LMFDB - Embedded newform 315.3.ca.b.37.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,3,Mod(37,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 4]))

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

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

chi := DirichletCharacter("315.37");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	315.ca (of order $12$, degree $4$, 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:	$8.58312832735$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$16$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			37.12
Character	$\chi$	$=$	315.37
Dual form			315.3.ca.b.298.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.91023 - 0.511845i) q^{2} +(-0.0771041 + 0.0445161i) q^{4} +(4.99333 + 0.258093i) q^{5} +(6.99587 + 0.240410i) q^{7} +(-5.71805 + 5.71805i) q^{8} +O(q^{10})$	\(q+(1.91023 - 0.511845i) q^{2} +(-0.0771041 + 0.0445161i) q^{4} +(4.99333 + 0.258093i) q^{5} +(6.99587 + 0.240410i) q^{7} +(-5.71805 + 5.71805i) q^{8} +(9.67053 - 2.06280i) q^{10} +(-1.58449 - 2.74441i) q^{11} +(11.0592 - 11.0592i) q^{13} +(13.4868 - 3.12156i) q^{14} +(-7.81797 + 13.5411i) q^{16} +(-4.27411 + 15.9512i) q^{17} +(24.9472 + 14.4033i) q^{19} +(-0.396496 + 0.202384i) q^{20} +(-4.43145 - 4.43145i) q^{22} +(2.86298 + 10.6848i) q^{23} +(24.8668 + 2.57749i) q^{25} +(15.4650 - 26.7862i) q^{26} +(-0.550112 + 0.292892i) q^{28} -20.9038i q^{29} +(-30.4426 - 52.7281i) q^{31} +(0.368622 - 1.37572i) q^{32} +32.6581i q^{34} +(34.8707 + 3.00603i) q^{35} +(-4.96117 + 1.32934i) q^{37} +(55.0271 + 14.7445i) q^{38} +(-30.0279 + 27.0763i) q^{40} -0.605481 q^{41} +(16.0752 - 16.0752i) q^{43} +(0.244341 + 0.141070i) q^{44} +(10.9379 + 18.9450i) q^{46} +(-34.1202 + 9.14247i) q^{47} +(48.8844 + 3.36376i) q^{49} +(48.8206 - 7.80433i) q^{50} +(-0.360397 + 1.34502i) q^{52} +(-60.8242 - 16.2978i) q^{53} +(-7.20355 - 14.1127i) q^{55} +(-41.3774 + 38.6280i) q^{56} +(-10.6995 - 39.9312i) q^{58} +(-88.6860 + 51.2029i) q^{59} +(-16.9814 + 29.4127i) q^{61} +(-85.1410 - 85.1410i) q^{62} -65.3604i q^{64} +(58.0765 - 52.3679i) q^{65} +(-13.4604 + 50.2349i) q^{67} +(-0.380533 - 1.42017i) q^{68} +(68.1497 - 12.1062i) q^{70} -25.3750 q^{71} +(-86.1585 - 23.0861i) q^{73} +(-8.79656 + 5.07870i) q^{74} -2.56471 q^{76} +(-10.4251 - 19.5805i) q^{77} +(6.66046 + 3.84542i) q^{79} +(-42.5326 + 65.5976i) q^{80} +(-1.15661 + 0.309913i) q^{82} +(-81.1873 + 81.1873i) q^{83} +(-25.4589 + 78.5465i) q^{85} +(22.4793 - 38.9354i) q^{86} +(24.7528 + 6.63250i) q^{88} +(35.6866 + 20.6037i) q^{89} +(80.0273 - 74.7098i) q^{91} +(-0.696392 - 0.696392i) q^{92} +(-60.4979 + 34.9285i) q^{94} +(120.852 + 78.3590i) q^{95} +(1.74125 + 1.74125i) q^{97} +(95.1022 - 18.5957i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 4 q^{5} - 4 q^{7} - 24 q^{8}+O(q^{10}) $ 64 * q - 4 * q^5 - 4 * q^7 - 24 * q^8	$ 64 q - 4 q^{5} - 4 q^{7} - 24 q^{8} - 16 q^{10} - 16 q^{11} + 80 q^{16} - 56 q^{17} - 96 q^{22} - 72 q^{23} - 4 q^{25} + 288 q^{26} - 380 q^{28} - 136 q^{31} + 48 q^{32} - 76 q^{35} - 28 q^{37} + 68 q^{38} + 164 q^{40} - 128 q^{41} + 344 q^{43} + 240 q^{46} - 412 q^{47} + 72 q^{50} + 388 q^{52} + 40 q^{53} - 8 q^{55} + 864 q^{56} + 56 q^{58} - 216 q^{61} + 912 q^{62} - 20 q^{65} - 368 q^{67} + 492 q^{68} + 416 q^{70} - 784 q^{71} - 316 q^{73} - 32 q^{76} - 844 q^{77} - 908 q^{80} + 556 q^{82} - 1408 q^{83} - 536 q^{85} - 1024 q^{86} + 372 q^{88} - 1064 q^{91} + 1704 q^{92} - 260 q^{95} + 352 q^{97} - 272 q^{98}+O(q^{100}) $ 64 * q - 4 * q^5 - 4 * q^7 - 24 * q^8 - 16 * q^10 - 16 * q^11 + 80 * q^16 - 56 * q^17 - 96 * q^22 - 72 * q^23 - 4 * q^25 + 288 * q^26 - 380 * q^28 - 136 * q^31 + 48 * q^32 - 76 * q^35 - 28 * q^37 + 68 * q^38 + 164 * q^40 - 128 * q^41 + 344 * q^43 + 240 * q^46 - 412 * q^47 + 72 * q^50 + 388 * q^52 + 40 * q^53 - 8 * q^55 + 864 * q^56 + 56 * q^58 - 216 * q^61 + 912 * q^62 - 20 * q^65 - 368 * q^67 + 492 * q^68 + 416 * q^70 - 784 * q^71 - 316 * q^73 - 32 * q^76 - 844 * q^77 - 908 * q^80 + 556 * q^82 - 1408 * q^83 - 536 * q^85 - 1024 * q^86 + 372 * q^88 - 1064 * q^91 + 1704 * q^92 - 260 * q^95 + 352 * q^97 - 272 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	1.91023	−	0.511845i	0.955116	−	0.255922i	0.252584	−	0.967575i	$-0.418720\pi$
$2$	1.91023	−	0.511845i	0.955116	−	0.255922i	0.702532	+	0.711653i	$0.252053\pi$
$3$		0			0
$3$		0			0
$4$	−0.0771041	+	0.0445161i	−0.0192760	+	0.0111290i
$5$	4.99333	+	0.258093i	0.998667	+	0.0516186i
$5$	4.99333	+	0.258093i	0.998667	+	0.0516186i
$6$		0			0
$7$	6.99587	+	0.240410i	0.999410	+	0.0343443i
$7$	6.99587	+	0.240410i	0.999410	+	0.0343443i
$8$	−5.71805	+	5.71805i	−0.714756	+	0.714756i
$9$		0			0
$10$	9.67053	−	2.06280i	0.967053	−	0.206280i
$11$	−1.58449	−	2.74441i	−0.144044	−	0.249492i	0.784972	−	0.619532i	$-0.212677\pi$
$11$	−1.58449	−	2.74441i	−0.144044	−	0.249492i	−0.929016	+	0.370040i	$0.879344\pi$
$12$		0			0
$13$	11.0592	−	11.0592i	0.850706	−	0.850706i	−0.139514	−	0.990220i	$-0.544554\pi$
$13$	11.0592	−	11.0592i	0.850706	−	0.850706i	0.990220	+	0.139514i	$0.0445541\pi$
$14$	13.4868	−	3.12156i	0.963342	−	0.222969i
$15$		0			0
$16$	−7.81797	+	13.5411i	−0.488623	+	0.846320i
$17$	−4.27411	+	15.9512i	−0.251418	+	0.938305i	0.718630	+	0.695392i	$0.244769\pi$
$17$	−4.27411	+	15.9512i	−0.251418	+	0.938305i	−0.970048	+	0.242912i	$0.921897\pi$
$18$		0			0
$19$	24.9472	+	14.4033i	1.31301	+	0.758066i	0.982593	−	0.185769i	$-0.0594778\pi$
$19$	24.9472	+	14.4033i	1.31301	+	0.758066i	0.330416	+	0.943836i	$0.392811\pi$
$20$	−0.396496	+	0.202384i	−0.0198248	+	0.0101192i
$21$		0			0
$22$	−4.43145	−	4.43145i	−0.201429	−	0.201429i
$23$	2.86298	+	10.6848i	0.124477	+	0.464556i	0.999820	−	0.0189465i	$-0.00603122\pi$
$23$	2.86298	+	10.6848i	0.124477	+	0.464556i	−0.875343	+	0.483502i	$0.839365\pi$
$24$		0			0
$25$	24.8668	+	2.57749i	0.994671	+	0.103100i
$26$	15.4650	−	26.7862i	0.594808	−	1.03024i
$27$		0			0
$28$	−0.550112	+	0.292892i	−0.0196469	+	0.0104604i
$29$		−	20.9038i		−	0.720822i	−0.932794	−	0.360411i	$-0.882636\pi$
$29$		−	20.9038i		−	0.720822i	0.932794	−	0.360411i	$-0.117364\pi$
$30$		0			0
$31$	−30.4426	−	52.7281i	−0.982019	−	1.70091i	−0.654501	−	0.756061i	$-0.727121\pi$
$31$	−30.4426	−	52.7281i	−0.982019	−	1.70091i	−0.327518	−	0.944845i	$-0.606212\pi$
$32$	0.368622	−	1.37572i	0.0115194	−	0.0429912i
$33$		0			0
$34$			32.6581i			0.960533i
$35$	34.8707	+	3.00603i	0.996305	+	0.0858867i
$36$		0			0
$37$	−4.96117	+	1.32934i	−0.134086	+	0.0359281i	−0.325238	−	0.945632i	$-0.605444\pi$
$37$	−4.96117	+	1.32934i	−0.134086	+	0.0359281i	0.191152	+	0.981560i	$0.438778\pi$
$38$	55.0271	+	14.7445i	1.44808	+	0.388012i
$39$		0			0
$40$	−30.0279	+	27.0763i	−0.750698	+	0.676908i
$41$	−0.605481			−0.0147678			−0.00738392	−	0.999973i	$-0.502350\pi$
$41$	−0.605481			−0.0147678			−0.00738392	+	0.999973i	$0.502350\pi$
$42$		0			0
$43$	16.0752	−	16.0752i	0.373842	−	0.373842i	−0.495032	−	0.868874i	$-0.664844\pi$
$43$	16.0752	−	16.0752i	0.373842	−	0.373842i	0.868874	+	0.495032i	$0.164844\pi$
$44$	0.244341	+	0.141070i	0.00555320	+	0.00320614i
$45$		0			0
$46$	10.9379	+	18.9450i	0.237780	+	0.411848i
$47$	−34.1202	+	9.14247i	−0.725961	+	0.194521i	−0.602830	−	0.797870i	$-0.705960\pi$
$47$	−34.1202	+	9.14247i	−0.725961	+	0.194521i	−0.123131	+	0.992390i	$0.539294\pi$
$48$		0			0
$49$	48.8844	+	3.36376i	0.997641	+	0.0686481i
$50$	48.8206	−	7.80433i	0.976411	−	0.156087i
$51$		0			0
$52$	−0.360397	+	1.34502i	−0.00693070	+	0.0258657i
$53$	−60.8242	−	16.2978i	−1.14763	−	0.307506i	−0.365613	−	0.930767i	$-0.619141\pi$
$53$	−60.8242	−	16.2978i	−1.14763	−	0.307506i	−0.782014	+	0.623261i	$0.785807\pi$
$54$		0			0
$55$	−7.20355	−	14.1127i	−0.130974	−	0.256595i
$56$	−41.3774	+	38.6280i	−0.738882	+	0.689786i
$57$		0			0
$58$	−10.6995	−	39.9312i	−0.184475	−	0.688469i
$59$	−88.6860	+	51.2029i	−1.50315	+	0.867845i	−0.503159	+	0.864194i	$0.667829\pi$
