LMFDB - Embedded newform 1100.2.n.e.401.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1100,2,Mod(201,1100)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1100, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 8]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1100.201");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1100 = 2^{2} \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1100.n (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$8.78354422234$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 3 x^{15} + 13 x^{14} - 15 x^{13} + 59 x^{12} + 4 x^{11} + 369 x^{10} + 618 x^{9} + 1481 x^{8} + \cdots + 400 $ x^16 - 3x^15 + 13x^14 - 15x^13 + 59x^12 + 4x^11 + 369x^10 + 618x^9 + 1481x^8 + 1013x^7 + 1564x^6 + 276x^5 + 1041x^4 + 220x^3 + 240x^2 + 200*x + 400
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			401.3
Root			$0.286660 - 0.882247i$ of defining polynomial
Character	$\chi$	$=$	1100.401
Dual form			1100.2.n.e.801.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.750484 + 0.545259i) q^{3} +(-0.472607 + 0.343369i) q^{7} +(-0.661131 - 2.03475i) q^{9} +O(q^{10})$	\(q+(0.750484 + 0.545259i) q^{3} +(-0.472607 + 0.343369i) q^{7} +(-0.661131 - 2.03475i) q^{9} +(-2.68926 + 1.94110i) q^{11} +(-1.64305 - 5.05679i) q^{13} +(1.72302 - 5.30292i) q^{17} +(-4.85320 - 3.52606i) q^{19} -0.541910 q^{21} -1.46478 q^{23} +(1.47328 - 4.53428i) q^{27} +(5.97092 - 4.33813i) q^{29} +(1.99414 + 6.13734i) q^{31} +(-3.07665 - 0.00957748i) q^{33} +(1.41243 - 1.02619i) q^{37} +(1.52418 - 4.69093i) q^{39} +(0.772467 + 0.561230i) q^{41} +6.82687 q^{43} +(-10.1421 - 7.36865i) q^{47} +(-2.05766 + 6.33284i) q^{49} +(4.18457 - 3.04027i) q^{51} +(-1.58459 - 4.87686i) q^{53} +(-1.71964 - 5.29250i) q^{57} +(0.541544 - 0.393454i) q^{59} +(-2.67951 + 8.24668i) q^{61} +(1.01113 + 0.734627i) q^{63} +5.37489 q^{67} +(-1.09929 - 0.798683i) q^{69} +(-1.70217 + 5.23873i) q^{71} +(4.10181 - 2.98014i) q^{73} +(0.604450 - 1.84079i) q^{77} +(-3.18802 - 9.81171i) q^{79} +(-1.61457 + 1.17305i) q^{81} +(-1.56683 + 4.82222i) q^{83} +6.84648 q^{87} -4.22913 q^{89} +(2.51287 + 1.82570i) q^{91} +(-1.84987 + 5.69330i) q^{93} +(-5.19726 - 15.9955i) q^{97} +(5.72762 + 4.18866i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 2 q^{3}+O(q^{10}) $ 16 * q + 2 * q^3	$ 16 q + 2 q^{3} - 5 q^{11} - q^{13} - 8 q^{17} + 13 q^{19} - 6 q^{21} - 16 q^{23} - 37 q^{27} - 7 q^{29} + 2 q^{31} + 14 q^{33} - 8 q^{37} - 17 q^{39} - 15 q^{41} - 18 q^{47} - 24 q^{49} + 13 q^{51} - 6 q^{53} - 31 q^{57} + 6 q^{59} + 24 q^{61} + 5 q^{63} + 18 q^{67} - 53 q^{69} + 36 q^{71} - 9 q^{73} + 45 q^{77} - 45 q^{79} + 17 q^{81} - 14 q^{83} + 18 q^{87} + 18 q^{89} + 38 q^{91} - 29 q^{93} + 49 q^{97} + 40 q^{99}+O(q^{100}) $ 16 * q + 2 * q^3 - 5 * q^11 - q^13 - 8 * q^17 + 13 * q^19 - 6 * q^21 - 16 * q^23 - 37 * q^27 - 7 * q^29 + 2 * q^31 + 14 * q^33 - 8 * q^37 - 17 * q^39 - 15 * q^41 - 18 * q^47 - 24 * q^49 + 13 * q^51 - 6 * q^53 - 31 * q^57 + 6 * q^59 + 24 * q^61 + 5 * q^63 + 18 * q^67 - 53 * q^69 + 36 * q^71 - 9 * q^73 + 45 * q^77 - 45 * q^79 + 17 * q^81 - 14 * q^83 + 18 * q^87 + 18 * q^89 + 38 * q^91 - 29 * q^93 + 49 * q^97 + 40 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1100\mathbb{Z}\right)^\times$.

$n$	$101$	$177$	$551$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$1$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	0.750484	+	0.545259i	0.433292	+	0.314805i	0.782964	−	0.622067i	$-0.213707\pi$
$3$	0.750484	+	0.545259i	0.433292	+	0.314805i	−0.349672	+	0.936872i	$0.613707\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−0.472607	+	0.343369i	−0.178629	+	0.129781i	−0.673507	−	0.739181i	$-0.735213\pi$
$7$	−0.472607	+	0.343369i	−0.178629	+	0.129781i	0.494878	+	0.868962i	$0.335213\pi$
$8$		0			0
$9$	−0.661131	−	2.03475i	−0.220377	−	0.678251i
$10$		0			0
$11$	−2.68926	+	1.94110i	−0.810843	+	0.585264i
$11$	−2.68926	+	1.94110i	−0.810843	+	0.585264i
$12$		0			0
$13$	−1.64305	−	5.05679i	−0.455701	−	1.40250i	−0.870311	−	0.492503i	$-0.836082\pi$
$13$	−1.64305	−	5.05679i	−0.455701	−	1.40250i	0.414610	−	0.909999i	$-0.363918\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	1.72302	−	5.30292i	0.417895	−	1.28615i	−0.491741	−	0.870741i	$-0.663639\pi$
$17$	1.72302	−	5.30292i	0.417895	−	1.28615i	0.909636	−	0.415406i	$-0.136361\pi$
$18$		0			0
$19$	−4.85320	−	3.52606i	−1.11340	−	0.808933i	−0.130205	−	0.991487i	$-0.541564\pi$
$19$	−4.85320	−	3.52606i	−1.11340	−	0.808933i	−0.983196	+	0.182554i	$0.941564\pi$
$20$		0			0
$21$	−0.541910			−0.118254
$22$		0			0
$23$	−1.46478			−0.305427			−0.152714	−	0.988270i	$-0.548801\pi$
$23$	−1.46478			−0.305427			−0.152714	+	0.988270i	$0.548801\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	1.47328	−	4.53428i	0.283532	−	0.872623i
$28$		0			0
$29$	5.97092	−	4.33813i	1.10877	−	0.805570i	0.126302	−	0.991992i	$-0.459689\pi$
$29$	5.97092	−	4.33813i	1.10877	−	0.805570i	0.982470	+	0.186422i	$0.0596892\pi$
$30$		0			0
$31$	1.99414	+	6.13734i	0.358159	+	1.10230i	0.954155	+	0.299312i	$0.0967572\pi$
$31$	1.99414	+	6.13734i	0.358159	+	1.10230i	−0.595997	+	0.802987i	$0.703243\pi$
$32$		0			0
$33$	−3.07665	−	0.00957748i	−0.535576	−	0.00166722i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	1.41243	−	1.02619i	0.232202	−	0.168705i	−0.465600	−	0.884995i	$-0.654161\pi$
$37$	1.41243	−	1.02619i	0.232202	−	0.168705i	0.697802	+	0.716291i	$0.254161\pi$
$38$		0			0
$39$	1.52418	−	4.69093i	0.244064	−	0.751151i
$40$		0			0
$41$	0.772467	+	0.561230i	0.120639	+	0.0876495i	0.646469	−	0.762940i	$-0.276245\pi$
$41$	0.772467	+	0.561230i	0.120639	+	0.0876495i	−0.525830	+	0.850590i	$0.676245\pi$
$42$		0			0
$43$	6.82687			1.04109			0.520544	−	0.853835i	$-0.325729\pi$
$43$	6.82687			1.04109			0.520544	+	0.853835i	$0.325729\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−10.1421	−	7.36865i	−1.47937	−	1.07483i	−0.977758	−	0.209737i	$-0.932739\pi$
$47$	−10.1421	−	7.36865i	−1.47937	−	1.07483i	−0.501616	−	0.865090i	$-0.667261\pi$
$48$		0			0
$49$	−2.05766	+	6.33284i	−0.293952	+	0.904691i
$50$		0			0
$51$	4.18457	−	3.04027i	0.585957	−	0.425722i
$52$		0			0
$53$	−1.58459	−	4.87686i	−0.217660	−	0.669889i	−0.998954	−	0.0457256i	$-0.985440\pi$
$53$	−1.58459	−	4.87686i	−0.217660	−	0.669889i	0.781294	−	0.624163i	$-0.214560\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−1.71964	−	5.29250i	−0.227772	−	0.701009i
$58$		0			0
$59$	0.541544	−	0.393454i	0.0705030	−	0.0512234i	−0.551976	−	0.833860i	$-0.686126\pi$
