LMFDB - Embedded newform 165.4.c.a.34.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [165,4,Mod(34,165)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(165, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

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

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

chi := DirichletCharacter("165.34");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 165 = 3 \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	165.c (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:	$9.73531515095$
Analytic rank:	$0$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} + 97x^{12} + 3674x^{10} + 68702x^{8} + 656605x^{6} + 2988841x^{4} + 5502384x^{2} + 3385600 $ x^14 + 97x^12 + 3674x^10 + 68702x^8 + 656605x^6 + 2988841x^4 + 5502384x^2 + 3385600
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4}\cdot 3^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			34.3
Root			$-4.31207i$ of defining polynomial
Character	$\chi$	$=$	165.34
Dual form			165.4.c.a.34.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.31207i q^{2} -3.00000i q^{3} -10.5939 q^{4} +(7.94512 - 7.86608i) q^{5} -12.9362 q^{6} -9.06309i q^{7} +11.1853i q^{8} -9.00000 q^{9} +O(q^{10})$	\(q-4.31207i q^{2} -3.00000i q^{3} -10.5939 q^{4} +(7.94512 - 7.86608i) q^{5} -12.9362 q^{6} -9.06309i q^{7} +11.1853i q^{8} -9.00000 q^{9} +(-33.9191 - 34.2599i) q^{10} -11.0000 q^{11} +31.7818i q^{12} -40.4128i q^{13} -39.0807 q^{14} +(-23.5982 - 23.8353i) q^{15} -36.5198 q^{16} +76.4137i q^{17} +38.8086i q^{18} +44.7264 q^{19} +(-84.1701 + 83.3328i) q^{20} -27.1893 q^{21} +47.4328i q^{22} +50.4845i q^{23} +33.5559 q^{24} +(1.24972 - 124.994i) q^{25} -174.263 q^{26} +27.0000i q^{27} +96.0139i q^{28} +81.1094 q^{29} +(-102.780 + 101.757i) q^{30} +100.171 q^{31} +246.958i q^{32} +33.0000i q^{33} +329.501 q^{34} +(-71.2910 - 72.0073i) q^{35} +95.3455 q^{36} +38.7941i q^{37} -192.863i q^{38} -121.238 q^{39} +(87.9843 + 88.8684i) q^{40} +18.6954 q^{41} +117.242i q^{42} -40.8344i q^{43} +116.533 q^{44} +(-71.5060 + 70.7947i) q^{45} +217.693 q^{46} +36.4307i q^{47} +109.559i q^{48} +260.860 q^{49} +(-538.982 - 5.38888i) q^{50} +229.241 q^{51} +428.131i q^{52} -652.838i q^{53} +116.426 q^{54} +(-87.3963 + 86.5268i) q^{55} +101.373 q^{56} -134.179i q^{57} -349.749i q^{58} -744.649 q^{59} +(249.998 + 252.510i) q^{60} -516.203 q^{61} -431.945i q^{62} +81.5678i q^{63} +772.743 q^{64} +(-317.890 - 321.084i) q^{65} +142.298 q^{66} -430.849i q^{67} -809.523i q^{68} +151.453 q^{69} +(-310.501 + 307.412i) q^{70} -272.484 q^{71} -100.668i q^{72} -692.483i q^{73} +167.283 q^{74} +(-374.981 - 3.74916i) q^{75} -473.829 q^{76} +99.6940i q^{77} +522.788i q^{78} +1086.01 q^{79} +(-290.154 + 287.268i) q^{80} +81.0000 q^{81} -80.6157i q^{82} -595.328i q^{83} +288.042 q^{84} +(601.076 + 607.116i) q^{85} -176.081 q^{86} -243.328i q^{87} -123.038i q^{88} +706.539 q^{89} +(305.272 + 308.339i) q^{90} -366.265 q^{91} -534.830i q^{92} -300.513i q^{93} +157.092 q^{94} +(355.356 - 351.821i) q^{95} +740.875 q^{96} -1311.14i q^{97} -1124.85i q^{98} +99.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 82 q^{4} - 14 q^{5} + 18 q^{6} - 126 q^{9}+O(q^{10}) $ 14 * q - 82 * q^4 - 14 * q^5 + 18 * q^6 - 126 * q^9	$ 14 q - 82 q^{4} - 14 q^{5} + 18 q^{6} - 126 q^{9} - 28 q^{10} - 154 q^{11} - 284 q^{14} + 362 q^{16} - 52 q^{19} + 226 q^{20} + 300 q^{21} - 126 q^{24} - 366 q^{25} + 952 q^{26} - 1144 q^{29} - 582 q^{30} - 280 q^{31} + 1612 q^{34} - 600 q^{35} + 738 q^{36} - 144 q^{39} + 176 q^{40} + 1792 q^{41} + 902 q^{44} + 126 q^{45} - 688 q^{46} - 590 q^{49} + 388 q^{50} + 228 q^{51} - 162 q^{54} + 154 q^{55} + 3044 q^{56} - 2632 q^{59} - 1140 q^{60} - 772 q^{61} - 1738 q^{64} - 904 q^{65} - 198 q^{66} - 1368 q^{69} + 84 q^{70} + 1608 q^{71} + 1496 q^{74} - 300 q^{75} - 3396 q^{76} + 748 q^{79} - 2606 q^{80} + 1134 q^{81} - 5040 q^{84} + 2508 q^{85} - 5068 q^{86} - 1388 q^{89} + 252 q^{90} - 6752 q^{91} + 5840 q^{94} + 1724 q^{95} + 5946 q^{96} + 1386 q^{99}+O(q^{100}) $ 14 * q - 82 * q^4 - 14 * q^5 + 18 * q^6 - 126 * q^9 - 28 * q^10 - 154 * q^11 - 284 * q^14 + 362 * q^16 - 52 * q^19 + 226 * q^20 + 300 * q^21 - 126 * q^24 - 366 * q^25 + 952 * q^26 - 1144 * q^29 - 582 * q^30 - 280 * q^31 + 1612 * q^34 - 600 * q^35 + 738 * q^36 - 144 * q^39 + 176 * q^40 + 1792 * q^41 + 902 * q^44 + 126 * q^45 - 688 * q^46 - 590 * q^49 + 388 * q^50 + 228 * q^51 - 162 * q^54 + 154 * q^55 + 3044 * q^56 - 2632 * q^59 - 1140 * q^60 - 772 * q^61 - 1738 * q^64 - 904 * q^65 - 198 * q^66 - 1368 * q^69 + 84 * q^70 + 1608 * q^71 + 1496 * q^74 - 300 * q^75 - 3396 * q^76 + 748 * q^79 - 2606 * q^80 + 1134 * q^81 - 5040 * q^84 + 2508 * q^85 - 5068 * q^86 - 1388 * q^89 + 252 * q^90 - 6752 * q^91 + 5840 * q^94 + 1724 * q^95 + 5946 * q^96 + 1386 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/165\mathbb{Z}\right)^\times$.

$n$	$46$	$56$	$67$
$\chi(n)$	$1$	$1$	$-1$

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 $

$2$		−	4.31207i		−	1.52455i	−0.647255	−	0.762274i	$-0.724083\pi$
$2$		−	4.31207i		−	1.52455i	0.647255	−	0.762274i	$-0.275917\pi$
$3$		−	3.00000i		−	0.577350i
$3$		−	3.00000i		−	0.577350i
$4$	−10.5939			−1.32424
$5$	7.94512	−	7.86608i	0.710633	−	0.703563i
$5$	7.94512	−	7.86608i	0.710633	−	0.703563i
$6$	−12.9362			−0.880198
$7$		−	9.06309i		−	0.489361i	−0.969604	−	0.244680i	$-0.921317\pi$
$7$		−	9.06309i		−	0.489361i	0.969604	−	0.244680i	$-0.0786831\pi$
$8$			11.1853i			0.494325i
$9$	−9.00000			−0.333333
$10$	−33.9191	−	34.2599i	−1.07262	−	1.08339i
$11$	−11.0000			−0.301511
$11$	−11.0000			−0.301511
$12$			31.7818i			0.764552i
$13$		−	40.4128i		−	0.862192i	−0.902306	−	0.431096i	$-0.858127\pi$
$13$		−	40.4128i		−	0.862192i	0.902306	−	0.431096i	$-0.141873\pi$
$14$	−39.0807			−0.746054
$15$	−23.5982	−	23.8353i	−0.406202	−	0.410284i
$16$	−36.5198			−0.570622
$17$			76.4137i			1.09018i	0.838378	+	0.545089i	$0.183504\pi$
$17$			76.4137i			1.09018i	−0.838378	+	0.545089i	$0.816496\pi$
$18$			38.8086i			0.508182i
$19$	44.7264			0.540050			0.270025	−	0.962853i	$-0.412968\pi$
$19$	44.7264			0.540050			0.270025	+	0.962853i	$0.412968\pi$
$20$	−84.1701	+	83.3328i	−0.941051	+	0.931689i
$21$	−27.1893			−0.282533
$22$			47.4328i			0.459668i
$23$			50.4845i			0.457685i	0.973464	+	0.228842i	$0.0734940\pi$
$23$			50.4845i			0.457685i	−0.973464	+	0.228842i	$0.926506\pi$
$24$	33.5559			0.285399
$25$	1.24972	−	124.994i	0.00999775	−	0.999950i
$26$	−174.263			−1.31445
$27$			27.0000i			0.192450i
$28$			96.0139i			0.648033i
$29$	81.1094			0.519367			0.259683	−	0.965694i	$-0.416382\pi$
$29$	81.1094			0.519367			0.259683	+	0.965694i	$0.416382\pi$
$30$	−102.780	+	101.757i	−0.625497	+	0.619275i
$31$	100.171			0.580363			0.290182	−	0.956972i	$-0.406284\pi$
$31$	100.171			0.580363			0.290182	+	0.956972i	$0.406284\pi$
$32$			246.958i			1.36427i
$33$			33.0000i			0.174078i
$34$	329.501			1.66203
$35$	−71.2910	−	72.0073i	−0.344296	−	0.347756i
$36$	95.3455			0.441415
$37$			38.7941i			0.172371i	0.996279	+	0.0861853i	$0.0274677\pi$
$37$			38.7941i			0.172371i	−0.996279	+	0.0861853i	$0.972532\pi$
$38$		−	192.863i		−	0.823331i
$39$	−121.238			−0.497787
$40$	87.9843	+	88.8684i	0.347789	+	0.351283i
$41$	18.6954			0.0712128			0.0356064	−	0.999366i	$-0.488664\pi$
$41$	18.6954			0.0712128			0.0356064	+	0.999366i	$0.488664\pi$
