LMFDB - Embedded newform 1050.3.c.b.449.16

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			449.16
Character	$\chi$	$=$	1050.449
Dual form			1050.3.c.b.449.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.41421 q^{2} +(2.98306 + 0.318317i) q^{3} +2.00000 q^{4} +(-4.21869 - 0.450168i) q^{6} +2.64575i q^{7} -2.82843 q^{8} +(8.79735 + 1.89912i) q^{9} +O(q^{10})$	\(q-1.41421 q^{2} +(2.98306 + 0.318317i) q^{3} +2.00000 q^{4} +(-4.21869 - 0.450168i) q^{6} +2.64575i q^{7} -2.82843 q^{8} +(8.79735 + 1.89912i) q^{9} +2.46124i q^{11} +(5.96613 + 0.636634i) q^{12} +5.95665i q^{13} -3.74166i q^{14} +4.00000 q^{16} +17.1483 q^{17} +(-12.4413 - 2.68576i) q^{18} +10.3642 q^{19} +(-0.842187 + 7.89245i) q^{21} -3.48072i q^{22} -25.4573 q^{23} +(-8.43738 - 0.900336i) q^{24} -8.42398i q^{26} +(25.6385 + 8.46554i) q^{27} +5.29150i q^{28} -2.22108i q^{29} +8.60441 q^{31} -5.65685 q^{32} +(-0.783453 + 7.34203i) q^{33} -24.2514 q^{34} +(17.5947 + 3.79824i) q^{36} +24.2274i q^{37} -14.6572 q^{38} +(-1.89610 + 17.7691i) q^{39} -10.9247i q^{41} +(1.19103 - 11.1616i) q^{42} +63.9354i q^{43} +4.92247i q^{44} +36.0021 q^{46} +53.3023 q^{47} +(11.9323 + 1.27327i) q^{48} -7.00000 q^{49} +(51.1546 + 5.45861i) q^{51} +11.9133i q^{52} -64.5180 q^{53} +(-36.2584 - 11.9721i) q^{54} -7.48331i q^{56} +(30.9172 + 3.29911i) q^{57} +3.14108i q^{58} +25.0383i q^{59} +72.3424 q^{61} -12.1685 q^{62} +(-5.02460 + 23.2756i) q^{63} +8.00000 q^{64} +(1.10797 - 10.3832i) q^{66} +76.9249i q^{67} +34.2967 q^{68} +(-75.9409 - 8.10350i) q^{69} -43.1374i q^{71} +(-24.8827 - 5.37152i) q^{72} +96.2952i q^{73} -34.2628i q^{74} +20.7284 q^{76} -6.51182 q^{77} +(2.68149 - 25.1293i) q^{78} +56.4860 q^{79} +(73.7867 + 33.4144i) q^{81} +15.4498i q^{82} -10.9616 q^{83} +(-1.68437 + 15.7849i) q^{84} -90.4183i q^{86} +(0.707008 - 6.62563i) q^{87} -6.96143i q^{88} -161.438i q^{89} -15.7598 q^{91} -50.9147 q^{92} +(25.6675 + 2.73893i) q^{93} -75.3809 q^{94} +(-16.8748 - 1.80067i) q^{96} +167.772i q^{97} +9.89949 q^{98} +(-4.67418 + 21.6524i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	2.98306	+	0.318317i	0.994355	+	0.106106i
$3$	2.98306	+	0.318317i	0.994355	+	0.106106i
$4$	2.00000			0.500000
$5$		0			0
$5$		0			0
$6$	−4.21869	−	0.450168i	−0.703115	−	0.0750280i
$7$			2.64575i			0.377964i
$7$			2.64575i			0.377964i
$8$	−2.82843			−0.353553
$9$	8.79735	+	1.89912i	0.977483	+	0.211013i
$10$		0			0
$11$			2.46124i			0.223749i	0.993722	+	0.111874i	$0.0356854\pi$
$11$			2.46124i			0.223749i	−0.993722	+	0.111874i	$0.964315\pi$
$12$	5.96613	+	0.636634i	0.497177	+	0.0530528i
$13$			5.95665i			0.458204i	0.973402	+	0.229102i	$0.0735789\pi$
$13$			5.95665i			0.458204i	−0.973402	+	0.229102i	$0.926421\pi$
$14$		−	3.74166i		−	0.267261i
$15$		0			0
$16$	4.00000			0.250000
$17$	17.1483			1.00873			0.504363	−	0.863492i	$-0.331727\pi$
$17$	17.1483			1.00873			0.504363	+	0.863492i	$0.331727\pi$
$18$	−12.4413	−	2.68576i	−0.691185	−	0.149209i
$19$	10.3642			0.545486			0.272743	−	0.962087i	$-0.412069\pi$
$19$	10.3642			0.545486			0.272743	+	0.962087i	$0.412069\pi$
$20$		0			0
$21$	−0.842187	+	7.89245i	−0.0401042	+	0.375831i
$22$		−	3.48072i		−	0.158214i
$23$	−25.4573			−1.10684			−0.553420	−	0.832902i	$-0.686678\pi$
$23$	−25.4573			−1.10684			−0.553420	+	0.832902i	$0.686678\pi$
$24$	−8.43738	−	0.900336i	−0.351558	−	0.0375140i
$25$		0			0
$26$		−	8.42398i		−	0.323999i
$27$	25.6385	+	8.46554i	0.949575	+	0.313539i
$28$			5.29150i			0.188982i
$29$		−	2.22108i		−	0.0765890i	−0.999266	−	0.0382945i	$-0.987807\pi$
$29$		−	2.22108i		−	0.0765890i	0.999266	−	0.0382945i	$-0.0121925\pi$
$30$		0			0
$31$	8.60441			0.277562			0.138781	−	0.990323i	$-0.455682\pi$
$31$	8.60441			0.277562			0.138781	+	0.990323i	$0.455682\pi$
$32$	−5.65685			−0.176777
$33$	−0.783453	+	7.34203i	−0.0237410	+	0.222486i
$34$	−24.2514			−0.713277
$35$		0			0
$36$	17.5947	+	3.79824i	0.488742	+	0.105507i
$37$			24.2274i			0.654796i	0.944887	+	0.327398i	$0.106172\pi$
$37$			24.2274i			0.654796i	−0.944887	+	0.327398i	$0.893828\pi$
$38$	−14.6572			−0.385717
$39$	−1.89610	+	17.7691i	−0.0486180	+	0.455617i
$40$		0			0
$41$		−	10.9247i		−	0.266455i	−0.991085	−	0.133228i	$-0.957466\pi$
$41$		−	10.9247i		−	0.266455i	0.991085	−	0.133228i	$-0.0425342\pi$
$42$	1.19103	−	11.1616i	0.0283579	−	0.265753i
$43$			63.9354i			1.48687i	0.668808	+	0.743435i	$0.266805\pi$
$43$			63.9354i			1.48687i	−0.668808	+	0.743435i	$0.733195\pi$
$44$			4.92247i			0.111874i
$45$		0			0
$46$	36.0021			0.782654
$47$	53.3023			1.13409			0.567046	−	0.823686i	$-0.308086\pi$
$47$	53.3023			1.13409			0.567046	+	0.823686i	$0.308086\pi$
$48$	11.9323	+	1.27327i	0.248589	+	0.0265264i
$49$	−7.00000			−0.142857
$50$		0			0
$51$	51.1546	+	5.45861i	1.00303	+	0.107031i
$52$			11.9133i			0.229102i
$53$	−64.5180			−1.21732			−0.608660	−	0.793431i	$-0.708293\pi$
$53$	−64.5180			−1.21732			−0.608660	+	0.793431i	$0.708293\pi$
$54$	−36.2584	−	11.9721i	−0.671451	−	0.221705i
$55$		0			0
$56$		−	7.48331i		−	0.133631i
$57$	30.9172	+	3.29911i	0.542406	+	0.0578791i
$58$			3.14108i			0.0541566i
$59$			25.0383i			0.424378i	0.977229	+	0.212189i	$0.0680593\pi$
$59$			25.0383i			0.424378i	−0.977229	+	0.212189i	$0.931941\pi$
$60$		0			0
$61$	72.3424			1.18594			0.592970	−	0.805224i	$-0.297955\pi$
$61$	72.3424			1.18594			0.592970	+	0.805224i	$0.297955\pi$
$62$	−12.1685			−0.196266
$63$	−5.02460	+	23.2756i	−0.0797555	+	0.369454i
$64$	8.00000			0.125000
$65$		0			0
$66$	1.10797	−	10.3832i	0.0167874	−	0.157321i
$67$			76.9249i			1.14813i	0.818809	+	0.574067i	$0.194635\pi$
$67$			76.9249i			1.14813i	−0.818809	+	0.574067i	$0.805365\pi$
$68$	34.2967			0.504363
$69$	−75.9409	−	8.10350i	−1.10059	−	0.117442i
$70$		0			0
$71$		−	43.1374i		−	0.607569i	−0.952741	−	0.303784i	$-0.901750\pi$
$71$		−	43.1374i		−	0.607569i	0.952741	−	0.303784i	$-0.0982503\pi$
$72$	−24.8827	−	5.37152i	−0.345592	−	0.0746045i
$73$			96.2952i			1.31911i	0.751655	+	0.659556i	$0.229256\pi$
$73$			96.2952i			1.31911i	−0.751655	+	0.659556i	$0.770744\pi$
$74$		−	34.2628i		−	0.463011i
$75$		0			0
$76$	20.7284			0.272743
$77$	−6.51182			−0.0845691
$78$	2.68149	−	25.1293i	0.0343781	−	0.322170i
$79$	56.4860			0.715013			0.357506	−	0.933911i	$-0.383627\pi$
$79$	56.4860			0.715013			0.357506	+	0.933911i	$0.383627\pi$
$80$		0			0
$81$	73.7867	+	33.4144i	0.910947	+	0.412524i
$82$			15.4498i			0.188412i
$83$	−10.9616			−0.132067			−0.0660337	−	0.997817i	$-0.521035\pi$
$83$	−10.9616			−0.132067			−0.0660337	+	0.997817i	$0.521035\pi$
$84$	−1.68437	+	15.7849i	−0.0200521	+	0.187915i
$85$		0			0