$59$	0.541544	−	0.393454i	0.0705030	−	0.0512234i	0.622478	+	0.782637i	$0.286126\pi$
$60$		0			0
$61$	−2.67951	+	8.24668i	−0.343076	+	1.05588i	0.619530	+	0.784973i	$0.287323\pi$
$61$	−2.67951	+	8.24668i	−0.343076	+	1.05588i	−0.962606	+	0.270906i	$0.912677\pi$
$62$		0			0
$63$	1.01113	+	0.734627i	0.127390	+	0.0925543i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	5.37489			0.656648			0.328324	−	0.944565i	$-0.393516\pi$
$67$	5.37489			0.656648			0.328324	+	0.944565i	$0.393516\pi$
$68$		0			0
$69$	−1.09929	−	0.798683i	−0.132339	−	0.0961501i
$70$		0			0
$71$	−1.70217	+	5.23873i	−0.202010	+	0.621723i	0.797813	+	0.602905i	$0.205990\pi$
$71$	−1.70217	+	5.23873i	−0.202010	+	0.621723i	−0.999823	+	0.0188180i	$0.994010\pi$
$72$		0			0
$73$	4.10181	−	2.98014i	0.480080	−	0.348799i	−0.321276	−	0.946985i	$-0.604112\pi$
$73$	4.10181	−	2.98014i	0.480080	−	0.348799i	0.801357	+	0.598187i	$0.204112\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	0.604450	−	1.84079i	0.0688835	−	0.209777i
$78$		0			0
$79$	−3.18802	−	9.81171i	−0.358680	−	1.10390i	−0.953845	−	0.300300i	$-0.902913\pi$
$79$	−3.18802	−	9.81171i	−0.358680	−	1.10390i	0.595165	−	0.803604i	$-0.297087\pi$
$80$		0			0
$81$	−1.61457	+	1.17305i	−0.179396	+	0.130339i
$82$		0			0
$83$	−1.56683	+	4.82222i	−0.171982	+	0.529307i	−0.999483	−	0.0321577i	$-0.989762\pi$
$83$	−1.56683	+	4.82222i	−0.171982	+	0.529307i	0.827500	+	0.561465i	$0.189762\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	6.84648			0.734020
$88$		0			0
$89$	−4.22913			−0.448287			−0.224144	−	0.974556i	$-0.571958\pi$
$89$	−4.22913			−0.448287			−0.224144	+	0.974556i	$0.571958\pi$
$90$		0			0
$91$	2.51287	+	1.82570i	0.263420	+	0.191386i
$92$		0			0
$93$	−1.84987	+	5.69330i	−0.191822	+	0.590368i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−5.19726	−	15.9955i	−0.527702	−	1.62410i	−0.758911	−	0.651195i	$-0.774268\pi$
$97$	−5.19726	−	15.9955i	−0.527702	−	1.62410i	0.231209	−	0.972904i	$-0.425732\pi$
$98$		0			0
$99$	5.72762	+	4.18866i	0.575647	+	0.420976i
$100$		0			0
$101$	1.25890	+	3.87449i	0.125265	+	0.385526i	0.993949	−	0.109840i	$-0.0350339\pi$
$101$	1.25890	+	3.87449i	0.125265	+	0.385526i	−0.868684	+	0.495366i	$0.835034\pi$
$102$		0			0
$103$	5.64712	−	4.10287i	0.556427	−	0.404268i	−0.273722	−	0.961809i	$-0.588255\pi$
$103$	5.64712	−	4.10287i	0.556427	−	0.404268i	0.830150	+	0.557541i	$0.188255\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	2.64365	+	1.92072i	0.255571	+	0.185683i	0.708192	−	0.706020i	$-0.249511\pi$
$107$	2.64365	+	1.92072i	0.255571	+	0.185683i	−0.452621	+	0.891703i	$0.649511\pi$
$108$		0			0
$109$	12.6448			1.21116			0.605578	−	0.795786i	$-0.292942\pi$
$109$	12.6448			1.21116			0.605578	+	0.795786i	$0.292942\pi$
$110$		0			0
$111$	1.61955			0.153720
$112$		0			0
$113$	−13.7435	−	9.98521i	−1.29288	−	0.939330i	−0.293017	−	0.956107i	$-0.594659\pi$
$113$	−13.7435	−	9.98521i	−1.29288	−	0.939330i	−0.999859	+	0.0167775i	$0.994659\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−9.20306	+	6.68641i	−0.850823	+	0.618159i
$118$		0			0
$119$	1.00655	+	3.09783i	0.0922700	+	0.283978i
$120$		0			0
$121$	3.46425	−	10.4403i	0.314932	−	0.949114i
$122$		0			0
$123$	0.273709	+	0.842389i	0.0246795	+	0.0759557i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	2.07703	−	6.39245i	0.184307	−	0.567239i	−0.815629	−	0.578576i	$-0.803609\pi$
$127$	2.07703	−	6.39245i	0.184307	−	0.567239i	0.999936	+	0.0113371i	$0.00360878\pi$
$128$		0			0
$129$	5.12346	+	3.72241i	0.451095	+	0.327740i
$130$		0			0
$131$	−8.97490			−0.784141			−0.392071	−	0.919935i	$-0.628241\pi$
$131$	−8.97490			−0.784141			−0.392071	+	0.919935i	$0.628241\pi$
$132$		0			0
$133$	3.50440			0.303870
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−5.91054	+	18.1908i	−0.504971	+	1.55414i	0.295848	+	0.955235i	$0.404398\pi$
$137$	−5.91054	+	18.1908i	−0.504971	+	1.55414i	−0.800819	+	0.598907i	$0.795602\pi$
$138$		0			0
$139$	−8.02866	+	5.83316i	−0.680982	+	0.494762i	−0.873683	−	0.486495i	$-0.838275\pi$
$139$	−8.02866	+	5.83316i	−0.680982	+	0.494762i	0.192701	+	0.981257i	$0.438275\pi$
$140$		0			0
$141$	−3.59365	−	11.0601i	−0.302640	−	0.931429i
$142$		0			0
$143$	14.2343	+	10.4097i	1.19034	+	0.870504i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−4.99728	+	3.63074i	−0.412169	+	0.299458i
$148$		0			0
$149$	−0.628274	+	1.93363i	−0.0514702	+	0.158409i	−0.973488	−	0.228739i	$-0.926540\pi$
$149$	−0.628274	+	1.93363i	−0.0514702	+	0.158409i	0.922018	+	0.387148i	$0.126540\pi$
$150$		0			0
$151$	1.77218	+	1.28757i	0.144218	+	0.104781i	0.657555	−	0.753407i	$-0.271591\pi$
$151$	1.77218	+	1.28757i	0.144218	+	0.104781i	−0.513337	+	0.858187i	$0.671591\pi$
$152$		0			0
$153$	−11.9293			−0.964425
$154$		0			0
$155$		0			0
$156$		0			0
$157$	6.13265	+	4.45563i	0.489439	+	0.355598i	0.804968	−	0.593318i	$-0.202182\pi$
$157$	6.13265	+	4.45563i	0.489439	+	0.355598i	−0.315530	+	0.948916i	$0.602182\pi$
$158$		0			0
$159$	1.46994	−	4.52402i	0.116574	−	0.358778i
$160$		0			0
$161$	0.692264	−	0.502959i	0.0545581	−	0.0396388i
$162$		0			0
$163$	4.06822	+	12.5207i	0.318648	+	0.980697i	0.974227	+	0.225570i	$0.0724246\pi$
$163$	4.06822	+	12.5207i	0.318648	+	0.980697i	−0.655579	+	0.755126i	$0.727575\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	5.11405	+	15.7394i	0.395737	+	1.21795i	0.928386	+	0.371618i	$0.121197\pi$
$167$	5.11405	+	15.7394i	0.395737	+	1.21795i	−0.532648	+	0.846337i	$0.678803\pi$
$168$		0			0
$169$	−12.3543	+	8.97594i	−0.950333	+	0.690457i
$170$		0			0
$171$	−3.96605	+	12.2063i	−0.303292	+	0.933436i
$172$		0			0
$173$	−4.29519	−	3.12064i	−0.326557	−	0.237258i	0.412411	−	0.910998i	$-0.364687\pi$
$173$	−4.29519	−	3.12064i	−0.326557	−	0.237258i	−0.738968	+	0.673740i	$0.764687\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	0.620955			0.0466738
$178$		0			0
$179$	−18.4946	−	13.4371i	−1.38235	−	1.00434i	−0.996656	−	0.0817132i	$-0.973961\pi$
$179$	−18.4946	−	13.4371i	−1.38235	−	1.00434i	−0.385698	−	0.922625i	$-0.626039\pi$
$180$		0			0
$181$	7.98786	−	24.5841i	0.593733	−	1.82732i	0.0327984	−	0.999462i	$-0.489558\pi$
$181$	7.98786	−	24.5841i	0.593733	−	1.82732i	0.560935	−	0.827860i	$-0.310442\pi$
$182$		0			0
$183$	−6.50750	+	4.72798i	−0.481049	+	0.349502i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	5.65985	+	17.6055i	0.413889	+	1.28744i
$188$		0			0
$189$	0.860651	+	2.64881i	0.0626032	+	0.192673i
$190$		0			0
$191$	13.4832	−	9.79613i	0.975611	−	0.708823i	0.0188877	−	0.999822i	$-0.493988\pi$
