LMFDB - Embedded newform 1650.2.d.c.1451.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1650,2,Mod(1451,1650)] 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, 0, 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("1650.1451"); 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.d (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,-8,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == 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:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 330)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1451.4
Root			$0.356500i$ of defining polynomial
Character	$\chi$	$=$	1650.1451
Dual form			1650.2.d.c.1451.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.00000 q^{2} +(-1.25820 + 1.19035i) q^{3} +1.00000 q^{4} +(1.25820 - 1.19035i) q^{6} -3.22941i q^{7} -1.00000 q^{8} +(0.166154 - 2.99540i) q^{9} +(2.73719 - 1.87291i) q^{11} +(-1.25820 + 1.19035i) q^{12} -0.713000i q^{13} +3.22941i q^{14} +1.00000 q^{16} +6.12651 q^{17} +(-0.166154 + 2.99540i) q^{18} -2.33231i q^{19} +(3.84411 + 4.06325i) q^{21} +(-2.73719 + 1.87291i) q^{22} +3.03282i q^{23} +(1.25820 - 1.19035i) q^{24} +0.713000i q^{26} +(3.35650 + 3.96660i) q^{27} -3.22941i q^{28} -5.27779 q^{29} -9.55251 q^{31} -1.00000 q^{32} +(-1.21454 + 5.61470i) q^{33} -6.12651 q^{34} +(0.166154 - 2.99540i) q^{36} -9.73661 q^{37} +2.33231i q^{38} +(0.848716 + 0.897099i) q^{39} +0.761383 q^{41} +(-3.84411 - 4.06325i) q^{42} -5.79420i q^{43} +(2.73719 - 1.87291i) q^{44} -3.03282i q^{46} -11.7942i q^{47} +(-1.25820 + 1.19035i) q^{48} -3.42907 q^{49} +(-7.70840 + 7.29266i) q^{51} -0.713000i q^{52} -1.09369i q^{53} +(-3.35650 - 3.96660i) q^{54} +3.22941i q^{56} +(2.77625 + 2.93452i) q^{57} +5.27779 q^{58} -1.95162i q^{59} +2.19331i q^{61} +9.55251 q^{62} +(-9.67335 - 0.536580i) q^{63} +1.00000 q^{64} +(1.21454 - 5.61470i) q^{66} -2.80977 q^{67} +6.12651 q^{68} +(-3.61010 - 3.81590i) q^{69} +11.7366i q^{71} +(-0.166154 + 2.99540i) q^{72} +14.6946i q^{73} +9.73661 q^{74} -2.33231i q^{76} +(-6.04838 - 8.83951i) q^{77} +(-0.848716 - 0.897099i) q^{78} -13.5400i q^{79} +(-8.94479 - 0.995395i) q^{81} -0.761383 q^{82} +7.72857 q^{83} +(3.84411 + 4.06325i) q^{84} +5.79420i q^{86} +(6.64054 - 6.28240i) q^{87} +(-2.73719 + 1.87291i) q^{88} -3.04203i q^{89} -2.30257 q^{91} +3.03282i q^{92} +(12.0190 - 11.3708i) q^{93} +11.7942i q^{94} +(1.25820 - 1.19035i) q^{96} -10.6462 q^{97} +3.42907 q^{98} +(-5.15530 - 8.51016i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{2} - 2 q^{3} + 8 q^{4} + 2 q^{6} - 8 q^{8} + 2 q^{9} + 6 q^{11} - 2 q^{12} + 8 q^{16} - 4 q^{17} - 2 q^{18} - 8 q^{21} - 6 q^{22} + 2 q^{24} + 22 q^{27} - 4 q^{29} - 4 q^{31} - 8 q^{32} + 2 q^{33}+ \cdots - 6 q^{99}+O(q^{100}) $ 8 * q - 8 * q^2 - 2 * q^3 + 8 * q^4 + 2 * q^6 - 8 * q^8 + 2 * q^9 + 6 * q^11 - 2 * q^12 + 8 * q^16 - 4 * q^17 - 2 * q^18 - 8 * q^21 - 6 * q^22 + 2 * q^24 + 22 * q^27 - 4 * q^29 - 4 * q^31 - 8 * q^32 + 2 * q^33 + 4 * q^34 + 2 * q^36 + 12 * q^37 - 8 * q^39 - 16 * q^41 + 8 * q^42 + 6 * q^44 - 2 * q^48 - 4 * q^49 - 28 * q^51 - 22 * q^54 - 14 * q^57 + 4 * q^58 + 4 * q^62 - 14 * q^63 + 8 * q^64 - 2 * q^66 + 12 * q^67 - 4 * q^68 + 8 * q^69 - 2 * q^72 - 12 * q^74 - 36 * q^77 + 8 * q^78 + 2 * q^81 + 16 * q^82 + 72 * q^83 - 8 * q^84 + 22 * q^87 - 6 * q^88 - 48 * q^91 - 8 * q^93 + 2 * q^96 + 8 * q^97 + 4 * q^98 - 6 * 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 $

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$	−1.25820	+	1.19035i	−0.726424	+	0.687246i
$3$	−1.25820	+	1.19035i	−0.726424	+	0.687246i
$4$	1.00000			0.500000
$5$		0			0
$5$		0			0
$6$	1.25820	−	1.19035i	0.513660	−	0.485957i
$7$		−	3.22941i		−	1.22060i	−0.792170	−	0.610301i	$-0.791049\pi$
$7$		−	3.22941i		−	1.22060i	0.792170	−	0.610301i	$-0.208951\pi$
$8$	−1.00000			−0.353553
$9$	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
$12$	−1.25820	+	1.19035i	−0.363212	+	0.343623i
$13$		−	0.713000i		−	0.197751i	−0.995100	−	0.0988753i	$-0.968476\pi$
$13$		−	0.713000i		−	0.197751i	0.995100	−	0.0988753i	$-0.0315245\pi$
$14$			3.22941i			0.863096i
$15$		0			0
$16$	1.00000			0.250000
$17$	6.12651			1.48590			0.742948	−	0.669349i	$-0.233427\pi$
$17$	6.12651			1.48590			0.742948	+	0.669349i	$0.233427\pi$
$18$	−0.166154	+	2.99540i	−0.0391629	+	0.706021i
$19$		−	2.33231i		−	0.535068i	−0.963548	−	0.267534i	$-0.913791\pi$
$19$		−	2.33231i		−	0.535068i	0.963548	−	0.267534i	$-0.0862088\pi$
$20$		0			0
$21$	3.84411	+	4.06325i	0.838854	+	0.886675i
$22$	−2.73719	+	1.87291i	−0.583571	+	0.399305i
$23$			3.03282i			0.632386i	0.948695	+	0.316193i	$0.102405\pi$
$23$			3.03282i			0.632386i	−0.948695	+	0.316193i	$0.897595\pi$
$24$	1.25820	−	1.19035i	0.256830	−	0.242978i
$25$		0			0
$26$			0.713000i			0.139831i
$27$	3.35650	+	3.96660i	0.645959	+	0.763372i
$28$		−	3.22941i		−	0.610301i
$29$	−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	$0.828194\pi$
$32$	−1.00000			−0.176777
$33$	−1.21454	+	5.61470i	−0.211424	+	0.977394i
$34$	−6.12651			−1.05069
$35$		0			0
$36$	0.166154	−	2.99540i	0.0276924	−	0.499233i
$37$	−9.73661			−1.60069			−0.800344	−	0.599541i	$-0.795350\pi$
$37$	−9.73661			−1.60069			−0.800344	+	0.599541i	$0.795350\pi$
$38$			2.33231i			0.378350i
$39$	0.848716	+	0.897099i	0.135903	+	0.143651i
$40$		0			0
$41$	0.761383			0.118908			0.0594540	−	0.998231i	$-0.481064\pi$
$41$	0.761383			0.118908			0.0594540	+	0.998231i	$0.481064\pi$
$42$	−3.84411	−	4.06325i	−0.593159	−	0.626974i
$43$		−	5.79420i		−	0.883607i	−0.897112	−	0.441803i	$-0.854339\pi$
$43$		−	5.79420i		−	0.883607i	0.897112	−	0.441803i	$-0.145661\pi$
$44$	2.73719	−	1.87291i	0.412647	−	0.282351i
$45$		0			0
$46$		−	3.03282i		−	0.447164i
$47$		−	11.7942i		−	1.72036i	−0.509990	−	0.860180i	$-0.670351\pi$
$47$		−	11.7942i		−	1.72036i	0.509990	−	0.860180i	$-0.329649\pi$
$48$	−1.25820	+	1.19035i	−0.181606	+	0.171812i
$49$	−3.42907			−0.489868
$50$		0			0
$51$	−7.70840	+	7.29266i	−1.07939	+	1.02118i
$52$		−	0.713000i		−	0.0988753i
$53$		−	1.09369i		−	0.150230i	−0.997175	−	0.0751150i	$-0.976068\pi$
$53$		−	1.09369i		−	0.150230i	0.997175	−	0.0751150i	$-0.0239324\pi$
$54$	−3.35650	−	3.96660i	−0.456762	−	0.539786i
$55$		0			0
$56$			3.22941i			0.431548i
$57$	2.77625	+	2.93452i	0.367724	+	0.388687i
$58$	5.27779			0.693008
$59$		−	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	$0.955157\pi$
$62$	9.55251			1.21317
$63$	−9.67335	−	0.536580i	−1.21873	−	0.0676027i
$64$	1.00000			0.125000
$65$		0			0
$66$	1.21454	−	5.61470i	0.149499	−	0.691122i
