LMFDB - Embedded newform 234.3.bb.d.145.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [234,3,Mod(19,234)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(234, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 5]))

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

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

chi := DirichletCharacter("234.19");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 234 = 2 \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	234.bb (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.37603818603$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + 2x^{6} + 82x^{5} + 5053x^{4} - 6736x^{3} + 6728x^{2} + 275384x + 5635876 $ x^8 - 2x^7 + 2x^6 + 82x^5 + 5053x^4 - 6736x^3 + 6728x^2 + 275384*x + 5635876
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 78)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			145.2
Root			$-5.39181 - 5.39181i$ of defining polynomial
Character	$\chi$	$=$	234.145
Dual form			234.3.bb.d.163.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.36603 - 0.366025i) q^{2} +(1.73205 + 1.00000i) q^{4} +(6.39181 - 6.39181i) q^{5} +(9.23137 - 2.47354i) q^{7} +(-2.00000 - 2.00000i) q^{8} +O(q^{10})$	\(q+(-1.36603 - 0.366025i) q^{2} +(1.73205 + 1.00000i) q^{4} +(6.39181 - 6.39181i) q^{5} +(9.23137 - 2.47354i) q^{7} +(-2.00000 - 2.00000i) q^{8} +(-11.0709 + 6.39181i) q^{10} +(-4.21503 + 15.7307i) q^{11} +(-3.81310 - 12.4282i) q^{13} -13.5157 q^{14} +(2.00000 + 3.46410i) q^{16} +(-8.31934 - 4.80317i) q^{17} +(2.56168 + 9.56033i) q^{19} +(17.4627 - 4.67913i) q^{20} +(11.5157 - 19.9457i) q^{22} +(23.6929 - 13.6791i) q^{23} -56.7105i q^{25} +(0.659759 + 18.3729i) q^{26} +(18.4627 + 4.94708i) q^{28} +(13.8023 + 23.9063i) q^{29} +(11.5613 - 11.5613i) q^{31} +(-1.46410 - 5.46410i) q^{32} +(9.60634 + 9.60634i) q^{34} +(43.1948 - 74.8156i) q^{35} +(-5.45615 + 20.3626i) q^{37} -13.9973i q^{38} -25.5672 q^{40} +(-39.1030 - 10.4776i) q^{41} +(-30.9095 - 17.8456i) q^{43} +(-23.0313 + 23.0313i) q^{44} +(-37.3721 + 10.0138i) q^{46} +(-25.5184 - 25.5184i) q^{47} +(36.6646 - 21.1683i) q^{49} +(-20.7575 + 77.4679i) q^{50} +(5.82371 - 25.3394i) q^{52} +39.0697 q^{53} +(73.6060 + 127.489i) q^{55} +(-23.4098 - 13.5157i) q^{56} +(-10.1040 - 37.7086i) q^{58} +(46.0300 - 12.3337i) q^{59} +(-35.2717 + 61.0923i) q^{61} +(-20.0248 + 11.5613i) q^{62} +8.00000i q^{64} +(-103.811 - 55.0661i) q^{65} +(38.7250 + 10.3763i) q^{67} +(-9.60634 - 16.6387i) q^{68} +(-86.3896 + 86.3896i) q^{70} +(8.28114 + 30.9056i) q^{71} +(-9.68320 - 9.68320i) q^{73} +(14.9065 - 25.8188i) q^{74} +(-5.12337 + 19.1207i) q^{76} +155.642i q^{77} -56.1543 q^{79} +(34.9255 + 9.35826i) q^{80} +(49.5806 + 28.6254i) q^{82} +(-4.59931 + 4.59931i) q^{83} +(-83.8766 + 22.4747i) q^{85} +(35.6912 + 35.6912i) q^{86} +(39.8915 - 23.0313i) q^{88} +(-29.9479 + 111.767i) q^{89} +(-65.9418 - 105.298i) q^{91} +54.7165 q^{92} +(25.5184 + 44.1991i) q^{94} +(77.4816 + 44.7340i) q^{95} +(-9.04249 - 33.7470i) q^{97} +(-57.8330 + 15.4963i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{2} + 6 q^{5} + 10 q^{7} - 16 q^{8}+O(q^{10}) $ 8 * q - 4 * q^2 + 6 * q^5 + 10 * q^7 - 16 * q^8	$ 8 q - 4 q^{2} + 6 q^{5} + 10 q^{7} - 16 q^{8} - 6 q^{10} - 24 q^{11} - 4 q^{14} + 16 q^{16} + 84 q^{17} + 10 q^{19} + 12 q^{20} - 12 q^{22} + 12 q^{23} - 26 q^{26} + 20 q^{28} - 36 q^{29} - 94 q^{31} + 16 q^{32} + 60 q^{34} + 204 q^{35} + 140 q^{37} - 24 q^{40} - 72 q^{41} - 222 q^{43} + 24 q^{44} - 84 q^{46} - 300 q^{47} + 42 q^{49} + 62 q^{50} + 44 q^{52} - 84 q^{53} + 396 q^{55} - 36 q^{56} - 66 q^{58} + 60 q^{59} - 90 q^{61} - 198 q^{62} + 108 q^{65} + 304 q^{67} - 60 q^{68} - 408 q^{70} + 192 q^{71} + 16 q^{73} + 46 q^{74} - 20 q^{76} - 96 q^{79} + 24 q^{80} + 114 q^{82} - 390 q^{85} - 168 q^{86} + 72 q^{88} - 354 q^{89} - 218 q^{91} + 288 q^{92} + 300 q^{94} + 576 q^{95} - 460 q^{97} - 58 q^{98}+O(q^{100}) $ 8 * q - 4 * q^2 + 6 * q^5 + 10 * q^7 - 16 * q^8 - 6 * q^10 - 24 * q^11 - 4 * q^14 + 16 * q^16 + 84 * q^17 + 10 * q^19 + 12 * q^20 - 12 * q^22 + 12 * q^23 - 26 * q^26 + 20 * q^28 - 36 * q^29 - 94 * q^31 + 16 * q^32 + 60 * q^34 + 204 * q^35 + 140 * q^37 - 24 * q^40 - 72 * q^41 - 222 * q^43 + 24 * q^44 - 84 * q^46 - 300 * q^47 + 42 * q^49 + 62 * q^50 + 44 * q^52 - 84 * q^53 + 396 * q^55 - 36 * q^56 - 66 * q^58 + 60 * q^59 - 90 * q^61 - 198 * q^62 + 108 * q^65 + 304 * q^67 - 60 * q^68 - 408 * q^70 + 192 * q^71 + 16 * q^73 + 46 * q^74 - 20 * q^76 - 96 * q^79 + 24 * q^80 + 114 * q^82 - 390 * q^85 - 168 * q^86 + 72 * q^88 - 354 * q^89 - 218 * q^91 + 288 * q^92 + 300 * q^94 + 576 * q^95 - 460 * q^97 - 58 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/234\mathbb{Z}\right)^\times$.

$n$	$145$	$209$
$\chi(n)$	$e\left(\frac{1}{12}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.36603	−	0.366025i	−0.683013	−	0.183013i
$2$	−1.36603	−	0.366025i	−0.683013	−	0.183013i
$3$		0			0
$3$		0			0
$4$	1.73205	+	1.00000i	0.433013	+	0.250000i
$5$	6.39181	−	6.39181i	1.27836	−	1.27836i	0.336778	−	0.941584i	$-0.390663\pi$
$5$	6.39181	−	6.39181i	1.27836	−	1.27836i	0.941584	−	0.336778i	$-0.109337\pi$
$6$		0			0
$7$	9.23137	−	2.47354i	1.31877	−	0.353363i	0.470252	−	0.882532i	$-0.344163\pi$
$7$	9.23137	−	2.47354i	1.31877	−	0.353363i	0.848516	+	0.529170i	$0.177496\pi$
$8$	−2.00000	−	2.00000i	−0.250000	−	0.250000i
$9$		0			0
$10$	−11.0709	+	6.39181i	−1.10709	+	0.639181i
$11$	−4.21503	+	15.7307i	−0.383184	+	1.43006i	0.457825	+	0.889042i	$0.348629\pi$
$11$	−4.21503	+	15.7307i	−0.383184	+	1.43006i	−0.841009	+	0.541021i	$0.818038\pi$
$12$		0			0
$13$	−3.81310	−	12.4282i	−0.293316	−	0.956016i
$13$	−3.81310	−	12.4282i	−0.293316	−	0.956016i
$14$	−13.5157			−0.965405
$15$		0			0
$16$	2.00000	+	3.46410i	0.125000	+	0.216506i
$17$	−8.31934	−	4.80317i	−0.489373	−	0.282540i	0.234941	−	0.972010i	$-0.424510\pi$
$17$	−8.31934	−	4.80317i	−0.489373	−	0.282540i	−0.724314	+	0.689470i	$0.757843\pi$
$18$		0			0
$19$	2.56168	+	9.56033i	0.134825	+	0.503175i	0.999999	+	0.00170204i	$0.000541777\pi$
$19$	2.56168	+	9.56033i	0.134825	+	0.503175i	−0.865173	+	0.501473i	$0.832792\pi$
$20$	17.4627	−	4.67913i	0.873137	−	0.233956i
$21$		0			0
$22$	11.5157	−	19.9457i	0.523440	−	0.906624i
$23$	23.6929	−	13.6791i	1.03013	−	0.594745i	0.113107	−	0.993583i	$-0.463920\pi$
$23$	23.6929	−	13.6791i	1.03013	−	0.594745i	0.917021	+	0.398838i	$0.130586\pi$
$24$		0			0
$25$		−	56.7105i		−	2.26842i
$26$	0.659759	+	18.3729i	0.0253754	+	0.706651i
$27$		0			0
$28$	18.4627	+	4.94708i	0.659384	+	0.176681i
$29$	13.8023	+	23.9063i	0.475942	+	0.824356i	0.999620	−	0.0275606i	$-0.00877392\pi$
$29$	13.8023	+	23.9063i	0.475942	+	0.824356i	−0.523678	+	0.851916i	$0.675441\pi$
$30$		0			0
$31$	11.5613	−	11.5613i	0.372946	−	0.372946i	−0.495603	−	0.868549i	$-0.665053\pi$
$31$	11.5613	−	11.5613i	0.372946	−	0.372946i	0.868549	+	0.495603i	$0.165053\pi$
$32$	−1.46410	−	5.46410i	−0.0457532	−	0.170753i
$33$		0			0
$34$	9.60634	+	9.60634i	0.282540	+	0.282540i
$35$	43.1948	−	74.8156i	1.23414	−	2.13759i
$36$		0			0
$37$	−5.45615	+	20.3626i	−0.147464	+	0.550342i	0.852170	+	0.523265i	$0.175286\pi$
$37$	−5.45615	+	20.3626i	−0.147464	+	0.550342i	−0.999633	+	0.0270763i	$0.991380\pi$
$38$		−	13.9973i		−	0.368350i
$39$		0			0
$40$	−25.5672			−0.639181
$41$	−39.1030	−	10.4776i	−0.953731	−	0.255551i	−0.251786	−	0.967783i	$-0.581018\pi$
$41$	−39.1030	−	10.4776i	−0.953731	−	0.255551i	−0.701945	+	0.712232i	$0.747685\pi$
$42$		0			0
$43$	−30.9095	−	17.8456i	−0.718826	−	0.415014i	0.0954945	−	0.995430i	$-0.469557\pi$
$43$	−30.9095	−	17.8456i	−0.718826	−	0.415014i	−0.814320	+	0.580416i	$0.802890\pi$
$44$	−23.0313	+	23.0313i	−0.523440	+	0.523440i
$45$		0			0
$46$	−37.3721	+	10.0138i	−0.812436	+	0.217692i
$47$	−25.5184	−	25.5184i	−0.542944	−	0.542944i	0.381447	−	0.924391i	$-0.375426\pi$
$47$	−25.5184	−	25.5184i	−0.542944	−	0.542944i	−0.924391	+	0.381447i	$0.875426\pi$