$191$	13.4832	−	9.79613i	0.975611	−	0.708823i	0.956723	+	0.290999i	$0.0939875\pi$
$192$		0			0
$193$	5.65234	−	17.3961i	0.406864	−	1.25220i	−0.512464	−	0.858708i	$-0.671267\pi$
$193$	5.65234	−	17.3961i	0.406864	−	1.25220i	0.919329	−	0.393491i	$-0.128733\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	24.1745			1.72236			0.861180	−	0.508300i	$-0.169726\pi$
$197$	24.1745			1.72236			0.861180	+	0.508300i	$0.169726\pi$
$198$		0			0
$199$	−11.4788			−0.813709			−0.406855	−	0.913493i	$-0.633374\pi$
$199$	−11.4788			−0.813709			−0.406855	+	0.913493i	$0.633374\pi$
$200$		0			0
$201$	4.03377	+	2.93071i	0.284521	+	0.206716i
$202$		0			0
$203$	−1.33232	+	4.10046i	−0.0935105	+	0.287796i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	0.968410	+	2.98046i	0.0673091	+	0.207156i
$208$		0			0
$209$	19.8960	+	0.0619353i	1.37623	+	0.00428415i
$210$		0			0
$211$	−3.44028	−	10.5881i	−0.236839	−	0.728915i	−0.996872	−	0.0790310i	$-0.974817\pi$
$211$	−3.44028	−	10.5881i	−0.236839	−	0.728915i	0.760033	−	0.649884i	$-0.225183\pi$
$212$		0			0
$213$	−4.13392	+	3.00347i	−0.283251	+	0.205794i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−3.04982	−	2.21583i	−0.207035	−	0.150420i
$218$		0			0
$219$	4.70329			0.317819
$220$		0			0
$221$	−29.6468			−1.99426
$222$		0			0
$223$	7.47318	+	5.42958i	0.500441	+	0.363592i	0.809185	−	0.587553i	$-0.199909\pi$
$223$	7.47318	+	5.42958i	0.500441	+	0.363592i	−0.308744	+	0.951145i	$0.599909\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−10.5784	+	7.68564i	−0.702111	+	0.510114i	−0.880619	−	0.473825i	$-0.842873\pi$
$227$	−10.5784	+	7.68564i	−0.702111	+	0.510114i	0.178508	+	0.983938i	$0.442873\pi$
$228$		0			0
$229$	5.58774	+	17.1973i	0.369248	+	1.13643i	0.947278	+	0.320413i	$0.103822\pi$
$229$	5.58774	+	17.1973i	0.369248	+	1.13643i	−0.578030	+	0.816016i	$0.696178\pi$
$230$		0			0
$231$	1.45734	−	1.05190i	0.0958857	−	0.0692100i
$232$		0			0
$233$	0.926030	+	2.85003i	0.0606662	+	0.186711i	0.976797	−	0.214169i	$-0.0687043\pi$
$233$	0.926030	+	2.85003i	0.0606662	+	0.186711i	−0.916130	+	0.400880i	$0.868704\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	2.95736	−	9.10183i	0.192101	−	0.591227i
$238$		0			0
$239$	12.2850	+	8.92554i	0.794648	+	0.577345i	0.909339	−	0.416056i	$-0.136588\pi$
$239$	12.2850	+	8.92554i	0.794648	+	0.577345i	−0.114691	+	0.993401i	$0.536588\pi$
$240$		0			0
$241$	−6.06753			−0.390844			−0.195422	−	0.980719i	$-0.562608\pi$
$241$	−6.06753			−0.390844			−0.195422	+	0.980719i	$0.562608\pi$
$242$		0			0
$243$	−16.1542			−1.03629
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−9.85649	+	30.3351i	−0.627153	+	1.93018i
$248$		0			0
$249$	−3.80524	+	2.76467i	−0.241147	+	0.175204i
$250$		0			0
$251$	5.83306	+	17.9523i	0.368180	+	1.13314i	0.947966	+	0.318372i	$0.103136\pi$
$251$	5.83306	+	17.9523i	0.368180	+	1.13314i	−0.579786	+	0.814769i	$0.696864\pi$
$252$		0			0
$253$	3.93917	−	2.84328i	0.247653	−	0.178755i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−20.2081	+	14.6821i	−1.26055	+	0.915843i	−0.998785	−	0.0492890i	$-0.984304\pi$
$257$	−20.2081	+	14.6821i	−1.26055	+	0.915843i	−0.261765	+	0.965132i	$0.584304\pi$
$258$		0			0
$259$	−0.315162	+	0.969970i	−0.0195832	+	0.0602710i
$260$		0			0
$261$	−12.7746	−	9.28127i	−0.790726	−	0.574496i
$262$		0			0
$263$	15.9640			0.984381			0.492191	−	0.870487i	$-0.336196\pi$
$263$	15.9640			0.984381			0.492191	+	0.870487i	$0.336196\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−3.17390	−	2.30597i	−0.194239	−	0.141123i
$268$		0			0
$269$	−7.77440	+	23.9271i	−0.474013	+	1.45886i	0.373270	+	0.927723i	$0.378236\pi$
$269$	−7.77440	+	23.9271i	−0.474013	+	1.45886i	−0.847284	+	0.531141i	$0.821764\pi$
$270$		0			0
$271$	14.9872	−	10.8888i	0.910408	−	0.661450i	−0.0307099	−	0.999528i	$-0.509777\pi$
$271$	14.9872	−	10.8888i	0.910408	−	0.661450i	0.941118	+	0.338078i	$0.109777\pi$
$272$		0			0
$273$	0.890386	+	2.74033i	0.0538886	+	0.165852i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−0.0756448	−	0.232811i	−0.00454506	−	0.0139882i	0.948758	−	0.316003i	$-0.102341\pi$
$277$	−0.0756448	−	0.232811i	−0.00454506	−	0.0139882i	−0.953303	+	0.302015i	$0.902341\pi$
$278$		0			0
$279$	11.1696	−	8.11518i	0.668706	−	0.485843i
$280$		0			0
$281$	4.41618	−	13.5916i	0.263447	−	0.810807i	−0.728600	−	0.684939i	$-0.759829\pi$
$281$	4.41618	−	13.5916i	0.263447	−	0.810807i	0.992047	−	0.125867i	$-0.0401713\pi$
$282$		0			0
$283$	13.2134	+	9.60011i	0.785456	+	0.570667i	0.906612	−	0.421966i	$-0.138660\pi$
$283$	13.2134	+	9.60011i	0.785456	+	0.570667i	−0.121155	+	0.992634i	$0.538660\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−0.557783			−0.0329249
$288$		0			0
$289$	−11.3989	−	8.28177i	−0.670523	−	0.487163i
$290$		0			0
$291$	4.82124	−	14.8382i	0.282626	−	0.869833i
$292$		0			0
$293$	−11.7963	+	8.57049i	−0.689145	+	0.500693i	−0.876379	−	0.481622i	$-0.840048\pi$
$293$	−11.7963	+	8.57049i	−0.689145	+	0.500693i	0.187234	+	0.982315i	$0.440048\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	4.83947	+	15.0536i	0.280814	+	0.873501i
$298$		0			0
$299$	2.40670	+	7.40708i	0.139183	+	0.428362i
$300$		0			0
$301$	−3.22643	+	2.34414i	−0.185968	+	0.135114i
$302$		0			0
$303$	−1.16782	+	3.59417i	−0.0670892	+	0.206479i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	26.7487			1.52663			0.763313	−	0.646029i	$-0.223571\pi$
$307$	26.7487			1.52663			0.763313	+	0.646029i	$0.223571\pi$
$308$		0			0
$309$	6.47520			0.368361
$310$		0			0
$311$	8.09997	+	5.88497i	0.459307	+	0.333706i	0.793259	−	0.608884i	$-0.208382\pi$
$311$	8.09997	+	5.88497i	0.459307	+	0.333706i	−0.333952	+	0.942590i	$0.608382\pi$
$312$		0			0
$313$	0.555729	−	1.71036i	0.0314117	−	0.0966752i	−0.934121	−	0.356955i	$-0.883815\pi$
$313$	0.555729	−	1.71036i	0.0314117	−	0.0966752i	0.965533	+	0.260280i	$0.0838149\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−0.955007	−	2.93921i	−0.0536386	−	0.165083i	0.920649	−	0.390392i	$-0.127661\pi$
$317$	−0.955007	−	2.93921i	−0.0536386	−	0.165083i	−0.974287	+	0.225310i	$0.927661\pi$
$318$		0			0
$319$	−7.63662	+	23.2565i	−0.427569	+	1.30211i
$320$		0			0
$321$	0.936726	+	2.88295i	0.0522830	+	0.160910i
$322$		0			0
$323$	−27.0606	+	19.6607i	−1.50569	+	1.09395i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	9.48976	+	6.89472i	0.524785	+	0.381279i
$328$		0			0
$329$	7.32339			0.403751
$330$		0			0
$331$	27.6900			1.52198			0.760990	−	0.648764i	$-0.224714\pi$
$331$	27.6900			1.52198			0.760990	+	0.648764i	$0.224714\pi$