$67$	−2.80977			−0.343268			−0.171634	−	0.985161i	$-0.554905\pi$
$67$	−2.80977			−0.343268			−0.171634	+	0.985161i	$0.554905\pi$
$68$	6.12651			0.742948
$69$	−3.61010	−	3.81590i	−0.434605	−	0.459380i
$70$		0			0
$71$			11.7366i			1.39288i	0.717616	+	0.696439i	$0.245234\pi$
$71$			11.7366i			1.39288i	−0.717616	+	0.696439i	$0.754766\pi$
$72$	−0.166154	+	2.99540i	−0.0195815	+	0.353011i
$73$			14.6946i			1.71987i	0.510403	+	0.859935i	$0.329496\pi$
$73$			14.6946i			1.71987i	−0.510403	+	0.859935i	$0.670504\pi$
$74$	9.73661			1.13186
$75$		0			0
$76$		−	2.33231i		−	0.267534i
$77$	−6.04838	−	8.83951i	−0.689277	−	1.00736i
$78$	−0.848716	−	0.897099i	−0.0960982	−	0.101576i
$79$		−	13.5400i		−	1.52337i	−0.647947	−	0.761685i	$-0.724372\pi$
$79$		−	13.5400i		−	1.52337i	0.647947	−	0.761685i	$-0.275628\pi$
$80$		0			0
$81$	−8.94479	−	0.995395i	−0.993865	−	0.110599i
$82$	−0.761383			−0.0840807
$83$	7.72857			0.848320			0.424160	−	0.905587i	$-0.360569\pi$
$83$	7.72857			0.848320			0.424160	+	0.905587i	$0.360569\pi$
$84$	3.84411	+	4.06325i	0.419427	+	0.443337i
$85$		0			0
$86$			5.79420i			0.624804i
$87$	6.64054	−	6.28240i	0.711940	−	0.673543i
$88$	−2.73719	+	1.87291i	−0.291786	+	0.199653i
$89$		−	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
$92$			3.03282i			0.316193i
$93$	12.0190	−	11.3708i	1.24631	−	1.17910i
$94$			11.7942i			1.21648i
$95$		0			0
$96$	1.25820	−	1.19035i	0.128415	−	0.121489i
$97$	−10.6462			−1.08096			−0.540479	−	0.841358i	$-0.681757\pi$
$97$	−10.6462			−1.08096			−0.540479	+	0.841358i	$0.681757\pi$
$98$	3.42907			0.346389
$99$	−5.15530	−	8.51016i	−0.518127	−	0.855303i
$100$		0			0
$101$	14.5072			1.44352			0.721760	−	0.692143i	$-0.243333\pi$
$101$	14.5072			1.44352			0.721760	+	0.692143i	$0.243333\pi$
$102$	7.70840	−	7.29266i	0.763245	−	0.722081i
$103$	7.79420			0.767985			0.383993	−	0.923336i	$-0.374549\pi$
$103$	7.79420			0.767985			0.383993	+	0.923336i	$0.374549\pi$
$104$			0.713000i			0.0699154i
$105$		0			0
$106$			1.09369i			0.106229i
$107$	5.30425			0.512781			0.256391	−	0.966573i	$-0.417467\pi$
$107$	5.30425			0.512781			0.256391	+	0.966573i	$0.417467\pi$
$108$	3.35650	+	3.96660i	0.322979	+	0.381686i
$109$		−	11.9643i		−	1.14598i	−0.819564	−	0.572988i	$-0.805784\pi$
$109$		−	11.9643i		−	1.14598i	0.819564	−	0.572988i	$-0.194216\pi$
$110$		0			0
$111$	12.2506	−	11.5899i	1.16278	−	1.10007i
$112$		−	3.22941i		−	0.305150i
$113$		−	3.28700i		−	0.309215i	−0.987976	−	0.154607i	$-0.950589\pi$
$113$		−	3.28700i		−	0.309215i	0.987976	−	0.154607i	$-0.0494113\pi$
$114$	−2.77625	−	2.93452i	−0.260020	−	0.274843i
$115$		0			0
$116$	−5.27779			−0.490031
$117$	−2.13572	−	0.118468i	−0.197447	−	0.0109524i
$118$			1.95162i			0.179661i
$119$		−	19.7850i		−	1.81369i
$120$		0			0
$121$	3.98443	−	10.2530i	0.362221	−	0.932092i
$122$		−	2.19331i		−	0.198573i
$123$	−0.957975	+	0.906309i	−0.0863777	+	0.0817191i
$124$	−9.55251			−0.857840
$125$		0			0
$126$	9.67335	+	0.536580i	0.861771	+	0.0478023i
$127$		−	17.7631i		−	1.57622i	−0.615536	−	0.788109i	$-0.711061\pi$
$127$		−	17.7631i		−	1.57622i	0.615536	−	0.788109i	$-0.288939\pi$
$128$	−1.00000			−0.0883883
$129$	6.89710	+	7.29028i	0.607256	+	0.641874i
$130$		0			0
$131$	−15.0720			−1.31685			−0.658423	−	0.752648i	$-0.728776\pi$
$131$	−15.0720			−1.31685			−0.658423	+	0.752648i	$0.728776\pi$
$132$	−1.21454	+	5.61470i	−0.105712	+	0.488697i
$133$	−7.53198			−0.653105
$134$	2.80977			0.242727
$135$		0			0
$136$	−6.12651			−0.525344
$137$			4.53833i			0.387736i	0.981028	+	0.193868i	$0.0621033\pi$
$137$			4.53833i			0.387736i	−0.981028	+	0.193868i	$0.937897\pi$
$138$	3.61010	+	3.81590i	0.307312	+	0.324831i
$139$			10.4404i			0.885543i	0.896635	+	0.442771i	$0.146005\pi$
$139$			10.4404i			0.885543i	−0.896635	+	0.442771i	$0.853995\pi$
$140$		0			0
$141$	14.0392	+	14.8395i	1.18231	+	1.24971i
$142$		−	11.7366i		−	0.984914i
$143$	−1.33538	−	1.95162i	−0.111670	−	0.163202i
$144$	0.166154	−	2.99540i	0.0138462	−	0.249616i
$145$		0			0
$146$		−	14.6946i		−	1.21613i
$147$	4.31447	−	4.08178i	0.355852	−	0.336660i
$148$	−9.73661			−0.800344
$149$	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	$-0.137937\pi$
$152$			2.33231i			0.189175i
$153$	1.01795	−	18.3513i	0.0822960	−	1.48362i
$154$	6.04838	+	8.83951i	0.487393	+	0.712308i
$155$		0			0
$156$	0.848716	+	0.897099i	0.0679517	+	0.0718254i
$157$	−11.2778			−0.900066			−0.450033	−	0.893012i	$-0.648588\pi$
$157$	−11.2778			−0.900066			−0.450033	+	0.893012i	$0.648588\pi$
$158$			13.5400i			1.07719i
$159$	1.30187	+	1.37609i	0.103245	+	0.109131i
$160$		0			0
$161$	9.79420			0.771891
$162$	8.94479	+	0.995395i	0.702769	+	0.0782056i
$163$	−6.51641			−0.510404			−0.255202	−	0.966888i	$-0.582142\pi$
$163$	−6.51641			−0.510404			−0.255202	+	0.966888i	$0.582142\pi$
$164$	0.761383			0.0594540
$165$		0			0
$166$	−7.72857			−0.599853
$167$	−8.61646			−0.666761			−0.333381	−	0.942792i	$-0.608189\pi$
$167$	−8.61646			−0.666761			−0.333381	+	0.942792i	$0.608189\pi$
$168$	−3.84411	−	4.06325i	−0.296580	−	0.313487i
$169$	12.4916			0.960895
$170$		0			0
$171$	−6.98619	−	0.387523i	−0.534247	−	0.0296346i
$172$		−	5.79420i		−	0.441803i
$173$	−12.0656			−0.917333			−0.458666	−	0.888608i	$-0.651673\pi$
$173$	−12.0656			−0.917333			−0.458666	+	0.888608i	$0.651673\pi$
$174$	−6.64054	+	6.28240i	−0.503418	+	0.476267i
$175$		0			0
$176$	2.73719	−	1.87291i	0.206324	−	0.141176i
$177$	2.32310	+	2.45553i	0.174615	+	0.184569i
$178$			3.04203i			0.228009i
$179$			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	$0.690172\pi$
$182$	2.30257			0.170678
$183$	−2.61080	−	2.75963i	−0.192996	−	0.203998i
$184$		−	3.03282i		−	0.223582i
$185$		0			0
$186$	−12.0190	+	11.3708i	−0.881276	+	0.833746i
$187$	16.7694	−	11.4744i	1.22630	−	0.839090i
$188$		−	11.7942i		−	0.860180i
$189$	12.8098	−	10.8395i	0.931773	−	0.788458i
$190$		0			0
$191$		−	8.93152i		−	0.646262i	−0.946354	−	0.323131i	$-0.895265\pi$
$191$		−	8.93152i		−	0.646262i	0.946354	−	0.323131i	$-0.104735\pi$
$192$	−1.25820	+	1.19035i	−0.0908030	+	0.0859058i
$193$		−	20.5820i		−	1.48153i	−0.671766	−	0.740764i	$-0.734464\pi$
$193$		−	20.5820i		−	1.48153i	0.671766	−	0.740764i	$-0.265536\pi$
$194$	10.6462			0.764352
$195$		0			0
$196$	−3.42907			−0.244934
$197$	−13.7631			−0.980578			−0.490289	−	0.871560i	$-0.663109\pi$
$197$	−13.7631			−0.980578			−0.490289	+	0.871560i	$0.663109\pi$
$198$	5.15530	+	8.51016i	0.366371	+	0.604791i
$199$	18.3139			1.29824			0.649119	−	0.760687i	$-0.275138\pi$
