LMFDB - Embedded newform 672.2.bi.c.593.21

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [672,2,Mod(17,672)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("672.17"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(672, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 3, 3, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 672 = 2^{5} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	672.bi (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [48,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$5.36594701583$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 168)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			593.21
Character	$\chi$	$=$	672.593
Dual form			672.2.bi.c.17.21

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.52791 + 0.815778i) q^{3} +(0.461663 + 0.266541i) q^{5} +(-0.489180 + 2.60014i) q^{7} +(1.66901 + 2.49287i) q^{9} +(2.28733 + 3.96177i) q^{11} -4.97924 q^{13} +(0.487941 + 0.783866i) q^{15} +(-2.16139 - 3.74363i) q^{17} +(-0.921087 + 1.59537i) q^{19} +(-2.86856 + 3.57371i) q^{21} +(-0.103387 - 0.0596907i) q^{23} +(-2.35791 - 4.08402i) q^{25} +(0.516471 + 5.17042i) q^{27} +7.74542 q^{29} +(1.93668 - 1.11814i) q^{31} +(0.262906 + 7.91918i) q^{33} +(-0.918880 + 1.07000i) q^{35} +(7.02261 + 4.05451i) q^{37} +(-7.60783 - 4.06195i) q^{39} +2.60914 q^{41} +1.87217i q^{43} +(0.106069 + 1.59573i) q^{45} +(2.91482 - 5.04861i) q^{47} +(-6.52141 - 2.54387i) q^{49} +(-0.248430 - 7.48314i) q^{51} +(2.29287 + 3.97137i) q^{53} +2.43867i q^{55} +(-2.70880 + 1.68618i) q^{57} +(5.71492 - 3.29951i) q^{59} +(1.07564 - 1.86306i) q^{61} +(-7.29824 + 3.12020i) q^{63} +(-2.29873 - 1.32717i) q^{65} +(-10.4812 + 6.05131i) q^{67} +(-0.109272 - 0.175543i) q^{69} -6.20627i q^{71} +(8.35520 - 4.82388i) q^{73} +(-0.271018 - 8.16355i) q^{75} +(-11.4201 + 4.00935i) q^{77} +(0.0228792 - 0.0396280i) q^{79} +(-3.42880 + 8.32126i) q^{81} +3.86459i q^{83} -2.30440i q^{85} +(11.8343 + 6.31854i) q^{87} +(8.23362 - 14.2610i) q^{89} +(2.43575 - 12.9467i) q^{91} +(3.87123 - 0.128520i) q^{93} +(-0.850463 + 0.491015i) q^{95} +7.18828i q^{97} +(-6.05860 + 12.3143i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 4 q^{7} - 14 q^{9} - 4 q^{15} - 8 q^{25} - 48 q^{31} - 42 q^{33} + 8 q^{39} - 36 q^{49} + 4 q^{57} + 6 q^{63} - 36 q^{73} + 56 q^{79} + 42 q^{81} + 132 q^{87}+O(q^{100}) $ 48 * q + 4 * q^7 - 14 * q^9 - 4 * q^15 - 8 * q^25 - 48 * q^31 - 42 * q^33 + 8 * q^39 - 36 * q^49 + 4 * q^57 + 6 * q^63 - 36 * q^73 + 56 * q^79 + 42 * q^81 + 132 * q^87

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/672\mathbb{Z}\right)^\times$.

$n$	$127$	$421$	$449$	$577$
$\chi(n)$	$1$	$-1$	$-1$	$e\left(\frac{5}{6}\right)$

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
$3$	1.52791	+	0.815778i	0.882139	+	0.470990i
$3$	1.52791	+	0.815778i	0.882139	+	0.470990i
$4$		0			0
$5$	0.461663	+	0.266541i	0.206462	+	0.119201i	0.599666	−	0.800250i	$-0.295300\pi$
$5$	0.461663	+	0.266541i	0.206462	+	0.119201i	−0.393204	+	0.919451i	$0.628633\pi$
$6$		0			0
$7$	−0.489180	+	2.60014i	−0.184893	+	0.982759i
$7$	−0.489180	+	2.60014i	−0.184893	+	0.982759i
$8$		0			0
$9$	1.66901	+	2.49287i	0.556337	+	0.830956i
$10$		0			0
$11$	2.28733	+	3.96177i	0.689656	+	1.19452i	0.971949	+	0.235191i	$0.0755716\pi$
$11$	2.28733	+	3.96177i	0.689656	+	1.19452i	−0.282293	+	0.959328i	$0.591095\pi$
$12$		0			0
$13$	−4.97924			−1.38099			−0.690496	−	0.723336i	$-0.742608\pi$
$13$	−4.97924			−1.38099			−0.690496	+	0.723336i	$0.742608\pi$
$14$		0			0
$15$	0.487941	+	0.783866i	0.125986	+	0.202393i
$16$		0			0
$17$	−2.16139	−	3.74363i	−0.524213	−	0.907964i	−0.999603	−	0.0281884i	$-0.991026\pi$
$17$	−2.16139	−	3.74363i	−0.524213	−	0.907964i	0.475389	−	0.879775i	$-0.342307\pi$
$18$		0			0
$19$	−0.921087	+	1.59537i	−0.211312	+	0.366003i	−0.952125	−	0.305708i	$-0.901107\pi$
$19$	−0.921087	+	1.59537i	−0.211312	+	0.366003i	0.740814	+	0.671711i	$0.234440\pi$
$20$		0			0
$21$	−2.86856	+	3.57371i	−0.625970	+	0.779847i
$22$		0			0
$23$	−0.103387	−	0.0596907i	−0.0215577	−	0.0124464i	0.489182	−	0.872182i	$-0.337295\pi$
$23$	−0.103387	−	0.0596907i	−0.0215577	−	0.0124464i	−0.510740	+	0.859735i	$0.670629\pi$
$24$		0			0
$25$	−2.35791	−	4.08402i	−0.471582	−	0.816804i
$26$		0			0
$27$	0.516471	+	5.17042i	0.0993949	+	0.995048i
$28$		0			0
$29$	7.74542			1.43829			0.719144	−	0.694861i	$-0.244534\pi$
$29$	7.74542			1.43829			0.719144	+	0.694861i	$0.244534\pi$
$30$		0			0
$31$	1.93668	−	1.11814i	0.347838	−	0.200825i	−0.315894	−	0.948794i	$-0.602305\pi$
$31$	1.93668	−	1.11814i	0.347838	−	0.200825i	0.663733	+	0.747970i	$0.268971\pi$
$32$		0			0
$33$	0.262906	+	7.91918i	0.0457660	+	1.37855i
$34$		0			0
$35$	−0.918880	+	1.07000i	−0.155319	+	0.180863i
$36$		0			0
$37$	7.02261	+	4.05451i	1.15451	+	0.666557i	0.949982	−	0.312304i	$-0.101101\pi$
$37$	7.02261	+	4.05451i	1.15451	+	0.666557i	0.204528	+	0.978861i	$0.434434\pi$
$38$		0			0
$39$	−7.60783	−	4.06195i	−1.21823	−	0.650433i
$40$		0			0
$41$	2.60914			0.407479			0.203740	−	0.979025i	$-0.434690\pi$
$41$	2.60914			0.407479			0.203740	+	0.979025i	$0.434690\pi$
$42$		0			0
$43$			1.87217i			0.285503i	0.989759	+	0.142752i	$0.0455950\pi$
$43$			1.87217i			0.285503i	−0.989759	+	0.142752i	$0.954405\pi$
$44$		0			0
$45$	0.106069	+	1.59573i	0.0158118	+	0.237877i
$46$		0			0
$47$	2.91482	−	5.04861i	0.425170	−	0.736415i	−0.571267	−	0.820764i	$-0.693548\pi$
$47$	2.91482	−	5.04861i	0.425170	−	0.736415i	0.996436	+	0.0843492i	$0.0268811\pi$
$48$		0			0
$49$	−6.52141	−	2.54387i	−0.931629	−	0.363410i
$50$		0			0
$51$	−0.248430	−	7.48314i	−0.0347871	−	1.04785i
$52$		0			0
$53$	2.29287	+	3.97137i	0.314950	+	0.545510i	0.979427	−	0.201799i	$-0.0646788\pi$
$53$	2.29287	+	3.97137i	0.314950	+	0.545510i	−0.664476	+	0.747309i	$0.731345\pi$
$54$		0			0
$55$			2.43867i			0.328830i
$56$		0			0
$57$	−2.70880	+	1.68618i	−0.358790	+	0.223339i
$58$		0			0
$59$	5.71492	−	3.29951i	0.744019	−	0.429559i	−0.0795100	−	0.996834i	$-0.525336\pi$
$59$	5.71492	−	3.29951i	0.744019	−	0.429559i	0.823529	+	0.567275i	$0.192002\pi$
$60$		0			0
$61$	1.07564	−	1.86306i	0.137722	−	0.238541i	−0.788912	−	0.614506i	$-0.789355\pi$
$61$	1.07564	−	1.86306i	0.137722	−	0.238541i	0.926634	+	0.375965i	$0.122689\pi$
$62$		0			0
$63$	−7.29824	+	3.12020i	−0.919492	+	0.393108i
$64$		0			0
$65$	−2.29873	−	1.32717i	−0.285123	−	0.164616i
$66$		0			0
$67$	−10.4812	+	6.05131i	−1.28048	+	0.739285i	−0.976936	−	0.213532i	$-0.931503\pi$
$67$	−10.4812	+	6.05131i	−1.28048	+	0.739285i	−0.303544	+	0.952817i	$0.598170\pi$
$68$		0			0
$69$	−0.109272	−	0.175543i	−0.0131548	−	0.0211329i
$70$		0			0
$71$		−	6.20627i		−	0.736549i	−0.929717	−	0.368275i	$-0.879949\pi$
$71$		−	6.20627i		−	0.736549i	0.929717	−	0.368275i	$-0.120051\pi$
