LMFDB - Embedded newform 504.2.t.c.193.5

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			193.5
Character	$\chi$	$=$	504.193
Dual form			504.2.t.c.457.5

$q$-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 $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

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

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	0.00983976	−	0.999952i	$-0.496868\pi$
$13$	3.14009	−	5.43879i	0.870903	−	1.50845i	0.861064	−	0.508497i	$-0.169799\pi$
$14$		0			0
$15$	1.45648	−	2.72430i	0.376062	−	0.703410i
$16$		0			0
$17$	0.646279	−	1.11939i	0.156746	−	0.271491i	−0.776948	−	0.629565i	$-0.783233\pi$
$17$	0.646279	−	1.11939i	0.156746	−	0.271491i	0.933693	+	0.358074i	$0.116566\pi$
$18$		0			0
$19$	0.559062	+	0.968324i	0.128258	+	0.222149i	0.923002	−	0.384796i	$-0.125728\pi$
$19$	0.559062	+	0.968324i	0.128258	+	0.222149i	−0.794744	+	0.606945i	$0.792395\pi$
$20$		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	0.681929	−	0.731418i	$-0.261141\pi$
$29$	−1.57496	−	2.72791i	−0.292462	−	0.506560i	−0.974391	+	0.224859i	$0.927808\pi$
$30$		0			0
$31$	−0.501553	−	0.868716i	−0.0900816	−	0.156026i	0.817464	−	0.575980i	$-0.195379\pi$
$31$	−0.501553	−	0.868716i	−0.0900816	−	0.156026i	−0.907545	+	0.419954i	$0.862046\pi$
$32$		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	−0.659642	−	0.751580i	$-0.729292\pi$
$37$	−5.96542	−	10.3324i	−0.980708	−	1.69864i	−0.321067	−	0.947057i	$-0.604041\pi$
$38$		0			0
$39$	5.74327	+	9.23778i	0.919659	+	1.47923i
$40$		0			0
$41$	4.14160	−	7.17347i	0.646810	−	1.12031i	−0.337071	−	0.941479i	$-0.609436\pi$
$41$	4.14160	−	7.17347i	0.646810	−	1.12031i	0.983880	−	0.178828i	$-0.0572306\pi$
$42$		0			0
$43$	2.34804	+	4.06693i	0.358073	+	0.620200i	0.987639	−	0.156747i	$-0.0501006\pi$
$43$	2.34804	+	4.06693i	0.358073	+	0.620200i	−0.629566	+	0.776947i	$0.716767\pi$
$44$		0			0
$45$	2.97186	+	4.44943i	0.443018	+	0.663282i
$46$		0			0
$47$	0.972001	−	1.68356i	0.141781	−	0.245572i	−0.786386	−	0.617735i	$-0.788050\pi$
$47$	0.972001	−	1.68356i	0.141781	−	0.245572i	0.928167	+	0.372163i	$0.121384\pi$
$48$		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	0.378180	+	0.925732i	$0.376550\pi$
$53$	−4.45992	+	7.72481i	−0.612617	+	1.06108i	−0.990798	+	0.135352i	$0.956783\pi$
$54$		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	−0.998548	−	0.0538778i	$-0.982842\pi$
$59$	−4.19339	−	7.26317i	−0.545933	−	0.945584i	0.452614	−	0.891706i	$-0.350491\pi$
$60$		0			0
$61$	−2.41288	+	4.17923i	−0.308937	+	0.535095i	−0.978130	−	0.207994i	$-0.933307\pi$
$61$	−2.41288	+	4.17923i	−0.308937	+	0.535095i	0.669193	+	0.743089i	$0.266640\pi$
$62$		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	0.933477	−	0.358637i	$-0.116758\pi$
$67$	1.27814	+	2.21380i	0.156150	+	0.270459i	−0.777327	+	0.629096i	$0.783425\pi$
$68$		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	−0.315145	−	0.949044i	$-0.602053\pi$
$73$	5.67598	−	9.83109i	0.664323	−	1.15064i	0.979468	−	0.201598i	$-0.0646135\pi$
$74$		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	0.187295	+	0.982304i	$0.440028\pi$
$79$	−6.72883	+	11.6547i	−0.757052	+	1.31125i	−0.944348	+	0.328949i	$0.893305\pi$
