LMFDB - Embedded newform 1050.3.c.b.449.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1050,3,Mod(449,1050)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1050, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("1050.449");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	1050.c (of order $2$, degree $1$, not 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:	$28.6104277578$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			449.12
Character	$\chi$	$=$	1050.449
Dual form			1050.3.c.b.449.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.41421 q^{2} +(2.24820 + 1.98636i) q^{3} +2.00000 q^{4} +(-3.17943 - 2.80913i) q^{6} +2.64575i q^{7} -2.82843 q^{8} +(1.10878 + 8.93144i) q^{9} +O(q^{10})$	\(q-1.41421 q^{2} +(2.24820 + 1.98636i) q^{3} +2.00000 q^{4} +(-3.17943 - 2.80913i) q^{6} +2.64575i q^{7} -2.82843 q^{8} +(1.10878 + 8.93144i) q^{9} -12.4599i q^{11} +(4.49639 + 3.97271i) q^{12} +2.47926i q^{13} -3.74166i q^{14} +4.00000 q^{16} +3.20137 q^{17} +(-1.56805 - 12.6310i) q^{18} +8.55673 q^{19} +(-5.25540 + 5.94817i) q^{21} +17.6209i q^{22} +34.1813 q^{23} +(-6.35886 - 5.61826i) q^{24} -3.50620i q^{26} +(-15.2483 + 22.2821i) q^{27} +5.29150i q^{28} -12.2244i q^{29} +15.9972 q^{31} -5.65685 q^{32} +(24.7498 - 28.0123i) q^{33} -4.52742 q^{34} +(2.21756 + 17.8629i) q^{36} +64.7939i q^{37} -12.1010 q^{38} +(-4.92468 + 5.57385i) q^{39} +57.2669i q^{41} +(7.43226 - 8.41198i) q^{42} +6.52459i q^{43} -24.9198i q^{44} -48.3396 q^{46} +35.0960 q^{47} +(8.99279 + 7.94542i) q^{48} -7.00000 q^{49} +(7.19731 + 6.35906i) q^{51} +4.95851i q^{52} +68.4964 q^{53} +(21.5643 - 31.5116i) q^{54} -7.48331i q^{56} +(19.2372 + 16.9967i) q^{57} +17.2879i q^{58} -31.3955i q^{59} -114.931 q^{61} -22.6235 q^{62} +(-23.6304 + 2.93356i) q^{63} +8.00000 q^{64} +(-35.0014 + 39.6153i) q^{66} +115.213i q^{67} +6.40274 q^{68} +(76.8463 + 67.8962i) q^{69} -14.3641i q^{71} +(-3.13610 - 25.2619i) q^{72} -1.78508i q^{73} -91.6324i q^{74} +17.1135 q^{76} +32.9657 q^{77} +(6.96455 - 7.88262i) q^{78} +16.1159 q^{79} +(-78.5412 + 19.8060i) q^{81} -80.9876i q^{82} +90.7978 q^{83} +(-10.5108 + 11.8963i) q^{84} -9.22717i q^{86} +(24.2820 - 27.4829i) q^{87} +35.2419i q^{88} +1.88927i q^{89} -6.55949 q^{91} +68.3626 q^{92} +(35.9649 + 31.7762i) q^{93} -49.6332 q^{94} +(-12.7177 - 11.2365i) q^{96} -106.996i q^{97} +9.89949 q^{98} +(111.285 - 13.8153i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 64 q^{4} - 16 q^{6} - 16 q^{9}+O(q^{10}) $ 32 * q + 64 * q^4 - 16 * q^6 - 16 * q^9	$ 32 q + 64 q^{4} - 16 q^{6} - 16 q^{9} + 128 q^{16} + 48 q^{19} + 56 q^{21} - 32 q^{24} + 48 q^{31} + 256 q^{34} - 32 q^{36} + 192 q^{39} + 160 q^{46} - 224 q^{49} + 288 q^{51} - 80 q^{54} - 112 q^{61} + 256 q^{64} - 192 q^{66} + 344 q^{69} + 96 q^{76} - 256 q^{79} + 160 q^{81} + 112 q^{84} - 448 q^{91} + 416 q^{94} - 64 q^{96} - 304 q^{99}+O(q^{100}) $ 32 * q + 64 * q^4 - 16 * q^6 - 16 * q^9 + 128 * q^16 + 48 * q^19 + 56 * q^21 - 32 * q^24 + 48 * q^31 + 256 * q^34 - 32 * q^36 + 192 * q^39 + 160 * q^46 - 224 * q^49 + 288 * q^51 - 80 * q^54 - 112 * q^61 + 256 * q^64 - 192 * q^66 + 344 * q^69 + 96 * q^76 - 256 * q^79 + 160 * q^81 + 112 * q^84 - 448 * q^91 + 416 * q^94 - 64 * q^96 - 304 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times$.

$n$	$127$	$451$	$701$
$\chi(n)$	$-1$	$1$	$-1$

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 $

$2$	−1.41421			−0.707107
$2$	−1.41421			−0.707107
$3$	2.24820	+	1.98636i	0.749399	+	0.662119i
$3$	2.24820	+	1.98636i	0.749399	+	0.662119i
$4$	2.00000			0.500000
$5$		0			0
$5$		0			0
$6$	−3.17943	−	2.80913i	−0.529905	−	0.468189i
$7$			2.64575i			0.377964i
$7$			2.64575i			0.377964i
$8$	−2.82843			−0.353553
$9$	1.10878	+	8.93144i	0.123198	+	0.992382i
$10$		0			0
$11$		−	12.4599i		−	1.13272i	−0.824159	−	0.566358i	$-0.808352\pi$
$11$		−	12.4599i		−	1.13272i	0.824159	−	0.566358i	$-0.191648\pi$
$12$	4.49639	+	3.97271i	0.374700	+	0.331059i
$13$			2.47926i			0.190712i	0.995443	+	0.0953560i	$0.0303989\pi$
$13$			2.47926i			0.190712i	−0.995443	+	0.0953560i	$0.969601\pi$
$14$		−	3.74166i		−	0.267261i
$15$		0			0
$16$	4.00000			0.250000
$17$	3.20137			0.188316			0.0941580	−	0.995557i	$-0.469984\pi$
$17$	3.20137			0.188316			0.0941580	+	0.995557i	$0.469984\pi$
$18$	−1.56805	−	12.6310i	−0.0871140	−	0.701720i
$19$	8.55673			0.450354			0.225177	−	0.974318i	$-0.427704\pi$
$19$	8.55673			0.450354			0.225177	+	0.974318i	$0.427704\pi$
$20$		0			0
$21$	−5.25540	+	5.94817i	−0.250257	+	0.283246i
$22$			17.6209i			0.800951i
$23$	34.1813			1.48614			0.743072	−	0.669212i	$-0.233368\pi$
$23$	34.1813			1.48614			0.743072	+	0.669212i	$0.233368\pi$
$24$	−6.35886	−	5.61826i	−0.264953	−	0.234094i
$25$		0			0
$26$		−	3.50620i		−	0.134854i
$27$	−15.2483	+	22.2821i	−0.564750	+	0.825262i
$28$			5.29150i			0.188982i
$29$		−	12.2244i		−	0.421532i	−0.977537	−	0.210766i	$-0.932404\pi$
$29$		−	12.2244i		−	0.421532i	0.977537	−	0.210766i	$-0.0675957\pi$
$30$		0			0
$31$	15.9972			0.516040			0.258020	−	0.966140i	$-0.416930\pi$
$31$	15.9972			0.516040			0.258020	+	0.966140i	$0.416930\pi$
$32$	−5.65685			−0.176777
$33$	24.7498	−	28.0123i	0.749992	−	0.848856i
$34$	−4.52742			−0.133159
$35$		0			0
$36$	2.21756	+	17.8629i	0.0615989	+	0.496191i
$37$			64.7939i			1.75119i	0.483050	+	0.875593i	$0.339529\pi$
$37$			64.7939i			1.75119i	−0.483050	+	0.875593i	$0.660471\pi$
$38$	−12.1010			−0.318448
$39$	−4.92468	+	5.57385i	−0.126274	+	0.142919i
$40$		0			0
$41$			57.2669i			1.39675i	0.715730	+	0.698377i	$0.246094\pi$
$41$			57.2669i			1.39675i	−0.715730	+	0.698377i	$0.753906\pi$
$42$	7.43226	−	8.41198i	0.176959	−	0.200285i
$43$			6.52459i			0.151735i	0.997118	+	0.0758674i	$0.0241726\pi$
$43$			6.52459i			0.151735i	−0.997118	+	0.0758674i	$0.975827\pi$
$44$		−	24.9198i		−	0.566358i
$45$		0			0
$46$	−48.3396			−1.05086
$47$	35.0960			0.746722			0.373361	−	0.927686i	$-0.378205\pi$
$47$	35.0960			0.746722			0.373361	+	0.927686i	$0.378205\pi$
$48$	8.99279	+	7.94542i	0.187350	+	0.165530i
$49$	−7.00000			−0.142857
$50$		0			0
$51$	7.19731	+	6.35906i	0.141124	+	0.124687i
$52$			4.95851i			0.0953560i
$53$	68.4964			1.29238			0.646192	−	0.763175i	$-0.276360\pi$
$53$	68.4964			1.29238			0.646192	+	0.763175i	$0.276360\pi$
$54$	21.5643	−	31.5116i	0.399339	−	0.583548i
$55$		0			0
$56$		−	7.48331i		−	0.133631i
$57$	19.2372	+	16.9967i	0.337495	+	0.298188i
$58$			17.2879i			0.298068i
$59$		−	31.3955i		−	0.532126i	−0.963956	−	0.266063i	$-0.914277\pi$
$59$		−	31.3955i		−	0.532126i	0.963956	−	0.266063i	$-0.0857230\pi$
$60$		0			0
$61$	−114.931			−1.88411			−0.942055	−	0.335459i	$-0.891109\pi$
$61$	−114.931			−1.88411			−0.942055	+	0.335459i	$0.891109\pi$
$62$	−22.6235			−0.364895
$63$	−23.6304	+	2.93356i	−0.375085	+	0.0465644i
$64$	8.00000			0.125000
$65$		0			0
