LMFDB - Embedded newform 1205.2.b.c.724.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1205,2,Mod(724,1205)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1205, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("1205.724");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1205 = 5 \cdot 241 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1205.b (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:	$9.62197344356$
Analytic rank:	$0$
Dimension:	$46$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			724.2
Character	$\chi$	$=$	1205.724
Dual form			1205.2.b.c.724.45

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.67602i q^{2} +0.199289i q^{3} -5.16108 q^{4} +(-2.13713 + 0.657778i) q^{5} +0.533301 q^{6} +2.87374i q^{7} +8.45912i q^{8} +2.96028 q^{9} +O(q^{10})$	\(q-2.67602i q^{2} +0.199289i q^{3} -5.16108 q^{4} +(-2.13713 + 0.657778i) q^{5} +0.533301 q^{6} +2.87374i q^{7} +8.45912i q^{8} +2.96028 q^{9} +(1.76023 + 5.71900i) q^{10} -0.806904 q^{11} -1.02855i q^{12} -5.09752i q^{13} +7.69018 q^{14} +(-0.131088 - 0.425906i) q^{15} +12.3146 q^{16} +0.390647i q^{17} -7.92178i q^{18} -0.489734 q^{19} +(11.0299 - 3.39485i) q^{20} -0.572704 q^{21} +2.15929i q^{22} -1.83958i q^{23} -1.68581 q^{24} +(4.13465 - 2.81152i) q^{25} -13.6411 q^{26} +1.18782i q^{27} -14.8316i q^{28} +8.05368 q^{29} +(-1.13973 + 0.350794i) q^{30} -5.55127 q^{31} -16.0359i q^{32} -0.160807i q^{33} +1.04538 q^{34} +(-1.89028 - 6.14155i) q^{35} -15.2783 q^{36} +2.20153i q^{37} +1.31054i q^{38} +1.01588 q^{39} +(-5.56423 - 18.0782i) q^{40} -3.59719 q^{41} +1.53257i q^{42} -9.27459i q^{43} +4.16450 q^{44} +(-6.32651 + 1.94721i) q^{45} -4.92275 q^{46} -10.9779i q^{47} +2.45416i q^{48} -1.25837 q^{49} +(-7.52368 - 11.0644i) q^{50} -0.0778515 q^{51} +26.3087i q^{52} -1.68955i q^{53} +3.17863 q^{54} +(1.72446 - 0.530764i) q^{55} -24.3093 q^{56} -0.0975985i q^{57} -21.5518i q^{58} +5.02546 q^{59} +(0.676556 + 2.19814i) q^{60} +3.39923 q^{61} +14.8553i q^{62} +8.50708i q^{63} -18.2832 q^{64} +(3.35304 + 10.8941i) q^{65} -0.430323 q^{66} -12.9814i q^{67} -2.01616i q^{68} +0.366608 q^{69} +(-16.4349 + 5.05843i) q^{70} +8.48671 q^{71} +25.0414i q^{72} +13.1818i q^{73} +5.89135 q^{74} +(0.560304 + 0.823991i) q^{75} +2.52756 q^{76} -2.31883i q^{77} -2.71851i q^{78} -8.08502 q^{79} +(-26.3179 + 8.10028i) q^{80} +8.64413 q^{81} +9.62615i q^{82} +0.366678i q^{83} +2.95577 q^{84} +(-0.256959 - 0.834863i) q^{85} -24.8190 q^{86} +1.60501i q^{87} -6.82569i q^{88} +2.24259 q^{89} +(5.21078 + 16.9299i) q^{90} +14.6489 q^{91} +9.49422i q^{92} -1.10631i q^{93} -29.3772 q^{94} +(1.04662 - 0.322136i) q^{95} +3.19578 q^{96} -7.32434i q^{97} +3.36741i q^{98} -2.38866 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 46 q - 34 q^{4} - 8 q^{5} - 4 q^{6} - 34 q^{9}+O(q^{10}) $ 46 * q - 34 * q^4 - 8 * q^5 - 4 * q^6 - 34 * q^9	$ 46 q - 34 q^{4} - 8 q^{5} - 4 q^{6} - 34 q^{9} - 7 q^{10} - 64 q^{11} + 66 q^{14} + 5 q^{15} + 22 q^{16} - 2 q^{20} - 14 q^{21} + 50 q^{24} + 30 q^{25} - 60 q^{26} + 36 q^{29} + 7 q^{30} - 36 q^{31} - 12 q^{34} + 3 q^{35} - 34 q^{36} + 88 q^{39} - 30 q^{40} - 76 q^{41} + 100 q^{44} - 17 q^{45} - 12 q^{46} - 22 q^{49} - 14 q^{50} - 112 q^{51} + 26 q^{54} - 5 q^{55} - 120 q^{56} + 84 q^{59} - 33 q^{60} - 78 q^{61} - 28 q^{64} + 9 q^{65} - 2 q^{66} + 24 q^{69} + 88 q^{70} - 172 q^{71} + 16 q^{74} + 59 q^{75} - 18 q^{76} + 54 q^{79} + 63 q^{80} - 42 q^{81} - 44 q^{84} + 30 q^{85} - 80 q^{86} + 86 q^{89} + 17 q^{90} - 88 q^{91} - 4 q^{94} + q^{95} - 122 q^{96} + 148 q^{99}+O(q^{100}) $ 46 * q - 34 * q^4 - 8 * q^5 - 4 * q^6 - 34 * q^9 - 7 * q^10 - 64 * q^11 + 66 * q^14 + 5 * q^15 + 22 * q^16 - 2 * q^20 - 14 * q^21 + 50 * q^24 + 30 * q^25 - 60 * q^26 + 36 * q^29 + 7 * q^30 - 36 * q^31 - 12 * q^34 + 3 * q^35 - 34 * q^36 + 88 * q^39 - 30 * q^40 - 76 * q^41 + 100 * q^44 - 17 * q^45 - 12 * q^46 - 22 * q^49 - 14 * q^50 - 112 * q^51 + 26 * q^54 - 5 * q^55 - 120 * q^56 + 84 * q^59 - 33 * q^60 - 78 * q^61 - 28 * q^64 + 9 * q^65 - 2 * q^66 + 24 * q^69 + 88 * q^70 - 172 * q^71 + 16 * q^74 + 59 * q^75 - 18 * q^76 + 54 * q^79 + 63 * q^80 - 42 * q^81 - 44 * q^84 + 30 * q^85 - 80 * q^86 + 86 * q^89 + 17 * q^90 - 88 * q^91 - 4 * q^94 + q^95 - 122 * q^96 + 148 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1205\mathbb{Z}\right)^\times$.

$n$	$242$	$971$
$\chi(n)$	$-1$	$1$

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 $

$2$		−	2.67602i		−	1.89223i	−0.323828	−	0.946116i	$-0.604970\pi$
$2$		−	2.67602i		−	1.89223i	0.323828	−	0.946116i	$-0.395030\pi$
$3$			0.199289i			0.115060i	0.998344	+	0.0575298i	$0.0183224\pi$
$3$			0.199289i			0.115060i	−0.998344	+	0.0575298i	$0.981678\pi$
$4$	−5.16108			−2.58054
$5$	−2.13713	+	0.657778i	−0.955754	+	0.294167i
$5$	−2.13713	+	0.657778i	−0.955754	+	0.294167i
$6$	0.533301			0.217719
$7$			2.87374i			1.08617i	0.839678	+	0.543085i	$0.182744\pi$
$7$			2.87374i			1.08617i	−0.839678	+	0.543085i	$0.817256\pi$
$8$			8.45912i			2.99075i
$9$	2.96028			0.986761
$10$	1.76023	+	5.71900i	0.556633	+	1.80851i
$11$	−0.806904			−0.243291			−0.121645	−	0.992574i	$-0.538817\pi$
$11$	−0.806904			−0.243291			−0.121645	+	0.992574i	$0.538817\pi$
$12$		−	1.02855i		−	0.296916i
$13$		−	5.09752i		−	1.41380i	−0.707315	−	0.706899i	$-0.750094\pi$
$13$		−	5.09752i		−	1.41380i	0.707315	−	0.706899i	$-0.249906\pi$
$14$	7.69018			2.05529
$15$	−0.131088	−	0.425906i	−0.0338468	−	0.109969i
$16$	12.3146			3.07865
$17$			0.390647i			0.0947457i	0.998877	+	0.0473729i	$0.0150849\pi$
$17$			0.390647i			0.0947457i	−0.998877	+	0.0473729i	$0.984915\pi$
$18$		−	7.92178i		−	1.86718i
$19$	−0.489734			−0.112353			−0.0561763	−	0.998421i	$-0.517891\pi$
$19$	−0.489734			−0.112353			−0.0561763	+	0.998421i	$0.517891\pi$
$20$	11.0299	−	3.39485i	2.46636	−	0.759111i
$21$	−0.572704			−0.124974
$22$			2.15929i			0.460362i
$23$		−	1.83958i		−	0.383579i	−0.981436	−	0.191789i	$-0.938571\pi$
$23$		−	1.83958i		−	0.383579i	0.981436	−	0.191789i	$-0.0614291\pi$
$24$	−1.68581			−0.344114
$25$	4.13465	−	2.81152i	0.826931	−	0.562303i
$26$	−13.6411			−2.67523
$27$			1.18782i			0.228596i
$28$		−	14.8316i		−	2.80291i
$29$	8.05368			1.49553			0.747765	−	0.663963i	$-0.231127\pi$
$29$	8.05368			1.49553			0.747765	+	0.663963i	$0.231127\pi$
$30$	−1.13973	+	0.350794i	−0.208086	+	0.0640459i
$31$	−5.55127			−0.997038			−0.498519	−	0.866879i	$-0.666123\pi$
$31$	−5.55127			−0.997038			−0.498519	+	0.866879i	$0.666123\pi$
$32$		−	16.0359i		−	2.83477i
$33$		−	0.160807i		−	0.0279929i
$34$	1.04538			0.179281
$35$	−1.89028	−	6.14155i	−0.319516	−	1.03811i
$36$	−15.2783			−2.54638
$37$			2.20153i			0.361930i	0.983490	+	0.180965i	$0.0579220\pi$
$37$			2.20153i			0.361930i	−0.983490	+	0.180965i	$0.942078\pi$
$38$			1.31054i			0.212597i
$39$	1.01588			0.162671
$40$	−5.56423	−	18.0782i	−0.879781	−	2.85842i
$41$	−3.59719			−0.561787			−0.280893	−	0.959739i	$-0.590631\pi$
$41$	−3.59719			−0.561787			−0.280893	+	0.959739i	$0.590631\pi$
$42$			1.53257i			0.236480i
$43$		−	9.27459i		−	1.41436i	−0.707033	−	0.707181i	$-0.749967\pi$
$43$		−	9.27459i		−	1.41436i	0.707033	−	0.707181i	$-0.250033\pi$
$44$	4.16450			0.627821
$45$	−6.32651	+	1.94721i	−0.943101	+	0.290273i
$46$	−4.92275			−0.725820
$47$		−	10.9779i		−	1.60130i	−0.599134	−	0.800649i	$-0.704488\pi$
