LMFDB - Embedded newform 656.2.u.h.385.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [656,2,Mod(305,656)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(656, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

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

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

chi := DirichletCharacter("656.305");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 656 = 2^{4} \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	656.u (of order $5$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.23818637260$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{5})$
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} - 2 x^{19} + 7 x^{18} - 6 x^{17} + 60 x^{16} - 92 x^{15} + 603 x^{14} - 690 x^{13} + 2935 x^{12} + \cdots + 4096 $ x^20 - 2x^19 + 7x^18 - 6x^17 + 60x^16 - 92x^15 + 603x^14 - 690x^13 + 2935x^12 - 3168x^11 + 7811x^10 - 7928x^9 + 15482x^8 - 24314x^7 + 44829x^6 - 45930x^5 + 53273x^4 - 47528x^3 + 33216x^2 - 12800*x + 4096
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 328)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			385.1
Root			$0.688630 - 2.11938i$ of defining polynomial
Character	$\chi$	$=$	656.385
Dual form			656.2.u.h.305.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.22845 q^{3} +(2.81973 + 2.04866i) q^{5} +(1.29202 + 3.97642i) q^{7} +1.96600 q^{9} +O(q^{10})$	\(q-2.22845 q^{3} +(2.81973 + 2.04866i) q^{5} +(1.29202 + 3.97642i) q^{7} +1.96600 q^{9} +(0.394664 - 0.286740i) q^{11} +(0.535047 - 1.64671i) q^{13} +(-6.28364 - 4.56533i) q^{15} +(-5.48006 + 3.98150i) q^{17} +(0.775530 + 2.38683i) q^{19} +(-2.87920 - 8.86127i) q^{21} +(2.77905 - 8.55304i) q^{23} +(2.20882 + 6.79803i) q^{25} +2.30422 q^{27} +(-0.697111 - 0.506481i) q^{29} +(-6.34676 + 4.61119i) q^{31} +(-0.879490 + 0.638987i) q^{33} +(-4.50317 + 13.8593i) q^{35} +(1.27440 + 0.925902i) q^{37} +(-1.19233 + 3.66961i) q^{39} +(-4.65470 + 4.39702i) q^{41} +(0.128977 - 0.396951i) q^{43} +(5.54360 + 4.02766i) q^{45} +(-3.70970 + 11.4173i) q^{47} +(-8.47950 + 6.16072i) q^{49} +(12.2121 - 8.87258i) q^{51} +(10.1959 + 7.40779i) q^{53} +1.70028 q^{55} +(-1.72823 - 5.31895i) q^{57} +(0.698854 - 2.15085i) q^{59} +(-2.52557 - 7.77289i) q^{61} +(2.54011 + 7.81765i) q^{63} +(4.88222 - 3.54714i) q^{65} +(4.48719 + 3.26013i) q^{67} +(-6.19299 + 19.0601i) q^{69} +(6.10826 - 4.43791i) q^{71} -1.26830 q^{73} +(-4.92224 - 15.1491i) q^{75} +(1.65011 + 1.19888i) q^{77} +0.138508 q^{79} -11.0328 q^{81} -4.56299 q^{83} -23.6090 q^{85} +(1.55348 + 1.12867i) q^{87} +(-3.56822 - 10.9818i) q^{89} +7.23929 q^{91} +(14.1435 - 10.2758i) q^{93} +(-2.70302 + 8.31903i) q^{95} +(2.97618 + 2.16232i) q^{97} +(0.775910 - 0.563731i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 2 q^{3} + 2 q^{5} + 10 q^{9}+O(q^{10}) $ 20 * q - 2 * q^3 + 2 * q^5 + 10 * q^9	$ 20 q - 2 q^{3} + 2 q^{5} + 10 q^{9} - 9 q^{11} + 7 q^{13} - q^{15} - 8 q^{17} - q^{19} - 6 q^{21} + 11 q^{23} + 15 q^{25} - 2 q^{27} + 21 q^{29} + 5 q^{31} + 19 q^{33} - 4 q^{37} - 4 q^{39} + 9 q^{41} + 17 q^{43} + 11 q^{45} - 15 q^{47} - 25 q^{49} + 22 q^{51} + 10 q^{53} + 28 q^{55} - 20 q^{57} + 24 q^{59} + 15 q^{61} + 65 q^{63} - 29 q^{65} + 26 q^{67} - 47 q^{69} - 16 q^{71} + 14 q^{73} - 11 q^{75} + 12 q^{77} + 26 q^{79} - 60 q^{81} - 20 q^{83} - 94 q^{85} - 57 q^{87} + 5 q^{89} + 46 q^{91} + 43 q^{93} - 71 q^{95} - 22 q^{97} - 8 q^{99}+O(q^{100}) $ 20 * q - 2 * q^3 + 2 * q^5 + 10 * q^9 - 9 * q^11 + 7 * q^13 - q^15 - 8 * q^17 - q^19 - 6 * q^21 + 11 * q^23 + 15 * q^25 - 2 * q^27 + 21 * q^29 + 5 * q^31 + 19 * q^33 - 4 * q^37 - 4 * q^39 + 9 * q^41 + 17 * q^43 + 11 * q^45 - 15 * q^47 - 25 * q^49 + 22 * q^51 + 10 * q^53 + 28 * q^55 - 20 * q^57 + 24 * q^59 + 15 * q^61 + 65 * q^63 - 29 * q^65 + 26 * q^67 - 47 * q^69 - 16 * q^71 + 14 * q^73 - 11 * q^75 + 12 * q^77 + 26 * q^79 - 60 * q^81 - 20 * q^83 - 94 * q^85 - 57 * q^87 + 5 * q^89 + 46 * q^91 + 43 * q^93 - 71 * q^95 - 22 * q^97 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/656\mathbb{Z}\right)^\times$.

