LMFDB - Embedded newform 912.2.bo.d.769.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [912,2,Mod(289,912)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(912, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 0, 0, 2]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("912.289");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 912 = 2^{4} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	912.bo (of order $9$, 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:	$7.28235666434$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 114)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			769.1
Root			$-0.766044 + 0.642788i$ of defining polynomial
Character	$\chi$	$=$	912.769
Dual form			912.2.bo.d.625.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.766044 - 0.642788i) q^{3} +(2.20574 + 0.802823i) q^{5} +(1.78699 - 3.09516i) q^{7} +(0.173648 - 0.984808i) q^{9} +O(q^{10})$	\(q+(0.766044 - 0.642788i) q^{3} +(2.20574 + 0.802823i) q^{5} +(1.78699 - 3.09516i) q^{7} +(0.173648 - 0.984808i) q^{9} +(1.35844 + 2.35289i) q^{11} +(4.14543 + 3.47843i) q^{13} +(2.20574 - 0.802823i) q^{15} +(-0.673648 - 3.82045i) q^{17} +(-1.01114 + 4.24000i) q^{19} +(-0.620615 - 3.51968i) q^{21} +(-7.73783 + 2.81634i) q^{23} +(0.390530 + 0.327693i) q^{25} +(-0.500000 - 0.866025i) q^{27} +(0.613341 - 3.47843i) q^{29} +(3.26604 - 5.65695i) q^{31} +(2.55303 + 0.929228i) q^{33} +(6.42649 - 5.39246i) q^{35} +0.389185 q^{37} +5.41147 q^{39} +(-1.48886 + 1.24930i) q^{41} +(4.71941 + 1.71772i) q^{43} +(1.17365 - 2.03282i) q^{45} +(-0.518418 + 2.94010i) q^{47} +(-2.88666 - 4.99984i) q^{49} +(-2.97178 - 2.49362i) q^{51} +(-7.80453 + 2.84062i) q^{53} +(1.10741 + 6.28044i) q^{55} +(1.95084 + 3.89798i) q^{57} +(-0.474308 - 2.68993i) q^{59} +(-5.91147 + 2.15160i) q^{61} +(-2.73783 - 2.29731i) q^{63} +(6.35117 + 11.0005i) q^{65} +(2.59374 - 14.7098i) q^{67} +(-4.11721 + 7.13122i) q^{69} +(8.47818 + 3.08580i) q^{71} +(7.88326 - 6.61484i) q^{73} +0.509800 q^{75} +9.71007 q^{77} +(-9.96451 + 8.36121i) q^{79} +(-0.939693 - 0.342020i) q^{81} +(-4.08512 + 7.07564i) q^{83} +(1.58125 - 8.96773i) q^{85} +(-1.76604 - 3.05888i) q^{87} +(8.98158 + 7.53644i) q^{89} +(18.1741 - 6.61484i) q^{91} +(-1.13429 - 6.43285i) q^{93} +(-5.63429 + 8.54055i) q^{95} +(-1.49407 - 8.47329i) q^{97} +(2.55303 - 0.929228i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{5} + 3 q^{7}+O(q^{10}) $ 6 * q + 3 * q^5 + 3 * q^7	$ 6 q + 3 q^{5} + 3 q^{7} + 9 q^{13} + 3 q^{15} - 3 q^{17} - 15 q^{21} - 27 q^{23} - 15 q^{25} - 3 q^{27} - 3 q^{29} + 15 q^{31} + 3 q^{33} - 12 q^{35} - 6 q^{37} + 12 q^{39} - 15 q^{41} - 3 q^{43} + 6 q^{45} - 15 q^{47} - 24 q^{49} - 3 q^{51} + 6 q^{53} - 27 q^{55} + 27 q^{59} - 15 q^{61} + 3 q^{63} + 12 q^{65} + 3 q^{67} + 6 q^{69} - 3 q^{71} + 12 q^{73} + 6 q^{75} - 42 q^{77} - 27 q^{79} - 3 q^{83} + 12 q^{85} - 6 q^{87} + 42 q^{89} + 42 q^{91} + 3 q^{93} - 24 q^{95} + 18 q^{97} + 3 q^{99}+O(q^{100}) $ 6 * q + 3 * q^5 + 3 * q^7 + 9 * q^13 + 3 * q^15 - 3 * q^17 - 15 * q^21 - 27 * q^23 - 15 * q^25 - 3 * q^27 - 3 * q^29 + 15 * q^31 + 3 * q^33 - 12 * q^35 - 6 * q^37 + 12 * q^39 - 15 * q^41 - 3 * q^43 + 6 * q^45 - 15 * q^47 - 24 * q^49 - 3 * q^51 + 6 * q^53 - 27 * q^55 + 27 * q^59 - 15 * q^61 + 3 * q^63 + 12 * q^65 + 3 * q^67 + 6 * q^69 - 3 * q^71 + 12 * q^73 + 6 * q^75 - 42 * q^77 - 27 * q^79 - 3 * q^83 + 12 * q^85 - 6 * q^87 + 42 * q^89 + 42 * q^91 + 3 * q^93 - 24 * q^95 + 18 * q^97 + 3 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/912\mathbb{Z}\right)^\times$.

$n$	$97$	$229$	$305$	$799$
$\chi(n)$	$e\left(\frac{4}{9}\right)$	$1$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.766044	−	0.642788i	0.442276	−	0.371114i
$3$	0.766044	−	0.642788i	0.442276	−	0.371114i
$4$		0			0
$5$	2.20574	+	0.802823i	0.986436	+	0.359033i	0.784339	−	0.620332i	$-0.213002\pi$
$5$	2.20574	+	0.802823i	0.986436	+	0.359033i	0.202097	+	0.979366i	$0.435225\pi$
$6$		0			0
$7$	1.78699	−	3.09516i	0.675418	−	1.16986i	−0.300928	−	0.953647i	$-0.597296\pi$
$7$	1.78699	−	3.09516i	0.675418	−	1.16986i	0.976346	−	0.216212i	$-0.0693703\pi$
$8$		0			0
$9$	0.173648	−	0.984808i	0.0578827	−	0.328269i
$10$		0			0
$11$	1.35844	+	2.35289i	0.409585	+	0.709423i	0.994843	−	0.101425i	$-0.0323401\pi$
$11$	1.35844	+	2.35289i	0.409585	+	0.709423i	−0.585258	+	0.810847i	$0.699007\pi$
$12$		0			0
$13$	4.14543	+	3.47843i	1.14974	+	0.964742i	0.999713	−	0.0239402i	$-0.00762112\pi$
$13$	4.14543	+	3.47843i	1.14974	+	0.964742i	0.150022	+	0.988683i	$0.452066\pi$
$14$		0			0
$15$	2.20574	−	0.802823i	0.569519	−	0.207288i
$16$		0			0
$17$	−0.673648	−	3.82045i	−0.163384	−	0.926595i	−0.950715	−	0.310065i	$-0.899649\pi$
$17$	−0.673648	−	3.82045i	−0.163384	−	0.926595i	0.787332	−	0.616530i	$-0.211462\pi$
$18$		0			0
$19$	−1.01114	+	4.24000i	−0.231972	+	0.972722i
$19$	−1.01114	+	4.24000i	−0.231972	+	0.972722i
$20$		0			0
$21$	−0.620615	−	3.51968i	−0.135429	−	0.768057i
$22$		0			0
$23$	−7.73783	+	2.81634i	−1.61345	+	0.587247i	−0.982118	−	0.188267i	$-0.939713\pi$
$23$	−7.73783	+	2.81634i	−1.61345	+	0.587247i	−0.631330	+	0.775514i	$0.717491\pi$
$24$		0			0
$25$	0.390530	+	0.327693i	0.0781059	+	0.0655386i
$26$		0			0
$27$	−0.500000	−	0.866025i	−0.0962250	−	0.166667i
$28$		0			0
$29$	0.613341	−	3.47843i	0.113895	−	0.645928i	−0.873397	−	0.487009i	$-0.838088\pi$
$29$	0.613341	−	3.47843i	0.113895	−	0.645928i	0.987292	−	0.158919i	$-0.0508009\pi$
$30$		0			0
$31$	3.26604	−	5.65695i	0.586599	−	1.01602i	−0.408075	−	0.912948i	$-0.633800\pi$
$31$	3.26604	−	5.65695i	0.586599	−	1.01602i	0.994674	−	0.103071i	$-0.0328668\pi$
$32$		0			0
$33$	2.55303	+	0.929228i	0.444426	+	0.161758i
$34$		0			0
$35$	6.42649	−	5.39246i	1.08627	−	0.911493i
$36$		0			0
$37$	0.389185			0.0639817			0.0319908	−	0.999488i	$-0.489815\pi$
$37$	0.389185			0.0639817			0.0319908	+	0.999488i	$0.489815\pi$
$38$		0			0
$39$	5.41147			0.866529
$40$		0			0
$41$	−1.48886	+	1.24930i	−0.232520	+	0.195108i	−0.751602	−	0.659617i	$-0.770718\pi$
$41$	−1.48886	+	1.24930i	−0.232520	+	0.195108i	0.519082	+	0.854725i	$0.326274\pi$
$42$		0			0
$43$	4.71941	+	1.71772i	0.719703	+	0.261950i	0.675800	−	0.737085i	$-0.263798\pi$
$43$	4.71941	+	1.71772i	0.719703	+	0.261950i	0.0439033	+	0.999036i	$0.486021\pi$
$44$		0			0
$45$	1.17365	−	2.03282i	0.174957	−	0.303035i
$46$		0			0
$47$	−0.518418	+	2.94010i	−0.0756191	+	0.428857i	0.923370	+	0.383911i	$0.125423\pi$
$47$	−0.518418	+	2.94010i	−0.0756191	+	0.428857i	−0.998989	+	0.0449466i	$0.985688\pi$
$48$		0			0
$49$	−2.88666	−	4.99984i	−0.412380	−	0.714263i
$50$		0			0
$51$	−2.97178	−	2.49362i	−0.416133	−	0.349177i
$52$		0			0
$53$	−7.80453	+	2.84062i	−1.07203	+	0.390189i	−0.816937	−	0.576727i	$-0.804330\pi$
$53$	−7.80453	+	2.84062i	−1.07203	+	0.390189i	−0.255097	+	0.966915i	$0.582108\pi$
$54$		0			0
$55$	1.10741	+	6.28044i	0.149323	+	0.846854i
$56$		0			0
$57$	1.95084	+	3.89798i	0.258395	+	0.516300i
$58$		0			0
$59$	−0.474308	−	2.68993i	−0.0617496	−	0.350199i	−0.999991	−	0.00421836i	$-0.998657\pi$
$59$	−0.474308	−	2.68993i	−0.0617496	−	0.350199i	0.938241	−	0.345981i	$-0.112454\pi$
