LMFDB - Embedded newform 800.2.bq.d.223.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [800,2,Mod(63,800)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(800, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 0, 19]))

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

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

chi := DirichletCharacter("800.63");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 800 = 2^{5} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	800.bq (of order $20$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.38803216170$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$8$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			223.2
Character	$\chi$	$=$	800.223
Dual form			800.2.bq.d.287.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.927126 - 1.81959i) q^{3} +(2.22567 + 0.215379i) q^{5} +(-0.168186 - 0.168186i) q^{7} +(-0.687977 + 0.946919i) q^{9} +O(q^{10})$	\(q+(-0.927126 - 1.81959i) q^{3} +(2.22567 + 0.215379i) q^{5} +(-0.168186 - 0.168186i) q^{7} +(-0.687977 + 0.946919i) q^{9} +(3.26920 + 4.49966i) q^{11} +(0.749249 + 4.73057i) q^{13} +(-1.67158 - 4.24948i) q^{15} +(6.52141 + 3.32283i) q^{17} +(-2.15014 - 6.61744i) q^{19} +(-0.150100 + 0.461959i) q^{21} +(-0.984773 + 6.21761i) q^{23} +(4.90722 + 0.958724i) q^{25} +(-3.69024 - 0.584476i) q^{27} +(-0.403562 - 0.131125i) q^{29} +(6.52597 - 2.12042i) q^{31} +(5.15657 - 10.1203i) q^{33} +(-0.338104 - 0.410551i) q^{35} +(-10.6475 + 1.68639i) q^{37} +(7.91304 - 5.74916i) q^{39} +(-2.78034 - 2.02003i) q^{41} +(0.0127275 - 0.0127275i) q^{43} +(-1.73516 + 1.95936i) q^{45} +(3.27746 - 1.66995i) q^{47} -6.94343i q^{49} -14.9469i q^{51} +(3.62693 - 1.84801i) q^{53} +(6.30702 + 10.7189i) q^{55} +(-10.0476 + 10.0476i) q^{57} +(-5.38035 - 3.90905i) q^{59} +(7.47861 - 5.43353i) q^{61} +(0.274967 - 0.0435505i) q^{63} +(0.648719 + 10.6901i) q^{65} +(-1.62927 + 3.19763i) q^{67} +(12.2265 - 3.97263i) q^{69} +(5.30499 + 1.72369i) q^{71} +(3.26586 + 0.517262i) q^{73} +(-2.80513 - 9.81798i) q^{75} +(0.206948 - 1.30662i) q^{77} +(0.104302 - 0.321009i) q^{79} +(3.44288 + 10.5961i) q^{81} +(2.12185 + 1.08114i) q^{83} +(13.7989 + 8.80009i) q^{85} +(0.135559 + 0.855886i) q^{87} +(-5.36229 - 7.38056i) q^{89} +(0.669604 - 0.921631i) q^{91} +(-9.90868 - 9.90868i) q^{93} +(-3.36024 - 15.1913i) q^{95} +(-8.01709 - 15.7344i) q^{97} -6.50995 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 2 q^{5} + 4 q^{7}+O(q^{10}) $ 64 * q + 2 * q^5 + 4 * q^7	$ 64 q + 2 q^{5} + 4 q^{7} + 4 q^{13} + 22 q^{15} + 8 q^{17} - 18 q^{19} - 16 q^{21} + 8 q^{23} + 40 q^{25} + 18 q^{27} - 20 q^{31} + 44 q^{33} + 38 q^{35} - 10 q^{37} - 36 q^{39} - 16 q^{41} + 32 q^{43} + 14 q^{45} + 8 q^{47} - 22 q^{53} - 24 q^{55} - 8 q^{57} - 4 q^{59} - 36 q^{61} + 18 q^{63} - 24 q^{65} - 26 q^{67} + 60 q^{69} + 70 q^{71} - 12 q^{73} + 66 q^{75} + 48 q^{77} + 16 q^{79} - 24 q^{81} - 52 q^{83} - 46 q^{85} - 144 q^{87} - 60 q^{89} - 30 q^{91} + 20 q^{93} - 8 q^{95} - 56 q^{97} + 132 q^{99}+O(q^{100}) $ 64 * q + 2 * q^5 + 4 * q^7 + 4 * q^13 + 22 * q^15 + 8 * q^17 - 18 * q^19 - 16 * q^21 + 8 * q^23 + 40 * q^25 + 18 * q^27 - 20 * q^31 + 44 * q^33 + 38 * q^35 - 10 * q^37 - 36 * q^39 - 16 * q^41 + 32 * q^43 + 14 * q^45 + 8 * q^47 - 22 * q^53 - 24 * q^55 - 8 * q^57 - 4 * q^59 - 36 * q^61 + 18 * q^63 - 24 * q^65 - 26 * q^67 + 60 * q^69 + 70 * q^71 - 12 * q^73 + 66 * q^75 + 48 * q^77 + 16 * q^79 - 24 * q^81 - 52 * q^83 - 46 * q^85 - 144 * q^87 - 60 * q^89 - 30 * q^91 + 20 * q^93 - 8 * q^95 - 56 * q^97 + 132 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/800\mathbb{Z}\right)^\times$.

$n$	$101$	$351$	$577$
$\chi(n)$	$1$	$-1$	$e\left(\frac{11}{20}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.927126	−	1.81959i	−0.535276	−	1.05054i	−0.987350	−	0.158558i	$-0.949316\pi$
$3$	−0.927126	−	1.81959i	−0.535276	−	1.05054i	0.452073	−	0.891981i	$-0.350684\pi$
$4$		0			0
$5$	2.22567	+	0.215379i	0.995350	+	0.0963202i
$5$	2.22567	+	0.215379i	0.995350	+	0.0963202i
$6$		0			0
$7$	−0.168186	−	0.168186i	−0.0635684	−	0.0635684i	0.674608	−	0.738176i	$-0.264313\pi$
$7$	−0.168186	−	0.168186i	−0.0635684	−	0.0635684i	−0.738176	+	0.674608i	$0.764313\pi$
$8$		0			0
$9$	−0.687977	+	0.946919i	−0.229326	+	0.315640i
$10$		0			0
$11$	3.26920	+	4.49966i	0.985699	+	1.35670i	0.933702	+	0.358052i	$0.116559\pi$
$11$	3.26920	+	4.49966i	0.985699	+	1.35670i	0.0519977	+	0.998647i	$0.483441\pi$
$12$		0			0
$13$	0.749249	+	4.73057i	0.207804	+	1.31203i	0.842262	+	0.539068i	$0.181223\pi$
$13$	0.749249	+	4.73057i	0.207804	+	1.31203i	−0.634458	+	0.772957i	$0.718777\pi$
$14$		0			0
$15$	−1.67158	−	4.24948i	−0.431599	−	1.09721i
$16$		0			0
$17$	6.52141	+	3.32283i	1.58167	+	0.805903i	0.999972	−	0.00749806i	$-0.00238673\pi$
$17$	6.52141	+	3.32283i	1.58167	+	0.805903i	0.581703	+	0.813402i	$0.302387\pi$
$18$		0			0
$19$	−2.15014	−	6.61744i	−0.493275	−	1.51815i	−0.819627	−	0.572897i	$-0.805819\pi$
$19$	−2.15014	−	6.61744i	−0.493275	−	1.51815i	0.326352	−	0.945248i	$-0.394181\pi$
$20$		0			0
$21$	−0.150100	+	0.461959i	−0.0327544	+	0.100808i
$22$		0			0
$23$	−0.984773	+	6.21761i	−0.205339	+	1.29646i	0.642532	+	0.766259i	$0.277884\pi$
$23$	−0.984773	+	6.21761i	−0.205339	+	1.29646i	−0.847871	+	0.530203i	$0.822116\pi$
$24$		0			0
$25$	4.90722	+	0.958724i	0.981445	+	0.191745i
$26$		0			0
$27$	−3.69024	−	0.584476i	−0.710187	−	0.112483i
$28$		0			0
$29$	−0.403562	−	0.131125i	−0.0749396	−	0.0243494i	0.271307	−	0.962493i	$-0.412544\pi$
$29$	−0.403562	−	0.131125i	−0.0749396	−	0.0243494i	−0.346247	+	0.938143i	$0.612544\pi$
$30$		0			0
$31$	6.52597	−	2.12042i	1.17210	−	0.380838i	0.342673	−	0.939455i	$-0.388668\pi$
$31$	6.52597	−	2.12042i	1.17210	−	0.380838i	0.829426	+	0.558617i	$0.188668\pi$
$32$		0			0
$33$	5.15657	−	10.1203i	0.897643	−	1.76172i
$34$		0			0
$35$	−0.338104	−	0.410551i	−0.0571499	−	0.0693958i
$36$		0			0
$37$	−10.6475	+	1.68639i	−1.75043	+	0.277242i	−0.947716	−	0.319116i	$-0.896614\pi$
$37$	−10.6475	+	1.68639i	−1.75043	+	0.277242i	−0.802719	+	0.596358i	$0.796614\pi$
$38$		0			0
$39$	7.91304	−	5.74916i	1.26710	−	0.920603i
$40$		0			0
$41$	−2.78034	−	2.02003i	−0.434216	−	0.315476i	0.349117	−	0.937079i	$-0.386482\pi$
$41$	−2.78034	−	2.02003i	−0.434216	−	0.315476i	−0.783332	+	0.621603i	$0.786482\pi$
$42$		0			0
$43$	0.0127275	−	0.0127275i	0.00194093	−	0.00194093i	−0.706136	−	0.708077i	$-0.749563\pi$
$43$	0.0127275	−	0.0127275i	0.00194093	−	0.00194093i	0.708077	+	0.706136i	$0.249563\pi$
$44$		0			0
$45$	−1.73516	+	1.95936i	−0.258662	+	0.292083i
$46$		0			0
$47$	3.27746	−	1.66995i	0.478067	−	0.243587i	−0.198315	−	0.980138i	$-0.563547\pi$
$47$	3.27746	−	1.66995i	0.478067	−	0.243587i	0.676382	+	0.736551i	$0.263547\pi$
$48$		0			0
$49$		−	6.94343i		−	0.991918i
$50$		0			0
$51$		−	14.9469i		−	2.09299i
$52$		0			0
$53$	3.62693	−	1.84801i	0.498197	−	0.253844i	−0.186789	−	0.982400i	$-0.559808\pi$
$53$	3.62693	−	1.84801i	0.498197	−	0.253844i	0.684986	+	0.728556i	$0.259808\pi$
$54$		0			0
$55$	6.30702	+	10.7189i	0.850439	+	1.44533i
$56$		0			0
$57$	−10.0476	+	10.0476i	−1.33083	+	1.33083i
$58$		0			0
