LMFDB - Embedded newform 177.4.d.c.176.7

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			176.7
Character	$\chi$	$=$	177.176
Dual form			177.4.d.c.176.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.62765 q^{2} +(4.25578 - 2.98133i) q^{3} +13.4152 q^{4} -5.89622i q^{5} +(-19.6943 + 13.7966i) q^{6} +10.0941 q^{7} -25.0596 q^{8} +(9.22335 - 25.3758i) q^{9} +O(q^{10})$	\(q-4.62765 q^{2} +(4.25578 - 2.98133i) q^{3} +13.4152 q^{4} -5.89622i q^{5} +(-19.6943 + 13.7966i) q^{6} +10.0941 q^{7} -25.0596 q^{8} +(9.22335 - 25.3758i) q^{9} +27.2857i q^{10} +53.2996 q^{11} +(57.0921 - 39.9951i) q^{12} -28.7582i q^{13} -46.7120 q^{14} +(-17.5786 - 25.0930i) q^{15} +8.64556 q^{16} +131.636i q^{17} +(-42.6825 + 117.430i) q^{18} +46.0847 q^{19} -79.0989i q^{20} +(42.9583 - 30.0938i) q^{21} -246.652 q^{22} -74.5942 q^{23} +(-106.648 + 74.7108i) q^{24} +90.2346 q^{25} +133.083i q^{26} +(-36.4010 - 135.492i) q^{27} +135.414 q^{28} -76.0280i q^{29} +(81.3476 + 116.122i) q^{30} -6.76067i q^{31} +160.468 q^{32} +(226.832 - 158.904i) q^{33} -609.164i q^{34} -59.5171i q^{35} +(123.733 - 340.420i) q^{36} -329.691i q^{37} -213.264 q^{38} +(-85.7378 - 122.389i) q^{39} +147.757i q^{40} -319.534i q^{41} +(-198.796 + 139.264i) q^{42} +116.364i q^{43} +715.024 q^{44} +(-149.621 - 54.3829i) q^{45} +345.196 q^{46} +301.449 q^{47} +(36.7936 - 25.7753i) q^{48} -241.109 q^{49} -417.574 q^{50} +(392.449 + 560.212i) q^{51} -385.797i q^{52} -314.489i q^{53} +(168.451 + 627.008i) q^{54} -314.266i q^{55} -252.954 q^{56} +(196.126 - 137.394i) q^{57} +351.831i q^{58} +(-118.720 + 437.361i) q^{59} +(-235.820 - 336.627i) q^{60} -559.302i q^{61} +31.2860i q^{62} +(93.1014 - 256.146i) q^{63} -811.754 q^{64} -169.565 q^{65} +(-1049.70 + 735.351i) q^{66} +221.837i q^{67} +1765.91i q^{68} +(-317.456 + 222.390i) q^{69} +275.424i q^{70} -250.765i q^{71} +(-231.133 + 635.906i) q^{72} +450.880i q^{73} +1525.70i q^{74} +(384.019 - 269.019i) q^{75} +618.234 q^{76} +538.012 q^{77} +(396.765 + 566.373i) q^{78} -403.620 q^{79} -50.9761i q^{80} +(-558.860 - 468.099i) q^{81} +1478.69i q^{82} +341.648 q^{83} +(576.293 - 403.714i) q^{84} +776.152 q^{85} -538.491i q^{86} +(-226.665 - 323.559i) q^{87} -1335.67 q^{88} -1523.84 q^{89} +(692.395 + 251.665i) q^{90} -290.289i q^{91} -1000.69 q^{92} +(-20.1558 - 28.7719i) q^{93} -1395.00 q^{94} -271.726i q^{95} +(682.916 - 478.408i) q^{96} +1030.41i q^{97} +1115.77 q^{98} +(491.601 - 1352.52i) 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 $

$2$	−4.62765			−1.63612			−0.818061	−	0.575131i	$-0.804951\pi$
$2$	−4.62765			−1.63612			−0.818061	+	0.575131i	$0.804951\pi$
$3$	4.25578	−	2.98133i	0.819025	−	0.573757i
$3$	4.25578	−	2.98133i	0.819025	−	0.573757i
$4$	13.4152			1.67690
$5$		−	5.89622i		−	0.527374i	−0.964608	−	0.263687i	$-0.915061\pi$
$5$		−	5.89622i		−	0.527374i	0.964608	−	0.263687i	$-0.0849386\pi$
$6$	−19.6943	+	13.7966i	−1.34003	+	0.938737i
$7$	10.0941			0.545030			0.272515	−	0.962152i	$-0.412145\pi$
$7$	10.0941			0.545030			0.272515	+	0.962152i	$0.412145\pi$
$8$	−25.0596			−1.10749
$9$	9.22335	−	25.3758i	0.341605	−	0.939843i
$10$			27.2857i			0.862849i
$11$	53.2996			1.46095			0.730475	−	0.682940i	$-0.239299\pi$
$11$	53.2996			1.46095			0.730475	+	0.682940i	$0.239299\pi$
$12$	57.0921	−	39.9951i	1.37342	−	0.962132i
$13$		−	28.7582i		−	0.613546i	−0.951783	−	0.306773i	$-0.900751\pi$
$13$		−	28.7582i		−	0.613546i	0.951783	−	0.306773i	$-0.0992493\pi$
$14$	−46.7120			−0.891736
$15$	−17.5786	−	25.0930i	−0.302585	−	0.431933i
$16$	8.64556			0.135087
$17$			131.636i			1.87802i	0.343892	+	0.939009i	$0.388254\pi$
$17$			131.636i			1.87802i	−0.343892	+	0.939009i	$0.611746\pi$
$18$	−42.6825	+	117.430i	−0.558908	+	1.53770i
$19$	46.0847			0.556450			0.278225	−	0.960516i	$-0.410254\pi$
$19$	46.0847			0.556450			0.278225	+	0.960516i	$0.410254\pi$
$20$		−	79.0989i		−	0.884352i
$21$	42.9583	−	30.0938i	0.446394	−	0.312715i
$22$	−246.652			−2.39029
$23$	−74.5942			−0.676259			−0.338130	−	0.941100i	$-0.609794\pi$
$23$	−74.5942			−0.676259			−0.338130	+	0.941100i	$0.609794\pi$
$24$	−106.648	+	74.7108i	−0.907060	+	0.635428i
$25$	90.2346			0.721877
$26$			133.083i			1.00384i
$27$	−36.4010	−	135.492i	−0.259458	−	0.965754i
$28$	135.414			0.913960
$29$		−	76.0280i		−	0.486829i	−0.969922	−	0.243415i	$-0.921732\pi$
$29$		−	76.0280i		−	0.486829i	0.969922	−	0.243415i	$-0.0782676\pi$
$30$	81.3476	+	116.122i	0.495066	+	0.706695i
$31$		−	6.76067i		−	0.0391694i	−0.999808	−	0.0195847i	$-0.993766\pi$
$31$		−	6.76067i		−	0.0391694i	0.999808	−	0.0195847i	$-0.00623440\pi$
$32$	160.468			0.886468
$33$	226.832	−	158.904i	1.19655	−	0.838230i
$34$		−	609.164i		−	3.07267i
$35$		−	59.5171i		−	0.287435i
$36$	123.733	−	340.420i	0.572837	−	1.57602i
$37$		−	329.691i		−	1.46489i	−0.680826	−	0.732445i	$-0.738379\pi$
$37$		−	329.691i		−	1.46489i	0.680826	−	0.732445i	$-0.261621\pi$
$38$	−213.264			−0.910421
$39$	−85.7378	−	122.389i	−0.352027	−	0.502510i
$40$			147.757i			0.584060i
$41$		−	319.534i		−	1.21714i	−0.793500	−	0.608571i	$-0.791743\pi$
$41$		−	319.534i		−	1.21714i	0.793500	−	0.608571i	$-0.208257\pi$
$42$	−198.796	+	139.264i	−0.730355	+	0.511640i
$43$			116.364i			0.412681i	0.978480	+	0.206341i	$0.0661555\pi$
$43$			116.364i			0.412681i	−0.978480	+	0.206341i	$0.933845\pi$
$44$	715.024			2.44986
$45$	−149.621	−	54.3829i	−0.495649	−	0.180154i
$46$	345.196			1.10644
$47$	301.449			0.935550			0.467775	−	0.883848i	$-0.345056\pi$
$47$	301.449			0.935550			0.467775	+	0.883848i	$0.345056\pi$
$48$	36.7936	−	25.7753i	0.110640	−	0.0775071i
$49$	−241.109			−0.702942
$50$	−417.574			−1.18108
$51$	392.449	+	560.212i	1.07753	+	1.53814i
$52$		−	385.797i		−	1.02885i
$53$		−	314.489i		−	0.815064i	−0.913191	−	0.407532i	$-0.866389\pi$
$53$		−	314.489i		−	0.815064i	0.913191	−	0.407532i	$-0.133611\pi$
$54$	168.451	+	627.008i	0.424506	+	1.58009i
$55$		−	314.266i		−	0.770467i
$56$	−252.954			−0.603614
$57$	196.126	−	137.394i	0.455747	−	0.319267i
$58$			351.831i			0.796513i
$59$	−118.720	+	437.361i	−0.261966	+	0.965077i
$59$	−118.720	+	437.361i	−0.261966	+	0.965077i
$60$	−235.820	−	336.627i	−0.507403	−	0.724307i
$61$		−	559.302i		−	1.17396i	−0.809603	−	0.586978i	$-0.800318\pi$
$61$		−	559.302i		−	1.17396i	0.809603	−	0.586978i	$-0.199682\pi$
$62$			31.2860i			0.0640860i
$63$	93.1014	−	256.146i	0.186185	−	0.512243i
$64$	−811.754			−1.58546
$65$	−169.565			−0.323568
$66$	−1049.70	+	735.351i	−1.95771	+	1.37145i
$67$			221.837i			0.404502i	0.979334	+	0.202251i	$0.0648257\pi$
$67$			221.837i			0.404502i	−0.979334	+	0.202251i	$0.935174\pi$
$68$			1765.91i			3.14924i
$69$	−317.456	+	222.390i	−0.553873	+	0.388008i
$70$			275.424i			0.470279i
$71$		−	250.765i		−	0.419159i	−0.977792	−	0.209580i	$-0.932790\pi$
$71$		−	250.765i		−	0.419159i	0.977792	−	0.209580i	$-0.0672096\pi$
$72$	−231.133	+	635.906i	−0.378324	+	1.04086i
$73$			450.880i			0.722897i	0.932392	+	0.361448i	$0.117718\pi$
$73$			450.880i			0.722897i	−0.932392	+	0.361448i	$0.882282\pi$
$74$			1525.70i			2.39674i
$75$	384.019	−	269.019i	0.591235	−	0.414182i
$76$	618.234			0.933110
$77$	538.012			0.796261
$78$	396.765	+	566.373i	0.575959	+	0.822168i
