LMFDB - Embedded newform 1045.2.b.d.419.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1045,2,Mod(419,1045)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1045, 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("1045.419");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1045 = 5 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1045.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:	$8.34436701122$
Analytic rank:	$0$
Dimension:	$22$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			419.14
Character	$\chi$	$=$	1045.419
Dual form			1045.2.b.d.419.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.06190i q^{2} +2.29282i q^{3} +0.872373 q^{4} +(-1.55246 + 1.60931i) q^{5} -2.43474 q^{6} +3.97400i q^{7} +3.05017i q^{8} -2.25702 q^{9} +O(q^{10})$	\(q+1.06190i q^{2} +2.29282i q^{3} +0.872373 q^{4} +(-1.55246 + 1.60931i) q^{5} -2.43474 q^{6} +3.97400i q^{7} +3.05017i q^{8} -2.25702 q^{9} +(-1.70892 - 1.64855i) q^{10} -1.00000 q^{11} +2.00019i q^{12} -4.18176i q^{13} -4.21998 q^{14} +(-3.68986 - 3.55950i) q^{15} -1.49422 q^{16} +2.67370i q^{17} -2.39672i q^{18} +1.00000 q^{19} +(-1.35432 + 1.40392i) q^{20} -9.11166 q^{21} -1.06190i q^{22} -1.19584i q^{23} -6.99348 q^{24} +(-0.179760 - 4.99677i) q^{25} +4.44060 q^{26} +1.70352i q^{27} +3.46681i q^{28} +7.35774 q^{29} +(3.77983 - 3.91825i) q^{30} +8.19367 q^{31} +4.51363i q^{32} -2.29282i q^{33} -2.83919 q^{34} +(-6.39540 - 6.16946i) q^{35} -1.96896 q^{36} -1.43784i q^{37} +1.06190i q^{38} +9.58801 q^{39} +(-4.90866 - 4.73525i) q^{40} +1.11324 q^{41} -9.67565i q^{42} -2.88968i q^{43} -0.872373 q^{44} +(3.50392 - 3.63225i) q^{45} +1.26986 q^{46} -7.25799i q^{47} -3.42597i q^{48} -8.79266 q^{49} +(5.30606 - 0.190886i) q^{50} -6.13030 q^{51} -3.64805i q^{52} +12.2562i q^{53} -1.80896 q^{54} +(1.55246 - 1.60931i) q^{55} -12.1214 q^{56} +2.29282i q^{57} +7.81317i q^{58} +1.48555 q^{59} +(-3.21893 - 3.10521i) q^{60} +2.05410 q^{61} +8.70084i q^{62} -8.96939i q^{63} -7.78145 q^{64} +(6.72974 + 6.49199i) q^{65} +2.43474 q^{66} -5.82801i q^{67} +2.33246i q^{68} +2.74185 q^{69} +(6.55133 - 6.79126i) q^{70} +2.59387 q^{71} -6.88429i q^{72} -5.35063i q^{73} +1.52684 q^{74} +(11.4567 - 0.412156i) q^{75} +0.872373 q^{76} -3.97400i q^{77} +10.1815i q^{78} +1.43346 q^{79} +(2.31971 - 2.40466i) q^{80} -10.6769 q^{81} +1.18214i q^{82} +10.4465i q^{83} -7.94877 q^{84} +(-4.30281 - 4.15080i) q^{85} +3.06854 q^{86} +16.8700i q^{87} -3.05017i q^{88} -16.4907 q^{89} +(3.85707 + 3.72081i) q^{90} +16.6183 q^{91} -1.04322i q^{92} +18.7866i q^{93} +7.70724 q^{94} +(-1.55246 + 1.60931i) q^{95} -10.3489 q^{96} +4.87755i q^{97} -9.33691i q^{98} +2.25702 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - 32 q^{4} + 7 q^{5} - 12 q^{6} - 34 q^{9}+O(q^{10}) $ 22 * q - 32 * q^4 + 7 * q^5 - 12 * q^6 - 34 * q^9	$ 22 q - 32 q^{4} + 7 q^{5} - 12 q^{6} - 34 q^{9} + 2 q^{10} - 22 q^{11} + 8 q^{14} - 23 q^{15} + 40 q^{16} + 22 q^{19} - 22 q^{20} - 22 q^{21} + 22 q^{24} + 13 q^{25} + 16 q^{26} + 10 q^{29} - 22 q^{30} + 76 q^{31} - 56 q^{34} - 2 q^{35} + 104 q^{36} + 8 q^{39} - 20 q^{40} + 6 q^{41} + 32 q^{44} - 12 q^{45} + 88 q^{46} - 28 q^{49} - 20 q^{50} + 8 q^{51} - 38 q^{54} - 7 q^{55} + 44 q^{56} - 40 q^{59} + 78 q^{60} - 6 q^{61} - 140 q^{64} - 22 q^{65} + 12 q^{66} - 74 q^{69} - 24 q^{70} + 62 q^{71} + 26 q^{74} + 13 q^{75} - 32 q^{76} - 102 q^{79} + 142 q^{80} + 94 q^{81} + 38 q^{84} + 26 q^{85} + 28 q^{86} - 54 q^{89} + 118 q^{90} + 88 q^{91} - 36 q^{94} + 7 q^{95} + 2 q^{96} + 34 q^{99}+O(q^{100}) $ 22 * q - 32 * q^4 + 7 * q^5 - 12 * q^6 - 34 * q^9 + 2 * q^10 - 22 * q^11 + 8 * q^14 - 23 * q^15 + 40 * q^16 + 22 * q^19 - 22 * q^20 - 22 * q^21 + 22 * q^24 + 13 * q^25 + 16 * q^26 + 10 * q^29 - 22 * q^30 + 76 * q^31 - 56 * q^34 - 2 * q^35 + 104 * q^36 + 8 * q^39 - 20 * q^40 + 6 * q^41 + 32 * q^44 - 12 * q^45 + 88 * q^46 - 28 * q^49 - 20 * q^50 + 8 * q^51 - 38 * q^54 - 7 * q^55 + 44 * q^56 - 40 * q^59 + 78 * q^60 - 6 * q^61 - 140 * q^64 - 22 * q^65 + 12 * q^66 - 74 * q^69 - 24 * q^70 + 62 * q^71 + 26 * q^74 + 13 * q^75 - 32 * q^76 - 102 * q^79 + 142 * q^80 + 94 * q^81 + 38 * q^84 + 26 * q^85 + 28 * q^86 - 54 * q^89 + 118 * q^90 + 88 * q^91 - 36 * q^94 + 7 * q^95 + 2 * q^96 + 34 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1045\mathbb{Z}\right)^\times$.

$n$	$496$	$761$	$837$
$\chi(n)$	$1$	$1$	$-1$

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 $

$2$			1.06190i			0.750875i	0.926848	+	0.375438i	$0.122508\pi$
$2$			1.06190i			0.750875i	−0.926848	+	0.375438i	$0.877492\pi$
$3$			2.29282i			1.32376i	0.749610	+	0.661880i	$0.230241\pi$
$3$			2.29282i			1.32376i	−0.749610	+	0.661880i	$0.769759\pi$
$4$	0.872373			0.436187
$5$	−1.55246	+	1.60931i	−0.694280	+	0.719705i
$5$	−1.55246	+	1.60931i	−0.694280	+	0.719705i
$6$	−2.43474			−0.993978
$7$			3.97400i			1.50203i	0.660285	+	0.751015i	$0.270435\pi$
$7$			3.97400i			1.50203i	−0.660285	+	0.751015i	$0.729565\pi$
$8$			3.05017i			1.07840i
$9$	−2.25702			−0.752340
$10$	−1.70892	−	1.64855i	−0.540409	−	0.521317i
$11$	−1.00000			−0.301511
$11$	−1.00000			−0.301511
$12$			2.00019i			0.577406i
$13$		−	4.18176i		−	1.15981i	−0.814684	−	0.579905i	$-0.803090\pi$
$13$		−	4.18176i		−	1.15981i	0.814684	−	0.579905i	$-0.196910\pi$
$14$	−4.21998			−1.12784
$15$	−3.68986	−	3.55950i	−0.952717	−	0.919059i
$16$	−1.49422			−0.373555
$17$			2.67370i			0.648467i	0.945977	+	0.324233i	$0.105106\pi$
$17$			2.67370i			0.648467i	−0.945977	+	0.324233i	$0.894894\pi$
$18$		−	2.39672i		−	0.564913i
$19$	1.00000			0.229416
$19$	1.00000			0.229416
$20$	−1.35432	+	1.40392i	−0.302835	+	0.313926i
$21$	−9.11166			−1.98833
$22$		−	1.06190i		−	0.226397i
$23$		−	1.19584i		−	0.249351i	−0.992198	−	0.124675i	$-0.960211\pi$
$23$		−	1.19584i		−	0.249351i	0.992198	−	0.124675i	$-0.0397889\pi$
$24$	−6.99348			−1.42754
$25$	−0.179760	−	4.99677i	−0.0359519	−	0.999354i
$26$	4.44060			0.870873
$27$			1.70352i			0.327842i
$28$			3.46681i			0.655165i
$29$	7.35774			1.36630			0.683149	−	0.730279i	$-0.260610\pi$
$29$	7.35774			1.36630			0.683149	+	0.730279i	$0.260610\pi$
$30$	3.77983	−	3.91825i	0.690099	−	0.715372i
$31$	8.19367			1.47163			0.735814	−	0.677184i	$-0.236800\pi$
$31$	8.19367			1.47163			0.735814	+	0.677184i	$0.236800\pi$
$32$			4.51363i			0.797904i
$33$		−	2.29282i		−	0.399129i
$34$	−2.83919			−0.486918
$35$	−6.39540	−	6.16946i	−1.08102	−	1.04283i
$36$	−1.96896			−0.328161
$37$		−	1.43784i		−	0.236380i	−0.992991	−	0.118190i	$-0.962291\pi$
$37$		−	1.43784i		−	0.236380i	0.992991	−	0.118190i	$-0.0377092\pi$
$38$			1.06190i			0.172263i
$39$	9.58801			1.53531
$40$	−4.90866	−	4.73525i	−0.776128	−	0.748709i
$41$	1.11324			0.173858			0.0869292	−	0.996214i	$-0.472295\pi$
$41$	1.11324			0.173858			0.0869292	+	0.996214i	$0.472295\pi$
$42$		−	9.67565i		−	1.49299i
$43$		−	2.88968i		−	0.440672i	−0.975424	−	0.220336i	$-0.929285\pi$
$43$		−	2.88968i		−	0.440672i	0.975424	−	0.220336i	$-0.0707154\pi$
$44$	−0.872373			−0.131515
$45$	3.50392	−	3.63225i	0.522334	−	0.541463i
$46$	1.26986			0.187231
$47$		−	7.25799i		−	1.05869i	−0.848408	−	0.529343i	$-0.822438\pi$
$47$		−	7.25799i		−	1.05869i	0.848408	−	0.529343i	$-0.177562\pi$
$48$		−	3.42597i		−	0.494497i