$66$	−35.0014	+	39.6153i	−0.530325	+	0.600232i
$67$			115.213i			1.71960i	0.510633	+	0.859799i	$0.329411\pi$
$67$			115.213i			1.71960i	−0.510633	+	0.859799i	$0.670589\pi$
$68$	6.40274			0.0941580
$69$	76.8463	+	67.8962i	1.11371	+	0.984003i
$70$		0			0
$71$		−	14.3641i		−	0.202311i	−0.994871	−	0.101156i	$-0.967746\pi$
$71$		−	14.3641i		−	0.202311i	0.994871	−	0.101156i	$-0.0322540\pi$
$72$	−3.13610	−	25.2619i	−0.0435570	−	0.350860i
$73$		−	1.78508i		−	0.0244532i	−0.999925	−	0.0122266i	$-0.996108\pi$
$73$		−	1.78508i		−	0.0244532i	0.999925	−	0.0122266i	$-0.00389194\pi$
$74$		−	91.6324i		−	1.23828i
$75$		0			0
$76$	17.1135			0.225177
$77$	32.9657			0.428126
$78$	6.96455	−	7.88262i	0.0892891	−	0.101059i
$79$	16.1159			0.203998			0.101999	−	0.994784i	$-0.467476\pi$
$79$	16.1159			0.203998			0.101999	+	0.994784i	$0.467476\pi$
$80$		0			0
$81$	−78.5412	+	19.8060i	−0.969645	+	0.244519i
$82$		−	80.9876i		−	0.987654i
$83$	90.7978			1.09395			0.546975	−	0.837149i	$-0.315779\pi$
$83$	90.7978			1.09395			0.546975	+	0.837149i	$0.315779\pi$
$84$	−10.5108	+	11.8963i	−0.125129	+	0.141623i
$85$		0			0
$86$		−	9.22717i		−	0.107293i
$87$	24.2820	−	27.4829i	0.279104	−	0.315895i
$88$			35.2419i			0.400476i
$89$			1.88927i			0.0212278i	0.999944	+	0.0106139i	$0.00337857\pi$
$89$			1.88927i			0.0212278i	−0.999944	+	0.0106139i	$0.996621\pi$
$90$		0			0
$91$	−6.55949			−0.0720823
$92$	68.3626			0.743072
$93$	35.9649	+	31.7762i	0.386720	+	0.341680i
$94$	−49.6332			−0.528012
$95$		0			0
$96$	−12.7177	−	11.2365i	−0.132476	−	0.117047i
$97$		−	106.996i		−	1.10305i	−0.834158	−	0.551525i	$-0.814046\pi$
$97$		−	106.996i		−	1.10305i	0.834158	−	0.551525i	$-0.185954\pi$
$98$	9.89949			0.101015
$99$	111.285	−	13.8153i	1.12409	−	0.139548i
$100$		0			0
$101$			79.6009i			0.788127i	0.919083	+	0.394064i	$0.128931\pi$
$101$			79.6009i			0.788127i	−0.919083	+	0.394064i	$0.871069\pi$
$102$	−10.1785	−	8.99307i	−0.0997896	−	0.0881674i
$103$			11.3495i			0.110189i	0.998481	+	0.0550947i	$0.0175461\pi$
$103$			11.3495i			0.110189i	−0.998481	+	0.0550947i	$0.982454\pi$
$104$		−	7.01239i		−	0.0674268i
$105$		0			0
$106$	−96.8685			−0.913854
$107$	−34.2787			−0.320362			−0.160181	−	0.987088i	$-0.551208\pi$
$107$	−34.2787			−0.320362			−0.160181	+	0.987088i	$0.551208\pi$
$108$	−30.4965	+	44.5641i	−0.282375	+	0.412631i
$109$	−163.422			−1.49928			−0.749642	−	0.661844i	$-0.769774\pi$
$109$	−163.422			−1.49928			−0.749642	+	0.661844i	$0.769774\pi$
$110$		0			0
$111$	−128.704	+	145.669i	−1.15949	+	1.31234i
$112$			10.5830i			0.0944911i
$113$	38.1104			0.337260			0.168630	−	0.985679i	$-0.446066\pi$
$113$	38.1104			0.337260			0.168630	+	0.985679i	$0.446066\pi$
$114$	−27.2055	−	24.0370i	−0.238645	−	0.210851i
$115$		0			0
$116$		−	24.4488i		−	0.210766i
$117$	−22.1433	+	2.74895i	−0.189259	+	0.0234953i
$118$			44.3999i			0.376270i
$119$			8.47003i			0.0711767i
$120$		0			0
$121$	−34.2485			−0.283046
$122$	162.537			1.33227
$123$	−113.752	+	128.747i	−0.924817	+	1.04673i
$124$	31.9945			0.258020
$125$		0			0
$126$	33.4184	−	4.14868i	0.265225	−	0.0329260i
$127$			18.5686i			0.146209i	0.997324	+	0.0731047i	$0.0232907\pi$
$127$			18.5686i			0.146209i	−0.997324	+	0.0731047i	$0.976709\pi$
$128$	−11.3137			−0.0883883
$129$	−12.9602	+	14.6686i	−0.100466	+	0.113710i
$130$		0			0
$131$		−	46.8032i		−	0.357276i	−0.983915	−	0.178638i	$-0.942831\pi$
$131$		−	46.8032i		−	0.357276i	0.983915	−	0.178638i	$-0.0571692\pi$
$132$	49.4995	−	56.0245i	0.374996	−	0.424428i
$133$			22.6390i			0.170218i
$134$		−	162.936i		−	1.21594i
$135$		0			0
$136$	−9.05484			−0.0665797
$137$	−121.470			−0.886642			−0.443321	−	0.896363i	$-0.646200\pi$
$137$	−121.470			−0.886642			−0.443321	+	0.896363i	$0.646200\pi$
$138$	−108.677	−	96.0197i	−0.787515	−	0.695795i
$139$	20.6274			0.148399			0.0741994	−	0.997243i	$-0.476360\pi$
$139$	20.6274			0.148399			0.0741994	+	0.997243i	$0.476360\pi$
$140$		0			0
$141$	78.9026	+	69.7131i	0.559593	+	0.494419i
$142$			20.3139i			0.143056i
$143$	30.8912			0.216022
$144$	4.43512	+	35.7258i	0.0307994	+	0.248096i
$145$		0			0
$146$			2.52449i			0.0172910i
$147$	−15.7374	−	13.9045i	−0.107057	−	0.0945884i
$148$			129.588i			0.875593i
$149$		−	75.6888i		−	0.507979i	−0.967207	−	0.253989i	$-0.918257\pi$
$149$		−	75.6888i		−	0.507979i	0.967207	−	0.253989i	$-0.0817428\pi$
$150$		0			0
$151$	83.7633			0.554724			0.277362	−	0.960766i	$-0.410540\pi$
$151$	83.7633			0.554724			0.277362	+	0.960766i	$0.410540\pi$
$152$	−24.2021			−0.159224
$153$	3.54962	+	28.5928i	0.0232001	+	0.186881i
$154$	−46.6206			−0.302731
$155$		0			0
$156$	−9.84937	+	11.1477i	−0.0631370	+	0.0714597i
$157$			257.274i			1.63869i	0.573301	+	0.819345i	$0.305662\pi$
$157$			257.274i			1.63869i	−0.573301	+	0.819345i	$0.694338\pi$
$158$	−22.7913			−0.144249
$159$	153.993	+	136.058i	0.968512	+	0.855712i
$160$		0			0
$161$			90.4352i			0.561709i
$162$	111.074	−	28.0099i	0.685642	−	0.172901i
$163$			285.043i			1.74873i	0.485269	+	0.874365i	$0.338722\pi$
$163$			285.043i			1.74873i	−0.485269	+	0.874365i	$0.661278\pi$
$164$			114.534i			0.698377i
$165$		0			0
$166$	−128.407			−0.773539
$167$	−144.183			−0.863368			−0.431684	−	0.902025i	$-0.642081\pi$
$167$	−144.183			−0.863368			−0.431684	+	0.902025i	$0.642081\pi$
$168$	14.8645	−	16.8240i	0.0884793	−	0.100143i
$169$	162.853			0.963629
$170$		0			0
$171$	9.48753	+	76.4239i	0.0554826	+	0.446923i
$172$			13.0492i			0.0758674i
$173$	132.180			0.764047			0.382024	−	0.924153i	$-0.375227\pi$
$173$	132.180			0.764047			0.382024	+	0.924153i	$0.375227\pi$
$174$	−34.3400	+	38.8667i	−0.197356	+	0.223372i
$175$		0			0
$176$		−	49.8395i		−	0.283179i
$177$	62.3625	−	70.5832i	0.352331	−	0.398775i
$178$		−	2.67183i		−	0.0150103i
$179$			208.636i			1.16557i	0.812628	+	0.582783i	$0.198036\pi$
$179$			208.636i			1.16557i	−0.812628	+	0.582783i	$0.801964\pi$
$180$		0			0
$181$	179.829			0.993528			0.496764	−	0.867886i	$-0.334522\pi$
$181$	179.829			0.993528			0.496764	+	0.867886i	$0.334522\pi$
$182$	9.27652			0.0509699
$183$	−258.387	−	228.293i	−1.41195	−	1.24750i
$184$	−96.6793			−0.525431
$185$		0			0
$186$	−50.8621	−	44.9383i	−0.273452	−	0.241604i
$187$		−	39.8887i		−	0.213308i
$188$	70.1919			0.373361
$189$	−58.9528	−	40.3431i	−0.311920	−	0.213456i
$190$		0			0
$191$		−	97.7769i		−	0.511921i	−0.966687	−	0.255960i	$-0.917608\pi$
$191$		−	97.7769i		−	0.511921i	0.966687	−	0.255960i	$-0.0823917\pi$
$192$	17.9856	+	15.8908i	0.0936749	+	0.0827648i
$193$			55.2651i			0.286348i	0.989698	+	0.143174i	$0.0457308\pi$
$193$			55.2651i			0.286348i	−0.989698	+	0.143174i	$0.954269\pi$
$194$			151.315i			0.779975i
$195$		0			0
$196$	−14.0000			−0.0714286
$197$	249.499			1.26649			0.633246	−	0.773951i	$-0.281722\pi$
$197$	249.499			1.26649			0.633246	+	0.773951i	$0.281722\pi$
$198$	−157.380	+	19.5377i	−0.794850	+	0.0986754i
