LMFDB - Embedded newform 230.4.b.a.139.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [230,4,Mod(139,230)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(230, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("230.139");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	230.b (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:	$13.5704393013$
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} + 212 x^{12} + 17560 x^{10} + 728073 x^{8} + 16036416 x^{6} + 183184060 x^{4} + 961600400 x^{2} + 1560250000 $ x^14 + 212x^12 + 17560x^10 + 728073x^8 + 16036416x^6 + 183184060x^4 + 961600400x^2 + 1560250000
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			139.9
Root			$-4.96965i$ of defining polynomial
Character	$\chi$	$=$	230.139
Dual form			230.4.b.a.139.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.00000i q^{2} -3.96965i q^{3} -4.00000 q^{4} +(10.8788 + 2.57927i) q^{5} +7.93930 q^{6} -5.88989i q^{7} -8.00000i q^{8} +11.2419 q^{9} +O(q^{10})$	\(q+2.00000i q^{2} -3.96965i q^{3} -4.00000 q^{4} +(10.8788 + 2.57927i) q^{5} +7.93930 q^{6} -5.88989i q^{7} -8.00000i q^{8} +11.2419 q^{9} +(-5.15854 + 21.7575i) q^{10} -10.3431 q^{11} +15.8786i q^{12} +1.80406i q^{13} +11.7798 q^{14} +(10.2388 - 43.1848i) q^{15} +16.0000 q^{16} -74.8568i q^{17} +22.4838i q^{18} +19.0864 q^{19} +(-43.5150 - 10.3171i) q^{20} -23.3808 q^{21} -20.6862i q^{22} -23.0000i q^{23} -31.7572 q^{24} +(111.695 + 56.1185i) q^{25} -3.60811 q^{26} -151.807i q^{27} +23.5596i q^{28} +253.550 q^{29} +(86.3697 + 20.4776i) q^{30} +148.076 q^{31} +32.0000i q^{32} +41.0585i q^{33} +149.714 q^{34} +(15.1916 - 64.0747i) q^{35} -44.9676 q^{36} -199.885i q^{37} +38.1728i q^{38} +7.16147 q^{39} +(20.6342 - 87.0301i) q^{40} -26.2024 q^{41} -46.7616i q^{42} -207.766i q^{43} +41.3724 q^{44} +(122.298 + 28.9959i) q^{45} +46.0000 q^{46} -28.7333i q^{47} -63.5144i q^{48} +308.309 q^{49} +(-112.237 + 223.389i) q^{50} -297.155 q^{51} -7.21622i q^{52} +528.893i q^{53} +303.614 q^{54} +(-112.520 - 26.6776i) q^{55} -47.1191 q^{56} -75.7662i q^{57} +507.100i q^{58} -114.842 q^{59} +(-40.9552 + 172.739i) q^{60} +207.365 q^{61} +296.152i q^{62} -66.2135i q^{63} -64.0000 q^{64} +(-4.65315 + 19.6259i) q^{65} -82.1169 q^{66} +53.4749i q^{67} +299.427i q^{68} -91.3019 q^{69} +(128.149 + 30.3832i) q^{70} -848.654 q^{71} -89.9352i q^{72} +442.031i q^{73} +399.769 q^{74} +(222.771 - 443.389i) q^{75} -76.3455 q^{76} +60.9197i q^{77} +14.3229i q^{78} -703.848 q^{79} +(174.060 + 41.2683i) q^{80} -299.089 q^{81} -52.4048i q^{82} +343.440i q^{83} +93.5231 q^{84} +(193.076 - 814.349i) q^{85} +415.533 q^{86} -1006.50i q^{87} +82.7448i q^{88} -642.348 q^{89} +(-57.9918 + 244.596i) q^{90} +10.6257 q^{91} +92.0000i q^{92} -587.810i q^{93} +57.4667 q^{94} +(207.636 + 49.2290i) q^{95} +127.029 q^{96} -665.706i q^{97} +616.618i q^{98} -116.276 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 56 q^{4} - 6 q^{5} - 36 q^{6} - 68 q^{9}+O(q^{10}) $ 14 * q - 56 * q^4 - 6 * q^5 - 36 * q^6 - 68 * q^9	$ 14 q - 56 q^{4} - 6 q^{5} - 36 q^{6} - 68 q^{9} - 40 q^{10} - 146 q^{11} + 176 q^{14} - 206 q^{15} + 224 q^{16} + 154 q^{19} + 24 q^{20} - 220 q^{21} + 144 q^{24} - 286 q^{25} - 180 q^{26} + 790 q^{29} - 232 q^{30} - 320 q^{31} - 200 q^{34} - 426 q^{35} + 272 q^{36} + 1616 q^{39} + 160 q^{40} - 1904 q^{41} + 584 q^{44} + 622 q^{45} + 644 q^{46} + 610 q^{49} + 200 q^{50} - 1834 q^{51} + 192 q^{54} + 854 q^{55} - 704 q^{56} + 2814 q^{59} + 824 q^{60} - 3742 q^{61} - 896 q^{64} + 1730 q^{65} - 612 q^{66} + 414 q^{69} + 348 q^{70} - 3808 q^{71} + 268 q^{74} + 2904 q^{75} - 616 q^{76} - 1528 q^{79} - 96 q^{80} - 4618 q^{81} + 880 q^{84} + 2574 q^{85} - 2024 q^{86} + 2336 q^{89} + 2092 q^{90} - 3866 q^{91} + 456 q^{94} + 838 q^{95} - 576 q^{96} + 3342 q^{99}+O(q^{100}) $ 14 * q - 56 * q^4 - 6 * q^5 - 36 * q^6 - 68 * q^9 - 40 * q^10 - 146 * q^11 + 176 * q^14 - 206 * q^15 + 224 * q^16 + 154 * q^19 + 24 * q^20 - 220 * q^21 + 144 * q^24 - 286 * q^25 - 180 * q^26 + 790 * q^29 - 232 * q^30 - 320 * q^31 - 200 * q^34 - 426 * q^35 + 272 * q^36 + 1616 * q^39 + 160 * q^40 - 1904 * q^41 + 584 * q^44 + 622 * q^45 + 644 * q^46 + 610 * q^49 + 200 * q^50 - 1834 * q^51 + 192 * q^54 + 854 * q^55 - 704 * q^56 + 2814 * q^59 + 824 * q^60 - 3742 * q^61 - 896 * q^64 + 1730 * q^65 - 612 * q^66 + 414 * q^69 + 348 * q^70 - 3808 * q^71 + 268 * q^74 + 2904 * q^75 - 616 * q^76 - 1528 * q^79 - 96 * q^80 - 4618 * q^81 + 880 * q^84 + 2574 * q^85 - 2024 * q^86 + 2336 * q^89 + 2092 * q^90 - 3866 * q^91 + 456 * q^94 + 838 * q^95 - 576 * q^96 + 3342 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$-1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$			2.00000i			0.707107i
$2$			2.00000i			0.707107i
$3$		−	3.96965i		−	0.763959i	−0.924171	−	0.381980i	$-0.875242\pi$
$3$		−	3.96965i		−	0.763959i	0.924171	−	0.381980i	$-0.124758\pi$
$4$	−4.00000			−0.500000
$5$	10.8788	+	2.57927i	0.973026	+	0.230697i
$5$	10.8788	+	2.57927i	0.973026	+	0.230697i
$6$	7.93930			0.540201
$7$		−	5.88989i		−	0.318024i	−0.987277	−	0.159012i	$-0.949169\pi$
$7$		−	5.88989i		−	0.318024i	0.987277	−	0.159012i	$-0.0508309\pi$
$8$		−	8.00000i		−	0.353553i
$9$	11.2419			0.416367
$10$	−5.15854	+	21.7575i	−0.163127	+	0.688033i
$11$	−10.3431			−0.283506			−0.141753	−	0.989902i	$-0.545274\pi$
$11$	−10.3431			−0.283506			−0.141753	+	0.989902i	$0.545274\pi$
$12$			15.8786i			0.381980i
$13$			1.80406i			0.0384889i	0.999815	+	0.0192444i	$0.00612607\pi$
$13$			1.80406i			0.0384889i	−0.999815	+	0.0192444i	$0.993874\pi$
$14$	11.7798			0.224877
$15$	10.2388	−	43.1848i	0.176243	−	0.743352i
$16$	16.0000			0.250000
$17$		−	74.8568i		−	1.06797i	−0.845495	−	0.533983i	$-0.820695\pi$
$17$		−	74.8568i		−	1.06797i	0.845495	−	0.533983i	$-0.179305\pi$
$18$			22.4838i			0.294416i
$19$	19.0864			0.230459			0.115229	−	0.993339i	$-0.463240\pi$
$19$	19.0864			0.230459			0.115229	+	0.993339i	$0.463240\pi$
$20$	−43.5150	−	10.3171i	−0.486513	−	0.115348i
$21$	−23.3808			−0.242957
$22$		−	20.6862i		−	0.200469i
$23$		−	23.0000i		−	0.208514i
$23$		−	23.0000i		−	0.208514i
$24$	−31.7572			−0.270100
$25$	111.695	+	56.1185i	0.893558	+	0.448948i
$26$	−3.60811			−0.0272157
$27$		−	151.807i		−	1.08205i
$28$			23.5596i			0.159012i
$29$	253.550			1.62355			0.811777	−	0.583967i	$-0.198500\pi$
$29$	253.550			1.62355			0.811777	+	0.583967i	$0.198500\pi$
$30$	86.3697	+	20.4776i	0.525629	+	0.124623i
$31$	148.076			0.857912			0.428956	−	0.903325i	$-0.358882\pi$
$31$	148.076			0.857912			0.428956	+	0.903325i	$0.358882\pi$
$32$			32.0000i			0.176777i
$33$			41.0585i			0.216587i
$34$	149.714			0.755166
$35$	15.1916	−	64.0747i	0.0733672	−	0.309446i
$36$	−44.9676			−0.208183
$37$		−	199.885i		−	0.888131i	−0.895994	−	0.444065i	$-0.853536\pi$
$37$		−	199.885i		−	0.888131i	0.895994	−	0.444065i	$-0.146464\pi$
$38$			38.1728i			0.162959i
$39$	7.16147			0.0294039
$40$	20.6342	−	87.0301i	0.0815637	−	0.344017i
$41$	−26.2024			−0.0998080			−0.0499040	−	0.998754i	$-0.515892\pi$
$41$	−26.2024			−0.0998080			−0.0499040	+	0.998754i	$0.515892\pi$
$42$		−	46.7616i		−	0.171797i
$43$		−	207.766i		−	0.736839i	−0.929660	−	0.368419i	$-0.879899\pi$
$43$		−	207.766i		−	0.736839i	0.929660	−	0.368419i	$-0.120101\pi$
$44$	41.3724			0.141753
$45$	122.298	+	28.9959i	0.405135	+	0.0960545i
$46$	46.0000			0.147442