$72$		0			0
$73$	8.35520	−	4.82388i	0.977902	−	0.564592i	0.0762659	−	0.997088i	$-0.475700\pi$
$73$	8.35520	−	4.82388i	0.977902	−	0.564592i	0.901636	+	0.432496i	$0.142367\pi$
$74$		0			0
$75$	−0.271018	−	8.16355i	−0.0312945	−	0.942645i
$76$		0			0
$77$	−11.4201	+	4.00935i	−1.30144	+	0.456908i
$78$		0			0
$79$	0.0228792	−	0.0396280i	0.00257411	−	0.00445849i	−0.864735	−	0.502228i	$-0.832514\pi$
$79$	0.0228792	−	0.0396280i	0.00257411	−	0.00445849i	0.867310	+	0.497769i	$0.165847\pi$
$80$		0			0
$81$	−3.42880	+	8.32126i	−0.380977	+	0.924584i
$82$		0			0
$83$			3.86459i			0.424194i	0.977249	+	0.212097i	$0.0680292\pi$
$83$			3.86459i			0.424194i	−0.977249	+	0.212097i	$0.931971\pi$
$84$		0			0
$85$		−	2.30440i		−	0.249947i
$86$		0			0
$87$	11.8343	+	6.31854i	1.26877	+	0.677419i
$88$		0			0
$89$	8.23362	−	14.2610i	0.872762	−	1.51167i	0.0136336	−	0.999907i	$-0.495660\pi$
$89$	8.23362	−	14.2610i	0.872762	−	1.51167i	0.859128	−	0.511761i	$-0.171007\pi$
$90$		0			0
$91$	2.43575	−	12.9467i	0.255335	−	1.35718i
$92$		0			0
$93$	3.87123	−	0.128520i	0.401428	−	0.0133269i
$94$		0			0
$95$	−0.850463	+	0.491015i	−0.0872557	+	0.0503771i
$96$		0			0
$97$			7.18828i			0.729859i	0.931035	+	0.364930i	$0.118907\pi$
$97$			7.18828i			0.729859i	−0.931035	+	0.364930i	$0.881093\pi$
$98$		0			0
$99$	−6.05860	+	12.3143i	−0.608912	+	1.23763i
$100$		0			0
$101$	−3.33419	+	1.92499i	−0.331764	+	0.191544i	−0.656624	−	0.754218i	$-0.728016\pi$
$101$	−3.33419	+	1.92499i	−0.331764	+	0.191544i	0.324860	+	0.945762i	$0.394683\pi$
$102$		0			0
$103$	4.61020	+	2.66170i	0.454256	+	0.262265i	0.709626	−	0.704578i	$-0.248864\pi$
$103$	4.61020	+	2.66170i	0.454256	+	0.262265i	−0.255370	+	0.966843i	$0.582197\pi$
$104$		0			0
$105$	−2.27685	+	0.885260i	−0.222198	+	0.0863926i
$106$		0			0
$107$	4.60634	−	7.97842i	0.445312	−	0.771303i	−0.552762	−	0.833339i	$-0.686426\pi$
$107$	4.60634	−	7.97842i	0.445312	−	0.771303i	0.998074	+	0.0620363i	$0.0197594\pi$
$108$		0			0
$109$	4.24194	−	2.44909i	0.406304	−	0.234580i	−0.282896	−	0.959151i	$-0.591295\pi$
$109$	4.24194	−	2.44909i	0.406304	−	0.234580i	0.689201	+	0.724571i	$0.257962\pi$
$110$		0			0
$111$	7.42233	+	11.9238i	0.704497	+	1.13176i
$112$		0			0
$113$			3.87615i			0.364637i	0.983240	+	0.182319i	$0.0583602\pi$
$113$			3.87615i			0.364637i	−0.983240	+	0.182319i	$0.941640\pi$
$114$		0			0
$115$	−0.0318201	−	0.0551140i	−0.00296724	−	0.00513941i
$116$		0			0
$117$	−8.31041	−	12.4126i	−0.768298	−	1.14754i
$118$		0			0
$119$	10.7913	−	3.78859i	0.989233	−	0.347299i
$120$		0			0
$121$	−4.96376	+	8.59748i	−0.451251	+	0.781589i
$122$		0			0
$123$	3.98653	+	2.12848i	0.359453	+	0.191918i
$124$		0			0
$125$		−	5.17934i		−	0.463254i
$126$		0			0
$127$	−8.19005			−0.726750			−0.363375	−	0.931643i	$-0.618376\pi$
$127$	−8.19005			−0.726750			−0.363375	+	0.931643i	$0.618376\pi$
$128$		0			0
$129$	−1.52728	+	2.86051i	−0.134469	+	0.251854i
$130$		0			0
$131$	−18.5565	−	10.7136i	−1.62129	−	0.936053i	−0.986575	−	0.163306i	$-0.947784\pi$
$131$	−18.5565	−	10.7136i	−1.62129	−	0.936053i	−0.634715	−	0.772746i	$-0.718883\pi$
$132$		0			0
$133$	−3.69760	−	3.17537i	−0.320622	−	0.275340i
$134$		0			0
$135$	−1.13970	+	2.52465i	−0.0980894	+	0.217288i
$136$		0			0
$137$	3.91533	−	2.26052i	0.334509	−	0.193129i	−0.323332	−	0.946286i	$-0.604803\pi$
$137$	3.91533	−	2.26052i	0.334509	−	0.193129i	0.657841	+	0.753157i	$0.271470\pi$
$138$		0			0
$139$	14.8300			1.25786			0.628931	−	0.777461i	$-0.283493\pi$
$139$	14.8300			1.25786			0.628931	+	0.777461i	$0.283493\pi$
$140$		0			0
$141$	8.57212	−	5.33597i	0.721903	−	0.449370i
$142$		0			0
$143$	−11.3892	−	19.7266i	−0.952410	−	1.64962i
$144$		0			0
$145$	3.57577	+	2.06447i	0.296952	+	0.171445i
$146$		0			0
$147$	−7.88888	−	9.20682i	−0.650664	−	0.759366i
$148$		0			0
$149$	10.7714	−	18.6566i	0.882425	−	1.52841i	0.0337890	−	0.999429i	$-0.489243\pi$
$149$	10.7714	−	18.6566i	0.882425	−	1.52841i	0.848636	−	0.528977i	$-0.177424\pi$
$150$		0			0
$151$	−1.40767	−	2.43816i	−0.114555	−	0.198415i	0.803047	−	0.595916i	$-0.203211\pi$
$151$	−1.40767	−	2.43816i	−0.114555	−	0.198415i	−0.917602	+	0.397501i	$0.869878\pi$
$152$		0			0
$153$	5.72500	−	11.6362i	0.462839	−	0.940733i
$154$		0			0
$155$	1.19213			0.0957539
$156$		0			0
$157$	3.54427	+	6.13885i	0.282863	+	0.489933i	0.972089	−	0.234613i	$-0.0753824\pi$
$157$	3.54427	+	6.13885i	0.282863	+	0.489933i	−0.689226	+	0.724547i	$0.742049\pi$
$158$		0			0
$159$	0.263543	+	7.93838i	0.0209003	+	0.629554i
$160$		0			0
$161$	0.205779	−	0.239622i	0.0162176	−	0.0188848i
$162$		0			0
$163$	5.64257	+	3.25774i	0.441960	+	0.255166i	0.704429	−	0.709775i	$-0.251203\pi$
$163$	5.64257	+	3.25774i	0.441960	+	0.255166i	−0.262469	+	0.964941i	$0.584537\pi$
$164$		0			0
$165$	−1.98942	+	3.72607i	−0.154876	+	0.290074i
$166$		0			0
$167$	−17.2470			−1.33462			−0.667308	−	0.744782i	$-0.732553\pi$
$167$	−17.2470			−1.33462			−0.667308	+	0.744782i	$0.732553\pi$
$168$		0			0
$169$	11.7928			0.907141
$170$		0			0
$171$	−5.51435	+	0.366542i	−0.421693	+	0.0280301i
$172$		0			0
$173$	−14.5387	−	8.39395i	−1.10536	−	0.638180i	−0.167737	−	0.985832i	$-0.553646\pi$
$173$	−14.5387	−	8.39395i	−1.10536	−	0.638180i	−0.937624	+	0.347652i	$0.886979\pi$
$174$		0			0
$175$	11.7725	−	4.13307i	0.889914	−	0.312430i
$176$		0			0
$177$	11.4235	−	0.379246i	0.858646	−	0.0285058i
$178$		0			0
$179$	−2.00982	−	3.48110i	−0.150221	−	0.260190i	0.781088	−	0.624421i	$-0.214665\pi$
$179$	−2.00982	−	3.48110i	−0.150221	−	0.260190i	−0.931309	+	0.364231i	$0.881332\pi$
$180$		0			0
$181$	−14.8596			−1.10451			−0.552253	−	0.833676i	$-0.686232\pi$
$181$	−14.8596			−1.10451			−0.552253	+	0.833676i	$0.686232\pi$
$182$		0			0
$183$	3.16332	−	1.96911i	0.233840	−	0.145561i
$184$		0			0
$185$	2.16139	+	3.74363i	0.158908	+	0.275237i
$186$		0			0
$187$	9.88761	−	17.1258i	0.723053	−	1.25237i
$188$		0			0
$189$	−13.6964	−	1.18637i	−0.996270	−	0.0862959i
$190$		0			0
$191$	17.1154	+	9.88159i	1.23843	+	0.715006i	0.968773	−	0.247951i	$-0.0797570\pi$
$191$	17.1154	+	9.88159i	1.23843	+	0.715006i	0.269655	+	0.962957i	$0.413090\pi$
$192$		0			0
$193$	−6.29229	−	10.8986i	−0.452929	−	0.784496i	0.545638	−	0.838021i	$-0.316287\pi$
$193$	−6.29229	−	10.8986i	−0.452929	−	0.784496i	−0.998566	+	0.0535255i	$0.982954\pi$
$194$		0			0
$195$	−2.42957	−	3.90305i	−0.173985	−	0.279504i
$196$		0			0
$197$	−8.41804			−0.599761			−0.299880	−	0.953977i	$-0.596947\pi$
$197$	−8.41804			−0.599761			−0.299880	+	0.953977i	$0.596947\pi$
$198$		0			0
$199$	−12.3980	+	7.15800i	−0.878873	+	0.507417i	−0.870287	−	0.492546i	$-0.836066\pi$
$199$	−12.3980	+	7.15800i	−0.878873	+	0.507417i	−0.00858618	+	0.999963i	$0.502733\pi$
$200$		0			0
$201$	−20.9508	+	0.695538i	−1.47776	+	0.0490595i
