LMFDB - Embedded newform 220.3.h.a.199.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [220,3,Mod(199,220)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(220, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("220.199");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 220 = 2^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	220.h (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:	$5.99456581593$
Analytic rank:	$0$
Dimension:	$60$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			199.2
Character	$\chi$	$=$	220.199
Dual form			220.3.h.a.199.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.99644 + 0.119294i) q^{2} +0.337678 q^{3} +(3.97154 - 0.476326i) q^{4} +(1.42257 - 4.79336i) q^{5} +(-0.674153 + 0.0402829i) q^{6} -6.79613 q^{7} +(-7.87211 + 1.42474i) q^{8} -8.88597 q^{9} +(-2.26826 + 9.73935i) q^{10} +3.31662i q^{11} +(1.34110 - 0.160845i) q^{12} -7.56772i q^{13} +(13.5681 - 0.810737i) q^{14} +(0.480371 - 1.61861i) q^{15} +(15.5462 - 3.78349i) q^{16} +26.2930i q^{17} +(17.7403 - 1.06004i) q^{18} +14.2491i q^{19} +(3.36660 - 19.7146i) q^{20} -2.29490 q^{21} +(-0.395653 - 6.62144i) q^{22} -34.5573 q^{23} +(-2.65824 + 0.481102i) q^{24} +(-20.9526 - 13.6378i) q^{25} +(0.902784 + 15.1085i) q^{26} -6.03970 q^{27} +(-26.9911 + 3.23717i) q^{28} -19.2441 q^{29} +(-0.765941 + 3.28876i) q^{30} -44.2429i q^{31} +(-30.5857 + 9.40809i) q^{32} +1.11995i q^{33} +(-3.13660 - 52.4925i) q^{34} +(-9.66799 + 32.5763i) q^{35} +(-35.2910 + 4.23262i) q^{36} +46.5774i q^{37} +(-1.69983 - 28.4475i) q^{38} -2.55545i q^{39} +(-4.36937 + 39.7606i) q^{40} -67.4821 q^{41} +(4.58163 - 0.273768i) q^{42} +54.3809 q^{43} +(1.57979 + 13.1721i) q^{44} +(-12.6409 + 42.5937i) q^{45} +(68.9914 - 4.12247i) q^{46} -7.43139 q^{47} +(5.24961 - 1.27760i) q^{48} -2.81262 q^{49} +(43.4574 + 24.7275i) q^{50} +8.87858i q^{51} +(-3.60470 - 30.0555i) q^{52} -88.6475i q^{53} +(12.0579 - 0.720499i) q^{54} +(15.8978 + 4.71814i) q^{55} +(53.4999 - 9.68269i) q^{56} +4.81161i q^{57} +(38.4196 - 2.29570i) q^{58} -74.2727i q^{59} +(1.13683 - 6.65719i) q^{60} -21.7427 q^{61} +(5.27791 + 88.3283i) q^{62} +60.3902 q^{63} +(59.9403 - 22.4314i) q^{64} +(-36.2748 - 10.7656i) q^{65} +(-0.133603 - 2.23591i) q^{66} +53.3540 q^{67} +(12.5241 + 104.424i) q^{68} -11.6692 q^{69} +(15.4154 - 66.1899i) q^{70} +107.738i q^{71} +(69.9514 - 12.6602i) q^{72} +34.9727i q^{73} +(-5.55640 - 92.9889i) q^{74} +(-7.07522 - 4.60518i) q^{75} +(6.78723 + 56.5909i) q^{76} -22.5402i q^{77} +(0.304850 + 5.10180i) q^{78} -119.442i q^{79} +(3.97999 - 79.9009i) q^{80} +77.9343 q^{81} +(134.724 - 8.05021i) q^{82} -91.9838 q^{83} +(-9.11429 + 1.09312i) q^{84} +(126.032 + 37.4038i) q^{85} +(-108.568 + 6.48731i) q^{86} -6.49830 q^{87} +(-4.72532 - 26.1088i) q^{88} +32.6768 q^{89} +(20.1557 - 86.5436i) q^{90} +51.4312i q^{91} +(-137.245 + 16.4605i) q^{92} -14.9399i q^{93} +(14.8363 - 0.886520i) q^{94} +(68.3011 + 20.2704i) q^{95} +(-10.3281 + 3.17690i) q^{96} +13.3085i q^{97} +(5.61522 - 0.335528i) q^{98} -29.4714i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - 4 q^{4} + 4 q^{5} + 12 q^{6} + 180 q^{9} - 18 q^{10} - 56 q^{14} - 40 q^{16} + 84 q^{20} - 16 q^{21} + 104 q^{24} - 60 q^{25} + 28 q^{26} - 88 q^{29} - 166 q^{30} - 152 q^{34} - 248 q^{36} + 132 q^{40}+ \cdots + 216 q^{96}+O(q^{100}) $ 60 * q - 4 * q^4 + 4 * q^5 + 12 * q^6 + 180 * q^9 - 18 * q^10 - 56 * q^14 - 40 * q^16 + 84 * q^20 - 16 * q^21 + 104 * q^24 - 60 * q^25 + 28 * q^26 - 88 * q^29 - 166 * q^30 - 152 * q^34 - 248 * q^36 + 132 * q^40 - 200 * q^41 + 44 * q^44 + 84 * q^45 + 260 * q^46 + 420 * q^49 - 198 * q^50 - 116 * q^54 - 128 * q^56 - 4 * q^60 + 136 * q^61 + 116 * q^64 - 288 * q^65 - 544 * q^69 + 152 * q^70 + 436 * q^74 - 72 * q^76 - 176 * q^80 + 300 * q^81 - 136 * q^84 + 176 * q^85 - 348 * q^86 + 760 * q^89 + 40 * q^90 + 112 * q^94 + 216 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/220\mathbb{Z}\right)^\times$.

$n$	$101$	$111$	$177$
$\chi(n)$	$1$	$-1$	$-1$

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 $

$2$	−1.99644	+	0.119294i	−0.998220	+	0.0596470i
$2$	−1.99644	+	0.119294i	−0.998220	+	0.0596470i
$3$	0.337678			0.112559			0.0562796	−	0.998415i	$-0.482076\pi$
$3$	0.337678			0.112559			0.0562796	+	0.998415i	$0.482076\pi$
$4$	3.97154	−	0.476326i	0.992884	−	0.119082i
$5$	1.42257	−	4.79336i	0.284514	−	0.958672i
$5$	1.42257	−	4.79336i	0.284514	−	0.958672i
$6$	−0.674153	+	0.0402829i	−0.112359	+	0.00671382i
$7$	−6.79613			−0.970876			−0.485438	−	0.874271i	$-0.661340\pi$
$7$	−6.79613			−0.970876			−0.485438	+	0.874271i	$0.661340\pi$
$8$	−7.87211	+	1.42474i	−0.984014	+	0.178092i
$9$	−8.88597			−0.987330
$10$	−2.26826	+	9.73935i	−0.226826	+	0.973935i
$11$			3.31662i			0.301511i
$11$			3.31662i			0.301511i
$12$	1.34110	−	0.160845i	0.111758	−	0.0134037i
$13$		−	7.56772i		−	0.582133i	−0.956703	−	0.291066i	$-0.905990\pi$
$13$		−	7.56772i		−	0.582133i	0.956703	−	0.291066i	$-0.0940100\pi$
$14$	13.5681	−	0.810737i	0.969147	−	0.0579098i
$15$	0.480371	−	1.61861i	0.0320247	−	0.107907i
$16$	15.5462	−	3.78349i	0.971639	−	0.236468i
$17$			26.2930i			1.54665i	0.634010	+	0.773325i	$0.281408\pi$
$17$			26.2930i			1.54665i	−0.634010	+	0.773325i	$0.718592\pi$
$18$	17.7403	−	1.06004i	0.985573	−	0.0588913i
$19$			14.2491i			0.749953i	0.927034	+	0.374977i	$0.122349\pi$
$19$			14.2491i			0.749953i	−0.927034	+	0.374977i	$0.877651\pi$
$20$	3.36660	−	19.7146i	0.168330	−	0.985731i
$21$	−2.29490			−0.109281
$22$	−0.395653	−	6.62144i	−0.0179842	−	0.300975i
$23$	−34.5573			−1.50249			−0.751245	−	0.660024i	$-0.770546\pi$
$23$	−34.5573			−1.50249			−0.751245	+	0.660024i	$0.770546\pi$
$24$	−2.65824	+	0.481102i	−0.110760	+	0.0200459i
$25$	−20.9526	−	13.6378i	−0.838103	−	0.545512i
$26$	0.902784	+	15.1085i	0.0347224	+	0.581096i
$27$	−6.03970			−0.223692
$28$	−26.9911	+	3.23717i	−0.963967	+	0.115613i
$29$	−19.2441			−0.663589			−0.331794	−	0.943352i	$-0.607654\pi$
$29$	−19.2441			−0.663589			−0.331794	+	0.943352i	$0.607654\pi$
$30$	−0.765941	+	3.28876i	−0.0255314	+	0.109625i
$31$		−	44.2429i		−	1.42719i	−0.700558	−	0.713596i	$-0.747065\pi$
$31$		−	44.2429i		−	1.42719i	0.700558	−	0.713596i	$-0.252935\pi$
$32$	−30.5857	+	9.40809i	−0.955805	+	0.294003i
$33$			1.11995i			0.0339379i
$34$	−3.13660	−	52.4925i	−0.0922530	−	1.54390i
$35$	−9.66799	+	32.5763i	−0.276228	+	0.930751i
$36$	−35.2910	+	4.23262i	−0.980305	+	0.117573i
$37$			46.5774i			1.25885i	0.777062	+	0.629424i	$0.216709\pi$
$37$			46.5774i			1.25885i	−0.777062	+	0.629424i	$0.783291\pi$
$38$	−1.69983	−	28.4475i	−0.0447324	−	0.748618i
$39$		−	2.55545i		−	0.0655244i
$40$	−4.36937	+	39.7606i	−0.109234	+	0.994016i
$41$	−67.4821			−1.64591			−0.822953	−	0.568110i	$-0.807675\pi$
$41$	−67.4821			−1.64591			−0.822953	+	0.568110i	$0.807675\pi$
$42$	4.58163	−	0.273768i	0.109086	−	0.00651828i
$43$	54.3809			1.26467			0.632336	−	0.774695i	$-0.282096\pi$
$43$	54.3809			1.26467			0.632336	+	0.774695i	$0.282096\pi$
$44$	1.57979	+	13.1721i	0.0359044	+	0.299366i
$45$	−12.6409	+	42.5937i	−0.280910	+	0.946526i
$46$	68.9914	−	4.12247i	1.49981	−	0.0896189i
$47$	−7.43139			−0.158115			−0.0790574	−	0.996870i	$-0.525191\pi$
$47$	−7.43139			−0.158115			−0.0790574	+	0.996870i	$0.525191\pi$
$48$	5.24961	−	1.27760i	0.109367	−	0.0266167i
$49$	−2.81262			−0.0574004
$50$	43.4574	+	24.7275i	0.869149	+	0.494550i
$51$			8.87858i			0.174090i
$52$	−3.60470	−	30.0555i	−0.0693212	−	0.577990i
$53$		−	88.6475i		−	1.67259i	−0.548277	−	0.836297i	$-0.684716\pi$
$53$		−	88.6475i		−	1.67259i	0.548277	−	0.836297i	$-0.315284\pi$
$54$	12.0579	−	0.720499i	0.223294	−	0.0133426i
$55$	15.8978	+	4.71814i	0.289050	+	0.0857843i
$56$	53.4999	−	9.68269i	0.955355	−	0.172905i
$57$			4.81161i			0.0844142i
$58$	38.4196	−	2.29570i	0.662407	−	0.0395811i
$59$		−	74.2727i		−	1.25886i	−0.777057	−	0.629430i	$-0.783288\pi$
$59$		−	74.2727i		−	1.25886i	0.777057	−	0.629430i	$-0.216712\pi$
$60$	1.13683	−	6.65719i	0.0189471	−	0.110953i
$61$	−21.7427			−0.356438			−0.178219	−	0.983991i	$-0.557034\pi$
$61$	−21.7427			−0.356438			−0.178219	+	0.983991i	$0.557034\pi$
$62$	5.27791	+	88.3283i	0.0851276	+	1.42465i
$63$	60.3902			0.958575
