LMFDB - Embedded newform 92.2.e.a.29.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [92,2,Mod(9,92)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(92, base_ring=CyclotomicField(22))

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

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

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

chi := DirichletCharacter("92.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 92 = 2^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	92.e (of order $11$, degree $10$, 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:	$0.734623698596$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$2$ over $\Q(\zeta_{11})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 9 x^{19} + 51 x^{18} - 200 x^{17} + 633 x^{16} - 1688 x^{15} + 3957 x^{14} - 8161 x^{13} + \cdots + 529 $ x^20 - 9x^19 + 51x^18 - 200x^17 + 633x^16 - 1688x^15 + 3957x^14 - 8161x^13 + 14788x^12 - 23925x^11 + 35080x^10 - 43945x^9 + 57269x^8 - 57348x^7 + 52821x^6 - 34986x^5 + 26231x^4 + 96928x^3 + 49370x^2 + 8165*x + 529
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			29.1
Root			$0.291382 - 2.02660i$ of defining polynomial
Character	$\chi$	$=$	92.29
Dual form			92.2.e.a.73.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.96451 - 0.576832i) q^{3} +(3.22799 - 2.07450i) q^{5} +(0.267813 - 1.86268i) q^{7} +(1.00280 + 0.644459i) q^{9} +(0.804680 + 1.76200i) q^{11} +(-0.112273 - 0.780878i) q^{13} +(-7.53806 + 2.21337i) q^{15} +(-4.90640 + 5.66229i) q^{17} +(3.96265 + 4.57314i) q^{19} +(-1.60057 + 3.50477i) q^{21} +(-1.77773 - 4.45418i) q^{23} +(4.03929 - 8.84481i) q^{25} +(2.42411 + 2.79757i) q^{27} +(-1.75966 + 2.03076i) q^{29} +(2.65784 - 0.780411i) q^{31} +(-0.564421 - 3.92564i) q^{33} +(-2.99964 - 6.56830i) q^{35} +(8.29737 + 5.33239i) q^{37} +(-0.229873 + 1.59881i) q^{39} +(-5.52765 + 3.55240i) q^{41} +(-7.72022 - 2.26686i) q^{43} +4.57396 q^{45} -1.75371 q^{47} +(3.31859 + 0.974427i) q^{49} +(12.9049 - 8.29345i) q^{51} +(0.516246 - 3.59057i) q^{53} +(6.25279 + 4.01842i) q^{55} +(-5.14673 - 11.2698i) q^{57} +(0.999647 + 6.95269i) q^{59} +(-1.86952 + 0.548941i) q^{61} +(1.46898 - 1.69530i) q^{63} +(-1.98235 - 2.28776i) q^{65} +(4.08243 - 8.93929i) q^{67} +(0.923056 + 9.77572i) q^{69} +(-2.88802 + 6.32387i) q^{71} +(-8.63107 - 9.96078i) q^{73} +(-13.0372 + 15.0457i) q^{75} +(3.49756 - 1.02698i) q^{77} +(0.0541763 + 0.376804i) q^{79} +(-4.63402 - 10.1471i) q^{81} +(2.75842 + 1.77273i) q^{83} +(-4.09138 + 28.4562i) q^{85} +(4.62828 - 2.97442i) q^{87} +(-4.66512 - 1.36980i) q^{89} -1.48460 q^{91} -5.67151 q^{93} +(22.2784 + 6.54153i) q^{95} +(-7.65402 + 4.91894i) q^{97} +(-0.328608 + 2.28552i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 2 q^{3} + 2 q^{5} + 2 q^{7} - 4 q^{9} - 2 q^{11} + 6 q^{13} - 17 q^{15} - 9 q^{17} - 11 q^{19} - 47 q^{21} - 22 q^{23} - 16 q^{25} - 19 q^{27} - q^{29} - 13 q^{31} - 5 q^{33} + 14 q^{35} + 34 q^{37}+ \cdots - q^{99}+O(q^{100}) $ 20 * q + 2 * q^3 + 2 * q^5 + 2 * q^7 - 4 * q^9 - 2 * q^11 + 6 * q^13 - 17 * q^15 - 9 * q^17 - 11 * q^19 - 47 * q^21 - 22 * q^23 - 16 * q^25 - 19 * q^27 - q^29 - 13 * q^31 - 5 * q^33 + 14 * q^35 + 34 * q^37 + 30 * q^39 + 28 * q^41 + 44 * q^43 + 78 * q^45 + 26 * q^47 + 60 * q^49 + 62 * q^51 + 14 * q^53 + 26 * q^55 + 3 * q^57 - 10 * q^59 - 56 * q^61 - 27 * q^63 - 87 * q^65 - 44 * q^67 - 51 * q^69 - 37 * q^71 - 12 * q^73 - 53 * q^75 - 47 * q^77 - 6 * q^79 - 10 * q^81 - 25 * q^83 + 8 * q^85 + 48 * q^87 + 10 * q^89 + 26 * q^91 - 14 * q^93 + 29 * q^95 - q^97 - q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/92\mathbb{Z}\right)^\times$.

$n$	$5$	$47$
$\chi(n)$	$e\left(\frac{9}{11}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.96451	−	0.576832i	−1.13421	−	0.333034i	−0.339849	−	0.940480i	$-0.610376\pi$
$3$	−1.96451	−	0.576832i	−1.13421	−	0.333034i	−0.794361	+	0.607446i	$0.792194\pi$
$4$		0			0
$5$	3.22799	−	2.07450i	1.44360	−	0.927747i	0.444107	−	0.895974i	$-0.353521\pi$
$5$	3.22799	−	2.07450i	1.44360	−	0.927747i	0.999495	−	0.0317727i	$-0.0101153\pi$
$6$		0			0
$7$	0.267813	−	1.86268i	0.101224	−	0.704027i	−0.874500	−	0.485025i	$-0.838811\pi$
$7$	0.267813	−	1.86268i	0.101224	−	0.704027i	0.975724	−	0.219003i	$-0.0702803\pi$
$8$		0			0
$9$	1.00280	+	0.644459i	0.334266	+	0.214820i
$10$		0			0
$11$	0.804680	+	1.76200i	0.242620	+	0.531264i	0.991293	−	0.131676i	$-0.0420357\pi$
$11$	0.804680	+	1.76200i	0.242620	+	0.531264i	−0.748673	+	0.662940i	$0.769308\pi$
$12$		0			0
$13$	−0.112273	−	0.780878i	−0.0311390	−	0.216577i	0.968311	−	0.249749i	$-0.0803481\pi$
$13$	−0.112273	−	0.780878i	−0.0311390	−	0.216577i	−0.999450	+	0.0331723i	$0.989439\pi$
$14$		0			0
$15$	−7.53806	+	2.21337i	−1.94632	+	0.571491i
$16$		0			0
$17$	−4.90640	+	5.66229i	−1.18998	+	1.37331i	−0.279292	+	0.960206i	$0.590100\pi$
$17$	−4.90640	+	5.66229i	−1.18998	+	1.37331i	−0.910685	+	0.413101i	$0.864446\pi$
$18$		0			0
$19$	3.96265	+	4.57314i	0.909095	+	1.04915i	0.998586	+	0.0531635i	$0.0169304\pi$
$19$	3.96265	+	4.57314i	0.909095	+	1.04915i	−0.0894912	+	0.995988i	$0.528524\pi$
$20$		0			0
$21$	−1.60057	+	3.50477i	−0.349274	+	0.764804i
$22$		0			0
$23$	−1.77773	−	4.45418i	−0.370682	−	0.928760i
$23$	−1.77773	−	4.45418i	−0.370682	−	0.928760i
$24$		0			0
$25$	4.03929	−	8.84481i	0.807858	−	1.76896i
$26$		0			0
$27$	2.42411	+	2.79757i	0.466521	+	0.538394i
$28$		0			0
$29$	−1.75966	+	2.03076i	−0.326761	+	0.377103i	−0.895232	−	0.445601i	$-0.852990\pi$
$29$	−1.75966	+	2.03076i	−0.326761	+	0.377103i	0.568470	+	0.822704i	$0.307535\pi$
$30$		0			0
$31$	2.65784	−	0.780411i	0.477361	−	0.140166i	−0.0341959	−	0.999415i	$-0.510887\pi$
$31$	2.65784	−	0.780411i	0.477361	−	0.140166i	0.511557	+	0.859249i	$0.329069\pi$
$32$		0			0
$33$	−0.564421	−	3.92564i	−0.0982531	−	0.683366i
$34$		0			0
$35$	−2.99964	−	6.56830i	−0.507032	−	1.11025i
$36$		0			0
$37$	8.29737	+	5.33239i	1.36408	+	0.876640i	0.998533	−	0.0541530i	$-0.0172459\pi$
$37$	8.29737	+	5.33239i	1.36408	+	0.876640i	0.365546	+	0.930793i	$0.380882\pi$
$38$		0			0
$39$	−0.229873	+	1.59881i	−0.0368092	+	0.256014i
$40$		0			0
$41$	−5.52765	+	3.55240i	−0.863273	+	0.554792i	−0.895688	−	0.444682i	$-0.853317\pi$
$41$	−5.52765	+	3.55240i	−0.863273	+	0.554792i	0.0324150	+	0.999474i	$0.489680\pi$
$42$		0			0
$43$	−7.72022	−	2.26686i	−1.17732	−	0.345693i	−0.366181	−	0.930544i	$-0.619335\pi$
$43$	−7.72022	−	2.26686i	−1.17732	−	0.345693i	−0.811141	+	0.584851i	$0.801153\pi$
$44$		0			0
$45$	4.57396			0.681845
$46$		0			0
$47$	−1.75371			−0.255805			−0.127903	−	0.991787i	$-0.540824\pi$
$47$	−1.75371			−0.255805			−0.127903	+	0.991787i	$0.540824\pi$
$48$		0			0
$49$	3.31859	+	0.974427i	0.474085	+	0.139204i
$50$		0			0
$51$	12.9049	−	8.29345i	1.80704	−	1.16131i
$52$		0			0
$53$	0.516246	−	3.59057i	0.0709118	−	0.493203i	−0.923155	−	0.384429i	$-0.874398\pi$
$53$	0.516246	−	3.59057i	0.0709118	−	0.493203i	0.994067	−	0.108774i	$-0.0346925\pi$
$54$		0			0
$55$	6.25279	+	4.01842i	0.843126	+	0.541844i
$56$		0			0
$57$	−5.14673	−	11.2698i	−0.681701	−	1.49272i