$59$	−5.38035	−	3.90905i	−0.700461	−	0.508915i	0.179621	−	0.983736i	$-0.442513\pi$
$59$	−5.38035	−	3.90905i	−0.700461	−	0.508915i	−0.880082	+	0.474821i	$0.842513\pi$
$60$		0			0
$61$	7.47861	−	5.43353i	0.957537	−	0.695692i	0.00495997	−	0.999988i	$-0.498421\pi$
$61$	7.47861	−	5.43353i	0.957537	−	0.695692i	0.952578	+	0.304296i	$0.0984212\pi$
$62$		0			0
$63$	0.274967	−	0.0435505i	0.0346426	−	0.00548685i
$64$		0			0
$65$	0.648719	+	10.6901i	0.0804636	+	1.32594i
$66$		0			0
$67$	−1.62927	+	3.19763i	−0.199047	+	0.390653i	−0.968857	−	0.247621i	$-0.920351\pi$
$67$	−1.62927	+	3.19763i	−0.199047	+	0.390653i	0.769810	+	0.638274i	$0.220351\pi$
$68$		0			0
$69$	12.2265	−	3.97263i	1.47190	−	0.478248i
$70$		0			0
$71$	5.30499	+	1.72369i	0.629586	+	0.204565i	0.606392	−	0.795166i	$-0.292616\pi$
$71$	5.30499	+	1.72369i	0.629586	+	0.204565i	0.0231944	+	0.999731i	$0.492616\pi$
$72$		0			0
$73$	3.26586	+	0.517262i	0.382241	+	0.0605410i	0.344598	−	0.938750i	$-0.388015\pi$
$73$	3.26586	+	0.517262i	0.382241	+	0.0605410i	0.0376424	+	0.999291i	$0.488015\pi$
$74$		0			0
$75$	−2.80513	−	9.81798i	−0.323909	−	1.13368i
$76$		0			0
$77$	0.206948	−	1.30662i	0.0235839	−	0.148903i
$78$		0			0
$79$	0.104302	−	0.321009i	0.0117349	−	0.0361164i	−0.945018	−	0.327019i	$-0.893956\pi$
$79$	0.104302	−	0.321009i	0.0117349	−	0.0361164i	0.956753	+	0.290903i	$0.0939557\pi$
$80$		0			0
$81$	3.44288	+	10.5961i	0.382542	+	1.17734i
$82$		0			0
$83$	2.12185	+	1.08114i	0.232904	+	0.118670i	0.566548	−	0.824029i	$-0.308278\pi$
$83$	2.12185	+	1.08114i	0.232904	+	0.118670i	−0.333644	+	0.942699i	$0.608278\pi$
$84$		0			0
$85$	13.7989	+	8.80009i	1.49670	+	0.954504i
$86$		0			0
$87$	0.135559	+	0.855886i	0.0145335	+	0.0917606i
$88$		0			0
$89$	−5.36229	−	7.38056i	−0.568402	−	0.782338i	0.423963	−	0.905680i	$-0.360639\pi$
$89$	−5.36229	−	7.38056i	−0.568402	−	0.782338i	−0.992364	+	0.123342i	$0.960639\pi$
$90$		0			0
$91$	0.669604	−	0.921631i	0.0701936	−	0.0966132i
$92$		0			0
$93$	−9.90868	−	9.90868i	−1.02748	−	1.02748i
$94$		0			0
$95$	−3.36024	−	15.1913i	−0.344754	−	1.55860i
$96$		0			0
$97$	−8.01709	−	15.7344i	−0.814012	−	1.59759i	−0.801747	−	0.597663i	$-0.796096\pi$
$97$	−8.01709	−	15.7344i	−0.814012	−	1.59759i	−0.0122645	−	0.999925i	$-0.503904\pi$
$98$		0			0
$99$	−6.50995			−0.654274
$100$		0			0
$101$	−8.39592			−0.835426			−0.417713	−	0.908579i	$-0.637168\pi$
$101$	−8.39592			−0.835426			−0.417713	+	0.908579i	$0.637168\pi$
$102$		0			0
$103$	1.14089	+	2.23913i	0.112416	+	0.220628i	0.940359	−	0.340183i	$-0.110489\pi$
$103$	1.14089	+	2.23913i	0.112416	+	0.220628i	−0.827943	+	0.560812i	$0.810489\pi$
$104$		0			0
$105$	−0.433569	+	0.995841i	−0.0423120	+	0.0971842i
$106$		0			0
$107$	−1.59279	−	1.59279i	−0.153981	−	0.153981i	0.625913	−	0.779893i	$-0.284727\pi$
$107$	−1.59279	−	1.59279i	−0.153981	−	0.153981i	−0.779893	+	0.625913i	$0.784727\pi$
$108$		0			0
$109$	−2.07319	+	2.85351i	−0.198576	+	0.273316i	−0.896679	−	0.442681i	$-0.854028\pi$
$109$	−2.07319	+	2.85351i	−0.198576	+	0.273316i	0.698103	+	0.715997i	$0.254028\pi$
$110$		0			0
$111$	12.9401	+	17.8105i	1.22822	+	1.69050i
$112$		0			0
$113$	−1.13232	−	7.14918i	−0.106520	−	0.672539i	−0.981942	−	0.189180i	$-0.939417\pi$
$113$	−1.13232	−	7.14918i	−0.106520	−	0.672539i	0.875423	−	0.483358i	$-0.160583\pi$
$114$		0			0
$115$	−3.53092	+	13.6263i	−0.329260	+	1.27066i
$116$		0			0
$117$	−4.99494	−	2.54505i	−0.461782	−	0.235290i
$118$		0			0
$119$	−0.537958	−	1.65567i	−0.0493146	−	0.151775i
$120$		0			0
$121$	−6.16013	+	18.9589i	−0.560012	+	1.72354i
$122$		0			0
$123$	−1.09790	+	6.93189i	−0.0989946	+	0.625028i
$124$		0			0
$125$	10.7154	+	3.19071i	0.958413	+	0.285386i
$126$		0			0
$127$	5.07958	+	0.804526i	0.450740	+	0.0713902i	0.377678	−	0.925937i	$-0.376723\pi$
$127$	5.07958	+	0.804526i	0.450740	+	0.0713902i	0.0730623	+	0.997327i	$0.476723\pi$
$128$		0			0
$129$	−0.0349588	−	0.0113588i	−0.00307795	−	0.00100009i
$130$		0			0
$131$	−0.264250	+	0.0858600i	−0.0230876	+	0.00750162i	−0.320538	−	0.947236i	$-0.603864\pi$
$131$	−0.264250	+	0.0858600i	−0.0230876	+	0.00750162i	0.297450	+	0.954737i	$0.403864\pi$
$132$		0			0
$133$	−0.751340	+	1.47459i	−0.0651494	+	0.127863i
$134$		0			0
$135$	−8.08737	−	2.09565i	−0.696050	−	0.180365i
$136$		0			0
$137$	10.2820	−	1.62851i	0.878453	−	0.139133i	0.299112	−	0.954218i	$-0.403310\pi$
$137$	10.2820	−	1.62851i	0.878453	−	0.139133i	0.579342	+	0.815085i	$0.303310\pi$
$138$		0			0
$139$	−14.8128	+	10.7621i	−1.25640	+	0.912830i	−0.998575	−	0.0533604i	$-0.983007\pi$
$139$	−14.8128	+	10.7621i	−1.25640	+	0.912830i	−0.257828	+	0.966191i	$0.583007\pi$
$140$		0			0
$141$	−6.07724	−	4.41537i	−0.511796	−	0.371841i
$142$		0			0
$143$	−18.8365	+	18.8365i	−1.57519	+	1.57519i
$144$		0			0
$145$	−0.869955	−	0.378761i	−0.0722459	−	0.0314543i
$146$		0			0
$147$	−12.6342	+	6.43743i	−1.04205	+	0.530950i
$148$		0			0
$149$			4.43750i			0.363534i	0.983342	+	0.181767i	$0.0581817\pi$
$149$			4.43750i			0.363534i	−0.983342	+	0.181767i	$0.941818\pi$
$150$		0			0
$151$			12.9987i			1.05782i	0.848679	+	0.528908i	$0.177398\pi$
$151$			12.9987i			1.05782i	−0.848679	+	0.528908i	$0.822602\pi$
$152$		0			0
$153$	−7.63303	+	3.88922i	−0.617094	+	0.314425i
$154$		0			0
$155$	14.9814	−	3.31380i	1.20333	−	0.266171i
$156$		0			0
$157$	−14.4526	+	14.4526i	−1.15344	+	1.15344i	−0.167582	+	0.985858i	$0.553596\pi$
$157$	−14.4526	+	14.4526i	−1.15344	+	1.15344i	−0.985858	+	0.167582i	$0.946404\pi$
$158$		0			0
$159$	−6.72524	−	4.88617i	−0.533346	−	0.387499i
$160$		0			0
$161$	1.21134	−	0.880092i	0.0954672	−	0.0693610i
$162$		0			0
$163$	−12.1897	+	1.93067i	−0.954774	+	0.151221i	−0.614335	−	0.789045i	$-0.710576\pi$
$163$	−12.1897	+	1.93067i	−0.954774	+	0.151221i	−0.340439	+	0.940267i	$0.610576\pi$
$164$		0			0
$165$	13.6565	−	21.4139i	1.06316	−	1.66707i
$166$		0			0
$167$	−6.32280	+	12.4092i	−0.489273	+	0.960252i	0.505945	+	0.862566i	$0.331144\pi$
$167$	−6.32280	+	12.4092i	−0.489273	+	0.960252i	−0.995217	+	0.0976859i	$0.968856\pi$
$168$		0			0
$169$	−9.45323	+	3.07154i	−0.727171	+	0.236272i
$170$		0			0
$171$	7.74543	+	2.51664i	0.592308	+	0.192453i
$172$		0			0
$173$	0.286129	+	0.0453184i	0.0217540	+	0.00344549i	0.167302	−	0.985906i	$-0.446495\pi$
$173$	0.286129	+	0.0453184i	0.0217540	+	0.00344549i	−0.145548	+	0.989351i	$0.546495\pi$
$174$		0			0
$175$	−0.664084	−	0.986572i	−0.0502000	−	0.0745778i
$176$		0			0
$177$	−2.12460	+	13.4142i	−0.159695	+	1.00827i
$178$		0			0
$179$	4.52419	−	13.9240i	0.338154	−	1.04073i	−0.626994	−	0.779024i	$-0.715715\pi$
$179$	4.52419	−	13.9240i	0.338154	−	1.04073i	0.965148	−	0.261706i	$-0.0842851\pi$
$180$		0			0
$181$	−3.12477	−	9.61706i	−0.232263	−	0.714831i	−0.997473	−	0.0710501i	$-0.977365\pi$
$181$	−3.12477	−	9.61706i	−0.232263	−	0.714831i	0.765210	−	0.643780i	$-0.222635\pi$
$182$		0			0
$183$	−16.8204	−	8.57041i	−1.24340	−	0.633543i
$184$		0			0
$185$	−24.0610	+	1.46012i	−1.76900	+	0.107350i
$186$		0			0
$187$	6.36818	+	40.2071i	0.465687	+	2.94023i
$188$		0			0
$189$	0.522347	+	0.718948i	0.0379951	+	0.0522958i
$190$		0			0
$191$	−1.99419	+	2.74477i	−0.144295	+	0.198605i	−0.875047	−	0.484038i	$-0.839170\pi$
