LMFDB - Embedded newform 177.4.d.c.176.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [177,4,Mod(176,177)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(177, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("177.176");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	177.d (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$10.4433380710$
Analytic rank:	$0$
Dimension:	$52$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			176.19
Character	$\chi$	$=$	177.176
Dual form			177.4.d.c.176.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.52893 q^{2} +(0.100502 - 5.19518i) q^{3} -1.60453 q^{4} +17.9211i q^{5} +(-0.254162 + 13.1382i) q^{6} -4.91298 q^{7} +24.2892 q^{8} +(-26.9798 - 1.04425i) q^{9} +O(q^{10})$	\(q-2.52893 q^{2} +(0.100502 - 5.19518i) q^{3} -1.60453 q^{4} +17.9211i q^{5} +(-0.254162 + 13.1382i) q^{6} -4.91298 q^{7} +24.2892 q^{8} +(-26.9798 - 1.04425i) q^{9} -45.3212i q^{10} +38.0756 q^{11} +(-0.161258 + 8.33584i) q^{12} -51.2270i q^{13} +12.4246 q^{14} +(93.1035 + 1.80111i) q^{15} -48.5892 q^{16} -30.7171i q^{17} +(68.2299 + 2.64083i) q^{18} -45.5739 q^{19} -28.7550i q^{20} +(-0.493764 + 25.5238i) q^{21} -96.2904 q^{22} -137.131 q^{23} +(2.44110 - 126.187i) q^{24} -196.167 q^{25} +129.549i q^{26} +(-8.13658 + 140.060i) q^{27} +7.88305 q^{28} -12.5498i q^{29} +(-235.452 - 4.55486i) q^{30} -75.5324i q^{31} -71.4347 q^{32} +(3.82667 - 197.810i) q^{33} +77.6812i q^{34} -88.0462i q^{35} +(43.2900 + 1.67553i) q^{36} -152.739i q^{37} +115.253 q^{38} +(-266.133 - 5.14840i) q^{39} +435.289i q^{40} -272.870i q^{41} +(1.24869 - 64.5479i) q^{42} -364.987i q^{43} -61.0936 q^{44} +(18.7141 - 483.509i) q^{45} +346.793 q^{46} +430.845 q^{47} +(-4.88330 + 252.430i) q^{48} -318.863 q^{49} +496.092 q^{50} +(-159.581 - 3.08712i) q^{51} +82.1954i q^{52} -660.497i q^{53} +(20.5768 - 354.201i) q^{54} +682.358i q^{55} -119.332 q^{56} +(-4.58026 + 236.765i) q^{57} +31.7375i q^{58} +(-351.582 - 285.954i) q^{59} +(-149.388 - 2.88993i) q^{60} +251.217i q^{61} +191.016i q^{62} +(132.551 + 5.13038i) q^{63} +569.367 q^{64} +918.046 q^{65} +(-9.67736 + 500.246i) q^{66} -442.198i q^{67} +49.2865i q^{68} +(-13.7819 + 712.418i) q^{69} +222.662i q^{70} +639.306i q^{71} +(-655.316 - 25.3639i) q^{72} -36.1944i q^{73} +386.267i q^{74} +(-19.7151 + 1019.12i) q^{75} +73.1249 q^{76} -187.065 q^{77} +(673.032 + 13.0199i) q^{78} -485.902 q^{79} -870.774i q^{80} +(726.819 + 56.3473i) q^{81} +690.068i q^{82} -1376.64 q^{83} +(0.792260 - 40.9538i) q^{84} +550.485 q^{85} +923.025i q^{86} +(-65.1984 - 1.26128i) q^{87} +924.825 q^{88} +1250.69 q^{89} +(-47.3267 + 1222.76i) q^{90} +251.677i q^{91} +220.030 q^{92} +(-392.404 - 7.59114i) q^{93} -1089.58 q^{94} -816.736i q^{95} +(-7.17931 + 371.116i) q^{96} -1687.28i q^{97} +806.380 q^{98} +(-1027.27 - 39.7605i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q - 8 q^{3} + 268 q^{4} - 16 q^{7} - 4 q^{9}+O(q^{10}) $ 52 * q - 8 * q^3 + 268 * q^4 - 16 * q^7 - 4 * q^9	$ 52 q - 8 q^{3} + 268 q^{4} - 16 q^{7} - 4 q^{9} + 28 q^{12} + 114 q^{15} + 484 q^{16} - 184 q^{19} - 758 q^{21} - 60 q^{22} + 36 q^{25} + 742 q^{27} - 4 q^{28} - 888 q^{36} + 1402 q^{45} - 660 q^{46} - 488 q^{48} - 924 q^{49} - 1772 q^{51} - 630 q^{57} - 1880 q^{60} - 212 q^{63} + 7648 q^{64} + 1316 q^{66} - 1556 q^{75} - 5680 q^{76} + 3224 q^{78} - 1504 q^{79} - 276 q^{81} + 1228 q^{84} - 848 q^{85} + 3598 q^{87} + 5760 q^{88} + 888 q^{94}+O(q^{100}) $ 52 * q - 8 * q^3 + 268 * q^4 - 16 * q^7 - 4 * q^9 + 28 * q^12 + 114 * q^15 + 484 * q^16 - 184 * q^19 - 758 * q^21 - 60 * q^22 + 36 * q^25 + 742 * q^27 - 4 * q^28 - 888 * q^36 + 1402 * q^45 - 660 * q^46 - 488 * q^48 - 924 * q^49 - 1772 * q^51 - 630 * q^57 - 1880 * q^60 - 212 * q^63 + 7648 * q^64 + 1316 * q^66 - 1556 * q^75 - 5680 * q^76 + 3224 * q^78 - 1504 * q^79 - 276 * q^81 + 1228 * q^84 - 848 * q^85 + 3598 * q^87 + 5760 * q^88 + 888 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/177\mathbb{Z}\right)^\times$.

$n$	$61$	$119$
$\chi(n)$	$-1$	$-1$

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 $

$2$	−2.52893			−0.894110			−0.447055	−	0.894506i	$-0.647527\pi$
$2$	−2.52893			−0.894110			−0.447055	+	0.894506i	$0.647527\pi$
$3$	0.100502	−	5.19518i	0.0193416	−	0.999813i
$3$	0.100502	−	5.19518i	0.0193416	−	0.999813i
$4$	−1.60453			−0.200567
$5$			17.9211i			1.60291i	0.598052	+	0.801457i	$0.295942\pi$
$5$			17.9211i			1.60291i	−0.598052	+	0.801457i	$0.704058\pi$
$6$	−0.254162	+	13.1382i	−0.0172935	+	0.893943i
$7$	−4.91298			−0.265276			−0.132638	−	0.991165i	$-0.542345\pi$
$7$	−4.91298			−0.265276			−0.132638	+	0.991165i	$0.542345\pi$
$8$	24.2892			1.07344
$9$	−26.9798	−	1.04425i	−0.999252	−	0.0386759i
$10$		−	45.3212i		−	1.43318i
$11$	38.0756			1.04366			0.521829	−	0.853050i	$-0.325250\pi$
$11$	38.0756			1.04366			0.521829	+	0.853050i	$0.325250\pi$
$12$	−0.161258	+	8.33584i	−0.00387927	+	0.200529i
$13$		−	51.2270i		−	1.09291i	−0.837489	−	0.546454i	$-0.815977\pi$
$13$		−	51.2270i		−	1.09291i	0.837489	−	0.546454i	$-0.184023\pi$
$14$	12.4246			0.237186
$15$	93.1035	+	1.80111i	1.60261	+	0.0310029i
$16$	−48.5892			−0.759206
$17$		−	30.7171i		−	0.438234i	−0.975699	−	0.219117i	$-0.929682\pi$
$17$		−	30.7171i		−	0.438234i	0.975699	−	0.219117i	$-0.0703177\pi$
$18$	68.2299	+	2.64083i	0.893441	+	0.0345805i
$19$	−45.5739			−0.550283			−0.275141	−	0.961404i	$-0.588725\pi$
$19$	−45.5739			−0.550283			−0.275141	+	0.961404i	$0.588725\pi$
$20$		−	28.7550i		−	0.321491i
$21$	−0.493764	+	25.5238i	−0.00513086	+	0.265227i
$22$	−96.2904			−0.933145
$23$	−137.131			−1.24320			−0.621602	−	0.783333i	$-0.713518\pi$
$23$	−137.131			−1.24320			−0.621602	+	0.783333i	$0.713518\pi$
$24$	2.44110	−	126.187i	0.0207620	−	1.07324i
$25$	−196.167			−1.56934
$26$			129.549i			0.977181i
$27$	−8.13658	+	140.060i	−0.0579958	+	0.998317i
$28$	7.88305			0.0532056
$29$		−	12.5498i		−	0.0803598i	−0.999192	−	0.0401799i	$-0.987207\pi$
$29$		−	12.5498i		−	0.0803598i	0.999192	−	0.0401799i	$-0.0127931\pi$
$30$	−235.452	−	4.55486i	−1.43291	−	0.0277200i
$31$		−	75.5324i		−	0.437614i	−0.975768	−	0.218807i	$-0.929784\pi$
$31$		−	75.5324i		−	0.437614i	0.975768	−	0.218807i	$-0.0702164\pi$
$32$	−71.4347			−0.394625
$33$	3.82667	−	197.810i	0.0201860	−	1.04346i
$34$			77.6812i			0.391830i
$35$		−	88.0462i		−	0.425215i
$36$	43.2900	+	1.67553i	0.200417	+	0.00775710i
$37$		−	152.739i		−	0.678654i	−0.940668	−	0.339327i	$-0.889801\pi$
$37$		−	152.739i		−	0.678654i	0.940668	−	0.339327i	$-0.110199\pi$
$38$	115.253			0.492014
$39$	−266.133	−	5.14840i	−1.09270	−	0.0211386i
$40$			435.289i			1.72063i
$41$		−	272.870i		−	1.03939i	−0.854351	−	0.519697i	$-0.826045\pi$
$41$		−	272.870i		−	1.03939i	0.854351	−	0.519697i	$-0.173955\pi$
$42$	1.24869	−	64.5479i	0.00458756	−	0.237142i
$43$		−	364.987i		−	1.29442i	−0.762313	−	0.647209i	$-0.775936\pi$
$43$		−	364.987i		−	1.29442i	0.762313	−	0.647209i	$-0.224064\pi$
$44$	−61.0936			−0.209323
$45$	18.7141	−	483.509i	0.0619942	−	1.60172i
$46$	346.793			1.11156
$47$	430.845			1.33713			0.668567	−	0.743652i	$-0.266908\pi$
$47$	430.845			1.33713			0.668567	+	0.743652i	$0.266908\pi$
$48$	−4.88330	+	252.430i	−0.0146842	+	0.759064i
$49$	−318.863			−0.929629
$50$	496.092			1.40316
$51$	−159.581	−	3.08712i	−0.438152	−	0.00847614i
$52$			82.1954i			0.219201i
$53$		−	660.497i		−	1.71181i	−0.517129	−	0.855907i	$-0.672999\pi$
$53$		−	660.497i		−	1.71181i	0.517129	−	0.855907i	$-0.327001\pi$
$54$	20.5768	−	354.201i	0.0518546	−	0.892605i
$55$			682.358i			1.67289i
$56$	−119.332			−0.284758