$58$		0			0
$59$	0.999647	+	6.95269i	0.130143	+	0.905164i	0.945365	+	0.326015i	$0.105706\pi$
$59$	0.999647	+	6.95269i	0.130143	+	0.905164i	−0.815222	+	0.579149i	$0.803385\pi$
$60$		0			0
$61$	−1.86952	+	0.548941i	−0.239368	+	0.0702847i	−0.399216	−	0.916857i	$-0.630718\pi$
$61$	−1.86952	+	0.548941i	−0.239368	+	0.0702847i	0.159848	+	0.987142i	$0.448899\pi$
$62$		0			0
$63$	1.46898	−	1.69530i	0.185075	−	0.213587i
$64$		0			0
$65$	−1.98235	−	2.28776i	−0.245881	−	0.283761i
$66$		0			0
$67$	4.08243	−	8.93929i	0.498749	−	1.09211i	−0.478125	−	0.878292i	$-0.658683\pi$
$67$	4.08243	−	8.93929i	0.498749	−	1.09211i	0.976874	−	0.213816i	$-0.0685892\pi$
$68$		0			0
$69$	0.923056	+	9.77572i	0.111123	+	1.17686i
$70$		0			0
$71$	−2.88802	+	6.32387i	−0.342745	+	0.750506i	−0.999995	−	0.00316639i	$-0.998992\pi$
$71$	−2.88802	+	6.32387i	−0.342745	+	0.750506i	0.657250	+	0.753672i	$0.271719\pi$
$72$		0			0
$73$	−8.63107	−	9.96078i	−1.01019	−	1.16582i	−0.986107	−	0.166111i	$-0.946879\pi$
$73$	−8.63107	−	9.96078i	−1.01019	−	1.16582i	−0.0240830	−	0.999710i	$-0.507667\pi$
$74$		0			0
$75$	−13.0372	+	15.0457i	−1.50540	+	1.73733i
$76$		0			0
$77$	3.49756	−	1.02698i	0.398584	−	0.117035i
$78$		0			0
$79$	0.0541763	+	0.376804i	0.00609531	+	0.0423938i	0.992642	−	0.121085i	$-0.0386375\pi$
$79$	0.0541763	+	0.376804i	0.00609531	+	0.0423938i	−0.986547	+	0.163479i	$0.947728\pi$
$80$		0			0
$81$	−4.63402	−	10.1471i	−0.514891	−	1.12745i
$82$		0			0
$83$	2.75842	+	1.77273i	0.302776	+	0.194582i	0.683203	−	0.730229i	$-0.260587\pi$
$83$	2.75842	+	1.77273i	0.302776	+	0.194582i	−0.380427	+	0.924811i	$0.624223\pi$
$84$		0			0
$85$	−4.09138	+	28.4562i	−0.443773	+	3.08651i
$86$		0			0
$87$	4.62828	−	2.97442i	0.496204	−	0.318891i
$88$		0			0
$89$	−4.66512	−	1.36980i	−0.494501	−	0.145199i	0.0249672	−	0.999688i	$-0.492052\pi$
$89$	−4.66512	−	1.36980i	−0.494501	−	0.145199i	−0.519469	+	0.854490i	$0.673870\pi$
$90$		0			0
$91$	−1.48460			−0.155628
$92$		0			0
$93$	−5.67151			−0.588108
$94$		0			0
$95$	22.2784	+	6.54153i	2.28572	+	0.671147i
$96$		0			0
$97$	−7.65402	+	4.91894i	−0.777148	+	0.499443i	−0.868086	−	0.496414i	$-0.834650\pi$
$97$	−7.65402	+	4.91894i	−0.777148	+	0.499443i	0.0909378	+	0.995857i	$0.471014\pi$
$98$		0			0
$99$	−0.328608	+	2.28552i	−0.0330263	+	0.229703i
$100$		0			0
$101$	−2.57015	−	1.65173i	−0.255739	−	0.164353i	0.406489	−	0.913655i	$-0.366753\pi$
$101$	−2.57015	−	1.65173i	−0.255739	−	0.164353i	−0.662228	+	0.749302i	$0.730389\pi$
$102$		0			0
$103$	−3.24333	−	7.10191i	−0.319575	−	0.699772i	0.679861	−	0.733341i	$-0.262040\pi$
$103$	−3.24333	−	7.10191i	−0.319575	−	0.699772i	−0.999436	+	0.0335688i	$0.989313\pi$
$104$		0			0
$105$	2.10402	+	14.6338i	0.205331	+	1.42811i
$106$		0			0
$107$	−1.69097	+	0.496515i	−0.163473	+	0.0479999i	−0.362445	−	0.932005i	$-0.618058\pi$
$107$	−1.69097	+	0.496515i	−0.163473	+	0.0479999i	0.198972	+	0.980005i	$0.436240\pi$
$108$		0			0
$109$	5.60965	−	6.47388i	0.537307	−	0.620085i	−0.420572	−	0.907259i	$-0.638170\pi$
$109$	5.60965	−	6.47388i	0.537307	−	0.620085i	0.957878	+	0.287174i	$0.0927159\pi$
$110$		0			0
$111$	−13.2244	−	15.2617i	−1.25520	−	1.44858i
$112$		0			0
$113$	0.270448	−	0.592199i	0.0254416	−	0.0557094i	−0.896485	−	0.443075i	$-0.853888\pi$
$113$	0.270448	−	0.592199i	0.0254416	−	0.0557094i	0.921926	+	0.387366i	$0.126615\pi$
$114$		0			0
$115$	−14.9787	−	10.6901i	−1.39677	−	0.996860i
$116$		0			0
$117$	0.390657	−	0.855419i	0.0361162	−	0.0790835i
$118$		0			0
$119$	9.23304	+	10.6555i	0.846392	+	0.976788i
$120$		0			0
$121$	4.74632	−	5.47755i	0.431484	−	0.497959i
$122$		0			0
$123$	12.9082	−	3.79020i	1.16390	−	0.341751i
$124$		0			0
$125$	−2.57941	−	17.9402i	−0.230709	−	1.60462i
$126$		0			0
$127$	−0.830695	−	1.81897i	−0.0737122	−	0.161407i	0.869189	−	0.494480i	$-0.164642\pi$
$127$	−0.830695	−	1.81897i	−0.0737122	−	0.161407i	−0.942901	+	0.333073i	$0.891914\pi$
$128$		0			0
$129$	13.8588	+	8.90653i	1.22020	+	0.784177i
$130$		0			0
$131$	1.34552	−	9.35830i	0.117559	−	0.817639i	−0.842671	−	0.538428i	$-0.819018\pi$
$131$	1.34552	−	9.35830i	0.117559	−	0.817639i	0.960230	−	0.279210i	$-0.0900726\pi$
$132$		0			0
$133$	9.57956	−	6.15641i	0.830653	−	0.533828i
$134$		0			0
$135$	13.6286	+	4.00172i	1.17296	+	0.344413i
$136$		0			0
$137$	−2.06670			−0.176570			−0.0882850	−	0.996095i	$-0.528139\pi$
$137$	−2.06670			−0.176570			−0.0882850	+	0.996095i	$0.528139\pi$
$138$		0			0
$139$	1.69986			0.144180			0.0720900	−	0.997398i	$-0.477033\pi$
$139$	1.69986			0.144180			0.0720900	+	0.997398i	$0.477033\pi$
$140$		0			0
$141$	3.44518	+	1.01160i	0.290137	+	0.0851918i
$142$		0			0
$143$	1.28557	−	0.826184i	0.107504	−	0.0690889i
$144$		0			0
$145$	−1.46736	+	10.2057i	−0.121858	+	0.847538i
$146$		0			0
$147$	−5.95732	−	3.82854i	−0.491352	−	0.315773i
$148$		0			0
$149$	−7.27513	−	15.9303i	−0.596002	−	1.30506i	−0.931747	−	0.363109i	$-0.881715\pi$
$149$	−7.27513	−	15.9303i	−0.596002	−	1.30506i	0.335745	−	0.941953i	$-0.391012\pi$
$150$		0			0
$151$	1.18599	+	8.24877i	0.0965149	+	0.671276i	0.979436	+	0.201755i	$0.0646643\pi$
$151$	1.18599	+	8.24877i	0.0965149	+	0.671276i	−0.882921	+	0.469521i	$0.844427\pi$
$152$		0			0
$153$	−8.56924	+	2.51616i	−0.692782	+	0.203419i
$154$		0			0
$155$	6.96051	−	8.03285i	0.559081	−	0.645214i
$156$		0			0
$157$	4.40887	+	5.08810i	0.351866	+	0.406075i	0.903898	−	0.427748i	$-0.140693\pi$
$157$	4.40887	+	5.08810i	0.351866	+	0.406075i	−0.552032	+	0.833823i	$0.686147\pi$
$158$		0			0
$159$	−3.08532	+	6.75592i	−0.244682	+	0.535779i
$160$		0			0
$161$	−8.77281	+	2.11846i	−0.691394	+	0.166958i
$162$		0			0
$163$	−6.50265	+	14.2388i	−0.509327	+	1.11527i	0.463997	+	0.885837i	$0.346415\pi$
$163$	−6.50265	+	14.2388i	−0.509327	+	1.11527i	−0.973324	+	0.229434i	$0.926313\pi$
$164$		0			0
$165$	−9.96570	−	11.5010i	−0.775829	−	0.895354i
$166$		0			0
$167$	−12.5986	+	14.5396i	−0.974908	+	1.12510i	0.0172165	+	0.999852i	$0.494520\pi$
$167$	−12.5986	+	14.5396i	−0.974908	+	1.12510i	−0.992125	+	0.125252i	$0.960026\pi$
$168$		0			0
$169$	11.8762	−	3.48718i	0.913557	−	0.268245i
$170$		0			0
$171$	1.02653	+	7.13970i	0.0785010	+	0.545987i
$172$		0			0
$173$	3.59270	+	7.86692i	0.273148	+	0.598111i	0.995641	−	0.0932675i	$-0.0297312\pi$
$173$	3.59270	+	7.86692i	0.273148	+	0.598111i	−0.722493	+	0.691378i	$0.757004\pi$
$174$		0			0
$175$	−15.3933	−	9.89266i	−1.16362	−	0.747815i
$176$		0			0
$177$	2.04672	−	14.2353i	0.153841	−	1.06999i
$178$		0			0
$179$	−5.83152	+	3.74769i	−0.435868	+	0.280115i	−0.740118	−	0.672477i	$-0.765230\pi$
$179$	−5.83152	+	3.74769i	−0.435868	+	0.280115i	0.304250	+	0.952592i	$0.401594\pi$
$180$		0			0
$181$	4.88561	+	1.43455i	0.363145	+	0.106629i	0.458214	−	0.888842i	$-0.348489\pi$
$181$	4.88561	+	1.43455i	0.363145	+	0.106629i	−0.0950696	+	0.995471i	$0.530307\pi$
$182$		0			0
$183$	3.98934			0.294900
$184$		0			0
$185$	37.8459			2.78249
$186$		0			0
$187$	−13.9251	−	4.08877i	−1.01830	−	0.299000i
$188$		0			0
$189$	5.86020	−	3.76612i	0.426267	−	0.273945i
$190$		0			0
$191$	3.45452	−	24.0267i	0.249960	−	1.73851i	−0.348453	−	0.937326i	$-0.613293\pi$
