LMFDB - Embedded newform 280.2.bo.a.33.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [280,2,Mod(17,280)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(280, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 0, 3, 2]))

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

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

chi := DirichletCharacter("280.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 280 = 2^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	280.bo (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.23581125660$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			33.12
Character	$\chi$	$=$	280.33
Dual form			280.2.bo.a.17.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.19510 + 0.856125i) q^{3} +(0.672461 - 2.13256i) q^{5} +(-2.52104 + 0.802724i) q^{7} +(6.87765 + 3.97081i) q^{9} +O(q^{10})$	\(q+(3.19510 + 0.856125i) q^{3} +(0.672461 - 2.13256i) q^{5} +(-2.52104 + 0.802724i) q^{7} +(6.87765 + 3.97081i) q^{9} +(-1.05351 - 1.82473i) q^{11} +(-1.20510 + 1.20510i) q^{13} +(3.97432 - 6.23802i) q^{15} +(0.850985 - 3.17592i) q^{17} +(-2.36491 + 4.09614i) q^{19} +(-8.74221 + 0.406461i) q^{21} +(-4.00492 + 1.07312i) q^{23} +(-4.09559 - 2.86812i) q^{25} +(11.5583 + 11.5583i) q^{27} +3.65910i q^{29} +(-1.63858 + 0.946036i) q^{31} +(-1.80387 - 6.73212i) q^{33} +(0.0165540 + 5.91606i) q^{35} +(-2.65625 - 9.91327i) q^{37} +(-4.88214 + 2.81870i) q^{39} +0.826081i q^{41} +(4.70172 + 4.70172i) q^{43} +(13.0929 - 11.9968i) q^{45} +(3.90561 - 1.04650i) q^{47} +(5.71127 - 4.04740i) q^{49} +(5.43796 - 9.41883i) q^{51} +(-0.645746 + 2.40996i) q^{53} +(-4.59977 + 1.01960i) q^{55} +(-11.0629 + 11.0629i) q^{57} +(-1.15566 - 2.00166i) q^{59} +(1.44974 + 0.837008i) q^{61} +(-20.5263 - 4.48972i) q^{63} +(1.75956 + 3.38033i) q^{65} +(-12.2602 - 3.28512i) q^{67} -13.7149 q^{69} +10.7915 q^{71} +(-12.6133 - 3.37973i) q^{73} +(-10.6304 - 12.6703i) q^{75} +(4.12068 + 3.75453i) q^{77} +(8.29280 + 4.78785i) q^{79} +(15.1223 + 26.1925i) q^{81} +(-3.47691 + 3.47691i) q^{83} +(-6.20057 - 3.95045i) q^{85} +(-3.13265 + 11.6912i) q^{87} +(2.86698 - 4.96576i) q^{89} +(2.07074 - 4.00547i) q^{91} +(-6.04536 + 1.61985i) q^{93} +(7.14494 + 7.79779i) q^{95} +(-1.02714 - 1.02714i) q^{97} -16.7331i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 4 q^{7}+O(q^{10}) $ 48 * q - 4 * q^7	$ 48 q - 4 q^{7} + 4 q^{11} + 8 q^{15} - 4 q^{21} - 4 q^{23} - 8 q^{25} - 36 q^{33} + 24 q^{35} + 8 q^{37} - 16 q^{43} + 48 q^{45} + 24 q^{51} + 16 q^{53} - 96 q^{57} - 36 q^{61} - 68 q^{63} + 12 q^{65} - 16 q^{67} - 64 q^{71} - 48 q^{73} - 48 q^{75} + 4 q^{77} - 40 q^{85} - 12 q^{87} - 80 q^{91} + 24 q^{95}+O(q^{100}) $ 48 * q - 4 * q^7 + 4 * q^11 + 8 * q^15 - 4 * q^21 - 4 * q^23 - 8 * q^25 - 36 * q^33 + 24 * q^35 + 8 * q^37 - 16 * q^43 + 48 * q^45 + 24 * q^51 + 16 * q^53 - 96 * q^57 - 36 * q^61 - 68 * q^63 + 12 * q^65 - 16 * q^67 - 64 * q^71 - 48 * q^73 - 48 * q^75 + 4 * q^77 - 40 * q^85 - 12 * q^87 - 80 * q^91 + 24 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/280\mathbb{Z}\right)^\times$.

$n$	$57$	$71$	$141$	$241$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$1$	$e\left(\frac{5}{6}\right)$

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
$3$	3.19510	+	0.856125i	1.84469	+	0.494284i	0.999211	−	0.0397200i	$-0.0126466\pi$
$3$	3.19510	+	0.856125i	1.84469	+	0.494284i	0.845482	+	0.534004i	$0.179313\pi$
$4$		0			0
$5$	0.672461	−	2.13256i	0.300734	−	0.953708i
$5$	0.672461	−	2.13256i	0.300734	−	0.953708i
$6$		0			0
$7$	−2.52104	+	0.802724i	−0.952863	+	0.303401i
$7$	−2.52104	+	0.802724i	−0.952863	+	0.303401i
$8$		0			0
$9$	6.87765	+	3.97081i	2.29255	+	1.32360i
$10$		0			0
$11$	−1.05351	−	1.82473i	−0.317644	−	0.550175i	0.662352	−	0.749193i	$-0.269558\pi$
$11$	−1.05351	−	1.82473i	−0.317644	−	0.550175i	−0.979996	+	0.199017i	$0.936225\pi$
$12$		0			0
$13$	−1.20510	+	1.20510i	−0.334235	+	0.334235i	−0.854192	−	0.519957i	$-0.825948\pi$
$13$	−1.20510	+	1.20510i	−0.334235	+	0.334235i	0.519957	+	0.854192i	$0.325948\pi$
$14$		0			0
$15$	3.97432	−	6.23802i	1.02616	−	1.61065i
$16$		0			0
$17$	0.850985	−	3.17592i	0.206394	−	0.770273i	−0.782626	−	0.622492i	$-0.786120\pi$
$17$	0.850985	−	3.17592i	0.206394	−	0.770273i	0.989020	−	0.147781i	$-0.0472131\pi$
$18$		0			0
$19$	−2.36491	+	4.09614i	−0.542547	+	0.939718i	0.456210	+	0.889872i	$0.349206\pi$
$19$	−2.36491	+	4.09614i	−0.542547	+	0.939718i	−0.998757	+	0.0498463i	$0.984127\pi$
$20$		0			0
$21$	−8.74221	+	0.406461i	−1.90771	+	0.0886970i
$22$		0			0
$23$	−4.00492	+	1.07312i	−0.835084	+	0.223760i	−0.650931	−	0.759137i	$-0.725621\pi$
$23$	−4.00492	+	1.07312i	−0.835084	+	0.223760i	−0.184154	+	0.982897i	$0.558954\pi$
$24$		0			0
$25$	−4.09559	−	2.86812i	−0.819118	−	0.573624i
$26$		0			0
$27$	11.5583	+	11.5583i	2.22440	+	2.22440i
$28$		0			0
$29$			3.65910i			0.679478i	0.940520	+	0.339739i	$0.110339\pi$
$29$			3.65910i			0.679478i	−0.940520	+	0.339739i	$0.889661\pi$
$30$		0			0
$31$	−1.63858	+	0.946036i	−0.294298	+	0.169913i	−0.639879	−	0.768476i	$-0.721015\pi$
$31$	−1.63858	+	0.946036i	−0.294298	+	0.169913i	0.345581	+	0.938389i	$0.387682\pi$
$32$		0			0
$33$	−1.80387	−	6.73212i	−0.314013	−	1.17191i
$34$		0			0
$35$	0.0165540	+	5.91606i	0.00279813	+	0.999996i
$36$		0			0
$37$	−2.65625	−	9.91327i	−0.436685	−	1.62973i	−0.737001	−	0.675891i	$-0.763759\pi$
$37$	−2.65625	−	9.91327i	−0.436685	−	1.62973i	0.300316	−	0.953840i	$-0.402908\pi$
$38$		0			0
$39$	−4.88214	+	2.81870i	−0.781768	+	0.451354i
$40$		0			0
$41$			0.826081i			0.129012i	0.997917	+	0.0645061i	$0.0205472\pi$
$41$			0.826081i			0.129012i	−0.997917	+	0.0645061i	$0.979453\pi$
$42$		0			0
$43$	4.70172	+	4.70172i	0.717005	+	0.717005i	0.967991	−	0.250985i	$-0.0807546\pi$
$43$	4.70172	+	4.70172i	0.717005	+	0.717005i	−0.250985	+	0.967991i	$0.580755\pi$
$44$		0			0
$45$	13.0929	−	11.9968i	1.95178	−	1.78837i
$46$		0			0
$47$	3.90561	−	1.04650i	0.569692	−	0.152648i	0.0375365	−	0.999295i	$-0.488049\pi$
$47$	3.90561	−	1.04650i	0.569692	−	0.152648i	0.532155	+	0.846647i	$0.321382\pi$
$48$		0			0
$49$	5.71127	−	4.04740i	0.815896	−	0.578199i
$50$		0			0
$51$	5.43796	−	9.41883i	0.761467	−	1.31890i
$52$		0			0
$53$	−0.645746	+	2.40996i	−0.0887000	+	0.331033i	−0.995989	−	0.0894744i	$-0.971481\pi$
$53$	−0.645746	+	2.40996i	−0.0887000	+	0.331033i	0.907289	+	0.420507i	$0.138148\pi$
$54$		0			0
$55$	−4.59977	+	1.01960i	−0.620233	+	0.137483i
$56$		0			0
$57$	−11.0629	+	11.0629i	−1.46532	+	1.46532i
$58$		0			0
$59$	−1.15566	−	2.00166i	−0.150454	−	0.260594i	0.780940	−	0.624606i	$-0.214740\pi$
$59$	−1.15566	−	2.00166i	−0.150454	−	0.260594i	−0.931394	+	0.364011i	$0.881407\pi$
$60$		0			0
$61$	1.44974	+	0.837008i	0.185620	+	0.107168i	0.589931	−	0.807454i	$-0.299155\pi$
$61$	1.44974	+	0.837008i	0.185620	+	0.107168i	−0.404310	+	0.914622i	$0.632488\pi$
$62$		0			0
$63$	−20.5263	−	4.48972i	−2.58607	−	0.565651i
$64$		0			0
