LMFDB - Embedded newform 414.3.l.b.19.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [414,3,Mod(19,414)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(414, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 15]))

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

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

chi := DirichletCharacter("414.19");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 414 = 2 \cdot 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	414.l (of order $22$, degree $10$, 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:	$11.2806829445$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$8$ over $\Q(\zeta_{22})$
Twist minimal:	no (minimal twist has level 138)
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			19.1
Character	$\chi$	$=$	414.19
Dual form			414.3.l.b.109.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.587486 - 1.28641i) q^{2} +(-1.30972 + 1.51150i) q^{4} +(-5.01874 + 7.80931i) q^{5} +(5.11630 - 0.735612i) q^{7} +(2.71386 + 0.796860i) q^{8} +O(q^{10})$	\(q+(-0.587486 - 1.28641i) q^{2} +(-1.30972 + 1.51150i) q^{4} +(-5.01874 + 7.80931i) q^{5} +(5.11630 - 0.735612i) q^{7} +(2.71386 + 0.796860i) q^{8} +(12.9944 + 1.86832i) q^{10} +(-7.49739 - 3.42394i) q^{11} +(-0.170426 + 1.18534i) q^{13} +(-3.95205 - 6.14951i) q^{14} +(-0.569259 - 3.95929i) q^{16} +(0.695908 - 0.603008i) q^{17} +(5.83348 + 5.05474i) q^{19} +(-5.23062 - 17.8139i) q^{20} +11.6563i q^{22} +(-22.4434 - 5.02937i) q^{23} +(-25.4123 - 55.6451i) q^{25} +(1.62496 - 0.477131i) q^{26} +(-5.58904 + 8.69672i) q^{28} +(-4.59011 - 5.29727i) q^{29} +(-42.9090 - 12.5992i) q^{31} +(-4.75885 + 3.05833i) q^{32} +(-1.18455 - 0.540968i) q^{34} +(-19.9327 + 43.6466i) q^{35} +(-37.0310 - 57.6213i) q^{37} +(3.07540 - 10.4739i) q^{38} +(-19.8431 + 17.1941i) q^{40} +(-38.4365 - 24.7016i) q^{41} +(20.8057 + 70.8578i) q^{43} +(14.9948 - 6.84788i) q^{44} +(6.71532 + 31.8262i) q^{46} -3.73913 q^{47} +(-21.3798 + 6.27768i) q^{49} +(-56.6533 + 65.3814i) q^{50} +(-1.56843 - 1.81006i) q^{52} +(80.0444 - 11.5086i) q^{53} +(64.3661 - 41.3656i) q^{55} +(14.4711 + 2.08063i) q^{56} +(-4.11786 + 9.01685i) q^{58} +(6.19820 - 43.1094i) q^{59} +(-22.1247 + 75.3498i) q^{61} +(9.00060 + 62.6005i) q^{62} +(6.73003 + 4.32513i) q^{64} +(-8.40135 - 7.27981i) q^{65} +(-12.0908 + 5.52170i) q^{67} +1.84164i q^{68} +67.8578 q^{70} +(42.4315 + 92.9121i) q^{71} +(2.04467 - 2.35968i) q^{73} +(-52.3697 + 81.4889i) q^{74} +(-15.2805 + 2.19700i) q^{76} +(-40.8775 - 12.0027i) q^{77} +(-82.0100 - 11.7913i) q^{79} +(33.7763 + 15.4251i) q^{80} +(-9.19564 + 63.9571i) q^{82} +(-72.6596 - 113.061i) q^{83} +(1.21649 + 8.46091i) q^{85} +(78.9294 - 68.3927i) q^{86} +(-17.6184 - 15.2665i) q^{88} +(-41.1099 - 140.007i) q^{89} +6.18991i q^{91} +(36.9965 - 27.3361i) q^{92} +(2.19668 + 4.81006i) q^{94} +(-68.7508 + 20.1870i) q^{95} +(12.6094 - 19.6206i) q^{97} +(20.6360 + 23.8152i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 16 q^{4}+O(q^{10}) $ 80 * q - 16 * q^4	$ 80 q - 16 q^{4} - 16 q^{13} - 32 q^{16} - 220 q^{17} + 132 q^{19} - 88 q^{20} + 104 q^{23} - 336 q^{25} + 208 q^{26} - 264 q^{28} + 164 q^{29} - 268 q^{31} - 552 q^{35} + 352 q^{37} - 192 q^{41} + 88 q^{43} + 80 q^{46} + 64 q^{47} - 40 q^{49} - 160 q^{50} - 32 q^{52} + 352 q^{53} + 196 q^{55} + 312 q^{58} + 696 q^{59} + 616 q^{61} - 96 q^{62} - 64 q^{64} + 44 q^{67} - 32 q^{70} + 32 q^{71} - 284 q^{73} + 224 q^{77} - 440 q^{79} - 616 q^{82} - 352 q^{83} - 532 q^{85} - 88 q^{89} + 32 q^{92} + 16 q^{94} - 372 q^{95} - 264 q^{97} - 1184 q^{98}+O(q^{100}) $ 80 * q - 16 * q^4 - 16 * q^13 - 32 * q^16 - 220 * q^17 + 132 * q^19 - 88 * q^20 + 104 * q^23 - 336 * q^25 + 208 * q^26 - 264 * q^28 + 164 * q^29 - 268 * q^31 - 552 * q^35 + 352 * q^37 - 192 * q^41 + 88 * q^43 + 80 * q^46 + 64 * q^47 - 40 * q^49 - 160 * q^50 - 32 * q^52 + 352 * q^53 + 196 * q^55 + 312 * q^58 + 696 * q^59 + 616 * q^61 - 96 * q^62 - 64 * q^64 + 44 * q^67 - 32 * q^70 + 32 * q^71 - 284 * q^73 + 224 * q^77 - 440 * q^79 - 616 * q^82 - 352 * q^83 - 532 * q^85 - 88 * q^89 + 32 * q^92 + 16 * q^94 - 372 * q^95 - 264 * q^97 - 1184 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/414\mathbb{Z}\right)^\times$.

$n$	$47$	$235$
$\chi(n)$	$1$	$e\left(\frac{15}{22}\right)$

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 $

$2$	−0.587486	−	1.28641i	−0.293743	−	0.643207i
$2$	−0.587486	−	1.28641i	−0.293743	−	0.643207i
$3$		0			0
$3$		0			0
$4$	−1.30972	+	1.51150i	−0.327430	+	0.377875i
$5$	−5.01874	+	7.80931i	−1.00375	+	1.56186i	−0.189059	+	0.981966i	$0.560544\pi$
$5$	−5.01874	+	7.80931i	−1.00375	+	1.56186i	−0.814690	+	0.579897i	$0.803093\pi$
$6$		0			0
$7$	5.11630	−	0.735612i	0.730899	−	0.105087i	0.233190	−	0.972431i	$-0.425084\pi$
$7$	5.11630	−	0.735612i	0.730899	−	0.105087i	0.497710	+	0.867344i	$0.334175\pi$
$8$	2.71386	+	0.796860i	0.339232	+	0.0996075i
$9$		0			0
$10$	12.9944	+	1.86832i	1.29944	+	0.186832i
$11$	−7.49739	−	3.42394i	−0.681581	−	0.311267i	0.0443692	−	0.999015i	$-0.485872\pi$
$11$	−7.49739	−	3.42394i	−0.681581	−	0.311267i	−0.725950	+	0.687748i	$0.758599\pi$
$12$		0			0
$13$	−0.170426	+	1.18534i	−0.0131097	+	0.0911798i	−0.995326	−	0.0965739i	$-0.969212\pi$
$13$	−0.170426	+	1.18534i	−0.0131097	+	0.0911798i	0.982216	+	0.187754i	$0.0601207\pi$
$14$	−3.95205	−	6.14951i	−0.282289	−	0.439251i
$15$		0			0
$16$	−0.569259	−	3.95929i	−0.0355787	−	0.247455i
$17$	0.695908	−	0.603008i	0.0409358	−	0.0354711i	−0.634153	−	0.773208i	$-0.718651\pi$
$17$	0.695908	−	0.603008i	0.0409358	−	0.0354711i	0.675088	+	0.737737i	$0.264105\pi$
$18$		0			0
$19$	5.83348	+	5.05474i	0.307025	+	0.266039i	0.794721	−	0.606975i	$-0.207617\pi$
$19$	5.83348	+	5.05474i	0.307025	+	0.266039i	−0.487696	+	0.873014i	$0.662163\pi$
$20$	−5.23062	−	17.8139i	−0.261531	−	0.890693i
$21$		0			0
$22$			11.6563i			0.529830i
$23$	−22.4434	−	5.02937i	−0.975799	−	0.218668i
$23$	−22.4434	−	5.02937i	−0.975799	−	0.218668i
$24$		0			0
$25$	−25.4123	−	55.6451i	−1.01649	−	2.22580i
$26$	1.62496	−	0.477131i	0.0624984	−	0.0183512i
$27$		0			0
$28$	−5.58904	+	8.69672i	−0.199609	+	0.310597i
$29$	−4.59011	−	5.29727i	−0.158280	−	0.182664i	0.671071	−	0.741393i	$-0.265835\pi$
$29$	−4.59011	−	5.29727i	−0.158280	−	0.182664i	−0.829350	+	0.558729i	$0.811289\pi$
$30$		0			0
$31$	−42.9090	−	12.5992i	−1.38416	−	0.406426i	−0.496945	−	0.867782i	$-0.665545\pi$
$31$	−42.9090	−	12.5992i	−1.38416	−	0.406426i	−0.887215	+	0.461356i	$0.847363\pi$
$32$	−4.75885	+	3.05833i	−0.148714	+	0.0955727i
$33$		0			0
$34$	−1.18455	−	0.540968i	−0.0348398	−	0.0159108i
$35$	−19.9327	+	43.6466i	−0.569507	+	1.24705i
$36$		0			0
$37$	−37.0310	−	57.6213i	−1.00084	−	1.55733i	−0.818830	−	0.574037i	$-0.805377\pi$
$37$	−37.0310	−	57.6213i	−1.00084	−	1.55733i	−0.182008	−	0.983297i	$-0.558260\pi$
$38$	3.07540	−	10.4739i	0.0809316	−	0.275628i
$39$		0			0
$40$	−19.8431	+	17.1941i	−0.496077	+	0.429853i
$41$	−38.4365	−	24.7016i	−0.937475	−	0.602479i	−0.0197972	−	0.999804i	$-0.506302\pi$
$41$	−38.4365	−	24.7016i	−0.937475	−	0.602479i	−0.917678	+	0.397325i	$0.869938\pi$
$42$		0			0
$43$	20.8057	+	70.8578i	0.483854	+	1.64786i	0.733627	+	0.679552i	$0.237826\pi$
$43$	20.8057	+	70.8578i	0.483854	+	1.64786i	−0.249773	+	0.968304i	$0.580356\pi$
$44$	14.9948	−	6.84788i	0.340790	−	0.155634i
$45$		0			0
$46$	6.71532	+	31.8262i	0.145985	+	0.691873i
$47$	−3.73913			−0.0795559			−0.0397779	−	0.999209i	$-0.512665\pi$
$47$	−3.73913			−0.0795559			−0.0397779	+	0.999209i	$0.512665\pi$
$48$		0			0
$49$	−21.3798	+	6.27768i	−0.436322	+	0.128116i
$50$	−56.6533	+	65.3814i	−1.13307	+	1.30763i
$51$		0			0
$52$	−1.56843	−	1.81006i	−0.0301621	−	0.0348089i
$53$	80.0444	−	11.5086i	1.51027	−	0.217144i	0.663127	−	0.748507i	$-0.269229\pi$
$53$	80.0444	−	11.5086i	1.51027	−	0.217144i	0.847144	+	0.531363i	$0.178320\pi$
$54$		0			0
$55$	64.3661	−	41.3656i	1.17029	−	0.752101i