$42$			117.242i			0.430734i
$43$		−	40.8344i		−	0.144818i	−0.997375	−	0.0724091i	$-0.976931\pi$
$43$		−	40.8344i		−	0.144818i	0.997375	−	0.0724091i	$-0.0230687\pi$
$44$	116.533			0.399274
$45$	−71.5060	+	70.7947i	−0.236878	+	0.234521i
$46$	217.693			0.697762
$47$			36.4307i			0.113063i	0.998401	+	0.0565315i	$0.0180041\pi$
$47$			36.4307i			0.113063i	−0.998401	+	0.0565315i	$0.981996\pi$
$48$			109.559i			0.329449i
$49$	260.860			0.760526
$50$	−538.982	−	5.38888i	−1.52447	−	0.0152420i
$51$	229.241			0.629415
$52$			428.131i			1.14175i
$53$		−	652.838i		−	1.69197i	−0.533209	−	0.845983i	$-0.679014\pi$
$53$		−	652.838i		−	1.69197i	0.533209	−	0.845983i	$-0.320986\pi$
$54$	116.426			0.293399
$55$	−87.3963	+	86.5268i	−0.214264	+	0.212132i
$56$	101.373			0.241903
$57$		−	134.179i		−	0.311798i
$58$		−	349.749i		−	0.791799i
$59$	−744.649			−1.64314			−0.821568	−	0.570110i	$-0.806900\pi$
$59$	−744.649			−1.64314			−0.821568	+	0.570110i	$0.806900\pi$
$60$	249.998	+	252.510i	0.537911	+	0.543316i
$61$	−516.203			−1.08349			−0.541746	−	0.840542i	$-0.682237\pi$
$61$	−516.203			−1.08349			−0.541746	+	0.840542i	$0.682237\pi$
$62$		−	431.945i		−	0.884791i
$63$			81.5678i			0.163120i
$64$	772.743			1.50926
$65$	−317.890	−	321.084i	−0.606606	−	0.612702i
$66$	142.298			0.265390
$67$		−	430.849i		−	0.785621i	−0.919619	−	0.392811i	$-0.871503\pi$
$67$		−	430.849i		−	0.785621i	0.919619	−	0.392811i	$-0.128497\pi$
$68$		−	809.523i		−	1.44366i
$69$	151.453			0.264244
$70$	−310.501	+	307.412i	−0.530170	+	0.524896i
$71$	−272.484			−0.455464			−0.227732	−	0.973724i	$-0.573131\pi$
$71$	−272.484			−0.455464			−0.227732	+	0.973724i	$0.573131\pi$
$72$		−	100.668i		−	0.164775i
$73$		−	692.483i		−	1.11026i	−0.831763	−	0.555130i	$-0.812668\pi$
$73$		−	692.483i		−	1.11026i	0.831763	−	0.555130i	$-0.187332\pi$
$74$	167.283			0.262787
$75$	−374.981	−	3.74916i	−0.577321	−	0.00577220i
$76$	−473.829			−0.715157
$77$			99.6940i			0.147548i
$78$			522.788i			0.758899i
$79$	1086.01			1.54665			0.773324	−	0.634011i	$-0.218593\pi$
$79$	1086.01			1.54665			0.773324	+	0.634011i	$0.218593\pi$
$80$	−290.154	+	287.268i	−0.405503	+	0.401469i
$81$	81.0000			0.111111
$82$		−	80.6157i		−	0.108567i
$83$		−	595.328i		−	0.787299i	−0.919261	−	0.393649i	$-0.871212\pi$
$83$		−	595.328i		−	0.787299i	0.919261	−	0.393649i	$-0.128788\pi$
$84$	288.042			0.374142
$85$	601.076	+	607.116i	0.767010	+	0.774717i
$86$	−176.081			−0.220782
$87$		−	243.328i		−	0.299857i
$88$		−	123.038i		−	0.149045i
$89$	706.539			0.841494			0.420747	−	0.907178i	$-0.361768\pi$
$89$	706.539			0.841494			0.420747	+	0.907178i	$0.361768\pi$
$90$	305.272	+	308.339i	0.357538	+	0.361131i
$91$	−366.265			−0.421923
$92$		−	534.830i		−	0.606086i
$93$		−	300.513i		−	0.335073i
$94$	157.092			0.172370
$95$	355.356	−	351.821i	0.383777	−	0.379959i
$96$	740.875			0.787659
$97$		−	1311.14i		−	1.37244i	−0.727396	−	0.686218i	$-0.759270\pi$
$97$		−	1311.14i		−	1.37244i	0.727396	−	0.686218i	$-0.240730\pi$
$98$		−	1124.85i		−	1.15946i
$99$	99.0000			0.100504
$100$	−13.2395	+	1324.18i	−0.0132395	+	1.32418i
$101$	1377.31			1.35690			0.678452	−	0.734644i	$-0.262651\pi$
$101$	1377.31			1.35690			0.678452	+	0.734644i	$0.262651\pi$
$102$		−	988.503i		−	0.959573i
$103$		−	714.721i		−	0.683724i	−0.939750	−	0.341862i	$-0.888942\pi$
$103$		−	714.721i		−	0.683724i	0.939750	−	0.341862i	$-0.111058\pi$
$104$	452.029			0.426203
$105$	−216.022	+	213.873i	−0.200777	+	0.198780i
$106$	−2815.09			−2.57948
$107$			1495.34i			1.35102i	0.737349	+	0.675512i	$0.236078\pi$
$107$			1495.34i			1.35102i	−0.737349	+	0.675512i	$0.763922\pi$
$108$		−	286.037i		−	0.254851i
$109$	743.908			0.653702			0.326851	−	0.945076i	$-0.394013\pi$
$109$	743.908			0.653702			0.326851	+	0.945076i	$0.394013\pi$
$110$	373.110	+	376.859i	0.323406	+	0.326655i
$111$	116.382			0.0995182
$112$			330.983i			0.279240i
$113$			1639.90i			1.36521i	0.730789	+	0.682604i	$0.239153\pi$
$113$			1639.90i			1.36521i	−0.730789	+	0.682604i	$0.760847\pi$
$114$	−578.590			−0.475350
$115$	397.115	+	401.105i	0.322010	+	0.325246i
$116$	−859.269			−0.687768
$117$			363.715i			0.287397i
$118$			3210.98i			2.50504i
$119$	692.544			0.533491
$120$	266.605	−	263.953i	0.202814	−	0.200796i
$121$	121.000			0.0909091
$122$			2225.90i			1.65183i
$123$		−	56.0861i		−	0.0411147i
$124$	−1061.21			−0.768543
$125$	−973.281	−	1002.92i	−0.696423	−	0.717631i
$126$	351.726			0.248685
$127$			2329.48i			1.62762i	0.581131	+	0.813810i	$0.302610\pi$
$127$			2329.48i			1.62762i	−0.581131	+	0.813810i	$0.697390\pi$
$128$		−	1356.46i		−	0.936679i
$129$	−122.503			−0.0836108
$130$	−1384.54	+	1370.76i	−0.934092	+	0.924800i
$131$	1842.66			1.22896			0.614480	−	0.788932i	$-0.289366\pi$
$131$	1842.66			1.22896			0.614480	+	0.788932i	$0.289366\pi$
$132$		−	349.600i		−	0.230521i
$133$		−	405.360i		−	0.264279i
$134$	−1857.85			−1.19772
$135$	212.384	+	214.518i	0.135401	+	0.136761i
$136$	−854.709			−0.538902
$137$		−	893.224i		−	0.557031i	−0.960432	−	0.278516i	$-0.910158\pi$
$137$		−	893.224i		−	0.557031i	0.960432	−	0.278516i	$-0.0898424\pi$
$138$		−	653.078i		−	0.402853i
$139$	−2777.79			−1.69503			−0.847514	−	0.530773i	$-0.821902\pi$
$139$	−2777.79			−1.69503			−0.847514	+	0.530773i	$0.821902\pi$
$140$	755.253	+	762.842i	0.455932	+	0.460514i
$141$	109.292			0.0652770
$142$			1174.97i			0.694376i
$143$			444.541i			0.259961i
$144$	328.678			0.190207
$145$	644.424	−	638.013i	0.369079	−	0.365407i
$146$	−2986.04			−1.69264
$147$		−	782.581i		−	0.439090i
$148$		−	410.983i		−	0.228261i
$149$	−969.362			−0.532975			−0.266487	−	0.963838i	$-0.585863\pi$
$149$	−969.362			−0.532975			−0.266487	+	0.963838i	$0.585863\pi$
$150$	−16.1666	+	1616.95i	−0.00880000	+	0.880154i
$151$	3477.75			1.87428			0.937138	−	0.348959i	$-0.113465\pi$
$151$	3477.75			1.87428			0.937138	+	0.348959i	$0.113465\pi$
$152$			500.278i			0.266960i
$153$		−	687.723i		−	0.363393i
$154$	429.888			0.224944
$155$	795.871	−	787.954i	0.412425	−	0.408322i
$156$	1284.39			0.659191
$157$		−	2374.99i		−	1.20729i	−0.797252	−	0.603646i	$-0.793714\pi$
$157$		−	2374.99i		−	1.20729i	0.797252	−	0.603646i	$-0.206286\pi$
$158$		−	4682.93i		−	2.35794i
$159$	−1958.52			−0.976858
$160$	1942.59	+	1962.11i	0.959847	+	0.969492i
$161$	457.546			0.223973
$162$		−	349.278i		−	0.169394i
$163$			363.778i			0.174805i	0.996173	+	0.0874027i	$0.0278567\pi$
$163$			363.778i			0.174805i	−0.996173	+	0.0874027i	$0.972143\pi$
$164$	−198.058			−0.0943031
$165$	259.580	+	262.189i	0.122475	+	0.123705i
$166$	−2567.10			−1.20027
$167$			3804.91i			1.76307i	0.472119	+	0.881535i	$0.343489\pi$
$167$			3804.91i			1.76307i	−0.472119	+	0.881535i	$0.656511\pi$
$168$		−	304.120i		−	0.139663i
$169$	563.806			0.256625
$170$	2617.92	−	2591.88i	1.18109	−	1.16934i
$171$	−402.538			−0.180017
$172$			432.597i			0.191775i
$173$			1008.59i			0.443248i	0.975132	+	0.221624i	$0.0711357\pi$
$173$			1008.59i			0.443248i	−0.975132	+	0.221624i	$0.928864\pi$
$174$	−1049.25			−0.457145
$175$	−1132.83	−	11.3263i	−0.489337	−	0.00489251i
$176$	401.718			0.172049
$177$			2233.95i			0.948665i
$178$		−	3046.65i		−	1.28290i
$179$	−3347.66			−1.39785			−0.698926	−	0.715194i	$-0.746339\pi$
$179$	−3347.66			−1.39785			−0.698926	+	0.715194i	$0.746339\pi$
$180$	757.531	−	749.995i	0.313684	−	0.310563i