$48$		0			0
$49$	36.6646	−	21.1683i	0.748258	−	0.432007i
$50$	−20.7575	+	77.4679i	−0.415149	+	1.54936i
$51$		0			0
$52$	5.82371	−	25.3394i	0.111994	−	0.487296i
$53$	39.0697			0.737165			0.368582	−	0.929595i	$-0.379843\pi$
$53$	39.0697			0.737165			0.368582	+	0.929595i	$0.379843\pi$
$54$		0			0
$55$	73.6060	+	127.489i	1.33829	+	2.31799i
$56$	−23.4098	−	13.5157i	−0.418033	−	0.241351i
$57$		0			0
$58$	−10.1040	−	37.7086i	−0.174207	−	0.650149i
$59$	46.0300	−	12.3337i	0.780169	−	0.209046i	0.153310	−	0.988178i	$-0.451007\pi$
$59$	46.0300	−	12.3337i	0.780169	−	0.209046i	0.626859	+	0.779132i	$0.284340\pi$
$60$		0			0
$61$	−35.2717	+	61.0923i	−0.578224	+	1.00151i	0.417459	+	0.908696i	$0.362921\pi$
$61$	−35.2717	+	61.0923i	−0.578224	+	1.00151i	−0.995683	+	0.0928174i	$0.970413\pi$
$62$	−20.0248	+	11.5613i	−0.322981	+	0.186473i
$63$		0			0
$64$			8.00000i			0.125000i
$65$	−103.811	−	55.0661i	−1.59710	−	0.847170i
$66$		0			0
$67$	38.7250	+	10.3763i	0.577984	+	0.154870i	0.535956	−	0.844246i	$-0.319951\pi$
$67$	38.7250	+	10.3763i	0.577984	+	0.154870i	0.0420285	+	0.999116i	$0.486618\pi$
$68$	−9.60634	−	16.6387i	−0.141270	−	0.244686i
$69$		0			0
$70$	−86.3896	+	86.3896i	−1.23414	+	1.23414i
$71$	8.28114	+	30.9056i	0.116636	+	0.435291i	0.999404	−	0.0345180i	$-0.0109896\pi$
$71$	8.28114	+	30.9056i	0.116636	+	0.435291i	−0.882768	+	0.469809i	$0.844323\pi$
$72$		0			0
$73$	−9.68320	−	9.68320i	−0.132647	−	0.132647i	0.637666	−	0.770313i	$-0.279900\pi$
$73$	−9.68320	−	9.68320i	−0.132647	−	0.132647i	−0.770313	+	0.637666i	$0.779900\pi$
$74$	14.9065	−	25.8188i	0.201439	−	0.348903i
$75$		0			0
$76$	−5.12337	+	19.1207i	−0.0674127	+	0.251588i
$77$			155.642i			2.02132i
$78$		0			0
$79$	−56.1543			−0.710814			−0.355407	−	0.934712i	$-0.615658\pi$
$79$	−56.1543			−0.710814			−0.355407	+	0.934712i	$0.615658\pi$
$80$	34.9255	+	9.35826i	0.436569	+	0.116978i
$81$		0			0
$82$	49.5806	+	28.6254i	0.604641	+	0.349090i
$83$	−4.59931	+	4.59931i	−0.0554133	+	0.0554133i	−0.734270	−	0.678857i	$-0.762476\pi$
$83$	−4.59931	+	4.59931i	−0.0554133	+	0.0554133i	0.678857	+	0.734270i	$0.262476\pi$
$84$		0			0
$85$	−83.8766	+	22.4747i	−0.986783	+	0.264408i
$86$	35.6912	+	35.6912i	0.415014	+	0.415014i
$87$		0			0
$88$	39.8915	−	23.0313i	0.453312	−	0.261720i
$89$	−29.9479	+	111.767i	−0.336494	+	1.25581i	0.565747	+	0.824579i	$0.308588\pi$
$89$	−29.9479	+	111.767i	−0.336494	+	1.25581i	−0.902241	+	0.431233i	$0.858079\pi$
$90$		0			0
$91$	−65.9418	−	105.298i	−0.724636	−	1.15712i
$92$	54.7165			0.594745
$93$		0			0
$94$	25.5184	+	44.1991i	0.271472	+	0.470203i
$95$	77.4816	+	44.7340i	0.815596	+	0.470885i
$96$		0			0
$97$	−9.04249	−	33.7470i	−0.0932215	−	0.347908i	0.903522	−	0.428541i	$-0.140972\pi$
$97$	−9.04249	−	33.7470i	−0.0932215	−	0.347908i	−0.996744	+	0.0806336i	$0.974306\pi$
$98$	−57.8330	+	15.4963i	−0.590132	+	0.158126i
$99$		0			0
$100$	56.7105	−	98.2254i	0.567105	−	0.982254i
$101$	101.471	−	58.5846i	1.00467	−	0.580045i	0.0950419	−	0.995473i	$-0.469701\pi$
$101$	101.471	−	58.5846i	1.00467	−	0.580045i	0.909626	+	0.415428i	$0.136368\pi$
$102$		0			0
$103$			184.178i			1.78813i	0.447933	+	0.894067i	$0.352160\pi$
$103$			184.178i			1.78813i	−0.447933	+	0.894067i	$0.647840\pi$
$104$	−17.2302	+	32.4826i	−0.165675	+	0.312333i
$105$		0			0
$106$	−53.3702	−	14.3005i	−0.503493	−	0.134910i
$107$	3.57599	+	6.19380i	0.0334205	+	0.0578860i	0.882252	−	0.470778i	$-0.156027\pi$
$107$	3.57599	+	6.19380i	0.0334205	+	0.0578860i	−0.848831	+	0.528664i	$0.822693\pi$
$108$		0			0
$109$	8.07627	−	8.07627i	0.0740942	−	0.0740942i	−0.669089	−	0.743183i	$-0.733315\pi$
$109$	8.07627	−	8.07627i	0.0740942	−	0.0740942i	0.743183	+	0.669089i	$0.233315\pi$
$110$	−53.8833	−	201.095i	−0.489848	−	1.82814i
$111$		0			0
$112$	27.0313	+	27.0313i	0.241351	+	0.241351i
$113$	−58.2038	+	100.812i	−0.515077	+	0.892140i	0.484769	+	0.874642i	$0.338904\pi$
$113$	−58.2038	+	100.812i	−0.515077	+	0.892140i	−0.999847	+	0.0174984i	$0.994430\pi$
$114$		0			0
$115$	64.0064	−	238.875i	0.556578	−	2.07718i
$116$			55.2093i			0.475942i
$117$		0			0
$118$	−67.3926			−0.571124
$119$	−88.6798	−	23.7617i	−0.745208	−	0.199678i
$120$		0			0
$121$	−124.899	−	72.1107i	−1.03223	−	0.595956i
$122$	70.5433	−	70.5433i	0.578224	−	0.578224i
$123$		0			0
$124$	31.5861	−	8.46347i	0.254727	−	0.0682538i
$125$	−202.687	−	202.687i	−1.62150	−	1.62150i
$126$		0			0
$127$	−23.3984	+	13.5091i	−0.184240	+	0.106371i	−0.589283	−	0.807927i	$-0.700590\pi$
$127$	−23.3984	+	13.5091i	−0.184240	+	0.106371i	0.405043	+	0.914297i	$0.367256\pi$
$128$	2.92820	−	10.9282i	0.0228766	−	0.0853766i
$129$		0			0
$130$	121.653	+	113.219i	0.935795	+	0.870917i
$131$	64.5682			0.492887			0.246444	−	0.969157i	$-0.420738\pi$
$131$	64.5682			0.492887			0.246444	+	0.969157i	$0.420738\pi$
$132$		0			0
$133$	47.2957	+	81.9186i	0.355607	+	0.615929i
$134$	−49.1013	−	28.3486i	−0.366427	−	0.211557i
$135$		0			0
$136$	7.03233	+	26.2450i	0.0517083	+	0.192978i
$137$	−197.212	+	52.8428i	−1.43950	+	0.385714i	−0.892360	−	0.451325i	$-0.850951\pi$
$137$	−197.212	+	52.8428i	−1.43950	+	0.385714i	−0.547143	+	0.837039i	$0.684285\pi$
$138$		0			0
$139$	−31.8057	+	55.0890i	−0.228818	+	0.396324i	−0.957458	−	0.288573i	$-0.906819\pi$
$139$	−31.8057	+	55.0890i	−0.228818	+	0.396324i	0.728640	+	0.684897i	$0.240153\pi$
$140$	149.631	−	86.3896i	1.06879	−	0.617069i
$141$		0			0
$142$		−	45.2490i		−	0.318655i
$143$	211.577	−	7.59757i	1.47956	−	0.0531299i
$144$		0			0
$145$	241.026	+	64.5828i	1.66225	+	0.445399i
$146$	9.68320	+	16.7718i	0.0663233	+	0.114875i
$147$		0			0
$148$	−29.8130	+	29.8130i	−0.201439	+	0.201439i
$149$	−7.51093	−	28.0312i	−0.0504089	−	0.188129i	0.936130	−	0.351653i	$-0.114380\pi$
$149$	−7.51093	−	28.0312i	−0.0504089	−	0.188129i	−0.986539	+	0.163525i	$0.947714\pi$
$150$		0			0
$151$	31.6350	+	31.6350i	0.209503	+	0.209503i	0.804056	−	0.594553i	$-0.202671\pi$
$151$	31.6350	+	31.6350i	0.209503	+	0.209503i	−0.594553	+	0.804056i	$0.702671\pi$
$152$	13.9973	−	24.2440i	0.0920875	−	0.159500i
$153$		0			0
$154$	56.9689	−	212.611i	0.369928	−	1.38059i
$155$		−	147.796i		−	0.953520i
$156$		0			0
$157$	242.423			1.54409			0.772047	−	0.635566i	$-0.219233\pi$
$157$	242.423			1.54409			0.772047	+	0.635566i	$0.219233\pi$
$158$	76.7082	+	20.5539i	0.485495	+	0.130088i
$159$		0			0
$160$	−44.2838	−	25.5672i	−0.276773	−	0.159795i
$161$	184.883	−	184.883i	1.14834	−	1.14834i
$162$		0			0
$163$	−15.0812	+	4.04100i	−0.0925228	+	0.0247914i	−0.304783	−	0.952422i	$-0.598584\pi$
$163$	−15.0812	+	4.04100i	−0.0925228	+	0.0247914i	0.212261	+	0.977213i	$0.431917\pi$
$164$	−57.2507	−	57.2507i	−0.349090	−	0.349090i
$165$		0			0
$166$	7.96623	−	4.59931i	0.0479894	−	0.0277067i
$167$	−12.8137	+	47.8214i	−0.0767287	+	0.286355i	−0.993620	−	0.112782i	$-0.964024\pi$
$167$	−12.8137	+	47.8214i	−0.0767287	+	0.286355i	0.916891	+	0.399138i	$0.130690\pi$
$168$		0			0
$169$	−139.920	+	94.7801i	−0.827932	+	0.560829i
$170$	122.804			0.722376
$171$		0			0
$172$	−35.6912	−	61.8190i	−0.207507	−	0.359413i
$173$	145.860	+	84.2123i	0.843122	+	0.486776i	0.858324	−	0.513108i	$-0.171506\pi$
$173$	145.860	+	84.2123i	0.843122	+	0.486776i	−0.0152025	+	0.999884i	$0.504839\pi$
$174$		0			0
$175$	−140.276	−	523.516i	−0.801575	−	2.99152i
$176$	−62.9228	+	16.8601i	−0.357516	+	0.0957961i
$177$		0			0
$178$	81.8193	−	141.715i	0.459659	−	0.796153i
$179$	−271.106	+	156.523i	−1.51456	+	0.874432i	−0.514707	+	0.857366i	$0.672099\pi$
$179$	−271.106	+	156.523i	−1.51456	+	0.874432i	−0.999854	+	0.0170659i	$0.994567\pi$
$180$		0			0
$181$			19.4795i			0.107622i	0.998551	+	0.0538108i	$0.0171368\pi$
$181$			19.4795i			0.107622i	−0.998551	+	0.0538108i	$0.982863\pi$
$182$	51.5367	+	167.976i	0.283168	+	0.922942i
$183$		0			0
$184$	−74.7442	−	20.0276i	−0.406218	−	0.108846i
$185$	95.2795	+	165.029i	0.515024	+	0.892048i
$186$		0			0