$80$		0			0
$81$	−3.44714	+	8.31368i	−0.383016	+	0.923742i
$82$		0			0
$83$	−1.60203	−	2.77479i	−0.175845	−	0.304573i	0.764608	−	0.644495i	$-0.222933\pi$
$83$	−1.60203	−	2.77479i	−0.175845	−	0.304573i	−0.940453	+	0.339922i	$0.889599\pi$
$84$		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	0.843782	−	0.536686i	$-0.180324\pi$
$89$	−0.404646	−	0.700867i	−0.0428924	−	0.0742917i	−0.886675	+	0.462394i	$0.846991\pi$
$90$		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	0.916770	−	0.399415i	$-0.130787\pi$
$97$	1.10781	+	1.91879i	0.112481	+	0.194823i	−0.804289	+	0.594238i	$0.797454\pi$
$98$		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	0.654122	−	0.756389i	$-0.273038\pi$
$107$	−3.39276	−	5.87644i	−0.327991	−	0.568097i	−0.982113	+	0.188292i	$0.939705\pi$
$108$		0			0
$109$	0.681848	−	1.18099i	0.0653092	−	0.113119i	−0.831522	−	0.555492i	$-0.812530\pi$
$109$	0.681848	−	1.18099i	0.0653092	−	0.113119i	0.896831	+	0.442373i	$0.145863\pi$
$110$		0			0
$111$	20.6538	−	0.674275i	1.96037	−	0.0639993i
$112$		0			0
$113$	−2.76458	+	4.78840i	−0.260070	+	0.450455i	−0.966260	−	0.257568i	$-0.917079\pi$
$113$	−2.76458	+	4.78840i	−0.260070	+	0.450455i	0.706190	+	0.708022i	$0.250412\pi$
$114$		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	0.486036	+	0.873939i	$0.338442\pi$
$139$	−6.05803	+	10.4928i	−0.513835	+	0.889988i	−0.999871	+	0.0160496i	$0.994891\pi$
$140$		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	0.963961	−	0.266043i	$-0.0857165\pi$
$157$	3.15229	+	5.45993i	0.251580	+	0.435750i	−0.712381	+	0.701793i	$0.752383\pi$
$158$		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	0.879432	−	0.476024i	$-0.157922\pi$
$163$	0.350678	+	0.607392i	0.0274672	+	0.0475746i	−0.851965	+	0.523599i	$0.824589\pi$
$164$		0			0
$165$	−8.17686	+	15.2945i	−0.636567	+	1.19068i
$166$		0			0
$167$	3.53822	−	6.12839i	0.273796	−	0.474229i	−0.696035	−	0.718008i	$-0.745054\pi$
$167$	3.53822	−	6.12839i	0.273796	−	0.474229i	0.969831	+	0.243780i	$0.0783873\pi$
$168$		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	−0.964142	−	0.265388i	$-0.914500\pi$
$173$	−3.31767	+	5.74638i	−0.252238	+	0.436889i	0.711904	+	0.702277i	$0.247833\pi$
$174$		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	−0.574858	−	0.818253i	$-0.694943\pi$
$179$	5.63527	−	9.76057i	0.421200	−	0.729539i	0.996057	+	0.0887145i	$0.0282759\pi$
$180$		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	−0.643163	−	0.765729i	$-0.722378\pi$
$191$	4.72044	−	8.17604i	0.341559	−	0.591598i	0.984722	+	0.174131i	$0.0557117\pi$
$192$		0			0
$193$	3.14021	+	5.43900i	0.226037	+	0.391508i	0.956630	−	0.291305i	$-0.0940896\pi$
$193$	3.14021	+	5.43900i	0.226037	+	0.391508i	−0.730593	+	0.682813i	$0.760756\pi$
$194$		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	−0.777688	−	0.628650i	$-0.783608\pi$
$199$	2.19477	−	3.80145i	0.155583	−	0.269478i	0.933271	+	0.359173i	$0.116941\pi$
$200$		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	−0.452550	−	0.891739i	$-0.649486\pi$
$211$	7.93101	−	13.7369i	0.545993	−	0.945688i	0.998544	−	0.0539495i	$-0.0171810\pi$
$212$		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	0.999342	−	0.0362769i	$-0.0115498\pi$