$79$	−403.620			−0.574820			−0.287410	−	0.957808i	$-0.592794\pi$
$79$	−403.620			−0.574820			−0.287410	+	0.957808i	$0.592794\pi$
$80$		−	50.9761i		−	0.0712413i
$81$	−558.860	−	468.099i	−0.766611	−	0.642111i
$82$			1478.69i			1.99139i
$83$	341.648			0.451816			0.225908	−	0.974149i	$-0.427465\pi$
$83$	341.648			0.451816			0.225908	+	0.974149i	$0.427465\pi$
$84$	576.293	−	403.714i	0.748556	−	0.524391i
$85$	776.152			0.990418
$86$		−	538.491i		−	0.675197i
$87$	−226.665	−	323.559i	−0.279322	−	0.398726i
$88$	−1335.67			−1.61798
$89$	−1523.84			−1.81491			−0.907454	−	0.420151i	$-0.861977\pi$
$89$	−1523.84			−1.81491			−0.907454	+	0.420151i	$0.861977\pi$
$90$	692.395	+	251.665i	0.810943	+	0.294754i
$91$		−	290.289i		−	0.334401i
$92$	−1000.69			−1.13402
$93$	−20.1558	−	28.7719i	−0.0224737	−	0.0320807i
$94$	−1395.00			−1.53067
$95$		−	271.726i		−	0.293457i
$96$	682.916	−	478.408i	0.726040	−	0.508617i
$97$			1030.41i			1.07858i	0.842119	+	0.539291i	$0.181308\pi$
$97$			1030.41i			1.07858i	−0.842119	+	0.539291i	$0.818692\pi$
$98$	1115.77			1.15010
$99$	491.601	−	1352.52i	0.499068	−	1.37306i
$100$	1210.51			1.21051
$101$	1800.46			1.77378			0.886891	−	0.461979i	$-0.152860\pi$
$101$	1800.46			1.77378			0.886891	+	0.461979i	$0.152860\pi$
$102$	−1816.12	−	2592.47i	−1.76297	−	2.51659i
$103$			1115.61i			1.06723i	0.845727	+	0.533616i	$0.179167\pi$
$103$			1115.61i			1.06723i	−0.845727	+	0.533616i	$0.820833\pi$
$104$			720.669i			0.679494i
$105$	−177.440	−	253.292i	−0.164918	−	0.235416i
$106$			1455.35i			1.33354i
$107$			294.975i			0.266507i	0.991082	+	0.133254i	$0.0425425\pi$
$107$			294.975i			0.266507i	−0.991082	+	0.133254i	$0.957457\pi$
$108$	−488.326	−	1817.64i	−0.435085	−	1.61947i
$109$		−	408.894i		−	0.359311i	−0.983730	−	0.179655i	$-0.942502\pi$
$109$		−	408.894i		−	0.359311i	0.983730	−	0.179655i	$-0.0574983\pi$
$110$			1454.32i			1.26058i
$111$	−982.919	−	1403.09i	−0.840491	−	1.19978i
$112$	87.2691			0.0736264
$113$	−33.0548			−0.0275180			−0.0137590	−	0.999905i	$-0.504380\pi$
$113$	−33.0548			−0.0275180			−0.0137590	+	0.999905i	$0.504380\pi$
$114$	−907.605	+	635.810i	−0.745658	+	0.522360i
$115$			439.824i			0.356642i
$116$		−	1019.93i		−	0.816363i
$117$	−729.763	−	265.247i	−0.576637	−	0.209591i
$118$	549.393	−	2023.96i	0.428608	−	1.57898i
$119$			1328.74i			1.02358i
$120$	440.512	+	628.820i	0.335109	+	0.478360i
$121$	1509.85			1.13437
$122$			2588.26i			1.92074i
$123$	−952.636	−	1359.87i	−0.698344	−	0.996870i
$124$		−	90.6956i		−	0.0656831i
$125$		−	1269.07i		−	0.908073i
$126$	−430.841	+	1185.35i	−0.304622	+	0.838092i
$127$	−605.304			−0.422929			−0.211465	−	0.977386i	$-0.567823\pi$
$127$	−605.304			−0.422929			−0.211465	+	0.977386i	$0.567823\pi$
$128$	2472.77			1.70753
$129$	346.918	+	495.218i	0.236779	+	0.337996i
$130$	784.688			0.529398
$131$	279.269			0.186258			0.0931292	−	0.995654i	$-0.470313\pi$
$131$	279.269			0.186258			0.0931292	+	0.995654i	$0.470313\pi$
$132$	3042.99	−	2131.72i	2.00650	−	1.40563i
$133$	465.183			0.303282
$134$		−	1026.58i		−	0.661815i
$135$	−798.888	+	214.628i	−0.509314	+	0.136832i
$136$		−	3298.73i		−	2.07988i
$137$			1534.48i			0.956930i	0.878107	+	0.478465i	$0.158807\pi$
$137$			1534.48i			0.956930i	−0.878107	+	0.478465i	$0.841193\pi$
$138$	1469.08	−	1029.14i	0.906205	−	0.634829i
$139$	1166.12			0.711577			0.355789	−	0.934566i	$-0.384212\pi$
$139$	1166.12			0.711577			0.355789	+	0.934566i	$0.384212\pi$
$140$		−	798.432i		−	0.481999i
$141$	1282.90	−	898.719i	0.766239	−	0.536779i
$142$			1160.45i			0.685796i
$143$		−	1532.80i		−	0.896360i
$144$	79.7410	−	219.388i	0.0461464	−	0.126960i
$145$	−448.278			−0.256741
$146$		−	2086.51i		−	1.18275i
$147$	−1026.11	+	718.826i	−0.575728	+	0.403318i
$148$		−	4422.87i		−	2.45647i
$149$	−1325.90			−0.729009			−0.364505	−	0.931202i	$-0.618762\pi$
$149$	−1325.90			−0.729009			−0.364505	+	0.931202i	$0.618762\pi$
$150$	−1777.10	+	1244.93i	−0.967333	+	0.677652i
$151$			3043.52i			1.64025i	0.572184	+	0.820125i	$0.306096\pi$
$151$			3043.52i			1.64025i	−0.572184	+	0.820125i	$0.693904\pi$
$152$	−1154.86			−0.616261
$153$	3340.35	+	1214.12i	1.76504	+	0.641541i
$154$	−2489.73			−1.30278
$155$	−39.8624			−0.0206569
$156$	−1150.19	−	1641.87i	−0.590312	−	0.842658i
$157$			2731.12i			1.38832i	0.719819	+	0.694162i	$0.244225\pi$
$157$			2731.12i			1.38832i	−0.719819	+	0.694162i	$0.755775\pi$
$158$	1867.81			0.940475
$159$	−937.596	−	1338.40i	−0.467649	−	0.667558i
$160$		−	946.154i		−	0.467500i
$161$	−752.961			−0.368582
$162$	2586.21	+	2166.20i	1.25427	+	1.05057i
$163$	−513.998			−0.246991			−0.123495	−	0.992345i	$-0.539410\pi$
$163$	−513.998			−0.246991			−0.123495	+	0.992345i	$0.539410\pi$
$164$		−	4286.60i		−	2.04102i
$165$	−936.932	−	1337.45i	−0.442061	−	0.631032i
$166$	−1581.03			−0.739227
$167$		−	1602.55i		−	0.742571i	−0.928519	−	0.371286i	$-0.878917\pi$
$167$		−	1602.55i		−	0.742571i	0.928519	−	0.371286i	$-0.121083\pi$
$168$	−1076.52	+	754.138i	−0.494375	+	0.346328i
$169$	1369.96			0.623561
$170$	−3591.76			−1.62045
$171$	425.055	−	1169.43i	0.190086	−	0.522976i
$172$			1561.04i			0.692024i
$173$	−2474.48			−1.08746			−0.543731	−	0.839260i	$-0.682989\pi$
$173$	−2474.48			−1.08746			−0.543731	+	0.839260i	$0.682989\pi$
$174$	1048.93	+	1497.32i	0.457005	+	0.652364i
$175$	910.837			0.393444
$176$	460.805			0.197355
$177$	798.672	+	2215.26i	0.339163	+	0.940728i
$178$	7051.81			2.96941
$179$	−1696.42			−0.708360			−0.354180	−	0.935177i	$-0.615240\pi$
$179$	−1696.42			−0.708360			−0.354180	+	0.935177i	$0.615240\pi$
$180$	−2007.19	−	729.556i	−0.831153	−	0.302100i
$181$	2390.68			0.981756			0.490878	−	0.871228i	$-0.336676\pi$
$181$	2390.68			0.981756			0.490878	+	0.871228i	$0.336676\pi$
$182$			1343.35i			0.547121i
$183$	−1667.46	−	2380.27i	−0.673566	−	0.961500i
$184$	1869.30			0.748948
$185$	−1943.93			−0.772545
$186$	93.2740	+	133.146i	0.0367698	+	0.0524880i
$187$			7016.12i			2.74369i
$188$	4043.99			1.56882
$189$	−367.435	−	1367.67i	−0.141413	−	0.526365i
$190$			1257.45i			0.480132i
$191$	−2544.85			−0.964076			−0.482038	−	0.876150i	$-0.660103\pi$
$191$	−2544.85			−0.964076			−0.482038	+	0.876150i	$0.660103\pi$
$192$	−3454.65	+	2420.11i	−1.29853	+	0.909667i
$193$	−3082.48			−1.14965			−0.574824	−	0.818277i	$-0.694929\pi$
$193$	−3082.48			−1.14965			−0.574824	+	0.818277i	$0.694929\pi$
$194$		−	4768.39i		−	1.76469i
$195$	−721.631	+	505.529i	−0.265011	+	0.185650i
$196$	−3234.52			−1.17876
$197$			4018.40i			1.45330i	0.687010	+	0.726648i	$0.258923\pi$
$197$			4018.40i			1.45330i	−0.687010	+	0.726648i	$0.741077\pi$
$198$	−2274.96	+	6258.99i	−0.816537	+	2.24650i
$199$	4500.71			1.60325			0.801626	−	0.597826i	$-0.203969\pi$
$199$	4500.71			1.60325			0.801626	+	0.597826i	$0.203969\pi$
$200$	−2261.24			−0.799469
$201$	661.368	+	944.088i	0.232086	+	0.331298i
$202$	−8331.88			−2.90213
$203$		−	767.435i		−	0.265337i
$204$	5264.77	+	7515.34i	1.80690	+	2.57931i
$205$	−1884.04			−0.641889
$206$		−	5162.68i		−	1.74612i
$207$	−688.008	+	1892.88i	−0.231014	+	0.635578i
$208$		−	248.631i		−	0.0828820i
$209$	2456.30			0.812945
$210$	821.131	+	1172.15i	0.269826	+	0.385170i