$199$	−101.452			−0.509807			−0.254904	−	0.966966i	$-0.582044\pi$
$199$	−101.452			−0.509807			−0.254904	+	0.966966i	$0.582044\pi$
$200$		0			0
$201$	−228.854	+	259.022i	−1.13858	+	1.28866i
$202$		−	112.573i		−	0.557290i
$203$	32.3428			0.159324
$204$	14.3946	+	12.7181i	0.0705619	+	0.0623437i
$205$		0			0
$206$		−	16.0506i		−	0.0779157i
$207$	37.8995	+	305.288i	0.183090	+	1.47482i
$208$			9.91702i			0.0476780i
$209$		−	106.616i		−	0.510123i
$210$		0			0
$211$	261.848			1.24098			0.620492	−	0.784213i	$-0.286933\pi$
$211$	261.848			1.24098			0.620492	+	0.784213i	$0.286933\pi$
$212$	136.993			0.646192
$213$	28.5322	−	32.2933i	0.133954	−	0.151612i
$214$	48.4775			0.226530
$215$		0			0
$216$	43.1286	−	63.0232i	0.199669	−	0.291774i
$217$			42.3247i			0.195045i
$218$	231.113			1.06015
$219$	3.54581	−	4.01322i	0.0161909	−	0.0183252i
$220$		0			0
$221$			7.93701i			0.0359141i
$222$	182.015	−	206.008i	0.819885	−	0.927962i
$223$		−	120.347i		−	0.539672i	−0.962906	−	0.269836i	$-0.913030\pi$
$223$		−	120.347i		−	0.539672i	0.962906	−	0.269836i	$-0.0869695\pi$
$224$		−	14.9666i		−	0.0668153i
$225$		0			0
$226$	−53.8963			−0.238479
$227$	−338.276			−1.49020			−0.745102	−	0.666951i	$-0.767599\pi$
$227$	−338.276			−1.49020			−0.745102	+	0.666951i	$0.767599\pi$
$228$	38.4744	+	33.9934i	0.168747	+	0.149094i
$229$	427.514			1.86687			0.933436	−	0.358745i	$-0.116795\pi$
$229$	427.514			1.86687			0.933436	+	0.358745i	$0.116795\pi$
$230$		0			0
$231$	74.1135	+	65.4817i	0.320838	+	0.283470i
$232$			34.5759i			0.149034i
$233$	250.445			1.07487			0.537435	−	0.843305i	$-0.319393\pi$
$233$	250.445			1.07487			0.537435	+	0.843305i	$0.319393\pi$
$234$	31.3154	−	3.88760i	0.133826	−	0.0166137i
$235$		0			0
$236$		−	62.7909i		−	0.266063i
$237$	36.2317	+	32.0119i	0.152876	+	0.135071i
$238$		−	11.9784i		−	0.0503295i
$239$		−	47.6780i		−	0.199489i	−0.995013	−	0.0997447i	$-0.968197\pi$
$239$		−	47.6780i		−	0.199489i	0.995013	−	0.0997447i	$-0.0318026\pi$
$240$		0			0
$241$	415.411			1.72370			0.861848	−	0.507167i	$-0.169307\pi$
$241$	415.411			1.72370			0.861848	+	0.507167i	$0.169307\pi$
$242$	48.4347			0.200144
$243$	−215.918	−	111.483i	−0.888551	−	0.458778i
$244$	−229.861			−0.942055
$245$		0			0
$246$	160.870	−	182.076i	0.653944	−	0.740147i
$247$			21.2143i			0.0858879i
$248$	−45.2470			−0.182448
$249$	204.131	+	180.357i	0.819805	+	0.724324i
$250$		0			0
$251$			123.415i			0.491691i	0.969309	+	0.245846i	$0.0790657\pi$
$251$			123.415i			0.491691i	−0.969309	+	0.245846i	$0.920934\pi$
$252$	−47.2607	+	5.86711i	−0.187543	+	0.0232822i
$253$		−	425.895i		−	1.68338i
$254$		−	26.2599i		−	0.103386i
$255$		0			0
$256$	16.0000			0.0625000
$257$	−463.629			−1.80400			−0.902002	−	0.431732i	$-0.857903\pi$
$257$	−463.629			−1.80400			−0.902002	+	0.431732i	$0.857903\pi$
$258$	18.3284	−	20.7445i	0.0710405	−	0.0804050i
$259$	−171.428			−0.661886
$260$		0			0
$261$	109.182	−	13.5542i	0.418320	−	0.0519318i
$262$			66.1897i			0.252633i
$263$	−426.510			−1.62171			−0.810856	−	0.585246i	$-0.800998\pi$
$263$	−426.510			−1.62171			−0.810856	+	0.585246i	$0.800998\pi$
$264$	−70.0029	+	79.2306i	−0.265162	+	0.300116i
$265$		0			0
$266$		−	32.0163i		−	0.120362i
$267$	−3.75277	+	4.24745i	−0.0140553	+	0.0159081i
$268$			230.426i			0.859799i
$269$		−	502.450i		−	1.86784i	−0.357479	−	0.933921i	$-0.616364\pi$
$269$		−	502.450i		−	1.86784i	0.357479	−	0.933921i	$-0.383636\pi$
$270$		0			0
$271$	81.9593			0.302433			0.151216	−	0.988501i	$-0.451681\pi$
$271$	81.9593			0.302433			0.151216	+	0.988501i	$0.451681\pi$
$272$	12.8055			0.0470790
$273$	−14.7470	−	13.0295i	−0.0540184	−	0.0477271i
$274$	171.784			0.626951
$275$		0			0
$276$	153.693	+	135.792i	0.556857	+	0.492002i
$277$			158.868i			0.573531i	0.958001	+	0.286765i	$0.0925800\pi$
$277$			158.868i			0.573531i	−0.958001	+	0.286765i	$0.907420\pi$
$278$	−29.1716			−0.104934
$279$	17.7374	+	142.878i	0.0635750	+	0.512109i
$280$		0			0
$281$		−	221.971i		−	0.789933i	−0.918696	−	0.394966i	$-0.870756\pi$
$281$		−	221.971i		−	0.789933i	0.918696	−	0.394966i	$-0.129244\pi$
$282$	−111.585	−	98.5891i	−0.395692	−	0.349607i
$283$		−	301.727i		−	1.06617i	−0.846060	−	0.533087i	$-0.821032\pi$
$283$		−	301.727i		−	1.06617i	0.846060	−	0.533087i	$-0.178968\pi$
$284$		−	28.7282i		−	0.101156i
$285$		0			0
$286$	−43.6868			−0.152751
$287$	−151.514			−0.527923
$288$	−6.27221	−	50.5238i	−0.0217785	−	0.175430i
$289$	−278.751			−0.964537
$290$		0			0
$291$	212.532	−	240.548i	0.730350	−	0.826625i
$292$		−	3.57017i		−	0.0122266i
$293$	261.561			0.892698			0.446349	−	0.894859i	$-0.352724\pi$
$293$	261.561			0.892698			0.446349	+	0.894859i	$0.352724\pi$
$294$	22.2560	+	19.6639i	0.0757007	+	0.0668841i
$295$		0			0
$296$		−	183.265i		−	0.619138i
$297$	277.632	+	189.991i	0.934787	+	0.639702i
$298$			107.040i			0.359195i
$299$			84.7441i			0.283425i
$300$		0			0
$301$	−17.2625			−0.0573503
$302$	−118.459			−0.392249
$303$	−158.116	+	178.958i	−0.521834	+	0.590622i
$304$	34.2269			0.112588
$305$		0			0
$306$	−5.01991	−	40.4364i	−0.0164050	−	0.132145i
$307$		−	501.884i		−	1.63480i	−0.576069	−	0.817401i	$-0.695414\pi$
$307$		−	501.884i		−	1.63480i	0.576069	−	0.817401i	$-0.304586\pi$
$308$	65.9315			0.214063
$309$	−22.5442	+	25.5159i	−0.0729585	+	0.0825758i
$310$		0			0
$311$		−	494.525i		−	1.59011i	−0.606535	−	0.795056i	$-0.707441\pi$
$311$		−	494.525i		−	1.59011i	0.606535	−	0.795056i	$-0.292559\pi$
$312$	13.9291	−	15.7652i	0.0446446	−	0.0505296i
$313$		−	93.5395i		−	0.298848i	−0.988773	−	0.149424i	$-0.952258\pi$
$313$		−	93.5395i		−	0.298848i	0.988773	−	0.149424i	$-0.0477420\pi$
$314$		−	363.841i		−	1.15873i
$315$		0			0
$316$	32.2318			0.101999
$317$	−630.828			−1.98999			−0.994996	−	0.0999132i	$-0.968143\pi$
$317$	−630.828			−1.98999			−0.994996	+	0.0999132i	$0.968143\pi$
$318$	−217.780	−	192.415i	−0.684841	−	0.605080i
$319$	−152.315			−0.477476
$320$		0			0
$321$	−77.0654	−	68.0898i	−0.240079	−	0.212118i
$322$		−	127.895i		−	0.397188i
$323$	27.3932			0.0848088
$324$	−157.082	+	39.6120i	−0.484822	+	0.122259i
$325$		0			0
$326$		−	403.112i		−	1.23654i
$327$	−367.405	−	324.614i	−1.12356	−	0.992703i
$328$		−	161.975i		−	0.493827i
$329$			92.8552i			0.282235i
$330$		0			0
$331$	7.46596			0.0225558			0.0112779	−	0.999936i	$-0.496410\pi$
$331$	7.46596			0.0225558			0.0112779	+	0.999936i	$0.496410\pi$
$332$	181.596			0.546975
$333$	−578.703	+	71.8422i	−1.73785	+	0.215742i
$334$	203.905			0.610494
$335$		0			0
$336$	−21.0216	+	23.7927i	−0.0625643	+	0.0708116i
$337$			258.147i			0.766015i	0.923745	+	0.383007i	$0.125112\pi$
$337$			258.147i			0.766015i	−0.923745	+	0.383007i	$0.874888\pi$
$338$	−230.309			−0.681389
$339$	85.6797	+	75.7009i	0.252743	+	0.223306i
$340$		0			0
$341$		−	199.324i		−	0.584527i
$342$	−13.4174	−	108.080i	−0.0392321	−	0.316022i
