LMFDB - Embedded newform 102.4.f.c.13.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [102,4,Mod(13,102)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(102, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("102.13");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 102 = 2 \cdot 3 \cdot 17 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	102.f (of order $4$, 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:	$6.01819482059$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 886x^{10} + 292945x^{8} + 42943904x^{6} + 2387634208x^{4} + 5944075264x^{2} + 2089586944 $ x^12 + 886x^10 + 292945x^8 + 42943904x^6 + 2387634208x^4 + 5944075264*x^2 + 2089586944
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6}\cdot 3^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			13.3
Root			$-14.8987i$ of defining polynomial
Character	$\chi$	$=$	102.13
Dual form			102.4.f.c.55.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.00000i q^{2} +(-2.12132 - 2.12132i) q^{3} -4.00000 q^{4} +(12.9492 + 12.9492i) q^{5} +(-4.24264 + 4.24264i) q^{6} +(17.3340 - 17.3340i) q^{7} +8.00000i q^{8} +9.00000i q^{9} +(25.8984 - 25.8984i) q^{10} +(25.2530 - 25.2530i) q^{11} +(8.48528 + 8.48528i) q^{12} -13.4149 q^{13} +(-34.6680 - 34.6680i) q^{14} -54.9388i q^{15} +16.0000 q^{16} +(-16.8983 - 68.0254i) q^{17} +18.0000 q^{18} +15.6725i q^{19} +(-51.7968 - 51.7968i) q^{20} -73.5420 q^{21} +(-50.5060 - 50.5060i) q^{22} +(100.376 - 100.376i) q^{23} +(16.9706 - 16.9706i) q^{24} +210.364i q^{25} +26.8298i q^{26} +(19.0919 - 19.0919i) q^{27} +(-69.3360 + 69.3360i) q^{28} +(94.5834 + 94.5834i) q^{29} -109.878 q^{30} +(133.855 + 133.855i) q^{31} -32.0000i q^{32} -107.139 q^{33} +(-136.051 + 33.7965i) q^{34} +448.923 q^{35} -36.0000i q^{36} +(-193.968 - 193.968i) q^{37} +31.3450 q^{38} +(28.4573 + 28.4573i) q^{39} +(-103.594 + 103.594i) q^{40} +(171.528 - 171.528i) q^{41} +147.084i q^{42} +385.616i q^{43} +(-101.012 + 101.012i) q^{44} +(-116.543 + 116.543i) q^{45} +(-200.752 - 200.752i) q^{46} -533.009 q^{47} +(-33.9411 - 33.9411i) q^{48} -257.936i q^{49} +420.728 q^{50} +(-108.457 + 180.150i) q^{51} +53.6595 q^{52} +403.802i q^{53} +(-38.1838 - 38.1838i) q^{54} +654.012 q^{55} +(138.672 + 138.672i) q^{56} +(33.2464 - 33.2464i) q^{57} +(189.167 - 189.167i) q^{58} +266.868i q^{59} +219.755i q^{60} +(-484.097 + 484.097i) q^{61} +(267.710 - 267.710i) q^{62} +(156.006 + 156.006i) q^{63} -64.0000 q^{64} +(-173.712 - 173.712i) q^{65} +214.279i q^{66} -441.266 q^{67} +(67.5931 + 272.101i) q^{68} -425.859 q^{69} -897.847i q^{70} +(-303.839 - 303.839i) q^{71} -72.0000 q^{72} +(-86.3683 - 86.3683i) q^{73} +(-387.936 + 387.936i) q^{74} +(446.249 - 446.249i) q^{75} -62.6901i q^{76} -875.471i q^{77} +(56.9145 - 56.9145i) q^{78} +(-464.263 + 464.263i) q^{79} +(207.187 + 207.187i) q^{80} -81.0000 q^{81} +(-343.057 - 343.057i) q^{82} -1243.94i q^{83} +294.168 q^{84} +(662.055 - 1099.69i) q^{85} +771.231 q^{86} -401.283i q^{87} +(202.024 + 202.024i) q^{88} +1498.50 q^{89} +(233.086 + 233.086i) q^{90} +(-232.534 + 232.534i) q^{91} +(-401.503 + 401.503i) q^{92} -567.900i q^{93} +1066.02i q^{94} +(-202.947 + 202.947i) q^{95} +(-67.8823 + 67.8823i) q^{96} +(90.0409 + 90.0409i) q^{97} -515.871 q^{98} +(227.277 + 227.277i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 48 q^{4} + 16 q^{5} - 12 q^{7} + 32 q^{10} - 32 q^{11} - 68 q^{13} + 24 q^{14} + 192 q^{16} + 64 q^{17} + 216 q^{18} - 64 q^{20} - 168 q^{21} + 64 q^{22} - 112 q^{23} + 48 q^{28} - 296 q^{29} - 168 q^{30}+ \cdots - 288 q^{99}+O(q^{100}) $ 12 * q - 48 * q^4 + 16 * q^5 - 12 * q^7 + 32 * q^10 - 32 * q^11 - 68 * q^13 + 24 * q^14 + 192 * q^16 + 64 * q^17 + 216 * q^18 - 64 * q^20 - 168 * q^21 + 64 * q^22 - 112 * q^23 + 48 * q^28 - 296 * q^29 - 168 * q^30 + 520 * q^31 + 204 * q^33 + 144 * q^34 + 392 * q^35 - 828 * q^37 - 280 * q^38 + 312 * q^39 - 128 * q^40 + 8 * q^41 + 128 * q^44 - 144 * q^45 + 224 * q^46 - 2920 * q^47 + 752 * q^50 + 420 * q^51 + 272 * q^52 + 1156 * q^55 - 96 * q^56 + 312 * q^57 - 592 * q^58 - 1124 * q^61 + 1040 * q^62 - 108 * q^63 - 768 * q^64 + 3288 * q^65 - 2008 * q^67 - 256 * q^68 + 468 * q^69 - 2184 * q^71 - 864 * q^72 + 2456 * q^73 - 1656 * q^74 - 192 * q^75 + 624 * q^78 + 2652 * q^79 + 256 * q^80 - 972 * q^81 - 16 * q^82 + 672 * q^84 + 3444 * q^85 - 184 * q^86 - 256 * q^88 + 5304 * q^89 + 288 * q^90 - 1420 * q^91 + 448 * q^92 - 2920 * q^95 + 2688 * q^97 - 4168 * q^98 - 288 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/102\mathbb{Z}\right)^\times$.

$n$	$35$	$37$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$

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 $

$2$		−	2.00000i		−	0.707107i
$2$		−	2.00000i		−	0.707107i
$3$	−2.12132	−	2.12132i	−0.408248	−	0.408248i
$3$	−2.12132	−	2.12132i	−0.408248	−	0.408248i
$4$	−4.00000			−0.500000
$5$	12.9492	+	12.9492i	1.15821	+	1.15821i	0.984860	+	0.173353i	$0.0554600\pi$
$5$	12.9492	+	12.9492i	1.15821	+	1.15821i	0.173353	+	0.984860i	$0.444540\pi$
$6$	−4.24264	+	4.24264i	−0.288675	+	0.288675i
$7$	17.3340	−	17.3340i	0.935948	−	0.935948i	−0.0621202	−	0.998069i	$-0.519786\pi$
$7$	17.3340	−	17.3340i	0.935948	−	0.935948i	0.998069	+	0.0621202i	$0.0197862\pi$
$8$			8.00000i			0.353553i
$9$			9.00000i			0.333333i
$10$	25.8984	−	25.8984i	0.818980	−	0.818980i
$11$	25.2530	−	25.2530i	0.692187	−	0.692187i	−0.270525	−	0.962713i	$-0.587197\pi$
$11$	25.2530	−	25.2530i	0.692187	−	0.692187i	0.962713	+	0.270525i	$0.0871974\pi$
$12$	8.48528	+	8.48528i	0.204124	+	0.204124i
$13$	−13.4149			−0.286201			−0.143101	−	0.989708i	$-0.545707\pi$
$13$	−13.4149			−0.286201			−0.143101	+	0.989708i	$0.545707\pi$
$14$	−34.6680	−	34.6680i	−0.661816	−	0.661816i
$15$		−	54.9388i		−	0.945676i
$16$	16.0000			0.250000
$17$	−16.8983	−	68.0254i	−0.241084	−	0.970504i
$17$	−16.8983	−	68.0254i	−0.241084	−	0.970504i
$18$	18.0000			0.235702
$19$			15.6725i			0.189238i	0.995514	+	0.0946190i	$0.0301633\pi$
$19$			15.6725i			0.189238i	−0.995514	+	0.0946190i	$0.969837\pi$
$20$	−51.7968	−	51.7968i	−0.579106	−	0.579106i
$21$	−73.5420			−0.764199
$22$	−50.5060	−	50.5060i	−0.489450	−	0.489450i
$23$	100.376	−	100.376i	0.909992	−	0.909992i	−0.0862791	−	0.996271i	$-0.527498\pi$
$23$	100.376	−	100.376i	0.909992	−	0.909992i	0.996271	+	0.0862791i	$0.0274977\pi$
$24$	16.9706	−	16.9706i	0.144338	−	0.144338i
$25$			210.364i			1.68291i
$26$			26.8298i			0.202375i
$27$	19.0919	−	19.0919i	0.136083	−	0.136083i
$28$	−69.3360	+	69.3360i	−0.467974	+	0.467974i
$29$	94.5834	+	94.5834i	0.605645	+	0.605645i	0.941805	−	0.336160i	$-0.109128\pi$
$29$	94.5834	+	94.5834i	0.605645	+	0.605645i	−0.336160	+	0.941805i	$0.609128\pi$
$30$	−109.878			−0.668694
$31$	133.855	+	133.855i	0.775520	+	0.775520i	0.979065	−	0.203546i	$-0.0652466\pi$
$31$	133.855	+	133.855i	0.775520	+	0.775520i	−0.203546	+	0.979065i	$0.565247\pi$
$32$		−	32.0000i		−	0.176777i
$33$	−107.139			−0.565169
$34$	−136.051	+	33.7965i	−0.686250	+	0.170472i
$35$	448.923			2.16805
$36$		−	36.0000i		−	0.166667i
$37$	−193.968	−	193.968i	−0.861842	−	0.861842i	0.129710	−	0.991552i	$-0.458595\pi$
$37$	−193.968	−	193.968i	−0.861842	−	0.861842i	−0.991552	+	0.129710i	$0.958595\pi$
$38$	31.3450			0.133811
$39$	28.4573	+	28.4573i	0.116841	+	0.116841i
$40$	−103.594	+	103.594i	−0.409490	+	0.409490i
$41$	171.528	−	171.528i	0.653372	−	0.653372i	−0.300432	−	0.953803i	$-0.597131\pi$
$41$	171.528	−	171.528i	0.653372	−	0.653372i	0.953803	+	0.300432i	$0.0971307\pi$
$42$			147.084i			0.540370i
$43$			385.616i			1.36758i	0.729680	+	0.683789i	$0.239669\pi$
$43$			385.616i			1.36758i	−0.729680	+	0.683789i	$0.760331\pi$
$44$	−101.012	+	101.012i	−0.346094	+	0.346094i
$45$	−116.543	+	116.543i	−0.386071	+	0.386071i
$46$	−200.752	−	200.752i	−0.643461	−	0.643461i
$47$	−533.009			−1.65420			−0.827099	−	0.562056i	$-0.810011\pi$
$47$	−533.009			−1.65420			−0.827099	+	0.562056i	$0.810011\pi$
$48$	−33.9411	−	33.9411i	−0.102062	−	0.102062i
$49$		−	257.936i		−	0.751999i
$50$	420.728			1.19000
$51$	−108.457	+	180.150i	−0.297784	+	0.494629i
$52$	53.6595			0.143101
$53$			403.802i			1.04654i	0.852168	+	0.523268i	$0.175287\pi$
$53$			403.802i			1.04654i	−0.852168	+	0.523268i	$0.824713\pi$
$54$	−38.1838	−	38.1838i	−0.0962250	−	0.0962250i
$55$	654.012			1.60340