$49$	−8.79266			−1.25609
$50$	5.30606	−	0.190886i	0.750390	−	0.0269954i
$51$	−6.13030			−0.858414
$52$		−	3.64805i		−	0.505894i
$53$			12.2562i			1.68352i	0.539854	+	0.841758i	$0.318479\pi$
$53$			12.2562i			1.68352i	−0.539854	+	0.841758i	$0.681521\pi$
$54$	−1.80896			−0.246169
$55$	1.55246	−	1.60931i	0.209333	−	0.216999i
$56$	−12.1214			−1.61978
$57$			2.29282i			0.303691i
$58$			7.81317i			1.02592i
$59$	1.48555			0.193402			0.0967010	−	0.995313i	$-0.469171\pi$
$59$	1.48555			0.193402			0.0967010	+	0.995313i	$0.469171\pi$
$60$	−3.21893	−	3.10521i	−0.415562	−	0.400881i
$61$	2.05410			0.263001			0.131500	−	0.991316i	$-0.458021\pi$
$61$	2.05410			0.263001			0.131500	+	0.991316i	$0.458021\pi$
$62$			8.70084i			1.10501i
$63$		−	8.96939i		−	1.13004i
$64$	−7.78145			−0.972681
$65$	6.72974	+	6.49199i	0.834722	+	0.805233i
$66$	2.43474			0.299696
$67$		−	5.82801i		−	0.712005i	−0.934485	−	0.356002i	$-0.884139\pi$
$67$		−	5.82801i		−	0.712005i	0.934485	−	0.356002i	$-0.115861\pi$
$68$			2.33246i			0.282853i
$69$	2.74185			0.330080
$70$	6.55133	−	6.79126i	0.783034	−	0.811710i
$71$	2.59387			0.307836			0.153918	−	0.988084i	$-0.450811\pi$
$71$	2.59387			0.307836			0.153918	+	0.988084i	$0.450811\pi$
$72$		−	6.88429i		−	0.811321i
$73$		−	5.35063i		−	0.626244i	−0.949713	−	0.313122i	$-0.898625\pi$
$73$		−	5.35063i		−	0.626244i	0.949713	−	0.313122i	$-0.101375\pi$
$74$	1.52684			0.177492
$75$	11.4567	−	0.412156i	1.32290	−	0.0475917i
$76$	0.872373			0.100068
$77$		−	3.97400i		−	0.452879i
$78$			10.1815i			1.15283i
$79$	1.43346			0.161277			0.0806387	−	0.996743i	$-0.474304\pi$
$79$	1.43346			0.161277			0.0806387	+	0.996743i	$0.474304\pi$
$80$	2.31971	−	2.40466i	0.259351	−	0.268849i
$81$	−10.6769			−1.18632
$82$			1.18214i			0.130546i
$83$			10.4465i			1.14666i	0.819325	+	0.573329i	$0.194348\pi$
$83$			10.4465i			1.14666i	−0.819325	+	0.573329i	$0.805652\pi$
$84$	−7.94877			−0.867282
$85$	−4.30281	−	4.15080i	−0.466705	−	0.450217i
$86$	3.06854			0.330889
$87$			16.8700i			1.80865i
$88$		−	3.05017i		−	0.325149i
$89$	−16.4907			−1.74801			−0.874004	−	0.485919i	$-0.838485\pi$
$89$	−16.4907			−1.74801			−0.874004	+	0.485919i	$0.838485\pi$
$90$	3.85707	+	3.72081i	0.406571	+	0.392208i
$91$	16.6183			1.74207
$92$		−	1.04322i		−	0.108763i
$93$			18.7866i			1.94808i
$94$	7.70724			0.794941
$95$	−1.55246	+	1.60931i	−0.159279	+	0.165112i
$96$	−10.3489			−1.05623
$97$			4.87755i			0.495240i	0.968857	+	0.247620i	$0.0796484\pi$
$97$			4.87755i			0.495240i	−0.968857	+	0.247620i	$0.920352\pi$
$98$		−	9.33691i		−	0.943170i
$99$	2.25702			0.226839
$100$	−0.156817	−	4.35905i	−0.0156817	−	0.435905i
$101$	3.44281			0.342572			0.171286	−	0.985221i	$-0.445208\pi$
$101$	3.44281			0.342572			0.171286	+	0.985221i	$0.445208\pi$
$102$		−	6.50976i		−	0.644562i
$103$		−	10.7782i		−	1.06200i	−0.847370	−	0.531002i	$-0.821816\pi$
$103$		−	10.7782i		−	1.06200i	0.847370	−	0.531002i	$-0.178184\pi$
$104$	12.7551			1.25074
$105$	14.1455	−	14.6635i	1.38045	−	1.43101i
$106$	−13.0148			−1.26411
$107$		−	15.3737i		−	1.48623i	−0.669162	−	0.743116i	$-0.733347\pi$
$107$		−	15.3737i		−	1.48623i	0.669162	−	0.743116i	$-0.266653\pi$
$108$			1.48610i			0.143000i
$109$	−19.0396			−1.82366			−0.911832	−	0.410564i	$-0.865332\pi$
$109$	−19.0396			−1.82366			−0.911832	+	0.410564i	$0.865332\pi$
$110$	1.70892	+	1.64855i	0.162939	+	0.157183i
$111$	3.29672			0.312910
$112$		−	5.93802i		−	0.561090i
$113$		−	17.1961i		−	1.61768i	−0.588032	−	0.808838i	$-0.700097\pi$
$113$		−	17.1961i		−	1.61768i	0.588032	−	0.808838i	$-0.299903\pi$
$114$	−2.43474			−0.228034
$115$	1.92448	+	1.85649i	0.179459	+	0.173119i
$116$	6.41870			0.595961
$117$			9.43831i			0.872572i
$118$			1.57750i			0.145221i
$119$	−10.6253			−0.974017
$120$	10.8571	−	11.2547i	0.991111	−	1.02741i
$121$	1.00000			0.0909091
$122$			2.18125i			0.197481i
$123$			2.55245i			0.230147i
$124$	7.14794			0.641904
$125$	8.32042	+	7.46797i	0.744201	+	0.667956i
$126$	9.52458			0.848517
$127$			2.55331i			0.226569i	0.993563	+	0.113285i	$0.0361372\pi$
$127$			2.55331i			0.226569i	−0.993563	+	0.113285i	$0.963863\pi$
$128$			0.764153i			0.0675422i
$129$	6.62551			0.583344
$130$	−6.89383	+	7.14630i	−0.604629	+	0.626772i
$131$	9.70628			0.848042			0.424021	−	0.905652i	$-0.360618\pi$
$131$	9.70628			0.848042			0.424021	+	0.905652i	$0.360618\pi$
$132$		−	2.00019i		−	0.174095i
$133$			3.97400i			0.344589i
$134$	6.18875			0.534627
$135$	−2.74149	−	2.64464i	−0.235950	−	0.227614i
$136$	−8.15522			−0.699305
$137$			1.69495i			0.144809i	0.997375	+	0.0724046i	$0.0230673\pi$
$137$			1.69495i			0.144809i	−0.997375	+	0.0724046i	$0.976933\pi$
$138$			2.91157i			0.247849i
$139$	18.6021			1.57781			0.788904	−	0.614517i	$-0.210649\pi$
$139$	18.6021			1.57781			0.788904	+	0.614517i	$0.210649\pi$
$140$	−5.57917	−	5.38207i	−0.471526	−	0.454868i
$141$	16.6412			1.40145
$142$			2.75442i			0.231146i
$143$			4.18176i			0.349696i
$144$	3.37248			0.281040
$145$	−11.4226	+	11.8409i	−0.948593	+	0.983333i
$146$	5.68182			0.470231
$147$		−	20.1600i		−	1.66277i
$148$		−	1.25434i		−	0.103106i
$149$	1.76860			0.144889			0.0724447	−	0.997372i	$-0.476920\pi$
$149$	1.76860			0.144889			0.0724447	+	0.997372i	$0.476920\pi$
$150$	0.437668	+	12.1658i	0.0357354	+	0.993336i
$151$	−5.47826			−0.445815			−0.222907	−	0.974840i	$-0.571555\pi$
$151$	−5.47826			−0.445815			−0.222907	+	0.974840i	$0.571555\pi$
$152$			3.05017i			0.247401i
$153$		−	6.03459i		−	0.487868i
$154$	4.21998			0.340056
$155$	−12.7203	+	13.1862i	−1.02172	+	1.05914i
$156$	8.36432			0.669682
$157$			10.1222i			0.807842i	0.914794	+	0.403921i	$0.132353\pi$
$157$			10.1222i			0.807842i	−0.914794	+	0.403921i	$0.867647\pi$
$158$			1.52219i			0.121099i
$159$	−28.1012			−2.22857
$160$	−7.26383	−	7.00721i	−0.574256	−	0.553968i
$161$	4.75228			0.374532
$162$		−	11.3378i		−	0.890782i
$163$		−	6.10691i		−	0.478330i	−0.970979	−	0.239165i	$-0.923126\pi$
$163$		−	6.10691i		−	0.478330i	0.970979	−	0.239165i	$-0.0768737\pi$
$164$	0.971158			0.0758347
$165$	3.68986	+	3.55950i	0.287255	+	0.277107i
$166$	−11.0932			−0.860997
$167$			18.4489i			1.42762i	0.700342	+	0.713808i	$0.253031\pi$
$167$			18.4489i			1.42762i	−0.700342	+	0.713808i	$0.746969\pi$
$168$		−	27.7921i		−	2.14421i
$169$	−4.48708			−0.345160
$170$	4.40772	−	4.56914i	0.338057	−	0.350437i
$171$	−2.25702			−0.172599
$172$		−	2.52088i		−	0.192215i
$173$			25.5672i			1.94384i	0.235313	+	0.971920i	$0.424389\pi$
$173$			25.5672i			1.94384i	−0.235313	+	0.971920i	$0.575611\pi$
$174$	−17.9142			−1.35807
$175$	19.8571	−	0.714364i	1.50106	−	0.0540009i
$176$	1.49422			0.112631
$177$			3.40610i			0.256018i
$178$		−	17.5114i		−	1.31254i
$179$	−15.7992			−1.18089			−0.590444	−	0.807079i	$-0.701047\pi$
$179$	−15.7992			−1.18089			−0.590444	+	0.807079i	$0.701047\pi$
$180$	3.05673	−	3.16867i	0.227835	−	0.236179i
$181$	−2.24707			−0.167023			−0.0835117	−	0.996507i	$-0.526614\pi$
$181$	−2.24707			−0.167023			−0.0835117	+	0.996507i	$0.526614\pi$
$182$			17.6469i			1.30808i
$183$			4.70969i			0.348150i
$184$	3.64752			0.268899
$185$	2.31394	+	2.23219i	0.170124	+	0.164114i
$186$	−19.9495			−1.46277
$187$		−	2.67370i		−	0.195520i
$188$		−	6.33167i		−	0.461785i
$189$	−6.76978			−0.492429
