LMFDB - Embedded newform 1650.2.f.c.1649.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1650,2,Mod(1649,1650)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1650, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1650.1649"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1650 = 2 \cdot 3 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1650.f (of order $2$, degree $1$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,-4,-8,0,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$13.1753163335$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.2051727616.3
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 11x^{6} + 37x^{4} + 36x^{2} + 4 $ x^8 + 11x^6 + 37x^4 + 36*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 330)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1649.6
Root			$-0.356500i$ of defining polynomial
Character	$\chi$	$=$	1650.1649
Dual form			1650.2.f.c.1649.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000i q^{2} +(-1.19035 + 1.25820i) q^{3} -1.00000 q^{4} +(-1.25820 - 1.19035i) q^{6} +3.22941 q^{7} -1.00000i q^{8} +(-0.166154 - 2.99540i) q^{9} +(-2.73719 + 1.87291i) q^{11} +(1.19035 - 1.25820i) q^{12} -0.713000 q^{13} +3.22941i q^{14} +1.00000 q^{16} -6.12651i q^{17} +(2.99540 - 0.166154i) q^{18} +2.33231i q^{19} +(-3.84411 + 4.06325i) q^{21} +(-1.87291 - 2.73719i) q^{22} -3.03282 q^{23} +(1.25820 + 1.19035i) q^{24} -0.713000i q^{26} +(3.96660 + 3.35650i) q^{27} -3.22941 q^{28} -5.27779 q^{29} -9.55251 q^{31} +1.00000i q^{32} +(0.901704 - 5.67335i) q^{33} +6.12651 q^{34} +(0.166154 + 2.99540i) q^{36} -9.73661i q^{37} -2.33231 q^{38} +(0.848716 - 0.897099i) q^{39} -0.761383 q^{41} +(-4.06325 - 3.84411i) q^{42} -5.79420 q^{43} +(2.73719 - 1.87291i) q^{44} -3.03282i q^{46} -11.7942 q^{47} +(-1.19035 + 1.25820i) q^{48} +3.42907 q^{49} +(7.70840 + 7.29266i) q^{51} +0.713000 q^{52} +1.09369 q^{53} +(-3.35650 + 3.96660i) q^{54} -3.22941i q^{56} +(-2.93452 - 2.77625i) q^{57} -5.27779i q^{58} -1.95162i q^{59} +2.19331i q^{61} -9.55251i q^{62} +(-0.536580 - 9.67335i) q^{63} -1.00000 q^{64} +(5.67335 + 0.901704i) q^{66} -2.80977i q^{67} +6.12651i q^{68} +(3.61010 - 3.81590i) q^{69} -11.7366i q^{71} +(-2.99540 + 0.166154i) q^{72} +14.6946 q^{73} +9.73661 q^{74} -2.33231i q^{76} +(-8.83951 + 6.04838i) q^{77} +(0.897099 + 0.848716i) q^{78} +13.5400i q^{79} +(-8.94479 + 0.995395i) q^{81} -0.761383i q^{82} +7.72857i q^{83} +(3.84411 - 4.06325i) q^{84} -5.79420i q^{86} +(6.28240 - 6.64054i) q^{87} +(1.87291 + 2.73719i) q^{88} -3.04203i q^{89} -2.30257 q^{91} +3.03282 q^{92} +(11.3708 - 12.0190i) q^{93} -11.7942i q^{94} +(-1.25820 - 1.19035i) q^{96} -10.6462i q^{97} +3.42907i q^{98} +(6.06490 + 7.88778i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{3} - 8 q^{4} - 2 q^{6} - 2 q^{9} - 6 q^{11} + 4 q^{12} + 4 q^{13} + 8 q^{16} + 8 q^{21} + 6 q^{22} + 8 q^{23} + 2 q^{24} - 10 q^{27} - 4 q^{29} - 4 q^{31} + 4 q^{33} - 4 q^{34} + 2 q^{36} - 20 q^{38}+ \cdots + 10 q^{99}+O(q^{100}) $ 8 * q - 4 * q^3 - 8 * q^4 - 2 * q^6 - 2 * q^9 - 6 * q^11 + 4 * q^12 + 4 * q^13 + 8 * q^16 + 8 * q^21 + 6 * q^22 + 8 * q^23 + 2 * q^24 - 10 * q^27 - 4 * q^29 - 4 * q^31 + 4 * q^33 - 4 * q^34 + 2 * q^36 - 20 * q^38 - 8 * q^39 + 16 * q^41 - 6 * q^42 + 8 * q^43 + 6 * q^44 - 40 * q^47 - 4 * q^48 + 4 * q^49 + 28 * q^51 - 4 * q^52 - 12 * q^53 - 22 * q^54 + 12 * q^57 - 32 * q^63 - 8 * q^64 - 18 * q^66 - 8 * q^69 + 12 * q^73 - 12 * q^74 - 8 * q^77 - 20 * q^78 + 2 * q^81 - 8 * q^84 + 36 * q^87 - 6 * q^88 - 48 * q^91 - 8 * q^92 - 2 * q^93 - 2 * q^96 + 10 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1650\mathbb{Z}\right)^\times$.

$n$	$551$	$727$	$1201$
$\chi(n)$	$-1$	$-1$	$-1$

Coefficient data

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

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

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

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$	−1.19035	+	1.25820i	−0.687246	+	0.726424i
$3$	−1.19035	+	1.25820i	−0.687246	+	0.726424i
$4$	−1.00000			−0.500000
$5$		0			0
$5$		0			0
$6$	−1.25820	−	1.19035i	−0.513660	−	0.485957i
$7$	3.22941			1.22060			0.610301	−	0.792170i	$-0.291049\pi$
$7$	3.22941			1.22060			0.610301	+	0.792170i	$0.291049\pi$
$8$		−	1.00000i		−	0.353553i
$9$	−0.166154	−	2.99540i	−0.0553847	−	0.998465i
$10$		0			0
$11$	−2.73719	+	1.87291i	−0.825294	+	0.564703i
$11$	−2.73719	+	1.87291i	−0.825294	+	0.564703i
$12$	1.19035	−	1.25820i	0.343623	−	0.363212i
$13$	−0.713000			−0.197751			−0.0988753	−	0.995100i	$-0.531524\pi$
$13$	−0.713000			−0.197751			−0.0988753	+	0.995100i	$0.531524\pi$
$14$			3.22941i			0.863096i
$15$		0			0
$16$	1.00000			0.250000
$17$		−	6.12651i		−	1.48590i	−0.669349	−	0.742948i	$-0.733427\pi$
$17$		−	6.12651i		−	1.48590i	0.669349	−	0.742948i	$-0.266573\pi$
$18$	2.99540	−	0.166154i	0.706021	−	0.0391629i
$19$			2.33231i			0.535068i	0.963548	+	0.267534i	$0.0862088\pi$
$19$			2.33231i			0.535068i	−0.963548	+	0.267534i	$0.913791\pi$
$20$		0			0
$21$	−3.84411	+	4.06325i	−0.838854	+	0.886675i
$22$	−1.87291	−	2.73719i	−0.399305	−	0.583571i
$23$	−3.03282			−0.632386			−0.316193	−	0.948695i	$-0.602405\pi$
$23$	−3.03282			−0.632386			−0.316193	+	0.948695i	$0.602405\pi$
$24$	1.25820	+	1.19035i	0.256830	+	0.242978i
$25$		0			0
$26$		−	0.713000i		−	0.139831i
$27$	3.96660	+	3.35650i	0.763372	+	0.645959i
$28$	−3.22941			−0.610301
$29$	−5.27779			−0.980061			−0.490031	−	0.871705i	$-0.663014\pi$
$29$	−5.27779			−0.980061			−0.490031	+	0.871705i	$0.663014\pi$
$30$		0			0
$31$	−9.55251			−1.71568			−0.857840	−	0.513916i	$-0.828194\pi$
$31$	−9.55251			−1.71568			−0.857840	+	0.513916i	$0.828194\pi$
$32$			1.00000i			0.176777i
$33$	0.901704	−	5.67335i	0.156967	−	0.987604i
$34$	6.12651			1.05069
$35$		0			0
$36$	0.166154	+	2.99540i	0.0276924	+	0.499233i
$37$		−	9.73661i		−	1.60069i	−0.599541	−	0.800344i	$-0.704650\pi$
$37$		−	9.73661i		−	1.60069i	0.599541	−	0.800344i	$-0.295350\pi$
$38$	−2.33231			−0.378350
$39$	0.848716	−	0.897099i	0.135903	−	0.143651i
$40$		0			0
$41$	−0.761383			−0.118908			−0.0594540	−	0.998231i	$-0.518936\pi$
$41$	−0.761383			−0.118908			−0.0594540	+	0.998231i	$0.518936\pi$
$42$	−4.06325	−	3.84411i	−0.626974	−	0.593159i
$43$	−5.79420			−0.883607			−0.441803	−	0.897112i	$-0.645661\pi$
$43$	−5.79420			−0.883607			−0.441803	+	0.897112i	$0.645661\pi$
$44$	2.73719	−	1.87291i	0.412647	−	0.282351i
$45$		0			0
$46$		−	3.03282i		−	0.447164i
$47$	−11.7942			−1.72036			−0.860180	−	0.509990i	$-0.829649\pi$
$47$	−11.7942			−1.72036			−0.860180	+	0.509990i	$0.829649\pi$
$48$	−1.19035	+	1.25820i	−0.171812	+	0.181606i
$49$	3.42907			0.489868
$50$		0			0
$51$	7.70840	+	7.29266i	1.07939	+	1.02118i
$52$	0.713000			0.0988753
$53$	1.09369			0.150230			0.0751150	−	0.997175i	$-0.476068\pi$
$53$	1.09369			0.150230			0.0751150	+	0.997175i	$0.476068\pi$
$54$	−3.35650	+	3.96660i	−0.456762	+	0.539786i
$55$		0			0
$56$		−	3.22941i		−	0.431548i
$57$	−2.93452	−	2.77625i	−0.388687	−	0.367724i
$58$		−	5.27779i		−	0.693008i
$59$		−	1.95162i		−	0.254079i	−0.991898	−	0.127039i	$-0.959453\pi$
