LMFDB - Embedded newform 504.2.t.c.457.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(193,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2, 4]))

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

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

chi := DirichletCharacter("504.193");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.t (of order $3$, 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:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$22$
Relative dimension:	$11$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			457.5
Character	$\chi$	$=$	504.457
Dual form			504.2.t.c.193.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.816621 - 1.52746i) q^{3} -1.78355 q^{5} +(1.90167 + 1.83948i) q^{7} +(-1.66626 + 2.49471i) q^{9} +O(q^{10})$	\(q+(-0.816621 - 1.52746i) q^{3} -1.78355 q^{5} +(1.90167 + 1.83948i) q^{7} +(-1.66626 + 2.49471i) q^{9} -5.61411 q^{11} +(3.14009 + 5.43879i) q^{13} +(1.45648 + 2.72430i) q^{15} +(0.646279 + 1.11939i) q^{17} +(0.559062 - 0.968324i) q^{19} +(1.25678 - 4.40687i) q^{21} +7.61715 q^{23} -1.81896 q^{25} +(5.17127 + 0.507916i) q^{27} +(-1.57496 + 2.72791i) q^{29} +(-0.501553 + 0.868716i) q^{31} +(4.58460 + 8.57533i) q^{33} +(-3.39171 - 3.28079i) q^{35} +(-5.96542 + 10.3324i) q^{37} +(5.74327 - 9.23778i) q^{39} +(4.14160 + 7.17347i) q^{41} +(2.34804 - 4.06693i) q^{43} +(2.97186 - 4.44943i) q^{45} +(0.972001 + 1.68356i) q^{47} +(0.232662 + 6.99613i) q^{49} +(1.18205 - 1.90128i) q^{51} +(-4.45992 - 7.72481i) q^{53} +10.0130 q^{55} +(-1.93562 - 0.0631911i) q^{57} +(-4.19339 + 7.26317i) q^{59} +(-2.41288 - 4.17923i) q^{61} +(-7.75763 + 1.67905i) q^{63} +(-5.60050 - 9.70034i) q^{65} +(1.27814 - 2.21380i) q^{67} +(-6.22032 - 11.6349i) q^{69} -8.86178 q^{71} +(5.67598 + 9.83109i) q^{73} +(1.48540 + 2.77838i) q^{75} +(-10.6762 - 10.3270i) q^{77} +(-6.72883 - 11.6547i) q^{79} +(-3.44714 - 8.31368i) q^{81} +(-1.60203 + 2.77479i) q^{83} +(-1.15267 - 1.99648i) q^{85} +(5.45291 + 0.178018i) q^{87} +(-0.404646 + 0.700867i) q^{89} +(-4.03312 + 16.1189i) q^{91} +(1.73651 + 0.0566909i) q^{93} +(-0.997114 + 1.72705i) q^{95} +(1.10781 - 1.91879i) q^{97} +(9.35458 - 14.0056i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - 2 q^{3} - 2 q^{5} - q^{7}+O(q^{10}) $ 22 * q - 2 * q^3 - 2 * q^5 - q^7	$ 22 q - 2 q^{3} - 2 q^{5} - q^{7} - 6 q^{11} + 7 q^{13} - q^{15} - q^{17} + 13 q^{19} + 33 q^{21} + 44 q^{25} - 2 q^{27} - 7 q^{29} + 6 q^{31} + 9 q^{33} + 2 q^{35} + 6 q^{37} - 4 q^{39} + 4 q^{41} + 2 q^{43} + 17 q^{47} + 29 q^{49} - 25 q^{51} + q^{53} + 2 q^{55} - 21 q^{57} - 21 q^{59} + 31 q^{61} - 7 q^{63} - 3 q^{65} - 26 q^{67} - 40 q^{69} - 32 q^{71} + 17 q^{73} - 16 q^{75} - 4 q^{77} - 16 q^{79} - 36 q^{83} + 28 q^{85} + 7 q^{87} - 2 q^{89} + 15 q^{91} - 56 q^{93} - 24 q^{95} + 19 q^{97} + 24 q^{99}+O(q^{100}) $ 22 * q - 2 * q^3 - 2 * q^5 - q^7 - 6 * q^11 + 7 * q^13 - q^15 - q^17 + 13 * q^19 + 33 * q^21 + 44 * q^25 - 2 * q^27 - 7 * q^29 + 6 * q^31 + 9 * q^33 + 2 * q^35 + 6 * q^37 - 4 * q^39 + 4 * q^41 + 2 * q^43 + 17 * q^47 + 29 * q^49 - 25 * q^51 + q^53 + 2 * q^55 - 21 * q^57 - 21 * q^59 + 31 * q^61 - 7 * q^63 - 3 * q^65 - 26 * q^67 - 40 * q^69 - 32 * q^71 + 17 * q^73 - 16 * q^75 - 4 * q^77 - 16 * q^79 - 36 * q^83 + 28 * q^85 + 7 * q^87 - 2 * q^89 + 15 * q^91 - 56 * q^93 - 24 * q^95 + 19 * q^97 + 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

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
$3$	−0.816621	−	1.52746i	−0.471476	−	0.881879i
$3$	−0.816621	−	1.52746i	−0.471476	−	0.881879i
$4$		0			0
$5$	−1.78355			−0.797627			−0.398814	−	0.917032i	$-0.630578\pi$
$5$	−1.78355			−0.797627			−0.398814	+	0.917032i	$0.630578\pi$
$6$		0			0
$7$	1.90167	+	1.83948i	0.718762	+	0.695256i
$7$	1.90167	+	1.83948i	0.718762	+	0.695256i
$8$		0			0
$9$	−1.66626	+	2.49471i	−0.555421	+	0.831570i
$10$		0			0
$11$	−5.61411			−1.69272			−0.846359	−	0.532612i	$-0.821210\pi$
$11$	−5.61411			−1.69272			−0.846359	+	0.532612i	$0.821210\pi$
$12$		0			0
$13$	3.14009	+	5.43879i	0.870903	+	1.50845i	0.861064	+	0.508497i	$0.169799\pi$
$13$	3.14009	+	5.43879i	0.870903	+	1.50845i	0.00983976	+	0.999952i	$0.496868\pi$
$14$		0			0
$15$	1.45648	+	2.72430i	0.376062	+	0.703410i
$16$		0			0
$17$	0.646279	+	1.11939i	0.156746	+	0.271491i	0.933693	−	0.358074i	$-0.116566\pi$
$17$	0.646279	+	1.11939i	0.156746	+	0.271491i	−0.776948	+	0.629565i	$0.783233\pi$
$18$		0			0
$19$	0.559062	−	0.968324i	0.128258	−	0.222149i	−0.794744	−	0.606945i	$-0.792395\pi$
$19$	0.559062	−	0.968324i	0.128258	−	0.222149i	0.923002	+	0.384796i	$0.125728\pi$
$20$		0			0
$21$	1.25678	−	4.40687i	0.274253	−	0.961658i
$22$		0			0
$23$	7.61715			1.58828			0.794142	−	0.607732i	$-0.207920\pi$
$23$	7.61715			1.58828			0.794142	+	0.607732i	$0.207920\pi$
$24$		0			0
$25$	−1.81896			−0.363791
$26$		0			0
$27$	5.17127	+	0.507916i	0.995211	+	0.0977485i
$28$		0			0
$29$	−1.57496	+	2.72791i	−0.292462	+	0.506560i	−0.974391	−	0.224859i	$-0.927808\pi$
$29$	−1.57496	+	2.72791i	−0.292462	+	0.506560i	0.681929	+	0.731418i	$0.261141\pi$
$30$		0			0
$31$	−0.501553	+	0.868716i	−0.0900816	+	0.156026i	−0.907545	−	0.419954i	$-0.862046\pi$
$31$	−0.501553	+	0.868716i	−0.0900816	+	0.156026i	0.817464	+	0.575980i	$0.195379\pi$
$32$		0			0
$33$	4.58460	+	8.57533i	0.798076	+	1.49277i
$34$		0			0
$35$	−3.39171	−	3.28079i	−0.573304	−	0.554555i
$36$		0			0
$37$	−5.96542	+	10.3324i	−0.980708	+	1.69864i	−0.321067	+	0.947057i	$0.604041\pi$
$37$	−5.96542	+	10.3324i	−0.980708	+	1.69864i	−0.659642	+	0.751580i	$0.729292\pi$
$38$		0			0
$39$	5.74327	−	9.23778i	0.919659	−	1.47923i
$40$		0			0
$41$	4.14160	+	7.17347i	0.646810	+	1.12031i	0.983880	+	0.178828i	$0.0572306\pi$
$41$	4.14160	+	7.17347i	0.646810	+	1.12031i	−0.337071	+	0.941479i	$0.609436\pi$
$42$		0			0
$43$	2.34804	−	4.06693i	0.358073	−	0.620200i	−0.629566	−	0.776947i	$-0.716767\pi$
$43$	2.34804	−	4.06693i	0.358073	−	0.620200i	0.987639	+	0.156747i	$0.0501006\pi$
$44$		0			0
$45$	2.97186	−	4.44943i	0.443018	−	0.663282i
$46$		0			0
$47$	0.972001	+	1.68356i	0.141781	+	0.245572i	0.928167	−	0.372163i	$-0.121384\pi$
$47$	0.972001	+	1.68356i	0.141781	+	0.245572i	−0.786386	+	0.617735i	$0.788050\pi$
$48$		0			0
$49$	0.232662	+	6.99613i	0.0332374	+	0.999447i
$50$		0			0
$51$	1.18205	−	1.90128i	0.165521	−	0.266232i
$52$		0			0
$53$	−4.45992	−	7.72481i	−0.612617	−	1.06108i	−0.990798	−	0.135352i	$-0.956783\pi$
$53$	−4.45992	−	7.72481i	−0.612617	−	1.06108i	0.378180	−	0.925732i	$-0.376550\pi$
$54$		0			0
$55$	10.0130			1.35016
$56$		0			0
$57$	−1.93562	−	0.0631911i	−0.256379	−	0.00836987i
$58$		0			0
$59$	−4.19339	+	7.26317i	−0.545933	+	0.945584i	0.452614	+	0.891706i	$0.350491\pi$
$59$	−4.19339	+	7.26317i	−0.545933	+	0.945584i	−0.998548	+	0.0538778i	$0.982842\pi$
$60$		0			0
$61$	−2.41288	−	4.17923i	−0.308937	−	0.535095i	0.669193	−	0.743089i	$-0.266640\pi$
