LMFDB - Embedded newform 84.3.g.a.43.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [84,3,Mod(43,84)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(84, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("84.43");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 84 = 2^{2} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	84.g (of order $2$, degree $1$, 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:	$2.28883422063$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	12.0.489494783471841.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} + 7 x^{10} - 11 x^{9} + 18 x^{8} - 22 x^{7} + 33 x^{6} - 44 x^{5} + 72 x^{4} + \cdots + 64 $ x^12 - 3x^11 + 7x^10 - 11x^9 + 18x^8 - 22x^7 + 33x^6 - 44x^5 + 72x^4 - 88x^3 + 112x^2 - 96*x + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{16} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			43.5
Root			$1.10978 - 0.876576i$ of defining polynomial
Character	$\chi$	$=$	84.43
Dual form			84.3.g.a.43.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0345996 - 1.99970i) q^{2} -1.73205i q^{3} +(-3.99761 - 0.138378i) q^{4} -6.29204 q^{5} +(-3.46358 - 0.0599283i) q^{6} -2.64575i q^{7} +(-0.415030 + 7.98923i) q^{8} -3.00000 q^{9} +O(q^{10})$	\(q+(0.0345996 - 1.99970i) q^{2} -1.73205i q^{3} +(-3.99761 - 0.138378i) q^{4} -6.29204 q^{5} +(-3.46358 - 0.0599283i) q^{6} -2.64575i q^{7} +(-0.415030 + 7.98923i) q^{8} -3.00000 q^{9} +(-0.217702 + 12.5822i) q^{10} -16.5803i q^{11} +(-0.239677 + 6.92406i) q^{12} +14.1288 q^{13} +(-5.29071 - 0.0915421i) q^{14} +10.8981i q^{15} +(15.9617 + 1.10636i) q^{16} -20.4687 q^{17} +(-0.103799 + 5.99910i) q^{18} -6.39258i q^{19} +(25.1531 + 0.870679i) q^{20} -4.58258 q^{21} +(-33.1556 - 0.573671i) q^{22} -29.0945i q^{23} +(13.8377 + 0.718853i) q^{24} +14.5898 q^{25} +(0.488852 - 28.2534i) q^{26} +5.19615i q^{27} +(-0.366113 + 10.5767i) q^{28} +54.6984 q^{29} +(21.7930 + 0.377071i) q^{30} +14.7296i q^{31} +(2.76466 - 31.8803i) q^{32} -28.7179 q^{33} +(-0.708210 + 40.9313i) q^{34} +16.6472i q^{35} +(11.9928 + 0.415134i) q^{36} +26.8040 q^{37} +(-12.7833 - 0.221181i) q^{38} -24.4718i q^{39} +(2.61139 - 50.2685i) q^{40} -33.5802 q^{41} +(-0.158555 + 9.16378i) q^{42} -3.83239i q^{43} +(-2.29434 + 66.2814i) q^{44} +18.8761 q^{45} +(-58.1804 - 1.00666i) q^{46} +27.4693i q^{47} +(1.91627 - 27.6465i) q^{48} -7.00000 q^{49} +(0.504801 - 29.1752i) q^{50} +35.4528i q^{51} +(-56.4815 - 1.95512i) q^{52} -21.7113 q^{53} +(10.3907 + 0.179785i) q^{54} +104.324i q^{55} +(21.1375 + 1.09807i) q^{56} -11.0723 q^{57} +(1.89254 - 109.380i) q^{58} +54.1344i q^{59} +(1.50806 - 43.5664i) q^{60} -35.7188 q^{61} +(29.4549 + 0.509641i) q^{62} +7.93725i q^{63} +(-63.6555 - 6.63154i) q^{64} -88.8991 q^{65} +(-0.993628 + 57.4271i) q^{66} -95.4255i q^{67} +(81.8258 + 2.83241i) q^{68} -50.3932 q^{69} +(33.2894 + 0.575986i) q^{70} +55.6524i q^{71} +(1.24509 - 23.9677i) q^{72} +130.476 q^{73} +(0.927408 - 53.5999i) q^{74} -25.2702i q^{75} +(-0.884592 + 25.5550i) q^{76} -43.8673 q^{77} +(-48.9363 - 0.846717i) q^{78} -15.6309i q^{79} +(-100.432 - 6.96126i) q^{80} +9.00000 q^{81} +(-1.16186 + 67.1503i) q^{82} -49.4495i q^{83} +(18.3193 + 0.634127i) q^{84} +128.790 q^{85} +(-7.66363 - 0.132599i) q^{86} -94.7403i q^{87} +(132.464 + 6.88131i) q^{88} +39.2530 q^{89} +(0.653107 - 37.7466i) q^{90} -37.3813i q^{91} +(-4.02604 + 116.309i) q^{92} +25.5125 q^{93} +(54.9303 + 0.950427i) q^{94} +40.2224i q^{95} +(-55.2184 - 4.78853i) q^{96} -171.943 q^{97} +(-0.242198 + 13.9979i) q^{98} +49.7408i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 2 q^{2} + 2 q^{4} + 8 q^{5} - 12 q^{6} - 10 q^{8} - 36 q^{9}+O(q^{10}) $ 12 * q + 2 * q^2 + 2 * q^4 + 8 * q^5 - 12 * q^6 - 10 * q^8 - 36 * q^9	$ 12 q + 2 q^{2} + 2 q^{4} + 8 q^{5} - 12 q^{6} - 10 q^{8} - 36 q^{9} + 28 q^{10} + 24 q^{12} - 24 q^{13} - 14 q^{14} - 14 q^{16} - 40 q^{17} - 6 q^{18} - 20 q^{20} - 88 q^{22} - 36 q^{24} + 180 q^{25} + 100 q^{26} + 14 q^{28} + 72 q^{29} + 72 q^{30} + 142 q^{32} - 100 q^{34} - 6 q^{36} - 88 q^{37} + 128 q^{38} - 28 q^{40} - 200 q^{41} - 40 q^{44} - 24 q^{45} - 24 q^{46} + 48 q^{48} - 84 q^{49} - 346 q^{50} - 364 q^{52} + 104 q^{53} + 36 q^{54} + 98 q^{56} + 148 q^{58} + 96 q^{60} + 104 q^{61} + 64 q^{62} - 70 q^{64} + 176 q^{65} + 24 q^{66} + 188 q^{68} - 192 q^{69} - 84 q^{70} + 30 q^{72} + 312 q^{73} + 4 q^{74} + 432 q^{76} - 224 q^{77} + 48 q^{78} - 564 q^{80} + 108 q^{81} + 332 q^{82} + 352 q^{85} + 160 q^{86} + 328 q^{88} - 552 q^{89} - 84 q^{90} + 232 q^{92} - 48 q^{93} - 144 q^{94} - 108 q^{96} - 264 q^{97} - 14 q^{98}+O(q^{100}) $ 12 * q + 2 * q^2 + 2 * q^4 + 8 * q^5 - 12 * q^6 - 10 * q^8 - 36 * q^9 + 28 * q^10 + 24 * q^12 - 24 * q^13 - 14 * q^14 - 14 * q^16 - 40 * q^17 - 6 * q^18 - 20 * q^20 - 88 * q^22 - 36 * q^24 + 180 * q^25 + 100 * q^26 + 14 * q^28 + 72 * q^29 + 72 * q^30 + 142 * q^32 - 100 * q^34 - 6 * q^36 - 88 * q^37 + 128 * q^38 - 28 * q^40 - 200 * q^41 - 40 * q^44 - 24 * q^45 - 24 * q^46 + 48 * q^48 - 84 * q^49 - 346 * q^50 - 364 * q^52 + 104 * q^53 + 36 * q^54 + 98 * q^56 + 148 * q^58 + 96 * q^60 + 104 * q^61 + 64 * q^62 - 70 * q^64 + 176 * q^65 + 24 * q^66 + 188 * q^68 - 192 * q^69 - 84 * q^70 + 30 * q^72 + 312 * q^73 + 4 * q^74 + 432 * q^76 - 224 * q^77 + 48 * q^78 - 564 * q^80 + 108 * q^81 + 332 * q^82 + 352 * q^85 + 160 * q^86 + 328 * q^88 - 552 * q^89 - 84 * q^90 + 232 * q^92 - 48 * q^93 - 144 * q^94 - 108 * q^96 - 264 * q^97 - 14 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/84\mathbb{Z}\right)^\times$.

$n$	$29$	$43$	$73$
$\chi(n)$	$1$	$-1$	$1$

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 $

$2$	0.0345996	−	1.99970i	0.0172998	−	0.999850i
$2$	0.0345996	−	1.99970i	0.0172998	−	0.999850i
$3$		−	1.73205i		−	0.577350i
$3$		−	1.73205i		−	0.577350i
$4$	−3.99761	−	0.138378i	−0.999401	−	0.0345945i
$5$	−6.29204			−1.25841			−0.629204	−	0.777240i	$-0.716619\pi$
$5$	−6.29204			−1.25841			−0.629204	+	0.777240i	$0.716619\pi$
$6$	−3.46358	−	0.0599283i	−0.577264	−	0.00998806i
$7$		−	2.64575i		−	0.377964i
$7$		−	2.64575i		−	0.377964i
$8$	−0.415030	+	7.98923i	−0.0518788	+	0.998653i
$9$	−3.00000			−0.333333
$10$	−0.217702	+	12.5822i	−0.0217702	+	1.25822i
$11$		−	16.5803i		−	1.50730i	−0.657278	−	0.753649i	$-0.728292\pi$
$11$		−	16.5803i		−	1.50730i	0.657278	−	0.753649i	$-0.271708\pi$
$12$	−0.239677	+	6.92406i	−0.0199731	+	0.577005i
$13$	14.1288			1.08683			0.543416	−	0.839463i	$-0.317131\pi$
$13$	14.1288			1.08683			0.543416	+	0.839463i	$0.317131\pi$
$14$	−5.29071	−	0.0915421i	−0.377908	−	0.00653872i
$15$			10.8981i			0.726542i
$16$	15.9617	+	1.10636i	0.997606	+	0.0691475i
$17$	−20.4687			−1.20404			−0.602020	−	0.798481i	$-0.705637\pi$
$17$	−20.4687			−1.20404			−0.602020	+	0.798481i	$0.705637\pi$
$18$	−0.103799	+	5.99910i	−0.00576661	+	0.333283i
$19$		−	6.39258i		−	0.336452i	−0.985748	−	0.168226i	$-0.946196\pi$
$19$		−	6.39258i		−	0.336452i	0.985748	−	0.168226i	$-0.0538038\pi$
$20$	25.1531	+	0.870679i	1.25765	+	0.0435340i
$21$	−4.58258			−0.218218
$22$	−33.1556	−	0.573671i	−1.50707	−	0.0260760i
$23$		−	29.0945i		−	1.26498i	−0.774568	−	0.632490i	$-0.782033\pi$
$23$		−	29.0945i		−	1.26498i	0.774568	−	0.632490i	$-0.217967\pi$
$24$	13.8377	+	0.718853i	0.576573	+	0.0299522i
$25$	14.5898			0.583591
$26$	0.488852	−	28.2534i	0.0188020	−	1.08667i
$27$			5.19615i			0.192450i
$28$	−0.366113	+	10.5767i	−0.0130755	+	0.377738i
$29$	54.6984			1.88615			0.943075	−	0.332579i	$-0.107919\pi$
$29$	54.6984			1.88615			0.943075	+	0.332579i	$0.107919\pi$
$30$	21.7930	+	0.377071i	0.726433	+	0.0125690i
$31$			14.7296i			0.475150i	0.971369	+	0.237575i	$0.0763525\pi$
$31$			14.7296i			0.475150i	−0.971369	+	0.237575i	$0.923647\pi$
$32$	2.76466	−	31.8803i	0.0863956	−	0.996261i
$33$	−28.7179			−0.870238
$34$	−0.708210	+	40.9313i	−0.0208297	+	1.20386i
$35$			16.6472i			0.475633i
$36$	11.9928	+	0.415134i	0.333134	+	0.0115315i
$37$	26.8040			0.724431			0.362216	−	0.932094i	$-0.382020\pi$
$37$	26.8040			0.724431			0.362216	+	0.932094i	$0.382020\pi$
$38$	−12.7833	−	0.221181i	−0.336401	−	0.00582055i
$39$		−	24.4718i		−	0.627483i
$40$	2.61139	−	50.2685i	0.0652846	−	1.25671i
$41$	−33.5802			−0.819029			−0.409515	−	0.912304i	$-0.634302\pi$
$41$	−33.5802			−0.819029			−0.409515	+	0.912304i	$0.634302\pi$
$42$	−0.158555	+	9.16378i	−0.00377513	+	0.218185i
