LMFDB - Embedded newform 210.4.g.a.169.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [210,4,Mod(169,210)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(210, 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("210.169");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 210 = 2 \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	210.g (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:	$12.3904011012$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(i, \sqrt{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 9 $ x^4 + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			169.1
Root			$1.22474 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	210.169
Dual form			210.4.g.a.169.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.00000i q^{2} -3.00000i q^{3} -4.00000 q^{4} +(-10.7980 - 2.89898i) q^{5} -6.00000 q^{6} -7.00000i q^{7} +8.00000i q^{8} -9.00000 q^{9} +O(q^{10})$	\(q-2.00000i q^{2} -3.00000i q^{3} -4.00000 q^{4} +(-10.7980 - 2.89898i) q^{5} -6.00000 q^{6} -7.00000i q^{7} +8.00000i q^{8} -9.00000 q^{9} +(-5.79796 + 21.5959i) q^{10} -13.5959 q^{11} +12.0000i q^{12} -10.8082i q^{13} -14.0000 q^{14} +(-8.69694 + 32.3939i) q^{15} +16.0000 q^{16} +98.7878i q^{17} +18.0000i q^{18} -7.79796 q^{19} +(43.1918 + 11.5959i) q^{20} -21.0000 q^{21} +27.1918i q^{22} +95.3735i q^{23} +24.0000 q^{24} +(108.192 + 62.6061i) q^{25} -21.6163 q^{26} +27.0000i q^{27} +28.0000i q^{28} -0.202041 q^{29} +(64.7878 + 17.3939i) q^{30} -165.596 q^{31} -32.0000i q^{32} +40.7878i q^{33} +197.576 q^{34} +(-20.2929 + 75.5857i) q^{35} +36.0000 q^{36} +10.9694i q^{37} +15.5959i q^{38} -32.4245 q^{39} +(23.1918 - 86.3837i) q^{40} +12.3837 q^{41} +42.0000i q^{42} -358.929i q^{43} +54.3837 q^{44} +(97.1816 + 26.0908i) q^{45} +190.747 q^{46} +450.565i q^{47} -48.0000i q^{48} -49.0000 q^{49} +(125.212 - 216.384i) q^{50} +296.363 q^{51} +43.2327i q^{52} +286.504i q^{53} +54.0000 q^{54} +(146.808 + 39.4143i) q^{55} +56.0000 q^{56} +23.3939i q^{57} +0.404082i q^{58} -739.069 q^{59} +(34.7878 - 129.576i) q^{60} -407.716 q^{61} +331.192i q^{62} +63.0000i q^{63} -64.0000 q^{64} +(-31.3326 + 116.706i) q^{65} +81.5755 q^{66} +77.8796i q^{67} -395.151i q^{68} +286.120 q^{69} +(151.171 + 40.5857i) q^{70} -558.100 q^{71} -72.0000i q^{72} -28.8286i q^{73} +21.9388 q^{74} +(187.818 - 324.576i) q^{75} +31.1918 q^{76} +95.1714i q^{77} +64.8490i q^{78} -109.616 q^{79} +(-172.767 - 46.3837i) q^{80} +81.0000 q^{81} -24.7673i q^{82} -1262.75i q^{83} +84.0000 q^{84} +(286.384 - 1066.71i) q^{85} -717.857 q^{86} +0.606123i q^{87} -108.767i q^{88} -1390.97 q^{89} +(52.1816 - 194.363i) q^{90} -75.6571 q^{91} -381.494i q^{92} +496.788i q^{93} +901.131 q^{94} +(84.2020 + 22.6061i) q^{95} -96.0000 q^{96} +418.082i q^{97} +98.0000i q^{98} +122.363 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 16 q^{4} - 4 q^{5} - 24 q^{6} - 36 q^{9}+O(q^{10}) $ 4 * q - 16 * q^4 - 4 * q^5 - 24 * q^6 - 36 * q^9	$ 4 q - 16 q^{4} - 4 q^{5} - 24 q^{6} - 36 q^{9} + 16 q^{10} + 24 q^{11} - 56 q^{14} + 24 q^{15} + 64 q^{16} + 8 q^{19} + 16 q^{20} - 84 q^{21} + 96 q^{24} + 276 q^{25} - 400 q^{26} - 40 q^{29} + 24 q^{30} - 584 q^{31} + 320 q^{34} + 56 q^{35} + 144 q^{36} - 600 q^{39} - 64 q^{40} - 264 q^{41} - 96 q^{44} + 36 q^{45} - 256 q^{46} - 196 q^{49} + 736 q^{50} + 480 q^{51} + 216 q^{54} + 744 q^{55} + 224 q^{56} - 448 q^{59} - 96 q^{60} - 24 q^{61} - 256 q^{64} + 1168 q^{65} - 144 q^{66} - 384 q^{69} + 56 q^{70} - 312 q^{71} - 1088 q^{74} + 1104 q^{75} - 32 q^{76} - 752 q^{79} - 64 q^{80} + 324 q^{81} + 336 q^{84} + 832 q^{85} - 128 q^{86} - 1096 q^{89} - 144 q^{90} - 1400 q^{91} + 2272 q^{94} + 376 q^{95} - 384 q^{96} - 216 q^{99}+O(q^{100}) $ 4 * q - 16 * q^4 - 4 * q^5 - 24 * q^6 - 36 * q^9 + 16 * q^10 + 24 * q^11 - 56 * q^14 + 24 * q^15 + 64 * q^16 + 8 * q^19 + 16 * q^20 - 84 * q^21 + 96 * q^24 + 276 * q^25 - 400 * q^26 - 40 * q^29 + 24 * q^30 - 584 * q^31 + 320 * q^34 + 56 * q^35 + 144 * q^36 - 600 * q^39 - 64 * q^40 - 264 * q^41 - 96 * q^44 + 36 * q^45 - 256 * q^46 - 196 * q^49 + 736 * q^50 + 480 * q^51 + 216 * q^54 + 744 * q^55 + 224 * q^56 - 448 * q^59 - 96 * q^60 - 24 * q^61 - 256 * q^64 + 1168 * q^65 - 144 * q^66 - 384 * q^69 + 56 * q^70 - 312 * q^71 - 1088 * q^74 + 1104 * q^75 - 32 * q^76 - 752 * q^79 - 64 * q^80 + 324 * q^81 + 336 * q^84 + 832 * q^85 - 128 * q^86 - 1096 * q^89 - 144 * q^90 - 1400 * q^91 + 2272 * q^94 + 376 * q^95 - 384 * q^96 - 216 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/210\mathbb{Z}\right)^\times$.

$n$	$31$	$71$	$127$
$\chi(n)$	$1$	$1$	$-1$

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 $

$2$		−	2.00000i		−	0.707107i
$2$		−	2.00000i		−	0.707107i
$3$		−	3.00000i		−	0.577350i
$3$		−	3.00000i		−	0.577350i
$4$	−4.00000			−0.500000
$5$	−10.7980	−	2.89898i	−0.965799	−	0.259293i
$5$	−10.7980	−	2.89898i	−0.965799	−	0.259293i
$6$	−6.00000			−0.408248
$7$		−	7.00000i		−	0.377964i
$7$		−	7.00000i		−	0.377964i
$8$			8.00000i			0.353553i
$9$	−9.00000			−0.333333
$10$	−5.79796	+	21.5959i	−0.183348	+	0.682923i
$11$	−13.5959			−0.372666			−0.186333	−	0.982487i	$-0.559660\pi$
$11$	−13.5959			−0.372666			−0.186333	+	0.982487i	$0.559660\pi$
$12$			12.0000i			0.288675i
$13$		−	10.8082i		−	0.230588i	−0.993331	−	0.115294i	$-0.963219\pi$
$13$		−	10.8082i		−	0.230588i	0.993331	−	0.115294i	$-0.0367810\pi$
$14$	−14.0000			−0.267261
$15$	−8.69694	+	32.3939i	−0.149703	+	0.557604i
$16$	16.0000			0.250000
$17$			98.7878i			1.40939i	0.709513	+	0.704693i	$0.248915\pi$
$17$			98.7878i			1.40939i	−0.709513	+	0.704693i	$0.751085\pi$
$18$			18.0000i			0.235702i
$19$	−7.79796			−0.0941566			−0.0470783	−	0.998891i	$-0.514991\pi$
$19$	−7.79796			−0.0941566			−0.0470783	+	0.998891i	$0.514991\pi$
$20$	43.1918	+	11.5959i	0.482899	+	0.129646i
$21$	−21.0000			−0.218218
$22$			27.1918i			0.263514i
$23$			95.3735i			0.864641i	0.901720	+	0.432320i	$0.142305\pi$
$23$			95.3735i			0.864641i	−0.901720	+	0.432320i	$0.857695\pi$
$24$	24.0000			0.204124
$25$	108.192	+	62.6061i	0.865535	+	0.500849i
$26$	−21.6163			−0.163050
$27$			27.0000i			0.192450i
$28$			28.0000i			0.188982i
$29$	−0.202041			−0.00129373			−0.000646863	−	1.00000i	$-0.500206\pi$
$29$	−0.202041			−0.00129373			−0.000646863		1.00000i	$0.500206\pi$
$30$	64.7878	+	17.3939i	0.394286	+	0.105856i
$31$	−165.596			−0.959416			−0.479708	−	0.877428i	$-0.659257\pi$
$31$	−165.596			−0.959416			−0.479708	+	0.877428i	$0.659257\pi$
$32$		−	32.0000i		−	0.176777i
$33$			40.7878i			0.215159i
$34$	197.576			0.996586
$35$	−20.2929	+	75.5857i	−0.0980034	+	0.365038i
$36$	36.0000			0.166667
$37$			10.9694i			0.0487393i	0.999703	+	0.0243697i	$0.00775788\pi$
$37$			10.9694i			0.0487393i	−0.999703	+	0.0243697i	$0.992242\pi$
$38$			15.5959i			0.0665787i
$39$	−32.4245			−0.133130
$40$	23.1918	−	86.3837i	0.0916738	−	0.341461i
$41$	12.3837			0.0471708			0.0235854	−	0.999722i	$-0.492492\pi$
$41$	12.3837			0.0471708			0.0235854	+	0.999722i	$0.492492\pi$
$42$			42.0000i			0.154303i
$43$		−	358.929i		−	1.27293i	−0.771305	−	0.636466i	$-0.780395\pi$
$43$		−	358.929i		−	1.27293i	0.771305	−	0.636466i	$-0.219605\pi$
$44$	54.3837			0.186333
$45$	97.1816	+	26.0908i	0.321933	+	0.0864309i
$46$	190.747			0.611393
$47$			450.565i			1.39833i	0.714958	+	0.699167i	$0.246446\pi$
$47$			450.565i			1.39833i	−0.714958	+	0.699167i	$0.753554\pi$