$59$	−88.6860	+	51.2029i	−1.50315	+	0.867845i	−0.999993	+	0.00365152i	$0.998838\pi$
$60$		0			0
$61$	−16.9814	+	29.4127i	−0.278384	+	0.482175i	−0.970983	−	0.239147i	$-0.923132\pi$
$61$	−16.9814	+	29.4127i	−0.278384	+	0.482175i	0.692599	+	0.721322i	$0.256465\pi$
$62$	−85.1410	−	85.1410i	−1.37324	−	1.37324i
$63$		0			0
$64$		−	65.3604i		−	1.02126i
$65$	58.0765	−	52.3679i	0.893484	−	0.805659i
$66$		0			0
$67$	−13.4604	+	50.2349i	−0.200902	+	0.749775i	0.789758	+	0.613418i	$0.210206\pi$
$67$	−13.4604	+	50.2349i	−0.200902	+	0.749775i	−0.990660	+	0.136357i	$0.956461\pi$
$68$	−0.380533	−	1.42017i	−0.00559607	−	0.0208848i
$69$		0			0
$70$	68.1497	−	12.1062i	0.973567	−	0.172945i
$71$	−25.3750			−0.357395			−0.178697	−	0.983904i	$-0.557188\pi$
$71$	−25.3750			−0.357395			−0.178697	+	0.983904i	$0.557188\pi$
$72$		0			0
$73$	−86.1585	−	23.0861i	−1.18025	−	0.316248i	−0.385226	−	0.922822i	$-0.625877\pi$
$73$	−86.1585	−	23.0861i	−1.18025	−	0.316248i	−0.795027	+	0.606574i	$0.792543\pi$
$74$	−8.79656	+	5.07870i	−0.118872	+	0.0686310i
$75$		0			0
$76$	−2.56471			−0.0337461
$77$	−10.4251	−	19.5805i	−0.135391	−	0.254292i
$78$		0			0
$79$	6.66046	+	3.84542i	0.0843096	+	0.0486762i	0.541562	−	0.840661i	$-0.317833\pi$
$79$	6.66046	+	3.84542i	0.0843096	+	0.0486762i	−0.457253	+	0.889337i	$0.651166\pi$
$80$	−42.5326	+	65.5976i	−0.531658	+	0.819970i
$81$		0			0
$82$	−1.15661	+	0.309913i	−0.0141050	+	0.00377942i
$83$	−81.1873	+	81.1873i	−0.978160	+	0.978160i	−0.999767	−	0.0216065i	$-0.993122\pi$
$83$	−81.1873	+	81.1873i	−0.978160	+	0.978160i	0.0216065	+	0.999767i	$0.493122\pi$
$84$		0			0
$85$	−25.4589	+	78.5465i	−0.299517	+	0.924076i
$86$	22.4793	−	38.9354i	0.261388	−	0.452737i
$87$		0			0
$88$	24.7528	+	6.63250i	0.281282	+	0.0753693i
$89$	35.6866	+	20.6037i	0.400973	+	0.231502i	0.686904	−	0.726748i	$-0.258969\pi$
$89$	35.6866	+	20.6037i	0.400973	+	0.231502i	−0.285931	+	0.958250i	$0.592303\pi$
$90$		0			0
$91$	80.0273	−	74.7098i	0.879421	−	0.820987i
$92$	−0.696392	−	0.696392i	−0.00756947	−	0.00756947i
$93$		0			0
$94$	−60.4979	+	34.9285i	−0.643594	+	0.371579i
$95$	120.852	+	78.3590i	1.27213	+	0.824831i
$96$		0			0
$97$	1.74125	+	1.74125i	0.0179511	+	0.0179511i	0.716025	−	0.698074i	$-0.245959\pi$
$97$	1.74125	+	1.74125i	0.0179511	+	0.0179511i	−0.698074	+	0.716025i	$0.745959\pi$
$98$	95.1022	−	18.5957i	0.970431	−	0.189752i
$99$		0			0
$100$	−2.03207	+	0.908236i	−0.0203207	+	0.00908236i
$101$	−75.1492	−	130.162i	−0.744051	−	1.28873i	−0.950637	−	0.310306i	$-0.899569\pi$
$101$	−75.1492	−	130.162i	−0.744051	−	1.28873i	0.206586	−	0.978429i	$-0.433765\pi$
$102$		0			0
$103$	−38.0137	−	141.869i	−0.369065	−	1.37737i	−0.861825	−	0.507205i	$-0.830679\pi$
$103$	−38.0137	−	141.869i	−0.369065	−	1.37737i	0.492760	−	0.870165i	$-0.335988\pi$
$104$			126.474i			1.21609i
$105$		0			0
$106$	−124.530			−1.17481
$107$	98.2349	−	26.3220i	0.918083	−	0.246000i	0.231317	−	0.972878i	$-0.425696\pi$
$107$	98.2349	−	26.3220i	0.918083	−	0.246000i	0.686766	+	0.726879i	$0.259030\pi$
$108$		0			0
$109$	−104.505	+	60.3357i	−0.958757	+	0.553539i	−0.895790	−	0.444477i	$-0.853390\pi$
$109$	−104.505	+	60.3357i	−0.958757	+	0.553539i	−0.0629667	+	0.998016i	$0.520056\pi$
$110$	−20.9840	−	23.2714i	−0.190763	−	0.211558i
$111$		0			0
$112$	−57.9489	+	92.8524i	−0.517401	+	0.829040i
$113$	152.659	−	152.659i	1.35097	−	1.35097i	0.466383	−	0.884583i	$-0.345557\pi$
$113$	152.659	−	152.659i	1.35097	−	1.35097i	0.884583	−	0.466383i	$-0.154443\pi$
$114$		0			0
$115$	11.5381	+	54.0916i	0.100332	+	0.470362i
$116$	0.930557	+	1.61177i	0.00802204	+	0.0138946i
$117$		0			0
$118$	−143.203	+	143.203i	−1.21358	+	1.21358i
$119$	−33.7359	+	110.565i	−0.283495	+	0.929116i
$120$		0			0
$121$	55.4788	−	96.0921i	0.458503	−	0.794150i
$122$	−17.3837	+	64.8769i	−0.142489	+	0.531778i
$123$		0			0
$124$	4.69449	+	2.71037i	0.0378588	+	0.0218578i
$125$	123.503	+	19.2882i	0.988023	+	0.154306i
$126$		0			0
$127$	−42.9287	−	42.9287i	−0.338021	−	0.338021i	0.517601	−	0.855622i	$-0.326825\pi$
$127$	−42.9287	−	42.9287i	−0.338021	−	0.338021i	−0.855622	+	0.517601i	$0.826825\pi$
$128$	−31.9799	−	119.351i	−0.249843	−	0.932426i
$129$		0			0
$130$	84.1352	−	129.761i	0.647194	−	0.998160i
$131$	0.332730	−	0.576305i	0.00253992	−	0.00439928i	−0.864753	−	0.502198i	$-0.832525\pi$
$131$	0.332730	−	0.576305i	0.00253992	−	0.00439928i	0.867293	+	0.497799i	$0.165858\pi$
$132$		0			0
$133$	171.064	+	106.761i	1.28620	+	0.802713i
$134$			102.850i			0.767537i
$135$		0			0
$136$	−66.7700	−	115.649i	−0.490956	−	0.850361i
$137$	21.7413	−	81.1397i	0.158696	−	0.592261i	−0.840065	−	0.542486i	$-0.817483\pi$
$137$	21.7413	−	81.1397i	0.158696	−	0.592261i	0.998760	−	0.0497746i	$-0.0158503\pi$
$138$		0			0
$139$			178.979i			1.28762i	0.765185	+	0.643810i	$0.222647\pi$
$139$			178.979i			1.28762i	−0.765185	+	0.643810i	$0.777353\pi$
$140$	−2.82249	+	1.32053i	−0.0201606	+	0.00943234i
$141$		0			0
$142$	−48.4722	+	12.9881i	−0.341353	+	0.0914654i
$143$	−47.8740	−	12.8278i	−0.334783	−	0.0897049i
$144$		0			0
$145$	5.39513	−	104.380i	0.0372078	−	0.719861i
$146$	−176.399			−1.20821
$147$		0			0
$148$	0.323349	−	0.323349i	0.00218479	−	0.00218479i
$149$	5.12619	+	2.95961i	0.0344039	+	0.0198631i	0.517103	−	0.855923i	$-0.327010\pi$
$149$	5.12619	+	2.95961i	0.0344039	+	0.0198631i	−0.482699	+	0.875786i	$0.660344\pi$
$150$		0			0
$151$	41.9842	+	72.7188i	0.278041	+	0.481581i	0.970898	−	0.239494i	$-0.0769815\pi$
$151$	41.9842	+	72.7188i	0.278041	+	0.481581i	−0.692857	+	0.721075i	$0.743648\pi$
$152$	−225.008	+	60.2906i	−1.48031	+	0.396649i
$153$		0			0
$154$	−29.9365	−	32.0672i	−0.194393	−	0.208228i
$155$	−138.401	−	271.146i	−0.892911	−	1.74933i
$156$		0			0
$157$	22.8585	−	85.3089i	0.145595	−	0.543369i	−0.854133	−	0.520055i	$-0.825912\pi$
$157$	22.8585	−	85.3089i	0.145595	−	0.543369i	0.999728	−	0.0233142i	$-0.00742182\pi$
$158$	14.6913	+	3.93651i	0.0929827	+	0.0249146i
$159$		0			0
$160$	2.19572	−	6.77428i	0.0137232	−	0.0423392i
$161$	17.4603	+	75.4376i	0.108449	+	0.468557i
$162$		0			0
$163$	−43.7619	−	163.321i	−0.268478	−	1.00197i	−0.960087	−	0.279701i	$-0.909765\pi$
$163$	−43.7619	−	163.321i	−0.268478	−	1.00197i	0.691610	−	0.722272i	$-0.256902\pi$
$164$	0.0466851	−	0.0269537i	0.000284665	−	0.000164352i
$165$		0			0
$166$	−113.531	+	196.642i	−0.683923	+	1.18459i
$167$	152.203	+	152.203i	0.911395	+	0.911395i	0.996382	−	0.0849869i	$-0.0270848\pi$
$167$	152.203	+	152.203i	0.911395	+	0.911395i	−0.0849869	+	0.996382i	$0.527085\pi$
$168$		0			0
$169$		−	75.6107i		−	0.447401i
$170$	−8.42883	+	163.073i	−0.0495813	+	0.959252i
$171$		0			0
$172$	−0.523859	+	1.95507i	−0.00304569	+	0.0113667i
$173$	5.62237	+	20.9830i	0.0324993	+	0.121289i	0.980270	−	0.197664i	$-0.0633355\pi$
$173$	5.62237	+	20.9830i	0.0324993	+	0.121289i	−0.947771	+	0.318953i	$0.896669\pi$
$174$		0			0
$175$	173.345	+	24.0100i	0.990543	+	0.137200i
$176$	49.5499			0.281533
$177$		0			0
$178$	78.7155	+	21.0918i	0.442222	+	0.118493i
$179$	106.793	−	61.6572i	0.596612	−	0.344454i	−0.171096	−	0.985254i	$-0.554731\pi$
$179$	106.793	−	61.6572i	0.596612	−	0.344454i	0.767707	+	0.640801i	$0.221397\pi$
$180$		0			0
$181$	−58.5465			−0.323462			−0.161731	−	0.986835i	$-0.551708\pi$
$181$	−58.5465			−0.323462			−0.161731	+	0.986835i	$0.551708\pi$
$182$	114.631	−	183.675i	0.629839	−	1.00920i
$183$		0			0
$184$	−77.4667	−	44.7254i	−0.421015	−	0.243073i
$185$	−25.1159	+	5.35740i	−0.135761	+	0.0289589i
$186$		0			0
$187$	50.5488	−	13.5445i	0.270315	−	0.0724306i
$188$	2.22382	−	2.22382i	0.0118288	−	0.0118288i
$189$		0			0
$190$	270.963	+	87.8261i	1.42612	+	0.462243i
$191$	−138.752	+	240.325i	−0.726449	+	1.25825i	0.231925	+	0.972734i	$0.425498\pi$
$191$	−138.752	+	240.325i	−0.726449	+	1.25825i	−0.958375	+	0.285514i	$0.907836\pi$
$192$		0			0
$193$	361.420	+	96.8423i	1.87265	+	0.501774i	0.999908	+	0.0135835i	$0.00432391\pi$