$n$	$129$	$165$	$575$
$\chi(n)$	$e\left(\frac{3}{5}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−2.22845			−1.28660			−0.643299	−	0.765615i	$-0.722435\pi$
$3$	−2.22845			−1.28660			−0.643299	+	0.765615i	$0.722435\pi$
$4$		0			0
$5$	2.81973	+	2.04866i	1.26102	+	0.916186i	0.998807	−	0.0488230i	$-0.0155470\pi$
$5$	2.81973	+	2.04866i	1.26102	+	0.916186i	0.262215	+	0.965009i	$0.415547\pi$
$6$		0			0
$7$	1.29202	+	3.97642i	0.488337	+	1.50295i	0.827089	+	0.562071i	$0.189995\pi$
$7$	1.29202	+	3.97642i	0.488337	+	1.50295i	−0.338752	+	0.940876i	$0.610005\pi$
$8$		0			0
$9$	1.96600			0.655334
$10$		0			0
$11$	0.394664	−	0.286740i	0.118996	−	0.0864554i	−0.526696	−	0.850054i	$-0.676569\pi$
$11$	0.394664	−	0.286740i	0.118996	−	0.0864554i	0.645691	+	0.763599i	$0.276569\pi$
$12$		0			0
$13$	0.535047	−	1.64671i	0.148395	−	0.456714i	−0.849037	−	0.528334i	$-0.822817\pi$
$13$	0.535047	−	1.64671i	0.148395	−	0.456714i	0.997432	+	0.0716201i	$0.0228169\pi$
$14$		0			0
$15$	−6.28364	−	4.56533i	−1.62243	−	1.17876i
$16$		0			0
$17$	−5.48006	+	3.98150i	−1.32911	+	0.965655i	−0.329341	+	0.944211i	$0.606826\pi$
$17$	−5.48006	+	3.98150i	−1.32911	+	0.965655i	−0.999770	+	0.0214443i	$0.993174\pi$
$18$		0			0
$19$	0.775530	+	2.38683i	0.177919	+	0.547577i	0.999755	−	0.0221466i	$-0.00705007\pi$
$19$	0.775530	+	2.38683i	0.177919	+	0.547577i	−0.821836	+	0.569724i	$0.807050\pi$
$20$		0			0
$21$	−2.87920	−	8.86127i	−0.628293	−	1.93369i
$22$		0			0
$23$	2.77905	−	8.55304i	0.579473	−	1.78343i	−0.0409451	−	0.999161i	$-0.513037\pi$
$23$	2.77905	−	8.55304i	0.579473	−	1.78343i	0.620418	−	0.784272i	$-0.286963\pi$
$24$		0			0
$25$	2.20882	+	6.79803i	0.441763	+	1.35961i
$26$		0			0
$27$	2.30422			0.443447
$28$		0			0
$29$	−0.697111	−	0.506481i	−0.129450	−	0.0940512i	0.521176	−	0.853449i	$-0.325494\pi$
$29$	−0.697111	−	0.506481i	−0.129450	−	0.0940512i	−0.650626	+	0.759398i	$0.725494\pi$
$30$		0			0
$31$	−6.34676	+	4.61119i	−1.13991	+	0.828194i	−0.987107	−	0.160062i	$-0.948830\pi$
$31$	−6.34676	+	4.61119i	−1.13991	+	0.828194i	−0.152805	+	0.988256i	$0.548830\pi$
$32$		0			0
$33$	−0.879490	+	0.638987i	−0.153099	+	0.111233i
$34$		0			0
$35$	−4.50317	+	13.8593i	−0.761175	+	2.34266i
$36$		0			0
$37$	1.27440	+	0.925902i	0.209509	+	0.152217i	0.687592	−	0.726098i	$-0.258668\pi$
$37$	1.27440	+	0.925902i	0.209509	+	0.152217i	−0.478082	+	0.878315i	$0.658668\pi$
$38$		0			0
$39$	−1.19233	+	3.66961i	−0.190925	+	0.587607i
$40$		0			0
$41$	−4.65470	+	4.39702i	−0.726942	+	0.686699i
$41$	−4.65470	+	4.39702i	−0.726942	+	0.686699i
$42$		0			0
$43$	0.128977	−	0.396951i	0.0196688	−	0.0605344i	−0.940740	−	0.339128i	$-0.889868\pi$
$43$	0.128977	−	0.396951i	0.0196688	−	0.0605344i	0.960409	+	0.278593i	$0.0898681\pi$
$44$		0			0
$45$	5.54360	+	4.02766i	0.826391	+	0.600408i
$46$		0			0
$47$	−3.70970	+	11.4173i	−0.541116	+	1.66538i	0.188935	+	0.981990i	$0.439496\pi$
$47$	−3.70970	+	11.4173i	−0.541116	+	1.66538i	−0.730051	+	0.683393i	$0.760504\pi$
$48$		0			0
$49$	−8.47950	+	6.16072i	−1.21136	+	0.880103i
$50$		0			0
$51$	12.2121	−	8.87258i	1.71003	−	1.24241i
$52$		0			0
$53$	10.1959	+	7.40779i	1.40052	+	1.01754i	0.994617	+	0.103623i	$0.0330435\pi$
$53$	10.1959	+	7.40779i	1.40052	+	1.01754i	0.405905	+	0.913915i	$0.366956\pi$
$54$		0			0
$55$	1.70028			0.229265
$56$		0			0
$57$	−1.72823	−	5.31895i	−0.228910	−	0.704512i
$58$		0			0
$59$	0.698854	−	2.15085i	0.0909831	−	0.280017i	−0.895203	−	0.445659i	$-0.852969\pi$
$59$	0.698854	−	2.15085i	0.0909831	−	0.280017i	0.986186	+	0.165642i	$0.0529695\pi$
$60$		0			0
$61$	−2.52557	−	7.77289i	−0.323366	−	0.995217i	−0.972173	−	0.234264i	$-0.924732\pi$
$61$	−2.52557	−	7.77289i	−0.323366	−	0.995217i	0.648807	−	0.760953i	$-0.275268\pi$
$62$		0			0
$63$	2.54011	+	7.81765i	0.320024	+	0.984932i
$64$		0			0
$65$	4.88222	−	3.54714i	0.605565	−	0.439969i
$66$		0			0
$67$	4.48719	+	3.26013i	0.548197	+	0.398289i	0.827120	−	0.562025i	$-0.189977\pi$
$67$	4.48719	+	3.26013i	0.548197	+	0.398289i	−0.278923	+	0.960313i	$0.589977\pi$
$68$		0			0
$69$	−6.19299	+	19.0601i	−0.745548	+	2.29456i
$70$		0			0
$71$	6.10826	−	4.43791i	0.724917	−	0.526683i	−0.163035	−	0.986620i	$-0.552128\pi$
$71$	6.10826	−	4.43791i	0.724917	−	0.526683i	0.887951	+	0.459938i	$0.152128\pi$
$72$		0			0
$73$	−1.26830			−0.148444			−0.0742219	−	0.997242i	$-0.523647\pi$
$73$	−1.26830			−0.148444			−0.0742219	+	0.997242i	$0.523647\pi$
$74$		0			0
$75$	−4.92224	−	15.1491i	−0.568371	−	1.74927i
$76$		0			0
$77$	1.65011	+	1.19888i	0.188048	+	0.136625i
$78$		0			0
