LMFDB - Embedded newform 1805.2.b.k.1084.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1805,2,Mod(1084,1805)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1805, 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("1805.1084");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1805 = 5 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1805.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:	$14.4129975648$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	no (minimal twist has level 95)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1084.2
Character	$\chi$	$=$	1805.1084
Dual form			1805.2.b.k.1084.23

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.37097i q^{2} -2.28512i q^{3} -3.62149 q^{4} +(1.17411 + 1.90301i) q^{5} -5.41794 q^{6} +1.63677i q^{7} +3.84450i q^{8} -2.22176 q^{9} +O(q^{10})$	\(q-2.37097i q^{2} -2.28512i q^{3} -3.62149 q^{4} +(1.17411 + 1.90301i) q^{5} -5.41794 q^{6} +1.63677i q^{7} +3.84450i q^{8} -2.22176 q^{9} +(4.51198 - 2.78378i) q^{10} +2.72748 q^{11} +8.27553i q^{12} -6.19933i q^{13} +3.88073 q^{14} +(4.34861 - 2.68298i) q^{15} +1.87222 q^{16} -3.12451i q^{17} +5.26771i q^{18} +(-4.25204 - 6.89175i) q^{20} +3.74021 q^{21} -6.46676i q^{22} -7.29904i q^{23} +8.78514 q^{24} +(-2.24292 + 4.46870i) q^{25} -14.6984 q^{26} -1.77838i q^{27} -5.92756i q^{28} -2.22572 q^{29} +(-6.36127 - 10.3104i) q^{30} +4.42666 q^{31} +3.25005i q^{32} -6.23260i q^{33} -7.40811 q^{34} +(-3.11480 + 1.92175i) q^{35} +8.04607 q^{36} -2.04016i q^{37} -14.1662 q^{39} +(-7.31614 + 4.51388i) q^{40} +3.92482 q^{41} -8.86793i q^{42} -0.472856i q^{43} -9.87754 q^{44} +(-2.60859 - 4.22803i) q^{45} -17.3058 q^{46} +2.30160i q^{47} -4.27823i q^{48} +4.32098 q^{49} +(10.5952 + 5.31789i) q^{50} -7.13986 q^{51} +22.4508i q^{52} +6.36387i q^{53} -4.21648 q^{54} +(3.20237 + 5.19043i) q^{55} -6.29258 q^{56} +5.27711i q^{58} -12.2661 q^{59} +(-15.7484 + 9.71640i) q^{60} -4.79076 q^{61} -10.4955i q^{62} -3.63651i q^{63} +11.4502 q^{64} +(11.7974 - 7.27871i) q^{65} -14.7773 q^{66} -0.670960i q^{67} +11.3154i q^{68} -16.6791 q^{69} +(4.55642 + 7.38509i) q^{70} +2.63494 q^{71} -8.54155i q^{72} +6.51298i q^{73} -4.83714 q^{74} +(10.2115 + 5.12533i) q^{75} +4.46426i q^{77} +33.5876i q^{78} -4.12016 q^{79} +(2.19819 + 3.56285i) q^{80} -10.7291 q^{81} -9.30563i q^{82} -6.42396i q^{83} -13.5452 q^{84} +(5.94598 - 3.66852i) q^{85} -1.12113 q^{86} +5.08603i q^{87} +10.4858i q^{88} -17.3044 q^{89} +(-10.0245 + 6.18489i) q^{90} +10.1469 q^{91} +26.4334i q^{92} -10.1154i q^{93} +5.45702 q^{94} +7.42673 q^{96} -0.129944i q^{97} -10.2449i q^{98} -6.05979 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 18 q^{4} - 3 q^{5} - 12 q^{6} - 12 q^{9}+O(q^{10}) $ 24 * q - 18 * q^4 - 3 * q^5 - 12 * q^6 - 12 * q^9	$ 24 q - 18 q^{4} - 3 q^{5} - 12 q^{6} - 12 q^{9} - 6 q^{10} + 12 q^{11} - 24 q^{14} - 9 q^{15} + 6 q^{16} + 21 q^{20} + 6 q^{21} + 42 q^{24} - 3 q^{25} - 12 q^{26} - 36 q^{29} - 18 q^{30} + 42 q^{31} - 6 q^{34} + 27 q^{35} - 6 q^{36} - 24 q^{39} + 12 q^{40} + 60 q^{41} + 30 q^{44} + 9 q^{45} + 6 q^{46} - 12 q^{49} + 18 q^{50} + 30 q^{51} + 24 q^{54} + 33 q^{55} + 18 q^{56} - 60 q^{59} - 42 q^{60} + 30 q^{61} + 18 q^{65} + 36 q^{66} - 66 q^{69} + 9 q^{70} + 96 q^{71} - 24 q^{74} + 36 q^{75} - 72 q^{79} - 42 q^{80} - 96 q^{81} + 54 q^{84} - 27 q^{85} + 108 q^{86} - 84 q^{89} - 93 q^{90} + 96 q^{91} - 36 q^{94} - 120 q^{96}+O(q^{100}) $ 24 * q - 18 * q^4 - 3 * q^5 - 12 * q^6 - 12 * q^9 - 6 * q^10 + 12 * q^11 - 24 * q^14 - 9 * q^15 + 6 * q^16 + 21 * q^20 + 6 * q^21 + 42 * q^24 - 3 * q^25 - 12 * q^26 - 36 * q^29 - 18 * q^30 + 42 * q^31 - 6 * q^34 + 27 * q^35 - 6 * q^36 - 24 * q^39 + 12 * q^40 + 60 * q^41 + 30 * q^44 + 9 * q^45 + 6 * q^46 - 12 * q^49 + 18 * q^50 + 30 * q^51 + 24 * q^54 + 33 * q^55 + 18 * q^56 - 60 * q^59 - 42 * q^60 + 30 * q^61 + 18 * q^65 + 36 * q^66 - 66 * q^69 + 9 * q^70 + 96 * q^71 - 24 * q^74 + 36 * q^75 - 72 * q^79 - 42 * q^80 - 96 * q^81 + 54 * q^84 - 27 * q^85 + 108 * q^86 - 84 * q^89 - 93 * q^90 + 96 * q^91 - 36 * q^94 - 120 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1805\mathbb{Z}\right)^\times$.

$n$	$362$	$1446$
$\chi(n)$	$-1$	$1$

Coefficient data

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

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

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

$2$		−	2.37097i		−	1.67653i	−0.545265	−	0.838264i	$-0.683571\pi$
$2$		−	2.37097i		−	1.67653i	0.545265	−	0.838264i	$-0.316429\pi$
$3$		−	2.28512i		−	1.31931i	−0.751567	−	0.659656i	$-0.770702\pi$
$3$		−	2.28512i		−	1.31931i	0.751567	−	0.659656i	$-0.229298\pi$
$4$	−3.62149			−1.81075
$5$	1.17411	+	1.90301i	0.525079	+	0.851053i
$5$	1.17411	+	1.90301i	0.525079	+	0.851053i
$6$	−5.41794			−2.21186
$7$			1.63677i			0.618642i	0.950958	+	0.309321i	$0.100102\pi$
$7$			1.63677i			0.618642i	−0.950958	+	0.309321i	$0.899898\pi$
$8$			3.84450i			1.35924i
$9$	−2.22176			−0.740585
$10$	4.51198	−	2.78378i	1.42681	−	0.880310i
$11$	2.72748			0.822365			0.411183	−	0.911553i	$-0.365116\pi$
$11$	2.72748			0.822365			0.411183	+	0.911553i	$0.365116\pi$
$12$			8.27553i			2.38894i
$13$		−	6.19933i		−	1.71938i	−0.510812	−	0.859692i	$-0.670655\pi$
$13$		−	6.19933i		−	1.71938i	0.510812	−	0.859692i	$-0.329345\pi$
$14$	3.88073			1.03717
$15$	4.34861	−	2.68298i	1.12281	−	0.692743i
$16$	1.87222			0.468054
$17$		−	3.12451i		−	0.757804i	−0.925437	−	0.378902i	$-0.876302\pi$
$17$		−	3.12451i		−	0.757804i	0.925437	−	0.378902i	$-0.123698\pi$
$18$			5.26771i			1.24161i
$19$		0			0
$19$		0			0
$20$	−4.25204	−	6.89175i	−0.950785	−	1.54104i
$21$	3.74021			0.816182
$22$		−	6.46676i		−	1.37872i
$23$		−	7.29904i		−	1.52195i	−0.648779	−	0.760977i	$-0.724720\pi$
$23$		−	7.29904i		−	1.52195i	0.648779	−	0.760977i	$-0.275280\pi$
$24$	8.78514			1.79326
$25$	−2.24292	+	4.46870i	−0.448584	+	0.893741i
$26$	−14.6984			−2.88260
$27$		−	1.77838i		−	0.342249i
$28$		−	5.92756i		−	1.12020i
$29$	−2.22572			−0.413306			−0.206653	−	0.978414i	$-0.566257\pi$
$29$	−2.22572			−0.413306			−0.206653	+	0.978414i	$0.566257\pi$
$30$	−6.36127	−	10.3104i	−1.16140	−	1.88241i
$31$	4.42666			0.795051			0.397526	−	0.917591i	$-0.369869\pi$
$31$	4.42666			0.795051			0.397526	+	0.917591i	$0.369869\pi$
$32$			3.25005i			0.574532i
$33$		−	6.23260i		−	1.08496i
$34$	−7.40811			−1.27048
$35$	−3.11480	+	1.92175i	−0.526497	+	0.324836i
$36$	8.04607			1.34101
$37$		−	2.04016i		−	0.335400i	−0.985838	−	0.167700i	$-0.946366\pi$
$37$		−	2.04016i		−	0.335400i	0.985838	−	0.167700i	$-0.0536339\pi$
$38$		0			0
$39$	−14.1662			−2.26841
$40$	−7.31614	+	4.51388i	−1.15678	+	0.713707i
$41$	3.92482			0.612954			0.306477	−	0.951878i	$-0.400850\pi$
$41$	3.92482			0.612954			0.306477	+	0.951878i	$0.400850\pi$
$42$		−	8.86793i		−	1.36835i
$43$		−	0.472856i		−	0.0721099i	−0.999350	−	0.0360549i	$-0.988521\pi$
$43$		−	0.472856i		−	0.0721099i	0.999350	−	0.0360549i	$-0.0114791\pi$
$44$	−9.87754			−1.48909
$45$	−2.60859	−	4.22803i	−0.388866	−	0.630278i
$46$	−17.3058			−2.55160
$47$			2.30160i			0.335723i	0.985811	+	0.167862i	$0.0536862\pi$
$47$			2.30160i			0.335723i	−0.985811	+	0.167862i	$0.946314\pi$
$48$		−	4.27823i		−	0.617509i
