LMFDB - Embedded newform 1216.2.t.d.353.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1216,2,Mod(353,1216)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1216, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 4]))

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

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

chi := DirichletCharacter("1216.353");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1216 = 2^{6} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1216.t (of order $6$, degree $2$, 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:	$9.70980888579$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			353.7
Character	$\chi$	$=$	1216.353
Dual form			1216.2.t.d.1185.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.495361 + 0.285997i) q^{3} +(3.31453 + 1.91364i) q^{5} -2.37943 q^{7} +(-1.33641 - 2.31473i) q^{9} +O(q^{10})$	\(q+(0.495361 + 0.285997i) q^{3} +(3.31453 + 1.91364i) q^{5} -2.37943 q^{7} +(-1.33641 - 2.31473i) q^{9} +2.62170i q^{11} +(1.36594 - 0.788626i) q^{13} +(1.09459 + 1.89589i) q^{15} +(1.53509 - 2.65885i) q^{17} +(0.0442721 + 4.35867i) q^{19} +(-1.17868 - 0.680510i) q^{21} +(4.47737 + 7.75503i) q^{23} +(4.82405 + 8.35551i) q^{25} -3.24482i q^{27} +(8.05237 - 4.64904i) q^{29} +4.38612 q^{31} +(-0.749798 + 1.29869i) q^{33} +(-7.88669 - 4.55338i) q^{35} +7.00890i q^{37} +0.902177 q^{39} +(-6.22065 + 10.7745i) q^{41} +(2.35778 + 1.36127i) q^{43} -10.2297i q^{45} +(-1.15544 - 2.00129i) q^{47} -1.33830 q^{49} +(1.52085 - 0.878061i) q^{51} +(1.38780 - 0.801249i) q^{53} +(-5.01700 + 8.68970i) q^{55} +(-1.22464 + 2.17178i) q^{57} +(-10.4393 - 6.02711i) q^{59} +(0.477247 - 0.275539i) q^{61} +(3.17990 + 5.50775i) q^{63} +6.03659 q^{65} +(-7.64072 + 4.41137i) q^{67} +5.12205i q^{69} +(3.63270 - 6.29203i) q^{71} +(-1.80857 + 3.13253i) q^{73} +5.51865i q^{75} -6.23817i q^{77} +(1.99460 - 3.45475i) q^{79} +(-3.08123 + 5.33684i) q^{81} -8.25278i q^{83} +(10.1762 - 5.87522i) q^{85} +5.31844 q^{87} +(-4.83103 - 8.36758i) q^{89} +(-3.25016 + 1.87648i) q^{91} +(2.17271 + 1.25442i) q^{93} +(-8.19420 + 14.5317i) q^{95} +(6.67320 - 11.5583i) q^{97} +(6.06854 - 3.50367i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 6 q^{5} + 8 q^{9}+O(q^{10}) $ 24 * q - 6 * q^5 + 8 * q^9	$ 24 q - 6 q^{5} + 8 q^{9} + 30 q^{13} + 6 q^{17} + 24 q^{21} + 6 q^{25} + 42 q^{29} - 14 q^{33} - 24 q^{41} + 24 q^{49} - 18 q^{53} - 42 q^{57} + 18 q^{61} - 20 q^{65} - 16 q^{73} + 52 q^{81} - 78 q^{85} + 14 q^{89} + 60 q^{93} - 4 q^{97}+O(q^{100}) $ 24 * q - 6 * q^5 + 8 * q^9 + 30 * q^13 + 6 * q^17 + 24 * q^21 + 6 * q^25 + 42 * q^29 - 14 * q^33 - 24 * q^41 + 24 * q^49 - 18 * q^53 - 42 * q^57 + 18 * q^61 - 20 * q^65 - 16 * q^73 + 52 * q^81 - 78 * q^85 + 14 * q^89 + 60 * q^93 - 4 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1216\mathbb{Z}\right)^\times$.

$n$	$191$	$705$	$837$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$-1$

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
$3$	0.495361	+	0.285997i	0.285997	+	0.165120i	0.636135	−	0.771578i	$-0.280532\pi$
$3$	0.495361	+	0.285997i	0.285997	+	0.165120i	−0.350138	+	0.936698i	$0.613865\pi$
$4$		0			0
$5$	3.31453	+	1.91364i	1.48230	+	0.855807i	0.999798	−	0.0200876i	$-0.00639450\pi$
$5$	3.31453	+	1.91364i	1.48230	+	0.855807i	0.482503	+	0.875894i	$0.339728\pi$
$6$		0			0
$7$	−2.37943			−0.899341			−0.449671	−	0.893194i	$-0.648459\pi$
$7$	−2.37943			−0.899341			−0.449671	+	0.893194i	$0.648459\pi$
$8$		0			0
$9$	−1.33641	−	2.31473i	−0.445471	−	0.771578i
$10$		0			0
$11$			2.62170i			0.790473i	0.918579	+	0.395237i	$0.129337\pi$
$11$			2.62170i			0.790473i	−0.918579	+	0.395237i	$0.870663\pi$
$12$		0			0
$13$	1.36594	−	0.788626i	0.378844	−	0.218725i	−0.298471	−	0.954419i	$-0.596477\pi$
$13$	1.36594	−	0.788626i	0.378844	−	0.218725i	0.677315	+	0.735693i	$0.263143\pi$
$14$		0			0
$15$	1.09459	+	1.89589i	0.282622	+	0.489516i
$16$		0			0
$17$	1.53509	−	2.65885i	0.372314	−	0.644866i	−0.617607	−	0.786487i	$-0.711898\pi$
$17$	1.53509	−	2.65885i	0.372314	−	0.644866i	0.989921	+	0.141620i	$0.0452312\pi$
$18$		0			0
$19$	0.0442721	+	4.35867i	0.0101567	+	0.999948i
$19$	0.0442721	+	4.35867i	0.0101567	+	0.999948i
$20$		0			0
$21$	−1.17868	−	0.680510i	−0.257209	−	0.148499i
$22$		0			0
$23$	4.47737	+	7.75503i	0.933596	+	1.61704i	0.777119	+	0.629354i	$0.216680\pi$
$23$	4.47737	+	7.75503i	0.933596	+	1.61704i	0.156477	+	0.987682i	$0.449986\pi$
$24$		0			0
$25$	4.82405	+	8.35551i	0.964811	+	1.67110i
$26$		0			0
$27$		−	3.24482i		−	0.624465i
$28$		0			0
$29$	8.05237	−	4.64904i	1.49529	−	0.863305i	0.495302	−	0.868721i	$-0.335057\pi$
$29$	8.05237	−	4.64904i	1.49529	−	0.863305i	0.999985	+	0.00541604i	$0.00172399\pi$
$30$		0			0
$31$	4.38612			0.787771			0.393885	−	0.919160i	$-0.371131\pi$
$31$	4.38612			0.787771			0.393885	+	0.919160i	$0.371131\pi$
$32$		0			0
$33$	−0.749798	+	1.29869i	−0.130523	+	0.226073i
$34$		0			0
$35$	−7.88669	−	4.55338i	−1.33309	−	0.769662i
$36$		0			0
$37$			7.00890i			1.15226i	0.817359	+	0.576128i	$0.195437\pi$
$37$			7.00890i			1.15226i	−0.817359	+	0.576128i	$0.804563\pi$
$38$		0			0
$39$	0.902177			0.144464
$40$		0			0
$41$	−6.22065	+	10.7745i	−0.971502	+	1.68269i	−0.280475	+	0.959861i	$0.590492\pi$
$41$	−6.22065	+	10.7745i	−0.971502	+	1.68269i	−0.691027	+	0.722829i	$0.742841\pi$
$42$		0			0
$43$	2.35778	+	1.36127i	0.359559	+	0.207591i	0.668887	−	0.743364i	$-0.266771\pi$
$43$	2.35778	+	1.36127i	0.359559	+	0.207591i	−0.309329	+	0.950955i	$0.600104\pi$
$44$		0			0
$45$		−	10.2297i		−	1.52495i
$46$		0			0
$47$	−1.15544	−	2.00129i	−0.168539	−	0.291918i	0.769368	−	0.638806i	$-0.220571\pi$
$47$	−1.15544	−	2.00129i	−0.168539	−	0.291918i	−0.937906	+	0.346889i	$0.887238\pi$
$48$		0			0
$49$	−1.33830			−0.191185
$50$		0			0
$51$	1.52085	−	0.878061i	0.212961	−	0.122953i
$52$		0			0
$53$	1.38780	−	0.801249i	0.190630	−	0.110060i	−0.401648	−	0.915794i	$-0.631562\pi$
$53$	1.38780	−	0.801249i	0.190630	−	0.110060i	0.592277	+	0.805734i	$0.298229\pi$
$54$		0			0
$55$	−5.01700	+	8.68970i	−0.676492	+	1.17172i
$56$		0			0
$57$	−1.22464	+	2.17178i	−0.162207	+	0.287659i
$58$		0			0
$59$	−10.4393	−	6.02711i	−1.35908	−	0.784663i	−0.369577	−	0.929200i	$-0.620497\pi$
$59$	−10.4393	−	6.02711i	−1.35908	−	0.784663i	−0.989499	+	0.144537i	$0.953831\pi$
$60$		0			0
$61$	0.477247	−	0.275539i	0.0611052	−	0.0352791i	−0.469136	−	0.883126i	$-0.655435\pi$
$61$	0.477247	−	0.275539i	0.0611052	−	0.0352791i	0.530241	+	0.847847i	$0.322101\pi$
$62$		0			0
$63$	3.17990	+	5.50775i	0.400630	+	0.693912i
