LMFDB - Embedded newform 405.3.l.i.28.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [405,3,Mod(28,405)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(405, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([4, 9]))

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

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

chi := DirichletCharacter("405.28");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 405 = 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	405.l (of order $12$, degree $4$, 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:	$11.0354507066$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{12})$
Coefficient field:	8.0.49787136.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 3x^{6} + 5x^{4} + 12x^{2} + 16 $ x^8 + 3x^6 + 5x^4 + 12*x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			28.2
Root			$-0.228425 - 1.39564i$ of defining polynomial
Character	$\chi$	$=$	405.28
Dual form			405.3.l.i.217.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.99009 + 0.801193i) q^{2} +(4.83465 + 2.79129i) q^{4} +(3.54933 + 3.52168i) q^{5} +(12.0091 + 3.21783i) q^{7} +(3.46410 + 3.46410i) q^{8} +(7.79129 + 13.3739i) q^{10} +(-5.24383 - 9.08258i) q^{11} +(-15.8221 + 4.23952i) q^{13} +(33.3303 + 19.2433i) q^{14} +(-3.58258 - 6.20520i) q^{16} +(-1.17985 + 1.17985i) q^{17} +1.74773i q^{19} +(7.32976 + 26.9333i) q^{20} +(-8.40264 - 31.3591i) q^{22} +(19.0585 - 5.10670i) q^{23} +(0.195508 + 24.9992i) q^{25} -50.7062 q^{26} +(49.0780 + 49.0780i) q^{28} +(-5.62159 + 3.24563i) q^{29} +(18.5000 - 32.0429i) q^{31} +(-10.8125 - 40.3527i) q^{32} +(-4.47315 + 2.58258i) q^{34} +(31.2922 + 53.7135i) q^{35} +(-45.6170 + 45.6170i) q^{37} +(-1.40027 + 5.22587i) q^{38} +(0.0957797 + 24.4947i) q^{40} +(19.6524 - 34.0390i) q^{41} +(-9.40838 + 35.1125i) q^{43} -58.5481i q^{44} +61.0780 q^{46} +(24.6751 + 6.61167i) q^{47} +(91.4293 + 52.7867i) q^{49} +(-19.4446 + 74.9067i) q^{50} +(-88.3280 - 23.6674i) q^{52} +(-64.6779 - 64.6779i) q^{53} +(13.3739 - 50.7042i) q^{55} +(30.4539 + 52.7477i) q^{56} +(-19.4095 + 5.20075i) q^{58} +(-45.3784 - 26.1992i) q^{59} +(0.252273 + 0.436950i) q^{61} +(80.9893 - 80.9893i) q^{62} -100.661i q^{64} +(-71.0881 - 40.6729i) q^{65} +(0.245126 + 0.914823i) q^{67} +(-8.99747 + 2.41086i) q^{68} +(50.5316 + 185.679i) q^{70} -60.6616 q^{71} +(25.6261 + 25.6261i) q^{73} +(-172.947 + 99.8512i) q^{74} +(-4.87841 + 8.44965i) q^{76} +(-33.7475 - 125.948i) q^{77} +(98.7866 - 57.0345i) q^{79} +(9.13701 - 34.6410i) q^{80} +(86.0345 - 86.0345i) q^{82} +(33.1688 - 123.788i) q^{83} +(-8.34274 + 0.0326220i) q^{85} +(-56.2639 + 97.4519i) q^{86} +(13.2978 - 49.6281i) q^{88} -83.4245i q^{89} -203.652 q^{91} +(106.395 + 28.5085i) q^{92} +(68.4836 + 39.5390i) q^{94} +(-6.15494 + 6.20326i) q^{95} +(-90.4428 - 24.2341i) q^{97} +(231.090 + 231.090i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 6 q^{2} + 6 q^{5} + 26 q^{7} + 44 q^{10} - 28 q^{13} + 120 q^{14} + 8 q^{16} + 24 q^{20} + 46 q^{22} + 60 q^{23} + 32 q^{25} + 136 q^{28} + 120 q^{29} + 148 q^{31} - 168 q^{32} + 20 q^{37} - 54 q^{38}+ \cdots - 274 q^{97}+O(q^{100}) $ 8 * q + 6 * q^2 + 6 * q^5 + 26 * q^7 + 44 * q^10 - 28 * q^13 + 120 * q^14 + 8 * q^16 + 24 * q^20 + 46 * q^22 + 60 * q^23 + 32 * q^25 + 136 * q^28 + 120 * q^29 + 148 * q^31 - 168 * q^32 + 20 * q^37 - 54 * q^38 - 48 * q^40 + 2 * q^43 + 232 * q^46 + 6 * q^47 + 42 * q^50 - 112 * q^52 + 52 * q^55 - 66 * q^58 - 528 * q^59 + 112 * q^61 - 84 * q^65 - 76 * q^67 + 156 * q^68 + 396 * q^70 + 260 * q^73 - 852 * q^74 - 204 * q^76 - 318 * q^77 + 340 * q^82 + 582 * q^83 + 194 * q^85 - 72 * q^88 - 896 * q^91 + 228 * q^92 + 342 * q^95 - 274 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/405\mathbb{Z}\right)^\times$.

$n$	$82$	$326$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	2.99009	+	0.801193i	1.49505	+	0.400597i	0.911438	−	0.411438i	$-0.134973\pi$
$2$	2.99009	+	0.801193i	1.49505	+	0.400597i	0.583609	+	0.812035i	$0.301640\pi$
$3$		0			0
$3$		0			0
$4$	4.83465	+	2.79129i	1.20866	+	0.697822i
$5$	3.54933	+	3.52168i	0.709866	+	0.704336i
$5$	3.54933	+	3.52168i	0.709866	+	0.704336i
$6$		0			0
$7$	12.0091	+	3.21783i	1.71559	+	0.459691i	0.976784	−	0.214228i	$-0.0687236\pi$
$7$	12.0091	+	3.21783i	1.71559	+	0.459691i	0.738805	+	0.673919i	$0.235390\pi$
$8$	3.46410	+	3.46410i	0.433013	+	0.433013i
$9$		0			0
$10$	7.79129	+	13.3739i	0.779129	+	1.33739i
$11$	−5.24383	−	9.08258i	−0.476712	−	0.825689i	0.522932	−	0.852374i	$-0.324838\pi$
$11$	−5.24383	−	9.08258i	−0.476712	−	0.825689i	−0.999644	+	0.0266855i	$0.991505\pi$
$12$		0			0
$13$	−15.8221	+	4.23952i	−1.21708	+	0.326117i	−0.809538	−	0.587068i	$-0.800282\pi$
$13$	−15.8221	+	4.23952i	−1.21708	+	0.326117i	−0.407546	+	0.913185i	$0.633616\pi$
$14$	33.3303	+	19.2433i	2.38074	+	1.37452i
$15$		0			0
$16$	−3.58258	−	6.20520i	−0.223911	−	0.387825i
$17$	−1.17985	+	1.17985i	−0.0694030	+	0.0694030i	−0.740956	−	0.671553i	$-0.765627\pi$
$17$	−1.17985	+	1.17985i	−0.0694030	+	0.0694030i	0.671553	+	0.740956i	$0.265627\pi$
$18$		0			0
$19$			1.74773i			0.0919856i	0.998942	+	0.0459928i	$0.0146451\pi$
$19$			1.74773i			0.0919856i	−0.998942	+	0.0459928i	$0.985355\pi$
$20$	7.32976	+	26.9333i	0.366488	+	1.34667i
$21$		0			0
$22$	−8.40264	−	31.3591i	−0.381938	−	1.42541i
$23$	19.0585	−	5.10670i	0.828628	−	0.222030i	0.180513	−	0.983573i	$-0.442224\pi$
$23$	19.0585	−	5.10670i	0.828628	−	0.222030i	0.648115	+	0.761542i	$0.275557\pi$
$24$		0			0
$25$	0.195508	+	24.9992i	0.00782032	+	0.999969i
$26$	−50.7062			−1.95024
$27$		0			0
$28$	49.0780	+	49.0780i	1.75279	+	1.75279i
$29$	−5.62159	+	3.24563i	−0.193848	+	0.111918i	−0.593783	−	0.804625i	$-0.702366\pi$
$29$	−5.62159	+	3.24563i	−0.193848	+	0.111918i	0.399935	+	0.916544i	$0.369033\pi$
$30$		0			0
$31$	18.5000	−	32.0429i	0.596774	−	1.03364i	−0.396520	−	0.918026i	$-0.629782\pi$
$31$	18.5000	−	32.0429i	0.596774	−	1.03364i	0.993294	−	0.115617i	$-0.0368845\pi$
$32$	−10.8125	−	40.3527i	−0.337890	−	1.26102i
$33$		0			0
$34$	−4.47315	+	2.58258i	−0.131563	+	0.0759581i
$35$	31.2922	+	53.7135i	0.894062	+	1.53467i
$36$		0			0
$37$	−45.6170	+	45.6170i	−1.23289	+	1.23289i	−0.270046	+	0.962848i	$0.587039\pi$
$37$	−45.6170	+	45.6170i	−1.23289	+	1.23289i	−0.962848	+	0.270046i	$0.912961\pi$
$38$	−1.40027	+	5.22587i	−0.0368491	+	0.137523i
$39$		0			0
$40$	0.0957797	+	24.4947i	0.00239449	+	0.612368i
$41$	19.6524	−	34.0390i	0.479328	−	0.830220i	−0.520391	−	0.853928i	$-0.674214\pi$
$41$	19.6524	−	34.0390i	0.479328	−	0.830220i	0.999719	+	0.0237081i	$0.00754722\pi$
$42$		0			0
$43$	−9.40838	+	35.1125i	−0.218799	+	0.816571i	0.765995	+	0.642847i	$0.222247\pi$
$43$	−9.40838	+	35.1125i	−0.218799	+	0.816571i	−0.984794	+	0.173724i	$0.944420\pi$
$44$		−	58.5481i		−	1.33064i
$45$		0			0
$46$	61.0780			1.32778
$47$	24.6751	+	6.61167i	0.525002	+	0.140674i	0.511579	−	0.859236i	$-0.329061\pi$
$47$	24.6751	+	6.61167i	0.525002	+	0.140674i	0.0134225	+	0.999910i	$0.495727\pi$
$48$		0			0
$49$	91.4293	+	52.7867i	1.86590	+	1.07728i
$50$	−19.4446	+	74.9067i	−0.388893	+	1.49813i
$51$		0			0
$52$	−88.3280	−	23.6674i	−1.69862	−	0.455143i
$53$	−64.6779	−	64.6779i	−1.22034	−	1.22034i	−0.967512	−	0.252825i	$-0.918640\pi$
$53$	−64.6779	−	64.6779i	−1.22034	−	1.22034i	−0.252825	−	0.967512i	$-0.581360\pi$
$54$		0			0
$55$	13.3739	−	50.7042i	0.243161	−	0.921894i
$56$	30.4539	+	52.7477i	0.543820	+	0.941924i
$57$		0			0
$58$	−19.4095	+	5.20075i	−0.334646	+	0.0896681i
$59$	−45.3784	−	26.1992i	−0.769126	−	0.444055i	0.0634370	−	0.997986i	$-0.479794\pi$
$59$	−45.3784	−	26.1992i	−0.769126	−	0.444055i	−0.832563	+	0.553931i	$0.813127\pi$
$60$		0			0
$61$	0.252273	+	0.436950i	0.00413562	+	0.00716311i	0.868086	−	0.496414i	$-0.165350\pi$