$47$		−	28.7333i		−	0.0891742i	−0.999005	−	0.0445871i	$-0.985803\pi$
$47$		−	28.7333i		−	0.0891742i	0.999005	−	0.0445871i	$-0.0141972\pi$
$48$		−	63.5144i		−	0.190990i
$49$	308.309			0.898861
$50$	−112.237	+	223.389i	−0.317454	+	0.631841i
$51$	−297.155			−0.815883
$52$		−	7.21622i		−	0.0192444i
$53$			528.893i			1.37074i	0.728197	+	0.685368i	$0.240359\pi$
$53$			528.893i			1.37074i	−0.728197	+	0.685368i	$0.759641\pi$
$54$	303.614			0.765122
$55$	−112.520	−	26.6776i	−0.275858	−	0.0654039i
$56$	−47.1191			−0.112439
$57$		−	75.7662i		−	0.176061i
$58$			507.100i			1.14803i
$59$	−114.842			−0.253409			−0.126704	−	0.991941i	$-0.540440\pi$
$59$	−114.842			−0.253409			−0.126704	+	0.991941i	$0.540440\pi$
$60$	−40.9552	+	172.739i	−0.0881215	+	0.371676i
$61$	207.365			0.435252			0.217626	−	0.976032i	$-0.430169\pi$
$61$	207.365			0.435252			0.217626	+	0.976032i	$0.430169\pi$
$62$			296.152i			0.606635i
$63$		−	66.2135i		−	0.132415i
$64$	−64.0000			−0.125000
$65$	−4.65315	+	19.6259i	−0.00887926	+	0.0374506i
$66$	−82.1169			−0.153150
$67$			53.4749i			0.0975074i	0.998811	+	0.0487537i	$0.0155249\pi$
$67$			53.4749i			0.0975074i	−0.998811	+	0.0487537i	$0.984475\pi$
$68$			299.427i			0.533983i
$69$	−91.3019			−0.159296
$70$	128.149	+	30.3832i	0.218811	+	0.0518784i
$71$	−848.654			−1.41854			−0.709272	−	0.704935i	$-0.750976\pi$
$71$	−848.654			−1.41854			−0.709272	+	0.704935i	$0.750976\pi$
$72$		−	89.9352i		−	0.147208i
$73$			442.031i			0.708709i	0.935111	+	0.354355i	$0.115299\pi$
$73$			442.031i			0.708709i	−0.935111	+	0.354355i	$0.884701\pi$
$74$	399.769			0.628003
$75$	222.771	−	443.389i	0.342978	−	0.682642i
$76$	−76.3455			−0.115229
$77$			60.9197i			0.0901616i
$78$			14.3229i			0.0207917i
$79$	−703.848			−1.00239			−0.501197	−	0.865333i	$-0.667107\pi$
$79$	−703.848			−1.00239			−0.501197	+	0.865333i	$0.667107\pi$
$80$	174.060	+	41.2683i	0.243256	+	0.0576742i
$81$	−299.089			−0.410272
$82$		−	52.4048i		−	0.0705749i
$83$			343.440i			0.454186i	0.973873	+	0.227093i	$0.0729222\pi$
$83$			343.440i			0.454186i	−0.973873	+	0.227093i	$0.927078\pi$
$84$	93.5231			0.121479
$85$	193.076	−	814.349i	0.246377	−	1.03916i
$86$	415.533			0.521024
$87$		−	1006.50i		−	1.24033i
$88$			82.7448i			0.100234i
$89$	−642.348			−0.765042			−0.382521	−	0.923947i	$-0.624944\pi$
$89$	−642.348			−0.765042			−0.382521	+	0.923947i	$0.624944\pi$
$90$	−57.9918	+	244.596i	−0.0679208	+	0.286474i
$91$	10.6257			0.0122404
$92$			92.0000i			0.104257i
$93$		−	587.810i		−	0.655409i
$94$	57.4667			0.0630557
$95$	207.636	+	49.2290i	0.224242	+	0.0531661i
$96$	127.029			0.135050
$97$		−	665.706i		−	0.696827i	−0.937341	−	0.348414i	$-0.886720\pi$
$97$		−	665.706i		−	0.696827i	0.937341	−	0.348414i	$-0.113280\pi$
$98$			616.618i			0.635590i
$99$	−116.276			−0.118042
$100$	−446.779	−	224.474i	−0.446779	−	0.224474i
$101$	−381.441			−0.375790			−0.187895	−	0.982189i	$-0.560167\pi$
$101$	−381.441			−0.375790			−0.187895	+	0.982189i	$0.560167\pi$
$102$		−	594.310i		−	0.576916i
$103$			4.42735i			0.00423534i	0.999998	+	0.00211767i	$0.000674075\pi$
$103$			4.42735i			0.00423534i	−0.999998	+	0.00211767i	$0.999326\pi$
$104$	14.4324			0.0136079
$105$	−254.354	−	60.3054i	−0.236404	−	0.0560495i
$106$	−1057.79			−0.969257
$107$		−	775.047i		−	0.700248i	−0.936703	−	0.350124i	$-0.886139\pi$
$107$		−	775.047i		−	0.700248i	0.936703	−	0.350124i	$-0.113861\pi$
$108$			607.227i			0.541023i
$109$	−259.215			−0.227782			−0.113891	−	0.993493i	$-0.536332\pi$
$109$	−259.215			−0.227782			−0.113891	+	0.993493i	$0.536332\pi$
$110$	53.3553	−	225.040i	0.0462475	−	0.195061i
$111$	−793.472			−0.678496
$112$		−	94.2382i		−	0.0795060i
$113$		−	331.257i		−	0.275771i	−0.990448	−	0.137885i	$-0.955969\pi$
$113$		−	331.257i		−	0.275771i	0.990448	−	0.137885i	$-0.0440305\pi$
$114$	151.532			0.124494
$115$	59.3232	−	250.211i	0.0481036	−	0.202890i
$116$	−1014.20			−0.811777
$117$			20.2810i			0.0160255i
$118$		−	229.683i		−	0.179187i
$119$	−440.898			−0.339639
$120$	−345.479	−	81.9104i	−0.262815	−	0.0623113i
$121$	−1224.02			−0.919625
$122$			414.730i			0.307770i
$123$			104.014i			0.0762492i
$124$	−592.305			−0.428956
$125$	1070.36	+	898.591i	0.765884	+	0.642979i
$126$	132.427			0.0936313
$127$			2155.73i			1.50622i	0.657895	+	0.753110i	$0.271447\pi$
$127$			2155.73i			1.50622i	−0.657895	+	0.753110i	$0.728553\pi$
$128$		−	128.000i		−	0.0883883i
$129$	−824.759			−0.562915
$130$	−39.2518	−	9.30630i	−0.0264816	−	0.00627859i
$131$	−790.581			−0.527278			−0.263639	−	0.964621i	$-0.584923\pi$
$131$	−790.581			−0.527278			−0.263639	+	0.964621i	$0.584923\pi$
$132$		−	164.234i		−	0.108293i
$133$		−	112.417i		−	0.0732915i
$134$	−106.950			−0.0689482
$135$	391.551	−	1651.47i	0.249625	−	1.05286i
$136$	−598.854			−0.377583
$137$			2767.64i			1.72595i	0.505243	+	0.862977i	$0.331403\pi$
$137$			2767.64i			1.72595i	−0.505243	+	0.862977i	$0.668597\pi$
$138$		−	182.604i		−	0.112640i
$139$	−2144.52			−1.30860			−0.654301	−	0.756234i	$-0.727037\pi$
$139$	−2144.52			−1.30860			−0.654301	+	0.756234i	$0.727037\pi$
$140$	−60.7665	+	256.299i	−0.0366836	+	0.154723i
$141$	−114.061			−0.0681255
$142$		−	1697.31i		−	1.00306i
$143$		−	18.6595i		−	0.0109118i
$144$	179.870			0.104092
$145$	2758.31	+	653.974i	1.57976	+	0.374549i
$146$	−884.062			−0.501133
$147$		−	1223.88i		−	0.686693i
$148$			799.539i			0.444065i
$149$	3030.89			1.66644			0.833222	−	0.552938i	$-0.186493\pi$
$149$	3030.89			1.66644			0.833222	+	0.552938i	$0.186493\pi$
$150$	886.777	+	445.541i	0.482700	+	0.242522i
$151$	−485.413			−0.261605			−0.130803	−	0.991408i	$-0.541755\pi$
$151$	−485.413			−0.261605			−0.130803	+	0.991408i	$0.541755\pi$
$152$		−	152.691i		−	0.0814795i
$153$		−	841.532i		−	0.444666i
$154$	−121.839			−0.0637539
$155$	1610.88	+	381.928i	0.834770	+	0.197918i
$156$	−28.6459			−0.0147020
$157$			2698.02i			1.37150i	0.727837	+	0.685750i	$0.240526\pi$
$157$			2698.02i			1.37150i	−0.727837	+	0.685750i	$0.759474\pi$
$158$		−	1407.70i		−	0.708800i
$159$	2099.52			1.04719
$160$	−82.5367	+	348.120i	−0.0407818	+	0.172008i
$161$	−135.467			−0.0663126
$162$		−	598.177i		−	0.290106i
$163$			966.418i			0.464391i	0.972669	+	0.232195i	$0.0745908\pi$
$163$			966.418i			0.464391i	−0.972669	+	0.232195i	$0.925409\pi$
$164$	104.810			0.0499040
$165$	−105.901	+	446.665i	−0.0499659	+	0.210744i
$166$	−686.881			−0.321158
$167$			1939.34i			0.898625i	0.893375	+	0.449312i	$0.148331\pi$
$167$			1939.34i			0.898625i	−0.893375	+	0.449312i	$0.851669\pi$
$168$			187.046i			0.0858984i
$169$	2193.75			0.998519
$170$	1628.70	+	386.152i	0.734796	+	0.174215i
$171$	214.567			0.0959553
$172$			831.065i			0.368419i
$173$			1641.11i			0.721221i	0.932716	+	0.360611i	$0.117432\pi$
$173$			1641.11i			0.721221i	−0.932716	+	0.360611i	$0.882568\pi$
$174$	2013.01			0.877045
$175$	330.532	−	657.870i	0.142776	−	0.284173i
$176$	−165.490			−0.0708764
$177$			455.881i			0.193594i
$178$		−	1284.70i		−	0.540967i
$179$	2286.67			0.954827			0.477413	−	0.878679i	$-0.341574\pi$
$179$	2286.67			0.954827			0.477413	+	0.878679i	$0.341574\pi$
$180$	−489.191	−	115.984i	−0.202568	−	0.0480273i
$181$	−3113.10			−1.27843			−0.639213	−	0.769030i	$-0.720740\pi$
$181$	−3113.10			−1.27843			−0.639213	+	0.769030i	$0.720740\pi$
$182$			21.2514i			0.00865526i
$183$		−	823.166i		−	0.332515i
$184$	−184.000			−0.0737210
