LMFDB - Embedded newform 1610.2.e.d.1289.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1610,2,Mod(1289,1610)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1610, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1610.1289");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1610 = 2 \cdot 5 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1610.e (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:	$12.8559147254$
Analytic rank:	$0$
Dimension:	$22$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1289.2
Character	$\chi$	$=$	1610.1289
Dual form			1610.2.e.d.1289.21

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} -2.22125i q^{3} -1.00000 q^{4} +(1.30169 - 1.81813i) q^{5} -2.22125 q^{6} -1.00000i q^{7} +1.00000i q^{8} -1.93397 q^{9} +O(q^{10})$	\(q-1.00000i q^{2} -2.22125i q^{3} -1.00000 q^{4} +(1.30169 - 1.81813i) q^{5} -2.22125 q^{6} -1.00000i q^{7} +1.00000i q^{8} -1.93397 q^{9} +(-1.81813 - 1.30169i) q^{10} -0.423051 q^{11} +2.22125i q^{12} -6.61038i q^{13} -1.00000 q^{14} +(-4.03854 - 2.89138i) q^{15} +1.00000 q^{16} +0.741036i q^{17} +1.93397i q^{18} +7.14871 q^{19} +(-1.30169 + 1.81813i) q^{20} -2.22125 q^{21} +0.423051i q^{22} -1.00000i q^{23} +2.22125 q^{24} +(-1.61122 - 4.73328i) q^{25} -6.61038 q^{26} -2.36793i q^{27} +1.00000i q^{28} +1.48991 q^{29} +(-2.89138 + 4.03854i) q^{30} -4.48286 q^{31} -1.00000i q^{32} +0.939703i q^{33} +0.741036 q^{34} +(-1.81813 - 1.30169i) q^{35} +1.93397 q^{36} +3.24800i q^{37} -7.14871i q^{38} -14.6833 q^{39} +(1.81813 + 1.30169i) q^{40} -10.4907 q^{41} +2.22125i q^{42} +12.2838i q^{43} +0.423051 q^{44} +(-2.51742 + 3.51621i) q^{45} -1.00000 q^{46} -5.57120i q^{47} -2.22125i q^{48} -1.00000 q^{49} +(-4.73328 + 1.61122i) q^{50} +1.64603 q^{51} +6.61038i q^{52} +12.6198i q^{53} -2.36793 q^{54} +(-0.550679 + 0.769163i) q^{55} +1.00000 q^{56} -15.8791i q^{57} -1.48991i q^{58} +11.6469 q^{59} +(4.03854 + 2.89138i) q^{60} +12.4650 q^{61} +4.48286i q^{62} +1.93397i q^{63} -1.00000 q^{64} +(-12.0186 - 8.60465i) q^{65} +0.939703 q^{66} -6.33919i q^{67} -0.741036i q^{68} -2.22125 q^{69} +(-1.30169 + 1.81813i) q^{70} +2.02740 q^{71} -1.93397i q^{72} -5.32798i q^{73} +3.24800 q^{74} +(-10.5138 + 3.57893i) q^{75} -7.14871 q^{76} +0.423051i q^{77} +14.6833i q^{78} +0.0572756 q^{79} +(1.30169 - 1.81813i) q^{80} -11.0617 q^{81} +10.4907i q^{82} +1.32943i q^{83} +2.22125 q^{84} +(1.34730 + 0.964597i) q^{85} +12.2838 q^{86} -3.30948i q^{87} -0.423051i q^{88} -2.80832 q^{89} +(3.51621 + 2.51742i) q^{90} -6.61038 q^{91} +1.00000i q^{92} +9.95757i q^{93} -5.57120 q^{94} +(9.30538 - 12.9973i) q^{95} -2.22125 q^{96} -0.862650i q^{97} +1.00000i q^{98} +0.818166 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - 22 q^{4} + 8 q^{6} - 38 q^{9}+O(q^{10}) $ 22 * q - 22 * q^4 + 8 * q^6 - 38 * q^9	$ 22 q - 22 q^{4} + 8 q^{6} - 38 q^{9} - 2 q^{10} + 20 q^{11} - 22 q^{14} - 8 q^{15} + 22 q^{16} + 8 q^{21} - 8 q^{24} - 2 q^{25} + 20 q^{26} - 24 q^{29} - 24 q^{30} - 32 q^{34} - 2 q^{35} + 38 q^{36} - 24 q^{39} + 2 q^{40} + 16 q^{41} - 20 q^{44} - 40 q^{45} - 22 q^{46} - 22 q^{49} + 4 q^{50} + 8 q^{51} - 20 q^{54} - 8 q^{55} + 22 q^{56} + 12 q^{59} + 8 q^{60} - 20 q^{61} - 22 q^{64} - 16 q^{65} + 56 q^{66} + 8 q^{69} + 28 q^{71} - 28 q^{74} - 28 q^{75} + 24 q^{79} + 94 q^{81} - 8 q^{84} + 28 q^{85} + 60 q^{86} + 12 q^{89} + 30 q^{90} + 20 q^{91} - 52 q^{94} - 52 q^{95} + 8 q^{96} + 12 q^{99}+O(q^{100}) $ 22 * q - 22 * q^4 + 8 * q^6 - 38 * q^9 - 2 * q^10 + 20 * q^11 - 22 * q^14 - 8 * q^15 + 22 * q^16 + 8 * q^21 - 8 * q^24 - 2 * q^25 + 20 * q^26 - 24 * q^29 - 24 * q^30 - 32 * q^34 - 2 * q^35 + 38 * q^36 - 24 * q^39 + 2 * q^40 + 16 * q^41 - 20 * q^44 - 40 * q^45 - 22 * q^46 - 22 * q^49 + 4 * q^50 + 8 * q^51 - 20 * q^54 - 8 * q^55 + 22 * q^56 + 12 * q^59 + 8 * q^60 - 20 * q^61 - 22 * q^64 - 16 * q^65 + 56 * q^66 + 8 * q^69 + 28 * q^71 - 28 * q^74 - 28 * q^75 + 24 * q^79 + 94 * q^81 - 8 * q^84 + 28 * q^85 + 60 * q^86 + 12 * q^89 + 30 * q^90 + 20 * q^91 - 52 * q^94 - 52 * q^95 + 8 * q^96 + 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1610\mathbb{Z}\right)^\times$.

$n$	$281$	$967$	$1151$
$\chi(n)$	$1$	$-1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$		−	2.22125i		−	1.28244i	−0.767356	−	0.641221i	$-0.778428\pi$
$3$		−	2.22125i		−	1.28244i	0.767356	−	0.641221i	$-0.221572\pi$
$4$	−1.00000			−0.500000
$5$	1.30169	−	1.81813i	0.582132	−	0.813094i
$5$	1.30169	−	1.81813i	0.582132	−	0.813094i
$6$	−2.22125			−0.906823
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$			1.00000i			0.353553i
$9$	−1.93397			−0.644656
$10$	−1.81813	−	1.30169i	−0.574944	−	0.411630i
$11$	−0.423051			−0.127555			−0.0637773	−	0.997964i	$-0.520315\pi$
$11$	−0.423051			−0.127555			−0.0637773	+	0.997964i	$0.520315\pi$
$12$			2.22125i			0.641221i
$13$		−	6.61038i		−	1.83339i	−0.399587	−	0.916695i	$-0.630846\pi$
$13$		−	6.61038i		−	1.83339i	0.399587	−	0.916695i	$-0.369154\pi$
$14$	−1.00000			−0.267261
$15$	−4.03854	−	2.89138i	−1.04275	−	0.746550i
$16$	1.00000			0.250000
$17$			0.741036i			0.179728i	0.995954	+	0.0898638i	$0.0286432\pi$
$17$			0.741036i			0.179728i	−0.995954	+	0.0898638i	$0.971357\pi$
$18$			1.93397i			0.455841i
$19$	7.14871			1.64003			0.820013	−	0.572345i	$-0.193966\pi$
$19$	7.14871			1.64003			0.820013	+	0.572345i	$0.193966\pi$
$20$	−1.30169	+	1.81813i	−0.291066	+	0.406547i
$21$	−2.22125			−0.484717
$22$			0.423051i			0.0901947i
$23$		−	1.00000i		−	0.208514i
$23$		−	1.00000i		−	0.208514i
$24$	2.22125			0.453412
$25$	−1.61122	−	4.73328i	−0.322245	−	0.946656i
$26$	−6.61038			−1.29640
$27$		−	2.36793i		−	0.455708i
$28$			1.00000i			0.188982i
$29$	1.48991			0.276670			0.138335	−	0.990385i	$-0.455825\pi$
$29$	1.48991			0.276670			0.138335	+	0.990385i	$0.455825\pi$
$30$	−2.89138	+	4.03854i	−0.527891	+	0.737333i
$31$	−4.48286			−0.805145			−0.402573	−	0.915388i	$-0.631884\pi$
$31$	−4.48286			−0.805145			−0.402573	+	0.915388i	$0.631884\pi$
$32$		−	1.00000i		−	0.176777i
$33$			0.939703i			0.163581i
$34$	0.741036			0.127087
$35$	−1.81813	−	1.30169i	−0.307321	−	0.220025i
$36$	1.93397			0.322328
$37$			3.24800i			0.533967i	0.963701	+	0.266984i	$0.0860270\pi$
$37$			3.24800i			0.533967i	−0.963701	+	0.266984i	$0.913973\pi$
$38$		−	7.14871i		−	1.15967i
$39$	−14.6833			−2.35122
$40$	1.81813	+	1.30169i	0.287472	+	0.205815i
$41$	−10.4907			−1.63838			−0.819190	−	0.573523i	$-0.805576\pi$
$41$	−10.4907			−1.63838			−0.819190	+	0.573523i	$0.805576\pi$
$42$			2.22125i			0.342747i
$43$			12.2838i			1.87326i	0.350323	+	0.936629i	$0.386072\pi$
$43$			12.2838i			1.87326i	−0.350323	+	0.936629i	$0.613928\pi$
$44$	0.423051			0.0637773
$45$	−2.51742	+	3.51621i	−0.375275	+	0.524166i
$46$	−1.00000			−0.147442
$47$		−	5.57120i		−	0.812643i	−0.913730	−	0.406321i	$-0.866811\pi$
$47$		−	5.57120i		−	0.812643i	0.913730	−	0.406321i	$-0.133189\pi$
$48$		−	2.22125i		−	0.320610i
$49$	−1.00000			−0.142857
$50$	−4.73328	+	1.61122i	−0.669387	+	0.227861i
$51$	1.64603			0.230490
$52$			6.61038i			0.916695i
$53$			12.6198i			1.73346i	0.498780	+	0.866729i	$0.333782\pi$
$53$			12.6198i			1.73346i	−0.498780	+	0.866729i	$0.666218\pi$
$54$	−2.36793			−0.322234