$191$	−1.99419	+	2.74477i	−0.144295	+	0.198605i	0.730752	+	0.682643i	$0.239170\pi$
$192$		0			0
$193$	−11.7797	−	11.7797i	−0.847921	−	0.847921i	0.141953	−	0.989873i	$-0.454662\pi$
$193$	−11.7797	−	11.7797i	−0.847921	−	0.847921i	−0.989873	+	0.141953i	$0.954662\pi$
$194$		0			0
$195$	18.8501	−	11.0914i	1.34988	−	0.794275i
$196$		0			0
$197$	−1.70429	−	3.34485i	−0.121425	−	0.238311i	0.822290	−	0.569068i	$-0.192696\pi$
$197$	−1.70429	−	3.34485i	−0.121425	−	0.238311i	−0.943716	+	0.330757i	$0.892696\pi$
$198$		0			0
$199$	11.5184			0.816516			0.408258	−	0.912867i	$-0.366136\pi$
$199$	11.5184			0.816516			0.408258	+	0.912867i	$0.366136\pi$
$200$		0			0
$201$	7.32890			0.516941
$202$		0			0
$203$	0.0458202	+	0.0899271i	0.00321594	+	0.00631165i
$204$		0			0
$205$	−5.75305	−	5.09476i	−0.401810	−	0.355833i
$206$		0			0
$207$	−5.21008	−	5.21008i	−0.362125	−	0.362125i
$208$		0			0
$209$	22.7470	−	31.3086i	1.57345	−	2.16566i
$210$		0			0
$211$	−3.00957	−	4.14232i	−0.207188	−	0.285169i	0.692759	−	0.721169i	$-0.256395\pi$
$211$	−3.00957	−	4.14232i	−0.207188	−	0.285169i	−0.899947	+	0.436000i	$0.856395\pi$
$212$		0			0
$213$	−1.78198	−	11.2510i	−0.122099	−	0.770903i
$214$		0			0
$215$	0.0310685	−	0.0255860i	0.00211885	−	0.00174495i
$216$		0			0
$217$	−1.45420	−	0.740954i	−0.0987178	−	0.0502992i
$218$		0			0
$219$	−2.08666	−	6.42209i	−0.141004	−	0.433965i
$220$		0			0
$221$	−10.8327	+	33.3396i	−0.728687	+	2.24267i
$222$		0			0
$223$	0.978883	−	6.18042i	0.0655509	−	0.413872i	−0.932992	−	0.359898i	$-0.882811\pi$
$223$	0.978883	−	6.18042i	0.0655509	−	0.413872i	0.998542	−	0.0539735i	$-0.0171886\pi$
$224$		0			0
$225$	−4.28389	+	3.98717i	−0.285593	+	0.265811i
$226$		0			0
$227$	14.3054	+	2.26575i	0.949481	+	0.150383i	0.611919	−	0.790920i	$-0.290398\pi$
$227$	14.3054	+	2.26575i	0.949481	+	0.150383i	0.337562	+	0.941303i	$0.390398\pi$
$228$		0			0
$229$	3.29403	+	1.07030i	0.217676	+	0.0707272i	0.415825	−	0.909445i	$-0.363493\pi$
$229$	3.29403	+	1.07030i	0.217676	+	0.0707272i	−0.198149	+	0.980172i	$0.563493\pi$
$230$		0			0
$231$	−2.56937	+	0.834837i	−0.169052	+	0.0549283i
$232$		0			0
$233$	2.83861	−	5.57109i	0.185964	−	0.364974i	−0.779137	−	0.626854i	$-0.784342\pi$
$233$	2.83861	−	5.57109i	0.185964	−	0.364974i	0.965101	+	0.261880i	$0.0843423\pi$
$234$		0			0
$235$	7.65422	−	3.01086i	0.499306	−	0.196407i
$236$		0			0
$237$	−0.680805	+	0.107829i	−0.0442231	+	0.00700425i
$238$		0			0
$239$	−8.22346	+	5.97469i	−0.531931	+	0.386471i	−0.821080	−	0.570813i	$-0.806628\pi$
$239$	−8.22346	+	5.97469i	−0.531931	+	0.386471i	0.289148	+	0.957284i	$0.406628\pi$
$240$		0			0
$241$	1.89276	+	1.37517i	0.121924	+	0.0885827i	0.647076	−	0.762426i	$-0.275992\pi$
$241$	1.89276	+	1.37517i	0.121924	+	0.0885827i	−0.525152	+	0.851008i	$0.675992\pi$
$242$		0			0
$243$	8.16278	−	8.16278i	0.523643	−	0.523643i
$244$		0			0
$245$	1.49547	−	15.4538i	0.0955418	−	0.987306i
$246$		0			0
$247$	29.6933	−	15.1295i	1.88934	−	0.962667i
$248$		0			0
$249$		−	4.86325i		−	0.308196i
$250$		0			0
$251$		−	21.4483i		−	1.35381i	−0.736073	−	0.676903i	$-0.763322\pi$
$251$		−	21.4483i		−	1.35381i	0.736073	−	0.676903i	$-0.236678\pi$
$252$		0			0
$253$	−31.1966	+	15.8954i	−1.96131	+	0.999338i
$254$		0			0
$255$	3.21925	−	33.2670i	0.201597	−	2.08326i
$256$		0			0
$257$	3.74593	−	3.74593i	0.233665	−	0.233665i	−0.580556	−	0.814221i	$-0.697165\pi$
$257$	3.74593	−	3.74593i	0.233665	−	0.233665i	0.814221	+	0.580556i	$0.197165\pi$
$258$		0			0
$259$	2.07439	+	1.50713i	0.128896	+	0.0936486i
$260$		0			0
$261$	0.401807	−	0.291930i	0.0248712	−	0.0180700i
$262$		0			0
$263$	−12.9890	+	2.05726i	−0.800937	+	0.126856i	−0.543467	−	0.839430i	$-0.682889\pi$
$263$	−12.9890	+	2.05726i	−0.800937	+	0.126856i	−0.257470	+	0.966286i	$0.582889\pi$
$264$		0			0
$265$	8.47037	−	3.33191i	0.520331	−	0.204677i
$266$		0			0
$267$	−8.45805	+	16.5999i	−0.517624	+	1.01589i
$268$		0			0
$269$	13.7775	−	4.47658i	0.840030	−	0.272942i	0.142766	−	0.989757i	$-0.454400\pi$
$269$	13.7775	−	4.47658i	0.840030	−	0.272942i	0.697264	+	0.716814i	$0.254400\pi$
$270$		0			0
$271$	12.2811	+	3.99038i	0.746025	+	0.242398i	0.657270	−	0.753655i	$-0.271711\pi$
$271$	12.2811	+	3.99038i	0.746025	+	0.242398i	0.0887550	+	0.996053i	$0.471711\pi$
$272$		0			0
$273$	−2.29780	−	0.363935i	−0.139069	−	0.0220263i
$274$		0			0
$275$	11.7287	+	25.2151i	0.707270	+	1.52053i
$276$		0			0
$277$	3.89880	−	24.6161i	0.234256	−	1.47904i	−0.537579	−	0.843213i	$-0.680661\pi$
$277$	3.89880	−	24.6161i	0.234256	−	1.47904i	0.771835	−	0.635822i	$-0.219339\pi$
$278$		0			0
$279$	−2.48186	+	7.63837i	−0.148585	+	0.457297i
$280$		0			0
$281$	0.235463	+	0.724682i	0.0140466	+	0.0432309i	0.957834	−	0.287322i	$-0.0927649\pi$
$281$	0.235463	+	0.724682i	0.0140466	+	0.0432309i	−0.943788	+	0.330553i	$0.892765\pi$
$282$		0			0
$283$	−5.37459	−	2.73849i	−0.319486	−	0.162786i	0.286892	−	0.957963i	$-0.407378\pi$
$283$	−5.37459	−	2.73849i	−0.319486	−	0.162786i	−0.606378	+	0.795177i	$0.707378\pi$
$284$		0			0
$285$	−24.5266	+	20.1985i	−1.45283	+	1.19646i
$286$		0			0
$287$	0.127873	+	0.807357i	0.00754809	+	0.0476568i
$288$		0			0
$289$	21.4953	+	29.5857i	1.26443	+	1.74034i
$290$		0			0
$291$	−21.1973	+	29.1756i	−1.24261	+	1.71030i
$292$		0			0
$293$	4.87177	+	4.87177i	0.284612	+	0.284612i	0.834945	−	0.550333i	$-0.185499\pi$
$293$	4.87177	+	4.87177i	0.284612	+	0.284612i	−0.550333	+	0.834945i	$0.685499\pi$
$294$		0			0
$295$	−11.1330	−	9.85907i	−0.648186	−	0.574017i
$296$		0			0
$297$	−9.43416	−	18.5156i	−0.547426	−	1.07438i
$298$		0			0
$299$	−30.1507			−1.74366
$300$		0			0
$301$	−0.00428119			−0.000246764
$302$		0			0
$303$	7.78408	+	15.2771i	0.447183	+	0.877647i
$304$		0			0
$305$	17.8152	−	10.4825i	1.02009	−	0.600227i
$306$		0			0
$307$	5.21399	+	5.21399i	0.297578	+	0.297578i	0.840064	−	0.542487i	$-0.182517\pi$
$307$	5.21399	+	5.21399i	0.297578	+	0.297578i	−0.542487	+	0.840064i	$0.682517\pi$
$308$		0			0
$309$	3.01654	−	4.15191i	0.171605	−	0.236194i
$310$		0			0
$311$	−15.0545	−	20.7207i	−0.853661	−	1.17496i	−0.983044	−	0.183369i	$-0.941300\pi$
$311$	−15.0545	−	20.7207i	−0.853661	−	1.17496i	0.129383	−	0.991595i	$-0.458700\pi$
$312$		0			0
$313$	−0.0883443	−	0.557784i	−0.00499352	−	0.0315278i	0.985066	−	0.172178i	$-0.0550806\pi$
$313$	−0.0883443	−	0.557784i	−0.00499352	−	0.0315278i	−0.990059	+	0.140651i	$0.955081\pi$
$314$		0			0
$315$	0.621366	−	0.0377071i	0.0350100	−	0.00212456i
$316$		0			0
$317$	−13.5373	−	6.89762i	−0.760333	−	0.387409i	0.0304257	−	0.999537i	$-0.490314\pi$
$317$	−13.5373	−	6.89762i	−0.760333	−	0.387409i	−0.790759	+	0.612128i	$0.790314\pi$
$318$		0			0
$319$	−0.729304	−	2.24457i	−0.0408332	−	0.125672i
$320$		0			0
$321$	−1.42150	+	4.37493i	−0.0793404	+	0.244185i
$322$		0			0
$323$	7.96667	−	50.2996i	0.443278	−	2.79874i
$324$		0			0
$325$	−0.858579	+	23.9323i	−0.0476254	+	1.32753i
$326$		0			0
$327$	7.11431	+	1.12680i	0.393422	+	0.0623120i
$328$		0			0
$329$	−0.832087	−	0.270361i	−0.0458744	−	0.0149055i
$330$		0			0
$331$	31.4834	−	10.2296i	1.73049	−	0.562269i	0.736966	−	0.675930i	$-0.236258\pi$
$331$	31.4834	−	10.2296i	1.73049	−	0.562269i	0.993520	+	0.113661i	$0.0362577\pi$