$332$		0			0
$333$	−3.02185	−	2.19550i	−0.165596	−	0.120313i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−21.0575	+	15.2992i	−1.14708	+	0.833400i	−0.988089	−	0.153880i	$-0.950823\pi$
$337$	−21.0575	+	15.2992i	−1.14708	+	0.833400i	−0.158987	+	0.987281i	$0.550823\pi$
$338$		0			0
$339$	−4.86973	−	14.9875i	−0.264487	−	0.814009i
$340$		0			0
$341$	−17.2760	−	12.6341i	−0.935546	−	0.684174i
$342$		0			0
$343$	−2.46567	−	7.58857i	−0.133134	−	0.409744i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	8.51240	−	26.1985i	0.456970	−	1.40641i	−0.411837	−	0.911257i	$-0.635113\pi$
$347$	8.51240	−	26.1985i	0.456970	−	1.40641i	0.868807	−	0.495151i	$-0.164887\pi$
$348$		0			0
$349$	0.479396	+	0.348302i	0.0256615	+	0.0186442i	0.600542	−	0.799593i	$-0.294951\pi$
$349$	0.479396	+	0.348302i	0.0256615	+	0.0186442i	−0.574881	+	0.818237i	$0.694951\pi$
$350$		0			0
$351$	−25.3496			−1.35306
$352$		0			0
$353$	2.26339			0.120468			0.0602341	−	0.998184i	$-0.480815\pi$
$353$	2.26339			0.120468			0.0602341	+	0.998184i	$0.480815\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−0.933723	+	2.87370i	−0.0494179	+	0.152093i
$358$		0			0
$359$	−3.72534	+	2.70662i	−0.196616	+	0.142850i	−0.681737	−	0.731597i	$-0.738775\pi$
$359$	−3.72534	+	2.70662i	−0.196616	+	0.142850i	0.485122	+	0.874447i	$0.338775\pi$
$360$		0			0
$361$	5.24917	+	16.1553i	0.276272	+	0.850278i
$362$		0			0
$363$	8.29251	−	5.94633i	0.435244	−	0.312102i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	8.39003	−	6.09571i	0.437956	−	0.318193i	−0.346866	−	0.937915i	$-0.612754\pi$
$367$	8.39003	−	6.09571i	0.437956	−	0.318193i	0.784822	+	0.619721i	$0.212754\pi$
$368$		0			0
$369$	0.631263	−	1.94283i	0.0328622	−	0.101140i
$370$		0			0
$371$	2.42345	+	1.76074i	0.125819	+	0.0914132i
$372$		0			0
$373$	34.9818			1.81129			0.905645	−	0.424037i	$-0.139388\pi$
$373$	34.9818			1.81129			0.905645	+	0.424037i	$0.139388\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−31.7475	−	23.0659i	−1.63508	−	1.18796i
$378$		0			0
$379$	−5.85838	+	18.0302i	−0.300925	+	0.926150i	0.680242	+	0.732987i	$0.261875\pi$
$379$	−5.85838	+	18.0302i	−0.300925	+	0.926150i	−0.981167	+	0.193163i	$0.938125\pi$
$380$		0			0
$381$	5.04432	−	3.66492i	0.258429	−	0.187759i
$382$		0			0
$383$	0.420280	+	1.29349i	0.0214753	+	0.0660943i	0.961220	−	0.275783i	$-0.0889372\pi$
$383$	0.420280	+	1.29349i	0.0214753	+	0.0660943i	−0.939745	+	0.341878i	$0.888937\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−4.51346	−	13.8910i	−0.229432	−	0.706119i
$388$		0			0
$389$	10.7712	−	7.82573i	0.546121	−	0.396780i	−0.280232	−	0.959932i	$-0.590411\pi$
$389$	10.7712	−	7.82573i	0.546121	−	0.396780i	0.826353	+	0.563152i	$0.190411\pi$
$390$		0			0
$391$	−2.52385	+	7.76760i	−0.127636	+	0.392824i
$392$		0			0
$393$	−6.73553	−	4.89365i	−0.339762	−	0.246852i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	23.4959			1.17923			0.589613	−	0.807686i	$-0.299280\pi$
$397$	23.4959			1.17923			0.589613	+	0.807686i	$0.299280\pi$
$398$		0			0
$399$	2.63000	+	1.91080i	0.131665	+	0.0956599i
$400$		0			0
$401$	−0.834243	+	2.56753i	−0.0416601	+	0.128217i	−0.969723	−	0.244206i	$-0.921473\pi$
$401$	−0.834243	+	2.56753i	−0.0416601	+	0.128217i	0.928063	+	0.372422i	$0.121473\pi$
$402$		0			0
$403$	27.7588	−	20.1679i	1.38276	−	1.00464i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−1.80645	+	5.50136i	−0.0895426	+	0.272692i
$408$		0			0
$409$	−9.06751	−	27.9069i	−0.448360	−	1.37991i	−0.878757	−	0.477269i	$-0.841627\pi$
$409$	−9.06751	−	27.9069i	−0.448360	−	1.37991i	0.430398	−	0.902639i	$-0.358373\pi$
$410$		0			0
$411$	−14.3544	+	10.4291i	−0.708052	+	0.514430i
$412$		0			0
$413$	−0.120837	+	0.371899i	−0.00594601	+	0.0183000i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−9.20597			−0.450818
$418$		0			0
$419$	21.2025			1.03581			0.517906	−	0.855438i	$-0.326712\pi$
$419$	21.2025			1.03581			0.517906	+	0.855438i	$0.326712\pi$
$420$		0			0
$421$	24.1913	+	17.5760i	1.17901	+	0.856601i	0.992060	−	0.125768i	$-0.0401395\pi$
$421$	24.1913	+	17.5760i	1.17901	+	0.856601i	0.186951	+	0.982369i	$0.440140\pi$
$422$		0			0
$423$	−8.28814	+	25.5083i	−0.402983	+	1.24025i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−1.56530	−	4.81750i	−0.0757503	−	0.233135i
$428$		0			0
$429$	5.00667	+	15.5737i	0.241724	+	0.751907i
$430$		0			0
$431$	1.03755	+	3.19324i	0.0499768	+	0.153813i	0.972930	−	0.231099i	$-0.0742320\pi$
$431$	1.03755	+	3.19324i	0.0499768	+	0.153813i	−0.922954	+	0.384911i	$0.874232\pi$
$432$		0			0
$433$	1.02429	−	0.744188i	0.0492241	−	0.0357634i	−0.562901	−	0.826524i	$-0.690315\pi$
$433$	1.02429	−	0.744188i	0.0492241	−	0.0357634i	0.612125	+	0.790761i	$0.290315\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	7.10886	+	5.16489i	0.340063	+	0.247070i
$438$		0			0
$439$	23.1573			1.10524			0.552620	−	0.833433i	$-0.313628\pi$
$439$	23.1573			1.10524			0.552620	+	0.833433i	$0.313628\pi$
$440$		0			0
$441$	14.2461			0.678388
$442$		0			0
$443$	−14.0879	−	10.2354i	−0.669335	−	0.486300i	0.200468	−	0.979700i	$-0.435754\pi$
$443$	−14.0879	−	10.2354i	−0.669335	−	0.486300i	−0.869803	+	0.493400i	$0.835754\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−1.52584	+	1.10859i	−0.0721697	+	0.0524343i
$448$		0			0
$449$	−6.10622	−	18.7930i	−0.288170	−	0.886897i	−0.985430	−	0.170079i	$-0.945598\pi$
$449$	−6.10622	−	18.7930i	−0.288170	−	0.886897i	0.697260	−	0.716818i	$-0.254402\pi$
$450$		0			0
$451$	−3.16677	−	0.00985802i	−0.149117	−	0.000464196i
$452$		0			0
$453$	0.627939	+	1.93260i	0.0295031	+	0.0908014i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	12.5483	−	38.6198i	0.586986	−	1.80656i	−0.00415716	−	0.999991i	$-0.501323\pi$
$457$	12.5483	−	38.6198i	0.586986	−	1.80656i	0.591143	−	0.806566i	$-0.298677\pi$
$458$		0			0
$459$	−21.5064	−	15.6253i	−1.00383	−	0.729329i
$460$		0			0
$461$	−23.9503			−1.11548			−0.557738	−	0.830017i	$-0.688331\pi$
$461$	−23.9503			−1.11548			−0.557738	+	0.830017i	$0.688331\pi$
$462$		0			0
$463$	6.35715			0.295442			0.147721	−	0.989029i	$-0.452806\pi$
$463$	6.35715			0.295442			0.147721	+	0.989029i	$0.452806\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−3.68681	+	11.3468i	−0.170605	+	0.525068i	−0.999406	−	0.0344760i	$-0.989024\pi$
$467$	−3.68681	+	11.3468i	−0.170605	+	0.525068i	0.828801	+	0.559544i	$0.189024\pi$
$468$		0			0
$469$	−2.54021	+	1.84557i	−0.117296	+	0.0852207i
$470$		0			0
$471$	2.17299	+	6.68776i	0.100126	+	0.308156i
$472$		0			0
