LMFDB - Embedded newform 672.4.bb.a.271.42

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [672,4,Mod(271,672)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(672, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 3, 0, 5])) N = Newforms(chi, 4, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("672.271"); S:= CuspForms(chi, 4); N := Newforms(S);

Level:	$ N $	$=$	$ 672 = 2^{5} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	672.bb (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$39.6492835239$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$48$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 168)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			271.42
Character	$\chi$	$=$	672.271
Dual form			672.4.bb.a.367.42

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.59808 - 1.50000i) q^{3} +(5.68130 - 9.84030i) q^{5} +(1.38512 + 18.4684i) q^{7} +(4.50000 - 7.79423i) q^{9} +(9.93039 + 17.1999i) q^{11} +31.0152 q^{13} -34.0878i q^{15} +(37.4442 - 21.6184i) q^{17} +(30.9280 + 17.8563i) q^{19} +(31.3012 + 45.9046i) q^{21} +(-77.4445 - 44.7126i) q^{23} +(-2.05428 - 3.55811i) q^{25} -27.0000i q^{27} +149.567i q^{29} +(72.4769 + 125.534i) q^{31} +(51.5998 + 29.7912i) q^{33} +(189.604 + 91.2944i) q^{35} +(255.281 + 147.387i) q^{37} +(80.5798 - 46.5228i) q^{39} -340.542i q^{41} +382.268 q^{43} +(-51.1317 - 88.5627i) q^{45} +(46.6383 - 80.7798i) q^{47} +(-339.163 + 51.1619i) q^{49} +(64.8552 - 112.333i) q^{51} +(-629.932 + 363.692i) q^{53} +225.670 q^{55} +107.138 q^{57} +(495.394 - 286.016i) q^{59} +(-7.77051 + 13.4589i) q^{61} +(150.180 + 72.3118i) q^{63} +(176.206 - 305.198i) q^{65} +(55.2285 + 95.6585i) q^{67} -268.276 q^{69} -518.920i q^{71} +(948.097 - 547.384i) q^{73} +(-10.6743 - 6.16283i) q^{75} +(-303.901 + 207.222i) q^{77} +(-288.366 - 166.488i) q^{79} +(-40.5000 - 70.1481i) q^{81} -934.727i q^{83} -491.282i q^{85} +(224.350 + 388.586i) q^{87} +(361.563 + 208.749i) q^{89} +(42.9597 + 572.800i) q^{91} +(376.601 + 217.431i) q^{93} +(351.423 - 202.894i) q^{95} +477.327i q^{97} +178.747 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 432 q^{9} - 40 q^{11} - 1200 q^{25} - 456 q^{35} + 1616 q^{43} - 360 q^{49} - 336 q^{57} - 4128 q^{59} + 1440 q^{67} - 648 q^{73} - 3888 q^{81} + 104 q^{91} - 720 q^{99}+O(q^{100}) $ 96 * q + 432 * q^9 - 40 * q^11 - 1200 * q^25 - 456 * q^35 + 1616 * q^43 - 360 * q^49 - 336 * q^57 - 4128 * q^59 + 1440 * q^67 - 648 * q^73 - 3888 * q^81 + 104 * q^91 - 720 * q^99

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
$3$	2.59808	−	1.50000i	0.500000	−	0.288675i
$3$	2.59808	−	1.50000i	0.500000	−	0.288675i
$4$		0			0
$5$	5.68130	−	9.84030i	0.508151	−	0.880143i	−0.491805	−	0.870705i	$-0.663663\pi$
$5$	5.68130	−	9.84030i	0.508151	−	0.880143i	0.999955	−	0.00943729i	$-0.00300403\pi$
$6$		0			0
$7$	1.38512	+	18.4684i	0.0747894	+	0.997199i
$7$	1.38512	+	18.4684i	0.0747894	+	0.997199i
$8$		0			0
$9$	4.50000	−	7.79423i	0.166667	−	0.288675i
$10$		0			0
$11$	9.93039	+	17.1999i	0.272193	+	0.471453i	0.969423	−	0.245395i	$-0.0789177\pi$
$11$	9.93039	+	17.1999i	0.272193	+	0.471453i	−0.697230	+	0.716848i	$0.745584\pi$
$12$		0			0
$13$	31.0152			0.661697			0.330848	−	0.943684i	$-0.392665\pi$
$13$	31.0152			0.661697			0.330848	+	0.943684i	$0.392665\pi$
$14$		0			0
$15$		−	34.0878i		−	0.586762i
$16$		0			0
$17$	37.4442	−	21.6184i	0.534209	−	0.308426i	−0.208520	−	0.978018i	$-0.566865\pi$
$17$	37.4442	−	21.6184i	0.534209	−	0.308426i	0.742729	+	0.669593i	$0.233531\pi$
$18$		0			0
$19$	30.9280	+	17.8563i	0.373441	+	0.215606i	0.674961	−	0.737854i	$-0.264161\pi$
$19$	30.9280	+	17.8563i	0.373441	+	0.215606i	−0.301520	+	0.953460i	$0.597494\pi$
$20$		0			0
$21$	31.3012	+	45.9046i	0.325261	+	0.477010i
$22$		0			0
$23$	−77.4445	−	44.7126i	−0.702100	−	0.405357i	0.106029	−	0.994363i	$-0.466186\pi$
$23$	−77.4445	−	44.7126i	−0.702100	−	0.405357i	−0.808129	+	0.589006i	$0.799520\pi$
$24$		0			0
$25$	−2.05428	−	3.55811i	−0.0164342	−	0.0284649i
$26$		0			0
$27$		−	27.0000i		−	0.192450i
$28$		0			0
$29$			149.567i			0.957718i	0.877892	+	0.478859i	$0.158950\pi$
$29$			149.567i			0.957718i	−0.877892	+	0.478859i	$0.841050\pi$
$30$		0			0
$31$	72.4769	+	125.534i	0.419911	+	0.727307i	0.995930	−	0.0901295i	$-0.0287281\pi$
$31$	72.4769	+	125.534i	0.419911	+	0.727307i	−0.576019	+	0.817436i	$0.695395\pi$
$32$		0			0
$33$	51.5998	+	29.7912i	0.272193	+	0.157151i
$34$		0			0
$35$	189.604	+	91.2944i	0.915682	+	0.440902i
$36$		0			0
$37$	255.281	+	147.387i	1.13427	+	0.654871i	0.945005	−	0.327055i	$-0.106056\pi$
$37$	255.281	+	147.387i	1.13427	+	0.654871i	0.189265	+	0.981926i	$0.439390\pi$
$38$		0			0
$39$	80.5798	−	46.5228i	0.330848	−	0.191015i
$40$		0			0
$41$		−	340.542i		−	1.29716i	−0.761145	−	0.648582i	$-0.775362\pi$
$41$		−	340.542i		−	1.29716i	0.761145	−	0.648582i	$-0.224638\pi$
$42$		0			0
$43$	382.268			1.35571			0.677853	−	0.735197i	$-0.262910\pi$
$43$	382.268			1.35571			0.677853	+	0.735197i	$0.262910\pi$
$44$		0			0
$45$	−51.1317	−	88.5627i	−0.169384	−	0.293381i
$46$		0			0
$47$	46.6383	−	80.7798i	0.144742	−	0.250701i	−0.784534	−	0.620085i	$-0.787098\pi$
$47$	46.6383	−	80.7798i	0.144742	−	0.250701i	0.929277	+	0.369384i	$0.120431\pi$
$48$		0			0
$49$	−339.163	+	51.1619i	−0.988813	+	0.149160i
$50$		0			0
$51$	64.8552	−	112.333i	0.178070	−	0.308426i
$52$		0			0
$53$	−629.932	+	363.692i	−1.63260	+	0.942583i	−0.649314	+	0.760520i	$0.724944\pi$
$53$	−629.932	+	363.692i	−1.63260	+	0.942583i	−0.983287	+	0.182062i	$0.941723\pi$
$54$		0			0
$55$	225.670			0.553261
$56$		0			0
$57$	107.138			0.248961
$58$		0			0
$59$	495.394	−	286.016i	1.09313	−	0.631121i	0.158724	−	0.987323i	$-0.449262\pi$
$59$	495.394	−	286.016i	1.09313	−	0.631121i	0.934409	+	0.356202i	$0.115929\pi$
$60$		0			0
$61$	−7.77051	+	13.4589i	−0.0163100	+	0.0282498i	−0.874065	−	0.485809i	$-0.838525\pi$
$61$	−7.77051	+	13.4589i	−0.0163100	+	0.0282498i	0.857755	+	0.514058i	$0.171859\pi$
$62$		0			0
$63$	150.180	+	72.3118i	0.300332	+	0.144610i
$64$		0			0
$65$	176.206	−	305.198i	0.336242	−	0.582388i
$66$		0			0
$67$	55.2285	+	95.6585i	0.100705	+	0.174426i	0.911975	−	0.410245i	$-0.134557\pi$
$67$	55.2285	+	95.6585i	0.100705	+	0.174426i	−0.811270	+	0.584671i	$0.801224\pi$
$68$		0			0
$69$	−268.276			−0.468066
$70$		0			0
$71$		−	518.920i		−	0.867387i	−0.901060	−	0.433693i	$-0.857210\pi$
$71$		−	518.920i		−	0.867387i	0.901060	−	0.433693i	$-0.142790\pi$
$72$		0			0