$56$	138.672	+	138.672i	0.330908	+	0.330908i
$57$	33.2464	−	33.2464i	0.0772561	−	0.0772561i
$58$	189.167	−	189.167i	0.428255	−	0.428255i
$59$			266.868i			0.588868i	0.955672	+	0.294434i	$0.0951311\pi$
$59$			266.868i			0.588868i	−0.955672	+	0.294434i	$0.904869\pi$
$60$			219.755i			0.472838i
$61$	−484.097	+	484.097i	−1.01610	+	1.01610i	−0.0162344	+	0.999868i	$0.505168\pi$
$61$	−484.097	+	484.097i	−1.01610	+	1.01610i	−0.999868	+	0.0162344i	$0.994832\pi$
$62$	267.710	−	267.710i	0.548375	−	0.548375i
$63$	156.006	+	156.006i	0.311983	+	0.311983i
$64$	−64.0000			−0.125000
$65$	−173.712	−	173.712i	−0.331482	−	0.331482i
$66$			214.279i			0.399635i
$67$	−441.266			−0.804615			−0.402308	−	0.915505i	$-0.631792\pi$
$67$	−441.266			−0.804615			−0.402308	+	0.915505i	$0.631792\pi$
$68$	67.5931	+	272.101i	0.120542	+	0.485252i
$69$	−425.859			−0.743005
$70$		−	897.847i		−	1.53305i
$71$	−303.839	−	303.839i	−0.507873	−	0.507873i	0.406000	−	0.913873i	$-0.366923\pi$
$71$	−303.839	−	303.839i	−0.507873	−	0.507873i	−0.913873	+	0.406000i	$0.866923\pi$
$72$	−72.0000			−0.117851
$73$	−86.3683	−	86.3683i	−0.138475	−	0.138475i	0.634472	−	0.772946i	$-0.281218\pi$
$73$	−86.3683	−	86.3683i	−0.138475	−	0.138475i	−0.772946	+	0.634472i	$0.781218\pi$
$74$	−387.936	+	387.936i	−0.609414	+	0.609414i
$75$	446.249	−	446.249i	0.687046	−	0.687046i
$76$		−	62.6901i		−	0.0946190i
$77$		−	875.471i		−	1.29570i
$78$	56.9145	−	56.9145i	0.0826192	−	0.0826192i
$79$	−464.263	+	464.263i	−0.661186	+	0.661186i	−0.955660	−	0.294474i	$-0.904856\pi$
$79$	−464.263	+	464.263i	−0.661186	+	0.661186i	0.294474	+	0.955660i	$0.404856\pi$
$80$	207.187	+	207.187i	0.289553	+	0.289553i
$81$	−81.0000			−0.111111
$82$	−343.057	−	343.057i	−0.462004	−	0.462004i
$83$		−	1243.94i		−	1.64506i	−0.568721	−	0.822530i	$-0.692562\pi$
$83$		−	1243.94i		−	1.64506i	0.568721	−	0.822530i	$-0.307438\pi$
$84$	294.168			0.382099
$85$	662.055	−	1099.69i	0.844823	−	1.40328i
$86$	771.231			0.967023
$87$		−	401.283i		−	0.494507i
$88$	202.024	+	202.024i	0.244725	+	0.244725i
$89$	1498.50			1.78472			0.892362	−	0.451320i	$-0.149047\pi$
$89$	1498.50			1.78472			0.892362	+	0.451320i	$0.149047\pi$
$90$	233.086	+	233.086i	0.272993	+	0.272993i
$91$	−232.534	+	232.534i	−0.267870	+	0.267870i
$92$	−401.503	+	401.503i	−0.454996	+	0.454996i
$93$		−	567.900i		−	0.633209i
$94$			1066.02i			1.16970i
$95$	−202.947	+	202.947i	−0.219178	+	0.219178i
$96$	−67.8823	+	67.8823i	−0.0721688	+	0.0721688i
$97$	90.0409	+	90.0409i	0.0942502	+	0.0942502i	0.752660	−	0.658410i	$-0.228771\pi$
$97$	90.0409	+	90.0409i	0.0942502	+	0.0942502i	−0.658410	+	0.752660i	$0.728771\pi$
$98$	−515.871			−0.531744
$99$	227.277	+	227.277i	0.230729	+	0.230729i
$100$		−	841.456i		−	0.841456i
$101$	−1152.65			−1.13557			−0.567785	−	0.823177i	$-0.692200\pi$
$101$	−1152.65			−1.13557			−0.567785	+	0.823177i	$0.692200\pi$
$102$	360.300	+	216.914i	0.349755	+	0.210565i
$103$	128.042			0.122489			0.0612445	−	0.998123i	$-0.480493\pi$
$103$	128.042			0.122489			0.0612445	+	0.998123i	$0.480493\pi$
$104$		−	107.319i		−	0.101187i
$105$	−952.310	−	952.310i	−0.885104	−	0.885104i
$106$	807.603			0.740013
$107$	1170.71	+	1170.71i	1.05773	+	1.05773i	0.998228	+	0.0594973i	$0.0189498\pi$
$107$	1170.71	+	1170.71i	1.05773	+	1.05773i	0.0594973	+	0.998228i	$0.481050\pi$
$108$	−76.3675	+	76.3675i	−0.0680414	+	0.0680414i
$109$	−1181.52	+	1181.52i	−1.03825	+	1.03825i	−0.0390141	+	0.999239i	$0.512422\pi$
$109$	−1181.52	+	1181.52i	−1.03825	+	1.03825i	−0.999239	+	0.0390141i	$0.987578\pi$
$110$		−	1308.02i		−	1.13378i
$111$			822.937i			0.703691i
$112$	277.344	−	277.344i	0.233987	−	0.233987i
$113$	−127.056	+	127.056i	−0.105773	+	0.105773i	−0.758013	−	0.652240i	$-0.773830\pi$
$113$	−127.056	+	127.056i	−0.105773	+	0.105773i	0.652240	+	0.758013i	$0.273830\pi$
$114$	−66.4928	−	66.4928i	−0.0546283	−	0.0546283i
$115$	2599.58			2.10793
$116$	−378.334	−	378.334i	−0.302822	−	0.302822i
$117$		−	120.734i		−	0.0954005i
$118$	533.735			0.416392
$119$	−1472.07	−	886.237i	−1.13398	−	0.682700i
$120$	439.511			0.334347
$121$			55.5736i			0.0417533i
$122$	968.194	+	968.194i	0.718493	+	0.718493i
$123$	−727.734			−0.533476
$124$	−535.421	−	535.421i	−0.387760	−	0.387760i
$125$	−1105.40	+	1105.40i	−0.790957	+	0.790957i
$126$	312.012	−	312.012i	0.220605	−	0.220605i
$127$		−	1988.60i		−	1.38945i	−0.719277	−	0.694723i	$-0.755527\pi$
$127$		−	1988.60i		−	1.38945i	0.719277	−	0.694723i	$-0.244473\pi$
$128$			128.000i			0.0883883i
$129$	818.014	−	818.014i	0.558311	−	0.558311i
$130$	−347.424	+	347.424i	−0.234393	+	0.234393i
$131$	694.086	+	694.086i	0.462920	+	0.462920i	0.899611	−	0.436691i	$-0.143850\pi$
$131$	694.086	+	694.086i	0.462920	+	0.462920i	−0.436691	+	0.899611i	$0.643850\pi$
$132$	428.557			0.282584
$133$	271.667	+	271.667i	0.177117	+	0.177117i
$134$			882.532i			0.568949i
$135$	494.450			0.315225
$136$	544.203	−	135.186i	0.343125	−	0.0852361i
$137$	−2788.01			−1.73866			−0.869328	−	0.494236i	$-0.835448\pi$
$137$	−2788.01			−1.73866			−0.869328	+	0.494236i	$0.835448\pi$
$138$			851.717i			0.525384i
$139$	−118.311	−	118.311i	−0.0721944	−	0.0721944i	0.670088	−	0.742282i	$-0.266257\pi$
$139$	−118.311	−	118.311i	−0.0721944	−	0.0721944i	−0.742282	+	0.670088i	$0.766257\pi$
$140$	−1795.69			−1.08403
$141$	1130.68	+	1130.68i	0.675324	+	0.675324i
$142$	−607.677	+	607.677i	−0.359121	+	0.359121i
$143$	−338.766	+	338.766i	−0.198105	+	0.198105i
$144$			144.000i			0.0833333i
$145$			2449.56i			1.40293i
$146$	−172.737	+	172.737i	−0.0979163	+	0.0979163i
$147$	−547.164	+	547.164i	−0.307002	+	0.307002i
$148$	775.872	+	775.872i	0.430921	+	0.430921i
$149$	−2926.77			−1.60920			−0.804598	−	0.593820i	$-0.797619\pi$
$149$	−2926.77			−1.60920			−0.804598	+	0.593820i	$0.797619\pi$
$150$	−892.499	−	892.499i	−0.485815	−	0.485815i
$151$			2142.40i			1.15461i	0.816528	+	0.577306i	$0.195896\pi$
$151$			2142.40i			1.15461i	−0.816528	+	0.577306i	$0.804104\pi$
$152$	−125.380			−0.0669057
$153$	612.228	−	152.084i	0.323501	−	0.0803614i
$154$	−1750.94			−0.916201
$155$			3466.64i			1.79643i
$156$	−113.829	−	113.829i	−0.0584206	−	0.0584206i
$157$	1329.27			0.675714			0.337857	−	0.941197i	$-0.390298\pi$
$157$	1329.27			0.675714			0.337857	+	0.941197i	$0.390298\pi$
$158$	928.526	+	928.526i	0.467529	+	0.467529i
$159$	856.593	−	856.593i	0.427247	−	0.427247i
$160$	414.375	−	414.375i	0.204745	−	0.204745i
$161$		−	3479.83i		−	1.70341i
$162$			162.000i			0.0785674i
$163$	1846.81	−	1846.81i	0.887442	−	0.887442i	−0.106834	−	0.994277i	$-0.534071\pi$
$163$	1846.81	−	1846.81i	0.887442	−	0.887442i	0.994277	+	0.106834i	$0.0340715\pi$
$164$	−686.114	+	686.114i	−0.326686	+	0.326686i
$165$	−1387.37	−	1387.37i	−0.654585	−	0.654585i
$166$	−2487.88			−1.16323
$167$	884.150	+	884.150i	0.409686	+	0.409686i	0.881629	−	0.471943i	$-0.156447\pi$
$167$	884.150	+	884.150i	0.409686	+	0.409686i	−0.471943	+	0.881629i	$0.656447\pi$
$168$		−	588.336i		−	0.270185i
$169$	−2017.04			−0.918089
$170$	−2199.39	−	1324.11i	−0.992266	−	0.597380i
$171$	−141.053			−0.0630793
$172$		−	1542.46i		−	0.683789i
$173$	2434.54	+	2434.54i	1.06991	+	1.06991i	0.997365	+	0.0725474i	$0.0231128\pi$
$173$	2434.54	+	2434.54i	1.06991	+	1.06991i	0.0725474	+	0.997365i	$0.476887\pi$
$174$	−802.567			−0.349669
$175$	3646.45	+	3646.45i	1.57512	+	1.57512i
$176$	404.048	−	404.048i	0.173047	−	0.173047i
$177$	566.112	−	566.112i	0.240404	−	0.240404i
$178$		−	2997.00i		−	1.26199i
$179$		−	1640.52i		−	0.685019i	−0.939514	−	0.342509i	$-0.888723\pi$
$179$		−	1640.52i		−	0.685019i	0.939514	−	0.342509i	$-0.111277\pi$
$180$	466.172	−	466.172i	0.193035	−	0.193035i
$181$	185.058	−	185.058i	0.0759958	−	0.0759958i	−0.668087	−	0.744083i	$-0.732887\pi$
$181$	185.058	−	185.058i	0.0759958	−	0.0759958i	0.744083	+	0.668087i	$0.232887\pi$
$182$	465.067	+	465.067i	0.189413	+	0.189413i
$183$	2053.85			0.829644
$184$	803.007	+	803.007i	0.321731	+	0.321731i
$185$		−	5023.46i		−	1.99639i
$186$	−1135.80			−0.447746
$187$	−2144.57	−	1291.11i	−0.838646	−	0.504895i
$188$	2132.04			0.827099
$189$		−	661.878i		−	0.254733i
$190$	405.893	+	405.893i	0.154982	+	0.154982i
$191$	2598.60			0.984439			0.492219	−	0.870471i	$-0.336186\pi$
$191$	2598.60			0.984439			0.492219	+	0.870471i	$0.336186\pi$
$192$	135.765	+	135.765i	0.0510310	+	0.0510310i