$48$		−	48.0000i		−	0.144338i
$49$	−49.0000			−0.142857
$50$	125.212	−	216.384i	0.354154	−	0.612025i
$51$	296.363			0.813709
$52$			43.2327i			0.115294i
$53$			286.504i			0.742535i	0.928526	+	0.371268i	$0.121077\pi$
$53$			286.504i			0.742535i	−0.928526	+	0.371268i	$0.878923\pi$
$54$	54.0000			0.136083
$55$	146.808	+	39.4143i	0.359920	+	0.0966295i
$56$	56.0000			0.133631
$57$			23.3939i			0.0543613i
$58$			0.404082i			0.000914803i
$59$	−739.069			−1.63082			−0.815412	−	0.578881i	$-0.803490\pi$
$59$	−739.069			−1.63082			−0.815412	+	0.578881i	$0.803490\pi$
$60$	34.7878	−	129.576i	0.0748513	−	0.278802i
$61$	−407.716			−0.855782			−0.427891	−	0.903830i	$-0.640743\pi$
$61$	−407.716			−0.855782			−0.427891	+	0.903830i	$0.640743\pi$
$62$			331.192i			0.678410i
$63$			63.0000i			0.125988i
$64$	−64.0000			−0.125000
$65$	−31.3326	+	116.706i	−0.0597898	+	0.222702i
$66$	81.5755			0.152140
$67$			77.8796i			0.142008i	0.997476	+	0.0710038i	$0.0226202\pi$
$67$			77.8796i			0.142008i	−0.997476	+	0.0710038i	$0.977380\pi$
$68$		−	395.151i		−	0.704693i
$69$	286.120			0.499201
$70$	151.171	+	40.5857i	0.258121	+	0.0692989i
$71$	−558.100			−0.932877			−0.466439	−	0.884554i	$-0.654463\pi$
$71$	−558.100			−0.932877			−0.466439	+	0.884554i	$0.654463\pi$
$72$		−	72.0000i		−	0.117851i
$73$		−	28.8286i		−	0.0462210i	−0.999733	−	0.0231105i	$-0.992643\pi$
$73$		−	28.8286i		−	0.0462210i	0.999733	−	0.0231105i	$-0.00735695\pi$
$74$	21.9388			0.0344639
$75$	187.818	−	324.576i	0.289165	−	0.499717i
$76$	31.1918			0.0470783
$77$			95.1714i			0.140854i
$78$			64.8490i			0.0941372i
$79$	−109.616			−0.156111			−0.0780557	−	0.996949i	$-0.524871\pi$
$79$	−109.616			−0.156111			−0.0780557	+	0.996949i	$0.524871\pi$
$80$	−172.767	−	46.3837i	−0.241450	−	0.0648232i
$81$	81.0000			0.111111
$82$		−	24.7673i		−	0.0333548i
$83$		−	1262.75i		−	1.66993i	−0.550300	−	0.834967i	$-0.685487\pi$
$83$		−	1262.75i		−	1.66993i	0.550300	−	0.834967i	$-0.314513\pi$
$84$	84.0000			0.109109
$85$	286.384	−	1066.71i	0.365443	−	1.36118i
$86$	−717.857			−0.900099
$87$			0.606123i			0.000746934i
$88$		−	108.767i		−	0.131757i
$89$	−1390.97			−1.65665			−0.828327	−	0.560245i	$-0.810707\pi$
$89$	−1390.97			−1.65665			−0.828327	+	0.560245i	$0.810707\pi$
$90$	52.1816	−	194.363i	0.0611159	−	0.227641i
$91$	−75.6571			−0.0871541
$92$		−	381.494i		−	0.432320i
$93$			496.788i			0.553919i
$94$	901.131			0.988772
$95$	84.2020	+	22.6061i	0.0909363	+	0.0244141i
$96$	−96.0000			−0.102062
$97$			418.082i			0.437626i	0.975767	+	0.218813i	$0.0702185\pi$
$97$			418.082i			0.437626i	−0.975767	+	0.218813i	$0.929781\pi$
$98$			98.0000i			0.101015i
$99$	122.363			0.124222
$100$	−432.767	−	250.424i	−0.432767	−	0.250424i
$101$	−1619.37			−1.59538			−0.797690	−	0.603067i	$-0.793945\pi$
$101$	−1619.37			−1.59538			−0.797690	+	0.603067i	$0.793945\pi$
$102$		−	592.727i		−	0.575379i
$103$		−	1470.22i		−	1.40646i	−0.710964	−	0.703229i	$-0.751741\pi$
$103$		−	1470.22i		−	1.40646i	0.710964	−	0.703229i	$-0.248259\pi$
$104$	86.4653			0.0815252
$105$	226.757	+	60.8786i	0.210755	+	0.0565823i
$106$	573.008			0.525052
$107$			1201.39i			1.08545i	0.839911	+	0.542725i	$0.182607\pi$
$107$			1201.39i			1.08545i	−0.839911	+	0.542725i	$0.817393\pi$
$108$		−	108.000i		−	0.0962250i
$109$	917.718			0.806436			0.403218	−	0.915104i	$-0.367892\pi$
$109$	917.718			0.806436			0.403218	+	0.915104i	$0.367892\pi$
$110$	78.8286	−	293.616i	0.0683274	−	0.254502i
$111$	32.9082			0.0281397
$112$		−	112.000i		−	0.0944911i
$113$		−	774.827i		−	0.645040i	−0.946563	−	0.322520i	$-0.895470\pi$
$113$		−	774.827i		−	0.645040i	0.946563	−	0.322520i	$-0.104530\pi$
$114$	46.7878			0.0384393
$115$	276.486	−	1029.84i	0.224195	−	0.835069i
$116$	0.808164			0.000646863
$117$			97.2735i			0.0768627i
$118$			1478.14i			1.15317i
$119$	691.514			0.532698
$120$	−259.151	−	69.5755i	−0.197143	−	0.0529279i
$121$	−1146.15			−0.861120
$122$			815.433i			0.605130i
$123$		−	37.1510i		−	0.0272341i
$124$	662.384			0.479708
$125$	−986.757	−	989.664i	−0.706066	−	0.708146i
$126$	126.000			0.0890871
$127$		−	8.15916i		−	0.00570085i	−0.999996	−	0.00285043i	$-0.999093\pi$
$127$		−	8.15916i		−	0.00570085i	0.999996	−	0.00285043i	$-0.000907320\pi$
$128$			128.000i			0.0883883i
$129$	−1076.79			−0.734928
$130$	233.412	+	62.6653i	0.157474	+	0.0422778i
$131$	876.808			0.584787			0.292393	−	0.956298i	$-0.405548\pi$
$131$	876.808			0.584787			0.292393	+	0.956298i	$0.405548\pi$
$132$		−	163.151i		−	0.107579i
$133$			54.5857i			0.0355878i
$134$	155.759			0.100415
$135$	78.2724	−	291.545i	0.0499009	−	0.185868i
$136$	−790.302			−0.498293
$137$			1077.53i			0.671970i	0.941867	+	0.335985i	$0.109069\pi$
$137$			1077.53i			0.671970i	−0.941867	+	0.335985i	$0.890931\pi$
$138$		−	572.241i		−	0.352988i
$139$	1555.72			0.949310			0.474655	−	0.880172i	$-0.342573\pi$
$139$	1555.72			0.949310			0.474655	+	0.880172i	$0.342573\pi$
$140$	81.1714	−	302.343i	0.0490017	−	0.182519i
$141$	1351.70			0.807329
$142$			1116.20i			0.659644i
$143$			146.947i			0.0859323i
$144$	−144.000			−0.0833333
$145$	2.18163	+	0.585713i	0.00124948	+	0.000335454i
$146$	−57.6571			−0.0326831
$147$			147.000i			0.0824786i
$148$		−	43.8775i		−	0.0243697i
$149$	−1806.99			−0.993519			−0.496760	−	0.867888i	$-0.665477\pi$
$149$	−1806.99			−0.993519			−0.496760	+	0.867888i	$0.665477\pi$
$150$	−649.151	−	375.637i	−0.353353	−	0.204471i
$151$	949.612			0.511777			0.255889	−	0.966706i	$-0.417632\pi$
$151$	949.612			0.511777			0.255889	+	0.966706i	$0.417632\pi$
$152$		−	62.3837i		−	0.0332894i
$153$		−	889.090i		−	0.469795i
$154$	190.343			0.0995991
$155$	1788.10	+	480.059i	0.926603	+	0.248770i
$156$	129.698			0.0665651
$157$			3018.52i			1.53442i	0.641395	+	0.767211i	$0.278356\pi$
$157$			3018.52i			1.53442i	−0.641395	+	0.767211i	$0.721644\pi$
$158$			219.233i			0.110387i
$159$	859.512			0.428703
$160$	−92.7673	+	345.535i	−0.0458369	+	0.170731i
$161$	667.614			0.326804
$162$		−	162.000i		−	0.0785674i
$163$			741.231i			0.356182i	0.984014	+	0.178091i	$0.0569921\pi$
$163$			741.231i			0.356182i	−0.984014	+	0.178091i	$0.943008\pi$
$164$	−49.5347			−0.0235854
$165$	118.243	−	440.424i	0.0557891	−	0.207800i
$166$	−2525.49			−1.18082
$167$		−	52.2591i		−	0.0242152i	−0.999927	−	0.0121076i	$-0.996146\pi$
$167$		−	52.2591i		−	0.0242152i	0.999927	−	0.0121076i	$-0.00385406\pi$
$168$		−	168.000i		−	0.0771517i
$169$	2080.18			0.946829
$170$	−2133.41	−	572.767i	−0.962501	−	0.258407i
$171$	70.1816			0.0313855
$172$			1435.71i			0.636466i
$173$		−	155.378i		−	0.0682840i	−0.999417	−	0.0341420i	$-0.989130\pi$
$173$		−	155.378i		−	0.0682840i	0.999417	−	0.0341420i	$-0.0108699\pi$
$174$	1.21225			0.000528162
$175$	438.243	−	757.343i	0.189303	−	0.327141i
$176$	−217.535			−0.0931664
$177$			2217.21i			0.941557i
$178$			2781.93i			1.17143i
$179$	2442.07			1.01972			0.509858	−	0.860259i	$-0.329698\pi$
$179$	2442.07			1.01972			0.509858	+	0.860259i	$0.329698\pi$
$180$	−388.727	−	104.363i	−0.160966	−	0.0432154i
$181$	−1153.49			−0.473693			−0.236846	−	0.971547i	$-0.576114\pi$
$181$	−1153.49			−0.473693			−0.236846	+	0.971547i	$0.576114\pi$
$182$			151.314i			0.0616273i
$183$			1223.15i			0.494086i
$184$	−762.988			−0.305697
$185$	31.8000	−	118.447i	0.0126378	−	0.0470724i
$186$	993.576			0.391680
$187$		−	1343.11i		−	0.525230i