$191$	3.45452	−	24.0267i	0.249960	−	1.73851i	0.598414	−	0.801187i	$-0.295798\pi$
$192$		0			0
$193$	10.8361	+	6.96394i	0.779999	+	0.501275i	0.869033	−	0.494753i	$-0.164742\pi$
$193$	10.8361	+	6.96394i	0.779999	+	0.501275i	−0.0890340	+	0.996029i	$0.528378\pi$
$194$		0			0
$195$	2.57470	+	5.63780i	0.184378	+	0.403731i
$196$		0			0
$197$	0.304917	+	2.12074i	0.0217244	+	0.151097i	0.997796	−	0.0663514i	$-0.0211358\pi$
$197$	0.304917	+	2.12074i	0.0217244	+	0.151097i	−0.976072	+	0.217448i	$0.930227\pi$
$198$		0			0
$199$	−23.2441	+	6.82508i	−1.64773	+	0.483817i	−0.968272	−	0.249899i	$-0.919603\pi$
$199$	−23.2441	+	6.82508i	−1.64773	+	0.483817i	−0.679457	+	0.733716i	$0.737784\pi$
$200$		0			0
$201$	−13.1764	+	15.2064i	−0.929394	+	1.07258i
$202$		0			0
$203$	3.31140	+	3.82156i	0.232415	+	0.268221i
$204$		0			0
$205$	−10.4737	+	22.9343i	−0.731516	+	1.60180i
$206$		0			0
$207$	1.08783	−	5.61231i	0.0756094	−	0.390083i
$208$		0			0
$209$	−4.86923	+	10.6621i	−0.336812	+	0.737515i
$210$		0			0
$211$	−14.3395	−	16.5486i	−0.987169	−	1.13925i	−0.990256	−	0.139258i	$-0.955528\pi$
$211$	−14.3395	−	16.5486i	−0.987169	−	1.13925i	0.00308717	−	0.999995i	$-0.499017\pi$
$212$		0			0
$213$	9.32134	−	10.7574i	0.638688	−	0.737085i
$214$		0			0
$215$	−29.6234	+	8.69822i	−2.02030	+	0.593214i
$216$		0			0
$217$	−0.741854	−	5.15971i	−0.0503603	−	0.350264i
$218$		0			0
$219$	11.2101	+	24.5467i	0.757509	+	1.65871i
$220$		0			0
$221$	4.97242	+	3.19558i	0.334481	+	0.214958i
$222$		0			0
$223$	−0.738261	+	5.13472i	−0.0494376	+	0.343846i	0.950058	+	0.312075i	$0.101024\pi$
$223$	−0.738261	+	5.13472i	−0.0494376	+	0.343846i	−0.999495	+	0.0317713i	$0.989885\pi$
$224$		0			0
$225$	9.75070	−	6.26640i	0.650047	−	0.417760i
$226$		0			0
$227$	6.22585	+	1.82807i	0.413224	+	0.121334i	0.481735	−	0.876317i	$-0.340007\pi$
$227$	6.22585	+	1.82807i	0.413224	+	0.121334i	−0.0685112	+	0.997650i	$0.521825\pi$
$228$		0			0
$229$	−18.1325			−1.19823			−0.599116	−	0.800662i	$-0.704481\pi$
$229$	−18.1325			−1.19823			−0.599116	+	0.800662i	$0.704481\pi$
$230$		0			0
$231$	−7.46337			−0.491054
$232$		0			0
$233$	−14.1559	−	4.15654i	−0.927383	−	0.272304i	−0.217042	−	0.976162i	$-0.569641\pi$
$233$	−14.1559	−	4.15654i	−0.927383	−	0.272304i	−0.710341	+	0.703858i	$0.751459\pi$
$234$		0			0
$235$	−5.66097	+	3.63808i	−0.369281	+	0.237322i
$236$		0			0
$237$	0.110923	−	0.771486i	0.00720522	−	0.0501134i
$238$		0			0
$239$	13.9897	+	8.99062i	0.904917	+	0.581555i	0.908245	−	0.418440i	$-0.137423\pi$
$239$	13.9897	+	8.99062i	0.904917	+	0.581555i	−0.00332787	+	0.999994i	$0.501059\pi$
$240$		0			0
$241$	6.08552	+	13.3254i	0.392003	+	0.858366i	0.998019	+	0.0629140i	$0.0200394\pi$
$241$	6.08552	+	13.3254i	0.392003	+	0.858366i	−0.606016	+	0.795452i	$0.707233\pi$
$242$		0			0
$243$	1.66998	+	11.6149i	0.107129	+	0.745099i
$244$		0			0
$245$	12.7338	−	3.73899i	0.813535	−	0.238876i
$246$		0			0
$247$	3.12617	−	3.60779i	0.198913	−	0.229558i
$248$		0			0
$249$	−4.39637	−	5.07368i	−0.278609	−	0.321531i
$250$		0			0
$251$	7.88046	−	17.2558i	0.497410	−	1.08918i	−0.479892	−	0.877327i	$-0.659324\pi$
$251$	7.88046	−	17.2558i	0.497410	−	1.08918i	0.977302	−	0.211849i	$-0.0679484\pi$
$252$		0			0
$253$	6.41777	−	6.71655i	0.403482	−	0.422266i
$254$		0			0
$255$	24.4520	−	53.5424i	1.53124	−	3.35295i
$256$		0			0
$257$	12.8045	+	14.7771i	0.798720	+	0.921772i	0.998310	−	0.0581072i	$-0.0185065\pi$
$257$	12.8045	+	14.7771i	0.798720	+	0.921772i	−0.199590	+	0.979879i	$0.563961\pi$
$258$		0			0
$259$	12.1547	−	14.0273i	0.755256	−	0.871612i
$260$		0			0
$261$	−3.07333	+	0.902410i	−0.190234	+	0.0558578i
$262$		0			0
$263$	−0.718442	−	4.99688i	−0.0443010	−	0.308121i	−0.999909	−	0.0134798i	$-0.995709\pi$
$263$	−0.718442	−	4.99688i	−0.0443010	−	0.308121i	0.955608	−	0.294641i	$-0.0952000\pi$
$264$		0			0
$265$	−5.78221	−	12.6613i	−0.355199	−	0.777776i
$266$		0			0
$267$	8.37452	+	5.38197i	0.512512	+	0.329372i
$268$		0			0
$269$	2.21563	−	15.4101i	0.135090	−	0.939568i	−0.803690	−	0.595049i	$-0.797133\pi$
$269$	2.21563	−	15.4101i	0.135090	−	0.939568i	0.938779	−	0.344520i	$-0.111958\pi$
$270$		0			0
$271$	−14.8244	+	9.52705i	−0.900517	+	0.578727i	−0.906943	−	0.421252i	$-0.861591\pi$
$271$	−14.8244	+	9.52705i	−0.900517	+	0.578727i	0.00642675	+	0.999979i	$0.497954\pi$
$272$		0			0
$273$	2.91650	+	0.856362i	0.176515	+	0.0518294i
$274$		0			0
$275$	18.8349			1.13579
$276$		0			0
$277$	−2.75886			−0.165764			−0.0828820	−	0.996559i	$-0.526412\pi$
$277$	−2.75886			−0.165764			−0.0828820	+	0.996559i	$0.526412\pi$
$278$		0			0
$279$	3.16821	+	0.930272i	0.189676	+	0.0556939i
$280$		0			0
$281$	−1.04029	+	0.668553i	−0.0620584	+	0.0398825i	−0.571302	−	0.820740i	$-0.693562\pi$
$281$	−1.04029	+	0.668553i	−0.0620584	+	0.0398825i	0.509244	+	0.860622i	$0.329925\pi$
$282$		0			0
$283$	−0.120397	+	0.837378i	−0.00715685	+	0.0497770i	−0.993087	−	0.117381i	$-0.962550\pi$
$283$	−0.120397	+	0.837378i	−0.00715685	+	0.0497770i	0.985930	+	0.167158i	$0.0534591\pi$
$284$		0			0
$285$	−39.9928	−	25.7018i	−2.36897	−	1.52244i
$286$		0			0
$287$	5.13662	+	11.2476i	0.303205	+	0.663926i
$288$		0			0
$289$	−5.56939	−	38.7360i	−0.327611	−	2.27859i
$290$		0			0
$291$	17.8738	−	5.24822i	1.04778	−	0.307656i
$292$		0			0
$293$	−9.29563	+	10.7277i	−0.543057	+	0.626721i	−0.959251	−	0.282555i	$-0.908818\pi$
$293$	−9.29563	+	10.7277i	−0.543057	+	0.626721i	0.416195	+	0.909276i	$0.363364\pi$
$294$		0			0
$295$	17.6502	+	20.3695i	1.02764	+	1.18596i
$296$		0			0
$297$	−2.97870	+	6.52245i	−0.172842	+	0.378471i
$298$		0			0
$299$	−3.27858	+	1.88828i	−0.189605	+	0.109202i
$300$		0			0
$301$	−6.29002	+	13.7732i	−0.362550	+	0.793875i
$302$		0			0
$303$	4.09630	+	4.72738i	0.235326	+	0.271581i
$304$		0			0
$305$	−4.89602	+	5.65031i	−0.280345	+	0.323536i
$306$		0			0
$307$	15.0430	−	4.41703i	0.858551	−	0.252093i	0.177312	−	0.984155i	$-0.443260\pi$
$307$	15.0430	−	4.41703i	0.858551	−	0.252093i	0.681239	+	0.732061i	$0.261442\pi$
$308$		0			0
$309$	2.27495	+	15.8226i	0.129417	+	0.900117i
$310$		0			0
$311$	6.30890	+	13.8146i	0.357745	+	0.783352i	0.999860	+	0.0167438i	$0.00532996\pi$
$311$	6.30890	+	13.8146i	0.357745	+	0.783352i	−0.642115	+	0.766608i	$0.721943\pi$
$312$		0			0
$313$	0.201698	+	0.129623i	0.0114006	+	0.00732674i	0.546329	−	0.837571i	$-0.316025\pi$
$313$	0.201698	+	0.129623i	0.0114006	+	0.00732674i	−0.534928	+	0.844898i	$0.679661\pi$
$314$		0			0
$315$	1.22497	−	8.51982i	0.0690190	−	0.480038i
$316$		0			0
$317$	−1.79447	+	1.15324i	−0.100788	+	0.0647723i	−0.590064	−	0.807357i	$-0.700897\pi$
$317$	−1.79447	+	1.15324i	−0.100788	+	0.0647723i	0.489276	+	0.872129i	$0.337261\pi$
$318$		0			0
$319$	−4.99417	−	1.46642i	−0.279620	−	0.0821039i
$320$		0			0
$321$	3.60834			0.201398
$322$		0			0
$323$	−45.3368			−2.52261
$324$		0			0
$325$	−7.36022	−	2.16116i	−0.408272	−	0.119879i
$326$		0			0
$327$	−14.7545	+	9.48216i	−0.815928	+	0.524365i
$328$		0			0
$329$	−0.469667	+	3.26661i	−0.0258936	+	0.180094i
$330$		0			0
$331$	19.5337	+	12.5535i	1.07367	+	0.690005i	0.953086	−	0.302698i	$-0.0978875\pi$
