LMFDB - Embedded newform 1045.2.b.e.419.2

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:	$30$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			419.2
Character	$\chi$	$=$	1045.419
Dual form			1045.2.b.e.419.29

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.77451i q^{2} -2.74433i q^{3} -5.69792 q^{4} +(0.316248 + 2.21359i) q^{5} -7.61418 q^{6} +3.20844i q^{7} +10.2599i q^{8} -4.53135 q^{9} +O(q^{10})$	\(q-2.77451i q^{2} -2.74433i q^{3} -5.69792 q^{4} +(0.316248 + 2.21359i) q^{5} -7.61418 q^{6} +3.20844i q^{7} +10.2599i q^{8} -4.53135 q^{9} +(6.14164 - 0.877434i) q^{10} +1.00000 q^{11} +15.6370i q^{12} -3.87053i q^{13} +8.90186 q^{14} +(6.07483 - 0.867889i) q^{15} +17.0705 q^{16} +5.86570i q^{17} +12.5723i q^{18} -1.00000 q^{19} +(-1.80196 - 12.6129i) q^{20} +8.80502 q^{21} -2.77451i q^{22} +6.11891i q^{23} +28.1566 q^{24} +(-4.79997 + 1.40009i) q^{25} -10.7388 q^{26} +4.20253i q^{27} -18.2814i q^{28} -6.40440 q^{29} +(-2.40797 - 16.8547i) q^{30} +1.66215 q^{31} -26.8423i q^{32} -2.74433i q^{33} +16.2745 q^{34} +(-7.10217 + 1.01466i) q^{35} +25.8193 q^{36} +0.251830i q^{37} +2.77451i q^{38} -10.6220 q^{39} +(-22.7113 + 3.24468i) q^{40} +10.7565 q^{41} -24.4296i q^{42} +2.17536i q^{43} -5.69792 q^{44} +(-1.43303 - 10.0306i) q^{45} +16.9770 q^{46} +2.68163i q^{47} -46.8470i q^{48} -3.29408 q^{49} +(3.88456 + 13.3176i) q^{50} +16.0974 q^{51} +22.0540i q^{52} +8.89909i q^{53} +11.6600 q^{54} +(0.316248 + 2.21359i) q^{55} -32.9183 q^{56} +2.74433i q^{57} +17.7691i q^{58} +4.09447 q^{59} +(-34.6139 + 4.94516i) q^{60} +4.52319 q^{61} -4.61167i q^{62} -14.5386i q^{63} -40.3335 q^{64} +(8.56778 - 1.22405i) q^{65} -7.61418 q^{66} +2.61295i q^{67} -33.4223i q^{68} +16.7923 q^{69} +(2.81519 + 19.7051i) q^{70} -5.51722 q^{71} -46.4913i q^{72} +2.73480i q^{73} +0.698705 q^{74} +(3.84230 + 13.1727i) q^{75} +5.69792 q^{76} +3.20844i q^{77} +29.4709i q^{78} -8.17104 q^{79} +(5.39850 + 37.7870i) q^{80} -2.06093 q^{81} -29.8440i q^{82} +12.2337i q^{83} -50.1703 q^{84} +(-12.9843 + 1.85502i) q^{85} +6.03555 q^{86} +17.5758i q^{87} +10.2599i q^{88} +1.84048 q^{89} +(-27.8299 + 3.97596i) q^{90} +12.4184 q^{91} -34.8651i q^{92} -4.56150i q^{93} +7.44022 q^{94} +(-0.316248 - 2.21359i) q^{95} -73.6642 q^{96} -2.65645i q^{97} +9.13947i q^{98} -4.53135 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 42 q^{4} + 12 q^{6} - 40 q^{9}+O(q^{10}) $ 30 * q - 42 * q^4 + 12 * q^6 - 40 * q^9	$ 30 q - 42 q^{4} + 12 q^{6} - 40 q^{9} + 10 q^{10} + 30 q^{11} + 4 q^{14} + 4 q^{15} + 66 q^{16} - 30 q^{19} + 10 q^{20} + 14 q^{21} - 22 q^{24} - 6 q^{25} - 30 q^{29} + 14 q^{30} + 26 q^{31} - 12 q^{34} + 6 q^{35} + 78 q^{36} - 64 q^{39} - 20 q^{40} + 22 q^{41} - 42 q^{44} + 6 q^{45} + 28 q^{46} - 60 q^{49} + 64 q^{51} - 62 q^{54} - 32 q^{56} + 14 q^{59} - 28 q^{60} + 78 q^{61} - 90 q^{64} + 40 q^{65} + 12 q^{66} + 28 q^{69} + 12 q^{70} + 20 q^{71} - 42 q^{74} + 50 q^{75} + 42 q^{76} - 102 q^{79} - 40 q^{80} + 42 q^{81} - 98 q^{84} - 2 q^{85} - 52 q^{86} + 8 q^{89} + 22 q^{90} + 56 q^{91} - 40 q^{94} - 74 q^{96} - 40 q^{99}+O(q^{100}) $ 30 * q - 42 * q^4 + 12 * q^6 - 40 * q^9 + 10 * q^10 + 30 * q^11 + 4 * q^14 + 4 * q^15 + 66 * q^16 - 30 * q^19 + 10 * q^20 + 14 * q^21 - 22 * q^24 - 6 * q^25 - 30 * q^29 + 14 * q^30 + 26 * q^31 - 12 * q^34 + 6 * q^35 + 78 * q^36 - 64 * q^39 - 20 * q^40 + 22 * q^41 - 42 * q^44 + 6 * q^45 + 28 * q^46 - 60 * q^49 + 64 * q^51 - 62 * q^54 - 32 * q^56 + 14 * q^59 - 28 * q^60 + 78 * q^61 - 90 * q^64 + 40 * q^65 + 12 * q^66 + 28 * q^69 + 12 * q^70 + 20 * q^71 - 42 * q^74 + 50 * q^75 + 42 * q^76 - 102 * q^79 - 40 * q^80 + 42 * q^81 - 98 * q^84 - 2 * q^85 - 52 * q^86 + 8 * q^89 + 22 * q^90 + 56 * q^91 - 40 * q^94 - 74 * q^96 - 40 * 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 $

$2$		−	2.77451i		−	1.96188i	−0.194319	−	0.980938i	$-0.562250\pi$
$2$		−	2.77451i		−	1.96188i	0.194319	−	0.980938i	$-0.437750\pi$
$3$		−	2.74433i		−	1.58444i	−0.610236	−	0.792220i	$-0.708925\pi$
$3$		−	2.74433i		−	1.58444i	0.610236	−	0.792220i	$-0.291075\pi$
$4$	−5.69792			−2.84896
$5$	0.316248	+	2.21359i	0.141430	+	0.989948i
$5$	0.316248	+	2.21359i	0.141430	+	0.989948i
$6$	−7.61418			−3.10848
$7$			3.20844i			1.21268i	0.795207	+	0.606338i	$0.207362\pi$
$7$			3.20844i			1.21268i	−0.795207	+	0.606338i	$0.792638\pi$
$8$			10.2599i			3.62743i
$9$	−4.53135			−1.51045
$10$	6.14164	−	0.877434i	1.94216	−	0.277469i
$11$	1.00000			0.301511
$11$	1.00000			0.301511
$12$			15.6370i			4.51401i
$13$		−	3.87053i		−	1.07349i	−0.843744	−	0.536746i	$-0.819653\pi$
$13$		−	3.87053i		−	1.07349i	0.843744	−	0.536746i	$-0.180347\pi$
$14$	8.90186			2.37912
$15$	6.07483	−	0.867889i	1.56851	−	0.224088i
$16$	17.0705			4.26761
$17$			5.86570i			1.42264i	0.702867	+	0.711321i	$0.251903\pi$
$17$			5.86570i			1.42264i	−0.702867	+	0.711321i	$0.748097\pi$
$18$			12.5723i			2.96332i
$19$	−1.00000			−0.229416
$19$	−1.00000			−0.229416
$20$	−1.80196	−	12.6129i	−0.402930	−	2.82032i
$21$	8.80502			1.92141
$22$		−	2.77451i		−	0.591528i
$23$			6.11891i			1.27588i	0.770086	+	0.637940i	$0.220213\pi$
$23$			6.11891i			1.27588i	−0.770086	+	0.637940i	$0.779787\pi$
$24$	28.1566			5.74745
$25$	−4.79997	+	1.40009i	−0.959995	+	0.280018i
$26$	−10.7388			−2.10606
$27$			4.20253i			0.808777i
$28$		−	18.2814i		−	3.45487i
$29$	−6.40440			−1.18927			−0.594634	−	0.803997i	$-0.702703\pi$
$29$	−6.40440			−1.18927			−0.594634	+	0.803997i	$0.702703\pi$
$30$	−2.40797	−	16.8547i	−0.439633	−	3.07723i
$31$	1.66215			0.298532			0.149266	−	0.988797i	$-0.452309\pi$
$31$	1.66215			0.298532			0.149266	+	0.988797i	$0.452309\pi$
$32$		−	26.8423i		−	4.74510i
$33$		−	2.74433i		−	0.477727i
$34$	16.2745			2.79105
$35$	−7.10217	+	1.01466i	−1.20049	+	0.171509i
$36$	25.8193			4.30321
$37$			0.251830i			0.0414006i	0.999786	+	0.0207003i	$0.00658958\pi$
$37$			0.251830i			0.0414006i	−0.999786	+	0.0207003i	$0.993410\pi$
$38$			2.77451i			0.450085i
$39$	−10.6220			−1.70088
$40$	−22.7113	+	3.24468i	−3.59097	+	0.513029i
$41$	10.7565			1.67988			0.839941	−	0.542677i	$-0.182589\pi$
$41$	10.7565			1.67988			0.839941	+	0.542677i	$0.182589\pi$
$42$		−	24.4296i		−	3.76957i
$43$			2.17536i			0.331739i	0.986148	+	0.165869i	$0.0530430\pi$
$43$			2.17536i			0.331739i	−0.986148	+	0.165869i	$0.946957\pi$
$44$	−5.69792			−0.858994
$45$	−1.43303	−	10.0306i	−0.213624	−	1.49527i
$46$	16.9770			2.50312
$47$			2.68163i			0.391156i	0.980688	+	0.195578i	$0.0626583\pi$
$47$			2.68163i			0.391156i	−0.980688	+	0.195578i	$0.937342\pi$
$48$		−	46.8470i		−	6.76178i
$49$	−3.29408			−0.470583
$50$	3.88456	+	13.3176i	0.549360	+	1.88339i
$51$	16.0974			2.25409
$52$			22.0540i			3.05834i
$53$			8.89909i			1.22238i	0.791483	+	0.611192i	$0.209310\pi$
$53$			8.89909i			1.22238i	−0.791483	+	0.611192i	$0.790690\pi$
$54$	11.6600			1.58672
$55$	0.316248	+	2.21359i	0.0426429	+	0.298481i
$56$	−32.9183			−4.39890
$57$			2.74433i			0.363495i
$58$			17.7691i			2.33320i
$59$	4.09447			0.533054			0.266527	−	0.963827i	$-0.414124\pi$
$59$	4.09447			0.533054			0.266527	+	0.963827i	$0.414124\pi$