$188$		−	1802.26i		−	0.699167i
$189$	189.000			0.0727393
$190$	45.2122	−	168.404i	0.0172634	−	0.0643017i
$191$	4828.85			1.82934			0.914668	−	0.404206i	$-0.132452\pi$
$191$	4828.85			1.82934			0.914668	+	0.404206i	$0.132452\pi$
$192$			192.000i			0.0721688i
$193$			527.437i			0.196714i	0.995151	+	0.0983568i	$0.0313586\pi$
$193$			527.437i			0.196714i	−0.995151	+	0.0983568i	$0.968641\pi$
$194$	836.163			0.309449
$195$	350.118	+	93.9979i	0.128577	+	0.0345197i
$196$	196.000			0.0714286
$197$			2527.48i			0.914087i	0.889444	+	0.457044i	$0.151092\pi$
$197$			2527.48i			0.914087i	−0.889444	+	0.457044i	$0.848908\pi$
$198$		−	244.727i		−	0.0878382i
$199$	−5137.31			−1.83002			−0.915010	−	0.403431i	$-0.867817\pi$
$199$	−5137.31			−1.83002			−0.915010	+	0.403431i	$0.867817\pi$
$200$	−500.849	+	865.535i	−0.177077	+	0.306013i
$201$	233.639			0.0819881
$202$			3238.74i			1.12810i
$203$			1.41429i			0.000488983i
$204$	−1185.45			−0.406854
$205$	−133.718	−	35.9000i	−0.0455575	−	0.0122311i
$206$	−2940.44			−0.994516
$207$		−	858.361i		−	0.288214i
$208$		−	172.931i		−	0.0576470i
$209$	106.020			0.0350889
$210$	121.757	−	453.514i	0.0400097	−	0.149026i
$211$	5766.29			1.88137			0.940683	−	0.339288i	$-0.110186\pi$
$211$	5766.29			1.88137			0.940683	+	0.339288i	$0.110186\pi$
$212$		−	1146.02i		−	0.371268i
$213$			1674.30i			0.538597i
$214$	2402.79			0.767529
$215$	−1040.53	+	3875.70i	−0.330062	+	1.22940i
$216$	−216.000			−0.0680414
$217$			1159.17i			0.362625i
$218$		−	1835.44i		−	0.570236i
$219$	−86.4857			−0.0266857
$220$	−587.233	−	157.657i	−0.179960	−	0.0483147i
$221$	1067.71			0.324987
$222$		−	65.8163i		−	0.0198978i
$223$		−	1194.30i		−	0.358637i	−0.983791	−	0.179319i	$-0.942611\pi$
$223$		−	1194.30i		−	0.358637i	0.983791	−	0.179319i	$-0.0573893\pi$
$224$	−224.000			−0.0668153
$225$	−973.727	−	563.455i	−0.288512	−	0.166950i
$226$	−1549.65			−0.456112
$227$			3101.45i			0.906830i	0.891300	+	0.453415i	$0.149794\pi$
$227$			3101.45i			0.906830i	−0.891300	+	0.453415i	$0.850206\pi$
$228$		−	93.5755i		−	0.0271807i
$229$	−2161.00			−0.623594			−0.311797	−	0.950149i	$-0.600931\pi$
$229$	−2161.00			−0.623594			−0.311797	+	0.950149i	$0.600931\pi$
$230$	−2059.68	−	552.971i	−0.590483	−	0.158530i
$231$	285.514			0.0813223
$232$		−	1.61633i		−	0.000457401i
$233$		−	3124.28i		−	0.878449i	−0.898377	−	0.439225i	$-0.855253\pi$
$233$		−	3124.28i		−	0.878449i	0.898377	−	0.439225i	$-0.144747\pi$
$234$	194.547			0.0543501
$235$	1306.18	−	4865.19i	0.362578	−	1.35051i
$236$	2956.28			0.815412
$237$			328.849i			0.0901310i
$238$		−	1383.03i		−	0.376674i
$239$	−1632.89			−0.441937			−0.220969	−	0.975281i	$-0.570922\pi$
$239$	−1632.89			−0.441937			−0.220969	+	0.975281i	$0.570922\pi$
$240$	−139.151	+	518.302i	−0.0374257	+	0.139401i
$241$	−4947.81			−1.32247			−0.661237	−	0.750177i	$-0.729968\pi$
$241$	−4947.81			−1.32247			−0.661237	+	0.750177i	$0.729968\pi$
$242$			2292.30i			0.608904i
$243$		−	243.000i		−	0.0641500i
$244$	1630.87			0.427891
$245$	529.100	+	142.050i	0.137971	+	0.0370418i
$246$	−74.3020			−0.0192574
$247$			84.2816i			0.0217114i
$248$		−	1324.77i		−	0.339205i
$249$	−3788.24			−0.964137
$250$	−1979.33	+	1973.51i	−0.500735	+	0.499264i
$251$	6977.04			1.75453			0.877265	−	0.480006i	$-0.159365\pi$
$251$	6977.04			1.75453			0.877265	+	0.480006i	$0.159365\pi$
$252$		−	252.000i		−	0.0629941i
$253$		−	1296.69i		−	0.322222i
$254$	−16.3183			−0.00403111
$255$	−3200.12	−	859.151i	−0.785879	−	0.210989i
$256$	256.000			0.0625000
$257$			3164.36i			0.768045i	0.923324	+	0.384022i	$0.125461\pi$
$257$			3164.36i			0.768045i	−0.923324	+	0.384022i	$0.874539\pi$
$258$			2153.57i			0.519672i
$259$	76.7857			0.0184217
$260$	125.331	−	466.824i	0.0298949	−	0.111351i
$261$	1.81837			0.000431242
$262$		−	1753.62i		−	0.413507i
$263$			496.871i			0.116496i	0.998302	+	0.0582479i	$0.0185514\pi$
$263$			496.871i			0.116496i	−0.998302	+	0.0582479i	$0.981449\pi$
$264$	−326.302			−0.0760701
$265$	830.569	−	3093.66i	0.192534	−	0.717140i
$266$	109.171			0.0251644
$267$			4172.90i			0.956470i
$268$		−	311.518i		−	0.0710038i
$269$	−3897.19			−0.883330			−0.441665	−	0.897180i	$-0.645612\pi$
$269$	−3897.19			−0.883330			−0.441665	+	0.897180i	$0.645612\pi$
$270$	−583.090	−	156.545i	−0.131429	−	0.0352853i
$271$	−7309.63			−1.63848			−0.819240	−	0.573450i	$-0.805605\pi$
$271$	−7309.63			−1.63848			−0.819240	+	0.573450i	$0.805605\pi$
$272$			1580.60i			0.352346i
$273$			226.971i			0.0503185i
$274$	2155.07			0.475154
$275$	−1470.97	−	851.188i	−0.322555	−	0.186649i
$276$	−1144.48			−0.249600
$277$		−	8351.24i		−	1.81147i	−0.423844	−	0.905735i	$-0.639320\pi$
$277$		−	8351.24i		−	1.81147i	0.423844	−	0.905735i	$-0.360680\pi$
$278$		−	3111.43i		−	0.671264i
$279$	1490.36			0.319805
$280$	−604.686	−	162.343i	−0.129060	−	0.0346494i
$281$	3816.91			0.810311			0.405156	−	0.914248i	$-0.367217\pi$
$281$	3816.91			0.810311			0.405156	+	0.914248i	$0.367217\pi$
$282$		−	2703.39i		−	0.570868i
$283$		−	3683.58i		−	0.773733i	−0.922136	−	0.386866i	$-0.873557\pi$
$283$		−	3683.58i		−	0.773733i	0.922136	−	0.386866i	$-0.126443\pi$
$284$	2232.40			0.466439
$285$	67.8184	−	252.606i	0.0140955	−	0.0525021i
$286$	293.894			0.0607633
$287$		−	86.6857i		−	0.0178289i
$288$			288.000i			0.0589256i
$289$	−4846.02			−0.986367
$290$	1.17143	−	4.36326i	0.000237202	−	0.000883516i
$291$	1254.24			0.252664
$292$			115.314i			0.0231105i
$293$		−	8450.79i		−	1.68498i	−0.538709	−	0.842492i	$-0.681088\pi$
$293$		−	8450.79i		−	1.68498i	0.538709	−	0.842492i	$-0.318912\pi$
$294$	294.000			0.0583212
$295$	7980.44	+	2142.55i	1.57505	+	0.422861i
$296$	−87.7551			−0.0172320
$297$		−	367.090i		−	0.0717196i
$298$			3613.98i			0.702524i
$299$	1030.81			0.199376
$300$	−751.273	+	1298.30i	−0.144583	+	0.249858i
$301$	−2512.50			−0.481123
$302$		−	1899.22i		−	0.361881i
$303$			4858.11i			0.921094i
$304$	−124.767			−0.0235391
$305$	4402.50	+	1181.96i	0.826514	+	0.221898i
$306$	−1778.18			−0.332195
$307$		−	3323.79i		−	0.617911i	−0.951076	−	0.308956i	$-0.900021\pi$
$307$		−	3323.79i		−	0.617911i	0.951076	−	0.308956i	$-0.0999795\pi$
$308$		−	380.686i		−	0.0704272i
$309$	−4410.66			−0.812019
$310$	960.118	−	3576.20i	0.175907	−	0.655207i
$311$	1760.61			0.321013			0.160506	−	0.987035i	$-0.448687\pi$
$311$	1760.61			0.321013			0.160506	+	0.987035i	$0.448687\pi$
$312$		−	259.396i		−	0.0470686i
$313$			1717.91i			0.310230i	0.987896	+	0.155115i	$0.0495748\pi$
$313$			1717.91i			0.310230i	−0.987896	+	0.155115i	$0.950425\pi$
$314$	6037.04			1.08500
$315$	182.636	−	680.271i	0.0326678	−	0.121679i
$316$	438.465			0.0780557
$317$		−	9539.06i		−	1.69012i	−0.534674	−	0.845059i	$-0.679565\pi$
$317$		−	9539.06i		−	1.69012i	0.534674	−	0.845059i	$-0.320435\pi$
$318$		−	1719.02i		−	0.303139i
$319$	2.74693			0.000482128
$320$	691.069	+	185.535i	0.120725	+	0.0324116i
$321$	3604.18			0.626685
$322$		−	1335.23i		−	0.231085i
$323$		−	770.343i		−	0.132703i
$324$	−324.000			−0.0555556
$325$	676.657	−	1169.36i	0.115490	−	0.199582i
$326$	1482.46			0.251859
$327$		−	2753.16i		−	0.465596i
$328$			99.0694i			0.0166774i
$329$	3153.96			0.528521
$330$	−880.849	−	236.486i	−0.146937	−	0.0394488i
$331$	−452.359			−0.0751175			−0.0375588	−	0.999294i	$-0.511958\pi$
$331$	−452.359			−0.0751175			−0.0375588	+	0.999294i	$0.511958\pi$
$332$			5050.99i			0.834967i