$211$		−	4567.43i		−	1.49021i	−0.666946	−	0.745106i	$-0.732399\pi$
$211$		−	4567.43i		−	1.49021i	0.666946	−	0.745106i	$-0.267601\pi$
$212$		−	4218.93i		−	1.36678i
$213$	−747.613	−	1067.20i	−0.240496	−	0.343302i
$214$		−	1365.04i		−	0.436039i
$215$	686.106			0.217637
$216$	912.193	+	3395.36i	0.287347	+	1.06956i
$217$		−	68.2429i		−	0.0213485i
$218$			1892.22i			0.587877i
$219$	1344.22	+	1918.84i	0.414767	+	0.592071i
$220$		−	4215.94i		−	1.29199i
$221$	3785.61			1.15225
$222$	4548.61	+	6493.04i	1.37515	+	1.96299i
$223$	247.649			0.0743669			0.0371835	−	0.999308i	$-0.488161\pi$
$223$	247.649			0.0743669			0.0371835	+	0.999308i	$0.488161\pi$
$224$	1619.78			0.483152
$225$	832.265	−	2289.77i	0.246597	−	0.678451i
$226$	152.966			0.0450228
$227$	1175.81			0.343795			0.171897	−	0.985115i	$-0.445010\pi$
$227$	1175.81			0.343795			0.171897	+	0.985115i	$0.445010\pi$
$228$	2631.07	−	1843.16i	0.764241	−	0.535378i
$229$		−	3872.27i		−	1.11741i	−0.829367	−	0.558704i	$-0.811299\pi$
$229$		−	3872.27i		−	1.11741i	0.829367	−	0.558704i	$-0.188701\pi$
$230$		−	2035.35i		−	0.583509i
$231$	2289.66	−	1603.99i	0.652158	−	0.456861i
$232$			1905.23i			0.539157i
$233$	2609.60			0.733736			0.366868	−	0.930273i	$-0.380430\pi$
$233$	2609.60			0.733736			0.366868	+	0.930273i	$0.380430\pi$
$234$	3377.09	+	1227.47i	0.943449	+	0.342916i
$235$		−	1777.41i		−	0.493385i
$236$	−1592.64	+	5867.28i	−0.439290	+	1.61834i
$237$	−1717.72	+	1203.32i	−0.470792	+	0.329807i
$238$		−	6148.96i		−	1.67470i
$239$			5126.17i			1.38738i	0.720273	+	0.693691i	$0.244017\pi$
$239$			5126.17i			1.38738i	−0.720273	+	0.693691i	$0.755983\pi$
$240$	−151.977	−	216.943i	−0.0408752	−	0.0583485i
$241$	−3001.15			−0.802161			−0.401081	−	0.916043i	$-0.631365\pi$
$241$	−3001.15			−0.802161			−0.401081	+	0.916043i	$0.631365\pi$
$242$	−6987.06			−1.85597
$243$	−3773.94	−	325.983i	−0.996290	−	0.0860568i
$244$		−	7503.14i		−	1.96860i
$245$			1421.63i			0.370713i
$246$	4408.47	+	6292.99i	1.14258	+	1.63100i
$247$		−	1325.31i		−	0.341408i
$248$			169.419i			0.0433796i
$249$	1453.98	−	1018.57i	0.370049	−	0.259233i
$250$			5872.82i			1.48572i
$251$		−	5448.19i		−	1.37007i	−0.728512	−	0.685034i	$-0.759788\pi$
$251$		−	5448.19i		−	1.37007i	0.728512	−	0.685034i	$-0.240212\pi$
$252$	1248.97	−	3436.24i	0.312214	−	0.858979i
$253$	−3975.84			−0.987980
$254$	2801.14			0.691964
$255$	3303.13	−	2313.97i	0.811178	−	0.568260i
$256$	−4949.11			−1.20828
$257$			1304.07i			0.316519i	0.987398	+	0.158260i	$0.0505883\pi$
$257$			1304.07i			0.316519i	−0.987398	+	0.158260i	$0.949412\pi$
$258$	−1605.42	−	2291.70i	−0.387399	−	0.553003i
$259$		−	3327.94i		−	0.798409i
$260$	−2274.74			−0.542591
$261$	−1929.27	−	701.233i	−0.457543	−	0.166304i
$262$	−1292.36			−0.304742
$263$			41.3337i			0.00969105i	0.999988	+	0.00484552i	$0.00154238\pi$
$263$			41.3337i			0.00969105i	−0.999988	+	0.00484552i	$0.998458\pi$
$264$	−5684.30	+	3982.06i	−1.32517	+	0.928329i
$265$	−1854.30			−0.429844
$266$	−2152.71			−0.496207
$267$	−6485.13	+	4543.07i	−1.48646	+	1.04132i
$268$			2975.98i			0.678309i
$269$	6337.69			1.43649			0.718245	−	0.695791i	$-0.244946\pi$
$269$	6337.69			1.43649			0.718245	+	0.695791i	$0.244946\pi$
$270$	3696.98	−	993.226i	0.833300	−	0.223873i
$271$	4545.70			1.01893			0.509467	−	0.860490i	$-0.329842\pi$
$271$	4545.70			1.01893			0.509467	+	0.860490i	$0.329842\pi$
$272$			1138.06i			0.253696i
$273$	−865.446	−	1235.40i	−0.191865	−	0.273883i
$274$		−	7101.04i		−	1.56565i
$275$	4809.47			1.05462
$276$	−4258.73	+	2983.40i	−0.928789	+	0.650650i
$277$	6321.46			1.37119			0.685595	−	0.727983i	$-0.259542\pi$
$277$	6321.46			1.37119			0.685595	+	0.727983i	$0.259542\pi$
$278$	−5396.41			−1.16423
$279$	−171.557	−	62.3560i	−0.0368131	−	0.0133805i
$280$			1491.47i			0.318330i
$281$			2091.33i			0.443979i	0.975049	+	0.221989i	$0.0712551\pi$
$281$			2091.33i			0.443979i	−0.975049	+	0.221989i	$0.928745\pi$
$282$	−5936.82	+	4158.96i	−1.25366	+	0.878236i
$283$		−	7506.42i		−	1.57672i	−0.615217	−	0.788358i	$-0.710932\pi$
$283$		−	7506.42i		−	1.57672i	0.615217	−	0.788358i	$-0.289068\pi$
$284$		−	3364.05i		−	0.702887i
$285$	−810.104	−	1156.40i	−0.168373	−	0.240349i
$286$			7093.28i			1.46655i
$287$		−	3225.41i		−	0.663379i
$288$	1480.05	−	4072.00i	0.302822	−	0.833141i
$289$	−12414.9			−2.52695
$290$	2074.48			0.420060
$291$	3072.00	+	4385.21i	0.618845	+	0.883387i
$292$			6048.63i			1.21222i
$293$			7349.25i			1.46535i	0.680578	+	0.732675i	$0.261729\pi$
$293$			7349.25i			1.46535i	−0.680578	+	0.732675i	$0.738271\pi$
$294$	4748.47	−	3326.48i	0.941961	−	0.659878i
$295$	2578.78	+	699.997i	0.508957	+	0.138154i
$296$			8261.92i			1.62235i
$297$	−1940.16	−	7221.65i	−0.379055	−	1.41092i
$298$	6135.83			1.19275
$299$			2145.20i			0.414916i
$300$	5151.68	−	3608.94i	0.991441	−	0.694540i
$301$			1174.59i			0.224924i
$302$		−	14084.3i		−	2.68365i
$303$	7662.34	−	5367.75i	1.45277	−	1.01772i
$304$	398.428			0.0751691
$305$	−3297.77			−0.619114
$306$	−15458.0	−	5618.53i	−2.88783	−	1.04964i
$307$	4822.74			0.896574			0.448287	−	0.893890i	$-0.352034\pi$
$307$	4822.74			0.896574			0.448287	+	0.893890i	$0.352034\pi$
$308$	7217.52			1.33525
$309$	3326.02	+	4747.81i	0.612332	+	0.874090i
$310$	184.469			0.0337973
$311$			5273.14i			0.961454i	0.876870	+	0.480727i	$0.159627\pi$
$311$			5273.14i			0.961454i	−0.876870	+	0.480727i	$0.840373\pi$
$312$	2148.55	+	3067.01i	0.389865	+	0.556523i
$313$			8851.82i			1.59851i	0.600990	+	0.799256i	$0.294773\pi$
$313$			8851.82i			1.59851i	−0.600990	+	0.799256i	$0.705227\pi$
$314$		−	12638.7i		−	2.27147i
$315$	−1510.29	−	548.946i	−0.270144	−	0.0981893i
$316$	−5414.63			−0.963913
$317$			8125.27i			1.43962i	0.694169	+	0.719812i	$0.255772\pi$
$317$			8125.27i			1.43962i	−0.694169	+	0.719812i	$0.744228\pi$
$318$	4338.87	+	6193.64i	0.765131	+	1.09221i
$319$		−	4052.27i		−	0.711233i
$320$			4786.28i			0.836129i
$321$	879.417	+	1255.35i	0.152911	+	0.218276i
$322$	3484.44			0.603045
$323$			6066.38i			1.04502i
$324$	−7497.20	−	6279.63i	−1.28553	−	1.07675i
$325$		−	2594.99i		−	0.442905i
$326$	2378.61			0.404107
$327$	−1219.05	−	1740.16i	−0.206157	−	0.294285i
$328$			8007.38i			1.34797i
$329$	3042.86			0.509903
$330$	4335.80	+	6189.25i	0.723266	+	1.03245i
$331$	−11740.5			−1.94959			−0.974795	−	0.223104i	$-0.928381\pi$
$331$	−11740.5			−1.94959			−0.974795	+	0.223104i	$0.928381\pi$
$332$	4583.27			0.757650
$333$	−8366.18	−	3040.86i	−1.37677	−	0.500415i
$334$			7416.07i			1.21494i
$335$	1308.00			0.213324
$336$	371.398	−	260.178i	0.0603019	−	0.0422437i
$337$			7342.61i			1.18688i	0.804880	+	0.593438i	$0.202230\pi$
$337$			7342.61i			1.18688i	−0.804880	+	0.593438i	$0.797770\pi$
$338$	−6339.72			−1.02022
$339$	−140.674	+	98.5472i	−0.0225379	+	0.0157886i
$340$	10412.2			1.66083
$341$		−	360.341i		−	0.0572245i
$342$	−1967.01	+	5411.74i	−0.311005	+	0.855653i
$343$	−5896.06			−0.928155
$344$		−	2916.02i		−	0.457039i
$345$	1311.26	+	1871.79i	0.204626	+	0.292099i
$346$	11451.0			1.77922
$347$	−11274.9			−1.74429			−0.872144	−	0.489250i	$-0.837271\pi$
$347$	−11274.9			−1.74429			−0.872144	+	0.489250i	$0.837271\pi$
$348$	−3040.75	−	4340.60i	−0.468394	−	0.668622i