$181$	1470.36			0.603819			0.301909	−	0.953337i	$-0.402376\pi$
$181$	1470.36			0.603819			0.301909	+	0.953337i	$0.402376\pi$
$182$			1579.36i			0.643241i
$183$			1548.61i			0.625554i
$184$	−564.684			−0.226245
$185$	305.157	+	308.224i	0.121274	+	0.122492i
$186$	−1295.83			−0.510835
$187$		−	840.550i		−	0.328701i
$188$		−	385.945i		−	0.149723i
$189$	244.703			0.0941776
$190$	−1517.08	−	1532.32i	−0.579265	−	0.585086i
$191$	3232.07			1.22442			0.612210	−	0.790695i	$-0.290281\pi$
$191$	3232.07			1.22442			0.612210	+	0.790695i	$0.290281\pi$
$192$		−	2318.23i		−	0.871374i
$193$		−	3983.00i		−	1.48551i	−0.669566	−	0.742753i	$-0.733520\pi$
$193$		−	3983.00i		−	1.48551i	0.669566	−	0.742753i	$-0.266480\pi$
$194$	−5653.74			−2.09234
$195$	−963.253	+	953.670i	−0.353743	+	0.350224i
$196$	−2763.54			−1.00712
$197$			4893.00i			1.76960i	0.465967	+	0.884802i	$0.345707\pi$
$197$			4893.00i			1.76960i	−0.465967	+	0.884802i	$0.654293\pi$
$198$		−	426.895i		−	0.153223i
$199$	−254.519			−0.0906651			−0.0453326	−	0.998972i	$-0.514435\pi$
$199$	−254.519			−0.0906651			−0.0453326	+	0.998972i	$0.514435\pi$
$200$	1398.09	+	13.9785i	0.494300	+	0.00494214i
$201$	−1292.55			−0.453579
$202$		−	5939.05i		−	2.06867i
$203$		−	735.102i		−	0.254158i
$204$	−2428.57			−0.833499
$205$	148.537	−	147.059i	0.0506062	−	0.0501027i
$206$	−3081.93			−1.04237
$207$		−	454.360i		−	0.152562i
$208$			1475.87i			0.491986i
$209$	−491.990			−0.162831
$210$	922.235	+	931.502i	0.303049	+	0.306094i
$211$	−1289.71			−0.420794			−0.210397	−	0.977616i	$-0.567476\pi$
$211$	−1289.71			−0.420794			−0.210397	+	0.977616i	$0.567476\pi$
$212$			6916.14i			2.24058i
$213$			817.452i			0.262962i
$214$	6448.00			2.05970
$215$	−321.206	−	324.434i	−0.101889	−	0.102913i
$216$	−302.003			−0.0951328
$217$		−	907.860i		−	0.284007i
$218$		−	3207.78i		−	0.996599i
$219$	−2077.45			−0.641009
$220$	925.872	−	916.661i	0.283738	−	0.280915i
$221$	3088.09			0.939943
$222$		−	501.849i		−	0.151720i
$223$		−	1519.82i		−	0.456388i	−0.973616	−	0.228194i	$-0.926718\pi$
$223$		−	1519.82i		−	0.456388i	0.973616	−	0.228194i	$-0.0732820\pi$
$224$	2238.21			0.667618
$225$	−11.2475	+	1124.94i	−0.00333258	+	0.333317i
$226$	7071.35			2.08132
$227$			2735.43i			0.799809i	0.916557	+	0.399904i	$0.130957\pi$
$227$			2735.43i			0.799809i	−0.916557	+	0.399904i	$0.869043\pi$
$228$			1421.49i			0.412896i
$229$	−1529.19			−0.441274			−0.220637	−	0.975356i	$-0.570814\pi$
$229$	−1529.19			−0.441274			−0.220637	+	0.975356i	$0.570814\pi$
$230$	1729.59	−	1712.39i	0.495852	−	0.490919i
$231$	299.082			0.0851868
$232$			907.232i			0.256736i
$233$			1660.31i			0.466826i	0.972378	+	0.233413i	$0.0749895\pi$
$233$			1660.31i			0.466826i	−0.972378	+	0.233413i	$0.925011\pi$
$234$	1568.37			0.438151
$235$	286.567	+	289.446i	0.0795470	+	0.0803463i
$236$	7888.77			2.17591
$237$		−	3258.02i		−	0.892958i
$238$		−	2986.30i		−	0.813332i
$239$	−558.538			−0.151167			−0.0755834	−	0.997139i	$-0.524082\pi$
$239$	−558.538			−0.151167			−0.0755834	+	0.997139i	$0.524082\pi$
$240$	861.803	+	870.463i	0.231788	+	0.234117i
$241$	6132.52			1.63913			0.819565	−	0.572986i	$-0.194215\pi$
$241$	6132.52			1.63913			0.819565	+	0.572986i	$0.194215\pi$
$242$		−	521.760i		−	0.138595i
$243$		−	243.000i		−	0.0641500i
$244$	5468.63			1.43481
$245$	2072.57	−	2051.95i	0.540455	−	0.535078i
$246$	−241.847			−0.0626814
$247$		−	1807.52i		−	0.465626i
$248$			1120.44i			0.286888i
$249$	−1785.99			−0.454547
$250$	−4324.66	+	4196.86i	−1.09406	+	1.06173i
$251$	2130.42			0.535741			0.267870	−	0.963455i	$-0.413680\pi$
$251$	2130.42			0.535741			0.267870	+	0.963455i	$0.413680\pi$
$252$		−	864.125i		−	0.216011i
$253$		−	555.329i		−	0.137997i
$254$	10044.9			2.48138
$255$	1821.35	−	1803.23i	0.447283	−	0.442833i
$256$	332.812			0.0812530
$257$			2559.71i			0.621285i	0.950527	+	0.310643i	$0.100544\pi$
$257$			2559.71i			0.621285i	−0.950527	+	0.310643i	$0.899456\pi$
$258$			528.242i			0.127469i
$259$	351.595			0.0843515
$260$	3367.71	+	3401.55i	0.803295	+	0.811366i
$261$	−729.985			−0.173122
$262$		−	7945.67i		−	1.87361i
$263$		−	69.1920i		−	0.0162227i	−0.999967	−	0.00811133i	$-0.997418\pi$
$263$		−	69.1920i		−	0.0162227i	0.999967	−	0.00811133i	$-0.00258195\pi$
$264$	−369.115			−0.0860509
$265$	−5135.28	−	5186.88i	−1.19041	−	1.20237i
$266$	−1747.94			−0.402906
$267$		−	2119.62i		−	0.485837i
$268$			4564.40i			1.04035i
$269$	−2985.84			−0.676765			−0.338382	−	0.941009i	$-0.609880\pi$
$269$	−2985.84			−0.676765			−0.338382	+	0.941009i	$0.609880\pi$
$270$	925.017	−	915.815i	0.208499	−	0.206425i
$271$	337.747			0.0757073			0.0378536	−	0.999283i	$-0.487948\pi$
$271$	337.747			0.0757073			0.0378536	+	0.999283i	$0.487948\pi$
$272$		−	2790.61i		−	0.622080i
$273$			1098.79i			0.243597i
$274$	−3851.65			−0.849221
$275$	−13.7469	+	1374.93i	−0.00301444	+	0.301496i
$276$	−1604.49			−0.349924
$277$		−	5468.83i		−	1.18625i	−0.805112	−	0.593123i	$-0.797895\pi$
$277$		−	5468.83i		−	1.18625i	0.805112	−	0.593123i	$-0.202105\pi$
$278$			11978.0i			2.58415i
$279$	−901.540			−0.193454
$280$	805.423	−	797.410i	0.171904	−	0.170194i
$281$	−3846.36			−0.816563			−0.408282	−	0.912856i	$-0.633872\pi$
$281$	−3846.36			−0.816563			−0.408282	+	0.912856i	$0.633872\pi$
$282$		−	471.275i		−	0.0995178i
$283$			6289.97i			1.32120i	0.750737	+	0.660601i	$0.229698\pi$
$283$			6289.97i			1.32120i	−0.750737	+	0.660601i	$0.770302\pi$
$284$	2886.68			0.603145
$285$	−1055.46	−	1066.07i	−0.219369	−	0.221574i
$286$	1916.89			0.396322
$287$		−	169.438i		−	0.0348488i
$288$		−	2222.63i		−	0.454755i
$289$	−926.050			−0.188490
$290$	−2751.16	−	2778.80i	−0.557081	−	0.562678i
$291$	−3933.43			−0.792376
$292$			7336.13i			1.47026i
$293$			1660.81i			0.331146i	0.986198	+	0.165573i	$0.0529473\pi$
$293$			1660.81i			0.331146i	−0.986198	+	0.165573i	$0.947053\pi$
$294$	−3374.54			−0.669413
$295$	−5916.32	+	5857.46i	−1.16767	+	1.15605i
$296$	−433.923			−0.0852071
$297$		−	297.000i		−	0.0580259i
$298$			4179.96i			0.812545i
$299$	2040.22			0.394612
$300$	3972.53	+	39.7184i	0.764514	+	0.00764381i
$301$	−370.086			−0.0708684
$302$		−	14996.3i		−	2.85742i
$303$		−	4131.93i		−	0.783409i
$304$	−1633.40			−0.308164
$305$	−4101.29	+	4060.49i	−0.769965	+	0.762305i
$306$	−2965.51			−0.554010
$307$			4067.69i			0.756207i	0.925763	+	0.378103i	$0.123424\pi$
$307$			4067.69i			0.756207i	−0.925763	+	0.378103i	$0.876576\pi$
$308$		−	1056.15i		−	0.195389i
$309$	−2144.16			−0.394748
$310$	−3397.71	−	3431.85i	−0.622507	−	0.628762i
$311$	−3923.20			−0.715320			−0.357660	−	0.933852i	$-0.616425\pi$
$311$	−3923.20			−0.715320			−0.357660	+	0.933852i	$0.616425\pi$
$312$		−	1356.09i		−	0.246068i
$313$			806.771i			0.145691i	0.997343	+	0.0728457i	$0.0232081\pi$
$313$			806.771i			0.145691i	−0.997343	+	0.0728457i	$0.976792\pi$
$314$	−10241.1			−1.84057
$315$	641.619	+	648.066i	0.114765	+	0.115919i
$316$	−11505.1			−2.04814
$317$		−	8976.60i		−	1.59046i	−0.606307	−	0.795231i	$-0.707350\pi$
$317$		−	8976.60i		−	1.59046i	0.606307	−	0.795231i	$-0.292650\pi$
$318$			8445.26i			1.48927i
$319$	−892.203			−0.156595
$320$	6139.54	−	6078.46i	1.07253	−	1.06186i
$321$	4486.01			0.780015
$322$		−	1972.97i		−	0.341457i
$323$			3417.71i			0.588751i
$324$	−858.110			−0.147138
$325$	−5051.35	−	50.5046i	−0.862149	−	0.00861998i
$326$	1568.64			0.266499
$327$		−	2231.72i		−	0.377415i
$328$			209.113i			0.0352023i