$331$	19.5337	+	12.5535i	1.07367	+	0.690005i	0.120582	+	0.992703i	$0.461524\pi$
$332$		0			0
$333$	4.88407	+	10.6946i	0.267645	+	0.586062i
$334$		0			0
$335$	−5.36652	−	37.3250i	−0.293204	−	2.03928i
$336$		0			0
$337$	9.46693	−	2.77974i	0.515697	−	0.151422i	−0.0135206	−	0.999909i	$-0.504304\pi$
$337$	9.46693	−	2.77974i	0.515697	−	0.151422i	0.529217	+	0.848486i	$0.322486\pi$
$338$		0			0
$339$	−0.872896	+	1.00738i	−0.0474092	+	0.0547132i
$340$		0			0
$341$	3.51380	+	4.05514i	0.190283	+	0.219598i
$342$		0			0
$343$	8.17601	−	17.9030i	0.441463	−	0.966669i
$344$		0			0
$345$	23.2594	+	29.6410i	1.25224	+	1.59582i
$346$		0			0
$347$	−6.24758	+	13.6803i	−0.335388	+	0.734397i	−0.999917	−	0.0128652i	$-0.995905\pi$
$347$	−6.24758	+	13.6803i	−0.335388	+	0.734397i	0.664529	+	0.747262i	$0.268632\pi$
$348$		0			0
$349$	17.4702	+	20.1617i	0.935158	+	1.07923i	0.996704	+	0.0811261i	$0.0258516\pi$
$349$	17.4702	+	20.1617i	0.935158	+	1.07923i	−0.0615454	+	0.998104i	$0.519603\pi$
$350$		0			0
$351$	1.91240	−	2.20703i	0.102077	−	0.117803i
$352$		0			0
$353$	−10.0682	+	2.95629i	−0.535877	+	0.157348i	−0.538463	−	0.842649i	$-0.680995\pi$
$353$	−10.0682	+	2.95629i	−0.535877	+	0.157348i	0.00258650	+	0.999997i	$0.499177\pi$
$354$		0			0
$355$	3.79641	+	26.4046i	0.201493	+	1.40141i
$356$		0			0
$357$	−11.9920	−	26.2587i	−0.634682	−	1.38976i
$358$		0			0
$359$	−25.2421	−	16.2221i	−1.33223	−	0.856170i	−0.335908	−	0.941895i	$-0.609043\pi$
$359$	−25.2421	−	16.2221i	−1.33223	−	0.856170i	−0.996319	+	0.0857246i	$0.972679\pi$
$360$		0			0
$361$	−2.50705	+	17.4369i	−0.131950	+	0.917734i
$362$		0			0
$363$	−12.4838	+	8.02286i	−0.655230	+	0.421091i
$364$		0			0
$365$	−48.5247	−	14.2481i	−2.53990	−	0.745782i
$366$		0			0
$367$	−4.42878			−0.231181			−0.115590	−	0.993297i	$-0.536876\pi$
$367$	−4.42878			−0.231181			−0.115590	+	0.993297i	$0.536876\pi$
$368$		0			0
$369$	−7.83249			−0.407743
$370$		0			0
$371$	−6.54983	−	1.92320i	−0.340050	−	0.0998477i
$372$		0			0
$373$	11.9565	−	7.68400i	0.619086	−	0.397863i	−0.193168	−	0.981166i	$-0.561876\pi$
$373$	11.9565	−	7.68400i	0.619086	−	0.397863i	0.812255	+	0.583303i	$0.198240\pi$
$374$		0			0
$375$	−5.28119	+	36.7315i	−0.272720	+	1.89681i
$376$		0			0
$377$	1.78334	+	1.14608i	0.0918467	+	0.0590263i
$378$		0			0
$379$	−9.26397	−	20.2853i	−0.475858	−	1.04198i	−0.983582	−	0.180464i	$-0.942240\pi$
$379$	−9.26397	−	20.2853i	−0.475858	−	1.04198i	0.507723	−	0.861520i	$-0.330487\pi$
$380$		0			0
$381$	0.582668	+	4.05255i	0.0298510	+	0.207618i
$382$		0			0
$383$	32.9588	−	9.67757i	1.68412	−	0.494501i	0.707001	−	0.707213i	$-0.250048\pi$
$383$	32.9588	−	9.67757i	1.68412	−	0.494501i	0.977115	+	0.212712i	$0.0682296\pi$
$384$		0			0
$385$	9.15962	−	10.5708i	0.466817	−	0.538736i
$386$		0			0
$387$	−6.28092	−	7.24857i	−0.319277	−	0.368465i
$388$		0			0
$389$	3.70219	−	8.10666i	0.187708	−	0.411024i	−0.792258	−	0.610186i	$-0.791095\pi$
$389$	3.70219	−	8.10666i	0.187708	−	0.411024i	0.979967	+	0.199162i	$0.0638220\pi$
$390$		0			0
$391$	33.9431	+	11.7880i	1.71658	+	0.596142i
$392$		0			0
$393$	−8.04145	+	17.6083i	−0.405638	+	0.888222i
$394$		0			0
$395$	0.956563	+	1.10393i	0.0481299	+	0.0555449i
$396$		0			0
$397$	22.7369	−	26.2398i	1.14113	−	1.31694i	0.199653	−	0.979867i	$-0.436019\pi$
$397$	22.7369	−	26.2398i	1.14113	−	1.31694i	0.941480	−	0.337070i	$-0.109436\pi$
$398$		0			0
$399$	−22.3703	+	6.56852i	−1.11992	+	0.328837i
$400$		0			0
$401$	0.0741208	+	0.515522i	0.00370142	+	0.0257439i	0.991588	−	0.129431i	$-0.0413150\pi$
$401$	0.0741208	+	0.515522i	0.00370142	+	0.0257439i	−0.987887	+	0.155175i	$0.950406\pi$
$402$		0			0
$403$	−0.907810	−	1.98783i	−0.0452212	−	0.0990207i
$404$		0			0
$405$	−36.0087	−	23.1414i	−1.78929	−	1.14991i
$406$		0			0
$407$	−2.71897	+	18.9109i	−0.134774	+	0.937377i
$408$		0			0
$409$	5.70238	−	3.66470i	0.281965	−	0.181208i	−0.392012	−	0.919960i	$-0.628221\pi$
$409$	5.70238	−	3.66470i	0.281965	−	0.181208i	0.673977	+	0.738752i	$0.264585\pi$
$410$		0			0
$411$	4.06005	+	1.19214i	0.200267	+	0.0588038i
$412$		0			0
$413$	13.2184			0.650434
$414$		0			0
$415$	12.5817			0.617610
$416$		0			0
$417$	−3.33938	−	0.980532i	−0.163530	−	0.0480168i
$418$		0			0
$419$	5.04672	−	3.24333i	0.246548	−	0.158447i	−0.411531	−	0.911396i	$-0.635006\pi$
$419$	5.04672	−	3.24333i	0.246548	−	0.158447i	0.658079	+	0.752949i	$0.271369\pi$
$420$		0			0
$421$	−1.38237	+	9.61457i	−0.0673724	+	0.468585i	0.928007	+	0.372563i	$0.121521\pi$
$421$	−1.38237	+	9.61457i	−0.0673724	+	0.468585i	−0.995379	+	0.0960221i	$0.969388\pi$
$422$		0			0
$423$	−1.75862	−	1.13020i	−0.0855070	−	0.0549520i
$424$		0			0
$425$	30.2635	+	66.2678i	1.46800	+	3.21446i
$426$		0			0
$427$	0.521820	+	3.62934i	0.0252526	+	0.175636i
$428$		0			0
$429$	−3.00208	+	0.881489i	−0.144942	+	0.0425587i
$430$		0			0
$431$	8.73778	−	10.0839i	0.420884	−	0.485726i	−0.505222	−	0.862989i	$-0.668589\pi$
$431$	8.73778	−	10.0839i	0.420884	−	0.485726i	0.926106	+	0.377263i	$0.123135\pi$
$432$		0			0
$433$	−10.8888	−	12.5664i	−0.523283	−	0.603900i	0.431167	−	0.902272i	$-0.358102\pi$
$433$	−10.8888	−	12.5664i	−0.523283	−	0.603900i	−0.954450	+	0.298372i	$0.903556\pi$
$434$		0			0
$435$	8.76961	−	19.2028i	0.420471	−	0.920703i
$436$		0			0
$437$	13.3251	−	25.7802i	0.637424	−	1.23323i
$438$		0			0
$439$	15.0542	−	32.9642i	0.718499	−	1.57329i	−0.0974963	−	0.995236i	$-0.531083\pi$
$439$	15.0542	−	32.9642i	0.718499	−	1.57329i	0.815996	−	0.578058i	$-0.196189\pi$
$440$		0			0
$441$	2.69990	+	3.11585i	0.128567	+	0.148374i
$442$		0			0
$443$	−6.00878	+	6.93450i	−0.285486	+	0.329468i	−0.880320	−	0.474380i	$-0.842672\pi$
$443$	−6.00878	+	6.93450i	−0.285486	+	0.329468i	0.594834	+	0.803848i	$0.297218\pi$
$444$		0			0
$445$	−17.9006	+	5.25610i	−0.848571	+	0.249163i
$446$		0			0
$447$	5.10294	+	35.4918i	0.241361	+	1.67870i
$448$		0			0
$449$	−8.66462	−	18.9729i	−0.408909	−	0.895385i	−0.996289	−	0.0860740i	$-0.972568\pi$
$449$	−8.66462	−	18.9729i	−0.408909	−	0.895385i	0.587380	−	0.809311i	$-0.300159\pi$
$450$		0			0
$451$	−10.7073	−	6.88119i	−0.504189	−	0.324022i
$452$		0			0
$453$	2.42826	−	16.8889i	0.114090	−	0.793510i
$454$		0			0
$455$	−4.79226	+	3.07980i	−0.224665	+	0.144383i
$456$		0			0
$457$	7.71162	+	2.26434i	0.360734	+	0.105921i	0.457077	−	0.889427i	$-0.348896\pi$
$457$	7.71162	+	2.26434i	0.360734	+	0.105921i	−0.0963428	+	0.995348i	$0.530714\pi$
$458$		0			0
$459$	−27.7344			−1.29453
$460$		0			0
$461$	−3.23977			−0.150891			−0.0754455	−	0.997150i	$-0.524038\pi$
$461$	−3.23977			−0.150891			−0.0754455	+	0.997150i	$0.524038\pi$
$462$		0			0
$463$	8.62234	+	2.53175i	0.400714	+	0.117660i	0.475879	−	0.879511i	$-0.342130\pi$
$463$	8.62234	+	2.53175i	0.400714	+	0.117660i	−0.0751646	+	0.997171i	$0.523948\pi$
$464$		0			0
$465$	−18.3076	+	11.7656i	−0.848994	+	0.545615i
$466$		0			0
$467$	3.24689	−	22.5826i	0.150248	−	1.04500i	−0.765555	−	0.643370i	$-0.777536\pi$
$467$	3.24689	−	22.5826i	0.150248	−	1.04500i	0.915803	−	0.401627i	$-0.131555\pi$
$468$		0			0
$469$	−15.5577	−	9.99833i	−0.718388	−	0.461680i
$470$		0			0
