LMFDB - Embedded newform 162.3.f.a.89.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [162,3,Mod(17,162)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(162, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([11]))

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

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

chi := DirichletCharacter("162.17");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 162 = 2 \cdot 3^{4} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	162.f (of order $18$, degree $6$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.41418028264$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$6$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 54)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			89.5
Character	$\chi$	$=$	162.89
Dual form			162.3.f.a.71.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.39273 + 0.245576i) q^{2} +(1.87939 + 0.684040i) q^{4} +(1.49345 + 1.77982i) q^{5} +(5.91054 - 2.15126i) q^{7} +(2.44949 + 1.41421i) q^{8} +O(q^{10})$	\(q+(1.39273 + 0.245576i) q^{2} +(1.87939 + 0.684040i) q^{4} +(1.49345 + 1.77982i) q^{5} +(5.91054 - 2.15126i) q^{7} +(2.44949 + 1.41421i) q^{8} +(1.64289 + 2.84556i) q^{10} +(-1.00782 + 1.20107i) q^{11} +(1.33408 + 7.56595i) q^{13} +(8.76008 - 1.54464i) q^{14} +(3.06418 + 2.57115i) q^{16} +(20.1411 - 11.6285i) q^{17} +(-15.0781 + 26.1161i) q^{19} +(1.58929 + 4.36655i) q^{20} +(-1.69857 + 1.42527i) q^{22} +(7.69793 - 21.1499i) q^{23} +(3.40383 - 19.3041i) q^{25} +10.8649i q^{26} +12.5797 q^{28} +(-49.0949 - 8.65675i) q^{29} +(-27.8049 - 10.1202i) q^{31} +(3.63616 + 4.33340i) q^{32} +(30.9068 - 11.2492i) q^{34} +(12.6559 + 7.30691i) q^{35} +(14.5999 + 25.2877i) q^{37} +(-27.4132 + 32.6698i) q^{38} +(1.14114 + 6.47170i) q^{40} +(-17.1669 + 3.02698i) q^{41} +(-64.1027 - 53.7886i) q^{43} +(-2.71565 + 1.56788i) q^{44} +(15.9150 - 27.5656i) q^{46} +(-11.3382 - 31.1513i) q^{47} +(-7.22958 + 6.06634i) q^{49} +(9.48121 - 26.0494i) q^{50} +(-2.66816 + 15.1319i) q^{52} +86.0360i q^{53} -3.64280 q^{55} +(17.5202 + 3.08928i) q^{56} +(-66.2499 - 24.1130i) q^{58} +(-29.2986 - 34.9167i) q^{59} +(79.4407 - 28.9140i) q^{61} +(-36.2395 - 20.9229i) q^{62} +(4.00000 + 6.92820i) q^{64} +(-11.4736 + 13.6738i) q^{65} +(-8.80100 - 49.9130i) q^{67} +(45.8073 - 8.07706i) q^{68} +(15.8319 + 13.2845i) q^{70} +(32.5457 - 18.7903i) q^{71} +(-3.93896 + 6.82248i) q^{73} +(14.1236 + 38.8043i) q^{74} +(-46.2021 + 38.7682i) q^{76} +(-3.37293 + 9.26704i) q^{77} +(-12.5403 + 71.1198i) q^{79} +9.29356i q^{80} -24.6521 q^{82} +(25.4050 + 4.47959i) q^{83} +(50.7763 + 18.4811i) q^{85} +(-76.0685 - 90.6549i) q^{86} +(-4.16720 + 1.51674i) q^{88} +(23.4923 + 13.5633i) q^{89} +(24.1615 + 41.8489i) q^{91} +(28.9347 - 34.4831i) q^{92} +(-8.14096 - 46.1697i) q^{94} +(-69.0004 + 12.1666i) q^{95} +(-27.0251 - 22.6768i) q^{97} +(-11.5586 + 6.67336i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 18 q^{5}+O(q^{10}) $ 36 * q - 18 * q^5	$ 36 q - 18 q^{5} + 18 q^{11} + 36 q^{14} + 72 q^{20} + 36 q^{22} + 180 q^{23} + 18 q^{25} - 144 q^{29} - 90 q^{31} - 72 q^{34} - 486 q^{35} - 180 q^{38} + 90 q^{41} + 90 q^{43} + 378 q^{47} + 72 q^{49} + 72 q^{56} - 252 q^{59} - 144 q^{61} + 144 q^{64} - 18 q^{65} - 594 q^{67} + 180 q^{68} - 360 q^{70} + 648 q^{71} + 126 q^{73} + 504 q^{74} - 72 q^{76} + 342 q^{77} - 72 q^{79} - 594 q^{83} + 360 q^{85} - 540 q^{86} + 144 q^{88} - 648 q^{89} - 198 q^{91} - 396 q^{92} + 504 q^{94} - 252 q^{95} + 702 q^{97} - 648 q^{98}+O(q^{100}) $ 36 * q - 18 * q^5 + 18 * q^11 + 36 * q^14 + 72 * q^20 + 36 * q^22 + 180 * q^23 + 18 * q^25 - 144 * q^29 - 90 * q^31 - 72 * q^34 - 486 * q^35 - 180 * q^38 + 90 * q^41 + 90 * q^43 + 378 * q^47 + 72 * q^49 + 72 * q^56 - 252 * q^59 - 144 * q^61 + 144 * q^64 - 18 * q^65 - 594 * q^67 + 180 * q^68 - 360 * q^70 + 648 * q^71 + 126 * q^73 + 504 * q^74 - 72 * q^76 + 342 * q^77 - 72 * q^79 - 594 * q^83 + 360 * q^85 - 540 * q^86 + 144 * q^88 - 648 * q^89 - 198 * q^91 - 396 * q^92 + 504 * q^94 - 252 * q^95 + 702 * q^97 - 648 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/162\mathbb{Z}\right)^\times$.

$n$	$83$
$\chi(n)$	$e\left(\frac{1}{18}\right)$

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 $

$2$	1.39273	+	0.245576i	0.696364	+	0.122788i
$2$	1.39273	+	0.245576i	0.696364	+	0.122788i
$3$		0			0
$3$		0			0
$4$	1.87939	+	0.684040i	0.469846	+	0.171010i
$5$	1.49345	+	1.77982i	0.298689	+	0.355964i	0.894426	−	0.447216i	$-0.147584\pi$
$5$	1.49345	+	1.77982i	0.298689	+	0.355964i	−0.595737	+	0.803180i	$0.703140\pi$
$6$		0			0
$7$	5.91054	−	2.15126i	0.844363	−	0.307323i	0.116623	−	0.993176i	$-0.462793\pi$
$7$	5.91054	−	2.15126i	0.844363	−	0.307323i	0.727740	+	0.685853i	$0.240571\pi$
$8$	2.44949	+	1.41421i	0.306186	+	0.176777i
$9$		0			0
$10$	1.64289	+	2.84556i	0.164289	+	0.284556i
$11$	−1.00782	+	1.20107i	−0.0916196	+	0.109188i	−0.809906	−	0.586559i	$-0.800482\pi$
$11$	−1.00782	+	1.20107i	−0.0916196	+	0.109188i	0.718287	+	0.695747i	$0.244927\pi$
$12$		0			0
$13$	1.33408	+	7.56595i	0.102622	+	0.581996i	0.992144	+	0.125104i	$0.0399264\pi$
$13$	1.33408	+	7.56595i	0.102622	+	0.581996i	−0.889522	+	0.456892i	$0.848963\pi$
$14$	8.76008	−	1.54464i	0.625720	−	0.110331i
$15$		0			0
$16$	3.06418	+	2.57115i	0.191511	+	0.160697i
$17$	20.1411	−	11.6285i	1.18477	−	0.684028i	0.227658	−	0.973741i	$-0.426893\pi$
$17$	20.1411	−	11.6285i	1.18477	−	0.684028i	0.957114	+	0.289713i	$0.0935597\pi$
$18$		0			0
$19$	−15.0781	+	26.1161i	−0.793586	+	1.37453i	0.130147	+	0.991495i	$0.458455\pi$
$19$	−15.0781	+	26.1161i	−0.793586	+	1.37453i	−0.923733	+	0.383037i	$0.874878\pi$
$20$	1.58929	+	4.36655i	0.0794646	+	0.218327i
$21$		0			0
$22$	−1.69857	+	1.42527i	−0.0772076	+	0.0647848i
$23$	7.69793	−	21.1499i	0.334693	−	0.919560i	−0.652181	−	0.758064i	$-0.726146\pi$
$23$	7.69793	−	21.1499i	0.334693	−	0.919560i	0.986873	−	0.161497i	$-0.0516321\pi$
$24$		0			0
$25$	3.40383	−	19.3041i	0.136153	−	0.772162i
$26$			10.8649i			0.417882i
$27$		0			0
$28$	12.5797			0.449276
$29$	−49.0949	−	8.65675i	−1.69293	−	0.298509i	−0.757711	−	0.652590i	$-0.773682\pi$
$29$	−49.0949	−	8.65675i	−1.69293	−	0.298509i	−0.935215	+	0.354081i	$0.884794\pi$
$30$		0			0
$31$	−27.8049	−	10.1202i	−0.896933	−	0.326457i	−0.147910	−	0.989001i	$-0.547255\pi$
$31$	−27.8049	−	10.1202i	−0.896933	−	0.326457i	−0.749023	+	0.662544i	$0.769477\pi$
$32$	3.63616	+	4.33340i	0.113630	+	0.135419i
$33$		0			0
$34$	30.9068	−	11.2492i	0.909023	−	0.330857i
$35$	12.6559	+	7.30691i	0.361598	+	0.208769i
$36$		0			0
$37$	14.5999	+	25.2877i	0.394591	+	0.683452i	0.993049	−	0.117702i	$-0.0375529\pi$
$37$	14.5999	+	25.2877i	0.394591	+	0.683452i	−0.598458	+	0.801154i	$0.704220\pi$
$38$	−27.4132	+	32.6698i	−0.721401	+	0.859732i
$39$		0			0
$40$	1.14114	+	6.47170i	0.0285284	+	0.161793i
$41$	−17.1669	+	3.02698i	−0.418704	+	0.0738288i	−0.379031	−	0.925384i	$-0.623743\pi$
$41$	−17.1669	+	3.02698i	−0.418704	+	0.0738288i	−0.0396727	+	0.999213i	$0.512632\pi$
$42$		0			0
$43$	−64.1027	−	53.7886i	−1.49076	−	1.25090i	−0.893671	−	0.448722i	$-0.851879\pi$
$43$	−64.1027	−	53.7886i	−1.49076	−	1.25090i	−0.597089	−	0.802175i	$-0.703676\pi$
$44$	−2.71565	+	1.56788i	−0.0617194	+	0.0356337i
$45$		0			0
$46$	15.9150	−	27.5656i	0.345979	−	0.599253i
$47$	−11.3382	−	31.1513i	−0.241237	−	0.662794i	−0.999936	−	0.0113518i	$-0.996387\pi$
$47$	−11.3382	−	31.1513i	−0.241237	−	0.662794i	0.758698	−	0.651442i	$-0.225836\pi$
$48$		0			0
$49$	−7.22958	+	6.06634i	−0.147543	+	0.123803i
$50$	9.48121	−	26.0494i	0.189624	−	0.520988i
$51$		0			0
$52$	−2.66816	+	15.1319i	−0.0513108	+	0.290998i
$53$			86.0360i			1.62332i	0.584130	+	0.811660i	$0.301436\pi$
$53$			86.0360i			1.62332i	−0.584130	+	0.811660i	$0.698564\pi$
$54$		0			0
$55$	−3.64280			−0.0662328
$56$	17.5202	+	3.08928i	0.312860	+	0.0551657i
$57$		0			0
$58$	−66.2499	−	24.1130i	−1.14224	−	0.415741i