$329$	330.175			0.0553286
$330$	1130.58	−	1119.33i	0.188595	−	0.186718i
$331$	−7482.31			−1.24249			−0.621246	−	0.783615i	$-0.713373\pi$
$331$	−7482.31			−1.24249			−0.621246	+	0.783615i	$0.713373\pi$
$332$			6306.88i			1.04258i
$333$		−	349.147i		−	0.0574569i
$334$	16407.0			2.68788
$335$	−3389.09	−	3423.15i	−0.552734	−	0.558288i
$336$	992.948			0.161219
$337$			6904.38i			1.11604i	0.829827	+	0.558020i	$0.188439\pi$
$337$			6904.38i			1.11604i	−0.829827	+	0.558020i	$0.811561\pi$
$338$		−	2431.17i		−	0.391238i
$339$	4919.69			0.788203
$340$	−6367.77	−	6431.75i	−1.01571	−	1.02591i
$341$	−1101.88			−0.174986
$342$			1735.77i			0.274444i
$343$		−	5472.84i		−	0.861533i
$344$	456.744			0.0715872
$345$	1203.32	−	1191.34i	0.187781	−	0.185913i
$346$	4349.12			0.675752
$347$			6050.06i			0.935977i	0.883735	+	0.467989i	$0.155021\pi$
$347$			6050.06i			0.935977i	−0.883735	+	0.467989i	$0.844979\pi$
$348$			2577.81i			0.397083i
$349$	1697.12			0.260299			0.130150	−	0.991494i	$-0.458454\pi$
$349$	1697.12			0.260299			0.130150	+	0.991494i	$0.458454\pi$
$350$	−48.8399	+	4884.84i	−0.00745886	+	0.746017i
$351$	1091.15			0.165929
$352$		−	2716.54i		−	0.411341i
$353$		−	8505.96i		−	1.28251i	−0.767327	−	0.641256i	$-0.778414\pi$
$353$		−	8505.96i		−	1.28251i	0.767327	−	0.641256i	$-0.221586\pi$
$354$	9632.93			1.44628
$355$	−2164.92	+	2143.38i	−0.323667	+	0.320447i
$356$	−7485.04			−1.11434
$357$		−	2077.63i		−	0.308011i
$358$			14435.3i			2.13109i
$359$	4937.28			0.725848			0.362924	−	0.931819i	$-0.381778\pi$
$359$	4937.28			0.725848			0.362924	+	0.931819i	$0.381778\pi$
$360$	−791.859	−	799.816i	−0.115930	−	0.117094i
$361$	−4858.55			−0.708347
$362$		−	6340.31i		−	0.920550i
$363$		−	363.000i		−	0.0524864i
$364$	3880.19			0.558729
$365$	−5447.13	−	5501.86i	−0.781139	−	0.788988i
$366$	6677.71			0.953687
$367$			12698.5i			1.80614i	0.429490	+	0.903072i	$0.358693\pi$
$367$			12698.5i			1.80614i	−0.429490	+	0.903072i	$0.641307\pi$
$368$		−	1843.69i		−	0.261165i
$369$	−168.258			−0.0237376
$370$	1329.08	−	1315.86i	0.186745	−	0.184887i
$371$	−5916.73			−0.827983
$372$			3183.62i			0.443718i
$373$			1441.18i			0.200058i	0.994985	+	0.100029i	$0.0318935\pi$
$373$			1441.18i			0.200058i	−0.994985	+	0.100029i	$0.968106\pi$
$374$	−3624.51			−0.501121
$375$	−3008.76	+	2919.84i	−0.414325	+	0.402080i
$376$	−407.488			−0.0558899
$377$		−	3277.86i		−	0.447794i
$378$		−	1055.18i		−	0.143578i
$379$	−12908.9			−1.74957			−0.874785	−	0.484511i	$-0.838997\pi$
$379$	−12908.9			−1.74957			−0.874785	+	0.484511i	$0.838997\pi$
$380$	−3764.63	+	3727.18i	−0.508214	+	0.503158i
$381$	6988.43			0.939707
$382$		−	13936.9i		−	1.86669i
$383$			10281.2i			1.37166i	0.727762	+	0.685829i	$0.240560\pi$
$383$			10281.2i			1.37166i	−0.727762	+	0.685829i	$0.759440\pi$
$384$	−4069.37			−0.540792
$385$	784.201	+	792.080i	0.103809	+	0.104852i
$386$	−17175.0			−2.26472
$387$			367.509i			0.0482727i
$388$			13890.2i			1.81744i
$389$	11485.2			1.49698			0.748490	−	0.663146i	$-0.230779\pi$
$389$	11485.2			1.49698			0.748490	+	0.663146i	$0.230779\pi$
$390$	4112.29	+	4153.61i	0.533933	+	0.539299i
$391$	−3857.71			−0.498958
$392$			2917.80i			0.375947i
$393$		−	5527.97i		−	0.709541i
$394$	21099.0			2.69785
$395$	8628.44	−	8542.60i	1.09910	−	1.08816i
$396$	−1048.80			−0.133091
$397$			12163.2i			1.53766i	0.639452	+	0.768831i	$0.279161\pi$
$397$			12163.2i			1.53766i	−0.639452	+	0.768831i	$0.720839\pi$
$398$			1097.50i			0.138223i
$399$	−1216.08			−0.152582
$400$	−45.6395	+	4564.75i	−0.00570494	+	0.570594i
$401$	15307.9			1.90634			0.953169	−	0.302437i	$-0.0978003\pi$
$401$	15307.9			1.90634			0.953169	+	0.302437i	$0.0978003\pi$
$402$			5573.56i			0.691502i
$403$		−	4048.20i		−	0.500385i
$404$	−14591.1			−1.79687
$405$	643.554	−	637.152i	0.0789592	−	0.0781737i
$406$	−3169.81			−0.387476
$407$		−	426.735i		−	0.0519717i
$408$			2564.13i			0.311135i
$409$	10396.2			1.25686			0.628431	−	0.777865i	$-0.283697\pi$
$409$	10396.2			1.25686			0.628431	+	0.777865i	$0.283697\pi$
$410$	−634.129	−	640.501i	−0.0763840	−	0.0771515i
$411$	−2679.67			−0.321602
$412$			7571.72i			0.905417i
$413$			6748.82i			0.804087i
$414$	−1959.23			−0.232587
$415$	−4682.90	−	4729.95i	−0.553914	−	0.559480i
$416$	9980.28			1.17626
$417$			8333.36i			0.978625i
$418$			2121.50i			0.248244i
$419$	−1588.33			−0.185191			−0.0925953	−	0.995704i	$-0.529516\pi$
$419$	−1588.33			−0.185191			−0.0925953	+	0.995704i	$0.529516\pi$
$420$	2288.53	−	2265.76i	0.265878	−	0.263233i
$421$	3793.62			0.439168			0.219584	−	0.975594i	$-0.429530\pi$
$421$	3793.62			0.439168			0.219584	+	0.975594i	$0.429530\pi$
$422$			5561.34i			0.641521i
$423$		−	327.876i		−	0.0376877i
$424$	7302.19			0.836381
$425$	9551.23	+	95.4956i	1.09012	+	0.0108993i
$426$	3524.91			0.400898
$427$			4678.39i			0.530219i
$428$		−	15841.5i		−	1.78909i
$429$	1333.62			0.150088
$430$	−1398.98	+	1385.06i	−0.156895	+	0.155334i
$431$	−6013.25			−0.672037			−0.336018	−	0.941855i	$-0.609080\pi$
$431$	−6013.25			−0.672037			−0.336018	+	0.941855i	$0.609080\pi$
$432$		−	986.035i		−	0.109816i
$433$			2624.08i			0.291236i	0.989341	+	0.145618i	$0.0465171\pi$
$433$			2624.08i			0.291236i	−0.989341	+	0.145618i	$0.953483\pi$
$434$	−3914.76			−0.432982
$435$	−1914.04	−	1933.27i	−0.210968	−	0.213088i
$436$	−7880.93			−0.865660
$437$			2257.99i			0.247172i
$438$			8958.11i			0.977249i
$439$	−1085.10			−0.117971			−0.0589854	−	0.998259i	$-0.518787\pi$
$439$	−1085.10			−0.117971			−0.0589854	+	0.998259i	$0.518787\pi$
$440$	−967.828	−	977.553i	−0.104862	−	0.105916i
$441$	−2347.74			−0.253509
$442$		−	13316.1i		−	1.43299i
$443$			5173.59i			0.554864i	0.960745	+	0.277432i	$0.0894833\pi$
$443$			5173.59i			0.554864i	−0.960745	+	0.277432i	$0.910517\pi$
$444$	−1232.95			−0.131786
$445$	5613.53	−	5557.69i	0.597993	−	0.592044i
$446$	−6553.55			−0.695784
$447$			2908.09i			0.307713i
$448$		−	7003.44i		−	0.738575i
$449$	16047.9			1.68674			0.843370	−	0.537333i	$-0.180568\pi$
$449$	16047.9			1.68674			0.843370	+	0.537333i	$0.180568\pi$
$450$	4850.84	+	48.4999i	0.508157	+	0.00508068i
$451$	−205.649			−0.0214715
$452$		−	17373.0i		−	1.80787i
$453$		−	10433.3i		−	1.08211i
$454$	11795.4			1.21935
$455$	−2910.02	+	2881.07i	−0.299832	+	0.296849i
$456$	1500.83			0.154129
$457$			4243.55i			0.434365i	0.976131	+	0.217183i	$0.0696867\pi$
$457$			4243.55i			0.434365i	−0.976131	+	0.217183i	$0.930313\pi$
$458$			6593.98i			0.672743i
$459$	−2063.17			−0.209805
$460$	−4207.01	−	4249.29i	−0.426420	−	0.430704i
$461$	15118.3			1.52740			0.763698	−	0.645573i	$-0.223381\pi$
$461$	15118.3			1.52740			0.763698	+	0.645573i	$0.223381\pi$
$462$		−	1289.66i		−	0.129871i
$463$		−	3300.13i		−	0.331252i	−0.986189	−	0.165626i	$-0.947035\pi$
$463$		−	3300.13i		−	0.331252i	0.986189	−	0.165626i	$-0.0529645\pi$
$464$	−2962.10			−0.296362
$465$	−2363.86	−	2387.61i	−0.235745	−	0.238114i
$466$	7159.38			0.711699
$467$		−	1267.20i		−	0.125566i	−0.998027	−	0.0627829i	$-0.980002\pi$
$467$		−	1267.20i		−	0.125566i	0.998027	−	0.0627829i	$-0.0199976\pi$
$468$		−	3853.18i		−	0.380584i
$469$	−3904.83			−0.384452
$470$	1248.11	−	1235.70i	0.122492	−	0.121273i
$471$	−7124.97			−0.697031
$472$		−	8329.11i		−	0.812243i
$473$			449.178i			0.0436643i
$474$	−14048.8			−1.36136
$475$	55.8954	−	5590.52i	0.00539928	−	0.540023i
$476$	−7336.78			−0.706472