$79$	0.138508			0.0155833			0.00779166	−	0.999970i	$-0.497520\pi$
$79$	0.138508			0.0155833			0.00779166	+	0.999970i	$0.497520\pi$
$80$		0			0
$81$	−11.0328			−1.22587
$82$		0			0
$83$	−4.56299			−0.500853			−0.250426	−	0.968136i	$-0.580571\pi$
$83$	−4.56299			−0.500853			−0.250426	+	0.968136i	$0.580571\pi$
$84$		0			0
$85$	−23.6090			−2.56076
$86$		0			0
$87$	1.55348	+	1.12867i	0.166551	+	0.121006i
$88$		0			0
$89$	−3.56822	−	10.9818i	−0.378230	−	1.16407i	−0.941273	−	0.337645i	$-0.890370\pi$
$89$	−3.56822	−	10.9818i	−0.378230	−	1.16407i	0.563043	−	0.826427i	$-0.309630\pi$
$90$		0			0
$91$	7.23929			0.758883
$92$		0			0
$93$	14.1435	−	10.2758i	1.46661	−	1.06555i
$94$		0			0
$95$	−2.70302	+	8.31903i	−0.277324	+	0.853514i
$96$		0			0
$97$	2.97618	+	2.16232i	0.302185	+	0.219551i	0.728536	−	0.685007i	$-0.240201\pi$
$97$	2.97618	+	2.16232i	0.302185	+	0.219551i	−0.426351	+	0.904558i	$0.640201\pi$
$98$		0			0
$99$	0.775910	−	0.563731i	0.0779819	−	0.0566571i
$100$		0			0
$101$	−1.89313	−	5.82647i	−0.188374	−	0.579755i	0.811616	−	0.584191i	$-0.198588\pi$
$101$	−1.89313	−	5.82647i	−0.188374	−	0.579755i	−0.999990	+	0.00443558i	$0.998588\pi$
$102$		0			0
$103$	0.401788	+	1.23658i	0.0395894	+	0.121844i	0.968898	−	0.247461i	$-0.0795961\pi$
$103$	0.401788	+	1.23658i	0.0395894	+	0.121844i	−0.929309	+	0.369304i	$0.879596\pi$
$104$		0			0
$105$	10.0351	−	30.8849i	0.979327	−	3.01406i
$106$		0			0
$107$	0.0882599	+	0.271636i	0.00853240	+	0.0262600i	0.955232	−	0.295858i	$-0.0956054\pi$
$107$	0.0882599	+	0.271636i	0.00853240	+	0.0262600i	−0.946700	+	0.322118i	$0.895605\pi$
$108$		0			0
$109$	7.54739			0.722909			0.361454	−	0.932390i	$-0.382280\pi$
$109$	7.54739			0.722909			0.361454	+	0.932390i	$0.382280\pi$
$110$		0			0
$111$	−2.83993	−	2.06333i	−0.269554	−	0.195843i
$112$		0			0
$113$	6.58973	−	4.78772i	0.619910	−	0.450391i	−0.232980	−	0.972482i	$-0.574848\pi$
$113$	6.58973	−	4.78772i	0.619910	−	0.450391i	0.852890	+	0.522090i	$0.174848\pi$
$114$		0			0
$115$	25.3584	−	18.4240i	2.36469	−	1.71804i
$116$		0			0
$117$	1.05190	−	3.23743i	0.0972485	−	0.299300i
$118$		0			0
$119$	−22.9125	−	16.6469i	−2.10038	−	1.52602i
$120$		0			0
$121$	−3.32565	+	10.2353i	−0.302332	+	0.930481i
$122$		0			0
$123$	10.3728	−	9.79855i	0.935282	−	0.883505i
$124$		0			0
$125$	−2.31335	+	7.11977i	−0.206913	+	0.636811i
$126$		0			0
$127$	−0.390939	−	0.284034i	−0.0346903	−	0.0252039i	0.570305	−	0.821433i	$-0.306825\pi$
$127$	−0.390939	−	0.284034i	−0.0346903	−	0.0252039i	−0.604995	+	0.796229i	$0.706825\pi$
$128$		0			0
$129$	−0.287419	+	0.884586i	−0.0253059	+	0.0778835i
$130$		0			0
$131$	4.11227	−	2.98774i	0.359291	−	0.261040i	−0.393465	−	0.919339i	$-0.628724\pi$
$131$	4.11227	−	2.98774i	0.359291	−	0.261040i	0.752756	+	0.658299i	$0.228724\pi$
$132$		0			0
$133$	−8.48906	+	6.16767i	−0.736095	+	0.534805i
$134$		0			0
$135$	6.49727	+	4.72054i	0.559196	+	0.406280i
$136$		0			0
$137$	14.8688			1.27032			0.635162	−	0.772379i	$-0.280933\pi$
$137$	14.8688			1.27032			0.635162	+	0.772379i	$0.280933\pi$
$138$		0			0
$139$	−4.13756	−	12.7341i	−0.350943	−	1.08009i	−0.958325	−	0.285681i	$-0.907780\pi$
$139$	−4.13756	−	12.7341i	−0.350943	−	1.08009i	0.607382	−	0.794410i	$-0.292220\pi$
$140$		0			0
$141$	8.26690	−	25.4429i	0.696198	−	2.14268i
$142$		0			0
$143$	−0.261013	−	0.803314i	−0.0218270	−	0.0671765i
$144$		0			0
$145$	−0.928062	−	2.85628i	−0.0770714	−	0.237201i
$146$		0			0
$147$	18.8962	−	13.7289i	1.55853	−	1.13234i
$148$		0			0
$149$	−17.1854	−	12.4859i	−1.40788	−	1.02289i	−0.993626	−	0.112725i	$-0.964042\pi$
$149$	−17.1854	−	12.4859i	−1.40788	−	1.02289i	−0.414256	−	0.910161i	$-0.635958\pi$
$150$		0			0
$151$	−5.93057	+	18.2524i	−0.482623	+	1.48536i	0.352771	+	0.935710i	$0.385240\pi$
$151$	−5.93057	+	18.2524i	−0.482623	+	1.48536i	−0.835394	+	0.549652i	$0.814760\pi$
$152$		0			0
$153$	−10.7738	+	7.82764i	−0.871011	+	0.632827i
$154$		0			0
$155$	−27.3429			−2.19623
$156$		0			0
$157$	5.29196	+	16.2870i	0.422344	+	1.29984i	0.905515	+	0.424315i	$0.139485\pi$
$157$	5.29196	+	16.2870i	0.422344	+	1.29984i	−0.483171	+	0.875526i	$0.660515\pi$
$158$		0			0
$159$	−22.7212	−	16.5079i	−1.80191	−	1.30916i
$160$		0			0
$161$	37.6011			2.96338
$162$		0			0
$163$	−5.18413			−0.406052			−0.203026	−	0.979173i	$-0.565078\pi$
$163$	−5.18413			−0.406052			−0.203026	+	0.979173i	$0.565078\pi$
$164$		0			0
$165$	−3.78899			−0.294972
$166$		0			0
$167$	9.32715			0.721756			0.360878	−	0.932613i	$-0.382477\pi$
$167$	9.32715			0.721756			0.360878	+	0.932613i	$0.382477\pi$
$168$		0			0
$169$	8.09186	+	5.87908i	0.622451	+	0.452237i