$61$	0.252273	+	0.436950i	0.00413562	+	0.00716311i	−0.863950	+	0.503577i	$0.832017\pi$
$62$	80.9893	−	80.9893i	1.30628	−	1.30628i
$63$		0			0
$64$		−	100.661i		−	1.57282i
$65$	−71.0881	−	40.6729i	−1.09366	−	0.625737i
$66$		0			0
$67$	0.245126	+	0.914823i	0.00365860	+	0.0136541i	0.967731	−	0.251986i	$-0.0810835\pi$
$67$	0.245126	+	0.914823i	0.00365860	+	0.0136541i	−0.964072	+	0.265640i	$0.914417\pi$
$68$	−8.99747	+	2.41086i	−0.132316	+	0.0354539i
$69$		0			0
$70$	50.5316	+	185.679i	0.721881	+	2.65256i
$71$	−60.6616			−0.854388			−0.427194	−	0.904160i	$-0.640498\pi$
$71$	−60.6616			−0.854388			−0.427194	+	0.904160i	$0.640498\pi$
$72$		0			0
$73$	25.6261	+	25.6261i	0.351043	+	0.351043i	0.860498	−	0.509455i	$-0.170153\pi$
$73$	25.6261	+	25.6261i	0.351043	+	0.351043i	−0.509455	+	0.860498i	$0.670153\pi$
$74$	−172.947	+	99.8512i	−2.33713	+	1.34934i
$75$		0			0
$76$	−4.87841	+	8.44965i	−0.0641896	+	0.111180i
$77$	−33.7475	−	125.948i	−0.438280	−	1.63568i
$78$		0			0
$79$	98.7866	−	57.0345i	1.25046	−	0.721955i	0.279262	−	0.960215i	$-0.409910\pi$
$79$	98.7866	−	57.0345i	1.25046	−	0.721955i	0.971201	+	0.238260i	$0.0765769\pi$
$80$	9.13701	−	34.6410i	0.114213	−	0.433013i
$81$		0			0
$82$	86.0345	−	86.0345i	1.04920	−	1.04920i
$83$	33.1688	−	123.788i	0.399624	−	1.49142i	−0.414135	−	0.910215i	$-0.635916\pi$
$83$	33.1688	−	123.788i	0.399624	−	1.49142i	0.813759	−	0.581202i	$-0.197417\pi$
$84$		0			0
$85$	−8.34274	+	0.0326220i	−0.0981499	+	0.000383788i
$86$	−56.2639	+	97.4519i	−0.654231	+	1.13316i
$87$		0			0
$88$	13.2978	−	49.6281i	0.151112	−	0.563956i
$89$		−	83.4245i		−	0.937354i	−0.883370	−	0.468677i	$-0.844731\pi$
$89$		−	83.4245i		−	0.937354i	0.883370	−	0.468677i	$-0.155269\pi$
$90$		0			0
$91$	−203.652			−2.23793
$92$	106.395	+	28.5085i	1.15647	+	0.309875i
$93$		0			0
$94$	68.4836	+	39.5390i	0.728549	+	0.420628i
$95$	−6.15494	+	6.20326i	−0.0647888	+	0.0652975i
$96$		0			0
$97$	−90.4428	−	24.2341i	−0.932400	−	0.249836i	−0.239522	−	0.970891i	$-0.576991\pi$
$97$	−90.4428	−	24.2341i	−0.932400	−	0.249836i	−0.692878	+	0.721055i	$0.743657\pi$
$98$	231.090	+	231.090i	2.35806	+	2.35806i
$99$		0			0
$100$	−68.8348	+	121.408i	−0.688348	+	1.21408i
$101$	11.7152	+	20.2913i	0.115992	+	0.200904i	0.918176	−	0.396173i	$-0.129662\pi$
$101$	11.7152	+	20.2913i	0.115992	+	0.200904i	−0.802184	+	0.597077i	$0.796329\pi$
$102$		0			0
$103$	−63.9652	+	17.1394i	−0.621021	+	0.166402i	−0.555592	−	0.831455i	$-0.687508\pi$
$103$	−63.9652	+	17.1394i	−0.621021	+	0.166402i	−0.0654292	+	0.997857i	$0.520842\pi$
$104$	−69.4955	−	40.1232i	−0.668226	−	0.385800i
$105$		0			0
$106$	−141.573	−	245.212i	−1.33560	−	2.31333i
$107$	−129.833	+	129.833i	−1.21339	+	1.21339i	−0.243483	+	0.969905i	$0.578290\pi$
$107$	−129.833	+	129.833i	−1.21339	+	1.21339i	−0.969905	+	0.243483i	$0.921710\pi$
$108$		0			0
$109$			71.5045i			0.656005i	0.944677	+	0.328003i	$0.106375\pi$
$109$			71.5045i			0.656005i	−0.944677	+	0.328003i	$0.893625\pi$
$110$	80.6130	−	140.895i	0.732845	−	1.28087i
$111$		0			0
$112$	−23.0563	−	86.0472i	−0.205860	−	0.768278i
$113$	76.5430	−	20.5096i	0.677372	−	0.181501i	0.0962986	−	0.995352i	$-0.469300\pi$
$113$	76.5430	−	20.5096i	0.677372	−	0.181501i	0.581073	+	0.813851i	$0.302633\pi$
$114$		0			0
$115$	85.6289	+	48.9925i	0.744599	+	0.426021i
$116$	−36.2379			−0.312396
$117$		0			0
$118$	−114.695	−	114.695i	−0.971992	−	0.971992i
$119$	−17.9655	+	10.3724i	−0.150971	+	0.0871631i
$120$		0			0
$121$	5.50455	−	9.53415i	0.0454921	−	0.0787947i
$122$	0.404239	+	1.50864i	0.00331343	+	0.0123659i
$123$		0			0
$124$	178.882	−	103.278i	1.44260	−	0.832884i
$125$	−87.3454	+	89.4191i	−0.698764	+	0.715353i
$126$		0			0
$127$	9.86932	−	9.86932i	0.0777112	−	0.0777112i	−0.667183	−	0.744894i	$-0.732500\pi$
$127$	9.86932	−	9.86932i	0.0777112	−	0.0777112i	0.744894	+	0.667183i	$0.232500\pi$
$128$	37.3987	−	139.574i	0.292178	−	1.09042i
$129$		0			0
$130$	−179.973	−	178.571i	−1.38441	−	1.37362i
$131$	19.4261	−	33.6470i	0.148291	−	0.256847i	−0.782305	−	0.622895i	$-0.785956\pi$
$131$	19.4261	−	33.6470i	0.148291	−	0.256847i	0.930596	+	0.366048i	$0.119290\pi$
$132$		0			0
$133$	−5.62390	+	20.9887i	−0.0422849	+	0.157810i
$134$			2.93180i			0.0218791i
$135$		0			0
$136$	−8.17424			−0.0601047
$137$	8.99747	+	2.41086i	0.0656750	+	0.0175976i	0.291507	−	0.956569i	$-0.405843\pi$
$137$	8.99747	+	2.41086i	0.0656750	+	0.0175976i	−0.225832	+	0.974166i	$0.572510\pi$
$138$		0			0
$139$	−44.5130	−	25.6996i	−0.320238	−	0.184889i	0.331261	−	0.943539i	$-0.392526\pi$
$139$	−44.5130	−	25.6996i	−0.320238	−	0.184889i	−0.651499	+	0.758650i	$0.725859\pi$
$140$	1.35697	+	347.031i	0.00969264	+	2.47880i
$141$		0			0
$142$	−181.384	−	48.6017i	−1.27735	−	0.342265i
$143$	121.474	+	121.474i	0.849469	+	0.849469i
$144$		0			0
$145$	−31.3830	−	8.27765i	−0.216434	−	0.0570872i
$146$	56.0931	+	97.1561i	0.384199	+	0.665452i
$147$		0			0
$148$	−347.873	+	93.2123i	−2.35049	+	0.629813i
$149$	120.234	+	69.4172i	0.806940	+	0.465887i	0.845892	−	0.533354i	$-0.179069\pi$
$149$	120.234	+	69.4172i	0.806940	+	0.465887i	−0.0389520	+	0.999241i	$0.512402\pi$
$150$		0			0
$151$	58.6216	+	101.536i	0.388222	+	0.672421i	0.992211	−	0.124572i	$-0.0397559\pi$
$151$	58.6216	+	101.536i	0.388222	+	0.672421i	−0.603988	+	0.796993i	$0.706423\pi$
$152$	−6.05430	+	6.05430i	−0.0398309	+	0.0398309i
$153$		0			0
$154$		−	403.633i		−	2.62100i
$155$	178.508	−	48.5799i	1.15166	−	0.313419i
$156$		0			0
$157$	63.7900	+	238.068i	0.406306	+	1.51635i	0.801634	+	0.597815i	$0.203964\pi$
$157$	63.7900	+	238.068i	0.406306	+	1.51635i	−0.395328	+	0.918540i	$0.629369\pi$
$158$	341.077	−	91.3913i	2.15871	−	0.578426i
$159$		0			0
$160$	103.732	−	181.303i	0.648327	−	1.13314i
$161$	245.308			1.52365
$162$		0			0
$163$	157.626	+	157.626i	0.967032	+	0.967032i	0.999474	−	0.0324421i	$-0.0103285\pi$
$163$	157.626	+	157.626i	0.967032	+	0.967032i	−0.0324421	+	0.999474i	$0.510328\pi$
$164$	190.025	−	109.711i	1.15869	−	0.668971i
$165$		0			0
$166$	198.356	−	343.562i	1.19491	−	2.06965i
$167$	31.6857	+	118.253i	0.189735	+	0.708099i	0.993567	+	0.113244i	$0.0361241\pi$
$167$	31.6857	+	118.253i	0.189735	+	0.708099i	−0.803833	+	0.594856i	$0.797209\pi$
$168$		0			0
$169$	86.0068	−	49.6561i	0.508916	−	0.293823i
$170$	−24.9717	−	6.58660i	−0.146892	−	0.0387447i
$171$		0			0
$172$	−143.495	+	143.495i	−0.834276	+	0.834276i
$173$	−13.6072	+	50.7829i	−0.0786546	+	0.293543i	−0.994037	−	0.109042i	$-0.965222\pi$
$173$	−13.6072	+	50.7829i	−0.0786546	+	0.293543i	0.915383	+	0.402585i	$0.131888\pi$
$174$		0			0
$175$	−78.0955	+	300.848i	−0.446260	+	1.71913i
$176$	−37.5728	+	65.0780i	−0.213482	+	0.369762i
$177$		0			0
$178$	66.8391	−	249.447i	0.375501	−	1.40139i
$179$		−	140.296i		−	0.783777i	−0.920013	−	0.391889i	$-0.871822\pi$
$179$		−	140.296i		−	0.783777i	0.920013	−	0.391889i	$-0.128178\pi$
$180$		0			0
$181$	−242.720			−1.34100			−0.670498	−	0.741911i	$-0.733920\pi$
$181$	−242.720			−1.34100			−0.670498	+	0.741911i	$0.733920\pi$
$182$	−608.937	−	163.164i	−3.34581	−	0.896507i
$183$		0			0
$184$	83.7105	+	48.3303i	0.454949	+	0.262665i
$185$	−322.559	+	1.26128i	−1.74356	+	0.00681771i
$186$		0			0
$187$	16.9030	+	4.52915i	0.0903904	+	0.0242200i
$188$	100.840	+	100.840i	0.536385	+	0.536385i
$189$		0			0
$190$	−23.3739	+	13.6170i	−0.123020	+	0.0716687i
$191$	9.03378	+	15.6470i	0.0472973	+	0.0819213i	0.888705	−	0.458480i	$-0.151606\pi$
$191$	9.03378	+	15.6470i	0.0472973	+	0.0819213i	−0.841408	+	0.540401i	$0.818273\pi$
$192$		0			0
$193$	261.278	−	70.0092i	1.35377	−	0.362742i	0.492245	−	0.870457i	$-0.336176\pi$
$193$	261.278	−	70.0092i	1.35377	−	0.362742i	0.861525	+	0.507715i	$0.169510\pi$