$57$	−4.58026	+	236.765i	−0.0106433	+	0.550180i
$58$			31.7375i			0.0718506i
$59$	−351.582	−	285.954i	−0.775797	−	0.630983i
$59$	−351.582	−	285.954i	−0.775797	−	0.630983i
$60$	−149.388	−	2.88993i	−0.321431	−	0.00621815i
$61$			251.217i			0.527295i	0.964619	+	0.263648i	$0.0849256\pi$
$61$			251.217i			0.527295i	−0.964619	+	0.263648i	$0.915074\pi$
$62$			191.016i			0.391275i
$63$	132.551	+	5.13038i	0.265078	+	0.0102598i
$64$	569.367			1.11204
$65$	918.046			1.75184
$66$	−9.67736	+	500.246i	−0.0180485	+	0.932971i
$67$		−	442.198i		−	0.806314i	−0.915131	−	0.403157i	$-0.867913\pi$
$67$		−	442.198i		−	0.806314i	0.915131	−	0.403157i	$-0.132087\pi$
$68$			49.2865i			0.0878952i
$69$	−13.7819	+	712.418i	−0.0240455	+	1.24297i
$70$			222.662i			0.380189i
$71$			639.306i			1.06862i	0.845290	+	0.534308i	$0.179428\pi$
$71$			639.306i			1.06862i	−0.845290	+	0.534308i	$0.820572\pi$
$72$	−655.316	−	25.3639i	−1.07264	−	0.0415162i
$73$		−	36.1944i		−	0.0580305i	−0.999579	−	0.0290153i	$-0.990763\pi$
$73$		−	36.1944i		−	0.0580305i	0.999579	−	0.0290153i	$-0.00923714\pi$
$74$			386.267i			0.606792i
$75$	−19.7151	+	1019.12i	−0.0303534	+	1.56904i
$76$	73.1249			0.110368
$77$	−187.065			−0.276858
$78$	673.032	+	13.0199i	0.976998	+	0.0189002i
$79$	−485.902			−0.692003			−0.346001	−	0.938234i	$-0.612461\pi$
$79$	−485.902			−0.692003			−0.346001	+	0.938234i	$0.612461\pi$
$80$		−	870.774i		−	1.21694i
$81$	726.819	+	56.3473i	0.997008	+	0.0772939i
$82$			690.068i			0.929332i
$83$	−1376.64			−1.82056			−0.910278	−	0.413998i	$-0.864132\pi$
$83$	−1376.64			−1.82056			−0.910278	+	0.413998i	$0.864132\pi$
$84$	0.792260	−	40.9538i	0.00102908	−	0.0531956i
$85$	550.485			0.702452
$86$			923.025i			1.15735i
$87$	−65.1984	−	1.26128i	−0.0803448	−	0.00155429i
$88$	924.825			1.12030
$89$	1250.69			1.48959			0.744793	−	0.667295i	$-0.232548\pi$
$89$	1250.69			1.48959			0.744793	+	0.667295i	$0.232548\pi$
$90$	−47.3267	+	1222.76i	−0.0554296	+	1.43211i
$91$			251.677i			0.289923i
$92$	220.030			0.249345
$93$	−392.404	−	7.59114i	−0.437532	−	0.00846414i
$94$	−1089.58			−1.19554
$95$		−	816.736i		−	0.882056i
$96$	−7.17931	+	371.116i	−0.00763266	+	0.394551i
$97$		−	1687.28i		−	1.76616i	−0.469220	−	0.883081i	$-0.655465\pi$
$97$		−	1687.28i		−	1.76616i	0.469220	−	0.883081i	$-0.344535\pi$
$98$	806.380			0.831191
$99$	−1027.27	−	39.7605i	−1.04288	−	0.0403644i
$100$	314.756			0.314756
$101$	916.279			0.902704			0.451352	−	0.892346i	$-0.350942\pi$
$101$	916.279			0.902704			0.451352	+	0.892346i	$0.350942\pi$
$102$	403.568	+	7.80710i	0.391757	+	0.00757860i
$103$		−	178.532i		−	0.170789i	−0.996347	−	0.0853946i	$-0.972785\pi$
$103$		−	178.532i		−	0.170789i	0.996347	−	0.0853946i	$-0.0272151\pi$
$104$		−	1244.26i		−	1.17317i
$105$	−457.416	−	8.84880i	−0.425136	−	0.00822433i
$106$			1670.35i			1.53055i
$107$			1657.49i			1.49753i	0.662834	+	0.748766i	$0.269354\pi$
$107$			1657.49i			1.49753i	−0.662834	+	0.748766i	$0.730646\pi$
$108$	13.0554	−	224.731i	0.0116320	−	0.200229i
$109$		−	116.077i		−	0.102002i	−0.998699	−	0.0510009i	$-0.983759\pi$
$109$		−	116.077i		−	0.102002i	0.998699	−	0.0510009i	$-0.0162411\pi$
$110$		−	1725.63i		−	1.49575i
$111$	−793.509	−	15.3506i	−0.678527	−	0.0131262i
$112$	238.718			0.201399
$113$	1038.47			0.864522			0.432261	−	0.901749i	$-0.357716\pi$
$113$	1038.47			0.864522			0.432261	+	0.901749i	$0.357716\pi$
$114$	11.5831	−	598.761i	0.00951632	−	0.491922i
$115$		−	2457.53i		−	1.99275i
$116$			20.1365i			0.0161175i
$117$	−53.4938	+	1382.09i	−0.0422692	+	1.09209i
$118$	889.124	+	723.155i	0.693648	+	0.564168i
$119$			150.912i			0.116253i
$120$	2261.41	+	43.7473i	1.72031	+	0.0332797i
$121$	118.753			0.0892212
$122$		−	635.309i		−	0.471460i
$123$	−1417.61	−	27.4239i	−1.03920	−	0.0201035i
$124$			121.194i			0.0877707i
$125$		−	1275.39i		−	0.912596i
$126$	−335.213	−	12.9744i	−0.237009	−	0.00917339i
$127$	1213.40			0.847813			0.423906	−	0.905706i	$-0.360659\pi$
$127$	1213.40			0.847813			0.423906	+	0.905706i	$0.360659\pi$
$128$	−868.409			−0.599666
$129$	−1896.17	−	36.6818i	−1.29418	−	0.0250361i
$130$	−2321.67			−1.56634
$131$	−2467.88			−1.64595			−0.822975	−	0.568077i	$-0.807687\pi$
$131$	−2467.88			−1.64595			−0.822975	+	0.568077i	$0.807687\pi$
$132$	−6.14001	+	317.392i	−0.00404863	+	0.209284i
$133$	223.904			0.145977
$134$			1118.29i			0.720934i
$135$	−2510.03	−	145.817i	−1.60022	−	0.0929623i
$136$		−	746.091i		−	0.470418i
$137$			653.589i			0.407590i	0.979014	+	0.203795i	$0.0653276\pi$
$137$			653.589i			0.407590i	−0.979014	+	0.203795i	$0.934672\pi$
$138$	34.8533	−	1801.65i	0.0214994	−	1.11135i
$139$	−706.567			−0.431153			−0.215576	−	0.976487i	$-0.569163\pi$
$139$	−706.567			−0.431153			−0.215576	+	0.976487i	$0.569163\pi$
$140$			141.273i			0.0852840i
$141$	43.3007	−	2238.32i	0.0258623	−	1.33688i
$142$		−	1616.76i		−	0.955460i
$143$		−	1950.50i		−	1.14062i
$144$	1310.93	+	50.7393i	0.758638	+	0.0293630i
$145$	224.906			0.128810
$146$			91.5329i			0.0518857i
$147$	−32.0463	+	1656.55i	−0.0179805	+	0.929455i
$148$			245.075i			0.136115i
$149$	−1113.52			−0.612235			−0.306118	−	0.951994i	$-0.599030\pi$
$149$	−1113.52			−0.612235			−0.306118	+	0.951994i	$0.599030\pi$
$150$	49.8581	−	2577.29i	0.0271393	−	1.40290i
$151$		−	1135.35i		−	0.611879i	−0.952051	−	0.305939i	$-0.901029\pi$
$151$		−	1135.35i		−	0.611879i	0.952051	−	0.305939i	$-0.0989705\pi$
$152$	−1106.95			−0.590695
$153$	−32.0763	+	828.740i	−0.0169491	+	0.437906i
$154$	473.074			0.247541
$155$	1353.63			0.701457
$156$	427.020	+	8.26078i	0.219160	+	0.00423969i
$157$			1602.61i			0.814665i	0.913280	+	0.407332i	$0.133541\pi$
$157$			1602.61i			0.814665i	−0.913280	+	0.407332i	$0.866459\pi$
$158$	1228.81			0.618727
$159$	−3431.40	−	66.3811i	−1.71149	−	0.0331092i
$160$		−	1280.19i		−	0.632550i
$161$	673.720			0.329793
$162$	−1838.07	−	142.498i	−0.891436	−	0.0691093i
$163$	867.586			0.416899			0.208450	−	0.978033i	$-0.433158\pi$
$163$	867.586			0.416899			0.208450	+	0.978033i	$0.433158\pi$
$164$			437.829i			0.208468i
$165$	3544.97	+	68.5782i	1.67258	+	0.0323564i
$166$	3481.43			1.62778
$167$			3842.95i			1.78070i	0.455277	+	0.890350i	$0.349540\pi$
$167$			3842.95i			1.78070i	−0.455277	+	0.890350i	$0.650460\pi$
$168$	−11.9931	+	619.953i	−0.00550767	+	0.284705i
$169$	−427.204			−0.194449
$170$	−1392.13			−0.628070
$171$	1229.58	+	47.5905i	0.549871	+	0.0212827i
$172$			585.633i			0.259617i
$173$	2410.10			1.05917			0.529586	−	0.848256i	$-0.322347\pi$
$173$	2410.10			1.05917			0.529586	+	0.848256i	$0.322347\pi$
$174$	164.882	+	3.18967i	0.0718371	+	0.00138970i
$175$	963.765			0.416307
$176$	−1850.06			−0.792352
$177$	−1520.91	+	1797.79i	−0.645870	+	0.763448i
$178$	−3162.91			−1.33185
$179$	1229.32			0.513318			0.256659	−	0.966502i	$-0.417378\pi$
$179$	1229.32			0.513318			0.256659	+	0.966502i	$0.417378\pi$
$180$	−30.0274	+	775.805i	−0.0124340	+	0.321251i
$181$	−2553.60			−1.04866			−0.524329	−	0.851516i	$-0.675684\pi$
$181$	−2553.60			−1.04866			−0.524329	+	0.851516i	$0.675684\pi$
$182$		−	636.474i		−	0.259223i
$183$	1305.12	+	25.2477i	0.527197	+	0.0101987i
$184$	−3330.78			−1.33450
$185$	2737.26			1.08782
$186$	992.362	+	19.1974i	0.391202	+	0.00756787i
$187$		−	1169.57i		−	0.457367i
$188$	−691.306			−0.268184
$189$	39.9749	−	688.113i	0.0153849	−	0.264830i
$190$			2065.47i			0.788656i
$191$	−3086.92			−1.16943			−0.584716	−	0.811238i	$-0.698794\pi$
$191$	−3086.92			−1.16943			−0.584716	+	0.811238i	$0.698794\pi$
$192$	57.2224	−	2957.96i	0.0215087	−	1.11184i
$193$	−4387.11			−1.63622			−0.818111	−	0.575060i	$-0.804979\pi$
