LMFDB - Embedded newform 1210.2.b.k.969.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1210,2,Mod(969,1210)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1210, 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("1210.969");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1210 = 2 \cdot 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1210.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:	$9.66189864457$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.12904960000.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + 2x^{6} + 6x^{5} + 59x^{4} - 86x^{3} + 72x^{2} + 132x + 121 $ x^8 - 2x^7 + 2x^6 + 6x^5 + 59x^4 - 86x^3 + 72x^2 + 132*x + 121
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 110)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			969.7
Root			$2.16751 + 2.16751i$ of defining polynomial
Character	$\chi$	$=$	1210.969
Dual form			1210.2.b.k.969.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +1.61803i q^{3} -1.00000 q^{4} +(-0.549472 - 2.16751i) q^{5} -1.61803 q^{6} +5.01420i q^{7} -1.00000i q^{8} +0.381966 q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +1.61803i q^{3} -1.00000 q^{4} +(-0.549472 - 2.16751i) q^{5} -1.61803 q^{6} +5.01420i q^{7} -1.00000i q^{8} +0.381966 q^{9} +(2.16751 - 0.549472i) q^{10} -1.61803i q^{12} +2.33501i q^{13} -5.01420 q^{14} +(3.50710 - 0.889064i) q^{15} +1.00000 q^{16} -0.0611504i q^{17} +0.381966i q^{18} +2.06115 q^{19} +(0.549472 + 2.16751i) q^{20} -8.11314 q^{21} +3.91525i q^{23} +1.61803 q^{24} +(-4.39616 + 2.38197i) q^{25} -2.33501 q^{26} +5.47214i q^{27} -5.01420i q^{28} +4.13712 q^{29} +(0.889064 + 3.50710i) q^{30} -8.87707 q^{31} +1.00000i q^{32} +0.0611504 q^{34} +(10.8683 - 2.75516i) q^{35} -0.381966 q^{36} -4.55688i q^{37} +2.06115i q^{38} -3.77813 q^{39} +(-2.16751 + 0.549472i) q^{40} -4.57985 q^{41} -8.11314i q^{42} +3.61803i q^{43} +(-0.209880 - 0.827913i) q^{45} -3.91525 q^{46} -8.87707i q^{47} +1.61803i q^{48} -18.1422 q^{49} +(-2.38197 - 4.39616i) q^{50} +0.0989434 q^{51} -2.33501i q^{52} +2.22187i q^{53} -5.47214 q^{54} +5.01420 q^{56} +3.33501i q^{57} +4.13712i q^{58} -1.93885 q^{59} +(-3.50710 + 0.889064i) q^{60} -9.69338 q^{61} -8.87707i q^{62} +1.91525i q^{63} -1.00000 q^{64} +(5.06115 - 1.28302i) q^{65} -2.49573i q^{67} +0.0611504i q^{68} -6.33501 q^{69} +(2.75516 + 10.8683i) q^{70} +8.81631 q^{71} -0.381966i q^{72} +5.39616i q^{73} +4.55688 q^{74} +(-3.85410 - 7.11314i) q^{75} -2.06115 q^{76} -3.77813i q^{78} +6.65520 q^{79} +(-0.549472 - 2.16751i) q^{80} -7.70820 q^{81} -4.57985i q^{82} +11.0520i q^{83} +8.11314 q^{84} +(-0.132544 + 0.0336004i) q^{85} -3.61803 q^{86} +6.69401i q^{87} -6.09017 q^{89} +(0.827913 - 0.209880i) q^{90} -11.7082 q^{91} -3.91525i q^{92} -14.3634i q^{93} +8.87707 q^{94} +(-1.13254 - 4.46756i) q^{95} -1.61803 q^{96} +7.30225i q^{97} -18.1422i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{4} + 2 q^{5} - 4 q^{6} + 12 q^{9}+O(q^{10}) $ 8 * q - 8 * q^4 + 2 * q^5 - 4 * q^6 + 12 * q^9	$ 8 q - 8 q^{4} + 2 q^{5} - 4 q^{6} + 12 q^{9} + 2 q^{10} + 4 q^{14} + 6 q^{15} + 8 q^{16} + 12 q^{19} - 2 q^{20} - 8 q^{21} + 4 q^{24} + 12 q^{26} + 28 q^{29} - 6 q^{30} - 32 q^{31} - 4 q^{34} + 16 q^{35} - 12 q^{36} - 4 q^{39} - 2 q^{40} - 20 q^{41} - 2 q^{45} - 48 q^{49} - 28 q^{50} - 12 q^{51} - 8 q^{54} - 4 q^{56} - 20 q^{59} - 6 q^{60} - 20 q^{61} - 8 q^{64} + 36 q^{65} - 20 q^{69} + 8 q^{70} + 52 q^{71} + 32 q^{74} - 4 q^{75} - 12 q^{76} - 12 q^{79} + 2 q^{80} - 8 q^{81} + 8 q^{84} + 28 q^{85} - 20 q^{86} - 4 q^{89} - 2 q^{90} - 40 q^{91} + 32 q^{94} + 20 q^{95} - 4 q^{96}+O(q^{100}) $ 8 * q - 8 * q^4 + 2 * q^5 - 4 * q^6 + 12 * q^9 + 2 * q^10 + 4 * q^14 + 6 * q^15 + 8 * q^16 + 12 * q^19 - 2 * q^20 - 8 * q^21 + 4 * q^24 + 12 * q^26 + 28 * q^29 - 6 * q^30 - 32 * q^31 - 4 * q^34 + 16 * q^35 - 12 * q^36 - 4 * q^39 - 2 * q^40 - 20 * q^41 - 2 * q^45 - 48 * q^49 - 28 * q^50 - 12 * q^51 - 8 * q^54 - 4 * q^56 - 20 * q^59 - 6 * q^60 - 20 * q^61 - 8 * q^64 + 36 * q^65 - 20 * q^69 + 8 * q^70 + 52 * q^71 + 32 * q^74 - 4 * q^75 - 12 * q^76 - 12 * q^79 + 2 * q^80 - 8 * q^81 + 8 * q^84 + 28 * q^85 - 20 * q^86 - 4 * q^89 - 2 * q^90 - 40 * q^91 + 32 * q^94 + 20 * q^95 - 4 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1210\mathbb{Z}\right)^\times$.

$n$	$727$	$1091$
$\chi(n)$	$-1$	$1$

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 $

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$			1.61803i			0.934172i	0.884212	+	0.467086i	$0.154696\pi$
$3$			1.61803i			0.934172i	−0.884212	+	0.467086i	$0.845304\pi$
$4$	−1.00000			−0.500000
$5$	−0.549472	−	2.16751i	−0.245731	−	0.969338i
$5$	−0.549472	−	2.16751i	−0.245731	−	0.969338i
$6$	−1.61803			−0.660560
$7$			5.01420i			1.89519i	0.319477	+	0.947594i	$0.396493\pi$
$7$			5.01420i			1.89519i	−0.319477	+	0.947594i	$0.603507\pi$
$8$		−	1.00000i		−	0.353553i
$9$	0.381966			0.127322
$10$	2.16751	−	0.549472i	0.685425	−	0.173758i
$11$		0			0
$11$		0			0
$12$		−	1.61803i		−	0.467086i
$13$			2.33501i			0.647616i	0.946123	+	0.323808i	$0.104963\pi$
$13$			2.33501i			0.647616i	−0.946123	+	0.323808i	$0.895037\pi$
$14$	−5.01420			−1.34010
$15$	3.50710	−	0.889064i	0.905529	−	0.229555i
$16$	1.00000			0.250000
$17$		−	0.0611504i		−	0.0148311i	−0.999973	−	0.00741557i	$-0.997640\pi$
$17$		−	0.0611504i		−	0.0148311i	0.999973	−	0.00741557i	$-0.00236047\pi$
$18$			0.381966i			0.0900303i
$19$	2.06115			0.472860			0.236430	−	0.971648i	$-0.424023\pi$
$19$	2.06115			0.472860			0.236430	+	0.971648i	$0.424023\pi$
$20$	0.549472	+	2.16751i	0.122866	+	0.484669i
$21$	−8.11314			−1.77043
$22$		0			0
$23$			3.91525i			0.816387i	0.912896	+	0.408193i	$0.133841\pi$
$23$			3.91525i			0.816387i	−0.912896	+	0.408193i	$0.866159\pi$
$24$	1.61803			0.330280
$25$	−4.39616	+	2.38197i	−0.879232	+	0.476393i
$26$	−2.33501			−0.457933
$27$			5.47214i			1.05311i
$28$		−	5.01420i		−	0.947594i
$29$	4.13712			0.768245			0.384122	−	0.923282i	$-0.374504\pi$
$29$	4.13712			0.768245			0.384122	+	0.923282i	$0.374504\pi$
$30$	0.889064	+	3.50710i	0.162320	+	0.640306i
$31$	−8.87707			−1.59437			−0.797185	−	0.603736i	$-0.793678\pi$
$31$	−8.87707			−1.59437			−0.797185	+	0.603736i	$0.793678\pi$
$32$			1.00000i			0.176777i
$33$		0			0
$34$	0.0611504			0.0104872
$35$	10.8683	−	2.75516i	1.83708	−	0.465707i
$36$	−0.381966			−0.0636610
$37$		−	4.55688i		−	0.749147i	−0.927197	−	0.374574i	$-0.877789\pi$
$37$		−	4.55688i		−	0.749147i	0.927197	−	0.374574i	$-0.122211\pi$
$38$			2.06115i			0.334363i
$39$	−3.77813			−0.604985
$40$	−2.16751	+	0.549472i	−0.342713	+	0.0868791i
$41$	−4.57985			−0.715253			−0.357626	−	0.933865i	$-0.616414\pi$
$41$	−4.57985			−0.715253			−0.357626	+	0.933865i	$0.616414\pi$
$42$		−	8.11314i		−	1.25188i
$43$			3.61803i			0.551745i	0.961194	+	0.275873i	$0.0889668\pi$
$43$			3.61803i			0.551745i	−0.961194	+	0.275873i	$0.911033\pi$
$44$		0			0
$45$	−0.209880	−	0.827913i	−0.0312870	−	0.123418i
$46$	−3.91525			−0.577272
$47$		−	8.87707i		−	1.29485i	−0.762128	−	0.647427i	$-0.775845\pi$
$47$		−	8.87707i		−	1.29485i	0.762128	−	0.647427i	$-0.224155\pi$
$48$			1.61803i			0.233543i
$49$	−18.1422			−2.59174
$50$	−2.38197	−	4.39616i	−0.336861	−	0.621711i