$59$	−29.2986	−	34.9167i	−0.496586	−	0.591809i	0.458294	−	0.888801i	$-0.348461\pi$
$59$	−29.2986	−	34.9167i	−0.496586	−	0.591809i	−0.954880	+	0.296992i	$0.904016\pi$
$60$		0			0
$61$	79.4407	−	28.9140i	1.30231	−	0.474001i	0.404559	−	0.914512i	$-0.367425\pi$
$61$	79.4407	−	28.9140i	1.30231	−	0.474001i	0.897747	+	0.440511i	$0.145203\pi$
$62$	−36.2395	−	20.9229i	−0.584507	−	0.337465i
$63$		0			0
$64$	4.00000	+	6.92820i	0.0625000	+	0.108253i
$65$	−11.4736	+	13.6738i	−0.176518	+	0.210366i
$66$		0			0
$67$	−8.80100	−	49.9130i	−0.131358	−	0.744969i	−0.977327	−	0.211737i	$-0.932088\pi$
$67$	−8.80100	−	49.9130i	−0.131358	−	0.744969i	0.845969	−	0.533233i	$-0.179023\pi$
$68$	45.8073	−	8.07706i	0.673636	−	0.118780i
$69$		0			0
$70$	15.8319	+	13.2845i	0.226170	+	0.189779i
$71$	32.5457	−	18.7903i	0.458391	−	0.264652i	−0.252977	−	0.967472i	$-0.581410\pi$
$71$	32.5457	−	18.7903i	0.458391	−	0.264652i	0.711367	+	0.702820i	$0.248076\pi$
$72$		0			0
$73$	−3.93896	+	6.82248i	−0.0539584	+	0.0934587i	−0.891743	−	0.452542i	$-0.850517\pi$
$73$	−3.93896	+	6.82248i	−0.0539584	+	0.0934587i	0.837785	+	0.546001i	$0.183850\pi$
$74$	14.1236	+	38.8043i	0.190860	+	0.524383i
$75$		0			0
$76$	−46.2021	+	38.7682i	−0.607922	+	0.510107i
$77$	−3.37293	+	9.26704i	−0.0438042	+	0.120351i
$78$		0			0
$79$	−12.5403	+	71.1198i	−0.158738	+	0.900250i	0.796550	+	0.604573i	$0.206656\pi$
$79$	−12.5403	+	71.1198i	−0.158738	+	0.900250i	−0.955288	+	0.295677i	$0.904455\pi$
$80$			9.29356i			0.116170i
$81$		0			0
$82$	−24.6521			−0.300636
$83$	25.4050	+	4.47959i	0.306084	+	0.0539709i	0.324581	−	0.945858i	$-0.394777\pi$
$83$	25.4050	+	4.47959i	0.306084	+	0.0539709i	−0.0184964	+	0.999829i	$0.505888\pi$
$84$		0			0
$85$	50.7763	+	18.4811i	0.597368	+	0.217424i
$86$	−76.0685	−	90.6549i	−0.884518	−	1.05413i
$87$		0			0
$88$	−4.16720	+	1.51674i	−0.0473545	+	0.0172356i
$89$	23.4923	+	13.5633i	0.263958	+	0.152396i	0.626139	−	0.779712i	$-0.284634\pi$
$89$	23.4923	+	13.5633i	0.263958	+	0.152396i	−0.362181	+	0.932108i	$0.617968\pi$
$90$		0			0
$91$	24.1615	+	41.8489i	0.265511	+	0.459878i
$92$	28.9347	−	34.4831i	0.314508	−	0.374816i
$93$		0			0
$94$	−8.14096	−	46.1697i	−0.0866060	−	0.491167i
$95$	−69.0004	+	12.1666i	−0.726320	+	0.128070i
$96$		0			0
$97$	−27.0251	−	22.6768i	−0.278610	−	0.233781i	0.492765	−	0.870162i	$-0.335986\pi$
$97$	−27.0251	−	22.6768i	−0.278610	−	0.233781i	−0.771375	+	0.636381i	$0.780431\pi$
$98$	−11.5586	+	6.67336i	−0.117945	+	0.0680955i
$99$		0			0
$100$	19.6019	−	33.9514i	0.196019	−	0.339514i
$101$	1.81805	+	4.99504i	0.0180005	+	0.0494559i	0.948367	−	0.317174i	$-0.102734\pi$
$101$	1.81805	+	4.99504i	0.0180005	+	0.0494559i	−0.930367	+	0.366630i	$0.880512\pi$
$102$		0			0
$103$	51.6309	−	43.3235i	0.501271	−	0.420616i	−0.356774	−	0.934191i	$-0.616123\pi$
$103$	51.6309	−	43.3235i	0.501271	−	0.420616i	0.858045	+	0.513574i	$0.171679\pi$
$104$	−7.43205	+	20.4194i	−0.0714620	+	0.196340i
$105$		0			0
$106$	−21.1283	+	119.825i	−0.199324	+	1.13042i
$107$		−	0.744883i		−	0.00696152i	−0.999994	−	0.00348076i	$-0.998892\pi$
$107$		−	0.744883i		−	0.00696152i	0.999994	−	0.00348076i	$-0.00110796\pi$
$108$		0			0
$109$	56.8674			0.521719			0.260859	−	0.965377i	$-0.415994\pi$
$109$	56.8674			0.521719			0.260859	+	0.965377i	$0.415994\pi$
$110$	−5.07344	−	0.894584i	−0.0461221	−	0.00813258i
$111$		0			0
$112$	23.6422	+	8.60505i	0.211091	+	0.0768308i
$113$	137.389	+	163.733i	1.21583	+	1.44897i	0.856806	+	0.515638i	$0.172445\pi$
$113$	137.389	+	163.733i	1.21583	+	1.44897i	0.359022	+	0.933329i	$0.383110\pi$
$114$		0			0
$115$	49.1394	−	17.8853i	0.427300	−	0.155524i
$116$	−86.3466	−	49.8522i	−0.744367	−	0.429761i
$117$		0			0
$118$	−32.2303	−	55.8245i	−0.273138	−	0.473089i
$119$	94.0291	−	112.059i	0.790160	−	0.941676i
$120$		0			0
$121$	20.5846	+	116.741i	0.170120	+	0.964800i
$122$	117.740	−	20.7607i	0.965081	−	0.170170i
$123$		0			0
$124$	−45.3336	−	38.0394i	−0.365593	−	0.306769i
$125$	89.7441	−	51.8138i	0.717953	−	0.414510i
$126$		0			0
$127$	−24.6922	+	42.7682i	−0.194427	+	0.336758i	−0.946713	−	0.322080i	$-0.895618\pi$
$127$	−24.6922	+	42.7682i	−0.194427	+	0.336758i	0.752285	+	0.658837i	$0.228951\pi$
$128$	3.86952	+	10.6314i	0.0302306	+	0.0830579i
$129$		0			0
$130$	−19.3376	+	16.2262i	−0.148751	+	0.124817i
$131$	−16.8555	+	46.3101i	−0.128668	+	0.353513i	−0.987253	−	0.159159i	$-0.949122\pi$
$131$	−16.8555	+	46.3101i	−0.128668	+	0.353513i	0.858585	+	0.512671i	$0.171344\pi$
$132$		0			0
$133$	−32.9374	+	186.797i	−0.247650	+	1.40449i
$134$		−	71.6765i		−	0.534899i
$135$		0			0
$136$	65.7806			0.483681
$137$	133.137	+	23.4756i	0.971801	+	0.171355i	0.636940	−	0.770913i	$-0.280200\pi$
$137$	133.137	+	23.4756i	0.971801	+	0.171355i	0.334860	+	0.942268i	$0.391311\pi$
$138$		0			0
$139$	204.776	+	74.5324i	1.47321	+	0.536204i	0.948970	−	0.315367i	$-0.102128\pi$
$139$	204.776	+	74.5324i	1.47321	+	0.536204i	0.524239	+	0.851571i	$0.324350\pi$
$140$	18.7872	+	22.3897i	0.134194	+	0.159926i
$141$		0			0
$142$	49.9418	−	18.1773i	0.351703	−	0.128009i
$143$	−10.4317	−	6.02276i	−0.0729491	−	0.0421172i
$144$		0			0
$145$	−57.9131	−	100.308i	−0.399401	−	0.691782i
$146$	−7.16134	+	8.53455i	−0.0490503	+	0.0584558i
$147$		0			0
$148$	10.1410	+	57.5123i	0.0685201	+	0.388597i
$149$	−69.7907	+	12.3060i	−0.468394	+	0.0825905i	−0.402864	−	0.915260i	$-0.631985\pi$
$149$	−69.7907	+	12.3060i	−0.468394	+	0.0825905i	−0.0655305	+	0.997851i	$0.520874\pi$
$150$		0			0
$151$	−202.069	−	169.556i	−1.33821	−	1.12289i	−0.982083	−	0.188449i	$-0.939654\pi$
$151$	−202.069	−	169.556i	−1.33821	−	1.12289i	−0.356123	−	0.934439i	$-0.615902\pi$
$152$	−73.8675	+	42.6474i	−0.485970	+	0.280575i
$153$		0			0
$154$	−6.97333	+	12.0782i	−0.0452814	+	0.0784296i
$155$	−23.5131	−	64.6017i	−0.151697	−	0.416785i
$156$		0			0
$157$	74.3308	−	62.3709i	0.473444	−	0.397267i	−0.374605	−	0.927185i	$-0.622222\pi$
$157$	74.3308	−	62.3709i	0.473444	−	0.397267i	0.848049	+	0.529918i	$0.177777\pi$
$158$	−34.9306	+	95.9709i	−0.221079	+	0.607411i
$159$		0			0
$160$	−2.28227	+	12.9434i	−0.0142642	+	0.0808963i
$161$		−	141.568i		−	0.879302i
$162$		0			0
$163$	−166.799			−1.02331			−0.511654	−	0.859191i	$-0.670967\pi$
$163$	−166.799			−1.02331			−0.511654	+	0.859191i	$0.670967\pi$
$164$	−34.3337	−	6.05396i	−0.209352	−	0.0369144i
$165$		0			0
$166$	34.2822	+	12.4777i	0.206519	+	0.0751668i
$167$	13.4784	+	16.0630i	0.0807092	+	0.0961855i	0.804888	−	0.593427i	$-0.202225\pi$
$167$	13.4784	+	16.0630i	0.0807092	+	0.0961855i	−0.724179	+	0.689612i	$0.757781\pi$
$168$		0			0
$169$	103.344	−	37.6142i	0.611505	−	0.222569i
$170$	66.1791	+	38.2085i	0.389289	+	0.224756i
$171$		0			0
$172$	−83.6801	−	144.938i	−0.486512	−	0.842664i
$173$	−115.925	+	138.154i	−0.670088	+	0.798580i	−0.988796	−	0.149273i	$-0.952307\pi$
$173$	−115.925	+	138.154i	−0.670088	+	0.798580i	0.318708	+	0.947853i	$0.396751\pi$
$174$		0			0
$175$	−21.4096	−	121.420i	−0.122341	−	0.693829i
$176$	−6.17625	+	1.08904i	−0.0350923	+	0.00618773i
$177$		0			0
$178$	29.3876	+	24.6591i	0.165099	+	0.138534i
$179$	−200.580	+	115.805i	−1.12056	+	0.646955i	−0.941544	−	0.336891i	$-0.890625\pi$
$179$	−200.580	+	115.805i	−1.12056	+	0.646955i	−0.179016	+	0.983846i	$0.557291\pi$
$180$		0			0
$181$	48.1236	−	83.3525i	0.265876	−	0.460511i	−0.701917	−	0.712259i	$-0.747672\pi$
$181$	48.1236	−	83.3525i	0.265876	−	0.460511i	0.967793	+	0.251748i	$0.0810054\pi$
$182$	23.3733	+	64.2176i	0.128425	+	0.352844i
$183$		0			0
$184$	48.7665	−	40.9199i	0.265035	−	0.222391i
$185$	−23.2035	+	63.7510i	−0.125424	+	0.344600i
$186$		0			0
$187$	−6.33194	+	35.9102i	−0.0338606	+	0.192033i
$188$		−	66.3011i		−	0.352665i
$189$		0			0
$190$	−99.0866			−0.521509
$191$	−95.7785	−	16.8883i	−0.501458	−	0.0884206i	−0.0828031	−	0.996566i	$-0.526387\pi$
$191$	−95.7785	−	16.8883i	−0.501458	−	0.0884206i	−0.418655	+	0.908145i	$0.637498\pi$
$192$		0			0