$60$		0			0
$61$	−5.91147	+	2.15160i	−0.756887	+	0.275484i	−0.691501	−	0.722376i	$-0.743050\pi$
$61$	−5.91147	+	2.15160i	−0.756887	+	0.275484i	−0.0653860	+	0.997860i	$0.520828\pi$
$62$		0			0
$63$	−2.73783	−	2.29731i	−0.344934	−	0.289434i
$64$		0			0
$65$	6.35117	+	11.0005i	0.787765	+	1.36445i
$66$		0			0
$67$	2.59374	−	14.7098i	0.316876	−	1.79709i	−0.244627	−	0.969617i	$-0.578665\pi$
$67$	2.59374	−	14.7098i	0.316876	−	1.79709i	0.561503	−	0.827475i	$-0.310223\pi$
$68$		0			0
$69$	−4.11721	+	7.13122i	−0.495654	+	0.858498i
$70$		0			0
$71$	8.47818	+	3.08580i	1.00617	+	0.366218i	0.791963	−	0.610570i	$-0.209059\pi$
$71$	8.47818	+	3.08580i	1.00617	+	0.366218i	0.214212	+	0.976787i	$0.431282\pi$
$72$		0			0
$73$	7.88326	−	6.61484i	0.922665	−	0.774208i	−0.0518207	−	0.998656i	$-0.516502\pi$
$73$	7.88326	−	6.61484i	0.922665	−	0.774208i	0.974486	+	0.224448i	$0.0720580\pi$
$74$		0			0
$75$	0.509800			0.0588667
$76$		0			0
$77$	9.71007			1.10657
$78$		0			0
$79$	−9.96451	+	8.36121i	−1.12109	+	0.940710i	−0.998659	−	0.0517663i	$-0.983515\pi$
$79$	−9.96451	+	8.36121i	−1.12109	+	0.940710i	−0.122435	+	0.992476i	$0.539070\pi$
$80$		0			0
$81$	−0.939693	−	0.342020i	−0.104410	−	0.0380022i
$82$		0			0
$83$	−4.08512	+	7.07564i	−0.448400	+	0.776652i	−0.998282	−	0.0585902i	$-0.981339\pi$
$83$	−4.08512	+	7.07564i	−0.448400	+	0.776652i	0.549882	+	0.835243i	$0.314673\pi$
$84$		0			0
$85$	1.58125	−	8.96773i	0.171511	−	0.972686i
$86$		0			0
$87$	−1.76604	−	3.05888i	−0.189340	−	0.327946i
$88$		0			0
$89$	8.98158	+	7.53644i	0.952046	+	0.798861i	0.979641	−	0.200758i	$-0.0643405\pi$
$89$	8.98158	+	7.53644i	0.952046	+	0.798861i	−0.0275951	+	0.999619i	$0.508785\pi$
$90$		0			0
$91$	18.1741	−	6.61484i	1.90516	−	0.693423i
$92$		0			0
$93$	−1.13429	−	6.43285i	−0.117620	−	0.667056i
$94$		0			0
$95$	−5.63429	+	8.54055i	−0.578065	+	0.876242i
$96$		0			0
$97$	−1.49407	−	8.47329i	−0.151700	−	0.860333i	−0.961741	−	0.273960i	$-0.911666\pi$
$97$	−1.49407	−	8.47329i	−0.151700	−	0.860333i	0.810041	−	0.586373i	$-0.199445\pi$
$98$		0			0
$99$	2.55303	−	0.929228i	0.256590	−	0.0933909i
$100$		0			0
$101$	−0.984985	−	0.826501i	−0.0980097	−	0.0822399i	0.592466	−	0.805595i	$-0.298154\pi$
$101$	−0.984985	−	0.826501i	−0.0980097	−	0.0822399i	−0.690476	+	0.723355i	$0.742599\pi$
$102$		0			0
$103$	0.368241	+	0.637812i	0.0362839	+	0.0628455i	0.883597	−	0.468248i	$-0.155115\pi$
$103$	0.368241	+	0.637812i	0.0362839	+	0.0628455i	−0.847313	+	0.531094i	$0.821781\pi$
$104$		0			0
$105$	1.45677	−	8.26173i	0.142166	−	0.806263i
$106$		0			0
$107$	5.01367	−	8.68393i	0.484690	−	0.839507i	−0.515155	−	0.857097i	$-0.672266\pi$
$107$	5.01367	−	8.68393i	0.484690	−	0.839507i	0.999845	+	0.0175893i	$0.00559915\pi$
$108$		0			0
$109$	−13.0817	−	4.76136i	−1.25300	−	0.456055i	−0.371587	−	0.928398i	$-0.621186\pi$
$109$	−13.0817	−	4.76136i	−1.25300	−	0.456055i	−0.881415	+	0.472343i	$0.843408\pi$
$110$		0			0
$111$	0.298133	−	0.250164i	0.0282976	−	0.0237445i
$112$		0			0
$113$	−0.226682			−0.0213244			−0.0106622	−	0.999943i	$-0.503394\pi$
$113$	−0.226682			−0.0213244			−0.0106622	+	0.999943i	$0.503394\pi$
$114$		0			0
$115$	−19.3286			−1.80240
$116$		0			0
$117$	4.14543	−	3.47843i	0.383245	−	0.321581i
$118$		0			0
$119$	−13.0287	−	4.74205i	−1.19434	−	0.434703i
$120$		0			0
$121$	1.80928	−	3.13376i	0.164480	−	0.284887i
$122$		0			0
$123$	−0.337496	+	1.91404i	−0.0304310	+	0.172583i
$124$		0			0
$125$	−5.26991	−	9.12776i	−0.471356	−	0.816412i
$126$		0			0
$127$	−6.66044	−	5.58878i	−0.591019	−	0.495924i	0.297526	−	0.954714i	$-0.403839\pi$
$127$	−6.66044	−	5.58878i	−0.591019	−	0.495924i	−0.888545	+	0.458790i	$0.848283\pi$
$128$		0			0
$129$	4.71941	−	1.71772i	0.415521	−	0.151237i
$130$		0			0
$131$	2.19547	+	12.4511i	0.191819	+	1.08786i	0.916876	+	0.399172i	$0.130702\pi$
$131$	2.19547	+	12.4511i	0.191819	+	1.08786i	−0.725057	+	0.688689i	$0.758187\pi$
$132$		0			0
$133$	11.3166	+	10.7065i	0.981269	+	0.928370i
$134$		0			0
$135$	−0.407604	−	2.31164i	−0.0350809	−	0.198954i
$136$		0			0
$137$	−20.4795	+	7.45394i	−1.74968	+	0.636833i	−0.999697	−	0.0246200i	$-0.992162\pi$
$137$	−20.4795	+	7.45394i	−1.74968	+	0.636833i	−0.749987	+	0.661453i	$0.769940\pi$
$138$		0			0
$139$	8.60014	+	7.21637i	0.729454	+	0.612085i	0.929983	−	0.367603i	$-0.119822\pi$
$139$	8.60014	+	7.21637i	0.729454	+	0.612085i	−0.200529	+	0.979688i	$0.564266\pi$
$140$		0			0
$141$	1.49273	+	2.58548i	0.125710	+	0.217736i
$142$		0			0
$143$	−2.55303	+	14.4790i	−0.213495	+	1.21079i
$144$		0			0
$145$	4.14543	−	7.18009i	0.344259	−	0.596274i
$146$		0			0
$147$	−5.42514	−	1.97459i	−0.447458	−	0.162862i
$148$		0			0
$149$	−16.8366	+	14.1276i	−1.37931	+	1.15738i	−0.409843	+	0.912156i	$0.634416\pi$
$149$	−16.8366	+	14.1276i	−1.37931	+	1.15738i	−0.969467	+	0.245222i	$0.921139\pi$
$150$		0			0
$151$	−2.36184			−0.192204			−0.0961021	−	0.995371i	$-0.530638\pi$
$151$	−2.36184			−0.192204			−0.0961021	+	0.995371i	$0.530638\pi$
$152$		0			0
$153$	−3.87939			−0.313630
$154$		0			0
$155$	11.7456	−	9.85570i	0.943427	−	0.791629i
$156$		0			0
$157$	13.4893	+	4.90971i	1.07657	+	0.391838i	0.818628	−	0.574324i	$-0.194735\pi$
$157$	13.4893	+	4.90971i	1.07657	+	0.391838i	0.257937	+	0.966162i	$0.416957\pi$
$158$		0			0
$159$	−4.15270	+	7.19269i	−0.329331	+	0.570418i
$160$		0			0
$161$	−5.11040	+	28.9825i	−0.402756	+	2.28414i
$162$		0			0
$163$	−8.57057	−	14.8447i	−0.671299	−	1.16272i	−0.977536	−	0.210769i	$-0.932403\pi$
$163$	−8.57057	−	14.8447i	−0.671299	−	1.16272i	0.306237	−	0.951955i	$-0.400930\pi$
$164$		0			0
$165$	4.88532	+	4.09927i	0.380321	+	0.319127i
$166$		0			0
$167$	−13.7369	+	4.99984i	−1.06300	+	0.386899i	−0.813553	−	0.581490i	$-0.802470\pi$
$167$	−13.7369	+	4.99984i	−1.06300	+	0.386899i	−0.249444	+	0.968389i	$0.580248\pi$
$168$		0			0
$169$	2.82770	+	16.0367i	0.217515	+	1.23359i
$170$		0			0
$171$	4.00000	+	1.73205i	0.305888	+	0.132453i
$172$		0			0
$173$	−3.58899	−	20.3542i	−0.272866	−	1.54750i	−0.745660	−	0.666327i	$-0.767865\pi$
$173$	−3.58899	−	20.3542i	−0.272866	−	1.54750i	0.472794	−	0.881173i	$-0.343246\pi$
$174$		0			0
$175$	1.71213	−	0.623166i	0.129425	−	0.0471069i
$176$		0			0
$177$	−2.09240	−	1.75573i	−0.157274	−	0.131969i
$178$		0			0
$179$	2.84730	+	4.93166i	0.212817	+	0.368610i	0.952595	−	0.304241i	$-0.0984029\pi$
$179$	2.84730	+	4.93166i	0.212817	+	0.368610i	−0.739778	+	0.672851i	$0.765070\pi$
$180$		0			0
$181$	−3.85844	+	21.8823i	−0.286796	+	1.62650i	0.412004	+	0.911182i	$0.364829\pi$
$181$	−3.85844	+	21.8823i	−0.286796	+	1.62650i	−0.698800	+	0.715317i	$0.746282\pi$
$182$		0			0
$183$	−3.14543	+	5.44804i	−0.232517	+	0.402731i
$184$		0			0
$185$	0.858441	+	0.312447i	0.0631138	+	0.0229716i
$186$		0			0
$187$	8.07398	−	6.77487i	0.590428	−	0.495428i
$188$		0			0
$189$	−3.57398			−0.259969
$190$		0			0
$191$	−6.04694			−0.437541			−0.218771	−	0.975776i	$-0.570205\pi$
$191$	−6.04694			−0.437541			−0.218771	+	0.975776i	$0.570205\pi$
$192$		0			0
$193$	4.82501	−	4.04866i	0.347312	−	0.291429i	−0.452398	−	0.891816i	$-0.649431\pi$