$473$	−18.3592	+	13.2516i	−0.844159	+	0.609311i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−8.87559	+	6.44850i	−0.406386	+	0.295256i
$478$		0			0
$479$	11.5367	−	35.5064i	0.527126	−	1.62233i	−0.232947	−	0.972489i	$-0.574837\pi$
$479$	11.5367	−	35.5064i	0.527126	−	1.62233i	0.760073	−	0.649837i	$-0.225163\pi$
$480$		0			0
$481$	−7.50993	−	5.45628i	−0.342423	−	0.248785i
$482$		0			0
$483$	0.793777			0.0361181
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−32.5995	−	23.6850i	−1.47723	−	1.07327i	−0.978437	−	0.206544i	$-0.933778\pi$
$487$	−32.5995	−	23.6850i	−1.47723	−	1.07327i	−0.498789	−	0.866723i	$-0.666222\pi$
$488$		0			0
$489$	−3.77388	+	11.6148i	−0.170661	+	0.525240i
$490$		0			0
$491$	7.06759	−	5.13490i	0.318956	−	0.231735i	−0.416774	−	0.909010i	$-0.636839\pi$
$491$	7.06759	−	5.13490i	0.318956	−	0.231735i	0.735730	+	0.677275i	$0.236839\pi$
$492$		0			0
$493$	−12.7167	−	39.1380i	−0.572732	−	1.76269i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−0.994363	−	3.06034i	−0.0446033	−	0.137275i
$498$		0			0
$499$	−30.0283	+	21.8168i	−1.34425	+	0.976654i	−0.344973	+	0.938613i	$0.612112\pi$
$499$	−30.0283	+	21.8168i	−1.34425	+	0.976654i	−0.999276	+	0.0380416i	$0.987888\pi$
$500$		0			0
$501$	−4.74405	+	14.6007i	−0.211949	+	0.652311i
$502$		0			0
$503$	−32.9950	−	23.9723i	−1.47118	−	1.06887i	−0.980271	−	0.197658i	$-0.936667\pi$
$503$	−32.9950	−	23.9723i	−1.47118	−	1.06887i	−0.490904	−	0.871214i	$-0.663333\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−14.1659			−0.629132
$508$		0			0
$509$	−2.68960	−	1.95411i	−0.119214	−	0.0866143i	0.526580	−	0.850125i	$-0.323474\pi$
$509$	−2.68960	−	1.95411i	−0.119214	−	0.0866143i	−0.645795	+	0.763511i	$0.723474\pi$
$510$		0			0
$511$	−0.915257	+	2.81687i	−0.0404886	+	0.124611i
$512$		0			0
$513$	−23.1382	+	16.8109i	−1.02158	+	0.742220i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	41.5780	+	0.129430i	1.82860	+	0.00569234i
$518$		0			0
$519$	−1.52192	−	4.68398i	−0.0668047	−	0.205604i
$520$		0			0
$521$	21.2931	−	15.4703i	0.932866	−	0.677767i	−0.0138266	−	0.999904i	$-0.504401\pi$
$521$	21.2931	−	15.4703i	0.932866	−	0.677767i	0.946693	+	0.322137i	$0.104401\pi$
$522$		0			0
$523$	8.91329	−	27.4323i	0.389751	−	1.19953i	−0.543224	−	0.839588i	$-0.682796\pi$
$523$	8.91329	−	27.4323i	0.389751	−	1.19953i	0.932975	−	0.359942i	$-0.117204\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	35.9818			1.56739
$528$		0			0
$529$	−20.8544			−0.906714
$530$		0			0
$531$	−1.15861	−	0.841782i	−0.0502796	−	0.0365302i
$532$		0			0
$533$	1.56882	−	4.82834i	0.0679533	−	0.209139i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−6.55321	−	20.1687i	−0.282792	−	0.870344i
$538$		0			0
$539$	−6.75908	−	21.0248i	−0.291134	−	0.905602i
$540$		0			0
$541$	3.72788	+	11.4732i	0.160274	+	0.493273i	0.998657	−	0.0518088i	$-0.0164986\pi$
$541$	3.72788	+	11.4732i	0.160274	+	0.493273i	−0.838383	+	0.545082i	$0.816499\pi$
$542$		0			0
$543$	19.3995	−	14.0945i	0.832511	−	0.604854i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−10.1234	−	7.35507i	−0.432844	−	0.314480i	0.349941	−	0.936772i	$-0.386202\pi$
$547$	−10.1234	−	7.35507i	−0.432844	−	0.314480i	−0.782785	+	0.622292i	$0.786202\pi$
$548$		0			0
$549$	18.5515			0.791757
$550$		0			0
$551$	−44.2746			−1.88616
$552$		0			0
$553$	4.87572	+	3.54242i	0.207337	+	0.150639i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−4.52374	+	3.28669i	−0.191677	+	0.139261i	−0.679485	−	0.733690i	$-0.737797\pi$
$557$	−4.52374	+	3.28669i	−0.191677	+	0.139261i	0.487808	+	0.872951i	$0.337797\pi$
$558$		0			0
$559$	−11.2169	−	34.5221i	−0.474424	−	1.46013i
$560$		0			0
$561$	−5.35193	+	16.2987i	−0.225959	+	0.688133i
$562$		0			0
$563$	1.21280	+	3.73261i	0.0511134	+	0.157311i	0.973355	−	0.229303i	$-0.0736447\pi$
$563$	1.21280	+	3.73261i	0.0511134	+	0.157311i	−0.922242	+	0.386614i	$0.873645\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	0.360266	−	1.10879i	0.0151298	−	0.0465646i
$568$		0			0
$569$	−9.29128	−	6.75051i	−0.389511	−	0.282996i	0.375744	−	0.926723i	$-0.377387\pi$
$569$	−9.29128	−	6.75051i	−0.389511	−	0.282996i	−0.765255	+	0.643727i	$0.777387\pi$
$570$		0			0
$571$	8.08060			0.338163			0.169081	−	0.985602i	$-0.445920\pi$
$571$	8.08060			0.338163			0.169081	+	0.985602i	$0.445920\pi$
$572$		0			0
$573$	15.4604			0.645866
$574$		0			0
$575$		0			0
$576$		0			0
$577$	4.71016	−	14.4964i	0.196087	−	0.603492i	−0.803876	−	0.594797i	$-0.797232\pi$
$577$	4.71016	−	14.4964i	0.196087	−	0.603492i	0.999962	−	0.00869493i	$-0.00276772\pi$
$578$		0			0
$579$	13.7274	−	9.97352i	0.570490	−	0.414485i
$580$		0			0
$581$	−0.915305	−	2.81702i	−0.0379733	−	0.116870i
$582$		0			0
$583$	13.7279	+	10.0393i	0.568550	+	0.415786i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	10.3913	−	7.54969i	0.428893	−	0.311609i	−0.352313	−	0.935882i	$-0.614605\pi$
$587$	10.3913	−	7.54969i	0.428893	−	0.311609i	0.781206	+	0.624273i	$0.214605\pi$
$588$		0			0
$589$	11.9626	−	36.8172i	0.492912	−	1.51703i
$590$		0			0
$591$	18.1426	+	13.1813i	0.746285	+	0.542208i
$592$		0			0
$593$	−15.9637			−0.655552			−0.327776	−	0.944756i	$-0.606299\pi$
$593$	−15.9637			−0.655552			−0.327776	+	0.944756i	$0.606299\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−8.61465	−	6.25891i	−0.352574	−	0.256160i
$598$		0			0
$599$	−3.75253	+	11.5491i	−0.153324	+	0.471883i	−0.997987	−	0.0634149i	$-0.979801\pi$
$599$	−3.75253	+	11.5491i	−0.153324	+	0.471883i	0.844663	+	0.535298i	$0.179801\pi$
$600$		0			0
$601$	1.56665	−	1.13824i	0.0639048	−	0.0464296i	−0.555374	−	0.831601i	$-0.687425\pi$
$601$	1.56665	−	1.13824i	0.0639048	−	0.0464296i	0.619279	+	0.785171i	$0.287425\pi$
$602$		0			0
$603$	−3.55351	−	10.9366i	−0.144710	−	0.445372i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−11.7105	−	36.0412i	−0.475315	−	1.46287i	−0.845533	−	0.533924i	$-0.820717\pi$
$607$	−11.7105	−	36.0412i	−0.475315	−	1.46287i	0.370218	−	0.928945i	$-0.379283\pi$
$608$		0			0
$609$	−3.23570	+	2.35087i	−0.131117	+	0.0952621i
$610$		0			0
$611$	−20.5978	+	63.3935i	−0.833297	+	2.56462i
$612$		0			0
$613$	33.6577	+	24.4537i	1.35942	+	0.987676i	0.998482	+	0.0550868i	$0.0175436\pi$
$613$	33.6577	+	24.4537i	1.35942	+	0.987676i	0.360938	+	0.932590i	$0.382456\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−22.6801			−0.913065			−0.456532	−	0.889707i	$-0.650909\pi$
$617$	−22.6801			−0.913065			−0.456532	+	0.889707i	$0.650909\pi$
$618$		0			0
$619$	−12.2927	−	8.93117i	−0.494086	−	0.358974i	0.312668	−	0.949863i	$-0.398777\pi$