$193$	−46.9759	−	17.0978i	−0.243398	−	0.0885897i	0.217441	−	0.976074i	$-0.430229\pi$
$193$	−46.9759	−	17.0978i	−0.243398	−	0.0885897i	−0.460839	+	0.887484i	$0.652451\pi$
$194$	−32.0698	−	38.2193i	−0.165308	−	0.197007i
$195$		0			0
$196$	−17.7368	+	6.45567i	−0.0904939	+	0.0329371i
$197$	−229.122	−	132.284i	−1.16306	−	0.671491i	−0.211022	−	0.977481i	$-0.567679\pi$
$197$	−229.122	−	132.284i	−1.16306	−	0.671491i	−0.952035	+	0.305991i	$0.901012\pi$
$198$		0			0
$199$	−66.9711	−	115.997i	−0.336538	−	0.582901i	0.647241	−	0.762285i	$-0.275923\pi$
$199$	−66.9711	−	115.997i	−0.336538	−	0.582901i	−0.983779	+	0.179384i	$0.942589\pi$
$200$	35.6377	−	42.4714i	0.178189	−	0.212357i
$201$		0			0
$202$	1.30539	+	7.40321i	0.00646230	+	0.0366495i
$203$	−308.800	+	54.4498i	−1.52118	+	0.268226i
$204$		0			0
$205$	−31.0253	−	26.0333i	−0.151343	−	0.126992i
$206$	82.5471	−	47.6586i	0.400714	−	0.231352i
$207$		0			0
$208$	−15.3653	+	26.6135i	−0.0738718	+	0.127950i
$209$	−16.1712	−	44.4301i	−0.0773743	−	0.212584i
$210$		0			0
$211$	−51.7595	+	43.4314i	−0.245306	+	0.205836i	−0.757148	−	0.653244i	$-0.773408\pi$
$211$	−51.7595	+	43.4314i	−0.245306	+	0.205836i	0.511842	+	0.859080i	$0.328963\pi$
$212$	−58.8521	+	161.695i	−0.277604	+	0.762711i
$213$		0			0
$214$	0.182925	−	1.03742i	0.000854790	−	0.00484776i
$215$		−	194.422i		−	0.904287i
$216$		0			0
$217$	−186.113			−0.857665
$218$	79.2008	+	13.9652i	0.363306	+	0.0640607i
$219$		0			0
$220$	−6.84623	−	2.49182i	−0.0311192	−	0.0113265i
$221$	114.850	+	136.873i	0.519685	+	0.619336i
$222$		0			0
$223$	−212.711	+	77.4206i	−0.953863	+	0.347178i	−0.771626	−	0.636077i	$-0.780556\pi$
$223$	−212.711	+	77.4206i	−0.953863	+	0.347178i	−0.182237	+	0.983255i	$0.558334\pi$
$224$	30.8139	+	17.7904i	0.137562	+	0.0794216i
$225$		0			0
$226$	151.136	+	261.775i	0.668744	+	1.15830i
$227$	166.065	−	197.909i	0.731565	−	0.871845i	−0.264135	−	0.964486i	$-0.585086\pi$
$227$	166.065	−	197.909i	0.731565	−	0.871845i	0.995700	+	0.0926409i	$0.0295309\pi$
$228$		0			0
$229$	9.32712	+	52.8967i	0.0407298	+	0.230990i	0.998377	−	0.0569548i	$-0.0181391\pi$
$229$	9.32712	+	52.8967i	0.0407298	+	0.230990i	−0.957647	+	0.287945i	$0.907028\pi$
$230$	72.8301	−	12.8419i	0.316653	−	0.0558344i
$231$		0			0
$232$	−108.015	−	90.6352i	−0.465581	−	0.390669i
$233$	−93.1740	+	53.7940i	−0.399888	+	0.230876i	−0.686436	−	0.727190i	$-0.740826\pi$
$233$	−93.1740	+	53.7940i	−0.399888	+	0.230876i	0.286547	+	0.958066i	$0.407492\pi$
$234$		0			0
$235$	38.5108	−	66.7027i	0.163876	−	0.283841i
$236$	−31.1789	−	85.6634i	−0.132114	−	0.362980i
$237$		0			0
$238$	158.476	−	132.977i	0.665866	−	0.558728i
$239$	152.119	−	417.943i	0.636480	−	1.74872i	−0.0260287	−	0.999661i	$-0.508286\pi$
$239$	152.119	−	417.943i	0.636480	−	1.74872i	0.662509	−	0.749054i	$-0.269492\pi$
$240$		0			0
$241$	−35.4521	+	201.059i	−0.147104	+	0.834269i	0.818549	+	0.574436i	$0.194779\pi$
$241$	−35.4521	+	201.059i	−0.147104	+	0.834269i	−0.965654	+	0.259833i	$0.916333\pi$
$242$			167.643i			0.692741i
$243$		0			0
$244$	169.078			0.692943
$245$	−21.5940	−	3.80760i	−0.0881388	−	0.0155412i
$246$		0			0
$247$	−217.709	−	79.2394i	−0.881411	−	0.320807i
$248$	−53.7958	−	64.1114i	−0.216919	−	0.258514i
$249$		0			0
$250$	137.713	−	50.1236i	0.550853	−	0.200494i
$251$	298.670	+	172.437i	1.18992	+	0.687000i	0.958288	−	0.285803i	$-0.0922604\pi$
$251$	298.670	+	172.437i	1.18992	+	0.687000i	0.231631	+	0.972804i	$0.425594\pi$
$252$		0			0
$253$	17.6444	+	30.5609i	0.0697405	+	0.120794i
$254$	−44.8924	+	53.5007i	−0.176742	+	0.210633i
$255$		0			0
$256$	2.77837	+	15.7569i	0.0108530	+	0.0615505i
$257$	179.971	−	31.7338i	0.700278	−	0.123478i	0.187837	−	0.982200i	$-0.439852\pi$
$257$	179.971	−	31.7338i	0.700278	−	0.123478i	0.512441	+	0.858722i	$0.328741\pi$
$258$		0			0
$259$	140.694	+	118.056i	0.543219	+	0.455815i
$260$	−30.9168	+	17.8498i	−0.118911	+	0.0686532i
$261$		0			0
$262$	−34.8478	+	60.3582i	−0.133007	+	0.230375i
$263$	88.5587	+	243.313i	0.336725	+	0.925144i	0.986317	+	0.164861i	$0.0527176\pi$
$263$	88.5587	+	243.313i	0.336725	+	0.925144i	−0.649592	+	0.760283i	$0.725060\pi$
$264$		0			0
$265$	−153.129	+	128.490i	−0.577844	+	0.484869i
$266$	−91.7458	+	252.069i	−0.344909	+	0.947629i
$267$		0			0
$268$	17.6020	−	99.8259i	0.0656791	−	0.372485i
$269$		−	152.516i		−	0.566974i	−0.958976	−	0.283487i	$-0.908509\pi$
$269$		−	152.516i		−	0.566974i	0.958976	−	0.283487i	$-0.0914913\pi$
$270$		0			0
$271$	352.593			1.30108			0.650541	−	0.759471i	$-0.274542\pi$
$271$	352.593			1.30108			0.650541	+	0.759471i	$0.274542\pi$
$272$	91.6146	+	16.1541i	0.336818	+	0.0593901i
$273$		0			0
$274$	179.658	+	65.3903i	0.655687	+	0.238651i
$275$	19.7551	+	23.5432i	0.0718366	+	0.0856115i
$276$		0			0
$277$	318.950	−	116.088i	1.15145	−	0.419092i	0.305411	−	0.952221i	$-0.401206\pi$
$277$	318.950	−	116.088i	1.15145	−	0.419092i	0.846034	+	0.533129i	$0.178984\pi$
$278$	266.894	+	154.091i	0.960051	+	0.554286i
$279$		0			0
$280$	20.6671	+	35.7964i	0.0738109	+	0.127844i
$281$	−184.637	+	220.042i	−0.657072	+	0.783067i	−0.986962	−	0.160952i	$-0.948544\pi$
$281$	−184.637	+	220.042i	−0.657072	+	0.783067i	0.329891	+	0.944019i	$0.392988\pi$
$282$		0			0
$283$	21.4854	+	121.850i	0.0759202	+	0.430565i	0.998949	+	0.0458341i	$0.0145946\pi$
$283$	21.4854	+	121.850i	0.0759202	+	0.430565i	−0.923029	+	0.384731i	$0.874294\pi$
$284$	74.0193	−	13.0516i	0.260631	−	0.0459563i
$285$		0			0
$286$	−13.0495	−	10.9498i	−0.0456277	−	0.0382862i
$287$	−94.9536	+	54.8215i	−0.330849	+	0.191016i
$288$		0			0
$289$	125.943	−	218.140i	0.435790	−	0.754810i
$290$	−56.0239	−	153.924i	−0.193186	−	0.530774i
$291$		0			0
$292$	−12.0697	+	10.1277i	−0.0413345	+	0.0346838i
$293$	172.243	−	473.234i	0.587861	−	1.61513i	−0.186547	−	0.982446i	$-0.559730\pi$
$293$	172.243	−	473.234i	0.587861	−	1.61513i	0.774407	−	0.632688i	$-0.218048\pi$
$294$		0			0
$295$	18.3896	−	104.292i	0.0623376	−	0.353534i
$296$			82.5894i			0.279018i
$297$		0			0
$298$	−100.222			−0.336314
$299$	170.289	+	30.0265i	0.569527	+	0.100423i
$300$		0			0
$301$	−494.595	−	180.018i	−1.64317	−	0.598066i
$302$	−239.789	−	285.769i	−0.794002	−	0.946255i
$303$		0			0
$304$	−113.351	+	41.2562i	−0.372864	+	0.135711i
$305$	170.102	+	98.2086i	0.557712	+	0.321995i
$306$		0			0
$307$	303.015	+	524.837i	0.987018	+	1.70957i	0.632601	+	0.774478i	$0.281987\pi$
$307$	303.015	+	524.837i	0.987018	+	1.70957i	0.354417	+	0.935087i	$0.384679\pi$
$308$	−12.6781	+	15.1091i	−0.0411625	+	0.0490556i
$309$		0			0
$310$	−16.8828	−	95.7469i	−0.0544605	−	0.308861i
$311$	112.127	−	19.7711i	0.360538	−	0.0635725i	0.00955468	−	0.999954i	$-0.496959\pi$
$311$	112.127	−	19.7711i	0.360538	−	0.0635725i	0.350983	+	0.936382i	$0.385847\pi$
$312$		0			0
$313$	391.591	+	328.584i	1.25109	+	1.04979i	0.996573	+	0.0827197i	$0.0263606\pi$
$313$	391.591	+	328.584i	1.25109	+	1.04979i	0.254516	+	0.967069i	$0.418084\pi$
$314$	118.839	−	68.6119i	0.378469	−	0.218509i
$315$		0			0
$316$	−72.2169	+	125.083i	−0.228534	+	0.395833i
$317$	13.2129	+	36.3021i	0.0416810	+	0.114518i	0.958787	−	0.284126i	$-0.0917033\pi$
$317$	13.2129	+	36.3021i	0.0416810	+	0.114518i	−0.917106	+	0.398643i	$0.869481\pi$
$318$		0			0
$319$	59.8759	−	50.2418i	0.187699	−	0.157498i
$320$	−6.35717	+	17.4662i	−0.0198662	+	0.0545818i
$321$		0			0
$322$	34.7655	−	197.165i	0.107968	−	0.612314i
$323$			701.344i			2.17134i
$324$		0			0
$325$	150.594			0.463368
$326$	−232.306	−	40.9618i	−0.712595	−	0.125650i
$327$		0			0
$328$	−46.3308	−	16.8630i	−0.141253	−	0.0514117i
$329$	−134.029	−	159.730i	−0.407384	−	0.485501i
$330$		0			0
$331$	−99.6998	+	36.2878i	−0.301208	+	0.109631i	−0.488203	−	0.872730i	$-0.662347\pi$
$331$	−99.6998	+	36.2878i	−0.301208	+	0.109631i	0.186995	+	0.982361i	$0.440125\pi$
$332$	44.6815	+	25.7969i	0.134583	+	0.0777015i
$333$		0			0
$334$	14.8271	+	25.6814i	0.0443926	+	0.0768903i
