.331	−	179.810i	−0.189274	−	0.251482i
$716$	−6.17230	+	3.56358i	−0.00862052	+	0.00497706i
$717$	−221.706	+	69.2740i	−0.309213	+	0.0966165i
$718$	166.903			0.232455
$719$	−534.714	−	308.717i	−0.743692	−	0.429371i	0.0797184	−	0.996817i	$-0.474598\pi$
$719$	−534.714	−	308.717i	−0.743692	−	0.429371i	−0.823410	+	0.567447i	$0.807931\pi$
$720$	147.555	−	12.1411i	0.204937	−	0.0168626i
$721$	−196.879	+	341.004i	−0.273064	+	0.472960i
$722$	−31.2999	+	18.0710i	−0.0433517	+	0.0250291i
$723$	−85.6869	−	274.234i	−0.118516	−	0.379300i
$724$	−41.4178			−0.0572069
$725$	−1106.90	−	639.070i	−1.52676	−	0.881475i
$726$	26.2296	−	116.884i	0.0361290	−	0.160997i
$727$	−527.853	+	914.268i	−0.726070	+	1.25759i	0.232462	+	0.972605i	$0.425322\pi$
$727$	−527.853	+	914.268i	−0.726070	+	1.25759i	−0.958532	+	0.284984i	$0.908012\pi$
$728$	−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
$731$			1186.47i			1.62308i
$732$	35.7268	+	114.341i	0.0488072	+	0.156203i
$733$	435.712	+	754.675i	0.594422	+	1.02957i	0.993628	+	0.112708i	$0.0359526\pi$
$733$	435.712	+	754.675i	0.594422	+	1.02957i	−0.399206	+	0.916861i	$0.630714\pi$
$734$			43.6844i			0.0595155i
$735$	−17.0028	+	75.7673i	−0.0231331	+	0.103085i
$736$	125.097	−	216.674i	0.169968	−	0.294394i
$737$	966.253	+	557.866i	1.31106	+	0.756942i
$738$	−80.2968	+	55.6080i	−0.108803	+	0.0753496i
$739$	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
$741$	−486.359	+	677.294i	−0.656355	+	0.914027i
$742$	12.2388	+	21.1983i	0.0164944	+	0.0285691i
$743$	426.534	+	246.260i	0.574071	+	0.331440i	0.758773	−	0.651355i	$-0.225799\pi$
$743$	426.534	+	246.260i	0.574071	+	0.331440i	−0.184703	+	0.982794i	$0.559132\pi$
$744$	−350.215	+	109.428i	−0.470719	+	0.147080i
$745$	135.078	+	233.963i	0.181313	+	0.314044i
$746$		−	79.3373i		−	0.106350i
$747$	424.293	+	612.671i	0.567997	+	0.820175i
$748$	−820.349	+	1420.89i	−1.09672	+	1.89958i
$749$	−106.376	−	61.4160i	−0.142024	−	0.0819974i
$750$	−61.5415	−	13.8104i	−0.0820553	−	0.0184139i
$751$	−197.444	+	341.982i	−0.262907	+	0.455369i	−0.967013	−	0.254726i	$-0.918015\pi$
$751$	−197.444	+	341.982i	−0.262907	+	0.455369i	0.704106	+	0.710095i	$0.251348\pi$
$752$	49.8934	+	28.8060i	0.0663477	+	0.0383058i
$753$	930.916	+	857.465i	1.23628	+	1.13873i
$754$	261.894	−	32.0003i	0.347340	−	0.0424407i
$755$		−	306.117i		−	0.405453i
$756$	−74.0720	+	530.794i	−0.0979789	+	0.702109i
$757$	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	$0.814344\pi$
$758$	−124.323	+	71.7776i	−0.164014	+	0.0946934i
$759$	−445.463	+	483.622i	−0.586907	+	0.637183i
$760$	−72.5630			−0.0954776
$761$			749.692i			0.985140i	0.870273	+	0.492570i	$0.163942\pi$
$761$			749.692i			0.985140i	−0.870273	+	0.492570i	$0.836058\pi$
$762$	−11.2563	+	3.51715i	−0.0147721	+	0.00461568i
$763$	−15.0269	−	26.0273i	−0.0196944	−	0.0341118i
$764$	220.296	−	127.188i	0.288346	−	0.166477i
$765$	−263.636	−	124.599i	−0.344622	−	0.162874i
$766$	95.4934			0.124665
$767$	34.6939	+	283.940i	0.0452333	+	0.370195i
$768$	−498.283	−	111.819i	−0.648806	−	0.145597i
$769$	6.79598	−	11.7710i	0.00883743	−	0.0153069i	−0.861573	−	0.507634i	$-0.830520\pi$
$769$	6.79598	−	11.7710i	0.00883743	−	0.0153069i	0.870410	+