$185$	515.557	−	2174.50i	0.204889	−	0.864174i
$186$	1175.62			0.463444
$187$			774.251i			0.302774i
$188$			114.933i			0.0445871i
$189$	−894.126			−0.344117
$190$	−98.4579	+	415.272i	−0.0375941	+	0.158563i
$191$	4364.26			1.65333			0.826667	−	0.562691i	$-0.190234\pi$
$191$	4364.26			1.65333			0.826667	+	0.562691i	$0.190234\pi$
$192$			254.057i			0.0954949i
$193$		−	833.210i		−	0.310755i	−0.987855	−	0.155378i	$-0.950341\pi$
$193$		−	833.210i		−	0.310755i	0.987855	−	0.155378i	$-0.0496595\pi$
$194$	1331.41			0.492731
$195$	77.9079	+	18.4714i	0.0286108	+	0.00678339i
$196$	−1233.24			−0.449430
$197$			742.776i			0.268632i	0.990939	+	0.134316i	$0.0428838\pi$
$197$			742.776i			0.268632i	−0.990939	+	0.134316i	$0.957116\pi$
$198$		−	232.552i		−	0.0834685i
$199$	−640.502			−0.228161			−0.114080	−	0.993472i	$-0.536392\pi$
$199$	−640.502			−0.228161			−0.114080	+	0.993472i	$0.536392\pi$
$200$	448.948	−	893.558i	0.158727	−	0.315920i
$201$	212.276			0.0744917
$202$		−	762.882i		−	0.265724i
$203$		−	1493.38i		−	0.516330i
$204$	1188.62			0.407941
$205$	−285.050	−	67.5831i	−0.0971157	−	0.0230254i
$206$	−8.85470			−0.00299484
$207$		−	258.564i		−	0.0868184i
$208$			28.8649i			0.00962221i
$209$	−197.412			−0.0653364
$210$	120.611	−	508.708i	0.0396330	−	0.167163i
$211$	−5283.84			−1.72395			−0.861977	−	0.506947i	$-0.830774\pi$
$211$	−5283.84			−1.72395			−0.861977	+	0.506947i	$0.830774\pi$
$212$		−	2115.57i		−	0.685368i
$213$			3368.86i			1.08371i
$214$	1550.09			0.495150
$215$	535.886	−	2260.24i	0.169986	−	0.716963i
$216$	−1214.45			−0.382561
$217$		−	872.152i		−	0.272837i
$218$		−	518.430i		−	0.161066i
$219$	1754.71			0.541425
$220$	450.080	+	106.711i	0.137929	+	0.0327019i
$221$	135.046			0.0411048
$222$		−	1586.94i		−	0.479769i
$223$		−	2471.69i		−	0.742227i	−0.928587	−	0.371114i	$-0.878976\pi$
$223$		−	2471.69i		−	0.742227i	0.928587	−	0.371114i	$-0.121024\pi$
$224$	188.476			0.0562193
$225$	1255.66	+	630.879i	0.372048	+	0.186927i
$226$	662.515			0.194999
$227$			1348.56i			0.394305i	0.980373	+	0.197153i	$0.0631695\pi$
$227$			1348.56i			0.394305i	−0.980373	+	0.197153i	$0.936831\pi$
$228$			303.065i			0.0880305i
$229$	−3680.73			−1.06214			−0.531068	−	0.847329i	$-0.678209\pi$
$229$	−3680.73			−1.06214			−0.531068	+	0.847329i	$0.678209\pi$
$230$	500.423	+	118.646i	0.143465	+	0.0340144i
$231$	241.830			0.0688798
$232$		−	2028.40i		−	0.574013i
$233$		−	3116.65i		−	0.876301i	−0.898902	−	0.438151i	$-0.855634\pi$
$233$		−	3116.65i		−	0.876301i	0.898902	−	0.438151i	$-0.144366\pi$
$234$	−40.5620			−0.0113317
$235$	74.1111	−	312.583i	0.0205722	−	0.0867688i
$236$	459.367			0.126704
$237$			2794.03i			0.765788i
$238$		−	881.796i		−	0.240161i
$239$	4834.03			1.30832			0.654158	−	0.756358i	$-0.273023\pi$
$239$	4834.03			1.30832			0.654158	+	0.756358i	$0.273023\pi$
$240$	163.821	−	690.957i	0.0440608	−	0.185838i
$241$	−1350.04			−0.360845			−0.180423	−	0.983589i	$-0.557747\pi$
$241$	−1350.04			−0.360845			−0.180423	+	0.983589i	$0.557747\pi$
$242$		−	2448.04i		−	0.650273i
$243$		−	2911.51i		−	0.768615i
$244$	−829.460			−0.217626
$245$	3354.02	+	795.213i	0.874614	+	0.207364i
$246$	−208.029			−0.0539163
$247$			34.4329i			0.00887009i
$248$		−	1184.61i		−	0.303318i
$249$	1363.34			0.346980
$250$	−1797.18	+	2140.71i	−0.454655	+	0.541562i
$251$	−2006.92			−0.504684			−0.252342	−	0.967638i	$-0.581201\pi$
$251$	−2006.92			−0.504684			−0.252342	+	0.967638i	$0.581201\pi$
$252$			264.854i			0.0662073i
$253$			237.891i			0.0591150i
$254$	−4311.46			−1.06506
$255$	−3232.68	−	766.443i	−0.793875	−	0.188222i
$256$	256.000			0.0625000
$257$			6064.65i			1.47199i	0.676985	+	0.735997i	$0.263286\pi$
$257$			6064.65i			1.47199i	−0.676985	+	0.735997i	$0.736714\pi$
$258$		−	1649.52i		−	0.398041i
$259$	−1177.30			−0.282447
$260$	18.6126	−	78.5035i	0.00443963	−	0.0187253i
$261$	2850.38			0.675994
$262$		−	1581.16i		−	0.372842i
$263$		−	3527.38i		−	0.827026i	−0.910498	−	0.413513i	$-0.864302\pi$
$263$		−	3527.38i		−	0.827026i	0.910498	−	0.413513i	$-0.135698\pi$
$264$	328.468			0.0765749
$265$	−1364.16	+	5753.70i	−0.316225	+	1.33376i
$266$	224.833			0.0518249
$267$			2549.90i			0.584461i
$268$		−	213.900i		−	0.0487537i
$269$	5159.52			1.16945			0.584724	−	0.811232i	$-0.301203\pi$
$269$	5159.52			1.16945			0.584724	+	0.811232i	$0.301203\pi$
$270$	3302.94	+	783.102i	0.744483	+	0.176511i
$271$	2747.61			0.615888			0.307944	−	0.951404i	$-0.400359\pi$
$271$	2747.61			0.615888			0.307944	+	0.951404i	$0.400359\pi$
$272$		−	1197.71i		−	0.266992i
$273$		−	42.1802i		−	0.00935115i
$274$	−5535.29			−1.22043
$275$	−1155.27	−	580.439i	−0.253329	−	0.127279i
$276$	365.208			0.0796482
$277$		−	3301.88i		−	0.716211i	−0.933681	−	0.358106i	$-0.883423\pi$
$277$		−	3301.88i		−	0.716211i	0.933681	−	0.358106i	$-0.116577\pi$
$278$		−	4289.04i		−	0.925321i
$279$	1664.66			0.357206
$280$	−512.597	−	121.533i	−0.109406	−	0.0259392i
$281$	−4158.96			−0.882928			−0.441464	−	0.897279i	$-0.645541\pi$
$281$	−4158.96			−0.882928			−0.441464	+	0.897279i	$0.645541\pi$
$282$		−	228.123i		−	0.0481720i
$283$		−	1315.59i		−	0.276337i	−0.990409	−	0.138169i	$-0.955878\pi$
$283$		−	1315.59i		−	0.276337i	0.990409	−	0.138169i	$-0.0441216\pi$
$284$	3394.61			0.709272
$285$	195.422	−	824.242i	0.0406168	−	0.171312i
$286$	37.3191			0.00771581
$287$			154.329i			0.0317414i
$288$			359.741i			0.0736039i
$289$	−690.535			−0.140553
$290$	−1307.95	+	5516.62i	−0.264846	+	1.11706i
$291$	−2642.62			−0.532347
$292$		−	1768.12i		−	0.354355i
$293$			5010.28i			0.998988i	0.866317	+	0.499494i	$0.166481\pi$
$293$			5010.28i			0.998988i	−0.866317	+	0.499494i	$0.833519\pi$
$294$	2447.76			0.485565
$295$	−1249.33	−	296.208i	−0.246573	−	0.0584606i
$296$	−1599.08			−0.314002
$297$			1570.15i			0.306766i
$298$			6061.78i			1.17835i
$299$	41.4933			0.00802548
$300$	−891.083	+	1773.55i	−0.171489	+	0.341321i
$301$	−1223.72			−0.234333
$302$		−	970.827i		−	0.184983i
$303$			1514.19i			0.287088i
$304$	305.382			0.0576147
$305$	2255.87	+	534.850i	0.423511	+	0.100411i
$306$	1683.06			0.314426
$307$		−	5668.59i		−	1.05382i	−0.849920	−	0.526912i	$-0.823350\pi$
$307$		−	5668.59i		−	1.05382i	0.849920	−	0.526912i	$-0.176650\pi$
$308$		−	243.679i		−	0.0450808i
$309$	17.5750			0.00323562
$310$	−763.857	+	3221.77i	−0.139949	+	0.590272i
$311$	−2944.23			−0.536823			−0.268412	−	0.963304i	$-0.586499\pi$
$311$	−2944.23			−0.536823			−0.268412	+	0.963304i	$0.586499\pi$
$312$		−	57.2917i		−	0.0103959i
$313$			4484.81i			0.809892i	0.914341	+	0.404946i	$0.132710\pi$
$313$			4484.81i			0.809892i	−0.914341	+	0.404946i	$0.867290\pi$
$314$	−5396.04			−0.969797
$315$	170.783	−	720.321i	0.0305476	−	0.128843i
$316$	2815.39			0.501197
$317$			5210.77i			0.923236i	0.887079	+	0.461618i	$0.152731\pi$
$317$			5210.77i			0.923236i	−0.887079	+	0.461618i	$0.847269\pi$
$318$			4199.04i			0.740473i
$319$	−2622.49			−0.460287
$320$	−696.240	−	165.073i	−0.121628	−	0.0288371i
$321$	−3076.66			−0.534961
$322$		−	270.935i		−	0.0468901i
$323$		−	1428.74i		−	0.246122i
$324$	1196.35			0.205136
$325$	−101.241	+	201.504i	−0.0172795	+	0.0343920i
$326$	−1932.84			−0.328374
$327$			1028.99i			0.174016i
$328$			209.619i			0.0352875i
$329$	−169.236			−0.0283596
$330$	−893.330	−	211.802i	−0.149019	−	0.0353312i
$331$	2244.51			0.372717			0.186359	−	0.982482i	$-0.440331\pi$