$55$	−0.550679	+	0.769163i	−0.0742536	+	0.103714i
$56$	1.00000			0.133631
$57$		−	15.8791i		−	2.10324i
$58$		−	1.48991i		−	0.195635i
$59$	11.6469			1.51630			0.758148	−	0.652083i	$-0.226105\pi$
$59$	11.6469			1.51630			0.758148	+	0.652083i	$0.226105\pi$
$60$	4.03854	+	2.89138i	0.521373	+	0.373275i
$61$	12.4650			1.59598			0.797989	−	0.602672i	$-0.205897\pi$
$61$	12.4650			1.59598			0.797989	+	0.602672i	$0.205897\pi$
$62$			4.48286i			0.569324i
$63$			1.93397i			0.243657i
$64$	−1.00000			−0.125000
$65$	−12.0186	−	8.60465i	−1.49072	−	1.06728i
$66$	0.939703			0.115669
$67$		−	6.33919i		−	0.774455i	−0.921984	−	0.387228i	$-0.873433\pi$
$67$		−	6.33919i		−	0.774455i	0.921984	−	0.387228i	$-0.126567\pi$
$68$		−	0.741036i		−	0.0898638i
$69$	−2.22125			−0.267408
$70$	−1.30169	+	1.81813i	−0.155581	+	0.217309i
$71$	2.02740			0.240608			0.120304	−	0.992737i	$-0.461613\pi$
$71$	2.02740			0.240608			0.120304	+	0.992737i	$0.461613\pi$
$72$		−	1.93397i		−	0.227920i
$73$		−	5.32798i		−	0.623593i	−0.950149	−	0.311796i	$-0.899069\pi$
$73$		−	5.32798i		−	0.623593i	0.950149	−	0.311796i	$-0.100931\pi$
$74$	3.24800			0.377572
$75$	−10.5138	+	3.57893i	−1.21403	+	0.413260i
$76$	−7.14871			−0.820013
$77$			0.423051i			0.0482111i
$78$			14.6833i			1.66256i
$79$	0.0572756			0.00644401			0.00322200	−	0.999995i	$-0.498974\pi$
$79$	0.0572756			0.00644401			0.00322200	+	0.999995i	$0.498974\pi$
$80$	1.30169	−	1.81813i	0.145533	−	0.203274i
$81$	−11.0617			−1.22907
$82$			10.4907i			1.15851i
$83$			1.32943i			0.145924i	0.997335	+	0.0729621i	$0.0232452\pi$
$83$			1.32943i			0.145924i	−0.997335	+	0.0729621i	$0.976755\pi$
$84$	2.22125			0.242359
$85$	1.34730	+	0.964597i	0.146136	+	0.104625i
$86$	12.2838			1.32459
$87$		−	3.30948i		−	0.354813i
$88$		−	0.423051i		−	0.0450973i
$89$	−2.80832			−0.297682			−0.148841	−	0.988861i	$-0.547554\pi$
$89$	−2.80832			−0.297682			−0.148841	+	0.988861i	$0.547554\pi$
$90$	3.51621	+	2.51742i	0.370642	+	0.265360i
$91$	−6.61038			−0.692957
$92$			1.00000i			0.104257i
$93$			9.95757i			1.03255i
$94$	−5.57120			−0.574625
$95$	9.30538	−	12.9973i	0.954711	−	1.33350i
$96$	−2.22125			−0.226706
$97$		−	0.862650i		−	0.0875889i	−0.999041	−	0.0437944i	$-0.986055\pi$
$97$		−	0.862650i		−	0.0875889i	0.999041	−	0.0437944i	$-0.0139447\pi$
$98$			1.00000i			0.101015i
$99$	0.818166			0.0822288
$100$	1.61122	+	4.73328i	0.161122	+	0.473328i
$101$	18.9165			1.88226			0.941131	−	0.338041i	$-0.109764\pi$
$101$	18.9165			1.88226			0.941131	+	0.338041i	$0.109764\pi$
$102$		−	1.64603i		−	0.162981i
$103$			19.7990i			1.95086i	0.220314	+	0.975429i	$0.429292\pi$
$103$			19.7990i			1.95086i	−0.220314	+	0.975429i	$0.570708\pi$
$104$	6.61038			0.648202
$105$	−2.89138	+	4.03854i	−0.282169	+	0.394121i
$106$	12.6198			1.22574
$107$			3.40252i			0.328934i	0.986383	+	0.164467i	$0.0525904\pi$
$107$			3.40252i			0.328934i	−0.986383	+	0.164467i	$0.947410\pi$
$108$			2.36793i			0.227854i
$109$	−0.784096			−0.0751028			−0.0375514	−	0.999295i	$-0.511956\pi$
$109$	−0.784096			−0.0751028			−0.0375514	+	0.999295i	$0.511956\pi$
$110$	0.769163	+	0.550679i	0.0733368	+	0.0525052i
$111$	7.21463			0.684782
$112$		−	1.00000i		−	0.0944911i
$113$			6.50402i			0.611847i	0.952056	+	0.305923i	$0.0989651\pi$
$113$			6.50402i			0.611847i	−0.952056	+	0.305923i	$0.901035\pi$
$114$	−15.8791			−1.48721
$115$	−1.81813	−	1.30169i	−0.169542	−	0.121383i
$116$	−1.48991			−0.138335
$117$			12.7843i			1.18191i
$118$		−	11.6469i		−	1.07218i
$119$	0.741036			0.0679307
$120$	2.89138	−	4.03854i	0.263945	−	0.368666i
$121$	−10.8210			−0.983730
$122$		−	12.4650i		−	1.12853i
$123$			23.3026i			2.10113i
$124$	4.48286			0.402573
$125$	−10.7030	−	3.23183i	−0.957310	−	0.289064i
$126$	1.93397			0.172292
$127$			7.94586i			0.705081i	0.935796	+	0.352541i	$0.114682\pi$
$127$			7.94586i			0.705081i	−0.935796	+	0.352541i	$0.885318\pi$
$128$			1.00000i			0.0883883i
$129$	27.2854			2.40234
$130$	−8.60465	+	12.0186i	−0.754678	+	1.05410i
$131$	−5.01035			−0.437756			−0.218878	−	0.975752i	$-0.570240\pi$
$131$	−5.01035			−0.437756			−0.218878	+	0.975752i	$0.570240\pi$
$132$		−	0.939703i		−	0.0817906i
$133$		−	7.14871i		−	0.619871i
$134$	−6.33919			−0.547623
$135$	−4.30521	−	3.08230i	−0.370533	−	0.265282i
$136$	−0.741036			−0.0635433
$137$			16.5606i			1.41487i	0.706779	+	0.707434i	$0.250147\pi$
$137$			16.5606i			1.41487i	−0.706779	+	0.707434i	$0.749853\pi$
$138$			2.22125i			0.189086i
$139$	−2.51256			−0.213113			−0.106556	−	0.994307i	$-0.533982\pi$
$139$	−2.51256			−0.213113			−0.106556	+	0.994307i	$0.533982\pi$
$140$	1.81813	+	1.30169i	0.153660	+	0.110013i
$141$	−12.3750			−1.04217
$142$		−	2.02740i		−	0.170136i
$143$			2.79653i			0.233857i
$144$	−1.93397			−0.161164
$145$	1.93940	−	2.70886i	0.161059	−	0.224959i
$146$	−5.32798			−0.440947
$147$			2.22125i			0.183206i
$148$		−	3.24800i		−	0.266984i
$149$	−17.8007			−1.45829			−0.729144	−	0.684360i	$-0.760082\pi$
$149$	−17.8007			−1.45829			−0.729144	+	0.684360i	$0.760082\pi$
$150$	3.57893	+	10.5138i	0.292219	+	0.858450i
$151$	22.2476			1.81048			0.905241	−	0.424898i	$-0.139690\pi$
$151$	22.2476			1.81048			0.905241	+	0.424898i	$0.139690\pi$
$152$			7.14871i			0.579837i
$153$		−	1.43314i		−	0.115863i
$154$	0.423051			0.0340904
$155$	−5.83528	+	8.15044i	−0.468701	+	0.654659i
$156$	14.6833			1.17561
$157$		−	12.6617i		−	1.01051i	−0.862969	−	0.505257i	$-0.831398\pi$
$157$		−	12.6617i		−	1.01051i	0.862969	−	0.505257i	$-0.168602\pi$
$158$		−	0.0572756i		−	0.00455660i
$159$	28.0317			2.22306
$160$	−1.81813	−	1.30169i	−0.143736	−	0.102907i
$161$	−1.00000			−0.0788110
$162$			11.0617i			0.869087i
$163$		−	20.6656i		−	1.61866i	−0.587357	−	0.809328i	$-0.699832\pi$
$163$		−	20.6656i		−	1.61866i	0.587357	−	0.809328i	$-0.300168\pi$
$164$	10.4907			0.819190
$165$	1.70851	+	1.22320i	0.133007	+	0.0952259i
$166$	1.32943			0.103184
$167$			3.43535i			0.265836i	0.991127	+	0.132918i	$0.0424346\pi$
$167$			3.43535i			0.265836i	−0.991127	+	0.132918i	$0.957565\pi$
$168$		−	2.22125i		−	0.171373i
$169$	−30.6972			−2.36132
$170$	0.964597	−	1.34730i	0.0739812	−	0.103333i
$171$	−13.8254			−1.05725
$172$		−	12.2838i		−	0.936629i
$173$			2.86126i			0.217538i	0.994067	+	0.108769i	$0.0346908\pi$
$173$			2.86126i			0.217538i	−0.994067	+	0.108769i	$0.965309\pi$
$174$	−3.30948			−0.250891
$175$	−4.73328	+	1.61122i	−0.357803	+	0.121797i
$176$	−0.423051			−0.0318886
$177$		−	25.8707i		−	1.94456i
$178$			2.80832i			0.210493i
$179$	20.8676			1.55972			0.779858	−	0.625956i	$-0.215291\pi$
$179$	20.8676			1.55972			0.779858	+	0.625956i	$0.215291\pi$
$180$	2.51742	−	3.51621i	0.187638	−	0.262083i
$181$	−2.53257			−0.188244			−0.0941222	−	0.995561i	$-0.530004\pi$
$181$	−2.53257			−0.188244			−0.0941222	+	0.995561i	$0.530004\pi$
$182$			6.61038i			0.489994i
$183$		−	27.6879i		−	2.04675i
$184$	1.00000			0.0737210
$185$	5.90529	+	4.22787i	0.434166	+	0.310840i
$186$	9.95757			0.730124
$187$		−	0.313496i		−	0.0229251i
$188$			5.57120i			0.406321i
$189$	−2.36793			−0.172241
$190$	−12.9973	−	9.30538i	−0.942924	−	0.675083i
$191$	11.9803			0.866865			0.433433	−	0.901186i	$-0.357302\pi$
$191$	11.9803			0.866865			0.433433	+	0.901186i	$0.357302\pi$
$192$			2.22125i			0.160305i