$56$	14.4711	+	2.08063i	0.258412	+	0.0371540i
$57$		0			0
$58$	−4.11786	+	9.01685i	−0.0709975	+	0.155463i
$59$	6.19820	−	43.1094i	0.105054	−	0.730669i	−0.867406	−	0.497601i	$-0.834214\pi$
$59$	6.19820	−	43.1094i	0.105054	−	0.730669i	0.972460	−	0.233068i	$-0.0748764\pi$
$60$		0			0
$61$	−22.1247	+	75.3498i	−0.362700	+	1.23524i	0.552933	+	0.833226i	$0.313509\pi$
$61$	−22.1247	+	75.3498i	−0.362700	+	1.23524i	−0.915632	+	0.402016i	$0.868309\pi$
$62$	9.00060	+	62.6005i	0.145171	+	1.00969i
$63$		0			0
$64$	6.73003	+	4.32513i	0.105157	+	0.0675801i
$65$	−8.40135	−	7.27981i	−0.129252	−	0.111997i
$66$		0			0
$67$	−12.0908	+	5.52170i	−0.180460	+	0.0824135i	−0.503596	−	0.863939i	$-0.667990\pi$
$67$	−12.0908	+	5.52170i	−0.180460	+	0.0824135i	0.323136	+	0.946353i	$0.395263\pi$
$68$			1.84164i			0.0270829i
$69$		0			0
$70$	67.8578			0.969397
$71$	42.4315	+	92.9121i	0.597627	+	1.30862i	0.930722	+	0.365728i	$0.119180\pi$
$71$	42.4315	+	92.9121i	0.597627	+	1.30862i	−0.333095	+	0.942893i	$0.608093\pi$
$72$		0			0
$73$	2.04467	−	2.35968i	0.0280092	−	0.0323244i	−0.741572	−	0.670873i	$-0.765919\pi$
$73$	2.04467	−	2.35968i	0.0280092	−	0.0323244i	0.769581	+	0.638549i	$0.220465\pi$
$74$	−52.3697	+	81.4889i	−0.707699	+	1.10120i
$75$		0			0
$76$	−15.2805	+	2.19700i	−0.201059	+	0.0289079i
$77$	−40.8775	−	12.0027i	−0.530877	−	0.155880i
$78$		0			0
$79$	−82.0100	−	11.7913i	−1.03810	−	0.149256i	−0.397873	−	0.917441i	$-0.630251\pi$
$79$	−82.0100	−	11.7913i	−1.03810	−	0.149256i	−0.640229	+	0.768184i	$0.721160\pi$
$80$	33.7763	+	15.4251i	0.422203	+	0.192814i
$81$		0			0
$82$	−9.19564	+	63.9571i	−0.112142	+	0.779964i
$83$	−72.6596	−	113.061i	−0.875417	−	1.36218i	−0.931497	−	0.363750i	$-0.881496\pi$
$83$	−72.6596	−	113.061i	−0.875417	−	1.36218i	0.0560795	−	0.998426i	$-0.482140\pi$
$84$		0			0
$85$	1.21649	+	8.46091i	0.0143117	+	0.0995401i
$86$	78.9294	−	68.3927i	0.917784	−	0.795265i
$87$		0			0
$88$	−17.6184	−	15.2665i	−0.200209	−	0.173482i
$89$	−41.1099	−	140.007i	−0.461909	−	1.57312i	−0.780456	−	0.625211i	$-0.785013\pi$
$89$	−41.1099	−	140.007i	−0.461909	−	1.57312i	0.318547	−	0.947907i	$-0.396805\pi$
$90$		0			0
$91$			6.18991i			0.0680209i
$92$	36.9965	−	27.3361i	0.402135	−	0.297131i
$93$		0			0
$94$	2.19668	+	4.81006i	0.0233690	+	0.0511709i
$95$	−68.7508	+	20.1870i	−0.723692	+	0.212495i
$96$		0			0
$97$	12.6094	−	19.6206i	0.129994	−	0.202275i	−0.770155	−	0.637857i	$-0.779821\pi$
$97$	12.6094	−	19.6206i	0.129994	−	0.202275i	0.900149	+	0.435582i	$0.143458\pi$
$98$	20.6360	+	23.8152i	0.210572	+	0.243013i
$99$		0			0
$100$	117.390	+	34.4689i	1.17390	+	0.344689i
$101$	57.3813	−	36.8767i	0.568132	−	0.365116i	−0.224820	−	0.974400i	$-0.572179\pi$
$101$	57.3813	−	36.8767i	0.568132	−	0.365116i	0.792952	+	0.609284i	$0.208543\pi$
$102$		0			0
$103$	38.5403	+	17.6008i	0.374177	+	0.170881i	0.593622	−	0.804744i	$-0.297697\pi$
$103$	38.5403	+	17.6008i	0.374177	+	0.170881i	−0.219445	+	0.975625i	$0.570425\pi$
$104$	−1.40706	+	3.08103i	−0.0135294	+	0.0296253i
$105$		0			0
$106$	−61.8298	−	96.2090i	−0.583300	−	0.907632i
$107$	−27.6763	+	94.2567i	−0.258657	+	0.880904i	0.723097	+	0.690746i	$0.242718\pi$
$107$	−27.6763	+	94.2567i	−0.258657	+	0.880904i	−0.981754	+	0.190157i	$0.939100\pi$
$108$		0			0
$109$	69.3168	−	60.0634i	0.635934	−	0.551040i	−0.276113	−	0.961125i	$-0.589046\pi$
$109$	69.3168	−	60.0634i	0.635934	−	0.551040i	0.912047	+	0.410085i	$0.134501\pi$
$110$	−91.0274	−	58.4997i	−0.827522	−	0.531816i
$111$		0			0
$112$	−5.82500	−	19.8381i	−0.0520089	−	0.177126i
$113$	−138.663	+	63.3251i	−1.22710	+	0.560399i	−0.920240	−	0.391355i	$-0.872007\pi$
$113$	−138.663	+	63.3251i	−1.22710	+	0.560399i	−0.306863	+	0.951754i	$0.599279\pi$
$114$		0			0
$115$	151.913	−	150.026i	1.32099	−	1.30458i
$116$	14.0186			0.120850
$117$		0			0
$118$	−59.0979	+	17.3527i	−0.500830	+	0.147057i
$119$	3.11689	−	3.59708i	0.0261924	−	0.0302276i
$120$		0			0
$121$	−34.7507	−	40.1045i	−0.287196	−	0.331442i
$122$	109.929	−	15.8054i	0.901057	−	0.129552i
$123$		0			0
$124$	75.2425	−	48.3554i	0.606794	−	0.389963i
$125$	332.376	+	47.7884i	2.65901	+	0.382307i
$126$		0			0
$127$	−33.3217	+	72.9644i	−0.262376	+	0.574523i	−0.994270	−	0.106895i	$-0.965909\pi$
$127$	−33.3217	+	72.9644i	−0.262376	+	0.574523i	0.731895	+	0.681418i	$0.238636\pi$
$128$	1.61011	−	11.1986i	0.0125790	−	0.0874887i
$129$		0			0
$130$	−4.42918	+	15.0844i	−0.0340706	+	0.116034i
$131$	−19.3145	−	134.336i	−0.147439	−	1.02546i	−0.920391	−	0.390998i	$-0.872130\pi$
$131$	−19.3145	−	134.336i	−0.147439	−	1.02546i	0.772952	−	0.634464i	$-0.218779\pi$
$132$		0			0
$133$	33.5641	+	21.5704i	0.252362	+	0.162183i
$134$	14.2064	+	12.3099i	0.106018	+	0.0918650i
$135$		0			0
$136$	2.36911	−	1.08194i	0.0174199	−	0.00795540i
$137$			177.966i			1.29902i	0.760351	+	0.649512i	$0.225027\pi$
$137$			177.966i			1.29902i	−0.760351	+	0.649512i	$0.774973\pi$
$138$		0			0
$139$	−88.4277			−0.636170			−0.318085	−	0.948062i	$-0.603040\pi$
$139$	−88.4277			−0.636170			−0.318085	+	0.948062i	$0.603040\pi$
$140$	−39.8655	−	87.2932i	−0.284753	−	0.623523i
$141$		0			0
$142$	94.5955	−	109.169i	0.666165	−	0.768796i
$143$	5.33628	−	8.30341i	0.0373166	−	0.0580658i
$144$		0			0
$145$	64.4046	−	9.25999i	0.444170	−	0.0638620i
$146$	−4.23674	−	1.24402i	−0.0290188	−	0.00852068i
$147$		0			0
$148$	135.595	+	19.4956i	0.916182	+	0.131727i
$149$	193.192	+	88.2279i	1.29659	+	0.592134i	0.939696	−	0.342011i	$-0.111108\pi$
$149$	193.192	+	88.2279i	1.29659	+	0.592134i	0.356896	+	0.934144i	$0.383835\pi$
$150$		0			0
$151$	−36.5667	+	254.327i	−0.242164	+	1.68429i	0.399054	+	0.916927i	$0.369338\pi$
$151$	−36.5667	+	254.327i	−0.242164	+	1.68429i	−0.641218	+	0.767359i	$0.721571\pi$
$152$	11.8033	+	18.3663i	0.0776533	+	0.120831i
$153$		0			0
$154$	8.57449	+	59.6369i	0.0556785	+	0.387252i
$155$	313.740	−	271.857i	2.02413	−	1.75392i
$156$		0			0
$157$	55.9727	+	48.5006i	0.356514	+	0.308921i	0.814641	−	0.579966i	$-0.196934\pi$
$157$	55.9727	+	48.5006i	0.356514	+	0.308921i	−0.458127	+	0.888887i	$0.651480\pi$
$158$	33.0113	+	112.426i	0.208932	+	0.711557i
$159$		0			0
$160$		−	52.5123i		−	0.328202i
$161$	−118.527	−	9.22209i	−0.736190	−	0.0572801i
$162$		0			0
$163$	−42.9991	−	94.1549i	−0.263798	−	0.577637i	0.730663	−	0.682738i	$-0.239211\pi$
$163$	−42.9991	−	94.1549i	−0.263798	−	0.577637i	−0.994462	+	0.105100i	$0.966484\pi$
$164$	87.6776	−	25.7445i	0.534619	−	0.156978i
$165$		0			0
$166$	−102.756	+	159.892i	−0.619014	+	0.963204i
$167$	77.6168	+	89.5745i	0.464771	+	0.536374i	0.938950	−	0.344054i	$-0.111800\pi$
$167$	77.6168	+	89.5745i	0.464771	+	0.536374i	−0.474179	+	0.880429i	$0.657255\pi$
$168$		0			0
$169$	160.778	+	47.2088i	0.951351	+	0.279342i
$170$	10.1696	−	6.53558i	0.0598209	−	0.0384446i
$171$		0			0
$172$	−134.351	−	61.3562i	−0.781112	−	0.356722i
$173$	−25.9438	+	56.8089i	−0.149964	+	0.328375i	−0.969673	−	0.244404i	$-0.921408\pi$
$173$	−25.9438	+	56.8089i	−0.149964	+	0.328375i	0.819710	+	0.572779i	$0.194135\pi$
$174$		0			0
$175$	−170.950	−	266.003i	−0.976856	−	1.52002i
$176$	−9.28841	+	31.6334i	−0.0527750	+	0.179735i
$177$		0			0
$178$	−155.956	+	135.137i	−0.876158	+	0.759195i
$179$	−53.0668	−	34.1040i	−0.296463	−	0.190525i	0.383951	−	0.923354i	$-0.374563\pi$
$179$	−53.0668	−	34.1040i	−0.296463	−	0.190525i	−0.680413	+	0.732829i	$0.738200\pi$
$180$		0			0
$181$	−47.4150	−	161.481i	−0.261962	−	0.892159i	−0.980475	−	0.196646i	$-0.936995\pi$
$181$	−47.4150	−	161.481i	−0.261962	−	0.892159i	0.718513	−	0.695513i	$-0.244823\pi$
$182$	7.96278	−	3.63648i	0.0437515	−	0.0199807i
$183$		0			0
$184$	−56.9004	−	31.5332i	−0.309241	−	0.171376i
$185$	635.832			3.43693
$186$		0			0
$187$	−7.28216	+	2.13823i	−0.0389420	+	0.0114344i
$188$	4.89721	−	5.65168i	0.0260490	−	0.0300622i
$189$		0			0
$190$	66.3590	+	76.5824i	0.349258	+	0.403065i
$191$	−261.172	+	37.5508i	−1.36739	+	0.196601i	−0.786606	−	0.617456i	$-0.788163\pi$