$170$		0			0
$171$	1.52469	+	4.69252i	0.116596	+	0.358846i
$172$		0			0
$173$	15.7331			1.19617			0.598084	−	0.801434i	$-0.295929\pi$
$173$	15.7331			1.19617			0.598084	+	0.801434i	$0.295929\pi$
$174$		0			0
$175$	−24.1780	+	17.5664i	−1.82769	+	1.32789i
$176$		0			0
$177$	−1.55736	+	4.79307i	−0.117059	+	0.360269i
$178$		0			0
$179$	8.17557	+	5.93990i	0.611071	+	0.443969i	0.849791	−	0.527120i	$-0.176728\pi$
$179$	8.17557	+	5.93990i	0.611071	+	0.443969i	−0.238721	+	0.971088i	$0.576728\pi$
$180$		0			0
$181$	18.9473	−	13.7660i	1.40834	−	1.02322i	0.414780	−	0.909922i	$-0.363859\pi$
$181$	18.9473	−	13.7660i	1.40834	−	1.02322i	0.993561	−	0.113298i	$-0.0361414\pi$
$182$		0			0
$183$	5.62811	+	17.3215i	0.416041	+	1.28044i
$184$		0			0
$185$	1.69660	+	5.22159i	0.124736	+	0.383899i
$186$		0			0
$187$	−1.02113	+	3.14271i	−0.0746722	+	0.229817i
$188$		0			0
$189$	2.97709	+	9.16254i	0.216551	+	0.666476i
$190$		0			0
$191$	0.972608			0.0703754			0.0351877	−	0.999381i	$-0.488797\pi$
$191$	0.972608			0.0703754			0.0351877	+	0.999381i	$0.488797\pi$
$192$		0			0
$193$	8.69067	+	6.31414i	0.625568	+	0.454502i	0.854862	−	0.518855i	$-0.173642\pi$
$193$	8.69067	+	6.31414i	0.625568	+	0.454502i	−0.229294	+	0.973357i	$0.573642\pi$
$194$		0			0
$195$	−10.8798	+	7.90464i	−0.779119	+	0.566063i
$196$		0			0
$197$	15.5649	−	11.3085i	1.10895	−	0.805699i	0.126452	−	0.991973i	$-0.459641\pi$
$197$	15.5649	−	11.3085i	1.10895	−	0.805699i	0.982498	+	0.186274i	$0.0596411\pi$
$198$		0			0
$199$	−4.06236	+	12.5026i	−0.287973	+	0.886289i	0.697519	+	0.716566i	$0.254287\pi$
$199$	−4.06236	+	12.5026i	−0.287973	+	0.886289i	−0.985492	+	0.169723i	$0.945713\pi$
$200$		0			0
$201$	−9.99949	−	7.26505i	−0.705310	−	0.512437i
$202$		0			0
$203$	1.11330	−	3.42639i	0.0781385	−	0.240486i
$204$		0			0
$205$	−22.1330	+	2.86253i	−1.54583	+	0.199928i
$206$		0			0
$207$	5.46362	−	16.8153i	0.379748	−	1.16874i
$208$		0			0
$209$	0.990474	+	0.719622i	0.0685125	+	0.0497773i
$210$		0			0
$211$	−1.20467	+	3.70759i	−0.0829328	+	0.255241i	−0.983921	−	0.178602i	$-0.942843\pi$
$211$	−1.20467	+	3.70759i	−0.0829328	+	0.255241i	0.900989	+	0.433843i	$0.142843\pi$
$212$		0			0
$213$	−13.6120	+	9.88967i	−0.932676	+	0.677629i
$214$		0			0
$215$	1.17690	−	0.855065i	0.0802637	−	0.0583150i
$216$		0			0
$217$	−26.5362	−	19.2797i	−1.80139	−	1.30879i
$218$		0			0
$219$	2.82636			0.190988
$220$		0			0
$221$	3.62426	+	11.1543i	0.243794	+	0.750322i
$222$		0			0
$223$	1.33269	−	4.10158i	0.0892432	−	0.274662i	−0.896467	−	0.443110i	$-0.853875\pi$
$223$	1.33269	−	4.10158i	0.0892432	−	0.274662i	0.985711	+	0.168447i	$0.0538753\pi$
$224$		0			0
$225$	4.34253	+	13.3649i	0.289502	+	0.890997i
$226$		0			0
$227$	−3.66721	−	11.2865i	−0.243401	−	0.749112i	−0.995895	−	0.0905129i	$-0.971149\pi$
$227$	−3.66721	−	11.2865i	−0.243401	−	0.749112i	0.752494	−	0.658599i	$-0.228851\pi$
$228$		0			0
$229$	−19.5868	+	14.2307i	−1.29433	+	0.940389i	−0.999883	−	0.0152782i	$-0.995137\pi$
$229$	−19.5868	+	14.2307i	−1.29433	+	0.940389i	−0.294450	+	0.955667i	$0.595137\pi$
$230$		0			0
$231$	−3.67720	−	2.67164i	−0.241942	−	0.175781i
$232$		0			0
$233$	0.0205096	−	0.0631221i	0.00134363	−	0.00413526i	−0.950382	−	0.311084i	$-0.899308\pi$
$233$	0.0205096	−	0.0631221i	0.00134363	−	0.00413526i	0.951726	+	0.306949i	$0.0993080\pi$
$234$		0			0
$235$	−33.8505	+	24.5938i	−2.20816	+	1.60432i
$236$		0			0
$237$	−0.308657			−0.0200495
$238$		0			0
$239$	−7.46837	−	22.9853i	−0.483089	−	1.48679i	−0.834730	−	0.550659i	$-0.814376\pi$
$239$	−7.46837	−	22.9853i	−0.483089	−	1.48679i	0.351642	−	0.936135i	$-0.385624\pi$
$240$		0			0
$241$	−3.56415	−	2.58951i	−0.229587	−	0.166805i	0.467044	−	0.884234i	$-0.345319\pi$
$241$	−3.56415	−	2.58951i	−0.229587	−	0.166805i	−0.696632	+	0.717429i	$0.745319\pi$
$242$		0			0
$243$	17.6735			1.13376
$244$		0			0
$245$	−36.5311			−2.33389
$246$		0			0
$247$	4.34536			0.276489
$248$		0			0
$249$	10.1684			0.644396
$250$		0			0
$251$	19.7784	+	14.3699i	1.24840	+	0.907018i	0.998128	−	0.0611564i	$-0.0194788\pi$
$251$	19.7784	+	14.3699i	1.24840	+	0.907018i	0.250275	+	0.968175i	$0.419479\pi$
$252$		0			0
$253$	−1.35571	−	4.17244i	−0.0852327	−	0.262319i
$254$		0			0
$255$	52.6116			3.29467
$256$		0			0
$257$	10.5993	−	7.70084i	0.661166	−	0.480365i	−0.205890	−	0.978575i	$-0.566009\pi$
$257$	10.5993	−	7.70084i	0.661166	−	0.480365i	0.867057	+	0.498210i	$0.166009\pi$
$258$		0			0
$259$	−2.03524	+	6.26382i	−0.126463	+	0.389215i
$260$		0			0
$261$	−1.37052	−	0.995743i	−0.0848332	−	0.0616349i
$262$		0			0