$477$			5875.55i			0.563989i
$478$			2408.46i			0.230461i
$479$	2938.23			0.280274			0.140137	−	0.990132i	$-0.455246\pi$
$479$	2938.23			0.280274			0.140137	+	0.990132i	$0.455246\pi$
$480$	5886.34	−	5827.78i	0.559736	−	0.554168i
$481$	1567.78			0.148617
$482$		−	26443.9i		−	2.49893i
$483$		−	1372.64i		−	0.129311i
$484$	−1281.87			−0.120386
$485$	−10313.5	−	10417.2i	−0.965596	−	0.975298i
$486$	−1047.83			−0.0977997
$487$			5071.53i			0.471895i	0.971766	+	0.235948i	$0.0758194\pi$
$487$			5071.53i			0.471895i	−0.971766	+	0.235948i	$0.924181\pi$
$488$		−	5773.88i		−	0.535597i
$489$	1091.33			0.100924
$490$	−8848.14	−	8937.05i	−0.815752	−	0.823948i
$491$	1890.86			0.173795			0.0868976	−	0.996217i	$-0.472305\pi$
$491$	1890.86			0.173795			0.0868976	+	0.996217i	$0.472305\pi$
$492$			594.173i			0.0544459i
$493$			6197.87i			0.566203i
$494$	−7794.15			−0.709869
$495$	786.566	−	778.741i	0.0714213	−	0.0707108i
$496$	−3658.23			−0.331168
$497$			2469.55i			0.222886i
$498$			7701.29i			0.692978i
$499$	16537.6			1.48362			0.741808	−	0.670613i	$-0.233969\pi$
$499$	16537.6			1.48362			0.741808	+	0.670613i	$0.233969\pi$
$500$	10310.9	+	10624.9i	0.922234	+	0.950319i
$501$	11414.7			1.01791
$502$		−	9186.52i		−	0.816762i
$503$			8330.23i			0.738422i	0.929346	+	0.369211i	$0.120372\pi$
$503$			8330.23i			0.738422i	−0.929346	+	0.369211i	$0.879628\pi$
$504$	−912.360			−0.0806344
$505$	10942.9	−	10834.0i	0.964261	−	0.954668i
$506$	−2394.62			−0.210383
$507$		−	1691.42i		−	0.148163i
$508$		−	24678.4i		−	2.15537i
$509$	−20701.7			−1.80273			−0.901363	−	0.433064i	$-0.857432\pi$
$509$	−20701.7			−1.80273			−0.901363	+	0.433064i	$0.857432\pi$
$510$	−7775.64	−	7853.77i	−0.675120	−	0.681904i
$511$	−6276.04			−0.543318
$512$		−	12286.8i		−	1.06055i
$513$			1207.61i			0.103933i
$514$	11037.6			0.947178
$515$	−5622.05	−	5678.54i	−0.481043	−	0.485877i
$516$	1297.79			0.110721
$517$		−	400.738i		−	0.0340898i
$518$		−	1516.10i		−	0.128598i
$519$	3025.78			0.255909
$520$	3591.42	−	3555.69i	0.302874	−	0.299860i
$521$	9311.54			0.783005			0.391503	−	0.920177i	$-0.371955\pi$
$521$	9311.54			0.783005			0.391503	+	0.920177i	$0.371955\pi$
$522$			3147.74i			0.263933i
$523$		−	18192.0i		−	1.52099i	−0.649341	−	0.760497i	$-0.724955\pi$
$523$		−	18192.0i		−	1.52099i	0.649341	−	0.760497i	$-0.275045\pi$
$524$	−19521.0			−1.62744
$525$	−33.9790	+	3398.49i	−0.00282469	+	0.282519i
$526$	−298.361			−0.0247322
$527$			7654.45i			0.632700i
$528$		−	1205.15i		−	0.0993326i
$529$	9618.32			0.790525
$530$	−22366.2	+	22143.7i	−1.83307	+	1.81483i
$531$	6701.84			0.547712
$532$			4294.36i			0.349970i
$533$		−	755.532i		−	0.0613991i
$534$	−9139.94			−0.740681
$535$	11762.4	+	11880.6i	0.950531	+	0.960083i
$536$	4819.18			0.388352
$537$			10043.0i			0.807051i
$538$			12875.1i			1.03176i
$539$	−2869.46			−0.229307
$540$	−2249.99	−	2272.59i	−0.179304	−	0.181105i
$541$	−12799.7			−1.01720			−0.508598	−	0.861004i	$-0.669836\pi$
$541$	−12799.7			−1.01720			−0.508598	+	0.861004i	$0.669836\pi$
$542$		−	1456.39i		−	0.115419i
$543$		−	4411.09i		−	0.348615i
$544$	−18871.0			−1.48729
$545$	5910.44	−	5851.64i	0.464542	−	0.459920i
$546$	4738.08			0.371376
$547$		−	4564.37i		−	0.356779i	−0.983960	−	0.178390i	$-0.942911\pi$
$547$		−	4564.37i		−	0.356779i	0.983960	−	0.178390i	$-0.0570888\pi$
$548$			9462.77i			0.737645i
$549$	4645.83			0.361164
$550$	5928.80	+	59.2776i	0.459645	+	0.00459565i
$551$	3627.73			0.280484
$552$			1694.05i			0.130622i
$553$		−	9842.57i		−	0.756869i
$554$	−23582.0			−1.80849
$555$	924.671	−	915.472i	0.0707209	−	0.0700174i
$556$	29427.7			2.24463
$557$		−	14228.8i		−	1.08239i	−0.840896	−	0.541197i	$-0.817971\pi$
$557$		−	14228.8i		−	1.08239i	0.840896	−	0.541197i	$-0.182029\pi$
$558$			3887.50i			0.294930i
$559$	−1650.23			−0.124861
$560$	2603.53	+	2629.70i	0.196463	+	0.198437i
$561$	−2521.65			−0.189776
$562$			16585.8i			1.24489i
$563$			18321.3i			1.37149i	0.727840	+	0.685747i	$0.240524\pi$
$563$			18321.3i			1.37149i	−0.727840	+	0.685747i	$0.759476\pi$
$564$	−1157.83			−0.0864426
$565$	12899.6	+	13029.2i	0.960510	+	0.970161i
$566$	27122.8			2.01423
$567$		−	734.110i		−	0.0543734i
$568$		−	3047.81i		−	0.225147i
$569$	1949.83			0.143658			0.0718288	−	0.997417i	$-0.477116\pi$
$569$	1949.83			0.143658			0.0718288	+	0.997417i	$0.477116\pi$
$570$	−4596.97	+	4551.23i	−0.337799	+	0.334439i
$571$	−20121.3			−1.47469			−0.737347	−	0.675514i	$-0.763922\pi$
$571$	−20121.3			−1.47469			−0.737347	+	0.675514i	$0.763922\pi$
$572$		−	4709.44i		−	0.344251i
$573$		−	9696.21i		−	0.706919i
$574$	−730.628			−0.0531286
$575$	6310.25	+	63.0914i	0.457662	+	0.00457582i
$576$	−6954.69			−0.503088
$577$		−	4171.22i		−	0.300953i	−0.988614	−	0.150477i	$-0.951919\pi$
$577$		−	4171.22i		−	0.300953i	0.988614	−	0.150477i	$-0.0480809\pi$
$578$			3993.19i			0.287362i
$579$	−11949.0			−0.857657
$580$	−6826.99	+	6759.07i	−0.488751	+	0.483888i
$581$	−5395.52			−0.385273
$582$			16961.2i			1.20802i
$583$			7181.22i			0.510147i
$584$	7745.63			0.548829
$585$	2861.01	+	2889.76i	0.202202	+	0.204234i
$586$	7161.54			0.504847
$587$		−	3593.98i		−	0.252708i	−0.991985	−	0.126354i	$-0.959673\pi$
$587$		−	3593.98i		−	0.252708i	0.991985	−	0.126354i	$-0.0403275\pi$
$588$			8290.62i			0.581462i
$589$	4480.29			0.313425
$590$	25257.8	+	25511.6i	1.76245	+	1.78016i
$591$	14679.0			1.02168
$592$		−	1416.75i		−	0.0983585i
$593$			2893.64i			0.200384i	0.994968	+	0.100192i	$0.0319457\pi$
$593$			2893.64i			0.200384i	−0.994968	+	0.100192i	$0.968054\pi$
$594$	−1280.68			−0.0884632
$595$	5502.34	−	5447.60i	0.379116	−	0.375345i
$596$	10269.4			0.705789
$597$			763.556i			0.0523455i
$598$		−	8797.57i		−	0.601604i
$599$	−26534.5			−1.80997			−0.904984	−	0.425445i	$-0.860118\pi$
$599$	−26534.5			−1.80997			−0.904984	+	0.425445i	$0.860118\pi$
$600$	41.9354	−	4194.27i	0.00285334	−	0.285384i
$601$	2770.19			0.188017			0.0940085	−	0.995571i	$-0.470032\pi$
$601$	2770.19			0.188017			0.0940085	+	0.995571i	$0.470032\pi$
$602$			1595.84i			0.108042i
$603$			3877.64i			0.261874i
$604$	−36843.2			−2.48200
$605$	961.359	−	951.795i	0.0646030	−	0.0639603i
$606$	−17817.2			−1.19434
$607$			5653.45i			0.378034i	0.981974	+	0.189017i	$0.0605301\pi$
$607$			5653.45i			0.378034i	−0.981974	+	0.189017i	$0.939470\pi$
$608$			11045.6i			0.736771i
$609$	−2205.31			−0.146738
$610$	17509.1	+	17685.1i	1.16217	+	1.17385i
$611$	1472.27			0.0974820
$612$			7285.70i			0.481221i
$613$			2464.19i			0.162362i	0.996699	+	0.0811808i	$0.0258691\pi$
$613$			2464.19i			0.162362i	−0.996699	+	0.0811808i	$0.974131\pi$
$614$	17540.2			1.15287
$615$	−441.177	−	445.611i	−0.0289268	−	0.0292175i
$616$	−1115.11			−0.0729366
$617$		−	24848.9i		−	1.62136i	−0.585492	−	0.810678i	$-0.699098\pi$
$617$		−	24848.9i		−	1.62136i	0.585492	−	0.810678i	$-0.300902\pi$
$618$			9245.78i			0.601812i
$619$	12904.2			0.837905			0.418953	−	0.908008i	$-0.362397\pi$
$619$	12904.2			0.837905			0.418953	+	0.908008i	$0.362397\pi$
$620$	−8431.42	+	8347.54i	−0.546152	+	0.540718i
$621$	−1363.08			−0.0880814
$622$			16917.1i			1.09054i
$623$		−	6403.43i		−	0.411794i
$624$	4427.61			0.284048
$625$	−15621.9	−	312.414i	−0.999800	−	0.0199945i
$626$	3478.85			0.222113
$627$			1475.97i			0.0940106i
$628$			25160.5i			1.59875i
$629$	−2964.40			−0.187915
$630$	2794.51	−	2766.70i	0.176723	−	0.174965i