$193$	4.82501	−	4.04866i	0.347312	−	0.291429i	0.799709	+	0.600387i	$0.204987\pi$
$194$		0			0
$195$	11.9363	+	4.34445i	0.854775	+	0.311113i
$196$		0			0
$197$	−9.96838	+	17.2657i	−0.710218	+	1.23013i	0.254558	+	0.967058i	$0.418070\pi$
$197$	−9.96838	+	17.2657i	−0.710218	+	1.23013i	−0.964775	+	0.263075i	$0.915263\pi$
$198$		0			0
$199$	−2.23695	+	12.6864i	−0.158573	+	0.899313i	0.796873	+	0.604147i	$0.206486\pi$
$199$	−2.23695	+	12.6864i	−0.158573	+	0.899313i	−0.955446	+	0.295166i	$0.904625\pi$
$200$		0			0
$201$	−7.46838	−	12.9356i	−0.526779	−	0.912408i
$202$		0			0
$203$	−9.67024	−	8.11430i	−0.678718	−	0.569512i
$204$		0			0
$205$	−4.28699	+	1.56034i	−0.299416	+	0.108979i
$206$		0			0
$207$	1.42989	+	8.10932i	0.0993844	+	0.563637i
$208$		0			0
$209$	−11.3498	+	3.38068i	−0.785084	+	0.233846i
$210$		0			0
$211$	−0.401674	−	2.27801i	−0.0276524	−	0.156824i	0.967855	−	0.251509i	$-0.0809268\pi$
$211$	−0.401674	−	2.27801i	−0.0276524	−	0.156824i	−0.995507	+	0.0946847i	$0.969816\pi$
$212$		0			0
$213$	8.47818	−	3.08580i	0.580915	−	0.211436i
$214$		0			0
$215$	9.03074	+	7.57769i	0.615892	+	0.516794i
$216$		0			0
$217$	−11.6728	−	20.2178i	−0.792399	−	1.37248i
$218$		0			0
$219$	1.78699	−	10.1345i	0.120754	−	0.684827i
$220$		0			0
$221$	10.4966	−	18.1806i	0.706077	−	1.22296i
$222$		0			0
$223$	3.82547	+	1.39236i	0.256173	+	0.0932392i	0.466914	−	0.884303i	$-0.345366\pi$
$223$	3.82547	+	1.39236i	0.256173	+	0.0932392i	−0.210742	+	0.977542i	$0.567588\pi$
$224$		0			0
$225$	0.390530	−	0.327693i	0.0260353	−	0.0218462i
$226$		0			0
$227$	0.440570			0.0292417			0.0146208	−	0.999893i	$-0.495346\pi$
$227$	0.440570			0.0292417			0.0146208	+	0.999893i	$0.495346\pi$
$228$		0			0
$229$	−3.38919			−0.223964			−0.111982	−	0.993710i	$-0.535720\pi$
$229$	−3.38919			−0.223964			−0.111982	+	0.993710i	$0.535720\pi$
$230$		0			0
$231$	7.43835	−	6.24152i	0.489407	−	0.410662i
$232$		0			0
$233$	−1.98633	−	0.722965i	−0.130129	−	0.0473630i	0.276135	−	0.961119i	$-0.410946\pi$
$233$	−1.98633	−	0.722965i	−0.130129	−	0.0473630i	−0.406264	+	0.913756i	$0.633169\pi$
$234$		0			0
$235$	−3.50387	+	6.06888i	−0.228567	+	0.395890i
$236$		0			0
$237$	−2.25877	+	12.8101i	−0.146723	+	0.832107i
$238$		0			0
$239$	−2.01455	−	3.48930i	−0.130310	−	0.225704i	0.793486	−	0.608589i	$-0.208264\pi$
$239$	−2.01455	−	3.48930i	−0.130310	−	0.225704i	−0.923796	+	0.382885i	$0.874931\pi$
$240$		0			0
$241$	−7.79607	−	6.54168i	−0.502189	−	0.421387i	0.356181	−	0.934417i	$-0.384079\pi$
$241$	−7.79607	−	6.54168i	−0.502189	−	0.421387i	−0.858371	+	0.513030i	$0.828523\pi$
$242$		0			0
$243$	−0.939693	+	0.342020i	−0.0602813	+	0.0219406i
$244$		0			0
$245$	−2.35323	−	13.3458i	−0.150342	−	0.852632i
$246$		0			0
$247$	−18.9402	+	14.0594i	−1.20513	+	0.894580i
$248$		0			0
$249$	1.41875	+	8.04612i	0.0899095	+	0.509902i
$250$		0			0
$251$	2.73396	−	0.995078i	0.172566	−	0.0628088i	−0.254292	−	0.967127i	$-0.581843\pi$
$251$	2.73396	−	0.995078i	0.172566	−	0.0628088i	0.426858	+	0.904319i	$0.359620\pi$
$252$		0			0
$253$	−17.1379	−	14.3804i	−1.07745	−	0.904089i
$254$		0			0
$255$	−4.55303	−	7.88609i	−0.285122	−	0.493846i
$256$		0			0
$257$	−0.444440	+	2.52055i	−0.0277234	+	0.157227i	−0.995527	−	0.0944803i	$-0.969881\pi$
$257$	−0.444440	+	2.52055i	−0.0277234	+	0.157227i	0.967803	+	0.251708i	$0.0809922\pi$
$258$		0			0
$259$	0.695470	−	1.20459i	0.0432144	−	0.0748495i
$260$		0			0
$261$	−3.31908	−	1.20805i	−0.205446	−	0.0747761i
$262$		0			0
$263$	−12.2023	+	10.2390i	−0.752428	+	0.631362i	−0.936144	−	0.351617i	$-0.885632\pi$
$263$	−12.2023	+	10.2390i	−0.752428	+	0.631362i	0.183716	+	0.982979i	$0.441187\pi$
$264$		0			0
$265$	−19.4953			−1.19758
$266$		0			0
$267$	11.7246			0.717535
$268$		0			0
$269$	12.9422	−	10.8598i	0.789101	−	0.662134i	−0.156422	−	0.987690i	$-0.549996\pi$
$269$	12.9422	−	10.8598i	0.789101	−	0.662134i	0.945523	+	0.325556i	$0.105551\pi$
$270$		0			0
$271$	−0.585122	−	0.212967i	−0.0355436	−	0.0129368i	0.324187	−	0.945993i	$-0.394909\pi$
$271$	−0.585122	−	0.212967i	−0.0355436	−	0.0129368i	−0.359731	+	0.933056i	$0.617131\pi$
$272$		0			0
$273$	9.67024	−	16.7494i	0.585270	−	1.01372i
$274$		0			0
$275$	−0.240514	+	1.36402i	−0.0145036	+	0.0822538i
$276$		0			0
$277$	13.7383	+	23.7954i	0.825454	+	1.42973i	0.901572	+	0.432629i	$0.142414\pi$
$277$	13.7383	+	23.7954i	0.825454	+	1.42973i	−0.0761178	+	0.997099i	$0.524253\pi$
$278$		0			0
$279$	−5.00387	−	4.19875i	−0.299574	−	0.251372i
$280$		0			0
$281$	2.33110	−	0.848451i	0.139062	−	0.0506143i	−0.271552	−	0.962424i	$-0.587537\pi$
$281$	2.33110	−	0.848451i	0.139062	−	0.0506143i	0.410613	+	0.911810i	$0.365315\pi$
$282$		0			0
$283$	−0.396459	−	2.24843i	−0.0235671	−	0.133655i	0.970754	−	0.240076i	$-0.0771722\pi$
$283$	−0.396459	−	2.24843i	−0.0235671	−	0.133655i	−0.994321	+	0.106420i	$0.966061\pi$
$284$		0			0
$285$	1.17365	+	10.1641i	0.0695209	+	0.602069i
$286$		0			0
$287$	1.20620	+	6.84072i	0.0712000	+	0.403795i
$288$		0			0
$289$	1.83275	−	0.667066i	0.107809	−	0.0392392i
$290$		0			0
$291$	−6.59105	−	5.53055i	−0.386374	−	0.324207i
$292$		0			0
$293$	1.19800	+	2.07499i	0.0699877	+	0.121222i	0.898896	−	0.438163i	$-0.144371\pi$
$293$	1.19800	+	2.07499i	0.0699877	+	0.121222i	−0.828908	+	0.559385i	$0.811037\pi$
$294$		0			0
$295$	1.11334	−	6.31407i	0.0648212	−	0.367619i
$296$		0			0
$297$	1.35844	−	2.35289i	0.0788247	−	0.136528i
$298$		0			0
$299$	−41.8730	−	15.2405i	−2.42158	−	0.881383i
$300$		0			0
$301$	13.7502	−	11.5377i	0.792546	−	0.665025i
$302$		0			0
$303$	−1.28581			−0.0738677
$304$		0			0
$305$	−14.7665			−0.845528
$306$		0			0
$307$	4.00908	−	3.36402i	0.228811	−	0.191995i	−0.521174	−	0.853451i	$-0.674506\pi$
$307$	4.00908	−	3.36402i	0.228811	−	0.191995i	0.749984	+	0.661456i	$0.230061\pi$
$308$		0			0
$309$	0.692066	+	0.251892i	0.0393703	+	0.0143296i
$310$		0			0
$311$	−5.49660	+	9.52038i	−0.311683	+	0.539851i	−0.978727	−	0.205167i	$-0.934226\pi$
$311$	−5.49660	+	9.52038i	−0.311683	+	0.539851i	0.667044	+	0.745019i	$0.267559\pi$
$312$		0			0
$313$	−5.28787	+	29.9890i	−0.298888	+	1.69508i	0.352078	+	0.935971i	$0.385475\pi$
$313$	−5.28787	+	29.9890i	−0.298888	+	1.69508i	−0.650966	+	0.759107i	$0.725636\pi$
$314$		0			0
$315$	−4.19459	−	7.26525i	−0.236339	−	0.409350i
$316$		0			0
$317$	8.68660	+	7.28893i	0.487888	+	0.409387i	0.853269	−	0.521471i	$-0.174617\pi$
$317$	8.68660	+	7.28893i	0.487888	+	0.409387i	−0.365381	+	0.930858i	$0.619061\pi$
$318$		0			0
$319$	9.01754	−	3.28212i	0.504885	−	0.183763i
$320$		0			0
$321$	−1.74123	−	9.87500i	−0.0971860	−	0.551169i
$322$		0			0
$323$	16.8799	+	1.00676i	0.939220	+	0.0560175i
$324$		0			0
$325$	0.479055	+	2.71686i	0.0265732	+	0.150704i
$326$		0			0
$327$	−13.0817	+	4.76136i	−0.723421	+	0.263304i
$328$		0			0
$329$	8.17365	+	6.85851i	0.450628	+	0.378122i
$330$		0			0
$331$	6.46585	+	11.1992i	0.355395	+	0.615563i	0.987186	−	0.159577i	$-0.0510129\pi$
$331$	6.46585	+	11.1992i	0.355395	+	0.615563i	−0.631790	+	0.775139i	$0.717680\pi$
$332$		0			0
$333$	0.0675813	−	0.383273i	0.00370343	−	0.0210032i
$334$		0			0