$619$	−12.2927	−	8.93117i	−0.494086	−	0.358974i	−0.806753	+	0.590888i	$0.798777\pi$
$620$		0			0
$621$	−2.15802	+	6.64171i	−0.0865984	+	0.266523i
$622$		0			0
$623$	1.99872	−	1.45215i	0.0800770	−	0.0581793i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	14.8978	+	10.8949i	0.594963	+	0.435102i
$628$		0			0
$629$	−3.00816	−	9.25815i	−0.119943	−	0.369147i
$630$		0			0
$631$	27.6414	−	20.0826i	1.10039	−	0.799477i	0.119263	−	0.992863i	$-0.461947\pi$
$631$	27.6414	−	20.0826i	1.10039	−	0.799477i	0.981123	+	0.193385i	$0.0619467\pi$
$632$		0			0
$633$	3.19138	−	9.82205i	0.126846	−	0.390392i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	35.4047			1.40279
$638$		0			0
$639$	11.7849			0.466203
$640$		0			0
$641$	28.2614	+	20.5331i	1.11626	+	0.811010i	0.983638	−	0.180157i	$-0.0576607\pi$
$641$	28.2614	+	20.5331i	1.11626	+	0.811010i	0.132621	+	0.991167i	$0.457661\pi$
$642$		0			0
$643$	−4.75397	+	14.6312i	−0.187478	+	0.576999i	−0.999982	−	0.00595656i	$-0.998104\pi$
$643$	−4.75397	+	14.6312i	−0.187478	+	0.576999i	0.812504	+	0.582956i	$0.198104\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−13.0562	−	40.1827i	−0.513290	−	1.57975i	−0.786371	−	0.617754i	$-0.788043\pi$
$647$	−13.0562	−	40.1827i	−0.513290	−	1.57975i	0.273081	−	0.961991i	$-0.411957\pi$
$648$		0			0
$649$	−0.692617	+	2.10929i	−0.0271876	+	0.0827970i
$650$		0			0
$651$	−1.08065	−	3.32588i	−0.0423538	−	0.130352i
$652$		0			0
$653$	25.4338	−	18.4787i	0.995302	−	0.723129i	0.0342259	−	0.999414i	$-0.489103\pi$
$653$	25.4338	−	18.4787i	0.995302	−	0.723129i	0.961076	+	0.276285i	$0.0891034\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−8.77568	−	6.37591i	−0.342372	−	0.248748i
$658$		0			0
$659$	36.1078			1.40656			0.703281	−	0.710912i	$-0.251718\pi$
$659$	36.1078			1.40656			0.703281	+	0.710912i	$0.251718\pi$
$660$		0			0
$661$	21.9994			0.855679			0.427840	−	0.903855i	$-0.359275\pi$
$661$	21.9994			0.855679			0.427840	+	0.903855i	$0.359275\pi$
$662$		0			0
$663$	−22.2495	−	16.1652i	−0.864098	−	0.627804i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−8.74606	+	6.35439i	−0.338649	+	0.246043i
$668$		0			0
$669$	2.64798	+	8.14963i	0.102377	+	0.315083i
$670$		0			0
$671$	−8.80174	−	27.3787i	−0.339787	−	1.05694i
$672$		0			0
$673$	−3.73744	−	11.5027i	−0.144068	−	0.443395i	0.852822	−	0.522202i	$-0.174889\pi$
$673$	−3.73744	−	11.5027i	−0.144068	−	0.443395i	−0.996890	+	0.0788063i	$0.974889\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	8.55454	−	26.3282i	0.328778	−	1.01187i	−0.640929	−	0.767600i	$-0.721451\pi$
$677$	8.55454	−	26.3282i	0.328778	−	1.01187i	0.969706	−	0.244273i	$-0.0785493\pi$
$678$		0			0
$679$	7.94863	+	5.77502i	0.305041	+	0.221625i
$680$		0			0
$681$	−12.1296			−0.464806
$682$		0			0
$683$	−10.6890			−0.409004			−0.204502	−	0.978866i	$-0.565557\pi$
$683$	−10.6890			−0.409004			−0.204502	+	0.978866i	$0.565557\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−5.18346	+	15.9531i	−0.197761	+	0.608647i
$688$		0			0
$689$	−22.0577	+	16.0259i	−0.840333	+	0.610538i
$690$		0			0
$691$	−9.49889	−	29.2346i	−0.361355	−	1.11214i	−0.952232	−	0.305375i	$-0.901218\pi$
$691$	−9.49889	−	29.2346i	−0.361355	−	1.11214i	0.590877	−	0.806761i	$-0.298782\pi$
$692$		0			0
$693$	−4.14517	−	0.0129037i	−0.157462	−	0.000490172i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	4.30714	−	3.12932i	0.163145	−	0.118532i
$698$		0			0
$699$	−0.859031	+	2.64383i	−0.0324915	+	0.0999987i
$700$		0			0
$701$	2.15512	+	1.56579i	0.0813978	+	0.0591390i	0.627740	−	0.778423i	$-0.283980\pi$
$701$	2.15512	+	1.56579i	0.0813978	+	0.0591390i	−0.546342	+	0.837562i	$0.683980\pi$
$702$		0			0
$703$	−10.4732			−0.395005
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−1.92534	−	1.39884i	−0.0724100	−	0.0526089i
$708$		0			0
$709$	10.3209	−	31.7645i	0.387610	−	1.19294i	−0.546959	−	0.837159i	$-0.684215\pi$
$709$	10.3209	−	31.7645i	0.387610	−	1.19294i	0.934569	−	0.355781i	$-0.115785\pi$
$710$		0			0
$711$	−17.8567	+	12.9737i	−0.669679	+	0.486550i
$712$		0			0
$713$	−2.92098	−	8.98984i	−0.109391	−	0.336672i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	4.35294	+	13.3970i	0.162563	+	0.500319i
$718$		0			0
$719$	−10.0724	+	7.31800i	−0.375636	+	0.272915i	−0.759544	−	0.650456i	$-0.774578\pi$
$719$	−10.0724	+	7.31800i	−0.375636	+	0.272915i	0.383908	+	0.923371i	$0.374578\pi$
$720$		0			0
$721$	−1.26007	+	3.87810i	−0.0469275	+	0.144428i
$722$		0			0
$723$	−4.55359	−	3.30837i	−0.169350	−	0.123040i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−4.02460			−0.149264			−0.0746320	−	0.997211i	$-0.523778\pi$
$727$	−4.02460			−0.149264			−0.0746320	+	0.997211i	$0.523778\pi$
$728$		0			0
$729$	−7.27977	−	5.28906i	−0.269621	−	0.195891i
$730$		0			0
$731$	11.7629	−	36.2024i	0.435065	−	1.33899i
$732$		0			0
$733$	−26.9355	+	19.5698i	−0.994886	+	0.722827i	−0.960986	−	0.276598i	$-0.910793\pi$
$733$	−26.9355	+	19.5698i	−0.994886	+	0.722827i	−0.0339006	+	0.999425i	$0.510793\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−14.4545	+	10.4332i	−0.532438	+	0.384312i
$738$		0			0
$739$	15.1474	+	46.6189i	0.557206	+	1.71490i	0.690046	+	0.723765i	$0.257590\pi$
$739$	15.1474	+	46.6189i	0.557206	+	1.71490i	−0.132840	+	0.991137i	$0.542410\pi$
$740$		0			0
$741$	−23.9376	+	17.3917i	−0.879371	+	0.638901i
$742$		0			0
$743$	−3.68141	+	11.3302i	−0.135058	+	0.415665i	−0.995599	−	0.0937155i	$-0.970126\pi$
$743$	−3.68141	+	11.3302i	−0.135058	+	0.415665i	0.860541	+	0.509381i	$0.170126\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	10.8479			0.396904
$748$		0			0
$749$	−1.90893			−0.0697507
$750$		0			0
$751$	2.56611	+	1.86439i	0.0936388	+	0.0680325i	0.633620	−	0.773645i	$-0.281568\pi$
$751$	2.56611	+	1.86439i	0.0936388	+	0.0680325i	−0.539981	+	0.841677i	$0.681568\pi$
$752$		0			0
$753$	−5.41104	+	16.6535i	−0.197189	+	0.606886i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	2.35409	+	7.24516i	0.0855610	+	0.263330i	0.984679	−	0.174377i	$-0.0557910\pi$
$757$	2.35409	+	7.24516i	0.0855610	+	0.263330i	−0.899118	+	0.437706i	$0.855791\pi$
$758$		0			0
$759$	4.50661	+	0.0140289i	0.163579	+	0.000509216i
$760$		0			0
$761$	15.7071	+	48.3416i	0.569383	+	1.75238i	0.654554	+	0.756016i	$0.272857\pi$
$761$	15.7071	+	48.3416i	0.569383	+	1.75238i	−0.0851702	+	0.996366i	$0.527143\pi$
$762$		0			0
$763$	−5.97605	+	4.34185i	−0.216347	+	0.157186i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−2.87940	−	2.09201i	−0.103969	−	0.0755380i
$768$		0			0