$190$	−1.70892	−	1.64855i	−0.123978	−	0.119598i
$191$	−5.54345			−0.401110			−0.200555	−	0.979682i	$-0.564274\pi$
$191$	−5.54345			−0.401110			−0.200555	+	0.979682i	$0.564274\pi$
$192$		−	17.8414i		−	1.28760i
$193$			20.8236i			1.49892i	0.662051	+	0.749459i	$0.269686\pi$
$193$			20.8236i			1.49892i	−0.662051	+	0.749459i	$0.730314\pi$
$194$	−5.17946			−0.371863
$195$	−14.8850	+	15.4301i	−1.06593	+	1.10497i
$196$	−7.67048			−0.547892
$197$		−	21.2333i		−	1.51281i	−0.654105	−	0.756404i	$-0.726954\pi$
$197$		−	21.2333i		−	1.51281i	0.654105	−	0.756404i	$-0.273046\pi$
$198$			2.39672i			0.170328i
$199$	−14.7763			−1.04746			−0.523731	−	0.851884i	$-0.675460\pi$
$199$	−14.7763			−1.04746			−0.523731	+	0.851884i	$0.675460\pi$
$200$	15.2410	−	0.548297i	1.07770	−	0.0387704i
$201$	13.3626			0.942523
$202$			3.65591i			0.257229i
$203$			29.2397i			2.05222i
$204$	−5.34791			−0.374429
$205$	−1.72825	+	1.79154i	−0.120706	+	0.125127i
$206$	11.4453			0.797433
$207$			2.69904i			0.187596i
$208$			6.24846i			0.433252i
$209$	−1.00000			−0.0691714
$210$	15.5711	+	15.0210i	1.07451	+	1.03655i
$211$	15.1649			1.04399			0.521996	−	0.852948i	$-0.325187\pi$
$211$	15.1649			1.04399			0.521996	+	0.852948i	$0.325187\pi$
$212$			10.6920i			0.734328i
$213$			5.94727i			0.407500i
$214$	16.3253			1.11598
$215$	4.65039	+	4.48610i	0.317154	+	0.305949i
$216$	−5.19602			−0.353544
$217$			32.5616i			2.21043i
$218$		−	20.2181i		−	1.36934i
$219$	12.2680			0.828996
$220$	1.35432	−	1.40392i	0.0913083	−	0.0946522i
$221$	11.1807			0.752099
$222$			3.50077i			0.234957i
$223$		−	22.8207i		−	1.52819i	−0.645104	−	0.764095i	$-0.723186\pi$
$223$		−	22.8207i		−	1.52819i	0.645104	−	0.764095i	$-0.276814\pi$
$224$	−17.9371			−1.19848
$225$	0.405721	+	11.2778i	0.0270481	+	0.751854i
$226$	18.2605			1.21467
$227$			26.4129i			1.75309i	0.481323	+	0.876543i	$0.340156\pi$
$227$			26.4129i			1.75309i	−0.481323	+	0.876543i	$0.659844\pi$
$228$			2.00019i			0.132466i
$229$	−15.7805			−1.04280			−0.521402	−	0.853311i	$-0.674591\pi$
$229$	−15.7805			−1.04280			−0.521402	+	0.853311i	$0.674591\pi$
$230$	−1.97141	+	2.04360i	−0.129991	+	0.134751i
$231$	9.11166			0.599503
$232$			22.4423i			1.47341i
$233$		−	6.73979i		−	0.441538i	−0.975326	−	0.220769i	$-0.929143\pi$
$233$		−	6.73979i		−	0.441538i	0.975326	−	0.220769i	$-0.0708567\pi$
$234$	−10.0225			−0.655192
$235$	11.6804	+	11.2677i	0.761942	+	0.735024i
$236$	1.29595			0.0843594
$237$			3.28667i			0.213492i
$238$		−	11.2829i		−	0.731365i
$239$	0.567512			0.0367093			0.0183547	−	0.999832i	$-0.494157\pi$
$239$	0.567512			0.0367093			0.0183547	+	0.999832i	$0.494157\pi$
$240$	5.51345	+	5.31867i	0.355892	+	0.343319i
$241$	9.40952			0.606120			0.303060	−	0.952971i	$-0.401992\pi$
$241$	9.40952			0.606120			0.303060	+	0.952971i	$0.401992\pi$
$242$			1.06190i			0.0682614i
$243$		−	19.3697i		−	1.24257i
$244$	1.79194			0.114717
$245$	13.6502	−	14.1501i	0.872081	−	0.904018i
$246$	−2.71044			−0.172811
$247$		−	4.18176i		−	0.266079i
$248$			24.9921i			1.58700i
$249$	−23.9520			−1.51790
$250$	−7.93022	+	8.83543i	−0.501551	+	0.558802i
$251$	4.91876			0.310469			0.155235	−	0.987878i	$-0.450387\pi$
$251$	4.91876			0.310469			0.155235	+	0.987878i	$0.450387\pi$
$252$		−	7.82466i		−	0.492907i
$253$			1.19584i			0.0751820i
$254$	−2.71135			−0.170125
$255$	9.51703	−	9.86556i	0.595979	−	0.617806i
$256$	−16.3743			−1.02340
$257$			23.1171i			1.44200i	0.692933	+	0.721002i	$0.256318\pi$
$257$			23.1171i			1.44200i	−0.692933	+	0.721002i	$0.743682\pi$
$258$			7.03561i			0.438018i
$259$	5.71399			0.355050
$260$	5.87085	+	5.66344i	0.364095	+	0.351232i
$261$	−16.6066			−1.02792
$262$			10.3071i			0.636773i
$263$		−	8.80241i		−	0.542780i	−0.962469	−	0.271390i	$-0.912517\pi$
$263$		−	8.80241i		−	0.542780i	0.962469	−	0.271390i	$-0.0874833\pi$
$264$	6.99348			0.430419
$265$	−19.7240	−	19.0272i	−1.21164	−	1.16883i
$266$	−4.21998			−0.258744
$267$		−	37.8101i		−	2.31394i
$268$		−	5.08420i		−	0.310567i
$269$	−28.4095			−1.73216			−0.866080	−	0.499906i	$-0.833368\pi$
$269$	−28.4095			−1.73216			−0.866080	+	0.499906i	$0.833368\pi$
$270$	2.80834	−	2.91118i	0.170910	−	0.177169i
$271$	24.8817			1.51146			0.755728	−	0.654886i	$-0.227283\pi$
$271$	24.8817			1.51146			0.755728	+	0.654886i	$0.227283\pi$
$272$		−	3.99509i		−	0.242238i
$273$			38.1027i			2.30608i
$274$	−1.79986			−0.108734
$275$	0.179760	+	4.99677i	0.0108399	+	0.301316i
$276$	2.39192			0.143977
$277$		−	8.38659i		−	0.503901i	−0.967740	−	0.251951i	$-0.918928\pi$
$277$		−	8.38659i		−	0.503901i	0.967740	−	0.251951i	$-0.0810721\pi$
$278$			19.7535i			1.18474i
$279$	−18.4933			−1.10716
$280$	18.8179	−	19.5070i	1.12458	−	1.16577i
$281$	20.3224			1.21233			0.606166	−	0.795338i	$-0.292707\pi$
$281$	20.3224			1.21233			0.606166	+	0.795338i	$0.292707\pi$
$282$			17.6713i			1.05231i
$283$		−	6.49096i		−	0.385848i	−0.981214	−	0.192924i	$-0.938203\pi$
$283$		−	6.49096i		−	0.385848i	0.981214	−	0.192924i	$-0.0617970\pi$
$284$	2.26282			0.134274
$285$	−3.68986	−	3.55950i	−0.218568	−	0.210847i
$286$	−4.44060			−0.262578
$287$			4.42400i			0.261141i
$288$		−	10.1873i		−	0.600295i
$289$	9.85134			0.579491
$290$	−12.5738	−	12.1296i	−0.738360	−	0.712275i
$291$	−11.1833			−0.655579
$292$		−	4.66774i		−	0.273159i
$293$			15.0800i			0.880984i	0.897756	+	0.440492i	$0.145196\pi$
$293$			15.0800i			0.880984i	−0.897756	+	0.440492i	$0.854804\pi$
$294$	21.4078			1.24853
$295$	−2.30625	+	2.39071i	−0.134275	+	0.139192i
$296$	4.38566			0.254911
$297$		−	1.70352i		−	0.0988482i
$298$			1.87807i			0.108794i
$299$	−5.00072			−0.289199
$300$	9.99451	−	0.359554i	0.577033	−	0.0207589i
$301$	11.4836			0.661902
$302$		−	5.81735i		−	0.334751i
$303$			7.89374i			0.453484i
$304$	−1.49422			−0.0856993
$305$	−3.18890	+	3.30569i	−0.182596	+	0.189283i
$306$	6.40812			0.366328
$307$			31.3111i			1.78702i	0.449047	+	0.893508i	$0.351764\pi$
$307$			31.3111i			1.78702i	−0.449047	+	0.893508i	$0.648236\pi$
$308$		−	3.46681i		−	0.197540i
$309$	24.7124			1.40584
$310$	−14.0024	−	13.5077i	−0.795280	−	0.767185i
$311$	24.6549			1.39805			0.699025	−	0.715097i	$-0.253617\pi$
$311$	24.6549			1.39805			0.699025	+	0.715097i	$0.253617\pi$
$312$			29.2450i			1.65567i
$313$		−	7.22175i		−	0.408198i	−0.978950	−	0.204099i	$-0.934574\pi$
$313$		−	7.22175i		−	0.408198i	0.978950	−	0.204099i	$-0.0654264\pi$
$314$	−10.7488			−0.606588
$315$	14.4345	+	13.9246i	0.813294	+	0.784562i
$316$	1.25052			0.0703470
$317$		−	13.3791i		−	0.751448i	−0.926732	−	0.375724i	$-0.877394\pi$
$317$		−	13.3791i		−	0.751448i	0.926732	−	0.375724i	$-0.122606\pi$
$318$		−	29.8406i		−	1.67338i
$319$	−7.35774			−0.411955
$320$	12.0804	−	12.5228i	0.675312	−	0.700044i
$321$	35.2491			1.96742
$322$			5.04643i			0.281227i
$323$			2.67370i			0.148769i
$324$	−9.31426			−0.517459
$325$	−20.8953	+	0.751711i	−1.15906	+	0.0416974i
$326$	6.48492			0.359166
$327$		−	43.6544i		−	2.41409i
$328$			3.39556i			0.187488i
$329$	28.8432			1.59018
$330$	−3.77983	+	3.91825i	−0.208073	+	0.215693i
$331$	30.9625			1.70185			0.850927	−	0.525284i	$-0.176041\pi$
$331$	30.9625			1.70185			0.850927	+	0.525284i	$0.176041\pi$
$332$			9.11329i			0.500157i
$333$			3.24524i			0.177838i
$334$	−19.5908			−1.07196
$335$	9.37908	+	9.04773i	0.512434	+	0.494330i