$51$	0.0989434			0.0138548
$52$		−	2.33501i		−	0.323808i
$53$			2.22187i			0.305198i	0.988288	+	0.152599i	$0.0487642\pi$
$53$			2.22187i			0.305198i	−0.988288	+	0.152599i	$0.951236\pi$
$54$	−5.47214			−0.744663
$55$		0			0
$56$	5.01420			0.670050
$57$			3.33501i			0.441733i
$58$			4.13712i			0.543231i
$59$	−1.93885			−0.252417			−0.126208	−	0.992004i	$-0.540281\pi$
$59$	−1.93885			−0.252417			−0.126208	+	0.992004i	$0.540281\pi$
$60$	−3.50710	+	0.889064i	−0.452764	+	0.114778i
$61$	−9.69338			−1.24111			−0.620555	−	0.784163i	$-0.713093\pi$
$61$	−9.69338			−1.24111			−0.620555	+	0.784163i	$0.713093\pi$
$62$		−	8.87707i		−	1.12739i
$63$			1.91525i			0.241299i
$64$	−1.00000			−0.125000
$65$	5.06115	−	1.28302i	0.627758	−	0.159139i
$66$		0			0
$67$		−	2.49573i		−	0.304902i	−0.988311	−	0.152451i	$-0.951283\pi$
$67$		−	2.49573i		−	0.304902i	0.988311	−	0.152451i	$-0.0487167\pi$
$68$			0.0611504i			0.00741557i
$69$	−6.33501			−0.762646
$70$	2.75516	+	10.8683i	0.329304	+	1.29901i
$71$	8.81631			1.04630			0.523152	−	0.852240i	$-0.324756\pi$
$71$	8.81631			1.04630			0.523152	+	0.852240i	$0.324756\pi$
$72$		−	0.381966i		−	0.0450151i
$73$			5.39616i			0.631573i	0.948830	+	0.315786i	$0.102268\pi$
$73$			5.39616i			0.631573i	−0.948830	+	0.315786i	$0.897732\pi$
$74$	4.55688			0.529727
$75$	−3.85410	−	7.11314i	−0.445033	−	0.821355i
$76$	−2.06115			−0.236430
$77$		0			0
$78$		−	3.77813i		−	0.427789i
$79$	6.65520			0.748768			0.374384	−	0.927274i	$-0.377854\pi$
$79$	6.65520			0.748768			0.374384	+	0.927274i	$0.377854\pi$
$80$	−0.549472	−	2.16751i	−0.0614328	−	0.242335i
$81$	−7.70820			−0.856467
$82$		−	4.57985i		−	0.505760i
$83$			11.0520i			1.21311i	0.795040	+	0.606557i	$0.207450\pi$
$83$			11.0520i			1.21311i	−0.795040	+	0.606557i	$0.792550\pi$
$84$	8.11314			0.885216
$85$	−0.132544	+	0.0336004i	−0.0143764	+	0.00364447i
$86$	−3.61803			−0.390143
$87$			6.69401i			0.717673i
$88$		0			0
$89$	−6.09017			−0.645557			−0.322778	−	0.946475i	$-0.604617\pi$
$89$	−6.09017			−0.645557			−0.322778	+	0.946475i	$0.604617\pi$
$90$	0.827913	−	0.209880i	0.0872697	−	0.0221232i
$91$	−11.7082			−1.22735
$92$		−	3.91525i		−	0.408193i
$93$		−	14.3634i		−	1.48942i
$94$	8.87707			0.915600
$95$	−1.13254	−	4.46756i	−0.116197	−	0.458361i
$96$	−1.61803			−0.165140
$97$			7.30225i			0.741431i	0.928746	+	0.370716i	$0.120888\pi$
$97$			7.30225i			0.741431i	−0.928746	+	0.370716i	$0.879112\pi$
$98$		−	18.1422i		−	1.83263i
$99$		0			0
$100$	4.39616	−	2.38197i	0.439616	−	0.238197i
$101$	−0.221872			−0.0220771			−0.0110386	−	0.999939i	$-0.503514\pi$
$101$	−0.221872			−0.0220771			−0.0110386	+	0.999939i	$0.503514\pi$
$102$			0.0989434i			0.00979685i
$103$			0.566045i			0.0557741i	0.999611	+	0.0278870i	$0.00887787\pi$
$103$			0.566045i			0.0557741i	−0.999611	+	0.0278870i	$0.991122\pi$
$104$	2.33501			0.228967
$105$	4.45794	+	17.5853i	0.435050	+	1.71615i
$106$	−2.22187			−0.215807
$107$			2.23002i			0.215584i	0.994173	+	0.107792i	$0.0343780\pi$
$107$			2.23002i			0.215584i	−0.994173	+	0.107792i	$0.965622\pi$
$108$		−	5.47214i		−	0.526557i
$109$	−7.86288			−0.753127			−0.376563	−	0.926391i	$-0.622894\pi$
$109$	−7.86288			−0.753127			−0.376563	+	0.926391i	$0.622894\pi$
$110$		0			0
$111$	7.37319			0.699832
$112$			5.01420i			0.473797i
$113$		−	12.5617i		−	1.18170i	−0.806780	−	0.590852i	$-0.798792\pi$
$113$		−	12.5617i		−	1.18170i	0.806780	−	0.590852i	$-0.201208\pi$
$114$	−3.33501			−0.312352
$115$	8.48633	−	2.15132i	0.791355	−	0.200612i
$116$	−4.13712			−0.384122
$117$			0.891895i			0.0824557i
$118$		−	1.93885i		−	0.178486i
$119$	0.306620			0.0281078
$120$	−0.889064	−	3.50710i	−0.0811601	−	0.320153i
$121$		0			0
$122$		−	9.69338i		−	0.877597i
$123$		−	7.41036i		−	0.668169i
$124$	8.87707			0.797185
$125$	7.57849	+	8.21988i	0.677841	+	0.735209i
$126$	−1.91525			−0.170624
$127$		−	14.4630i		−	1.28338i	−0.766964	−	0.641691i	$-0.778233\pi$
$127$		−	14.4630i		−	1.28338i	0.766964	−	0.641691i	$-0.221767\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	−5.85410			−0.515425
$130$	1.28302	+	5.06115i	0.112529	+	0.443892i
$131$	15.3256			1.33900			0.669502	−	0.742810i	$-0.266507\pi$
$131$	15.3256			1.33900			0.669502	+	0.742810i	$0.266507\pi$
$132$		0			0
$133$			10.3350i			0.896159i
$134$	2.49573			0.215599
$135$	11.8609	−	3.00678i	1.02082	−	0.258783i
$136$	−0.0611504			−0.00524360
$137$			1.10437i			0.0943523i	0.998887	+	0.0471762i	$0.0150222\pi$
$137$			1.10437i			0.0943523i	−0.998887	+	0.0471762i	$0.984978\pi$
$138$		−	6.33501i		−	0.539272i
$139$	9.90609			0.840224			0.420112	−	0.907472i	$-0.361991\pi$
$139$	9.90609			0.840224			0.420112	+	0.907472i	$0.361991\pi$
$140$	−10.8683	+	2.75516i	−0.918539	+	0.232853i
$141$	14.3634			1.20962
$142$			8.81631i			0.739848i
$143$		0			0
$144$	0.381966			0.0318305
$145$	−2.27323	−	8.96724i	−0.188782	−	0.744689i
$146$	−5.39616			−0.446590
$147$		−	29.3546i		−	2.42113i
$148$			4.55688i			0.374574i
$149$	−8.79232			−0.720295			−0.360148	−	0.932895i	$-0.617274\pi$
$149$	−8.79232			−0.720295			−0.360148	+	0.932895i	$0.617274\pi$
$150$	7.11314	−	3.85410i	0.580785	−	0.314686i
$151$	21.5903			1.75699			0.878497	−	0.477747i	$-0.158547\pi$
$151$	21.5903			1.75699			0.878497	+	0.477747i	$0.158547\pi$
$152$		−	2.06115i		−	0.167181i
$153$		−	0.0233574i		−	0.00188833i
$154$		0			0
$155$	4.87770	+	19.2411i	0.391786	+	1.54548i
$156$	3.77813			0.302492
$157$		−	3.41472i		−	0.272525i	−0.990673	−	0.136262i	$-0.956491\pi$
$157$		−	3.41472i		−	0.272525i	0.990673	−	0.136262i	$-0.0435090\pi$
$158$			6.65520i			0.529459i
$159$	−3.59506			−0.285107
$160$	2.16751	−	0.549472i	0.171356	−	0.0434396i
$161$	−19.6318			−1.54721
$162$		−	7.70820i		−	0.605614i
$163$			17.4104i			1.36368i	0.731499	+	0.681842i	$0.238821\pi$
$163$			17.4104i			1.36368i	−0.731499	+	0.681842i	$0.761179\pi$
$164$	4.57985			0.357626
$165$		0			0
$166$	−11.0520			−0.857801
$167$		−	3.30599i		−	0.255825i	−0.991785	−	0.127913i	$-0.959172\pi$
$167$		−	3.30599i		−	0.255825i	0.991785	−	0.127913i	$-0.0408277\pi$
$168$			8.11314i			0.625942i
$169$	7.54772			0.580594
$170$	−0.0336004	−	0.132544i	−0.00257703	−	0.0101656i
$171$	0.787289			0.0602055
$172$		−	3.61803i		−	0.275873i
$173$			5.12859i			0.389920i	0.980811	+	0.194960i	$0.0624576\pi$
$173$			5.12859i			0.389920i	−0.980811	+	0.194960i	$0.937542\pi$
$174$	−6.69401			−0.507471
$175$	−11.9436	−	22.0432i	−0.902855	−	1.66631i
$176$		0			0
$177$		−	3.13712i		−	0.235801i
$178$		−	6.09017i		−	0.456478i
$179$	14.4394			1.07925			0.539625	−	0.841906i	$-0.318566\pi$
$179$	14.4394			1.07925			0.539625	+	0.841906i	$0.318566\pi$
$180$	0.209880	+	0.827913i	0.0156435	+	0.0617090i
$181$	11.9061			0.884973			0.442486	−	0.896775i	$-0.354097\pi$
$181$	11.9061			0.884973			0.442486	+	0.896775i	$0.354097\pi$
$182$		−	11.7082i		−	0.867870i
$183$		−	15.6842i		−	1.15941i
$184$	3.91525			0.288636
$185$	−9.87707	+	2.50388i	−0.726177	+	0.184089i
$186$	14.3634			1.05318
$187$		0			0
$188$			8.87707i			0.647427i
$189$	−27.4384			−1.99585
$190$	4.46756	−	1.13254i	0.324111	−	0.0821634i
$191$	10.5181			0.761061			0.380531	−	0.924768i	$-0.375741\pi$
$191$	10.5181			0.761061			0.380531	+	0.924768i	$0.375741\pi$