$73$	948.097	−	547.384i	1.52009	−	0.877623i	0.520368	−	0.853942i	$-0.325795\pi$
$73$	948.097	−	547.384i	1.52009	−	0.877623i	0.999720	−	0.0236803i	$-0.00753837\pi$
$74$		0			0
$75$	−10.6743	−	6.16283i	−0.0164342	−	0.00948829i
$76$		0			0
$77$	−303.901	+	207.222i	−0.449775	+	0.306691i
$78$		0			0
$79$	−288.366	−	166.488i	−0.410680	−	0.237106i	0.280402	−	0.959883i	$-0.409532\pi$
$79$	−288.366	−	166.488i	−0.410680	−	0.237106i	−0.691082	+	0.722777i	$0.742866\pi$
$80$		0			0
$81$	−40.5000	−	70.1481i	−0.0555556	−	0.0962250i
$82$		0			0
$83$		−	934.727i		−	1.23614i	−0.786123	−	0.618070i	$-0.787915\pi$
$83$		−	934.727i		−	1.23614i	0.786123	−	0.618070i	$-0.212085\pi$
$84$		0			0
$85$		−	491.282i		−	0.626907i
$86$		0			0
$87$	224.350	+	388.586i	0.276469	+	0.478859i
$88$		0			0
$89$	361.563	+	208.749i	0.430625	+	0.248621i	0.699613	−	0.714522i	$-0.253356\pi$
$89$	361.563	+	208.749i	0.430625	+	0.248621i	−0.268988	+	0.963144i	$0.586689\pi$
$90$		0			0
$91$	42.9597	+	572.800i	0.0494879	+	0.659844i
$92$		0			0
$93$	376.601	+	217.431i	0.419911	+	0.242436i
$94$		0			0
$95$	351.423	−	202.894i	0.379528	−	0.219121i
$96$		0			0
$97$			477.327i			0.499642i	0.968292	+	0.249821i	$0.0803717\pi$
$97$			477.327i			0.499642i	−0.968292	+	0.249821i	$0.919628\pi$
$98$		0			0
$99$	178.747			0.181462
$100$		0			0
$101$	330.374	+	572.225i	0.325480	+	0.563748i	0.981609	−	0.190901i	$-0.0611408\pi$
$101$	330.374	+	572.225i	0.325480	+	0.563748i	−0.656129	+	0.754648i	$0.727807\pi$
$102$		0			0
$103$	−452.718	+	784.131i	−0.433084	+	0.750124i	−0.997137	−	0.0756149i	$-0.975908\pi$
$103$	−452.718	+	784.131i	−0.433084	+	0.750124i	0.564053	+	0.825739i	$0.309241\pi$
$104$		0			0
$105$	629.546	−	47.2157i	0.585119	−	0.0438836i
$106$		0			0
$107$	680.592	−	1178.82i	0.614909	−	1.06505i	−0.375491	−	0.926826i	$-0.622526\pi$
$107$	680.592	−	1178.82i	0.614909	−	1.06505i	0.990400	−	0.138228i	$-0.0441406\pi$
$108$		0			0
$109$	841.623	−	485.911i	0.739568	−	0.426990i	−0.0823444	−	0.996604i	$-0.526241\pi$
$109$	841.623	−	485.911i	0.739568	−	0.426990i	0.821912	+	0.569614i	$0.192907\pi$
$110$		0			0
$111$	884.320			0.756180
$112$		0			0
$113$	−1694.16			−1.41038			−0.705189	−	0.709019i	$-0.749138\pi$
$113$	−1694.16			−1.41038			−0.705189	+	0.709019i	$0.749138\pi$
$114$		0			0
$115$	−879.970	+	508.051i	−0.713545	+	0.411965i
$116$		0			0
$117$	139.568	−	241.739i	0.110283	−	0.191015i
$118$		0			0
$119$	451.122	+	661.590i	0.347515	+	0.509646i
$120$		0			0
$121$	468.275	−	811.075i	0.351822	−	0.609373i
$122$		0			0
$123$	−510.813	−	884.754i	−0.374459	−	0.648582i
$124$		0			0
$125$	1373.64			0.982897
$126$		0			0
$127$			627.533i			0.438461i	0.975673	+	0.219231i	$0.0703547\pi$
$127$			627.533i			0.438461i	−0.975673	+	0.219231i	$0.929645\pi$
$128$		0			0
$129$	993.162	−	573.403i	0.677853	−	0.391359i
$130$		0			0
$131$	1540.25	+	889.263i	1.02727	+	0.593094i	0.916201	−	0.400719i	$-0.131240\pi$
$131$	1540.25	+	889.263i	1.02727	+	0.593094i	0.111067	+	0.993813i	$0.464573\pi$
$132$		0			0
$133$	−286.938	+	595.924i	−0.187073	+	0.388520i
$134$		0			0
$135$	−265.688	−	153.395i	−0.169384	−	0.0977936i
$136$		0			0
$137$	486.966	+	843.450i	0.303681	+	0.525991i	0.976967	−	0.213391i	$-0.0684509\pi$
$137$	486.966	+	843.450i	0.303681	+	0.525991i	−0.673286	+	0.739382i	$0.735118\pi$
$138$		0			0
$139$		−	2556.40i		−	1.55994i	−0.625819	−	0.779969i	$-0.715235\pi$
$139$		−	2556.40i		−	1.55994i	0.625819	−	0.779969i	$-0.284765\pi$
$140$		0			0
$141$		−	279.830i		−	0.167134i
$142$		0			0
$143$	307.993	+	533.459i	0.180109	+	0.311959i
$144$		0			0
$145$	1471.78	+	849.733i	0.842929	+	0.486665i
$146$		0			0
$147$	−804.428	+	641.667i	−0.451348	+	0.360026i
$148$		0			0
$149$	2474.68	+	1428.76i	1.36063	+	0.785559i	0.989707	−	0.143105i	$-0.0457088\pi$
$149$	2474.68	+	1428.76i	1.36063	+	0.785559i	0.370921	+	0.928664i	$0.379042\pi$
$150$		0			0
$151$	−2143.73	+	1237.68i	−1.15532	+	0.667027i	−0.950179	−	0.311705i	$-0.899100\pi$
$151$	−2143.73	+	1237.68i	−1.15532	+	0.667027i	−0.205145	+	0.978732i	$0.565767\pi$
$152$		0			0
$153$		−	389.131i		−	0.205617i
$154$		0			0
$155$	1647.05			0.853511
$156$		0			0
$157$	−1225.00	−	2121.76i	−0.622709	−	1.07856i	−0.988979	−	0.148056i	$-0.952699\pi$
$157$	−1225.00	−	2121.76i	−0.622709	−	1.07856i	0.366270	−	0.930509i	$-0.380635\pi$
$158$		0			0
$159$	−1091.07	+	1889.80i	−0.544200	+	0.942583i
$160$		0			0
$161$	718.500	−	1492.21i	0.351713	−	0.730450i
$162$		0			0
$163$	−1608.40	+	2785.83i	−0.772882	+	1.33867i	0.163095	+	0.986610i	$0.447852\pi$
$163$	−1608.40	+	2785.83i	−0.772882	+	1.33867i	−0.935977	+	0.352061i	$0.885481\pi$
$164$		0			0
$165$	586.308	−	338.505i	0.276630	−	0.159713i
$166$		0			0
$167$	882.107			0.408739			0.204370	−	0.978894i	$-0.434486\pi$
$167$	882.107			0.408739			0.204370	+	0.978894i	$0.434486\pi$
$168$		0			0
$169$	−1235.06			−0.562157
$170$		0			0
$171$	278.352	−	160.707i	0.124480	−	0.0718687i
$172$		0			0
$173$	−584.827	+	1012.95i	−0.257015	+	0.445163i	−0.965441	−	0.260622i	$-0.916072\pi$
$173$	−584.827	+	1012.95i	−0.257015	+	0.445163i	0.708426	+	0.705785i	$0.249406\pi$
$174$		0			0
$175$	62.8671	−	42.8676i	0.0271561	−	0.0185170i
$176$		0			0
$177$	858.048	−	1486.18i	0.364378	−	0.631121i
$178$		0			0
$179$	−216.382	−	374.785i	−0.0903528	−	0.156496i	0.817307	−	0.576203i	$-0.195466\pi$
$179$	−216.382	−	374.785i	−0.0903528	−	0.156496i	−0.907660	+	0.419707i	$0.862133\pi$
$180$		0			0
$181$	−698.293			−0.286761			−0.143380	−	0.989668i	$-0.545797\pi$
$181$	−698.293			−0.286761			−0.143380	+	0.989668i	$0.545797\pi$
$182$		0			0
$183$			46.6231i			0.0188332i
$184$		0			0
$185$	2900.66	−	1674.70i	1.15276	−	0.665546i
$186$		0			0
$187$	743.671	+	429.359i	0.290816	+	0.167903i
$188$		0			0
$189$	498.647	−	37.3982i	0.191911	−	0.0143932i
$190$		0			0
$191$	−2801.97	−	1617.72i	−1.06148	−	0.612848i	−0.135642	−	0.990758i	$-0.543310\pi$
$191$	−2801.97	−	1617.72i	−1.06148	−	0.612848i	−0.925842	+	0.377910i	$0.876643\pi$
$192$		0			0
$193$	1731.02	+	2998.21i	0.645603	+	1.11822i	0.984162	+	0.177271i	$0.0567270\pi$
$193$	1731.02	+	2998.21i	0.645603	+	1.11822i	−0.338559	+	0.940945i	$0.609940\pi$
$194$		0			0
$195$		−	1057.24i		−	0.388259i
$196$		0			0
$197$		−	2199.91i		−	0.795618i	−0.917468	−	0.397809i	$-0.869771\pi$
$197$		−	2199.91i		−	0.795618i	0.917468	−	0.397809i	$-0.130229\pi$
$198$		0			0
$199$	−1592.88	−	2758.94i	−0.567417	−	0.982795i	−0.996820	−	0.0796820i	$-0.974610\pi$
$199$	−1592.88	−	2758.94i	−0.567417	−	0.982795i	0.429404	−	0.903113i	$-0.358724\pi$
$200$		0			0