$193$	−2925.77	+	2925.77i	−1.09120	+	1.09120i	−0.0957997	+	0.995401i	$0.530541\pi$
$193$	−2925.77	+	2925.77i	−1.09120	+	1.09120i	−0.995401	+	0.0957997i	$0.969459\pi$
$194$	180.082	−	180.082i	0.0666449	−	0.0666449i
$195$			736.998i			0.270654i
$196$			1031.74i			0.376000i
$197$	−897.733	+	897.733i	−0.324674	+	0.324674i	−0.850557	−	0.525883i	$-0.823735\pi$
$197$	−897.733	+	897.733i	−0.324674	+	0.324674i	0.525883	+	0.850557i	$0.323735\pi$
$198$	454.554	−	454.554i	0.163150	−	0.163150i
$199$	−3823.88	−	3823.88i	−1.36215	−	1.36215i	−0.871174	−	0.490975i	$-0.836641\pi$
$199$	−3823.88	−	3823.88i	−1.36215	−	1.36215i	−0.490975	−	0.871174i	$-0.663359\pi$
$200$	−1682.91			−0.594999
$201$	936.066	+	936.066i	0.328483	+	0.328483i
$202$			2305.29i			0.802970i
$203$	3279.02			1.13370
$204$	433.828	−	720.601i	0.148892	−	0.247314i
$205$	4442.31			1.51349
$206$		−	256.084i		−	0.0866128i
$207$	903.383	+	903.383i	0.303331	+	0.303331i
$208$	−214.638			−0.0715503
$209$	395.778	+	395.778i	0.130988	+	0.130988i
$210$	−1904.62	+	1904.62i	−0.625863	+	0.625863i
$211$	2349.49	−	2349.49i	0.766567	−	0.766567i	−0.210933	−	0.977501i	$-0.567650\pi$
$211$	2349.49	−	2349.49i	0.766567	−	0.766567i	0.977501	+	0.210933i	$0.0676502\pi$
$212$		−	1615.21i		−	0.523268i
$213$			1289.08i			0.414677i
$214$	2341.42	−	2341.42i	0.747925	−	0.747925i
$215$	−4993.42	+	4993.42i	−1.58395	+	1.58395i
$216$	152.735	+	152.735i	0.0481125	+	0.0481125i
$217$	4640.49			1.45169
$218$	2363.05	+	2363.05i	0.734156	+	0.734156i
$219$			366.429i			0.113064i
$220$	−2616.05			−0.801700
$221$	226.688	+	912.552i	0.0689986	+	0.277760i
$222$	1645.87			0.497585
$223$		−	2244.32i		−	0.673951i	−0.941513	−	0.336975i	$-0.890596\pi$
$223$		−	2244.32i		−	0.673951i	0.941513	−	0.336975i	$-0.109404\pi$
$224$	−554.688	−	554.688i	−0.165454	−	0.165454i
$225$	−1893.28			−0.560971
$226$	254.111	+	254.111i	0.0747930	+	0.0747930i
$227$	2441.46	−	2441.46i	0.713856	−	0.713856i	−0.253484	−	0.967340i	$-0.581577\pi$
$227$	2441.46	−	2441.46i	0.713856	−	0.713856i	0.967340	+	0.253484i	$0.0815765\pi$
$228$	−132.986	+	132.986i	−0.0386280	+	0.0386280i
$229$		−	2682.67i		−	0.774130i	−0.922052	−	0.387065i	$-0.873489\pi$
$229$		−	2682.67i		−	0.774130i	0.922052	−	0.387065i	$-0.126511\pi$
$230$		−	5199.15i		−	1.49053i
$231$	−1857.15	+	1857.15i	−0.528969	+	0.528969i
$232$	−756.667	+	756.667i	−0.214128	+	0.214128i
$233$	−1116.03	−	1116.03i	−0.313791	−	0.313791i	0.532585	−	0.846376i	$-0.321220\pi$
$233$	−1116.03	−	1116.03i	−0.313791	−	0.313791i	−0.846376	+	0.532585i	$0.821220\pi$
$234$	−241.468			−0.0674583
$235$	−6902.04	−	6902.04i	−1.91591	−	1.91591i
$236$		−	1067.47i		−	0.294434i
$237$	1969.70			0.539856
$238$	−1772.47	+	2944.13i	−0.482742	+	0.801848i
$239$	5016.20			1.35762			0.678810	−	0.734314i	$-0.262496\pi$
$239$	5016.20			1.35762			0.678810	+	0.734314i	$0.262496\pi$
$240$		−	879.021i		−	0.236419i
$241$	−1150.94	−	1150.94i	−0.307629	−	0.307629i	0.536360	−	0.843989i	$-0.319799\pi$
$241$	−1150.94	−	1150.94i	−0.307629	−	0.307629i	−0.843989	+	0.536360i	$0.819799\pi$
$242$	111.147			0.0295240
$243$	171.827	+	171.827i	0.0453609	+	0.0453609i
$244$	1936.39	−	1936.39i	0.508051	−	0.508051i
$245$	3340.06	−	3340.06i	0.870975	−	0.870975i
$246$			1455.47i			0.377224i
$247$		−	210.245i		−	0.0541602i
$248$	−1070.84	+	1070.84i	−0.274188	+	0.274188i
$249$	−2638.79	+	2638.79i	−0.671593	+	0.671593i
$250$	2210.79	+	2210.79i	0.559291	+	0.559291i
$251$	296.264			0.0745021			0.0372510	−	0.999306i	$-0.488140\pi$
$251$	296.264			0.0745021			0.0372510	+	0.999306i	$0.488140\pi$
$252$	−624.024	−	624.024i	−0.155991	−	0.155991i
$253$		−	5069.58i		−	1.25977i
$254$	−3977.20			−0.982487
$255$	−3737.23	+	928.371i	−0.917783	+	0.227988i
$256$	256.000			0.0625000
$257$		−	2885.16i		−	0.700278i	−0.936698	−	0.350139i	$-0.886134\pi$
$257$		−	2885.16i		−	0.700278i	0.936698	−	0.350139i	$-0.113866\pi$
$258$	−1636.03	−	1636.03i	−0.394786	−	0.394786i
$259$	−6724.49			−1.61328
$260$	694.848	+	694.848i	0.165741	+	0.165741i
$261$	−851.250	+	851.250i	−0.201882	+	0.201882i
$262$	1388.17	−	1388.17i	0.327334	−	0.327334i
$263$			2958.63i			0.693677i	0.937925	+	0.346839i	$0.112745\pi$
$263$			2958.63i			0.693677i	−0.937925	+	0.346839i	$0.887255\pi$
$264$		−	857.115i		−	0.199817i
$265$	−5228.91	+	5228.91i	−1.21211	+	1.21211i
$266$	543.335	−	543.335i	0.125241	−	0.125241i
$267$	−3178.79	−	3178.79i	−0.728611	−	0.728611i
$268$	1765.06			0.402308
$269$	1852.83	+	1852.83i	0.419958	+	0.419958i	0.885189	−	0.465231i	$-0.154029\pi$
$269$	1852.83	+	1852.83i	0.419958	+	0.419958i	−0.465231	+	0.885189i	$0.654029\pi$
$270$		−	988.899i		−	0.222898i
$271$	−2252.27			−0.504856			−0.252428	−	0.967616i	$-0.581229\pi$
$271$	−2252.27			−0.504856			−0.252428	+	0.967616i	$0.581229\pi$
$272$	−270.372	−	1088.41i	−0.0602710	−	0.242626i
$273$	986.557			0.218715
$274$			5576.02i			1.22942i
$275$	5312.32	+	5312.32i	1.16489	+	1.16489i
$276$	1703.43			0.371503
$277$	3241.37	+	3241.37i	0.703087	+	0.703087i	0.965072	−	0.261985i	$-0.0843771\pi$
$277$	3241.37	+	3241.37i	0.703087	+	0.703087i	−0.261985	+	0.965072i	$0.584377\pi$
$278$	−236.622	+	236.622i	−0.0510492	+	0.0510492i
$279$	−1204.70	+	1204.70i	−0.258507	+	0.258507i
$280$			3591.39i			0.766523i
$281$			5686.53i			1.20722i	0.797278	+	0.603612i	$0.206272\pi$
$281$			5686.53i			1.20722i	−0.797278	+	0.603612i	$0.793728\pi$
$282$	2261.37	−	2261.37i	0.477526	−	0.477526i
$283$	−389.733	+	389.733i	−0.0818629	+	0.0818629i	−0.746853	−	0.664990i	$-0.768436\pi$
$283$	−389.733	+	389.733i	−0.0818629	+	0.0818629i	0.664990	+	0.746853i	$0.268436\pi$
$284$	1215.35	+	1215.35i	0.253937	+	0.253937i
$285$	861.030			0.178958
$286$	677.531	+	677.531i	0.140081	+	0.140081i
$287$		−	5946.55i		−	1.22304i
$288$	288.000			0.0589256
$289$	−4341.90	+	2299.02i	−0.883757	+	0.467946i
$290$	4899.12			0.992021
$291$		−	382.011i		−	0.0769550i
$292$	345.473	+	345.473i	0.0692373	+	0.0692373i
$293$	5505.48			1.09772			0.548862	−	0.835913i	$-0.315061\pi$
$293$	5505.48			1.09772			0.548862	+	0.835913i	$0.315061\pi$
$294$	1094.33	+	1094.33i	0.217083	+	0.217083i
$295$	−3455.72	+	3455.72i	−0.682034	+	0.682034i
$296$	1551.74	−	1551.74i	0.304707	−	0.304707i
$297$		−	964.254i		−	0.188390i
$298$			5853.54i			1.13787i
$299$	−1346.53	+	1346.53i	−0.260441	+	0.260441i
$300$	−1785.00	+	1785.00i	−0.343523	+	0.343523i
$301$	6684.27	+	6684.27i	1.27998	+	1.27998i
$302$	4284.81			0.816433
$303$	2445.13	+	2445.13i	0.463595	+	0.463595i
$304$			250.760i			0.0473095i
$305$	−12537.3			−2.35373
$306$	−304.169	−	1224.46i	−0.0568241	−	0.228750i
$307$	−3279.39			−0.609657			−0.304829	−	0.952407i	$-0.598599\pi$
$307$	−3279.39			−0.609657			−0.304829	+	0.952407i	$0.598599\pi$
$308$			3501.88i			0.647852i
$309$	−271.618	−	271.618i	−0.0500059	−	0.0500059i
$310$	6933.28			1.27027
$311$	−6043.27	−	6043.27i	−1.10187	−	1.10187i	−0.994185	−	0.107687i	$-0.965656\pi$
$311$	−6043.27	−	6043.27i	−1.10187	−	1.10187i	−0.107687	−	0.994185i	$-0.534344\pi$
$312$	−227.658	+	227.658i	−0.0413096	+	0.0413096i
$313$	−1413.61	+	1413.61i	−0.255277	+	0.255277i	−0.823130	−	0.567853i	$-0.807774\pi$
$313$	−1413.61	+	1413.61i	−0.255277	+	0.255277i	0.567853	+	0.823130i	$0.307774\pi$
$314$		−	2658.54i		−	0.477802i
$315$			4040.31i			0.722685i
$316$	1857.05	−	1857.05i	0.330593	−	0.330593i
$317$	3348.70	−	3348.70i	0.593317	−	0.593317i	−0.345209	−	0.938526i	$-0.612192\pi$
$317$	3348.70	−	3348.70i	0.593317	−	0.593317i	0.938526	+	0.345209i	$0.112192\pi$
$318$	−1713.19	−	1713.19i	−0.302109	−	0.302109i
$319$	4777.03			0.838439
$320$	−828.749	−	828.749i	−0.144777	−	0.144777i
$321$		−	4966.90i		−	0.863629i
$322$	−6959.66			−1.20449
$323$	1066.13	−	264.838i	0.183656	−	0.0456223i
$324$	324.000			0.0555556
$325$		−	2822.01i		−	0.481652i
$326$	−3693.61	−	3693.61i	−0.627517	−	0.627517i
$327$	5012.79			0.847730
$328$	1372.23	+	1372.23i	0.231002	+	0.231002i
$329$	−9239.18	+	9239.18i	−1.54824	+	1.54824i
$330$	−2774.74	+	2774.74i	−0.462862	+	0.462862i
$331$			3878.09i			0.643985i	0.946742	+	0.321993i	$0.104353\pi$
$331$			3878.09i			0.643985i	−0.946742	+	0.321993i	$0.895647\pi$
$332$			4975.76i			0.822530i
$333$	1745.71	−	1745.71i	0.287281	−	0.287281i
$334$	1768.30	−	1768.30i	0.289692	−	0.289692i
$335$	−5714.04	−	5714.04i	−0.931915	−	0.931915i
$336$	−1176.67			−0.191050