$333$		−	98.7245i		−	0.0162464i
$334$	−104.518			−0.0171227
$335$	225.771	−	840.941i	0.0368215	−	0.137151i
$336$	−336.000			−0.0545545
$337$			5637.61i			0.911277i	0.890165	+	0.455638i	$0.150589\pi$
$337$			5637.61i			0.911277i	−0.890165	+	0.455638i	$0.849411\pi$
$338$		−	4160.37i		−	0.669509i
$339$	−2324.48			−0.372414
$340$	−1145.53	+	4266.82i	−0.182722	+	0.680591i
$341$	2251.43			0.357542
$342$		−	140.363i		−	0.0221929i
$343$			343.000i			0.0539949i
$344$	2871.43			0.450050
$345$	−3089.52	−	829.457i	−0.482127	−	0.129439i
$346$	−310.755			−0.0482841
$347$		−	12313.1i		−	1.90490i	−0.304696	−	0.952450i	$-0.598555\pi$
$347$		−	12313.1i		−	1.90490i	0.304696	−	0.952450i	$-0.401445\pi$
$348$		−	2.42449i		−	0.000373467i
$349$	−7203.55			−1.10486			−0.552432	−	0.833558i	$-0.686300\pi$
$349$	−7203.55			−1.10486			−0.552432	+	0.833558i	$0.686300\pi$
$350$	−1514.69	−	876.486i	−0.231324	−	0.133858i
$351$	291.820			0.0443767
$352$			435.069i			0.0658786i
$353$			7030.58i			1.06006i	0.847980	+	0.530028i	$0.177819\pi$
$353$			7030.58i			1.06006i	−0.847980	+	0.530028i	$0.822181\pi$
$354$	4434.42			0.665781
$355$	6026.34	+	1617.92i	0.900972	+	0.241888i
$356$	5563.87			0.828327
$357$		−	2074.54i		−	0.307553i
$358$		−	4884.15i		−	0.721048i
$359$	−5999.06			−0.881946			−0.440973	−	0.897520i	$-0.645366\pi$
$359$	−5999.06			−0.881946			−0.440973	+	0.897520i	$0.645366\pi$
$360$	−208.727	+	777.453i	−0.0305579	+	0.113820i
$361$	−6798.19			−0.991135
$362$			2306.98i			0.334951i
$363$			3438.45i			0.497168i
$364$	302.629			0.0435771
$365$	−83.5734	+	311.290i	−0.0119848	+	0.0446401i
$366$	2446.30			0.349372
$367$		−	9039.02i		−	1.28565i	−0.766014	−	0.642824i	$-0.777763\pi$
$367$		−	9039.02i		−	1.28565i	0.766014	−	0.642824i	$-0.222237\pi$
$368$			1525.98i			0.216160i
$369$	−111.453			−0.0157236
$370$	−236.894	−	63.6000i	−0.0332852	−	0.00893624i
$371$	2005.53			0.280652
$372$		−	1987.15i		−	0.276960i
$373$			12415.4i			1.72345i	0.507375	+	0.861726i	$0.330616\pi$
$373$			12415.4i			1.72345i	−0.507375	+	0.861726i	$0.669384\pi$
$374$	−2686.22			−0.371393
$375$	−2968.99	+	2960.27i	−0.408848	+	0.407647i
$376$	−3604.52			−0.494386
$377$			2.18369i			0.000298318i
$378$		−	378.000i		−	0.0514344i
$379$	−7339.39			−0.994721			−0.497360	−	0.867544i	$-0.665697\pi$
$379$	−7339.39			−0.994721			−0.497360	+	0.867544i	$0.665697\pi$
$380$	−336.808	−	90.4245i	−0.0454681	−	0.0122070i
$381$	−24.4775			−0.00329139
$382$		−	9657.69i		−	1.29354i
$383$			8054.27i			1.07455i	0.843406	+	0.537277i	$0.180547\pi$
$383$			8054.27i			1.07455i	−0.843406	+	0.537277i	$0.819453\pi$
$384$	384.000			0.0510310
$385$	275.900	−	1027.66i	0.0365225	−	0.136037i
$386$	1054.87			0.139098
$387$			3230.36i			0.424311i
$388$		−	1672.33i		−	0.218813i
$389$	−4405.48			−0.574208			−0.287104	−	0.957899i	$-0.592693\pi$
$389$	−4405.48			−0.574208			−0.287104	+	0.957899i	$0.592693\pi$
$390$	187.996	−	700.237i	0.0244091	−	0.0909176i
$391$	−9421.73			−1.21861
$392$		−	392.000i		−	0.0505076i
$393$		−	2630.42i		−	0.337627i
$394$	5054.95			0.646357
$395$	1183.63	+	317.775i	0.150772	+	0.0404785i
$396$	−489.453			−0.0621110
$397$			10950.6i			1.38437i	0.721721	+	0.692184i	$0.243351\pi$
$397$			10950.6i			1.38437i	−0.721721	+	0.692184i	$0.756649\pi$
$398$			10274.6i			1.29402i
$399$	163.757			0.0205466
$400$	1731.07	+	1001.70i	0.216384	+	0.125212i
$401$	−7942.59			−0.989112			−0.494556	−	0.869146i	$-0.664669\pi$
$401$	−7942.59			−0.989112			−0.494556	+	0.869146i	$0.664669\pi$
$402$		−	467.278i		−	0.0579743i
$403$			1789.79i			0.221230i
$404$	6477.49			0.797690
$405$	−874.635	−	234.817i	−0.107311	−	0.0288103i
$406$	2.82857			0.000345763
$407$		−	149.139i		−	0.0181635i
$408$			2370.91i			0.287690i
$409$	7094.02			0.857645			0.428822	−	0.903389i	$-0.358929\pi$
$409$	7094.02			0.857645			0.428822	+	0.903389i	$0.358929\pi$
$410$	−71.8000	+	267.437i	−0.00864866	+	0.0322140i
$411$	3232.60			0.387962
$412$			5880.88i			0.703229i
$413$			5173.49i			0.616394i
$414$	−1716.72			−0.203798
$415$	−3660.68	+	13635.1i	−0.433001	+	1.61282i
$416$	−345.861			−0.0407626
$417$		−	4667.15i		−	0.548085i
$418$		−	212.041i		−	0.0248116i
$419$	2491.00			0.290438			0.145219	−	0.989400i	$-0.453611\pi$
$419$	2491.00			0.290438			0.145219	+	0.989400i	$0.453611\pi$
$420$	−907.029	−	243.514i	−0.105377	−	0.0282911i
$421$	−1567.51			−0.181462			−0.0907311	−	0.995875i	$-0.528920\pi$
$421$	−1567.51			−0.181462			−0.0907311	+	0.995875i	$0.528920\pi$
$422$		−	11532.6i		−	1.33033i
$423$		−	4055.09i		−	0.466111i
$424$	−2292.03			−0.262526
$425$	−6184.72	+	10688.0i	−0.705889	+	1.21987i
$426$	3348.60			0.380846
$427$			2854.01i			0.323455i
$428$		−	4805.58i		−	0.542725i
$429$	440.841			0.0496130
$430$	7751.39	+	2081.05i	0.869315	+	0.233389i
$431$	715.843			0.0800022			0.0400011	−	0.999200i	$-0.487264\pi$
$431$	715.843			0.0800022			0.0400011	+	0.999200i	$0.487264\pi$
$432$			432.000i			0.0481125i
$433$			3583.72i			0.397743i	0.980026	+	0.198871i	$0.0637276\pi$
$433$			3583.72i			0.397743i	−0.980026	+	0.198871i	$0.936272\pi$
$434$	2318.34			0.256415
$435$	1.75714	−	6.54489i	0.000193674	−	0.000721388i
$436$	−3670.87			−0.403218
$437$		−	743.718i		−	0.0814116i
$438$			172.971i			0.0188696i
$439$	10290.4			1.11875			0.559376	−	0.828914i	$-0.311041\pi$
$439$	10290.4			1.11875			0.559376	+	0.828914i	$0.311041\pi$
$440$	−315.314	+	1174.47i	−0.0341637	+	0.127251i
$441$	441.000			0.0476190
$442$		−	2135.43i		−	0.229801i
$443$			3716.40i			0.398581i	0.979940	+	0.199291i	$0.0638637\pi$
$443$			3716.40i			0.398581i	−0.979940	+	0.199291i	$0.936136\pi$
$444$	−131.633			−0.0140698
$445$	15019.6	+	4032.39i	1.59999	+	0.429558i
$446$	−2388.60			−0.253595
$447$			5420.97i			0.573609i
$448$			448.000i			0.0472456i
$449$	−10608.7			−1.11504			−0.557521	−	0.830163i	$-0.688247\pi$
$449$	−10608.7			−1.11504			−0.557521	+	0.830163i	$0.688247\pi$
$450$	−1126.91	+	1947.45i	−0.118051	+	0.204008i
$451$	−168.367			−0.0175790
$452$			3099.31i			0.322520i
$453$		−	2848.84i		−	0.295475i
$454$	6202.90			0.641226
$455$	816.943	+	219.329i	0.0841733	+	0.0225984i
$456$	−187.151			−0.0192196
$457$			8241.22i			0.843563i	0.906698	+	0.421781i	$0.138595\pi$
$457$			8241.22i			0.843563i	−0.906698	+	0.421781i	$0.861405\pi$
$458$			4322.00i			0.440948i
$459$	−2667.27			−0.271236
$460$	−1105.94	+	4119.36i	−0.112098	+	0.417535i
$461$	−15252.5			−1.54096			−0.770478	−	0.637467i	$-0.779982\pi$
$461$	−15252.5			−1.54096			−0.770478	+	0.637467i	$0.779982\pi$
$462$		−	571.029i		−	0.0575036i
$463$			3541.52i			0.355482i	0.984077	+	0.177741i	$0.0568790\pi$
$463$			3541.52i			0.355482i	−0.984077	+	0.177741i	$0.943121\pi$
$464$	−3.23266			−0.000323432
$465$	1440.18	−	5364.29i	0.143627	−	0.534975i
$466$	−6248.57			−0.621157
$467$		−	4220.46i		−	0.418200i	−0.977894	−	0.209100i	$-0.932947\pi$
$467$		−	4220.46i		−	0.418200i	0.977894	−	0.209100i	$-0.0670534\pi$
$468$		−	389.094i		−	0.0384314i
$469$	545.157			0.0536738
$470$	−9730.37	−	2612.36i	−0.954954	−	0.256381i
$471$	9055.57			0.885899
$472$		−	5912.55i		−	0.576583i
$473$			4879.96i			0.474378i
$474$	657.698			0.0637322
$475$	−843.675	−	488.200i	−0.0814958	−	0.0471582i
$476$	−2766.06			−0.266349
$477$		−	2578.54i		−	0.247512i
$478$			3265.78i			0.312497i
$479$	−6685.70			−0.637740			−0.318870	−	0.947798i	$-0.603303\pi$