$201$	286.975	+	165.685i	0.100705	+	0.0581420i
$202$		0			0
$203$	−2762.26	+	207.168i	−0.955036	+	0.0716272i
$204$		0			0
$205$	−3351.03	−	1934.72i	−1.14169	−	0.659154i
$206$		0			0
$207$	−697.000	+	402.413i	−0.234033	+	0.135119i
$208$		0			0
$209$			709.280i			0.234746i
$210$		0			0
$211$	−683.474			−0.222997			−0.111498	−	0.993765i	$-0.535565\pi$
$211$	−683.474			−0.222997			−0.111498	+	0.993765i	$0.535565\pi$
$212$		0			0
$213$	−778.380	−	1348.19i	−0.250393	−	0.433693i
$214$		0			0
$215$	2171.78	−	3761.63i	0.688903	−	1.19322i
$216$		0			0
$217$	−2218.01	+	1512.41i	−0.693865	+	0.473129i
$218$		0			0
$219$	1642.15	−	2844.29i	0.506696	−	0.877623i
$220$		0			0
$221$	1161.34	−	670.499i	0.353484	−	0.204084i
$222$		0			0
$223$	4932.98			1.48133			0.740665	−	0.671874i	$-0.234510\pi$
$223$	4932.98			1.48133			0.740665	+	0.671874i	$0.234510\pi$
$224$		0			0
$225$	−36.9770			−0.0109561
$226$		0			0
$227$	2717.56	−	1568.98i	0.794584	−	0.458753i	−0.0469897	−	0.998895i	$-0.514963\pi$
$227$	2717.56	−	1568.98i	0.794584	−	0.458753i	0.841574	+	0.540142i	$0.181629\pi$
$228$		0			0
$229$	−2141.45	+	3709.10i	−0.617952	+	1.07032i	0.371907	+	0.928270i	$0.378704\pi$
$229$	−2141.45	+	3709.10i	−0.617952	+	1.07032i	−0.989859	+	0.142054i	$0.954629\pi$
$230$		0			0
$231$	−478.723	+	994.230i	−0.136354	+	0.283184i
$232$		0			0
$233$	−150.884	+	261.339i	−0.0424238	+	0.0734802i	−0.886458	−	0.462810i	$-0.846841\pi$
$233$	−150.884	+	261.339i	−0.0424238	+	0.0734802i	0.844034	+	0.536290i	$0.180175\pi$
$234$		0			0
$235$	−529.932	−	917.868i	−0.147102	−	0.254788i
$236$		0			0
$237$	−998.929			−0.273787
$238$		0			0
$239$			3412.31i			0.923530i	0.887002	+	0.461765i	$0.152784\pi$
$239$			3412.31i			0.923530i	−0.887002	+	0.461765i	$0.847216\pi$
$240$		0			0
$241$	−3873.71	+	2236.49i	−1.03538	+	0.597779i	−0.918522	−	0.395369i	$-0.870617\pi$
$241$	−3873.71	+	2236.49i	−1.03538	+	0.597779i	−0.116861	+	0.993148i	$0.537283\pi$
$242$		0			0
$243$	−210.444	−	121.500i	−0.0555556	−	0.0320750i
$244$		0			0
$245$	−1423.44	+	3628.13i	−0.371184	+	0.946092i
$246$		0			0
$247$	959.238	+	553.816i	0.247105	+	0.142666i
$248$		0			0
$249$	−1402.09	−	2428.49i	−0.356843	−	0.618070i
$250$		0			0
$251$			2427.14i			0.610358i	0.952295	+	0.305179i	$0.0987164\pi$
$251$			2427.14i			0.610358i	−0.952295	+	0.305179i	$0.901284\pi$
$252$		0			0
$253$		−	1776.05i		−	0.441342i
$254$		0			0
$255$	−736.924	−	1276.39i	−0.180972	−	0.313453i
$256$		0			0
$257$	−5476.85	−	3162.06i	−1.32932	−	0.767486i	−0.344129	−	0.938922i	$-0.611826\pi$
$257$	−5476.85	−	3162.06i	−1.32932	−	0.767486i	−0.985195	+	0.171436i	$0.945159\pi$
$258$		0			0
$259$	−2368.40	+	4918.78i	−0.568206	+	1.18007i
$260$		0			0
$261$	1165.76	+	673.050i	0.276469	+	0.159620i
$262$		0			0
$263$	−1779.35	+	1027.31i	−0.417184	+	0.240862i	−0.693872	−	0.720098i	$-0.744097\pi$
$263$	−1779.35	+	1027.31i	−0.417184	+	0.240862i	0.276688	+	0.960960i	$0.410763\pi$
$264$		0			0
$265$			8264.96i			1.91590i
$266$		0			0
$267$	1252.49			0.287083
$268$		0			0
$269$	−61.4698	−	106.469i	−0.0139326	−	0.0241320i	0.858975	−	0.512017i	$-0.171102\pi$
$269$	−61.4698	−	106.469i	−0.0139326	−	0.0241320i	−0.872908	+	0.487885i	$0.837768\pi$
$270$		0			0
$271$	−206.365	+	357.435i	−0.0462576	+	0.0801204i	−0.888227	−	0.459405i	$-0.848063\pi$
$271$	−206.365	+	357.435i	−0.0462576	+	0.0801204i	0.841970	+	0.539525i	$0.181396\pi$
$272$		0			0
$273$	970.813	+	1423.74i	0.215224	+	0.315636i
$274$		0			0
$275$	40.7995	−	70.6669i	0.00894656	−	0.0154959i
$276$		0			0
$277$	1971.50	−	1138.25i	0.427639	−	0.246897i	−0.270701	−	0.962663i	$-0.587256\pi$
$277$	1971.50	−	1138.25i	0.427639	−	0.246897i	0.698340	+	0.715766i	$0.253922\pi$
$278$		0			0
$279$	1304.58			0.279940
$280$		0			0
$281$	−7937.53			−1.68510			−0.842551	−	0.538617i	$-0.818947\pi$
$281$	−7937.53			−1.68510			−0.842551	+	0.538617i	$0.818947\pi$
$282$		0			0
$283$	−6710.48	+	3874.30i	−1.40953	+	0.813792i	−0.995343	−	0.0963997i	$-0.969267\pi$
$283$	−6710.48	+	3874.30i	−1.40953	+	0.813792i	−0.414187	+	0.910192i	$0.635934\pi$
$284$		0			0
$285$	608.682	−	1054.27i	0.126509	−	0.219121i
$286$		0			0
$287$	6289.26	−	471.691i	1.29353	−	0.0970141i
$288$		0			0
$289$	−1521.79	+	2635.82i	−0.309747	+	0.536498i
$290$		0			0
$291$	715.991	+	1240.13i	0.144234	+	0.249821i
$292$		0			0
$293$	1805.31			0.359957			0.179978	−	0.983671i	$-0.442397\pi$
$293$	1805.31			0.359957			0.179978	+	0.983671i	$0.442397\pi$
$294$		0			0
$295$		−	6499.77i		−	1.28282i
$296$		0			0
$297$	464.399	−	268.121i	0.0907311	−	0.0523836i
$298$		0			0
$299$	−2401.95	−	1386.77i	−0.464577	−	0.268224i
$300$		0			0
$301$	529.487	+	7059.88i	0.101393	+	1.35191i
$302$		0			0
$303$	1716.67	+	991.123i	0.325480	+	0.187916i
$304$		0			0
$305$	88.2932	+	152.928i	0.0165759	+	0.0287103i
$306$		0			0
$307$			5699.24i			1.05952i	0.848148	+	0.529760i	$0.177718\pi$
$307$			5699.24i			1.05952i	−0.848148	+	0.529760i	$0.822282\pi$
$308$		0			0
$309$			2716.31i			0.500082i
$310$		0			0
$311$	−2294.28	−	3973.81i	−0.418317	−	0.724546i	0.577453	−	0.816424i	$-0.304047\pi$
$311$	−2294.28	−	3973.81i	−0.418317	−	0.724546i	−0.995770	+	0.0918773i	$0.970713\pi$
$312$		0			0
$313$	−5418.90	−	3128.61i	−0.978577	−	0.564982i	−0.0767366	−	0.997051i	$-0.524450\pi$
$313$	−5418.90	−	3128.61i	−0.978577	−	0.564982i	−0.901840	+	0.432070i	$0.857783\pi$
$314$		0			0
$315$	1564.79	−	1066.99i	0.279891	−	0.190851i
$316$		0			0
$317$	−5675.91	−	3276.99i	−1.00565	−	0.580612i	−0.0957345	−	0.995407i	$-0.530520\pi$
$317$	−5675.91	−	3276.99i	−1.00565	−	0.580612i	−0.909915	+	0.414795i	$0.863853\pi$
$318$		0			0
$319$	−2572.54	+	1485.26i	−0.451519	+	0.260685i
$320$		0			0
$321$		−	4083.55i		−	0.710036i
$322$		0			0
$323$	1544.10			0.265994
$324$		0			0
$325$	−63.7137	−	110.355i	−0.0108745	−	0.0188351i
$326$		0			0
$327$	1457.73	−	2524.87i	0.246523	−	0.426990i
$328$		0			0
$329$	1556.47	+	749.444i	0.260824	+	0.125587i
$330$		0			0
$331$	−5624.81	+	9742.45i	−0.934040	+	1.61781i	−0.157704	+	0.987486i	$0.550409\pi$
$331$	−5624.81	+	9742.45i	−0.934040	+	1.61781i	−0.776336	+	0.630319i	$0.782924\pi$
$332$		0			0
$333$	2297.53	−	1326.48i	0.378090	−	0.218290i
$334$		0			0
$335$	1255.08			0.204693
$336$		0			0
$337$	−4766.06			−0.770397			−0.385199	−	0.922834i	$-0.625867\pi$
$337$	−4766.06			−0.770397			−0.385199	+	0.922834i	$0.625867\pi$
$338$		0			0
$339$	−4401.55	+	2541.23i	−0.705189	+	0.407141i
$340$		0			0
$341$	−1439.45	+	2493.20i	−0.228594	+	0.395936i
$342$		0			0