$263$	25.7111	−	18.6802i	1.58541	−	1.15187i	0.675278	−	0.737564i	$-0.264024\pi$
$263$	25.7111	−	18.6802i	1.58541	−	1.15187i	0.910137	−	0.414307i	$-0.135976\pi$
$264$		0			0
$265$	13.5738	+	41.7760i	0.833834	+	2.56628i
$266$		0			0
$267$	7.95160	+	24.4725i	0.486630	+	1.49769i
$268$		0			0
$269$	−9.21560	+	28.3627i	−0.561885	+	1.72930i	0.115144	+	0.993349i	$0.463267\pi$
$269$	−9.21560	+	28.3627i	−0.561885	+	1.72930i	−0.677029	+	0.735956i	$0.736733\pi$
$270$		0			0
$271$	−0.361760	−	1.11338i	−0.0219754	−	0.0676332i	0.939467	−	0.342638i	$-0.111320\pi$
$271$	−0.361760	−	1.11338i	−0.0219754	−	0.0676332i	−0.961443	+	0.275005i	$0.911320\pi$
$272$		0			0
$273$	−16.1324			−0.976378
$274$		0			0
$275$	2.82101	+	2.04958i	0.170113	+	0.123594i
$276$		0			0
$277$	3.66183	−	2.66048i	0.220018	−	0.159853i	−0.472317	−	0.881429i	$-0.656582\pi$
$277$	3.66183	−	2.66048i	0.220018	−	0.159853i	0.692335	+	0.721576i	$0.256582\pi$
$278$		0			0
$279$	−12.4777	+	9.06561i	−0.747023	+	0.542744i
$280$		0			0
$281$	4.14405	−	12.7541i	0.247213	−	0.760844i	−0.748051	−	0.663641i	$-0.769010\pi$
$281$	4.14405	−	12.7541i	0.247213	−	0.760844i	0.995265	−	0.0972034i	$-0.0309897\pi$
$282$		0			0
$283$	9.64183	+	7.00520i	0.573147	+	0.416416i	0.836247	−	0.548353i	$-0.184745\pi$
$283$	9.64183	+	7.00520i	0.573147	+	0.416416i	−0.263100	+	0.964769i	$0.584745\pi$
$284$		0			0
$285$	6.02354	−	18.5386i	0.356804	−	1.09813i
$286$		0			0
$287$	−23.4984	−	12.8280i	−1.38706	−	0.757215i
$288$		0			0
$289$	8.92547	−	27.4698i	0.525028	−	1.61587i
$290$		0			0
$291$	−6.63228	−	4.81863i	−0.388791	−	0.282473i
$292$		0			0
$293$	1.80504	−	5.55534i	0.105452	−	0.324546i	−0.884385	−	0.466759i	$-0.845422\pi$
$293$	1.80504	−	5.55534i	0.105452	−	0.324546i	0.989836	+	0.142212i	$0.0454216\pi$
$294$		0			0
$295$	6.37694	−	4.63312i	0.371280	−	0.269750i
$296$		0			0
$297$	0.909391	−	0.660711i	0.0527682	−	0.0383383i
$298$		0			0
$299$	−12.5974	−	9.15256i	−0.728528	−	0.529306i
$300$		0			0
$301$	1.74508			0.100585
$302$		0			0
$303$	4.21876	+	12.9840i	0.242362	+	0.745912i
$304$		0			0
$305$	8.80256	−	27.0915i	0.504033	−	1.55125i
$306$		0			0
$307$	−8.90648	−	27.4113i	−0.508320	−	1.56445i	−0.795117	−	0.606456i	$-0.792591\pi$
$307$	−8.90648	−	27.4113i	−0.508320	−	1.56445i	0.286797	−	0.957991i	$-0.407409\pi$
$308$		0			0
$309$	−0.895366	−	2.75565i	−0.0509356	−	0.156764i
$310$		0			0
$311$	6.14159	−	4.46213i	0.348258	−	0.253024i	−0.399880	−	0.916567i	$-0.630948\pi$
$311$	6.14159	−	4.46213i	0.348258	−	0.253024i	0.748138	+	0.663543i	$0.230948\pi$
$312$		0			0
$313$	−3.86104	−	2.80521i	−0.218239	−	0.158560i	0.473295	−	0.880904i	$-0.343065\pi$
$313$	−3.86104	−	2.80521i	−0.218239	−	0.158560i	−0.691534	+	0.722344i	$0.743065\pi$
$314$		0			0
$315$	−8.85325	+	27.2475i	−0.498824	+	1.53522i
$316$		0			0
$317$	3.29427	−	2.39343i	0.185024	−	0.134428i	−0.491417	−	0.870924i	$-0.663521\pi$
$317$	3.29427	−	2.39343i	0.185024	−	0.134428i	0.676442	+	0.736496i	$0.263521\pi$
$318$		0			0
$319$	−0.420353			−0.0235353
$320$		0			0
$321$	−0.196683	−	0.605328i	−0.0109778	−	0.0337861i
$322$		0			0
$323$	−13.7531	−	9.99224i	−0.765245	−	0.555983i
$324$		0			0
$325$	12.3762			0.686507
$326$		0			0
$327$	−16.8190			−0.930093
$328$		0			0
$329$	−50.1930			−2.76723
$330$		0			0
$331$	23.0450			1.26667			0.633334	−	0.773879i	$-0.281686\pi$
$331$	23.0450			1.26667			0.633334	+	0.773879i	$0.281686\pi$
$332$		0			0
$333$	2.50546	+	1.82033i	0.137299	+	0.0997532i
$334$		0			0
$335$	5.97378	+	18.3854i	0.326383	+	1.00450i
$336$		0			0
$337$	15.0876			0.821876			0.410938	−	0.911663i	$-0.365201\pi$
$337$	15.0876			0.821876			0.410938	+	0.911663i	$0.365201\pi$
$338$		0			0
$339$	−14.6849	+	10.6692i	−0.797575	+	0.579472i
$340$		0			0
$341$	−1.18262	+	3.63974i	−0.0640426	+	0.197103i
$342$		0			0
$343$	−11.7755	−	8.55538i	−0.635816	−	0.461947i
$344$		0			0
$345$	−56.5100	+	41.0570i	−3.04240	+	2.21043i
$346$		0			0
$347$	−6.00861	−	18.4926i	−0.322559	−	0.992735i	−0.972530	−	0.232776i	$-0.925219\pi$
$347$	−6.00861	−	18.4926i	−0.322559	−	0.992735i	0.649971	−	0.759959i	$-0.274781\pi$
$348$		0			0
$349$	−0.0955985	−	0.294222i	−0.00511727	−	0.0157493i	0.948465	−	0.316881i	$-0.102636\pi$
$349$	−0.0955985	−	0.294222i	−0.00511727	−	0.0157493i	−0.953583	+	0.301132i	$0.902636\pi$
$350$		0			0
$351$	1.23286	−	3.79437i	0.0658054	−	0.202528i
$352$		0			0
$353$	−2.42246	−	7.45557i	−0.128935	−	0.396820i	0.865663	−	0.500627i	$-0.166897\pi$
$353$	−2.42246	−	7.45557i	−0.128935	−	0.396820i	−0.994597	+	0.103808i	$0.966897\pi$
$354$		0			0