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q-0.376029i q^{2} +(-2.92720 - 0.656887i) q^{3} +3.85860 q^{4} +(0.994641 - 0.574256i) q^{5} +(-0.247009 + 1.10071i) q^{6} +(-2.57212 - 4.45503i) q^{7} -2.95506i q^{8} +(8.13700 + 3.84568i) q^{9} +(-0.215937 - 0.374014i) q^{10} -15.0728i q^{11} +(-11.2949 - 2.53467i) q^{12} +(12.9040 - 1.57671i) q^{13} +(-1.67522 + 0.967190i) q^{14} +(-3.28873 + 1.02760i) q^{15} +14.3232 q^{16} +(-24.4307 - 14.1051i) q^{17} +(1.44609 - 3.05975i) q^{18} +(10.6901 - 18.5158i) q^{19} +(3.83792 - 2.21583i) q^{20} +(4.60264 + 14.7304i) q^{21} -5.66781 q^{22} +(12.5928 + 7.27045i) q^{23} +(-1.94114 + 8.65006i) 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} +53.9734i q^{29} +(0.386406 + 1.23666i) q^{30} +(20.6940 + 35.8431i) q^{31} -17.2062i q^{32} +(-9.90113 + 44.1211i) q^{33} +(-5.30391 + 9.18664i) q^{34} +(-5.11666 - 2.95411i) q^{35} +(31.3974 + 14.8390i) q^{36} +(26.5470 + 45.9807i) q^{37} +(-6.96249 - 4.01980i) q^{38} +(-38.8084 - 3.86114i) q^{39} +(-1.69696 - 2.93923i) q^{40} +(-24.9941 - 14.4303i) q^{41} +(5.53904 - 1.73073i) q^{42} +(-21.0292 - 36.4236i) q^{43} -58.1599i q^{44} +(10.3018 - 0.847651i) q^{45} +(2.73390 - 4.73525i) q^{46} +(3.48340 + 2.01114i) q^{47} +(-41.9269 - 9.40874i) q^{48} +(11.2684 - 19.5175i) q^{49} +(7.71171 + 4.45236i) q^{50} +(62.2480 + 57.3365i) q^{51} +(49.7915 - 6.08391i) q^{52} -12.6540i q^{53} +(-6.24290 + 8.00658i) q^{54} +(-8.65564 - 14.9920i) q^{55} +(-13.1649 + 7.60076i) q^{56} +(-43.4549 + 47.1774i) q^{57} +20.2956 q^{58} +22.0040i q^{59} +(-12.6899 + 3.96508i) q^{60} +(-5.17426 - 8.96208i) q^{61} +(13.4780 - 7.78155i) q^{62} +(-3.79666 - 46.1421i) q^{63} +50.8229 q^{64} +(11.9294 - 8.97848i) q^{65} +(16.5908 + 3.72311i) q^{66} +(-37.0115 + 64.1058i) q^{67} +(-94.2683 - 54.4258i) q^{68} +(-32.0857 - 29.5541i) q^{69} +(-1.11083 + 1.92401i) q^{70} +(34.1908 + 19.7401i) q^{71} +(11.3642 - 24.0453i) q^{72} -65.2913 q^{73} +(17.2901 - 9.98243i) q^{74} +(48.1310 - 52.2540i) q^{75} +(41.2489 - 71.4453i) q^{76} +(-67.1498 + 38.7690i) q^{77} +(-1.45190 + 14.5931i) q^{78} +(-9.78025 + 16.9399i) q^{79} +(14.2465 - 8.22520i) q^{80} +(51.4215 + 62.5846i) q^{81} +(-5.42622 + 9.39850i) q^{82} +(71.7112 + 41.4025i) q^{83} +(17.7598 + 56.8386i) q^{84} -32.3997 q^{85} +(-13.6963 + 7.90758i) q^{86} +(35.4544 - 157.991i) q^{87} -44.5410 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} +(-37.0306 - 118.513i) q^{93} +(0.756247 - 1.30986i) q^{94} -24.5555i q^{95} +(-11.3025 + 50.3660i) q^{96} +(-9.71984 - 16.8353i) q^{97} +(-7.33915 - 4.23726i) q^{98} +(57.9651 - 122.647i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q - q^{3} - 98 q^{4} - 6 q^{5} + 12 q^{6} - q^{7} - 3 q^{9} - 6 q^{10} - 39 q^{12} + 4 q^{13} - 6 q^{14} - 25 q^{15} + 166 q^{16} + 34 q^{18} + 5 q^{19} + 21 q^{20} - 91 q^{21} + 30 q^{22} - 75 q^{23}+ \cdots + 522 q^{99}+O(q^{100}) \) 52 * q - q^3 - 98 * q^4 - 6 * q^5 + 12 * q^6 - q^7 - 3 * q^9 - 6 * q^10 - 39 * q^12 + 4 * q^13 - 6 * q^14 - 25 * q^15 + 166 * q^16 + 34 * q^18 + 5 * q^19 + 21 * q^20 - 91 * q^21 + 30 * q^22 - 75 * q^23 - 24 * q^24 + 88 * q^25 - 132 * q^26 - 34 * q^27 - 22 * q^28 + 70 * q^30 + 14 * q^31 + 95 * q^33 - 6 * q^34 + 228 * q^35 - 58 * q^36 - 13 * q^37 - 192 * q^38 - 111 * q^39 + 72 * q^40 + 33 * q^41 + 159 * q^42 - 31 * q^43 - 47 * q^45 + 6 * q^46 - 69 * q^47 + 293 * q^48 - 123 * q^49 - 168 * q^50 + 235 * q^51 - 92 * q^52 - 339 * q^54 - 27 * q^55 + 168 * q^56 + 189 * q^57 + 210 * q^58 + 213 * q^60 + 8 * q^61 + 471 * q^62 + 169 * q^63 - 98 * q^64 - 246 * q^65 - 576 * q^66 - 34 * q^67 + 18 * q^68 - 193 * q^69 - 57 * q^70 + 144 * q^71 + 36 * q^72 - 106 * q^73 - 465 * q^74 - 58 * q^75 - 79 * q^76 + 282 * q^77 - 76 * q^78 - 25 * q^79 - 1050 * q^80 - 279 * q^81 + 81 * q^82 + 219 * q^83 + 395 * q^84 - 108 * q^85 - 24 * q^86 - 518 * q^87 + 30 * q^88 + 99 * q^89 + 183 * q^90 + 2 * q^91 + 888 * q^92 + 582 * q^93 + 303 * q^94 - 439 * q^96 + 212 * q^97 - 405 * q^98 + 522 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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