$349$			2405.99i			0.369025i	0.982830	+	0.184513i	$0.0590706\pi$
$349$			2405.99i			0.369025i	−0.982830	+	0.184513i	$0.940929\pi$
$350$	−4215.04			−0.643723
$351$	−3896.50	+	1046.83i	−0.592535	+	0.159190i
$352$	8552.88			1.29508
$353$	2454.37			0.370065			0.185033	−	0.982732i	$-0.440761\pi$
$353$	2454.37			0.370065			0.185033	+	0.982732i	$0.440761\pi$
$354$	−3695.98	−	10251.4i	−0.554913	−	1.53915i
$355$	−1478.57			−0.221054
$356$	−20442.6			−3.04341
$357$	3961.42	+	5654.84i	0.587284	+	0.838335i
$358$	7850.45			1.15896
$359$		−	3927.04i		−	0.577330i	−0.957430	−	0.288665i	$-0.906789\pi$
$359$		−	3927.04i		−	0.577330i	0.957430	−	0.288665i	$-0.0932113\pi$
$360$	3749.44	+	1362.81i	0.548925	+	0.199518i
$361$	−4735.20			−0.690363
$362$	−11063.2			−1.60627
$363$	6425.59	−	4501.36i	0.929080	−	0.650854i
$364$		−	3894.27i		−	0.560756i
$365$	2658.49			0.381237
$366$	7716.45	+	11015.1i	1.10204	+	1.57313i
$367$			11433.0i			1.62615i	0.582160	+	0.813074i	$0.302208\pi$
$367$			11433.0i			1.62615i	−0.582160	+	0.813074i	$0.697792\pi$
$368$	−644.908			−0.0913537
$369$	−8108.42	−	2947.17i	−1.14392	−	0.415782i
$370$	8995.85			1.26398
$371$		−	3174.48i		−	0.444234i
$372$	−270.393	−	385.980i	−0.0376861	−	0.0537961i
$373$	3095.15			0.429653			0.214827	−	0.976652i	$-0.431081\pi$
$373$	3095.15			0.429653			0.214827	+	0.976652i	$0.431081\pi$
$374$		−	32468.2i		−	4.48901i
$375$	−3783.52	−	5400.89i	−0.521013	−	0.743735i
$376$	−7554.18			−1.03611
$377$	−2186.43			−0.298692
$378$	1700.36	+	6329.08i	0.231368	+	0.861198i
$379$	3022.14			0.409597			0.204798	−	0.978804i	$-0.434346\pi$
$379$	3022.14			0.409597			0.204798	+	0.978804i	$0.434346\pi$
$380$		−	3645.25i		−	0.492098i
$381$	−2576.04	+	1804.61i	−0.346390	+	0.242659i
$382$	11776.7			1.57735
$383$		−	6729.51i		−	0.897812i	−0.893579	−	0.448906i	$-0.851814\pi$
$383$		−	6729.51i		−	0.897812i	0.893579	−	0.448906i	$-0.148186\pi$
$384$	10523.6	−	7372.15i	1.39851	−	0.979710i
$385$		−	3172.24i		−	0.419928i
$386$	14264.7			1.88096
$387$	2952.82	+	1073.26i	0.387856	+	0.140974i
$388$			13823.2i			1.80867i
$389$			4796.16i			0.625129i	0.949897	+	0.312564i	$0.101188\pi$
$389$			4796.16i			0.625129i	−0.949897	+	0.312564i	$0.898812\pi$
$390$	3339.46	−	2339.41i	0.433590	−	0.303746i
$391$		−	9819.24i		−	1.27003i
$392$	6042.09			0.778499
$393$	1188.51	−	832.593i	0.152550	−	0.106867i
$394$		−	18595.8i		−	2.37777i
$395$			2379.83i			0.303145i
$396$	6594.91	−	18144.3i	0.836886	−	2.30249i
$397$		−	6475.19i		−	0.818590i	−0.912402	−	0.409295i	$-0.865775\pi$
$397$		−	6475.19i		−	0.818590i	0.912402	−	0.409295i	$-0.134225\pi$
$398$	−20827.7			−2.62312
$399$	1979.72	−	1386.87i	0.248396	−	0.174010i
$400$	780.128			0.0975160
$401$	5689.94			0.708584			0.354292	−	0.935135i	$-0.384722\pi$
$401$	5689.94			0.708584			0.354292	+	0.935135i	$0.384722\pi$
$402$	−3060.58	−	4368.91i	−0.379721	−	0.542044i
$403$	−194.425			−0.0240322
$404$	24153.4			2.97445
$405$	−2760.02	+	3295.16i	−0.338633	+	0.404291i
$406$			3551.42i			0.434123i
$407$		−	17572.4i		−	2.14013i
$408$	−9834.60	−	14038.7i	−1.19335	−	1.70347i
$409$		−	6415.64i		−	0.775631i	−0.921737	−	0.387815i	$-0.873230\pi$
$409$		−	6415.64i		−	0.775631i	0.921737	−	0.387815i	$-0.126770\pi$
$410$	8718.70			1.05021
$411$	4574.79	+	6530.41i	0.549045	+	0.783750i
$412$			14966.2i			1.78964i
$413$	−1198.37	+	4414.77i	−0.142779	+	0.525996i
$414$	3183.86	−	8759.61i	0.377967	−	1.03988i
$415$		−	2014.43i		−	0.238276i
$416$		−	4614.77i		−	0.543889i
$417$	4962.76	−	3476.60i	0.582800	−	0.408273i
$418$	−11366.9			−1.33008
$419$	−56.4393			−0.00658052			−0.00329026	−	0.999995i	$-0.501047\pi$
$419$	−56.4393			−0.00658052			−0.00329026	+	0.999995i	$0.501047\pi$
$420$	−2380.39	−	3397.95i	−0.276550	−	0.394769i
$421$			6070.96i			0.702804i	0.936225	+	0.351402i	$0.114295\pi$
$421$			6070.96i			0.702804i	−0.936225	+	0.351402i	$0.885705\pi$
$422$			21136.5i			2.43817i
$423$	2780.37	−	7649.50i	0.319589	−	0.879271i
$424$			7880.96i			0.902673i
$425$			11878.1i			1.35570i
$426$	3459.69	+	4938.63i	0.393480	+	0.561684i
$427$		−	5645.65i		−	0.639841i
$428$			3957.14i			0.446906i
$429$	−4569.79	−	6523.28i	−0.514293	−	0.734142i
$430$	−3175.06			−0.356081
$431$	1006.47			0.112482			0.0562412	−	0.998417i	$-0.482088\pi$
$431$	1006.47			0.112482			0.0562412	+	0.998417i	$0.482088\pi$
$432$	−314.707	−	1171.40i	−0.0350494	−	0.130461i
$433$	−12899.6			−1.43167			−0.715836	−	0.698268i	$-0.753954\pi$
$433$	−12899.6			−1.43167			−0.715836	+	0.698268i	$0.753954\pi$
$434$			315.804i			0.0349288i
$435$	−1907.77	+	1336.47i	−0.210278	+	0.147307i
$436$		−	5485.38i		−	0.602528i
$437$	−3437.65			−0.376305
$438$	−6220.59	−	8879.75i	−0.678610	−	0.968700i
$439$	13595.9			1.47813			0.739064	−	0.673635i	$-0.235268\pi$
$439$	13595.9			1.47813			0.739064	+	0.673635i	$0.235268\pi$
$440$			7875.38i			0.853282i
$441$	−2223.83	+	6118.33i	−0.240129	+	0.660656i
$442$	−17518.5			−1.88522
$443$	16463.4			1.76569			0.882843	−	0.469668i	$-0.155626\pi$
$443$	16463.4			1.76569			0.882843	+	0.469668i	$0.155626\pi$
$444$	−13186.0	−	18822.8i	−1.40942	−	2.01191i
$445$			8984.90i			0.957136i
$446$	−1146.04			−0.121673
$447$	−5642.76	+	3952.96i	−0.597077	+	0.418274i
$448$	−8193.93			−0.864122
$449$			14660.1i			1.54088i	0.637513	+	0.770440i	$0.279963\pi$
$449$			14660.1i			1.54088i	−0.637513	+	0.770440i	$0.720037\pi$
$450$	−3851.43	+	10596.3i	−0.403463	+	1.11003i
$451$		−	17031.0i		−	1.77818i
$452$	−443.436			−0.0461448
$453$	9073.72	+	12952.5i	0.941105	+	1.34341i
$454$	−5441.25			−0.562490
$455$	−1711.61			−0.176355
$456$	−4914.84	+	3443.03i	−0.504734	+	0.353584i
$457$			1970.40i			0.201688i	0.994902	+	0.100844i	$0.0321543\pi$
$457$			1970.40i			0.201688i	−0.994902	+	0.100844i	$0.967846\pi$
$458$			17919.5i			1.82822i
$459$	17835.5	−	4791.66i	1.81370	−	0.487267i
$460$			5900.31i			0.598051i
$461$		−	10954.7i		−	1.10674i	−0.832934	−	0.553372i	$-0.813341\pi$
$461$		−	10954.7i		−	1.10674i	0.832934	−	0.553372i	$-0.186659\pi$
$462$	−10595.8	+	7422.71i	−1.06701	+	0.747480i
$463$			16309.2i			1.63704i	0.574475	+	0.818522i	$0.305206\pi$
$463$			16309.2i			1.63704i	−0.574475	+	0.818522i	$0.694794\pi$
$464$		−	657.305i		−	0.0657643i
$465$	−169.646	+	118.843i	−0.0169186	+	0.0118521i
$466$	−12076.3			−1.20048
$467$	−10124.7			−1.00324			−0.501622	−	0.865087i	$-0.667263\pi$
$467$	−10124.7			−1.00324			−0.501622	+	0.865087i	$0.667263\pi$
$468$	−9789.89	−	3558.34i	−0.966962	−	0.351462i
$469$			2239.24i			0.220466i
$470$			8225.24i			0.807238i
$471$	8142.36	+	11623.0i	0.796561	+	1.13707i
$472$	2975.06	−	10960.1i	0.290124	−	1.06881i
$473$			6202.14i			0.602906i
$474$	7949.00	−	5568.56i	0.770273	−	0.539604i
$475$	4158.43			0.401688
$476$			17825.3i			1.71643i
$477$	−7980.40	−	2900.64i	−0.766033	−	0.278430i
$478$		−	23722.1i		−	2.26993i
$479$		−	1871.94i		−	0.178562i	−0.996006	−	0.0892808i	$-0.971543\pi$
$479$		−	1871.94i		−	0.178562i	0.996006	−	0.0892808i	$-0.0284568\pi$
$480$	−2820.80	−	4026.62i	−0.268232	−	0.382895i
$481$	−9481.35			−0.898778
$482$	13888.3			1.31243
$483$	−3204.44	+	2244.82i	−0.301878	+	0.211476i
$484$	20254.9			1.90223
$485$	6075.54			0.568817