$631$	−5744.27			−0.362402			−0.181201	−	0.983446i	$-0.557998\pi$
$631$	−5744.27			−0.362402			−0.181201	+	0.983446i	$0.557998\pi$
$632$			12147.3i			0.764546i
$633$			3869.14i			0.242946i
$634$	−38707.7			−2.42473
$635$	18323.9	+	18508.0i	1.14513	+	1.15664i
$636$	20748.4			1.29360
$637$		−	10542.1i		−	0.655719i
$638$			3847.24i			0.238736i
$639$	2452.36			0.151821
$640$	−10670.0	−	10777.2i	−0.659013	−	0.665635i
$641$	−18325.2			−1.12917			−0.564587	−	0.825374i	$-0.690964\pi$
$641$	−18325.2			−1.12917			−0.564587	+	0.825374i	$0.690964\pi$
$642$		−	19344.0i		−	1.18917i
$643$		−	25589.3i		−	1.56943i	−0.619855	−	0.784716i	$-0.712809\pi$
$643$		−	25589.3i		−	1.56943i	0.619855	−	0.784716i	$-0.287191\pi$
$644$	−4847.21			−0.296595
$645$	−973.301	+	963.619i	−0.0594166	+	0.0588255i
$646$	14737.4			0.897578
$647$			10244.3i			0.622479i	0.950331	+	0.311240i	$0.100744\pi$
$647$			10244.3i			0.622479i	−0.950331	+	0.311240i	$0.899256\pi$
$648$			906.009i			0.0549250i
$649$	8191.14			0.495424
$650$	−217.780	+	21781.8i	−0.0131416	+	1.31439i
$651$	−2723.58			−0.163972
$652$		−	3853.85i		−	0.231485i
$653$		−	9356.38i		−	0.560710i	−0.959896	−	0.280355i	$-0.909548\pi$
$653$		−	9356.38i		−	0.560710i	0.959896	−	0.280355i	$-0.0904522\pi$
$654$	−9623.35			−0.575387
$655$	14640.1	−	14494.5i	0.873339	−	0.864651i
$656$	−682.752			−0.0406356
$657$			6232.35i			0.370087i
$658$		−	1423.74i		−	0.0843511i
$659$	8188.52			0.484036			0.242018	−	0.970272i	$-0.422191\pi$
$659$	8188.52			0.484036			0.242018	+	0.970272i	$0.422191\pi$
$660$	−2749.98	−	2777.61i	−0.162186	−	0.163816i
$661$	6886.53			0.405227			0.202613	−	0.979259i	$-0.435057\pi$
$661$	6886.53			0.405227			0.202613	+	0.979259i	$0.435057\pi$
$662$			32264.3i			1.89424i
$663$		−	9264.27i		−	0.542676i
$664$	6658.92			0.389181
$665$	−3188.59	−	3220.63i	−0.185937	−	0.187805i
$666$	−1505.55			−0.0875957
$667$			4094.77i			0.237706i
$668$		−	40309.0i		−	2.33473i
$669$	−4559.45			−0.263495
$670$	−14760.9	+	14614.0i	−0.851137	+	0.842669i
$671$	5678.23			0.326685
$672$		−	6714.62i		−	0.385450i
$673$			8450.15i			0.483996i	0.970277	+	0.241998i	$0.0778027\pi$
$673$			8450.15i			0.483996i	−0.970277	+	0.241998i	$0.922197\pi$
$674$	29772.2			1.70146
$675$	3374.83	+	33.7424i	0.192440	+	0.00192407i
$676$	−5972.93			−0.339835
$677$		−	23308.6i		−	1.32322i	−0.749846	−	0.661612i	$-0.769872\pi$
$677$		−	23308.6i		−	1.32322i	0.749846	−	0.661612i	$-0.230128\pi$
$678$		−	21214.0i		−	1.20165i
$679$	−11883.0			−0.671617
$680$	−6790.76	+	6723.21i	−0.382962	+	0.379152i
$681$	8206.28			0.461770
$682$			4751.39i			0.266775i
$683$		−	19580.0i		−	1.09693i	−0.836172	−	0.548467i	$-0.815212\pi$
$683$		−	19580.0i		−	1.09693i	0.836172	−	0.548467i	$-0.184788\pi$
$684$	4264.46			0.238386
$685$	−7026.17	−	7096.77i	−0.391907	−	0.395845i
$686$	−23599.3			−1.31345
$687$			4587.57i			0.254770i
$688$			1491.26i			0.0826365i
$689$	−26383.0			−1.45880
$690$	−5137.16	−	5188.78i	−0.283432	−	0.286280i
$691$	−33164.9			−1.82584			−0.912918	−	0.408142i	$-0.866177\pi$
$691$	−33164.9			−1.82584			−0.912918	+	0.408142i	$0.866177\pi$
$692$		−	10685.0i		−	0.586968i
$693$		−	897.246i		−	0.0491826i
$694$	26088.3			1.42694
$695$	−22069.8	+	21850.3i	−1.20454	+	1.19256i
$696$	2721.70			0.148227
$697$			1428.58i			0.0776347i
$698$		−	7318.08i		−	0.396839i
$699$	4980.93			0.269522
$700$	12001.1	+	119.990i	0.648001	+	0.00647887i
$701$	−20819.6			−1.12175			−0.560874	−	0.827901i	$-0.689535\pi$
$701$	−20819.6			−1.12175			−0.560874	+	0.827901i	$0.689535\pi$
$702$		−	4705.10i		−	0.252966i
$703$			1735.12i			0.0930887i
$704$	−8500.18			−0.455060
$705$	868.338	−	859.700i	0.0463880	−	0.0459265i
$706$	−36678.3			−1.95525
$707$		−	12482.7i		−	0.664016i
$708$		−	23666.3i		−	1.25626i
$709$	−14367.7			−0.761058			−0.380529	−	0.924769i	$-0.624258\pi$
$709$	−14367.7			−0.761058			−0.380529	+	0.924769i	$0.624258\pi$
$710$	9242.41	+	9335.28i	0.488537	+	0.493446i
$711$	−9774.05			−0.515549
$712$			7902.84i			0.415971i
$713$			5057.09i			0.265623i
$714$	−8958.90			−0.469577
$715$	3496.79	+	3531.93i	0.182899	+	0.184737i
$716$	35464.9			1.85110
$717$			1675.62i			0.0872762i
$718$		−	21289.9i		−	1.10659i
$719$	27403.4			1.42138			0.710691	−	0.703504i	$-0.248382\pi$
$719$	27403.4			1.42138			0.710691	+	0.703504i	$0.248382\pi$
$720$	2611.39	−	2585.41i	0.135168	−	0.133823i
$721$	−6477.58			−0.334588
$722$			20950.4i			1.07991i
$723$		−	18397.6i		−	0.946352i
$724$	−15576.9			−0.799603
$725$	101.364	−	10138.2i	0.00519250	−	0.519341i
$726$	−1565.28			−0.0800180
$727$			6652.03i			0.339354i	0.985500	+	0.169677i	$0.0542724\pi$
$727$			6652.03i			0.339354i	−0.985500	+	0.169677i	$0.945728\pi$
$728$		−	4096.78i		−	0.208567i
$729$	−729.000			−0.0370370
$730$	−23724.4	+	23488.4i	−1.20285	+	1.19088i
$731$	3120.30			0.157878
$732$		−	16405.9i		−	0.828386i
$733$		−	11674.6i		−	0.588285i	−0.955762	−	0.294142i	$-0.904966\pi$
$733$		−	11674.6i		−	0.588285i	0.955762	−	0.294142i	$-0.0950339\pi$
$734$	54756.7			2.75355
$735$	−6155.84	−	6217.70i	−0.308927	−	0.312032i
$736$	−12467.6			−0.624403
$737$			4739.34i			0.236874i
$738$			725.542i			0.0361891i
$739$	−6253.35			−0.311276			−0.155638	−	0.987814i	$-0.549743\pi$
$739$	−6253.35			−0.311276			−0.155638	+	0.987814i	$0.549743\pi$
$740$	−3232.82	−	3265.31i	−0.160596	−	0.162210i
$741$	−5422.56			−0.268829
$742$			25513.4i			1.26230i
$743$			5832.24i			0.287973i	0.989580	+	0.143987i	$0.0459923\pi$
$743$			5832.24i			0.287973i	−0.989580	+	0.143987i	$0.954008\pi$
$744$	3361.33			0.165635
$745$	−7701.69	+	7625.08i	−0.378749	+	0.374981i
$746$	6214.47			0.304997
$747$			5357.96i			0.262433i
$748$			8904.75i			0.435281i
$749$	13552.4			0.661139
$750$	12590.6	+	12974.0i	0.612990	+	0.631657i
$751$	−9600.53			−0.466483			−0.233241	−	0.972419i	$-0.574933\pi$
$751$	−9600.53			−0.466483			−0.233241	+	0.972419i	$0.574933\pi$
$752$		−	1330.44i		−	0.0645163i
$753$		−	6391.26i		−	0.309310i
$754$	−14134.4			−0.682683
$755$	27631.2	−	27356.3i	1.33192	−	1.31867i
$756$	−2592.38			−0.124714
$757$			18731.0i			0.899324i	0.893199	+	0.449662i	$0.148456\pi$
$757$			18731.0i			0.899324i	−0.893199	+	0.449662i	$0.851544\pi$
$758$			55664.2i			2.66730i
$759$	−1665.99			−0.0796726
$760$	3935.22	+	3974.77i	0.187823	+	0.189710i
$761$	23588.9			1.12365			0.561823	−	0.827257i	$-0.310100\pi$
$761$	23588.9			1.12365			0.561823	+	0.827257i	$0.310100\pi$
$762$		−	30134.6i		−	1.43263i
$763$		−	6742.11i		−	0.319896i
$764$	−34240.4			−1.62143
$765$	−5409.68	−	5464.04i	−0.255670	−	0.258239i
$766$	44333.3			2.09116
$767$			30093.3i			1.41670i
$768$		−	998.437i		−	0.0469114i
$769$	84.7916			0.00397616			0.00198808	−	0.999998i	$-0.499367\pi$
$769$	84.7916			0.00397616			0.00198808	+	0.999998i	$0.499367\pi$
$770$	3415.51	−	3381.53i	0.159852	−	0.158262i
$771$	7679.13			0.358699
$772$			42195.7i			1.96717i
$773$		−	17416.9i		−	0.810403i	−0.914227	−	0.405202i	$-0.867201\pi$
$773$		−	17416.9i		−	0.810403i	0.914227	−	0.405202i	$-0.132799\pi$
$774$	1584.73			0.0735941
$775$	125.186	−	12520.8i	0.00580233	−	0.580334i
$776$	14665.5			0.678429
$777$		−	1054.78i		−	0.0487003i
$778$		−	49525.2i		−	2.28222i
$779$	836.177			0.0384585
$780$	10204.7	−	10103.1i	0.468443	−	0.463782i
$781$	2997.32			0.137327
$782$			16634.7i			0.760685i
$783$			2189.95i			0.0999522i
$784$	−9526.58			−0.433973
$785$	−18681.9	−	18869.6i	−0.849406	−	0.857941i