$65$	1.75956	+	3.38033i	0.218247	+	0.419278i
$66$		0			0
$67$	−12.2602	−	3.28512i	−1.49783	−	0.401342i	−0.585456	−	0.810704i	$-0.699084\pi$
$67$	−12.2602	−	3.28512i	−1.49783	−	0.401342i	−0.912372	+	0.409363i	$0.865751\pi$
$68$		0			0
$69$	−13.7149			−1.65108
$70$		0			0
$71$	10.7915			1.28071			0.640356	−	0.768079i	$-0.278787\pi$
$71$	10.7915			1.28071			0.640356	+	0.768079i	$0.278787\pi$
$72$		0			0
$73$	−12.6133	−	3.37973i	−1.47628	−	0.395567i	−0.571198	−	0.820812i	$-0.693521\pi$
$73$	−12.6133	−	3.37973i	−1.47628	−	0.395567i	−0.905078	+	0.425245i	$0.860188\pi$
$74$		0			0
$75$	−10.6304	−	12.6703i	−1.22749	−	1.46304i
$76$		0			0
$77$	4.12068	+	3.75453i	0.469595	+	0.427868i
$78$		0			0
$79$	8.29280	+	4.78785i	0.933013	+	0.538675i	0.887763	−	0.460301i	$-0.152258\pi$
$79$	8.29280	+	4.78785i	0.933013	+	0.538675i	0.0452496	+	0.998976i	$0.485592\pi$
$80$		0			0
$81$	15.1223	+	26.1925i	1.68025	+	2.91028i
$82$		0			0
$83$	−3.47691	+	3.47691i	−0.381641	+	0.381641i	−0.871693	−	0.490052i	$-0.836978\pi$
$83$	−3.47691	+	3.47691i	−0.381641	+	0.381641i	0.490052	+	0.871693i	$0.336978\pi$
$84$		0			0
$85$	−6.20057	−	3.95045i	−0.672546	−	0.428487i
$86$		0			0
$87$	−3.13265	+	11.6912i	−0.335855	+	1.25343i
$88$		0			0
$89$	2.86698	−	4.96576i	0.303900	−	0.526370i	−0.673116	−	0.739537i	$-0.735045\pi$
$89$	2.86698	−	4.96576i	0.303900	−	0.526370i	0.977016	+	0.213167i	$0.0683779\pi$
$90$		0			0
$91$	2.07074	−	4.00547i	0.217073	−	0.419887i
$92$		0			0
$93$	−6.04536	+	1.61985i	−0.626875	+	0.167971i
$94$		0			0
$95$	7.14494	+	7.79779i	0.733055	+	0.800036i
$96$		0			0
$97$	−1.02714	−	1.02714i	−0.104290	−	0.104290i	0.653036	−	0.757327i	$-0.273495\pi$
$97$	−1.02714	−	1.02714i	−0.104290	−	0.104290i	−0.757327	+	0.653036i	$0.773495\pi$
$98$		0			0
$99$		−	16.7331i		−	1.68174i
$100$		0			0
$101$	1.11869	−	0.645878i	0.111314	−	0.0642672i	−0.443309	−	0.896369i	$-0.646196\pi$
$101$	1.11869	−	0.645878i	0.111314	−	0.0642672i	0.554623	+	0.832101i	$0.312862\pi$
$102$		0			0
$103$	−2.82954	−	10.5600i	−0.278803	−	1.04051i	−0.953250	−	0.302184i	$-0.902284\pi$
$103$	−2.82954	−	10.5600i	−0.278803	−	1.04051i	0.674447	−	0.738324i	$-0.264382\pi$
$104$		0			0
$105$	−5.01199	+	18.9166i	−0.489120	+	1.84607i
$106$		0			0
$107$	−0.770212	−	2.87447i	−0.0744592	−	0.277885i	0.918651	−	0.395070i	$-0.129280\pi$
$107$	−0.770212	−	2.87447i	−0.0744592	−	0.277885i	−0.993110	+	0.117185i	$0.962613\pi$
$108$		0			0
$109$	13.0694	−	7.54561i	1.25182	−	0.722739i	0.280349	−	0.959898i	$-0.409550\pi$
$109$	13.0694	−	7.54561i	1.25182	−	0.722739i	0.971471	+	0.237160i	$0.0762164\pi$
$110$		0			0
$111$		−	33.9480i		−	3.22220i
$112$		0			0
$113$	4.23171	+	4.23171i	0.398086	+	0.398086i	0.877558	−	0.479471i	$-0.159172\pi$
$113$	4.23171	+	4.23171i	0.398086	+	0.398086i	−0.479471	+	0.877558i	$0.659172\pi$
$114$		0			0
$115$	−0.404675	+	9.26236i	−0.0377361	+	0.863719i
$116$		0			0
$117$	−13.0735	+	3.50303i	−1.20865	+	0.323855i
$118$		0			0
$119$	0.404020	+	8.68972i	0.0370365	+	0.796585i
$120$		0			0
$121$	3.28025	−	5.68156i	0.298205	−	0.516506i
$122$		0			0
$123$	−0.707229	+	2.63941i	−0.0637687	+	0.237988i
$124$		0			0
$125$	−8.87056	+	6.80538i	−0.793407	+	0.608692i
$126$		0			0
$127$	−4.53114	+	4.53114i	−0.402073	+	0.402073i	−0.878963	−	0.476890i	$-0.841764\pi$
$127$	−4.53114	+	4.53114i	−0.402073	+	0.402073i	0.476890	+	0.878963i	$0.341764\pi$
$128$		0			0
$129$	10.9972	+	19.0477i	0.968250	+	1.67706i
$130$		0			0
$131$	−2.40936	−	1.39105i	−0.210507	−	0.121536i	0.391040	−	0.920374i	$-0.372115\pi$
$131$	−2.40936	−	1.39105i	−0.210507	−	0.121536i	−0.601547	+	0.798837i	$0.705449\pi$
$132$		0			0
$133$	2.67395	−	12.2249i	0.231861	−	1.06003i
$134$		0			0
$135$	32.4214	−	16.8763i	2.79039	−	1.45248i
$136$		0			0
$137$	21.7199	+	5.81982i	1.85565	+	0.497221i	0.999800	−	0.0199984i	$-0.00636610\pi$
$137$	21.7199	+	5.81982i	1.85565	+	0.497221i	0.855853	+	0.517219i	$0.173033\pi$
$138$		0			0
$139$	−8.33499			−0.706965			−0.353482	−	0.935441i	$-0.615003\pi$
$139$	−8.33499			−0.706965			−0.353482	+	0.935441i	$0.615003\pi$
$140$		0			0
$141$	13.3748			1.12636
$142$		0			0
$143$	3.46856	+	0.929398i	0.290056	+	0.0777202i
$144$		0			0
$145$	7.80324	+	2.46060i	0.648024	+	0.204342i
$146$		0			0
$147$	21.7132	−	8.04228i	1.79087	−	0.663316i
$148$		0			0
$149$	7.44844	+	4.30036i	0.610200	+	0.352299i	0.773044	−	0.634353i	$-0.218733\pi$
$149$	7.44844	+	4.30036i	0.610200	+	0.352299i	−0.162844	+	0.986652i	$0.552067\pi$
$150$		0			0
$151$	5.13200	+	8.88888i	0.417636	+	0.723366i	0.995701	−	0.0926240i	$-0.0295255\pi$
$151$	5.13200	+	8.88888i	0.417636	+	0.723366i	−0.578065	+	0.815990i	$0.696192\pi$
$152$		0			0
$153$	18.4637	−	18.4637i	1.49271	−	1.49271i
$154$		0			0
$155$	0.915592	+	4.13054i	0.0735421	+	0.331773i
$156$		0			0
$157$	2.63385	−	9.82966i	0.210204	−	0.784492i	−0.777596	−	0.628764i	$-0.783561\pi$
$157$	2.63385	−	9.82966i	0.210204	−	0.784492i	0.987800	−	0.155728i	$-0.0497723\pi$
$158$		0			0
$159$	−4.12645	+	7.14722i	−0.327249	+	0.566811i
$160$		0			0
$161$	9.23515	−	5.92022i	0.727832	−	0.466578i
$162$		0			0
$163$	2.79779	−	0.749665i	0.219140	−	0.0587183i	−0.147579	−	0.989050i	$-0.547148\pi$
$163$	2.79779	−	0.749665i	0.219140	−	0.0587183i	0.366718	+	0.930332i	$0.380481\pi$
$164$		0			0
$165$	−15.5696	−	0.680242i	−1.21210	−	0.0529567i
$166$		0			0
$167$	8.39226	+	8.39226i	0.649412	+	0.649412i	0.952851	−	0.303439i	$-0.0981347\pi$
$167$	8.39226	+	8.39226i	0.649412	+	0.649412i	−0.303439	+	0.952851i	$0.598135\pi$
$168$		0			0
$169$			10.0955i			0.776574i
$170$		0			0
$171$	−32.5300	+	18.7812i	−2.48763	+	1.43623i
$172$		0			0
$173$	0.0653257	+	0.243799i	0.00496662	+	0.0185357i	0.968365	−	0.249539i	$-0.0802792\pi$
$173$	0.0653257	+	0.243799i	0.00496662	+	0.0185357i	−0.963398	+	0.268075i	$0.913613\pi$
$174$		0			0
$175$	12.6275	+	3.94301i	0.954546	+	0.298064i
$176$		0			0
$177$	−1.97878	−	7.38490i	−0.148734	−	0.555083i
$178$		0			0
$179$	18.8244	−	10.8683i	1.40700	−	0.812331i	0.411901	−	0.911228i	$-0.364865\pi$
$179$	18.8244	−	10.8683i	1.40700	−	0.812331i	0.995098	+	0.0988972i	$0.0315315\pi$
$180$		0			0
$181$			3.06050i			0.227485i	0.993510	+	0.113743i	$0.0362839\pi$
$181$			3.06050i			0.227485i	−0.993510	+	0.113743i	$0.963716\pi$
$182$		0			0
$183$	3.91548	+	3.91548i	0.289441	+	0.289441i
$184$		0			0
$185$	−22.9268	−	1.00168i	−1.68561	−	0.0736449i
$186$		0			0
$187$	−6.69170	+	1.79303i	−0.489345	+	0.131120i
$188$		0			0
$189$	−38.4172	−	19.8609i	−2.79444	−	1.44467i
$190$		0			0
$191$	−10.5499	+	18.2729i	−0.763361	+	1.32218i	0.177748	+	0.984076i	$0.443119\pi$
$191$	−10.5499	+	18.2729i	−0.763361	+	1.32218i	−0.941109	+	0.338103i	$0.890215\pi$
$192$		0			0
$193$	−5.39085	+	20.1189i	−0.388042	+	1.44819i	0.445273	+	0.895395i	$0.353106\pi$
$193$	−5.39085	+	20.1189i	−0.388042	+	1.44819i	−0.833315	+	0.552798i	$0.813560\pi$
$194$		0			0
$195$	2.72800	+	12.3069i	0.195356	+	0.881316i
$196$		0			0
