LMFDB - Embedded newform 117.3.k.a.113.13

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			113.13
Character	$\chi$	$=$	117.113
Dual form			117.3.k.a.29.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+0.376029i 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 $\left(\mathbb{Z}/117\mathbb{Z}\right)^\times$.

$n$	$28$	$92$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$			0.376029i			0.188014i	0.995572	+	0.0940072i	$0.0299677\pi$
$2$			0.376029i			0.188014i	−0.995572	+	0.0940072i	$0.970032\pi$
$3$	−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	0.596155	−	0.802869i	$-0.296694\pi$
$5$	0.994641	+	0.574256i	0.198928	+	0.114851i	−0.397227	+	0.917720i	$0.630028\pi$
$6$	−0.247009	−	1.10071i	−0.0411681	−	0.183452i
$7$	−2.57212	+	4.45503i	−0.367445	+	0.636434i	−0.989165	−	0.146806i	$-0.953101\pi$
$7$	−2.57212	+	4.45503i	−0.367445	+	0.636434i	0.621720	+	0.783239i	$0.286434\pi$
$8$			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	$0.240253\pi$
$11$			15.0728i			1.37025i	−0.728424	+	0.685127i	$0.759747\pi$
$12$	−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	−0.997647	−	0.0685572i	$-0.978160\pi$
$17$	−24.4307	+	14.1051i	−1.43710	+	0.829709i	−0.439451	+	0.898266i	$0.644827\pi$
$18$	1.44609	+	3.05975i	0.0803382	+	0.169986i
$19$	10.6901	+	18.5158i	0.562638	+	0.974518i	0.997265	+	0.0739073i	$0.0235469\pi$
$19$	10.6901	+	18.5158i	0.562638	+	0.974518i	−0.434627	+	0.900611i	$0.643120\pi$
$20$	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	−0.200606	−	0.979672i	$-0.564291\pi$
$23$	12.5928	−	7.27045i	0.547512	−	0.316106i	0.748118	+	0.663566i	$0.230958\pi$
$24$	−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	$-0.619307\pi$
$29$		−	53.9734i		−	1.86115i	0.366100	−	0.930576i	$-0.380693\pi$
$30$	0.386406	−	1.23666i	0.0128802	−	0.0412220i
$31$	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	$-0.0659897\pi$
$32$			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	−0.244507	−	0.969647i	$-0.578626\pi$
$37$	26.5470	−	45.9807i	0.717486	−	1.24272i	0.961993	−	0.273074i	$-0.0880405\pi$
$38$	−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	−0.772813	−	0.634633i	$-0.781151\pi$
$41$	−24.9941	+	14.4303i	−0.609612	+	0.351959i	0.163202	+	0.986593i	$0.447818\pi$
$42$	5.53904	+	1.73073i	0.131882	+	0.0412078i
$43$	−21.0292	+	36.4236i	−0.489050	+	0.847060i	−0.999921	−	0.0125977i	$-0.995990\pi$
$43$	−21.0292	+	36.4236i	−0.489050	+	0.847060i	0.510870	+	0.859658i	$0.329323\pi$
$44$			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	−0.462485	−	0.886627i	$-0.653042\pi$
$47$	3.48340	−	2.01114i	0.0741148	−	0.0427902i	0.536599	+	0.843837i	$0.319709\pi$
$48$	−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	$0.0380899\pi$
$53$			12.6540i			0.238755i	−0.992849	+	0.119378i	$0.961910\pi$
$54$	−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	$-0.940294\pi$
$59$		−	22.0040i		−	0.372948i	0.982460	−	0.186474i	$-0.0597061\pi$
$60$	−12.6899	−	3.96508i	−0.211499	−	0.0660847i
$61$	−5.17426	+	8.96208i	−0.0848239	+	0.146919i	−0.905316	−	0.424738i	$-0.860366\pi$
$61$	−5.17426	+	8.96208i	−0.0848239	+	0.146919i	0.820492	+	0.571658i	$0.193699\pi$
$62$	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	−0.998100	−	0.0616149i	$-0.980375\pi$
$67$	−37.0115	−	64.1058i	−0.552410	−	0.956802i	0.445690	−	0.895187i	$-0.352958\pi$
$68$	−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	−0.239506	−	0.970895i	$-0.576985\pi$
$71$	34.1908	−	19.7401i	0.481561	−	0.278029i	0.721067	+	0.692865i	$0.243652\pi$
$72$	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	0.797463	−	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
$81$	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	−0.00135589	−	0.999999i	$-0.500432\pi$
$83$	71.7112	−	41.4025i	0.863991	−	0.498825i	0.865347	+	0.501174i	$0.167098\pi$
$84$	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	0.999846	+	0.0175212i	$0.00557746\pi$
$89$	134.830	+	77.8441i	1.51494	+	0.874653i	0.515097	+	0.857132i	$0.327756\pi$
$90$	−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	−0.911769	−	0.410704i	$-0.865283\pi$