$191$	−261.172	+	37.5508i	−1.36739	+	0.196601i	−0.580785	+	0.814057i	$0.697254\pi$
$192$		0			0
$193$	−44.0386	+	28.3019i	−0.228179	+	0.146642i	−0.649735	−	0.760160i	$-0.725120\pi$
$193$	−44.0386	+	28.3019i	−0.228179	+	0.146642i	0.421556	+	0.906802i	$0.361484\pi$
$194$	−32.6481	−	4.69409i	−0.168289	−	0.0241963i
$195$		0			0
$196$	18.5129	−	40.5376i	0.0944535	−	0.206824i
$197$	−24.2488	+	168.654i	−0.123090	+	0.856111i	0.830932	+	0.556374i	$0.187808\pi$
$197$	−24.2488	+	168.654i	−0.123090	+	0.856111i	−0.954022	+	0.299737i	$0.903101\pi$
$198$		0			0
$199$	26.4974	−	90.2417i	0.133153	−	0.453476i	−0.865742	−	0.500491i	$-0.833153\pi$
$199$	26.4974	−	90.2417i	0.133153	−	0.453476i	0.998894	+	0.0470152i	$0.0149709\pi$
$200$	−24.6239	−	171.263i	−0.123119	−	0.856314i
$201$		0			0
$202$	−81.1494	−	52.1516i	−0.401730	−	0.258176i
$203$	−27.3811	−	23.7259i	−0.134882	−	0.116876i
$204$		0			0
$205$	385.805	−	176.191i	1.88198	−	0.859471i
$206$		−	59.9189i		−	0.290869i
$207$		0			0
$208$	4.79011			0.0230294
$209$	−26.4287	−	57.8708i	−0.126453	−	0.276894i
$210$		0			0
$211$	−231.409	+	267.060i	−1.09672	+	1.26569i	−0.135245	+	0.990812i	$0.543182\pi$
$211$	−231.409	+	267.060i	−1.09672	+	1.26569i	−0.961480	+	0.274875i	$0.911363\pi$
$212$	−87.4405	+	136.060i	−0.412455	+	0.641793i
$213$		0			0
$214$	137.513	−	19.7713i	0.642582	−	0.0923893i
$215$	−657.770	−	193.139i	−3.05939	−	0.898319i
$216$		0			0
$217$	−228.803	−	32.8969i	−1.05439	−	0.151599i
$218$	−117.989	−	53.8838i	−0.541234	−	0.247173i
$219$		0			0
$220$	−21.7776	+	151.467i	−0.0989892	+	0.688485i
$221$	0.596167	+	0.927654i	0.00269759	+	0.00419753i
$222$		0			0
$223$	−31.5033	−	219.111i	−0.141271	−	0.982558i	−0.929932	−	0.367731i	$-0.880135\pi$
$223$	−31.5033	−	219.111i	−0.141271	−	0.982558i	0.788662	−	0.614827i	$-0.210774\pi$
$224$	−22.0979	+	19.1480i	−0.0986515	+	0.0854820i
$225$		0			0
$226$	162.925	+	141.175i	0.720905	+	0.624668i
$227$	47.0851	+	160.357i	0.207423	+	0.706419i	0.995827	+	0.0912611i	$0.0290898\pi$
$227$	47.0851	+	160.357i	0.207423	+	0.706419i	−0.788404	+	0.615158i	$0.789092\pi$
$228$		0			0
$229$			282.266i			1.23260i	0.787510	+	0.616302i	$0.211370\pi$
$229$			282.266i			1.23260i	−0.787510	+	0.616302i	$0.788630\pi$
$230$	−282.243	−	107.285i	−1.22714	−	0.466458i
$231$		0			0
$232$	−8.23571	−	18.0337i	−0.0354988	−	0.0777315i
$233$	−407.635	+	119.693i	−1.74951	+	0.513702i	−0.990516	−	0.137398i	$-0.956126\pi$
$233$	−407.635	+	119.693i	−1.74951	+	0.513702i	−0.758992	+	0.651100i	$0.774308\pi$
$234$		0			0
$235$	18.7657	−	29.2000i	0.0798541	−	0.124255i
$236$	57.0420	+	65.8299i	0.241703	+	0.278940i
$237$		0			0
$238$	−6.45847	−	1.89638i	−0.0271364	−	0.00796797i
$239$	79.2424	−	50.9260i	0.331558	−	0.213079i	−0.364260	−	0.931297i	$-0.618678\pi$
$239$	79.2424	−	50.9260i	0.331558	−	0.213079i	0.695818	+	0.718218i	$0.255042\pi$
$240$		0			0
$241$	297.373	+	135.806i	1.23391	+	0.563509i	0.922217	−	0.386673i	$-0.126376\pi$
$241$	297.373	+	135.806i	1.23391	+	0.563509i	0.311696	+	0.950182i	$0.399103\pi$
$242$	−31.1754	+	68.2646i	−0.128824	+	0.282085i
$243$		0			0
$244$	−84.9140	−	132.129i	−0.348008	−	0.541511i
$245$	58.2754	−	198.468i	0.237859	−	0.810072i
$246$		0			0
$247$	−6.98575	+	6.05319i	−0.0282824	+	0.0245068i
$248$	−106.409	−	68.3849i	−0.429068	−	0.275745i
$249$		0			0
$250$	−133.790	−	455.648i	−0.535161	−	1.82259i
$251$	189.975	−	86.7588i	0.756873	−	0.345652i	0.000679153	−	1.00000i	$-0.499784\pi$
$251$	189.975	−	86.7588i	0.756873	−	0.345652i	0.756194	+	0.654347i	$0.227057\pi$
$252$		0			0
$253$	151.046	+	114.552i	0.597022	+	0.452774i
$254$	113.438			0.446608
$255$		0			0
$256$	−15.3519	+	4.50772i	−0.0599683	+	0.0176083i
$257$	−192.135	+	221.735i	−0.747605	+	0.862783i	−0.994334	−	0.106302i	$-0.966099\pi$
$257$	−192.135	+	221.735i	−0.747605	+	0.862783i	0.246729	+	0.969085i	$0.420644\pi$
$258$		0			0
$259$	−231.848	−	267.567i	−0.895168	−	1.03308i
$260$	22.0069	−	3.16411i	0.0846418	−	0.0121697i
$261$		0			0
$262$	−161.464	+	103.767i	−0.616275	+	0.396056i
$263$	−78.0911	−	11.2278i	−0.296924	−	0.0426913i	−0.00775728	−	0.999970i	$-0.502469\pi$
$263$	−78.0911	−	11.2278i	−0.296924	−	0.0426913i	−0.289167	+	0.957279i	$0.593378\pi$
$264$		0			0
$265$	−311.847	+	682.851i	−1.17678	+	2.57679i
$266$	8.02997	−	55.8496i	0.0301878	−	0.209961i
$267$		0			0
$268$	7.48959	−	25.5072i	0.0279462	−	0.0951761i
$269$	56.8585	+	395.460i	0.211370	+	1.47011i	0.768588	+	0.639744i	$0.220960\pi$
$269$	56.8585	+	395.460i	0.211370	+	1.47011i	−0.557218	+	0.830366i	$0.688131\pi$
$270$		0			0
$271$	288.130	+	185.170i	1.06321	+	0.683283i	0.950620	−	0.310358i	$-0.100449\pi$
$271$	288.130	+	185.170i	1.06321	+	0.683283i	0.112590	+	0.993642i	$0.464085\pi$
$272$	−2.78363	−	2.41203i	−0.0102339	−	0.00886776i
$273$		0			0
$274$	228.938	−	104.553i	0.835542	−	0.381579i
$275$			504.203i			1.83346i
$276$		0			0
$277$	273.282			0.986578			0.493289	−	0.869865i	$-0.335794\pi$
$277$	273.282			0.986578			0.493289	+	0.869865i	$0.335794\pi$
$278$	51.9500	+	113.755i	0.186870	+	0.409189i
$279$		0			0
$280$	−88.8748	+	102.567i	−0.317410	+	0.366311i
$281$	−38.7929	+	60.3630i	−0.138053	+	0.214815i	−0.903395	−	0.428809i	$-0.858933\pi$
$281$	−38.7929	+	60.3630i	−0.138053	+	0.214815i	0.765342	+	0.643624i	$0.222570\pi$
$282$		0			0
$283$	−158.807	+	22.8331i	−0.561157	+	0.0806822i	−0.417056	−	0.908881i	$-0.636938\pi$
$283$	−158.807	+	22.8331i	−0.561157	+	0.0806822i	−0.144101	+	0.989563i	$0.546029\pi$
$284$	−196.010	−	57.5537i	−0.690176	−	0.202654i
$285$		0			0
$286$	−13.8166	−	1.98653i	−0.0483098	−	0.00694590i
$287$	−214.823	−	98.1065i	−0.748513	−	0.341834i
$288$		0			0
$289$	−41.0083	+	285.219i	−0.141897	+	0.986917i
$290$	−49.7490	−	77.4109i	−0.171548	−	0.266934i
$291$		0			0
$292$	0.888700	+	6.18104i	0.00304349	+	0.0211680i
$293$	178.229	−	154.436i	0.608291	−	0.527087i	−0.295344	−	0.955391i	$-0.595434\pi$
$293$	178.229	−	154.436i	0.608291	−	0.527087i	0.903635	+	0.428304i	$0.140889\pi$
$294$		0			0
$295$	305.548	+	264.759i	1.03576	+	0.897488i
$296$	−54.5806	−	185.885i	−0.184394	−	0.627988i
$297$		0			0
$298$		−	300.358i		−	1.00791i
$299$	9.78643	−	25.7459i	0.0327305	−	0.0861066i
$300$		0			0
$301$	158.572	+	347.225i	0.526818	+	1.15357i
$302$	348.652	−	102.374i	1.15448	−	0.338985i
$303$		0			0
$304$	16.6924	−	25.9739i	0.0549092	−	0.0854404i
$305$	−477.392	−	550.940i	−1.56522	−	1.80636i
$306$		0			0
$307$	−292.416	−	85.8611i	−0.952495	−	0.279678i	−0.231670	−	0.972794i	$-0.574419\pi$
$307$	−292.416	−	85.8611i	−0.952495	−	0.279678i	−0.720825	+	0.693117i	$0.756237\pi$
$308$	71.6803	−	46.0661i	0.232728	−	0.149565i
$309$		0			0
$310$	−534.039	−	243.887i	−1.72271	−	0.786734i
$311$	−58.4012	+	127.881i	−0.187785	+	0.411192i	−0.979985	−	0.199069i	$-0.936208\pi$
$311$	−58.4012	+	127.881i	−0.187785	+	0.411192i	0.792200	+	0.610261i	$0.208935\pi$
$312$		0			0
$313$	−75.0459	−	116.774i	−0.239763	−	0.373079i	0.700430	−	0.713722i	$-0.252992\pi$
$313$	−75.0459	−	116.774i	−0.239763	−	0.373079i	−0.940193	+	0.340642i	$0.889355\pi$
$314$	29.5087	−	100.497i	0.0939768	−	0.320056i
$315$		0			0
$316$	125.233	−	108.515i	0.396306	−	0.343401i
$317$	−205.902	−	132.325i	−0.649532	−	0.417429i	0.173963	−	0.984752i	$-0.444343\pi$
$317$	−205.902	−	132.325i	−0.649532	−	0.417429i	−0.823495	+	0.567324i	$0.807979\pi$
$318$		0			0
$319$	16.2763	+	55.4319i	0.0510228	+	0.173768i
$320$	−67.5526	+	30.8502i	−0.211102	+	0.0964069i
$321$		0			0
$322$	57.7693	+	157.892i	0.179408	+	0.490348i
$323$	7.10761			0.0220050
$324$		0			0
$325$	70.2891	−	20.6387i	0.216274	−	0.0635038i
$326$	−95.8608	+	110.629i	−0.294052	+	0.339354i
$327$		0			0
$328$	−84.6273	−	97.6651i	−0.258010	−	0.297760i
$329$	−19.1305	+	2.75055i	−0.0581473	+	0.00836032i
$330$		0			0
$331$	−300.008	+	192.803i	−0.906368	+	0.582487i	−0.908672	−	0.417510i	$-0.862903\pi$
$331$	−300.008	+	192.803i	−0.906368	+	0.582487i	0.00230465	+	0.999997i	$0.499266\pi$