$192$		−	1.61803i		−	0.116772i
$193$			4.86869i			0.350456i	0.984528	+	0.175228i	$0.0560662\pi$
$193$			4.86869i			0.350456i	−0.984528	+	0.175228i	$0.943934\pi$
$194$	−7.30225			−0.524271
$195$	2.07597	+	8.18911i	0.148664	+	0.586435i
$196$	18.1422			1.29587
$197$			15.9760i			1.13824i	0.822253	+	0.569122i	$0.192717\pi$
$197$			15.9760i			1.13824i	−0.822253	+	0.569122i	$0.807283\pi$
$198$		0			0
$199$	−16.7076			−1.18437			−0.592184	−	0.805803i	$-0.701734\pi$
$199$	−16.7076			−1.18437			−0.592184	+	0.805803i	$0.701734\pi$
$200$	2.38197	+	4.39616i	0.168430	+	0.310856i
$201$	4.03818			0.284831
$202$		−	0.221872i		−	0.0156109i
$203$			20.7444i			1.45597i
$204$	−0.0989434			−0.00692742
$205$	2.51650	+	9.92686i	0.175760	+	0.693322i
$206$	−0.566045			−0.0394382
$207$			1.49549i			0.103944i
$208$			2.33501i			0.161904i
$209$		0			0
$210$	−17.5853	+	4.45794i	−1.21350	+	0.307627i
$211$	−15.7460			−1.08400			−0.542000	−	0.840379i	$-0.682333\pi$
$211$	−15.7460			−1.08400			−0.542000	+	0.840379i	$0.682333\pi$
$212$		−	2.22187i		−	0.152599i
$213$			14.2651i			0.977428i
$214$	−2.23002			−0.152441
$215$	7.84211	−	1.98801i	0.534827	−	0.135581i
$216$	5.47214			0.372332
$217$		−	44.5114i		−	3.02163i
$218$		−	7.86288i		−	0.532541i
$219$	−8.73117			−0.589998
$220$		0			0
$221$	0.142787			0.00960488
$222$			7.37319i			0.494856i
$223$			14.5556i			0.974717i	0.873202	+	0.487358i	$0.162039\pi$
$223$			14.5556i			0.974717i	−0.873202	+	0.487358i	$0.837961\pi$
$224$	−5.01420			−0.335025
$225$	−1.67918	+	0.909830i	−0.111946	+	0.0606553i
$226$	12.5617			0.835590
$227$			9.83656i			0.652875i	0.945219	+	0.326438i	$0.105848\pi$
$227$			9.83656i			0.652875i	−0.945219	+	0.326438i	$0.894152\pi$
$228$		−	3.33501i		−	0.220867i
$229$	15.5479			1.02743			0.513716	−	0.857960i	$-0.328268\pi$
$229$	15.5479			1.02743			0.513716	+	0.857960i	$0.328268\pi$
$230$	2.15132	+	8.48633i	0.141854	+	0.559572i
$231$		0			0
$232$		−	4.13712i		−	0.271616i
$233$			25.8967i			1.69655i	0.529557	+	0.848274i	$0.322358\pi$
$233$			25.8967i			1.69655i	−0.529557	+	0.848274i	$0.677642\pi$
$234$	−0.891895			−0.0583050
$235$	−19.2411	+	4.87770i	−1.25515	+	0.318186i
$236$	1.93885			0.126208
$237$			10.7683i			0.699479i
$238$			0.306620i			0.0198752i
$239$	−19.9960			−1.29344			−0.646718	−	0.762730i	$-0.723859\pi$
$239$	−19.9960			−1.29344			−0.646718	+	0.762730i	$0.723859\pi$
$240$	3.50710	−	0.889064i	0.226382	−	0.0573888i
$241$	9.01381			0.580630			0.290315	−	0.956931i	$-0.406240\pi$
$241$	9.01381			0.580630			0.290315	+	0.956931i	$0.406240\pi$
$242$		0			0
$243$			3.94427i			0.253025i
$244$	9.69338			0.620555
$245$	9.96860	+	39.3232i	0.636871	+	2.51227i
$246$	7.41036			0.472467
$247$			4.81281i			0.306232i
$248$			8.87707i			0.563695i
$249$	−17.8825			−1.13326
$250$	−8.21988	+	7.57849i	−0.519871	+	0.479306i
$251$	1.31165			0.0827909			0.0413954	−	0.999143i	$-0.486820\pi$
$251$	1.31165			0.0827909			0.0413954	+	0.999143i	$0.486820\pi$
$252$		−	1.91525i		−	0.120650i
$253$		0			0
$254$	14.4630			0.907488
$255$	−0.0543666	−	0.214460i	−0.00340457	−	0.0134300i
$256$	1.00000			0.0625000
$257$		−	4.46399i		−	0.278456i	−0.990260	−	0.139228i	$-0.955538\pi$
$257$		−	4.46399i		−	0.278456i	0.990260	−	0.139228i	$-0.0444621\pi$
$258$		−	5.85410i		−	0.364460i
$259$	22.8491			1.41977
$260$	−5.06115	+	1.28302i	−0.313879	+	0.0795697i
$261$	1.58024			0.0978145
$262$			15.3256i			0.946819i
$263$			14.1791i			0.874320i	0.899384	+	0.437160i	$0.144016\pi$
$263$			14.1791i			0.874320i	−0.899384	+	0.437160i	$0.855984\pi$
$264$		0			0
$265$	4.81592	−	1.22086i	0.295840	−	0.0749966i
$266$	−10.3350			−0.633680
$267$		−	9.85410i		−	0.603061i
$268$			2.49573i			0.152451i
$269$	31.9952			1.95078			0.975392	−	0.220477i	$-0.0707613\pi$
$269$	31.9952			1.95078			0.975392	+	0.220477i	$0.0707613\pi$
$270$	3.00678	+	11.8609i	0.182987	+	0.721831i
$271$	1.06139			0.0644749			0.0322374	−	0.999480i	$-0.489737\pi$
$271$	1.06139			0.0644749			0.0322374	+	0.999480i	$0.489737\pi$
$272$		−	0.0611504i		−	0.00370779i
$273$		−	18.9443i		−	1.14656i
$274$	−1.10437			−0.0667172
$275$		0			0
$276$	6.33501			0.381323
$277$			6.63325i			0.398553i	0.979943	+	0.199277i	$0.0638592\pi$
$277$			6.63325i			0.398553i	−0.979943	+	0.199277i	$0.936141\pi$
$278$			9.90609i			0.594128i
$279$	−3.39074			−0.202998
$280$	−2.75516	−	10.8683i	−0.164652	−	0.649505i
$281$	15.6464			0.933387			0.466694	−	0.884419i	$-0.345445\pi$
$281$	15.6464			0.933387			0.466694	+	0.884419i	$0.345445\pi$
$282$			14.3634i			0.855328i
$283$			22.5005i			1.33752i	0.743479	+	0.668759i	$0.233174\pi$
$283$			22.5005i			1.33752i	−0.743479	+	0.668759i	$0.766826\pi$
$284$	−8.81631			−0.523152
$285$	7.22866	−	1.83249i	0.428189	−	0.108548i
$286$		0			0
$287$		−	22.9643i		−	1.35554i
$288$			0.381966i			0.0225076i
$289$	16.9963			0.999780
$290$	8.96724	−	2.27323i	0.526575	−	0.133489i
$291$	−11.8153			−0.692625
$292$		−	5.39616i		−	0.315786i
$293$			18.1887i			1.06260i	0.847185	+	0.531298i	$0.178296\pi$
$293$			18.1887i			1.06260i	−0.847185	+	0.531298i	$0.821704\pi$
$294$	29.3546			1.71200
$295$	1.06534	+	4.20247i	0.0620267	+	0.244677i
$296$	−4.55688			−0.264863
$297$		0			0
$298$		−	8.79232i		−	0.509326i
$299$	−9.14216			−0.528705
$300$	3.85410	+	7.11314i	0.222517	+	0.410677i
$301$	−18.1415			−1.04566
$302$			21.5903i			1.24238i
$303$		−	0.358997i		−	0.0206238i
$304$	2.06115			0.118215
$305$	5.32624	+	21.0105i	0.304979	+	1.20306i
$306$	0.0233574			0.00133525
$307$			12.3820i			0.706676i	0.935496	+	0.353338i	$0.114953\pi$
$307$			12.3820i			0.706676i	−0.935496	+	0.353338i	$0.885047\pi$
$308$		0			0
$309$	−0.915880			−0.0521026
$310$	−19.2411	+	4.87770i	−1.09282	+	0.277035i
$311$	9.40997			0.533590			0.266795	−	0.963753i	$-0.414035\pi$
$311$	9.40997			0.533590			0.266795	+	0.963753i	$0.414035\pi$
$312$			3.77813i			0.213894i
$313$		−	15.2317i		−	0.860947i	−0.902603	−	0.430473i	$-0.858347\pi$
$313$		−	15.2317i		−	0.860947i	0.902603	−	0.430473i	$-0.141653\pi$
$314$	3.41472			0.192704
$315$	4.15132	−	1.05238i	0.233900	−	0.0592947i
$316$	−6.65520			−0.374384
$317$		−	13.4567i		−	0.755803i	−0.925846	−	0.377901i	$-0.876646\pi$
$317$		−	13.4567i		−	0.755803i	0.925846	−	0.377901i	$-0.123354\pi$
$318$		−	3.59506i		−	0.201601i
$319$		0			0
$320$	0.549472	+	2.16751i	0.0307164	+	0.121167i
$321$	−3.60824			−0.201393
$322$		−	19.6318i		−	1.09404i
$323$		−	0.126040i		−	0.00701306i
$324$	7.70820			0.428234
$325$	−5.56192	−	10.2651i	−0.308520	−	0.569405i
$326$	−17.4104			−0.964271
$327$		−	12.7224i		−	0.703550i
$328$			4.57985i			0.252880i
$329$	44.5114			2.45399
$330$		0			0
$331$	−3.82236			−0.210096			−0.105048	−	0.994467i	$-0.533500\pi$
$331$	−3.82236			−0.210096			−0.105048	+	0.994467i	$0.533500\pi$
$332$		−	11.0520i		−	0.606557i
$333$		−	1.74057i		−	0.0953829i
$334$	3.30599			0.180896
$335$	−5.40952	+	1.37133i	−0.295553	+	0.0749240i
$336$	−8.11314			−0.442608
$337$		−	9.46671i		−	0.515685i	−0.966187	−	0.257842i	$-0.916988\pi$
$337$		−	9.46671i		−	0.515685i	0.966187	−	0.257842i	$-0.0830115\pi$
$338$			7.54772i			0.410542i
$339$	20.3252			1.10391
$340$	0.132544	−	0.0336004i	0.00718820	−	0.00182224i