$479$	−6685.70			−0.637740			−0.318870	+	0.947798i	$0.603303\pi$
$480$	1036.60	+	278.302i	0.0985714	+	0.0264639i
$481$	118.559			0.0112387
$482$			9895.62i			0.935131i
$483$		−	2002.84i		−	0.188680i
$484$	4584.60			0.430560
$485$	1212.01	−	4514.43i	0.113473	−	0.422659i
$486$	−486.000			−0.0453609
$487$		−	5921.10i		−	0.550946i	−0.961309	−	0.275473i	$-0.911166\pi$
$487$		−	5921.10i		−	0.550946i	0.961309	−	0.275473i	$-0.0888345\pi$
$488$		−	3261.73i		−	0.302565i
$489$	2223.69			0.205642
$490$	284.100	−	1058.20i	0.0261925	−	0.0975604i
$491$	−1625.67			−0.149420			−0.0747100	−	0.997205i	$-0.523803\pi$
$491$	−1625.67			−0.149420			−0.0747100	+	0.997205i	$0.523803\pi$
$492$			148.604i			0.0136170i
$493$		−	19.9592i		−	0.00182336i
$494$	168.563			0.0153523
$495$	−1321.27	−	354.729i	−0.119973	−	0.0322098i
$496$	−2649.53			−0.239854
$497$			3906.70i			0.352594i
$498$			7576.48i			0.681748i
$499$	20263.3			1.81786			0.908929	−	0.416952i	$-0.136902\pi$
$499$	20263.3			1.81786			0.908929	+	0.416952i	$0.136902\pi$
$500$	3947.03	+	3958.66i	0.353033	+	0.354073i
$501$	−156.777			−0.0139806
$502$		−	13954.1i		−	1.24064i
$503$		−	13300.9i		−	1.17904i	−0.807753	−	0.589521i	$-0.799316\pi$
$503$		−	13300.9i		−	1.17904i	0.807753	−	0.589521i	$-0.200684\pi$
$504$	−504.000			−0.0445435
$505$	17485.9	+	4694.52i	1.54082	+	0.413670i
$506$	−2593.38			−0.227845
$507$		−	6240.55i		−	0.546652i
$508$			32.6366i			0.00285043i
$509$	12280.6			1.06941			0.534704	−	0.845039i	$-0.320423\pi$
$509$	12280.6			1.06941			0.534704	+	0.845039i	$0.320423\pi$
$510$	−1718.30	+	6400.24i	−0.149192	+	0.555700i
$511$	−201.800			−0.0174699
$512$		−	512.000i		−	0.0441942i
$513$		−	210.545i		−	0.0181204i
$514$	6328.73			0.543090
$515$	−4262.14	+	15875.4i	−0.364684	+	1.35835i
$516$	4307.14			0.367464
$517$		−	6125.85i		−	0.521111i
$518$		−	153.571i		−	0.0130261i
$519$	−466.133			−0.0394238
$520$	−933.649	−	250.661i	−0.0787369	−	0.0211389i
$521$	18174.1			1.52826			0.764128	−	0.645064i	$-0.223169\pi$
$521$	18174.1			1.52826			0.764128	+	0.645064i	$0.223169\pi$
$522$		−	3.63674i		−	0.000304934i
$523$		−	8750.68i		−	0.731626i	−0.930688	−	0.365813i	$-0.880791\pi$
$523$		−	8750.68i		−	0.731626i	0.930688	−	0.365813i	$-0.119209\pi$
$524$	−3507.23			−0.292393
$525$	−2272.03	−	1314.73i	−0.188875	−	0.109294i
$526$	993.743			0.0823750
$527$		−	16358.8i		−	1.35219i
$528$			652.604i			0.0537897i
$529$	3070.90			0.252396
$530$	−6187.32	−	1661.14i	−0.507094	−	0.136142i
$531$	6651.62			0.543608
$532$		−	218.343i		−	0.0177939i
$533$		−	133.845i		−	0.0108770i
$534$	8345.80			0.676326
$535$	3482.82	−	12972.6i	0.281449	−	1.04833i
$536$	−623.037			−0.0502073
$537$		−	7326.22i		−	0.588733i
$538$			7794.38i			0.624609i
$539$	666.200			0.0532380
$540$	−313.090	+	1166.18i	−0.0249504	+	0.0929340i
$541$	−656.045			−0.0521360			−0.0260680	−	0.999660i	$-0.508299\pi$
$541$	−656.045			−0.0521360			−0.0260680	+	0.999660i	$0.508299\pi$
$542$			14619.3i			1.15858i
$543$			3460.48i			0.273487i
$544$	3161.21			0.249146
$545$	−9909.49	−	2660.45i	−0.778855	−	0.209103i
$546$	453.943			0.0355805
$547$			5798.36i			0.453236i	0.973984	+	0.226618i	$0.0727669\pi$
$547$			5798.36i			0.453236i	−0.973984	+	0.226618i	$0.927233\pi$
$548$		−	4310.13i		−	0.335985i
$549$	3669.45			0.285261
$550$	−1702.38	+	2941.93i	−0.131981	+	0.228081i
$551$	1.57551			0.000121813
$552$			2288.96i			0.176494i
$553$			767.314i			0.0590046i
$554$	−16702.5			−1.28090
$555$	−355.341	−	95.4001i	−0.0271773	−	0.00729641i
$556$	−6222.87			−0.474655
$557$		−	10841.0i		−	0.824680i	−0.911030	−	0.412340i	$-0.864712\pi$
$557$		−	10841.0i		−	0.824680i	0.911030	−	0.412340i	$-0.135288\pi$
$558$		−	2980.73i		−	0.226137i
$559$	−3879.36			−0.293523
$560$	−324.686	+	1209.37i	−0.0245008	+	0.0912594i
$561$	−4029.33			−0.303241
$562$		−	7633.81i		−	0.572977i
$563$		−	844.473i		−	0.0632155i	−0.999500	−	0.0316077i	$-0.989937\pi$
$563$		−	844.473i		−	0.0632155i	0.999500	−	0.0316077i	$-0.0100627\pi$
$564$	−5406.78			−0.403664
$565$	−2246.21	+	8366.54i	−0.167254	+	0.622979i
$566$	−7367.17			−0.547112
$567$		−	567.000i		−	0.0419961i
$568$		−	4464.80i		−	0.329822i
$569$	12991.7			0.957187			0.478593	−	0.878037i	$-0.341147\pi$
$569$	12991.7			0.957187			0.478593	+	0.878037i	$0.341147\pi$
$570$	−505.212	−	135.637i	−0.0371246	−	0.00996701i
$571$	5989.62			0.438980			0.219490	−	0.975615i	$-0.429561\pi$
$571$	5989.62			0.438980			0.219490	+	0.975615i	$0.429561\pi$
$572$		−	587.788i		−	0.0429661i
$573$		−	14486.5i		−	1.05617i
$574$	−173.371			−0.0126069
$575$	−5970.96	+	10318.6i	−0.433055	+	0.748377i
$576$	576.000			0.0416667
$577$			7876.11i			0.568261i	0.958786	+	0.284130i	$0.0917049\pi$
$577$			7876.11i			0.568261i	−0.958786	+	0.284130i	$0.908295\pi$
$578$			9692.04i			0.697467i
$579$	1582.31			0.113573
$580$	−8.72652	−	2.34285i	−0.000624740	−	0.000167727i
$581$	−8839.23			−0.631176
$582$		−	2508.49i		−	0.178660i
$583$		−	3895.29i		−	0.276717i
$584$	230.629			0.0163416
$585$	281.994	−	1050.36i	0.0199299	−	0.0742339i
$586$	−16901.6			−1.19146
$587$		−	18207.9i		−	1.28028i	−0.768260	−	0.640138i	$-0.778877\pi$
$587$		−	18207.9i		−	1.28028i	0.768260	−	0.640138i	$-0.221123\pi$
$588$		−	588.000i		−	0.0412393i
$589$	1291.31			0.0903353
$590$	4285.09	−	15960.9i	0.299008	−	1.11373i
$591$	7582.43			0.527748
$592$			175.510i			0.0121848i
$593$			11709.0i			0.810848i	0.914129	+	0.405424i	$0.132876\pi$
$593$			11709.0i			0.810848i	−0.914129	+	0.405424i	$0.867124\pi$
$594$	−734.180			−0.0507134
$595$	−7466.94	−	2004.69i	−0.514479	−	0.138125i
$596$	7227.96			0.496760
$597$			15411.9i			1.05656i
$598$		−	2061.62i		−	0.140980i
$599$	−20376.3			−1.38990			−0.694952	−	0.719056i	$-0.744574\pi$
$599$	−20376.3			−1.38990			−0.694952	+	0.719056i	$0.744574\pi$
$600$	2596.60	+	1502.55i	0.176677	+	0.102235i
$601$	−13509.9			−0.916937			−0.458469	−	0.888711i	$-0.651602\pi$
$601$	−13509.9			−0.916937			−0.458469	+	0.888711i	$0.651602\pi$
$602$			5025.00i			0.340205i
$603$		−	700.916i		−	0.0473359i
$604$	−3798.45			−0.255889
$605$	12376.1	+	3322.67i	0.831669	+	0.223282i
$606$	9716.23			0.651312
$607$		−	24253.6i		−	1.62179i	−0.585193	−	0.810894i	$-0.698981\pi$
$607$		−	24253.6i		−	1.62179i	0.585193	−	0.810894i	$-0.301019\pi$
$608$			249.535i			0.0166447i
$609$	4.24286			0.000282314
$610$	2363.92	−	8805.01i	0.156906	−	0.584433i
$611$	4869.78			0.322439
$612$			3556.36i			0.234898i
$613$			696.145i			0.0458679i	0.999737	+	0.0229340i	$0.00730074\pi$
$613$			696.145i			0.0458679i	−0.999737	+	0.0229340i	$0.992699\pi$
$614$	−6647.58			−0.436929
$615$	−107.700	+	401.155i	−0.00706160	+	0.0263027i
$616$	−761.371			−0.0497996
$617$		−	19894.8i		−	1.29811i	−0.760740	−	0.649056i	$-0.775164\pi$
$617$		−	19894.8i		−	1.29811i	0.760740	−	0.649056i	$-0.224836\pi$
$618$			8821.32i			0.574184i
$619$	−5616.19			−0.364675			−0.182337	−	0.983236i	$-0.558366\pi$
$619$	−5616.19			−0.364675			−0.182337	+	0.983236i	$0.558366\pi$
$620$	−7152.39	−	1920.24i	−0.463302	−	0.124385i
$621$	−2575.08			−0.166400
$622$		−	3521.22i		−	0.226990i
$623$			9736.77i			0.626157i
$624$	−518.792			−0.0332825
$625$	7785.95	+	13546.9i	0.498301	+	0.867004i
$626$	3435.82			0.219366
$627$		−	318.061i		−	0.0202586i
$628$		−	12074.1i		−	0.767211i
$629$	−1083.64			−0.0686925
$630$	−1360.54	−	365.271i	−0.0860402	−	0.0230996i
$631$	−27234.6			−1.71821			−0.859106	−	0.511798i	$-0.828980\pi$