$786$	−23837.0			−1.08173
$787$		−	8941.25i		−	0.404983i	−0.979284	−	0.202491i	$-0.935096\pi$
$787$		−	8941.25i		−	0.404983i	0.979284	−	0.202491i	$-0.0649038\pi$
$788$		−	51836.2i		−	2.34339i
$789$	−207.576			−0.00936616
$790$	−36836.3	−	37206.4i	−1.65896	−	1.67563i
$791$	14862.5			0.668079
$792$			1107.34i			0.0496815i
$793$			20861.2i			0.934178i
$794$	52448.4			2.34424
$795$	−15560.6	+	15405.8i	−0.694187	+	0.687281i
$796$	2696.36			0.120063
$797$			24769.1i			1.10084i	0.834889	+	0.550419i	$0.185532\pi$
$797$			24769.1i			1.10084i	−0.834889	+	0.550419i	$0.814468\pi$
$798$			5243.82i			0.232618i
$799$	−2783.80			−0.123259
$800$	30868.3	+	308.629i	1.36420	+	0.0136396i
$801$	−6358.85			−0.280498
$802$		−	66008.9i		−	2.90630i
$803$			7617.32i			0.334756i
$804$	13693.2			0.600649
$805$	3635.25	−	3599.09i	0.159163	−	0.157579i
$806$	−17456.1			−0.762860
$807$			8957.51i			0.390730i
$808$			15405.6i			0.670752i
$809$	882.312			0.0383442			0.0191721	−	0.999816i	$-0.493897\pi$
$809$	882.312			0.0383442			0.0191721	+	0.999816i	$0.493897\pi$
$810$	−2747.44	−	2775.05i	−0.119179	−	0.120377i
$811$	41973.3			1.81736			0.908682	−	0.417490i	$-0.137090\pi$
$811$	41973.3			1.81736			0.908682	+	0.417490i	$0.137090\pi$
$812$			7787.63i			0.336567i
$813$		−	1013.24i		−	0.0437096i
$814$	−1840.11			−0.0792333
$815$	2861.50	+	2890.26i	0.122987	+	0.124222i
$816$	−8371.84			−0.359158
$817$		−	1826.37i		−	0.0782090i
$818$		−	44829.0i		−	1.91615i
$819$	3296.38			0.140641
$820$	−1573.59	+	1557.94i	−0.0670149	+	0.0663482i
$821$	−32888.4			−1.39807			−0.699033	−	0.715089i	$-0.746386\pi$
$821$	−32888.4			−1.39807			−0.699033	+	0.715089i	$0.746386\pi$
$822$			11554.9i			0.490298i
$823$		−	36607.4i		−	1.55049i	−0.631661	−	0.775245i	$-0.717627\pi$
$823$		−	36607.4i		−	1.55049i	0.631661	−	0.775245i	$-0.282373\pi$
$824$	7994.36			0.337982
$825$	4124.79	+	41.2407i	0.174069	+	0.00174039i
$826$	29101.4			1.22587
$827$		−	41798.2i		−	1.75752i	−0.477266	−	0.878759i	$-0.658372\pi$
$827$		−	41798.2i		−	1.75752i	0.477266	−	0.878759i	$-0.341628\pi$
$828$			4813.47i			0.202029i
$829$	18948.8			0.793872			0.396936	−	0.917846i	$-0.370074\pi$
$829$	18948.8			0.793872			0.396936	+	0.917846i	$0.370074\pi$
$830$	−20395.9	+	20193.0i	−0.852954	+	0.844468i
$831$	−16406.5			−0.684879
$832$		−	31228.7i		−	1.30128i
$833$			19933.3i			0.829109i
$834$	35934.0			1.49196
$835$	29929.7	+	30230.4i	1.24043	+	1.25290i
$836$	5212.12			0.215628
$837$			2704.62i			0.111691i
$838$			6848.98i			0.282332i
$839$	25373.5			1.04409			0.522045	−	0.852918i	$-0.325169\pi$
$839$	25373.5			1.04409			0.522045	+	0.852918i	$0.325169\pi$
$840$	−2392.23	−	2416.27i	−0.0982617	−	0.0992490i
$841$	−17810.3			−0.730258
$842$		−	16358.4i		−	0.669533i
$843$			11539.1i			0.471443i
$844$	13663.2			0.557234
$845$	4479.50	−	4434.94i	0.182366	−	0.180552i
$846$	−1413.83			−0.0574566
$847$		−	1096.63i		−	0.0444874i
$848$			23841.5i			0.965474i
$849$	18869.9			0.762796
$850$	411.784	−	41185.6i	0.0166166	−	1.66195i
$851$	−1958.50			−0.0788914
$852$		−	8660.05i		−	0.348226i
$853$		−	3778.34i		−	0.151662i	−0.997121	−	0.0758310i	$-0.975839\pi$
$853$		−	3778.34i		−	0.151662i	0.997121	−	0.0758310i	$-0.0241610\pi$
$854$	20173.6			0.808343
$855$	−3198.21	+	3166.39i	−0.127926	+	0.126653i
$856$	−16725.8			−0.667845
$857$			22069.1i			0.879655i	0.898082	+	0.439828i	$0.144960\pi$
$857$			22069.1i			0.879655i	−0.898082	+	0.439828i	$0.855040\pi$
$858$		−	5750.67i		−	0.228817i
$859$	42408.4			1.68447			0.842234	−	0.539113i	$-0.181240\pi$
$859$	42408.4			1.68447			0.842234	+	0.539113i	$0.181240\pi$
$860$	3402.84	+	3437.04i	0.134926	+	0.136281i
$861$	−508.313			−0.0201200
$862$			25929.5i			1.02455i
$863$			19295.8i			0.761110i	0.924758	+	0.380555i	$0.124267\pi$
$863$			19295.8i			0.761110i	−0.924758	+	0.380555i	$0.875733\pi$
$864$	−6667.88			−0.262553
$865$	7933.66	+	8013.38i	0.311853	+	0.314986i
$866$	11315.2			0.444003
$867$			2778.15i			0.108825i
$868$			9617.83i			0.376095i
$869$	−11946.1			−0.466332
$870$	−8336.40	+	8253.47i	−0.324863	+	0.321631i
$871$	−17411.8			−0.677356
$872$			8320.83i			0.323141i
$873$			11800.3i			0.457479i
$874$	9736.61			0.376826
$875$	−9089.56	+	8820.94i	−0.351181	+	0.340802i
$876$	22008.4			0.848853
$877$			32873.7i			1.26575i	0.774253	+	0.632877i	$0.218126\pi$
$877$			32873.7i			1.26575i	−0.774253	+	0.632877i	$0.781874\pi$
$878$			4679.05i			0.179852i
$879$	4982.44			0.191187
$880$	3191.70	−	3159.95i	0.122264	−	0.121047i
$881$	−44772.8			−1.71218			−0.856092	−	0.516823i	$-0.827114\pi$
$881$	−44772.8			−1.71218			−0.856092	+	0.516823i	$0.827114\pi$
$882$			10123.6i			0.386486i
$883$			30710.6i			1.17043i	0.810877	+	0.585217i	$0.198991\pi$
$883$			30710.6i			1.17043i	−0.810877	+	0.585217i	$0.801009\pi$
$884$	−32715.1			−1.24471
$885$	17572.4	+	17749.0i	0.667446	+	0.674152i
$886$	22308.9			0.845916
$887$			65.5662i			0.00248196i	0.999999	+	0.00124098i	$0.000395016\pi$
$887$			65.5662i			0.00248196i	−0.999999	+	0.00124098i	$0.999605\pi$
$888$			1301.77i			0.0491943i
$889$	21112.3			0.796494
$890$	−23965.1	−	24206.0i	−0.902599	−	0.911669i
$891$	−891.000			−0.0335013
$892$			16100.9i			0.604368i
$893$			1629.41i			0.0610596i
$894$	12539.9			0.469123
$895$	−26597.5	+	26332.9i	−0.993360	+	0.983478i
$896$	−12293.7			−0.458374
$897$		−	6120.66i		−	0.227829i
$898$		−	69199.6i		−	2.57152i
$899$	8124.82			0.301422
$900$	119.155	−	11917.6i	0.00441315	−	0.441392i
$901$	49885.8			1.84455
$902$			886.773i			0.0327343i
$903$			1110.26i			0.0409159i
$904$	−18342.7			−0.674856
$905$	11682.2	−	11566.0i	0.429093	−	0.424825i
$906$	−44989.0			−1.64973
$907$			30133.2i			1.10315i	0.834125	+	0.551575i	$0.185973\pi$
$907$			30133.2i			1.10315i	−0.834125	+	0.551575i	$0.814027\pi$
$908$		−	28979.0i		−	1.05914i
$909$	−12395.8			−0.452302
$910$	12423.4	+	12548.2i	0.452561	+	0.457108i
$911$	−52126.0			−1.89573			−0.947865	−	0.318671i	$-0.896763\pi$
$911$	−52126.0			−1.89573			−0.947865	+	0.318671i	$0.896763\pi$
$912$			4900.20i			0.177919i
$913$			6548.61i			0.237379i
$914$	18298.5			0.662210
$915$	12181.5	+	12303.9i	0.440117	+	0.444539i
$916$	16200.2			0.584354
$917$		−	16700.2i		−	0.601405i
$918$			8896.53i			0.319858i
$919$	16211.2			0.581891			0.290945	−	0.956740i	$-0.406030\pi$
$919$	16211.2			0.581891			0.290945	+	0.956740i	$0.406030\pi$
$920$	−4486.48	+	4441.84i	−0.160777	+	0.159177i
$921$	12203.1			0.436596
$922$		−	65191.2i		−	2.32859i
$923$			11011.8i			0.392697i
$924$	−3168.46			−0.112808
$925$	4849.02	+	48.4817i	0.172362	+	0.00172332i
$926$	−14230.4			−0.505010
$927$			6432.49i			0.227908i
$928$			20030.6i			0.708554i
$929$	−46797.6			−1.65272			−0.826362	−	0.563139i	$-0.809594\pi$
$929$	−46797.6			−1.65272			−0.826362	+	0.563139i	$0.809594\pi$
$930$	−10295.6	+	10193.1i	−0.363016	+	0.359404i
$931$	11667.3			0.410722
$932$		−	17589.2i		−	0.618192i
$933$			11769.6i			0.412990i
$934$	−5464.27			−0.191431
$935$	−6611.83	−	6678.27i	−0.231262	−	0.233586i
$936$	−4068.26			−0.142068
$937$		−	31594.6i		−	1.10155i	−0.834654	−	0.550775i	$-0.814332\pi$
$937$		−	31594.6i		−	1.10155i	0.834654	−	0.550775i	$-0.185668\pi$
$938$			16837.9i			0.586116i
$939$	2420.31			0.0841149
$940$	−3035.87	−	3066.38i	−0.105340	−	0.106398i
$941$	−54758.6			−1.89700			−0.948501	−	0.316775i	$-0.897400\pi$
$941$	−54758.6			−1.89700			−0.948501	+	0.316775i	$0.897400\pi$