$337$	−1904.95	−	1904.95i	−0.307921	−	0.307921i	0.536182	−	0.844103i	$-0.319866\pi$
$337$	−1904.95	−	1904.95i	−0.307921	−	0.307921i	−0.844103	+	0.536182i	$0.819866\pi$
$338$			4034.08i			0.649187i
$339$	539.051			0.0863636
$340$	−2648.22	+	4398.77i	−0.422412	+	0.701638i
$341$	6760.49			1.07361
$342$			282.105i			0.0446038i
$343$	1474.51	+	1474.51i	0.232116	+	0.232116i
$344$	−3084.93			−0.483512
$345$	−5514.53	−	5514.53i	−0.860558	−	0.860558i
$346$	4869.08	−	4869.08i	0.756542	−	0.756542i
$347$	5068.32	−	5068.32i	0.784098	−	0.784098i	−0.196422	−	0.980519i	$-0.562932\pi$
$347$	5068.32	−	5068.32i	0.784098	−	0.784098i	0.980519	+	0.196422i	$0.0629322\pi$
$348$			1605.13i			0.247253i
$349$		−	1517.31i		−	0.232722i	−0.993207	−	0.116361i	$-0.962877\pi$
$349$		−	1517.31i		−	0.232722i	0.993207	−	0.116361i	$-0.0371230\pi$
$350$	7292.90	−	7292.90i	1.11378	−	1.11378i
$351$	−256.115	+	256.115i	−0.0389471	+	0.0389471i
$352$	−808.095	−	808.095i	−0.122363	−	0.122363i
$353$	4647.31			0.700711			0.350356	−	0.936617i	$-0.386061\pi$
$353$	4647.31			0.700711			0.350356	+	0.936617i	$0.386061\pi$
$354$	−1132.22	−	1132.22i	−0.169991	−	0.169991i
$355$		−	7868.94i		−	1.17645i
$356$	−5993.99			−0.892362
$357$	1242.73	+	5002.72i	0.184236	+	0.741658i
$358$	−3281.04			−0.484381
$359$			2365.09i			0.347702i	0.984772	+	0.173851i	$0.0556210\pi$
$359$			2365.09i			0.347702i	−0.984772	+	0.173851i	$0.944379\pi$
$360$	−932.343	−	932.343i	−0.136497	−	0.136497i
$361$	6613.37			0.964189
$362$	−370.116	−	370.116i	−0.0537372	−	0.0537372i
$363$	117.889	−	117.889i	0.0170457	−	0.0170457i
$364$	930.134	−	930.134i	0.133935	−	0.133935i
$365$		−	2236.80i		−	0.320766i
$366$		−	4107.70i		−	0.586647i
$367$	−0.150296	+	0.150296i	−2.13771e−5	+	2.13771e-5i	−0.707117	−	0.707096i	$-0.750005\pi$
$367$	−0.150296	+	0.150296i	−2.13771e−5	+	2.13771e-5i	0.707096	+	0.707117i	$0.250005\pi$
$368$	1606.01	−	1606.01i	0.227498	−	0.227498i
$369$	1543.76	+	1543.76i	0.217791	+	0.217791i
$370$	−10046.9			−1.41166
$371$	6999.50	+	6999.50i	0.979504	+	0.979504i
$372$			2271.60i			0.316605i
$373$	8478.48			1.17694			0.588471	−	0.808519i	$-0.299730\pi$
$373$	8478.48			1.17694			0.588471	+	0.808519i	$0.299730\pi$
$374$	−2582.22	+	4289.15i	−0.357015	+	0.593012i
$375$	4689.80			0.645814
$376$		−	4264.07i		−	0.584848i
$377$	−1268.82	−	1268.82i	−0.173336	−	0.173336i
$378$	−1323.76			−0.180123
$379$	−4121.44	−	4121.44i	−0.558586	−	0.558586i	0.370319	−	0.928905i	$-0.379248\pi$
$379$	−4121.44	−	4121.44i	−0.558586	−	0.558586i	−0.928905	+	0.370319i	$0.879248\pi$
$380$	811.787	−	811.787i	0.109589	−	0.109589i
$381$	−4218.46	+	4218.46i	−0.567239	+	0.567239i
$382$		−	5197.19i		−	0.696103i
$383$		−	1561.85i		−	0.208373i	−0.994558	−	0.104187i	$-0.966776\pi$
$383$		−	1561.85i		−	0.208373i	0.994558	−	0.104187i	$-0.0332240\pi$
$384$	271.529	−	271.529i	0.0360844	−	0.0360844i
$385$	11336.7	−	11336.7i	1.50070	−	1.50070i
$386$	5851.54	+	5851.54i	0.771595	+	0.771595i
$387$	−3470.54			−0.455859
$388$	−360.164	−	360.164i	−0.0471251	−	0.0471251i
$389$		−	7043.78i		−	0.918081i	−0.888415	−	0.459041i	$-0.848193\pi$
$389$		−	7043.78i		−	0.918081i	0.888415	−	0.459041i	$-0.151807\pi$
$390$	1474.00			0.191381
$391$	−8524.28	−	5131.93i	−1.10254	−	0.663766i
$392$	2063.49			0.265872
$393$		−	2944.76i		−	0.377973i
$394$	1795.47	+	1795.47i	0.229579	+	0.229579i
$395$	−12023.7			−1.53159
$396$	−909.107	−	909.107i	−0.115365	−	0.115365i
$397$	−8311.58	+	8311.58i	−1.05075	+	1.05075i	−0.0521045	+	0.998642i	$0.516593\pi$
$397$	−8311.58	+	8311.58i	−1.05075	+	1.05075i	−0.998642	+	0.0521045i	$0.983407\pi$
$398$	−7647.76	+	7647.76i	−0.963185	+	0.963185i
$399$		−	1152.59i		−	0.144615i
$400$			3365.82i			0.420728i
$401$	191.110	−	191.110i	0.0237995	−	0.0237995i	−0.695107	−	0.718906i	$-0.744643\pi$
$401$	191.110	−	191.110i	0.0237995	−	0.0237995i	0.718906	+	0.695107i	$0.244643\pi$
$402$	1872.13	−	1872.13i	0.232272	−	0.232272i
$403$	−1795.65	−	1795.65i	−0.221955	−	0.221955i
$404$	4610.59			0.567785
$405$	−1048.89	−	1048.89i	−0.128690	−	0.128690i
$406$		−	6558.04i		−	0.801650i
$407$	−9796.54			−1.19311
$408$	−1441.20	−	867.656i	−0.174878	−	0.105283i
$409$	−10961.4			−1.32520			−0.662598	−	0.748975i	$-0.730546\pi$
$409$	−10961.4			−1.32520			−0.662598	+	0.748975i	$0.730546\pi$
$410$		−	8884.63i		−	1.07020i
$411$	5914.26	+	5914.26i	0.709803	+	0.709803i
$412$	−512.168			−0.0612445
$413$	4625.88	+	4625.88i	0.551150	+	0.551150i
$414$	1806.77	−	1806.77i	0.214487	−	0.214487i
$415$	16108.0	−	16108.0i	1.90533	−	1.90533i
$416$			429.276i			0.0505937i
$417$			501.952i			0.0589465i
$418$	791.555	−	791.555i	0.0926226	−	0.0926226i
$419$	−8128.39	+	8128.39i	−0.947727	+	0.947727i	−0.998700	−	0.0509730i	$-0.983768\pi$
$419$	−8128.39	+	8128.39i	−0.947727	+	0.947727i	0.0509730	+	0.998700i	$0.483768\pi$
$420$	3809.24	+	3809.24i	0.442552	+	0.442552i
$421$	11175.3			1.29371			0.646854	−	0.762614i	$-0.276084\pi$
$421$	11175.3			1.29371			0.646854	+	0.762614i	$0.276084\pi$
$422$	−4698.99	−	4698.99i	−0.542045	−	0.542045i
$423$		−	4797.08i		−	0.551400i
$424$	−3230.41			−0.370006
$425$	14310.1	−	3554.79i	1.63327	−	0.405723i
$426$	2578.16			0.293221
$427$			16782.7i			1.90204i
$428$	−4682.83	−	4682.83i	−0.528863	−	0.528863i
$429$	1437.26			0.161752
$430$	9986.84	+	9986.84i	1.12002	+	1.12002i
$431$	−8830.33	+	8830.33i	−0.986873	+	0.986873i	−0.999915	−	0.0130424i	$-0.995848\pi$
$431$	−8830.33	+	8830.33i	−0.986873	+	0.986873i	0.0130424	+	0.999915i	$0.495848\pi$
$432$	305.470	−	305.470i	0.0340207	−	0.0340207i
$433$		−	2035.22i		−	0.225881i	−0.993602	−	0.112940i	$-0.963973\pi$
$433$		−	2035.22i		−	0.225881i	0.993602	−	0.112940i	$-0.0360269\pi$
$434$		−	9280.99i		−	1.02650i
$435$	5196.30	−	5196.30i	0.572744	−	0.572744i
$436$	4726.10	−	4726.10i	0.519126	−	0.519126i
$437$	1573.14	+	1573.14i	0.172205	+	0.172205i
$438$	732.859			0.0799483
$439$	−6948.56	−	6948.56i	−0.755437	−	0.755437i	0.220051	−	0.975488i	$-0.429378\pi$
$439$	−6948.56	−	6948.56i	−0.755437	−	0.755437i	−0.975488	+	0.220051i	$0.929378\pi$
$440$			5232.10i			0.566888i
$441$	2321.42			0.250666
$442$	1825.10	−	453.376i	0.196406	−	0.0487894i
$443$	−1404.92			−0.150677			−0.0753385	−	0.997158i	$-0.524004\pi$
$443$	−1404.92			−0.150677			−0.0753385	+	0.997158i	$0.524004\pi$
$444$		−	3291.75i		−	0.351845i
$445$	19404.4	+	19404.4i	2.06709	+	2.06709i
$446$	−4488.65			−0.476555
$447$	6208.61	+	6208.61i	0.656952	+	0.656952i
$448$	−1109.38	+	1109.38i	−0.116994	+	0.116994i
$449$	4441.50	−	4441.50i	0.466831	−	0.466831i	−0.434055	−	0.900886i	$-0.642918\pi$
$449$	4441.50	−	4441.50i	0.466831	−	0.466831i	0.900886	+	0.434055i	$0.142918\pi$
$450$			3786.55i			0.396666i
$451$		−	8663.21i		−	0.904511i
$452$	508.222	−	508.222i	0.0528867	−	0.0528867i
$453$	4544.72	−	4544.72i	0.471368	−	0.471368i
$454$	−4882.91	−	4882.91i	−0.504772	−	0.504772i
$455$	−6022.25			−0.620500
$456$	265.971	+	265.971i	0.0273141	+	0.0273141i
$457$			16304.1i			1.66887i	0.551106	+	0.834435i	$0.314206\pi$
$457$			16304.1i			1.66887i	−0.551106	+	0.834435i	$0.685794\pi$
$458$	−5365.34			−0.547393
$459$	−1621.35	−	976.112i	−0.164876	−	0.0992615i
$460$	−10398.3			−1.05396
$461$			80.0065i			0.00808302i	0.999992	+	0.00404151i	$0.00128646\pi$
$461$			80.0065i			0.00808302i	−0.999992	+	0.00404151i	$0.998714\pi$
$462$	3714.31	+	3714.31i	0.374037	+	0.374037i
$463$	2619.71			0.262955			0.131477	−	0.991319i	$-0.458028\pi$
$463$	2619.71			0.262955			0.131477	+	0.991319i	$0.458028\pi$
$464$	1513.33	+	1513.33i	0.151411	+	0.151411i
$465$	7353.85	−	7353.85i	0.733391	−	0.733391i
$466$	−2232.05	+	2232.05i	−0.221884	+	0.221884i
$467$			1360.07i			0.134768i	0.997727	+	0.0673839i	$0.0214652\pi$
$467$			1360.07i			0.134768i	−0.997727	+	0.0673839i	$0.978535\pi$
$468$			482.936i			0.0477002i
$469$	−7648.91	+	7648.91i	−0.753078	+	0.753078i
$470$	−13804.1	+	13804.1i	−1.35476	+	1.35476i
$471$	−2819.80	−	2819.80i	−0.275859	−	0.275859i
$472$	−2134.94			−0.208196
$473$	9737.95	+	9737.95i	0.946620	+	0.946620i
$474$		−	3939.40i		−	0.381736i
$475$	−3296.93			−0.318471
$476$	5888.27	+	3544.95i	0.566992	+	0.341350i
$477$	−3634.21			−0.348845
$478$		−	10032.4i		−	0.959983i
$479$	−6950.26	−	6950.26i	−0.662976	−	0.662976i	0.293105	−	0.956080i	$-0.405312\pi$
$479$	−6950.26	−	6950.26i	−0.662976	−	0.662976i	−0.956080	+	0.293105i	$0.905312\pi$