$60$	−34.6139	+	4.94516i	−4.46863	+	0.638418i
$61$	4.52319			0.579135			0.289567	−	0.957158i	$-0.406489\pi$
$61$	4.52319			0.579135			0.289567	+	0.957158i	$0.406489\pi$
$62$		−	4.61167i		−	0.585682i
$63$		−	14.5386i		−	1.83169i
$64$	−40.3335			−5.04169
$65$	8.56778	−	1.22405i	1.06270	−	0.151824i
$66$	−7.61418			−0.937241
$67$			2.61295i			0.319222i	0.987180	+	0.159611i	$0.0510240\pi$
$67$			2.61295i			0.319222i	−0.987180	+	0.159611i	$0.948976\pi$
$68$		−	33.4223i		−	4.05305i
$69$	16.7923			2.02156
$70$	2.81519	+	19.7051i	0.336480	+	2.35521i
$71$	−5.51722			−0.654774			−0.327387	−	0.944890i	$-0.606168\pi$
$71$	−5.51722			−0.654774			−0.327387	+	0.944890i	$0.606168\pi$
$72$		−	46.4913i		−	5.47905i
$73$			2.73480i			0.320084i	0.987110	+	0.160042i	$0.0511630\pi$
$73$			2.73480i			0.320084i	−0.987110	+	0.160042i	$0.948837\pi$
$74$	0.698705			0.0812229
$75$	3.84230	+	13.1727i	0.443671	+	1.52105i
$76$	5.69792			0.653596
$77$			3.20844i			0.365636i
$78$			29.4709i			3.33692i
$79$	−8.17104			−0.919313			−0.459657	−	0.888097i	$-0.652028\pi$
$79$	−8.17104			−0.919313			−0.459657	+	0.888097i	$0.652028\pi$
$80$	5.39850	+	37.7870i	0.603570	+	4.22472i
$81$	−2.06093			−0.228992
$82$		−	29.8440i		−	3.29572i
$83$			12.2337i			1.34283i	0.741083	+	0.671413i	$0.234312\pi$
$83$			12.2337i			1.34283i	−0.741083	+	0.671413i	$0.765688\pi$
$84$	−50.1703			−5.47403
$85$	−12.9843	+	1.85502i	−1.40834	+	0.201205i
$86$	6.03555			0.650830
$87$			17.5758i			1.88432i
$88$			10.2599i			1.09371i
$89$	1.84048			0.195091			0.0975454	−	0.995231i	$-0.468901\pi$
$89$	1.84048			0.195091			0.0975454	+	0.995231i	$0.468901\pi$
$90$	−27.8299	+	3.97596i	−2.93353	+	0.419103i
$91$	12.4184			1.30180
$92$		−	34.8651i		−	3.63493i
$93$		−	4.56150i		−	0.473005i
$94$	7.44022			0.767400
$95$	−0.316248	−	2.21359i	−0.0324464	−	0.227110i
$96$	−73.6642			−7.51832
$97$		−	2.65645i		−	0.269722i	−0.990865	−	0.134861i	$-0.956941\pi$
$97$		−	2.65645i		−	0.269722i	0.990865	−	0.134861i	$-0.0430588\pi$
$98$			9.13947i			0.923226i
$99$	−4.53135			−0.455418
$100$	27.3499	−	7.97759i	2.73499	−	0.797759i
$101$	3.36522			0.334852			0.167426	−	0.985885i	$-0.446454\pi$
$101$	3.36522			0.334852			0.167426	+	0.985885i	$0.446454\pi$
$102$		−	44.6625i		−	4.42225i
$103$			19.1222i			1.88416i	0.335381	+	0.942082i	$0.391135\pi$
$103$			19.1222i			1.88416i	−0.335381	+	0.942082i	$0.608865\pi$
$104$	39.7114			3.89402
$105$	2.78457	+	19.4907i	0.271746	+	1.90210i
$106$	24.6906			2.39817
$107$		−	19.1096i		−	1.84739i	−0.383125	−	0.923697i	$-0.625152\pi$
$107$		−	19.1096i		−	1.84739i	0.383125	−	0.923697i	$-0.374848\pi$
$108$		−	23.9457i		−	2.30417i
$109$	2.04217			0.195605			0.0978023	−	0.995206i	$-0.468819\pi$
$109$	2.04217			0.195605			0.0978023	+	0.995206i	$0.468819\pi$
$110$	6.14164	−	0.877434i	0.585582	−	0.0836601i
$111$	0.691105			0.0655968
$112$			54.7695i			5.17523i
$113$		−	2.01233i		−	0.189305i	−0.995510	−	0.0946523i	$-0.969826\pi$
$113$		−	2.01233i		−	0.189305i	0.995510	−	0.0946523i	$-0.0301739\pi$
$114$	7.61418			0.713133
$115$	−13.5448	+	1.93509i	−1.26306	+	0.180448i
$116$	36.4918			3.38818
$117$			17.5387i			1.62146i
$118$		−	11.3601i		−	1.04579i
$119$	−18.8197			−1.72520
$120$	8.90448	+	62.3273i	0.812864	+	5.68967i
$121$	1.00000			0.0909091
$122$		−	12.5496i		−	1.13619i
$123$		−	29.5194i		−	2.66167i
$124$	−9.47082			−0.850505
$125$	−4.61720	−	10.1824i	−0.412975	−	0.910742i
$126$	−40.3374			−3.59354
$127$			17.6725i			1.56818i	0.620648	+	0.784090i	$0.286870\pi$
$127$			17.6725i			1.56818i	−0.620648	+	0.784090i	$0.713130\pi$
$128$			58.2211i			5.14607i
$129$	5.96990			0.525620
$130$	−3.39614	−	23.7714i	−0.297861	−	2.08489i
$131$	−4.85389			−0.424086			−0.212043	−	0.977260i	$-0.568012\pi$
$131$	−4.85389			−0.424086			−0.212043	+	0.977260i	$0.568012\pi$
$132$			15.6370i			1.36102i
$133$		−	3.20844i		−	0.278207i
$134$	7.24965			0.626274
$135$	−9.30268	+	1.32904i	−0.800647	+	0.114386i
$136$	−60.1817			−5.16054
$137$		−	0.470694i		−	0.0402141i	−0.999798	−	0.0201071i	$-0.993599\pi$
$137$		−	0.470694i		−	0.0402141i	0.999798	−	0.0201071i	$-0.00640071\pi$
$138$		−	46.5905i		−	3.96604i
$139$	−10.2256			−0.867325			−0.433663	−	0.901075i	$-0.642779\pi$
$139$	−10.2256			−0.867325			−0.433663	+	0.901075i	$0.642779\pi$
$140$	40.4676	−	5.78147i	3.42014	−	0.488623i
$141$	7.35929			0.619764
$142$			15.3076i			1.28459i
$143$		−	3.87053i		−	0.323670i
$144$	−77.3522			−6.44601
$145$	−2.02538	−	14.1767i	−0.168199	−	1.17731i
$146$	7.58774			0.627965
$147$			9.04005i			0.745611i
$148$		−	1.43491i		−	0.117949i
$149$	19.2747			1.57905			0.789523	−	0.613721i	$-0.210328\pi$
$149$	19.2747			1.57905			0.789523	+	0.613721i	$0.210328\pi$
$150$	36.5479	−	10.6605i	2.98412	−	0.870428i
$151$	−9.24566			−0.752401			−0.376200	−	0.926538i	$-0.622770\pi$
$151$	−9.24566			−0.752401			−0.376200	+	0.926538i	$0.622770\pi$
$152$		−	10.2599i		−	0.832190i
$153$		−	26.5795i		−	2.14883i
$154$	8.90186			0.717332
$155$	0.525653	+	3.67933i	0.0422215	+	0.295531i
$156$	60.5234			4.84575
$157$			9.10320i			0.726514i	0.931689	+	0.363257i	$0.118335\pi$
$157$			9.10320i			0.726514i	−0.931689	+	0.363257i	$0.881665\pi$
$158$			22.6706i			1.80358i
$159$	24.4220			1.93679
$160$	59.4180	−	8.48883i	4.69740	−	0.671101i
$161$	−19.6321			−1.54723
$162$			5.71806i			0.449253i
$163$		−	13.1874i		−	1.03292i	−0.856313	−	0.516458i	$-0.827250\pi$
$163$		−	13.1874i		−	1.03292i	0.856313	−	0.516458i	$-0.172750\pi$
$164$	−61.2897			−4.78592
$165$	6.07483	−	0.867889i	0.472925	−	0.0675651i
$166$	33.9426			2.63446
$167$		−	7.56734i		−	0.585578i	−0.956177	−	0.292789i	$-0.905417\pi$
$167$		−	7.56734i		−	0.585578i	0.956177	−	0.292789i	$-0.0945834\pi$
$168$			90.3388i			6.96979i
$169$	−1.98102			−0.152386
$170$	5.14677	+	36.0250i	0.394739	+	2.76299i
$171$	4.53135			0.346521
$172$		−	12.3950i		−	0.945110i
$173$			12.3483i			0.938825i	0.882979	+	0.469412i	$0.155534\pi$
$173$			12.3483i			0.938825i	−0.882979	+	0.469412i	$0.844466\pi$
$174$	48.7643			3.69681
$175$	−4.49210	−	15.4004i	−0.339571	−	1.16416i
$176$	17.0705			1.28673
$177$		−	11.2366i		−	0.844592i
$178$		−	5.10644i		−	0.382744i
$179$	−9.75082			−0.728810			−0.364405	−	0.931241i	$-0.618728\pi$
$179$	−9.75082			−0.728810			−0.364405	+	0.931241i	$0.618728\pi$
$180$	8.16529	+	57.1533i	0.608605	+	4.25996i
$181$	−3.06931			−0.228140			−0.114070	−	0.993473i	$-0.536389\pi$
$181$	−3.06931			−0.228140			−0.114070	+	0.993473i	$0.536389\pi$
$182$		−	34.4549i		−	2.55397i
$183$		−	12.4131i		−	0.917604i
$184$	−62.7796			−4.62817
$185$	−0.557449	+	0.0796407i	−0.0409844	+	0.00585530i
$186$	−12.6559			−0.927978
$187$			5.86570i			0.428943i
$188$		−	15.2797i		−	1.11439i
$189$	−13.4836			−0.980784
$190$	−6.14164	+	0.877434i	−0.445561	+	0.0636558i
$191$	11.5267			0.834040			0.417020	−	0.908897i	$-0.363075\pi$
$191$	11.5267			0.834040			0.417020	+	0.908897i	$0.363075\pi$
$192$			110.688i			7.98825i
$193$		−	6.25518i		−	0.450258i	−0.974329	−	0.225129i	$-0.927720\pi$
$193$		−	6.25518i		−	0.450258i	0.974329	−	0.225129i	$-0.0722803\pi$
$194$	−7.37036			−0.529161
$195$	−3.35919	−	23.5128i	−0.240557	−	1.68379i