$332$	266.055	+	38.2529i	0.801370	+	0.115220i
$333$		0			0
$334$	69.6312	−	152.471i	0.208477	−	0.456500i
$335$	17.5601	−	122.133i	0.0524182	−	0.364577i
$336$		0			0
$337$	114.565	−	390.174i	0.339957	−	1.15779i	−0.595208	−	0.803572i	$-0.702930\pi$
$337$	114.565	−	390.174i	0.339957	−	1.15779i	0.935164	−	0.354214i	$-0.115252\pi$
$338$	−33.7249	−	234.562i	−0.0997779	−	0.693970i
$339$		0			0
$340$	−14.3819	−	9.24270i	−0.0422998	−	0.0271844i
$341$	278.566	+	241.379i	0.816909	+	0.707856i
$342$		0			0
$343$	−335.156	+	153.061i	−0.977131	+	0.446241i
$344$			208.877i			0.607201i
$345$		0			0
$346$	88.3213			0.255264
$347$	122.720	+	268.719i	0.353659	+	0.774406i	0.999936	+	0.0113028i	$0.00359787\pi$
$347$	122.720	+	268.719i	0.353659	+	0.774406i	−0.646277	+	0.763103i	$0.723675\pi$
$348$		0			0
$349$	34.8964	−	40.2726i	0.0999898	−	0.115394i	−0.703549	−	0.710647i	$-0.748402\pi$
$349$	34.8964	−	40.2726i	0.0999898	−	0.115394i	0.803539	+	0.595252i	$0.202948\pi$
$350$	−241.760	+	376.185i	−0.690741	+	1.07481i
$351$		0			0
$352$	46.1505	−	6.63543i	0.131109	−	0.0188507i
$353$	−313.757	−	92.1274i	−0.888830	−	0.260984i	−0.194725	−	0.980858i	$-0.562381\pi$
$353$	−313.757	−	92.1274i	−0.888830	−	0.260984i	−0.694105	+	0.719874i	$0.744200\pi$
$354$		0			0
$355$	−938.533	−	134.941i	−2.64375	−	0.380114i
$356$	265.464	+	121.233i	0.745685	+	0.340543i
$357$		0			0
$358$	−12.6958	+	88.3014i	−0.0354632	+	0.246652i
$359$	44.7692	+	69.6622i	0.124705	+	0.194045i	0.897993	−	0.440011i	$-0.145025\pi$
$359$	44.7692	+	69.6622i	0.124705	+	0.194045i	−0.773287	+	0.634056i	$0.781389\pi$
$360$		0			0
$361$	−42.8966	−	298.352i	−0.118827	−	0.826460i
$362$	−179.875	+	155.863i	−0.496894	+	0.430561i
$363$		0			0
$364$	−9.35604	−	8.10705i	−0.0257034	−	0.0222721i
$365$	8.16579	+	27.8101i	0.0223720	+	0.0761921i
$366$		0			0
$367$		−	394.115i		−	1.07388i	−0.843619	−	0.536942i	$-0.819579\pi$
$367$		−	394.115i		−	1.07388i	0.843619	−	0.536942i	$-0.180421\pi$
$368$	−7.13659	+	91.7228i	−0.0193929	+	0.249247i
$369$		0			0
$370$	−373.542	−	817.943i	−1.00957	−	2.21066i
$371$	401.065	−	117.763i	1.08104	−	0.317421i
$372$		0			0
$373$	220.123	−	342.518i	0.590142	−	0.918279i	−0.409839	−	0.912158i	$-0.634415\pi$
$373$	220.123	−	342.518i	0.590142	−	0.918279i	0.999981	−	0.00612124i	$-0.00194846\pi$
$374$	7.02881	+	8.11168i	0.0187936	+	0.0216890i
$375$		0			0
$376$	−10.1474	−	2.97956i	−0.0269879	−	0.00792436i
$377$	7.06133	−	4.53804i	0.0187303	−	0.0120372i
$378$		0			0
$379$	177.399	+	81.0155i	0.468072	+	0.213761i	0.635466	−	0.772129i	$-0.280808\pi$
$379$	177.399	+	81.0155i	0.468072	+	0.213761i	−0.167394	+	0.985890i	$0.553535\pi$
$380$	59.5317	−	130.356i	0.156662	−	0.343043i
$381$		0			0
$382$	201.740	+	313.914i	0.528116	+	0.821765i
$383$	120.949	−	411.915i	0.315794	−	1.07550i	−0.636744	−	0.771076i	$-0.719719\pi$
$383$	120.949	−	411.915i	0.315794	−	1.07550i	0.952538	−	0.304420i	$-0.0984628\pi$
$384$		0			0
$385$	298.887	−	258.987i	0.776330	−	0.672693i
$386$	62.2799	+	40.0249i	0.161347	+	0.103691i
$387$		0			0
$388$	13.1417	+	44.7567i	0.0338705	+	0.115352i
$389$	439.584	−	200.751i	1.13004	−	0.516070i	0.239460	−	0.970906i	$-0.423029\pi$
$389$	439.584	−	200.751i	1.13004	−	0.516070i	0.890575	+	0.454836i	$0.150302\pi$
$390$		0			0
$391$	−18.6513	+	10.0336i	−0.0477015	+	0.0256613i
$392$	−63.0241			−0.160776
$393$		0			0
$394$	231.205	−	67.8878i	0.586814	−	0.172304i
$395$	503.669	−	581.265i	1.27511	−	1.47156i
$396$		0			0
$397$	26.5554	+	30.6466i	0.0668901	+	0.0771953i	0.788208	−	0.615408i	$-0.211009\pi$
$397$	26.5554	+	30.6466i	0.0668901	+	0.0771953i	−0.721318	+	0.692604i	$0.756463\pi$
$398$	−131.655	+	18.9291i	−0.330792	+	0.0475606i
$399$		0			0
$400$	−205.849	+	132.291i	−0.514621	+	0.330727i
$401$	76.9762	+	11.0675i	0.191961	+	0.0275998i	0.237624	−	0.971357i	$-0.423631\pi$
$401$	76.9762	+	11.0675i	0.191961	+	0.0275998i	−0.0456639	+	0.998957i	$0.514540\pi$
$402$		0			0
$403$	22.2471	−	48.7144i	0.0552038	−	0.120879i
$404$	−19.4144	+	135.030i	−0.0480554	+	0.334233i
$405$		0			0
$406$	−14.4353	+	49.1620i	−0.0355548	+	0.121089i
$407$	80.3435	+	558.801i	0.197404	+	1.37298i
$408$		0			0
$409$	188.593	+	121.202i	0.461108	+	0.296336i	0.750495	−	0.660876i	$-0.229815\pi$
$409$	188.593	+	121.202i	0.461108	+	0.296336i	−0.289387	+	0.957212i	$0.593451\pi$
$410$	−453.310	−	392.796i	−1.10563	−	0.958038i
$411$		0			0
$412$	−77.0806	+	35.2015i	−0.187089	+	0.0854406i
$413$		−	225.120i		−	0.545085i
$414$		0			0
$415$	1247.59			3.00623
$416$	−2.81412	−	6.16206i	−0.00676471	−	0.0148126i
$417$		0			0
$418$	−58.9193	+	67.9965i	−0.140955	+	0.162671i
$419$	−165.928	+	258.189i	−0.396009	+	0.616202i	−0.980808	−	0.194976i	$-0.937537\pi$
$419$	−165.928	+	258.189i	−0.396009	+	0.616202i	0.584799	+	0.811178i	$0.301173\pi$
$420$		0			0
$421$	−311.380	+	44.7697i	−0.739621	+	0.106341i	−0.501819	−	0.864972i	$-0.667336\pi$
$421$	−311.380	+	44.7697i	−0.739621	+	0.106341i	−0.237801	+	0.971314i	$0.576427\pi$
$422$	479.499	+	140.794i	1.13625	+	0.333634i
$423$		0			0
$424$	226.400	+	32.5514i	0.533961	+	0.0767721i
$425$	−51.2390	−	23.4001i	−0.120562	−	0.0550590i
$426$		0			0
$427$	−57.7682	+	401.787i	−0.135289	+	0.940953i
$428$	−106.221	−	165.283i	−0.248179	−	0.386174i
$429$		0			0
$430$	137.974	+	959.630i	0.320870	+	2.23170i
$431$	−0.556780	+	0.482452i	−0.00129183	+	0.00111938i	−0.655506	−	0.755190i	$-0.727545\pi$
$431$	−0.556780	+	0.482452i	−0.00129183	+	0.00111938i	0.654215	+	0.756309i	$0.272999\pi$
$432$		0			0
$433$	−600.536	−	520.368i	−1.38692	−	1.20177i	−0.953802	−	0.300436i	$-0.902868\pi$
$433$	−600.536	−	520.368i	−1.38692	−	1.20177i	−0.433118	−	0.901337i	$-0.642587\pi$
$434$	92.0994	+	313.662i	0.212211	+	0.722723i
$435$		0			0
$436$			183.439i			0.420731i
$437$	−105.501	−	142.784i	−0.241421	−	0.326737i
$438$		0			0
$439$	−281.090	−	615.501i	−0.640296	−	1.40205i	−0.899796	−	0.436310i	$-0.856285\pi$
$439$	−281.090	−	615.501i	−0.640296	−	1.40205i	0.259500	−	0.965743i	$-0.416442\pi$
$440$	207.643	−	60.9694i	0.471916	−	0.138567i
$441$		0			0
$442$	0.843108	−	1.31190i	0.00190748	−	0.00296810i
$443$	162.883	+	187.977i	0.367681	+	0.424327i	0.909199	−	0.416363i	$-0.136695\pi$
$443$	162.883	+	187.977i	0.367681	+	0.424327i	−0.541517	+	0.840690i	$0.682150\pi$
$444$		0			0
$445$	1299.68	+	381.621i	2.92064	+	0.857576i
$446$	−263.359	+	169.251i	−0.590491	+	0.379486i
$447$		0			0
$448$	37.6144	+	17.1779i	0.0839608	+	0.0383436i
$449$	31.5058	−	68.9881i	0.0701688	−	0.153648i	−0.871298	−	0.490755i	$-0.836721\pi$
$449$	31.5058	−	68.9881i	0.0701688	−	0.153648i	0.941466	+	0.337107i	$0.109448\pi$
$450$		0			0
$451$	203.596	+	316.802i	0.451433	+	0.702443i
$452$	85.8936	−	292.527i	0.190030	−	0.647183i
$453$		0			0
$454$	178.624	−	154.779i	0.393445	−	0.340922i
$455$	−48.3389	−	31.0655i	−0.106239	−	0.0682759i
$456$		0			0
$457$	22.0460	+	75.0817i	0.0482406	+	0.164292i	0.980090	−	0.198552i	$-0.0636238\pi$
$457$	22.0460	+	75.0817i	0.0482406	+	0.164292i	−0.931850	+	0.362844i	$0.881806\pi$
$458$	363.111	−	165.827i	0.792819	−	0.362068i
$459$		0			0
$460$	27.8004	+	426.110i	0.0604357	+	0.926326i
$461$	−830.321			−1.80113			−0.900565	−	0.434722i	$-0.856847\pi$
$461$	−830.321			−1.80113			−0.900565	+	0.434722i	$0.856847\pi$
$462$		0			0
$463$	−503.042	+	147.706i	−1.08648	+	0.319020i	−0.775469	−	0.631385i	$-0.782487\pi$
$463$	−503.042	+	147.706i	−1.08648	+	0.319020i	−0.311014	+	0.950405i	$0.600668\pi$
$464$	−18.3604	+	21.1891i	−0.0395699	+	0.0456661i
$465$		0			0
$466$	393.454	+	454.070i	0.844322	+	0.974399i
$467$	−503.211	+	72.3509i	−1.07754	+	0.154927i	−0.658156	−	0.752882i	$-0.728663\pi$
$467$	−503.211	+	72.3509i	−1.07754	+	0.154927i	−0.419385	+	0.907809i	$0.637754\pi$
$468$		0			0
$469$	−57.7985	+	37.1448i	−0.123238	+	0.0792001i
$470$	−48.5879	−	6.98588i	−0.103378	−	0.0148636i
$471$		0			0
$472$	51.1732	−	112.054i	0.108418	−	0.237402i
$473$	86.6244	−	602.486i	0.183138	−	1.27376i
$474$		0			0