$202$		0			0
$203$	−3.78890	+	20.1391i	−0.265929	+	1.41349i
$204$		0			0
$205$	1.20454	+	0.695443i	0.0841290	+	0.0485719i
$206$		0			0
$207$	−0.0237536	−	0.357356i	−0.00165099	−	0.0248379i
$208$		0			0
$209$	−8.42732			−0.582930
$210$		0			0
$211$			9.62315i			0.662485i	0.943546	+	0.331243i	$0.107468\pi$
$211$			9.62315i			0.662485i	−0.943546	+	0.331243i	$0.892532\pi$
$212$		0			0
$213$	5.06294	−	9.48262i	0.346907	−	0.649739i
$214$		0			0
$215$	−0.499011	+	0.864312i	−0.0340323	+	0.0589456i
$216$		0			0
$217$	1.95994	+	5.58261i	0.133049	+	0.378972i
$218$		0			0
$219$	16.7012	−	0.554457i	1.12856	−	0.0374667i
$220$		0			0
$221$	10.7621	+	18.6404i	0.723935	+	1.25389i
$222$		0			0
$223$		−	20.1840i		−	1.35162i	−0.737076	−	0.675810i	$-0.763794\pi$
$223$		−	20.1840i		−	1.35162i	0.737076	−	0.675810i	$-0.236206\pi$
$224$		0			0
$225$	6.24555	−	12.6942i	0.416370	−	0.846283i
$226$		0			0
$227$	1.03403	−	0.597000i	0.0686313	−	0.0396243i	−0.465292	−	0.885157i	$-0.654051\pi$
$227$	1.03403	−	0.597000i	0.0686313	−	0.0396243i	0.533923	+	0.845533i	$0.320717\pi$
$228$		0			0
$229$	11.4021	−	19.7490i	0.753472	−	1.30505i	−0.192658	−	0.981266i	$-0.561711\pi$
$229$	11.4021	−	19.7490i	0.753472	−	1.30505i	0.946130	−	0.323786i	$-0.104956\pi$
$230$		0			0
$231$	−20.7195	−	3.19031i	−1.36325	−	0.209907i
$232$		0			0
$233$	−14.1080	−	8.14528i	−0.924249	−	0.533615i	−0.0392607	−	0.999229i	$-0.512500\pi$
$233$	−14.1080	−	8.14528i	−0.924249	−	0.533615i	−0.884988	+	0.465614i	$0.845834\pi$
$234$		0			0
$235$	2.69133	−	1.55384i	0.175563	−	0.101361i
$236$		0			0
$237$	0.0672850	−	0.0418836i	0.00437063	−	0.00272063i
$238$		0			0
$239$			20.2417i			1.30933i	0.755920	+	0.654664i	$0.227190\pi$
$239$			20.2417i			1.30933i	−0.755920	+	0.654664i	$0.772810\pi$
$240$		0			0
$241$	−7.99312	+	4.61483i	−0.514882	+	0.297267i	−0.734838	−	0.678242i	$-0.762742\pi$
$241$	−7.99312	+	4.61483i	−0.514882	+	0.297267i	0.219956	+	0.975510i	$0.429409\pi$
$242$		0			0
$243$	−12.0272	+	9.91699i	−0.771545	+	0.636175i
$244$		0			0
$245$	−2.33265	−	2.91263i	−0.149027	−	0.186081i
$246$		0			0
$247$	4.58631	−	7.94372i	0.291820	−	0.505447i
$248$		0			0
$249$	−3.15265	+	5.90474i	−0.199791	+	0.374198i
$250$		0			0
$251$			8.22152i			0.518938i	0.965751	+	0.259469i	$0.0835475\pi$
$251$			8.22152i			0.518938i	−0.965751	+	0.259469i	$0.916452\pi$
$252$		0			0
$253$		−	0.546129i		−	0.0343349i
$254$		0			0
$255$	1.87987	−	3.52091i	0.117722	−	0.220488i
$256$		0			0
$257$	6.71468	−	11.6302i	0.418850	−	0.725470i	−0.576974	−	0.816763i	$-0.695767\pi$
$257$	6.71468	−	11.6302i	0.418850	−	0.725470i	0.995824	+	0.0912928i	$0.0290999\pi$
$258$		0			0
$259$	−13.9776	+	16.2763i	−0.868525	+	1.01136i
$260$		0			0
$261$	12.9272	+	19.3083i	0.800174	+	1.19515i
$262$		0			0
$263$	13.0415	−	7.52949i	0.804170	−	0.464288i	−0.0407569	−	0.999169i	$-0.512977\pi$
$263$	13.0415	−	7.52949i	0.804170	−	0.464288i	0.844927	+	0.534881i	$0.179644\pi$
$264$		0			0
$265$			2.44458i			0.150170i
$266$		0			0
$267$	24.2141	−	15.0728i	1.48188	−	0.922439i
$268$		0			0
$269$	11.5014	−	6.64035i	0.701254	−	0.404869i	−0.106560	−	0.994306i	$-0.533984\pi$
$269$	11.5014	−	6.64035i	0.701254	−	0.404869i	0.807814	+	0.589437i	$0.200650\pi$
$270$		0			0
$271$	−16.2954	−	9.40818i	−0.989878	−	0.571506i	−0.0846401	−	0.996412i	$-0.526974\pi$
$271$	−16.2954	−	9.40818i	−0.989878	−	0.571506i	−0.905238	+	0.424905i	$0.860307\pi$
$272$		0			0
$273$	14.2832	−	17.7943i	0.864460	−	1.07696i
$274$		0			0
$275$	10.7866	−	18.6830i	0.650459	−	1.12663i
$276$		0			0
$277$	−20.1344	+	11.6246i	−1.20976	+	0.698454i	−0.962706	−	0.270548i	$-0.912795\pi$
$277$	−20.1344	+	11.6246i	−1.20976	+	0.698454i	−0.247052	+	0.969002i	$0.579462\pi$
$278$		0			0
$279$	6.01973	+	2.96170i	0.360392	+	0.177312i
$280$		0			0
$281$			21.2736i			1.26908i	0.772892	+	0.634538i	$0.218810\pi$
$281$			21.2736i			1.26908i	−0.772892	+	0.634538i	$0.781190\pi$
$282$		0			0
$283$	−4.31186	−	7.46836i	−0.256314	−	0.443948i	0.708938	−	0.705271i	$-0.249175\pi$
$283$	−4.31186	−	7.46836i	−0.256314	−	0.443948i	−0.965251	+	0.261323i	$0.915841\pi$
$284$		0			0
$285$	−1.69999	+	0.0564373i	−0.100699	+	0.00334306i
$286$		0			0
$287$	−1.27634	+	6.78411i	−0.0753399	+	0.400454i
$288$		0			0
$289$	−0.843181	+	1.46043i	−0.0495989	+	0.0859078i
$290$		0			0
$291$	−5.86404	+	10.9830i	−0.343756	+	0.643837i
$292$		0			0
$293$			22.7441i			1.32872i	0.747411	+	0.664362i	$0.231297\pi$
$293$			22.7441i			1.32872i	−0.747411	+	0.664362i	$0.768703\pi$
$294$		0			0
$295$	3.51782			0.204815
$296$		0			0
$297$	−19.3027	+	13.8726i	−1.12006	+	0.804970i
$298$		0			0
$299$	0.514790	+	0.297214i	0.0297711	+	0.0171883i
$300$		0			0
$301$	−4.86790	−	0.915828i	−0.280581	−	0.0527875i
$302$		0			0
$303$	−6.66470	+	0.221259i	−0.382877	+	0.0127110i
$304$		0			0
$305$	0.993166	−	0.573405i	0.0568685	−	0.0328331i
$306$		0			0
$307$	−22.8169			−1.30223			−0.651114	−	0.758980i	$-0.725698\pi$
$307$	−22.8169			−1.30223			−0.651114	+	0.758980i	$0.725698\pi$
$308$		0			0
$309$	4.87261	+	7.82773i	0.277193	+	0.445304i
$310$		0			0
$311$	11.9871	+	20.7622i	0.679725	+	1.17732i	0.975064	+	0.221925i	$0.0712341\pi$
$311$	11.9871	+	20.7622i	0.679725	+	1.17732i	−0.295339	+	0.955393i	$0.595433\pi$
$312$		0			0
$313$	19.4419	+	11.2248i	1.09892	+	0.634463i	0.935938	−	0.352166i	$-0.114555\pi$
$313$	19.4419	+	11.2248i	1.09892	+	0.634463i	0.162984	+	0.986629i	$0.447888\pi$
$314$		0			0
$315$	−4.20099	−	0.504805i	−0.236699	−	0.0284425i
$316$		0			0
$317$	1.06072	−	1.83723i	0.0595762	−	0.103189i	−0.834699	−	0.550706i	$-0.814358\pi$
$317$	1.06072	−	1.83723i	0.0595762	−	0.103189i	0.894275	+	0.447517i	$0.147692\pi$
$318$		0			0
$319$	17.7163	+	30.6856i	0.991924	+	1.71806i
$320$		0			0
$321$	13.5467	−	8.43255i	0.756103	−	0.470659i
$322$		0			0
$323$	7.96330			0.443090
$324$		0			0
$325$	11.7406	+	20.3353i	0.651252	+	1.12800i
$326$		0			0
$327$	8.47921	−	0.281498i	0.468902	−	0.0155669i
$328$		0			0
$329$	11.7012	+	10.0486i	0.645108	+	0.553997i
$330$		0			0
$331$	1.25478	+	0.724448i	0.0689689	+	0.0398192i	0.534088	−	0.845429i	$-0.320655\pi$
$331$	1.25478	+	0.724448i	0.0689689	+	0.0398192i	−0.465119	+	0.885248i	$0.653988\pi$
$332$		0			0
$333$	1.61347	+	24.2735i	0.0884176	+	1.33018i
$334$		0			0
$335$	−6.45170			−0.352494
$336$		0			0
$337$	−21.6680			−1.18033			−0.590165	−	0.807282i	$-0.700937\pi$
$337$	−21.6680			−1.18033			−0.590165	+	0.807282i	$0.700937\pi$
$338$		0			0
$339$	−3.16208	+	5.92240i	−0.171740	+	0.321661i
$340$		0			0
$341$	8.85966	+	5.11513i	0.479778	+	0.277000i
$342$		0			0
$343$	9.80454	−	15.7121i	0.529396	−	0.848375i
$344$		0			0
$345$	−0.00365740	−	0.110167i	−0.000196908	−	0.00593121i
$346$		0			0
$347$	13.7374	+	23.7939i	0.737463	+	1.27732i	0.953634	+	0.300969i	$0.0973099\pi$