$193$	−4387.11			−1.63622			−0.818111	+	0.575060i	$0.804979\pi$
$194$			4267.02i			1.57914i
$195$	92.2652	−	4769.41i	0.0338833	−	1.75151i
$196$	511.626			0.186452
$197$		−	1321.27i		−	0.477852i	−0.971038	−	0.238926i	$-0.923205\pi$
$197$		−	1321.27i		−	0.477852i	0.971038	−	0.238926i	$-0.0767953\pi$
$198$	2597.90	+	100.551i	0.932447	+	0.0360902i
$199$	2247.81			0.800718			0.400359	−	0.916358i	$-0.368885\pi$
$199$	2247.81			0.800718			0.400359	+	0.916358i	$0.368885\pi$
$200$	−4764.73			−1.68459
$201$	−2297.30	−	44.4416i	−0.806163	−	0.0155954i
$202$	−2317.20			−0.807117
$203$			61.6569i			0.0213176i
$204$	256.052	+	4.95338i	0.0878787	+	0.00170003i
$205$	4890.14			1.66606
$206$			451.494i			0.152704i
$207$	3699.75	+	143.199i	1.24227	+	0.0480820i
$208$			2489.08i			0.829743i
$209$	−1735.26			−0.574307
$210$	1156.77	+	22.3780i	0.380118	+	0.00735346i
$211$		−	238.261i		−	0.0777372i	−0.999244	−	0.0388686i	$-0.987625\pi$
$211$		−	238.261i		−	0.0777372i	0.999244	−	0.0388686i	$-0.0123754\pi$
$212$			1059.79i			0.343333i
$213$	3321.31	+	64.2514i	1.06842	+	0.0206687i
$214$		−	4191.68i		−	1.33896i
$215$	6540.98			2.07484
$216$	−197.631	+	3401.94i	−0.0622549	+	1.07163i
$217$			371.090i			0.116088i
$218$			293.551i			0.0912008i
$219$	−188.036	−	3.63760i	−0.0580197	−	0.00112240i
$220$		−	1094.87i		−	0.335527i
$221$	−1573.54			−0.478950
$222$	2006.72	+	38.8205i	0.606678	+	0.0117363i
$223$	2110.45			0.633750			0.316875	−	0.948467i	$-0.397366\pi$
$223$	2110.45			0.633750			0.316875	+	0.948467i	$0.397366\pi$
$224$	350.958			0.104685
$225$	5292.54	+	204.847i	1.56816	+	0.0606955i
$226$	−2626.21			−0.772978
$227$	2633.15			0.769904			0.384952	−	0.922937i	$-0.374218\pi$
$227$	2633.15			0.769904			0.384952	+	0.922937i	$0.374218\pi$
$228$	7.34918	−	379.897i	0.00213470	−	0.110348i
$229$		−	811.669i		−	0.234221i	−0.993119	−	0.117110i	$-0.962637\pi$
$229$		−	811.669i		−	0.234221i	0.993119	−	0.117110i	$-0.0373631\pi$
$230$			6214.92i			1.78174i
$231$	−18.8004	+	971.836i	−0.00535486	+	0.276806i
$232$		−	304.824i		−	0.0862614i
$233$	−4623.35			−1.29994			−0.649970	−	0.759960i	$-0.725219\pi$
$233$	−4623.35			−1.29994			−0.649970	+	0.759960i	$0.725219\pi$
$234$	135.282	−	3495.21i	0.0377934	−	0.976450i
$235$			7721.24i			2.14331i
$236$	564.124	+	458.822i	0.155599	+	0.126554i
$237$	−48.8340	+	2524.35i	−0.0133844	+	0.691873i
$238$		−	381.646i		−	0.103943i
$239$		−	4107.24i		−	1.11161i	−0.831312	−	0.555806i	$-0.812410\pi$
$239$		−	4107.24i		−	1.11161i	0.831312	−	0.555806i	$-0.187590\pi$
$240$	−4523.83	−	87.5143i	−1.21672	−	0.0235376i
$241$	−1369.49			−0.366045			−0.183023	−	0.983109i	$-0.558588\pi$
$241$	−1369.49			−0.366045			−0.183023	+	0.983109i	$0.558588\pi$
$242$	−300.319			−0.0797736
$243$	365.781	−	3770.29i	0.0965632	−	0.995327i
$244$		−	403.086i		−	0.105758i
$245$		−	5714.38i		−	1.49012i
$246$	3585.03	+	69.3530i	0.929159	+	0.0179748i
$247$			2334.61i			0.601409i
$248$		−	1834.62i		−	0.469752i
$249$	−138.355	+	7151.91i	−0.0352124	+	1.82022i
$250$			3225.37i			0.815962i
$251$			581.170i			0.146148i	0.997327	+	0.0730740i	$0.0232809\pi$
$251$			581.170i			0.146148i	−0.997327	+	0.0730740i	$0.976719\pi$
$252$	−212.683	−	8.23187i	−0.0531658	−	0.00205777i
$253$	−5221.33			−1.29748
$254$	−3068.61			−0.758038
$255$	55.3247	−	2859.87i	0.0135865	−	0.702321i
$256$	−2358.79			−0.575877
$257$		−	1366.48i		−	0.331667i	−0.986154	−	0.165834i	$-0.946969\pi$
$257$		−	1366.48i		−	0.331667i	0.986154	−	0.165834i	$-0.0530315\pi$
$258$	4795.28	+	92.7656i	1.15714	+	0.0223850i
$259$			750.406i			0.180031i
$260$	−1473.03			−0.351360
$261$	−13.1051	+	338.591i	−0.00310799	+	0.0802997i
$262$	6241.08			1.47166
$263$		−	3753.52i		−	0.880046i	−0.897986	−	0.440023i	$-0.854970\pi$
$263$		−	3753.52i		−	0.880046i	0.897986	−	0.440023i	$-0.145030\pi$
$264$	92.9465	−	4804.63i	0.0216684	−	1.12009i
$265$	11836.8			2.74389
$266$	−566.237			−0.130520
$267$	125.697	−	6497.58i	0.0288110	−	1.48931i
$268$			709.521i			0.161720i
$269$	−2795.74			−0.633678			−0.316839	−	0.948479i	$-0.602621\pi$
$269$	−2795.74			−0.633678			−0.316839	+	0.948479i	$0.602621\pi$
$270$	6347.69	+	368.760i	1.43077	+	0.0831185i
$271$	−8440.91			−1.89206			−0.946031	−	0.324076i	$-0.894946\pi$
$271$	−8440.91			−1.89206			−0.946031	+	0.324076i	$0.894946\pi$
$272$			1492.52i			0.332710i
$273$	1307.51	+	25.2940i	0.289868	+	0.00560756i
$274$		−	1652.88i		−	0.364431i
$275$	−7469.18			−1.63785
$276$	22.1135	−	1143.10i	0.00482273	−	0.249299i
$277$	2260.98			0.490430			0.245215	−	0.969469i	$-0.421141\pi$
$277$	2260.98			0.490430			0.245215	+	0.969469i	$0.421141\pi$
$278$	1786.86			0.385498
$279$	−78.8747	+	2037.85i	−0.0169251	+	0.437286i
$280$		−	2138.57i		−	0.456443i
$281$			6580.58i			1.39703i	0.715597	+	0.698513i	$0.246155\pi$
$281$			6580.58i			1.39703i	−0.715597	+	0.698513i	$0.753845\pi$
$282$	−109.504	+	5660.54i	−0.0231237	+	1.19532i
$283$			5314.23i			1.11625i	0.829758	+	0.558124i	$0.188479\pi$
$283$			5314.23i			1.11625i	−0.829758	+	0.558124i	$0.811521\pi$
$284$		−	1025.79i		−	0.214329i
$285$	−4243.09	−	82.0834i	−0.881891	−	0.0170604i
$286$			4932.67i			1.01984i
$287$			1340.61i			0.275726i
$288$	1927.29	+	74.5957i	0.394330	+	0.0152625i
$289$	3969.46			0.807951
$290$	−568.771			−0.115170
$291$	−8765.74	−	169.575i	−1.76583	−	0.0341604i
$292$			58.0750i			0.0116390i
$293$			3526.60i			0.703161i	0.936158	+	0.351580i	$0.114356\pi$
$293$			3526.60i			0.703161i	−0.936158	+	0.351580i	$0.885644\pi$
$294$	81.0426	−	4189.29i	0.0160765	−	0.831035i
$295$	5124.61	−	6300.74i	1.01141	−	1.24354i
$296$		−	3709.91i		−	0.728494i
$297$	−309.805	+	5332.87i	−0.0605277	+	1.04190i
$298$	2816.01			0.547406
$299$			7024.78i			1.35871i
$300$	31.6336	−	1635.22i	0.00608788	−	0.314697i
$301$			1793.17i			0.343378i
$302$			2871.22i			0.547087i
$303$	92.0876	−	4760.23i	0.0174597	−	0.902535i
$304$	2214.40			0.417778
$305$	−4502.09			−0.845209
$306$	81.1185	−	2095.82i	0.0151544	−	0.391537i
$307$	−6528.33			−1.21365			−0.606827	−	0.794834i	$-0.707558\pi$
$307$	−6528.33			−1.21365			−0.606827	+	0.794834i	$0.707558\pi$
$308$	300.152			0.0555284
$309$	−927.506	−	17.9428i	−0.170757	−	0.00330333i
$310$	−3423.22			−0.627180
$311$		−	4105.29i		−	0.748519i	−0.927324	−	0.374260i	$-0.877897\pi$
$311$		−	4105.29i		−	0.748519i	0.927324	−	0.374260i	$-0.122103\pi$
$312$	−6464.16	−	125.050i	−1.17295	−	0.0226910i
$313$			5568.41i			1.00558i	0.864410	+	0.502788i	$0.167692\pi$
$313$			5568.41i			1.00558i	−0.864410	+	0.502788i	$0.832308\pi$
$314$		−	4052.89i		−	0.728400i
$315$	−91.9423	+	2375.47i	−0.0164456	+	0.424897i
$316$	779.645			0.138793
$317$			6372.94i			1.12915i	0.825382	+	0.564574i	$0.190960\pi$
$317$			6372.94i			1.12915i	−0.825382	+	0.564574i	$0.809040\pi$
$318$	8677.75	+	167.873i	1.53027	+	0.0296033i
$319$		−	477.841i		−	0.0838682i
$320$			10203.7i			1.78251i
$321$	8610.98	+	166.581i	1.49725	+	0.0289646i
$322$	−1703.79			−0.294871
$323$			1399.90i			0.241153i
$324$	−1166.21	−	90.4111i	−0.199967	−	0.0155026i
$325$			10049.0i			1.71514i
$326$	−2194.06			−0.372754
$327$	−603.042	−	11.6660i	−0.101983	−	0.00197287i
$328$		−	6627.78i		−	1.11573i
$329$	−2116.74			−0.354710
$330$	−8964.98	−	173.429i	−1.49547	−	0.0289302i
$331$	7783.40			1.29249			0.646246	−	0.763129i	$-0.276338\pi$
$331$	7783.40			1.29249			0.646246	+	0.763129i	$0.276338\pi$
$332$	2208.87			0.365143
$333$	−159.498	+	4120.88i	−0.0262476	+	0.678146i
$334$		−	9718.55i		−	1.59214i
$335$	7924.68			1.29245
$336$	23.9916	−	1240.18i	0.00389538	−	0.201362i
$337$		−	607.505i		−	0.0981986i	−0.998794	−	0.0490993i	$-0.984365\pi$