$59$		−	1.95162i		−	0.254079i	0.991898	−	0.127039i	$-0.0405475\pi$
$60$		0			0
$61$			2.19331i			0.280824i	0.990093	+	0.140412i	$0.0448428\pi$
$61$			2.19331i			0.280824i	−0.990093	+	0.140412i	$0.955157\pi$
$62$		−	9.55251i		−	1.21317i
$63$	−0.536580	−	9.67335i	−0.0676027	−	1.21873i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	5.67335	+	0.901704i	0.698341	+	0.110992i
$67$		−	2.80977i		−	0.343268i	−0.985161	−	0.171634i	$-0.945095\pi$
$67$		−	2.80977i		−	0.343268i	0.985161	−	0.171634i	$-0.0549046\pi$
$68$			6.12651i			0.742948i
$69$	3.61010	−	3.81590i	0.434605	−	0.459380i
$70$		0			0
$71$		−	11.7366i		−	1.39288i	−0.717616	−	0.696439i	$-0.754766\pi$
$71$		−	11.7366i		−	1.39288i	0.717616	−	0.696439i	$-0.245234\pi$
$72$	−2.99540	+	0.166154i	−0.353011	+	0.0195815i
$73$	14.6946			1.71987			0.859935	−	0.510403i	$-0.170504\pi$
$73$	14.6946			1.71987			0.859935	+	0.510403i	$0.170504\pi$
$74$	9.73661			1.13186
$75$		0			0
$76$		−	2.33231i		−	0.267534i
$77$	−8.83951	+	6.04838i	−1.00736	+	0.689277i
$78$	0.897099	+	0.848716i	0.101576	+	0.0960982i
$79$			13.5400i			1.52337i	0.647947	+	0.761685i	$0.275628\pi$
$79$			13.5400i			1.52337i	−0.647947	+	0.761685i	$0.724372\pi$
$80$		0			0
$81$	−8.94479	+	0.995395i	−0.993865	+	0.110599i
$82$		−	0.761383i		−	0.0840807i
$83$			7.72857i			0.848320i	0.905587	+	0.424160i	$0.139431\pi$
$83$			7.72857i			0.848320i	−0.905587	+	0.424160i	$0.860569\pi$
$84$	3.84411	−	4.06325i	0.419427	−	0.443337i
$85$		0			0
$86$		−	5.79420i		−	0.624804i
$87$	6.28240	−	6.64054i	0.673543	−	0.711940i
$88$	1.87291	+	2.73719i	0.199653	+	0.291786i
$89$		−	3.04203i		−	0.322454i	−0.986917	−	0.161227i	$-0.948455\pi$
$89$		−	3.04203i		−	0.322454i	0.986917	−	0.161227i	$-0.0515451\pi$
$90$		0			0
$91$	−2.30257			−0.241375
$92$	3.03282			0.316193
$93$	11.3708	−	12.0190i	1.17910	−	1.24631i
$94$		−	11.7942i		−	1.21648i
$95$		0			0
$96$	−1.25820	−	1.19035i	−0.128415	−	0.121489i
$97$		−	10.6462i		−	1.08096i	−0.841358	−	0.540479i	$-0.818243\pi$
$97$		−	10.6462i		−	1.08096i	0.841358	−	0.540479i	$-0.181757\pi$
$98$			3.42907i			0.346389i
$99$	6.06490	+	7.88778i	0.609545	+	0.792752i
$100$		0			0
$101$	−14.5072			−1.44352			−0.721760	−	0.692143i	$-0.756667\pi$
$101$	−14.5072			−1.44352			−0.721760	+	0.692143i	$0.756667\pi$
$102$	−7.29266	+	7.70840i	−0.722081	+	0.763245i
$103$		−	7.79420i		−	0.767985i	−0.923336	−	0.383993i	$-0.874549\pi$
$103$		−	7.79420i		−	0.767985i	0.923336	−	0.383993i	$-0.125451\pi$
$104$			0.713000i			0.0699154i
$105$		0			0
$106$			1.09369i			0.106229i
$107$		−	5.30425i		−	0.512781i	−0.966573	−	0.256391i	$-0.917467\pi$
$107$		−	5.30425i		−	0.512781i	0.966573	−	0.256391i	$-0.0825333\pi$
$108$	−3.96660	−	3.35650i	−0.381686	−	0.322979i
$109$			11.9643i			1.14598i	0.819564	+	0.572988i	$0.194216\pi$
$109$			11.9643i			1.14598i	−0.819564	+	0.572988i	$0.805784\pi$
$110$		0			0
$111$	12.2506	+	11.5899i	1.16278	+	1.10007i
$112$	3.22941			0.305150
$113$	3.28700			0.309215			0.154607	−	0.987976i	$-0.450589\pi$
$113$	3.28700			0.309215			0.154607	+	0.987976i	$0.450589\pi$
$114$	2.77625	−	2.93452i	0.260020	−	0.274843i
$115$		0			0
$116$	5.27779			0.490031
$117$	0.118468	+	2.13572i	0.0109524	+	0.197447i
$118$	1.95162			0.179661
$119$		−	19.7850i		−	1.81369i
$120$		0			0
$121$	3.98443	−	10.2530i	0.362221	−	0.932092i
$122$	−2.19331			−0.198573
$123$	0.906309	−	0.957975i	0.0817191	−	0.0863777i
$124$	9.55251			0.857840
$125$		0			0
$126$	9.67335	−	0.536580i	0.861771	−	0.0478023i
$127$	17.7631			1.57622			0.788109	−	0.615536i	$-0.211061\pi$
$127$	17.7631			1.57622			0.788109	+	0.615536i	$0.211061\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	6.89710	−	7.29028i	0.607256	−	0.641874i
$130$		0			0
$131$	15.0720			1.31685			0.658423	−	0.752648i	$-0.271224\pi$
$131$	15.0720			1.31685			0.658423	+	0.752648i	$0.271224\pi$
$132$	−0.901704	+	5.67335i	−0.0784833	+	0.493802i
$133$			7.53198i			0.653105i
$134$	2.80977			0.242727
$135$		0			0
$136$	−6.12651			−0.525344
$137$	4.53833			0.387736			0.193868	−	0.981028i	$-0.437897\pi$
$137$	4.53833			0.387736			0.193868	+	0.981028i	$0.437897\pi$
$138$	3.81590	+	3.61010i	0.324831	+	0.307312i
$139$		−	10.4404i		−	0.885543i	−0.896635	−	0.442771i	$-0.853995\pi$
$139$		−	10.4404i		−	0.885543i	0.896635	−	0.442771i	$-0.146005\pi$
$140$		0			0
$141$	14.0392	−	14.8395i	1.18231	−	1.24971i
$142$	11.7366			0.984914
$143$	1.95162	−	1.33538i	0.163202	−	0.111670i
$144$	−0.166154	−	2.99540i	−0.0138462	−	0.249616i
$145$		0			0
$146$			14.6946i			1.21613i
$147$	−4.08178	+	4.31447i	−0.336660	+	0.355852i
$148$			9.73661i			0.800344i
$149$	0.691075			0.0566151			0.0283075	−	0.999599i	$-0.490988\pi$
$149$	0.691075			0.0566151			0.0283075	+	0.999599i	$0.490988\pi$
$150$		0			0
$151$		−	10.3198i		−	0.839815i	−0.907567	−	0.419907i	$-0.862063\pi$
$151$		−	10.3198i		−	0.839815i	0.907567	−	0.419907i	$-0.137937\pi$
$152$	2.33231			0.189175
$153$	−18.3513	+	1.01795i	−1.48362	+	0.0822960i
$154$	−6.04838	−	8.83951i	−0.487393	−	0.712308i
$155$		0			0
$156$	−0.848716	+	0.897099i	−0.0679517	+	0.0718254i
$157$		−	11.2778i		−	0.900066i	−0.893012	−	0.450033i	$-0.851412\pi$
$157$		−	11.2778i		−	0.900066i	0.893012	−	0.450033i	$-0.148588\pi$
$158$	−13.5400			−1.07719
$159$	−1.30187	+	1.37609i	−0.103245	+	0.109131i
$160$		0			0
$161$	−9.79420			−0.771891
$162$	−0.995395	−	8.94479i	−0.0782056	−	0.702769i
$163$			6.51641i			0.510404i	0.966888	+	0.255202i	$0.0821420\pi$
$163$			6.51641i			0.510404i	−0.966888	+	0.255202i	$0.917858\pi$
$164$	0.761383			0.0594540
$165$		0			0
$166$	−7.72857			−0.599853
$167$			8.61646i			0.666761i	0.942792	+	0.333381i	$0.108189\pi$
$167$			8.61646i			0.666761i	−0.942792	+	0.333381i	$0.891811\pi$
$168$	4.06325	+	3.84411i	0.313487	+	0.296580i
$169$	−12.4916			−0.960895
$170$		0			0
$171$	6.98619	−	0.387523i	0.534247	−	0.0296346i
$172$	5.79420			0.441803
$173$		−	12.0656i		−	0.917333i	−0.888608	−	0.458666i	$-0.848327\pi$
$173$		−	12.0656i		−	0.917333i	0.888608	−	0.458666i	$-0.151673\pi$
$174$	6.64054	+	6.28240i	0.503418	+	0.476267i
$175$		0			0
$176$	−2.73719	+	1.87291i	−0.206324	+	0.141176i
$177$	2.45553	+	2.32310i	0.184569	+	0.174615i
$178$	3.04203			0.228009
$179$			3.49280i			0.261064i	0.991444	+	0.130532i	$0.0416686\pi$
$179$			3.49280i			0.261064i	−0.991444	+	0.130532i	$0.958331\pi$
$180$		0			0
$181$	−15.1361			−1.12506			−0.562531	−	0.826777i	$-0.690172\pi$
$181$	−15.1361			−1.12506			−0.562531	+	0.826777i	$0.690172\pi$
$182$		−	2.30257i		−	0.170678i
$183$	−2.75963	−	2.61080i	−0.203998	−	0.192996i
$184$			3.03282i			0.223582i
$185$		0			0
$186$	12.0190	+	11.3708i	0.881276	+	0.833746i
$187$	11.4744	+	16.7694i	0.839090	+	1.22630i
$188$	11.7942			0.860180
$189$	12.8098	+	10.8395i	0.931773	+	0.788458i
$190$		0			0
$191$			8.93152i			0.646262i	0.946354	+	0.323131i	$0.104735\pi$
$191$			8.93152i			0.646262i	−0.946354	+	0.323131i	$0.895265\pi$
$192$	1.19035	−	1.25820i	0.0859058	−	0.0908030i
$193$	−20.5820			−1.48153			−0.740764	−	0.671766i	$-0.765536\pi$
$193$	−20.5820			−1.48153			−0.740764	+	0.671766i	$0.765536\pi$
$194$	10.6462			0.764352