$942$			30723.4i			1.06266i
$943$			943.826i			0.0325930i
$944$	27194.5			0.937610
$945$	1944.20	−	1924.86i	0.0669257	−	0.0662599i
$946$	1936.89			0.0665683
$947$			32471.6i			1.11424i	0.830432	+	0.557120i	$0.188094\pi$
$947$			32471.6i			1.11424i	−0.830432	+	0.557120i	$0.811906\pi$
$948$			34515.3i			1.18249i
$949$	−27985.2			−0.957258
$950$	−24106.7	−	241.025i	−0.823290	−	0.00823146i
$951$	−26929.8			−0.918253
$952$			7746.31i			0.263718i
$953$			721.649i			0.0245294i	0.999925	+	0.0122647i	$0.00390407\pi$
$953$			721.649i			0.0245294i	−0.999925	+	0.0122647i	$0.996096\pi$
$954$	25335.8			0.859828
$955$	25679.2	−	25423.7i	0.870113	−	0.861457i
$956$	5917.13			0.200182
$957$			2676.61i			0.0904102i
$958$		−	12669.9i		−	0.427291i
$959$	−8095.37			−0.272589
$960$	−18235.4	−	18418.6i	−0.613067	−	0.619227i
$961$	−19756.7			−0.663178
$962$		−	6760.37i		−	0.226573i
$963$		−	13458.0i		−	0.450342i
$964$	−64967.6			−2.17061
$965$	−31330.6	−	31645.4i	−1.04515	−	1.05565i
$966$	−5918.91			−0.197140
$967$		−	45604.2i		−	1.51658i	−0.651917	−	0.758290i	$-0.726035\pi$
$967$		−	45604.2i		−	1.51658i	0.651917	−	0.758290i	$-0.273965\pi$
$968$			1353.42i			0.0449386i
$969$	10253.1			0.339915
$970$	−44919.6	+	44472.7i	−1.48689	+	1.47210i
$971$	35321.3			1.16737			0.583685	−	0.811980i	$-0.301610\pi$
$971$	35321.3			1.16737			0.583685	+	0.811980i	$0.301610\pi$
$972$			2574.33i			0.0849503i
$973$			25175.3i			0.829480i
$974$	21868.8			0.719426
$975$	−151.514	+	15154.0i	−0.00497675	+	0.497762i
$976$	18851.6			0.618265
$977$			29255.2i			0.957991i	0.877817	+	0.478996i	$0.158999\pi$
$977$			29255.2i			0.957991i	−0.877817	+	0.478996i	$0.841001\pi$
$978$		−	4705.91i		−	0.153863i
$979$	−7771.93			−0.253720
$980$	−21956.7	+	21738.2i	−0.715694	+	0.708574i
$981$	−6695.17			−0.217901
$982$		−	8153.54i		−	0.264959i
$983$			4054.06i			0.131541i	0.997835	+	0.0657703i	$0.0209505\pi$
$983$			4054.06i			0.131541i	−0.997835	+	0.0657703i	$0.979050\pi$
$984$	627.339			0.0203240
$985$	38488.7	+	38875.5i	1.24503	+	1.25754i
$986$	26725.6			0.863203
$987$		−	990.524i		−	0.0319440i
$988$			19148.8i			0.616603i
$989$	2061.50			0.0662811
$990$	−3357.99	−	3391.73i	−0.107802	−	0.108885i
$991$	−9972.08			−0.319650			−0.159825	−	0.987145i	$-0.551093\pi$
$991$	−9972.08			−0.319650			−0.159825	+	0.987145i	$0.551093\pi$
$992$			24738.1i			0.791770i
$993$			22446.9i			0.717353i
$994$	10648.9			0.339800
$995$	−2022.18	+	2002.06i	−0.0644296	+	0.0637886i
$996$	18920.6			0.601931
$997$		−	7920.62i		−	0.251603i	−0.992055	−	0.125802i	$-0.959850\pi$
$997$		−	7920.62i		−	0.251603i	0.992055	−	0.125802i	$-0.0401503\pi$
$998$		−	71311.2i		−	2.26184i
$999$	−1047.44			−0.0331727

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	165.4.c.a.34.3	✓	14
3.2	odd	2		495.4.c.c.199.12		14
5.2	odd	4		825.4.a.bb.1.6		7
5.3	odd	4		825.4.a.bc.1.2		7
5.4	even	2	inner	165.4.c.a.34.12	yes	14
15.2	even	4		2475.4.a.br.1.2		7
15.8	even	4		2475.4.a.bq.1.6		7
15.14	odd	2		495.4.c.c.199.3		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.4.c.a.34.3	✓	14	1.1	even	1	trivial
165.4.c.a.34.12	yes	14	5.4	even	2	inner
495.4.c.c.199.3		14	15.14	odd	2
495.4.c.c.199.12		14	3.2	odd	2
825.4.a.bb.1.6		7	5.2	odd	4
825.4.a.bc.1.2		7	5.3	odd	4
2475.4.a.bq.1.6		7	15.8	even	4
2475.4.a.br.1.2		7	15.2	even	4

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:	\( N \)	\(=\)	\( 165 = 3 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	165.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-4.31207i q^{2} -3.00000i q^{3} -10.5939 q^{4} +(7.94512 - 7.86608i) q^{5} -12.9362 q^{6} -9.06309i q^{7} +11.1853i q^{8} -9.00000 q^{9} +O(q^{10})\)	\(q-4.31207i q^{2} -3.00000i q^{3} -10.5939 q^{4} +(7.94512 - 7.86608i) q^{5} -12.9362 q^{6} -9.06309i q^{7} +11.1853i q^{8} -9.00000 q^{9} +(-33.9191 - 34.2599i) q^{10} -11.0000 q^{11} +31.7818i q^{12} -40.4128i q^{13} -39.0807 q^{14} +(-23.5982 - 23.8353i) q^{15} -36.5198 q^{16} +76.4137i q^{17} +38.8086i q^{18} +44.7264 q^{19} +(-84.1701 + 83.3328i) q^{20} -27.1893 q^{21} +47.4328i q^{22} +50.4845i q^{23} +33.5559 q^{24} +(1.24972 - 124.994i) q^{25} -174.263 q^{26} +27.0000i q^{27} +96.0139i q^{28} +81.1094 q^{29} +(-102.780 + 101.757i) q^{30} +100.171 q^{31} +246.958i q^{32} +33.0000i q^{33} +329.501 q^{34} +(-71.2910 - 72.0073i) q^{35} +95.3455 q^{36} +38.7941i q^{37} -192.863i q^{38} -121.238 q^{39} +(87.9843 + 88.8684i) q^{40} +18.6954 q^{41} +117.242i q^{42} -40.8344i q^{43} +116.533 q^{44} +(-71.5060 + 70.7947i) q^{45} +217.693 q^{46} +36.4307i q^{47} +109.559i q^{48} +260.860 q^{49} +(-538.982 - 5.38888i) q^{50} +229.241 q^{51} +428.131i q^{52} -652.838i q^{53} +116.426 q^{54} +(-87.3963 + 86.5268i) q^{55} +101.373 q^{56} -134.179i q^{57} -349.749i q^{58} -744.649 q^{59} +(249.998 + 252.510i) q^{60} -516.203 q^{61} -431.945i q^{62} +81.5678i q^{63} +772.743 q^{64} +(-317.890 - 321.084i) q^{65} +142.298 q^{66} -430.849i q^{67} -809.523i q^{68} +151.453 q^{69} +(-310.501 + 307.412i) q^{70} -272.484 q^{71} -100.668i q^{72} -692.483i q^{73} +167.283 q^{74} +(-374.981 - 3.74916i) q^{75} -473.829 q^{76} +99.6940i q^{77} +522.788i q^{78} +1086.01 q^{79} +(-290.154 + 287.268i) q^{80} +81.0000 q^{81} -80.6157i q^{82} -595.328i q^{83} +288.042 q^{84} +(601.076 + 607.116i) q^{85} -176.081 q^{86} -243.328i q^{87} -123.038i q^{88} +706.539 q^{89} +(305.272 + 308.339i) q^{90} -366.265 q^{91} -534.830i q^{92} -300.513i q^{93} +157.092 q^{94} +(355.356 - 351.821i) q^{95} +740.875 q^{96} -1311.14i q^{97} -1124.85i q^{98} +99.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 82 q^{4} - 14 q^{5} + 18 q^{6} - 126 q^{9}+O(q^{10}) \) 14 * q - 82 * q^4 - 14 * q^5 + 18 * q^6 - 126 * q^9	\( 14 q - 82 q^{4} - 14 q^{5} + 18 q^{6} - 126 q^{9} - 28 q^{10} - 154 q^{11} - 284 q^{14} + 362 q^{16} - 52 q^{19} + 226 q^{20} + 300 q^{21} - 126 q^{24} - 366 q^{25} + 952 q^{26} - 1144 q^{29} - 582 q^{30} - 280 q^{31} + 1612 q^{34} - 600 q^{35} + 738 q^{36} - 144 q^{39} + 176 q^{40} + 1792 q^{41} + 902 q^{44} + 126 q^{45} - 688 q^{46} - 590 q^{49} + 388 q^{50} + 228 q^{51} - 162 q^{54} + 154 q^{55} + 3044 q^{56} - 2632 q^{59} - 1140 q^{60} - 772 q^{61} - 1738 q^{64} - 904 q^{65} - 198 q^{66} - 1368 q^{69} + 84 q^{70} + 1608 q^{71} + 1496 q^{74} - 300 q^{75} - 3396 q^{76} + 748 q^{79} - 2606 q^{80} + 1134 q^{81} - 5040 q^{84} + 2508 q^{85} - 5068 q^{86} - 1388 q^{89} + 252 q^{90} - 6752 q^{91} + 5840 q^{94} + 1724 q^{95} + 5946 q^{96} + 1386 q^{99}+O(q^{100}) \) 14 * q - 82 * q^4 - 14 * q^5 + 18 * q^6 - 126 * q^9 - 28 * q^10 - 154 * q^11 - 284 * q^14 + 362 * q^16 - 52 * q^19 + 226 * q^20 + 300 * q^21 - 126 * q^24 - 366 * q^25 + 952 * q^26 - 1144 * q^29 - 582 * q^30 - 280 * q^31 + 1612 * q^34 - 600 * q^35 + 738 * q^36 - 144 * q^39 + 176 * q^40 + 1792 * q^41 + 902 * q^44 + 126 * q^45 - 688 * q^46 - 590 * q^49 + 388 * q^50 + 228 * q^51 - 162 * q^54 + 154 * q^55 + 3044 * q^56 - 2632 * q^59 - 1140 * q^60 - 772 * q^61 - 1738 * q^64 - 904 * q^65 - 198 * q^66 - 1368 * q^69 + 84 * q^70 + 1608 * q^71 + 1496 * q^74 - 300 * q^75 - 3396 * q^76 + 748 * q^79 - 2606 * q^80 + 1134 * q^81 - 5040 * q^84 + 2508 * q^85 - 5068 * q^86 - 1388 * q^89 + 252 * q^90 - 6752 * q^91 + 5840 * q^94 + 1724 * q^95 + 5946 * q^96 + 1386 * q^99

Introduction

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