$341$		0			0
$342$			0.787289i			0.0425717i
$343$		−	55.8690i		−	3.01664i
$344$	3.61803			0.195071
$345$	3.48091	+	13.7312i	0.187406	+	0.739262i
$346$	−5.12859			−0.275715
$347$		−	16.5424i		−	0.888045i	−0.896016	−	0.444023i	$-0.853551\pi$
$347$		−	16.5424i		−	0.888045i	0.896016	−	0.444023i	$-0.146449\pi$
$348$		−	6.69401i		−	0.358837i
$349$	−29.2269			−1.56448			−0.782240	−	0.622977i	$-0.785923\pi$
$349$	−29.2269			−1.56448			−0.782240	+	0.622977i	$0.785923\pi$
$350$	22.0432	−	11.9436i	1.17826	−	0.638415i
$351$	−12.7775			−0.682012
$352$		0			0
$353$		−	27.9200i		−	1.48603i	−0.669272	−	0.743017i	$-0.733394\pi$
$353$		−	27.9200i		−	1.48603i	0.669272	−	0.743017i	$-0.266606\pi$
$354$	3.13712			0.166736
$355$	−4.84431	−	19.1094i	−0.257109	−	1.01422i
$356$	6.09017			0.322778
$357$			0.496121i			0.0262575i
$358$			14.4394i			0.763145i
$359$	−17.0142			−0.897975			−0.448987	−	0.893538i	$-0.648215\pi$
$359$	−17.0142			−0.897975			−0.448987	+	0.893538i	$0.648215\pi$
$360$	−0.827913	+	0.209880i	−0.0436349	+	0.0110616i
$361$	−14.7517			−0.776403
$362$			11.9061i			0.625770i
$363$		0			0
$364$	11.7082			0.613677
$365$	11.6962	−	2.96504i	0.612208	−	0.155197i
$366$	15.6842			0.819827
$367$		−	29.4391i		−	1.53671i	−0.640024	−	0.768355i	$-0.721075\pi$
$367$		−	29.4391i		−	1.53671i	0.640024	−	0.768355i	$-0.278925\pi$
$368$			3.91525i			0.204097i
$369$	−1.74935			−0.0910674
$370$	−2.50388	−	9.87707i	−0.130170	−	0.513484i
$371$	−11.1409			−0.578407
$372$			14.3634i			0.744708i
$373$		−	16.0743i		−	0.832297i	−0.909297	−	0.416149i	$-0.863380\pi$
$373$		−	16.0743i		−	0.832297i	0.909297	−	0.416149i	$-0.136620\pi$
$374$		0			0
$375$	−13.3000	+	12.2623i	−0.686812	+	0.633220i
$376$	−8.87707			−0.457800
$377$			9.66023i			0.497527i
$378$		−	27.4384i		−	1.41128i
$379$	−18.1230			−0.930914			−0.465457	−	0.885070i	$-0.654110\pi$
$379$	−18.1230			−0.930914			−0.465457	+	0.885070i	$0.654110\pi$
$380$	1.13254	+	4.46756i	0.0580983	+	0.229181i
$381$	23.4016			1.19890
$382$			10.5181i			0.538151i
$383$			13.2121i			0.675106i	0.941307	+	0.337553i	$0.109599\pi$
$383$			13.2121i			0.675106i	−0.941307	+	0.337553i	$0.890401\pi$
$384$	1.61803			0.0825700
$385$		0			0
$386$	−4.86869			−0.247810
$387$			1.38197i			0.0702493i
$388$		−	7.30225i		−	0.370716i
$389$	26.5245			1.34485			0.672423	−	0.740167i	$-0.265254\pi$
$389$	26.5245			1.34485			0.672423	+	0.740167i	$0.265254\pi$
$390$	−8.18911	+	2.07597i	−0.414672	+	0.105121i
$391$	0.239419			0.0121079
$392$			18.1422i			0.916317i
$393$			24.7974i			1.25086i
$394$	−15.9760			−0.804860
$395$	−3.65684	−	14.4252i	−0.183996	−	0.725810i
$396$		0			0
$397$		−	30.3246i		−	1.52195i	−0.648783	−	0.760974i	$-0.724722\pi$
$397$		−	30.3246i		−	1.52195i	0.648783	−	0.760974i	$-0.275278\pi$
$398$		−	16.7076i		−	0.837475i
$399$	−16.7224			−0.837167
$400$	−4.39616	+	2.38197i	−0.219808	+	0.119098i
$401$	19.4762			0.972593			0.486296	−	0.873794i	$-0.338348\pi$
$401$	19.4762			0.972593			0.486296	+	0.873794i	$0.338348\pi$
$402$			4.03818i			0.201406i
$403$		−	20.7281i		−	1.03254i
$404$	0.221872			0.0110386
$405$	4.23544	+	16.7076i	0.210461	+	0.830206i
$406$	−20.7444			−1.02952
$407$		0			0
$408$		−	0.0989434i		−	0.00489843i
$409$	28.3303			1.40084			0.700420	−	0.713730i	$-0.252996\pi$
$409$	28.3303			1.40084			0.700420	+	0.713730i	$0.252996\pi$
$410$	−9.92686	+	2.51650i	−0.490253	+	0.124281i
$411$	−1.78690			−0.0881413
$412$		−	0.566045i		−	0.0278870i
$413$		−	9.72177i		−	0.478377i
$414$	−1.49549			−0.0734995
$415$	23.9552	−	6.07275i	1.17592	−	0.298100i
$416$	−2.33501			−0.114483
$417$			16.0284i			0.784914i
$418$		0			0
$419$	15.4826			0.756374			0.378187	−	0.925729i	$-0.376548\pi$
$419$	15.4826			0.756374			0.378187	+	0.925729i	$0.376548\pi$
$420$	−4.45794	−	17.5853i	−0.217525	−	0.858074i
$421$	21.4863			1.04718			0.523590	−	0.851970i	$-0.324592\pi$
$421$	21.4863			1.04718			0.523590	+	0.851970i	$0.324592\pi$
$422$		−	15.7460i		−	0.766503i
$423$		−	3.39074i		−	0.164863i
$424$	2.22187			0.107904
$425$	0.145658	+	0.268827i	0.00706546	+	0.0130400i
$426$	−14.2651			−0.691146
$427$		−	48.6045i		−	2.35214i
$428$		−	2.23002i		−	0.107792i
$429$		0			0
$430$	1.98801	+	7.84211i	0.0958702	+	0.378180i
$431$	26.4390			1.27352			0.636761	−	0.771062i	$-0.280274\pi$
$431$	26.4390			1.27352			0.636761	+	0.771062i	$0.280274\pi$
$432$			5.47214i			0.263278i
$433$			32.8819i			1.58020i	0.612977	+	0.790101i	$0.289972\pi$
$433$			32.8819i			1.58020i	−0.612977	+	0.790101i	$0.710028\pi$
$434$	44.5114			2.13661
$435$	14.5093	−	3.67817i	0.695668	−	0.176355i
$436$	7.86288			0.376563
$437$			8.06992i			0.386037i
$438$		−	8.73117i		−	0.417192i
$439$	12.1796			0.581299			0.290649	−	0.956830i	$-0.406129\pi$
$439$	12.1796			0.581299			0.290649	+	0.956830i	$0.406129\pi$
$440$		0			0
$441$	−6.92969			−0.329985
$442$			0.142787i			0.00679168i
$443$		−	16.6090i		−	0.789118i	−0.918871	−	0.394559i	$-0.870897\pi$
$443$		−	16.6090i		−	0.789118i	0.918871	−	0.394559i	$-0.129103\pi$
$444$	−7.37319			−0.349916
$445$	3.34638	+	13.2005i	0.158633	+	0.625763i
$446$	−14.5556			−0.689229
$447$		−	14.2263i		−	0.672880i
$448$		−	5.01420i		−	0.236898i
$449$	5.36364			0.253126			0.126563	−	0.991959i	$-0.459605\pi$
$449$	5.36364			0.253126			0.126563	+	0.991959i	$0.459605\pi$
$450$	−0.909830	−	1.67918i	−0.0428898	−	0.0791575i
$451$		0			0
$452$			12.5617i			0.590852i
$453$			34.9339i			1.64134i
$454$	−9.83656			−0.461652
$455$	6.43333	+	25.3776i	0.301599	+	1.18972i
$456$	3.33501			0.156176
$457$			3.61237i			0.168980i	0.996424	+	0.0844898i	$0.0269260\pi$
$457$			3.61237i			0.168980i	−0.996424	+	0.0844898i	$0.973074\pi$
$458$			15.5479i			0.726504i
$459$	0.334623			0.0156189
$460$	−8.48633	+	2.15132i	−0.395677	+	0.100306i
$461$	−40.6625			−1.89384			−0.946922	−	0.321464i	$-0.895825\pi$
$461$	−40.6625			−1.89384			−0.946922	+	0.321464i	$0.895825\pi$
$462$		0			0
$463$		−	2.11880i		−	0.0984690i	−0.998787	−	0.0492345i	$-0.984322\pi$
$463$		−	2.11880i		−	0.0984690i	0.998787	−	0.0492345i	$-0.0156782\pi$
$464$	4.13712			0.192061
$465$	−31.1328	+	7.89228i	−1.44375	+	0.365996i
$466$	−25.8967			−1.19964
$467$			13.7549i			0.636502i	0.948007	+	0.318251i	$0.103095\pi$
$467$			13.7549i			0.636502i	−0.948007	+	0.318251i	$0.896905\pi$
$468$		−	0.891895i		−	0.0412279i
$469$	12.5141			0.577847
$470$	−4.87770	−	19.2411i	−0.224991	−	0.887526i
$471$	5.52514			0.254585
$472$			1.93885i			0.0892428i
$473$		0			0
$474$	−10.7683			−0.494606
$475$	−9.06115	+	4.90959i	−0.415754	+	0.225267i
$476$	−0.306620			−0.0140539
$477$			0.848680i			0.0388584i
$478$		−	19.9960i		−	0.914597i
$479$	−31.4107			−1.43519			−0.717597	−	0.696459i	$-0.754758\pi$
$479$	−31.4107			−1.43519			−0.717597	+	0.696459i	$0.754758\pi$
$480$	0.889064	+	3.50710i	0.0405800	+	0.160076i
$481$	10.6404			0.485159
$482$			9.01381i			0.410568i
$483$		−	31.7650i		−	1.44536i
$484$		0			0
$485$	15.8277	−	4.01238i	0.718698	−	0.182193i
$486$	−3.94427			−0.178916
$487$			7.51032i			0.340325i	0.985416	+	0.170162i	$0.0544293\pi$
$487$			7.51032i			0.340325i	−0.985416	+	0.170162i	$0.945571\pi$
$488$			9.69338i			0.438799i
$489$	−28.1706			−1.27392
$490$	−39.3232	+	9.96860i	−1.77644	+	0.450336i