$97$	−9.71984	+	16.8353i	−0.100205	+	0.173559i	0.811564	+	0.584263i	$0.198616\pi$
$98$	−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	$-0.865400\pi$
$101$		−	82.8944i		−	0.820737i	0.911920	−	0.410369i	$-0.134600\pi$
$102$	21.5602	+	23.4071i	0.211374	+	0.229481i
$103$	−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	$0.287847\pi$
$104$	−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	0.593507	−	0.804829i	$-0.297743\pi$
$107$	20.6786	+	11.9388i	0.193258	+	0.111578i	−0.400249	+	0.916407i	$0.631076\pi$
$108$	−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	$-0.798989\pi$
$113$		−	133.419i		−	1.18070i	0.807146	−	0.590351i	$-0.201011\pi$
$114$	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	−0.844713	−	0.535220i	$-0.820229\pi$
$127$	5.22700	−	9.05343i	0.0411575	−	0.0712869i	0.885870	+	0.463933i	$0.153562\pi$
$128$			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	0.189064	−	0.981965i	$-0.439455\pi$
$131$	−74.2522	−	42.8695i	−0.566811	−	0.327248i	−0.755875	+	0.654716i	$0.772788\pi$
$132$	−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	0.808079	−	0.589075i	$-0.200508\pi$
$137$	96.1691	+	55.5233i	0.701964	+	0.405279i	−0.106114	+	0.994354i	$0.533841\pi$
$138$	−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	$-0.710423\pi$
$149$		−	235.223i		−	1.57868i	0.613957	−	0.789340i	$-0.289577\pi$
$150$	−19.6490	+	18.0987i	−0.130993	+	0.120658i
$151$	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
$153$	−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	−0.758587	−	0.651572i	$-0.774110\pi$
$157$	29.0426	−	50.3033i	0.184985	−	0.320403i	0.943571	+	0.331169i	$0.107443\pi$
$158$	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	0.840106	−	0.542422i	$-0.182493\pi$
$163$	−8.10087	−	14.0311i	−0.0496986	−	0.0860805i	−0.889805	+	0.456342i	$0.849159\pi$
$164$	−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	−0.578922	−	0.815383i	$-0.696526\pi$
$167$	−27.0940	+	15.6427i	−0.162240	+	0.0936691i	0.416682	+	0.909052i	$0.363193\pi$
$168$	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	0.510780	−	0.859712i	$-0.329357\pi$
$173$	3.74325	+	2.16116i	0.0216373	+	0.0124923i	−0.489142	+	0.872204i	$0.662690\pi$
$174$	−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	0.495525	−	0.868594i	$-0.334976\pi$
$179$	−1.59962	−	0.923541i	−0.00893642	−	0.00515945i	−0.504462	+	0.863434i	$0.668309\pi$
$180$	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	0.641954	−	0.766743i	$-0.278124\pi$
$191$	57.0922	+	32.9622i	0.298912	+	0.172577i	−0.343042	+	0.939320i	$0.611457\pi$
$192$	−148.769	+	33.3849i	−0.774837	+	0.173880i
$193$	55.9292	+	96.8723i	0.289789	+	0.501929i	0.973759	−	0.227581i	$-0.0730816\pi$
$193$	55.9292	+	96.8723i	0.289789	+	0.501929i	−0.683970	+	0.729510i	$0.739748\pi$
$194$	−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	0.525593	−	0.850736i	$-0.323844\pi$
$197$	10.1710	+	5.87226i	0.0516297	+	0.0298084i	−0.473963	+	0.880545i	$0.657177\pi$
$198$	−46.1189	+	21.7966i	−0.232924	+	0.110084i
$199$	9.23826	+	16.0011i	0.0464234	+	0.0804077i	0.888303	−	0.459257i	$-0.151884\pi$
$199$	9.23826	+	16.0011i	0.0464234	+	0.0804077i	−0.841880	+	0.539665i	$0.818551\pi$
$200$	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	0.833336	−	0.552767i	$-0.186428\pi$
$211$	−13.0910	−	22.6743i	−0.0620426	−	0.107461i	−0.895378	+	0.445306i	$0.853095\pi$
$212$			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	0.898382	−	0.439216i	$-0.144744\pi$
$227$	219.554	+	126.760i	0.967200	+	0.558413i	0.0688188	+	0.997629i	$0.478077\pi$
$228$	−167.675	−	182.039i	−0.735418	−	0.798415i
$229$	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	$-0.00799781\pi$
$230$			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	$-0.970645\pi$
$233$		−	42.9145i		−	0.184182i	0.995751	−	0.0920912i	$-0.0293551\pi$
$234$	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	0.633674	−	0.773600i	$-0.281546\pi$
$239$	67.0524	+	38.7127i	0.280554	+	0.161978i	−0.353120	+	0.935578i	$0.614879\pi$
$240$	−47.1053	−	14.7185i	−0.196272	−	0.0613270i