$337$		−	607.505i		−	0.0981986i	0.998794	−	0.0490993i	$-0.0156351\pi$
$338$	1080.37			0.173859
$339$	104.368	−	5395.04i	0.0167212	−	0.864360i
$340$	−883.271			−0.140888
$341$		−	2875.94i		−	0.456719i
$342$	−3109.50	−	120.353i	−0.491646	−	0.0190291i
$343$	3251.72			0.511885
$344$		−	8865.22i		−	1.38948i
$345$	−12767.3	−	246.987i	−1.99238	−	0.0385429i
$346$	−6094.97			−0.947017
$347$	8204.92			1.26935			0.634673	−	0.772780i	$-0.281135\pi$
$347$	8204.92			1.26935			0.634673	+	0.772780i	$0.281135\pi$
$348$	104.613	+	2.02376i	0.0161145	+	0.000311738i
$349$		−	12249.4i		−	1.87878i	−0.342854	−	0.939389i	$-0.611394\pi$
$349$		−	12249.4i		−	1.87878i	0.342854	−	0.939389i	$-0.388606\pi$
$350$	−2437.29			−0.372225
$351$	7174.85	+	416.813i	1.09107	+	0.0633841i
$352$	−2719.92			−0.411853
$353$	10546.0			1.59010			0.795051	−	0.606542i	$-0.207444\pi$
$353$	10546.0			1.59010			0.795051	+	0.606542i	$0.207444\pi$
$354$	3846.28	−	4546.48i	0.577479	−	0.682606i
$355$	−11457.1			−1.71290
$356$	−2006.78			−0.298761
$357$	784.017	+	15.1670i	0.116231	+	0.00224852i
$358$	−3108.87			−0.458963
$359$		−	4715.89i		−	0.693301i	−0.937994	−	0.346651i	$-0.887319\pi$
$359$		−	4715.89i		−	0.693301i	0.937994	−	0.346651i	$-0.112681\pi$
$360$	454.550	−	11744.0i	0.0665470	−	1.71934i
$361$	−4782.02			−0.697189
$362$	6457.85			0.937617
$363$	11.9349	−	616.946i	0.00172568	−	0.0892045i
$364$		−	403.825i		−	0.0581488i
$365$	648.644			0.0930180
$366$	−3300.54	−	63.8496i	−0.471372	−	0.00911878i
$367$		−	3339.88i		−	0.475042i	−0.971382	−	0.237521i	$-0.923665\pi$
$367$		−	3339.88i		−	0.475042i	0.971382	−	0.237521i	$-0.0763348\pi$
$368$	6663.06			0.943848
$369$	−284.944	+	7361.98i	−0.0401995	+	1.03862i
$370$	−6922.33			−0.972635
$371$			3245.01i			0.454104i
$372$	629.626	+	12.1802i	0.0877543	+	0.00169762i
$373$	8644.93			1.20005			0.600023	−	0.799982i	$-0.295158\pi$
$373$	8644.93			1.20005			0.600023	+	0.799982i	$0.295158\pi$
$374$			2957.76i			0.408936i
$375$	−6625.89	−	128.179i	−0.912425	−	0.0176510i
$376$	10464.9			1.43533
$377$	−642.887			−0.0878260
$378$	−101.094	+	1740.19i	−0.0137558	+	0.236787i
$379$	−10504.2			−1.42365			−0.711825	−	0.702356i	$-0.752131\pi$
$379$	−10504.2			−1.42365			−0.711825	+	0.702356i	$0.752131\pi$
$380$			1310.48i			0.176911i
$381$	121.949	−	6303.85i	0.0163980	−	0.847654i
$382$	7806.59			1.04560
$383$		−	3695.29i		−	0.493004i	−0.969142	−	0.246502i	$-0.920719\pi$
$383$		−	3695.29i		−	0.493004i	0.969142	−	0.246502i	$-0.0792812\pi$
$384$	−87.2766	+	4511.54i	−0.0115985	+	0.599554i
$385$		−	3352.42i		−	0.443779i
$386$	11094.7			1.46296
$387$	−381.137	+	9847.27i	−0.0500628	+	1.29345i
$388$			2707.30i			0.354233i
$389$		−	12641.4i		−	1.64767i	−0.566832	−	0.823833i	$-0.691831\pi$
$389$		−	12641.4i		−	1.64767i	0.566832	−	0.823833i	$-0.308169\pi$
$390$	−233.332	+	12061.5i	−0.0302954	+	1.56604i
$391$			4212.25i			0.544815i
$392$	−7744.90			−0.997900
$393$	−248.026	+	12821.1i	−0.0318353	+	1.64564i
$394$			3341.40i			0.427252i
$395$		−	8707.91i		−	1.10922i
$396$	1648.29	+	63.7970i	0.209166	+	0.00809575i
$397$		−	13140.9i		−	1.66127i	−0.556821	−	0.830633i	$-0.687979\pi$
$397$		−	13140.9i		−	1.66127i	0.556821	−	0.830633i	$-0.312021\pi$
$398$	−5684.54			−0.715931
$399$	22.5027	−	1163.22i	0.00282342	−	0.145950i
$400$	9531.60			1.19145
$401$	−4936.62			−0.614770			−0.307385	−	0.951585i	$-0.599454\pi$
$401$	−4936.62			−0.614770			−0.307385	+	0.951585i	$0.599454\pi$
$402$	5809.69	+	112.390i	0.720799	+	0.0139440i
$403$	−3869.30			−0.478272
$404$	−1470.20			−0.181052
$405$	−1009.81	+	13025.4i	−0.123896	+	1.59812i
$406$		−	155.926i		−	0.0190603i
$407$		−	5815.65i		−	0.708282i
$408$	−3876.08	−	74.9835i	−0.470330	−	0.00909862i
$409$		−	5911.21i		−	0.714647i	−0.933981	−	0.357323i	$-0.883689\pi$
$409$		−	5911.21i		−	0.714647i	0.933981	−	0.357323i	$-0.116311\pi$
$410$	−12366.8			−1.48964
$411$	3395.51	+	65.6868i	0.407514	+	0.00788344i
$412$			286.460i			0.0342546i
$413$	1727.31	+	1404.89i	0.205800	+	0.167385i
$414$	−9356.40	−	362.138i	−1.11073	−	0.0429907i
$415$		−	24671.0i		−	2.91820i
$416$			3659.39i			0.431289i
$417$	−71.0113	+	3670.74i	−0.00833918	+	0.431072i
$418$	4388.33			0.513494
$419$	−14149.6			−1.64976			−0.824882	−	0.565304i	$-0.808759\pi$
$419$	−14149.6			−1.64976			−0.824882	+	0.565304i	$0.808759\pi$
$420$	733.939	+	14.1982i	0.0852680	+	0.00164953i
$421$			4735.46i			0.548200i	0.961701	+	0.274100i	$0.0883799\pi$
$421$			4735.46i			0.548200i	−0.961701	+	0.274100i	$0.911620\pi$
$422$			602.544i			0.0695057i
$423$	−11624.1	−	449.910i	−1.33613	−	0.0517148i
$424$		−	16042.9i		−	1.83753i
$425$			6025.67i			0.687737i
$426$	−8399.35	−	162.487i	−0.955281	−	0.0184801i
$427$		−	1234.22i		−	0.139879i
$428$		−	2659.50i		−	0.300355i
$429$	−10133.2	−	196.029i	−1.14041	−	0.0220614i
$430$	−16541.6			−1.85514
$431$	10921.4			1.22057			0.610287	−	0.792180i	$-0.291054\pi$
$431$	10921.4			1.22057			0.610287	+	0.792180i	$0.291054\pi$
$432$	395.350	−	6805.40i	0.0440308	−	0.757929i
$433$	1855.12			0.205893			0.102946	−	0.994687i	$-0.467173\pi$
$433$	1855.12			0.205893			0.102946	+	0.994687i	$0.467173\pi$
$434$		−	938.458i		−	0.103796i
$435$	22.6035	−	1168.43i	0.00249139	−	0.128786i
$436$			186.250i			0.0204581i
$437$	6249.58			0.684114
$438$	475.530	+	9.19921i	0.0518760	+	0.00100355i
$439$	9335.14			1.01490			0.507451	−	0.861681i	$-0.330588\pi$
$439$	9335.14			1.01490			0.507451	+	0.861681i	$0.330588\pi$
$440$			16573.9i			1.79575i
$441$	8602.85	+	332.972i	0.928933	+	0.0359542i
$442$	3979.37			0.428234
$443$	−2399.08			−0.257300			−0.128650	−	0.991690i	$-0.541064\pi$
$443$	−2399.08			−0.257300			−0.128650	+	0.991690i	$0.541064\pi$
$444$	1273.21	+	24.6305i	0.136090	+	0.00263268i
$445$			22413.8i			2.38768i
$446$	−5337.17			−0.566642
$447$	−111.911	+	5784.94i	−0.0118416	+	0.612121i
$448$	−2797.29			−0.294999
$449$		−	8641.91i		−	0.908323i	−0.890919	−	0.454162i	$-0.849939\pi$
$449$		−	8641.91i		−	0.908323i	0.890919	−	0.454162i	$-0.150061\pi$
$450$	−13384.5	−	518.044i	−1.40211	−	0.0542685i
$451$		−	10389.7i		−	1.08477i
$452$	−1666.26			−0.173394
$453$	−5898.36	−	114.105i	−0.611764	−	0.0118347i
$454$	−6659.04			−0.688379
$455$	−4510.34			−0.464721
$456$	−111.251	+	5750.82i	−0.0114250	+	0.590585i
$457$			14348.7i			1.46872i	0.678762	+	0.734359i	$0.262517\pi$
$457$			14348.7i			1.46872i	−0.678762	+	0.734359i	$0.737483\pi$
$458$			2052.65i			0.209419i
$459$	4302.23	+	249.932i	0.437497	+	0.0254157i
$460$			3943.19i			0.399679i
$461$		−	8909.98i		−	0.900172i	−0.892985	−	0.450086i	$-0.851393\pi$
$461$		−	8909.98i		−	0.900172i	0.892985	−	0.450086i	$-0.148607\pi$
$462$	47.5447	−	2457.70i	0.00478784	−	0.247495i
$463$			13537.1i			1.35880i	0.733769	+	0.679400i	$0.237760\pi$
$463$			13537.1i			1.35880i	−0.733769	+	0.679400i	$0.762240\pi$
$464$			609.784i			0.0610097i
$465$	136.042	−	7032.33i	0.0135673	−	0.701326i
$466$	11692.1			1.16229
$467$	10252.9			1.01595			0.507976	−	0.861371i	$-0.330394\pi$
$467$	10252.9			1.01595			0.507976	+	0.861371i	$0.330394\pi$
$468$	85.8325	−	2217.62i	0.00847780	−	0.219037i
$469$			2172.51i			0.213896i
$470$		−	19526.4i		−	1.91636i
$471$	8325.86	+	161.065i	0.814512	+	0.0157569i
$472$	−8539.62	−	6945.57i	−0.832771	−	0.677322i
$473$		−	13897.1i		−	1.35093i
$474$	123.498	−	6383.89i	0.0119671	−	0.618611i
$475$	8940.10			0.863578
$476$		−	242.144i		−	0.0233165i
$477$	−689.723	+	17820.1i	−0.0662060	+	1.71053i
$478$			10386.9i			0.993905i
$479$			9800.56i			0.934862i	0.884029	+	0.467431i	$0.154820\pi$
$479$			9800.56i			0.934862i	−0.884029	+	0.467431i	$0.845180\pi$