$193$	361.420	+	96.8423i	1.87265	+	0.501774i	0.872737	+	0.488190i	$0.162343\pi$
$194$	4.21745	+	2.43494i	0.0217394	+	0.0125513i
$195$		0			0
$196$	−3.91893	+	1.91678i	−0.0199945	+	0.00977950i
$197$	−96.9859	−	96.9859i	−0.492314	−	0.492314i	0.416720	−	0.909035i	$-0.363179\pi$
$197$	−96.9859	−	96.9859i	−0.492314	−	0.492314i	−0.909035	+	0.416720i	$0.863179\pi$
$198$		0			0
$199$	−78.0408	+	45.0569i	−0.392165	+	0.226416i	−0.683098	−	0.730327i	$-0.739368\pi$
$199$	−78.0408	+	45.0569i	−0.392165	+	0.226416i	0.290933	+	0.956743i	$0.406034\pi$
$200$	−156.928	+	127.451i	−0.784638	+	0.637256i
$201$		0			0
$202$	−210.175	−	210.175i	−1.04047	−	1.04047i
$203$	5.02550	−	146.241i	0.0247562	−	0.720397i
$204$		0			0
$205$	−3.02337	−	0.156270i	−0.0147482	−	0.000762295i
$206$	−145.230	−	251.546i	−0.705000	−	1.22110i
$207$		0			0
$208$	63.2934	+	236.214i	0.304295	+	1.13564i
$209$		−	91.2870i		−	0.436780i
$210$		0			0
$211$	−3.83967			−0.0181975			−0.00909873	−	0.999959i	$-0.502896\pi$
$211$	−3.83967			−0.0181975			−0.00909873	+	0.999959i	$0.502896\pi$
$212$	5.41531	−	1.45103i	0.0255439	−	0.00684447i
$213$		0			0
$214$	174.179	−	100.562i	0.813919	−	0.469916i
$215$	84.4178	−	76.1200i	0.392641	−	0.354046i
$216$		0			0
$217$	−200.296	−	376.198i	−0.923023	−	1.73363i
$218$	−168.745	+	168.745i	−0.774061	+	0.774061i
$219$		0			0
$220$	1.18367	+	0.767473i	0.00538030	+	0.00348851i
$221$	129.139	+	223.675i	0.584338	+	1.01210i
$222$		0			0
$223$	−68.8218	+	68.8218i	−0.308618	+	0.308618i	−0.844373	−	0.535755i	$-0.820027\pi$
$223$	−68.8218	+	68.8218i	−0.308618	+	0.308618i	0.535755	+	0.844373i	$0.320027\pi$
$224$	2.90957	−	9.53572i	0.0129892	−	0.0425702i
$225$		0			0
$226$	213.476	−	369.752i	0.944586	−	1.63607i
$227$	36.4264	−	135.945i	0.160469	−	0.598878i	−0.838106	−	0.545508i	$-0.816337\pi$
$227$	36.4264	−	135.945i	0.160469	−	0.598878i	0.998575	−	0.0533705i	$-0.0169964\pi$
$228$		0			0
$229$	143.125	+	82.6334i	0.625001	+	0.360844i	0.778813	−	0.627256i	$-0.215822\pi$
$229$	143.125	+	82.6334i	0.625001	+	0.360844i	−0.153813	+	0.988100i	$0.549155\pi$
$230$	49.7270	+	97.4217i	0.216204	+	0.423573i
$231$		0			0
$232$	119.529	+	119.529i	0.515212	+	0.515212i
$233$	−68.7110	−	256.433i	−0.294897	−	1.10057i	−0.941299	−	0.337574i	$-0.890394\pi$
$233$	−68.7110	−	256.433i	−0.294897	−	1.10057i	0.646402	−	0.762997i	$-0.276273\pi$
$234$		0			0
$235$	−172.733	+	36.8452i	−0.735034	+	0.156788i
$236$	4.55870	−	7.89590i	0.0193165	−	0.0334572i
$237$		0			0
$238$	−7.85135	+	228.472i	−0.0329889	+	0.959966i
$239$			373.238i			1.56167i	0.624739	+	0.780834i	$0.285205\pi$
$239$			373.238i			1.56167i	−0.624739	+	0.780834i	$0.714795\pi$
$240$		0			0
$241$	193.813	+	335.694i	0.804204	+	1.39292i	0.916827	+	0.399284i	$0.130741\pi$
$241$	193.813	+	335.694i	0.804204	+	1.39292i	−0.112624	+	0.993638i	$0.535925\pi$
$242$	56.7931	−	211.955i	0.234682	−	0.875846i
$243$		0			0
$244$		−	3.02378i		−	0.0123926i
$245$	243.228	+	29.4131i	0.992767	+	0.120053i
$246$		0			0
$247$	435.183	−	116.607i	1.76188	−	0.472093i
$248$	475.574	+	127.430i	1.91764	+	0.513829i
$249$		0			0
$250$	245.792	−	26.3694i	0.983167	−	0.105478i
$251$	24.1190			0.0960917			0.0480458	−	0.998845i	$-0.484701\pi$
$251$	24.1190			0.0960917			0.0480458	+	0.998845i	$0.484701\pi$
$252$		0			0
$253$	24.7871	−	24.7871i	0.0979726	−	0.0979726i
$254$	−103.977	−	60.0309i	−0.409357	−	0.236342i
$255$		0			0
$256$	8.54282	+	14.7966i	0.0333704	+	0.0577992i
$257$	194.693	−	52.1677i	0.757558	−	0.202987i	0.140690	−	0.990054i	$-0.455068\pi$
$257$	194.693	−	52.1677i	0.757558	−	0.202987i	0.616868	+	0.787067i	$0.288401\pi$
$258$		0			0
$259$	−35.0273	+	8.10718i	−0.135240	+	0.0313019i
$260$	−2.14672	+	6.62311i	−0.00825662	+	0.0254735i
$261$		0			0
$262$	0.340612	−	1.27118i	0.00130005	−	0.00485184i
$263$	156.656	+	41.9758i	0.595649	+	0.159604i	0.544034	−	0.839063i	$-0.316896\pi$
$263$	156.656	+	41.9758i	0.595649	+	0.159604i	0.0516156	+	0.998667i	$0.483563\pi$
$264$		0			0
$265$	−299.509	−	97.0786i	−1.13022	−	0.366334i
$266$	381.418	+	116.379i	1.43390	+	0.437517i
$267$		0			0
$268$	−1.19841	−	4.47252i	−0.00447168	−	0.0166885i
$269$	−69.3332	+	40.0295i	−0.257744	+	0.148809i	−0.623305	−	0.781979i	$-0.714211\pi$
$269$	−69.3332	+	40.0295i	−0.257744	+	0.148809i	0.365561	+	0.930787i	$0.380877\pi$
$270$		0			0
$271$	−230.600	+	399.411i	−0.850923	+	1.47384i	0.0294543	+	0.999566i	$0.490623\pi$
$271$	−230.600	+	399.411i	−0.850923	+	1.47384i	−0.880377	+	0.474275i	$0.842710\pi$
$272$	−182.582	−	182.582i	−0.671258	−	0.671258i
$273$		0			0
$274$		−	166.124i		−	0.606291i
$275$	−32.3274	−	72.3286i	−0.117554	−	0.263013i
$276$		0			0
$277$	44.5632	−	166.312i	0.160878	−	0.600405i	−0.837652	−	0.546204i	$-0.816072\pi$
$277$	44.5632	−	166.312i	0.160878	−	0.600405i	0.998530	−	0.0542008i	$-0.0172611\pi$
$278$	91.6096	+	341.892i	0.329531	+	1.22983i
$279$		0			0
$280$	−216.581	+	182.203i	−0.773503	+	0.650727i
$281$	−40.4440			−0.143929			−0.0719644	−	0.997407i	$-0.522927\pi$
$281$	−40.4440			−0.143929			−0.0719644	+	0.997407i	$0.522927\pi$
$282$		0			0
$283$	−147.124	−	39.4218i	−0.519874	−	0.139300i	−0.0106656	−	0.999943i	$-0.503395\pi$
$283$	−147.124	−	39.4218i	−0.519874	−	0.139300i	−0.509208	+	0.860643i	$0.670062\pi$
$284$	1.95652	−	1.12960i	0.00688915	−	0.00397745i
$285$		0			0
$286$	−98.0163			−0.342714
$287$	−4.23587	−	0.145564i	−0.0147591	−	0.000507192i
$288$		0			0
$289$	14.1092	+	8.14597i	0.0488209	+	0.0281867i
$290$	−43.1204	−	202.151i	−0.148691	−	0.697073i
$291$		0			0
$292$	7.67087	−	2.05540i	0.0262701	−	0.00703906i
$293$	106.571	−	106.571i	0.363722	−	0.363722i	−0.501459	−	0.865181i	$-0.667203\pi$
$293$	106.571	−	106.571i	0.363722	−	0.363722i	0.865181	+	0.501459i	$0.167203\pi$
$294$		0			0
$295$	−456.054	+	232.784i	−1.54595	+	0.789098i
$296$	20.7670	−	35.9694i	0.0701586	−	0.121518i
$297$		0			0
$298$	11.3071	+	3.02972i	0.0379432	+	0.0101668i
$299$	149.827	+	86.5027i	0.501094	+	0.289307i
$300$		0			0
$301$	116.325	−	108.595i	0.386461	−	0.360782i
$302$	117.420	+	117.420i	0.388809	+	0.388809i
$303$		0			0
$304$	−390.073	+	225.209i	−1.28313	+	0.740817i
$305$	−92.3851	+	142.485i	−0.302902	+	0.467162i
$306$		0			0
$307$	196.397	+	196.397i	0.639729	+	0.639729i	0.950489	−	0.310759i	$-0.100583\pi$
$307$	196.397	+	196.397i	0.639729	+	0.639729i	−0.310759	+	0.950489i	$0.600583\pi$
$308$	1.67546	+	1.04565i	0.00543981	+	0.00339497i
$309$		0			0
$310$	−403.163	−	447.112i	−1.30053	−	1.44230i
$311$	−92.9088	−	160.923i	−0.298742	−	0.517437i	0.677106	−	0.735885i	$-0.263234\pi$
$311$	−92.9088	−	160.923i	−0.298742	−	0.517437i	−0.975848	+	0.218449i	$0.929900\pi$
$312$		0			0
$313$	−141.985	−	529.896i	−0.453627	−	1.69296i	−0.692094	−	0.721807i	$-0.743312\pi$
$313$	−141.985	−	529.896i	−0.453627	−	1.69296i	0.238468	−	0.971150i	$-0.423355\pi$
$314$		−	174.660i		−	0.556241i
$315$		0			0
$316$	−0.684731			−0.00216687
$317$	47.1593	−	12.6363i	0.148768	−	0.0398622i	−0.183667	−	0.982989i	$-0.558797\pi$
$317$	47.1593	−	12.6363i	0.148768	−	0.0398622i	0.332434	+	0.943126i	$0.392130\pi$
$318$		0			0
$319$	−57.3687	+	33.1218i	−0.179839	+	0.103830i
$320$	16.8691	−	326.366i	0.0527158	−	1.01989i
$321$		0			0
$322$	71.9655	+	135.166i	0.223495	+	0.419771i
$323$	−336.376	+	336.376i	−1.04141	+	1.04141i
$324$		0			0
$325$	303.511	−	246.501i	0.933880	−	0.758465i
$326$	−167.191	−	289.583i	−0.512854	−	0.888290i
$327$		0			0
$328$	3.46217	−	3.46217i	0.0105554	−	0.0105554i
$329$	−240.898	+	55.7567i	−0.732213	+	0.169473i
$330$		0			0
$331$	−11.1043	+	19.2332i	−0.0335477	+	0.0581063i	−0.882312	−	0.470665i	$-0.844014\pi$
$331$	−11.1043	+	19.2332i	−0.0335477	+	0.0581063i	0.848764	+	0.528772i	$0.177347\pi$
$332$	2.64573	−	9.87401i	0.00796908	−	0.0297410i
$333$		0			0
$334$	368.647	+	212.839i	1.10373	+	0.637241i
$335$	−80.1776	+	247.366i	−0.239336	+	0.738405i
$336$		0			0
$337$	229.038	+	229.038i	0.679638	+	0.679638i	0.959918	−	0.280280i	$-0.0904275\pi$