$336$	13.6148			0.742749
$337$		−	11.3436i		−	0.617924i	−0.951074	−	0.308962i	$-0.900018\pi$
$337$		−	11.3436i		−	0.617924i	0.951074	−	0.308962i	$-0.0999817\pi$
$338$		−	4.76482i		−	0.259172i
$339$	39.4276			2.14141
$340$	−3.75366	−	3.62105i	−0.203571	−	0.196379i
$341$	−8.19367			−0.443712
$342$		−	2.39672i		−	0.129600i
$343$		−	7.12403i		−	0.384662i
$344$	8.81400			0.475219
$345$	−4.25661	+	4.41249i	−0.229168	+	0.237561i
$346$	−27.1498			−1.45958
$347$			5.13673i			0.275754i	0.990449	+	0.137877i	$0.0440279\pi$
$347$			5.13673i			0.275754i	−0.990449	+	0.137877i	$0.955972\pi$
$348$			14.7169i			0.788909i
$349$	−9.51024			−0.509071			−0.254536	−	0.967063i	$-0.581923\pi$
$349$	−9.51024			−0.509071			−0.254536	+	0.967063i	$0.581923\pi$
$350$	0.758582	+	21.0863i	0.0405479	+	1.12711i
$351$	7.12370			0.380235
$352$		−	4.51363i		−	0.240577i
$353$			21.6537i			1.15251i	0.817269	+	0.576256i	$0.195487\pi$
$353$			21.6537i			1.15251i	−0.817269	+	0.576256i	$0.804513\pi$
$354$	−3.61692			−0.192237
$355$	−4.02687	+	4.17434i	−0.213724	+	0.221551i
$356$	−14.3860			−0.762457
$357$		−	24.3618i		−	1.28936i
$358$		−	16.7771i		−	0.886699i
$359$	−1.79729			−0.0948574			−0.0474287	−	0.998875i	$-0.515103\pi$
$359$	−1.79729			−0.0948574			−0.0474287	+	0.998875i	$0.515103\pi$
$360$	11.0790	+	10.6876i	0.583912	+	0.563284i
$361$	1.00000			0.0526316
$362$		−	2.38616i		−	0.125414i
$363$			2.29282i			0.120342i
$364$	14.4974			0.759868
$365$	8.61082	+	8.30661i	0.450711	+	0.434788i
$366$	−5.00120			−0.261417
$367$		−	36.4138i		−	1.90078i	−0.311055	−	0.950392i	$-0.600682\pi$
$367$		−	36.4138i		−	1.90078i	0.311055	−	0.950392i	$-0.399318\pi$
$368$			1.78685i			0.0931460i
$369$	−2.51260			−0.130801
$370$	−2.37036	+	2.45716i	−0.123229	+	0.127742i
$371$	−48.7061			−2.52869
$372$			16.3889i			0.849727i
$373$		−	22.3236i		−	1.15587i	−0.816083	−	0.577935i	$-0.803859\pi$
$373$		−	22.3236i		−	1.15587i	0.816083	−	0.577935i	$-0.196141\pi$
$374$	2.83919			0.146811
$375$	−17.1227	+	19.0772i	−0.884213	+	0.985143i
$376$	22.1381			1.14168
$377$		−	30.7683i		−	1.58465i
$378$		−	7.18882i		−	0.369753i
$379$	−13.6221			−0.699718			−0.349859	−	0.936802i	$-0.613771\pi$
$379$	−13.6221			−0.699718			−0.349859	+	0.936802i	$0.613771\pi$
$380$	−1.35432	+	1.40392i	−0.0694752	+	0.0720195i
$381$	−5.85427			−0.299924
$382$		−	5.88657i		−	0.301183i
$383$		−	28.6568i		−	1.46429i	−0.681147	−	0.732146i	$-0.738519\pi$
$383$		−	28.6568i		−	1.46429i	0.681147	−	0.732146i	$-0.261481\pi$
$384$	−1.75206			−0.0894096
$385$	6.39540	+	6.16946i	0.325940	+	0.314425i
$386$	−22.1126			−1.12550
$387$			6.52206i			0.331535i
$388$			4.25504i			0.216017i
$389$	−11.7318			−0.594828			−0.297414	−	0.954749i	$-0.596124\pi$
$389$	−11.7318			−0.594828			−0.297414	+	0.954749i	$0.596124\pi$
$390$	−16.3852	−	15.8063i	−0.829695	−	0.800384i
$391$	3.19732			0.161696
$392$		−	26.8191i		−	1.35457i
$393$			22.2547i			1.12260i
$394$	22.5476			1.13593
$395$	−2.22539	+	2.30689i	−0.111972	+	0.116072i
$396$	1.96896			0.0989442
$397$			32.3652i			1.62436i	0.583404	+	0.812182i	$0.301720\pi$
$397$			32.3652i			1.62436i	−0.583404	+	0.812182i	$0.698280\pi$
$398$		−	15.6909i		−	0.786513i
$399$	−9.11166			−0.456154
$400$	0.268600	+	7.46626i	0.0134300	+	0.373313i
$401$	−28.1976			−1.40812			−0.704061	−	0.710140i	$-0.748632\pi$
$401$	−28.1976			−1.40812			−0.704061	+	0.710140i	$0.748632\pi$
$402$			14.1897i			0.707717i
$403$		−	34.2639i		−	1.70681i
$404$	3.00342			0.149426
$405$	16.5755	−	17.1825i	0.823641	−	0.853804i
$406$	−31.0495			−1.54096
$407$			1.43784i			0.0712713i
$408$		−	18.6985i		−	0.925711i
$409$	31.1557			1.54055			0.770275	−	0.637711i	$-0.220119\pi$
$409$	31.1557			1.54055			0.770275	+	0.637711i	$0.220119\pi$
$410$	−1.90244	−	1.83523i	−0.0939546	−	0.0906354i
$411$	−3.88621			−0.191693
$412$		−	9.40259i		−	0.463232i
$413$			5.90357i			0.290496i
$414$	−2.86611			−0.140861
$415$	−16.8117	−	16.2178i	−0.825256	−	0.796101i
$416$	18.8749			0.925417
$417$			42.6512i			2.08864i
$418$		−	1.06190i		−	0.0519391i
$419$	15.5968			0.761953			0.380976	−	0.924585i	$-0.375588\pi$
$419$	15.5968			0.761953			0.380976	+	0.924585i	$0.375588\pi$
$420$	12.3401	−	12.7920i	0.602136	−	0.624187i
$421$	−9.69298			−0.472407			−0.236204	−	0.971704i	$-0.575903\pi$
$421$	−9.69298			−0.472407			−0.236204	+	0.971704i	$0.575903\pi$
$422$			16.1035i			0.783908i
$423$			16.3814i			0.796492i
$424$	−37.3834			−1.81550
$425$	13.3598	−	0.480623i	0.648048	−	0.0233136i
$426$	−6.31540			−0.305982
$427$			8.16300i			0.395035i
$428$		−	13.4116i		−	0.648275i
$429$	−9.58801			−0.462913
$430$	−4.76378	+	4.93824i	−0.229730	+	0.238143i
$431$	−35.7997			−1.72441			−0.862205	−	0.506560i	$-0.830917\pi$
$431$	−35.7997			−1.72441			−0.862205	+	0.506560i	$0.830917\pi$
$432$		−	2.54543i		−	0.122467i
$433$		−	2.32394i		−	0.111682i	−0.998440	−	0.0558408i	$-0.982216\pi$
$433$		−	2.32394i		−	0.111682i	0.998440	−	0.0558408i	$-0.0177839\pi$
$434$	−34.5771			−1.65976
$435$	−27.1490	−	26.1899i	−1.30170	−	1.25571i
$436$	−16.6096			−0.795458
$437$		−	1.19584i		−	0.0572049i
$438$			13.0274i			0.622472i
$439$	−13.4385			−0.641384			−0.320692	−	0.947183i	$-0.603916\pi$
$439$	−13.4385			−0.641384			−0.320692	+	0.947183i	$0.603916\pi$
$440$	4.90866	+	4.73525i	0.234011	+	0.225744i
$441$	19.8452			0.945010
$442$			11.8728i			0.564732i
$443$		−	15.5860i		−	0.740516i	−0.928929	−	0.370258i	$-0.879269\pi$
$443$		−	15.5860i		−	0.740516i	0.928929	−	0.370258i	$-0.120731\pi$
$444$	2.87597			0.136487
$445$	25.6010	−	26.5386i	1.21361	−	1.25805i
$446$	24.2333			1.14748
$447$			4.05508i			0.191799i
$448$		−	30.9235i		−	1.46100i
$449$	23.0527			1.08793			0.543963	−	0.839109i	$-0.316923\pi$
$449$	23.0527			1.08793			0.543963	+	0.839109i	$0.316923\pi$
$450$	−11.9759	+	0.430834i	−0.564548	+	0.0203097i
$451$	−1.11324			−0.0524203
$452$		−	15.0014i		−	0.705608i
$453$		−	12.5607i		−	0.590151i
$454$	−28.0478			−1.31635
$455$	−25.7992	+	26.7440i	−1.20948	+	1.25378i
$456$	−6.99348			−0.327500
$457$		−	20.9075i		−	0.978013i	−0.872280	−	0.489007i	$-0.837359\pi$
$457$		−	20.9075i		−	0.978013i	0.872280	−	0.489007i	$-0.162641\pi$
$458$		−	16.7573i		−	0.783015i
$459$	−4.55469			−0.212595
$460$	1.67887	+	1.61956i	0.0782776	+	0.0755122i
$461$	6.85175			0.319118			0.159559	−	0.987188i	$-0.448993\pi$
$461$	6.85175			0.319118			0.159559	+	0.987188i	$0.448993\pi$
$462$			9.67565i			0.450152i
$463$			24.2362i			1.12635i	0.826338	+	0.563175i	$0.190420\pi$
$463$			24.2362i			1.12635i	−0.826338	+	0.563175i	$0.809580\pi$
$464$	−10.9941			−0.510387
$465$	−30.2335	−	29.1654i	−1.40204	−	1.35251i
$466$	7.15697			0.331540
$467$		−	15.8851i		−	0.735076i	−0.930008	−	0.367538i	$-0.880201\pi$
$467$		−	15.8851i		−	0.735076i	0.930008	−	0.367538i	$-0.119799\pi$
$468$			8.23373i			0.380604i
$469$	23.1605			1.06945
$470$	−11.9652	+	12.4033i	−0.551911	+	0.572123i
$471$	−23.2084			−1.06939
$472$			4.53117i			0.208564i
$473$			2.88968i			0.132868i
$474$	−3.49011			−0.160306
$475$	−0.179760	−	4.99677i	−0.00824794	−	0.229267i
$476$	−9.26920			−0.424853
$477$		−	27.6625i		−	1.26658i
$478$			0.602640i			0.0275641i
$479$	17.9382			0.819616			0.409808	−	0.912172i	$-0.365596\pi$
$479$	17.9382			0.819616			0.409808	+	0.912172i	$0.365596\pi$