$64$		0			0
$65$	6.03659			0.748747
$66$		0			0
$67$	−7.64072	+	4.41137i	−0.933463	+	0.538935i	−0.887905	−	0.460027i	$-0.847840\pi$
$67$	−7.64072	+	4.41137i	−0.933463	+	0.538935i	−0.0455578	+	0.998962i	$0.514507\pi$
$68$		0			0
$69$			5.12205i			0.616622i
$70$		0			0
$71$	3.63270	−	6.29203i	0.431123	−	0.746726i	−0.565848	−	0.824510i	$-0.691451\pi$
$71$	3.63270	−	6.29203i	0.431123	−	0.746726i	0.996970	+	0.0777836i	$0.0247843\pi$
$72$		0			0
$73$	−1.80857	+	3.13253i	−0.211677	+	0.366635i	−0.952239	−	0.305352i	$-0.901226\pi$
$73$	−1.80857	+	3.13253i	−0.211677	+	0.366635i	0.740563	+	0.671987i	$0.234559\pi$
$74$		0			0
$75$			5.51865i			0.637239i
$76$		0			0
$77$		−	6.23817i		−	0.710905i
$78$		0			0
$79$	1.99460	−	3.45475i	0.224410	−	0.388690i	−0.731732	−	0.681592i	$-0.761288\pi$
$79$	1.99460	−	3.45475i	0.224410	−	0.388690i	0.956142	+	0.292903i	$0.0946212\pi$
$80$		0			0
$81$	−3.08123	+	5.33684i	−0.342359	+	0.592983i
$82$		0			0
$83$		−	8.25278i		−	0.905861i	−0.891546	−	0.452930i	$-0.850379\pi$
$83$		−	8.25278i		−	0.905861i	0.891546	−	0.452930i	$-0.149621\pi$
$84$		0			0
$85$	10.1762	−	5.87522i	1.10376	−	0.637257i
$86$		0			0
$87$	5.31844			0.570196
$88$		0			0
$89$	−4.83103	−	8.36758i	−0.512088	−	0.886962i	−0.999902	−	0.0140145i	$-0.995539\pi$
$89$	−4.83103	−	8.36758i	−0.512088	−	0.886962i	0.487814	−	0.872948i	$-0.337794\pi$
$90$		0			0
$91$	−3.25016	+	1.87648i	−0.340710	+	0.196709i
$92$		0			0
$93$	2.17271	+	1.25442i	0.225300	+	0.130077i
$94$		0			0
$95$	−8.19420	+	14.5317i	−0.840707	+	1.49092i
$96$		0			0
$97$	6.67320	−	11.5583i	0.677561	−	1.17357i	−0.298153	−	0.954518i	$-0.596370\pi$
$97$	6.67320	−	11.5583i	0.677561	−	1.17357i	0.975713	−	0.219051i	$-0.0702963\pi$
$98$		0			0
$99$	6.06854	−	3.50367i	0.609911	−	0.352133i
$100$		0			0
$101$	−1.57668	+	0.910298i	−0.156886	+	0.0905780i	−0.576388	−	0.817176i	$-0.695538\pi$
$101$	−1.57668	+	0.910298i	−0.156886	+	0.0905780i	0.419502	+	0.907754i	$0.362205\pi$
$102$		0			0
$103$	−9.94561			−0.979970			−0.489985	−	0.871731i	$-0.662998\pi$
$103$	−9.94561			−0.979970			−0.489985	+	0.871731i	$0.662998\pi$
$104$		0			0
$105$	−2.60450	−	4.51113i	−0.254174	−	0.440242i
$106$		0			0
$107$		−	13.2581i		−	1.28171i	−0.767662	−	0.640855i	$-0.778580\pi$
$107$		−	13.2581i		−	1.28171i	0.767662	−	0.640855i	$-0.221420\pi$
$108$		0			0
$109$	6.54713	+	3.77999i	0.627102	+	0.362057i	0.779629	−	0.626242i	$-0.215408\pi$
$109$	6.54713	+	3.77999i	0.627102	+	0.362057i	−0.152527	+	0.988299i	$0.548741\pi$
$110$		0			0
$111$	−2.00452	+	3.47193i	−0.190261	+	0.329541i
$112$		0			0
$113$	7.07753			0.665798			0.332899	−	0.942963i	$-0.391973\pi$
$113$	7.07753			0.665798			0.332899	+	0.942963i	$0.391973\pi$
$114$		0			0
$115$			34.2723i			3.19591i
$116$		0			0
$117$	−3.65092	−	2.10786i	−0.337527	−	0.194871i
$118$		0			0
$119$	−3.65264	+	6.32656i	−0.334837	+	0.579955i
$120$		0			0
$121$	4.12668			0.375152
$122$		0			0
$123$	−6.16293	+	3.55817i	−0.555692	+	0.320829i
$124$		0			0
$125$			17.7896i			1.59115i
$126$		0			0
$127$	2.91907	+	5.05597i	0.259025	+	0.448645i	0.965981	−	0.258613i	$-0.0832654\pi$
$127$	2.91907	+	5.05597i	0.259025	+	0.448645i	−0.706956	+	0.707258i	$0.749932\pi$
$128$		0			0
$129$	0.778635	+	1.34864i	0.0685550	+	0.118741i
$130$		0			0
$131$	12.2631	+	7.08012i	1.07143	+	0.618593i	0.928573	−	0.371150i	$-0.121036\pi$
$131$	12.2631	+	7.08012i	1.07143	+	0.618593i	0.142861	+	0.989743i	$0.454370\pi$
$132$		0			0
$133$	−0.105343	−	10.3712i	−0.00913436	−	0.899295i
$134$		0			0
$135$	6.20942	−	10.7550i	0.534422	−	0.925646i
$136$		0			0
$137$	0.616142	+	1.06719i	0.0526405	+	0.0911761i	0.891145	−	0.453719i	$-0.149903\pi$
$137$	0.616142	+	1.06719i	0.0526405	+	0.0911761i	−0.838504	+	0.544895i	$0.816570\pi$
$138$		0			0
$139$	5.20766	−	3.00664i	0.441708	−	0.255020i	−0.262614	−	0.964901i	$-0.584585\pi$
$139$	5.20766	−	3.00664i	0.441708	−	0.255020i	0.704322	+	0.709881i	$0.251251\pi$
$140$		0			0
$141$		−	1.32181i		−	0.111317i
$142$		0			0
$143$	2.06754	+	3.58109i	0.172897	+	0.299466i
$144$		0			0
$145$	35.5864			2.95529
$146$		0			0
$147$	−0.662940	−	0.382749i	−0.0546784	−	0.0315686i
$148$		0			0
$149$	0.499112	+	0.288162i	0.0408888	+	0.0236072i	0.520305	−	0.853980i	$-0.325818\pi$
$149$	0.499112	+	0.288162i	0.0408888	+	0.0236072i	−0.479416	+	0.877588i	$0.659152\pi$
$150$		0			0
$151$	13.2393			1.07740			0.538700	−	0.842498i	$-0.318916\pi$
$151$	13.2393			1.07740			0.538700	+	0.842498i	$0.318916\pi$
$152$		0			0
$153$	−8.20604			−0.663419
$154$		0			0
$155$	14.5379	+	8.39347i	1.16771	+	0.674180i
$156$		0			0
$157$	−15.3009	−	8.83396i	−1.22114	−	0.705027i	−0.255981	−	0.966682i	$-0.582399\pi$
$157$	−15.3009	−	8.83396i	−1.22114	−	0.705027i	−0.965162	+	0.261655i	$0.915732\pi$
$158$		0			0
$159$	0.916618			0.0726925
$160$		0			0
$161$	−10.6536	−	18.4526i	−0.839621	−	1.45427i
$162$		0			0
$163$		−	18.7739i		−	1.47049i	−0.677803	−	0.735244i	$-0.737068\pi$
$163$		−	18.7739i		−	1.47049i	0.677803	−	0.735244i	$-0.262932\pi$
$164$		0			0
$165$	−4.97045	+	2.86969i	−0.386949	+	0.223405i
$166$		0			0
$167$	−2.37890	−	4.12037i	−0.184085	−	0.318844i	0.759183	−	0.650877i	$-0.225599\pi$
$167$	−2.37890	−	4.12037i	−0.184085	−	0.318844i	−0.943268	+	0.332033i	$0.892265\pi$
$168$		0			0
$169$	−5.25614	+	9.10390i	−0.404318	+	0.700300i
$170$		0			0
$171$	10.0300	−	5.92746i	0.767013	−	0.453284i
$172$		0			0
$173$	14.4488	+	8.34203i	1.09852	+	0.634233i	0.935833	−	0.352445i	$-0.114649\pi$
$173$	14.4488	+	8.34203i	1.09852	+	0.634233i	0.162690	+	0.986677i	$0.447983\pi$
$174$		0			0
$175$	−11.4785	−	19.8814i	−0.867694	−	1.50289i
$176$		0			0
$177$	−3.44747	−	5.97119i	−0.259128	−	0.448822i
$178$		0			0
$179$		−	17.2627i		−	1.29027i	−0.764067	−	0.645136i	$-0.776801\pi$
$179$		−	17.2627i		−	1.29027i	0.764067	−	0.645136i	$-0.223199\pi$
$180$		0			0
$181$	−0.358255	+	0.206838i	−0.0266289	+	0.0153742i	−0.513255	−	0.858236i	$-0.671561\pi$
$181$	−0.358255	+	0.206838i	−0.0266289	+	0.0153742i	0.486626	+	0.873610i	$0.338227\pi$
$182$		0			0
$183$	0.315213			0.0233012
$184$		0			0
$185$	−13.4125	+	23.2312i	−0.986109	+	1.70799i
$186$		0			0
$187$	6.97072	+	4.02455i	0.509749	+	0.294304i
$188$		0			0
$189$			7.72082i			0.561607i
$190$		0			0
$191$	−24.8774			−1.80006			−0.900031	−	0.435825i	$-0.856457\pi$
$191$	−24.8774			−1.80006			−0.900031	+	0.435825i	$0.856457\pi$
$192$		0			0
$193$	−4.75804	+	8.24117i	−0.342491	+	0.593212i	−0.984895	−	0.173154i	$-0.944604\pi$
$193$	−4.75804	+	8.24117i	−0.342491	+	0.593212i	0.642403	+	0.766367i	$0.277937\pi$
$194$		0			0