$223$	6.99253	+	12.1114i	0.468254	+	0.811040i	−0.531088	+	0.847317i	$0.678216\pi$
$224$		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	0.848815	−	0.528690i	$-0.177316\pi$
$233$	−0.510606	−	0.884395i	−0.0334509	−	0.0579387i	−0.882266	+	0.470751i	$0.843983\pi$
$234$		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	−0.998416	−	0.0562640i	$-0.982081\pi$
$239$	−6.96428	+	12.0625i	−0.450482	+	0.780258i	0.547934	+	0.836522i	$0.315414\pi$
$240$		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	−0.749173	−	0.662374i	$-0.769549\pi$
$269$	3.26461	−	5.65446i	0.199047	−	0.344759i	0.948220	+	0.317616i	$0.102882\pi$
$270$		0			0
$271$	−5.64494	−	9.77733i	−0.342906	−	0.593930i	0.642065	−	0.766650i	$-0.278078\pi$
$271$	−5.64494	−	9.77733i	−0.342906	−	0.593930i	−0.984971	+	0.172720i	$0.944745\pi$
$272$		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	0.763033	−	0.646360i	$-0.223710\pi$
$281$	−2.98798	−	5.17533i	−0.178248	−	0.308734i	−0.941280	+	0.337626i	$0.890376\pi$
$282$		0			0
$283$	9.99760	+	17.3163i	0.594295	+	1.02935i	0.993646	+	0.112552i	$0.0359024\pi$
$283$	9.99760	+	17.3163i	0.594295	+	1.02935i	−0.399350	+	0.916798i	$0.630764\pi$
$284$		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	−0.973638	−	0.228099i	$-0.926749\pi$
$293$	−4.95166	+	8.57652i	−0.289279	+	0.501046i	0.684359	+	0.729145i	$0.260082\pi$
$294$		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	−0.995841	−	0.0911122i	$-0.970958\pi$
$311$	−10.1724	−	17.6192i	−0.576826	−	0.999092i	0.419015	−	0.907979i	$-0.362376\pi$
$312$		0			0
$313$	−4.85936	+	8.41665i	−0.274667	+	0.475737i	−0.970051	−	0.242901i	$-0.921901\pi$
$313$	−4.85936	+	8.41665i	−0.274667	+	0.475737i	0.695384	+	0.718638i	$0.255234\pi$
$314$		0			0
$315$	13.8361	+	2.99467i	0.779576	+	0.168731i
$316$		0			0
$317$	1.66419	−	2.88246i	0.0934703	−	0.161895i	−0.815499	−	0.578759i	$-0.803537\pi$
$317$	1.66419	−	2.88246i	0.0934703	−	0.161895i	0.908969	+	0.416863i	$0.136871\pi$
$318$		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	−0.845638	−	0.533758i	$-0.820779\pi$
$331$	0.717346	−	1.24248i	0.0394289	−	0.0682929i	0.885066	+	0.465465i	$0.154113\pi$
$332$		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	−0.865955	−	0.500121i	$-0.833289\pi$
$337$	0.00257316	−	0.00445685i	0.000140169	−	0.000242780i	0.866095	+	0.499879i	$0.166622\pi$
$338$		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	−0.989443	−	0.144924i	$-0.953706\pi$
$347$	−11.5536	−	20.0114i	−0.620229	−	1.07427i	0.369214	−	0.929344i	$-0.379627\pi$
$348$		0			0
$349$	6.09723	+	10.5607i	0.326377	+	0.565302i	0.981790	−	0.189969i	$-0.0608387\pi$
$349$	6.09723	+	10.5607i	0.326377	+	0.565302i	−0.655413	+	0.755271i	$0.727505\pi$
$350$		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	0.997128	−	0.0757407i	$-0.0241321\pi$
$359$	8.20362	+	14.2091i	0.432970	+	0.749927i	−0.564157	+	0.825667i	$0.690799\pi$
$360$		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	0.993057	−	0.117636i	$-0.0375315\pi$
$397$	7.86340	+	13.6198i	0.394653	+	0.683559i	−0.598404	+	0.801195i	$0.704198\pi$
$398$		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	0.997344	−	0.0728314i	$-0.0232035\pi$