$86$		−	90.4183i		−	1.05138i
$87$	0.707008	−	6.62563i	0.00812652	−	0.0761567i
$88$		−	6.96143i		−	0.0791072i
$89$		−	161.438i		−	1.81391i	−0.421223	−	0.906957i	$-0.638399\pi$
$89$		−	161.438i		−	1.81391i	0.421223	−	0.906957i	$-0.361601\pi$
$90$		0			0
$91$	−15.7598			−0.173185
$92$	−50.9147			−0.553420
$93$	25.6675	+	2.73893i	0.275995	+	0.0294508i
$94$	−75.3809			−0.801924
$95$		0			0
$96$	−16.8748	−	1.80067i	−0.175779	−	0.0187570i
$97$			167.772i			1.72960i	0.502113	+	0.864802i	$0.332556\pi$
$97$			167.772i			1.72960i	−0.502113	+	0.864802i	$0.667444\pi$
$98$	9.89949			0.101015
$99$	−4.67418	+	21.6524i	−0.0472140	+	0.218711i
$100$		0			0
$101$		−	113.437i		−	1.12314i	−0.827429	−	0.561570i	$-0.810198\pi$
$101$		−	113.437i		−	1.12314i	0.827429	−	0.561570i	$-0.189802\pi$
$102$	−72.3435	−	7.71963i	−0.709250	−	0.0756827i
$103$			11.0672i			0.107448i	0.998556	+	0.0537242i	$0.0171092\pi$
$103$			11.0672i			0.107448i	−0.998556	+	0.0537242i	$0.982891\pi$
$104$		−	16.8480i		−	0.162000i
$105$		0			0
$106$	91.2422			0.860776
$107$	−19.2928			−0.180307			−0.0901534	−	0.995928i	$-0.528736\pi$
$107$	−19.2928			−0.180307			−0.0901534	+	0.995928i	$0.528736\pi$
$108$	51.2771	+	16.9311i	0.474788	+	0.156769i
$109$	−29.3391			−0.269166			−0.134583	−	0.990902i	$-0.542970\pi$
$109$	−29.3391			−0.269166			−0.134583	+	0.990902i	$0.542970\pi$
$110$		0			0
$111$	−7.71200	+	72.2720i	−0.0694775	+	0.651099i
$112$			10.5830i			0.0944911i
$113$	33.2693			0.294418			0.147209	−	0.989105i	$-0.452971\pi$
$113$	33.2693			0.294418			0.147209	+	0.989105i	$0.452971\pi$
$114$	−43.7235	−	4.66564i	−0.383539	−	0.0409267i
$115$		0			0
$116$		−	4.44216i		−	0.0382945i
$117$	−11.3124	+	52.4027i	−0.0966871	+	0.447887i
$118$		−	35.4095i		−	0.300081i
$119$			45.3702i			0.381263i
$120$		0			0
$121$	114.942			0.949936
$122$	−102.308			−0.838587
$123$	3.47751	−	32.5890i	0.0282724	−	0.264951i
$124$	17.2088			0.138781
$125$		0			0
$126$	7.10585	−	32.9167i	0.0563957	−	0.261243i
$127$		−	154.615i		−	1.21744i	−0.793386	−	0.608719i	$-0.791684\pi$
$127$		−	154.615i		−	1.21744i	0.793386	−	0.608719i	$-0.208316\pi$
$128$	−11.3137			−0.0883883
$129$	−20.3517	+	190.723i	−0.157765	+	1.47848i
$130$		0			0
$131$			191.400i			1.46107i	0.682875	+	0.730535i	$0.260729\pi$
$131$			191.400i			1.46107i	−0.682875	+	0.730535i	$0.739271\pi$
$132$	−1.56691	+	14.6841i	−0.0118705	+	0.111243i
$133$			27.4212i			0.206174i
$134$		−	108.788i		−	0.811853i
$135$		0			0
$136$	−48.5028			−0.356638
$137$	−30.7427			−0.224399			−0.112199	−	0.993686i	$-0.535790\pi$
$137$	−30.7427			−0.224399			−0.112199	+	0.993686i	$0.535790\pi$
$138$	107.397	+	11.4601i	0.778236	+	0.0830440i
$139$	−26.4077			−0.189983			−0.0949917	−	0.995478i	$-0.530282\pi$
$139$	−26.4077			−0.189983			−0.0949917	+	0.995478i	$0.530282\pi$
$140$		0			0
$141$	159.004	+	16.9670i	1.12769	+	0.120334i
$142$			61.0055i			0.429616i
$143$	−14.6607			−0.102523
$144$	35.1894	+	7.59648i	0.244371	+	0.0527533i
$145$		0			0
$146$		−	136.182i		−	0.932753i
$147$	−20.8815	−	2.22822i	−0.142051	−	0.0151579i
$148$			48.4549i			0.327398i
$149$		−	0.905723i		−	0.00607868i	−0.999995	−	0.00303934i	$-0.999033\pi$
$149$		−	0.905723i		−	0.00607868i	0.999995	−	0.00303934i	$-0.000967453\pi$
$150$		0			0
$151$	−93.4124			−0.618625			−0.309313	−	0.950960i	$-0.600099\pi$
$151$	−93.4124			−0.618625			−0.309313	+	0.950960i	$0.600099\pi$
$152$	−29.3145			−0.192858
$153$	150.860	+	32.5667i	0.986013	+	0.212855i
$154$	9.20911			0.0597994
$155$		0			0
$156$	−3.79220	+	35.5381i	−0.0243090	+	0.227809i
$157$		−	32.6815i		−	0.208162i	−0.994569	−	0.104081i	$-0.966810\pi$
$157$		−	32.6815i		−	0.208162i	0.994569	−	0.104081i	$-0.0331902\pi$
$158$	−79.8832			−0.505590
$159$	−192.461	−	20.5372i	−1.21045	−	0.129165i
$160$		0			0
$161$		−	67.3538i		−	0.418346i
$162$	−104.350	−	47.2551i	−0.644137	−	0.291698i
$163$		−	124.070i		−	0.761167i	−0.924747	−	0.380584i	$-0.875723\pi$
$163$		−	124.070i		−	0.761167i	0.924747	−	0.380584i	$-0.124277\pi$
$164$		−	21.8493i		−	0.133228i
$165$		0			0
$166$	15.5020			0.0933858
$167$	183.213			1.09708			0.548542	−	0.836123i	$-0.315183\pi$
$167$	183.213			1.09708			0.548542	+	0.836123i	$0.315183\pi$
$168$	2.38207	−	22.3232i	0.0141790	−	0.132876i
$169$	133.518			0.790049
$170$		0			0
$171$	91.1777	+	19.6829i	0.533203	+	0.115105i
$172$			127.871i			0.743435i
$173$	−70.8439			−0.409502			−0.204751	−	0.978814i	$-0.565639\pi$
$173$	−70.8439			−0.409502			−0.204751	+	0.978814i	$0.565639\pi$
$174$	−0.999860	+	9.37005i	−0.00574632	+	0.0538509i
$175$		0			0
$176$			9.84495i			0.0559372i
$177$	−7.97012	+	74.6909i	−0.0450289	+	0.421983i
$178$			228.308i			1.28263i
$179$			305.073i			1.70432i	0.523282	+	0.852160i	$0.324707\pi$
$179$			305.073i			1.70432i	−0.523282	+	0.852160i	$0.675293\pi$
$180$		0			0
$181$	−69.3954			−0.383400			−0.191700	−	0.981454i	$-0.561400\pi$
$181$	−69.3954			−0.383400			−0.191700	+	0.981454i	$0.561400\pi$
$182$	22.2877			0.122460
$183$	215.802	+	23.0278i	1.17925	+	0.125835i
$184$	72.0042			0.391327
$185$		0			0
$186$	−36.2993	−	3.87343i	−0.195158	−	0.0208249i
$187$			42.2061i			0.225701i
$188$	106.605			0.567046
$189$	−22.3977	+	67.8332i	−0.118506	+	0.358906i
$190$		0			0
$191$			165.339i			0.865648i	0.901478	+	0.432824i	$0.142483\pi$
$191$			165.339i			0.865648i	−0.901478	+	0.432824i	$0.857517\pi$
$192$	23.8645	+	2.54653i	0.124294	+	0.0132632i
$193$			321.908i			1.66792i	0.551828	+	0.833958i	$0.313930\pi$
$193$			321.908i			1.66792i	−0.551828	+	0.833958i	$0.686070\pi$
$194$		−	237.265i		−	1.22301i
$195$		0			0
$196$	−14.0000			−0.0714286
$197$	354.728			1.80065			0.900325	−	0.435218i	$-0.143329\pi$
$197$	354.728			1.80065			0.900325	+	0.435218i	$0.143329\pi$
$198$	6.61029	−	30.6211i	0.0333853	−	0.154652i
$199$	252.929			1.27100			0.635501	−	0.772100i	$-0.280794\pi$
$199$	252.929			1.27100			0.635501	+	0.772100i	$0.280794\pi$
$200$		0			0
$201$	−24.4865	+	229.472i	−0.121823	+	1.14165i
$202$			160.424i			0.794180i
$203$	5.87643			0.0289479
$204$	102.309	+	10.9172i	0.501516	+	0.0535157i
$205$		0			0
$206$		−	15.6514i		−	0.0759774i
$207$	−223.957	−	48.3465i	−1.08192	−	0.233558i
$208$			23.8266i			0.114551i
$209$			25.5088i			0.122052i
$210$		0			0
$211$	40.9685			0.194163			0.0970817	−	0.995276i	$-0.469049\pi$
$211$	40.9685			0.194163			0.0970817	+	0.995276i	$0.469049\pi$
$212$	−129.036			−0.608660
$213$	13.7314	−	128.682i	0.0644665	−	0.604139i
$214$	27.2842			0.127496
$215$		0			0
$216$	−72.5167	−	23.9442i	−0.335726	−	0.110853i
$217$			22.7651i			0.104908i
$218$	41.4918			0.190329