$347$	13.7374	+	23.7939i	0.737463	+	1.27732i	−0.216171	+	0.976356i	$0.569357\pi$
$348$		0			0
$349$	15.6203			0.836134			0.418067	−	0.908416i	$-0.362708\pi$
$349$	15.6203			0.836134			0.418067	+	0.908416i	$0.362708\pi$
$350$		0			0
$351$	−2.57163	−	25.7448i	−0.137264	−	1.37415i
$352$		0			0
$353$	6.72613	+	11.6500i	0.357996	+	0.620067i	0.987626	−	0.156828i	$-0.0501268\pi$
$353$	6.72613	+	11.6500i	0.357996	+	0.620067i	−0.629630	+	0.776895i	$0.716793\pi$
$354$		0			0
$355$	1.65423	−	2.86521i	0.0877973	−	0.152069i
$356$		0			0
$357$	19.5787	+	3.01465i	1.03621	+	0.159552i
$358$		0			0
$359$	−19.9816	−	11.5364i	−1.05459	−	0.608867i	−0.130658	−	0.991428i	$-0.541709\pi$
$359$	−19.9816	−	11.5364i	−1.05459	−	0.608867i	−0.923930	+	0.382561i	$0.875042\pi$
$360$		0			0
$361$	7.80320	+	13.5155i	0.410695	+	0.711344i
$362$		0			0
$363$	−14.5978	+	9.08684i	−0.766186	+	0.476936i
$364$		0			0
$365$	5.14305			0.269200
$366$		0			0
$367$	−18.6893	+	10.7903i	−0.975574	+	0.563248i	−0.900931	−	0.433963i	$-0.857115\pi$
$367$	−18.6893	+	10.7903i	−0.975574	+	0.563248i	−0.0746427	+	0.997210i	$0.523782\pi$
$368$		0			0
$369$	4.35469	+	6.50424i	0.226696	+	0.338597i
$370$		0			0
$371$	−11.4477	+	4.01907i	−0.594337	+	0.208659i
$372$		0			0
$373$	0.158888	+	0.0917338i	0.00822689	+	0.00474980i	0.504108	−	0.863641i	$-0.331821\pi$
$373$	0.158888	+	0.0917338i	0.00822689	+	0.00474980i	−0.495881	+	0.868391i	$0.665155\pi$
$374$		0			0
$375$	4.22519	−	7.91356i	0.218188	−	0.408654i
$376$		0			0
$377$	−38.5663			−1.98627
$378$		0			0
$379$			2.93359i			0.150688i	0.997158	+	0.0753441i	$0.0240055\pi$
$379$			2.93359i			0.150688i	−0.997158	+	0.0753441i	$0.975994\pi$
$380$		0			0
$381$	−12.5137	−	6.68127i	−0.641094	−	0.342292i
$382$		0			0
$383$	7.67488	−	13.2933i	0.392168	−	0.679255i	−0.600567	−	0.799574i	$-0.705058\pi$
$383$	7.67488	−	13.2933i	0.392168	−	0.679255i	0.992735	+	0.120319i	$0.0383918\pi$
$384$		0			0
$385$	−6.34088	−	1.19295i	−0.323161	−	0.0607983i
$386$		0			0
$387$	−4.66708	+	3.12468i	−0.237241	+	0.158836i
$388$		0			0
$389$	−2.00060	−	3.46513i	−0.101434	−	0.175689i	0.810842	−	0.585266i	$-0.199010\pi$
$389$	−2.00060	−	3.46513i	−0.101434	−	0.175689i	−0.912276	+	0.409577i	$0.865676\pi$
$390$		0			0
$391$			0.516059i			0.0260982i
$392$		0			0
$393$	−19.6127	−	31.5074i	−0.989332	−	1.58934i
$394$		0			0
$395$	0.0211250	−	0.0121965i	0.00106291	−	0.000613673i
$396$		0			0
$397$	−11.7195	+	20.2987i	−0.588183	+	1.01876i	0.406288	+	0.913745i	$0.366823\pi$
$397$	−11.7195	+	20.2987i	−0.588183	+	1.01876i	−0.994470	+	0.105017i	$0.966510\pi$
$398$		0			0
$399$	−3.05919	−	7.86810i	−0.153151	−	0.393898i
$400$		0			0
$401$	14.5441	+	8.39703i	0.726297	+	0.419328i	0.817066	−	0.576544i	$-0.195599\pi$
$401$	14.5441	+	8.39703i	0.726297	+	0.419328i	−0.0907689	+	0.995872i	$0.528932\pi$
$402$		0			0
$403$	−9.64320	+	5.56751i	−0.480362	+	0.277337i
$404$		0			0
$405$	−3.80091	+	2.92770i	−0.188869	+	0.145479i
$406$		0			0
$407$			37.0960i			1.83878i
$408$		0			0
$409$	11.9749	−	6.91372i	0.592121	−	0.341861i	−0.173815	−	0.984778i	$-0.555609\pi$
$409$	11.9749	−	6.91372i	0.592121	−	0.341861i	0.765936	+	0.642917i	$0.222276\pi$
$410$		0			0
$411$	7.82635	−	0.259824i	0.386045	−	0.0128162i
$412$		0			0
$413$	5.78354	+	16.4736i	0.284590	+	0.810613i
$414$		0			0
$415$	−1.03007	+	1.78414i	−0.0505643	+	0.0875799i
$416$		0			0
$417$	22.6588	+	12.0980i	1.10961	+	0.592440i
$418$		0			0
$419$		−	17.5573i		−	0.857728i	−0.903369	−	0.428864i	$-0.858914\pi$
$419$		−	17.5573i		−	0.857728i	0.903369	−	0.428864i	$-0.141086\pi$
$420$		0			0
$421$			19.8896i			0.969362i	0.874691	+	0.484681i	$0.161064\pi$
$421$			19.8896i			0.969362i	−0.874691	+	0.484681i	$0.838936\pi$
$422$		0			0
$423$	17.4504	−	1.15994i	0.848467	−	0.0563980i
$424$		0			0
$425$	−10.1927	+	17.6543i	−0.494419	+	0.856359i
$426$		0			0
$427$	4.31803	+	3.70818i	0.208964	+	0.179451i
$428$		0			0
$429$	−1.30907	−	39.4315i	−0.0632026	−	1.90377i
$430$		0			0
$431$	−25.3821	+	14.6544i	−1.22261	+	0.705876i	−0.965474	−	0.260498i	$-0.916113\pi$
$431$	−25.3821	+	14.6544i	−1.22261	+	0.705876i	−0.257139	+	0.966374i	$0.582780\pi$
$432$		0			0
$433$		−	12.5427i		−	0.602763i	−0.953504	−	0.301381i	$-0.902552\pi$
$433$		−	12.5427i		−	0.602763i	0.953504	−	0.301381i	$-0.0974477\pi$
$434$		0			0
$435$	3.77930	+	6.07137i	0.181204	+	0.291100i
$436$		0			0
$437$	0.190457	−	0.109961i	0.00911081	−	0.00526013i
$438$		0			0
$439$	−11.7921	−	6.80818i	−0.562807	−	0.324937i	0.191464	−	0.981500i	$-0.438676\pi$
$439$	−11.7921	−	6.80818i	−0.562807	−	0.324937i	−0.754271	+	0.656563i	$0.772010\pi$
$440$		0			0
$441$	−4.54277	−	20.5028i	−0.216323	−	0.976322i
$442$		0			0
$443$	−6.72205	+	11.6429i	−0.319374	+	0.553172i	−0.980358	−	0.197228i	$-0.936806\pi$
$443$	−6.72205	+	11.6429i	−0.319374	+	0.553172i	0.660984	+	0.750400i	$0.270139\pi$
$444$		0			0
$445$	7.60232	−	4.38920i	0.360384	−	0.208068i
$446$		0			0
$447$	31.6773	−	19.7185i	1.49828	−	0.932653i
$448$		0			0
$449$			16.3428i			0.771266i	0.922652	+	0.385633i	$0.126017\pi$
$449$			16.3428i			0.771266i	−0.922652	+	0.385633i	$0.873983\pi$
$450$		0			0
$451$	5.96796	+	10.3368i	0.281020	+	0.486742i
$452$		0			0
$453$	−0.161798	−	4.87364i	−0.00760194	−	0.228984i
$454$		0			0
$455$	4.57532	−	5.32779i	0.214494	−	0.249770i
$456$		0			0
$457$	14.6395	−	25.3564i	0.684808	−	1.18612i	−0.288689	−	0.957423i	$-0.593219\pi$
$457$	14.6395	−	25.3564i	0.684808	−	1.18612i	0.973497	−	0.228699i	$-0.0734472\pi$
$458$		0			0
$459$	18.2399	−	13.1088i	0.851364	−	0.611864i
$460$		0			0
$461$		−	6.06975i		−	0.282696i	−0.989960	−	0.141348i	$-0.954856\pi$
$461$		−	6.06975i		−	0.282696i	0.989960	−	0.141348i	$-0.0451437\pi$
$462$		0			0
$463$	3.30400			0.153550			0.0767750	−	0.997048i	$-0.475538\pi$
$463$	3.30400			0.153550			0.0767750	+	0.997048i	$0.475538\pi$
$464$		0			0
$465$	1.82146	+	0.972510i	0.0844682	+	0.0450991i
$466$		0			0
$467$	7.03895	+	4.06394i	0.325724	+	0.188057i	0.653941	−	0.756546i	$-0.273114\pi$
$467$	7.03895	+	4.06394i	0.325724	+	0.188057i	−0.328217	+	0.944602i	$0.606448\pi$
$468$		0			0
$469$	−10.6070	−	30.2127i	−0.489788	−	1.39509i
$470$		0			0
$471$	0.407378	+	12.2709i	0.0187710	+	0.565415i
$472$		0			0
$473$	−7.41711	+	4.28227i	−0.341039	+	0.196899i
$474$		0			0
$475$	8.68736			0.398604
$476$		0			0
$477$	−6.07328	+	12.3441i	−0.278076	+	0.565198i
$478$		0			0
$479$	0.425876	+	0.737638i	0.0194588	+	0.0337035i	0.875591	−	0.483054i	$-0.160472\pi$
$479$	0.425876	+	0.737638i	0.0194588	+	0.0337035i	−0.856132	+	0.516757i	$0.827139\pi$
$480$		0			0
$481$	−34.9673	−	20.1884i	−1.59437	−	0.920510i
$482$		0			0
$483$	0.509889	−	0.198250i	0.0232008	−	0.00902069i
$484$		0			0
$485$	−1.91597	+	3.31856i	−0.0869999	+	0.150688i