$49$	4.32098			0.617282
$50$	10.5952	+	5.31789i	1.49838	+	0.752063i
$51$	−7.13986			−0.999781
$52$			22.4508i			3.11337i
$53$			6.36387i			0.874145i	0.899426	+	0.437072i	$0.143985\pi$
$53$			6.36387i			0.874145i	−0.899426	+	0.437072i	$0.856015\pi$
$54$	−4.21648			−0.573790
$55$	3.20237	+	5.19043i	0.431807	+	0.699877i
$56$	−6.29258			−0.840881
$57$		0			0
$58$			5.27711i			0.692919i
$59$	−12.2661			−1.59691			−0.798454	−	0.602056i	$-0.794348\pi$
$59$	−12.2661			−1.59691			−0.798454	+	0.602056i	$0.794348\pi$
$60$	−15.7484	+	9.71640i	−2.03311	+	1.25438i
$61$	−4.79076			−0.613393			−0.306697	−	0.951807i	$-0.599224\pi$
$61$	−4.79076			−0.613393			−0.306697	+	0.951807i	$0.599224\pi$
$62$		−	10.4955i		−	1.33293i
$63$		−	3.63651i		−	0.458157i
$64$	11.4502			1.43127
$65$	11.7974	−	7.27871i	1.46329	−	0.902813i
$66$	−14.7773			−1.81896
$67$		−	0.670960i		−	0.0819708i	−0.999160	−	0.0409854i	$-0.986950\pi$
$67$		−	0.670960i		−	0.0819708i	0.999160	−	0.0409854i	$-0.0130497\pi$
$68$			11.3154i			1.37219i
$69$	−16.6791			−2.00793
$70$	4.55642	+	7.38509i	0.544596	+	0.882687i
$71$	2.63494			0.312710			0.156355	−	0.987701i	$-0.450026\pi$
$71$	2.63494			0.312710			0.156355	+	0.987701i	$0.450026\pi$
$72$		−	8.54155i		−	1.00663i
$73$			6.51298i			0.762287i	0.924516	+	0.381143i	$0.124470\pi$
$73$			6.51298i			0.762287i	−0.924516	+	0.381143i	$0.875530\pi$
$74$	−4.83714			−0.562307
$75$	10.2115	+	5.12533i	1.17912	+	0.591822i
$76$		0			0
$77$			4.46426i			0.508750i
$78$			33.5876i			3.80305i
$79$	−4.12016			−0.463555			−0.231777	−	0.972769i	$-0.574454\pi$
$79$	−4.12016			−0.463555			−0.231777	+	0.972769i	$0.574454\pi$
$80$	2.19819	+	3.56285i	0.245765	+	0.398339i
$81$	−10.7291			−1.19212
$82$		−	9.30563i		−	1.02763i
$83$		−	6.42396i		−	0.705121i	−0.935789	−	0.352560i	$-0.885311\pi$
$83$		−	6.42396i		−	0.705121i	0.935789	−	0.352560i	$-0.114689\pi$
$84$	−13.5452			−1.47790
$85$	5.94598	−	3.66852i	0.644932	−	0.397907i
$86$	−1.12113			−0.120894
$87$			5.08603i			0.545280i
$88$			10.4858i			1.11779i
$89$	−17.3044			−1.83426			−0.917130	−	0.398589i	$-0.869500\pi$
$89$	−17.3044			−1.83426			−0.917130	+	0.398589i	$0.869500\pi$
$90$	−10.0245	+	6.18489i	−1.05668	+	0.651945i
$91$	10.1469			1.06368
$92$			26.4334i			2.75587i
$93$		−	10.1154i		−	1.04892i
$94$	5.45702			0.562849
$95$		0			0
$96$	7.42673			0.757988
$97$		−	0.129944i		−	0.0131938i	−0.999978	−	0.00659689i	$-0.997900\pi$
$97$		−	0.129944i		−	0.0131938i	0.999978	−	0.00659689i	$-0.00209987\pi$
$98$		−	10.2449i		−	1.03489i
$99$	−6.05979			−0.609032
$100$	8.12271	−	16.1834i	0.812271	−	1.61834i
$101$	3.73547			0.371693			0.185846	−	0.982579i	$-0.440497\pi$
$101$	3.73547			0.371693			0.185846	+	0.982579i	$0.440497\pi$
$102$			16.9284i			1.67616i
$103$			6.59954i			0.650272i	0.945667	+	0.325136i	$0.105410\pi$
$103$			6.59954i			0.650272i	−0.945667	+	0.325136i	$0.894590\pi$
$104$	23.8333			2.33705
$105$	4.39143	+	7.11768i	0.428560	+	0.694614i
$106$	15.0885			1.46553
$107$		−	11.7953i		−	1.14029i	−0.821543	−	0.570146i	$-0.806886\pi$
$107$		−	11.7953i		−	1.14029i	0.821543	−	0.570146i	$-0.193114\pi$
$108$			6.44038i			0.619726i
$109$	−7.23806			−0.693281			−0.346640	−	0.937998i	$-0.612678\pi$
$109$	−7.23806			−0.693281			−0.346640	+	0.937998i	$0.612678\pi$
$110$	12.3063	−	7.59271i	1.17336	−	0.723936i
$111$	−4.66199			−0.442497
$112$			3.06439i			0.289558i
$113$		−	13.2879i		−	1.25002i	−0.780616	−	0.625010i	$-0.785095\pi$
$113$		−	13.2879i		−	1.25002i	0.780616	−	0.625010i	$-0.214905\pi$
$114$		0			0
$115$	13.8902	−	8.56989i	1.29526	−	0.799146i
$116$	8.06043			0.748392
$117$			13.7734i			1.27335i
$118$			29.0825i			2.67726i
$119$	5.11411			0.468809
$120$	10.3147	+	16.7182i	0.941603	+	1.52616i
$121$	−3.56087			−0.323715
$122$			11.3587i			1.02837i
$123$		−	8.96867i		−	0.808678i
$124$	−16.0311			−1.43964
$125$	−11.1374	+	0.978456i	−0.996163	+	0.0875158i
$126$	−8.62205			−0.768113
$127$		−	8.69369i		−	0.771440i	−0.922616	−	0.385720i	$-0.873953\pi$
$127$		−	8.69369i		−	0.771440i	0.922616	−	0.385720i	$-0.126047\pi$
$128$		−	20.6479i		−	1.82504i
$129$	−1.08053			−0.0951355
$130$	−17.2576	−	27.9713i	−1.51359	−	2.45324i
$131$	10.5459			0.921402			0.460701	−	0.887555i	$-0.347598\pi$
$131$	10.5459			0.921402			0.460701	+	0.887555i	$0.347598\pi$
$132$			22.5713i			1.96458i
$133$		0			0
$134$	−1.59083			−0.137426
$135$	3.38428	−	2.08801i	0.291272	−	0.179708i
$136$	12.0122			1.03004
$137$			0.397219i			0.0339367i	0.999856	+	0.0169683i	$0.00540145\pi$
$137$			0.397219i			0.0339367i	−0.999856	+	0.0169683i	$0.994599\pi$
$138$			39.5457i			3.36636i
$139$	7.50543			0.636602			0.318301	−	0.947990i	$-0.396888\pi$
$139$	7.50543			0.636602			0.318301	+	0.947990i	$0.396888\pi$
$140$	11.2802	−	6.95962i	0.953352	−	0.588195i
$141$	5.25943			0.442924
$142$		−	6.24735i		−	0.524266i
$143$		−	16.9085i		−	1.41396i
$144$	−4.15961			−0.346634
$145$	−2.61325	−	4.23558i	−0.217018	−	0.351745i
$146$	15.4421			1.27800
$147$		−	9.87393i		−	0.814388i
$148$			7.38841i			0.607323i
$149$	3.68581			0.301953			0.150977	−	0.988537i	$-0.451758\pi$
$149$	3.68581			0.301953			0.150977	+	0.988537i	$0.451758\pi$
$150$	12.1520	−	24.2112i	0.992207	−	1.97683i
$151$	−4.49051			−0.365433			−0.182716	−	0.983166i	$-0.558489\pi$
$151$	−4.49051			−0.365433			−0.182716	+	0.983166i	$0.558489\pi$
$152$		0			0
$153$			6.94189i			0.561219i
$154$	10.5846			0.852933
$155$	5.19740	+	8.42399i	0.417465	+	0.676631i
$156$	51.3027			4.10751
$157$		−	20.2651i		−	1.61733i	−0.588266	−	0.808667i	$-0.700189\pi$
$157$		−	20.2651i		−	1.61733i	0.588266	−	0.808667i	$-0.299811\pi$
$158$			9.76878i			0.777162i
$159$	14.5422			1.15327
$160$	−6.18488	+	3.81592i	−0.488958	+	0.301675i
$161$	11.9469			0.941544
$162$			25.4383i			1.99862i
$163$			15.6590i			1.22651i	0.789887	+	0.613253i	$0.210139\pi$
$163$			15.6590i			1.22651i	−0.789887	+	0.613253i	$0.789861\pi$
$164$	−14.2137			−1.10990
$165$	11.8607	−	7.31778i	0.923356	−	0.569688i
$166$	−15.2310			−1.18215
$167$		−	6.04571i		−	0.467831i	−0.972257	−	0.233915i	$-0.924846\pi$
$167$		−	6.04571i		−	0.467831i	0.972257	−	0.233915i	$-0.0751539\pi$
$168$			14.3793i			1.10938i
$169$	−25.4317			−1.95628
$170$	−8.69795	−	14.0977i	−0.667103	−	1.08125i
$171$		0			0
$172$			1.71244i			0.130573i
$173$			1.64040i			0.124717i	0.998054	+	0.0623586i	$0.0198623\pi$
$173$			1.64040i			0.124717i	−0.998054	+	0.0623586i	$0.980138\pi$
$174$	12.0588			0.914177
$175$	−7.31425	−	3.67115i	−0.552905	−	0.277513i
$176$	5.10642			0.384911
$177$			28.0294i			2.10682i
$178$			41.0281i			3.07519i
$179$	14.1885			1.06050			0.530248	−	0.847842i	$-0.322099\pi$
$179$	14.1885			1.06050			0.530248	+	0.847842i	$0.322099\pi$
$180$	9.44699	+	15.3118i	0.704137	+	1.14127i
$181$	22.9459			1.70555			0.852776	−	0.522277i	$-0.174917\pi$
$181$	22.9459			1.70555			0.852776	+	0.522277i	$0.174917\pi$
$182$		−	24.0580i		−	1.78329i
$183$			10.9474i			0.809258i
$184$	28.0612			2.06870
$185$	3.88244	−	2.39537i	0.285443	−	0.176111i
$186$	−23.9834			−1.75855
$187$		−	8.52202i		−	0.623192i
$188$		−	8.33523i		−	0.607909i
$189$	2.91080			0.211729
$190$		0			0
$191$	10.2099			0.738762			0.369381	−	0.929278i	$-0.379570\pi$