$43$		−	3.83239i		−	0.0891253i	−0.999007	−	0.0445627i	$-0.985811\pi$
$43$		−	3.83239i		−	0.0891253i	0.999007	−	0.0445627i	$-0.0141894\pi$
$44$	−2.29434	+	66.2814i	−0.0521441	+	1.50639i
$45$	18.8761			0.419469
$46$	−58.1804	−	1.00666i	−1.26479	−	0.0218839i
$47$			27.4693i			0.584453i	0.956349	+	0.292226i	$0.0943961\pi$
$47$			27.4693i			0.584453i	−0.956349	+	0.292226i	$0.905604\pi$
$48$	1.91627	−	27.6465i	0.0399223	−	0.575968i
$49$	−7.00000			−0.142857
$50$	0.504801	−	29.1752i	0.0100960	−	0.583503i
$51$			35.4528i			0.695153i
$52$	−56.4815	−	1.95512i	−1.08618	−	0.0375984i
$53$	−21.7113			−0.409648			−0.204824	−	0.978799i	$-0.565662\pi$
$53$	−21.7113			−0.409648			−0.204824	+	0.978799i	$0.565662\pi$
$54$	10.3907	+	0.179785i	0.192421	+	0.00332935i
$55$			104.324i			1.89679i
$56$	21.1375	+	1.09807i	0.377456	+	0.0196083i
$57$	−11.0723			−0.194250
$58$	1.89254	−	109.380i	0.0326301	−	1.88587i
$59$			54.1344i			0.917532i	0.888557	+	0.458766i	$0.151708\pi$
$59$			54.1344i			0.917532i	−0.888557	+	0.458766i	$0.848292\pi$
$60$	1.50806	−	43.5664i	0.0251343	−	0.726107i
$61$	−35.7188			−0.585554			−0.292777	−	0.956181i	$-0.594579\pi$
$61$	−35.7188			−0.585554			−0.292777	+	0.956181i	$0.594579\pi$
$62$	29.4549	+	0.509641i	0.475079	+	0.00822001i
$63$			7.93725i			0.125988i
$64$	−63.6555	−	6.63154i	−0.994617	−	0.103618i
$65$	−88.8991			−1.36768
$66$	−0.993628	+	57.4271i	−0.0150550	+	0.870108i
$67$		−	95.4255i		−	1.42426i	−0.702047	−	0.712131i	$-0.747730\pi$
$67$		−	95.4255i		−	1.42426i	0.702047	−	0.712131i	$-0.252270\pi$
$68$	81.8258	+	2.83241i	1.20332	+	0.0416532i
$69$	−50.3932			−0.730337
$70$	33.2894	+	0.575986i	0.475562	+	0.00822837i
$71$			55.6524i			0.783837i	0.920000	+	0.391919i	$0.128189\pi$
$71$			55.6524i			0.783837i	−0.920000	+	0.391919i	$0.871811\pi$
$72$	1.24509	−	23.9677i	0.0172929	−	0.332884i
$73$	130.476			1.78735			0.893673	−	0.448719i	$-0.148119\pi$
$73$	130.476			1.78735			0.893673	+	0.448719i	$0.148119\pi$
$74$	0.927408	−	53.5999i	0.0125325	−	0.724323i
$75$		−	25.2702i		−	0.336936i
$76$	−0.884592	+	25.5550i	−0.0116394	+	0.336250i
$77$	−43.8673			−0.569705
$78$	−48.9363	−	0.846717i	−0.627389	−	0.0108553i
$79$		−	15.6309i		−	0.197859i	−0.995094	−	0.0989295i	$-0.968458\pi$
$79$		−	15.6309i		−	0.197859i	0.995094	−	0.0989295i	$-0.0315418\pi$
$80$	−100.432	−	6.96126i	−1.25540	−	0.0870158i
$81$	9.00000			0.111111
$82$	−1.16186	+	67.1503i	−0.0141691	+	0.818907i
$83$		−	49.4495i		−	0.595777i	−0.954601	−	0.297889i	$-0.903718\pi$
$83$		−	49.4495i		−	0.595777i	0.954601	−	0.297889i	$-0.0962824\pi$
$84$	18.3193	+	0.634127i	0.218087	+	0.00754913i
$85$	128.790			1.51517
$86$	−7.66363	−	0.132599i	−0.0891120	−	0.00154185i
$87$		−	94.7403i		−	1.08897i
$88$	132.464	+	6.88131i	1.50527	+	0.0781967i
$89$	39.2530			0.441045			0.220522	−	0.975382i	$-0.429224\pi$
$89$	39.2530			0.441045			0.220522	+	0.975382i	$0.429224\pi$
$90$	0.653107	−	37.7466i	0.00725674	−	0.419407i
$91$		−	37.3813i		−	0.410784i
$92$	−4.02604	+	116.309i	−0.0437613	+	1.26422i
$93$	25.5125			0.274328
$94$	54.9303	+	0.950427i	0.584365	+	0.0101109i
$95$			40.2224i			0.423394i
$96$	−55.2184	−	4.78853i	−0.575192	−	0.0498805i
$97$	−171.943			−1.77261			−0.886303	−	0.463106i	$-0.846735\pi$
$97$	−171.943			−1.77261			−0.886303	+	0.463106i	$0.846735\pi$
$98$	−0.242198	+	13.9979i	−0.00247140	+	0.142836i
$99$			49.7408i			0.502432i
$100$	−58.3241	−	2.01890i	−0.583241	−	0.0201890i
$101$	113.883			1.12755			0.563777	−	0.825927i	$-0.309348\pi$
$101$	113.883			1.12755			0.563777	+	0.825927i	$0.309348\pi$
$102$	70.8950	+	1.22665i	0.695049	+	0.0120260i
$103$		−	93.7629i		−	0.910319i	−0.890410	−	0.455160i	$-0.849582\pi$
$103$		−	93.7629i		−	0.910319i	0.890410	−	0.455160i	$-0.150418\pi$
$104$	−5.86389	+	112.878i	−0.0563835	+	1.08537i
$105$	28.8337			0.274607
$106$	−0.751204	+	43.4161i	−0.00708683	+	0.409586i
$107$		−	48.2088i		−	0.450549i	−0.974295	−	0.225275i	$-0.927672\pi$
$107$		−	48.2088i		−	0.450549i	0.974295	−	0.225275i	$-0.0723279\pi$
$108$	0.719032	−	20.7722i	0.00665771	−	0.192335i
$109$	89.3790			0.819991			0.409996	−	0.912088i	$-0.365530\pi$
$109$	89.3790			0.819991			0.409996	+	0.912088i	$0.365530\pi$
$110$	208.616	+	3.60956i	1.89651	+	0.0328142i
$111$		−	46.4258i		−	0.418251i
$112$	2.92715	−	42.2307i	0.0261353	−	0.377060i
$113$	93.4667			0.827139			0.413569	−	0.910473i	$-0.364282\pi$
$113$	93.4667			0.827139			0.413569	+	0.910473i	$0.364282\pi$
$114$	−0.383097	+	22.1412i	−0.00336050	+	0.194221i
$115$			183.064i			1.59186i
$116$	−218.662	−	7.56904i	−1.88502	−	0.0652504i
$117$	−42.3865			−0.362277
$118$	108.253	+	1.87303i	0.917395	+	0.0158731i
$119$			54.1551i			0.455085i
$120$	−87.0677	−	4.52305i	−0.725564	−	0.0376921i
$121$	−153.905			−1.27194
$122$	−1.23586	+	71.4269i	−0.0101300	+	0.585466i
$123$			58.1626i			0.472867i
$124$	2.03826	−	58.8833i	0.0164376	−	0.474866i
$125$	65.5016			0.524013
$126$	15.8721	+	0.274626i	0.125969	+	0.00217957i
$127$		−	208.300i		−	1.64016i	−0.572248	−	0.820081i	$-0.693929\pi$
$127$		−	208.300i		−	1.64016i	0.572248	−	0.820081i	$-0.306071\pi$
$128$	−15.4635	+	127.062i	−0.120809	+	0.992676i
$129$	−6.63789			−0.0514565
$130$	−3.07588	+	177.772i	−0.0236606	+	1.36747i
$131$		−	67.7695i		−	0.517324i	−0.965968	−	0.258662i	$-0.916718\pi$
$131$		−	67.7695i		−	0.517324i	0.965968	−	0.258662i	$-0.0832816\pi$
$132$	114.803	+	3.97392i	0.869718	+	0.0301054i
$133$	−16.9132			−0.127167
$134$	−190.823	−	3.30169i	−1.42405	−	0.0246395i
$135$		−	32.6944i		−	0.242181i
$136$	8.49512	−	163.529i	0.0624641	−	1.20242i
$137$	−13.4127			−0.0979029			−0.0489514	−	0.998801i	$-0.515588\pi$
$137$	−13.4127			−0.0979029			−0.0489514	+	0.998801i	$0.515588\pi$
$138$	−1.74359	+	100.771i	−0.0126347	+	0.730227i
$139$		−	160.382i		−	1.15383i	−0.816804	−	0.576915i	$-0.804256\pi$
$139$		−	160.382i		−	1.15383i	0.816804	−	0.576915i	$-0.195744\pi$
$140$	2.30360	−	66.5488i	0.0164543	−	0.475349i
$141$	47.5782			0.337434
$142$	111.288	+	1.92555i	0.783720	+	0.0135602i
$143$		−	234.260i		−	1.63818i
$144$	−47.8851	−	3.31908i	−0.332535	−	0.0230492i
$145$	−344.164			−2.37355
$146$	4.51443	−	260.914i	0.0309208	−	1.78708i
$147$			12.1244i			0.0824786i
$148$	−107.152	−	3.70908i	−0.723998	−	0.0250613i
$149$	−130.824			−0.878015			−0.439007	−	0.898483i	$-0.644670\pi$
$149$	−130.824			−0.878015			−0.439007	+	0.898483i	$0.644670\pi$
$150$	−50.5329	−	0.874340i	−0.336886	−	0.00582894i
$151$			175.855i			1.16460i	0.812974	+	0.582300i	$0.197847\pi$
$151$			175.855i			1.16460i	−0.812974	+	0.582300i	$0.802153\pi$
$152$	51.0718	+	2.65311i	0.335999	+	0.0174547i
$153$	61.4061			0.401347
$154$	−1.51779	+	87.7214i	−0.00985579	+	0.569620i
$155$		−	92.6795i		−	0.597932i
$156$	−3.38636	+	97.8288i	−0.0217074	+	0.627107i
$157$	−167.199			−1.06496			−0.532482	−	0.846441i	$-0.678741\pi$
$157$	−167.199			−1.06496			−0.532482	+	0.846441i	$0.678741\pi$
$158$	−31.2570	−	0.540822i	−0.197829	−	0.00342293i
$159$			37.6051i			0.236510i
$160$	−17.3953	+	200.592i	−0.108721	+	1.25370i
$161$	−76.9769			−0.478118
$162$	0.311397	−	17.9973i	0.00192220	−	0.111094i
$163$			220.591i			1.35332i	0.736295	+	0.676661i	$0.236574\pi$
$163$			220.591i			1.35332i	−0.736295	+	0.676661i	$0.763426\pi$
$164$	134.240	+	4.64676i	0.818539	+	0.0283339i
$165$	180.694			1.09511
$166$	−98.8842	−	1.71093i	−0.595688	−	0.0103068i
$167$			64.6529i			0.387143i	0.981086	+	0.193572i	$0.0620072\pi$
$167$			64.6529i			0.387143i	−0.981086	+	0.193572i	$0.937993\pi$
$168$	1.90191	−	36.6112i	0.0113209	−	0.217924i
$169$	30.6236			0.181205
$170$	4.45608	−	257.541i	0.0262123	−	1.51495i
$171$			19.1777i			0.112151i
$172$	−0.530318	+	15.3204i	−0.00308324	+	0.0890720i
$173$	237.146			1.37078			0.685392	−	0.728174i	$-0.259631\pi$
$173$	237.146			1.37078			0.685392	+	0.728174i	$0.259631\pi$
$174$	−189.452	−	3.27798i	−1.08881	−	0.0188390i
$175$		−	38.6009i		−	0.220577i
$176$	18.3438	−	264.649i	0.104226	−	1.50369i
$177$	93.7636			0.529738
$178$	1.35814	−	78.4942i	0.00763000	−	0.440979i
$179$			103.153i			0.576275i	0.957589	+	0.288137i	$0.0930360\pi$
$179$			103.153i			0.576275i	−0.957589	+	0.288137i	$0.906964\pi$
$180$	−75.4593	−	2.61204i	−0.419218	−	0.0145113i
$181$	43.5702			0.240719			0.120360	−	0.992730i	$-0.461595\pi$
$181$	43.5702			0.240719			0.120360	+	0.992730i	$0.461595\pi$