$64$	59.9403	−	22.4314i	0.936566	−	0.350490i
$65$	−36.2748	−	10.7656i	−0.558074	−	0.165625i
$66$	−0.133603	−	2.23591i	−0.00202429	−	0.0338775i
$67$	53.3540			0.796328			0.398164	−	0.917314i	$-0.369647\pi$
$67$	53.3540			0.796328			0.398164	+	0.917314i	$0.369647\pi$
$68$	12.5241	+	104.424i	0.184177	+	1.53564i
$69$	−11.6692			−0.169119
$70$	15.4154	−	66.1899i	0.220220	−	0.945570i
$71$			107.738i			1.51744i	0.651419	+	0.758719i	$0.274174\pi$
$71$			107.738i			1.51744i	−0.651419	+	0.758719i	$0.725826\pi$
$72$	69.9514	−	12.6602i	0.971547	−	0.175836i
$73$			34.9727i			0.479078i	0.970887	+	0.239539i	$0.0769963\pi$
$73$			34.9727i			0.479078i	−0.970887	+	0.239539i	$0.923004\pi$
$74$	−5.55640	−	92.9889i	−0.0750865	−	1.25661i
$75$	−7.07522	−	4.60518i	−0.0943362	−	0.0614024i
$76$	6.78723	+	56.5909i	0.0893056	+	0.744617i
$77$		−	22.5402i		−	0.292730i
$78$	0.304850	+	5.10180i	0.00390833	+	0.0654078i
$79$		−	119.442i		−	1.51193i	−0.654614	−	0.755963i	$-0.727169\pi$
$79$		−	119.442i		−	1.51193i	0.654614	−	0.755963i	$-0.272831\pi$
$80$	3.97999	−	79.9009i	0.0497498	−	0.998762i
$81$	77.9343			0.962152
$82$	134.724	−	8.05021i	1.64297	−	0.0981732i
$83$	−91.9838			−1.10824			−0.554119	−	0.832437i	$-0.686945\pi$
$83$	−91.9838			−1.10824			−0.554119	+	0.832437i	$0.686945\pi$
$84$	−9.11429	+	1.09312i	−0.108503	+	0.0130134i
$85$	126.032	+	37.4038i	1.48273	+	0.440044i
$86$	−108.568	+	6.48731i	−1.26242	+	0.0754338i
$87$	−6.49830			−0.0746931
$88$	−4.72532	−	26.1088i	−0.0536968	−	0.296691i
$89$	32.6768			0.367155			0.183577	−	0.983005i	$-0.441232\pi$
$89$	32.6768			0.367155			0.183577	+	0.983005i	$0.441232\pi$
$90$	20.1557	−	86.5436i	0.223952	−	0.961596i
$91$			51.4312i			0.565178i
$92$	−137.245	+	16.4605i	−1.49180	+	0.178919i
$93$		−	14.9399i		−	0.160644i
$94$	14.8363	−	0.886520i	0.157833	−	0.00943106i
$95$	68.3011	+	20.2704i	0.718959	+	0.213373i
$96$	−10.3281	+	3.17690i	−0.107585	+	0.0330927i
$97$			13.3085i			0.137201i	0.997644	+	0.0686006i	$0.0218534\pi$
$97$			13.3085i			0.137201i	−0.997644	+	0.0686006i	$0.978147\pi$
$98$	5.61522	−	0.335528i	0.0572982	−	0.00342376i
$99$		−	29.4714i		−	0.297691i
$100$	−89.7100	−	44.1828i	−0.897100	−	0.441828i
$101$	40.3501			0.399506			0.199753	−	0.979846i	$-0.435986\pi$
$101$	40.3501			0.399506			0.199753	+	0.979846i	$0.435986\pi$
$102$	−1.05916	−	17.7255i	−0.0103839	−	0.173780i
$103$	65.9697			0.640483			0.320241	−	0.947336i	$-0.396236\pi$
$103$	65.9697			0.640483			0.320241	+	0.947336i	$0.396236\pi$
$104$	10.7820	+	59.5740i	0.103673	+	0.572827i
$105$	−3.26466	+	11.0003i	−0.0310920	+	0.104765i
$106$	10.5751	+	176.979i	0.0997652	+	1.66962i
$107$	−42.8379			−0.400355			−0.200177	−	0.979760i	$-0.564152\pi$
$107$	−42.8379			−0.400355			−0.200177	+	0.979760i	$0.564152\pi$
$108$	−23.9869	+	2.87686i	−0.222101	+	0.0266376i
$109$	33.8101			0.310184			0.155092	−	0.987900i	$-0.450433\pi$
$109$	33.8101			0.310184			0.155092	+	0.987900i	$0.450433\pi$
$110$	−32.3018	−	7.52297i	−0.293653	−	0.0683906i
$111$			15.7282i			0.141695i
$112$	−105.654	+	25.7131i	−0.943341	+	0.229581i
$113$		−	130.528i		−	1.15511i	−0.816351	−	0.577556i	$-0.804006\pi$
$113$		−	130.528i		−	1.15511i	0.816351	−	0.577556i	$-0.195994\pi$
$114$	−0.573996	−	9.60608i	−0.00503505	−	0.0842639i
$115$	−49.1602	+	165.645i	−0.427480	+	1.44039i
$116$	−76.4286	+	9.16646i	−0.658867	+	0.0790212i
$117$			67.2466i			0.574757i
$118$	8.86029	+	148.281i	0.0750872	+	1.25662i
$119$		−	178.691i		−	1.50160i
$120$	−1.47544	+	13.4263i	−0.0122953	+	0.111886i
$121$	−11.0000			−0.0909091
$122$	43.4080	−	2.59377i	0.355803	−	0.0212604i
$123$	−22.7872			−0.185262
$124$	−21.0741	−	175.713i	−0.169952	−	1.41704i
$125$	−95.1774	+	81.0325i	−0.761419	+	0.648260i
$126$	−120.565	+	7.20419i	−0.956868	+	0.0571761i
$127$	5.97899			0.0470787			0.0235393	−	0.999723i	$-0.492507\pi$
$127$	5.97899			0.0470787			0.0235393	+	0.999723i	$0.492507\pi$
$128$	−116.991	+	51.9334i	−0.913993	+	0.405729i
$129$	18.3632			0.142350
$130$	73.7047	+	17.1656i	0.566960	+	0.132043i
$131$		−	11.3591i		−	0.0867105i	−0.999060	−	0.0433552i	$-0.986195\pi$
$131$		−	11.3591i		−	0.0867105i	0.999060	−	0.0433552i	$-0.0138047\pi$
$132$	0.533462	+	4.44793i	0.00404138	+	0.0336964i
$133$		−	96.8388i		−	0.728112i
$134$	−106.518	+	6.36481i	−0.794910	+	0.0474985i
$135$	−8.59190	+	28.9504i	−0.0636437	+	0.214448i
$136$	−37.4607	−	206.982i	−0.275446	−	1.52192i
$137$			97.9040i			0.714628i	0.933984	+	0.357314i	$0.116307\pi$
$137$			97.9040i			0.714628i	−0.933984	+	0.357314i	$0.883693\pi$
$138$	23.2969	−	1.39207i	0.168818	−	0.0100874i
$139$			83.2834i			0.599161i	0.954071	+	0.299581i	$0.0968468\pi$
$139$			83.2834i			0.599161i	−0.954071	+	0.299581i	$0.903153\pi$
$140$	−22.8798	+	133.983i	−0.163427	+	0.957022i
$141$	−2.50942			−0.0177973
$142$	−12.8525	−	215.092i	−0.0905105	−	1.51474i
$143$	25.0993			0.175520
$144$	−138.143	+	33.6200i	−0.959329	+	0.233472i
$145$	−27.3761	+	92.2438i	−0.188801	+	0.636164i
$146$	−4.17203	−	69.8209i	−0.0285756	−	0.478225i
$147$	−0.949759			−0.00646094
$148$	22.1860	+	184.984i	0.149906	+	1.24989i
$149$	143.283			0.961632			0.480816	−	0.876822i	$-0.340341\pi$
$149$	143.283			0.961632			0.480816	+	0.876822i	$0.340341\pi$
$150$	14.6746	+	8.34993i	0.0978308	+	0.0556662i
$151$		−	19.1317i		−	0.126700i	−0.997991	−	0.0633500i	$-0.979822\pi$
$151$		−	19.1317i		−	0.126700i	0.997991	−	0.0633500i	$-0.0201784\pi$
$152$	−20.3012	−	112.171i	−0.133561	−	0.737965i
$153$		−	233.639i		−	1.52705i
$154$	2.68891	+	45.0002i	0.0174605	+	0.292209i
$155$	−212.072	−	62.9388i	−1.36821	−	0.406057i
$156$	−1.21723	−	10.1491i	−0.00780275	−	0.0650582i
$157$		−	226.543i		−	1.44295i	−0.692442	−	0.721474i	$-0.743465\pi$
$157$		−	226.543i		−	1.44295i	0.692442	−	0.721474i	$-0.256535\pi$
$158$	14.2487	+	238.459i	0.0901818	+	1.50923i
$159$		−	29.9343i		−	0.188266i
$160$	1.58589	+	159.992i	0.00991183	+	0.999951i
$161$	234.856			1.45873
$162$	−155.591	+	9.29709i	−0.960439	+	0.0573894i
$163$	−249.137			−1.52845			−0.764225	−	0.644950i	$-0.776878\pi$
$163$	−249.137			−1.52845			−0.764225	+	0.644950i	$0.776878\pi$
$164$	−268.008	+	32.1435i	−1.63419	+	0.195997i
$165$	5.36832	+	1.59321i	0.0325353	+	0.00965582i
$166$	183.640	−	10.9731i	1.10627	−	0.0661031i
$167$	−60.2805			−0.360961			−0.180481	−	0.983579i	$-0.557765\pi$
$167$	−60.2805			−0.360961			−0.180481	+	0.983579i	$0.557765\pi$
$168$	18.0657	−	3.26963i	0.107534	−	0.0194621i
$169$	111.730			0.661122
$170$	−256.077	−	59.6395i	−1.50634	−	0.350821i
$171$		−	126.617i		−	0.740452i
$172$	215.976	−	25.9030i	1.25567	−	0.150599i
$173$			24.9330i			0.144121i	0.997400	+	0.0720607i	$0.0229575\pi$
$173$			24.9330i			0.144121i	−0.997400	+	0.0720607i	$0.977042\pi$
$174$	12.9735	−	0.775207i	0.0745601	−	0.00445521i
$175$	142.396	+	92.6843i	0.813694	+	0.529624i
$176$	12.5484	+	51.5610i	0.0712979	+	0.292960i
$177$		−	25.0803i		−	0.141696i
$178$	−65.2372	+	3.89814i	−0.366501	+	0.0218997i
$179$			273.560i			1.52827i	0.645058	+	0.764134i	$0.276833\pi$
$179$			273.560i			1.52827i	−0.645058	+	0.764134i	$0.723167\pi$
$180$	−29.9155	+	175.184i	−0.166197	+	0.973242i
$181$	−149.211			−0.824368			−0.412184	−	0.911101i	$-0.635234\pi$
$181$	−149.211			−0.824368			−0.412184	+	0.911101i	$0.635234\pi$
$182$	−6.13543	−	102.679i	−0.0337112	−	0.564172i
$183$	−7.34203			−0.0401204
$184$	272.039	−	49.2350i	1.47847	−	0.267581i
$185$	223.262	+	66.2597i	1.20682	+	0.358161i
$186$	1.78223	+	29.8265i	0.00958190	+	0.160358i
$187$	−87.2042			−0.466332
$188$	−29.5141	+	3.53977i	−0.156990	+	0.0188285i
$189$	41.0466			0.217178
$190$	−138.777	−	32.3207i	−0.730406	−	0.170109i
$191$			227.027i			1.18862i	0.804235	+	0.594312i	$0.202576\pi$
$191$			227.027i			1.18862i	−0.804235	+	0.594312i	$0.797424\pi$
$192$	20.2405	−	7.57457i	0.105419	−	0.0394509i
$193$		−	255.756i		−	1.32516i	−0.748991	−	0.662580i	$-0.769461\pi$
$193$		−	255.756i		−	1.32516i	0.748991	−	0.662580i	$-0.230539\pi$
$194$	−1.58763	−	26.5697i	−0.00818364	−	0.136957i
$195$	−12.2492	−	3.63532i	−0.0628164	−	0.0186426i
$196$	−11.1704	+	1.33972i	−0.0569919	+	0.00683532i
$197$		−	120.032i		−	0.609301i	−0.952464	−	0.304650i	$-0.901460\pi$
$197$		−	120.032i		−	0.609301i	0.952464	−	0.304650i	$-0.0985396\pi$