$196$	18.7694			1.34067
$197$		−	6.53160i		−	0.465357i	−0.972554	−	0.232678i	$-0.925251\pi$
$197$		−	6.53160i		−	0.465357i	0.972554	−	0.232678i	$-0.0747490\pi$
$198$			12.5723i			0.893473i
$199$	−11.4237			−0.809808			−0.404904	−	0.914359i	$-0.632695\pi$
$199$	−11.4237			−0.809808			−0.404904	+	0.914359i	$0.632695\pi$
$200$	−14.3648	−	49.2474i	−1.01574	−	3.48232i
$201$	7.17079			0.505788
$202$		−	9.33686i		−	0.656939i
$203$		−	20.5481i		−	1.44220i
$204$	−91.7218			−6.42181
$205$	3.40172	+	23.8105i	0.237587	+	1.66300i
$206$	53.0547			3.69650
$207$		−	27.7269i		−	1.92715i
$208$		−	66.0717i		−	4.58125i
$209$	−1.00000			−0.0691714
$210$	54.0772	−	7.72582i	3.73168	−	0.533132i
$211$	−0.159122			−0.0109544			−0.00547722	−	0.999985i	$-0.501743\pi$
$211$	−0.159122			−0.0109544			−0.00547722	+	0.999985i	$0.501743\pi$
$212$		−	50.7063i		−	3.48252i
$213$			15.1411i			1.03745i
$214$	−53.0198			−3.62436
$215$	−4.81535	+	0.687952i	−0.328404	+	0.0469179i
$216$	−43.1176			−2.93378
$217$			5.33292i			0.362022i
$218$		−	5.66603i		−	0.383752i
$219$	7.50519			0.507154
$220$	−1.80196	−	12.6129i	−0.121488	−	0.850359i
$221$	22.7034			1.52720
$222$		−	1.91748i		−	0.128693i
$223$			0.537456i			0.0359907i	0.999838	+	0.0179954i	$0.00572841\pi$
$223$			0.537456i			0.0359907i	−0.999838	+	0.0179954i	$0.994272\pi$
$224$	86.1220			5.75427
$225$	21.7504	−	6.34429i	1.45002	−	0.422952i
$226$	−5.58325			−0.371392
$227$		−	13.5232i		−	0.897565i	−0.893641	−	0.448783i	$-0.851858\pi$
$227$		−	13.5232i		−	0.897565i	0.893641	−	0.448783i	$-0.148142\pi$
$228$		−	15.6370i		−	1.03558i
$229$	10.6187			0.701704			0.350852	−	0.936431i	$-0.385892\pi$
$229$	10.6187			0.701704			0.350852	+	0.936431i	$0.385892\pi$
$230$	5.36894	+	37.5801i	0.354017	+	2.47796i
$231$	8.80502			0.579328
$232$		−	65.7087i		−	4.31399i
$233$			7.83409i			0.513228i	0.966514	+	0.256614i	$0.0826069\pi$
$233$			7.83409i			0.513228i	−0.966514	+	0.256614i	$0.917393\pi$
$234$	48.6614			3.18110
$235$	−5.93604	+	0.848061i	−0.387225	+	0.0553214i
$236$	−23.3299			−1.51865
$237$			22.4240i			1.45660i
$238$			52.2156i			3.38464i
$239$	−25.3402			−1.63912			−0.819560	−	0.572994i	$-0.805782\pi$
$239$	−25.3402			−1.63912			−0.819560	+	0.572994i	$0.805782\pi$
$240$	103.700	−	14.8153i	6.69381	−	0.956321i
$241$	−30.0559			−1.93607			−0.968035	−	0.250814i	$-0.919302\pi$
$241$	−30.0559			−1.93607			−0.968035	+	0.250814i	$0.919302\pi$
$242$		−	2.77451i		−	0.178352i
$243$			18.2634i			1.17160i
$244$	−25.7728			−1.64993
$245$	−1.04175	−	7.29175i	−0.0665548	−	0.465853i
$246$	−81.9019			−5.22188
$247$			3.87053i			0.246276i
$248$			17.0536i			1.08290i
$249$	33.5734			2.12763
$250$	−28.2512	+	12.8105i	−1.78676	+	0.810207i
$251$	24.0428			1.51757			0.758783	−	0.651344i	$-0.225794\pi$
$251$	24.0428			1.51757			0.758783	+	0.651344i	$0.225794\pi$
$252$			82.8395i			5.21840i
$253$			6.11891i			0.384693i
$254$	49.0325			3.07657
$255$	5.09078	+	35.6331i	0.318797	+	2.23143i
$256$	80.8682			5.05426
$257$			6.58227i			0.410591i	0.978700	+	0.205295i	$0.0658155\pi$
$257$			6.58227i			0.410591i	−0.978700	+	0.205295i	$0.934185\pi$
$258$		−	16.5635i		−	1.03120i
$259$	−0.807981			−0.0502055
$260$	−48.8185	+	6.97453i	−3.02760	+	0.432542i
$261$	29.0206			1.79633
$262$			13.4672i			0.832005i
$263$		−	16.0460i		−	0.989442i	−0.869052	−	0.494721i	$-0.835270\pi$
$263$		−	16.0460i		−	0.989442i	0.869052	−	0.494721i	$-0.164730\pi$
$264$	28.1566			1.73292
$265$	−19.6989	+	2.81432i	−1.21010	+	0.172882i
$266$	−8.90186			−0.545808
$267$		−	5.05089i		−	0.309110i
$268$		−	14.8884i		−	0.909451i
$269$	17.0574			1.04001			0.520005	−	0.854163i	$-0.325930\pi$
$269$	17.0574			1.04001			0.520005	+	0.854163i	$0.325930\pi$
$270$	3.68744	+	25.8104i	0.224410	+	1.57077i
$271$	14.8456			0.901807			0.450904	−	0.892573i	$-0.351102\pi$
$271$	14.8456			0.901807			0.450904	+	0.892573i	$0.351102\pi$
$272$			100.130i			6.07128i
$273$		−	34.0801i		−	2.06262i
$274$	−1.30595			−0.0788951
$275$	−4.79997	+	1.40009i	−0.289449	+	0.0844285i
$276$	−95.6812			−5.75933
$277$			8.59398i			0.516362i	0.966097	+	0.258181i	$0.0831232\pi$
$277$			8.59398i			0.516362i	−0.966097	+	0.258181i	$0.916877\pi$
$278$			28.3711i			1.70158i
$279$	−7.53180			−0.450917
$280$	−10.4104	−	72.8678i	−0.622138	−	4.35468i
$281$	−13.4669			−0.803368			−0.401684	−	0.915778i	$-0.631575\pi$
$281$	−13.4669			−0.803368			−0.401684	+	0.915778i	$0.631575\pi$
$282$		−	20.4184i		−	1.21590i
$283$		−	14.2887i		−	0.849374i	−0.905340	−	0.424687i	$-0.860384\pi$
$283$		−	14.2887i		−	0.849374i	0.905340	−	0.424687i	$-0.139616\pi$
$284$	31.4367			1.86542
$285$	−6.07483	+	0.867889i	−0.359842	+	0.0514093i
$286$	−10.7388			−0.635001
$287$			34.5116i			2.03715i
$288$			121.632i			7.16723i
$289$	−17.4065			−1.02391
$290$	−39.3335	+	5.61944i	−2.30974	+	0.329985i
$291$	−7.29019			−0.427358
$292$		−	15.5827i		−	0.911907i
$293$			29.5456i			1.72607i	0.505143	+	0.863036i	$0.331440\pi$
$293$			29.5456i			1.72607i	−0.505143	+	0.863036i	$0.668560\pi$
$294$	25.0817			1.46280
$295$	1.29487	+	9.06348i	0.0753901	+	0.527696i
$296$	−2.58376			−0.150178
$297$			4.20253i			0.243855i
$298$		−	53.4779i		−	3.09789i
$299$	23.6834			1.36965
$300$	−21.8931	−	75.0571i	−1.26400	−	4.33342i
$301$	−6.97950			−0.402292
$302$			25.6522i			1.47612i
$303$		−	9.23529i		−	0.530553i
$304$	−17.0705			−0.979058
$305$	1.43045	+	10.0125i	0.0819072	+	0.573313i
$306$	−73.7453			−4.21574
$307$		−	21.6031i		−	1.23295i	−0.787373	−	0.616477i	$-0.788559\pi$
$307$		−	21.6031i		−	1.23295i	0.787373	−	0.616477i	$-0.211441\pi$
$308$		−	18.2814i		−	1.04168i
$309$	52.4776			2.98535
$310$	10.2083	−	1.45843i	0.579795	−	0.0828333i
$311$	21.4045			1.21374			0.606870	−	0.794801i	$-0.292425\pi$
$311$	21.4045			1.21374			0.606870	+	0.794801i	$0.292425\pi$
$312$		−	108.981i		−	6.16984i
$313$			22.7332i			1.28496i	0.766304	+	0.642478i	$0.222094\pi$
$313$			22.7332i			1.28496i	−0.766304	+	0.642478i	$0.777906\pi$
$314$	25.2569			1.42533
$315$	32.1824	−	4.59779i	1.81327	−	0.259056i
$316$	46.5579			2.61909
$317$		−	1.29414i		−	0.0726859i	−0.999339	−	0.0363430i	$-0.988429\pi$
$317$		−	1.29414i		−	0.0726859i	0.999339	−	0.0363430i	$-0.0115709\pi$
$318$		−	67.7592i		−	3.79975i
$319$	−6.40440			−0.358578
$320$	−12.7554	−	89.2819i	−0.713048	−	4.99101i
$321$	−52.4430			−2.92708
$322$			54.4696i			3.03547i
$323$		−	5.86570i		−	0.326376i
$324$	11.7430			0.652388
$325$	5.41908	+	18.5785i	0.300597	+	1.03055i
$326$	−36.5885			−2.02645
$327$		−	5.60440i		−	0.309924i
$328$			110.361i			6.09366i
$329$	−8.60386			−0.474346
$330$	−2.40797	−	16.8547i	−0.132554	−	0.927820i
$331$	−22.3804			−1.23014			−0.615068	−	0.788474i	$-0.710872\pi$
$331$	−22.3804			−1.23014			−0.615068	+	0.788474i	$0.710872\pi$
$332$		−	69.7068i		−	3.82566i
$333$		−	1.14113i		−	0.0625335i
$334$	−20.9957			−1.14883
$335$	−5.78399	+	0.826339i	−0.316013	+	0.0451477i
$336$	150.306			8.19984
$337$		−	19.7453i		−	1.07560i	−0.843074	−	0.537798i	$-0.819256\pi$
$337$		−	19.7453i		−	1.07560i	0.843074	−	0.537798i	$-0.180744\pi$
$338$			5.49636i			0.298962i
$339$	−5.52251			−0.299942