$343$		−	18.5203i		−	0.0539949i
$344$		−	18.4543i		−	0.0536463i
$345$		0			0
$346$	−186.931			−0.540263
$347$	−249.954			−0.720329			−0.360164	−	0.932889i	$-0.617279\pi$
$347$	−249.954			−0.720329			−0.360164	+	0.932889i	$0.617279\pi$
$348$	48.5641	−	54.9658i	0.139552	−	0.157948i
$349$	−260.211			−0.745590			−0.372795	−	0.927914i	$-0.621601\pi$
$349$	−260.211			−0.745590			−0.372795	+	0.927914i	$0.621601\pi$
$350$		0			0
$351$	−55.2429	−	37.8043i	−0.157387	−	0.107705i
$352$			70.4837i			0.200238i
$353$	596.278			1.68917			0.844587	−	0.535419i	$-0.179846\pi$
$353$	596.278			1.68917			0.844587	+	0.535419i	$0.179846\pi$
$354$	−88.1940	+	99.8197i	−0.249135	+	0.281976i
$355$		0			0
$356$			3.77854i			0.0106139i
$357$	−16.8245	+	19.0423i	−0.0471274	+	0.0533398i
$358$		−	295.056i		−	0.824180i
$359$			547.426i			1.52486i	0.647068	+	0.762432i	$0.275995\pi$
$359$			547.426i			1.52486i	−0.647068	+	0.762432i	$0.724005\pi$
$360$		0			0
$361$	−287.782			−0.797181
$362$	−254.316			−0.702530
$363$	−76.9974	−	68.0298i	−0.212114	−	0.187410i
$364$	−13.1190			−0.0360412
$365$		0			0
$366$	365.414	+	322.855i	0.998399	+	0.882119i
$367$		−	257.617i		−	0.701954i	−0.936384	−	0.350977i	$-0.885850\pi$
$367$		−	257.617i		−	0.701954i	0.936384	−	0.350977i	$-0.114150\pi$
$368$	136.725			0.371536
$369$	−511.476	+	63.4964i	−1.38611	+	0.172077i
$370$		0			0
$371$			181.224i			0.488476i
$372$	71.9299	+	63.5524i	0.193360	+	0.170840i
$373$		−	594.804i		−	1.59465i	−0.603551	−	0.797325i	$-0.706248\pi$
$373$		−	594.804i		−	1.59465i	0.603551	−	0.797325i	$-0.293752\pi$
$374$			56.4111i			0.150832i
$375$		0			0
$376$	−99.2663			−0.264006
$377$	30.3074			0.0803911
$378$	83.3719	+	57.0538i	0.220560	+	0.150936i
$379$	533.207			1.40688			0.703439	−	0.710756i	$-0.251647\pi$
$379$	533.207			1.40688			0.703439	+	0.710756i	$0.251647\pi$
$380$		0			0
$381$	−36.8838	+	41.7458i	−0.0968079	+	0.109569i
$382$			138.277i			0.361983i
$383$	−76.1257			−0.198762			−0.0993808	−	0.995049i	$-0.531686\pi$
$383$	−76.1257			−0.198762			−0.0993808	+	0.995049i	$0.531686\pi$
$384$	−25.4354	−	22.4731i	−0.0662381	−	0.0585236i
$385$		0			0
$386$		−	78.1567i		−	0.202479i
$387$	−58.2740	+	7.23434i	−0.150579	+	0.0186934i
$388$		−	213.992i		−	0.551525i
$389$		−	661.924i		−	1.70160i	−0.525486	−	0.850802i	$-0.676116\pi$
$389$		−	661.924i		−	1.70160i	0.525486	−	0.850802i	$-0.323884\pi$
$390$		0			0
$391$	109.427			0.279864
$392$	19.7990			0.0505076
$393$	92.9678	−	105.223i	0.236559	−	0.267743i
$394$	−352.845			−0.895545
$395$		0			0
$396$	222.569	−	27.6305i	0.562044	−	0.0697741i
$397$		−	710.566i		−	1.78984i	−0.446227	−	0.894920i	$-0.647233\pi$
$397$		−	710.566i		−	1.78984i	0.446227	−	0.894920i	$-0.352767\pi$
$398$	143.474			0.360488
$399$	−44.9690	+	50.8969i	−0.112704	+	0.127561i
$400$		0			0
$401$		−	443.448i		−	1.10586i	−0.833229	−	0.552928i	$-0.813511\pi$
$401$		−	443.448i		−	1.10586i	0.833229	−	0.552928i	$-0.186489\pi$
$402$	323.649	−	366.312i	0.805096	−	0.911223i
$403$			39.6612i			0.0984149i
$404$			159.202i			0.394064i
$405$		0			0
$406$	−45.7396			−0.112659
$407$	807.324			1.98360
$408$	−20.3571	−	17.9861i	−0.0498948	−	0.0440837i
$409$	−337.790			−0.825893			−0.412946	−	0.910755i	$-0.635500\pi$
$409$	−337.790			−0.825893			−0.412946	+	0.910755i	$0.635500\pi$
$410$		0			0
$411$	−273.088	−	241.283i	−0.664449	−	0.587062i
$412$			22.6990i			0.0550947i
$413$	83.0646			0.201125
$414$	−53.5980	−	431.743i	−0.129464	−	1.04286i
$415$		0			0
$416$		−	14.0248i		−	0.0337134i
$417$	46.3745	+	40.9734i	0.111210	+	0.0982576i
$418$			150.777i			0.360712i
$419$			135.979i			0.324532i	0.986747	+	0.162266i	$0.0518802\pi$
$419$			135.979i			0.324532i	−0.986747	+	0.162266i	$0.948120\pi$
$420$		0			0
$421$	508.532			1.20792			0.603958	−	0.797016i	$-0.293590\pi$
$421$	508.532			1.20792			0.603958	+	0.797016i	$0.293590\pi$
$422$	−370.308			−0.877508
$423$	38.9137	+	313.457i	0.0919945	+	0.741034i
$424$	−193.737			−0.456927
$425$		0			0
$426$	−40.3506	+	45.6696i	−0.0947197	+	0.107206i
$427$		−	304.078i		−	0.712127i
$428$	−68.5575			−0.160181
$429$	69.4495	+	61.3609i	0.161887	+	0.143033i
$430$		0			0
$431$		−	403.006i		−	0.935050i	−0.883980	−	0.467525i	$-0.845146\pi$
$431$		−	403.006i		−	0.935050i	0.883980	−	0.467525i	$-0.154854\pi$
$432$	−60.9930	+	89.1283i	−0.141188	+	0.206315i
$433$		−	262.462i		−	0.606149i	−0.952967	−	0.303074i	$-0.901987\pi$
$433$		−	262.462i		−	0.606149i	0.952967	−	0.303074i	$-0.0980131\pi$
$434$		−	59.8562i		−	0.137917i
$435$		0			0
$436$	−326.844			−0.749642
$437$	292.480			0.669290
$438$	−5.01453	+	5.67555i	−0.0114487	+	0.0129579i
$439$	−524.676			−1.19516			−0.597581	−	0.801808i	$-0.703871\pi$
$439$	−524.676			−1.19516			−0.597581	+	0.801808i	$0.703871\pi$
$440$		0			0
$441$	−7.76146	−	62.5201i	−0.0175997	−	0.141769i
$442$		−	11.2246i		−	0.0253951i
$443$	649.400			1.46591			0.732957	−	0.680275i	$-0.238139\pi$
$443$	649.400			1.46591			0.732957	+	0.680275i	$0.238139\pi$
$444$	−257.407	+	291.339i	−0.579746	+	0.656169i
$445$		0			0
$446$			170.196i			0.381606i
$447$	150.345	−	170.163i	0.336342	−	0.380679i
$448$			21.1660i			0.0472456i
$449$		−	75.5075i		−	0.168168i	−0.996459	−	0.0840840i	$-0.973204\pi$
$449$		−	75.5075i		−	0.168168i	0.996459	−	0.0840840i	$-0.0267964\pi$
$450$		0			0
$451$	713.539			1.58213
$452$	76.2208			0.168630
$453$	188.316	+	166.384i	0.415709	+	0.367293i
$454$	478.395			1.05373
$455$		0			0
$456$	−54.4110	−	48.0739i	−0.119322	−	0.105425i
$457$		−	621.978i		−	1.36100i	−0.732747	−	0.680501i	$-0.761762\pi$
$457$		−	621.978i		−	1.36100i	0.732747	−	0.680501i	$-0.238238\pi$
$458$	−604.595			−1.32008
$459$	−48.8153	+	71.3332i	−0.106351	+	0.155410i
$460$		0			0
$461$			152.681i			0.331196i	0.986193	+	0.165598i	$0.0529554\pi$
$461$			152.681i			0.331196i	−0.986193	+	0.165598i	$0.947045\pi$
$462$	−104.812	−	92.6051i	−0.226866	−	0.200444i
$463$			306.697i			0.662413i	0.943558	+	0.331207i	$0.107456\pi$
$463$			306.697i			0.662413i	−0.943558	+	0.331207i	$0.892544\pi$
$464$		−	48.8977i		−	0.105383i
$465$		0			0
$466$	−354.182			−0.760047
$467$	95.8983			0.205350			0.102675	−	0.994715i	$-0.467260\pi$
$467$	95.8983			0.205350			0.102675	+	0.994715i	$0.467260\pi$
$468$	−44.2866	+	5.49790i	−0.0946296	+	0.0117476i
$469$	−304.825			−0.649947
$470$		0			0
$471$	−511.038	+	578.403i	−1.08501	+	1.22803i
$472$			88.7998i			0.188135i
$473$	81.2956			0.171872
$474$	−51.2393	−	45.2716i	−0.108100	−	0.0955097i
$475$		0			0
$476$			16.9401i			0.0355884i
$477$	75.9474	+	611.771i	0.159219	+	1.28254i
$478$			67.4268i			0.141060i
$479$		−	335.144i		−	0.699675i	−0.936810	−	0.349838i	$-0.886237\pi$
$479$		−	335.144i		−	0.699675i	0.936810	−	0.349838i	$-0.113763\pi$
$480$		0			0
$481$	−160.641			−0.333972
$482$	−587.479			−1.21884
$483$	−179.636	+	203.316i	−0.371918	+	0.420944i
$484$	−68.4971			−0.141523