$409$	8.80943	+	15.2584i	0.435598	+	0.754478i	−0.561746	+	0.827310i	$0.689870\pi$
$410$		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	−0.529365	−	0.848394i	$-0.677570\pi$
$419$	9.62164	−	16.6652i	0.470048	−	0.814147i	0.999413	+	0.0342470i	$0.0109033\pi$
$420$		0			0
$421$	7.77999	+	13.4753i	0.379174	+	0.656748i	0.990942	−	0.134289i	$-0.0428750\pi$
$421$	7.77999	+	13.4753i	0.379174	+	0.656748i	−0.611769	+	0.791037i	$0.709542\pi$
$422$		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	0.0895020	+	0.995987i	$0.471472\pi$
$431$	−16.9779	+	29.4067i	−0.817799	+	1.41647i	−0.907301	+	0.420482i	$0.861861\pi$
$432$		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	−0.989764	−	0.142712i	$-0.954418\pi$
$439$	−7.77938	+	13.4743i	−0.371290	+	0.643093i	0.618475	+	0.785805i	$0.287751\pi$
$440$		0			0
$441$	−17.8410	+	11.0770i	−0.849571	+	0.527474i
$442$		0			0
$443$	−9.16212	+	15.8693i	−0.435305	+	0.753971i	−0.997321	−	0.0731560i	$-0.976693\pi$
$443$	−9.16212	+	15.8693i	−0.435305	+	0.753971i	0.562015	+	0.827127i	$0.310026\pi$
$444$		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	−0.999825	−	0.0187018i	$-0.994047\pi$
$457$	−10.3407	+	17.9106i	−0.483716	+	0.837821i	0.516109	+	0.856523i	$0.327380\pi$
$458$		0			0
$459$	2.77353	−	6.11691i	0.129457	−	0.285513i
$460$		0			0
$461$	6.40670	+	11.0967i	0.298390	+	0.516826i	0.975768	−	0.218809i	$-0.0702172\pi$
$461$	6.40670	+	11.0967i	0.298390	+	0.516826i	−0.677378	+	0.735635i	$0.736884\pi$
$462$		0			0
$463$	5.54704	−	9.60775i	0.257793	−	0.446510i	−0.707858	−	0.706355i	$-0.750338\pi$
$463$	5.54704	−	9.60775i	0.257793	−	0.446510i	0.965650	+	0.259845i	$0.0836715\pi$
$464$		0			0
$465$	−3.09714	+	0.101111i	−0.143627	+	0.00468891i
$466$		0			0
$467$	5.36754	+	9.29686i	0.248380	+	0.430207i	0.963077	−	0.269228i	$-0.0867684\pi$
$467$	5.36754	+	9.29686i	0.248380	+	0.430207i	−0.714696	+	0.699435i	$0.753435\pi$
$468$		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	−0.352331	−	0.935875i	$-0.614611\pi$
$487$	13.9984	−	24.2459i	0.634326	−	1.09868i	0.986657	−	0.162810i	$-0.0520557\pi$
$488$		0			0
$489$	−1.21414	+	0.0396373i	−0.0549052	+	0.00179246i
$490$		0			0
$491$	−12.1227	+	20.9971i	−0.547089	+	0.947586i	0.451383	+	0.892330i	$0.350931\pi$
$491$	−12.1227	+	20.9971i	−0.547089	+	0.947586i	−0.998472	+	0.0552556i	$0.982403\pi$
$492$		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	−0.0498617	−	0.998756i	$-0.515878\pi$
$521$	19.1738	−	33.2099i	0.840017	−	1.45495i	0.889879	−	0.456197i	$-0.150789\pi$
$522$		0			0
$523$	20.6021	+	35.6838i	0.900865	+	1.56034i	0.826374	+	0.563122i	$0.190400\pi$
$523$	20.6021	+	35.6838i	0.900865	+	1.56034i	0.0744911	+	0.997222i	$0.476267\pi$
$524$		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	0.601609	−	0.798791i	$-0.294527\pi$
$541$	−9.09371	−	15.7508i	−0.390969	−	0.677178i	−0.992578	+	0.121613i	$0.961193\pi$
$542$		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	0.873175	−	0.487406i	$-0.162057\pi$
$547$	0.338699	+	0.586644i	0.0144817	+	0.0250831i	−0.858694	+	0.512489i	$0.828723\pi$
$548$		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	−0.357687	−	0.933842i	$-0.616435\pi$
$557$	14.8659	−	25.7484i	0.629887	−	1.09100i	0.987574	−	0.157155i	$-0.0502322\pi$