$195$		0			0
$196$	−3.42907			−0.244934
$197$			13.7631i			0.980578i	0.871560	+	0.490289i	$0.163109\pi$
$197$			13.7631i			0.980578i	−0.871560	+	0.490289i	$0.836891\pi$
$198$	−7.88778	+	6.06490i	−0.560560	+	0.431013i
$199$	−18.3139			−1.29824			−0.649119	−	0.760687i	$-0.724862\pi$
$199$	−18.3139			−1.29824			−0.649119	+	0.760687i	$0.724862\pi$
$200$		0			0
$201$	3.53526	+	3.34459i	0.249358	+	0.235909i
$202$		−	14.5072i		−	1.02072i
$203$	−17.0441			−1.19626
$204$	−7.70840	−	7.29266i	−0.539696	−	0.510588i
$205$		0			0
$206$	7.79420			0.543048
$207$	0.503915	+	9.08448i	0.0350245	+	0.631415i
$208$	−0.713000			−0.0494376
$209$	−4.36820	−	6.38397i	−0.302155	−	0.441589i
$210$		0			0
$211$			1.12483i			0.0774362i	0.999250	+	0.0387181i	$0.0123274\pi$
$211$			1.12483i			0.0774362i	−0.999250	+	0.0387181i	$0.987673\pi$
$212$	−1.09369			−0.0751150
$213$	14.7670	+	13.9706i	1.01182	+	0.957251i
$214$	5.30425			0.362591
$215$		0			0
$216$	3.35650	−	3.96660i	0.228381	−	0.269893i
$217$	−30.8489			−2.09416
$218$	−11.9643			−0.810327
$219$	−17.4916	+	18.4888i	−1.18197	+	1.24936i
$220$		0			0
$221$			4.36820i			0.293837i
$222$	−11.5899	+	12.2506i	−0.777865	+	0.822209i
$223$		−	5.12343i		−	0.343090i	−0.985176	−	0.171545i	$-0.945124\pi$
$223$		−	5.12343i		−	0.343090i	0.985176	−	0.171545i	$-0.0548760\pi$
$224$			3.22941i			0.215774i
$225$		0			0
$226$			3.28700i			0.218648i
$227$			26.9648i			1.78972i	0.446347	+	0.894860i	$0.352725\pi$
$227$			26.9648i			1.78972i	−0.446347	+	0.894860i	$0.647275\pi$
$228$	2.93452	+	2.77625i	0.194343	+	0.183862i
$229$	5.51005			0.364114			0.182057	−	0.983288i	$-0.441724\pi$
$229$	5.51005			0.364114			0.182057	+	0.983288i	$0.441724\pi$
$230$		0			0
$231$	2.91197	−	18.3216i	0.191594	−	1.20547i
$232$			5.27779i			0.346504i
$233$		−	17.7399i		−	1.16218i	−0.813840	−	0.581089i	$-0.802627\pi$
$233$		−	17.7399i		−	1.16218i	0.813840	−	0.581089i	$-0.197373\pi$
$234$	−2.13572	+	0.118468i	−0.139616	+	0.00774449i
$235$		0			0
$236$			1.95162i			0.127039i
$237$	−17.0361	−	16.1173i	−1.10661	−	1.04693i
$238$	19.7850			1.28247
$239$	−5.03938			−0.325971			−0.162985	−	0.986629i	$-0.552112\pi$
$239$	−5.03938			−0.325971			−0.162985	+	0.986629i	$0.552112\pi$
$240$		0			0
$241$			10.4588i			0.673712i	0.941556	+	0.336856i	$0.109363\pi$
$241$			10.4588i			0.673712i	−0.941556	+	0.336856i	$0.890637\pi$
$242$	10.2530	+	3.98443i	0.659089	+	0.256129i
$243$	9.39498	−	12.4392i	0.602688	−	0.797977i
$244$		−	2.19331i		−	0.140412i
$245$		0			0
$246$	0.957975	+	0.906309i	0.0610782	+	0.0577841i
$247$		−	1.66294i		−	0.105810i
$248$			9.55251i			0.606585i
$249$	−9.72411	−	9.19967i	−0.616241	−	0.583005i
$250$		0			0
$251$			19.2374i			1.21426i	0.794604	+	0.607128i	$0.207679\pi$
$251$			19.2374i			1.21426i	−0.794604	+	0.607128i	$0.792321\pi$
$252$	0.536580	+	9.67335i	0.0338013	+	0.609364i
$253$	8.30140	−	5.68018i	0.521904	−	0.357110i
$254$			17.7631i			1.11455i
$255$		0			0
$256$	1.00000			0.0625000
$257$	−9.72740			−0.606778			−0.303389	−	0.952867i	$-0.598118\pi$
$257$	−9.72740			−0.606778			−0.303389	+	0.952867i	$0.598118\pi$
$258$	7.29028	+	6.89710i	0.453873	+	0.429395i
$259$		−	31.4435i		−	1.95380i
$260$		0			0
$261$	0.876927	+	15.8091i	0.0542804	+	0.978557i
$262$			15.0720i			0.931151i
$263$			9.76446i			0.602102i	0.953608	+	0.301051i	$0.0973375\pi$
$263$			9.76446i			0.602102i	−0.953608	+	0.301051i	$0.902663\pi$
$264$	−5.67335	−	0.901704i	−0.349171	−	0.0554960i
$265$		0			0
$266$	−7.53198			−0.461815
$267$	3.82749	+	3.62106i	0.234238	+	0.221605i
$268$			2.80977i			0.171634i
$269$			16.8270i			1.02596i	0.858400	+	0.512981i	$0.171459\pi$
$269$			16.8270i			1.02596i	−0.858400	+	0.512981i	$0.828541\pi$
$270$		0			0
$271$		−	31.8836i		−	1.93679i	−0.249415	−	0.968397i	$-0.580238\pi$
$271$		−	31.8836i		−	1.93679i	0.249415	−	0.968397i	$-0.419762\pi$
$272$		−	6.12651i		−	0.371474i
$273$	2.74085	−	2.89710i	0.165884	−	0.175340i
$274$			4.53833i			0.274171i
$275$		0			0
$276$	−3.61010	+	3.81590i	−0.217302	+	0.229690i
$277$	0.0483829			0.00290705			0.00145352	−	0.999999i	$-0.499537\pi$
$277$	0.0483829			0.00290705			0.00145352	+	0.999999i	$0.499537\pi$
$278$	10.4404			0.626173
$279$	1.58719	+	28.6135i	0.0950226	+	1.71305i
$280$		0			0
$281$	−4.52445			−0.269906			−0.134953	−	0.990852i	$-0.543088\pi$
$281$	−4.52445			−0.269906			−0.134953	+	0.990852i	$0.543088\pi$
$282$	14.8395	+	14.0392i	0.883680	+	0.836021i
$283$	−23.5950			−1.40257			−0.701287	−	0.712879i	$-0.747391\pi$
$283$	−23.5950			−1.40257			−0.701287	+	0.712879i	$0.747391\pi$
$284$			11.7366i			0.696439i
$285$		0			0
$286$	1.33538	+	1.95162i	0.0789629	+	0.115402i
$287$	−2.45882			−0.145139
$288$	2.99540	−	0.166154i	0.176505	−	0.00979073i
$289$	−20.5341			−1.20789
$290$		0			0
$291$	13.3951	+	12.6727i	0.785234	+	0.742884i
$292$	−14.6946			−0.859935
$293$			24.6151i			1.43803i	0.694996	+	0.719014i	$0.255406\pi$
$293$			24.6151i			1.43803i	−0.694996	+	0.719014i	$0.744594\pi$
$294$	−4.31447	−	4.08178i	−0.251625	−	0.238054i
$295$		0			0
$296$	−9.73661			−0.565929
$297$	−17.1438	−	1.75831i	−0.994782	−	0.102027i
$298$			0.691075i			0.0400329i
$299$	2.16240			0.125055
$300$		0			0
$301$	−18.7118			−1.07853
$302$	10.3198			0.593839
$303$	17.2686	−	18.2530i	0.992054	−	1.04861i
$304$			2.33231i			0.133767i
$305$		0			0
$306$	−1.01795	−	18.3513i	−0.0581920	−	1.04907i
$307$	25.8725			1.47662			0.738312	−	0.674459i	$-0.235623\pi$
$307$	25.8725			1.47662			0.738312	+	0.674459i	$0.235623\pi$
$308$	8.83951	−	6.04838i	0.503678	−	0.344639i
$309$	9.80669	+	9.27779i	0.557883	+	0.527795i
$310$		0			0
$311$		−	10.7038i		−	0.606956i	−0.952838	−	0.303478i	$-0.901852\pi$
$311$		−	10.7038i		−	0.606956i	0.952838	−	0.303478i	$-0.0981479\pi$
$312$	−0.897099	−	0.848716i	−0.0507882	−	0.0480491i
$313$		−	14.3682i		−	0.812139i	−0.913842	−	0.406069i	$-0.866899\pi$
$313$		−	14.3682i		−	0.812139i	0.913842	−	0.406069i	$-0.133101\pi$
$314$	11.2778			0.636443
$315$		0			0
$316$		−	13.5400i		−	0.761685i
$317$	34.7727			1.95303			0.976515	−	0.215450i	$-0.0691219\pi$
$317$	34.7727			1.95303			0.976515	+	0.215450i	$0.0691219\pi$
$318$	−1.37609	−	1.30187i	−0.0771671	−	0.0730053i
$319$	14.4463	−	9.88482i	0.808839	−	0.553443i
$320$		0			0
$321$	6.67383	+	6.31389i	0.372497	+	0.352407i
$322$		−	9.79420i		−	0.545809i
$323$	14.2889			0.795056
$324$	8.94479	−	0.995395i	0.496933	−	0.0552997i
$325$		0			0
$326$	−6.51641			−0.360910
$327$	−15.0536	−	14.2417i	−0.832464	−	0.787567i
$328$			0.761383i			0.0420403i
$329$	−38.0883			−2.09987
$330$		0			0
$331$	−13.7942			−0.758198			−0.379099	−	0.925356i	$-0.623766\pi$
$331$	−13.7942			−0.758198			−0.379099	+	0.925356i	$0.623766\pi$
$332$		−	7.72857i		−	0.424160i
$333$	−29.1650	+	1.61778i	−1.59823	+	0.0886537i
$334$	−8.61646			−0.471472
$335$		0			0
$336$	−3.84411	+	4.06325i	−0.209713	+	0.221669i
$337$	−13.3868			−0.729227			−0.364613	−	0.931159i	$-0.618799\pi$
$337$	−13.3868			−0.729227			−0.364613	+	0.931159i	$0.618799\pi$
$338$		−	12.4916i		−	0.679455i
$339$	−3.91267	+	4.13572i	−0.212507	+	0.224621i
$340$		0			0
$341$	26.1470	−	17.8910i	1.41594	−	0.968850i