$491$	11.2618			0.508236			0.254118	−	0.967173i	$-0.418215\pi$
$491$	11.2618			0.508236			0.254118	+	0.967173i	$0.418215\pi$
$492$			7.41036i			0.334085i
$493$		−	0.252987i		−	0.0113939i
$494$	−4.81281			−0.216539
$495$		0			0
$496$	−8.87707			−0.398592
$497$			44.2067i			1.98294i
$498$		−	17.8825i		−	0.801334i
$499$	26.9808			1.20783			0.603913	−	0.797050i	$-0.293607\pi$
$499$	26.9808			1.20783			0.603913	+	0.797050i	$0.293607\pi$
$500$	−7.57849	−	8.21988i	−0.338920	−	0.367604i
$501$	5.34921			0.238985
$502$			1.31165i			0.0585420i
$503$		−	32.1556i		−	1.43375i	−0.697204	−	0.716873i	$-0.745573\pi$
$503$		−	32.1556i		−	1.43375i	0.697204	−	0.716873i	$-0.254427\pi$
$504$	1.91525			0.0853121
$505$	0.121913	+	0.480909i	0.00542504	+	0.0214002i
$506$		0			0
$507$			12.2125i			0.542375i
$508$			14.4630i			0.641691i
$509$	−11.7809			−0.522177			−0.261089	−	0.965315i	$-0.584081\pi$
$509$	−11.7809			−0.522177			−0.261089	+	0.965315i	$0.584081\pi$
$510$	0.214460	−	0.0543666i	0.00949646	−	0.00240739i
$511$	−27.0574			−1.19695
$512$			1.00000i			0.0441942i
$513$			11.2789i			0.497975i
$514$	4.46399			0.196898
$515$	1.22691	−	0.311026i	0.0540640	−	0.0137054i
$516$	5.85410			0.257712
$517$		0			0
$518$			22.8491i			1.00393i
$519$	−8.29823			−0.364252
$520$	−1.28302	−	5.06115i	−0.0562643	−	0.221946i
$521$	2.32624			0.101914			0.0509572	−	0.998701i	$-0.483773\pi$
$521$	2.32624			0.101914			0.0509572	+	0.998701i	$0.483773\pi$
$522$			1.58024i			0.0691653i
$523$			1.53391i			0.0670734i	0.999437	+	0.0335367i	$0.0106771\pi$
$523$			1.53391i			0.0670734i	−0.999437	+	0.0335367i	$0.989323\pi$
$524$	−15.3256			−0.669502
$525$	35.6667	−	19.3252i	1.55662	−	0.843422i
$526$	−14.1791			−0.618237
$527$			0.542836i			0.0236463i
$528$		0			0
$529$	7.67080			0.333513
$530$	1.22086	+	4.81592i	0.0530306	+	0.209190i
$531$	−0.740575			−0.0321382
$532$		−	10.3350i		−	0.448080i
$533$		−	10.6940i		−	0.463209i
$534$	9.85410			0.426429
$535$	4.83358	−	1.22533i	0.208974	−	0.0529757i
$536$	−2.49573			−0.107799
$537$			23.3634i			1.00821i
$538$			31.9952i			1.37941i
$539$		0			0
$540$	−11.8609	+	3.00678i	−0.510411	+	0.129391i
$541$	−15.4419			−0.663897			−0.331949	−	0.943297i	$-0.607706\pi$
$541$	−15.4419			−0.663897			−0.331949	+	0.943297i	$0.607706\pi$
$542$			1.06139i			0.0455906i
$543$			19.2645i			0.826717i
$544$	0.0611504			0.00262180
$545$	4.32043	+	17.0428i	0.185067	+	0.730035i
$546$	18.9443			0.810740
$547$			10.6472i			0.455241i	0.973750	+	0.227621i	$0.0730946\pi$
$547$			10.6472i			0.455241i	−0.973750	+	0.227621i	$0.926905\pi$
$548$		−	1.10437i		−	0.0471762i
$549$	−3.70254			−0.158021
$550$		0			0
$551$	8.52724			0.363272
$552$			6.33501i			0.269636i
$553$			33.3705i			1.41906i
$554$	−6.63325			−0.281820
$555$	−4.05136	−	15.9814i	−0.171971	−	0.678374i
$556$	−9.90609			−0.420112
$557$		−	33.9197i		−	1.43722i	−0.695412	−	0.718611i	$-0.744778\pi$
$557$		−	33.9197i		−	1.43722i	0.695412	−	0.718611i	$-0.255222\pi$
$558$		−	3.39074i		−	0.143541i
$559$	−8.44815			−0.357319
$560$	10.8683	−	2.75516i	0.459269	−	0.116427i
$561$		0			0
$562$			15.6464i			0.660005i
$563$			1.34378i			0.0566338i	0.999599	+	0.0283169i	$0.00901475\pi$
$563$			1.34378i			0.0566338i	−0.999599	+	0.0283169i	$0.990985\pi$
$564$	−14.3634			−0.604808
$565$	−27.2275	+	6.90229i	−1.14547	+	0.290381i
$566$	−22.5005			−0.945768
$567$		−	38.6504i		−	1.62317i
$568$		−	8.81631i		−	0.369924i
$569$	31.4091			1.31674			0.658369	−	0.752695i	$-0.271247\pi$
$569$	31.4091			1.31674			0.658369	+	0.752695i	$0.271247\pi$
$570$	1.83249	+	7.22866i	0.0767547	+	0.302775i
$571$	9.25361			0.387252			0.193626	−	0.981075i	$-0.437975\pi$
$571$	9.25361			0.387252			0.193626	+	0.981075i	$0.437975\pi$
$572$		0			0
$573$			17.0186i			0.710962i
$574$	22.9643			0.958510
$575$	−9.32600	−	17.2121i	−0.388921	−	0.717793i
$576$	−0.381966			−0.0159153
$577$		−	43.3829i		−	1.80605i	−0.429585	−	0.903026i	$-0.641340\pi$
$577$		−	43.3829i		−	1.80605i	0.429585	−	0.903026i	$-0.358660\pi$
$578$			16.9963i			0.706951i
$579$	−7.87770			−0.327386
$580$	2.27323	+	8.96724i	0.0943909	+	0.372344i
$581$	−55.4168			−2.29908
$582$		−	11.8153i		−	0.489760i
$583$		0			0
$584$	5.39616			0.223295
$585$	1.93319	−	0.490071i	0.0799275	−	0.0202619i
$586$	−18.1887			−0.751369
$587$			3.21247i			0.132593i	0.997800	+	0.0662964i	$0.0211183\pi$
$587$			3.21247i			0.132593i	−0.997800	+	0.0662964i	$0.978882\pi$
$588$			29.3546i			1.21056i
$589$	−18.2970			−0.753914
$590$	−4.20247	+	1.06534i	−0.173013	+	0.0438595i
$591$	−25.8497			−1.06332
$592$		−	4.55688i		−	0.187287i
$593$			0.0315027i			0.00129366i	1.00000		0.000646829i	$0.000205892\pi$
$593$			0.0315027i			0.00129366i	−1.00000		0.000646829i	$0.999794\pi$
$594$		0			0
$595$	−0.168479	−	0.664600i	−0.00690696	−	0.0272460i
$596$	8.79232			0.360148
$597$		−	27.0334i		−	1.10640i
$598$		−	9.14216i		−	0.373851i
$599$	10.5189			0.429789			0.214894	−	0.976637i	$-0.431059\pi$
$599$	10.5189			0.429789			0.214894	+	0.976637i	$0.431059\pi$
$600$	−7.11314	+	3.85410i	−0.290393	+	0.157343i
$601$	24.1186			0.983817			0.491908	−	0.870647i	$-0.336300\pi$
$601$	24.1186			0.983817			0.491908	+	0.870647i	$0.336300\pi$
$602$		−	18.1415i		−	0.739394i
$603$		−	0.953285i		−	0.0388208i
$604$	−21.5903			−0.878497
$605$		0			0
$606$	0.358997			0.0145833
$607$		−	2.48968i		−	0.101053i	−0.998723	−	0.0505266i	$-0.983910\pi$
$607$		−	2.48968i		−	0.101053i	0.998723	−	0.0505266i	$-0.0160900\pi$
$608$			2.06115i			0.0835907i
$609$	−33.5651			−1.36013
$610$	−21.0105	+	5.32624i	−0.850689	+	0.215653i
$611$	20.7281			0.838568
$612$			0.0233574i			0.000944165i
$613$		−	37.5728i		−	1.51755i	−0.651353	−	0.758775i	$-0.725798\pi$
$613$		−	37.5728i		−	1.51755i	0.651353	−	0.758775i	$-0.274202\pi$
$614$	−12.3820			−0.499695
$615$	−16.0620	+	4.07178i	−0.647682	+	0.164190i
$616$		0			0
$617$			45.5803i			1.83499i	0.397744	+	0.917496i	$0.369793\pi$
$617$			45.5803i			1.83499i	−0.397744	+	0.917496i	$0.630207\pi$
$618$		−	0.915880i		−	0.0368421i
$619$	−5.74019			−0.230718			−0.115359	−	0.993324i	$-0.536802\pi$
$619$	−5.74019			−0.230718			−0.115359	+	0.993324i	$0.536802\pi$
$620$	−4.87770	−	19.2411i	−0.195893	−	0.772741i
$621$	−21.4248			−0.859747
$622$			9.40997i			0.377305i
$623$		−	30.5373i		−	1.22345i
$624$	−3.77813			−0.151246
$625$	13.6525	−	20.9430i	0.546099	−	0.837721i
$626$	15.2317			0.608781
$627$		0			0
$628$			3.41472i			0.136262i
$629$	−0.278655			−0.0111107
$630$	1.05238	+	4.15132i	0.0419277	+	0.165393i
$631$	11.9768			0.476789			0.238394	−	0.971168i	$-0.423379\pi$
$631$	11.9768			0.476789			0.238394	+	0.971168i	$0.423379\pi$
$632$		−	6.65520i		−	0.264730i
$633$		−	25.4776i		−	1.01264i
$634$	13.4567			0.534433
$635$	−31.3486	+	7.94699i	−1.24403	+	0.315367i
$636$	3.59506			0.142554
$637$		−	42.3621i		−	1.67845i
$638$		0			0
$639$	3.36753			0.133217
$640$	−2.16751	+	0.549472i	−0.0856782	+	0.0217198i
$641$	−35.1196			−1.38714			−0.693571	−	0.720389i	$-0.743964\pi$
$641$	−35.1196			−1.38714			−0.693571	+	0.720389i	$0.743964\pi$
$642$		−	3.60824i		−	0.142406i
$643$			35.6472i			1.40579i	0.711294	+	0.702894i	$0.248109\pi$
$643$			35.6472i			1.40579i	−0.711294	+	0.702894i	$0.751891\pi$