$475$	133.029	−	453.057i	0.280062	−	0.953804i
$476$	1.35473	+	9.42236i	0.00284607	+	0.0197949i
$477$		0			0
$478$	−112.066	−	72.0202i	−0.234447	−	0.150670i
$479$	586.790	+	508.456i	1.22503	+	1.06150i	0.996116	+	0.0880487i	$0.0280631\pi$
$479$	586.790	+	508.456i	1.22503	+	1.06150i	0.228915	+	0.973447i	$0.426482\pi$
$480$		0			0
$481$	74.6118	−	34.0741i	0.155118	−	0.0708401i
$482$		−	462.328i		−	0.959188i
$483$		0			0
$484$	106.132			0.219280
$485$	89.9403	+	196.942i	0.185444	+	0.406066i
$486$		0			0
$487$	103.977	−	119.996i	0.213505	−	0.246398i	−0.638888	−	0.769300i	$-0.720605\pi$
$487$	103.977	−	119.996i	0.213505	−	0.246398i	0.852393	+	0.522902i	$0.175151\pi$
$488$	−120.086	+	186.858i	−0.246079	+	0.382906i
$489$		0			0
$490$	−289.547	+	41.6306i	−0.590913	+	0.0849605i
$491$	149.147	+	43.7934i	0.303761	+	0.0891922i	0.430061	−	0.902800i	$-0.358492\pi$
$491$	149.147	+	43.7934i	0.303761	+	0.0891922i	−0.126300	+	0.991992i	$0.540310\pi$
$492$		0			0
$493$	−6.38859	−	0.918540i	−0.0129586	−	0.00186317i
$494$	11.8909	+	5.43041i	0.0240707	+	0.0109927i
$495$		0			0
$496$	−25.4575	+	177.061i	−0.0513257	+	0.356978i
$497$	285.440	+	444.153i	0.574325	+	0.893667i
$498$		0			0
$499$	−7.59472	−	52.8224i	−0.0152199	−	0.105857i	0.980795	−	0.195040i	$-0.0624835\pi$
$499$	−7.59472	−	52.8224i	−0.0152199	−	0.105857i	−0.996015	+	0.0891829i	$0.971574\pi$
$500$	−507.552	+	439.796i	−1.01510	+	0.879593i
$501$		0			0
$502$	−223.215	−	193.417i	−0.444652	−	0.385293i
$503$	−44.1794	−	150.461i	−0.0878318	−	0.299128i	0.903849	−	0.427853i	$-0.140730\pi$
$503$	−44.1794	−	150.461i	−0.0878318	−	0.299128i	−0.991680	+	0.128725i	$0.958912\pi$
$504$		0			0
$505$			633.183i			1.25383i
$506$	58.6236	−	261.606i	0.115857	−	0.517008i
$507$		0			0
$508$	−66.6434	−	145.929i	−0.131188	−	0.287261i
$509$	538.828	−	158.214i	1.05860	−	0.310833i	0.294313	−	0.955709i	$-0.404909\pi$
$509$	538.828	−	158.214i	1.05860	−	0.310833i	0.764287	+	0.644876i	$0.223091\pi$
$510$		0			0
$511$	8.72534	−	13.5769i	0.0170750	−	0.0265693i
$512$	14.8178	+	17.1007i	0.0289410	+	0.0333997i
$513$		0			0
$514$	398.119	+	116.898i	0.774551	+	0.227429i
$515$	−330.874	+	212.640i	−0.642473	+	0.412892i
$516$		0			0
$517$	28.0337	+	12.8025i	0.0542237	+	0.0247631i
$518$	−207.995	+	455.445i	−0.401534	+	0.879238i
$519$		0			0
$520$	−16.9991	−	26.4511i	−0.0326905	−	0.0508674i
$521$	243.125	−	828.008i	0.466651	−	1.58927i	−0.304433	−	0.952534i	$-0.598467\pi$
$521$	243.125	−	828.008i	0.466651	−	1.58927i	0.771084	−	0.636733i	$-0.219715\pi$
$522$		0			0
$523$	−439.532	+	380.857i	−0.840406	+	0.728216i	−0.964508	−	0.264053i	$-0.914940\pi$
$523$	−439.532	+	380.857i	−0.840406	+	0.728216i	0.124102	+	0.992269i	$0.460395\pi$
$524$	228.345	+	146.748i	0.435772	+	0.280054i
$525$		0			0
$526$	31.4338	+	107.054i	0.0597601	+	0.203524i
$527$	−37.4581	+	17.1065i	−0.0710780	+	0.0324602i
$528$		0			0
$529$	478.411	+	225.752i	0.904369	+	0.426752i
$530$	1061.63			2.00308
$531$		0			0
$532$	−76.5632	+	22.4810i	−0.143916	+	0.0422575i
$533$	35.8303	−	41.3504i	0.0672239	−	0.0775805i
$534$		0			0
$535$	−597.180	−	689.183i	−1.11622	−	1.28819i
$536$	−37.2128	+	5.35040i	−0.0694269	+	0.00998209i
$537$		0			0
$538$	475.321	−	305.470i	0.883497	−	0.567789i
$539$	181.787	+	26.1370i	0.337267	+	0.0484917i
$540$		0			0
$541$	−153.889	+	336.969i	−0.284452	+	0.622864i	−0.996884	−	0.0788772i	$-0.974866\pi$
$541$	−153.889	+	336.969i	−0.284452	+	0.622864i	0.712432	+	0.701741i	$0.247594\pi$
$542$	68.9329	−	479.439i	0.127182	−	0.884573i
$543$		0			0
$544$	−1.46753	+	4.99794i	−0.00269766	+	0.00918738i
$545$	121.171	+	842.759i	0.222331	+	1.54635i
$546$		0			0
$547$	148.039	+	95.1392i	0.270639	+	0.173929i	0.668920	−	0.743334i	$-0.266757\pi$
$547$	148.039	+	95.1392i	0.270639	+	0.173929i	−0.398281	+	0.917263i	$0.630393\pi$
$548$	−268.996	−	233.086i	−0.490869	−	0.425340i
$549$		0			0
$550$	648.613	−	296.212i	1.17930	−	0.538567i
$551$		−	54.1033i		−	0.0981911i
$552$		0			0
$553$	−428.261			−0.774433
$554$	−160.549	−	351.554i	−0.289800	−	0.634574i
$555$		0			0
$556$	115.816	−	133.658i	0.208302	−	0.240393i
$557$	256.851	−	399.668i	0.461133	−	0.717537i	−0.530349	−	0.847779i	$-0.677939\pi$
$557$	256.851	−	399.668i	0.461133	−	0.717537i	0.991482	+	0.130242i	$0.0415755\pi$
$558$		0			0
$559$	−87.5363	+	12.5858i	−0.156594	+	0.0225149i
$560$	184.156	+	54.0732i	0.328851	+	0.0965592i
$561$		0			0
$562$	100.442	+	14.4414i	0.178722	+	0.0256964i
$563$	46.4988	+	21.2353i	0.0825911	+	0.0377181i	0.456282	−	0.889835i	$-0.349181\pi$
$563$	46.4988	+	21.2353i	0.0825911	+	0.0377181i	−0.373691	+	0.927553i	$0.621908\pi$
$564$		0			0
$565$	201.386	−	1400.67i	0.356436	−	2.47907i
$566$	122.670	+	190.878i	0.216731	+	0.337240i
$567$		0			0
$568$	41.1151	+	285.962i	0.0723858	+	0.503454i
$569$	−220.503	+	191.067i	−0.387528	+	0.335795i	−0.826736	−	0.562591i	$-0.809805\pi$
$569$	−220.503	+	191.067i	−0.387528	+	0.335795i	0.439208	+	0.898386i	$0.355259\pi$
$570$		0			0
$571$	−454.507	−	393.832i	−0.795984	−	0.689724i	0.158706	−	0.987326i	$-0.449268\pi$
$571$	−454.507	−	393.832i	−0.795984	−	0.689724i	−0.954690	+	0.297602i	$0.903813\pi$
$572$	5.56156	+	18.9409i	0.00972300	+	0.0331135i
$573$		0			0
$574$			333.988i			0.581860i
$575$	290.478	+	1376.67i	0.505178	+	2.39421i
$576$		0			0
$577$	14.0359	+	30.7343i	0.0243256	+	0.0532657i	0.921405	−	0.388604i	$-0.127043\pi$
$577$	14.0359	+	30.7343i	0.0243256	+	0.0532657i	−0.897079	+	0.441870i	$0.854315\pi$
$578$	391.002	−	114.808i	0.676473	−	0.198631i
$579$		0			0
$580$	−70.3556	+	109.476i	−0.121303	+	0.188751i
$581$	−454.917	−	525.002i	−0.782990	−	0.903618i
$582$		0			0
$583$	−639.528	−	187.782i	−1.09696	−	0.322097i
$584$	7.42928	−	4.77451i	0.0127214	−	0.00817553i
$585$		0			0
$586$	−303.376	−	138.547i	−0.517707	−	0.236429i
$587$	−178.372	+	390.581i	−0.303871	+	0.665385i	−0.998544	−	0.0539405i	$-0.982822\pi$
$587$	−178.372	+	390.581i	−0.303871	+	0.665385i	0.694673	+	0.719326i	$0.255549\pi$
$588$		0			0
$589$	−186.623	−	290.391i	−0.316847	−	0.493023i
$590$	161.084	−	548.603i	0.273025	−	0.929836i
$591$		0			0
$592$	−207.059	+	179.418i	−0.349762	+	0.303071i
$593$	59.7013	+	38.3677i	0.100677	+	0.0647010i	0.590010	−	0.807396i	$-0.299124\pi$
$593$	59.7013	+	38.3677i	0.100677	+	0.0647010i	−0.489334	+	0.872097i	$0.662760\pi$
$594$		0			0
$595$	12.4479	+	42.3936i	0.0209208	+	0.0712498i
$596$	−386.384	+	176.456i	−0.648296	+	0.296067i
$597$		0			0
$598$	−38.8692	+	2.53592i	−0.0649987	+	0.00424067i
$599$	−566.394			−0.945565			−0.472783	−	0.881179i	$-0.656750\pi$
$599$	−566.394			−0.945565			−0.472783	+	0.881179i	$0.656750\pi$
$600$		0			0
$601$	465.332	−	136.634i	0.774263	−	0.227344i	0.129349	−	0.991599i	$-0.458711\pi$
$601$	465.332	−	136.634i	0.774263	−	0.227344i	0.644914	+	0.764255i	$0.276893\pi$
$602$	353.516	−	407.979i	0.587236	−	0.677706i
$603$		0			0
$604$	−336.523	−	388.368i	−0.557157	−	0.642994i
$605$	487.593	−	70.1054i	0.805940	−	0.115877i
$606$		0			0
$607$	211.499	−	135.922i	0.348433	−	0.223924i	−0.354704	−	0.934979i	$-0.615418\pi$
$607$	211.499	−	135.922i	0.348433	−	0.223924i	0.703137	+	0.711054i	$0.251782\pi$
$608$	−43.2197	−	6.21405i	−0.0710850	−	0.0102205i
$609$		0			0
$610$	−428.276	+	937.793i	−0.702091	+	1.53737i
$611$	0.637244	−	4.43213i	0.00104295	−	0.00725389i
$612$		0			0
$613$	267.867	−	912.271i	0.436977	−	1.48821i	−0.387265	−	0.921969i	$-0.626580\pi$
$613$	267.867	−	912.271i	0.436977	−	1.48821i	0.824242	−	0.566238i	$-0.191602\pi$
$614$	61.3373	+	426.610i	0.0998979	+	0.694805i
$615$		0			0
$616$	−101.371	−	65.1473i	−0.164564	−	0.105759i
$617$	469.393	+	406.731i	0.760767	+	0.659208i	0.946249	−	0.323440i	$-0.104839\pi$
$617$	469.393	+	406.731i	0.760767	+	0.659208i	−0.185482	+	0.982648i	$0.559385\pi$
$618$		0			0
$619$	−274.369	+	125.300i	−0.443246	+	0.202424i	−0.624520	−	0.781009i	$-0.714705\pi$
$619$	−274.369	+	125.300i	−0.443246	+	0.202424i	0.181274	+	0.983433i	$0.441978\pi$