$219$	−30.6524	+	287.255i	−0.139965	+	1.31167i
$220$		0			0
$221$			102.147i			0.462202i
$222$	10.9064	−	102.208i	0.0491280	−	0.460397i
$223$		−	217.935i		−	0.977289i	−0.872483	−	0.488645i	$-0.837491\pi$
$223$		−	217.935i		−	0.977289i	0.872483	−	0.488645i	$-0.162509\pi$
$224$		−	14.9666i		−	0.0668153i
$225$		0			0
$226$	−47.0499			−0.208185
$227$	130.607			0.575361			0.287680	−	0.957726i	$-0.407116\pi$
$227$	130.607			0.575361			0.287680	+	0.957726i	$0.407116\pi$
$228$	61.8343	+	6.59821i	0.271203	+	0.0289395i
$229$	−176.250			−0.769652			−0.384826	−	0.922989i	$-0.625739\pi$
$229$	−176.250			−0.769652			−0.384826	+	0.922989i	$0.625739\pi$
$230$		0			0
$231$	−19.4252	−	2.07282i	−0.0840917	−	0.00897326i
$232$			6.28217i			0.0270783i
$233$	−383.463			−1.64576			−0.822882	−	0.568213i	$-0.807635\pi$
$233$	−383.463			−1.64576			−0.822882	+	0.568213i	$0.807635\pi$
$234$	15.9981	−	74.1087i	0.0683681	−	0.316704i
$235$		0			0
$236$			50.0767i			0.212189i
$237$	168.501	+	17.9804i	0.710976	+	0.0758668i
$238$		−	64.1632i		−	0.269593i
$239$		−	157.348i		−	0.658361i	−0.944267	−	0.329181i	$-0.893228\pi$
$239$		−	157.348i		−	0.658361i	0.944267	−	0.329181i	$-0.106772\pi$
$240$		0			0
$241$	104.975			0.435580			0.217790	−	0.975996i	$-0.430115\pi$
$241$	104.975			0.435580			0.217790	+	0.975996i	$0.430115\pi$
$242$	−162.553			−0.671707
$243$	209.474	+	123.165i	0.862033	+	0.506852i
$244$	144.685			0.592970
$245$		0			0
$246$	−4.91794	+	46.0878i	−0.0199916	+	0.187349i
$247$			61.7361i			0.249944i
$248$	−24.3369			−0.0981328
$249$	−32.6992	−	3.48926i	−0.131322	−	0.0140131i
$250$		0			0
$251$		−	85.3203i		−	0.339921i	−0.985451	−	0.169961i	$-0.945636\pi$
$251$		−	85.3203i		−	0.339921i	0.985451	−	0.169961i	$-0.0543641\pi$
$252$	−10.0492	+	46.5512i	−0.0398778	+	0.184727i
$253$		−	62.6565i		−	0.247654i
$254$			218.658i			0.860858i
$255$		0			0
$256$	16.0000			0.0625000
$257$	342.067			1.33100			0.665499	−	0.746398i	$-0.268219\pi$
$257$	342.067			1.33100			0.665499	+	0.746398i	$0.268219\pi$
$258$	28.7817	−	269.724i	0.111557	−	1.04544i
$259$	−64.0998			−0.247490
$260$		0			0
$261$	4.21810	−	19.5396i	0.0161613	−	0.0748645i
$262$		−	270.681i		−	1.03313i
$263$	−491.050			−1.86711			−0.933555	−	0.358433i	$-0.883311\pi$
$263$	−491.050			−1.86711			−0.933555	+	0.358433i	$0.883311\pi$
$264$	2.21594	−	20.7664i	0.00839371	−	0.0786606i
$265$		0			0
$266$		−	38.7794i		−	0.145787i
$267$	51.3885	−	481.581i	0.192466	−	1.80367i
$268$			153.850i			0.574067i
$269$			77.8232i			0.289305i	0.989482	+	0.144653i	$0.0462065\pi$
$269$			77.8232i			0.289305i	−0.989482	+	0.144653i	$0.953793\pi$
$270$		0			0
$271$	−395.316			−1.45873			−0.729366	−	0.684124i	$-0.760185\pi$
$271$	−395.316			−1.45873			−0.729366	+	0.684124i	$0.760185\pi$
$272$	68.5934			0.252181
$273$	−47.0125	−	5.01661i	−0.172207	−	0.0183759i
$274$	43.4767			0.158674
$275$		0			0
$276$	−151.882	−	16.2070i	−0.550296	−	0.0587210i
$277$		−	544.962i		−	1.96737i	−0.179896	−	0.983686i	$-0.557576\pi$
$277$		−	544.962i		−	1.96737i	0.179896	−	0.983686i	$-0.442424\pi$
$278$	37.3461			0.134339
$279$	75.6960	+	16.3408i	0.271312	+	0.0585692i
$280$		0			0
$281$		−	239.047i		−	0.850703i	−0.905028	−	0.425351i	$-0.860151\pi$
$281$		−	239.047i		−	0.850703i	0.905028	−	0.425351i	$-0.139849\pi$
$282$	−224.866	−	23.9950i	−0.797397	−	0.0850887i
$283$		−	409.774i		−	1.44796i	−0.689819	−	0.723982i	$-0.742310\pi$
$283$		−	409.774i		−	1.44796i	0.689819	−	0.723982i	$-0.257690\pi$
$284$		−	86.2748i		−	0.303784i
$285$		0			0
$286$	20.7334			0.0724944
$287$	28.9040			0.100711
$288$	−49.7653	−	10.7430i	−0.172796	−	0.0373022i
$289$	5.06559			0.0175280
$290$		0			0
$291$	−53.4045	+	500.473i	−0.183521	+	1.71984i
$292$			192.590i			0.659556i
$293$	−253.198			−0.864158			−0.432079	−	0.901836i	$-0.642220\pi$
$293$	−253.198			−0.864158			−0.432079	+	0.901836i	$0.642220\pi$
$294$	29.5308	+	3.15118i	0.100445	+	0.0107183i
$295$		0			0
$296$		−	68.5256i		−	0.231505i
$297$	−20.8357	+	63.1025i	−0.0701539	+	0.212466i
$298$			1.28089i			0.00429827i
$299$		−	151.640i		−	0.507159i
$300$		0			0
$301$	−169.157			−0.561984
$302$	132.105			0.437434
$303$	36.1089	−	338.390i	0.119171	−	1.11680i
$304$	41.4569			0.136371
$305$		0			0
$306$	−213.348	−	46.0563i	−0.697216	−	0.150511i
$307$		−	107.521i		−	0.350230i	−0.984548	−	0.175115i	$-0.943970\pi$
$307$		−	107.521i		−	0.350230i	0.984548	−	0.175115i	$-0.0560298\pi$
$308$	−13.0236			−0.0422846
$309$	−3.52287	+	33.0141i	−0.0114009	+	0.106842i
$310$		0			0
$311$		−	164.570i		−	0.529162i	−0.964363	−	0.264581i	$-0.914766\pi$
$311$		−	164.570i		−	0.529162i	0.964363	−	0.264581i	$-0.0852337\pi$
$312$	5.36299	−	50.2585i	0.0171891	−	0.161085i
$313$		−	558.672i		−	1.78489i	−0.451153	−	0.892447i	$-0.648987\pi$
$313$		−	558.672i		−	1.78489i	0.451153	−	0.892447i	$-0.351013\pi$
$314$			46.2186i			0.147193i
$315$		0			0
$316$	112.972			0.357506
$317$	183.286			0.578190			0.289095	−	0.957300i	$-0.406646\pi$
$317$	183.286			0.578190			0.289095	+	0.957300i	$0.406646\pi$
$318$	272.181	+	29.0439i	0.855917	+	0.0913331i
$319$	5.46661			0.0171367
$320$		0			0
$321$	−57.5517	−	6.14123i	−0.179289	−	0.0191316i
$322$			95.2526i			0.295816i
$323$	177.729			0.550245
$324$	147.573	+	66.8289i	0.455473	+	0.206262i
$325$		0			0
$326$			175.462i			0.538227i
$327$	−87.5205	−	9.33913i	−0.267647	−	0.0285600i
$328$			30.8996i			0.0942062i
$329$			141.025i			0.428647i
$330$		0			0
$331$	−566.039			−1.71009			−0.855043	−	0.518557i	$-0.826469\pi$
$331$	−566.039			−1.71009			−0.855043	+	0.518557i	$0.826469\pi$
$332$	−21.9232			−0.0660337
$333$	−46.0108	+	213.137i	−0.138171	+	0.640052i
$334$	−259.102			−0.775756
$335$		0			0
$336$	−3.36875	+	31.5698i	−0.0100260	+	0.0939577i
$337$		−	533.027i		−	1.58168i	−0.612022	−	0.790841i	$-0.709643\pi$
$337$		−	533.027i		−	1.58168i	0.612022	−	0.790841i	$-0.290357\pi$
$338$	−188.823			−0.558649
$339$	99.2444	+	10.5902i	0.292756	+	0.0312394i
$340$		0			0
$341$			21.1775i			0.0621041i
$342$	−128.945	−	27.8358i	−0.377031	−	0.0813913i
$343$		−	18.5203i		−	0.0539949i
$344$		−	180.837i		−	0.525688i
$345$		0			0
$346$	100.188			0.289562
$347$	−390.990			−1.12677			−0.563386	−	0.826194i	$-0.690501\pi$
$347$	−390.990			−1.12677			−0.563386	+	0.826194i	$0.690501\pi$
$348$	1.41402	−	13.2513i	0.00406326	−	0.0380783i
$349$	−283.402			−0.812041			−0.406021	−	0.913864i	$-0.633084\pi$
$349$	−283.402			−0.812041			−0.406021	+	0.913864i	$0.633084\pi$
$350$		0			0
$351$	−50.4263	+	152.720i	−0.143665	+	0.435099i
$352$		−	13.9229i		−	0.0395536i
$353$	−580.549			−1.64461			−0.822307	−	0.569044i	$-0.807314\pi$