$335$	75.6923	−	90.2065i	0.225947	−	0.269273i
$336$		0			0
$337$	−0.873000	−	4.95103i	−0.00259051	−	0.0146915i	0.983485	−	0.180989i	$-0.0579299\pi$
$337$	−0.873000	−	4.95103i	−0.00259051	−	0.0146915i	−0.986076	+	0.166298i	$0.946819\pi$
$338$	153.168	−	27.0076i	0.453159	−	0.0799041i
$339$		0			0
$340$	82.7864	+	69.4661i	0.243490	+	0.204312i
$341$	40.1772	−	23.1963i	0.117822	−	0.0680245i
$342$		0			0
$343$	−183.782	+	318.320i	−0.535808	+	0.928047i
$344$	−80.9504	−	222.409i	−0.235321	−	0.646539i
$345$		0			0
$346$	−195.380	+	163.943i	−0.564681	+	0.473824i
$347$	77.4742	−	212.859i	0.223268	−	0.613425i	−0.776594	−	0.630001i	$-0.783054\pi$
$347$	77.4742	−	212.859i	0.223268	−	0.613425i	0.999863	+	0.0165761i	$0.00527659\pi$
$348$		0			0
$349$	85.4880	−	484.827i	0.244951	−	1.38919i	−0.575655	−	0.817693i	$-0.695253\pi$
$349$	85.4880	−	484.827i	0.244951	−	1.38919i	0.820606	−	0.571495i	$-0.193636\pi$
$350$		−	174.363i		−	0.498179i
$351$		0			0
$352$	−8.86928			−0.0251968
$353$	−440.404	−	77.6551i	−1.24760	−	0.219986i	−0.489432	−	0.872042i	$-0.662796\pi$
$353$	−440.404	−	77.6551i	−1.24760	−	0.219986i	−0.758171	+	0.652056i	$0.773907\pi$
$354$		0			0
$355$	82.0487	+	29.8633i	0.231123	+	0.0841219i
$356$	34.8732	+	41.5603i	0.0979585	+	0.116742i
$357$		0			0
$358$	−307.793	+	112.027i	−0.859756	+	0.312926i
$359$	−62.2367	−	35.9324i	−0.173361	−	0.100090i	0.410809	−	0.911722i	$-0.365246\pi$
$359$	−62.2367	−	35.9324i	−0.173361	−	0.100090i	−0.584170	+	0.811631i	$0.698580\pi$
$360$		0			0
$361$	−274.201	−	474.930i	−0.759559	−	1.31559i
$362$	87.4925	−	104.269i	0.241692	−	0.288037i
$363$		0			0
$364$	16.7824	+	95.1776i	0.0461054	+	0.261477i
$365$	−18.0254	+	3.17837i	−0.0493847	+	0.00870786i
$366$		0			0
$367$	−106.401	−	89.2809i	−0.289920	−	0.243272i	0.486214	−	0.873840i	$-0.338378\pi$
$367$	−106.401	−	89.2809i	−0.289920	−	0.243272i	−0.776134	+	0.630568i	$0.782822\pi$
$368$	77.9674	−	45.0145i	0.211868	−	0.122322i
$369$		0			0
$370$	−47.9718	+	83.0897i	−0.129654	+	0.224567i
$371$	185.086	+	508.519i	0.498884	+	1.37067i
$372$		0			0
$373$	−498.940	+	418.661i	−1.33764	+	1.12241i	−0.355416	+	0.934708i	$0.615661\pi$
$373$	−498.940	+	418.661i	−1.33764	+	1.12241i	−0.982225	+	0.187706i	$0.939895\pi$
$374$	−17.6373	+	48.4582i	−0.0471587	+	0.129567i
$375$		0			0
$376$	16.2819	−	92.3394i	0.0433030	−	0.245584i
$377$		−	382.998i		−	1.01591i
$378$		0			0
$379$	379.153			1.00040			0.500202	−	0.865909i	$-0.333259\pi$
$379$	379.153			1.00040			0.500202	+	0.865909i	$0.333259\pi$
$380$	−138.001	−	24.3333i	−0.363160	−	0.0640349i
$381$		0			0
$382$	−129.246	−	47.0417i	−0.338341	−	0.123146i
$383$	−103.347	−	123.164i	−0.269835	−	0.321577i	0.614062	−	0.789258i	$-0.289534\pi$
$383$	−103.347	−	123.164i	−0.269835	−	0.321577i	−0.883898	+	0.467680i	$0.845090\pi$
$384$		0			0
$385$	−21.5309	+	7.83662i	−0.0559245	+	0.0203549i
$386$	−61.2258	−	35.3487i	−0.158616	−	0.0915771i
$387$		0			0
$388$	−35.2788	−	61.1047i	−0.0909248	−	0.157486i
$389$	−255.119	+	304.040i	−0.655834	+	0.781593i	−0.986781	−	0.162057i	$-0.948187\pi$
$389$	−255.119	+	304.040i	−0.655834	+	0.781593i	0.330947	+	0.943649i	$0.392632\pi$
$390$		0			0
$391$	−90.8961	−	515.498i	−0.232471	−	1.31841i
$392$	−26.2879	+	4.63527i	−0.0670610	+	0.0118247i
$393$		0			0
$394$	−286.619	−	240.502i	−0.727460	−	0.610411i
$395$	−145.309	+	83.8940i	−0.367870	+	0.212390i
$396$		0			0
$397$	−19.8819	+	34.4365i	−0.0500804	+	0.0867418i	−0.889979	−	0.456002i	$-0.849281\pi$
$397$	−19.8819	+	34.4365i	−0.0500804	+	0.0867418i	0.839898	+	0.542744i	$0.182614\pi$
$398$	−64.7864	−	177.999i	−0.162780	−	0.447234i
$399$		0			0
$400$	60.0636	−	50.3993i	0.150159	−	0.125998i
$401$	−151.169	+	415.334i	−0.376981	+	1.03575i	0.595620	+	0.803266i	$0.296906\pi$
$401$	−151.169	+	415.334i	−0.376981	+	1.03575i	−0.972601	+	0.232480i	$0.925316\pi$
$402$		0			0
$403$	39.4746	−	223.872i	0.0979519	−	0.555513i
$404$			10.6312i			0.0263149i
$405$		0			0
$406$	−443.446			−1.09223
$407$	−45.0863	−	7.94992i	−0.110777	−	0.0195330i
$408$		0			0
$409$	130.597	+	47.5333i	0.319307	+	0.116218i	0.496701	−	0.867922i	$-0.334544\pi$
$409$	130.597	+	47.5333i	0.319307	+	0.116218i	−0.177394	+	0.984140i	$0.556767\pi$
$410$	−36.8166	−	43.8764i	−0.0897967	−	0.107015i
$411$		0			0
$412$	126.669	−	46.1039i	0.307450	−	0.111903i
$413$	−248.286	−	143.348i	−0.601176	−	0.347089i
$414$		0			0
$415$	29.9681	+	51.9063i	0.0722124	+	0.125076i
$416$	−27.9354	+	33.2921i	−0.0671523	+	0.0800290i
$417$		0			0
$418$	−11.6112	−	65.8503i	−0.0277780	−	0.157537i
$419$	−67.2764	+	11.8626i	−0.160564	+	0.0283118i	−0.253352	−	0.967374i	$-0.581533\pi$
$419$	−67.2764	+	11.8626i	−0.160564	+	0.0283118i	0.0927881	+	0.995686i	$0.470422\pi$
$420$		0			0
$421$	266.680	+	223.771i	0.633444	+	0.531522i	0.901997	−	0.431742i	$-0.142101\pi$
$421$	266.680	+	223.771i	0.633444	+	0.531522i	−0.268553	+	0.963265i	$0.586546\pi$
$422$	−82.7527	+	47.7773i	−0.196096	+	0.113216i
$423$		0			0
$424$	−121.673	+	210.744i	−0.286965	+	0.497038i
$425$	−155.920	−	428.387i	−0.366871	−	1.00797i
$426$		0			0
$427$	407.336	−	341.795i	0.953948	−	0.800458i
$428$	0.509530	−	1.39992i	0.00119049	−	0.00327085i
$429$		0			0
$430$	47.7452	−	270.777i	0.111035	−	0.629713i
$431$			350.668i			0.813615i	0.913514	+	0.406807i	$0.133358\pi$
$431$			350.668i			0.813615i	−0.913514	+	0.406807i	$0.866642\pi$
$432$		0			0
$433$	−177.240			−0.409330			−0.204665	−	0.978832i	$-0.565610\pi$
$433$	−177.240			−0.409330			−0.204665	+	0.978832i	$0.565610\pi$
$434$	−259.205	−	45.7049i	−0.597247	−	0.105311i
$435$		0			0
$436$	106.876	+	38.8996i	0.245128	+	0.0892192i
$437$	436.282	+	519.941i	0.998357	+	1.18980i
$438$		0			0
$439$	2.67961	−	0.975298i	0.00610389	−	0.00222163i	−0.338966	−	0.940798i	$-0.610077\pi$
$439$	2.67961	−	0.975298i	0.00610389	−	0.00222163i	0.345070	+	0.938577i	$0.387855\pi$
$440$	−8.92301	−	5.15170i	−0.0202796	−	0.0117084i
$441$		0			0
$442$	126.343	+	218.832i	0.285843	+	0.495095i
$443$	−343.331	+	409.166i	−0.775014	+	0.923626i	−0.998697	−	0.0510363i	$-0.983748\pi$
$443$	−343.331	+	409.166i	−0.775014	+	0.923626i	0.223683	+	0.974662i	$0.428192\pi$
$444$		0			0
$445$	10.9443	+	62.0681i	0.0245939	+	0.139479i
$446$	−315.262	+	55.5892i	−0.706865	+	0.124639i
$447$		0			0
$448$	38.5466	+	32.3444i	0.0860414	+	0.0721973i
$449$	573.148	−	330.907i	1.27650	−	0.736987i	0.300296	−	0.953846i	$-0.402915\pi$
$449$	573.148	−	330.907i	1.27650	−	0.736987i	0.976203	+	0.216859i	$0.0695813\pi$
$450$		0			0
$451$	13.6654	−	23.6692i	0.0303003	−	0.0524816i
$452$	146.206	+	401.697i	0.323464	+	0.888711i
$453$		0			0
$454$	279.885	−	234.852i	0.616487	−	0.517294i
$455$	−38.3997	+	105.502i	−0.0843948	+	0.231873i
$456$		0			0
$457$	106.695	−	605.098i	0.233468	−	1.32407i	−0.612347	−	0.790589i	$-0.709774\pi$
$457$	106.695	−	605.098i	0.233468	−	1.32407i	0.845815	−	0.533476i	$-0.179115\pi$
$458$			75.9613i			0.165854i
$459$		0			0
$460$	104.586			0.227361
$461$	397.986	+	70.1756i	0.863310	+	0.152225i	0.587734	−	0.809054i	$-0.300020\pi$
$461$	397.986	+	70.1756i	0.863310	+	0.152225i	0.275576	+	0.961279i	$0.411131\pi$
$462$		0			0
$463$	390.527	+	142.140i	0.843470	+	0.306998i	0.727375	−	0.686240i	$-0.240740\pi$
$463$	390.527	+	142.140i	0.843470	+	0.306998i	0.116095	+	0.993238i	$0.462962\pi$
$464$	−128.178	−	152.756i	−0.276245	−	0.329216i
$465$		0			0
$466$	−142.977	+	52.0392i	−0.306817	+	0.111672i
$467$	−161.324	−	93.1404i	−0.345448	−	0.199444i	0.317231	−	0.948348i	$-0.397247\pi$
$467$	−161.324	−	93.1404i	−0.345448	−	0.199444i	−0.662678	+	0.748904i	$0.730580\pi$
$468$		0			0
$469$	−159.395	−	276.079i	−0.339860	−	0.588655i
$470$	70.0157	−	83.4414i	0.148970	−	0.177535i
$471$		0			0
$472$	−22.3869	−	126.963i	−0.0474299	−	0.268989i
$473$	129.207	−	22.7828i	0.273166	−	0.0481665i
$474$		0			0
$475$	452.824	+	379.964i	0.953313	+	0.799924i
$476$	253.370	−	146.283i	0.532290	−	0.307318i
$477$		0			0
$478$	314.497	−	544.724i	0.657943	−	1.13959i