$47$		−	10.9779i		−	1.60130i	0.599134	−	0.800649i	$-0.295512\pi$
$48$			2.45416i			0.354228i
$49$	−1.25837			−0.179767
$50$	−7.52368	−	11.0644i	−1.06401	−	1.56475i
$51$	−0.0778515			−0.0109014
$52$			26.3087i			3.64836i
$53$		−	1.68955i		−	0.232077i	−0.993245	−	0.116039i	$-0.962980\pi$
$53$		−	1.68955i		−	0.232077i	0.993245	−	0.116039i	$-0.0370197\pi$
$54$	3.17863			0.432556
$55$	1.72446	−	0.530764i	0.232526	−	0.0715682i
$56$	−24.3093			−3.24847
$57$		−	0.0975985i		−	0.0129272i
$58$		−	21.5518i		−	2.82989i
$59$	5.02546			0.654259			0.327130	−	0.944979i	$-0.393919\pi$
$59$	5.02546			0.654259			0.327130	+	0.944979i	$0.393919\pi$
$60$	0.676556	+	2.19814i	0.0873430	+	0.283778i
$61$	3.39923			0.435227			0.217613	−	0.976035i	$-0.430173\pi$
$61$	3.39923			0.435227			0.217613	+	0.976035i	$0.430173\pi$
$62$			14.8553i			1.88663i
$63$			8.50708i			1.07179i
$64$	−18.2832			−2.28539
$65$	3.35304	+	10.8941i	0.415893	+	1.35124i
$66$	−0.430323			−0.0529690
$67$		−	12.9814i		−	1.58594i	−0.609263	−	0.792968i	$-0.708535\pi$
$67$		−	12.9814i		−	1.58594i	0.609263	−	0.792968i	$-0.291465\pi$
$68$		−	2.01616i		−	0.244495i
$69$	0.366608			0.0441344
$70$	−16.4349	+	5.05843i	−1.96435	+	0.604598i
$71$	8.48671			1.00719			0.503594	−	0.863941i	$-0.332011\pi$
$71$	8.48671			1.00719			0.503594	+	0.863941i	$0.332011\pi$
$72$			25.0414i			2.95116i
$73$			13.1818i			1.54281i	0.636346	+	0.771404i	$0.280445\pi$
$73$			13.1818i			1.54281i	−0.636346	+	0.771404i	$0.719555\pi$
$74$	5.89135			0.684855
$75$	0.560304	+	0.823991i	0.0646984	+	0.0951463i
$76$	2.52756			0.289931
$77$		−	2.31883i		−	0.264255i
$78$		−	2.71851i		−	0.307811i
$79$	−8.08502			−0.909636			−0.454818	−	0.890584i	$-0.650296\pi$
$79$	−8.08502			−0.909636			−0.454818	+	0.890584i	$0.650296\pi$
$80$	−26.3179	+	8.10028i	−2.94243	+	0.905639i
$81$	8.64413			0.960459
$82$			9.62615i			1.06303i
$83$			0.366678i			0.0402481i	0.999797	+	0.0201240i	$0.00640611\pi$
$83$			0.366678i			0.0402481i	−0.999797	+	0.0201240i	$0.993594\pi$
$84$	2.95577			0.322501
$85$	−0.256959	−	0.834863i	−0.0278711	−	0.0905536i
$86$	−24.8190			−2.67630
$87$			1.60501i			0.172075i
$88$		−	6.82569i		−	0.727621i
$89$	2.24259			0.237715			0.118857	−	0.992911i	$-0.462077\pi$
$89$	2.24259			0.237715			0.118857	+	0.992911i	$0.462077\pi$
$90$	5.21078	+	16.9299i	0.549264	+	1.78457i
$91$	14.6489			1.53563
$92$			9.49422i			0.989841i
$93$		−	1.10631i		−	0.114719i
$94$	−29.3772			−3.03003
$95$	1.04662	−	0.322136i	0.107381	−	0.0330505i
$96$	3.19578			0.326168
$97$		−	7.32434i		−	0.743674i	−0.928298	−	0.371837i	$-0.878728\pi$
$97$		−	7.32434i		−	0.743674i	0.928298	−	0.371837i	$-0.121272\pi$
$98$			3.36741i			0.340160i
$99$	−2.38866			−0.240070
$100$	−21.3393	+	14.5105i	−2.13393	+	1.45105i
$101$	3.65598			0.363783			0.181892	−	0.983319i	$-0.441778\pi$
$101$	3.65598			0.363783			0.181892	+	0.983319i	$0.441778\pi$
$102$			0.208332i			0.0206280i
$103$		−	19.1218i		−	1.88413i	−0.335434	−	0.942064i	$-0.608883\pi$
$103$		−	19.1218i		−	1.88413i	0.335434	−	0.942064i	$-0.391117\pi$
$104$	43.1205			4.22832
$105$	1.22394	−	0.376712i	0.119445	−	0.0367634i
$106$	−4.52127			−0.439144
$107$		−	6.56240i		−	0.634411i	−0.948357	−	0.317205i	$-0.897256\pi$
$107$		−	6.56240i		−	0.634411i	0.948357	−	0.317205i	$-0.102744\pi$
$108$		−	6.13043i		−	0.589901i
$109$	15.2722			1.46282			0.731408	−	0.681940i	$-0.238864\pi$
$109$	15.2722			1.46282			0.731408	+	0.681940i	$0.238864\pi$
$110$	−1.42033	−	4.61468i	−0.135424	−	0.439993i
$111$	−0.438741			−0.0416435
$112$			35.3889i			3.34394i
$113$			0.183036i			0.0172186i	0.999963	+	0.00860929i	$0.00274046\pi$
$113$			0.183036i			0.0172186i	−0.999963	+	0.00860929i	$0.997260\pi$
$114$	−0.261176			−0.0244613
$115$	1.21004	+	3.93142i	0.112836	+	0.366607i
$116$	−41.5657			−3.85928
$117$		−	15.0901i		−	1.39508i
$118$		−	13.4482i		−	1.23801i
$119$	−1.12262			−0.102910
$120$	3.60279	−	1.10889i	0.328889	−	0.101227i
$121$	−10.3489			−0.940810
$122$		−	9.09640i		−	0.823550i
$123$		−	0.716880i		−	0.0646389i
$124$	28.6506			2.57290
$125$	−6.98694	+	8.72827i	−0.624931	+	0.780680i
$126$	22.7651			2.02808
$127$		−	15.1585i		−	1.34510i	−0.740051	−	0.672551i	$-0.765199\pi$
$127$		−	15.1585i		−	1.34510i	0.740051	−	0.672551i	$-0.234801\pi$
$128$			16.8543i			1.48972i
$129$	1.84832			0.162736
$130$	29.1527	−	8.97280i	2.55686	−	0.786967i
$131$	7.10114			0.620430			0.310215	−	0.950667i	$-0.399599\pi$
$131$	7.10114			0.620430			0.310215	+	0.950667i	$0.399599\pi$
$132$			0.829938i			0.0722368i
$133$		−	1.40737i		−	0.122034i
$134$	−34.7386			−3.00096
$135$	−0.781321	−	2.53852i	−0.0672454	−	0.218481i
$136$	−3.30453			−0.283361
$137$			7.60403i			0.649656i	0.945773	+	0.324828i	$0.105306\pi$
$137$			7.60403i			0.649656i	−0.945773	+	0.324828i	$0.894694\pi$
$138$		−	0.981050i		−	0.0835125i
$139$	21.2414			1.80167			0.900835	−	0.434161i	$-0.142955\pi$
$139$	21.2414			1.80167			0.900835	+	0.434161i	$0.142955\pi$
$140$	9.75590	+	31.6971i	0.824524	+	2.67889i
$141$	2.18778			0.184245
$142$		−	22.7106i		−	1.90583i
$143$			4.11321i			0.343964i
$144$	36.4547			3.03789
$145$	−17.2118	+	5.29754i	−1.42936	+	0.439936i
$146$	35.2746			2.91935
$147$		−	0.250778i		−	0.0206839i
$148$		−	11.3623i		−	0.933975i
$149$	16.0916			1.31827			0.659137	−	0.752023i	$-0.270922\pi$
$149$	16.0916			1.31827			0.659137	+	0.752023i	$0.270922\pi$
$150$	2.20502	−	1.49939i	0.180039	−	0.122424i
$151$	−10.5518			−0.858695			−0.429348	−	0.903139i	$-0.641256\pi$
$151$	−10.5518			−0.858695			−0.429348	+	0.903139i	$0.641256\pi$
$152$		−	4.14272i		−	0.336019i
$153$			1.15642i			0.0934914i
$154$	−6.20523			−0.500032
$155$	11.8638	−	3.65151i	0.952923	−	0.293296i
$156$	−5.24304			−0.419779
$157$		−	0.254366i		−	0.0203006i	−0.999948	−	0.0101503i	$-0.996769\pi$
$157$		−	0.254366i		−	0.0203006i	0.999948	−	0.0101503i	$-0.00323100\pi$
$158$			21.6357i			1.72124i
$159$	0.336708			0.0267027
$160$	10.5481	+	34.2708i	0.833898	+	2.70934i
$161$	5.28647			0.416632
$162$		−	23.1319i		−	1.81741i
$163$			8.82845i			0.691497i	0.938327	+	0.345749i	$0.112375\pi$
$163$			8.82845i			0.691497i	−0.938327	+	0.345749i	$0.887625\pi$
$164$	18.5654			1.44971
$165$	0.105775	+	0.343665i	0.00823460	+	0.0267543i
$166$	0.981236			0.0761587
$167$			3.04162i			0.235367i	0.993051	+	0.117684i	$0.0375469\pi$
$167$			3.04162i			0.235367i	−0.993051	+	0.117684i	$0.962453\pi$
$168$		−	4.84457i		−	0.373767i
$169$	−12.9847			−0.998824
$170$	−2.23411	+	0.687627i	−0.171348	+	0.0527386i
$171$	−1.44975			−0.110865
$172$			47.8669i			3.64982i
$173$			6.02560i			0.458118i	0.973413	+	0.229059i	$0.0735648\pi$
$173$			6.02560i			0.458118i	−0.973413	+	0.229059i	$0.926435\pi$
$174$	4.29504			0.325606
$175$	8.07956	+	11.8819i	0.610757	+	0.898188i
$176$	−9.93670			−0.749007
$177$			1.00152i			0.0752787i
$178$		−	6.00123i		−	0.449811i
$179$	−7.72419			−0.577333			−0.288667	−	0.957430i	$-0.593212\pi$
$179$	−7.72419			−0.577333			−0.288667	+	0.957430i	$0.593212\pi$
$180$	32.6517	−	10.0497i	2.43371	−	0.749062i
$181$	−10.3144			−0.766662			−0.383331	−	0.923611i	$-0.625223\pi$
$181$	−10.3144			−0.766662			−0.383331	+	0.923611i	$0.625223\pi$
$182$		−	39.2008i		−	2.90576i
$183$			0.677429i			0.0500770i
$184$	15.5612			1.14719