$353$	−580.549			−1.64461			−0.822307	+	0.569044i	$0.807314\pi$
$354$	11.2715	−	105.629i	0.0318403	−	0.298387i
$355$		0			0
$356$		−	322.877i		−	0.906957i
$357$	−14.4421	+	135.342i	−0.0404541	+	0.379110i
$358$		−	431.439i		−	1.20514i
$359$		−	465.159i		−	1.29571i	−0.761765	−	0.647854i	$-0.775667\pi$
$359$		−	465.159i		−	1.29571i	0.761765	−	0.647854i	$-0.224333\pi$
$360$		0			0
$361$	−253.583			−0.702446
$362$	98.1399			0.271105
$363$	342.880	+	36.5881i	0.944574	+	0.100794i
$364$	−31.5196			−0.0865924
$365$		0			0
$366$	−305.190	−	32.5662i	−0.833853	−	0.0889788i
$367$		−	486.978i		−	1.32691i	−0.748214	−	0.663457i	$-0.769088\pi$
$367$		−	486.978i		−	1.32691i	0.748214	−	0.663457i	$-0.230912\pi$
$368$	−101.829			−0.276710
$369$	20.7473	−	96.1081i	0.0562256	−	0.260456i
$370$		0			0
$371$		−	170.699i		−	0.460104i
$372$	51.3350	+	5.47786i	0.137997	+	0.0147254i
$373$		−	90.3262i		−	0.242161i	−0.992643	−	0.121081i	$-0.961364\pi$
$373$		−	90.3262i		−	0.242161i	0.992643	−	0.121081i	$-0.0386360\pi$
$374$		−	59.6885i		−	0.159595i
$375$		0			0
$376$	−150.762			−0.400962
$377$	13.2302			0.0350934
$378$	31.6752	−	95.9306i	0.0837967	−	0.253785i
$379$	580.355			1.53128			0.765640	−	0.643269i	$-0.222422\pi$
$379$	580.355			1.53128			0.765640	+	0.643269i	$0.222422\pi$
$380$		0			0
$381$	49.2164	−	461.225i	0.129177	−	1.21056i
$382$		−	233.824i		−	0.612106i
$383$	−106.999			−0.279371			−0.139685	−	0.990196i	$-0.544609\pi$
$383$	−106.999			−0.279371			−0.139685	+	0.990196i	$0.544609\pi$
$384$	−33.7495	−	3.60134i	−0.0878894	−	0.00937850i
$385$		0			0
$386$		−	455.246i		−	1.17939i
$387$	−121.421	+	562.462i	−0.313749	+	1.45339i
$388$			335.543i			0.864802i
$389$		−	474.997i		−	1.22107i	−0.791988	−	0.610536i	$-0.790954\pi$
$389$		−	474.997i		−	1.22107i	0.791988	−	0.610536i	$-0.209046\pi$
$390$		0			0
$391$	−436.551			−1.11650
$392$	19.7990			0.0505076
$393$	−60.9259	+	570.959i	−0.155028	+	1.45282i
$394$	−501.661			−1.27325
$395$		0			0
$396$	−9.34837	+	43.3047i	−0.0236070	+	0.109355i
$397$			543.180i			1.36821i	0.729383	+	0.684106i	$0.239807\pi$
$397$			543.180i			1.36821i	−0.729383	+	0.684106i	$0.760193\pi$
$398$	−357.696			−0.898734
$399$	−8.72862	+	81.7991i	−0.0218762	+	0.205010i
$400$		0			0
$401$			113.348i			0.282662i	0.989962	+	0.141331i	$0.0451382\pi$
$401$			113.348i			0.282662i	−0.989962	+	0.141331i	$0.954862\pi$
$402$	34.6291	−	324.522i	0.0861421	−	0.807270i
$403$			51.2535i			0.127180i
$404$		−	226.874i		−	0.561570i
$405$		0			0
$406$	−8.31053			−0.0204693
$407$	−59.6295			−0.146510
$408$	−144.687	−	15.4393i	−0.354625	−	0.0378413i
$409$	507.919			1.24186			0.620928	−	0.783867i	$-0.286756\pi$
$409$	507.919			1.24186			0.620928	+	0.783867i	$0.286756\pi$
$410$		0			0
$411$	−91.7073	−	9.78590i	−0.223132	−	0.0238100i
$412$			22.1344i			0.0537242i
$413$	−66.2452			−0.160400
$414$	316.723	+	68.3723i	0.765031	+	0.165150i
$415$		0			0
$416$		−	33.6959i		−	0.0809998i
$417$	−78.7758	−	8.40601i	−0.188911	−	0.0201583i
$418$		−	36.0749i		−	0.0863036i
$419$			8.79015i			0.0209789i	0.999945	+	0.0104894i	$0.00333895\pi$
$419$			8.79015i			0.0209789i	−0.999945	+	0.0104894i	$0.996661\pi$
$420$		0			0
$421$	182.651			0.433851			0.216926	−	0.976188i	$-0.430397\pi$
$421$	182.651			0.433851			0.216926	+	0.976188i	$0.430397\pi$
$422$	−57.9382			−0.137294
$423$	468.919	+	101.228i	1.10856	+	0.239309i
$424$	182.484			0.430388
$425$		0			0
$426$	−19.4191	+	181.983i	−0.0455847	+	0.427191i
$427$			191.400i			0.448244i
$428$	−38.5857			−0.0901534
$429$	−43.7339	−	4.66676i	−0.101944	−	0.0108782i
$430$		0			0
$431$		−	109.256i		−	0.253493i	−0.991935	−	0.126747i	$-0.959546\pi$
$431$		−	109.256i		−	0.253493i	0.991935	−	0.126747i	$-0.0404535\pi$
$432$	102.554	+	33.8622i	0.237394	+	0.0783846i
$433$		−	241.349i		−	0.557387i	−0.960380	−	0.278694i	$-0.910099\pi$
$433$		−	241.349i		−	0.557387i	0.960380	−	0.278694i	$-0.0899014\pi$
$434$		−	32.1947i		−	0.0741815i
$435$		0			0
$436$	−58.6782			−0.134583
$437$	−263.845			−0.603765
$438$	43.3490	−	406.240i	0.0989704	−	0.927488i
$439$	78.9565			0.179855			0.0899277	−	0.995948i	$-0.471336\pi$
$439$	78.9565			0.179855			0.0899277	+	0.995948i	$0.471336\pi$
$440$		0			0
$441$	−61.5814	−	13.2938i	−0.139640	−	0.0301448i
$442$		−	144.457i		−	0.326826i
$443$	348.992			0.787791			0.393896	−	0.919155i	$-0.371127\pi$
$443$	348.992			0.787791			0.393896	+	0.919155i	$0.371127\pi$
$444$	−15.4240	+	144.544i	−0.0347388	+	0.325550i
$445$		0			0
$446$			308.207i			0.691048i
$447$	0.288307	−	2.70183i	0.000644982	−	0.00604436i
$448$			21.1660i			0.0472456i
$449$		−	401.895i		−	0.895088i	−0.894262	−	0.447544i	$-0.852299\pi$
$449$		−	401.895i		−	0.895088i	0.894262	−	0.447544i	$-0.147701\pi$
$450$		0			0
$451$	26.8882			0.0596191
$452$	66.5385			0.147209
$453$	−278.655	−	29.7347i	−0.615133	−	0.0656396i
$454$	−184.706			−0.406842
$455$		0			0
$456$	−87.4469	−	9.33128i	−0.191770	−	0.0204633i
$457$			80.5571i			0.176274i	0.996108	+	0.0881369i	$0.0280913\pi$
$457$			80.5571i			0.176274i	−0.996108	+	0.0881369i	$0.971909\pi$
$458$	249.256			0.544226
$459$	439.658	+	145.170i	0.957861	+	0.316274i
$460$		0			0
$461$		−	670.208i		−	1.45381i	−0.686736	−	0.726907i	$-0.740957\pi$
$461$		−	670.208i		−	1.45381i	0.686736	−	0.726907i	$-0.259043\pi$
$462$	27.4714	+	2.93141i	0.0594618	+	0.00634505i
$463$			384.490i			0.830433i	0.909723	+	0.415216i	$0.136294\pi$
$463$			384.490i			0.830433i	−0.909723	+	0.415216i	$0.863706\pi$
$464$		−	8.88433i		−	0.0191473i
$465$		0			0
$466$	542.298			1.16373
$467$	−524.245			−1.12258			−0.561290	−	0.827619i	$-0.689695\pi$
$467$	−524.245			−1.12258			−0.561290	+	0.827619i	$0.689695\pi$
$468$	−22.6248	+	104.805i	−0.0483435	+	0.223943i
$469$	−203.524			−0.433953
$470$		0			0
$471$	10.4031	−	97.4910i	0.0220872	−	0.206987i
$472$		−	70.8191i		−	0.150040i
$473$	−157.360			−0.332685
$474$	−238.297	−	25.4282i	−0.502736	−	0.0536460i
$475$		0			0
$476$			90.7405i			0.190631i
$477$	−567.587	−	122.527i	−1.18991	−	0.256871i
$478$			222.524i			0.465532i
$479$			238.920i			0.498790i	0.968402	+	0.249395i	$0.0802317\pi$
$479$			238.920i			0.498790i	−0.968402	+	0.249395i	$0.919768\pi$
$480$		0			0
$481$	−144.314			−0.300030
$482$	−148.457			−0.308002
$483$	21.4398	−	200.921i	0.0443889	−	0.415985i
$484$	229.885			0.474968
$485$		0			0
$486$	−296.241	−	174.182i	−0.609550	−	0.358398i
$487$			109.180i			0.224188i	0.993698	+	0.112094i	$0.0357558\pi$
$487$			109.180i			0.224188i	−0.993698	+	0.112094i	$0.964244\pi$
$488$	−204.615			−0.419293
$489$	39.4937	−	370.110i	0.0807641	−	0.756870i
$490$		0			0