$199$	18.3139			1.29824			0.649119	+	0.760687i	$0.275138\pi$
$200$		0			0
$201$	3.53526	−	3.34459i	0.249358	−	0.235909i
$202$	−14.5072			−1.02072
$203$			17.0441i			1.19626i
$204$	−7.70840	+	7.29266i	−0.539696	+	0.510588i
$205$		0			0
$206$	−7.79420			−0.543048
$207$	9.08448	+	0.503915i	0.631415	+	0.0350245i
$208$		−	0.713000i		−	0.0494376i
$209$	−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	$0.987673\pi$
$212$		−	1.09369i		−	0.0751150i
$213$	−13.9706	−	14.7670i	−0.957251	−	1.01182i
$214$	−5.30425			−0.362591
$215$		0			0
$216$	−3.35650	−	3.96660i	−0.228381	−	0.269893i
$217$			30.8489i			2.09416i
$218$			11.9643i			0.810327i
$219$	−17.4916	−	18.4888i	−1.18197	−	1.24936i
$220$		0			0
$221$		−	4.36820i		−	0.293837i
$222$	−12.2506	+	11.5899i	−0.822209	+	0.777865i
$223$	5.12343			0.343090			0.171545	−	0.985176i	$-0.445124\pi$
$223$	5.12343			0.343090			0.171545	+	0.985176i	$0.445124\pi$
$224$			3.22941i			0.215774i
$225$		0			0
$226$			3.28700i			0.218648i
$227$	−26.9648			−1.78972			−0.894860	−	0.446347i	$-0.852725\pi$
$227$	−26.9648			−1.78972			−0.894860	+	0.446347i	$0.852725\pi$
$228$	2.77625	+	2.93452i	0.183862	+	0.194343i
$229$	−5.51005			−0.364114			−0.182057	−	0.983288i	$-0.558276\pi$
$229$	−5.51005			−0.364114			−0.182057	+	0.983288i	$0.558276\pi$
$230$		0			0
$231$	18.1322	+	3.92224i	1.19301	+	0.258064i
$232$	5.27779			0.346504
$233$	−17.7399			−1.16218			−0.581089	−	0.813840i	$-0.697373\pi$
$233$	−17.7399			−1.16218			−0.581089	+	0.813840i	$0.697373\pi$
$234$	2.13572	+	0.118468i	0.139616	+	0.00774449i
$235$		0			0
$236$		−	1.95162i		−	0.127039i
$237$	16.1173	+	17.0361i	1.04693	+	1.10661i
$238$			19.7850i			1.28247i
$239$	−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	$0.890637\pi$
$242$	−3.98443	+	10.2530i	−0.256129	+	0.659089i
$243$	12.4392	−	9.39498i	0.797977	−	0.602688i
$244$			2.19331i			0.140412i
$245$		0			0
$246$	0.957975	−	0.906309i	0.0610782	−	0.0577841i
$247$	−1.66294			−0.105810
$248$	9.55251			0.606585
$249$	−9.72411	+	9.19967i	−0.616241	+	0.583005i
$250$		0			0
$251$		−	19.2374i		−	1.21426i	−0.794604	−	0.607128i	$-0.792321\pi$
$251$		−	19.2374i		−	1.21426i	0.794604	−	0.607128i	$-0.207679\pi$
$252$	−9.67335	−	0.536580i	−0.609364	−	0.0338013i
$253$	5.68018	+	8.30140i	0.357110	+	0.521904i
$254$			17.7631i			1.11455i
$255$		0			0
$256$	1.00000			0.0625000
$257$		−	9.72740i		−	0.606778i	−0.952867	−	0.303389i	$-0.901882\pi$
$257$		−	9.72740i		−	0.606778i	0.952867	−	0.303389i	$-0.0981182\pi$
$258$	−6.89710	−	7.29028i	−0.429395	−	0.453873i
$259$			31.4435i			1.95380i
$260$		0			0
$261$	−0.876927	+	15.8091i	−0.0542804	+	0.978557i
$262$	15.0720			0.931151
$263$	9.76446			0.602102			0.301051	−	0.953608i	$-0.402663\pi$
$263$	9.76446			0.602102			0.301051	+	0.953608i	$0.402663\pi$
$264$	1.21454	−	5.61470i	0.0747496	−	0.345561i
$265$		0			0
$266$	7.53198			0.461815
$267$	3.62106	+	3.82749i	0.221605	+	0.234238i
$268$	−2.80977			−0.171634
$269$			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	$-0.419762\pi$
$272$	6.12651			0.371474
$273$	2.89710	−	2.74085i	0.175340	−	0.165884i
$274$		−	4.53833i		−	0.274171i
$275$		0			0
$276$	−3.61010	−	3.81590i	−0.217302	−	0.229690i
$277$		−	0.0483829i		−	0.00290705i	−0.999999	−	0.00145352i	$-0.999537\pi$
$277$		−	0.0483829i		−	0.00290705i	0.999999	−	0.00145352i	$-0.000462671\pi$
$278$		−	10.4404i		−	0.626173i
$279$	−1.58719	+	28.6135i	−0.0950226	+	1.71305i
$280$		0			0
$281$	4.52445			0.269906			0.134953	−	0.990852i	$-0.456912\pi$
$281$	4.52445			0.269906			0.134953	+	0.990852i	$0.456912\pi$
$282$	−14.0392	−	14.8395i	−0.836021	−	0.883680i
$283$		−	23.5950i		−	1.40257i	−0.712879	−	0.701287i	$-0.752609\pi$
$283$		−	23.5950i		−	1.40257i	0.712879	−	0.701287i	$-0.247391\pi$
$284$			11.7366i			0.696439i
$285$		0			0
$286$	1.33538	+	1.95162i	0.0789629	+	0.115402i
$287$		−	2.45882i		−	0.145139i
$288$	−0.166154	+	2.99540i	−0.00979073	+	0.176505i
$289$	20.5341			1.20789
$290$		0			0
$291$	13.3951	−	12.6727i	0.785234	−	0.742884i
$292$			14.6946i			0.859935i
$293$	24.6151			1.43803			0.719014	−	0.694996i	$-0.244594\pi$
$293$	24.6151			1.43803			0.719014	+	0.694996i	$0.244594\pi$
$294$	−4.31447	+	4.08178i	−0.251625	+	0.238054i
$295$		0			0
$296$	9.73661			0.565929
$297$	16.6165	+	4.57093i	0.964185	+	0.265232i
$298$	−0.691075			−0.0400329
$299$	2.16240			0.125055
$300$		0			0
$301$	−18.7118			−1.07853
$302$			10.3198i			0.593839i
$303$	−18.2530	+	17.2686i	−1.04861	+	0.992054i
$304$		−	2.33231i		−	0.133767i
$305$		0			0
$306$	−1.01795	+	18.3513i	−0.0581920	+	1.04907i
$307$		−	25.8725i		−	1.47662i	−0.674459	−	0.738312i	$-0.735623\pi$
$307$		−	25.8725i		−	1.47662i	0.674459	−	0.738312i	$-0.264377\pi$
$308$	−6.04838	−	8.83951i	−0.344639	−	0.503678i
$309$	−9.80669	+	9.27779i	−0.557883	+	0.527795i
$310$		0			0
$311$			10.7038i			0.606956i	0.952838	+	0.303478i	$0.0981479\pi$
$311$			10.7038i			0.606956i	−0.952838	+	0.303478i	$0.901852\pi$
$312$	−0.848716	−	0.897099i	−0.0480491	−	0.0507882i
$313$	14.3682			0.812139			0.406069	−	0.913842i	$-0.366899\pi$
$313$	14.3682			0.812139			0.406069	+	0.913842i	$0.366899\pi$
$314$	11.2778			0.636443
$315$		0			0
$316$		−	13.5400i		−	0.761685i
$317$			34.7727i			1.95303i	0.215450	+	0.976515i	$0.430878\pi$
$317$			34.7727i			1.95303i	−0.215450	+	0.976515i	$0.569122\pi$
$318$	−1.30187	−	1.37609i	−0.0730053	−	0.0771671i
$319$	−14.4463	+	9.88482i	−0.808839	+	0.553443i
$320$		0			0
$321$	−6.67383	+	6.31389i	−0.372497	+	0.352407i
$322$	−9.79420			−0.545809
$323$		−	14.2889i		−	0.795056i
$324$	−8.94479	−	0.995395i	−0.496933	−	0.0552997i
$325$		0			0
$326$	6.51641			0.360910
$327$	14.2417	+	15.0536i	0.787567	+	0.832464i
$328$	−0.761383			−0.0420403
$329$	−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	$0.623766\pi$
$332$	7.72857			0.424160
$333$	−1.61778	+	29.1650i	−0.0886537	+	1.59823i
$334$	8.61646			0.471472
$335$		0			0
$336$	3.84411	+	4.06325i	0.209713	+	0.221669i
$337$			13.3868i			0.729227i	0.931159	+	0.364613i	$0.118799\pi$
$337$			13.3868i			0.729227i	−0.931159	+	0.364613i	$0.881201\pi$
$338$	−12.4916			−0.679455
$339$	3.91267	+	4.13572i	0.212507	+	0.224621i
$340$		0			0
$341$	−26.1470	+	17.8910i	−1.41594	+	0.968850i
$342$	6.98619	+	0.387523i	0.377770	+	0.0209548i
$343$		−	11.5320i		−	0.622668i
$344$			5.79420i			0.312402i
$345$		0			0
$346$	12.0656			0.648652
$347$	19.3699			1.03983			0.519915	−	0.854218i	$-0.325964\pi$
$347$	19.3699			1.03983			0.519915	+	0.854218i	$0.325964\pi$
$348$	6.64054	−	6.28240i	0.355970	−	0.336772i