$185$	−1.44812	−	4.70496i	−0.106468	−	0.345916i
$186$	−2.96050			−0.217074
$187$		−	0.315214i		−	0.0230507i
$188$			56.6581i			4.13221i
$189$	−3.41348			−0.248294
$190$	−0.862043	−	2.80079i	−0.0625392	−	0.203191i
$191$	−16.6263			−1.20304			−0.601519	−	0.798858i	$-0.705438\pi$
$191$	−16.6263			−1.20304			−0.601519	+	0.798858i	$0.705438\pi$
$192$		−	3.64363i		−	0.262956i
$193$		−	26.5699i		−	1.91254i	−0.292481	−	0.956271i	$-0.594481\pi$
$193$		−	26.5699i		−	1.91254i	0.292481	−	0.956271i	$-0.405519\pi$
$194$	−19.6001			−1.40720
$195$	−2.17107	+	0.668223i	−0.155473	+	0.0478525i
$196$	6.49453			0.463895
$197$			4.42875i			0.315536i	0.987476	+	0.157768i	$0.0504298\pi$
$197$			4.42875i			0.315536i	−0.987476	+	0.157768i	$0.949570\pi$
$198$			6.39211i			0.454268i
$199$	−3.44630			−0.244302			−0.122151	−	0.992512i	$-0.538979\pi$
$199$	−3.44630			−0.244302			−0.122151	+	0.992512i	$0.538979\pi$
$200$	23.7830	+	34.9755i	1.68171	+	2.47314i
$201$	2.58706			0.182477
$202$		−	9.78347i		−	0.688362i
$203$			23.1442i			1.62440i
$204$	0.401798			0.0281315
$205$	7.68767	−	2.36615i	0.536930	−	0.165259i
$206$	−51.1703			−3.56521
$207$		−	5.44568i		−	0.378501i
$208$		−	62.7740i		−	4.35259i
$209$	0.395168			0.0273343
$210$	−1.00809	−	3.27530i	−0.0695648	−	0.226017i
$211$	−0.758471			−0.0522153			−0.0261076	−	0.999659i	$-0.508311\pi$
$211$	−0.758471			−0.0522153			−0.0261076	+	0.999659i	$0.508311\pi$
$212$			8.71990i			0.598885i
$213$			1.69131i			0.115886i
$214$	−17.5611			−1.20045
$215$	6.10063	+	19.8210i	0.416059	+	1.35178i
$216$	−10.0479			−0.683673
$217$		−	15.9529i		−	1.08295i
$218$		−	40.8688i		−	2.76799i
$219$	−2.62698			−0.177515
$220$	−8.90007	+	2.73932i	−0.600043	+	0.184685i
$221$	1.99133			0.133951
$222$			1.17408i			0.0787991i
$223$		−	0.994567i		−	0.0666011i	−0.999445	−	0.0333006i	$-0.989398\pi$
$223$		−	0.994567i		−	0.0666011i	0.999445	−	0.0333006i	$-0.0106019\pi$
$224$	46.0830			3.07905
$225$	12.2398	−	8.32289i	0.815984	−	0.554859i
$226$	0.489808			0.0325815
$227$			9.15012i			0.607315i	0.952781	+	0.303657i	$0.0982078\pi$
$227$			9.15012i			0.607315i	−0.952781	+	0.303657i	$0.901792\pi$
$228$			0.503714i			0.0333593i
$229$	−24.8061			−1.63924			−0.819618	−	0.572910i	$-0.805814\pi$
$229$	−24.8061			−1.63924			−0.819618	+	0.572910i	$0.805814\pi$
$230$	10.5206	−	3.23808i	0.693706	−	0.213513i
$231$	0.462117			0.0304051
$232$			68.1270i			4.47276i
$233$			20.8307i			1.36466i	0.731042	+	0.682332i	$0.239034\pi$
$233$			20.8307i			1.36466i	−0.731042	+	0.682332i	$0.760966\pi$
$234$	−40.3814			−2.63982
$235$	7.22105	+	23.4613i	0.471050	+	1.53045i
$236$	−25.9368			−1.68834
$237$		−	1.61126i		−	0.104662i
$238$			3.00414i			0.194730i
$239$	27.2186			1.76062			0.880311	−	0.474397i	$-0.157334\pi$
$239$	27.2186			1.76062			0.880311	+	0.474397i	$0.157334\pi$
$240$	−1.61430	−	5.24487i	−0.104202	−	0.338555i
$241$	1.00000			0.0644157
$241$	1.00000			0.0644157
$242$			27.6939i			1.78023i
$243$			5.28614i			0.339106i
$244$	−17.5437			−1.12312
$245$	2.68929	−	0.827726i	0.171813	−	0.0528815i
$246$	−1.91839			−0.122312
$247$			2.49643i			0.158844i
$248$		−	46.9589i		−	2.98189i
$249$	−0.0730748			−0.00463093
$250$	23.3570	+	18.6972i	1.47723	+	1.18251i
$251$	17.6839			1.11620			0.558100	−	0.829774i	$-0.311531\pi$
$251$	17.6839			1.11620			0.558100	+	0.829774i	$0.311531\pi$
$252$		−	43.9057i		−	2.76580i
$253$			1.48436i			0.0933211i
$254$	−40.5645			−2.54524
$255$	0.166379	−	0.0512091i	0.0104191	−	0.00320684i
$256$	8.53615			0.533509
$257$			24.6433i			1.53721i	0.639725	+	0.768604i	$0.279048\pi$
$257$			24.6433i			1.53721i	−0.639725	+	0.768604i	$0.720952\pi$
$258$		−	4.94615i		−	0.307934i
$259$	−6.32663			−0.393118
$260$	−17.3053	−	56.2252i	−1.07323	−	3.48694i
$261$	23.8412			1.47573
$262$		−	19.0028i		−	1.17400i
$263$		−	21.3217i		−	1.31475i	−0.753563	−	0.657376i	$-0.771666\pi$
$263$		−	21.3217i		−	1.31475i	0.753563	−	0.657376i	$-0.228334\pi$
$264$	1.36029			0.0837198
$265$	1.11135	+	3.61079i	0.0682696	+	0.221809i
$266$	−3.76614			−0.230917
$267$			0.446924i			0.0273513i
$268$			66.9983i			4.09257i
$269$	−21.8448			−1.33190			−0.665951	−	0.745996i	$-0.731974\pi$
$269$	−21.8448			−1.33190			−0.665951	+	0.745996i	$0.731974\pi$
$270$	−6.79314	+	2.09083i	−0.413417	+	0.127244i
$271$	1.65986			0.100830			0.0504148	−	0.998728i	$-0.483946\pi$
$271$	1.65986			0.100830			0.0504148	+	0.998728i	$0.483946\pi$
$272$			4.81066i			0.291689i
$273$			2.91937i			0.176688i
$274$	20.3485			1.22930
$275$	−3.33627	+	2.26862i	−0.201185	+	0.136803i
$276$	−1.89209			−0.113891
$277$		−	17.1120i		−	1.02816i	−0.857742	−	0.514080i	$-0.828134\pi$
$277$		−	17.1120i		−	1.02816i	0.857742	−	0.514080i	$-0.171866\pi$
$278$		−	56.8424i		−	3.40918i
$279$	−16.4333			−0.983839
$280$	51.9521	−	15.9901i	3.10473	−	0.955593i
$281$	26.8613			1.60241			0.801205	−	0.598390i	$-0.204193\pi$
$281$	26.8613			1.60241			0.801205	+	0.598390i	$0.204193\pi$
$282$		−	5.85455i		−	0.348633i
$283$		−	4.41536i		−	0.262466i	−0.991352	−	0.131233i	$-0.958106\pi$
$283$		−	4.41536i		−	0.262466i	0.991352	−	0.131233i	$-0.0418936\pi$
$284$	−43.8006			−2.59909
$285$	0.0641982	+	0.208581i	0.00380277	+	0.0123553i
$286$	11.0070			0.650859
$287$		−	10.3374i		−	0.610196i
$288$		−	47.4708i		−	2.79724i
$289$	16.8474			0.991023
$290$	14.1763	+	46.0590i	0.832462	+	2.70468i
$291$	1.45966			0.0855668
$292$		−	68.0321i		−	3.98128i
$293$			27.4208i			1.60194i	0.598703	+	0.800971i	$0.295683\pi$
$293$			27.4208i			1.60194i	−0.598703	+	0.800971i	$0.704317\pi$
$294$	−0.671088			−0.0391387
$295$	−10.7401	+	3.30564i	−0.625311	+	0.192462i
$296$	−18.6230			−1.08244
$297$		−	0.958455i		−	0.0556152i
$298$		−	43.0614i		−	2.49448i
$299$	−9.37730			−0.542303
$300$	−2.89178	−	4.25268i	−0.166957	−	0.245529i
$301$	26.6527			1.53624
$302$			28.2369i			1.62485i
$303$			0.728596i			0.0418567i
$304$	−6.03088			−0.345895
$305$	−7.26460	+	2.23594i	−0.415970	+	0.128030i
$306$	3.09462			0.176907
$307$		−	22.4558i		−	1.28162i	−0.767700	−	0.640809i	$-0.778599\pi$
$307$		−	22.4558i		−	1.28162i	0.767700	−	0.640809i	$-0.221401\pi$
$308$			11.9677i			0.681921i
$309$	3.81076			0.216787
$310$	−9.77151	−	31.7478i	−0.554984	−	1.80315i
$311$	−17.0158			−0.964880			−0.482440	−	0.875929i	$-0.660249\pi$
$311$	−17.0158			−0.964880			−0.482440	+	0.875929i	$0.660249\pi$
$312$			8.59344i			0.486508i
$313$		−	30.6076i		−	1.73004i	−0.501734	−	0.865022i	$-0.667304\pi$
$313$		−	30.6076i		−	1.73004i	0.501734	−	0.865022i	$-0.332696\pi$
$314$	−0.680689			−0.0384135
$315$	−5.59577	−	18.1807i	−0.315286	−	1.02437i
$316$	41.7275			2.34735
$317$			13.1196i			0.736869i	0.929654	+	0.368434i	$0.120106\pi$
$317$			13.1196i			0.736869i	−0.929654	+	0.368434i	$0.879894\pi$
$318$		−	0.901039i		−	0.0505277i
$319$	−6.49854			−0.363848
$320$	39.0735	−	12.0263i	2.18428	−	0.672289i
$321$	1.30781			0.0729950
$322$		−	14.1467i		−	0.788365i
$323$		−	0.191313i		−	0.0106449i
$324$	−44.6131			−2.47850
$325$	−14.3318	−	21.0765i	−0.794983	−	1.16911i
$326$	23.6251			1.30847
$327$			3.04359i			0.168311i
$328$		−	30.4291i		−	1.68016i
$329$	31.5477			1.73928
$330$	0.919655	−	0.283057i	0.0506254	−	0.0155818i
$331$	20.2977			1.11566			0.557832	−	0.829954i	$-0.311633\pi$
$331$	20.2977			1.11566			0.557832	+	0.829954i	$0.311633\pi$
$332$		−	1.89245i		−	0.103862i