$331$	2244.51			0.372717			0.186359	+	0.982482i	$0.440331\pi$
$332$		−	1373.76i		−	0.227093i
$333$		−	2247.08i		−	0.369788i
$334$	−3878.67			−0.635424
$335$	−137.926	+	581.740i	−0.0224947	+	0.0948772i
$336$	−374.093			−0.0607394
$337$			3098.16i			0.500794i	0.968143	+	0.250397i	$0.0805611\pi$
$337$			3098.16i			0.500794i	−0.968143	+	0.250397i	$0.919439\pi$
$338$			4387.49i			0.706059i
$339$	−1314.98			−0.210677
$340$	−772.303	+	3257.39i	−0.123188	+	0.519579i
$341$	−1531.57			−0.243223
$342$			429.134i			0.0678507i
$343$		−	3836.14i		−	0.603884i
$344$	−1662.13			−0.260512
$345$	−993.251	−	235.492i	−0.155000	−	0.0367492i
$346$	−3282.22			−0.509980
$347$			2041.00i			0.315753i	0.987459	+	0.157877i	$0.0504648\pi$
$347$			2041.00i			0.315753i	−0.987459	+	0.157877i	$0.949535\pi$
$348$			4026.02i			0.620165i
$349$	−12032.8			−1.84556			−0.922779	−	0.385330i	$-0.874088\pi$
$349$	−12032.8			−1.84556			−0.922779	+	0.385330i	$0.874088\pi$
$350$	1315.74	+	661.064i	0.200941	+	0.100958i
$351$	273.868			0.0416467
$352$		−	330.979i		−	0.0501172i
$353$		−	792.405i		−	0.119477i	−0.998214	−	0.0597386i	$-0.980973\pi$
$353$		−	792.405i		−	0.119477i	0.998214	−	0.0597386i	$-0.0190267\pi$
$354$	−911.762			−0.136891
$355$	−9232.30	−	2188.91i	−1.38028	−	0.327254i
$356$	2569.39			0.382521
$357$			1750.21i			0.259470i
$358$			4573.35i			0.675165i
$359$	249.989			0.0367518			0.0183759	−	0.999831i	$-0.494150\pi$
$359$	249.989			0.0367518			0.0183759	+	0.999831i	$0.494150\pi$
$360$	231.967	−	978.383i	0.0339604	−	0.143237i
$361$	−6494.71			−0.946889
$362$		−	6226.20i		−	0.903984i
$363$			4858.93i			0.702556i
$364$	−42.5028			−0.00612019
$365$	−1140.12	+	4808.75i	−0.163497	+	0.689593i
$366$	1646.33			0.235123
$367$		−	11460.9i		−	1.63012i	−0.579375	−	0.815061i	$-0.696703\pi$
$367$		−	11460.9i		−	1.63012i	0.579375	−	0.815061i	$-0.303297\pi$
$368$		−	368.000i		−	0.0521286i
$369$	−294.565			−0.0415567
$370$	4348.99	+	1031.11i	0.611063	+	0.144878i
$371$	3115.12			0.435927
$372$			2351.24i			0.327705i
$373$		−	9995.86i		−	1.38758i	−0.720179	−	0.693788i	$-0.755940\pi$
$373$		−	9995.86i		−	1.38758i	0.720179	−	0.693788i	$-0.244060\pi$
$374$	−1548.50			−0.214094
$375$	3567.09	−	4248.93i	0.491210	−	0.585104i
$376$	−229.867			−0.0315279
$377$			457.419i			0.0624888i
$378$		−	1788.25i		−	0.243327i
$379$	1068.57			0.144826			0.0724128	−	0.997375i	$-0.476930\pi$
$379$	1068.57			0.144826			0.0724128	+	0.997375i	$0.476930\pi$
$380$	−830.545	−	196.916i	−0.112121	−	0.0265831i
$381$	8557.48			1.15069
$382$			8728.52i			1.16908i
$383$		−	14296.3i		−	1.90732i	−0.300879	−	0.953662i	$-0.597280\pi$
$383$		−	14296.3i		−	1.90732i	0.300879	−	0.953662i	$-0.402720\pi$
$384$	−508.115			−0.0675251
$385$	−157.128	+	662.731i	−0.0208000	+	0.0877296i
$386$	1666.42			0.219737
$387$		−	2335.69i		−	0.306795i
$388$			2662.83i			0.348414i
$389$	3987.30			0.519702			0.259851	−	0.965649i	$-0.416327\pi$
$389$	3987.30			0.519702			0.259851	+	0.965649i	$0.416327\pi$
$390$	−36.9427	+	155.816i	−0.00479658	+	0.0202309i
$391$	−1721.71			−0.222686
$392$		−	2466.47i		−	0.317795i
$393$			3138.33i			0.402819i
$394$	−1485.55			−0.189952
$395$	−7656.99	−	1815.42i	−0.975355	−	0.231249i
$396$	465.104			0.0590211
$397$		−	2852.09i		−	0.360560i	−0.983615	−	0.180280i	$-0.942300\pi$
$397$		−	2852.09i		−	0.360560i	0.983615	−	0.180280i	$-0.0577004\pi$
$398$		−	1281.00i		−	0.161334i
$399$	−446.255			−0.0559917
$400$	1787.12	+	897.896i	0.223389	+	0.112237i
$401$	−6601.37			−0.822087			−0.411043	−	0.911616i	$-0.634835\pi$
$401$	−6601.37			−0.822087			−0.411043	+	0.911616i	$0.634835\pi$
$402$			424.553i			0.0526736i
$403$			267.138i			0.0330200i
$404$	1525.76			0.187895
$405$	−3253.71	−	771.430i	−0.399206	−	0.0946486i
$406$	2986.76			0.365100
$407$			2067.43i			0.251790i
$408$			2377.24i			0.288458i
$409$	8048.66			0.973058			0.486529	−	0.873665i	$-0.338263\pi$
$409$	8048.66			0.973058			0.486529	+	0.873665i	$0.338263\pi$
$410$	135.166	−	570.099i	0.0162814	−	0.0686712i
$411$	10986.6			1.31856
$412$		−	17.7094i		−	0.00211767i
$413$			676.405i			0.0805901i
$414$	517.127			0.0613899
$415$	−885.826	+	3736.20i	−0.104779	+	0.441935i
$416$	−57.7298			−0.00680393
$417$			8512.98i			0.999718i
$418$		−	394.825i		−	0.0461998i
$419$	−6294.39			−0.733893			−0.366946	−	0.930242i	$-0.619597\pi$
$419$	−6294.39			−0.733893			−0.366946	+	0.930242i	$0.619597\pi$
$420$	1017.42	+	241.221i	0.118202	+	0.0280248i
$421$	8227.18			0.952419			0.476210	−	0.879332i	$-0.342010\pi$
$421$	8227.18			0.952419			0.476210	+	0.879332i	$0.342010\pi$
$422$		−	10567.7i		−	1.21902i
$423$		−	323.017i		−	0.0371292i
$424$	4231.14			0.484628
$425$	4200.85	−	8361.11i	0.479462	−	0.954290i
$426$	−6737.71			−0.766299
$427$		−	1221.36i		−	0.138421i
$428$			3100.19i			0.350124i
$429$	−74.0717			−0.00833617
$430$	4520.48	+	1071.77i	0.506969	+	0.120199i
$431$	6826.51			0.762927			0.381463	−	0.924384i	$-0.375420\pi$
$431$	6826.51			0.762927			0.381463	+	0.924384i	$0.375420\pi$
$432$		−	2428.91i		−	0.270512i
$433$		−	795.073i		−	0.0882420i	−0.999026	−	0.0441210i	$-0.985951\pi$
$433$		−	795.073i		−	0.0882420i	0.999026	−	0.0441210i	$-0.0140487\pi$
$434$	1744.30			0.192925
$435$	2596.05	−	10949.5i	0.286140	−	1.20687i
$436$	1036.86			0.113891
$437$		−	438.987i		−	0.0480540i
$438$			3509.41i			0.382845i
$439$	4062.85			0.441707			0.220854	−	0.975307i	$-0.429116\pi$
$439$	4062.85			0.441707			0.220854	+	0.975307i	$0.429116\pi$
$440$	−213.421	+	900.160i	−0.0231238	+	0.0975306i
$441$	3465.98			0.374256
$442$			270.092i			0.0290655i
$443$		−	75.2836i		−	0.00807412i	−0.999992	−	0.00403706i	$-0.998715\pi$
$443$		−	75.2836i		−	0.00807412i	0.999992	−	0.00403706i	$-0.00128504\pi$
$444$	3173.89			0.339248
$445$	−6987.95	−	1656.79i	−0.744406	−	0.176493i
$446$	4943.38			0.524834
$447$		−	12031.6i		−	1.27310i
$448$			376.953i			0.0397530i
$449$	3264.03			0.343072			0.171536	−	0.985178i	$-0.445127\pi$
$449$	3264.03			0.343072			0.171536	+	0.985178i	$0.445127\pi$
$450$	−1261.76	+	2511.32i	−0.132177	+	0.263077i
$451$	271.014			0.0282961
$452$			1325.03i			0.137885i
$453$			1926.92i			0.199856i
$454$	−2697.13			−0.278816
$455$	115.594	+	27.4065i	0.0119102	+	0.00282382i
$456$	−606.130			−0.0622470
$457$			1083.03i			0.110858i	0.998463	+	0.0554288i	$0.0176526\pi$
$457$			1083.03i			0.110858i	−0.998463	+	0.0554288i	$0.982347\pi$
$458$		−	7361.45i		−	0.751044i
$459$	−11363.8			−1.15559
$460$	−237.293	+	1000.85i	−0.0240518	+	0.101445i
$461$	−3088.22			−0.312002			−0.156001	−	0.987757i	$-0.549860\pi$
$461$	−3088.22			−0.312002			−0.156001	+	0.987757i	$0.549860\pi$
$462$			483.660i			0.0487054i
$463$			11971.1i			1.20161i	0.799396	+	0.600804i	$0.205153\pi$
$463$			11971.1i			1.20161i	−0.799396	+	0.600804i	$0.794847\pi$
$464$	4056.80			0.405889
$465$	1516.12	−	6394.64i	0.151201	−	0.637730i
$466$	6233.29			0.619639
$467$		−	1448.39i		−	0.143519i	−0.997422	−	0.0717596i	$-0.977139\pi$
$467$		−	1448.39i		−	0.143519i	0.997422	−	0.0717596i	$-0.0228615\pi$
$468$		−	81.1240i		−	0.00801274i
$469$	314.961			0.0310097
$470$	625.166	+	148.222i	0.0613548	+	0.0145468i
$471$	10710.2			1.04777
$472$			918.733i			0.0895935i
$473$			2148.95i			0.208898i
$474$	−5588.06			−0.541494
$475$	2131.85	+	1071.10i	0.205928	+	0.103464i
$476$	1763.59			0.169820
$477$			5945.76i			0.570729i