$343$	−1414.66	−	6192.93i	−0.222695	−	0.974888i
$344$		0			0
$345$	−1524.15	+	2639.91i	−0.237848	+	0.411965i
$346$		0			0
$347$	2363.60	+	4093.87i	0.365662	+	0.633344i	0.988882	−	0.148702i	$-0.0475094\pi$
$347$	2363.60	+	4093.87i	0.365662	+	0.633344i	−0.623221	+	0.782046i	$0.714176\pi$
$348$		0			0
$349$	−3269.10			−0.501407			−0.250703	−	0.968064i	$-0.580662\pi$
$349$	−3269.10			−0.501407			−0.250703	+	0.968064i	$0.580662\pi$
$350$		0			0
$351$		−	837.410i		−	0.127344i
$352$		0			0
$353$	5356.02	−	3092.30i	0.807571	−	0.466251i	−0.0385409	−	0.999257i	$-0.512271\pi$
$353$	5356.02	−	3092.30i	0.807571	−	0.466251i	0.846112	+	0.533006i	$0.178938\pi$
$354$		0			0
$355$	−5106.33	−	2948.14i	−0.763424	−	0.440763i
$356$		0			0
$357$	2164.43	+	1042.18i	0.320879	+	0.154504i
$358$		0			0
$359$	−10170.1	−	5871.73i	−1.49515	−	0.863226i	−0.495167	−	0.868798i	$-0.664893\pi$
$359$	−10170.1	−	5871.73i	−1.49515	−	0.863226i	−0.999984	+	0.00557116i	$0.998227\pi$
$360$		0			0
$361$	−2791.80	−	4835.55i	−0.407028	−	0.704993i
$362$		0			0
$363$		−	2809.65i		−	0.406249i
$364$		0			0
$365$		−	12439.4i		−	1.78386i
$366$		0			0
$367$	−1562.19	−	2705.80i	−0.222196	−	0.384855i	0.733279	−	0.679928i	$-0.237989\pi$
$367$	−1562.19	−	2705.80i	−0.222196	−	0.384855i	−0.955474	+	0.295074i	$0.904656\pi$
$368$		0			0
$369$	−2654.26	−	1532.44i	−0.374459	−	0.216194i
$370$		0			0
$371$	−7589.33	−	11130.1i	−1.06204	−	1.55753i
$372$		0			0
$373$	−5214.58	−	3010.64i	−0.723862	−	0.417922i	0.0923105	−	0.995730i	$-0.470575\pi$
$373$	−5214.58	−	3010.64i	−0.723862	−	0.417922i	−0.816172	+	0.577808i	$0.803908\pi$
$374$		0			0
$375$	3568.82	−	2060.46i	0.491449	−	0.283738i
$376$		0			0
$377$			4638.84i			0.633719i
$378$		0			0
$379$	11131.0			1.50860			0.754300	−	0.656530i	$-0.227976\pi$
$379$	11131.0			1.50860			0.754300	+	0.656530i	$0.227976\pi$
$380$		0			0
$381$	941.299	+	1630.38i	0.126573	+	0.219231i
$382$		0			0
$383$	−7412.83	+	12839.4i	−0.988977	+	1.71296i	−0.366254	+	0.930515i	$0.619360\pi$
$383$	−7412.83	+	12839.4i	−0.988977	+	1.71296i	−0.622722	+	0.782443i	$0.713973\pi$
$384$		0			0
$385$	312.580	+	4167.76i	0.0413781	+	0.551711i
$386$		0			0
$387$	1720.21	−	2979.49i	0.225951	−	0.391359i
$388$		0			0
$389$	−1408.72	+	813.323i	−0.183611	+	0.106008i	−0.588988	−	0.808142i	$-0.700474\pi$
$389$	−1408.72	+	813.323i	−0.183611	+	0.106008i	0.405377	+	0.914150i	$0.367140\pi$
$390$		0			0
$391$	−3866.46			−0.500090
$392$		0			0
$393$	5335.58			0.684845
$394$		0			0
$395$	−3276.59	+	1891.74i	−0.417374	+	0.240971i
$396$		0			0
$397$	4545.33	−	7872.74i	0.574618	−	0.995268i	−0.421465	−	0.906845i	$-0.638484\pi$
$397$	4545.33	−	7872.74i	0.574618	−	0.995268i	0.996083	−	0.0884234i	$-0.0281828\pi$
$398$		0			0
$399$	148.399	+	1978.66i	0.0186196	+	0.248263i
$400$		0			0
$401$	2090.65	−	3621.11i	0.260354	−	0.450947i	−0.705982	−	0.708230i	$-0.749494\pi$
$401$	2090.65	−	3621.11i	0.260354	−	0.450947i	0.966336	+	0.257283i	$0.0828273\pi$
$402$		0			0
$403$	2247.88	+	3893.45i	0.277854	+	0.481257i
$404$		0			0
$405$	−920.370			−0.112922
$406$		0			0
$407$			5854.43i			0.713006i
$408$		0			0
$409$	−10120.3	+	5842.94i	−1.22351	+	0.706393i	−0.965664	−	0.259793i	$-0.916346\pi$
$409$	−10120.3	+	5842.94i	−1.22351	+	0.706393i	−0.257845	+	0.966186i	$0.583012\pi$
$410$		0			0
$411$	2530.35	+	1460.90i	0.303681	+	0.175330i
$412$		0			0
$413$	5968.44	+	8752.97i	0.711108	+	1.04287i
$414$		0			0
$415$	−9197.99	−	5310.46i	−1.08798	−	0.628146i
$416$		0			0
$417$	−3834.60	−	6641.73i	−0.450315	−	0.779969i
$418$		0			0
$419$		−	6630.39i		−	0.773068i	−0.922275	−	0.386534i	$-0.873672\pi$
$419$		−	6630.39i		−	0.773068i	0.922275	−	0.386534i	$-0.126328\pi$
$420$		0			0
$421$		−	8062.94i		−	0.933406i	−0.884414	−	0.466703i	$-0.845442\pi$
$421$		−	8062.94i		−	0.933406i	0.884414	−	0.466703i	$-0.154558\pi$
$422$		0			0
$423$	−419.744	−	727.018i	−0.0482474	−	0.0835670i
$424$		0			0
$425$	−153.841	−	88.8203i	−0.0175586	−	0.0101375i
$426$		0			0
$427$	−259.328	−	124.867i	−0.0293905	−	0.0141516i
$428$		0			0
$429$	1600.38	+	923.978i	0.180109	+	0.103986i
$430$		0			0
$431$	11197.4	−	6464.82i	1.25141	−	0.722505i	0.280024	−	0.959993i	$-0.409657\pi$
$431$	11197.4	−	6464.82i	1.25141	−	0.722505i	0.971390	+	0.237488i	$0.0763242\pi$
$432$		0			0
$433$			15425.1i			1.71197i	0.516999	+	0.855986i	$0.327049\pi$
$433$			15425.1i			1.71197i	−0.516999	+	0.855986i	$0.672951\pi$
$434$		0			0
$435$	5098.40			0.561953
$436$		0			0
$437$	−1596.80	−	2765.74i	−0.174795	−	0.302754i
$438$		0			0
$439$	−7687.49	+	13315.1i	−0.835772	+	1.44760i	0.0576279	+	0.998338i	$0.481646\pi$
$439$	−7687.49	+	13315.1i	−0.835772	+	1.44760i	−0.893400	+	0.449262i	$0.851687\pi$
$440$		0			0
$441$	−1127.47	+	2873.74i	−0.121743	+	0.310306i
$442$		0			0
$443$	−2141.57	+	3709.31i	−0.229682	+	0.397820i	−0.957714	−	0.287723i	$-0.907102\pi$
$443$	−2141.57	+	3709.31i	−0.229682	+	0.397820i	0.728032	+	0.685543i	$0.240435\pi$
$444$		0			0
$445$	4108.29	−	2371.92i	0.437645	−	0.252674i
$446$		0			0
$447$	8572.54			0.907086
$448$		0			0
$449$	14674.6			1.54240			0.771201	−	0.636592i	$-0.219656\pi$
$449$	14674.6			1.54240			0.771201	+	0.636592i	$0.219656\pi$
$450$		0			0
$451$	5857.30	−	3381.71i	0.611551	−	0.353079i
$452$		0			0
$453$	−3713.04	+	6431.18i	−0.385108	+	0.667027i
$454$		0			0
$455$	5880.59	+	2831.51i	0.605904	+	0.291744i
$456$		0			0
$457$	8662.00	−	15003.0i	0.886633	−	1.53569i	0.0428020	−	0.999084i	$-0.486372\pi$
$457$	8662.00	−	15003.0i	0.886633	−	1.53569i	0.843831	−	0.536609i	$-0.180295\pi$
$458$		0			0
$459$	−583.697	−	1010.99i	−0.0593565	−	0.102809i
$460$		0			0
$461$	−6377.83			−0.644349			−0.322175	−	0.946680i	$-0.604414\pi$
$461$	−6377.83			−0.644349			−0.322175	+	0.946680i	$0.604414\pi$
$462$		0			0
$463$			7592.70i			0.762123i	0.924550	+	0.381061i	$0.124441\pi$
$463$			7592.70i			0.762123i	−0.924550	+	0.381061i	$0.875559\pi$
$464$		0			0
$465$	4279.16	−	2470.58i	0.426756	−	0.246388i
$466$		0			0
$467$	−4571.40	−	2639.30i	−0.452975	−	0.261525i	0.256111	−	0.966647i	$-0.417559\pi$
$467$	−4571.40	−	2639.30i	−0.452975	−	0.261525i	−0.709086	+	0.705122i	$0.750892\pi$
$468$		0			0
$469$	−1690.16	+	1152.48i	−0.166406	+	0.113468i
$470$		0			0
$471$	−6365.27	−	3674.99i	−0.622709	−	0.359521i
$472$		0			0
$473$	3796.07	+	6574.99i	0.369014	+	0.639151i
$474$		0			0
$475$		−	146.727i		−	0.0141733i
$476$		0			0
$477$			6546.45i			0.628388i
$478$		0			0
$479$	7795.95	+	13503.0i	0.743645	+	1.28803i	0.950825	+	0.309728i	$0.100238\pi$