$198$	3.51576	+	58.8379i	0.0177564	+	0.297161i
$199$		−	144.902i		−	0.728152i	−0.931369	−	0.364076i	$-0.881385\pi$
$199$		−	144.902i		−	0.728152i	0.931369	−	0.364076i	$-0.118615\pi$
$200$	184.371	+	77.5064i	0.921856	+	0.387532i
$201$	18.0165			0.0896341
$202$	−80.5565	+	4.81352i	−0.398795	+	0.0238293i
$203$	130.785			0.644262
$204$	4.22910	+	35.2616i	0.0207309	+	0.172851i
$205$	−95.9982	+	323.466i	−0.468284	+	1.57788i
$206$	−131.705	+	7.86979i	−0.639342	+	0.0382029i
$207$	307.075			1.48345
$208$	−28.6324	−	117.650i	−0.137656	−	0.565623i
$209$	−47.2590			−0.226119
$210$	5.20544	−	22.3509i	0.0247878	−	0.106433i
$211$		−	117.572i		−	0.557211i	−0.960406	−	0.278605i	$-0.910128\pi$
$211$		−	117.572i		−	0.557211i	0.960406	−	0.278605i	$-0.0898722\pi$
$212$	−42.2251	−	352.067i	−0.199175	−	1.66069i
$213$			36.3807i			0.170802i
$214$	85.5233	−	5.11031i	0.399642	−	0.0238799i
$215$	77.3607	−	260.667i	0.359817	−	1.21240i
$216$	47.5452	−	8.60497i	0.220116	−	0.0398378i
$217$			300.681i			1.38563i
$218$	−67.4997	+	4.03334i	−0.309632	+	0.0185015i
$219$			11.8095i			0.0539247i
$220$	65.3860	+	11.1657i	0.297209	+	0.0507534i
$221$	198.979			0.900355
$222$	−1.87627	−	31.4003i	−0.00845168	−	0.141443i
$223$	262.174			1.17567			0.587833	−	0.808982i	$-0.299981\pi$
$223$	262.174			1.17567			0.587833	+	0.808982i	$0.299981\pi$
$224$	207.865	−	63.9386i	0.927967	−	0.285440i
$225$	186.184	+	121.185i	0.827485	+	0.538601i
$226$	15.5712	+	260.591i	0.0688990	+	1.15306i
$227$	−269.481			−1.18714			−0.593571	−	0.804781i	$-0.702283\pi$
$227$	−269.481			−1.18714			−0.593571	+	0.804781i	$0.702283\pi$
$228$	2.29190	+	19.1095i	0.0100522	+	0.0838135i
$229$	−289.225			−1.26299			−0.631496	−	0.775379i	$-0.717559\pi$
$229$	−289.225			−1.26299			−0.631496	+	0.775379i	$0.717559\pi$
$230$	78.3849	−	336.565i	0.340804	−	1.46333i
$231$		−	7.61133i		−	0.0329495i
$232$	151.492	−	27.4177i	0.652981	−	0.118180i
$233$			40.9655i			0.175817i	0.996129	+	0.0879087i	$0.0280184\pi$
$233$			40.9655i			0.175817i	−0.996129	+	0.0879087i	$0.971982\pi$
$234$	−8.02211	−	134.254i	−0.0342825	−	0.573734i
$235$	−10.5717	+	35.6213i	−0.0449859	+	0.151580i
$236$	−35.3780	−	294.977i	−0.149907	−	1.24990i
$237$		−	40.3330i		−	0.170181i
$238$	21.3167	+	356.746i	0.0895662	+	1.49893i
$239$			318.508i			1.33267i	0.745653	+	0.666334i	$0.232138\pi$
$239$			318.508i			1.33267i	−0.745653	+	0.666334i	$0.767862\pi$
$240$	1.34395	−	26.9808i	0.00559981	−	0.112420i
$241$	−236.574			−0.981635			−0.490817	−	0.871262i	$-0.663302\pi$
$241$	−236.574			−0.981635			−0.490817	+	0.871262i	$0.663302\pi$
$242$	21.9608	−	1.31223i	0.0907472	−	0.00542245i
$243$	80.6739			0.331992
$244$	−86.3520	+	10.3566i	−0.353902	+	0.0424452i
$245$	−4.00115	+	13.4819i	−0.0163312	+	0.0550281i
$246$	45.4933	−	2.71838i	0.184932	−	0.0110503i
$247$	107.833			0.436572
$248$	63.0345	+	348.285i	0.254171	+	1.40438i
$249$	−31.0609			−0.124742
$250$	180.349	−	173.130i	0.721397	−	0.692522i
$251$		−	296.486i		−	1.18122i	−0.806957	−	0.590610i	$-0.798887\pi$
$251$		−	296.486i		−	1.18122i	0.806957	−	0.590610i	$-0.201113\pi$
$252$	239.842	−	28.7654i	0.951754	−	0.114149i
$253$		−	114.613i		−	0.453018i
$254$	−11.9367	+	0.713258i	−0.0469949	+	0.00280810i
$255$	42.5582	+	12.6304i	0.166895	+	0.0495311i
$256$	227.370	−	117.638i	0.888165	−	0.459524i
$257$		−	53.1586i		−	0.206843i	−0.994638	−	0.103421i	$-0.967021\pi$
$257$		−	53.1586i		−	0.206843i	0.994638	−	0.103421i	$-0.0329790\pi$
$258$	−36.6610	+	2.19062i	−0.142097	+	0.00849077i
$259$		−	316.546i		−	1.22219i
$260$	−149.195	−	25.4775i	−0.573826	−	0.0979903i
$261$	171.002			0.655181
$262$	1.35507	+	22.6777i	0.00517202	+	0.0865561i
$263$	−84.2123			−0.320199			−0.160100	−	0.987101i	$-0.551182\pi$
$263$	−84.2123			−0.320199			−0.160100	+	0.987101i	$0.551182\pi$
$264$	−1.59563	−	8.81637i	−0.00604407	−	0.0333954i
$265$	−424.919	−	126.107i	−1.60347	−	0.475877i
$266$	11.5523	+	193.333i	0.0434296	+	0.726815i
$267$	11.0342			0.0413267
$268$	211.897	−	25.4139i	0.790662	−	0.0948280i
$269$	8.89157			0.0330542			0.0165271	−	0.999863i	$-0.494739\pi$
$269$	8.89157			0.0330542			0.0165271	+	0.999863i	$0.494739\pi$
$270$	13.6996	−	58.8227i	0.0507393	−	0.217862i
$271$		−	139.790i		−	0.515831i	−0.966168	−	0.257915i	$-0.916964\pi$
$271$		−	139.790i		−	0.515831i	0.966168	−	0.257915i	$-0.0830356\pi$
$272$	99.4796	+	408.758i	0.365734	+	1.50279i
$273$			17.3672i			0.0636161i
$274$	−11.6794	−	195.459i	−0.0426254	−	0.713355i
$275$	45.2315	−	69.4918i	0.164478	−	0.252698i
$276$	−46.3447	+	5.55835i	−0.167916	+	0.0201390i
$277$			280.193i			1.01153i	0.862672	+	0.505764i	$0.168789\pi$
$277$			280.193i			1.01153i	−0.862672	+	0.505764i	$0.831211\pi$
$278$	−9.93521	−	166.270i	−0.0357381	−	0.598094i
$279$			393.142i			1.40911i
$280$	29.6948	−	270.218i	0.106053	−	0.965066i
$281$	−441.298			−1.57045			−0.785227	−	0.619208i	$-0.787454\pi$
$281$	−441.298			−1.57045			−0.785227	+	0.619208i	$0.787454\pi$
$282$	5.00990	−	0.299358i	0.0177656	−	0.00106155i
$283$	12.2834			0.0434042			0.0217021	−	0.999764i	$-0.493091\pi$
$283$	12.2834			0.0434042			0.0217021	+	0.999764i	$0.493091\pi$
$284$	51.3184	+	427.886i	0.180699	+	1.50664i
$285$	23.0638	+	6.84486i	0.0809255	+	0.0240171i
$286$	−50.1092	+	2.99419i	−0.175207	+	0.0104692i
$287$	458.617			1.59797
$288$	271.784	−	83.6000i	0.943695	−	0.290278i
$289$	−402.324			−1.39213
$290$	43.6506	−	187.425i	0.150519	−	0.646293i
$291$			4.49399i			0.0154433i
$292$	16.6584	+	138.895i	0.0570494	+	0.475669i
$293$			25.7448i			0.0878663i	0.999034	+	0.0439331i	$0.0139889\pi$
$293$			25.7448i			0.0878663i	−0.999034	+	0.0439331i	$0.986011\pi$
$294$	1.89614	−	0.113300i	0.00644944	−	0.000385376i
$295$	−356.016	−	105.658i	−1.20683	−	0.358164i
$296$	−66.3605	−	366.662i	−0.224191	−	1.23872i
$297$		−	20.0314i		−	0.0674458i
$298$	−286.056	+	17.0928i	−0.959920	+	0.0573584i
$299$			261.520i			0.874648i
$300$	−30.2931	−	14.9195i	−0.100977	−	0.0497318i
$301$	−369.579			−1.22784
$302$	2.28230	+	38.1953i	0.00755727	+	0.126474i
$303$	13.6253			0.0449681
$304$	53.9115	+	221.520i	0.177340	+	0.728684i
$305$	−30.9306	+	104.221i	−0.101412	+	0.341707i
$306$	27.8718	+	466.447i	0.0910842	+	1.52434i
$307$	−201.655			−0.656858			−0.328429	−	0.944529i	$-0.606519\pi$
$307$	−201.655			−0.656858			−0.328429	+	0.944529i	$0.606519\pi$
$308$	−10.7365	−	89.5193i	−0.0348587	−	0.290647i
$309$	22.2765			0.0720923
$310$	430.898	+	100.355i	1.38999	+	0.323724i
$311$			319.387i			1.02697i	0.858099	+	0.513484i	$0.171645\pi$
$311$			319.387i			1.02697i	−0.858099	+	0.513484i	$0.828355\pi$
$312$	3.64085	+	20.1168i	0.0116694	+	0.0644769i
$313$		−	184.025i		−	0.587940i	−0.955815	−	0.293970i	$-0.905023\pi$
$313$		−	184.025i		−	0.587940i	0.955815	−	0.293970i	$-0.0949765\pi$
$314$	27.0252	+	452.279i	0.0860674	+	1.44038i
$315$	85.9095	−	289.472i	0.272729	−	0.918959i
$316$	−56.8934	−	474.369i	−0.180042	−	1.50117i
$317$		−	96.9360i		−	0.305792i	−0.988242	−	0.152896i	$-0.951140\pi$
$317$		−	96.9360i		−	0.305792i	0.988242	−	0.152896i	$-0.0488599\pi$
$318$	3.57098	+	59.7620i	0.0112295	+	0.187931i
$319$		−	63.8254i		−	0.200080i
$320$	−22.2522	−	319.225i	−0.0695382	−	0.997579i
$321$	−14.4654			−0.0450636
$322$	−468.875	+	28.0168i	−1.45613	+	0.0870088i
$323$	−374.653			−1.15992
$324$	309.519	−	37.1221i	0.955306	−	0.114575i
$325$	−103.207	+	158.563i	−0.317560	+	0.487887i
$326$	497.387	−	29.7206i	1.52573	−	0.0911673i
$327$	11.4169			0.0349141
$328$	531.227	−	96.1442i	1.61959	−	0.293123i
$329$	50.5047			0.153510
$330$	−10.9076	−	2.54034i	−0.0330533	−	0.00769800i
$331$			129.543i			0.391370i	0.980667	+	0.195685i	$0.0626930\pi$
$331$			129.543i			0.391370i	−0.980667	+	0.195685i	$0.937307\pi$
$332$	−365.317	+	43.8143i	−1.10035	+	0.131971i
$333$		−	413.886i		−	1.24290i
$334$	120.346	−	7.19110i	0.360318	−	0.0215302i
$335$	75.8999	−	255.745i	0.226567	−	0.763417i
$336$	−35.6771	+	8.68275i	−0.106182	+	0.0258415i
$337$			435.350i			1.29184i	0.763406	+	0.645919i	$0.223526\pi$
$337$			435.350i			1.29184i	−0.763406	+	0.645919i	$0.776474\pi$
$338$	−223.061	+	13.3287i	−0.659944	+	0.0394339i
$339$		−	44.0763i		−	0.130019i
$340$	518.357	+	88.5181i	1.52458	+	0.260347i
$341$	146.737			0.430314