$620$			830.275i			1.33915i
$621$		0			0
$622$	198.817			0.319642
$623$	−313.322	−	686.079i	−0.502924	−	1.10125i
$624$		0			0
$625$	−1039.81	+	1200.00i	−1.66369	+	1.92000i
$626$	−106.131	+	165.143i	−0.169538	+	0.263807i
$627$		0			0
$628$	−146.617	+	21.0804i	−0.233467	+	0.0335675i
$629$	−60.5163	−	17.7692i	−0.0962103	−	0.0282499i
$630$		0			0
$631$	255.944	+	36.7992i	0.405617	+	0.0583189i	0.342104	−	0.939662i	$-0.388860\pi$
$631$	255.944	+	36.7992i	0.405617	+	0.0583189i	0.0635130	+	0.997981i	$0.479770\pi$
$632$	−213.167	−	97.3503i	−0.337290	−	0.154035i
$633$		0			0
$634$	−49.2604	+	342.614i	−0.0776978	+	0.540400i
$635$	−402.569	−	626.409i	−0.633967	−	0.986471i
$636$		0			0
$637$	−3.79750	−	26.4122i	−0.00596153	−	0.0414634i
$638$	61.7463	−	53.5035i	0.0967811	−	0.0838613i
$639$		0			0
$640$	79.3723	+	68.7765i	0.124019	+	0.107463i
$641$	139.085	+	473.679i	0.216981	+	0.738969i	0.993989	+	0.109479i	$0.0349181\pi$
$641$	139.085	+	473.679i	0.216981	+	0.738969i	−0.777008	+	0.629490i	$0.783264\pi$
$642$		0			0
$643$			743.051i			1.15560i	0.816178	+	0.577800i	$0.196089\pi$
$643$			743.051i			1.15560i	−0.816178	+	0.577800i	$0.803911\pi$
$644$	169.176	−	167.075i	0.262696	−	0.259433i
$645$		0			0
$646$	−4.17562	−	9.14333i	−0.00646381	−	0.0141538i
$647$	−365.373	+	107.283i	−0.564718	+	0.165816i	−0.551616	−	0.834098i	$-0.685989\pi$
$647$	−365.373	+	107.283i	−0.564718	+	0.165816i	−0.0131019	+	0.999914i	$0.504171\pi$
$648$		0			0
$649$	−194.075	+	301.986i	−0.299036	+	0.465309i
$650$	−67.8438	−	78.2959i	−0.104375	−	0.120455i
$651$		0			0
$652$	198.632	+	58.3236i	0.304650	+	0.0894534i
$653$	107.592	−	69.1450i	0.164765	−	0.105888i	−0.455660	−	0.890154i	$-0.650597\pi$
$653$	107.592	−	69.1450i	0.164765	−	0.105888i	0.620425	+	0.784266i	$0.286960\pi$
$654$		0			0
$655$	1146.00	+	523.362i	1.74962	+	0.799026i
$656$	−75.9205	+	166.243i	−0.115732	+	0.253419i
$657$		0			0
$658$	14.7772	+	22.9938i	0.0224578	+	0.0349450i
$659$	214.616	−	730.914i	0.325669	−	1.10913i	−0.620164	−	0.784472i	$-0.712934\pi$
$659$	214.616	−	730.914i	0.325669	−	1.10913i	0.945833	−	0.324654i	$-0.105248\pi$
$660$		0			0
$661$	−303.138	+	262.671i	−0.458606	+	0.397384i	−0.853293	−	0.521431i	$-0.825398\pi$
$661$	−303.138	+	262.671i	−0.458606	+	0.397384i	0.394687	+	0.918815i	$0.370853\pi$
$662$	424.275	+	272.665i	0.640899	+	0.411881i
$663$		0			0
$664$	−107.094	−	364.730i	−0.161287	−	0.549292i
$665$	−336.899	+	153.857i	−0.506616	+	0.231364i
$666$		0			0
$667$	76.3757	+	141.974i	0.114506	+	0.212855i
$668$	−237.048			−0.354862
$669$		0			0
$670$	−167.430	+	49.1619i	−0.249896	+	0.0733760i
$671$	423.871	−	489.173i	0.631700	−	0.729021i
$672$		0			0
$673$	−534.794	−	617.185i	−0.794642	−	0.917065i	0.203433	−	0.979089i	$-0.434790\pi$
$673$	−534.794	−	617.185i	−0.794642	−	0.917065i	−0.998075	+	0.0620236i	$0.980245\pi$
$674$	−569.230	+	81.8430i	−0.844556	+	0.121429i
$675$		0			0
$676$	−281.931	+	181.186i	−0.417057	+	0.268027i
$677$	−773.254	−	111.177i	−1.14218	−	0.164220i	−0.454850	−	0.890568i	$-0.650307\pi$
$677$	−773.254	−	111.177i	−1.14218	−	0.164220i	−0.687327	+	0.726348i	$0.741216\pi$
$678$		0			0
$679$	50.0803	−	109.661i	0.0737560	−	0.161503i
$680$	−3.44077	+	23.9311i	−0.00505995	+	0.0351927i
$681$		0			0
$682$	146.860	−	500.158i	0.215337	−	0.733369i
$683$	−139.702	−	971.649i	−0.204542	−	1.42262i	−0.790592	−	0.612344i	$-0.790227\pi$
$683$	−139.702	−	971.649i	−0.204542	−	1.42262i	0.586050	−	0.810275i	$-0.300682\pi$
$684$		0			0
$685$	−1389.80	−	893.167i	−2.02890	−	1.30389i
$686$	393.798	+	341.228i	0.574050	+	0.497417i
$687$		0			0
$688$	268.703	−	122.712i	0.390556	−	0.178361i
$689$			96.8410i			0.140553i
$690$		0			0
$691$	1105.82			1.60031			0.800156	−	0.599792i	$-0.204750\pi$
$691$	1105.82			1.60031			0.800156	+	0.599792i	$0.204750\pi$
$692$	−51.8875	−	113.618i	−0.0749819	−	0.164188i
$693$		0			0
$694$	273.588	−	315.737i	0.394218	−	0.454952i
$695$	443.796	−	690.560i	0.638555	−	0.993611i
$696$		0			0
$697$	−41.6435	+	5.98744i	−0.0597468	+	0.00859029i
$698$	−72.3084	−	21.2317i	−0.103594	−	0.0304179i
$699$		0			0
$700$	625.960	+	89.9995i	0.894229	+	0.128571i
$701$	−205.907	−	94.0347i	−0.293734	−	0.134144i	0.263098	−	0.964769i	$-0.415256\pi$
$701$	−205.907	−	94.0347i	−0.293734	−	0.134144i	−0.556831	+	0.830626i	$0.687983\pi$
$702$		0			0
$703$	75.2413	−	523.315i	0.107029	−	0.744403i
$704$	−35.6486	−	55.4704i	−0.0506373	−	0.0787931i
$705$		0			0
$706$	65.8138	+	457.745i	0.0932206	+	0.648364i
$707$	266.453	−	230.883i	0.376878	−	0.326567i
$708$		0			0
$709$	322.922	+	279.814i	0.455461	+	0.394660i	0.852153	−	0.523292i	$-0.175296\pi$
$709$	322.922	+	279.814i	0.455461	+	0.394660i	−0.396692	+	0.917952i	$0.629842\pi$
$710$	377.785	+	1286.62i	0.532091	+	1.81214i
$711$		0			0
$712$		−	412.719i		−	0.579662i
$713$	899.656	+	498.574i	1.26179	+	0.699262i
$714$		0			0
$715$	38.0625	+	83.3453i	0.0532343	+	0.116567i
$716$	121.051	−	35.5437i	0.169065	−	0.0496421i
$717$		0			0
$718$	63.3132	−	98.5172i	0.0881799	−	0.137211i
$719$	−699.990	−	807.832i	−0.973561	−	1.12355i	−0.992317	−	0.123725i	$-0.960516\pi$
$719$	−699.990	−	807.832i	−0.973561	−	1.12355i	0.0187557	−	0.999824i	$-0.494030\pi$
$720$		0			0
$721$	210.131	+	61.7000i	0.291444	+	0.0855755i
$722$	−358.603	+	230.460i	−0.496680	+	0.319197i
$723$		0			0
$724$	306.179	+	139.827i	0.422899	+	0.193131i
$725$	−178.122	+	390.033i	−0.245685	+	0.537976i
$726$		0			0
$727$	−153.822	−	239.352i	−0.211585	−	0.329233i	0.719198	−	0.694805i	$-0.244509\pi$
$727$	−153.822	−	239.352i	−0.211585	−	0.329233i	−0.930783	+	0.365573i	$0.880873\pi$
$728$	−4.93249	+	16.7985i	−0.00677540	+	0.0230749i
$729$		0			0
$730$	30.9780	−	26.8426i	0.0424357	−	0.0367707i
$731$	57.2067	+	36.7645i	0.0782582	+	0.0502935i
$732$		0			0
$733$	69.0218	+	235.067i	0.0941634	+	0.320691i	0.993082	−	0.117425i	$-0.0374640\pi$
$733$	69.0218	+	235.067i	0.0941634	+	0.320691i	−0.898918	+	0.438116i	$0.855646\pi$
$734$	−506.996	+	231.537i	−0.690730	+	0.315446i
$735$		0			0
$736$	122.186	−	44.7052i	0.166014	−	0.0607408i
$737$	109.556			0.148651
$738$		0			0
$739$	863.478	−	253.540i	1.16844	−	0.343085i	0.360734	−	0.932669i	$-0.382526\pi$
$739$	863.478	−	253.540i	1.16844	−	0.343085i	0.807708	+	0.589583i	$0.200708\pi$
$740$	−832.763	+	961.060i	−1.12536	+	1.29873i
$741$		0			0
$742$	−387.112	−	446.751i	−0.521714	−	0.602090i
$743$	−1259.47	+	181.084i	−1.69511	+	0.243720i	−0.921064	−	0.389410i	$-0.872679\pi$
$743$	−1259.47	+	181.084i	−1.69511	+	0.243720i	−0.774045	+	0.633130i	$0.781770\pi$
$744$		0			0
$745$	−1658.58	+	1065.91i	−2.22628	+	1.43075i
$746$	−569.939	−	81.9449i	−0.763993	−	0.109846i
$747$		0			0
$748$	6.30566	−	13.8075i	0.00843002	−	0.0184592i
$749$	−72.2636	+	502.604i	−0.0964800	+	0.671033i
$750$		0			0
$751$	359.302	−	1223.67i	0.478432	−	1.62939i	−0.267637	−	0.963520i	$-0.586243\pi$
$751$	359.302	−	1223.67i	0.478432	−	1.62939i	0.746069	−	0.665869i	$-0.231939\pi$
$752$	2.12853	+	14.8043i	0.00283049	+	0.0196865i
$753$		0			0
$754$	−9.98622	−	6.41776i	−0.0132443	−	0.00851161i
$755$	−1802.60	−	1561.96i	−2.38755	−	2.06883i
$756$		0			0
$757$	823.638	−	376.143i	1.08803	−	0.496886i	0.211079	−	0.977469i	$-0.432302\pi$
$757$	823.638	−	376.143i	1.08803	−	0.496886i	0.876949	+	0.480583i	$0.159575\pi$
$758$		−	275.804i		−	0.363858i
$759$		0			0
$760$	−202.666			−0.266666
$761$	128.233	+	280.790i	0.168505	+	0.368975i	0.974980	−	0.222294i	$-0.0713544\pi$
$761$	128.233	+	280.790i	0.168505	+	0.368975i	−0.806474	+	0.591269i	$0.798627\pi$
$762$		0			0
$763$	310.462	−	358.292i	0.406896	−	0.469584i
$764$	285.304	−	443.942i	0.373435	−	0.581076i
$765$		0			0
$766$	−600.949	+	86.4034i	−0.784529	+	0.112798i
$767$	50.0429	+	14.6939i	0.0652450	+	0.0191577i
$768$		0			0
$769$	96.3741	+	13.8565i	0.125324	+	0.0180189i	0.204691	−	0.978827i	$-0.434381\pi$
$769$	96.3741	+	13.8565i	0.125324	+	0.0180189i	−0.0793674	+	0.996845i	$0.525290\pi$