$480$	−6650.82	−	128.661i	−0.632431	−	0.0122345i
$481$	−7824.38			−0.741707
$482$	3463.35			0.327285
$483$	67.7101	−	3500.10i	0.00637871	−	0.329731i
$484$	−190.544			−0.0178948
$485$	30238.0			2.83101
$486$	−925.033	+	9534.79i	−0.0863382	+	0.889932i
$487$	−1932.83			−0.179846			−0.0899229	−	0.995949i	$-0.528662\pi$
$487$	−1932.83			−0.179846			−0.0899229	+	0.995949i	$0.528662\pi$
$488$			6101.84i			0.566019i
$489$	87.1939	−	4507.26i	0.00806349	−	0.416821i
$490$			14451.2i			1.33233i
$491$			10380.0i			0.954061i	0.878887	+	0.477031i	$0.158287\pi$
$491$			10380.0i			0.954061i	−0.878887	+	0.477031i	$0.841713\pi$
$492$	2274.60	+	44.0026i	0.208429	+	0.00403209i
$493$	−385.492			−0.0352164
$494$		−	5904.07i		−	0.537726i
$495$	712.552	−	18409.9i	0.0647007	−	1.67164i
$496$			3670.06i			0.332239i
$497$		−	3140.90i		−	0.283478i
$498$	349.890	−	18086.6i	0.0314838	−	1.62747i
$499$	−8109.16			−0.727487			−0.363743	−	0.931499i	$-0.618501\pi$
$499$	−8109.16			−0.727487			−0.363743	+	0.931499i	$0.618501\pi$
$500$			2046.41i			0.183036i
$501$	19964.8	+	386.224i	1.78037	+	0.0344415i
$502$		−	1469.74i		−	0.130672i
$503$	−3825.79			−0.339132			−0.169566	−	0.985519i	$-0.554237\pi$
$503$	−3825.79			−0.339132			−0.169566	+	0.985519i	$0.554237\pi$
$504$	3219.56	+	124.613i	0.284545	+	0.0110133i
$505$			16420.8i			1.44696i
$506$	13204.4			1.16009
$507$	−42.9348	+	2219.40i	−0.00376095	+	0.194413i
$508$	−1946.95			−0.170043
$509$	19008.0			1.65524			0.827618	−	0.561291i	$-0.189695\pi$
$509$	19008.0			1.65524			0.827618	+	0.561291i	$0.189695\pi$
$510$	−139.912	+	7232.39i	−0.0121479	+	0.627952i
$511$			177.822i			0.0153941i
$512$	12912.5			1.11456
$513$	370.816	−	6383.08i	0.0319141	−	0.549357i
$514$			3455.72i			0.296547i
$515$	3199.50			0.273760
$516$	3042.47	+	58.8572i	0.259568	+	0.00502140i
$517$	16404.7			1.39551
$518$		−	1897.72i		−	0.160967i
$519$	242.220	−	12520.9i	0.0204861	−	1.05897i
$520$	22298.5			1.88049
$521$			18365.1i			1.54432i	0.635428	+	0.772160i	$0.280824\pi$
$521$			18365.1i			1.54432i	−0.635428	+	0.772160i	$0.719176\pi$
$522$	33.1418	−	856.270i	0.00277889	−	0.0717968i
$523$	13117.1			1.09669			0.548346	−	0.836252i	$-0.315258\pi$
$523$	13117.1			1.09669			0.548346	+	0.836252i	$0.315258\pi$
$524$	3959.79			0.330123
$525$	96.8601	−	5006.93i	0.00805204	−	0.416230i
$526$			9492.38i			0.786858i
$527$	−2320.13			−0.191777
$528$	−185.935	+	9611.42i	−0.0153253	+	0.792203i
$529$	6637.78			0.545556
$530$	−29934.5			−2.45334
$531$	9186.99	+	8082.11i	0.750813	+	0.660515i
$532$	−359.261			−0.0292781
$533$	−13978.3			−1.13596
$534$	−317.878	+	16431.9i	−0.0257602	+	1.33161i
$535$	−29704.2			−2.40042
$536$		−	10740.6i		−	0.865529i
$537$	123.549	−	6386.55i	0.00992838	−	0.513222i
$538$	7070.22			0.566578
$539$	−12140.9			−0.970214
$540$	4027.43	+	233.968i	0.320950	+	0.0186451i
$541$		−	1040.15i		−	0.0826605i	−0.999146	−	0.0413303i	$-0.986840\pi$
$541$		−	1040.15i		−	0.0826605i	0.999146	−	0.0413303i	$-0.0131596\pi$
$542$	21346.4			1.69171
$543$	−256.641	+	13266.4i	−0.0202827	+	1.04846i
$544$			2194.26i			0.172938i
$545$	2080.24			0.163500
$546$	−3306.60	−	63.9667i	−0.259174	−	0.00501378i
$547$	270.011			0.0211057			0.0105529	−	0.999944i	$-0.496641\pi$
$547$	270.011			0.0211057			0.0105529	+	0.999944i	$0.496641\pi$
$548$		−	1048.70i		−	0.0817490i
$549$	262.333	−	6777.78i	0.0203936	−	0.526901i
$550$	18889.0			1.46442
$551$			571.943i			0.0442206i
$552$	−334.750	+	17304.0i	−0.0258114	+	1.33425i
$553$	2387.23			0.183572
$554$	−5717.86			−0.438499
$555$	275.100	−	14220.6i	0.0210402	−	1.08762i
$556$	1133.71			0.0864749
$557$		−	19341.3i		−	1.47130i	−0.677359	−	0.735652i	$-0.736876\pi$
$557$		−	19341.3i		−	1.47130i	0.677359	−	0.735652i	$-0.263124\pi$
$558$	199.468	−	5153.57i	0.0151329	−	0.390982i
$559$	−18697.2			−1.41468
$560$			4278.10i			0.322826i
$561$	−6076.14	−	117.544i	−0.457281	−	0.00884619i
$562$		−	16641.8i		−	1.24910i
$563$	−24978.5			−1.86983			−0.934917	−	0.354866i	$-0.884527\pi$
$563$	−24978.5			−1.86983			−0.934917	+	0.354866i	$0.884527\pi$
$564$	−69.4774	+	3591.46i	−0.00518711	+	0.268134i
$565$			18610.5i			1.38576i
$566$		−	13439.3i		−	0.998048i
$567$	−3570.85	−	276.833i	−0.264483	−	0.0205042i
$568$			15528.2i			1.14709i
$569$	−3828.07			−0.282041			−0.141020	−	0.990007i	$-0.545038\pi$
$569$	−3828.07			−0.282041			−0.141020	+	0.990007i	$0.545038\pi$
$570$	10730.5	+	207.583i	0.788508	+	0.0152538i
$571$			19204.9i			1.40753i	0.710432	+	0.703765i	$0.248499\pi$
$571$			19204.9i			1.40753i	−0.710432	+	0.703765i	$0.751501\pi$
$572$			3129.64i			0.228771i
$573$	−310.241	+	16037.1i	−0.0226187	+	1.16921i
$574$		−	3390.29i		−	0.246530i
$575$	26900.5			1.95100
$576$	−15361.4	−	594.561i	−1.11121	−	0.0430093i
$577$	−12909.8			−0.931445			−0.465723	−	0.884931i	$-0.654206\pi$
$577$	−12909.8			−0.931445			−0.465723	+	0.884931i	$0.654206\pi$
$578$	−10038.5			−0.722397
$579$	−440.912	+	22791.8i	−0.0316471	+	1.63592i
$580$	−360.869			−0.0258350
$581$	6763.42			0.482950
$582$	22167.9	+	428.843i	1.57885	+	0.0305431i
$583$		−	25148.8i		−	1.78655i
$584$		−	879.130i		−	0.0622923i
$585$	−24768.7	−	958.669i	−1.75053	−	0.0677540i
$586$		−	8918.51i		−	0.628703i
$587$	4715.16			0.331543			0.165771	−	0.986164i	$-0.446989\pi$
$587$	4715.16			0.331543			0.165771	+	0.986164i	$0.446989\pi$
$588$	51.4193	−	2657.99i	0.00360628	−	0.186418i
$589$			3442.31i			0.240811i
$590$	−12959.8	+	15934.1i	−0.904313	+	1.11186i
$591$	−6864.25	−	132.790i	−0.477763	−	0.00924241i
$592$			7421.48i			0.515238i
$593$			15022.0i			1.04027i	0.854084	+	0.520135i	$0.174118\pi$
$593$			15022.0i			1.04027i	−0.854084	+	0.520135i	$0.825882\pi$
$594$	783.475	−	13486.4i	0.0541185	−	0.931574i
$595$	−2704.52			−0.186344
$596$	1786.68			0.122794
$597$	225.909	−	11677.8i	0.0154872	−	0.800569i
$598$		−	17765.2i		−	1.21484i
$599$			20568.7i			1.40303i	0.712655	+	0.701515i	$0.247493\pi$
$599$			20568.7i			1.40303i	−0.712655	+	0.701515i	$0.752507\pi$
$600$	−478.864	+	24753.6i	−0.0325825	+	1.68427i
$601$		−	12269.7i		−	0.832764i	−0.909190	−	0.416382i	$-0.863298\pi$
$601$		−	12269.7i		−	0.832764i	0.909190	−	0.416382i	$-0.136702\pi$
$602$		−	4534.81i		−	0.307018i
$603$	−461.765	+	11930.4i	−0.0311849	+	0.805711i
$604$			1821.71i			0.122722i
$605$			2128.20i			0.143014i
$606$	−232.883	+	12038.3i	−0.0156109	+	0.806966i
$607$	−11719.7			−0.783673			−0.391837	−	0.920035i	$-0.628160\pi$
$607$	−11719.7			−0.783673			−0.391837	+	0.920035i	$0.628160\pi$
$608$	3255.56			0.217155
$609$	320.319	+	6.19662i	0.0213136	+	0.000412315i
$610$	11385.4			0.755710
$611$		−	22070.9i		−	1.46136i
$612$	51.4675	−	1329.74i	0.00339943	−	0.0878294i
$613$			331.561i			0.0218460i	0.999940	+	0.0109230i	$0.00347697\pi$
$613$			331.561i			0.0218460i	−0.999940	+	0.0109230i	$0.996523\pi$
$614$	16509.7			1.08514
$615$	491.467	−	25405.1i	0.0322242	−	1.66575i
$616$	−4543.65			−0.297190
$617$			22795.3i			1.48736i	0.668533	+	0.743682i	$0.266923\pi$
$617$			22795.3i			1.48736i	−0.668533	+	0.743682i	$0.733077\pi$
$618$	2345.59	+	45.3760i	0.152676	+	0.00295354i
$619$	−14271.8			−0.926708			−0.463354	−	0.886173i	$-0.653354\pi$
$619$	−14271.8			−0.926708			−0.463354	+	0.886173i	$0.653354\pi$
$620$	−2171.94			−0.140689
$621$	1115.77	−	19206.5i	0.0721006	−	1.24111i
$622$			10382.0i			0.669259i
$623$	−6144.64			−0.395152
$624$	12931.2	+	250.157i	0.829588	+	0.0160485i
$625$	−1664.40			−0.106522
$626$		−	14082.1i		−	0.899096i
$627$	−174.396	+	9014.97i	−0.0111080	+	0.574199i
$628$		−	2571.44i		−	0.163395i
$629$	−4691.70			−0.297409