$342$	15.1047	+	252.784i	0.0441657	+	0.739134i
$343$	352.125			1.02660
$344$	−428.092	+	77.4784i	−1.24445	+	0.225228i
$345$	−16.6003	+	55.9347i	−0.0481168	+	0.162130i
$346$	−2.97436	−	49.7772i	−0.00859640	−	0.143865i
$347$	−419.782			−1.20975			−0.604873	−	0.796322i	$-0.706776\pi$
$347$	−419.782			−1.20975			−0.604873	+	0.796322i	$0.706776\pi$
$348$	−25.8082	+	3.09531i	−0.0741616	+	0.00889456i
$349$	−573.417			−1.64303			−0.821514	−	0.570189i	$-0.806870\pi$
$349$	−573.417			−1.64303			−0.821514	+	0.570189i	$0.806870\pi$
$350$	−295.342	−	168.051i	−0.843836	−	0.480147i
$351$			45.7068i			0.130219i
$352$	−31.2031	−	101.441i	−0.0886452	−	0.288186i
$353$		−	4.05432i		−	0.0114853i	−0.999984	−	0.00574266i	$-0.998172\pi$
$353$		−	4.05432i		−	0.0114853i	0.999984	−	0.00574266i	$-0.00182796\pi$
$354$	2.99192	+	50.0712i	0.00845176	+	0.141444i
$355$	516.427	+	153.265i	1.45472	+	0.431733i
$356$	129.777	−	15.5648i	0.364542	−	0.0437213i
$357$		−	60.3400i		−	0.169020i
$358$	−32.6340	−	546.146i	−0.0911565	−	1.52555i
$359$		−	661.143i		−	1.84163i	−0.390005	−	0.920813i	$-0.627527\pi$
$359$		−	661.143i		−	1.84163i	0.390005	−	0.920813i	$-0.372473\pi$
$360$	38.8262	−	353.312i	0.107850	−	0.981422i
$361$	157.963			0.437570
$362$	297.890	−	17.7999i	0.822901	−	0.0491711i
$363$	−3.71446			−0.0102327
$364$	24.4980	+	204.261i	0.0673023	+	0.561157i
$365$	167.637	+	49.7512i	0.459279	+	0.136305i
$366$	14.6579	−	0.875860i	0.0400490	−	0.00239306i
$367$	210.234			0.572845			0.286423	−	0.958103i	$-0.407534\pi$
$367$	210.234			0.572845			0.286423	+	0.958103i	$0.407534\pi$
$368$	−537.235	+	130.747i	−1.45988	+	0.355291i
$369$	599.644			1.62505
$370$	−453.634	−	105.650i	−1.22604	−	0.285540i
$371$			602.460i			1.62388i
$372$	−7.11624	−	59.3342i	−0.0191297	−	0.159501i
$373$		−	63.7890i		−	0.171016i	−0.996337	−	0.0855080i	$-0.972749\pi$
$373$		−	63.7890i		−	0.171016i	0.996337	−	0.0855080i	$-0.0272513\pi$
$374$	174.098	−	10.4029i	0.465502	−	0.0278153i
$375$	−32.1393	+	27.3629i	−0.0857048	+	0.0729676i
$376$	58.5007	−	10.5878i	0.155587	−	0.0281590i
$377$			145.634i			0.386297i
$378$	−81.9469	+	4.89660i	−0.216791	+	0.0129540i
$379$			553.999i			1.46174i	0.682518	+	0.730869i	$0.260885\pi$
$379$			553.999i			1.46174i	−0.682518	+	0.730869i	$0.739115\pi$
$380$	280.916	+	47.9711i	0.739252	+	0.126240i
$381$	2.01897			0.00529914
$382$	−27.0830	−	453.246i	−0.0708978	−	1.18651i
$383$	36.9752			0.0965411			0.0482705	−	0.998834i	$-0.484629\pi$
$383$	36.9752			0.0965411			0.0482705	+	0.998834i	$0.484629\pi$
$384$	−39.5053	+	17.5367i	−0.102878	+	0.0456686i
$385$	−108.043	−	32.0651i	−0.280632	−	0.0832859i
$386$	30.5101	+	510.601i	0.0790418	+	1.32280i
$387$	−483.227			−1.24865
$388$	6.33920	+	52.8553i	0.0163381	+	0.136225i
$389$	560.923			1.44196			0.720981	−	0.692955i	$-0.243691\pi$
$389$	560.923			1.44196			0.720981	+	0.692955i	$0.243691\pi$
$390$	24.8885	+	5.79643i	0.0638165	+	0.0148626i
$391$		−	908.616i		−	2.32382i
$392$	22.1412	−	4.00724i	0.0564828	−	0.0102225i
$393$		−	3.83571i		−	0.00976006i
$394$	14.3191	+	239.637i	0.0363430	+	0.608216i
$395$	−572.529	−	169.915i	−1.44944	−	0.430165i
$396$	−14.0380	−	117.047i	−0.0354495	−	0.295573i
$397$			421.348i			1.06133i	0.847581	+	0.530665i	$0.178058\pi$
$397$			421.348i			1.06133i	−0.847581	+	0.530665i	$0.821942\pi$
$398$	17.2860	+	289.288i	0.0434321	+	0.726856i
$399$		−	32.7003i		−	0.0819557i
$400$	−377.332	−	132.742i	−0.943330	−	0.331856i
$401$	9.67014			0.0241151			0.0120575	−	0.999927i	$-0.496162\pi$
$401$	9.67014			0.0241151			0.0120575	+	0.999927i	$0.496162\pi$
$402$	−35.9687	+	2.14925i	−0.0894745	+	0.00534640i
$403$	−334.818			−0.830815
$404$	160.252	−	19.2198i	0.396663	−	0.0475738i
$405$	110.867	−	373.567i	0.273746	−	0.922388i
$406$	−261.105	+	15.6019i	−0.643115	+	0.0384283i
$407$	−154.480			−0.379557
$408$	−12.6496	−	69.8931i	−0.0310040	−	0.171307i
$409$	−95.1201			−0.232568			−0.116284	−	0.993216i	$-0.537098\pi$
$409$	−95.1201			−0.232568			−0.116284	+	0.993216i	$0.537098\pi$
$410$	153.067	−	657.232i	0.373334	−	1.60301i
$411$			33.0600i			0.0804380i
$412$	262.001	−	31.4231i	0.635925	−	0.0762697i
$413$			504.767i			1.22220i
$414$	−613.056	+	36.6322i	−1.48081	+	0.0884835i
$415$	−130.854	+	440.911i	−0.315310	+	1.06244i
$416$	71.1978	+	231.465i	0.171149	+	0.556405i
$417$			28.1230i			0.0674411i
$418$	94.3497	−	5.63771i	0.225717	−	0.0134873i
$419$			638.390i			1.52360i	0.647810	+	0.761802i	$0.275685\pi$
$419$			638.390i			1.52360i	−0.647810	+	0.761802i	$0.724315\pi$
$420$	−7.72601	+	45.2431i	−0.0183953	+	0.107722i
$421$	19.9200			0.0473160			0.0236580	−	0.999720i	$-0.492469\pi$
$421$	19.9200			0.0473160			0.0236580	+	0.999720i	$0.492469\pi$
$422$	14.0256	+	234.724i	0.0332359	+	0.556219i
$423$	66.0352			0.156111
$424$	126.299	+	697.843i	0.297876	+	1.64586i
$425$	358.579	−	550.907i	0.843716	−	1.29625i
$426$	−4.34000	−	72.6319i	−0.0101878	−	0.170497i
$427$	147.766			0.346057
$428$	−170.132	+	20.4048i	−0.397506	+	0.0476748i
$429$	8.47548			0.0197564
$430$	−123.350	+	529.634i	−0.286860	+	1.23171i
$431$			117.730i			0.273155i	0.990629	+	0.136577i	$0.0436103\pi$
$431$			117.730i			0.273155i	−0.990629	+	0.136577i	$0.956390\pi$
$432$	−93.8945	+	22.8512i	−0.217348	+	0.0528962i
$433$		−	8.18765i		−	0.0189091i	−0.999955	−	0.00945457i	$-0.996990\pi$
$433$		−	8.18765i		−	0.0189091i	0.999955	−	0.00945457i	$-0.00300953\pi$
$434$	−35.8694	−	600.291i	−0.0826484	−	1.38316i
$435$	−9.24430	+	31.1487i	−0.0212513	+	0.0716061i
$436$	134.278	−	16.1046i	0.307977	−	0.0369372i
$437$		−	492.410i		−	1.12680i
$438$	−1.40880	−	23.5770i	−0.00321644	−	0.0538287i
$439$			424.336i			0.966597i	0.875456	+	0.483298i	$0.160561\pi$
$439$			424.336i			0.966597i	−0.875456	+	0.483298i	$0.839439\pi$
$440$	−131.871	−	14.4916i	−0.299707	−	0.0329354i
$441$	24.9929			0.0566731
$442$	−397.249	+	23.7369i	−0.898752	+	0.0537035i
$443$	−381.909			−0.862098			−0.431049	−	0.902329i	$-0.641856\pi$
$443$	−381.909			−0.862098			−0.431049	+	0.902329i	$0.641856\pi$
$444$	7.49173	+	62.4650i	0.0168733	+	0.140687i
$445$	46.4851	−	156.631i	0.104461	−	0.351981i
$446$	−523.414	+	31.2757i	−1.17357	+	0.0701249i
$447$	48.3835			0.108241
$448$	−407.362	+	152.446i	−0.909290	+	0.340282i
$449$	−665.089			−1.48127			−0.740634	−	0.671909i	$-0.765475\pi$
$449$	−665.089			−1.48127			−0.740634	+	0.671909i	$0.765475\pi$
$450$	−386.162	−	219.728i	−0.858137	−	0.488285i
$451$		−	223.813i		−	0.496259i
$452$	−62.1738	−	518.396i	−0.137553	−	1.14689i
$453$		−	6.46035i		−	0.0142613i
$454$	538.003	−	32.1475i	1.18503	−	0.0708095i
$455$	246.528	+	73.1647i	0.541821	+	0.160801i
$456$	−6.85528	−	37.8775i	−0.0150335	−	0.0830647i
$457$		−	36.2416i		−	0.0793033i	−0.999214	−	0.0396517i	$-0.987375\pi$
$457$		−	36.2416i		−	0.0793033i	0.999214	−	0.0396517i	$-0.0126248\pi$
$458$	577.421	−	34.5028i	1.26074	−	0.0753337i
$459$		−	158.802i		−	0.345974i
$460$	−116.340	+	681.283i	−0.252914	+	1.48105i
$461$	87.1977			0.189149			0.0945745	−	0.995518i	$-0.469851\pi$
$461$	87.1977			0.189149			0.0945745	+	0.995518i	$0.469851\pi$
$462$	0.907985	+	15.1956i	0.00196534	+	0.0328908i
$463$	−244.001			−0.527001			−0.263500	−	0.964659i	$-0.584877\pi$
$463$	−244.001			−0.527001			−0.263500	+	0.964659i	$0.584877\pi$
$464$	−299.173	+	72.8099i	−0.644769	+	0.156918i
$465$	−71.6121	−	21.2530i	−0.154005	−	0.0457054i
$466$	−4.88693	−	81.7851i	−0.0104870	−	0.175504i
$467$	138.792			0.297200			0.148600	−	0.988897i	$-0.452523\pi$
$467$	138.792			0.297200			0.148600	+	0.988897i	$0.452523\pi$
$468$	32.0313	+	267.072i	0.0684430	+	0.570668i
$469$	−362.601			−0.773136
$470$	16.8563	−	72.3770i	0.0358645	−	0.153994i
$471$		−	76.4985i		−	0.162417i
$472$	105.819	+	584.683i	0.224193	+	1.23874i
$473$			180.361i			0.381313i
$474$	4.81148	+	80.5223i	0.0101508	+	0.169878i
$475$	194.327	−	298.556i	0.409109	−	0.628538i
$476$	−85.1152	−	709.678i	−0.178813	−	1.49092i
$477$			787.719i			1.65140i
$478$	−37.9960	−	635.881i	−0.0794896	−	1.33030i
$479$		−	639.640i		−	1.33537i	−0.744446	−	0.667683i	$-0.767286\pi$
$479$		−	639.640i		−	1.33537i	0.744446	−	0.667683i	$-0.232714\pi$
$480$	0.535521	+	54.0258i	0.00111567	+	0.112554i
$481$	352.485			0.732817
$482$	472.306	−	28.2218i	0.979887	−	0.0585515i