$187$	110.623	−	110.623i	0.591569	−	0.591569i
$188$	−18.6807	−	69.7175i	−0.0993657	−	0.370838i
$189$		0			0
$190$	−89.4681	−	89.4681i	−0.470885	−	0.470885i
$191$	71.4756	−	123.799i	0.374218	−	0.648164i	−0.615992	−	0.787752i	$-0.711245\pi$
$191$	71.4756	−	123.799i	0.374218	−	0.648164i	0.990210	+	0.139588i	$0.0445780\pi$
$192$		0			0
$193$	−43.4334	+	162.096i	−0.225044	+	0.839874i	0.757344	+	0.653017i	$0.226497\pi$
$193$	−43.4334	+	162.096i	−0.225044	+	0.839874i	−0.982387	+	0.186857i	$0.940170\pi$
$194$			49.4091i			0.254686i
$195$		0			0
$196$	84.6734			0.432007
$197$	−164.580	−	44.0992i	−0.835434	−	0.223854i	−0.184351	−	0.982860i	$-0.559018\pi$
$197$	−164.580	−	44.0992i	−0.835434	−	0.223854i	−0.651083	+	0.759007i	$0.725685\pi$
$198$		0			0
$199$	140.059	+	80.8629i	0.703813	+	0.406346i	0.808766	−	0.588131i	$-0.200136\pi$
$199$	140.059	+	80.8629i	0.703813	+	0.406346i	−0.104953	+	0.994477i	$0.533469\pi$
$200$	−113.421	+	113.421i	−0.567105	+	0.567105i
$201$		0			0
$202$	−160.056	+	42.8869i	−0.792357	+	0.212311i
$203$	186.548	+	186.548i	0.918953	+	0.918953i
$204$		0			0
$205$	−316.910	+	182.968i	−1.54590	+	0.892526i
$206$	67.4138	−	251.592i	0.327251	−	1.22132i
$207$		0			0
$208$	35.4264	−	38.0654i	0.170319	−	0.183007i
$209$	−161.188			−0.771236
$210$		0			0
$211$	89.9377	+	155.777i	0.426245	+	0.738278i	0.996536	−	0.0831651i	$-0.0265029\pi$
$211$	89.9377	+	155.777i	0.426245	+	0.738278i	−0.570291	+	0.821443i	$0.693170\pi$
$212$	67.6707	+	39.0697i	0.319202	+	0.184291i
$213$		0			0
$214$	−2.61781	−	9.76979i	−0.0122327	−	0.0456532i
$215$	−311.634	+	83.5020i	−1.44946	+	0.388381i
$216$		0			0
$217$	78.1295	−	135.324i	0.360044	−	0.623614i
$218$	−13.9885	+	8.07627i	−0.0641675	+	0.0370471i
$219$		0			0
$220$			294.424i			1.33829i
$221$	−27.9723	+	121.709i	−0.126571	+	0.550721i
$222$		0			0
$223$	376.519	+	100.888i	1.68843	+	0.452413i	0.969983	−	0.243171i	$-0.0781877\pi$
$223$	376.519	+	100.888i	1.68843	+	0.452413i	0.718445	+	0.695584i	$0.244854\pi$
$224$	−27.0313	−	46.8197i	−0.120676	−	0.209016i
$225$		0			0
$226$	116.408	−	116.408i	0.515077	−	0.515077i
$227$	−34.5070	−	128.782i	−0.152013	−	0.567321i	−0.999343	−	0.0362535i	$-0.988458\pi$
$227$	−34.5070	−	128.782i	−0.152013	−	0.567321i	0.847329	−	0.531068i	$-0.178209\pi$
$228$		0			0
$229$	−304.866	−	304.866i	−1.33129	−	1.33129i	−0.904215	−	0.427077i	$-0.859543\pi$
$229$	−304.866	−	304.866i	−1.33129	−	1.33129i	−0.427077	−	0.904215i	$-0.640457\pi$
$230$	−174.869	+	302.882i	−0.760299	+	1.31688i
$231$		0			0
$232$	20.2080	−	75.4172i	0.0871034	−	0.325074i
$233$			44.1414i			0.189448i	0.995504	+	0.0947240i	$0.0301969\pi$
$233$			44.1414i			0.189448i	−0.995504	+	0.0947240i	$0.969803\pi$
$234$		0			0
$235$	−326.217			−1.38816
$236$	92.0600	+	24.6674i	0.390085	+	0.104523i
$237$		0			0
$238$	112.441	+	64.9181i	0.472443	+	0.272765i
$239$	15.8448	−	15.8448i	0.0662964	−	0.0662964i	−0.673181	−	0.739478i	$-0.735073\pi$
$239$	15.8448	−	15.8448i	0.0662964	−	0.0662964i	0.739478	+	0.673181i	$0.235073\pi$
$240$		0			0
$241$	−464.593	+	124.487i	−1.92777	+	0.516545i	−0.947076	+	0.321010i	$0.895978\pi$
$241$	−464.593	+	124.487i	−1.92777	+	0.516545i	−0.980697	+	0.195535i	$0.937356\pi$
$242$	144.221	+	144.221i	0.595956	+	0.595956i
$243$		0			0
$244$	−122.185	+	70.5433i	−0.500757	+	0.289112i
$245$	99.0494	−	369.657i	0.404283	−	1.50881i
$246$		0			0
$247$	109.050	−	68.2917i	0.441497	−	0.276484i
$248$	−46.2453			−0.186473
$249$		0			0
$250$	202.687	+	351.065i	0.810749	+	1.40426i
$251$	183.403	+	105.888i	0.730691	+	0.421865i	0.818675	−	0.574257i	$-0.194709\pi$
$251$	183.403	+	105.888i	0.730691	+	0.421865i	−0.0879839	+	0.996122i	$0.528042\pi$
$252$		0			0
$253$	115.316	+	430.365i	0.455794	+	1.70105i
$254$	36.9075	−	9.88934i	0.145305	−	0.0389344i
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$	−235.923	+	136.210i	−0.917990	+	0.530002i	−0.882993	−	0.469386i	$-0.844475\pi$
$257$	−235.923	+	136.210i	−0.917990	+	0.530002i	−0.0349966	+	0.999387i	$0.511142\pi$
$258$		0			0
$259$			201.471i			0.777881i
$260$	−124.740	−	199.189i	−0.479771	−	0.766110i
$261$		0			0
$262$	−88.2018	−	23.6336i	−0.336648	−	0.0902046i
$263$	118.171	+	204.679i	0.449321	+	0.778247i	0.998342	−	0.0575615i	$-0.0183325\pi$
$263$	118.171	+	204.679i	0.449321	+	0.778247i	−0.549021	+	0.835809i	$0.684999\pi$
$264$		0			0
$265$	249.726	−	249.726i	0.942363	−	0.942363i
$266$	−34.6229	−	129.214i	−0.130161	−	0.485768i
$267$		0			0
$268$	56.6973	+	56.6973i	0.211557	+	0.211557i
$269$	233.180	−	403.880i	0.866842	−	1.50141i	0.00163514	−	0.999999i	$-0.499480\pi$
$269$	233.180	−	403.880i	0.866842	−	1.50141i	0.865207	−	0.501415i	$-0.167187\pi$
$270$		0			0
$271$	−119.372	+	445.502i	−0.440486	+	1.64392i	0.287099	+	0.957901i	$0.407309\pi$
$271$	−119.372	+	445.502i	−0.440486	+	1.64392i	−0.727586	+	0.686017i	$0.759358\pi$
$272$		−	38.4254i		−	0.141270i
$273$		0			0
$274$	288.738			1.05379
$275$	892.095	+	239.036i	3.24398	+	0.869223i
$276$		0			0
$277$	−21.2638	−	12.2766i	−0.0767645	−	0.0443200i	0.461126	−	0.887334i	$-0.347445\pi$
$277$	−21.2638	−	12.2766i	−0.0767645	−	0.0443200i	−0.537891	+	0.843014i	$0.680779\pi$
$278$	63.6113	−	63.6113i	0.228818	−	0.228818i
$279$		0			0
$280$	−236.021	+	63.2416i	−0.842931	+	0.225863i
$281$	−276.591	−	276.591i	−0.984311	−	0.984311i	0.0155674	−	0.999879i	$-0.495045\pi$
$281$	−276.591	−	276.591i	−0.984311	−	0.984311i	−0.999879	+	0.0155674i	$0.995045\pi$
$282$		0			0
$283$	339.231	−	195.855i	1.19870	−	0.692068i	0.238432	−	0.971159i	$-0.423366\pi$
$283$	339.231	−	195.855i	1.19870	−	0.692068i	0.960265	+	0.279091i	$0.0900331\pi$
$284$	−16.5623	+	61.8113i	−0.0583179	+	0.217645i
$285$		0			0
$286$	−291.800	−	67.0640i	−1.02028	−	0.234489i
$287$	−386.891			−1.34805
$288$		0			0
$289$	−98.3591	−	170.363i	−0.340343	−	0.589491i
$290$	−305.609	−	176.444i	−1.05382	−	0.608426i
$291$		0			0
$292$	−7.08860	−	26.4550i	−0.0242760	−	0.0905993i
$293$	−286.280	+	76.7084i	−0.977064	+	0.261804i	−0.711808	−	0.702374i	$-0.752123\pi$
$293$	−286.280	+	76.7084i	−0.977064	+	0.261804i	−0.265256	+	0.964178i	$0.585457\pi$
$294$		0			0
$295$	215.380	−	373.050i	0.730103	−	1.26457i
$296$	51.6376	−	29.8130i	0.174451	−	0.100720i
$297$		0			0
$298$			41.0405i			0.137720i
$299$	−260.351	−	242.301i	−0.870738	−	0.810371i
$300$		0			0
$301$	−329.479	−	88.2837i	−1.09462	−	0.293301i
$302$	−31.6350	−	54.7934i	−0.104752	−	0.181435i
$303$		0			0
$304$	−27.9946	+	27.9946i	−0.0920875	+	0.0920875i
$305$	165.041	+	615.940i	0.541117	+	2.01948i
$306$		0			0
$307$	221.215	+	221.215i	0.720571	+	0.720571i	0.968722	−	0.248150i	$-0.0798227\pi$
$307$	221.215	+	221.215i	0.720571	+	0.720571i	−0.248150	+	0.968722i	$0.579823\pi$
$308$	−155.642	+	269.580i	−0.505331	+	0.875259i
$309$		0			0
$310$	−54.0969	+	201.892i	−0.174506	+	0.651266i
$311$		−	12.5556i		−	0.0403716i	−0.999796	−	0.0201858i	$-0.993574\pi$
$311$		−	12.5556i		−	0.0403716i	0.999796	−	0.0201858i	$-0.00642578\pi$
$312$		0			0
$313$	590.956			1.88804			0.944018	−	0.329893i	$-0.107013\pi$
$313$	590.956			1.88804			0.944018	+	0.329893i	$0.107013\pi$
$314$	−331.156	−	88.7329i	−1.05464	−	0.282589i
$315$		0			0
$316$	−97.2622	−	56.1543i	−0.307792	−	0.177704i
$317$	−54.7137	+	54.7137i	−0.172598	+	0.172598i	−0.788120	−	0.615522i	$-0.788945\pi$
$317$	−54.7137	+	54.7137i	−0.172598	+	0.172598i	0.615522	+	0.788120i	$0.288945\pi$
$318$		0			0
$319$	−434.240	+	116.354i	−1.36125	+	0.364747i
$320$	51.1345	+	51.1345i	0.159795	+	0.159795i
$321$		0			0
$322$	−320.226	+	184.883i	−0.994491	+	0.574170i
$323$	24.6084	−	91.8398i	0.0761870	−	0.284334i
$324$		0			0
$325$	−704.809	+	216.243i	−2.16864	+	0.665363i
$326$	22.0804			0.0677314
$327$		0			0
$328$	57.2507	+	99.1611i	0.174545	+	0.302321i
$329$	−298.690	−	172.449i	−0.907874	−	0.524161i
$330$		0			0
$331$	−5.29073	−	19.7453i	−0.0159841	−	0.0596534i	0.957473	−	0.288522i	$-0.0931640\pi$