$197$	−9.29732	+	9.29732i	−0.662406	+	0.662406i	−0.955947	−	0.293540i	$-0.905167\pi$
$197$	−9.29732	+	9.29732i	−0.662406	+	0.662406i	0.293540	+	0.955947i	$0.405167\pi$
$198$		0			0
$199$	3.77827	+	6.54415i	0.267834	+	0.463902i	0.968302	−	0.249781i	$-0.0803587\pi$
$199$	3.77827	+	6.54415i	0.267834	+	0.463902i	−0.700468	+	0.713684i	$0.747025\pi$
$200$		0			0
$201$	−36.3603	−	20.9926i	−2.56465	−	1.48070i
$202$		0			0
$203$	−2.93725	−	9.22474i	−0.206154	−	0.647450i
$204$		0			0
$205$	1.76167	+	0.555508i	0.123040	+	0.0387983i
$206$		0			0
$207$	−31.8056	−	8.52229i	−2.21064	−	0.592340i
$208$		0			0
$209$	9.96577			0.689347
$210$		0			0
$211$	−1.32737			−0.0913799			−0.0456900	−	0.998956i	$-0.514549\pi$
$211$	−1.32737			−0.0913799			−0.0456900	+	0.998956i	$0.514549\pi$
$212$		0			0
$213$	34.4798	+	9.23884i	2.36252	+	0.633035i
$214$		0			0
$215$	13.1884	−	6.86496i	0.899442	−	0.468186i
$216$		0			0
$217$	3.37152	−	3.70032i	0.228874	−	0.251194i
$218$		0			0
$219$	−37.4074	−	21.5971i	−2.52775	−	1.45940i
$220$		0			0
$221$	2.80178	+	4.85282i	0.188468	+	0.326436i
$222$		0			0
$223$	−7.24966	+	7.24966i	−0.485473	+	0.485473i	−0.906874	−	0.421401i	$-0.861538\pi$
$223$	−7.24966	+	7.24966i	−0.485473	+	0.485473i	0.421401	+	0.906874i	$0.361538\pi$
$224$		0			0
$225$	−16.7793	−	35.9888i	−1.11862	−	2.39925i
$226$		0			0
$227$	7.76791	−	28.9902i	0.515574	−	1.92415i	0.171618	−	0.985164i	$-0.445101\pi$
$227$	7.76791	−	28.9902i	0.515574	−	1.92415i	0.343956	−	0.938986i	$-0.388233\pi$
$228$		0			0
$229$	10.3484	−	17.9239i	0.683841	−	1.18445i	−0.289958	−	0.957039i	$-0.593641\pi$
$229$	10.3484	−	17.9239i	0.683841	−	1.18445i	0.973800	−	0.227408i	$-0.0730252\pi$
$230$		0			0
$231$	9.95164	+	15.5239i	0.654770	+	1.02140i
$232$		0			0
$233$	3.82659	−	1.02533i	0.250688	−	0.0671717i	−0.131287	−	0.991344i	$-0.541911\pi$
$233$	3.82659	−	1.02533i	0.250688	−	0.0671717i	0.381975	+	0.924173i	$0.375244\pi$
$234$		0			0
$235$	0.394639	−	9.03266i	0.0257434	−	0.589226i
$236$		0			0
$237$	22.3973	+	22.3973i	1.45486	+	1.45486i
$238$		0			0
$239$			14.2588i			0.922325i	0.887316	+	0.461163i	$0.152568\pi$
$239$			14.2588i			0.922325i	−0.887316	+	0.461163i	$0.847432\pi$
$240$		0			0
$241$	−4.21711	+	2.43475i	−0.271648	+	0.156836i	−0.629636	−	0.776890i	$-0.716796\pi$
$241$	−4.21711	+	2.43475i	−0.271648	+	0.156836i	0.357989	+	0.933726i	$0.383463\pi$
$242$		0			0
$243$	13.2012	+	49.2674i	0.846854	+	3.16050i
$244$		0			0
$245$	−4.79069	−	14.9013i	−0.306066	−	0.952010i
$246$		0			0
$247$	−2.08631	−	7.78621i	−0.132749	−	0.495425i
$248$		0			0
$249$	−14.0858	+	8.13241i	−0.892648	+	0.515371i
$250$		0			0
$251$		−	16.5118i		−	1.04222i	−0.853491	−	0.521108i	$-0.825519\pi$
$251$		−	16.5118i		−	1.04222i	0.853491	−	0.521108i	$-0.174481\pi$
$252$		0			0
$253$	6.17735	+	6.17735i	0.388367	+	0.388367i
$254$		0			0
$255$	−16.4294	−	17.9306i	−1.02885	−	1.12286i
$256$		0			0
$257$	−9.47367	+	2.53846i	−0.590951	+	0.158345i	−0.541888	−	0.840451i	$-0.682290\pi$
$257$	−9.47367	+	2.53846i	−0.590951	+	0.158345i	−0.0490634	+	0.998796i	$0.515624\pi$
$258$		0			0
$259$	14.6541	+	22.8595i	0.910563	+	1.42042i
$260$		0			0
$261$	−14.5296	+	25.1660i	−0.899360	+	1.55774i
$262$		0			0
$263$	3.21180	−	11.9866i	0.198048	−	0.739125i	−0.793409	−	0.608689i	$-0.791696\pi$
$263$	3.21180	−	11.9866i	0.198048	−	0.739125i	0.991457	−	0.130436i	$-0.0416376\pi$
$264$		0			0
$265$	4.70513	+	2.99769i	0.289034	+	0.184147i
$266$		0			0
$267$	13.4116	−	13.4116i	0.820778	−	0.820778i
$268$		0			0
$269$	1.86530	+	3.23079i	0.113729	+	0.196985i	0.917271	−	0.398264i	$-0.130387\pi$
$269$	1.86530	+	3.23079i	0.113729	+	0.196985i	−0.803542	+	0.595248i	$0.797054\pi$
$270$		0			0
$271$	−1.43539	−	0.828725i	−0.0871940	−	0.0503415i	0.455769	−	0.890098i	$-0.349364\pi$
$271$	−1.43539	−	0.828725i	−0.0871940	−	0.0503415i	−0.542963	+	0.839757i	$0.682698\pi$
$272$		0			0
$273$	10.0454	−	11.0251i	0.607976	−	0.667268i
$274$		0			0
$275$	−0.918805	+	10.4949i	−0.0554060	+	0.632867i
$276$		0			0
$277$	−14.7235	−	3.94516i	−0.884652	−	0.237042i	−0.212239	−	0.977218i	$-0.568076\pi$
$277$	−14.7235	−	3.94516i	−0.884652	−	0.237042i	−0.672413	+	0.740176i	$0.734742\pi$
$278$		0			0
$279$	−15.0261			−0.899590
$280$		0			0
$281$	−2.25722			−0.134655			−0.0673273	−	0.997731i	$-0.521447\pi$
$281$	−2.25722			−0.134655			−0.0673273	+	0.997731i	$0.521447\pi$
$282$		0			0
$283$	−5.87101	−	1.57313i	−0.348995	−	0.0935130i	0.0800631	−	0.996790i	$-0.474488\pi$
$283$	−5.87101	−	1.57313i	−0.348995	−	0.0935130i	−0.429058	+	0.903277i	$0.641154\pi$
$284$		0			0
$285$	16.1529	+	31.0317i	0.956816	+	1.83816i
$286$		0			0
$287$	−0.663115	−	2.08258i	−0.0391425	−	0.122931i
$288$		0			0
$289$	5.36015	+	3.09469i	0.315303	+	0.182040i
$290$		0			0
$291$	−2.40246	−	4.16118i	−0.140834	−	0.243932i
$292$		0			0
$293$	−17.5770	+	17.5770i	−1.02686	+	1.02686i	−0.0272289	+	0.999629i	$0.508668\pi$
$293$	−17.5770	+	17.5770i	−1.02686	+	1.02686i	−0.999629	+	0.0272289i	$0.991332\pi$
$294$		0			0
$295$	−5.04579	+	1.11847i	−0.293777	+	0.0651198i
$296$		0			0
$297$	8.91403	−	33.2676i	0.517244	−	1.93038i
$298$		0			0
$299$	3.53313	−	6.11955i	0.204326	−	0.353903i
$300$		0			0
$301$	−15.6274	−	8.07903i	−0.900748	−	0.465668i
$302$		0			0
$303$	4.12729	−	1.10590i	0.237107	−	0.0635325i
$304$		0			0
$305$	2.75986	−	2.52880i	0.158029	−	0.144798i
$306$		0			0
$307$	−21.1121	−	21.1121i	−1.20493	−	1.20493i	−0.972648	−	0.232283i	$-0.925380\pi$
$307$	−21.1121	−	21.1121i	−1.20493	−	1.20493i	−0.232283	−	0.972648i	$-0.574620\pi$
$308$		0			0
$309$		−	36.1627i		−	2.05722i
$310$		0			0
$311$	16.3420	−	9.43506i	0.926670	−	0.535013i	0.0409129	−	0.999163i	$-0.486973\pi$
$311$	16.3420	−	9.43506i	0.926670	−	0.535013i	0.885757	+	0.464150i	$0.153640\pi$
$312$		0			0
$313$	6.71594	+	25.0642i	0.379607	+	1.41671i	0.846495	+	0.532397i	$0.178709\pi$
$313$	6.71594	+	25.0642i	0.379607	+	1.41671i	−0.466888	+	0.884317i	$0.654625\pi$
$314$		0			0
$315$	−23.3777	+	40.7543i	−1.31718	+	2.29624i
$316$		0			0
$317$	0.370421	+	1.38243i	0.0208049	+	0.0776451i	0.975548	−	0.219787i	$-0.0705364\pi$
$317$	0.370421	+	1.38243i	0.0208049	+	0.0776451i	−0.954743	+	0.297432i	$0.903870\pi$
$318$		0			0
$319$	6.67686	−	3.85489i	0.373832	−	0.215832i
$320$		0			0
$321$		−	9.84362i		−	0.549417i
$322$		0			0
$323$	10.9965	+	10.9965i	0.611861	+	0.611861i
$324$		0			0
$325$	8.39198	−	1.47923i	0.465503	−	0.0820527i
$326$		0			0
$327$	48.2180	−	12.9200i	2.66646	−	0.714476i
$328$		0			0
$329$	−9.00614	+	5.77340i	−0.496524	+	0.318298i
$330$		0			0
$331$	−8.21858	+	14.2350i	−0.451734	+	0.782426i	−0.998494	−	0.0548631i	$-0.982528\pi$
$331$	−8.21858	+	14.2350i	−0.451734	+	0.782426i	0.546760	+	0.837290i	$0.315861\pi$
$332$		0			0
$333$	21.0950	−	78.7275i	1.15600	−	4.31424i
$334$		0			0
$335$	−15.2502	+	23.9365i	−0.833210	+	1.30779i
$336$		0			0
$337$	16.4453	−	16.4453i	0.895835	−	0.895835i	−0.0992293	−	0.995065i	$-0.531638\pi$