$486$		0			0
$487$	2.45804	+	4.25745i	0.111384	+	0.192923i	0.916329	−	0.400427i	$-0.131138\pi$
$487$	2.45804	+	4.25745i	0.111384	+	0.192923i	−0.804944	+	0.593350i	$0.797805\pi$
$488$		0			0
$489$	5.96374	+	9.58062i	0.269690	+	0.433250i
$490$		0			0
$491$	5.07434			0.229002			0.114501	−	0.993423i	$-0.463473\pi$
$491$	5.07434			0.229002			0.114501	+	0.993423i	$0.463473\pi$
$492$		0			0
$493$	−16.7408	−	28.9960i	−0.753970	−	1.30591i
$494$		0			0
$495$	−6.07929	+	4.07017i	−0.273244	+	0.182941i
$496$		0			0
$497$	16.1372	+	3.03599i	0.723850	+	0.136183i
$498$		0			0
$499$	17.6743	+	10.2042i	0.791209	+	0.456805i	0.840388	−	0.541985i	$-0.182327\pi$
$499$	17.6743	+	10.2042i	0.791209	+	0.456805i	−0.0491790	+	0.998790i	$0.515660\pi$
$500$		0			0
$501$	−26.3519	−	14.0697i	−1.17732	−	0.628590i
$502$		0			0
$503$	−26.6102			−1.18649			−0.593245	−	0.805022i	$-0.702153\pi$
$503$	−26.6102			−1.18649			−0.593245	+	0.805022i	$0.702153\pi$
$504$		0			0
$505$	−2.05236			−0.0913289
$506$		0			0
$507$	18.0184	+	9.62033i	0.800224	+	0.427254i
$508$		0			0
$509$	−24.9978	−	14.4325i	−1.10801	−	0.639710i	−0.169697	−	0.985496i	$-0.554279\pi$
$509$	−24.9978	−	14.4325i	−1.10801	−	0.639710i	−0.938313	+	0.345787i	$0.887612\pi$
$510$		0			0
$511$	8.45553	+	24.0844i	0.374051	+	1.06543i
$512$		0			0
$513$	−8.72444	−	3.93844i	−0.385194	−	0.173887i
$514$		0			0
$515$	1.41891	+	2.45762i	0.0625245	+	0.108296i
$516$		0			0
$517$	26.6686			1.17288
$518$		0			0
$519$	−15.3663	−	24.6856i	−0.674505	−	1.08358i
$520$		0			0
$521$	−12.5564	−	21.7483i	−0.550105	−	0.952811i	−0.998266	−	0.0588577i	$-0.981254\pi$
$521$	−12.5564	−	21.7483i	−0.550105	−	0.952811i	0.448161	−	0.893953i	$-0.352079\pi$
$522$		0			0
$523$	1.54754	−	2.68042i	0.0676692	−	0.117206i	−0.830206	−	0.557457i	$-0.811777\pi$
$523$	1.54754	−	2.68042i	0.0676692	−	0.117206i	0.897875	+	0.440251i	$0.145110\pi$
$524$		0			0
$525$	21.3589	+	3.28876i	0.932179	+	0.143533i
$526$		0			0
$527$	−8.37183	−	4.83348i	−0.364683	−	0.210550i
$528$		0			0
$529$	−11.4929	−	19.9062i	−0.499690	−	0.865489i
$530$		0			0
$531$	17.7635	+	8.73962i	0.770871	+	0.379267i
$532$		0			0
$533$	−12.9915			−0.562726
$534$		0			0
$535$	4.25316	−	2.45556i	0.183880	−	0.106163i
$536$		0			0
$537$	−0.231008	−	6.95837i	−0.00996875	−	0.300276i
$538$		0			0
$539$	−4.83838	−	31.6550i	−0.208404	−	1.36348i
$540$		0			0
$541$	−23.8925	−	13.7944i	−1.02722	−	0.593066i	−0.111033	−	0.993817i	$-0.535416\pi$
$541$	−23.8925	−	13.7944i	−1.02722	−	0.593066i	−0.916187	+	0.400751i	$0.868749\pi$
$542$		0			0
$543$	−22.7041	−	12.1221i	−0.974328	−	0.520211i
$544$		0			0
$545$	2.61113			0.111849
$546$		0			0
$547$		−	32.0757i		−	1.37146i	−0.727856	−	0.685730i	$-0.759483\pi$
$547$		−	32.0757i		−	1.37146i	0.727856	−	0.685730i	$-0.240517\pi$
$548$		0			0
$549$	6.43963	−	0.428045i	0.274837	−	0.0182685i
$550$		0			0
$551$	−7.13420	+	12.3568i	−0.303927	+	0.526417i
$552$		0			0
$553$	0.0918460	+	0.0788743i	0.00390569	+	0.00335407i
$554$		0			0
$555$	0.248430	+	7.48314i	0.0105453	+	0.317642i
$556$		0			0
$557$	−8.23577	−	14.2648i	−0.348961	−	0.604417i	0.637104	−	0.770777i	$-0.280132\pi$
$557$	−8.23577	−	14.2648i	−0.348961	−	0.604417i	−0.986065	+	0.166360i	$0.946799\pi$
$558$		0			0
$559$		−	9.32199i		−	0.394278i
$560$		0			0
$561$	29.0782	−	18.1006i	1.22768	−	0.764209i
$562$		0			0
$563$	−14.5542	+	8.40290i	−0.613388	+	0.354140i	−0.774290	−	0.632830i	$-0.781893\pi$
$563$	−14.5542	+	8.40290i	−0.613388	+	0.354140i	0.160902	+	0.986970i	$0.448560\pi$
$564$		0			0
$565$	−1.03315	+	1.78947i	−0.0434651	+	0.0752837i
$566$		0			0
$567$	−19.9591	−	12.9859i	−0.838203	−	0.545358i
$568$		0			0
$569$	32.1947	+	18.5876i	1.34967	+	0.779235i	0.988203	−	0.153149i	$-0.0489414\pi$
$569$	32.1947	+	18.5876i	1.34967	+	0.779235i	0.361471	+	0.932383i	$0.382275\pi$
$570$		0			0
$571$	−6.80801	+	3.93061i	−0.284906	+	0.164491i	−0.635642	−	0.771984i	$-0.719265\pi$
$571$	−6.80801	+	3.93061i	−0.284906	+	0.164491i	0.350736	+	0.936474i	$0.385931\pi$
$572$		0			0
$573$	18.0896	+	29.0605i	0.755704	+	1.21402i
$574$		0			0
$575$			0.562982i			0.0234780i
$576$		0			0
$577$	14.7236	−	8.50067i	0.612951	−	0.353888i	−0.161168	−	0.986927i	$-0.551526\pi$
$577$	14.7236	−	8.50067i	0.612951	−	0.353888i	0.774120	+	0.633039i	$0.218193\pi$
$578$		0			0
$579$	−0.723236	−	21.7851i	−0.0300567	−	0.905359i
$580$		0			0
$581$	−10.0484	−	1.89048i	−0.416880	−	0.0784303i
$582$		0			0
$583$	−10.4891	+	18.1677i	−0.434415	+	0.752429i
$584$		0			0
$585$	−0.528142	−	7.94551i	−0.0218360	−	0.328506i
$586$		0			0
$587$		−	24.3750i		−	1.00606i	−0.864268	−	0.503032i	$-0.832218\pi$
$587$		−	24.3750i		−	1.00606i	0.864268	−	0.503032i	$-0.167782\pi$
$588$		0			0
$589$			4.11963i			0.169746i
$590$		0			0
$591$	−12.8620	−	6.86725i	−0.529072	−	0.282481i
$592$		0			0
$593$	−0.0286004	+	0.0495374i	−0.00117448	+	0.00203426i	−0.866612	−	0.498983i	$-0.833707\pi$
$593$	−0.0286004	+	0.0495374i	−0.00117448	+	0.00203426i	0.865438	+	0.501017i	$0.167041\pi$
$594$		0			0
$595$	5.99174	+	1.12726i	0.245637	+	0.0462133i
$596$		0			0
$597$	−24.7824	+	0.822741i	−1.01428	+	0.0336726i
$598$		0			0
$599$	35.8620	−	20.7049i	1.46528	−	0.845980i	0.466033	−	0.884768i	$-0.345683\pi$
$599$	35.8620	−	20.7049i	1.46528	−	0.845980i	0.999247	+	0.0387877i	$0.0123496\pi$
$600$		0			0
$601$			23.8559i			0.973104i	0.873652	+	0.486552i	$0.161746\pi$
$601$			23.8559i			0.973104i	−0.873652	+	0.486552i	$0.838254\pi$
$602$		0			0
$603$	−32.5783	−	16.0285i	−1.32669	−	0.652731i
$604$		0			0
$605$	−4.58317	+	2.64609i	−0.186332	+	0.107579i
$606$		0			0
$607$	33.6542	+	19.4303i	1.36598	+	0.788650i	0.990412	−	0.138144i	$-0.0441136\pi$
$607$	33.6542	+	19.4303i	1.36598	+	0.788650i	0.375570	+	0.926794i	$0.377447\pi$
$608$		0			0
$609$	−22.2182	+	27.6799i	−0.900325	+	1.12164i
$610$		0			0
$611$	−14.5136	+	25.1382i	−0.587156	+	1.01698i
$612$		0			0
$613$	16.8751	−	9.74286i	0.681580	−	0.393510i	−0.118870	−	0.992910i	$-0.537927\pi$
$613$	16.8751	−	9.74286i	0.681580	−	0.393510i	0.800450	+	0.599400i	$0.204594\pi$
$614$		0			0
$615$	1.27311	+	2.04521i	0.0513366	+	0.0824710i
$616$		0			0
$617$			21.5819i			0.868854i	0.900707	+	0.434427i	$0.143049\pi$
$617$			21.5819i			0.868854i	−0.900707	+	0.434427i	$0.856951\pi$
$618$		0			0
$619$	−5.60757	−	9.71259i	−0.225387	−	0.390382i	0.731048	−	0.682326i	$-0.239031\pi$
$619$	−5.60757	−	9.71259i	−0.225387	−	0.390382i	−0.956436	+	0.291944i	$0.905698\pi$
$620$		0			0
$621$	0.255230	−	0.565385i	0.0102420	−	0.0226881i
$622$		0			0
$623$	33.0529	+	28.3847i	1.32424	+	1.13721i
$624$		0			0
$625$	−10.4090	+	18.0290i	−0.416362	+	0.721160i
$626$		0			0
$627$	−12.8762	−	6.87482i	−0.514225	−	0.274554i
$628$		0			0
$629$		−	35.0534i		−	1.39767i
$630$		0			0