$479$	7795.95	+	13503.0i	0.743645	+	1.28803i	−0.207180	+	0.978303i	$0.566429\pi$
$480$		0			0
$481$	7917.59	+	4571.22i	0.750543	+	0.433326i
$482$		0			0
$483$	−371.594	−	4954.62i	−0.0350064	−	0.466756i
$484$		0			0
$485$	4697.04	+	2711.84i	0.439756	+	0.253893i
$486$		0			0
$487$	9084.27	−	5244.80i	0.845272	−	0.488018i	−0.0137808	−	0.999905i	$-0.504387\pi$
$487$	9084.27	−	5244.80i	0.845272	−	0.488018i	0.859053	+	0.511887i	$0.171053\pi$
$488$		0			0
$489$			9650.41i			0.892447i
$490$		0			0
$491$	−7949.83			−0.730694			−0.365347	−	0.930871i	$-0.619050\pi$
$491$	−7949.83			−0.730694			−0.365347	+	0.930871i	$0.619050\pi$
$492$		0			0
$493$	3233.39	+	5600.40i	0.295385	+	0.511621i
$494$		0			0
$495$	1015.52	−	1758.92i	0.0922101	−	0.159713i
$496$		0			0
$497$	9583.62	−	718.766i	0.864958	−	0.0648714i
$498$		0			0
$499$	2422.80	−	4196.41i	0.217353	−	0.376467i	−0.736645	−	0.676280i	$-0.763591\pi$
$499$	2422.80	−	4196.41i	0.217353	−	0.376467i	0.953998	+	0.299813i	$0.0969242\pi$
$500$		0			0
$501$	2291.78	−	1323.16i	0.204370	−	0.117993i
$502$		0			0
$503$	−546.557			−0.0484488			−0.0242244	−	0.999707i	$-0.507712\pi$
$503$	−546.557			−0.0484488			−0.0242244	+	0.999707i	$0.507712\pi$
$504$		0			0
$505$	7507.82			0.661571
$506$		0			0
$507$	−3208.78	+	1852.59i	−0.281079	+	0.162281i
$508$		0			0
$509$	1123.03	−	1945.14i	0.0977944	−	0.169385i	−0.812977	−	0.582296i	$-0.802155\pi$
$509$	1123.03	−	1945.14i	0.0977944	−	0.169385i	0.910771	+	0.412911i	$0.135488\pi$
$510$		0			0
$511$	11422.5	+	16751.6i	0.988851	+	1.45019i
$512$		0			0
$513$	482.120	−	835.057i	0.0414934	−	0.0718687i
$514$		0			0
$515$	5144.05	+	8909.76i	0.440144	+	0.762352i
$516$		0			0
$517$	1852.54			0.157592
$518$		0			0
$519$			3508.96i			0.296775i
$520$		0			0
$521$	6742.95	−	3893.04i	0.567013	−	0.327365i	−0.188942	−	0.981988i	$-0.560506\pi$
$521$	6742.95	−	3893.04i	0.567013	−	0.327365i	0.755956	+	0.654623i	$0.227173\pi$
$522$		0			0
$523$	−10196.9	−	5887.21i	−0.852545	−	0.492217i	0.00896379	−	0.999960i	$-0.497147\pi$
$523$	−10196.9	−	5887.21i	−0.852545	−	0.492217i	−0.861509	+	0.507743i	$0.830480\pi$
$524$		0			0
$525$	99.0323	−	205.674i	0.00823261	−	0.0170978i
$526$		0			0
$527$	5427.67	+	3133.67i	0.448640	+	0.259022i
$528$		0			0
$529$	−2085.07	−	3611.44i	−0.171371	−	0.296823i
$530$		0			0
$531$		−	5148.29i		−	0.420747i
$532$		0			0
$533$		−	10562.0i		−	0.858329i
$534$		0			0
$535$	−7733.29	−	13394.4i	−0.624933	−	1.08242i
$536$		0			0
$537$	−1124.35	−	649.146i	−0.0903528	−	0.0521652i
$538$		0			0
$539$	−4248.00	−	5325.53i	−0.339470	−	0.425578i
$540$		0			0
$541$	5410.37	+	3123.68i	0.429963	+	0.248239i	0.699331	−	0.714798i	$-0.253481\pi$
$541$	5410.37	+	3123.68i	0.429963	+	0.248239i	−0.269368	+	0.963037i	$0.586815\pi$
$542$		0			0
$543$	−1814.22	+	1047.44i	−0.143380	+	0.0827807i
$544$		0			0
$545$		−	11042.4i		−	0.867900i
$546$		0			0
$547$	3021.26			0.236160			0.118080	−	0.993004i	$-0.462326\pi$
$547$	3021.26			0.236160			0.118080	+	0.993004i	$0.462326\pi$
$548$		0			0
$549$	69.9346	+	121.130i	0.00543668	+	0.00941660i
$550$		0			0
$551$	−2670.71	+	4625.80i	−0.206490	+	0.357651i
$552$		0			0
$553$	2675.35	−	5556.26i	0.205728	−	0.427263i
$554$		0			0
$555$	5024.09	−	8701.97i	0.384253	−	0.665546i
$556$		0			0
$557$	5016.95	−	2896.54i	0.381643	−	0.220342i	−0.296890	−	0.954912i	$-0.595949\pi$
$557$	5016.95	−	2896.54i	0.381643	−	0.220342i	0.678533	+	0.734570i	$0.262616\pi$
$558$		0			0
$559$	11856.1			0.897067
$560$		0			0
$561$	2576.15			0.193877
$562$		0			0
$563$	20719.3	−	11962.3i	1.55100	−	0.895470i	0.552939	−	0.833221i	$-0.313506\pi$
$563$	20719.3	−	11962.3i	1.55100	−	0.895470i	0.998061	−	0.0622488i	$-0.0198272\pi$
$564$		0			0
$565$	−9625.01	+	16671.0i	−0.716685	+	1.24133i
$566$		0			0
$567$	1239.42	−	845.133i	0.0918006	−	0.0625966i
$568$		0			0
$569$	4267.57	−	7391.65i	0.314422	−	0.544594i	−0.664893	−	0.746939i	$-0.731523\pi$
$569$	4267.57	−	7391.65i	0.314422	−	0.544594i	0.979314	+	0.202345i	$0.0648561\pi$
$570$		0			0
$571$	4647.94	+	8050.46i	0.340648	+	0.590020i	0.984553	−	0.175086i	$-0.0560202\pi$
$571$	4647.94	+	8050.46i	0.340648	+	0.590020i	−0.643905	+	0.765105i	$0.722687\pi$
$572$		0			0
$573$	−9706.31			−0.707656
$574$		0			0
$575$			367.408i			0.0266469i
$576$		0			0
$577$	−8890.70	+	5133.05i	−0.641464	+	0.370349i	−0.785178	−	0.619270i	$-0.787429\pi$
$577$	−8890.70	+	5133.05i	−0.641464	+	0.370349i	0.143714	+	0.989619i	$0.454095\pi$
$578$		0			0
$579$	8994.63	+	5193.05i	0.645603	+	0.372739i
$580$		0			0
$581$	17262.9	−	1294.71i	1.23268	−	0.0924502i
$582$		0			0
$583$	−12510.9	−	7223.20i	−0.888766	−	0.513129i
$584$		0			0
$585$	−1585.86	−	2746.79i	−0.112081	−	0.194129i
$586$		0			0
$587$			9195.89i			0.646601i	0.946296	+	0.323301i	$0.104792\pi$
$587$			9195.89i			0.646601i	−0.946296	+	0.323301i	$0.895208\pi$
$588$		0			0
$589$			5176.68i			0.362141i
$590$		0			0
$591$	−3299.86	−	5715.52i	−0.229675	−	0.397809i
$592$		0			0
$593$	−12551.0	−	7246.30i	−0.869150	−	0.501804i	−0.00208435	−	0.999998i	$-0.500663\pi$
$593$	−12551.0	−	7246.30i	−0.869150	−	0.501804i	−0.867066	+	0.498194i	$0.833997\pi$
$594$		0			0
$595$	9073.19	−	680.485i	0.625151	−	0.0468860i
$596$		0			0
$597$	−8276.82	−	4778.63i	−0.567417	−	0.327598i
$598$		0			0
$599$	8877.36	−	5125.35i	0.605541	−	0.349609i	−0.165677	−	0.986180i	$-0.552981\pi$
$599$	8877.36	−	5125.35i	0.605541	−	0.349609i	0.771218	+	0.636571i	$0.219648\pi$
$600$		0			0
$601$		−	7735.54i		−	0.525024i	−0.964929	−	0.262512i	$-0.915449\pi$
$601$		−	7735.54i		−	0.525024i	0.964929	−	0.262512i	$-0.0845509\pi$
$602$		0			0
$603$	994.112			0.0671366
$604$		0			0
$605$	−5320.81	−	9215.92i	−0.357557	−	0.619307i
$606$		0			0
$607$	−11358.6	+	19673.6i	−0.759523	+	1.31553i	0.183572	+	0.983006i	$0.441234\pi$
$607$	−11358.6	+	19673.6i	−0.759523	+	1.31553i	−0.943094	+	0.332525i	$0.892099\pi$
$608$		0			0
$609$	−6865.80	+	4681.62i	−0.456841	+	0.311509i
$610$		0			0
$611$	1446.49	−	2505.40i	0.0957755	−	0.165888i
$612$		0			0
$613$	11301.1	−	6524.70i	0.744613	−	0.429902i	−0.0791312	−	0.996864i	$-0.525215\pi$
$613$	11301.1	−	6524.70i	0.744613	−	0.429902i	0.823744	+	0.566962i	$0.191881\pi$
$614$		0			0
$615$	−11608.3			−0.761126
$616$		0			0
$617$	3941.58			0.257183			0.128592	−	0.991698i	$-0.458954\pi$
$617$	3941.58			0.257183			0.128592	+	0.991698i	$0.458954\pi$
$618$		0			0
$619$	11457.4	−	6614.93i	0.743960	−	0.429526i	−0.0795473	−	0.996831i	$-0.525347\pi$
$619$	11457.4	−	6614.93i	0.743960	−	0.429526i	0.823507	+	0.567306i	$0.192014\pi$