$191$	10.2099			0.738762			0.369381	+	0.929278i	$0.379570\pi$
$192$		−	26.1650i		−	1.88830i
$193$		−	11.8312i		−	0.851631i	−0.904810	−	0.425816i	$-0.859987\pi$
$193$		−	11.8312i		−	0.851631i	0.904810	−	0.425816i	$-0.140013\pi$
$194$	−0.308092			−0.0221197
$195$	−16.6327	−	26.9584i	−1.19109	−	1.93053i
$196$	−15.6484			−1.11774
$197$		−	2.72674i		−	0.194273i	−0.995271	−	0.0971363i	$-0.969032\pi$
$197$		−	2.72674i		−	0.194273i	0.995271	−	0.0971363i	$-0.0309683\pi$
$198$			14.3676i			1.02106i
$199$	−4.47838			−0.317464			−0.158732	−	0.987322i	$-0.550741\pi$
$199$	−4.47838			−0.317464			−0.158732	+	0.987322i	$0.550741\pi$
$200$	−17.1799	−	8.62291i	−1.21481	−	0.609732i
$201$	−1.53322			−0.108145
$202$		−	8.85667i		−	0.623153i
$203$		−	3.64300i		−	0.255688i
$204$	25.8569			1.81035
$205$	4.60818	+	7.46899i	0.321849	+	0.521657i
$206$	15.6473			1.09020
$207$			16.2167i			1.12714i
$208$		−	11.6065i		−	0.804764i
$209$		0			0
$210$	16.8758	−	10.4119i	1.16454	−	0.718493i
$211$	−7.34023			−0.505322			−0.252661	−	0.967555i	$-0.581306\pi$
$211$	−7.34023			−0.505322			−0.252661	+	0.967555i	$0.581306\pi$
$212$		−	23.0467i		−	1.58285i
$213$		−	6.02114i		−	0.412562i
$214$	−27.9662			−1.91173
$215$	0.899852	−	0.555186i	0.0613694	−	0.0378634i
$216$	6.83698			0.465197
$217$			7.24543i			0.491852i
$218$			17.1612i			1.16230i
$219$	14.8829			1.00569
$220$	−11.5973	−	18.7971i	−0.781892	−	1.26730i
$221$	−19.3699			−1.30296
$222$			11.0534i			0.741858i
$223$			16.5811i			1.11035i	0.831733	+	0.555176i	$0.187349\pi$
$223$			16.5811i			1.11035i	−0.831733	+	0.555176i	$0.812651\pi$
$224$	−5.31958			−0.355430
$225$	4.98322	−	9.92837i	0.332215	−	0.661891i
$226$	−31.5052			−2.09569
$227$			11.7828i			0.782052i	0.920380	+	0.391026i	$0.127880\pi$
$227$			11.7828i			0.782052i	−0.920380	+	0.391026i	$0.872120\pi$
$228$		0			0
$229$	7.82331			0.516979			0.258490	−	0.966014i	$-0.416775\pi$
$229$	7.82331			0.516979			0.258490	+	0.966014i	$0.416775\pi$
$230$	−20.3189	−	32.9331i	−1.33979	−	2.17155i
$231$	10.2014			0.671200
$232$		−	8.55679i		−	0.561781i
$233$			6.71975i			0.440225i	0.975474	+	0.220113i	$0.0706425\pi$
$233$			6.71975i			0.440225i	−0.975474	+	0.220113i	$0.929358\pi$
$234$	32.6563			2.13481
$235$	−4.37998	+	2.70234i	−0.285718	+	0.176281i
$236$	44.4215			2.89159
$237$			9.41505i			0.611573i
$238$		−	12.1254i		−	0.785972i
$239$	15.9746			1.03331			0.516654	−	0.856194i	$-0.327177\pi$
$239$	15.9746			1.03331			0.516654	+	0.856194i	$0.327177\pi$
$240$	8.14153	−	5.02312i	0.525533	−	0.324241i
$241$	10.4554			0.673493			0.336747	−	0.941595i	$-0.390673\pi$
$241$	10.4554			0.673493			0.336747	+	0.941595i	$0.390673\pi$
$242$			8.44270i			0.542717i
$243$			19.1820i			1.23053i
$244$	17.3497			1.11070
$245$	5.07331	+	8.22288i	0.324122	+	0.525340i
$246$	−21.2644			−1.35577
$247$		0			0
$248$			17.0183i			1.08066i
$249$	−14.6795			−0.930275
$250$	2.31989	+	26.4065i	0.146723	+	1.67010i
$251$	−11.8661			−0.748984			−0.374492	−	0.927230i	$-0.622183\pi$
$251$	−11.8661			−0.748984			−0.374492	+	0.927230i	$0.622183\pi$
$252$			13.1696i			0.829606i
$253$		−	19.9080i		−	1.25160i
$254$	−20.6125			−1.29334
$255$	−8.38300	−	13.5873i	−0.524964	−	0.850867i
$256$	−26.0552			−1.62845
$257$			3.81629i			0.238053i	0.992891	+	0.119027i	$0.0379774\pi$
$257$			3.81629i			0.238053i	−0.992891	+	0.119027i	$0.962023\pi$
$258$			2.56191i			0.159497i
$259$	3.33927			0.207492
$260$	−42.7242	+	26.3598i	−2.64964	+	1.63476i
$261$	4.94501			0.306088
$262$		−	25.0041i		−	1.54476i
$263$		−	2.11957i		−	0.130699i	−0.997862	−	0.0653493i	$-0.979184\pi$
$263$		−	2.11957i		−	0.130699i	0.997862	−	0.0653493i	$-0.0208161\pi$
$264$	23.9613			1.47471
$265$	−12.1105	+	7.47190i	−0.743944	+	0.458995i
$266$		0			0
$267$			39.5425i			2.41996i
$268$			2.42988i			0.148428i
$269$	3.92827			0.239511			0.119755	−	0.992803i	$-0.461789\pi$
$269$	3.92827			0.239511			0.119755	+	0.992803i	$0.461789\pi$
$270$	−4.95062	−	8.02401i	−0.301285	−	0.488326i
$271$	18.9358			1.15027			0.575135	−	0.818058i	$-0.304949\pi$
$271$	18.9358			1.15027			0.575135	+	0.818058i	$0.304949\pi$
$272$		−	5.84975i		−	0.354693i
$273$		−	23.1868i		−	1.40333i
$274$	0.941793			0.0568958
$275$	−6.11751	+	12.1883i	−0.368900	+	0.734982i
$276$	60.4034			3.63586
$277$		−	15.0274i		−	0.902909i	−0.892294	−	0.451454i	$-0.850905\pi$
$277$		−	15.0274i		−	0.902909i	0.892294	−	0.451454i	$-0.149095\pi$
$278$		−	17.7951i		−	1.06728i
$279$	−9.83496			−0.588803
$280$	−7.38819	−	11.9749i	−0.441529	−	0.715635i
$281$	27.4830			1.63950			0.819750	−	0.572722i	$-0.194112\pi$
$281$	27.4830			1.63950			0.819750	+	0.572722i	$0.194112\pi$
$282$		−	12.4699i		−	0.742574i
$283$			20.3357i			1.20883i	0.796669	+	0.604415i	$0.206593\pi$
$283$			20.3357i			1.20883i	−0.796669	+	0.604415i	$0.793407\pi$
$284$	−9.54240			−0.566237
$285$		0			0
$286$	−40.0896			−2.37055
$287$			6.42404i			0.379199i
$288$		−	7.22081i		−	0.425490i
$289$	7.23745			0.425732
$290$	−10.0424	+	6.19593i	−0.589711	+	0.363837i
$291$	−0.296936			−0.0174067
$292$		−	23.5867i		−	1.38031i
$293$			4.58659i			0.267951i	0.990985	+	0.133976i	$0.0427744\pi$
$293$			4.58659i			0.267951i	−0.990985	+	0.133976i	$0.957226\pi$
$294$	−23.4108			−1.36534
$295$	−14.4018	−	23.3425i	−0.838503	−	1.35905i
$296$	7.84339			0.455888
$297$		−	4.85048i		−	0.281454i
$298$		−	8.73893i		−	0.506233i
$299$	−45.2491			−2.61682
$300$	−36.9809	−	18.5613i	−2.13509	−	1.07164i
$301$	0.773958			0.0446102
$302$			10.6469i			0.612658i
$303$		−	8.53597i		−	0.490379i
$304$		0			0
$305$	−5.62489	−	9.11687i	−0.322080	−	0.522031i
$306$	16.4590			0.940899
$307$			24.3228i			1.38818i	0.719890	+	0.694088i	$0.244192\pi$
$307$			24.3228i			1.38818i	−0.719890	+	0.694088i	$0.755808\pi$
$308$		−	16.1673i		−	0.921216i
$309$	15.0807			0.857911
$310$	19.9730	−	12.3229i	1.13439	−	0.699891i
$311$	22.0205			1.24867			0.624334	−	0.781157i	$-0.285370\pi$
$311$	22.0205			1.24867			0.624334	+	0.781157i	$0.285370\pi$
$312$		−	54.4620i		−	3.08330i
$313$		−	29.4817i		−	1.66640i	−0.552969	−	0.833202i	$-0.686505\pi$
$313$		−	29.4817i		−	1.66640i	0.552969	−	0.833202i	$-0.313495\pi$
$314$	−48.0480			−2.71151
$315$	6.92032	−	4.26967i	0.389916	−	0.240569i
$316$	14.9211			0.839379
$317$		−	8.04314i		−	0.451748i	−0.974157	−	0.225874i	$-0.927476\pi$
$317$		−	8.04314i		−	0.451748i	0.974157	−	0.225874i	$-0.0725237\pi$
$318$		−	34.4791i		−	1.93349i
$319$	−6.07060			−0.339889
$320$	13.4438	+	21.7899i	0.751532	+	1.21809i
$321$	−26.9536			−1.50440
$322$		−	28.3256i		−	1.57853i
$323$		0			0
$324$	38.8552			2.15862
$325$	27.7030	+	13.9046i	1.53668	+	0.771288i
$326$	37.1269			2.05627
$327$			16.5398i			0.914654i
$328$			15.0890i			0.833150i
$329$	−3.76720			−0.207692
$330$	−17.3502	−	28.1214i	−0.955098	−	1.54803i
$331$	18.2183			1.00137			0.500685	−	0.865630i	$-0.333082\pi$
$331$	18.2183			1.00137			0.500685	+	0.865630i	$0.333082\pi$
$332$			23.2643i			1.27679i
$333$			4.53273i			0.248392i
$334$	−14.3342			−0.784331
$335$	1.27685	−	0.787783i	0.0697615	−	0.0430412i
$336$	7.00249			0.382017
$337$			9.60328i			0.523124i	0.965187	+	0.261562i	$0.0842376\pi$
$337$			9.60328i			0.523124i	−0.965187	+	0.261562i	$0.915762\pi$
$338$			60.2977i			3.27976i