$480$	16.0663	−	16.6546i	0.733321	−	0.760177i
$481$	−6.01271			−0.274156
$482$			9.99195i			0.455121i
$483$			10.8961i			0.495790i
$484$	0.872373			0.0396533
$485$	−7.84949	−	7.57218i	−0.356427	−	0.343835i
$486$	20.5686			0.933012
$487$		−	1.52634i		−	0.0691652i	−0.999402	−	0.0345826i	$-0.988990\pi$
$487$		−	1.52634i		−	0.0691652i	0.999402	−	0.0345826i	$-0.0110102\pi$
$488$			6.26536i			0.283619i
$489$	14.0020			0.633194
$490$	15.0260	+	14.4951i	0.678805	+	0.654824i
$491$	4.24560			0.191601			0.0958005	−	0.995401i	$-0.469459\pi$
$491$	4.24560			0.191601			0.0958005	+	0.995401i	$0.469459\pi$
$492$			2.22669i			0.100387i
$493$			19.6724i			0.885999i
$494$	4.44060			0.199792
$495$	−3.50392	+	3.63225i	−0.157490	+	0.163257i
$496$	−12.2431			−0.549733
$497$			10.3080i			0.462378i
$498$		−	25.4346i		−	1.13975i
$499$	9.48978			0.424821			0.212410	−	0.977181i	$-0.431869\pi$
$499$	9.48978			0.424821			0.212410	+	0.977181i	$0.431869\pi$
$500$	7.25851	+	6.51486i	0.324610	+	0.291353i
$501$	−42.2999			−1.88982
$502$			5.22321i			0.233123i
$503$		−	20.2931i		−	0.904827i	−0.891808	−	0.452413i	$-0.850563\pi$
$503$		−	20.2931i		−	0.904827i	0.891808	−	0.452413i	$-0.149437\pi$
$504$	27.3581			1.21863
$505$	−5.34481	+	5.54055i	−0.237841	+	0.246551i
$506$	−1.26986			−0.0564523
$507$		−	10.2881i		−	0.456909i
$508$			2.22744i			0.0988266i
$509$	−0.290145			−0.0128604			−0.00643022	−	0.999979i	$-0.502047\pi$
$509$	−0.290145			−0.0128604			−0.00643022	+	0.999979i	$0.502047\pi$
$510$	10.4762	+	10.1061i	0.463895	+	0.447506i
$511$	21.2634			0.940637
$512$		−	15.8596i		−	0.700901i
$513$			1.70352i			0.0752122i
$514$	−24.5480			−1.08276
$515$	17.3454	+	16.7326i	0.764331	+	0.737328i
$516$	5.77992			0.254447
$517$			7.25799i			0.319206i
$518$			6.06767i			0.266598i
$519$	−58.6210			−2.57318
$520$	−19.8017	+	20.5268i	−0.868360	+	0.900161i
$521$	14.9754			0.656085			0.328043	−	0.944663i	$-0.393611\pi$
$521$	14.9754			0.656085			0.328043	+	0.944663i	$0.393611\pi$
$522$		−	17.6345i		−	0.771840i
$523$			5.79311i			0.253315i	0.991947	+	0.126657i	$0.0404249\pi$
$523$			5.79311i			0.253315i	−0.991947	+	0.126657i	$0.959575\pi$
$524$	8.46750			0.369904
$525$	1.63791	+	45.5288i	0.0714842	+	1.98704i
$526$	9.34726			0.407560
$527$			21.9074i			0.954302i
$528$			3.42597i			0.149096i
$529$	21.5700			0.937824
$530$	20.2049	−	20.9449i	0.877646	−	0.909787i
$531$	−3.35291			−0.145504
$532$			3.46681i			0.150305i
$533$		−	4.65529i		−	0.201643i
$534$	40.1505			1.73748
$535$	24.7411	+	23.8670i	1.06965	+	1.03186i
$536$	17.7764			0.767824
$537$		−	36.2247i		−	1.56321i
$538$		−	30.1680i		−	1.30064i
$539$	8.79266			0.378727
$540$	−2.39160	−	2.30711i	−0.102918	−	0.0992823i
$541$	18.0927			0.777864			0.388932	−	0.921266i	$-0.372844\pi$
$541$	18.0927			0.777864			0.388932	+	0.921266i	$0.372844\pi$
$542$			26.4218i			1.13491i
$543$		−	5.15213i		−	0.221099i
$544$	−12.0681			−0.517414
$545$	29.5581	−	30.6406i	1.26613	−	1.31250i
$546$	−40.4612			−1.73158
$547$		−	30.3317i		−	1.29689i	−0.761261	−	0.648446i	$-0.775419\pi$
$547$		−	30.3317i		−	1.29689i	0.761261	−	0.648446i	$-0.224581\pi$
$548$			1.47863i			0.0631639i
$549$	−4.63615			−0.197866
$550$	−5.30606	+	0.190886i	−0.226251	+	0.00813942i
$551$	7.35774			0.313450
$552$			8.36311i			0.355957i
$553$			5.69658i			0.242243i
$554$	8.90570			0.378367
$555$	−5.11801	+	5.30544i	−0.217247	+	0.225203i
$556$	16.2280			0.688218
$557$			39.4118i			1.66993i	0.550301	+	0.834966i	$0.314513\pi$
$557$			39.4118i			1.66993i	−0.550301	+	0.834966i	$0.685487\pi$
$558$		−	19.6380i		−	0.831342i
$559$	−12.0839			−0.511096
$560$	9.55612	+	9.21852i	0.403820	+	0.389553i
$561$	6.13030			0.258822
$562$			21.5803i			0.910311i
$563$			21.6096i			0.910734i	0.890304	+	0.455367i	$0.150492\pi$
$563$			21.6096i			0.910734i	−0.890304	+	0.455367i	$0.849508\pi$
$564$	14.5174			0.611292
$565$	27.6739	+	26.6962i	1.16425	+	1.12312i
$566$	6.89274			0.289723
$567$		−	42.4301i		−	1.78190i
$568$			7.91173i			0.331969i
$569$	6.12575			0.256805			0.128402	−	0.991722i	$-0.459015\pi$
$569$	6.12575			0.256805			0.128402	+	0.991722i	$0.459015\pi$
$570$	3.77983	−	3.91825i	0.158320	−	0.164117i
$571$	−4.18229			−0.175023			−0.0875117	−	0.996163i	$-0.527892\pi$
$571$	−4.18229			−0.175023			−0.0875117	+	0.996163i	$0.527892\pi$
$572$			3.64805i			0.152533i
$573$		−	12.7101i		−	0.530973i
$574$	−4.69784			−0.196084
$575$	−5.97535	+	0.214964i	−0.249189	+	0.00896463i
$576$	17.5629			0.731787
$577$		−	2.00273i		−	0.0833748i	−0.999131	−	0.0416874i	$-0.986727\pi$
$577$		−	2.00273i		−	0.0833748i	0.999131	−	0.0416874i	$-0.0132734\pi$
$578$			10.4611i			0.435125i
$579$	−47.7448			−1.98421
$580$	−9.96475	+	10.3297i	−0.413764	+	0.428917i
$581$	−41.5146			−1.72231
$582$		−	11.8756i		−	0.492258i
$583$		−	12.2562i		−	0.507599i
$584$	16.3203			0.675339
$585$	−15.1892	−	14.6526i	−0.627995	−	0.605809i
$586$	−16.0134			−0.661509
$587$		−	28.9666i		−	1.19558i	−0.801652	−	0.597791i	$-0.796045\pi$
$587$		−	28.9666i		−	1.19558i	0.801652	−	0.597791i	$-0.203955\pi$
$588$		−	17.5870i		−	0.725277i
$589$	8.19367			0.337614
$590$	−2.53869	−	2.44900i	−0.104516	−	0.100824i
$591$	48.6841			2.00259
$592$			2.14845i			0.0883009i
$593$		−	8.57526i		−	0.352144i	−0.984377	−	0.176072i	$-0.943661\pi$
$593$		−	8.57526i		−	0.352144i	0.984377	−	0.176072i	$-0.0563391\pi$
$594$	1.80896			0.0742227
$595$	16.4953	−	17.0994i	0.676240	−	0.701005i
$596$	1.54288			0.0631988
$597$		−	33.8793i		−	1.38659i
$598$		−	5.31026i		−	0.217153i
$599$	−23.9694			−0.979363			−0.489682	−	0.871901i	$-0.662887\pi$
$599$	−23.9694			−0.979363			−0.489682	+	0.871901i	$0.662887\pi$
$600$	1.25715	+	34.9448i	0.0513227	+	1.42662i
$601$	8.92319			0.363985			0.181992	−	0.983300i	$-0.441745\pi$
$601$	8.92319			0.363985			0.181992	+	0.983300i	$0.441745\pi$
$602$			12.1944i			0.497006i
$603$			13.1539i			0.535670i
$604$	−4.77909			−0.194458
$605$	−1.55246	+	1.60931i	−0.0631163	+	0.0654278i
$606$	−8.38235			−0.340510
$607$		−	14.6248i		−	0.593601i	−0.954940	−	0.296800i	$-0.904080\pi$
$607$		−	14.6248i		−	0.593601i	0.954940	−	0.296800i	$-0.0959196\pi$
$608$			4.51363i			0.183052i
$609$	−67.0413			−2.71665
$610$	−3.51030	−	3.38629i	−0.142128	−	0.137107i
$611$	−30.3511			−1.22788
$612$		−	5.26441i		−	0.212801i
$613$		−	26.9022i		−	1.08657i	−0.839548	−	0.543285i	$-0.817180\pi$
$613$		−	26.9022i		−	1.08657i	0.839548	−	0.543285i	$-0.182820\pi$
$614$	−33.2491			−1.34183
$615$	−4.10769	−	3.96257i	−0.165638	−	0.159786i
$616$	12.1214			0.488383
$617$		−	46.7800i		−	1.88329i	−0.336605	−	0.941646i	$-0.609279\pi$
$617$		−	46.7800i		−	1.88329i	0.336605	−	0.941646i	$-0.390721\pi$
$618$			26.2420i			1.05561i
$619$	−7.13924			−0.286950			−0.143475	−	0.989654i	$-0.545828\pi$
$619$	−7.13924			−0.286950			−0.143475	+	0.989654i	$0.545828\pi$
$620$	−11.0969	+	11.5033i	−0.445661	+	0.461982i
$621$	2.03714			0.0817477
$622$			26.1810i			1.04976i
$623$		−	65.5339i		−	2.62556i
$624$	−14.3266			−0.573522
$625$	−24.9354	+	1.79643i	−0.997415	+	0.0718574i
$626$	7.66876			0.306505
$627$		−	2.29282i		−	0.0915664i
$628$			8.83036i			0.352370i
$629$	3.84436			0.153285
$630$	−14.7865	+	15.3280i	−0.589108	+	0.610682i
$631$	37.9146			1.50936			0.754679	−	0.656094i	$-0.227793\pi$