$479$	−117.100	−	321.729i	−0.244467	−	0.671668i	−0.999865	−	0.0164023i	$-0.994779\pi$
$479$	−117.100	−	321.729i	−0.244467	−	0.671668i	0.755398	−	0.655266i	$-0.227443\pi$
$480$		0			0
$481$	−171.848	+	144.198i	−0.357273	+	0.299787i
$482$	−98.7503	+	271.314i	−0.204876	+	0.562892i
$483$		0			0
$484$	−41.1691	+	233.482i	−0.0850602	+	0.482400i
$485$		−	81.9665i		−	0.169003i
$486$		0			0
$487$	−483.112			−0.992016			−0.496008	−	0.868318i	$-0.665201\pi$
$487$	−483.112			−0.992016			−0.496008	+	0.868318i	$0.665201\pi$
$488$	235.480	+	41.5214i	0.482541	+	0.0850849i
$489$		0			0
$490$	−29.1395	−	10.6059i	−0.0594684	−	0.0216447i
$491$	160.343	+	191.089i	0.326564	+	0.389184i	0.904199	−	0.427111i	$-0.140469\pi$
$491$	160.343	+	191.089i	0.326564	+	0.389184i	−0.577635	+	0.816295i	$0.696024\pi$
$492$		0			0
$493$	−1089.49	+	396.542i	−2.20992	+	0.804345i
$494$	−283.750	−	163.823i	−0.574392	−	0.331625i
$495$		0			0
$496$	−59.1788	−	102.501i	−0.119312	−	0.206655i
$497$	151.940	−	181.075i	0.305715	−	0.364336i
$498$		0			0
$499$	57.5888	+	326.602i	0.115408	+	0.654513i	0.986547	+	0.163476i	$0.0522708\pi$
$499$	57.5888	+	326.602i	0.115408	+	0.654513i	−0.871139	+	0.491037i	$0.836618\pi$
$500$	204.106	−	35.9895i	0.408213	−	0.0719789i
$501$		0			0
$502$	373.620	+	313.504i	0.744262	+	0.624510i
$503$	212.097	−	122.454i	0.421664	−	0.243448i	−0.274125	−	0.961694i	$-0.588388\pi$
$503$	212.097	−	122.454i	0.421664	−	0.243448i	0.695789	+	0.718246i	$0.255055\pi$
$504$		0			0
$505$	−6.17512	+	10.6956i	−0.0122280	+	0.0211795i
$506$	17.0688	+	46.8961i	0.0337328	+	0.0926800i
$507$		0			0
$508$	−75.6614	+	63.4875i	−0.148940	+	0.124975i
$509$	302.898	−	832.205i	0.595084	−	1.63498i	−0.165850	−	0.986151i	$-0.553037\pi$
$509$	302.898	−	832.205i	0.595084	−	1.63498i	0.760934	−	0.648829i	$-0.224741\pi$
$510$		0			0
$511$	−8.60446	+	48.7983i	−0.0168385	+	0.0954957i
$512$			22.6274i			0.0441942i
$513$		0			0
$514$	258.444			0.502810
$515$	154.216	+	27.1925i	0.299449	+	0.0528009i
$516$		0			0
$517$	48.8416	+	17.7769i	0.0944712	+	0.0343847i
$518$	166.956	+	198.971i	0.322310	+	0.384114i
$519$		0			0
$520$	−47.4422	+	17.2675i	−0.0912350	+	0.0332068i
$521$	−285.381	−	164.765i	−0.547756	−	0.316247i	0.200461	−	0.979702i	$-0.435756\pi$
$521$	−285.381	−	164.765i	−0.547756	−	0.316247i	−0.748216	+	0.663455i	$0.769089\pi$
$522$		0			0
$523$	145.262	+	251.600i	0.277747	+	0.481071i	0.970824	−	0.239791i	$-0.0770791\pi$
$523$	145.262	+	251.600i	0.277747	+	0.481071i	−0.693078	+	0.720863i	$0.743746\pi$
$524$	−63.3560	+	75.5048i	−0.120908	+	0.144093i
$525$		0			0
$526$	63.5865	+	360.617i	0.120887	+	0.685583i
$527$	−677.705	+	119.498i	−1.28597	+	0.226751i
$528$		0			0
$529$	17.1780	+	14.4140i	0.0324726	+	0.0272477i
$530$	−244.821	+	141.347i	−0.461926	+	0.266693i
$531$		0			0
$532$	−189.679	+	328.534i	−0.356540	+	0.617545i
$533$	−45.8039	−	125.845i	−0.0859361	−	0.236107i
$534$		0			0
$535$	1.32576	−	1.11244i	0.00247805	−	0.00207933i
$536$	49.0296	−	134.708i	0.0914732	−	0.251320i
$537$		0			0
$538$	37.4542	−	212.413i	0.0696175	−	0.394820i
$539$		−	14.7970i		−	0.0274526i
$540$		0			0
$541$	−385.680			−0.712901			−0.356451	−	0.934314i	$-0.616013\pi$
$541$	−385.680			−0.712901			−0.356451	+	0.934314i	$0.616013\pi$
$542$	491.067	+	86.5883i	0.906027	+	0.159757i
$543$		0			0
$544$	123.627	+	44.9966i	0.227256	+	0.0827143i
$545$	84.9284	+	101.214i	0.155832	+	0.185713i
$546$		0			0
$547$	−621.520	+	226.215i	−1.13623	+	0.413556i	−0.840552	−	0.541731i	$-0.817769\pi$
$547$	−621.520	+	226.215i	−1.13623	+	0.413556i	−0.295683	+	0.955286i	$0.595547\pi$
$548$	234.157	+	135.191i	0.427294	+	0.246698i
$549$		0			0
$550$	21.7318	+	37.6406i	0.0395124	+	0.0684374i
$551$	966.340	−	1151.64i	1.75379	−	2.09009i
$552$		0			0
$553$	78.8770	+	447.334i	0.142635	+	0.808922i
$554$	472.720	−	83.3532i	0.853285	−	0.150457i
$555$		0			0
$556$	333.870	+	280.150i	0.600485	+	0.503867i
$557$	−352.046	+	203.254i	−0.632040	+	0.364909i	−0.781542	−	0.623853i	$-0.785566\pi$
$557$	−352.046	+	203.254i	−0.632040	+	0.364909i	0.149502	+	0.988761i	$0.452233\pi$
$558$		0			0
$559$	321.443	−	556.756i	0.575033	−	0.995986i
$560$	19.9929	+	54.9300i	0.0357016	+	0.0980893i
$561$		0			0
$562$	−311.186	+	261.116i	−0.553712	+	0.464620i
$563$	−338.582	+	930.245i	−0.601388	+	1.65230i	0.147076	+	0.989125i	$0.453014\pi$
$563$	−338.582	+	930.245i	−0.601388	+	1.65230i	−0.748464	+	0.663175i	$0.769208\pi$
$564$		0			0
$565$	−86.2334	+	489.054i	−0.152626	+	0.865582i
$566$			174.980i			0.309152i
$567$		0			0
$568$	106.294			0.187137
$569$	115.486	+	20.3632i	0.202963	+	0.0357878i	0.274205	−	0.961671i	$-0.411585\pi$
$569$	115.486	+	20.3632i	0.202963	+	0.0357878i	−0.0712425	+	0.997459i	$0.522696\pi$
$570$		0			0
$571$	399.543	+	145.422i	0.699725	+	0.254679i	0.667294	−	0.744795i	$-0.267453\pi$
$571$	399.543	+	145.422i	0.699725	+	0.254679i	0.0324316	+	0.999474i	$0.489675\pi$
$572$	−15.4854	−	18.4548i	−0.0270724	−	0.0322636i
$573$		0			0
$574$	−145.707	+	53.0332i	−0.253846	+	0.0923923i
$575$	−382.076	−	220.592i	−0.664480	−	0.383638i
$576$		0			0
$577$	−3.24056	−	5.61282i	−0.00561623	−	0.00972759i	0.863204	−	0.504856i	$-0.168454\pi$
$577$	−3.24056	−	5.61282i	−0.00561623	−	0.00972759i	−0.868820	+	0.495128i	$0.835121\pi$
$578$	228.975	−	272.881i	0.396150	−	0.472113i
$579$		0			0
$580$	−40.2260	−	228.133i	−0.0693552	−	0.393333i
$581$	159.794	−	28.1760i	0.275033	−	0.0484957i
$582$		0			0
$583$	−103.335	−	86.7084i	−0.177247	−	0.148728i
$584$	−19.2969	+	11.1411i	−0.0330426	+	0.0190772i
$585$		0			0
$586$	356.103	−	616.788i	0.607684	−	1.05254i
$587$	149.791	+	411.548i	0.255181	+	0.701105i	0.999448	+	0.0332222i	$0.0105769\pi$
$587$	149.791	+	411.548i	0.255181	+	0.701105i	−0.744267	+	0.667882i	$0.767201\pi$
$588$		0			0
$589$	683.546	−	573.563i	1.16052	−	0.973792i
$590$	51.2234	−	140.735i	0.0868193	−	0.238534i
$591$		0			0
$592$	−20.2819	+	115.025i	−0.0342600	+	0.194298i
$593$		−	328.720i		−	0.554334i	−0.960822	−	0.277167i	$-0.910604\pi$
$593$		−	328.720i		−	0.554334i	0.960822	−	0.277167i	$-0.0893956\pi$
$594$		0			0
$595$	339.873			0.571215
$596$	−139.581	−	24.6120i	−0.234197	−	0.0412953i
$597$		0			0
$598$	229.792	+	83.6374i	0.384267	+	0.139862i
$599$	−348.296	−	415.083i	−0.581463	−	0.692960i	0.392479	−	0.919761i	$-0.371618\pi$
$599$	−348.296	−	415.083i	−0.581463	−	0.692960i	−0.973941	+	0.226801i	$0.927173\pi$
$600$		0			0
$601$	148.519	−	54.0563i	0.247119	−	0.0899440i	−0.215491	−	0.976506i	$-0.569135\pi$
$601$	148.519	−	54.0563i	0.247119	−	0.0899440i	0.462610	+	0.886562i	$0.346913\pi$
$602$	−644.629	−	372.177i	−1.07081	−	0.618233i
$603$		0			0
$604$	−263.783	−	456.885i	−0.436726	−	0.756432i
$605$	−177.036	+	210.983i	−0.292621	+	0.348732i
$606$		0			0
$607$	16.1881	+	91.8071i	0.0266690	+	0.151247i	0.995234	−	0.0975118i	$-0.0310884\pi$
$607$	16.1881	+	91.8071i	0.0266690	+	0.151247i	−0.968565	+	0.248759i	$0.919977\pi$
$608$	−167.998	+	29.6226i	−0.276313	+	0.0487214i
$609$		0			0
$610$	212.789	+	178.551i	0.348834	+	0.292706i
$611$	220.563	−	127.342i	0.360987	−	0.208416i
$612$		0			0
$613$	−17.1815	+	29.7593i	−0.0280286	+	0.0485469i	−0.879699	−	0.475530i	$-0.842256\pi$
$613$	−17.1815	+	29.7593i	−0.0280286	+	0.0485469i	0.851671	+	0.524077i	$0.175590\pi$
$614$	293.130	+	805.368i	0.477410	+	1.31167i
$615$		0			0
$616$	−21.3675	+	17.9295i	−0.0346875	+	0.0291063i
$617$	−239.022	+	656.706i	−0.387393	+	1.06435i	0.580777	+	0.814062i	$0.302749\pi$
$617$	−239.022	+	656.706i	−0.387393	+	1.06435i	−0.968171	+	0.250291i	$0.919474\pi$
$618$		0			0
$619$	−17.1006	+	96.9823i	−0.0276262	+	0.156676i	−0.995500	−	0.0947600i	$-0.969792\pi$
$619$	−17.1006	+	96.9823i	−0.0276262	+	0.156676i	0.967874	+	0.251436i	$0.0809027\pi$
$620$		−	137.495i		−	0.221767i
$621$		0			0
$622$	161.018			0.258871
$623$	168.030	+	29.6283i	0.269711	+	0.0475574i
$624$		0			0
$625$	−234.246	−	85.2585i	−0.374793	−	0.136414i