$332$		0			0
$333$	5.72834	−	11.2425i	0.313911	−	0.616085i
$334$		0			0
$335$	−4.31493	+	6.76596i	−0.235750	+	0.369664i
$336$		0			0
$337$	−10.7567	+	1.70369i	−0.585952	+	0.0928057i	−0.442370	−	0.896833i	$-0.645862\pi$
$337$	−10.7567	+	1.70369i	−0.585952	+	0.0928057i	−0.143582	+	0.989638i	$0.545862\pi$
$338$		0			0
$339$	−11.9588	+	8.68854i	−0.649510	+	0.471897i
$340$		0			0
$341$	30.8758	+	22.4326i	1.67202	+	1.21479i
$342$		0			0
$343$	−2.34509	+	2.34509i	−0.126623	+	0.126623i
$344$		0			0
$345$	28.0678	−	6.20844i	1.51112	−	0.334251i
$346$		0			0
$347$	18.3766	−	9.36335i	0.986508	−	0.502651i	0.115176	−	0.993345i	$-0.463257\pi$
$347$	18.3766	−	9.36335i	0.986508	−	0.502651i	0.871332	+	0.490694i	$0.163257\pi$
$348$		0			0
$349$		−	3.64296i		−	0.195003i	−0.995235	−	0.0975016i	$-0.968915\pi$
$349$		−	3.64296i		−	0.195003i	0.995235	−	0.0975016i	$-0.0310851\pi$
$350$		0			0
$351$		−	17.8949i		−	0.955157i
$352$		0			0
$353$	5.68052	−	2.89437i	0.302344	−	0.154052i	−0.296237	−	0.955115i	$-0.595732\pi$
$353$	5.68052	−	2.89437i	0.302344	−	0.154052i	0.598580	+	0.801063i	$0.295732\pi$
$354$		0			0
$355$	11.4359	+	4.97896i	0.606955	+	0.264256i
$356$		0			0
$357$	−2.51387	+	2.51387i	−0.133048	+	0.133048i
$358$		0			0
$359$	12.7336	+	9.25148i	0.672052	+	0.488274i	0.870711	−	0.491794i	$-0.163659\pi$
$359$	12.7336	+	9.25148i	0.672052	+	0.488274i	−0.198660	+	0.980069i	$0.563659\pi$
$360$		0			0
$361$	−23.7961	+	17.2889i	−1.25243	+	0.909943i
$362$		0			0
$363$	40.2086	−	6.36842i	2.11040	−	0.334255i
$364$		0			0
$365$	7.15733	+	1.85465i	0.374632	+	0.0970769i
$366$		0			0
$367$	−9.54972	+	18.7424i	−0.498491	+	0.978344i	0.495471	+	0.868624i	$0.334995\pi$
$367$	−9.54972	+	18.7424i	−0.498491	+	0.978344i	−0.993963	+	0.109720i	$0.965005\pi$
$368$		0			0
$369$	3.82562	−	1.24302i	0.199154	−	0.0647090i
$370$		0			0
$371$	−0.920810	−	0.299189i	−0.0478061	−	0.0155331i
$372$		0			0
$373$	2.39195	+	0.378848i	0.123851	+	0.0196160i	0.218052	−	0.975937i	$-0.430030\pi$
$373$	2.39195	+	0.378848i	0.123851	+	0.0196160i	−0.0942013	+	0.995553i	$0.530030\pi$
$374$		0			0
$375$	−4.12872	−	22.4558i	−0.213206	−	1.15961i
$376$		0			0
$377$	0.317929	−	2.00733i	0.0163742	−	0.103383i
$378$		0			0
$379$	−2.63288	+	8.10317i	−0.135242	+	0.416232i	−0.995628	−	0.0934116i	$-0.970223\pi$
$379$	−2.63288	+	8.10317i	−0.135242	+	0.416232i	0.860386	+	0.509644i	$0.170223\pi$
$380$		0			0
$381$	−3.24550	−	9.98863i	−0.166272	−	0.511733i
$382$		0			0
$383$	−21.6410	−	11.0266i	−1.10580	−	0.563434i	−0.196891	−	0.980425i	$-0.563084\pi$
$383$	−21.6410	−	11.0266i	−1.10580	−	0.563434i	−0.908910	+	0.416992i	$0.863084\pi$
$384$		0			0
$385$	0.742014	−	2.86352i	0.0378165	−	0.145939i
$386$		0			0
$387$	0.00329569	+	0.0208082i	0.000167529	+	0.00105774i
$388$		0			0
$389$	−21.8577	−	30.0846i	−1.10823	−	1.52535i	−0.823999	−	0.566591i	$-0.808262\pi$
$389$	−21.8577	−	30.0846i	−1.10823	−	1.52535i	−0.284231	−	0.958756i	$-0.591738\pi$
$390$		0			0
$391$	−27.0821	+	37.2754i	−1.36960	+	1.88510i
$392$		0			0
$393$	0.401223	+	0.401223i	0.0202390	+	0.0202390i
$394$		0			0
$395$	0.301281	−	0.691997i	0.0151591	−	0.0348181i
$396$		0			0
$397$	9.53727	+	18.7179i	0.478662	+	0.939427i	0.996472	+	0.0839308i	$0.0267475\pi$
$397$	9.53727	+	18.7179i	0.478662	+	0.939427i	−0.517810	+	0.855496i	$0.673253\pi$
$398$		0			0
$399$	3.37972			0.169198
$400$		0			0
$401$	0.240390			0.0120045			0.00600224	−	0.999982i	$-0.498089\pi$
$401$	0.240390			0.0120045			0.00600224	+	0.999982i	$0.498089\pi$
$402$		0			0
$403$	14.9204	+	29.2829i	0.743237	+	1.45868i
$404$		0			0
$405$	5.38055	+	24.3250i	0.267362	+	1.20872i
$406$		0			0
$407$	−42.3969	−	42.3969i	−2.10154	−	2.10154i
$408$		0			0
$409$	−10.5101	+	14.4659i	−0.519689	+	0.715291i	−0.985515	−	0.169585i	$-0.945757\pi$
$409$	−10.5101	+	14.4659i	−0.519689	+	0.715291i	0.465826	+	0.884876i	$0.345757\pi$
$410$		0			0
$411$	−12.4960	−	17.1992i	−0.616380	−	0.848374i
$412$		0			0
$413$	0.247452	+	1.56235i	0.0121763	+	0.0768782i
$414$		0			0
$415$	4.48970	+	2.86326i	0.220391	+	0.140552i
$416$		0			0
$417$	33.3159	+	16.9753i	1.63149	+	0.831284i
$418$		0			0
$419$	8.19593	+	25.2245i	0.400397	+	1.23230i	0.924678	+	0.380751i	$0.124334\pi$
$419$	8.19593	+	25.2245i	0.400397	+	1.23230i	−0.524280	+	0.851546i	$0.675666\pi$
$420$		0			0
$421$	−9.91324	+	30.5098i	−0.483142	+	1.48696i	0.351512	+	0.936183i	$0.385668\pi$
$421$	−9.91324	+	30.5098i	−0.483142	+	1.48696i	−0.834654	+	0.550774i	$0.814332\pi$
$422$		0			0
$423$	−0.673511	+	4.25238i	−0.0327472	+	0.206758i
$424$		0			0
$425$	28.8164	+	22.5581i	1.39780	+	1.09423i
$426$		0			0
$427$	−2.17164	−	0.343955i	−0.105093	−	0.0166451i
$428$		0			0
$429$	51.7386	+	16.8109i	2.49796	+	0.811637i
$430$		0			0
$431$	−3.83506	+	1.24609i	−0.184728	+	0.0600218i	−0.399920	−	0.916550i	$-0.630962\pi$
$431$	−3.83506	+	1.24609i	−0.184728	+	0.0600218i	0.215192	+	0.976572i	$0.430962\pi$
$432$		0			0
$433$	−9.43578	+	18.5188i	−0.453455	+	0.889955i	0.545210	+	0.838299i	$0.316450\pi$
$433$	−9.43578	+	18.5188i	−0.453455	+	0.889955i	−0.998665	+	0.0516556i	$0.983550\pi$
$434$		0			0
$435$	0.117370	+	1.93412i	0.00562748	+	0.0927338i
$436$		0			0
$437$	43.2621	−	6.85204i	2.06951	−	0.327778i
$438$		0			0
$439$	28.1811	−	20.4747i	1.34501	−	0.977206i	0.345765	−	0.938321i	$-0.387620\pi$
$439$	28.1811	−	20.4747i	1.34501	−	0.977206i	0.999244	−	0.0388844i	$-0.0123804\pi$
$440$		0			0
$441$	6.57487	+	4.77692i	0.313089	+	0.227472i
$442$		0			0
$443$	−20.1399	+	20.1399i	−0.956878	+	0.956878i	−0.999108	−	0.0422301i	$-0.986554\pi$
$443$	−20.1399	+	20.1399i	−0.956878	+	0.956878i	0.0422301	+	0.999108i	$0.486554\pi$
$444$		0			0
$445$	−10.3451	−	17.5816i	−0.490404	−	0.833449i
$446$		0			0
$447$	8.07442	−	4.11412i	0.381907	−	0.194591i
$448$		0			0
$449$			9.00855i			0.425140i	0.977146	+	0.212570i	$0.0681833\pi$
$449$			9.00855i			0.425140i	−0.977146	+	0.212570i	$0.931817\pi$
$450$		0			0
$451$		−	19.1145i		−	0.900065i
$452$		0			0
$453$	23.6522	−	12.0514i	1.11128	−	0.566224i
$454$		0			0
$455$	1.68882	−	1.90703i	0.0791730	−	0.0894029i
$456$		0			0
$457$	−0.668687	+	0.668687i	−0.0312799	+	0.0312799i	−0.722574	−	0.691294i	$-0.757041\pi$
$457$	−0.668687	+	0.668687i	−0.0312799	+	0.0312799i	0.691294	+	0.722574i	$0.257041\pi$
$458$		0			0
$459$	−22.1234	−	16.0736i	−1.03263	−	0.750253i
$460$		0			0
$461$	17.5838	−	12.7754i	0.818959	−	0.595009i	−0.0974548	−	0.995240i	$-0.531070\pi$
$461$	17.5838	−	12.7754i	0.818959	−	0.595009i	0.916414	+	0.400231i	$0.131070\pi$
$462$		0			0
$463$	−18.9491	+	3.00124i	−0.880639	+	0.139480i	−0.580348	−	0.814368i	$-0.697084\pi$
$463$	−18.9491	+	3.00124i	−0.880639	+	0.139480i	−0.300291	+	0.953848i	$0.597084\pi$
$464$		0			0
$465$	−19.9193	−	24.1876i	−0.923737	−	1.12167i
$466$		0			0
$467$	−1.92708	+	3.78211i	−0.0891748	+	0.175015i	−0.931286	−	0.364288i	$-0.881312\pi$
$467$	−1.92708	+	3.78211i	−0.0891748	+	0.175015i	0.842112	+	0.539303i	$0.181312\pi$
$468$		0			0
$469$	0.811819	−	0.263776i	0.0374863	−	0.0121800i
$470$		0			0
$471$	39.6970	+	12.8983i	1.82914	+	0.594324i
$472$		0			0
$473$	0.0988782	+	0.0156608i	0.00454643	+	0.000720083i