$61$	−2.41288	−	4.17923i	−0.308937	−	0.535095i	−0.978130	+	0.207994i	$0.933307\pi$
$62$		0			0
$63$	−7.75763	+	1.67905i	−0.977369	+	0.211541i
$64$		0			0
$65$	−5.60050	−	9.70034i	−0.694656	−	1.20318i
$66$		0			0
$67$	1.27814	−	2.21380i	0.156150	−	0.270459i	−0.777327	−	0.629096i	$-0.783425\pi$
$67$	1.27814	−	2.21380i	0.156150	−	0.270459i	0.933477	+	0.358637i	$0.116758\pi$
$68$		0			0
$69$	−6.22032	−	11.6349i	−0.748838	−	1.40067i
$70$		0			0
$71$	−8.86178			−1.05170			−0.525850	−	0.850577i	$-0.676253\pi$
$71$	−8.86178			−1.05170			−0.525850	+	0.850577i	$0.676253\pi$
$72$		0			0
$73$	5.67598	+	9.83109i	0.664323	+	1.15064i	0.979468	+	0.201598i	$0.0646135\pi$
$73$	5.67598	+	9.83109i	0.664323	+	1.15064i	−0.315145	+	0.949044i	$0.602053\pi$
$74$		0			0
$75$	1.48540	+	2.77838i	0.171519	+	0.320820i
$76$		0			0
$77$	−10.6762	−	10.3270i	−1.21666	−	1.17687i
$78$		0			0
$79$	−6.72883	−	11.6547i	−0.757052	−	1.31125i	−0.944348	−	0.328949i	$-0.893305\pi$
$79$	−6.72883	−	11.6547i	−0.757052	−	1.31125i	0.187295	−	0.982304i	$-0.440028\pi$
$80$		0			0
$81$	−3.44714	−	8.31368i	−0.383016	−	0.923742i
$82$		0			0
$83$	−1.60203	+	2.77479i	−0.175845	+	0.304573i	−0.940453	−	0.339922i	$-0.889599\pi$
$83$	−1.60203	+	2.77479i	−0.175845	+	0.304573i	0.764608	+	0.644495i	$0.222933\pi$
$84$		0			0
$85$	−1.15267	−	1.99648i	−0.125025	−	0.216549i
$86$		0			0
$87$	5.45291	+	0.178018i	0.584613	+	0.0190856i
$88$		0			0
$89$	−0.404646	+	0.700867i	−0.0428924	+	0.0742917i	−0.886675	−	0.462394i	$-0.846991\pi$
$89$	−0.404646	+	0.700867i	−0.0428924	+	0.0742917i	0.843782	+	0.536686i	$0.180324\pi$
$90$		0			0
$91$	−4.03312	+	16.1189i	−0.422786	+	1.68972i
$92$		0			0
$93$	1.73651	+	0.0566909i	0.180067	+	0.00587857i
$94$		0			0
$95$	−0.997114	+	1.72705i	−0.102302	+	0.177192i
$96$		0			0
$97$	1.10781	−	1.91879i	0.112481	−	0.194823i	−0.804289	−	0.594238i	$-0.797454\pi$
$97$	1.10781	−	1.91879i	0.112481	−	0.194823i	0.916770	+	0.399415i	$0.130787\pi$
$98$		0			0
$99$	9.35458	−	14.0056i	0.940171	−	1.40761i
$100$		0			0
$101$	9.40267			0.935601			0.467801	−	0.883834i	$-0.345047\pi$
$101$	9.40267			0.935601			0.467801	+	0.883834i	$0.345047\pi$
$102$		0			0
$103$	−3.52698			−0.347524			−0.173762	−	0.984788i	$-0.555592\pi$
$103$	−3.52698			−0.347524			−0.173762	+	0.984788i	$0.555592\pi$
$104$		0			0
$105$	−2.24153	+	7.85986i	−0.218751	+	0.767044i
$106$		0			0
$107$	−3.39276	+	5.87644i	−0.327991	+	0.568097i	−0.982113	−	0.188292i	$-0.939705\pi$
$107$	−3.39276	+	5.87644i	−0.327991	+	0.568097i	0.654122	+	0.756389i	$0.273038\pi$
$108$		0			0
$109$	0.681848	+	1.18099i	0.0653092	+	0.113119i	0.896831	−	0.442373i	$-0.145863\pi$
$109$	0.681848	+	1.18099i	0.0653092	+	0.113119i	−0.831522	+	0.555492i	$0.812530\pi$
$110$		0			0
$111$	20.6538	+	0.674275i	1.96037	+	0.0639993i
$112$		0			0
$113$	−2.76458	−	4.78840i	−0.260070	−	0.450455i	0.706190	−	0.708022i	$-0.250412\pi$
$113$	−2.76458	−	4.78840i	−0.260070	−	0.450455i	−0.966260	+	0.257568i	$0.917079\pi$
$114$		0			0
$115$	−13.5855			−1.26686
$116$		0			0
$117$	−18.8004	−	1.22885i	−1.73810	−	0.113607i
$118$		0			0
$119$	−0.830080	+	3.31752i	−0.0760933	+	0.304116i
$120$		0			0
$121$	20.5183			1.86530
$122$		0			0
$123$	7.57506	−	12.1841i	0.683020	−	1.09861i
$124$		0			0
$125$	12.1619			1.08780
$126$		0			0
$127$	−12.8209			−1.13767			−0.568837	−	0.822450i	$-0.692606\pi$
$127$	−12.8209			−1.13767			−0.568837	+	0.822450i	$0.692606\pi$
$128$		0			0
$129$	−8.12952	−	0.265401i	−0.715764	−	0.0233672i
$130$		0			0
$131$	−5.81910			−0.508417			−0.254208	−	0.967149i	$-0.581815\pi$
$131$	−5.81910			−0.508417			−0.254208	+	0.967149i	$0.581815\pi$
$132$		0			0
$133$	2.84436	−	0.813047i	0.246637	−	0.0705001i
$134$		0			0
$135$	−9.22321	−	0.905892i	−0.793807	−	0.0779668i
$136$		0			0
$137$	−15.3409			−1.31066			−0.655332	−	0.755341i	$-0.727471\pi$
$137$	−15.3409			−1.31066			−0.655332	+	0.755341i	$0.727471\pi$
$138$		0			0
$139$	−6.05803	−	10.4928i	−0.513835	−	0.889988i	−0.999871	−	0.0160496i	$-0.994891\pi$
$139$	−6.05803	−	10.4928i	−0.513835	−	0.889988i	0.486036	−	0.873939i	$-0.338442\pi$
$140$		0			0
$141$	1.77781	−	2.85952i	0.149718	−	0.240815i
$142$		0			0
$143$	−17.6288	−	30.5340i	−1.47419	−	2.55338i
$144$		0			0
$145$	2.80901	−	4.86535i	0.233276	−	0.404046i
$146$		0			0
$147$	10.4963	−	6.06857i	0.865721	−	0.500527i
$148$		0			0
$149$	4.73699			0.388069			0.194035	−	0.980995i	$-0.437843\pi$
$149$	4.73699			0.388069			0.194035	+	0.980995i	$0.437843\pi$
$150$		0			0
$151$	24.3690			1.98312			0.991559	−	0.129657i	$-0.0413876\pi$
$151$	24.3690			1.98312			0.991559	+	0.129657i	$0.0413876\pi$
$152$		0			0
$153$	−3.86942	−	0.252916i	−0.312824	−	0.0204470i
$154$		0			0
$155$	0.894545	−	1.54940i	0.0718516	−	0.124451i
$156$		0			0
$157$	3.15229	−	5.45993i	0.251580	−	0.435750i	−0.712381	−	0.701793i	$-0.752383\pi$
$157$	3.15229	−	5.45993i	0.251580	−	0.435750i	0.963961	+	0.266043i	$0.0857165\pi$
$158$		0			0
$159$	−8.15727	+	13.1206i	−0.646913	+	1.04053i
$160$		0			0
$161$	14.4853	+	14.0116i	1.14160	+	1.10426i
$162$		0			0
$163$	0.350678	−	0.607392i	0.0274672	−	0.0475746i	−0.851965	−	0.523599i	$-0.824589\pi$
$163$	0.350678	−	0.607392i	0.0274672	−	0.0475746i	0.879432	+	0.476024i	$0.157922\pi$
$164$		0			0
$165$	−8.17686	−	15.2945i	−0.636567	−	1.19068i
$166$		0			0
$167$	3.53822	+	6.12839i	0.273796	+	0.474229i	0.969831	−	0.243780i	$-0.0783873\pi$
$167$	3.53822	+	6.12839i	0.273796	+	0.474229i	−0.696035	+	0.718008i	$0.745054\pi$
$168$		0			0
$169$	−13.2203	+	22.8982i	−1.01695	+	1.76140i
$170$		0			0
$171$	1.48414	+	3.00818i	0.113495	+	0.230041i
$172$		0			0
$173$	−3.31767	−	5.74638i	−0.252238	−	0.436889i	0.711904	−	0.702277i	$-0.247833\pi$
$173$	−3.31767	−	5.74638i	−0.252238	−	0.436889i	−0.964142	+	0.265388i	$0.914500\pi$
$174$		0			0
$175$	−3.45904	−	3.34592i	−0.261479	−	0.252928i
$176$		0			0
$177$	14.5186	+	0.473982i	1.09129	+	0.0356267i
$178$		0			0
$179$	5.63527	+	9.76057i	0.421200	+	0.729539i	0.996057	−	0.0887145i	$-0.0282759\pi$
$179$	5.63527	+	9.76057i	0.421200	+	0.729539i	−0.574858	+	0.818253i	$0.694943\pi$
$180$		0			0
$181$	21.1800			1.57430			0.787149	−	0.616762i	$-0.211556\pi$
$181$	21.1800			1.57430			0.787149	+	0.616762i	$0.211556\pi$
$182$		0			0
$183$	−4.41319	+	7.09841i	−0.326233	+	0.524730i
$184$		0			0
$185$	10.6396	−	18.4283i	0.782240	−	1.35488i
$186$		0			0
$187$	−3.62828	−	6.28437i	−0.265326	−	0.459559i
$188$		0			0
$189$	8.89972	+	10.4783i	0.647360	+	0.762185i
$190$		0			0
$191$	4.72044	+	8.17604i	0.341559	+	0.591598i	0.984722	−	0.174131i	$-0.0557117\pi$
$191$	4.72044	+	8.17604i	0.341559	+	0.591598i	−0.643163	+	0.765729i	$0.722378\pi$
$192$		0			0
$193$	3.14021	−	5.43900i	0.226037	−	0.391508i	−0.730593	−	0.682813i	$-0.760756\pi$
$193$	3.14021	−	5.43900i	0.226037	−	0.391508i	0.956630	+	0.291305i	$0.0940896\pi$
$194$		0			0
$195$	−10.2434	+	16.4760i	−0.733545	+	1.17987i
$196$		0			0