$355$	26.3154			1.39668
$356$		0			0
$357$	51.0593	+	37.0968i	2.70235	+	1.96337i
$358$		0			0
$359$	17.1695	−	12.4744i	0.906170	−	0.658371i	−0.0338732	−	0.999426i	$-0.510784\pi$
$359$	17.1695	−	12.4744i	0.906170	−	0.658371i	0.940043	+	0.341055i	$0.110784\pi$
$360$		0			0
$361$	10.2758	−	7.46580i	0.540831	−	0.392937i
$362$		0			0
$363$	7.41105	−	22.8089i	0.388979	−	1.19715i
$364$		0			0
$365$	−3.57628	−	2.59832i	−0.187191	−	0.136002i
$366$		0			0
$367$	−4.97909	+	15.3241i	−0.259907	+	0.799910i	0.732917	+	0.680318i	$0.238159\pi$
$367$	−4.97909	+	15.3241i	−0.259907	+	0.799910i	−0.992823	+	0.119592i	$0.961841\pi$
$368$		0			0
$369$	−9.15115	+	8.64454i	−0.476390	+	0.450017i
$370$		0			0
$371$	−16.2832	+	50.1144i	−0.845379	+	2.60181i
$372$		0			0
$373$	8.40686	+	6.10794i	0.435291	+	0.316257i	0.783761	−	0.621063i	$-0.213299\pi$
$373$	8.40686	+	6.10794i	0.435291	+	0.316257i	−0.348470	+	0.937320i	$0.613299\pi$
$374$		0			0
$375$	5.15520	−	15.8661i	0.266213	−	0.819320i
$376$		0			0
$377$	−1.20701	+	0.876946i	−0.0621643	+	0.0451650i
$378$		0			0
$379$	−11.7664	+	8.54880i	−0.604400	+	0.439122i	−0.847438	−	0.530895i	$-0.821856\pi$
$379$	−11.7664	+	8.54880i	−0.604400	+	0.439122i	0.243038	+	0.970017i	$0.421856\pi$
$380$		0			0
$381$	0.871190	+	0.632956i	0.0446324	+	0.0324273i
$382$		0			0
$383$	−9.23623			−0.471949			−0.235975	−	0.971759i	$-0.575828\pi$
$383$	−9.23623			−0.471949			−0.235975	+	0.971759i	$0.575828\pi$
$384$		0			0
$385$	2.19679	+	6.76102i	0.111959	+	0.344574i
$386$		0			0
$387$	0.253569	−	0.780406i	0.0128897	−	0.0396703i
$388$		0			0
$389$	−6.82693	−	21.0111i	−0.346139	−	1.06531i	−0.960971	−	0.276648i	$-0.910776\pi$
$389$	−6.82693	−	21.0111i	−0.346139	−	1.06531i	0.614832	−	0.788658i	$-0.289224\pi$
$390$		0			0
$391$	18.8246	+	57.9360i	0.951999	+	2.92995i
$392$		0			0
$393$	−9.16400	+	6.65804i	−0.462263	+	0.335854i
$394$		0			0
$395$	0.390554	+	0.283754i	0.0196509	+	0.0142772i
$396$		0			0
$397$	−8.94659	+	27.5348i	−0.449016	+	1.38193i	0.429002	+	0.903304i	$0.358865\pi$
$397$	−8.94659	+	27.5348i	−0.449016	+	1.38193i	−0.878018	+	0.478627i	$0.841135\pi$
$398$		0			0
$399$	18.9175	−	13.7444i	0.947059	−	0.688078i
$400$		0			0
$401$	−4.21426			−0.210450			−0.105225	−	0.994448i	$-0.533556\pi$
$401$	−4.21426			−0.210450			−0.105225	+	0.994448i	$0.533556\pi$
$402$		0			0
$403$	4.19746	+	12.9184i	0.209090	+	0.643514i
$404$		0			0
$405$	−31.1097	−	22.6025i	−1.54585	−	1.12313i
$406$		0			0
$407$	0.768451			0.0380907
$408$		0			0
$409$	37.9408			1.87605			0.938026	−	0.346565i	$-0.112652\pi$
$409$	37.9408			1.87605			0.938026	+	0.346565i	$0.112652\pi$
$410$		0			0
$411$	−33.1343			−1.63440
$412$		0			0
$413$	9.45563			0.465281
$414$		0			0
$415$	−12.8664	−	9.34798i	−0.631587	−	0.458874i
$416$		0			0
$417$	9.22035	+	28.3773i	0.451523	+	1.38964i
$418$		0			0
$419$	18.5755			0.907474			0.453737	−	0.891136i	$-0.350091\pi$
$419$	18.5755			0.907474			0.453737	+	0.891136i	$0.350091\pi$
$420$		0			0
$421$	−28.1585	+	20.4583i	−1.37236	+	0.997079i	−0.374812	+	0.927101i	$0.622293\pi$
$421$	−28.1585	+	20.4583i	−1.37236	+	0.997079i	−0.997549	+	0.0699779i	$0.977707\pi$
$422$		0			0
$423$	−7.29328	+	22.4464i	−0.354611	+	1.09138i
$424$		0			0
$425$	−39.1708	−	28.4593i	−1.90006	−	1.38048i
$426$		0			0
$427$	27.6452	−	20.0854i	1.33785	−	0.972002i
$428$		0			0
$429$	0.581654	+	1.79015i	0.0280825	+	0.0864292i
$430$		0			0
$431$	−5.67824	−	17.4758i	−0.273511	−	0.841781i	−0.989609	−	0.143782i	$-0.954074\pi$
$431$	−5.67824	−	17.4758i	−0.273511	−	0.841781i	0.716098	−	0.698000i	$-0.245926\pi$
$432$		0			0
$433$	−5.31801	+	16.3672i	−0.255567	+	0.786555i	0.738150	+	0.674636i	$0.235700\pi$
$433$	−5.31801	+	16.3672i	−0.255567	+	0.786555i	−0.993717	+	0.111919i	$0.964300\pi$
$434$		0			0
$435$	2.06814	+	6.36509i	0.0991599	+	0.305183i
$436$		0			0
$437$	22.5699			1.07967
$438$		0			0
$439$	−22.8734	−	16.6185i	−1.09169	−	0.793159i	−0.112005	−	0.993708i	$-0.535727\pi$
$439$	−22.8734	−	16.6185i	−1.09169	−	0.793159i	−0.979684	+	0.200549i	$0.935727\pi$
$440$		0			0
$441$	−16.6707	+	12.1120i	−0.793844	+	0.576761i
$442$		0			0
$443$	12.4887	−	9.07354i	0.593354	−	0.431097i	−0.250160	−	0.968205i	$-0.580483\pi$
$443$	12.4887	−	9.07354i	0.593354	−	0.431097i	0.843514	+	0.537108i	$0.180483\pi$
$444$		0			0
$445$	12.4366	−	38.2759i	0.589551	−	1.81445i
$446$		0			0
$447$	38.2968	+	27.8243i	1.81138	+	1.31604i
$448$		0			0
$449$	−1.11968	+	3.44603i	−0.0528411	+	0.162628i	−0.973995	−	0.226571i	$-0.927248\pi$
$449$	−1.11968	+	3.44603i	−0.0528411	+	0.162628i	0.921153	+	0.389200i	$0.127248\pi$