$474$		0			0
$475$	−4.20691	−	34.5347i	−0.193026	−	1.58456i
$476$		0			0
$477$	−0.745326	+	4.70580i	−0.0341261	+	0.215464i
$478$		0			0
$479$	8.35905	−	25.7265i	0.381935	−	1.17547i	−0.556745	−	0.830684i	$-0.687950\pi$
$479$	8.35905	−	25.7265i	0.381935	−	1.17547i	0.938680	−	0.344791i	$-0.112050\pi$
$480$		0			0
$481$	−15.9552	−	49.1052i	−0.727496	−	2.23900i
$482$		0			0
$483$	−2.72447	−	1.38819i	−0.123968	−	0.0631647i
$484$		0			0
$485$	−14.4545	−	36.7463i	−0.656347	−	1.66857i
$486$		0			0
$487$	−4.96193	−	31.3284i	−0.224847	−	1.41963i	−0.799223	−	0.601034i	$-0.794755\pi$
$487$	−4.96193	−	31.3284i	−0.224847	−	1.41963i	0.574377	−	0.818591i	$-0.305245\pi$
$488$		0			0
$489$	14.8144	+	20.3903i	0.669932	+	0.922082i
$490$		0			0
$491$	9.44164	−	12.9953i	0.426095	−	0.586470i	−0.540956	−	0.841051i	$-0.681938\pi$
$491$	9.44164	−	12.9953i	0.426095	−	0.586470i	0.967051	+	0.254581i	$0.0819376\pi$
$492$		0			0
$493$	−2.19609	−	2.19609i	−0.0989069	−	0.0989069i
$494$		0			0
$495$	−14.4890	−	1.40210i	−0.651232	−	0.0630198i
$496$		0			0
$497$	−0.602324	−	1.18213i	−0.0270179	−	0.0530257i
$498$		0			0
$499$	30.8676			1.38182			0.690912	−	0.722939i	$-0.257209\pi$
$499$	30.8676			1.38182			0.690912	+	0.722939i	$0.257209\pi$
$500$		0			0
$501$	28.4416			1.27068
$502$		0			0
$503$	−19.4699	−	38.2118i	−0.868120	−	1.70378i	−0.695163	−	0.718852i	$-0.744668\pi$
$503$	−19.4699	−	38.2118i	−0.868120	−	1.70378i	−0.172957	−	0.984929i	$-0.555332\pi$
$504$		0			0
$505$	−18.6866	−	1.80830i	−0.831541	−	0.0804684i
$506$		0			0
$507$	14.3533	+	14.3533i	0.637451	+	0.637451i
$508$		0			0
$509$	−15.8794	+	21.8562i	−0.703844	+	0.968758i	0.296064	+	0.955168i	$0.404326\pi$
$509$	−15.8794	+	21.8562i	−0.703844	+	0.968758i	−0.999908	+	0.0135895i	$0.995674\pi$
$510$		0			0
$511$	−0.462277	−	0.636270i	−0.0204499	−	0.0281469i
$512$		0			0
$513$	4.06678	+	25.6766i	0.179553	+	1.13365i
$514$		0			0
$515$	2.05699	+	5.22929i	0.0906420	+	0.230430i
$516$		0			0
$517$	18.2289	+	9.28807i	0.801705	+	0.408489i
$518$		0			0
$519$	−0.182817	−	0.562652i	−0.00802477	−	0.0246977i
$520$		0			0
$521$	−8.57078	+	26.3782i	−0.375493	+	1.15565i	0.567653	+	0.823268i	$0.307852\pi$
$521$	−8.57078	+	26.3782i	−0.375493	+	1.15565i	−0.943146	+	0.332380i	$0.892148\pi$
$522$		0			0
$523$	−0.484481	+	3.05889i	−0.0211849	+	0.133756i	−0.996014	−	0.0891975i	$-0.971570\pi$
$523$	−0.484481	+	3.05889i	−0.0211849	+	0.133756i	0.974829	+	0.222953i	$0.0715698\pi$
$524$		0			0
$525$	−1.17946	+	2.12303i	−0.0514760	+	0.0926568i
$526$		0			0
$527$	49.6043	+	7.85655i	2.16080	+	0.342237i
$528$		0			0
$529$	−15.8146	−	5.13848i	−0.687592	−	0.223412i
$530$		0			0
$531$	7.40311	−	2.40542i	0.321268	−	0.104386i
$532$		0			0
$533$	7.47275	−	14.6661i	0.323681	−	0.635260i
$534$		0			0
$535$	−3.20197	−	3.88807i	−0.138433	−	0.168096i
$536$		0			0
$537$	−29.5305	+	4.67716i	−1.27433	+	0.201835i
$538$		0			0
$539$	31.2431	−	22.6994i	1.34573	−	0.977733i
$540$		0			0
$541$	−30.1498	−	21.9051i	−1.29624	−	0.941773i	−0.296328	−	0.955086i	$-0.595762\pi$
$541$	−30.1498	−	21.9051i	−1.29624	−	0.941773i	−0.999911	+	0.0133133i	$0.995762\pi$
$542$		0			0
$543$	−14.6020	+	14.6020i	−0.626633	+	0.626633i
$544$		0			0
$545$	−5.22883	+	5.90444i	−0.223978	+	0.252919i
$546$		0			0
$547$	−12.7351	+	6.48883i	−0.544512	+	0.277443i	−0.704533	−	0.709671i	$-0.748844\pi$
$547$	−12.7351	+	6.48883i	−0.544512	+	0.277443i	0.160022	+	0.987114i	$0.448844\pi$
$548$		0			0
$549$			10.8198i			0.461777i
$550$		0			0
$551$			2.95249i			0.125780i
$552$		0			0
$553$	−0.0715316	+	0.0364472i	−0.00304183	+	0.00154989i
$554$		0			0
$555$	24.9644	+	42.4273i	1.05968	+	1.80094i
$556$		0			0
$557$	−13.4999	+	13.4999i	−0.572008	+	0.572008i	−0.932689	−	0.360681i	$-0.882544\pi$
$557$	−13.4999	+	13.4999i	−0.572008	+	0.572008i	0.360681	+	0.932689i	$0.382544\pi$
$558$		0			0
$559$	0.0697446	+	0.0506724i	0.00294988	+	0.00214321i
$560$		0			0
$561$	67.2562	−	48.8645i	2.83956	−	2.06306i
$562$		0			0
$563$	39.7636	−	6.29793i	1.67584	−	0.265426i	0.755099	−	0.655611i	$-0.227589\pi$
$563$	39.7636	−	6.29793i	1.67584	−	0.265426i	0.920737	+	0.390185i	$0.127589\pi$
$564$		0			0
$565$	−0.980390	−	16.1556i	−0.0412453	−	0.679672i
$566$		0			0
$567$	1.20307	−	2.36116i	0.0505243	−	0.0991596i
$568$		0			0
$569$	−25.7278	+	8.35947i	−1.07857	+	0.350447i	−0.793818	−	0.608155i	$-0.791910\pi$
$569$	−25.7278	+	8.35947i	−1.07857	+	0.350447i	−0.284748	+	0.958602i	$0.591910\pi$
$570$		0			0
$571$	−31.1343	−	10.1162i	−1.30293	−	0.423348i	−0.426331	−	0.904567i	$-0.640194\pi$
$571$	−31.1343	−	10.1162i	−1.30293	−	0.423348i	−0.876600	+	0.481219i	$0.840194\pi$
$572$		0			0
$573$	6.84322	+	1.08386i	0.285880	+	0.0452789i
$574$		0			0
$575$	−10.7935	+	29.5671i	−0.450119	+	1.23303i
$576$		0			0
$577$	−2.03537	+	12.8508i	−0.0847334	+	0.534985i	0.908410	+	0.418081i	$0.137297\pi$
$577$	−2.03537	+	12.8508i	−0.0847334	+	0.534985i	−0.993143	+	0.116905i	$0.962703\pi$
$578$		0			0
$579$	−10.5129	+	32.3554i	−0.436902	+	1.34465i
$580$		0			0
$581$	−0.175034	−	0.538700i	−0.00726164	−	0.0223490i
$582$		0			0
$583$	20.1726	+	10.2784i	0.835463	+	0.425689i
$584$		0			0
$585$	−10.5689	−	6.74024i	−0.436972	−	0.278675i
$586$		0			0
$587$	−2.94061	−	18.5663i	−0.121372	−	0.766313i	−0.971026	−	0.238973i	$-0.923189\pi$
$587$	−2.94061	−	18.5663i	−0.121372	−	0.766313i	0.849654	−	0.527340i	$-0.176811\pi$
$588$		0			0
$589$	−28.0635	−	38.6261i	−1.15634	−	1.59156i
$590$		0			0
$591$	−4.50616	+	6.20220i	−0.185359	+	0.255124i
$592$		0			0
$593$	−13.8864	−	13.8864i	−0.570246	−	0.570246i	0.361951	−	0.932197i	$-0.382111\pi$
$593$	−13.8864	−	13.8864i	−0.570246	−	0.570246i	−0.932197	+	0.361951i	$0.882111\pi$
$594$		0			0
$595$	−0.840724	−	3.80083i	−0.0344663	−	0.155819i
$596$		0			0
$597$	−10.6790	−	20.9587i	−0.437061	−	0.857781i
$598$		0			0
$599$	−16.1249			−0.658847			−0.329424	−	0.944182i	$-0.606854\pi$
$599$	−16.1249			−0.658847			−0.329424	+	0.944182i	$0.606854\pi$
$600$		0			0
$601$	10.3476			0.422086			0.211043	−	0.977477i	$-0.432314\pi$
$601$	10.3476			0.422086			0.211043	+	0.977477i	$0.432314\pi$
$602$		0			0
$603$	−1.90699	−	3.74269i	−0.0776588	−	0.152414i
$604$		0			0
$605$	−17.7938	+	40.8696i	−0.723419	+	1.66158i
$606$		0			0
$607$	5.17523	+	5.17523i	0.210056	+	0.210056i	0.804291	−	0.594235i	$-0.202545\pi$
$607$	5.17523	+	5.17523i	0.210056	+	0.210056i	−0.594235	+	0.804291i	$0.702545\pi$
$608$		0			0
$609$	0.121149	−	0.166747i	0.00490921	−	0.00675695i
$610$		0			0
$611$	10.3555	+	14.2531i	0.418937	+	0.576617i
$612$		0			0
$613$	5.92933	+	37.4363i	0.239483	+	1.51204i	0.755323	+	0.655353i	$0.227480\pi$
$613$	5.92933	+	37.4363i	0.239483	+	1.51204i	−0.515840	+	0.856685i	$0.672520\pi$
$614$		0			0
$615$	−3.93655	+	15.1916i	−0.158737	+	0.612586i
$616$		0			0
$617$	−16.8172	−	8.56877i	−0.677033	−	0.344966i	0.0814321	−	0.996679i	$-0.474051\pi$
$617$	−16.8172	−	8.56877i	−0.677033	−	0.344966i	−0.758466	+	0.651713i	$0.774051\pi$
$618$		0			0
$619$	−9.60558	−	29.5629i	−0.386081	−	1.18823i	−0.935693	−	0.352815i	$-0.885225\pi$
$619$	−9.60558	−	29.5629i	−0.386081	−	1.18823i	0.549613	−	0.835420i	$-0.314775\pi$