$193$		−	25.6425i		−	1.84579i	−0.385056	−	0.922893i	$-0.625818\pi$
$193$		−	25.6425i		−	1.84579i	0.385056	−	0.922893i	$-0.374182\pi$
$194$	−0.862650			−0.0619347
$195$	−19.1131	+	26.6963i	−1.36872	+	1.91176i
$196$	1.00000			0.0714286
$197$		−	5.15174i		−	0.367047i	−0.983015	−	0.183523i	$-0.941250\pi$
$197$		−	5.15174i		−	0.367047i	0.983015	−	0.183523i	$-0.0587503\pi$
$198$		−	0.818166i		−	0.0581446i
$199$	9.88220			0.700531			0.350265	−	0.936651i	$-0.386091\pi$
$199$	9.88220			0.700531			0.350265	+	0.936651i	$0.386091\pi$
$200$	4.73328	−	1.61122i	0.334694	−	0.113931i
$201$	−14.0809			−0.993194
$202$		−	18.9165i		−	1.33096i
$203$		−	1.48991i		−	0.104571i
$204$	−1.64603			−0.115245
$205$	−13.6557	+	19.0736i	−0.953753	+	1.33216i
$206$	19.7990			1.37946
$207$			1.93397i			0.134420i
$208$		−	6.61038i		−	0.458348i
$209$	−3.02426			−0.209193
$210$	4.03854	+	2.89138i	0.278686	+	0.199524i
$211$	−9.53535			−0.656440			−0.328220	−	0.944601i	$-0.606449\pi$
$211$	−9.53535			−0.656440			−0.328220	+	0.944601i	$0.606449\pi$
$212$		−	12.6198i		−	0.866729i
$213$		−	4.50338i		−	0.308566i
$214$	3.40252			0.232591
$215$	22.3335	+	15.9896i	1.52314	+	1.09048i
$216$	2.36793			0.161117
$217$			4.48286i			0.304316i
$218$			0.784096i			0.0531057i
$219$	−11.8348			−0.799721
$220$	0.550679	−	0.769163i	0.0371268	−	0.0518569i
$221$	4.89853			0.329511
$222$		−	7.21463i		−	0.484214i
$223$			5.97117i			0.399859i	0.979810	+	0.199930i	$0.0640714\pi$
$223$			5.97117i			0.399859i	−0.979810	+	0.199930i	$0.935929\pi$
$224$	−1.00000			−0.0668153
$225$	3.11605	+	9.15402i	0.207737	+	0.610268i
$226$	6.50402			0.432641
$227$		−	14.7700i		−	0.980317i	−0.871633	−	0.490158i	$-0.836939\pi$
$227$		−	14.7700i		−	0.980317i	0.871633	−	0.490158i	$-0.163061\pi$
$228$			15.8791i			1.05162i
$229$	−18.0549			−1.19310			−0.596552	−	0.802574i	$-0.703463\pi$
$229$	−18.0549			−1.19310			−0.596552	+	0.802574i	$0.703463\pi$
$230$	−1.30169	+	1.81813i	−0.0858307	+	0.119884i
$231$	0.939703			0.0618279
$232$			1.48991i			0.0978177i
$233$			6.52961i			0.427769i	0.976859	+	0.213885i	$0.0686116\pi$
$233$			6.52961i			0.427769i	−0.976859	+	0.213885i	$0.931388\pi$
$234$	12.7843			0.835734
$235$	−10.1292	−	7.25195i	−0.660755	−	0.473065i
$236$	−11.6469			−0.758148
$237$		−	0.127224i		−	0.00826406i
$238$		−	0.741036i		−	0.0480342i
$239$	15.5053			1.00295			0.501477	−	0.865171i	$-0.332790\pi$
$239$	15.5053			1.00295			0.501477	+	0.865171i	$0.332790\pi$
$240$	−4.03854	−	2.89138i	−0.260686	−	0.186638i
$241$	−2.16241			−0.139293			−0.0696466	−	0.997572i	$-0.522187\pi$
$241$	−2.16241			−0.139293			−0.0696466	+	0.997572i	$0.522187\pi$
$242$			10.8210i			0.695602i
$243$			17.4670i			1.12051i
$244$	−12.4650			−0.797989
$245$	−1.30169	+	1.81813i	−0.0831617	+	0.116156i
$246$	23.3026			1.48572
$247$		−	47.2557i		−	3.00681i
$248$		−	4.48286i		−	0.284662i
$249$	2.95301			0.187139
$250$	−3.23183	+	10.7030i	−0.204399	+	0.676920i
$251$	1.81655			0.114660			0.0573299	−	0.998355i	$-0.481741\pi$
$251$	1.81655			0.114660			0.0573299	+	0.998355i	$0.481741\pi$
$252$		−	1.93397i		−	0.121829i
$253$			0.423051i			0.0265970i
$254$	7.94586			0.498568
$255$	2.14261	−	2.99270i	0.134176	−	0.187410i
$256$	1.00000			0.0625000
$257$		−	3.31608i		−	0.206851i	−0.994637	−	0.103426i	$-0.967020\pi$
$257$		−	3.31608i		−	0.206851i	0.994637	−	0.103426i	$-0.0329804\pi$
$258$		−	27.2854i		−	1.69871i
$259$	3.24800			0.201821
$260$	12.0186	+	8.60465i	0.745360	+	0.533638i
$261$	−2.88145			−0.178357
$262$			5.01035i			0.309540i
$263$			24.9863i			1.54072i	0.637609	+	0.770360i	$0.279923\pi$
$263$			24.9863i			1.54072i	−0.637609	+	0.770360i	$0.720077\pi$
$264$	−0.939703			−0.0578347
$265$	22.9444	+	16.4270i	1.40946	+	1.00910i
$266$	−7.14871			−0.438315
$267$			6.23800i			0.381759i
$268$			6.33919i			0.387228i
$269$	−5.93220			−0.361693			−0.180846	−	0.983511i	$-0.557884\pi$
$269$	−5.93220			−0.361693			−0.180846	+	0.983511i	$0.557884\pi$
$270$	−3.08230	+	4.30521i	−0.187583	+	0.262007i
$271$	−5.05492			−0.307065			−0.153532	−	0.988144i	$-0.549065\pi$
$271$	−5.05492			−0.307065			−0.153532	+	0.988144i	$0.549065\pi$
$272$			0.741036i			0.0449319i
$273$			14.6833i			0.888676i
$274$	16.5606			1.00046
$275$	0.681629	+	2.00242i	0.0411038	+	0.120750i
$276$	2.22125			0.133704
$277$		−	19.4524i		−	1.16878i	−0.811473	−	0.584390i	$-0.801334\pi$
$277$		−	19.4524i		−	1.16878i	0.811473	−	0.584390i	$-0.198666\pi$
$278$			2.51256i			0.150693i
$279$	8.66971			0.519042
$280$	1.30169	−	1.81813i	0.0777907	−	0.108654i
$281$	−20.1244			−1.20052			−0.600259	−	0.799806i	$-0.704936\pi$
$281$	−20.1244			−1.20052			−0.600259	+	0.799806i	$0.704936\pi$
$282$			12.3750i			0.736923i
$283$			13.9032i			0.826460i	0.910627	+	0.413230i	$0.135600\pi$
$283$			13.9032i			0.826460i	−0.910627	+	0.413230i	$0.864400\pi$
$284$	−2.02740			−0.120304
$285$	−28.8703	−	20.6696i	−1.71013	−	1.22436i
$286$	2.79653			0.165362
$287$			10.4907i			0.619249i
$288$			1.93397i			0.113960i
$289$	16.4509			0.967698
$290$	−2.70886	−	1.93940i	−0.159070	−	0.113886i
$291$	−1.91617			−0.112328
$292$			5.32798i			0.311796i
$293$		−	8.74867i		−	0.511103i	−0.966795	−	0.255551i	$-0.917743\pi$
$293$		−	8.74867i		−	0.511103i	0.966795	−	0.255551i	$-0.0822570\pi$
$294$	2.22125			0.129546
$295$	15.1606	−	21.1756i	0.882684	−	1.23289i
$296$	−3.24800			−0.188786
$297$			1.00175i			0.0581276i
$298$			17.8007i			1.03117i
$299$	−6.61038			−0.382288
$300$	10.5138	−	3.57893i	0.607016	−	0.206630i
$301$	12.2838			0.708025
$302$		−	22.2476i		−	1.28020i
$303$		−	42.0184i		−	2.41389i
$304$	7.14871			0.410006
$305$	16.2255	−	22.6630i	0.929070	−	1.29768i
$306$	−1.43314			−0.0819272
$307$		−	22.6861i		−	1.29477i	−0.762165	−	0.647383i	$-0.775863\pi$
$307$		−	22.6861i		−	1.29477i	0.762165	−	0.647383i	$-0.224137\pi$
$308$		−	0.423051i		−	0.0241055i
$309$	43.9787			2.50186
$310$	8.15044	+	5.83528i	0.462914	+	0.331422i
$311$	−7.97690			−0.452328			−0.226164	−	0.974089i	$-0.572619\pi$
$311$	−7.97690			−0.452328			−0.226164	+	0.974089i	$0.572619\pi$
$312$		−	14.6833i		−	0.831281i
$313$		−	13.4710i		−	0.761425i	−0.924694	−	0.380712i	$-0.875679\pi$
$313$		−	13.4710i		−	0.761425i	0.924694	−	0.380712i	$-0.124321\pi$
$314$	−12.6617			−0.714542
$315$	3.51621	+	2.51742i	0.198116	+	0.141841i
$316$	−0.0572756			−0.00322200
$317$		−	15.9884i		−	0.897999i	−0.893532	−	0.448999i	$-0.851781\pi$
$317$		−	15.9884i		−	0.897999i	0.893532	−	0.448999i	$-0.148219\pi$
$318$		−	28.0317i		−	1.57194i
$319$	−0.630309			−0.0352905
$320$	−1.30169	+	1.81813i	−0.0727665	+	0.101637i
$321$	7.55785			0.421838
$322$			1.00000i			0.0557278i
$323$			5.29745i			0.294758i
$324$	11.0617			0.614537
$325$	−31.2888	+	10.6508i	−1.73559	+	0.590800i
$326$	−20.6656			−1.14456
$327$			1.74168i			0.0963150i
$328$		−	10.4907i		−	0.579255i
$329$	−5.57120			−0.307150
$330$	1.22320	−	1.70851i	0.0673349	−	0.0940501i
$331$	0.228787			0.0125753			0.00628764	−	0.999980i	$-0.497999\pi$
$331$	0.228787			0.0125753			0.00628764	+	0.999980i	$0.497999\pi$
$332$		−	1.32943i		−	0.0729621i
$333$		−	6.28152i		−	0.344225i
$334$	3.43535			0.187974
$335$	−11.5255	−	8.25164i	−0.629705	−	0.450835i
$336$	−2.22125			−0.121179
$337$		−	35.8929i		−	1.95521i	−0.210443	−	0.977606i	$-0.567491\pi$