$631$	22.3220			0.888626			0.444313	−	0.895872i	$-0.353448\pi$
$631$	22.3220			0.888626			0.444313	+	0.895872i	$0.353448\pi$
$632$		0			0
$633$	−7.85036	+	14.7033i	−0.312024	+	0.584404i
$634$		0			0
$635$	−3.78105	−	2.18299i	−0.150046	−	0.0866292i
$636$		0			0
$637$	32.4716	+	12.6665i	1.28657	+	0.501866i
$638$		0			0
$639$	15.4714	−	10.3583i	0.612040	−	0.409770i
$640$		0			0
$641$	10.9414	−	6.31703i	0.432160	−	0.249508i	−0.268107	−	0.963389i	$-0.586398\pi$
$641$	10.9414	−	6.31703i	0.432160	−	0.249508i	0.700266	+	0.713882i	$0.253065\pi$
$642$		0			0
$643$	−25.9092			−1.02176			−0.510879	−	0.859652i	$-0.670680\pi$
$643$	−25.9092			−1.02176			−0.510879	+	0.859652i	$0.670680\pi$
$644$		0			0
$645$	−1.46753	+	0.913508i	−0.0577839	+	0.0359693i
$646$		0			0
$647$	−8.29783	−	14.3723i	−0.326221	−	0.565032i	0.655538	−	0.755163i	$-0.272442\pi$
$647$	−8.29783	−	14.3723i	−0.326221	−	0.565032i	−0.981759	+	0.190131i	$0.939109\pi$
$648$		0			0
$649$	26.1438	+	15.0941i	1.02623	+	0.592496i
$650$		0			0
$651$	−1.55956	+	10.1286i	−0.0611240	+	0.396971i
$652$		0			0
$653$	2.57443	−	4.45904i	0.100745	−	0.174496i	−0.811247	−	0.584704i	$-0.801211\pi$
$653$	2.57443	−	4.45904i	0.100745	−	0.174496i	0.911992	+	0.410208i	$0.134544\pi$
$654$		0			0
$655$	−5.71124	−	9.89216i	−0.223157	−	0.386519i
$656$		0			0
$657$	25.9702	+	12.7773i	1.01319	+	0.498490i
$658$		0			0
$659$	−20.6891			−0.805934			−0.402967	−	0.915214i	$-0.632021\pi$
$659$	−20.6891			−0.805934			−0.402967	+	0.915214i	$0.632021\pi$
$660$		0			0
$661$	−12.3911	−	21.4621i	−0.481960	−	0.834779i	0.517826	−	0.855486i	$-0.326742\pi$
$661$	−12.3911	−	21.4621i	−0.481960	−	0.834779i	−0.999786	+	0.0207072i	$0.993408\pi$
$662$		0			0
$663$	1.23699	+	37.2603i	0.0480408	+	1.44707i
$664$		0			0
$665$	−0.860676	−	2.45151i	−0.0333756	−	0.0950657i
$666$		0			0
$667$	−0.800778	−	0.462329i	−0.0310063	−	0.0179015i
$668$		0			0
$669$	16.4657	−	30.8393i	0.636599	−	1.19232i
$670$		0			0
$671$	9.84137			0.379922
$672$		0			0
$673$	0.492833			0.0189973			0.00949866	−	0.999955i	$-0.496976\pi$
$673$	0.492833			0.0189973			0.00949866	+	0.999955i	$0.496976\pi$
$674$		0			0
$675$	19.8983	−	14.3007i	0.765887	−	0.550433i
$676$		0			0
$677$	35.2987	+	20.3797i	1.35664	+	0.783256i	0.989169	−	0.146779i	$-0.0468905\pi$
$677$	35.2987	+	20.3797i	1.35664	+	0.783256i	0.367471	+	0.930035i	$0.380224\pi$
$678$		0			0
$679$	−18.6905	−	3.51636i	−0.717276	−	0.134946i
$680$		0			0
$681$	2.06693	−	0.0686192i	0.0792049	−	0.00262949i
$682$		0			0
$683$	−14.8402	−	25.7039i	−0.567843	−	0.983532i	−0.996779	−	0.0801976i	$-0.974445\pi$
$683$	−14.8402	−	25.7039i	−0.567843	−	0.983532i	0.428936	−	0.903335i	$-0.358888\pi$
$684$		0			0
$685$	2.41009			0.0920846
$686$		0			0
$687$	33.5322	−	20.8731i	1.27933	−	0.796360i
$688$		0			0
$689$	−11.4168	−	19.7744i	−0.434944	−	0.753346i
$690$		0			0
$691$	−3.83116	+	6.63576i	−0.145744	+	0.252436i	−0.929650	−	0.368443i	$-0.879891\pi$
$691$	−3.83116	+	6.63576i	−0.145744	+	0.252436i	0.783906	+	0.620879i	$0.213224\pi$
$692$		0			0
$693$	−29.0550	−	21.7771i	−1.10371	−	0.827242i
$694$		0			0
$695$	6.84645	+	3.95280i	0.259701	+	0.149938i
$696$		0			0
$697$	−5.63936	−	9.76765i	−0.213606	−	0.369976i
$698$		0			0
$699$	−14.9111	−	23.9543i	−0.563988	−	0.906034i
$700$		0			0
$701$	−6.75507			−0.255136			−0.127568	−	0.991830i	$-0.540717\pi$
$701$	−6.75507			−0.255136			−0.127568	+	0.991830i	$0.540717\pi$
$702$		0			0
$703$	−12.9369	+	7.46910i	−0.487923	+	0.281702i
$704$		0			0
$705$	5.37969	−	0.178598i	0.202611	−	0.00672640i
$706$		0			0
$707$	−3.37423	−	9.61100i	−0.126901	−	0.361459i
$708$		0			0
$709$	36.0884	+	20.8357i	1.35533	+	0.782499i	0.988990	−	0.147982i	$-0.0472778\pi$
$709$	36.0884	+	20.8357i	1.35533	+	0.782499i	0.366339	+	0.930482i	$0.380611\pi$
$710$		0			0
$711$	0.136973	−	0.00910466i	0.00513689	−	0.000341452i
$712$		0			0
$713$	−0.266971			−0.00999815
$714$		0			0
$715$		−	12.1427i		−	0.454112i
$716$		0			0
$717$	−16.5127	+	30.9275i	−0.616680	+	1.15501i
$718$		0			0
$719$	23.2782	−	40.3190i	0.868131	−	1.50365i	0.00422645	−	0.999991i	$-0.498655\pi$
$719$	23.2782	−	40.3190i	0.868131	−	1.50365i	0.863904	−	0.503656i	$-0.168012\pi$
$720$		0			0
$721$	−9.17600	+	10.6851i	−0.341732	+	0.397934i
$722$		0			0
$723$	−15.9774	+	0.530429i	−0.594208	+	0.0197269i
$724$		0			0
$725$	−18.2630	−	31.6325i	−0.678271	−	1.17480i
$726$		0			0
$727$			10.7218i			0.397651i	0.980035	+	0.198825i	$0.0637127\pi$
$727$			10.7218i			0.397651i	−0.980035	+	0.198825i	$0.936287\pi$
$728$		0			0
$729$	−26.4665	+	5.34075i	−0.980241	+	0.197805i
$730$		0			0
$731$	7.00871	−	4.04648i	0.259227	−	0.149665i
$732$		0			0
$733$	−12.5202	+	21.6857i	−0.462445	+	0.800979i	−0.999082	−	0.0428345i	$-0.986361\pi$
$733$	−12.5202	+	21.6857i	−0.462445	+	0.800979i	0.536637	+	0.843813i	$0.319695\pi$
$734$		0			0
$735$	−1.18801	−	6.35316i	−0.0438203	−	0.234340i
$736$		0			0
$737$	−47.9478	−	27.6827i	−1.76618	−	1.01971i
$738$		0			0
$739$	45.0173	−	25.9908i	1.65599	−	0.956086i	0.681452	−	0.731863i	$-0.261349\pi$
$739$	45.0173	−	25.9908i	1.65599	−	0.956086i	0.974538	−	0.224224i	$-0.0719846\pi$
$740$		0			0
$741$	13.4878	−	8.39588i	0.495486	−	0.308430i
$742$		0			0
$743$			26.4603i			0.970735i	0.874310	+	0.485367i	$0.161314\pi$
$743$			26.4603i			0.970735i	−0.874310	+	0.485367i	$0.838686\pi$
$744$		0			0
$745$	9.94549	−	5.74203i	0.364375	−	0.210372i
$746$		0			0
$747$	−9.63391	+	6.45004i	−0.352486	+	0.235995i
$748$		0			0
$749$	18.4916	+	15.8800i	0.675670	+	0.580242i
$750$		0			0
$751$	9.69510	−	16.7924i	0.353779	−	0.612763i	−0.633129	−	0.774046i	$-0.718230\pi$
$751$	9.69510	−	16.7924i	0.353779	−	0.612763i	0.986908	+	0.161283i	$0.0515631\pi$
$752$		0			0
$753$	−6.70694	+	12.5617i	−0.244414	+	0.457775i
$754$		0			0
$755$		−	1.50081i		−	0.0546202i
$756$		0			0
$757$			5.19772i			0.188914i	0.995529	+	0.0944572i	$0.0301115\pi$
$757$			5.19772i			0.188914i	−0.995529	+	0.0944572i	$0.969888\pi$
$758$		0			0
$759$	0.445520	−	0.834436i	0.0161714	−	0.0302881i
$760$		0			0
$761$	18.8681	−	32.6805i	0.683969	−	1.18467i	−0.289791	−	0.957090i	$-0.593586\pi$
$761$	18.8681	−	32.6805i	0.683969	−	1.18467i	0.973760	−	0.227578i	$-0.0730808\pi$
$762$		0			0
$763$	4.29288	+	12.2277i	0.155413	+	0.442671i
$764$		0			0
$765$	5.74456	−	3.84606i	0.207695	−	0.139055i
$766$		0			0
$767$	−28.4559	+	16.4290i	−1.02748	+	0.593218i
$768$		0			0
$769$			13.9517i			0.503110i	0.967843	+	0.251555i	$0.0809419\pi$
$769$			13.9517i			0.503110i	−0.967843	+	0.251555i	$0.919058\pi$
$770$		0			0
$771$	19.7471	−	12.2921i	0.711173	−	0.442691i
$772$		0			0
$773$	−21.5519	+	12.4430i	−0.775169	+	0.447544i	−0.834715	−	0.550682i	$-0.814368\pi$
$773$	−21.5519	+	12.4430i	−0.775169	+	0.447544i	0.0595465	+	0.998226i	$0.481035\pi$