$486$	17464.5	+	1508.53i	1.63005	+	0.140799i
$487$	−5575.34			−0.518773			−0.259387	−	0.965774i	$-0.583520\pi$
$487$	−5575.34			−0.518773			−0.259387	+	0.965774i	$0.583520\pi$
$488$			14015.9i			1.30014i
$489$	−2187.47	+	1532.40i	−0.202292	+	0.141713i
$490$		−	6578.83i		−	0.606533i
$491$			386.189i			0.0354959i	0.999842	+	0.0177479i	$0.00564964\pi$
$491$			386.189i			0.0354959i	−0.999842	+	0.0177479i	$0.994350\pi$
$492$	−12779.8	−	18242.8i	−1.17105	−	1.67165i
$493$	10008.0			0.914274
$494$			6133.10i			0.558585i
$495$	−7974.75	−	2898.59i	−0.724118	−	0.263196i
$496$		−	58.4498i		−	0.00529127i
$497$		−	2531.25i		−	0.228454i
$498$	−6728.51	+	4713.57i	−0.605446	+	0.424137i
$499$	7220.37			0.647752			0.323876	−	0.946100i	$-0.395014\pi$
$499$	7220.37			0.647752			0.323876	+	0.946100i	$0.395014\pi$
$500$		−	17024.8i		−	1.52275i
$501$	−4777.74	−	6820.12i	−0.426055	−	0.608185i
$502$			25212.3i			2.24160i
$503$	−5269.99			−0.467152			−0.233576	−	0.972339i	$-0.575043\pi$
$503$	−5269.99			−0.467152			−0.233576	+	0.972339i	$0.575043\pi$
$504$	−2333.08	+	6418.90i	−0.206198	+	0.567302i
$505$		−	10615.9i		−	0.935447i
$506$	18398.8			1.61646
$507$	5830.27	−	4084.31i	0.510712	−	0.357773i
$508$	−8120.26			−0.709209
$509$	−21337.4			−1.85808			−0.929039	−	0.369982i	$-0.879364\pi$
$509$	−21337.4			−1.85808			−0.929039	+	0.369982i	$0.879364\pi$
$510$	−15285.8	+	10708.2i	−1.32719	+	0.929742i
$511$			4551.22i			0.394001i
$512$	3120.57			0.269357
$513$	−1677.53	−	6244.09i	−0.144376	−	0.537394i
$514$		−	6034.77i		−	0.517864i
$515$	6577.91			0.562830
$516$	4653.97	+	6643.44i	0.397054	+	0.566785i
$517$	16067.1			1.36679
$518$			15400.5i			1.30630i
$519$	−10530.8	+	7377.23i	−0.890659	+	0.623939i
$520$	4249.22			0.358348
$521$			2794.35i			0.234976i	0.993074	+	0.117488i	$0.0374842\pi$
$521$			2794.35i			0.234976i	−0.993074	+	0.117488i	$0.962516\pi$
$522$	8927.99	+	3245.06i	0.748597	+	0.272093i
$523$	16502.9			1.37977			0.689886	−	0.723918i	$-0.257661\pi$
$523$	16502.9			1.37977			0.689886	+	0.723918i	$0.257661\pi$
$524$	3746.44			0.312336
$525$	3876.32	−	2715.50i	0.322241	−	0.225742i
$526$		−	191.278i		−	0.0158557i
$527$	889.944			0.0735609
$528$	1961.09	−	1373.81i	0.161639	−	0.113234i
$529$	−6602.71			−0.542674
$530$	8581.05			0.703277
$531$	10003.4	+	7046.54i	0.817533	+	0.575882i
$532$	6240.52			0.508573
$533$	−9189.23			−0.746773
$534$	30011.0	−	21023.8i	2.43202	−	1.70372i
$535$	1739.24			0.140549
$536$		−	5559.13i		−	0.447981i
$537$	−7219.60	+	5057.59i	−0.580165	+	0.406427i
$538$	−29328.6			−2.35027
$539$	−12851.0			−1.02696
$540$	−10717.2	+	2879.28i	−0.854067	+	0.229453i
$541$		−	13410.8i		−	1.06576i	−0.846192	−	0.532878i	$-0.821111\pi$
$541$		−	13410.8i		−	1.06576i	0.846192	−	0.532878i	$-0.178889\pi$
$542$	−21035.9			−1.66710
$543$	10174.2	−	7127.41i	0.804083	−	0.563290i
$544$			21123.3i			1.66480i
$545$	−2410.93			−0.189491
$546$	4004.98	+	5717.02i	0.313915	+	0.448106i
$547$	6557.46			0.512572			0.256286	−	0.966601i	$-0.417501\pi$
$547$	6557.46			0.512572			0.256286	+	0.966601i	$0.417501\pi$
$548$			20585.3i			1.60467i
$549$	−14192.7	−	5158.64i	−1.10333	−	0.401030i
$550$	−22256.6			−1.72550
$551$		−	3503.73i		−	0.270896i
$552$	7955.32	−	5572.99i	0.613407	−	0.429714i
$553$	−4074.18			−0.313294
$554$	−29253.5			−2.24344
$555$	−8272.96	+	5795.51i	−0.632734	+	0.443253i
$556$	15643.7			1.19324
$557$			17276.0i			1.31420i	0.753805	+	0.657099i	$0.228217\pi$
$557$			17276.0i			1.31420i	−0.753805	+	0.657099i	$0.771783\pi$
$558$	793.907	+	288.562i	0.0602308	+	0.0218921i
$559$	3346.41			0.253199
$560$		−	514.558i		−	0.0388287i
$561$	20917.4	+	29859.1i	1.57421	+	2.24715i
$562$		−	9677.93i		−	0.726404i
$563$	15957.9			1.19457			0.597285	−	0.802029i	$-0.296246\pi$
$563$	15957.9			1.19457			0.597285	+	0.802029i	$0.296246\pi$
$564$	17210.3	−	12056.5i	1.28490	−	0.900122i
$565$			194.898i			0.0145123i
$566$			34737.1i			2.57970i
$567$	−5641.19	−	4725.04i	−0.417826	−	0.349970i
$568$			6284.06i			0.464213i
$569$	16378.5			1.20672			0.603358	−	0.797471i	$-0.293829\pi$
$569$	16378.5			1.20672			0.603358	+	0.797471i	$0.293829\pi$
$570$	3748.88	+	5351.44i	0.275479	+	0.393241i
$571$			5837.15i			0.427806i	0.976855	+	0.213903i	$0.0686177\pi$
$571$			5837.15i			0.427806i	−0.976855	+	0.213903i	$0.931382\pi$
$572$		−	20562.8i		−	1.50310i
$573$	−10830.3	+	7587.02i	−0.789603	+	0.553146i
$574$			14926.1i			1.08537i
$575$	−6730.97			−0.488176
$576$	−7487.09	+	20598.9i	−0.541601	+	1.49008i
$577$	−24908.4			−1.79714			−0.898572	−	0.438826i	$-0.855394\pi$
$577$	−24908.4			−1.79714			−0.898572	+	0.438826i	$0.855394\pi$
$578$	57451.9			4.13440
$579$	−13118.4	+	9189.89i	−0.941590	+	0.659618i
$580$	−6013.73			−0.430529
$581$	3448.63			0.246254
$582$	−14216.1	−	20293.2i	−1.01251	−	1.44533i
$583$		−	16762.1i		−	1.19077i
$584$		−	11298.8i		−	0.800598i
$585$	−1563.96	+	4302.84i	−0.110533	+	0.304104i
$586$		−	34009.8i		−	2.39749i
$587$	−24884.5			−1.74973			−0.874866	−	0.484365i	$-0.839051\pi$
$587$	−24884.5			−1.74973			−0.874866	+	0.484365i	$0.839051\pi$
$588$	−13765.4	+	9643.18i	−0.965436	+	0.676323i
$589$		−	311.563i		−	0.0217958i
$590$	−11933.7	−	3239.35i	−0.832716	−	0.226037i
$591$	11980.2	+	17101.4i	0.833839	+	1.19029i
$592$		−	2850.37i		−	0.197887i
$593$			4214.97i			0.291885i	0.989293	+	0.145943i	$0.0466215\pi$
$593$			4214.97i			0.291885i	−0.989293	+	0.145943i	$0.953378\pi$
$594$	8978.38	+	33419.3i	0.620181	+	2.30843i
$595$	7834.56			0.539808
$596$	−17787.2			−1.22247
$597$	19154.0	−	13418.1i	1.31310	−	0.919877i
$598$		−	9927.23i		−	0.678854i
$599$		−	26573.3i		−	1.81261i	−0.422620	−	0.906307i	$-0.638890\pi$
$599$		−	26573.3i		−	1.81261i	0.422620	−	0.906307i	$-0.361110\pi$
$600$	−9623.34	+	6741.50i	−0.654785	+	0.458701i
$601$		−	20051.3i		−	1.36092i	−0.732787	−	0.680458i	$-0.761781\pi$
$601$		−	20051.3i		−	1.36092i	0.732787	−	0.680458i	$-0.238219\pi$
$602$		−	5435.58i		−	0.368003i
$603$	5629.28	+	2046.08i	0.380169	+	0.138180i
$604$			40829.3i			2.75053i
$605$		−	8902.41i		−	0.598239i
$606$	−35458.7	+	24840.1i	−2.37691	+	1.66511i
$607$	−12265.2			−0.820145			−0.410072	−	0.912053i	$-0.634497\pi$
$607$	−12265.2			−0.820145			−0.410072	+	0.912053i	$0.634497\pi$
$608$	7395.11			0.493275
$609$	−2287.98	−	3266.03i	−0.152239	−	0.217318i
$610$	15260.9			1.01295
$611$		−	8669.14i		−	0.574003i
$612$	44811.4	+	16287.6i	2.95980	+	1.07580i
$613$		−	12455.2i		−	0.820657i	−0.911938	−	0.410328i	$-0.865414\pi$
$613$		−	12455.2i		−	0.820657i	0.911938	−	0.410328i	$-0.134586\pi$
$614$	−22318.0			−1.46691
$615$	−8018.07	+	5616.95i	−0.525723	+	0.368288i
$616$	−13482.3			−0.881849
$617$			13837.4i			0.902872i	0.892304	+	0.451436i	$0.149088\pi$
$617$			13837.4i			0.902872i	−0.892304	+	0.451436i	$0.850912\pi$
$618$	−15391.6	−	21971.2i	−1.00185	−	1.43012i
$619$	−751.124			−0.0487726			−0.0243863	−	0.999703i	$-0.507763\pi$
$619$	−751.124			−0.0487726			−0.0243863	+	0.999703i	$0.507763\pi$
$620$	−534.761			−0.0346396
$621$	2715.30	+	10106.9i	0.175461	+	0.653100i
$622$		−	24402.2i		−	1.57306i
$623$	−15381.8			−0.989180
$624$	−741.251	−	1058.12i	−0.0475542	−	0.0678825i
$625$	3796.60			0.242982