$194$	−251.016	−	144.924i	−1.29390	−	0.747033i
$195$		0			0
$196$	294.686	+	510.411i	1.50350	+	2.60414i
$197$	−13.5148	+	13.5148i	−0.0686031	+	0.0686031i	−0.740576	−	0.671973i	$-0.765447\pi$
$197$	−13.5148	+	13.5148i	−0.0686031	+	0.0686031i	0.671973	+	0.740576i	$0.265447\pi$
$198$		0			0
$199$			141.964i			0.713385i	0.934222	+	0.356693i	$0.116096\pi$
$199$			141.964i			0.713385i	−0.934222	+	0.356693i	$0.883904\pi$
$200$	−85.9226	+	87.2772i	−0.429613	+	0.436386i
$201$		0			0
$202$	18.7723	+	70.0590i	0.0929319	+	0.346827i
$203$	−77.9543	+	20.8878i	−0.384011	+	0.102895i
$204$		0			0
$205$	189.628	−	51.6061i	0.925013	−	0.251737i
$206$	−204.994			−0.995116
$207$		0			0
$208$	82.9909	+	82.9909i	0.398995	+	0.398995i
$209$	15.8739	−	9.16478i	0.0759515	−	0.0438506i
$210$		0			0
$211$	−96.9864	+	167.985i	−0.459651	+	0.796139i	−0.998942	−	0.0459804i	$-0.985359\pi$
$211$	−96.9864	+	167.985i	−0.459651	+	0.796139i	0.539291	+	0.842119i	$0.318692\pi$
$212$	−132.160	−	493.230i	−0.623399	−	2.32656i
$213$		0			0
$214$	−492.232	+	284.191i	−2.30015	+	1.32799i
$215$	−157.049	+	91.4927i	−0.730459	+	0.425548i
$216$		0			0
$217$	325.278	−	325.278i	1.49898	−	1.49898i
$218$	−57.2890	+	213.805i	−0.262793	+	0.980758i
$219$		0			0
$220$	206.188	−	207.807i	0.937218	−	0.944576i
$221$	13.6657	−	23.6697i	0.0618358	−	0.107103i
$222$		0			0
$223$	−5.14959	+	19.2185i	−0.0230923	+	0.0861817i	−0.976510	−	0.215471i	$-0.930871\pi$
$223$	−5.14959	+	19.2185i	−0.0230923	+	0.0861817i	0.953418	+	0.301652i	$0.0975382\pi$
$224$		−	519.393i		−	2.31872i
$225$		0			0
$226$	245.303			1.08541
$227$	202.908	+	54.3692i	0.893870	+	0.239512i	0.676382	−	0.736551i	$-0.263547\pi$
$227$	202.908	+	54.3692i	0.893870	+	0.239512i	0.217488	+	0.976063i	$0.430214\pi$
$228$		0			0
$229$	62.6399	+	36.1652i	0.273537	+	0.157926i	0.630494	−	0.776194i	$-0.282852\pi$
$229$	62.6399	+	36.1652i	0.273537	+	0.157926i	−0.356957	+	0.934121i	$0.616186\pi$
$230$	216.786	+	215.097i	0.942549	+	0.935206i
$231$		0			0
$232$	−30.7169	−	8.23058i	−0.132401	−	0.0354766i
$233$	−113.160	−	113.160i	−0.485663	−	0.485663i	0.421271	−	0.906935i	$-0.361584\pi$
$233$	−113.160	−	113.160i	−0.485663	−	0.485663i	−0.906935	+	0.421271i	$0.861584\pi$
$234$		0			0
$235$	64.2958	+	110.365i	0.273599	+	0.469637i
$236$	−146.259	−	253.328i	−0.619742	−	1.07343i
$237$		0			0
$238$	−62.0289	+	16.6206i	−0.260626	+	0.0698345i
$239$	−245.505	−	141.742i	−1.02722	−	0.593063i	−0.111030	−	0.993817i	$-0.535415\pi$
$239$	−245.505	−	141.742i	−1.02722	−	0.593063i	−0.916186	+	0.400754i	$0.868748\pi$
$240$		0			0
$241$	−240.856	−	417.174i	−0.999401	−	1.73101i	−0.529667	−	0.848206i	$-0.677683\pi$
$241$	−240.856	−	417.174i	−0.999401	−	1.73101i	−0.469734	−	0.882808i	$-0.655650\pi$
$242$	24.0978	−	24.0978i	0.0995777	−	0.0995777i
$243$		0			0
$244$			2.81667i			0.0115437i
$245$	138.615	+	509.343i	0.565775	+	2.07895i
$246$		0			0
$247$	−7.40952	−	27.6527i	−0.0299981	−	0.111954i
$248$	175.086	−	46.9141i	0.705991	−	0.189170i
$249$		0			0
$250$	−332.813	+	197.391i	−1.33125	+	0.789564i
$251$	87.5245			0.348703			0.174352	−	0.984683i	$-0.444217\pi$
$251$	87.5245			0.348703			0.174352	+	0.984683i	$0.444217\pi$
$252$		0			0
$253$	−146.321	−	146.321i	−0.578345	−	0.578345i
$254$	37.4174	−	21.6030i	0.147313	−	0.0850510i
$255$		0			0
$256$	22.3303	−	38.6772i	0.0872277	−	0.151083i
$257$	−47.7982	−	178.385i	−0.185985	−	0.694106i	−0.994418	−	0.105517i	$-0.966350\pi$
$257$	−47.7982	−	178.385i	−0.185985	−	0.694106i	0.808432	−	0.588589i	$-0.200316\pi$
$258$		0			0
$259$	−694.609	+	401.033i	−2.68189	+	1.54839i
$260$	−230.156	−	395.067i	−0.885217	−	1.51949i
$261$		0			0
$262$	85.0436	−	85.0436i	0.324594	−	0.324594i
$263$	−79.2760	+	295.862i	−0.301430	+	1.12495i	0.634546	+	0.772885i	$0.281187\pi$
$263$	−79.2760	+	295.862i	−0.301430	+	1.12495i	−0.935975	+	0.352065i	$0.885480\pi$
$264$		0			0
$265$	−1.78829	−	457.338i	−0.00674828	−	1.72580i
$266$	−33.6320	+	58.2523i	−0.126436	+	0.218994i
$267$		0			0
$268$	−1.36844	+	5.10707i	−0.00510610	+	0.0190562i
$269$			283.047i			1.05222i	0.850416	+	0.526110i	$0.176350\pi$
$269$			283.047i			1.05222i	−0.850416	+	0.526110i	$0.823650\pi$
$270$		0			0
$271$	−130.991			−0.483361			−0.241681	−	0.970356i	$-0.577699\pi$
$271$	−130.991			−0.483361			−0.241681	+	0.970356i	$0.577699\pi$
$272$	11.5481	+	3.09431i	0.0424563	+	0.0113761i
$273$		0			0
$274$	24.9717	+	14.4174i	0.0911376	+	0.0526183i
$275$	226.032	−	132.867i	0.821935	−	0.483154i
$276$		0			0
$277$	156.081	+	41.8219i	0.563471	+	0.150981i	0.529300	−	0.848435i	$-0.322454\pi$
$277$	156.081	+	41.8219i	0.563471	+	0.150981i	0.0341702	+	0.999416i	$0.489121\pi$
$278$	−112.508	−	112.508i	−0.404705	−	0.404705i
$279$		0			0
$280$	−77.6697	+	294.468i	−0.277392	+	1.05167i
$281$	12.3706	+	21.4265i	0.0440235	+	0.0762509i	0.887198	−	0.461390i	$-0.152649\pi$
$281$	12.3706	+	21.4265i	0.0440235	+	0.0762509i	−0.843174	+	0.537641i	$0.819316\pi$
$282$		0			0
$283$	113.925	−	30.5262i	0.402564	−	0.107867i	−0.0518555	−	0.998655i	$-0.516514\pi$
$283$	113.925	−	30.5262i	0.402564	−	0.107867i	0.454419	+	0.890788i	$0.349847\pi$
$284$	−293.278	−	169.324i	−1.03267	−	0.596211i
$285$		0			0
$286$	265.895	+	460.543i	0.929702	+	1.61029i
$287$	345.540	−	345.540i	1.20397	−	1.20397i
$288$		0			0
$289$			286.216i			0.990366i
$290$	−87.2060	−	49.8948i	−0.300710	−	0.172051i
$291$		0			0
$292$	52.3635	+	195.423i	0.179327	+	0.669258i
$293$	281.150	−	75.3340i	0.959558	−	0.257113i	0.255145	−	0.966903i	$-0.417877\pi$
$293$	281.150	−	75.3340i	0.959558	−	0.257113i	0.704413	+	0.709790i	$0.251210\pi$
$294$		0			0
$295$	−68.7976	−	252.798i	−0.233212	−	0.856943i
$296$	−316.044			−1.06772
$297$		0			0
$298$	303.895	+	303.895i	1.01978	+	1.01978i
$299$	−279.895	+	161.597i	−0.936103	+	0.540459i
$300$		0			0
$301$	−225.973	+	391.396i	−0.750740	+	1.30032i
$302$	93.9345	+	350.568i	0.311041	+	1.16082i
$303$		0			0
$304$	10.8450	−	6.26136i	0.0356743	−	0.0205966i
$305$	−0.643397	+	2.43930i	−0.00210950	+	0.00799772i
$306$		0			0
$307$	61.6534	−	61.6534i	0.200825	−	0.200825i	−0.599528	−	0.800354i	$-0.704645\pi$
$307$	61.6534	−	61.6534i	0.200825	−	0.200825i	0.800354	+	0.599528i	$0.204645\pi$
$308$	188.398	−	703.112i	0.611682	−	2.28283i
$309$		0			0
$310$	572.677	−	2.23929i	1.84734	−	0.00722353i
$311$	−306.228	+	530.402i	−0.984655	+	1.70547i	−0.341195	+	0.939993i	$0.610832\pi$
$311$	−306.228	+	530.402i	−0.984655	+	1.70547i	−0.643460	+	0.765480i	$0.722502\pi$
$312$		0			0
$313$	27.0473	−	100.942i	0.0864132	−	0.322499i	−0.909165	−	0.416436i	$-0.863279\pi$
$313$	27.0473	−	100.942i	0.0864132	−	0.322499i	0.995578	+	0.0939379i	$0.0299455\pi$
$314$			762.953i			2.42979i
$315$		0			0
$316$	636.798			2.01519
$317$	404.227	+	108.312i	1.27516	+	0.341679i	0.832007	−	0.554765i	$-0.187192\pi$
$317$	404.227	+	108.312i	1.27516	+	0.341679i	0.443156	+	0.896444i	$0.353859\pi$
$318$		0			0
$319$	58.9573	+	34.0390i	0.184819	+	0.106705i
$320$	354.495	−	357.278i	1.10780	−	1.11649i
$321$		0			0
$322$	733.494	+	196.539i	2.27793	+	0.610370i
$323$	−2.06206	−	2.06206i	−0.00638408	−	0.00638408i
$324$		0			0
$325$	−109.078	−	394.711i	−0.335625	−	1.21450i
$326$	345.028	+	597.606i	1.05837	+	1.83315i
$327$		0			0
$328$	185.993	−	49.8366i	0.567051	−	0.151941i
$329$	275.051	+	158.801i	0.836021	+	0.482677i
$330$		0			0
$331$	110.378	+	191.181i	0.333470	+	0.577586i	0.983190	−	0.182587i	$-0.0584472\pi$
$331$	110.378	+	191.181i	0.333470	+	0.577586i	−0.649720	+	0.760174i	$0.725114\pi$
$332$	505.887	−	505.887i	1.52375	−	1.52375i
$333$		0			0
$334$			378.973i			1.13465i
$335$	−2.35168	+	4.11027i	−0.00701995	+	0.0122695i
$336$		0			0
$337$	22.3880	+	83.5532i	0.0664332	+	0.247932i	0.991155	−	0.132713i	$-0.0423687\pi$