$630$	232.515	−	6007.39i	0.0147042	−	0.379905i
$631$	−5033.55			−0.317563			−0.158782	−	0.987314i	$-0.550757\pi$
$631$	−5033.55			−0.317563			−0.158782	+	0.987314i	$0.550757\pi$
$632$	−11802.1			−0.742823
$633$	−1237.81	−	23.9456i	−0.0777227	−	0.00150356i
$634$		−	16116.7i		−	1.00958i
$635$			21745.6i			1.35897i
$636$	5505.79	+	106.511i	0.343269	+	0.00664060i
$637$			16334.4i			1.01600i
$638$			1208.42i			0.0749874i
$639$	667.595	−	17248.4i	0.0413297	−	1.06782i
$640$		−	15562.9i		−	0.961213i
$641$		−	15611.3i		−	0.961948i	−0.876735	−	0.480974i	$-0.840283\pi$
$641$		−	15611.3i		−	0.961948i	0.876735	−	0.480974i	$-0.159717\pi$
$642$	−21776.5	−	421.271i	−1.33871	−	0.0258976i
$643$	23418.0			1.43626			0.718130	−	0.695909i	$-0.244998\pi$
$643$	23418.0			1.43626			0.718130	+	0.695909i	$0.244998\pi$
$644$	−1081.01			−0.0661454
$645$	657.380	−	33981.6i	0.0401307	−	2.07445i
$646$		−	3540.24i		−	0.215617i
$647$		−	17281.7i		−	1.05010i	−0.851072	−	0.525048i	$-0.824047\pi$
$647$		−	17281.7i		−	1.05010i	0.851072	−	0.525048i	$-0.175953\pi$
$648$	17653.8	+	1368.63i	1.07023	+	0.0829703i
$649$	−13386.7	−	10887.9i	−0.809666	−	0.658530i
$650$		−	25413.3i		−	1.53352i
$651$	1927.88	+	37.2952i	0.116067	+	0.00224533i
$652$	−1392.07			−0.0836161
$653$			2766.26i			0.165777i	0.996559	+	0.0828884i	$0.0264145\pi$
$653$			2766.26i			0.165777i	−0.996559	+	0.0828884i	$0.973585\pi$
$654$	1525.05	+	29.5024i	0.0911837	+	0.00176397i
$655$		−	44227.2i		−	2.63832i
$656$			13258.5i			0.789114i
$657$	−37.7959	+	976.517i	−0.00224438	+	0.0579871i
$658$	5353.07			0.317150
$659$	14505.0			0.857412			0.428706	−	0.903444i	$-0.358970\pi$
$659$	14505.0			0.857412			0.428706	+	0.903444i	$0.358970\pi$
$660$	−5688.03	−	110.036i	−0.335464	−	0.00648961i
$661$	2069.11			0.121754			0.0608769	−	0.998145i	$-0.480610\pi$
$661$	2069.11			0.121754			0.0608769	+	0.998145i	$0.480610\pi$
$662$	−19683.7			−1.15563
$663$	−158.144	+	8174.84i	−0.00926365	+	0.478860i
$664$	−33437.5			−1.95426
$665$			4012.61i			0.233989i
$666$	403.359	−	10421.4i	0.0234682	−	0.606338i
$667$			1720.96i			0.0999037i
$668$		−	6166.15i		−	0.357149i
$669$	212.104	−	10964.2i	0.0122577	−	0.633631i
$670$	−20040.9			−1.15560
$671$			9565.24i			0.550316i
$672$	35.2719	−	1823.29i	0.00202476	−	0.104665i
$673$		−	19658.6i		−	1.12598i	−0.826465	−	0.562988i	$-0.809652\pi$
$673$		−	19658.6i		−	1.12598i	0.826465	−	0.562988i	$-0.190348\pi$
$674$			1536.34i			0.0878004i
$675$	1596.13	−	27475.1i	0.0910148	−	1.56669i
$676$	685.464			0.0390000
$677$		−	6768.57i		−	0.384250i	−0.981370	−	0.192125i	$-0.938462\pi$
$677$		−	6768.57i		−	0.384250i	0.981370	−	0.192125i	$-0.0615379\pi$
$678$	−263.939	+	13643.6i	−0.0149506	+	0.772834i
$679$			8289.60i			0.468521i
$680$	13370.8			0.754040
$681$	264.636	−	13679.7i	0.0148912	−	0.769760i
$682$			7273.05i			0.408357i
$683$	−27264.9			−1.52747			−0.763734	−	0.645531i	$-0.776636\pi$
$683$	−27264.9			−1.52747			−0.763734	+	0.645531i	$0.776636\pi$
$684$	−1972.89	−	76.3606i	−0.110286	−	0.00426860i
$685$	−11713.1			−0.653332
$686$	−8223.36			−0.457681
$687$	−4216.76	−	81.5741i	−0.234177	−	0.00453020i
$688$			17734.4i			0.982730i
$689$	−33835.3			−1.87086
$690$	32287.6	+	624.611i	1.78141	+	0.0344616i
$691$			5793.00i			0.318923i	0.987204	+	0.159462i	$0.0509758\pi$
$691$			5793.00i			0.318923i	−0.987204	+	0.159462i	$0.949024\pi$
$692$	−3867.09			−0.212435
$693$	5046.98	+	195.343i	0.276650	+	0.0107077i
$694$	−20749.6			−1.13494
$695$		−	12662.5i		−	0.691101i
$696$	−1583.61	−	30.6353i	−0.0862453	−	0.00166843i
$697$	−8381.76			−0.455498
$698$			30977.7i			1.67983i
$699$	−464.655	+	24019.2i	−0.0251429	+	1.29970i
$700$	−1546.39			−0.0834974
$701$	1161.05			0.0625565			0.0312783	−	0.999511i	$-0.490042\pi$
$701$	1161.05			0.0625565			0.0312783	+	0.999511i	$0.490042\pi$
$702$	−18144.7	−	1054.09i	−0.975536	−	0.0566724i
$703$			6960.93i			0.373452i
$704$	21679.0			1.16059
$705$	40113.2	+	775.998i	2.14291	+	0.0414550i
$706$	−26670.0			−1.42173
$707$	−4501.66			−0.239466
$708$	2440.36	−	2884.61i	0.129540	−	0.153122i
$709$	2589.53			0.137167			0.0685837	−	0.997645i	$-0.478152\pi$
$709$	2589.53			0.137167			0.0685837	+	0.997645i	$0.478152\pi$
$710$	28974.1			1.53152
$711$	13109.5	+	507.403i	0.691485	+	0.0267638i
$712$	30378.3			1.59898
$713$			10357.8i			0.544043i
$714$	−1982.72	−	38.3561i	−0.103924	−	0.00201042i
$715$	34955.2			1.82832
$716$	−1972.49			−0.102954
$717$	−21337.9	−	412.785i	−1.11141	−	0.0215003i
$718$			11926.1i			0.619888i
$719$	−25261.8			−1.31030			−0.655152	−	0.755497i	$-0.727395\pi$
$719$	−25261.8			−1.31030			−0.655152	+	0.755497i	$0.727395\pi$
$720$	−909.305	+	23493.3i	−0.0470664	+	1.21603i
$721$			877.125i			0.0453063i
$722$	12093.4			0.623364
$723$	−137.637	+	7114.77i	−0.00707989	+	0.365977i
$724$	4097.33			0.210326
$725$			2461.85i			0.126112i
$726$	−30.1826	+	1560.21i	−0.00154295	+	0.0797587i
$727$	−6751.37			−0.344422			−0.172211	−	0.985060i	$-0.555091\pi$
$727$	−6751.37			−0.344422			−0.172211	+	0.985060i	$0.555091\pi$
$728$			6113.03i			0.311214i
$729$	−19550.6	−	2279.22i	−0.993273	−	0.115796i
$730$	−1640.37			−0.0831684
$731$	−11211.3			−0.567258
$732$	−2094.10	−	40.5108i	−0.105738	−	0.00204552i
$733$	5684.58			0.286446			0.143223	−	0.989690i	$-0.454253\pi$
$733$	5684.58			0.286446			0.143223	+	0.989690i	$0.454253\pi$
$734$			8446.31i			0.424740i
$735$	−29687.2	−	574.305i	−1.48984	−	0.0288212i
$736$	9795.88			0.490599
$737$		−	16837.0i		−	0.841516i
$738$	720.603	−	18617.9i	0.0359428	−	0.928637i
$739$		−	22799.0i		−	1.13488i	−0.823416	−	0.567438i	$-0.807935\pi$
$739$		−	22799.0i		−	1.13488i	0.823416	−	0.567438i	$-0.192065\pi$
$740$	−4392.03			−0.218181
$741$	12128.7	+	234.633i	0.601296	+	0.0116322i
$742$		−	8206.39i		−	0.406019i
$743$		−	4680.60i		−	0.231110i	−0.993301	−	0.115555i	$-0.963135\pi$
$743$		−	4680.60i		−	0.231110i	0.993301	−	0.115555i	$-0.0368646\pi$
$744$	−9531.17	−	184.382i	−0.469664	−	0.00908573i
$745$		−	19955.5i		−	0.981361i
$746$	−21862.4			−1.07297
$747$	37141.5	+	1437.56i	1.81919	+	0.0704117i
$748$			1876.62i			0.0917325i
$749$		−	8143.24i		−	0.397260i
$750$	16756.4	+	324.156i	0.815809	+	0.0157820i
$751$		−	24749.5i		−	1.20256i	−0.799039	−	0.601279i	$-0.794658\pi$
$751$		−	24749.5i		−	1.20256i	0.799039	−	0.601279i	$-0.205342\pi$
$752$	−20934.4			−1.01516
$753$	3019.28	+	58.4086i	0.146121	+	0.00282673i
$754$	1625.81			0.0785261
$755$	20346.8			0.980790
$756$	−64.1411	+	1104.10i	−0.00308570	+	0.0531160i
$757$	24788.0			1.19014			0.595069	−	0.803675i	$-0.297125\pi$
$757$	24788.0			1.19014			0.595069	+	0.803675i	$0.297125\pi$
$758$	26564.3			1.27290
$759$	−524.753	+	27125.8i	−0.0250953	+	1.29724i
$760$		−	19837.8i		−	0.946834i
$761$			21981.9i			1.04710i	0.851995	+	0.523549i	$0.175392\pi$
$761$			21981.9i			1.04710i	−0.851995	+	0.523549i	$0.824608\pi$
$762$	−308.401	+	15942.0i	−0.0146616	+	0.757896i
$763$			570.286i			0.0270586i
$764$	4953.06			0.234549
$765$	−14852.0	−	574.843i	−0.701927	−	0.0271680i
$766$			9345.12i			0.440800i
$767$	−14648.5	+	18010.5i	−0.689606	+	0.847875i
$768$	−237.063	+	12254.4i	−0.0111384	+	0.575769i
$769$		−	33444.5i		−	1.56832i	−0.620556	−	0.784162i	$-0.713093\pi$
$769$		−	33444.5i		−	1.56832i	0.620556	−	0.784162i	$-0.286907\pi$
$770$			8478.01i			0.396787i
$771$	−7099.09	−	137.333i	−0.331605	−	0.00641497i
$772$	7039.26			0.328172
$773$	25499.6			1.18649			0.593246	−	0.805021i	$-0.297846\pi$
$773$	25499.6			1.18649			0.593246	+	0.805021i	$0.297846\pi$
$774$	963.868	−	24903.0i	0.0447617	−	1.15649i
$775$			14817.0i			0.686762i