$631$	37.9146			1.50936			0.754679	+	0.656094i	$0.227793\pi$
$632$			4.37231i			0.173921i
$633$			34.7703i			1.38200i
$634$	14.2073			0.564243
$635$	−4.10906	−	3.96390i	−0.163063	−	0.157303i
$636$	−24.5148			−0.972073
$637$			36.7688i			1.45683i
$638$		−	7.81317i		−	0.309326i
$639$	−5.85441			−0.231597
$640$	−1.22976	−	1.18631i	−0.0486105	−	0.0468932i
$641$	6.64283			0.262376			0.131188	−	0.991358i	$-0.458121\pi$
$641$	6.64283			0.262376			0.131188	+	0.991358i	$0.458121\pi$
$642$			37.4310i			1.47728i
$643$			0.0628819i			0.00247982i	0.999999	+	0.00123991i	$0.000394676\pi$
$643$			0.0628819i			0.00247982i	−0.999999	+	0.00123991i	$0.999605\pi$
$644$	4.14576			0.163366
$645$	−10.2858	+	10.6625i	−0.405004	+	0.419836i
$646$	−2.83919			−0.111707
$647$		−	44.0501i		−	1.73179i	−0.500228	−	0.865894i	$-0.666750\pi$
$647$		−	44.0501i		−	1.73179i	0.500228	−	0.865894i	$-0.333250\pi$
$648$		−	32.5664i		−	1.27933i
$649$	−1.48555			−0.0583129
$650$	−0.798240	−	22.1886i	−0.0313095	−	0.870310i
$651$	−74.6580			−2.92608
$652$		−	5.32751i		−	0.208641i
$653$		−	21.6203i		−	0.846066i	−0.906114	−	0.423033i	$-0.860965\pi$
$653$		−	21.6203i		−	0.846066i	0.906114	−	0.423033i	$-0.139035\pi$
$654$	46.3565			1.81268
$655$	−15.0686	+	15.6204i	−0.588778	+	0.610340i
$656$	−1.66342			−0.0649456
$657$			12.0765i			0.471148i
$658$			30.6286i			1.19403i
$659$	18.1043			0.705242			0.352621	−	0.935766i	$-0.385291\pi$
$659$	18.1043			0.705242			0.352621	+	0.935766i	$0.385291\pi$
$660$	3.21893	+	3.10521i	0.125297	+	0.120870i
$661$	2.83007			0.110077			0.0550384	−	0.998484i	$-0.482472\pi$
$661$	2.83007			0.110077			0.0550384	+	0.998484i	$0.482472\pi$
$662$			32.8790i			1.27788i
$663$			25.6354i			0.995598i
$664$	−31.8637			−1.23655
$665$	−6.39540	−	6.16946i	−0.248003	−	0.239241i
$666$	−3.44611			−0.133534
$667$		−	8.79871i		−	0.340687i
$668$			16.0943i			0.622707i
$669$	52.3238			2.02296
$670$	−9.60777	+	9.95962i	−0.371180	+	0.384774i
$671$	−2.05410			−0.0792978
$672$		−	41.1266i		−	1.58649i
$673$			34.9461i			1.34707i	0.739154	+	0.673536i	$0.235226\pi$
$673$			34.9461i			1.34707i	−0.739154	+	0.673536i	$0.764774\pi$
$674$	12.0457			0.463984
$675$	8.51209	−	0.306224i	0.327630	−	0.0117866i
$676$	−3.91441			−0.150554
$677$		−	9.09646i		−	0.349605i	−0.984603	−	0.174803i	$-0.944071\pi$
$677$		−	9.09646i		−	0.349605i	0.984603	−	0.174803i	$-0.0559288\pi$
$678$			41.8681i			1.60793i
$679$	−19.3834			−0.743865
$680$	12.6606	−	13.1243i	0.485513	−	0.503293i
$681$	−60.5600			−2.32067
$682$		−	8.70084i		−	0.333173i
$683$		−	11.5565i		−	0.442196i	−0.975252	−	0.221098i	$-0.929036\pi$
$683$		−	11.5565i		−	0.442196i	0.975252	−	0.221098i	$-0.0709641\pi$
$684$	−1.96896			−0.0752852
$685$	−2.72770	−	2.63133i	−0.104220	−	0.100538i
$686$	7.56500			0.288833
$687$		−	36.1818i		−	1.38042i
$688$			4.31781i			0.164615i
$689$	51.2524			1.95256
$690$	−4.68561	−	4.52008i	−0.178378	−	0.172076i
$691$	29.0986			1.10696			0.553481	−	0.832862i	$-0.313299\pi$
$691$	29.0986			1.10696			0.553481	+	0.832862i	$0.313299\pi$
$692$			22.3042i			0.847877i
$693$			8.96939i			0.340719i
$694$	−5.45468			−0.207057
$695$	−28.8789	+	29.9365i	−1.09544	+	1.13556i
$696$	−51.4562			−1.95044
$697$			2.97646i			0.112741i
$698$		−	10.0989i		−	0.382249i
$699$	15.4531			0.584491
$700$	17.3228	−	0.623192i	0.654742	−	0.0235545i
$701$	−7.70772			−0.291117			−0.145558	−	0.989350i	$-0.546498\pi$
$701$	−7.70772			−0.291117			−0.145558	+	0.989350i	$0.546498\pi$
$702$			7.56464i			0.285509i
$703$		−	1.43784i		−	0.0542293i
$704$	7.78145			0.293274
$705$	−25.8348	+	26.7809i	−0.972995	+	1.00863i
$706$	−22.9941			−0.865393
$707$			13.6817i			0.514554i
$708$			2.97139i			0.111672i
$709$	5.82452			0.218744			0.109372	−	0.994001i	$-0.465116\pi$
$709$	5.82452			0.218744			0.109372	+	0.994001i	$0.465116\pi$
$710$	−4.43272	−	4.27612i	−0.166357	−	0.160480i
$711$	−3.23536			−0.121335
$712$		−	50.2993i		−	1.88505i
$713$		−	9.79835i		−	0.366951i
$714$	25.8698			0.968151
$715$	−6.72974	−	6.49199i	−0.251678	−	0.242787i
$716$	−13.7828			−0.515087
$717$			1.30120i			0.0485943i
$718$		−	1.90854i		−	0.0712260i
$719$	−20.0263			−0.746854			−0.373427	−	0.927660i	$-0.621817\pi$
$719$	−20.0263			−0.746854			−0.373427	+	0.927660i	$0.621817\pi$
$720$	−5.23563	+	5.42737i	−0.195120	+	0.202266i
$721$	42.8324			1.59516
$722$			1.06190i			0.0395197i
$723$			21.5743i			0.802358i
$724$	−1.96028			−0.0728534
$725$	−1.32263	−	36.7649i	−0.0491211	−	1.36542i
$726$	−2.43474			−0.0903617
$727$		−	41.4107i		−	1.53584i	−0.640548	−	0.767918i	$-0.721293\pi$
$727$		−	41.4107i		−	1.53584i	0.640548	−	0.767918i	$-0.278707\pi$
$728$			50.6886i			1.87864i
$729$	12.3804			0.458535
$730$	−8.82077	+	9.14381i	−0.326471	+	0.338428i
$731$	7.72613			0.285761
$732$			4.10860i			0.151858i
$733$			28.8233i			1.06461i	0.846552	+	0.532306i	$0.178674\pi$
$733$			28.8233i			1.06461i	−0.846552	+	0.532306i	$0.821326\pi$
$734$	38.6677			1.42725
$735$	32.4437	+	31.2975i	1.19670	+	1.15443i
$736$	5.39759			0.198958
$737$			5.82801i			0.214678i
$738$		−	2.66812i		−	0.0982149i
$739$	−37.3953			−1.37561			−0.687804	−	0.725896i	$-0.741425\pi$
$739$	−37.3953			−1.37561			−0.687804	+	0.725896i	$0.741425\pi$
$740$	2.01862	+	1.94730i	0.0742058	+	0.0715843i
$741$	9.58801			0.352224
$742$		−	51.7209i		−	1.89873i
$743$			19.1716i			0.703340i	0.936124	+	0.351670i	$0.114386\pi$
$743$			19.1716i			0.703340i	−0.936124	+	0.351670i	$0.885614\pi$
$744$	−57.3023			−2.10080
$745$	−2.74567	+	2.84623i	−0.100594	+	0.104278i
$746$	23.7053			0.867914
$747$		−	23.5781i		−	0.862676i
$748$		−	2.33246i		−	0.0852833i
$749$	61.0951			2.23237
$750$	−20.2581	−	18.1826i	−0.739719	−	0.663934i
$751$	−38.6860			−1.41167			−0.705836	−	0.708376i	$-0.749428\pi$
$751$	−38.6860			−1.41167			−0.705836	+	0.708376i	$0.749428\pi$
$752$			10.8450i			0.395477i
$753$			11.2778i			0.410986i
$754$	32.6728			1.18987
$755$	8.50476	−	8.81622i	0.309520	−	0.320855i
$756$	−5.90578			−0.214791
$757$		−	15.5683i		−	0.565839i	−0.959144	−	0.282920i	$-0.908697\pi$
$757$		−	15.5683i		−	0.565839i	0.959144	−	0.282920i	$-0.0913030\pi$
$758$		−	14.4652i		−	0.525401i
$759$	−2.74185			−0.0995229
$760$	−4.90866	−	4.73525i	−0.178056	−	0.171766i
$761$	13.1758			0.477622			0.238811	−	0.971066i	$-0.423242\pi$
$761$	13.1758			0.477622			0.238811	+	0.971066i	$0.423242\pi$
$762$		−	6.21664i		−	0.225205i
$763$		−	75.6633i		−	2.73920i
$764$	−4.83595			−0.174959
$765$	9.71152	+	9.36843i	0.351121	+	0.338716i
$766$	30.4306			1.09950
$767$		−	6.21220i		−	0.224310i
$768$		−	37.5434i		−	1.35473i
$769$	−3.76231			−0.135673			−0.0678363	−	0.997696i	$-0.521610\pi$
$769$	−3.76231			−0.135673			−0.0678363	+	0.997696i	$0.521610\pi$
$770$	−6.55133	+	6.79126i	−0.236094	+	0.244740i
$771$	−53.0033			−1.90887
$772$			18.1660i			0.653808i
$773$			21.5173i			0.773925i	0.922096	+	0.386962i	$0.126476\pi$
$773$			21.5173i			0.773925i	−0.922096	+	0.386962i	$0.873524\pi$
$774$	−6.92576			−0.248941
$775$	−1.47289	−	40.9419i	−0.0529078	−	1.47068i
$776$	−14.8773			−0.534065
$777$			13.1011i			0.470001i
$778$		−	12.4580i		−	0.446641i
$779$	1.11324			0.0398859
$780$	−12.9852	+	13.4608i	−0.464946	+	0.481974i
$781$	−2.59387			−0.0928159