$195$	2.99029	+	1.72644i	0.214139	+	0.123633i
$196$		0			0
$197$		−	5.85154i		−	0.416905i	−0.978033	−	0.208452i	$-0.933157\pi$
$197$		−	5.85154i		−	0.416905i	0.978033	−	0.208452i	$-0.0668426\pi$
$198$		0			0
$199$	−8.39537	−	14.5412i	−0.595132	−	1.03080i	−0.993528	−	0.113585i	$-0.963767\pi$
$199$	−8.39537	−	14.5412i	−0.595132	−	1.03080i	0.398397	−	0.917213i	$-0.369567\pi$
$200$		0			0
$201$	−5.04655			−0.355956
$202$		0			0
$203$	−19.1601	+	11.0621i	−1.34477	+	0.776405i
$204$		0			0
$205$	−41.2370	+	23.8082i	−2.88012	+	1.66284i
$206$		0			0
$207$	11.9672	−	20.7278i	0.831779	−	1.44068i
$208$		0			0
$209$	−11.4271	+	0.116068i	−0.790432	+	0.00802862i
$210$		0			0
$211$	−3.15685	−	1.82261i	−0.217327	−	0.125474i	0.387385	−	0.921918i	$-0.373378\pi$
$211$	−3.15685	−	1.82261i	−0.217327	−	0.125474i	−0.604712	+	0.796444i	$0.706712\pi$
$212$		0			0
$213$	3.59900	−	2.07788i	0.246599	−	0.142374i
$214$		0			0
$215$	5.20995	+	9.02391i	0.355316	+	0.615425i
$216$		0			0
$217$	−10.4365			−0.708475
$218$		0			0
$219$	−1.79179	+	1.03449i	−0.121078	+	0.0699042i
$220$		0			0
$221$		−	4.84244i		−	0.325738i
$222$		0			0
$223$	8.66306	−	15.0049i	0.580121	−	1.00480i	−0.415343	−	0.909665i	$-0.636338\pi$
$223$	8.66306	−	15.0049i	0.580121	−	1.00480i	0.995464	−	0.0951349i	$-0.0303283\pi$
$224$		0			0
$225$	12.8938	−	22.3328i	0.859590	−	1.48885i
$226$		0			0
$227$		−	15.0900i		−	1.00156i	−0.865575	−	0.500779i	$-0.833047\pi$
$227$		−	15.0900i		−	1.00156i	0.865575	−	0.500779i	$-0.166953\pi$
$228$		0			0
$229$		−	9.04237i		−	0.597536i	−0.954326	−	0.298768i	$-0.903424\pi$
$229$		−	9.04237i		−	0.597536i	0.954326	−	0.298768i	$-0.0965757\pi$
$230$		0			0
$231$	1.78409	−	3.09014i	0.117385	−	0.203316i
$232$		0			0
$233$	−5.64804	+	9.78269i	−0.370015	+	0.640885i	−0.989567	−	0.144070i	$-0.953981\pi$
$233$	−5.64804	+	9.78269i	−0.370015	+	0.640885i	0.619552	+	0.784955i	$0.287314\pi$
$234$		0			0
$235$		−	8.84442i		−	0.576946i
$236$		0			0
$237$	1.97609	−	1.14090i	0.128361	−	0.0741093i
$238$		0			0
$239$	6.47049			0.418541			0.209271	−	0.977858i	$-0.432891\pi$
$239$	6.47049			0.418541			0.209271	+	0.977858i	$0.432891\pi$
$240$		0			0
$241$	−10.1454	−	17.5724i	−0.653524	−	1.13194i	−0.982262	−	0.187516i	$-0.939956\pi$
$241$	−10.1454	−	17.5724i	−0.653524	−	1.13194i	0.328737	−	0.944421i	$-0.393377\pi$
$242$		0			0
$243$	−11.4829	+	6.62967i	−0.736630	+	0.425293i
$244$		0			0
$245$	−4.43582	−	2.56102i	−0.283394	−	0.163618i
$246$		0			0
$247$	3.49784	+	5.91877i	0.222562	+	0.376602i
$248$		0			0
$249$	2.36027	−	4.08810i	0.149576	−	0.259073i
$250$		0			0
$251$	9.81627	−	5.66742i	0.619597	−	0.357725i	−0.157115	−	0.987580i	$-0.550219\pi$
$251$	9.81627	−	5.66742i	0.619597	−	0.357725i	0.776712	+	0.629856i	$0.216886\pi$
$252$		0			0
$253$	−20.3314	+	11.7383i	−1.27822	+	0.737982i
$254$		0			0
$255$	6.72118			0.420896
$256$		0			0
$257$	−2.33679	−	4.04744i	−0.145765	−	0.252472i	0.783893	−	0.620896i	$-0.213231\pi$
$257$	−2.33679	−	4.04744i	−0.145765	−	0.252472i	−0.929658	+	0.368424i	$0.879898\pi$
$258$		0			0
$259$		−	16.6772i		−	1.03627i
$260$		0			0
$261$	−21.5226	−	12.4261i	−1.33221	−	0.769154i
$262$		0			0
$263$	5.51632	−	9.55454i	0.340151	−	0.589158i	−0.644310	−	0.764765i	$-0.722855\pi$
$263$	5.51632	−	9.55454i	0.340151	−	0.589158i	0.984460	+	0.175606i	$0.0561886\pi$
$264$		0			0
$265$	6.13322			0.376761
$266$		0			0
$267$		−	5.52663i		−	0.338224i
$268$		0			0
$269$	12.9884	+	7.49889i	0.791920	+	0.457215i	0.840638	−	0.541597i	$-0.182180\pi$
$269$	12.9884	+	7.49889i	0.791920	+	0.457215i	−0.0487182	+	0.998813i	$0.515514\pi$
$270$		0			0
$271$	−8.33304	+	14.4332i	−0.506196	+	0.876757i	0.493778	+	0.869588i	$0.335615\pi$
$271$	−8.33304	+	14.4332i	−0.506196	+	0.876757i	−0.999974	+	0.00716938i	$0.997718\pi$
$272$		0			0
$273$	−2.14667			−0.129922
$274$		0			0
$275$	−21.9057	+	12.6472i	−1.32096	+	0.762657i
$276$		0			0
$277$		−	15.6486i		−	0.940235i	−0.882604	−	0.470118i	$-0.844211\pi$
$277$		−	15.6486i		−	0.940235i	0.882604	−	0.470118i	$-0.155789\pi$
$278$		0			0
$279$	−5.86167	−	10.1527i	−0.350929	−	0.607826i
$280$		0			0
$281$	3.50045	+	6.06295i	0.208819	+	0.361685i	0.951343	−	0.308134i	$-0.0997047\pi$
$281$	3.50045	+	6.06295i	0.208819	+	0.361685i	−0.742524	+	0.669820i	$0.766371\pi$
$282$		0			0
$283$	1.72756	+	0.997408i	0.102693	+	0.0592897i	0.550467	−	0.834857i	$-0.314450\pi$
$283$	1.72756	+	0.997408i	0.102693	+	0.0592897i	−0.447774	+	0.894147i	$0.647783\pi$
$284$		0			0
$285$	−8.21509	+	4.85490i	−0.486620	+	0.287579i
$286$		0			0
$287$	14.8016	−	25.6371i	0.873712	−	1.51331i
$288$		0			0
$289$	3.78700	+	6.55928i	0.222765	+	0.385840i
$290$		0			0
$291$	6.61128	−	3.81703i	0.387560	−	0.223758i
$292$		0			0
$293$			17.9363i			1.04785i	0.851765	+	0.523924i	$0.175532\pi$
$293$			17.9363i			1.04785i	−0.851765	+	0.523924i	$0.824468\pi$
$294$		0			0
$295$	−23.0675	−	39.9540i	−1.34304	−	2.32621i
$296$		0			0
$297$	8.50695			0.493623
$298$		0			0
$299$	12.2316	+	7.06194i	0.707373	+	0.408402i
$300$		0			0
$301$	−5.61019	−	3.23904i	−0.323366	−	0.186695i
$302$		0			0
$303$	−1.04137			−0.0598250
$304$		0			0
$305$	2.10913			0.120768
$306$		0			0
$307$	25.5431	+	14.7473i	1.45782	+	0.841673i	0.998904	−	0.0468072i	$-0.0149046\pi$
$307$	25.5431	+	14.7473i	1.45782	+	0.841673i	0.458916	+	0.888480i	$0.348238\pi$
$308$		0			0
$309$	−4.92666	−	2.84441i	−0.280268	−	0.161813i
$310$		0			0
$311$	−18.2270			−1.03356			−0.516779	−	0.856119i	$-0.672869\pi$
$311$	−18.2270			−1.03356			−0.516779	+	0.856119i	$0.672869\pi$
$312$		0			0
$313$	−14.9213	−	25.8444i	−0.843401	−	1.46081i	−0.887003	−	0.461764i	$-0.847217\pi$
$313$	−14.9213	−	25.8444i	−0.843401	−	1.46081i	0.0436015	−	0.999049i	$-0.486117\pi$
$314$		0			0
$315$			24.3408i			1.37145i
$316$		0			0
$317$	5.53123	−	3.19346i	0.310665	−	0.179363i	−0.336559	−	0.941662i	$-0.609263\pi$
$317$	5.53123	−	3.19346i	0.310665	−	0.179363i	0.647224	+	0.762300i	$0.275930\pi$
$318$		0			0
$319$	12.1884	+	21.1109i	0.682419	+	1.18198i
$320$		0			0
$321$	3.79177	−	6.56754i	0.211636	−	0.366565i
$322$		0			0
$323$	11.6570	+	6.57324i	0.648615	+	0.365745i
$324$		0			0
$325$	13.1787	+	7.60875i	0.731025	+	0.422057i
$326$		0			0
$327$	2.16213	+	3.74492i	0.119566	+	0.207094i
$328$		0			0
$329$	2.74930	+	4.76193i	0.151574	+	0.262533i
$330$		0			0
$331$		−	6.22210i		−	0.341997i	−0.985271	−	0.170999i	$-0.945301\pi$
$331$		−	6.22210i		−	0.341997i	0.985271	−	0.170999i	$-0.0546994\pi$
$332$		0			0
$333$	16.2237	−	9.36678i	0.889055	−	0.513296i
$334$		0			0
$335$	−33.7672			−1.84490
$336$		0			0