$480$	−1758.04			−0.167174
$481$	2602.06	+	2602.06i	0.246660	+	0.246660i
$482$	−2301.88	+	2301.88i	−0.217527	+	0.217527i
$483$	−7381.84	+	7381.84i	−0.695415	+	0.695415i
$484$		−	222.294i		−	0.0208766i
$485$			2331.92i			0.218323i
$486$	343.654	−	343.654i	0.0320750	−	0.0320750i
$487$	5165.25	−	5165.25i	0.480616	−	0.480616i	−0.424712	−	0.905328i	$-0.639625\pi$
$487$	5165.25	−	5165.25i	0.480616	−	0.480616i	0.905328	+	0.424712i	$0.139625\pi$
$488$	−3872.78	−	3872.78i	−0.359247	−	0.359247i
$489$	−7835.34			−0.724594
$490$	−6680.13	−	6680.13i	−0.615872	−	0.615872i
$491$			18687.3i			1.71761i	0.512305	+	0.858803i	$0.328792\pi$
$491$			18687.3i			1.71761i	−0.512305	+	0.858803i	$0.671208\pi$
$492$	2910.93			0.266738
$493$	4835.77	−	8032.36i	0.441769	−	0.733792i
$494$	−420.490			−0.0382970
$495$			5886.11i			0.534467i
$496$	2141.68	+	2141.68i	0.193880	+	0.193880i
$497$	−10533.5			−0.950686
$498$	5277.59	+	5277.59i	0.474888	+	0.474888i
$499$	5768.60	−	5768.60i	0.517511	−	0.517511i	−0.399307	−	0.916817i	$-0.630749\pi$
$499$	5768.60	−	5768.60i	0.517511	−	0.517511i	0.916817	+	0.399307i	$0.130749\pi$
$500$	4421.59	−	4421.59i	0.395479	−	0.395479i
$501$		−	3751.13i		−	0.334507i
$502$		−	592.528i		−	0.0526809i
$503$	3807.34	−	3807.34i	0.337497	−	0.337497i	−0.517928	−	0.855424i	$-0.673296\pi$
$503$	3807.34	−	3807.34i	0.337497	−	0.337497i	0.855424	+	0.517928i	$0.173296\pi$
$504$	−1248.05	+	1248.05i	−0.110303	+	0.110303i
$505$	−14925.9	−	14925.9i	−1.31523	−	1.31523i
$506$	−10139.2			−0.890792
$507$	4278.79	+	4278.79i	0.374808	+	0.374808i
$508$			7954.40i			0.694723i
$509$	12438.1			1.08313			0.541563	−	0.840660i	$-0.317833\pi$
$509$	12438.1			1.08313			0.541563	+	0.840660i	$0.317833\pi$
$510$	1856.74	+	7474.47i	0.161212	+	0.648971i
$511$	−2994.22			−0.259210
$512$		−	512.000i		−	0.0441942i
$513$	299.218	+	299.218i	0.0257520	+	0.0257520i
$514$	−5770.33			−0.495172
$515$	1658.04	+	1658.04i	0.141868	+	0.141868i
$516$	−3272.06	+	3272.06i	−0.279156	+	0.279156i
$517$	−13460.1	+	13460.1i	−1.14502	+	1.14502i
$518$			13449.0i			1.14076i
$519$		−	10328.9i		−	0.873580i
$520$	1389.70	−	1389.70i	0.117197	−	0.117197i
$521$	−1409.93	+	1409.93i	−0.118561	+	0.118561i	−0.763898	−	0.645337i	$-0.776717\pi$
$521$	−1409.93	+	1409.93i	−0.118561	+	0.118561i	0.645337	+	0.763898i	$0.276717\pi$
$522$	1702.50	+	1702.50i	0.142752	+	0.142752i
$523$	−171.269			−0.0143194			−0.00715970	−	0.999974i	$-0.502279\pi$
$523$	−171.269			−0.0143194			−0.00715970	+	0.999974i	$0.502279\pi$
$524$	−2776.34	−	2776.34i	−0.231460	−	0.231460i
$525$		−	15470.6i		−	1.28608i
$526$	5917.27			0.490504
$527$	6843.63	−	11367.5i	0.565680	−	0.939610i
$528$	−1714.23			−0.141292
$529$		−	7983.63i		−	0.656171i
$530$	10457.8	+	10457.8i	0.857092	+	0.857092i
$531$	−2401.81			−0.196289
$532$	−1086.67	−	1086.67i	−0.0885585	−	0.0885585i
$533$	−2301.03	+	2301.03i	−0.186996	+	0.186996i
$534$	−6357.59	+	6357.59i	−0.515206	+	0.515206i
$535$			30319.5i			2.45014i
$536$		−	3530.13i		−	0.284474i
$537$	−3480.07	+	3480.07i	−0.279658	+	0.279658i
$538$	3705.65	−	3705.65i	0.296955	−	0.296955i
$539$	−6513.65	−	6513.65i	−0.520524	−	0.520524i
$540$	−1977.80			−0.157613
$541$	11243.1	+	11243.1i	0.893492	+	0.893492i	0.994850	−	0.101358i	$-0.0323187\pi$
$541$	11243.1	+	11243.1i	0.893492	+	0.893492i	−0.101358	+	0.994850i	$0.532319\pi$
$542$			4504.55i			0.356987i
$543$	−785.134			−0.0620503
$544$	−2176.81	+	540.744i	−0.171563	+	0.0426181i
$545$	−30599.6			−2.40503
$546$		−	1973.11i		−	0.154655i
$547$	−598.801	−	598.801i	−0.0468060	−	0.0468060i	0.683316	−	0.730122i	$-0.260537\pi$
$547$	−598.801	−	598.801i	−0.0468060	−	0.0468060i	−0.730122	+	0.683316i	$0.760537\pi$
$548$	11152.0			0.869328
$549$	−4356.87	−	4356.87i	−0.338701	−	0.338701i
$550$	10624.6	−	10624.6i	0.823702	−	0.823702i
$551$	−1482.36	+	1482.36i	−0.114611	+	0.114611i
$552$		−	3406.87i		−	0.262692i
$553$			16095.1i			1.23767i
$554$	6482.74	−	6482.74i	0.497158	−	0.497158i
$555$	−10656.4	+	10656.4i	−0.815024	+	0.815024i
$556$	473.245	+	473.245i	0.0360972	+	0.0360972i
$557$	7243.67			0.551031			0.275515	−	0.961297i	$-0.411152\pi$
$557$	7243.67			0.551031			0.275515	+	0.961297i	$0.411152\pi$
$558$	2409.39	+	2409.39i	0.182792	+	0.182792i
$559$		−	5172.99i		−	0.391403i
$560$	7182.77			0.542014
$561$	1810.47	+	7288.19i	0.136253	+	0.548499i
$562$	11373.1			0.853636
$563$		−	4072.87i		−	0.304887i	−0.988312	−	0.152443i	$-0.951286\pi$
$563$		−	4072.87i		−	0.304887i	0.988312	−	0.152443i	$-0.0487142\pi$
$564$	−4522.73	−	4522.73i	−0.337662	−	0.337662i
$565$	−3290.54			−0.245016
$566$	779.466	+	779.466i	0.0578858	+	0.0578858i
$567$	−1404.05	+	1404.05i	−0.103994	+	0.103994i
$568$	2430.71	−	2430.71i	0.179560	−	0.179560i
$569$		−	17415.3i		−	1.28311i	−0.767079	−	0.641553i	$-0.778291\pi$
$569$		−	17415.3i		−	1.28311i	0.767079	−	0.641553i	$-0.221709\pi$
$570$		−	1722.06i		−	0.126542i
$571$	−3510.31	+	3510.31i	−0.257271	+	0.257271i	−0.823943	−	0.566672i	$-0.808231\pi$
$571$	−3510.31	+	3510.31i	−0.257271	+	0.257271i	0.566672	+	0.823943i	$0.308231\pi$
$572$	1355.06	−	1355.06i	0.0990525	−	0.0990525i
$573$	−5512.45	−	5512.45i	−0.401895	−	0.401895i
$574$	−11893.1			−0.864823
$575$	21115.5	+	21115.5i	1.53144	+	1.53144i
$576$		−	576.000i		−	0.0416667i
$577$	2943.90			0.212402			0.106201	−	0.994345i	$-0.466131\pi$
$577$	2943.90			0.212402			0.106201	+	0.994345i	$0.466131\pi$
$578$	4598.04	+	8683.79i	0.330888	+	0.624910i
$579$	12413.0			0.890961
$580$		−	9798.24i		−	0.701465i
$581$	−21562.4	−	21562.4i	−1.53969	−	1.53969i
$582$	−764.022			−0.0544154
$583$	10197.2	+	10197.2i	0.724399	+	0.724399i
$584$	690.946	−	690.946i	0.0489581	−	0.0489581i
$585$	1563.41	−	1563.41i	0.110494	−	0.110494i
$586$		−	11011.0i		−	0.776209i
$587$		−	3580.59i		−	0.251767i	−0.992045	−	0.125883i	$-0.959824\pi$
$587$		−	3580.59i		−	0.251767i	0.992045	−	0.125883i	$-0.0401765\pi$
$588$	2188.66	−	2188.66i	0.153501	−	0.153501i
$589$	−2097.85	+	2097.85i	−0.146758	+	0.146758i
$590$	6911.45	+	6911.45i	0.482271	+	0.482271i
$591$	3808.76			0.265095
$592$	−3103.49	−	3103.49i	−0.215460	−	0.215460i
$593$		−	23081.4i		−	1.59838i	−0.601077	−	0.799191i	$-0.705262\pi$
$593$		−	23081.4i		−	1.59838i	0.601077	−	0.799191i	$-0.294738\pi$
$594$	−1928.51			−0.133212
$595$	−7586.03	−	30538.2i	−0.522684	−	2.10411i
$596$	11707.1			0.804598
$597$			16223.3i			1.11219i
$598$	2693.06	+	2693.06i	0.184160	+	0.184160i
$599$	−3524.31			−0.240400			−0.120200	−	0.992750i	$-0.538354\pi$
$599$	−3524.31			−0.240400			−0.120200	+	0.992750i	$0.538354\pi$
$600$	3570.00	+	3570.00i	0.242907	+	0.242907i
$601$	9933.96	−	9933.96i	0.674234	−	0.674234i	−0.284455	−	0.958689i	$-0.591813\pi$
$601$	9933.96	−	9933.96i	0.674234	−	0.674234i	0.958689	+	0.284455i	$0.0918126\pi$
$602$	13368.5	−	13368.5i	0.905084	−	0.905084i
$603$		−	3971.39i		−	0.268205i
$604$		−	8569.61i		−	0.577306i
$605$	−719.634	+	719.634i	−0.0483591	+	0.0483591i
$606$	4890.27	−	4890.27i	0.327811	−	0.327811i
$607$	6396.01	+	6396.01i	0.427687	+	0.427687i	0.887840	−	0.460153i	$-0.152205\pi$
$607$	6396.01	+	6396.01i	0.427687	+	0.427687i	−0.460153	+	0.887840i	$0.652205\pi$
$608$	501.520			0.0334529
$609$	−6955.85	−	6955.85i	−0.462833	−	0.462833i
$610$			25074.7i			1.66434i
$611$	7150.25			0.473434
$612$	−2448.91	+	608.337i	−0.161751	+	0.0401807i
$613$	−17364.1			−1.14409			−0.572047	−	0.820221i	$-0.693851\pi$
$613$	−17364.1			−1.14409			−0.572047	+	0.820221i	$0.693851\pi$
$614$			6558.78i			0.431093i
$615$	−9423.57	−	9423.57i	−0.617878	−	0.617878i
$616$	7003.77			0.458100
$617$	−16029.9	−	16029.9i	−1.04593	−	1.04593i	−0.998893	−	0.0470409i	$-0.985021\pi$
$617$	−16029.9	−	16029.9i	−1.04593	−	1.04593i	−0.0470409	−	0.998893i	$-0.514979\pi$
$618$	−543.237	+	543.237i	−0.0353595	+	0.0353595i
$619$	−664.009	+	664.009i	−0.0431160	+	0.0431160i	−0.728336	−	0.685220i	$-0.759706\pi$
$619$	−664.009	+	664.009i	−0.0431160	+	0.0431160i	0.685220	+	0.728336i	$0.259706\pi$
$620$		−	13866.6i		−	0.898216i
$621$		−	3832.73i		−	0.247668i
$622$	−12086.5	+	12086.5i	−0.779141	+	0.779141i
$623$	25975.0	−	25975.0i	1.67041	−	1.67041i
$624$	455.316	+	455.316i	0.0292103	+	0.0292103i
$625$	−2332.51			−0.149281
$626$	2827.22	+	2827.22i	0.180508	+	0.180508i
$627$		−	1679.14i		−	0.106951i