$644$	19.6318			0.773603
$645$	3.21666	+	12.6888i	0.126656	+	0.499621i
$646$	0.126040			0.00495898
$647$			20.1564i			0.792428i	0.918158	+	0.396214i	$0.129676\pi$
$647$			20.1564i			0.792428i	−0.918158	+	0.396214i	$0.870324\pi$
$648$			7.70820i			0.302807i
$649$		0			0
$650$	10.2651	−	5.56192i	0.402630	−	0.218156i
$651$	72.0209			2.82272
$652$		−	17.4104i		−	0.681842i
$653$		−	24.3839i		−	0.954215i	−0.878845	−	0.477108i	$-0.841685\pi$
$653$		−	24.3839i		−	0.954215i	0.878845	−	0.477108i	$-0.158315\pi$
$654$	12.7224			0.497485
$655$	−8.42099	−	33.2183i	−0.329035	−	1.29795i
$656$	−4.57985			−0.178813
$657$			2.06115i			0.0804131i
$658$			44.5114i			1.73523i
$659$	6.98788			0.272209			0.136104	−	0.990694i	$-0.456542\pi$
$659$	6.98788			0.272209			0.136104	+	0.990694i	$0.456542\pi$
$660$		0			0
$661$	−3.61827			−0.140735			−0.0703673	−	0.997521i	$-0.522417\pi$
$661$	−3.61827			−0.140735			−0.0703673	+	0.997521i	$0.522417\pi$
$662$		−	3.82236i		−	0.148560i
$663$			0.231034i			0.00897261i
$664$	11.0520			0.428900
$665$	22.4012	−	5.67880i	0.868681	−	0.220214i
$666$	1.74057			0.0674459
$667$			16.1979i			0.627185i
$668$			3.30599i			0.127913i
$669$	−23.5515			−0.910554
$670$	−1.37133	−	5.40952i	−0.0529793	−	0.208988i
$671$		0			0
$672$		−	8.11314i		−	0.312971i
$673$		−	7.96850i		−	0.307163i	−0.988136	−	0.153581i	$-0.950919\pi$
$673$		−	7.96850i		−	0.307163i	0.988136	−	0.153581i	$-0.0490808\pi$
$674$	9.46671			0.364644
$675$	−13.0344	−	24.0564i	−0.501696	−	0.925931i
$676$	−7.54772			−0.290297
$677$			14.4346i			0.554766i	0.960759	+	0.277383i	$0.0894671\pi$
$677$			14.4346i			0.554766i	−0.960759	+	0.277383i	$0.910533\pi$
$678$			20.3252i			0.780585i
$679$	−36.6149			−1.40515
$680$	0.0336004	+	0.132544i	0.00128852	+	0.00508282i
$681$	−15.9159			−0.609898
$682$		0			0
$683$			29.6723i			1.13538i	0.823242	+	0.567690i	$0.192163\pi$
$683$			29.6723i			1.13538i	−0.823242	+	0.567690i	$0.807837\pi$
$684$	−0.787289			−0.0301028
$685$	2.39372	−	0.606818i	0.0914593	−	0.0231853i
$686$	55.8690			2.13309
$687$			25.1570i			0.959799i
$688$			3.61803i			0.137936i
$689$	−5.18810			−0.197651
$690$	−13.7312	+	3.48091i	−0.522737	+	0.132516i
$691$	32.3618			1.23110			0.615550	−	0.788098i	$-0.288934\pi$
$691$	32.3618			1.23110			0.615550	+	0.788098i	$0.288934\pi$
$692$		−	5.12859i		−	0.194960i
$693$		0			0
$694$	16.5424			0.627943
$695$	−5.44312	−	21.4715i	−0.206469	−	0.814461i
$696$	6.69401			0.253736
$697$			0.280060i			0.0106080i
$698$		−	29.2269i		−	1.10625i
$699$	−41.9017			−1.58487
$700$	11.9436	+	22.0432i	0.451427	+	0.833155i
$701$	18.9662			0.716344			0.358172	−	0.933656i	$-0.383400\pi$
$701$	18.9662			0.716344			0.358172	+	0.933656i	$0.383400\pi$
$702$		−	12.7775i		−	0.482256i
$703$		−	9.39242i		−	0.354242i
$704$		0			0
$705$	−7.89228	−	31.1328i	−0.297241	−	1.17253i
$706$	27.9200			1.05078
$707$		−	1.11251i		−	0.0418403i
$708$			3.13712i			0.117900i
$709$	−8.38816			−0.315024			−0.157512	−	0.987517i	$-0.550347\pi$
$709$	−8.38816			−0.315024			−0.157512	+	0.987517i	$0.550347\pi$
$710$	19.1094	−	4.84431i	0.717163	−	0.181804i
$711$	2.54206			0.0953347
$712$			6.09017i			0.228239i
$713$		−	34.7560i		−	1.30162i
$714$	−0.496121			−0.0185669
$715$		0			0
$716$	−14.4394			−0.539625
$717$		−	32.3542i		−	1.20829i
$718$		−	17.0142i		−	0.634964i
$719$	−7.54709			−0.281459			−0.140730	−	0.990048i	$-0.544945\pi$
$719$	−7.54709			−0.281459			−0.140730	+	0.990048i	$0.544945\pi$
$720$	−0.209880	−	0.827913i	−0.00782175	−	0.0308545i
$721$	−2.83826			−0.105702
$722$		−	14.7517i		−	0.549000i
$723$			14.5846i			0.542409i
$724$	−11.9061			−0.442486
$725$	−18.1875	+	9.85449i	−0.675466	+	0.365987i
$726$		0			0
$727$		−	24.2826i		−	0.900593i	−0.892879	−	0.450297i	$-0.851318\pi$
$727$		−	24.2826i		−	0.900593i	0.892879	−	0.450297i	$-0.148682\pi$
$728$			11.7082i			0.433935i
$729$	−29.5066			−1.09284
$730$	2.96504	+	11.6962i	0.109741	+	0.432896i
$731$	0.221244			0.00818301
$732$			15.6842i			0.579705i
$733$			21.4016i			0.790486i	0.918577	+	0.395243i	$0.129340\pi$
$733$			21.4016i			0.790486i	−0.918577	+	0.395243i	$0.870660\pi$
$734$	29.4391			1.08662
$735$	−63.6263	+	16.1295i	−2.34689	+	0.594947i
$736$	−3.91525			−0.144318
$737$		0			0
$738$		−	1.74935i		−	0.0643944i
$739$	−35.1561			−1.29324			−0.646619	−	0.762813i	$-0.723818\pi$
$739$	−35.1561			−1.29324			−0.646619	+	0.762813i	$0.723818\pi$
$740$	9.87707	−	2.50388i	0.363088	−	0.0920444i
$741$	−7.78729			−0.286073
$742$		−	11.1409i		−	0.408995i
$743$		−	34.1000i		−	1.25101i	−0.780221	−	0.625504i	$-0.784893\pi$
$743$		−	34.1000i		−	1.25101i	0.780221	−	0.625504i	$-0.215107\pi$
$744$	−14.3634			−0.526588
$745$	4.83113	+	19.0574i	0.176999	+	0.698210i
$746$	16.0743			0.588523
$747$			4.22148i			0.154456i
$748$		0			0
$749$	−11.1817			−0.408572
$750$	−12.2623	−	13.3000i	−0.447754	−	0.485649i
$751$	−35.8201			−1.30709			−0.653547	−	0.756886i	$-0.726720\pi$
$751$	−35.8201			−1.30709			−0.653547	+	0.756886i	$0.726720\pi$
$752$		−	8.87707i		−	0.323713i
$753$			2.12230i			0.0773409i
$754$	−9.66023			−0.351805
$755$	−11.8633	−	46.7971i	−0.431748	−	1.70312i
$756$	27.4384			0.997924
$757$		−	24.2280i		−	0.880580i	−0.897856	−	0.440290i	$-0.854876\pi$
$757$		−	24.2280i		−	0.880580i	0.897856	−	0.440290i	$-0.145124\pi$
$758$		−	18.1230i		−	0.658256i
$759$		0			0
$760$	−4.46756	+	1.13254i	−0.162055	+	0.0410817i
$761$	10.6573			0.386326			0.193163	−	0.981167i	$-0.438125\pi$
$761$	10.6573			0.386326			0.193163	+	0.981167i	$0.438125\pi$
$762$			23.4016i			0.847750i
$763$		−	39.4260i		−	1.42732i
$764$	−10.5181			−0.380531
$765$	−0.0506272	+	0.0128342i	−0.00183043	+	0.000464022i
$766$	−13.2121			−0.477372
$767$		−	4.52724i		−	0.163469i
$768$			1.61803i			0.0583858i
$769$	−25.8297			−0.931444			−0.465722	−	0.884931i	$-0.654205\pi$
$769$	−25.8297			−0.931444			−0.465722	+	0.884931i	$0.654205\pi$
$770$		0			0
$771$	7.22289			0.260126
$772$		−	4.86869i		−	0.175228i
$773$		−	12.0580i		−	0.433698i	−0.976205	−	0.216849i	$-0.930422\pi$
$773$		−	12.0580i		−	0.433698i	0.976205	−	0.216849i	$-0.0695778\pi$
$774$	−1.38197			−0.0496737
$775$	39.0250	−	21.1449i	1.40182	−	0.759547i
$776$	7.30225			0.262136
$777$			36.9706i			1.32631i
$778$			26.5245i			0.950950i
$779$	−9.43977			−0.338215
$780$	−2.07597	−	8.18911i	−0.0743318	−	0.293217i
$781$		0			0
$782$			0.239419i			0.00856161i
$783$			22.6389i			0.809049i
$784$	−18.1422			−0.647934
$785$	−7.40144	+	1.87629i	−0.264169	+	0.0669678i
$786$	−24.7974			−0.884492
$787$			18.1572i			0.647235i	0.946188	+	0.323618i	$0.104899\pi$
$787$			18.1572i			0.647235i	−0.946188	+	0.323618i	$0.895101\pi$
$788$		−	15.9760i		−	0.569122i
$789$	−22.9422			−0.816765
$790$	14.4252	−	3.65684i	0.513225	−	0.130105i
$791$	62.9867			2.23955
$792$		0			0
$793$		−	22.6342i		−	0.803762i
$794$	30.3246			1.07618
$795$	1.97539	+	7.79232i	0.0700597	+	0.276365i
$796$	16.7076			0.592184
$797$		−	1.61067i		−	0.0570527i	−0.999593	−	0.0285263i	$-0.990919\pi$
$797$		−	1.61067i		−	0.0570527i	0.999593	−	0.0285263i	$-0.00908145\pi$
$798$		−	16.7224i		−	0.591967i
$799$	−0.542836			−0.0192042
$800$	−2.38197	−	4.39616i	−0.0842152	−	0.155428i