$337$	14.7925	−	25.6213i	0.805797	−	1.39568i	−0.109954	−	0.993937i	$-0.535070\pi$
$337$	14.7925	−	25.6213i	0.805797	−	1.39568i	0.915752	−	0.401745i	$-0.131596\pi$
$338$		0			0
$339$	3.50593	+	2.02415i	0.190416	+	0.109937i
$340$		0			0
$341$			11.4991i			0.622712i
$342$		0			0
$343$	19.8404			1.07128
$344$		0			0
$345$	−9.80177	+	16.9772i	−0.527710	+	0.914020i
$346$		0			0
$347$	−5.78717	−	3.34122i	−0.310671	−	0.179366i	0.336555	−	0.941664i	$-0.390738\pi$
$347$	−5.78717	−	3.34122i	−0.310671	−	0.179366i	−0.647227	+	0.762297i	$0.724071\pi$
$348$		0			0
$349$		−	17.1074i		−	0.915736i	−0.889020	−	0.457868i	$-0.848613\pi$
$349$		−	17.1074i		−	0.915736i	0.889020	−	0.457868i	$-0.151387\pi$
$350$		0			0
$351$	−2.55895	−	4.43222i	−0.136586	−	0.236575i
$352$		0			0
$353$	0.857173			0.0456227			0.0228114	−	0.999740i	$-0.492738\pi$
$353$	0.857173			0.0456227			0.0228114	+	0.999740i	$0.492738\pi$
$354$		0			0
$355$	24.0814	−	13.9034i	1.27811	−	0.737915i
$356$		0			0
$357$	−3.61875	+	2.08929i	−0.191525	+	0.110577i
$358$		0			0
$359$	−17.9279	+	31.0520i	−0.946198	+	1.63886i	−0.192863	+	0.981226i	$0.561777\pi$
$359$	−17.9279	+	31.0520i	−0.946198	+	1.63886i	−0.753335	+	0.657637i	$0.771556\pi$
$360$		0			0
$361$	−18.9961	+	0.385936i	−0.999794	+	0.0203124i
$362$		0			0
$363$	2.04419	+	1.18022i	0.107292	+	0.0619452i
$364$		0			0
$365$	−11.9891	+	6.92190i	−0.627537	+	0.362309i
$366$		0			0
$367$	3.60358	+	6.24158i	0.188105	+	0.325808i	0.944618	−	0.328171i	$-0.106432\pi$
$367$	3.60358	+	6.24158i	0.188105	+	0.325808i	−0.756513	+	0.653978i	$0.773099\pi$
$368$		0			0
$369$	33.2534			1.73110
$370$		0			0
$371$	−3.30219	+	1.90652i	−0.171441	+	0.0989815i
$372$		0			0
$373$		−	1.23956i		−	0.0641818i	−0.999485	−	0.0320909i	$-0.989783\pi$
$373$		−	1.23956i		−	0.0641818i	0.999485	−	0.0320909i	$-0.0102166\pi$
$374$		0			0
$375$	−5.08778	+	8.81229i	−0.262732	+	0.455064i
$376$		0			0
$377$	7.33270	−	12.7006i	0.377653	−	0.654115i
$378$		0			0
$379$		−	7.69864i		−	0.395453i	−0.980257	−	0.197726i	$-0.936644\pi$
$379$		−	7.69864i		−	0.395453i	0.980257	−	0.197726i	$-0.0633558\pi$
$380$		0			0
$381$			3.33937i			0.171081i
$382$		0			0
$383$	−6.13360	+	10.6237i	−0.313413	+	0.542846i	−0.979099	−	0.203385i	$-0.934806\pi$
$383$	−6.13360	+	10.6237i	−0.313413	+	0.542846i	0.665686	+	0.746232i	$0.268139\pi$
$384$		0			0
$385$	11.9376	−	20.6766i	0.608397	−	1.05378i
$386$		0			0
$387$		−	7.27685i		−	0.369903i
$388$		0			0
$389$	−23.7105	+	13.6893i	−1.20217	+	0.694074i	−0.961038	−	0.276417i	$-0.910853\pi$
$389$	−23.7105	+	13.6893i	−1.20217	+	0.694074i	−0.241135	+	0.970492i	$0.577520\pi$
$390$		0			0
$391$	27.4926			1.39036
$392$		0			0
$393$	4.04978	+	7.01443i	0.204284	+	0.353831i
$394$		0			0
$395$	13.2223	−	7.63390i	0.665286	−	0.384103i
$396$		0			0
$397$	−2.94101	−	1.69799i	−0.147605	−	0.0852197i	0.424379	−	0.905485i	$-0.360493\pi$
$397$	−2.94101	−	1.69799i	−0.147605	−	0.0852197i	−0.571984	+	0.820265i	$0.693826\pi$
$398$		0			0
$399$	2.91394	−	5.16760i	0.145879	−	0.258704i
$400$		0			0
$401$	−12.4586	+	21.5789i	−0.622151	+	1.07760i	0.366934	+	0.930247i	$0.380408\pi$
$401$	−12.4586	+	21.5789i	−0.622151	+	1.07760i	−0.989084	+	0.147350i	$0.952926\pi$
$402$		0			0
$403$	5.99118	−	3.45901i	0.298442	−	0.172306i
$404$		0			0
$405$	−20.4256	+	11.7927i	−1.01496	+	0.585986i
$406$		0			0
$407$	−18.3753			−0.910827
$408$		0			0
$409$	5.57567	+	9.65734i	0.275699	+	0.477525i	0.970311	−	0.241860i	$-0.0777574\pi$
$409$	5.57567	+	9.65734i	0.275699	+	0.477525i	−0.694612	+	0.719384i	$0.744424\pi$
$410$		0			0
$411$			0.704858i			0.0347681i
$412$		0			0
$413$	24.8395	+	14.3411i	1.22227	+	0.705680i
$414$		0			0
$415$	15.7929	−	27.3541i	0.775242	−	1.34276i
$416$		0			0
$417$	3.43956			0.168436
$418$		0			0
$419$			5.54457i			0.270870i	0.990786	+	0.135435i	$0.0432432\pi$
$419$			5.54457i			0.270870i	−0.990786	+	0.135435i	$0.956757\pi$
$420$		0			0
$421$	19.9281	+	11.5055i	0.971235	+	0.560743i	0.899612	−	0.436689i	$-0.143849\pi$
$421$	19.9281	+	11.5055i	0.971235	+	0.560743i	0.0716223	+	0.997432i	$0.477182\pi$
$422$		0			0
$423$	−3.08830	+	5.34908i	−0.150158	+	0.260081i
$424$		0			0
$425$	29.6214			1.43685
$426$		0			0
$427$	−1.13558	+	0.655626i	−0.0549544	+	0.0317280i
$428$		0			0
$429$			2.36524i			0.114195i
$430$		0			0
$431$	3.84478	+	6.65935i	0.185196	+	0.320770i	0.943643	−	0.330966i	$-0.107375\pi$
$431$	3.84478	+	6.65935i	0.185196	+	0.320770i	−0.758446	+	0.651736i	$0.774041\pi$
$432$		0			0
$433$	−13.8560	−	23.9994i	−0.665879	−	1.15334i	−0.979046	−	0.203639i	$-0.934723\pi$
$433$	−13.8560	−	23.9994i	−0.665879	−	1.15334i	0.313167	−	0.949698i	$-0.398610\pi$
$434$		0			0
$435$	17.6281	+	10.1776i	0.845203	+	0.487978i
$436$		0			0
$437$	−33.6034	+	19.8587i	−1.60747	+	0.949971i
$438$		0			0
$439$	−17.4148	+	30.1634i	−0.831165	+	1.43962i	0.0659505	+	0.997823i	$0.478992\pi$
$439$	−17.4148	+	30.1634i	−0.831165	+	1.43962i	−0.897115	+	0.441797i	$0.854341\pi$
$440$		0			0
$441$	1.78852	+	3.09780i	0.0851675	+	0.147514i
$442$		0			0
$443$	−6.78938	+	3.91985i	−0.322573	+	0.186238i	−0.652539	−	0.757755i	$-0.726296\pi$
$443$	−6.78938	+	3.91985i	−0.322573	+	0.186238i	0.329966	+	0.943993i	$0.392963\pi$
$444$		0			0
$445$		−	36.9794i		−	1.75299i
$446$		0			0
$447$	0.164827	+	0.285488i	0.00779604	+	0.0135031i
$448$		0			0
$449$	−22.7057			−1.07155			−0.535775	−	0.844361i	$-0.679980\pi$
$449$	−22.7057			−1.07155			−0.535775	+	0.844361i	$0.679980\pi$
$450$		0			0
$451$	−28.2475	−	16.3087i	−1.33012	−	0.767946i
$452$		0			0
$453$	6.55823	+	3.78640i	0.308133	+	0.177900i
$454$		0			0
$455$	−14.3637			−0.673379
$456$		0			0
$457$	−34.5207			−1.61481			−0.807405	−	0.589998i	$-0.799129\pi$
$457$	−34.5207			−1.61481			−0.807405	+	0.589998i	$0.799129\pi$
$458$		0			0
$459$	−8.62749	−	4.98108i	−0.402697	−	0.232497i
$460$		0			0
$461$	−11.7449	−	6.78091i	−0.547014	−	0.315819i	0.200903	−	0.979611i	$-0.435612\pi$
$461$	−11.7449	−	6.78091i	−0.547014	−	0.315819i	−0.747917	+	0.663793i	$0.768946\pi$
$462$		0			0
$463$	−16.0544			−0.746112			−0.373056	−	0.927809i	$-0.621690\pi$
$463$	−16.0544			−0.746112			−0.373056	+	0.927809i	$0.621690\pi$
$464$		0			0
$465$	4.80101	+	8.31559i	0.222641	+	0.385626i
$466$		0			0
$467$			36.4819i			1.68818i	0.536201	+	0.844091i	$0.319859\pi$
$467$			36.4819i			1.68818i	−0.536201	+	0.844091i	$0.680141\pi$
$468$		0			0
$469$	18.1806	−	10.4966i	0.839502	−	0.484686i
$470$		0			0
$471$	−5.05297	−	8.75200i	−0.232828	−	0.403271i
$472$		0			0
$473$	−3.56884	+	6.18141i	−0.164095	+	0.284221i
$474$		0			0
$475$	−36.2054	+	21.3964i	−1.66122	+	0.981734i