$337$		−	35.8929i		−	1.95521i	0.210443	−	0.977606i	$-0.432509\pi$
$338$			30.6972i			1.66971i
$339$	14.4471			0.784657
$340$	−1.34730	−	0.964597i	−0.0730678	−	0.0523126i
$341$	1.89648			0.102700
$342$			13.8254i			0.747591i
$343$			1.00000i			0.0539949i
$344$	−12.2838			−0.662297
$345$	−2.89138	+	4.03854i	−0.155667	+	0.217428i
$346$	2.86126			0.153822
$347$		−	17.6010i		−	0.944869i	−0.881366	−	0.472435i	$-0.843375\pi$
$347$		−	17.6010i		−	0.944869i	0.881366	−	0.472435i	$-0.156625\pi$
$348$			3.30948i			0.177407i
$349$	−19.9182			−1.06620			−0.533098	−	0.846054i	$-0.678972\pi$
$349$	−19.9182			−1.06620			−0.533098	+	0.846054i	$0.678972\pi$
$350$	1.61122	+	4.73328i	0.0861235	+	0.253005i
$351$	−15.6529			−0.835490
$352$			0.423051i			0.0225487i
$353$			20.0085i			1.06494i	0.846447	+	0.532472i	$0.178737\pi$
$353$			20.0085i			1.06494i	−0.846447	+	0.532472i	$0.821263\pi$
$354$	−25.8707			−1.37501
$355$	2.63904	−	3.68609i	0.140066	−	0.195637i
$356$	2.80832			0.148841
$357$		−	1.64603i		−	0.0871171i
$358$		−	20.8676i		−	1.10289i
$359$	16.0834			0.848850			0.424425	−	0.905463i	$-0.360476\pi$
$359$	16.0834			0.848850			0.424425	+	0.905463i	$0.360476\pi$
$360$	−3.51621	−	2.51742i	−0.185321	−	0.132680i
$361$	32.1040			1.68968
$362$			2.53257i			0.133109i
$363$			24.0363i			1.26158i
$364$	6.61038			0.346478
$365$	−9.68698	−	6.93536i	−0.507040	−	0.363013i
$366$	−27.6879			−1.44727
$367$		−	32.3235i		−	1.68727i	−0.536916	−	0.843636i	$-0.680411\pi$
$367$		−	32.3235i		−	1.68727i	0.536916	−	0.843636i	$-0.319589\pi$
$368$		−	1.00000i		−	0.0521286i
$369$	20.2888			1.05619
$370$	4.22787	−	5.90529i	0.219797	−	0.307002i
$371$	12.6198			0.655185
$372$		−	9.95757i		−	0.516276i
$373$			17.4855i			0.905366i	0.891672	+	0.452683i	$0.149533\pi$
$373$			17.4855i			0.905366i	−0.891672	+	0.452683i	$0.850467\pi$
$374$	−0.313496			−0.0162105
$375$	−7.17872	+	23.7742i	−0.370708	+	1.22769i
$376$	5.57120			0.287313
$377$		−	9.84891i		−	0.507245i
$378$			2.36793i			0.121793i
$379$	17.7356			0.911018			0.455509	−	0.890231i	$-0.349457\pi$
$379$	17.7356			0.911018			0.455509	+	0.890231i	$0.349457\pi$
$380$	−9.30538	+	12.9973i	−0.477356	+	0.666748i
$381$	17.6498			0.904226
$382$		−	11.9803i		−	0.612966i
$383$		−	23.5765i		−	1.20470i	−0.798232	−	0.602351i	$-0.794231\pi$
$383$		−	23.5765i		−	1.20470i	0.798232	−	0.602351i	$-0.205769\pi$
$384$	2.22125			0.113353
$385$	0.769163	+	0.550679i	0.0392002	+	0.0280652i
$386$	−25.6425			−1.30517
$387$		−	23.7564i		−	1.20761i
$388$			0.862650i			0.0437944i
$389$	−23.4162			−1.18725			−0.593624	−	0.804743i	$-0.702303\pi$
$389$	−23.4162			−1.18725			−0.593624	+	0.804743i	$0.702303\pi$
$390$	26.6963	+	19.1131i	1.35182	+	0.967830i
$391$	0.741036			0.0374758
$392$		−	1.00000i		−	0.0505076i
$393$			11.1293i			0.561397i
$394$	−5.15174			−0.259541
$395$	0.0745549	−	0.104135i	0.00375126	−	0.00523959i
$396$	−0.818166			−0.0411144
$397$			11.6273i			0.583557i	0.956486	+	0.291778i	$0.0942470\pi$
$397$			11.6273i			0.583557i	−0.956486	+	0.291778i	$0.905753\pi$
$398$		−	9.88220i		−	0.495350i
$399$	−15.8791			−0.794949
$400$	−1.61122	−	4.73328i	−0.0805611	−	0.236664i
$401$	−6.97339			−0.348235			−0.174117	−	0.984725i	$-0.555707\pi$
$401$	−6.97339			−0.348235			−0.174117	+	0.984725i	$0.555707\pi$
$402$			14.0809i			0.702294i
$403$			29.6334i			1.47615i
$404$	−18.9165			−0.941131
$405$	−14.3988	+	20.1116i	−0.715484	+	0.999353i
$406$	−1.48991			−0.0739432
$407$		−	1.37407i		−	0.0681100i
$408$			1.64603i			0.0814906i
$409$	−4.20460			−0.207904			−0.103952	−	0.994582i	$-0.533149\pi$
$409$	−4.20460			−0.207904			−0.103952	+	0.994582i	$0.533149\pi$
$410$	19.0736	+	13.6557i	0.941977	+	0.674405i
$411$	36.7853			1.81449
$412$		−	19.7990i		−	0.975429i
$413$		−	11.6469i		−	0.573106i
$414$	1.93397			0.0950494
$415$	2.41709	+	1.73050i	0.118650	+	0.0849471i
$416$	−6.61038			−0.324101
$417$			5.58103i			0.273304i
$418$			3.02426i			0.147922i
$419$	32.2281			1.57445			0.787223	−	0.616669i	$-0.211518\pi$
$419$	32.2281			1.57445			0.787223	+	0.616669i	$0.211518\pi$
$420$	2.89138	−	4.03854i	0.141085	−	0.197060i
$421$	26.2570			1.27969			0.639844	−	0.768505i	$-0.278999\pi$
$421$	26.2570			1.27969			0.639844	+	0.768505i	$0.278999\pi$
$422$			9.53535i			0.464174i
$423$			10.7745i			0.523875i
$424$	−12.6198			−0.612870
$425$	3.50753	−	1.19397i	0.170140	−	0.0579163i
$426$	−4.50338			−0.218189
$427$		−	12.4650i		−	0.603223i
$428$		−	3.40252i		−	0.164467i
$429$	6.21180			0.299908
$430$	15.9896	−	22.3335i	0.771088	−	1.07702i
$431$	4.69106			0.225960			0.112980	−	0.993597i	$-0.463960\pi$
$431$	4.69106			0.225960			0.112980	+	0.993597i	$0.463960\pi$
$432$		−	2.36793i		−	0.113927i
$433$			8.60159i			0.413366i	0.978408	+	0.206683i	$0.0662669\pi$
$433$			8.60159i			0.413366i	−0.978408	+	0.206683i	$0.933733\pi$
$434$	4.48286			0.215184
$435$	−6.01708	−	4.30790i	−0.288497	−	0.206548i
$436$	0.784096			0.0375514
$437$		−	7.14871i		−	0.341969i
$438$			11.8348i			0.565488i
$439$	4.94309			0.235921			0.117960	−	0.993018i	$-0.462364\pi$
$439$	4.94309			0.235921			0.117960	+	0.993018i	$0.462364\pi$
$440$	−0.769163	−	0.550679i	−0.0366684	−	0.0262526i
$441$	1.93397			0.0920937
$442$		−	4.89853i		−	0.232999i
$443$		−	28.0556i		−	1.33296i	−0.745523	−	0.666480i	$-0.767800\pi$
$443$		−	28.0556i		−	1.33296i	0.745523	−	0.666480i	$-0.232200\pi$
$444$	−7.21463			−0.342391
$445$	−3.65556	+	5.10591i	−0.173290	+	0.242043i
$446$	5.97117			0.282743
$447$			39.5398i			1.87017i
$448$			1.00000i			0.0472456i
$449$	−27.9104			−1.31717			−0.658586	−	0.752506i	$-0.728845\pi$
$449$	−27.9104			−1.31717			−0.658586	+	0.752506i	$0.728845\pi$
$450$	9.15402	−	3.11605i	0.431525	−	0.146892i
$451$	4.43812			0.208983
$452$		−	6.50402i		−	0.305923i
$453$		−	49.4175i		−	2.32184i
$454$	−14.7700			−0.693189
$455$	−8.60465	+	12.0186i	−0.403392	+	0.563439i
$456$	15.8791			0.743607
$457$			5.63199i			0.263454i	0.991286	+	0.131727i	$0.0420522\pi$
$457$			5.63199i			0.263454i	−0.991286	+	0.131727i	$0.957948\pi$
$458$			18.0549i			0.843652i
$459$	1.75472			0.0819033
$460$	1.81813	+	1.30169i	0.0847709	+	0.0606915i
$461$	−21.6674			−1.00915			−0.504577	−	0.863367i	$-0.668351\pi$
$461$	−21.6674			−1.00915			−0.504577	+	0.863367i	$0.668351\pi$
$462$		−	0.939703i		−	0.0437189i
$463$		−	10.9004i		−	0.506582i	−0.967390	−	0.253291i	$-0.918487\pi$
$463$		−	10.9004i		−	0.506582i	0.967390	−	0.253291i	$-0.0815131\pi$
$464$	1.48991			0.0691675
$465$	18.1042	+	12.9616i	0.839562	+	0.601081i
$466$	6.52961			0.302478
$467$			27.8840i			1.29032i	0.764048	+	0.645159i	$0.223209\pi$
$467$			27.8840i			1.29032i	−0.764048	+	0.645159i	$0.776791\pi$
$468$		−	12.7843i		−	0.590953i
$469$	−6.33919			−0.292717
$470$	−7.25195	+	10.1292i	−0.334508	+	0.467224i
$471$	−28.1249			−1.29593
$472$			11.6469i			0.536091i
$473$		−	5.19666i		−	0.238943i
$474$	−0.127224			−0.00584357
$475$	−11.5182	−	33.8368i	−0.528489	−	1.55254i
$476$	−0.741036			−0.0339653
$477$		−	24.4062i		−	1.11748i
$478$		−	15.5053i		−	0.709196i
$479$	12.7425			0.582221			0.291111	−	0.956689i	$-0.405975\pi$
$479$	12.7425			0.582221			0.291111	+	0.956689i	$0.405975\pi$
$480$	−2.89138	+	4.03854i	−0.131973	+	0.184333i