$337$	22.3880	+	83.5532i	0.0664332	+	0.247932i	−0.924721	+	0.380645i	$0.875702\pi$
$338$	296.953	−	79.5682i	0.878558	−	0.235409i
$339$		0			0
$340$	−40.4253	−	23.1293i	−0.118898	−	0.0680273i
$341$	−388.043			−1.13796
$342$		0			0
$343$	497.354	+	497.354i	1.45001	+	1.45001i
$344$	−154.225	+	89.0418i	−0.448328	+	0.258843i
$345$		0			0
$346$	−81.3739	+	140.944i	−0.235185	+	0.407352i
$347$	112.526	+	419.953i	0.324283	+	1.21024i	0.915031	+	0.403384i	$0.132166\pi$
$347$	112.526	+	419.953i	0.324283	+	1.21024i	−0.590748	+	0.806856i	$0.701167\pi$
$348$		0			0
$349$	336.701	−	194.395i	0.964761	−	0.557005i	0.0671257	−	0.997745i	$-0.478617\pi$
$349$	336.701	−	194.395i	0.964761	−	0.557005i	0.897635	+	0.440740i	$0.145284\pi$
$350$	−474.550	+	836.994i	−1.35586	+	2.39141i
$351$		0			0
$352$	−309.808	+	309.808i	−0.880135	+	0.880135i
$353$	5.91365	−	22.0701i	0.0167526	−	0.0625214i	−0.957044	−	0.289944i	$-0.906363\pi$
$353$	5.91365	−	22.0701i	0.0167526	−	0.0625214i	0.973796	+	0.227423i	$0.0730299\pi$
$354$		0			0
$355$	−215.308	−	213.631i	−0.606502	−	0.601777i
$356$	232.862	−	403.328i	0.654106	−	1.13294i
$357$		0			0
$358$	112.404	−	419.499i	0.313979	−	1.17178i
$359$			105.473i			0.293796i	0.989152	+	0.146898i	$0.0469289\pi$
$359$			105.473i			0.293796i	−0.989152	+	0.146898i	$0.953071\pi$
$360$		0			0
$361$	357.945			0.991539
$362$	−725.757	−	194.466i	−2.00485	−	0.537199i
$363$		0			0
$364$	−984.584	−	568.450i	−2.70490	−	1.56168i
$365$	0.708543	+	181.203i	0.00194121	+	0.496446i
$366$		0			0
$367$	178.498	+	47.8284i	0.486371	+	0.130323i	0.493668	−	0.869651i	$-0.335656\pi$
$367$	178.498	+	47.8284i	0.486371	+	0.130323i	−0.00729667	+	0.999973i	$0.502323\pi$
$368$	−99.9664	−	99.9664i	−0.271648	−	0.271648i
$369$		0			0
$370$	−965.492	−	254.661i	−2.60944	−	0.688272i
$371$	−568.602	−	984.847i	−1.53262	−	2.65458i
$372$		0			0
$373$	−291.888	+	78.2112i	−0.782542	+	0.209681i	−0.627905	−	0.778290i	$-0.716087\pi$
$373$	−291.888	+	78.2112i	−0.782542	+	0.209681i	−0.154637	+	0.987971i	$0.549421\pi$
$374$	46.9129	+	27.0852i	0.125436	+	0.0724202i
$375$		0			0
$376$	62.5735	+	108.380i	0.166419	+	0.288246i
$377$	75.1854	−	75.1854i	0.199431	−	0.199431i
$378$		0			0
$379$			142.748i			0.376643i	0.982107	+	0.188322i	$0.0603047\pi$
$379$			142.748i			0.376643i	−0.982107	+	0.188322i	$0.939695\pi$
$380$	−47.0721	+	12.8104i	−0.123874	+	0.0337116i
$381$		0			0
$382$	14.4756	+	54.0237i	0.0378943	+	0.141423i
$383$	308.517	−	82.6668i	0.805526	−	0.215840i	0.167517	−	0.985869i	$-0.446425\pi$
$383$	308.517	−	82.6668i	0.805526	−	0.215840i	0.638009	+	0.770029i	$0.279758\pi$
$384$		0			0
$385$	323.766	−	565.878i	0.840951	−	1.46981i
$386$	837.336			2.16926
$387$		0			0
$388$	−369.615	−	369.615i	−0.952616	−	0.952616i
$389$	67.7205	−	39.0984i	0.174089	−	0.100510i	−0.410424	−	0.911895i	$-0.634619\pi$
$389$	67.7205	−	39.0984i	0.174089	−	0.100510i	0.584512	+	0.811385i	$0.301286\pi$
$390$		0			0
$391$	−16.4610	+	28.5113i	−0.0420997	+	0.0729188i
$392$	133.862	+	499.579i	0.341484	+	1.27444i
$393$		0			0
$394$	−51.2385	+	29.5826i	−0.130047	+	0.0750827i
$395$	551.484	+	145.461i	1.39616	+	0.368255i
$396$		0			0
$397$	−140.027	+	140.027i	−0.352714	+	0.352714i	−0.861118	−	0.508405i	$-0.830235\pi$
$397$	−140.027	+	140.027i	−0.352714	+	0.352714i	0.508405	+	0.861118i	$0.330235\pi$
$398$	−113.740	+	424.485i	−0.285780	+	1.06654i
$399$		0			0
$400$	154.425	−	90.7748i	0.386062	−	0.226937i
$401$	−172.582	+	298.920i	−0.430378	+	0.745437i	−0.996906	−	0.0786061i	$-0.974953\pi$
$401$	−172.582	+	298.920i	−0.430378	+	0.745437i	0.566528	+	0.824043i	$0.308286\pi$
$402$		0			0
$403$	−156.862	+	585.417i	−0.389236	+	1.45265i
$404$			130.802i			0.323767i
$405$		0			0
$406$	−249.826			−0.615334
$407$	653.528	+	175.112i	1.60572	+	0.430251i
$408$		0			0
$409$	−243.075	−	140.339i	−0.594315	−	0.343128i	0.172487	−	0.985012i	$-0.444820\pi$
$409$	−243.075	−	140.339i	−0.594315	−	0.343128i	−0.766802	+	0.641884i	$0.778153\pi$
$410$	608.351	−	2.37879i	1.48378	−	0.00580192i
$411$		0			0
$412$	−357.090	−	95.6821i	−0.866724	−	0.232238i
$413$	−460.650	−	460.650i	−1.11538	−	1.11538i
$414$		0			0
$415$	553.668	−	322.553i	1.33414	−	0.777237i
$416$	342.152	+	592.624i	0.822480	+	1.42458i
$417$		0			0
$418$	54.8071	−	14.6855i	0.131117	−	0.0351328i
$419$	−427.301	−	246.702i	−1.01981	−	0.588789i	−0.105762	−	0.994391i	$-0.533728\pi$
$419$	−427.301	−	246.702i	−1.01981	−	0.588789i	−0.914049	+	0.405603i	$0.867062\pi$
$420$		0			0
$421$	−197.500	−	342.080i	−0.469121	−	0.812542i	0.530256	−	0.847838i	$-0.322096\pi$
$421$	−197.500	−	342.080i	−0.469121	−	0.812542i	−0.999377	+	0.0352961i	$0.988763\pi$
$422$	−424.587	+	424.587i	−1.00613	+	1.00613i
$423$		0			0
$424$		−	448.102i		−	1.05684i
$425$	−29.7260	−	29.2647i	−0.0699436	−	0.0688581i
$426$		0			0
$427$	1.62355	+	6.05915i	0.00380221	+	0.0141901i
$428$	−990.095	+	265.295i	−2.31331	+	0.619848i
$429$		0			0
$430$	−542.894	+	147.746i	−1.26254	+	0.343594i
$431$	23.0490			0.0534779			0.0267389	−	0.999642i	$-0.491488\pi$
$431$	23.0490			0.0534779			0.0267389	+	0.999642i	$0.491488\pi$
$432$		0			0
$433$	−357.486	−	357.486i	−0.825604	−	0.825604i	0.161302	−	0.986905i	$-0.448431\pi$
$433$	−357.486	−	357.486i	−0.825604	−	0.825604i	−0.986905	+	0.161302i	$0.948431\pi$
$434$	1233.22	−	712.001i	2.84152	−	1.64055i
$435$		0			0
$436$	−199.590	+	345.700i	−0.457775	+	0.792889i
$437$	8.92511	+	33.3090i	0.0204236	+	0.0762219i
$438$		0			0
$439$	−596.116	+	344.168i	−1.35790	+	0.783981i	−0.989340	−	0.145624i	$-0.953481\pi$
$439$	−596.116	+	344.168i	−1.35790	+	0.783981i	−0.368556	+	0.929606i	$0.620148\pi$
$440$	221.973	−	129.316i	0.504484	−	0.293900i
$441$		0			0
$442$	59.8258	−	59.8258i	0.135352	−	0.135352i
$443$	87.0946	−	325.041i	0.196602	−	0.733728i	−0.795245	−	0.606289i	$-0.792658\pi$
$443$	87.0946	−	325.041i	0.196602	−	0.733728i	0.991846	−	0.127439i	$-0.0406757\pi$
$444$		0			0
$445$	293.795	−	296.101i	0.660212	−	0.665396i
$446$	−30.7955	+	53.3394i	−0.0690482	+	0.119595i
$447$		0			0
$448$	323.909	−	1208.85i	0.723012	−	2.69832i
$449$			387.090i			0.862115i	0.902324	+	0.431058i	$0.141859\pi$
$449$			387.090i			0.862115i	−0.902324	+	0.431058i	$0.858141\pi$
$450$		0			0
$451$	−412.216			−0.914004
$452$	427.307	+	114.497i	0.945370	+	0.253311i
$453$		0			0
$454$	563.155	+	325.138i	1.24043	+	0.716163i
$455$	−722.827	−	717.196i	−1.58863	−	1.57625i
$456$		0			0
$457$	193.284	+	51.7902i	0.422940	+	0.113327i	0.464010	−	0.885830i	$-0.346410\pi$
$457$	193.284	+	51.7902i	0.422940	+	0.113327i	−0.0410700	+	0.999156i	$0.513077\pi$
$458$	158.324	+	158.324i	0.345685	+	0.345685i
$459$		0			0
$460$	277.234	+	475.877i	0.602683	+	1.03451i
$461$	−352.588	−	610.700i	−0.764832	−	1.32473i	−0.940335	−	0.340249i	$-0.889489\pi$
$461$	−352.588	−	610.700i	−0.764832	−	1.32473i	0.175503	−	0.984479i	$-0.443845\pi$
$462$		0			0
$463$	−163.673	+	43.8559i	−0.353505	+	0.0947213i	−0.431201	−	0.902256i	$-0.641910\pi$
$463$	−163.673	+	43.8559i	−0.353505	+	0.0947213i	0.0776967	+	0.996977i	$0.475243\pi$
$464$	40.2795	+	23.2554i	0.0868094	+	0.0501194i
$465$		0			0
$466$	−247.695	−	429.020i	−0.531534	−	0.920645i
$467$	−47.2065	+	47.2065i	−0.101085	+	0.101085i	−0.755840	−	0.654756i	$-0.772771\pi$
$467$	−47.2065	+	47.2065i	−0.101085	+	0.101085i	0.654756	+	0.755840i	$0.272771\pi$
$468$		0			0
$469$			11.7750i			0.0251066i
$470$	103.827	+	381.514i	0.220909	+	0.811733i
$471$		0			0
$472$	−66.4386	−	247.952i	−0.140760	−	0.525323i
$473$	368.248	−	98.6718i	0.778538	−	0.208609i
$474$		0			0
$475$	−43.6918	+	0.341695i	−0.0919828	+	0.000719357i
$476$	−115.809			−0.243297
$477$		0			0
$478$	−620.519	−	620.519i	−1.29816	−	1.29816i
$479$	−463.239	+	267.451i	−0.967095	+	0.558353i	−0.898349	−	0.439281i	$-0.855233\pi$