$197$	15.4780			1.10276			0.551382	−	0.834253i	$-0.314101\pi$
$197$	15.4780			1.10276			0.551382	+	0.834253i	$0.314101\pi$
$198$		0			0
$199$	2.19477	+	3.80145i	0.155583	+	0.269478i	0.933271	−	0.359173i	$-0.116941\pi$
$199$	2.19477	+	3.80145i	0.155583	+	0.269478i	−0.777688	+	0.628650i	$0.783608\pi$
$200$		0			0
$201$	−4.42525	−	0.144469i	−0.312133	−	0.0101901i
$202$		0			0
$203$	−8.01296	+	2.29047i	−0.562400	+	0.160759i
$204$		0			0
$205$	−7.38675	−	12.7942i	−0.515913	−	0.893587i
$206$		0			0
$207$	−12.6922	+	19.0026i	−0.882166	+	1.32077i
$208$		0			0
$209$	−3.13864	+	5.43628i	−0.217104	+	0.376035i
$210$		0			0
$211$	7.93101	+	13.7369i	0.545993	+	0.945688i	0.998544	+	0.0539495i	$0.0171810\pi$
$211$	7.93101	+	13.7369i	0.545993	+	0.945688i	−0.452550	+	0.891739i	$0.649486\pi$
$212$		0			0
$213$	7.23671	+	13.5360i	0.495851	+	0.927472i
$214$		0			0
$215$	−4.18784	+	7.25356i	−0.285609	+	0.494689i
$216$		0			0
$217$	−2.55177	+	0.729412i	−0.173225	+	0.0495157i
$218$		0			0
$219$	10.3815	−	16.6981i	0.701514	−	1.12835i
$220$		0			0
$221$	−4.05874	+	7.02995i	−0.273021	+	0.472886i
$222$		0			0
$223$	6.99253	−	12.1114i	0.468254	−	0.811040i	−0.531088	−	0.847317i	$-0.678216\pi$
$223$	6.99253	−	12.1114i	0.468254	−	0.811040i	0.999342	+	0.0362769i	$0.0115498\pi$
$224$		0			0
$225$	3.03086	−	4.53776i	0.202057	−	0.302518i
$226$		0			0
$227$	10.7673			0.714650			0.357325	−	0.933980i	$-0.383689\pi$
$227$	10.7673			0.714650			0.357325	+	0.933980i	$0.383689\pi$
$228$		0			0
$229$	−1.61003			−0.106394			−0.0531969	−	0.998584i	$-0.516941\pi$
$229$	−1.61003			−0.106394			−0.0531969	+	0.998584i	$0.516941\pi$
$230$		0			0
$231$	−7.05573	+	24.7407i	−0.464233	+	1.62782i
$232$		0			0
$233$	−0.510606	+	0.884395i	−0.0334509	+	0.0579387i	−0.882266	−	0.470751i	$-0.843983\pi$
$233$	−0.510606	+	0.884395i	−0.0334509	+	0.0579387i	0.848815	+	0.528690i	$0.177316\pi$
$234$		0			0
$235$	−1.73361	−	3.00270i	−0.113088	−	0.195875i
$236$		0			0
$237$	−12.3071	+	19.7955i	−0.799434	+	1.28585i
$238$		0			0
$239$	−6.96428	−	12.0625i	−0.450482	−	0.780258i	0.547934	−	0.836522i	$-0.315414\pi$
$239$	−6.96428	−	12.0625i	−0.450482	−	0.780258i	−0.998416	+	0.0562640i	$0.982081\pi$
$240$		0			0
$241$	−14.5758			−0.938908			−0.469454	−	0.882957i	$-0.655549\pi$
$241$	−14.5758			−0.938908			−0.469454	+	0.882957i	$0.655549\pi$
$242$		0			0
$243$	−9.88379	+	12.0545i	−0.634045	+	0.773296i
$244$		0			0
$245$	−0.414964	−	12.4779i	−0.0265111	−	0.797186i
$246$		0			0
$247$	7.02201			0.446800
$248$		0			0
$249$	5.54663	+	0.181078i	0.351503	+	0.0114754i
$250$		0			0
$251$	18.0287			1.13796			0.568981	−	0.822350i	$-0.307338\pi$
$251$	18.0287			1.13796			0.568981	+	0.822350i	$0.307338\pi$
$252$		0			0
$253$	−42.7635			−2.68852
$254$		0			0
$255$	−2.10825	+	3.39102i	−0.132024	+	0.212354i
$256$		0			0
$257$	26.9266			1.67964			0.839818	−	0.542869i	$-0.182662\pi$
$257$	26.9266			1.67964			0.839818	+	0.542869i	$0.182662\pi$
$258$		0			0
$259$	−30.3504	+	8.67554i	−1.88588	+	0.539072i
$260$		0			0
$261$	−4.18104	−	8.47447i	−0.258800	−	0.524556i
$262$		0			0
$263$	1.53884			0.0948888			0.0474444	−	0.998874i	$-0.484892\pi$
$263$	1.53884			0.0948888			0.0474444	+	0.998874i	$0.484892\pi$
$264$		0			0
$265$	7.95448	+	13.7776i	0.488640	+	0.846349i
$266$		0			0
$267$	1.40099	+	0.0457374i	0.0857390	+	0.00279908i
$268$		0			0
$269$	3.26461	+	5.65446i	0.199047	+	0.344759i	0.948220	−	0.317616i	$-0.102882\pi$
$269$	3.26461	+	5.65446i	0.199047	+	0.344759i	−0.749173	+	0.662374i	$0.769549\pi$
$270$		0			0
$271$	−5.64494	+	9.77733i	−0.342906	+	0.593930i	−0.984971	−	0.172720i	$-0.944745\pi$
$271$	−5.64494	+	9.77733i	−0.342906	+	0.593930i	0.642065	+	0.766650i	$0.278078\pi$
$272$		0			0
$273$	27.9144	−	7.00257i	1.68946	−	0.423815i
$274$		0			0
$275$	10.2118			0.615796
$276$		0			0
$277$	1.81188			0.108865			0.0544325	−	0.998517i	$-0.482665\pi$
$277$	1.81188			0.108865			0.0544325	+	0.998517i	$0.482665\pi$
$278$		0			0
$279$	−1.33147	−	2.69874i	−0.0797133	−	0.161569i
$280$		0			0
$281$	−2.98798	+	5.17533i	−0.178248	+	0.308734i	−0.941280	−	0.337626i	$-0.890376\pi$
$281$	−2.98798	+	5.17533i	−0.178248	+	0.308734i	0.763033	+	0.646360i	$0.223710\pi$
$282$		0			0
$283$	9.99760	−	17.3163i	0.594295	−	1.02935i	−0.399350	−	0.916798i	$-0.630764\pi$
$283$	9.99760	−	17.3163i	0.594295	−	1.02935i	0.993646	−	0.112552i	$-0.0359024\pi$
$284$		0			0
$285$	3.45227	+	0.112704i	0.204495	+	0.00667604i
$286$		0			0
$287$	−5.31947	+	21.2599i	−0.313998	+	1.25493i
$288$		0			0
$289$	7.66465	−	13.2756i	0.450862	−	0.780915i
$290$		0			0
$291$	−3.83553	−	0.125217i	−0.224843	−	0.00734033i
$292$		0			0
$293$	−4.95166	−	8.57652i	−0.289279	−	0.501046i	0.684359	−	0.729145i	$-0.260082\pi$
$293$	−4.95166	−	8.57652i	−0.289279	−	0.501046i	−0.973638	+	0.228099i	$0.926749\pi$
$294$		0			0
$295$	7.47912	−	12.9542i	0.435451	−	0.754224i
$296$		0			0
$297$	−29.0321	−	2.85150i	−1.68461	−	0.165461i
$298$		0			0
$299$	23.9185	+	41.4281i	1.38324	+	2.39585i
$300$		0			0
$301$	11.9462	−	3.41477i	0.688567	−	0.196824i
$302$		0			0
$303$	−7.67842	−	14.3622i	−0.441114	−	0.825087i
$304$		0			0
$305$	4.30348	+	7.45385i	0.246417	+	0.426806i
$306$		0			0
$307$	−23.7122			−1.35332			−0.676662	−	0.736293i	$-0.736574\pi$
$307$	−23.7122			−1.35332			−0.676662	+	0.736293i	$0.736574\pi$
$308$		0			0
$309$	2.88021	+	5.38732i	0.163849	+	0.306474i
$310$		0			0
$311$	−10.1724	+	17.6192i	−0.576826	+	0.999092i	0.419015	+	0.907979i	$0.362376\pi$
$311$	−10.1724	+	17.6192i	−0.576826	+	0.999092i	−0.995841	+	0.0911122i	$0.970958\pi$
$312$		0			0
$313$	−4.85936	−	8.41665i	−0.274667	−	0.475737i	0.695384	−	0.718638i	$-0.255234\pi$
$313$	−4.85936	−	8.41665i	−0.274667	−	0.475737i	−0.970051	+	0.242901i	$0.921901\pi$
$314$		0			0
$315$	13.8361	−	2.99467i	0.779576	−	0.168731i
$316$		0			0
$317$	1.66419	+	2.88246i	0.0934703	+	0.161895i	0.908969	−	0.416863i	$-0.136871\pi$
$317$	1.66419	+	2.88246i	0.0934703	+	0.161895i	−0.815499	+	0.578759i	$0.803537\pi$
$318$		0			0
$319$	8.84199	−	15.3148i	0.495056	−	0.857463i
$320$		0			0
$321$	11.7466	+	0.383486i	0.655633	+	0.0214041i
$322$		0			0
$323$	1.44524			0.0804153
$324$		0			0
$325$	−5.71168	−	9.89292i	−0.316827	−	0.548760i
$326$		0			0
$327$	1.24711	−	2.00592i	0.0689654	−	0.110928i
$328$		0			0
$329$	−1.24844	+	4.98953i	−0.0688286	+	0.275082i
$330$		0			0
$331$	0.717346	+	1.24248i	0.0394289	+	0.0682929i	0.885066	−	0.465465i	$-0.154113\pi$
$331$	0.717346	+	1.24248i	0.0394289	+	0.0682929i	−0.845638	+	0.533758i	$0.820779\pi$
$332$		0			0
$333$	−15.8364	−	32.0985i	−0.867829	−	1.75899i
$334$		0			0
$335$	−2.27962	+	3.94843i	−0.124549	+	0.215726i
$336$		0			0
$337$	0.00257316	+	0.00445685i	0.000140169	+	0.000242780i	0.866095	−	0.499879i	$-0.166622\pi$
$337$	0.00257316	+	0.00445685i	0.000140169	+	0.000242780i	−0.865955	+	0.500121i	$0.833289\pi$
$338$		0			0
$339$	−5.05647	+	8.13309i	−0.274630	+	0.441729i