$471$	−5.72628	−	12.5388i	−0.263853	−	0.577757i
$472$		0			0
$473$	−2.21809	−	15.4272i	−0.101988	−	0.709341i
$474$		0			0
$475$	56.4549	−	16.5766i	2.59033	−	0.760589i
$476$		0			0
$477$	2.83166	−	3.26792i	0.129653	−	0.149628i
$478$		0			0
$479$	−0.320654	−	0.370054i	−0.0146511	−	0.0169082i	0.748377	−	0.663274i	$-0.230834\pi$
$479$	−0.320654	−	0.370054i	−0.0146511	−	0.0169082i	−0.763028	+	0.646366i	$0.776288\pi$
$480$		0			0
$481$	3.23238	−	7.07792i	0.147384	−	0.322725i
$482$		0			0
$483$	18.4563	+	0.898706i	0.839788	+	0.0408925i
$484$		0			0
$485$	−14.5028	+	31.7566i	−0.658536	+	1.44199i
$486$		0			0
$487$	8.88989	+	10.2595i	0.402839	+	0.464901i	0.920533	−	0.390665i	$-0.127755\pi$
$487$	8.88989	+	10.2595i	0.402839	+	0.464901i	−0.517694	+	0.855566i	$0.673209\pi$
$488$		0			0
$489$	20.9879	−	24.2213i	0.949106	−	1.09533i
$490$		0			0
$491$	10.3852	−	3.04937i	0.468677	−	0.137616i	−0.0388622	−	0.999245i	$-0.512373\pi$
$491$	10.3852	−	3.04937i	0.468677	−	0.137616i	0.507539	+	0.861629i	$0.330555\pi$
$492$		0			0
$493$	−2.86513	−	19.9275i	−0.129039	−	0.897487i
$494$		0			0
$495$	3.68057	+	8.05933i	0.165429	+	0.362240i
$496$		0			0
$497$	11.0059	+	7.07307i	0.493683	+	0.317271i
$498$		0			0
$499$	5.04370	−	35.0797i	0.225787	−	1.57038i	−0.489784	−	0.871844i	$-0.662925\pi$
$499$	5.04370	−	35.0797i	0.225787	−	1.57038i	0.715571	−	0.698540i	$-0.246166\pi$
$500$		0			0
$501$	33.1369	−	21.2958i	1.48045	−	0.951426i
$502$		0			0
$503$	21.3170	+	6.25923i	0.950478	+	0.279085i	0.719986	−	0.693989i	$-0.244148\pi$
$503$	21.3170	+	6.25923i	0.950478	+	0.279085i	0.230492	+	0.973074i	$0.425966\pi$
$504$		0			0
$505$	−11.7229			−0.521664
$506$		0			0
$507$	−25.3425			−1.12550
$508$		0			0
$509$	30.5783	+	8.97860i	1.35536	+	0.397970i	0.877125	−	0.480262i	$-0.159459\pi$
$509$	30.5783	+	8.97860i	1.35536	+	0.397970i	0.478235	+	0.878232i	$0.341277\pi$
$510$		0			0
$511$	−20.8653	+	13.4093i	−0.923026	+	0.593193i
$512$		0			0
$513$	−3.18780	+	22.1716i	−0.140745	+	0.978901i
$514$		0			0
$515$	−25.2024	−	16.1966i	−1.11055	−	0.713707i
$516$		0			0
$517$	−1.41118	−	3.09005i	−0.0620635	−	0.135900i
$518$		0			0
$519$	−2.52000	−	17.5270i	−0.110616	−	0.769350i
$520$		0			0
$521$	−23.2469	+	6.82590i	−1.01846	+	0.299048i	−0.748012	−	0.663685i	$-0.768992\pi$
$521$	−23.2469	+	6.82590i	−1.01846	+	0.299048i	−0.270453	+	0.962733i	$0.587173\pi$
$522$		0			0
$523$	−27.0894	+	31.2628i	−1.18454	+	1.36703i	−0.269831	+	0.962908i	$0.586968\pi$
$523$	−27.0894	+	31.2628i	−1.18454	+	1.36703i	−0.914706	+	0.404121i	$0.867578\pi$
$524$		0			0
$525$	24.5338	+	28.3136i	1.07074	+	1.23570i
$526$		0			0
$527$	−8.62150	+	18.8784i	−0.375558	+	0.822358i
$528$		0			0
$529$	−16.6794	+	15.8366i	−0.725189	+	0.688550i
$530$		0			0
$531$	−3.47828	+	7.61638i	−0.150945	+	0.330523i
$532$		0			0
$533$	3.39460	+	3.91758i	0.147037	+	0.169689i
$534$		0			0
$535$	−4.42843	+	5.11068i	−0.191458	+	0.220954i
$536$		0			0
$537$	13.6178	−	3.99856i	0.587654	−	0.172551i
$538$		0			0
$539$	0.953462	+	6.63148i	0.0410685	+	0.285638i
$540$		0			0
$541$	16.5874	+	36.3214i	0.713149	+	1.56158i	0.823264	+	0.567659i	$0.192151\pi$
$541$	16.5874	+	36.3214i	0.713149	+	1.56158i	−0.110116	+	0.993919i	$0.535122\pi$
$542$		0			0
$543$	−8.77034	−	5.63635i	−0.376371	−	0.241879i
$544$		0			0
$545$	4.67781	−	32.5349i	0.200375	−	1.39364i
$546$		0			0
$547$	−29.5547	+	18.9937i	−1.26367	+	0.812111i	−0.988782	−	0.149366i	$-0.952277\pi$
$547$	−29.5547	+	18.9937i	−1.26367	+	0.812111i	−0.274887	+	0.961477i	$0.588640\pi$
$548$		0			0
$549$	−2.22852	−	0.654353i	−0.0951110	−	0.0279271i
$550$		0			0
$551$	−16.2599			−0.692695
$552$		0			0
$553$	0.716375			0.0304634
$554$		0			0
$555$	−74.3486	−	21.8307i	−3.15592	−	0.926662i
$556$		0			0
$557$	−32.8275	+	21.0970i	−1.39095	+	0.893907i	−0.999653	−	0.0263580i	$-0.991609\pi$
$557$	−32.8275	+	21.0970i	−1.39095	+	0.893907i	−0.391295	+	0.920265i	$0.627973\pi$
$558$		0			0
$559$	−0.903368	+	6.28306i	−0.0382084	+	0.265745i
$560$		0			0
$561$	24.9974	+	16.0648i	1.05539	+	0.678258i
$562$		0			0
$563$	15.0969	+	33.0575i	0.636257	+	1.39321i	0.903084	+	0.429463i	$0.141297\pi$
$563$	15.0969	+	33.0575i	0.636257	+	1.39321i	−0.266828	+	0.963744i	$0.585976\pi$
$564$		0			0
$565$	−0.355515	−	2.47266i	−0.0149566	−	0.104025i
$566$		0			0
$567$	−20.1418	+	5.91418i	−0.845878	+	0.248372i
$568$		0			0
$569$	24.1240	−	27.8406i	1.01133	−	1.16714i	0.0254519	−	0.999676i	$-0.491898\pi$
$569$	24.1240	−	27.8406i	1.01133	−	1.16714i	0.985879	−	0.167462i	$-0.0535570\pi$
$570$		0			0
$571$	4.36811	+	5.04106i	0.182800	+	0.210962i	0.839752	−	0.542970i	$-0.182700\pi$
$571$	4.36811	+	5.04106i	0.182800	+	0.210962i	−0.656953	+	0.753932i	$0.728155\pi$
$572$		0			0
$573$	−20.6458	+	45.2080i	−0.862491	+	1.88859i
$574$		0			0
$575$	−46.5771	−	2.26802i	−1.94240	−	0.0945829i
$576$		0			0
$577$	2.74466	−	6.00998i	0.114262	−	0.250199i	−0.843858	−	0.536567i	$-0.819721\pi$
$577$	2.74466	−	6.00998i	0.114262	−	0.250199i	0.958120	+	0.286368i	$0.0924481\pi$
$578$		0			0
$579$	−17.2706	−	19.9313i	−0.717741	−	0.828317i
$580$		0			0
$581$	4.04077	−	4.66329i	0.167639	−	0.193466i
$582$		0			0
$583$	6.74201	−	1.97963i	0.279226	−	0.0819880i
$584$		0			0
$585$	−0.513533	−	3.57170i	−0.0212320	−	0.147672i
$586$		0			0
$587$	15.6309	+	34.2268i	0.645155	+	1.41269i	0.895731	+	0.444596i	$0.146653\pi$
$587$	15.6309	+	34.2268i	0.645155	+	1.41269i	−0.250576	+	0.968097i	$0.580620\pi$
$588$		0			0
$589$	14.1010	+	9.06217i	0.581022	+	0.373400i
$590$		0			0
$591$	0.624300	−	4.34210i	0.0256803	−	0.178610i
$592$		0			0
$593$	18.3734	−	11.8079i	0.754507	−	0.484892i	−0.105978	−	0.994369i	$-0.533797\pi$
$593$	18.3734	−	11.8079i	0.754507	−	0.484892i	0.860485	+	0.509476i	$0.170161\pi$
$594$		0			0
$595$	51.9091	+	15.2419i	2.12806	+	0.624856i
$596$		0			0
$597$	49.6001			2.03000
$598$		0			0
$599$	24.6893			1.00878			0.504389	−	0.863477i	$-0.331718\pi$
$599$	24.6893			1.00878			0.504389	+	0.863477i	$0.331718\pi$
$600$		0			0
$601$	−28.3417	−	8.32189i	−1.15608	−	0.339457i	−0.353174	−	0.935558i	$-0.614898\pi$
$601$	−28.3417	−	8.32189i	−1.15608	−	0.339457i	−0.802910	+	0.596101i	$0.796716\pi$
$602$		0			0
$603$	9.85486	−	6.33333i	0.401321	−	0.257913i
$604$		0			0
$605$	3.95789	−	27.5277i	0.160911	−	1.11916i
$606$		0			0
$607$	−19.0056	−	12.2142i	−0.771414	−	0.495757i	0.0947603	−	0.995500i	$-0.469792\pi$
$607$	−19.0056	−	12.2142i	−0.771414	−	0.495757i	−0.866174	+	0.499743i	$0.833428\pi$
$608$		0			0
$609$	−4.30087	−	9.41760i	−0.174280	−	0.381620i
$610$		0			0
$611$	0.196895	+	1.36944i	0.00796553	+	0.0554014i
$612$		0			0
$613$	26.2691	−	7.71331i	1.06100	−	0.311538i	0.295746	−	0.955266i	$-0.404432\pi$
$613$	26.2691	−	7.71331i	1.06100	−	0.311538i	0.765254	+	0.643729i	$0.222613\pi$
$614$		0			0
$615$	33.8049	−	39.0130i	1.36315	−	1.57315i
$616$		0			0
$617$	−23.5656	−	27.1961i	−0.948714	−	1.09487i	−0.995385	−	0.0959635i	$-0.969407\pi$
$617$	−23.5656	−	27.1961i	−0.948714	−	1.09487i	0.0466713	−	0.998910i	$-0.485139\pi$
$618$		0			0
$619$	−8.77016	+	19.2040i	−0.352503	+	0.771873i	0.647450	+	0.762108i	$0.275836\pi$