$476$		0			0
$477$	−3.70936	−	2.14160i	−0.169840	−	0.0980570i
$478$		0			0
$479$	−6.04549	−	10.4711i	−0.276225	−	0.478437i	0.694218	−	0.719765i	$-0.255750\pi$
$479$	−6.04549	−	10.4711i	−0.276225	−	0.478437i	−0.970444	+	0.241328i	$0.922417\pi$
$480$		0			0
$481$	5.52740	+	9.57373i	0.252028	+	0.436525i
$482$		0			0
$483$		−	12.1876i		−	0.554554i
$484$		0			0
$485$	44.2370	−	25.5402i	2.00870	−	1.15972i
$486$		0			0
$487$	33.9780			1.53969			0.769845	−	0.638231i	$-0.220334\pi$
$487$	33.9780			1.53969			0.769845	+	0.638231i	$0.220334\pi$
$488$		0			0
$489$	5.36928	−	9.29987i	0.242807	−	0.420555i
$490$		0			0
$491$	−8.85946	−	5.11501i	−0.399822	−	0.230837i	0.286585	−	0.958055i	$-0.407480\pi$
$491$	−8.85946	−	5.11501i	−0.399822	−	0.230837i	−0.686407	+	0.727218i	$0.740813\pi$
$492$		0			0
$493$		−	28.5467i		−	1.28568i
$494$		0			0
$495$	26.8191			1.20543
$496$		0			0
$497$	−8.64377	+	14.9715i	−0.387726	+	0.671562i
$498$		0			0
$499$	−24.9924	−	14.4294i	−1.11881	−	0.645947i	−0.177716	−	0.984082i	$-0.556871\pi$
$499$	−24.9924	−	14.4294i	−1.11881	−	0.645947i	−0.941098	+	0.338135i	$0.890204\pi$
$500$		0			0
$501$		−	2.72143i		−	0.121584i
$502$		0			0
$503$	13.5515	+	23.4718i	0.604229	+	1.04656i	0.992173	+	0.124873i	$0.0398523\pi$
$503$	13.5515	+	23.4718i	0.604229	+	1.04656i	−0.387943	+	0.921683i	$0.626814\pi$
$504$		0			0
$505$	−6.96794			−0.310069
$506$		0			0
$507$	−5.20737	+	3.00648i	−0.231267	+	0.133522i
$508$		0			0
$509$	20.2327	−	11.6814i	0.896798	−	0.517767i	0.0206383	−	0.999787i	$-0.493430\pi$
$509$	20.2327	−	11.6814i	0.896798	−	0.517767i	0.876160	+	0.482020i	$0.160097\pi$
$510$		0			0
$511$	4.30336	−	7.45364i	0.190370	−	0.329730i
$512$		0			0
$513$	14.1431	−	0.143655i	0.624433	−	0.00634252i
$514$		0			0
$515$	−32.9650	−	19.0323i	−1.45261	−	0.838665i
$516$		0			0
$517$	5.24678	−	3.02923i	0.230753	−	0.133225i
$518$		0			0
$519$	4.77158	+	8.26463i	0.209449	+	0.362777i
$520$		0			0
$521$	2.49127			0.109144			0.0545722	−	0.998510i	$-0.482621\pi$
$521$	2.49127			0.109144			0.0545722	+	0.998510i	$0.482621\pi$
$522$		0			0
$523$	24.6860	−	14.2525i	1.07944	−	0.623217i	0.148697	−	0.988883i	$-0.452492\pi$
$523$	24.6860	−	14.2525i	1.07944	−	0.623217i	0.930746	+	0.365666i	$0.119159\pi$
$524$		0			0
$525$		−	13.1313i		−	0.573095i
$526$		0			0
$527$	6.73309	−	11.6621i	0.293298	−	0.508007i
$528$		0			0
$529$	−28.5937	+	49.5257i	−1.24320	+	2.15329i
$530$		0			0
$531$			32.2188i			1.39818i
$532$		0			0
$533$			19.6230i			0.849968i
$534$		0			0
$535$	25.3713	−	43.9443i	1.09690	−	1.89988i
$536$		0			0
$537$	4.93707	−	8.55125i	0.213050	−	0.369014i
$538$		0			0
$539$		−	3.50862i		−	0.151127i
$540$		0			0
$541$	5.26285	−	3.03851i	0.226267	−	0.130636i	−0.382581	−	0.923922i	$-0.624965\pi$
$541$	5.26285	−	3.03851i	0.226267	−	0.130636i	0.608849	+	0.793286i	$0.291632\pi$
$542$		0			0
$543$	−0.236620			−0.0101544
$544$		0			0
$545$	14.4671	+	25.0577i	0.619702	+	1.07336i
$546$		0			0
$547$	16.7508	−	9.67108i	0.716212	−	0.413505i	−0.0971447	−	0.995270i	$-0.530971\pi$
$547$	16.7508	−	9.67108i	0.716212	−	0.413505i	0.813357	+	0.581765i	$0.197638\pi$
$548$		0			0
$549$	−1.27560	−	0.736466i	−0.0544412	−	0.0314316i
$550$		0			0
$551$	20.6201	+	34.8918i	0.878447	+	1.48644i
$552$		0			0
$553$	−4.74602	+	8.22034i	−0.201821	+	0.349564i
$554$		0			0
$555$	−13.2881	+	7.67188i	−0.564047	+	0.325653i
$556$		0			0
$557$	19.3179	−	11.1532i	0.818525	−	0.472576i	−0.0313823	−	0.999507i	$-0.509991\pi$
$557$	19.3179	−	11.1532i	0.818525	−	0.472576i	0.849908	+	0.526932i	$0.176658\pi$
$558$		0			0
$559$	4.29412			0.181622
$560$		0			0
$561$	2.30201	+	3.98720i	0.0971911	+	0.168340i
$562$		0			0
$563$		−	25.2448i		−	1.06394i	−0.846763	−	0.531970i	$-0.821452\pi$
$563$		−	25.2448i		−	1.06394i	0.846763	−	0.531970i	$-0.178548\pi$
$564$		0			0
$565$	23.4586	+	13.5439i	0.986913	+	0.569794i
$566$		0			0
$567$	7.33158	−	12.6987i	0.307897	−	0.533294i
$568$		0			0
$569$	−17.1784			−0.720155			−0.360078	−	0.932922i	$-0.617250\pi$
$569$	−17.1784			−0.720155			−0.360078	+	0.932922i	$0.617250\pi$
$570$		0			0
$571$		−	8.64144i		−	0.361633i	−0.983517	−	0.180816i	$-0.942126\pi$
$571$		−	8.64144i		−	0.361633i	0.983517	−	0.180816i	$-0.0578740\pi$
$572$		0			0
$573$	−12.3233	−	7.11484i	−0.514812	−	0.297227i
$574$		0			0
$575$	−43.1981	+	74.8214i	−1.80149	+	3.12027i
$576$		0			0
$577$	24.5806			1.02331			0.511653	−	0.859192i	$-0.329034\pi$
$577$	24.5806			1.02331			0.511653	+	0.859192i	$0.329034\pi$
$578$		0			0
$579$	−4.71389	+	2.72157i	−0.195903	+	0.113104i
$580$		0			0
$581$			19.6369i			0.814678i
$582$		0			0
$583$	2.10064	+	3.63841i	0.0869995	+	0.150688i
$584$		0			0
$585$	−8.06737	−	13.9731i	−0.333545	−	0.577716i
$586$		0			0
$587$	−33.7781	−	19.5018i	−1.39417	−	0.804926i	−0.400399	−	0.916341i	$-0.631128\pi$
$587$	−33.7781	−	19.5018i	−1.39417	−	0.804926i	−0.993774	+	0.111415i	$0.964462\pi$
$588$		0			0
$589$	0.194183	+	19.1177i	0.00800117	+	0.787730i
$590$		0			0
$591$	1.67352	−	2.89862i	0.0688394	−	0.119233i
$592$		0			0
$593$	−3.40127	−	5.89117i	−0.139673	−	0.241921i	0.787700	−	0.616059i	$-0.211272\pi$
$593$	−3.40127	−	5.89117i	−0.139673	−	0.241921i	−0.927373	+	0.374138i	$0.877939\pi$
$594$		0			0
$595$	−24.2135	+	13.9797i	−0.992659	+	0.573112i
$596$		0			0
$597$		−	9.60418i		−	0.393073i
$598$		0			0
$599$	−18.1953	−	31.5152i	−0.743439	−	1.28767i	−0.950921	−	0.309435i	$-0.899860\pi$
$599$	−18.1953	−	31.5152i	−0.743439	−	1.28767i	0.207481	−	0.978239i	$-0.433473\pi$
$600$		0			0
$601$	−0.372849			−0.0152088			−0.00760441	−	0.999971i	$-0.502421\pi$
$601$	−0.372849			−0.0152088			−0.00760441	+	0.999971i	$0.502421\pi$
$602$		0			0
$603$	20.4223	+	11.7908i	0.831661	+	0.480159i
$604$		0			0
$605$	13.6780	+	7.89698i	0.556089	+	0.321058i
$606$		0			0
$607$	31.5367			1.28003			0.640017	−	0.768361i	$-0.278927\pi$
$607$	31.5367			1.28003			0.640017	+	0.768361i	$0.278927\pi$
$608$		0			0
$609$	−12.6549			−0.512801
$610$		0			0
$611$	−3.15653	−	1.82242i	−0.127700	−	0.0737274i
$612$		0			0
$613$	−16.9009	−	9.75775i	−0.682621	−	0.394112i	0.118221	−	0.992987i	$-0.462281\pi$
$613$	−16.9009	−	9.75775i	−0.682621	−	0.394112i	−0.800842	+	0.598876i	$0.795614\pi$
$614$		0			0
$615$	−27.2362			−1.09827
$616$		0			0
$617$	18.5156	+	32.0700i	0.745410	+	1.29109i	0.950003	+	0.312241i	$0.101080\pi$
$617$	18.5156	+	32.0700i	0.745410	+	1.29109i	−0.204592	+	0.978847i	$0.565587\pi$
$618$		0			0
$619$		−	8.86666i		−	0.356381i	−0.983996	−	0.178190i	$-0.942976\pi$
$619$		−	8.86666i		−	0.356381i	0.983996	−	0.178190i	$-0.0570243\pi$
$620$		0			0