$342$	0.387523	+	6.98619i	0.0209548	+	0.377770i
$343$	−11.5320			−0.622668
$344$			5.79420i			0.312402i
$345$		0			0
$346$	12.0656			0.648652
$347$		−	19.3699i		−	1.03983i	−0.854218	−	0.519915i	$-0.825964\pi$
$347$		−	19.3699i		−	1.03983i	0.854218	−	0.519915i	$-0.174036\pi$
$348$	−6.28240	+	6.64054i	−0.336772	+	0.355970i
$349$		−	2.53833i		−	0.135874i	−0.997690	−	0.0679369i	$-0.978358\pi$
$349$		−	2.53833i		−	0.135874i	0.997690	−	0.0679369i	$-0.0216417\pi$
$350$		0			0
$351$	−2.82818	−	2.39318i	−0.150957	−	0.127739i
$352$	−1.87291	−	2.73719i	−0.0998263	−	0.145893i
$353$	−32.9476			−1.75362			−0.876812	−	0.480834i	$-0.840334\pi$
$353$	−32.9476			−1.75362			−0.876812	+	0.480834i	$0.840334\pi$
$354$	−2.32310	+	2.45553i	−0.123471	+	0.130510i
$355$		0			0
$356$			3.04203i			0.161227i
$357$	24.8936	+	23.5510i	1.31751	+	1.24645i
$358$	−3.49280			−0.184600
$359$	−16.6212			−0.877234			−0.438617	−	0.898674i	$-0.644532\pi$
$359$	−16.6212			−0.877234			−0.438617	+	0.898674i	$0.644532\pi$
$360$		0			0
$361$	13.5603			0.713702
$362$		−	15.1361i		−	0.795538i
$363$	8.15753	+	17.2179i	0.428159	+	0.903703i
$364$	2.30257			0.120687
$365$		0			0
$366$	2.61080	−	2.75963i	0.136468	−	0.144248i
$367$			11.1361i			0.581302i	0.956829	+	0.290651i	$0.0938719\pi$
$367$			11.1361i			0.581302i	−0.956829	+	0.290651i	$0.906128\pi$
$368$	−3.03282			−0.158096
$369$	0.126507	+	2.28064i	0.00658569	+	0.118726i
$370$		0			0
$371$	3.53198			0.183371
$372$	−11.3708	+	12.0190i	−0.589548	+	0.623156i
$373$	−4.69458			−0.243076			−0.121538	−	0.992587i	$-0.538783\pi$
$373$	−4.69458			−0.243076			−0.121538	+	0.992587i	$0.538783\pi$
$374$	−16.7694	+	11.4744i	−0.867126	+	0.593326i
$375$		0			0
$376$			11.7942i			0.608239i
$377$	3.76306			0.193808
$378$	−10.8395	+	12.8098i	−0.557524	+	0.658863i
$379$	−22.6339			−1.16263			−0.581313	−	0.813680i	$-0.697461\pi$
$379$	−22.6339			−1.16263			−0.581313	+	0.813680i	$0.697461\pi$
$380$		0			0
$381$	−21.1442	+	22.3496i	−1.08325	+	1.14500i
$382$	−8.93152			−0.456976
$383$	34.2412			1.74964			0.874821	−	0.484447i	$-0.160979\pi$
$383$	34.2412			1.74964			0.874821	+	0.484447i	$0.160979\pi$
$384$	1.25820	+	1.19035i	0.0642075	+	0.0607446i
$385$		0			0
$386$		−	20.5820i		−	1.04760i
$387$	0.962731	+	17.3559i	0.0489383	+	0.882251i
$388$			10.6462i			0.540479i
$389$		−	3.67901i		−	0.186533i	−0.995641	−	0.0932667i	$-0.970269\pi$
$389$		−	3.67901i		−	0.186533i	0.995641	−	0.0932667i	$-0.0297309\pi$
$390$		0			0
$391$			18.5806i			0.939660i
$392$		−	3.42907i		−	0.173194i
$393$	−17.9409	+	18.9636i	−0.904998	+	0.956589i
$394$	−13.7631			−0.693373
$395$		0			0
$396$	−6.06490	−	7.88778i	−0.304772	−	0.396376i
$397$		−	1.07505i		−	0.0539552i	−0.999636	−	0.0269776i	$-0.991412\pi$
$397$		−	1.07505i		−	0.0539552i	0.999636	−	0.0269776i	$-0.00858828\pi$
$398$		−	18.3139i		−	0.917992i
$399$	−9.47676	−	8.96565i	−0.474431	−	0.448844i
$400$		0			0
$401$		−	28.8428i		−	1.44034i	−0.693798	−	0.720170i	$-0.744064\pi$
$401$		−	28.8428i		−	1.44034i	0.693798	−	0.720170i	$-0.255936\pi$
$402$	−3.34459	+	3.53526i	−0.166813	+	0.176323i
$403$	6.81094			0.339277
$404$	14.5072			0.721760
$405$		0			0
$406$		−	17.0441i		−	0.845886i
$407$	18.2358	+	26.6510i	0.903913	+	1.32104i
$408$	7.29266	−	7.70840i	0.361041	−	0.381622i
$409$		−	3.23862i		−	0.160139i	−0.996789	−	0.0800697i	$-0.974486\pi$
$409$		−	3.23862i		−	0.160139i	0.996789	−	0.0800697i	$-0.0255143\pi$
$410$		0			0
$411$	−5.40218	+	5.71015i	−0.266470	+	0.281661i
$412$			7.79420i			0.383993i
$413$		−	6.30257i		−	0.310129i
$414$	−9.08448	+	0.503915i	−0.446478	+	0.0247661i
$415$		0			0
$416$		−	0.713000i		−	0.0349577i
$417$	13.1361	+	12.4277i	0.643280	+	0.608586i
$418$	6.38397	−	4.36820i	0.312250	−	0.213656i
$419$			8.74413i			0.427179i	0.976924	+	0.213589i	$0.0685155\pi$
$419$			8.74413i			0.427179i	−0.976924	+	0.213589i	$0.931485\pi$
$420$		0			0
$421$	−28.4749			−1.38778			−0.693891	−	0.720080i	$-0.744105\pi$
$421$	−28.4749			−1.38778			−0.693891	+	0.720080i	$0.744105\pi$
$422$	−1.12483			−0.0547557
$423$	1.95966	+	35.3283i	0.0952817	+	1.71772i
$424$		−	1.09369i		−	0.0531143i
$425$		0			0
$426$	−13.9706	+	14.7670i	−0.676879	+	0.715466i
$427$			7.08309i			0.342775i
$428$			5.30425i			0.256391i
$429$	−0.642915	+	4.04510i	−0.0310402	+	0.195299i
$430$		0			0
$431$	−11.9032			−0.573359			−0.286679	−	0.958027i	$-0.592551\pi$
$431$	−11.9032			−0.573359			−0.286679	+	0.958027i	$0.592551\pi$
$432$	3.96660	+	3.35650i	0.190843	+	0.161490i
$433$		−	20.9488i		−	1.00673i	−0.864073	−	0.503367i	$-0.832094\pi$
$433$		−	20.9488i		−	1.00673i	0.864073	−	0.503367i	$-0.167906\pi$
$434$		−	30.8489i		−	1.48080i
$435$		0			0
$436$		−	11.9643i		−	0.572988i
$437$		−	7.07346i		−	0.338370i
$438$	−18.4888	−	17.4916i	−0.883428	−	0.835782i
$439$			32.8386i			1.56730i	0.621203	+	0.783649i	$0.286644\pi$
$439$			32.8386i			1.56730i	−0.621203	+	0.783649i	$0.713356\pi$
$440$		0			0
$441$	−0.569755	−	10.2714i	−0.0271312	−	0.489116i
$442$	−4.36820			−0.207774
$443$	5.39604			0.256373			0.128187	−	0.991750i	$-0.459084\pi$
$443$	5.39604			0.256373			0.128187	+	0.991750i	$0.459084\pi$
$444$	−12.2506	−	11.5899i	−0.581389	−	0.550034i
$445$		0			0
$446$	5.12343			0.242602
$447$	−0.822618	+	0.869513i	−0.0389085	+	0.0411266i
$448$	−3.22941			−0.152575
$449$		−	4.00000i		−	0.188772i	−0.995536	−	0.0943858i	$-0.969911\pi$
$449$		−	4.00000i		−	0.188772i	0.995536	−	0.0943858i	$-0.0300887\pi$
$450$		0			0
$451$	2.08405	−	1.42600i	0.0981341	−	0.0671477i
$452$	−3.28700			−0.154607
$453$	12.9844	+	12.2841i	0.610062	+	0.577160i
$454$	−26.9648			−1.26552
$455$		0			0
$456$	−2.77625	+	2.93452i	−0.130010	+	0.137421i
$457$	−16.1359			−0.754807			−0.377404	−	0.926049i	$-0.623183\pi$
$457$	−16.1359			−0.754807			−0.377404	+	0.926049i	$0.623183\pi$
$458$			5.51005i			0.257468i
$459$	20.5636	−	24.3014i	0.959828	−	1.13429i
$460$		0			0
$461$	5.29621			0.246669			0.123335	−	0.992365i	$-0.460641\pi$
$461$	5.29621			0.246669			0.123335	+	0.992365i	$0.460641\pi$
$462$	18.3216	+	2.91197i	0.852397	+	0.135477i
$463$			11.9159i			0.553781i	0.960901	+	0.276891i	$0.0893040\pi$
$463$			11.9159i			0.553781i	−0.960901	+	0.276891i	$0.910696\pi$
$464$	−5.27779			−0.245015
$465$		0			0
$466$	17.7399			0.821785
$467$	−4.56807			−0.211385			−0.105693	−	0.994399i	$-0.533706\pi$
$467$	−4.56807			−0.211385			−0.105693	+	0.994399i	$0.533706\pi$
$468$	−0.118468	−	2.13572i	−0.00547618	−	0.0987235i
$469$		−	9.07388i		−	0.418993i
$470$		0			0
$471$	14.1898	+	13.4245i	0.653830	+	0.618567i
$472$	−1.95162			−0.0898305
$473$	15.8598	−	10.8520i	0.729236	−	0.498975i
$474$	16.1173	−	17.0361i	0.740292	−	0.782494i
$475$		0			0
$476$			19.7850i			0.906843i
$477$	−0.181721	−	3.27604i	−0.00832045	−	0.149999i
$478$		−	5.03938i		−	0.230496i
$479$	25.4010			1.16060			0.580301	−	0.814402i	$-0.302935\pi$
$479$	25.4010			1.16060			0.580301	+	0.814402i	$0.302935\pi$
$480$		0			0
$481$			6.94220i			0.316537i
$482$	−10.4588			−0.476386
$483$	11.6585	−	12.3231i	0.530479	−	0.560720i
$484$	−3.98443	+	10.2530i	−0.181111	+	0.466046i
$485$		0			0
$486$	12.4392	+	9.39498i	0.564255	+	0.426165i