$631$	−27234.6			−1.71821			−0.859106	+	0.511798i	$0.828980\pi$
$632$		−	876.931i		−	0.0551937i
$633$		−	17298.9i		−	1.08621i
$634$	−19078.1			−1.19509
$635$	−23.6532	+	88.1023i	−0.00147819	+	0.00550588i
$636$	−3438.05			−0.214351
$637$			529.600i			0.0329412i
$638$		−	5.49387i		−	0.000340916i
$639$	5022.90			0.310959
$640$	371.069	−	1382.14i	0.0229184	−	0.0853654i
$641$	−18064.7			−1.11313			−0.556563	−	0.830806i	$-0.687880\pi$
$641$	−18064.7			−1.11313			−0.556563	+	0.830806i	$0.687880\pi$
$642$		−	7208.36i		−	0.443133i
$643$		−	2169.88i		−	0.133082i	−0.997784	−	0.0665409i	$-0.978804\pi$
$643$		−	2169.88i		−	0.133082i	0.997784	−	0.0665409i	$-0.0211963\pi$
$644$	−2670.46			−0.163402
$645$	11627.1	+	3121.58i	0.709792	+	0.190561i
$646$	−1540.69			−0.0938351
$647$			10954.9i			0.665657i	0.942987	+	0.332829i	$0.108003\pi$
$647$			10954.9i			0.665657i	−0.942987	+	0.332829i	$0.891997\pi$
$648$			648.000i			0.0392837i
$649$	10048.3			0.607752
$650$	−2338.71	−	1353.31i	−0.141126	−	0.0816636i
$651$	3477.51			0.209362
$652$		−	2964.92i		−	0.178091i
$653$		−	23846.3i		−	1.42906i	−0.699603	−	0.714532i	$-0.746640\pi$
$653$		−	23846.3i		−	1.42906i	0.699603	−	0.714532i	$-0.253360\pi$
$654$	−5506.31			−0.329226
$655$	−9467.74	−	2541.85i	−0.564787	−	0.151631i
$656$	198.139			0.0117927
$657$			259.457i			0.0154070i
$658$		−	6307.91i		−	0.373721i
$659$	−29345.7			−1.73467			−0.867334	−	0.497726i	$-0.834168\pi$
$659$	−29345.7			−1.73467			−0.867334	+	0.497726i	$0.834168\pi$
$660$	−472.971	+	1761.70i	−0.0278945	+	0.103900i
$661$	19909.3			1.17153			0.585764	−	0.810482i	$-0.300794\pi$
$661$	19909.3			1.17153			0.585764	+	0.810482i	$0.300794\pi$
$662$			904.718i			0.0531161i
$663$		−	3203.14i		−	0.187632i
$664$	10102.0			0.590411
$665$	158.243	−	589.414i	0.00922766	−	0.0343707i
$666$	−197.449			−0.0114880
$667$		−	19.2694i		−	0.00111861i
$668$			209.037i			0.0121076i
$669$	−3582.89			−0.207059
$670$	−1681.88	−	451.543i	−0.0969802	−	0.0260367i
$671$	5543.28			0.318921
$672$			672.000i			0.0385758i
$673$		−	14940.2i		−	0.855722i	−0.903845	−	0.427861i	$-0.859267\pi$
$673$		−	14940.2i		−	0.855722i	0.903845	−	0.427861i	$-0.140733\pi$
$674$	11275.2			0.644370
$675$	−1690.37	+	2921.18i	−0.0963884	+	0.166572i
$676$	−8320.73			−0.473415
$677$		−	22193.1i		−	1.25989i	−0.776638	−	0.629947i	$-0.783076\pi$
$677$		−	22193.1i		−	1.25989i	0.776638	−	0.629947i	$-0.216924\pi$
$678$			4648.96i			0.263337i
$679$	2926.57			0.165407
$680$	8533.65	+	2291.07i	0.481251	+	0.129204i
$681$	9304.35			0.523559
$682$		−	4502.86i		−	0.252820i
$683$			31363.3i			1.75708i	0.477670	+	0.878539i	$0.341482\pi$
$683$			31363.3i			1.75708i	−0.477670	+	0.878539i	$0.658518\pi$
$684$	−280.727			−0.0156928
$685$	3123.74	−	11635.2i	0.174237	−	0.648987i
$686$	686.000			0.0381802
$687$			6483.01i			0.360032i
$688$		−	5742.86i		−	0.318233i
$689$	3096.58			0.171220
$690$	−1658.91	+	6179.03i	−0.0915272	+	0.340916i
$691$	3043.95			0.167579			0.0837897	−	0.996483i	$-0.473298\pi$
$691$	3043.95			0.167579			0.0837897	+	0.996483i	$0.473298\pi$
$692$			621.510i			0.0341420i
$693$		−	856.543i		−	0.0469515i
$694$	−24626.1			−1.34697
$695$	−16798.6	−	4509.99i	−0.916843	−	0.246149i
$696$	−4.84898			−0.000264081
$697$			1223.36i			0.0664819i
$698$			14407.1i			0.781256i
$699$	−9372.85			−0.507173
$700$	−1752.97	+	3029.37i	−0.0946516	+	0.163571i
$701$	24625.6			1.32681			0.663405	−	0.748260i	$-0.269110\pi$
$701$	24625.6			1.32681			0.663405	+	0.748260i	$0.269110\pi$
$702$		−	583.641i		−	0.0313791i
$703$		−	85.5388i		−	0.00458913i
$704$	870.139			0.0465832
$705$	−14595.6	−	3918.54i	−0.779717	−	0.209334i
$706$	14061.2			0.749573
$707$			11335.6i			0.602997i
$708$		−	8868.83i		−	0.470778i
$709$	29005.6			1.53643			0.768215	−	0.640192i	$-0.221145\pi$
$709$	29005.6			1.53643			0.768215	+	0.640192i	$0.221145\pi$
$710$	3235.84	−	12052.7i	0.171041	−	0.637083i
$711$	986.547			0.0520371
$712$		−	11127.7i		−	0.585716i
$713$		−	15793.5i		−	0.829551i
$714$	−4149.09			−0.217473
$715$	425.996	−	1586.73i	0.0222816	−	0.0829933i
$716$	−9768.29			−0.509858
$717$			4898.68i			0.255153i
$718$			11998.1i			0.623630i
$719$	−2287.47			−0.118648			−0.0593242	−	0.998239i	$-0.518895\pi$
$719$	−2287.47			−0.118648			−0.0593242	+	0.998239i	$0.518895\pi$
$720$	1554.91	+	417.453i	0.0804832	+	0.0216077i
$721$	−10291.5			−0.531591
$722$			13596.4i			0.700838i
$723$			14843.4i			0.763531i
$724$	4613.97			0.236846
$725$	−21.8592	−	12.6490i	−0.00111977	−	0.000647962i
$726$	6876.91			0.351551
$727$			36915.8i			1.88326i	0.336645	+	0.941632i	$0.390708\pi$
$727$			36915.8i			1.88326i	−0.336645	+	0.941632i	$0.609292\pi$
$728$		−	605.257i		−	0.0308136i
$729$	−729.000			−0.0370370
$730$	622.580	+	167.147i	0.0315653	+	0.00847450i
$731$	35457.7			1.79405
$732$		−	4892.60i		−	0.247043i
$733$		−	7943.12i		−	0.400254i	−0.979770	−	0.200127i	$-0.935865\pi$
$733$		−	7943.12i		−	0.400254i	0.979770	−	0.200127i	$-0.0641354\pi$
$734$	−18078.0			−0.909091
$735$	426.150	−	1587.30i	0.0213861	−	0.0796577i
$736$	3051.95			0.152848
$737$		−	1058.84i		−	0.0529214i
$738$			222.906i			0.0111183i
$739$	3388.38			0.168665			0.0843327	−	0.996438i	$-0.473124\pi$
$739$	3388.38			0.168665			0.0843327	+	0.996438i	$0.473124\pi$
$740$	−127.200	+	473.788i	−0.00631888	+	0.0235362i
$741$	252.845			0.0125351
$742$		−	4011.06i		−	0.198451i
$743$			26530.0i			1.30995i	0.755652	+	0.654973i	$0.227320\pi$
$743$			26530.0i			1.30995i	−0.755652	+	0.654973i	$0.772680\pi$
$744$	−3974.30			−0.195840
$745$	19511.8	+	5238.43i	0.959540	+	0.257612i
$746$	24830.9			1.21866
$747$			11364.7i			0.556645i
$748$			5372.44i			0.262615i
$749$	8409.76			0.410261
$750$	5920.54	+	5937.99i	0.288250	+	0.289099i
$751$	11544.9			0.560956			0.280478	−	0.959860i	$-0.409507\pi$
$751$	11544.9			0.560956			0.280478	+	0.959860i	$0.409507\pi$
$752$			7209.04i			0.349584i
$753$		−	20931.1i		−	1.01298i
$754$	4.36739			0.000210943
$755$	−10253.9	−	2752.91i	−0.494274	−	0.132700i
$756$	−756.000			−0.0363696
$757$			38521.4i			1.84952i	0.380555	+	0.924758i	$0.375733\pi$
$757$			38521.4i			1.84952i	−0.380555	+	0.924758i	$0.624267\pi$
$758$			14678.8i			0.703374i
$759$	−3890.07			−0.186035
$760$	−180.849	+	673.616i	−0.00863169	+	0.0321508i
$761$	23725.7			1.13017			0.565083	−	0.825034i	$-0.308844\pi$
$761$	23725.7			1.13017			0.565083	+	0.825034i	$0.308844\pi$
$762$			48.9550i			0.00232736i
$763$		−	6424.03i		−	0.304804i
$764$	−19315.4			−0.914668
$765$	−2577.45	+	9600.36i	−0.121814	+	0.453728i
$766$	16108.5			0.759824
$767$			7987.98i			0.376049i
$768$		−	768.000i		−	0.0360844i
$769$	39110.5			1.83402			0.917009	−	0.398866i	$-0.130596\pi$
$769$	39110.5			1.83402			0.917009	+	0.398866i	$0.130596\pi$
$770$	−2055.31	−	551.800i	−0.0961927	−	0.0258253i
$771$	9493.09			0.443431
$772$		−	2109.75i		−	0.0983568i
$773$			35966.5i			1.67351i	0.547577	+	0.836755i	$0.315550\pi$
$773$			35966.5i			1.67351i	−0.547577	+	0.836755i	$0.684450\pi$
$774$	6460.71			0.300033
$775$	−17916.1	−	10367.3i	−0.830408	−	0.480523i
$776$	−3344.65			−0.154724
$777$		−	230.357i		−	0.0106358i
$778$			8810.97i			0.406026i
$779$	−96.5674			−0.00444144
$780$	−1400.47	−	375.992i	−0.0642884	−	0.0172598i
$781$	7587.88			0.347651
$782$			18843.5i			0.861689i
$783$		−	5.45511i		−	0.000248978i
$784$	−784.000			−0.0357143