$801$	−2.32624			−0.0821936
$802$			19.4762i			0.687727i
$803$		0			0
$804$	−4.03818			−0.142416
$805$	10.7871	+	42.5521i	0.380197	+	1.49977i
$806$	20.7281			0.730115
$807$			51.7694i			1.82237i
$808$			0.221872i			0.00780544i
$809$	−25.6203			−0.900763			−0.450382	−	0.892836i	$-0.648712\pi$
$809$	−25.6203			−0.900763			−0.450382	+	0.892836i	$0.648712\pi$
$810$	−16.7076	+	4.23544i	−0.587044	+	0.148818i
$811$	43.8508			1.53981			0.769904	−	0.638160i	$-0.220304\pi$
$811$	43.8508			1.53981			0.769904	+	0.638160i	$0.220304\pi$
$812$		−	20.7444i		−	0.727984i
$813$			1.71737i			0.0602306i
$814$		0			0
$815$	37.7370	−	9.56650i	1.32187	−	0.335100i
$816$	0.0989434			0.00346371
$817$			7.45731i			0.260898i
$818$			28.3303i			0.990544i
$819$	−4.47214			−0.156269
$820$	−2.51650	−	9.92686i	−0.0878800	−	0.346661i
$821$	−17.6022			−0.614321			−0.307160	−	0.951658i	$-0.599379\pi$
$821$	−17.6022			−0.614321			−0.307160	+	0.951658i	$0.599379\pi$
$822$		−	1.78690i		−	0.0623253i
$823$		−	12.6552i		−	0.441133i	−0.975372	−	0.220566i	$-0.929209\pi$
$823$		−	12.6552i		−	0.441133i	0.975372	−	0.220566i	$-0.0707905\pi$
$824$	0.566045			0.0197191
$825$		0			0
$826$	9.72177			0.338264
$827$		−	8.84431i		−	0.307547i	−0.988106	−	0.153773i	$-0.950857\pi$
$827$		−	8.84431i		−	0.307547i	0.988106	−	0.153773i	$-0.0491426\pi$
$828$		−	1.49549i		−	0.0519720i
$829$	−37.7230			−1.31017			−0.655087	−	0.755553i	$-0.727368\pi$
$829$	−37.7230			−1.31017			−0.655087	+	0.755553i	$0.727368\pi$
$830$	6.07275	+	23.9552i	0.210788	+	0.831499i
$831$	−10.7328			−0.372317
$832$		−	2.33501i		−	0.0809520i
$833$			1.10940i			0.0384384i
$834$	−16.0284			−0.555018
$835$	−7.16576	+	1.81655i	−0.247981	+	0.0628643i
$836$		0			0
$837$		−	48.5765i		−	1.67905i
$838$			15.4826i			0.534837i
$839$	38.4879			1.32875			0.664374	−	0.747400i	$-0.268698\pi$
$839$	38.4879			1.32875			0.664374	+	0.747400i	$0.268698\pi$
$840$	17.5853	−	4.45794i	0.606750	−	0.153814i
$841$	−11.8842			−0.409800
$842$			21.4863i			0.740468i
$843$			25.3164i			0.871945i
$844$	15.7460			0.542000
$845$	−4.14726	−	16.3597i	−0.142670	−	0.562792i
$846$	3.39074			0.116576
$847$		0			0
$848$			2.22187i			0.0762994i
$849$	−36.4066			−1.24947
$850$	−0.268827	+	0.145658i	−0.00922069	+	0.00499603i
$851$	17.8413			0.611594
$852$		−	14.2651i		−	0.488714i
$853$			50.8896i			1.74243i	0.490905	+	0.871213i	$0.336666\pi$
$853$			50.8896i			1.74243i	−0.490905	+	0.871213i	$0.663334\pi$
$854$	48.6045			1.66321
$855$	−0.432593	−	1.70645i	−0.0147944	−	0.0583595i
$856$	2.23002			0.0762204
$857$		−	11.5197i		−	0.393506i	−0.980453	−	0.196753i	$-0.936960\pi$
$857$		−	11.5197i		−	0.393506i	0.980453	−	0.196753i	$-0.0630397\pi$
$858$		0			0
$859$	−23.9497			−0.817153			−0.408577	−	0.912724i	$-0.633975\pi$
$859$	−23.9497			−0.817153			−0.408577	+	0.912724i	$0.633975\pi$
$860$	−7.84211	+	1.98801i	−0.267414	+	0.0677905i
$861$	37.1570			1.26631
$862$			26.4390i			0.900516i
$863$		−	40.0096i		−	1.36194i	−0.732310	−	0.680971i	$-0.761558\pi$
$863$		−	40.0096i		−	1.36194i	0.732310	−	0.680971i	$-0.238442\pi$
$864$	−5.47214			−0.186166
$865$	11.1163	−	2.81802i	0.377964	−	0.0958154i
$866$	−32.8819			−1.11737
$867$			27.5005i			0.933967i
$868$			44.5114i			1.51081i
$869$		0			0
$870$	3.67817	+	14.5093i	0.124702	+	0.491911i
$871$	5.82757			0.197460
$872$			7.86288i			0.266271i
$873$			2.78921i			0.0944005i
$874$	−8.06992			−0.272969
$875$	−41.2161	+	38.0000i	−1.39336	+	1.28464i
$876$	8.73117			0.294999
$877$			25.9821i			0.877353i	0.898645	+	0.438677i	$0.144553\pi$
$877$			25.9821i			0.877353i	−0.898645	+	0.438677i	$0.855447\pi$
$878$			12.1796i			0.411040i
$879$	−29.4300			−0.992648
$880$		0			0
$881$	25.1372			0.846893			0.423446	−	0.905921i	$-0.360820\pi$
$881$	25.1372			0.846893			0.423446	+	0.905921i	$0.360820\pi$
$882$		−	6.92969i		−	0.233335i
$883$			43.4707i			1.46291i	0.681892	+	0.731453i	$0.261157\pi$
$883$			43.4707i			1.46291i	−0.681892	+	0.731453i	$0.738843\pi$
$884$	−0.142787			−0.00480244
$885$	−6.79974	+	1.72376i	−0.228571	+	0.0579436i
$886$	16.6090			0.557991
$887$			28.6080i			0.960563i	0.877114	+	0.480281i	$0.159465\pi$
$887$			28.6080i			0.960563i	−0.877114	+	0.480281i	$0.840535\pi$
$888$		−	7.37319i		−	0.247428i
$889$	72.5202			2.43225
$890$	−13.2005	+	3.34638i	−0.442481	+	0.112171i
$891$		0			0
$892$		−	14.5556i		−	0.487358i
$893$		−	18.2970i		−	0.612285i
$894$	14.2263			0.475798
$895$	−7.93403	−	31.2974i	−0.265205	−	1.04616i
$896$	5.01420			0.167513
$897$		−	14.7923i		−	0.493901i
$898$			5.36364i			0.178987i
$899$	−36.7255			−1.22487
$900$	1.67918	−	0.909830i	0.0559728	−	0.0303277i
$901$	0.135868			0.00452643
$902$		0			0
$903$		−	29.3536i		−	0.976827i
$904$	−12.5617			−0.417795
$905$	−6.54206	−	25.8065i	−0.217465	−	0.857838i
$906$	−34.9339			−1.16060
$907$			47.7110i			1.58422i	0.610381	+	0.792108i	$0.291017\pi$
$907$			47.7110i			1.58422i	−0.610381	+	0.792108i	$0.708983\pi$
$908$		−	9.83656i		−	0.326438i
$909$	−0.0847477			−0.00281090
$910$	−25.3776	+	6.43333i	−0.841259	+	0.213263i
$911$	49.8139			1.65041			0.825203	−	0.564836i	$-0.191060\pi$
$911$	49.8139			1.65041			0.825203	+	0.564836i	$0.191060\pi$
$912$			3.33501i			0.110433i
$913$		0			0
$914$	−3.61237			−0.119487
$915$	−33.9956	+	8.61803i	−1.12386	+	0.284903i
$916$	−15.5479			−0.513716
$917$			76.8456i			2.53767i
$918$			0.334623i			0.0110442i
$919$	42.8988			1.41510			0.707550	−	0.706664i	$-0.249801\pi$
$919$	42.8988			1.41510			0.707550	+	0.706664i	$0.249801\pi$
$920$	−2.15132	−	8.48633i	−0.0709269	−	0.279786i
$921$	−20.0344			−0.660157
$922$		−	40.6625i		−	1.33915i
$923$			20.5862i			0.677602i
$924$		0			0
$925$	10.8543	+	20.0328i	0.356889	+	0.658674i
$926$	2.11880			0.0696281
$927$			0.216210i			0.00710127i
$928$			4.13712i			0.135808i
$929$	3.96430			0.130065			0.0650323	−	0.997883i	$-0.479285\pi$
$929$	3.96430			0.130065			0.0650323	+	0.997883i	$0.479285\pi$
$930$	−7.89228	−	31.1328i	−0.258798	−	1.02088i
$931$	−37.3937			−1.22553
$932$		−	25.8967i		−	0.848274i
$933$			15.2257i			0.498465i
$934$	−13.7549			−0.450075
$935$		0			0
$936$	0.891895			0.0291525
$937$		−	2.11919i		−	0.0692309i	−0.999401	−	0.0346155i	$-0.988979\pi$
$937$		−	2.11919i		−	0.0692309i	0.999401	−	0.0346155i	$-0.0110206\pi$
$938$			12.5141i			0.408600i
$939$	24.6454			0.804273
$940$	19.2411	−	4.87770i	0.627576	−	0.159093i
$941$	5.04462			0.164450			0.0822250	−	0.996614i	$-0.473797\pi$
$941$	5.04462			0.164450			0.0822250	+	0.996614i	$0.473797\pi$
$942$			5.52514i			0.180019i
$943$		−	17.9313i		−	0.583923i
$944$	−1.93885			−0.0631042
$945$	15.0766	+	59.4728i	0.490442	+	1.93465i
$946$		0			0
$947$		−	0.986192i		−	0.0320470i	−0.999872	−	0.0160235i	$-0.994899\pi$
$947$		−	0.986192i		−	0.0320470i	0.999872	−	0.0160235i	$-0.00510065\pi$
$948$		−	10.7683i		−	0.349739i
$949$	−12.6001			−0.409017
$950$	−4.90959	−	9.06115i	−0.159288	−	0.293983i
$951$	21.7734			0.706050
$952$		−	0.306620i		−	0.00993761i
$953$		−	22.9625i		−	0.743828i	−0.928267	−	0.371914i	$-0.878702\pi$
$953$		−	22.9625i		−	0.743828i	0.928267	−	0.371914i	$-0.121298\pi$
$954$	−0.848680			−0.0274770
$955$	−5.77938	−	22.7980i	−0.187016	−	0.737725i
$956$	19.9960			0.646718
$957$		0			0