$340$		0			0
$341$	2.81578	−	4.87707i	0.152483	−	0.264108i
$342$		0			0
$343$	−12.4268	+	13.7323i	−0.670982	+	0.741473i
$344$		0			0
$345$	11.0942	+	20.7514i	0.597294	+	1.11722i
$346$		0			0
$347$	−11.5536	+	20.0114i	−0.620229	+	1.07427i	0.369214	+	0.929344i	$0.379627\pi$
$347$	−11.5536	+	20.0114i	−0.620229	+	1.07427i	−0.989443	+	0.144924i	$0.953706\pi$
$348$		0			0
$349$	6.09723	−	10.5607i	0.326377	−	0.565302i	−0.655413	−	0.755271i	$-0.727505\pi$
$349$	6.09723	−	10.5607i	0.326377	−	0.565302i	0.981790	+	0.189969i	$0.0608387\pi$
$350$		0			0
$351$	13.4758	+	29.7203i	0.719284	+	1.58635i
$352$		0			0
$353$	24.7072			1.31503			0.657515	−	0.753441i	$-0.271608\pi$
$353$	24.7072			1.31503			0.657515	+	0.753441i	$0.271608\pi$
$354$		0			0
$355$	15.8054			0.838864
$356$		0			0
$357$	5.74523	−	1.44124i	0.304070	−	0.0762784i
$358$		0			0
$359$	8.20362	−	14.2091i	0.432970	−	0.749927i	−0.564157	−	0.825667i	$-0.690799\pi$
$359$	8.20362	−	14.2091i	0.432970	−	0.749927i	0.997128	+	0.0757407i	$0.0241321\pi$
$360$		0			0
$361$	8.87490	+	15.3718i	0.467100	+	0.809041i
$362$		0			0
$363$	−16.7556	−	31.3408i	−0.879443	−	1.64497i
$364$		0			0
$365$	−10.1234	−	17.5342i	−0.529882	−	0.917783i
$366$		0			0
$367$	−5.81801			−0.303698			−0.151849	−	0.988404i	$-0.548523\pi$
$367$	−5.81801			−0.303698			−0.151849	+	0.988404i	$0.548523\pi$
$368$		0			0
$369$	−24.7967	−	1.62078i	−1.29086	−	0.0843744i
$370$		0			0
$371$	5.72832	−	22.8939i	0.297399	−	1.18859i
$372$		0			0
$373$	8.84966			0.458218			0.229109	−	0.973401i	$-0.426419\pi$
$373$	8.84966			0.458218			0.229109	+	0.973401i	$0.426419\pi$
$374$		0			0
$375$	−9.93169	−	18.5769i	−0.512870	−	0.959305i
$376$		0			0
$377$	−19.7820			−1.01883
$378$		0			0
$379$	17.3300			0.890181			0.445091	−	0.895486i	$-0.353171\pi$
$379$	17.3300			0.890181			0.445091	+	0.895486i	$0.353171\pi$
$380$		0			0
$381$	10.4698	+	19.5834i	0.536386	+	1.00329i
$382$		0			0
$383$	7.09090			0.362328			0.181164	−	0.983453i	$-0.442014\pi$
$383$	7.09090			0.362328			0.181164	+	0.983453i	$0.442014\pi$
$384$		0			0
$385$	19.0415	+	18.4187i	0.970442	+	0.938706i
$386$		0			0
$387$	6.23335	+	12.6342i	0.316859	+	0.642235i
$388$		0			0
$389$	6.64240			0.336783			0.168392	−	0.985720i	$-0.446143\pi$
$389$	6.64240			0.336783			0.168392	+	0.985720i	$0.446143\pi$
$390$		0			0
$391$	4.92280	+	8.52654i	0.248957	+	0.431206i
$392$		0			0
$393$	4.75199	+	8.88843i	0.239706	+	0.448362i
$394$		0			0
$395$	12.0012	+	20.7867i	0.603845	+	1.04589i
$396$		0			0
$397$	7.86340	−	13.6198i	0.394653	−	0.683559i	−0.598404	−	0.801195i	$-0.704198\pi$
$397$	7.86340	−	13.6198i	0.394653	−	0.683559i	0.993057	+	0.117636i	$0.0375315\pi$
$398$		0			0
$399$	−3.56466	−	3.68069i	−0.178456	−	0.184265i
$400$		0			0
$401$	5.96559			0.297907			0.148954	−	0.988844i	$-0.452409\pi$
$401$	5.96559			0.297907			0.148954	+	0.988844i	$0.452409\pi$
$402$		0			0
$403$	−6.29968			−0.313810
$404$		0			0
$405$	6.14815	+	14.8278i	0.305504	+	0.736801i
$406$		0			0
$407$	33.4905	−	58.0073i	1.66006	−	2.87531i
$408$		0			0
$409$	8.80943	−	15.2584i	0.435598	−	0.754478i	−0.561746	−	0.827310i	$-0.689870\pi$
$409$	8.80943	−	15.2584i	0.435598	−	0.754478i	0.997344	+	0.0728314i	$0.0232035\pi$
$410$		0			0
$411$	12.5277	+	23.4326i	0.617947	+	1.15585i
$412$		0			0
$413$	−21.3349	+	6.09848i	−1.04982	+	0.300086i
$414$		0			0
$415$	2.85729	−	4.94897i	0.140259	−	0.242936i
$416$		0			0
$417$	−11.0802	+	17.8220i	−0.542601	+	0.872748i
$418$		0			0
$419$	9.62164	+	16.6652i	0.470048	+	0.814147i	0.999413	−	0.0342470i	$-0.0109033\pi$
$419$	9.62164	+	16.6652i	0.470048	+	0.814147i	−0.529365	+	0.848394i	$0.677570\pi$
$420$		0			0
$421$	7.77999	−	13.4753i	0.379174	−	0.656748i	−0.611769	−	0.791037i	$-0.709542\pi$
$421$	7.77999	−	13.4753i	0.379174	−	0.656748i	0.990942	+	0.134289i	$0.0428750\pi$
$422$		0			0
$423$	−5.81959	−	0.380384i	−0.282958	−	0.0184949i
$424$		0			0
$425$	−1.17555	−	2.03612i	−0.0570227	−	0.0987662i
$426$		0			0
$427$	3.09910	−	12.3859i	0.149976	−	0.599397i
$428$		0			0
$429$	−32.2434	+	51.8620i	−1.55672	+	2.50392i
$430$		0			0
$431$	−16.9779	−	29.4067i	−0.817799	−	1.41647i	−0.907301	−	0.420482i	$-0.861861\pi$
$431$	−16.9779	−	29.4067i	−0.817799	−	1.41647i	0.0895020	−	0.995987i	$-0.471472\pi$
$432$		0			0
$433$	−34.8338			−1.67401			−0.837004	−	0.547197i	$-0.815695\pi$
$433$	−34.8338			−1.67401			−0.837004	+	0.547197i	$0.815695\pi$
$434$		0			0
$435$	−9.72553	−	0.317505i	−0.466303	−	0.0152232i
$436$		0			0
$437$	4.25846	−	7.37587i	0.203710	−	0.352835i
$438$		0			0
$439$	−7.77938	−	13.4743i	−0.371290	−	0.643093i	0.618475	−	0.785805i	$-0.287751\pi$
$439$	−7.77938	−	13.4743i	−0.371290	−	0.643093i	−0.989764	+	0.142712i	$0.954418\pi$
$440$		0			0
$441$	−17.8410	−	11.0770i	−0.849571	−	0.527474i
$442$		0			0
$443$	−9.16212	−	15.8693i	−0.435305	−	0.753971i	0.562015	−	0.827127i	$-0.310026\pi$
$443$	−9.16212	−	15.8693i	−0.435305	−	0.753971i	−0.997321	+	0.0731560i	$0.976693\pi$
$444$		0			0
$445$	0.721705	−	1.25003i	0.0342121	−	0.0592571i
$446$		0			0
$447$	−3.86832	−	7.23555i	−0.182965	−	0.342230i
$448$		0			0
$449$	−2.75072			−0.129815			−0.0649073	−	0.997891i	$-0.520675\pi$
$449$	−2.75072			−0.129815			−0.0649073	+	0.997891i	$0.520675\pi$
$450$		0			0
$451$	−23.2514	−	40.2727i	−1.09487	−	1.89637i
$452$		0			0
$453$	−19.9002	−	37.2226i	−0.934993	−	1.74887i
$454$		0			0
$455$	7.19327	−	28.7488i	0.337226	−	1.34776i
$456$		0			0
$457$	−10.3407	−	17.9106i	−0.483716	−	0.837821i	0.516109	−	0.856523i	$-0.327380\pi$
$457$	−10.3407	−	17.9106i	−0.483716	−	0.837821i	−0.999825	+	0.0187018i	$0.994047\pi$
$458$		0			0
$459$	2.77353	+	6.11691i	0.129457	+	0.285513i
$460$		0			0
$461$	6.40670	−	11.0967i	0.298390	−	0.516826i	−0.677378	−	0.735635i	$-0.736884\pi$
$461$	6.40670	−	11.0967i	0.298390	−	0.516826i	0.975768	+	0.218809i	$0.0702172\pi$
$462$		0			0
$463$	5.54704	+	9.60775i	0.257793	+	0.446510i	0.965650	−	0.259845i	$-0.0836715\pi$
$463$	5.54704	+	9.60775i	0.257793	+	0.446510i	−0.707858	+	0.706355i	$0.750338\pi$
$464$		0			0
$465$	−3.09714	−	0.101111i	−0.143627	−	0.00468891i
$466$		0			0
$467$	5.36754	−	9.29686i	0.248380	−	0.430207i	−0.714696	−	0.699435i	$-0.753435\pi$
$467$	5.36754	−	9.29686i	0.248380	−	0.430207i	0.963077	+	0.269228i	$0.0867684\pi$
$468$		0			0
$469$	6.50283	−	1.85881i	0.300273	−	0.0858317i
$470$		0			0
$471$	−10.9140	−	0.356305i	−0.502892	−	0.0164177i
$472$		0			0
$473$	−13.1822	+	22.8322i	−0.606117	+	1.04982i
$474$		0			0
$475$	−1.01691	+	1.76134i	−0.0466590	+	0.0808157i
$476$		0			0
$477$	26.7025	+	1.74535i	1.22263	+	0.0799141i
$478$		0			0
$479$	−7.79508			−0.356166			−0.178083	−	0.984015i	$-0.556990\pi$
$479$	−7.79508			−0.356166			−0.178083	+	0.984015i	$0.556990\pi$
$480$		0			0
$481$	−74.9277			−3.41641
$482$		0			0
$483$	9.57311	−	33.5678i	0.435591	−	1.52739i
$484$		0			0
$485$	−1.97583	+	3.42225i	−0.0897180	+	0.155396i