$491$			418.094i			0.851515i	0.904837	+	0.425758i	$0.139992\pi$
$491$			418.094i			0.851515i	−0.904837	+	0.425758i	$0.860008\pi$
$492$	6.95501	−	65.1780i	0.0141362	−	0.132476i
$493$		−	38.0879i		−	0.0772573i
$494$		−	87.3080i		−	0.176737i
$495$		0			0
$496$	34.4176			0.0693904
$497$	114.131			0.229639
$498$	46.2436	+	4.93456i	0.0928586	+	0.00990876i
$499$	−288.979			−0.579115			−0.289558	−	0.957161i	$-0.593508\pi$
$499$	−288.979			−0.579115			−0.289558	+	0.957161i	$0.593508\pi$
$500$		0			0
$501$	546.536	+	58.3198i	1.09089	+	0.116407i
$502$			120.661i			0.240361i
$503$	868.307			1.72626			0.863128	−	0.504986i	$-0.168502\pi$
$503$	868.307			1.72626			0.863128	+	0.504986i	$0.168502\pi$
$504$	14.2117	−	65.8333i	0.0281978	−	0.130622i
$505$		0			0
$506$			88.6097i			0.175118i
$507$	398.294	+	42.5011i	0.785589	+	0.0838287i
$508$		−	309.229i		−	0.608719i
$509$			125.512i			0.246586i	0.992370	+	0.123293i	$0.0393455\pi$
$509$			125.512i			0.246586i	−0.992370	+	0.123293i	$0.960654\pi$
$510$		0			0
$511$	−254.773			−0.498578
$512$	−22.6274			−0.0441942
$513$	265.724	+	87.7388i	0.517980	+	0.171031i
$514$	−483.755			−0.941158
$515$		0			0
$516$	−40.7034	+	381.447i	−0.0788826	+	0.739238i
$517$			131.190i			0.253752i
$518$	90.6508			0.175002
$519$	−211.332	−	22.5508i	−0.407191	−	0.0434505i
$520$		0			0
$521$		−	238.393i		−	0.457569i	−0.973477	−	0.228784i	$-0.926525\pi$
$521$		−	238.393i		−	0.457569i	0.973477	−	0.228784i	$-0.0734751\pi$
$522$	−5.96529	+	27.6332i	−0.0114278	+	0.0529372i
$523$		−	554.925i		−	1.06104i	−0.847672	−	0.530521i	$-0.821996\pi$
$523$		−	554.925i		−	1.06104i	0.847672	−	0.530521i	$-0.178004\pi$
$524$			382.800i			0.730535i
$525$		0			0
$526$	694.450			1.32025
$527$	147.551			0.279984
$528$	−3.13381	+	29.3681i	−0.00593525	+	0.0556214i
$529$	119.076			0.225096
$530$		0			0
$531$	−47.5508	+	220.271i	−0.0895495	+	0.414823i
$532$			54.8423i			0.103087i
$533$	65.0744			0.122091
$534$	−72.6744	+	681.058i	−0.136094	+	1.27539i
$535$		0			0
$536$		−	217.577i		−	0.405926i
$537$	−97.1099	+	910.053i	−0.180838	+	1.69470i
$538$		−	110.059i		−	0.204570i
$539$		−	17.2287i		−	0.0319641i
$540$		0			0
$541$	−271.258			−0.501401			−0.250701	−	0.968065i	$-0.580661\pi$
$541$	−271.258			−0.501401			−0.250701	+	0.968065i	$0.580661\pi$
$542$	559.062			1.03148
$543$	−207.011	−	22.0897i	−0.381236	−	0.0406809i
$544$	−97.0057			−0.178319
$545$		0			0
$546$	66.4858	+	7.09456i	0.121769	+	0.0129937i
$547$		−	1053.10i		−	1.92523i	−0.270873	−	0.962615i	$-0.587312\pi$
$547$		−	1053.10i		−	1.92523i	0.270873	−	0.962615i	$-0.412688\pi$
$548$	−61.4853			−0.112199
$549$	636.421	+	137.387i	1.15924	+	0.250249i
$550$		0			0
$551$		−	23.0198i		−	0.0417782i
$552$	214.793	+	22.9201i	0.389118	+	0.0415220i
$553$			149.448i			0.270249i
$554$			770.692i			1.39114i
$555$		0			0
$556$	−52.8154			−0.0949917
$557$	−198.443			−0.356271			−0.178136	−	0.984006i	$-0.557007\pi$
$557$	−198.443			−0.356271			−0.178136	+	0.984006i	$0.557007\pi$
$558$	−107.050	−	23.1094i	−0.191846	−	0.0414147i
$559$	−380.841			−0.681290
$560$		0			0
$561$	−13.4349	+	125.904i	−0.0239482	+	0.224427i
$562$			338.064i			0.601538i
$563$	22.4619			0.0398968			0.0199484	−	0.999801i	$-0.493650\pi$
$563$	22.4619			0.0398968			0.0199484	+	0.999801i	$0.493650\pi$
$564$	318.009	+	33.9341i	0.563845	+	0.0601668i
$565$		0			0
$566$			579.508i			1.02387i
$567$	−88.4063	+	195.221i	−0.155919	+	0.344306i
$568$			122.011i			0.214808i
$569$		−	1019.36i		−	1.79150i	−0.444562	−	0.895748i	$-0.646641\pi$
$569$		−	1019.36i		−	1.79150i	0.444562	−	0.895748i	$-0.353359\pi$
$570$		0			0
$571$	162.612			0.284784			0.142392	−	0.989810i	$-0.454521\pi$
$571$	162.612			0.284784			0.142392	+	0.989810i	$0.454521\pi$
$572$	−29.3215			−0.0512613
$573$	−52.6301	+	493.216i	−0.0918501	+	0.860761i
$574$	−40.8764			−0.0712132
$575$		0			0
$576$	70.3788	+	15.1930i	0.122185	+	0.0263767i
$577$		−	589.353i		−	1.02141i	−0.859756	−	0.510704i	$-0.829385\pi$
$577$		−	589.353i		−	1.02141i	0.859756	−	0.510704i	$-0.170615\pi$
$578$	−7.16383			−0.0123942
$579$	−102.469	+	960.271i	−0.176975	+	1.65850i
$580$		0			0
$581$		−	29.0017i		−	0.0499168i
$582$	75.5254	−	707.776i	0.129769	−	1.21611i
$583$		−	158.794i		−	0.272374i
$584$		−	272.364i		−	0.466377i
$585$		0			0
$586$	358.076			0.611052
$587$	529.888			0.902705			0.451352	−	0.892346i	$-0.350942\pi$
$587$	529.888			0.902705			0.451352	+	0.892346i	$0.350942\pi$
$588$	−41.7629	−	4.45644i	−0.0710253	−	0.00757897i
$589$	89.1780			0.151406
$590$		0			0
$591$	1058.18	+	112.916i	1.79049	+	0.191059i
$592$			96.9098i			0.163699i
$593$	−471.654			−0.795369			−0.397684	−	0.917522i	$-0.630186\pi$
$593$	−471.654			−0.795369			−0.397684	+	0.917522i	$0.630186\pi$
$594$	29.4661	−	89.2404i	0.0496063	−	0.150236i
$595$		0			0
$596$		−	1.81145i		−	0.00303934i
$597$	754.505	+	80.5117i	1.26383	+	0.134860i
$598$			214.452i			0.358615i
$599$			477.503i			0.797167i	0.917132	+	0.398583i	$0.130498\pi$
$599$			477.503i			0.797167i	−0.917132	+	0.398583i	$0.869502\pi$
$600$		0			0
$601$	−731.782			−1.21761			−0.608804	−	0.793321i	$-0.708350\pi$
$601$	−731.782			−1.21761			−0.608804	+	0.793321i	$0.708350\pi$
$602$	239.224			0.397383
$603$	−146.090	+	676.735i	−0.242271	+	1.12228i
$604$	−186.825			−0.309313
$605$		0			0
$606$	−51.0658	+	478.556i	−0.0842669	+	0.789697i
$607$			659.688i			1.08680i	0.839474	+	0.543401i	$0.182864\pi$
$607$			659.688i			1.08680i	−0.839474	+	0.543401i	$0.817136\pi$
$608$	−58.6289			−0.0964291
$609$	17.5298	+	1.87057i	0.0287845	+	0.00307154i
$610$		0			0
$611$			317.503i			0.519646i
$612$	301.720	+	65.1335i	0.493006	+	0.106427i
$613$		−	214.842i		−	0.350476i	−0.984526	−	0.175238i	$-0.943931\pi$
$613$		−	214.842i		−	0.350476i	0.984526	−	0.175238i	$-0.0560694\pi$
$614$			152.057i			0.247650i
$615$		0			0
$616$	18.4182			0.0298997
$617$	72.1435			0.116926			0.0584631	−	0.998290i	$-0.481380\pi$
$617$	72.1435			0.116926			0.0584631	+	0.998290i	$0.481380\pi$
$618$	4.98209	−	46.6890i	0.00806163	−	0.0755485i
$619$	166.270			0.268610			0.134305	−	0.990940i	$-0.457120\pi$
$619$	166.270			0.268610			0.134305	+	0.990940i	$0.457120\pi$
$620$		0			0
$621$	−652.689	−	215.510i	−1.05103	−	0.347037i
$622$			232.736i			0.374174i
$623$	427.126			0.685595
$624$	−7.58441	+	71.0763i	−0.0121545	+	0.113904i
$625$		0			0
$626$			790.081i			1.26211i
$627$	−8.11989	+	76.0944i	−0.0129504	+	0.121363i
$628$		−	65.3630i		−	0.104081i
$629$			415.460i			0.660509i
$630$		0			0
$631$	948.332			1.50290			0.751451	−	0.659788i	$-0.229354\pi$
$631$	948.332			1.50290			0.751451	+	0.659788i	$0.229354\pi$