$478$			9668.06i			0.925119i
$479$	−17893.5			−1.70683			−0.853417	−	0.521228i	$-0.825474\pi$
$479$	−17893.5			−1.70683			−0.853417	+	0.521228i	$0.825474\pi$
$480$	1381.91	+	327.641i	0.131407	+	0.0311557i
$481$	360.603			0.0341831
$482$		−	2700.08i		−	0.255156i
$483$			537.758i			0.0506601i
$484$	4896.08			0.459812
$485$	1717.04	−	7242.06i	0.160756	−	0.678031i
$486$	5823.02			0.543493
$487$			19059.2i			1.77342i	0.462323	+	0.886712i	$0.347016\pi$
$487$			19059.2i			1.77342i	−0.462323	+	0.886712i	$0.652984\pi$
$488$		−	1658.92i		−	0.153885i
$489$	3836.34			0.354775
$490$	−1590.43	+	6708.04i	−0.146629	+	0.618446i
$491$	8915.68			0.819469			0.409734	−	0.912205i	$-0.365621\pi$
$491$	8915.68			0.819469			0.409734	+	0.912205i	$0.365621\pi$
$492$		−	416.057i		−	0.0381246i
$493$		−	18979.9i		−	1.73390i
$494$	−68.8658			−0.00627210
$495$	−1264.94	−	299.907i	−0.114858	−	0.0272320i
$496$	2369.22			0.214478
$497$			4998.48i			0.451131i
$498$			2726.67i			0.245352i
$499$	−7117.31			−0.638506			−0.319253	−	0.947669i	$-0.603432\pi$
$499$	−7117.31			−0.638506			−0.319253	+	0.947669i	$0.603432\pi$
$500$	−4281.42	−	3594.36i	−0.382942	−	0.321490i
$501$	7698.48			0.686512
$502$		−	4013.84i		−	0.356866i
$503$			20158.2i			1.78690i	0.449163	+	0.893450i	$0.351722\pi$
$503$			20158.2i			1.78690i	−0.449163	+	0.893450i	$0.648278\pi$
$504$	−529.708			−0.0468156
$505$	−4149.61	−	983.840i	−0.365654	−	0.0866937i
$506$	−475.783			−0.0418006
$507$		−	8708.40i		−	0.762827i
$508$		−	8622.91i		−	0.753110i
$509$	15511.1			1.35073			0.675363	−	0.737486i	$-0.263987\pi$
$509$	15511.1			1.35073			0.675363	+	0.737486i	$0.263987\pi$
$510$	1532.89	−	6465.35i	0.133093	−	0.561354i
$511$	2603.51			0.225387
$512$			512.000i			0.0441942i
$513$		−	2897.44i		−	0.249367i
$514$	−12129.3			−1.04086
$515$	−11.4193	+	48.1641i	−0.000977079	+	0.00412109i
$516$	3299.04			0.281457
$517$			297.192i			0.0252814i
$518$		−	2354.60i		−	0.199720i
$519$	6514.63			0.550983
$520$	157.007	+	37.2252i	0.0132408	+	0.00313929i
$521$	13448.6			1.13089			0.565447	−	0.824785i	$-0.308704\pi$
$521$	13448.6			1.13089			0.565447	+	0.824785i	$0.308704\pi$
$522$			5700.77i			0.478000i
$523$			9720.80i			0.812736i	0.913710	+	0.406368i	$0.133205\pi$
$523$			9720.80i			0.812736i	−0.913710	+	0.406368i	$0.866795\pi$
$524$	3162.32			0.263639
$525$	−2611.51	−	1312.10i	−0.217096	−	0.109075i
$526$	7054.77			0.584795
$527$		−	11084.5i		−	0.916221i
$528$			656.935i			0.0541467i
$529$	−529.000			−0.0434783
$530$	−11507.4	−	2728.32i	−0.943112	−	0.223605i
$531$	−1291.04			−0.105511
$532$			449.667i			0.0366457i
$533$		−	47.2706i		−	0.00384150i
$534$	−5099.79			−0.413276
$535$	1999.05	−	8431.54i	0.161545	−	0.681360i
$536$	427.799			0.0344741
$537$		−	9077.29i		−	0.729449i
$538$			10319.0i			0.826925i
$539$	−3188.87			−0.254832
$540$	−1566.20	+	6605.88i	−0.124812	+	0.526429i
$541$	−8566.75			−0.680801			−0.340401	−	0.940281i	$-0.610563\pi$
$541$	−8566.75			−0.680801			−0.340401	+	0.940281i	$0.610563\pi$
$542$			5495.23i			0.435499i
$543$			12357.9i			0.976665i
$544$	2395.42			0.188792
$545$	−2819.93	−	668.585i	−0.221638	−	0.0525487i
$546$	84.3605			0.00661226
$547$			21803.6i			1.70430i	0.523295	+	0.852151i	$0.324702\pi$
$547$			21803.6i			1.70430i	−0.523295	+	0.852151i	$0.675298\pi$
$548$		−	11070.6i		−	0.862977i
$549$	2331.18			0.181224
$550$	1160.88	−	2310.54i	0.0900001	−	0.179130i
$551$	4839.36			0.374162
$552$			730.415i			0.0563198i
$553$			4145.59i			0.318785i
$554$	6603.75			0.506438
$555$	−8631.99	−	2046.58i	−0.660194	−	0.156527i
$556$	8578.07			0.654301
$557$		−	4212.85i		−	0.320474i	−0.987079	−	0.160237i	$-0.948774\pi$
$557$		−	4212.85i		−	0.320474i	0.987079	−	0.160237i	$-0.0512259\pi$
$558$			3329.31i			0.252583i
$559$	374.822			0.0283601
$560$	243.066	−	1025.19i	0.0183418	−	0.0773614i
$561$	3073.50			0.231307
$562$		−	8317.92i		−	0.624324i
$563$		−	9283.37i		−	0.694933i	−0.937692	−	0.347467i	$-0.887042\pi$
$563$		−	9283.37i		−	0.694933i	0.937692	−	0.347467i	$-0.112958\pi$
$564$	456.245			0.0340627
$565$	854.402	−	3603.67i	0.0636194	−	0.268332i
$566$	2631.17			0.195400
$567$			1761.60i			0.130477i
$568$			6789.23i			0.501531i
$569$	2997.26			0.220829			0.110415	−	0.993886i	$-0.464782\pi$
$569$	2997.26			0.220829			0.110415	+	0.993886i	$0.464782\pi$
$570$	1648.48	+	390.843i	0.121136	+	0.0287204i
$571$	12384.7			0.907679			0.453840	−	0.891083i	$-0.350054\pi$
$571$	12384.7			0.907679			0.453840	+	0.891083i	$0.350054\pi$
$572$			74.6381i			0.00545590i
$573$		−	17324.6i		−	1.26308i
$574$	−308.659			−0.0224445
$575$	1290.73	−	2568.98i	0.0936122	−	0.186320i
$576$	−719.481			−0.0520458
$577$		−	142.143i		−	0.0102556i	−0.999987	−	0.00512782i	$-0.998368\pi$
$577$		−	142.143i		−	0.0102556i	0.999987	−	0.00512782i	$-0.00163224\pi$
$578$		−	1381.07i		−	0.0993856i
$579$	−3307.55			−0.237404
$580$	−11033.2	−	2615.90i	−0.789880	−	0.187275i
$581$	2022.83			0.144442
$582$		−	5285.24i		−	0.376426i
$583$		−	5470.39i		−	0.388611i
$584$	3536.25			0.250567
$585$	−52.3102	+	220.632i	−0.00369703	+	0.0155932i
$586$	−10020.6			−0.706391
$587$			8307.77i			0.584154i	0.956395	+	0.292077i	$0.0943463\pi$
$587$			8307.77i			0.584154i	−0.956395	+	0.292077i	$0.905654\pi$
$588$			4895.52i			0.343346i
$589$	2826.24			0.197713
$590$	592.415	−	2498.67i	0.0413379	−	0.174354i
$591$	2948.56			0.205224
$592$		−	3198.15i		−	0.222033i
$593$			18562.1i			1.28542i	0.766109	+	0.642711i	$0.222190\pi$
$593$			18562.1i			1.28542i	−0.766109	+	0.642711i	$0.777810\pi$
$594$	−3140.31			−0.216916
$595$	−4796.42	−	1137.20i	−0.330478	−	0.0783537i
$596$	−12123.6			−0.833222
$597$			2542.57i			0.174305i
$598$			82.9866i			0.00567487i
$599$	18439.8			1.25781			0.628907	−	0.777481i	$-0.283503\pi$
$599$	18439.8			1.25781			0.628907	+	0.777481i	$0.283503\pi$
$600$	−3547.11	−	1782.17i	−0.241350	−	0.121261i
$601$	12557.5			0.852299			0.426150	−	0.904653i	$-0.359870\pi$
$601$	12557.5			0.852299			0.426150	+	0.904653i	$0.359870\pi$
$602$		−	2447.44i		−	0.165698i
$603$			601.159i			0.0405988i
$604$	1941.65			0.130803
$605$	−13315.8	−	3157.08i	−0.894818	−	0.212155i
$606$	−3028.37			−0.203002
$607$		−	6309.83i		−	0.421924i	−0.977494	−	0.210962i	$-0.932340\pi$
$607$		−	6309.83i		−	0.421924i	0.977494	−	0.210962i	$-0.0676597\pi$
$608$			610.764i			0.0407397i
$609$	−5928.20			−0.394455
$610$	−1069.70	+	4511.75i	−0.0710015	+	0.299468i
$611$	51.8366			0.00343221
$612$			3366.13i			0.222333i
$613$		−	25462.8i		−	1.67770i	−0.544361	−	0.838851i	$-0.683228\pi$
$613$		−	25462.8i		−	1.67770i	0.544361	−	0.838851i	$-0.316772\pi$
$614$	11337.2			0.745166
$615$	−268.281	+	1131.55i	−0.0175905	+	0.0741925i
$616$	487.358			0.0318769
$617$			19574.4i			1.27720i	0.769537	+	0.638602i	$0.220487\pi$
$617$			19574.4i			1.27720i	−0.769537	+	0.638602i	$0.779513\pi$
$618$			35.1500i			0.00228793i
$619$	−18795.2			−1.22043			−0.610213	−	0.792237i	$-0.708916\pi$
$619$	−18795.2			−1.22043			−0.610213	+	0.792237i	$0.708916\pi$
$620$	−6443.54	−	1527.71i	−0.417385	−	0.0989588i
$621$	−3491.56			−0.225622
$622$		−	5888.46i		−	0.379591i
$623$			3783.36i			0.243302i
$624$	114.583			0.00735098
$625$	9326.42	+	12536.3i	0.596891	+	0.802322i
$626$	−8969.62			−0.572680
$627$			783.657i			0.0499143i
$628$		−	10792.1i		−	0.685750i
$629$	−14962.7			−0.948494
$630$	1440.64	+	341.565i	0.0911056	+	0.0216004i