$340$	73.9833	−	10.5697i	4.01231	−	0.573224i
$341$	1.66215			0.0900107
$342$		−	12.5723i		−	0.679831i
$343$			11.8902i			0.642011i
$344$	−22.3190			−1.20336
$345$	5.31053	+	37.1713i	0.285910	+	2.00124i
$346$	34.2605			1.84186
$347$			21.6561i			1.16256i	0.813704	+	0.581279i	$0.197448\pi$
$347$			21.6561i			1.16256i	−0.813704	+	0.581279i	$0.802552\pi$
$348$		−	100.145i		−	5.36836i
$349$	−4.59915			−0.246187			−0.123093	−	0.992395i	$-0.539281\pi$
$349$	−4.59915			−0.246187			−0.123093	+	0.992395i	$0.539281\pi$
$350$	−42.7287	+	12.4634i	−2.28394	+	0.666196i
$351$	16.2660			0.868216
$352$		−	26.8423i		−	1.43070i
$353$		−	0.690423i		−	0.0367475i	−0.999831	−	0.0183737i	$-0.994151\pi$
$353$		−	0.690423i		−	0.0367475i	0.999831	−	0.0183737i	$-0.00584887\pi$
$354$	−31.1760			−1.65699
$355$	−1.74481	−	12.2129i	−0.0926049	−	0.648192i
$356$	−10.4869			−0.555806
$357$			51.6476i			2.73348i
$358$			27.0538i			1.42984i
$359$	−0.484355			−0.0255633			−0.0127816	−	0.999918i	$-0.504069\pi$
$359$	−0.484355			−0.0255633			−0.0127816	+	0.999918i	$0.504069\pi$
$360$	102.913	−	14.7028i	5.42398	−	0.774905i
$361$	1.00000			0.0526316
$362$			8.51583i			0.447582i
$363$		−	2.74433i		−	0.144040i
$364$	−70.7589			−3.70877
$365$	−6.05373	+	0.864875i	−0.316867	+	0.0452696i
$366$	−34.4403			−1.80023
$367$		−	10.4333i		−	0.544614i	−0.962210	−	0.272307i	$-0.912213\pi$
$367$		−	10.4333i		−	0.544614i	0.962210	−	0.272307i	$-0.0877866\pi$
$368$			104.453i			5.44497i
$369$	−48.7414			−2.53738
$370$	0.220964	+	1.54665i	0.0114874	+	0.0804064i
$371$	−28.5522			−1.48236
$372$			25.9911i			1.34757i
$373$		−	12.4034i		−	0.642226i	−0.947041	−	0.321113i	$-0.895943\pi$
$373$		−	12.4034i		−	0.642226i	0.947041	−	0.321113i	$-0.104057\pi$
$374$	16.2745			0.841533
$375$	−27.9439	+	12.6711i	−1.44302	+	0.654335i
$376$	−27.5134			−1.41889
$377$			24.7884i			1.27667i
$378$			37.4103i			1.92418i
$379$	17.1068			0.878719			0.439359	−	0.898311i	$-0.355205\pi$
$379$	17.1068			0.878719			0.439359	+	0.898311i	$0.355205\pi$
$380$	1.80196	+	12.6129i	0.0924384	+	0.647026i
$381$	48.4991			2.48469
$382$		−	31.9809i		−	1.63628i
$383$		−	27.5259i		−	1.40651i	−0.710939	−	0.703253i	$-0.751730\pi$
$383$		−	27.5259i		−	1.40651i	0.710939	−	0.703253i	$-0.248270\pi$
$384$	159.778			8.15363
$385$	−7.10217	+	1.01466i	−0.361960	+	0.0517120i
$386$	−17.3551			−0.883350
$387$		−	9.85730i		−	0.501075i
$388$			15.1363i			0.768427i
$389$	29.4568			1.49352			0.746760	−	0.665094i	$-0.231609\pi$
$389$	29.4568			1.49352			0.746760	+	0.665094i	$0.231609\pi$
$390$	−65.2366	+	9.32012i	−3.30338	+	0.471943i
$391$	−35.8917			−1.81512
$392$		−	33.7970i		−	1.70701i
$393$			13.3207i			0.671939i
$394$	−18.1220			−0.912973
$395$	−2.58407	−	18.0873i	−0.130019	−	0.910073i
$396$	25.8193			1.29747
$397$			0.725541i			0.0364138i	0.999834	+	0.0182069i	$0.00579576\pi$
$397$			0.725541i			0.0364138i	−0.999834	+	0.0182069i	$0.994204\pi$
$398$			31.6953i			1.58874i
$399$	−8.80502			−0.440802
$400$	−81.9377	+	23.9001i	−4.09689	+	1.19501i
$401$	25.0438			1.25063			0.625314	−	0.780373i	$-0.284971\pi$
$401$	25.0438			1.25063			0.625314	+	0.780373i	$0.284971\pi$
$402$		−	19.8954i		−	0.992294i
$403$		−	6.43342i		−	0.320471i
$404$	−19.1748			−0.953981
$405$	−0.651764	−	4.56205i	−0.0323864	−	0.226690i
$406$	−57.0111			−2.82941
$407$			0.251830i			0.0124827i
$408$			165.158i			8.17656i
$409$	38.9407			1.92550			0.962748	−	0.270401i	$-0.0871563\pi$
$409$	38.9407			1.92550			0.962748	+	0.270401i	$0.0871563\pi$
$410$	66.0625	−	9.43812i	3.26260	−	0.466116i
$411$	−1.29174			−0.0637168
$412$		−	108.957i		−	5.36791i
$413$			13.1368i			0.646422i
$414$	−76.9287			−3.78084
$415$	−27.0805	+	3.86889i	−1.32933	+	0.189916i
$416$	−103.894			−5.09383
$417$			28.0625i			1.37422i
$418$			2.77451i			0.135706i
$419$	−35.0064			−1.71018			−0.855088	−	0.518482i	$-0.826497\pi$
$419$	−35.0064			−1.71018			−0.855088	+	0.518482i	$0.826497\pi$
$420$	−15.8663	−	111.057i	−0.774194	−	5.41900i
$421$	−6.05787			−0.295242			−0.147621	−	0.989044i	$-0.547162\pi$
$421$	−6.05787			−0.295242			−0.147621	+	0.989044i	$0.547162\pi$
$422$			0.441487i			0.0214913i
$423$		−	12.1514i		−	0.590822i
$424$	−91.3040			−4.43411
$425$	−8.21250	−	28.1552i	−0.398365	−	1.36573i
$426$	42.0091			2.03535
$427$			14.5124i			0.702303i
$428$			108.885i			5.26315i
$429$	−10.6220			−0.512836
$430$	1.90873	+	13.3602i	0.0920472	+	0.644288i
$431$	−9.48475			−0.456864			−0.228432	−	0.973560i	$-0.573360\pi$
$431$	−9.48475			−0.456864			−0.228432	+	0.973560i	$0.573360\pi$
$432$			71.7390i			3.45155i
$433$			25.8710i			1.24328i	0.783302	+	0.621641i	$0.213534\pi$
$433$			25.8710i			1.24328i	−0.783302	+	0.621641i	$0.786466\pi$
$434$	14.7963			0.710243
$435$	−38.9056	+	5.55831i	−1.86538	+	0.266501i
$436$	−11.6361			−0.557270
$437$		−	6.11891i		−	0.292707i
$438$		−	20.8233i		−	0.994974i
$439$	1.01956			0.0486612			0.0243306	−	0.999704i	$-0.492255\pi$
$439$	1.01956			0.0486612			0.0243306	+	0.999704i	$0.492255\pi$
$440$	−22.7113	+	3.24468i	−1.08272	+	0.154684i
$441$	14.9266			0.710792
$442$		−	62.9908i		−	2.99617i
$443$			17.3007i			0.821982i	0.911639	+	0.410991i	$0.134817\pi$
$443$			17.3007i			0.821982i	−0.911639	+	0.410991i	$0.865183\pi$
$444$	−3.93786			−0.186883
$445$	0.582049	+	4.07408i	0.0275918	+	0.193130i
$446$	1.49118			0.0706094
$447$		−	52.8962i		−	2.50190i
$448$		−	129.408i		−	6.11393i
$449$	30.9651			1.46133			0.730667	−	0.682734i	$-0.239209\pi$
$449$	30.9651			1.46133			0.730667	+	0.682734i	$0.239209\pi$
$450$	−17.6023	−	60.3466i	−0.829780	−	2.84477i
$451$	10.7565			0.506504
$452$			11.4661i			0.539321i
$453$			25.3731i			1.19213i
$454$	−37.5202			−1.76091
$455$	3.92728	+	27.4892i	0.184114	+	1.28871i
$456$	−28.1566			−1.31855
$457$			38.9037i			1.81984i	0.414784	+	0.909920i	$0.363857\pi$
$457$			38.9037i			1.81984i	−0.414784	+	0.909920i	$0.636143\pi$
$458$		−	29.4618i		−	1.37666i
$459$	−24.6508			−1.15060
$460$	77.1770	−	11.0260i	3.59840	−	0.514090i
$461$	−24.5284			−1.14240			−0.571200	−	0.820811i	$-0.693522\pi$
$461$	−24.5284			−1.14240			−0.571200	+	0.820811i	$0.693522\pi$
$462$		−	24.4296i		−	1.13657i
$463$			5.44017i			0.252826i	0.991978	+	0.126413i	$0.0403465\pi$
$463$			5.44017i			0.252826i	−0.991978	+	0.126413i	$0.959654\pi$
$464$	−109.326			−5.07533
$465$	10.0973	−	1.44257i	0.468251	−	0.0668974i
$466$	21.7358			1.00689
$467$			14.4461i			0.668487i	0.942487	+	0.334243i	$0.108481\pi$
$467$			14.4461i			0.668487i	−0.942487	+	0.334243i	$0.891519\pi$
$468$		−	99.9343i		−	4.61946i
$469$	−8.38348			−0.387113
$470$	2.35296	+	16.4696i	0.108534	+	0.759687i
$471$	24.9822			1.15112
$472$			42.0089i			1.93362i
$473$			2.17536i			0.100023i
$474$	62.2157			2.85766
$475$	4.79997	−	1.40009i	0.220238	−	0.0642404i
$476$	107.233			4.91504
$477$		−	40.3249i		−	1.84635i
$478$			70.3066i			3.21575i
$479$	−25.0982			−1.14677			−0.573383	−	0.819288i	$-0.694369\pi$
$479$	−25.0982			−1.14677			−0.573383	+	0.819288i	$0.694369\pi$
$480$	−23.2962	−	163.063i	−1.06332	−	7.44275i
$481$	0.974716			0.0444432
$482$			83.3905i			3.79833i
$483$			53.8771i			2.45149i
$484$	−5.69792			−0.258996