$481$	21.4705			0.978971
$482$			2.16241i			0.0984952i
$483$			2.22125i			0.101071i
$484$	10.8210			0.491865
$485$	−1.56841	−	1.12290i	−0.0712180	−	0.0509883i
$486$	17.4670			0.792319
$487$			27.0056i			1.22374i	0.790959	+	0.611869i	$0.209582\pi$
$487$			27.0056i			1.22374i	−0.790959	+	0.611869i	$0.790418\pi$
$488$			12.4650i			0.564264i
$489$	−45.9036			−2.07583
$490$	1.81813	+	1.30169i	0.0821349	+	0.0588042i
$491$	14.9364			0.674069			0.337034	−	0.941492i	$-0.390576\pi$
$491$	14.9364			0.674069			0.337034	+	0.941492i	$0.390576\pi$
$492$		−	23.3026i		−	1.05056i
$493$			1.10408i			0.0497253i
$494$	−47.2557			−2.12613
$495$	1.06500	−	1.48754i	0.0478680	−	0.0668598i
$496$	−4.48286			−0.201286
$497$		−	2.02740i		−	0.0909415i
$498$		−	2.95301i		−	0.132327i
$499$	−25.4725			−1.14030			−0.570152	−	0.821539i	$-0.693116\pi$
$499$	−25.4725			−1.14030			−0.570152	+	0.821539i	$0.693116\pi$
$500$	10.7030	+	3.23183i	0.478655	+	0.144532i
$501$	7.63079			0.340919
$502$		−	1.81655i		−	0.0810767i
$503$			19.1156i			0.852324i	0.904647	+	0.426162i	$0.140135\pi$
$503$			19.1156i			0.852324i	−0.904647	+	0.426162i	$0.859865\pi$
$504$	−1.93397			−0.0861458
$505$	24.6234	−	34.3927i	1.09573	−	1.53046i
$506$	0.423051			0.0188069
$507$			68.1862i			3.02826i
$508$		−	7.94586i		−	0.352541i
$509$	−1.40129			−0.0621111			−0.0310556	−	0.999518i	$-0.509887\pi$
$509$	−1.40129			−0.0621111			−0.0310556	+	0.999518i	$0.509887\pi$
$510$	−2.99270	−	2.14261i	−0.132519	−	0.0948766i
$511$	−5.32798			−0.235696
$512$		−	1.00000i		−	0.0441942i
$513$		−	16.9276i		−	0.747372i
$514$	−3.31608			−0.146266
$515$	35.9973	+	25.7722i	1.58623	+	1.13566i
$516$	−27.2854			−1.20117
$517$			2.35690i			0.103656i
$518$		−	3.24800i		−	0.142709i
$519$	6.35559			0.278979
$520$	8.60465	−	12.0186i	0.377339	−	0.527049i
$521$	1.94883			0.0853796			0.0426898	−	0.999088i	$-0.486407\pi$
$521$	1.94883			0.0853796			0.0426898	+	0.999088i	$0.486407\pi$
$522$			2.88145i			0.126118i
$523$		−	31.4935i		−	1.37712i	−0.725181	−	0.688558i	$-0.758244\pi$
$523$		−	31.4935i		−	1.37712i	0.725181	−	0.688558i	$-0.241756\pi$
$524$	5.01035			0.218878
$525$	3.57893	+	10.5138i	0.156198	+	0.458861i
$526$	24.9863			1.08945
$527$		−	3.32196i		−	0.144707i
$528$			0.939703i			0.0408953i
$529$	−1.00000			−0.0434783
$530$	16.4270	−	22.9444i	0.713542	−	0.996642i
$531$	−22.5247			−0.977489
$532$			7.14871i			0.309936i
$533$			69.3479i			3.00379i
$534$	6.23800			0.269945
$535$	6.18623	+	4.42901i	0.267454	+	0.191483i
$536$	6.33919			0.273811
$537$		−	46.3522i		−	2.00025i
$538$			5.93220i			0.255755i
$539$	0.423051			0.0182221
$540$	4.30521	+	3.08230i	0.185267	+	0.132641i
$541$	28.2578			1.21490			0.607449	−	0.794358i	$-0.292193\pi$
$541$	28.2578			1.21490			0.607449	+	0.794358i	$0.292193\pi$
$542$			5.05492i			0.217128i
$543$			5.62548i			0.241413i
$544$	0.741036			0.0317717
$545$	−1.02065	+	1.42559i	−0.0437198	+	0.0610657i
$546$	14.6833			0.628389
$547$		−	20.4360i		−	0.873781i	−0.899515	−	0.436890i	$-0.856080\pi$
$547$		−	20.4360i		−	0.873781i	0.899515	−	0.436890i	$-0.143920\pi$
$548$		−	16.5606i		−	0.707434i
$549$	−24.1069			−1.02886
$550$	2.00242	−	0.681629i	0.0853834	−	0.0290647i
$551$	10.6510			0.453746
$552$		−	2.22125i		−	0.0945428i
$553$		−	0.0572756i		−	0.00243561i
$554$	−19.4524			−0.826452
$555$	9.39118	−	13.1172i	0.398634	−	0.556792i
$556$	2.51256			0.106556
$557$		−	42.4246i		−	1.79759i	−0.438371	−	0.898794i	$-0.644444\pi$
$557$		−	42.4246i		−	1.79759i	0.438371	−	0.898794i	$-0.355556\pi$
$558$		−	8.66971i		−	0.367018i
$559$	81.2005			3.43441
$560$	−1.81813	−	1.30169i	−0.0768302	−	0.0550063i
$561$	−0.696354			−0.0294001
$562$			20.1244i			0.848895i
$563$			38.2486i			1.61199i	0.591924	+	0.805994i	$0.298368\pi$
$563$			38.2486i			1.61199i	−0.591924	+	0.805994i	$0.701632\pi$
$564$	12.3750			0.521083
$565$	11.8252	+	8.46620i	0.497489	+	0.356176i
$566$	13.9032			0.584396
$567$			11.0617i			0.464547i
$568$			2.02740i			0.0850679i
$569$	28.3741			1.18950			0.594752	−	0.803910i	$-0.297250\pi$
$569$	28.3741			1.18950			0.594752	+	0.803910i	$0.297250\pi$
$570$	−20.6696	+	28.8703i	−0.865754	+	1.20924i
$571$	21.8367			0.913838			0.456919	−	0.889508i	$-0.348953\pi$
$571$	21.8367			0.913838			0.456919	+	0.889508i	$0.348953\pi$
$572$		−	2.79653i		−	0.116929i
$573$		−	26.6113i		−	1.11170i
$574$	10.4907			0.437875
$575$	−4.73328	+	1.61122i	−0.197392	+	0.0671926i
$576$	1.93397			0.0805820
$577$			14.4664i			0.602245i	0.953585	+	0.301123i	$0.0973613\pi$
$577$			14.4664i			0.602245i	−0.953585	+	0.301123i	$0.902639\pi$
$578$		−	16.4509i		−	0.684266i
$579$	−56.9585			−2.36711
$580$	−1.93940	+	2.70886i	−0.0805293	+	0.112479i
$581$	1.32943			0.0551541
$582$			1.91617i			0.0794276i
$583$		−	5.33880i		−	0.221110i
$584$	5.32798			0.220473
$585$	23.2435	+	16.6411i	0.961002	+	0.688026i
$586$	−8.74867			−0.361404
$587$			24.5816i			1.01459i	0.861772	+	0.507296i	$0.169355\pi$
$587$			24.5816i			1.01459i	−0.861772	+	0.507296i	$0.830645\pi$
$588$		−	2.22125i		−	0.0916030i
$589$	−32.0466			−1.32046
$590$	−21.1756	−	15.1606i	−0.871786	−	0.624152i
$591$	−11.4433			−0.470716
$592$			3.24800i			0.133492i
$593$			15.0307i			0.617238i	0.951186	+	0.308619i	$0.0998668\pi$
$593$			15.0307i			0.617238i	−0.951186	+	0.308619i	$0.900133\pi$
$594$	1.00175			0.0411024
$595$	0.964597	−	1.34730i	0.0395446	−	0.0552340i
$596$	17.8007			0.729144
$597$		−	21.9509i		−	0.898389i
$598$			6.61038i			0.270319i
$599$	−25.6328			−1.04733			−0.523664	−	0.851925i	$-0.675435\pi$
$599$	−25.6328			−1.04733			−0.523664	+	0.851925i	$0.675435\pi$
$600$	−3.57893	−	10.5138i	−0.146109	−	0.429225i
$601$	−15.0596			−0.614294			−0.307147	−	0.951662i	$-0.599374\pi$
$601$	−15.0596			−0.614294			−0.307147	+	0.951662i	$0.599374\pi$
$602$		−	12.2838i		−	0.500649i
$603$			12.2598i			0.499257i
$604$	−22.2476			−0.905241
$605$	−14.0856	+	19.6741i	−0.572661	+	0.799865i
$606$	−42.0184			−1.70688
$607$			21.4240i			0.869572i	0.900534	+	0.434786i	$0.143176\pi$
$607$			21.4240i			0.869572i	−0.900534	+	0.434786i	$0.856824\pi$
$608$		−	7.14871i		−	0.289918i
$609$	−3.30948			−0.134107
$610$	−22.6630	−	16.2255i	−0.917599	−	0.656952i
$611$	−36.8278			−1.48989
$612$			1.43314i			0.0579313i
$613$			44.9215i			1.81436i	0.420739	+	0.907182i	$0.361771\pi$
$613$			44.9215i			1.81436i	−0.420739	+	0.907182i	$0.638229\pi$
$614$	−22.6861			−0.915538
$615$	42.3673	+	30.3327i	1.70841	+	1.22313i
$616$	−0.423051			−0.0170452
$617$		−	30.8333i		−	1.24130i	−0.784087	−	0.620651i	$-0.786869\pi$
$617$		−	30.8333i		−	1.24130i	0.784087	−	0.620651i	$-0.213131\pi$
$618$		−	43.9787i		−	1.76908i
$619$	−18.5806			−0.746817			−0.373409	−	0.927667i	$-0.621811\pi$
$619$	−18.5806			−0.746817			−0.373409	+	0.927667i	$0.621811\pi$
$620$	5.83528	−	8.15044i	0.234350	−	0.327330i
$621$	−2.36793			−0.0950216
$622$			7.97690i			0.319844i
$623$			2.80832i			0.112513i
$624$	−14.6833			−0.587804
$625$	−19.8079	+	15.2527i	−0.792317	+	0.610110i
$626$	−13.4710			−0.538408
$627$			6.71766i			0.268277i
$628$			12.6617i			0.505257i
$629$	−2.40688			−0.0959687
$630$	2.51742	−	3.51621i	0.100296	−	0.140089i
$631$	23.7396			0.945058			0.472529	−	0.881315i	$-0.343341\pi$