$337$	229.038	+	229.038i	0.679638	+	0.679638i	−0.280280	+	0.959918i	$0.590427\pi$
$338$	−38.7010	−	144.434i	−0.114500	−	0.427319i
$339$		0			0
$340$	−1.53359	−	7.18958i	−0.00451056	−	0.0211458i
$341$	−96.4717	+	167.094i	−0.282908	+	0.490011i
$342$		0			0
$343$	341.180	+	35.2847i	0.994695	+	0.102871i
$344$			183.838i			0.534412i
$345$		0			0
$346$	21.4801	+	37.2045i	0.0620811	+	0.107528i
$347$	−161.490	+	602.689i	−0.465389	+	1.73686i	0.190206	+	0.981744i	$0.439084\pi$
$347$	−161.490	+	602.689i	−0.465389	+	1.73686i	−0.655595	+	0.755112i	$0.727582\pi$
$348$		0			0
$349$		−	121.709i		−	0.348736i	−0.984681	−	0.174368i	$-0.944212\pi$
$349$		−	121.709i		−	0.348736i	0.984681	−	0.174368i	$-0.0557882\pi$
$350$	343.419	−	42.8611i	0.981196	−	0.122460i
$351$		0			0
$352$	−4.35961	+	1.16815i	−0.0123853	+	0.00331862i
$353$	47.2091	+	12.6496i	0.133737	+	0.0358347i	0.325067	−	0.945691i	$-0.394613\pi$
$353$	47.2091	+	12.6496i	0.133737	+	0.0358347i	−0.191330	+	0.981526i	$0.561280\pi$
$354$		0			0
$355$	−126.706	−	6.54912i	−0.356918	−	0.0184482i
$356$	−3.66878			−0.0103056
$357$		0			0
$358$	172.441	−	172.441i	0.481680	−	0.481680i
$359$	−439.021	−	253.469i	−1.22290	−	0.706042i	−0.257365	−	0.966314i	$-0.582854\pi$
$359$	−439.021	−	253.469i	−1.22290	−	0.706042i	−0.965535	+	0.260273i	$0.916188\pi$
$360$		0			0
$361$	234.408	+	406.006i	0.649328	+	1.12467i
$362$	−111.837	+	29.9667i	−0.308943	+	0.0827811i
$363$		0			0
$364$	−2.84464	+	9.32293i	−0.00781496	+	0.0256125i
$365$	−424.260	−	137.514i	−1.16236	−	0.376749i
$366$		0			0
$367$	85.7047	−	319.854i	0.233528	−	0.871538i	−0.745279	−	0.666753i	$-0.767684\pi$
$367$	85.7047	−	319.854i	0.233528	−	0.871538i	0.978807	−	0.204785i	$-0.0656496\pi$
$368$	−167.067	−	44.7654i	−0.453985	−	0.121645i
$369$		0			0
$370$	−45.2349	+	23.0893i	−0.122257	+	0.0624035i
$371$	−421.600	−	128.640i	−1.13639	−	0.346739i
$372$		0			0
$373$	−55.0306	−	205.377i	−0.147535	−	0.550608i	−0.999629	−	0.0272202i	$-0.991334\pi$
$373$	−55.0306	−	205.377i	−0.147535	−	0.550608i	0.852094	−	0.523388i	$-0.175332\pi$
$374$	89.6272	−	51.7463i	0.239645	−	0.138359i
$375$		0			0
$376$	142.824	−	247.378i	0.379850	−	0.657919i
$377$	−231.179	−	231.179i	−0.613208	−	0.613208i
$378$		0			0
$379$		−	147.615i		−	0.389487i	−0.980854	−	0.194743i	$-0.937613\pi$
$379$		−	147.615i		−	0.389487i	0.980854	−	0.194743i	$-0.0623874\pi$
$380$	−12.8064	−	0.661932i	−0.0337011	−	0.00174193i
$381$		0			0
$382$	−142.039	+	530.096i	−0.371829	+	1.38769i
$383$	−12.2398	−	45.6796i	−0.0319578	−	0.119268i	0.948104	−	0.317959i	$-0.102998\pi$
$383$	−12.2398	−	45.6796i	−0.0319578	−	0.119268i	−0.980062	+	0.198691i	$0.936331\pi$
$384$		0			0
$385$	−47.0023	−	100.462i	−0.122084	−	0.260941i
$386$	739.965			1.91701
$387$		0			0
$388$	−0.211771	−	0.0567440i	−0.000545803	−	0.000146247i
$389$	289.878	−	167.361i	0.745187	−	0.430234i	−0.0787651	−	0.996893i	$-0.525098\pi$
$389$	289.878	−	167.361i	0.745187	−	0.430234i	0.823952	+	0.566659i	$0.191764\pi$
$390$		0			0
$391$	−182.671			−0.467190
$392$	−298.757	+	260.289i	−0.762136	+	0.664003i
$393$		0			0
$394$	−234.907	−	135.624i	−0.596211	−	0.344223i
$395$	32.2654	+	20.9205i	0.0816846	+	0.0529632i
$396$		0			0
$397$	−450.996	+	120.844i	−1.13601	+	0.304393i	−0.777346	−	0.629073i	$-0.783434\pi$
$397$	−450.996	+	120.844i	−1.13601	+	0.304393i	−0.358665	+	0.933466i	$0.616768\pi$
$398$	−126.014	+	126.014i	−0.316618	+	0.316618i
$399$		0			0
$400$	−229.310	+	316.573i	−0.573275	+	0.791433i
$401$	13.7234	−	23.7697i	0.0342230	−	0.0592759i	−0.848407	−	0.529345i	$-0.822438\pi$
$401$	13.7234	−	23.7697i	0.0342230	−	0.0592759i	0.882630	+	0.470069i	$0.155771\pi$
$402$		0			0
$403$	−919.799	−	246.459i	−2.28238	−	0.611562i
$404$	11.5886	+	6.69069i	0.0286847	+	0.0165611i
$405$		0			0
$406$	−65.2526	−	281.926i	−0.160721	−	0.694398i
$407$	11.5092	+	11.5092i	0.0282780	+	0.0282780i
$408$		0			0
$409$	−418.429	+	241.580i	−1.02305	+	0.590660i	−0.914987	−	0.403484i	$-0.867799\pi$
$409$	−418.429	+	241.580i	−1.02305	+	0.590660i	−0.108066	+	0.994144i	$0.534466\pi$
$410$	−5.85532	+	1.24898i	−0.0142813	+	0.00304630i
$411$		0			0
$412$	9.24647	+	9.24647i	0.0224429	+	0.0224429i
$413$	−632.745	+	336.888i	−1.53207	+	0.815709i
$414$		0			0
$415$	−426.349	+	384.441i	−1.02735	+	0.926365i
$416$	−11.1376	−	19.2910i	−0.0267732	−	0.0463725i
$417$		0			0
$418$	−46.7248	−	174.379i	−0.111782	−	0.417175i
$419$		−	666.615i		−	1.59097i	−0.605975	−	0.795484i	$-0.707217\pi$
$419$		−	666.615i		−	1.59097i	0.605975	−	0.795484i	$-0.292783\pi$
$420$		0			0
$421$	−468.859			−1.11368			−0.556840	−	0.830620i	$-0.687986\pi$
$421$	−468.859			−1.11368			−0.556840	+	0.830620i	$0.687986\pi$
$422$	−7.33465	+	1.96531i	−0.0173807	+	0.00465714i
$423$		0			0
$424$	440.987	−	254.604i	1.04006	−	0.600481i
$425$	−147.397	+	385.638i	−0.346817	+	0.907383i
$426$		0			0
$427$	−125.871	+	201.685i	−0.294780	+	0.472330i
$428$	−6.40256	+	6.40256i	−0.0149593	+	0.0149593i
$429$		0			0
$430$	122.296	−	188.616i	0.284409	−	0.438641i
$431$	128.770	+	223.036i	0.298769	+	0.517484i	0.975855	−	0.218421i	$-0.0700905\pi$
$431$	128.770	+	223.036i	0.298769	+	0.517484i	−0.677085	+	0.735905i	$0.736757\pi$
$432$		0			0
$433$	25.8365	−	25.8365i	0.0596685	−	0.0596685i	−0.676643	−	0.736311i	$-0.736566\pi$
$433$	25.8365	−	25.8365i	0.0596685	−	0.0596685i	0.736311	+	0.676643i	$0.236566\pi$
$434$	−575.166	−	616.104i	−1.32527	−	1.41959i
$435$		0			0
$436$	5.37182	−	9.30426i	0.0123207	−	0.0213400i
$437$	−82.4724	+	307.791i	−0.188724	+	0.704328i
$438$		0			0
$439$	−65.8274	−	38.0054i	−0.149948	−	0.0865728i	0.423149	−	0.906060i	$-0.360925\pi$
$439$	−65.8274	−	38.0054i	−0.149948	−	0.0865728i	−0.573097	+	0.819488i	$0.694258\pi$
$440$	121.887	+	39.5068i	0.277017	+	0.0897882i
$441$		0			0
$442$	361.172	+	361.172i	0.817131	+	0.817131i
$443$	−69.5026	−	259.387i	−0.156891	−	0.585524i	−0.998936	−	0.0461173i	$-0.985315\pi$
$443$	−69.5026	−	259.387i	−0.156891	−	0.585524i	0.842045	−	0.539407i	$-0.181351\pi$
$444$		0			0
$445$	172.877	+	112.091i	0.388489	+	0.251891i
$446$	−96.2394	+	166.692i	−0.215783	+	0.373748i
$447$		0			0
$448$	15.7133	−	457.253i	0.0350744	−	1.02065i
$449$		−	458.330i		−	1.02078i	−0.859943	−	0.510390i	$-0.829501\pi$
$449$		−	458.330i		−	1.02078i	0.859943	−	0.510390i	$-0.170499\pi$
$450$		0			0
$451$	0.959377	+	1.66169i	0.00212722	+	0.00368446i
$452$	−4.97486	+	18.5664i	−0.0110063	+	0.0410762i
$453$		0			0
$454$		−	278.332i		−	0.613065i
$455$	418.885	−	352.397i	0.920627	−	0.774498i
$456$		0			0
$457$	−569.001	+	152.463i	−1.24508	+	0.333618i	−0.820433	−	0.571742i	$-0.806268\pi$
$457$	−569.001	+	152.463i	−1.24508	+	0.333618i	−0.424645	+	0.905360i	$0.639601\pi$
$458$	315.698	+	84.5909i	0.689296	+	0.184696i
$459$		0			0
$460$	−3.29758	−	3.65705i	−0.00716866	−	0.00795011i
$461$	520.350			1.12874			0.564371	−	0.825521i	$-0.309119\pi$
$461$	520.350			1.12874			0.564371	+	0.825521i	$0.309119\pi$
$462$		0			0
$463$	−457.986	+	457.986i	−0.989171	+	0.989171i	−0.999942	−	0.0107714i	$-0.996571\pi$
$463$	−457.986	+	457.986i	−0.989171	+	0.989171i	0.0107714	+	0.999942i	$0.496571\pi$
$464$	283.062	+	163.426i	0.610047	+	0.352211i
$465$		0			0
$466$	−262.508	−	454.677i	−0.563322	−	0.975702i
$467$	137.951	−	36.9638i	0.295398	−	0.0791516i	−0.108077	−	0.994143i	$-0.534469\pi$
$467$	137.951	−	36.9638i	0.295398	−	0.0791516i	0.403474	+	0.914991i	$0.367802\pi$
$468$		0			0
$469$	−106.244	+	348.201i	−0.226534	+	0.742433i
$470$	−311.101	+	158.795i	−0.661917	+	0.337863i
$471$		0			0
$472$	214.330	−	799.891i	0.454089	−	1.69468i
$473$	−69.5879	−	18.6460i	−0.147120	−	0.0394208i
$474$		0			0
$475$	583.231	+	422.464i	1.22786	+	0.889397i
$476$	−2.32073	−	10.0268i	−0.00487549	−	0.0210647i
$477$		0			0
$478$	191.040	+	712.972i	0.399666	+	1.49157i
$479$	−220.224	+	127.146i	−0.459758	+	0.265441i	−0.711942	−	0.702238i	$-0.752184\pi$
$479$	−220.224	+	127.146i	−0.459758	+	0.265441i	0.252185	+	0.967679i	$0.418851\pi$