$485$	5.88030	−	0.840098i	0.267011	−	0.0381469i
$486$	50.6721			2.29854
$487$			27.8647i			1.26267i	0.775510	+	0.631336i	$0.217493\pi$
$487$			27.8647i			1.26267i	−0.775510	+	0.631336i	$0.782507\pi$
$488$			46.4075i			2.10077i
$489$	−36.1905			−1.63659
$490$	−20.2311	+	2.89034i	−0.913946	+	0.130572i
$491$	−5.39887			−0.243648			−0.121824	−	0.992552i	$-0.538874\pi$
$491$	−5.39887			−0.243648			−0.121824	+	0.992552i	$0.538874\pi$
$492$			168.199i			7.58300i
$493$		−	37.5663i		−	1.69190i
$494$	10.7388			0.483163
$495$	−1.43303	−	10.0306i	−0.0644099	−	0.450840i
$496$	28.3737			1.27402
$497$		−	17.7017i		−	0.794028i
$498$		−	93.1498i		−	4.17414i
$499$	40.0954			1.79492			0.897458	−	0.441100i	$-0.145411\pi$
$499$	40.0954			1.79492			0.897458	+	0.441100i	$0.145411\pi$
$500$	26.3085	+	58.0185i	1.17655	+	2.59467i
$501$	−20.7673			−0.927813
$502$		−	66.7069i		−	2.97728i
$503$		−	19.3594i		−	0.863193i	−0.902067	−	0.431596i	$-0.857950\pi$
$503$		−	19.3594i		−	0.863193i	0.902067	−	0.431596i	$-0.142050\pi$
$504$	149.165			6.64432
$505$	1.06425	+	7.44923i	0.0473583	+	0.331486i
$506$	16.9770			0.754719
$507$			5.43657i			0.241446i
$508$		−	100.696i		−	4.46768i
$509$	29.1426			1.29172			0.645862	−	0.763454i	$-0.276498\pi$
$509$	29.1426			1.29172			0.645862	+	0.763454i	$0.276498\pi$
$510$	98.8645	−	14.1244i	4.37780	−	0.625440i
$511$	−8.77444			−0.388158
$512$		−	107.928i		−	4.76977i
$513$		−	4.20253i		−	0.185546i
$514$	18.2626			0.805528
$515$	−42.3287	+	6.04735i	−1.86523	+	0.266478i
$516$	−34.0160			−1.49747
$517$			2.68163i			0.117938i
$518$			2.24175i			0.0984970i
$519$	33.8878			1.48751
$520$	12.5586	+	87.9047i	0.550733	+	3.85488i
$521$	36.9334			1.61808			0.809042	−	0.587751i	$-0.199987\pi$
$521$	36.9334			1.61808			0.809042	+	0.587751i	$0.199987\pi$
$522$		−	80.5180i		−	3.52418i
$523$		−	43.8433i		−	1.91713i	−0.284867	−	0.958567i	$-0.591950\pi$
$523$		−	43.8433i		−	1.91713i	0.284867	−	0.958567i	$-0.408050\pi$
$524$	27.6571			1.20820
$525$	−42.2639	+	12.3278i	−1.84455	+	0.538029i
$526$	−44.5200			−1.94116
$527$			9.74970i			0.424704i
$528$		−	46.8470i		−	2.03875i
$529$	−14.4410			−0.627872
$530$	7.80836	+	54.6550i	0.339174	+	2.37406i
$531$	−18.5535			−0.805151
$532$			18.2814i			0.792601i
$533$		−	41.6334i		−	1.80334i
$534$	−14.0138			−0.606435
$535$	42.3008	−	6.04337i	1.82882	−	0.261278i
$536$	−26.8086			−1.15796
$537$			26.7595i			1.15476i
$538$		−	47.3260i		−	2.04037i
$539$	−3.29408			−0.141886
$540$	53.0059	−	7.57277i	2.28101	−	0.325880i
$541$	26.3462			1.13271			0.566355	−	0.824161i	$-0.308353\pi$
$541$	26.3462			1.13271			0.566355	+	0.824161i	$0.308353\pi$
$542$		−	41.1894i		−	1.76923i
$543$			8.42319i			0.361474i
$544$	157.449			6.75058
$545$	0.645833	+	4.52054i	0.0276644	+	0.193638i
$546$	−94.5557			−4.04661
$547$		−	13.6728i		−	0.584609i	−0.956325	−	0.292304i	$-0.905578\pi$
$547$		−	13.6728i		−	0.584609i	0.956325	−	0.292304i	$-0.0944220\pi$
$548$			2.68198i			0.114568i
$549$	−20.4961			−0.874754
$550$	3.88456	+	13.3176i	0.165638	+	0.567864i
$551$	6.40440			0.272837
$552$			172.288i			7.33306i
$553$		−	26.2163i		−	1.11483i
$554$	23.8441			1.01304
$555$	0.218560	+	1.52982i	0.00927738	+	0.0649374i
$556$	58.2647			2.47097
$557$			13.0278i			0.552007i	0.961157	+	0.276004i	$0.0890102\pi$
$557$			13.0278i			0.552007i	−0.961157	+	0.276004i	$0.910990\pi$
$558$			20.8971i			0.884644i
$559$	8.41978			0.356119
$560$	−121.237	+	17.3207i	−5.12321	+	0.731935i
$561$	16.0974			0.679634
$562$			37.3641i			1.57611i
$563$		−	26.1689i		−	1.10289i	−0.834211	−	0.551445i	$-0.814077\pi$
$563$		−	26.1689i		−	1.10289i	0.834211	−	0.551445i	$-0.185923\pi$
$564$	−41.9326			−1.76568
$565$	4.45449	−	0.636397i	0.187402	−	0.0267734i
$566$	−39.6441			−1.66637
$567$		−	6.61235i		−	0.277693i
$568$		−	56.6063i		−	2.37515i
$569$	−24.2618			−1.01711			−0.508554	−	0.861030i	$-0.669820\pi$
$569$	−24.2618			−1.01711			−0.508554	+	0.861030i	$0.669820\pi$
$570$	2.40797	+	16.8547i	0.100859	+	0.705965i
$571$	6.25197			0.261637			0.130818	−	0.991406i	$-0.458240\pi$
$571$	6.25197			0.261637			0.130818	+	0.991406i	$0.458240\pi$
$572$			22.0540i			0.922123i
$573$		−	31.6330i		−	1.32149i
$574$	95.7528			3.99664
$575$	−8.56701	−	29.3706i	−0.357269	−	1.22484i
$576$	182.765			7.61521
$577$		−	5.41416i		−	0.225395i	−0.993629	−	0.112697i	$-0.964051\pi$
$577$		−	5.41416i		−	0.225395i	0.993629	−	0.112697i	$-0.0359490\pi$
$578$			48.2944i			2.00878i
$579$	−17.1663			−0.713406
$580$	11.5405	+	80.7779i	0.479191	+	3.35412i
$581$	−39.2512			−1.62841
$582$			20.2267i			0.838424i
$583$			8.89909i			0.368562i
$584$	−28.0588			−1.16108
$585$	−38.8236	+	5.54659i	−1.60516	+	0.229323i
$586$	81.9746			3.38634
$587$		−	29.2069i		−	1.20550i	−0.797931	−	0.602749i	$-0.794072\pi$
$587$		−	29.2069i		−	1.20550i	0.797931	−	0.602749i	$-0.205928\pi$
$588$		−	51.5095i		−	2.12422i
$589$	−1.66215			−0.0684879
$590$	25.1467	−	3.59262i	1.03527	−	0.147906i
$591$	−17.9249			−0.737330
$592$			4.29885i			0.176682i
$593$		−	13.3606i		−	0.548653i	−0.961637	−	0.274326i	$-0.911545\pi$
$593$		−	13.3606i		−	0.548653i	0.961637	−	0.274326i	$-0.0884549\pi$
$594$	11.6600			0.478414
$595$	−5.95171	−	41.6592i	−0.243996	−	1.70786i
$596$	−109.826			−4.49864
$597$			31.3505i			1.28309i
$598$		−	65.7100i		−	2.68708i
$599$	−7.63307			−0.311879			−0.155939	−	0.987767i	$-0.549840\pi$
$599$	−7.63307			−0.311879			−0.155939	+	0.987767i	$0.549840\pi$
$600$	−135.151	+	39.4217i	−5.51752	+	1.60939i
$601$	−33.4520			−1.36454			−0.682269	−	0.731102i	$-0.739006\pi$
$601$	−33.4520			−1.36454			−0.682269	+	0.731102i	$0.739006\pi$
$602$			19.3647i			0.789246i
$603$		−	11.8402i		−	0.482169i
$604$	52.6810			2.14356
$605$	0.316248	+	2.21359i	0.0128573	+	0.0899953i
$606$	−25.6234			−1.04088
$607$			1.87063i			0.0759265i	0.999279	+	0.0379633i	$0.0120870\pi$
$607$			1.87063i			0.0759265i	−0.999279	+	0.0379633i	$0.987913\pi$
$608$			26.8423i			1.08860i
$609$	−56.3909			−2.28507
$610$	27.7798	−	3.96880i	1.12477	−	0.160692i
$611$	10.3793			0.419903
$612$			151.448i			6.12193i
$613$		−	30.9265i		−	1.24911i	−0.780980	−	0.624556i	$-0.785280\pi$
$613$		−	30.9265i		−	1.24911i	0.780980	−	0.624556i	$-0.214720\pi$
$614$	−59.9381			−2.41890
$615$	65.3439	−	9.33545i	2.63492	−	0.376442i
$616$	−32.9183			−1.32632
$617$		−	1.25799i		−	0.0506447i	−0.999679	−	0.0253224i	$-0.991939\pi$
$617$		−	1.25799i		−	0.0506447i	0.999679	−	0.0253224i	$-0.00806122\pi$
$618$		−	145.600i		−	5.85688i
$619$	−15.5642			−0.625578			−0.312789	−	0.949823i	$-0.601263\pi$
$619$	−15.5642			−0.625578			−0.312789	+	0.949823i	$0.601263\pi$
$620$	−2.99513	−	20.9645i	−0.120287	−	0.841956i
$621$	−25.7149			−1.03190
$622$		−	59.3871i		−	2.38121i
$623$			5.90508i			0.236582i
$624$	−181.323			−7.25872
$625$	21.0795	−	13.4408i	0.843180	−	0.537631i
$626$	63.0736			2.52093
$627$			2.74433i			0.109598i
$628$		−	51.8693i		−	2.06981i
$629$	−1.47716			−0.0588982
$630$	−12.7566	−	89.2905i	−0.508236	−	3.55742i
$631$	−33.5188			−1.33436			−0.667182	−	0.744895i	$-0.732500\pi$
$631$	−33.5188			−1.33436			−0.667182	+	0.744895i	$0.732500\pi$