$331$	−5.29073	−	19.7453i	−0.0159841	−	0.0596534i	−0.973457	+	0.228869i	$0.926497\pi$
$332$	−12.5655	+	3.36693i	−0.0378480	+	0.0101413i
$333$		0			0
$334$	35.0077	−	60.6351i	0.104813	−	0.181542i
$335$	313.846	−	181.199i	0.936854	−	0.540893i
$336$		0			0
$337$		−	202.326i		−	0.600375i	−0.953880	−	0.300188i	$-0.902951\pi$
$337$		−	202.326i		−	0.600375i	0.953880	−	0.300188i	$-0.0970493\pi$
$338$	225.827	−	78.2575i	0.668127	−	0.231531i
$339$		0			0
$340$	−167.753	−	44.9493i	−0.493392	−	0.132204i
$341$	133.136	+	230.599i	0.390429	+	0.676243i
$342$		0			0
$343$	−45.0296	+	45.0296i	−0.131282	+	0.131282i
$344$	26.1278	+	97.5103i	0.0759529	+	0.283460i
$345$		0			0
$346$	−168.425	−	168.425i	−0.486776	−	0.486776i
$347$	278.263	−	481.966i	0.801911	−	1.38895i	−0.116446	−	0.993197i	$-0.537150\pi$
$347$	278.263	−	481.966i	0.801911	−	1.38895i	0.918357	−	0.395753i	$-0.129517\pi$
$348$		0			0
$349$	119.978	−	447.764i	0.343777	−	1.28299i	−0.550258	−	0.834995i	$-0.685471\pi$
$349$	119.978	−	447.764i	0.343777	−	1.28299i	0.894035	−	0.447998i	$-0.147863\pi$
$350$			766.480i			2.18994i
$351$		0			0
$352$	92.1254			0.261720
$353$	272.941	+	73.1344i	0.773205	+	0.207180i	0.623787	−	0.781595i	$-0.285593\pi$
$353$	272.941	+	73.1344i	0.773205	+	0.207180i	0.149418	+	0.988774i	$0.452260\pi$
$354$		0			0
$355$	250.474	+	144.611i	0.705562	+	0.407356i
$356$	−163.639	+	163.639i	−0.459659	+	0.459659i
$357$		0			0
$358$	427.630	−	114.583i	1.19450	−	0.320064i
$359$	280.398	+	280.398i	0.781054	+	0.781054i	0.980009	−	0.198955i	$-0.0637547\pi$
$359$	280.398	+	280.398i	0.781054	+	0.781054i	−0.198955	+	0.980009i	$0.563755\pi$
$360$		0			0
$361$	227.797	−	131.519i	0.631018	−	0.364318i
$362$	7.12999	−	26.6095i	0.0196961	−	0.0735069i
$363$		0			0
$364$	−8.91709	−	248.323i	−0.0244975	−	0.682205i
$365$	−123.786			−0.339141
$366$		0			0
$367$	−295.943	−	512.588i	−0.806384	−	1.39670i	−0.915353	−	0.402653i	$-0.868088\pi$
$367$	−295.943	−	512.588i	−0.806384	−	1.39670i	0.108968	−	0.994045i	$-0.465245\pi$
$368$	94.7718	+	54.7165i	0.257532	+	0.148686i
$369$		0			0
$370$	−69.7494	−	260.308i	−0.188512	−	0.703536i
$371$	360.667	−	96.6405i	0.972149	−	0.260487i
$372$		0			0
$373$	255.943	−	443.306i	0.686174	−	1.18849i	−0.286892	−	0.957963i	$-0.592622\pi$
$373$	255.943	−	443.306i	0.686174	−	1.18849i	0.973066	−	0.230525i	$-0.0740445\pi$
$374$	−191.606	+	110.623i	−0.512314	+	0.295785i
$375$		0			0
$376$			102.073i			0.271472i
$377$	244.483	−	262.695i	0.648496	−	0.696804i
$378$		0			0
$379$	197.686	+	52.9699i	0.521600	+	0.139762i	0.510006	−	0.860171i	$-0.329643\pi$
$379$	197.686	+	52.9699i	0.521600	+	0.139762i	0.0115932	+	0.999933i	$0.496310\pi$
$380$	89.4681	+	154.963i	0.235442	+	0.407798i
$381$		0			0
$382$	−142.951	+	142.951i	−0.374218	+	0.374218i
$383$	−84.9951	−	317.206i	−0.221919	−	0.828214i	−0.983615	−	0.180280i	$-0.942300\pi$
$383$	−84.9951	−	317.206i	−0.221919	−	0.828214i	0.761696	−	0.647934i	$-0.224367\pi$
$384$		0			0
$385$	994.834	+	994.834i	2.58398	+	2.58398i
$386$	118.662	−	205.529i	0.307415	−	0.532459i
$387$		0			0
$388$	18.0850	−	67.4941i	0.0466108	−	0.173954i
$389$		−	393.984i		−	1.01281i	−0.862295	−	0.506406i	$-0.830974\pi$
$389$		−	393.984i		−	1.01281i	0.862295	−	0.506406i	$-0.169026\pi$
$390$		0			0
$391$	−262.813			−0.672156
$392$	−115.666	−	30.9926i	−0.295066	−	0.0790628i
$393$		0			0
$394$	208.680	+	120.481i	0.529644	+	0.305790i
$395$	−358.928	+	358.928i	−0.908678	+	0.908678i
$396$		0			0
$397$	−115.976	+	31.0756i	−0.292130	+	0.0782760i	−0.401908	−	0.915680i	$-0.631653\pi$
$397$	−115.976	+	31.0756i	−0.292130	+	0.0782760i	0.109778	+	0.993956i	$0.464986\pi$
$398$	−161.726	−	161.726i	−0.406346	−	0.406346i
$399$		0			0
$400$	196.451	−	113.421i	0.491127	−	0.283552i
$401$	−85.9977	+	320.948i	−0.214458	+	0.800368i	0.771899	+	0.635746i	$0.219307\pi$
$401$	−85.9977	+	320.948i	−0.214458	+	0.800368i	−0.986357	+	0.164623i	$0.947359\pi$
$402$		0			0
$403$	−187.771	−	99.6019i	−0.465933	−	0.247151i
$404$	234.338			0.580045
$405$		0			0
$406$	−186.548	−	323.110i	−0.459477	−	0.795837i
$407$	−297.321	−	171.658i	−0.730518	−	0.421765i
$408$		0			0
$409$	−113.840	−	424.856i	−0.278337	−	1.03877i	−0.953572	−	0.301165i	$-0.902625\pi$
$409$	−113.840	−	424.856i	−0.278337	−	1.03877i	0.675235	−	0.737603i	$-0.264042\pi$
$410$	499.877	−	133.942i	1.21921	−	0.326687i
$411$		0			0
$412$	−184.178	+	319.005i	−0.447034	+	0.774285i
$413$	394.412	−	227.714i	0.954993	−	0.551366i
$414$		0			0
$415$			58.7958i			0.141677i
$416$	−62.3262	+	39.0313i	−0.149823	+	0.0938253i
$417$		0			0
$418$	220.187	+	58.9990i	0.526764	+	0.141146i
$419$	−62.4764	−	108.212i	−0.149108	−	0.258263i	0.781790	−	0.623542i	$-0.214307\pi$
$419$	−62.4764	−	108.212i	−0.149108	−	0.258263i	−0.930898	+	0.365279i	$0.880974\pi$
$420$		0			0
$421$	9.46318	−	9.46318i	0.0224779	−	0.0224779i	−0.695779	−	0.718256i	$-0.744940\pi$
$421$	9.46318	−	9.46318i	0.0224779	−	0.0224779i	0.718256	+	0.695779i	$0.244940\pi$
$422$	−65.8389	−	245.714i	−0.156016	−	0.582261i
$423$		0			0
$424$	−78.1394	−	78.1394i	−0.184291	−	0.184291i
$425$	−272.390	+	471.794i	−0.640918	+	1.11010i
$426$		0			0
$427$	−174.492	+	651.212i	−0.408646	+	1.52509i
$428$			14.3040i			0.0334205i
$429$		0			0
$430$	456.263			1.06108
$431$	−698.341	−	187.120i	−1.62028	−	0.434153i	−0.669197	−	0.743085i	$-0.733362\pi$
$431$	−698.341	−	187.120i	−1.62028	−	0.434153i	−0.951084	+	0.308932i	$0.900028\pi$
$432$		0			0
$433$	35.4730	+	20.4803i	0.0819237	+	0.0472987i	0.540402	−	0.841407i	$-0.318272\pi$
$433$	35.4730	+	20.4803i	0.0819237	+	0.0472987i	−0.458479	+	0.888705i	$0.651605\pi$
$434$	−156.259	+	156.259i	−0.360044	+	0.360044i
$435$		0			0
$436$	22.0648	−	5.91224i	0.0506073	−	0.0135602i
$437$	191.471	+	191.471i	0.438148	+	0.438148i
$438$		0			0
$439$	−576.214	+	332.678i	−1.31256	+	0.757808i	−0.982520	−	0.186159i	$-0.940396\pi$
$439$	−576.214	+	332.678i	−1.31256	+	0.757808i	−0.330042	+	0.943966i	$0.607063\pi$
$440$	107.767	−	402.191i	0.244924	−	0.914069i
$441$		0			0
$442$	82.7596	−	156.020i	0.187239	−	0.352985i
$443$	−267.578			−0.604013			−0.302006	−	0.953306i	$-0.597656\pi$
$443$	−267.578			−0.604013			−0.302006	+	0.953306i	$0.597656\pi$
$444$		0			0
$445$	522.973	+	905.816i	1.17522	+	2.03554i
$446$	−477.408	−	275.631i	−1.07042	−	0.618008i
$447$		0			0
$448$	19.7883	+	73.8510i	0.0441703	+	0.164846i
$449$	543.945	−	145.750i	1.21146	−	0.324610i	0.404125	−	0.914704i	$-0.367576\pi$
$449$	543.945	−	145.750i	1.21146	−	0.324610i	0.807335	+	0.590094i	$0.200909\pi$
$450$		0			0
$451$	329.640	−	570.953i	0.730909	−	1.26597i
$452$	−201.624	+	116.408i	−0.446070	+	0.257539i
$453$		0			0
$454$			188.550i			0.415308i
$455$	−1094.53	−	251.554i	−2.40556	−	0.552866i
$456$		0			0
$457$	−643.576	−	172.446i	−1.40826	−	0.377343i	−0.526958	−	0.849891i	$-0.676668\pi$
$457$	−643.576	−	172.446i	−1.40826	−	0.377343i	−0.881305	+	0.472548i	$0.843334\pi$
$458$	304.866	+	528.043i	0.665646	+	1.15293i
$459$		0			0
$460$	349.738	−	349.738i	0.760299	−	0.760299i
$461$	92.7172	+	346.025i	0.201122	+	0.750597i	0.990597	+	0.136814i	$0.0436863\pi$
$461$	92.7172	+	346.025i	0.201122	+	0.750597i	−0.789475	+	0.613783i	$0.789647\pi$
$462$		0			0
$463$	−630.292	−	630.292i	−1.36132	−	1.36132i	−0.872236	−	0.489084i	$-0.837331\pi$
$463$	−630.292	−	630.292i	−1.36132	−	1.36132i	−0.489084	−	0.872236i	$-0.662669\pi$
$464$	−55.2093	+	95.6252i	−0.118985	+	0.206089i
$465$		0			0
$466$	16.1569	−	60.2983i	0.0346714	−	0.129395i
$467$		−	425.264i		−	0.910630i	−0.890331	−	0.455315i	$-0.849527\pi$
$467$		−	425.264i		−	0.910630i	0.890331	−	0.455315i	$-0.150473\pi$
$468$		0			0
$469$	383.151			0.816953
$470$	445.621	+	119.404i	0.948130	+	0.254051i
$471$		0			0
$472$	−116.727	−	67.3926i	−0.247304	−	0.142781i
$473$	411.009	−	411.009i	0.868940	−	0.868940i
$474$		0			0
$475$	542.171	−	145.274i	1.14141	−	0.305841i
$476$	−129.836	−	129.836i	−0.272765	−	0.272765i