$626$		−	40963.2i		−	2.61536i
$627$	10453.5	−	7323.03i	0.665823	−	0.466433i
$628$			36638.4i			2.32808i
$629$	43399.1			2.75109
$630$	6989.10	+	2540.33i	0.441988	+	0.160650i
$631$	8416.49			0.530991			0.265495	−	0.964112i	$-0.414465\pi$
$631$	8416.49			0.530991			0.265495	+	0.964112i	$0.414465\pi$
$632$	10114.5			0.636605
$633$	−13617.0	−	19438.0i	−0.855020	−	1.22052i
$634$		−	37600.9i		−	2.35540i
$635$			3569.00i			0.223042i
$636$	−12578.0	−	17954.8i	−0.784199	−	1.11943i
$637$			6933.88i			0.431287i
$638$			18752.5i			1.16366i
$639$	−6363.35	−	2312.89i	−0.393944	−	0.143187i
$640$		−	14580.0i		−	0.900509i
$641$			3885.41i			0.239414i	0.992809	+	0.119707i	$0.0381955\pi$
$641$			3885.41i			0.239414i	−0.992809	+	0.119707i	$0.961804\pi$
$642$	−4069.64	−	5809.32i	−0.250180	−	0.357127i
$643$	−1897.58			−0.116382			−0.0581908	−	0.998305i	$-0.518533\pi$
$643$	−1897.58			−0.116382			−0.0581908	+	0.998305i	$0.518533\pi$
$644$	−10101.1			−0.618073
$645$	2919.92	−	2045.51i	0.178251	−	0.124871i
$646$		−	28073.1i		−	1.70979i
$647$		−	17928.3i		−	1.08939i	−0.838635	−	0.544694i	$-0.816646\pi$
$647$		−	17928.3i		−	1.08939i	0.838635	−	0.544694i	$-0.183354\pi$
$648$	14004.8	+	11730.4i	0.849012	+	0.711130i
$649$	−6327.71	+	23311.2i	−0.382719	+	1.40993i
$650$			12008.7i			0.724646i
$651$	−203.454	−	290.427i	−0.0122489	−	0.0174850i
$652$	−6895.38			−0.414178
$653$			1789.92i			0.107266i	0.998561	+	0.0536331i	$0.0170801\pi$
$653$			1789.92i			0.107266i	−0.998561	+	0.0536331i	$0.982920\pi$
$654$	5641.32	+	8052.86i	0.337299	+	0.481486i
$655$		−	1646.63i		−	0.0982279i
$656$		−	2762.55i		−	0.164420i
$657$	11441.4	+	4158.62i	0.679410	+	0.246945i
$658$	−14081.3			−0.834264
$659$	−15179.7			−0.897298			−0.448649	−	0.893708i	$-0.648095\pi$
$659$	−15179.7			−0.897298			−0.448649	+	0.893708i	$0.648095\pi$
$660$	−12569.1	−	17942.1i	−0.741291	−	1.05818i
$661$	−23153.2			−1.36241			−0.681207	−	0.732091i	$-0.738545\pi$
$661$	−23153.2			−1.36241			−0.681207	+	0.732091i	$0.738545\pi$
$662$	54330.8			3.18977
$663$	16110.7	−	11286.1i	0.943723	−	0.661112i
$664$	−8561.55			−0.500381
$665$		−	2742.83i		−	0.159943i
$666$	38715.8	+	14072.0i	2.25256	+	0.818740i
$667$			5671.25i			0.329223i
$668$		−	21498.5i		−	1.24522i
$669$	1053.94	−	738.324i	0.0609084	−	0.0426686i
$670$	−6052.96			−0.349024
$671$		−	29810.6i		−	1.71509i
$672$	6893.42	−	4829.09i	0.395714	−	0.277212i
$673$		−	20396.6i		−	1.16825i	−0.811664	−	0.584125i	$-0.801438\pi$
$673$		−	20396.6i		−	1.16825i	0.811664	−	0.584125i	$-0.198562\pi$
$674$		−	33979.0i		−	1.94188i
$675$	−3284.63	−	12226.0i	−0.187297	−	0.697155i
$676$	18378.3			1.04565
$677$		−	19292.1i		−	1.09521i	−0.836738	−	0.547603i	$-0.815540\pi$
$677$		−	19292.1i		−	1.09521i	0.836738	−	0.547603i	$-0.184460\pi$
$678$	650.990	−	456.042i	0.0368748	−	0.0258321i
$679$			10401.1i			0.587860i
$680$	−19450.0			−1.09687
$681$	5004.00	−	3505.48i	0.281577	−	0.197255i
$682$			1667.53i			0.0936263i
$683$	29395.9			1.64685			0.823427	−	0.567422i	$-0.192059\pi$
$683$	29395.9			1.64685			0.823427	+	0.567422i	$0.192059\pi$
$684$	5702.19	−	15688.2i	0.318755	−	0.876977i
$685$	9047.63			0.504660
$686$	27284.9			1.51858
$687$	−11544.5	−	16479.5i	−0.641121	−	0.915186i
$688$			1006.03i			0.0557478i
$689$	−9044.15			−0.500079
$690$	−6068.06	−	8662.01i	−0.334793	−	0.477909i
$691$			19024.6i			1.04736i	0.851914	+	0.523682i	$0.175442\pi$
$691$			19024.6i			1.04736i	−0.851914	+	0.523682i	$0.824558\pi$
$692$	−33195.5			−1.82356
$693$	4962.27	−	13652.5i	0.272007	−	0.748361i
$694$	52176.3			2.85387
$695$		−	6875.72i		−	0.375268i
$696$	5680.12	+	8108.24i	0.309345	+	0.441583i
$697$	42062.0			2.28581
$698$		−	11134.1i		−	0.603770i
$699$	11105.9	−	7780.08i	0.600949	−	0.420987i
$700$	12219.0			0.659766
$701$	−29699.6			−1.60020			−0.800099	−	0.599868i	$-0.795220\pi$
$701$	−29699.6			−1.60020			−0.800099	+	0.599868i	$0.795220\pi$
$702$	18031.6	−	4844.36i	0.969460	−	0.260454i
$703$		−	15193.7i		−	0.815139i
$704$	−43266.2			−2.31627
$705$	−5299.05	−	7564.27i	−0.283083	−	0.404095i
$706$	−11358.0			−0.605472
$707$	18174.0			0.966765
$708$	10714.3	+	29718.0i	0.568742	+	1.57750i
$709$	10911.1			0.577961			0.288981	−	0.957335i	$-0.406684\pi$
$709$	10911.1			0.577961			0.288981	+	0.957335i	$0.406684\pi$
$710$	6842.29			0.361671
$711$	−3722.72	+	10242.2i	−0.196362	+	0.540240i
$712$	38186.8			2.00999
$713$			504.306i			0.0264887i
$714$	−18332.1	−	26168.6i	−0.960869	−	1.37162i
$715$	−9037.75			−0.472717
$716$	−22757.8			−1.18785
$717$	15282.8	+	21815.9i	0.796020	+	1.13630i
$718$			18173.0i			0.944582i
$719$	−1121.25			−0.0581579			−0.0290790	−	0.999577i	$-0.509257\pi$
$719$	−1121.25			−0.0581579			−0.0290790	+	0.999577i	$0.509257\pi$
$720$	−1293.56	−	470.171i	−0.0669557	−	0.0243364i
$721$			11261.1i			0.581673i
$722$	21912.9			1.12952
$723$	−12772.2	+	8947.41i	−0.656991	+	0.460246i
$724$	32071.4			1.64630
$725$		−	6860.36i		−	0.351431i
$726$	−29735.4	+	20830.7i	−1.52009	+	1.06488i
$727$	−8366.74			−0.426830			−0.213415	−	0.976962i	$-0.568459\pi$
$727$	−8366.74			−0.426830			−0.213415	+	0.976962i	$0.568459\pi$
$728$			7274.50i			0.370345i
$729$	−17032.9	+	9864.06i	−0.865363	+	0.501146i
$730$	−12302.6			−0.623751
$731$	−15317.6			−0.775023
$732$	−22369.3	−	31931.7i	−1.12950	−	1.61234i
$733$	−13068.8			−0.658535			−0.329267	−	0.944237i	$-0.606802\pi$
$733$	−13068.8			−0.658535			−0.329267	+	0.944237i	$0.606802\pi$
$734$		−	52907.9i		−	2.66058i
$735$	4238.36	+	6050.16i	0.212700	+	0.303624i
$736$	−11970.0			−0.599482
$737$			11823.8i			0.590957i
$738$	37523.0	+	13638.5i	1.87160	+	0.680271i
$739$		−	27498.4i		−	1.36880i	−0.729105	−	0.684402i	$-0.760063\pi$
$739$		−	27498.4i		−	1.36880i	0.729105	−	0.684402i	$-0.239937\pi$
$740$	−26078.2			−1.29548
$741$	−3951.20	−	5640.25i	−0.195885	−	0.279622i
$742$			14690.4i			0.726822i
$743$		−	15660.2i		−	0.773241i	−0.922239	−	0.386621i	$-0.873642\pi$
$743$		−	15660.2i		−	0.773241i	0.922239	−	0.386621i	$-0.126358\pi$
$744$	505.095	+	721.012i	0.0248894	+	0.0355290i
$745$			7817.83i			0.384461i
$746$	−14323.3			−0.702965
$747$	3151.14	−	8669.59i	0.154343	−	0.424637i
$748$			94122.6i			4.60088i
$749$			2977.51i			0.145255i
$750$	17508.8	+	24993.4i	0.852442	+	1.21684i
$751$		−	8067.62i		−	0.392000i	−0.980604	−	0.196000i	$-0.937205\pi$
$751$		−	8067.62i		−	0.392000i	0.980604	−	0.196000i	$-0.0627952\pi$
$752$	2606.20			0.126381
$753$	−16242.9	−	23186.3i	−0.786086	−	1.12212i
$754$	10118.1			0.488697
$755$	17945.2			0.865026
$756$	−4929.21	−	18347.5i	−0.237134	−	0.882660i
$757$	11714.4			0.562438			0.281219	−	0.959644i	$-0.409261\pi$
$757$	11714.4			0.562438			0.281219	+	0.959644i	$0.409261\pi$
$758$	−13985.4			−0.670150
$759$	−16920.3	+	11853.3i	−0.809181	+	0.566861i
$760$			6809.32i			0.325000i
$761$			27554.7i			1.31256i	0.754517	+	0.656280i	$0.227871\pi$
$761$			27554.7i			1.31256i	−0.754517	+	0.656280i	$0.772129\pi$
$762$	11921.0	−	8351.11i	0.566736	−	0.397019i
$763$		−	4127.41i		−	0.195835i
$764$	−34139.6			−1.61666
$765$	7158.72	−	19695.5i	0.338332	−	0.930838i
$766$			31141.9i			1.46893i
$767$	12577.7	+	3414.17i	0.592119	+	0.160728i
$768$	−21062.3	+	14754.9i	−0.989611	+	0.693258i