$626$	464.688	+	553.793i	0.742312	+	0.884653i
$627$		0			0
$628$	182.360	−	66.3737i	0.290383	−	0.105691i
$629$	588.116	+	339.549i	0.935001	+	0.539823i
$630$		0			0
$631$	−167.835	−	290.699i	−0.265983	−	0.460696i	0.701838	−	0.712337i	$-0.252363\pi$
$631$	−167.835	−	290.699i	−0.265983	−	0.460696i	−0.967821	+	0.251641i	$0.919030\pi$
$632$	−131.296	+	156.472i	−0.207747	+	0.247583i
$633$		0			0
$634$	9.48705	+	53.8037i	0.0149638	+	0.0848639i
$635$	−112.996	+	19.9243i	−0.177947	+	0.0313768i
$636$		0			0
$637$	−55.5425	−	46.6057i	−0.0871938	−	0.0731643i
$638$	95.7290	−	55.2692i	0.150045	−	0.0866288i
$639$		0			0
$640$	−13.1431	+	22.7645i	−0.0205361	+	0.0355695i
$641$	−341.193	−	937.419i	−0.532282	−	1.46243i	−0.856349	−	0.516398i	$-0.827273\pi$
$641$	−341.193	−	937.419i	−0.532282	−	1.46243i	0.324067	−	0.946034i	$-0.394950\pi$
$642$		0			0
$643$	478.514	−	401.521i	0.744189	−	0.624449i	−0.189770	−	0.981829i	$-0.560774\pi$
$643$	478.514	−	401.521i	0.744189	−	0.624449i	0.933959	+	0.357380i	$0.116330\pi$
$644$	96.8379	−	266.060i	0.150369	−	0.413137i
$645$		0			0
$646$	−172.233	+	976.781i	−0.266614	+	1.51205i
$647$			550.714i			0.851181i	0.904916	+	0.425591i	$0.139934\pi$
$647$			550.714i			0.851181i	−0.904916	+	0.425591i	$0.860066\pi$
$648$		0			0
$649$	71.4649			0.110115
$650$	209.737	+	36.9823i	0.322673	+	0.0568959i
$651$		0			0
$652$	−313.480	−	114.097i	−0.480798	−	0.174996i
$653$	−435.250	−	518.711i	−0.666539	−	0.794350i	0.321770	−	0.946818i	$-0.395722\pi$
$653$	−435.250	−	518.711i	−0.666539	−	0.794350i	−0.988308	+	0.152468i	$0.951278\pi$
$654$		0			0
$655$	−107.597	+	39.1619i	−0.164270	+	0.0597892i
$656$	−60.3851	−	34.8634i	−0.0920505	−	0.0531454i
$657$		0			0
$658$	−147.441	−	255.375i	−0.224074	−	0.388107i
$659$	307.922	−	366.967i	0.467257	−	0.556855i	−0.480026	−	0.877254i	$-0.659373\pi$
$659$	307.922	−	366.967i	0.467257	−	0.556855i	0.947283	+	0.320399i	$0.103817\pi$
$660$		0			0
$661$	−166.498	−	944.257i	−0.251888	−	1.42853i	−0.803936	−	0.594716i	$-0.797265\pi$
$661$	−166.498	−	944.257i	−0.251888	−	1.42853i	0.552048	−	0.833812i	$-0.313846\pi$
$662$	−147.766	+	26.0552i	−0.223212	+	0.0393583i
$663$		0			0
$664$	55.8942	+	46.9008i	0.0841780	+	0.0706337i
$665$	−381.656	+	220.349i	−0.573919	+	0.331352i
$666$		0			0
$667$	−561.018	+	971.711i	−0.841106	+	1.45684i
$668$	14.3435	+	39.4083i	0.0214722	+	0.0589945i
$669$		0			0
$670$	127.571	−	107.045i	0.190405	−	0.159769i
$671$	−45.3338	+	124.554i	−0.0675616	+	0.185624i
$672$		0			0
$673$	34.1556	−	193.706i	0.0507513	−	0.287825i	−0.948860	−	0.315696i	$-0.897762\pi$
$673$	34.1556	−	193.706i	0.0507513	−	0.287825i	0.999612	+	0.0278717i	$0.00887300\pi$
$674$		−	7.10983i		−	0.0105487i
$675$		0			0
$676$	219.953			0.325375
$677$	705.776	+	124.447i	1.04250	+	0.183822i	0.668582	−	0.743638i	$-0.266902\pi$
$677$	705.776	+	124.447i	1.04250	+	0.183822i	0.373922	+	0.927460i	$0.378013\pi$
$678$		0			0
$679$	−208.517	−	75.8940i	−0.307094	−	0.111773i
$680$	98.2399	+	117.078i	0.144470	+	0.172173i
$681$		0			0
$682$	61.6524	−	22.4397i	0.0903995	−	0.0329027i
$683$	−223.152	−	128.837i	−0.326723	−	0.188633i	0.327662	−	0.944795i	$-0.393739\pi$
$683$	−223.152	−	128.837i	−0.326723	−	0.188633i	−0.654385	+	0.756161i	$0.727072\pi$
$684$		0			0
$685$	157.050	+	272.019i	0.229270	+	0.397108i
$686$	−334.130	+	398.201i	−0.487071	+	0.580468i
$687$		0			0
$688$	−58.1236	−	329.635i	−0.0844820	−	0.479121i
$689$	−650.944	+	114.779i	−0.944766	+	0.166588i
$690$		0			0
$691$	−224.575	−	188.440i	−0.324999	−	0.272707i	0.465659	−	0.884964i	$-0.345817\pi$
$691$	−224.575	−	188.440i	−0.324999	−	0.272707i	−0.790659	+	0.612257i	$0.790262\pi$
$692$	−312.371	+	180.348i	−0.451403	+	0.260618i
$693$		0			0
$694$	160.173	−	277.428i	0.230797	−	0.399753i
$695$	173.168	+	475.775i	0.249162	+	0.684568i
$696$		0			0
$697$	−310.561	+	260.591i	−0.445568	+	0.373876i
$698$	238.123	−	654.238i	0.341151	−	0.937304i
$699$		0			0
$700$	42.8192	−	242.840i	0.0611703	−	0.346914i
$701$		−	414.603i		−	0.591445i	−0.955274	−	0.295722i	$-0.904440\pi$
$701$		−	414.603i		−	0.591445i	0.955274	−	0.295722i	$-0.0955603\pi$
$702$		0			0
$703$	−880.556			−1.25257
$704$	−12.3525	−	2.17808i	−0.0175462	−	0.00309386i
$705$		0			0
$706$	−594.293	−	216.305i	−0.841774	−	0.306381i
$707$	21.4913	+	25.6123i	0.0303979	+	0.0362268i
$708$		0			0
$709$	−502.572	+	182.921i	−0.708846	+	0.257999i	−0.671183	−	0.741291i	$-0.734214\pi$
$709$	−502.572	+	182.921i	−0.708846	+	0.257999i	−0.0376632	+	0.999290i	$0.511991\pi$
$710$	106.938	+	61.7406i	0.150617	+	0.0869586i
$711$		0			0
$712$	38.3627	+	66.4462i	0.0538802	+	0.0933233i
$713$	−428.081	+	510.167i	−0.600394	+	0.715521i
$714$		0			0
$715$	−4.85979	−	27.5613i	−0.00679691	−	0.0385472i
$716$	−456.183	+	80.4373i	−0.637127	+	0.112343i
$717$		0			0
$718$	−77.8547	−	65.3279i	−0.108433	−	0.0909859i
$719$	829.644	−	478.995i	1.15389	−	0.666196i	0.204055	−	0.978959i	$-0.434588\pi$
$719$	829.644	−	478.995i	1.15389	−	0.666196i	0.949831	+	0.312763i	$0.101255\pi$
$720$		0			0
$721$	211.967	−	367.137i	0.293990	−	0.509205i
$722$	−265.256	−	728.785i	−0.367391	−	1.00940i
$723$		0			0
$724$	147.459	−	123.733i	0.203673	−	0.170902i
$725$	−334.221	+	918.264i	−0.460994	+	1.26657i
$726$		0			0
$727$	132.512	−	751.513i	0.182272	−	1.03372i	−0.747138	−	0.664669i	$-0.768573\pi$
$727$	132.512	−	751.513i	0.182272	−	1.03372i	0.929410	−	0.369048i	$-0.120316\pi$
$728$			136.678i			0.187744i
$729$		0			0
$730$	−25.8851			−0.0354590
$731$	−1916.58	−	337.945i	−2.62186	−	0.462305i
$732$		0			0
$733$	386.707	+	140.750i	0.527568	+	0.192019i	0.592052	−	0.805900i	$-0.298318\pi$
$733$	386.707	+	140.750i	0.527568	+	0.192019i	−0.0644843	+	0.997919i	$0.520540\pi$
$734$	−126.262	−	150.473i	−0.172019	−	0.205005i
$735$		0			0
$736$	119.642	−	43.5461i	0.162557	−	0.0591658i
$737$	68.8186	+	39.7324i	0.0933767	+	0.0539111i
$738$		0			0
$739$	−310.367	−	537.571i	−0.419982	−	0.727431i	0.575955	−	0.817481i	$-0.304630\pi$
$739$	−310.367	−	537.571i	−0.419982	−	0.727431i	−0.995937	+	0.0900509i	$0.971297\pi$
$740$	−87.2166	+	103.941i	−0.117860	+	0.140460i
$741$		0			0
$742$	132.894	+	753.682i	0.179103	+	1.01574i
$743$	892.676	−	157.403i	1.20145	−	0.211848i	0.463124	−	0.886293i	$-0.346728\pi$
$743$	892.676	−	157.403i	1.20145	−	0.211848i	0.738325	+	0.674446i	$0.235617\pi$
$744$		0			0
$745$	−126.131	−	105.837i	−0.169304	−	0.142063i
$746$	−797.701	+	460.553i	−1.06930	+	0.617363i
$747$		0			0
$748$	−36.4642	+	63.1578i	−0.0487489	+	0.0844356i
$749$	−1.60244	−	4.40266i	−0.00213944	−	0.00587805i
$750$		0			0
$751$	−262.258	+	220.060i	−0.349211	+	0.293023i	−0.800473	−	0.599369i	$-0.795418\pi$
$751$	−262.258	+	220.060i	−0.349211	+	0.293023i	0.451262	+	0.892391i	$0.350974\pi$
$752$	45.3526	−	124.605i	0.0603093	−	0.165699i
$753$		0			0
$754$	94.0549	−	533.412i	0.124741	−	0.707443i
$755$		−	612.870i		−	0.811748i
$756$		0			0
$757$	546.517			0.721951			0.360975	−	0.932575i	$-0.382444\pi$
$757$	546.517			0.721951			0.360975	+	0.932575i	$0.382444\pi$
$758$	528.057	+	93.1108i	0.696646	+	0.122837i
$759$		0			0
$760$	−186.222	−	67.7792i	−0.245029	−	0.0891832i
$761$	48.9259	+	58.3077i	0.0642916	+	0.0766198i	0.797232	−	0.603673i	$-0.206297\pi$
$761$	48.9259	+	58.3077i	0.0642916	+	0.0766198i	−0.732940	+	0.680293i	$0.761852\pi$
$762$		0			0
$763$	336.117	−	122.337i	0.440520	−	0.160336i
$764$	−168.452	−	97.2561i	−0.220487	−	0.127299i
$765$		0			0
$766$	−113.688	−	196.914i	−0.148418	−	0.257067i
$767$	225.091	−	268.253i	0.293470	−	0.349744i
$768$		0			0
$769$	150.408	+	853.005i	0.195589	+	1.10924i	0.911578	+	0.411127i	$0.134865\pi$
$769$	150.408	+	853.005i	0.195589	+	1.10924i	−0.715989	+	0.698111i	$0.754024\pi$
$770$	−31.9112	+	5.62681i	−0.0414432	+	0.00730755i
$771$		0			0
$772$	−76.5902	−	64.2668i	−0.0992100	−	0.0832471i
$773$	−390.015	+	225.175i	−0.504547	+	0.291301i	−0.730589	−	0.682817i	$-0.760755\pi$