$621$	25.1637	−	14.5282i	1.00978	−	0.582998i
$622$		0			0
$623$	11.4951	+	19.9101i	0.460542	+	0.797682i
$624$		0			0
$625$	−9.92273	+	17.1867i	−0.396909	+	0.687467i
$626$		0			0
$627$	−5.69375	−	3.21063i	−0.227387	−	0.128220i
$628$		0			0
$629$	18.6356	+	10.7593i	0.743051	+	0.429001i
$630$		0			0
$631$	−2.13344	−	3.69522i	−0.0849307	−	0.147104i	0.820431	−	0.571746i	$-0.193734\pi$
$631$	−2.13344	−	3.69522i	−0.0849307	−	0.147104i	−0.905362	+	0.424641i	$0.860400\pi$
$632$		0			0
$633$	−1.04252	−	1.80570i	−0.0414364	−	0.0717700i
$634$		0			0
$635$			22.3442i			0.886702i
$636$		0			0
$637$	−1.82803	+	1.05542i	−0.0724294	+	0.0418171i
$638$		0			0
$639$	−19.4192			−0.768210
$640$		0			0
$641$	−11.7085	+	20.2797i	−0.462458	+	0.801000i	−0.999083	−	0.0428208i	$-0.986366\pi$
$641$	−11.7085	+	20.2797i	−0.462458	+	0.801000i	0.536625	+	0.843821i	$0.319699\pi$
$642$		0			0
$643$	18.6718	+	10.7802i	0.736344	+	0.425128i	0.820739	−	0.571304i	$-0.193562\pi$
$643$	18.6718	+	10.7802i	0.736344	+	0.425128i	−0.0843944	+	0.996432i	$0.526896\pi$
$644$		0			0
$645$			5.96012i			0.234679i
$646$		0			0
$647$	27.5504			1.08312			0.541559	−	0.840663i	$-0.317834\pi$
$647$	27.5504			1.08312			0.541559	+	0.840663i	$0.317834\pi$
$648$		0			0
$649$	15.8013	−	27.3686i	0.620255	−	1.07431i
$650$		0			0
$651$	−5.16982	−	2.98480i	−0.202621	−	0.116984i
$652$		0			0
$653$		−	11.9425i		−	0.467348i	−0.972315	−	0.233674i	$-0.924925\pi$
$653$		−	11.9425i		−	0.467348i	0.972315	−	0.233674i	$-0.0750748\pi$
$654$		0			0
$655$	27.0976	+	46.9345i	1.05879	+	1.83388i
$656$		0			0
$657$	9.66796			0.377183
$658$		0			0
$659$	−30.7336	+	17.7441i	−1.19721	+	0.691211i	−0.959933	−	0.280231i	$-0.909589\pi$
$659$	−30.7336	+	17.7441i	−1.19721	+	0.691211i	−0.237279	+	0.971442i	$0.576256\pi$
$660$		0			0
$661$	−15.5565	+	8.98158i	−0.605080	+	0.349343i	−0.771037	−	0.636790i	$-0.780262\pi$
$661$	−15.5565	+	8.98158i	−0.605080	+	0.349343i	0.165958	+	0.986133i	$0.446928\pi$
$662$		0			0
$663$	1.38492	−	2.39876i	0.0537859	−	0.0931599i
$664$		0			0
$665$	19.4976	−	34.5771i	0.756083	−	1.34084i
$666$		0			0
$667$	72.1069	+	41.6309i	2.79199	+	1.61196i
$668$		0			0
$669$	8.58268	−	4.95521i	0.331826	−	0.191580i
$670$		0			0
$671$	0.722381	+	1.25120i	0.0278872	+	0.0483020i
$672$		0			0
$673$	−28.4280			−1.09582			−0.547909	−	0.836538i	$-0.684576\pi$
$673$	−28.4280			−1.09582			−0.547909	+	0.836538i	$0.684576\pi$
$674$		0			0
$675$	27.1121	−	15.6532i	1.04354	−	0.602491i
$676$		0			0
$677$		−	42.7219i		−	1.64194i	−0.570974	−	0.820968i	$-0.693434\pi$
$677$		−	42.7219i		−	1.64194i	0.570974	−	0.820968i	$-0.306566\pi$
$678$		0			0
$679$	−15.8784	+	27.5023i	−0.609358	+	1.05544i
$680$		0			0
$681$	4.31569	−	7.47499i	0.165377	−	0.286442i
$682$		0			0
$683$		−	5.28834i		−	0.202353i	−0.994869	−	0.101176i	$-0.967739\pi$
$683$		−	5.28834i		−	0.202353i	0.994869	−	0.101176i	$-0.0322606\pi$
$684$		0			0
$685$			4.71630i			0.180201i
$686$		0			0
$687$	2.58609	−	4.47923i	0.0986654	−	0.170893i
$688$		0			0
$689$	1.26377	−	2.18892i	0.0481458	−	0.0833911i
$690$		0			0
$691$			2.46172i			0.0936482i	0.998903	+	0.0468241i	$0.0149100\pi$
$691$			2.46172i			0.0936482i	−0.998903	+	0.0468241i	$0.985090\pi$
$692$		0			0
$693$	−14.4397	+	8.33676i	−0.548518	+	0.316687i
$694$		0			0
$695$	23.0146			0.872992
$696$		0			0
$697$	19.0985	+	33.0796i	0.723407	+	1.25298i
$698$		0			0
$699$	−5.59563	+	3.23064i	−0.211646	+	0.122194i
$700$		0			0
$701$	31.3878	+	18.1217i	1.18550	+	0.684449i	0.957280	−	0.289161i	$-0.0933763\pi$
$701$	31.3878	+	18.1217i	1.18550	+	0.684449i	0.228220	+	0.973610i	$0.426710\pi$
$702$		0			0
$703$	−30.5495	+	0.310299i	−1.15220	+	0.0117031i
$704$		0			0
$705$	2.52947	−	4.38118i	0.0952655	−	0.165005i
$706$		0			0
$707$	3.75161	−	2.16599i	0.141094	−	0.0814605i
$708$		0			0
$709$	11.9138	−	6.87845i	0.447433	−	0.258325i	−0.259313	−	0.965793i	$-0.583496\pi$
$709$	11.9138	−	6.87845i	0.447433	−	0.258325i	0.706745	+	0.707468i	$0.250163\pi$
$710$		0			0
$711$	−10.6624			−0.399872
$712$		0			0
$713$	19.6383	+	34.0145i	0.735460	+	1.27385i
$714$		0			0
$715$			15.8261i			0.591864i
$716$		0			0
$717$	3.20523	+	1.85054i	0.119701	+	0.0691097i
$718$		0			0
$719$	−21.5301	+	37.2913i	−0.802938	+	1.39073i	0.114736	+	0.993396i	$0.463398\pi$
$719$	−21.5301	+	37.2913i	−0.802938	+	1.39073i	−0.917674	+	0.397334i	$0.869935\pi$
$720$		0			0
$721$	23.6649			0.881328
$722$		0			0
$723$		−	11.6062i		−	0.431640i
$724$		0			0
$725$	77.6901	+	44.8544i	2.88534	+	1.66585i
$726$		0			0
$727$	10.5087	−	18.2017i	0.389747	−	0.675062i	−0.602668	−	0.797992i	$-0.705896\pi$
$727$	10.5087	−	18.2017i	0.389747	−	0.675062i	0.992415	+	0.122930i	$0.0392290\pi$
$728$		0			0
$729$	10.9031			0.403819
$730$		0			0
$731$	7.23881	−	4.17933i	0.267737	−	0.154578i
$732$		0			0
$733$			39.1556i			1.44624i	0.690720	+	0.723122i	$0.257294\pi$
$733$			39.1556i			1.44624i	−0.690720	+	0.723122i	$0.742706\pi$
$734$		0			0
$735$	−1.46489	−	2.53726i	−0.0540332	−	0.0935883i
$736$		0			0
$737$	−11.5653	−	20.0317i	−0.426014	−	0.737877i
$738$		0			0
$739$	−13.9285	−	8.04160i	−0.512367	−	0.295815i	0.221439	−	0.975174i	$-0.428925\pi$
$739$	−13.9285	−	8.04160i	−0.512367	−	0.295815i	−0.733806	+	0.679359i	$0.762258\pi$
$740$		0			0
$741$	0.0399413	+	3.93230i	0.00146728	+	0.144457i
$742$		0			0
$743$	−17.2042	+	29.7985i	−0.631161	+	1.09320i	0.356154	+	0.934427i	$0.384088\pi$
$743$	−17.2042	+	29.7985i	−0.631161	+	1.09320i	−0.987315	+	0.158775i	$0.949245\pi$
$744$		0			0
$745$	1.10288	+	1.91024i	0.0404063	+	0.0699858i
$746$		0			0
$747$	−19.1030	+	11.0291i	−0.698942	+	0.403534i
$748$		0			0
$749$			31.5468i			1.15269i
$750$		0			0
$751$	16.1770	+	28.0194i	0.590307	+	1.02244i	0.994191	+	0.107631i	$0.0343266\pi$
$751$	16.1770	+	28.0194i	0.590307	+	1.02244i	−0.403884	+	0.914810i	$0.632340\pi$
$752$		0			0
$753$	6.48346			0.236270
$754$		0			0
$755$	43.8820	+	25.3353i	1.59703	+	0.922046i
$756$		0			0
$757$	−32.1757	−	18.5767i	−1.16945	−	0.675180i	−0.215896	−	0.976416i	$-0.569267\pi$
$757$	−32.1757	−	18.5767i	−1.16945	−	0.675180i	−0.953550	+	0.301236i	$0.902601\pi$
$758$		0			0
$759$	−13.4285			−0.487423
$760$		0			0
$761$	43.8152			1.58830			0.794150	−	0.607721i	$-0.207916\pi$
$761$	43.8152			1.58830			0.794150	+	0.607721i	$0.207916\pi$
$762$		0			0
$763$	−15.5785	−	8.99423i	−0.563978	−	0.325613i
$764$		0			0
$765$	−27.1991	−	15.7034i	−0.983387	−	0.567759i
$766$		0			0
$767$	−19.0125			−0.686503
$768$		0			0
$769$	−5.81793	−	10.0770i	−0.209800	−	0.363384i	0.741851	−	0.670564i	$-0.233948\pi$