$485$		0			0
$486$	305.354	+	157.661i	0.628300	+	0.324405i
$487$			137.863i			0.283085i	0.989932	+	0.141543i	$0.0452063\pi$
$487$			137.863i			0.283085i	−0.989932	+	0.141543i	$0.954794\pi$
$488$	325.073			0.666133
$489$	−566.197	+	640.833i	−1.15787	+	1.31050i
$490$		0			0
$491$			94.4698i			0.192403i	0.995362	+	0.0962014i	$0.0306693\pi$
$491$			94.4698i			0.192403i	−0.995362	+	0.0962014i	$0.969331\pi$
$492$	−227.505	+	257.495i	−0.462408	+	0.523363i
$493$		−	39.1349i		−	0.0793811i
$494$		−	30.0016i		−	0.0607319i
$495$		0			0
$496$	63.9889			0.129010
$497$	38.0038			0.0764664
$498$	−288.685	−	255.063i	−0.579689	−	0.512175i
$499$	329.132			0.659583			0.329792	−	0.944054i	$-0.393022\pi$
$499$	329.132			0.659583			0.329792	+	0.944054i	$0.393022\pi$
$500$		0			0
$501$	−324.151	−	286.398i	−0.647007	−	0.571652i
$502$		−	174.535i		−	0.347678i
$503$	−520.315			−1.03442			−0.517212	−	0.855858i	$-0.673030\pi$
$503$	−520.315			−1.03442			−0.517212	+	0.855858i	$0.673030\pi$
$504$	66.8368	−	8.29735i	0.132613	−	0.0164630i
$505$		0			0
$506$			602.306i			1.19033i
$507$	366.126	+	323.485i	0.722143	+	0.638037i
$508$			37.1372i			0.0731047i
$509$		−	58.8506i		−	0.115620i	−0.998328	−	0.0578101i	$-0.981588\pi$
$509$		−	58.8506i		−	0.115620i	0.998328	−	0.0578101i	$-0.0184118\pi$
$510$		0			0
$511$	4.72289			0.00924244
$512$	−22.6274			−0.0441942
$513$	−130.475	+	190.662i	−0.254338	+	0.371660i
$514$	655.670			1.27562
$515$		0			0
$516$	−25.9203	+	29.3371i	−0.0502332	+	0.0568549i
$517$		−	437.291i		−	0.845824i
$518$	242.437			0.468024
$519$	297.167	+	262.557i	0.572576	+	0.505890i
$520$		0			0
$521$		−	648.248i		−	1.24424i	−0.782922	−	0.622119i	$-0.786272\pi$
$521$		−	648.248i		−	1.24424i	0.782922	−	0.622119i	$-0.213728\pi$
$522$	−154.406	+	19.1685i	−0.295797	+	0.0367213i
$523$			761.495i			1.45601i	0.685570	+	0.728007i	$0.259553\pi$
$523$			761.495i			1.45601i	−0.685570	+	0.728007i	$0.740447\pi$
$524$		−	93.6064i		−	0.178638i
$525$		0			0
$526$	603.176			1.14672
$527$	51.2131			0.0971785
$528$	98.9990	−	112.049i	0.187498	−	0.212214i
$529$	639.361			1.20862
$530$		0			0
$531$	280.407	−	34.8107i	0.528073	−	0.0655568i
$532$			45.2779i			0.0851089i
$533$	−141.979			−0.266378
$534$	5.30721	−	6.00681i	0.00993860	−	0.0112487i
$535$		0			0
$536$		−	325.872i		−	0.607969i
$537$	−414.426	+	469.055i	−0.771743	+	0.873474i
$538$			710.571i			1.32076i
$539$			87.2191i			0.161817i
$540$		0			0
$541$	−1.76954			−0.00327086			−0.00163543	−	0.999999i	$-0.500521\pi$
$541$	−1.76954			−0.00327086			−0.00163543	+	0.999999i	$0.500521\pi$
$542$	−115.908			−0.213852
$543$	404.290	+	357.203i	0.744549	+	0.657833i
$544$	−18.1097			−0.0332899
$545$		0			0
$546$	20.8555	+	18.4265i	0.0381968	+	0.0337481i
$547$			685.643i			1.25346i	0.779236	+	0.626730i	$0.215607\pi$
$547$			685.643i			1.25346i	−0.779236	+	0.626730i	$0.784393\pi$
$548$	−242.940			−0.443321
$549$	−127.433	−	1026.50i	−0.232118	−	1.86976i
$550$		0			0
$551$		−	104.601i		−	0.189838i
$552$	−217.354	−	192.039i	−0.393757	−	0.347898i
$553$			42.6386i			0.0771042i
$554$		−	224.673i		−	0.405548i
$555$		0			0
$556$	41.2549			0.0741994
$557$	493.482			0.885964			0.442982	−	0.896531i	$-0.353921\pi$
$557$	493.482			0.885964			0.442982	+	0.896531i	$0.353921\pi$
$558$	−25.0845	−	202.060i	−0.0449543	−	0.362116i
$559$	−16.1761			−0.0289376
$560$		0			0
$561$	79.2331	−	89.6776i	0.141236	−	0.159853i
$562$			313.915i			0.558567i
$563$	−613.695			−1.09004			−0.545022	−	0.838421i	$-0.683479\pi$
$563$	−613.695			−1.09004			−0.545022	+	0.838421i	$0.683479\pi$
$564$	157.805	+	139.426i	0.279797	+	0.247209i
$565$		0			0
$566$			426.707i			0.753899i
$567$	−52.4018	−	207.801i	−0.0924193	−	0.366491i
$568$			40.6278i			0.0715278i
$569$			743.272i			1.30628i	0.757239	+	0.653138i	$0.226548\pi$
$569$			743.272i			1.30628i	−0.757239	+	0.653138i	$0.773452\pi$
$570$		0			0
$571$	−172.272			−0.301702			−0.150851	−	0.988556i	$-0.548201\pi$
$571$	−172.272			−0.301702			−0.150851	+	0.988556i	$0.548201\pi$
$572$	61.7824			0.108011
$573$	194.220	−	219.822i	0.338952	−	0.383633i
$574$	214.273			0.373298
$575$		0			0
$576$	8.87024	+	71.4515i	0.0153997	+	0.124048i
$577$			416.282i			0.721459i	0.932670	+	0.360730i	$0.117472\pi$
$577$			416.282i			0.721459i	−0.932670	+	0.360730i	$0.882528\pi$
$578$	394.214			0.682031
$579$	−109.776	+	124.247i	−0.189596	+	0.214589i
$580$		0			0
$581$			240.228i			0.413474i
$582$	−300.566	+	340.186i	−0.516436	+	0.584512i
$583$		−	853.457i		−	1.46391i
$584$			5.04898i			0.00864551i
$585$		0			0
$586$	−369.902			−0.631233
$587$	442.053			0.753072			0.376536	−	0.926402i	$-0.377115\pi$
$587$	442.053			0.753072			0.376536	+	0.926402i	$0.377115\pi$
$588$	−31.4748	−	27.8090i	−0.0535285	−	0.0472942i
$589$	136.884			0.232401
$590$		0			0
$591$	560.922	+	495.593i	0.949107	+	0.838568i
$592$			259.176i			0.437796i
$593$	254.468			0.429119			0.214560	−	0.976711i	$-0.431168\pi$
$593$	254.468			0.429119			0.214560	+	0.976711i	$0.431168\pi$
$594$	−392.631	−	268.689i	−0.660994	−	0.452338i
$595$		0			0
$596$		−	151.378i		−	0.253989i
$597$	−228.083	−	201.519i	−0.382049	−	0.337553i
$598$		−	119.846i		−	0.200412i
$599$			159.505i			0.266285i	0.991097	+	0.133142i	$0.0425067\pi$
$599$			159.505i			0.266285i	−0.991097	+	0.133142i	$0.957493\pi$
$600$		0			0
$601$	−803.694			−1.33726			−0.668631	−	0.743594i	$-0.733119\pi$
$601$	−803.694			−1.33726			−0.668631	+	0.743594i	$0.733119\pi$
$602$	24.4128			0.0405528
$603$	−1029.02	+	127.746i	−1.70650	+	0.211851i
$604$	167.527			0.277362
$605$		0			0
$606$	223.609	−	253.085i	0.368992	−	0.417633i
$607$		−	533.032i		−	0.878142i	−0.898452	−	0.439071i	$-0.855308\pi$
$607$		−	533.032i		−	0.878142i	0.898452	−	0.439071i	$-0.144692\pi$
$608$	−48.4041			−0.0796121
$609$	72.7129	+	64.2442i	0.119397	+	0.105491i
$610$		0			0
$611$			87.0118i			0.142409i
$612$	7.09923	+	57.1857i	0.0116001	+	0.0934407i
$613$		−	1027.03i		−	1.67541i	−0.546119	−	0.837707i	$-0.683895\pi$
$613$		−	1027.03i		−	1.67541i	0.546119	−	0.837707i	$-0.316105\pi$
$614$			709.772i			1.15598i
$615$		0			0
$616$	−93.2412			−0.151366
$617$	1001.53			1.62322			0.811612	−	0.584197i	$-0.198590\pi$
$617$	1001.53			1.62322			0.811612	+	0.584197i	$0.198590\pi$
$618$	31.8823	−	36.0850i	0.0515894	−	0.0583899i
$619$	783.615			1.26594			0.632969	−	0.774177i	$-0.281836\pi$
$619$	783.615			1.26594			0.632969	+	0.774177i	$0.281836\pi$
$620$		0			0
$621$	−521.205	+	761.630i	−0.839300	+	1.22646i
$622$			699.364i			1.12438i
$623$	−4.99854			−0.00802334
$624$	−19.6987	+	22.2954i	−0.0315685	+	0.0357298i
$625$		0			0
$626$			132.285i			0.211318i
$627$	211.777	−	239.693i	0.337762	−	0.382286i
$628$			514.548i			0.819345i
$629$			207.429i			0.329776i
$630$		0			0
$631$	486.331			0.770731			0.385366	−	0.922764i	$-0.374075\pi$