$335$	17.5305	−	30.3637i	0.957793	−	1.65895i
$336$		0			0
$337$	−10.0988	−	3.67566i	−0.550116	−	0.200226i	0.0519819	−	0.998648i	$-0.483446\pi$
$337$	−10.0988	−	3.67566i	−0.550116	−	0.200226i	−0.602098	+	0.798422i	$0.705668\pi$
$338$		0			0
$339$	−0.173648	+	0.145708i	−0.00943127	+	0.00791378i
$340$		0			0
$341$	17.7469			0.961049
$342$		0			0
$343$	4.38413			0.236721
$344$		0			0
$345$	−14.8066	+	12.4242i	−0.797160	+	0.668897i
$346$		0			0
$347$	21.4281	+	7.79920i	1.15032	+	0.418683i	0.845631	−	0.533768i	$-0.179224\pi$
$347$	21.4281	+	7.79920i	1.15032	+	0.418683i	0.304692	+	0.952451i	$0.401447\pi$
$348$		0			0
$349$	12.6814	−	21.9648i	0.678819	−	1.17575i	−0.296518	−	0.955027i	$-0.595825\pi$
$349$	12.6814	−	21.9648i	0.678819	−	1.17575i	0.975337	−	0.220722i	$-0.0708413\pi$
$350$		0			0
$351$	0.939693	−	5.32926i	0.0501571	−	0.284455i
$352$		0			0
$353$	6.09627	+	10.5590i	0.324472	+	0.562001i	0.981405	−	0.191947i	$-0.0614802\pi$
$353$	6.09627	+	10.5590i	0.324472	+	0.562001i	−0.656934	+	0.753948i	$0.728147\pi$
$354$		0			0
$355$	16.2233	+	13.6129i	0.861042	+	0.722500i
$356$		0			0
$357$	−13.0287	+	4.74205i	−0.689551	+	0.250976i
$358$		0			0
$359$	−5.06418	−	28.7204i	−0.267277	−	1.51580i	−0.762472	−	0.647022i	$-0.776014\pi$
$359$	−5.06418	−	28.7204i	−0.267277	−	1.51580i	0.495195	−	0.868782i	$-0.335097\pi$
$360$		0			0
$361$	−16.9552	−	8.57450i	−0.892378	−	0.451290i
$362$		0			0
$363$	−0.628356	−	3.56358i	−0.0329801	−	0.187040i
$364$		0			0
$365$	22.6989	−	8.26173i	1.18812	−	0.432439i
$366$		0			0
$367$	−10.7187	−	8.99405i	−0.559511	−	0.469486i	0.318635	−	0.947877i	$-0.396775\pi$
$367$	−10.7187	−	8.99405i	−0.559511	−	0.469486i	−0.878147	+	0.478392i	$0.841220\pi$
$368$		0			0
$369$	0.971782	+	1.68317i	0.0505889	+	0.0876226i
$370$		0			0
$371$	−5.15446	+	29.2324i	−0.267606	+	1.51767i
$372$		0			0
$373$	3.41013	−	5.90652i	0.176570	−	0.305828i	−0.764134	−	0.645058i	$-0.776833\pi$
$373$	3.41013	−	5.90652i	0.176570	−	0.305828i	0.940703	+	0.339230i	$0.110167\pi$
$374$		0			0
$375$	−9.90420	−	3.60483i	−0.511451	−	0.186153i
$376$		0			0
$377$	14.6420	−	12.2861i	0.754103	−	0.632767i
$378$		0			0
$379$	−31.9341			−1.64034			−0.820171	−	0.572118i	$-0.806122\pi$
$379$	−31.9341			−1.64034			−0.820171	+	0.572118i	$0.806122\pi$
$380$		0			0
$381$	−8.69459			−0.445437
$382$		0			0
$383$	28.2049	−	23.6667i	1.44120	−	1.20931i	0.502501	−	0.864577i	$-0.332413\pi$
$383$	28.2049	−	23.6667i	1.44120	−	1.20931i	0.938700	−	0.344734i	$-0.112031\pi$
$384$		0			0
$385$	21.4179	+	7.79547i	1.09156	+	0.397294i
$386$		0			0
$387$	2.51114	−	4.34943i	0.127649	−	0.221094i
$388$		0			0
$389$	−0.582596	+	3.30407i	−0.0295388	+	0.167523i	−0.996009	−	0.0892575i	$-0.971551\pi$
$389$	−0.582596	+	3.30407i	−0.0295388	+	0.167523i	0.966470	+	0.256780i	$0.0826617\pi$
$390$		0			0
$391$	15.9722	+	27.6647i	0.807751	+	1.39907i
$392$		0			0
$393$	9.68526	+	8.12690i	0.488557	+	0.409948i
$394$		0			0
$395$	−28.6917	+	10.4429i	−1.44363	+	0.525440i
$396$		0			0
$397$	1.19547	+	6.77985i	0.0599989	+	0.340271i	1.00000		0.000901796i	$-0.000287051\pi$
$397$	1.19547	+	6.77985i	0.0599989	+	0.340271i	−0.940001	+	0.341173i	$0.889176\pi$
$398$		0			0
$399$	15.5510	+	0.927500i	0.778522	+	0.0464331i
$400$		0			0
$401$	−0.873455	−	4.95361i	−0.0436183	−	0.247372i	0.955201	−	0.295959i	$-0.0956392\pi$
$401$	−0.873455	−	4.95361i	−0.0436183	−	0.247372i	−0.998819	+	0.0485874i	$0.984528\pi$
$402$		0			0
$403$	33.2165	−	12.0898i	1.65463	−	0.602236i
$404$		0			0
$405$	−1.79813	−	1.50881i	−0.0893500	−	0.0749735i
$406$		0			0
$407$	0.528685	+	0.915710i	0.0262060	+	0.0453901i
$408$		0			0
$409$	−1.80747	+	10.2507i	−0.0893735	+	0.506862i	0.906953	+	0.421231i	$0.138402\pi$
$409$	−1.80747	+	10.2507i	−0.0893735	+	0.506862i	−0.996327	+	0.0856312i	$0.972709\pi$
$410$		0			0
$411$	−10.8969	+	18.8740i	−0.537506	+	0.930987i
$412$		0			0
$413$	−9.17334	−	3.33882i	−0.451391	−	0.164293i
$414$		0			0
$415$	−14.6912	+	12.3274i	−0.721162	+	0.605127i
$416$		0			0
$417$	11.2267			0.549773
$418$		0			0
$419$	6.22256			0.303992			0.151996	−	0.988381i	$-0.451430\pi$
$419$	6.22256			0.303992			0.151996	+	0.988381i	$0.451430\pi$
$420$		0			0
$421$	−20.3917	+	17.1107i	−0.993831	+	0.833923i	−0.986118	−	0.166047i	$-0.946900\pi$
$421$	−20.3917	+	17.1107i	−0.993831	+	0.833923i	−0.00771335	+	0.999970i	$0.502455\pi$
$422$		0			0
$423$	2.80541	+	1.02108i	0.136404	+	0.0496468i
$424$		0			0
$425$	0.988856	−	1.71275i	0.0479665	−	0.0830805i
$426$		0			0
$427$	−3.90420	+	22.1418i	−0.188937	+	1.07152i
$428$		0			0
$429$	7.35117	+	12.7326i	0.354918	+	0.614735i
$430$		0			0
$431$	10.5196	+	8.82699i	0.506711	+	0.425181i	0.859970	−	0.510344i	$-0.170482\pi$
$431$	10.5196	+	8.82699i	0.506711	+	0.425181i	−0.353259	+	0.935526i	$0.614926\pi$
$432$		0			0
$433$	23.2053	−	8.44605i	1.11518	−	0.405891i	0.282287	−	0.959330i	$-0.408907\pi$
$433$	23.2053	−	8.44605i	1.11518	−	0.405891i	0.832890	+	0.553439i	$0.186685\pi$
$434$		0			0
$435$	−1.43969	−	8.16490i	−0.0690280	−	0.391477i
$436$		0			0
$437$	−4.11721	−	35.6561i	−0.196953	−	1.70566i
$438$		0			0
$439$	−3.15018	−	17.8655i	−0.150350	−	0.852676i	−0.962915	−	0.269805i	$-0.913041\pi$
$439$	−3.15018	−	17.8655i	−0.150350	−	0.852676i	0.812565	−	0.582870i	$-0.198070\pi$
$440$		0			0
$441$	−5.42514	+	1.97459i	−0.258340	+	0.0940282i
$442$		0			0
$443$	9.85323	+	8.26784i	0.468141	+	0.392817i	0.846116	−	0.532999i	$-0.178935\pi$
$443$	9.85323	+	8.26784i	0.468141	+	0.392817i	−0.377975	+	0.925816i	$0.623379\pi$
$444$		0			0
$445$	13.7606	+	23.8340i	0.652314	+	1.12984i
$446$		0			0
$447$	−3.81655	+	21.6447i	−0.180517	+	1.02376i
$448$		0			0
$449$	10.9659	−	18.9934i	0.517511	−	0.896355i	−0.482283	−	0.876016i	$-0.660192\pi$
$449$	10.9659	−	18.9934i	0.517511	−	0.896355i	0.999793	−	0.0203389i	$-0.00647451\pi$
$450$		0			0
$451$	−4.96198	−	1.80601i	−0.233651	−	0.0850419i
$452$		0			0
$453$	−1.80928	+	1.51816i	−0.0850073	+	0.0713296i
$454$		0			0
$455$	45.3979			2.12828
$456$		0			0
$457$	30.8452			1.44288			0.721440	−	0.692477i	$-0.243481\pi$
$457$	30.8452			1.44288			0.721440	+	0.692477i	$0.243481\pi$
$458$		0			0
$459$	−2.97178	+	2.49362i	−0.138711	+	0.116392i
$460$		0			0
$461$	11.5770	+	4.21367i	0.539193	+	0.196250i	0.597239	−	0.802064i	$-0.296265\pi$
$461$	11.5770	+	4.21367i	0.539193	+	0.196250i	−0.0580453	+	0.998314i	$0.518487\pi$
$462$		0			0
$463$	6.10472	−	10.5737i	0.283711	−	0.491401i	−0.688585	−	0.725156i	$-0.741768\pi$
$463$	6.10472	−	10.5737i	0.283711	−	0.491401i	0.972296	+	0.233754i	$0.0751012\pi$
$464$		0			0
$465$	2.66250	−	15.0998i	0.123471	−	0.700237i
$466$		0			0
$467$	−13.3701	−	23.1576i	−0.618692	−	1.07161i	−0.989725	−	0.142986i	$-0.954329\pi$
$467$	−13.3701	−	23.1576i	−0.618692	−	1.07161i	0.371032	−	0.928620i	$-0.379004\pi$
$468$		0			0
$469$	−40.8942	−	34.3143i	−1.88832	−	1.58449i
$470$		0			0
$471$	13.4893	−	4.90971i	0.621555	−	0.226228i
$472$		0			0
$473$	2.36942	+	13.4377i	0.108946	+	0.617865i
$474$		0			0
$475$	−1.78430	+	1.32450i	−0.0818693	+	0.0607722i
$476$		0			0
$477$	1.44222	+	8.17923i	0.0660347	+	0.374501i
$478$		0			0