$776$		−	40982.7i		−	1.89587i
$777$	3898.50	+	75.4171i	0.179997	+	0.00348208i
$778$			31969.1i			1.47320i
$779$			12435.8i			0.571960i
$780$	−148.043	+	7652.68i	−0.00679586	+	0.351295i
$781$			24342.0i			1.11527i
$782$		−	10652.5i		−	0.487124i
$783$	1757.72	+	102.112i	0.0802246	+	0.00466053i
$784$	15493.3			0.705780
$785$	−28720.6			−1.30584
$786$	627.240	−	32423.5i	0.0284642	−	1.47139i
$787$	37441.0			1.69584			0.847922	−	0.530121i	$-0.177854\pi$
$787$	37441.0			1.69584			0.847922	+	0.530121i	$0.177854\pi$
$788$			2120.03i			0.0958412i
$789$	−19500.2	−	377.236i	−0.879882	−	0.0170215i
$790$			22021.7i			0.991766i
$791$	−5101.98			−0.229337
$792$	−24951.6	−	965.748i	−1.11946	−	0.0433287i
$793$	12869.1			0.576285
$794$			33232.3i			1.48535i
$795$	1189.62	−	61494.6i	0.0530712	−	2.74338i
$796$	−3606.68			−0.160597
$797$	−8316.21			−0.369605			−0.184803	−	0.982776i	$-0.559165\pi$
$797$	−8316.21			−0.369605			−0.184803	+	0.982776i	$0.559165\pi$
$798$	−56.9078	+	2941.70i	−0.00252445	+	0.130495i
$799$		−	13234.3i		−	0.585978i
$800$	14013.1			0.619299
$801$	−33743.5	−	1306.04i	−1.48847	−	0.0576111i
$802$	12484.3			0.549673
$803$		−	1378.12i		−	0.0605640i
$804$	3686.09	+	71.3081i	0.161689	+	0.00312791i
$805$			12073.8i			0.528629i
$806$	9785.17			0.427628
$807$	−280.977	+	14524.4i	−0.0122563	+	0.633559i
$808$	22255.6			0.968998
$809$	−6961.54			−0.302540			−0.151270	−	0.988493i	$-0.548336\pi$
$809$	−6961.54			−0.302540			−0.151270	+	0.988493i	$0.548336\pi$
$810$	2553.73	−	32940.3i	0.110776	−	1.42890i
$811$			34293.9i			1.48486i	0.669924	+	0.742430i	$0.266327\pi$
$811$			34293.9i			1.48486i	−0.669924	+	0.742430i	$0.733673\pi$
$812$		−	98.9305i		−	0.00427559i
$813$	−848.326	+	43852.0i	−0.0365955	+	1.89171i
$814$			14707.3i			0.633283i
$815$			15548.1i			0.668254i
$816$	7753.90	+	150.001i	0.332648	+	0.00643514i
$817$			16633.9i			0.712296i
$818$			14949.0i			0.638973i
$819$	262.814	−	6790.21i	0.0112130	−	0.289706i
$820$	−7846.39			−0.334156
$821$	23025.8			0.978812			0.489406	−	0.872056i	$-0.337214\pi$
$821$	23025.8			0.978812			0.489406	+	0.872056i	$0.337214\pi$
$822$	−8587.00	−	166.117i	−0.364363	−	0.00704866i
$823$		−	8497.80i		−	0.359921i	−0.983674	−	0.179960i	$-0.942403\pi$
$823$		−	8497.80i		−	0.359921i	0.983674	−	0.179960i	$-0.0575970\pi$
$824$		−	4336.39i		−	0.183332i
$825$	−750.666	+	38803.7i	−0.0316786	+	1.63754i
$826$	−4368.25	−	3552.85i	−0.184008	−	0.149660i
$827$		−	26223.3i		−	1.10263i	−0.834298	−	0.551314i	$-0.814127\pi$
$827$		−	26223.3i		−	1.10263i	0.834298	−	0.551314i	$-0.185873\pi$
$828$	−5936.38	−	229.767i	−0.249159	−	0.00964365i
$829$	16393.2			0.686801			0.343400	−	0.939189i	$-0.388421\pi$
$829$	16393.2			0.686801			0.343400	+	0.939189i	$0.388421\pi$
$830$			62391.1i			2.60919i
$831$	227.233	−	11746.2i	0.00948570	−	0.490339i
$832$		−	29166.9i		−	1.21536i
$833$			9794.52i			0.407395i
$834$	179.582	−	9283.04i	0.00745614	−	0.385426i
$835$	−68870.1			−2.85431
$836$	2784.28			0.115187
$837$	10579.1	+	614.576i	0.436877	+	0.0253797i
$838$	35783.2			1.47507
$839$	−7868.35			−0.323773			−0.161886	−	0.986809i	$-0.551758\pi$
$839$	−7868.35			−0.323773			−0.161886	+	0.986809i	$0.551758\pi$
$840$	−11110.3	−	214.930i	−0.456357	−	0.00882832i
$841$	24231.5			0.993542
$842$		−	11975.6i		−	0.490151i
$843$	34187.3	+	661.360i	1.39676	+	0.0270207i
$844$			382.298i			0.0155915i
$845$		−	7655.99i		−	0.311685i
$846$	29396.5	+	1137.79i	1.19465	+	0.0462388i
$847$	−583.434			−0.0236683
$848$			32093.0i			1.29962i
$849$	27608.4	+	534.089i	1.11604	+	0.0215900i
$850$		−	15238.5i		−	0.614912i
$851$			20945.2i			0.843705i
$852$	−5329.15	−	103.094i	−0.214289	−	0.00414545i
$853$	5741.45			0.230461			0.115231	−	0.993339i	$-0.463239\pi$
$853$	5741.45			0.230461			0.115231	+	0.993339i	$0.463239\pi$
$854$			3121.26i			0.125067i
$855$	−852.876	+	22035.4i	−0.0341143	+	0.881397i
$856$			40259.1i			1.60751i
$857$	−11416.1			−0.455039			−0.227519	−	0.973774i	$-0.573062\pi$
$857$	−11416.1			−0.455039			−0.227519	+	0.973774i	$0.573062\pi$
$858$	25626.1	+	495.742i	1.01965	+	0.0197254i
$859$		−	31759.3i		−	1.26148i	−0.775994	−	0.630741i	$-0.782751\pi$
$859$		−	31759.3i		−	1.26148i	0.775994	−	0.630741i	$-0.217249\pi$
$860$	−10495.2			−0.416144
$861$	6964.69	+	134.733i	0.275675	+	0.00533298i
$862$	−27619.5			−1.09133
$863$	−30393.6			−1.19885			−0.599426	−	0.800430i	$-0.704604\pi$
$863$	−30393.6			−1.19885			−0.599426	+	0.800430i	$0.704604\pi$
$864$	581.234	−	10005.1i	0.0228866	−	0.393961i
$865$			43191.8i			1.69776i
$866$	−4691.47			−0.184091
$867$	398.938	−	20622.1i	0.0156270	−	0.807800i
$868$		−	595.425i		−	0.0232835i
$869$	−18501.0			−0.722214
$870$	−57.1625	+	2954.87i	−0.00222758	+	0.115149i
$871$	−22652.5			−0.881227
$872$		−	2819.42i		−	0.109493i
$873$	−1761.95	+	45522.6i	−0.0683079	+	1.76484i
$874$	−15804.7			−0.611673
$875$			6265.98i			0.242090i
$876$	301.710	+	5.83665i	0.0116368	+	0.000225116i
$877$	39884.5			1.53569			0.767847	−	0.640634i	$-0.221328\pi$
$877$	39884.5			1.53569			0.767847	+	0.640634i	$0.221328\pi$
$878$	−23607.9			−0.907434
$879$	18321.3	+	354.429i	0.703029	+	0.0136002i
$880$		−	33155.3i		−	1.27007i
$881$	38240.4			1.46237			0.731187	−	0.682178i	$-0.238967\pi$
$881$	38240.4			1.46237			0.731187	+	0.682178i	$0.238967\pi$
$882$	−21756.0	−	842.062i	−0.830569	−	0.0321471i
$883$	39560.2			1.50771			0.753855	−	0.657041i	$-0.228192\pi$
$883$	39560.2			1.50771			0.753855	+	0.657041i	$0.228192\pi$
$884$	2524.80			0.0960614
$885$	−32218.4	−	27256.5i	−1.22374	−	1.03527i
$886$	6067.10			0.230054
$887$	−40841.4			−1.54602			−0.773011	−	0.634393i	$-0.781250\pi$
$887$	−40841.4			−1.54602			−0.773011	+	0.634393i	$0.781250\pi$
$888$	−19273.7	−	372.852i	−0.728357	−	0.0140902i
$889$	−5961.44			−0.224905
$890$		−	56682.9i		−	2.13485i
$891$	27674.1	+	2145.46i	1.04054	+	0.0806684i
$892$	−3386.29			−0.127109
$893$	−19635.3			−0.735801
$894$	283.014	−	14629.7i	0.0105877	−	0.547304i
$895$			22030.9i			0.822805i
$896$	4266.48			0.159077
$897$	36495.0	+	706.003i	1.35845	+	0.0262796i
$898$			21854.8i			0.812141i
$899$	−947.915			−0.0351666
$900$	−8492.06	−	328.684i	−0.314521	−	0.0121735i
$901$	−20288.5			−0.750176
$902$			26274.8i			0.969905i
$903$	9315.87	+	180.217i	0.343314	+	0.00664148i
$904$	25223.5			0.928012
$905$		−	45763.3i		−	1.68091i
$906$	14916.5	+	288.563i	0.546985	+	0.0105815i
$907$	−37591.7			−1.37620			−0.688099	−	0.725617i	$-0.741554\pi$
$907$	−37591.7			−1.37620			−0.688099	+	0.725617i	$0.741554\pi$
$908$	−4224.98			−0.154417
$909$	−24721.0	−	956.824i	−0.902029	−	0.0349129i
$910$	11406.3			0.415512
$911$			34725.7i			1.26291i	0.775411	+	0.631457i	$0.217543\pi$
$911$			34725.7i			1.26291i	−0.775411	+	0.631457i	$0.782457\pi$
$912$	222.551	−	11504.2i	0.00808049	−	0.417700i
$913$	−52416.5			−1.90004
$914$		−	36286.8i		−	1.31320i
$915$	−452.468	+	23389.2i	−0.0163477	+	0.845051i
$916$			1302.35i			0.0469769i
$917$	12124.6			0.436631
$918$	−10880.0	−	632.059i	−0.391170	−	0.0227245i
$919$			12927.0i			0.464007i	0.972715	+	0.232004i	$0.0745281\pi$
$919$			12927.0i			0.464007i	−0.972715	+	0.232004i	$0.925472\pi$
$920$		−	59691.4i		−	2.13910i
$921$	−656.109	+	33915.9i	−0.0234740	+	1.21343i
$922$			22532.7i			0.804853i
$923$	32749.7			1.16790
$924$	30.1658	−	1559.34i	0.00107401	−	0.0555180i
$925$			29962.4i			1.06504i
$926$		−	34234.4i		−	1.21492i
$927$	−186.432	+	4816.76i	−0.00660543	+	0.170661i
$928$			896.490i			0.0317120i
$929$	30295.2			1.06992			0.534958	−	0.844878i	$-0.320327\pi$
$929$	30295.2			1.06992			0.534958	+	0.844878i	$0.320327\pi$