$339$	−30.3644			−1.64917
$340$	−21.5333	+	13.2855i	−1.16781	+	0.720509i
$341$	12.0736			0.653823
$342$		0			0
$343$			18.5299i			1.00052i
$344$	1.81790			0.0980144
$345$	−19.5832	−	31.7406i	−1.05432	−	1.70886i
$346$	3.88934			0.209092
$347$			1.26627i			0.0679771i	0.999422	+	0.0339885i	$0.0108210\pi$
$347$			1.26627i			0.0679771i	−0.999422	+	0.0339885i	$0.989179\pi$
$348$		−	18.4190i		−	0.987363i
$349$	−26.6148			−1.42466			−0.712330	−	0.701845i	$-0.752360\pi$
$349$	−26.6148			−1.42466			−0.712330	+	0.701845i	$0.752360\pi$
$350$	−8.70418	+	17.3419i	−0.465258	+	0.926961i
$351$	−11.0247			−0.588457
$352$			8.86443i			0.472475i
$353$			26.8743i			1.43037i	0.698934	+	0.715187i	$0.253658\pi$
$353$			26.8743i			1.43037i	−0.698934	+	0.715187i	$0.746342\pi$
$354$	66.4568			3.53214
$355$	3.09371	+	5.01432i	0.164197	+	0.266133i
$356$	62.6676			3.32138
$357$		−	11.6863i		−	0.618506i
$358$		−	33.6404i		−	1.77795i
$359$	21.0567			1.11133			0.555664	−	0.831407i	$-0.312464\pi$
$359$	21.0567			1.11133			0.555664	+	0.831407i	$0.312464\pi$
$360$	16.2547	−	10.0287i	0.856697	−	0.528561i
$361$		0			0
$362$		−	54.4039i		−	2.85940i
$363$			8.13699i			0.427081i
$364$	−36.7469			−1.92606
$365$	−12.3943	+	7.64697i	−0.648747	+	0.400261i
$366$	25.9560			1.35674
$367$		−	11.0177i		−	0.575118i	−0.957763	−	0.287559i	$-0.907156\pi$
$367$		−	11.0177i		−	0.575118i	0.957763	−	0.287559i	$-0.0928437\pi$
$368$		−	13.6654i		−	0.712356i
$369$	−8.72000			−0.453945
$370$	−5.67935	−	9.20515i	−0.295255	−	0.478553i
$371$	−10.4162			−0.540782
$372$			36.6329i			1.89933i
$373$		−	4.83309i		−	0.250248i	−0.992141	−	0.125124i	$-0.960067\pi$
$373$		−	4.83309i		−	0.250248i	0.992141	−	0.125124i	$-0.0399328\pi$
$374$	−20.2055			−1.04480
$375$	2.23589	+	25.4504i	0.115461	+	1.31425i
$376$	−8.84852			−0.456327
$377$			13.7980i			0.710632i
$378$		−	6.90141i		−	0.354970i
$379$	−2.03721			−0.104644			−0.0523221	−	0.998630i	$-0.516662\pi$
$379$	−2.03721			−0.104644			−0.0523221	+	0.998630i	$0.516662\pi$
$380$		0			0
$381$	−19.8661			−1.01777
$382$		−	24.2073i		−	1.23856i
$383$			34.5805i			1.76698i	0.468451	+	0.883489i	$0.344812\pi$
$383$			34.5805i			1.76698i	−0.468451	+	0.883489i	$0.655188\pi$
$384$	−47.1829			−2.40779
$385$	−8.49554	+	5.24154i	−0.432973	+	0.267134i
$386$	−28.0515			−1.42778
$387$			1.05057i			0.0534035i
$388$			0.470590i			0.0238906i
$389$	4.53021			0.229691			0.114845	−	0.993383i	$-0.463363\pi$
$389$	4.53021			0.229691			0.114845	+	0.993383i	$0.463363\pi$
$390$	−63.9176	+	39.4356i	−3.23659	+	1.99690i
$391$	−22.8059			−1.15334
$392$			16.6120i			0.839033i
$393$		−	24.0987i		−	1.21562i
$394$	−6.46503			−0.325703
$395$	−4.83754	−	7.84073i	−0.243403	−	0.394510i
$396$	21.9455			1.10280
$397$		−	25.1348i		−	1.26148i	−0.775995	−	0.630739i	$-0.782752\pi$
$397$		−	25.1348i		−	1.26148i	0.775995	−	0.630739i	$-0.217248\pi$
$398$			10.6181i			0.532237i
$399$		0			0
$400$	−4.19923	+	8.36637i	−0.209961	+	0.418319i
$401$	28.9116			1.44378			0.721888	−	0.692010i	$-0.243275\pi$
$401$	28.9116			1.44378			0.721888	+	0.692010i	$0.243275\pi$
$402$			3.63522i			0.181308i
$403$		−	27.4423i		−	1.36700i
$404$	−13.5280			−0.673041
$405$	−12.5971	−	20.4176i	−0.625957	−	1.01456i
$406$	−8.63743			−0.428669
$407$		−	5.56448i		−	0.275821i
$408$		−	27.4492i		−	1.35894i
$409$	22.9616			1.13538			0.567689	−	0.823243i	$-0.307837\pi$
$409$	22.9616			1.13538			0.567689	+	0.823243i	$0.307837\pi$
$410$	17.7087	−	10.9259i	0.874572	−	0.539589i
$411$	0.907691			0.0447731
$412$		−	23.9002i		−	1.17748i
$413$		−	20.0768i		−	0.987913i
$414$	38.4492			1.88968
$415$	12.2249	−	7.54245i	0.600096	−	0.370244i
$416$	20.1481			0.987842
$417$		−	17.1508i		−	0.839877i
$418$		0			0
$419$	−8.98058			−0.438730			−0.219365	−	0.975643i	$-0.570399\pi$
$419$	−8.98058			−0.438730			−0.219365	+	0.975643i	$0.570399\pi$
$420$	−15.9035	−	25.7766i	−0.776013	−	1.25777i
$421$	−34.0406			−1.65904			−0.829519	−	0.558478i	$-0.811385\pi$
$421$	−34.0406			−1.65904			−0.829519	+	0.558478i	$0.811385\pi$
$422$			17.4034i			0.847187i
$423$		−	5.11360i		−	0.248632i
$424$	−24.4659			−1.18817
$425$	13.9625	+	7.00802i	0.677281	+	0.339939i
$426$	−14.2759			−0.691671
$427$		−	7.84138i		−	0.379471i
$428$			42.7165i			2.06478i
$429$	−38.6380			−1.86546
$430$	−1.31633	−	2.13352i	−0.0634790	−	0.102887i
$431$	37.9730			1.82909			0.914547	−	0.404480i	$-0.132547\pi$
$431$	37.9730			1.82909			0.914547	+	0.404480i	$0.132547\pi$
$432$		−	3.32950i		−	0.160191i
$433$		−	36.9800i		−	1.77714i	−0.458738	−	0.888572i	$-0.651698\pi$
$433$		−	36.9800i		−	1.77714i	0.458738	−	0.888572i	$-0.348302\pi$
$434$	17.1787			0.824603
$435$	−9.67878	+	5.97157i	−0.464062	+	0.286315i
$436$	26.2126			1.25535
$437$		0			0
$438$		−	35.2869i		−	1.68607i
$439$	−22.1830			−1.05874			−0.529369	−	0.848392i	$-0.677571\pi$
$439$	−22.1830			−1.05874			−0.529369	+	0.848392i	$0.677571\pi$
$440$	−19.9546	+	12.3115i	−0.951299	+	0.586928i
$441$	−9.60016			−0.457150
$442$			45.9253i			2.18444i
$443$		−	9.84880i		−	0.467931i	−0.972245	−	0.233965i	$-0.924830\pi$
$443$		−	9.84880i		−	0.467931i	0.972245	−	0.233965i	$-0.0751702\pi$
$444$	16.8834			0.801249
$445$	−20.3173	−	32.9304i	−0.963131	−	1.56105i
$446$	39.3133			1.86154
$447$		−	8.42250i		−	0.398370i
$448$			18.7413i			0.885445i
$449$	37.3039			1.76048			0.880240	−	0.474528i	$-0.157381\pi$
$449$	37.3039			1.76048			0.880240	+	0.474528i	$0.157381\pi$
$450$	−23.5399	−	11.8151i	−1.10968	−	0.556967i
$451$	10.7049			0.504072
$452$			48.1220i			2.26347i
$453$			10.2613i			0.482120i
$454$	27.9367			1.31113
$455$	11.9136	+	19.3097i	0.558518	+	0.905251i
$456$		0			0
$457$		−	14.0343i		−	0.656498i	−0.944591	−	0.328249i	$-0.893542\pi$
$457$		−	14.0343i		−	0.656498i	0.944591	−	0.328249i	$-0.106458\pi$
$458$		−	18.5488i		−	0.866730i
$459$	−5.55655			−0.259358
$460$	−50.3031	+	31.0358i	−2.34539	+	1.44705i
$461$	−10.1359			−0.472077			−0.236039	−	0.971744i	$-0.575849\pi$
$461$	−10.1359			−0.472077			−0.236039	+	0.971744i	$0.575849\pi$
$462$		−	24.1871i		−	1.12528i
$463$		−	0.722130i		−	0.0335602i	−0.999859	−	0.0167801i	$-0.994658\pi$
$463$		−	0.722130i		−	0.0335602i	0.999859	−	0.0167801i	$-0.00534153\pi$
$464$	−4.16703			−0.193449
$465$	19.2498	−	11.8767i	0.892688	−	0.550767i
$466$	15.9323			0.738050
$467$			35.0172i			1.62040i	0.586152	+	0.810201i	$0.300642\pi$
$467$			35.0172i			1.62040i	−0.586152	+	0.810201i	$0.699358\pi$
$468$		−	49.8802i		−	2.30572i
$469$	1.09821			0.0507106
$470$	6.40716	+	10.3848i	0.295540	+	0.479015i
$471$	−46.3082			−2.13377
$472$		−	47.1570i		−	2.17058i
$473$		−	1.28970i		−	0.0593007i
$474$	22.3228			1.02532
$475$		0			0
$476$	−18.5207			−0.848895
$477$		−	14.1390i		−	0.647379i
$478$		−	37.8752i		−	1.73237i
$479$	26.9601			1.23184			0.615920	−	0.787809i	$-0.288784\pi$
$479$	26.9601			1.23184			0.615920	+	0.787809i	$0.288784\pi$
$480$	8.71982	+	14.1332i	0.398003	+	0.645088i
$481$	−12.6476			−0.576681
$482$		−	24.7895i		−	1.12913i
$483$		−	27.3000i		−	1.24219i
$484$	12.8956			0.586166
$485$	0.247285	−	0.152569i	0.0112286	−	0.00692778i
$486$	45.4800			2.06301
$487$		−	3.06758i		−	0.139005i	−0.997582	−	0.0695026i	$-0.977859\pi$
$487$		−	3.06758i		−	0.139005i	0.997582	−	0.0695026i	$-0.0221412\pi$