$483$	79.3055			0.164194
$484$	−43.6869	+	5.23959i	−0.0902622	+	0.0108256i
$485$	63.7925	+	18.9323i	0.131531	+	0.0390357i
$486$	−161.061	+	9.62391i	−0.331400	+	0.0198023i
$487$	−369.872			−0.759490			−0.379745	−	0.925091i	$-0.623988\pi$
$487$	−369.872			−0.759490			−0.379745	+	0.925091i	$0.623988\pi$
$488$	171.161	−	30.9776i	0.350740	−	0.0634788i
$489$	−84.1281			−0.172041
$490$	6.37975	−	27.3931i	0.0130199	−	0.0559042i
$491$		−	572.905i		−	1.16681i	−0.812180	−	0.583407i	$-0.801719\pi$
$491$		−	572.905i		−	1.16681i	0.812180	−	0.583407i	$-0.198281\pi$
$492$	−90.5003	+	10.8541i	−0.183944	+	0.0220613i
$493$		−	505.985i		−	1.02634i
$494$	−215.283	+	12.8639i	−0.435795	+	0.0260402i
$495$	−141.267	−	41.9253i	−0.285388	−	0.0846975i
$496$	−167.393	−	687.811i	−0.337486	−	1.38672i
$497$		−	732.202i		−	1.47324i
$498$	62.0112	−	3.70537i	0.124520	−	0.00744051i
$499$			746.848i			1.49669i	0.663310	+	0.748345i	$0.269151\pi$
$499$			746.848i			1.49669i	−0.663310	+	0.748345i	$0.730849\pi$
$500$	−339.403	+	367.159i	−0.678806	+	0.734318i
$501$	−20.3554			−0.0406295
$502$	35.3690	+	591.917i	0.0704562	+	1.17912i
$503$	701.770			1.39517			0.697584	−	0.716503i	$-0.254258\pi$
$503$	701.770			1.39517			0.697584	+	0.716503i	$0.254258\pi$
$504$	−475.399	+	86.0402i	−0.943251	+	0.170715i
$505$	57.4010	−	193.413i	0.113665	−	0.382995i
$506$	13.6727	+	228.819i	0.0270211	+	0.452211i
$507$	37.7286			0.0744153
$508$	23.7458	−	2.84795i	0.0467437	−	0.00560620i
$509$	652.960			1.28283			0.641415	−	0.767194i	$-0.278348\pi$
$509$	652.960			1.28283			0.641415	+	0.767194i	$0.278348\pi$
$510$	−86.4716	−	20.1389i	−0.169552	−	0.0394881i
$511$		−	237.679i		−	0.465125i
$512$	−439.898	+	261.981i	−0.859175	+	0.511682i
$513$		−	86.0603i		−	0.167759i
$514$	6.34150	+	106.128i	0.0123375	+	0.206474i
$515$	93.8467	−	316.217i	0.182227	−	0.614013i
$516$	72.9302	−	8.74688i	0.141338	−	0.0169513i
$517$		−	24.6471i		−	0.0476734i
$518$	37.7620	+	631.965i	0.0728997	+	1.22001i
$519$			8.41932i			0.0162222i
$520$	300.898	+	33.0662i	0.578649	+	0.0635889i
$521$	150.656			0.289167			0.144583	−	0.989493i	$-0.453816\pi$
$521$	150.656			0.289167			0.144583	+	0.989493i	$0.453816\pi$
$522$	−341.396	+	20.3995i	−0.654015	+	0.0390796i
$523$	286.395			0.547600			0.273800	−	0.961787i	$-0.411719\pi$
$523$	286.395			0.547600			0.273800	+	0.961787i	$0.411719\pi$
$524$	−5.41062	−	45.1130i	−0.0103256	−	0.0860935i
$525$	48.0841	+	31.2974i	0.0915888	+	0.0596141i
$526$	168.125	−	10.0460i	0.319629	−	0.0190989i
$527$	1163.28			2.20737
$528$	4.23733	+	17.4110i	0.00802524	+	0.0329754i
$529$	665.204			1.25747
$530$	863.369	+	201.076i	1.62900	+	0.379388i
$531$			659.986i			1.24291i
$532$	−46.1269	−	384.599i	−0.0867046	−	0.722931i
$533$			510.686i			0.958135i
$534$	−22.0291	+	1.31632i	−0.0412531	+	0.00246501i
$535$	−60.9401	+	205.338i	−0.113907	+	0.383809i
$536$	−420.008	+	76.0154i	−0.783598	+	0.141820i
$537$			92.3751i			0.172021i
$538$	−17.7515	+	1.06071i	−0.0329953	+	0.00197158i
$539$		−	9.32840i		−	0.0173069i
$540$	−20.3332	+	119.070i	−0.0376541	+	0.220500i
$541$	80.1371			0.148128			0.0740639	−	0.997254i	$-0.476403\pi$
$541$	80.1371			0.148128			0.0740639	+	0.997254i	$0.476403\pi$
$542$	16.6761	+	279.082i	0.0307677	+	0.514912i
$543$	−50.3851			−0.0927903
$544$	−247.367	−	804.193i	−0.454719	−	1.47830i
$545$	48.0973	−	162.064i	0.0882519	−	0.297365i
$546$	−2.07180	−	34.6725i	−0.00379450	−	0.0635028i
$547$	97.7575			0.178716			0.0893579	−	0.996000i	$-0.471519\pi$
$547$	97.7575			0.178716			0.0893579	+	0.996000i	$0.471519\pi$
$548$	46.6342	+	388.830i	0.0850990	+	0.709543i
$549$	193.205			0.351922
$550$	−82.0119	+	144.132i	−0.149113	+	0.262058i
$551$		−	274.211i		−	0.497661i
$552$	91.8614	−	16.6256i	0.166415	−	0.0301188i
$553$			811.745i			1.46789i
$554$	−33.4254	−	559.389i	−0.0603346	−	1.00973i
$555$	75.3907	+	22.3744i	0.135839	+	0.0403143i
$556$	39.6701	+	330.763i	0.0713490	+	0.594898i
$557$		−	864.931i		−	1.55284i	−0.630216	−	0.776420i	$-0.717034\pi$
$557$		−	864.931i		−	1.55284i	0.630216	−	0.776420i	$-0.282966\pi$
$558$	−46.8994	−	784.883i	−0.0840491	−	1.40660i
$559$		−	411.539i		−	0.736206i
$560$	−27.0485	+	543.017i	−0.0483009	+	0.969673i
$561$	−29.4469			−0.0524900
$562$	881.024	−	52.6441i	1.56766	−	0.0936728i
$563$	336.183			0.597128			0.298564	−	0.954390i	$-0.403492\pi$
$563$	336.183			0.597128			0.298564	+	0.954390i	$0.403492\pi$
$564$	−9.96624	+	1.19530i	−0.0176706	+	0.00211933i
$565$	−625.666	−	185.685i	−1.10737	−	0.328646i
$566$	−24.5230	+	1.46533i	−0.0433269	+	0.00258893i
$567$	−529.652			−0.934130
$568$	−153.498	−	848.126i	−0.270243	−	1.49318i
$569$	557.759			0.980245			0.490122	−	0.871654i	$-0.336952\pi$
$569$	557.759			0.980245			0.490122	+	0.871654i	$0.336952\pi$
$570$	−46.8620	−	10.9140i	−0.0822140	−	0.0191473i
$571$		−	196.621i		−	0.344346i	−0.985067	−	0.172173i	$-0.944921\pi$
$571$		−	196.621i		−	0.344346i	0.985067	−	0.172173i	$-0.0550788\pi$
$572$	99.6828	−	11.9555i	0.174271	−	0.0209011i
$573$			76.6620i			0.133791i
$574$	−915.601	+	54.7102i	−1.59512	+	0.0953140i
$575$	724.063	+	471.285i	1.25924	+	0.819626i
$576$	−532.628	+	199.325i	−0.924701	+	0.346050i
$577$		−	121.469i		−	0.210518i	−0.994445	−	0.105259i	$-0.966433\pi$
$577$		−	121.469i		−	0.210518i	0.994445	−	0.105259i	$-0.0335671\pi$
$578$	803.216	−	47.9949i	1.38965	−	0.0830361i
$579$		−	86.3631i		−	0.149159i
$580$	−64.7871	+	379.390i	−0.111702	+	0.654120i
$581$	625.134			1.07596
$582$	−0.536106	−	8.97198i	−0.000921144	−	0.0154158i
$583$	294.010			0.504306
$584$	−49.8269	−	275.309i	−0.0853200	−	0.471420i
$585$	322.337	+	95.6632i	0.551004	+	0.163527i
$586$	−3.07120	−	51.3980i	−0.00524096	−	0.0877098i
$587$	651.846			1.11047			0.555235	−	0.831693i	$-0.312628\pi$
$587$	651.846			1.11047			0.555235	+	0.831693i	$0.312628\pi$
$588$	−3.77200	+	0.452395i	−0.00641497	+	0.000769379i
$589$	630.423			1.07033
$590$	723.368	+	168.470i	1.22605	+	0.285542i
$591$		−	40.5322i		−	0.0685825i
$592$	176.225	+	724.103i	0.297678	+	1.22315i
$593$			723.673i			1.22036i	0.792263	+	0.610180i	$0.208903\pi$
$593$			723.673i			1.22036i	−0.792263	+	0.610180i	$0.791097\pi$
$594$	2.38962	+	39.9915i	0.00402294	+	0.0673257i
$595$	−856.530	−	254.201i	−1.43955	−	0.427228i
$596$	569.054	−	68.2495i	0.954789	−	0.114513i
$597$		−	48.9303i		−	0.0819602i
$598$	−31.1977	−	522.108i	−0.0521701	−	0.873091i
$599$			511.958i			0.854687i	0.904089	+	0.427344i	$0.140551\pi$
$599$			511.958i			0.854687i	−0.904089	+	0.427344i	$0.859449\pi$
$600$	62.2581	+	26.1722i	0.103763	+	0.0436203i
$601$	568.906			0.946598			0.473299	−	0.880902i	$-0.343063\pi$
$601$	568.906			0.946598			0.473299	+	0.880902i	$0.343063\pi$
$602$	737.843	−	44.0886i	1.22565	−	0.0732368i
$603$	−474.102			−0.786239
$604$	−9.11293	−	75.9823i	−0.0150876	−	0.125798i
$605$	−15.6483	+	52.7269i	−0.0258650	+	0.0871520i
$606$	−27.2022	+	1.62542i	−0.0448880	+	0.00268221i
$607$	−618.530			−1.01899			−0.509497	−	0.860472i	$-0.670169\pi$
$607$	−618.530			−1.01899			−0.509497	+	0.860472i	$0.670169\pi$
$608$	−134.057	−	435.820i	−0.220488	−	0.716809i
$609$	44.1633			0.0725177
$610$	49.3181	−	211.760i	0.0808494	−	0.347148i
$611$			56.2387i			0.0920437i
$612$	−111.289	−	927.907i	−0.181844	−	1.51619i
$613$			189.349i			0.308889i	0.988001	+	0.154445i	$0.0493588\pi$
$613$			189.349i			0.308889i	−0.988001	+	0.154445i	$0.950641\pi$
$614$	402.593	−	24.0563i	0.655688	−	0.0391796i
$615$	−32.4165	+	109.227i	−0.0527097	+	0.177605i
$616$	32.1139	+	177.439i	0.0521329	+	0.288050i
$617$		−	615.603i		−	0.997737i	−0.866678	−	0.498868i	$-0.833749\pi$
$617$		−	615.603i		−	0.997737i	0.866678	−	0.498868i	$-0.166251\pi$
$618$	−44.4737	+	2.65745i	−0.0719639	+	0.00430008i
$619$			819.178i			1.32339i	0.749773	+	0.661695i	$0.230163\pi$
$619$			819.178i			1.32339i	−0.749773	+	0.661695i	$0.769837\pi$
$620$	−872.233	−	148.948i	−1.40683	−	0.240239i
$621$	208.715			0.336095
$622$	−38.1009	−	637.636i	−0.0612555	−	1.02514i
$623$	−222.076			−0.356462
$624$	−9.66854	−	39.7276i	−0.0154945	−	0.0636661i
$625$	253.021	+	571.494i	0.404833	+	0.914390i
$626$	21.9531	+	367.395i	0.0350688	+	0.586893i
$627$	−15.9583			−0.0254518
$628$	−107.908	−	899.723i	−0.171828	−	1.43268i
$629$	−1224.66			−1.94700