$349$			2.53833i			0.135874i	0.997690	+	0.0679369i	$0.0216417\pi$
$349$			2.53833i			0.135874i	−0.997690	+	0.0679369i	$0.978358\pi$
$350$		0			0
$351$	2.82818	−	2.39318i	0.150957	−	0.127739i
$352$	−2.73719	+	1.87291i	−0.145893	+	0.0998263i
$353$			32.9476i			1.75362i	0.480834	+	0.876812i	$0.340334\pi$
$353$			32.9476i			1.75362i	−0.480834	+	0.876812i	$0.659666\pi$
$354$	−2.32310	−	2.45553i	−0.123471	−	0.130510i
$355$		0			0
$356$		−	3.04203i		−	0.161227i
$357$	23.5510	+	24.8936i	1.24645	+	1.31751i
$358$		−	3.49280i		−	0.184600i
$359$	−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
$362$	15.1361			0.795538
$363$	7.19140	+	17.6432i	0.377451	+	0.926030i
$364$	−2.30257			−0.120687
$365$		0			0
$366$	2.61080	+	2.75963i	0.136468	+	0.144248i
$367$	11.1361			0.581302			0.290651	−	0.956829i	$-0.406128\pi$
$367$	11.1361			0.581302			0.290651	+	0.956829i	$0.406128\pi$
$368$			3.03282i			0.158096i
$369$	0.126507	−	2.28064i	0.00658569	−	0.118726i
$370$		0			0
$371$	−3.53198			−0.183371
$372$	12.0190	−	11.3708i	0.623156	−	0.589548i
$373$		−	4.69458i		−	0.243076i	−0.992587	−	0.121538i	$-0.961217\pi$
$373$		−	4.69458i		−	0.243076i	0.992587	−	0.121538i	$-0.0387827\pi$
$374$	−16.7694	+	11.4744i	−0.867126	+	0.593326i
$375$		0			0
$376$			11.7942i			0.608239i
$377$			3.76306i			0.193808i
$378$	−12.8098	+	10.8395i	−0.658863	+	0.557524i
$379$	22.6339			1.16263			0.581313	−	0.813680i	$-0.302539\pi$
$379$	22.6339			1.16263			0.581313	+	0.813680i	$0.302539\pi$
$380$		0			0
$381$	21.1442	+	22.3496i	1.08325	+	1.14500i
$382$			8.93152i			0.456976i
$383$		−	34.2412i		−	1.74964i	−0.484447	−	0.874821i	$-0.660979\pi$
$383$		−	34.2412i		−	1.74964i	0.484447	−	0.874821i	$-0.339021\pi$
$384$	1.25820	−	1.19035i	0.0642075	−	0.0607446i
$385$		0			0
$386$			20.5820i			1.04760i
$387$	−17.3559	−	0.962731i	−0.882251	−	0.0489383i
$388$	−10.6462			−0.540479
$389$		−	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
$392$	3.42907			0.173194
$393$	18.9636	−	17.9409i	0.956589	−	0.904998i
$394$	13.7631			0.693373
$395$		0			0
$396$	−5.15530	−	8.51016i	−0.259064	−	0.427652i
$397$	−1.07505			−0.0539552			−0.0269776	−	0.999636i	$-0.508588\pi$
$397$	−1.07505			−0.0539552			−0.0269776	+	0.999636i	$0.508588\pi$
$398$	−18.3139			−0.917992
$399$	9.47676	−	8.96565i	0.474431	−	0.448844i
$400$		0			0
$401$			28.8428i			1.44034i	0.693798	+	0.720170i	$0.255936\pi$
$401$			28.8428i			1.44034i	−0.693798	+	0.720170i	$0.744064\pi$
$402$	−3.53526	+	3.34459i	−0.176323	+	0.166813i
$403$			6.81094i			0.339277i
$404$	14.5072			0.721760
$405$		0			0
$406$		−	17.0441i		−	0.845886i
$407$	−26.6510	+	18.2358i	−1.32104	+	0.903913i
$408$	7.70840	−	7.29266i	0.381622	−	0.361041i
$409$			3.23862i			0.160139i	0.996789	+	0.0800697i	$0.0255143\pi$
$409$			3.23862i			0.160139i	−0.996789	+	0.0800697i	$0.974486\pi$
$410$		0			0
$411$	−5.40218	−	5.71015i	−0.266470	−	0.281661i
$412$	7.79420			0.383993
$413$	−6.30257			−0.310129
$414$	−9.08448	−	0.503915i	−0.446478	−	0.0247661i
$415$		0			0
$416$			0.713000i			0.0349577i
$417$	−12.4277	−	13.1361i	−0.608586	−	0.643280i
$418$	4.36820	+	6.38397i	0.213656	+	0.312250i
$419$			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	$0.744105\pi$
$422$		−	1.12483i		−	0.0547557i
$423$	−35.3283	−	1.95966i	−1.71772	−	0.0952817i
$424$			1.09369i			0.0531143i
$425$		0			0
$426$	13.9706	+	14.7670i	0.676879	+	0.715466i
$427$	7.08309			0.342775
$428$	5.30425			0.256391
$429$	4.00328	+	0.865965i	0.193280	+	0.0418092i
$430$		0			0
$431$	11.9032			0.573359			0.286679	−	0.958027i	$-0.407449\pi$
$431$	11.9032			0.573359			0.286679	+	0.958027i	$0.407449\pi$
$432$	3.35650	+	3.96660i	0.161490	+	0.190843i
$433$	20.9488			1.00673			0.503367	−	0.864073i	$-0.332094\pi$
$433$	20.9488			1.00673			0.503367	+	0.864073i	$0.332094\pi$
$434$		−	30.8489i		−	1.48080i
$435$		0			0
$436$		−	11.9643i		−	0.572988i
$437$	7.07346			0.338370
$438$	17.4916	+	18.4888i	0.835782	+	0.883428i
$439$		−	32.8386i		−	1.56730i	−0.621203	−	0.783649i	$-0.713356\pi$
$439$		−	32.8386i		−	1.56730i	0.621203	−	0.783649i	$-0.286644\pi$
$440$		0			0
$441$	−0.569755	+	10.2714i	−0.0271312	+	0.489116i
$442$			4.36820i			0.207774i
$443$		−	5.39604i		−	0.256373i	−0.991750	−	0.128187i	$-0.959084\pi$
$443$		−	5.39604i		−	0.256373i	0.991750	−	0.128187i	$-0.0409157\pi$
$444$	12.2506	−	11.5899i	0.581389	−	0.550034i
$445$		0			0
$446$	−5.12343			−0.242602
$447$	−0.869513	+	0.822618i	−0.0411266	+	0.0389085i
$448$		−	3.22941i		−	0.152575i
$449$		−	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
$452$		−	3.28700i		−	0.154607i
$453$	12.2841	+	12.9844i	0.577160	+	0.610062i
$454$	26.9648			1.26552
$455$		0			0
$456$	−2.77625	−	2.93452i	−0.130010	−	0.137421i
$457$			16.1359i			0.754807i	0.926049	+	0.377404i	$0.123183\pi$
$457$			16.1359i			0.754807i	−0.926049	+	0.377404i	$0.876817\pi$
$458$	5.51005			0.257468
$459$	20.5636	+	24.3014i	0.959828	+	1.13429i
$460$		0			0
$461$	−5.29621			−0.246669			−0.123335	−	0.992365i	$-0.539359\pi$
$461$	−5.29621			−0.246669			−0.123335	+	0.992365i	$0.539359\pi$
$462$	−18.1322	−	3.92224i	−0.843585	−	0.182479i
$463$	−11.9159			−0.553781			−0.276891	−	0.960901i	$-0.589304\pi$
$463$	−11.9159			−0.553781			−0.276891	+	0.960901i	$0.589304\pi$
$464$	−5.27779			−0.245015
$465$		0			0
$466$	17.7399			0.821785
$467$		−	4.56807i		−	0.211385i	−0.994399	−	0.105693i	$-0.966294\pi$
$467$		−	4.56807i		−	0.211385i	0.994399	−	0.105693i	$-0.0337060\pi$
$468$	−2.13572	−	0.118468i	−0.0987235	−	0.00547618i
$469$			9.07388i			0.418993i
$470$		0			0
$471$	14.1898	−	13.4245i	0.653830	−	0.618567i
$472$			1.95162i			0.0898305i
$473$	−10.8520	−	15.8598i	−0.498975	−	0.729236i
$474$	−16.1173	−	17.0361i	−0.740292	−	0.782494i
$475$		0			0
$476$		−	19.7850i		−	0.906843i
$477$	−3.27604	−	0.181721i	−0.149999	−	0.00832045i
$478$	5.03938			0.230496
$479$	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
$482$		−	10.4588i		−	0.476386i
$483$	−12.3231	+	11.6585i	−0.560720	+	0.530479i
$484$	3.98443	−	10.2530i	0.181111	−	0.466046i
$485$		0			0
$486$	−12.4392	+	9.39498i	−0.564255	+	0.426165i
$487$	−4.36205			−0.197663			−0.0988317	−	0.995104i	$-0.531511\pi$
$487$	−4.36205			−0.197663			−0.0988317	+	0.995104i	$0.531511\pi$
$488$		−	2.19331i		−	0.0992864i
$489$	8.19897	−	7.75678i	0.370770	−	0.350774i
$490$		0			0
$491$	−13.4156			−0.605438			−0.302719	−	0.953080i	$-0.597894\pi$
$491$	−13.4156			−0.605438			−0.302719	+	0.953080i	$0.597894\pi$
$492$	−0.957975	+	0.906309i	−0.0431888	+	0.0408596i
$493$	−32.3344			−1.45627
$494$	1.66294			0.0748190