$479$	7.26991	−	2.64603i	0.332171	−	0.120900i	−0.170550	−	0.985349i	$-0.554555\pi$
$479$	7.26991	−	2.64603i	0.332171	−	0.120900i	0.502721	+	0.864449i	$0.332332\pi$
$480$		0			0
$481$	1.61334	+	1.35375i	0.0735620	+	0.0617259i
$482$		0			0
$483$	14.7148	+	25.4868i	0.669548	+	1.15969i
$484$		0			0
$485$	3.50703	−	19.8893i	0.159246	−	0.903128i
$486$		0			0
$487$	6.69594	−	11.5977i	0.303422	−	0.525542i	−0.673487	−	0.739199i	$-0.735204\pi$
$487$	6.69594	−	11.5977i	0.303422	−	0.525542i	0.976909	+	0.213657i	$0.0685375\pi$
$488$		0			0
$489$	−16.1074	−	5.86262i	−0.728402	−	0.265117i
$490$		0			0
$491$	15.5103	−	13.0147i	0.699969	−	0.587343i	−0.221796	−	0.975093i	$-0.571192\pi$
$491$	15.5103	−	13.0147i	0.699969	−	0.587343i	0.921765	+	0.387750i	$0.126748\pi$
$492$		0			0
$493$	−13.7023			−0.617122
$494$		0			0
$495$	6.37733			0.286639
$496$		0			0
$497$	24.7015	−	20.7270i	1.10801	−	0.929732i
$498$		0			0
$499$	−4.45171	−	1.62029i	−0.199286	−	0.0725342i	0.240449	−	0.970662i	$-0.422705\pi$
$499$	−4.45171	−	1.62029i	−0.199286	−	0.0725342i	−0.439735	+	0.898128i	$0.644928\pi$
$500$		0			0
$501$	−7.30928	+	12.6600i	−0.326554	+	0.565609i
$502$		0			0
$503$	−1.49319	+	8.46832i	−0.0665782	+	0.377584i	0.933253	+	0.359219i	$0.116957\pi$
$503$	−1.49319	+	8.46832i	−0.0665782	+	0.377584i	−0.999831	+	0.0183643i	$0.994154\pi$
$504$		0			0
$505$	−1.50908	−	2.61381i	−0.0671534	−	0.116313i
$506$		0			0
$507$	12.4743	+	10.4672i	0.554003	+	0.464864i
$508$		0			0
$509$	−5.03936	+	1.83418i	−0.223366	+	0.0812985i	−0.451279	−	0.892383i	$-0.649032\pi$
$509$	−5.03936	+	1.83418i	−0.223366	+	0.0812985i	0.227913	+	0.973681i	$0.426810\pi$
$510$		0			0
$511$	−6.38666	−	36.2205i	−0.282529	−	1.60230i
$512$		0			0
$513$	4.17752	−	1.24432i	0.184442	−	0.0549382i
$514$		0			0
$515$	0.300193	+	1.70248i	0.0132281	+	0.0750201i
$516$		0			0
$517$	−7.62196	+	2.77417i	−0.335213	+	0.122008i
$518$		0			0
$519$	−15.8327	−	13.2853i	−0.694981	−	0.583158i
$520$		0			0
$521$	11.8576	+	20.5379i	0.519489	+	0.899782i	0.999743	+	0.0226524i	$0.00721111\pi$
$521$	11.8576	+	20.5379i	0.519489	+	0.899782i	−0.480254	+	0.877129i	$0.659456\pi$
$522$		0			0
$523$	5.43794	−	30.8401i	0.237784	−	1.34854i	−0.598885	−	0.800835i	$-0.704389\pi$
$523$	5.43794	−	30.8401i	0.237784	−	1.34854i	0.836670	−	0.547708i	$-0.184499\pi$
$524$		0			0
$525$	0.911007	−	1.57791i	0.0397596	−	0.0688657i
$526$		0			0
$527$	−23.8123	−	8.66696i	−1.03728	−	0.377539i
$528$		0			0
$529$	34.3232	−	28.8006i	1.49231	−	1.25220i
$530$		0			0
$531$	−2.73143			−0.118534
$532$		0			0
$533$	−10.5175			−0.455565
$534$		0			0
$535$	18.0305	−	15.1294i	0.779526	−	0.654100i
$536$		0			0
$537$	5.35117	+	1.94767i	0.230920	+	0.0840480i
$538$		0			0
$539$	7.84271	−	13.5840i	0.337809	−	0.585103i
$540$		0			0
$541$	1.66519	−	9.44377i	0.0715922	−	0.406020i	−0.927860	−	0.372928i	$-0.878354\pi$
$541$	1.66519	−	9.44377i	0.0715922	−	0.406020i	0.999452	−	0.0330912i	$-0.0105352\pi$
$542$		0			0
$543$	11.1099	+	19.2430i	0.476773	+	0.825795i
$544$		0			0
$545$	−25.0323	−	21.0046i	−1.07227	−	0.899738i
$546$		0			0
$547$	9.65570	−	3.51439i	0.412848	−	0.150264i	−0.127242	−	0.991872i	$-0.540612\pi$
$547$	9.65570	−	3.51439i	0.412848	−	0.150264i	0.540090	+	0.841607i	$0.318390\pi$
$548$		0			0
$549$	1.09240	+	6.19529i	0.0466223	+	0.264408i
$550$		0			0
$551$	14.1284	+	6.11776i	0.601888	+	0.260625i
$552$		0			0
$553$	8.07280	+	45.7831i	0.343290	+	1.94690i
$554$		0			0
$555$	0.858441	−	0.312447i	0.0364388	−	0.0132626i
$556$		0			0
$557$	−12.7756	−	10.7200i	−0.541319	−	0.454221i	0.330669	−	0.943747i	$-0.392725\pi$
$557$	−12.7756	−	10.7200i	−0.541319	−	0.454221i	−0.871989	+	0.489526i	$0.837170\pi$
$558$		0			0
$559$	13.5890	+	23.5368i	0.574753	+	0.995502i
$560$		0			0
$561$	1.83022	−	10.3797i	0.0772720	−	0.438232i
$562$		0			0
$563$	1.71554	−	2.97140i	0.0723013	−	0.125229i	−0.827608	−	0.561306i	$-0.810299\pi$
$563$	1.71554	−	2.97140i	0.0723013	−	0.125229i	0.899910	+	0.436077i	$0.143632\pi$
$564$		0			0
$565$	−0.500000	−	0.181985i	−0.0210352	−	0.00765617i
$566$		0			0
$567$	−2.73783	+	2.29731i	−0.114978	+	0.0964779i
$568$		0			0
$569$	−43.5681			−1.82647			−0.913235	−	0.407433i	$-0.866424\pi$
$569$	−43.5681			−1.82647			−0.913235	+	0.407433i	$0.866424\pi$
$570$		0			0
$571$	8.14115			0.340696			0.170348	−	0.985384i	$-0.445511\pi$
$571$	8.14115			0.340696			0.170348	+	0.985384i	$0.445511\pi$
$572$		0			0
$573$	−4.63223	+	3.88690i	−0.193514	+	0.162378i
$574$		0			0
$575$	−3.94475	−	1.43577i	−0.164507	−	0.0598757i
$576$		0			0
$577$	−17.5248	+	30.3539i	−0.729568	+	1.26365i	0.227499	+	0.973778i	$0.426945\pi$
$577$	−17.5248	+	30.3539i	−0.729568	+	1.26365i	−0.957066	+	0.289870i	$0.906388\pi$
$578$		0			0
$579$	1.09374	−	6.20291i	0.0454543	−	0.257784i
$580$		0			0
$581$	14.6001	+	25.2882i	0.605716	+	1.04913i
$582$		0			0
$583$	−17.2856	−	14.5044i	−0.715898	−	0.600710i
$584$		0			0
$585$	11.9363	−	4.34445i	0.493505	−	0.179621i
$586$		0			0
$587$	−1.69594	−	9.61814i	−0.0699988	−	0.396983i	−0.999596	−	0.0284070i	$-0.990957\pi$
$587$	−1.69594	−	9.61814i	−0.0699988	−	0.396983i	0.929598	−	0.368576i	$-0.120155\pi$
$588$		0			0
$589$	20.6830	+	19.5680i	0.852230	+	0.806286i
$590$		0			0
$591$	3.46198	+	19.6339i	0.142407	+	0.807630i
$592$		0			0
$593$	30.7254	−	11.1831i	1.26174	−	0.459236i	0.377388	−	0.926055i	$-0.376822\pi$
$593$	30.7254	−	11.1831i	1.26174	−	0.459236i	0.884353	+	0.466819i	$0.154600\pi$
$594$		0			0
$595$	−24.9308	−	20.9194i	−1.02206	−	0.857614i
$596$		0			0
$597$	6.44104	+	11.1562i	0.263614	+	0.456593i
$598$		0			0
$599$	1.53580	−	8.70994i	0.0627510	−	0.355878i	−0.937223	−	0.348729i	$-0.886613\pi$
$599$	1.53580	−	8.70994i	0.0627510	−	0.355878i	0.999974	−	0.00714909i	$-0.00227565\pi$
$600$		0			0
$601$	10.9076	−	18.8925i	0.444930	−	0.770642i	−0.553117	−	0.833104i	$-0.686562\pi$
$601$	10.9076	−	18.8925i	0.444930	−	0.770642i	0.998047	+	0.0624615i	$0.0198951\pi$
$602$		0			0
$603$	−14.0360	−	5.10867i	−0.571588	−	0.208041i
$604$		0			0
$605$	6.50665	−	5.45972i	0.264533	−	0.221969i
$606$		0			0
$607$	26.5963			1.07951			0.539755	−	0.841822i	$-0.318517\pi$
$607$	26.5963			1.07951			0.539755	+	0.841822i	$0.318517\pi$
$608$		0			0
$609$	−12.6236			−0.511534
$610$		0			0
$611$	−12.3760	+	10.3847i	−0.500679	+	0.420119i
$612$		0			0
$613$	14.2280	+	5.17858i	0.574665	+	0.209161i	0.612971	−	0.790105i	$-0.289974\pi$
$613$	14.2280	+	5.17858i	0.574665	+	0.209161i	−0.0383067	+	0.999266i	$0.512196\pi$
$614$		0			0
$615$	−2.28106	+	3.95091i	−0.0919812	+	0.159316i
$616$		0			0
$617$	−5.10338	+	28.9427i	−0.205454	+	1.16519i	0.691269	+	0.722598i	$0.257052\pi$
$617$	−5.10338	+	28.9427i	−0.205454	+	1.16519i	−0.896723	+	0.442592i	$0.854059\pi$
$618$		0			0
$619$	15.7219	+	27.2312i	0.631918	+	1.09451i	0.987159	+	0.159739i	$0.0510653\pi$
$619$	15.7219	+	27.2312i	0.631918	+	1.09451i	−0.355241	+	0.934775i	$0.615601\pi$
$620$		0			0
$621$	6.30793	+	5.29298i	0.253129	+	0.212400i
$622$		0			0
$623$	39.3764	−	14.3319i	1.57758	−	0.574194i
$624$		0			0
$625$	−4.73870	−	26.8745i	−0.189548	−	1.07498i
$626$		0			0