$337$	16.4453	−	16.4453i	0.895835	−	0.895835i	0.995065	+	0.0992293i	$0.0316377\pi$
$338$		0			0
$339$	9.89788	+	17.1436i	0.537579	+	0.931115i
$340$		0			0
$341$	3.45251	+	1.99331i	0.186964	+	0.107944i
$342$		0			0
$343$	−11.1494	+	14.7882i	−0.602010	+	0.798488i
$344$		0			0
$345$	−9.22271	+	29.2477i	−0.496534	+	1.57464i
$346$		0			0
$347$	−3.43767	−	0.921122i	−0.184544	−	0.0494484i	0.165363	−	0.986233i	$-0.447120\pi$
$347$	−3.43767	−	0.921122i	−0.184544	−	0.0494484i	−0.349907	+	0.936784i	$0.613787\pi$
$348$		0			0
$349$	−8.16515			−0.437070			−0.218535	−	0.975829i	$-0.570128\pi$
$349$	−8.16515			−0.437070			−0.218535	+	0.975829i	$0.570128\pi$
$350$		0			0
$351$	−27.8580			−1.48695
$352$		0			0
$353$	−0.779678	−	0.208914i	−0.0414981	−	0.0111194i	0.238010	−	0.971263i	$-0.423505\pi$
$353$	−0.779678	−	0.208914i	−0.0414981	−	0.0111194i	−0.279508	+	0.960143i	$0.590171\pi$
$354$		0			0
$355$	7.25684	−	23.0134i	0.385153	−	1.22142i
$356$		0			0
$357$	−6.14860	+	28.1104i	−0.325418	+	1.48776i
$358$		0			0
$359$	−23.7687	−	13.7228i	−1.25446	−	0.724264i	−0.282469	−	0.959276i	$-0.591154\pi$
$359$	−23.7687	−	13.7228i	−1.25446	−	0.724264i	−0.971992	+	0.235012i	$0.924487\pi$
$360$		0			0
$361$	−1.68556	−	2.91947i	−0.0887136	−	0.153656i
$362$		0			0
$363$	15.3449	−	15.3449i	0.805396	−	0.805396i
$364$		0			0
$365$	−15.6894	+	24.6259i	−0.821222	+	1.28898i
$366$		0			0
$367$	−3.44136	+	12.8433i	−0.179637	+	0.670416i	0.816078	+	0.577942i	$0.196144\pi$
$367$	−3.44136	+	12.8433i	−0.179637	+	0.670416i	−0.995715	+	0.0924739i	$0.970523\pi$
$368$		0			0
$369$	−3.28021	+	5.68150i	−0.170761	+	0.295767i
$370$		0			0
$371$	−0.306579	−	6.59395i	−0.0159168	−	0.342341i
$372$		0			0
$373$	−12.3794	+	3.31706i	−0.640982	+	0.171751i	−0.564648	−	0.825332i	$-0.690988\pi$
$373$	−12.3794	+	3.31706i	−0.640982	+	0.171751i	−0.0763341	+	0.997082i	$0.524322\pi$
$374$		0			0
$375$	−34.1686	+	14.1496i	−1.76446	+	0.730681i
$376$		0			0
$377$	−4.40959	−	4.40959i	−0.227105	−	0.227105i
$378$		0			0
$379$			3.65754i			0.187875i	0.995578	+	0.0939375i	$0.0299454\pi$
$379$			3.65754i			0.187875i	−0.995578	+	0.0939375i	$0.970055\pi$
$380$		0			0
$381$	−18.3567	+	10.5982i	−0.940441	+	0.542964i
$382$		0			0
$383$	−7.80691	−	29.1358i	−0.398915	−	1.48877i	−0.815009	−	0.579448i	$-0.803268\pi$
$383$	−7.80691	−	29.1358i	−0.398915	−	1.48877i	0.416095	−	0.909321i	$-0.363399\pi$
$384$		0			0
$385$	10.7777	−	6.26281i	0.549285	−	0.319182i
$386$		0			0
$387$	13.6671	+	51.0064i	0.694739	+	2.59280i
$388$		0			0
$389$	−5.17854	+	2.98983i	−0.262562	+	0.151591i	−0.625503	−	0.780222i	$-0.715106\pi$
$389$	−5.17854	+	2.98983i	−0.262562	+	0.151591i	0.362940	+	0.931812i	$0.381773\pi$
$390$		0			0
$391$			13.6325i			0.689426i
$392$		0			0
$393$	−6.50725	−	6.50725i	−0.328247	−	0.328247i
$394$		0			0
$395$	15.7869	−	14.4652i	0.794327	−	0.727824i
$396$		0			0
$397$	−1.45836	+	0.390768i	−0.0731932	+	0.0196121i	−0.295230	−	0.955426i	$-0.595396\pi$
$397$	−1.45836	+	0.390768i	−0.0731932	+	0.0196121i	0.222037	+	0.975038i	$0.428730\pi$
$398$		0			0
$399$	19.0096	−	36.7705i	0.951669	−	1.84083i
$400$		0			0
$401$	12.6011	−	21.8258i	0.629269	−	1.08993i	−0.358429	−	0.933557i	$-0.616688\pi$
$401$	12.6011	−	21.8258i	0.629269	−	1.08993i	0.987699	−	0.156370i	$-0.0499791\pi$
$402$		0			0
$403$	0.834588	−	3.11473i	0.0415738	−	0.155156i
$404$		0			0
$405$	66.0262	−	14.6356i	3.28087	−	0.727250i
$406$		0			0
$407$	−15.2906	+	15.2906i	−0.757928	+	0.757928i
$408$		0			0
$409$	−11.7806	−	20.4046i	−0.582513	−	1.00894i	−0.995180	−	0.0980604i	$-0.968736\pi$
$409$	−11.7806	−	20.4046i	−0.582513	−	1.00894i	0.412667	−	0.910882i	$-0.364597\pi$
$410$		0			0
$411$	64.4147	+	37.1898i	3.17734	+	1.83444i
$412$		0			0
$413$	4.52024	+	4.11859i	0.222427	+	0.202663i
$414$		0			0
$415$	5.07662	+	9.75280i	0.249202	+	0.478746i
$416$		0			0
$417$	−26.6312	−	7.13580i	−1.30413	−	0.349441i
$418$		0			0
$419$	−0.614382			−0.0300145			−0.0150073	−	0.999887i	$-0.504777\pi$
$419$	−0.614382			−0.0300145			−0.0150073	+	0.999887i	$0.504777\pi$
$420$		0			0
$421$	13.0643			0.636713			0.318356	−	0.947971i	$-0.396869\pi$
$421$	13.0643			0.636713			0.318356	+	0.947971i	$0.396869\pi$
$422$		0			0
$423$	31.0169	+	8.31095i	1.50809	+	0.404092i
$424$		0			0
$425$	−12.5942	+	10.5665i	−0.610909	+	0.512552i
$426$		0			0
$427$	−4.32674	−	0.946388i	−0.209385	−	0.0457989i
$428$		0			0
$429$	10.2867	+	5.93904i	0.496648	+	0.286740i
$430$		0			0
$431$	−7.52522	−	13.0341i	−0.362477	−	0.627828i	0.625891	−	0.779911i	$-0.284735\pi$
$431$	−7.52522	−	13.0341i	−0.362477	−	0.627828i	−0.988368	+	0.152082i	$0.951402\pi$
$432$		0			0
$433$	−18.5694	+	18.5694i	−0.892387	+	0.892387i	−0.994747	−	0.102361i	$-0.967360\pi$
$433$	−18.5694	+	18.5694i	−0.892387	+	0.892387i	0.102361	+	0.994747i	$0.467360\pi$
$434$		0			0
$435$	22.8256	+	14.5424i	1.09440	+	0.697256i
$436$		0			0
$437$	5.07564	−	18.9425i	0.242801	−	0.906144i
$438$		0			0
$439$	−3.96987	+	6.87601i	−0.189471	+	0.328174i	−0.945074	−	0.326856i	$-0.894011\pi$
$439$	−3.96987	+	6.87601i	−0.189471	+	0.328174i	0.755603	+	0.655030i	$0.227344\pi$
$440$		0			0
$441$	55.3516	−	5.15819i	2.63579	−	0.245628i
$442$		0			0
$443$	9.70480	−	2.60039i	0.461089	−	0.123548i	−0.0207943	−	0.999784i	$-0.506620\pi$
$443$	9.70480	−	2.60039i	0.461089	−	0.123548i	0.481883	+	0.876235i	$0.339953\pi$
$444$		0			0
$445$	−8.66183	−	9.45329i	−0.410610	−	0.448129i
$446$		0			0
$447$	20.1169	+	20.1169i	0.951496	+	0.951496i
$448$		0			0
$449$			15.6484i			0.738492i	0.929332	+	0.369246i	$0.120384\pi$
$449$			15.6484i			0.738492i	−0.929332	+	0.369246i	$0.879616\pi$
$450$		0			0
$451$	1.50737	−	0.870282i	0.0709794	−	0.0409800i
$452$		0			0
$453$	8.78726	+	32.7945i	0.412861	+	1.54082i
$454$		0			0
$455$	−7.14940	−	7.10950i	−0.335169	−	0.333298i
$456$		0			0
$457$	−6.39543	−	23.8681i	−0.299165	−	1.11650i	−0.937853	−	0.347034i	$-0.887189\pi$
$457$	−6.39543	−	23.8681i	−0.299165	−	1.11650i	0.638687	−	0.769467i	$-0.279478\pi$
$458$		0			0
$459$	46.5443	−	26.8724i	2.17250	−	1.25430i
$460$		0			0
$461$		−	17.2862i		−	0.805099i	−0.915398	−	0.402550i	$-0.868124\pi$
$461$		−	17.2862i		−	0.805099i	0.915398	−	0.402550i	$-0.131876\pi$
$462$		0			0
$463$	−5.61564	−	5.61564i	−0.260981	−	0.260981i	0.564472	−	0.825453i	$-0.309080\pi$
$463$	−5.61564	−	5.61564i	−0.260981	−	0.260981i	−0.825453	+	0.564472i	$0.809080\pi$
$464$		0			0
$465$	−0.610849	+	13.9814i	−0.0283274	+	0.648370i
$466$		0			0
$467$	−40.3828	+	10.8205i	−1.86869	+	0.500715i	−0.868709	+	0.495322i	$0.835050\pi$
$467$	−40.3828	+	10.8205i	−1.86869	+	0.500715i	−0.999985	+	0.00539309i	$0.998283\pi$
$468$		0			0
$469$	33.5456	−	1.55967i	1.54899	−	0.0720189i
$470$		0			0
$471$	16.8308	−	29.1519i	0.775524	−	1.34325i
$472$		0			0
$473$	3.62606	−	13.5326i	0.166726	−	0.622231i
$474$		0			0
$475$	21.4339	−	9.99327i	0.983455	−	0.458523i
$476$		0			0
$477$	−14.0107	+	14.0107i	−0.641506	+	0.641506i
$478$		0			0