$630$	−136.981	+	588.162i	−0.217430	+	0.933590i
$631$			347.524i			0.550751i	0.961337	+	0.275375i	$0.0888021\pi$
$631$			347.524i			0.550751i	−0.961337	+	0.275375i	$0.911198\pi$
$632$	170.174	+	940.262i	0.269262	+	1.48776i
$633$		−	39.7013i		−	0.0627193i
$634$	11.5639	+	193.527i	0.0182395	+	0.305247i
$635$	8.50555	−	28.6595i	0.0133946	−	0.0451330i
$636$	−14.2585	−	118.885i	−0.0224190	−	0.186926i
$637$			21.2851i			0.0334146i
$638$	7.61398	+	127.423i	0.0119341	+	0.199723i
$639$		−	957.357i		−	1.49821i
$640$	82.5069	+	634.659i	0.128917	+	0.991655i
$641$	−34.9339			−0.0544990			−0.0272495	−	0.999629i	$-0.508675\pi$
$641$	−34.9339			−0.0544990			−0.0272495	+	0.999629i	$0.508675\pi$
$642$	28.8793	−	1.72564i	0.0449834	−	0.00268791i
$643$	−710.122			−1.10439			−0.552194	−	0.833715i	$-0.686209\pi$
$643$	−710.122			−1.10439			−0.552194	+	0.833715i	$0.686209\pi$
$644$	932.738	−	111.868i	1.44835	−	0.173708i
$645$	26.1230	−	88.0214i	0.0405008	−	0.136467i
$646$	747.971	−	44.6938i	1.15785	−	0.0691854i
$647$	−190.839			−0.294960			−0.147480	−	0.989065i	$-0.547116\pi$
$647$	−190.839			−0.294960			−0.147480	+	0.989065i	$0.547116\pi$
$648$	−613.507	+	111.036i	−0.946771	+	0.171352i
$649$	246.335			0.379561
$650$	187.131	−	328.874i	0.287894	−	0.505960i
$651$			101.533i			0.155965i
$652$	−989.458	+	118.671i	−1.51757	+	0.182010i
$653$		−	106.664i		−	0.163344i	−0.996659	−	0.0816720i	$-0.973974\pi$
$653$		−	106.664i		−	0.163344i	0.996659	−	0.0816720i	$-0.0260260\pi$
$654$	−22.7932	+	1.36197i	−0.0348519	+	0.00208252i
$655$	−54.4481	−	16.1591i	−0.0831269	−	0.0246704i
$656$	−1049.09	+	255.318i	−1.59923	+	0.389205i
$657$		−	310.767i		−	0.473008i
$658$	−100.830	+	6.02490i	−0.153236	+	0.00915639i
$659$		−	924.093i		−	1.40227i	−0.713031	−	0.701133i	$-0.752678\pi$
$659$		−	924.093i		−	1.40227i	0.713031	−	0.701133i	$-0.247322\pi$
$660$	22.0794	+	3.77042i	0.0334536	+	0.00571276i
$661$	−1044.05			−1.57951			−0.789753	−	0.613425i	$-0.789791\pi$
$661$	−1044.05			−1.57951			−0.789753	+	0.613425i	$0.789791\pi$
$662$	−15.4537	−	258.626i	−0.0233440	−	0.390673i
$663$	67.1906			0.101343
$664$	724.107	−	131.053i	1.09052	−	0.197368i
$665$	−464.183	−	137.760i	−0.698020	−	0.207158i
$666$	49.3740	+	826.297i	0.0741352	+	1.24069i
$667$	665.022			0.997035
$668$	−239.406	+	28.7132i	−0.358393	+	0.0429838i
$669$	88.5302			0.132332
$670$	−121.021	+	519.633i	−0.180628	+	0.775572i
$671$		−	72.1124i		−	0.107470i
$672$	70.1913	−	21.5906i	0.104451	−	0.0321289i
$673$			327.324i			0.486365i	0.969981	+	0.243183i	$0.0781914\pi$
$673$			327.324i			0.486365i	−0.969981	+	0.243183i	$0.921809\pi$
$674$	−51.9346	−	869.149i	−0.0770542	−	1.28954i
$675$	126.547	+	82.3682i	0.187477	+	0.122027i
$676$	443.738	−	53.2197i	0.656417	−	0.0787274i
$677$		−	402.278i		−	0.594206i	−0.954845	−	0.297103i	$-0.903979\pi$
$677$		−	402.278i		−	0.594206i	0.954845	−	0.297103i	$-0.0960205\pi$
$678$	5.25804	+	87.9957i	0.00775522	+	0.129787i
$679$		−	90.4465i		−	0.133205i
$680$	−1045.43	−	114.884i	−1.53739	−	0.168947i
$681$	−90.9979			−0.133624
$682$	−292.952	+	17.5049i	−0.429548	+	0.0256670i
$683$	1136.74			1.66433			0.832166	−	0.554526i	$-0.187101\pi$
$683$	1136.74			1.66433			0.832166	+	0.554526i	$0.187101\pi$
$684$	−60.3111	−	502.865i	−0.0881741	−	0.735183i
$685$	469.289	+	139.276i	0.685094	+	0.203322i
$686$	−702.997	+	42.0064i	−1.02478	+	0.0612338i
$687$	−97.6650			−0.142162
$688$	845.417	−	205.750i	1.22880	−	0.299055i
$689$	−670.860			−0.973672
$690$	26.4688	−	113.651i	0.0383606	−	0.164711i
$691$		−	280.686i		−	0.406202i	−0.979158	−	0.203101i	$-0.934898\pi$
$691$		−	280.686i		−	0.406202i	0.979158	−	0.203101i	$-0.0651021\pi$
$692$	11.8762	+	99.0224i	0.0171622	+	0.143096i
$693$			200.292i			0.289021i
$694$	838.069	−	50.0774i	1.20759	−	0.0721577i
$695$	399.207	+	118.477i	0.574399	+	0.170470i
$696$	51.1553	−	9.25836i	0.0734990	−	0.0133022i
$697$		−	1774.31i		−	2.54564i
$698$	1144.79	−	68.4051i	1.64010	−	0.0980016i
$699$			13.8331i			0.0197899i
$700$	609.681	+	300.272i	0.870972	+	0.428960i
$701$	−1131.37			−1.61393			−0.806967	−	0.590597i	$-0.798892\pi$
$701$	−1131.37			−1.61393			−0.806967	+	0.590597i	$0.798892\pi$
$702$	−5.45254	−	91.2507i	−0.00776715	−	0.129987i
$703$	−663.687			−0.944078
$704$	74.3964	+	198.799i	0.105677	+	0.282385i
$705$	−3.56983	+	12.0285i	−0.00506358	+	0.0170617i
$706$	0.483655	+	8.09420i	0.000685064	+	0.0114649i
$707$	−274.225			−0.387871
$708$	−11.9464	−	99.6072i	−0.0168734	−	0.140688i
$709$	−123.300			−0.173907			−0.0869535	−	0.996212i	$-0.527713\pi$
$709$	−123.300			−0.173907			−0.0869535	+	0.996212i	$0.527713\pi$
$710$	−1049.30	−	244.378i	−1.47789	−	0.344194i
$711$			1061.36i			1.49277i
$712$	−257.235	+	46.5558i	−0.361285	+	0.0653873i
$713$			1528.91i			2.14434i
$714$	7.19819	+	120.465i	0.0100815	+	0.168719i
$715$	35.7056	−	120.310i	0.0499379	−	0.168266i
$716$	130.304	+	1086.45i	0.181988	+	1.51739i
$717$			107.553i			0.150004i
$718$	78.8704	+	1319.93i	0.109847	+	1.83835i
$719$		−	832.447i		−	1.15778i	−0.815404	−	0.578892i	$-0.803485\pi$
$719$		−	832.447i		−	1.15778i	0.815404	−	0.578892i	$-0.196515\pi$
$720$	−35.3661	+	709.998i	−0.0491195	+	0.986108i
$721$	−448.339			−0.621829
$722$	−315.363	+	18.8440i	−0.436791	+	0.0260997i
$723$	−79.8858			−0.110492
$724$	−592.596	+	71.0729i	−0.818502	+	0.0981670i
$725$	403.213	+	262.447i	0.556156	+	0.361996i
$726$	7.41568	−	0.443112i	0.0102144	−	0.000610347i
$727$	−436.428			−0.600314			−0.300157	−	0.953890i	$-0.597039\pi$
$727$	−436.428			−0.600314			−0.300157	+	0.953890i	$0.597039\pi$
$728$	−73.2760	−	404.872i	−0.100654	−	0.556143i
$729$	−674.167			−0.924783
$730$	−340.612	−	79.3272i	−0.466591	−	0.108667i
$731$			1429.84i			1.95600i
$732$	−29.1592	+	3.49720i	−0.0398349	+	0.00477760i
$733$			269.567i			0.367759i	0.982949	+	0.183879i	$0.0588655\pi$
$733$			269.567i			0.367759i	−0.982949	+	0.183879i	$0.941134\pi$
$734$	−419.720	+	25.0797i	−0.571826	+	0.0341685i
$735$	−1.35110	+	4.55253i	−0.00183823	+	0.00619392i
$736$	1056.96	−	325.118i	1.43609	−	0.441736i
$737$			176.955i			0.240102i
$738$	−1197.15	+	71.5339i	−1.62216	+	0.0969294i
$739$		−	717.958i		−	0.971526i	−0.874091	−	0.485763i	$-0.838542\pi$
$739$		−	717.958i		−	0.971526i	0.874091	−	0.485763i	$-0.161458\pi$
$740$	918.255	+	156.807i	1.24089	+	0.211902i
$741$	36.4129			0.0491403
$742$	−71.8698	−	1202.77i	−0.0968596	−	1.62099i
$743$	−836.208			−1.12545			−0.562724	−	0.826645i	$-0.690247\pi$
$743$	−836.208			−1.12545			−0.562724	+	0.826645i	$0.690247\pi$
$744$	21.2854	+	117.608i	0.0286094	+	0.158076i
$745$	203.831	−	686.807i	0.273598	−	0.921889i
$746$	7.60964	+	127.351i	0.0102006	+	0.170712i
$747$	817.366			1.09420
$748$	−346.335	+	41.5376i	−0.463014	+	0.0555316i
$749$	291.132			0.388694
$750$	60.8999	−	58.4623i	0.0811999	−	0.0779497i
$751$			86.4880i			0.115164i	0.998341	+	0.0575819i	$0.0183390\pi$
$751$			86.4880i			0.115164i	−0.998341	+	0.0575819i	$0.981661\pi$
$752$	−115.530	+	28.1166i	−0.153630	+	0.0373891i
$753$		−	100.117i		−	0.132957i
$754$	−17.3732	−	290.749i	−0.0230414	−	0.385609i
$755$	−91.7051	−	27.2162i	−0.121464	−	0.0360480i
$756$	163.018	−	19.5515i	0.215632	−	0.0258618i
$757$			595.235i			0.786308i	0.919473	+	0.393154i	$0.128616\pi$
$757$			595.235i			0.786308i	−0.919473	+	0.393154i	$0.871384\pi$
$758$	−66.0887	−	1106.02i	−0.0871882	−	1.45914i
$759$		−	38.7024i		−	0.0509913i
$760$	−566.554	−	62.2597i	−0.745466	−	0.0819207i
$761$	549.658			0.722283			0.361142	−	0.932511i	$-0.382387\pi$
$761$	549.658			0.722283			0.361142	+	0.932511i	$0.382387\pi$
$762$	−4.03076	+	0.240851i	−0.00528971	+	0.000316078i
$763$	−229.778			−0.301150
$764$	108.139	+	901.647i	0.141543	+	1.18017i
$765$	−1119.92	−	332.369i	−1.46394	−	0.434469i
$766$	−73.8188	+	4.41092i	−0.0963692	+	0.00575838i
$767$	−562.076			−0.732824
$768$	76.7779	−	39.7238i	0.0999712	−	0.0517237i
$769$	−1135.49			−1.47658			−0.738291	−	0.674483i	$-0.764367\pi$
$769$	−1135.49			−1.47658			−0.738291	+	0.674483i	$0.764367\pi$
$770$	219.527	+	51.1271i	0.285100	+	0.0663988i
$771$		−	17.9505i		−	0.0232821i
$772$	−121.823	−	1015.74i	−0.157802	−	1.31573i
$773$			1116.93i			1.44493i	0.691410	+	0.722463i	$0.256990\pi$