$620$		0			0
$621$	7.26809	−	22.3689i	0.291659	−	0.897633i
$622$		0			0
$623$	−0.339445	+	2.14317i	−0.0135996	+	0.0858644i
$624$		0			0
$625$	23.1617	+	9.40934i	0.926468	+	0.376374i
$626$		0			0
$627$	−78.0581	−	12.3632i	−3.11734	−	0.493738i
$628$		0			0
$629$	−75.0402	−	24.3820i	−2.99205	−	0.972175i
$630$		0			0
$631$	−22.9072	+	7.44299i	−0.911920	+	0.296301i	−0.727148	−	0.686481i	$-0.759155\pi$
$631$	−22.9072	+	7.44299i	−0.911920	+	0.296301i	−0.184772	+	0.982781i	$0.559155\pi$
$632$		0			0
$633$	−4.74706	+	9.31664i	−0.188679	+	0.370303i
$634$		0			0
$635$	11.1322	+	2.88464i	0.441768	+	0.114474i
$636$		0			0
$637$	32.8464	−	5.20236i	1.30142	−	0.206125i
$638$		0			0
$639$	−5.28191	+	3.83753i	−0.208949	+	0.151810i
$640$		0			0
$641$	−34.0912	−	24.7687i	−1.34652	−	0.978306i	−0.999177	−	0.0405694i	$-0.987083\pi$
$641$	−34.0912	−	24.7687i	−1.34652	−	0.978306i	−0.347346	−	0.937737i	$-0.612917\pi$
$642$		0			0
$643$	9.28007	−	9.28007i	0.365970	−	0.365970i	−0.500035	−	0.866005i	$-0.666680\pi$
$643$	9.28007	−	9.28007i	0.365970	−	0.365970i	0.866005	+	0.500035i	$0.166680\pi$
$644$		0			0
$645$	−0.0753604	−	0.0328104i	−0.00296731	−	0.00129191i
$646$		0			0
$647$	−4.61885	+	2.35342i	−0.181586	+	0.0925225i	−0.542420	−	0.840107i	$-0.682492\pi$
$647$	−4.61885	+	2.35342i	−0.181586	+	0.0925225i	0.360835	+	0.932630i	$0.382492\pi$
$648$		0			0
$649$		−	36.9892i		−	1.45195i
$650$		0			0
$651$			3.33301i			0.130631i
$652$		0			0
$653$	11.1410	−	5.67663i	0.435981	−	0.222144i	−0.222203	−	0.975000i	$-0.571325\pi$
$653$	11.1410	−	5.67663i	0.435981	−	0.222144i	0.658184	+	0.752857i	$0.271325\pi$
$654$		0			0
$655$	−0.606626	+	0.134182i	−0.0237028	+	0.00524294i
$656$		0			0
$657$	−2.73665	+	2.73665i	−0.106767	+	0.106767i
$658$		0			0
$659$	−18.5877	−	13.5047i	−0.724073	−	0.526070i	0.163610	−	0.986525i	$-0.447686\pi$
$659$	−18.5877	−	13.5047i	−0.724073	−	0.526070i	−0.887683	+	0.460455i	$0.847686\pi$
$660$		0			0
$661$	−22.6531	+	16.4585i	−0.881104	+	0.640160i	−0.933543	−	0.358464i	$-0.883300\pi$
$661$	−22.6531	+	16.4585i	−0.881104	+	0.640160i	0.0524392	+	0.998624i	$0.483300\pi$
$662$		0			0
$663$	70.7077	−	11.1990i	2.74606	−	0.434933i
$664$		0			0
$665$	−1.98983	+	3.12012i	−0.0771623	+	0.120993i
$666$		0			0
$667$	1.21270	−	2.38007i	0.0469561	−	0.0921565i
$668$		0			0
$669$	−12.1534	+	3.94887i	−0.469876	+	0.152672i
$670$		0			0
$671$	48.8981	+	15.8879i	1.88769	+	0.613347i
$672$		0			0
$673$	27.5085	+	4.35692i	1.06037	+	0.167947i	0.662173	−	0.749351i	$-0.269634\pi$
$673$	27.5085	+	4.35692i	1.06037	+	0.167947i	0.398201	+	0.917298i	$0.369634\pi$
$674$		0			0
$675$	−17.5485	−	6.40608i	−0.675441	−	0.246570i
$676$		0			0
$677$	−0.515741	+	3.25626i	−0.0198216	+	0.125148i	−0.995615	−	0.0935460i	$-0.970180\pi$
$677$	−0.515741	+	3.25626i	−0.0198216	+	0.125148i	0.975793	+	0.218694i	$0.0701798\pi$
$678$		0			0
$679$	−1.29795	+	3.99468i	−0.0498107	+	0.153302i
$680$		0			0
$681$	−9.14015	−	28.1305i	−0.350251	−	1.07796i
$682$		0			0
$683$	−23.9199	−	12.1878i	−0.915271	−	0.466354i	−0.0681026	−	0.997678i	$-0.521695\pi$
$683$	−23.9199	−	12.1878i	−0.915271	−	0.466354i	−0.847168	+	0.531324i	$0.821695\pi$
$684$		0			0
$685$	23.2352	−	1.41001i	0.887770	−	0.0538736i
$686$		0			0
$687$	−1.10649	−	6.98608i	−0.0422151	−	0.266536i
$688$		0			0
$689$	11.4596	+	15.7728i	0.436577	+	0.600897i
$690$		0			0
$691$	−15.9131	+	21.9024i	−0.605361	+	0.833208i	−0.996186	−	0.0872569i	$-0.972190\pi$
$691$	−15.9131	+	21.9024i	−0.605361	+	0.833208i	0.390825	+	0.920465i	$0.372190\pi$
$692$		0			0
$693$	1.09488	+	1.09488i	0.0415912	+	0.0415912i
$694$		0			0
$695$	−35.2863	+	20.7626i	−1.33849	+	0.787569i
$696$		0			0
$697$	−11.4195	−	22.4120i	−0.432545	−	0.848917i
$698$		0			0
$699$	−12.7688			−0.482962
$700$		0			0
$701$	14.5677			0.550214			0.275107	−	0.961414i	$-0.411287\pi$
$701$	14.5677			0.550214			0.275107	+	0.961414i	$0.411287\pi$
$702$		0			0
$703$	34.0532	+	66.8331i	1.28434	+	2.52066i
$704$		0			0
$705$	−12.5750	−	11.1361i	−0.473600	−	0.419409i
$706$		0			0
$707$	1.41208	+	1.41208i	0.0531067	+	0.0531067i
$708$		0			0
$709$	−23.5444	+	32.4061i	−0.884228	+	1.21704i	0.0910033	+	0.995851i	$0.470993\pi$
$709$	−23.5444	+	32.4061i	−0.884228	+	1.21704i	−0.975232	+	0.221185i	$0.929007\pi$
$710$		0			0
$711$	0.232212	+	0.319613i	0.00870864	+	0.0119864i
$712$		0			0
$713$	6.75733	+	42.6641i	0.253064	+	1.59778i
$714$		0			0
$715$	−45.9809	+	37.8670i	−1.71959	+	1.41614i
$716$		0			0
$717$	18.4957	+	9.42401i	0.690733	+	0.351946i
$718$		0			0
$719$	10.7723	+	33.1537i	0.401738	+	1.23642i	0.923588	+	0.383386i	$0.125242\pi$
$719$	10.7723	+	33.1537i	0.401738	+	1.23642i	−0.521850	+	0.853037i	$0.674758\pi$
$720$		0			0
$721$	0.184708	−	0.568474i	0.00687890	−	0.0211711i
$722$		0			0
$723$	0.747417	−	4.71901i	0.0277967	−	0.175502i
$724$		0			0
$725$	−1.85466	−	1.03037i	−0.0688803	−	0.0382668i
$726$		0			0
$727$	−25.6487	−	4.06236i	−0.951258	−	0.150664i	−0.338528	−	0.940956i	$-0.609929\pi$
$727$	−25.6487	−	4.06236i	−0.951258	−	0.150664i	−0.612730	+	0.790292i	$0.709929\pi$
$728$		0			0
$729$	9.36749	+	3.04368i	0.346944	+	0.112729i
$730$		0			0
$731$	0.125293	−	0.0407101i	0.00463412	−	0.00150572i
$732$		0			0
$733$	20.5592	−	40.3496i	0.759370	−	1.49035i	−0.108791	−	0.994065i	$-0.534698\pi$
$733$	20.5592	−	40.3496i	0.759370	−	1.49035i	0.868161	−	0.496282i	$-0.165302\pi$
$734$		0			0
$735$	−29.5060	+	11.6065i	−1.08834	+	0.428111i
$736$		0			0
$737$	−19.7147	+	3.12250i	−0.726199	+	0.115019i
$738$		0			0
$739$	3.16515	−	2.29962i	0.116432	−	0.0845928i	−0.528046	−	0.849216i	$-0.677075\pi$
$739$	3.16515	−	2.29962i	0.116432	−	0.0845928i	0.644477	+	0.764623i	$0.277075\pi$
$740$		0			0
$741$	−55.0589	−	40.0026i	−2.02264	−	1.46953i
$742$		0			0
$743$	7.89174	−	7.89174i	0.289520	−	0.289520i	−0.547371	−	0.836890i	$-0.684371\pi$
$743$	7.89174	−	7.89174i	0.289520	−	0.289520i	0.836890	+	0.547371i	$0.184371\pi$
$744$		0			0
$745$	−0.955743	+	9.87642i	−0.0350157	+	0.361844i
$746$		0			0
$747$	−2.48354	+	1.26543i	−0.0908679	+	0.0462995i
$748$		0			0
$749$			0.535770i			0.0195766i
$750$		0			0
$751$		−	33.7646i		−	1.23209i	−0.787712	−	0.616044i	$-0.788734\pi$
$751$		−	33.7646i		−	1.23209i	0.787712	−	0.616044i	$-0.211266\pi$
$752$		0			0
$753$	−39.0270	+	19.8853i	−1.42222	+	0.724660i
$754$		0			0
$755$	−2.79963	+	28.9308i	−0.101889	+	1.05290i
$756$		0			0
$757$	−9.32683	+	9.32683i	−0.338989	+	0.338989i	−0.855987	−	0.516997i	$-0.827050\pi$
$757$	−9.32683	+	9.32683i	−0.338989	+	0.338989i	0.516997	+	0.855987i	$0.327050\pi$
$758$		0			0
$759$	57.8463	+	42.0278i	2.09969	+	1.52551i
$760$		0			0
$761$	4.34693	−	3.15823i	0.157576	−	0.114486i	−0.506203	−	0.862414i	$-0.668951\pi$
$761$	4.34693	−	3.15823i	0.157576	−	0.114486i	0.663779	+	0.747928i	$0.268951\pi$
$762$		0			0
$763$	0.828603	−	0.131238i	0.0299974	−	0.00475113i
$764$		0			0
$765$	−17.8263	+	7.01214i	−0.644510	+	0.253524i
$766$		0			0
$767$	14.4608	−	28.3810i	0.522150	−	1.02478i
$768$		0			0
$769$	11.4718	−	3.72742i	0.413685	−	0.134414i	−0.0947777	−	0.995498i	$-0.530214\pi$
$769$	11.4718	−	3.72742i	0.413685	−	0.134414i	0.508463	+	0.861084i	$0.330214\pi$