$241$	47.8848	−	82.9389i	0.198692	−	0.344145i	−0.749412	−	0.662103i	$-0.769664\pi$
$241$	47.8848	−	82.9389i	0.198692	−	0.344145i	0.948105	+	0.317959i	$0.102997\pi$
$242$		−	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	−0.998791	−	0.0491566i	$-0.984347\pi$
$251$	−365.360	+	210.940i	−1.45562	+	0.840400i	−0.456825	+	0.889557i	$0.651013\pi$
$252$	−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	0.326783	−	0.945100i	$-0.394035\pi$
$257$	336.324	−	194.177i	1.30865	−	0.755552i	0.981872	+	0.189548i	$0.0607022\pi$
$258$	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	$-0.902007\pi$
$263$		−	159.385i		−	0.606027i	0.952986	−	0.303014i	$-0.0979928\pi$
$264$	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	−0.734262	−	0.678866i	$-0.762472\pi$
$269$	−138.125	+	79.7468i	−0.513478	+	0.296456i	0.220784	+	0.975323i	$0.429138\pi$
$270$	−1.61161	−	11.5487i	−0.00596894	−	0.0427729i
$271$	−96.7532	+	167.581i	−0.357023	+	0.618382i	−0.987462	−	0.157857i	$-0.949542\pi$
$271$	−96.7532	+	167.581i	−0.357023	+	0.618382i	0.630439	+	0.776239i	$0.282875\pi$
$272$	−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	−0.414183	−	0.910194i	$-0.635933\pi$
$277$	160.981	−	278.828i	0.581159	−	1.00660i	0.995342	−	0.0964039i	$-0.0307340\pi$
$278$		−	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	−0.975444	−	0.220246i	$-0.929314\pi$
$281$	−357.552	+	206.433i	−1.27243	+	0.734637i	−0.296984	+	0.954883i	$0.595981\pi$
$282$	−3.07411	−	3.33745i	−0.0109011	−	0.0118349i
$283$	−243.879	−	422.411i	−0.861764	−	1.49262i	−0.870225	−	0.492654i	$-0.836027\pi$
$283$	−243.879	−	422.411i	−0.861764	−	1.49262i	0.00846154	−	0.999964i	$-0.497307\pi$
$284$	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	$0.385719\pi$
$293$			548.637i			1.87248i	−0.351360	+	0.936240i	$0.614281\pi$
$294$	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	−0.284255	−	0.958749i	$-0.591746\pi$
$311$	−390.829	−	225.645i	−1.25668	−	0.725547i	−0.972428	+	0.233202i	$0.925080\pi$
$312$	−11.4099	−	114.681i	−0.0365702	−	0.367568i
$313$	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
$315$	−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	−0.320047	−	0.947402i	$-0.603699\pi$
$317$	107.908	−	62.3008i	0.340404	−	0.196532i	0.660451	+	0.750869i	$0.270365\pi$
$318$	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	0.494567	+	0.869139i	$0.335327\pi$
$331$	−167.292	+	289.758i	−0.505413	+	0.875401i	−0.999980	+	0.00626172i	$0.998007\pi$
$332$	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	0.446342	+	0.894862i	$0.352726\pi$
$337$	−185.957	+	322.088i	−0.551802	+	0.955750i	−0.998145	+	0.0608873i	$0.980607\pi$
$338$	−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	$-0.920848\pi$
$347$		−	170.800i		−	0.492219i	0.969242	−	0.246110i	$-0.0791523\pi$
$348$	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	$0.0575621\pi$
$353$			126.976i			0.359705i	−0.983694	+	0.179853i	$0.942438\pi$
$354$	−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	$-0.787869\pi$
$359$		−	443.856i		−	1.23637i	0.786034	−	0.618184i	$-0.212131\pi$
$360$	−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	0.496341	+	0.868127i	$0.334676\pi$
$379$	−190.883	+	330.619i	−0.503650	+	0.872347i	−0.999991	+	0.00421947i	$0.998657\pi$
$380$			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	$-0.892435\pi$
$383$		−	253.952i		−	0.663061i	0.943445	−	0.331530i	$-0.107565\pi$
$384$	−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	−0.825358	−	0.564610i	$-0.809027\pi$
$389$	−291.388	+	168.233i	−0.749070	+	0.432476i	0.0762879	+	0.997086i	$0.475693\pi$
$390$	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	0.664835	−	0.746990i	$-0.268502\pi$
$397$	−124.854	−	216.254i	−0.314494	−	0.544720i	−0.979330	+	0.202269i	$0.935168\pi$
$398$	−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	−0.964003	−	0.265893i	$-0.914333\pi$
$401$	−487.509	+	281.464i	−1.21573	+	0.701904i	−0.251731	+	0.967797i	$0.581000\pi$
$402$	−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	0.0393673	−	0.999225i	$-0.487466\pi$