$769$			10523.3i			0.493471i	0.969083	+	0.246735i	$0.0793579\pi$
$769$			10523.3i			0.493471i	−0.969083	+	0.246735i	$0.920642\pi$
$770$			14680.0i			0.687053i
$771$	3887.85	+	5549.82i	0.181605	+	0.259237i
$772$	−41352.0			−1.92784
$773$	9615.25			0.447395			0.223698	−	0.974659i	$-0.428187\pi$
$773$	9615.25			0.447395			0.223698	+	0.974659i	$0.428187\pi$
$774$	−13664.6	−	4966.69i	−0.634579	−	0.230651i
$775$		−	610.046i		−	0.0282755i
$776$		−	25821.7i		−	1.19452i
$777$	−9921.68	−	14163.0i	−0.458093	−	0.653918i
$778$		−	22195.0i		−	1.02279i
$779$		−	14725.6i		−	0.677279i
$780$	−9680.81	+	6781.76i	−0.444396	+	0.311315i
$781$		−	13365.7i		−	0.612370i
$782$			45440.1i			2.07792i
$783$	−10301.2	+	2767.50i	−0.470158	+	0.126312i
$784$	−2084.52			−0.0949582
$785$	16103.3			0.732166
$786$	−5500.00	+	3852.95i	−0.249591	+	0.174848i
$787$	−2154.13			−0.0975685			−0.0487843	−	0.998809i	$-0.515535\pi$
$787$	−2154.13			−0.0975685			−0.0487843	+	0.998809i	$0.515535\pi$
$788$			53907.6i			2.43703i
$789$	123.229	+	175.907i	0.00556031	+	0.00793721i
$790$		−	11013.0i		−	0.495982i
$791$	−333.658			−0.0149981
$792$	−12319.3	+	33893.5i	−0.552711	+	1.52065i
$793$	−16084.5			−0.720276
$794$			29964.9i			1.33931i
$795$	−7891.48	+	5528.27i	−0.352053	+	0.246626i
$796$	60377.9			2.68849
$797$	7133.48			0.317040			0.158520	−	0.987356i	$-0.449328\pi$
$797$	7133.48			0.317040			0.158520	+	0.987356i	$0.449328\pi$
$798$	−9161.45	+	6417.93i	−0.406406	+	0.284702i
$799$			39681.4i			1.75698i
$800$	14479.7			0.639920
$801$	−14054.9	+	38668.6i	−0.619982	+	1.70573i
$802$	−26331.1			−1.15933
$803$			24031.7i			1.05612i
$804$	8872.37	+	12665.1i	0.389184	+	0.555552i
$805$			4439.63i			0.194380i
$806$	899.731			0.0393197
$807$	26971.8	−	18894.7i	1.17652	−	0.824196i
$808$	−45118.6			−1.96444
$809$	9019.73			0.391986			0.195993	−	0.980605i	$-0.437207\pi$
$809$	9019.73			0.391986			0.195993	+	0.980605i	$0.437207\pi$
$810$	12772.4	−	15248.9i	0.554045	−	0.661470i
$811$			21944.8i			0.950168i	0.879940	+	0.475084i	$0.157582\pi$
$811$			21944.8i			0.950168i	−0.879940	+	0.475084i	$0.842418\pi$
$812$		−	10295.3i		−	0.444942i
$813$	19345.5	−	13552.2i	0.834533	−	0.584621i
$814$			81319.1i			3.50152i
$815$			3030.65i			0.130256i
$816$	3392.94	+	4843.35i	0.145560	+	0.207783i
$817$			5362.58i			0.229636i
$818$			29689.4i			1.26903i
$819$	−7366.30	−	2677.43i	−0.314285	−	0.114233i
$820$	−25274.8			−1.07638
$821$	−6364.35			−0.270545			−0.135272	−	0.990808i	$-0.543191\pi$
$821$	−6364.35			−0.270545			−0.135272	+	0.990808i	$0.543191\pi$
$822$	−21170.5	−	30220.5i	−0.898306	−	1.28231i
$823$		−	35235.2i		−	1.49237i	−0.665739	−	0.746185i	$-0.731883\pi$
$823$		−	35235.2i		−	1.49237i	0.665739	−	0.746185i	$-0.268117\pi$
$824$		−	27956.8i		−	1.18194i
$825$	20468.0	−	14338.6i	0.863765	−	0.605099i
$826$	5545.63	−	20430.0i	0.233604	−	0.860594i
$827$			6231.54i			0.262021i	0.991381	+	0.131011i	$0.0418222\pi$
$827$			6231.54i			0.262021i	−0.991381	+	0.131011i	$0.958178\pi$
$828$	−9229.75	+	25393.4i	−0.387386	+	1.06580i
$829$	−26098.6			−1.09342			−0.546708	−	0.837323i	$-0.684119\pi$
$829$	−26098.6			−1.09342			−0.546708	+	0.837323i	$0.684119\pi$
$830$			9322.10i			0.389849i
$831$	26902.7	−	18846.4i	1.12304	−	0.786730i
$832$			23344.6i			0.972751i
$833$		−	31738.5i		−	1.32014i
$834$	−22966.0	+	16088.5i	−0.953532	+	0.667984i
$835$	−9449.02			−0.391613
$836$	32951.7			1.36323
$837$	−916.014	+	246.095i	−0.0378280	+	0.0101628i
$838$	261.181			0.0107665
$839$	4962.97			0.204220			0.102110	−	0.994773i	$-0.467441\pi$
$839$	4962.97			0.204220			0.102110	+	0.994773i	$0.467441\pi$
$840$	4446.57	+	6347.38i	0.182644	+	0.260721i
$841$	18608.7			0.762997
$842$		−	28094.3i		−	1.14987i
$843$	6234.93	+	8900.23i	0.254736	+	0.363630i
$844$		−	61272.8i		−	2.49893i
$845$		−	8077.61i		−	0.328850i
$846$	−12866.6	+	35399.2i	−0.522887	+	1.43859i
$847$	15240.6			0.618267
$848$		−	2718.93i		−	0.110104i
$849$	−22379.1	−	31945.7i	−0.904652	−	1.29137i
$850$		−	54967.6i		−	2.21809i
$851$			24593.1i			0.990645i
$852$	−10029.4	−	14316.7i	−0.403286	−	0.575682i
$853$	11139.2			0.447128			0.223564	−	0.974689i	$-0.428231\pi$
$853$	11139.2			0.447128			0.223564	+	0.974689i	$0.428231\pi$
$854$			26126.1i			1.04686i
$855$	−6895.25	−	2506.22i	−0.275804	−	0.100247i
$856$		−	7391.94i		−	0.295153i
$857$	−23620.2			−0.941483			−0.470741	−	0.882271i	$-0.656013\pi$
$857$	−23620.2			−0.941483			−0.470741	+	0.882271i	$0.656013\pi$
$858$	21147.4	+	30187.5i	0.841446	+	1.20115i
$859$			31829.2i			1.26426i	0.774862	+	0.632130i	$0.217819\pi$
$859$			31829.2i			1.26426i	−0.774862	+	0.632130i	$0.782181\pi$
$860$	9204.23			0.364955
$861$	−9616.00	−	13726.6i	−0.380618	−	0.543324i
$862$	−4657.59			−0.184035
$863$	−8224.22			−0.324398			−0.162199	−	0.986758i	$-0.551859\pi$
$863$	−8224.22			−0.324398			−0.162199	+	0.986758i	$0.551859\pi$
$864$	−5841.19	−	21742.0i	−0.230002	−	0.856110i
$865$			14590.1i			0.573499i
$866$	59694.8			2.34239
$867$	−52835.2	+	37013.0i	−2.06964	+	1.44986i
$868$		−	915.490i		−	0.0357993i
$869$	−21512.8			−0.839782
$870$	8828.52	−	6184.70i	0.344040	−	0.241013i
$871$	6379.63			0.248181
$872$			10246.7i			0.397932i
$873$	26147.5	+	9503.85i	1.01370	+	0.368450i
$874$	15908.2			0.615680
$875$		−	12810.1i		−	0.494927i
$876$	18033.0	+	25741.6i	0.695522	+	0.992842i
$877$	27049.7			1.04151			0.520755	−	0.853706i	$-0.325650\pi$
$877$	27049.7			1.04151			0.520755	+	0.853706i	$0.325650\pi$
$878$	−62917.2			−2.41840
$879$	21910.5	+	31276.8i	0.840756	+	1.20016i
$880$		−	2717.01i		−	0.104080i
$881$	−38603.4			−1.47625			−0.738127	−	0.674662i	$-0.764290\pi$
$881$	−38603.4			−1.47625			−0.738127	+	0.674662i	$0.764290\pi$
$882$	10291.1	−	28313.5i	0.392880	−	1.08091i
$883$	−39937.9			−1.52210			−0.761052	−	0.648690i	$-0.775317\pi$
$883$	−39937.9			−1.52210			−0.761052	+	0.648690i	$0.775317\pi$
$884$	50784.6			1.93221
$885$	13061.6	−	4709.15i	0.496115	−	0.178866i
$886$	−76186.8			−2.88888
$887$	−38978.7			−1.47551			−0.737754	−	0.675070i	$-0.764113\pi$
$887$	−38978.7			−1.47551			−0.737754	+	0.675070i	$0.764113\pi$
$888$	24631.5	+	35160.9i	0.930833	+	1.32874i
$889$	−6110.00			−0.230509
$890$		−	41579.0i		−	1.56599i
$891$	−29787.0	−	24949.5i	−1.11998	−	0.938092i
$892$	3322.26			0.124706
$893$	13892.2			0.520587
$894$	26112.7	−	18292.9i	0.976891	−	0.684348i
$895$			10002.5i			0.373571i
$896$	24960.4			0.930658
$897$	6395.54	+	9129.49i	0.238061	+	0.339827i
$898$		−	67842.1i		−	2.52107i
$899$	−514.000			−0.0190688
$900$	11165.0	−	30717.7i	0.413518	−	1.13769i
$901$	41397.9			1.53070
$902$			78813.7i			2.90932i
$903$	3501.83	+	4998.78i	0.129052	+	0.184218i
$904$	828.338			0.0304758
$905$		−	14096.0i		−	0.517753i
$906$	−41990.0	−	59939.9i	−1.53976	−	2.19798i
$907$	−12606.7			−0.461518			−0.230759	−	0.973011i	$-0.574121\pi$
$907$	−12606.7			−0.461518			−0.230759	+	0.973011i	$0.574121\pi$
$908$	15773.7			0.576508
$909$	16606.2	−	45687.9i	0.605934	−	1.66708i
$910$	7920.72			0.288538
$911$		−	7996.20i		−	0.290808i	−0.989372	−	0.145404i	$-0.953552\pi$
$911$		−	7996.20i		−	0.290808i	0.989372	−	0.145404i	$-0.0464482\pi$