$620$		0			0
$621$	−1207.24	+	2091.00i	−0.0780111	+	0.135119i
$622$		0			0
$623$	−3354.44	+	6966.63i	−0.215719	+	0.448013i
$624$		0			0
$625$	8060.84	−	13961.8i	0.515894	−	0.893555i
$626$		0			0
$627$	1063.92	+	1842.76i	0.0677654	+	0.117373i
$628$		0			0
$629$	12745.1			0.807916
$630$		0			0
$631$		−	20182.5i		−	1.27330i	−0.771154	−	0.636649i	$-0.780320\pi$
$631$		−	20182.5i		−	1.27330i	0.771154	−	0.636649i	$-0.219680\pi$
$632$		0			0
$633$	−1775.72	+	1025.21i	−0.111498	+	0.0643736i
$634$		0			0
$635$	6175.11	+	3565.20i	0.385908	+	0.222804i
$636$		0			0
$637$	−10519.2	+	1586.79i	−0.654295	+	0.0986987i
$638$		0			0
$639$	−4044.58	−	2335.14i	−0.250393	−	0.144564i
$640$		0			0
$641$	8885.98	+	15391.0i	0.547543	+	0.948373i	0.998442	+	0.0557977i	$0.0177702\pi$
$641$	8885.98	+	15391.0i	0.547543	+	0.948373i	−0.450899	+	0.892575i	$0.648896\pi$
$642$		0			0
$643$		−	7636.64i		−	0.468366i	−0.972192	−	0.234183i	$-0.924758\pi$
$643$		−	7636.64i		−	0.468366i	0.972192	−	0.234183i	$-0.0752416\pi$
$644$		0			0
$645$		−	13030.7i		−	0.795477i
$646$		0			0
$647$	−2958.17	−	5123.70i	−0.179749	−	0.311335i	0.762045	−	0.647524i	$-0.224195\pi$
$647$	−2958.17	−	5123.70i	−0.179749	−	0.311335i	−0.941795	+	0.336189i	$0.890862\pi$
$648$		0			0
$649$	9838.92	+	5680.50i	0.595087	+	0.343574i
$650$		0			0
$651$	−3493.96	+	7256.38i	−0.210352	+	0.436866i
$652$		0			0
$653$	−16261.3	−	9388.47i	−0.974509	−	0.562633i	−0.0739010	−	0.997266i	$-0.523545\pi$
$653$	−16261.3	−	9388.47i	−0.974509	−	0.562633i	−0.900608	+	0.434633i	$0.856878\pi$
$654$		0			0
$655$	17501.2	−	10104.3i	1.04401	−	0.602762i
$656$		0			0
$657$		−	9852.91i		−	0.585082i
$658$		0			0
$659$	1477.88			0.0873594			0.0436797	−	0.999046i	$-0.486092\pi$
$659$	1477.88			0.0873594			0.0436797	+	0.999046i	$0.486092\pi$
$660$		0			0
$661$	12988.8	+	22497.3i	0.764307	+	1.32382i	0.940612	+	0.339484i	$0.110252\pi$
$661$	12988.8	+	22497.3i	0.764307	+	1.32382i	−0.176305	+	0.984336i	$0.556414\pi$
$662$		0			0
$663$	2011.50	−	3484.01i	0.117828	−	0.204084i
$664$		0			0
$665$	4233.89	+	6209.18i	0.246892	+	0.362078i
$666$		0			0
$667$	6687.51	−	11583.1i	0.388218	−	0.672414i
$668$		0			0
$669$	12816.3	−	7399.47i	0.740665	−	0.427623i
$670$		0			0
$671$	−308.657			−0.0177579
$672$		0			0
$673$	3291.08			0.188502			0.0942509	−	0.995548i	$-0.469954\pi$
$673$	3291.08			0.188502			0.0942509	+	0.995548i	$0.469954\pi$
$674$		0			0
$675$	−96.0690	+	55.4654i	−0.00547807	+	0.00316276i
$676$		0			0
$677$	−9665.86	+	16741.8i	−0.548728	+	0.950425i	0.449634	+	0.893213i	$0.351555\pi$
$677$	−9665.86	+	16741.8i	−0.548728	+	0.950425i	−0.998362	+	0.0572123i	$0.981779\pi$
$678$		0			0
$679$	−8815.46	+	661.155i	−0.498242	+	0.0373679i
$680$		0			0
$681$	4706.95	−	8152.67i	0.264861	−	0.458753i
$682$		0			0
$683$	−1480.32	−	2563.99i	−0.0829325	−	0.143643i	0.821576	−	0.570099i	$-0.193095\pi$
$683$	−1480.32	−	2563.99i	−0.0829325	−	0.143643i	−0.904508	+	0.426456i	$0.859762\pi$
$684$		0			0
$685$	11066.4			0.617263
$686$		0			0
$687$			12848.7i			0.713549i
$688$		0			0
$689$	−19537.5	+	11280.0i	−1.08029	+	0.623704i
$690$		0			0
$691$	−19776.3	−	11417.8i	−1.08875	−	0.628589i	−0.155506	−	0.987835i	$-0.549701\pi$
$691$	−19776.3	−	11417.8i	−1.08875	−	0.628589i	−0.933243	+	0.359246i	$0.883034\pi$
$692$		0			0
$693$	247.586	+	3301.17i	0.0135715	+	0.180954i
$694$		0			0
$695$	−25155.8	−	14523.7i	−1.37297	−	0.792683i
$696$		0			0
$697$	−7361.97	−	12751.3i	−0.400078	−	0.692956i
$698$		0			0
$699$			905.304i			0.0489868i
$700$		0			0
$701$			34253.9i			1.84558i	0.385300	+	0.922791i	$0.374098\pi$
$701$			34253.9i			1.84558i	−0.385300	+	0.922791i	$0.625902\pi$
$702$		0			0
$703$	5263.56	+	9116.76i	0.282388	+	0.489111i
$704$		0			0
$705$	−2753.60	−	1589.79i	−0.147102	−	0.0849293i
$706$		0			0
$707$	−10110.5	+	6894.08i	−0.537826	+	0.366731i
$708$		0			0
$709$	−20019.3	−	11558.2i	−1.06042	−	0.612237i	−0.134875	−	0.990863i	$-0.543063\pi$
$709$	−20019.3	−	11558.2i	−1.06042	−	0.612237i	−0.925550	+	0.378626i	$0.876397\pi$
$710$		0			0
$711$	−2595.29	+	1498.39i	−0.136893	+	0.0790354i
$712$		0			0
$713$		−	12962.5i		−	0.680856i
$714$		0			0
$715$	6999.20			0.366091
$716$		0			0
$717$	5118.46	+	8865.43i	0.266600	+	0.461765i
$718$		0			0
$719$	−5504.81	+	9534.61i	−0.285528	+	0.494550i	−0.972737	−	0.231910i	$-0.925502\pi$
$719$	−5504.81	+	9534.61i	−0.285528	+	0.494550i	0.687209	+	0.726460i	$0.258836\pi$
$720$		0			0
$721$	−15108.7	−	7274.86i	−0.780413	−	0.375770i
$722$		0			0
$723$	−6709.46	+	11621.1i	−0.345128	+	0.597779i
$724$		0			0
$725$	532.175	−	307.251i	0.0272613	−	0.0157393i
$726$		0			0
$727$	31122.9			1.58774			0.793869	−	0.608089i	$-0.208064\pi$
$727$	31122.9			1.58774			0.793869	+	0.608089i	$0.208064\pi$
$728$		0			0
$729$	−729.000			−0.0370370
$730$		0			0
$731$	14313.7	−	8264.03i	0.724230	−	0.418134i
$732$		0			0
$733$	−15353.3	+	26592.7i	−0.773653	+	1.34001i	0.161896	+	0.986808i	$0.448239\pi$
$733$	−15353.3	+	26592.7i	−0.773653	+	1.34001i	−0.935549	+	0.353198i	$0.885094\pi$
$734$		0			0
$735$	1743.99	+	11561.3i	0.0875214	+	0.580198i
$736$		0			0
$737$	−1096.88	+	1899.85i	−0.0548224	+	0.0949552i
$738$		0			0
$739$	2219.89	+	3844.96i	0.110501	+	0.191393i	0.915972	−	0.401242i	$-0.131421\pi$
$739$	2219.89	+	3844.96i	0.110501	+	0.191393i	−0.805472	+	0.592634i	$0.798088\pi$
$740$		0			0
$741$	3322.90			0.164736
$742$		0			0
$743$		−	20548.4i		−	1.01460i	−0.861770	−	0.507299i	$-0.830644\pi$
$743$		−	20548.4i		−	1.01460i	0.861770	−	0.507299i	$-0.169356\pi$
$744$		0			0
$745$	28118.8	−	16234.4i	1.38281	−	0.798365i
$746$		0			0
$747$	−7285.48	−	4206.27i	−0.356843	−	0.206023i
$748$		0			0
$749$	22713.6	+	10936.6i	1.10806	+	0.533532i
$750$		0			0
$751$	18835.5	+	10874.7i	0.915205	+	0.528394i	0.882102	−	0.471058i	$-0.156128\pi$
$751$	18835.5	+	10874.7i	0.915205	+	0.528394i	0.0331028	+	0.999452i	$0.489461\pi$
$752$		0			0
$753$	3640.72	+	6305.90i	0.176195	+	0.305179i
$754$		0			0
$755$			28126.5i			1.35580i
$756$		0			0
$757$		−	29296.1i		−	1.40658i	−0.710901	−	0.703292i	$-0.751713\pi$
$757$		−	29296.1i		−	1.40658i	0.710901	−	0.703292i	$-0.248287\pi$
$758$		0			0
$759$	−2664.08	−	4614.33i	−0.127405	−	0.220671i
$760$		0			0
$761$	−24098.1	−	13913.1i	−1.14791	−	0.662744i	−0.199530	−	0.979892i	$-0.563942\pi$
$761$	−24098.1	−	13913.1i	−1.14791	−	0.662744i	−0.948376	+	0.317148i	$0.897275\pi$
$762$		0			0
$763$	10139.8	+	14870.4i	0.481106	+	0.705562i
$764$		0			0