$632$	−159.766			−0.252795
$633$	122.212	+	13.0410i	0.193067	+	0.0206018i
$634$	−259.206			−0.408842
$635$		0			0
$636$	−384.923	−	41.0743i	−0.605224	−	0.0645823i
$637$		−	41.6966i		−	0.0654577i
$638$	−7.73095			−0.0121175
$639$	81.9231	−	379.495i	0.128205	−	0.593888i
$640$		0			0
$641$			11.6929i			0.0182417i	0.999958	+	0.00912085i	$0.00290330\pi$
$641$			11.6929i			0.0182417i	−0.999958	+	0.00912085i	$0.997097\pi$
$642$	81.3905	+	8.68501i	0.126776	+	0.0135281i
$643$			515.459i			0.801647i	0.916155	+	0.400823i	$0.131276\pi$
$643$			515.459i			0.801647i	−0.916155	+	0.400823i	$0.868724\pi$
$644$		−	134.708i		−	0.209173i
$645$		0			0
$646$	−251.347			−0.389082
$647$	−1235.46			−1.90951			−0.954757	−	0.297387i	$-0.903885\pi$
$647$	−1235.46			−1.90951			−0.954757	+	0.297387i	$0.903885\pi$
$648$	−208.700	−	94.5103i	−0.322068	−	0.145849i
$649$	−61.6253			−0.0949542
$650$		0			0
$651$	−7.24652	+	67.9098i	−0.0111314	+	0.104316i
$652$		−	248.141i		−	0.380584i
$653$	414.510			0.634778			0.317389	−	0.948295i	$-0.397194\pi$
$653$	414.510			0.634778			0.317389	+	0.948295i	$0.397194\pi$
$654$	123.773	+	13.2075i	0.189255	+	0.0201950i
$655$		0			0
$656$		−	43.6987i		−	0.0666138i
$657$	−182.876	+	847.142i	−0.278350	+	1.28941i
$658$		−	199.439i		−	0.303099i
$659$			433.365i			0.657609i	0.944398	+	0.328805i	$0.106646\pi$
$659$			433.365i			0.657609i	−0.944398	+	0.328805i	$0.893354\pi$
$660$		0			0
$661$	979.636			1.48205			0.741025	−	0.671477i	$-0.234340\pi$
$661$	979.636			1.48205			0.741025	+	0.671477i	$0.234340\pi$
$662$	800.499			1.20921
$663$	−32.5150	+	304.710i	−0.0490422	+	0.459593i
$664$	31.0041			0.0466929
$665$		0			0
$666$	65.0691	−	301.422i	0.0977014	−	0.452585i
$667$			56.5428i			0.0847718i
$668$	366.426			0.548542
$669$	69.3725	−	650.116i	0.103696	−	0.971772i
$670$		0			0
$671$			178.052i			0.265353i
$672$	4.76413	−	44.6464i	0.00708948	−	0.0664381i
$673$			654.898i			0.973103i	0.873652	+	0.486551i	$0.161745\pi$
$673$			654.898i			0.973103i	−0.873652	+	0.486551i	$0.838255\pi$
$674$			753.814i			1.11842i
$675$		0			0
$676$	267.037			0.395025
$677$	−314.756			−0.464928			−0.232464	−	0.972605i	$-0.574679\pi$
$677$	−314.756			−0.464928			−0.232464	+	0.972605i	$0.574679\pi$
$678$	−140.353	−	14.9768i	−0.207010	−	0.0220896i
$679$	−443.882			−0.653729
$680$		0			0
$681$	389.609	+	41.5744i	0.572113	+	0.0610490i
$682$		−	29.9495i		−	0.0439142i
$683$	978.165			1.43216			0.716079	−	0.698019i	$-0.245935\pi$
$683$	978.165			1.43216			0.716079	+	0.698019i	$0.245935\pi$
$684$	182.355	+	39.3658i	0.266601	+	0.0575523i
$685$		0			0
$686$			26.1916i			0.0381802i
$687$	−525.766	−	56.1035i	−0.765308	−	0.0816644i
$688$			255.742i			0.371718i
$689$		−	384.311i		−	0.557781i
$690$		0			0
$691$	928.182			1.34325			0.671623	−	0.740893i	$-0.265598\pi$
$691$	928.182			1.34325			0.671623	+	0.740893i	$0.265598\pi$
$692$	−141.688			−0.204751
$693$	−57.2868	−	12.3667i	−0.0826649	−	0.0178452i
$694$	552.943			0.796748
$695$		0			0
$696$	−1.99972	+	18.7401i	−0.00287316	+	0.0269254i
$697$		−	187.340i		−	0.268780i
$698$	400.792			0.574200
$699$	−1143.89	−	122.063i	−1.63647	−	0.174625i
$700$		0			0
$701$		−	1177.79i		−	1.68015i	−0.542468	−	0.840077i	$-0.682510\pi$
$701$		−	1177.79i		−	1.68015i	0.542468	−	0.840077i	$-0.317490\pi$
$702$	71.3135	−	215.978i	0.101586	−	0.307662i
$703$			251.099i			0.357182i
$704$			19.6899i			0.0279686i
$705$		0			0
$706$	821.020			1.16292
$707$	300.126			0.424507
$708$	−15.9402	+	149.382i	−0.0225145	+	0.210991i
$709$	−1177.46			−1.66074			−0.830369	−	0.557214i	$-0.811870\pi$
$709$	−1177.46			−1.66074			−0.830369	+	0.557214i	$0.811870\pi$
$710$		0			0
$711$	496.927	+	107.274i	0.698913	+	0.150877i
$712$			456.617i			0.641315i
$713$	−219.045			−0.307216
$714$	20.4242	−	191.403i	0.0286054	−	0.268071i
$715$		0			0
$716$			610.146i			0.852160i
$717$	50.0866	−	469.380i	0.0698558	−	0.654645i
$718$			657.834i			0.916203i
$719$			862.273i			1.19927i	0.800275	+	0.599634i	$0.204687\pi$
$719$			862.273i			1.19927i	−0.800275	+	0.599634i	$0.795313\pi$
$720$		0			0
$721$	−29.2810			−0.0406116
$722$	358.620			0.496704
$723$	313.147	+	33.4152i	0.433121	+	0.0462175i
$724$	−138.791			−0.191700
$725$		0			0
$726$	−484.906	−	51.7433i	−0.667915	−	0.0712718i
$727$			1195.80i			1.64484i	0.568882	+	0.822419i	$0.307376\pi$
$727$			1195.80i			1.64484i	−0.568882	+	0.822419i	$0.692624\pi$
$728$	44.5755			0.0612301
$729$	585.669	+	434.088i	0.803387	+	0.595457i
$730$		0			0
$731$			1096.39i			1.49984i
$732$	431.604	+	46.0556i	0.589623	+	0.0629175i
$733$		−	1037.50i		−	1.41541i	−0.706506	−	0.707707i	$-0.749730\pi$
$733$		−	1037.50i		−	1.41541i	0.706506	−	0.707707i	$-0.250270\pi$
$734$			688.690i			0.938270i
$735$		0			0
$736$	144.008			0.195664
$737$	−189.330			−0.256893
$738$	−29.3410	+	135.917i	−0.0397575	+	0.184170i
$739$	−333.738			−0.451608			−0.225804	−	0.974173i	$-0.572501\pi$
$739$	−333.738			−0.451608			−0.225804	+	0.974173i	$0.572501\pi$
$740$		0			0
$741$	−19.6516	+	184.163i	−0.0265204	+	0.248533i
$742$			241.404i			0.325343i
$743$	746.025			1.00407			0.502036	−	0.864847i	$-0.332585\pi$
$743$	746.025			1.00407			0.502036	+	0.864847i	$0.332585\pi$
$744$	−72.5987	−	7.74686i	−0.0975789	−	0.0104124i
$745$		0			0
$746$			127.740i			0.171234i
$747$	−96.4330	−	20.8174i	−0.129094	−	0.0278680i
$748$			84.4123i			0.112851i
$749$		−	51.0440i		−	0.0681496i
$750$		0			0
$751$	518.562			0.690495			0.345248	−	0.938512i	$-0.387795\pi$
$751$	518.562			0.690495			0.345248	+	0.938512i	$0.387795\pi$
$752$	213.209			0.283523
$753$	27.1589	−	254.516i	0.0360676	−	0.338002i
$754$	−18.7103			−0.0248148
$755$		0			0
$756$	−44.7954	+	135.666i	−0.0592532	+	0.179453i
$757$		−	1172.19i		−	1.54846i	−0.632903	−	0.774231i	$-0.718137\pi$
$757$		−	1172.19i		−	1.54846i	0.632903	−	0.774231i	$-0.281863\pi$
$758$	−820.746			−1.08278
$759$	19.9446	−	186.908i	0.0262775	−	0.246256i
$760$		0			0
$761$		−	682.033i		−	0.896233i	−0.893975	−	0.448116i	$-0.852095\pi$
$761$		−	682.033i		−	0.896233i	0.893975	−	0.448116i	$-0.147905\pi$
$762$	−69.6025	+	652.271i	−0.0913419	+	0.855998i
$763$		−	77.6240i		−	0.101735i
$764$			330.678i			0.432824i
$765$		0			0
$766$	151.319			0.197545
$767$	−149.145			−0.194452
$768$	47.7290	+	5.09307i	0.0621472	+	0.00663160i
$769$	−711.176			−0.924807			−0.462403	−	0.886670i	$-0.653013\pi$
$769$	−711.176			−0.924807			−0.462403	+	0.886670i	$0.653013\pi$
$770$		0			0
$771$	1020.41	+	108.886i	1.32348	+	0.141226i
$772$			643.815i			0.833958i
$773$	−657.862			−0.851050			−0.425525	−	0.904947i	$-0.639911\pi$