$479$	−18.2812	−	31.6639i	−0.835287	−	1.44676i	−0.893796	−	0.448473i	$-0.851968\pi$
$479$	−18.2812	−	31.6639i	−0.835287	−	1.44676i	0.0585091	−	0.998287i	$-0.481365\pi$
$480$		0			0
$481$	15.1475	+	8.74544i	0.690669	+	0.398758i
$482$		0			0
$483$	34.5757	−	11.0092i	1.57325	−	0.500938i
$484$		0			0
$485$	−2.88114	+	1.49972i	−0.130826	+	0.0680989i
$486$		0			0
$487$	3.00674	+	0.805655i	0.136249	+	0.0365077i	0.326299	−	0.945267i	$-0.394198\pi$
$487$	3.00674	+	0.805655i	0.136249	+	0.0365077i	−0.190050	+	0.981774i	$0.560865\pi$
$488$		0			0
$489$	9.58102			0.433269
$490$		0			0
$491$	−32.3286			−1.45897			−0.729484	−	0.683998i	$-0.760240\pi$
$491$	−32.3286			−1.45897			−0.729484	+	0.683998i	$0.760240\pi$
$492$		0			0
$493$	11.6210	+	3.11384i	0.523384	+	0.140240i
$494$		0			0
$495$	−35.6843	−	11.2524i	−1.60389	−	0.505756i
$496$		0			0
$497$	−27.2057	+	8.66257i	−1.22034	+	0.388569i
$498$		0			0
$499$	−19.3372	−	11.1643i	−0.865651	−	0.499784i	0.000249428	−	1.00000i	$-0.499921\pi$
$499$	−19.3372	−	11.1643i	−0.865651	−	0.499784i	−0.865901	+	0.500216i	$0.833254\pi$
$500$		0			0
$501$	19.6293	+	33.9989i	0.876972	+	1.51896i
$502$		0			0
$503$	20.3631	−	20.3631i	0.907947	−	0.907947i	−0.0881596	−	0.996106i	$-0.528099\pi$
$503$	20.3631	−	20.3631i	0.907947	−	0.907947i	0.996106	+	0.0881596i	$0.0280985\pi$
$504$		0			0
$505$	−0.625093	−	2.82000i	−0.0278163	−	0.125489i
$506$		0			0
$507$	−8.64298	+	32.2560i	−0.383848	+	1.43254i
$508$		0			0
$509$	−16.5423	+	28.6521i	−0.733224	+	1.26998i	0.222274	+	0.974984i	$0.428652\pi$
$509$	−16.5423	+	28.6521i	−0.733224	+	1.26998i	−0.955498	+	0.294997i	$0.904681\pi$
$510$		0			0
$511$	34.5116	−	1.60459i	1.52670	−	0.0709827i
$512$		0			0
$513$	−74.6790	+	20.0102i	−3.29716	+	0.883471i
$514$		0			0
$515$	−24.4225	−	1.06703i	−1.07619	−	0.0470188i
$516$		0			0
$517$	−6.02417	−	6.02417i	−0.264943	−	0.264943i
$518$		0			0
$519$			0.834889i			0.0366475i
$520$		0			0
$521$	−20.9365	+	12.0877i	−0.917246	+	0.529572i	−0.882755	−	0.469833i	$-0.844314\pi$
$521$	−20.9365	+	12.0877i	−0.917246	+	0.529572i	−0.0344903	+	0.999405i	$0.510981\pi$
$522$		0			0
$523$	−6.17690	−	23.0525i	−0.270097	−	1.00801i	−0.959056	−	0.283215i	$-0.908599\pi$
$523$	−6.17690	−	23.0525i	−0.270097	−	1.00801i	0.688960	−	0.724800i	$-0.258068\pi$
$524$		0			0
$525$	36.9703	+	23.4090i	1.61352	+	1.02165i
$526$		0			0
$527$	1.61012	+	6.00906i	0.0701381	+	0.261759i
$528$		0			0
$529$	−5.03074	+	2.90450i	−0.218728	+	0.126283i
$530$		0			0
$531$		−	18.3556i		−	0.796566i
$532$		0			0
$533$	−0.995512	−	0.995512i	−0.0431204	−	0.0431204i
$534$		0			0
$535$	−6.64790	−	0.290448i	−0.287414	−	0.0125572i
$536$		0			0
$537$	69.4503	−	18.6092i	2.99700	−	0.803045i
$538$		0			0
$539$	−13.4022	−	6.15754i	−0.577275	−	0.265224i
$540$		0			0
$541$	0.226204	−	0.391797i	0.00972527	−	0.0168447i	−0.861122	−	0.508399i	$-0.830238\pi$
$541$	0.226204	−	0.391797i	0.00972527	−	0.0168447i	0.870847	+	0.491554i	$0.163571\pi$
$542$		0			0
$543$	−2.62017	+	9.77860i	−0.112442	+	0.419640i
$544$		0			0
$545$	−7.30279	−	32.9453i	−0.312817	−	1.41122i
$546$		0			0
$547$	24.0665	−	24.0665i	1.02901	−	1.02901i	0.0294424	−	0.999566i	$-0.490627\pi$
$547$	24.0665	−	24.0665i	1.02901	−	1.02901i	0.999566	−	0.0294424i	$-0.00937316\pi$
$548$		0			0
$549$	6.64720	+	11.5133i	0.283696	+	0.491375i
$550$		0			0
$551$	−14.9882	−	8.65343i	−0.638518	−	0.368649i
$552$		0			0
$553$	−24.7498	−	5.41353i	−1.05247	−	0.230207i
$554$		0			0
$555$	−72.3960	−	22.8287i	−3.07304	−	0.969024i
$556$		0			0
$557$	43.9643	+	11.7802i	1.86283	+	0.499143i	0.999980	−	0.00632392i	$-0.00201298\pi$
$557$	43.9643	+	11.7802i	1.86283	+	0.499143i	0.862846	+	0.505467i	$0.168680\pi$
$558$		0			0
$559$	−11.3321			−0.479297
$560$		0			0
$561$	−22.9157			−0.967502
$562$		0			0
$563$	−22.3526	−	5.98936i	−0.942050	−	0.252422i	−0.245065	−	0.969507i	$-0.578809\pi$
$563$	−22.3526	−	5.98936i	−0.942050	−	0.252422i	−0.696986	+	0.717085i	$0.745476\pi$
$564$		0			0
$565$	11.8700	−	6.17871i	0.499376	−	0.259940i
$566$		0			0
$567$	−59.1492	−	53.8934i	−2.48403	−	2.26331i
$568$		0			0
$569$	6.46781	+	3.73419i	0.271145	+	0.156545i	0.629408	−	0.777075i	$-0.283298\pi$
$569$	6.46781	+	3.73419i	0.271145	+	0.156545i	−0.358263	+	0.933621i	$0.616631\pi$
$570$		0			0
$571$	0.421350	+	0.729799i	0.0176329	+	0.0305412i	0.874707	−	0.484652i	$-0.161054\pi$
$571$	0.421350	+	0.729799i	0.0176329	+	0.0305412i	−0.857074	+	0.515193i	$0.827720\pi$
$572$		0			0
$573$	−49.3517	+	49.3517i	−2.06170	+	2.06170i
$574$		0			0
$575$	19.4804	+	7.09156i	0.812387	+	0.295739i
$576$		0			0
$577$	−9.36558	+	34.9528i	−0.389894	+	1.45511i	0.440411	+	0.897796i	$0.354833\pi$
$577$	−9.36558	+	34.9528i	−0.389894	+	1.45511i	−0.830305	+	0.557309i	$0.811834\pi$
$578$		0			0
$579$	−34.4486	+	59.6668i	−1.43164	+	2.47967i
$580$		0			0
$581$	5.97443	−	11.5564i	0.247861	−	0.479441i
$582$		0			0
$583$	5.07781	−	1.36059i	0.210301	−	0.0563500i
$584$		0			0
$585$	−1.32100	+	30.2356i	−0.0546167	+	1.25009i
$586$		0			0
$587$	−0.777106	−	0.777106i	−0.0320746	−	0.0320746i	0.690888	−	0.722962i	$-0.257220\pi$
$587$	−0.777106	−	0.777106i	−0.0320746	−	0.0320746i	−0.722962	+	0.690888i	$0.757220\pi$
$588$		0			0
$589$		−	8.94914i		−	0.368743i
$590$		0			0
$591$	−37.6655	+	21.7462i	−1.54935	+	0.894519i
$592$		0			0
$593$	−5.14887	−	19.2159i	−0.211439	−	0.789101i	−0.987390	−	0.158307i	$-0.949396\pi$
$593$	−5.14887	−	19.2159i	−0.211439	−	0.789101i	0.775951	−	0.630793i	$-0.217270\pi$
$594$		0			0
$595$	18.8030	+	4.98190i	0.770848	+	0.204238i
$596$		0			0
$597$	6.46934	+	24.1439i	0.264772	+	0.988144i
$598$		0			0
$599$	19.4628	−	11.2369i	0.795229	−	0.459126i	−0.0465712	−	0.998915i	$-0.514829\pi$
$599$	19.4628	−	11.2369i	0.795229	−	0.459126i	0.841800	+	0.539789i	$0.181496\pi$
$600$		0			0
$601$			30.0046i			1.22391i	0.790891	+	0.611957i	$0.209618\pi$
$601$			30.0046i			1.22391i	−0.790891	+	0.611957i	$0.790382\pi$
$602$		0			0
$603$	−71.2771	−	71.2771i	−2.90263	−	2.90263i
$604$		0			0
$605$	−9.91041	−	10.8159i	−0.402915	−	0.439731i
$606$		0			0
$607$	−4.14580	+	1.11086i	−0.168273	+	0.0450886i	−0.341972	−	0.939710i	$-0.611095\pi$
$607$	−4.14580	+	1.11086i	−0.168273	+	0.0450886i	0.173699	+	0.984799i	$0.444428\pi$
$608$		0			0
$609$	−1.48728	−	31.9886i	−0.0602677	−	1.29624i
$610$		0			0
$611$	−3.44551	+	5.96780i	−0.139390	+	0.241431i
$612$		0			0
$613$	−6.74007	+	25.1543i	−0.272229	+	1.01597i	0.685447	+	0.728123i	$0.259607\pi$
$613$	−6.74007	+	25.1543i	−0.272229	+	1.01597i	−0.957676	+	0.287850i	$0.907060\pi$
$614$		0			0
$615$	5.15312	+	3.28311i	0.207794	+	0.132388i
$616$		0			0
$617$	18.5489	−	18.5489i	0.746750	−	0.746750i	−0.227117	−	0.973867i	$-0.572930\pi$
$617$	18.5489	−	18.5489i	0.746750	−	0.746750i	0.973867	+	0.227117i	$0.0729300\pi$
$618$		0			0
$619$	14.9263	+	25.8532i	0.599940	+	1.03913i	0.992829	+	0.119541i	$0.0381422\pi$
$619$	14.9263	+	25.8532i	0.599940	+	1.03913i	−0.392889	+	0.919586i	$0.628524\pi$