$480$		0			0
$481$	−40.1650	+	69.5678i	−0.0835031	+	0.144632i
$482$	542.051	+	542.051i	1.12459	+	1.12459i
$483$		0			0
$484$			9.87879i			0.0204107i
$485$	8.24525	+	9.14406i	0.0170005	+	0.0188537i
$486$		0			0
$487$	50.6027	−	188.852i	0.103907	−	0.387786i	−0.894312	−	0.447444i	$-0.852334\pi$
$487$	50.6027	−	188.852i	0.103907	−	0.387786i	0.998219	+	0.0596581i	$0.0190011\pi$
$488$	−71.0825	−	265.284i	−0.145661	−	0.543614i
$489$		0			0
$490$	479.677	−	68.3092i	0.978932	−	0.139407i
$491$	627.569			1.27814			0.639072	−	0.769147i	$-0.279319\pi$
$491$	627.569			1.27814			0.639072	+	0.769147i	$0.279319\pi$
$492$		0			0
$493$	333.441	+	89.3452i	0.676351	+	0.181228i
$494$	771.616	−	445.493i	1.56198	−	0.901807i
$495$		0			0
$496$	951.997			1.91935
$497$	−177.520	−	6.10042i	−0.357184	−	0.0122745i
$498$		0			0
$499$	796.995	+	460.145i	1.59718	+	0.922135i	0.992027	+	0.126029i	$0.0402231\pi$
$499$	796.995	+	460.145i	1.59718	+	0.922135i	0.605157	+	0.796106i	$0.293110\pi$
$500$	−10.3812	+	4.01066i	−0.0207624	+	0.00802133i
$501$		0			0
$502$	46.0729	−	12.3452i	0.0917787	−	0.0245920i
$503$	−414.553	+	414.553i	−0.824162	+	0.824162i	−0.986702	−	0.162540i	$-0.948031\pi$
$503$	−414.553	+	414.553i	−0.824162	+	0.824162i	0.162540	+	0.986702i	$0.448031\pi$
$504$		0			0
$505$	−341.651	−	669.339i	−0.676537	−	1.32542i
$506$	34.6619	−	60.0361i	0.0685018	−	0.118649i
$507$		0			0
$508$	5.22100	+	1.39896i	0.0102775	+	0.00275386i
$509$	722.536	+	417.156i	1.41952	+	0.819561i	0.996257	−	0.0864459i	$-0.0275510\pi$
$509$	722.536	+	417.156i	1.41952	+	0.819561i	0.423264	+	0.906006i	$0.360884\pi$
$510$		0			0
$511$	−597.204	−	182.221i	−1.16870	−	0.356596i
$512$	373.375	+	373.375i	0.729248	+	0.729248i
$513$		0			0
$514$	345.206	−	199.305i	0.671607	−	0.387752i
$515$	−153.200	−	718.211i	−0.297475	−	1.39458i
$516$		0			0
$517$	79.1536	+	79.1536i	0.153102	+	0.153102i
$518$	−62.7606	+	33.4151i	−0.121159	+	0.0645079i
$519$		0			0
$520$	−32.6420	+	631.526i	−0.0627730	+	1.21447i
$521$	222.489	+	385.363i	0.427043	+	0.739660i	0.996609	−	0.0822856i	$-0.0262220\pi$
$521$	222.489	+	385.363i	0.427043	+	0.739660i	−0.569566	+	0.821946i	$0.692889\pi$
$522$		0			0
$523$	69.1669	+	258.134i	0.132250	+	0.493565i	0.999994	−	0.00344695i	$-0.00109720\pi$
$523$	69.1669	+	258.134i	0.132250	+	0.493565i	−0.867744	+	0.497012i	$0.834431\pi$
$524$			0.0592473i			0.000113067i
$525$		0			0
$526$	320.734			0.609760
$527$	971.190	−	260.230i	1.84287	−	0.493794i
$528$		0			0
$529$	352.160	−	203.319i	0.665708	−	0.384347i
$530$	−621.821	−	32.1404i	−1.17325	−	0.0606422i
$531$		0			0
$532$	−17.9423	−	0.616582i	−0.0337262	−	0.00115899i
$533$	−6.69613	+	6.69613i	−0.0125631	+	0.0125631i
$534$		0			0
$535$	497.313	−	106.081i	0.929558	−	0.198282i
$536$	−210.278	−	364.213i	−0.392311	−	0.679502i
$537$		0			0
$538$	−111.953	+	111.953i	−0.208092	+	0.208092i
$539$	−68.2251	−	139.489i	−0.126577	−	0.258792i
$540$		0			0
$541$	97.3418	−	168.601i	0.179929	−	0.311647i	−0.761927	−	0.647663i	$-0.775746\pi$
$541$	97.3418	−	168.601i	0.179929	−	0.311647i	0.941856	+	0.336016i	$0.109080\pi$
$542$	−236.063	+	880.999i	−0.435540	+	1.62546i
$543$		0			0
$544$	20.3688	+	11.7599i	0.0374426	+	0.0216175i
$545$	−537.398	+	274.304i	−0.986052	+	0.503311i
$546$		0			0
$547$	256.595	+	256.595i	0.469095	+	0.469095i	0.901621	−	0.432526i	$-0.142378\pi$
$547$	256.595	+	256.595i	0.469095	+	0.469095i	−0.432526	+	0.901621i	$0.642378\pi$
$548$	1.93568	+	7.22404i	0.00353226	+	0.0131826i
$549$		0			0
$550$	−98.7738	−	121.618i	−0.179589	−	0.221123i
$551$	301.083	−	521.492i	0.546431	−	0.946446i
$552$		0			0
$553$	45.6712	+	28.5033i	0.0825881	+	0.0515430i
$554$		−	340.504i		−	0.614629i
$555$		0			0
$556$	−7.96745	−	13.8000i	−0.0143300	−	0.0248202i
$557$	150.923	−	563.251i	0.270957	−	1.01122i	−0.687546	−	0.726141i	$-0.741312\pi$
$557$	150.923	−	563.251i	0.270957	−	1.01122i	0.958503	−	0.285083i	$-0.0920212\pi$
$558$		0			0
$559$		−	355.557i		−	0.636059i
$560$	−313.323	+	448.687i	−0.559505	+	0.801227i
$561$		0			0
$562$	−77.2574	+	20.7010i	−0.137469	+	0.0368346i
$563$	799.735	+	214.288i	1.42049	+	0.380619i	0.885657	−	0.464340i	$-0.153708\pi$
$563$	799.735	+	214.288i	1.42049	+	0.380619i	0.534831	+	0.844959i	$0.320375\pi$
$564$		0			0
$565$	801.678	−	722.878i	1.41890	−	1.27943i
$566$	−301.219			−0.532189
$567$		0			0
$568$	145.096	−	145.096i	0.255450	−	0.255450i
$569$	683.193	+	394.442i	1.20069	+	0.693219i	0.960709	−	0.277558i	$-0.0895252\pi$
$569$	683.193	+	394.442i	1.20069	+	0.693219i	0.239982	+	0.970777i	$0.422859\pi$
$570$		0			0
$571$	272.727	+	472.377i	0.477631	+	0.827281i	0.999671	−	0.0256398i	$-0.00816230\pi$
$571$	272.727	+	472.377i	0.477631	+	0.827281i	−0.522040	+	0.852921i	$0.674829\pi$
$572$	4.26233	−	1.14209i	0.00745162	−	0.00199666i
$573$		0			0
$574$	−8.16600	+	1.89005i	−0.0142265	+	0.00329277i
$575$	43.6531	+	273.075i	0.0759185	+	0.474914i
$576$		0			0
$577$	−285.030	+	1063.75i	−0.493987	+	1.84358i	0.0416465	+	0.999132i	$0.486740\pi$
$577$	−285.030	+	1063.75i	−0.493987	+	1.84358i	−0.535633	+	0.844451i	$0.679927\pi$
$578$	31.1214	+	8.33894i	0.0538432	+	0.0144272i
$579$		0			0
$580$	4.23060	+	8.28829i	0.00729413	+	0.0142901i
$581$	−587.494	+	548.457i	−1.01118	+	0.943989i
$582$		0			0
$583$	51.6472	+	192.750i	0.0885888	+	0.330618i
$584$	624.666	−	360.651i	1.06963	−	0.617553i
$585$		0			0
$586$	149.027	−	258.122i	0.254312	−	0.440482i
$587$	−161.386	−	161.386i	−0.274934	−	0.274934i	0.556149	−	0.831083i	$-0.312278\pi$
$587$	−161.386	−	161.386i	−0.274934	−	0.274934i	−0.831083	+	0.556149i	$0.812278\pi$
$588$		0			0
$589$		−	1753.89i		−	2.97774i
$590$	−752.019	+	678.100i	−1.27461	+	1.14932i
$591$		0			0
$592$	20.7855	−	77.5725i	0.0351106	−	0.131035i
$593$	−261.697	−	976.667i	−0.441310	−	1.64699i	−0.725498	−	0.688224i	$-0.758391\pi$
$593$	−261.697	−	976.667i	−0.441310	−	1.64699i	0.284188	−	0.958769i	$-0.408276\pi$
$594$		0			0
$595$	−196.991	+	543.380i	−0.331077	+	0.913244i
$596$	−0.527000			−0.000884228
$597$		0			0
$598$	330.480	+	88.5519i	0.552642	+	0.148080i
$599$	−999.469	+	577.044i	−1.66856	+	0.963345i	−0.700149	+	0.713996i	$0.746883\pi$
$599$	−999.469	+	577.044i	−1.66856	+	0.963345i	−0.968414	+	0.249349i	$0.919783\pi$
$600$		0			0
$601$	586.294			0.975531			0.487766	−	0.872975i	$-0.337812\pi$
$601$	586.294			0.975531			0.487766	+	0.872975i	$0.337812\pi$
$602$	166.623	−	266.983i	0.276783	−	0.443493i
$603$		0			0
$604$	−6.47431	−	3.73794i	−0.0107191	−	0.00618865i
$605$	301.825	−	465.501i	0.498884	−	0.769424i
$606$		0			0
$607$	−743.260	+	199.156i	−1.22448	+	0.328099i	−0.812428	−	0.583061i	$-0.801855\pi$
$607$	−743.260	+	199.156i	−1.22448	+	0.328099i	−0.412053	+	0.911160i	$0.635188\pi$
$608$	29.0109	−	29.0109i	0.0477153	−	0.0477153i
$609$		0			0
$610$	−103.547	+	319.465i	−0.169749	+	0.523714i
$611$	−276.233	+	478.449i	−0.452099	+	0.783059i
$612$		0			0
$613$	−182.550	−	48.9141i	−0.297797	−	0.0797946i	0.106827	−	0.994278i	$-0.465931\pi$
$613$	−182.550	−	48.9141i	−0.297797	−	0.0797946i	−0.404624	+	0.914483i	$0.632598\pi$
$614$	475.688	+	274.639i	0.774736	+	0.447294i
$615$		0			0
$616$	171.573	+	52.3509i	0.278528	+	0.0849853i
$617$	−362.020	−	362.020i	−0.586742	−	0.586742i	0.350006	−	0.936748i	$-0.386180\pi$
$617$	−362.020	−	362.020i	−0.586742	−	0.586742i	−0.936748	+	0.350006i	$0.886180\pi$
$618$		0			0
$619$	−608.882	+	351.538i	−0.983654	+	0.567913i	−0.903371	−	0.428859i	$-0.858916\pi$
$619$	−608.882	+	351.538i	−0.983654	+	0.567913i	−0.0802824	+	0.996772i	$0.525582\pi$
$620$	22.7417	+	14.7454i	0.0366801	+	0.0237829i
$621$		0			0
$622$	−259.845	−	259.845i	−0.417757	−	0.417757i
$623$	244.705	+	152.720i	0.392786	+	0.245136i
$624$		0			0
$625$	611.713	+	128.188i	0.978741	+	0.205100i
$626$	−542.449	−	939.549i	−0.866532	−	1.50088i
$627$		0			0
$628$	2.03514	+	7.59524i	0.00324066	+	0.0120943i
$629$		−	84.8182i		−	0.134846i
$630$		0			0