$558$		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	0.548524	−	0.836135i	$-0.315190\pi$
$563$	−10.6739	−	18.4878i	−0.449852	−	0.779167i	−0.998376	+	0.0569680i	$0.981857\pi$
$564$		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	−0.662844	−	0.748757i	$-0.730651\pi$
$569$	7.56212	−	13.0980i	0.317021	−	0.549096i	0.979865	+	0.199661i	$0.0639842\pi$
$570$		0			0
$571$	−9.94314	−	17.2220i	−0.416107	−	0.720719i	0.579437	−	0.815017i	$-0.303273\pi$
$571$	−9.94314	−	17.2220i	−0.416107	−	0.720719i	−0.995544	+	0.0942981i	$0.969939\pi$
$572$		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	−0.0775179	−	0.996991i	$-0.524700\pi$
$577$	19.8090	−	34.3102i	0.824661	−	1.42835i	0.902178	−	0.431363i	$-0.141967\pi$
$578$		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	0.888455	−	0.458963i	$-0.151779\pi$
$587$	1.13275	+	1.96199i	0.0467537	+	0.0809798i	−0.841701	+	0.539943i	$0.818446\pi$
$588$		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	0.962210	−	0.272308i	$-0.0877869\pi$
$593$	5.97295	+	10.3454i	0.245280	+	0.424837i	−0.716931	+	0.697145i	$0.754454\pi$
$594$		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	0.894610	−	0.446849i	$-0.147454\pi$
$599$	1.47636	+	2.55713i	0.0603224	+	0.104481i	−0.834287	+	0.551330i	$0.814120\pi$
$600$		0			0
$601$	15.9751	+	27.6697i	0.651638	+	1.12867i	0.982725	+	0.185071i	$0.0592514\pi$
$601$	15.9751	+	27.6697i	0.651638	+	1.12867i	−0.331087	+	0.943600i	$0.607415\pi$
$602$		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	−0.712510	−	0.701662i	$-0.752442\pi$
$613$	6.22441	−	10.7810i	0.251402	−	0.435441i	0.963912	+	0.266221i	$0.0857751\pi$
$614$		0			0
$615$	−13.5105	−	21.7310i	−0.544795	−	0.876278i
$616$		0			0
$617$	−4.70100	+	8.14237i	−0.189255	+	0.327799i	−0.945002	−	0.327064i	$-0.893941\pi$
$617$	−4.70100	+	8.14237i	−0.189255	+	0.327799i	0.755747	+	0.654864i	$0.227274\pi$
$618$		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	−0.596470	−	0.802635i	$-0.703431\pi$
$643$	10.0635	−	17.4306i	0.396867	−	0.687394i	0.993338	+	0.115241i	$0.0367640\pi$
$644$		0			0
$645$	14.4994	−	0.473355i	0.570913	−	0.0186383i
$646$		0			0
$647$	−11.1891	+	19.3800i	−0.439887	+	0.761907i	−0.997680	−	0.0680731i	$-0.978315\pi$
$647$	−11.1891	+	19.3800i	−0.439887	+	0.761907i	0.557793	+	0.829980i	$0.311648\pi$
$648$		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	0.976064	−	0.217484i	$-0.0697851\pi$
$659$	7.69321	+	13.3250i	0.299685	+	0.519070i	−0.676379	+	0.736554i	$0.736452\pi$
$660$		0			0
$661$	−24.5736	−	42.5628i	−0.955804	−	1.65550i	−0.732518	−	0.680747i	$-0.761655\pi$
$661$	−24.5736	−	42.5628i	−0.955804	−	1.65550i	−0.223285	−	0.974753i	$-0.571678\pi$
$662$		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	0.698999	−	0.715123i	$-0.253629\pi$
$673$	−6.99961	−	12.1237i	−0.269815	−	0.467334i	−0.968814	+	0.247789i	$0.920296\pi$
$674$		0			0
$675$	−9.40631	+	0.923876i	−0.362049	+	0.0355600i
$676$		0			0
$677$	23.3870	−	40.5075i	0.898836	−	1.55683i	0.0698517	−	0.997557i	$-0.477747\pi$
$677$	23.3870	−	40.5075i	0.898836	−	1.55683i	0.828984	−	0.559272i	$-0.188919\pi$
$678$		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	−0.0727571	−	0.997350i	$-0.523180\pi$