$628$	−5317.07			−0.337857
$629$	−9917.02	+	16472.5i	−0.628645	+	1.04420i
$630$	8080.62			0.511015
$631$			10145.6i			0.640079i	0.947404	+	0.320040i	$0.103696\pi$
$631$			10145.6i			0.640079i	−0.947404	+	0.320040i	$0.896304\pi$
$632$	−3714.10	−	3714.10i	−0.233764	−	0.233764i
$633$	−9968.05			−0.625900
$634$	−6697.40	−	6697.40i	−0.419539	−	0.419539i
$635$	25750.8	−	25750.8i	1.60927	−	1.60927i
$636$	−3426.37	+	3426.37i	−0.213623	+	0.213623i
$637$			3460.18i			0.215223i
$638$		−	9554.05i		−	0.592866i
$639$	2734.55	−	2734.55i	0.169291	−	0.169291i
$640$	−1657.50	+	1657.50i	−0.102372	+	0.102372i
$641$	2416.01	+	2416.01i	0.148871	+	0.148871i	0.777614	−	0.628742i	$-0.216430\pi$
$641$	2416.01	+	2416.01i	0.148871	+	0.148871i	−0.628742	+	0.777614i	$0.716430\pi$
$642$	−9933.79			−0.610678
$643$	−11621.0	−	11621.0i	−0.712736	−	0.712736i	0.254371	−	0.967107i	$-0.418132\pi$
$643$	−11621.0	−	11621.0i	−0.712736	−	0.712736i	−0.967107	+	0.254371i	$0.918132\pi$
$644$			13919.3i			0.851706i
$645$	21185.3			1.29329
$646$	−529.676	−	2132.26i	−0.0322598	−	0.129865i
$647$	9019.31			0.548046			0.274023	−	0.961723i	$-0.411646\pi$
$647$	9019.31			0.548046			0.274023	+	0.961723i	$0.411646\pi$
$648$		−	648.000i		−	0.0392837i
$649$	6739.20	+	6739.20i	0.407607	+	0.407607i
$650$	−5644.01			−0.340579
$651$	−9843.98	−	9843.98i	−0.592651	−	0.592651i
$652$	−7387.23	+	7387.23i	−0.443721	+	0.443721i
$653$	−9946.84	+	9946.84i	−0.596095	+	0.596095i	−0.939271	−	0.343176i	$-0.888497\pi$
$653$	−9946.84	+	9946.84i	−0.596095	+	0.596095i	0.343176	+	0.939271i	$0.388497\pi$
$654$		−	10025.6i		−	0.599436i
$655$			17975.7i			1.07232i
$656$	2744.45	−	2744.45i	0.163343	−	0.163343i
$657$	777.314	−	777.314i	0.0461582	−	0.0461582i
$658$	18478.4	+	18478.4i	1.09477	+	1.09477i
$659$	18759.1			1.10888			0.554438	−	0.832225i	$-0.312933\pi$
$659$	18759.1			1.10888			0.554438	+	0.832225i	$0.312933\pi$
$660$	5549.48	+	5549.48i	0.327293	+	0.327293i
$661$			22941.6i			1.34996i	0.737836	+	0.674980i	$0.235848\pi$
$661$			22941.6i			1.34996i	−0.737836	+	0.674980i	$0.764152\pi$
$662$	7756.18			0.455366
$663$	1454.94	−	2416.69i	0.0852263	−	0.141563i
$664$	9951.51			0.581617
$665$			7035.76i			0.410278i
$666$	−3491.42	−	3491.42i	−0.203138	−	0.203138i
$667$	18987.8			1.10226
$668$	−3536.60	−	3536.60i	−0.204843	−	0.204843i
$669$	−4760.93	+	4760.93i	−0.275139	+	0.275139i
$670$	−11428.1	+	11428.1i	−0.658964	+	0.658964i
$671$			24449.8i			1.40667i
$672$			2353.34i			0.135093i
$673$	7783.39	−	7783.39i	0.445807	−	0.445807i	−0.448151	−	0.893958i	$-0.647917\pi$
$673$	7783.39	−	7783.39i	0.445807	−	0.445807i	0.893958	+	0.448151i	$0.147917\pi$
$674$	−3809.90	+	3809.90i	−0.217733	+	0.217733i
$675$	4016.24	+	4016.24i	0.229015	+	0.229015i
$676$	8068.16			0.459044
$677$	6957.54	+	6957.54i	0.394978	+	0.394978i	0.876457	−	0.481480i	$-0.159900\pi$
$677$	6957.54	+	6957.54i	0.394978	+	0.394978i	−0.481480	+	0.876457i	$0.659900\pi$
$678$		−	1078.10i		−	0.0610683i
$679$	3121.54			0.176427
$680$	8797.55	+	5296.44i	0.496133	+	0.298690i
$681$	−10358.2			−0.582861
$682$		−	13521.0i		−	0.759157i
$683$	−13910.7	−	13910.7i	−0.779323	−	0.779323i	0.200392	−	0.979716i	$-0.435778\pi$
$683$	−13910.7	−	13910.7i	−0.779323	−	0.779323i	−0.979716	+	0.200392i	$0.935778\pi$
$684$	564.210			0.0315397
$685$	−36102.5	−	36102.5i	−2.01373	−	2.01373i
$686$	2949.01	−	2949.01i	0.164131	−	0.164131i
$687$	−5690.80	+	5690.80i	−0.316037	+	0.316037i
$688$			6169.85i			0.341894i
$689$		−	5416.95i		−	0.299520i
$690$	−11029.1	+	11029.1i	−0.608506	+	0.608506i
$691$	6593.82	−	6593.82i	0.363011	−	0.363011i	−0.501909	−	0.864920i	$-0.667369\pi$
$691$	6593.82	−	6593.82i	0.363011	−	0.363011i	0.864920	+	0.501909i	$0.167369\pi$
$692$	−9738.17	−	9738.17i	−0.534956	−	0.534956i
$693$	7879.24			0.431901
$694$	−10136.6	−	10136.6i	−0.554441	−	0.554441i
$695$		−	3064.07i		−	0.167233i
$696$	3210.27			0.174835
$697$	−14566.8	−	8769.75i	−0.791618	−	0.476582i
$698$	−3034.63			−0.164559
$699$			4734.89i			0.256209i
$700$	−14585.8	−	14585.8i	−0.787559	−	0.787559i
$701$	4811.86			0.259260			0.129630	−	0.991562i	$-0.458621\pi$
$701$	4811.86			0.259260			0.129630	+	0.991562i	$0.458621\pi$
$702$	512.231	+	512.231i	0.0275397	+	0.0275397i
$703$	3039.97	−	3039.97i	0.163093	−	0.163093i
$704$	−1616.19	+	1616.19i	−0.0865234	+	0.0865234i
$705$			29282.9i			1.56434i
$706$		−	9294.61i		−	0.495478i
$707$	−19980.0	+	19980.0i	−1.06284	+	1.06284i
$708$	−2264.45	+	2264.45i	−0.120202	+	0.120202i
$709$	19747.1	+	19747.1i	1.04600	+	1.04600i	0.998890	+	0.0471139i	$0.0150024\pi$
$709$	19747.1	+	19747.1i	1.04600	+	1.04600i	0.0471139	+	0.998890i	$0.484998\pi$
$710$	−15737.9			−0.831876
$711$	−4178.37	−	4178.37i	−0.220395	−	0.220395i
$712$			11988.0i			0.630995i
$713$	26871.7			1.41143
$714$	10005.4	−	2485.46i	0.524431	−	0.130275i
$715$	−8773.50			−0.458895
$716$			6562.09i			0.342509i
$717$	−10641.0	−	10641.0i	−0.554246	−	0.554246i
$718$	4730.19			0.245862
$719$	−6565.65	−	6565.65i	−0.340553	−	0.340553i	0.516022	−	0.856575i	$-0.327412\pi$
$719$	−6565.65	−	6565.65i	−0.340553	−	0.340553i	−0.856575	+	0.516022i	$0.827412\pi$
$720$	−1864.69	+	1864.69i	−0.0965177	+	0.0965177i
$721$	2219.48	−	2219.48i	0.114643	−	0.114643i
$722$		−	13226.7i		−	0.681785i
$723$			4883.03i			0.251178i
$724$	−740.232	+	740.232i	−0.0379979	+	0.0379979i
$725$	−19896.9	+	19896.9i	−1.01925	+	1.01925i
$726$	−235.779	−	235.779i	−0.0120531	−	0.0120531i
$727$	−3740.62			−0.190828			−0.0954140	−	0.995438i	$-0.530418\pi$
$727$	−3740.62			−0.190828			−0.0954140	+	0.995438i	$0.530418\pi$
$728$	−1860.27	−	1860.27i	−0.0947063	−	0.0947063i
$729$		−	729.000i		−	0.0370370i
$730$	−4473.60			−0.226816
$731$	26231.6	−	6516.23i	1.32724	−	0.329701i
$732$	−8215.40			−0.414822
$733$		−	23222.5i		−	1.17018i	−0.810967	−	0.585092i	$-0.801059\pi$
$733$		−	23222.5i		−	1.17018i	0.810967	−	0.585092i	$-0.198941\pi$
$734$	0.300592	+	0.300592i	1.51159e−5	+	1.51159e-5i
$735$	−14170.7			−0.711148
$736$	−3212.03	−	3212.03i	−0.160865	−	0.160865i
$737$	−11143.3	+	11143.3i	−0.556944	+	0.556944i
$738$	3087.51	−	3087.51i	0.154001	−	0.154001i
$739$		−	9987.91i		−	0.497173i	−0.968610	−	0.248587i	$-0.920034\pi$
$739$		−	9987.91i		−	0.497173i	0.968610	−	0.248587i	$-0.0799661\pi$
$740$			20093.9i			0.998196i
$741$	−445.997	+	445.997i	−0.0221108	+	0.0221108i
$742$	13999.0	−	13999.0i	0.692614	−	0.692614i
$743$	25752.7	+	25752.7i	1.27157	+	1.27157i	0.945266	+	0.326302i	$0.105803\pi$
$743$	25752.7	+	25752.7i	1.27157	+	1.27157i	0.326302	+	0.945266i	$0.394197\pi$
$744$	4543.20			0.223873
$745$	−37899.3	−	37899.3i	−1.86379	−	1.86379i
$746$		−	16957.0i		−	0.832223i
$747$	11195.5			0.548354
$748$	8578.30	+	5164.45i	0.419323	+	0.252448i
$749$	40586.1			1.97995
$750$		−	9379.60i		−	0.456659i
$751$	−10329.3	−	10329.3i	−0.501894	−	0.501894i	0.410132	−	0.912026i	$-0.365483\pi$
$751$	−10329.3	−	10329.3i	−0.501894	−	0.501894i	−0.912026	+	0.410132i	$0.865483\pi$
$752$	−8528.14			−0.413550
$753$	−628.471	−	628.471i	−0.0304153	−	0.0304153i
$754$	−2537.65	+	2537.65i	−0.122567	+	0.122567i
$755$	−27742.4	+	27742.4i	−1.33728	+	1.33728i
$756$			2647.51i			0.127366i
$757$			25138.4i			1.20696i	0.797378	+	0.603481i	$0.206220\pi$
$757$			25138.4i			1.20696i	−0.797378	+	0.603481i	$0.793780\pi$
$758$	−8242.87	+	8242.87i	−0.394980	+	0.394980i
$759$	−10754.2	+	10754.2i	−0.514299	+	0.514299i
$760$	−1623.57	−	1623.57i	−0.0774910	−	0.0774910i
$761$	−13550.5			−0.645473			−0.322737	−	0.946489i	$-0.604603\pi$
$761$	−13550.5			−0.645473			−0.322737	+	0.946489i	$0.604603\pi$
$762$	8436.92	+	8436.92i	0.401099	+	0.401099i
$763$			40961.1i			1.94350i
$764$	−10394.4			−0.492219
$765$	9897.24	+	5958.50i	0.467759	+	0.281608i
$766$	−3123.71			−0.147342
$767$		−	3580.00i		−	0.168535i
$768$	−543.058	−	543.058i	−0.0255155	−	0.0255155i
$769$	30080.8			1.41059			0.705294	−	0.708915i	$-0.250815\pi$
$769$	30080.8			1.41059			0.705294	+	0.708915i	$0.250815\pi$
$770$	−22673.3	−	22673.3i	−1.06116	−	1.06116i
$771$	−6120.36	+	6120.36i	−0.285887	+	0.285887i
$772$	11703.1	−	11703.1i	0.545600	−	0.545600i
$773$		−	11588.8i		−	0.539226i	−0.962969	−	0.269613i	$-0.913104\pi$
$773$		−	11588.8i		−	0.539226i	0.962969	−	0.269613i	$-0.0868958\pi$
$774$			6941.08i			0.322341i
$775$	−28158.3	+	28158.3i	−1.30513	+	1.30513i