$495$		0			0
$496$	−9.55251			−0.428920
$497$	37.9023			1.70015
$498$	9.72411	−	9.19967i	0.435748	−	0.412247i
$499$	−20.6278			−0.923426			−0.461713	−	0.887029i	$-0.652765\pi$
$499$	−20.6278			−0.923426			−0.461713	+	0.887029i	$0.652765\pi$
$500$		0			0
$501$	10.8413	−	10.2566i	0.484352	−	0.458229i
$502$			19.2374i			0.858609i
$503$	−1.14800			−0.0511868			−0.0255934	−	0.999672i	$-0.508148\pi$
$503$	−1.14800			−0.0511868			−0.0255934	+	0.999672i	$0.508148\pi$
$504$	9.67335	+	0.536580i	0.430885	+	0.0239012i
$505$		0			0
$506$	−5.68018	−	8.30140i	−0.252515	−	0.369042i
$507$	−15.7170	+	14.8694i	−0.698017	+	0.660371i
$508$		−	17.7631i		−	0.788109i
$509$		−	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
$512$	−1.00000			−0.0441942
$513$	9.25133	−	7.82839i	0.408456	−	0.345632i
$514$			9.72740i			0.429057i
$515$		0			0
$516$	6.89710	+	7.29028i	0.303628	+	0.320937i
$517$	−22.0894	−	32.2830i	−0.971493	−	1.41980i
$518$		−	31.4435i		−	1.38155i
$519$	15.1810	−	14.3623i	0.666373	−	0.630434i
$520$		0			0
$521$		−	31.1768i		−	1.36588i	−0.730474	−	0.682940i	$-0.760701\pi$
$521$		−	31.1768i		−	1.36588i	0.730474	−	0.682940i	$-0.239299\pi$
$522$	0.876927	−	15.8091i	0.0383821	−	0.691944i
$523$			32.9337i			1.44009i	0.693927	+	0.720045i	$0.255879\pi$
$523$			32.9337i			1.44009i	−0.693927	+	0.720045i	$0.744121\pi$
$524$	−15.0720			−0.658423
$525$		0			0
$526$	−9.76446			−0.425751
$527$	−58.5235			−2.54932
$528$	−1.21454	+	5.61470i	−0.0528559	+	0.244349i
$529$	13.8020			0.600088
$530$		0			0
$531$	−5.84586	−	0.324269i	−0.253689	−	0.0140721i
$532$	−7.53198			−0.326553
$533$		−	0.542866i		−	0.0235141i
$534$	−3.62106	−	3.82749i	−0.156699	−	0.165632i
$535$		0			0
$536$	2.80977			0.121363
$537$	−4.15764	−	4.39466i	−0.179415	−	0.189643i
$538$		−	16.8270i		−	0.725464i
$539$	−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	$0.733002\pi$
$542$			31.8836i			1.36952i
$543$	19.0444	−	18.0172i	0.817272	−	0.773194i
$544$	−6.12651			−0.262672
$545$		0			0
$546$	−2.89710	+	2.74085i	−0.123984	+	0.117298i
$547$			28.8647i			1.23417i	0.786898	+	0.617083i	$0.211686\pi$
$547$			28.8647i			1.23417i	−0.786898	+	0.617083i	$0.788314\pi$
$548$			4.53833i			0.193868i
$549$	6.56983	+	0.364428i	0.280393	+	0.0155534i
$550$		0			0
$551$			12.3094i			0.524400i
$552$	3.61010	+	3.81590i	0.153656	+	0.162416i
$553$	−43.7262			−1.85943
$554$			0.0483829i			0.00205559i
$555$		0			0
$556$			10.4404i			0.442771i
$557$	15.4076			0.652840			0.326420	−	0.945225i	$-0.394158\pi$
$557$	15.4076			0.652840			0.326420	+	0.945225i	$0.394158\pi$
$558$	1.58719	−	28.6135i	0.0671911	−	1.21131i
$559$	−4.13126			−0.174734
$560$		0			0
$561$	−7.44087	+	34.3985i	−0.314154	+	1.45231i
$562$	−4.52445			−0.190852
$563$	40.8624			1.72214			0.861072	−	0.508483i	$-0.169794\pi$
$563$	40.8624			1.72214			0.861072	+	0.508483i	$0.169794\pi$
$564$	14.0392	+	14.8395i	0.591156	+	0.624856i
$565$		0			0
$566$			23.5950i			0.991770i
$567$	−3.21454	+	28.8864i	−0.134998	+	1.21311i
$568$		−	11.7366i		−	0.492457i
$569$	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	$0.963707\pi$
$572$	−1.33538	−	1.95162i	−0.0558352	−	0.0816012i
$573$	10.6316	+	11.2377i	0.444141	+	0.469460i
$574$			2.45882i			0.102629i
$575$		0			0
$576$	0.166154	−	2.99540i	0.00692309	−	0.124808i
$577$	12.5556			0.522696			0.261348	−	0.965245i	$-0.415833\pi$
$577$	12.5556			0.522696			0.261348	+	0.965245i	$0.415833\pi$
$578$	−20.5341			−0.854105
$579$	24.4997	+	25.8964i	1.01817	+	1.07622i
$580$		0			0
$581$		−	24.9587i		−	1.03546i
$582$	−13.3951	+	12.6727i	−0.555244	+	0.525298i
$583$	−2.04838	−	2.99364i	−0.0848354	−	0.123984i
$584$		−	14.6946i		−	0.608066i
$585$		0			0
$586$	−24.6151			−1.01684
$587$		−	31.9380i		−	1.31822i	−0.752046	−	0.659110i	$-0.770933\pi$
$587$		−	31.9380i		−	1.31822i	0.752046	−	0.659110i	$-0.229067\pi$
$588$	4.31447	−	4.08178i	0.177926	−	0.168330i
$589$			22.2794i			0.918006i
$590$		0			0
$591$	17.3167	−	16.3828i	0.712316	−	0.673899i
$592$	−9.73661			−0.400172
$593$	14.0345			0.576328			0.288164	−	0.957581i	$-0.406955\pi$
$593$	14.0345			0.576328			0.288164	+	0.957581i	$0.406955\pi$
$594$	−16.6165	−	4.57093i	−0.681781	−	0.187547i
$595$		0			0
$596$	0.691075			0.0283075
$597$	−23.0426	+	21.7999i	−0.943071	+	0.892209i
$598$	−2.16240			−0.0884270
$599$		−	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	$-0.139177\pi$
$602$	18.7118			0.762637
$603$	−0.466854	+	8.41636i	−0.0190118	+	0.342741i
$604$		−	10.3198i		−	0.419907i
$605$		0			0
$606$	18.2530	−	17.2686i	0.741478	−	0.701488i
$607$		−	15.1326i		−	0.614215i	−0.951675	−	0.307107i	$-0.900639\pi$
$607$		−	15.1326i		−	0.614215i	0.951675	−	0.307107i	$-0.0993611\pi$
$608$			2.33231i			0.0945876i
$609$	−20.2884	−	21.4450i	−0.822128	−	0.868995i
$610$		0			0
$611$	−8.40926			−0.340202
$612$	1.01795	−	18.3513i	0.0411480	−	0.741808i
$613$			26.3137i			1.06280i	0.847121	+	0.531399i	$0.178334\pi$
$613$			26.3137i			1.06280i	−0.847121	+	0.531399i	$0.821666\pi$
$614$			25.8725i			1.04413i
$615$		0			0
$616$	6.04838	+	8.83951i	0.243696	+	0.356154i
$617$		−	2.21735i		−	0.0892670i	−0.999003	−	0.0446335i	$-0.985788\pi$
$617$		−	2.21735i		−	0.0892670i	0.999003	−	0.0446335i	$-0.0142120\pi$
$618$	9.80669	−	9.27779i	0.394483	−	0.373207i
$619$	−49.1338			−1.97485			−0.987427	−	0.158074i	$-0.949471\pi$
$619$	−49.1338			−1.97485			−0.987427	+	0.158074i	$0.949471\pi$
$620$		0			0
$621$	−12.0300	+	10.1796i	−0.482746	+	0.408495i
$622$		−	10.7038i		−	0.429183i
$623$	−9.82394			−0.393588
$624$	0.848716	+	0.897099i	0.0339758	+	0.0359127i
$625$		0			0
$626$	−14.3682			−0.574269
$627$	13.0952	+	2.83268i	0.522973	+	0.113126i
$628$	−11.2778			−0.450033
$629$	−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	$0.619260\pi$
$632$			13.5400i			0.538593i
$633$	−1.33893	−	1.41526i	−0.0532177	−	0.0562515i
$634$		−	34.7727i		−	1.38100i
$635$		0			0
$636$	1.30187	+	1.37609i	0.0516225	+	0.0545654i
$637$			2.44493i			0.0968716i
$638$	14.4463	−	9.88482i	0.571935	−	0.391344i
$639$	35.1558	+	1.95009i	1.39074	+	0.0771442i
$640$		0			0
$641$			8.97639i			0.354546i	0.984162	+	0.177273i	$0.0567276\pi$
$641$			8.97639i			0.354546i	−0.984162	+	0.177273i	$0.943272\pi$
$642$	6.67383	−	6.31389i	0.263395	−	0.249189i
$643$	29.0097			1.14403			0.572016	−	0.820243i	$-0.306162\pi$
$643$	29.0097			1.14403			0.572016	+	0.820243i	$0.306162\pi$
$644$	9.79420			0.385945
$645$		0			0
$646$			14.2889i			0.562189i
$647$		−	21.7880i		−	0.856577i	−0.903642	−	0.428288i	$-0.859117\pi$
$647$		−	21.7880i		−	0.856577i	0.903642	−	0.428288i	$-0.140883\pi$