$620$		0			0
$621$	−58.6938	−	33.8869i	−2.35530	−	1.35983i
$622$		0			0
$623$	−3.24164	+	14.8203i	−0.129874	+	0.593762i
$624$		0			0
$625$	8.54776	+	23.4933i	0.341910	+	0.939733i
$626$		0			0
$627$	31.8416	+	8.53194i	1.27163	+	0.340733i
$628$		0			0
$629$	−33.7441			−1.34547
$630$		0			0
$631$	0.755612			0.0300804			0.0150402	−	0.999887i	$-0.495212\pi$
$631$	0.755612			0.0300804			0.0150402	+	0.999887i	$0.495212\pi$
$632$		0			0
$633$	−4.24108	−	1.13639i	−0.168568	−	0.0451676i
$634$		0			0
$635$	6.61589	+	12.7099i	0.262544	+	0.504378i
$636$		0			0
$637$	−2.00514	+	11.7602i	−0.0794464	+	0.465955i
$638$		0			0
$639$	74.2199	+	42.8509i	2.93609	+	1.69515i
$640$		0			0
$641$	−10.1050	−	17.5023i	−0.399122	−	0.691299i	0.594496	−	0.804099i	$-0.297352\pi$
$641$	−10.1050	−	17.5023i	−0.399122	−	0.691299i	−0.993618	+	0.112799i	$0.964018\pi$
$642$		0			0
$643$	0.933128	−	0.933128i	0.0367990	−	0.0367990i	−0.688468	−	0.725267i	$-0.741716\pi$
$643$	0.933128	−	0.933128i	0.0367990	−	0.0367990i	0.725267	+	0.688468i	$0.241716\pi$
$644$		0			0
$645$	48.0155	−	10.6433i	1.89061	−	0.419080i
$646$		0			0
$647$	−7.85058	+	29.2988i	−0.308638	+	1.15185i	0.621130	+	0.783708i	$0.286674\pi$
$647$	−7.85058	+	29.2988i	−0.308638	+	1.15185i	−0.929768	+	0.368146i	$0.879993\pi$
$648$		0			0
$649$	−2.43499	+	4.21752i	−0.0955816	+	0.165552i
$650$		0			0
$651$	13.9403	−	8.93646i	0.546363	−	0.350247i
$652$		0			0
$653$	40.0331	−	10.7268i	1.56662	−	0.419774i	0.631867	−	0.775077i	$-0.282289\pi$
$653$	40.0331	−	10.7268i	1.56662	−	0.419774i	0.934751	+	0.355303i	$0.115622\pi$
$654$		0			0
$655$	−4.58669	+	4.20268i	−0.179217	+	0.164212i
$656$		0			0
$657$	−73.3297	−	73.3297i	−2.86086	−	2.86086i
$658$		0			0
$659$			7.54235i			0.293808i	0.989151	+	0.146904i	$0.0469309\pi$
$659$			7.54235i			0.293808i	−0.989151	+	0.146904i	$0.953069\pi$
$660$		0			0
$661$	−40.6248	+	23.4548i	−1.58012	+	0.912284i	−0.585282	+	0.810830i	$0.699016\pi$
$661$	−40.6248	+	23.4548i	−1.58012	+	0.912284i	−0.994840	+	0.101455i	$0.967650\pi$
$662$		0			0
$663$	4.79735	+	17.9039i	0.186314	+	0.695332i
$664$		0			0
$665$	−24.2721	−	13.9231i	−0.941233	−	0.539915i
$666$		0			0
$667$	−3.92664	−	14.6544i	−0.152040	−	0.567422i
$668$		0			0
$669$	−29.3700	+	16.9568i	−1.13551	+	0.655588i
$670$		0			0
$671$		−	3.52717i		−	0.136165i
$672$		0			0
$673$	29.6391	+	29.6391i	1.14250	+	1.14250i	0.987991	+	0.154511i	$0.0493803\pi$
$673$	29.6391	+	29.6391i	1.14250	+	1.14250i	0.154511	+	0.987991i	$0.450620\pi$
$674$		0			0
$675$	−14.1875	−	80.4890i	−0.546078	−	3.09802i
$676$		0			0
$677$	38.0992	−	10.2087i	1.46427	−	0.392351i	0.563309	−	0.826246i	$-0.309528\pi$
$677$	38.0992	−	10.2087i	1.46427	−	0.392351i	0.900963	+	0.433896i	$0.142861\pi$
$678$		0			0
$679$	3.41397	+	1.76495i	0.131016	+	0.0677325i
$680$		0			0
$681$	49.6385	−	85.9764i	1.90215	−	3.29462i
$682$		0			0
$683$	1.10186	−	4.11219i	0.0421615	−	0.157349i	−0.941636	−	0.336633i	$-0.890712\pi$
$683$	1.10186	−	4.11219i	0.0421615	−	0.157349i	0.983797	+	0.179285i	$0.0573783\pi$
$684$		0			0
$685$	27.0169	−	42.4052i	1.03226	−	1.62022i
$686$		0			0
$687$	48.4093	−	48.4093i	1.84693	−	1.84693i
$688$		0			0
$689$	−2.12605	−	3.68243i	−0.0809961	−	0.140289i
$690$		0			0
$691$	0.538345	+	0.310814i	0.0204796	+	0.0118239i	0.510205	−	0.860053i	$-0.329570\pi$
$691$	0.538345	+	0.310814i	0.0204796	+	0.0118239i	−0.489725	+	0.871877i	$0.662903\pi$
$692$		0			0
$693$	13.4321	+	42.1848i	0.510242	+	1.60247i
$694$		0			0
$695$	−5.60496	+	17.7748i	−0.212608	+	0.674238i
$696$		0			0
$697$	2.62357	+	0.702983i	0.0993747	+	0.0266274i
$698$		0			0
$699$	13.1042			0.495645
$700$		0			0
$701$	−30.9626			−1.16944			−0.584721	−	0.811235i	$-0.698796\pi$
$701$	−30.9626			−1.16944			−0.584721	+	0.811235i	$0.698796\pi$
$702$		0			0
$703$	46.8879	+	12.5636i	1.76841	+	0.473844i
$704$		0			0
$705$	8.99400	−	28.5224i	0.338734	−	1.07422i
$706$		0			0
$707$	−2.30181	+	2.52628i	−0.0865683	+	0.0950107i
$708$		0			0
$709$	−26.5831	−	15.3478i	−0.998350	−	0.576398i	−0.0905903	−	0.995888i	$-0.528875\pi$
$709$	−26.5831	−	15.3478i	−0.998350	−	0.576398i	−0.907760	+	0.419491i	$0.862209\pi$
$710$		0			0
$711$	38.0233	+	65.8583i	1.42599	+	2.46988i
$712$		0			0
$713$	5.54719	−	5.54719i	0.207744	−	0.207744i
$714$		0			0
$715$	4.31446	−	6.77192i	0.161352	−	0.253255i
$716$		0			0
$717$	−12.2073	+	45.5583i	−0.455891	+	1.70141i
$718$		0			0
$719$	−4.00357	+	6.93439i	−0.149308	+	0.258609i	−0.930972	−	0.365091i	$-0.881038\pi$
$719$	−4.00357	+	6.93439i	−0.149308	+	0.258609i	0.781664	+	0.623700i	$0.214371\pi$
$720$		0			0
$721$	15.6101	+	24.3508i	0.581352	+	0.906871i
$722$		0			0
$723$	−15.5585	+	4.16889i	−0.578628	+	0.155043i
$724$		0			0
$725$	10.4948	−	14.9862i	0.389765	−	0.556573i
$726$		0			0
$727$	2.24335	+	2.24335i	0.0832011	+	0.0832011i	0.747483	−	0.664281i	$-0.231262\pi$
$727$	2.24335	+	2.24335i	0.0832011	+	0.0832011i	−0.664281	+	0.747483i	$0.731262\pi$
$728$		0			0
$729$			77.9825i			2.88824i
$730$		0			0
$731$	18.9334	−	10.9312i	0.700276	−	0.404304i
$732$		0			0
$733$	−9.69369	−	36.1773i	−0.358045	−	1.33624i	−0.876610	−	0.481202i	$-0.840200\pi$
$733$	−9.69369	−	36.1773i	−0.358045	−	1.33624i	0.518565	−	0.855038i	$-0.326466\pi$
$734$		0			0
$735$	−2.54936	−	51.7127i	−0.0940347	−	1.90745i
$736$		0			0
$737$	6.92179	+	25.8325i	0.254967	+	0.951552i
$738$		0			0
$739$	−8.55973	+	4.94196i	−0.314875	+	0.181793i	−0.649106	−	0.760698i	$-0.724857\pi$
$739$	−8.55973	+	4.94196i	−0.314875	+	0.181793i	0.334231	+	0.942491i	$0.391523\pi$
$740$		0			0
$741$		−	26.6639i		−	0.979522i
$742$		0			0
$743$	23.1188	+	23.1188i	0.848147	+	0.848147i	0.989902	−	0.141755i	$-0.0452746\pi$
$743$	23.1188	+	23.1188i	0.848147	+	0.848147i	−0.141755	+	0.989902i	$0.545275\pi$
$744$		0			0
$745$	14.1795	−	12.9924i	0.519498	−	0.476005i
$746$		0			0
$747$	−37.7191	+	10.1068i	−1.38007	+	0.369789i
$748$		0			0
$749$	4.24914	+	6.62838i	0.155260	+	0.242196i
$750$		0			0
$751$	−19.0861	+	33.0582i	−0.696463	+	1.20631i	0.273222	+	0.961951i	$0.411911\pi$
$751$	−19.0861	+	33.0582i	−0.696463	+	1.20631i	−0.969685	+	0.244358i	$0.921423\pi$
$752$		0			0
$753$	14.1362	−	52.7569i	0.515150	−	1.92257i
$754$		0			0
$755$	22.4071	−	4.96685i	0.815478	−	0.180762i
$756$		0			0
$757$	−24.5560	+	24.5560i	−0.892504	+	0.892504i	−0.994758	−	0.102255i	$-0.967394\pi$
$757$	−24.5560	+	24.5560i	−0.892504	+	0.892504i	0.102255	+	0.994758i	$0.467394\pi$
$758$		0			0
$759$	14.4487	+	25.0259i	0.524454	+	0.908381i
$760$		0			0
$761$	11.7157	+	6.76405i	0.424693	+	0.245197i	0.697083	−	0.716990i	$-0.254481\pi$
$761$	11.7157	+	6.76405i	0.424693	+	0.245197i	−0.272390	+	0.962187i	$0.587814\pi$
$762$		0			0
$763$	−26.8914	+	29.5139i	−0.973533	+	1.06847i
$764$		0			0
$765$	−26.9588	−	51.7911i	−0.974699	−	1.87251i
$766$		0			0
$767$	3.80489	+	1.01952i	0.137387	+	0.0368126i
$768$		0			0
$769$	39.3025			1.41728			0.708641	−	0.705569i	$-0.249308\pi$