$912$	1695.62	−	1187.84i	0.0615654	−	0.0431288i
$913$	18209.7			0.660081
$914$		−	9118.31i		−	0.329986i
$915$	−14034.6	+	9831.74i	−0.507070	+	0.355221i
$916$		−	51947.1i		−	1.87378i
$917$	2818.97			0.101516
$918$	−82536.5	+	22174.2i	−2.96744	+	0.797229i
$919$			40590.8i			1.45698i	0.685056	+	0.728491i	$0.259778\pi$
$919$			40590.8i			1.45698i	−0.685056	+	0.728491i	$0.740222\pi$
$920$		−	11021.8i		−	0.394976i
$921$	20524.5	−	14378.2i	0.734317	−	0.514416i
$922$			50694.4i			1.81077i
$923$	−7211.56			−0.257174
$924$	30716.2	−	21517.8i	1.09360	−	0.766108i
$925$		−	29749.6i		−	1.05747i
$926$		−	75473.2i		−	2.67841i
$927$	28309.6	+	10289.7i	1.00303	+	0.364572i
$928$		−	12200.1i		−	0.431559i
$929$	−3584.68			−0.126598			−0.0632991	−	0.997995i	$-0.520162\pi$
$929$	−3584.68			−0.126598			−0.0632991	+	0.997995i	$0.520162\pi$
$930$	785.061	−	549.964i	0.0276808	−	0.0193914i
$931$	−11111.4			−0.391152
$932$	35008.2			1.23040
$933$	15721.0	+	22441.3i	0.551641	+	0.787455i
$934$	46853.5			1.64143
$935$	41368.6			1.44695
$936$	18287.5	+	6646.98i	0.638618	+	0.232119i
$937$			1948.62i			0.0679388i	0.999423	+	0.0339694i	$0.0108149\pi$
$937$			1948.62i			0.0679388i	−0.999423	+	0.0339694i	$0.989185\pi$
$938$		−	10362.4i		−	0.360709i
$939$	26390.2	+	37671.4i	0.917158	+	1.30922i
$940$		−	23844.3i		−	0.827356i
$941$	8750.04			0.303128			0.151564	−	0.988447i	$-0.451569\pi$
$941$	8750.04			0.303128			0.151564	+	0.988447i	$0.451569\pi$
$942$	−37680.0	−	53787.4i	−1.30327	−	1.86039i
$943$			23835.4i			0.823103i
$944$	−1026.40	+	3781.23i	−0.0353881	+	0.130369i
$945$	−8064.06	+	2166.48i	−0.277591	+	0.0745774i
$946$		−	28701.3i		−	0.986428i
$947$		−	7137.19i		−	0.244908i	−0.992474	−	0.122454i	$-0.960924\pi$
$947$		−	7137.19i		−	0.244908i	0.992474	−	0.122454i	$-0.0390763\pi$
$948$	−23043.5	+	16142.8i	−0.789470	+	0.553052i
$949$	12966.5			0.443531
$950$	−19243.8			−0.657211
$951$	24224.1	+	34579.4i	0.825994	+	1.17909i
$952$		−	33297.7i		−	1.13360i
$953$			7562.46i			0.257054i	0.991706	+	0.128527i	$0.0410249\pi$
$953$			7562.46i			0.257054i	−0.991706	+	0.128527i	$0.958975\pi$
$954$	36930.5	+	13423.2i	1.25332	+	0.455546i
$955$			15005.0i			0.508429i
$956$			68768.5i			2.32650i
$957$	−12081.1	−	17245.6i	−0.408075	−	0.582518i
$958$			8662.68i			0.292149i
$959$			15489.2i			0.521556i
$960$	14269.5	+	20369.4i	0.479735	+	0.684811i
$961$	29745.3			0.998466
$962$	43876.4			1.47051
$963$	7485.22	+	2720.66i	0.250475	+	0.0910404i
$964$	−40260.9			−1.34514
$965$			18175.0i			0.606294i
$966$	14829.0	−	10388.3i	0.493909	−	0.346001i
$967$		−	21113.6i		−	0.702138i	−0.936350	−	0.351069i	$-0.885818\pi$
$967$		−	21113.6i		−	0.702138i	0.936350	−	0.351069i	$-0.114182\pi$
$968$	−37836.2			−1.25630
$969$	18085.9	+	25817.2i	0.599590	+	0.855901i
$970$	−28115.5			−0.930654
$971$		−	14513.2i		−	0.479660i	−0.970815	−	0.239830i	$-0.922908\pi$
$971$		−	14513.2i		−	0.479660i	0.970815	−	0.239830i	$-0.0770918\pi$
$972$	−50628.1	−	4373.11i	−1.67068	−	0.144308i
$973$	11771.0			0.387831
$974$	25800.7			0.848777
$975$	−7736.51	−	11043.7i	−0.254120	−	0.362750i
$976$		−	4835.48i		−	0.158586i
$977$	33445.8			1.09522			0.547608	−	0.836735i	$-0.315538\pi$
$977$	33445.8			1.09522			0.547608	+	0.836735i	$0.315538\pi$
$978$	10122.8	−	7091.41i	0.330974	−	0.231859i
$979$	−81220.1			−2.65149
$980$			19071.5i			0.621648i
$981$	−10376.0	−	3771.37i	−0.337696	−	0.122743i
$982$		−	1787.15i		−	0.0580756i
$983$	−45100.3			−1.46335			−0.731677	−	0.681652i	$-0.761262\pi$
$983$	−45100.3			−1.46335			−0.731677	+	0.681652i	$0.761262\pi$
$984$	23872.6	+	34077.7i	0.773406	+	1.10402i
$985$	23693.4			0.766430
$986$	−46313.5			−1.49587
$987$	12949.7	−	9071.76i	0.417624	−	0.292561i
$988$		−	17779.3i		−	0.572506i
$989$		−	8680.05i		−	0.279079i
$990$	36904.4	+	13413.7i	1.18475	+	0.430620i
$991$		−	22423.7i		−	0.718782i	−0.933187	−	0.359391i	$-0.882984\pi$
$991$		−	22423.7i		−	0.718782i	0.933187	−	0.359391i	$-0.117016\pi$
$992$		−	1084.87i		−	0.0347224i
$993$	−49964.8	+	35002.2i	−1.59676	+	1.11859i
$994$			11713.7i			0.373779i
$995$		−	26537.2i		−	0.845513i
$996$	19505.4	−	13664.2i	0.620534	−	0.434707i
$997$	−27130.8			−0.861828			−0.430914	−	0.902393i	$-0.641809\pi$
$997$	−27130.8			−0.861828			−0.430914	+	0.902393i	$0.641809\pi$
$998$	−33413.4			−1.05980
$999$	−44670.4	+	12001.1i	−1.41472	+	0.380078i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.4.d.c.176.7	✓	52
3.2	odd	2	inner	177.4.d.c.176.46	yes	52
59.58	odd	2	inner	177.4.d.c.176.45	yes	52
177.176	even	2	inner	177.4.d.c.176.8	yes	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.4.d.c.176.7	✓	52	1.1	even	1	trivial
177.4.d.c.176.8	yes	52	177.176	even	2	inner
177.4.d.c.176.45	yes	52	59.58	odd	2	inner
177.4.d.c.176.46	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)

\(f(q)\)	\(=\)	\(q-4.62765 q^{2} +(4.25578 - 2.98133i) q^{3} +13.4152 q^{4} -5.89622i q^{5} +(-19.6943 + 13.7966i) q^{6} +10.0941 q^{7} -25.0596 q^{8} +(9.22335 - 25.3758i) q^{9} +O(q^{10})\)	\(q-4.62765 q^{2} +(4.25578 - 2.98133i) q^{3} +13.4152 q^{4} -5.89622i q^{5} +(-19.6943 + 13.7966i) q^{6} +10.0941 q^{7} -25.0596 q^{8} +(9.22335 - 25.3758i) q^{9} +27.2857i q^{10} +53.2996 q^{11} +(57.0921 - 39.9951i) q^{12} -28.7582i q^{13} -46.7120 q^{14} +(-17.5786 - 25.0930i) q^{15} +8.64556 q^{16} +131.636i q^{17} +(-42.6825 + 117.430i) q^{18} +46.0847 q^{19} -79.0989i q^{20} +(42.9583 - 30.0938i) q^{21} -246.652 q^{22} -74.5942 q^{23} +(-106.648 + 74.7108i) q^{24} +90.2346 q^{25} +133.083i q^{26} +(-36.4010 - 135.492i) q^{27} +135.414 q^{28} -76.0280i q^{29} +(81.3476 + 116.122i) q^{30} -6.76067i q^{31} +160.468 q^{32} +(226.832 - 158.904i) q^{33} -609.164i q^{34} -59.5171i q^{35} +(123.733 - 340.420i) q^{36} -329.691i q^{37} -213.264 q^{38} +(-85.7378 - 122.389i) q^{39} +147.757i q^{40} -319.534i q^{41} +(-198.796 + 139.264i) q^{42} +116.364i q^{43} +715.024 q^{44} +(-149.621 - 54.3829i) q^{45} +345.196 q^{46} +301.449 q^{47} +(36.7936 - 25.7753i) q^{48} -241.109 q^{49} -417.574 q^{50} +(392.449 + 560.212i) q^{51} -385.797i q^{52} -314.489i q^{53} +(168.451 + 627.008i) q^{54} -314.266i q^{55} -252.954 q^{56} +(196.126 - 137.394i) q^{57} +351.831i q^{58} +(-118.720 + 437.361i) q^{59} +(-235.820 - 336.627i) q^{60} -559.302i q^{61} +31.2860i q^{62} +(93.1014 - 256.146i) q^{63} -811.754 q^{64} -169.565 q^{65} +(-1049.70 + 735.351i) q^{66} +221.837i q^{67} +1765.91i q^{68} +(-317.456 + 222.390i) q^{69} +275.424i q^{70} -250.765i q^{71} +(-231.133 + 635.906i) q^{72} +450.880i q^{73} +1525.70i q^{74} +(384.019 - 269.019i) q^{75} +618.234 q^{76} +538.012 q^{77} +(396.765 + 566.373i) q^{78} -403.620 q^{79} -50.9761i q^{80} +(-558.860 - 468.099i) q^{81} +1478.69i q^{82} +341.648 q^{83} +(576.293 - 403.714i) q^{84} +776.152 q^{85} -538.491i q^{86} +(-226.665 - 323.559i) q^{87} -1335.67 q^{88} -1523.84 q^{89} +(692.395 + 251.665i) q^{90} -290.289i q^{91} -1000.69 q^{92} +(-20.1558 - 28.7719i) q^{93} -1395.00 q^{94} -271.726i q^{95} +(682.916 - 478.408i) q^{96} +1030.41i q^{97} +1115.77 q^{98} +(491.601 - 1352.52i) 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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