$773$	−390.015	+	225.175i	−0.504547	+	0.291301i	0.226042	+	0.974118i	$0.427421\pi$
$774$		0			0
$775$	−290.003	+	502.301i	−0.374198	+	0.648130i
$776$	−34.1280	−	93.7659i	−0.0439794	−	0.120832i
$777$		0			0
$778$	−429.977	+	360.793i	−0.552670	+	0.463745i
$779$	179.791	−	493.973i	0.230798	−	0.634111i
$780$		0			0
$781$	−10.2317	+	58.0268i	−0.0131007	+	0.0742980i
$782$		−	740.270i		−	0.946637i
$783$		0			0
$784$	−37.7502			−0.0481508
$785$	222.018	+	39.1478i	0.282826	+	0.0498698i
$786$		0			0
$787$	−736.238	−	267.969i	−0.935499	−	0.340494i	−0.171112	−	0.985252i	$-0.554736\pi$
$787$	−736.238	−	267.969i	−0.935499	−	0.340494i	−0.764387	+	0.644758i	$0.776958\pi$
$788$	−340.121	−	405.341i	−0.431626	−	0.514392i
$789$		0			0
$790$	−222.978	+	81.1573i	−0.282251	+	0.102731i
$791$	1164.27	+	672.194i	1.47190	+	0.849803i
$792$		0			0
$793$	324.742	+	562.470i	0.409511	+	0.709294i
$794$	−36.1469	+	43.0782i	−0.0455250	+	0.0542546i
$795$		0			0
$796$	−46.5176	−	263.815i	−0.0584392	−	0.331425i
$797$	823.055	−	145.127i	1.03269	−	0.182091i	0.368480	−	0.929636i	$-0.379878\pi$
$797$	823.055	−	145.127i	1.03269	−	0.182091i	0.664212	+	0.747544i	$0.268767\pi$
$798$		0			0
$799$	−590.606	−	495.577i	−0.739181	−	0.620247i
$800$	96.0291	−	55.4424i	0.120036	−	0.0693030i
$801$		0			0
$802$	−312.534	+	541.325i	−0.389693	+	0.674968i
$803$	−4.22452	−	11.6068i	−0.00526092	−	0.0144543i
$804$		0			0
$805$	251.965	−	211.424i	0.313000	−	0.262638i
$806$	109.955	−	302.099i	0.136420	−	0.374812i
$807$		0			0
$808$	−2.61077	+	14.8064i	−0.00323115	+	0.0183248i
$809$			1495.47i			1.84854i	0.381735	+	0.924272i	$0.375327\pi$
$809$			1495.47i			1.84854i	−0.381735	+	0.924272i	$0.624673\pi$
$810$		0			0
$811$	584.404			0.720597			0.360299	−	0.932837i	$-0.382675\pi$
$811$	584.404			0.720597			0.360299	+	0.932837i	$0.382675\pi$
$812$	−617.600	−	108.900i	−0.760592	−	0.134113i
$813$		0			0
$814$	−60.8406	−	22.1442i	−0.0747428	−	0.0272041i
$815$	−249.106	−	296.873i	−0.305651	−	0.364261i
$816$		0			0
$817$	2371.30	−	863.082i	2.90244	−	1.05640i
$818$	170.213	+	98.2724i	0.208084	+	0.120137i
$819$		0			0
$820$	−40.5006	−	70.1491i	−0.0493910	−	0.0855477i
$821$	−691.162	+	823.695i	−0.841854	+	1.00328i	0.158021	+	0.987436i	$0.449489\pi$
$821$	−691.162	+	823.695i	−0.841854	+	1.00328i	−0.999874	+	0.0158465i	$0.994956\pi$
$822$		0			0
$823$	61.8166	+	350.579i	0.0751113	+	0.425977i	0.999056	+	0.0434502i	$0.0138350\pi$
$823$	61.8166	+	350.579i	0.0751113	+	0.425977i	−0.923944	+	0.382527i	$0.875054\pi$
$824$	187.738	−	33.1033i	0.227838	−	0.0401739i
$825$		0			0
$826$	−310.592	−	260.617i	−0.376019	−	0.315517i
$827$	−924.163	+	533.566i	−1.11749	+	0.645182i	−0.940759	−	0.339077i	$-0.889885\pi$
$827$	−924.163	+	533.566i	−1.11749	+	0.645182i	−0.176730	+	0.984259i	$0.556552\pi$
$828$		0			0
$829$	−54.2240	+	93.9188i	−0.0654090	+	0.113292i	−0.896875	−	0.442283i	$-0.854169\pi$
$829$	−54.2240	+	93.9188i	−0.0654090	+	0.113292i	0.831466	+	0.555575i	$0.187502\pi$
$830$	28.9906	+	79.6509i	0.0349284	+	0.0959649i
$831$		0			0
$832$	−47.0821	+	39.5066i	−0.0565891	+	0.0474839i
$833$	−75.0696	+	206.252i	−0.0901196	+	0.247601i
$834$		0			0
$835$	−8.45989	+	47.9784i	−0.0101316	+	0.0574592i
$836$		−	94.5630i		−	0.113114i
$837$		0			0
$838$	−96.6109			−0.115287
$839$	−1323.91	−	233.440i	−1.57796	−	0.278236i	−0.685056	−	0.728490i	$-0.740222\pi$
$839$	−1323.91	−	233.440i	−1.57796	−	0.278236i	−0.892901	+	0.450254i	$0.851334\pi$
$840$		0			0
$841$	1545.08	+	562.364i	1.83720	+	0.668685i
$842$	316.460	+	377.142i	0.375843	+	0.447912i
$843$		0			0
$844$	−126.985	+	46.2187i	−0.150456	+	0.0547615i
$845$	221.286	+	127.759i	0.261877	+	0.151195i
$846$		0			0
$847$	372.806	+	645.719i	0.440149	+	0.762360i
$848$	−221.211	+	263.630i	−0.260863	+	0.310884i
$849$		0			0
$850$	−111.953	−	634.917i	−0.131709	−	0.746961i
$851$	647.221	−	114.123i	0.760542	−	0.134104i
$852$		0			0
$853$	−582.882	−	489.096i	−0.683332	−	0.573383i	0.233646	−	0.972322i	$-0.424934\pi$
$853$	−582.882	−	489.096i	−0.683332	−	0.573383i	−0.916978	+	0.398938i	$0.869379\pi$
$854$	651.245	−	375.996i	0.762582	−	0.440277i
$855$		0			0
$856$	1.05342	−	1.82458i	0.00123063	−	0.00213152i
$857$	18.4563	+	50.7082i	0.0215359	+	0.0591694i	0.949995	−	0.312266i	$-0.101088\pi$
$857$	18.4563	+	50.7082i	0.0215359	+	0.0591694i	−0.928459	+	0.371435i	$0.878866\pi$
$858$		0			0
$859$	−626.704	+	525.867i	−0.729573	+	0.612185i	−0.930015	−	0.367521i	$-0.880207\pi$
$859$	−626.704	+	525.867i	−0.729573	+	0.612185i	0.200442	+	0.979706i	$0.435762\pi$
$860$	132.992	−	365.393i	0.154642	−	0.424876i
$861$		0			0
$862$	−86.1155	+	488.385i	−0.0999020	+	0.566572i
$863$		−	879.385i		−	1.01899i	−0.860475	−	0.509493i	$-0.829833\pi$
$863$		−	879.385i		−	1.01899i	0.860475	−	0.509493i	$-0.170167\pi$
$864$		0			0
$865$	−419.018			−0.484414
$866$	−246.847	−	43.5258i	−0.285043	−	0.0502607i
$867$		0			0
$868$	−349.779	−	127.309i	−0.402971	−	0.146669i
$869$	−72.7813	−	86.7374i	−0.0837529	−	0.0998129i
$870$		0			0
$871$	365.897	−	133.176i	0.420089	−	0.152900i
$872$	139.296	+	80.4226i	0.159743	+	0.0922277i
$873$		0			0
$874$	479.938	+	831.277i	0.549128	+	0.951118i
$875$	418.971	−	499.311i	0.478824	−	0.570641i
$876$		0			0
$877$	−116.280	−	659.457i	−0.132588	−	0.751947i	−0.976509	−	0.215478i	$-0.930869\pi$
$877$	−116.280	−	659.457i	−0.132588	−	0.751947i	0.843920	−	0.536469i	$-0.180242\pi$
$878$	3.97148	−	0.700278i	0.00452332	−	0.000797584i
$879$		0			0
$880$	−11.1622	−	9.36620i	−0.0126843	−	0.0106434i
$881$	1369.90	−	790.915i	1.55494	−	0.897747i	0.557215	−	0.830368i	$-0.311870\pi$
$881$	1369.90	−	790.915i	1.55494	−	0.897747i	0.997727	−	0.0673788i	$-0.0214636\pi$
$882$		0			0
$883$	478.719	−	829.166i	0.542151	−	0.939033i	−0.456629	−	0.889657i	$-0.650943\pi$
$883$	478.719	−	829.166i	0.542151	−	0.939033i	0.998780	−	0.0493760i	$-0.0157233\pi$
$884$	122.221	+	335.800i	0.138259	+	0.379864i
$885$		0			0
$886$	−578.648	+	485.544i	−0.653102	+	0.548018i
$887$	−51.4063	+	141.238i	−0.0579552	+	0.159231i	−0.965291	−	0.261175i	$-0.915890\pi$
$887$	−51.4063	+	141.238i	−0.0579552	+	0.159231i	0.907336	+	0.420406i	$0.138112\pi$
$888$		0			0
$889$	−53.9389	+	305.903i	−0.0606737	+	0.344098i
$890$			89.1316i			0.100148i
$891$		0			0
$892$	−452.726			−0.507540
$893$	984.509	+	173.596i	1.10247	+	0.194396i
$894$		0			0
$895$	−505.668	−	184.048i	−0.564992	−	0.205640i
$896$	45.7419	+	54.5131i	0.0510512	+	0.0608405i
$897$		0			0
$898$	879.502	−	320.113i	0.979401	−	0.356473i
$899$	1277.47	+	737.548i	1.42099	+	0.820410i
$900$		0			0
$901$	1000.47	+	1732.86i	1.11040	+	1.92326i
$902$	24.8448	−	29.6089i	0.0275441	−	0.0328258i
$903$		0			0
$904$	104.978	+	595.360i	0.116126	+	0.658584i
$905$	220.223	−	38.8312i	0.243340	−	0.0429074i
$906$		0			0
$907$	437.395	+	367.018i	0.482243	+	0.404650i	0.851237	−	0.524782i	$-0.175853\pi$
$907$	437.395	+	367.018i	0.482243	+	0.404650i	−0.368994	+	0.929432i	$0.620298\pi$
$908$	447.478	−	258.352i	0.492817	−	0.284528i
$909$		0			0
$910$	−79.3890	+	137.506i	−0.0872407	+	0.151105i
$911$	−25.3171	−	69.5582i	−0.0277905	−	0.0763537i	0.925022	−	0.379915i	$-0.124047\pi$
$911$	−25.3171	−	69.5582i	−0.0277905	−	0.0763537i	−0.952812	+	0.303561i	$0.901824\pi$
$912$		0			0
$913$	−30.9838	+	25.9985i	−0.0339363	+	0.0284759i
$914$	297.195	−	816.536i	0.325158	−	0.893365i
$915$		0			0
$916$	−18.6542	+	105.793i	−0.0203649	+	0.115495i
$917$			309.979i			0.338036i
$918$		0			0
$919$	−124.230			−0.135179			−0.0675897	−	0.997713i	$-0.521531\pi$
$919$	−124.230			−0.135179			−0.0675897	+	0.997713i	$0.521531\pi$
$920$	145.660	+	25.6838i	0.158326	+	0.0279172i
$921$		0			0
$922$	537.053	+	195.471i	0.582487	+	0.212008i
$923$	185.585	+	221.172i	0.201067	+	0.239622i
$924$		0			0
$925$	537.851	−	195.762i	0.581461	−	0.211634i
$926$	508.991	+	293.866i	0.549667	+	0.317350i
$927$		0			0
$928$	−141.003	−	244.225i	−0.151943	−	0.263173i