$769$	39.3025			1.41728			0.708641	+	0.705569i	$0.249308\pi$
$770$		0			0
$771$	−32.4426			−1.16839
$772$		0			0
$773$	−27.5742	−	7.38848i	−0.991774	−	0.265745i	−0.273778	−	0.961793i	$-0.588274\pi$
$773$	−27.5742	−	7.38848i	−0.991774	−	0.265745i	−0.717995	+	0.696048i	$0.754940\pi$
$774$		0			0
$775$	9.42431	+	0.825076i	0.338531	+	0.0296376i
$776$		0			0
$777$	27.2509	+	85.5842i	0.977619	+	3.07031i
$778$		0			0
$779$	−3.38374	−	1.95360i	−0.121235	−	0.0699952i
$780$		0			0
$781$	−11.3689	−	19.6915i	−0.406810	−	0.704616i
$782$		0			0
$783$	−42.2932	+	42.2932i	−1.51143	+	1.51143i
$784$		0			0
$785$	−19.1911	−	12.2269i	−0.684961	−	0.436397i
$786$		0			0
$787$	4.15609	−	15.5107i	0.148149	−	0.552898i	−0.851446	−	0.524442i	$-0.824274\pi$
$787$	4.15609	−	15.5107i	0.148149	−	0.552898i	0.999595	−	0.0284567i	$-0.00905928\pi$
$788$		0			0
$789$	20.5240	−	35.5487i	0.730675	−	1.26557i
$790$		0			0
$791$	−14.0652	−	7.27142i	−0.500101	−	0.258542i
$792$		0			0
$793$	−2.75576	+	0.738404i	−0.0978600	+	0.0262215i
$794$		0			0
$795$	12.4670	+	13.6061i	0.442158	+	0.482559i
$796$		0			0
$797$	11.4141	+	11.4141i	0.404310	+	0.404310i	0.879749	−	0.475439i	$-0.157711\pi$
$797$	11.4141	+	11.4141i	0.404310	+	0.404310i	−0.475439	+	0.879749i	$0.657711\pi$
$798$		0			0
$799$		−	13.2945i		−	0.470324i
$800$		0			0
$801$	39.4362	−	22.7685i	1.39341	−	0.804486i
$802$		0			0
$803$	7.12113	+	26.5764i	0.251299	+	0.937861i
$804$		0			0
$805$	−6.41491	−	23.6756i	−0.226096	−	0.834455i
$806$		0			0
$807$	3.19385	+	11.9196i	0.112429	+	0.419591i
$808$		0			0
$809$	15.1396	−	8.74085i	0.532280	−	0.307312i	−0.209665	−	0.977773i	$-0.567237\pi$
$809$	15.1396	−	8.74085i	0.532280	−	0.307312i	0.741944	+	0.670461i	$0.233904\pi$
$810$		0			0
$811$			51.1883i			1.79747i	0.438497	+	0.898733i	$0.355511\pi$
$811$			51.1883i			1.79747i	−0.438497	+	0.898733i	$0.644489\pi$
$812$		0			0
$813$	−3.87674	−	3.87674i	−0.135963	−	0.135963i
$814$		0			0
$815$	0.282700	−	6.47056i	0.00990256	−	0.226654i
$816$		0			0
$817$	−30.3780	+	8.13976i	−1.06279	+	0.284774i
$818$		0			0
$819$	30.1468	−	19.3257i	1.05341	−	0.675294i
$820$		0			0
$821$	0.0218989	−	0.0379301i	0.000764278	−	0.00132377i	−0.865643	−	0.500662i	$-0.833090\pi$
$821$	0.0218989	−	0.0379301i	0.000764278	−	0.00132377i	0.866407	+	0.499338i	$0.166423\pi$
$822$		0			0
$823$	1.97965	−	7.38815i	0.0690062	−	0.257535i	−0.922801	−	0.385276i	$-0.874106\pi$
$823$	1.97965	−	7.38815i	0.0690062	−	0.257535i	0.991807	+	0.127742i	$0.0407728\pi$
$824$		0			0
$825$	−11.9206	+	32.7457i	−0.415023	+	1.14006i
$826$		0			0
$827$	−25.9919	+	25.9919i	−0.903826	+	0.903826i	−0.995765	−	0.0919384i	$-0.970694\pi$
$827$	−25.9919	+	25.9919i	−0.903826	+	0.903826i	0.0919384	+	0.995765i	$0.470694\pi$
$828$		0			0
$829$	10.5010	+	18.1883i	0.364715	+	0.631704i	0.988730	−	0.149708i	$-0.0478332\pi$
$829$	10.5010	+	18.1883i	0.364715	+	0.631704i	−0.624016	+	0.781412i	$0.714500\pi$
$830$		0			0
$831$	−43.6657	−	25.2104i	−1.51475	−	0.874539i
$832$		0			0
$833$	−7.99399	−	21.5828i	−0.276975	−	0.747799i
$834$		0			0
$835$	23.5404	−	12.2535i	0.814650	−	0.424050i
$836$		0			0
$837$	−29.8739	−	8.00469i	−1.03259	−	0.276683i
$838$		0			0
$839$	43.5751			1.50438			0.752189	−	0.658947i	$-0.228998\pi$
$839$	43.5751			1.50438			0.752189	+	0.658947i	$0.228998\pi$
$840$		0			0
$841$	15.6110			0.538309
$842$		0			0
$843$	−7.21205	−	1.93246i	−0.248396	−	0.0665576i
$844$		0			0
$845$	21.5291	+	6.78880i	0.740625	+	0.233542i
$846$		0			0
$847$	−3.70891	+	16.9566i	−0.127440	+	0.582635i
$848$		0			0
$849$	−17.4117	−	10.0526i	−0.597567	−	0.345005i
$850$		0			0
$851$	21.2762	+	36.8514i	0.729338	+	1.26325i
$852$		0			0
$853$	17.6117	−	17.6117i	0.603014	−	0.603014i	−0.338098	−	0.941111i	$-0.609783\pi$
$853$	17.6117	−	17.6117i	0.603014	−	0.603014i	0.941111	+	0.338098i	$0.109783\pi$
$854$		0			0
$855$	18.1768	+	82.0016i	0.621634	+	2.80440i
$856$		0			0
$857$	9.04624	−	33.7610i	0.309014	−	1.15325i	−0.620422	−	0.784268i	$-0.713038\pi$
$857$	9.04624	−	33.7610i	0.309014	−	1.15325i	0.929435	−	0.368986i	$-0.120295\pi$
$858$		0			0
$859$	17.2794	−	29.9288i	0.589565	−	1.02116i	−0.404724	−	0.914439i	$-0.632633\pi$
$859$	17.2794	−	29.9288i	0.589565	−	1.02116i	0.994289	−	0.106718i	$-0.0340341\pi$
$860$		0			0
$861$	−0.335770	−	7.22177i	−0.0114430	−	0.246117i
$862$		0			0
$863$	42.6135	−	11.4183i	1.45058	−	0.388682i	0.554355	−	0.832280i	$-0.312965\pi$
$863$	42.6135	−	11.4183i	1.45058	−	0.388682i	0.896226	+	0.443598i	$0.146298\pi$
$864$		0			0
$865$	0.563844	+	0.0246345i	0.0191713	+	0.000837597i
$866$		0			0
$867$	14.4768	+	14.4768i	0.491658	+	0.491658i
$868$		0			0
$869$		−	20.1761i		−	0.684428i
$870$		0			0
$871$	18.7337	−	10.8159i	0.634769	−	0.366484i
$872$		0			0
$873$	−2.98573	−	11.1429i	−0.101052	−	0.377130i
$874$		0			0
$875$	16.9002	−	24.2772i	0.571330	−	0.820720i
$876$		0			0
$877$	−0.217309	−	0.811006i	−0.00733799	−	0.0273857i	0.962160	−	0.272486i	$-0.0878458\pi$
$877$	−0.217309	−	0.811006i	−0.00733799	−	0.0273857i	−0.969498	+	0.245100i	$0.921179\pi$
$878$		0			0
$879$	−71.2083	+	41.1121i	−2.40180	+	1.38668i
$880$		0			0
$881$			39.6633i			1.33629i	0.744031	+	0.668145i	$0.232911\pi$
$881$			39.6633i			1.33629i	−0.744031	+	0.668145i	$0.767089\pi$
$882$		0			0
$883$	−28.9598	−	28.9598i	−0.974576	−	0.974576i	0.0251084	−	0.999685i	$-0.492007\pi$
$883$	−28.9598	−	28.9598i	−0.974576	−	0.974576i	−0.999685	+	0.0251084i	$0.992007\pi$
$884$		0			0
$885$	−17.0794	−	0.746202i	−0.574117	−	0.0250833i
$886$		0			0
$887$	−5.40217	+	1.44751i	−0.181387	+	0.0486025i	−0.348369	−	0.937357i	$-0.613264\pi$
$887$	−5.40217	+	1.44751i	−0.181387	+	0.0486025i	0.166982	+	0.985960i	$0.446598\pi$
$888$		0			0
$889$	7.78592	−	15.0604i	0.261131	−	0.505110i
$890$		0			0
$891$	31.8628	−	55.1880i	1.06744	−	1.84887i
$892$		0			0
$893$	−4.94977	+	18.4728i	−0.165638	+	0.618168i
$894$		0			0
$895$	−10.5185	−	47.4525i	−0.351595	−	1.58616i
$896$		0			0
$897$	16.5278	−	16.5278i	0.551847	−	0.551847i
$898$		0			0
$899$	−3.46164	−	5.99574i	−0.115452	−	0.199969i
$900$		0			0
$901$	7.10430	+	4.10167i	0.236679	+	0.136646i
$902$		0			0
$903$	−43.0145	−	39.1923i	−1.43143	−	1.30424i
$904$		0			0
$905$	6.52668	+	2.05807i	0.216954	+	0.0684124i
$906$		0			0
$907$	−20.2095	−	5.41512i	−0.671046	−	0.179806i	−0.0928200	−	0.995683i	$-0.529588\pi$
$907$	−20.2095	−	5.41512i	−0.671046	−	0.179806i	−0.578226	+	0.815877i	$0.696255\pi$
$908$		0			0
$909$	10.2586			0.340258
$910$		0			0
$911$	−13.0212			−0.431413			−0.215707	−	0.976458i	$-0.569205\pi$
$911$	−13.0212			−0.431413			−0.215707	+	0.976458i	$0.569205\pi$
$912$		0			0
$913$	10.0074	+	2.68146i	0.331195	+	0.0887435i
$914$		0			0
$915$	10.9830	−	5.71698i	0.363087	−	0.188997i
$916$		0			0
$917$	7.19072	+	1.57283i	0.237459	+	0.0519394i
$918$		0			0
$919$	−4.38681	−	2.53273i	−0.144708	−	0.0835470i	0.425898	−	0.904771i	$-0.359958\pi$
$919$	−4.38681	−	2.53273i	−0.144708	−	0.0835470i	−0.570606	+	0.821224i	$0.693292\pi$