$419$	387.326	−	223.623i	0.924405	−	0.533705i	0.885038	+	0.465519i	$0.154132\pi$
$420$	50.3045	−	46.3354i	0.119773	−	0.110322i
$421$	−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
$423$	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	0.613189	−	0.789936i	$-0.289886\pi$
$431$	101.578	+	58.6459i	0.235679	+	0.136069i	−0.377510	+	0.926005i	$0.623220\pi$
$432$	−304.976	+	237.796i	−0.705964	+	0.550455i
$433$	211.520	+	366.363i	0.488498	+	0.846104i	0.999912	−	0.0132303i	$-0.00421145\pi$
$433$	211.520	+	366.363i	0.488498	+	0.846104i	−0.511414	+	0.859334i	$0.670878\pi$
$434$	−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	−0.461964	−	0.886899i	$-0.652855\pi$
$443$	33.2832	−	19.2161i	0.0751314	−	0.0433771i	0.537095	+	0.843522i	$0.319522\pi$
$444$	−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	−0.951913	−	0.306370i	$-0.900886\pi$
$449$	−521.983	+	301.367i	−1.16254	+	0.671196i	−0.210632	+	0.977565i	$0.567552\pi$
$450$	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	−0.0945820	−	0.995517i	$-0.530151\pi$
$461$	−462.851	−	267.227i	−1.00402	−	0.579669i	−0.909434	+	0.415848i	$0.863485\pi$
$462$	−26.0869	+	83.4889i	−0.0564651	+	0.180712i
$463$	−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	$0.935476\pi$
$464$		−	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	$-0.914777\pi$
$467$		−	247.090i		−	0.529100i	0.964372	−	0.264550i	$-0.0852234\pi$
$468$	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	$0.327216\pi$
$479$			820.294i			1.71251i	−0.516550	+	0.856257i	$0.672784\pi$
$480$	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	−0.945574	−	0.325407i	$-0.894499\pi$
$487$	−367.489	−	636.510i	−0.754598	−	1.30700i	0.190976	−	0.981595i	$-0.438835\pi$
$488$	−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	−0.380389	−	0.924827i	$-0.624210\pi$
$491$	113.097	−	65.2966i	0.230340	−	0.132987i	0.610729	+	0.791840i	$0.290876\pi$
$492$	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	−0.880164	−	0.474670i	$-0.842568\pi$
$499$	−14.4740	+	25.0696i	−0.0290059	+	0.0502397i	0.851158	+	0.524909i	$0.175901\pi$
$500$		−	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	−0.731701	−	0.681626i	$-0.761273\pi$
$503$	−255.144	+	147.308i	−0.507245	+	0.292858i	0.224455	+	0.974484i	$0.427940\pi$
$504$	−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	0.132425	−	0.991193i	$-0.457724\pi$
$509$	538.032	−	310.633i	1.05704	−	0.610280i	0.924611	+	0.380913i	$0.124390\pi$
$510$	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	$0.0511071\pi$
$521$			166.583i			0.319738i	−0.987138	+	0.159869i	$0.948893\pi$
$522$	165.145	−	78.0502i	0.316370	−	0.149522i
$523$	−51.1561	+	88.6049i	−0.0978127	+	0.169417i	−0.910779	−	0.412894i	$-0.864518\pi$
$523$	−51.1561	+	88.6049i	−0.0978127	+	0.169417i	0.812966	+	0.582311i	$0.197851\pi$
$524$	−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	0.541370	−	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
$549$	−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	0.291663	−	0.956521i	$-0.405791\pi$
$557$	−217.719	−	125.700i	−0.390877	−	0.225673i	−0.682540	+	0.730848i	$0.739125\pi$
$558$	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	$-0.767285\pi$
$563$		−	751.814i		−	1.33537i	0.744443	−	0.667685i	$-0.232715\pi$
$564$	−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	$-0.843811\pi$
$569$		−	536.258i		−	0.942456i	0.882011	−	0.471228i	$-0.156189\pi$
$570$	27.0285	−	6.06541i	0.0474184	−	0.0106411i
$571$	−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	$0.195116\pi$
$572$	−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	$-0.853255\pi$
$587$		−	522.260i		−	0.889711i	0.895602	−	0.444855i	$-0.146745\pi$
$588$	−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	$0.176561\pi$
$593$			624.635i			1.05335i	−0.850068	+	0.526674i	$0.823439\pi$
$594$	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	0.0502581	−	0.998736i	$-0.483996\pi$
$599$	−472.937	−	273.050i	−0.789544	−	0.455843i	−0.839802	+	0.542893i	$0.817329\pi$
$600$	−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	0.481725	+	0.876322i	$0.340010\pi$