$785$	8750.63	−	32593.9i	0.397864	−	1.48194i
$786$	−5260.85			−0.238738
$787$		−	13194.2i		−	0.597614i	−0.954313	−	0.298807i	$-0.903411\pi$
$787$		−	13194.2i		−	0.597614i	0.954313	−	0.298807i	$-0.0965888\pi$
$788$		−	10109.9i		−	0.457044i
$789$	1490.61			0.0672589
$790$	635.551	−	2367.27i	0.0286226	−	0.106612i
$791$	−5423.79			−0.243802
$792$			978.906i			0.0439191i
$793$			4406.66i			0.197333i
$794$	21901.2			0.978896
$795$	−9280.98	−	2491.71i	−0.414041	−	0.111159i
$796$	20549.2			0.915010
$797$		−	10384.7i		−	0.461537i	−0.973009	−	0.230769i	$-0.925876\pi$
$797$		−	10384.7i		−	0.461537i	0.973009	−	0.230769i	$-0.0741240\pi$
$798$		−	327.514i		−	0.0145287i
$799$	−44510.3			−1.97079
$800$	2003.40	−	3462.14i	0.0885384	−	0.153006i
$801$	12518.7			0.552218
$802$			15885.2i			0.699408i
$803$			391.951i			0.0172250i
$804$	−934.555			−0.0409941
$805$	−7208.87	−	1935.40i	−0.315627	−	0.0847378i
$806$	3579.58			0.156433
$807$			11691.6i			0.509991i
$808$		−	12955.0i		−	0.564052i
$809$	−1318.94			−0.0573196			−0.0286598	−	0.999589i	$-0.509124\pi$
$809$	−1318.94			−0.0573196			−0.0286598	+	0.999589i	$0.509124\pi$
$810$	−469.635	+	1749.27i	−0.0203720	+	0.0758803i
$811$	−23639.6			−1.02355			−0.511774	−	0.859120i	$-0.671012\pi$
$811$	−23639.6			−1.02355			−0.511774	+	0.859120i	$0.671012\pi$
$812$		−	5.65715i		−	0.000244491i
$813$			21928.9i			0.945977i
$814$	−298.278			−0.0128435
$815$	2148.81	−	8003.78i	0.0923554	−	0.344000i
$816$	4741.81			0.203427
$817$			2798.91i			0.119855i
$818$		−	14188.0i		−	0.606446i
$819$	680.914			0.0290514
$820$	534.874	+	143.600i	0.0227788	+	0.00611553i
$821$	−23351.9			−0.992677			−0.496338	−	0.868129i	$-0.665322\pi$
$821$	−23351.9			−0.992677			−0.496338	+	0.868129i	$0.665322\pi$
$822$		−	6465.20i		−	0.274330i
$823$			5675.84i			0.240398i	0.992750	+	0.120199i	$0.0383533\pi$
$823$			5675.84i			0.240398i	−0.992750	+	0.120199i	$0.961647\pi$
$824$	11761.8			0.497258
$825$	−2553.56	+	4412.90i	−0.107762	+	0.186227i
$826$	10347.0			0.435856
$827$			8698.65i			0.365758i	0.983135	+	0.182879i	$0.0585416\pi$
$827$			8698.65i			0.365758i	−0.983135	+	0.182879i	$0.941458\pi$
$828$			3433.44i			0.144107i
$829$	−19561.7			−0.819551			−0.409775	−	0.912186i	$-0.634393\pi$
$829$	−19561.7			−0.819551			−0.409775	+	0.912186i	$0.634393\pi$
$830$	27270.2	+	7321.35i	1.14044	+	0.306178i
$831$	−25053.7			−1.04585
$832$			691.723i			0.0288235i
$833$		−	4840.60i		−	0.201341i
$834$	−9334.30			−0.387554
$835$	−151.498	+	564.292i	−0.00627882	+	0.0233870i
$836$	−424.082			−0.0175445
$837$		−	4471.09i		−	0.184640i
$838$		−	4982.00i		−	0.205370i
$839$	32967.7			1.35658			0.678290	−	0.734794i	$-0.262721\pi$
$839$	32967.7			1.35658			0.678290	+	0.734794i	$0.262721\pi$
$840$	−487.029	+	1814.06i	−0.0200049	+	0.0745130i
$841$	−24389.0			−0.999998
$842$			3135.01i			0.128313i
$843$		−	11450.7i		−	0.467834i
$844$	−23065.2			−0.940683
$845$	−22461.7	−	6030.41i	−0.914446	−	0.245506i
$846$	−8110.18			−0.329591
$847$			8023.06i			0.325473i
$848$			4584.07i			0.185634i
$849$	−11050.8			−0.446715
$850$	21376.1	+	12369.4i	0.862580	+	0.499139i
$851$	−1046.19			−0.0421420
$852$		−	6697.20i		−	0.269298i
$853$			22005.6i			0.883302i	0.897187	+	0.441651i	$0.145607\pi$
$853$			22005.6i			0.883302i	−0.897187	+	0.441651i	$0.854393\pi$
$854$	5708.03			0.228717
$855$	−757.818	−	203.455i	−0.0303121	−	0.00813803i
$856$	−9611.15			−0.383764
$857$			8008.58i			0.319216i	0.987181	+	0.159608i	$0.0510229\pi$
$857$			8008.58i			0.319216i	−0.987181	+	0.159608i	$0.948977\pi$
$858$		−	881.681i		−	0.0350817i
$859$	21100.9			0.838130			0.419065	−	0.907956i	$-0.362358\pi$
$859$	21100.9			0.838130			0.419065	+	0.907956i	$0.362358\pi$
$860$	4162.11	−	15502.8i	0.165031	−	0.614698i
$861$	−260.057			−0.0102935
$862$		−	1431.69i		−	0.0565701i
$863$		−	30473.1i		−	1.20199i	−0.799253	−	0.600994i	$-0.794771\pi$
$863$		−	30473.1i		−	1.20199i	0.799253	−	0.600994i	$-0.205229\pi$
$864$	864.000			0.0340207
$865$	−450.436	+	1677.76i	−0.0177055	+	0.0659486i
$866$	7167.44			0.281246
$867$			14538.1i			0.569479i
$868$		−	4636.69i		−	0.181313i
$869$	1490.33			0.0581774
$870$	−13.0898	−	3.51428i	−0.000510098	−	0.000136948i
$871$	841.735			0.0327453
$872$			7341.75i			0.285118i
$873$		−	3762.73i		−	0.145875i
$874$	−1487.44			−0.0575667
$875$	−6927.65	+	6907.30i	−0.267654	+	0.266868i
$876$	345.943			0.0133428
$877$			19268.9i			0.741921i	0.928649	+	0.370961i	$0.120972\pi$
$877$			19268.9i			0.741921i	−0.928649	+	0.370961i	$0.879028\pi$
$878$		−	20580.7i		−	0.791077i
$879$	−25352.4			−0.972826
$880$	2348.93	+	630.629i	0.0899800	+	0.0241574i
$881$	−25810.9			−0.987049			−0.493525	−	0.869732i	$-0.664292\pi$
$881$	−25810.9			−0.987049			−0.493525	+	0.869732i	$0.664292\pi$
$882$		−	882.000i		−	0.0336718i
$883$		−	2908.02i		−	0.110830i	−0.998463	−	0.0554149i	$-0.982352\pi$
$883$		−	2908.02i		−	0.110830i	0.998463	−	0.0554149i	$-0.0176482\pi$
$884$	−4270.86			−0.162494
$885$	6427.64	−	23941.3i	0.244139	−	0.909355i
$886$	7432.80			0.281839
$887$			50742.2i			1.92081i	0.278615	+	0.960403i	$0.410125\pi$
$887$			50742.2i			1.92081i	−0.278615	+	0.960403i	$0.589875\pi$
$888$			263.265i			0.00994888i
$889$	−57.1141			−0.00215472
$890$	8064.77	−	30039.2i	0.303744	−	1.13137i
$891$	−1101.27			−0.0414073
$892$			4777.19i			0.179319i
$893$		−	3513.49i		−	0.131662i
$894$	10841.9			0.405603
$895$	−26369.4	−	7079.52i	−0.984840	−	0.264405i
$896$	896.000			0.0334077
$897$		−	3092.44i		−	0.115110i
$898$			21217.3i			0.788453i
$899$	33.4572			0.00124122
$900$	3894.91	+	2253.82i	0.144256	+	0.0834748i
$901$	−28303.1			−1.04652
$902$			336.735i			0.0124302i
$903$			7537.50i			0.277777i
$904$	6198.61			0.228056
$905$	12455.4	+	3343.95i	0.457492	+	0.122825i
$906$	−5697.67			−0.208932
$907$		−	14210.5i		−	0.520235i	−0.965577	−	0.260117i	$-0.916239\pi$
$907$		−	14210.5i		−	0.520235i	0.965577	−	0.260117i	$-0.0837612\pi$
$908$		−	12405.8i		−	0.453415i
$909$	14574.3			0.531794
$910$	438.657	−	1633.89i	0.0159795	−	0.0595195i
$911$	14523.3			0.528188			0.264094	−	0.964497i	$-0.414927\pi$
$911$	14523.3			0.528188			0.264094	+	0.964497i	$0.414927\pi$
$912$			374.302i			0.0135903i
$913$			17168.2i			0.622327i
$914$	16482.4			0.596489
$915$	3545.88	−	13207.5i	0.128113	−	0.477188i
$916$	8644.01			0.311797
$917$		−	6137.66i		−	0.221029i
$918$			5334.54i			0.191793i
$919$	−24513.7			−0.879905			−0.439953	−	0.898021i	$-0.645005\pi$
$919$	−24513.7			−0.879905			−0.439953	+	0.898021i	$0.645005\pi$
$920$	8238.71	+	2211.89i	0.295242	+	0.0792649i
$921$	−9971.38			−0.356751
$922$			30505.0i			1.08962i
$923$			6032.04i			0.215110i
$924$	−1142.06			−0.0406612
$925$	−686.751	+	1186.80i	−0.0244111	+	0.0421856i
$926$	7083.04			0.251364
$927$			13232.0i			0.468819i
$928$			6.46531i			0.000228701i
$929$	27502.6			0.971291			0.485646	−	0.874156i	$-0.338585\pi$
$929$	27502.6			0.971291			0.485646	+	0.874156i	$0.338585\pi$
$930$	−10728.6	−	2880.36i	−0.378284	−	0.101560i
$931$	382.100			0.0134509
$932$			12497.1i			0.439225i
$933$		−	5281.82i		−	0.185337i
$934$	−8440.91			−0.295712
$935$	−3893.65	+	14502.8i	−0.136188	+	0.507266i
$936$	−778.188			−0.0271751
$937$			52359.0i			1.82550i	0.408520	+	0.912749i	$0.366045\pi$
$937$			52359.0i			1.82550i	−0.408520	+	0.912749i	$0.633955\pi$
$938$		−	1090.31i		−	0.0379531i
$939$	5153.73			0.179111