$487$		−	4.36205i		−	0.197663i	−0.995104	−	0.0988317i	$-0.968489\pi$
$487$		−	4.36205i		−	0.197663i	0.995104	−	0.0988317i	$-0.0315105\pi$
$488$	2.19331			0.0992864
$489$	−8.19897	−	7.75678i	−0.370770	−	0.350774i
$490$		0			0
$491$	13.4156			0.605438			0.302719	−	0.953080i	$-0.402106\pi$
$491$	13.4156			0.605438			0.302719	+	0.953080i	$0.402106\pi$
$492$	−0.906309	+	0.957975i	−0.0408596	+	0.0431888i
$493$			32.3344i			1.45627i
$494$	1.66294			0.0748190
$495$		0			0
$496$	−9.55251			−0.428920
$497$		−	37.9023i		−	1.70015i
$498$	9.19967	−	9.72411i	0.412247	−	0.435748i
$499$	20.6278			0.923426			0.461713	−	0.887029i	$-0.347235\pi$
$499$	20.6278			0.923426			0.461713	+	0.887029i	$0.347235\pi$
$500$		0			0
$501$	−10.8413	−	10.2566i	−0.484352	−	0.458229i
$502$	−19.2374			−0.858609
$503$		−	1.14800i		−	0.0511868i	−0.999672	−	0.0255934i	$-0.991852\pi$
$503$		−	1.14800i		−	0.0511868i	0.999672	−	0.0255934i	$-0.00814752\pi$
$504$	−9.67335	+	0.536580i	−0.430885	+	0.0239012i
$505$		0			0
$506$	5.68018	+	8.30140i	0.252515	+	0.369042i
$507$	14.8694	−	15.7170i	0.660371	−	0.698017i
$508$	−17.7631			−0.788109
$509$		−	2.81430i		−	0.124742i	−0.998053	−	0.0623708i	$-0.980134\pi$
$509$		−	2.81430i		−	0.124742i	0.998053	−	0.0623708i	$-0.0198661\pi$
$510$		0			0
$511$	47.4548			2.09928
$512$			1.00000i			0.0441942i
$513$	−7.82839	+	9.25133i	−0.345632	+	0.408456i
$514$		−	9.72740i		−	0.429057i
$515$		0			0
$516$	−6.89710	+	7.29028i	−0.303628	+	0.320937i
$517$	32.2830	−	22.0894i	1.41980	−	0.971493i
$518$	31.4435			1.38155
$519$	15.1810	+	14.3623i	0.666373	+	0.630434i
$520$		0			0
$521$			31.1768i			1.36588i	0.730474	+	0.682940i	$0.239299\pi$
$521$			31.1768i			1.36588i	−0.730474	+	0.682940i	$0.760701\pi$
$522$	−15.8091	+	0.876927i	−0.691944	+	0.0383821i
$523$	32.9337			1.44009			0.720045	−	0.693927i	$-0.244121\pi$
$523$	32.9337			1.44009			0.720045	+	0.693927i	$0.244121\pi$
$524$	−15.0720			−0.658423
$525$		0			0
$526$	−9.76446			−0.425751
$527$			58.5235i			2.54932i
$528$	0.901704	−	5.67335i	0.0392416	−	0.246901i
$529$	−13.8020			−0.600088
$530$		0			0
$531$	−5.84586	+	0.324269i	−0.253689	+	0.0140721i
$532$		−	7.53198i		−	0.326553i
$533$	0.542866			0.0235141
$534$	−3.62106	+	3.82749i	−0.156699	+	0.165632i
$535$		0			0
$536$	−2.80977			−0.121363
$537$	−4.39466	−	4.15764i	−0.189643	−	0.179415i
$538$	−16.8270			−0.725464
$539$	−9.38603	+	6.42234i	−0.404285	+	0.276630i
$540$		0			0
$541$			34.6026i			1.48768i	0.668357	+	0.743840i	$0.266998\pi$
$541$			34.6026i			1.48768i	−0.668357	+	0.743840i	$0.733002\pi$
$542$	31.8836			1.36952
$543$	18.0172	−	19.0444i	0.773194	−	0.817272i
$544$	6.12651			0.262672
$545$		0			0
$546$	2.89710	+	2.74085i	0.123984	+	0.117298i
$547$	−28.8647			−1.23417			−0.617083	−	0.786898i	$-0.711686\pi$
$547$	−28.8647			−1.23417			−0.617083	+	0.786898i	$0.711686\pi$
$548$	−4.53833			−0.193868
$549$	6.56983	−	0.364428i	0.280393	−	0.0155534i
$550$		0			0
$551$		−	12.3094i		−	0.524400i
$552$	−3.81590	−	3.61010i	−0.162416	−	0.153656i
$553$			43.7262i			1.85943i
$554$			0.0483829i			0.00205559i
$555$		0			0
$556$			10.4404i			0.442771i
$557$		−	15.4076i		−	0.652840i	−0.945225	−	0.326420i	$-0.894158\pi$
$557$		−	15.4076i		−	0.652840i	0.945225	−	0.326420i	$-0.105842\pi$
$558$	−28.6135	+	1.58719i	−1.21131	+	0.0671911i
$559$	4.13126			0.174734
$560$		0			0
$561$	−34.7578	−	5.52430i	−1.46748	−	0.233236i
$562$		−	4.52445i		−	0.190852i
$563$			40.8624i			1.72214i	0.508483	+	0.861072i	$0.330206\pi$
$563$			40.8624i			1.72214i	−0.508483	+	0.861072i	$0.669794\pi$
$564$	−14.0392	+	14.8395i	−0.591156	+	0.624856i
$565$		0			0
$566$		−	23.5950i		−	0.991770i
$567$	−28.8864	+	3.21454i	−1.21311	+	0.134998i
$568$	−11.7366			−0.492457
$569$	38.0817			1.59647			0.798234	−	0.602347i	$-0.205768\pi$
$569$	38.0817			1.59647			0.798234	+	0.602347i	$0.205768\pi$
$570$		0			0
$571$			5.43732i			0.227545i	0.993507	+	0.113772i	$0.0362935\pi$
$571$			5.43732i			0.227545i	−0.993507	+	0.113772i	$0.963707\pi$
$572$	−1.95162	+	1.33538i	−0.0816012	+	0.0558352i
$573$	−11.2377	−	10.6316i	−0.469460	−	0.444141i
$574$		−	2.45882i		−	0.102629i
$575$		0			0
$576$	0.166154	+	2.99540i	0.00692309	+	0.124808i
$577$			12.5556i			0.522696i	0.965245	+	0.261348i	$0.0841670\pi$
$577$			12.5556i			0.522696i	−0.965245	+	0.261348i	$0.915833\pi$
$578$		−	20.5341i		−	0.854105i
$579$	24.4997	−	25.8964i	1.01817	−	1.07622i
$580$		0			0
$581$			24.9587i			1.03546i
$582$	−12.6727	+	13.3951i	−0.525298	+	0.555244i
$583$	−2.99364	+	2.04838i	−0.123984	+	0.0848354i
$584$		−	14.6946i		−	0.608066i
$585$		0			0
$586$	−24.6151			−1.01684
$587$	−31.9380			−1.31822			−0.659110	−	0.752046i	$-0.729067\pi$
$587$	−31.9380			−1.31822			−0.659110	+	0.752046i	$0.729067\pi$
$588$	4.08178	−	4.31447i	0.168330	−	0.177926i
$589$		−	22.2794i		−	0.918006i
$590$		0			0
$591$	−17.3167	−	16.3828i	−0.712316	−	0.673899i
$592$		−	9.73661i		−	0.400172i
$593$			14.0345i			0.576328i	0.957581	+	0.288164i	$0.0930448\pi$
$593$			14.0345i			0.576328i	−0.957581	+	0.288164i	$0.906955\pi$
$594$	1.75831	−	17.1438i	0.0721443	−	0.703417i
$595$		0			0
$596$	−0.691075			−0.0283075
$597$	21.7999	−	23.0426i	0.892209	−	0.943071i
$598$			2.16240i			0.0884270i
$599$		−	10.7383i		−	0.438755i	−0.975640	−	0.219377i	$-0.929597\pi$
$599$		−	10.7383i		−	0.438755i	0.975640	−	0.219377i	$-0.0704026\pi$
$600$		0			0
$601$		−	20.7614i		−	0.846874i	−0.905925	−	0.423437i	$-0.860823\pi$
$601$		−	20.7614i		−	0.846874i	0.905925	−	0.423437i	$-0.139177\pi$
$602$		−	18.7118i		−	0.762637i
$603$	−8.41636	+	0.466854i	−0.342741	+	0.0190118i
$604$			10.3198i			0.419907i
$605$		0			0
$606$	18.2530	+	17.2686i	0.741478	+	0.701488i
$607$	15.1326			0.614215			0.307107	−	0.951675i	$-0.400639\pi$
$607$	15.1326			0.614215			0.307107	+	0.951675i	$0.400639\pi$
$608$	−2.33231			−0.0945876
$609$	20.2884	−	21.4450i	0.822128	−	0.868995i
$610$		0			0
$611$	8.40926			0.340202
$612$	18.3513	−	1.01795i	0.741808	−	0.0411480i
$613$	26.3137			1.06280			0.531399	−	0.847121i	$-0.321666\pi$
$613$	26.3137			1.06280			0.531399	+	0.847121i	$0.321666\pi$
$614$			25.8725i			1.04413i
$615$		0			0
$616$	6.04838	+	8.83951i	0.243696	+	0.356154i
$617$	−2.21735			−0.0892670			−0.0446335	−	0.999003i	$-0.514212\pi$
$617$	−2.21735			−0.0892670			−0.0446335	+	0.999003i	$0.514212\pi$
$618$	−9.27779	+	9.80669i	−0.373207	+	0.394483i
$619$	49.1338			1.97485			0.987427	−	0.158074i	$-0.0505286\pi$
$619$	49.1338			1.97485			0.987427	+	0.158074i	$0.0505286\pi$
$620$		0			0
$621$	−12.0300	−	10.1796i	−0.482746	−	0.408495i
$622$	10.7038			0.429183
$623$		−	9.82394i		−	0.393588i
$624$	0.848716	−	0.897099i	0.0339758	−	0.0359127i
$625$		0			0
$626$	14.3682			0.574269
$627$	13.2320	+	2.10305i	0.528436	+	0.0839878i
$628$			11.2778i			0.450033i
$629$	−59.6514			−2.37846
$630$		0			0
$631$	−18.3857			−0.731922			−0.365961	−	0.930630i	$-0.619260\pi$
$631$	−18.3857			−0.731922			−0.365961	+	0.930630i	$0.619260\pi$
$632$	13.5400			0.538593
$633$	−1.41526	−	1.33893i	−0.0562515	−	0.0532177i
$634$			34.7727i			1.38100i
$635$		0			0