$450$		0			0
$451$	−0.576241	+	3.07003i	−0.0271341	+	0.144562i
$452$		0			0
$453$	13.2160	−	40.6747i	0.620942	−	1.91106i
$454$		0			0
$455$	20.4128	+	14.8308i	0.956969	+	0.695279i
$456$		0			0
$457$	−8.36603	+	25.7480i	−0.391346	+	1.20444i	0.540424	+	0.841393i	$0.318264\pi$
$457$	−8.36603	+	25.7480i	−0.391346	+	1.20444i	−0.931771	+	0.363048i	$0.881736\pi$
$458$		0			0
$459$	−12.6273	+	9.17424i	−0.589390	+	0.428217i
$460$		0			0
$461$	2.36625	−	1.71918i	0.110207	−	0.0800703i	−0.531317	−	0.847173i	$-0.678303\pi$
$461$	2.36625	−	1.71918i	0.110207	−	0.0800703i	0.641524	+	0.767103i	$0.278303\pi$
$462$		0			0
$463$	−15.4154	−	11.1999i	−0.716412	−	0.520504i	0.168824	−	0.985646i	$-0.446003\pi$
$463$	−15.4154	−	11.1999i	−0.716412	−	0.520504i	−0.885236	+	0.465142i	$0.846003\pi$
$464$		0			0
$465$	60.9324			2.82567
$466$		0			0
$467$	−0.619069	−	1.90530i	−0.0286471	−	0.0881667i	0.935711	−	0.352768i	$-0.114760\pi$
$467$	−0.619069	−	1.90530i	−0.0286471	−	0.0881667i	−0.964358	+	0.264602i	$0.914760\pi$
$468$		0			0
$469$	−7.16614	+	22.0551i	−0.330902	+	1.01841i
$470$		0			0
$471$	−11.7929	−	36.2947i	−0.543387	−	1.67237i
$472$		0			0
$473$	−0.0629191	−	0.193645i	−0.00289302	−	0.00890381i
$474$		0			0
$475$	−14.5128	+	10.5442i	−0.665892	+	0.483799i
$476$		0			0
$477$	20.0453	+	14.5637i	0.917809	+	0.666827i
$478$		0			0
$479$	−9.29151	+	28.5963i	−0.424540	+	1.30660i	0.478894	+	0.877873i	$0.341038\pi$
$479$	−9.29151	+	28.5963i	−0.424540	+	1.30660i	−0.903434	+	0.428727i	$0.858962\pi$
$480$		0			0
$481$	2.20655	−	1.60315i	0.100610	−	0.0730974i
$482$		0			0
$483$	−83.7923			−3.81268
$484$		0			0
$485$	3.96218	+	12.1943i	0.179913	+	0.553716i
$486$		0			0
$487$	17.1297	+	12.4455i	0.776222	+	0.563958i	0.903843	−	0.427865i	$-0.140734\pi$
$487$	17.1297	+	12.4455i	0.776222	+	0.563958i	−0.127621	+	0.991823i	$0.540734\pi$
$488$		0			0
$489$	11.5526			0.522426
$490$		0			0
$491$	9.53579			0.430344			0.215172	−	0.976576i	$-0.430969\pi$
$491$	9.53579			0.430344			0.215172	+	0.976576i	$0.430969\pi$
$492$		0			0
$493$	5.83677			0.262875
$494$		0			0
$495$	3.34275			0.150245
$496$		0			0
$497$	25.5390	+	18.5551i	1.14558	+	0.832312i
$498$		0			0
$499$	−1.50567	−	4.63399i	−0.0674032	−	0.207446i	0.911682	−	0.410897i	$-0.134784\pi$
$499$	−1.50567	−	4.63399i	−0.0674032	−	0.207446i	−0.979085	+	0.203451i	$0.934784\pi$
$500$		0			0
$501$	−20.7851			−0.928610
$502$		0			0
$503$	−0.450996	+	0.327668i	−0.0201089	+	0.0146100i	−0.597794	−	0.801650i	$-0.703956\pi$
$503$	−0.450996	+	0.327668i	−0.0201089	+	0.0146100i	0.577685	+	0.816260i	$0.303956\pi$
$504$		0			0
$505$	6.59830	−	20.3075i	0.293620	−	0.903670i
$506$		0			0
$507$	−18.0323	−	13.1012i	−0.800844	−	0.581847i
$508$		0			0
$509$	14.6624	−	10.6528i	0.649899	−	0.472179i	−0.213338	−	0.976978i	$-0.568434\pi$
$509$	14.6624	−	10.6528i	0.649899	−	0.472179i	0.863237	+	0.504800i	$0.168434\pi$
$510$		0			0
$511$	−1.63867	−	5.04332i	−0.0724906	−	0.223103i
$512$		0			0
$513$	1.78699	+	5.49978i	0.0788974	+	0.242821i
$514$		0			0
$515$	−1.40038	+	4.30994i	−0.0617083	+	0.189919i
$516$		0			0
$517$	1.80971	+	5.56971i	0.0795909	+	0.244956i
$518$		0			0
$519$	−35.0605			−1.53899
$520$		0			0
$521$	−10.8838	−	7.90757i	−0.476830	−	0.346437i	0.323267	−	0.946308i	$-0.395219\pi$
$521$	−10.8838	−	7.90757i	−0.476830	−	0.346437i	−0.800097	+	0.599871i	$0.795219\pi$
$522$		0			0
$523$	6.17598	−	4.48711i	0.270057	−	0.196208i	−0.444512	−	0.895773i	$-0.646623\pi$
$523$	6.17598	−	4.48711i	0.270057	−	0.196208i	0.714569	+	0.699565i	$0.246623\pi$
$524$		0			0
$525$	53.8796	−	39.1458i	2.35150	−	1.70846i
$526$		0			0
$527$	16.4212	−	50.5392i	0.715318	−	2.20152i
$528$		0			0
$529$	−46.8240	−	34.0197i	−2.03583	−	1.47912i
$530$		0			0
$531$	1.37395	−	4.22858i	0.0596243	−	0.183505i
$532$		0			0
$533$	4.75011	+	10.0175i	0.205750	+	0.433907i
$534$		0			0
$535$	−0.307619	+	0.946754i	−0.0132995	+	0.0409318i
$536$		0			0
$537$	−18.2189	−	13.2368i	−0.786202	−	0.571209i
$538$		0			0
$539$	−1.58003	+	4.86283i	−0.0680566	+	0.209457i
$540$		0			0
$541$	−19.0273	+	13.8241i	−0.818047	+	0.594346i	−0.916152	−	0.400830i	$-0.868722\pi$
$541$	−19.0273	+	13.8241i	−0.818047	+	0.594346i	0.0981056	+	0.995176i	$0.468722\pi$
$542$		0			0
$543$	−42.2231	+	30.6769i	−1.81197	+	1.31647i
$544$		0			0
$545$	21.2816	+	15.4620i	0.911604	+	0.662319i
$546$		0			0
$547$	37.0650			1.58478			0.792392	−	0.610012i	$-0.208835\pi$
$547$	37.0650			1.58478			0.792392	+	0.610012i	$0.208835\pi$
$548$		0			0
$549$	−4.96527	−	15.2815i	−0.211912	−	0.652200i