$333$			6.51716i			0.357138i
$334$	8.13942			0.445369
$335$	8.53892	+	27.7430i	0.466531	+	1.51576i
$336$	−7.05262			−0.384752
$337$			10.6212i			0.578575i	0.957242	+	0.289287i	$0.0934183\pi$
$337$			10.6212i			0.578575i	−0.957242	+	0.289287i	$0.906582\pi$
$338$			34.7473i			1.89001i
$339$	−0.0364771			−0.00198116
$340$	1.32619	+	4.30880i	0.0719225	+	0.233677i
$341$	4.47934			0.242570
$342$			3.87956i			0.209783i
$343$			16.4999i			0.890913i
$344$	78.4549			4.23000
$345$	−0.783489	+	0.241147i	−0.0421816	+	0.0129829i
$346$	16.1246			0.866865
$347$		−	1.73240i		−	0.0930001i	−0.998918	−	0.0465001i	$-0.985193\pi$
$347$		−	1.73240i		−	0.0930001i	0.998918	−	0.0465001i	$-0.0148068\pi$
$348$		−	8.28358i		−	0.444047i
$349$	31.0836			1.66387			0.831933	−	0.554876i	$-0.187234\pi$
$349$	31.0836			1.66387			0.831933	+	0.554876i	$0.187234\pi$
$350$	31.7962	−	21.6211i	1.69958	−	1.15569i
$351$	6.05493			0.323188
$352$			12.9394i			0.689673i
$353$			33.0003i			1.75643i	0.478268	+	0.878214i	$0.341265\pi$
$353$			33.0003i			1.75643i	−0.478268	+	0.878214i	$0.658735\pi$
$354$	2.68008			0.142445
$355$	−18.1372	+	5.58237i	−0.962623	+	0.296282i
$356$	−11.5742			−0.613432
$357$		−	0.223725i		−	0.0118408i
$358$			20.6701i			1.09245i
$359$	−32.1190			−1.69518			−0.847589	−	0.530654i	$-0.821946\pi$
$359$	−32.1190			−1.69518			−0.847589	+	0.530654i	$0.821946\pi$
$360$	−16.4717	−	53.5167i	−0.868134	−	2.82058i
$361$	−18.7602			−0.987377
$362$			27.6015i			1.45070i
$363$		−	2.06242i		−	0.108249i
$364$	−75.6044			−3.96275
$365$	−8.67067	−	28.1711i	−0.453844	−	1.47454i
$366$	1.81281			0.0947572
$367$		−	1.93764i		−	0.101144i	−0.998720	−	0.0505719i	$-0.983896\pi$
$367$		−	1.93764i		−	0.101144i	0.998720	−	0.0505719i	$-0.0161044\pi$
$368$		−	22.6537i		−	1.18091i
$369$	−10.6487			−0.554349
$370$	−12.5906	+	3.87520i	−0.654553	+	0.201462i
$371$	4.85532			0.252076
$372$			5.70974i			0.296036i
$373$		−	8.78738i		−	0.454993i	−0.973779	−	0.227497i	$-0.926946\pi$
$373$		−	8.78738i		−	0.454993i	0.973779	−	0.227497i	$-0.0730541\pi$
$374$	−0.843519			−0.0436173
$375$	−1.73945	−	1.39242i	−0.0898246	−	0.0719043i
$376$	92.8637			4.78908
$377$		−	41.0538i		−	2.11438i
$378$			9.13454i			0.469830i
$379$	−15.6012			−0.801378			−0.400689	−	0.916214i	$-0.631229\pi$
$379$	−15.6012			−0.801378			−0.400689	+	0.916214i	$0.631229\pi$
$380$	−5.40172	+	1.66257i	−0.277102	+	0.0852881i
$381$	3.02093			0.154767
$382$			44.4924i			2.27643i
$383$		−	3.43332i		−	0.175435i	−0.996145	−	0.0877173i	$-0.972043\pi$
$383$		−	3.43332i		−	0.175435i	0.996145	−	0.0877173i	$-0.0279572\pi$
$384$	−3.35888			−0.171407
$385$	1.52528	+	4.95564i	0.0777352	+	0.252563i
$386$	−71.1016			−3.61897
$387$		−	27.4554i		−	1.39564i
$388$			37.8015i			1.91908i
$389$	16.1302			0.817836			0.408918	−	0.912571i	$-0.365906\pi$
$389$	16.1302			0.817836			0.408918	+	0.912571i	$0.365906\pi$
$390$	1.78818	+	5.80982i	0.0905480	+	0.294192i
$391$	0.718626			0.0363425
$392$		−	10.6447i		−	0.537637i
$393$			1.41518i			0.0713863i
$394$	11.8514			0.597067
$395$	17.2788	−	5.31815i	0.869388	−	0.267585i
$396$	12.3281			0.619510
$397$			4.27325i			0.214468i	0.994234	+	0.107234i	$0.0341995\pi$
$397$			4.27325i			0.214468i	−0.994234	+	0.107234i	$0.965801\pi$
$398$			9.22236i			0.462275i
$399$	0.280472			0.0140412
$400$	50.9167	−	34.6227i	2.54583	−	1.73114i
$401$	−0.0337541			−0.00168560			−0.000842800	−	1.00000i	$-0.500268\pi$
$401$	−0.0337541			−0.00168560			−0.000842800		1.00000i	$0.500268\pi$
$402$		−	6.92302i		−	0.345289i
$403$			28.2977i			1.40961i
$404$	−18.8688			−0.938758
$405$	−18.4736	+	5.68592i	−0.917963	+	0.282536i
$406$	61.9342			3.07374
$407$		−	1.77642i		−	0.0880541i
$408$		−	0.658555i		−	0.0326034i
$409$	−12.7748			−0.631672			−0.315836	−	0.948814i	$-0.602285\pi$
$409$	−12.7748			−0.631672			−0.315836	+	0.948814i	$0.602285\pi$
$410$	−6.33188	−	20.5723i	−0.312709	−	1.01600i
$411$	−1.51540			−0.0747491
$412$			98.6892i			4.86207i
$413$			14.4419i			0.710637i
$414$	−14.5727			−0.716211
$415$	−0.241193	−	0.783638i	−0.0118397	−	0.0384673i
$416$	−81.7433			−4.00780
$417$			4.23317i			0.207299i
$418$		−	1.05748i		−	0.0517229i
$419$	37.5266			1.83329			0.916646	−	0.399699i	$-0.130885\pi$
$419$	37.5266			1.83329			0.916646	+	0.399699i	$0.130885\pi$
$420$	−6.31687	+	1.94424i	−0.308232	+	0.0948694i
$421$	−9.23835			−0.450250			−0.225125	−	0.974330i	$-0.572279\pi$
$421$	−9.23835			−0.450250			−0.225125	+	0.974330i	$0.572279\pi$
$422$			2.02968i			0.0988034i
$423$		−	32.4978i		−	1.58010i
$424$	14.2921			0.694086
$425$	1.09831	+	1.61519i	0.0532758	+	0.0783482i
$426$	4.52597			0.219284
$427$			9.76849i			0.472730i
$428$			33.8691i			1.63712i
$429$	−0.819717			−0.0395763
$430$	53.0414	−	16.3254i	2.55788	−	0.787281i
$431$	−28.2694			−1.36169			−0.680845	−	0.732427i	$-0.738387\pi$
$431$	−28.2694			−1.36169			−0.680845	+	0.732427i	$0.738387\pi$
$432$			14.6275i			0.703767i
$433$		−	2.19007i		−	0.105248i	−0.998614	−	0.0526239i	$-0.983242\pi$
$433$		−	2.19007i		−	0.105248i	0.998614	−	0.0526239i	$-0.0167585\pi$
$434$	−42.6903			−2.04920
$435$	−1.05574	−	3.43011i	−0.0506189	−	0.164461i
$436$	−78.8213			−3.77486
$437$			0.900904i			0.0430961i
$438$			7.02984i			0.335899i
$439$	−16.6956			−0.796839			−0.398419	−	0.917203i	$-0.630441\pi$
$439$	−16.6956			−0.796839			−0.398419	+	0.917203i	$0.630441\pi$
$440$	4.48979	+	14.5874i	0.214043	+	0.695427i
$441$	−3.72512			−0.177387
$442$		−	5.32884i		−	0.253467i
$443$		−	10.7664i		−	0.511529i	−0.966739	−	0.255764i	$-0.917673\pi$
$443$		−	10.7664i		−	0.511529i	0.966739	−	0.255764i	$-0.0823271\pi$
$444$	2.26438			0.107463
$445$	−4.79272	+	1.47513i	−0.227197	+	0.0699279i
$446$	−2.66148			−0.126025
$447$			3.20688i			0.151680i
$448$		−	52.5410i		−	2.48233i
$449$	32.2748			1.52314			0.761571	−	0.648082i	$-0.224429\pi$
$449$	32.2748			1.52314			0.761571	+	0.648082i	$0.224429\pi$
$450$	−22.2722	−	32.7538i	−1.04992	−	1.54403i
$451$	2.90259			0.136677
$452$		−	0.944664i		−	0.0444333i
$453$		−	2.10286i		−	0.0988011i
$454$	24.4859			1.14918
$455$	−31.3067	+	9.63575i	−1.46768	+	0.451731i
$456$	0.825597			0.0386621
$457$		−	19.5040i		−	0.912358i	−0.889888	−	0.456179i	$-0.849218\pi$
$457$		−	19.5040i		−	0.912358i	0.889888	−	0.456179i	$-0.150782\pi$
$458$			66.3817i			3.10181i
$459$	−0.464017			−0.0216585
$460$	−6.24510	−	20.2904i	−0.291179	−	0.946045i
$461$	−7.59585			−0.353774			−0.176887	−	0.984231i	$-0.556603\pi$
$461$	−7.59585			−0.353774			−0.176887	+	0.984231i	$0.556603\pi$
$462$		−	1.23663i		−	0.0575334i
$463$			12.5155i			0.581644i	0.956777	+	0.290822i	$0.0939288\pi$
$463$			12.5155i			0.581644i	−0.956777	+	0.290822i	$0.906071\pi$
$464$	99.1779			4.60422
$465$	0.727705	+	2.36432i	0.0337465	+	0.109643i
$466$	55.7433			2.58226
$467$		−	11.4282i		−	0.528833i	−0.964409	−	0.264416i	$-0.914821\pi$
$467$		−	11.4282i		−	0.528833i	0.964409	−	0.264416i	$-0.0851793\pi$
$468$			77.8813i			3.60006i
$469$	37.3053			1.72260
$470$	62.7829	−	19.3237i	2.89596	−	0.891335i
$471$	0.0506924			0.00233578
$472$			42.5110i			1.95673i
$473$			7.48370i			0.344101i
$474$	−4.31175			−0.198045
$475$	−2.02488	+	1.37689i	−0.0929079	+	0.0631763i
$476$	5.79391			0.265564
$477$		−	5.00155i		−	0.229005i
$478$		−	72.8374i		−	3.33150i