$636$	1.30187	−	1.37609i	0.0516225	−	0.0545654i
$637$	−2.44493			−0.0968716
$638$	9.88482	+	14.4463i	0.391344	+	0.571935i
$639$	−35.1558	+	1.95009i	−1.39074	+	0.0771442i
$640$		0			0
$641$		−	8.97639i		−	0.354546i	−0.984162	−	0.177273i	$-0.943272\pi$
$641$		−	8.97639i		−	0.354546i	0.984162	−	0.177273i	$-0.0567276\pi$
$642$	−6.31389	+	6.67383i	−0.249189	+	0.263395i
$643$		−	29.0097i		−	1.14403i	−0.820243	−	0.572016i	$-0.806162\pi$
$643$		−	29.0097i		−	1.14403i	0.820243	−	0.572016i	$-0.193838\pi$
$644$	9.79420			0.385945
$645$		0			0
$646$			14.2889i			0.562189i
$647$	−21.7880			−0.856577			−0.428288	−	0.903642i	$-0.640883\pi$
$647$	−21.7880			−0.856577			−0.428288	+	0.903642i	$0.640883\pi$
$648$	0.995395	+	8.94479i	0.0391028	+	0.351384i
$649$	3.65520	+	5.34195i	0.143479	+	0.209690i
$650$		0			0
$651$	36.7209	−	38.8143i	1.43921	−	1.52125i
$652$		−	6.51641i		−	0.255202i
$653$	2.13307			0.0834736			0.0417368	−	0.999129i	$-0.486711\pi$
$653$	2.13307			0.0834736			0.0417368	+	0.999129i	$0.486711\pi$
$654$	14.2417	−	15.0536i	0.556894	−	0.588641i
$655$		0			0
$656$	−0.761383			−0.0297270
$657$	−2.44157	−	44.0161i	−0.0952546	−	1.71723i
$658$		−	38.0883i		−	1.48484i
$659$	28.7576			1.12024			0.560118	−	0.828413i	$-0.310756\pi$
$659$	28.7576			1.12024			0.560118	+	0.828413i	$0.310756\pi$
$660$		0			0
$661$	−20.3371			−0.791020			−0.395510	−	0.918462i	$-0.629432\pi$
$661$	−20.3371			−0.791020			−0.395510	+	0.918462i	$0.629432\pi$
$662$		−	13.7942i		−	0.536127i
$663$	−5.49608	−	5.19967i	−0.213450	−	0.201938i
$664$	7.72857			0.299927
$665$		0			0
$666$	−1.61778	−	29.1650i	−0.0626876	−	1.13012i
$667$	16.0066			0.619777
$668$		−	8.61646i		−	0.333381i
$669$	6.44632	+	6.09866i	0.249229	+	0.235788i
$670$		0			0
$671$	−4.10787	−	6.00351i	−0.158582	−	0.231763i
$672$	−4.06325	−	3.84411i	−0.156743	−	0.148290i
$673$	−12.5820			−0.485002			−0.242501	−	0.970151i	$-0.577968\pi$
$673$	−12.5820			−0.485002			−0.242501	+	0.970151i	$0.577968\pi$
$674$		−	13.3868i		−	0.515641i
$675$		0			0
$676$	12.4916			0.480447
$677$		−	16.6085i		−	0.638316i	−0.947701	−	0.319158i	$-0.896600\pi$
$677$		−	16.6085i		−	0.638316i	0.947701	−	0.319158i	$-0.103400\pi$
$678$	−4.13572	−	3.91267i	−0.158831	−	0.150265i
$679$		−	34.3809i		−	1.31942i
$680$		0			0
$681$	−33.9273	−	32.0975i	−1.30010	−	1.22998i
$682$	17.8910	+	26.1470i	0.685080	+	1.00122i
$683$	−36.0597			−1.37979			−0.689893	−	0.723911i	$-0.742343\pi$
$683$	−36.0597			−1.37979			−0.689893	+	0.723911i	$0.742343\pi$
$684$	−6.98619	+	0.387523i	−0.267123	+	0.0148173i
$685$		0			0
$686$		−	11.5320i		−	0.440293i
$687$	−6.55886	+	6.93277i	−0.250236	+	0.264502i
$688$	−5.79420			−0.220902
$689$	−0.779802			−0.0297081
$690$		0			0
$691$	27.3396			1.04005			0.520024	−	0.854152i	$-0.325923\pi$
$691$	27.3396			1.04005			0.520024	+	0.854152i	$0.325923\pi$
$692$			12.0656i			0.458666i
$693$	19.5860	+	25.4729i	0.744011	+	0.967634i
$694$	19.3699			0.735271
$695$		0			0
$696$	−6.64054	−	6.28240i	−0.251709	−	0.238134i
$697$			4.66462i			0.176685i
$698$	2.53833			0.0960773
$699$	22.3204	+	21.1166i	0.844235	+	0.798703i
$700$		0			0
$701$	6.68771			0.252591			0.126296	−	0.991993i	$-0.459691\pi$
$701$	6.68771			0.252591			0.126296	+	0.991993i	$0.459691\pi$
$702$	2.39318	−	2.82818i	0.0903249	−	0.106743i
$703$	22.7088			0.856477
$704$	2.73719	−	1.87291i	0.103162	−	0.0705879i
$705$		0			0
$706$		−	32.9476i		−	1.24000i
$707$	−46.8497			−1.76196
$708$	−2.45553	−	2.32310i	−0.0922846	−	0.0873074i
$709$	34.9431			1.31231			0.656157	−	0.754624i	$-0.272181\pi$
$709$	34.9431			1.31231			0.656157	+	0.754624i	$0.272181\pi$
$710$		0			0
$711$	40.5577	−	2.24973i	1.52103	−	0.0843715i
$712$	−3.04203			−0.114005
$713$	28.9710			1.08497
$714$	−23.5510	+	24.8936i	−0.881373	+	0.931618i
$715$		0			0
$716$		−	3.49280i		−	0.130532i
$717$	5.99861	−	6.34057i	0.224022	−	0.236793i
$718$		−	16.6212i		−	0.620298i
$719$			37.5534i			1.40051i	0.713894	+	0.700254i	$0.246930\pi$
$719$			37.5534i			1.40051i	−0.713894	+	0.700254i	$0.753070\pi$
$720$		0			0
$721$		−	25.1706i		−	0.937404i
$722$			13.5603i			0.504663i
$723$	−13.1593	−	12.4496i	−0.489400	−	0.463006i
$724$	15.1361			0.562531
$725$		0			0
$726$	−17.2179	+	8.15753i	−0.639015	+	0.302754i
$727$			29.6479i			1.09958i	0.835303	+	0.549789i	$0.185292\pi$
$727$			29.6479i			1.09958i	−0.835303	+	0.549789i	$0.814708\pi$
$728$			2.30257i			0.0853388i
$729$	4.46782	+	26.6278i	0.165475	+	0.986214i
$730$		0			0
$731$			35.4982i			1.31295i
$732$	2.75963	+	2.61080i	0.101999	+	0.0964978i
$733$	34.2703			1.26580			0.632901	−	0.774233i	$-0.281864\pi$
$733$	34.2703			1.26580			0.632901	+	0.774233i	$0.281864\pi$
$734$	−11.1361			−0.411043
$735$		0			0
$736$		−	3.03282i		−	0.111791i
$737$	5.26243	+	7.69087i	0.193844	+	0.283297i
$738$	−2.28064	+	0.126507i	−0.0839516	+	0.00465679i
$739$		−	49.1457i		−	1.80785i	−0.427689	−	0.903926i	$-0.640672\pi$
$739$		−	49.1457i		−	1.80785i	0.427689	−	0.903926i	$-0.359328\pi$
$740$		0			0
$741$	2.09231	+	1.97947i	0.0768630	+	0.0727176i
$742$			3.53198i			0.129663i
$743$		−	29.6654i		−	1.08832i	−0.838983	−	0.544158i	$-0.816849\pi$
$743$		−	29.6654i		−	1.08832i	0.838983	−	0.544158i	$-0.183151\pi$
$744$	−12.0190	−	11.3708i	−0.440638	−	0.416873i
$745$		0			0
$746$		−	4.69458i		−	0.171881i
$747$	23.1501	−	1.28413i	0.847018	−	0.0469840i
$748$	−11.4744	−	16.7694i	−0.419545	−	0.613151i
$749$		−	17.1296i		−	0.625901i
$750$		0			0
$751$	9.45574			0.345045			0.172522	−	0.985006i	$-0.444808\pi$
$751$	9.45574			0.345045			0.172522	+	0.985006i	$0.444808\pi$
$752$	−11.7942			−0.430090
$753$	−24.2046	−	22.8992i	−0.882066	−	0.834494i
$754$			3.76306i			0.137043i
$755$		0			0
$756$	−12.8098	−	10.8395i	−0.465887	−	0.394229i
$757$			39.5154i			1.43621i	0.695933	+	0.718107i	$0.254991\pi$
$757$			39.5154i			1.43621i	−0.695933	+	0.718107i	$0.745009\pi$
$758$		−	22.6339i		−	0.822101i
$759$	−2.73470	+	17.2062i	−0.0992634	+	0.624547i
$760$		0			0
$761$	10.0538			0.364449			0.182225	−	0.983257i	$-0.441670\pi$
$761$	10.0538			0.364449			0.182225	+	0.983257i	$0.441670\pi$
$762$	−22.3496	−	21.1442i	−0.809639	−	0.765973i
$763$			38.6377i			1.39878i
$764$		−	8.93152i		−	0.323131i
$765$		0			0
$766$			34.2412i			1.23718i
$767$			1.39150i			0.0502443i
$768$	−1.19035	+	1.25820i	−0.0429529	+	0.0454015i
$769$			52.0226i			1.87598i	0.346656	+	0.937992i	$0.387317\pi$
$769$			52.0226i			1.87598i	−0.346656	+	0.937992i	$0.612683\pi$
$770$		0			0
$771$	11.5790	−	12.2390i	0.417006	−	0.440779i
$772$	20.5820			0.740764
$773$	6.51969			0.234497			0.117248	−	0.993103i	$-0.462593\pi$
$773$	6.51969			0.234497			0.117248	+	0.993103i	$0.462593\pi$
$774$	−17.3559	+	0.962731i	−0.623845	+	0.0346046i
$775$		0			0
$776$	−10.6462			−0.382176
$777$	39.5623	+	37.4286i	1.41929	+	1.34274i
$778$	3.67901			0.131899
$779$		−	1.77578i		−	0.0636239i
$780$		0			0
$781$	21.9816	+	32.1253i	0.786563	+	1.14953i
$782$	−18.5806			−0.664440
$783$	−20.9349	−	17.7149i	−0.748152	−	0.633079i
$784$	3.42907			0.122467
$785$		0			0
$786$	−18.9636	−	17.9409i	−0.676410	−	0.639930i
$787$	−27.3330			−0.974318			−0.487159	−	0.873313i	$-0.661967\pi$