$619$	−8.77016	+	19.2040i	−0.352503	+	0.771873i	−0.999952	+	0.00976497i	$0.996892\pi$
$620$		0			0
$621$	8.15147	−	15.7708i	0.327107	−	0.632859i
$622$		0			0
$623$	−3.80088	+	8.32278i	−0.152279	+	0.333445i
$624$		0			0
$625$	−13.7056	−	15.8171i	−0.548222	−	0.632682i
$626$		0			0
$627$	15.7159	−	18.1371i	0.627632	−	0.724326i
$628$		0			0
$629$	−70.9038	+	20.8192i	−2.82712	+	0.830117i
$630$		0			0
$631$	−2.20429	−	15.3312i	−0.0877514	−	0.610324i	−0.985482	−	0.169780i	$-0.945694\pi$
$631$	−2.20429	−	15.3312i	−0.0877514	−	0.610324i	0.897731	−	0.440545i	$-0.145215\pi$
$632$		0			0
$633$	18.6242	+	40.7813i	0.740246	+	1.62091i
$634$		0			0
$635$	−6.45493	−	4.14833i	−0.256156	−	0.164622i
$636$		0			0
$637$	0.388319	−	2.70082i	0.0153858	−	0.107010i
$638$		0			0
$639$	−6.97157	+	4.48036i	−0.275791	+	0.177240i
$640$		0			0
$641$	−14.9918	−	4.40200i	−0.592142	−	0.173869i	−0.0280867	−	0.999605i	$-0.508941\pi$
$641$	−14.9918	−	4.40200i	−0.592142	−	0.173869i	−0.564056	+	0.825737i	$0.690760\pi$
$642$		0			0
$643$	−10.4115			−0.410590			−0.205295	−	0.978700i	$-0.565815\pi$
$643$	−10.4115			−0.410590			−0.205295	+	0.978700i	$0.565815\pi$
$644$		0			0
$645$	63.2129			2.48900
$646$		0			0
$647$	5.31858	+	1.56168i	0.209095	+	0.0613958i	0.384603	−	0.923082i	$-0.374338\pi$
$647$	5.31858	+	1.56168i	0.209095	+	0.0613958i	−0.175508	+	0.984478i	$0.556157\pi$
$648$		0			0
$649$	−11.4463	+	7.35608i	−0.449306	+	0.288751i
$650$		0			0
$651$	−1.51890	+	10.5642i	−0.0595305	+	0.414044i
$652$		0			0
$653$	22.1268	+	14.2200i	0.865889	+	0.556473i	0.896493	−	0.443058i	$-0.146107\pi$
$653$	22.1268	+	14.2200i	0.865889	+	0.556473i	−0.0306034	+	0.999532i	$0.509743\pi$
$654$		0			0
$655$	−15.0705	−	32.9998i	−0.588853	−	1.28941i
$656$		0			0
$657$	−2.23590	−	15.5510i	−0.0872307	−	0.606703i
$658$		0			0
$659$	−35.3457	+	10.3784i	−1.37687	+	0.404287i	−0.884680	−	0.466198i	$-0.845623\pi$
$659$	−35.3457	+	10.3784i	−1.37687	+	0.404287i	−0.492194	+	0.870485i	$0.663805\pi$
$660$		0			0
$661$	−27.1782	+	31.3653i	−1.05711	+	1.21997i	−0.0823732	+	0.996602i	$0.526250\pi$
$661$	−27.1782	+	31.3653i	−1.05711	+	1.21997i	−0.974735	+	0.223366i	$0.928295\pi$
$662$		0			0
$663$	−7.92505	−	9.14599i	−0.307783	−	0.355201i
$664$		0			0
$665$	18.1512	−	39.7457i	0.703875	−	1.54127i
$666$		0			0
$667$	12.1736	+	4.22771i	0.471362	+	0.163697i
$668$		0			0
$669$	4.41219	−	9.66134i	0.170585	−	0.373529i
$670$		0			0
$671$	−2.47160	−	2.85238i	−0.0954152	−	0.110115i
$672$		0			0
$673$	−13.6694	+	15.7753i	−0.526917	+	0.608095i	−0.955349	−	0.295479i	$-0.904521\pi$
$673$	−13.6694	+	15.7753i	−0.526917	+	0.608095i	0.428432	+	0.903574i	$0.359066\pi$
$674$		0			0
$675$	34.5357	−	10.1406i	1.32928	−	0.390312i
$676$		0			0
$677$	1.72691	+	12.0109i	0.0663707	+	0.461618i	0.995720	+	0.0924175i	$0.0294594\pi$
$677$	1.72691	+	12.0109i	0.0663707	+	0.461618i	−0.929350	+	0.369201i	$0.879631\pi$
$678$		0			0
$679$	7.11257	+	15.5744i	0.272956	+	0.597689i
$680$		0			0
$681$	−11.1762	−	7.18253i	−0.428274	−	0.275235i
$682$		0			0
$683$	0.172392	−	1.19902i	0.00659641	−	0.0458791i	−0.986257	−	0.165216i	$-0.947168\pi$
$683$	0.172392	−	1.19902i	0.00659641	−	0.0458791i	0.992854	+	0.119337i	$0.0380769\pi$
$684$		0			0
$685$	−6.67128	+	4.28737i	−0.254897	+	0.163812i
$686$		0			0
$687$	35.6215	+	10.4594i	1.35905	+	0.399052i
$688$		0			0
$689$	−2.86176			−0.109024
$690$		0			0
$691$	8.65337			0.329190			0.164595	−	0.986361i	$-0.447368\pi$
$691$	8.65337			0.329190			0.164595	+	0.986361i	$0.447368\pi$
$692$		0			0
$693$	4.16918	+	1.22418i	0.158374	+	0.0465029i
$694$		0			0
$695$	5.48713	−	3.52636i	0.208139	−	0.133763i
$696$		0			0
$697$	7.00612	−	48.7287i	0.265376	−	1.84573i
$698$		0			0
$699$	25.4117	+	16.3311i	0.961160	+	0.617700i
$700$		0			0
$701$	−0.323088	−	0.707464i	−0.0122029	−	0.0267205i	0.903432	−	0.428730i	$-0.141039\pi$
$701$	−0.323088	−	0.707464i	−0.0122029	−	0.0267205i	−0.915635	+	0.402010i	$0.868312\pi$
$702$		0			0
$703$	8.49377	+	59.0755i	0.320349	+	2.22807i
$704$		0			0
$705$	13.2196	−	3.88162i	0.497878	−	0.146190i
$706$		0			0
$707$	−3.76497	+	4.34501i	−0.141596	+	0.163411i
$708$		0			0
$709$	−13.7169	−	15.8302i	−0.515151	−	0.594516i	0.437259	−	0.899335i	$-0.355949\pi$
$709$	−13.7169	−	15.8302i	−0.515151	−	0.594516i	−0.952410	+	0.304820i	$0.901404\pi$
$710$		0			0
$711$	−0.188507	+	0.412773i	−0.00706957	+	0.0154802i
$712$		0			0
$713$	−8.20100	−	10.4511i	−0.307130	−	0.391397i
$714$		0			0
$715$	2.43588	−	5.33383i	0.0910967	−	0.199474i
$716$		0			0
$717$	−22.2968	−	25.7318i	−0.832688	−	0.960973i
$718$		0			0
$719$	30.7857	−	35.5286i	1.14811	−	1.32499i	0.210385	−	0.977619i	$-0.432528\pi$
$719$	30.7857	−	35.5286i	1.14811	−	1.32499i	0.937727	−	0.347373i	$-0.112926\pi$
$720$		0			0
$721$	−14.0972	+	4.13931i	−0.525007	+	0.154156i
$722$		0			0
$723$	−4.26852	−	29.6882i	−0.158748	−	1.10412i
$724$		0			0
$725$	10.8539	+	23.7667i	0.403103	+	0.882673i
$726$		0			0
$727$	−18.6601	−	11.9921i	−0.692064	−	0.444763i	0.146755	−	0.989173i	$-0.453117\pi$
$727$	−18.6601	−	11.9921i	−0.692064	−	0.444763i	−0.838819	+	0.544410i	$0.816754\pi$
$728$		0			0
$729$	−1.34345	+	9.34387i	−0.0497572	+	0.346069i
$730$		0			0
$731$	50.7141	−	32.5920i	1.87573	−	1.20546i
$732$		0			0
$733$	28.6349	+	8.40795i	1.05765	+	0.310555i	0.763905	−	0.645328i	$-0.223279\pi$
$733$	28.6349	+	8.40795i	1.05765	+	0.310555i	0.293747	+	0.955883i	$0.405098\pi$
$734$		0			0
$735$	−27.1725			−1.00227
$736$		0			0
$737$	19.0361			0.701204
$738$		0			0
$739$	39.1921	+	11.5079i	1.44171	+	0.423323i	0.906790	−	0.421582i	$-0.138525\pi$
$739$	39.1921	+	11.5079i	1.44171	+	0.423323i	0.534916	+	0.844905i	$0.320343\pi$
$740$		0			0
$741$	−8.22247	+	5.28426i	−0.302060	+	0.194122i
$742$		0			0
$743$	1.51739	−	10.5537i	0.0556678	−	0.387178i	−0.942872	−	0.333155i	$-0.891887\pi$
$743$	1.51739	−	10.5537i	0.0556678	−	0.387178i	0.998540	−	0.0540226i	$-0.0172043\pi$
$744$		0			0
$745$	−56.5316	−	36.3306i	−2.07116	−	1.33105i
$746$		0			0
$747$	1.62368	+	3.55537i	0.0594075	+	0.130084i
$748$		0			0
$749$	0.471984	+	3.28272i	0.0172459	+	0.119948i
$750$		0			0
$751$	−8.48857	+	2.49247i	−0.309752	+	0.0909514i	−0.432914	−	0.901435i	$-0.642515\pi$
$751$	−8.48857	+	2.49247i	−0.309752	+	0.0909514i	0.123162	+	0.992387i	$0.460697\pi$
$752$		0			0
$753$	−25.4349	+	29.3535i	−0.926900	+	1.06970i
$754$		0			0
$755$	20.9405	+	24.1666i	0.762103	+	0.879514i
$756$		0			0
$757$	−8.58531	+	18.7992i	−0.312038	+	0.683269i	−0.999059	−	0.0433692i	$-0.986191\pi$
$757$	−8.58531	+	18.7992i	−0.312038	+	0.683269i	0.687021	+	0.726638i	$0.258918\pi$
$758$		0			0
$759$	−16.4821	+	9.49275i	−0.598262	+	0.344565i
$760$		0			0
$761$	−1.44451	+	3.16303i	−0.0523634	+	0.114660i	−0.934005	−	0.357259i	$-0.883711\pi$
$761$	−1.44451	+	3.16303i	−0.0523634	+	0.114660i	0.881642	+	0.471919i	$0.156439\pi$
$762$		0			0
$763$	−10.5564	−	12.1828i	−0.382169	−	0.441046i
$764$		0			0
$765$	−22.4417	+	25.8991i	−0.811380	+	0.936383i
$766$		0			0
$767$	5.31698	−	1.56120i	0.191985	−	0.0563718i
$768$		0			0