$613$	−317.568	+	550.044i	−0.518055	+	0.897298i	−0.999780	+	0.0209752i	$0.993323\pi$
$614$			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	$0.0165637\pi$
$617$			64.1839i			0.104026i	−0.998646	+	0.0520129i	$0.983436\pi$
$618$	82.4182	+	25.7523i	0.133363	+	0.0416704i
$619$	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
$621$	−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	0.977541	+	0.210743i	$0.0675884\pi$
$631$	423.578	+	733.658i	0.671280	+	1.16269i	−0.306262	+	0.951947i	$0.599078\pi$
$632$	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	0.998374	−	0.0570099i	$-0.0181567\pi$
$641$	928.289	+	535.948i	1.44819	+	0.836112i	0.449815	+	0.893122i	$0.351490\pi$
$642$	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	0.987936	−	0.154865i	$-0.0494943\pi$
$647$	872.018	+	503.460i	1.34779	+	0.778145i	0.359851	+	0.933010i	$0.382828\pi$
$648$	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	−0.530573	+	0.847639i	$0.678023\pi$
$653$	−999.048	+	576.801i	−1.52994	+	0.883309i	−0.999364	+	0.0356698i	$0.988644\pi$
$654$	−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	0.281737	−	0.959492i	$-0.409089\pi$
$659$	−269.095	−	155.362i	−0.408338	−	0.235754i	−0.690076	+	0.723737i	$0.742423\pi$
$660$	59.7649	−	191.272i	0.0905528	−	0.289807i
$661$	257.855	+	446.618i	0.390099	+	0.675670i	0.992462	−	0.122551i	$-0.0391076\pi$
$661$	257.855	+	446.618i	0.390099	+	0.675670i	−0.602364	+	0.798222i	$0.705774\pi$
$662$	−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	−0.491169	−	0.871064i	$-0.663430\pi$
$677$	11.9220	−	6.88315i	0.0176100	−	0.0101671i	0.508779	+	0.860897i	$0.330097\pi$
$678$	−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	−0.175138	−	0.984544i	$-0.556037\pi$
$683$	402.924	−	232.628i	0.589933	−	0.340598i	0.765071	+	0.643946i	$0.222704\pi$
$684$	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	$0.186443\pi$
$701$			775.035i			1.10561i	−0.833310	+	0.552806i	$0.813557\pi$
$702$	−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	−0.997313	−	0.0732533i	$-0.976662\pi$
$709$	−308.569	+	534.457i	−0.435217	+	0.753819i	0.562096	+	0.827072i	$0.309995\pi$
$710$			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	−0.823410	−	0.567447i	$-0.807931\pi$
$719$	−534.714	+	308.717i	−0.743692	+	0.429371i	0.0797184	+	0.996817i	$0.474598\pi$
$720$	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	−0.958532	−	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
$731$		−	1186.47i		−	1.62308i
$732$	35.7268	−	114.341i	0.0488072	−	0.156203i
$733$	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	$-0.0359526\pi$
$734$		−	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	−0.839081	−	0.544007i	$-0.816907\pi$
$739$	38.1201	−	66.0259i	0.0515833	−	0.0893449i	0.890664	+	0.454662i	$0.150240\pi$
$740$	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	−0.184703	−	0.982794i	$-0.559132\pi$
$743$	426.534	−	246.260i	0.574071	−	0.331440i	0.758773	+	0.651355i	$0.225799\pi$
$744$	−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	0.704106	−	0.710095i	$-0.251348\pi$
$751$	−197.444	−	341.982i	−0.262907	−	0.455369i	−0.967013	+	0.254726i	$0.918015\pi$
$752$	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	−0.834675	−	0.550743i	$-0.814344\pi$
$757$	45.1326	−	78.1720i	0.0596204	−	0.103266i	0.894295	+	0.447478i	$0.147678\pi$
$758$	−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	$-0.836058\pi$
$761$		−	749.692i		−	0.985140i	0.870273	−	0.492570i	$-0.163942\pi$
$762$	−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	0.870410	−	0.492327i	$-0.163854\pi$
$769$	6.79598	+	11.7710i	0.00883743	+	0.0153069i	−0.861573	+	0.507634i	$0.830520\pi$
$770$	29.0003	−	16.7433i	0.0376627	−	0.0217445i
$771$	−856.936	+	789.321i	−1.11146	+	1.02376i
$772$	215.809	+	373.792i	0.279545	+	0.484186i
$773$	−20.8183	+	12.0195i	−0.0269318	+	0.0155491i	−0.513405	−	0.858146i	$-0.671616\pi$
$773$	−20.8183	+	12.0195i	−0.0269318	+	0.0155491i	0.486474	+	0.873695i	$0.338283\pi$
$774$	−141.857	−	11.6723i	−0.183278	−	0.0150804i
$775$	−980.106			−1.26465