$683$	21.6222	−	37.4508i	0.827352	−	1.43302i	0.900109	−	0.435665i	$-0.143487\pi$
$684$		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	−0.732751	−	0.680497i	$-0.761764\pi$
$691$	5.86072	−	10.1511i	0.222952	−	0.386165i	0.955703	+	0.294332i	$0.0950972\pi$
$692$		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	−0.875940	−	0.482420i	$-0.839758\pi$
$709$	−0.537388	+	0.930783i	−0.0201820	+	0.0349563i	0.855758	+	0.517376i	$0.173091\pi$
$710$		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	0.999638	−	0.0268932i	$-0.00856140\pi$
$719$	12.7777	+	22.1317i	0.476529	+	0.825372i	−0.523109	+	0.852266i	$0.675228\pi$
$720$		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	0.957849	−	0.287273i	$-0.0927486\pi$
$727$	6.20522	+	10.7478i	0.230139	+	0.398612i	−0.727710	+	0.685885i	$0.759415\pi$
$728$		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	−0.687288	−	0.726385i	$-0.741199\pi$
$739$	7.75910	−	13.4392i	0.285423	−	0.494368i	0.972712	+	0.232017i	$0.0745325\pi$
$740$		0			0
$741$	−5.73432	+	10.7258i	−0.210656	+	0.394024i
$742$		0			0
$743$	−13.6333	+	23.6136i	−0.500159	+	0.866301i	0.499841	+	0.866117i	$0.333392\pi$
$743$	−13.6333	+	23.6136i	−0.500159	+	0.866301i	−1.00000		0.000183414i	$0.999942\pi$
$744$		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	−0.999774	−	0.0212548i	$-0.993234\pi$
$769$	−13.3518	+	23.1261i	−0.481480	+	0.833948i	0.518294	+	0.855202i	$0.326567\pi$
$770$		0			0
$771$	−21.9888	+	41.1293i	−0.791908	+	1.48123i
$772$		0			0
$773$	−13.5143	+	23.4074i	−0.486074	+	0.841905i	−0.999872	−	0.0160062i	$-0.994905\pi$
$773$	−13.5143	+	23.4074i	−0.486074	+	0.841905i	0.513798	+	0.857911i	$0.328238\pi$
$774$		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	−0.855056	−	0.518535i	$-0.826478\pi$
$787$	−24.5915	−	42.5937i	−0.876593	−	1.51830i	−0.0215363	−	0.999768i	$-0.506856\pi$
$788$		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	−0.144434	−	0.989514i	$-0.546136\pi$
$797$	22.1538	−	38.3715i	0.784728	−	1.35919i	0.929162	−	0.369674i	$-0.120531\pi$
$798$		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	0.406040	+	0.913855i	$0.366909\pi$
$809$	−16.7359	+	28.9874i	−0.588402	+	1.01914i	−0.994442	+	0.105286i	$0.966424\pi$
$810$		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	−0.599968	−	0.800024i	$-0.704820\pi$
$821$	11.2566	−	19.4970i	0.392857	−	0.680449i	0.992825	+	0.119575i	$0.0381533\pi$
$822$		0			0
$823$	−7.33674	−	12.7076i	−0.255743	−	0.442959i	0.709354	−	0.704852i	$-0.248987\pi$
$823$	−7.33674	−	12.7076i	−0.255743	−	0.442959i	−0.965097	+	0.261893i	$0.915653\pi$
$824$		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	−0.243992	−	0.969777i	$-0.578457\pi$
$829$	20.6688	−	35.7993i	0.717856	−	1.24336i	0.961848	−	0.273585i	$-0.0882095\pi$
$830$		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	0.899161	−	0.437617i	$-0.144177\pi$
$839$	2.04477	+	3.54164i	0.0705932	+	0.122271i	−0.828568	+	0.559888i	$0.810844\pi$
$840$		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	−0.959998	−	0.280006i	$-0.909664\pi$
$853$	−21.1012	−	36.5484i	−0.722491	−	1.25139i	0.237507	−	0.971386i	$-0.423670\pi$