$477$		0			0
$478$	−27.4441	+	15.8448i	−0.0574144	+	0.0331482i
$479$	71.3059	−	266.117i	0.148864	−	0.555568i	−0.850689	−	0.525670i	$-0.823815\pi$
$479$	71.3059	−	266.117i	0.148864	−	0.555568i	0.999553	−	0.0298988i	$-0.00951850\pi$
$480$		0			0
$481$	273.876	−	9.83470i	0.569389	−	0.0204464i
$482$	680.212			1.41123
$483$		0			0
$484$	−144.221	−	249.799i	−0.297978	−	0.516113i
$485$	−273.502	−	157.907i	−0.563923	−	0.325581i
$486$		0			0
$487$	−165.703	−	618.410i	−0.340252	−	1.26984i	−0.898062	−	0.439868i	$-0.855025\pi$
$487$	−165.703	−	618.410i	−0.340252	−	1.26984i	0.557811	−	0.829968i	$-0.311641\pi$
$488$	192.728	−	51.6413i	0.394934	−	0.105822i
$489$		0			0
$490$	−270.608	+	468.707i	−0.552261	+	0.956545i
$491$	−490.748	+	283.333i	−0.999486	+	0.577053i	−0.908096	−	0.418762i	$-0.862464\pi$
$491$	−490.748	+	283.333i	−0.999486	+	0.577053i	−0.0913898	+	0.995815i	$0.529131\pi$
$492$		0			0
$493$		−	265.180i		−	0.537890i
$494$	−173.961	+	53.3732i	−0.352148	+	0.108043i
$495$		0			0
$496$	63.1722	+	16.9269i	0.127363	+	0.0341269i
$497$	152.893	+	264.818i	0.307631	+	0.532833i
$498$		0			0
$499$	−409.292	+	409.292i	−0.820224	+	0.820224i	−0.986140	−	0.165916i	$-0.946942\pi$
$499$	−409.292	+	409.292i	−0.820224	+	0.820224i	0.165916	+	0.986140i	$0.446942\pi$
$500$	−148.377	−	553.752i	−0.296755	−	1.10750i
$501$		0			0
$502$	−211.776	−	211.776i	−0.421865	−	0.421865i
$503$	111.621	−	193.333i	0.221910	−	0.384360i	−0.733478	−	0.679714i	$-0.762104\pi$
$503$	111.621	−	193.333i	0.221910	−	0.384360i	0.955388	+	0.295354i	$0.0954374\pi$
$504$		0			0
$505$	274.125	−	1023.05i	0.542822	−	2.02584i
$506$		−	630.097i		−	1.24525i
$507$		0			0
$508$	−54.0363			−0.106371
$509$	414.332	+	111.020i	0.814012	+	0.218114i	0.641727	−	0.766933i	$-0.278218\pi$
$509$	414.332	+	111.020i	0.814012	+	0.218114i	0.172285	+	0.985047i	$0.444885\pi$
$510$		0			0
$511$	−113.341	−	65.4375i	−0.221802	−	0.128058i
$512$	16.0000	−	16.0000i	0.0312500	−	0.0312500i
$513$		0			0
$514$	372.134	−	99.7130i	0.723996	−	0.193994i
$515$	1177.23	+	1177.23i	2.28588	+	2.28588i
$516$		0			0
$517$	508.983	−	293.861i	0.984492	−	0.568397i
$518$	73.7436	−	275.215i	0.142362	−	0.531303i
$519$		0			0
$520$	97.4906	+	317.755i	0.187482	+	0.611067i
$521$	470.908			0.903854			0.451927	−	0.892055i	$-0.350737\pi$
$521$	470.908			0.903854			0.451927	+	0.892055i	$0.350737\pi$
$522$		0			0
$523$	455.785	+	789.442i	0.871481	+	1.50945i	0.860464	+	0.509511i	$0.170174\pi$
$523$	455.785	+	789.442i	0.871481	+	1.50945i	0.0110172	+	0.999939i	$0.496493\pi$
$524$	111.835	+	64.5682i	0.213426	+	0.123222i
$525$		0			0
$526$	−86.5075	−	322.851i	−0.164463	−	0.613784i
$527$	−151.714	+	40.6515i	−0.287881	+	0.0771376i
$528$		0			0
$529$	109.737	−	190.070i	0.207443	−	0.359301i
$530$	−432.539	+	249.726i	−0.816110	+	0.471182i
$531$		0			0
$532$			189.183i			0.355607i
$533$	18.8858	+	525.932i	0.0354331	+	0.986739i
$534$		0			0
$535$	62.4466	+	16.7325i	0.116723	+	0.0312758i
$536$	−56.6973	−	98.2025i	−0.105778	−	0.183214i
$537$		0			0
$538$	−466.361	+	466.361i	−0.866842	+	0.866842i
$539$	178.450	+	665.986i	0.331077	+	1.23559i
$540$		0			0
$541$	−393.572	−	393.572i	−0.727490	−	0.727490i	0.242629	−	0.970119i	$-0.421990\pi$
$541$	−393.572	−	393.572i	−0.727490	−	0.727490i	−0.970119	+	0.242629i	$0.921990\pi$
$542$	326.130	−	564.873i	0.601716	−	1.04220i
$543$		0			0
$544$	−14.0647	+	52.4900i	−0.0258542	+	0.0964890i
$545$		−	103.244i		−	0.189438i
$546$		0			0
$547$	−388.679			−0.710565			−0.355283	−	0.934759i	$-0.615615\pi$
$547$	−388.679			−0.710565			−0.355283	+	0.934759i	$0.615615\pi$
$548$	−394.424	−	105.686i	−0.719751	−	0.192857i
$549$		0			0
$550$	−1131.13	−	653.059i	−2.05660	−	1.18738i
$551$	−193.195	+	193.195i	−0.350626	+	0.350626i
$552$		0			0
$553$	−518.382	+	138.900i	−0.937399	+	0.251175i
$554$	24.5533	+	24.5533i	0.0443200	+	0.0443200i
$555$		0			0
$556$	−110.178	+	63.6113i	−0.198162	+	0.114409i
$557$	−183.042	+	683.123i	−0.328622	+	1.22643i	0.581999	+	0.813190i	$0.302271\pi$
$557$	−183.042	+	683.123i	−0.328622	+	1.22643i	−0.910621	+	0.413244i	$0.864396\pi$
$558$		0			0
$559$	−103.928	+	452.197i	−0.185917	+	0.808939i
$560$	345.558			0.617069
$561$		0			0
$562$	276.591	+	479.071i	0.492156	+	0.852439i
$563$	514.657	+	297.138i	0.914134	+	0.527776i	0.881759	−	0.471700i	$-0.156360\pi$
$563$	514.657	+	297.138i	0.914134	+	0.527776i	0.0323751	+	0.999476i	$0.489693\pi$
$564$		0			0
$565$	272.343	+	1016.40i	0.482023	+	1.79893i
$566$	−535.087	+	143.376i	−0.945383	+	0.253314i
$567$		0			0
$568$	45.2490	−	78.3735i	0.0796637	−	0.137982i
$569$	−101.268	+	58.4673i	−0.177976	+	0.102754i	−0.586341	−	0.810064i	$-0.699432\pi$
$569$	−101.268	+	58.4673i	−0.177976	+	0.102754i	0.408365	+	0.912819i	$0.366099\pi$
$570$		0			0
$571$			137.505i			0.240815i	0.992725	+	0.120408i	$0.0384201\pi$
$571$			137.505i			0.240815i	−0.992725	+	0.120408i	$0.961580\pi$
$572$	374.059	+	198.417i	0.653949	+	0.346883i
$573$		0			0
$574$	528.503	+	141.612i	0.920736	+	0.246711i
$575$	−775.750	−	1343.64i	−1.34913	−	2.33676i
$576$		0			0
$577$	−617.016	+	617.016i	−1.06935	+	1.06935i	−0.0719422	+	0.997409i	$0.522920\pi$
$577$	−617.016	+	617.016i	−1.06935	+	1.06935i	−0.997409	+	0.0719422i	$0.977080\pi$
$578$	72.0038	+	268.722i	0.124574	+	0.464917i
$579$		0			0
$580$	352.887	+	352.887i	0.608426	+	0.608426i
$581$	−31.0814	+	53.8345i	−0.0534963	+	0.0926583i
$582$		0			0
$583$	−164.680	+	614.594i	−0.282470	+	1.05419i
$584$			38.7328i			0.0663233i
$585$		0			0
$586$	419.143			0.715261
$587$	−373.261	−	100.015i	−0.635878	−	0.170383i	−0.0735425	−	0.997292i	$-0.523430\pi$
$587$	−373.261	−	100.015i	−0.635878	−	0.170383i	−0.562336	+	0.826909i	$0.690097\pi$
$588$		0			0
$589$	140.146	+	80.9136i	0.237940	+	0.137375i
$590$	−430.761	+	430.761i	−0.730103	+	0.730103i
$591$		0			0
$592$	−81.4506	+	21.8246i	−0.137585	+	0.0368659i
$593$	−536.353	−	536.353i	−0.904473	−	0.904473i	0.0913459	−	0.995819i	$-0.470883\pi$
$593$	−536.353	−	536.353i	−0.904473	−	0.904473i	−0.995819	+	0.0913459i	$0.970883\pi$
$594$		0			0
$595$	−718.704	+	414.944i	−1.20791	+	0.697385i
$596$	15.0219	−	56.0623i	0.0252045	−	0.0940643i
$597$		0			0
$598$	266.957	+	426.284i	0.446417	+	0.712850i
$599$	−344.623			−0.575331			−0.287666	−	0.957731i	$-0.592879\pi$
$599$	−344.623			−0.575331			−0.287666	+	0.957731i	$0.592879\pi$
$600$		0			0
$601$	−445.870	−	772.269i	−0.741879	−	1.28497i	−0.951639	−	0.307220i	$-0.900601\pi$
$601$	−445.870	−	772.269i	−0.741879	−	1.28497i	0.209759	−	0.977753i	$-0.432732\pi$
$602$	417.763	+	241.195i	0.693958	+	0.400657i
$603$		0			0
$604$	23.1584	+	86.4284i	0.0383417	+	0.143093i
$605$	−1259.25	+	337.415i	−2.08141	+	0.557711i
$606$		0			0
$607$	−232.733	+	403.106i	−0.383416	+	0.664096i	−0.991548	−	0.129740i	$-0.958586\pi$
$607$	−232.733	+	403.106i	−0.383416	+	0.664096i	0.608132	+	0.793836i	$0.291919\pi$
$608$	48.4881	−	27.9946i	0.0797501	−	0.0460437i
$609$		0			0
$610$		−	901.799i		−	1.47836i
$611$	−219.843	+	414.452i	−0.359809	+	0.678317i
$612$		0			0
$613$	851.290	+	228.103i	1.38873	+	0.372109i	0.874284	−	0.485415i	$-0.161332\pi$
$613$	851.290	+	228.103i	1.38873	+	0.372109i	0.514444	+	0.857524i	$0.327998\pi$
$614$	−221.215	−	383.156i	−0.360286	−	0.624033i
$615$		0			0
$616$	311.284	−	311.284i	0.505331	−	0.505331i
$617$	−293.787	−	1096.43i	−0.476154	−	1.77703i	−0.616960	−	0.786995i	$-0.711636\pi$
$617$	−293.787	−	1096.43i	−0.476154	−	1.77703i	0.140805	−	0.990037i	$-0.455031\pi$
$618$		0			0
$619$	69.6384	+	69.6384i	0.112501	+	0.112501i	0.761117	−	0.648615i	$-0.224651\pi$
$619$	69.6384	+	69.6384i	0.112501	+	0.112501i	−0.648615	+	0.761117i	$0.724651\pi$
$620$	147.796	−	255.989i	0.238380	−	0.412886i
$621$		0			0
$622$	−4.59566	+	17.1512i	−0.00738852	+	0.0275743i
$623$			1105.84i			1.77503i
$624$		0			0
$625$	−1173.32			−1.87731
$626$	−807.260	−	216.305i	−1.28955	−	0.345535i
$627$		0			0