$773$			1116.93i			1.44493i	−0.691410	+	0.722463i	$0.743010\pi$
$774$	964.733	−	57.6460i	1.24643	−	0.0744781i
$775$	−603.376	+	927.004i	−0.778550	+	1.19613i
$776$	−18.9611	−	104.766i	−0.0244345	−	0.135008i
$777$		−	106.891i		−	0.137568i
$778$	−1119.85	+	66.9148i	−1.43940	+	0.0860087i
$779$		−	961.560i		−	1.23435i
$780$	−50.3798	−	8.60318i	−0.0645894	−	0.0110297i
$781$	−357.327			−0.457525
$782$	108.392	+	1814.00i	0.138609	+	2.31969i
$783$	116.228			0.148440
$784$	−43.7256	+	10.6415i	−0.0557724	+	0.0135734i
$785$	−1085.90	−	322.274i	−1.38331	−	0.410540i
$786$	0.457576	+	7.65775i	0.000582158	+	0.00974269i
$787$	−211.481			−0.268718			−0.134359	−	0.990933i	$-0.542898\pi$
$787$	−211.481			−0.268718			−0.134359	+	0.990933i	$0.542898\pi$
$788$	−57.1745	−	476.713i	−0.0725565	−	0.604965i
$789$	−28.4366			−0.0360414
$790$	1163.29	+	270.926i	1.47252	+	0.342944i
$791$			887.084i			1.12147i
$792$	41.9890	+	232.002i	0.0530165	+	0.292932i
$793$			164.543i			0.207494i
$794$	−50.2643	−	841.196i	−0.0633052	−	1.05944i
$795$	−143.486	−	42.5837i	−0.180485	−	0.0535644i
$796$	−69.0207	−	575.485i	−0.0867094	−	0.722971i
$797$		−	192.909i		−	0.242044i	−0.992650	−	0.121022i	$-0.961383\pi$
$797$		−	192.909i		−	0.242044i	0.992650	−	0.121022i	$-0.0386171\pi$
$798$	3.90095	+	65.2842i	0.00488841	+	0.0818098i
$799$		−	195.394i		−	0.244548i
$800$	769.156	+	219.999i	0.961445	+	0.274998i
$801$	−290.365			−0.362503
$802$	−19.3058	+	1.15359i	−0.0240721	+	0.00143839i
$803$	−115.991			−0.144448
$804$	71.5530	−	8.58171i	0.0889963	−	0.0106738i
$805$	334.099	−	1125.75i	0.415030	−	1.39844i
$806$	668.445	−	39.9418i	0.829336	−	0.0495556i
$807$	3.00249			0.00372055
$808$	−317.641	+	57.4883i	−0.393119	+	0.0711489i
$809$	−198.401			−0.245242			−0.122621	−	0.992454i	$-0.539130\pi$
$809$	−198.401			−0.245242			−0.122621	+	0.992454i	$0.539130\pi$
$810$	−176.775	+	759.030i	−0.218241	+	0.937074i
$811$		−	348.393i		−	0.429585i	−0.976660	−	0.214792i	$-0.931092\pi$
$811$		−	348.393i		−	0.429585i	0.976660	−	0.214792i	$-0.0689075\pi$
$812$	519.419	−	62.2964i	0.639678	−	0.0767197i
$813$		−	47.2040i		−	0.0580615i
$814$	308.409	−	18.4285i	0.378881	−	0.0226394i
$815$	−354.416	+	1194.20i	−0.434866	+	1.46528i
$816$	33.5920	+	138.028i	0.0411667	+	0.169152i
$817$			774.879i			0.948445i
$818$	189.902	−	11.3473i	0.232153	−	0.0138719i
$819$		−	457.017i		−	0.558018i
$820$	−227.185	+	1330.38i	−0.277055	+	1.62242i
$821$	−1087.94			−1.32514			−0.662571	−	0.748999i	$-0.730535\pi$
$821$	−1087.94			−1.32514			−0.662571	+	0.748999i	$0.730535\pi$
$822$	−3.94386	−	66.0023i	−0.00479788	−	0.0802948i
$823$	−499.591			−0.607036			−0.303518	−	0.952826i	$-0.598161\pi$
$823$	−499.591			−0.607036			−0.303518	+	0.952826i	$0.598161\pi$
$824$	−519.321	+	93.9895i	−0.630244	+	0.114065i
$825$	15.2737	−	23.4658i	0.0185135	−	0.0284434i
$826$	−60.2157	−	1007.74i	−0.0729003	−	1.22002i
$827$	−1141.91			−1.38078			−0.690392	−	0.723436i	$-0.742562\pi$
$827$	−1141.91			−1.38078			−0.690392	+	0.723436i	$0.742562\pi$
$828$	1219.56	−	146.268i	1.47290	−	0.176652i
$829$	1005.42			1.21281			0.606404	−	0.795157i	$-0.292611\pi$
$829$	1005.42			1.21281			0.606404	+	0.795157i	$0.292611\pi$
$830$	208.643	−	895.863i	0.251377	−	1.07935i
$831$			94.6151i			0.113857i
$832$	−169.754	−	453.611i	−0.204032	−	0.545206i
$833$		−	73.9523i		−	0.0887783i
$834$	−3.35490	−	56.1458i	−0.00402266	−	0.0673211i
$835$	−85.7534	+	288.946i	−0.102699	+	0.346043i
$836$	−187.691	+	22.5107i	−0.224511	+	0.0269267i
$837$			267.214i			0.319252i
$838$	−76.1560	−	1274.51i	−0.0908783	−	1.52089i
$839$		−	401.529i		−	0.478581i	−0.970948	−	0.239290i	$-0.923085\pi$
$839$		−	401.529i		−	0.478581i	0.970948	−	0.239290i	$-0.0769148\pi$
$840$	10.0273	−	91.2468i	0.0119372	−	0.108627i
$841$	−470.666			−0.559650
$842$	−39.7691	+	2.37634i	−0.0472317	+	0.00282225i
$843$	−149.016			−0.176769
$844$	−56.0024	−	466.940i	−0.0663535	−	0.553246i
$845$	158.943	−	535.560i	0.188099	−	0.633799i
$846$	−131.835	+	7.87759i	−0.155834	+	0.00931158i
$847$	74.7574			0.0882614
$848$	−335.397	−	1378.13i	−0.395516	−	1.62516i
$849$	4.14782			0.00488554
$850$	−650.162	+	1142.63i	−0.764896	+	1.34427i
$851$		−	1609.59i		−	1.89141i
$852$	17.3291	+	144.487i	0.0203393	+	0.169586i
$853$			298.364i			0.349782i	0.984588	+	0.174891i	$0.0559574\pi$
$853$			298.364i			0.349782i	−0.984588	+	0.174891i	$0.944043\pi$
$854$	−295.006	+	17.6276i	−0.345441	+	0.0206412i
$855$	−606.922	−	180.122i	−0.709850	−	0.210669i
$856$	337.225	−	61.0328i	0.393954	−	0.0713000i
$857$			1380.73i			1.61112i	0.592515	+	0.805560i	$0.298135\pi$
$857$			1380.73i			1.61112i	−0.592515	+	0.805560i	$0.701865\pi$
$858$	−16.9208	+	1.01107i	−0.0197212	+	0.00117841i
$859$			313.865i			0.365384i	0.983170	+	0.182692i	$0.0584811\pi$
$859$			313.865i			0.365384i	−0.983170	+	0.182692i	$0.941519\pi$
$860$	183.079	−	1072.10i	0.212882	−	1.24663i
$861$	154.865			0.179866
$862$	−14.0444	−	235.040i	−0.0162929	−	0.272669i
$863$	742.534			0.860410			0.430205	−	0.902731i	$-0.358441\pi$
$863$	742.534			0.860410			0.430205	+	0.902731i	$0.358441\pi$
$864$	184.729	−	56.8220i	0.213806	−	0.0657662i
$865$	119.513	+	35.4690i	0.138165	+	0.0410046i
$866$	0.976737	+	16.3462i	0.00112787	+	0.0188755i
$867$	−135.856			−0.156697
$868$	143.222	+	1194.17i	0.165002	+	1.37577i
$869$	396.145			0.455863
$870$	14.7398	−	63.2892i	0.0169423	−	0.0727462i
$871$		−	403.768i		−	0.463569i
$872$	−266.157	+	48.1704i	−0.305225	+	0.0552413i
$873$		−	118.259i		−	0.135463i
$874$	58.7416	+	983.067i	0.0672100	+	1.12479i
$875$	646.838	−	550.707i	0.739244	−	0.629380i
$876$	5.62518	+	46.9019i	0.00642143	+	0.0535410i
$877$			1053.23i			1.20095i	0.799645	+	0.600473i	$0.205021\pi$
$877$			1053.23i			1.20095i	−0.799645	+	0.600473i	$0.794979\pi$
$878$	−50.6207	−	847.161i	−0.0576546	−	0.964876i
$879$			8.69345i			0.00989016i
$880$	265.001	+	13.2001i	0.301138	+	0.0150001i
$881$	−265.004			−0.300799			−0.150400	−	0.988625i	$-0.548056\pi$
$881$	−265.004			−0.300799			−0.150400	+	0.988625i	$0.548056\pi$
$882$	−49.8967	+	2.98150i	−0.0565722	+	0.00338038i
$883$	−207.575			−0.235079			−0.117540	−	0.993068i	$-0.537501\pi$
$883$	−207.575			−0.235079			−0.117540	+	0.993068i	$0.537501\pi$
$884$	790.251	−	94.7787i	0.893949	−	0.107216i
$885$	−120.219	−	35.6785i	−0.135840	−	0.0403147i
$886$	762.459	−	45.5595i	0.860563	−	0.0514215i
$887$	1182.03			1.33262			0.666308	−	0.745676i	$-0.267874\pi$
$887$	1182.03			1.33262			0.666308	+	0.745676i	$0.267874\pi$
$888$	−22.4085	−	123.814i	−0.0252348	−	0.139430i
$889$	−40.6340			−0.0457076
$890$	−74.1194	+	318.251i	−0.0832802	+	0.357585i
$891$			258.479i			0.290100i
$892$	1041.23	−	124.880i	1.16730	−	0.140000i
$893$		−	105.891i		−	0.118579i
$894$	−96.5948	+	5.77186i	−0.108048	+	0.00645622i
$895$	1311.27	+	389.159i	1.46511	+	0.434814i
$896$	795.087	−	352.946i	0.887374	−	0.393913i
$897$			88.3094i			0.0984497i
$898$	1327.81	−	79.3411i	1.47863	−	0.0883531i
$899$			851.415i			0.947069i
$900$	797.161	+	392.607i	0.885734	+	0.436230i
$901$	2330.81			2.58692
$902$	26.6995	+	446.829i	0.0296003	+	0.495376i
$903$	−124.799			−0.138205
$904$	185.968	+	1027.53i	0.205716	+	1.13665i
$905$	−212.263	+	715.220i	−0.234545	+	0.790299i
$906$	0.770681	+	12.8977i	0.000850641	+	0.0142359i
$907$	1636.73			1.80455			0.902277	−	0.431156i	$-0.141894\pi$
$907$	1636.73			1.80455			0.902277	+	0.431156i	$0.141894\pi$
$908$	−1070.26	+	128.361i	−1.17870	+	0.141367i
$909$	−358.550			−0.394444
$910$	−500.907	−	116.659i	−0.550447	−	0.128197i
$911$		−	24.0881i		−	0.0264414i	−0.999913	−	0.0132207i	$-0.995792\pi$
$911$		−	24.0881i		−	0.0264414i	0.999913	−	0.0132207i	$-0.00420841\pi$
$912$	18.2047	+	74.8024i	0.0199613	+	0.0820201i
$913$		−	305.076i		−	0.334146i
$914$	4.32341	+	72.3542i	0.00473020	+	0.0791621i
$915$	−10.4446	+	35.1930i	−0.0114148	+	0.0384623i
$916$	−1148.67	+	137.766i	−1.25401	+	0.150399i
$917$			77.1977i			0.0841851i
$918$	18.9441	+	317.039i	0.0206363	+	0.345358i
$919$			418.233i			0.455095i	0.973767	+	0.227548i	$0.0730707\pi$
$919$			418.233i			0.455095i	−0.973767	+	0.227548i	$0.926929\pi$
$920$	150.994	−	1374.02i	0.164123	−	1.49350i
$921$	−68.0945			−0.0739354
$922$	−174.085	+	10.4022i	−0.188812	+	0.0112822i
$923$	815.332			0.883350