$770$		0			0
$771$	−10.2890	−	3.34310i	−0.370549	−	0.120399i
$772$		0			0
$773$	26.0288	+	4.12255i	0.936190	+	0.148278i	0.605845	−	0.795582i	$-0.292835\pi$
$773$	26.0288	+	4.12255i	0.936190	+	0.148278i	0.330345	+	0.943860i	$0.392835\pi$
$774$		0			0
$775$	34.0573	−	4.14876i	1.22337	−	0.149028i
$776$		0			0
$777$	0.819137	−	5.17183i	0.0293864	−	0.185538i
$778$		0			0
$779$	−7.38935	+	22.7421i	−0.264751	+	0.814820i
$780$		0			0
$781$	9.58700	+	29.5057i	0.343050	+	1.05580i
$782$		0			0
$783$	1.41260	+	0.719756i	0.0504823	+	0.0257220i
$784$		0			0
$785$	−35.2794	+	29.0539i	−1.25918	+	1.03698i
$786$		0			0
$787$	−2.08619	−	13.1717i	−0.0743645	−	0.469519i	−0.996565	−	0.0828082i	$-0.973611\pi$
$787$	−2.08619	−	13.1717i	−0.0743645	−	0.469519i	0.922201	−	0.386711i	$-0.126389\pi$
$788$		0			0
$789$	15.7858	+	21.7273i	0.561990	+	0.773513i
$790$		0			0
$791$	−1.01195	+	1.39284i	−0.0359809	+	0.0495235i
$792$		0			0
$793$	31.3070	+	31.3070i	1.11175	+	1.11175i
$794$		0			0
$795$	−13.9158	−	12.3235i	−0.493542	−	0.437069i
$796$		0			0
$797$	12.6437	+	24.8147i	0.447863	+	0.878981i	0.999006	+	0.0445700i	$0.0141918\pi$
$797$	12.6437	+	24.8147i	0.447863	+	0.878981i	−0.551143	+	0.834411i	$0.685808\pi$
$798$		0			0
$799$	26.9226			0.952454
$800$		0			0
$801$	10.6779			0.377286
$802$		0			0
$803$	8.34924	+	16.3863i	0.294638	+	0.578260i
$804$		0			0
$805$	2.88560	−	1.69790i	0.101704	−	0.0598430i
$806$		0			0
$807$	−20.9190	−	20.9190i	−0.736384	−	0.736384i
$808$		0			0
$809$	4.37116	−	6.01639i	0.153682	−	0.211525i	−0.725233	−	0.688503i	$-0.758268\pi$
$809$	4.37116	−	6.01639i	0.153682	−	0.211525i	0.878915	+	0.476978i	$0.158268\pi$
$810$		0			0
$811$	−12.7904	−	17.6045i	−0.449132	−	0.618178i	0.523079	−	0.852284i	$-0.324783\pi$
$811$	−12.7904	−	17.6045i	−0.449132	−	0.618178i	−0.972211	+	0.234107i	$0.924783\pi$
$812$		0			0
$813$	−4.12530	−	26.0461i	−0.144681	−	0.913478i
$814$		0			0
$815$	−27.5462	+	1.67162i	−0.964901	+	0.0585542i
$816$		0			0
$817$	−0.111590	−	0.0568577i	−0.00390402	−	0.00198920i
$818$		0			0
$819$	0.412038	+	1.26812i	0.0143978	+	0.0443118i
$820$		0			0
$821$	1.39473	−	4.29253i	0.0486763	−	0.149810i	−0.923764	−	0.382962i	$-0.874904\pi$
$821$	1.39473	−	4.29253i	0.0486763	−	0.149810i	0.972440	+	0.233152i	$0.0749039\pi$
$822$		0			0
$823$	−2.87447	+	18.1487i	−0.100198	+	0.632623i	0.885570	+	0.464507i	$0.153768\pi$
$823$	−2.87447	+	18.1487i	−0.100198	+	0.632623i	−0.985767	+	0.168116i	$0.946232\pi$
$824$		0			0
$825$	35.0070	−	44.7190i	1.21879	−	1.55692i
$826$		0			0
$827$	−21.9045	−	3.46934i	−0.761695	−	0.120641i	−0.236510	−	0.971629i	$-0.576004\pi$
$827$	−21.9045	−	3.46934i	−0.761695	−	0.120641i	−0.525185	+	0.850988i	$0.676004\pi$
$828$		0			0
$829$	−6.77427	−	2.20109i	−0.235280	−	0.0764472i	0.189004	−	0.981976i	$-0.439474\pi$
$829$	−6.77427	−	2.20109i	−0.235280	−	0.0764472i	−0.424284	+	0.905529i	$0.639474\pi$
$830$		0			0
$831$	−48.4057	+	15.7280i	−1.67918	+	0.545597i
$832$		0			0
$833$	23.0718	−	45.2809i	0.799390	−	1.56889i
$834$		0			0
$835$	−16.7451	+	26.2570i	−0.579490	+	0.908660i
$836$		0			0
$837$	−25.3217	+	4.01057i	−0.875247	+	0.138625i
$838$		0			0
$839$	−28.4718	+	20.6860i	−0.982955	+	0.714159i	−0.958367	−	0.285539i	$-0.907827\pi$
$839$	−28.4718	+	20.6860i	−0.982955	+	0.714159i	−0.0245883	+	0.999698i	$0.507827\pi$
$840$		0			0
$841$	−23.3158	−	16.9399i	−0.803994	−	0.584136i
$842$		0			0
$843$	1.10032	−	1.10032i	0.0378969	−	0.0378969i
$844$		0			0
$845$	−21.7013	+	4.80022i	−0.746548	+	0.165132i
$846$		0			0
$847$	4.22468	−	2.15258i	0.145162	−	0.0739636i
$848$		0			0
$849$			12.3185i			0.422768i
$850$		0			0
$851$		−	67.8626i		−	2.32630i
$852$		0			0
$853$	−19.8794	+	10.1290i	−0.680656	+	0.346812i	−0.759897	−	0.650044i	$-0.774751\pi$
$853$	−19.8794	+	10.1290i	−0.680656	+	0.346812i	0.0792405	+	0.996856i	$0.474751\pi$
$854$		0			0
$855$	16.6968	+	7.26942i	0.571017	+	0.248609i
$856$		0			0
$857$	41.1208	−	41.1208i	1.40466	−	1.40466i	0.620270	−	0.784388i	$-0.287023\pi$
$857$	41.1208	−	41.1208i	1.40466	−	1.40466i	0.784388	−	0.620270i	$-0.212977\pi$
$858$		0			0
$859$	43.1893	+	31.3789i	1.47360	+	1.07063i	0.979550	+	0.201201i	$0.0644846\pi$
$859$	43.1893	+	31.3789i	1.47360	+	1.07063i	0.494052	+	0.869433i	$0.335515\pi$
$860$		0			0
$861$	1.35050	−	0.981197i	0.0460250	−	0.0334391i
$862$		0			0
$863$	−31.7199	+	5.02393i	−1.07976	+	0.171017i	−0.670875	−	0.741571i	$-0.734081\pi$
$863$	−31.7199	+	5.02393i	−1.07976	+	0.171017i	−0.408882	+	0.912587i	$0.634081\pi$
$864$		0			0
$865$	0.627069	+	0.162490i	0.0213210	+	0.00552482i
$866$		0			0
$867$	33.9050	−	66.5422i	1.15147	−	2.25989i
$868$		0			0
$869$	1.78542	−	0.580117i	0.0605661	−	0.0196791i
$870$		0			0
$871$	−16.3474	−	5.31158i	−0.553909	−	0.179976i
$872$		0			0
$873$	20.4148	+	3.23339i	0.690936	+	0.109434i
$874$		0			0
$875$	−1.26555	−	2.33881i	−0.0427832	−	0.0790663i
$876$		0			0
$877$	−0.0206403	+	0.130318i	−0.000696974	+	0.00440052i	−0.988034	−	0.154234i	$-0.950709\pi$
$877$	−0.0206403	+	0.130318i	−0.000696974	+	0.00440052i	0.987337	+	0.158634i	$0.0507091\pi$
$878$		0			0
$879$	4.34786	−	13.3814i	0.146650	−	0.451342i
$880$		0			0
$881$	7.65764	+	23.5678i	0.257993	+	0.794020i	0.993225	+	0.116205i	$0.0370729\pi$
$881$	7.65764	+	23.5678i	0.257993	+	0.794020i	−0.735233	+	0.677815i	$0.762927\pi$
$882$		0			0
$883$	−1.88893	−	0.962459i	−0.0635676	−	0.0323893i	0.421918	−	0.906634i	$-0.361357\pi$
$883$	−1.88893	−	0.962459i	−0.0635676	−	0.0323893i	−0.485485	+	0.874245i	$0.661357\pi$
$884$		0			0
$885$	−7.61778	+	29.3980i	−0.256069	+	0.988202i
$886$		0			0
$887$	6.01209	+	37.9589i	0.201866	+	1.27453i	0.855532	+	0.517750i	$0.173230\pi$
$887$	6.01209	+	37.9589i	0.201866	+	1.27453i	−0.653665	+	0.756784i	$0.726770\pi$
$888$		0			0
$889$	−0.719005	−	0.989626i	−0.0241147	−	0.0331910i
$890$		0			0
$891$	−36.4234	+	50.1325i	−1.22023	+	1.67950i
$892$		0			0
$893$	−18.0978	−	18.0978i	−0.605620	−	0.605620i
$894$		0			0
$895$	13.0683	−	30.0159i	0.436825	−	1.00332i
$896$		0			0
$897$	27.9535	+	54.8618i	0.933340	+	1.83178i
$898$		0			0
$899$	−2.91168			−0.0971098
$900$		0			0
$901$	29.7933			0.992560
$902$		0			0
$903$	0.00396920	+	0.00778999i	0.000132087	+	0.000259235i
$904$		0			0
$905$	−4.88341	−	22.0774i	−0.162330	−	0.733878i
$906$		0			0
$907$	29.8016	+	29.8016i	0.989548	+	0.989548i	0.999946	−	0.0103984i	$-0.00330997\pi$
$907$	29.8016	+	29.8016i	0.989548	+	0.989548i	−0.0103984	+	0.999946i	$0.503310\pi$
$908$		0			0
$909$	5.77620	−	7.95026i	0.191585	−	0.263694i
$910$		0			0
$911$	−4.04439	−	5.56662i	−0.133997	−	0.184431i	0.736746	−	0.676170i	$-0.236361\pi$
$911$	−4.04439	−	5.56662i	−0.133997	−	0.184431i	−0.870743	+	0.491739i	$0.836361\pi$
$912$		0			0
$913$	2.07200	+	13.0821i	0.0685731	+	0.432954i
$914$		0			0
$915$	−35.5907	−	22.6977i	−1.17659	−	0.750362i
$916$		0			0
$917$	0.0588837	+	0.0300027i	0.00194451	+	0.000990778i
$918$		0			0
$919$	−3.53804	−	10.8890i	−0.116709	−	0.359194i	0.875591	−	0.483054i	$-0.160473\pi$
$919$	−3.53804	−	10.8890i	−0.116709	−	0.359194i	−0.992300	+	0.123860i	$0.960473\pi$
$920$		0			0
$921$	4.65328	−	14.3213i	0.153331	−	0.471904i