$631$	23.7396			0.945058			0.472529	+	0.881315i	$0.343341\pi$
$632$			0.0572756i			0.00227830i
$633$			21.1804i			0.841847i
$634$	−15.9884			−0.634981
$635$	14.4466	+	10.3430i	0.573298	+	0.410450i
$636$	−28.0317			−1.11153
$637$			6.61038i			0.261913i
$638$			0.630309i			0.0249542i
$639$	−3.92093			−0.155110
$640$	1.81813	+	1.30169i	0.0718681	+	0.0514537i
$641$	18.9187			0.747245			0.373623	−	0.927581i	$-0.378116\pi$
$641$	18.9187			0.747245			0.373623	+	0.927581i	$0.378116\pi$
$642$		−	7.55785i		−	0.298285i
$643$		−	8.19325i		−	0.323110i	−0.986864	−	0.161555i	$-0.948349\pi$
$643$		−	8.19325i		−	0.323110i	0.986864	−	0.161555i	$-0.0516510\pi$
$644$	1.00000			0.0394055
$645$	35.5170	−	49.6085i	1.39848	−	1.95333i
$646$	5.29745			0.208425
$647$			14.6884i			0.577459i	0.957411	+	0.288730i	$0.0932329\pi$
$647$			14.6884i			0.577459i	−0.957411	+	0.288730i	$0.906767\pi$
$648$		−	11.0617i		−	0.434543i
$649$	−4.92722			−0.193410
$650$	10.6508	+	31.2888i	0.417759	+	1.22725i
$651$	9.95757			0.390268
$652$			20.6656i			0.809328i
$653$			31.1138i			1.21758i	0.793333	+	0.608788i	$0.208344\pi$
$653$			31.1138i			1.21758i	−0.793333	+	0.608788i	$0.791656\pi$
$654$	1.74168			0.0681050
$655$	−6.52191	+	9.10949i	−0.254832	+	0.355937i
$656$	−10.4907			−0.409595
$657$			10.3041i			0.402003i
$658$			5.57120i			0.217188i
$659$	−3.87091			−0.150789			−0.0753947	−	0.997154i	$-0.524022\pi$
$659$	−3.87091			−0.150789			−0.0753947	+	0.997154i	$0.524022\pi$
$660$	−1.70851	−	1.22320i	−0.0665035	−	0.0476129i
$661$	21.4407			0.833946			0.416973	−	0.908919i	$-0.363091\pi$
$661$	21.4407			0.833946			0.416973	+	0.908919i	$0.363091\pi$
$662$		−	0.228787i		−	0.00889206i
$663$		−	10.8809i		−	0.422579i
$664$	−1.32943			−0.0515920
$665$	−12.9973	−	9.30538i	−0.504014	−	0.360847i
$666$	−6.28152			−0.243404
$667$		−	1.48991i		−	0.0576897i
$668$		−	3.43535i		−	0.132918i
$669$	13.2635			0.512796
$670$	−8.25164	+	11.5255i	−0.318789	+	0.445269i
$671$	−5.27332			−0.203574
$672$			2.22125i			0.0856867i
$673$		−	22.7974i		−	0.878775i	−0.898298	−	0.439387i	$-0.855196\pi$
$673$		−	22.7974i		−	0.878775i	0.898298	−	0.439387i	$-0.144804\pi$
$674$	−35.8929			−1.38254
$675$	−11.2081	+	3.81526i	−0.431399	+	0.146849i
$676$	30.6972			1.18066
$677$			37.3421i			1.43517i	0.696470	+	0.717586i	$0.254753\pi$
$677$			37.3421i			1.43517i	−0.696470	+	0.717586i	$0.745247\pi$
$678$		−	14.4471i		−	0.554837i
$679$	−0.862650			−0.0331055
$680$	−0.964597	+	1.34730i	−0.0369906	+	0.0516667i
$681$	−32.8078			−1.25720
$682$		−	1.89648i		−	0.0726198i
$683$			0.922387i			0.0352942i	0.999844	+	0.0176471i	$0.00561753\pi$
$683$			0.922387i			0.0352942i	−0.999844	+	0.0176471i	$0.994382\pi$
$684$	13.8254			0.528626
$685$	30.1094	+	21.5567i	1.15042	+	0.823640i
$686$	1.00000			0.0381802
$687$			40.1046i			1.53009i
$688$			12.2838i			0.468315i
$689$	83.4215			3.17811
$690$	4.03854	+	2.89138i	0.153744	+	0.110073i
$691$	46.9651			1.78664			0.893319	−	0.449423i	$-0.148370\pi$
$691$	46.9651			1.78664			0.893319	+	0.449423i	$0.148370\pi$
$692$		−	2.86126i		−	0.108769i
$693$		−	0.818166i		−	0.0310796i
$694$	−17.6010			−0.668123
$695$	−3.27057	+	4.56817i	−0.124060	+	0.173281i
$696$	3.30948			0.125445
$697$		−	7.77402i		−	0.294462i
$698$			19.9182i			0.753914i
$699$	14.5039			0.548589
$700$	4.73328	−	1.61122i	0.178901	−	0.0608985i
$701$	−33.0666			−1.24891			−0.624455	−	0.781061i	$-0.714679\pi$
$701$	−33.0666			−1.24891			−0.624455	+	0.781061i	$0.714679\pi$
$702$			15.6529i			0.590781i
$703$			23.2190i			0.875720i
$704$	0.423051			0.0159443
$705$	−16.1084	+	22.4995i	−0.606679	+	0.847380i
$706$	20.0085			0.753029
$707$		−	18.9165i		−	0.711428i
$708$			25.8707i			0.972280i
$709$	1.46422			0.0549899			0.0274949	−	0.999622i	$-0.491247\pi$
$709$	1.46422			0.0549899			0.0274949	+	0.999622i	$0.491247\pi$
$710$	−3.68609	−	2.63904i	−0.138337	−	0.0990416i
$711$	−0.110769			−0.00415417
$712$		−	2.80832i		−	0.105246i
$713$			4.48286i			0.167884i
$714$	−1.64603			−0.0616011
$715$	5.08446	+	3.64020i	0.190148	+	0.136136i
$716$	−20.8676			−0.779858
$717$		−	34.4412i		−	1.28623i
$718$		−	16.0834i		−	0.600228i
$719$	−19.0617			−0.710881			−0.355441	−	0.934699i	$-0.615669\pi$
$719$	−19.0617			−0.710881			−0.355441	+	0.934699i	$0.615669\pi$
$720$	−2.51742	+	3.51621i	−0.0938188	+	0.131042i
$721$	19.7990			0.737355
$722$		−	32.1040i		−	1.19479i
$723$			4.80327i			0.178635i
$724$	2.53257			0.0941222
$725$	−2.40058	−	7.05219i	−0.0891555	−	0.261912i
$726$	24.0363			0.892069
$727$			5.26247i			0.195174i	0.995227	+	0.0975872i	$0.0311125\pi$
$727$			5.26247i			0.195174i	−0.995227	+	0.0975872i	$0.968888\pi$
$728$		−	6.61038i		−	0.244997i
$729$	5.61363			0.207912
$730$	−6.93536	+	9.68698i	−0.256689	+	0.358531i
$731$	−9.10272			−0.336676
$732$			27.6879i			1.02337i
$733$		−	47.5088i		−	1.75478i	−0.479780	−	0.877389i	$-0.659283\pi$
$733$		−	47.5088i		−	1.75478i	0.479780	−	0.877389i	$-0.340717\pi$
$734$	−32.3235			−1.19308
$735$	4.03854	+	2.89138i	0.148964	+	0.106650i
$736$	−1.00000			−0.0368605
$737$			2.68180i			0.0987853i
$738$		−	20.2888i		−	0.746840i
$739$	34.8410			1.28165			0.640823	−	0.767688i	$-0.278593\pi$
$739$	34.8410			1.28165			0.640823	+	0.767688i	$0.278593\pi$
$740$	−5.90529	−	4.22787i	−0.217083	−	0.155420i
$741$	−104.967			−3.85605
$742$		−	12.6198i		−	0.463286i
$743$			20.9392i			0.768185i	0.923295	+	0.384092i	$0.125486\pi$
$743$			20.9392i			0.768185i	−0.923295	+	0.384092i	$0.874514\pi$
$744$	−9.95757			−0.365062
$745$	−23.1709	+	32.3640i	−0.848917	+	1.18573i
$746$	17.4855			0.640190
$747$		−	2.57108i		−	0.0940709i
$748$			0.313496i			0.0114625i
$749$	3.40252			0.124325
$750$	23.7742	+	7.17872i	0.868111	+	0.262130i
$751$	−19.2299			−0.701709			−0.350854	−	0.936430i	$-0.614109\pi$
$751$	−19.2299			−0.701709			−0.350854	+	0.936430i	$0.614109\pi$
$752$		−	5.57120i		−	0.203161i
$753$		−	4.03502i		−	0.147044i
$754$	−9.84891			−0.358676
$755$	28.9594	−	40.4491i	1.05394	−	1.47209i
$756$	2.36793			0.0861206
$757$			12.8205i			0.465967i	0.972481	+	0.232984i	$0.0748489\pi$
$757$			12.8205i			0.465967i	−0.972481	+	0.232984i	$0.925151\pi$
$758$		−	17.7356i		−	0.644187i
$759$	0.939703			0.0341090
$760$	12.9973	+	9.30538i	0.471462	+	0.337541i
$761$	43.3004			1.56964			0.784819	−	0.619725i	$-0.212756\pi$
$761$	43.3004			1.56964			0.784819	+	0.619725i	$0.212756\pi$
$762$		−	17.6498i		−	0.639384i
$763$			0.784096i			0.0283862i
$764$	−11.9803			−0.433433
$765$	−2.60564	−	1.86550i	−0.0942072	−	0.0674473i
$766$	−23.5765			−0.851853
$767$		−	76.9904i		−	2.77996i
$768$		−	2.22125i		−	0.0801526i
$769$	−26.9969			−0.973534			−0.486767	−	0.873532i	$-0.661824\pi$
$769$	−26.9969			−0.973534			−0.486767	+	0.873532i	$0.661824\pi$
$770$	0.550679	−	0.769163i	0.0198451	−	0.0277187i
$771$	−7.36585			−0.265275
$772$			25.6425i			0.922893i
$773$			32.6878i			1.17570i	0.808971	+	0.587849i	$0.200025\pi$
$773$			32.6878i			1.17570i	−0.808971	+	0.587849i	$0.799975\pi$
$774$	−23.7564			−0.853907
$775$	7.22288	+	21.2186i	0.259454	+	0.762196i
$776$	0.862650			0.0309673
$777$		−	7.21463i		−	0.258823i
$778$			23.4162i			0.839511i
$779$	−74.9953			−2.68698
$780$	19.1131	−	26.6963i	0.684359	−	0.955880i
$781$	−0.857694			−0.0306907