$488$		−	18.4181i		−	0.833747i
$489$	35.7826			1.61814
$490$	19.4962	−	12.0287i	0.880748	−	0.543400i
$491$	1.24888			0.0563613			0.0281806	−	0.999603i	$-0.491029\pi$
$491$	1.24888			0.0563613			0.0281806	+	0.999603i	$0.491029\pi$
$492$			32.4800i			1.46431i
$493$			6.95428i			0.313205i
$494$		0			0
$495$	−7.11488	−	11.5319i	−0.319790	−	0.518319i
$496$	8.28766			0.372127
$497$			4.31279i			0.193455i
$498$			34.8046i			1.55963i
$499$	−19.5720			−0.876165			−0.438083	−	0.898935i	$-0.644342\pi$
$499$	−19.5720			−0.876165			−0.438083	+	0.898935i	$0.644342\pi$
$500$	40.3341	−	3.54347i	1.80380	−	0.158469i
$501$	−13.8151			−0.617215
$502$			28.1342i			1.25569i
$503$		−	5.11859i		−	0.228227i	−0.993468	−	0.114113i	$-0.963597\pi$
$503$		−	5.11859i		−	0.228227i	0.993468	−	0.114113i	$-0.0364027\pi$
$504$	13.9806			0.622744
$505$	4.38586	+	7.10864i	0.195168	+	0.316330i
$506$	−47.2011			−2.09835
$507$			58.1144i			2.58095i
$508$			31.4841i			1.39688i
$509$	15.8349			0.701871			0.350935	−	0.936400i	$-0.385864\pi$
$509$	15.8349			0.701871			0.350935	+	0.936400i	$0.385864\pi$
$510$	−32.2150	+	19.8758i	−1.42650	+	0.880117i
$511$	−10.6603			−0.471582
$512$			20.4803i			0.905108i
$513$		0			0
$514$	9.04830			0.399103
$515$	−12.5590	+	7.74860i	−0.553416	+	0.341444i
$516$	3.91313			0.172266
$517$			6.27757i			0.276087i
$518$		−	7.91730i		−	0.347866i
$519$	3.74850			0.164541
$520$	27.9830	+	45.3552i	1.22714	+	1.98896i
$521$	−29.9732			−1.31315			−0.656575	−	0.754261i	$-0.727996\pi$
$521$	−29.9732			−1.31315			−0.656575	+	0.754261i	$0.727996\pi$
$522$		−	11.7245i		−	0.513166i
$523$			30.3765i			1.32827i	0.747611	+	0.664136i	$0.231201\pi$
$523$			30.3765i			1.32827i	−0.747611	+	0.664136i	$0.768799\pi$
$524$	−38.1920			−1.66843
$525$	−8.38900	+	16.7139i	−0.366126	+	0.729455i
$526$	−5.02544			−0.219120
$527$		−	13.8311i		−	0.602493i
$528$		−	11.6688i		−	0.507818i
$529$	−30.2759			−1.31635
$530$	17.7156	+	28.7137i	0.769518	+	1.24724i
$531$	27.2522			1.18265
$532$		0			0
$533$		−	24.3313i		−	1.05390i
$534$	93.7540			4.05713
$535$	22.4466	−	13.8490i	0.970450	−	0.598744i
$536$	2.57951			0.111418
$537$		−	32.4223i		−	1.39913i
$538$		−	9.31380i		−	0.401546i
$539$	11.7854			0.507632
$540$	−12.2561	+	7.56173i	−0.527420	+	0.325405i
$541$	−23.8593			−1.02579			−0.512895	−	0.858451i	$-0.671427\pi$
$541$	−23.8593			−1.02579			−0.512895	+	0.858451i	$0.671427\pi$
$542$		−	44.8963i		−	1.92846i
$543$		−	52.4339i		−	2.25016i
$544$	10.1548			0.435383
$545$	−8.49830	−	13.7741i	−0.364027	−	0.590019i
$546$	−54.9752			−2.35272
$547$			13.7402i			0.587489i	0.955884	+	0.293745i	$0.0949015\pi$
$547$			13.7402i			0.587489i	−0.955884	+	0.293745i	$0.905098\pi$
$548$		−	1.43852i		−	0.0614507i
$549$	10.6439			0.454270
$550$	28.8980	+	14.5044i	1.23222	+	0.618471i
$551$		0			0
$552$		−	64.1230i		−	2.72926i
$553$		−	6.74377i		−	0.286774i
$554$	−35.6295			−1.51375
$555$	−5.47370	−	8.87183i	−0.232346	−	0.376588i
$556$	−27.1808			−1.15272
$557$			27.0314i			1.14536i	0.819780	+	0.572679i	$0.194096\pi$
$557$			27.0314i			1.14536i	−0.819780	+	0.572679i	$0.805904\pi$
$558$			23.3184i			0.987145i
$559$	−2.93139			−0.123985
$560$	−5.83157	+	3.59794i	−0.246429	+	0.152041i
$561$	−19.4738			−0.822185
$562$		−	65.1614i		−	2.74867i
$563$			38.1678i			1.60858i	0.594237	+	0.804290i	$0.297454\pi$
$563$			38.1678i			1.60858i	−0.594237	+	0.804290i	$0.702546\pi$
$564$	−19.0470			−0.802022
$565$	25.2871	−	15.6015i	1.06383	−	0.656360i
$566$	48.2153			2.02664
$567$		−	17.5610i		−	0.737494i
$568$			10.1300i			0.425046i
$569$	−2.28061			−0.0956082			−0.0478041	−	0.998857i	$-0.515222\pi$
$569$	−2.28061			−0.0956082			−0.0478041	+	0.998857i	$0.515222\pi$
$570$		0			0
$571$	−14.4656			−0.605367			−0.302683	−	0.953091i	$-0.597883\pi$
$571$	−14.4656			−0.605367			−0.302683	+	0.953091i	$0.597883\pi$
$572$			61.2341i			2.56033i
$573$		−	23.3308i		−	0.974658i
$574$	15.2312			0.635738
$575$	32.6172	+	16.3712i	1.36023	+	0.682724i
$576$	−25.4395			−1.05998
$577$		−	8.17830i		−	0.340467i	−0.985404	−	0.170234i	$-0.945548\pi$
$577$		−	8.17830i		−	0.340467i	0.985404	−	0.170234i	$-0.0544522\pi$
$578$		−	17.1598i		−	0.713752i
$579$	−27.0358			−1.12357
$580$	9.46385	+	15.3391i	0.392965	+	0.636922i
$581$	10.5146			0.436217
$582$			0.704027i			0.0291829i
$583$			17.3573i			0.718867i
$584$	−25.0392			−1.03613
$585$	−26.2110	+	16.1715i	−1.08369	+	0.668610i
$586$	10.8746			0.449228
$587$		−	34.4354i		−	1.42130i	−0.703544	−	0.710651i	$-0.748400\pi$
$587$		−	34.4354i		−	1.42130i	0.703544	−	0.710651i	$-0.251600\pi$
$588$			35.7584i			1.47465i
$589$		0			0
$590$	−55.3443	+	34.1461i	−2.27849	+	1.40577i
$591$	−6.23093			−0.256306
$592$		−	3.81961i		−	0.156985i
$593$		−	2.65119i		−	0.108871i	−0.998517	−	0.0544357i	$-0.982664\pi$
$593$		−	2.65119i		−	0.108871i	0.998517	−	0.0544357i	$-0.0173360\pi$
$594$	−11.5003			−0.471865
$595$	6.00454	+	9.73221i	0.246162	+	0.398982i
$596$	−13.3481			−0.546760
$597$			10.2336i			0.418834i
$598$			107.284i			4.38718i
$599$	2.45464			0.100294			0.0501469	−	0.998742i	$-0.484031\pi$
$599$	2.45464			0.100294			0.0501469	+	0.998742i	$0.484031\pi$
$600$	−19.7044	+	39.2582i	−0.804427	+	1.60271i
$601$	14.9631			0.610356			0.305178	−	0.952295i	$-0.401284\pi$
$601$	14.9631			0.610356			0.305178	+	0.952295i	$0.401284\pi$
$602$		−	1.83503i		−	0.0747902i
$603$			1.49071i			0.0607064i
$604$	16.2623			0.661705
$605$	−4.18086	−	6.77638i	−0.169976	−	0.275499i
$606$	−20.2385			−0.822134
$607$		−	43.0431i		−	1.74706i	−0.486767	−	0.873532i	$-0.661824\pi$
$607$		−	43.0431i		−	1.74706i	0.486767	−	0.873532i	$-0.338176\pi$
$608$		0			0
$609$	−8.32467			−0.337333
$610$	−21.6158	+	13.3364i	−0.875199	+	0.539976i
$611$	14.2684			0.577237
$612$		−	25.1400i		−	1.01622i
$613$			39.1922i			1.58296i	0.611198	+	0.791478i	$0.290688\pi$
$613$			39.1922i			1.58296i	−0.611198	+	0.791478i	$0.709312\pi$
$614$	57.6686			2.32732
$615$	17.0675	−	10.5302i	0.688228	−	0.424620i
$616$	−17.1629			−0.691511
$617$			27.9028i			1.12332i	0.827367	+	0.561662i	$0.189838\pi$
$617$			27.9028i			1.12332i	−0.827367	+	0.561662i	$0.810162\pi$
$618$		−	35.7559i		−	1.43831i
$619$	24.8596			0.999193			0.499597	−	0.866258i	$-0.333482\pi$
$619$	24.8596			0.999193			0.499597	+	0.866258i	$0.333482\pi$
$620$	−18.8223	−	30.5074i	−0.755923	−	1.22521i
$621$	−12.9804			−0.520887
$622$		−	52.2099i		−	2.09343i
$623$		−	28.3233i		−	1.13475i
$624$	−26.5222			−1.06174
$625$	−14.9386	−	20.0459i	−0.597545	−	0.801835i
$626$	−69.9001			−2.79377
$627$		0			0
$628$			73.3901i			2.92858i
$629$	−6.37448			−0.254167
$630$	−10.1233	−	16.4079i	−0.403320	−	0.653705i
$631$	44.2670			1.76224			0.881120	−	0.472893i	$-0.156790\pi$
$631$	44.2670			1.76224			0.881120	+	0.472893i	$0.156790\pi$
$632$		−	15.8400i		−	0.630081i
$633$			16.7733i			0.666678i
$634$	−19.0700			−0.757368
$635$	16.5442	−	10.2074i	0.656537	−	0.405067i
$636$	−52.6644			−2.08828
$637$		−	26.7872i		−	1.06135i
$638$			14.3932i			0.569833i
$639$	−5.85419			−0.231588
$640$	39.2933	−	24.2430i	1.55320	−	0.958289i
$641$	20.3402			0.803389			0.401695	−	0.915774i	$-0.368421\pi$
$641$	20.3402			0.803389			0.401695	+	0.915774i	$0.368421\pi$