$486$		0			0
$487$	13.9984	+	24.2459i	0.634326	+	1.09868i	0.986657	+	0.162810i	$0.0520557\pi$
$487$	13.9984	+	24.2459i	0.634326	+	1.09868i	−0.352331	+	0.935875i	$0.614611\pi$
$488$		0			0
$489$	−1.21414	−	0.0396373i	−0.0549052	−	0.00179246i
$490$		0			0
$491$	−12.1227	−	20.9971i	−0.547089	−	0.947586i	−0.998472	−	0.0552556i	$-0.982403\pi$
$491$	−12.1227	−	20.9971i	−0.547089	−	0.947586i	0.451383	−	0.892330i	$-0.350931\pi$
$492$		0			0
$493$	−4.07145			−0.183369
$494$		0			0
$495$	−16.6843	+	24.9796i	−0.749906	+	1.12275i
$496$		0			0
$497$	−16.8521	−	16.3010i	−0.755922	−	0.731201i
$498$		0			0
$499$	−33.7748			−1.51197			−0.755984	−	0.654590i	$-0.772841\pi$
$499$	−33.7748			−1.51197			−0.755984	+	0.654590i	$0.772841\pi$
$500$		0			0
$501$	6.47147	−	10.4091i	0.289124	−	0.465042i
$502$		0			0
$503$	−1.09819			−0.0489661			−0.0244830	−	0.999700i	$-0.507794\pi$
$503$	−1.09819			−0.0489661			−0.0244830	+	0.999700i	$0.507794\pi$
$504$		0			0
$505$	−16.7701			−0.746261
$506$		0			0
$507$	45.7720	+	1.49430i	2.03281	+	0.0663641i
$508$		0			0
$509$	16.2134			0.718648			0.359324	−	0.933213i	$-0.383007\pi$
$509$	16.2134			0.718648			0.359324	+	0.933213i	$0.383007\pi$
$510$		0			0
$511$	−7.29023	+	29.1363i	−0.322501	+	1.28891i
$512$		0			0
$513$	3.38289	−	4.72351i	0.149358	−	0.208548i
$514$		0			0
$515$	6.29054			0.277194
$516$		0			0
$517$	−5.45692	−	9.45167i	−0.239995	−	0.415684i
$518$		0			0
$519$	−6.06807	+	9.76021i	−0.266359	+	0.428426i
$520$		0			0
$521$	19.1738	+	33.2099i	0.840017	+	1.45495i	0.889879	+	0.456197i	$0.150789\pi$
$521$	19.1738	+	33.2099i	0.840017	+	1.45495i	−0.0498617	+	0.998756i	$0.515878\pi$
$522$		0			0
$523$	20.6021	−	35.6838i	0.900865	−	1.56034i	0.0744911	−	0.997222i	$-0.476267\pi$
$523$	20.6021	−	35.6838i	0.900865	−	1.56034i	0.826374	−	0.563122i	$-0.190400\pi$
$524$		0			0
$525$	−2.28603	+	8.01590i	−0.0997707	+	0.349843i
$526$		0			0
$527$	−1.29657			−0.0564796
$528$		0			0
$529$	35.0209			1.52265
$530$		0			0
$531$	−11.1322	−	22.5636i	−0.483097	−	0.979178i
$532$		0			0
$533$	−26.0100	+	45.0506i	−1.12662	+	1.95136i
$534$		0			0
$535$	6.05116	−	10.4809i	0.261614	−	0.453129i
$536$		0			0
$537$	10.3070	−	16.5783i	0.444779	−	0.715407i
$538$		0			0
$539$	−1.30619	−	39.2771i	−0.0562616	−	1.69178i
$540$		0			0
$541$	−9.09371	+	15.7508i	−0.390969	+	0.677178i	−0.992578	−	0.121613i	$-0.961193\pi$
$541$	−9.09371	+	15.7508i	−0.390969	+	0.677178i	0.601609	+	0.798791i	$0.294527\pi$
$542$		0			0
$543$	−17.2960	−	32.3516i	−0.742244	−	1.38834i
$544$		0			0
$545$	−1.21611	−	2.10636i	−0.0520924	−	0.0902266i
$546$		0			0
$547$	0.338699	−	0.586644i	0.0144817	−	0.0250831i	−0.858694	−	0.512489i	$-0.828723\pi$
$547$	0.338699	−	0.586644i	0.0144817	−	0.0250831i	0.873175	+	0.487406i	$0.162057\pi$
$548$		0			0
$549$	14.4464	+	0.944258i	0.616559	+	0.0403000i
$550$		0			0
$551$	1.76100	+	3.05014i	0.0750211	+	0.129940i
$552$		0			0
$553$	8.64250	−	34.5408i	0.367516	−	1.46882i
$554$		0			0
$555$	−36.8371	−	1.20260i	−1.56365	−	0.0510476i
$556$		0			0
$557$	14.8659	+	25.7484i	0.629887	+	1.09100i	0.987574	+	0.157155i	$0.0502322\pi$
$557$	14.8659	+	25.7484i	0.629887	+	1.09100i	−0.357687	+	0.933842i	$0.616435\pi$
$558$		0			0
$559$	29.4922			1.24739
$560$		0			0
$561$	−6.63619	+	10.6740i	−0.280180	+	0.450657i
$562$		0			0
$563$	−10.6739	+	18.4878i	−0.449852	+	0.779167i	−0.998376	−	0.0569680i	$-0.981857\pi$
$563$	−10.6739	+	18.4878i	−0.449852	+	0.779167i	0.548524	+	0.836135i	$0.315190\pi$
$564$		0			0
$565$	4.93077	+	8.54034i	0.207439	+	0.359295i
$566$		0			0
$567$	8.73749	−	22.1508i	0.366940	−	0.930245i
$568$		0			0
$569$	7.56212	+	13.0980i	0.317021	+	0.549096i	0.979865	−	0.199661i	$-0.0639842\pi$
$569$	7.56212	+	13.0980i	0.317021	+	0.549096i	−0.662844	+	0.748757i	$0.730651\pi$
$570$		0			0
$571$	−9.94314	+	17.2220i	−0.416107	+	0.720719i	−0.995544	−	0.0942981i	$-0.969939\pi$
$571$	−9.94314	+	17.2220i	−0.416107	+	0.720719i	0.579437	+	0.815017i	$0.303273\pi$
$572$		0			0
$573$	8.63376	−	13.8870i	0.360681	−	0.580138i
$574$		0			0
$575$	−13.8553			−0.577804
$576$		0			0
$577$	19.8090	+	34.3102i	0.824661	+	1.42835i	0.902178	+	0.431363i	$0.141967\pi$
$577$	19.8090	+	34.3102i	0.824661	+	1.42835i	−0.0775179	+	0.996991i	$0.524700\pi$
$578$		0			0
$579$	−10.8722	−	0.354940i	−0.451834	−	0.0147508i
$580$		0			0
$581$	−8.15068	+	2.32984i	−0.338147	+	0.0966579i
$582$		0			0
$583$	25.0385	+	43.3679i	1.03699	+	1.79612i
$584$		0			0
$585$	33.5314	+	2.19170i	1.38635	+	0.0906158i
$586$		0			0
$587$	1.13275	−	1.96199i	0.0467537	−	0.0809798i	−0.841701	−	0.539943i	$-0.818446\pi$
$587$	1.13275	−	1.96199i	0.0467537	−	0.0809798i	0.888455	+	0.458963i	$0.151779\pi$
$588$		0			0
$589$	0.560799	+	0.971332i	0.0231073	+	0.0400230i
$590$		0			0
$591$	−12.6397	−	23.6421i	−0.519927	−	0.972504i
$592$		0			0
$593$	5.97295	−	10.3454i	0.245280	−	0.424837i	−0.716931	−	0.697145i	$-0.754454\pi$
$593$	5.97295	−	10.3454i	0.245280	−	0.424837i	0.962210	+	0.272308i	$0.0877869\pi$
$594$		0			0
$595$	1.48049	−	5.91695i	0.0606941	−	0.242571i
$596$		0			0
$597$	4.01426	−	6.45676i	0.164293	−	0.264257i
$598$		0			0
$599$	1.47636	−	2.55713i	0.0603224	−	0.104481i	−0.834287	−	0.551330i	$-0.814120\pi$
$599$	1.47636	−	2.55713i	0.0603224	−	0.104481i	0.894610	+	0.446849i	$0.147454\pi$
$600$		0			0
$601$	15.9751	−	27.6697i	0.651638	−	1.12867i	−0.331087	−	0.943600i	$-0.607415\pi$
$601$	15.9751	−	27.6697i	0.651638	−	1.12867i	0.982725	−	0.185071i	$-0.0592514\pi$
$602$		0			0
$603$	3.39308	+	6.87736i	0.138177	+	0.280068i
$604$		0			0
$605$	−36.5953			−1.48781
$606$		0			0
$607$	10.4014			0.422179			0.211089	−	0.977467i	$-0.432299\pi$
$607$	10.4014			0.422179			0.211089	+	0.977467i	$0.432299\pi$
$608$		0			0
$609$	10.0421	+	10.3690i	0.406928	+	0.420174i
$610$		0			0
$611$	−6.10433	+	10.5730i	−0.246955	+	0.427739i
$612$		0			0
$613$	6.22441	+	10.7810i	0.251402	+	0.435441i	0.963912	−	0.266221i	$-0.0857751\pi$
$613$	6.22441	+	10.7810i	0.251402	+	0.435441i	−0.712510	+	0.701662i	$0.752442\pi$
$614$		0			0
$615$	−13.5105	+	21.7310i	−0.544795	+	0.876278i
$616$		0			0
$617$	−4.70100	−	8.14237i	−0.189255	−	0.327799i	0.755747	−	0.654864i	$-0.227274\pi$
$617$	−4.70100	−	8.14237i	−0.189255	−	0.327799i	−0.945002	+	0.327064i	$0.893941\pi$
$618$		0			0
$619$	−22.1196			−0.889062			−0.444531	−	0.895763i	$-0.646630\pi$
$619$	−22.1196			−0.889062			−0.444531	+	0.895763i	$0.646630\pi$
$620$		0			0
$621$	39.3903	+	3.86887i	1.58068	+	0.155252i
$622$		0			0
$623$	−2.05873	+	0.588479i	−0.0824812	+	0.0235769i
$624$		0			0
$625$	−12.5966			−0.503865
$626$		0			0
$627$	10.8668	+	0.354762i	0.433977	+	0.0141678i
$628$		0			0
$629$	−15.4213			−0.614887
$630$		0			0
$631$	18.3705			0.731316			0.365658	−	0.930749i	$-0.380844\pi$
$631$	18.3705			0.731316			0.365658	+	0.930749i	$0.380844\pi$
$632$		0			0
$633$	14.5059	−	23.3321i	0.576560	−	0.927370i
$634$		0			0