$769$	−5.81793	−	10.0770i	−0.209800	−	0.363384i	−0.951651	+	0.307180i	$0.900615\pi$
$770$		0			0
$771$		−	2.67325i		−	0.0962749i
$772$		0			0
$773$	−20.2046	+	11.6652i	−0.726711	+	0.419567i	−0.817218	−	0.576329i	$-0.804485\pi$
$773$	−20.2046	+	11.6652i	−0.726711	+	0.419567i	0.0905070	+	0.995896i	$0.471151\pi$
$774$		0			0
$775$	21.1589	+	36.6483i	0.760050	+	1.31645i
$776$		0			0
$777$	4.76963	−	8.26123i	0.171109	−	0.296370i
$778$		0			0
$779$	−47.2378	−	26.6368i	−1.69247	−	0.954361i
$780$		0			0
$781$	16.4958	+	9.52387i	0.590267	+	0.340791i
$782$		0			0
$783$	−15.0853	−	26.1285i	−0.539104	−	0.933755i
$784$		0			0
$785$	−33.8101	−	58.5608i	−1.20673	−	2.09012i
$786$		0			0
$787$			47.9991i			1.71098i	0.517815	+	0.855492i	$0.326745\pi$
$787$			47.9991i			1.71098i	−0.517815	+	0.855492i	$0.673255\pi$
$788$		0			0
$789$	5.46514	−	3.15530i	0.194564	−	0.112332i
$790$		0			0
$791$	−16.8405			−0.598779
$792$		0			0
$793$	0.434594	−	0.752739i	0.0154329	−	0.0267305i
$794$		0			0
$795$	3.03815	+	1.75408i	0.107752	+	0.0622108i
$796$		0			0
$797$		−	15.8257i		−	0.560576i	−0.959916	−	0.280288i	$-0.909570\pi$
$797$		−	15.8257i		−	0.560576i	0.959916	−	0.280288i	$-0.0904299\pi$
$798$		0			0
$799$	−7.09483			−0.250997
$800$		0			0
$801$	−12.9125	+	22.3651i	−0.456240	+	0.790231i
$802$		0			0
$803$	−8.21256	−	4.74152i	−0.289815	−	0.167325i
$804$		0			0
$805$		−	81.5487i		−	2.87421i
$806$		0			0
$807$	4.28931	+	7.42931i	0.150991	+	0.261524i
$808$		0			0
$809$	−15.5885			−0.548063			−0.274031	−	0.961721i	$-0.588357\pi$
$809$	−15.5885			−0.548063			−0.274031	+	0.961721i	$0.588357\pi$
$810$		0			0
$811$	30.1683	−	17.4177i	1.05935	−	0.611618i	0.134100	−	0.990968i	$-0.457186\pi$
$811$	30.1683	−	17.4177i	1.05935	−	0.611618i	0.925253	+	0.379350i	$0.123852\pi$
$812$		0			0
$813$	−8.25572	+	4.76644i	−0.289541	+	0.167166i
$814$		0			0
$815$	35.9266	−	62.2267i	1.25845	−	2.17971i
$816$		0			0
$817$	−5.82893	+	10.3371i	−0.203929	+	0.361648i
$818$		0			0
$819$	8.68711	+	5.01551i	0.303552	+	0.175256i
$820$		0			0
$821$	35.5478	−	20.5235i	1.24063	−	0.716276i	0.271404	−	0.962465i	$-0.412512\pi$
$821$	35.5478	−	20.5235i	1.24063	−	0.716276i	0.969222	+	0.246190i	$0.0791786\pi$
$822$		0			0
$823$	3.83395	+	6.64060i	0.133643	+	0.231477i	0.925078	−	0.379776i	$-0.123999\pi$
$823$	3.83395	+	6.64060i	0.133643	+	0.231477i	−0.791435	+	0.611253i	$0.790666\pi$
$824$		0			0
$825$	−14.4683			−0.503720
$826$		0			0
$827$	10.6903	−	6.17207i	0.371740	−	0.214624i	−0.302478	−	0.953156i	$-0.597814\pi$
$827$	10.6903	−	6.17207i	0.371740	−	0.214624i	0.674218	+	0.738532i	$0.264481\pi$
$828$		0			0
$829$		−	27.6662i		−	0.960887i	−0.877026	−	0.480444i	$-0.840476\pi$
$829$		−	27.6662i		−	0.960887i	0.877026	−	0.480444i	$-0.159524\pi$
$830$		0			0
$831$	4.47546	−	7.75172i	0.155252	−	0.268904i
$832$		0			0
$833$	−2.05441	+	3.55834i	−0.0711810	+	0.123289i
$834$		0			0
$835$		−	18.2095i		−	0.630164i
$836$		0			0
$837$		−	14.2322i		−	0.491936i
$838$		0			0
$839$	7.03223	−	12.1802i	0.242779	−	0.420506i	−0.718726	−	0.695294i	$-0.755274\pi$
$839$	7.03223	−	12.1802i	0.242779	−	0.420506i	0.961505	+	0.274788i	$0.0886076\pi$
$840$		0			0
$841$	28.7271	−	49.7568i	0.990590	−	1.71575i
$842$		0			0
$843$			4.00446i			0.137921i
$844$		0			0
$845$	−34.8432	+	20.1167i	−1.19864	+	0.692037i
$846$		0			0
$847$	−9.81915			−0.337390
$848$		0			0
$849$	0.570510	+	0.988153i	0.0195799	+	0.0339133i
$850$		0			0
$851$	−54.3542	+	31.3814i	−1.86324	+	1.07574i
$852$		0			0
$853$	7.50368	+	4.33225i	0.256921	+	0.148333i	0.622929	−	0.782278i	$-0.285942\pi$
$853$	7.50368	+	4.33225i	0.256921	+	0.148333i	−0.366008	+	0.930612i	$0.619276\pi$
$854$		0			0
$855$	44.5877	−	0.452889i	1.52487	−	0.0154885i
$856$		0			0
$857$	−6.95703	+	12.0499i	−0.237648	+	0.411618i	−0.960039	−	0.279867i	$-0.909710\pi$
$857$	−6.95703	+	12.0499i	−0.237648	+	0.411618i	0.722391	+	0.691485i	$0.243043\pi$
$858$		0			0
$859$	−12.5401	+	7.24001i	−0.427861	+	0.247026i	−0.698435	−	0.715673i	$-0.746120\pi$
$859$	−12.5401	+	7.24001i	−0.427861	+	0.247026i	0.270574	+	0.962699i	$0.412787\pi$
$860$		0			0
$861$	14.6643	−	8.46642i	0.499757	−	0.288535i
$862$		0			0
$863$	26.5065			0.902291			0.451145	−	0.892450i	$-0.351016\pi$
$863$	26.5065			0.902291			0.451145	+	0.892450i	$0.351016\pi$
$864$		0			0
$865$	31.9273	+	55.2997i	1.08556	+	1.88025i
$866$		0			0
$867$			4.33228i			0.147132i
$868$		0			0
$869$	9.05732	+	5.22925i	0.307249	+	0.177390i
$870$		0			0
$871$	−6.95785	+	12.0513i	−0.235758	+	0.408344i
$872$		0			0
$873$	−35.6726			−1.20733
$874$		0			0
$875$		−	42.3292i		−	1.43099i
$876$		0			0
$877$	15.4900	+	8.94317i	0.523061	+	0.301989i	0.738186	−	0.674597i	$-0.235683\pi$
$877$	15.4900	+	8.94317i	0.523061	+	0.301989i	−0.215125	+	0.976586i	$0.569016\pi$
$878$		0			0
$879$	−5.12971	+	8.88491i	−0.173021	+	0.299681i
$880$		0			0
$881$	−16.0705			−0.541427			−0.270714	−	0.962660i	$-0.587260\pi$
$881$	−16.0705			−0.541427			−0.270714	+	0.962660i	$0.587260\pi$
$882$		0			0
$883$	−14.4924	+	8.36718i	−0.487708	+	0.281578i	−0.723623	−	0.690196i	$-0.757525\pi$
$883$	−14.4924	+	8.36718i	−0.487708	+	0.281578i	0.235915	+	0.971774i	$0.424191\pi$
$884$		0			0
$885$		−	26.3889i		−	0.887052i
$886$		0			0
$887$	−23.8735	−	41.3502i	−0.801595	−	1.38840i	−0.918566	−	0.395268i	$-0.870652\pi$
$887$	−23.8735	−	41.3502i	−0.801595	−	1.38840i	0.116971	−	0.993135i	$-0.462681\pi$
$888$		0			0
$889$	−6.94572	−	12.0303i	−0.232952	−	0.403485i
$890$		0			0
$891$	−13.9916	−	8.07807i	−0.468737	−	0.270625i
$892$		0			0
$893$	8.67180	−	5.12480i	0.290191	−	0.171495i
$894$		0			0
$895$	33.0346	−	57.2176i	1.10422	−	1.91257i
$896$		0			0
$897$	4.03938	+	6.99641i	0.134871	+	0.233603i
$898$		0			0
$899$	35.3187	−	20.3913i	1.17794	−	0.680086i
$900$		0			0
$901$		−	4.91995i		−	0.163907i
$902$		0			0
$903$	−1.85271	−	3.20899i	−0.0616543	−	0.106788i
$904$		0			0
$905$	−1.58326			−0.0526293
$906$		0			0
$907$	21.5036	+	12.4151i	0.714016	+	0.412237i	0.812546	−	0.582897i	$-0.198081\pi$
$907$	21.5036	+	12.4151i	0.714016	+	0.412237i	−0.0985303	+	0.995134i	$0.531414\pi$
$908$		0			0
$909$	4.21419	+	2.43306i	0.139776	+	0.0806997i
$910$		0			0
$911$	12.9835			0.430161			0.215081	−	0.976596i	$-0.430999\pi$
$911$	12.9835			0.430161			0.215081	+	0.976596i	$0.430999\pi$
$912$		0			0
$913$	21.6363			0.716058
$914$		0			0
$915$	1.04478	+	0.603204i	0.0345394	+	0.0199413i
$916$		0			0
$917$	−29.1793	−	16.8467i	−0.963585	−	0.556326i
$918$		0			0
$919$	−49.4768			−1.63209			−0.816045	−	0.577988i	$-0.803838\pi$
$919$	−49.4768			−1.63209			−0.816045	+	0.577988i	$0.803838\pi$