$922$		0			0
$923$	−4.17931	+	26.3871i	−0.137564	+	0.868542i
$924$		0			0
$925$	−53.8663	−	1.93247i	−1.77111	−	0.0635392i
$926$		0			0
$927$	−2.90519	−	0.460136i	−0.0954188	−	0.0151129i
$928$		0			0
$929$	−7.59176	−	2.46671i	−0.249078	−	0.0809302i	0.181817	−	0.983332i	$-0.441802\pi$
$929$	−7.59176	−	2.46671i	−0.249078	−	0.0809302i	−0.430895	+	0.902402i	$0.641802\pi$
$930$		0			0
$931$	−45.9477	+	14.9293i	−1.50588	+	0.489289i
$932$		0			0
$933$	−23.7457	+	46.6036i	−0.777401	+	1.52573i
$934$		0			0
$935$	5.51373	+	90.8594i	0.180318	+	2.97142i
$936$		0			0
$937$	9.77156	−	1.54766i	0.319223	−	0.0505600i	0.00523318	−	0.999986i	$-0.498334\pi$
$937$	9.77156	−	1.54766i	0.319223	−	0.0505600i	0.313990	+	0.949426i	$0.398334\pi$
$938$		0			0
$939$	−0.933030	+	0.677886i	−0.0304483	+	0.0221220i
$940$		0			0
$941$	−18.7002	−	13.5865i	−0.609610	−	0.442908i	0.239667	−	0.970855i	$-0.422962\pi$
$941$	−18.7002	−	13.5865i	−0.609610	−	0.442908i	−0.849277	+	0.527947i	$0.822962\pi$
$942$		0			0
$943$	15.2978	−	15.2978i	0.498165	−	0.498165i
$944$		0			0
$945$	1.00773	+	1.71264i	0.0327813	+	0.0557123i
$946$		0			0
$947$	−4.48566	+	2.28556i	−0.145764	+	0.0742707i	−0.525351	−	0.850885i	$-0.676066\pi$
$947$	−4.48566	+	2.28556i	−0.145764	+	0.0742707i	0.379587	+	0.925156i	$0.376066\pi$
$948$		0			0
$949$			15.8370i			0.514090i
$950$		0			0
$951$			31.0273i			1.00613i
$952$		0			0
$953$	8.83504	−	4.50168i	0.286195	−	0.145824i	−0.305000	−	0.952352i	$-0.598656\pi$
$953$	8.83504	−	4.50168i	0.286195	−	0.145824i	0.591195	+	0.806529i	$0.298656\pi$
$954$		0			0
$955$	−5.02959	+	5.67946i	−0.162754	+	0.183783i
$956$		0			0
$957$	−3.40803	+	3.40803i	−0.110166	+	0.110166i
$958$		0			0
$959$	−2.00319	−	1.45540i	−0.0646864	−	0.0469974i
$960$		0			0
$961$	13.0126	−	9.45422i	0.419762	−	0.304975i
$962$		0			0
$963$	2.60404	−	0.412440i	0.0839141	−	0.0132907i
$964$		0			0
$965$	−23.6806	−	28.7548i	−0.762306	−	0.925650i
$966$		0			0
$967$	−2.92888	+	5.74826i	−0.0941866	+	0.184852i	−0.933293	−	0.359116i	$-0.883078\pi$
$967$	−2.92888	+	5.74826i	−0.0941866	+	0.184852i	0.839107	+	0.543967i	$0.183078\pi$
$968$		0			0
$969$	−98.9106	+	32.1380i	−3.17747	+	1.03242i
$970$		0			0
$971$	49.5154	+	16.0885i	1.58903	+	0.516306i	0.964362	−	0.264587i	$-0.0852358\pi$
$971$	49.5154	+	16.0885i	1.58903	+	0.516306i	0.624664	+	0.780893i	$0.285236\pi$
$972$		0			0
$973$	4.30135	+	0.681266i	0.137895	+	0.0218404i
$974$		0			0
$975$	44.3429	−	20.6260i	1.42011	−	0.660561i
$976$		0			0
$977$	4.35642	−	27.5053i	0.139374	−	0.879973i	−0.814587	−	0.580042i	$-0.803036\pi$
$977$	4.35642	−	27.5053i	0.139374	−	0.879973i	0.953961	−	0.299932i	$-0.0969638\pi$
$978$		0			0
$979$	15.6796	−	48.2570i	0.501124	−	1.54230i
$980$		0			0
$981$	−1.27573	−	3.92629i	−0.0407309	−	0.125357i
$982$		0			0
$983$	6.45182	+	3.28737i	0.205781	+	0.104851i	0.553844	−	0.832621i	$-0.313160\pi$
$983$	6.45182	+	3.28737i	0.205781	+	0.104851i	−0.348063	+	0.937471i	$0.613160\pi$
$984$		0			0
$985$	−3.07277	−	7.81161i	−0.0979067	−	0.248898i
$986$		0			0
$987$	0.279503	+	1.76471i	0.00889668	+	0.0561714i
$988$		0			0
$989$	0.0666010	+	0.0916685i	0.00211779	+	0.00291489i
$990$		0			0
$991$	16.4038	−	22.5778i	0.521082	−	0.717209i	−0.464656	−	0.885491i	$-0.653822\pi$
$991$	16.4038	−	22.5778i	0.521082	−	0.717209i	0.985739	+	0.168283i	$0.0538221\pi$
$992$		0			0
$993$	−47.8027	−	47.8027i	−1.51697	−	1.51697i
$994$		0			0
$995$	25.6361	+	2.48081i	0.812719	+	0.0786470i
$996$		0			0
$997$	−10.4842	−	20.5765i	−0.332040	−	0.651664i	0.663273	−	0.748378i	$-0.269167\pi$
$997$	−10.4842	−	20.5765i	−0.332040	−	0.651664i	−0.995312	+	0.0967135i	$0.969167\pi$
$998$		0			0
$999$	40.2774			1.27432

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	800.2.bq.d.223.2	yes	64
4.3	odd	2		800.2.bq.c.223.7	✓	64
25.12	odd	20		800.2.bq.c.287.7	yes	64
100.87	even	20	inner	800.2.bq.d.287.2	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
800.2.bq.c.223.7	✓	64	4.3	odd	2
800.2.bq.c.287.7	yes	64	25.12	odd	20
800.2.bq.d.223.2	yes	64	1.1	even	1	trivial
800.2.bq.d.287.2	yes	64	100.87	even	20	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:	\( N \)	\(=\)	\( 800 = 2^{5} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	800.bq (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.927126 - 1.81959i) q^{3} +(2.22567 + 0.215379i) q^{5} +(-0.168186 - 0.168186i) q^{7} +(-0.687977 + 0.946919i) q^{9} +O(q^{10})\)	\(q+(-0.927126 - 1.81959i) q^{3} +(2.22567 + 0.215379i) q^{5} +(-0.168186 - 0.168186i) q^{7} +(-0.687977 + 0.946919i) q^{9} +(3.26920 + 4.49966i) q^{11} +(0.749249 + 4.73057i) q^{13} +(-1.67158 - 4.24948i) q^{15} +(6.52141 + 3.32283i) q^{17} +(-2.15014 - 6.61744i) q^{19} +(-0.150100 + 0.461959i) q^{21} +(-0.984773 + 6.21761i) q^{23} +(4.90722 + 0.958724i) q^{25} +(-3.69024 - 0.584476i) q^{27} +(-0.403562 - 0.131125i) q^{29} +(6.52597 - 2.12042i) q^{31} +(5.15657 - 10.1203i) q^{33} +(-0.338104 - 0.410551i) q^{35} +(-10.6475 + 1.68639i) q^{37} +(7.91304 - 5.74916i) q^{39} +(-2.78034 - 2.02003i) q^{41} +(0.0127275 - 0.0127275i) q^{43} +(-1.73516 + 1.95936i) q^{45} +(3.27746 - 1.66995i) q^{47} -6.94343i q^{49} -14.9469i q^{51} +(3.62693 - 1.84801i) q^{53} +(6.30702 + 10.7189i) q^{55} +(-10.0476 + 10.0476i) q^{57} +(-5.38035 - 3.90905i) q^{59} +(7.47861 - 5.43353i) q^{61} +(0.274967 - 0.0435505i) q^{63} +(0.648719 + 10.6901i) q^{65} +(-1.62927 + 3.19763i) q^{67} +(12.2265 - 3.97263i) q^{69} +(5.30499 + 1.72369i) q^{71} +(3.26586 + 0.517262i) q^{73} +(-2.80513 - 9.81798i) q^{75} +(0.206948 - 1.30662i) q^{77} +(0.104302 - 0.321009i) q^{79} +(3.44288 + 10.5961i) q^{81} +(2.12185 + 1.08114i) q^{83} +(13.7989 + 8.80009i) q^{85} +(0.135559 + 0.855886i) q^{87} +(-5.36229 - 7.38056i) q^{89} +(0.669604 - 0.921631i) q^{91} +(-9.90868 - 9.90868i) q^{93} +(-3.36024 - 15.1913i) q^{95} +(-8.01709 - 15.7344i) q^{97} -6.50995 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 2 q^{5} + 4 q^{7}+O(q^{10}) \) 64 * q + 2 * q^5 + 4 * q^7	\( 64 q + 2 q^{5} + 4 q^{7} + 4 q^{13} + 22 q^{15} + 8 q^{17} - 18 q^{19} - 16 q^{21} + 8 q^{23} + 40 q^{25} + 18 q^{27} - 20 q^{31} + 44 q^{33} + 38 q^{35} - 10 q^{37} - 36 q^{39} - 16 q^{41} + 32 q^{43} + 14 q^{45} + 8 q^{47} - 22 q^{53} - 24 q^{55} - 8 q^{57} - 4 q^{59} - 36 q^{61} + 18 q^{63} - 24 q^{65} - 26 q^{67} + 60 q^{69} + 70 q^{71} - 12 q^{73} + 66 q^{75} + 48 q^{77} + 16 q^{79} - 24 q^{81} - 52 q^{83} - 46 q^{85} - 144 q^{87} - 60 q^{89} - 30 q^{91} + 20 q^{93} - 8 q^{95} - 56 q^{97} + 132 q^{99}+O(q^{100}) \) 64 * q + 2 * q^5 + 4 * q^7 + 4 * q^13 + 22 * q^15 + 8 * q^17 - 18 * q^19 - 16 * q^21 + 8 * q^23 + 40 * q^25 + 18 * q^27 - 20 * q^31 + 44 * q^33 + 38 * q^35 - 10 * q^37 - 36 * q^39 - 16 * q^41 + 32 * q^43 + 14 * q^45 + 8 * q^47 - 22 * q^53 - 24 * q^55 - 8 * q^57 - 4 * q^59 - 36 * q^61 + 18 * q^63 - 24 * q^65 - 26 * q^67 + 60 * q^69 + 70 * q^71 - 12 * q^73 + 66 * q^75 + 48 * q^77 + 16 * q^79 - 24 * q^81 - 52 * q^83 - 46 * q^85 - 144 * q^87 - 60 * q^89 - 30 * q^91 + 20 * q^93 - 8 * q^95 - 56 * q^97 + 132 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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