$776$	−720.327	+	720.327i	−0.0333225	+	0.0333225i
$777$	14264.8	+	14264.8i	0.658618	+	0.658618i
$778$	−14087.6			−0.649182
$779$	2688.28	+	2688.28i	0.123643	+	0.123643i
$780$		−	2947.99i		−	0.135327i
$781$	−15345.7			−0.703087
$782$	−10263.9	+	17048.6i	−0.469354	+	0.779610i
$783$	3611.55			0.164836
$784$		−	4126.97i		−	0.188000i
$785$	17213.0	+	17213.0i	0.782620	+	0.782620i
$786$	−5889.51			−0.267267
$787$	3121.23	+	3121.23i	0.141372	+	0.141372i	0.774251	−	0.632879i	$-0.218127\pi$
$787$	3121.23	+	3121.23i	0.141372	+	0.141372i	−0.632879	+	0.774251i	$0.718127\pi$
$788$	3590.93	−	3590.93i	0.162337	−	0.162337i
$789$	6276.21	−	6276.21i	0.283193	−	0.283193i
$790$			24047.4i			1.08300i
$791$			4404.77i			0.197997i
$792$	−1818.21	+	1818.21i	−0.0815751	+	0.0815751i
$793$	6494.10	−	6494.10i	0.290810	−	0.290810i
$794$	16623.2	+	16623.2i	0.742990	+	0.742990i
$795$	22184.4			0.989685
$796$	15295.5	+	15295.5i	0.681074	+	0.681074i
$797$		−	36966.3i		−	1.64293i	−0.570260	−	0.821464i	$-0.693157\pi$
$797$		−	36966.3i		−	1.64293i	0.570260	−	0.821464i	$-0.306843\pi$
$798$	−2305.17			−0.102259
$799$	9006.92	+	36258.1i	0.398801	+	1.60541i
$800$	6731.65			0.297500
$801$			13486.5i			0.594908i
$802$	−382.221	−	382.221i	−0.0168288	−	0.0168288i
$803$	−4362.11			−0.191701
$804$	−3744.27	−	3744.27i	−0.164241	−	0.164241i
$805$	45061.1	−	45061.1i	1.97291	−	1.97291i
$806$	−3591.30	+	3591.30i	−0.156946	+	0.156946i
$807$		−	7860.87i		−	0.342895i
$808$		−	9221.17i		−	0.401485i
$809$	−23264.9	+	23264.9i	−1.01106	+	1.01106i	−0.0111248	+	0.999938i	$0.503541\pi$
$809$	−23264.9	+	23264.9i	−1.01106	+	1.01106i	−0.999938	+	0.0111248i	$0.996459\pi$
$810$	−2097.77	+	2097.77i	−0.0909978	+	0.0909978i
$811$	−12867.2	−	12867.2i	−0.557126	−	0.557126i	0.371362	−	0.928488i	$-0.378891\pi$
$811$	−12867.2	−	12867.2i	−0.557126	−	0.557126i	−0.928488	+	0.371362i	$0.878891\pi$
$812$	−13116.1			−0.566852
$813$	4777.79	+	4777.79i	0.206106	+	0.206106i
$814$			19593.1i			0.843658i
$815$	47829.4			2.05569
$816$	−1735.31	+	2882.40i	−0.0744461	+	0.123657i
$817$	−6043.57			−0.258798
$818$			21922.7i			0.937055i
$819$	−2092.80	−	2092.80i	−0.0892899	−	0.0892899i
$820$	−17769.3			−0.756743
$821$	10846.1	+	10846.1i	0.461060	+	0.461060i	0.899003	−	0.437943i	$-0.144293\pi$
$821$	10846.1	+	10846.1i	0.461060	+	0.461060i	−0.437943	+	0.899003i	$0.644293\pi$
$822$	11828.5	−	11828.5i	0.501907	−	0.501907i
$823$	22850.1	−	22850.1i	0.967807	−	0.967807i	−0.0316911	−	0.999498i	$-0.510089\pi$
$823$	22850.1	−	22850.1i	0.967807	−	0.967807i	0.999498	+	0.0316911i	$0.0100893\pi$
$824$			1024.34i			0.0433064i
$825$		−	22538.3i		−	0.951129i
$826$	9251.77	−	9251.77i	0.389722	−	0.389722i
$827$	8154.95	−	8154.95i	0.342896	−	0.342896i	−0.514559	−	0.857455i	$-0.672044\pi$
$827$	8154.95	−	8154.95i	0.342896	−	0.342896i	0.857455	+	0.514559i	$0.172044\pi$
$828$	−3613.53	−	3613.53i	−0.151665	−	0.151665i
$829$	28488.7			1.19355			0.596774	−	0.802409i	$-0.296449\pi$
$829$	28488.7			1.19355			0.596774	+	0.802409i	$0.296449\pi$
$830$	−32216.1	−	32216.1i	−1.34727	−	1.34727i
$831$		−	13752.0i		−	0.574068i
$832$	858.552			0.0357752
$833$	−17546.2	+	4358.67i	−0.729818	+	0.181295i
$834$	1003.90			0.0416815
$835$			22898.1i			0.949007i
$836$	−1583.11	−	1583.11i	−0.0654941	−	0.0654941i
$837$	5111.10			0.211070
$838$	16256.8	+	16256.8i	0.670144	+	0.670144i
$839$	13682.6	−	13682.6i	0.563021	−	0.563021i	−0.367143	−	0.930164i	$-0.619664\pi$
$839$	13682.6	−	13682.6i	0.563021	−	0.563021i	0.930164	+	0.367143i	$0.119664\pi$
$840$	7618.48	−	7618.48i	0.312932	−	0.312932i
$841$		−	6496.97i		−	0.266389i
$842$		−	22350.6i		−	0.914789i
$843$	12063.0	−	12063.0i	0.492847	−	0.492847i
$844$	−9397.97	+	9397.97i	−0.383284	+	0.383284i
$845$	−26119.1	−	26119.1i	−1.06334	−	1.06334i
$846$	−9594.16			−0.389898
$847$	963.313	+	963.313i	0.0390789	+	0.0390789i
$848$			6460.83i			0.261634i
$849$	1653.50			0.0668408
$850$	−7109.57	−	28620.2i	−0.286890	−	1.15490i
$851$	−38939.4			−1.56854
$852$		−	5156.31i		−	0.207338i
$853$	−16798.3	−	16798.3i	−0.674281	−	0.674281i	0.284419	−	0.958700i	$-0.408199\pi$
$853$	−16798.3	−	16798.3i	−0.674281	−	0.674281i	−0.958700	+	0.284419i	$0.908199\pi$
$854$	33565.4			1.34494
$855$	−1826.52	−	1826.52i	−0.0730592	−	0.0730592i
$856$	−9365.67	+	9365.67i	−0.373963	+	0.373963i
$857$	3594.51	−	3594.51i	0.143274	−	0.143274i	−0.631831	−	0.775106i	$-0.717697\pi$
$857$	3594.51	−	3594.51i	0.143274	−	0.143274i	0.775106	+	0.631831i	$0.217697\pi$
$858$		−	2874.52i		−	0.114376i
$859$		−	32488.7i		−	1.29046i	−0.763990	−	0.645228i	$-0.776763\pi$
$859$		−	32488.7i		−	1.29046i	0.763990	−	0.645228i	$-0.223237\pi$
$860$	19973.7	−	19973.7i	0.791973	−	0.791973i
$861$	−12614.5	+	12614.5i	−0.499306	+	0.499306i
$862$	17660.7	+	17660.7i	0.697824	+	0.697824i
$863$	−30304.2			−1.19532			−0.597662	−	0.801748i	$-0.703904\pi$
$863$	−30304.2			−1.19532			−0.597662	+	0.801748i	$0.703904\pi$
$864$	−610.940	−	610.940i	−0.0240563	−	0.0240563i
$865$			63050.8i			2.47837i
$866$	−4070.44			−0.159722
$867$	14087.5	+	4333.60i	0.551831	+	0.169754i
$868$	−18562.0			−0.725846
$869$			23448.1i			0.915329i
$870$	−10392.6	−	10392.6i	−0.404991	−	0.404991i
$871$	5919.53			0.230282
$872$	−9452.20	−	9452.20i	−0.367078	−	0.367078i
$873$	−810.368	+	810.368i	−0.0314167	+	0.0314167i
$874$	3146.28	−	3146.28i	0.121767	−	0.121767i
$875$			38321.9i			1.48059i
$876$		−	1465.72i		−	0.0565320i
$877$	−15323.5	+	15323.5i	−0.590009	+	0.590009i	−0.937634	−	0.347624i	$-0.886988\pi$
$877$	−15323.5	+	15323.5i	−0.590009	+	0.590009i	0.347624	+	0.937634i	$0.386988\pi$
$878$	−13897.1	+	13897.1i	−0.534175	+	0.534175i
$879$	−11678.9	−	11678.9i	−0.448144	−	0.448144i
$880$	10464.2			0.400850
$881$	−24765.1	−	24765.1i	−0.947056	−	0.947056i	0.0516111	−	0.998667i	$-0.483564\pi$
$881$	−24765.1	−	24765.1i	−0.947056	−	0.947056i	−0.998667	+	0.0516111i	$0.983564\pi$
$882$		−	4642.84i		−	0.177248i
$883$	35916.7			1.36885			0.684425	−	0.729084i	$-0.260054\pi$
$883$	35916.7			1.36885			0.684425	+	0.729084i	$0.260054\pi$
$884$	−906.753	−	3650.21i	−0.0344993	−	0.138880i
$885$	14661.4			0.556878
$886$			2809.85i			0.106545i
$887$	−17482.6	−	17482.6i	−0.661790	−	0.661790i	0.294012	−	0.955802i	$-0.405010\pi$
$887$	−17482.6	−	17482.6i	−0.661790	−	0.661790i	−0.955802	+	0.294012i	$0.905010\pi$
$888$	−6583.49			−0.248792
$889$	−34470.4	−	34470.4i	−1.30045	−	1.30045i
$890$	38808.7	−	38808.7i	1.46165	−	1.46165i
$891$	−2045.49	+	2045.49i	−0.0769097	+	0.0769097i
$892$			8977.29i			0.336975i
$893$		−	8353.59i		−	0.313037i
$894$	12417.2	−	12417.2i	0.464535	−	0.464535i
$895$	21243.5	−	21243.5i	0.793397	−	0.793397i
$896$	2218.75	+	2218.75i	0.0827269	+	0.0827269i
$897$	5712.84			0.212649
$898$	−8882.99	−	8882.99i	−0.330099	−	0.330099i
$899$			25321.0i			0.939378i
$900$	7573.10			0.280485
$901$	27468.7	−	6823.55i	1.01567	−	0.252303i
$902$	−17326.4			−0.639586
$903$		−	28358.9i		−	1.04510i
$904$	−1016.44	−	1016.44i	−0.0373965	−	0.0373965i
$905$	4792.71			0.176039
$906$	−9089.45	−	9089.45i	−0.333308	−	0.333308i
$907$	−5525.49	+	5525.49i	−0.202283	+	0.202283i	−0.800978	−	0.598694i	$-0.795686\pi$
$907$	−5525.49	+	5525.49i	−0.202283	+	0.202283i	0.598694	+	0.800978i	$0.295686\pi$
$908$	−9765.83	+	9765.83i	−0.356928	+	0.356928i
$909$		−	10373.8i		−	0.378524i
$910$			12044.5i			0.438760i
$911$	−11064.3	+	11064.3i	−0.402390	+	0.402390i	−0.879074	−	0.476684i	$-0.841838\pi$
$911$	−11064.3	+	11064.3i	−0.402390	+	0.402390i	0.476684	+	0.879074i	$0.341838\pi$
$912$	531.943	−	531.943i	0.0193140	−	0.0193140i
$913$	−31413.2	−	31413.2i	−1.13869	−	1.13869i
$914$	32608.2			1.18007
$915$	26595.7	+	26595.7i	0.960904	+	0.960904i
$916$			10730.7i			0.387065i
$917$	24062.6			0.866539
$918$	−1952.22	+	3242.70i	−0.0701885	+	0.116585i
$919$	−54133.9			−1.94310			−0.971552	−	0.236825i	$-0.923893\pi$
$919$	−54133.9			−1.94310			−0.971552	+	0.236825i	$0.923893\pi$
$920$			20796.6i			0.745265i
$921$	6956.64	+	6956.64i	0.248892	+	0.248892i
$922$	160.013			0.00571556
$923$	4075.96	+	4075.96i	0.145354	+	0.145354i
$924$	7428.62	−	7428.62i	0.264484	−	0.264484i
$925$	40803.9	−	40803.9i	1.45040	−	1.45040i
$926$		−	5239.41i		−	0.185937i
$927$			1152.38i			0.0408297i
$928$	3026.67	−	3026.67i	0.107064	−	0.107064i
$929$	−2614.28	+	2614.28i	−0.0923270	+	0.0923270i	−0.751762	−	0.659435i	$-0.770796\pi$