$773$	−657.862			−0.851050			−0.425525	+	0.904947i	$0.639911\pi$
$774$	171.715	−	795.442i	0.221854	−	1.02770i
$775$		0			0
$776$		−	474.530i		−	0.611507i
$777$	−191.214	−	20.4040i	−0.246092	−	0.0262600i
$778$			671.747i			0.863428i
$779$		−	113.226i		−	0.145348i
$780$		0			0
$781$	106.171			0.135943
$782$	617.376			0.789484
$783$	18.8027	−	56.9453i	0.0240136	−	0.0727270i
$784$	−28.0000			−0.0357143
$785$		0			0
$786$	86.1622	−	807.458i	0.109621	−	1.02730i
$787$			1054.23i			1.33955i	0.742565	+	0.669775i	$0.233609\pi$
$787$			1054.23i			1.33955i	−0.742565	+	0.669775i	$0.766391\pi$
$788$	709.456			0.900325
$789$	−1464.83	−	156.310i	−1.85657	−	0.198111i
$790$		0			0
$791$			88.0222i			0.111280i
$792$	13.2206	−	61.2421i	0.0166927	−	0.0773259i
$793$			430.918i			0.543403i
$794$		−	768.173i		−	0.967472i
$795$		0			0
$796$	505.859			0.635501
$797$	−284.062			−0.356414			−0.178207	−	0.983993i	$-0.557030\pi$
$797$	−284.062			−0.356414			−0.178207	+	0.983993i	$0.557030\pi$
$798$	12.3441	−	115.681i	0.0154688	−	0.144964i
$799$	914.047			1.14399
$800$		0			0
$801$	306.591	−	1420.23i	0.382760	−	1.77307i
$802$		−	160.298i		−	0.199872i
$803$	−237.005			−0.295150
$804$	−48.9730	+	458.944i	−0.0609117	+	0.570826i
$805$		0			0
$806$		−	72.4833i		−	0.0899297i
$807$	−24.7724	+	232.152i	−0.0306969	+	0.287672i
$808$			320.849i			0.397090i
$809$		−	736.234i		−	0.910054i	−0.890478	−	0.455027i	$-0.849630\pi$
$809$		−	736.234i		−	0.910054i	0.890478	−	0.455027i	$-0.150370\pi$
$810$		0			0
$811$	−537.651			−0.662948			−0.331474	−	0.943464i	$-0.607546\pi$
$811$	−537.651			−0.662948			−0.331474	+	0.943464i	$0.607546\pi$
$812$	11.7529			0.0144740
$813$	−1179.25	−	125.836i	−1.45050	−	0.154780i
$814$	84.3288			0.103598
$815$		0			0
$816$	204.618	+	21.8344i	0.250758	+	0.0267579i
$817$			662.641i			0.811066i
$818$	−718.307			−0.878125
$819$	−138.645	−	29.9298i	−0.169285	−	0.0365443i
$820$		0			0
$821$			616.599i			0.751034i	0.926816	+	0.375517i	$0.122535\pi$
$821$			616.599i			0.751034i	−0.926816	+	0.375517i	$0.877465\pi$
$822$	129.694	+	13.8394i	0.157778	+	0.0168362i
$823$			1135.48i			1.37968i	0.723962	+	0.689839i	$0.242319\pi$
$823$			1135.48i			1.37968i	−0.723962	+	0.689839i	$0.757681\pi$
$824$		−	31.3027i		−	0.0379887i
$825$		0			0
$826$	93.6848			0.113420
$827$	−912.460			−1.10334			−0.551669	−	0.834063i	$-0.686009\pi$
$827$	−912.460			−1.10334			−0.551669	+	0.834063i	$0.686009\pi$
$828$	−447.914	−	96.6930i	−0.540959	−	0.116779i
$829$	−199.050			−0.240108			−0.120054	−	0.992767i	$-0.538307\pi$
$829$	−199.050			−0.240108			−0.120054	+	0.992767i	$0.538307\pi$
$830$		0			0
$831$	173.471	−	1625.66i	0.208749	−	1.95627i
$832$			47.6532i			0.0572755i
$833$	−120.038			−0.144104
$834$	111.406	+	11.8879i	0.133580	+	0.0142541i
$835$		0			0
$836$			51.0176i			0.0610259i
$837$	220.604	+	72.8410i	0.263566	+	0.0870262i
$838$		−	12.4312i		−	0.0148343i
$839$			28.6559i			0.0341548i	0.999854	+	0.0170774i	$0.00543617\pi$
$839$			28.6559i			0.0341548i	−0.999854	+	0.0170774i	$0.994564\pi$
$840$		0			0
$841$	836.067			0.994134
$842$	−258.308			−0.306779
$843$	76.0928	−	713.094i	0.0902643	−	0.845900i
$844$	81.9370			0.0970817
$845$		0			0
$846$	−663.152	−	143.157i	−0.783868	−	0.169217i
$847$			304.109i			0.359042i
$848$	−258.072			−0.304330
$849$	130.438	−	1222.38i	0.153637	−	1.43979i
$850$		0			0
$851$		−	616.766i		−	0.724754i
$852$	27.4627	−	257.363i	0.0322332	−	0.302070i
$853$		−	1093.16i		−	1.28154i	−0.767731	−	0.640772i	$-0.778614\pi$
$853$		−	1093.16i		−	1.28154i	0.767731	−	0.640772i	$-0.221386\pi$
$854$		−	270.680i		−	0.316956i
$855$		0			0
$856$	54.5684			0.0637481
$857$	−407.107			−0.475037			−0.237519	−	0.971383i	$-0.576334\pi$
$857$	−407.107			−0.475037			−0.237519	+	0.971383i	$0.576334\pi$
$858$	61.8491	+	6.59979i	0.0720852	+	0.00769206i
$859$	1041.16			1.21206			0.606032	−	0.795440i	$-0.292760\pi$
$859$	1041.16			1.21206			0.606032	+	0.795440i	$0.292760\pi$
$860$		0			0
$861$	86.2224	+	9.20062i	0.100142	+	0.0106860i
$862$			154.511i			0.179247i
$863$	1485.61			1.72145			0.860727	−	0.509067i	$-0.170009\pi$
$863$	1485.61			1.72145			0.860727	+	0.509067i	$0.170009\pi$
$864$	−145.033	−	47.8883i	−0.167863	−	0.0554263i
$865$		0			0
$866$			341.319i			0.394132i
$867$	15.1110	+	1.61246i	0.0174291	+	0.00185982i
$868$			45.5303i			0.0524542i
$869$			139.025i			0.159983i
$870$		0			0
$871$	−458.215			−0.526079
$872$	82.9835			0.0951646
$873$	−318.618	+	1475.95i	−0.364969	+	1.69066i
$874$	373.134			0.426927
$875$		0			0
$876$	−61.3048	+	574.510i	−0.0699826	+	0.655833i
$877$		−	285.779i		−	0.325860i	−0.986638	−	0.162930i	$-0.947906\pi$
$877$		−	285.779i		−	0.325860i	0.986638	−	0.162930i	$-0.0520944\pi$
$878$	−111.661			−0.127177
$879$	−755.307	−	80.5973i	−0.859279	−	0.0916920i
$880$		0			0
$881$		−	134.739i		−	0.152938i	−0.997072	−	0.0764692i	$-0.975635\pi$
$881$		−	134.739i		−	0.152938i	0.997072	−	0.0764692i	$-0.0243647\pi$
$882$	87.0893	+	18.8003i	0.0987407	+	0.0213156i
$883$			49.4924i			0.0560503i	0.999607	+	0.0280252i	$0.00892185\pi$
$883$			49.4924i			0.0560503i	−0.999607	+	0.0280252i	$0.991078\pi$
$884$			204.293i			0.231101i
$885$		0			0
$886$	−493.549			−0.557053
$887$	−1334.66			−1.50469			−0.752345	−	0.658769i	$-0.771077\pi$
$887$	−1334.66			−1.50469			−0.752345	+	0.658769i	$0.771077\pi$
$888$	21.8128	−	204.416i	0.0245640	−	0.230198i
$889$	409.072			0.460148
$890$		0			0
$891$	−82.2408	+	181.607i	−0.0923017	+	0.203823i
$892$		−	435.871i		−	0.488645i
$893$	552.437			0.618631
$894$	−0.407728	+	3.82097i	−0.000456071	+	0.00427401i
$895$		0			0
$896$		−	29.9333i		−	0.0334077i
$897$	48.2697	−	452.353i	0.0538124	−	0.504296i
$898$			568.365i			0.632923i
$899$		−	19.1111i		−	0.0212582i
$900$		0			0
$901$	−1106.38			−1.22794
$902$	−38.0257			−0.0421571
$903$	−504.607	−	53.8456i	−0.558812	−	0.0596297i
$904$	−94.0997			−0.104093
$905$		0			0
$906$	394.078	+	42.0513i	0.434965	+	0.0464142i
$907$		−	368.808i		−	0.406624i	−0.979114	−	0.203312i	$-0.934829\pi$
$907$		−	368.808i		−	0.406624i	0.979114	−	0.203312i	$-0.0651706\pi$
$908$	261.214			0.287680
$909$	215.431	−	997.946i	0.236997	−	1.09785i
$910$		0			0
$911$		−	371.365i		−	0.407645i	−0.979008	−	0.203822i	$-0.934663\pi$
$911$		−	371.365i		−	0.407645i	0.979008	−	0.203822i	$-0.0653365\pi$
$912$	123.669	+	13.1964i	0.135602	+	0.0144698i
$913$		−	26.9791i		−	0.0295499i
$914$		−	113.925i		−	0.124644i
$915$		0			0
$916$	−352.501			−0.384826
$917$	−506.397			−0.552232
$918$	−621.771	−	205.301i	−0.677310	−	0.223640i
$919$	4.28269			0.00466017			0.00233008	−	0.999997i	$-0.499258\pi$