$776$	−49.7493	−	28.7227i	−0.0641099	−	0.0370138i
$777$	−555.126	−	602.679i	−0.714448	−	0.775649i
$778$	−63.2605	−	109.570i	−0.0813117	−	0.140836i
$779$	−534.379	−	308.524i	−0.685981	−	0.396052i
$780$	−157.499	−	71.1739i	−0.201922	−	0.0912486i
$781$	297.538	+	515.351i	0.380971	+	0.659861i
$782$	−133.582	−	77.1236i	−0.170821	−	0.0986235i
$783$	896.075	+	1149.23i	1.14441	+	1.46772i
$784$	161.400	+	279.554i	0.205868	+	0.356574i
$785$	57.7739	−	33.3558i	0.0735974	−	0.0424915i
$786$	−28.8461	+	92.3195i	−0.0366999	+	0.117455i
$787$	−564.709			−0.717546			−0.358773	−	0.933425i	$-0.616805\pi$
$787$	−564.709			−0.717546			−0.358773	+	0.933425i	$0.616805\pi$
$788$	39.2460	+	22.6587i	0.0498046	+	0.0287547i
$789$	104.698	+	466.552i	0.132697	+	0.591321i
$790$	8.44767			0.0106933
$791$	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
$795$	13.0032	−	41.6157i	0.0163562	−	0.0523468i
$796$	35.6468	+	61.7420i	0.0447824	+	0.0775654i
$797$		−	410.342i		−	0.514858i	−0.966297	−	0.257429i	$-0.917125\pi$
$797$		−	410.342i		−	0.514858i	0.966297	−	0.257429i	$-0.0828754\pi$
$798$	27.1672	+	121.062i	0.0340441	+	0.151706i
$799$	−56.7345	+	98.2670i	−0.0710068	+	0.122987i
$800$	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
$803$		−	984.123i		−	1.22556i
$804$	580.528	+	630.256i	0.722049	+	0.783901i
$805$	−42.9553	+	74.4008i	−0.0533607	+	0.0924234i
$806$	161.652	+	121.664i	0.200560	+	0.150948i
$807$	351.936	−	324.168i	0.436104	−	0.401695i
$808$	244.958			0.303166
$809$	−518.289	−	299.234i	−0.640654	−	0.369882i	0.144212	−	0.989547i	$-0.453935\pi$
$809$	−518.289	−	299.234i	−0.640654	−	0.369882i	−0.784867	+	0.619665i	$0.787269\pi$
$810$	12.3037	+	32.7467i	0.0151898	+	0.0404280i
$811$	−427.373			−0.526971			−0.263485	−	0.964663i	$-0.584872\pi$
$811$	−427.373			−0.526971			−0.263485	+	0.964663i	$0.584872\pi$
$812$	927.814	+	535.673i	1.14263	+	0.659696i
$813$	173.134	−	554.100i	0.212957	−	0.681550i
$814$	−150.463	+	260.610i	−0.184844	+	0.320159i
$815$		−	18.6079i		−	0.0228318i
$816$	891.592	−	821.244i	1.09264	−	1.00643i
$817$	−899.218			−1.10063
$818$		−	278.426i		−	0.340374i
$819$	−121.745	+	589.433i	−0.148651	+	0.719699i
$820$	−127.900			−0.155976
$821$			515.147i			0.627463i	0.949512	+	0.313732i	$0.101579\pi$
$821$			515.147i			0.627463i	−0.949512	+	0.313732i	$0.898421\pi$
$822$	37.3605	−	119.569i	0.0454507	−	0.145461i
$823$	−992.582			−1.20605			−0.603026	−	0.797721i	$-0.706039\pi$
$823$	−992.582			−1.20605			−0.603026	+	0.797721i	$0.706039\pi$
$824$	−195.887	−	113.095i	−0.237727	−	0.137252i
$825$	−787.613	+	725.469i	−0.954683	+	0.879356i
$826$	−21.2820	+	36.8615i	−0.0257651	+	0.0446265i
$827$		−	943.762i		−	1.14119i	−0.821233	−	0.570594i	$-0.806713\pi$
$827$		−	943.762i		−	1.14119i	0.821233	−	0.570594i	$-0.193287\pi$
$828$	287.495	−	415.137i	0.347217	−	0.501373i
$829$	133.486	−	231.205i	0.161021	−	0.278896i	−0.774214	−	0.632924i	$-0.781855\pi$
$829$	133.486	−	231.205i	0.161021	−	0.278896i	0.935235	+	0.354027i	$0.115188\pi$
$830$			35.7613i			0.0430859i
$831$	−288.066	+	921.930i	−0.346650	+	1.10942i
$832$	655.820	+	80.1331i	0.788245	+	0.0963138i
$833$	−550.591	−	317.884i	−0.660974	−	0.381614i
$834$	50.1041	+	223.272i	0.0600768	+	0.267712i
$835$	−35.9318			−0.0430320
$836$	−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
$839$	702.552	+	405.618i	0.837368	+	0.483455i	0.856369	−	0.516365i	$-0.172715\pi$
$839$	702.552	+	405.618i	0.837368	+	0.483455i	−0.0190007	+	0.999819i	$0.506048\pi$
$840$	35.4854	+	38.5251i	0.0422445	+	0.0458632i
$841$	−2072.13			−2.46388
$842$	103.850	−	59.9578i	0.123337	−	0.0712088i
$843$	911.024	−	839.142i	1.08069	−	0.995423i
$844$	−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
$848$			181.246i			0.213734i
$849$	991.359	+	1076.28i	1.16768	+	1.26770i
$850$	−125.601	+	217.548i	−0.147766	+	0.255939i
$851$		−	772.033i		−	0.907207i
$852$	−336.148	+	309.625i	−0.394539	+	0.363409i
$853$	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
$855$	94.4325	+	199.808i	0.110447	+	0.233693i
$856$	−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	$-0.0326830\pi$