$635$	22.8668			0.907439
$636$		0			0
$637$	−37.3199	+	23.2339i	−1.47867	+	0.920559i
$638$		0			0
$639$	14.7660	−	22.1076i	0.584136	−	0.874562i
$640$		0			0
$641$	−33.7233			−1.33199			−0.665995	−	0.745956i	$-0.731993\pi$
$641$	−33.7233			−1.33199			−0.665995	+	0.745956i	$0.731993\pi$
$642$		0			0
$643$	10.0635	+	17.4306i	0.396867	+	0.687394i	0.993338	−	0.115241i	$-0.0367640\pi$
$643$	10.0635	+	17.4306i	0.396867	+	0.687394i	−0.596470	+	0.802635i	$0.703431\pi$
$644$		0			0
$645$	14.4994	+	0.473355i	0.570913	+	0.0186383i
$646$		0			0
$647$	−11.1891	−	19.3800i	−0.439887	−	0.761907i	0.557793	−	0.829980i	$-0.311648\pi$
$647$	−11.1891	−	19.3800i	−0.439887	−	0.761907i	−0.997680	+	0.0680731i	$0.978315\pi$
$648$		0			0
$649$	23.5422	−	40.7763i	0.924112	−	1.60061i
$650$		0			0
$651$	3.19797	+	3.30207i	0.125338	+	0.129418i
$652$		0			0
$653$	−40.6754			−1.59175			−0.795875	−	0.605460i	$-0.792989\pi$
$653$	−40.6754			−1.59175			−0.795875	+	0.605460i	$0.792989\pi$
$654$		0			0
$655$	10.3786			0.405527
$656$		0			0
$657$	−33.9834	−	2.22124i	−1.32582	−	0.0866590i
$658$		0			0
$659$	7.69321	−	13.3250i	0.299685	−	0.519070i	−0.676379	−	0.736554i	$-0.736452\pi$
$659$	7.69321	−	13.3250i	0.299685	−	0.519070i	0.976064	+	0.217484i	$0.0697851\pi$
$660$		0			0
$661$	−24.5736	+	42.5628i	−0.955804	+	1.65550i	−0.223285	+	0.974753i	$0.571678\pi$
$661$	−24.5736	+	42.5628i	−0.955804	+	1.65550i	−0.732518	+	0.680747i	$0.761655\pi$
$662$		0			0
$663$	14.0524	+	0.458762i	0.545751	+	0.0178169i
$664$		0			0
$665$	−5.07305	+	1.45011i	−0.196724	+	0.0562328i
$666$		0			0
$667$	−11.9967	+	20.7789i	−0.464513	+	0.804561i
$668$		0			0
$669$	−24.2099	−	0.790370i	−0.936010	−	0.0305575i
$670$		0			0
$671$	13.5462	+	23.4627i	0.522944	+	0.905766i
$672$		0			0
$673$	−6.99961	+	12.1237i	−0.269815	+	0.467334i	−0.968814	−	0.247789i	$-0.920296\pi$
$673$	−6.99961	+	12.1237i	−0.269815	+	0.467334i	0.698999	+	0.715123i	$0.253629\pi$
$674$		0			0
$675$	−9.40631	−	0.923876i	−0.362049	−	0.0355600i
$676$		0			0
$677$	23.3870	+	40.5075i	0.898836	+	1.55683i	0.828984	+	0.559272i	$0.188919\pi$
$677$	23.3870	+	40.5075i	0.898836	+	1.55683i	0.0698517	+	0.997557i	$0.477747\pi$
$678$		0			0
$679$	5.63624	−	1.61110i	0.216299	−	0.0618282i
$680$		0			0
$681$	−8.79279	−	16.4466i	−0.336940	−	0.630235i
$682$		0			0
$683$	21.6222	+	37.4508i	0.827352	+	1.43302i	0.900109	+	0.435665i	$0.143487\pi$
$683$	21.6222	+	37.4508i	0.827352	+	1.43302i	−0.0727571	+	0.997350i	$0.523180\pi$
$684$		0			0
$685$	27.3613			1.04542
$686$		0			0
$687$	1.31478	+	2.45925i	0.0501621	+	0.0938264i
$688$		0			0
$689$	28.0091	−	48.5131i	1.06706	−	1.84820i
$690$		0			0
$691$	5.86072	+	10.1511i	0.222952	+	0.386165i	0.955703	−	0.294332i	$-0.0950972\pi$
$691$	5.86072	+	10.1511i	0.222952	+	0.386165i	−0.732751	+	0.680497i	$0.761764\pi$
$692$		0			0
$693$	43.5522	−	9.42640i	1.65441	−	0.358079i
$694$		0			0
$695$	10.8048	+	18.7144i	0.409849	+	0.709879i
$696$		0			0
$697$	−5.35326	+	9.27212i	−0.202769	+	0.351207i
$698$		0			0
$699$	1.76785	+	0.0577141i	0.0668662	+	0.00218295i
$700$		0			0
$701$	0.0120975			0.000456915			0.000228458	−	1.00000i	$-0.499927\pi$
$701$	0.0120975			0.000456915			0.000228458		1.00000i	$0.499927\pi$
$702$		0			0
$703$	6.67008	+	11.5529i	0.251567	+	0.435726i
$704$		0			0
$705$	−3.17080	+	5.10009i	−0.119419	+	0.192080i
$706$		0			0
$707$	17.8807	+	17.2960i	0.672474	+	0.650483i
$708$		0			0
$709$	−0.537388	−	0.930783i	−0.0201820	−	0.0349563i	0.855758	−	0.517376i	$-0.173091\pi$
$709$	−0.537388	−	0.930783i	−0.0201820	−	0.0349563i	−0.875940	+	0.482420i	$0.839758\pi$
$710$		0			0
$711$	40.2870	+	2.63327i	1.51088	+	0.0987552i
$712$		0			0
$713$	−3.82041	+	6.61714i	−0.143075	+	0.247814i
$714$		0			0
$715$	31.4418	+	54.4588i	1.17586	+	2.03664i
$716$		0			0
$717$	−12.7378	+	20.4881i	−0.475701	+	0.765143i
$718$		0			0
$719$	12.7777	−	22.1317i	0.476529	−	0.825372i	−0.523109	−	0.852266i	$-0.675228\pi$
$719$	12.7777	−	22.1317i	0.476529	−	0.825372i	0.999638	+	0.0268932i	$0.00856140\pi$
$720$		0			0
$721$	−6.70714	−	6.48779i	−0.249787	−	0.241618i
$722$		0			0
$723$	11.9029	+	22.2639i	0.442672	+	0.828003i
$724$		0			0
$725$	2.86478	−	4.96194i	0.106395	−	0.184282i
$726$		0			0
$727$	6.20522	−	10.7478i	0.230139	−	0.398612i	−0.727710	−	0.685885i	$-0.759415\pi$
$727$	6.20522	−	10.7478i	0.230139	−	0.398612i	0.957849	+	0.287273i	$0.0927486\pi$
$728$		0			0
$729$	26.4840	+	5.25314i	0.980890	+	0.194561i
$730$		0			0
$731$	6.06996			0.224505
$732$		0			0
$733$	29.4189			1.08661			0.543307	−	0.839534i	$-0.317172\pi$
$733$	29.4189			1.08661			0.543307	+	0.839534i	$0.317172\pi$
$734$		0			0
$735$	−18.7207	+	10.8236i	−0.690522	+	0.399234i
$736$		0			0
$737$	−7.17562	+	12.4285i	−0.264317	+	0.457811i
$738$		0			0
$739$	7.75910	+	13.4392i	0.285423	+	0.494368i	0.972712	−	0.232017i	$-0.0745325\pi$
$739$	7.75910	+	13.4392i	0.285423	+	0.494368i	−0.687288	+	0.726385i	$0.741199\pi$
$740$		0			0
$741$	−5.73432	−	10.7258i	−0.210656	−	0.394024i
$742$		0			0
$743$	−13.6333	−	23.6136i	−0.500159	−	0.866301i	−1.00000		0.000183414i	$-0.999942\pi$
$743$	−13.6333	−	23.6136i	−0.500159	−	0.866301i	0.499841	−	0.866117i	$-0.333392\pi$
$744$		0			0
$745$	−8.44865			−0.309534
$746$		0			0
$747$	−4.25290	−	8.62012i	−0.155606	−	0.315394i
$748$		0			0
$749$	−17.2615	+	4.93412i	−0.630720	+	0.180289i
$750$		0			0
$751$	−9.14353			−0.333652			−0.166826	−	0.985986i	$-0.553352\pi$
$751$	−9.14353			−0.333652			−0.166826	+	0.985986i	$0.553352\pi$
$752$		0			0
$753$	−14.7226	−	27.5381i	−0.536522	−	1.00355i
$754$		0			0
$755$	−43.4632			−1.58179
$756$		0			0
$757$	−20.6307			−0.749834			−0.374917	−	0.927058i	$-0.622329\pi$
$757$	−20.6307			−0.749834			−0.374917	+	0.927058i	$0.622329\pi$
$758$		0			0
$759$	34.9216	+	65.3195i	1.26757	+	2.37095i
$760$		0			0
$761$	−0.478417			−0.0173426			−0.00867130	−	0.999962i	$-0.502760\pi$
$761$	−0.478417			−0.0173426			−0.00867130	+	0.999962i	$0.502760\pi$
$762$		0			0
$763$	−0.875765	+	3.50010i	−0.0317048	+	0.126712i
$764$		0			0
$765$	6.90129	+	0.451087i	0.249517	+	0.0163091i
$766$		0			0
$767$	−52.6705			−1.90182
$768$		0			0
$769$	−13.3518	−	23.1261i	−0.481480	−	0.833948i	0.518294	−	0.855202i	$-0.326567\pi$
$769$	−13.3518	−	23.1261i	−0.481480	−	0.833948i	−0.999774	+	0.0212548i	$0.993234\pi$
$770$		0			0
$771$	−21.9888	−	41.1293i	−0.791908	−	1.48123i
$772$		0			0
$773$	−13.5143	−	23.4074i	−0.486074	−	0.841905i	0.513798	−	0.857911i	$-0.328238\pi$
$773$	−13.5143	−	23.4074i	−0.486074	−	0.841905i	−0.999872	+	0.0160062i	$0.994905\pi$
$774$		0			0
$775$	0.912303	−	1.58016i	0.0327709	−	0.0567609i
$776$		0			0
$777$	38.0363	+	39.2744i	1.36455	+	1.40896i
$778$		0			0
$779$	9.26165			0.331833
$780$		0			0
$781$	49.7510			1.78023
$782$		0			0
$783$	−9.53008	+	13.3068i	−0.340577	+	0.475546i
$784$		0			0
$785$	−5.62226	+	9.73804i	−0.200667	+	0.347566i
$786$		0			0