$628$	419.888	+	242.423i	0.668612	+	0.386023i
$629$	143.197	−	143.197i	0.227658	−	0.227658i
$630$		0			0
$631$	616.962	−	165.314i	0.977752	−	0.261988i	0.265655	−	0.964068i	$-0.414412\pi$
$631$	616.962	−	165.314i	0.977752	−	0.261988i	0.712098	+	0.702080i	$0.247745\pi$
$632$	112.309	+	112.309i	0.177704	+	0.177704i
$633$		0			0
$634$	94.7669	−	54.7137i	0.149475	−	0.0862992i
$635$	−63.2108	+	235.906i	−0.0995445	+	0.371505i
$636$		0			0
$637$	−402.891	−	374.959i	−0.632481	−	0.588632i
$638$	635.772			0.996507
$639$		0			0
$640$	−51.1345	−	88.5675i	−0.0798976	−	0.138387i
$641$	792.951	+	457.811i	1.23705	+	0.714213i	0.968491	−	0.249049i	$-0.0801181\pi$
$641$	792.951	+	457.811i	1.23705	+	0.714213i	0.268563	+	0.963262i	$0.413451\pi$
$642$		0			0
$643$	109.397	+	408.276i	0.170136	+	0.634955i	0.997329	+	0.0730378i	$0.0232694\pi$
$643$	109.397	+	408.276i	0.170136	+	0.634955i	−0.827194	+	0.561917i	$0.810064\pi$
$644$	505.109	−	135.343i	0.784330	−	0.210161i
$645$		0			0
$646$	−67.2314	+	116.448i	−0.104073	+	0.180260i
$647$	−557.382	+	321.805i	−0.861487	+	0.497380i	−0.864510	−	0.502616i	$-0.832371\pi$
$647$	−557.382	+	321.805i	−0.861487	+	0.497380i	0.00302290	+	0.999995i	$0.499038\pi$
$648$		0			0
$649$			776.071i			1.19579i
$650$	1041.94	−	37.4153i	1.60298	−	0.0575619i
$651$		0			0
$652$	−30.1624	−	8.08200i	−0.0462614	−	0.0123957i
$653$	−149.123	−	258.289i	−0.228366	−	0.395542i	0.728958	−	0.684559i	$-0.240005\pi$
$653$	−149.123	−	258.289i	−0.228366	−	0.395542i	−0.957324	+	0.289016i	$0.906672\pi$
$654$		0			0
$655$	412.708	−	412.708i	0.630088	−	0.630088i
$656$	−41.9104	−	156.412i	−0.0638878	−	0.238433i
$657$		0			0
$658$	344.898	+	344.898i	0.524161	+	0.524161i
$659$	−322.944	+	559.356i	−0.490052	+	0.848794i	−0.999934	−	0.0114495i	$-0.996355\pi$
$659$	−322.944	+	559.356i	−0.490052	+	0.848794i	0.509883	+	0.860244i	$0.329689\pi$
$660$		0			0
$661$	251.425	−	938.332i	0.380371	−	1.41956i	−0.464965	−	0.885329i	$-0.653933\pi$
$661$	251.425	−	938.332i	0.380371	−	1.41956i	0.845336	−	0.534235i	$-0.179400\pi$
$662$			28.9091i			0.0436693i
$663$		0			0
$664$	18.3972			0.0277067
$665$	825.913	+	221.303i	1.24197	+	0.332786i
$666$		0			0
$667$	654.035	+	377.607i	0.980562	+	0.566128i
$668$	−70.0153	+	70.0153i	−0.104813	+	0.104813i
$669$		0			0
$670$	−495.045	+	132.647i	−0.738873	+	0.197981i
$671$	−812.354	−	812.354i	−1.21066	−	1.21066i
$672$		0			0
$673$	−712.407	+	411.308i	−1.05855	+	0.611156i	−0.925032	−	0.379890i	$-0.875962\pi$
$673$	−712.407	+	411.308i	−1.05855	+	0.611156i	−0.133522	+	0.991046i	$0.542629\pi$
$674$	−74.0566	+	276.383i	−0.109876	+	0.410064i
$675$		0			0
$676$	−337.129	+	24.2434i	−0.498712	+	0.0358631i
$677$	−195.713			−0.289089			−0.144544	−	0.989498i	$-0.546172\pi$
$677$	−195.713			−0.289089			−0.144544	+	0.989498i	$0.546172\pi$
$678$		0			0
$679$	−166.949	−	289.165i	−0.245875	−	0.425868i
$680$	212.702	+	122.804i	0.312798	+	0.180594i
$681$		0			0
$682$	−97.4626	−	363.735i	−0.142907	−	0.533336i
$683$	628.395	−	168.378i	0.920052	−	0.246527i	0.232444	−	0.972610i	$-0.425328\pi$
$683$	628.395	−	168.378i	0.920052	−	0.246527i	0.687607	+	0.726083i	$0.258661\pi$
$684$		0			0
$685$	−922.780	+	1598.30i	−1.34712	+	2.33329i
$686$	77.9936	−	45.0296i	0.113693	−	0.0656408i
$687$		0			0
$688$		−	142.765i		−	0.207507i
$689$	−148.977	−	485.566i	−0.216222	−	0.704741i
$690$		0			0
$691$	−303.752	−	81.3900i	−0.439583	−	0.117786i	0.0322384	−	0.999480i	$-0.489736\pi$
$691$	−303.752	−	81.3900i	−0.439583	−	0.117786i	−0.471821	+	0.881694i	$0.656403\pi$
$692$	168.425	+	291.720i	0.243388	+	0.421561i
$693$		0			0
$694$	−556.526	+	556.526i	−0.801911	+	0.801911i
$695$	148.823	+	555.414i	0.214134	+	0.799157i
$696$		0			0
$697$	274.985	+	274.985i	0.394526	+	0.394526i
$698$	−327.786	+	567.742i	−0.469608	+	0.813385i
$699$		0			0
$700$	280.551	−	1047.03i	0.400787	−	1.49576i
$701$		−	769.901i		−	1.09829i	−0.835727	−	0.549145i	$-0.814954\pi$
$701$		−	769.901i		−	1.09829i	0.835727	−	0.549145i	$-0.185046\pi$
$702$		0			0
$703$	−208.651			−0.296800
$704$	−125.846	−	33.7202i	−0.178758	−	0.0478980i
$705$		0			0
$706$	−346.076	−	199.807i	−0.490192	−	0.283013i
$707$	791.810	−	791.810i	1.11996	−	1.11996i
$708$		0			0
$709$	918.547	−	246.124i	1.29555	−	0.347142i	0.455786	−	0.890089i	$-0.349358\pi$
$709$	918.547	−	246.124i	1.29555	−	0.347142i	0.839767	+	0.542947i	$0.182692\pi$
$710$	−289.223	−	289.223i	−0.407356	−	0.407356i
$711$		0			0
$712$	283.430	−	163.639i	0.398076	−	0.229829i
$713$	115.773	−	432.071i	0.162374	−	0.605990i
$714$		0			0
$715$	1303.80	−	1400.92i	1.82349	−	1.95933i
$716$	−626.093			−0.874432
$717$		0			0
$718$	−280.398	−	485.664i	−0.390527	−	0.676412i
$719$	1165.21	+	672.733i	1.62060	+	0.935651i	0.986761	+	0.162183i	$0.0518535\pi$
$719$	1165.21	+	672.733i	1.62060	+	0.935651i	0.633835	+	0.773468i	$0.281480\pi$
$720$		0			0
$721$	455.571	+	1700.21i	0.631860	+	2.35813i
$722$	−359.316	+	96.2785i	−0.497668	+	0.133350i
$723$		0			0
$724$	−19.4795	+	33.7395i	−0.0269054	+	0.0466015i
$725$	1355.74	−	782.736i	1.86998	−	1.07964i
$726$		0			0
$727$		−	681.807i		−	0.937837i	−0.883241	−	0.468918i	$-0.844644\pi$
$727$		−	681.807i		−	0.937837i	0.883241	−	0.468918i	$-0.155356\pi$
$728$	−78.7114	+	342.479i	−0.108120	+	0.470438i
$729$		0			0
$730$	169.095	+	45.3090i	0.231637	+	0.0620671i
$731$	171.431	+	296.927i	0.234516	+	0.406193i
$732$		0			0
$733$	760.545	−	760.545i	1.03758	−	1.03758i	0.0383126	−	0.999266i	$-0.487802\pi$
$733$	760.545	−	760.545i	1.03758	−	1.03758i	0.999266	−	0.0383126i	$-0.0121983\pi$
$734$	216.645	+	808.531i	0.295157	+	1.10154i
$735$		0			0
$736$	−109.433	−	109.433i	−0.148686	−	0.148686i
$737$	−326.454	+	565.434i	−0.442949	+	0.767210i
$738$		0			0
$739$	202.762	−	756.716i	0.274373	−	1.02397i	−0.681888	−	0.731457i	$-0.738841\pi$
$739$	202.762	−	756.716i	0.274373	−	1.02397i	0.956260	−	0.292517i	$-0.0944927\pi$
$740$			381.118i			0.515024i
$741$		0			0
$742$	−528.053			−0.711662
$743$	−779.633	−	208.902i	−1.04930	−	0.281160i	−0.307340	−	0.951600i	$-0.599439\pi$
$743$	−779.633	−	208.902i	−1.04930	−	0.281160i	−0.741964	+	0.670440i	$0.766106\pi$
$744$		0			0
$745$	−227.178	−	131.161i	−0.304937	−	0.176056i
$746$	−511.886	+	511.886i	−0.686174	+	0.686174i
$747$		0			0
$748$	302.229	−	80.9820i	0.404049	−	0.108265i
$749$	48.3319	+	48.3319i	0.0645286	+	0.0645286i
$750$		0			0
$751$	858.524	−	495.669i	1.14317	−	0.660012i	0.195959	−	0.980612i	$-0.437218\pi$
$751$	858.524	−	495.669i	1.14317	−	0.660012i	0.947215	+	0.320600i	$0.103885\pi$
$752$	37.3615	−	139.435i	0.0496828	−	0.185419i
$753$		0			0
$754$	−430.123	+	269.361i	−0.570455	+	0.357243i
$755$	404.410			0.535642
$756$		0			0
$757$	−370.164	−	641.143i	−0.488988	−	0.846952i	0.510932	−	0.859621i	$-0.329301\pi$
$757$	−370.164	−	641.143i	−0.488988	−	0.846952i	−0.999920	+	0.0126691i	$0.995967\pi$
$758$	−250.656	−	144.716i	−0.330681	−	0.190919i
$759$		0			0
$760$	−65.4952	−	244.431i	−0.0861778	−	0.321620i
$761$	−762.920	+	204.424i	−1.00252	+	0.268625i	−0.722502	−	0.691368i	$-0.757008\pi$
$761$	−762.920	+	204.424i	−1.00252	+	0.268625i	−0.280021	+	0.959994i	$0.590341\pi$
$762$		0			0
$763$	54.5781	−	94.5320i	0.0715309	−	0.123895i
$764$	247.599	−	142.951i	0.324082	−	0.187109i
$765$		0			0
$766$			464.422i			0.606295i
$767$	−328.803	−	525.040i	−0.428687	−	0.684538i
$768$		0			0
$769$	12.3641	+	3.31296i	0.0160782	+	0.00430814i	0.266849	−	0.963738i	$-0.414017\pi$
$769$	12.3641	+	3.31296i	0.0160782	+	0.00430814i	−0.250771	+	0.968046i	$0.580684\pi$
$770$	−994.834	−	1723.10i	−1.29199	−	2.23780i
$771$		0			0
$772$	−237.325	+	237.325i	−0.307415	+	0.307415i
$773$	−24.6452	−	91.9770i	−0.0318825	−	0.118987i	0.948151	−	0.317821i	$-0.102951\pi$
$773$	−24.6452	−	91.9770i	−0.0318825	−	0.118987i	−0.980033	+	0.198834i	$0.936284\pi$
$774$		0			0
$775$	−655.648	−	655.648i	−0.845997	−	0.845997i
$776$	−49.4091	+	85.5790i	−0.0636715	+	0.110282i
$777$		0			0