$648$	8.94479	+	0.995395i	0.351384	+	0.0391028i
$649$	−3.65520	−	5.34195i	−0.143479	−	0.209690i
$650$		0			0
$651$	−36.7209	−	38.8143i	−1.43921	−	1.52125i
$652$	−6.51641			−0.255202
$653$		−	2.13307i		−	0.0834736i	−0.999129	−	0.0417368i	$-0.986711\pi$
$653$		−	2.13307i		−	0.0834736i	0.999129	−	0.0417368i	$-0.0132891\pi$
$654$	−14.2417	−	15.0536i	−0.556894	−	0.588641i
$655$		0			0
$656$	0.761383			0.0297270
$657$	44.0161	+	2.44157i	1.71723	+	0.0952546i
$658$	38.0883			1.48484
$659$	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	$0.629432\pi$
$662$	13.7942			0.536127
$663$	5.19967	+	5.49608i	0.201938	+	0.213450i
$664$	−7.72857			−0.299927
$665$		0			0
$666$	1.61778	−	29.1650i	0.0626876	−	1.13012i
$667$		−	16.0066i		−	0.619777i
$668$	−8.61646			−0.333381
$669$	−6.44632	+	6.09866i	−0.249229	+	0.235788i
$670$		0			0
$671$	4.10787	+	6.00351i	0.158582	+	0.231763i
$672$	−3.84411	−	4.06325i	−0.148290	−	0.156743i
$673$		−	12.5820i		−	0.485002i	−0.970151	−	0.242501i	$-0.922032\pi$
$673$		−	12.5820i		−	0.485002i	0.970151	−	0.242501i	$-0.0779678\pi$
$674$		−	13.3868i		−	0.515641i
$675$		0			0
$676$	12.4916			0.480447
$677$	16.6085			0.638316			0.319158	−	0.947701i	$-0.396600\pi$
$677$	16.6085			0.638316			0.319158	+	0.947701i	$0.396600\pi$
$678$	−3.91267	−	4.13572i	−0.150265	−	0.158831i
$679$			34.3809i			1.31942i
$680$		0			0
$681$	33.9273	−	32.0975i	1.30010	−	1.22998i
$682$	26.1470	−	17.8910i	1.00122	−	0.685080i
$683$			36.0597i			1.37979i	0.723911	+	0.689893i	$0.242343\pi$
$683$			36.0597i			1.37979i	−0.723911	+	0.689893i	$0.757657\pi$
$684$	−6.98619	−	0.387523i	−0.267123	−	0.0148173i
$685$		0			0
$686$			11.5320i			0.440293i
$687$	6.93277	−	6.55886i	0.264502	−	0.250236i
$688$		−	5.79420i		−	0.220902i
$689$	−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	$0.325923\pi$
$692$	−12.0656			−0.458666
$693$	−27.4828	+	16.6486i	−1.04398	+	0.632427i
$694$	−19.3699			−0.735271
$695$		0			0
$696$	−6.64054	+	6.28240i	−0.251709	+	0.238134i
$697$	4.66462			0.176685
$698$		−	2.53833i		−	0.0960773i
$699$	22.3204	−	21.1166i	0.844235	−	0.798703i
$700$		0			0
$701$	−6.68771			−0.252591			−0.126296	−	0.991993i	$-0.540309\pi$
$701$	−6.68771			−0.252591			−0.126296	+	0.991993i	$0.540309\pi$
$702$	−2.82818	+	2.39318i	−0.106743	+	0.0903249i
$703$			22.7088i			0.856477i
$704$	2.73719	−	1.87291i	0.103162	−	0.0705879i
$705$		0			0
$706$		−	32.9476i		−	1.24000i
$707$		−	46.8497i		−	1.76196i
$708$	2.32310	+	2.45553i	0.0873074	+	0.0922846i
$709$	−34.9431			−1.31231			−0.656157	−	0.754624i	$-0.727819\pi$
$709$	−34.9431			−1.31231			−0.656157	+	0.754624i	$0.727819\pi$
$710$		0			0
$711$	−40.5577	−	2.24973i	−1.52103	−	0.0843715i
$712$			3.04203i			0.114005i
$713$		−	28.9710i		−	1.08497i
$714$	−23.5510	−	24.8936i	−0.881373	−	0.931618i
$715$		0			0
$716$			3.49280i			0.130532i
$717$	6.34057	−	5.99861i	0.236793	−	0.224022i
$718$	16.6212			0.620298
$719$			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
$722$	−13.5603			−0.504663
$723$	−12.4496	−	13.1593i	−0.463006	−	0.489400i
$724$	−15.1361			−0.562531
$725$		0			0
$726$	−7.19140	−	17.6432i	−0.266898	−	0.654802i
$727$	29.6479			1.09958			0.549789	−	0.835303i	$-0.314708\pi$
$727$	29.6479			1.09958			0.549789	+	0.835303i	$0.314708\pi$
$728$	2.30257			0.0853388
$729$	−4.46782	+	26.6278i	−0.165475	+	0.986214i
$730$		0			0
$731$		−	35.4982i		−	1.31295i
$732$	−2.61080	−	2.75963i	−0.0964978	−	0.101999i
$733$			34.2703i			1.26580i	0.774233	+	0.632901i	$0.218136\pi$
$733$			34.2703i			1.26580i	−0.774233	+	0.632901i	$0.781864\pi$
$734$	−11.1361			−0.411043
$735$		0			0
$736$		−	3.03282i		−	0.111791i
$737$	−7.69087	+	5.26243i	−0.283297	+	0.193844i
$738$	−0.126507	+	2.28064i	−0.00465679	+	0.0839516i
$739$			49.1457i			1.80785i	0.427689	+	0.903926i	$0.359328\pi$
$739$			49.1457i			1.80785i	−0.427689	+	0.903926i	$0.640672\pi$
$740$		0			0
$741$	2.09231	−	1.97947i	0.0768630	−	0.0727176i
$742$	3.53198			0.129663
$743$	−29.6654			−1.08832			−0.544158	−	0.838983i	$-0.683151\pi$
$743$	−29.6654			−1.08832			−0.544158	+	0.838983i	$0.683151\pi$
$744$	−12.0190	+	11.3708i	−0.440638	+	0.416873i
$745$		0			0
$746$			4.69458i			0.171881i
$747$	1.28413	−	23.1501i	0.0469840	−	0.847018i
$748$	16.7694	−	11.4744i	0.613151	−	0.419545i
$749$		−	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	$0.444808\pi$
$752$		−	11.7942i		−	0.430090i
$753$	22.8992	+	24.2046i	0.834494	+	0.882066i
$754$		−	3.76306i		−	0.137043i
$755$		0			0
$756$	12.8098	−	10.8395i	0.465887	−	0.394229i
$757$	39.5154			1.43621			0.718107	−	0.695933i	$-0.245009\pi$
$757$	39.5154			1.43621			0.718107	+	0.695933i	$0.245009\pi$
$758$	−22.6339			−0.822101
$759$	−17.0284	−	3.68347i	−0.618090	−	0.133701i
$760$		0			0
$761$	−10.0538			−0.364449			−0.182225	−	0.983257i	$-0.558330\pi$
$761$	−10.0538			−0.364449			−0.182225	+	0.983257i	$0.558330\pi$
$762$	−21.1442	−	22.3496i	−0.765973	−	0.809639i
$763$	−38.6377			−1.39878
$764$		−	8.93152i		−	0.323131i
$765$		0			0
$766$			34.2412i			1.23718i
$767$	−1.39150			−0.0502443
$768$	−1.25820	+	1.19035i	−0.0454015	+	0.0429529i
$769$		−	52.0226i		−	1.87598i	−0.346656	−	0.937992i	$-0.612683\pi$
$769$		−	52.0226i		−	1.87598i	0.346656	−	0.937992i	$-0.387317\pi$
$770$		0			0
$771$	11.5790	+	12.2390i	0.417006	+	0.440779i
$772$		−	20.5820i		−	0.740764i
$773$		−	6.51969i		−	0.234497i	−0.993103	−	0.117248i	$-0.962593\pi$
$773$		−	6.51969i		−	0.234497i	0.993103	−	0.117248i	$-0.0374074\pi$
$774$	17.3559	+	0.962731i	0.623845	+	0.0346046i
$775$		0			0
$776$	10.6462			0.382176
$777$	−37.4286	−	39.5623i	−1.34274	−	1.41929i
$778$			3.67901i			0.131899i
$779$		−	1.77578i		−	0.0636239i
$780$		0			0
$781$	21.9816	+	32.1253i	0.786563	+	1.14953i
$782$		−	18.5806i		−	0.664440i
$783$	−17.7149	−	20.9349i	−0.633079	−	0.748152i
$784$	−3.42907			−0.122467
$785$		0			0
$786$	−18.9636	+	17.9409i	−0.676410	+	0.639930i
$787$			27.3330i			0.974318i	0.873313	+	0.487159i	$0.161967\pi$
$787$			27.3330i			0.974318i	−0.873313	+	0.487159i	$0.838033\pi$
$788$	−13.7631			−0.490289
$789$	−12.2857	+	11.6231i	−0.437382	+	0.413793i
$790$		0			0
$791$	−10.6151			−0.377428
$792$	5.15530	+	8.51016i	0.183186	+	0.302395i
$793$	1.56383			0.0555332
$794$	1.07505			0.0381521
$795$		0			0
$796$	18.3139			0.649119
$797$		−	43.6885i		−	1.54753i	−0.633475	−	0.773763i	$-0.718372\pi$
$797$		−	43.6885i		−	1.54753i	0.633475	−	0.773763i	$-0.281628\pi$
$798$	−9.47676	+	8.96565i	−0.335474	+	0.317381i
$799$		−	72.2572i		−	2.55628i
$800$		0			0