$774$		0			0
$775$	−9.13305	−	5.27297i	−0.328069	−	0.189411i
$776$		0			0
$777$	−34.6344	+	13.4662i	−1.24250	+	0.483096i
$778$		0			0
$779$	−2.40324	+	4.16254i	−0.0861051	+	0.149138i
$780$		0			0
$781$	24.5878	−	14.1958i	0.879822	−	0.507966i
$782$		0			0
$783$	4.00028	+	40.0471i	0.142958	+	1.43117i
$784$		0			0
$785$			3.77877i			0.134870i
$786$		0			0
$787$	−4.90837	−	8.50154i	−0.174964	−	0.303047i	0.765185	−	0.643811i	$-0.222648\pi$
$787$	−4.90837	−	8.50154i	−0.174964	−	0.303047i	−0.940149	+	0.340764i	$0.889314\pi$
$788$		0			0
$789$	26.0685	−	0.865440i	0.928065	−	0.0308105i
$790$		0			0
$791$	−10.0785	−	1.89613i	−0.358350	−	0.0674188i
$792$		0			0
$793$	−5.35587	+	9.27663i	−0.190192	+	0.329423i
$794$		0			0
$795$	−1.99424	+	3.73510i	−0.0707283	+	0.132470i
$796$		0			0
$797$			11.3322i			0.401406i	0.979652	+	0.200703i	$0.0643226\pi$
$797$			11.3322i			0.401406i	−0.979652	+	0.200703i	$0.935677\pi$
$798$		0			0
$799$	−25.2002			−0.891518
$800$		0			0
$801$	49.2929	−	3.27653i	1.74168	−	0.115770i
$802$		0			0
$803$	38.2222	+	22.0676i	1.34883	+	0.778748i
$804$		0			0
$805$	0.158870	−	0.0557758i	0.00559942	−	0.00196584i
$806$		0			0
$807$	22.9902	−	0.763242i	0.809292	−	0.0268674i
$808$		0			0
$809$	19.0031	−	10.9714i	0.668113	−	0.385735i	−0.127248	−	0.991871i	$-0.540615\pi$
$809$	19.0031	−	10.9714i	0.668113	−	0.385735i	0.795361	+	0.606136i	$0.207281\pi$
$810$		0			0
$811$	−12.2220			−0.429171			−0.214586	−	0.976705i	$-0.568840\pi$
$811$	−12.2220			−0.429171			−0.214586	+	0.976705i	$0.568840\pi$
$812$		0			0
$813$	−17.2230	−	27.6683i	−0.604036	−	0.970370i
$814$		0			0
$815$	1.73664	+	3.00796i	0.0608320	+	0.105364i
$816$		0			0
$817$	−2.98680	−	1.72443i	−0.104495	−	0.0603302i
$818$		0			0
$819$	36.3397	−	15.5362i	1.26981	−	0.542879i
$820$		0			0
$821$	−22.2720	+	38.5763i	−0.777299	+	1.34632i	0.156195	+	0.987726i	$0.450077\pi$
$821$	−22.2720	+	38.5763i	−0.777299	+	1.34632i	−0.933493	+	0.358595i	$0.883256\pi$
$822$		0			0
$823$	−13.6219	−	23.5938i	−0.474830	−	0.822429i	0.524755	−	0.851254i	$-0.324157\pi$
$823$	−13.6219	−	23.5938i	−0.474830	−	0.822429i	−0.999584	+	0.0288241i	$0.990824\pi$
$824$		0			0
$825$	31.7222	−	19.7464i	1.10443	−	0.687483i
$826$		0			0
$827$	−10.2913			−0.357864			−0.178932	−	0.983861i	$-0.557264\pi$
$827$	−10.2913			−0.357864			−0.178932	+	0.983861i	$0.557264\pi$
$828$		0			0
$829$	16.2859	+	28.2081i	0.565634	+	0.979707i	0.996990	+	0.0775252i	$0.0247018\pi$
$829$	16.2859	+	28.2081i	0.565634	+	0.979707i	−0.431356	+	0.902182i	$0.641965\pi$
$830$		0			0
$831$	−40.2466	+	1.33613i	−1.39614	+	0.0463499i
$832$		0			0
$833$	4.57197	+	29.9120i	0.158409	+	1.03639i
$834$		0			0
$835$	−7.96232	−	4.59705i	−0.275547	−	0.159087i
$836$		0			0
$837$	6.78151	+	9.43597i	0.234403	+	0.326155i
$838$		0			0
$839$	4.55619			0.157297			0.0786486	−	0.996902i	$-0.474939\pi$
$839$	4.55619			0.157297			0.0786486	+	0.996902i	$0.474939\pi$
$840$		0			0
$841$	30.9915			1.06867
$842$		0			0
$843$	−17.3545	+	32.5041i	−0.597722	+	1.11950i
$844$		0			0
$845$	5.44432	+	3.14328i	0.187290	+	0.108132i
$846$		0			0
$847$	−19.9264	−	17.1122i	−0.684681	−	0.587981i
$848$		0			0
$849$	−0.495606	−	14.9285i	−0.0170091	−	0.512345i
$850$		0			0
$851$	−0.484032	−	0.838369i	−0.0165924	−	0.0287389i
$852$		0			0
$853$	−50.6930			−1.73570			−0.867848	−	0.496830i	$-0.834497\pi$
$853$	−50.6930			−1.73570			−0.867848	+	0.496830i	$0.834497\pi$
$854$		0			0
$855$	−2.64347	−	1.30058i	−0.0904048	−	0.0444790i
$856$		0			0
$857$	−3.66887	−	6.35467i	−0.125326	−	0.217071i	0.796534	−	0.604594i	$-0.206664\pi$
$857$	−3.66887	−	6.35467i	−0.125326	−	0.217071i	−0.921860	+	0.387522i	$0.873331\pi$
$858$		0			0
$859$	−28.8455	+	49.9619i	−0.984195	+	1.70468i	−0.338737	+	0.940881i	$0.610000\pi$
$859$	−28.8455	+	49.9619i	−0.984195	+	1.70468i	−0.645458	+	0.763795i	$0.723334\pi$
$860$		0			0
$861$	−7.48446	+	9.32430i	−0.255070	+	0.317771i
$862$		0			0
$863$	−31.1345	−	17.9755i	−1.05983	−	0.611894i	−0.134445	−	0.990921i	$-0.542925\pi$
$863$	−31.1345	−	17.9755i	−1.05983	−	0.611894i	−0.925385	+	0.379027i	$0.876259\pi$
$864$		0			0
$865$	−4.47467	−	7.75035i	−0.152143	−	0.263520i
$866$		0			0
$867$	−2.47969	+	1.54356i	−0.0842148	+	0.0524220i
$868$		0			0
$869$	0.209329			0.00710101
$870$		0			0
$871$	52.1883	−	30.1309i	1.76833	−	1.02095i
$872$		0			0
$873$	−17.9194	+	11.9973i	−0.606481	+	0.406048i
$874$		0			0
$875$	13.4670	+	2.53363i	0.455267	+	0.0856523i
$876$		0			0
$877$	−43.3964	−	25.0550i	−1.46539	−	0.846046i	−0.466142	−	0.884710i	$-0.654356\pi$
$877$	−43.3964	−	25.0550i	−1.46539	−	0.846046i	−0.999252	+	0.0386646i	$0.987690\pi$
$878$		0			0
$879$	−18.5541	+	34.7509i	−0.625815	+	1.17212i
$880$		0			0
$881$	−47.9585			−1.61576			−0.807882	−	0.589344i	$-0.799386\pi$
$881$	−47.9585			−1.61576			−0.807882	+	0.589344i	$0.799386\pi$
$882$		0			0
$883$		−	0.345258i		−	0.0116188i	−0.999983	−	0.00580942i	$-0.998151\pi$
$883$		−	0.345258i		−	0.0116188i	0.999983	−	0.00580942i	$-0.00184921\pi$
$884$		0			0
$885$	5.37491	+	2.86976i	0.180676	+	0.0964660i
$886$		0			0
$887$	13.7032	−	23.7346i	0.460109	−	0.796931i	−0.538857	−	0.842397i	$-0.681144\pi$
$887$	13.7032	−	23.7346i	0.460109	−	0.796931i	0.998966	+	0.0454656i	$0.0144771\pi$
$888$		0			0
$889$	4.00641	−	21.2952i	0.134371	−	0.714220i
$890$		0			0
$891$	−40.8097	+	5.44936i	−1.36718	+	0.182560i
$892$		0			0
$893$	5.36959	+	9.30041i	0.179687	+	0.311226i
$894$		0			0
$895$		−	2.14280i		−	0.0716258i
$896$		0			0
$897$	0.544092	+	0.874071i	0.0181667	+	0.0291844i
$898$		0			0
$899$	15.0004	−	8.66049i	0.500292	−	0.288844i
$900$		0			0
$901$	9.91157	−	17.1673i	0.330202	−	0.571927i
$902$		0			0
$903$	−6.69059	−	5.37043i	−0.222649	−	0.178717i
$904$		0			0
$905$	−6.86014	−	3.96070i	−0.228039	−	0.131658i
$906$		0			0
$907$	−7.67380	+	4.43047i	−0.254804	+	0.147111i	−0.621962	−	0.783047i	$-0.713664\pi$
$907$	−7.67380	+	4.43047i	−0.254804	+	0.147111i	0.367158	+	0.930159i	$0.380331\pi$
$908$		0			0
$909$	−10.3636	−	5.09885i	−0.343737	−	0.169118i
$910$		0			0
$911$		−	17.2124i		−	0.570272i	−0.958487	−	0.285136i	$-0.907961\pi$
$911$		−	17.2124i		−	0.570272i	0.958487	−	0.285136i	$-0.0920388\pi$
$912$		0			0
$913$	−15.3106	+	8.83959i	−0.506707	+	0.292548i
$914$		0			0
$915$	1.98524	−	0.0659072i	0.0656300	−	0.00217882i
$916$		0			0
$917$	36.9343	−	43.0086i	1.21968	−	1.42027i
$918$		0			0
$919$	−2.91012	+	5.04048i	−0.0959961	+	0.166270i	−0.910024	−	0.414556i	$-0.863937\pi$
$919$	−2.91012	+	5.04048i	−0.0959961	+	0.166270i	0.814028	+	0.580826i	$0.197270\pi$
$920$		0			0
$921$	−34.8621	−	18.6135i	−1.14875	−	0.613336i
$922$		0			0
$923$			30.9025i			1.01717i
$924$		0			0
$925$		−	38.2407i		−	1.25734i
$926$		0			0
$927$	1.05921	+	15.9350i	0.0347890	+	0.523375i