$858$	219.959	−	21.8842i	0.256362	−	0.0255060i
$859$	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	$0.0845054\pi$
$860$	−161.417	+	93.1939i	−0.187694	+	0.108365i
$861$	97.5254	+	434.589i	0.113270	+	0.504750i
$862$	−22.0526	+	38.1962i	−0.0255830	+	0.0443111i
$863$		−	1057.49i		−	1.22536i	−0.790331	−	0.612680i	$-0.790091\pi$
$863$		−	1057.49i		−	1.22536i	0.790331	−	0.612680i	$-0.209909\pi$
$864$	−285.660	−	366.362i	−0.330625	−	0.424030i
$865$	2.48212	+	4.29916i	0.00286951	+	0.00497013i
$866$	−137.763	+	79.5376i	−0.159080	+	0.0918448i
$867$	−453.453	+	1451.24i	−0.523014	+	1.67386i
$868$	410.767	+	711.468i	0.473233	+	0.819664i
$869$	255.331	−	147.416i	0.293822	−	0.169638i
$870$	−66.7467	−	20.8556i	−0.0767203	−	0.0239720i
$871$	−376.521	−	885.579i	−0.432286	−	1.01674i
$872$			17.2641i			0.0197983i
$873$	−14.3473	+	174.368i	−0.0164345	+	0.199734i
$874$	−58.4514	+	101.241i	−0.0668781	+	0.115836i
$875$	249.084	+	143.809i	0.284667	+	0.164353i
$876$	737.459	−	165.492i	0.841848	−	0.188918i
$877$	152.759			0.174184			0.0870920	−	0.996200i	$-0.472243\pi$
$877$	152.759			0.174184			0.0870920	+	0.996200i	$0.472243\pi$
$878$		−	101.008i		−	0.115043i
$879$	−360.393	−	1605.97i	−0.410003	−	1.82704i
$880$	−123.977	+	214.734i	−0.140883	+	0.244016i
$881$	1343.46	+	775.645i	1.52492	+	0.880414i	0.999564	+	0.0295323i	$0.00940179\pi$
$881$	1343.46	+	775.645i	1.52492	+	0.880414i	0.525358	+	0.850882i	$0.323932\pi$
$882$	−43.4235	+	62.7026i	−0.0492330	+	0.0710914i
$883$	−613.125			−0.694366			−0.347183	−	0.937797i	$-0.612862\pi$
$883$	−613.125			−0.694366			−0.347183	+	0.937797i	$0.612862\pi$
$884$	−1302.25	+	553.678i	−1.47314	+	0.626333i
$885$	−22.6112	+	72.3651i	−0.0255493	+	0.0817685i
$886$	7.22579	+	12.5154i	0.00815552	+	0.0141258i
$887$	809.756	−	467.513i	0.912916	−	0.527072i	0.0315475	−	0.999502i	$-0.489956\pi$
$887$	809.756	−	467.513i	0.912916	−	0.527072i	0.881368	+	0.472430i	$0.156623\pi$
$888$	−449.267	−	140.378i	−0.505932	−	0.158083i
$889$	26.8889	+	46.5729i	0.0302462	+	0.0523880i
$890$	−58.2295	+	33.6188i	−0.0654265	+	0.0377740i
$891$	943.325	+	775.065i	1.05873	+	0.869883i
$892$	−1246.02			−1.39688
$893$	74.4759	+	42.9987i	0.0833996	+	0.0481508i
$894$	−258.913	+	58.1022i	−0.289612	+	0.0649913i
$895$	−1.06070	−	1.83718i	−0.00118514	−	0.00205272i
$896$	−391.756	−	226.181i	−0.437228	−	0.252434i
$897$	−460.634	+	330.777i	−0.513527	+	0.368759i
$898$	−113.323	−	196.281i	−0.126195	−	0.218575i
$899$	−1934.57	−	1116.93i	−2.15192	−	1.24241i
$900$	−676.081	−	468.207i	−0.751202	−	0.520230i
$901$	−178.486	−	309.146i	−0.198097	−	0.343115i
$902$	141.662	−	81.7884i	0.157053	−	0.0906745i
$903$	439.743	+	477.412i	0.486980	+	0.528695i
$904$	394.263			0.436131
$905$	−10.6764	−	6.16400i	−0.0117971	−	0.00681105i
$906$	221.154	−	203.704i	0.244099	−	0.224839i
$907$	1149.05			1.26687			0.633433	−	0.773797i	$-0.281645\pi$
$907$	1149.05			1.26687			0.633433	+	0.773797i	$0.281645\pi$
$908$	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	$0.242570\pi$
$912$	−622.415	−	675.732i	−0.682472	−	0.740934i
$913$	624.051	+	1080.89i	0.683517	+	1.18389i
$914$			97.6180i			0.106803i
$915$	26.2261	−	24.1568i	0.0286625	−	0.0264009i
$916$	460.896	−	798.295i	0.503161	−	0.871501i
$917$	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	0.984799	−	0.173695i	$-0.0555708\pi$
$919$	314.275	+	544.341i	0.341975	+	0.592318i	−0.642824	+	0.766014i	$0.722237\pi$
$920$			49.3507i			0.0536421i
$921$	−229.330	+	51.4636i	−0.249001	+	0.0558779i
$922$	100.485	−	174.046i	0.108986	−	0.188770i
$923$	472.324	−	200.818i	0.511727	−	0.217570i
$924$	856.717	+	267.689i	0.927183	+	0.289707i
$925$	−1257.31			−1.35926
$926$	−200.265	−	115.623i	−0.216269	−	0.124863i
$927$	−56.4924	+	686.572i	−0.0609411	+	0.740638i
$928$	928.677			1.00073
$929$	203.102	+	117.261i	0.218625	+	0.126223i	0.605313	−	0.795987i	$-0.293048\pi$
$929$	203.102	+	117.261i	0.218625	+	0.126223i	−0.386689	+	0.922210i	$0.626381\pi$
$930$	−36.3294	−	39.4414i	−0.0390639	−	0.0424101i
$931$	−240.922	+	417.289i	−0.258778	+	0.448216i
$932$		−	165.590i		−	0.177672i