$778$	−144.208	+	538.192i	−0.185358	+	0.691764i
$779$		−	400.678i		−	0.514349i
$780$		0			0
$781$	−521.072			−0.667186
$782$	359.009	+	96.1962i	0.459091	+	0.123013i
$783$		0			0
$784$	146.659	+	84.6734i	0.187064	+	0.108002i
$785$	1549.52	−	1549.52i	1.97391	−	1.97391i
$786$		0			0
$787$	−869.425	+	232.962i	−1.10473	+	0.296012i	−0.764690	−	0.644398i	$-0.777108\pi$
$787$	−869.425	+	232.962i	−1.10473	+	0.296012i	−0.340042	+	0.940410i	$0.610441\pi$
$788$	−240.963	−	240.963i	−0.305790	−	0.305790i
$789$		0			0
$790$	621.681	−	358.928i	0.786938	−	0.454339i
$791$	−287.939	+	1074.60i	−0.364018	+	1.35854i
$792$		0			0
$793$	893.762	+	205.412i	1.12706	+	0.259032i
$794$	169.800			0.213854
$795$		0			0
$796$	161.726	+	280.117i	0.203173	+	0.351906i
$797$	559.840	+	323.224i	0.702435	+	0.405551i	0.808254	−	0.588835i	$-0.200413\pi$
$797$	559.840	+	323.224i	0.702435	+	0.405551i	−0.105819	+	0.994385i	$0.533746\pi$
$798$		0			0
$799$	89.7268	+	334.865i	0.112299	+	0.419105i
$800$	−309.872	+	83.0299i	−0.387340	+	0.103787i
$801$		0			0
$802$	234.950	−	406.945i	0.292955	−	0.507413i
$803$	193.139	−	111.509i	0.240521	−	0.138865i
$804$		0			0
$805$		−	2363.47i		−	2.93599i
$806$	220.043	+	204.788i	0.273006	+	0.254079i
$807$		0			0
$808$	−320.112	−	85.7738i	−0.396178	−	0.106156i
$809$	−572.693	−	991.934i	−0.707903	−	1.22612i	−0.965634	−	0.259907i	$-0.916308\pi$
$809$	−572.693	−	991.934i	−0.707903	−	1.22612i	0.257731	−	0.966217i	$-0.417025\pi$
$810$		0			0
$811$	394.302	−	394.302i	0.486192	−	0.486192i	−0.420910	−	0.907102i	$-0.638289\pi$
$811$	394.302	−	394.302i	0.486192	−	0.486192i	0.907102	+	0.420910i	$0.138289\pi$
$812$	136.562	+	509.657i	0.168180	+	0.627657i
$813$		0			0
$814$	343.316	+	343.316i	0.421765	+	0.421765i
$815$	−70.5670	+	122.226i	−0.0865853	+	0.149970i
$816$		0			0
$817$	91.4296	−	341.220i	0.111909	−	0.417650i
$818$			622.032i			0.760431i
$819$		0			0
$820$	−731.871			−0.892526
$821$	684.846	+	183.504i	0.834161	+	0.223513i	0.650528	−	0.759482i	$-0.274548\pi$
$821$	684.846	+	183.504i	0.834161	+	0.223513i	0.183633	+	0.982995i	$0.441214\pi$
$822$		0			0
$823$	479.938	+	277.093i	0.583157	+	0.336686i	0.762387	−	0.647121i	$-0.224027\pi$
$823$	479.938	+	277.093i	0.583157	+	0.336686i	−0.179230	+	0.983807i	$0.557361\pi$
$824$	368.356	−	368.356i	0.447034	−	0.447034i
$825$		0			0
$826$	−622.126	+	166.698i	−0.753179	+	0.201814i
$827$	−140.395	−	140.395i	−0.169764	−	0.169764i	0.617112	−	0.786876i	$-0.288303\pi$
$827$	−140.395	−	140.395i	−0.169764	−	0.169764i	−0.786876	+	0.617112i	$0.788303\pi$
$828$		0			0
$829$	446.523	−	257.800i	0.538628	−	0.310977i	−0.205894	−	0.978574i	$-0.566010\pi$
$829$	446.523	−	257.800i	0.538628	−	0.310977i	0.744523	+	0.667597i	$0.232677\pi$
$830$	21.5208	−	80.3165i	0.0259286	−	0.0967669i
$831$		0			0
$832$	99.4256	−	30.5048i	0.119502	−	0.0366645i
$833$	−406.701			−0.488236
$834$		0			0
$835$	223.762	+	387.568i	0.267979	+	0.464153i
$836$	−279.186	−	161.188i	−0.333955	−	0.192809i
$837$		0			0
$838$	45.7359	+	170.689i	0.0545775	+	0.203686i
$839$	840.624	−	225.244i	1.00194	−	0.268468i	0.279679	−	0.960094i	$-0.409772\pi$
$839$	840.624	−	225.244i	1.00194	−	0.268468i	0.722256	+	0.691626i	$0.243105\pi$
$840$		0			0
$841$	39.4922	−	68.4025i	0.0469586	−	0.0813348i
$842$	−16.3907	+	9.46318i	−0.0194664	+	0.0112389i
$843$		0			0
$844$			359.751i			0.426245i
$845$	−288.529	+	1500.16i	−0.341454	+	1.77534i
$846$		0			0
$847$	−1331.36	−	356.737i	−1.57186	−	0.421177i
$848$	78.1394	+	135.341i	0.0921456	+	0.159601i
$849$		0			0
$850$	544.780	−	544.780i	0.640918	−	0.640918i
$851$	149.271	+	557.087i	0.175406	+	0.654626i
$852$		0			0
$853$	−42.9256	−	42.9256i	−0.0503230	−	0.0503230i	0.681497	−	0.731820i	$-0.261329\pi$
$853$	−42.9256	−	42.9256i	−0.0503230	−	0.0503230i	−0.731820	+	0.681497i	$0.761329\pi$
$854$	476.720	−	825.703i	0.558220	−	0.966866i
$855$		0			0
$856$	5.23561	−	19.5396i	0.00611637	−	0.0228266i
$857$		−	236.541i		−	0.276011i	−0.990431	−	0.138005i	$-0.955931\pi$
$857$		−	236.541i		−	0.276011i	0.990431	−	0.138005i	$-0.0440692\pi$
$858$		0			0
$859$	−646.957			−0.753151			−0.376575	−	0.926386i	$-0.622898\pi$
$859$	−646.957			−0.753151			−0.376575	+	0.926386i	$0.622898\pi$
$860$	−623.267	−	167.004i	−0.724729	−	0.194191i
$861$		0			0
$862$	885.461	+	511.221i	1.02722	+	0.593064i
$863$	344.605	−	344.605i	0.399310	−	0.399310i	−0.478680	−	0.877990i	$-0.658884\pi$
$863$	344.605	−	344.605i	0.399310	−	0.399310i	0.877990	+	0.478680i	$0.158884\pi$
$864$		0			0
$865$	1470.58	−	394.040i	1.70009	−	0.455538i
$866$	−40.9607	−	40.9607i	−0.0472987	−	0.0472987i
$867$		0			0
$868$	270.649	−	156.259i	0.311807	−	0.180022i
$869$	236.692	−	883.347i	0.272373	−	1.01651i
$870$		0			0
$871$	−18.7033	−	520.848i	−0.0214733	−	0.597988i
$872$	−32.3051			−0.0370471
$873$		0			0
$874$	−191.471	−	331.637i	−0.219074	−	0.379448i
$875$	−2372.44	−	1369.73i	−2.71136	−	1.56540i
$876$		0			0
$877$	227.669	+	849.673i	0.259600	+	0.968840i	0.965473	+	0.260502i	$0.0838881\pi$
$877$	227.669	+	849.673i	0.259600	+	0.968840i	−0.705873	+	0.708338i	$0.749445\pi$
$878$	908.892	−	243.537i	1.03518	−	0.277377i
$879$		0			0
$880$	−294.424	+	509.957i	−0.334573	+	0.579497i
$881$	−35.9052	+	20.7299i	−0.0407551	+	0.0235299i	−0.520239	−	0.854021i	$-0.674157\pi$
$881$	−35.9052	+	20.7299i	−0.0407551	+	0.0235299i	0.479484	+	0.877551i	$0.340824\pi$
$882$		0			0
$883$		−	28.0736i		−	0.0317934i	−0.999874	−	0.0158967i	$-0.994940\pi$
$883$		−	28.0736i		−	0.0317934i	0.999874	−	0.0158967i	$-0.00506029\pi$
$884$	−170.159	+	182.835i	−0.192487	+	0.206826i
$885$		0			0
$886$	365.518	+	97.9402i	0.412548	+	0.110542i
$887$	68.9319	+	119.393i	0.0777135	+	0.134604i	0.902263	−	0.431186i	$-0.141905\pi$
$887$	68.9319	+	119.393i	0.0777135	+	0.134604i	−0.824550	+	0.565790i	$0.808571\pi$
$888$		0			0
$889$	−182.584	+	182.584i	−0.205382	+	0.205382i
$890$	−382.843	−	1428.79i	−0.430161	−	1.60538i
$891$		0			0
$892$	551.263	+	551.263i	0.618008	+	0.618008i
$893$	178.594	−	309.334i	0.199993	−	0.346399i
$894$		0			0
$895$	−732.393	+	2733.33i	−0.818316	+	3.05400i
$896$		−	108.125i		−	0.120676i
$897$		0			0
$898$	−796.391			−0.886850
$899$	435.962	+	116.816i	0.484941	+	0.129939i
$900$		0			0
$901$	−325.034	−	187.659i	−0.360748	−	0.208278i
$902$	−659.280	+	659.280i	−0.730909	+	0.730909i
$903$		0			0
$904$	318.031	−	85.2162i	0.351804	−	0.0942657i
$905$	124.509	+	124.509i	0.137579	+	0.137579i
$906$		0			0
$907$	776.354	−	448.228i	0.855958	−	0.494187i	−0.00669893	−	0.999978i	$-0.502132\pi$
$907$	776.354	−	448.228i	0.855958	−	0.494187i	0.862657	+	0.505790i	$0.168799\pi$
$908$	69.0140	−	257.564i	0.0760066	−	0.283661i
$909$		0			0
$910$	1403.08	+	744.255i	1.54185	+	0.817863i
$911$	318.659			0.349791			0.174895	−	0.984587i	$-0.444041\pi$
$911$	318.659			0.349791			0.174895	+	0.984587i	$0.444041\pi$
$912$		0			0
$913$	−52.9641	−	91.7365i	−0.0580111	−	0.100478i
$914$	816.022	+	471.131i	0.892803	+	0.515460i
$915$		0			0
$916$	−223.177	−	832.909i	−0.243643	−	0.909289i
$917$	596.053	−	159.712i	0.650004	−	0.174168i
$918$		0			0
$919$	50.2641	−	87.0600i	0.0546944	−	0.0947334i	−0.837382	−	0.546618i	$-0.815915\pi$
$919$	50.2641	−	87.0600i	0.0546944	−	0.0947334i	0.892076	+	0.451885i	$0.149248\pi$
$920$	−605.763	+	349.738i	−0.658438	+	0.380150i
$921$		0			0
$922$		−	506.616i		−	0.549475i
$923$	352.525	−	220.766i	0.381934	−	0.239183i
$924$		0			0
$925$	1154.78	+	309.421i	1.24841	+	0.334509i
$926$	630.292	+	1091.70i	0.680660	+	1.17894i
$927$		0			0
$928$	110.419	−	110.419i	0.118985	−	0.118985i
$929$	287.719	+	1073.78i	0.309709	+	1.15585i	0.928816	+	0.370542i	$0.120828\pi$
$929$	287.719	+	1073.78i	0.309709	+	1.15585i	−0.619107	+	0.785306i	$0.712505\pi$
$930$		0			0
$931$	296.300	+	296.300i	0.318259	+	0.318259i
$932$	−44.1414	+	76.4552i	−0.0473620	+	0.0820334i
$933$		0			0
$934$	−155.657	+	580.921i	−0.166657	+	0.621972i
$935$		−	1414.17i		−	1.51248i