$479$	−463.239	+	267.451i	−0.967095	+	0.558353i	−0.0687458	+	0.997634i	$0.521900\pi$
$480$		0			0
$481$	528.363	−	915.151i	1.09847	−	1.90260i
$482$	−385.944	−	1440.36i	−0.800714	−	2.98830i
$483$		0			0
$484$	53.2251	−	30.7295i	0.109969	−	0.0634908i
$485$	−235.667	−	404.525i	−0.485911	−	0.834073i
$486$		0			0
$487$	284.693	−	284.693i	0.584586	−	0.584586i	−0.351574	−	0.936160i	$-0.614354\pi$
$487$	284.693	−	284.693i	0.584586	−	0.584586i	0.936160	+	0.351574i	$0.114354\pi$
$488$	−0.639738	+	2.38754i	−0.00131094	+	0.00489249i
$489$		0			0
$490$	6.38946	+	1634.04i	0.0130397	+	3.33478i
$491$	−29.1153	+	50.4292i	−0.0592979	+	0.102707i	−0.894150	−	0.447767i	$-0.852220\pi$
$491$	−29.1153	+	50.4292i	−0.0592979	+	0.102707i	0.834853	+	0.550474i	$0.185553\pi$
$492$		0			0
$493$	2.80328	−	10.4620i	0.00568617	−	0.0212211i
$494$		−	88.6206i		−	0.179394i
$495$		0			0
$496$	−265.111			−0.534497
$497$	−728.492	−	195.199i	−1.46578	−	0.392754i
$498$		0			0
$499$	−5.51828	−	3.18598i	−0.0110587	−	0.00638474i	0.494460	−	0.869200i	$-0.335366\pi$
$499$	−5.51828	−	3.18598i	−0.0110587	−	0.00638474i	−0.505519	+	0.862815i	$0.668699\pi$
$500$	−671.879	+	188.504i	−1.34376	+	0.377008i
$501$		0			0
$502$	261.707	+	70.1241i	0.521328	+	0.139689i
$503$	452.328	+	452.328i	0.899261	+	0.899261i	0.995371	−	0.0961100i	$-0.0306401\pi$
$503$	452.328	+	452.328i	0.899261	+	0.899261i	−0.0961100	+	0.995371i	$0.530640\pi$
$504$		0			0
$505$	−29.8784	+	113.278i	−0.0591652	+	0.224312i
$506$	−320.283	−	554.746i	−0.632970	−	1.09634i
$507$		0			0
$508$	75.2628	−	20.1666i	0.148155	−	0.0396981i
$509$	505.851	+	292.053i	0.993814	+	0.573779i	0.906412	−	0.422395i	$-0.138810\pi$
$509$	505.851	+	292.053i	0.993814	+	0.573779i	0.0874016	+	0.996173i	$0.472144\pi$
$510$		0			0
$511$	225.287	+	390.208i	0.440874	+	0.763617i
$512$	−310.943	+	310.943i	−0.607311	+	0.607311i
$513$		0			0
$514$		−	571.684i		−	1.11223i
$515$	−287.393	−	164.432i	−0.558045	−	0.319285i
$516$		0			0
$517$	−69.3409	−	258.784i	−0.134122	−	0.500549i
$518$	−2398.25	+	642.609i	−4.62983	+	1.24056i
$519$		0			0
$520$	−105.361	−	387.152i	−0.202618	−	0.744522i
$521$	512.704			0.984076			0.492038	−	0.870574i	$-0.336252\pi$
$521$	512.704			0.984076			0.492038	+	0.870574i	$0.336252\pi$
$522$		0			0
$523$	−562.973	−	562.973i	−1.07643	−	1.07643i	−0.996827	−	0.0796030i	$-0.974635\pi$
$523$	−562.973	−	562.973i	−1.07643	−	1.07643i	−0.0796030	−	0.996827i	$-0.525365\pi$
$524$	187.837	−	108.448i	0.358467	−	0.206961i
$525$		0			0
$526$	−474.085	+	821.140i	−0.901303	+	1.56110i
$527$	15.9786	+	59.6331i	0.0303200	+	0.113156i
$528$		0			0
$529$	−120.981	+	69.8485i	−0.228698	+	0.132039i
$530$	361.069	−	1368.92i	0.681263	−	2.58286i
$531$		0			0
$532$	−85.7750	+	85.7750i	−0.161231	+	0.161231i
$533$	−166.634	+	621.885i	−0.312634	+	1.16676i
$534$		0			0
$535$	−918.047	+	3.58977i	−1.71598	+	0.00670985i
$536$	−2.31990	+	4.01818i	−0.00432817	+	0.00749661i
$537$		0			0
$538$	−226.776	+	846.338i	−0.421516	+	1.57312i
$539$		−	1107.22i		−	2.05421i
$540$		0			0
$541$	−943.675			−1.74432			−0.872158	−	0.489224i	$-0.837280\pi$
$541$	−943.675			−1.74432			−0.872158	+	0.489224i	$0.837280\pi$
$542$	−391.675	−	104.949i	−0.722648	−	0.193633i
$543$		0			0
$544$	60.3672	+	34.8530i	0.110969	+	0.0640681i
$545$	−251.816	+	253.793i	−0.462048	+	0.465676i
$546$		0			0
$547$	−284.867	−	76.3299i	−0.520781	−	0.139543i	−0.0111530	−	0.999938i	$-0.503550\pi$
$547$	−284.867	−	76.3299i	−0.520781	−	0.139543i	−0.509628	+	0.860395i	$0.670217\pi$
$548$	36.7702	+	36.7702i	0.0670989	+	0.0670989i
$549$		0			0
$550$	782.310	−	216.191i	1.42238	−	0.393074i
$551$	−5.67247	−	9.82501i	−0.0102949	−	0.0178312i
$552$		0			0
$553$	1369.87	−	367.055i	2.47716	−	0.663752i
$554$	433.191	+	250.103i	0.781932	+	0.451449i
$555$		0			0
$556$	−143.470	−	248.497i	−0.258040	−	0.446938i
$557$	154.478	−	154.478i	0.277340	−	0.277340i	−0.554706	−	0.832046i	$-0.687169\pi$
$557$	154.478	−	154.478i	0.277340	−	0.277340i	0.832046	+	0.554706i	$0.187169\pi$
$558$		0			0
$559$		−	595.441i		−	1.06519i
$560$	221.196	−	386.607i	0.394994	−	0.690369i
$561$		0			0
$562$	19.8225	+	73.9786i	0.0352713	+	0.131634i
$563$	445.578	−	119.392i	0.791436	−	0.212065i	0.159615	−	0.987179i	$-0.448975\pi$
$563$	445.578	−	119.392i	0.791436	−	0.212065i	0.631821	+	0.775115i	$0.282308\pi$
$564$		0			0
$565$	343.905	+	196.765i	0.608681	+	0.348256i
$566$	365.105			0.645062
$567$		0			0
$568$	−210.138	−	210.138i	−0.369961	−	0.369961i
$569$	−461.670	+	266.546i	−0.811372	+	0.468446i	−0.847432	−	0.530904i	$-0.821852\pi$
$569$	−461.670	+	266.546i	−0.811372	+	0.468446i	0.0360604	+	0.999350i	$0.488519\pi$
$570$		0			0
$571$	29.7159	−	51.4695i	0.0520419	−	0.0901392i	−0.838831	−	0.544392i	$-0.816760\pi$
$571$	29.7159	−	51.4695i	0.0520419	−	0.0901392i	0.890873	+	0.454253i	$0.150094\pi$
$572$	248.216	+	926.354i	0.433944	+	1.61950i
$573$		0			0
$574$	1310.04	−	756.354i	2.28231	−	1.31769i
$575$	131.390	+	475.448i	0.228504	+	0.826867i
$576$		0			0
$577$	410.356	−	410.356i	0.711188	−	0.711188i	−0.255595	−	0.966784i	$-0.582272\pi$
$577$	410.356	−	410.356i	0.711188	−	0.711188i	0.966784	+	0.255595i	$0.0822715\pi$
$578$	−229.314	+	855.813i	−0.396738	+	1.48064i
$579$		0			0
$580$	−128.620	−	127.618i	−0.221759	−	0.220032i
$581$	796.656	−	1379.85i	1.37118	−	2.37496i
$582$		0			0
$583$	−248.282	+	926.601i	−0.425870	+	1.58937i
$584$			177.543i			0.304012i
$585$		0			0
$586$	901.023			1.53758
$587$	−553.331	−	148.264i	−0.942642	−	0.252580i	−0.245405	−	0.969421i	$-0.578921\pi$
$587$	−553.331	−	148.264i	−0.942642	−	0.252580i	−0.697237	+	0.716841i	$0.745587\pi$
$588$		0			0
$589$	56.0023	+	32.3330i	0.0950803	+	0.0548947i
$590$	−3.17123	−	811.010i	−0.00537497	−	1.37459i
$591$		0			0
$592$	446.490	+	119.637i	0.754205	+	0.202089i
$593$	−526.790	−	526.790i	−0.888347	−	0.888347i	0.106017	−	0.994364i	$-0.466190\pi$
$593$	−526.790	−	526.790i	−0.888347	−	0.888347i	−0.994364	+	0.106017i	$0.966190\pi$
$594$		0			0
$595$	−100.294	−	26.4538i	−0.168561	−	0.0444602i
$596$	387.527	+	671.216i	0.650213	+	1.12620i
$597$		0			0
$598$	−966.382	+	258.941i	−1.61602	+	0.433012i
$599$	−372.062	−	214.810i	−0.621139	−	0.358615i	0.156173	−	0.987730i	$-0.450084\pi$
$599$	−372.062	−	214.810i	−0.621139	−	0.358615i	−0.777312	+	0.629115i	$0.783418\pi$
$600$		0			0
$601$	−207.594	−	359.564i	−0.345415	−	0.598276i	0.640014	−	0.768363i	$-0.278928\pi$
$601$	−207.594	−	359.564i	−0.345415	−	0.598276i	−0.985429	+	0.170087i	$0.945595\pi$
$602$	−989.264	+	989.264i	−1.64330	+	1.64330i
$603$		0			0
$604$			654.519i			1.08364i
$605$	53.1137	−	14.4546i	0.0877913	−	0.0238919i
$606$		0			0
$607$	−192.319	−	717.743i	−0.316835	−	1.18244i	−0.922269	−	0.386548i	$-0.873667\pi$
$607$	−192.319	−	717.743i	−0.316835	−	1.18244i	0.605434	−	0.795895i	$-0.292999\pi$
$608$	70.5255	−	18.8972i	0.115996	−	0.0310810i
$609$		0			0
$610$	−3.87817	+	6.77826i	−0.00635766	+	0.0111119i
$611$	−418.442			−0.684847
$612$		0			0
$613$	764.432	+	764.432i	1.24703	+	1.24703i	0.957023	+	0.290010i	$0.0936588\pi$
$613$	764.432	+	764.432i	1.24703	+	1.24703i	0.290010	+	0.957023i	$0.406341\pi$
$614$	233.746	−	134.953i	0.380694	−	0.219794i
$615$		0			0
$616$	319.390	−	553.200i	0.518491	−	0.898052i
$617$	194.165	+	724.634i	0.314692	+	1.17445i	0.924276	+	0.381725i	$0.124670\pi$
$617$	194.165	+	724.634i	0.314692	+	1.17445i	−0.609584	+	0.792722i	$0.708663\pi$
$618$		0			0
$619$	1042.50	−	601.886i	1.68416	−	0.972352i	0.725320	−	0.688412i	$-0.241692\pi$
$619$	1042.50	−	601.886i	1.68416	−	0.972352i	0.958842	−	0.283940i	$-0.0916416\pi$
$620$	998.623	+	263.399i	1.61068	+	0.424838i
$621$		0			0
$622$	−1340.60	+	1340.60i	−2.15531	+	2.15531i
$623$	268.446	−	1001.85i	0.430893	−	1.60811i