$929$	−2614.28	+	2614.28i	−0.0923270	+	0.0923270i	0.659435	+	0.751762i	$0.270796\pi$
$930$	−14707.7	−	14707.7i	−0.518585	−	0.518585i
$931$	4042.50			0.142307
$932$	4464.10	+	4464.10i	0.156895	+	0.156895i
$933$			25639.4i			0.899675i
$934$	2720.14			0.0952952
$935$	−11051.7	−	44489.4i	−0.386554	−	1.55611i
$936$	965.871			0.0337292
$937$		−	9888.38i		−	0.344759i	−0.985031	−	0.172380i	$-0.944854\pi$
$937$		−	9888.38i		−	0.344759i	0.985031	−	0.172380i	$-0.0551456\pi$
$938$	15297.8	+	15297.8i	0.532507	+	0.532507i
$939$	5997.43			0.208433
$940$	27608.2	+	27608.2i	0.957957	+	0.957957i
$941$	−1174.44	+	1174.44i	−0.0406860	+	0.0406860i	−0.727157	−	0.686471i	$-0.759159\pi$
$941$	−1174.44	+	1174.44i	−0.0406860	+	0.0406860i	0.686471	+	0.727157i	$0.259159\pi$
$942$	−5639.60	+	5639.60i	−0.195062	+	0.195062i
$943$		−	34434.6i		−	1.18913i
$944$			4269.88i			0.147217i
$945$	8570.79	−	8570.79i	0.295035	−	0.295035i
$946$	19475.9	−	19475.9i	0.669361	−	0.669361i
$947$	−16396.0	−	16396.0i	−0.562618	−	0.562618i	0.367433	−	0.930050i	$-0.380237\pi$
$947$	−16396.0	−	16396.0i	−0.562618	−	0.562618i	−0.930050	+	0.367433i	$0.880237\pi$
$948$	−7878.80			−0.269928
$949$	1158.62	+	1158.62i	0.0396316	+	0.0396316i
$950$			6593.87i			0.225193i
$951$	−14207.3			−0.484442
$952$	7089.90	−	11776.5i	0.241371	−	0.400924i
$953$	−1163.54			−0.0395495			−0.0197748	−	0.999804i	$-0.506295\pi$
$953$	−1163.54			−0.0395495			−0.0197748	+	0.999804i	$0.506295\pi$
$954$			7268.43i			0.246671i
$955$	33649.8	+	33649.8i	1.14019	+	1.14019i
$956$	−20064.8			−0.678810
$957$	−10133.6	−	10133.6i	−0.342291	−	0.342291i
$958$	−13900.5	+	13900.5i	−0.468795	+	0.468795i
$959$	−48327.4	+	48327.4i	−1.62729	+	1.62729i
$960$			3516.09i			0.118210i
$961$			6043.44i			0.202861i
$962$	5204.11	−	5204.11i	0.174415	−	0.174415i
$963$	−10536.4	+	10536.4i	−0.352575	+	0.352575i
$964$	4603.76	+	4603.76i	0.153815	+	0.153815i
$965$	−75772.9			−2.52768
$966$	14763.7	+	14763.7i	0.491732	+	0.491732i
$967$		−	31087.8i		−	1.03383i	−0.856036	−	0.516916i	$-0.827080\pi$
$967$		−	31087.8i		−	1.03383i	0.856036	−	0.516916i	$-0.172920\pi$
$968$	−444.589			−0.0147620
$969$	−2823.41	−	1699.79i	−0.0936026	−	0.0563521i
$970$	4663.83			0.154378
$971$		−	5352.03i		−	0.176885i	−0.996081	−	0.0884423i	$-0.971811\pi$
$971$		−	5352.03i		−	0.176885i	0.996081	−	0.0884423i	$-0.0281889\pi$
$972$	−687.308	−	687.308i	−0.0226805	−	0.0226805i
$973$	−4101.62			−0.135141
$974$	−10330.5	−	10330.5i	−0.339847	−	0.339847i
$975$	−5986.38	+	5986.38i	−0.196633	+	0.196633i
$976$	−7745.55	+	7745.55i	−0.254026	+	0.254026i
$977$			27767.7i			0.909282i	0.890675	+	0.454641i	$0.150232\pi$
$977$			27767.7i			0.909282i	−0.890675	+	0.454641i	$0.849768\pi$
$978$			15670.7i			0.512365i
$979$	37841.5	−	37841.5i	1.23536	−	1.23536i
$980$	−13360.3	+	13360.3i	−0.435487	+	0.435487i
$981$	−10633.7	−	10633.7i	−0.346084	−	0.346084i
$982$	37374.6			1.21453
$983$	−20541.2	−	20541.2i	−0.666492	−	0.666492i	0.290410	−	0.956902i	$-0.406208\pi$
$983$	−20541.2	−	20541.2i	−0.666492	−	0.666492i	−0.956902	+	0.290410i	$0.906208\pi$
$984$		−	5821.87i		−	0.188612i
$985$	−23249.9			−0.752083
$986$	−16064.7	−	9671.55i	−0.518869	−	0.312378i
$987$	39198.5			1.26414
$988$			840.979i			0.0270801i
$989$	38706.5	+	38706.5i	1.24448	+	1.24448i
$990$	11772.2			0.377925
$991$	16947.4	+	16947.4i	0.543242	+	0.543242i	0.924478	−	0.381236i	$-0.124501\pi$
$991$	16947.4	+	16947.4i	0.543242	+	0.543242i	−0.381236	+	0.924478i	$0.624501\pi$
$992$	4283.37	−	4283.37i	0.137094	−	0.137094i
$993$	8226.67	−	8226.67i	0.262906	−	0.262906i
$994$			21067.0i			0.672237i
$995$		−	99032.4i		−	3.15532i
$996$	10555.2	−	10555.2i	0.335797	−	0.335797i
$997$	−29861.9	+	29861.9i	−0.948582	+	0.948582i	−0.998741	−	0.0501591i	$-0.984027\pi$
$997$	−29861.9	+	29861.9i	−0.948582	+	0.948582i	0.0501591	+	0.998741i	$0.484027\pi$
$998$	−11537.2	−	11537.2i	−0.365936	−	0.365936i
$999$	−7406.43			−0.234564

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	102.4.f.c.13.3	✓	12
3.2	odd	2		306.4.g.g.217.1		12
17.2	even	8		1734.4.a.bd.1.1		6
17.4	even	4	inner	102.4.f.c.55.3	yes	12
17.15	even	8		1734.4.a.be.1.6		6
51.38	odd	4		306.4.g.g.55.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
102.4.f.c.13.3	✓	12	1.1	even	1	trivial
102.4.f.c.55.3	yes	12	17.4	even	4	inner
306.4.g.g.55.1		12	51.38	odd	4
306.4.g.g.217.1		12	3.2	odd	2
1734.4.a.bd.1.1		6	17.2	even	8
1734.4.a.be.1.6		6	17.15	even	8

Overview	Random
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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:	\( N \)	\(=\)	\( 102 = 2 \cdot 3 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	102.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-2.00000i q^{2} +(-2.12132 - 2.12132i) q^{3} -4.00000 q^{4} +(12.9492 + 12.9492i) q^{5} +(-4.24264 + 4.24264i) q^{6} +(17.3340 - 17.3340i) q^{7} +8.00000i q^{8} +9.00000i q^{9} +(25.8984 - 25.8984i) q^{10} +(25.2530 - 25.2530i) q^{11} +(8.48528 + 8.48528i) q^{12} -13.4149 q^{13} +(-34.6680 - 34.6680i) q^{14} -54.9388i q^{15} +16.0000 q^{16} +(-16.8983 - 68.0254i) q^{17} +18.0000 q^{18} +15.6725i q^{19} +(-51.7968 - 51.7968i) q^{20} -73.5420 q^{21} +(-50.5060 - 50.5060i) q^{22} +(100.376 - 100.376i) q^{23} +(16.9706 - 16.9706i) q^{24} +210.364i q^{25} +26.8298i q^{26} +(19.0919 - 19.0919i) q^{27} +(-69.3360 + 69.3360i) q^{28} +(94.5834 + 94.5834i) q^{29} -109.878 q^{30} +(133.855 + 133.855i) q^{31} -32.0000i q^{32} -107.139 q^{33} +(-136.051 + 33.7965i) q^{34} +448.923 q^{35} -36.0000i q^{36} +(-193.968 - 193.968i) q^{37} +31.3450 q^{38} +(28.4573 + 28.4573i) q^{39} +(-103.594 + 103.594i) q^{40} +(171.528 - 171.528i) q^{41} +147.084i q^{42} +385.616i q^{43} +(-101.012 + 101.012i) q^{44} +(-116.543 + 116.543i) q^{45} +(-200.752 - 200.752i) q^{46} -533.009 q^{47} +(-33.9411 - 33.9411i) q^{48} -257.936i q^{49} +420.728 q^{50} +(-108.457 + 180.150i) q^{51} +53.6595 q^{52} +403.802i q^{53} +(-38.1838 - 38.1838i) q^{54} +654.012 q^{55} +(138.672 + 138.672i) q^{56} +(33.2464 - 33.2464i) q^{57} +(189.167 - 189.167i) q^{58} +266.868i q^{59} +219.755i q^{60} +(-484.097 + 484.097i) q^{61} +(267.710 - 267.710i) q^{62} +(156.006 + 156.006i) q^{63} -64.0000 q^{64} +(-173.712 - 173.712i) q^{65} +214.279i q^{66} -441.266 q^{67} +(67.5931 + 272.101i) q^{68} -425.859 q^{69} -897.847i q^{70} +(-303.839 - 303.839i) q^{71} -72.0000 q^{72} +(-86.3683 - 86.3683i) q^{73} +(-387.936 + 387.936i) q^{74} +(446.249 - 446.249i) q^{75} -62.6901i q^{76} -875.471i q^{77} +(56.9145 - 56.9145i) q^{78} +(-464.263 + 464.263i) q^{79} +(207.187 + 207.187i) q^{80} -81.0000 q^{81} +(-343.057 - 343.057i) q^{82} -1243.94i q^{83} +294.168 q^{84} +(662.055 - 1099.69i) q^{85} +771.231 q^{86} -401.283i q^{87} +(202.024 + 202.024i) q^{88} +1498.50 q^{89} +(233.086 + 233.086i) q^{90} +(-232.534 + 232.534i) q^{91} +(-401.503 + 401.503i) q^{92} -567.900i q^{93} +1066.02i q^{94} +(-202.947 + 202.947i) q^{95} +(-67.8823 + 67.8823i) q^{96} +(90.0409 + 90.0409i) q^{97} -515.871 q^{98} +(227.277 + 227.277i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 48 q^{4} + 16 q^{5} - 12 q^{7} + 32 q^{10} - 32 q^{11} - 68 q^{13} + 24 q^{14} + 192 q^{16} + 64 q^{17} + 216 q^{18} - 64 q^{20} - 168 q^{21} + 64 q^{22} - 112 q^{23} + 48 q^{28} - 296 q^{29} - 168 q^{30}+ \cdots - 288 q^{99}+O(q^{100}) \) 12 * q - 48 * q^4 + 16 * q^5 - 12 * q^7 + 32 * q^10 - 32 * q^11 - 68 * q^13 + 24 * q^14 + 192 * q^16 + 64 * q^17 + 216 * q^18 - 64 * q^20 - 168 * q^21 + 64 * q^22 - 112 * q^23 + 48 * q^28 - 296 * q^29 - 168 * q^30 + 520 * q^31 + 204 * q^33 + 144 * q^34 + 392 * q^35 - 828 * q^37 - 280 * q^38 + 312 * q^39 - 128 * q^40 + 8 * q^41 + 128 * q^44 - 144 * q^45 + 224 * q^46 - 2920 * q^47 + 752 * q^50 + 420 * q^51 + 272 * q^52 + 1156 * q^55 - 96 * q^56 + 312 * q^57 - 592 * q^58 - 1124 * q^61 + 1040 * q^62 - 108 * q^63 - 768 * q^64 + 3288 * q^65 - 2008 * q^67 - 256 * q^68 + 468 * q^69 - 2184 * q^71 - 864 * q^72 + 2456 * q^73 - 1656 * q^74 - 192 * q^75 + 624 * q^78 + 2652 * q^79 + 256 * q^80 - 972 * q^81 - 16 * q^82 + 672 * q^84 + 3444 * q^85 - 184 * q^86 - 256 * q^88 + 5304 * q^89 + 288 * q^90 - 1420 * q^91 + 448 * q^92 - 2920 * q^95 + 2688 * q^97 - 4168 * q^98 - 288 * q^99

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