$631$	7244.63			0.457059			0.228529	−	0.973537i	$-0.426608\pi$
$631$	7244.63			0.457059			0.228529	+	0.973537i	$0.426608\pi$
$632$			5630.79i			0.354400i
$633$			20975.0i			1.31703i
$634$	−10421.5			−0.652827
$635$	−5560.21	+	23451.6i	−0.347480	+	1.46559i
$636$	−8398.07			−0.523593
$637$			556.207i			0.0345961i
$638$		−	5244.99i		−	0.325472i
$639$	−9540.48			−0.590634
$640$	330.147	−	1392.48i	0.0203909	−	0.0860041i
$641$	4925.25			0.303488			0.151744	−	0.988420i	$-0.451511\pi$
$641$	4925.25			0.303488			0.151744	+	0.988420i	$0.451511\pi$
$642$		−	6153.32i		−	0.378275i
$643$			14417.3i			0.884237i	0.896957	+	0.442118i	$0.145773\pi$
$643$			14417.3i			0.884237i	−0.896957	+	0.442118i	$0.854227\pi$
$644$	541.870			0.0331563
$645$	−8972.36	−	2127.28i	−0.547730	−	0.129863i
$646$	2857.49			0.174035
$647$			30802.0i			1.87164i	0.352481	+	0.935819i	$0.385338\pi$
$647$			30802.0i			1.87164i	−0.352481	+	0.935819i	$0.614662\pi$
$648$			2392.71i			0.145053i
$649$	1187.82			0.0718428
$650$	−403.007	−	202.482i	−0.0243188	−	0.0122185i
$651$	−3462.14			−0.208436
$652$		−	3865.67i		−	0.232195i
$653$		−	21169.3i		−	1.26864i	−0.773072	−	0.634318i	$-0.781281\pi$
$653$		−	21169.3i		−	1.26864i	0.773072	−	0.634318i	$-0.218719\pi$
$654$	−2057.98			−0.123048
$655$	−8600.54	−	2039.12i	−0.513055	−	0.121641i
$656$	−419.238			−0.0249520
$657$			4969.26i			0.295083i
$658$		−	338.472i		−	0.0200532i
$659$	−2766.37			−0.163524			−0.0817622	−	0.996652i	$-0.526055\pi$
$659$	−2766.37			−0.163524			−0.0817622	+	0.996652i	$0.526055\pi$
$660$	423.603	−	1786.66i	0.0249829	−	0.105372i
$661$	−18361.5			−1.08045			−0.540226	−	0.841520i	$-0.681661\pi$
$661$	−18361.5			−1.08045			−0.540226	+	0.841520i	$0.681661\pi$
$662$			4489.02i			0.263551i
$663$		−	536.084i		−	0.0314024i
$664$	2747.52			0.160579
$665$	289.953	−	1222.95i	0.0169081	−	0.0713145i
$666$	4494.17			0.261480
$667$		−	5831.65i		−	0.338535i
$668$		−	7757.34i		−	0.449312i
$669$	−9811.74			−0.567031
$670$	−1163.48	−	275.852i	−0.0670883	−	0.0159061i
$671$	−2144.80			−0.123396
$672$		−	748.185i		−	0.0429492i
$673$			14934.8i			0.855416i	0.903917	+	0.427708i	$0.140679\pi$
$673$			14934.8i			0.855416i	−0.903917	+	0.427708i	$0.859321\pi$
$674$	−6196.32			−0.354115
$675$	8519.18	−	16956.0i	0.485783	−	0.966871i
$676$	−8774.98			−0.499259
$677$		−	23189.8i		−	1.31648i	−0.752808	−	0.658241i	$-0.771301\pi$
$677$		−	23189.8i		−	1.31648i	0.752808	−	0.658241i	$-0.228699\pi$
$678$		−	2629.95i		−	0.148971i
$679$	−3920.94			−0.221608
$680$	−6514.79	−	1544.61i	−0.367398	−	0.0871073i
$681$	5353.32			0.301233
$682$		−	3063.13i		−	0.171984i
$683$			21266.1i			1.19140i	0.803207	+	0.595700i	$0.203125\pi$
$683$			21266.1i			1.19140i	−0.803207	+	0.595700i	$0.796875\pi$
$684$	−858.269			−0.0479777
$685$	−7138.50	+	30108.5i	−0.398172	+	1.67940i
$686$	7672.28			0.427010
$687$			14611.2i			0.811428i
$688$		−	3324.26i		−	0.184210i
$689$	−954.152			−0.0527581
$690$	470.985	−	1986.50i	0.0259856	−	0.109601i
$691$	10423.3			0.573838			0.286919	−	0.957955i	$-0.407369\pi$
$691$	10423.3			0.573838			0.286919	+	0.957955i	$0.407369\pi$
$692$		−	6564.44i		−	0.360611i
$693$			684.853i			0.0375403i
$694$	−4081.99			−0.223271
$695$	−23329.7	−	5531.29i	−1.27330	−	0.301891i
$696$	−8052.04			−0.438523
$697$			1961.43i			0.106592i
$698$		−	24065.5i		−	1.30501i
$699$	−12372.0			−0.669458
$700$	−1322.13	+	2631.48i	−0.0713882	+	0.142086i
$701$	−18475.9			−0.995472			−0.497736	−	0.867329i	$-0.665835\pi$
$701$	−18475.9			−0.995472			−0.497736	+	0.867329i	$0.665835\pi$
$702$			547.736i			0.0294487i
$703$		−	3815.08i		−	0.204678i
$704$	661.958			0.0354382
$705$	−1240.84	−	294.195i	−0.0662878	−	0.0157163i
$706$	1584.81			0.0844832
$707$			2246.65i			0.119510i
$708$		−	1823.52i		−	0.0967969i
$709$	−11361.5			−0.601820			−0.300910	−	0.953653i	$-0.597290\pi$
$709$	−11361.5			−0.601820			−0.300910	+	0.953653i	$0.597290\pi$
$710$	4377.81	−	18464.6i	0.231403	−	0.976005i
$711$	−7912.59			−0.417363
$712$			5138.78i			0.270483i
$713$		−	3405.75i		−	0.178887i
$714$	−3500.42			−0.183473
$715$	48.1280	−	202.992i	0.00251732	−	0.0106175i
$716$	−9146.69			−0.477413
$717$		−	19189.4i		−	0.999500i
$718$			499.977i			0.0259874i
$719$	34802.5			1.80516			0.902582	−	0.430518i	$-0.141669\pi$
$719$	34802.5			1.80516			0.902582	+	0.430518i	$0.141669\pi$
$720$	1956.77	+	463.934i	0.101284	+	0.0240136i
$721$	26.0766			0.00134694
$722$		−	12989.4i		−	0.669551i
$723$			5359.19i			0.275671i
$724$	12452.4			0.639213
$725$	28320.2	+	14228.9i	1.45074	+	0.728892i
$726$	−9717.86			−0.496782
$727$		−	6027.34i		−	0.307485i	−0.988111	−	0.153743i	$-0.950867\pi$
$727$		−	6027.34i		−	0.307485i	0.988111	−	0.153743i	$-0.0491326\pi$
$728$		−	85.0055i		−	0.00432763i
$729$	−19633.1			−0.997463
$730$	−9617.49	−	2280.23i	−0.487616	−	0.115610i
$731$	−15552.7			−0.786919
$732$			3292.66i			0.166257i
$733$		−	22491.6i		−	1.13335i	−0.823942	−	0.566675i	$-0.808230\pi$
$733$		−	22491.6i		−	1.13335i	0.823942	−	0.566675i	$-0.191770\pi$
$734$	22921.8			1.15267
$735$	3156.71	−	13314.3i	0.158418	−	0.668170i
$736$	736.000			0.0368605
$737$		−	553.096i		−	0.0276439i
$738$		−	589.129i		−	0.0293850i
$739$	16613.4			0.826976			0.413488	−	0.910510i	$-0.364310\pi$
$739$	16613.4			0.826976			0.413488	+	0.910510i	$0.364310\pi$
$740$	−2062.23	+	8697.99i	−0.102445	+	0.432087i
$741$	136.687			0.00677639
$742$			6230.24i			0.308247i
$743$			26293.8i			1.29829i	0.760667	+	0.649143i	$0.224872\pi$
$743$			26293.8i			1.29829i	−0.760667	+	0.649143i	$0.775128\pi$
$744$	−4702.48			−0.231722
$745$	32972.3	+	7817.49i	1.62149	+	0.384444i
$746$	19991.7			0.981165
$747$			3860.92i			0.189108i
$748$		−	3097.00i		−	0.151387i
$749$	−4564.94			−0.222696
$750$	8497.86	+	7134.18i	0.413731	+	0.347338i
$751$	−36012.3			−1.74981			−0.874904	−	0.484296i	$-0.839076\pi$
$751$	−36012.3			−1.74981			−0.874904	+	0.484296i	$0.839076\pi$
$752$		−	459.734i		−	0.0222936i
$753$			7966.77i			0.385558i
$754$	−914.837			−0.0441862
$755$	−5280.70	−	1252.01i	−0.254549	−	0.0603515i
$756$	3576.50			0.172058
$757$		−	5490.25i		−	0.263602i	−0.991276	−	0.131801i	$-0.957924\pi$
$757$		−	5490.25i		−	0.263602i	0.991276	−	0.131801i	$-0.0420760\pi$
$758$			2137.15i			0.102407i
$759$	944.344			0.0451614
$760$	393.832	−	1661.09i	0.0187971	−	0.0792816i
$761$	−7912.14			−0.376892			−0.188446	−	0.982084i	$-0.560345\pi$
$761$	−7912.14			−0.376892			−0.188446	+	0.982084i	$0.560345\pi$
$762$			17115.0i			0.813661i
$763$			1526.75i			0.0724403i
$764$	−17457.0			−0.826667
$765$	2170.54	−	9154.82i	0.102583	−	0.432671i
$766$	28592.5			1.34868
$767$		−	207.181i		−	0.00975341i
$768$		−	1016.23i		−	0.0477474i
$769$	−11919.8			−0.558959			−0.279479	−	0.960152i	$-0.590162\pi$
$769$	−11919.8			−0.558959			−0.279479	+	0.960152i	$0.590162\pi$
$770$	−1325.46	−	314.257i	−0.0620342	−	0.0147078i
$771$	24074.5			1.12454
$772$			3332.84i			0.155378i
$773$		−	21228.0i		−	0.987732i	−0.869538	−	0.493866i	$-0.835583\pi$
$773$		−	21228.0i		−	0.987732i	0.869538	−	0.493866i	$-0.164417\pi$
$774$	4671.38			0.216937
$775$	16539.3	+	8309.81i	0.766594	+	0.385158i
$776$	−5325.65			−0.246366
$777$			4673.46i			0.215778i
$778$			7974.60i			0.367485i
$779$	−500.109			−0.0230016
$780$	−311.631	−	73.8854i	−0.0143054	−	0.00339170i
$781$	8777.71			0.402165
$782$		−	3443.41i		−	0.157463i