$624$		0			0
$625$	−624.924	+	9.77511i	−0.999878	+	0.0156402i
$626$	161.748	−	280.156i	0.258384	−	0.447534i
$627$		0			0
$628$	−356.113	+	1329.03i	−0.567059	+	2.11629i
$629$		−	107.643i		−	0.171133i
$630$		0			0
$631$	133.973			0.212318			0.106159	−	0.994349i	$-0.466145\pi$
$631$	133.973			0.212318			0.106159	+	0.994349i	$0.466145\pi$
$632$	539.780	+	144.634i	0.854082	+	0.228851i
$633$		0			0
$634$	1121.90	+	647.728i	1.76955	+	1.02165i
$635$	69.7861	−	0.272879i	0.109899	−	0.000429731i
$636$		0			0
$637$	−1670.39	−	447.581i	−2.62228	−	0.702638i
$638$	149.016	+	149.016i	0.233568	+	0.233568i
$639$		0			0
$640$	624.276	−	363.688i	0.975431	−	0.568262i
$641$	181.019	+	313.534i	0.282401	+	0.489133i	0.971976	−	0.235082i	$-0.0755357\pi$
$641$	181.019	+	313.534i	0.282401	+	0.489133i	−0.689574	+	0.724215i	$0.742202\pi$
$642$		0			0
$643$	332.053	−	88.9734i	0.516413	−	0.138372i	0.00880592	−	0.999961i	$-0.497197\pi$
$643$	332.053	−	88.9734i	0.516413	−	0.138372i	0.507607	+	0.861589i	$0.330530\pi$
$644$	1185.98	+	684.725i	1.84158	+	1.06324i
$645$		0			0
$646$	−4.51364	−	7.81785i	−0.00698705	−	0.0121019i
$647$	−627.638	+	627.638i	−0.970075	+	0.970075i	−0.999565	−	0.0294903i	$-0.990612\pi$
$647$	−627.638	+	627.638i	−0.970075	+	0.970075i	0.0294903	+	0.999565i	$0.490612\pi$
$648$		0			0
$649$			549.537i			0.846744i
$650$	−9.91348	−	1267.62i	−0.0152515	−	1.95018i
$651$		0			0
$652$	322.088	+	1202.05i	0.493999	+	1.84363i
$653$	−468.983	+	125.664i	−0.718197	+	0.192440i	−0.599367	−	0.800474i	$-0.704581\pi$
$653$	−468.983	+	125.664i	−0.718197	+	0.192440i	−0.118830	+	0.992915i	$0.537914\pi$
$654$		0			0
$655$	187.444	−	51.0117i	0.286173	−	0.0778805i
$656$	−281.625			−0.429307
$657$		0			0
$658$	695.198	+	695.198i	1.05653	+	1.05653i
$659$	1042.51	−	601.892i	1.58195	−	0.913342i	0.587380	−	0.809311i	$-0.300159\pi$
$659$	1042.51	−	601.892i	1.58195	−	0.913342i	0.994574	−	0.104031i	$-0.0331740\pi$
$660$		0			0
$661$	394.072	−	682.552i	0.596175	−	1.03261i	−0.397205	−	0.917730i	$-0.630020\pi$
$661$	394.072	−	682.552i	0.596175	−	1.03261i	0.993380	−	0.114875i	$-0.0366468\pi$
$662$	176.869	+	660.084i	0.267174	+	0.997105i
$663$		0			0
$664$	543.713	−	313.913i	0.818845	−	0.472760i
$665$	−93.8765	+	54.6902i	−0.141168	+	0.0822408i
$666$		0			0
$667$	−90.5644	+	90.5644i	−0.135779	+	0.135779i
$668$	−176.888	+	660.154i	−0.264802	+	0.988254i
$669$		0			0
$670$	−10.3249	+	10.4059i	−0.0154103	+	0.0155312i
$671$	2.64575	−	4.58258i	0.00394300	−	0.00682947i
$672$		0			0
$673$	73.1765	−	273.098i	0.108732	−	0.405793i	−0.890010	−	0.455941i	$-0.849303\pi$
$673$	73.1765	−	273.098i	0.108732	−	0.405793i	0.998742	+	0.0501484i	$0.0159694\pi$
$674$			267.769i			0.397283i
$675$		0			0
$676$	554.417			0.820144
$677$	678.626	+	181.837i	1.00240	+	0.268593i	0.722451	−	0.691422i	$-0.243015\pi$
$677$	678.626	+	181.837i	1.00240	+	0.268593i	0.279950	+	0.960015i	$0.409682\pi$
$678$		0			0
$679$	−1008.16	−	582.060i	−1.48477	−	0.857231i
$680$	−29.0131	−	28.7871i	−0.0426663	−	0.0423340i
$681$		0			0
$682$	−1160.29	−	310.898i	−1.70130	−	0.455862i
$683$	328.645	+	328.645i	0.481179	+	0.481179i	0.905508	−	0.424329i	$-0.139490\pi$
$683$	328.645	+	328.645i	0.481179	+	0.481179i	−0.424329	+	0.905508i	$0.639490\pi$
$684$		0			0
$685$	23.4447	+	40.2432i	0.0342258	+	0.0587492i
$686$	1088.66	+	1885.61i	1.58697	+	2.74870i
$687$		0			0
$688$	251.587	−	67.4125i	0.365678	−	0.0979832i
$689$	1297.54	+	749.136i	1.88323	+	1.08728i
$690$		0			0
$691$	13.7659	+	23.8433i	0.0199217	+	0.0345054i	0.875814	−	0.482648i	$-0.160325\pi$
$691$	13.7659	+	23.8433i	0.0199217	+	0.0345054i	−0.855893	+	0.517153i	$0.826992\pi$
$692$	−207.536	+	207.536i	−0.299908	+	0.299908i
$693$		0			0
$694$			1345.85i			1.93927i
$695$	−67.4857	−	247.977i	−0.0971017	−	0.356802i
$696$		0			0
$697$	16.9740	+	63.3479i	0.0243530	+	0.0908865i
$698$	1162.52	−	311.495i	1.66550	−	0.446269i
$699$		0			0
$700$	−1217.32	+	1236.51i	−1.73903	+	1.76644i
$701$	520.641			0.742712			0.371356	−	0.928491i	$-0.378893\pi$
$701$	520.641			0.742712			0.371356	+	0.928491i	$0.378893\pi$
$702$		0			0
$703$	−79.7261	−	79.7261i	−0.113408	−	0.113408i
$704$	−914.258	+	527.847i	−1.29866	+	0.749782i
$705$		0			0
$706$	35.3648	−	61.2536i	0.0500917	−	0.0867614i
$707$	75.3950	+	281.378i	0.106641	+	0.397989i
$708$		0			0
$709$	806.321	−	465.530i	1.13727	−	0.656601i	0.191514	−	0.981490i	$-0.438660\pi$
$709$	806.321	−	465.530i	1.13727	−	0.656601i	0.945752	+	0.324889i	$0.105327\pi$
$710$	−472.632	−	811.280i	−0.665679	−	1.14265i
$711$		0			0
$712$	288.991	−	288.991i	0.405886	−	0.405886i
$713$	188.948	−	705.163i	0.265004	−	0.989008i
$714$		0			0
$715$	3.35866	+	858.945i	0.00469743	+	1.20132i
$716$	391.607	−	678.283i	0.546937	−	0.947323i
$717$		0			0
$718$	−84.5040	+	315.373i	−0.117694	+	0.439239i
$719$			441.340i			0.613824i	0.951738	+	0.306912i	$0.0992958\pi$
$719$			441.340i			0.613824i	−0.951738	+	0.306912i	$0.900704\pi$
$720$		0			0
$721$	−823.317			−1.14191
$722$	1070.29	+	286.784i	1.48240	+	0.397207i
$723$		0			0
$724$	−1173.47	−	677.503i	−1.62081	−	0.935777i
$725$	−82.2373	−	139.901i	−0.113431	−	0.192967i
$726$		0			0
$727$	256.079	+	68.6162i	0.352241	+	0.0943826i	0.430601	−	0.902542i	$-0.358302\pi$
$727$	256.079	+	68.6162i	0.352241	+	0.0943826i	−0.0783600	+	0.996925i	$0.524968\pi$
$728$	−705.470	−	705.470i	−0.969052	−	0.969052i
$729$		0			0
$730$	−143.060	+	542.381i	−0.195972	+	0.742988i
$731$	−30.3271	−	52.5280i	−0.0414871	−	0.0718578i
$732$		0			0
$733$	289.109	−	77.4665i	0.394419	−	0.105684i	−0.0561580	−	0.998422i	$-0.517885\pi$
$733$	289.109	−	77.4665i	0.394419	−	0.105684i	0.450577	+	0.892738i	$0.351218\pi$
$734$	495.406	+	286.023i	0.674941	+	0.389677i
$735$		0			0
$736$	−412.138	−	713.844i	−0.559970	−	0.969896i
$737$	7.02355	−	7.02355i	0.00952992	−	0.00952992i
$738$		0			0
$739$			784.720i			1.06187i	0.847413	+	0.530934i	$0.178159\pi$
$739$			784.720i			1.06187i	−0.847413	+	0.530934i	$0.821841\pi$
$740$	−1562.98	−	894.256i	−2.11214	−	1.20845i
$741$		0			0
$742$	−911.120	−	3400.35i	−1.22792	−	4.58268i
$743$	−1172.26	+	314.107i	−1.57774	+	0.422755i	−0.938226	−	0.346022i	$-0.887532\pi$
$743$	−1172.26	+	314.107i	−1.57774	+	0.422755i	−0.639517	+	0.768777i	$0.720866\pi$
$744$		0			0
$745$	182.285	+	669.811i	0.244678	+	0.899075i
$746$	−935.435			−1.25393
$747$		0			0
$748$	69.0780	+	69.0780i	0.0923503	+	0.0923503i
$749$	−1976.95	+	1141.40i	−2.63946	+	1.52389i
$750$		0			0
$751$	−55.7023	+	96.4792i	−0.0741708	+	0.128468i	−0.900725	−	0.434389i	$-0.856964\pi$
$751$	−55.7023	+	96.4792i	−0.0741708	+	0.128468i	0.826555	+	0.562857i	$0.190298\pi$
$752$	−47.3736	−	176.801i	−0.0629968	−	0.235107i
$753$		0			0
$754$	285.050	−	164.573i	0.378050	−	0.218267i
$755$	−149.509	+	566.830i	−0.198025	+	0.750768i
$756$		0			0
$757$	668.748	−	668.748i	0.883418	−	0.883418i	−0.110462	−	0.993880i	$-0.535233\pi$
$757$	668.748	−	668.748i	0.883418	−	0.883418i	0.993880	+	0.110462i	$0.0352330\pi$
$758$	−114.369	+	426.829i	−0.150882	+	0.563099i
$759$		0			0
$760$	−42.8101	+	0.167397i	−0.0563290	+	0.000220259i
$761$	627.722	−	1087.25i	0.824864	−	1.42871i	−0.0771588	−	0.997019i	$-0.524585\pi$
$761$	627.722	−	1087.25i	0.824864	−	1.42871i	0.902023	−	0.431688i	$-0.142082\pi$
$762$		0			0
$763$	−230.090	+	858.707i	−0.301559	+	1.12543i
$764$			100.864i			0.132020i
$765$		0			0
$766$	988.726			1.29076
$767$	829.054	+	222.144i	1.08090	+	0.289627i
$768$		0			0
$769$	456.845	+	263.759i	0.594076	+	0.342990i	0.766708	−	0.641996i	$-0.221894\pi$
$769$	456.845	+	263.759i	0.594076	+	0.342990i	−0.172631	+	0.984987i	$0.555227\pi$
$770$	1421.47	−	1432.63i	1.84606	−	1.86056i
$771$		0			0
$772$	1458.60	+	390.831i	1.88938	+	0.506258i