$787$	−27.3330			−0.974318			−0.487159	+	0.873313i	$0.661967\pi$
$788$		−	13.7631i		−	0.490289i
$789$	−12.2857	−	11.6231i	−0.437382	−	0.413793i
$790$		0			0
$791$	10.6151			0.377428
$792$	7.88778	−	6.06490i	0.280280	−	0.215507i
$793$		−	1.56383i		−	0.0555332i
$794$	1.07505			0.0381521
$795$		0			0
$796$	18.3139			0.649119
$797$	−43.6885			−1.54753			−0.773763	−	0.633475i	$-0.781628\pi$
$797$	−43.6885			−1.54753			−0.773763	+	0.633475i	$0.781628\pi$
$798$	8.96565	−	9.47676i	0.317381	−	0.335474i
$799$			72.2572i			2.55628i
$800$		0			0
$801$	−9.11207	+	0.505445i	−0.321959	+	0.0178590i
$802$	28.8428			1.01847
$803$	−40.2219	+	27.5216i	−1.41940	+	0.971216i
$804$	−3.53526	−	3.34459i	−0.124679	−	0.117955i
$805$		0			0
$806$			6.81094i			0.239905i
$807$	−21.1718	−	20.0300i	−0.745283	−	0.705088i
$808$			14.5072i			0.510361i
$809$	46.6684			1.64077			0.820387	−	0.571808i	$-0.193758\pi$
$809$	46.6684			1.64077			0.820387	+	0.571808i	$0.193758\pi$
$810$		0			0
$811$		−	10.0543i		−	0.353055i	−0.984296	−	0.176527i	$-0.943514\pi$
$811$		−	10.0543i		−	0.353055i	0.984296	−	0.176527i	$-0.0564864\pi$
$812$	17.0441			0.598132
$813$	40.1161	+	37.9526i	1.40693	+	1.33105i
$814$	−26.6510	+	18.2358i	−0.934115	+	0.639163i
$815$		0			0
$816$	7.70840	+	7.29266i	0.269848	+	0.255294i
$817$		−	13.5139i		−	0.472790i
$818$	3.23862			0.113236
$819$	0.382581	+	6.89710i	0.0133685	+	0.241004i
$820$		0			0
$821$	−8.34480			−0.291236			−0.145618	−	0.989341i	$-0.546517\pi$
$821$	−8.34480			−0.291236			−0.145618	+	0.989341i	$0.546517\pi$
$822$	−5.71015	−	5.40218i	−0.199164	−	0.188423i
$823$		−	1.96316i		−	0.0684315i	−0.999414	−	0.0342158i	$-0.989107\pi$
$823$		−	1.96316i		−	0.0684315i	0.999414	−	0.0342158i	$-0.0108933\pi$
$824$	−7.79420			−0.271524
$825$		0			0
$826$	6.30257			0.219294
$827$		−	24.1152i		−	0.838567i	−0.907855	−	0.419284i	$-0.862281\pi$
$827$		−	24.1152i		−	0.838567i	0.907855	−	0.419284i	$-0.137719\pi$
$828$	−0.503915	−	9.08448i	−0.0175123	−	0.315708i
$829$	−43.2329			−1.50154			−0.750771	−	0.660563i	$-0.770318\pi$
$829$	−43.2329			−1.50154			−0.750771	+	0.660563i	$0.770318\pi$
$830$		0			0
$831$	−0.0575924	+	0.0608756i	−0.00199786	+	0.00211175i
$832$	0.713000			0.0247188
$833$		−	21.0082i		−	0.727893i
$834$	−12.4277	+	13.1361i	−0.430335	+	0.454868i
$835$		0			0
$836$	4.36820	+	6.38397i	0.151077	+	0.220794i
$837$	−37.8910	−	32.0630i	−1.30970	−	1.10826i
$838$	−8.74413			−0.302061
$839$			3.70811i			0.128018i	0.997949	+	0.0640092i	$0.0203887\pi$
$839$			3.70811i			0.128018i	−0.997949	+	0.0640092i	$0.979611\pi$
$840$		0			0
$841$	−1.14493			−0.0394802
$842$		−	28.4749i		−	0.981310i
$843$	5.38566	−	5.69268i	0.185492	−	0.196066i
$844$		−	1.12483i		−	0.0387181i
$845$		0			0
$846$	−35.3283	+	1.95966i	−1.21461	+	0.0673744i
$847$	12.8674	−	33.1112i	0.442128	−	1.13771i
$848$	1.09369			0.0375575
$849$	28.0862	−	29.6873i	0.963915	−	1.01886i
$850$		0			0
$851$			29.5293i			1.01225i
$852$	−14.7670	−	13.9706i	−0.505911	−	0.478626i
$853$	−32.9542			−1.12833			−0.564164	−	0.825662i	$-0.690802\pi$
$853$	−32.9542			−1.12833			−0.564164	+	0.825662i	$0.690802\pi$
$854$	−7.08309			−0.242378
$855$		0			0
$856$	−5.30425			−0.181295
$857$			24.5788i			0.839594i	0.907618	+	0.419797i	$0.137899\pi$
$857$			24.5788i			0.839594i	−0.907618	+	0.419797i	$0.862101\pi$
$858$	−4.04510	−	0.642915i	−0.138097	−	0.0219488i
$859$	24.9776			0.852223			0.426112	−	0.904671i	$-0.359883\pi$
$859$	24.9776			0.852223			0.426112	+	0.904671i	$0.359883\pi$
$860$		0			0
$861$	2.92684	−	3.09369i	0.0997465	−	0.105433i
$862$		−	11.9032i		−	0.405426i
$863$	−30.3314			−1.03249			−0.516246	−	0.856440i	$-0.672671\pi$
$863$	−30.3314			−1.03249			−0.516246	+	0.856440i	$0.672671\pi$
$864$	−3.35650	+	3.96660i	−0.114190	+	0.134946i
$865$		0			0
$866$	20.9488			0.711868
$867$	24.4427	−	25.8361i	0.830116	−	0.877439i
$868$	30.8489			1.04708
$869$	−25.3592	−	37.0616i	−0.860252	−	1.25723i
$870$		0			0
$871$			2.00336i			0.0678814i
$872$	11.9643			0.405163
$873$	−31.8896	+	1.76891i	−1.07930	+	0.0598686i
$874$	7.07346			0.239263
$875$		0			0
$876$	17.4916	−	18.4888i	0.590987	−	0.624678i
$877$	15.2497			0.514946			0.257473	−	0.966285i	$-0.417110\pi$
$877$	15.2497			0.514946			0.257473	+	0.966285i	$0.417110\pi$
$878$	−32.8386			−1.10825
$879$	−30.9708	−	29.3004i	−1.04462	−	0.988279i
$880$		0			0
$881$			53.1457i			1.79052i	0.445541	+	0.895261i	$0.353011\pi$
$881$			53.1457i			1.79052i	−0.445541	+	0.895261i	$0.646989\pi$
$882$	10.2714	−	0.569755i	0.345857	−	0.0191847i
$883$		−	34.7231i		−	1.16852i	−0.811565	−	0.584262i	$-0.801384\pi$
$883$		−	34.7231i		−	1.16852i	0.811565	−	0.584262i	$-0.198616\pi$
$884$		−	4.36820i		−	0.146918i
$885$		0			0
$886$			5.39604i			0.181283i
$887$		−	16.7241i		−	0.561540i	−0.959775	−	0.280770i	$-0.909410\pi$
$887$		−	16.7241i		−	0.561540i	0.959775	−	0.280770i	$-0.0905899\pi$
$888$	11.5899	−	12.2506i	0.388932	−	0.411104i
$889$	57.3642			1.92393
$890$		0			0
$891$	22.6193	−	19.4773i	0.757775	−	0.652516i
$892$			5.12343i			0.171545i
$893$		−	27.5077i		−	0.920510i
$894$	−0.869513	−	0.822618i	−0.0290809	−	0.0275125i
$895$		0			0
$896$		−	3.22941i		−	0.107887i
$897$	−2.57400	+	2.72074i	−0.0859434	+	0.0908428i
$898$	4.00000			0.133482
$899$	50.4161			1.68147
$900$		0			0
$901$		−	6.70051i		−	0.223226i
$902$	1.42600	+	2.08405i	0.0474806	+	0.0693913i
$903$	22.2735	−	23.5433i	0.741217	−	0.783472i
$904$		−	3.28700i		−	0.109324i
$905$		0			0
$906$	−12.2841	+	12.9844i	−0.408113	+	0.431379i
$907$		−	46.9073i		−	1.55753i	−0.627316	−	0.778765i	$-0.715847\pi$
$907$		−	46.9073i		−	1.55753i	0.627316	−	0.778765i	$-0.284153\pi$
$908$		−	26.9648i		−	0.894860i
$909$	2.41043	+	43.4548i	0.0799490	+	1.44130i
$910$		0			0
$911$		−	11.4463i		−	0.379233i	−0.981858	−	0.189617i	$-0.939276\pi$
$911$		−	11.4463i		−	0.379233i	0.981858	−	0.189617i	$-0.0607245\pi$
$912$	−2.93452	−	2.77625i	−0.0971717	−	0.0919309i
$913$	−14.4749	−	21.1546i	−0.479049	−	0.700114i
$914$		−	16.1359i		−	0.533729i
$915$		0			0
$916$	−5.51005			−0.182057
$917$	48.6736			1.60734
$918$	24.3014	+	20.5636i	0.802066	+	0.678701i
$919$		−	19.8836i		−	0.655901i	−0.944695	−	0.327950i	$-0.893642\pi$
$919$		−	19.8836i		−	0.655901i	0.944695	−	0.327950i	$-0.106358\pi$
$920$		0			0
$921$	−30.7973	+	32.5529i	−1.01480	+	1.07266i
$922$			5.29621i			0.174421i
$923$			8.36820i			0.275443i
$924$	−2.91197	+	18.3216i	−0.0957968	+	0.602735i
$925$		0			0
$926$	−11.9159			−0.391582
$927$	−23.3467	+	1.29504i	−0.766806	+	0.0425347i
$928$		−	5.27779i		−	0.173252i
$929$			27.5136i			0.902690i	0.892349	+	0.451345i	$0.149056\pi$
$929$			27.5136i			0.902690i	−0.892349	+	0.451345i	$0.850944\pi$
$930$		0			0
$931$			7.99766i			0.262113i
$932$			17.7399i			0.581089i
$933$	13.4676	+	12.7412i	0.440908	+	0.417129i
$934$		−	4.56807i		−	0.149472i
$935$		0			0
$936$	2.13572	−	0.118468i	0.0698081	−	0.00387225i
$937$	−30.4642			−0.995222			−0.497611	−	0.867400i	$-0.665789\pi$
$937$	−30.4642			−0.995222			−0.497611	+	0.867400i	$0.665789\pi$
$938$	9.07388			0.296273
$939$	18.0781	+	17.1031i	0.589957	+	0.558139i
$940$		0			0