$765$	−3829.17	−	2210.77i	−0.180972	−	0.104484i
$766$		0			0
$767$	15364.7	−	8870.84i	0.723323	−	0.417611i
$768$		0			0
$769$		−	3210.87i		−	0.150568i	−0.997162	−	0.0752840i	$-0.976014\pi$
$769$		−	3210.87i		−	0.150568i	0.997162	−	0.0752840i	$-0.0239863\pi$
$770$		0			0
$771$	−18972.4			−0.886216
$772$		0			0
$773$	−4752.28	−	8231.20i	−0.221123	−	0.382996i	0.734027	−	0.679121i	$-0.237639\pi$
$773$	−4752.28	−	8231.20i	−0.221123	−	0.382996i	−0.955149	+	0.296125i	$0.904305\pi$
$774$		0			0
$775$	297.775	−	515.761i	0.0138018	−	0.0239054i
$776$		0			0
$777$	1224.89	+	16332.0i	0.0565543	+	0.754062i
$778$		0			0
$779$	6080.82	−	10532.3i	0.279676	−	0.484414i
$780$		0			0
$781$	8925.40	−	5153.08i	0.408932	−	0.236097i
$782$		0			0
$783$	4038.30			0.184313
$784$		0			0
$785$	−27838.3			−1.26572
$786$		0			0
$787$	4458.68	−	2574.22i	0.201950	−	0.116596i	−0.395615	−	0.918417i	$-0.629468\pi$
$787$	4458.68	−	2574.22i	0.201950	−	0.116596i	0.597565	+	0.801821i	$0.296135\pi$
$788$		0			0
$789$	−3081.93	+	5338.05i	−0.139061	+	0.240862i
$790$		0			0
$791$	−2346.61	−	31288.3i	−0.105481	−	1.40643i
$792$		0			0
$793$	−241.004	+	417.431i	−0.0107923	+	0.0186928i
$794$		0			0
$795$	12397.4	+	21473.0i	0.553072	+	0.957948i
$796$		0			0
$797$	−24018.5			−1.06748			−0.533738	−	0.845650i	$-0.679213\pi$
$797$	−24018.5			−1.06748			−0.533738	+	0.845650i	$0.679213\pi$
$798$		0			0
$799$		−	4032.98i		−	0.178569i
$800$		0			0
$801$	3254.07	−	1878.74i	0.143542	−	0.0828738i
$802$		0			0
$803$	18830.0	+	10871.5i	0.827515	+	0.477766i
$804$		0			0
$805$	−10601.8	−	15547.9i	−0.464177	−	0.680736i
$806$		0			0
$807$	−319.407	−	184.409i	−0.0139326	−	0.00804402i
$808$		0			0
$809$	17874.7	+	30959.8i	0.776810	+	1.34547i	0.933771	+	0.357870i	$0.116497\pi$
$809$	17874.7	+	30959.8i	0.776810	+	1.34547i	−0.156961	+	0.987605i	$0.550170\pi$
$810$		0			0
$811$		−	36313.3i		−	1.57230i	−0.618037	−	0.786149i	$-0.712072\pi$
$811$		−	36313.3i		−	1.57230i	0.618037	−	0.786149i	$-0.287928\pi$
$812$		0			0
$813$			1238.19i			0.0534136i
$814$		0			0
$815$	18275.6	+	31654.3i	0.785481	+	1.36049i
$816$		0			0
$817$	11822.8	+	6825.90i	0.506276	+	0.292299i
$818$		0			0
$819$	4657.86	+	2242.76i	0.198728	+	0.0956880i
$820$		0			0
$821$	−7083.90	−	4089.89i	−0.301133	−	0.173859i	0.341819	−	0.939766i	$-0.388957\pi$
$821$	−7083.90	−	4089.89i	−0.301133	−	0.173859i	−0.642952	+	0.765907i	$0.722290\pi$
$822$		0			0
$823$	6930.59	−	4001.38i	0.293542	−	0.169477i	−0.345996	−	0.938236i	$-0.612459\pi$
$823$	6930.59	−	4001.38i	0.293542	−	0.169477i	0.639538	+	0.768759i	$0.279126\pi$
$824$		0			0
$825$		−	244.797i		−	0.0103306i
$826$		0			0
$827$	4176.53			0.175613			0.0878065	−	0.996138i	$-0.472014\pi$
$827$	4176.53			0.175613			0.0878065	+	0.996138i	$0.472014\pi$
$828$		0			0
$829$	3732.41	+	6464.72i	0.156371	+	0.270843i	0.933558	−	0.358428i	$-0.116687\pi$
$829$	3732.41	+	6464.72i	0.156371	+	0.270843i	−0.777186	+	0.629271i	$0.783354\pi$
$830$		0			0
$831$	3414.74	−	5914.50i	0.142546	−	0.246897i
$832$		0			0
$833$	−11593.6	+	9247.87i	−0.482228	+	0.384658i
$834$		0			0
$835$	5011.51	−	8680.19i	0.207701	−	0.359749i
$836$		0			0
$837$	3389.41	−	1956.88i	0.139970	−	0.0808118i
$838$		0			0
$839$	−26786.2			−1.10222			−0.551110	−	0.834432i	$-0.685796\pi$
$839$	−26786.2			−1.10222			−0.551110	+	0.834432i	$0.685796\pi$
$840$		0			0
$841$	2018.81			0.0827754
$842$		0			0
$843$	−20622.3	+	11906.3i	−0.842551	+	0.486447i
$844$		0			0
$845$	−7016.74	+	12153.3i	−0.285661	+	0.494779i
$846$		0			0
$847$	15627.9	+	7524.84i	0.633979	+	0.305262i
$848$		0			0
$849$	−11622.9	+	20131.5i	−0.469843	+	0.813792i
$850$		0			0
$851$	−13180.1	−	22828.6i	−0.530914	−	0.919569i
$852$		0			0
$853$	18794.9			0.754425			0.377212	−	0.926127i	$-0.376883\pi$
$853$	18794.9			0.754425			0.377212	+	0.926127i	$0.376883\pi$
$854$		0			0
$855$		−	3652.09i		−	0.146081i
$856$		0			0
$857$	−21918.7	+	12654.8i	−0.873662	+	0.504409i	−0.868564	−	0.495578i	$-0.834956\pi$
$857$	−21918.7	+	12654.8i	−0.873662	+	0.504409i	−0.00509890	+	0.999987i	$0.501623\pi$
$858$		0			0
$859$	−14459.6	−	8348.25i	−0.574337	−	0.331593i	0.184543	−	0.982824i	$-0.440920\pi$
$859$	−14459.6	−	8348.25i	−0.574337	−	0.331593i	−0.758880	+	0.651231i	$0.774253\pi$
$860$		0			0
$861$	15632.4	−	10659.4i	0.618760	−	0.421917i
$862$		0			0
$863$	−4012.90	−	2316.85i	−0.158286	−	0.0913864i	0.418765	−	0.908095i	$-0.362463\pi$
$863$	−4012.90	−	2316.85i	−0.158286	−	0.0913864i	−0.577051	+	0.816708i	$0.695797\pi$
$864$		0			0
$865$	6645.15	+	11509.7i	0.261205	+	0.452420i
$866$		0			0
$867$			9130.73i			0.357666i
$868$		0			0
$869$		−	6613.17i		−	0.258155i
$870$		0			0
$871$	1712.92	+	2966.86i	0.0666361	+	0.115417i
$872$		0			0
$873$	3720.40	+	2147.97i	0.144234	+	0.0832736i
$874$		0			0
$875$	1902.66	+	25368.9i	0.0735103	+	0.980144i
$876$		0			0
$877$	−26477.8	−	15287.0i	−1.01949	−	0.588602i	−0.105533	−	0.994416i	$-0.533655\pi$
$877$	−26477.8	−	15287.0i	−1.01949	−	0.588602i	−0.913956	+	0.405814i	$0.866988\pi$
$878$		0			0
$879$	4690.33	−	2707.97i	0.179978	−	0.103911i
$880$		0			0
$881$		−	13856.1i		−	0.529881i	−0.964265	−	0.264941i	$-0.914648\pi$
$881$		−	13856.1i		−	0.529881i	0.964265	−	0.264941i	$-0.0853524\pi$
$882$		0			0
$883$	7762.38			0.295838			0.147919	−	0.988999i	$-0.452742\pi$
$883$	7762.38			0.295838			0.147919	+	0.988999i	$0.452742\pi$
$884$		0			0
$885$	−9749.65	−	16886.9i	−0.370318	−	0.641409i
$886$		0			0
$887$	−5247.14	+	9088.31i	−0.198626	+	0.344031i	−0.948083	−	0.318022i	$-0.896981\pi$
$887$	−5247.14	+	9088.31i	−0.198626	+	0.344031i	0.749457	+	0.662053i	$0.230315\pi$
$888$		0			0
$889$	−11589.5	+	869.208i	−0.437233	+	0.0327923i
$890$		0			0
$891$	804.362	−	1393.20i	0.0302437	−	0.0523836i
$892$		0			0
$893$	2884.86	−	1665.57i	0.108105	−	0.0624147i
$894$		0			0
$895$	−4917.32			−0.183651
$896$		0			0
$897$	−8320.61			−0.309718
$898$		0			0
$899$	−18775.6	+	10840.1i	−0.696555	+	0.402156i
$900$		0			0
$901$	−15724.9	+	27236.3i	−0.581433	+	1.00707i
$902$		0			0
$903$	11965.5	+	17547.9i	0.440959	+	0.646685i
$904$		0			0
$905$	−3967.21	+	6871.41i	−0.145718	+	0.252391i
$906$		0			0
$907$	184.106	+	318.881i	0.00673995	+	0.0116739i	0.869376	−	0.494152i	$-0.164521\pi$
$907$	184.106	+	318.881i	0.00673995	+	0.0116739i	−0.862636	+	0.505826i	$0.831188\pi$
$908$		0			0
$909$	5946.74			0.216987
$910$		0			0
$911$		−	14957.6i		−	0.543980i	−0.962300	−	0.271990i	$-0.912318\pi$
$911$		−	14957.6i		−	0.543980i	0.962300	−	0.271990i	$-0.0876818\pi$
$912$		0			0