$773$	−97.6183	−	97.6183i	−0.126285	−	0.126285i	0.641139	−	0.767424i	$-0.278462\pi$
$773$	−97.6183	−	97.6183i	−0.126285	−	0.126285i	−0.767424	+	0.641139i	$0.778462\pi$
$774$		0			0
$775$	804.666	+	456.221i	1.03828	+	0.588673i
$776$	−229.354	−	397.252i	−0.295559	−	0.511923i
$777$		0			0
$778$	233.816	−	62.6508i	0.300535	−	0.0805280i
$779$	59.4909	+	34.3471i	0.0763683	+	0.0440913i
$780$		0			0
$781$	318.099	+	550.963i	0.407297	+	0.705459i
$782$	−72.0629	+	72.0629i	−0.0921521	+	0.0921521i
$783$		0			0
$784$		−	756.450i		−	0.964860i
$785$	−611.987	+	1069.63i	−0.779601	+	1.36259i
$786$		0			0
$787$	−6.55255	−	24.4544i	−0.00832598	−	0.0310730i	0.961638	−	0.274322i	$-0.0884534\pi$
$787$	−6.55255	−	24.4544i	−0.00832598	−	0.0310730i	−0.969964	+	0.243249i	$0.921787\pi$
$788$	−103.063	+	27.6157i	−0.130791	+	0.0350453i
$789$		0			0
$790$	1532.45	+	876.787i	1.93981	+	1.10986i
$791$	985.211			1.24553
$792$		0			0
$793$	−5.84394	−	5.84394i	−0.00736941	−	0.00736941i
$794$	−530.884	+	306.506i	−0.668619	+	0.386028i
$795$		0			0
$796$	−396.261	+	686.345i	−0.497816	+	0.862242i
$797$	−39.8418	−	148.692i	−0.0499897	−	0.186564i	0.936416	−	0.350891i	$-0.114121\pi$
$797$	−39.8418	−	148.692i	−0.0499897	−	0.186564i	−0.986406	+	0.164327i	$0.947455\pi$
$798$		0			0
$799$	−36.9137	+	21.3121i	−0.0461998	+	0.0266735i
$800$	1006.67	−	278.193i	1.25834	−	0.347741i
$801$		0			0
$802$	−755.528	+	755.528i	−0.942055	+	0.942055i
$803$	98.3723	−	367.130i	0.122506	−	0.457198i
$804$		0			0
$805$	870.679	+	863.896i	1.08159	+	1.07316i
$806$	−938.065	+	1624.78i	−1.16385	+	2.01585i
$807$		0			0
$808$	−29.7085	+	110.874i	−0.0367680	+	0.137220i
$809$		−	992.609i		−	1.22696i	−0.789711	−	0.613479i	$-0.789769\pi$
$809$		−	992.609i		−	1.22696i	0.789711	−	0.613479i	$-0.210231\pi$
$810$		0			0
$811$	815.730			1.00583			0.502916	−	0.864335i	$-0.332261\pi$
$811$	815.730			1.00583			0.502916	+	0.864335i	$0.332261\pi$
$812$	−435.186	−	116.608i	−0.535943	−	0.143605i
$813$		0			0
$814$	1813.81	+	1047.20i	2.22827	+	1.28649i
$815$	4.35824	+	1114.58i	0.00534754	+	1.36758i
$816$		0			0
$817$	−61.3671	−	16.4433i	−0.0751128	−	0.0201264i
$818$	−614.378	−	614.378i	−0.751073	−	0.751073i
$819$		0			0
$820$	1060.83	+	279.808i	1.29370	+	0.341229i
$821$	−589.787	−	1021.54i	−0.718377	−	1.24427i	−0.961643	−	0.274305i	$-0.911552\pi$
$821$	−589.787	−	1021.54i	−0.718377	−	1.24427i	0.243266	−	0.969960i	$-0.421781\pi$
$822$		0			0
$823$	−1199.38	+	321.372i	−1.45732	+	0.390489i	−0.898565	−	0.438841i	$-0.855389\pi$
$823$	−1199.38	+	321.372i	−1.45732	+	0.390489i	−0.558759	+	0.829330i	$0.688722\pi$
$824$	−280.955	−	162.209i	−0.340964	−	0.196856i
$825$		0			0
$826$	−1008.32	−	1746.46i	−1.22072	−	2.11435i
$827$	537.516	−	537.516i	0.649959	−	0.649959i	−0.303024	−	0.952983i	$-0.597996\pi$
$827$	537.516	−	537.516i	0.649959	−	0.649959i	0.952983	+	0.303024i	$0.0979962\pi$
$828$		0			0
$829$		−	600.964i		−	0.724926i	−0.931998	−	0.362463i	$-0.881936\pi$
$829$		−	600.964i		−	0.724926i	0.931998	−	0.362463i	$-0.118064\pi$
$830$	1913.95	−	520.870i	2.30596	−	0.627554i
$831$		0			0
$832$	426.752	+	1592.66i	0.512923	+	1.91426i
$833$	−170.153	+	45.5925i	−0.204266	+	0.0547328i
$834$		0			0
$835$	−303.985	+	531.304i	−0.364054	+	0.636293i
$836$	102.326			0.122400
$837$		0			0
$838$	−1080.01	−	1080.01i	−1.28880	−	1.28880i
$839$	83.9864	−	48.4895i	0.100103	−	0.0577945i	−0.449113	−	0.893475i	$-0.648260\pi$
$839$	83.9864	−	48.4895i	0.100103	−	0.0577945i	0.549216	+	0.835681i	$0.314927\pi$
$840$		0			0
$841$	−399.432	+	691.836i	−0.474949	+	0.822635i
$842$	−316.471	−	1181.09i	−0.375857	−	1.40272i
$843$		0			0
$844$	−937.791	+	541.434i	−1.11113	+	0.641509i
$845$	480.140	+	126.643i	0.568213	+	0.149873i
$846$		0			0
$847$	96.7841	−	96.7841i	0.114267	−	0.114267i
$848$	−169.626	+	633.053i	−0.200031	+	0.746525i
$849$		0			0
$850$	−65.4370	−	111.320i	−0.0769847	−	0.130965i
$851$	−636.438	+	1102.34i	−0.747871	+	1.29535i
$852$		0			0
$853$	222.628	−	830.861i	0.260995	−	0.974045i	−0.703662	−	0.710535i	$-0.748453\pi$
$853$	222.628	−	830.861i	0.260995	−	0.974045i	0.964657	−	0.263510i	$-0.0848803\pi$
$854$			19.4182i			0.0227380i
$855$		0			0
$856$	−899.506			−1.05082
$857$	1302.12	+	348.902i	1.51939	+	0.407120i	0.919541	−	0.392993i	$-0.128560\pi$
$857$	1302.12	+	348.902i	1.51939	+	0.407120i	0.599850	+	0.800113i	$0.295227\pi$
$858$		0			0
$859$	124.517	+	71.8901i	0.144956	+	0.0836905i	0.570724	−	0.821142i	$-0.306663\pi$
$859$	124.517	+	71.8901i	0.144956	+	0.0836905i	−0.425768	+	0.904832i	$0.639996\pi$
$860$	−1014.66	+	3.96754i	−1.17984	+	0.00461342i
$861$		0			0
$862$	68.9186	+	18.4667i	0.0799519	+	0.0214231i
$863$	−945.308	−	945.308i	−1.09537	−	1.09537i	−0.994944	−	0.100430i	$-0.967978\pi$
$863$	−945.308	−	945.308i	−1.09537	−	1.09537i	−0.100430	−	0.994944i	$-0.532022\pi$
$864$		0			0
$865$	−227.138	+	132.325i	−0.262587	+	0.152977i
$866$	−782.502	−	1355.33i	−0.903582	−	1.56505i
$867$		0			0
$868$	2480.55	−	664.661i	2.85777	−	0.765738i
$869$	−1036.04	−	598.158i	−1.19222	−	0.688329i
$870$		0			0
$871$	−7.75682	−	13.4352i	−0.00890565	−	0.0154250i
$872$	−247.699	+	247.699i	−0.284059	+	0.284059i
$873$		0			0
$874$			106.748i			0.122137i
$875$	−1336.68	+	792.782i	−1.52763	+	0.906036i
$876$		0			0
$877$	299.426	+	1117.47i	0.341421	+	1.27420i	0.896738	+	0.442561i	$0.145930\pi$
$877$	299.426	+	1117.47i	0.341421	+	1.27420i	−0.555318	+	0.831638i	$0.687403\pi$
$878$	−2058.19	+	551.490i	−2.34418	+	0.628121i
$879$		0			0
$880$	−362.543	+	98.6640i	−0.411980	+	0.112118i
$881$	−1608.71			−1.82601			−0.913003	−	0.407952i	$-0.866243\pi$
$881$	−1608.71			−1.82601			−0.913003	+	0.407952i	$0.866243\pi$
$882$		0			0
$883$	−12.3011	−	12.3011i	−0.0139311	−	0.0139311i	0.700107	−	0.714038i	$-0.253136\pi$
$883$	−12.3011	−	12.3011i	−0.0139311	−	0.0139311i	−0.714038	+	0.700107i	$0.753136\pi$
$884$	132.138	−	76.2898i	0.149477	−	0.0863007i
$885$		0			0
$886$	520.842	−	902.125i	0.587858	−	1.01820i
$887$	−86.4257	−	322.545i	−0.0974360	−	0.363636i	0.899942	−	0.436011i	$-0.143609\pi$
$887$	−86.4257	−	322.545i	−0.0974360	−	0.363636i	−0.997378	+	0.0723746i	$0.976942\pi$
$888$		0			0
$889$	150.280	−	86.7640i	0.169044	−	0.0975973i
$890$	1115.71	−	649.984i	1.25360	−	0.730319i
$891$		0			0
$892$	−78.5409	+	78.5409i	−0.0880504	+	0.0880504i
$893$	−11.5554	+	43.1253i	−0.0129400	+	0.0482926i
$894$		0			0
$895$	494.078	−	497.957i	0.552043	−	0.556377i
$896$	898.252	−	1555.82i	1.00251	−	1.73640i
$897$		0			0
$898$	−310.134	+	1157.43i	−0.345361	+	1.28890i
$899$			240.176i			0.267159i
$900$		0			0
$901$	152.620			0.169390
$902$	−1232.56	−	330.265i	−1.36648	−	0.366147i
$903$		0			0
$904$	336.200	+	194.105i	0.371903	+	0.214718i
$905$	−861.495	−	854.784i	−0.951929	−	0.944513i
$906$		0			0
$907$	−171.869	−	46.0521i	−0.189491	−	0.0507741i	0.162825	−	0.986655i	$-0.447939\pi$
$907$	−171.869	−	46.0521i	−0.189491	−	0.0507741i	−0.352317	+	0.935881i	$0.614606\pi$
$908$	829.232	+	829.232i	0.913251	+	0.913251i
$909$		0			0
$910$	−1586.71	−	2723.61i	−1.74363	−	2.99298i
$911$	604.208	+	1046.52i	0.663236	+	1.14876i	0.979760	+	0.200175i	$0.0641510\pi$
$911$	604.208	+	1046.52i	0.663236	+	1.14876i	−0.316524	+	0.948585i	$0.602516\pi$
$912$		0			0
$913$	−1298.24	+	347.863i	−1.42195	+	0.381011i
$914$	536.443	+	309.715i	0.586918	+	0.338857i
$915$		0			0
$916$	201.895	+	349.692i	0.220409	+	0.381760i
$917$	341.561	−	341.561i	0.372476	−	0.372476i
$918$		0			0
$919$		−	58.7205i		−	0.0638960i	−0.999490	−	0.0319480i	$-0.989829\pi$
$919$		−	58.7205i		−	0.0638960i	0.999490	−	0.0319480i	$-0.0101711\pi$
$920$	126.912	+	466.342i	0.137948	+	0.506894i
$921$		0			0
$922$	−564.982	−	2108.54i	−0.612778	−	2.28692i
$923$	959.793	−	257.176i	1.03986	−	0.278630i