$631$	259.497			0.411247			0.205623	−	0.978631i	$-0.434078\pi$
$631$	259.497			0.411247			0.205623	+	0.978631i	$0.434078\pi$
$632$	−60.0731	+	16.0965i	−0.0950523	+	0.0254692i
$633$		0			0
$634$	83.6174	−	48.2765i	0.131889	−	0.0761459i
$635$	−203.278	−	225.437i	−0.320122	−	0.355019i
$636$		0			0
$637$	577.822	−	503.421i	0.907098	−	0.790300i
$638$	−92.6343	+	92.6343i	−0.145195	+	0.145195i
$639$		0			0
$640$	−128.883	−	604.211i	−0.201379	−	0.944080i
$641$	451.476	+	781.979i	0.704330	+	1.21994i	0.966933	+	0.255032i	$0.0820859\pi$
$641$	451.476	+	781.979i	0.704330	+	1.21994i	−0.262602	+	0.964904i	$0.584581\pi$
$642$		0			0
$643$	−359.258	+	359.258i	−0.558722	+	0.558722i	−0.928944	−	0.370222i	$-0.879282\pi$
$643$	−359.258	+	359.258i	−0.558722	+	0.558722i	0.370222	+	0.928944i	$0.379282\pi$
$644$	−4.70445	−	5.03929i	−0.00730504	−	0.00782498i
$645$		0			0
$646$	−470.383	+	814.728i	−0.728147	+	1.26119i
$647$	−184.661	+	689.165i	−0.285411	+	1.06517i	0.663127	+	0.748507i	$0.269229\pi$
$647$	−184.661	+	689.165i	−0.285411	+	1.06517i	−0.948538	+	0.316663i	$0.897438\pi$
$648$		0			0
$649$	281.043	+	162.260i	0.433041	+	0.250016i
$650$	453.606	−	626.225i	0.697855	−	0.963423i
$651$		0			0
$652$	10.6446	+	10.6446i	0.0163261	+	0.0163261i
$653$	−127.162	−	474.577i	−0.194736	−	0.726764i	−0.992335	−	0.123576i	$-0.960564\pi$
$653$	−127.162	−	474.577i	−0.194736	−	0.726764i	0.797599	−	0.603188i	$-0.206103\pi$
$654$		0			0
$655$	1.81017	−	2.79181i	0.00276362	−	0.00426230i
$656$	4.73364	−	8.19890i	0.00721591	−	0.0124983i
$657$		0			0
$658$	−431.632	+	229.811i	−0.655976	+	0.349256i
$659$		−	379.448i		−	0.575793i	−0.957662	−	0.287897i	$-0.907044\pi$
$659$		−	379.448i		−	0.575793i	0.957662	−	0.287897i	$-0.0929559\pi$
$660$		0			0
$661$	−404.533	−	700.672i	−0.612002	−	1.06002i	−0.990903	−	0.134581i	$-0.957031\pi$
$661$	−404.533	−	700.672i	−0.612002	−	1.06002i	0.378900	−	0.925437i	$-0.376302\pi$
$662$	−11.3673	+	42.4235i	−0.0171712	+	0.0640838i
$663$		0			0
$664$		−	928.465i		−	1.39829i
$665$	826.628	+	577.243i	1.24305	+	0.868035i
$666$		0			0
$667$	223.353	−	59.8472i	0.334862	−	0.0897260i
$668$	−18.5110	−	4.95999i	−0.0277110	−	0.00742514i
$669$		0			0
$670$	−26.5449	+	513.564i	−0.0396192	+	0.766514i
$671$	107.627			0.160398
$672$		0			0
$673$	536.016	−	536.016i	0.796458	−	0.796458i	−0.186077	−	0.982535i	$-0.559577\pi$
$673$	536.016	−	536.016i	0.796458	−	0.796458i	0.982535	+	0.186077i	$0.0595775\pi$
$674$	554.747	+	320.283i	0.823067	+	0.475198i
$675$		0			0
$676$	3.36589	+	5.82989i	0.00497913	+	0.00862410i
$677$	121.106	−	32.4502i	0.178886	−	0.0479323i	−0.168264	−	0.985742i	$-0.553816\pi$
$677$	121.106	−	32.4502i	0.178886	−	0.0479323i	0.347150	+	0.937810i	$0.387149\pi$
$678$		0			0
$679$	11.7630	+	12.6002i	0.0173240	+	0.0185570i
$680$	−303.557	−	594.708i	−0.446407	−	0.874570i
$681$		0			0
$682$	−98.7570	+	368.566i	−0.144805	+	0.540420i
$683$	−671.930	−	180.043i	−0.983792	−	0.263606i	−0.269151	−	0.963098i	$-0.586743\pi$
$683$	−671.930	−	180.043i	−0.983792	−	0.263606i	−0.714641	+	0.699492i	$0.753410\pi$
$684$		0			0
$685$	129.503	−	399.547i	0.189056	−	0.583280i
$686$	669.793	−	107.229i	0.976375	−	0.156311i
$687$		0			0
$688$	92.0009	+	343.352i	0.133722	+	0.499058i
$689$	−852.906	+	492.425i	−1.23789	+	0.714696i
$690$		0			0
$691$	−320.368	+	554.894i	−0.463630	+	0.803030i	−0.999139	−	0.0414993i	$-0.986787\pi$
$691$	−320.368	+	554.894i	−0.463630	+	0.803030i	0.535509	+	0.844530i	$0.320120\pi$
$692$	−1.36759	−	1.36759i	−0.00197628	−	0.00197628i
$693$		0			0
$694$			1233.93i			1.77800i
$695$	−46.1933	+	893.703i	−0.0664652	+	1.28590i
$696$		0			0
$697$	2.58789	−	9.65814i	0.00371290	−	0.0138567i
$698$	−62.2960	−	232.492i	−0.0892493	−	0.333083i
$699$		0			0
$700$	−14.4344	+	5.86537i	−0.0206206	+	0.00837910i
$701$	−271.882			−0.387849			−0.193924	−	0.981016i	$-0.562122\pi$
$701$	−271.882			−0.387849			−0.193924	+	0.981016i	$0.562122\pi$
$702$		0			0
$703$	−142.914	−	38.2937i	−0.203291	−	0.0544718i
$704$	−179.376	+	103.563i	−0.254795	+	0.147106i
$705$		0			0
$706$	96.6549			0.136905
$707$	−494.441	−	928.664i	−0.699351	−	1.31353i
$708$		0			0
$709$	−208.885	−	120.600i	−0.294619	−	0.170099i	0.345404	−	0.938454i	$-0.387742\pi$
$709$	−208.885	−	120.600i	−0.294619	−	0.170099i	−0.640023	+	0.768356i	$0.721075\pi$
$710$	−245.390	+	52.3435i	−0.345620	+	0.0737233i
$711$		0			0
$712$	−321.870	+	86.2449i	−0.452065	+	0.121130i
$713$	476.232	−	476.232i	0.667926	−	0.667926i
$714$		0			0
$715$	−235.740	−	76.4095i	−0.329707	−	0.106866i
$716$	−5.48948	+	9.50805i	−0.00766687	+	0.0132794i
$717$		0			0
$718$	−968.368	−	259.474i	−1.34870	−	0.361384i
$719$	−1158.13	−	668.644i	−1.61075	−	0.929964i	−0.989198	−	0.146589i	$-0.953171\pi$
$719$	−1158.13	−	668.644i	−1.61075	−	0.929964i	−0.621548	−	0.783376i	$-0.713496\pi$
$720$		0			0
$721$	−231.832	−	1001.64i	−0.321543	−	1.38923i
$722$	655.585	+	655.585i	0.908012	+	0.908012i
$723$		0			0
$724$	4.51418	−	2.60626i	0.00623505	−	0.00359981i
$725$	53.8794	−	519.811i	0.0743164	−	0.716981i
$726$		0			0
$727$	711.809	+	711.809i	0.979105	+	0.979105i	0.999786	−	0.0206810i	$-0.00658344\pi$
$727$	711.809	+	711.809i	0.979105	+	0.979105i	−0.0206810	+	0.999786i	$0.506583\pi$
$728$	−30.4056	+	884.794i	−0.0417659	+	1.21538i
$729$		0			0
$730$	−880.820	−	45.5274i	−1.20660	−	0.0623663i
$731$	187.711	+	325.126i	0.256787	+	0.444768i
$732$		0			0
$733$	77.9360	+	290.861i	0.106325	+	0.396809i	0.998492	−	0.0548957i	$-0.0174826\pi$
$733$	77.9360	+	290.861i	0.106325	+	0.396809i	−0.892167	+	0.451705i	$0.850816\pi$
$734$		−	654.863i		−	0.892184i
$735$		0			0
$736$	15.7546			0.0214057
$737$	159.193	−	42.6557i	0.216001	−	0.0578774i
$738$		0			0
$739$	−233.165	+	134.618i	−0.315514	+	0.182162i	−0.649391	−	0.760454i	$-0.724976\pi$
$739$	−233.165	+	134.618i	−0.315514	+	0.182162i	0.333877	+	0.942617i	$0.391643\pi$
$740$	1.69805	−	1.53114i	0.00229466	−	0.00206910i
$741$		0			0
$742$	−871.197	−	29.9383i	−1.17412	−	0.0403482i
$743$	490.075	−	490.075i	0.659589	−	0.659589i	−0.295694	−	0.955283i	$-0.595551\pi$
$743$	490.075	−	490.075i	0.659589	−	0.659589i	0.955283	+	0.295694i	$0.0955508\pi$
$744$		0			0
$745$	24.8329	+	16.1013i	0.0333328	+	0.0216125i
$746$	−210.242	−	364.150i	−0.281826	−	0.488137i
$747$		0			0
$748$	−3.29457	+	3.29457i	−0.00440451	+	0.00440451i
$749$	693.567	−	160.528i	0.925991	−	0.214324i
$750$		0			0
$751$	497.864	−	862.326i	0.662935	−	1.14824i	−0.316906	−	0.948457i	$-0.602644\pi$
$751$	497.864	−	862.326i	0.662935	−	1.14824i	0.979841	−	0.199780i	$-0.0640227\pi$
$752$	142.951	−	533.501i	0.190095	−	0.709443i
$753$		0			0
$754$	−559.934	−	323.278i	−0.742618	−	0.428751i
$755$	190.873	+	373.945i	0.252812	+	0.495291i
$756$		0			0
$757$	−111.675	−	111.675i	−0.147523	−	0.147523i	0.629488	−	0.777010i	$-0.283265\pi$
$757$	−111.675	−	111.675i	−0.147523	−	0.147523i	−0.777010	+	0.629488i	$0.783265\pi$
$758$	−75.5562	−	281.980i	−0.0996784	−	0.372005i
$759$		0			0
$760$	−1139.10	+	242.978i	−1.49881	+	0.319708i
$761$	−290.882	+	503.823i	−0.382237	+	0.662054i	−0.991382	−	0.131005i	$-0.958180\pi$
$761$	−290.882	+	503.823i	−0.382237	+	0.662054i	0.609145	+	0.793059i	$0.291513\pi$
$762$		0			0
$763$	−745.605	+	396.977i	−0.977202	+	0.520284i
$764$		−	24.7067i		−	0.0323387i
$765$		0			0
$766$	−46.7618	−	80.9938i	−0.0610467	−	0.105736i
$767$	−414.532	+	1547.06i	−0.540459	+	2.01702i
$768$		0			0
$769$		−	26.5351i		−	0.0345060i	−0.999851	−	0.0172530i	$-0.994508\pi$
$769$		−	26.5351i		−	0.0345060i	0.999851	−	0.0172530i	$-0.00549207\pi$
$770$	−141.206	−	167.849i	−0.183385	−	0.217985i
$771$		0			0
$772$	−32.1780	+	8.62208i	−0.0416814	+	0.0111685i
$773$	−361.326	−	96.8169i	−0.467433	−	0.125248i	0.0174120	−	0.999848i	$-0.494457\pi$
$773$	−361.326	−	96.8169i	−0.467433	−	0.125248i	−0.484845	+	0.874600i	$0.661124\pi$
$774$		0			0
$775$	−621.103	−	1389.64i	−0.801423	−	1.79309i
$776$	−19.9131			−0.0256612
$777$		0			0