$479$	−24.3966			−1.11471			−0.557354	−	0.830275i	$-0.688183\pi$
$479$	−24.3966			−1.11471			−0.557354	+	0.830275i	$0.688183\pi$
$480$	−6.82979	+	2.10211i	−0.311736	+	0.0959479i
$481$	11.2224			0.511696
$482$		−	2.67602i		−	0.121889i
$483$			1.05353i			0.0479375i
$484$	53.4116			2.42780
$485$	4.81779	+	15.6531i	0.218765	+	0.710769i
$486$	14.1458			0.641667
$487$			32.5012i			1.47277i	0.676563	+	0.736385i	$0.263469\pi$
$487$			32.5012i			1.47277i	−0.676563	+	0.736385i	$0.736531\pi$
$488$			28.7545i			1.30165i
$489$	−1.75941			−0.0795633
$490$	−2.21501	−	7.19660i	−0.100064	−	0.325109i
$491$	15.3890			0.694498			0.347249	−	0.937773i	$-0.387116\pi$
$491$	15.3890			0.694498			0.347249	+	0.937773i	$0.387116\pi$
$492$			3.69988i			0.166803i
$493$			3.14614i			0.141695i
$494$	6.68049			0.300569
$495$	5.10489	−	1.57121i	0.229448	−	0.0706207i
$496$	−68.3618			−3.06953
$497$			24.3886i			1.09398i
$498$			0.195550i			0.00876278i
$499$	33.4862			1.49905			0.749525	−	0.661976i	$-0.230282\pi$
$499$	33.4862			1.49905			0.749525	+	0.661976i	$0.230282\pi$
$500$	36.0602	−	45.0473i	1.61266	−	2.01458i
$501$	−0.606160			−0.0270812
$502$		−	47.3225i		−	2.11211i
$503$		−	38.0060i		−	1.69460i	−0.531111	−	0.847302i	$-0.678225\pi$
$503$		−	38.0060i		−	1.69460i	0.531111	−	0.847302i	$-0.321775\pi$
$504$	−71.9624			−3.20546
$505$	−7.81330	+	2.40482i	−0.347687	+	0.107013i
$506$	3.97219			0.176585
$507$		−	2.58771i		−	0.114924i
$508$			78.2344i			3.47109i
$509$	−28.9990			−1.28536			−0.642679	−	0.766136i	$-0.722177\pi$
$509$	−28.9990			−1.28536			−0.642679	+	0.766136i	$0.722177\pi$
$510$	−0.137036	−	0.445233i	−0.00606808	−	0.0197153i
$511$	−37.8809			−1.67575
$512$			10.8657i			0.480202i
$513$		−	0.581715i		−	0.0256833i
$514$	65.9460			2.90875
$515$	12.5779	+	40.8658i	0.554249	+	1.80076i
$516$	−9.53935			−0.419946
$517$			8.85814i			0.389581i
$518$			16.9302i			0.743870i
$519$	−1.20083			−0.0527108
$520$	−92.1542	+	28.3638i	−4.04123	+	1.24383i
$521$	−8.52198			−0.373355			−0.186677	−	0.982421i	$-0.559772\pi$
$521$	−8.52198			−0.373355			−0.186677	+	0.982421i	$0.559772\pi$
$522$		−	63.7995i		−	2.79243i
$523$		−	6.18981i		−	0.270662i	−0.990800	−	0.135331i	$-0.956790\pi$
$523$		−	6.18981i		−	0.270662i	0.990800	−	0.135331i	$-0.0432097\pi$
$524$	−36.6496			−1.60104
$525$	−2.36793	+	1.61017i	−0.103345	+	0.0702735i
$526$	−57.0573			−2.48782
$527$		−	2.16859i		−	0.0944651i
$528$		−	1.98027i		−	0.0861804i
$529$	19.6159			0.852867
$530$	9.66254	−	2.97399i	0.419714	−	0.129182i
$531$	14.8768			0.645598
$532$			7.26353i			0.314914i
$533$			18.3367i			0.794253i
$534$	1.19598			0.0517550
$535$	4.31660	+	14.0247i	0.186623	+	0.606341i
$536$	109.812			4.74314
$537$		−	1.53935i		−	0.0664277i
$538$			58.4572i			2.52027i
$539$	1.01538			0.0437355
$540$	4.03246	+	13.1015i	0.173530	+	0.563800i
$541$	23.0092			0.989244			0.494622	−	0.869108i	$-0.335306\pi$
$541$	23.0092			0.989244			0.494622	+	0.869108i	$0.335306\pi$
$542$		−	4.44183i		−	0.190793i
$543$		−	2.05554i		−	0.0882117i
$544$	6.26437			0.268583
$545$	−32.6388	+	10.0458i	−1.39809	+	0.430313i
$546$	7.81229			0.334335
$547$			34.2241i			1.46332i	0.681672	+	0.731658i	$0.261253\pi$
$547$			34.2241i			1.46332i	−0.681672	+	0.731658i	$0.738747\pi$
$548$		−	39.2450i		−	1.67646i
$549$	10.0627			0.429465
$550$	6.07088	+	8.92792i	0.258863	+	0.380688i
$551$	−3.94416			−0.168027
$552$			3.10118i			0.131995i
$553$		−	23.2342i		−	0.988020i
$554$	−45.7920			−1.94552
$555$	0.937647	−	0.288594i	0.0398009	−	0.0122502i
$556$	−109.629			−4.64929
$557$		−	8.34480i		−	0.353580i	−0.984249	−	0.176790i	$-0.943429\pi$
$557$		−	8.34480i		−	0.353580i	0.984249	−	0.176790i	$-0.0565714\pi$
$558$			43.9760i			1.86165i
$559$	−47.2774			−1.99962
$560$	−23.2781	−	75.6308i	−0.983679	−	3.19598i
$561$	0.0628187			0.00265221
$562$		−	71.8813i		−	3.03213i
$563$			21.1210i			0.890146i	0.895494	+	0.445073i	$0.146822\pi$
$563$			21.1210i			0.890146i	−0.895494	+	0.445073i	$0.853178\pi$
$564$	−11.2913			−0.475451
$565$	−0.120397	−	0.391172i	−0.00506515	−	0.0164567i
$566$	−11.8156			−0.496647
$567$			24.8410i			1.04322i
$568$			71.7901i			3.01225i
$569$	−38.2880			−1.60512			−0.802559	−	0.596573i	$-0.796529\pi$
$569$	−38.2880			−1.60512			−0.802559	+	0.596573i	$0.796529\pi$
$570$	0.558166	−	0.171796i	0.0233790	−	0.00719573i
$571$	4.36826			0.182806			0.0914031	−	0.995814i	$-0.470865\pi$
$571$	4.36826			0.182806			0.0914031	+	0.995814i	$0.470865\pi$
$572$		−	21.2286i		−	0.887612i
$573$		−	3.31344i		−	0.138421i
$574$	−27.6630			−1.15463
$575$	−5.17201	−	7.60603i	−0.215688	−	0.317193i
$576$	−54.1233			−2.25514
$577$			9.27981i			0.386324i	0.981167	+	0.193162i	$0.0618742\pi$
$577$			9.27981i			0.386324i	−0.981167	+	0.193162i	$0.938126\pi$
$578$		−	45.0840i		−	1.87525i
$579$	5.29508			0.220056
$580$	88.8313	−	27.3410i	3.68852	−	1.13527i
$581$	−1.05373			−0.0437163
$582$		−	3.90608i		−	0.161912i
$583$			1.36330i			0.0564623i
$584$	−111.506			−4.61415
$585$	9.92595	+	32.2495i	0.410387	+	1.33335i
$586$	73.3787			3.03125
$587$		−	12.4373i		−	0.513342i	−0.966499	−	0.256671i	$-0.917374\pi$
$587$		−	12.4373i		−	0.513342i	0.966499	−	0.256671i	$-0.0826256\pi$
$588$			1.29429i			0.0533755i
$589$	2.71865			0.112020
$590$	8.84596	+	28.7406i	0.364182	+	1.18323i
$591$	−0.882602			−0.0363054
$592$			27.1110i			1.11426i
$593$			37.5611i			1.54245i	0.636563	+	0.771225i	$0.280356\pi$
$593$			37.5611i			1.54245i	−0.636563	+	0.771225i	$0.719644\pi$
$594$	−2.56484			−0.105237
$595$	2.39918	−	0.738432i	0.0983567	−	0.0302728i
$596$	−83.0500			−3.40186
$597$		−	0.686809i		−	0.0281092i
$598$			25.0938i			1.02616i
$599$	22.2278			0.908204			0.454102	−	0.890950i	$-0.349960\pi$
$599$	22.2278			0.908204			0.454102	+	0.890950i	$0.349960\pi$
$600$	−6.97024	+	4.73968i	−0.284559	+	0.193497i
$601$	−46.9863			−1.91661			−0.958305	−	0.285747i	$-0.907758\pi$
$601$	−46.9863			−1.91661			−0.958305	+	0.285747i	$0.907758\pi$
$602$		−	71.3233i		−	2.90692i
$603$		−	38.4288i		−	1.56494i
$604$	54.4588			2.21590
$605$	22.1170	−	6.80729i	0.899183	−	0.276756i
$606$	1.94974			0.0792026
$607$			0.527341i			0.0214041i	0.999943	+	0.0107021i	$0.00340664\pi$
$607$			0.527341i			0.0214041i	−0.999943	+	0.0107021i	$0.996593\pi$
$608$			7.85332i			0.318494i
$609$	−4.61237			−0.186903
$610$	5.98342	+	19.4402i	0.242262	+	0.787111i
$611$	−55.9603			−2.26391
$612$		−	5.96840i		−	0.241258i
$613$		−	9.71818i		−	0.392514i	−0.980553	−	0.196257i	$-0.937121\pi$
$613$		−	9.71818i		−	0.392514i	0.980553	−	0.196257i	$-0.0628786\pi$
$614$	−60.0921			−2.42512
$615$	0.471548	+	1.53207i	0.0190147	+	0.0617789i
$616$	19.6153			0.790321
$617$		−	2.81867i		−	0.113476i	−0.998389	−	0.0567378i	$-0.981930\pi$
$617$		−	2.81867i		−	0.113476i	0.998389	−	0.0567378i	$-0.0180699\pi$
$618$		−	10.1977i		−	0.410211i
$619$	2.75560			0.110757			0.0553785	−	0.998465i	$-0.482363\pi$
$619$	2.75560			0.110757			0.0553785	+	0.998465i	$0.482363\pi$
$620$	−61.2300	+	18.8457i	−2.45906	+	0.756863i
$621$	2.18509			0.0876845
$622$			45.5347i			1.82578i
$623$			6.44463i			0.258199i
$624$	12.5102			0.500807
$625$	9.19074	−	23.2493i	0.367630	−	0.929972i
$626$	−81.9065			−3.27364
$627$			0.0787526i			0.00314507i
$628$			1.31281i			0.0523866i
$629$	−0.860022			−0.0342913
$630$	−48.6520	+	14.9744i	−1.93834	+	0.596594i