$920$		0			0
$921$	−49.3807	−	85.5299i	−1.62715	−	2.81831i
$922$		0			0
$923$	−13.0048	+	13.0048i	−0.428059	+	0.428059i
$924$		0			0
$925$	−17.5535	+	48.2192i	−0.577157	+	1.58544i
$926$		0			0
$927$	22.4712	−	83.8635i	0.738050	−	2.75444i
$928$		0			0
$929$	−24.7411	+	42.8528i	−0.811728	+	1.40595i	0.0999258	+	0.994995i	$0.468139\pi$
$929$	−24.7411	+	42.8528i	−0.811728	+	1.40595i	−0.911654	+	0.410959i	$0.865194\pi$
$930$		0			0
$931$	3.07207	+	32.9658i	0.100683	+	1.08041i
$932$		0			0
$933$	60.2919	−	16.1552i	1.97387	−	0.528897i
$934$		0			0
$935$	−0.676157	+	15.4762i	−0.0221127	+	0.506125i
$936$		0			0
$937$	22.1742	+	22.1742i	0.724399	+	0.724399i	0.969498	−	0.245099i	$-0.0788204\pi$
$937$	22.1742	+	22.1742i	0.724399	+	0.724399i	−0.245099	+	0.969498i	$0.578820\pi$
$938$		0			0
$939$			85.8324i			2.80103i
$940$		0			0
$941$	26.5134	−	15.3075i	0.864313	−	0.499011i	−0.00114123	−	0.999999i	$-0.500363\pi$
$941$	26.5134	−	15.3075i	0.864313	−	0.499011i	0.865454	+	0.500988i	$0.167030\pi$
$942$		0			0
$943$	−0.886481	−	3.30839i	−0.0288678	−	0.107736i
$944$		0			0
$945$	−68.1885	+	68.5712i	−2.21817	+	2.23062i
$946$		0			0
$947$	5.48860	+	20.4837i	0.178355	+	0.665632i	0.995956	+	0.0898453i	$0.0286373\pi$
$947$	5.48860	+	20.4837i	0.178355	+	0.665632i	−0.817600	+	0.575786i	$0.804696\pi$
$948$		0			0
$949$	19.2732	−	11.1274i	0.625636	−	0.361211i
$950$		0			0
$951$			4.73414i			0.153515i
$952$		0			0
$953$	−30.4466	−	30.4466i	−0.986262	−	0.986262i	0.0136447	−	0.999907i	$-0.495657\pi$
$953$	−30.4466	−	30.4466i	−0.986262	−	0.986262i	−0.999907	+	0.0136447i	$0.995657\pi$
$954$		0			0
$955$	31.8736	+	34.7860i	1.03140	+	1.12565i
$956$		0			0
$957$	24.6335	−	6.60053i	0.796288	−	0.213365i
$958$		0			0
$959$	−59.4283	+	2.76306i	−1.91904	+	0.0892240i
$960$		0			0
$961$	−13.7100	+	23.7465i	−0.442259	+	0.766015i
$962$		0			0
$963$	6.11673	−	22.8280i	0.197109	−	0.735620i
$964$		0			0
$965$	39.2796	+	25.0255i	1.26446	+	0.805599i
$966$		0			0
$967$	40.2212	−	40.2212i	1.29343	−	1.29343i	0.360774	−	0.932653i	$-0.382513\pi$
$967$	40.2212	−	40.2212i	1.29343	−	1.29343i	0.932653	−	0.360774i	$-0.117487\pi$
$968$		0			0
$969$	25.7205	+	44.5493i	0.826263	+	1.43113i
$970$		0			0
$971$	−11.4574	−	6.61493i	−0.367685	−	0.212283i	0.304761	−	0.952429i	$-0.401423\pi$
$971$	−11.4574	−	6.61493i	−0.367685	−	0.212283i	−0.672447	+	0.740145i	$0.734757\pi$
$972$		0			0
$973$	21.0128	−	6.69070i	0.673641	−	0.214494i
$974$		0			0
$975$	28.0796	+	2.45830i	0.899268	+	0.0787288i
$976$		0			0
$977$	28.2330	+	7.56500i	0.903253	+	0.242026i	0.680413	−	0.732829i	$-0.261800\pi$
$977$	28.2330	+	7.56500i	0.903253	+	0.242026i	0.222840	+	0.974855i	$0.428467\pi$
$978$		0			0
$979$	−12.0815			−0.386128
$980$		0			0
$981$	119.849			3.82648
$982$		0			0
$983$	13.3912	+	3.58817i	0.427114	+	0.114445i	0.465971	−	0.884800i	$-0.345705\pi$
$983$	13.3912	+	3.58817i	0.427114	+	0.114445i	−0.0388569	+	0.999245i	$0.512372\pi$
$984$		0			0
$985$	13.5750	+	26.0791i	0.432534	+	0.830950i
$986$		0			0
$987$	−33.7183	+	10.7362i	−1.07326	+	0.341738i
$988$		0			0
$989$	−23.8755	−	13.7845i	−0.759197	−	0.438323i
$990$		0			0
$991$	2.37408	+	4.11203i	0.0754152	+	0.130623i	0.901267	−	0.433265i	$-0.142638\pi$
$991$	2.37408	+	4.11203i	0.0754152	+	0.130623i	−0.825852	+	0.563888i	$0.809305\pi$
$992$		0			0
$993$	−38.4461	+	38.4461i	−1.22005	+	1.22005i
$994$		0			0
$995$	16.4965	−	3.65668i	0.522974	−	0.115925i
$996$		0			0
$997$	1.26721	−	4.72928i	0.0401329	−	0.149778i	−0.942952	−	0.332929i	$-0.891963\pi$
$997$	1.26721	−	4.72928i	0.0401329	−	0.149778i	0.983085	+	0.183151i	$0.0586297\pi$
$998$		0			0
$999$	83.8791	−	145.283i	2.65382	−	4.59655i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	280.2.bo.a.33.12	yes	48
4.3	odd	2		560.2.ci.e.33.1		48
5.2	odd	4	inner	280.2.bo.a.257.12	yes	48
7.3	odd	6	inner	280.2.bo.a.73.12	yes	48
20.7	even	4		560.2.ci.e.257.1		48
28.3	even	6		560.2.ci.e.353.1		48
35.17	even	12	inner	280.2.bo.a.17.12	✓	48
140.87	odd	12		560.2.ci.e.17.1		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.bo.a.17.12	✓	48	35.17	even	12	inner
280.2.bo.a.33.12	yes	48	1.1	even	1	trivial
280.2.bo.a.73.12	yes	48	7.3	odd	6	inner
280.2.bo.a.257.12	yes	48	5.2	odd	4	inner
560.2.ci.e.17.1		48	140.87	odd	12
560.2.ci.e.33.1		48	4.3	odd	2
560.2.ci.e.257.1		48	20.7	even	4
560.2.ci.e.353.1		48	28.3	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:	\( N \)	\(=\)	\( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	280.bo (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(3.19510 + 0.856125i) q^{3} +(0.672461 - 2.13256i) q^{5} +(-2.52104 + 0.802724i) q^{7} +(6.87765 + 3.97081i) q^{9} +O(q^{10})\)	\(q+(3.19510 + 0.856125i) q^{3} +(0.672461 - 2.13256i) q^{5} +(-2.52104 + 0.802724i) q^{7} +(6.87765 + 3.97081i) q^{9} +(-1.05351 - 1.82473i) q^{11} +(-1.20510 + 1.20510i) q^{13} +(3.97432 - 6.23802i) q^{15} +(0.850985 - 3.17592i) q^{17} +(-2.36491 + 4.09614i) q^{19} +(-8.74221 + 0.406461i) q^{21} +(-4.00492 + 1.07312i) q^{23} +(-4.09559 - 2.86812i) q^{25} +(11.5583 + 11.5583i) q^{27} +3.65910i q^{29} +(-1.63858 + 0.946036i) q^{31} +(-1.80387 - 6.73212i) q^{33} +(0.0165540 + 5.91606i) q^{35} +(-2.65625 - 9.91327i) q^{37} +(-4.88214 + 2.81870i) q^{39} +0.826081i q^{41} +(4.70172 + 4.70172i) q^{43} +(13.0929 - 11.9968i) q^{45} +(3.90561 - 1.04650i) q^{47} +(5.71127 - 4.04740i) q^{49} +(5.43796 - 9.41883i) q^{51} +(-0.645746 + 2.40996i) q^{53} +(-4.59977 + 1.01960i) q^{55} +(-11.0629 + 11.0629i) q^{57} +(-1.15566 - 2.00166i) q^{59} +(1.44974 + 0.837008i) q^{61} +(-20.5263 - 4.48972i) q^{63} +(1.75956 + 3.38033i) q^{65} +(-12.2602 - 3.28512i) q^{67} -13.7149 q^{69} +10.7915 q^{71} +(-12.6133 - 3.37973i) q^{73} +(-10.6304 - 12.6703i) q^{75} +(4.12068 + 3.75453i) q^{77} +(8.29280 + 4.78785i) q^{79} +(15.1223 + 26.1925i) q^{81} +(-3.47691 + 3.47691i) q^{83} +(-6.20057 - 3.95045i) q^{85} +(-3.13265 + 11.6912i) q^{87} +(2.86698 - 4.96576i) q^{89} +(2.07074 - 4.00547i) q^{91} +(-6.04536 + 1.61985i) q^{93} +(7.14494 + 7.79779i) q^{95} +(-1.02714 - 1.02714i) q^{97} -16.7331i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{7}+O(q^{10}) \) 48 * q - 4 * q^7	\( 48 q - 4 q^{7} + 4 q^{11} + 8 q^{15} - 4 q^{21} - 4 q^{23} - 8 q^{25} - 36 q^{33} + 24 q^{35} + 8 q^{37} - 16 q^{43} + 48 q^{45} + 24 q^{51} + 16 q^{53} - 96 q^{57} - 36 q^{61} - 68 q^{63} + 12 q^{65} - 16 q^{67} - 64 q^{71} - 48 q^{73} - 48 q^{75} + 4 q^{77} - 40 q^{85} - 12 q^{87} - 80 q^{91} + 24 q^{95}+O(q^{100}) \) 48 * q - 4 * q^7 + 4 * q^11 + 8 * q^15 - 4 * q^21 - 4 * q^23 - 8 * q^25 - 36 * q^33 + 24 * q^35 + 8 * q^37 - 16 * q^43 + 48 * q^45 + 24 * q^51 + 16 * q^53 - 96 * q^57 - 36 * q^61 - 68 * q^63 + 12 * q^65 - 16 * q^67 - 64 * q^71 - 48 * q^73 - 48 * q^75 + 4 * q^77 - 40 * q^85 - 12 * q^87 - 80 * q^91 + 24 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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