$778$	468.071	−	468.071i	0.601633	−	0.601633i
$779$	−15.1050	−	8.72090i	−0.0193903	−	0.0111950i
$780$		0			0
$781$	40.2064	+	69.6395i	0.0514806	+	0.0891671i
$782$	−348.945	+	93.4995i	−0.446221	+	0.119565i
$783$		0			0
$784$	−427.726	+	635.652i	−0.545569	+	0.810781i
$785$	136.158	−	420.076i	0.173449	−	0.535129i
$786$		0			0
$787$	−190.095	+	709.443i	−0.241544	+	0.901453i	0.733546	+	0.679640i	$0.237864\pi$
$787$	−190.095	+	709.443i	−0.241544	+	0.901453i	−0.975089	+	0.221813i	$0.928803\pi$
$788$	11.7954	+	3.16058i	0.0149688	+	0.00401089i
$789$		0			0
$790$	72.3424	+	23.4480i	0.0915727	+	0.0296811i
$791$	1104.68	−	1031.28i	1.39657	−	1.30377i
$792$		0			0
$793$	137.479	+	513.080i	0.173366	+	0.647012i
$794$	−799.654	+	461.680i	−1.00712	+	0.581461i
$795$		0			0
$796$	4.01151	−	6.94814i	0.00503958	−	0.00872882i
$797$	246.070	+	246.070i	0.308745	+	0.308745i	0.844423	−	0.535677i	$-0.179944\pi$
$797$	246.070	+	246.070i	0.308745	+	0.308745i	−0.535677	+	0.844423i	$0.679944\pi$
$798$		0			0
$799$		−	583.333i		−	0.730078i
$800$	12.7123	−	33.2595i	0.0158904	−	0.0415744i
$801$		0			0
$802$	14.0485	−	52.4298i	0.0175169	−	0.0653738i
$803$	73.1592	+	273.034i	0.0911073	+	0.340017i
$804$		0			0
$805$	67.7152	+	381.192i	0.0841182	+	0.473530i
$806$	−1883.18			−2.33645
$807$		0			0
$808$	1173.98	+	314.567i	1.45295	+	0.389315i
$809$	524.873	−	303.035i	0.648792	−	0.374580i	−0.139201	−	0.990264i	$-0.544454\pi$
$809$	524.873	−	303.035i	0.648792	−	0.374580i	0.787993	+	0.615684i	$0.211120\pi$
$810$		0			0
$811$	158.508			0.195448			0.0977240	−	0.995214i	$-0.468844\pi$
$811$	158.508			0.195448			0.0977240	+	0.995214i	$0.468844\pi$
$812$	6.12257	+	11.4995i	0.00754011	+	0.0141619i
$813$		0			0
$814$	27.8760	+	16.0942i	0.0342458	+	0.0197718i
$815$	−176.365	−	826.813i	−0.216399	−	1.01450i
$816$		0			0
$817$	632.566	−	169.496i	0.774255	−	0.207461i
$818$	−675.644	+	675.644i	−0.825970	+	0.825970i
$819$		0			0
$820$	0.240071	−	0.122540i	0.000292769	−	0.000149438i
$821$	−169.327	+	293.282i	−0.206244	+	0.357226i	−0.950529	−	0.310637i	$-0.899458\pi$
$821$	−169.327	+	293.282i	−0.206244	+	0.357226i	0.744284	+	0.667863i	$0.232791\pi$
$822$		0			0
$823$	−575.604	−	154.233i	−0.699398	−	0.187403i	−0.108437	−	0.994103i	$-0.534585\pi$
$823$	−575.604	−	154.233i	−0.699398	−	0.187403i	−0.590961	+	0.806700i	$0.701251\pi$
$824$	1028.58	+	593.850i	1.24827	+	0.720692i
$825$		0			0
$826$	−1036.26	+	967.401i	−1.25455	+	1.17119i
$827$	−108.883	−	108.883i	−0.131660	−	0.131660i	0.638206	−	0.769866i	$-0.279677\pi$
$827$	−108.883	−	108.883i	−0.131660	−	0.131660i	−0.769866	+	0.638206i	$0.779677\pi$
$828$		0			0
$829$	−264.922	+	152.953i	−0.319568	+	0.184503i	−0.651200	−	0.758906i	$-0.725734\pi$
$829$	−264.922	+	152.953i	−0.319568	+	0.184503i	0.331632	+	0.943409i	$0.392401\pi$
$830$	−617.651	+	952.596i	−0.744158	+	1.14771i
$831$		0			0
$832$	−722.832	−	722.832i	−0.868789	−	0.868789i
$833$	−262.593	+	765.387i	−0.315238	+	0.918832i
$834$		0			0
$835$	720.718	+	799.283i	0.863135	+	0.957225i
$836$	4.06374	+	7.03860i	0.00486093	+	0.00841938i
$837$		0			0
$838$	−341.204	−	1273.39i	−0.407164	−	1.51956i
$839$			762.350i			0.908641i	0.890838	+	0.454321i	$0.150118\pi$
$839$			762.350i			0.908641i	−0.890838	+	0.454321i	$0.849882\pi$
$840$		0			0
$841$	404.029			0.480415
$842$	−895.629	+	239.983i	−1.06369	+	0.285016i
$843$		0			0
$844$	0.296054	−	0.170927i	0.000350775	−	0.000202520i
$845$	19.5146	−	377.550i	0.0230942	−	0.446804i
$846$		0			0
$847$	411.224	−	658.910i	0.485507	−	0.777934i
$848$	696.212	−	696.212i	0.821005	−	0.821005i
$849$		0			0
$850$	−84.1759	+	812.102i	−0.0990305	+	0.955414i
$851$	−28.4074	−	49.2031i	−0.0333812	−	0.0578180i
$852$		0			0
$853$	582.940	−	582.940i	0.683400	−	0.683400i	−0.277365	−	0.960765i	$-0.589461\pi$
$853$	582.940	−	582.940i	0.683400	−	0.683400i	0.960765	+	0.277365i	$0.0894610\pi$
$854$	−137.211	+	449.691i	−0.160669	+	0.526570i
$855$		0			0
$856$	−411.202	+	712.222i	−0.480376	+	0.832035i
$857$	288.117	−	1075.27i	0.336193	−	1.25469i	−0.566377	−	0.824146i	$-0.691655\pi$
$857$	288.117	−	1075.27i	0.336193	−	1.25469i	0.902570	−	0.430543i	$-0.141678\pi$
$858$		0			0
$859$	600.525	+	346.713i	0.699097	+	0.403624i	0.807011	−	0.590536i	$-0.201084\pi$
$859$	600.525	+	346.713i	0.699097	+	0.403624i	−0.107914	+	0.994160i	$0.534417\pi$
$860$	−3.12039	+	9.62711i	−0.00362837	+	0.0111943i
$861$		0			0
$862$	360.139	+	360.139i	0.417795	+	0.417795i
$863$	190.009	+	709.122i	0.220172	+	0.821694i	0.984281	+	0.176607i	$0.0565121\pi$
$863$	190.009	+	709.122i	0.220172	+	0.821694i	−0.764109	+	0.645087i	$0.776821\pi$
$864$		0			0
$865$	22.6588	+	106.226i	0.0261952	+	0.122805i
$866$	36.1294	−	62.5779i	0.0417198	−	0.0722608i
$867$		0			0
$868$	32.1905	+	20.0900i	0.0370858	+	0.0231451i
$869$		−	24.3720i		−	0.0280461i
$870$		0			0
$871$	406.696	+	704.418i	0.466930	+	0.808746i
$872$	252.559	−	942.564i	0.289632	−	1.08092i
$873$		0			0
$874$			630.165i			0.721013i
$875$	859.373	+	164.629i	0.982141	+	0.188148i
$876$		0			0
$877$	1011.30	−	270.978i	1.15314	−	0.308983i	0.368918	−	0.929462i	$-0.379728\pi$
$877$	1011.30	−	270.978i	1.15314	−	0.308983i	0.784223	+	0.620479i	$0.213062\pi$
$878$	−145.198	−	38.9058i	−0.165374	−	0.0443118i
$879$		0			0
$880$	247.419	+	12.7885i	0.281158	+	0.0145324i
$881$	1628.97			1.84900			0.924501	−	0.381180i	$-0.124482\pi$
$881$	1628.97			1.84900			0.924501	+	0.381180i	$0.124482\pi$
$882$		0			0
$883$	363.615	−	363.615i	0.411795	−	0.411795i	−0.470569	−	0.882363i	$-0.655951\pi$
$883$	363.615	−	363.615i	0.411795	−	0.411795i	0.882363	+	0.470569i	$0.155951\pi$
$884$	−19.9143	−	11.4975i	−0.0225274	−	0.0130062i
$885$		0			0
$886$	−265.532	−	459.915i	−0.299698	−	0.519091i
$887$	164.352	−	44.0381i	0.185290	−	0.0496483i	−0.164981	−	0.986297i	$-0.552756\pi$
$887$	164.352	−	44.0381i	0.185290	−	0.0496483i	0.350271	+	0.936648i	$0.386090\pi$
$888$		0			0
$889$	−290.003	−	310.644i	−0.326213	−	0.349431i
$890$	387.609	+	125.634i	0.435516	+	0.141162i
$891$		0			0
$892$	2.24277	−	8.37011i	0.00251431	−	0.00938353i
$893$	−982.883	−	263.363i	−1.10065	−	0.294919i
$894$		0			0
$895$	549.169	−	280.313i	0.613597	−	0.313198i
$896$	−195.034	−	842.650i	−0.217672	−	0.940457i
$897$		0			0
$898$	−234.594	−	875.516i	−0.261240	−	0.974962i
$899$	−1102.22	+	636.367i	−1.22605	+	0.707861i
$900$		0			0
$901$	519.938	−	900.559i	0.577068	−	0.999511i
$902$	2.68316	+	2.68316i	0.00297468	+	0.00297468i
$903$		0			0
$904$			1745.82i			1.93122i
$905$	−292.342	−	15.1104i	−0.323030	−	0.0166966i
$906$		0			0
$907$	333.960	−	1246.36i	0.368203	−	1.37415i	−0.494824	−	0.868993i	$-0.664767\pi$
$907$	333.960	−	1246.36i	0.368203	−	1.37415i	0.863027	−	0.505159i	$-0.168566\pi$
$908$	3.24312	+	12.1035i	0.00357172	+	0.0133298i
$909$		0			0
$910$	619.795	−	887.563i	0.681093	−	0.975344i
$911$	758.411			0.832504			0.416252	−	0.909249i	$-0.363343\pi$
$911$	758.411			0.832504			0.416252	+	0.909249i	$0.363343\pi$
$912$		0			0
$913$	351.451	+	94.1711i	0.384941	+	0.103145i
$914$	−1008.89	+	582.480i	−1.10381	+	0.637287i
$915$		0			0
$916$	−14.7141			−0.0160634
$917$	2.46628	−	3.95176i	0.00268951	−	0.00430945i
$918$		0			0
$919$	−9.29930	−	5.36895i	−0.0101189	−	0.00584217i	0.494932	−	0.868932i	$-0.335193\pi$
$919$	−9.29930	−	5.36895i	−0.0101189	−	0.00584217i	−0.505051	+	0.863090i	$0.668526\pi$
$920$	−375.274	−	243.323i	−0.407906	−	0.264481i
$921$		0			0
$922$	993.989	−	266.339i	1.07808	−	0.288870i
$923$	−280.627	+	280.627i	−0.304038	+	0.304038i
$924$		0			0
$925$	−126.795	+	20.2691i	−0.137075	+	0.0219125i
$926$	−640.441	+	1109.28i	−0.691621	+	1.19792i
$927$		0			0
$928$	−28.7578	−	7.70563i	−0.0309890	−	0.00830348i
$929$	−764.432	−	441.345i	−0.822854	−	0.475075i	0.0285454	−	0.999592i	$-0.490912\pi$
$929$	−764.432	−	441.345i	−0.822854	−	0.475075i	−0.851400	+	0.524517i	$0.824246\pi$
$930$		0			0
$931$	1171.08	+	788.011i	1.25787	+	0.846413i
$932$	16.7133	+	16.7133i	0.0179327	+	0.0179327i