$958$		−	31.4107i		−	1.01484i
$959$	−5.53751			−0.178815
$960$	−3.50710	+	0.889064i	−0.113191	+	0.0286944i
$961$	47.8024			1.54201
$962$			10.6404i			0.343059i
$963$			0.851791i			0.0274486i
$964$	−9.01381			−0.290315
$965$	10.5529	−	2.67521i	0.339710	−	0.0861179i
$966$	31.7650			1.02202
$967$			20.1267i			0.647231i	0.946189	+	0.323616i	$0.104898\pi$
$967$			20.1267i			0.647231i	−0.946189	+	0.323616i	$0.895102\pi$
$968$		0			0
$969$	0.203937			0.00655141
$970$	4.01238	+	15.8277i	0.128830	+	0.508196i
$971$	−21.9357			−0.703951			−0.351976	−	0.936009i	$-0.614490\pi$
$971$	−21.9357			−0.703951			−0.351976	+	0.936009i	$0.614490\pi$
$972$		−	3.94427i		−	0.126513i
$973$			49.6711i			1.59238i
$974$	−7.51032			−0.240646
$975$	16.6093	−	8.99937i	0.531922	−	0.288211i
$976$	−9.69338			−0.310278
$977$			59.0578i			1.88943i	0.327896	+	0.944714i	$0.393660\pi$
$977$			59.0578i			1.88943i	−0.327896	+	0.944714i	$0.606340\pi$
$978$		−	28.1706i		−	0.900795i
$979$		0			0
$980$	−9.96860	−	39.3232i	−0.318435	−	1.25613i
$981$	−3.00335			−0.0958896
$982$			11.2618i			0.359377i
$983$		−	48.3411i		−	1.54184i	−0.636931	−	0.770921i	$-0.719796\pi$
$983$		−	48.3411i		−	1.54184i	0.636931	−	0.770921i	$-0.280204\pi$
$984$	−7.41036			−0.236234
$985$	34.6281	−	8.77837i	1.10334	−	0.279702i
$986$	0.252987			0.00805674
$987$			72.0209i			2.29245i
$988$		−	4.81281i		−	0.153116i
$989$	−14.1655			−0.450437
$990$		0			0
$991$	−55.0154			−1.74762			−0.873811	−	0.486266i	$-0.838359\pi$
$991$	−55.0154			−1.74762			−0.873811	+	0.486266i	$0.838359\pi$
$992$		−	8.87707i		−	0.281847i
$993$		−	6.18471i		−	0.196266i
$994$	−44.2067			−1.40215
$995$	9.18034	+	36.2138i	0.291036	+	1.14805i
$996$	17.8825			0.566628
$997$		−	22.9699i		−	0.727465i	−0.931503	−	0.363733i	$-0.881502\pi$
$997$		−	22.9699i		−	0.727465i	0.931503	−	0.363733i	$-0.118498\pi$
$998$			26.9808i			0.854063i
$999$	24.9359			0.788937

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1210.2.b.k.969.7		8
5.2	odd	4		6050.2.a.dd.1.3		4
5.3	odd	4		6050.2.a.di.1.2		4
5.4	even	2	inner	1210.2.b.k.969.1		8
11.5	even	5		110.2.j.b.69.2	yes	16
11.9	even	5		110.2.j.b.59.4	yes	16
11.10	odd	2		1210.2.b.l.969.3		8
33.5	odd	10		990.2.ba.h.289.3		16
33.20	odd	10		990.2.ba.h.829.1		16
44.27	odd	10		880.2.cd.b.289.4		16
44.31	odd	10		880.2.cd.b.609.2		16
55.9	even	10		110.2.j.b.59.2	✓	16
55.27	odd	20		550.2.h.n.201.1		8
55.32	even	4		6050.2.a.dl.1.4		4
55.38	odd	20		550.2.h.j.201.2		8
55.42	odd	20		550.2.h.n.301.1		8
55.43	even	4		6050.2.a.da.1.1		4
55.49	even	10		110.2.j.b.69.4	yes	16
55.53	odd	20		550.2.h.j.301.2		8
55.54	odd	2		1210.2.b.l.969.5		8
165.104	odd	10		990.2.ba.h.289.1		16
165.119	odd	10		990.2.ba.h.829.3		16
220.119	odd	10		880.2.cd.b.609.4		16
220.159	odd	10		880.2.cd.b.289.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
110.2.j.b.59.2	✓	16	55.9	even	10
110.2.j.b.59.4	yes	16	11.9	even	5
110.2.j.b.69.2	yes	16	11.5	even	5
110.2.j.b.69.4	yes	16	55.49	even	10
550.2.h.j.201.2		8	55.38	odd	20
550.2.h.j.301.2		8	55.53	odd	20
550.2.h.n.201.1		8	55.27	odd	20
550.2.h.n.301.1		8	55.42	odd	20
880.2.cd.b.289.2		16	220.159	odd	10
880.2.cd.b.289.4		16	44.27	odd	10
880.2.cd.b.609.2		16	44.31	odd	10
880.2.cd.b.609.4		16	220.119	odd	10
990.2.ba.h.289.1		16	165.104	odd	10
990.2.ba.h.289.3		16	33.5	odd	10
990.2.ba.h.829.1		16	33.20	odd	10
990.2.ba.h.829.3		16	165.119	odd	10
1210.2.b.k.969.1		8	5.4	even	2	inner
1210.2.b.k.969.7		8	1.1	even	1	trivial
1210.2.b.l.969.3		8	11.10	odd	2
1210.2.b.l.969.5		8	55.54	odd	2
6050.2.a.da.1.1		4	55.43	even	4
6050.2.a.dd.1.3		4	5.2	odd	4
6050.2.a.di.1.2		4	5.3	odd	4
6050.2.a.dl.1.4		4	55.32	even	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:	\( N \)	\(=\)	\( 1210 = 2 \cdot 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1210.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +1.61803i q^{3} -1.00000 q^{4} +(-0.549472 - 2.16751i) q^{5} -1.61803 q^{6} +5.01420i q^{7} -1.00000i q^{8} +0.381966 q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +1.61803i q^{3} -1.00000 q^{4} +(-0.549472 - 2.16751i) q^{5} -1.61803 q^{6} +5.01420i q^{7} -1.00000i q^{8} +0.381966 q^{9} +(2.16751 - 0.549472i) q^{10} -1.61803i q^{12} +2.33501i q^{13} -5.01420 q^{14} +(3.50710 - 0.889064i) q^{15} +1.00000 q^{16} -0.0611504i q^{17} +0.381966i q^{18} +2.06115 q^{19} +(0.549472 + 2.16751i) q^{20} -8.11314 q^{21} +3.91525i q^{23} +1.61803 q^{24} +(-4.39616 + 2.38197i) q^{25} -2.33501 q^{26} +5.47214i q^{27} -5.01420i q^{28} +4.13712 q^{29} +(0.889064 + 3.50710i) q^{30} -8.87707 q^{31} +1.00000i q^{32} +0.0611504 q^{34} +(10.8683 - 2.75516i) q^{35} -0.381966 q^{36} -4.55688i q^{37} +2.06115i q^{38} -3.77813 q^{39} +(-2.16751 + 0.549472i) q^{40} -4.57985 q^{41} -8.11314i q^{42} +3.61803i q^{43} +(-0.209880 - 0.827913i) q^{45} -3.91525 q^{46} -8.87707i q^{47} +1.61803i q^{48} -18.1422 q^{49} +(-2.38197 - 4.39616i) q^{50} +0.0989434 q^{51} -2.33501i q^{52} +2.22187i q^{53} -5.47214 q^{54} +5.01420 q^{56} +3.33501i q^{57} +4.13712i q^{58} -1.93885 q^{59} +(-3.50710 + 0.889064i) q^{60} -9.69338 q^{61} -8.87707i q^{62} +1.91525i q^{63} -1.00000 q^{64} +(5.06115 - 1.28302i) q^{65} -2.49573i q^{67} +0.0611504i q^{68} -6.33501 q^{69} +(2.75516 + 10.8683i) q^{70} +8.81631 q^{71} -0.381966i q^{72} +5.39616i q^{73} +4.55688 q^{74} +(-3.85410 - 7.11314i) q^{75} -2.06115 q^{76} -3.77813i q^{78} +6.65520 q^{79} +(-0.549472 - 2.16751i) q^{80} -7.70820 q^{81} -4.57985i q^{82} +11.0520i q^{83} +8.11314 q^{84} +(-0.132544 + 0.0336004i) q^{85} -3.61803 q^{86} +6.69401i q^{87} -6.09017 q^{89} +(0.827913 - 0.209880i) q^{90} -11.7082 q^{91} -3.91525i q^{92} -14.3634i q^{93} +8.87707 q^{94} +(-1.13254 - 4.46756i) q^{95} -1.61803 q^{96} +7.30225i q^{97} -18.1422i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{4} + 2 q^{5} - 4 q^{6} + 12 q^{9}+O(q^{10}) \) 8 * q - 8 * q^4 + 2 * q^5 - 4 * q^6 + 12 * q^9	\( 8 q - 8 q^{4} + 2 q^{5} - 4 q^{6} + 12 q^{9} + 2 q^{10} + 4 q^{14} + 6 q^{15} + 8 q^{16} + 12 q^{19} - 2 q^{20} - 8 q^{21} + 4 q^{24} + 12 q^{26} + 28 q^{29} - 6 q^{30} - 32 q^{31} - 4 q^{34} + 16 q^{35} - 12 q^{36} - 4 q^{39} - 2 q^{40} - 20 q^{41} - 2 q^{45} - 48 q^{49} - 28 q^{50} - 12 q^{51} - 8 q^{54} - 4 q^{56} - 20 q^{59} - 6 q^{60} - 20 q^{61} - 8 q^{64} + 36 q^{65} - 20 q^{69} + 8 q^{70} + 52 q^{71} + 32 q^{74} - 4 q^{75} - 12 q^{76} - 12 q^{79} + 2 q^{80} - 8 q^{81} + 8 q^{84} + 28 q^{85} - 20 q^{86} - 4 q^{89} - 2 q^{90} - 40 q^{91} + 32 q^{94} + 20 q^{95} - 4 q^{96}+O(q^{100}) \) 8 * q - 8 * q^4 + 2 * q^5 - 4 * q^6 + 12 * q^9 + 2 * q^10 + 4 * q^14 + 6 * q^15 + 8 * q^16 + 12 * q^19 - 2 * q^20 - 8 * q^21 + 4 * q^24 + 12 * q^26 + 28 * q^29 - 6 * q^30 - 32 * q^31 - 4 * q^34 + 16 * q^35 - 12 * q^36 - 4 * q^39 - 2 * q^40 - 20 * q^41 - 2 * q^45 - 48 * q^49 - 28 * q^50 - 12 * q^51 - 8 * q^54 - 4 * q^56 - 20 * q^59 - 6 * q^60 - 20 * q^61 - 8 * q^64 + 36 * q^65 - 20 * q^69 + 8 * q^70 + 52 * q^71 + 32 * q^74 - 4 * q^75 - 12 * q^76 - 12 * q^79 + 2 * q^80 - 8 * q^81 + 8 * q^84 + 28 * q^85 - 20 * q^86 - 4 * q^89 - 2 * q^90 - 40 * q^91 + 32 * q^94 + 20 * q^95 - 4 * q^96

Introduction

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