$924$		0			0
$925$	−1149.31	−	1131.47i	−1.24250	−	1.22321i
$926$	−524.534			−0.566451
$927$		0			0
$928$	191.753	+	191.753i	0.206630	+	0.206630i
$929$	1322.56	−	763.581i	1.42364	−	0.821939i	0.427032	−	0.904237i	$-0.359559\pi$
$929$	1322.56	−	763.581i	1.42364	−	0.821939i	0.996608	+	0.0822977i	$0.0262258\pi$
$930$		0			0
$931$	−92.2568	+	159.793i	−0.0990943	+	0.171636i
$932$	−231.226	−	862.948i	−0.248097	−	0.925910i
$933$		0			0
$934$	−178.973	+	103.330i	−0.191620	+	0.110632i
$935$	44.0442	+	75.6025i	0.0471061	+	0.0808583i
$936$		0			0
$937$	−566.027	+	566.027i	−0.604085	+	0.604085i	−0.941394	−	0.337309i	$-0.890483\pi$
$937$	−566.027	+	566.027i	−0.604085	+	0.604085i	0.337309	+	0.941394i	$0.390483\pi$
$938$	−9.43405	+	35.2084i	−0.0100576	+	0.0375356i
$939$		0			0
$940$	2.78816	+	713.043i	0.00296613	+	0.758557i
$941$	−532.845	+	922.914i	−0.566254	+	0.980780i	0.430678	+	0.902506i	$0.358274\pi$
$941$	−532.845	+	922.914i	−0.566254	+	0.980780i	−0.996932	+	0.0782748i	$0.975059\pi$
$942$		0			0
$943$	200.718	−	749.090i	0.212851	−	0.794369i
$944$			375.443i			0.397715i
$945$		0			0
$946$	1180.15			1.24752
$947$	493.784	+	132.309i	0.521419	+	0.139714i	0.509923	−	0.860220i	$-0.329674\pi$
$947$	493.784	+	132.309i	0.521419	+	0.139714i	0.0114960	+	0.999934i	$0.496341\pi$
$948$		0			0
$949$	−514.102	−	296.817i	−0.541730	−	0.312768i
$950$	−130.916	−	33.9839i	−0.137807	−	0.0357725i
$951$		0			0
$952$	−98.1655	−	26.3034i	−0.103115	−	0.0276296i
$953$	−477.641	−	477.641i	−0.501198	−	0.501198i	0.410612	−	0.911810i	$-0.365315\pi$
$953$	−477.641	−	477.641i	−0.501198	−	0.501198i	−0.911810	+	0.410612i	$0.865315\pi$
$954$		0			0
$955$	−23.0398	+	87.3504i	−0.0241254	+	0.0914664i
$956$	−791.286	−	1370.55i	−0.827705	−	1.43363i
$957$		0			0
$958$	−1599.41	+	428.560i	−1.66953	+	0.447349i
$959$	100.294	+	57.9047i	0.104582	+	0.0603803i
$960$		0			0
$961$	−204.000	−	353.338i	−0.212279	−	0.367678i
$962$	2313.07	−	2313.07i	2.40444	−	2.40444i
$963$		0			0
$964$		−	2689.19i		−	2.78962i
$965$	1173.91	+	671.651i	1.21649	+	0.696012i
$966$		0			0
$967$	124.204	+	463.536i	0.128443	+	0.479355i	0.999939	−	0.0110472i	$-0.00351651\pi$
$967$	124.204	+	463.536i	0.128443	+	0.479355i	−0.871496	+	0.490402i	$0.836850\pi$
$968$	52.0956	−	13.9590i	0.0538177	−	0.0144204i
$969$		0			0
$970$	−380.563	−	1398.38i	−0.392333	−	1.44163i
$971$	−364.302			−0.375182			−0.187591	−	0.982247i	$-0.560068\pi$
$971$	−364.302			−0.375182			−0.187591	+	0.982247i	$0.560068\pi$
$972$		0			0
$973$	−451.866	−	451.866i	−0.464404	−	0.464404i
$974$	1079.35	−	623.165i	1.10817	−	0.639800i
$975$		0			0
$976$	1.80757	−	3.13081i	0.00185202	−	0.00320780i
$977$	−21.6947	−	80.9659i	−0.0222055	−	0.0828719i	0.953934	−	0.300017i	$-0.0969923\pi$
$977$	−21.6947	−	80.9659i	−0.0222055	−	0.0828719i	−0.976139	+	0.217145i	$0.930326\pi$
$978$		0			0
$979$	−757.709	+	437.464i	−0.773962	+	0.446847i
$980$	−751.567	+	2849.41i	−0.766906	+	2.90756i
$981$		0			0
$982$	−127.461	+	127.461i	−0.129797	+	0.129797i
$983$	−4.93067	+	18.4015i	−0.00501595	+	0.0187198i	−0.968388	−	0.249447i	$-0.919751\pi$
$983$	−4.93067	+	18.4015i	−0.00501595	+	0.0187198i	0.963373	+	0.268167i	$0.0864178\pi$
$984$		0			0
$985$	−95.5634	+	0.373674i	−0.0970187	+	0.000379365i
$986$	16.7642	−	29.0364i	0.0170022	−	0.0294486i
$987$		0			0
$988$	41.3642	−	154.373i	0.0418666	−	0.156248i
$989$			717.237i			0.725214i
$990$		0			0
$991$	522.405			0.527149			0.263574	−	0.964639i	$-0.415099\pi$
$991$	522.405			0.527149			0.263574	+	0.964639i	$0.415099\pi$
$992$	−1493.05	−	400.061i	−1.50509	−	0.403288i
$993$		0			0
$994$	−2021.87	−	1167.33i	−2.03407	−	1.17437i
$995$	−499.951	+	503.876i	−0.502463	+	0.506408i
$996$		0			0
$997$	−573.696	−	153.721i	−0.575422	−	0.154184i	−0.0406400	−	0.999174i	$-0.512940\pi$
$997$	−573.696	−	153.721i	−0.575422	−	0.154184i	−0.534782	+	0.844990i	$0.679606\pi$
$998$	−13.9476	−	13.9476i	−0.0139756	−	0.0139756i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	405.3.l.i.28.2		8
3.2	odd	2		405.3.l.e.28.1		8
5.2	odd	4		405.3.l.e.352.1		8
9.2	odd	6	inner	405.3.l.i.298.2		8
9.4	even	3		405.3.g.d.163.1	yes	8
9.5	odd	6		405.3.g.d.163.4	yes	8
9.7	even	3		405.3.l.e.298.1		8
15.2	even	4	inner	405.3.l.i.352.2		8
45.2	even	12		405.3.l.e.217.1		8
45.7	odd	12	inner	405.3.l.i.217.2		8
45.22	odd	12		405.3.g.d.82.1	✓	8
45.32	even	12		405.3.g.d.82.4	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
405.3.g.d.82.1	✓	8	45.22	odd	12
405.3.g.d.82.4	yes	8	45.32	even	12
405.3.g.d.163.1	yes	8	9.4	even	3
405.3.g.d.163.4	yes	8	9.5	odd	6
405.3.l.e.28.1		8	3.2	odd	2
405.3.l.e.217.1		8	45.2	even	12
405.3.l.e.298.1		8	9.7	even	3
405.3.l.e.352.1		8	5.2	odd	4
405.3.l.i.28.2		8	1.1	even	1	trivial
405.3.l.i.217.2		8	45.7	odd	12	inner
405.3.l.i.298.2		8	9.2	odd	6	inner
405.3.l.i.352.2		8	15.2	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 405 = 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	405.l (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.99009 + 0.801193i) q^{2} +(4.83465 + 2.79129i) q^{4} +(3.54933 + 3.52168i) q^{5} +(12.0091 + 3.21783i) q^{7} +(3.46410 + 3.46410i) q^{8} +(7.79129 + 13.3739i) q^{10} +(-5.24383 - 9.08258i) q^{11} +(-15.8221 + 4.23952i) q^{13} +(33.3303 + 19.2433i) q^{14} +(-3.58258 - 6.20520i) q^{16} +(-1.17985 + 1.17985i) q^{17} +1.74773i q^{19} +(7.32976 + 26.9333i) q^{20} +(-8.40264 - 31.3591i) q^{22} +(19.0585 - 5.10670i) q^{23} +(0.195508 + 24.9992i) q^{25} -50.7062 q^{26} +(49.0780 + 49.0780i) q^{28} +(-5.62159 + 3.24563i) q^{29} +(18.5000 - 32.0429i) q^{31} +(-10.8125 - 40.3527i) q^{32} +(-4.47315 + 2.58258i) q^{34} +(31.2922 + 53.7135i) q^{35} +(-45.6170 + 45.6170i) q^{37} +(-1.40027 + 5.22587i) q^{38} +(0.0957797 + 24.4947i) q^{40} +(19.6524 - 34.0390i) q^{41} +(-9.40838 + 35.1125i) q^{43} -58.5481i q^{44} +61.0780 q^{46} +(24.6751 + 6.61167i) q^{47} +(91.4293 + 52.7867i) q^{49} +(-19.4446 + 74.9067i) q^{50} +(-88.3280 - 23.6674i) q^{52} +(-64.6779 - 64.6779i) q^{53} +(13.3739 - 50.7042i) q^{55} +(30.4539 + 52.7477i) q^{56} +(-19.4095 + 5.20075i) q^{58} +(-45.3784 - 26.1992i) q^{59} +(0.252273 + 0.436950i) q^{61} +(80.9893 - 80.9893i) q^{62} -100.661i q^{64} +(-71.0881 - 40.6729i) q^{65} +(0.245126 + 0.914823i) q^{67} +(-8.99747 + 2.41086i) q^{68} +(50.5316 + 185.679i) q^{70} -60.6616 q^{71} +(25.6261 + 25.6261i) q^{73} +(-172.947 + 99.8512i) q^{74} +(-4.87841 + 8.44965i) q^{76} +(-33.7475 - 125.948i) q^{77} +(98.7866 - 57.0345i) q^{79} +(9.13701 - 34.6410i) q^{80} +(86.0345 - 86.0345i) q^{82} +(33.1688 - 123.788i) q^{83} +(-8.34274 + 0.0326220i) q^{85} +(-56.2639 + 97.4519i) q^{86} +(13.2978 - 49.6281i) q^{88} -83.4245i q^{89} -203.652 q^{91} +(106.395 + 28.5085i) q^{92} +(68.4836 + 39.5390i) q^{94} +(-6.15494 + 6.20326i) q^{95} +(-90.4428 - 24.2341i) q^{97} +(231.090 + 231.090i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 6 q^{2} + 6 q^{5} + 26 q^{7} + 44 q^{10} - 28 q^{13} + 120 q^{14} + 8 q^{16} + 24 q^{20} + 46 q^{22} + 60 q^{23} + 32 q^{25} + 136 q^{28} + 120 q^{29} + 148 q^{31} - 168 q^{32} + 20 q^{37} - 54 q^{38}+ \cdots - 274 q^{97}+O(q^{100}) \) 8 * q + 6 * q^2 + 6 * q^5 + 26 * q^7 + 44 * q^10 - 28 * q^13 + 120 * q^14 + 8 * q^16 + 24 * q^20 + 46 * q^22 + 60 * q^23 + 32 * q^25 + 136 * q^28 + 120 * q^29 + 148 * q^31 - 168 * q^32 + 20 * q^37 - 54 * q^38 - 48 * q^40 + 2 * q^43 + 232 * q^46 + 6 * q^47 + 42 * q^50 - 112 * q^52 + 52 * q^55 - 66 * q^58 - 528 * q^59 + 112 * q^61 - 84 * q^65 - 76 * q^67 + 156 * q^68 + 396 * q^70 + 260 * q^73 - 852 * q^74 - 204 * q^76 - 318 * q^77 + 340 * q^82 + 582 * q^83 + 194 * q^85 - 72 * q^88 - 896 * q^91 + 228 * q^92 + 342 * q^95 - 274 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more