$783$		−	38490.7i		−	1.75676i
$784$	4932.95			0.224715
$785$	−6958.93	+	29351.1i	−0.316401	+	1.33450i
$786$	−6276.66			−0.284836
$787$		−	37174.0i		−	1.68375i	−0.539675	−	0.841874i	$-0.681453\pi$
$787$		−	37174.0i		−	1.68375i	0.539675	−	0.841874i	$-0.318547\pi$
$788$		−	2971.10i		−	0.134316i
$789$	−14002.5			−0.631814
$790$	3630.83	−	15314.0i	0.163518	−	0.689680i
$791$	−1951.07			−0.0877017
$792$			930.208i			0.0417342i
$793$			374.098i			0.0167523i
$794$	5704.18			0.254954
$795$	22840.1	+	5415.23i	1.01894	+	0.241583i
$796$	2562.01			0.114080
$797$		−	13532.6i		−	0.601441i	−0.953712	−	0.300721i	$-0.902773\pi$
$797$		−	13532.6i		−	0.601441i	0.953712	−	0.300721i	$-0.0972272\pi$
$798$		−	892.509i		−	0.0395921i
$799$	−2150.89			−0.0952351
$800$	−1795.79	+	3574.23i	−0.0793636	+	0.157960i
$801$	−7221.21			−0.318538
$802$		−	13202.7i		−	0.581303i
$803$		−	4571.97i		−	0.200923i
$804$	−849.106			−0.0372458
$805$	−1473.72	−	349.407i	−0.0645239	−	0.0152981i
$806$	−534.275			−0.0233487
$807$		−	20481.5i		−	0.893411i
$808$			3051.53i			0.132862i
$809$	19942.7			0.866686			0.433343	−	0.901229i	$-0.357334\pi$
$809$	19942.7			0.866686			0.433343	+	0.901229i	$0.357334\pi$
$810$	1542.86	−	6507.42i	0.0669267	−	0.282281i
$811$	27737.0			1.20096			0.600479	−	0.799641i	$-0.294977\pi$
$811$	27737.0			1.20096			0.600479	+	0.799641i	$0.294977\pi$
$812$			5973.53i			0.258165i
$813$		−	10907.1i		−	0.470513i
$814$	−4134.85			−0.178042
$815$	−2492.65	+	10513.4i	−0.107133	+	0.451864i
$816$	−4754.48			−0.203971
$817$		−	3965.51i		−	0.169811i
$818$			16097.3i			0.688056i
$819$	119.453			0.00509649
$820$	1140.20	+	270.332i	0.0485579	+	0.0115127i
$821$	−40546.9			−1.72363			−0.861813	−	0.507226i	$-0.830671\pi$
$821$	−40546.9			−1.72363			−0.861813	+	0.507226i	$0.830671\pi$
$822$			21973.1i			0.932362i
$823$			17120.1i			0.725113i	0.931962	+	0.362556i	$0.118096\pi$
$823$			17120.1i			0.725113i	−0.931962	+	0.362556i	$0.881904\pi$
$824$	35.4188			0.00149742
$825$	−2304.14	+	4586.01i	−0.0972362	+	0.193533i
$826$	−1352.81			−0.0569858
$827$			11547.9i			0.485563i	0.970081	+	0.242782i	$0.0780598\pi$
$827$			11547.9i			0.485563i	−0.970081	+	0.242782i	$0.921940\pi$
$828$			1034.25i			0.0434092i
$829$	18830.6			0.788917			0.394459	−	0.918914i	$-0.370932\pi$
$829$	18830.6			0.788917			0.394459	+	0.918914i	$0.370932\pi$
$830$	−7472.41	−	1771.65i	−0.312495	−	0.0740903i
$831$	−13107.3			−0.547156
$832$		−	115.460i		−	0.00481111i
$833$		−	23079.0i		−	0.959953i
$834$	−17026.0			−0.706908
$835$	−5002.07	+	21097.6i	−0.207310	+	0.874385i
$836$	789.649			0.0326682
$837$		−	22479.0i		−	0.928300i
$838$		−	12588.8i		−	0.518940i
$839$	−19588.7			−0.806050			−0.403025	−	0.915189i	$-0.632041\pi$
$839$	−19588.7			−0.806050			−0.403025	+	0.915189i	$0.632041\pi$
$840$	−482.443	+	2034.83i	−0.0198165	+	0.0835814i
$841$	39898.7			1.63593
$842$			16454.4i			0.673462i
$843$			16509.6i			0.674521i
$844$	21135.3			0.861977
$845$	23865.2	+	5658.26i	0.971584	+	0.230355i
$846$	646.035			0.0262543
$847$			7209.34i			0.292463i
$848$			8462.29i			0.342684i
$849$	−5222.41			−0.211110
$850$	16722.2	+	8401.70i	0.674785	+	0.339031i
$851$	−4597.35			−0.185188
$852$		−	13475.4i		−	0.541855i
$853$		−	35784.6i		−	1.43639i	−0.695842	−	0.718195i	$-0.744969\pi$
$853$		−	35784.6i		−	1.43639i	0.695842	−	0.718195i	$-0.255031\pi$
$854$	2442.71			0.0978781
$855$	2334.22	+	553.427i	0.0933670	+	0.0221366i
$856$	−6200.37			−0.247575
$857$			45368.8i			1.80836i	0.427147	+	0.904182i	$0.359519\pi$
$857$			45368.8i			1.80836i	−0.427147	+	0.904182i	$0.640481\pi$
$858$		−	148.143i		−	0.00589456i
$859$	−12024.2			−0.477604			−0.238802	−	0.971068i	$-0.576755\pi$
$859$	−12024.2			−0.477604			−0.238802	+	0.971068i	$0.576755\pi$
$860$	−2143.54	+	9040.96i	−0.0849932	+	0.358482i
$861$	612.633			0.0242491
$862$			13653.0i			0.539471i
$863$			42287.9i			1.66801i	0.551754	+	0.834007i	$0.313959\pi$
$863$			42287.9i			1.66801i	−0.551754	+	0.834007i	$0.686041\pi$
$864$	4857.82			0.191281
$865$	−4232.87	+	17853.2i	−0.166384	+	0.701767i
$866$	1590.15			0.0623965
$867$			2741.18i			0.107376i
$868$			3488.61i			0.136418i
$869$	7279.97			0.284184
$870$	21899.0	+	5192.10i	0.853387	+	0.202332i
$871$	−96.4717			−0.00375295
$872$			2073.72i			0.0805332i
$873$		−	7483.80i		−	0.290136i
$874$	877.974			0.0339793
$875$	5292.60	−	6304.27i	0.204483	−	0.243569i
$876$	−7018.83			−0.270713
$877$		−	21824.3i		−	0.840311i	−0.907452	−	0.420156i	$-0.861976\pi$
$877$		−	21824.3i		−	0.840311i	0.907452	−	0.420156i	$-0.138024\pi$
$878$			8125.71i			0.312334i
$879$	19889.0			0.763186
$880$	−1800.32	−	426.842i	−0.0689645	−	0.0163510i
$881$	−19684.2			−0.752756			−0.376378	−	0.926466i	$-0.622831\pi$
$881$	−19684.2			−0.752756			−0.376378	+	0.926466i	$0.622831\pi$
$882$			6931.96i			0.264639i
$883$			9507.33i			0.362341i	0.983452	+	0.181170i	$0.0579886\pi$
$883$			9507.33i			0.362341i	−0.983452	+	0.181170i	$0.942011\pi$
$884$	−540.183			−0.0205524
$885$	−1175.84	+	4959.42i	−0.0446615	+	0.188372i
$886$	150.567			0.00570926
$887$		−	25386.6i		−	0.960991i	−0.876997	−	0.480495i	$-0.840457\pi$
$887$		−	25386.6i		−	0.960991i	0.876997	−	0.480495i	$-0.159543\pi$
$888$			6347.77i			0.239884i
$889$	12697.0			0.479014
$890$	3313.58	−	13975.9i	0.124799	−	0.526374i
$891$	3093.50			0.116314
$892$			9886.76i			0.371114i
$893$		−	548.416i		−	0.0205510i
$894$	24063.1			0.900214
$895$	24876.2	+	5897.95i	0.929071	+	0.220276i
$896$	−753.906			−0.0281096
$897$		−	164.714i		−	0.00613114i
$898$			6528.07i			0.242588i
$899$	37544.7			1.39287
$900$	−5022.64	−	2523.51i	−0.186024	−	0.0934635i
$901$	39591.2			1.46390
$902$			542.028i			0.0200084i
$903$			4857.74i			0.179020i
$904$	−2650.06			−0.0974996
$905$	−33866.7	−	8029.53i	−1.24394	−	0.294929i
$906$	−3853.84			−0.141319
$907$		−	44576.2i		−	1.63189i	−0.578127	−	0.815947i	$-0.696216\pi$
$907$		−	44576.2i		−	1.63189i	0.578127	−	0.815947i	$-0.303784\pi$
$908$		−	5394.26i		−	0.197153i
$909$	−4288.12			−0.156467
$910$	−54.8131	+	231.189i	−0.00199674	+	0.00842179i
$911$	5820.92			0.211697			0.105848	−	0.994382i	$-0.466244\pi$
$911$	5820.92			0.211697			0.105848	+	0.994382i	$0.466244\pi$
$912$		−	1212.26i		−	0.0440153i
$913$		−	3552.24i		−	0.128764i
$914$	−2166.06			−0.0783881
$915$	2123.17	−	8955.02i	0.0767101	−	0.323545i
$916$	14722.9			0.531068
$917$			4656.43i			0.167687i
$918$		−	22727.5i		−	0.817125i
$919$	33134.8			1.18935			0.594677	−	0.803965i	$-0.297280\pi$
$919$	33134.8			1.18935			0.594677	+	0.803965i	$0.297280\pi$
$920$	−2001.69	−	474.586i	−0.0717324	−	0.0170072i
$921$	−22502.3			−0.805078
$922$		−	6176.44i		−	0.220619i
$923$		−	1531.02i		−	0.0545981i
$924$	−967.319			−0.0344399
$925$	11217.2	−	22326.1i	0.398725	−	0.793596i
$926$	−23942.2			−0.849665
$927$			49.7718i			0.00176345i
$928$			8113.61i			0.287007i
$929$	8140.79			0.287504			0.143752	−	0.989614i	$-0.454083\pi$
$929$	8140.79			0.287504			0.143752	+	0.989614i	$0.454083\pi$
$930$	12789.3	+	3032.24i	0.450943	+	0.106915i
$931$	5884.51			0.207150
$932$			12466.6i			0.438151i
$933$			11687.6i			0.410111i
$934$	2896.78			0.101483
$935$	−1997.00	+	8422.89i	−0.0698492	+	0.294607i
$936$	162.248			0.00566586
$937$		−	26813.4i		−	0.934850i	−0.884033	−	0.467425i	$-0.845182\pi$
$937$		−	26813.4i		−	0.934850i	0.884033	−	0.467425i	$-0.154818\pi$