$769$	−2.06897	−	14.3900i	−0.0746090	−	0.518917i	−0.992515	−	0.122120i	$-0.961031\pi$
$769$	−2.06897	−	14.3900i	−0.0746090	−	0.518917i	0.917906	−	0.396797i	$-0.129878\pi$
$770$		0			0
$771$	−16.6305	−	36.4158i	−0.598935	−	1.31148i
$772$		0			0
$773$	32.3451	+	20.7870i	1.16337	+	0.747655i	0.972258	−	0.233912i	$-0.0751529\pi$
$773$	32.3451	+	20.7870i	1.16337	+	0.747655i	0.191116	+	0.981567i	$0.438789\pi$
$774$		0			0
$775$	3.83318	−	26.6604i	0.137692	−	0.957668i
$776$		0			0
$777$	−31.9694	+	20.5455i	−1.14689	+	0.737065i
$778$		0			0
$779$	−38.1498	−	11.2018i	−1.36686	−	0.401346i
$780$		0			0
$781$	−13.4666			−0.481874
$782$		0			0
$783$	−9.94683			−0.355471
$784$		0			0
$785$	24.7871	+	7.27814i	0.884689	+	0.259768i
$786$		0			0
$787$	−0.556296	+	0.357510i	−0.0198298	+	0.0127438i	−0.550518	−	0.834823i	$-0.685570\pi$
$787$	−0.556296	+	0.357510i	−0.0198298	+	0.0127438i	0.530688	+	0.847567i	$0.321933\pi$
$788$		0			0
$789$	−1.47097	+	10.2308i	−0.0523679	+	0.364227i
$790$		0			0
$791$	−1.03065	−	0.662357i	−0.0366456	−	0.0235507i
$792$		0			0
$793$	0.638554	+	1.39824i	0.0226757	+	0.0496529i
$794$		0			0
$795$	4.05578	+	28.2086i	0.143844	+	1.00045i
$796$		0			0
$797$	8.55630	−	2.51236i	0.303080	−	0.0889923i	−0.126657	−	0.991947i	$-0.540425\pi$
$797$	8.55630	−	2.51236i	0.303080	−	0.0889923i	0.429736	+	0.902954i	$0.358606\pi$
$798$		0			0
$799$	8.60442	−	9.93003i	0.304402	−	0.351299i
$800$		0			0
$801$	−3.79539	−	4.38011i	−0.134103	−	0.154764i
$802$		0			0
$803$	10.6057	−	23.2232i	0.374267	−	0.819530i
$804$		0			0
$805$	−23.9238	+	25.0376i	−0.843203	+	0.882459i
$806$		0			0
$807$	−13.2416	+	28.9952i	−0.466128	+	1.02068i
$808$		0			0
$809$	25.2724	+	29.1659i	0.888531	+	1.02542i	0.999501	+	0.0315959i	$0.0100590\pi$
$809$	25.2724	+	29.1659i	0.888531	+	1.02542i	−0.110970	+	0.993824i	$0.535396\pi$
$810$		0			0
$811$	−17.7831	+	20.5228i	−0.624449	+	0.720653i	−0.976546	−	0.215311i	$-0.930923\pi$
$811$	−17.7831	+	20.5228i	−0.624449	+	0.720653i	0.352096	+	0.935964i	$0.385469\pi$
$812$		0			0
$813$	34.6181	−	10.1648i	1.21411	−	0.356495i
$814$		0			0
$815$	8.54799	+	59.4526i	0.299423	+	2.08253i
$816$		0			0
$817$	−20.2259	−	44.2884i	−0.707613	−	1.54946i
$818$		0			0
$819$	−1.48875	−	0.956761i	−0.0520211	−	0.0334319i
$820$		0			0
$821$	−1.23523	+	8.59123i	−0.0431099	+	0.299836i	0.956847	+	0.290591i	$0.0938519\pi$
$821$	−1.23523	+	8.59123i	−0.0431099	+	0.299836i	−0.999957	+	0.00924507i	$0.997057\pi$
$822$		0			0
$823$	−5.68274	+	3.65208i	−0.198088	+	0.127303i	−0.635925	−	0.771751i	$-0.719381\pi$
$823$	−5.68274	+	3.65208i	−0.198088	+	0.127303i	0.437837	+	0.899054i	$0.355745\pi$
$824$		0			0
$825$	−37.0014	−	10.8646i	−1.28822	−	0.378256i
$826$		0			0
$827$	54.2431			1.88622			0.943109	−	0.332484i	$-0.107887\pi$
$827$	54.2431			1.88622			0.943109	+	0.332484i	$0.107887\pi$
$828$		0			0
$829$	−52.3288			−1.81745			−0.908727	−	0.417392i	$-0.862944\pi$
$829$	−52.3288			−1.81745			−0.908727	+	0.417392i	$0.862944\pi$
$830$		0			0
$831$	5.41981	+	1.59140i	0.188011	+	0.0552050i
$832$		0			0
$833$	−21.7998	+	14.0099i	−0.755320	+	0.485414i
$834$		0			0
$835$	−10.5058	+	73.0694i	−0.363568	+	2.52867i
$836$		0			0
$837$	8.62615	+	5.54369i	0.298163	+	0.191618i
$838$		0			0
$839$	−7.41634	−	16.2395i	−0.256041	−	0.560651i	0.737340	−	0.675522i	$-0.236082\pi$
$839$	−7.41634	−	16.2395i	−0.256041	−	0.560651i	−0.993380	+	0.114871i	$0.963354\pi$
$840$		0			0
$841$	3.09956	+	21.5579i	0.106881	+	0.743376i
$842$		0			0
$843$	2.42930	−	0.713306i	0.0836694	−	0.0245676i
$844$		0			0
$845$	31.1022	−	35.8939i	1.06995	−	1.23479i
$846$		0			0
$847$	−8.93180	−	10.3078i	−0.306900	−	0.354182i
$848$		0			0
$849$	0.719547	−	1.57559i	0.0246948	−	0.0540740i
$850$		0			0
$851$	9.00094	−	46.4375i	0.308548	−	1.59186i
$852$		0			0
$853$	−3.14859	+	6.89446i	−0.107806	+	0.236062i	−0.955845	−	0.293872i	$-0.905056\pi$
$853$	−3.14859	+	6.89446i	−0.107806	+	0.236062i	0.848039	+	0.529934i	$0.177783\pi$
$854$		0			0
$855$	18.1250	+	20.9174i	0.619862	+	0.715358i
$856$		0			0
$857$	−32.9446	+	38.0201i	−1.12537	+	1.29874i	−0.176062	+	0.984379i	$0.556336\pi$
$857$	−32.9446	+	38.0201i	−1.12537	+	1.29874i	−0.949303	+	0.314362i	$0.898210\pi$
$858$		0			0
$859$	30.3209	−	8.90301i	1.03453	−	0.303767i	0.279981	−	0.960005i	$-0.409672\pi$
$859$	30.3209	−	8.90301i	1.03453	−	0.303767i	0.754553	+	0.656239i	$0.227853\pi$
$860$		0			0
$861$	−3.60294	−	25.0590i	−0.122788	−	0.854009i
$862$		0			0
$863$	−13.6266	−	29.8382i	−0.463856	−	1.01570i	−0.986592	−	0.163208i	$-0.947816\pi$
$863$	−13.6266	−	29.8382i	−0.463856	−	1.01570i	0.522736	−	0.852495i	$-0.324912\pi$
$864$		0			0
$865$	27.9172	+	17.9413i	0.949212	+	0.610022i
$866$		0			0
$867$	−11.4030	+	79.3098i	−0.387267	+	2.69350i
$868$		0			0
$869$	−0.620336	+	0.398666i	−0.0210435	+	0.0135238i
$870$		0			0
$871$	−7.43884	−	2.18424i	−0.252056	−	0.0740102i
$872$		0			0
$873$	−10.8455			−0.367064
$874$		0			0
$875$	−34.1076			−1.15305
$876$		0			0
$877$	−22.5735	−	6.62818i	−0.762253	−	0.223818i	−0.122574	−	0.992459i	$-0.539115\pi$
$877$	−22.5735	−	6.62818i	−0.762253	−	0.223818i	−0.639679	+	0.768642i	$0.720933\pi$
$878$		0			0
$879$	24.4494	−	15.7127i	0.824659	−	0.529976i
$880$		0			0
$881$	−1.33403	+	9.27840i	−0.0449447	+	0.312597i	0.954931	+	0.296828i	$0.0959288\pi$
$881$	−1.33403	+	9.27840i	−0.0449447	+	0.312597i	−0.999876	+	0.0157693i	$0.994980\pi$
$882$		0			0
$883$	12.9552	+	8.32577i	0.435976	+	0.280185i	0.740163	−	0.672428i	$-0.234748\pi$
$883$	12.9552	+	8.32577i	0.435976	+	0.280185i	−0.304187	+	0.952612i	$0.598385\pi$
$884$		0			0
$885$	−22.9243	−	50.1972i	−0.770592	−	1.68736i
$886$		0			0
$887$	−5.45902	−	37.9683i	−0.183296	−	1.27485i	−0.848903	−	0.528549i	$-0.822736\pi$
$887$	−5.45902	−	37.9683i	−0.183296	−	1.27485i	0.665607	−	0.746302i	$-0.268173\pi$
$888$		0			0
$889$	−3.61063	+	1.06018i	−0.121097	+	0.0355572i
$890$		0			0
$891$	14.1503	−	16.3303i	0.474053	−	0.547086i
$892$		0			0
$893$	−6.94935	−	8.01998i	−0.232551	−	0.268378i
$894$		0			0
$895$	−11.0495	+	24.1950i	−0.369344	+	0.808750i
$896$		0			0
$897$	7.53001	−	1.81835i	0.251420	−	0.0607128i
$898$		0			0
$899$	−3.09207	+	6.77069i	−0.103126	+	0.225815i
$900$		0			0
$901$	17.7979	+	20.5399i	0.592935	+	0.684284i
$902$		0			0
$903$	20.3016	−	23.4293i	0.675595	−	0.779679i
$904$		0			0
$905$	18.7467	−	5.50453i	0.623161	−	0.182977i
$906$		0			0
$907$	−3.19434	−	22.2171i	−0.106066	−	0.737708i	−0.971561	−	0.236790i	$-0.923905\pi$
$907$	−3.19434	−	22.2171i	−0.106066	−	0.737708i	0.865494	−	0.500918i	$-0.167004\pi$
$908$		0			0
$909$	−1.51286	−	3.31271i	−0.0501785	−	0.109876i
$910$		0			0
$911$	23.9713	+	15.4054i	0.794204	+	0.510404i	0.873720	−	0.486430i	$-0.161701\pi$
$911$	23.9713	+	15.4054i	0.794204	+	0.510404i	−0.0795160	+	0.996834i	$0.525337\pi$
$912$		0			0
$913$	−0.903908	+	6.28682i	−0.0299150	+	0.208063i
$914$		0			0
$915$	12.8775	−	8.27590i	0.425718	−	0.273593i
$916$		0			0
$917$	−17.0712	−	5.01255i	−0.563740	−	0.165529i
$918$		0			0
$919$	−32.9290			−1.08623			−0.543113	−	0.839660i	$-0.682755\pi$
$919$	−32.9290			−1.08623			−0.543113	+	0.839660i	$0.682755\pi$