$924$	−3.62547	−	30.2287i	−0.00392367	−	0.0327150i
$925$	635.213	−	975.917i	0.686717	−	1.05504i
$926$	487.134	−	29.1079i	0.526063	−	0.0314340i
$927$	−586.205			−0.632368
$928$	588.594	−	181.050i	0.634261	−	0.195097i
$929$	1173.64			1.26334			0.631671	−	0.775237i	$-0.282370\pi$
$929$	1173.64			1.26334			0.631671	+	0.775237i	$0.282370\pi$
$930$	145.505	+	33.8875i	0.156456	+	0.0364382i
$931$		−	40.0773i		−	0.0430476i
$932$	19.5129	+	162.696i	0.0209366	+	0.174566i
$933$			107.850i			0.115595i
$934$	−277.090	+	16.5571i	−0.296671	+	0.0177271i
$935$	−124.054	+	418.001i	−0.132678	+	0.447060i
$936$	−95.8087	−	529.373i	−0.102360	−	0.565569i
$937$		−	553.381i		−	0.590588i	−0.955406	−	0.295294i	$-0.904582\pi$
$937$		−	553.381i		−	0.590588i	0.955406	−	0.295294i	$-0.0954175\pi$
$938$	723.910	−	43.2560i	0.771759	−	0.0461152i
$939$		−	62.1412i		−	0.0661780i
$940$	−25.0185	+	146.507i	−0.0266154	+	0.155859i
$941$	1581.26			1.68040			0.840202	−	0.542273i	$-0.182436\pi$
$941$	1581.26			1.68040			0.840202	+	0.542273i	$0.182436\pi$
$942$	9.12580	+	152.725i	0.00968769	+	0.162128i
$943$	2332.00			2.47295
$944$	−281.011	−	1154.66i	−0.297681	−	1.22316i
$945$	58.3917	−	196.751i	0.0617902	−	0.208202i
$946$	−21.5160	−	360.080i	−0.0227441	−	0.380634i
$947$	−154.003			−0.162622			−0.0813108	−	0.996689i	$-0.525911\pi$
$947$	−154.003			−0.162622			−0.0813108	+	0.996689i	$0.525911\pi$
$948$	−19.2116	−	160.184i	−0.0202654	−	0.168970i
$949$	264.664			0.278887
$950$	−352.345	+	619.230i	−0.370890	+	0.651821i
$951$		−	32.7331i		−	0.0344197i
$952$	254.588	+	1406.68i	0.267424	+	1.47760i
$953$		−	1091.92i		−	1.14577i	−0.819636	−	0.572885i	$-0.805824\pi$
$953$		−	1091.92i		−	1.14577i	0.819636	−	0.572885i	$-0.194176\pi$
$954$	−93.9701	−	1572.63i	−0.0985012	−	1.64846i
$955$	1088.22	+	322.963i	1.13950	+	0.338181i
$956$	151.714	+	1264.97i	0.158696	+	1.32319i
$957$		−	21.5524i		−	0.0225208i
$958$	76.3052	+	1277.00i	0.0796505	+	1.33299i
$959$		−	665.368i		−	0.693815i
$960$	−7.51408	−	107.795i	−0.00782717	−	0.112287i
$961$	−996.438			−1.03688
$962$	−703.715	+	42.0493i	−0.731512	+	0.0437103i
$963$	380.657			0.395282
$964$	−939.563	+	112.686i	−0.974650	+	0.116895i
$965$	−1225.93	−	363.831i	−1.27039	−	0.377027i
$966$	−158.329	+	9.46066i	−0.163901	+	0.00979365i
$967$	−1164.42			−1.20415			−0.602077	−	0.798438i	$-0.705660\pi$
$967$	−1164.42			−1.20415			−0.602077	+	0.798438i	$0.705660\pi$
$968$	86.5932	−	15.6721i	0.0894558	−	0.0161902i
$969$	−126.512			−0.130559
$970$	−129.616	−	30.1872i	−0.133625	−	0.0311208i
$971$		−	1070.67i		−	1.10264i	−0.834293	−	0.551321i	$-0.814124\pi$
$971$		−	1070.67i		−	1.10264i	0.834293	−	0.551321i	$-0.185876\pi$
$972$	320.400	−	38.4271i	0.329629	−	0.0395341i
$973$		−	566.005i		−	0.581711i
$974$	738.426	−	44.1234i	0.758138	−	0.0453013i
$975$	−34.8507	+	53.5433i	−0.0357444	+	0.0549162i
$976$	−338.017	+	82.2634i	−0.346329	+	0.0842863i
$977$		−	846.227i		−	0.866149i	−0.901358	−	0.433074i	$-0.857429\pi$
$977$		−	846.227i		−	0.866149i	0.901358	−	0.433074i	$-0.142571\pi$
$978$	167.957	−	10.0360i	0.171735	−	0.0102617i
$979$			108.377i			0.110701i
$980$	−9.46896	+	55.4497i	−0.00966220	+	0.0565813i
$981$	−300.435			−0.306254
$982$	68.3441	+	1143.77i	0.0695969	+	1.16474i
$983$	−1825.55			−1.85712			−0.928560	−	0.371182i	$-0.878952\pi$
$983$	−1825.55			−1.85712			−0.928560	+	0.371182i	$0.878952\pi$
$984$	179.383	−	32.4658i	0.182300	−	0.0329937i
$985$	−575.358	−	170.755i	−0.584120	−	0.173355i
$986$	60.3610	+	1010.17i	0.0612180	+	1.02451i
$987$	17.0543			0.0172789
$988$	428.264	−	51.3639i	0.433466	−	0.0519877i
$989$	−1879.25			−1.90015
$990$	287.033	+	66.8489i	0.289932	+	0.0675241i
$991$		−	240.199i		−	0.242381i	−0.992629	−	0.121190i	$-0.961329\pi$
$991$		−	240.199i		−	0.242381i	0.992629	−	0.121190i	$-0.0386711\pi$
$992$	416.241	+	1353.20i	0.419598	+	1.36412i
$993$			43.7439i			0.0440523i
$994$	87.3472	+	1461.80i	0.0878745	+	1.47062i
$995$	−694.568	−	206.134i	−0.698059	−	0.207170i
$996$	−123.359	+	14.7951i	−0.123855	+	0.0148545i
$997$		−	799.638i		−	0.802044i	−0.916068	−	0.401022i	$-0.868655\pi$
$997$		−	799.638i		−	0.802044i	0.916068	−	0.401022i	$-0.131345\pi$
$998$	−89.0945	−	1491.04i	−0.0892730	−	1.49403i
$999$		−	281.313i		−	0.281595i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	220.3.h.a.199.2	yes	60
4.3	odd	2	inner	220.3.h.a.199.60	yes	60
5.4	even	2	inner	220.3.h.a.199.59	yes	60
20.19	odd	2	inner	220.3.h.a.199.1	✓	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
220.3.h.a.199.1	✓	60	20.19	odd	2	inner
220.3.h.a.199.2	yes	60	1.1	even	1	trivial
220.3.h.a.199.59	yes	60	5.4	even	2	inner
220.3.h.a.199.60	yes	60	4.3	odd	2	inner

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:	\( N \)	\(=\)	\( 220 = 2^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	220.h (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.99644 + 0.119294i) q^{2} +0.337678 q^{3} +(3.97154 - 0.476326i) q^{4} +(1.42257 - 4.79336i) q^{5} +(-0.674153 + 0.0402829i) q^{6} -6.79613 q^{7} +(-7.87211 + 1.42474i) q^{8} -8.88597 q^{9} +(-2.26826 + 9.73935i) q^{10} +3.31662i q^{11} +(1.34110 - 0.160845i) q^{12} -7.56772i q^{13} +(13.5681 - 0.810737i) q^{14} +(0.480371 - 1.61861i) q^{15} +(15.5462 - 3.78349i) q^{16} +26.2930i q^{17} +(17.7403 - 1.06004i) q^{18} +14.2491i q^{19} +(3.36660 - 19.7146i) q^{20} -2.29490 q^{21} +(-0.395653 - 6.62144i) q^{22} -34.5573 q^{23} +(-2.65824 + 0.481102i) q^{24} +(-20.9526 - 13.6378i) q^{25} +(0.902784 + 15.1085i) q^{26} -6.03970 q^{27} +(-26.9911 + 3.23717i) q^{28} -19.2441 q^{29} +(-0.765941 + 3.28876i) q^{30} -44.2429i q^{31} +(-30.5857 + 9.40809i) q^{32} +1.11995i q^{33} +(-3.13660 - 52.4925i) q^{34} +(-9.66799 + 32.5763i) q^{35} +(-35.2910 + 4.23262i) q^{36} +46.5774i q^{37} +(-1.69983 - 28.4475i) q^{38} -2.55545i q^{39} +(-4.36937 + 39.7606i) q^{40} -67.4821 q^{41} +(4.58163 - 0.273768i) q^{42} +54.3809 q^{43} +(1.57979 + 13.1721i) q^{44} +(-12.6409 + 42.5937i) q^{45} +(68.9914 - 4.12247i) q^{46} -7.43139 q^{47} +(5.24961 - 1.27760i) q^{48} -2.81262 q^{49} +(43.4574 + 24.7275i) q^{50} +8.87858i q^{51} +(-3.60470 - 30.0555i) q^{52} -88.6475i q^{53} +(12.0579 - 0.720499i) q^{54} +(15.8978 + 4.71814i) q^{55} +(53.4999 - 9.68269i) q^{56} +4.81161i q^{57} +(38.4196 - 2.29570i) q^{58} -74.2727i q^{59} +(1.13683 - 6.65719i) q^{60} -21.7427 q^{61} +(5.27791 + 88.3283i) q^{62} +60.3902 q^{63} +(59.9403 - 22.4314i) q^{64} +(-36.2748 - 10.7656i) q^{65} +(-0.133603 - 2.23591i) q^{66} +53.3540 q^{67} +(12.5241 + 104.424i) q^{68} -11.6692 q^{69} +(15.4154 - 66.1899i) q^{70} +107.738i q^{71} +(69.9514 - 12.6602i) q^{72} +34.9727i q^{73} +(-5.55640 - 92.9889i) q^{74} +(-7.07522 - 4.60518i) q^{75} +(6.78723 + 56.5909i) q^{76} -22.5402i q^{77} +(0.304850 + 5.10180i) q^{78} -119.442i q^{79} +(3.97999 - 79.9009i) q^{80} +77.9343 q^{81} +(134.724 - 8.05021i) q^{82} -91.9838 q^{83} +(-9.11429 + 1.09312i) q^{84} +(126.032 + 37.4038i) q^{85} +(-108.568 + 6.48731i) q^{86} -6.49830 q^{87} +(-4.72532 - 26.1088i) q^{88} +32.6768 q^{89} +(20.1557 - 86.5436i) q^{90} +51.4312i q^{91} +(-137.245 + 16.4605i) q^{92} -14.9399i q^{93} +(14.8363 - 0.886520i) q^{94} +(68.3011 + 20.2704i) q^{95} +(-10.3281 + 3.17690i) q^{96} +13.3085i q^{97} +(5.61522 - 0.335528i) q^{98} -29.4714i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 4 q^{4} + 4 q^{5} + 12 q^{6} + 180 q^{9} - 18 q^{10} - 56 q^{14} - 40 q^{16} + 84 q^{20} - 16 q^{21} + 104 q^{24} - 60 q^{25} + 28 q^{26} - 88 q^{29} - 166 q^{30} - 152 q^{34} - 248 q^{36} + 132 q^{40}+ \cdots + 216 q^{96}+O(q^{100}) \) 60 * q - 4 * q^4 + 4 * q^5 + 12 * q^6 + 180 * q^9 - 18 * q^10 - 56 * q^14 - 40 * q^16 + 84 * q^20 - 16 * q^21 + 104 * q^24 - 60 * q^25 + 28 * q^26 - 88 * q^29 - 166 * q^30 - 152 * q^34 - 248 * q^36 + 132 * q^40 - 200 * q^41 + 44 * q^44 + 84 * q^45 + 260 * q^46 + 420 * q^49 - 198 * q^50 - 116 * q^54 - 128 * q^56 - 4 * q^60 + 136 * q^61 + 116 * q^64 - 288 * q^65 - 544 * q^69 + 152 * q^70 + 436 * q^74 - 72 * q^76 - 176 * q^80 + 300 * q^81 - 136 * q^84 + 176 * q^85 - 348 * q^86 + 760 * q^89 + 40 * q^90 + 112 * q^94 + 216 * q^96

Introduction

L-functions

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