$642$			63.9061i			2.52217i
$643$			30.3707i			1.19770i	0.800860	+	0.598852i	$0.204376\pi$
$643$			30.3707i			1.19770i	−0.800860	+	0.598852i	$0.795624\pi$
$644$	−43.2654			−1.70490
$645$	−1.26867	−	2.05627i	−0.0499536	−	0.0809654i
$646$		0			0
$647$			48.5913i			1.91032i	0.296087	+	0.955161i	$0.404318\pi$
$647$			48.5913i			1.91032i	−0.296087	+	0.955161i	$0.595682\pi$
$648$		−	41.2479i		−	1.62037i
$649$	−33.4554			−1.31324
$650$	32.9674	−	65.6829i	1.29309	−	2.57629i
$651$	16.5567			0.648906
$652$		−	56.7088i		−	2.22089i
$653$		−	19.9555i		−	0.780918i	−0.920620	−	0.390459i	$-0.872316\pi$
$653$		−	19.9555i		−	0.780918i	0.920620	−	0.390459i	$-0.127684\pi$
$654$	39.2154			1.53344
$655$	12.3821	+	20.0690i	0.483809	+	0.784163i
$656$	7.34811			0.286895
$657$		−	14.4703i		−	0.564539i
$658$			8.93191i			0.348202i
$659$	17.0285			0.663335			0.331667	−	0.943396i	$-0.392389\pi$
$659$	17.0285			0.663335			0.331667	+	0.943396i	$0.392389\pi$
$660$	−42.9535	+	26.5013i	−1.67196	+	1.03156i
$661$	−27.5335			−1.07093			−0.535464	−	0.844558i	$-0.679863\pi$
$661$	−27.5335			−1.07093			−0.535464	+	0.844558i	$0.679863\pi$
$662$		−	43.1951i		−	1.67882i
$663$			44.2624i			1.71901i
$664$	24.6969			0.958427
$665$		0			0
$666$	10.7470			0.416436
$667$			16.2456i			0.629033i
$668$			21.8945i			0.847122i
$669$	37.8897			1.46490
$670$	−1.86781	−	3.02736i	−0.0721597	−	0.116957i
$671$	−13.0667			−0.504434
$672$			12.1559i			0.468923i
$673$		−	37.2560i		−	1.43611i	−0.695984	−	0.718057i	$-0.745032\pi$
$673$		−	37.2560i		−	1.43611i	0.695984	−	0.718057i	$-0.254968\pi$
$674$	22.7691			0.877032
$675$	7.94704	+	3.98876i	0.305882	+	0.153527i
$676$	92.1006			3.54233
$677$		−	22.7880i		−	0.875815i	−0.899020	−	0.437907i	$-0.855720\pi$
$677$		−	22.7880i		−	0.875815i	0.899020	−	0.437907i	$-0.144280\pi$
$678$			71.9930i			2.76488i
$679$	0.212688			0.00816223
$680$	14.1037	+	22.8593i	0.540850	+	0.876616i
$681$	26.9251			1.03177
$682$		−	28.6262i		−	1.09615i
$683$		−	4.61408i		−	0.176553i	−0.996096	−	0.0882764i	$-0.971864\pi$
$683$		−	4.61408i		−	0.176553i	0.996096	−	0.0882764i	$-0.0281359\pi$
$684$		0			0
$685$	−0.755912	+	0.466379i	−0.0288819	+	0.0178194i
$686$	43.9337			1.67740
$687$		−	17.8772i		−	0.682057i
$688$		−	0.885288i		−	0.0337513i
$689$	39.4517			1.50299
$690$	−75.2561	+	46.4311i	−2.86495	+	1.76760i
$691$	35.7599			1.36037			0.680186	−	0.733040i	$-0.261899\pi$
$691$	35.7599			1.36037			0.680186	+	0.733040i	$0.261899\pi$
$692$		−	5.94069i		−	0.225831i
$693$		−	9.91850i		−	0.376773i
$694$	3.00229			0.113965
$695$	8.81222	+	14.2829i	0.334267	+	0.541783i
$696$	−19.5533			−0.741165
$697$		−	12.2631i		−	0.464499i
$698$			63.1030i			2.38848i
$699$	15.3554			0.580795
$700$	26.4885	+	13.2950i	1.00117	+	0.502505i
$701$	32.8766			1.24173			0.620865	−	0.783917i	$-0.286781\pi$
$701$	32.8766			1.24173			0.620865	+	0.783917i	$0.286781\pi$
$702$			26.1393i			0.986565i
$703$		0			0
$704$	31.2301			1.17703
$705$	6.17516	+	10.0088i	0.232570	+	0.376952i
$706$	63.7180			2.39806
$707$			6.11411i			0.229945i
$708$		−	101.508i		−	3.81491i
$709$	−44.4229			−1.66834			−0.834169	−	0.551510i	$-0.814052\pi$
$709$	−44.4229			−1.66834			−0.834169	+	0.551510i	$0.814052\pi$
$710$	11.8888	−	7.33510i	0.446179	−	0.275281i
$711$	9.15400			0.343302
$712$		−	66.5267i		−	2.49319i
$713$		−	32.3103i		−	1.21003i
$714$	−27.7079			−1.03694
$715$	32.1772	−	19.8525i	1.20336	−	0.742442i
$716$	−51.3834			−1.92029
$717$		−	36.5037i		−	1.36326i
$718$		−	49.9247i		−	1.86317i
$719$	20.0859			0.749079			0.374540	−	0.927211i	$-0.377801\pi$
$719$	20.0859			0.749079			0.374540	+	0.927211i	$0.377801\pi$
$720$	−4.88385	−	7.91579i	−0.182010	−	0.295004i
$721$	−10.8019			−0.402285
$722$		0			0
$723$		−	23.8919i		−	0.888548i
$724$	−83.0982			−3.08832
$725$	4.99211	−	9.94609i	0.185402	−	0.369388i
$726$	19.2926			0.716014
$727$			0.729793i			0.0270665i	0.999908	+	0.0135333i	$0.00430790\pi$
$727$			0.729793i			0.0270665i	−0.999908	+	0.0135333i	$0.995692\pi$
$728$			39.0098i			1.44580i
$729$	11.6460			0.431333
$730$	18.1307	+	29.3865i	0.671049	+	1.08764i
$731$	−1.47744			−0.0546452
$732$		−	39.6460i		−	1.46536i
$733$		−	29.4948i		−	1.08941i	−0.838626	−	0.544707i	$-0.816641\pi$
$733$		−	29.4948i		−	1.08941i	0.838626	−	0.544707i	$-0.183359\pi$
$734$	−26.1226			−0.964201
$735$	18.7902	−	11.5931i	0.693088	−	0.427618i
$736$	23.7222			0.874412
$737$		−	1.83003i		−	0.0674100i
$738$			20.6748i			0.761051i
$739$	40.4996			1.48980			0.744901	−	0.667175i	$-0.232497\pi$
$739$	40.4996			1.48980			0.744901	+	0.667175i	$0.232497\pi$
$740$	−14.0602	+	8.67482i	−0.516864	+	0.318893i
$741$		0			0
$742$			24.6965i			0.906637i
$743$		−	19.4337i		−	0.712955i	−0.934304	−	0.356477i	$-0.883978\pi$
$743$		−	19.4337i		−	0.712955i	0.934304	−	0.356477i	$-0.116022\pi$
$744$	38.8888			1.42573
$745$	4.32755	+	7.01414i	0.158549	+	0.256978i
$746$	−11.4591			−0.419547
$747$			14.2725i			0.522202i
$748$			30.8624i			1.12844i
$749$	19.3062			0.705433
$750$	60.3420	−	5.30122i	2.20338	−	0.193573i
$751$	5.66378			0.206674			0.103337	−	0.994646i	$-0.467048\pi$
$751$	5.66378			0.206674			0.103337	+	0.994646i	$0.467048\pi$
$752$			4.30909i			0.157136i
$753$			27.1155i			0.988144i
$754$	32.7146			1.19139
$755$	−5.27236	−	8.54550i	−0.191881	−	0.311003i
$756$	−10.5414			−0.383388
$757$			12.5786i			0.457176i	0.973523	+	0.228588i	$0.0734109\pi$
$757$			12.5786i			0.457176i	−0.973523	+	0.228588i	$0.926589\pi$
$758$			4.83015i			0.175439i
$759$	−45.4920			−1.65126
$760$		0			0
$761$	50.0335			1.81371			0.906857	−	0.421439i	$-0.138475\pi$
$761$	50.0335			1.81371			0.906857	+	0.421439i	$0.138475\pi$
$762$			47.1019i			1.70632i
$763$		−	11.8471i		−	0.428892i
$764$	−36.9750			−1.33771
$765$	−13.2105	+	8.15057i	−0.477627	+	0.294684i
$766$	81.9892			2.96239
$767$			76.0414i			2.74570i
$768$			59.5392i			2.14844i
$769$	31.7447			1.14474			0.572371	−	0.819994i	$-0.306024\pi$
$769$	31.7447			1.14474			0.572371	+	0.819994i	$0.306024\pi$
$770$	12.4275	+	20.1427i	0.447857	+	0.725891i
$771$	8.72066			0.314067
$772$			42.8467i			1.54209i
$773$		−	11.4374i		−	0.411373i	−0.978618	−	0.205687i	$-0.934057\pi$
$773$		−	11.4374i		−	0.411373i	0.978618	−	0.205687i	$-0.0659428\pi$
$774$	2.49087			0.0895325
$775$	−9.92864	+	19.7814i	−0.356647	+	0.710570i
$776$	0.499569			0.0179335
$777$		−	7.63062i		−	0.273747i
$778$		−	10.7410i		−	0.385083i
$779$		0			0
$780$	60.2352	+	97.6298i	2.15677	+	3.49571i
$781$	7.18673			0.257162
$782$			54.0721i			1.93361i
$783$			3.95817i			0.141453i
$784$	8.08980			0.288921
$785$	38.5648	−	23.7936i	1.37644	−	0.849229i
$786$	−57.1372			−2.03802
$787$			6.64024i			0.236699i	0.992972	+	0.118350i	$0.0377603\pi$
$787$			6.64024i			0.236699i	−0.992972	+	0.118350i	$0.962240\pi$
$788$			9.87488i			0.351778i
$789$	−4.84347			−0.172432
$790$	−18.5901	+	11.4696i	−0.661407	+	0.408072i
$791$	21.7493			0.773315
$792$		−	23.2969i		−	0.827819i
$793$			29.6995i			1.05466i
$794$	−59.5938			−2.11490
$795$	17.0742	+	27.6740i	0.605558	+	0.981495i
$796$	16.2184			0.574847
$797$		−	0.186468i		−	0.00660502i	−0.999995	−	0.00330251i	$-0.998949\pi$
$797$		−	0.186468i		−	0.00660502i	0.999995	−	0.00330251i	$-0.00105122\pi$