$920$		0			0
$921$	−32.1000			−1.05773
$922$		0			0
$923$	5.26242	+	1.54519i	0.173215	+	0.0508605i
$924$		0			0
$925$	80.6795	−	51.8495i	2.65272	−	1.70480i
$926$		0			0
$927$	1.32448	−	9.21197i	0.0435017	−	0.302561i
$928$		0			0
$929$	35.5977	+	22.8773i	1.16792	+	0.750578i	0.973128	−	0.230266i	$-0.0739595\pi$
$929$	35.5977	+	22.8773i	1.16792	+	0.750578i	0.194795	+	0.980844i	$0.437596\pi$
$930$		0			0
$931$	8.69423	+	19.0377i	0.284942	+	0.623936i
$932$		0			0
$933$	−4.42521	−	30.7780i	−0.144875	−	1.00763i
$934$		0			0
$935$	−53.4322	+	15.6891i	−1.74742	+	0.513088i
$936$		0			0
$937$	13.9629	−	16.1140i	0.456147	−	0.526421i	−0.480360	−	0.877072i	$-0.659494\pi$
$937$	13.9629	−	16.1140i	0.456147	−	0.526421i	0.936507	+	0.350650i	$0.114039\pi$
$938$		0			0
$939$	−0.321466	−	0.370992i	−0.0104907	−	0.0121069i
$940$		0			0
$941$	15.8083	−	34.6153i	0.515336	−	1.12843i	−0.455840	−	0.890062i	$-0.650661\pi$
$941$	15.8083	−	34.6153i	0.515336	−	1.12843i	0.971175	−	0.238366i	$-0.0766117\pi$
$942$		0			0
$943$	25.6497	+	18.3059i	0.835269	+	0.596122i
$944$		0			0
$945$	11.1038	−	24.3140i	0.361208	−	0.790935i
$946$		0			0
$947$	−6.34168	−	7.31869i	−0.206077	−	0.237826i	0.643297	−	0.765616i	$-0.277566\pi$
$947$	−6.34168	−	7.31869i	−0.206077	−	0.237826i	−0.849374	+	0.527791i	$0.823020\pi$
$948$		0			0
$949$	−6.80912	+	7.85814i	−0.221033	+	0.255086i
$950$		0			0
$951$	4.19048	−	1.23044i	0.135886	−	0.0398997i
$952$		0			0
$953$	−7.74379	−	53.8593i	−0.250846	−	1.74467i	−0.593157	−	0.805086i	$-0.702119\pi$
$953$	−7.74379	−	53.8593i	−0.250846	−	1.74467i	0.342311	−	0.939587i	$-0.388790\pi$
$954$		0			0
$955$	−38.6924	−	84.7245i	−1.25206	−	2.74162i
$956$		0			0
$957$	8.96522	+	5.76160i	0.289804	+	0.186246i
$958$		0			0
$959$	−0.553489	+	3.84960i	−0.0178731	+	0.124310i
$960$		0			0
$961$	−19.6238	+	12.6115i	−0.633026	+	0.406821i
$962$		0			0
$963$	−2.01569	−	0.591859i	−0.0649546	−	0.0190724i
$964$		0			0
$965$	49.4256			1.59106
$966$		0			0
$967$	43.2998			1.39243			0.696214	−	0.717834i	$-0.254866\pi$
$967$	43.2998			1.39243			0.696214	+	0.717834i	$0.254866\pi$
$968$		0			0
$969$	89.0646	+	26.1517i	2.86117	+	0.840114i
$970$		0			0
$971$	14.2880	−	9.18234i	0.458524	−	0.294675i	−0.290915	−	0.956749i	$-0.593960\pi$
$971$	14.2880	−	9.18234i	0.458524	−	0.294675i	0.749439	+	0.662073i	$0.230323\pi$
$972$		0			0
$973$	0.455244	−	3.16629i	0.0145945	−	0.101507i
$974$		0			0
$975$	13.2126	+	8.49122i	0.423142	+	0.271937i
$976$		0			0
$977$	−0.236343	−	0.517520i	−0.00756130	−	0.0165569i	0.905814	−	0.423676i	$-0.139261\pi$
$977$	−0.236343	−	0.517520i	−0.00756130	−	0.0165569i	−0.913375	+	0.407119i	$0.866533\pi$
$978$		0			0
$979$	−1.34033	−	9.32221i	−0.0428372	−	0.297939i
$980$		0			0
$981$	9.79749	−	2.87680i	0.312810	−	0.0918492i
$982$		0			0
$983$	−7.31141	+	8.43782i	−0.233198	+	0.269125i	−0.860272	−	0.509835i	$-0.829707\pi$
$983$	−7.31141	+	8.43782i	−0.233198	+	0.269125i	0.627075	+	0.778959i	$0.284252\pi$
$984$		0			0
$985$	5.38376	+	6.21319i	0.171541	+	0.197969i
$986$		0			0
$987$	2.80695	−	6.14636i	0.0893461	−	0.195641i
$988$		0			0
$989$	3.62747	+	38.4171i	0.115347	+	1.22159i
$990$		0			0
$991$	5.73064	−	12.5483i	0.182040	−	0.398611i	−0.796509	−	0.604627i	$-0.793322\pi$
$991$	5.73064	−	12.5483i	0.182040	−	0.398611i	0.978549	+	0.206015i	$0.0660496\pi$
$992$		0			0
$993$	−31.1328	−	35.9292i	−0.987970	−	1.14018i
$994$		0			0
$995$	−60.8730	+	70.2512i	−1.92980	+	2.22711i
$996$		0			0
$997$	−6.84252	+	2.00914i	−0.216705	+	0.0636302i	−0.388283	−	0.921540i	$-0.626932\pi$
$997$	−6.84252	+	2.00914i	−0.216705	+	0.0636302i	0.171578	+	0.985171i	$0.445113\pi$
$998$		0			0
$999$	5.19598	+	36.1388i	0.164394	+	1.14338i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	92.2.e.a.29.1	✓	20
3.2	odd	2		828.2.q.a.397.1		20
4.3	odd	2		368.2.m.d.305.2		20
23.2	even	11		2116.2.a.j.1.7		10
23.4	even	11	inner	92.2.e.a.73.1	yes	20
23.21	odd	22		2116.2.a.i.1.7		10
69.50	odd	22		828.2.q.a.73.1		20
92.27	odd	22		368.2.m.d.257.2		20
92.67	even	22		8464.2.a.cd.1.4		10
92.71	odd	22		8464.2.a.ce.1.4		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
92.2.e.a.29.1	✓	20	1.1	even	1	trivial
92.2.e.a.73.1	yes	20	23.4	even	11	inner
368.2.m.d.257.2		20	92.27	odd	22
368.2.m.d.305.2		20	4.3	odd	2
828.2.q.a.73.1		20	69.50	odd	22
828.2.q.a.397.1		20	3.2	odd	2
2116.2.a.i.1.7		10	23.21	odd	22
2116.2.a.j.1.7		10	23.2	even	11
8464.2.a.cd.1.4		10	92.67	even	22
8464.2.a.ce.1.4		10	92.71	odd	22

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:	\( N \)	\(=\)	\( 92 = 2^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	92.e (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.96451 - 0.576832i) q^{3} +(3.22799 - 2.07450i) q^{5} +(0.267813 - 1.86268i) q^{7} +(1.00280 + 0.644459i) q^{9} +(0.804680 + 1.76200i) q^{11} +(-0.112273 - 0.780878i) q^{13} +(-7.53806 + 2.21337i) q^{15} +(-4.90640 + 5.66229i) q^{17} +(3.96265 + 4.57314i) q^{19} +(-1.60057 + 3.50477i) q^{21} +(-1.77773 - 4.45418i) q^{23} +(4.03929 - 8.84481i) q^{25} +(2.42411 + 2.79757i) q^{27} +(-1.75966 + 2.03076i) q^{29} +(2.65784 - 0.780411i) q^{31} +(-0.564421 - 3.92564i) q^{33} +(-2.99964 - 6.56830i) q^{35} +(8.29737 + 5.33239i) q^{37} +(-0.229873 + 1.59881i) q^{39} +(-5.52765 + 3.55240i) q^{41} +(-7.72022 - 2.26686i) q^{43} +4.57396 q^{45} -1.75371 q^{47} +(3.31859 + 0.974427i) q^{49} +(12.9049 - 8.29345i) q^{51} +(0.516246 - 3.59057i) q^{53} +(6.25279 + 4.01842i) q^{55} +(-5.14673 - 11.2698i) q^{57} +(0.999647 + 6.95269i) q^{59} +(-1.86952 + 0.548941i) q^{61} +(1.46898 - 1.69530i) q^{63} +(-1.98235 - 2.28776i) q^{65} +(4.08243 - 8.93929i) q^{67} +(0.923056 + 9.77572i) q^{69} +(-2.88802 + 6.32387i) q^{71} +(-8.63107 - 9.96078i) q^{73} +(-13.0372 + 15.0457i) q^{75} +(3.49756 - 1.02698i) q^{77} +(0.0541763 + 0.376804i) q^{79} +(-4.63402 - 10.1471i) q^{81} +(2.75842 + 1.77273i) q^{83} +(-4.09138 + 28.4562i) q^{85} +(4.62828 - 2.97442i) q^{87} +(-4.66512 - 1.36980i) q^{89} -1.48460 q^{91} -5.67151 q^{93} +(22.2784 + 6.54153i) q^{95} +(-7.65402 + 4.91894i) q^{97} +(-0.328608 + 2.28552i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 2 q^{3} + 2 q^{5} + 2 q^{7} - 4 q^{9} - 2 q^{11} + 6 q^{13} - 17 q^{15} - 9 q^{17} - 11 q^{19} - 47 q^{21} - 22 q^{23} - 16 q^{25} - 19 q^{27} - q^{29} - 13 q^{31} - 5 q^{33} + 14 q^{35} + 34 q^{37}+ \cdots - q^{99}+O(q^{100}) \) 20 * q + 2 * q^3 + 2 * q^5 + 2 * q^7 - 4 * q^9 - 2 * q^11 + 6 * q^13 - 17 * q^15 - 9 * q^17 - 11 * q^19 - 47 * q^21 - 22 * q^23 - 16 * q^25 - 19 * q^27 - q^29 - 13 * q^31 - 5 * q^33 + 14 * q^35 + 34 * q^37 + 30 * q^39 + 28 * q^41 + 44 * q^43 + 78 * q^45 + 26 * q^47 + 60 * q^49 + 62 * q^51 + 14 * q^53 + 26 * q^55 + 3 * q^57 - 10 * q^59 - 56 * q^61 - 27 * q^63 - 87 * q^65 - 44 * q^67 - 51 * q^69 - 37 * q^71 - 12 * q^73 - 53 * q^75 - 47 * q^77 - 6 * q^79 - 10 * q^81 - 25 * q^83 + 8 * q^85 + 48 * q^87 + 10 * q^89 + 26 * q^91 - 14 * q^93 + 29 * q^95 - q^97 - q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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