$782$		−	0.741036i		−	0.0264994i
$783$		−	3.52801i		−	0.126081i
$784$	−1.00000			−0.0357143
$785$	−23.0207	−	16.4816i	−0.821643	−	0.588253i
$786$	11.1293			0.396967
$787$			5.83587i			0.208026i	0.994576	+	0.104013i	$0.0331684\pi$
$787$			5.83587i			0.208026i	−0.994576	+	0.104013i	$0.966832\pi$
$788$			5.15174i			0.183523i
$789$	55.5009			1.97588
$790$	−0.104135	−	0.0745549i	−0.00370495	−	0.00265254i
$791$	6.50402			0.231256
$792$			0.818166i			0.0290723i
$793$		−	82.3984i		−	2.92605i
$794$	11.6273			0.412637
$795$	36.4885	−	50.9654i	1.29411	−	1.80756i
$796$	−9.88220			−0.350265
$797$		−	5.60035i		−	0.198374i	−0.995069	−	0.0991872i	$-0.968376\pi$
$797$		−	5.60035i		−	0.198374i	0.995069	−	0.0991872i	$-0.0316243\pi$
$798$			15.8791i			0.562114i
$799$	4.12846			0.146054
$800$	−4.73328	+	1.61122i	−0.167347	+	0.0569653i
$801$	5.43121			0.191902
$802$			6.97339i			0.246239i
$803$			2.25400i			0.0795421i
$804$	14.0809			0.496597
$805$	−1.30169	+	1.81813i	−0.0458784	+	0.0640808i
$806$	29.6334			1.04379
$807$			13.1769i			0.463850i
$808$			18.9165i			0.665480i
$809$	38.3586			1.34862			0.674308	−	0.738450i	$-0.264442\pi$
$809$	38.3586			1.34862			0.674308	+	0.738450i	$0.264442\pi$
$810$	20.1116	+	14.3988i	0.706650	+	0.505923i
$811$	−15.6066			−0.548022			−0.274011	−	0.961727i	$-0.588350\pi$
$811$	−15.6066			−0.548022			−0.274011	+	0.961727i	$0.588350\pi$
$812$			1.48991i			0.0522857i
$813$			11.2283i			0.393792i
$814$	−1.37407			−0.0481610
$815$	−37.5729	−	26.9002i	−1.31612	−	0.942272i
$816$	1.64603			0.0576226
$817$			87.8131i			3.07219i
$818$			4.20460i			0.147010i
$819$	12.7843			0.446719
$820$	13.6557	−	19.0736i	0.476877	−	0.666078i
$821$	4.06427			0.141844			0.0709221	−	0.997482i	$-0.477406\pi$
$821$	4.06427			0.141844			0.0709221	+	0.997482i	$0.477406\pi$
$822$		−	36.7853i		−	1.28304i
$823$		−	26.2729i		−	0.915816i	−0.888999	−	0.457908i	$-0.848599\pi$
$823$		−	26.2729i		−	0.915816i	0.888999	−	0.457908i	$-0.151401\pi$
$824$	−19.7990			−0.689732
$825$	4.44788	−	1.51407i	0.154855	−	0.0527132i
$826$	−11.6469			−0.405247
$827$			42.9896i			1.49489i	0.664321	+	0.747447i	$0.268721\pi$
$827$			42.9896i			1.49489i	−0.664321	+	0.747447i	$0.731279\pi$
$828$		−	1.93397i		−	0.0672101i
$829$	17.2201			0.598078			0.299039	−	0.954241i	$-0.403334\pi$
$829$	17.2201			0.598078			0.299039	+	0.954241i	$0.403334\pi$
$830$	1.73050	−	2.41709i	0.0600667	−	0.0838983i
$831$	−43.2086			−1.49889
$832$			6.61038i			0.229174i
$833$		−	0.741036i		−	0.0256754i
$834$	5.58103			0.193255
$835$	6.24593	+	4.47175i	0.216149	+	0.154751i
$836$	3.02426			0.104596
$837$			10.6151i			0.366911i
$838$		−	32.2281i		−	1.11330i
$839$	−16.6646			−0.575325			−0.287662	−	0.957732i	$-0.592878\pi$
$839$	−16.6646			−0.575325			−0.287662	+	0.957732i	$0.592878\pi$
$840$	−4.03854	−	2.89138i	−0.139343	−	0.0997620i
$841$	−26.7802			−0.923454
$842$		−	26.2570i		−	0.904876i
$843$			44.7013i			1.53959i
$844$	9.53535			0.328220
$845$	−39.9581	+	55.8116i	−1.37460	+	1.91998i
$846$	10.7745			0.370436
$847$			10.8210i			0.371815i
$848$			12.6198i			0.433364i
$849$	30.8826			1.05989
$850$	−1.19397	−	3.50753i	−0.0409530	−	0.120307i
$851$	3.24800			0.111340
$852$			4.50338i			0.154283i
$853$			4.51328i			0.154532i	0.997011	+	0.0772658i	$0.0246190\pi$
$853$			4.51328i			0.154532i	−0.997011	+	0.0772658i	$0.975381\pi$
$854$	−12.4650			−0.426543
$855$	−17.9963	+	25.1364i	−0.615461	+	0.859646i
$856$	−3.40252			−0.116296
$857$		−	2.91185i		−	0.0994669i	−0.998763	−	0.0497334i	$-0.984163\pi$
$857$		−	2.91185i		−	0.0994669i	0.998763	−	0.0497334i	$-0.0158372\pi$
$858$		−	6.21180i		−	0.212067i
$859$	−55.4404			−1.89160			−0.945800	−	0.324748i	$-0.894720\pi$
$859$	−55.4404			−1.89160			−0.945800	+	0.324748i	$0.894720\pi$
$860$	−22.3335	−	15.9896i	−0.761568	−	0.545242i
$861$	23.3026			0.794151
$862$		−	4.69106i		−	0.159778i
$863$		−	29.9382i		−	1.01911i	−0.860439	−	0.509554i	$-0.829811\pi$
$863$		−	29.9382i		−	1.01911i	0.860439	−	0.509554i	$-0.170189\pi$
$864$	−2.36793			−0.0805585
$865$	5.20216	+	3.72447i	0.176879	+	0.126636i
$866$	8.60159			0.292294
$867$		−	36.5415i		−	1.24102i
$868$		−	4.48286i		−	0.152158i
$869$	−0.0242305			−0.000821962
$870$	−4.30790	+	6.01708i	−0.146052	+	0.203998i
$871$	−41.9045			−1.41988
$872$		−	0.784096i		−	0.0265529i
$873$			1.66834i			0.0564647i
$874$	−7.14871			−0.241809
$875$	−3.23183	+	10.7030i	−0.109256	+	0.361829i
$876$	11.8348			0.399861
$877$		−	0.885235i		−	0.0298923i	−0.999888	−	0.0149461i	$-0.995242\pi$
$877$		−	0.885235i		−	0.0298923i	0.999888	−	0.0149461i	$-0.00475768\pi$
$878$		−	4.94309i		−	0.166821i
$879$	−19.4330			−0.655460
$880$	−0.550679	+	0.769163i	−0.0185634	+	0.0259285i
$881$	33.6712			1.13441			0.567206	−	0.823576i	$-0.308024\pi$
$881$	33.6712			1.13441			0.567206	+	0.823576i	$0.308024\pi$
$882$		−	1.93397i		−	0.0651201i
$883$			16.7223i			0.562750i	0.959598	+	0.281375i	$0.0907905\pi$
$883$			16.7223i			0.562750i	−0.959598	+	0.281375i	$0.909210\pi$
$884$	−4.89853			−0.164756
$885$	−47.0364	−	33.6755i	−1.58111	−	1.13199i
$886$	−28.0556			−0.942546
$887$			39.3534i			1.32136i	0.750668	+	0.660680i	$0.229732\pi$
$887$			39.3534i			1.32136i	−0.750668	+	0.660680i	$0.770268\pi$
$888$			7.21463i			0.242107i
$889$	7.94586			0.266496
$890$	5.10591	+	3.65556i	0.171150	+	0.122535i
$891$	4.67965			0.156774
$892$		−	5.97117i		−	0.199930i
$893$		−	39.8268i		−	1.33275i
$894$	39.5398			1.32241
$895$	27.1631	−	37.9401i	0.907961	−	1.26820i
$896$	1.00000			0.0334077
$897$			14.6833i			0.490263i
$898$			27.9104i			0.931381i
$899$	−6.67908			−0.222760
$900$	−3.11605	−	9.15402i	−0.103868	−	0.305134i
$901$	−9.35170			−0.311550
$902$		−	4.43812i		−	0.147773i
$903$		−	27.2854i		−	0.908001i
$904$	−6.50402			−0.216320
$905$	−3.29661	+	4.60455i	−0.109583	+	0.153061i
$906$	−49.4175			−1.64179
$907$			7.12458i			0.236568i	0.992980	+	0.118284i	$0.0377393\pi$
$907$			7.12458i			0.236568i	−0.992980	+	0.118284i	$0.962261\pi$
$908$			14.7700i			0.490158i
$909$	−36.5839			−1.21341
$910$	12.0186	+	8.60465i	0.398412	+	0.285241i
$911$	−43.0059			−1.42485			−0.712424	−	0.701749i	$-0.752403\pi$
$911$	−43.0059			−1.42485			−0.712424	+	0.701749i	$0.752403\pi$
$912$		−	15.8791i		−	0.525809i
$913$		−	0.562417i		−	0.0186133i
$914$	5.63199			0.186290
$915$	−50.3403	−	36.0410i	−1.66420	−	1.19148i
$916$	18.0549			0.596552
$917$			5.01035i			0.165456i
$918$		−	1.75472i		−	0.0579144i
$919$	49.6755			1.63864			0.819322	−	0.573333i	$-0.194350\pi$
$919$	49.6755			1.63864			0.819322	+	0.573333i	$0.194350\pi$
$920$	1.30169	−	1.81813i	0.0429153	−	0.0599421i
$921$	−50.3917			−1.66046
$922$			21.6674i			0.713579i
$923$		−	13.4019i		−	0.441129i
$924$	−0.939703			−0.0309139
$925$	15.3737	−	5.23325i	0.505484	−	0.172068i
$926$	−10.9004			−0.358208
$927$		−	38.2907i		−	1.25763i
$928$		−	1.48991i		−	0.0489088i
$929$	40.5769			1.33129			0.665643	−	0.746271i	$-0.268158\pi$
$929$	40.5769			1.33129			0.665643	+	0.746271i	$0.268158\pi$
$930$	12.9616	−	18.1042i	0.425029	−	0.593660i
$931$	−7.14871			−0.234289
$932$		−	6.52961i		−	0.213885i
$933$			17.7187i			0.580085i
$934$	27.8840			0.912392
$935$	−0.569977	−	0.408073i	−0.0186402	−	0.0133454i
$936$	−12.7843			−0.417867