$631$	486.331			0.770731			0.385366	+	0.922764i	$0.374075\pi$
$632$	−45.5826			−0.0721243
$633$	588.685	+	520.123i	0.929992	+	0.821679i
$634$	892.125			1.40714
$635$		0			0
$636$	307.987	+	272.116i	0.484256	+	0.427856i
$637$		−	17.3548i		−	0.0272446i
$638$	215.406			0.337626
$639$	128.292	−	15.9266i	0.200770	−	0.0249243i
$640$		0			0
$641$			218.729i			0.341230i	0.985338	+	0.170615i	$0.0545755\pi$
$641$			218.729i			0.341230i	−0.985338	+	0.170615i	$0.945425\pi$
$642$	108.987	+	96.2935i	0.169762	+	0.149990i
$643$			932.912i			1.45087i	0.688289	+	0.725437i	$0.258362\pi$
$643$			932.912i			1.45087i	−0.688289	+	0.725437i	$0.741638\pi$
$644$			180.870i			0.280855i
$645$		0			0
$646$	−38.7399			−0.0599689
$647$	192.297			0.297213			0.148607	−	0.988896i	$-0.452521\pi$
$647$	192.297			0.297213			0.148607	+	0.988896i	$0.452521\pi$
$648$	222.148	−	56.0198i	0.342821	−	0.0864504i
$649$	−391.183			−0.602748
$650$		0			0
$651$	−84.0719	+	95.1543i	−0.129143	+	0.146166i
$652$			570.086i			0.874365i
$653$	−282.013			−0.431874			−0.215937	−	0.976407i	$-0.569281\pi$
$653$	−282.013			−0.431874			−0.215937	+	0.976407i	$0.569281\pi$
$654$	519.588	+	459.073i	0.794478	+	0.701947i
$655$		0			0
$656$			229.068i			0.349188i
$657$	15.9434	−	1.97926i	0.0242669	−	0.00301258i
$658$		−	131.317i		−	0.199570i
$659$		−	994.977i		−	1.50983i	−0.655823	−	0.754914i	$-0.727678\pi$
$659$		−	994.977i		−	1.50983i	0.655823	−	0.754914i	$-0.272322\pi$
$660$		0			0
$661$	−1075.15			−1.62655			−0.813274	−	0.581881i	$-0.802317\pi$
$661$	−1075.15			−1.62655			−0.813274	+	0.581881i	$0.802317\pi$
$662$	−10.5585			−0.0159493
$663$	−15.7657	+	17.8440i	−0.0237794	+	0.0269140i
$664$	−256.815			−0.386769
$665$		0			0
$666$	818.409	−	101.600i	1.22884	−	0.152553i
$667$		−	417.846i		−	0.626456i
$668$	−288.365			−0.431684
$669$	239.052	−	270.564i	0.357327	−	0.404430i
$670$		0			0
$671$			1432.02i			2.13416i
$672$	29.7291	−	33.6479i	0.0442397	−	0.0500713i
$673$		−	544.654i		−	0.809293i	−0.914473	−	0.404647i	$-0.867395\pi$
$673$		−	544.654i		−	0.809293i	0.914473	−	0.404647i	$-0.132605\pi$
$674$		−	365.075i		−	0.541654i
$675$		0			0
$676$	325.707			0.481814
$677$	−1134.78			−1.67619			−0.838097	−	0.545521i	$-0.816332\pi$
$677$	−1134.78			−1.67619			−0.838097	+	0.545521i	$0.816332\pi$
$678$	−121.169	−	107.057i	−0.178716	−	0.157901i
$679$	283.085			0.416914
$680$		0			0
$681$	−760.511	−	671.937i	−1.11676	−	0.986691i
$682$			281.886i			0.413323i
$683$	−481.970			−0.705666			−0.352833	−	0.935686i	$-0.614782\pi$
$683$	−481.970			−0.705666			−0.352833	+	0.935686i	$0.614782\pi$
$684$	18.9751	+	152.848i	0.0277413	+	0.223462i
$685$		0			0
$686$			26.1916i			0.0381802i
$687$	961.135	+	849.194i	1.39903	+	1.23609i
$688$			26.0984i			0.0379337i
$689$			169.820i			0.246473i
$690$		0			0
$691$	941.656			1.36274			0.681372	−	0.731938i	$-0.261384\pi$
$691$	941.656			1.36274			0.681372	+	0.731938i	$0.261384\pi$
$692$	264.360			0.382024
$693$	36.5517	+	294.431i	0.0527442	+	0.424865i
$694$	353.488			0.509349
$695$		0			0
$696$	−68.6800	+	77.7334i	−0.0986781	+	0.111686i
$697$			183.333i			0.263031i
$698$	367.994			0.527212
$699$	563.049	+	497.472i	0.805506	+	0.711691i
$700$		0			0
$701$			310.157i			0.442449i	0.975223	+	0.221224i	$0.0710054\pi$
$701$			310.157i			0.442449i	−0.975223	+	0.221224i	$0.928995\pi$
$702$	78.1253	+	53.4634i	0.111290	+	0.0761587i
$703$			554.423i			0.788654i
$704$		−	99.6790i		−	0.141590i
$705$		0			0
$706$	−843.265			−1.19443
$707$	−210.604			−0.297884
$708$	124.725	−	141.166i	0.176165	−	0.199387i
$709$	346.625			0.488892			0.244446	−	0.969663i	$-0.421394\pi$
$709$	346.625			0.488892			0.244446	+	0.969663i	$0.421394\pi$
$710$		0			0
$711$	17.8690	+	143.938i	0.0251322	+	0.202444i
$712$		−	5.34367i		−	0.00750515i
$713$	546.806			0.766909
$714$	23.7934	−	26.9299i	0.0333241	−	0.0377169i
$715$		0			0
$716$			417.273i			0.582783i
$717$	94.7054	−	107.189i	0.132086	−	0.149497i
$718$		−	774.178i		−	1.07824i
$719$		−	643.186i		−	0.894556i	−0.894395	−	0.447278i	$-0.852393\pi$
$719$		−	643.186i		−	0.894556i	0.894395	−	0.447278i	$-0.147607\pi$
$720$		0			0
$721$	−30.0280			−0.0416477
$722$	406.986			0.563692
$723$	933.925	+	825.153i	1.29174	+	1.14129i
$724$	359.657			0.496764
$725$		0			0
$726$	108.891	+	96.2086i	0.149987	+	0.132519i
$727$		−	571.442i		−	0.786028i	−0.919533	−	0.393014i	$-0.871432\pi$
$727$		−	571.442i		−	0.786028i	0.919533	−	0.393014i	$-0.128568\pi$
$728$	18.5530			0.0254850
$729$	−263.981	−	679.526i	−0.362114	−	0.932134i
$730$		0			0
$731$			20.8876i			0.0285741i
$732$	−516.774	−	456.587i	−0.705975	−	0.623752i
$733$			1236.27i			1.68658i	0.537456	+	0.843292i	$0.319385\pi$
$733$			1236.27i			1.68658i	−0.537456	+	0.843292i	$0.680615\pi$
$734$			364.325i			0.496356i
$735$		0			0
$736$	−193.359			−0.262715
$737$	1435.54			1.94782
$738$	723.336	−	89.7975i	0.980130	−	0.121677i
$739$	−470.354			−0.636473			−0.318237	−	0.948011i	$-0.603091\pi$
$739$	−470.354			−0.636473			−0.318237	+	0.948011i	$0.603091\pi$
$740$		0			0
$741$	−42.1392	+	47.6939i	−0.0568680	+	0.0643643i
$742$		−	256.290i		−	0.345404i
$743$	−647.901			−0.872007			−0.436004	−	0.899945i	$-0.643606\pi$
$743$	−647.901			−0.872007			−0.436004	+	0.899945i	$0.643606\pi$
$744$	−101.724	−	89.8767i	−0.136726	−	0.120802i
$745$		0			0
$746$			841.180i			1.12759i
$747$	100.675	+	810.955i	0.134772	+	1.08562i
$748$		−	79.7774i		−	0.106654i
$749$		−	90.6930i		−	0.121085i
$750$		0			0
$751$	−1200.64			−1.59872			−0.799359	−	0.600853i	$-0.794828\pi$
$751$	−1200.64			−1.59872			−0.799359	+	0.600853i	$0.794828\pi$
$752$	140.384			0.186681
$753$	−245.145	+	277.460i	−0.325558	+	0.368473i
$754$	−42.8612			−0.0568451
$755$		0			0
$756$	−117.906	−	80.6862i	−0.155960	−	0.106728i
$757$			412.699i			0.545177i	0.962131	+	0.272589i	$0.0878798\pi$
$757$			412.699i			0.545177i	−0.962131	+	0.272589i	$0.912120\pi$
$758$	−754.068			−0.994813
$759$	845.978	−	957.495i	1.11460	−	1.26152i
$760$		0			0
$761$		−	21.4803i		−	0.0282264i	−0.999900	−	0.0141132i	$-0.995507\pi$
$761$		−	21.4803i		−	0.0282264i	0.999900	−	0.0141132i	$-0.00449252\pi$
$762$	52.1616	−	59.0375i	0.0684535	−	0.0774771i
$763$		−	432.374i		−	0.566676i
$764$		−	195.554i		−	0.255960i
$765$		0			0
$766$	107.658			0.140546
$767$	77.8373			0.101483
$768$	35.9712	+	31.7817i	0.0468374	+	0.0413824i
$769$	−512.111			−0.665944			−0.332972	−	0.942937i	$-0.608051\pi$
$769$	−512.111			−0.665944			−0.332972	+	0.942937i	$0.608051\pi$
$770$		0			0
$771$	−1042.33	−	920.932i	−1.35192	−	1.19446i
$772$			110.530i			0.143174i
$773$	−403.273			−0.521699			−0.260849	−	0.965380i	$-0.584003\pi$
$773$	−403.273			−0.521699			−0.260849	+	0.965380i	$0.584003\pi$
$774$	82.4119	−	10.2309i	0.106475	−	0.0132182i
$775$		0			0
$776$			302.630i			0.389987i
$777$	−385.405	−	340.518i	−0.496017	−	0.438247i
$778$			936.102i			1.20322i