$941$	−32.6542			−1.06450			−0.532249	−	0.846588i	$-0.678653\pi$
$941$	−32.6542			−1.06450			−0.532249	+	0.846588i	$0.678653\pi$
$942$	−13.4245	+	14.1898i	−0.437393	+	0.462327i
$943$	2.30913			0.0751957
$944$		−	1.95162i		−	0.0635197i
$945$		0			0
$946$	10.8520	+	15.8598i	0.352829	+	0.515648i
$947$	23.7449			0.771605			0.385802	−	0.922581i	$-0.373925\pi$
$947$	23.7449			0.771605			0.385802	+	0.922581i	$0.373925\pi$
$948$	17.0361	+	16.1173i	0.553307	+	0.523465i
$949$	−10.4772			−0.340105
$950$		0			0
$951$	−41.3915	+	43.7512i	−1.34221	+	1.41873i
$952$	−19.7850			−0.641235
$953$		−	23.0691i		−	0.747282i	−0.927573	−	0.373641i	$-0.878109\pi$
$953$		−	23.0691i		−	0.747282i	0.927573	−	0.373641i	$-0.121891\pi$
$954$	3.27604	−	0.181721i	0.106066	−	0.00588345i
$955$		0			0
$956$	5.03938			0.162985
$957$	−4.75900	+	29.9428i	−0.153837	+	0.967912i
$958$			25.4010i			0.820670i
$959$	14.6561			0.473271
$960$		0			0
$961$	60.2504			1.94356
$962$	−6.94220			−0.223825
$963$	−15.8883	+	0.881323i	−0.511994	+	0.0284003i
$964$		−	10.4588i		−	0.336856i
$965$		0			0
$966$	12.3231	+	11.6585i	0.396489	+	0.375106i
$967$	−2.79237			−0.0897967			−0.0448983	−	0.998992i	$-0.514296\pi$
$967$	−2.79237			−0.0897967			−0.0448983	+	0.998992i	$0.514296\pi$
$968$	−10.2530	−	3.98443i	−0.329544	−	0.128065i
$969$	−17.0087	+	17.9784i	−0.546399	+	0.577548i
$970$		0			0
$971$		−	21.5150i		−	0.690450i	−0.938520	−	0.345225i	$-0.887803\pi$
$971$		−	21.5150i		−	0.690450i	0.938520	−	0.345225i	$-0.112197\pi$
$972$	−9.39498	+	12.4392i	−0.301344	+	0.398988i
$973$		−	33.7163i		−	1.08089i
$974$	4.36205			0.139769
$975$		0			0
$976$			2.19331i			0.0702061i
$977$	−5.27428			−0.168739			−0.0843697	−	0.996435i	$-0.526888\pi$
$977$	−5.27428			−0.168739			−0.0843697	+	0.996435i	$0.526888\pi$
$978$	7.75678	−	8.19897i	0.248034	−	0.262174i
$979$	5.69743	+	8.32660i	0.182091	+	0.266119i
$980$		0			0
$981$	35.8379	−	1.98792i	1.14422	−	0.0634695i
$982$			13.4156i			0.428110i
$983$	−28.1850			−0.898963			−0.449482	−	0.893290i	$-0.648391\pi$
$983$	−28.1850			−0.898963			−0.449482	+	0.893290i	$0.648391\pi$
$984$	−0.957975	−	0.906309i	−0.0305391	−	0.0288921i
$985$		0			0
$986$	−32.3344			−1.02974
$987$	45.3382	−	47.9228i	1.44313	−	1.52540i
$988$			1.66294i			0.0529050i
$989$	17.5727			0.558781
$990$		0			0
$991$	0.602794			0.0191484			0.00957419	−	0.999954i	$-0.496952\pi$
$991$	0.602794			0.0191484			0.00957419	+	0.999954i	$0.496952\pi$
$992$		−	9.55251i		−	0.303292i
$993$	16.4199	−	17.3559i	0.521069	−	0.550773i
$994$	37.9023			1.20219
$995$		0			0
$996$	9.72411	+	9.19967i	0.308120	+	0.291503i
$997$	23.2502			0.736340			0.368170	−	0.929758i	$-0.379984\pi$
$997$	23.2502			0.736340			0.368170	+	0.929758i	$0.379984\pi$
$998$			20.6278i			0.652961i
$999$	32.6809	−	38.6212i	1.03398	−	1.22192i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1650.2.f.c.1649.6		8
3.2	odd	2		1650.2.f.f.1649.3		8
5.2	odd	4		330.2.d.a.131.6	yes	8
5.3	odd	4		1650.2.d.f.1451.3		8
5.4	even	2		1650.2.f.e.1649.3		8
11.10	odd	2		1650.2.f.d.1649.2		8
15.2	even	4		330.2.d.b.131.5	yes	8
15.8	even	4		1650.2.d.c.1451.4		8
15.14	odd	2		1650.2.f.d.1649.6		8
20.7	even	4		2640.2.f.b.1121.3		8
33.32	even	2		1650.2.f.e.1649.7		8
55.32	even	4		330.2.d.b.131.6	yes	8
55.43	even	4		1650.2.d.c.1451.3		8
55.54	odd	2		1650.2.f.f.1649.7		8
60.47	odd	4		2640.2.f.a.1121.4		8
165.32	odd	4		330.2.d.a.131.5	✓	8
165.98	odd	4		1650.2.d.f.1451.4		8
165.164	even	2	inner	1650.2.f.c.1649.2		8
220.87	odd	4		2640.2.f.a.1121.3		8
660.527	even	4		2640.2.f.b.1121.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
330.2.d.a.131.5	✓	8	165.32	odd	4
330.2.d.a.131.6	yes	8	5.2	odd	4
330.2.d.b.131.5	yes	8	15.2	even	4
330.2.d.b.131.6	yes	8	55.32	even	4
1650.2.d.c.1451.3		8	55.43	even	4
1650.2.d.c.1451.4		8	15.8	even	4
1650.2.d.f.1451.3		8	5.3	odd	4
1650.2.d.f.1451.4		8	165.98	odd	4
1650.2.f.c.1649.2		8	165.164	even	2	inner
1650.2.f.c.1649.6		8	1.1	even	1	trivial
1650.2.f.d.1649.2		8	11.10	odd	2
1650.2.f.d.1649.6		8	15.14	odd	2
1650.2.f.e.1649.3		8	5.4	even	2
1650.2.f.e.1649.7		8	33.32	even	2
1650.2.f.f.1649.3		8	3.2	odd	2
1650.2.f.f.1649.7		8	55.54	odd	2
2640.2.f.a.1121.3		8	220.87	odd	4
2640.2.f.a.1121.4		8	60.47	odd	4
2640.2.f.b.1121.3		8	20.7	even	4
2640.2.f.b.1121.4		8	660.527	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1650 = 2 \cdot 3 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1650.f (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +(-1.19035 + 1.25820i) q^{3} -1.00000 q^{4} +(-1.25820 - 1.19035i) q^{6} +3.22941 q^{7} -1.00000i q^{8} +(-0.166154 - 2.99540i) q^{9} +(-2.73719 + 1.87291i) q^{11} +(1.19035 - 1.25820i) q^{12} -0.713000 q^{13} +3.22941i q^{14} +1.00000 q^{16} -6.12651i q^{17} +(2.99540 - 0.166154i) q^{18} +2.33231i q^{19} +(-3.84411 + 4.06325i) q^{21} +(-1.87291 - 2.73719i) q^{22} -3.03282 q^{23} +(1.25820 + 1.19035i) q^{24} -0.713000i q^{26} +(3.96660 + 3.35650i) q^{27} -3.22941 q^{28} -5.27779 q^{29} -9.55251 q^{31} +1.00000i q^{32} +(0.901704 - 5.67335i) q^{33} +6.12651 q^{34} +(0.166154 + 2.99540i) q^{36} -9.73661i q^{37} -2.33231 q^{38} +(0.848716 - 0.897099i) q^{39} -0.761383 q^{41} +(-4.06325 - 3.84411i) q^{42} -5.79420 q^{43} +(2.73719 - 1.87291i) q^{44} -3.03282i q^{46} -11.7942 q^{47} +(-1.19035 + 1.25820i) q^{48} +3.42907 q^{49} +(7.70840 + 7.29266i) q^{51} +0.713000 q^{52} +1.09369 q^{53} +(-3.35650 + 3.96660i) q^{54} -3.22941i q^{56} +(-2.93452 - 2.77625i) q^{57} -5.27779i q^{58} -1.95162i q^{59} +2.19331i q^{61} -9.55251i q^{62} +(-0.536580 - 9.67335i) q^{63} -1.00000 q^{64} +(5.67335 + 0.901704i) q^{66} -2.80977i q^{67} +6.12651i q^{68} +(3.61010 - 3.81590i) q^{69} -11.7366i q^{71} +(-2.99540 + 0.166154i) q^{72} +14.6946 q^{73} +9.73661 q^{74} -2.33231i q^{76} +(-8.83951 + 6.04838i) q^{77} +(0.897099 + 0.848716i) q^{78} +13.5400i q^{79} +(-8.94479 + 0.995395i) q^{81} -0.761383i q^{82} +7.72857i q^{83} +(3.84411 - 4.06325i) q^{84} -5.79420i q^{86} +(6.28240 - 6.64054i) q^{87} +(1.87291 + 2.73719i) q^{88} -3.04203i q^{89} -2.30257 q^{91} +3.03282 q^{92} +(11.3708 - 12.0190i) q^{93} -11.7942i q^{94} +(-1.25820 - 1.19035i) q^{96} -10.6462i q^{97} +3.42907i q^{98} +(6.06490 + 7.88778i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{3} - 8 q^{4} - 2 q^{6} - 2 q^{9} - 6 q^{11} + 4 q^{12} + 4 q^{13} + 8 q^{16} + 8 q^{21} + 6 q^{22} + 8 q^{23} + 2 q^{24} - 10 q^{27} - 4 q^{29} - 4 q^{31} + 4 q^{33} - 4 q^{34} + 2 q^{36} - 20 q^{38}+ \cdots + 10 q^{99}+O(q^{100}) \) 8 * q - 4 * q^3 - 8 * q^4 - 2 * q^6 - 2 * q^9 - 6 * q^11 + 4 * q^12 + 4 * q^13 + 8 * q^16 + 8 * q^21 + 6 * q^22 + 8 * q^23 + 2 * q^24 - 10 * q^27 - 4 * q^29 - 4 * q^31 + 4 * q^33 - 4 * q^34 + 2 * q^36 - 20 * q^38 - 8 * q^39 + 16 * q^41 - 6 * q^42 + 8 * q^43 + 6 * q^44 - 40 * q^47 - 4 * q^48 + 4 * q^49 + 28 * q^51 - 4 * q^52 - 12 * q^53 - 22 * q^54 + 12 * q^57 - 32 * q^63 - 8 * q^64 - 18 * q^66 - 8 * q^69 + 12 * q^73 - 12 * q^74 - 8 * q^77 - 20 * q^78 + 2 * q^81 - 8 * q^84 + 36 * q^87 - 6 * q^88 - 48 * q^91 - 8 * q^92 - 2 * q^93 - 2 * q^96 + 10 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more