$182$	−74.7515	−	1.29338i	−0.410723	−	0.00710649i
$183$			61.8668i			0.338070i
$184$	232.443	+	12.0751i	1.26328	+	0.0656256i
$185$	−168.652			−0.911630
$186$	0.882723	−	51.0174i	0.00474582	−	0.274287i
$187$			339.376i			1.81485i
$188$	3.80114	−	109.811i	0.0202188	−	0.584103i
$189$	13.7477			0.0727393
$190$	80.4327	+	1.39168i	0.423330	+	0.00732463i
$191$			219.309i			1.14822i	0.818779	+	0.574109i	$0.194651\pi$
$191$			219.309i			1.14822i	−0.818779	+	0.574109i	$0.805349\pi$
$192$	−11.4862	+	110.255i	−0.0598238	+	0.574243i
$193$	9.40273			0.0487188			0.0243594	−	0.999703i	$-0.492245\pi$
$193$	9.40273			0.0487188			0.0243594	+	0.999703i	$0.492245\pi$
$194$	−5.94916	+	343.834i	−0.0306658	+	1.77234i
$195$			153.978i			0.789630i
$196$	27.9832	+	0.968645i	0.142772	+	0.00494207i
$197$	329.193			1.67103			0.835514	−	0.549469i	$-0.185170\pi$
$197$	329.193			1.67103			0.835514	+	0.549469i	$0.185170\pi$
$198$	99.4667	+	1.72101i	0.502357	+	0.00869199i
$199$			63.0050i			0.316608i	0.987390	+	0.158304i	$0.0506026\pi$
$199$			63.0050i			0.316608i	−0.987390	+	0.158304i	$0.949397\pi$
$200$	−6.05519	+	116.561i	−0.0302760	+	0.582805i
$201$	−165.282			−0.822298
$202$	3.94031	−	227.732i	0.0195065	−	1.12739i
$203$		−	144.718i		−	0.712898i
$204$	4.90589	−	141.726i	0.0240485	−	0.694737i
$205$	211.288			1.03067
$206$	−187.498	−	3.24416i	−0.910183	−	0.0157484i
$207$			87.2836i			0.421660i
$208$	225.520	+	15.6316i	1.08423	+	0.0751518i
$209$	−105.991			−0.507133
$210$	0.997637	−	57.6589i	0.00475065	−	0.274566i
$211$		−	0.702405i		−	0.00332893i	−0.999999	−	0.00166447i	$-0.999470\pi$
$211$		−	0.702405i		−	0.00332893i	0.999999	−	0.00166447i	$-0.000529817\pi$
$212$	86.7933	+	3.00437i	0.409402	+	0.0141715i
$213$	96.3929			0.452549
$214$	−96.4031	−	1.66801i	−0.450482	−	0.00779442i
$215$			24.1135i			0.112156i
$216$	−41.5132	−	2.15656i	−0.192191	−	0.00998407i
$217$	38.9710			0.179590
$218$	3.09248	−	178.731i	0.0141857	−	0.819868i
$219$		−	225.992i		−	1.03192i
$220$	14.4361	−	417.045i	0.0656186	−	1.89566i
$221$	−289.199			−1.30859
$222$	−92.8378	−	1.60632i	−0.418188	−	0.00723566i
$223$		−	260.543i		−	1.16835i	−0.811627	−	0.584177i	$-0.801418\pi$
$223$		−	260.543i		−	1.16835i	0.811627	−	0.584177i	$-0.198582\pi$
$224$	−84.3475	−	7.31460i	−0.376551	−	0.0326545i
$225$	−43.7693			−0.194530
$226$	3.23391	−	186.905i	0.0143094	−	0.827015i
$227$		−	222.146i		−	0.978617i	−0.872111	−	0.489308i	$-0.837249\pi$
$227$		−	222.146i		−	0.978617i	0.872111	−	0.489308i	$-0.162751\pi$
$228$	44.2626	+	1.53216i	0.194134	+	0.00671999i
$229$	124.781			0.544893			0.272447	−	0.962171i	$-0.412167\pi$
$229$	124.781			0.544893			0.272447	+	0.962171i	$0.412167\pi$
$230$	366.073	+	6.33395i	1.59162	+	0.0275389i
$231$			75.9803i			0.328919i
$232$	−22.7015	+	436.998i	−0.0978511	+	1.88361i
$233$	332.321			1.42627			0.713135	−	0.701027i	$-0.247275\pi$
$233$	332.321			1.42627			0.713135	+	0.701027i	$0.247275\pi$
$234$	−1.46656	+	84.7602i	−0.00626734	+	0.362223i
$235$		−	172.838i		−	0.735480i
$236$	7.49100	−	216.408i	0.0317415	−	0.916983i
$237$	−27.0734			−0.114234
$238$	108.294	+	1.87375i	0.455017	+	0.00787288i
$239$			285.085i			1.19282i	0.802679	+	0.596412i	$0.203407\pi$
$239$			285.085i			1.19282i	−0.802679	+	0.596412i	$0.796593\pi$
$240$	−12.0573	+	173.953i	−0.0502386	+	0.724803i
$241$	89.2332			0.370262			0.185131	−	0.982714i	$-0.440729\pi$
$241$	89.2332			0.370262			0.185131	+	0.982714i	$0.440729\pi$
$242$	−5.32507	+	307.765i	−0.0220044	+	1.27175i
$243$		−	15.5885i		−	0.0641500i
$244$	142.790	+	4.94269i	0.585204	+	0.0202569i
$245$	44.0443			0.179773
$246$	116.308	+	2.01241i	0.472796	+	0.00818051i
$247$		−	90.3197i		−	0.365667i
$248$	−117.679	−	6.11325i	−0.474510	−	0.0246502i
$249$	−85.6490			−0.343972
$250$	2.26633	−	130.984i	0.00906533	−	0.523935i
$251$			83.4611i			0.332514i	0.986082	+	0.166257i	$0.0531682\pi$
$251$			83.4611i			0.332514i	−0.986082	+	0.166257i	$0.946832\pi$
$252$	1.09834	−	31.7300i	0.00435849	−	0.125913i
$253$	−482.395			−1.90670
$254$	−416.539	−	7.20712i	−1.63992	−	0.0283745i
$255$		−	223.071i		−	0.874786i
$256$	253.552	+	35.3188i	0.990437	+	0.137964i
$257$	−29.8619			−0.116194			−0.0580971	−	0.998311i	$-0.518503\pi$
$257$	−29.8619			−0.116194			−0.0580971	+	0.998311i	$0.518503\pi$
$258$	−0.229669	+	13.2738i	−0.000890189	+	0.0514488i
$259$		−	70.9166i		−	0.273809i
$260$	355.384	+	12.3017i	1.36686	+	0.0473141i
$261$	−164.095			−0.628717
$262$	−135.519	−	2.34480i	−0.517247	−	0.00894962i
$263$			245.304i			0.932717i	0.884596	+	0.466358i	$0.154434\pi$
$263$			245.304i			0.932717i	−0.884596	+	0.466358i	$0.845566\pi$
$264$	11.9188	−	229.434i	0.0451469	−	0.869067i
$265$	136.608			0.515504
$266$	−0.585190	+	33.8213i	−0.00219996	+	0.127148i
$267$		−	67.9882i		−	0.254637i
$268$	−13.2048	+	381.474i	−0.0492716	+	1.42341i
$269$	−18.9441			−0.0704241			−0.0352120	−	0.999380i	$-0.511211\pi$
$269$	−18.9441			−0.0704241			−0.0352120	+	0.999380i	$0.511211\pi$
$270$	−65.3790	−	1.13121i	−0.242144	−	0.00418968i
$271$			278.928i			1.02925i	0.857414	+	0.514626i	$0.172069\pi$
$271$			278.928i			1.02925i	−0.857414	+	0.514626i	$0.827931\pi$
$272$	−326.715	−	22.6458i	−1.20116	−	0.0832564i
$273$	−64.7464			−0.237166
$274$	−0.464074	+	26.8214i	−0.00169370	+	0.0978882i
$275$		−	241.902i		−	0.879644i
$276$	201.452	+	6.97331i	0.729899	+	0.0252656i
$277$	−206.348			−0.744938			−0.372469	−	0.928045i	$-0.621489\pi$
$277$	−206.348			−0.744938			−0.372469	+	0.928045i	$0.621489\pi$
$278$	−320.717	−	5.54917i	−1.15366	−	0.0199610i
$279$		−	44.1889i		−	0.158383i
$280$	−132.998	−	6.90908i	−0.474993	−	0.0246753i
$281$	−262.775			−0.935142			−0.467571	−	0.883956i	$-0.654871\pi$
$281$	−262.775			−0.935142			−0.467571	+	0.883956i	$0.654871\pi$
$282$	1.64619	−	95.1421i	0.00583755	−	0.337383i
$283$			543.508i			1.92052i	0.279101	+	0.960262i	$0.409963\pi$
$283$			543.508i			1.92052i	−0.279101	+	0.960262i	$0.590037\pi$
$284$	7.70107	−	222.477i	0.0271164	−	0.783368i
$285$	69.6672			0.244446
$286$	−468.449	−	8.10530i	−1.63793	−	0.0283402i
$287$			88.8448i			0.309564i
$288$	−8.29398	+	95.6410i	−0.0287985	+	0.332087i
$289$	129.967			0.449714
$290$	−11.9080	+	688.226i	−0.0410619	+	2.37319i
$291$			297.814i			1.02341i
$292$	−521.593	−	18.0550i	−1.78628	−	0.0618323i
$293$	19.1934			0.0655064			0.0327532	−	0.999463i	$-0.489572\pi$
$293$	19.1934			0.0655064			0.0327532	+	0.999463i	$0.489572\pi$
$294$	24.2451	+	0.419498i	0.0824663	+	0.00142687i
$295$		−	340.616i		−	1.15463i
$296$	−11.1245	+	214.143i	−0.0375826	+	0.723456i
$297$	86.1536			0.290079
$298$	−4.52647	+	261.609i	−0.0151895	+	0.877883i
$299$		−	411.072i		−	1.37482i
$300$	−3.49684	+	101.020i	−0.0116561	+	0.336734i
$301$	−10.1395			−0.0336862
$302$	351.657	+	6.08451i	1.16443	+	0.0201474i
$303$		−	197.251i		−	0.650994i
$304$	7.07250	−	102.037i	0.0232648	−	0.335646i
$305$	224.744			0.736866
$306$	2.12463	−	122.794i	0.00694323	−	0.401287i
$307$		−	543.121i		−	1.76912i	−0.466423	−	0.884562i	$-0.654458\pi$
$307$		−	543.121i		−	1.76912i	0.466423	−	0.884562i	$-0.345542\pi$
$308$	175.364	+	6.07026i	0.569364	+	0.0197086i
$309$	−162.402			−0.525573
$310$	−185.331	−	3.20668i	−0.597843	−	0.0103441i
$311$		−	183.154i		−	0.588920i	−0.955664	−	0.294460i	$-0.904860\pi$
$311$		−	183.154i		−	0.588920i	0.955664	−	0.294460i	$-0.0951398\pi$
$312$	195.511	+	10.1565i	0.626638	+	0.0325530i
$313$	513.858			1.64172			0.820859	−	0.571131i	$-0.193495\pi$
$313$	513.858			1.64172			0.820859	+	0.571131i	$0.193495\pi$
$314$	−5.78504	+	334.349i	−0.0184237	+	1.06481i
$315$		−	49.9415i		−	0.158544i
$316$	−2.16297	+	62.4860i	−0.00684483	+	0.197741i
$317$	−559.731			−1.76571			−0.882857	−	0.469642i	$-0.844383\pi$
$317$	−559.731			−1.76571			−0.882857	+	0.469642i	$0.844383\pi$
$318$	75.1990	+	1.30112i	0.236475	+	0.00409158i
$319$		−	906.914i		−	2.84299i
$320$	400.523	+	41.7259i	1.25163	+	0.130393i
$321$	−83.5000			−0.260125
$322$	−2.66337	+	153.931i	−0.00827135	+	0.478046i
$323$			130.848i			0.405102i
$324$	−35.9785	−	1.24540i	−0.111045	−	0.00384383i
$325$	206.136			0.634265
$326$	441.117	+	7.63239i	1.35312	+	0.0234122i
$327$		−	154.809i		−	0.473422i
$328$	13.9368	−	268.280i	0.0424902	−	0.817926i
$329$	72.6769			0.220902
$330$	6.25195	−	361.334i	0.0189453	−	1.09495i
$331$			379.794i			1.14741i	0.819061	+	0.573707i	$0.194495\pi$
$331$			379.794i			1.14741i	−0.819061	+	0.573707i	$0.805505\pi$