$913$	16077.3	−	9282.21i	0.582782	−	0.336469i
$914$		0			0
$915$	458.785	+	264.880i	0.0165759	+	0.00957011i
$916$		0			0
$917$	−14289.8	+	29677.6i	−0.514604	+	1.06875i
$918$		0			0
$919$	−30202.0	−	17437.1i	−1.08408	−	0.625895i	−0.152087	−	0.988367i	$-0.548599\pi$
$919$	−30202.0	−	17437.1i	−1.08408	−	0.625895i	−0.931995	+	0.362472i	$0.881933\pi$
$920$		0			0
$921$	8548.86	+	14807.1i	0.305857	+	0.529760i
$922$		0			0
$923$		−	16094.4i		−	0.573947i
$924$		0			0
$925$		−	1211.09i		−	0.0430491i
$926$		0			0
$927$	4074.46	+	7057.18i	0.144361	+	0.250041i
$928$		0			0
$929$	29680.6	+	17136.1i	1.04821	+	0.605186i	0.922148	−	0.386837i	$-0.126432\pi$
$929$	29680.6	+	17136.1i	1.04821	+	0.605186i	0.126064	+	0.992022i	$0.459766\pi$
$930$		0			0
$931$	−11403.2	−	4473.86i	−0.401423	−	0.157492i
$932$		0			0
$933$	−11921.4	−	6882.84i	−0.418317	−	0.241515i
$934$		0			0
$935$	8450.03	−	4878.63i	0.295557	−	0.170640i
$936$		0			0
$937$		−	7971.69i		−	0.277933i	−0.990297	−	0.138967i	$-0.955622\pi$
$937$		−	7971.69i		−	0.277933i	0.990297	−	0.138967i	$-0.0443781\pi$
$938$		0			0
$939$	−18771.6			−0.652385
$940$		0			0
$941$	−19868.3	−	34412.9i	−0.688298	−	1.19217i	−0.972388	−	0.233370i	$-0.925025\pi$
$941$	−19868.3	−	34412.9i	−0.688298	−	1.19217i	0.284090	−	0.958798i	$-0.408309\pi$
$942$		0			0
$943$	−15226.5	+	26373.1i	−0.525815	+	0.910738i
$944$		0			0
$945$	2464.95	−	5119.30i	0.0848517	−	0.176223i
$946$		0			0
$947$	−12920.5	+	22378.9i	−0.443357	+	0.767916i	−0.997936	−	0.0642144i	$-0.979546\pi$
$947$	−12920.5	+	22378.9i	−0.443357	+	0.767916i	0.554579	+	0.832131i	$0.312879\pi$
$948$		0			0
$949$	29405.4	−	16977.2i	1.00584	−	0.580720i
$950$		0			0
$951$	−19661.9			−0.670433
$952$		0			0
$953$	−28798.7			−0.978891			−0.489445	−	0.872034i	$-0.662801\pi$
$953$	−28798.7			−0.978891			−0.489445	+	0.872034i	$0.662801\pi$
$954$		0			0
$955$	−31837.7	+	18381.5i	−1.07879	+	0.622838i
$956$		0			0
$957$	−4455.77	+	7717.62i	−0.150506	+	0.260685i
$958$		0			0
$959$	−14902.7	+	10161.8i	−0.501806	+	0.342169i
$960$		0			0
$961$	4389.71	−	7603.20i	0.147350	−	0.255218i
$962$		0			0
$963$	−6125.32	−	10609.4i	−0.204970	−	0.355018i
$964$		0			0
$965$	39337.7			1.31225
$966$		0			0
$967$		−	34186.3i		−	1.13687i	−0.822727	−	0.568437i	$-0.807548\pi$
$967$		−	34186.3i		−	1.13687i	0.822727	−	0.568437i	$-0.192452\pi$
$968$		0			0
$969$	4011.69	−	2316.15i	0.132997	−	0.0767858i
$970$		0			0
$971$	−1588.97	−	917.394i	−0.0525155	−	0.0303198i	0.473512	−	0.880787i	$-0.342986\pi$
$971$	−1588.97	−	917.394i	−0.0525155	−	0.0303198i	−0.526028	+	0.850467i	$0.676319\pi$
$972$		0			0
$973$	47212.7	−	3540.92i	1.55557	−	0.116667i
$974$		0			0
$975$	−331.066	−	191.141i	−0.0108745	−	0.00627837i
$976$		0			0
$977$	−10982.2	−	19021.7i	−0.359622	−	0.622884i	0.628276	−	0.777991i	$-0.283761\pi$
$977$	−10982.2	−	19021.7i	−0.359622	−	0.622884i	−0.987898	+	0.155107i	$0.950428\pi$
$978$		0			0
$979$			8291.82i			0.270692i
$980$		0			0
$981$		−	8746.41i		−	0.284660i
$982$		0			0
$983$	−9107.15	−	15774.0i	−0.295496	−	0.511815i	0.679604	−	0.733579i	$-0.262152\pi$
$983$	−9107.15	−	15774.0i	−0.295496	−	0.511815i	−0.975100	+	0.221765i	$0.928818\pi$
$984$		0			0
$985$	−21647.7	−	12498.3i	−0.700258	−	0.404294i
$986$		0			0
$987$	5168.00	−	387.597i	0.166666	−	0.0124999i
$988$		0			0
$989$	−29604.6	−	17092.2i	−0.951841	−	0.549546i
$990$		0			0
$991$	−42443.0	+	24504.5i	−1.36049	+	0.785479i	−0.989689	−	0.143234i	$-0.954250\pi$
$991$	−42443.0	+	24504.5i	−1.36049	+	0.785479i	−0.370801	+	0.928713i	$0.620917\pi$
$992$		0			0
$993$			33748.8i			1.07854i
$994$		0			0
$995$	−36198.4			−1.15333
$996$		0			0
$997$	−10050.3	−	17407.7i	−0.319255	−	0.552967i	0.661077	−	0.750318i	$-0.270099\pi$
$997$	−10050.3	−	17407.7i	−0.319255	−	0.552967i	−0.980333	+	0.197351i	$0.936766\pi$
$998$		0			0
$999$	3979.44	−	6892.59i	0.126030	−	0.218290i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	672.4.bb.a.271.42		96
4.3	odd	2		168.4.t.a.19.46	yes	96
7.3	odd	6	inner	672.4.bb.a.367.41		96
8.3	odd	2	inner	672.4.bb.a.271.41		96
8.5	even	2		168.4.t.a.19.14	✓	96
28.3	even	6		168.4.t.a.115.14	yes	96
56.3	even	6	inner	672.4.bb.a.367.42		96
56.45	odd	6		168.4.t.a.115.46	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.4.t.a.19.14	✓	96	8.5	even	2
168.4.t.a.19.46	yes	96	4.3	odd	2
168.4.t.a.115.14	yes	96	28.3	even	6
168.4.t.a.115.46	yes	96	56.45	odd	6
672.4.bb.a.271.41		96	8.3	odd	2	inner
672.4.bb.a.271.42		96	1.1	even	1	trivial
672.4.bb.a.367.41		96	7.3	odd	6	inner
672.4.bb.a.367.42		96	56.3	even	6	inner

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:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	672.bb (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.59808 - 1.50000i) q^{3} +(5.68130 - 9.84030i) q^{5} +(1.38512 + 18.4684i) q^{7} +(4.50000 - 7.79423i) q^{9} +(9.93039 + 17.1999i) q^{11} +31.0152 q^{13} -34.0878i q^{15} +(37.4442 - 21.6184i) q^{17} +(30.9280 + 17.8563i) q^{19} +(31.3012 + 45.9046i) q^{21} +(-77.4445 - 44.7126i) q^{23} +(-2.05428 - 3.55811i) q^{25} -27.0000i q^{27} +149.567i q^{29} +(72.4769 + 125.534i) q^{31} +(51.5998 + 29.7912i) q^{33} +(189.604 + 91.2944i) q^{35} +(255.281 + 147.387i) q^{37} +(80.5798 - 46.5228i) q^{39} -340.542i q^{41} +382.268 q^{43} +(-51.1317 - 88.5627i) q^{45} +(46.6383 - 80.7798i) q^{47} +(-339.163 + 51.1619i) q^{49} +(64.8552 - 112.333i) q^{51} +(-629.932 + 363.692i) q^{53} +225.670 q^{55} +107.138 q^{57} +(495.394 - 286.016i) q^{59} +(-7.77051 + 13.4589i) q^{61} +(150.180 + 72.3118i) q^{63} +(176.206 - 305.198i) q^{65} +(55.2285 + 95.6585i) q^{67} -268.276 q^{69} -518.920i q^{71} +(948.097 - 547.384i) q^{73} +(-10.6743 - 6.16283i) q^{75} +(-303.901 + 207.222i) q^{77} +(-288.366 - 166.488i) q^{79} +(-40.5000 - 70.1481i) q^{81} -934.727i q^{83} -491.282i q^{85} +(224.350 + 388.586i) q^{87} +(361.563 + 208.749i) q^{89} +(42.9597 + 572.800i) q^{91} +(376.601 + 217.431i) q^{93} +(351.423 - 202.894i) q^{95} +477.327i q^{97} +178.747 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 432 q^{9} - 40 q^{11} - 1200 q^{25} - 456 q^{35} + 1616 q^{43} - 360 q^{49} - 336 q^{57} - 4128 q^{59} + 1440 q^{67} - 648 q^{73} - 3888 q^{81} + 104 q^{91} - 720 q^{99}+O(q^{100}) \) 96 * q + 432 * q^9 - 40 * q^11 - 1200 * q^25 - 456 * q^35 + 1616 * q^43 - 360 * q^49 - 336 * q^57 - 4128 * q^59 + 1440 * q^67 - 648 * q^73 - 3888 * q^81 + 104 * q^91 - 720 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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