$769$	−17.6599			−0.636832			−0.318416	−	0.947951i	$-0.603151\pi$
$769$	−17.6599			−0.636832			−0.318416	+	0.947951i	$0.603151\pi$
$770$		0			0
$771$	−23.1714			−0.834499
$772$		0			0
$773$	5.31773	+	3.86356i	0.191265	+	0.138963i	0.679297	−	0.733864i	$-0.262285\pi$
$773$	5.31773	+	3.86356i	0.191265	+	0.138963i	−0.488031	+	0.872826i	$0.662285\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−0.765409	+	0.556102i	−0.0274589	+	0.0199501i
$778$		0			0
$779$	−1.77001	−	5.44753i	−0.0634172	−	0.195178i
$780$		0			0
$781$	−5.59134	−	17.3924i	−0.200074	−	0.622349i
$782$		0			0
$783$	−10.8735	−	33.4651i	−0.388586	−	1.19594i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−3.06584	+	9.43570i	−0.109286	+	0.336346i	−0.990712	−	0.135974i	$-0.956584\pi$
$787$	−3.06584	+	9.43570i	−0.109286	+	0.336346i	0.881427	+	0.472321i	$0.156584\pi$
$788$		0			0
$789$	11.9807	+	8.70450i	0.426525	+	0.309888i
$790$		0			0
$791$	9.92388			0.352852
$792$		0			0
$793$	46.1043			1.63721
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−17.1505	+	52.7837i	−0.607500	+	1.86969i	−0.128907	+	0.991657i	$0.541147\pi$
$797$	−17.1505	+	52.7837i	−0.607500	+	1.86969i	−0.478593	+	0.878037i	$0.658853\pi$
$798$		0			0
$799$	−56.5504	+	41.0863i	−2.00061	+	1.45353i
$800$		0			0
$801$	2.79601	+	8.60524i	0.0987922	+	0.304051i
$802$		0			0
$803$	−5.24609	+	15.9764i	−0.185130	+	0.563795i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−18.8810	+	13.7179i	−0.664644	+	0.482892i
$808$		0			0
$809$	7.90044	−	24.3151i	0.277765	−	0.854872i	−0.710710	−	0.703485i	$-0.751626\pi$
$809$	7.90044	−	24.3151i	0.277765	−	0.854872i	0.988475	−	0.151387i	$-0.0483738\pi$
$810$		0			0
$811$	−3.81345	−	2.77063i	−0.133908	−	0.0972900i	0.518815	−	0.854887i	$-0.326373\pi$
$811$	−3.81345	−	2.77063i	−0.133908	−	0.0972900i	−0.652723	+	0.757597i	$0.726373\pi$
$812$		0			0
$813$	17.1849			0.602701
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−33.1322	−	24.0719i	−1.15915	−	0.842171i
$818$		0			0
$819$	2.05352	−	6.32009i	0.0717559	−	0.220842i
$820$		0			0
$821$	−7.26632	+	5.27929i	−0.253596	+	0.184248i	−0.707319	−	0.706894i	$-0.750096\pi$
$821$	−7.26632	+	5.27929i	−0.253596	+	0.184248i	0.453723	+	0.891143i	$0.350096\pi$
$822$		0			0
$823$	9.60505	+	29.5613i	0.334811	+	1.03044i	0.966815	+	0.255477i	$0.0822325\pi$
$823$	9.60505	+	29.5613i	0.334811	+	1.03044i	−0.632004	+	0.774965i	$0.717768\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−10.4046	−	32.0219i	−0.361802	−	1.11351i	−0.951959	−	0.306224i	$-0.900934\pi$
$827$	−10.4046	−	32.0219i	−0.361802	−	1.11351i	0.590157	−	0.807288i	$-0.299066\pi$
$828$		0			0
$829$	14.0103	−	10.1791i	0.486599	−	0.353535i	−0.317276	−	0.948333i	$-0.602768\pi$
$829$	14.0103	−	10.1791i	0.486599	−	0.353535i	0.803875	+	0.594798i	$0.202768\pi$
$830$		0			0
$831$	0.0701719	−	0.215967i	0.00243424	−	0.00749181i
$832$		0			0
$833$	30.0371	+	21.8233i	1.04073	+	0.756131i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	30.7663			1.06344
$838$		0			0
$839$	7.14476	+	5.19097i	0.246665	+	0.179212i	0.704247	−	0.709955i	$-0.251285\pi$
$839$	7.14476	+	5.19097i	0.246665	+	0.179212i	−0.457583	+	0.889167i	$0.651285\pi$
$840$		0			0
$841$	7.87103	−	24.2245i	0.271415	−	0.835329i
$842$		0			0
$843$	10.7252	−	7.79232i	0.369396	−	0.268382i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	1.94763	+	6.12366i	0.0669214	+	0.210411i
$848$		0			0
$849$	4.68192	+	14.4095i	0.160683	+	0.494532i
$850$		0			0
$851$	−2.06889	+	1.50314i	−0.0709208	+	0.0515270i
$852$		0			0
$853$	−0.167803	+	0.516444i	−0.00574546	+	0.0176827i	−0.953888	−	0.300162i	$-0.902959\pi$
$853$	−0.167803	+	0.516444i	−0.00574546	+	0.0176827i	0.948143	+	0.317845i	$0.102959\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	30.9856			1.05845			0.529225	−	0.848482i	$-0.322483\pi$
$857$	30.9856			1.05845			0.529225	+	0.848482i	$0.322483\pi$
$858$		0			0
$859$	43.0688			1.46949			0.734745	−	0.678344i	$-0.237302\pi$
$859$	43.0688			1.46949			0.734745	+	0.678344i	$0.237302\pi$
$860$		0			0
$861$	−0.418608	−	0.304136i	−0.0142661	−	0.0103649i
$862$		0			0
$863$	15.8717	−	48.8482i	0.540280	−	1.66281i	−0.191676	−	0.981458i	$-0.561392\pi$
$863$	15.8717	−	48.8482i	0.540280	−	1.66281i	0.731956	−	0.681352i	$-0.238608\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−4.03897	−	12.4307i	−0.137171	−	0.422168i
$868$		0			0
$869$	27.6189	+	20.1980i	0.936908	+	0.685170i
$870$		0			0
$871$	−8.83123	−	27.1797i	−0.299235	−	0.920950i
$872$		0			0
$873$	−29.1109	+	21.1503i	−0.985254	+	0.715829i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	30.7253	+	22.3233i	1.03752	+	0.753803i	0.969800	−	0.243901i	$-0.0784272\pi$
$877$	30.7253	+	22.3233i	1.03752	+	0.753803i	0.0677212	+	0.997704i	$0.478427\pi$
$878$		0			0
$879$	−13.5261			−0.456222
$880$		0			0
$881$	54.2562			1.82794			0.913970	−	0.405783i	$-0.133001\pi$
$881$	54.2562			1.82794			0.913970	+	0.405783i	$0.133001\pi$
$882$		0			0
$883$	−36.8126	−	26.7459i	−1.23884	−	0.900073i	−0.241323	−	0.970445i	$-0.577581\pi$
$883$	−36.8126	−	26.7459i	−1.23884	−	0.900073i	−0.997521	+	0.0703719i	$0.977581\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	11.4702	−	8.33357i	0.385131	−	0.279814i	−0.378326	−	0.925672i	$-0.623500\pi$
$887$	11.4702	−	8.33357i	0.385131	−	0.279814i	0.763457	+	0.645858i	$0.223500\pi$
$888$		0			0
$889$	1.21335	+	3.73431i	0.0406945	+	0.125245i
$890$		0			0
$891$	2.06498	−	6.28868i	0.0691794	−	0.210679i
$892$		0			0
$893$	23.2393	+	71.5231i	0.777672	+	2.39343i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−2.23258	+	6.87117i	−0.0745436	+	0.229422i
$898$		0			0
$899$	38.5314	+	27.9947i	1.28509	+	0.933676i
$900$		0			0
$901$	−28.5919			−0.952535
$902$		0			0
$903$	−3.69955			−0.123113
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−8.61569	+	26.5164i	−0.286079	+	0.880462i	0.699994	+	0.714149i	$0.253186\pi$
$907$	−8.61569	+	26.5164i	−0.286079	+	0.880462i	−0.986073	+	0.166313i	$0.946814\pi$
$908$		0			0
$909$	7.05133	−	5.12309i	0.233878	−	0.169922i
$910$		0			0
$911$	8.15642	+	25.1029i	0.270234	+	0.831696i	0.990441	+	0.137936i	$0.0440469\pi$
$911$	8.15642	+	25.1029i	0.270234	+	0.831696i	−0.720207	+	0.693759i	$0.755953\pi$
$912$		0			0
$913$	−5.14679	−	16.0096i	−0.170334	−	0.529840i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	4.24161	−	3.08171i	0.140070	−	0.101767i
$918$		0			0
$919$	−8.20788	+	25.2613i	−0.270753	+	0.833292i	0.719559	+	0.694431i	$0.244344\pi$
$919$	−8.20788	+	25.2613i	−0.270753	+	0.833292i	−0.990312	+	0.138861i	$0.955656\pi$