$627$	−6.52141	+	9.88527i	−0.260440	+	0.394780i
$628$		0			0
$629$	−0.262174	−	1.48686i	−0.0104536	−	0.0592851i
$630$		0			0
$631$	−28.0736	+	10.2179i	−1.11759	+	0.406770i	−0.833773	−	0.552108i	$-0.813824\pi$
$631$	−28.0736	+	10.2179i	−1.11759	+	0.406770i	−0.283819	+	0.958878i	$0.591601\pi$
$632$		0			0
$633$	−1.77197	−	1.48686i	−0.0704297	−	0.0590975i
$634$		0			0
$635$	−10.2044	−	17.6745i	−0.404949	−	0.701392i
$636$		0			0
$637$	5.42514	−	30.7675i	0.214952	−	1.21905i
$638$		0			0
$639$	4.51114	−	7.81353i	0.178458	−	0.309099i
$640$		0			0
$641$	−6.75150	−	2.45734i	−0.266668	−	0.0970592i	0.205226	−	0.978715i	$-0.434207\pi$
$641$	−6.75150	−	2.45734i	−0.266668	−	0.0970592i	−0.471894	+	0.881655i	$0.656429\pi$
$642$		0			0
$643$	−6.95858	+	5.83894i	−0.274420	+	0.230265i	−0.769602	−	0.638523i	$-0.779546\pi$
$643$	−6.95858	+	5.83894i	−0.274420	+	0.230265i	0.495183	+	0.868789i	$0.335101\pi$
$644$		0			0
$645$	11.7888			0.464184
$646$		0			0
$647$	−37.5749			−1.47722			−0.738611	−	0.674132i	$-0.764518\pi$
$647$	−37.5749			−1.47722			−0.738611	+	0.674132i	$0.764518\pi$
$648$		0			0
$649$	5.68479	−	4.77011i	0.223148	−	0.187243i
$650$		0			0
$651$	−21.9376	−	7.98465i	−0.859804	−	0.312943i
$652$		0			0
$653$	−0.870767	+	1.50821i	−0.0340758	+	0.0590209i	−0.882560	−	0.470199i	$-0.844182\pi$
$653$	−0.870767	+	1.50821i	−0.0340758	+	0.0590209i	0.848485	+	0.529220i	$0.177515\pi$
$654$		0			0
$655$	−5.15342	+	29.2265i	−0.201361	+	1.14197i
$656$		0			0
$657$	−5.14543	−	8.91215i	−0.200742	−	0.347696i
$658$		0			0
$659$	3.98680	+	3.34532i	0.155304	+	0.130315i	0.717128	−	0.696941i	$-0.245456\pi$
$659$	3.98680	+	3.34532i	0.155304	+	0.130315i	−0.561825	+	0.827256i	$0.689901\pi$
$660$		0			0
$661$	23.3427	−	8.49605i	0.907926	−	0.330458i	0.154502	−	0.987993i	$-0.450623\pi$
$661$	23.3427	−	8.49605i	0.907926	−	0.330458i	0.753425	+	0.657534i	$0.228401\pi$
$662$		0			0
$663$	−3.64543	−	20.6743i	−0.141577	−	0.802922i
$664$		0			0
$665$	16.3659	+	32.7009i	0.634644	+	1.26809i
$666$		0			0
$667$	5.05051	+	28.6428i	0.195556	+	1.10906i
$668$		0			0
$669$	3.82547	−	1.39236i	0.147901	−	0.0538317i
$670$		0			0
$671$	−13.0929	−	10.9862i	−0.505444	−	0.424118i
$672$		0			0
$673$	−4.49613	−	7.78752i	−0.173313	−	0.300187i	0.766263	−	0.642527i	$-0.222114\pi$
$673$	−4.49613	−	7.78752i	−0.173313	−	0.300187i	−0.939576	+	0.342340i	$0.888781\pi$
$674$		0			0
$675$	0.0885259	−	0.502055i	0.00340736	−	0.0193241i
$676$		0			0
$677$	−3.20780	+	5.55607i	−0.123286	+	0.213537i	−0.921062	−	0.389417i	$-0.872676\pi$
$677$	−3.20780	+	5.55607i	−0.123286	+	0.213537i	0.797776	+	0.602954i	$0.206010\pi$
$678$		0			0
$679$	−28.8960	−	10.5173i	−1.10893	−	0.403617i
$680$		0			0
$681$	0.337496	−	0.283193i	0.0129329	−	0.0108520i
$682$		0			0
$683$	26.0000			0.994862			0.497431	−	0.867503i	$-0.334277\pi$
$683$	26.0000			0.994862			0.497431	+	0.867503i	$0.334277\pi$
$684$		0			0
$685$	−51.1566			−1.95459
$686$		0			0
$687$	−2.59627	+	2.17853i	−0.0990538	+	0.0831160i
$688$		0			0
$689$	−42.2340	−	15.3719i	−1.60899	−	0.585624i
$690$		0			0
$691$	−22.1509	+	38.3666i	−0.842662	+	1.45953i	0.0449746	+	0.998988i	$0.485679\pi$
$691$	−22.1509	+	38.3666i	−0.842662	+	1.45953i	−0.887636	+	0.460545i	$0.847654\pi$
$692$		0			0
$693$	1.68614	−	9.56256i	0.0640510	−	0.363251i
$694$		0			0
$695$	13.1762	+	22.8218i	0.499801	+	0.865680i
$696$		0			0
$697$	5.77584	+	4.84651i	0.218776	+	0.183575i
$698$		0			0
$699$	−1.98633	+	0.722965i	−0.0751299	+	0.0273450i
$700$		0			0
$701$	−8.11334	−	46.0130i	−0.306437	−	1.73789i	−0.616664	−	0.787226i	$-0.711516\pi$
$701$	−8.11334	−	46.0130i	−0.306437	−	1.73789i	0.310228	−	0.950662i	$-0.399595\pi$
$702$		0			0
$703$	−0.393523	+	1.65015i	−0.0148420	+	0.0622364i
$704$		0			0
$705$	1.21688	+	6.90128i	0.0458304	+	0.259917i
$706$		0			0
$707$	−4.31831	+	1.57173i	−0.162407	+	0.0591112i
$708$		0			0
$709$	−11.6400	−	9.76709i	−0.437148	−	0.366811i	0.397493	−	0.917605i	$-0.369880\pi$
$709$	−11.6400	−	9.76709i	−0.437148	−	0.366811i	−0.834641	+	0.550794i	$0.814325\pi$
$710$		0			0
$711$	6.50387	+	11.2650i	0.243914	+	0.422472i
$712$		0			0
$713$	−9.34018	+	52.9708i	−0.349793	+	1.98377i
$714$		0			0
$715$	−17.2554	+	29.8872i	−0.645314	+	1.11772i
$716$		0			0
$717$	−3.78611	−	1.37803i	−0.141395	−	0.0514635i
$718$		0			0
$719$	−17.9231	+	15.0393i	−0.668418	+	0.560870i	−0.912597	−	0.408861i	$-0.865926\pi$
$719$	−17.9231	+	15.0393i	−0.668418	+	0.560870i	0.244178	+	0.969730i	$0.421482\pi$
$720$		0			0
$721$	2.63217			0.0980271
$722$		0			0
$723$	−10.1771			−0.378489
$724$		0			0
$725$	1.37939	−	1.15744i	0.0512291	−	0.0429863i
$726$		0			0
$727$	32.0266	+	11.6567i	1.18780	+	0.432325i	0.858951	−	0.512057i	$-0.171117\pi$
$727$	32.0266	+	11.6567i	1.18780	+	0.432325i	0.328851	+	0.944382i	$0.393339\pi$
$728$		0			0
$729$	−0.500000	+	0.866025i	−0.0185185	+	0.0320750i
$730$		0			0
$731$	3.38326	−	19.1874i	0.125134	−	0.709671i
$732$		0			0
$733$	15.0064	+	25.9918i	0.554274	+	0.960031i	0.997960	+	0.0638481i	$0.0203373\pi$
$733$	15.0064	+	25.9918i	0.554274	+	0.960031i	−0.443686	+	0.896182i	$0.646329\pi$
$734$		0			0
$735$	−10.3812	−	8.71086i	−0.382916	−	0.321305i
$736$		0			0
$737$	38.1340	−	13.8797i	1.40469	−	0.511264i
$738$		0			0
$739$	−4.14022	−	23.4803i	−0.152300	−	0.863738i	−0.961213	−	0.275808i	$-0.911054\pi$
$739$	−4.14022	−	23.4803i	−0.152300	−	0.863738i	0.808912	−	0.587929i	$-0.200057\pi$
$740$		0			0
$741$	−5.47178	+	22.9446i	−0.201011	+	0.842892i
$742$		0			0
$743$	−5.38207	−	30.5233i	−0.197449	−	1.11979i	−0.908888	−	0.417041i	$-0.863067\pi$
$743$	−5.38207	−	30.5233i	−0.197449	−	1.11979i	0.711438	−	0.702748i	$-0.248044\pi$
$744$		0			0
$745$	−48.4791	+	17.6450i	−1.77614	+	0.646461i
$746$		0			0
$747$	6.25877	+	5.25173i	0.228996	+	0.192151i
$748$		0			0
$749$	−17.9187	−	31.0362i	−0.654737	−	1.13404i
$750$		0			0
$751$	−3.82800	+	21.7097i	−0.139686	+	0.792197i	0.831796	+	0.555082i	$0.187313\pi$
$751$	−3.82800	+	21.7097i	−0.139686	+	0.792197i	−0.971482	+	0.237115i	$0.923798\pi$
$752$		0			0
$753$	1.45471	−	2.51963i	0.0530125	−	0.0918203i
$754$		0			0
$755$	−5.20961	−	1.89614i	−0.189597	−	0.0690077i
$756$		0			0
$757$	−10.9736	+	9.20794i	−0.398842	+	0.334668i	−0.820046	−	0.572298i	$-0.806052\pi$
$757$	−10.9736	+	9.20794i	−0.398842	+	0.334668i	0.421204	+	0.906966i	$0.361608\pi$
$758$		0			0
$759$	−22.3719			−0.812050
$760$		0			0
$761$	17.2635			0.625802			0.312901	−	0.949786i	$-0.398699\pi$
$761$	17.2635			0.625802			0.312901	+	0.949786i	$0.398699\pi$
$762$		0			0
$763$	−38.1140	+	31.9815i	−1.37982	+	1.15781i
$764$		0			0
$765$	−8.55690	−	3.11446i	−0.309376	−	0.112603i
$766$		0			0
$767$	7.39053	−	12.8008i	0.266857	−	0.462209i
$768$		0			0
$769$	3.18123	−	18.0416i	0.114718	−	0.650598i	−0.872171	−	0.489200i	$-0.837289\pi$
$769$	3.18123	−	18.0416i	0.114718	−	0.650598i	0.986889	−	0.161398i	$-0.0516002\pi$
$770$		0			0
$771$	1.27972	+	2.21653i	0.0460878	+	0.0798264i
$772$		0			0
$773$	−31.5180	−	26.4467i	−1.13362	−	0.951223i	−0.134412	−	0.990925i	$-0.542915\pi$
$773$	−31.5180	−	26.4467i	−1.13362	−	0.951223i	−0.999212	+	0.0397020i	$0.987359\pi$