$919$	4.28269			0.00466017			0.00233008	+	0.999997i	$0.499258\pi$
$920$		0			0
$921$	34.2256	−	320.741i	0.0371614	−	0.348253i
$922$			947.817i			1.02800i
$923$	256.954			0.278390
$924$	−38.8504	−	4.14564i	−0.0420459	−	0.00448663i
$925$		0			0
$926$		−	543.752i		−	0.587205i
$927$	−21.0179	+	97.3618i	−0.0226730	+	0.105029i
$928$			12.5643i			0.0135392i
$929$			1323.53i			1.42468i	0.701833	+	0.712341i	$0.252365\pi$
$929$			1323.53i			1.42468i	−0.701833	+	0.712341i	$0.747635\pi$
$930$		0			0
$931$	−72.5496			−0.0779265
$932$	−766.926			−0.822882
$933$	52.3852	−	490.921i	0.0561471	−	0.526175i
$934$	741.394			0.793784
$935$		0			0
$936$	31.9963	−	148.217i	0.0341841	−	0.158352i
$937$			1514.47i			1.61630i	0.588977	+	0.808150i	$0.299531\pi$
$937$			1514.47i			1.61630i	−0.588977	+	0.808150i	$0.700469\pi$
$938$	287.827			0.306851
$939$	177.835	−	1666.55i	0.189387	−	1.77482i
$940$		0			0
$941$			1235.73i			1.31320i	0.754237	+	0.656602i	$0.228007\pi$
$941$			1235.73i			1.31320i	−0.754237	+	0.656602i	$0.771993\pi$
$942$	−14.7122	+	137.873i	−0.0156180	+	0.146362i
$943$			278.113i			0.294924i
$944$			100.153i			0.106095i
$945$		0			0
$946$	222.541			0.235244
$947$	1424.36			1.50407			0.752036	−	0.659122i	$-0.229072\pi$
$947$	1424.36			1.50407			0.752036	+	0.659122i	$0.229072\pi$
$948$	337.003	+	35.9609i	0.355488	+	0.0379334i
$949$	−573.597			−0.604422
$950$		0			0
$951$	546.755	+	58.3431i	0.574927	+	0.0613493i
$952$		−	128.326i		−	0.134797i
$953$	544.301			0.571145			0.285573	−	0.958357i	$-0.407816\pi$
$953$	544.301			0.571145			0.285573	+	0.958357i	$0.407816\pi$
$954$	802.690	+	173.280i	0.841394	+	0.181635i
$955$		0			0
$956$		−	314.697i		−	0.329181i
$957$	16.3072	+	1.74011i	0.0170400	+	0.00181830i
$958$		−	337.884i		−	0.352698i
$959$		−	81.3374i		−	0.0848148i
$960$		0			0
$961$	−886.964			−0.922960
$962$	204.091			0.212153
$963$	−169.726	−	36.6394i	−0.176247	−	0.0380471i
$964$	209.950			0.217790
$965$		0			0
$966$	−30.3205	+	284.145i	−0.0313877	+	0.294146i
$967$		−	1312.39i		−	1.35718i	−0.734518	−	0.678590i	$-0.762591\pi$
$967$		−	1312.39i		−	1.35718i	0.734518	−	0.678590i	$-0.237409\pi$
$968$	−325.106			−0.335853
$969$	530.178	+	56.5742i	0.547139	+	0.0583841i
$970$		0			0
$971$			194.087i			0.199884i	0.994993	+	0.0999419i	$0.0318657\pi$
$971$			194.087i			0.199884i	−0.994993	+	0.0999419i	$0.968134\pi$
$972$	418.948	+	246.330i	0.431017	+	0.253426i
$973$		−	69.8682i		−	0.0718070i
$974$		−	154.403i		−	0.158525i
$975$		0			0
$976$	289.370			0.296485
$977$	1340.42			1.37198			0.685989	−	0.727612i	$-0.259370\pi$
$977$	1340.42			1.37198			0.685989	+	0.727612i	$0.259370\pi$
$978$	−55.8525	+	523.414i	−0.0571089	+	0.535188i
$979$	397.338			0.405861
$980$		0			0
$981$	−258.106	−	55.7185i	−0.263105	−	0.0567976i
$982$		−	591.274i		−	0.602112i
$983$	−508.734			−0.517532			−0.258766	−	0.965940i	$-0.583316\pi$
$983$	−508.734			−0.517532			−0.258766	+	0.965940i	$0.583316\pi$
$984$	−9.83587	+	92.1756i	−0.00999581	+	0.0936744i
$985$		0			0
$986$			53.8644i			0.0546292i
$987$	−44.8906	+	420.686i	−0.0454818	+	0.426227i
$988$			123.472i			0.124972i
$989$		−	1627.62i		−	1.64573i
$990$		0			0
$991$	−1087.94			−1.09782			−0.548912	−	0.835880i	$-0.684958\pi$
$991$	−1087.94			−1.09782			−0.548912	+	0.835880i	$0.684958\pi$
$992$	−48.6739			−0.0490664
$993$	−1688.53	−	180.180i	−1.70043	−	0.181450i
$994$	−161.405			−0.162380
$995$		0			0
$996$	−65.3983	−	6.97853i	−0.0656610	−	0.00700655i
$997$		−	1221.50i		−	1.22518i	−0.790402	−	0.612588i	$-0.790128\pi$
$997$		−	1221.50i		−	1.22518i	0.790402	−	0.612588i	$-0.209872\pi$
$998$	408.677			0.409496
$999$	−205.098	+	621.156i	−0.205304	+	0.621778i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.3.c.b.449.16		32
3.2	odd	2	inner	1050.3.c.b.449.18		32
5.2	odd	4		1050.3.e.c.701.4	yes	16
5.3	odd	4		1050.3.e.b.701.13	yes	16
5.4	even	2	inner	1050.3.c.b.449.17		32
15.2	even	4		1050.3.e.c.701.12	yes	16
15.8	even	4		1050.3.e.b.701.5	✓	16
15.14	odd	2	inner	1050.3.c.b.449.15		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1050.3.c.b.449.15		32	15.14	odd	2	inner
1050.3.c.b.449.16		32	1.1	even	1	trivial
1050.3.c.b.449.17		32	5.4	even	2	inner
1050.3.c.b.449.18		32	3.2	odd	2	inner
1050.3.e.b.701.5	✓	16	15.8	even	4
1050.3.e.b.701.13	yes	16	5.3	odd	4
1050.3.e.c.701.4	yes	16	5.2	odd	4
1050.3.e.c.701.12	yes	16	15.2	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1050.c (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-1.41421 q^{2} +(2.98306 + 0.318317i) q^{3} +2.00000 q^{4} +(-4.21869 - 0.450168i) q^{6} +2.64575i q^{7} -2.82843 q^{8} +(8.79735 + 1.89912i) q^{9} +O(q^{10})\)	\(q-1.41421 q^{2} +(2.98306 + 0.318317i) q^{3} +2.00000 q^{4} +(-4.21869 - 0.450168i) q^{6} +2.64575i q^{7} -2.82843 q^{8} +(8.79735 + 1.89912i) q^{9} +2.46124i q^{11} +(5.96613 + 0.636634i) q^{12} +5.95665i q^{13} -3.74166i q^{14} +4.00000 q^{16} +17.1483 q^{17} +(-12.4413 - 2.68576i) q^{18} +10.3642 q^{19} +(-0.842187 + 7.89245i) q^{21} -3.48072i q^{22} -25.4573 q^{23} +(-8.43738 - 0.900336i) q^{24} -8.42398i q^{26} +(25.6385 + 8.46554i) q^{27} +5.29150i q^{28} -2.22108i q^{29} +8.60441 q^{31} -5.65685 q^{32} +(-0.783453 + 7.34203i) q^{33} -24.2514 q^{34} +(17.5947 + 3.79824i) q^{36} +24.2274i q^{37} -14.6572 q^{38} +(-1.89610 + 17.7691i) q^{39} -10.9247i q^{41} +(1.19103 - 11.1616i) q^{42} +63.9354i q^{43} +4.92247i q^{44} +36.0021 q^{46} +53.3023 q^{47} +(11.9323 + 1.27327i) q^{48} -7.00000 q^{49} +(51.1546 + 5.45861i) q^{51} +11.9133i q^{52} -64.5180 q^{53} +(-36.2584 - 11.9721i) q^{54} -7.48331i q^{56} +(30.9172 + 3.29911i) q^{57} +3.14108i q^{58} +25.0383i q^{59} +72.3424 q^{61} -12.1685 q^{62} +(-5.02460 + 23.2756i) q^{63} +8.00000 q^{64} +(1.10797 - 10.3832i) q^{66} +76.9249i q^{67} +34.2967 q^{68} +(-75.9409 - 8.10350i) q^{69} -43.1374i q^{71} +(-24.8827 - 5.37152i) q^{72} +96.2952i q^{73} -34.2628i q^{74} +20.7284 q^{76} -6.51182 q^{77} +(2.68149 - 25.1293i) q^{78} +56.4860 q^{79} +(73.7867 + 33.4144i) q^{81} +15.4498i q^{82} -10.9616 q^{83} +(-1.68437 + 15.7849i) q^{84} -90.4183i q^{86} +(0.707008 - 6.62563i) q^{87} -6.96143i q^{88} -161.438i q^{89} -15.7598 q^{91} -50.9147 q^{92} +(25.6675 + 2.73893i) q^{93} -75.3809 q^{94} +(-16.8748 - 1.80067i) q^{96} +167.772i q^{97} +9.89949 q^{98} +(-4.67418 + 21.6524i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 64 q^{4} - 16 q^{6} - 16 q^{9}+O(q^{10}) \) 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

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Database

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