$929$	−576.612	+	687.179i	−0.620680	+	0.739697i	−0.981187	−	0.193059i	$-0.938159\pi$
$929$	−576.612	+	687.179i	−0.620680	+	0.739697i	0.360507	+	0.932756i	$0.382604\pi$
$930$		0			0
$931$	−49.4205	−	280.278i	−0.0530833	−	0.301050i
$932$	−211.907	+	37.3649i	−0.227368	+	0.0400911i
$933$		0			0
$934$	−201.807	−	169.337i	−0.216068	−	0.181303i
$935$	−73.3702	+	42.3603i	−0.0784708	+	0.0453051i
$936$		0			0
$937$	−710.201	+	1230.10i	−0.757951	+	1.31281i	0.185942	+	0.982561i	$0.440466\pi$
$937$	−710.201	+	1230.10i	−0.757951	+	1.31281i	−0.943894	+	0.330250i	$0.892867\pi$
$938$	−154.195	−	423.647i	−0.164387	−	0.451649i
$939$		0			0
$940$	118.004	−	99.0171i	0.125536	−	0.105337i
$941$	397.724	−	1092.74i	0.422661	−	1.16125i	−0.527517	−	0.849545i	$-0.676877\pi$
$941$	397.724	−	1092.74i	0.422661	−	1.16125i	0.950178	−	0.311708i	$-0.100901\pi$
$942$		0			0
$943$	−68.1290	+	386.379i	−0.0722470	+	0.409733i
$944$		−	182.322i		−	0.193138i
$945$		0			0
$946$	185.546			0.196137
$947$	553.877	+	97.6635i	0.584875	+	0.103129i	0.458253	−	0.888822i	$-0.348475\pi$
$947$	553.877	+	97.6635i	0.584875	+	0.103129i	0.126622	+	0.991951i	$0.459586\pi$
$948$		0			0
$949$	−56.8734	−	20.7002i	−0.0599299	−	0.0218127i
$950$	537.350	+	640.389i	0.565632	+	0.674094i
$951$		0			0
$952$	388.799	−	141.511i	0.408403	−	0.148646i
$953$	1273.41	+	735.202i	1.33621	+	0.771461i	0.986243	−	0.165302i	$-0.0528598\pi$
$953$	1273.41	+	735.202i	1.33621	+	0.771461i	0.349966	+	0.936762i	$0.386193\pi$
$954$		0			0
$955$	−112.982	−	195.690i	−0.118306	−	0.204911i
$956$	571.780	−	681.420i	0.598096	−	0.712783i
$957$		0			0
$958$	−84.0794	−	476.838i	−0.0877656	−	0.497743i
$959$	837.412	−	147.658i	0.873214	−	0.153971i
$960$		0			0
$961$	−65.4723	−	54.9378i	−0.0681294	−	0.0571673i
$962$	−274.749	+	158.627i	−0.285602	+	0.164893i
$963$		0			0
$964$	−204.160	+	353.616i	−0.211785	+	0.366822i
$965$	−39.7249	−	109.143i	−0.0411657	−	0.113102i
$966$		0			0
$967$	151.344	−	126.993i	0.156509	−	0.131326i	−0.561171	−	0.827700i	$-0.689649\pi$
$967$	151.344	−	126.993i	0.156509	−	0.131326i	0.717679	+	0.696374i	$0.245204\pi$
$968$	−114.675	+	315.066i	−0.118466	+	0.325482i
$969$		0			0
$970$	20.1290	−	114.157i	0.0207515	−	0.117688i
$971$		−	983.699i		−	1.01308i	−0.862217	−	0.506539i	$-0.830925\pi$
$971$		−	983.699i		−	1.01308i	0.862217	−	0.506539i	$-0.169075\pi$
$972$		0			0
$973$	1370.68			1.40871
$974$	−672.843	−	118.640i	−0.690804	−	0.121807i
$975$		0			0
$976$	317.763	+	115.656i	0.325577	+	0.118500i
$977$	−594.062	−	707.975i	−0.608047	−	0.724642i	0.370919	−	0.928665i	$-0.379043\pi$
$977$	−594.062	−	707.975i	−0.608047	−	0.724642i	−0.978966	+	0.204023i	$0.934598\pi$
$978$		0			0
$979$	−39.9663	+	14.5465i	−0.0408236	+	0.0148586i
$980$	−37.9789	−	21.9271i	−0.0387540	−	0.0223746i
$981$		0			0
$982$	176.387	+	305.512i	0.179621	+	0.311112i
$983$	−782.330	+	932.344i	−0.795860	+	0.948468i	−0.999533	−	0.0305705i	$-0.990268\pi$
$983$	−782.330	+	932.344i	−0.795860	+	0.948468i	0.203673	+	0.979039i	$0.434712\pi$
$984$		0			0
$985$	−106.740	−	605.355i	−0.108366	−	0.614573i
$986$	−1614.75	+	284.723i	−1.63767	+	0.288766i
$987$		0			0
$988$	−354.955	−	297.843i	−0.359266	−	0.301460i
$989$	−1631.08	+	941.704i	−1.64922	+	0.952178i
$990$		0			0
$991$	370.185	−	641.179i	0.373547	−	0.647002i	−0.616562	−	0.787307i	$-0.711475\pi$
$991$	370.185	−	641.179i	0.373547	−	0.647002i	0.990108	+	0.140305i	$0.0448082\pi$
$992$	−57.2483	−	157.288i	−0.0577100	−	0.158557i
$993$		0			0
$994$	256.079	−	214.876i	0.257625	−	0.216173i
$995$	106.437	−	292.432i	0.106971	−	0.293902i
$996$		0			0
$997$	−210.084	+	1191.45i	−0.210717	+	1.19503i	0.677470	+	0.735550i	$0.263076\pi$
$997$	−210.084	+	1191.45i	−0.210717	+	1.19503i	−0.888187	+	0.459483i	$0.848035\pi$
$998$			469.010i			0.469950i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	162.3.f.a.89.5		36
3.2	odd	2		54.3.f.a.29.3	✓	36
12.11	even	2		432.3.bc.c.353.2		36
27.11	odd	18		1458.3.b.c.1457.7		36
27.13	even	9		54.3.f.a.41.3	yes	36
27.14	odd	18	inner	162.3.f.a.71.5		36
27.16	even	9		1458.3.b.c.1457.30		36
108.67	odd	18		432.3.bc.c.257.2		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
54.3.f.a.29.3	✓	36	3.2	odd	2
54.3.f.a.41.3	yes	36	27.13	even	9
162.3.f.a.71.5		36	27.14	odd	18	inner
162.3.f.a.89.5		36	1.1	even	1	trivial
432.3.bc.c.257.2		36	108.67	odd	18
432.3.bc.c.353.2		36	12.11	even	2
1458.3.b.c.1457.7		36	27.11	odd	18
1458.3.b.c.1457.30		36	27.16	even	9

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:	\( N \)	\(=\)	\( 162 = 2 \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	162.f (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.39273 + 0.245576i) q^{2} +(1.87939 + 0.684040i) q^{4} +(1.49345 + 1.77982i) q^{5} +(5.91054 - 2.15126i) q^{7} +(2.44949 + 1.41421i) q^{8} +O(q^{10})\)	\(q+(1.39273 + 0.245576i) q^{2} +(1.87939 + 0.684040i) q^{4} +(1.49345 + 1.77982i) q^{5} +(5.91054 - 2.15126i) q^{7} +(2.44949 + 1.41421i) q^{8} +(1.64289 + 2.84556i) q^{10} +(-1.00782 + 1.20107i) q^{11} +(1.33408 + 7.56595i) q^{13} +(8.76008 - 1.54464i) q^{14} +(3.06418 + 2.57115i) q^{16} +(20.1411 - 11.6285i) q^{17} +(-15.0781 + 26.1161i) q^{19} +(1.58929 + 4.36655i) q^{20} +(-1.69857 + 1.42527i) q^{22} +(7.69793 - 21.1499i) q^{23} +(3.40383 - 19.3041i) q^{25} +10.8649i q^{26} +12.5797 q^{28} +(-49.0949 - 8.65675i) q^{29} +(-27.8049 - 10.1202i) q^{31} +(3.63616 + 4.33340i) q^{32} +(30.9068 - 11.2492i) q^{34} +(12.6559 + 7.30691i) q^{35} +(14.5999 + 25.2877i) q^{37} +(-27.4132 + 32.6698i) q^{38} +(1.14114 + 6.47170i) q^{40} +(-17.1669 + 3.02698i) q^{41} +(-64.1027 - 53.7886i) q^{43} +(-2.71565 + 1.56788i) q^{44} +(15.9150 - 27.5656i) q^{46} +(-11.3382 - 31.1513i) q^{47} +(-7.22958 + 6.06634i) q^{49} +(9.48121 - 26.0494i) q^{50} +(-2.66816 + 15.1319i) q^{52} +86.0360i q^{53} -3.64280 q^{55} +(17.5202 + 3.08928i) q^{56} +(-66.2499 - 24.1130i) q^{58} +(-29.2986 - 34.9167i) q^{59} +(79.4407 - 28.9140i) q^{61} +(-36.2395 - 20.9229i) q^{62} +(4.00000 + 6.92820i) q^{64} +(-11.4736 + 13.6738i) q^{65} +(-8.80100 - 49.9130i) q^{67} +(45.8073 - 8.07706i) q^{68} +(15.8319 + 13.2845i) q^{70} +(32.5457 - 18.7903i) q^{71} +(-3.93896 + 6.82248i) q^{73} +(14.1236 + 38.8043i) q^{74} +(-46.2021 + 38.7682i) q^{76} +(-3.37293 + 9.26704i) q^{77} +(-12.5403 + 71.1198i) q^{79} +9.29356i q^{80} -24.6521 q^{82} +(25.4050 + 4.47959i) q^{83} +(50.7763 + 18.4811i) q^{85} +(-76.0685 - 90.6549i) q^{86} +(-4.16720 + 1.51674i) q^{88} +(23.4923 + 13.5633i) q^{89} +(24.1615 + 41.8489i) q^{91} +(28.9347 - 34.4831i) q^{92} +(-8.14096 - 46.1697i) q^{94} +(-69.0004 + 12.1666i) q^{95} +(-27.0251 - 22.6768i) q^{97} +(-11.5586 + 6.67336i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 18 q^{5}+O(q^{10}) \) 36 * q - 18 * q^5	\( 36 q - 18 q^{5} + 18 q^{11} + 36 q^{14} + 72 q^{20} + 36 q^{22} + 180 q^{23} + 18 q^{25} - 144 q^{29} - 90 q^{31} - 72 q^{34} - 486 q^{35} - 180 q^{38} + 90 q^{41} + 90 q^{43} + 378 q^{47} + 72 q^{49} + 72 q^{56} - 252 q^{59} - 144 q^{61} + 144 q^{64} - 18 q^{65} - 594 q^{67} + 180 q^{68} - 360 q^{70} + 648 q^{71} + 126 q^{73} + 504 q^{74} - 72 q^{76} + 342 q^{77} - 72 q^{79} - 594 q^{83} + 360 q^{85} - 540 q^{86} + 144 q^{88} - 648 q^{89} - 198 q^{91} - 396 q^{92} + 504 q^{94} - 252 q^{95} + 702 q^{97} - 648 q^{98}+O(q^{100}) \) 36 * q - 18 * q^5 + 18 * q^11 + 36 * q^14 + 72 * q^20 + 36 * q^22 + 180 * q^23 + 18 * q^25 - 144 * q^29 - 90 * q^31 - 72 * q^34 - 486 * q^35 - 180 * q^38 + 90 * q^41 + 90 * q^43 + 378 * q^47 + 72 * q^49 + 72 * q^56 - 252 * q^59 - 144 * q^61 + 144 * q^64 - 18 * q^65 - 594 * q^67 + 180 * q^68 - 360 * q^70 + 648 * q^71 + 126 * q^73 + 504 * q^74 - 72 * q^76 + 342 * q^77 - 72 * q^79 - 594 * q^83 + 360 * q^85 - 540 * q^86 + 144 * q^88 - 648 * q^89 - 198 * q^91 - 396 * q^92 + 504 * q^94 - 252 * q^95 + 702 * q^97 - 648 * q^98

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