$938$			629.922i			0.0219272i
$939$	17803.1			0.618725
$940$	−296.444	+	1250.33i	−0.0102861	+	0.0433844i
$941$	−9639.89			−0.333955			−0.166977	−	0.985961i	$-0.553401\pi$
$941$	−9639.89			−0.333955			−0.166977	+	0.985961i	$0.553401\pi$
$942$			21420.4i			0.740885i
$943$			602.655i			0.0208114i
$944$	−1837.47			−0.0633522
$945$	−9726.98	−	2306.19i	−0.334834	−	0.0793867i
$946$	−4297.90			−0.147713
$947$			18265.7i			0.626775i	0.949625	+	0.313387i	$0.101464\pi$
$947$			18265.7i			0.626775i	−0.949625	+	0.313387i	$0.898536\pi$
$948$		−	11176.1i		−	0.382894i
$949$	−797.448			−0.0272774
$950$	−2142.20	+	4263.70i	−0.0731601	+	0.145613i
$951$	20684.9			0.705315
$952$			3527.18i			0.120081i
$953$		−	12095.3i		−	0.411127i	−0.978644	−	0.205564i	$-0.934097\pi$
$953$		−	12095.3i		−	0.411127i	0.978644	−	0.205564i	$-0.0659027\pi$
$954$	−11891.5			−0.403566
$955$	47477.7	+	11256.6i	1.60874	+	0.381419i
$956$	−19336.1			−0.654158
$957$			10410.4i			0.351640i
$958$		−	35787.0i		−	1.20691i
$959$	16301.1			0.548895
$960$	−655.283	+	2763.83i	−0.0220304	+	0.0929190i
$961$	−7864.46			−0.263988
$962$			721.206i			0.0241711i
$963$		−	8712.99i		−	0.291560i
$964$	5400.16			0.180423
$965$	2149.07	−	9064.29i	0.0716903	−	0.302373i
$966$	−1075.52			−0.0358221
$967$		−	30934.3i		−	1.02873i	−0.857572	−	0.514364i	$-0.828028\pi$
$967$		−	30934.3i		−	1.02873i	0.857572	−	0.514364i	$-0.171972\pi$
$968$			9792.16i			0.325136i
$969$	−5671.61			−0.188027
$970$	14484.1	+	3434.07i	0.479440	+	0.113672i
$971$	27951.5			0.923797			0.461899	−	0.886933i	$-0.347168\pi$
$971$	27951.5			0.923797			0.461899	+	0.886933i	$0.347168\pi$
$972$			11646.0i			0.384307i
$973$			12631.0i			0.416167i
$974$	−38118.5			−1.25400
$975$	799.898	+	401.891i	0.0262741	+	0.0132008i
$976$	3317.84			0.108813
$977$		−	4883.24i		−	0.159907i	−0.996799	−	0.0799533i	$-0.974523\pi$
$977$		−	4883.24i		−	0.159907i	0.996799	−	0.0799533i	$-0.0254771\pi$
$978$			7672.67i			0.250864i
$979$	6643.87			0.216894
$980$	−13416.1	−	3180.85i	−0.437307	−	0.103682i
$981$	−2914.07			−0.0948409
$982$			17831.4i			0.579452i
$983$			26472.1i			0.858932i	0.903083	+	0.429466i	$0.141298\pi$
$983$			26472.1i			0.858932i	−0.903083	+	0.429466i	$0.858702\pi$
$984$	832.115			0.0269582
$985$	−1915.82	+	8080.48i	−0.0619727	+	0.261386i
$986$	37959.9			1.22605
$987$			671.808i			0.0216655i
$988$		−	137.732i		−	0.00443505i
$989$	−4778.63			−0.153642
$990$	599.815	−	2529.88i	0.0192559	−	0.0812170i
$991$	−61862.2			−1.98297			−0.991483	−	0.130237i	$-0.958426\pi$
$991$	−61862.2			−1.98297			−0.991483	+	0.130237i	$0.958426\pi$
$992$			4738.44i			0.151659i
$993$		−	8909.92i		−	0.284741i
$994$	−9996.95			−0.318998
$995$	−6967.87	−	1652.03i	−0.222006	−	0.0526360i
$996$	−5453.35			−0.173490
$997$		−	42340.9i		−	1.34498i	−0.740104	−	0.672492i	$-0.765224\pi$
$997$		−	42340.9i		−	1.34498i	0.740104	−	0.672492i	$-0.234776\pi$
$998$		−	14234.6i		−	0.451492i
$999$	−30343.9			−0.960998

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.4.b.a.139.9	yes	14
5.2	odd	4		1150.4.a.y.1.2		7
5.3	odd	4		1150.4.a.z.1.6		7
5.4	even	2	inner	230.4.b.a.139.6	✓	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.4.b.a.139.6	✓	14	5.4	even	2	inner
230.4.b.a.139.9	yes	14	1.1	even	1	trivial
1150.4.a.y.1.2		7	5.2	odd	4
1150.4.a.z.1.6		7	5.3	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:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	230.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+2.00000i q^{2} -3.96965i q^{3} -4.00000 q^{4} +(10.8788 + 2.57927i) q^{5} +7.93930 q^{6} -5.88989i q^{7} -8.00000i q^{8} +11.2419 q^{9} +O(q^{10})\)	\(q+2.00000i q^{2} -3.96965i q^{3} -4.00000 q^{4} +(10.8788 + 2.57927i) q^{5} +7.93930 q^{6} -5.88989i q^{7} -8.00000i q^{8} +11.2419 q^{9} +(-5.15854 + 21.7575i) q^{10} -10.3431 q^{11} +15.8786i q^{12} +1.80406i q^{13} +11.7798 q^{14} +(10.2388 - 43.1848i) q^{15} +16.0000 q^{16} -74.8568i q^{17} +22.4838i q^{18} +19.0864 q^{19} +(-43.5150 - 10.3171i) q^{20} -23.3808 q^{21} -20.6862i q^{22} -23.0000i q^{23} -31.7572 q^{24} +(111.695 + 56.1185i) q^{25} -3.60811 q^{26} -151.807i q^{27} +23.5596i q^{28} +253.550 q^{29} +(86.3697 + 20.4776i) q^{30} +148.076 q^{31} +32.0000i q^{32} +41.0585i q^{33} +149.714 q^{34} +(15.1916 - 64.0747i) q^{35} -44.9676 q^{36} -199.885i q^{37} +38.1728i q^{38} +7.16147 q^{39} +(20.6342 - 87.0301i) q^{40} -26.2024 q^{41} -46.7616i q^{42} -207.766i q^{43} +41.3724 q^{44} +(122.298 + 28.9959i) q^{45} +46.0000 q^{46} -28.7333i q^{47} -63.5144i q^{48} +308.309 q^{49} +(-112.237 + 223.389i) q^{50} -297.155 q^{51} -7.21622i q^{52} +528.893i q^{53} +303.614 q^{54} +(-112.520 - 26.6776i) q^{55} -47.1191 q^{56} -75.7662i q^{57} +507.100i q^{58} -114.842 q^{59} +(-40.9552 + 172.739i) q^{60} +207.365 q^{61} +296.152i q^{62} -66.2135i q^{63} -64.0000 q^{64} +(-4.65315 + 19.6259i) q^{65} -82.1169 q^{66} +53.4749i q^{67} +299.427i q^{68} -91.3019 q^{69} +(128.149 + 30.3832i) q^{70} -848.654 q^{71} -89.9352i q^{72} +442.031i q^{73} +399.769 q^{74} +(222.771 - 443.389i) q^{75} -76.3455 q^{76} +60.9197i q^{77} +14.3229i q^{78} -703.848 q^{79} +(174.060 + 41.2683i) q^{80} -299.089 q^{81} -52.4048i q^{82} +343.440i q^{83} +93.5231 q^{84} +(193.076 - 814.349i) q^{85} +415.533 q^{86} -1006.50i q^{87} +82.7448i q^{88} -642.348 q^{89} +(-57.9918 + 244.596i) q^{90} +10.6257 q^{91} +92.0000i q^{92} -587.810i q^{93} +57.4667 q^{94} +(207.636 + 49.2290i) q^{95} +127.029 q^{96} -665.706i q^{97} +616.618i q^{98} -116.276 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 56 q^{4} - 6 q^{5} - 36 q^{6} - 68 q^{9}+O(q^{10}) \) 14 * q - 56 * q^4 - 6 * q^5 - 36 * q^6 - 68 * q^9	\( 14 q - 56 q^{4} - 6 q^{5} - 36 q^{6} - 68 q^{9} - 40 q^{10} - 146 q^{11} + 176 q^{14} - 206 q^{15} + 224 q^{16} + 154 q^{19} + 24 q^{20} - 220 q^{21} + 144 q^{24} - 286 q^{25} - 180 q^{26} + 790 q^{29} - 232 q^{30} - 320 q^{31} - 200 q^{34} - 426 q^{35} + 272 q^{36} + 1616 q^{39} + 160 q^{40} - 1904 q^{41} + 584 q^{44} + 622 q^{45} + 644 q^{46} + 610 q^{49} + 200 q^{50} - 1834 q^{51} + 192 q^{54} + 854 q^{55} - 704 q^{56} + 2814 q^{59} + 824 q^{60} - 3742 q^{61} - 896 q^{64} + 1730 q^{65} - 612 q^{66} + 414 q^{69} + 348 q^{70} - 3808 q^{71} + 268 q^{74} + 2904 q^{75} - 616 q^{76} - 1528 q^{79} - 96 q^{80} - 4618 q^{81} + 880 q^{84} + 2574 q^{85} - 2024 q^{86} + 2336 q^{89} + 2092 q^{90} - 3866 q^{91} + 456 q^{94} + 838 q^{95} - 576 q^{96} + 3342 q^{99}+O(q^{100}) \) 14 * q - 56 * q^4 - 6 * q^5 - 36 * q^6 - 68 * q^9 - 40 * q^10 - 146 * q^11 + 176 * q^14 - 206 * q^15 + 224 * q^16 + 154 * q^19 + 24 * q^20 - 220 * q^21 + 144 * q^24 - 286 * q^25 - 180 * q^26 + 790 * q^29 - 232 * q^30 - 320 * q^31 - 200 * q^34 - 426 * q^35 + 272 * q^36 + 1616 * q^39 + 160 * q^40 - 1904 * q^41 + 584 * q^44 + 622 * q^45 + 644 * q^46 + 610 * q^49 + 200 * q^50 - 1834 * q^51 + 192 * q^54 + 854 * q^55 - 704 * q^56 + 2814 * q^59 + 824 * q^60 - 3742 * q^61 - 896 * q^64 + 1730 * q^65 - 612 * q^66 + 414 * q^69 + 348 * q^70 - 3808 * q^71 + 268 * q^74 + 2904 * q^75 - 616 * q^76 - 1528 * q^79 - 96 * q^80 - 4618 * q^81 + 880 * q^84 + 2574 * q^85 - 2024 * q^86 + 2336 * q^89 + 2092 * q^90 - 3866 * q^91 + 456 * q^94 + 838 * q^95 - 576 * q^96 + 3342 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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