$940$	−5224.72	+	19460.7i	−0.181289	+	0.675255i
$941$	−873.156			−0.0302487			−0.0151244	−	0.999886i	$-0.504814\pi$
$941$	−873.156			−0.0302487			−0.0151244	+	0.999886i	$0.504814\pi$
$942$		−	18111.1i		−	0.626425i
$943$			1181.07i			0.0407858i
$944$	−11825.1			−0.407706
$945$	−2040.81	−	547.907i	−0.0702515	−	0.0188608i
$946$	9759.93			0.335436
$947$		−	25333.0i		−	0.869283i	−0.900604	−	0.434641i	$-0.856875\pi$
$947$		−	25333.0i		−	0.869283i	0.900604	−	0.434641i	$-0.143125\pi$
$948$		−	1315.40i		−	0.0450655i
$949$	−311.584			−0.0106580
$950$	−976.400	+	1687.35i	−0.0333459	+	0.0576262i
$951$	−28617.2			−0.975790
$952$			5532.11i			0.188337i
$953$		−	28335.5i		−	0.963145i	−0.876406	−	0.481573i	$-0.840066\pi$
$953$		−	28335.5i		−	0.963145i	0.876406	−	0.481573i	$-0.159934\pi$
$954$	−5157.07			−0.175017
$955$	−52141.7	−	13998.7i	−1.76677	−	0.474333i
$956$	6531.57			0.220969
$957$		−	8.24080i		−	0.000278357i
$958$			13371.4i			0.450950i
$959$	7542.73			0.253981
$960$	556.604	−	2073.21i	0.0187128	−	0.0697005i
$961$	−2368.99			−0.0795204
$962$		−	237.118i		−	0.00794697i
$963$		−	10812.5i		−	0.361817i
$964$	19791.2			0.661237
$965$	1529.03	−	5695.24i	0.0510064	−	0.189986i
$966$	−4005.69			−0.133417
$967$			12644.3i			0.420490i	0.977649	+	0.210245i	$0.0674262\pi$
$967$			12644.3i			0.420490i	−0.977649	+	0.210245i	$0.932574\pi$
$968$		−	9169.21i		−	0.304452i
$969$	−2311.03			−0.0766160
$970$	−9028.86	−	2424.02i	−0.298865	−	0.0802377i
$971$	41862.8			1.38357			0.691783	−	0.722106i	$-0.256826\pi$
$971$	41862.8			1.38357			0.691783	+	0.722106i	$0.256826\pi$
$972$			972.000i			0.0320750i
$973$		−	10890.0i		−	0.358806i
$974$	−11842.2			−0.389578
$975$	−3508.07	−	2029.97i	−0.115229	−	0.0666781i
$976$	−6523.46			−0.213946
$977$		−	12362.4i		−	0.404818i	−0.979301	−	0.202409i	$-0.935123\pi$
$977$		−	12362.4i		−	0.404818i	0.979301	−	0.202409i	$-0.0648770\pi$
$978$		−	4447.38i		−	0.145411i
$979$	18911.5			0.617378
$980$	−2116.40	−	568.200i	−0.0689856	−	0.0185209i
$981$	−8259.47			−0.268812
$982$			3251.33i			0.105656i
$983$		−	25887.9i		−	0.839976i	−0.907530	−	0.419988i	$-0.862034\pi$
$983$		−	25887.9i		−	0.839976i	0.907530	−	0.419988i	$-0.137966\pi$
$984$	297.208			0.00962871
$985$	7327.10	−	27291.6i	0.237016	−	0.882824i
$986$	−39.9184			−0.00128931
$987$		−	9461.87i		−	0.305142i
$988$		−	337.126i		−	0.0108557i
$989$	34232.3			1.10063
$990$	−709.457	+	2642.55i	−0.0227758	+	0.0848340i
$991$	9414.31			0.301771			0.150886	−	0.988551i	$-0.451787\pi$
$991$	9414.31			0.301771			0.150886	+	0.988551i	$0.451787\pi$
$992$			5299.07i			0.169602i
$993$			1357.08i			0.0433691i
$994$	7813.40			0.249322
$995$	55472.4	+	14892.9i	1.76743	+	0.474511i
$996$	15153.0			0.482068
$997$		−	12125.8i		−	0.385183i	−0.981279	−	0.192592i	$-0.938311\pi$
$997$		−	12125.8i		−	0.385183i	0.981279	−	0.192592i	$-0.0616892\pi$
$998$		−	40526.6i		−	1.28542i
$999$	−296.173			−0.00937989

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	210.4.g.a.169.1	✓	4
3.2	odd	2		630.4.g.e.379.4		4
5.2	odd	4		1050.4.a.bg.1.1		2
5.3	odd	4		1050.4.a.bc.1.1		2
5.4	even	2	inner	210.4.g.a.169.3	yes	4
15.14	odd	2		630.4.g.e.379.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.4.g.a.169.1	✓	4	1.1	even	1	trivial
210.4.g.a.169.3	yes	4	5.4	even	2	inner
630.4.g.e.379.2		4	15.14	odd	2
630.4.g.e.379.4		4	3.2	odd	2
1050.4.a.bc.1.1		2	5.3	odd	4
1050.4.a.bg.1.1		2	5.2	odd	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:	\( N \)	\(=\)	\( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	210.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.00000i q^{2} -3.00000i q^{3} -4.00000 q^{4} +(-10.7980 - 2.89898i) q^{5} -6.00000 q^{6} -7.00000i q^{7} +8.00000i q^{8} -9.00000 q^{9} +O(q^{10})\)	\(q-2.00000i q^{2} -3.00000i q^{3} -4.00000 q^{4} +(-10.7980 - 2.89898i) q^{5} -6.00000 q^{6} -7.00000i q^{7} +8.00000i q^{8} -9.00000 q^{9} +(-5.79796 + 21.5959i) q^{10} -13.5959 q^{11} +12.0000i q^{12} -10.8082i q^{13} -14.0000 q^{14} +(-8.69694 + 32.3939i) q^{15} +16.0000 q^{16} +98.7878i q^{17} +18.0000i q^{18} -7.79796 q^{19} +(43.1918 + 11.5959i) q^{20} -21.0000 q^{21} +27.1918i q^{22} +95.3735i q^{23} +24.0000 q^{24} +(108.192 + 62.6061i) q^{25} -21.6163 q^{26} +27.0000i q^{27} +28.0000i q^{28} -0.202041 q^{29} +(64.7878 + 17.3939i) q^{30} -165.596 q^{31} -32.0000i q^{32} +40.7878i q^{33} +197.576 q^{34} +(-20.2929 + 75.5857i) q^{35} +36.0000 q^{36} +10.9694i q^{37} +15.5959i q^{38} -32.4245 q^{39} +(23.1918 - 86.3837i) q^{40} +12.3837 q^{41} +42.0000i q^{42} -358.929i q^{43} +54.3837 q^{44} +(97.1816 + 26.0908i) q^{45} +190.747 q^{46} +450.565i q^{47} -48.0000i q^{48} -49.0000 q^{49} +(125.212 - 216.384i) q^{50} +296.363 q^{51} +43.2327i q^{52} +286.504i q^{53} +54.0000 q^{54} +(146.808 + 39.4143i) q^{55} +56.0000 q^{56} +23.3939i q^{57} +0.404082i q^{58} -739.069 q^{59} +(34.7878 - 129.576i) q^{60} -407.716 q^{61} +331.192i q^{62} +63.0000i q^{63} -64.0000 q^{64} +(-31.3326 + 116.706i) q^{65} +81.5755 q^{66} +77.8796i q^{67} -395.151i q^{68} +286.120 q^{69} +(151.171 + 40.5857i) q^{70} -558.100 q^{71} -72.0000i q^{72} -28.8286i q^{73} +21.9388 q^{74} +(187.818 - 324.576i) q^{75} +31.1918 q^{76} +95.1714i q^{77} +64.8490i q^{78} -109.616 q^{79} +(-172.767 - 46.3837i) q^{80} +81.0000 q^{81} -24.7673i q^{82} -1262.75i q^{83} +84.0000 q^{84} +(286.384 - 1066.71i) q^{85} -717.857 q^{86} +0.606123i q^{87} -108.767i q^{88} -1390.97 q^{89} +(52.1816 - 194.363i) q^{90} -75.6571 q^{91} -381.494i q^{92} +496.788i q^{93} +901.131 q^{94} +(84.2020 + 22.6061i) q^{95} -96.0000 q^{96} +418.082i q^{97} +98.0000i q^{98} +122.363 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 16 q^{4} - 4 q^{5} - 24 q^{6} - 36 q^{9}+O(q^{10}) \) 4 * q - 16 * q^4 - 4 * q^5 - 24 * q^6 - 36 * q^9	\( 4 q - 16 q^{4} - 4 q^{5} - 24 q^{6} - 36 q^{9} + 16 q^{10} + 24 q^{11} - 56 q^{14} + 24 q^{15} + 64 q^{16} + 8 q^{19} + 16 q^{20} - 84 q^{21} + 96 q^{24} + 276 q^{25} - 400 q^{26} - 40 q^{29} + 24 q^{30} - 584 q^{31} + 320 q^{34} + 56 q^{35} + 144 q^{36} - 600 q^{39} - 64 q^{40} - 264 q^{41} - 96 q^{44} + 36 q^{45} - 256 q^{46} - 196 q^{49} + 736 q^{50} + 480 q^{51} + 216 q^{54} + 744 q^{55} + 224 q^{56} - 448 q^{59} - 96 q^{60} - 24 q^{61} - 256 q^{64} + 1168 q^{65} - 144 q^{66} - 384 q^{69} + 56 q^{70} - 312 q^{71} - 1088 q^{74} + 1104 q^{75} - 32 q^{76} - 752 q^{79} - 64 q^{80} + 324 q^{81} + 336 q^{84} + 832 q^{85} - 128 q^{86} - 1096 q^{89} - 144 q^{90} - 1400 q^{91} + 2272 q^{94} + 376 q^{95} - 384 q^{96} - 216 q^{99}+O(q^{100}) \) 4 * q - 16 * q^4 - 4 * q^5 - 24 * q^6 - 36 * q^9 + 16 * q^10 + 24 * q^11 - 56 * q^14 + 24 * q^15 + 64 * q^16 + 8 * q^19 + 16 * q^20 - 84 * q^21 + 96 * q^24 + 276 * q^25 - 400 * q^26 - 40 * q^29 + 24 * q^30 - 584 * q^31 + 320 * q^34 + 56 * q^35 + 144 * q^36 - 600 * q^39 - 64 * q^40 - 264 * q^41 - 96 * q^44 + 36 * q^45 - 256 * q^46 - 196 * q^49 + 736 * q^50 + 480 * q^51 + 216 * q^54 + 744 * q^55 + 224 * q^56 - 448 * q^59 - 96 * q^60 - 24 * q^61 - 256 * q^64 + 1168 * q^65 - 144 * q^66 - 384 * q^69 + 56 * q^70 - 312 * q^71 - 1088 * q^74 + 1104 * q^75 - 32 * q^76 - 752 * q^79 - 64 * q^80 + 324 * q^81 + 336 * q^84 + 832 * q^85 - 128 * q^86 - 1096 * q^89 - 144 * q^90 - 1400 * q^91 + 2272 * q^94 + 376 * q^95 - 384 * q^96 - 216 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more