$632$		−	83.8342i		−	3.33475i
$633$			0.436685i			0.0173567i
$634$	−3.59060			−0.142601
$635$	−39.1197	+	5.58889i	−1.55242	+	0.221788i
$636$	−139.155			−5.51785
$637$			12.7499i			0.505168i
$638$			17.7691i			0.703485i
$639$	25.0005			0.989003
$640$	−128.878	+	18.4123i	−5.09434	+	0.727810i
$641$	1.89938			0.0750211			0.0375106	−	0.999296i	$-0.488057\pi$
$641$	1.89938			0.0750211			0.0375106	+	0.999296i	$0.488057\pi$
$642$			145.504i			5.74258i
$643$		−	19.4308i		−	0.766277i	−0.923691	−	0.383138i	$-0.874843\pi$
$643$		−	19.4308i		−	0.766277i	0.923691	−	0.383138i	$-0.125157\pi$
$644$	111.862			4.40800
$645$	1.88797	+	13.2149i	0.0743387	+	0.520337i
$646$	−16.2745			−0.640310
$647$			7.80761i			0.306949i	0.988153	+	0.153474i	$0.0490463\pi$
$647$			7.80761i			0.306949i	−0.988153	+	0.153474i	$0.950954\pi$
$648$		−	21.1449i		−	0.830652i
$649$	4.09447			0.160722
$650$	51.5462	−	15.0353i	2.02181	−	0.589734i
$651$	14.6353			0.573602
$652$			75.1406i			2.94273i
$653$		−	21.0194i		−	0.822553i	−0.911511	−	0.411277i	$-0.865083\pi$
$653$		−	21.0194i		−	0.822553i	0.911511	−	0.411277i	$-0.134917\pi$
$654$	−15.5495			−0.608032
$655$	−1.53503	−	10.7445i	−0.0599787	−	0.419823i
$656$	183.618			7.16909
$657$		−	12.3923i		−	0.483471i
$658$			23.8715i			0.930608i
$659$	−32.1192			−1.25119			−0.625594	−	0.780149i	$-0.715143\pi$
$659$	−32.1192			−1.25119			−0.625594	+	0.780149i	$0.715143\pi$
$660$	−34.6139	+	4.94516i	−1.34734	+	0.192490i
$661$	−26.8022			−1.04248			−0.521242	−	0.853409i	$-0.674531\pi$
$661$	−26.8022			−1.04248			−0.521242	+	0.853409i	$0.674531\pi$
$662$			62.0946i			2.41338i
$663$		−	62.3056i		−	2.41975i
$664$	−125.517			−4.87101
$665$	7.10217	−	1.01466i	0.275410	−	0.0393469i
$666$	−3.16608			−0.122683
$667$		−	39.1880i		−	1.51736i
$668$			43.1181i			1.66829i
$669$	1.47496			0.0570252
$670$	2.29269	+	16.0478i	0.0885742	+	0.619979i
$671$	4.52319			0.174616
$672$		−	236.347i		−	9.11729i
$673$		−	13.3416i		−	0.514281i	−0.966374	−	0.257140i	$-0.917220\pi$
$673$		−	13.3416i		−	0.514281i	0.966374	−	0.257140i	$-0.0827803\pi$
$674$	−54.7837			−2.11019
$675$	−5.88391	−	20.1720i	−0.226472	−	0.776421i
$676$	11.2877			0.434142
$677$		−	35.2641i		−	1.35531i	−0.735381	−	0.677654i	$-0.762997\pi$
$677$		−	35.2641i		−	1.35531i	0.735381	−	0.677654i	$-0.237003\pi$
$678$			15.3223i			0.588449i
$679$	8.52307			0.327085
$680$	−19.0323	−	133.218i	−0.729857	−	5.10866i
$681$	−37.1121			−1.42214
$682$		−	4.61167i		−	0.176590i
$683$			22.6519i			0.866753i	0.901213	+	0.433376i	$0.142678\pi$
$683$			22.6519i			0.866753i	−0.901213	+	0.433376i	$0.857322\pi$
$684$	−25.8193			−0.987224
$685$	1.04192	−	0.148856i	0.0398099	−	0.00568750i
$686$	32.9895			1.25955
$687$		−	29.1413i		−	1.11181i
$688$			37.1343i			1.41573i
$689$	34.4442			1.31222
$690$	103.132	−	14.7341i	3.92618	−	0.560919i
$691$	13.6411			0.518930			0.259465	−	0.965752i	$-0.416454\pi$
$691$	13.6411			0.518930			0.259465	+	0.965752i	$0.416454\pi$
$692$		−	70.3597i		−	2.67467i
$693$		−	14.5386i		−	0.552274i
$694$	60.0850			2.28080
$695$	−3.23383	−	22.6353i	−0.122666	−	0.858607i
$696$	−180.326			−6.83525
$697$			63.0944i			2.38987i
$698$			12.7604i			0.482988i
$699$	21.4993			0.813179
$700$	25.5956	+	87.7504i	0.967423	+	3.31665i
$701$	5.88833			0.222399			0.111200	−	0.993798i	$-0.464531\pi$
$701$	5.88833			0.222399			0.111200	+	0.993798i	$0.464531\pi$
$702$		−	45.1303i		−	1.70333i
$703$		−	0.251830i		−	0.00949795i
$704$	−40.3335			−1.52013
$705$	2.32736	+	16.2905i	0.0876534	+	0.613534i
$706$	−1.91559			−0.0720940
$707$			10.7971i			0.406067i
$708$			64.0251i			2.40621i
$709$	20.0746			0.753919			0.376960	−	0.926230i	$-0.376970\pi$
$709$	20.0746			0.753919			0.376960	+	0.926230i	$0.376970\pi$
$710$	−33.8848	+	4.84100i	−1.27167	+	0.181679i
$711$	37.0258			1.38858
$712$			18.8832i			0.707678i
$713$			10.1706i			0.380891i
$714$	143.297			5.36275
$715$	8.56778	−	1.22405i	0.320417	−	0.0457768i
$716$	55.5594			2.07635
$717$			69.5418i			2.59709i
$718$			1.34385i			0.0501520i
$719$	19.9007			0.742171			0.371086	−	0.928599i	$-0.378986\pi$
$719$	19.9007			0.742171			0.371086	+	0.928599i	$0.378986\pi$
$720$	−24.4625	−	171.226i	−0.911662	−	6.38122i
$721$	−61.3524			−2.28488
$722$		−	2.77451i		−	0.103257i
$723$			82.4833i			3.06759i
$724$	17.4887			0.649961
$725$	30.7410	−	8.96673i	1.14169	−	0.333016i
$726$	−7.61418			−0.282589
$727$			2.48983i			0.0923426i	0.998934	+	0.0461713i	$0.0147020\pi$
$727$			2.48983i			0.0923426i	−0.998934	+	0.0461713i	$0.985298\pi$
$728$			127.412i			4.72219i
$729$	43.9381			1.62734
$730$	2.39961	+	16.7961i	0.0888134	+	0.621653i
$731$	−12.7600			−0.471945
$732$			70.7289i			2.61422i
$733$			1.67302i			0.0617945i	0.999523	+	0.0308973i	$0.00983647\pi$
$733$			1.67302i			0.0617945i	−0.999523	+	0.0308973i	$0.990164\pi$
$734$	−28.9473			−1.06847
$735$	−20.0110	+	2.85890i	−0.738116	+	0.105452i
$736$	164.246			6.05418
$737$			2.61295i			0.0962491i
$738$			135.234i			4.97802i
$739$	−12.3807			−0.455432			−0.227716	−	0.973728i	$-0.573126\pi$
$739$	−12.3807			−0.455432			−0.227716	+	0.973728i	$0.573126\pi$
$740$	3.17630	−	0.453787i	0.116763	−	0.0166815i
$741$	10.6220			0.390210
$742$			79.2184i			2.90820i
$743$		−	2.41474i		−	0.0885881i	−0.999019	−	0.0442940i	$-0.985896\pi$
$743$		−	2.41474i		−	0.0885881i	0.999019	−	0.0442940i	$-0.0141038\pi$
$744$	46.8006			1.71579
$745$	6.09559	+	42.6663i	0.223325	+	1.56317i
$746$	−34.4135			−1.25997
$747$		−	55.4353i		−	2.02827i
$748$		−	33.4223i		−	1.22204i
$749$	61.3119			2.24029
$750$	35.1562	+	77.5307i	1.28372	+	2.83102i
$751$	7.67280			0.279984			0.139992	−	0.990153i	$-0.455292\pi$
$751$	7.67280			0.279984			0.139992	+	0.990153i	$0.455292\pi$
$752$			45.7767i			1.66930i
$753$		−	65.9813i		−	2.40449i
$754$	68.7759			2.50467
$755$	−2.92392	−	20.4661i	−0.106412	−	0.744838i
$756$	76.8282			2.79421
$757$		−	7.03423i		−	0.255663i	−0.991796	−	0.127832i	$-0.959198\pi$
$757$		−	7.03423i		−	0.255663i	0.991796	−	0.127832i	$-0.0408017\pi$
$758$		−	47.4631i		−	1.72394i
$759$	16.7923			0.609522
$760$	22.7113	−	3.24468i	0.823825	−	0.117697i
$761$	8.98118			0.325567			0.162784	−	0.986662i	$-0.447953\pi$
$761$	8.98118			0.325567			0.162784	+	0.986662i	$0.447953\pi$
$762$		−	134.561i		−	4.87465i
$763$			6.55219i			0.237205i
$764$	−65.6780			−2.37615
$765$	58.8362	−	8.40573i	2.12723	−	0.303910i
$766$	−76.3709			−2.75939
$767$		−	15.8478i		−	0.572230i
$768$		−	221.929i		−	8.00817i
$769$	−47.2240			−1.70294			−0.851470	−	0.524404i	$-0.824288\pi$
$769$	−47.2240			−1.70294			−0.851470	+	0.524404i	$0.824288\pi$
$770$	2.81519	+	19.7051i	0.101453	+	0.710121i
$771$	18.0639			0.650556
$772$			35.6415i			1.28277i
$773$		−	30.3348i		−	1.09107i	−0.838089	−	0.545533i	$-0.816327\pi$
$773$		−	30.3348i		−	1.09107i	0.838089	−	0.545533i	$-0.183673\pi$
$774$	−27.3492			−0.983046
$775$	−7.97830	+	2.32716i	−0.286589	+	0.0835941i
$776$	27.2550			0.978398
$777$			2.21737i			0.0795476i
$778$		−	81.7283i		−	2.93010i
$779$	−10.7565			−0.385392
$780$	19.1404	+	133.974i	0.685337	+	4.79704i
$781$	−5.51722			−0.197422
$782$			99.5820i			3.56104i