$933$		0			0
$934$	244.598	−	141.219i	0.261882	−	0.151198i
$935$	255.903	−	54.5860i	0.273693	−	0.0583808i
$936$		0			0
$937$	−861.453	−	861.453i	−0.919373	−	0.919373i	0.0776103	−	0.996984i	$-0.475271\pi$
$937$	−861.453	−	861.453i	−0.919373	−	0.919373i	−0.996984	+	0.0776103i	$0.975271\pi$
$938$	−24.7262	+	719.525i	−0.0263605	+	0.767084i
$939$		0			0
$940$	11.6782	−	10.5303i	0.0124236	−	0.0112025i
$941$	−253.129	−	438.432i	−0.269000	−	0.465921i	0.699604	−	0.714531i	$-0.253360\pi$
$941$	−253.129	−	438.432i	−0.269000	−	0.465921i	−0.968604	+	0.248610i	$0.920026\pi$
$942$		0			0
$943$	−1.73348	−	6.46944i	−0.00183826	−	0.00686048i
$944$		−	1601.21i		−	1.69620i
$945$		0			0
$946$	−142.473			−0.150606
$947$	1135.56	−	304.272i	1.19911	−	0.321301i	0.396630	−	0.917978i	$-0.370179\pi$
$947$	1135.56	−	304.272i	1.19911	−	0.321301i	0.802481	+	0.596677i	$0.203513\pi$
$948$		0			0
$949$	−1208.16	+	697.529i	−1.27308	+	0.735014i
$950$	1330.34	+	508.479i	1.40036	+	0.535241i
$951$		0			0
$952$	−439.311	−	825.118i	−0.461461	−	0.866721i
$953$	363.579	−	363.579i	0.381510	−	0.381510i	−0.490136	−	0.871646i	$-0.663053\pi$
$953$	363.579	−	363.579i	0.381510	−	0.381510i	0.871646	+	0.490136i	$0.163053\pi$
$954$		0			0
$955$	−754.861	+	1164.21i	−0.790430	+	1.21907i
$956$	−16.6151	−	28.7782i	−0.0173798	−	0.0301027i
$957$		0			0
$958$	−355.600	+	355.600i	−0.371189	+	0.371189i
$959$	171.606	−	562.416i	0.178943	−	0.586461i
$960$		0			0
$961$	−1373.00	+	2378.11i	−1.42872	+	2.47462i
$962$	−41.1165	+	153.449i	−0.0427406	+	0.159510i
$963$		0			0
$964$	−29.8876	−	17.2556i	−0.0310037	−	0.0179000i
$965$	1779.70	+	576.846i	1.84425	+	0.597768i
$966$		0			0
$967$	−741.851	−	741.851i	−0.767168	−	0.767168i	0.210439	−	0.977607i	$-0.432511\pi$
$967$	−741.851	−	741.851i	−0.767168	−	0.767168i	−0.977607	+	0.210439i	$0.932511\pi$
$968$	232.229	+	866.690i	0.239906	+	0.895340i
$969$		0			0
$970$	20.4307	+	13.2470i	0.0210626	+	0.0136567i
$971$	−375.989	+	651.232i	−0.387218	+	0.670682i	−0.992074	−	0.125653i	$-0.959897\pi$
$971$	−375.989	+	651.232i	−0.387218	+	0.670682i	0.604856	+	0.796335i	$0.293231\pi$
$972$		0			0
$973$	−43.0285	+	1252.12i	−0.0442225	+	1.28686i
$974$		−	386.651i		−	0.396972i
$975$		0			0
$976$	−265.520	−	459.895i	−0.272050	−	0.471204i
$977$	248.716	−	928.222i	0.254572	−	0.950074i	−0.713757	−	0.700394i	$-0.753008\pi$
$977$	248.716	−	928.222i	0.254572	−	0.950074i	0.968328	−	0.249680i	$-0.0803255\pi$
$978$		0			0
$979$		−	130.585i		−	0.133386i
$980$	−20.0632	+	8.55969i	−0.0204727	+	0.00873437i
$981$		0			0
$982$	1198.80	−	321.218i	1.22077	−	0.327106i
$983$	1582.53	+	424.037i	1.60989	+	0.431370i	0.948011	−	0.318237i	$-0.103091\pi$
$983$	1582.53	+	424.037i	1.60989	+	0.431370i	0.661883	+	0.749607i	$0.269757\pi$
$984$		0			0
$985$	−459.252	−	509.315i	−0.466246	−	0.517071i
$986$	682.680			0.692373
$987$		0			0
$988$	−28.3635	+	28.3635i	−0.0287080	+	0.0287080i
$989$	217.783	+	125.737i	0.220205	+	0.127136i
$990$		0			0
$991$	−686.253	−	1188.63i	−0.692485	−	1.19942i	−0.971021	−	0.238994i	$-0.923182\pi$
$991$	−686.253	−	1188.63i	−0.692485	−	1.19942i	0.278536	−	0.960426i	$-0.410151\pi$
$992$	−83.7608	+	22.4436i	−0.0844363	+	0.0226246i
$993$		0			0
$994$	−342.228	+	79.2097i	−0.344293	+	0.0796879i
$995$	−401.313	+	204.842i	−0.403329	+	0.205872i
$996$		0			0
$997$	−145.327	+	542.368i	−0.145764	+	0.544000i	0.853956	+	0.520346i	$0.174197\pi$
$997$	−145.327	+	542.368i	−0.145764	+	0.544000i	−0.999720	+	0.0236546i	$0.992470\pi$
$998$	1757.97	+	471.046i	1.76149	+	0.471990i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.3.ca.b.37.12		64
3.2	odd	2		105.3.v.a.37.5	✓	64
5.3	odd	4	inner	315.3.ca.b.163.5		64
7.4	even	3	inner	315.3.ca.b.172.5		64
15.8	even	4		105.3.v.a.58.12	yes	64
21.11	odd	6		105.3.v.a.67.12	yes	64
35.18	odd	12	inner	315.3.ca.b.298.12		64
105.53	even	12		105.3.v.a.88.5	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.v.a.37.5	✓	64	3.2	odd	2
105.3.v.a.58.12	yes	64	15.8	even	4
105.3.v.a.67.12	yes	64	21.11	odd	6
105.3.v.a.88.5	yes	64	105.53	even	12
315.3.ca.b.37.12		64	1.1	even	1	trivial
315.3.ca.b.163.5		64	5.3	odd	4	inner
315.3.ca.b.172.5		64	7.4	even	3	inner
315.3.ca.b.298.12		64	35.18	odd	12	inner

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:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	315.ca (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.91023 - 0.511845i) q^{2} +(-0.0771041 + 0.0445161i) q^{4} +(4.99333 + 0.258093i) q^{5} +(6.99587 + 0.240410i) q^{7} +(-5.71805 + 5.71805i) q^{8} +O(q^{10})\)	\(q+(1.91023 - 0.511845i) q^{2} +(-0.0771041 + 0.0445161i) q^{4} +(4.99333 + 0.258093i) q^{5} +(6.99587 + 0.240410i) q^{7} +(-5.71805 + 5.71805i) q^{8} +(9.67053 - 2.06280i) q^{10} +(-1.58449 - 2.74441i) q^{11} +(11.0592 - 11.0592i) q^{13} +(13.4868 - 3.12156i) q^{14} +(-7.81797 + 13.5411i) q^{16} +(-4.27411 + 15.9512i) q^{17} +(24.9472 + 14.4033i) q^{19} +(-0.396496 + 0.202384i) q^{20} +(-4.43145 - 4.43145i) q^{22} +(2.86298 + 10.6848i) q^{23} +(24.8668 + 2.57749i) q^{25} +(15.4650 - 26.7862i) q^{26} +(-0.550112 + 0.292892i) q^{28} -20.9038i q^{29} +(-30.4426 - 52.7281i) q^{31} +(0.368622 - 1.37572i) q^{32} +32.6581i q^{34} +(34.8707 + 3.00603i) q^{35} +(-4.96117 + 1.32934i) q^{37} +(55.0271 + 14.7445i) q^{38} +(-30.0279 + 27.0763i) q^{40} -0.605481 q^{41} +(16.0752 - 16.0752i) q^{43} +(0.244341 + 0.141070i) q^{44} +(10.9379 + 18.9450i) q^{46} +(-34.1202 + 9.14247i) q^{47} +(48.8844 + 3.36376i) q^{49} +(48.8206 - 7.80433i) q^{50} +(-0.360397 + 1.34502i) q^{52} +(-60.8242 - 16.2978i) q^{53} +(-7.20355 - 14.1127i) q^{55} +(-41.3774 + 38.6280i) q^{56} +(-10.6995 - 39.9312i) q^{58} +(-88.6860 + 51.2029i) q^{59} +(-16.9814 + 29.4127i) q^{61} +(-85.1410 - 85.1410i) q^{62} -65.3604i q^{64} +(58.0765 - 52.3679i) q^{65} +(-13.4604 + 50.2349i) q^{67} +(-0.380533 - 1.42017i) q^{68} +(68.1497 - 12.1062i) q^{70} -25.3750 q^{71} +(-86.1585 - 23.0861i) q^{73} +(-8.79656 + 5.07870i) q^{74} -2.56471 q^{76} +(-10.4251 - 19.5805i) q^{77} +(6.66046 + 3.84542i) q^{79} +(-42.5326 + 65.5976i) q^{80} +(-1.15661 + 0.309913i) q^{82} +(-81.1873 + 81.1873i) q^{83} +(-25.4589 + 78.5465i) q^{85} +(22.4793 - 38.9354i) q^{86} +(24.7528 + 6.63250i) q^{88} +(35.6866 + 20.6037i) q^{89} +(80.0273 - 74.7098i) q^{91} +(-0.696392 - 0.696392i) q^{92} +(-60.4979 + 34.9285i) q^{94} +(120.852 + 78.3590i) q^{95} +(1.74125 + 1.74125i) q^{97} +(95.1022 - 18.5957i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 4 q^{5} - 4 q^{7} - 24 q^{8}+O(q^{10}) \) 64 * q - 4 * q^5 - 4 * q^7 - 24 * q^8	\( 64 q - 4 q^{5} - 4 q^{7} - 24 q^{8} - 16 q^{10} - 16 q^{11} + 80 q^{16} - 56 q^{17} - 96 q^{22} - 72 q^{23} - 4 q^{25} + 288 q^{26} - 380 q^{28} - 136 q^{31} + 48 q^{32} - 76 q^{35} - 28 q^{37} + 68 q^{38} + 164 q^{40} - 128 q^{41} + 344 q^{43} + 240 q^{46} - 412 q^{47} + 72 q^{50} + 388 q^{52} + 40 q^{53} - 8 q^{55} + 864 q^{56} + 56 q^{58} - 216 q^{61} + 912 q^{62} - 20 q^{65} - 368 q^{67} + 492 q^{68} + 416 q^{70} - 784 q^{71} - 316 q^{73} - 32 q^{76} - 844 q^{77} - 908 q^{80} + 556 q^{82} - 1408 q^{83} - 536 q^{85} - 1024 q^{86} + 372 q^{88} - 1064 q^{91} + 1704 q^{92} - 260 q^{95} + 352 q^{97} - 272 q^{98}+O(q^{100}) \) 64 * q - 4 * q^5 - 4 * q^7 - 24 * q^8 - 16 * q^10 - 16 * q^11 + 80 * q^16 - 56 * q^17 - 96 * q^22 - 72 * q^23 - 4 * q^25 + 288 * q^26 - 380 * q^28 - 136 * q^31 + 48 * q^32 - 76 * q^35 - 28 * q^37 + 68 * q^38 + 164 * q^40 - 128 * q^41 + 344 * q^43 + 240 * q^46 - 412 * q^47 + 72 * q^50 + 388 * q^52 + 40 * q^53 - 8 * q^55 + 864 * q^56 + 56 * q^58 - 216 * q^61 + 912 * q^62 - 20 * q^65 - 368 * q^67 + 492 * q^68 + 416 * q^70 - 784 * q^71 - 316 * q^73 - 32 * q^76 - 844 * q^77 - 908 * q^80 + 556 * q^82 - 1408 * q^83 - 536 * q^85 - 1024 * q^86 + 372 * q^88 - 1064 * q^91 + 1704 * q^92 - 260 * q^95 + 352 * q^97 - 272 * q^98

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