$798$		0			0
$799$	7.19137			0.254412
$800$	−14.5235	−	7.28959i	−0.513483	−	0.257726i
$801$	38.4461			1.35843
$802$		−	68.5485i		−	2.42053i
$803$			17.7640i			0.626878i
$804$	5.55255			0.195823
$805$	14.0270	+	22.7350i	0.494385	+	0.801305i
$806$	−65.0649			−2.29181
$807$		−	8.97655i		−	0.315989i
$808$			14.3610i			0.505219i
$809$	−1.21997			−0.0428918			−0.0214459	−	0.999770i	$-0.506827\pi$
$809$	−1.21997			−0.0428918			−0.0214459	+	0.999770i	$0.506827\pi$
$810$	−48.4094	+	29.8674i	−1.70093	+	1.04943i
$811$	−19.0938			−0.670474			−0.335237	−	0.942134i	$-0.608816\pi$
$811$	−19.0938			−0.670474			−0.335237	+	0.942134i	$0.608816\pi$
$812$			13.1931i			0.462986i
$813$		−	43.2706i		−	1.51757i
$814$	−13.1932			−0.462422
$815$	−29.7992	+	18.3854i	−1.04382	+	0.644012i
$816$	−13.3674			−0.467951
$817$		0			0
$818$		−	54.4413i		−	1.90349i
$819$	−22.5439			−0.787748
$820$	−16.6885	−	27.0489i	−0.582787	−	0.944587i
$821$	−9.97729			−0.348210			−0.174105	−	0.984727i	$-0.555703\pi$
$821$	−9.97729			−0.348210			−0.174105	+	0.984727i	$0.555703\pi$
$822$		−	2.15211i		−	0.0750633i
$823$			28.2077i			0.983260i	0.870804	+	0.491630i	$0.163599\pi$
$823$			28.2077i			0.983260i	−0.870804	+	0.491630i	$0.836401\pi$
$824$	−25.3719			−0.883873
$825$	27.8517	+	13.9792i	0.969670	+	0.486694i
$826$	−47.6014			−1.65626
$827$			8.85297i			0.307848i	0.988083	+	0.153924i	$0.0491911\pi$
$827$			8.85297i			0.307848i	−0.988083	+	0.153924i	$0.950809\pi$
$828$		−	58.7286i		−	2.04096i
$829$	−45.6892			−1.58685			−0.793425	−	0.608668i	$-0.791704\pi$
$829$	−45.6892			−1.58685			−0.793425	+	0.608668i	$0.791704\pi$
$830$	−17.8829	−	28.9848i	−0.620725	−	1.00608i
$831$	−34.3393			−1.19122
$832$		−	70.9835i		−	2.46091i
$833$		−	13.5009i		−	0.467779i
$834$	−40.6640			−1.40808
$835$	11.5051	−	7.09834i	0.398149	−	0.245648i
$836$		0			0
$837$		−	7.87227i		−	0.272105i
$838$			21.2927i			0.735543i
$839$	−0.182558			−0.00630259			−0.00315130	−	0.999995i	$-0.501003\pi$
$839$	−0.182558			−0.00630259			−0.00315130	+	0.999995i	$0.501003\pi$
$840$	−27.3639	+	16.8829i	−0.944146	+	0.582515i
$841$	−24.0462			−0.829178
$842$			80.7092i			2.78142i
$843$		−	62.8019i		−	2.16301i
$844$	26.5826			0.915010
$845$	−29.8597	−	48.3968i	−1.02720	−	1.66490i
$846$	−12.1242			−0.416838
$847$		−	5.82833i		−	0.200264i
$848$			11.9145i			0.409147i
$849$	46.4694			1.59483
$850$	16.6158	−	33.1046i	0.569917	−	1.13548i
$851$	−14.8912			−0.510463
$852$			21.8055i			0.747044i
$853$		−	49.2184i		−	1.68520i	−0.538537	−	0.842602i	$-0.681023\pi$
$853$		−	49.2184i		−	1.68520i	0.538537	−	0.842602i	$-0.318977\pi$
$854$	−18.5917			−0.636193
$855$		0			0
$856$	45.3470			1.54993
$857$		−	31.5699i		−	1.07841i	−0.842175	−	0.539204i	$-0.818725\pi$
$857$		−	31.5699i		−	1.07841i	0.842175	−	0.539204i	$-0.181275\pi$
$858$			91.6094i			3.12749i
$859$	10.6896			0.364723			0.182362	−	0.983232i	$-0.441626\pi$
$859$	10.6896			0.364723			0.182362	+	0.983232i	$0.441626\pi$
$860$	−3.25880	+	2.01060i	−0.111124	+	0.0685610i
$861$	14.6797			0.500282
$862$		−	90.0327i		−	3.06653i
$863$			25.5826i			0.870841i	0.900227	+	0.435420i	$0.143400\pi$
$863$			25.5826i			0.870841i	−0.900227	+	0.435420i	$0.856600\pi$
$864$	5.77981			0.196633
$865$	−3.12170	+	1.92601i	−0.106141	+	0.0654864i
$866$	−87.6783			−2.97943
$867$		−	16.5384i		−	0.561674i
$868$		−	26.2393i		−	0.890619i
$869$	−11.2377			−0.381211
$870$	14.1584	+	22.9481i	0.480015	+	0.778013i
$871$	−4.15950			−0.140939
$872$		−	27.8268i		−	0.942333i
$873$			0.288703i			0.00977113i
$874$		0			0
$875$	−1.60151	−	18.2295i	−0.0541409	−	0.616268i
$876$	−53.8984			−1.82106
$877$			31.0952i			1.05001i	0.851099	+	0.525005i	$0.175937\pi$
$877$			31.0952i			1.05001i	−0.851099	+	0.525005i	$0.824063\pi$
$878$			52.5953i			1.77500i
$879$	10.4809			0.353511
$880$	5.99552	+	9.71759i	0.202109	+	0.327580i
$881$	−47.4465			−1.59851			−0.799257	−	0.600990i	$-0.794773\pi$
$881$	−47.4465			−1.59851			−0.799257	+	0.600990i	$0.794773\pi$
$882$			22.7617i			0.766425i
$883$			14.5332i			0.489082i	0.969639	+	0.244541i	$0.0786372\pi$
$883$			14.5332i			0.489082i	−0.969639	+	0.244541i	$0.921363\pi$
$884$	70.1477			2.35932
$885$	−53.3403	+	32.9097i	−1.79302	+	1.10625i
$886$	−23.3512			−0.784498
$887$			37.1270i			1.24660i	0.781982	+	0.623301i	$0.214209\pi$
$887$			37.1270i			1.24660i	−0.781982	+	0.623301i	$0.785791\pi$
$888$		−	17.9230i		−	0.601458i
$889$	14.2296			0.477245
$890$	−78.0770	+	48.1716i	−2.61715	+	1.61472i
$891$	−29.2633			−0.980357
$892$		−	60.0483i		−	2.01057i
$893$		0			0
$894$	−19.9695			−0.667879
$895$	16.6589	+	27.0009i	0.556845	+	0.902539i
$896$	33.7960			1.12904
$897$			103.400i			3.45241i
$898$		−	88.4464i		−	2.95150i
$899$	−9.85251			−0.328600
$900$	−18.0467	+	35.9555i	−0.601556	+	1.19852i
$901$	19.8840			0.662431
$902$		−	25.3809i		−	0.845091i
$903$		−	1.76858i		−	0.0588548i
$904$	51.0854			1.69907
$905$	26.9410	+	43.6663i	0.895550	+	1.45152i
$906$	24.3293			0.808287
$907$		−	10.8657i		−	0.360789i	−0.983594	−	0.180394i	$-0.942263\pi$
$907$		−	10.8657i		−	0.360789i	0.983594	−	0.180394i	$-0.0577374\pi$
$908$		−	42.6713i		−	1.41610i
$909$	−8.29929			−0.275270
$910$	45.7826	−	28.2467i	1.51768	−	0.936371i
$911$	−39.5522			−1.31042			−0.655211	−	0.755446i	$-0.727420\pi$
$911$	−39.5522			−1.31042			−0.655211	+	0.755446i	$0.727420\pi$
$912$		0			0
$913$		−	17.5212i		−	0.579867i
$914$	−33.2749			−1.10064
$915$	−20.8331	+	12.8535i	−0.688722	+	0.424924i
$916$	−28.3321			−0.936117
$917$			17.2613i			0.570018i
$918$			13.1744i			0.434820i
$919$	−32.1565			−1.06074			−0.530372	−	0.847765i	$-0.677948\pi$
$919$	−32.1565			−1.06074			−0.530372	+	0.847765i	$0.677948\pi$
$920$	32.9470	+	53.4008i	1.08623	+	1.76057i
$921$	55.5805			1.83144
$922$			24.0320i			0.791451i
$923$		−	16.3348i		−	0.537668i
$924$	−36.9441			−1.21537
$925$	9.11685	+	4.57590i	0.299760	+	0.150455i
$926$	−1.71215			−0.0562647
$927$		−	14.6626i		−	0.481582i
$928$		−	7.23369i		−	0.237458i
$929$	10.9336			0.358719			0.179359	−	0.983784i	$-0.442598\pi$
$929$	10.9336			0.358719			0.179359	+	0.983784i	$0.442598\pi$
$930$	−28.1592	−	45.6407i	−0.923376	−	1.49662i
$931$		0			0
$932$		−	24.3355i		−	0.797136i
$933$		−	50.3194i		−	1.64738i
$934$	83.0247			2.71665
$935$	16.2175	−	10.0058i	0.530370	−	0.327225i
$936$	−52.9519			−1.73079
$937$			45.0301i			1.47107i	0.677487	+	0.735535i	$0.263069\pi$
$937$			45.0301i			1.47107i	−0.677487	+	0.735535i	$0.736931\pi$
$938$		−	2.60382i		−	0.0850177i
$939$	−67.3691			−2.19851
$940$	15.8621	−	9.78650i	0.517363	−	0.319200i
$941$	−42.6516			−1.39040			−0.695201	−	0.718816i	$-0.744685\pi$
$941$	−42.6516			−1.39040			−0.695201	+	0.718816i	$0.744685\pi$
$942$			109.795i			3.57733i
$943$		−	28.6474i		−	0.932888i
$944$	−22.9647			−0.747438
$945$	3.41760	+	5.53929i	0.111175	+	0.180193i
$946$	−3.05785			−0.0994192
$947$			24.7131i			0.803069i	0.915844	+	0.401535i	$0.131523\pi$
$947$			24.7131i			0.803069i	−0.915844	+	0.401535i	$0.868477\pi$
$948$		−	34.0965i		−	1.10740i
$949$	40.3761			1.31066
$950$		0			0
$951$	−18.3795			−0.595996
$952$			19.6612i			0.637223i
$953$			15.5170i			0.502646i	0.967903	+	0.251323i	$0.0808657\pi$
$953$			15.5170i			0.502646i	−0.967903	+	0.251323i	$0.919134\pi$