$332$	−6.84271	+	197.680i	−0.0206106	+	0.595420i
$333$	−80.4119			−0.241477
$334$	129.286	+	2.23697i	0.387085	+	0.00669751i
$335$			600.421i			1.79230i
$336$	−73.1457	−	5.06998i	−0.217696	−	0.0150892i
$337$	−117.618			−0.349015			−0.174507	−	0.984656i	$-0.555833\pi$
$337$	−117.618			−0.349015			−0.174507	+	0.984656i	$0.555833\pi$
$338$	1.05957	−	61.2380i	0.00313481	−	0.181178i
$339$		−	161.889i		−	0.477549i
$340$	−514.851	−	17.8217i	−1.51427	−	0.0524167i
$341$	244.222			0.716192
$342$	38.3498	+	0.663543i	0.112134	+	0.00194018i
$343$			18.5203i			0.0539949i
$344$	30.6178	+	1.59056i	0.0890053	+	0.00462371i
$345$	317.076			0.919061
$346$	8.20516	−	474.221i	0.0237143	−	1.37058i
$347$		−	302.706i		−	0.872351i	−0.899862	−	0.436175i	$-0.856333\pi$
$347$		−	302.706i		−	0.872351i	0.899862	−	0.436175i	$-0.143667\pi$
$348$	−13.1100	+	378.735i	−0.0376723	+	1.08832i
$349$	83.1588			0.238277			0.119139	−	0.992878i	$-0.461987\pi$
$349$	83.1588			0.238277			0.119139	+	0.992878i	$0.461987\pi$
$350$	−77.1902	−	1.33558i	−0.220543	−	0.00381593i
$351$			73.4155i			0.209161i
$352$	−528.585	−	45.8388i	−1.50166	−	0.130224i
$353$	−277.478			−0.786057			−0.393028	−	0.919526i	$-0.628573\pi$
$353$	−277.478			−0.786057			−0.393028	+	0.919526i	$0.628573\pi$
$354$	3.24419	−	187.499i	0.00916437	−	0.529658i
$355$		−	350.167i		−	0.986387i
$356$	−156.918	−	5.43175i	−0.440781	−	0.0152577i
$357$	93.7993			0.262743
$358$	206.276	+	3.56906i	0.576189	+	0.00996945i
$359$			76.3214i			0.212594i	0.994334	+	0.106297i	$0.0338995\pi$
$359$			76.3214i			0.212594i	−0.994334	+	0.106297i	$0.966101\pi$
$360$	−7.83416	+	150.806i	−0.0217615	+	0.418904i
$361$	320.135			0.886800
$362$	1.50751	−	87.1273i	0.00416440	−	0.240683i
$363$			266.572i			0.734358i
$364$	−5.17275	+	149.436i	−0.0142109	+	0.410538i
$365$	−820.962			−2.24921
$366$	123.715	+	2.14057i	0.338019	+	0.00584855i
$367$			176.403i			0.480663i	0.970691	+	0.240332i	$0.0772562\pi$
$367$			176.403i			0.480663i	−0.970691	+	0.240332i	$0.922744\pi$
$368$	32.1890	−	464.398i	0.0874702	−	1.26195i
$369$	100.741			0.273010
$370$	−5.83529	+	337.253i	−0.0157710	+	0.911494i
$371$			57.4428i			0.154832i
$372$	−101.989	−	3.53037i	−0.274164	−	0.00949023i
$373$	57.5272			0.154229			0.0771143	−	0.997022i	$-0.475429\pi$
$373$	57.5272			0.154229			0.0771143	+	0.997022i	$0.475429\pi$
$374$	678.651	+	11.7423i	1.81458	+	0.0313965i
$375$		−	113.452i		−	0.302539i
$376$	−219.458	−	11.4006i	−0.583666	−	0.0303207i
$377$	772.823			2.04993
$378$	0.475666	−	27.4913i	0.00125838	−	0.0727284i
$379$			412.402i			1.08813i	0.839042	+	0.544066i	$0.183116\pi$
$379$			412.402i			1.08813i	−0.839042	+	0.544066i	$0.816884\pi$
$380$	5.56589	−	160.793i	0.0146471	−	0.423140i
$381$	−360.787			−0.946948
$382$	438.553	+	7.58803i	1.14805	+	0.0198640i
$383$			583.323i			1.52304i	0.648143	+	0.761518i	$0.275546\pi$
$383$			583.323i			1.52304i	−0.648143	+	0.761518i	$0.724454\pi$
$384$	220.079	+	26.7837i	0.573122	+	0.0697491i
$385$	276.015			0.716921
$386$	0.325331	−	18.8026i	0.000842826	−	0.0487115i
$387$			11.4972i			0.0297084i
$388$	687.360	+	23.7931i	1.77155	+	0.0613224i
$389$	64.4937			0.165794			0.0828968	−	0.996558i	$-0.473583\pi$
$389$	64.4937			0.165794			0.0828968	+	0.996558i	$0.473583\pi$
$390$	307.909	+	5.32758i	0.789511	+	0.0136605i
$391$			595.527i			1.52309i
$392$	2.90521	−	55.9246i	0.00741125	−	0.142665i
$393$	−117.380			−0.298677
$394$	11.3899	−	658.287i	0.0289085	−	1.67078i
$395$			98.3500i			0.248987i
$396$	6.88303	−	198.844i	0.0173814	−	0.502132i
$397$	−0.702051			−0.00176839			−0.000884195	−	1.00000i	$-0.500281\pi$
$397$	−0.702051			−0.00176839			−0.000884195		1.00000i	$0.500281\pi$
$398$	125.991	+	2.17995i	0.316561	+	0.00547727i
$399$			29.2945i			0.0734198i
$400$	232.877	+	16.1415i	0.582194	+	0.0403538i
$401$	61.3178			0.152912			0.0764561	−	0.997073i	$-0.475640\pi$
$401$	61.3178			0.152912			0.0764561	+	0.997073i	$0.475640\pi$
$402$	−5.71869	+	330.514i	−0.0142256	+	0.822175i
$403$			208.113i			0.516408i
$404$	−455.259	−	15.7589i	−1.12688	−	0.0390071i
$405$	−56.6284			−0.139823
$406$	−289.393	−	5.00720i	−0.712791	−	0.0123330i
$407$		−	444.417i		−	1.09193i
$408$	−283.241	−	14.7140i	−0.694217	−	0.0360637i
$409$	−109.489			−0.267700			−0.133850	−	0.991002i	$-0.542734\pi$
$409$	−109.489			−0.267700			−0.133850	+	0.991002i	$0.542734\pi$
$410$	7.31049	−	422.513i	0.0178305	−	1.03052i
$411$			23.2315i			0.0565242i
$412$	−12.9747	+	374.827i	−0.0314920	+	0.909774i
$413$	143.226			0.346795
$414$	174.541	+	3.01998i	0.421597	+	0.00729464i
$415$			311.138i			0.749731i
$416$	39.0614	−	450.432i	0.0938975	−	1.08277i
$417$	−277.790			−0.666164
$418$	−3.66724	+	211.950i	−0.00877331	+	0.507057i
$419$		−	312.627i		−	0.746128i	−0.927806	−	0.373064i	$-0.878307\pi$
$419$		−	312.627i		−	0.746128i	0.927806	−	0.373064i	$-0.121693\pi$
$420$	−115.266	−	3.98995i	−0.274443	−	0.00949989i
$421$	633.267			1.50420			0.752099	−	0.659050i	$-0.229042\pi$
$421$	633.267			1.50420			0.752099	+	0.659050i	$0.229042\pi$
$422$	−1.40460	−	0.0243030i	−0.00332844	−	5.75900e-5i
$423$		−	82.4078i		−	0.194818i
$424$	9.01085	−	173.457i	0.0212520	−	0.409096i
$425$	−298.633			−0.702667
$426$	3.33516	−	192.757i	0.00782901	−	0.452481i
$427$			94.5031i			0.221319i
$428$	−6.67103	+	192.720i	−0.0155865	+	0.450280i
$429$	−405.750			−0.945803
$430$	48.2199	+	0.834320i	0.112139	+	0.00194028i
$431$		−	46.7851i		−	0.108550i	−0.998526	−	0.0542750i	$-0.982715\pi$
$431$		−	46.7851i		−	0.108550i	0.998526	−	0.0542750i	$-0.0172848\pi$
$432$	−5.74882	+	82.9394i	−0.0133074	+	0.191989i
$433$	71.4224			0.164948			0.0824739	−	0.996593i	$-0.473718\pi$
$433$	71.4224			0.164948			0.0824739	+	0.996593i	$0.473718\pi$
$434$	1.34838	−	77.9303i	0.00310687	−	0.179563i
$435$			596.110i			1.37037i
$436$	−357.302	−	12.3681i	−0.819500	−	0.0283672i
$437$	−185.989			−0.425605
$438$	−451.915	−	7.81923i	−1.03177	−	0.0178521i
$439$			0.829943i			0.00189053i	1.00000		0.000945266i	$0.000300887\pi$
$439$			0.829943i			0.00189053i	−1.00000		0.000945266i	$0.999699\pi$
$440$	−833.466	−	43.2975i	−1.89424	−	0.0984033i
$441$	21.0000			0.0476190
$442$	−10.0062	+	578.311i	−0.0226384	+	1.30839i
$443$		−	770.065i		−	1.73830i	−0.494552	−	0.869148i	$-0.664668\pi$
$443$		−	770.065i		−	1.73830i	0.494552	−	0.869148i	$-0.335332\pi$
$444$	−6.42431	+	185.592i	−0.0144692	+	0.418000i
$445$	−246.981			−0.555014
$446$	−521.008	−	9.01469i	−1.16818	−	0.0202123i
$447$			226.594i			0.506922i
$448$	−17.5454	+	168.417i	−0.0391638	+	0.375930i
$449$	−80.0955			−0.178386			−0.0891932	−	0.996014i	$-0.528429\pi$
$449$	−80.0955			−0.178386			−0.0891932	+	0.996014i	$0.528429\pi$
$450$	−1.51440	+	87.5255i	−0.00336534	+	0.194501i
$451$			556.769i			1.23452i
$452$	−373.643	−	12.9337i	−0.826644	−	0.0286144i
$453$	304.589			0.672382
$454$	−444.226	−	7.68617i	−0.978470	−	0.0169299i
$455$			235.205i			0.516934i
$456$	4.59533	−	88.4589i	0.0100775	−	0.193989i
$457$	−178.912			−0.391493			−0.195747	−	0.980654i	$-0.562713\pi$
$457$	−178.912			−0.391493			−0.195747	+	0.980654i	$0.562713\pi$
$458$	4.31736	−	249.524i	0.00942656	−	0.544812i
$459$		−	106.358i		−	0.231718i
$460$	25.3320	−	731.818i	0.0550696	−	1.59091i
$461$	−320.864			−0.696017			−0.348009	−	0.937491i	$-0.613142\pi$
$461$	−320.864			−0.696017			−0.348009	+	0.937491i	$0.613142\pi$
$462$	151.938	+	2.62889i	0.328870	+	0.00569024i
$463$		−	597.651i		−	1.29082i	−0.763835	−	0.645411i	$-0.776686\pi$
$463$		−	597.651i		−	1.29082i	0.763835	−	0.645411i	$-0.223314\pi$
$464$	873.079	+	60.5161i	1.88164	+	0.130423i
$465$	−160.526			−0.345216
$466$	11.4982	−	664.542i	0.0246742	−	1.42606i
$467$		−	578.307i		−	1.23834i	−0.785255	−	0.619172i	$-0.787468\pi$
$467$		−	578.307i		−	1.23834i	0.785255	−	0.619172i	$-0.212532\pi$
$468$	169.444	+	5.86535i	0.362061	+	0.0125328i
$469$	−252.472			−0.538320
$470$	−345.624	−	5.98013i	−0.735370	−	0.0127237i
$471$			289.598i			0.614858i
$472$	−432.492	−	22.4674i	−0.916297	−	0.0476004i
$473$	−63.5420			−0.134338
$474$	−0.936732	+	54.1388i	−0.00197623	+	0.114217i
$475$		−	93.2663i		−	0.196350i
$476$	7.49386	−	216.491i	0.0157434	−	0.454812i
$477$	65.1340			0.136549
$478$	570.084	+	9.86383i	1.19264	+	0.0206356i
$479$			543.921i			1.13554i	0.823189	+	0.567768i	$0.192193\pi$
$479$			543.921i			1.13554i	−0.823189	+	0.567768i	$0.807807\pi$