$930$	−344.040	+	17784.2i	−0.0121307	+	0.627063i
$931$	14531.8			0.511559
$932$	7418.32			0.260725
$933$	−21327.7	−	412.589i	−0.748379	−	0.0144775i
$934$	−25928.9			−0.908373
$935$	20960.0			0.733120
$936$	−1299.32	+	33569.9i	−0.0453734	+	1.17229i
$937$		−	45047.4i		−	1.57058i	−0.619128	−	0.785290i	$-0.712514\pi$
$937$		−	45047.4i		−	1.57058i	0.619128	−	0.785290i	$-0.287486\pi$
$938$		−	5494.12i		−	0.191247i
$939$	28928.9	+	559.635i	1.00539	+	0.0194494i
$940$		−	12389.0i		−	0.429877i
$941$	−36531.8			−1.26557			−0.632786	−	0.774327i	$-0.718089\pi$
$941$	−36531.8			−1.26557			−0.632786	+	0.774327i	$0.718089\pi$
$942$	−21055.5	−	407.322i	−0.728264	−	0.0140884i
$943$			37418.8i			1.29218i
$944$	17083.1	+	13894.3i	0.588990	+	0.479046i
$945$	12331.8	+	716.396i	0.424499	+	0.0246607i
$946$			35144.7i			1.20788i
$947$		−	14825.2i		−	0.508715i	−0.967110	−	0.254358i	$-0.918136\pi$
$947$		−	14825.2i		−	0.508715i	0.967110	−	0.254358i	$-0.0818640\pi$
$948$	78.3557	−	4050.40i	0.00268447	−	0.138767i
$949$	−1854.13			−0.0634221
$950$	−22608.8			−0.772134
$951$	33108.6	+	640.492i	1.12894	+	0.0218395i
$952$			3665.54i			0.124791i
$953$		−	32250.8i		−	1.09623i	−0.836403	−	0.548114i	$-0.815346\pi$
$953$		−	32250.8i		−	1.09623i	0.836403	−	0.548114i	$-0.184654\pi$
$954$	1744.26	−	45065.6i	0.0591955	−	1.52941i
$955$		−	55321.1i		−	1.87450i
$956$			6590.21i			0.222952i
$957$	−2482.47	−	48.0238i	−0.0838525	−	0.00162214i
$958$		−	24784.9i		−	0.835870i
$959$		−	3211.07i		−	0.108124i
$960$	53010.0	+	1025.49i	1.78218	+	0.0344766i
$961$	24085.9			0.808494
$962$	19787.3			0.663168
$963$	1730.84	−	44718.9i	0.0579184	−	1.49641i
$964$	2197.40			0.0734165
$965$		−	78621.9i		−	2.62272i
$966$	−171.234	+	8851.49i	−0.00570327	+	0.294816i
$967$		−	51811.0i		−	1.72299i	−0.507767	−	0.861494i	$-0.669529\pi$
$967$		−	51811.0i		−	1.72299i	0.507767	−	0.861494i	$-0.330471\pi$
$968$	2884.42			0.0957736
$969$	7272.72	+	140.692i	0.241108	+	0.00466427i
$970$	−76469.8			−2.53123
$971$			7631.82i			0.252232i	0.992016	+	0.126116i	$0.0402511\pi$
$971$			7631.82i			0.252232i	−0.992016	+	0.126116i	$0.959749\pi$
$972$	−586.908	+	6049.56i	−0.0193674	+	0.199629i
$973$	3471.35			0.114375
$974$	4887.98			0.160802
$975$	52206.6	+	1009.95i	1.71482	+	0.0331735i
$976$		−	12206.4i		−	0.400326i
$977$	50178.4			1.64314			0.821570	−	0.570107i	$-0.193098\pi$
$977$	50178.4			1.64314			0.821570	+	0.570107i	$0.193098\pi$
$978$	−220.507	+	11398.5i	−0.00720965	+	0.372684i
$979$	47620.9			1.55462
$980$			9168.91i			0.298867i
$981$	−121.214	+	3131.74i	−0.00394501	+	0.101925i
$982$		−	26250.3i		−	0.853036i
$983$	−37252.2			−1.20871			−0.604354	−	0.796716i	$-0.706569\pi$
$983$	−37252.2			−1.20871			−0.604354	+	0.796716i	$0.706569\pi$
$984$	−34432.5	−	666.104i	−1.11552	−	0.0215799i
$985$	23678.7			0.765956
$986$	974.882			0.0314874
$987$	−212.736	+	10996.8i	−0.00686064	+	0.354643i
$988$		−	3745.97i		−	0.120623i
$989$			50050.8i			1.60923i
$990$	−1801.99	+	46557.2i	−0.0578496	+	1.49463i
$991$			20189.7i			0.647172i	0.946199	+	0.323586i	$0.104889\pi$
$991$			20189.7i			0.647172i	−0.946199	+	0.323586i	$0.895111\pi$
$992$			5395.64i			0.172693i
$993$	782.246	−	40436.2i	0.0249988	−	1.29225i
$994$			7943.11i			0.253461i
$995$			40283.3i			1.28348i
$996$	221.995	−	11475.5i	0.00706244	−	0.365074i
$997$	−10466.4			−0.332472			−0.166236	−	0.986086i	$-0.553161\pi$
$997$	−10466.4			−0.332472			−0.166236	+	0.986086i	$0.553161\pi$
$998$	20507.5			0.650453
$999$	21392.7	+	1242.78i	0.677512	+	0.0393591i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.4.d.c.176.19	✓	52
3.2	odd	2	inner	177.4.d.c.176.34	yes	52
59.58	odd	2	inner	177.4.d.c.176.33	yes	52
177.176	even	2	inner	177.4.d.c.176.20	yes	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.4.d.c.176.19	✓	52	1.1	even	1	trivial
177.4.d.c.176.20	yes	52	177.176	even	2	inner
177.4.d.c.176.33	yes	52	59.58	odd	2	inner
177.4.d.c.176.34	yes	52	3.2	odd	2	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 177 = 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	177.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.52893 q^{2} +(0.100502 - 5.19518i) q^{3} -1.60453 q^{4} +17.9211i q^{5} +(-0.254162 + 13.1382i) q^{6} -4.91298 q^{7} +24.2892 q^{8} +(-26.9798 - 1.04425i) q^{9} +O(q^{10})\)	\(q-2.52893 q^{2} +(0.100502 - 5.19518i) q^{3} -1.60453 q^{4} +17.9211i q^{5} +(-0.254162 + 13.1382i) q^{6} -4.91298 q^{7} +24.2892 q^{8} +(-26.9798 - 1.04425i) q^{9} -45.3212i q^{10} +38.0756 q^{11} +(-0.161258 + 8.33584i) q^{12} -51.2270i q^{13} +12.4246 q^{14} +(93.1035 + 1.80111i) q^{15} -48.5892 q^{16} -30.7171i q^{17} +(68.2299 + 2.64083i) q^{18} -45.5739 q^{19} -28.7550i q^{20} +(-0.493764 + 25.5238i) q^{21} -96.2904 q^{22} -137.131 q^{23} +(2.44110 - 126.187i) q^{24} -196.167 q^{25} +129.549i q^{26} +(-8.13658 + 140.060i) q^{27} +7.88305 q^{28} -12.5498i q^{29} +(-235.452 - 4.55486i) q^{30} -75.5324i q^{31} -71.4347 q^{32} +(3.82667 - 197.810i) q^{33} +77.6812i q^{34} -88.0462i q^{35} +(43.2900 + 1.67553i) q^{36} -152.739i q^{37} +115.253 q^{38} +(-266.133 - 5.14840i) q^{39} +435.289i q^{40} -272.870i q^{41} +(1.24869 - 64.5479i) q^{42} -364.987i q^{43} -61.0936 q^{44} +(18.7141 - 483.509i) q^{45} +346.793 q^{46} +430.845 q^{47} +(-4.88330 + 252.430i) q^{48} -318.863 q^{49} +496.092 q^{50} +(-159.581 - 3.08712i) q^{51} +82.1954i q^{52} -660.497i q^{53} +(20.5768 - 354.201i) q^{54} +682.358i q^{55} -119.332 q^{56} +(-4.58026 + 236.765i) q^{57} +31.7375i q^{58} +(-351.582 - 285.954i) q^{59} +(-149.388 - 2.88993i) q^{60} +251.217i q^{61} +191.016i q^{62} +(132.551 + 5.13038i) q^{63} +569.367 q^{64} +918.046 q^{65} +(-9.67736 + 500.246i) q^{66} -442.198i q^{67} +49.2865i q^{68} +(-13.7819 + 712.418i) q^{69} +222.662i q^{70} +639.306i q^{71} +(-655.316 - 25.3639i) q^{72} -36.1944i q^{73} +386.267i q^{74} +(-19.7151 + 1019.12i) q^{75} +73.1249 q^{76} -187.065 q^{77} +(673.032 + 13.0199i) q^{78} -485.902 q^{79} -870.774i q^{80} +(726.819 + 56.3473i) q^{81} +690.068i q^{82} -1376.64 q^{83} +(0.792260 - 40.9538i) q^{84} +550.485 q^{85} +923.025i q^{86} +(-65.1984 - 1.26128i) q^{87} +924.825 q^{88} +1250.69 q^{89} +(-47.3267 + 1222.76i) q^{90} +251.677i q^{91} +220.030 q^{92} +(-392.404 - 7.59114i) q^{93} -1089.58 q^{94} -816.736i q^{95} +(-7.17931 + 371.116i) q^{96} -1687.28i q^{97} +806.380 q^{98} +(-1027.27 - 39.7605i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q - 8 q^{3} + 268 q^{4} - 16 q^{7} - 4 q^{9}+O(q^{10}) \) 52 * q - 8 * q^3 + 268 * q^4 - 16 * q^7 - 4 * q^9	\( 52 q - 8 q^{3} + 268 q^{4} - 16 q^{7} - 4 q^{9} + 28 q^{12} + 114 q^{15} + 484 q^{16} - 184 q^{19} - 758 q^{21} - 60 q^{22} + 36 q^{25} + 742 q^{27} - 4 q^{28} - 888 q^{36} + 1402 q^{45} - 660 q^{46} - 488 q^{48} - 924 q^{49} - 1772 q^{51} - 630 q^{57} - 1880 q^{60} - 212 q^{63} + 7648 q^{64} + 1316 q^{66} - 1556 q^{75} - 5680 q^{76} + 3224 q^{78} - 1504 q^{79} - 276 q^{81} + 1228 q^{84} - 848 q^{85} + 3598 q^{87} + 5760 q^{88} + 888 q^{94}+O(q^{100}) \) 52 * q - 8 * q^3 + 268 * q^4 - 16 * q^7 - 4 * q^9 + 28 * q^12 + 114 * q^15 + 484 * q^16 - 184 * q^19 - 758 * q^21 - 60 * q^22 + 36 * q^25 + 742 * q^27 - 4 * q^28 - 888 * q^36 + 1402 * q^45 - 660 * q^46 - 488 * q^48 - 924 * q^49 - 1772 * q^51 - 630 * q^57 - 1880 * q^60 - 212 * q^63 + 7648 * q^64 + 1316 * q^66 - 1556 * q^75 - 5680 * q^76 + 3224 * q^78 - 1504 * q^79 - 276 * q^81 + 1228 * q^84 - 848 * q^85 + 3598 * q^87 + 5760 * q^88 + 888 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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