$779$			490.017i			0.629034i
$780$		0			0
$781$	−178.975			−0.229161
$782$	−154.753			−0.197894
$783$	272.385	+	186.401i	0.347874	+	0.238060i
$784$	−28.0000			−0.0357143
$785$		0			0
$786$	−131.476	+	148.808i	−0.167273	+	0.189323i
$787$			780.597i			0.991864i	0.868361	+	0.495932i	$0.165173\pi$
$787$			780.597i			0.991864i	−0.868361	+	0.495932i	$0.834827\pi$
$788$	498.998			0.633246
$789$	−958.879	−	847.201i	−1.21531	−	1.07377i
$790$		0			0
$791$			100.831i			0.127472i
$792$	−314.760	+	39.0755i	−0.397425	+	0.0493377i
$793$		−	284.943i		−	0.359322i
$794$			1004.89i			1.26561i
$795$		0			0
$796$	−202.903			−0.254904
$797$	−1371.43			−1.72074			−0.860372	−	0.509667i	$-0.829769\pi$
$797$	−1371.43			−1.72074			−0.860372	+	0.509667i	$0.829769\pi$
$798$	63.5958	−	71.9790i	0.0796940	−	0.0901993i
$799$	112.355			0.140620
$800$		0			0
$801$	−16.8739	+	2.09479i	−0.0210661	+	0.00261521i
$802$			627.130i			0.781958i
$803$	−22.2419			−0.0276985
$804$	−457.708	+	518.043i	−0.569289	+	0.644332i
$805$		0			0
$806$		−	56.0894i		−	0.0695899i
$807$	998.044	−	1129.61i	1.23673	−	1.39976i
$808$		−	225.145i		−	0.278645i
$809$		−	1241.62i		−	1.53476i	−0.641195	−	0.767378i	$-0.721561\pi$
$809$		−	1241.62i		−	1.53476i	0.641195	−	0.767378i	$-0.278439\pi$
$810$		0			0
$811$	−712.149			−0.878112			−0.439056	−	0.898460i	$-0.644687\pi$
$811$	−712.149			−0.878112			−0.439056	+	0.898460i	$0.644687\pi$
$812$	64.6855			0.0796620
$813$	184.261	+	162.800i	0.226643	+	0.200246i
$814$	−1141.73			−1.40261
$815$		0			0
$816$	28.7892	+	25.4362i	0.0352809	+	0.0311719i
$817$			55.8292i			0.0683343i
$818$	477.707			0.583994
$819$	−7.27303	−	58.5857i	−0.00888038	−	0.0715332i
$820$		0			0
$821$		−	637.492i		−	0.776483i	−0.921558	−	0.388241i	$-0.873083\pi$
$821$		−	637.492i		−	0.776483i	0.921558	−	0.388241i	$-0.126917\pi$
$822$	386.205	+	341.225i	0.469836	+	0.415116i
$823$			956.777i			1.16255i	0.813708	+	0.581274i	$0.197446\pi$
$823$			956.777i			1.16255i	−0.813708	+	0.581274i	$0.802554\pi$
$824$		−	32.1013i		−	0.0389578i
$825$		0			0
$826$	−117.471			−0.142217
$827$	1491.85			1.80393			0.901967	−	0.431806i	$-0.142123\pi$
$827$	1491.85			1.80393			0.901967	+	0.431806i	$0.142123\pi$
$828$	75.7991	+	610.576i	0.0915448	+	0.737411i
$829$	51.5821			0.0622221			0.0311111	−	0.999516i	$-0.490095\pi$
$829$	51.5821			0.0622221			0.0311111	+	0.999516i	$0.490095\pi$
$830$		0			0
$831$	−315.568	+	357.167i	−0.379745	+	0.429803i
$832$			19.8340i			0.0238390i
$833$	−22.4096			−0.0269023
$834$	−65.5835	−	57.9452i	−0.0786373	−	0.0694786i
$835$		0			0
$836$		−	213.231i		−	0.255062i
$837$	−243.930	+	356.451i	−0.291434	+	0.425868i
$838$		−	192.303i		−	0.229479i
$839$		−	156.683i		−	0.186750i	−0.995631	−	0.0933748i	$-0.970235\pi$
$839$		−	156.683i		−	0.186750i	0.995631	−	0.0933748i	$-0.0297655\pi$
$840$		0			0
$841$	691.564			0.822311
$842$	−719.173			−0.854125
$843$	440.914	−	499.035i	0.523029	−	0.591975i
$844$	523.695			0.620492
$845$		0			0
$846$	−55.0323	−	443.296i	−0.0650500	−	0.523990i
$847$		−	90.6131i		−	0.106981i
$848$	273.986			0.323096
$849$	599.338	−	678.342i	0.705934	−	0.798990i
$850$		0			0
$851$			2214.74i			2.60251i
$852$	57.0644	−	64.5866i	0.0669770	−	0.0758059i
$853$			222.657i			0.261028i	0.991446	+	0.130514i	$0.0416628\pi$
$853$			222.657i			0.261028i	−0.991446	+	0.130514i	$0.958337\pi$
$854$			430.031i			0.503550i
$855$		0			0
$856$	96.9549			0.113265
$857$	−737.700			−0.860793			−0.430396	−	0.902640i	$-0.641626\pi$
$857$	−737.700			−0.860793			−0.430396	+	0.902640i	$0.641626\pi$
$858$	−98.2165	−	86.7775i	−0.114471	−	0.101139i
$859$	−1615.88			−1.88112			−0.940560	−	0.339628i	$-0.889699\pi$
$859$	−1615.88			−1.88112			−0.940560	+	0.339628i	$0.889699\pi$
$860$		0			0
$861$	−340.633	−	300.961i	−0.395625	−	0.349548i
$862$			569.937i			0.661180i
$863$	−581.527			−0.673844			−0.336922	−	0.941533i	$-0.609386\pi$
$863$	−581.527			−0.673844			−0.336922	+	0.941533i	$0.609386\pi$
$864$	86.2572	−	126.046i	0.0998347	−	0.145887i
$865$		0			0
$866$			371.178i			0.428612i
$867$	−626.688	−	553.699i	−0.722823	−	0.638638i
$868$			84.6494i			0.0975224i
$869$		−	200.802i		−	0.231072i
$870$		0			0
$871$	−285.642			−0.327948
$872$	462.227			0.530077
$873$	955.627	−	118.635i	1.09465	−	0.135893i
$874$	−413.629			−0.473260
$875$		0			0
$876$	7.09162	−	8.02644i	0.00809546	−	0.00916260i
$877$		−	964.404i		−	1.09966i	−0.835276	−	0.549831i	$-0.814692\pi$
$877$		−	964.404i		−	1.09966i	0.835276	−	0.549831i	$-0.185308\pi$
$878$	742.004			0.845108
$879$	588.040	+	519.552i	0.668987	+	0.591072i
$880$		0			0
$881$		−	948.772i		−	1.07693i	−0.842649	−	0.538463i	$-0.819005\pi$
$881$		−	948.772i		−	1.07693i	0.842649	−	0.538463i	$-0.180995\pi$
$882$	10.9764	+	88.4167i	0.0124449	+	0.100246i
$883$		−	408.920i		−	0.463103i	−0.972823	−	0.231551i	$-0.925620\pi$
$883$		−	408.920i		−	0.463103i	0.972823	−	0.231551i	$-0.0743801\pi$
$884$			15.8740i			0.0179570i
$885$		0			0
$886$	−918.391			−1.03656
$887$	738.870			0.832999			0.416500	−	0.909136i	$-0.363257\pi$
$887$	738.870			0.832999			0.416500	+	0.909136i	$0.363257\pi$
$888$	364.029	−	412.015i	0.409943	−	0.463981i
$889$	−49.1278			−0.0552619
$890$		0			0
$891$	246.780	+	978.614i	0.276970	+	1.09833i
$892$		−	240.694i		−	0.269836i
$893$	300.306			0.336289
$894$	−212.620	+	240.647i	−0.237830	+	0.269180i
$895$		0			0
$896$		−	29.9333i		−	0.0334077i
$897$	−168.332	+	190.522i	−0.187661	+	0.212399i
$898$			106.784i			0.118913i
$899$		−	195.557i		−	0.217527i
$900$		0			0
$901$	219.282			0.243377
$902$	−1009.10			−1.11873
$903$	−38.8094	−	34.2894i	−0.0429783	−	0.0379727i
$904$	−107.793			−0.119240
$905$		0			0
$906$	−266.320	−	235.302i	−0.293951	−	0.259715i
$907$		−	317.100i		−	0.349614i	−0.984603	−	0.174807i	$-0.944070\pi$
$907$		−	317.100i		−	0.349614i	0.984603	−	0.174807i	$-0.0559301\pi$
$908$	−676.552			−0.745102
$909$	−710.950	+	88.2599i	−0.782124	+	0.0970956i
$910$		0			0
$911$		−	201.300i		−	0.220966i	−0.993878	−	0.110483i	$-0.964760\pi$
$911$		−	201.300i		−	0.220966i	0.993878	−	0.110483i	$-0.0352398\pi$
$912$	76.9488	+	67.9868i	0.0843737	+	0.0745469i
$913$		−	1131.33i		−	1.23913i
$914$			879.610i			0.962374i
$915$		0			0
$916$	855.027			0.933436
$917$	123.830			0.135038
$918$	69.0353	−	100.880i	0.0752019	−	0.109891i
$919$	−333.069			−0.362425			−0.181213	−	0.983444i	$-0.558002\pi$
$919$	−333.069			−0.362425			−0.181213	+	0.983444i	$0.558002\pi$
$920$		0			0
$921$	996.921	−	1128.34i	1.08243	−	1.22512i
$922$		−	215.924i		−	0.234191i
$923$	35.6122			0.0385831
$924$	148.227	+	130.963i	0.160419	+	0.141735i
$925$		0			0
$926$		−	433.736i		−	0.468397i
$927$	−101.367	+	12.5841i	−0.109350	+	0.0135751i
$928$			69.1517i			0.0745170i
$929$			1265.71i			1.36245i	0.732076	+	0.681223i	$0.238551\pi$
$929$			1265.71i			1.36245i	−0.732076	+	0.681223i	$0.761449\pi$