$801$	−9.11207	−	0.505445i	−0.321959	−	0.0178590i
$802$		−	28.8428i		−	1.01847i
$803$	27.5216	+	40.2219i	0.971216	+	1.41940i
$804$	3.53526	−	3.34459i	0.124679	−	0.117955i
$805$		0			0
$806$		−	6.81094i		−	0.239905i
$807$	−20.0300	−	21.1718i	−0.705088	−	0.745283i
$808$	−14.5072			−0.510361
$809$	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	$-0.0564864\pi$
$812$			17.0441i			0.598132i
$813$	37.9526	+	40.1161i	1.33105	+	1.40693i
$814$	26.6510	−	18.2358i	0.934115	−	0.639163i
$815$		0			0
$816$	−7.70840	+	7.29266i	−0.269848	+	0.255294i
$817$	−13.5139			−0.472790
$818$		−	3.23862i		−	0.113236i
$819$	−0.382581	+	6.89710i	−0.0133685	+	0.241004i
$820$		0			0
$821$	8.34480			0.291236			0.145618	−	0.989341i	$-0.453483\pi$
$821$	8.34480			0.291236			0.145618	+	0.989341i	$0.453483\pi$
$822$	5.40218	+	5.71015i	0.188423	+	0.199164i
$823$	1.96316			0.0684315			0.0342158	−	0.999414i	$-0.489107\pi$
$823$	1.96316			0.0684315			0.0342158	+	0.999414i	$0.489107\pi$
$824$	−7.79420			−0.271524
$825$		0			0
$826$	6.30257			0.219294
$827$	24.1152			0.838567			0.419284	−	0.907855i	$-0.362281\pi$
$827$	24.1152			0.838567			0.419284	+	0.907855i	$0.362281\pi$
$828$	9.08448	+	0.503915i	0.315708	+	0.0175123i
$829$	43.2329			1.50154			0.750771	−	0.660563i	$-0.229682\pi$
$829$	43.2329			1.50154			0.750771	+	0.660563i	$0.229682\pi$
$830$		0			0
$831$	0.0575924	+	0.0608756i	0.00199786	+	0.00211175i
$832$		−	0.713000i		−	0.0247188i
$833$	−21.0082			−0.727893
$834$	12.4277	+	13.1361i	0.430335	+	0.454868i
$835$		0			0
$836$	−4.36820	−	6.38397i	−0.151077	−	0.220794i
$837$	−32.0630	−	37.8910i	−1.10826	−	1.30970i
$838$		−	8.74413i		−	0.302061i
$839$			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
$842$	28.4749			0.981310
$843$	−5.69268	+	5.38566i	−0.196066	+	0.185492i
$844$			1.12483i			0.0387181i
$845$		0			0
$846$	35.3283	+	1.95966i	1.21461	+	0.0673744i
$847$	−33.1112	−	12.8674i	−1.13771	−	0.442128i
$848$		−	1.09369i		−	0.0375575i
$849$	28.0862	+	29.6873i	0.963915	+	1.01886i
$850$		0			0
$851$		−	29.5293i		−	1.01225i
$852$	−13.9706	−	14.7670i	−0.478626	−	0.505911i
$853$		−	32.9542i		−	1.12833i	−0.825662	−	0.564164i	$-0.809198\pi$
$853$		−	32.9542i		−	1.12833i	0.825662	−	0.564164i	$-0.190802\pi$
$854$	−7.08309			−0.242378
$855$		0			0
$856$	−5.30425			−0.181295
$857$	−24.5788			−0.839594			−0.419797	−	0.907618i	$-0.637899\pi$
$857$	−24.5788			−0.839594			−0.419797	+	0.907618i	$0.637899\pi$
$858$	−4.00328	−	0.865965i	−0.136670	−	0.0295636i
$859$	−24.9776			−0.852223			−0.426112	−	0.904671i	$-0.640117\pi$
$859$	−24.9776			−0.852223			−0.426112	+	0.904671i	$0.640117\pi$
$860$		0			0
$861$	2.92684	+	3.09369i	0.0997465	+	0.105433i
$862$	−11.9032			−0.405426
$863$			30.3314i			1.03249i	0.856440	+	0.516246i	$0.172671\pi$
$863$			30.3314i			1.03249i	−0.856440	+	0.516246i	$0.827329\pi$
$864$	−3.35650	−	3.96660i	−0.114190	−	0.134946i
$865$		0			0
$866$	−20.9488			−0.711868
$867$	−25.8361	+	24.4427i	−0.877439	+	0.830116i
$868$			30.8489i			1.04708i
$869$	−25.3592	−	37.0616i	−0.860252	−	1.25723i
$870$		0			0
$871$			2.00336i			0.0678814i
$872$			11.9643i			0.405163i
$873$	−1.76891	+	31.8896i	−0.0598686	+	1.07930i
$874$	−7.07346			−0.239263
$875$		0			0
$876$	−17.4916	−	18.4888i	−0.590987	−	0.624678i
$877$		−	15.2497i		−	0.514946i	−0.966285	−	0.257473i	$-0.917110\pi$
$877$		−	15.2497i		−	0.514946i	0.966285	−	0.257473i	$-0.0828899\pi$
$878$			32.8386i			1.10825i
$879$	−30.9708	+	29.3004i	−1.04462	+	0.988279i
$880$		0			0
$881$		−	53.1457i		−	1.79052i	−0.445541	−	0.895261i	$-0.646989\pi$
$881$		−	53.1457i		−	1.79052i	0.445541	−	0.895261i	$-0.353011\pi$
$882$	0.569755	−	10.2714i	0.0191847	−	0.345857i
$883$	34.7231			1.16852			0.584262	−	0.811565i	$-0.301384\pi$
$883$	34.7231			1.16852			0.584262	+	0.811565i	$0.301384\pi$
$884$		−	4.36820i		−	0.146918i
$885$		0			0
$886$			5.39604i			0.181283i
$887$	16.7241			0.561540			0.280770	−	0.959775i	$-0.409410\pi$
$887$	16.7241			0.561540			0.280770	+	0.959775i	$0.409410\pi$
$888$	−12.2506	+	11.5899i	−0.411104	+	0.388932i
$889$	−57.3642			−1.92393
$890$		0			0
$891$	−26.3479	+	14.0282i	−0.882687	+	0.469961i
$892$	5.12343			0.171545
$893$	−27.5077			−0.920510
$894$	0.869513	−	0.822618i	0.0290809	−	0.0275125i
$895$		0			0
$896$			3.22941i			0.107887i
$897$	−2.72074	+	2.57400i	−0.0908428	+	0.0859434i
$898$			4.00000i			0.133482i
$899$	50.4161			1.68147
$900$		0			0
$901$		−	6.70051i		−	0.223226i
$902$	−2.08405	+	1.42600i	−0.0693913	+	0.0474806i
$903$	23.5433	−	22.2735i	0.783472	−	0.741217i
$904$			3.28700i			0.109324i
$905$		0			0
$906$	−12.2841	−	12.9844i	−0.408113	−	0.431379i
$907$	−46.9073			−1.55753			−0.778765	−	0.627316i	$-0.784153\pi$
$907$	−46.9073			−1.55753			−0.778765	+	0.627316i	$0.784153\pi$
$908$	−26.9648			−0.894860
$909$	2.41043	−	43.4548i	0.0799490	−	1.44130i
$910$		0			0
$911$			11.4463i			0.379233i	0.981858	+	0.189617i	$0.0607245\pi$
$911$			11.4463i			0.379233i	−0.981858	+	0.189617i	$0.939276\pi$
$912$	2.77625	+	2.93452i	0.0919309	+	0.0971717i
$913$	21.1546	−	14.4749i	0.700114	−	0.479049i
$914$		−	16.1359i		−	0.533729i
$915$		0			0
$916$	−5.51005			−0.182057
$917$			48.6736i			1.60734i
$918$	−20.5636	−	24.3014i	−0.678701	−	0.802066i
$919$			19.8836i			0.655901i	0.944695	+	0.327950i	$0.106358\pi$
$919$			19.8836i			0.655901i	−0.944695	+	0.327950i	$0.893642\pi$
$920$		0			0
$921$	30.7973	+	32.5529i	1.01480	+	1.07266i
$922$	5.29621			0.174421
$923$	8.36820			0.275443
$924$	18.1322	+	3.92224i	0.596505	+	0.129032i
$925$		0			0
$926$	11.9159			0.391582
$927$	1.29504	−	23.3467i	0.0425347	−	0.766806i
$928$	5.27779			0.173252
$929$			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
$932$	−17.7399			−0.581089
$933$	−12.7412	−	13.4676i	−0.417129	−	0.440908i
$934$			4.56807i			0.149472i
$935$		0			0
$936$	2.13572	+	0.118468i	0.0698081	+	0.00387225i
$937$			30.4642i			0.995222i	0.867400	+	0.497611i	$0.165789\pi$
$937$			30.4642i			0.995222i	−0.867400	+	0.497611i	$0.834211\pi$
$938$		−	9.07388i		−	0.296273i
$939$	−18.0781	+	17.1031i	−0.589957	+	0.558139i
$940$		0			0
$941$	32.6542			1.06450			0.532249	−	0.846588i	$-0.321347\pi$
$941$	32.6542			1.06450			0.532249	+	0.846588i	$0.321347\pi$
$942$	−14.1898	+	13.4245i	−0.462327	+	0.437393i
$943$			2.30913i			0.0751957i
$944$		−	1.95162i		−	0.0635197i
$945$		0			0
$946$	10.8520	+	15.8598i	0.352829	+	0.515648i
$947$			23.7449i			0.771605i	0.922581	+	0.385802i	$0.126075\pi$
$947$			23.7449i			0.771605i	−0.922581	+	0.385802i	$0.873925\pi$
$948$	16.1173	+	17.0361i	0.523465	+	0.553307i