$774$		0			0
$775$	3.12923	−	1.13895i	0.112405	−	0.0409122i
$776$		0			0
$777$	−0.241534	−	1.36981i	−0.00866499	−	0.0491416i
$778$		0			0
$779$	−3.79157	−	7.57597i	−0.135847	−	0.271437i
$780$		0			0
$781$	4.25655	+	24.1401i	0.152311	+	0.863800i
$782$		0			0
$783$	−3.31908	+	1.20805i	−0.118614	+	0.0431720i
$784$		0			0
$785$	25.8123	+	21.6591i	0.921279	+	0.773045i
$786$		0			0
$787$	6.83662	+	11.8414i	0.243699	+	0.422099i	0.961765	−	0.273876i	$-0.0883057\pi$
$787$	6.83662	+	11.8414i	0.243699	+	0.422099i	−0.718066	+	0.695975i	$0.754972\pi$
$788$		0			0
$789$	−2.76604	+	15.6870i	−0.0984738	+	0.558473i
$790$		0			0
$791$	−0.405078	+	0.701615i	−0.0144029	+	0.0249466i
$792$		0			0
$793$	−31.9898	−	11.6433i	−1.13599	−	0.413467i
$794$		0			0
$795$	−14.9342	+	12.5313i	−0.529663	+	0.444440i
$796$		0			0
$797$	33.4935			1.18640			0.593200	−	0.805055i	$-0.297864\pi$
$797$	33.4935			1.18640			0.593200	+	0.805055i	$0.297864\pi$
$798$		0			0
$799$	11.5817			0.409732
$800$		0			0
$801$	8.98158	−	7.53644i	0.317349	−	0.266287i
$802$		0			0
$803$	26.2729	+	9.56256i	0.927151	+	0.337455i
$804$		0			0
$805$	−34.5400	+	59.8251i	−1.21738	+	2.10856i
$806$		0			0
$807$	2.93376	−	16.6382i	0.103273	−	0.585692i
$808$		0			0
$809$	−5.19207	−	8.99292i	−0.182543	−	0.316174i	0.760203	−	0.649686i	$-0.225100\pi$
$809$	−5.19207	−	8.99292i	−0.182543	−	0.316174i	−0.942746	+	0.333512i	$0.891766\pi$
$810$		0			0
$811$	−23.7362	−	19.9171i	−0.833492	−	0.699383i	0.122598	−	0.992456i	$-0.460877\pi$
$811$	−23.7362	−	19.9171i	−0.833492	−	0.699383i	−0.956090	+	0.293074i	$0.905322\pi$
$812$		0			0
$813$	−0.585122	+	0.212967i	−0.0205211	+	0.00746908i
$814$		0			0
$815$	−6.98680	−	39.6241i	−0.244737	−	1.38797i
$816$		0			0
$817$	−12.0551	+	18.2734i	−0.421756	+	0.639306i
$818$		0			0
$819$	−3.35844	−	19.0467i	−0.117353	−	0.665544i
$820$		0			0
$821$	41.6019	−	15.1419i	1.45192	−	0.528455i	0.508792	−	0.860890i	$-0.330092\pi$
$821$	41.6019	−	15.1419i	1.45192	−	0.528455i	0.943126	+	0.332435i	$0.107870\pi$
$822$		0			0
$823$	15.2947	+	12.8338i	0.533141	+	0.447358i	0.869184	−	0.494488i	$-0.164644\pi$
$823$	15.2947	+	12.8338i	0.533141	+	0.447358i	−0.336044	+	0.941846i	$0.609089\pi$
$824$		0			0
$825$	0.692533	+	1.19950i	0.0241109	+	0.0417613i
$826$		0			0
$827$	−1.46363	+	8.30066i	−0.0508954	+	0.288642i	−0.999623	−	0.0274523i	$-0.991261\pi$
$827$	−1.46363	+	8.30066i	−0.0508954	+	0.288642i	0.948728	+	0.316095i	$0.102372\pi$
$828$		0			0
$829$	−2.12361	+	3.67820i	−0.0737559	+	0.127749i	−0.900545	−	0.434764i	$-0.856832\pi$
$829$	−2.12361	+	3.67820i	−0.0737559	+	0.127749i	0.826789	+	0.562513i	$0.190165\pi$
$830$		0			0
$831$	25.8195	+	9.39755i	0.895670	+	0.325997i
$832$		0			0
$833$	−17.1570	+	14.3965i	−0.594456	+	0.498808i
$834$		0			0
$835$	−34.3141			−1.18749
$836$		0			0
$837$	−6.53209			−0.225782
$838$		0			0
$839$	−4.63357	+	3.88803i	−0.159969	+	0.134230i	−0.719259	−	0.694743i	$-0.755518\pi$
$839$	−4.63357	+	3.88803i	−0.159969	+	0.134230i	0.559290	+	0.828972i	$0.311074\pi$
$840$		0			0
$841$	15.5278	+	5.65166i	0.535442	+	0.194885i
$842$		0			0
$843$	1.24035	−	2.14835i	0.0427200	−	0.0739932i
$844$		0			0
$845$	−6.63744	+	37.6428i	−0.228335	+	1.29495i
$846$		0			0
$847$	−6.46632	−	11.2000i	−0.222185	−	0.384836i
$848$		0			0
$849$	−1.74897	−	1.46756i	−0.0600245	−	0.0503665i
$850$		0			0
$851$	−3.01145	+	1.09608i	−0.103231	+	0.0375731i
$852$		0			0
$853$	−4.47296	−	25.3674i	−0.153151	−	0.868564i	−0.960456	−	0.278430i	$-0.910186\pi$
$853$	−4.47296	−	25.3674i	−0.153151	−	0.868564i	0.807305	−	0.590134i	$-0.200925\pi$
$854$		0			0
$855$	7.43242	+	7.03174i	0.254183	+	0.240480i
$856$		0			0
$857$	−10.1083	−	57.3273i	−0.345294	−	1.95826i	−0.278234	−	0.960513i	$-0.589749\pi$
$857$	−10.1083	−	57.3273i	−0.345294	−	1.95826i	−0.0670607	−	0.997749i	$-0.521362\pi$
$858$		0			0
$859$	−9.50609	+	3.45993i	−0.324344	+	0.118051i	−0.499060	−	0.866567i	$-0.666321\pi$
$859$	−9.50609	+	3.45993i	−0.324344	+	0.118051i	0.174716	+	0.984619i	$0.444099\pi$
$860$		0			0
$861$	5.32114	+	4.46496i	0.181344	+	0.152166i
$862$		0			0
$863$	−18.1707	−	31.4726i	−0.618538	−	1.07134i	−0.989753	−	0.142792i	$-0.954392\pi$
$863$	−18.1707	−	31.4726i	−0.618538	−	1.07134i	0.371214	−	0.928547i	$-0.378941\pi$
$864$		0			0
$865$	8.42443	−	47.7773i	0.286439	−	1.62448i
$866$		0			0
$867$	0.975185	−	1.68907i	0.0331190	−	0.0573638i
$868$		0			0
$869$	−33.2092	−	12.0872i	−1.12654	−	0.410029i
$870$		0			0
$871$	61.9193	−	51.9564i	2.09805	−	1.76048i
$872$		0			0
$873$	−8.60401			−0.291202
$874$		0			0
$875$	−37.6691			−1.27345
$876$		0			0
$877$	−5.49975	+	4.61484i	−0.185713	+	0.155832i	−0.730905	−	0.682480i	$-0.760902\pi$
$877$	−5.49975	+	4.61484i	−0.185713	+	0.155832i	0.545191	+	0.838312i	$0.316457\pi$
$878$		0			0
$879$	2.25150	+	0.819478i	0.0759411	+	0.0276403i
$880$		0			0
$881$	−6.58559	+	11.4066i	−0.221874	+	0.384297i	−0.955377	−	0.295389i	$-0.904551\pi$
$881$	−6.58559	+	11.4066i	−0.221874	+	0.384297i	0.733503	+	0.679686i	$0.237884\pi$
$882$		0			0
$883$	2.17634	−	12.3426i	0.0732396	−	0.415362i	−0.926041	−	0.377424i	$-0.876810\pi$
$883$	2.17634	−	12.3426i	0.0732396	−	0.415362i	0.999280	−	0.0379381i	$-0.0120790\pi$
$884$		0			0
$885$	−3.20574	−	5.55250i	−0.107760	−	0.186645i
$886$		0			0
$887$	40.6015	+	34.0687i	1.36327	+	1.14392i	0.974959	+	0.222386i	$0.0713846\pi$
$887$	40.6015	+	34.0687i	1.36327	+	1.14392i	0.388308	+	0.921530i	$0.373060\pi$
$888$		0			0
$889$	−29.2003	+	10.6280i	−0.979346	+	0.356453i
$890$		0			0
$891$	−0.471782	−	2.67561i	−0.0158053	−	0.0896362i
$892$		0			0
$893$	−11.9418	−	5.17095i	−0.399617	−	0.173039i
$894$		0			0
$895$	2.32114	+	13.1638i	0.0775871	+	0.440018i
$896$		0			0
$897$	−41.8730	+	15.2405i	−1.39810	+	0.508867i
$898$		0			0
$899$	−17.6741	−	14.8303i	−0.589465	−	0.494620i
$900$		0			0
$901$	16.1099	+	27.9032i	0.536700	+	0.929591i
$902$		0			0
$903$	3.11691	−	17.6769i	0.103724	−	0.588249i
$904$		0			0
$905$	−26.0783	+	45.1690i	−0.866873	+	1.50147i
$906$		0			0
$907$	20.8268	+	7.58034i	0.691543	+	0.251701i	0.663796	−	0.747914i	$-0.268944\pi$
$907$	20.8268	+	7.58034i	0.691543	+	0.251701i	0.0277473	+	0.999615i	$0.491167\pi$
$908$		0			0
$909$	−0.984985	+	0.826501i	−0.0326699	+	0.0274133i
$910$		0			0
$911$	−37.1908			−1.23219			−0.616093	−	0.787674i	$-0.711285\pi$
$911$	−37.1908			−1.23219			−0.616093	+	0.787674i	$0.711285\pi$
$912$		0			0
$913$	−22.1976			−0.734633
$914$		0			0
$915$	−11.3118	+	9.49173i	−0.373957	+	0.313787i
$916$		0			0
$917$	42.4615	+	15.4547i	1.40220	+	0.510359i
$918$		0			0
$919$	5.57785	−	9.66112i	0.183996	−	0.318691i	−0.759242	−	0.650809i	$-0.774430\pi$
$919$	5.57785	−	9.66112i	0.183996	−	0.318691i	0.943238	+	0.332118i	$0.107763\pi$
$920$		0			0
$921$	0.908786	−	5.15398i	0.0299455	−	0.169829i
$922$		0			0
$923$	24.4119	+	42.2827i	0.803529	+	1.39175i
$924$		0			0
$925$	0.151988	+	0.127533i	0.00499735	+	0.00419327i
$926$		0			0
$927$	0.692066	−	0.251892i	0.0227304	−	0.00827321i
$928$		0			0
$929$	−2.15539	−	12.2238i	−0.0707161	−	0.401051i	−0.999534	−	0.0305152i	$-0.990285\pi$