$631$	−21.5819			−0.859161			−0.429580	−	0.903029i	$-0.641338\pi$
$631$	−21.5819			−0.859161			−0.429580	+	0.903029i	$0.641338\pi$
$632$		−	68.3922i		−	2.72050i
$633$		−	0.151155i		−	0.00600787i
$634$	35.1083			1.39433
$635$	9.97095	+	32.3958i	0.395685	+	1.28559i
$636$	−1.73778			−0.0689075
$637$			6.41455i			0.254154i
$638$			17.3902i			0.688486i
$639$	25.1231			0.993853
$640$	−11.0864	−	36.0199i	−0.438228	−	1.42381i
$641$	−21.4224			−0.846135			−0.423068	−	0.906098i	$-0.639047\pi$
$641$	−21.4224			−0.846135			−0.423068	+	0.906098i	$0.639047\pi$
$642$		−	3.49973i		−	0.138123i
$643$			29.1001i			1.14760i	0.818997	+	0.573798i	$0.194531\pi$
$643$			29.1001i			1.14760i	−0.818997	+	0.573798i	$0.805469\pi$
$644$	−27.2839			−1.07514
$645$	−3.95011	+	1.21579i	−0.155535	+	0.0478716i
$646$	−0.511957			−0.0201427
$647$			8.60753i			0.338397i	0.985582	+	0.169198i	$0.0541179\pi$
$647$			8.60753i			0.338397i	−0.985582	+	0.169198i	$0.945882\pi$
$648$			73.1218i			2.87249i
$649$	−4.05506			−0.159175
$650$	−56.4011	+	38.3521i	−2.21223	+	1.50429i
$651$	3.17924			0.124604
$652$		−	45.5643i		−	1.78444i
$653$		−	10.3765i		−	0.406062i	−0.979172	−	0.203031i	$-0.934921\pi$
$653$		−	10.3765i		−	0.406062i	0.979172	−	0.203031i	$-0.0650792\pi$
$654$	8.14470			0.318483
$655$	−15.1761	+	4.67098i	−0.592978	+	0.182510i
$656$	−44.2980			−1.72955
$657$			39.0217i			1.52238i
$658$		−	84.4223i		−	3.29113i
$659$	39.6868			1.54598			0.772990	−	0.634418i	$-0.218760\pi$
$659$	39.6868			1.54598			0.772990	+	0.634418i	$0.218760\pi$
$660$	−0.545915	−	1.77369i	−0.0212497	−	0.0690406i
$661$	−37.6874			−1.46587			−0.732934	−	0.680300i	$-0.761850\pi$
$661$	−37.6874			−1.46587			−0.732934	+	0.680300i	$0.761850\pi$
$662$		−	54.3171i		−	2.11109i
$663$			0.396850i			0.0154124i
$664$	−3.10177			−0.120372
$665$	0.925735	+	3.00772i	0.0358985	+	0.116635i
$666$	17.4401			0.675789
$667$		−	14.8154i		−	0.573654i
$668$		−	15.6980i		−	0.607375i
$669$	0.198206			0.00766309
$670$	74.2409	−	22.8503i	2.86818	−	0.882784i
$671$	−2.74285			−0.105887
$672$			9.18382i			0.354274i
$673$			31.7217i			1.22278i	0.791329	+	0.611390i	$0.209390\pi$
$673$			31.7217i			1.22278i	−0.791329	+	0.611390i	$0.790610\pi$
$674$	28.4226			1.09480
$675$	3.33957	+	4.91122i	0.128540	+	0.189033i
$676$	67.0152			2.57751
$677$		−	45.3409i		−	1.74259i	−0.490757	−	0.871297i	$-0.663280\pi$
$677$		−	45.3409i		−	1.74259i	0.490757	−	0.871297i	$-0.336720\pi$
$678$			0.0976133i			0.00374882i
$679$	21.0482			0.807757
$680$	7.06220	−	2.17365i	0.270823	−	0.0833555i
$681$	−1.82352			−0.0698773
$682$		−	11.9868i		−	0.458999i
$683$			7.82593i			0.299451i	0.988728	+	0.149726i	$0.0478390\pi$
$683$			7.82593i			0.299451i	−0.988728	+	0.149726i	$0.952161\pi$
$684$	7.48228			0.286092
$685$	−5.00177	−	16.2508i	−0.191108	−	0.620911i
$686$	44.1542			1.68581
$687$		−	4.94359i		−	0.188610i
$688$		−	114.213i		−	4.35433i
$689$	−8.61251			−0.328111
$690$	0.645314	+	2.09663i	0.0245667	+	0.0798174i
$691$	−35.0023			−1.33155			−0.665775	−	0.746152i	$-0.731899\pi$
$691$	−35.0023			−1.33155			−0.665775	+	0.746152i	$0.731899\pi$
$692$		−	31.0986i		−	1.18219i
$693$		−	6.86439i		−	0.260757i
$694$	−4.63594			−0.175978
$695$	−45.3956	+	13.9721i	−1.72195	+	0.529993i
$696$	−13.5770			−0.514633
$697$		−	1.40523i		−	0.0532269i
$698$		−	83.1803i		−	3.14842i
$699$	−4.15133			−0.157018
$700$	−41.6993	−	61.3235i	−1.57608	−	2.31781i
$701$	−8.28122			−0.312778			−0.156389	−	0.987696i	$-0.549985\pi$
$701$	−8.28122			−0.312778			−0.156389	+	0.987696i	$0.549985\pi$
$702$		−	16.2031i		−	0.611547i
$703$		−	1.07816i		−	0.0406638i
$704$	14.7527			0.556015
$705$	−4.67558	+	1.43908i	−0.176092	+	0.0541987i
$706$	88.3094			3.32357
$707$			10.5063i			0.395131i
$708$		−	5.16892i		−	0.194260i
$709$	23.7901			0.893458			0.446729	−	0.894669i	$-0.352589\pi$
$709$	23.7901			0.893458			0.446729	+	0.894669i	$0.352589\pi$
$710$	14.9385	+	48.5355i	0.560634	+	1.82151i
$711$	−23.9340			−0.897594
$712$			18.9704i			0.710945i
$713$			10.2120i			0.382443i
$714$	−0.598692			−0.0224055
$715$	−2.70558	−	8.79046i	−0.101183	−	0.328745i
$716$	39.8652			1.48983
$717$			5.42436i			0.202576i
$718$			85.9512i			3.20767i
$719$	−33.8950			−1.26407			−0.632035	−	0.774940i	$-0.717780\pi$
$719$	−33.8950			−1.26407			−0.632035	+	0.774940i	$0.717780\pi$
$720$	−77.9085	+	23.9791i	−2.90348	+	0.893650i
$721$	54.9510			2.04648
$722$			50.2026i			1.86835i
$723$			0.199289i			0.00741163i
$724$	53.2334			1.97840
$725$	33.2992	−	22.6431i	1.23670	−	0.840942i
$726$	−5.51908			−0.204832
$727$		−	26.5707i		−	0.985451i	−0.870185	−	0.492725i	$-0.836001\pi$
$727$		−	26.5707i		−	0.985451i	0.870185	−	0.492725i	$-0.163999\pi$
$728$			123.917i			4.59267i
$729$	24.8789			0.921442
$730$	−75.3865	+	23.2029i	−2.79018	+	0.858778i
$731$	3.62309			0.134005
$732$		−	3.49627i		−	0.129226i
$733$			50.9266i			1.88102i	0.339768	+	0.940509i	$0.389651\pi$
$733$			50.9266i			1.88102i	−0.339768	+	0.940509i	$0.610349\pi$
$734$	−5.18516			−0.191388
$735$	0.164957	+	0.535946i	0.00608452	+	0.0197687i
$736$	−29.4993			−1.08736
$737$			10.4748i			0.385843i
$738$			28.4961i			1.04896i
$739$	−37.8448			−1.39214			−0.696071	−	0.717973i	$-0.745070\pi$
$739$	−37.8448			−1.39214			−0.696071	+	0.717973i	$0.745070\pi$
$740$	7.47387	+	24.2827i	0.274745	+	0.892650i
$741$	−0.497510			−0.0182765
$742$		−	12.9929i		−	0.476986i
$743$			18.8351i			0.690992i	0.938420	+	0.345496i	$0.112289\pi$
$743$			18.8351i			0.690992i	−0.938420	+	0.345496i	$0.887711\pi$
$744$	9.35839			0.343095
$745$	−34.3898	+	10.5847i	−1.25995	+	0.387794i
$746$	−23.5152			−0.860953
$747$			1.08547i			0.0397153i
$748$			1.62685i			0.0594834i
$749$	18.8586			0.689079
$750$	−3.72614	+	4.65479i	−0.136060	+	0.169969i
$751$	40.1498			1.46509			0.732544	−	0.680720i	$-0.238333\pi$
$751$	40.1498			1.46509			0.732544	+	0.680720i	$0.238333\pi$
$752$		−	135.189i		−	4.92984i
$753$			3.52421i			0.128429i
$754$	−109.861			−4.00089
$755$	22.5506	−	6.94076i	0.820701	−	0.252600i
$756$	17.6172			0.640733
$757$		−	11.3231i		−	0.411546i	−0.978600	−	0.205773i	$-0.934029\pi$
$757$		−	11.3231i		−	0.411546i	0.978600	−	0.205773i	$-0.0659708\pi$
$758$			41.7490i			1.51639i
$759$	−0.295817			−0.0107375
$760$	2.72499	+	8.85352i	0.0988457	+	0.321151i
$761$	27.9931			1.01475			0.507374	−	0.861726i	$-0.330616\pi$
$761$	27.9931			1.01475			0.507374	+	0.861726i	$0.330616\pi$
$762$		−	8.08406i		−	0.292855i
$763$			43.8884i			1.58887i
$764$	85.8098			3.10449
$765$	−0.760671	−	2.47143i	−0.0275021	−	0.0893548i
$766$	−9.18764			−0.331963
$767$		−	25.6174i		−	0.924990i
$768$			1.70116i			0.0613853i
$769$	8.32041			0.300042			0.150021	−	0.988683i	$-0.452066\pi$
$769$	8.32041			0.300042			0.150021	+	0.988683i	$0.452066\pi$
$770$	13.2614	−	4.08167i	0.477907	−	0.147093i
$771$	−4.91114			−0.176870
$772$			137.129i			4.93539i
$773$		−	11.4321i		−	0.411183i	−0.978638	−	0.205591i	$-0.934088\pi$
$773$		−	11.4321i		−	0.411183i	0.978638	−	0.205591i	$-0.0659118\pi$
$774$	−73.4713			−2.64087
$775$	−22.9526	+	15.6075i	−0.824482	+	0.560638i
$776$	61.9575			2.22414
$777$		−	1.26083i		−	0.0452319i
$778$		−	43.1649i		−	1.54754i
$779$	1.76167			0.0631182
$780$	11.2051	−	3.44876i	0.401205	−	0.123485i
$781$	−6.84796			−0.245039
$782$		−	1.92306i		−	0.0687684i