$930$		0			0
$931$	−59.8971			−0.0643363
$932$	500.889			0.537435
$933$	982.303	−	1111.79i	1.05284	−	1.19163i
$934$	−135.621			−0.145204
$935$		0			0
$936$	62.6308	−	7.77520i	0.0669132	−	0.00830684i
$937$		−	1010.57i		−	1.07851i	−0.842142	−	0.539256i	$-0.818706\pi$
$937$		−	1010.57i		−	1.07851i	0.842142	−	0.539256i	$-0.181294\pi$
$938$	431.088			0.459582
$939$	185.803	−	210.295i	0.197873	−	0.223957i
$940$		0			0
$941$		−	934.431i		−	0.993019i	−0.868031	−	0.496510i	$-0.834615\pi$
$941$		−	934.431i		−	0.993019i	0.868031	−	0.496510i	$-0.165385\pi$
$942$	722.717	−	817.986i	0.767216	−	0.868350i
$943$			1957.46i			2.07578i
$944$		−	125.582i		−	0.133032i
$945$		0			0
$946$	−114.969			−0.121532
$947$	−464.364			−0.490353			−0.245176	−	0.969479i	$-0.578846\pi$
$947$	−464.364			−0.490353			−0.245176	+	0.969479i	$0.578846\pi$
$948$	72.4633	+	64.0237i	0.0764381	+	0.0675356i
$949$	4.42568			0.00466351
$950$		0			0
$951$	−1418.22	−	1253.05i	−1.49130	−	1.31761i
$952$		−	23.9569i		−	0.0251648i
$953$	341.847			0.358706			0.179353	−	0.983785i	$-0.442600\pi$
$953$	341.847			0.358706			0.179353	+	0.983785i	$0.442600\pi$
$954$	−107.406	−	865.175i	−0.112585	−	0.906893i
$955$		0			0
$956$		−	95.3559i		−	0.0997447i
$957$	−342.433	−	302.551i	−0.357820	−	0.316145i
$958$			473.966i			0.494745i
$959$		−	321.379i		−	0.335119i
$960$		0			0
$961$	−705.089			−0.733703
$962$	227.180			0.236154
$963$	−38.0076	−	306.159i	−0.0394679	−	0.317922i
$964$	830.821			0.861848
$965$		0			0
$966$	254.044	−	287.532i	0.262986	−	0.297653i
$967$			989.971i			1.02375i	0.859059	+	0.511877i	$0.171050\pi$
$967$			989.971i			1.02375i	−0.859059	+	0.511877i	$0.828950\pi$
$968$	96.8695			0.100072
$969$	61.5854	+	54.4127i	0.0635556	+	0.0561535i
$970$		0			0
$971$			1338.46i			1.37843i	0.724556	+	0.689216i	$0.242045\pi$
$971$			1338.46i			1.37843i	−0.724556	+	0.689216i	$0.757955\pi$
$972$	−431.836	−	222.966i	−0.444276	−	0.229389i
$973$			54.5751i			0.0560895i
$974$		−	194.967i		−	0.200172i
$975$		0			0
$976$	−459.723			−0.471027
$977$	1266.08			1.29589			0.647944	−	0.761688i	$-0.275629\pi$
$977$	1266.08			1.29589			0.647944	+	0.761688i	$0.275629\pi$
$978$	800.723	−	906.275i	0.818736	−	0.926661i
$979$	23.5401			0.0240450
$980$		0			0
$981$	−181.199	−	1459.59i	−0.184708	−	1.48786i
$982$		−	133.600i		−	0.136049i
$983$	−1487.36			−1.51308			−0.756539	−	0.653949i	$-0.773111\pi$
$983$	−1487.36			−1.51308			−0.756539	+	0.653949i	$0.773111\pi$
$984$	321.741	−	364.152i	0.326972	−	0.370073i
$985$		0			0
$986$			55.3451i			0.0561309i
$987$	−184.443	+	208.757i	−0.186873	+	0.211506i
$988$			42.4286i			0.0429439i
$989$			223.019i			0.225500i
$990$		0			0
$991$	1014.75			1.02396			0.511982	−	0.858996i	$-0.328911\pi$
$991$	1014.75			1.02396			0.511982	+	0.858996i	$0.328911\pi$
$992$	−90.4940			−0.0912238
$993$	16.7849	+	14.8300i	0.0169033	+	0.0149346i
$994$	−53.7455			−0.0540699
$995$		0			0
$996$	408.263	+	360.713i	0.409902	+	0.362162i
$997$		−	104.700i		−	0.105015i	−0.998621	−	0.0525074i	$-0.983279\pi$
$997$		−	104.700i		−	0.105015i	0.998621	−	0.0525074i	$-0.0167213\pi$
$998$	−465.463			−0.466396
$999$	−1443.74	−	987.994i	−1.44519	−	0.988983i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.3.c.b.449.12		32
3.2	odd	2	inner	1050.3.c.b.449.22		32
5.2	odd	4		1050.3.e.b.701.6	✓	16
5.3	odd	4		1050.3.e.c.701.11	yes	16
5.4	even	2	inner	1050.3.c.b.449.21		32
15.2	even	4		1050.3.e.b.701.14	yes	16
15.8	even	4		1050.3.e.c.701.3	yes	16
15.14	odd	2	inner	1050.3.c.b.449.11		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1050.3.c.b.449.11		32	15.14	odd	2	inner
1050.3.c.b.449.12		32	1.1	even	1	trivial
1050.3.c.b.449.21		32	5.4	even	2	inner
1050.3.c.b.449.22		32	3.2	odd	2	inner
1050.3.e.b.701.6	✓	16	5.2	odd	4
1050.3.e.b.701.14	yes	16	15.2	even	4
1050.3.e.c.701.3	yes	16	15.8	even	4
1050.3.e.c.701.11	yes	16	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:	\( N \)	\(=\)	\( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1050.c (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-1.41421 q^{2} +(2.24820 + 1.98636i) q^{3} +2.00000 q^{4} +(-3.17943 - 2.80913i) q^{6} +2.64575i q^{7} -2.82843 q^{8} +(1.10878 + 8.93144i) q^{9} +O(q^{10})\)	\(q-1.41421 q^{2} +(2.24820 + 1.98636i) q^{3} +2.00000 q^{4} +(-3.17943 - 2.80913i) q^{6} +2.64575i q^{7} -2.82843 q^{8} +(1.10878 + 8.93144i) q^{9} -12.4599i q^{11} +(4.49639 + 3.97271i) q^{12} +2.47926i q^{13} -3.74166i q^{14} +4.00000 q^{16} +3.20137 q^{17} +(-1.56805 - 12.6310i) q^{18} +8.55673 q^{19} +(-5.25540 + 5.94817i) q^{21} +17.6209i q^{22} +34.1813 q^{23} +(-6.35886 - 5.61826i) q^{24} -3.50620i q^{26} +(-15.2483 + 22.2821i) q^{27} +5.29150i q^{28} -12.2244i q^{29} +15.9972 q^{31} -5.65685 q^{32} +(24.7498 - 28.0123i) q^{33} -4.52742 q^{34} +(2.21756 + 17.8629i) q^{36} +64.7939i q^{37} -12.1010 q^{38} +(-4.92468 + 5.57385i) q^{39} +57.2669i q^{41} +(7.43226 - 8.41198i) q^{42} +6.52459i q^{43} -24.9198i q^{44} -48.3396 q^{46} +35.0960 q^{47} +(8.99279 + 7.94542i) q^{48} -7.00000 q^{49} +(7.19731 + 6.35906i) q^{51} +4.95851i q^{52} +68.4964 q^{53} +(21.5643 - 31.5116i) q^{54} -7.48331i q^{56} +(19.2372 + 16.9967i) q^{57} +17.2879i q^{58} -31.3955i q^{59} -114.931 q^{61} -22.6235 q^{62} +(-23.6304 + 2.93356i) q^{63} +8.00000 q^{64} +(-35.0014 + 39.6153i) q^{66} +115.213i q^{67} +6.40274 q^{68} +(76.8463 + 67.8962i) q^{69} -14.3641i q^{71} +(-3.13610 - 25.2619i) q^{72} -1.78508i q^{73} -91.6324i q^{74} +17.1135 q^{76} +32.9657 q^{77} +(6.96455 - 7.88262i) q^{78} +16.1159 q^{79} +(-78.5412 + 19.8060i) q^{81} -80.9876i q^{82} +90.7978 q^{83} +(-10.5108 + 11.8963i) q^{84} -9.22717i q^{86} +(24.2820 - 27.4829i) q^{87} +35.2419i q^{88} +1.88927i q^{89} -6.55949 q^{91} +68.3626 q^{92} +(35.9649 + 31.7762i) q^{93} -49.6332 q^{94} +(-12.7177 - 11.2365i) q^{96} -106.996i q^{97} +9.89949 q^{98} +(111.285 - 13.8153i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 64 q^{4} - 16 q^{6} - 16 q^{9}+O(q^{10}) \) 32 * q + 64 * q^4 - 16 * q^6 - 16 * q^9	\( 32 q + 64 q^{4} - 16 q^{6} - 16 q^{9} + 128 q^{16} + 48 q^{19} + 56 q^{21} - 32 q^{24} + 48 q^{31} + 256 q^{34} - 32 q^{36} + 192 q^{39} + 160 q^{46} - 224 q^{49} + 288 q^{51} - 80 q^{54} - 112 q^{61} + 256 q^{64} - 192 q^{66} + 344 q^{69} + 96 q^{76} - 256 q^{79} + 160 q^{81} + 112 q^{84} - 448 q^{91} + 416 q^{94} - 64 q^{96} - 304 q^{99}+O(q^{100}) \) 32 * q + 64 * q^4 - 16 * q^6 - 16 * q^9 + 128 * q^16 + 48 * q^19 + 56 * q^21 - 32 * q^24 + 48 * q^31 + 256 * q^34 - 32 * q^36 + 192 * q^39 + 160 * q^46 - 224 * q^49 + 288 * q^51 - 80 * q^54 - 112 * q^61 + 256 * q^64 - 192 * q^66 + 344 * q^69 + 96 * q^76 - 256 * q^79 + 160 * q^81 + 112 * q^84 - 448 * q^91 + 416 * q^94 - 64 * q^96 - 304 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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