$480$	347.436	+	30.1296i	0.723826	+	0.0627700i
$481$	378.708			0.787336
$482$	3.08744	−	178.440i	0.00640547	−	0.370207i
$483$			133.328i			0.276041i
$484$	615.253	+	21.2971i	1.27118	+	0.0440022i
$485$	1081.87			2.23066
$486$	−31.1722	−	0.539355i	−0.0641404	−	0.00110978i
$487$		−	25.1657i		−	0.0516750i	−0.999666	−	0.0258375i	$-0.991775\pi$
$487$		−	25.1657i		−	0.0516750i	0.999666	−	0.0258375i	$-0.00822524\pi$
$488$	14.8244	−	285.366i	0.0303778	−	0.584766i
$489$	382.076			0.781341
$490$	1.52392	−	88.0754i	0.00311003	−	0.179746i
$491$			876.015i			1.78414i	0.451894	+	0.892072i	$0.350749\pi$
$491$			876.015i			1.78414i	−0.451894	+	0.892072i	$0.649251\pi$
$492$	8.04842	−	232.511i	0.0163586	−	0.472584i
$493$	−1119.60			−2.27100
$494$	−180.612	−	3.12503i	−0.365612	−	0.00632597i
$495$		−	312.971i		−	0.632265i
$496$	−16.2963	+	235.110i	−0.0328554	+	0.474013i
$497$	147.243			0.296263
$498$	−2.96343	+	171.272i	−0.00595065	+	0.343921i
$499$			9.06767i			0.0181717i	0.999959	+	0.00908584i	$0.00289215\pi$
$499$			9.06767i			0.0181717i	−0.999959	+	0.00908584i	$0.997108\pi$
$500$	−261.850	−	9.06397i	−0.523699	−	0.0181279i
$501$	111.982			0.223517
$502$	166.897	+	2.88772i	0.332465	+	0.00575244i
$503$		−	433.976i		−	0.862774i	−0.902167	−	0.431387i	$-0.858024\pi$
$503$		−	433.976i		−	0.862774i	0.902167	−	0.431387i	$-0.141976\pi$
$504$	−63.4125	−	3.29420i	−0.125819	−	0.00653611i
$505$	−716.556			−1.41892
$506$	−16.6907	+	964.646i	−0.0329856	+	1.90642i
$507$		−	53.0416i		−	0.104619i
$508$	−28.8242	+	832.703i	−0.0567405	+	1.63918i
$509$	−335.775			−0.659675			−0.329838	−	0.944038i	$-0.606994\pi$
$509$	−335.775			−0.659675			−0.329838	+	0.944038i	$0.606994\pi$
$510$	−446.074	−	7.71816i	−0.874656	−	0.0151337i
$511$		−	345.208i		−	0.675553i
$512$	79.3998	−	505.806i	0.155078	−	0.987902i
$513$	33.2168			0.0647502
$514$	−1.03321	+	59.7149i	−0.00201014	+	0.116177i
$515$			589.960i			1.14555i
$516$	26.5357	+	0.918537i	0.0514257	+	0.00178011i
$517$	455.448			0.880944
$518$	−141.812	−	2.45369i	−0.273768	−	0.00473685i
$519$		−	410.748i		−	0.791423i
$520$	36.8958	−	710.235i	0.0709535	−	1.36584i
$521$	540.822			1.03805			0.519023	−	0.854760i	$-0.326296\pi$
$521$	540.822			1.03805			0.519023	+	0.854760i	$0.326296\pi$
$522$	−5.67763	+	328.141i	−0.0108767	+	0.628623i
$523$		−	337.109i		−	0.644568i	−0.946643	−	0.322284i	$-0.895549\pi$
$523$		−	337.109i		−	0.644568i	0.946643	−	0.322284i	$-0.104451\pi$
$524$	−9.37780	+	270.916i	−0.0178966	+	0.517015i
$525$	−66.8587			−0.127350
$526$	490.535	+	8.48745i	0.932577	+	0.0161358i
$527$		−	301.497i		−	0.572100i
$528$	−458.386	−	31.7723i	−0.868155	−	0.0601748i
$529$	−317.492			−0.600175
$530$	4.72661	−	273.176i	0.00891812	−	0.515427i
$531$		−	162.403i		−	0.305844i
$532$	67.6122	+	2.34041i	0.127091	+	0.00439927i
$533$	−474.449			−0.890147
$534$	−135.956	−	2.35237i	−0.254599	−	0.00440518i
$535$			303.331i			0.566975i
$536$	762.376	+	39.6045i	1.42234	+	0.0738889i
$537$	178.667			0.332712
$538$	−0.655458	+	37.8825i	−0.00121832	+	0.0704135i
$539$			116.062i			0.215328i
$540$	−4.52418	+	130.699i	−0.00837811	+	0.242036i
$541$	210.355			0.388827			0.194413	−	0.980920i	$-0.437720\pi$
$541$	210.355			0.388827			0.194413	+	0.980920i	$0.437720\pi$
$542$	557.772	+	9.65079i	1.02910	+	0.0178059i
$543$		−	75.4657i		−	0.138979i
$544$	−56.5890	+	652.549i	−0.104024	+	1.19954i
$545$	−562.376			−1.03188
$546$	−2.24020	+	129.473i	−0.00410293	+	0.237131i
$547$		−	228.588i		−	0.417894i	−0.977927	−	0.208947i	$-0.932996\pi$
$547$		−	228.588i		−	0.417894i	0.977927	−	0.208947i	$-0.0670036\pi$
$548$	53.6187	+	1.85602i	0.0978443	+	0.00338690i
$549$	107.156			0.195185
$550$	−483.732	−	8.36973i	−0.879513	−	0.0152177i
$551$		−	349.664i		−	0.634599i
$552$	20.9147	−	402.603i	0.0378890	−	0.729353i
$553$	−41.3554			−0.0747837
$554$	−7.13956	+	412.634i	−0.0128873	+	0.744826i
$555$			292.113i			0.526330i
$556$	−22.1934	+	641.145i	−0.0399161	+	1.15314i
$557$	129.632			0.232732			0.116366	−	0.993206i	$-0.462875\pi$
$557$	129.632			0.232732			0.116366	+	0.993206i	$0.462875\pi$
$558$	−88.3647	−	1.52892i	−0.158360	−	0.00274000i
$559$		−	54.1471i		−	0.0968643i
$560$	−18.4178	+	265.717i	−0.0328889	+	0.474495i
$561$	587.817			1.04780
$562$	−9.09192	+	525.471i	−0.0161778	+	0.935002i
$563$		−	718.440i		−	1.27609i	−0.769998	−	0.638046i	$-0.779743\pi$
$563$		−	718.440i		−	1.27609i	0.769998	−	0.638046i	$-0.220257\pi$
$564$	−190.199	−	6.58377i	−0.337232	−	0.0116733i
$565$	−588.096			−1.04088
$566$	1086.85	+	18.8052i	1.92024	+	0.0332247i
$567$		−	23.8118i		−	0.0419961i
$568$	−444.620	−	23.0974i	−0.782782	−	0.0406645i
$569$	736.365			1.29414			0.647069	−	0.762431i	$-0.275994\pi$
$569$	736.365			1.29414			0.647069	+	0.762431i	$0.275994\pi$
$570$	2.41046	−	139.314i	0.00422888	−	0.244410i
$571$		−	161.022i		−	0.282001i	−0.990010	−	0.141000i	$-0.954968\pi$
$571$		−	161.022i		−	0.282001i	0.990010	−	0.141000i	$-0.0450319\pi$
$572$	−32.4163	+	936.478i	−0.0566719	+	1.63720i
$573$	379.855			0.662923
$574$	177.663	+	3.07400i	0.309518	+	0.00535540i
$575$		−	424.483i		−	0.738230i
$576$	190.967	+	19.8946i	0.331539	+	0.0345393i
$577$	748.940			1.29799			0.648995	−	0.760793i	$-0.275190\pi$
$577$	748.940			1.29799			0.648995	+	0.760793i	$0.275190\pi$
$578$	4.49683	−	259.896i	0.00777998	−	0.449647i
$579$		−	16.2860i		−	0.0281278i
$580$	1375.83	+	47.6247i	2.37213	+	0.0821116i
$581$	−130.831			−0.225183
$582$	595.538	+	10.3042i	1.02326	+	0.0177049i
$583$			359.980i			0.617461i
$584$	−54.1516	+	1042.40i	−0.0927253	+	1.78494i
$585$	266.697			0.455893
$586$	0.664084	−	38.3810i	0.00113325	−	0.0654966i
$587$		−	261.696i		−	0.445819i	−0.974839	−	0.222910i	$-0.928444\pi$
$587$		−	261.696i		−	0.445819i	0.974839	−	0.222910i	$-0.0715555\pi$
$588$	1.67774	−	48.4684i	0.00285330	−	0.0824292i
$589$	94.1605			0.159865
$590$	−681.130	−	11.7852i	−1.15446	−	0.0199749i
$591$		−	570.178i		−	0.964769i
$592$	427.837	+	29.6548i	0.722698	+	0.0500926i
$593$	−284.492			−0.479750			−0.239875	−	0.970804i	$-0.577106\pi$
$593$	−284.492			−0.479750			−0.239875	+	0.970804i	$0.577106\pi$
$594$	2.98088	−	172.281i	0.00501832	−	0.290036i
$595$		−	340.746i		−	0.572682i
$596$	522.984	+	18.1032i	0.877489	+	0.0303745i
$597$	109.128			0.182794
$598$	−822.020	−	14.2229i	−1.37462	−	0.0237842i
$599$		−	358.608i		−	0.598678i	−0.954147	−	0.299339i	$-0.903234\pi$
$599$		−	358.608i		−	0.598678i	0.954147	−	0.299339i	$-0.0967662\pi$
$600$	201.889	+	10.4879i	0.336482	+	0.0174798i
$601$	−404.112			−0.672399			−0.336200	−	0.941791i	$-0.609142\pi$
$601$	−404.112			−0.672399			−0.336200	+	0.941791i	$0.609142\pi$
$602$	−0.350825	+	20.2761i	−0.000582765	+	0.0336812i
$603$			286.277i			0.474754i
$604$	24.3344	−	702.997i	0.0402887	−	1.16390i
$605$	968.378			1.60063
$606$	−394.443	−	6.82482i	−0.650896	−	0.0112621i
$607$			608.215i			1.00200i	0.865447	+	0.501001i	$0.167035\pi$
$607$			608.215i			1.00200i	−0.865447	+	0.501001i	$0.832965\pi$
$608$	−203.798	−	17.6733i	−0.335194	−	0.0290679i
$609$	−250.659			−0.411592
$610$	7.77607	−	449.421i	0.0127476	−	0.736756i
$611$			388.108i			0.635202i
$612$	−245.477	−	8.49724i	−0.401107	−	0.0138844i
$613$	−741.906			−1.21029			−0.605143	−	0.796117i	$-0.706884\pi$
$613$	−741.906			−1.21029			−0.605143	+	0.796117i	$0.706884\pi$
$614$	−1086.08	−	18.7918i	−1.76886	−	0.0306055i
$615$		−	365.961i		−	0.595059i
$616$	18.2062	−	350.466i	0.0295556	−	0.568938i
$617$	788.372			1.27775			0.638875	−	0.769310i	$-0.279400\pi$
$617$	788.372			1.27775			0.638875	+	0.769310i	$0.279400\pi$
$618$	−5.61905	+	324.755i	−0.00909232	+	0.525494i
$619$		−	1053.85i		−	1.70251i	−0.524754	−	0.851254i	$-0.675843\pi$
$619$		−	1053.85i		−	1.70251i	0.524754	−	0.851254i	$-0.324157\pi$
$620$	−12.8248	+	370.496i	−0.0206852	+	0.597575i
$621$	151.180			0.243446
$622$	−366.253	−	6.33707i	−0.588832	−	0.0101882i
$623$		−	103.854i		−	0.166699i
$624$	27.0747	−	390.612i	0.0433889	−	0.625981i
$625$	−776.883			−1.24301
$626$	17.7793	−	1027.56i	0.0284014	−	1.64147i
$627$			183.581i			0.292793i
$628$	668.398	+	23.1367i	1.06433	+	0.0368419i
$629$	−548.642			−0.872245
$630$	−99.8681	−	1.72796i	−0.158521	−	0.00274279i
$631$		−	729.494i		−	1.15609i	−0.816004	−	0.578046i	$-0.803815\pi$
$631$		−	729.494i		−	1.15609i	0.816004	−	0.578046i	$-0.196185\pi$
$632$	124.879	+	6.48728i	0.197593	+	0.0102647i