$782$			3.39523i			0.121413i
$783$			12.5341i			0.447931i
$784$	13.1382			0.469220
$785$	−16.2898	−	15.7143i	−0.581408	−	0.560868i
$786$	−23.6323			−0.842935
$787$			42.7128i			1.52255i	0.648430	+	0.761274i	$0.275426\pi$
$787$			42.7128i			1.52255i	−0.648430	+	0.761274i	$0.724574\pi$
$788$		−	18.5233i		−	0.659867i
$789$	20.1823			0.718510
$790$	−2.44968	−	2.36314i	−0.0871557	−	0.0840766i
$791$	68.3374			2.42980
$792$			6.88429i			0.244622i
$793$		−	8.58976i		−	0.305031i
$794$	−34.3685			−1.21969
$795$	43.6259	−	45.2236i	1.54725	−	1.60392i
$796$	−12.8904			−0.456889
$797$		−	8.75980i		−	0.310288i	−0.987892	−	0.155144i	$-0.950416\pi$
$797$		−	8.75980i		−	0.310288i	0.987892	−	0.155144i	$-0.0495841\pi$
$798$		−	9.67565i		−	0.342514i
$799$	19.4057			0.686523
$800$	22.5535	−	0.811368i	0.797388	−	0.0286862i
$801$	37.2198			1.31510
$802$		−	29.9430i		−	1.05732i
$803$			5.35063i			0.188820i
$804$	11.6572			0.411116
$805$	−7.37770	+	7.64789i	−0.260030	+	0.269553i
$806$	36.3848			1.28160
$807$		−	65.1379i		−	2.29296i
$808$			10.5011i			0.369429i
$809$	32.8429			1.15469			0.577347	−	0.816499i	$-0.304088\pi$
$809$	32.8429			1.15469			0.577347	+	0.816499i	$0.304088\pi$
$810$	18.2460	+	17.6014i	0.641100	+	0.618451i
$811$	−31.1503			−1.09383			−0.546917	−	0.837187i	$-0.684199\pi$
$811$	−31.1503			−1.09383			−0.546917	+	0.837187i	$0.684199\pi$
$812$			25.5079i			0.895152i
$813$			57.0492i			2.00080i
$814$	−1.52684			−0.0535158
$815$	9.82792	+	9.48071i	0.344257	+	0.332095i
$816$	9.16001			0.320665
$817$		−	2.88968i		−	0.101097i
$818$			33.0842i			1.15676i
$819$	−37.5078			−1.31063
$820$	−1.50768	+	1.56289i	−0.0526505	+	0.0545787i
$821$	54.6095			1.90589			0.952943	−	0.303150i	$-0.0980384\pi$
$821$	54.6095			1.90589			0.952943	+	0.303150i	$0.0980384\pi$
$822$		−	4.12676i		−	0.143937i
$823$		−	8.88620i		−	0.309753i	−0.987934	−	0.154877i	$-0.950502\pi$
$823$		−	8.88620i		−	0.309753i	0.987934	−	0.154877i	$-0.0494980\pi$
$824$	32.8752			1.14526
$825$	−11.4567	+	0.412156i	−0.398871	+	0.0143494i
$826$	−6.26899			−0.218126
$827$			3.12848i			0.108788i	0.998520	+	0.0543939i	$0.0173227\pi$
$827$			3.12848i			0.108788i	−0.998520	+	0.0543939i	$0.982677\pi$
$828$			2.35457i			0.0818270i
$829$	22.3752			0.777123			0.388562	−	0.921423i	$-0.372972\pi$
$829$	22.3752			0.777123			0.388562	+	0.921423i	$0.372972\pi$
$830$	17.2217	−	17.8523i	0.597772	−	0.619664i
$831$	19.2289			0.667044
$832$			32.5401i			1.12813i
$833$		−	23.5089i		−	0.814536i
$834$	−45.2912			−1.56831
$835$	−29.6899	−	28.6410i	−1.02746	−	0.991164i
$836$	−0.872373			−0.0301717
$837$			13.9581i			0.482462i
$838$			16.5622i			0.572131i
$839$	−34.4806			−1.19040			−0.595201	−	0.803577i	$-0.702928\pi$
$839$	−34.4806			−1.19040			−0.595201	+	0.803577i	$0.702928\pi$
$840$	44.7261	+	43.1460i	1.54320	+	1.48868i
$841$	25.1364			0.866772
$842$		−	10.2930i		−	0.354719i
$843$			46.5956i			1.60484i
$844$	13.2294			0.455376
$845$	6.96600	−	7.22111i	0.239638	−	0.248414i
$846$	−17.3954			−0.598066
$847$			3.97400i			0.136548i
$848$		−	18.3134i		−	0.628885i
$849$	14.8826			0.510769
$850$	0.510372	+	14.1868i	0.0175056	+	0.486603i
$851$	−1.71944			−0.0589415
$852$			5.18824i			0.177746i
$853$			29.4993i			1.01004i	0.863108	+	0.505019i	$0.168515\pi$
$853$			29.4993i			1.01004i	−0.863108	+	0.505019i	$0.831485\pi$
$854$	−8.66827			−0.296622
$855$	3.50392	−	3.63225i	0.119832	−	0.124220i
$856$	46.8924			1.60275
$857$			8.21774i			0.280713i	0.990101	+	0.140356i	$0.0448248\pi$
$857$			8.21774i			0.280713i	−0.990101	+	0.140356i	$0.955175\pi$
$858$		−	10.1815i		−	0.347590i
$859$	−8.79058			−0.299931			−0.149965	−	0.988691i	$-0.547916\pi$
$859$	−8.79058			−0.299931			−0.149965	+	0.988691i	$0.547916\pi$
$860$	4.05688	+	3.91355i	0.138338	+	0.133451i
$861$	−10.1434			−0.345687
$862$		−	38.0156i		−	1.29482i
$863$		−	36.7130i		−	1.24972i	−0.780735	−	0.624862i	$-0.785155\pi$
$863$		−	36.7130i		−	1.24972i	0.780735	−	0.624862i	$-0.214845\pi$
$864$	−7.68905			−0.261587
$865$	−41.1456	−	39.6920i	−1.39899	−	1.34957i
$866$	2.46779			0.0838590
$867$			22.5873i			0.767107i
$868$			28.4059i			0.964159i
$869$	−1.43346			−0.0486269
$870$	27.8110	−	28.8295i	0.942881	−	0.977411i
$871$	−24.3713			−0.825791
$872$		−	58.0740i		−	1.96663i
$873$		−	11.0087i		−	0.372589i
$874$	1.26986			0.0429538
$875$	−29.6777	+	33.0653i	−1.00329	+	1.11781i
$876$	10.7023			0.361597
$877$			21.9461i			0.741068i	0.928819	+	0.370534i	$0.120825\pi$
$877$			21.9461i			0.741068i	−0.928819	+	0.370534i	$0.879175\pi$
$878$		−	14.2703i		−	0.481600i
$879$	−34.5758			−1.16621
$880$	−2.31971	+	2.40466i	−0.0781974	+	0.0810611i
$881$	−53.7080			−1.80947			−0.904734	−	0.425978i	$-0.859930\pi$
$881$	−53.7080			−1.80947			−0.904734	+	0.425978i	$0.859930\pi$
$882$			21.0736i			0.709585i
$883$			44.1058i			1.48428i	0.670245	+	0.742140i	$0.266189\pi$
$883$			44.1058i			1.48428i	−0.670245	+	0.742140i	$0.733811\pi$
$884$	9.75379			0.328055
$885$	−5.48146	−	5.28781i	−0.184257	−	0.177748i
$886$	16.5508			0.556035
$887$			32.4804i			1.09059i	0.838245	+	0.545293i	$0.183582\pi$
$887$			32.4804i			1.09059i	−0.838245	+	0.545293i	$0.816418\pi$
$888$			10.0555i			0.337442i
$889$	−10.1468			−0.340314
$890$	28.1813	+	27.1857i	0.944639	+	0.911266i
$891$	10.6769			0.357690
$892$		−	19.9082i		−	0.666576i
$893$		−	7.25799i		−	0.242879i
$894$	−4.30608			−0.144017
$895$	24.5276	−	25.4258i	0.819866	−	0.849891i
$896$	−3.03674			−0.101450
$897$		−	11.4658i		−	0.382830i
$898$			24.4797i			0.816897i
$899$	60.2870			2.01068
$900$	0.353940	+	9.83845i	0.0117980	+	0.327948i
$901$	−32.7693			−1.09170
$902$		−	1.18214i		−	0.0393611i
$903$			26.3298i			0.876200i
$904$	52.4510			1.74450
$905$	3.48848	−	3.61623i	0.115961	−	0.120208i
$906$	13.3381			0.443130
$907$			33.4864i			1.11190i	0.831216	+	0.555949i	$0.187645\pi$
$907$			33.4864i			1.11190i	−0.831216	+	0.555949i	$0.812355\pi$
$908$			23.0419i			0.764673i
$909$	−7.77049			−0.257731
$910$	−28.3994	−	27.3961i	−0.941430	−	0.908171i
$911$	−0.918244			−0.0304228			−0.0152114	−	0.999884i	$-0.504842\pi$
$911$	−0.918244			−0.0304228			−0.0152114	+	0.999884i	$0.504842\pi$
$912$		−	3.42597i		−	0.113445i
$913$		−	10.4465i		−	0.345730i
$914$	22.2017			0.734366
$915$	−7.57935	−	7.31158i	−0.250565	−	0.241713i
$916$	−13.7665			−0.454857
$917$			38.5727i			1.27378i
$918$		−	4.83662i		−	0.159632i
$919$	−55.1738			−1.82002			−0.910008	−	0.414591i	$-0.863925\pi$
$919$	−55.1738			−1.82002			−0.910008	+	0.414591i	$0.863925\pi$
$920$	−5.66262	+	5.86999i	−0.186691	+	0.193528i
$921$	−71.7906			−2.36558
$922$			7.27585i			0.239618i
$923$		−	10.8469i		−	0.357031i
$924$	7.94877			0.261495
$925$	−7.18457	+	0.258466i	−0.236227	+	0.00849832i
$926$	−25.7363			−0.845748
$927$			24.3265i			0.798988i
$928$			33.2101i			1.09018i
$929$	34.5843			1.13468			0.567338	−	0.823485i	$-0.307973\pi$
$929$	34.5843			1.13468			0.567338	+	0.823485i	$0.307973\pi$
$930$	30.9707	−	32.1049i	1.01557	−	1.05276i
$931$	−8.79266			−0.288168
$932$		−	5.87961i		−	0.192593i
$933$			56.5292i			1.85068i
$934$	16.8684			0.551950
$935$	4.30281	+	4.15080i	0.140717	+	0.135746i
$936$	−28.7884			−0.940978
$937$			14.3184i			0.467762i	0.972265	+	0.233881i	$0.0751426\pi$
$937$			14.3184i			0.467762i	−0.972265	+	0.233881i	$0.924857\pi$