$936$		0			0
$937$	−99.5793			−0.106275			−0.0531373	−	0.998587i	$-0.516922\pi$
$937$	−99.5793			−0.106275			−0.0531373	+	0.998587i	$0.516922\pi$
$938$	−523.394	−	140.243i	−0.557989	−	0.149513i
$939$		0			0
$940$	−565.025	−	326.217i	−0.601090	−	0.347040i
$941$	−795.092	+	795.092i	−0.844943	+	0.844943i	−0.989497	−	0.144554i	$-0.953825\pi$
$941$	−795.092	+	795.092i	−0.844943	+	0.844943i	0.144554	+	0.989497i	$0.453825\pi$
$942$		0			0
$943$	−1069.79	+	286.649i	−1.13445	+	0.303976i
$944$	134.785	+	134.785i	0.142781	+	0.142781i
$945$		0			0
$946$	−711.888	+	411.009i	−0.752524	+	0.434470i
$947$	−94.5423	+	352.837i	−0.0998335	+	0.372584i	−0.997708	−	0.0676681i	$-0.978444\pi$
$947$	−94.5423	+	352.837i	−0.0998335	+	0.372584i	0.897874	+	0.440252i	$0.145111\pi$
$948$		0			0
$949$	−83.4217	+	157.268i	−0.0879049	+	0.165720i
$950$	−793.793			−0.835572
$951$		0			0
$952$	129.836	+	224.883i	0.136383	+	0.236221i
$953$	262.250	+	151.410i	0.275184	+	0.158877i	0.631241	−	0.775587i	$-0.282546\pi$
$953$	262.250	+	151.410i	0.275184	+	0.158877i	−0.356057	+	0.934464i	$0.615879\pi$
$954$		0			0
$955$	−334.443	−	1248.16i	−0.350203	−	1.30697i
$956$	43.2889	−	11.5992i	0.0452813	−	0.0121331i
$957$		0			0
$958$	−194.811	+	337.423i	−0.203352	+	0.352216i
$959$	−1689.83	+	975.623i	−1.76207	+	1.01733i
$960$		0			0
$961$			693.672i			0.721823i
$962$	−377.721	−	86.8111i	−0.392642	−	0.0902403i
$963$		0			0
$964$	−929.186	−	248.975i	−0.963886	−	0.258273i
$965$	758.467	+	1313.70i	0.785976	+	1.36135i
$966$		0			0
$967$	228.726	−	228.726i	0.236532	−	0.236532i	−0.578881	−	0.815412i	$-0.696510\pi$
$967$	228.726	−	228.726i	0.236532	−	0.236532i	0.815412	+	0.578881i	$0.196510\pi$
$968$	105.577	+	394.020i	0.109068	+	0.407046i
$969$		0			0
$970$	315.813	+	315.813i	0.325581	+	0.325581i
$971$	−297.774	+	515.760i	−0.306668	+	0.531164i	−0.977631	−	0.210326i	$-0.932547\pi$
$971$	−297.774	+	515.760i	−0.306668	+	0.531164i	0.670964	+	0.741490i	$0.265881\pi$
$972$		0			0
$973$	−157.345	+	587.220i	−0.161711	+	0.603515i
$974$			905.415i			0.929585i
$975$		0			0
$976$	−282.173			−0.289112
$977$	−922.516	−	247.187i	−0.944233	−	0.253007i	−0.246320	−	0.969189i	$-0.579221\pi$
$977$	−922.516	−	247.187i	−0.944233	−	0.253007i	−0.697914	+	0.716182i	$0.745888\pi$
$978$		0			0
$979$	−1631.95	−	942.204i	−1.66695	−	0.962415i
$980$	541.216	−	541.216i	0.552261	−	0.552261i
$981$		0			0
$982$	774.081	−	207.414i	0.788270	−	0.211216i
$983$	−265.546	−	265.546i	−0.270138	−	0.270138i	0.559018	−	0.829156i	$-0.311178\pi$
$983$	−265.546	−	265.546i	−0.270138	−	0.270138i	−0.829156	+	0.559018i	$0.811178\pi$
$984$		0			0
$985$	−1333.84	+	770.093i	−1.35415	+	0.781821i
$986$	−97.0625	+	362.242i	−0.0984406	+	0.367385i
$987$		0			0
$988$	257.171	−	9.23485i	0.260295	−	0.00934701i
$989$	−976.450			−0.987310
$990$		0			0
$991$	−72.5775	−	125.708i	−0.0732366	−	0.126850i	0.827081	−	0.562082i	$-0.189999\pi$
$991$	−72.5775	−	125.708i	−0.0732366	−	0.126850i	−0.900318	+	0.435233i	$0.856666\pi$
$992$	−80.0992	−	46.2453i	−0.0807451	−	0.0466182i
$993$		0			0
$994$	−111.925	−	417.710i	−0.112601	−	0.420232i
$995$	1412.09	−	378.368i	1.41919	−	0.380269i
$996$		0			0
$997$	−292.161	+	506.038i	−0.293040	+	0.507561i	−0.974527	−	0.224270i	$-0.928000\pi$
$997$	−292.161	+	506.038i	−0.293040	+	0.507561i	0.681487	+	0.731830i	$0.261334\pi$
$998$	708.914	−	409.292i	0.710335	−	0.410112i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	234.3.bb.d.145.2		8
3.2	odd	2		78.3.l.c.67.1	yes	8
13.7	odd	12	inner	234.3.bb.d.163.2		8
39.2	even	12		1014.3.f.j.775.2		8
39.11	even	12		1014.3.f.h.775.1		8
39.20	even	12		78.3.l.c.7.1	✓	8
39.23	odd	6		1014.3.f.j.577.2		8
39.29	odd	6		1014.3.f.h.577.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
78.3.l.c.7.1	✓	8	39.20	even	12
78.3.l.c.67.1	yes	8	3.2	odd	2
234.3.bb.d.145.2		8	1.1	even	1	trivial
234.3.bb.d.163.2		8	13.7	odd	12	inner
1014.3.f.h.577.1		8	39.29	odd	6
1014.3.f.h.775.1		8	39.11	even	12
1014.3.f.j.577.2		8	39.23	odd	6
1014.3.f.j.775.2		8	39.2	even	12

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:	\( N \)	\(=\)	\( 234 = 2 \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	234.bb (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.36603 - 0.366025i) q^{2} +(1.73205 + 1.00000i) q^{4} +(6.39181 - 6.39181i) q^{5} +(9.23137 - 2.47354i) q^{7} +(-2.00000 - 2.00000i) q^{8} +O(q^{10})\)	\(q+(-1.36603 - 0.366025i) q^{2} +(1.73205 + 1.00000i) q^{4} +(6.39181 - 6.39181i) q^{5} +(9.23137 - 2.47354i) q^{7} +(-2.00000 - 2.00000i) q^{8} +(-11.0709 + 6.39181i) q^{10} +(-4.21503 + 15.7307i) q^{11} +(-3.81310 - 12.4282i) q^{13} -13.5157 q^{14} +(2.00000 + 3.46410i) q^{16} +(-8.31934 - 4.80317i) q^{17} +(2.56168 + 9.56033i) q^{19} +(17.4627 - 4.67913i) q^{20} +(11.5157 - 19.9457i) q^{22} +(23.6929 - 13.6791i) q^{23} -56.7105i q^{25} +(0.659759 + 18.3729i) q^{26} +(18.4627 + 4.94708i) q^{28} +(13.8023 + 23.9063i) q^{29} +(11.5613 - 11.5613i) q^{31} +(-1.46410 - 5.46410i) q^{32} +(9.60634 + 9.60634i) q^{34} +(43.1948 - 74.8156i) q^{35} +(-5.45615 + 20.3626i) q^{37} -13.9973i q^{38} -25.5672 q^{40} +(-39.1030 - 10.4776i) q^{41} +(-30.9095 - 17.8456i) q^{43} +(-23.0313 + 23.0313i) q^{44} +(-37.3721 + 10.0138i) q^{46} +(-25.5184 - 25.5184i) q^{47} +(36.6646 - 21.1683i) q^{49} +(-20.7575 + 77.4679i) q^{50} +(5.82371 - 25.3394i) q^{52} +39.0697 q^{53} +(73.6060 + 127.489i) q^{55} +(-23.4098 - 13.5157i) q^{56} +(-10.1040 - 37.7086i) q^{58} +(46.0300 - 12.3337i) q^{59} +(-35.2717 + 61.0923i) q^{61} +(-20.0248 + 11.5613i) q^{62} +8.00000i q^{64} +(-103.811 - 55.0661i) q^{65} +(38.7250 + 10.3763i) q^{67} +(-9.60634 - 16.6387i) q^{68} +(-86.3896 + 86.3896i) q^{70} +(8.28114 + 30.9056i) q^{71} +(-9.68320 - 9.68320i) q^{73} +(14.9065 - 25.8188i) q^{74} +(-5.12337 + 19.1207i) q^{76} +155.642i q^{77} -56.1543 q^{79} +(34.9255 + 9.35826i) q^{80} +(49.5806 + 28.6254i) q^{82} +(-4.59931 + 4.59931i) q^{83} +(-83.8766 + 22.4747i) q^{85} +(35.6912 + 35.6912i) q^{86} +(39.8915 - 23.0313i) q^{88} +(-29.9479 + 111.767i) q^{89} +(-65.9418 - 105.298i) q^{91} +54.7165 q^{92} +(25.5184 + 44.1991i) q^{94} +(77.4816 + 44.7340i) q^{95} +(-9.04249 - 33.7470i) q^{97} +(-57.8330 + 15.4963i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{2} + 6 q^{5} + 10 q^{7} - 16 q^{8}+O(q^{10}) \) 8 * q - 4 * q^2 + 6 * q^5 + 10 * q^7 - 16 * q^8	\( 8 q - 4 q^{2} + 6 q^{5} + 10 q^{7} - 16 q^{8} - 6 q^{10} - 24 q^{11} - 4 q^{14} + 16 q^{16} + 84 q^{17} + 10 q^{19} + 12 q^{20} - 12 q^{22} + 12 q^{23} - 26 q^{26} + 20 q^{28} - 36 q^{29} - 94 q^{31} + 16 q^{32} + 60 q^{34} + 204 q^{35} + 140 q^{37} - 24 q^{40} - 72 q^{41} - 222 q^{43} + 24 q^{44} - 84 q^{46} - 300 q^{47} + 42 q^{49} + 62 q^{50} + 44 q^{52} - 84 q^{53} + 396 q^{55} - 36 q^{56} - 66 q^{58} + 60 q^{59} - 90 q^{61} - 198 q^{62} + 108 q^{65} + 304 q^{67} - 60 q^{68} - 408 q^{70} + 192 q^{71} + 16 q^{73} + 46 q^{74} - 20 q^{76} - 96 q^{79} + 24 q^{80} + 114 q^{82} - 390 q^{85} - 168 q^{86} + 72 q^{88} - 354 q^{89} - 218 q^{91} + 288 q^{92} + 300 q^{94} + 576 q^{95} - 460 q^{97} - 58 q^{98}+O(q^{100}) \) 8 * q - 4 * q^2 + 6 * q^5 + 10 * q^7 - 16 * q^8 - 6 * q^10 - 24 * q^11 - 4 * q^14 + 16 * q^16 + 84 * q^17 + 10 * q^19 + 12 * q^20 - 12 * q^22 + 12 * q^23 - 26 * q^26 + 20 * q^28 - 36 * q^29 - 94 * q^31 + 16 * q^32 + 60 * q^34 + 204 * q^35 + 140 * q^37 - 24 * q^40 - 72 * q^41 - 222 * q^43 + 24 * q^44 - 84 * q^46 - 300 * q^47 + 42 * q^49 + 62 * q^50 + 44 * q^52 - 84 * q^53 + 396 * q^55 - 36 * q^56 - 66 * q^58 + 60 * q^59 - 90 * q^61 - 198 * q^62 + 108 * q^65 + 304 * q^67 - 60 * q^68 - 408 * q^70 + 192 * q^71 + 16 * q^73 + 46 * q^74 - 20 * q^76 - 96 * q^79 + 24 * q^80 + 114 * q^82 - 390 * q^85 - 168 * q^86 + 72 * q^88 - 354 * q^89 - 218 * q^91 + 288 * q^92 + 300 * q^94 + 576 * q^95 - 460 * q^97 - 58 * q^98

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