$770$	−508.756	−	232.341i	−0.660722	−	0.301742i
$771$		0			0
$772$	14.9000	−	103.632i	0.0193005	−	0.134238i
$773$	−605.893	−	942.788i	−0.783820	−	1.21965i	−0.971412	−	0.237401i	$-0.923704\pi$
$773$	−605.893	−	942.788i	−0.783820	−	1.21965i	0.187591	−	0.982247i	$-0.439932\pi$
$774$		0			0
$775$	389.330	+	2707.85i	0.502361	+	3.49400i
$776$	49.8550	−	43.1996i	0.0642462	−	0.0556696i
$777$		0			0
$778$	−516.498	−	447.548i	−0.663879	−	0.575255i
$779$	−99.3581	−	338.383i	−0.127546	−	0.434381i
$780$		0			0
$781$		−	841.881i		−	1.07795i
$782$	23.8647	+	18.0987i	0.0305175	+	0.0231441i
$783$		0			0
$784$	37.0258	+	81.0751i	0.0472267	+	0.103412i
$785$	−659.669	+	193.696i	−0.840343	+	0.246747i
$786$		0			0
$787$	−138.725	+	215.860i	−0.176270	+	0.274282i	−0.918135	−	0.396268i	$-0.870305\pi$
$787$	−138.725	+	215.860i	−0.176270	+	0.274282i	0.741865	+	0.670549i	$0.233942\pi$
$788$	−223.161	−	257.542i	−0.283199	−	0.326830i
$789$		0			0
$790$	−1043.65	−	306.442i	−1.32107	−	0.387901i
$791$	−662.856	+	425.992i	−0.837998	+	0.538548i
$792$		0			0
$793$	−85.5443	−	39.0668i	−0.107874	−	0.0492646i
$794$	23.8232	−	52.1656i	0.0300041	−	0.0656998i
$795$		0			0
$796$	101.696	+	158.242i	0.127759	+	0.198797i
$797$	41.1574	−	140.169i	0.0516403	−	0.175871i	−0.929635	−	0.368482i	$-0.879878\pi$
$797$	41.1574	−	140.169i	0.0516403	−	0.175871i	0.981275	+	0.192611i	$0.0616957\pi$
$798$		0			0
$799$	−2.60209	+	2.25472i	−0.00325668	+	0.00282193i
$800$	291.114	+	187.088i	0.363892	+	0.233859i
$801$		0			0
$802$	−30.9850	−	105.525i	−0.0386347	−	0.131578i
$803$	−23.4091	+	10.6906i	−0.0291521	+	0.0133133i
$804$		0			0
$805$	666.873	−	879.329i	0.828414	−	1.09233i
$806$	−75.7367			−0.0939661
$807$		0			0
$808$	185.110	−	54.3533i	0.229097	−	0.0672689i
$809$	−112.748	+	130.119i	−0.139368	+	0.160839i	−0.821143	−	0.570723i	$-0.806663\pi$
$809$	−112.748	+	130.119i	−0.139368	+	0.160839i	0.681775	+	0.731562i	$0.261208\pi$
$810$		0			0
$811$	57.2945	+	66.1214i	0.0706467	+	0.0815307i	0.789973	−	0.613142i	$-0.210095\pi$
$811$	57.2945	+	66.1214i	0.0706467	+	0.0815307i	−0.719326	+	0.694673i	$0.755549\pi$
$812$	71.7232	−	10.3122i	0.0883291	−	0.0126998i
$813$		0			0
$814$	671.649	−	431.643i	0.825122	−	0.530274i
$815$	951.087	+	136.746i	1.16698	+	0.167786i
$816$		0			0
$817$	−236.798	+	518.515i	−0.289838	+	0.634658i
$818$	45.1195	−	313.813i	0.0551583	−	0.383635i
$819$		0			0
$820$	−238.984	+	813.906i	−0.291444	+	0.992569i
$821$	227.091	+	1579.45i	0.276603	+	1.92382i	0.371712	+	0.928348i	$0.378771\pi$
$821$	227.091	+	1579.45i	0.276603	+	1.92382i	−0.0951089	+	0.995467i	$0.530320\pi$
$822$		0			0
$823$	−182.708	−	117.419i	−0.222003	−	0.142672i	0.424913	−	0.905234i	$-0.360305\pi$
$823$	−182.708	−	117.419i	−0.222003	−	0.142672i	−0.646915	+	0.762562i	$0.723941\pi$
$824$	90.5674	+	78.4771i	0.109912	+	0.0952392i
$825$		0			0
$826$	−289.598	+	132.255i	−0.350603	+	0.160115i
$827$			145.920i			0.176444i	0.996101	+	0.0882222i	$0.0281186\pi$
$827$			145.920i			0.176444i	−0.996101	+	0.0882222i	$0.971881\pi$
$828$		0			0
$829$	−820.455			−0.989692			−0.494846	−	0.868981i	$-0.664776\pi$
$829$	−820.455			−0.989692			−0.494846	+	0.868981i	$0.664776\pi$
$830$	−732.939	−	1604.91i	−0.883059	−	1.93363i
$831$		0			0
$832$	−6.27371	+	7.24024i	−0.00754051	+	0.00870222i
$833$	−11.0929	+	17.2609i	−0.0133168	+	0.0207213i
$834$		0			0
$835$	−1089.05	+	156.582i	−1.30426	+	0.187524i
$836$	122.086	+	35.8477i	0.146036	+	0.0428800i
$837$		0			0
$838$	429.617	+	61.7697i	0.512670	+	0.0737108i
$839$	−115.714	−	52.8447i	−0.137919	−	0.0629853i	0.345260	−	0.938507i	$-0.387791\pi$
$839$	−115.714	−	52.8447i	−0.137919	−	0.0629853i	−0.483179	+	0.875522i	$0.660518\pi$
$840$		0			0
$841$	112.695	−	783.810i	0.134001	−	0.931997i
$842$	240.524	+	374.262i	0.285658	+	0.444492i
$843$		0			0
$844$	−100.580	−	699.549i	−0.119171	−	0.828849i
$845$	−1175.57	+	1018.64i	−1.39121	+	1.20549i
$846$		0			0
$847$	−207.296	−	179.623i	−0.244742	−	0.212070i
$848$	−91.1320	−	310.367i	−0.107467	−	0.365999i
$849$		0			0
$850$			79.6618i			0.0937197i
$851$	541.302	+	1479.46i	0.636078	+	1.73850i
$852$		0			0
$853$	190.270	+	416.632i	0.223059	+	0.488432i	0.987765	−	0.155948i	$-0.0498431\pi$
$853$	190.270	+	416.632i	0.223059	+	0.488432i	−0.764706	+	0.644379i	$0.777116\pi$
$854$	550.802	−	161.730i	0.644968	−	0.189380i
$855$		0			0
$856$	−150.219	+	233.745i	−0.175489	+	0.273067i
$857$	−299.813	−	346.002i	−0.349840	−	0.403736i	0.553370	−	0.832935i	$-0.313341\pi$
$857$	−299.813	−	346.002i	−0.349840	−	0.403736i	−0.903210	+	0.429199i	$0.858796\pi$
$858$		0			0
$859$	871.398	+	255.865i	1.01443	+	0.297864i	0.746366	−	0.665536i	$-0.231797\pi$
$859$	871.398	+	255.865i	1.01443	+	0.297864i	0.268067	+	0.963400i	$0.413615\pi$
$860$	1153.42	−	741.261i	1.34119	−	0.861931i
$861$		0			0
$862$	0.947733	+	0.432815i	0.00109946	+	0.000502106i
$863$	158.736	−	347.583i	0.183935	−	0.402761i	−0.795093	−	0.606487i	$-0.792578\pi$
$863$	158.736	−	347.583i	0.183935	−	0.402761i	0.979028	+	0.203727i	$0.0653053\pi$
$864$		0			0
$865$	−313.434	−	487.712i	−0.362351	−	0.563829i
$866$	−316.602	+	1078.25i	−0.365591	+	1.24509i
$867$		0			0
$868$	349.392	−	302.750i	0.402525	−	0.348790i
$869$	574.488	+	369.201i	0.661091	+	0.424857i
$870$		0			0
$871$	−4.48449	−	15.2728i	−0.00514867	−	0.0175348i
$872$	235.978	−	107.768i	0.270617	−	0.123587i
$873$		0			0
$874$	−121.699	+	219.601i	−0.139244	+	0.251260i
$875$	1735.69			1.98364
$876$		0			0
$877$	178.885	−	52.5255i	0.203974	−	0.0598922i	−0.178149	−	0.984003i	$-0.557011\pi$
$877$	178.885	−	52.5255i	0.203974	−	0.0598922i	0.382124	+	0.924111i	$0.375193\pi$
$878$	−626.653	+	723.196i	−0.713728	+	0.823686i
$879$		0			0
$880$	−200.419	−	231.296i	−0.227749	−	0.262836i
$881$	760.883	−	109.398i	0.863658	−	0.124175i	0.303772	−	0.952745i	$-0.401754\pi$
$881$	760.883	−	109.398i	0.863658	−	0.124175i	0.559886	+	0.828570i	$0.310845\pi$
$882$		0			0
$883$	−442.850	+	284.603i	−0.501529	+	0.322313i	−0.766828	−	0.641853i	$-0.778166\pi$
$883$	−442.850	+	284.603i	−0.501529	+	0.322313i	0.265298	+	0.964166i	$0.414530\pi$
$884$	−2.18296	−	0.313863i	−0.00246941	−	0.000355048i
$885$		0			0
$886$	146.125	−	319.968i	0.164926	−	0.361138i
$887$	−64.6344	+	449.542i	−0.0728685	+	0.506812i	0.920400	+	0.390978i	$0.127863\pi$
$887$	−64.6344	+	449.542i	−0.0728685	+	0.506812i	−0.993269	+	0.115834i	$0.963046\pi$
$888$		0			0
$889$	−116.810	+	397.819i	−0.131395	+	0.447491i
$890$	−272.622	−	1896.13i	−0.306317	−	2.13048i
$891$		0			0
$892$	372.446	+	239.356i	0.417540	+	0.268337i
$893$	−21.8121	−	18.9003i	−0.0244257	−	0.0211650i
$894$		0			0
$895$	532.657	−	243.256i	0.595148	−	0.271795i
$896$		−	58.4795i		−	0.0652673i
$897$		0			0
$898$	−107.256			−0.119439
$899$	130.215	+	285.132i	0.144845	+	0.317166i
$900$		0			0
$901$	48.7637	−	56.2763i	0.0541218	−	0.0624599i
$902$	287.928	−	448.025i	0.319211	−	0.496702i
$903$		0			0
$904$	−426.772	+	61.3605i	−0.472092	+	0.0678766i
$905$	1499.02	+	440.151i	1.65637	+	0.486355i
$906$		0			0
$907$	−644.769	−	92.7037i	−0.710880	−	0.102209i	−0.222618	−	0.974906i	$-0.571460\pi$
$907$	−644.769	−	92.7037i	−0.710880	−	0.102209i	−0.488263	+	0.872697i	$0.662369\pi$
$908$	−304.048	−	138.854i	−0.334855	−	0.152923i
$909$		0			0
$910$	−11.5647	+	80.4344i	−0.0127085	+	0.0883895i
$911$	667.347	+	1038.41i	0.732543	+	1.13986i	0.985051	+	0.172264i	$0.0551082\pi$
$911$	667.347	+	1038.41i	0.732543	+	1.13986i	−0.252508	+	0.967595i	$0.581255\pi$
$912$		0			0
$913$	157.644	+	1096.44i	0.172666	+	1.20092i
$914$	83.6344	−	72.4696i	0.0915037	−	0.0792884i
$915$		0			0
$916$	−426.645	−	369.690i	−0.465770	−	0.403592i
$917$	−197.638	−	673.092i	−0.215526	−	0.734016i
$918$		0			0
$919$			1367.95i			1.48852i	0.667888	+	0.744262i	$0.267199\pi$
$919$			1367.95i			1.48852i	−0.667888	+	0.744262i	$0.732801\pi$
$920$	531.821	−	286.096i	0.578067	−	0.310974i
$921$		0			0
$922$	487.802	+	1068.14i	0.529069	+	1.15850i