$783$			9.56631i			0.341872i
$784$	−15.4963			−0.553439
$785$	0.167317	+	0.543614i	0.00597179	+	0.0194024i
$786$	3.78705			0.135079
$787$		−	11.5127i		−	0.410384i	−0.978722	−	0.205192i	$-0.934218\pi$
$787$		−	11.5127i		−	0.410384i	0.978722	−	0.205192i	$-0.0657819\pi$
$788$		−	22.8572i		−	0.814253i
$789$	4.24918			0.151275
$790$	−14.2315	−	46.2383i	−0.506334	−	1.64508i
$791$	−0.525997			−0.0187023
$792$		−	20.2060i		−	0.717989i
$793$		−	17.3276i		−	0.615323i
$794$	11.4353			0.405824
$795$	−0.719590	+	0.221480i	−0.0255212	+	0.00785507i
$796$	17.7866			0.630430
$797$		−	8.19431i		−	0.290257i	−0.989413	−	0.145129i	$-0.953640\pi$
$797$		−	8.19431i		−	0.290257i	0.989413	−	0.145129i	$-0.0463596\pi$
$798$		−	0.750550i		−	0.0265692i
$799$	4.28850			0.151716
$800$	−45.0852	−	66.3029i	−1.59400	−	2.34416i
$801$	6.63872			0.234568
$802$			0.0903266i			0.00318954i
$803$		−	10.6364i		−	0.375351i
$804$	−13.3520			−0.470889
$805$	−11.2979	+	3.47733i	−0.398198	+	0.122560i
$806$	75.7253			2.66731
$807$		−	4.35343i		−	0.153248i
$808$			30.9263i			1.08799i
$809$	−9.19094			−0.323136			−0.161568	−	0.986862i	$-0.551655\pi$
$809$	−9.19094			−0.323136			−0.161568	+	0.986862i	$0.551655\pi$
$810$	15.2156	+	49.4358i	0.534623	+	1.73700i
$811$	−23.9711			−0.841740			−0.420870	−	0.907121i	$-0.638275\pi$
$811$	−23.9711			−0.841740			−0.420870	+	0.907121i	$0.638275\pi$
$812$		−	119.449i		−	4.19183i
$813$			0.330793i			0.0116014i
$814$	−4.75375			−0.166619
$815$	−5.80716	−	18.8675i	−0.203416	−	0.660901i
$816$	−0.958711			−0.0335616
$817$			4.54208i			0.158907i
$818$			34.1856i			1.19527i
$819$	43.3650			1.51530
$820$	−39.6767	+	12.2119i	−1.38557	+	0.426459i
$821$	−5.58377			−0.194875			−0.0974375	−	0.995242i	$-0.531065\pi$
$821$	−5.58377			−0.194875			−0.0974375	+	0.995242i	$0.531065\pi$
$822$			4.05524i			0.141443i
$823$			2.02001i			0.0704131i	0.999380	+	0.0352066i	$0.0112089\pi$
$823$			2.02001i			0.0704131i	−0.999380	+	0.0352066i	$0.988791\pi$
$824$	161.754			5.63495
$825$	−0.452111	−	0.664881i	−0.0157405	−	0.0231482i
$826$	38.6467			1.34469
$827$		−	24.2638i		−	0.843735i	−0.906658	−	0.421867i	$-0.861375\pi$
$827$		−	24.2638i		−	0.843735i	0.906658	−	0.421867i	$-0.138625\pi$
$828$			28.1056i			0.976737i
$829$	−0.464596			−0.0161361			−0.00806805	−	0.999967i	$-0.502568\pi$
$829$	−0.464596			−0.0161361			−0.00806805	+	0.999967i	$0.502568\pi$
$830$	−2.09703	+	0.645436i	−0.0727890	+	0.0224034i
$831$	3.41023			0.118299
$832$			93.1988i			3.23109i
$833$		−	0.491577i		−	0.0170321i
$834$	11.3281			0.392258
$835$	−2.00071	−	6.50033i	−0.0692374	−	0.224953i
$836$	−2.03949			−0.0705374
$837$		−	6.59391i		−	0.227919i
$838$		−	100.422i		−	3.46901i
$839$	−11.0915			−0.382921			−0.191461	−	0.981500i	$-0.561322\pi$
$839$	−11.0915			−0.382921			−0.191461	+	0.981500i	$0.561322\pi$
$840$	3.18665	+	10.3535i	0.109950	+	0.357229i
$841$	35.8617			1.23661
$842$			24.7220i			0.851977i
$843$			5.35316i			0.184372i
$844$	3.91453			0.134744
$845$	27.7500	−	8.54106i	0.954630	−	0.293822i
$846$	−86.9648			−2.98991
$847$		−	29.7400i		−	1.02188i
$848$		−	20.8061i		−	0.714486i
$849$	0.879933			0.0301992
$850$	4.32228	−	2.93910i	0.148253	−	0.100810i
$851$	4.04990			0.138829
$852$		−	8.72897i		−	0.299050i
$853$		−	38.1172i		−	1.30511i	−0.757743	−	0.652553i	$-0.773698\pi$
$853$		−	38.1172i		−	1.30511i	0.757743	−	0.652553i	$-0.226302\pi$
$854$	26.1407			0.894516
$855$	3.09831	−	0.953615i	0.105960	−	0.0326129i
$856$	55.5121			1.89736
$857$			17.6418i			0.602634i	0.953524	+	0.301317i	$0.0974262\pi$
$857$			17.6418i			0.602634i	−0.953524	+	0.301317i	$0.902574\pi$
$858$			2.19358i			0.0748875i
$859$	27.4875			0.937862			0.468931	−	0.883235i	$-0.344639\pi$
$859$	27.4875			0.937862			0.468931	+	0.883235i	$0.344639\pi$
$860$	−31.4858	−	102.298i	−1.07366	−	3.48833i
$861$	2.06013			0.0702089
$862$			75.6495i			2.57663i
$863$		−	19.2496i		−	0.655263i	−0.944806	−	0.327632i	$-0.893750\pi$
$863$		−	19.2496i		−	0.655263i	0.944806	−	0.327632i	$-0.106250\pi$
$864$	19.0477			0.648017
$865$	−3.96351	−	12.8775i	−0.134763	−	0.437848i
$866$	−5.86066			−0.199153
$867$			3.35750i			0.114027i
$868$			82.3342i			2.79461i
$869$	6.52383			0.221306
$870$	−9.17905	+	2.82518i	−0.311199	+	0.0957826i
$871$	−66.1732			−2.24219
$872$			129.190i			4.37492i
$873$		−	21.6821i		−	0.733829i
$874$	2.41084			0.0815478
$875$	−25.0827	−	20.0786i	−0.847952	−	0.678782i
$876$	13.5580			0.458084
$877$			41.2611i			1.39329i	0.717417	+	0.696644i	$0.245324\pi$
$877$			41.2611i			1.39329i	−0.717417	+	0.696644i	$0.754676\pi$
$878$			44.6778i			1.50780i
$879$	−5.46467			−0.184319
$880$	21.2360	−	6.53615i	0.715866	−	0.220333i
$881$	32.1377			1.08275			0.541373	−	0.840783i	$-0.317905\pi$
$881$	32.1377			1.08275			0.541373	+	0.840783i	$0.317905\pi$
$882$			9.96850i			0.335657i
$883$			9.13498i			0.307416i	0.988116	+	0.153708i	$0.0491216\pi$
$883$			9.13498i			0.307416i	−0.988116	+	0.153708i	$0.950878\pi$
$884$	−10.2774			−0.345667
$885$	−0.658777	−	2.14038i	−0.0221446	−	0.0719479i
$886$	−28.8112			−0.967931
$887$		−	13.8765i		−	0.465928i	−0.972485	−	0.232964i	$-0.925158\pi$
$887$		−	13.8765i		−	0.465928i	0.972485	−	0.232964i	$-0.0748424\pi$
$888$		−	3.71136i		−	0.124545i
$889$	43.5616			1.46101
$890$	3.94748	+	12.8254i	0.132320	+	0.429909i
$891$	−6.97498			−0.233671
$892$			5.13304i			0.171867i
$893$			5.37627i			0.179910i
$894$	8.58167			0.287014
$895$	16.5076	−	5.08081i	0.551788	−	0.169833i
$896$	−48.4349			−1.61809
$897$		−	1.86879i		−	0.0623971i
$898$		−	86.3680i		−	2.88214i
$899$	−44.7082			−1.49110
$900$	−63.1704	+	42.9551i	−2.10568	+	1.43184i
$901$	0.660017			0.0219883
$902$		−	7.76738i		−	0.258625i
$903$			5.31160i			0.176759i
$904$	−1.54832			−0.0514965
$905$	22.0432	−	6.78458i	0.732740	−	0.225527i
$906$	−5.62730			−0.186954
$907$			20.5930i			0.683778i	0.939740	+	0.341889i	$0.111067\pi$
$907$			20.5930i			0.683778i	−0.939740	+	0.341889i	$0.888933\pi$
$908$		−	47.2245i		−	1.56720i
$909$	10.8227			0.358967
$910$	25.7855	+	83.7773i	0.854780	+	2.77719i
$911$	−29.8513			−0.989018			−0.494509	−	0.869173i	$-0.664652\pi$
$911$	−29.8513			−0.989018			−0.494509	+	0.869173i	$0.664652\pi$
$912$		−	1.20189i		−	0.0397985i
$913$		−	0.295873i		−	0.00979198i
$914$	−52.1931			−1.72639
$915$	−0.445598	−	1.44775i	−0.0147310	−	0.0478613i
$916$	128.027			4.23012
$917$			20.4068i			0.673892i
$918$			1.24172i			0.0409828i
$919$	44.8288			1.47877			0.739383	−	0.673285i	$-0.235117\pi$
$919$	44.8288			1.47877			0.739383	+	0.673285i	$0.235117\pi$
$920$	−33.2564	+	10.2358i	−1.09643	+	0.337466i
$921$	4.47519			0.147462
$922$			20.3266i			0.669422i
$923$		−	43.2612i		−	1.42396i
$924$	−2.38502			−0.0784615
$925$	6.18965	+	9.10258i	0.203514	+	0.299291i
$926$	33.4917			1.10061
$927$		−	56.6060i		−	1.85918i
$928$		−	129.148i		−	4.23949i
$929$	53.9902			1.77136			0.885681	−	0.464294i	$-0.153692\pi$
$929$	53.9902			1.77136			0.885681	+	0.464294i	$0.153692\pi$
$930$	6.32698	−	1.94735i	0.207470	−	0.0638562i
$931$	0.616264			0.0201972
$932$		−	107.509i		−	3.52157i
$933$		−	3.39107i		−	0.111019i
$934$	−30.5820			−1.00067
$935$	0.207341	+	0.673654i	0.00678078	+	0.0220308i
$936$	127.649			4.17234
$937$		−	41.8090i		−	1.36584i	−0.730493	−	0.682920i	$-0.760710\pi$