$920$		0			0
$921$	20.0744	+	14.5849i	0.661475	+	0.480590i
$922$		0			0
$923$	29.2879			0.964025
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−12.0818	−	8.77796i	−0.396819	−	0.288306i
$928$		0			0
$929$	−5.37534	+	16.5436i	−0.176359	+	0.542778i	−0.999693	−	0.0247798i	$-0.992112\pi$
$929$	−5.37534	+	16.5436i	−0.176359	+	0.542778i	0.823334	+	0.567557i	$0.192112\pi$
$930$		0			0
$931$	32.3162	−	23.4791i	1.05912	−	0.769497i
$932$		0			0
$933$	2.87007	+	8.83316i	0.0939618	+	0.289185i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	8.37826	+	25.7856i	0.273706	+	0.842380i	0.989559	+	0.144129i	$0.0460381\pi$
$937$	8.37826	+	25.7856i	0.273706	+	0.842380i	−0.715853	+	0.698251i	$0.753962\pi$
$938$		0			0
$939$	1.34965	−	0.980581i	0.0440443	−	0.0320001i
$940$		0			0
$941$	14.8539	−	45.7158i	0.484225	−	1.49029i	−0.348876	−	0.937169i	$-0.613436\pi$
$941$	14.8539	−	45.7158i	0.484225	−	1.49029i	0.833100	−	0.553122i	$-0.186564\pi$
$942$		0			0
$943$	−1.13149	−	0.822077i	−0.0368465	−	0.0267705i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−11.5867			−0.376517			−0.188259	−	0.982119i	$-0.560284\pi$
$947$	−11.5867			−0.376517			−0.188259	+	0.982119i	$0.560284\pi$
$948$		0			0
$949$	−21.8094	−	15.8455i	−0.707964	−	0.514366i
$950$		0			0
$951$	0.885912	−	2.72656i	0.0287277	−	0.0884147i
$952$		0			0
$953$	−30.8298	+	22.3992i	−0.998676	+	0.725581i	−0.961804	−	0.273739i	$-0.911739\pi$
$953$	−30.8298	+	22.3992i	−0.998676	+	0.725581i	−0.0368724	+	0.999320i	$0.511739\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−18.4120	+	13.2897i	−0.595175	+	0.429595i
$958$		0			0
$959$	−3.45279	−	10.6266i	−0.111496	−	0.343150i
$960$		0			0
$961$	−8.61083	+	6.25613i	−0.277769	+	0.201811i
$962$		0			0
$963$	2.16040	−	6.64903i	0.0696179	−	0.214262i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	11.0115			0.354105			0.177053	−	0.984201i	$-0.443344\pi$
$967$	11.0115			0.354105			0.177053	+	0.984201i	$0.443344\pi$
$968$		0			0
$969$	−31.0287			−0.996786
$970$		0			0
$971$	−47.7129	−	34.6655i	−1.53118	−	1.11247i	−0.955578	−	0.294737i	$-0.904768\pi$
$971$	−47.7129	−	34.6655i	−1.53118	−	1.11247i	−0.575601	−	0.817730i	$-0.695232\pi$
$972$		0			0
$973$	1.79147	−	5.51359i	0.0574320	−	0.176758i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	16.4975	+	50.7740i	0.527801	+	1.62440i	0.758710	+	0.651429i	$0.225830\pi$
$977$	16.4975	+	50.7740i	0.527801	+	1.62440i	−0.230909	+	0.972975i	$0.574170\pi$
$978$		0			0
$979$	11.3732	−	8.20917i	0.363490	−	0.262366i
$980$		0			0
$981$	−8.35991	−	25.7291i	−0.266911	−	0.821468i
$982$		0			0
$983$	−12.6381	+	9.18213i	−0.403093	+	0.292864i	−0.770800	−	0.637078i	$-0.780143\pi$
$983$	−12.6381	+	9.18213i	−0.403093	+	0.292864i	0.367707	+	0.929942i	$0.380143\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	5.49609	+	3.99314i	0.174942	+	0.127103i
$988$		0			0
$989$	−9.99984			−0.317976
$990$		0			0
$991$	−11.6086			−0.368759			−0.184380	−	0.982855i	$-0.559028\pi$
$991$	−11.6086			−0.368759			−0.184380	+	0.982855i	$0.559028\pi$
$992$		0			0
$993$	20.7809	+	15.0982i	0.659462	+	0.479127i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	9.98154	−	7.25202i	0.316119	−	0.229674i	−0.418399	−	0.908263i	$-0.637409\pi$
$997$	9.98154	−	7.25202i	0.316119	−	0.229674i	0.734517	+	0.678590i	$0.237409\pi$
$998$		0			0
$999$	−2.57213	−	7.91621i	−0.0813787	−	0.250458i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1100.2.n.e.401.3	yes	16
5.2	odd	4		1100.2.cb.d.49.5		32
5.3	odd	4		1100.2.cb.d.49.4		32
5.4	even	2		1100.2.n.d.401.2	✓	16
11.9	even	5	inner	1100.2.n.e.801.3	yes	16
55.9	even	10		1100.2.n.d.801.2	yes	16
55.42	odd	20		1100.2.cb.d.449.4		32
55.53	odd	20		1100.2.cb.d.449.5		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1100.2.n.d.401.2	✓	16	5.4	even	2
1100.2.n.d.801.2	yes	16	55.9	even	10
1100.2.n.e.401.3	yes	16	1.1	even	1	trivial
1100.2.n.e.801.3	yes	16	11.9	even	5	inner
1100.2.cb.d.49.4		32	5.3	odd	4
1100.2.cb.d.49.5		32	5.2	odd	4
1100.2.cb.d.449.4		32	55.42	odd	20
1100.2.cb.d.449.5		32	55.53	odd	20

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1100 = 2^{2} \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1100.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.750484 + 0.545259i) q^{3} +(-0.472607 + 0.343369i) q^{7} +(-0.661131 - 2.03475i) q^{9} +O(q^{10})\)	\(q+(0.750484 + 0.545259i) q^{3} +(-0.472607 + 0.343369i) q^{7} +(-0.661131 - 2.03475i) q^{9} +(-2.68926 + 1.94110i) q^{11} +(-1.64305 - 5.05679i) q^{13} +(1.72302 - 5.30292i) q^{17} +(-4.85320 - 3.52606i) q^{19} -0.541910 q^{21} -1.46478 q^{23} +(1.47328 - 4.53428i) q^{27} +(5.97092 - 4.33813i) q^{29} +(1.99414 + 6.13734i) q^{31} +(-3.07665 - 0.00957748i) q^{33} +(1.41243 - 1.02619i) q^{37} +(1.52418 - 4.69093i) q^{39} +(0.772467 + 0.561230i) q^{41} +6.82687 q^{43} +(-10.1421 - 7.36865i) q^{47} +(-2.05766 + 6.33284i) q^{49} +(4.18457 - 3.04027i) q^{51} +(-1.58459 - 4.87686i) q^{53} +(-1.71964 - 5.29250i) q^{57} +(0.541544 - 0.393454i) q^{59} +(-2.67951 + 8.24668i) q^{61} +(1.01113 + 0.734627i) q^{63} +5.37489 q^{67} +(-1.09929 - 0.798683i) q^{69} +(-1.70217 + 5.23873i) q^{71} +(4.10181 - 2.98014i) q^{73} +(0.604450 - 1.84079i) q^{77} +(-3.18802 - 9.81171i) q^{79} +(-1.61457 + 1.17305i) q^{81} +(-1.56683 + 4.82222i) q^{83} +6.84648 q^{87} -4.22913 q^{89} +(2.51287 + 1.82570i) q^{91} +(-1.84987 + 5.69330i) q^{93} +(-5.19726 - 15.9955i) q^{97} +(5.72762 + 4.18866i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 2 q^{3}+O(q^{10}) \) 16 * q + 2 * q^3	\( 16 q + 2 q^{3} - 5 q^{11} - q^{13} - 8 q^{17} + 13 q^{19} - 6 q^{21} - 16 q^{23} - 37 q^{27} - 7 q^{29} + 2 q^{31} + 14 q^{33} - 8 q^{37} - 17 q^{39} - 15 q^{41} - 18 q^{47} - 24 q^{49} + 13 q^{51} - 6 q^{53} - 31 q^{57} + 6 q^{59} + 24 q^{61} + 5 q^{63} + 18 q^{67} - 53 q^{69} + 36 q^{71} - 9 q^{73} + 45 q^{77} - 45 q^{79} + 17 q^{81} - 14 q^{83} + 18 q^{87} + 18 q^{89} + 38 q^{91} - 29 q^{93} + 49 q^{97} + 40 q^{99}+O(q^{100}) \) 16 * q + 2 * q^3 - 5 * q^11 - q^13 - 8 * q^17 + 13 * q^19 - 6 * q^21 - 16 * q^23 - 37 * q^27 - 7 * q^29 + 2 * q^31 + 14 * q^33 - 8 * q^37 - 17 * q^39 - 15 * q^41 - 18 * q^47 - 24 * q^49 + 13 * q^51 - 6 * q^53 - 31 * q^57 + 6 * q^59 + 24 * q^61 + 5 * q^63 + 18 * q^67 - 53 * q^69 + 36 * q^71 - 9 * q^73 + 45 * q^77 - 45 * q^79 + 17 * q^81 - 14 * q^83 + 18 * q^87 + 18 * q^89 + 38 * q^91 - 29 * q^93 + 49 * q^97 + 40 * q^99

Introduction

L-functions

Modular forms

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