$787$	−24.5915	+	42.5937i	−0.876593	+	1.51830i	−0.0215363	+	0.999768i	$0.506856\pi$
$787$	−24.5915	+	42.5937i	−0.876593	+	1.51830i	−0.855056	+	0.518535i	$0.826478\pi$
$788$		0			0
$789$	−1.25665	−	2.35051i	−0.0447378	−	0.0836804i
$790$		0			0
$791$	3.55083	−	14.1913i	0.126253	−	0.504585i
$792$		0			0
$793$	15.1533	−	26.2463i	0.538109	−	0.932032i
$794$		0			0
$795$	14.5489	−	23.4012i	0.515995	−	0.829955i
$796$		0			0
$797$	22.1538	+	38.3715i	0.784728	+	1.35919i	0.929162	+	0.369674i	$0.120531\pi$
$797$	22.1538	+	38.3715i	0.784728	+	1.35919i	−0.144434	+	0.989514i	$0.546136\pi$
$798$		0			0
$799$	−1.25637	+	2.17609i	−0.0444471	+	0.0769846i
$800$		0			0
$801$	−1.07421	−	2.17730i	−0.0379555	−	0.0769311i
$802$		0			0
$803$	−31.8656	−	55.1928i	−1.12451	−	1.94771i
$804$		0			0
$805$	−25.8352	−	24.9903i	−0.910570	−	0.880792i
$806$		0			0
$807$	5.97102	−	9.60410i	0.210190	−	0.338080i
$808$		0			0
$809$	−16.7359	−	28.9874i	−0.588402	−	1.01914i	−0.994442	−	0.105286i	$-0.966424\pi$
$809$	−16.7359	−	28.9874i	−0.588402	−	1.01914i	0.406040	−	0.913855i	$-0.366909\pi$
$810$		0			0
$811$	−43.7383			−1.53586			−0.767929	−	0.640535i	$-0.778713\pi$
$811$	−43.7383			−1.53586			−0.767929	+	0.640535i	$0.778713\pi$
$812$		0			0
$813$	19.5442	+	0.638051i	0.685446	+	0.0223774i
$814$		0			0
$815$	−0.625451	+	1.08331i	−0.0219086	+	0.0379468i
$816$		0			0
$817$	−2.62540	−	4.54733i	−0.0918512	−	0.159091i
$818$		0			0
$819$	−33.4916	−	36.9197i	−1.17029	−	1.29008i
$820$		0			0
$821$	11.2566	+	19.4970i	0.392857	+	0.680449i	0.992825	−	0.119575i	$-0.0381533\pi$
$821$	11.2566	+	19.4970i	0.392857	+	0.680449i	−0.599968	+	0.800024i	$0.704820\pi$
$822$		0			0
$823$	−7.33674	+	12.7076i	−0.255743	+	0.442959i	−0.965097	−	0.261893i	$-0.915653\pi$
$823$	−7.33674	+	12.7076i	−0.255743	+	0.442959i	0.709354	+	0.704852i	$0.248987\pi$
$824$		0			0
$825$	−8.33919	−	15.5981i	−0.290333	−	0.543058i
$826$		0			0
$827$	45.0520			1.56661			0.783306	−	0.621636i	$-0.213532\pi$
$827$	45.0520			1.56661			0.783306	+	0.621636i	$0.213532\pi$
$828$		0			0
$829$	20.6688	+	35.7993i	0.717856	+	1.24336i	0.961848	+	0.273585i	$0.0882095\pi$
$829$	20.6688	+	35.7993i	0.717856	+	1.24336i	−0.243992	+	0.969777i	$0.578457\pi$
$830$		0			0
$831$	−1.47961	−	2.76756i	−0.0513273	−	0.0960058i
$832$		0			0
$833$	−7.68102	+	4.78189i	−0.266132	+	0.165683i
$834$		0			0
$835$	−6.31059	−	10.9303i	−0.218387	−	0.378258i
$836$		0			0
$837$	−3.03490	+	4.23762i	−0.104902	+	0.146473i
$838$		0			0
$839$	2.04477	−	3.54164i	0.0705932	−	0.122271i	−0.828568	−	0.559888i	$-0.810844\pi$
$839$	2.04477	−	3.54164i	0.0705932	−	0.122271i	0.899161	+	0.437617i	$0.144177\pi$
$840$		0			0
$841$	9.53902	+	16.5221i	0.328932	+	0.569726i
$842$		0			0
$843$	10.3451	+	0.337733i	0.356306	+	0.0116321i
$844$		0			0
$845$	23.5790	−	40.8401i	0.811143	−	1.40494i
$846$		0			0
$847$	39.0189	+	37.7428i	1.34070	+	1.29686i
$848$		0			0
$849$	−34.6143	−	1.13003i	−1.18796	−	0.0387827i
$850$		0			0
$851$	−45.4394	+	78.7034i	−1.55764	+	2.69792i
$852$		0			0
$853$	−21.1012	+	36.5484i	−0.722491	+	1.25139i	0.237507	+	0.971386i	$0.423670\pi$
$853$	−21.1012	+	36.5484i	−0.722491	+	1.25139i	−0.959998	+	0.280006i	$0.909664\pi$
$854$		0			0
$855$	−2.64704	−	5.36523i	−0.0905269	−	0.183487i
$856$		0			0
$857$	−55.1245			−1.88302			−0.941509	−	0.336987i	$-0.890592\pi$
$857$	−55.1245			−1.88302			−0.941509	+	0.336987i	$0.890592\pi$
$858$		0			0
$859$	−37.9534			−1.29495			−0.647476	−	0.762086i	$-0.724176\pi$
$859$	−37.9534			−1.29495			−0.647476	+	0.762086i	$0.724176\pi$
$860$		0			0
$861$	36.8176	−	9.23600i	1.25474	−	0.314762i
$862$		0			0
$863$	6.27205	−	10.8635i	0.213503	−	0.369798i	−0.739305	−	0.673370i	$-0.764846\pi$
$863$	6.27205	−	10.8635i	0.213503	−	0.369798i	0.952809	+	0.303572i	$0.0981793\pi$
$864$		0			0
$865$	5.91723	+	10.2489i	0.201192	+	0.348474i
$866$		0			0
$867$	−26.5370	−	0.866340i	−0.901243	−	0.0294224i
$868$		0			0
$869$	37.7764	+	65.4306i	1.28148	+	2.21958i
$870$		0			0
$871$	16.0539			0.543965
$872$		0			0
$873$	2.94091	+	5.96086i	0.0995346	+	0.201745i
$874$		0			0
$875$	23.1279	+	22.3716i	0.781867	+	0.756297i
$876$		0			0
$877$	9.70673			0.327773			0.163887	−	0.986479i	$-0.447597\pi$
$877$	9.70673			0.327773			0.163887	+	0.986479i	$0.447597\pi$
$878$		0			0
$879$	−9.05666	+	14.5672i	−0.305474	+	0.491340i
$880$		0			0
$881$	−11.6652			−0.393012			−0.196506	−	0.980503i	$-0.562959\pi$
$881$	−11.6652			−0.393012			−0.196506	+	0.980503i	$0.562959\pi$
$882$		0			0
$883$	−13.1758			−0.443401			−0.221701	−	0.975115i	$-0.571161\pi$
$883$	−13.1758			−0.443401			−0.221701	+	0.975115i	$0.571161\pi$
$884$		0			0
$885$	−25.8946	−	0.845370i	−0.870439	−	0.0284168i
$886$		0			0
$887$	−0.830721			−0.0278929			−0.0139464	−	0.999903i	$-0.504439\pi$
$887$	−0.830721			−0.0278929			−0.0139464	+	0.999903i	$0.504439\pi$
$888$		0			0
$889$	−24.3811	−	23.5838i	−0.817717	−	0.790975i
$890$		0			0
$891$	19.3527	+	46.6739i	0.648338	+	1.56364i
$892$		0			0
$893$	2.17364			0.0727379
$894$		0			0
$895$	−10.0508	−	17.4084i	−0.335960	−	0.581900i
$896$		0			0
$897$	43.7473	−	70.3655i	1.46068	−	2.34944i
$898$		0			0
$899$	−1.57985	−	2.73638i	−0.0526910	−	0.0912634i
$900$		0			0
$901$	5.76470	−	9.98476i	0.192050	−	0.332641i
$902$		0			0
$903$	−14.9714	−	15.4588i	−0.498218	−	0.514435i
$904$		0			0
$905$	−37.7756			−1.25570
$906$		0			0
$907$	33.3176			1.10629			0.553146	−	0.833084i	$-0.313427\pi$
$907$	33.3176			1.10629			0.553146	+	0.833084i	$0.313427\pi$
$908$		0			0
$909$	−15.6673	+	23.4569i	−0.519652	+	0.778017i
$910$		0			0
$911$	−11.1353	+	19.2870i	−0.368930	+	0.639006i	−0.989399	−	0.145226i	$-0.953609\pi$
$911$	−11.1353	+	19.2870i	−0.368930	+	0.639006i	0.620469	+	0.784231i	$0.286942\pi$
$912$		0			0
$913$	8.99396	−	15.5780i	0.297657	−	0.515556i
$914$		0			0
$915$	7.87114	−	12.6604i	0.260212	−	0.418539i
$916$		0			0
$917$	−11.0660	−	10.7041i	−0.365431	−	0.353480i
$918$		0			0
$919$	10.7906	−	18.6899i	0.355949	−	0.616522i	−0.631331	−	0.775514i	$-0.717491\pi$
$919$	10.7906	−	18.6899i	0.355949	−	0.616522i	0.987280	+	0.158992i	$0.0508243\pi$
$920$		0			0
$921$	19.3638	+	36.2194i	0.638060	+	1.19347i
$922$		0			0
$923$	−27.8268	−	48.1974i	−0.915929	−	1.58644i
$924$		0			0
$925$	10.8508	−	18.7942i	0.356773	−	0.617949i
$926$		0			0
$927$	5.87687	−	8.79879i	0.193022	−	0.288990i
$928$		0			0
$929$	18.5780	+	32.1780i	0.609523	+	1.05572i	0.991319	+	0.131478i	$0.0419724\pi$
$929$	18.5780	+	32.1780i	0.609523	+	1.05572i	−0.381796	+	0.924247i	$0.624694\pi$
$930$		0			0
$931$	6.90460	+	3.68598i	0.226289	+	0.120803i
$932$		0			0
$933$	35.2196	+	1.14980i	1.15304	+	0.0376427i
$934$		0			0
$935$	6.47122	+	11.2085i	0.211631	+	0.366556i
$936$		0			0
$937$	21.5238			0.703152			0.351576	−	0.936159i	$-0.385646\pi$
$937$	21.5238			0.703152			0.351576	+	0.936159i	$0.385646\pi$
$938$		0			0
$939$	−8.88784	+	14.2957i	−0.290044	+	0.466522i
$940$		0			0