$937$		−	41.8090i		−	1.36584i	0.730493	−	0.682920i	$-0.239290\pi$
$938$		−	99.8296i		−	3.25955i
$939$	6.09975			0.199058
$940$	−37.2685	−	121.086i	−1.21556	−	3.94938i
$941$	17.5326			0.571548			0.285774	−	0.958297i	$-0.407749\pi$
$941$	17.5326			0.571548			0.285774	+	0.958297i	$0.407749\pi$
$942$		−	0.135654i		−	0.00441984i
$943$			6.61732i			0.215490i
$944$	61.8866			2.01424
$945$	7.29505	−	2.24531i	0.237308	−	0.0730400i
$946$	20.0265			0.651119
$947$		−	60.8556i		−	1.97754i	−0.149444	−	0.988770i	$-0.547748\pi$
$947$		−	60.8556i		−	1.97754i	0.149444	−	0.988770i	$-0.452252\pi$
$948$			8.31582i			0.270085i
$949$	67.1943			2.18122
$950$	3.68460	+	5.41862i	0.119544	+	0.175803i
$951$	−2.61459			−0.0847838
$952$		−	9.49634i		−	0.307778i
$953$			47.7538i			1.54690i	0.633859	+	0.773449i	$0.281470\pi$
$953$			47.7538i			1.54690i	−0.633859	+	0.773449i	$0.718530\pi$
$954$	−13.3842			−0.433331
$955$	35.5326	−	10.9364i	1.14981	−	0.353895i
$956$	−140.477			−4.54336
$957$		−	1.29509i		−	0.0418642i
$958$			65.2857i			2.10928i
$959$	−21.8520			−0.705637
$960$	2.39670	+	7.78692i	0.0773532	+	0.251322i
$961$	−0.183358			−0.00591476
$962$		−	30.0313i		−	0.968247i
$963$		−	19.4266i		−	0.626012i
$964$	−5.16108			−0.166227
$965$	17.4771	+	56.7833i	0.562608	+	1.82792i
$966$	2.81928			0.0907088
$967$		−	10.5625i		−	0.339666i	−0.985473	−	0.169833i	$-0.945677\pi$
$967$		−	10.5625i		−	0.339666i	0.985473	−	0.169833i	$-0.0543229\pi$
$968$		−	87.5426i		−	2.81373i
$969$	0.0381265			0.00122480
$970$	41.8879	−	12.8925i	1.34494	−	0.413954i
$971$	−42.2601			−1.35619			−0.678096	−	0.734973i	$-0.737195\pi$
$971$	−42.2601			−1.35619			−0.678096	+	0.734973i	$0.737195\pi$
$972$		−	27.2822i		−	0.875076i
$973$			61.0422i			1.95692i
$974$	86.9739			2.78682
$975$	4.20031	−	2.85616i	0.134518	−	0.0914704i
$976$	41.8602			1.33991
$977$			0.878630i			0.0281099i	0.999901	+	0.0140549i	$0.00447397\pi$
$977$			0.878630i			0.0281099i	−0.999901	+	0.0140549i	$0.995526\pi$
$978$			4.70822i			0.150552i
$979$	−1.80956			−0.0578337
$980$	−13.8797	+	4.27196i	−0.443370	+	0.136463i
$981$	45.2102			1.44345
$982$		−	41.1814i		−	1.31415i
$983$		−	20.9666i		−	0.668731i	−0.942444	−	0.334365i	$-0.891478\pi$
$983$		−	20.9666i		−	0.668731i	0.942444	−	0.334365i	$-0.108522\pi$
$984$	6.06417			0.193319
$985$	−2.91314	−	9.46483i	−0.0928203	−	0.301574i
$986$	8.41914			0.268120
$987$			6.28711i			0.200121i
$988$		−	12.8843i		−	0.409903i
$989$	−17.0614			−0.542519
$990$	−4.20459	−	13.6608i	−0.133631	−	0.434168i
$991$	3.56254			0.113168			0.0565840	−	0.998398i	$-0.481979\pi$
$991$	3.56254			0.113168			0.0565840	+	0.998398i	$0.481979\pi$
$992$			89.0196i			2.82638i
$993$			4.04511i			0.128368i
$994$	65.2643			2.07006
$995$	7.36519	−	2.26690i	0.233492	−	0.0718656i
$996$	0.377145			0.0119503
$997$			5.26746i			0.166822i	0.996515	+	0.0834111i	$0.0265815\pi$
$997$			5.26746i			0.166822i	−0.996515	+	0.0834111i	$0.973419\pi$
$998$		−	89.6098i		−	2.83655i
$999$	−2.61502			−0.0827356

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1205.2.b.c.724.2	✓	46
5.2	odd	4		6025.2.a.p.1.45		46
5.3	odd	4		6025.2.a.p.1.2		46
5.4	even	2	inner	1205.2.b.c.724.45	yes	46

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1205.2.b.c.724.2	✓	46	1.1	even	1	trivial
1205.2.b.c.724.45	yes	46	5.4	even	2	inner
6025.2.a.p.1.2		46	5.3	odd	4
6025.2.a.p.1.45		46	5.2	odd	4

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:	\( N \)	\(=\)	\( 1205 = 5 \cdot 241 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1205.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.67602i q^{2} +0.199289i q^{3} -5.16108 q^{4} +(-2.13713 + 0.657778i) q^{5} +0.533301 q^{6} +2.87374i q^{7} +8.45912i q^{8} +2.96028 q^{9} +O(q^{10})\)	\(q-2.67602i q^{2} +0.199289i q^{3} -5.16108 q^{4} +(-2.13713 + 0.657778i) q^{5} +0.533301 q^{6} +2.87374i q^{7} +8.45912i q^{8} +2.96028 q^{9} +(1.76023 + 5.71900i) q^{10} -0.806904 q^{11} -1.02855i q^{12} -5.09752i q^{13} +7.69018 q^{14} +(-0.131088 - 0.425906i) q^{15} +12.3146 q^{16} +0.390647i q^{17} -7.92178i q^{18} -0.489734 q^{19} +(11.0299 - 3.39485i) q^{20} -0.572704 q^{21} +2.15929i q^{22} -1.83958i q^{23} -1.68581 q^{24} +(4.13465 - 2.81152i) q^{25} -13.6411 q^{26} +1.18782i q^{27} -14.8316i q^{28} +8.05368 q^{29} +(-1.13973 + 0.350794i) q^{30} -5.55127 q^{31} -16.0359i q^{32} -0.160807i q^{33} +1.04538 q^{34} +(-1.89028 - 6.14155i) q^{35} -15.2783 q^{36} +2.20153i q^{37} +1.31054i q^{38} +1.01588 q^{39} +(-5.56423 - 18.0782i) q^{40} -3.59719 q^{41} +1.53257i q^{42} -9.27459i q^{43} +4.16450 q^{44} +(-6.32651 + 1.94721i) q^{45} -4.92275 q^{46} -10.9779i q^{47} +2.45416i q^{48} -1.25837 q^{49} +(-7.52368 - 11.0644i) q^{50} -0.0778515 q^{51} +26.3087i q^{52} -1.68955i q^{53} +3.17863 q^{54} +(1.72446 - 0.530764i) q^{55} -24.3093 q^{56} -0.0975985i q^{57} -21.5518i q^{58} +5.02546 q^{59} +(0.676556 + 2.19814i) q^{60} +3.39923 q^{61} +14.8553i q^{62} +8.50708i q^{63} -18.2832 q^{64} +(3.35304 + 10.8941i) q^{65} -0.430323 q^{66} -12.9814i q^{67} -2.01616i q^{68} +0.366608 q^{69} +(-16.4349 + 5.05843i) q^{70} +8.48671 q^{71} +25.0414i q^{72} +13.1818i q^{73} +5.89135 q^{74} +(0.560304 + 0.823991i) q^{75} +2.52756 q^{76} -2.31883i q^{77} -2.71851i q^{78} -8.08502 q^{79} +(-26.3179 + 8.10028i) q^{80} +8.64413 q^{81} +9.62615i q^{82} +0.366678i q^{83} +2.95577 q^{84} +(-0.256959 - 0.834863i) q^{85} -24.8190 q^{86} +1.60501i q^{87} -6.82569i q^{88} +2.24259 q^{89} +(5.21078 + 16.9299i) q^{90} +14.6489 q^{91} +9.49422i q^{92} -1.10631i q^{93} -29.3772 q^{94} +(1.04662 - 0.322136i) q^{95} +3.19578 q^{96} -7.32434i q^{97} +3.36741i q^{98} -2.38866 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 46 q - 34 q^{4} - 8 q^{5} - 4 q^{6} - 34 q^{9}+O(q^{10}) \) 46 * q - 34 * q^4 - 8 * q^5 - 4 * q^6 - 34 * q^9	\( 46 q - 34 q^{4} - 8 q^{5} - 4 q^{6} - 34 q^{9} - 7 q^{10} - 64 q^{11} + 66 q^{14} + 5 q^{15} + 22 q^{16} - 2 q^{20} - 14 q^{21} + 50 q^{24} + 30 q^{25} - 60 q^{26} + 36 q^{29} + 7 q^{30} - 36 q^{31} - 12 q^{34} + 3 q^{35} - 34 q^{36} + 88 q^{39} - 30 q^{40} - 76 q^{41} + 100 q^{44} - 17 q^{45} - 12 q^{46} - 22 q^{49} - 14 q^{50} - 112 q^{51} + 26 q^{54} - 5 q^{55} - 120 q^{56} + 84 q^{59} - 33 q^{60} - 78 q^{61} - 28 q^{64} + 9 q^{65} - 2 q^{66} + 24 q^{69} + 88 q^{70} - 172 q^{71} + 16 q^{74} + 59 q^{75} - 18 q^{76} + 54 q^{79} + 63 q^{80} - 42 q^{81} - 44 q^{84} + 30 q^{85} - 80 q^{86} + 86 q^{89} + 17 q^{90} - 88 q^{91} - 4 q^{94} + q^{95} - 122 q^{96} + 148 q^{99}+O(q^{100}) \) 46 * q - 34 * q^4 - 8 * q^5 - 4 * q^6 - 34 * q^9 - 7 * q^10 - 64 * q^11 + 66 * q^14 + 5 * q^15 + 22 * q^16 - 2 * q^20 - 14 * q^21 + 50 * q^24 + 30 * q^25 - 60 * q^26 + 36 * q^29 + 7 * q^30 - 36 * q^31 - 12 * q^34 + 3 * q^35 - 34 * q^36 + 88 * q^39 - 30 * q^40 - 76 * q^41 + 100 * q^44 - 17 * q^45 - 12 * q^46 - 22 * q^49 - 14 * q^50 - 112 * q^51 + 26 * q^54 - 5 * q^55 - 120 * q^56 + 84 * q^59 - 33 * q^60 - 78 * q^61 - 28 * q^64 + 9 * q^65 - 2 * q^66 + 24 * q^69 + 88 * q^70 - 172 * q^71 + 16 * q^74 + 59 * q^75 - 18 * q^76 + 54 * q^79 + 63 * q^80 - 42 * q^81 - 44 * q^84 + 30 * q^85 - 80 * q^86 + 86 * q^89 + 17 * q^90 - 88 * q^91 - 4 * q^94 + q^95 - 122 * q^96 + 148 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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