$949$	10.4772			0.340105
$950$		0			0
$951$	−41.3915	−	43.7512i	−1.34221	−	1.41873i
$952$			19.7850i			0.641235i
$953$	−23.0691			−0.747282			−0.373641	−	0.927573i	$-0.621891\pi$
$953$	−23.0691			−0.747282			−0.373641	+	0.927573i	$0.621891\pi$
$954$	3.27604	+	0.181721i	0.106066	+	0.00588345i
$955$		0			0
$956$	−5.03938			−0.162985
$957$	6.41007	−	29.6332i	0.207208	−	0.957906i
$958$	−25.4010			−0.820670
$959$	14.6561			0.473271
$960$		0			0
$961$	60.2504			1.94356
$962$		−	6.94220i		−	0.223825i
$963$	0.881323	−	15.8883i	0.0284003	−	0.511994i
$964$			10.4588i			0.336856i
$965$		0			0
$966$	12.3231	−	11.6585i	0.396489	−	0.375106i
$967$			2.79237i			0.0897967i	0.998992	+	0.0448983i	$0.0142964\pi$
$967$			2.79237i			0.0897967i	−0.998992	+	0.0448983i	$0.985704\pi$
$968$	−3.98443	+	10.2530i	−0.128065	+	0.329544i
$969$	17.0087	+	17.9784i	0.546399	+	0.577548i
$970$		0			0
$971$			21.5150i			0.690450i	0.938520	+	0.345225i	$0.112197\pi$
$971$			21.5150i			0.690450i	−0.938520	+	0.345225i	$0.887803\pi$
$972$	12.4392	−	9.39498i	0.398988	−	0.301344i
$973$	33.7163			1.08089
$974$	4.36205			0.139769
$975$		0			0
$976$			2.19331i			0.0702061i
$977$		−	5.27428i		−	0.168739i	−0.996435	−	0.0843697i	$-0.973112\pi$
$977$		−	5.27428i		−	0.168739i	0.996435	−	0.0843697i	$-0.0268877\pi$
$978$	−8.19897	+	7.75678i	−0.262174	+	0.248034i
$979$	−5.69743	−	8.32660i	−0.182091	−	0.266119i
$980$		0			0
$981$	−35.8379	−	1.98792i	−1.14422	−	0.0634695i
$982$	13.4156			0.428110
$983$			28.1850i			0.898963i	0.893290	+	0.449482i	$0.148391\pi$
$983$			28.1850i			0.898963i	−0.893290	+	0.449482i	$0.851609\pi$
$984$	0.957975	−	0.906309i	0.0305391	−	0.0288921i
$985$		0			0
$986$	32.3344			1.02974
$987$	47.9228	−	45.3382i	1.52540	−	1.44313i
$988$	−1.66294			−0.0529050
$989$	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	$0.496952\pi$
$992$	9.55251			0.303292
$993$	17.3559	−	16.4199i	0.550773	−	0.521069i
$994$	−37.9023			−1.20219
$995$		0			0
$996$	−9.72411	+	9.19967i	−0.308120	+	0.291503i
$997$		−	23.2502i		−	0.736340i	−0.929758	−	0.368170i	$-0.879984\pi$
$997$		−	23.2502i		−	0.736340i	0.929758	−	0.368170i	$-0.120016\pi$
$998$	20.6278			0.652961
$999$	−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.d.c.1451.4		8
3.2	odd	2		1650.2.d.f.1451.3		8
5.2	odd	4		1650.2.f.f.1649.3		8
5.3	odd	4		1650.2.f.d.1649.6		8
5.4	even	2		330.2.d.b.131.5	yes	8
11.10	odd	2		1650.2.d.f.1451.4		8
15.2	even	4		1650.2.f.c.1649.6		8
15.8	even	4		1650.2.f.e.1649.3		8
15.14	odd	2		330.2.d.a.131.6	yes	8
20.19	odd	2		2640.2.f.a.1121.4		8
33.32	even	2	inner	1650.2.d.c.1451.3		8
55.32	even	4		1650.2.f.e.1649.7		8
55.43	even	4		1650.2.f.c.1649.2		8
55.54	odd	2		330.2.d.a.131.5	✓	8
60.59	even	2		2640.2.f.b.1121.3		8
165.32	odd	4		1650.2.f.d.1649.2		8
165.98	odd	4		1650.2.f.f.1649.7		8
165.164	even	2		330.2.d.b.131.6	yes	8
220.219	even	2		2640.2.f.b.1121.4		8
660.659	odd	2		2640.2.f.a.1121.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
330.2.d.a.131.5	✓	8	55.54	odd	2
330.2.d.a.131.6	yes	8	15.14	odd	2
330.2.d.b.131.5	yes	8	5.4	even	2
330.2.d.b.131.6	yes	8	165.164	even	2
1650.2.d.c.1451.3		8	33.32	even	2	inner
1650.2.d.c.1451.4		8	1.1	even	1	trivial
1650.2.d.f.1451.3		8	3.2	odd	2
1650.2.d.f.1451.4		8	11.10	odd	2
1650.2.f.c.1649.2		8	55.43	even	4
1650.2.f.c.1649.6		8	15.2	even	4
1650.2.f.d.1649.2		8	165.32	odd	4
1650.2.f.d.1649.6		8	5.3	odd	4
1650.2.f.e.1649.3		8	15.8	even	4
1650.2.f.e.1649.7		8	55.32	even	4
1650.2.f.f.1649.3		8	5.2	odd	4
1650.2.f.f.1649.7		8	165.98	odd	4
2640.2.f.a.1121.3		8	660.659	odd	2
2640.2.f.a.1121.4		8	20.19	odd	2
2640.2.f.b.1121.3		8	60.59	even	2
2640.2.f.b.1121.4		8	220.219	even	2

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.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +(-1.25820 + 1.19035i) q^{3} +1.00000 q^{4} +(1.25820 - 1.19035i) q^{6} -3.22941i q^{7} -1.00000 q^{8} +(0.166154 - 2.99540i) q^{9} +(2.73719 - 1.87291i) q^{11} +(-1.25820 + 1.19035i) q^{12} -0.713000i q^{13} +3.22941i q^{14} +1.00000 q^{16} +6.12651 q^{17} +(-0.166154 + 2.99540i) q^{18} -2.33231i q^{19} +(3.84411 + 4.06325i) q^{21} +(-2.73719 + 1.87291i) q^{22} +3.03282i q^{23} +(1.25820 - 1.19035i) q^{24} +0.713000i q^{26} +(3.35650 + 3.96660i) q^{27} -3.22941i q^{28} -5.27779 q^{29} -9.55251 q^{31} -1.00000 q^{32} +(-1.21454 + 5.61470i) q^{33} -6.12651 q^{34} +(0.166154 - 2.99540i) q^{36} -9.73661 q^{37} +2.33231i q^{38} +(0.848716 + 0.897099i) q^{39} +0.761383 q^{41} +(-3.84411 - 4.06325i) q^{42} -5.79420i q^{43} +(2.73719 - 1.87291i) q^{44} -3.03282i q^{46} -11.7942i q^{47} +(-1.25820 + 1.19035i) q^{48} -3.42907 q^{49} +(-7.70840 + 7.29266i) q^{51} -0.713000i q^{52} -1.09369i q^{53} +(-3.35650 - 3.96660i) q^{54} +3.22941i q^{56} +(2.77625 + 2.93452i) q^{57} +5.27779 q^{58} -1.95162i q^{59} +2.19331i q^{61} +9.55251 q^{62} +(-9.67335 - 0.536580i) q^{63} +1.00000 q^{64} +(1.21454 - 5.61470i) q^{66} -2.80977 q^{67} +6.12651 q^{68} +(-3.61010 - 3.81590i) q^{69} +11.7366i q^{71} +(-0.166154 + 2.99540i) q^{72} +14.6946i q^{73} +9.73661 q^{74} -2.33231i q^{76} +(-6.04838 - 8.83951i) q^{77} +(-0.848716 - 0.897099i) q^{78} -13.5400i q^{79} +(-8.94479 - 0.995395i) q^{81} -0.761383 q^{82} +7.72857 q^{83} +(3.84411 + 4.06325i) q^{84} +5.79420i q^{86} +(6.64054 - 6.28240i) q^{87} +(-2.73719 + 1.87291i) q^{88} -3.04203i q^{89} -2.30257 q^{91} +3.03282i q^{92} +(12.0190 - 11.3708i) q^{93} +11.7942i q^{94} +(1.25820 - 1.19035i) q^{96} -10.6462 q^{97} +3.42907 q^{98} +(-5.15530 - 8.51016i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{2} - 2 q^{3} + 8 q^{4} + 2 q^{6} - 8 q^{8} + 2 q^{9} + 6 q^{11} - 2 q^{12} + 8 q^{16} - 4 q^{17} - 2 q^{18} - 8 q^{21} - 6 q^{22} + 2 q^{24} + 22 q^{27} - 4 q^{29} - 4 q^{31} - 8 q^{32} + 2 q^{33}+ \cdots - 6 q^{99}+O(q^{100}) \) 8 * q - 8 * q^2 - 2 * q^3 + 8 * q^4 + 2 * q^6 - 8 * q^8 + 2 * q^9 + 6 * q^11 - 2 * q^12 + 8 * q^16 - 4 * q^17 - 2 * q^18 - 8 * q^21 - 6 * q^22 + 2 * q^24 + 22 * q^27 - 4 * q^29 - 4 * q^31 - 8 * q^32 + 2 * q^33 + 4 * q^34 + 2 * q^36 + 12 * q^37 - 8 * q^39 - 16 * q^41 + 8 * q^42 + 6 * q^44 - 2 * q^48 - 4 * q^49 - 28 * q^51 - 22 * q^54 - 14 * q^57 + 4 * q^58 + 4 * q^62 - 14 * q^63 + 8 * q^64 - 2 * q^66 + 12 * q^67 - 4 * q^68 + 8 * q^69 - 2 * q^72 - 12 * q^74 - 36 * q^77 + 8 * q^78 + 2 * q^81 + 16 * q^82 + 72 * q^83 - 8 * q^84 + 22 * q^87 - 6 * q^88 - 48 * q^91 - 8 * q^93 + 2 * q^96 + 8 * q^97 + 4 * q^98 - 6 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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