$633$	−1.21660			−0.00192196
$634$	−19.3665	+	1119.30i	−0.0305465	+	1.76545i
$635$			1310.63i			2.06399i
$636$	5.20371	−	150.330i	0.00818194	−	0.236369i
$637$	−98.9018			−0.155262
$638$	−1813.56	−	31.3789i	−2.84256	−	0.0491832i
$639$		−	166.957i		−	0.261279i
$640$	97.2973	−	799.482i	0.152027	−	1.24919i
$641$	258.186			0.402787			0.201393	−	0.979510i	$-0.435453\pi$
$641$	258.186			0.402787			0.201393	+	0.979510i	$0.435453\pi$
$642$	−2.88907	+	166.975i	−0.00450011	+	0.260086i
$643$			844.440i			1.31328i	0.754203	+	0.656641i	$0.228023\pi$
$643$			844.440i			1.31328i	−0.754203	+	0.656641i	$0.771977\pi$
$644$	307.723	+	10.6519i	0.477831	+	0.0165402i
$645$	41.7659			0.0647533
$646$	261.656	+	4.52729i	0.405041	+	0.00700819i
$647$			94.5538i			0.146142i	0.997327	+	0.0730709i	$0.0232799\pi$
$647$			94.5538i			0.146142i	−0.997327	+	0.0730709i	$0.976720\pi$
$648$	−3.73527	+	71.9030i	−0.00576431	+	0.110961i
$649$	897.563			1.38299
$650$	7.13224	−	412.211i	0.0109727	−	0.634170i
$651$		−	67.4997i		−	0.103686i
$652$	30.5250	−	881.838i	0.0468174	−	1.35251i
$653$	−239.621			−0.366954			−0.183477	−	0.983024i	$-0.558735\pi$
$653$	−239.621			−0.366954			−0.183477	+	0.983024i	$0.558735\pi$
$654$	−309.572	−	5.35634i	−0.473351	−	0.00819012i
$655$			426.408i			0.651005i
$656$	−535.997	−	37.1518i	−0.817069	−	0.0566338i
$657$	−391.429			−0.595782
$658$	2.51459	−	145.332i	0.00382157	−	0.220869i
$659$			150.618i			0.228555i	0.993449	+	0.114278i	$0.0364553\pi$
$659$			150.618i			0.228555i	−0.993449	+	0.114278i	$0.963545\pi$
$660$	−722.343	−	25.0040i	−1.09446	−	0.0378849i
$661$	−575.893			−0.871246			−0.435623	−	0.900129i	$-0.643472\pi$
$661$	−575.893			−0.871246			−0.435623	+	0.900129i	$0.643472\pi$
$662$	759.474	+	13.1407i	1.14724	+	0.0198500i
$663$			500.907i			0.755515i
$664$	395.063	+	20.5230i	0.594975	+	0.0309082i
$665$	106.418			0.160028
$666$	−2.78222	+	160.800i	−0.00417751	+	0.241441i
$667$		−	1591.42i		−	2.38594i
$668$	8.94653	−	258.457i	0.0133930	−	0.386912i
$669$	−451.273			−0.674549
$670$	1200.66	+	20.7744i	1.79203	+	0.0310065i
$671$			592.227i			0.882604i
$672$	−12.6693	+	146.094i	−0.0188531	+	0.217402i
$673$	−614.833			−0.913571			−0.456785	−	0.889577i	$-0.650999\pi$
$673$	−614.833			−0.913571			−0.456785	+	0.889577i	$0.650999\pi$
$674$	−4.06954	+	235.201i	−0.00603789	+	0.348962i
$675$			75.8106i			0.112312i
$676$	−122.421	−	4.23763i	−0.181096	−	0.00626868i
$677$	−308.666			−0.455933			−0.227966	−	0.973669i	$-0.573208\pi$
$677$	−308.666			−0.455933			−0.227966	+	0.973669i	$0.573208\pi$
$678$	−323.730	−	5.60130i	−0.477477	−	0.00826151i
$679$			454.918i			0.669982i
$680$	−53.4517	+	1028.93i	−0.0786054	+	1.51313i
$681$	−384.768			−0.565005
$682$	8.44998	−	488.370i	0.0123900	−	0.716085i
$683$			143.442i			0.210018i	0.994471	+	0.105009i	$0.0334871\pi$
$683$			143.442i			0.210018i	−0.994471	+	0.105009i	$0.966513\pi$
$684$	2.65378	−	76.6651i	0.00387979	−	0.112083i
$685$	84.3932			0.123202
$686$	37.0350	+	0.640794i	0.0539868	+	0.000934103i
$687$		−	216.126i		−	0.314594i
$688$	4.24000	−	61.1715i	0.00616279	−	0.0889120i
$689$	−306.755			−0.445218
$690$	10.9707	−	634.057i	0.0158996	−	0.918924i
$691$		−	366.656i		−	0.530616i	−0.964164	−	0.265308i	$-0.914526\pi$
$691$		−	366.656i		−	0.530616i	0.964164	−	0.265308i	$-0.0854737\pi$
$692$	−948.015	−	32.8157i	−1.36996	−	0.0474216i
$693$	131.602			0.189902
$694$	−605.321	−	10.4735i	−0.872220	−	0.0150915i
$695$			1009.13i			1.45199i
$696$	756.902	+	39.3201i	1.08750	+	0.0564944i
$697$	687.343			0.986145
$698$	2.87726	−	166.293i	0.00412215	−	0.238242i
$699$		−	575.597i		−	0.823457i
$700$	−5.34151	+	154.311i	−0.00763073	+	0.220444i
$701$	125.995			0.179736			0.0898681	−	0.995954i	$-0.471355\pi$
$701$	125.995			0.179736			0.0898681	+	0.995954i	$0.471355\pi$
$702$	146.809	+	2.54015i	0.209130	+	0.00361845i
$703$		−	171.347i		−	0.243736i
$704$	−109.953	+	1055.43i	−0.156183	+	1.49918i
$705$	−299.364			−0.424630
$706$	−9.60064	+	554.873i	−0.0135986	+	0.785939i
$707$		−	301.306i		−	0.426175i
$708$	−374.830	−	12.9748i	−0.529421	−	0.0183260i
$709$	−159.688			−0.225230			−0.112615	−	0.993639i	$-0.535923\pi$
$709$	−159.688			−0.225230			−0.112615	+	0.993639i	$0.535923\pi$
$710$	−700.230	−	12.1157i	−0.986239	−	0.0170643i
$711$			46.8926i			0.0659530i
$712$	−16.2912	+	313.601i	−0.0228809	+	0.440451i
$713$	428.552			0.601055
$714$	3.24542	−	187.571i	0.00454541	−	0.262704i
$715$			1473.97i			2.06150i
$716$	14.2741	−	412.366i	0.0199359	−	0.575930i
$717$	493.781			0.688677
$718$	152.620	+	2.64069i	0.212563	+	0.00367785i
$719$			1368.60i			1.90348i	0.306899	+	0.951742i	$0.400708\pi$
$719$			1368.60i			1.90348i	−0.306899	+	0.951742i	$0.599292\pi$
$720$	301.295	+	20.8838i	0.418465	+	0.0290053i
$721$	−248.073			−0.344068
$722$	11.0766	−	640.174i	0.0153415	−	0.886668i
$723$		−	154.556i		−	0.213771i
$724$	−174.176	−	6.02914i	−0.240575	−	0.00832755i
$725$	798.036			1.10074
$726$	533.064	+	9.22329i	0.734248	+	0.0127043i
$727$		−	510.747i		−	0.702540i	−0.936274	−	0.351270i	$-0.885750\pi$
$727$		−	510.747i		−	0.702540i	0.936274	−	0.351270i	$-0.114250\pi$
$728$	298.648	+	15.5144i	0.410231	+	0.0213110i
$729$	−27.0000			−0.0370370
$730$	−28.4050	+	1641.68i	−0.0389109	+	2.24887i
$731$			78.4440i			0.107311i
$732$	8.56099	−	247.319i	0.0116953	−	0.337867i
$733$	−774.969			−1.05726			−0.528628	−	0.848853i	$-0.677293\pi$
$733$	−774.969			−1.05726			−0.528628	+	0.848853i	$0.677293\pi$
$734$	352.754	+	6.10350i	0.480592	+	0.00831539i
$735$		−	76.2869i		−	0.103792i
$736$	−927.544	−	80.4365i	−1.26025	−	0.109289i
$737$	−1582.18			−2.14679
$738$	3.48559	−	201.451i	0.00472302	−	0.272969i
$739$			1349.26i			1.82579i	0.408194	+	0.912895i	$0.366159\pi$
$739$			1349.26i			1.82579i	−0.408194	+	0.912895i	$0.633841\pi$
$740$	674.203	+	23.3376i	0.911085	+	0.0315374i
$741$	−156.438			−0.211118
$742$	114.868	+	1.98750i	0.154809	+	0.00267857i
$743$		−	853.994i		−	1.14939i	−0.818369	−	0.574693i	$-0.805122\pi$
$743$		−	853.994i		−	1.14939i	0.818369	−	0.574693i	$-0.194878\pi$
$744$	−10.5885	+	203.825i	−0.0142318	+	0.273959i
$745$	823.151			1.10490
$746$	1.99042	−	115.037i	0.00266813	−	0.154205i
$747$			148.348i			0.198592i
$748$	46.9622	−	1356.69i	0.0627837	−	1.81376i
$749$	−127.548			−0.170292
$750$	−226.870	−	3.92540i	−0.302494	−	0.00523387i
$751$			509.524i			0.678460i	0.940703	+	0.339230i	$0.110167\pi$
$751$			509.524i			0.678460i	−0.940703	+	0.339230i	$0.889833\pi$
$752$	−30.3909	+	438.456i	−0.0404135	+	0.583054i
$753$	144.559			0.191977
$754$	26.7394	−	1545.42i	0.0354634	−	2.04962i
$755$		−	1106.48i		−	1.46554i
$756$	−54.9580	−	1.90238i	−0.0726958	−	0.00251638i
$757$	1373.83			1.81484			0.907418	−	0.420228i	$-0.138050\pi$
$757$	1373.83			1.81484			0.907418	+	0.420228i	$0.138050\pi$
$758$	824.681	+	14.2690i	1.08797	+	0.0188245i
$759$			835.533i			1.10083i
$760$	−321.346	−	16.6935i	−0.422823	−	0.0219651i
$761$	−1165.32			−1.53130			−0.765652	−	0.643255i	$-0.777583\pi$
$761$	−1165.32			−1.53130			−0.765652	+	0.643255i	$0.777583\pi$
$762$	−12.4831	+	721.466i	−0.0163820	+	0.946806i
$763$		−	236.475i		−	0.309927i
$764$	30.3476	−	876.713i	0.0397220	−	1.14753i
$765$	−386.370			−0.505058
$766$	1166.47	+	20.1828i	1.52281	+	0.0263483i
$767$			764.855i			0.997204i
$768$	61.1739	−	439.165i	0.0796536	−	0.571829i
$769$	−686.335			−0.892503			−0.446251	−	0.894908i	$-0.647241\pi$
$769$	−686.335			−0.892503			−0.446251	+	0.894908i	$0.647241\pi$
$770$	9.55001	−	551.947i	0.0124026	−	0.716814i
$771$			51.7223i			0.0670848i
$772$	−37.5884	−	1.30113i	−0.0486896	−	0.00168540i
$773$	244.058			0.315729			0.157864	−	0.987461i	$-0.449539\pi$
$773$	244.058			0.315729			0.157864	+	0.987461i	$0.449539\pi$
$774$	22.9909	+	0.397798i	0.0297040	+	0.000513951i
$775$			214.902i			0.277293i
$776$	71.3614	−	1373.69i	0.0919606	−	1.77022i
$777$	−122.831			−0.158084
$778$	2.23146	−	128.968i	0.00286820	−	0.165769i
$779$			214.664i			0.275564i
$780$	21.3071	−	615.542i	0.0273168	−	0.789157i
$781$	922.733			1.18148
$782$	1190.88	+	20.6050i	1.52286	+	0.0263491i
$783$			284.221i			0.362990i
$784$	−111.732	−	7.74452i	−0.142515	−	0.00987822i
$785$	1052.03			1.34016
$786$	−4.06131	+	234.725i	−0.00516707	+	0.298633i
$787$			959.027i			1.21859i	0.792945	+	0.609293i	$0.208547\pi$
$787$			959.027i			1.21859i	−0.792945	+	0.609293i	$0.791453\pi$