$937$		−	54.6988i		−	1.78693i	−0.449132	−	0.893465i	$-0.648267\pi$
$937$		−	54.6988i		−	1.78693i	0.449132	−	0.893465i	$-0.351733\pi$
$938$			6.33919i			0.206982i
$939$	−29.9225			−0.976482
$940$	10.1292	+	7.25195i	0.330378	+	0.236533i
$941$	−34.8224			−1.13518			−0.567589	−	0.823312i	$-0.692124\pi$
$941$	−34.8224			−1.13518			−0.567589	+	0.823312i	$0.692124\pi$
$942$			28.1249i			0.916358i
$943$			10.4907i			0.341626i
$944$	11.6469			0.379074
$945$	−3.08230	+	4.30521i	−0.100267	+	0.140048i
$946$	−5.19666			−0.168958
$947$			50.0861i			1.62758i	0.581160	+	0.813790i	$0.302599\pi$
$947$			50.0861i			1.62758i	−0.581160	+	0.813790i	$0.697401\pi$
$948$			0.127224i			0.00413203i
$949$	−35.2200			−1.14329
$950$	−33.8368	+	11.5182i	−1.09781	+	0.373698i
$951$	−35.5143			−1.15163
$952$			0.741036i			0.0240171i
$953$			32.6977i			1.05918i	0.848253	+	0.529591i	$0.177655\pi$
$953$			32.6977i			1.05918i	−0.848253	+	0.529591i	$0.822345\pi$
$954$	−24.4062			−0.790181
$955$	15.5946	−	21.7818i	0.504630	−	0.704843i
$956$	−15.5053			−0.501477
$957$			1.40008i			0.0452580i
$958$		−	12.7425i		−	0.411693i
$959$	16.5606			0.534770
$960$	4.03854	+	2.89138i	0.130343	+	0.0933188i
$961$	−10.9040			−0.351741
$962$		−	21.4705i		−	0.692237i
$963$		−	6.58036i		−	0.212049i
$964$	2.16241			0.0696466
$965$	−46.6215	−	33.3785i	−1.50080	−	1.07449i
$966$	2.22125			0.0714677
$967$			29.2546i			0.940765i	0.882463	+	0.470383i	$0.155884\pi$
$967$			29.2546i			0.940765i	−0.882463	+	0.470383i	$0.844116\pi$
$968$		−	10.8210i		−	0.347801i
$969$	11.7670			0.378010
$970$	−1.12290	+	1.56841i	−0.0360542	+	0.0503587i
$971$	2.76121			0.0886114			0.0443057	−	0.999018i	$-0.485892\pi$
$971$	2.76121			0.0886114			0.0443057	+	0.999018i	$0.485892\pi$
$972$		−	17.4670i		−	0.560254i
$973$			2.51256i			0.0805490i
$974$	27.0056			0.865314
$975$	23.6581	+	69.5004i	0.757667	+	2.22579i
$976$	12.4650			0.398995
$977$			5.45041i			0.174374i	0.996192	+	0.0871870i	$0.0277878\pi$
$977$			5.45041i			0.174374i	−0.996192	+	0.0871870i	$0.972212\pi$
$978$			45.9036i			1.46783i
$979$	1.18806			0.0379706
$980$	1.30169	−	1.81813i	0.0415809	−	0.0580782i
$981$	1.51642			0.0484155
$982$		−	14.9364i		−	0.476638i
$983$			40.3255i			1.28618i	0.765789	+	0.643091i	$0.222348\pi$
$983$			40.3255i			1.28618i	−0.765789	+	0.643091i	$0.777652\pi$
$984$	−23.3026			−0.742860
$985$	−9.36656	−	6.70596i	−0.298443	−	0.213670i
$986$	1.10408			0.0351611
$987$			12.3750i			0.393902i
$988$			47.2557i			1.50340i
$989$	12.2838			0.390601
$990$	−1.48754	−	1.06500i	−0.0472770	−	0.0338478i
$991$	31.8160			1.01067			0.505335	−	0.862923i	$-0.331369\pi$
$991$	31.8160			1.01067			0.505335	+	0.862923i	$0.331369\pi$
$992$			4.48286i			0.142331i
$993$		−	0.508194i		−	0.0161271i
$994$	−2.02740			−0.0643053
$995$	12.8635	−	17.9672i	0.407801	−	0.569597i
$996$	−2.95301			−0.0935696
$997$			25.7226i			0.814644i	0.913285	+	0.407322i	$0.133537\pi$
$997$			25.7226i			0.814644i	−0.913285	+	0.407322i	$0.866463\pi$
$998$			25.4725i			0.806317i
$999$	7.69102			0.243333

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1610.2.e.d.1289.2	✓	22
5.2	odd	4		8050.2.a.cj.1.2		11
5.3	odd	4		8050.2.a.ci.1.10		11
5.4	even	2	inner	1610.2.e.d.1289.21	yes	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1610.2.e.d.1289.2	✓	22	1.1	even	1	trivial
1610.2.e.d.1289.21	yes	22	5.4	even	2	inner
8050.2.a.ci.1.10		11	5.3	odd	4
8050.2.a.cj.1.2		11	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:	\( N \)	\(=\)	\( 1610 = 2 \cdot 5 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1610.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} -2.22125i q^{3} -1.00000 q^{4} +(1.30169 - 1.81813i) q^{5} -2.22125 q^{6} -1.00000i q^{7} +1.00000i q^{8} -1.93397 q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} -2.22125i q^{3} -1.00000 q^{4} +(1.30169 - 1.81813i) q^{5} -2.22125 q^{6} -1.00000i q^{7} +1.00000i q^{8} -1.93397 q^{9} +(-1.81813 - 1.30169i) q^{10} -0.423051 q^{11} +2.22125i q^{12} -6.61038i q^{13} -1.00000 q^{14} +(-4.03854 - 2.89138i) q^{15} +1.00000 q^{16} +0.741036i q^{17} +1.93397i q^{18} +7.14871 q^{19} +(-1.30169 + 1.81813i) q^{20} -2.22125 q^{21} +0.423051i q^{22} -1.00000i q^{23} +2.22125 q^{24} +(-1.61122 - 4.73328i) q^{25} -6.61038 q^{26} -2.36793i q^{27} +1.00000i q^{28} +1.48991 q^{29} +(-2.89138 + 4.03854i) q^{30} -4.48286 q^{31} -1.00000i q^{32} +0.939703i q^{33} +0.741036 q^{34} +(-1.81813 - 1.30169i) q^{35} +1.93397 q^{36} +3.24800i q^{37} -7.14871i q^{38} -14.6833 q^{39} +(1.81813 + 1.30169i) q^{40} -10.4907 q^{41} +2.22125i q^{42} +12.2838i q^{43} +0.423051 q^{44} +(-2.51742 + 3.51621i) q^{45} -1.00000 q^{46} -5.57120i q^{47} -2.22125i q^{48} -1.00000 q^{49} +(-4.73328 + 1.61122i) q^{50} +1.64603 q^{51} +6.61038i q^{52} +12.6198i q^{53} -2.36793 q^{54} +(-0.550679 + 0.769163i) q^{55} +1.00000 q^{56} -15.8791i q^{57} -1.48991i q^{58} +11.6469 q^{59} +(4.03854 + 2.89138i) q^{60} +12.4650 q^{61} +4.48286i q^{62} +1.93397i q^{63} -1.00000 q^{64} +(-12.0186 - 8.60465i) q^{65} +0.939703 q^{66} -6.33919i q^{67} -0.741036i q^{68} -2.22125 q^{69} +(-1.30169 + 1.81813i) q^{70} +2.02740 q^{71} -1.93397i q^{72} -5.32798i q^{73} +3.24800 q^{74} +(-10.5138 + 3.57893i) q^{75} -7.14871 q^{76} +0.423051i q^{77} +14.6833i q^{78} +0.0572756 q^{79} +(1.30169 - 1.81813i) q^{80} -11.0617 q^{81} +10.4907i q^{82} +1.32943i q^{83} +2.22125 q^{84} +(1.34730 + 0.964597i) q^{85} +12.2838 q^{86} -3.30948i q^{87} -0.423051i q^{88} -2.80832 q^{89} +(3.51621 + 2.51742i) q^{90} -6.61038 q^{91} +1.00000i q^{92} +9.95757i q^{93} -5.57120 q^{94} +(9.30538 - 12.9973i) q^{95} -2.22125 q^{96} -0.862650i q^{97} +1.00000i q^{98} +0.818166 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 22 q^{4} + 8 q^{6} - 38 q^{9}+O(q^{10}) \) 22 * q - 22 * q^4 + 8 * q^6 - 38 * q^9	\( 22 q - 22 q^{4} + 8 q^{6} - 38 q^{9} - 2 q^{10} + 20 q^{11} - 22 q^{14} - 8 q^{15} + 22 q^{16} + 8 q^{21} - 8 q^{24} - 2 q^{25} + 20 q^{26} - 24 q^{29} - 24 q^{30} - 32 q^{34} - 2 q^{35} + 38 q^{36} - 24 q^{39} + 2 q^{40} + 16 q^{41} - 20 q^{44} - 40 q^{45} - 22 q^{46} - 22 q^{49} + 4 q^{50} + 8 q^{51} - 20 q^{54} - 8 q^{55} + 22 q^{56} + 12 q^{59} + 8 q^{60} - 20 q^{61} - 22 q^{64} - 16 q^{65} + 56 q^{66} + 8 q^{69} + 28 q^{71} - 28 q^{74} - 28 q^{75} + 24 q^{79} + 94 q^{81} - 8 q^{84} + 28 q^{85} + 60 q^{86} + 12 q^{89} + 30 q^{90} + 20 q^{91} - 52 q^{94} - 52 q^{95} + 8 q^{96} + 12 q^{99}+O(q^{100}) \) 22 * q - 22 * q^4 + 8 * q^6 - 38 * q^9 - 2 * q^10 + 20 * q^11 - 22 * q^14 - 8 * q^15 + 22 * q^16 + 8 * q^21 - 8 * q^24 - 2 * q^25 + 20 * q^26 - 24 * q^29 - 24 * q^30 - 32 * q^34 - 2 * q^35 + 38 * q^36 - 24 * q^39 + 2 * q^40 + 16 * q^41 - 20 * q^44 - 40 * q^45 - 22 * q^46 - 22 * q^49 + 4 * q^50 + 8 * q^51 - 20 * q^54 - 8 * q^55 + 22 * q^56 + 12 * q^59 + 8 * q^60 - 20 * q^61 - 22 * q^64 - 16 * q^65 + 56 * q^66 + 8 * q^69 + 28 * q^71 - 28 * q^74 - 28 * q^75 + 24 * q^79 + 94 * q^81 - 8 * q^84 + 28 * q^85 + 60 * q^86 + 12 * q^89 + 30 * q^90 + 20 * q^91 - 52 * q^94 - 52 * q^95 + 8 * q^96 + 12 * q^99

Introduction

L-functions

Modular forms

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Database

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