$929$	−2.15539	−	12.2238i	−0.0707161	−	0.401051i	0.928818	−	0.370536i	$-0.120826\pi$
$930$		0			0
$931$	24.1181	−	7.18387i	0.790440	−	0.235442i
$932$		0			0
$933$	1.90895	+	10.8262i	0.0624961	+	0.354433i
$934$		0			0
$935$	23.2481	−	8.46161i	0.760294	−	0.276724i
$936$		0			0
$937$	10.8439	+	9.09911i	0.354255	+	0.297255i	0.802496	−	0.596658i	$-0.203505\pi$
$937$	10.8439	+	9.09911i	0.354255	+	0.297255i	−0.448241	+	0.893913i	$0.647949\pi$
$938$		0			0
$939$	15.2258	+	26.3719i	0.496875	+	0.860613i
$940$		0			0
$941$	3.23870	−	18.3676i	0.105579	−	0.598767i	−0.885409	−	0.464813i	$-0.846122\pi$
$941$	3.23870	−	18.3676i	0.105579	−	0.598767i	0.990988	−	0.133954i	$-0.0427673\pi$
$942$		0			0
$943$	8.00206	−	13.8600i	0.260583	−	0.451343i
$944$		0			0
$945$	−7.88326	−	2.86927i	−0.256442	−	0.0933374i
$946$		0			0
$947$	32.8901	−	27.5981i	1.06879	−	0.896817i	0.0738434	−	0.997270i	$-0.476473\pi$
$947$	32.8901	−	27.5981i	1.06879	−	0.896817i	0.994942	+	0.100453i	$0.0320291\pi$
$948$		0			0
$949$	55.6887			1.80773
$950$		0			0
$951$	11.3396			0.367710
$952$		0			0
$953$	28.6117	−	24.0081i	0.926825	−	0.777699i	−0.0484193	−	0.998827i	$-0.515418\pi$
$953$	28.6117	−	24.0081i	0.926825	−	0.777699i	0.975245	+	0.221128i	$0.0709739\pi$
$954$		0			0
$955$	−13.3380	−	4.85462i	−0.431606	−	0.157092i
$956$		0			0
$957$	4.79813	−	8.31061i	0.155102	−	0.268644i
$958$		0			0
$959$	−13.5256	+	76.7074i	−0.436764	+	2.47701i
$960$		0			0
$961$	−5.83409	−	10.1049i	−0.188197	−	0.325966i
$962$		0			0
$963$	−7.68139	−	6.44545i	−0.247529	−	0.207702i
$964$		0			0
$965$	13.8931	−	5.05666i	0.447233	−	0.162780i
$966$		0			0
$967$	4.52001	+	25.6343i	0.145354	+	0.824342i	0.967082	+	0.254463i	$0.0818988\pi$
$967$	4.52001	+	25.6343i	0.145354	+	0.824342i	−0.821729	+	0.569879i	$0.806990\pi$
$968$		0			0
$969$	13.5778	−	10.0789i	0.436183	−	0.323782i
$970$		0			0
$971$	1.16250	+	6.59289i	0.0373065	+	0.211576i	0.997763	−	0.0668555i	$-0.0212967\pi$
$971$	1.16250	+	6.59289i	0.0373065	+	0.211576i	−0.960456	+	0.278431i	$0.910186\pi$
$972$		0			0
$973$	37.7041	−	13.7232i	1.20874	−	0.439945i
$974$		0			0
$975$	2.11334	+	1.77330i	0.0676811	+	0.0567912i
$976$		0			0
$977$	2.43969	+	4.22567i	0.0780527	+	0.135191i	0.902410	−	0.430879i	$-0.141796\pi$
$977$	2.43969	+	4.22567i	0.0780527	+	0.135191i	−0.824357	+	0.566070i	$0.808463\pi$
$978$		0			0
$979$	−5.53146	+	31.3705i	−0.176786	+	1.00260i
$980$		0			0
$981$	−6.96064	+	12.0562i	−0.222236	+	0.384924i
$982$		0			0
$983$	−5.84611	−	2.12781i	−0.186462	−	0.0678666i	0.247102	−	0.968990i	$-0.420522\pi$
$983$	−5.84611	−	2.12781i	−0.186462	−	0.0678666i	−0.433564	+	0.901123i	$0.642744\pi$
$984$		0			0
$985$	−35.8489	+	30.0808i	−1.14224	+	0.958455i
$986$		0			0
$987$	10.6699			0.339628
$988$		0			0
$989$	−41.3556			−1.31503
$990$		0			0
$991$	7.14480	−	5.99520i	0.226962	−	0.190444i	−0.522214	−	0.852814i	$-0.674894\pi$
$991$	7.14480	−	5.99520i	0.226962	−	0.190444i	0.749176	+	0.662370i	$0.230449\pi$
$992$		0			0
$993$	12.1518	+	4.42290i	0.385627	+	0.140357i
$994$		0			0
$995$	−15.1190	+	26.1869i	−0.479305	+	0.830181i
$996$		0			0
$997$	−4.08337	+	23.1579i	−0.129322	+	0.733419i	0.849325	+	0.527870i	$0.177009\pi$
$997$	−4.08337	+	23.1579i	−0.129322	+	0.733419i	−0.978647	+	0.205549i	$0.934102\pi$
$998$		0			0
$999$	−0.194593	−	0.337044i	−0.00615664	−	0.0106636i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	912.2.bo.d.769.1		6
4.3	odd	2		114.2.i.c.85.1	yes	6
12.11	even	2		342.2.u.b.199.1		6
19.17	even	9	inner	912.2.bo.d.625.1		6
76.51	even	18		2166.2.a.p.1.2		3
76.55	odd	18		114.2.i.c.55.1	✓	6
76.63	odd	18		2166.2.a.r.1.2		3
228.131	even	18		342.2.u.b.55.1		6
228.203	odd	18		6498.2.a.bu.1.2		3
228.215	even	18		6498.2.a.bp.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
114.2.i.c.55.1	✓	6	76.55	odd	18
114.2.i.c.85.1	yes	6	4.3	odd	2
342.2.u.b.55.1		6	228.131	even	18
342.2.u.b.199.1		6	12.11	even	2
912.2.bo.d.625.1		6	19.17	even	9	inner
912.2.bo.d.769.1		6	1.1	even	1	trivial
2166.2.a.p.1.2		3	76.51	even	18
2166.2.a.r.1.2		3	76.63	odd	18
6498.2.a.bp.1.2		3	228.215	even	18
6498.2.a.bu.1.2		3	228.203	odd	18

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:	\( N \)	\(=\)	\( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	912.bo (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.766044 - 0.642788i) q^{3} +(2.20574 + 0.802823i) q^{5} +(1.78699 - 3.09516i) q^{7} +(0.173648 - 0.984808i) q^{9} +O(q^{10})\)	\(q+(0.766044 - 0.642788i) q^{3} +(2.20574 + 0.802823i) q^{5} +(1.78699 - 3.09516i) q^{7} +(0.173648 - 0.984808i) q^{9} +(1.35844 + 2.35289i) q^{11} +(4.14543 + 3.47843i) q^{13} +(2.20574 - 0.802823i) q^{15} +(-0.673648 - 3.82045i) q^{17} +(-1.01114 + 4.24000i) q^{19} +(-0.620615 - 3.51968i) q^{21} +(-7.73783 + 2.81634i) q^{23} +(0.390530 + 0.327693i) q^{25} +(-0.500000 - 0.866025i) q^{27} +(0.613341 - 3.47843i) q^{29} +(3.26604 - 5.65695i) q^{31} +(2.55303 + 0.929228i) q^{33} +(6.42649 - 5.39246i) q^{35} +0.389185 q^{37} +5.41147 q^{39} +(-1.48886 + 1.24930i) q^{41} +(4.71941 + 1.71772i) q^{43} +(1.17365 - 2.03282i) q^{45} +(-0.518418 + 2.94010i) q^{47} +(-2.88666 - 4.99984i) q^{49} +(-2.97178 - 2.49362i) q^{51} +(-7.80453 + 2.84062i) q^{53} +(1.10741 + 6.28044i) q^{55} +(1.95084 + 3.89798i) q^{57} +(-0.474308 - 2.68993i) q^{59} +(-5.91147 + 2.15160i) q^{61} +(-2.73783 - 2.29731i) q^{63} +(6.35117 + 11.0005i) q^{65} +(2.59374 - 14.7098i) q^{67} +(-4.11721 + 7.13122i) q^{69} +(8.47818 + 3.08580i) q^{71} +(7.88326 - 6.61484i) q^{73} +0.509800 q^{75} +9.71007 q^{77} +(-9.96451 + 8.36121i) q^{79} +(-0.939693 - 0.342020i) q^{81} +(-4.08512 + 7.07564i) q^{83} +(1.58125 - 8.96773i) q^{85} +(-1.76604 - 3.05888i) q^{87} +(8.98158 + 7.53644i) q^{89} +(18.1741 - 6.61484i) q^{91} +(-1.13429 - 6.43285i) q^{93} +(-5.63429 + 8.54055i) q^{95} +(-1.49407 - 8.47329i) q^{97} +(2.55303 - 0.929228i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{5} + 3 q^{7}+O(q^{10}) \) 6 * q + 3 * q^5 + 3 * q^7	\( 6 q + 3 q^{5} + 3 q^{7} + 9 q^{13} + 3 q^{15} - 3 q^{17} - 15 q^{21} - 27 q^{23} - 15 q^{25} - 3 q^{27} - 3 q^{29} + 15 q^{31} + 3 q^{33} - 12 q^{35} - 6 q^{37} + 12 q^{39} - 15 q^{41} - 3 q^{43} + 6 q^{45} - 15 q^{47} - 24 q^{49} - 3 q^{51} + 6 q^{53} - 27 q^{55} + 27 q^{59} - 15 q^{61} + 3 q^{63} + 12 q^{65} + 3 q^{67} + 6 q^{69} - 3 q^{71} + 12 q^{73} + 6 q^{75} - 42 q^{77} - 27 q^{79} - 3 q^{83} + 12 q^{85} - 6 q^{87} + 42 q^{89} + 42 q^{91} + 3 q^{93} - 24 q^{95} + 18 q^{97} + 3 q^{99}+O(q^{100}) \) 6 * q + 3 * q^5 + 3 * q^7 + 9 * q^13 + 3 * q^15 - 3 * q^17 - 15 * q^21 - 27 * q^23 - 15 * q^25 - 3 * q^27 - 3 * q^29 + 15 * q^31 + 3 * q^33 - 12 * q^35 - 6 * q^37 + 12 * q^39 - 15 * q^41 - 3 * q^43 + 6 * q^45 - 15 * q^47 - 24 * q^49 - 3 * q^51 + 6 * q^53 - 27 * q^55 + 27 * q^59 - 15 * q^61 + 3 * q^63 + 12 * q^65 + 3 * q^67 + 6 * q^69 - 3 * q^71 + 12 * q^73 + 6 * q^75 - 42 * q^77 - 27 * q^79 - 3 * q^83 + 12 * q^85 - 6 * q^87 + 42 * q^89 + 42 * q^91 + 3 * q^93 - 24 * q^95 + 18 * q^97 + 3 * q^99

Introduction

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