$941$	23.7032	−	41.0551i	0.772702	−	1.33836i	−0.163375	−	0.986564i	$-0.552238\pi$
$941$	23.7032	−	41.0551i	0.772702	−	1.33836i	0.936077	−	0.351795i	$-0.114429\pi$
$942$		0			0
$943$	31.5472	+	54.6413i	1.02732	+	1.77937i
$944$		0			0
$945$	−15.8731	−	18.6886i	−0.516352	−	0.607939i
$946$		0			0
$947$	1.25059	+	2.16608i	0.0406386	+	0.0703881i	0.885629	−	0.464393i	$-0.153727\pi$
$947$	1.25059	+	2.16608i	0.0406386	+	0.0703881i	−0.844991	+	0.534781i	$0.820394\pi$
$948$		0			0
$949$	−35.6461	+	61.7409i	−1.15712	+	2.00420i
$950$		0			0
$951$	3.04383	−	4.89586i	0.0987031	−	0.158759i
$952$		0			0
$953$	−7.89914			−0.255878			−0.127939	−	0.991782i	$-0.540836\pi$
$953$	−7.89914			−0.255878			−0.127939	+	0.991782i	$0.540836\pi$
$954$		0			0
$955$	−8.41913	−	14.5824i	−0.272437	−	0.471874i
$956$		0			0
$957$	−30.6132	−	0.999416i	−0.989586	−	0.0323065i
$958$		0			0
$959$	−29.1733	−	28.2193i	−0.942055	−	0.911247i
$960$		0			0
$961$	14.9969	+	25.9754i	0.483771	+	0.837915i
$962$		0			0
$963$	−9.00677	−	18.2556i	−0.290239	−	0.588280i
$964$		0			0
$965$	−5.60071	+	9.70072i	−0.180293	+	0.312277i
$966$		0			0
$967$	5.76591	+	9.98684i	0.185419	+	0.321155i	0.943718	−	0.330752i	$-0.107302\pi$
$967$	5.76591	+	9.98684i	0.185419	+	0.321155i	−0.758299	+	0.651907i	$0.773969\pi$
$968$		0			0
$969$	−1.18021	−	2.20755i	−0.0379139	−	0.0709166i
$970$		0			0
$971$	−9.14669	+	15.8425i	−0.293531	+	0.508411i	−0.974642	−	0.223769i	$-0.928164\pi$
$971$	−9.14669	+	15.8425i	−0.293531	+	0.508411i	0.681111	+	0.732180i	$0.261497\pi$
$972$		0			0
$973$	7.78092	−	31.0974i	0.249445	−	0.996937i
$974$		0			0
$975$	−10.4468	+	16.8031i	−0.334564	+	0.538130i
$976$		0			0
$977$	14.9541	−	25.9013i	0.478425	−	0.828656i	−0.521269	−	0.853392i	$-0.674541\pi$
$977$	14.9541	−	25.9013i	0.478425	−	0.828656i	0.999694	+	0.0247361i	$0.00787454\pi$
$978$		0			0
$979$	2.27173	−	3.93475i	0.0726047	−	0.125755i
$980$		0			0
$981$	−4.08238	−	0.266835i	−0.130340	−	0.00851939i
$982$		0			0
$983$	14.5445			0.463897			0.231948	−	0.972728i	$-0.425490\pi$
$983$	14.5445			0.463897			0.231948	+	0.972728i	$0.425490\pi$
$984$		0			0
$985$	−27.6058			−0.879594
$986$		0			0
$987$	8.64080	−	2.16762i	0.275040	−	0.0689960i
$988$		0			0
$989$	17.8854	−	30.9784i	0.568722	−	0.985055i
$990$		0			0
$991$	−14.3753	−	24.8987i	−0.456646	−	0.790935i	0.542135	−	0.840292i	$-0.317616\pi$
$991$	−14.3753	−	24.8987i	−0.456646	−	0.790935i	−0.998781	+	0.0493567i	$0.984283\pi$
$992$		0			0
$993$	1.31204	−	2.11035i	0.0416363	−	0.0669700i
$994$		0			0
$995$	−3.91447	−	6.78007i	−0.124097	−	0.214943i
$996$		0			0
$997$	35.8938			1.13677			0.568384	−	0.822763i	$-0.307569\pi$
$997$	35.8938			1.13677			0.568384	+	0.822763i	$0.307569\pi$
$998$		0			0
$999$	−36.0968	+	50.4017i	−1.14205	+	1.59464i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.t.c.457.5	yes	22
3.2	odd	2		1512.2.t.c.289.8		22
4.3	odd	2		1008.2.t.l.961.7		22
7.4	even	3		504.2.q.c.25.4	✓	22
9.4	even	3		504.2.q.c.121.4	yes	22
9.5	odd	6		1512.2.q.d.793.4		22
12.11	even	2		3024.2.t.k.289.8		22
21.11	odd	6		1512.2.q.d.1369.4		22
28.11	odd	6		1008.2.q.l.529.8		22
36.23	even	6		3024.2.q.l.2305.4		22
36.31	odd	6		1008.2.q.l.625.8		22
63.4	even	3	inner	504.2.t.c.193.5	yes	22
63.32	odd	6		1512.2.t.c.361.8		22
84.11	even	6		3024.2.q.l.2881.4		22
252.67	odd	6		1008.2.t.l.193.7		22
252.95	even	6		3024.2.t.k.1873.8		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.q.c.25.4	✓	22	7.4	even	3
504.2.q.c.121.4	yes	22	9.4	even	3
504.2.t.c.193.5	yes	22	63.4	even	3	inner
504.2.t.c.457.5	yes	22	1.1	even	1	trivial
1008.2.q.l.529.8		22	28.11	odd	6
1008.2.q.l.625.8		22	36.31	odd	6
1008.2.t.l.193.7		22	252.67	odd	6
1008.2.t.l.961.7		22	4.3	odd	2
1512.2.q.d.793.4		22	9.5	odd	6
1512.2.q.d.1369.4		22	21.11	odd	6
1512.2.t.c.289.8		22	3.2	odd	2
1512.2.t.c.361.8		22	63.32	odd	6
3024.2.q.l.2305.4		22	36.23	even	6
3024.2.q.l.2881.4		22	84.11	even	6
3024.2.t.k.289.8		22	12.11	even	2
3024.2.t.k.1873.8		22	252.95	even	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:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.t (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.816621 - 1.52746i) q^{3} -1.78355 q^{5} +(1.90167 + 1.83948i) q^{7} +(-1.66626 + 2.49471i) q^{9} +O(q^{10})\)	\(q+(-0.816621 - 1.52746i) q^{3} -1.78355 q^{5} +(1.90167 + 1.83948i) q^{7} +(-1.66626 + 2.49471i) q^{9} -5.61411 q^{11} +(3.14009 + 5.43879i) q^{13} +(1.45648 + 2.72430i) q^{15} +(0.646279 + 1.11939i) q^{17} +(0.559062 - 0.968324i) q^{19} +(1.25678 - 4.40687i) q^{21} +7.61715 q^{23} -1.81896 q^{25} +(5.17127 + 0.507916i) q^{27} +(-1.57496 + 2.72791i) q^{29} +(-0.501553 + 0.868716i) q^{31} +(4.58460 + 8.57533i) q^{33} +(-3.39171 - 3.28079i) q^{35} +(-5.96542 + 10.3324i) q^{37} +(5.74327 - 9.23778i) q^{39} +(4.14160 + 7.17347i) q^{41} +(2.34804 - 4.06693i) q^{43} +(2.97186 - 4.44943i) q^{45} +(0.972001 + 1.68356i) q^{47} +(0.232662 + 6.99613i) q^{49} +(1.18205 - 1.90128i) q^{51} +(-4.45992 - 7.72481i) q^{53} +10.0130 q^{55} +(-1.93562 - 0.0631911i) q^{57} +(-4.19339 + 7.26317i) q^{59} +(-2.41288 - 4.17923i) q^{61} +(-7.75763 + 1.67905i) q^{63} +(-5.60050 - 9.70034i) q^{65} +(1.27814 - 2.21380i) q^{67} +(-6.22032 - 11.6349i) q^{69} -8.86178 q^{71} +(5.67598 + 9.83109i) q^{73} +(1.48540 + 2.77838i) q^{75} +(-10.6762 - 10.3270i) q^{77} +(-6.72883 - 11.6547i) q^{79} +(-3.44714 - 8.31368i) q^{81} +(-1.60203 + 2.77479i) q^{83} +(-1.15267 - 1.99648i) q^{85} +(5.45291 + 0.178018i) q^{87} +(-0.404646 + 0.700867i) q^{89} +(-4.03312 + 16.1189i) q^{91} +(1.73651 + 0.0566909i) q^{93} +(-0.997114 + 1.72705i) q^{95} +(1.10781 - 1.91879i) q^{97} +(9.35458 - 14.0056i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 2 q^{3} - 2 q^{5} - q^{7}+O(q^{10}) \) 22 * q - 2 * q^3 - 2 * q^5 - q^7	\( 22 q - 2 q^{3} - 2 q^{5} - q^{7} - 6 q^{11} + 7 q^{13} - q^{15} - q^{17} + 13 q^{19} + 33 q^{21} + 44 q^{25} - 2 q^{27} - 7 q^{29} + 6 q^{31} + 9 q^{33} + 2 q^{35} + 6 q^{37} - 4 q^{39} + 4 q^{41} + 2 q^{43} + 17 q^{47} + 29 q^{49} - 25 q^{51} + q^{53} + 2 q^{55} - 21 q^{57} - 21 q^{59} + 31 q^{61} - 7 q^{63} - 3 q^{65} - 26 q^{67} - 40 q^{69} - 32 q^{71} + 17 q^{73} - 16 q^{75} - 4 q^{77} - 16 q^{79} - 36 q^{83} + 28 q^{85} + 7 q^{87} - 2 q^{89} + 15 q^{91} - 56 q^{93} - 24 q^{95} + 19 q^{97} + 24 q^{99}+O(q^{100}) \) 22 * q - 2 * q^3 - 2 * q^5 - q^7 - 6 * q^11 + 7 * q^13 - q^15 - q^17 + 13 * q^19 + 33 * q^21 + 44 * q^25 - 2 * q^27 - 7 * q^29 + 6 * q^31 + 9 * q^33 + 2 * q^35 + 6 * q^37 - 4 * q^39 + 4 * q^41 + 2 * q^43 + 17 * q^47 + 29 * q^49 - 25 * q^51 + q^53 + 2 * q^55 - 21 * q^57 - 21 * q^59 + 31 * q^61 - 7 * q^63 - 3 * q^65 - 26 * q^67 - 40 * q^69 - 32 * q^71 + 17 * q^73 - 16 * q^75 - 4 * q^77 - 16 * q^79 - 36 * q^83 + 28 * q^85 + 7 * q^87 - 2 * q^89 + 15 * q^91 - 56 * q^93 - 24 * q^95 + 19 * q^97 + 24 * q^99

Introduction

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