$920$		0			0
$921$	8.43535	+	14.6105i	0.277954	+	0.481431i
$922$		0			0
$923$		−	11.4594i		−	0.377190i
$924$		0			0
$925$	−58.5629	+	33.8113i	−1.92554	+	1.11171i
$926$		0			0
$927$	13.2914	+	23.0214i	0.436548	+	0.756123i
$928$		0			0
$929$	−9.58486	+	16.6015i	−0.314469	+	0.544676i	−0.979324	−	0.202296i	$-0.935160\pi$
$929$	−9.58486	+	16.6015i	−0.314469	+	0.544676i	0.664856	+	0.746972i	$0.268493\pi$
$930$		0			0
$931$	−0.0592493	−	5.83321i	−0.00194182	−	0.191176i
$932$		0			0
$933$	−9.02894	−	5.21286i	−0.295594	−	0.170661i
$934$		0			0
$935$	15.4031	+	26.6789i	0.503735	+	0.872494i
$936$		0			0
$937$	−21.9199	−	37.9663i	−0.716091	−	1.24031i	−0.962537	−	0.271149i	$-0.912596\pi$
$937$	−21.9199	−	37.9663i	−0.716091	−	1.24031i	0.246447	−	0.969156i	$-0.420737\pi$
$938$		0			0
$939$		−	17.0698i		−	0.557050i
$940$		0			0
$941$	−25.4920	+	14.7178i	−0.831017	+	0.479788i	−0.854201	−	0.519944i	$-0.825953\pi$
$941$	−25.4920	+	14.7178i	−0.831017	+	0.479788i	0.0231840	+	0.999731i	$0.492620\pi$
$942$		0			0
$943$	−111.409			−3.62796
$944$		0			0
$945$	−14.7749	+	25.5909i	−0.480627	+	0.832471i
$946$		0			0
$947$	−1.17630	−	0.679140i	−0.0382248	−	0.0220691i	0.480766	−	0.876849i	$-0.340359\pi$
$947$	−1.17630	−	0.679140i	−0.0382248	−	0.0220691i	−0.518991	+	0.854780i	$0.673692\pi$
$948$		0			0
$949$			5.70513i			0.185196i
$950$		0			0
$951$	3.65327			0.118466
$952$		0			0
$953$	19.0604	−	33.0136i	0.617428	−	1.06942i	−0.372525	−	0.928022i	$-0.621508\pi$
$953$	19.0604	−	33.0136i	0.617428	−	1.06942i	0.989953	−	0.141395i	$-0.0451587\pi$
$954$		0			0
$955$	−82.4567	−	47.6064i	−2.66824	−	1.54051i
$956$		0			0
$957$			13.9434i			0.450725i
$958$		0			0
$959$	−1.46607	−	2.53930i	−0.0473418	−	0.0819984i
$960$		0			0
$961$	−11.7619			−0.379417
$962$		0			0
$963$	−30.6890	+	17.7183i	−0.988938	+	0.570964i
$964$		0			0
$965$	−31.5413	+	18.2104i	−1.01535	+	0.586213i
$966$		0			0
$967$	9.12156	−	15.7990i	0.293330	−	0.508062i	−0.681265	−	0.732037i	$-0.738570\pi$
$967$	9.12156	−	15.7990i	0.293330	−	0.508062i	0.974595	+	0.223975i	$0.0719033\pi$
$968$		0			0
$969$	3.89451	+	6.59000i	0.125110	+	0.211701i
$970$		0			0
$971$	33.6284	+	19.4153i	1.07919	+	0.623068i	0.930677	−	0.365843i	$-0.119219\pi$
$971$	33.6284	+	19.4153i	1.07919	+	0.623068i	0.148509	+	0.988911i	$0.452553\pi$
$972$		0			0
$973$	−12.3913	+	7.15411i	−0.397246	+	0.229350i
$974$		0			0
$975$	4.35215	+	7.53815i	0.139380	+	0.241414i
$976$		0			0
$977$	−4.02782			−0.128861			−0.0644306	−	0.997922i	$-0.520523\pi$
$977$	−4.02782			−0.128861			−0.0644306	+	0.997922i	$0.520523\pi$
$978$		0			0
$979$	21.9373	−	12.6655i	0.701120	−	0.404792i
$980$		0			0
$981$		−	20.2065i		−	0.645143i
$982$		0			0
$983$	21.2147	−	36.7449i	0.676643	−	1.17198i	−0.299342	−	0.954146i	$-0.596767\pi$
$983$	21.2147	−	36.7449i	0.676643	−	1.17198i	0.975986	−	0.217835i	$-0.0698995\pi$
$984$		0			0
$985$	11.1977	−	19.3951i	0.356790	−	0.617978i
$986$		0			0
$987$			3.14516i			0.100112i
$988$		0			0
$989$			24.3796i			0.775225i
$990$		0			0
$991$	29.4383	−	50.9886i	0.935138	−	1.61971i	0.160751	−	0.986995i	$-0.448608\pi$
$991$	29.4383	−	50.9886i	0.935138	−	1.61971i	0.774387	−	0.632712i	$-0.218058\pi$
$992$		0			0
$993$	1.77950	−	3.08218i	0.0564707	−	0.0978101i
$994$		0			0
$995$		−	64.2629i		−	2.03727i
$996$		0			0
$997$	−42.1664	+	24.3448i	−1.33542	+	0.771007i	−0.986125	−	0.166005i	$-0.946913\pi$
$997$	−42.1664	+	24.3448i	−1.33542	+	0.771007i	−0.349298	+	0.937012i	$0.613580\pi$
$998$		0			0
$999$	22.7426			0.719544

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1216.2.t.d.353.7	yes	24
4.3	odd	2	inner	1216.2.t.d.353.5	✓	24
8.3	odd	2		1216.2.t.e.353.7	yes	24
8.5	even	2		1216.2.t.e.353.5	yes	24
19.7	even	3		1216.2.t.e.1185.5	yes	24
76.7	odd	6		1216.2.t.e.1185.7	yes	24
152.45	even	6	inner	1216.2.t.d.1185.7	yes	24
152.83	odd	6	inner	1216.2.t.d.1185.5	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1216.2.t.d.353.5	✓	24	4.3	odd	2	inner
1216.2.t.d.353.7	yes	24	1.1	even	1	trivial
1216.2.t.d.1185.5	yes	24	152.83	odd	6	inner
1216.2.t.d.1185.7	yes	24	152.45	even	6	inner
1216.2.t.e.353.5	yes	24	8.5	even	2
1216.2.t.e.353.7	yes	24	8.3	odd	2
1216.2.t.e.1185.5	yes	24	19.7	even	3
1216.2.t.e.1185.7	yes	24	76.7	odd	6

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:	\( N \)	\(=\)	\( 1216 = 2^{6} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1216.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.495361 + 0.285997i) q^{3} +(3.31453 + 1.91364i) q^{5} -2.37943 q^{7} +(-1.33641 - 2.31473i) q^{9} +O(q^{10})\)	\(q+(0.495361 + 0.285997i) q^{3} +(3.31453 + 1.91364i) q^{5} -2.37943 q^{7} +(-1.33641 - 2.31473i) q^{9} +2.62170i q^{11} +(1.36594 - 0.788626i) q^{13} +(1.09459 + 1.89589i) q^{15} +(1.53509 - 2.65885i) q^{17} +(0.0442721 + 4.35867i) q^{19} +(-1.17868 - 0.680510i) q^{21} +(4.47737 + 7.75503i) q^{23} +(4.82405 + 8.35551i) q^{25} -3.24482i q^{27} +(8.05237 - 4.64904i) q^{29} +4.38612 q^{31} +(-0.749798 + 1.29869i) q^{33} +(-7.88669 - 4.55338i) q^{35} +7.00890i q^{37} +0.902177 q^{39} +(-6.22065 + 10.7745i) q^{41} +(2.35778 + 1.36127i) q^{43} -10.2297i q^{45} +(-1.15544 - 2.00129i) q^{47} -1.33830 q^{49} +(1.52085 - 0.878061i) q^{51} +(1.38780 - 0.801249i) q^{53} +(-5.01700 + 8.68970i) q^{55} +(-1.22464 + 2.17178i) q^{57} +(-10.4393 - 6.02711i) q^{59} +(0.477247 - 0.275539i) q^{61} +(3.17990 + 5.50775i) q^{63} +6.03659 q^{65} +(-7.64072 + 4.41137i) q^{67} +5.12205i q^{69} +(3.63270 - 6.29203i) q^{71} +(-1.80857 + 3.13253i) q^{73} +5.51865i q^{75} -6.23817i q^{77} +(1.99460 - 3.45475i) q^{79} +(-3.08123 + 5.33684i) q^{81} -8.25278i q^{83} +(10.1762 - 5.87522i) q^{85} +5.31844 q^{87} +(-4.83103 - 8.36758i) q^{89} +(-3.25016 + 1.87648i) q^{91} +(2.17271 + 1.25442i) q^{93} +(-8.19420 + 14.5317i) q^{95} +(6.67320 - 11.5583i) q^{97} +(6.06854 - 3.50367i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 6 q^{5} + 8 q^{9}+O(q^{10}) \) 24 * q - 6 * q^5 + 8 * q^9	\( 24 q - 6 q^{5} + 8 q^{9} + 30 q^{13} + 6 q^{17} + 24 q^{21} + 6 q^{25} + 42 q^{29} - 14 q^{33} - 24 q^{41} + 24 q^{49} - 18 q^{53} - 42 q^{57} + 18 q^{61} - 20 q^{65} - 16 q^{73} + 52 q^{81} - 78 q^{85} + 14 q^{89} + 60 q^{93} - 4 q^{97}+O(q^{100}) \) 24 * q - 6 * q^5 + 8 * q^9 + 30 * q^13 + 6 * q^17 + 24 * q^21 + 6 * q^25 + 42 * q^29 - 14 * q^33 - 24 * q^41 + 24 * q^49 - 18 * q^53 - 42 * q^57 + 18 * q^61 - 20 * q^65 - 16 * q^73 + 52 * q^81 - 78 * q^85 + 14 * q^89 + 60 * q^93 - 4 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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