$938$			24.5941i			0.803025i
$939$	16.5582			0.540356
$940$	10.1896	+	9.82964i	0.332349	+	0.320608i
$941$	−26.8186			−0.874260			−0.437130	−	0.899398i	$-0.644005\pi$
$941$	−26.8186			−0.874260			−0.437130	+	0.899398i	$0.644005\pi$
$942$		−	24.6450i		−	0.802977i
$943$		−	1.33126i		−	0.0433517i
$944$	−2.21973			−0.0722462
$945$	10.5098	−	10.8947i	0.341884	−	0.354404i
$946$	−3.06854			−0.0997669
$947$			39.3789i			1.27964i	0.768524	+	0.639821i	$0.220992\pi$
$947$			39.3789i			1.27964i	−0.768524	+	0.639821i	$0.779008\pi$
$948$			2.86721i			0.0931226i
$949$	−22.3750			−0.726324
$950$	5.30606	−	0.190886i	0.172151	−	0.00619317i
$951$	30.6760			0.994736
$952$		−	32.4088i		−	1.05038i
$953$		−	57.8455i		−	1.87380i	−0.349600	−	0.936899i	$-0.613683\pi$
$953$		−	57.8455i		−	1.87380i	0.349600	−	0.936899i	$-0.386317\pi$
$954$	29.3747			0.951041
$955$	8.60596	−	8.92113i	0.278482	−	0.288681i
$956$	0.495082			0.0160121
$957$		−	16.8700i		−	0.545329i
$958$			19.0485i			0.615429i
$959$	−6.73573			−0.217508
$960$	28.7124	+	27.6981i	0.926690	+	0.893951i
$961$	36.1363			1.16569
$962$		−	6.38488i		−	0.205857i
$963$			34.6988i			1.11815i
$964$	8.20861			0.264382
$965$	−33.5117	−	32.3278i	−1.07878	−	1.04067i
$966$	−11.5706			−0.372277
$967$		−	24.5575i		−	0.789715i	−0.918742	−	0.394858i	$-0.870794\pi$
$967$		−	24.5575i		−	0.789715i	0.918742	−	0.394858i	$-0.129206\pi$
$968$			3.05017i			0.0980361i
$969$	−6.13030			−0.196934
$970$	8.04088	−	8.33535i	0.258177	−	0.267632i
$971$	42.0688			1.35005			0.675026	−	0.737794i	$-0.264132\pi$
$971$	42.0688			1.35005			0.675026	+	0.737794i	$0.264132\pi$
$972$		−	16.8976i		−	0.541991i
$973$			73.9246i			2.36991i
$974$	1.62082			0.0519345
$975$	−1.72354	−	47.9091i	−0.0551974	−	1.53432i
$976$	−3.06928			−0.0982452
$977$			21.0445i			0.673272i	0.941635	+	0.336636i	$0.109289\pi$
$977$			21.0445i			0.673272i	−0.941635	+	0.336636i	$0.890711\pi$
$978$			14.8687i			0.475450i
$979$	16.4907			0.527044
$980$	11.9081	−	12.3442i	0.380390	−	0.394321i
$981$	42.9728			1.37201
$982$			4.50839i			0.143868i
$983$		−	12.0650i		−	0.384813i	−0.981315	−	0.192406i	$-0.938371\pi$
$983$		−	12.0650i		−	0.384813i	0.981315	−	0.192406i	$-0.0616292\pi$
$984$	−7.78540			−0.248190
$985$	34.1709	+	32.9637i	1.08878	+	1.05031i
$986$	−20.8901			−0.665275
$987$			66.1323i			2.10501i
$988$		−	3.64805i		−	0.116060i
$989$	−3.45560			−0.109882
$990$	−3.85707	−	3.72081i	−0.122586	−	0.118255i
$991$	47.0928			1.49595			0.747975	−	0.663726i	$-0.231026\pi$
$991$	47.0928			1.49595			0.747975	+	0.663726i	$0.231026\pi$
$992$			36.9832i			1.17422i
$993$			70.9914i			2.25285i
$994$	−10.9461			−0.347188
$995$	22.9395	−	23.7796i	0.727231	−	0.753864i
$996$	−20.8951			−0.662087
$997$		−	28.5202i		−	0.903245i	−0.892209	−	0.451623i	$-0.850845\pi$
$997$		−	28.5202i		−	0.903245i	0.892209	−	0.451623i	$-0.149155\pi$
$998$			10.0772i			0.318987i
$999$	2.44939			0.0774954

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1045.2.b.d.419.14	yes	22
5.2	odd	4		5225.2.a.bb.1.9		22
5.3	odd	4		5225.2.a.bb.1.14		22
5.4	even	2	inner	1045.2.b.d.419.9	✓	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1045.2.b.d.419.9	✓	22	5.4	even	2	inner
1045.2.b.d.419.14	yes	22	1.1	even	1	trivial
5225.2.a.bb.1.9		22	5.2	odd	4
5225.2.a.bb.1.14		22	5.3	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:	\( N \)	\(=\)	\( 1045 = 5 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1045.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.06190i q^{2} +2.29282i q^{3} +0.872373 q^{4} +(-1.55246 + 1.60931i) q^{5} -2.43474 q^{6} +3.97400i q^{7} +3.05017i q^{8} -2.25702 q^{9} +O(q^{10})\)	\(q+1.06190i q^{2} +2.29282i q^{3} +0.872373 q^{4} +(-1.55246 + 1.60931i) q^{5} -2.43474 q^{6} +3.97400i q^{7} +3.05017i q^{8} -2.25702 q^{9} +(-1.70892 - 1.64855i) q^{10} -1.00000 q^{11} +2.00019i q^{12} -4.18176i q^{13} -4.21998 q^{14} +(-3.68986 - 3.55950i) q^{15} -1.49422 q^{16} +2.67370i q^{17} -2.39672i q^{18} +1.00000 q^{19} +(-1.35432 + 1.40392i) q^{20} -9.11166 q^{21} -1.06190i q^{22} -1.19584i q^{23} -6.99348 q^{24} +(-0.179760 - 4.99677i) q^{25} +4.44060 q^{26} +1.70352i q^{27} +3.46681i q^{28} +7.35774 q^{29} +(3.77983 - 3.91825i) q^{30} +8.19367 q^{31} +4.51363i q^{32} -2.29282i q^{33} -2.83919 q^{34} +(-6.39540 - 6.16946i) q^{35} -1.96896 q^{36} -1.43784i q^{37} +1.06190i q^{38} +9.58801 q^{39} +(-4.90866 - 4.73525i) q^{40} +1.11324 q^{41} -9.67565i q^{42} -2.88968i q^{43} -0.872373 q^{44} +(3.50392 - 3.63225i) q^{45} +1.26986 q^{46} -7.25799i q^{47} -3.42597i q^{48} -8.79266 q^{49} +(5.30606 - 0.190886i) q^{50} -6.13030 q^{51} -3.64805i q^{52} +12.2562i q^{53} -1.80896 q^{54} +(1.55246 - 1.60931i) q^{55} -12.1214 q^{56} +2.29282i q^{57} +7.81317i q^{58} +1.48555 q^{59} +(-3.21893 - 3.10521i) q^{60} +2.05410 q^{61} +8.70084i q^{62} -8.96939i q^{63} -7.78145 q^{64} +(6.72974 + 6.49199i) q^{65} +2.43474 q^{66} -5.82801i q^{67} +2.33246i q^{68} +2.74185 q^{69} +(6.55133 - 6.79126i) q^{70} +2.59387 q^{71} -6.88429i q^{72} -5.35063i q^{73} +1.52684 q^{74} +(11.4567 - 0.412156i) q^{75} +0.872373 q^{76} -3.97400i q^{77} +10.1815i q^{78} +1.43346 q^{79} +(2.31971 - 2.40466i) q^{80} -10.6769 q^{81} +1.18214i q^{82} +10.4465i q^{83} -7.94877 q^{84} +(-4.30281 - 4.15080i) q^{85} +3.06854 q^{86} +16.8700i q^{87} -3.05017i q^{88} -16.4907 q^{89} +(3.85707 + 3.72081i) q^{90} +16.6183 q^{91} -1.04322i q^{92} +18.7866i q^{93} +7.70724 q^{94} +(-1.55246 + 1.60931i) q^{95} -10.3489 q^{96} +4.87755i q^{97} -9.33691i q^{98} +2.25702 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 32 q^{4} + 7 q^{5} - 12 q^{6} - 34 q^{9}+O(q^{10}) \) 22 * q - 32 * q^4 + 7 * q^5 - 12 * q^6 - 34 * q^9	\( 22 q - 32 q^{4} + 7 q^{5} - 12 q^{6} - 34 q^{9} + 2 q^{10} - 22 q^{11} + 8 q^{14} - 23 q^{15} + 40 q^{16} + 22 q^{19} - 22 q^{20} - 22 q^{21} + 22 q^{24} + 13 q^{25} + 16 q^{26} + 10 q^{29} - 22 q^{30} + 76 q^{31} - 56 q^{34} - 2 q^{35} + 104 q^{36} + 8 q^{39} - 20 q^{40} + 6 q^{41} + 32 q^{44} - 12 q^{45} + 88 q^{46} - 28 q^{49} - 20 q^{50} + 8 q^{51} - 38 q^{54} - 7 q^{55} + 44 q^{56} - 40 q^{59} + 78 q^{60} - 6 q^{61} - 140 q^{64} - 22 q^{65} + 12 q^{66} - 74 q^{69} - 24 q^{70} + 62 q^{71} + 26 q^{74} + 13 q^{75} - 32 q^{76} - 102 q^{79} + 142 q^{80} + 94 q^{81} + 38 q^{84} + 26 q^{85} + 28 q^{86} - 54 q^{89} + 118 q^{90} + 88 q^{91} - 36 q^{94} + 7 q^{95} + 2 q^{96} + 34 q^{99}+O(q^{100}) \) 22 * q - 32 * q^4 + 7 * q^5 - 12 * q^6 - 34 * q^9 + 2 * q^10 - 22 * q^11 + 8 * q^14 - 23 * q^15 + 40 * q^16 + 22 * q^19 - 22 * q^20 - 22 * q^21 + 22 * q^24 + 13 * q^25 + 16 * q^26 + 10 * q^29 - 22 * q^30 + 76 * q^31 - 56 * q^34 - 2 * q^35 + 104 * q^36 + 8 * q^39 - 20 * q^40 + 6 * q^41 + 32 * q^44 - 12 * q^45 + 88 * q^46 - 28 * q^49 - 20 * q^50 + 8 * q^51 - 38 * q^54 - 7 * q^55 + 44 * q^56 - 40 * q^59 + 78 * q^60 - 6 * q^61 - 140 * q^64 - 22 * q^65 + 12 * q^66 - 74 * q^69 - 24 * q^70 + 62 * q^71 + 26 * q^74 + 13 * q^75 - 32 * q^76 - 102 * q^79 + 142 * q^80 + 94 * q^81 + 38 * q^84 + 26 * q^85 + 28 * q^86 - 54 * q^89 + 118 * q^90 + 88 * q^91 - 36 * q^94 + 7 * q^95 + 2 * q^96 + 34 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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