$928$		0			0
$929$	3.36170	−	5.82263i	0.110294	−	0.191034i	−0.805595	−	0.592467i	$-0.798154\pi$
$929$	3.36170	−	5.82263i	0.110294	−	0.191034i	0.915889	+	0.401432i	$0.131488\pi$
$930$		0			0
$931$	10.0652	−	8.06092i	0.329873	−	0.264186i
$932$		0			0
$933$	1.37780	+	41.5016i	0.0451070	+	1.35870i
$934$		0			0
$935$	9.12949	−	5.27091i	0.298566	−	0.172377i
$936$		0			0
$937$		−	5.64519i		−	0.184420i	−0.995740	−	0.0922102i	$-0.970607\pi$
$937$		−	5.64519i		−	0.184420i	0.995740	−	0.0922102i	$-0.0293932\pi$
$938$		0			0
$939$	20.5485	+	33.0107i	0.670576	+	1.07726i
$940$		0			0
$941$	39.2739	−	22.6748i	1.28029	−	0.739177i	0.303391	−	0.952866i	$-0.401881\pi$
$941$	39.2739	−	22.6748i	1.28029	−	0.739177i	0.976902	+	0.213689i	$0.0685479\pi$
$942$		0			0
$943$	−0.269752	−	0.155741i	−0.00878433	−	0.00507164i
$944$		0			0
$945$	−6.00692	−	4.19837i	−0.195405	−	0.136573i
$946$		0			0
$947$	−0.0324938	+	0.0562810i	−0.00105591	+	0.00182889i	−0.866553	−	0.499085i	$-0.833669\pi$
$947$	−0.0324938	+	0.0562810i	−0.00105591	+	0.00182889i	0.865497	+	0.500914i	$0.167003\pi$
$948$		0			0
$949$	−41.6025	+	24.0192i	−1.35048	+	0.779697i
$950$		0			0
$951$	3.11946	−	1.94180i	0.101155	−	0.0629672i
$952$		0			0
$953$		−	33.3269i		−	1.07956i	−0.841805	−	0.539781i	$-0.818507\pi$
$953$		−	33.3269i		−	1.07956i	0.841805	−	0.539781i	$-0.181493\pi$
$954$		0			0
$955$	5.26770	+	9.12393i	0.170459	+	0.295243i
$956$		0			0
$957$	2.03632	+	61.3374i	0.0658247	+	1.98276i
$958$		0			0
$959$	3.96235	+	11.2862i	0.127951	+	0.364450i
$960$		0			0
$961$	−12.9995	+	22.5158i	−0.419339	+	0.726316i
$962$		0			0
$963$	27.5772	−	1.83307i	0.888663	−	0.0590699i
$964$		0			0
$965$		−	6.70862i		−	0.215958i
$966$		0			0
$967$	−8.68323			−0.279234			−0.139617	−	0.990206i	$-0.544587\pi$
$967$	−8.68323			−0.279234			−0.139617	+	0.990206i	$0.544587\pi$
$968$		0			0
$969$	12.1672	+	6.49628i	0.390867	+	0.208691i
$970$		0			0
$971$	37.7352	+	21.7864i	1.21098	+	0.699159i	0.962973	−	0.269599i	$-0.0868912\pi$
$971$	37.7352	+	21.7864i	1.21098	+	0.699159i	0.248007	+	0.968758i	$0.420225\pi$
$972$		0			0
$973$	−7.25453	+	38.5599i	−0.232569	+	1.23617i
$974$		0			0
$975$	1.34947	+	40.6483i	0.0432175	+	1.30179i
$976$		0			0
$977$	−16.6770	+	9.62846i	−0.533544	+	0.308042i	−0.742458	−	0.669892i	$-0.766340\pi$
$977$	−16.6770	+	9.62846i	−0.533544	+	0.308042i	0.208914	+	0.977934i	$0.433007\pi$
$978$		0			0
$979$	75.3320			2.40762
$980$		0			0
$981$	13.1851	+	6.48705i	0.420968	+	0.207116i
$982$		0			0
$983$	−12.6512	−	21.9125i	−0.403510	−	0.698900i	0.590637	−	0.806938i	$-0.298877\pi$
$983$	−12.6512	−	21.9125i	−0.403510	−	0.698900i	−0.994147	+	0.108037i	$0.965543\pi$
$984$		0			0
$985$	−3.88630	−	2.24376i	−0.123828	−	0.0714920i
$986$		0			0
$987$	9.68094	+	24.8989i	0.308148	+	0.792541i
$988$		0			0
$989$	0.111751	−	0.193559i	0.00355348	−	0.00615481i
$990$		0			0
$991$	−6.86308	−	11.8872i	−0.218013	−	0.377609i	0.736187	−	0.676778i	$-0.236624\pi$
$991$	−6.86308	−	11.8872i	−0.218013	−	0.377609i	−0.954200	+	0.299168i	$0.903291\pi$
$992$		0			0
$993$	1.32620	+	2.13051i	0.0420857	+	0.0676098i
$994$		0			0
$995$	−7.63161			−0.241938
$996$		0			0
$997$	1.12122	+	1.94201i	0.0355094	+	0.0615041i	0.883234	−	0.468933i	$-0.155361\pi$
$997$	1.12122	+	1.94201i	0.0355094	+	0.0615041i	−0.847725	+	0.530437i	$0.822028\pi$
$998$		0			0
$999$	−17.3365	+	38.4039i	−0.548503	+	1.21505i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	672.2.bi.c.593.21		48
3.2	odd	2	inner	672.2.bi.c.593.12		48
4.3	odd	2		168.2.ba.c.5.3	✓	48
7.3	odd	6	inner	672.2.bi.c.17.13		48
8.3	odd	2		168.2.ba.c.5.6	yes	48
8.5	even	2	inner	672.2.bi.c.593.4		48
12.11	even	2		168.2.ba.c.5.22	yes	48
21.17	even	6	inner	672.2.bi.c.17.4		48
24.5	odd	2	inner	672.2.bi.c.593.13		48
24.11	even	2		168.2.ba.c.5.19	yes	48
28.3	even	6		168.2.ba.c.101.19	yes	48
56.3	even	6		168.2.ba.c.101.22	yes	48
56.45	odd	6	inner	672.2.bi.c.17.12		48
84.59	odd	6		168.2.ba.c.101.6	yes	48
168.59	odd	6		168.2.ba.c.101.3	yes	48
168.101	even	6	inner	672.2.bi.c.17.21		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.2.ba.c.5.3	✓	48	4.3	odd	2
168.2.ba.c.5.6	yes	48	8.3	odd	2
168.2.ba.c.5.19	yes	48	24.11	even	2
168.2.ba.c.5.22	yes	48	12.11	even	2
168.2.ba.c.101.3	yes	48	168.59	odd	6
168.2.ba.c.101.6	yes	48	84.59	odd	6
168.2.ba.c.101.19	yes	48	28.3	even	6
168.2.ba.c.101.22	yes	48	56.3	even	6
672.2.bi.c.17.4		48	21.17	even	6	inner
672.2.bi.c.17.12		48	56.45	odd	6	inner
672.2.bi.c.17.13		48	7.3	odd	6	inner
672.2.bi.c.17.21		48	168.101	even	6	inner
672.2.bi.c.593.4		48	8.5	even	2	inner
672.2.bi.c.593.12		48	3.2	odd	2	inner
672.2.bi.c.593.13		48	24.5	odd	2	inner
672.2.bi.c.593.21		48	1.1	even	1	trivial

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 672 = 2^{5} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	672.bi (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.52791 + 0.815778i) q^{3} +(0.461663 + 0.266541i) q^{5} +(-0.489180 + 2.60014i) q^{7} +(1.66901 + 2.49287i) q^{9} +(2.28733 + 3.96177i) q^{11} -4.97924 q^{13} +(0.487941 + 0.783866i) q^{15} +(-2.16139 - 3.74363i) q^{17} +(-0.921087 + 1.59537i) q^{19} +(-2.86856 + 3.57371i) q^{21} +(-0.103387 - 0.0596907i) q^{23} +(-2.35791 - 4.08402i) q^{25} +(0.516471 + 5.17042i) q^{27} +7.74542 q^{29} +(1.93668 - 1.11814i) q^{31} +(0.262906 + 7.91918i) q^{33} +(-0.918880 + 1.07000i) q^{35} +(7.02261 + 4.05451i) q^{37} +(-7.60783 - 4.06195i) q^{39} +2.60914 q^{41} +1.87217i q^{43} +(0.106069 + 1.59573i) q^{45} +(2.91482 - 5.04861i) q^{47} +(-6.52141 - 2.54387i) q^{49} +(-0.248430 - 7.48314i) q^{51} +(2.29287 + 3.97137i) q^{53} +2.43867i q^{55} +(-2.70880 + 1.68618i) q^{57} +(5.71492 - 3.29951i) q^{59} +(1.07564 - 1.86306i) q^{61} +(-7.29824 + 3.12020i) q^{63} +(-2.29873 - 1.32717i) q^{65} +(-10.4812 + 6.05131i) q^{67} +(-0.109272 - 0.175543i) q^{69} -6.20627i q^{71} +(8.35520 - 4.82388i) q^{73} +(-0.271018 - 8.16355i) q^{75} +(-11.4201 + 4.00935i) q^{77} +(0.0228792 - 0.0396280i) q^{79} +(-3.42880 + 8.32126i) q^{81} +3.86459i q^{83} -2.30440i q^{85} +(11.8343 + 6.31854i) q^{87} +(8.23362 - 14.2610i) q^{89} +(2.43575 - 12.9467i) q^{91} +(3.87123 - 0.128520i) q^{93} +(-0.850463 + 0.491015i) q^{95} +7.18828i q^{97} +(-6.05860 + 12.3143i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 4 q^{7} - 14 q^{9} - 4 q^{15} - 8 q^{25} - 48 q^{31} - 42 q^{33} + 8 q^{39} - 36 q^{49} + 4 q^{57} + 6 q^{63} - 36 q^{73} + 56 q^{79} + 42 q^{81} + 132 q^{87}+O(q^{100}) \) 48 * q + 4 * q^7 - 14 * q^9 - 4 * q^15 - 8 * q^25 - 48 * q^31 - 42 * q^33 + 8 * q^39 - 36 * q^49 + 4 * q^57 + 6 * q^63 - 36 * q^73 + 56 * q^79 + 42 * q^81 + 132 * q^87

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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