$923$	−117.364	+	34.4611i	−0.127155	+	0.0373359i
$924$		0			0
$925$	−2265.30	+	3524.88i	−2.44898	+	3.81068i
$926$	485.541	+	560.344i	0.524342	+	0.605123i
$927$		0			0
$928$	38.0444	+	11.1708i	0.0409961	+	0.0120376i
$929$	−183.192	+	117.730i	−0.197193	+	0.126728i	−0.635511	−	0.772092i	$-0.719211\pi$
$929$	−183.192	+	117.730i	−0.197193	+	0.126728i	0.438318	+	0.898820i	$0.355574\pi$
$930$		0			0
$931$	−156.451	−	71.4486i	−0.168046	−	0.0767439i
$932$	352.974	−	772.904i	0.378727	−	0.829296i
$933$		0			0
$934$	388.703	+	604.833i	0.416170	+	0.647573i
$935$	19.8491	−	67.5999i	0.0212290	−	0.0722993i
$936$		0			0
$937$	727.821	−	630.660i	0.776756	−	0.673063i	−0.173395	−	0.984852i	$-0.555474\pi$
$937$	727.821	−	630.660i	0.776756	−	0.673063i	0.950151	+	0.311789i	$0.100928\pi$
$938$	81.7394	+	52.5307i	0.0871422	+	0.0560029i
$939$		0			0
$940$	19.5579	+	66.6082i	0.0208063	+	0.0708598i
$941$	1285.19	−	586.928i	1.36577	−	0.623728i	0.408460	−	0.912776i	$-0.366066\pi$
$941$	1285.19	−	586.928i	1.36577	−	0.623728i	0.957315	+	0.289048i	$0.0933386\pi$
$942$		0			0
$943$	738.411	+	747.699i	0.783045	+	0.792894i
$944$	−174.211			−0.184546
$945$		0			0
$946$	−825.937	+	242.517i	−0.873084	+	0.256361i
$947$	−1086.74	+	1254.17i	−1.14756	+	1.32436i	−0.209536	+	0.977801i	$0.567195\pi$
$947$	−1086.74	+	1254.17i	−1.14756	+	1.32436i	−0.938028	+	0.346559i	$0.887350\pi$
$948$		0			0
$949$	2.44855	+	2.82578i	0.00258014	+	0.00297764i
$950$	−660.971	+	95.0333i	−0.695759	+	0.100035i
$951$		0			0
$952$	11.3252	−	7.27824i	0.0118962	−	0.00764521i
$953$	−815.261	−	117.217i	−0.855468	−	0.122998i	−0.299393	−	0.954130i	$-0.596784\pi$
$953$	−815.261	−	117.217i	−0.855468	−	0.122998i	−0.556075	+	0.831132i	$0.687693\pi$
$954$		0			0
$955$	1017.51	−	2228.03i	1.06545	−	2.33301i
$956$	−26.8109	+	186.474i	−0.0280448	+	0.195056i
$957$		0			0
$958$	309.355	−	1053.57i	0.322917	−	1.09975i
$959$	130.914	+	910.528i	0.136511	+	0.949456i
$960$		0			0
$961$	873.994	+	561.682i	0.909463	+	0.584476i
$962$	−87.6667	−	75.9636i	−0.0911296	−	0.0789643i
$963$		0			0
$964$	−594.746	+	271.611i	−0.616956	+	0.281754i
$965$		−	485.951i		−	0.503576i
$966$		0			0
$967$	1235.01			1.27715			0.638577	−	0.769558i	$-0.279523\pi$
$967$	1235.01			1.27715			0.638577	+	0.769558i	$0.279523\pi$
$968$	−62.3508	−	136.529i	−0.0644120	−	0.141043i
$969$		0			0
$970$	200.510	−	231.401i	0.206711	−	0.238558i
$971$	−273.858	+	426.131i	−0.282037	+	0.438858i	−0.953150	−	0.302497i	$-0.902180\pi$
$971$	−273.858	+	426.131i	−0.282037	+	0.438858i	0.671114	+	0.741355i	$0.265816\pi$
$972$		0			0
$973$	−452.422	+	65.0485i	−0.464977	+	0.0668535i
$974$	−215.449	−	63.2615i	−0.221200	−	0.0649503i
$975$		0			0
$976$	310.926	+	44.7044i	0.318572	+	0.0458037i
$977$	164.661	+	75.1983i	0.168538	+	0.0769686i	0.497897	−	0.867236i	$-0.334106\pi$
$977$	164.661	+	75.1983i	0.168538	+	0.0769686i	−0.329360	+	0.944205i	$0.606833\pi$
$978$		0			0
$979$	−171.161	+	1190.45i	−0.174832	+	1.21598i
$980$	223.659	+	348.020i	0.228224	+	0.355123i
$981$		0			0
$982$	−31.2850	−	217.592i	−0.0318585	−	0.221581i
$983$	662.692	−	574.226i	0.674152	−	0.584156i	−0.249041	−	0.968493i	$-0.580115\pi$
$983$	662.692	−	574.226i	0.674152	−	0.584156i	0.923193	+	0.384337i	$0.125570\pi$
$984$		0			0
$985$	−1195.37	−	1035.80i	−1.21358	−	1.05157i
$986$	2.57158	+	8.75800i	0.00260809	+	0.00888235i
$987$		0			0
$988$		−	18.4869i		−	0.0187115i
$989$	−110.581	−	1694.93i	−0.111811	−	1.71378i
$990$		0			0
$991$	−302.545	−	662.482i	−0.305293	−	0.668498i	0.693349	−	0.720602i	$-0.256135\pi$
$991$	−302.545	−	662.482i	−0.305293	−	0.668498i	−0.998642	+	0.0521040i	$0.983407\pi$
$992$	242.730	−	71.2719i	0.244687	−	0.0718466i
$993$		0			0
$994$	403.672	−	628.127i	0.406109	−	0.631918i
$995$	571.743	+	659.826i	0.574616	+	0.663142i
$996$		0			0
$997$	−905.605	−	265.910i	−0.908330	−	0.266710i	−0.205992	−	0.978554i	$-0.566042\pi$
$997$	−905.605	−	265.910i	−0.908330	−	0.266710i	−0.702338	+	0.711844i	$0.747860\pi$
$998$	−63.4897	+	40.8024i	−0.0636170	+	0.0408841i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	414.3.l.b.19.1		80
3.2	odd	2		138.3.h.a.19.6	✓	80
23.17	odd	22	inner	414.3.l.b.109.1		80
69.17	even	22		138.3.h.a.109.6	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
138.3.h.a.19.6	✓	80	3.2	odd	2
138.3.h.a.109.6	yes	80	69.17	even	22
414.3.l.b.19.1		80	1.1	even	1	trivial
414.3.l.b.109.1		80	23.17	odd	22	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:	\( N \)	\(=\)	\( 414 = 2 \cdot 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	414.l (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.587486 - 1.28641i) q^{2} +(-1.30972 + 1.51150i) q^{4} +(-5.01874 + 7.80931i) q^{5} +(5.11630 - 0.735612i) q^{7} +(2.71386 + 0.796860i) q^{8} +O(q^{10})\)	\(q+(-0.587486 - 1.28641i) q^{2} +(-1.30972 + 1.51150i) q^{4} +(-5.01874 + 7.80931i) q^{5} +(5.11630 - 0.735612i) q^{7} +(2.71386 + 0.796860i) q^{8} +(12.9944 + 1.86832i) q^{10} +(-7.49739 - 3.42394i) q^{11} +(-0.170426 + 1.18534i) q^{13} +(-3.95205 - 6.14951i) q^{14} +(-0.569259 - 3.95929i) q^{16} +(0.695908 - 0.603008i) q^{17} +(5.83348 + 5.05474i) q^{19} +(-5.23062 - 17.8139i) q^{20} +11.6563i q^{22} +(-22.4434 - 5.02937i) q^{23} +(-25.4123 - 55.6451i) q^{25} +(1.62496 - 0.477131i) q^{26} +(-5.58904 + 8.69672i) q^{28} +(-4.59011 - 5.29727i) q^{29} +(-42.9090 - 12.5992i) q^{31} +(-4.75885 + 3.05833i) q^{32} +(-1.18455 - 0.540968i) q^{34} +(-19.9327 + 43.6466i) q^{35} +(-37.0310 - 57.6213i) q^{37} +(3.07540 - 10.4739i) q^{38} +(-19.8431 + 17.1941i) q^{40} +(-38.4365 - 24.7016i) q^{41} +(20.8057 + 70.8578i) q^{43} +(14.9948 - 6.84788i) q^{44} +(6.71532 + 31.8262i) q^{46} -3.73913 q^{47} +(-21.3798 + 6.27768i) q^{49} +(-56.6533 + 65.3814i) q^{50} +(-1.56843 - 1.81006i) q^{52} +(80.0444 - 11.5086i) q^{53} +(64.3661 - 41.3656i) q^{55} +(14.4711 + 2.08063i) q^{56} +(-4.11786 + 9.01685i) q^{58} +(6.19820 - 43.1094i) q^{59} +(-22.1247 + 75.3498i) q^{61} +(9.00060 + 62.6005i) q^{62} +(6.73003 + 4.32513i) q^{64} +(-8.40135 - 7.27981i) q^{65} +(-12.0908 + 5.52170i) q^{67} +1.84164i q^{68} +67.8578 q^{70} +(42.4315 + 92.9121i) q^{71} +(2.04467 - 2.35968i) q^{73} +(-52.3697 + 81.4889i) q^{74} +(-15.2805 + 2.19700i) q^{76} +(-40.8775 - 12.0027i) q^{77} +(-82.0100 - 11.7913i) q^{79} +(33.7763 + 15.4251i) q^{80} +(-9.19564 + 63.9571i) q^{82} +(-72.6596 - 113.061i) q^{83} +(1.21649 + 8.46091i) q^{85} +(78.9294 - 68.3927i) q^{86} +(-17.6184 - 15.2665i) q^{88} +(-41.1099 - 140.007i) q^{89} +6.18991i q^{91} +(36.9965 - 27.3361i) q^{92} +(2.19668 + 4.81006i) q^{94} +(-68.7508 + 20.1870i) q^{95} +(12.6094 - 19.6206i) q^{97} +(20.6360 + 23.8152i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 16 q^{4}+O(q^{10}) \) 80 * q - 16 * q^4	\( 80 q - 16 q^{4} - 16 q^{13} - 32 q^{16} - 220 q^{17} + 132 q^{19} - 88 q^{20} + 104 q^{23} - 336 q^{25} + 208 q^{26} - 264 q^{28} + 164 q^{29} - 268 q^{31} - 552 q^{35} + 352 q^{37} - 192 q^{41} + 88 q^{43} + 80 q^{46} + 64 q^{47} - 40 q^{49} - 160 q^{50} - 32 q^{52} + 352 q^{53} + 196 q^{55} + 312 q^{58} + 696 q^{59} + 616 q^{61} - 96 q^{62} - 64 q^{64} + 44 q^{67} - 32 q^{70} + 32 q^{71} - 284 q^{73} + 224 q^{77} - 440 q^{79} - 616 q^{82} - 352 q^{83} - 532 q^{85} - 88 q^{89} + 32 q^{92} + 16 q^{94} - 372 q^{95} - 264 q^{97} - 1184 q^{98}+O(q^{100}) \) 80 * q - 16 * q^4 - 16 * q^13 - 32 * q^16 - 220 * q^17 + 132 * q^19 - 88 * q^20 + 104 * q^23 - 336 * q^25 + 208 * q^26 - 264 * q^28 + 164 * q^29 - 268 * q^31 - 552 * q^35 + 352 * q^37 - 192 * q^41 + 88 * q^43 + 80 * q^46 + 64 * q^47 - 40 * q^49 - 160 * q^50 - 32 * q^52 + 352 * q^53 + 196 * q^55 + 312 * q^58 + 696 * q^59 + 616 * q^61 - 96 * q^62 - 64 * q^64 + 44 * q^67 - 32 * q^70 + 32 * q^71 - 284 * q^73 + 224 * q^77 - 440 * q^79 - 616 * q^82 - 352 * q^83 - 532 * q^85 - 88 * q^89 + 32 * q^92 + 16 * q^94 - 372 * q^95 - 264 * q^97 - 1184 * q^98

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