$783$		−	26.9147i		−	0.961852i
$784$	−56.2315			−2.00827
$785$	−20.1508	+	2.87887i	−0.719211	+	0.102751i
$786$	36.9584			1.31826
$787$			3.82340i			0.136289i	0.997675	+	0.0681447i	$0.0217080\pi$
$787$			3.82340i			0.136289i	−0.997675	+	0.0681447i	$0.978292\pi$
$788$			37.2165i			1.32578i
$789$	−44.0356			−1.56771
$790$	−50.1835	+	7.16955i	−1.78545	+	0.255081i
$791$	6.45645			0.229565
$792$		−	46.4913i		−	1.65200i
$793$		−	17.5071i		−	0.621697i
$794$	2.01302			0.0714395
$795$	7.72342	+	54.0604i	0.273921	+	1.91732i
$796$	65.0916			2.30711
$797$			32.7856i			1.16133i	0.814144	+	0.580663i	$0.197207\pi$
$797$			32.7856i			1.16133i	−0.814144	+	0.580663i	$0.802793\pi$
$798$			24.4296i			0.864800i
$799$	−15.7297			−0.556475
$800$	37.5816	+	128.843i	1.32871	+	4.55527i
$801$	−8.33987			−0.294675
$802$		−	69.4844i		−	2.45358i
$803$			2.73480i			0.0965090i
$804$	−40.8586			−1.44097
$805$	−6.20863	−	43.4576i	−0.218825	−	1.53168i
$806$	−17.8496			−0.628725
$807$		−	46.8112i		−	1.64783i
$808$			34.5270i			1.21465i
$809$	−24.8694			−0.874361			−0.437181	−	0.899374i	$-0.644023\pi$
$809$	−24.8694			−0.874361			−0.437181	+	0.899374i	$0.644023\pi$
$810$	−12.6575	+	1.80833i	−0.444738	+	0.0635381i
$811$	−20.4421			−0.717821			−0.358910	−	0.933372i	$-0.616852\pi$
$811$	−20.4421			−0.717821			−0.358910	+	0.933372i	$0.616852\pi$
$812$			117.082i			4.10876i
$813$		−	40.7413i		−	1.42886i
$814$	0.698705			0.0244896
$815$	29.1915	−	4.17048i	1.02253	−	0.146086i
$816$	274.790			9.61958
$817$		−	2.17536i		−	0.0761061i
$818$		−	108.042i		−	3.77758i
$819$	−56.2719			−1.96630
$820$	−19.3827	−	135.670i	−0.676875	−	4.73781i
$821$	53.8539			1.87951			0.939757	−	0.341843i	$-0.111051\pi$
$821$	53.8539			1.87951			0.939757	+	0.341843i	$0.111051\pi$
$822$			3.58395i			0.125005i
$823$			40.2952i			1.40460i	0.711880	+	0.702301i	$0.247844\pi$
$823$			40.2952i			1.40460i	−0.711880	+	0.702301i	$0.752156\pi$
$824$	−196.192			−6.83468
$825$	3.84230	+	13.1727i	0.133772	+	0.458615i
$826$	36.4484			1.26820
$827$			33.1923i			1.15421i	0.816670	+	0.577105i	$0.195818\pi$
$827$			33.1923i			1.15421i	−0.816670	+	0.577105i	$0.804182\pi$
$828$			157.986i			5.49038i
$829$	−28.6178			−0.993937			−0.496969	−	0.867769i	$-0.665554\pi$
$829$	−28.6178			−0.993937			−0.496969	+	0.867769i	$0.665554\pi$
$830$	10.7343	+	75.1351i	0.372593	+	2.60798i
$831$	23.5847			0.818145
$832$			156.112i			5.41221i
$833$		−	19.3221i		−	0.669471i
$834$	77.8596			2.69606
$835$	16.7510	−	2.39316i	0.579692	−	0.0828186i
$836$	5.69792			0.197067
$837$			6.98525i			0.241445i
$838$			97.1258i			3.35516i
$839$	5.00397			0.172756			0.0863781	−	0.996262i	$-0.472471\pi$
$839$	5.00397			0.172756			0.0863781	+	0.996262i	$0.472471\pi$
$840$	−199.973	+	28.5695i	−6.89973	+	0.985740i
$841$	12.0164			0.414358
$842$			16.8076i			0.579229i
$843$			36.9576i			1.27289i
$844$	0.906667			0.0312088
$845$	−0.626493	−	4.38516i	−0.0215520	−	0.150854i
$846$	−33.7142			−1.15912
$847$			3.20844i			0.110243i
$848$			151.911i			5.21666i
$849$	−39.2129			−1.34578
$850$	−78.1170	+	22.7857i	−2.67939	+	0.781542i
$851$	−1.54092			−0.0528222
$852$		−	86.2726i		−	2.95565i
$853$			14.8401i			0.508117i	0.967189	+	0.254058i	$0.0817655\pi$
$853$			14.8401i			0.508117i	−0.967189	+	0.254058i	$0.918234\pi$
$854$	40.2647			1.37783
$855$	1.43303	+	10.0306i	0.0490086	+	0.343038i
$856$	196.063			6.70129
$857$			9.89677i			0.338067i	0.985610	+	0.169034i	$0.0540646\pi$
$857$			9.89677i			0.338067i	−0.985610	+	0.169034i	$0.945935\pi$
$858$			29.4709i			1.00612i
$859$	21.7867			0.743352			0.371676	−	0.928363i	$-0.378783\pi$
$859$	21.7867			0.743352			0.371676	+	0.928363i	$0.378783\pi$
$860$	27.4375	−	3.91990i	0.935610	−	0.133667i
$861$	94.7112			3.22775
$862$			26.3155i			0.896311i
$863$		−	24.4284i		−	0.831553i	−0.909467	−	0.415776i	$-0.863510\pi$
$863$		−	24.4284i		−	0.831553i	0.909467	−	0.415776i	$-0.136490\pi$
$864$	112.806			3.83772
$865$	−27.3341	+	3.90513i	−0.929388	+	0.132778i
$866$	71.7795			2.43917
$867$			47.7691i			1.62232i
$868$		−	30.3865i		−	1.03139i
$869$	−8.17104			−0.277183
$870$	15.4216	+	107.944i	0.522841	+	3.65965i
$871$	10.1135			0.342682
$872$			20.9525i			0.709542i
$873$			12.0373i			0.407401i
$874$	−16.9770			−0.574255
$875$	32.6696	−	14.8140i	1.10444	−	0.500805i
$876$	−42.7640			−1.44486
$877$		−	24.9962i		−	0.844062i	−0.906581	−	0.422031i	$-0.861317\pi$
$877$		−	24.9962i		−	0.844062i	0.906581	−	0.422031i	$-0.138683\pi$
$878$		−	2.82879i		−	0.0954672i
$879$	81.0828			2.73486
$880$	5.39850	+	37.7870i	0.181983	+	1.27380i
$881$	−25.3991			−0.855719			−0.427859	−	0.903845i	$-0.640732\pi$
$881$	−25.3991			−0.855719			−0.427859	+	0.903845i	$0.640732\pi$
$882$		−	41.4141i		−	1.39449i
$883$			48.3559i			1.62731i	0.581351	+	0.813653i	$0.302524\pi$
$883$			48.3559i			1.62731i	−0.581351	+	0.813653i	$0.697476\pi$
$884$	−129.362			−4.35092
$885$	24.8732	−	3.55354i	0.836103	−	0.119451i
$886$	48.0010			1.61263
$887$			22.8073i			0.765793i	0.923791	+	0.382897i	$0.125073\pi$
$887$			22.8073i			0.765793i	−0.923791	+	0.382897i	$0.874927\pi$
$888$			7.09068i			0.237948i
$889$	−56.7011			−1.90169
$890$	11.3036	−	1.61490i	0.378897	−	0.0541316i
$891$	−2.06093			−0.0690436
$892$		−	3.06238i		−	0.102536i
$893$		−	2.68163i		−	0.0897374i
$894$	−146.761			−4.90843
$895$	−3.08368	−	21.5843i	−0.103076	−	0.721484i
$896$	−186.799			−6.24051
$897$		−	64.9952i		−	2.17013i
$898$		−	85.9131i		−	2.86696i
$899$	−10.6451			−0.355034
$900$	−123.932	+	36.1492i	−4.13106	+	1.20497i
$901$	−52.1994			−1.73901
$902$		−	29.8440i		−	0.993698i
$903$			19.1540i			0.637407i
$904$	20.6464			0.686689
$905$	−0.970663	−	6.79419i	−0.0322659	−	0.225847i
$906$	70.3981			2.33882
$907$			4.89927i			0.162678i	0.996687	+	0.0813388i	$0.0259196\pi$
$907$			4.89927i			0.162678i	−0.996687	+	0.0813388i	$0.974080\pi$
$908$			77.0540i			2.55713i
$909$	−15.2490			−0.505778
$910$	76.2691	−	10.8963i	2.52830	−	0.361209i
$911$	14.2078			0.470727			0.235364	−	0.971907i	$-0.424372\pi$
$911$	14.2078			0.470727			0.235364	+	0.971907i	$0.424372\pi$
$912$			46.8470i			1.55126i
$913$			12.2337i			0.404877i
$914$	107.939			3.57030
$915$	27.4776	−	3.92562i	0.908380	−	0.129777i
$916$	−60.5046			−1.99913
$917$		−	15.5734i		−	0.514279i
$918$			68.3939i			2.25733i
$919$	−37.3984			−1.23366			−0.616830	−	0.787096i	$-0.711583\pi$
$919$	−37.3984			−1.23366			−0.616830	+	0.787096i	$0.711583\pi$
$920$	−19.8539	−	138.968i	−0.654564	−	4.58165i
$921$	−59.2861			−1.95354
$922$			68.0542i			2.24125i
$923$			21.3546i			0.702895i
$924$	−50.1703			−1.65048
$925$	−0.352584	−	1.20878i	−0.0115929	−	0.0397444i
$926$	15.0938			0.496013
$927$		−	86.6493i		−	2.84594i
$928$			171.909i			5.64319i
$929$	−18.4186			−0.604294			−0.302147	−	0.953261i	$-0.597703\pi$
$929$	−18.4186			−0.604294			−0.302147	+	0.953261i	$0.597703\pi$
$930$	−4.00241	−	28.0151i	−0.131244	−	0.918650i
$931$	3.29408			0.107959
$932$		−	44.6380i		−	1.46217i
$933$		−	58.7411i		−	1.92310i
$934$	40.0810			1.31149
$935$	−12.9843	+	1.85502i	−0.424631	+	0.0606655i
$936$	−179.946			−5.88172
$937$		−	59.8435i		−	1.95500i	−0.210930	−	0.977501i	$-0.567649\pi$