$854$		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	0.952809	−	0.303572i	$-0.0981793\pi$
$863$	6.27205	+	10.8635i	0.213503	+	0.369798i	−0.739305	+	0.673370i	$0.764846\pi$
$864$		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	0.620469	−	0.784231i	$-0.286942\pi$
$911$	−11.1353	−	19.2870i	−0.368930	−	0.639006i	−0.989399	+	0.145226i	$0.953609\pi$
$912$		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	0.987280	−	0.158992i	$-0.0508243\pi$
$919$	10.7906	+	18.6899i	0.355949	+	0.616522i	−0.631331	+	0.775514i	$0.717491\pi$
$920$		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	−0.381796	−	0.924247i	$-0.624694\pi$
$929$	18.5780	−	32.1780i	0.609523	−	1.05572i	0.991319	−	0.131478i	$-0.0419724\pi$
$930$		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	0.936077	+	0.351795i	$0.114429\pi$
$941$	23.7032	+	41.0551i	0.772702	+	1.33836i	−0.163375	+	0.986564i	$0.552238\pi$
$942$		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	−0.844991	−	0.534781i	$-0.820394\pi$
$947$	1.25059	−	2.16608i	0.0406386	−	0.0703881i	0.885629	+	0.464393i	$0.153727\pi$
$948$		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	−0.758299	−	0.651907i	$-0.773969\pi$
$967$	5.76591	−	9.98684i	0.185419	−	0.321155i	0.943718	+	0.330752i	$0.107302\pi$
$968$		0			0
$969$	−1.18021	+	2.20755i	−0.0379139	+	0.0709166i
$970$		0			0
$971$	−9.14669	−	15.8425i	−0.293531	−	0.508411i	0.681111	−	0.732180i	$-0.261497\pi$
$971$	−9.14669	−	15.8425i	−0.293531	−	0.508411i	−0.974642	+	0.223769i	$0.928164\pi$
$972$		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	0.999694	−	0.0247361i	$-0.00787454\pi$
$977$	14.9541	+	25.9013i	0.478425	+	0.828656i	−0.521269	+	0.853392i	$0.674541\pi$
$978$		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	−0.998781	−	0.0493567i	$-0.984283\pi$
$991$	−14.3753	+	24.8987i	−0.456646	+	0.790935i	0.542135	+	0.840292i	$0.317616\pi$
$992$		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.193.5	yes	22
3.2	odd	2		1512.2.t.c.361.8		22
4.3	odd	2		1008.2.t.l.193.7		22
7.2	even	3		504.2.q.c.121.4	yes	22
9.2	odd	6		1512.2.q.d.1369.4		22
9.7	even	3		504.2.q.c.25.4	✓	22
12.11	even	2		3024.2.t.k.1873.8		22
21.2	odd	6		1512.2.q.d.793.4		22
28.23	odd	6		1008.2.q.l.625.8		22
36.7	odd	6		1008.2.q.l.529.8		22
36.11	even	6		3024.2.q.l.2881.4		22
63.2	odd	6		1512.2.t.c.289.8		22
63.16	even	3	inner	504.2.t.c.457.5	yes	22
84.23	even	6		3024.2.q.l.2305.4		22
252.79	odd	6		1008.2.t.l.961.7		22
252.191	even	6		3024.2.t.k.289.8		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.q.c.25.4	✓	22	9.7	even	3
504.2.q.c.121.4	yes	22	7.2	even	3
504.2.t.c.193.5	yes	22	1.1	even	1	trivial
504.2.t.c.457.5	yes	22	63.16	even	3	inner
1008.2.q.l.529.8		22	36.7	odd	6
1008.2.q.l.625.8		22	28.23	odd	6
1008.2.t.l.193.7		22	4.3	odd	2
1008.2.t.l.961.7		22	252.79	odd	6
1512.2.q.d.793.4		22	21.2	odd	6
1512.2.q.d.1369.4		22	9.2	odd	6
1512.2.t.c.289.8		22	63.2	odd	6
1512.2.t.c.361.8		22	3.2	odd	2
3024.2.q.l.2305.4		22	84.23	even	6
3024.2.q.l.2881.4		22	36.11	even	6
3024.2.t.k.289.8		22	252.191	even	6
3024.2.t.k.1873.8		22	12.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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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