$788$	−1315.98	−	45.5530i	−1.67003	−	0.0578083i
$789$	424.880			0.538504
$790$	196.671	+	3.40288i	0.248950	+	0.00430744i
$791$		−	247.290i		−	0.312629i
$792$	−397.391	−	20.6439i	−0.501756	−	0.0260656i
$793$	−504.665			−0.636399
$794$	−0.0242907	+	1.40389i	−3.05928e−5	+	0.00176812i
$795$		−	236.613i		−	0.297626i
$796$	8.71850	−	251.869i	0.0109529	−	0.316419i
$797$	24.5322			0.0307807			0.0153903	−	0.999882i	$-0.495101\pi$
$797$	24.5322			0.0307807			0.0153903	+	0.999882i	$0.495101\pi$
$798$	58.5802	+	1.01358i	0.0734088	+	0.00127015i
$799$		−	562.260i		−	0.703705i
$800$	40.3357	−	465.127i	0.0504196	−	0.581408i
$801$	−117.759			−0.147015
$802$	2.12157	−	122.617i	0.00264535	−	0.152889i
$803$		−	2163.33i		−	2.69406i
$804$	660.732	+	22.8714i	0.821806	+	0.0284470i
$805$	484.342			0.601667
$806$	416.163	+	7.20062i	0.516331	+	0.00893377i
$807$			32.8121i			0.0406594i
$808$	−47.2649	+	909.837i	−0.0584961	+	1.12604i
$809$	673.148			0.832074			0.416037	−	0.909348i	$-0.363419\pi$
$809$	673.148			0.832074			0.416037	+	0.909348i	$0.363419\pi$
$810$	−1.95932	+	113.240i	−0.00241891	+	0.139802i
$811$			386.219i			0.476226i	0.971237	+	0.238113i	$0.0765288\pi$
$811$			386.219i			0.476226i	−0.971237	+	0.238113i	$0.923471\pi$
$812$	−20.0258	+	578.527i	−0.0246623	+	0.712471i
$813$	483.117			0.594239
$814$	−888.701	−	15.3767i	−1.09177	−	0.0188903i
$815$		−	1387.97i		−	1.70303i
$816$	−39.2236	+	565.887i	−0.0480681	+	0.693489i
$817$	−24.4989			−0.0299864
$818$	−3.78830	+	218.946i	−0.00463117	+	0.267660i
$819$			112.144i			0.136928i
$820$	−844.646	−	29.2376i	−1.03006	−	0.0356556i
$821$	5.93033			0.00722330			0.00361165	−	0.999993i	$-0.498850\pi$
$821$	5.93033			0.00722330			0.00361165	+	0.999993i	$0.498850\pi$
$822$	46.4560	+	0.803800i	0.0565158	+	0.000977859i
$823$		−	365.439i		−	0.444033i	−0.975043	−	0.222016i	$-0.928736\pi$
$823$		−	365.439i		−	0.444033i	0.975043	−	0.222016i	$-0.0712638\pi$
$824$	749.093	+	38.9144i	0.909093	+	0.0472262i
$825$	−418.987			−0.507863
$826$	4.95558	−	286.410i	0.00599949	−	0.346743i
$827$			1236.80i			1.49552i	0.663968	+	0.747761i	$0.268871\pi$
$827$			1236.80i			1.49552i	−0.663968	+	0.747761i	$0.731129\pi$
$828$	12.0781	−	348.926i	0.0145871	−	0.421408i
$829$	899.957			1.08559			0.542797	−	0.839864i	$-0.317365\pi$
$829$	899.957			1.08559			0.542797	+	0.839864i	$0.317365\pi$
$830$	622.183	+	10.7653i	0.749618	+	0.0129702i
$831$			357.405i			0.430090i
$832$	−899.377	−	93.6958i	−1.08098	−	0.112615i
$833$	143.281			0.172006
$834$	−9.61144	+	555.497i	−0.0115245	+	0.666064i
$835$		−	406.799i		−	0.487184i
$836$	423.709	+	14.6668i	0.506829	+	0.0175440i
$837$	−76.5375			−0.0914427
$838$	−625.161	−	10.8168i	−0.746016	−	0.0129079i
$839$			473.095i			0.563880i	0.959432	+	0.281940i	$0.0909779\pi$
$839$			473.095i			0.563880i	−0.959432	+	0.281940i	$0.909022\pi$
$840$	−11.9669	+	230.359i	−0.0142463	+	0.274237i
$841$	2150.91			2.55756
$842$	21.9108	−	1266.35i	0.0260224	−	1.50397i
$843$			455.140i			0.539905i
$844$	−0.0971973	+	2.80794i	−0.000115163	+	0.00332694i
$845$	−192.685			−0.228029
$846$	−164.791	−	2.85128i	−0.194788	−	0.00337031i
$847$			407.195i			0.480750i
$848$	−346.550	−	24.0205i	−0.408667	−	0.0283261i
$849$	941.384			1.10881
$850$	−10.3326	+	597.177i	−0.0121560	+	0.702562i
$851$		−	779.849i		−	0.916391i
$852$	−385.341	−	13.3386i	−0.452278	−	0.0156557i
$853$	−456.925			−0.535668			−0.267834	−	0.963465i	$-0.586308\pi$
$853$	−456.925			−0.535668			−0.267834	+	0.963465i	$0.586308\pi$
$854$	188.978	+	3.26977i	0.221286	+	0.00382877i
$855$		−	120.667i		−	0.141131i
$856$	385.151	+	20.0081i	0.449943	+	0.0233739i
$857$	−1460.48			−1.70417			−0.852087	−	0.523401i	$-0.824663\pi$
$857$	−1460.48			−1.70417			−0.852087	+	0.523401i	$0.824663\pi$
$858$	−14.0388	+	811.378i	−0.0163622	+	0.945662i
$859$		−	329.072i		−	0.383087i	−0.981484	−	0.191544i	$-0.938651\pi$
$859$		−	329.072i		−	0.383087i	0.981484	−	0.191544i	$-0.0613493\pi$
$860$	3.33678	−	96.3964i	0.00387998	−	0.112089i
$861$	153.884			0.178727
$862$	−93.5562	−	1.61875i	−0.108534	−	0.00187790i
$863$			528.421i			0.612307i	0.951982	+	0.306154i	$0.0990421\pi$
$863$			528.421i			0.612307i	−0.951982	+	0.306154i	$0.900958\pi$
$864$	165.655	+	14.3656i	0.191731	+	0.0166268i
$865$	−1492.13			−1.72501
$866$	2.47119	−	142.823i	0.00285357	−	0.164923i
$867$		−	225.110i		−	0.259643i
$868$	−155.791	−	5.39272i	−0.179482	−	0.00621281i
$869$	−259.164			−0.298232
$870$	1192.04	+	20.6252i	1.37016	+	0.0237071i
$871$		−	1348.25i		−	1.54793i
$872$	−37.0950	+	714.069i	−0.0425401	+	0.818887i
$873$	515.828			0.590869
$874$	−6.43516	+	371.923i	−0.00736289	+	0.425541i
$875$		−	173.301i		−	0.198058i
$876$	−31.2722	+	903.425i	−0.0356989	+	1.03131i
$877$	532.559			0.607250			0.303625	−	0.952792i	$-0.401803\pi$
$877$	532.559			0.607250			0.303625	+	0.952792i	$0.401803\pi$
$878$	1.65964	+	0.0287157i	0.00189025	+	3.27058e-5i
$879$		−	33.2439i		−	0.0378201i
$880$	−115.420	+	1665.18i	−0.131159	+	1.89225i
$881$	−326.517			−0.370621			−0.185310	−	0.982680i	$-0.559329\pi$
$881$	−326.517			−0.370621			−0.185310	+	0.982680i	$0.559329\pi$
$882$	0.726593	−	41.9937i	0.000823801	−	0.0476119i
$883$			31.0138i			0.0351232i	0.999846	+	0.0175616i	$0.00559032\pi$
$883$			31.0138i			0.0351232i	−0.999846	+	0.0175616i	$0.994410\pi$
$884$	1156.10	+	40.0187i	1.30781	+	0.0452700i
$885$	−589.964			−0.666626
$886$	−1539.90	−	26.6440i	−1.73804	−	0.0300722i
$887$		−	414.448i		−	0.467247i	−0.972327	−	0.233623i	$-0.924942\pi$
$887$		−	414.448i		−	0.467247i	0.972327	−	0.233623i	$-0.0750583\pi$
$888$	370.906	+	19.2681i	0.417687	+	0.0216983i
$889$	−551.111			−0.619923
$890$	−8.54547	+	493.889i	−0.00960165	+	0.554931i
$891$		−	149.222i		−	0.167477i
$892$	−36.0534	+	1041.55i	−0.0404186	+	1.16765i
$893$	175.600			0.196640
$894$	453.121	+	7.84008i	0.506846	+	0.00876966i
$895$		−	649.044i		−	0.725189i
$896$	336.176	+	40.9127i	0.375196	+	0.0456615i
$897$	−711.997			−0.793753
$898$	−2.77127	+	160.167i	−0.00308605	+	0.178360i
$899$			805.688i			0.896204i
$900$	174.972	+	6.05670i	0.194414	+	0.00672967i
$901$	444.402			0.493232
$902$	1113.37	+	19.2640i	1.23434	+	0.0213570i
$903$			17.5622i			0.0194487i
$904$	−38.7915	+	746.726i	−0.0429109	+	0.826025i
$905$	−274.145			−0.302923
$906$	10.5387	−	609.087i	0.0116321	−	0.672282i
$907$			388.080i			0.427872i	0.976848	+	0.213936i	$0.0686283\pi$
$907$			388.080i			0.427872i	−0.976848	+	0.213936i	$0.931372\pi$
$908$	−30.7401	+	888.052i	−0.0338547	+	0.978031i
$909$	−341.649			−0.375851
$910$	470.339	+	8.13801i	0.516857	+	0.00894286i
$911$		−	891.807i		−	0.978932i	−0.872023	−	0.489466i	$-0.837192\pi$
$911$		−	891.807i		−	0.978932i	0.872023	−	0.489466i	$-0.162808\pi$
$912$	−176.732	−	12.2499i	−0.193786	−	0.0134319i
$913$	−819.886			−0.898013
$914$	−6.19031	+	357.771i	−0.00677277	+	0.391435i
$915$		−	389.268i		−	0.425430i
$916$	−498.824	−	17.2669i	−0.544567	−	0.0188503i
$917$	−179.301			−0.195530
$918$	−212.685	−	3.67996i	−0.231683	−	0.00400868i
$919$			390.619i			0.425048i	0.977156	+	0.212524i	$0.0681684\pi$
$919$			390.619i			0.425048i	−0.977156	+	0.212524i	$0.931832\pi$
$920$	−1462.54	−	75.9771i	−1.58972	−	0.0825838i
$921$	−940.713			−1.02140
$922$	−11.1018	+	641.632i	−0.0120410	+	0.695913i
$923$			786.304i			0.851900i
$924$	10.5140	−	303.739i	0.0113788	−	0.328722i
$925$	391.064			0.422771
$926$	−1195.12	−	20.6785i	−1.29063	−	0.0223310i
$927$			281.289i			0.303440i
$928$	151.222	−	1743.80i	0.162955	−	1.87910i
$929$	−241.450			−0.259903			−0.129952	−	0.991520i	$-0.541482\pi$
$929$	−241.450			−0.259903			−0.129952	+	0.991520i	$0.541482\pi$
$930$	−5.55413	+	321.003i	−0.00597218	+	0.345165i
$931$			44.7481i			0.0480645i
$932$	−1328.49	−	45.9859i	−1.42542	−	0.0493410i
$933$	−317.232			−0.340013
$934$	−1156.44	−	20.0092i	−1.23816	−	0.0214231i
$935$		−	2135.37i		−	2.28382i
$936$	17.5917	−	338.635i	0.0187945	−	0.361790i
$937$	−753.075			−0.803709			−0.401855	−	0.915703i	$-0.631634\pi$
$937$	−753.075			−0.803709			−0.401855	+	0.915703i	$0.631634\pi$
$938$	−8.73545	+	504.869i	−0.00931285	+	0.538240i
$939$		−	890.028i		−	0.947847i
$940$	−23.9169	+	690.937i	−0.0254435	+	0.735040i
$941$	1372.35			1.45840			0.729199	−	0.684302i	$-0.239893\pi$
$941$	1372.35			1.45840			0.729199	+	0.684302i	$0.239893\pi$
$942$	579.109	+	10.0200i	0.614766	+	0.0106369i