$937$		−	59.8435i		−	1.95500i	0.210930	−	0.977501i	$-0.432351\pi$
$938$			23.2601i			0.759468i
$939$	62.3874			2.03594
$940$	33.8231	−	4.83218i	1.10319	−	0.157608i
$941$	14.5570			0.474545			0.237272	−	0.971443i	$-0.423747\pi$
$941$	14.5570			0.474545			0.237272	+	0.971443i	$0.423747\pi$
$942$		−	69.3134i		−	2.25835i
$943$			65.8180i			2.14333i
$944$	69.8944			2.27487
$945$	−4.26415	−	29.8471i	−0.138713	−	0.970925i
$946$	6.03555			0.196233
$947$		−	15.6623i		−	0.508955i	−0.967079	−	0.254478i	$-0.918097\pi$
$947$		−	15.6623i		−	0.508955i	0.967079	−	0.254478i	$-0.0819035\pi$
$948$		−	127.770i		−	4.14979i
$949$	10.5851			0.343608
$950$	−3.88456	−	13.3176i	−0.126032	−	0.432080i
$951$	−3.55154			−0.115166
$952$		−	193.089i		−	6.25806i
$953$		−	27.6656i		−	0.896176i	−0.893990	−	0.448088i	$-0.852105\pi$
$953$		−	27.6656i		−	0.896176i	0.893990	−	0.448088i	$-0.147895\pi$
$954$	−111.882			−3.62231
$955$	3.64528	+	25.5153i	0.117959	+	0.825656i
$956$	144.386			4.66979
$957$			17.5758i			0.568145i
$958$			69.6352i			2.24981i
$959$	1.51019			0.0487667
$960$	−245.019	+	35.0050i	−7.90795	+	1.12978i
$961$	−28.2372			−0.910879
$962$		−	2.70436i		−	0.0871921i
$963$			86.5922i			2.79039i
$964$	171.256			5.51579
$965$	13.8464	−	1.97819i	0.445732	−	0.0636801i
$966$	149.483			4.80953
$967$			2.39400i			0.0769857i	0.999259	+	0.0384929i	$0.0122557\pi$
$967$			2.39400i			0.0769857i	−0.999259	+	0.0384929i	$0.987744\pi$
$968$			10.2599i			0.329766i
$969$	−16.0974			−0.517124
$970$	−2.33086	−	16.3150i	−0.0748395	−	0.523842i
$971$	9.52917			0.305806			0.152903	−	0.988241i	$-0.451138\pi$
$971$	9.52917			0.305806			0.152903	+	0.988241i	$0.451138\pi$
$972$		−	104.064i		−	3.33784i
$973$		−	32.8083i		−	1.05178i
$974$	77.3111			2.47721
$975$	50.9854	−	14.8718i	1.63284	−	0.476277i
$976$	77.2128			2.47152
$977$		−	17.6663i		−	0.565194i	−0.959239	−	0.282597i	$-0.908804\pi$
$977$		−	17.6663i		−	0.565194i	0.959239	−	0.282597i	$-0.0911959\pi$
$978$			100.411i			3.21079i
$979$	1.84048			0.0588221
$980$	5.93579	+	41.5478i	0.189612	+	1.32720i
$981$	−9.25380			−0.295451
$982$			14.9792i			0.478007i
$983$			3.24817i			0.103601i	0.998657	+	0.0518003i	$0.0164959\pi$
$983$			3.24817i			0.103601i	−0.998657	+	0.0518003i	$0.983504\pi$
$984$	302.867			9.65504
$985$	14.4583	−	2.06560i	0.460679	−	0.0658156i
$986$	−104.228			−3.31930
$987$			23.6118i			0.751573i
$988$		−	22.0540i		−	0.701631i
$989$	−13.3108			−0.423259
$990$	−27.8299	+	3.97596i	−0.884492	+	0.126364i
$991$	−15.8274			−0.502774			−0.251387	−	0.967887i	$-0.580887\pi$
$991$	−15.8274			−0.502774			−0.251387	+	0.967887i	$0.580887\pi$
$992$		−	44.6161i		−	1.41656i
$993$			61.4191i			1.94908i
$994$	−49.1135			−1.55779
$995$	−3.61274	−	25.2875i	−0.114531	−	0.801668i
$996$	−191.298			−6.06152
$997$			47.5564i			1.50613i	0.657948	+	0.753063i	$0.271425\pi$
$997$			47.5564i			1.50613i	−0.657948	+	0.753063i	$0.728575\pi$
$998$		−	111.245i		−	3.52140i
$999$	−1.05832			−0.0334838

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1045.2.b.e.419.2	✓	30
5.2	odd	4		5225.2.a.bc.1.29		30
5.3	odd	4		5225.2.a.bc.1.2		30
5.4	even	2	inner	1045.2.b.e.419.29	yes	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1045.2.b.e.419.2	✓	30	1.1	even	1	trivial
1045.2.b.e.419.29	yes	30	5.4	even	2	inner
5225.2.a.bc.1.2		30	5.3	odd	4
5225.2.a.bc.1.29		30	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:	\( N \)	\(=\)	\( 1045 = 5 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1045.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.77451i q^{2} -2.74433i q^{3} -5.69792 q^{4} +(0.316248 + 2.21359i) q^{5} -7.61418 q^{6} +3.20844i q^{7} +10.2599i q^{8} -4.53135 q^{9} +O(q^{10})\)	\(q-2.77451i q^{2} -2.74433i q^{3} -5.69792 q^{4} +(0.316248 + 2.21359i) q^{5} -7.61418 q^{6} +3.20844i q^{7} +10.2599i q^{8} -4.53135 q^{9} +(6.14164 - 0.877434i) q^{10} +1.00000 q^{11} +15.6370i q^{12} -3.87053i q^{13} +8.90186 q^{14} +(6.07483 - 0.867889i) q^{15} +17.0705 q^{16} +5.86570i q^{17} +12.5723i q^{18} -1.00000 q^{19} +(-1.80196 - 12.6129i) q^{20} +8.80502 q^{21} -2.77451i q^{22} +6.11891i q^{23} +28.1566 q^{24} +(-4.79997 + 1.40009i) q^{25} -10.7388 q^{26} +4.20253i q^{27} -18.2814i q^{28} -6.40440 q^{29} +(-2.40797 - 16.8547i) q^{30} +1.66215 q^{31} -26.8423i q^{32} -2.74433i q^{33} +16.2745 q^{34} +(-7.10217 + 1.01466i) q^{35} +25.8193 q^{36} +0.251830i q^{37} +2.77451i q^{38} -10.6220 q^{39} +(-22.7113 + 3.24468i) q^{40} +10.7565 q^{41} -24.4296i q^{42} +2.17536i q^{43} -5.69792 q^{44} +(-1.43303 - 10.0306i) q^{45} +16.9770 q^{46} +2.68163i q^{47} -46.8470i q^{48} -3.29408 q^{49} +(3.88456 + 13.3176i) q^{50} +16.0974 q^{51} +22.0540i q^{52} +8.89909i q^{53} +11.6600 q^{54} +(0.316248 + 2.21359i) q^{55} -32.9183 q^{56} +2.74433i q^{57} +17.7691i q^{58} +4.09447 q^{59} +(-34.6139 + 4.94516i) q^{60} +4.52319 q^{61} -4.61167i q^{62} -14.5386i q^{63} -40.3335 q^{64} +(8.56778 - 1.22405i) q^{65} -7.61418 q^{66} +2.61295i q^{67} -33.4223i q^{68} +16.7923 q^{69} +(2.81519 + 19.7051i) q^{70} -5.51722 q^{71} -46.4913i q^{72} +2.73480i q^{73} +0.698705 q^{74} +(3.84230 + 13.1727i) q^{75} +5.69792 q^{76} +3.20844i q^{77} +29.4709i q^{78} -8.17104 q^{79} +(5.39850 + 37.7870i) q^{80} -2.06093 q^{81} -29.8440i q^{82} +12.2337i q^{83} -50.1703 q^{84} +(-12.9843 + 1.85502i) q^{85} +6.03555 q^{86} +17.5758i q^{87} +10.2599i q^{88} +1.84048 q^{89} +(-27.8299 + 3.97596i) q^{90} +12.4184 q^{91} -34.8651i q^{92} -4.56150i q^{93} +7.44022 q^{94} +(-0.316248 - 2.21359i) q^{95} -73.6642 q^{96} -2.65645i q^{97} +9.13947i q^{98} -4.53135 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 42 q^{4} + 12 q^{6} - 40 q^{9}+O(q^{10}) \) 30 * q - 42 * q^4 + 12 * q^6 - 40 * q^9	\( 30 q - 42 q^{4} + 12 q^{6} - 40 q^{9} + 10 q^{10} + 30 q^{11} + 4 q^{14} + 4 q^{15} + 66 q^{16} - 30 q^{19} + 10 q^{20} + 14 q^{21} - 22 q^{24} - 6 q^{25} - 30 q^{29} + 14 q^{30} + 26 q^{31} - 12 q^{34} + 6 q^{35} + 78 q^{36} - 64 q^{39} - 20 q^{40} + 22 q^{41} - 42 q^{44} + 6 q^{45} + 28 q^{46} - 60 q^{49} + 64 q^{51} - 62 q^{54} - 32 q^{56} + 14 q^{59} - 28 q^{60} + 78 q^{61} - 90 q^{64} + 40 q^{65} + 12 q^{66} + 28 q^{69} + 12 q^{70} + 20 q^{71} - 42 q^{74} + 50 q^{75} + 42 q^{76} - 102 q^{79} - 40 q^{80} + 42 q^{81} - 98 q^{84} - 2 q^{85} - 52 q^{86} + 8 q^{89} + 22 q^{90} + 56 q^{91} - 40 q^{94} - 74 q^{96} - 40 q^{99}+O(q^{100}) \) 30 * q - 42 * q^4 + 12 * q^6 - 40 * q^9 + 10 * q^10 + 30 * q^11 + 4 * q^14 + 4 * q^15 + 66 * q^16 - 30 * q^19 + 10 * q^20 + 14 * q^21 - 22 * q^24 - 6 * q^25 - 30 * q^29 + 14 * q^30 + 26 * q^31 - 12 * q^34 + 6 * q^35 + 78 * q^36 - 64 * q^39 - 20 * q^40 + 22 * q^41 - 42 * q^44 + 6 * q^45 + 28 * q^46 - 60 * q^49 + 64 * q^51 - 62 * q^54 - 32 * q^56 + 14 * q^59 - 28 * q^60 + 78 * q^61 - 90 * q^64 + 40 * q^65 + 12 * q^66 + 28 * q^69 + 12 * q^70 + 20 * q^71 - 42 * q^74 + 50 * q^75 + 42 * q^76 - 102 * q^79 - 40 * q^80 + 42 * q^81 - 98 * q^84 - 2 * q^85 - 52 * q^86 + 8 * q^89 + 22 * q^90 + 56 * q^91 - 40 * q^94 - 74 * q^96 - 40 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more