$933$	1292.26	+	403.778i	1.38506	+	0.432773i
$934$	92.9128			0.0994784
$935$		−	488.353i		−	0.522303i
$936$	108.732	+	328.200i	0.116166	+	0.350641i
$937$	−598.868			−0.639133			−0.319567	−	0.947564i	$-0.603537\pi$
$937$	−598.868			−0.639133			−0.319567	+	0.947564i	$0.603537\pi$
$938$			143.189i			0.152653i
$939$	−478.950	−	519.978i	−0.510064	−	0.553757i
$940$	17.8253			0.0189631
$941$	−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	$0.709650\pi$
$942$	−62.5432	−	19.5422i	−0.0663941	−	0.0207454i
$943$	−209.830	+	363.436i	−0.222513	+	0.385404i
$944$		−	315.167i		−	0.333864i
$945$	59.9017	−	147.848i	0.0633880	−	0.156453i
$946$	119.189	−	206.442i	0.125993	−	0.218226i
$947$			1553.39i			1.64033i	0.572130	+	0.820163i	$0.306117\pi$
$947$			1553.39i			1.64033i	−0.572130	+	0.820163i	$0.693883\pi$
$948$	153.404	+	166.545i	0.161818	+	0.175680i
$949$	−842.521	−	102.946i	−0.887799	−	0.108478i
$950$	164.878	+	95.1925i	0.173556	+	0.100203i
$951$	−274.944	+	253.250i	−0.289110	+	0.266299i
$952$	428.837			0.450459
$953$	373.494	−	215.637i	0.391914	−	0.226272i	−0.291075	−	0.956700i	$-0.594013\pi$
$953$	373.494	−	215.637i	0.391914	−	0.226272i	0.682989	+	0.730429i	$0.260680\pi$
$954$	−38.7181	+	18.2988i	−0.0405850	+	0.0191811i
$955$	37.8575	+	65.5711i	0.0396414	+	0.0686609i
$956$	258.729	+	149.377i	0.270637	+	0.156252i
$957$	−2381.36	+	534.397i	−2.48836	+	0.558409i
$958$	−308.454			−0.321978
$959$	−494.716	+	285.624i	−0.515867	+	0.297836i
$960$	−167.143	−	52.2253i	−0.174107	−	0.0544014i
$961$	−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
$965$			128.471i			0.133130i
$966$	82.3352	−	18.4767i	0.0852331	−	0.0191270i
$967$	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	$-0.0251671\pi$
$968$		−	313.795i		−	0.324169i
$969$	1727.07	+	539.640i	1.78233	+	0.556904i
$970$	−4.19775	−	7.27071i	−0.00432757	−	0.00749558i
$971$	88.2684	−	50.9618i	0.0909046	−	0.0524838i	−0.453859	−	0.891074i	$-0.649953\pi$
$971$	88.2684	−	50.9618i	0.0909046	−	0.0524838i	0.544763	+	0.838590i	$0.316620\pi$
$972$	−422.169	+	837.223i	−0.434331	+	0.861341i
$973$	521.736	−	903.674i	0.536214	−	0.928750i
$974$	239.346	−	138.187i	0.245735	−	0.141875i
$975$	538.695	+	750.176i	0.552507	+	0.769411i
$976$	−74.1120	+	128.366i	−0.0759345	+	0.131522i
$977$	874.681	−	504.997i	0.895272	−	0.516886i	0.0196090	−	0.999808i	$-0.493758\pi$
$977$	874.681	−	504.997i	0.895272	−	0.516886i	0.875663	+	0.482922i	$0.160425\pi$
$978$	−13.4432	+	12.3825i	−0.0137456	+	0.0126611i
$979$	−1173.33	+	2032.26i	−1.19850	+	2.07586i
$980$			99.8756i			0.101914i
$981$	47.5381	−	22.4673i	0.0484588	−	0.0229024i
$982$	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	$0.595230\pi$
$984$	173.340	+	188.189i	0.176159	+	0.191249i
$985$	6.74436	+	11.6816i	0.00684706	+	0.0118595i
$986$	−495.834	+	286.270i	−0.502874	+	0.290335i
$987$	−13.5920	−	60.5682i	−0.0137710	−	0.0613660i
$988$	419.629	+	986.969i	0.424726	+	0.998957i
$989$			611.566i			0.618368i
$990$	−58.3886	−	4.80432i	−0.0589784	−	0.00485285i
$991$	−698.522	+	1209.87i	−0.704865	+	1.22086i	0.261875	+	0.965102i	$0.415659\pi$
$991$	−698.522	+	1209.87i	−0.704865	+	1.22086i	−0.966740	+	0.255761i	$0.917674\pi$
$992$	616.723	+	356.065i	0.621696	+	0.358937i
$993$	299.358	−	958.071i	0.301468	−	0.964824i
$994$	−76.3697			−0.0768307
$995$			21.2205i			0.0213272i
$996$	−705.030	+	649.401i	−0.707861	+	0.652009i
$997$	682.194	−	1181.60i	0.684247	−	1.18515i	−0.289426	−	0.957200i	$-0.593464\pi$
$997$	682.194	−	1181.60i	0.684247	−	1.18515i	0.973673	−	0.227950i	$-0.0732023\pi$
$998$	−9.42691	−	5.44263i	−0.00944580	−	0.00545354i
$999$	198.129	+	1419.78i	0.198328	+	1.42120i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.3.k.a.29.14	✓	52	117.29	odd	6	inner
117.3.k.a.113.13	yes	52	1.1	even	1	trivial
117.3.u.a.68.14	yes	52	13.3	even	3
117.3.u.a.74.14	yes	52	9.2	odd	6
351.3.k.a.152.14		52	3.2	odd	2
351.3.k.a.224.13		52	117.16	even	3
351.3.u.a.35.13		52	9.7	even	3
351.3.u.a.341.13		52	39.29	odd	6

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

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