$954$	−33.5231			−1.08535
$955$	11.9876	+	19.4296i	0.387909	+	0.628726i
$956$	−57.8517			−1.87106
$957$			13.8720i			0.448419i
$958$		−	63.9217i		−	2.06521i
$959$	−0.650157			−0.0209946
$960$	49.7923	−	30.7207i	1.60704	−	0.991505i
$961$	−11.4047			−0.367893
$962$			29.9871i			0.966821i
$963$			26.2062i			0.844484i
$964$	−37.8642			−1.21952
$965$	22.5150	−	13.8912i	0.724784	−	0.447174i
$966$	−64.7274			−2.08257
$967$			16.0510i			0.516166i	0.966123	+	0.258083i	$0.0830909\pi$
$967$			16.0510i			0.516166i	−0.966123	+	0.258083i	$0.916909\pi$
$968$		−	13.6898i		−	0.440006i
$969$		0			0
$970$	−0.361735	−	0.586304i	−0.0116146	−	0.0188251i
$971$	−5.76925			−0.185144			−0.0925720	−	0.995706i	$-0.529509\pi$
$971$	−5.76925			−0.185144			−0.0925720	+	0.995706i	$0.529509\pi$
$972$		−	69.4676i		−	2.22817i
$973$			12.2847i			0.393829i
$974$	−7.27312			−0.233046
$975$	31.7736	−	63.3045i	1.01757	−	2.02737i
$976$	−8.96933			−0.287101
$977$			46.7724i			1.49638i	0.663484	+	0.748190i	$0.269077\pi$
$977$			46.7724i			1.49638i	−0.663484	+	0.748190i	$0.730923\pi$
$978$		−	84.8394i		−	2.71286i
$979$	−47.1973			−1.50843
$980$	−18.3730	−	29.7791i	−0.586903	−	0.951258i
$981$	16.0812			0.513434
$982$		−	2.96106i		−	0.0944912i
$983$			33.6039i			1.07180i	0.844282	+	0.535900i	$0.180028\pi$
$983$			33.6039i			1.07180i	−0.844282	+	0.535900i	$0.819972\pi$
$984$	34.4801			1.09919
$985$	5.18903	−	3.20151i	0.165336	−	0.102008i
$986$	16.4884			0.525097
$987$			8.60848i			0.274011i
$988$		0			0
$989$	−3.45139			−0.109748
$990$	−27.3417	+	16.8691i	−0.868976	+	0.536137i
$991$	−45.6040			−1.44866			−0.724329	−	0.689454i	$-0.757850\pi$
$991$	−45.6040			−1.44866			−0.724329	+	0.689454i	$0.757850\pi$
$992$			14.3868i			0.456783i
$993$		−	41.6310i		−	1.32112i
$994$	10.2255			0.324333
$995$	−5.25812	−	8.52242i	−0.166694	−	0.270179i
$996$	53.1616			1.68449
$997$			4.80126i			0.152057i	0.997106	+	0.0760287i	$0.0242241\pi$
$997$			4.80126i			0.152057i	−0.997106	+	0.0760287i	$0.975776\pi$
$998$			46.4047i			1.46892i
$999$	−3.62817			−0.114790

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1805.2.b.k.1084.2		24
5.2	odd	4		9025.2.a.cu.1.23		24
5.3	odd	4		9025.2.a.cu.1.2		24
5.4	even	2	inner	1805.2.b.k.1084.23		24
19.9	even	9		95.2.p.a.24.8	yes	48
19.17	even	9		95.2.p.a.4.1	✓	48
19.18	odd	2		1805.2.b.l.1084.23		24
57.17	odd	18		855.2.da.b.289.8		48
57.47	odd	18		855.2.da.b.784.1		48
95.9	even	18		95.2.p.a.24.1	yes	48
95.17	odd	36		475.2.l.f.251.1		48
95.18	even	4		9025.2.a.ct.1.23		24
95.28	odd	36		475.2.l.f.176.8		48
95.37	even	4		9025.2.a.ct.1.2		24
95.47	odd	36		475.2.l.f.176.1		48
95.74	even	18		95.2.p.a.4.8	yes	48
95.93	odd	36		475.2.l.f.251.8		48
95.94	odd	2		1805.2.b.l.1084.2		24
285.74	odd	18		855.2.da.b.289.1		48
285.104	odd	18		855.2.da.b.784.8		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.p.a.4.1	✓	48	19.17	even	9
95.2.p.a.4.8	yes	48	95.74	even	18
95.2.p.a.24.1	yes	48	95.9	even	18
95.2.p.a.24.8	yes	48	19.9	even	9
475.2.l.f.176.1		48	95.47	odd	36
475.2.l.f.176.8		48	95.28	odd	36
475.2.l.f.251.1		48	95.17	odd	36
475.2.l.f.251.8		48	95.93	odd	36
855.2.da.b.289.1		48	285.74	odd	18
855.2.da.b.289.8		48	57.17	odd	18
855.2.da.b.784.1		48	57.47	odd	18
855.2.da.b.784.8		48	285.104	odd	18
1805.2.b.k.1084.2		24	1.1	even	1	trivial
1805.2.b.k.1084.23		24	5.4	even	2	inner
1805.2.b.l.1084.2		24	95.94	odd	2
1805.2.b.l.1084.23		24	19.18	odd	2
9025.2.a.ct.1.2		24	95.37	even	4
9025.2.a.ct.1.23		24	95.18	even	4
9025.2.a.cu.1.2		24	5.3	odd	4
9025.2.a.cu.1.23		24	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:	\( N \)	\(=\)	\( 1805 = 5 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1805.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.37097i q^{2} -2.28512i q^{3} -3.62149 q^{4} +(1.17411 + 1.90301i) q^{5} -5.41794 q^{6} +1.63677i q^{7} +3.84450i q^{8} -2.22176 q^{9} +O(q^{10})\)	\(q-2.37097i q^{2} -2.28512i q^{3} -3.62149 q^{4} +(1.17411 + 1.90301i) q^{5} -5.41794 q^{6} +1.63677i q^{7} +3.84450i q^{8} -2.22176 q^{9} +(4.51198 - 2.78378i) q^{10} +2.72748 q^{11} +8.27553i q^{12} -6.19933i q^{13} +3.88073 q^{14} +(4.34861 - 2.68298i) q^{15} +1.87222 q^{16} -3.12451i q^{17} +5.26771i q^{18} +(-4.25204 - 6.89175i) q^{20} +3.74021 q^{21} -6.46676i q^{22} -7.29904i q^{23} +8.78514 q^{24} +(-2.24292 + 4.46870i) q^{25} -14.6984 q^{26} -1.77838i q^{27} -5.92756i q^{28} -2.22572 q^{29} +(-6.36127 - 10.3104i) q^{30} +4.42666 q^{31} +3.25005i q^{32} -6.23260i q^{33} -7.40811 q^{34} +(-3.11480 + 1.92175i) q^{35} +8.04607 q^{36} -2.04016i q^{37} -14.1662 q^{39} +(-7.31614 + 4.51388i) q^{40} +3.92482 q^{41} -8.86793i q^{42} -0.472856i q^{43} -9.87754 q^{44} +(-2.60859 - 4.22803i) q^{45} -17.3058 q^{46} +2.30160i q^{47} -4.27823i q^{48} +4.32098 q^{49} +(10.5952 + 5.31789i) q^{50} -7.13986 q^{51} +22.4508i q^{52} +6.36387i q^{53} -4.21648 q^{54} +(3.20237 + 5.19043i) q^{55} -6.29258 q^{56} +5.27711i q^{58} -12.2661 q^{59} +(-15.7484 + 9.71640i) q^{60} -4.79076 q^{61} -10.4955i q^{62} -3.63651i q^{63} +11.4502 q^{64} +(11.7974 - 7.27871i) q^{65} -14.7773 q^{66} -0.670960i q^{67} +11.3154i q^{68} -16.6791 q^{69} +(4.55642 + 7.38509i) q^{70} +2.63494 q^{71} -8.54155i q^{72} +6.51298i q^{73} -4.83714 q^{74} +(10.2115 + 5.12533i) q^{75} +4.46426i q^{77} +33.5876i q^{78} -4.12016 q^{79} +(2.19819 + 3.56285i) q^{80} -10.7291 q^{81} -9.30563i q^{82} -6.42396i q^{83} -13.5452 q^{84} +(5.94598 - 3.66852i) q^{85} -1.12113 q^{86} +5.08603i q^{87} +10.4858i q^{88} -17.3044 q^{89} +(-10.0245 + 6.18489i) q^{90} +10.1469 q^{91} +26.4334i q^{92} -10.1154i q^{93} +5.45702 q^{94} +7.42673 q^{96} -0.129944i q^{97} -10.2449i q^{98} -6.05979 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 18 q^{4} - 3 q^{5} - 12 q^{6} - 12 q^{9}+O(q^{10}) \) 24 * q - 18 * q^4 - 3 * q^5 - 12 * q^6 - 12 * q^9	\( 24 q - 18 q^{4} - 3 q^{5} - 12 q^{6} - 12 q^{9} - 6 q^{10} + 12 q^{11} - 24 q^{14} - 9 q^{15} + 6 q^{16} + 21 q^{20} + 6 q^{21} + 42 q^{24} - 3 q^{25} - 12 q^{26} - 36 q^{29} - 18 q^{30} + 42 q^{31} - 6 q^{34} + 27 q^{35} - 6 q^{36} - 24 q^{39} + 12 q^{40} + 60 q^{41} + 30 q^{44} + 9 q^{45} + 6 q^{46} - 12 q^{49} + 18 q^{50} + 30 q^{51} + 24 q^{54} + 33 q^{55} + 18 q^{56} - 60 q^{59} - 42 q^{60} + 30 q^{61} + 18 q^{65} + 36 q^{66} - 66 q^{69} + 9 q^{70} + 96 q^{71} - 24 q^{74} + 36 q^{75} - 72 q^{79} - 42 q^{80} - 96 q^{81} + 54 q^{84} - 27 q^{85} + 108 q^{86} - 84 q^{89} - 93 q^{90} + 96 q^{91} - 36 q^{94} - 120 q^{96}+O(q^{100}) \) 24 * q - 18 * q^4 - 3 * q^5 - 12 * q^6 - 12 * q^9 - 6 * q^10 + 12 * q^11 - 24 * q^14 - 9 * q^15 + 6 * q^16 + 21 * q^20 + 6 * q^21 + 42 * q^24 - 3 * q^25 - 12 * q^26 - 36 * q^29 - 18 * q^30 + 42 * q^31 - 6 * q^34 + 27 * q^35 - 6 * q^36 - 24 * q^39 + 12 * q^40 + 60 * q^41 + 30 * q^44 + 9 * q^45 + 6 * q^46 - 12 * q^49 + 18 * q^50 + 30 * q^51 + 24 * q^54 + 33 * q^55 + 18 * q^56 - 60 * q^59 - 42 * q^60 + 30 * q^61 + 18 * q^65 + 36 * q^66 - 66 * q^69 + 9 * q^70 + 96 * q^71 - 24 * q^74 + 36 * q^75 - 72 * q^79 - 42 * q^80 - 96 * q^81 + 54 * q^84 - 27 * q^85 + 108 * q^86 - 84 * q^89 - 93 * q^90 + 96 * q^91 - 36 * q^94 - 120 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more