$943$			977.000i			1.03606i
$944$	−59.8922	+	864.077i	−0.0634451	+	0.915336i
$945$	−86.5012			−0.0915357
$946$	−2.19853	+	127.065i	−0.00232403	+	0.134318i
$947$		−	498.081i		−	0.525957i	−0.964802	−	0.262979i	$-0.915295\pi$
$947$		−	498.081i		−	0.525957i	0.964802	−	0.262979i	$-0.0847048\pi$
$948$	108.229	+	3.74637i	0.114166	+	0.00395186i
$949$	1843.48			1.94255
$950$	−186.505	−	3.22698i	−0.196321	−	0.00339682i
$951$			969.483i			1.01944i
$952$	−432.657	−	22.4760i	−0.454472	−	0.0236092i
$953$	−117.526			−0.123322			−0.0616610	−	0.998097i	$-0.519640\pi$
$953$	−117.526			−0.123322			−0.0616610	+	0.998097i	$0.519640\pi$
$954$	2.25361	−	130.248i	0.00236228	−	0.136529i
$955$		−	1379.90i		−	1.44493i
$956$	39.4494	−	1139.66i	0.0412651	−	1.19211i
$957$	−1570.82			−1.64140
$958$	1087.68	+	18.8195i	1.13537	+	0.0196446i
$959$			35.4867i			0.0370038i
$960$	72.2714	−	693.726i	0.0752827	−	0.722631i
$961$	744.037			0.774233
$962$	13.1032	−	757.304i	0.0136208	−	0.787218i
$963$			144.626i			0.150183i
$964$	−356.719	−	12.3479i	−0.370041	−	0.0128090i
$965$	−59.1623			−0.0613081
$966$	266.616	+	4.61310i	0.276000	+	0.00477546i
$967$			1016.54i			1.05123i	0.850723	+	0.525614i	$0.176164\pi$
$967$			1016.54i			1.05123i	−0.850723	+	0.525614i	$0.823836\pi$
$968$	63.8753	−	1229.58i	0.0659869	−	1.27023i
$969$	226.635			0.233886
$970$	37.4324	−	2163.42i	0.0385901	−	2.23033i
$971$		−	760.606i		−	0.783323i	−0.920109	−	0.391661i	$-0.871900\pi$
$971$		−	760.606i		−	0.783323i	0.920109	−	0.391661i	$-0.128100\pi$
$972$	−2.15710	+	62.3165i	−0.00221924	+	0.0641116i
$973$	−424.332			−0.436107
$974$	−50.3239	−	0.870724i	−0.0516672	−	0.000893967i
$975$		−	357.038i		−	0.366193i
$976$	−570.133	−	39.5179i	−0.584153	−	0.0404896i
$977$	−1823.13			−1.86605			−0.933026	−	0.359809i	$-0.882842\pi$
$977$	−1823.13			−1.86605			−0.933026	+	0.359809i	$0.882842\pi$
$978$	13.2197	−	764.037i	0.0135171	−	0.781224i
$979$		−	650.825i		−	0.664786i
$980$	−176.072	−	6.09475i	−0.179665	−	0.00621914i
$981$	−268.137			−0.273330
$982$	1751.77	+	30.3098i	1.78388	+	0.0308654i
$983$			1400.51i			1.42473i	0.701809	+	0.712365i	$0.252376\pi$
$983$			1400.51i			1.42473i	−0.701809	+	0.712365i	$0.747624\pi$
$984$	−464.674	−	24.1392i	−0.472230	−	0.0245317i
$985$	−2071.29			−2.10284
$986$	−38.7379	+	2238.87i	−0.0392879	+	2.27066i
$987$		−	125.880i		−	0.127538i
$988$	−12.4982	+	361.062i	−0.0126500	+	0.365448i
$989$	−111.502			−0.112742
$990$	−625.849	−	10.8287i	−0.632170	−	0.0109381i
$991$		−	508.288i		−	0.512904i	−0.966557	−	0.256452i	$-0.917446\pi$
$991$		−	508.288i		−	0.512904i	0.966557	−	0.256452i	$-0.0825536\pi$
$992$	469.586	+	40.7225i	0.473373	+	0.0410509i
$993$	657.822			0.662459
$994$	5.09454	−	294.441i	0.00512529	−	0.296218i
$995$		−	396.430i		−	0.398422i
$996$	342.391	+	11.8519i	0.343766	+	0.0118995i
$997$	1357.91			1.36199			0.680997	−	0.732286i	$-0.261547\pi$
$997$	1357.91			1.36199			0.680997	+	0.732286i	$0.261547\pi$
$998$	18.1326	+	0.313738i	0.0181690	+	0.000314367i
$999$			139.277i			0.139417i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	84.3.g.a.43.5	✓	12
3.2	odd	2		252.3.g.b.127.8		12
4.3	odd	2	inner	84.3.g.a.43.6	yes	12
7.6	odd	2		588.3.g.d.295.5		12
8.3	odd	2		1344.3.m.e.127.5		12
8.5	even	2		1344.3.m.e.127.11		12
12.11	even	2		252.3.g.b.127.7		12
28.27	even	2		588.3.g.d.295.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.3.g.a.43.5	✓	12	1.1	even	1	trivial
84.3.g.a.43.6	yes	12	4.3	odd	2	inner
252.3.g.b.127.7		12	12.11	even	2
252.3.g.b.127.8		12	3.2	odd	2
588.3.g.d.295.5		12	7.6	odd	2
588.3.g.d.295.6		12	28.27	even	2
1344.3.m.e.127.5		12	8.3	odd	2
1344.3.m.e.127.11		12	8.5	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 84 = 2^{2} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	84.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0345996 - 1.99970i) q^{2} -1.73205i q^{3} +(-3.99761 - 0.138378i) q^{4} -6.29204 q^{5} +(-3.46358 - 0.0599283i) q^{6} -2.64575i q^{7} +(-0.415030 + 7.98923i) q^{8} -3.00000 q^{9} +O(q^{10})\)	\(q+(0.0345996 - 1.99970i) q^{2} -1.73205i q^{3} +(-3.99761 - 0.138378i) q^{4} -6.29204 q^{5} +(-3.46358 - 0.0599283i) q^{6} -2.64575i q^{7} +(-0.415030 + 7.98923i) q^{8} -3.00000 q^{9} +(-0.217702 + 12.5822i) q^{10} -16.5803i q^{11} +(-0.239677 + 6.92406i) q^{12} +14.1288 q^{13} +(-5.29071 - 0.0915421i) q^{14} +10.8981i q^{15} +(15.9617 + 1.10636i) q^{16} -20.4687 q^{17} +(-0.103799 + 5.99910i) q^{18} -6.39258i q^{19} +(25.1531 + 0.870679i) q^{20} -4.58258 q^{21} +(-33.1556 - 0.573671i) q^{22} -29.0945i q^{23} +(13.8377 + 0.718853i) q^{24} +14.5898 q^{25} +(0.488852 - 28.2534i) q^{26} +5.19615i q^{27} +(-0.366113 + 10.5767i) q^{28} +54.6984 q^{29} +(21.7930 + 0.377071i) q^{30} +14.7296i q^{31} +(2.76466 - 31.8803i) q^{32} -28.7179 q^{33} +(-0.708210 + 40.9313i) q^{34} +16.6472i q^{35} +(11.9928 + 0.415134i) q^{36} +26.8040 q^{37} +(-12.7833 - 0.221181i) q^{38} -24.4718i q^{39} +(2.61139 - 50.2685i) q^{40} -33.5802 q^{41} +(-0.158555 + 9.16378i) q^{42} -3.83239i q^{43} +(-2.29434 + 66.2814i) q^{44} +18.8761 q^{45} +(-58.1804 - 1.00666i) q^{46} +27.4693i q^{47} +(1.91627 - 27.6465i) q^{48} -7.00000 q^{49} +(0.504801 - 29.1752i) q^{50} +35.4528i q^{51} +(-56.4815 - 1.95512i) q^{52} -21.7113 q^{53} +(10.3907 + 0.179785i) q^{54} +104.324i q^{55} +(21.1375 + 1.09807i) q^{56} -11.0723 q^{57} +(1.89254 - 109.380i) q^{58} +54.1344i q^{59} +(1.50806 - 43.5664i) q^{60} -35.7188 q^{61} +(29.4549 + 0.509641i) q^{62} +7.93725i q^{63} +(-63.6555 - 6.63154i) q^{64} -88.8991 q^{65} +(-0.993628 + 57.4271i) q^{66} -95.4255i q^{67} +(81.8258 + 2.83241i) q^{68} -50.3932 q^{69} +(33.2894 + 0.575986i) q^{70} +55.6524i q^{71} +(1.24509 - 23.9677i) q^{72} +130.476 q^{73} +(0.927408 - 53.5999i) q^{74} -25.2702i q^{75} +(-0.884592 + 25.5550i) q^{76} -43.8673 q^{77} +(-48.9363 - 0.846717i) q^{78} -15.6309i q^{79} +(-100.432 - 6.96126i) q^{80} +9.00000 q^{81} +(-1.16186 + 67.1503i) q^{82} -49.4495i q^{83} +(18.3193 + 0.634127i) q^{84} +128.790 q^{85} +(-7.66363 - 0.132599i) q^{86} -94.7403i q^{87} +(132.464 + 6.88131i) q^{88} +39.2530 q^{89} +(0.653107 - 37.7466i) q^{90} -37.3813i q^{91} +(-4.02604 + 116.309i) q^{92} +25.5125 q^{93} +(54.9303 + 0.950427i) q^{94} +40.2224i q^{95} +(-55.2184 - 4.78853i) q^{96} -171.943 q^{97} +(-0.242198 + 13.9979i) q^{98} +49.7408i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{2} + 2 q^{4} + 8 q^{5} - 12 q^{6} - 10 q^{8} - 36 q^{9}+O(q^{10}) \) 12 * q + 2 * q^2 + 2 * q^4 + 8 * q^5 - 12 * q^6 - 10 * q^8 - 36 * q^9	\( 12 q + 2 q^{2} + 2 q^{4} + 8 q^{5} - 12 q^{6} - 10 q^{8} - 36 q^{9} + 28 q^{10} + 24 q^{12} - 24 q^{13} - 14 q^{14} - 14 q^{16} - 40 q^{17} - 6 q^{18} - 20 q^{20} - 88 q^{22} - 36 q^{24} + 180 q^{25} + 100 q^{26} + 14 q^{28} + 72 q^{29} + 72 q^{30} + 142 q^{32} - 100 q^{34} - 6 q^{36} - 88 q^{37} + 128 q^{38} - 28 q^{40} - 200 q^{41} - 40 q^{44} - 24 q^{45} - 24 q^{46} + 48 q^{48} - 84 q^{49} - 346 q^{50} - 364 q^{52} + 104 q^{53} + 36 q^{54} + 98 q^{56} + 148 q^{58} + 96 q^{60} + 104 q^{61} + 64 q^{62} - 70 q^{64} + 176 q^{65} + 24 q^{66} + 188 q^{68} - 192 q^{69} - 84 q^{70} + 30 q^{72} + 312 q^{73} + 4 q^{74} + 432 q^{76} - 224 q^{77} + 48 q^{78} - 564 q^{80} + 108 q^{81} + 332 q^{82} + 352 q^{85} + 160 q^{86} + 328 q^{88} - 552 q^{89} - 84 q^{90} + 232 q^{92} - 48 q^{93} - 144 q^{94} - 108 q^{96} - 264 q^{97} - 14 q^{98}+O(q^{100}) \) 12 * q + 2 * q^2 + 2 * q^4 + 8 * q^5 - 12 * q^6 - 10 * q^8 - 36 * q^9 + 28 * q^10 + 24 * q^12 - 24 * q^13 - 14 * q^14 - 14 * q^16 - 40 * q^17 - 6 * q^18 - 20 * q^20 - 88 * q^22 - 36 * q^24 + 180 * q^25 + 100 * q^26 + 14 * q^28 + 72 * q^29 + 72 * q^30 + 142 * q^32 - 100 * q^34 - 6 * q^36 - 88 * q^37 + 128 * q^38 - 28 * q^40 - 200 * q^41 - 40 * q^44 - 24 * q^45 - 24 * q^46 + 48 * q^48 - 84 * q^49 - 346 * q^50 - 364 * q^52 + 104 * q^53 + 36 * q^54 + 98 * q^56 + 148 * q^58 + 96 * q^60 + 104 * q^61 + 64 * q^62 - 70 * q^64 + 176 * q^65 + 24 * q^66 + 188 * q^68 - 192 * q^69 - 84 * q^70 + 30 * q^72 + 312 * q^73 + 4 * q^74 + 432 * q^76 - 224 * q^77 + 48 * q^78 - 564 * q^80 + 108 * q^81 + 332 * q^82 + 352 * q^85 + 160 * q^86 + 328 * q^88 - 552 * q^89 - 84 * q^90 + 232 * q^92 - 48 * q^93 - 144 * q^94 - 108 * q^96 - 264 * q^97 - 14 * q^98

Introduction

L-functions

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