$550$		0			0
$551$	0.668256	−	2.05668i	0.0284687	−	0.0876176i
$552$		0			0
$553$	0.178954	+	0.550764i	0.00760991	+	0.0234209i
$554$		0			0
$555$	−3.78079	−	11.6361i	−0.160486	−	0.493924i
$556$		0			0
$557$	−2.78053	+	2.02017i	−0.117815	+	0.0855975i	−0.645132	−	0.764071i	$-0.723198\pi$
$557$	−2.78053	+	2.02017i	−0.117815	+	0.0855975i	0.527318	+	0.849668i	$0.323198\pi$
$558$		0			0
$559$	−0.584652	−	0.424775i	−0.0247282	−	0.0179661i
$560$		0			0
$561$	2.27553	−	7.00337i	0.0960731	−	0.295683i
$562$		0			0
$563$	−2.04571	+	1.48630i	−0.0862165	+	0.0626400i	−0.630058	−	0.776548i	$-0.716969\pi$
$563$	−2.04571	+	1.48630i	−0.0862165	+	0.0626400i	0.543842	+	0.839188i	$0.316969\pi$
$564$		0			0
$565$	28.3897			1.19436
$566$		0			0
$567$	−14.2546	−	43.8712i	−0.598638	−	1.84242i
$568$		0			0
$569$	−3.24312	−	2.35626i	−0.135958	−	0.0987796i	0.517727	−	0.855546i	$-0.326778\pi$
$569$	−3.24312	−	2.35626i	−0.135958	−	0.0987796i	−0.653686	+	0.756766i	$0.726778\pi$
$570$		0			0
$571$	−23.1438			−0.968536			−0.484268	−	0.874920i	$-0.660914\pi$
$571$	−23.1438			−0.968536			−0.484268	+	0.874920i	$0.660914\pi$
$572$		0			0
$573$	−2.16741			−0.0905449
$574$		0			0
$575$	64.2823			2.68076
$576$		0			0
$577$	−3.76954			−0.156928			−0.0784640	−	0.996917i	$-0.525002\pi$
$577$	−3.76954			−0.156928			−0.0784640	+	0.996917i	$0.525002\pi$
$578$		0			0
$579$	−19.3667	−	14.0708i	−0.804854	−	0.584761i
$580$		0			0
$581$	−5.89546	−	18.1444i	−0.244585	−	0.752755i
$582$		0			0
$583$	6.14808			0.254628
$584$		0			0
$585$	9.59846	−	6.97369i	0.396847	−	0.288326i
$586$		0			0
$587$	−3.63443	+	11.1856i	−0.150009	+	0.461680i	−0.997621	−	0.0689365i	$-0.978039\pi$
$587$	−3.63443	+	11.1856i	−0.150009	+	0.461680i	0.847612	+	0.530616i	$0.178039\pi$
$588$		0			0
$589$	−15.9282	−	11.5725i	−0.656312	−	0.476839i
$590$		0			0
$591$	−34.6855	+	25.2005i	−1.42677	+	1.03661i
$592$		0			0
$593$	−3.22213	−	9.91668i	−0.132317	−	0.407229i	0.862846	−	0.505467i	$-0.168680\pi$
$593$	−3.22213	−	9.91668i	−0.132317	−	0.407229i	−0.995163	+	0.0982372i	$0.968680\pi$
$594$		0			0
$595$	−30.5033	−	93.8795i	−1.25051	−	3.84868i
$596$		0			0
$597$	9.05277	−	27.8616i	0.370505	−	1.14030i
$598$		0			0
$599$	10.4275	+	32.0926i	0.426056	+	1.31127i	0.901979	+	0.431779i	$0.142114\pi$
$599$	10.4275	+	32.0926i	0.426056	+	1.31127i	−0.475923	+	0.879487i	$0.657886\pi$
$600$		0			0
$601$	9.64124			0.393274			0.196637	−	0.980476i	$-0.436998\pi$
$601$	9.64124			0.393274			0.196637	+	0.980476i	$0.436998\pi$
$602$		0			0
$603$	8.82182	+	6.40943i	0.359252	+	0.261012i
$604$		0			0
$605$	−30.3460	+	22.0477i	−1.23374	+	0.896365i
$606$		0			0
$607$	22.6399	−	16.4489i	0.918926	−	0.667639i	−0.0243307	−	0.999704i	$-0.507745\pi$
$607$	22.6399	−	16.4489i	0.918926	−	0.667639i	0.943256	+	0.332065i	$0.107745\pi$
$608$		0			0
$609$	−2.48094	+	7.63555i	−0.100533	+	0.309408i
$610$		0			0
$611$	16.8160	+	12.2176i	0.680304	+	0.494270i
$612$		0			0
$613$	10.2812	−	31.6424i	0.415256	−	1.27803i	−0.496766	−	0.867884i	$-0.665479\pi$
$613$	10.2812	−	31.6424i	0.415256	−	1.27803i	0.912022	−	0.410141i	$-0.134521\pi$
$614$		0			0
$615$	49.3223	−	6.37902i	1.98887	−	0.257227i
$616$		0			0
$617$	−9.15209	+	28.1672i	−0.368449	+	1.13397i	0.579343	+	0.815084i	$0.303309\pi$
$617$	−9.15209	+	28.1672i	−0.368449	+	1.13397i	−0.947793	+	0.318887i	$0.896691\pi$
$618$		0			0
$619$	16.8594	+	12.2491i	0.677637	+	0.492332i	0.872573	−	0.488484i	$-0.162450\pi$
$619$	16.8594	+	12.2491i	0.677637	+	0.492332i	−0.194936	+	0.980816i	$0.562450\pi$
$620$		0			0
$621$	6.40354	−	19.7081i	0.256965	−	0.790857i
$622$		0			0
$623$	39.0582	−	28.3775i	1.56484	−	1.13692i
$624$		0			0
$625$	7.80478	−	5.67051i	0.312191	−	0.226820i
$626$		0			0
$627$	−2.20723	−	1.60364i	−0.0881481	−	0.0640433i
$628$		0			0
$629$	−10.6702			−0.425451
$630$		0			0
$631$	−6.87583	−	21.1616i	−0.273722	−	0.842431i	−0.989555	−	0.144158i	$-0.953953\pi$
$631$	−6.87583	−	21.1616i	−0.273722	−	0.842431i	0.715832	−	0.698272i	$-0.246047\pi$
$632$		0			0
$633$	2.68455	−	8.26218i	0.106701	−	0.328392i
$634$		0			0
$635$	−0.520456	−	1.60180i	−0.0206537	−	0.0635655i
$636$		0			0
$637$	5.60796	+	17.2595i	0.222195	+	0.683847i
$638$		0			0
$639$	12.0088	−	8.72493i	0.475062	−	0.345153i
$640$		0			0
$641$	17.1235	+	12.4409i	0.676337	+	0.491388i	0.872141	−	0.489255i	$-0.162731\pi$
$641$	17.1235	+	12.4409i	0.676337	+	0.491388i	−0.195803	+	0.980643i	$0.562731\pi$
$642$		0			0
$643$	−2.33980	+	7.20115i	−0.0922726	+	0.283986i	−0.986533	−	0.163561i	$-0.947702\pi$
$643$	−2.33980	+	7.20115i	−0.0922726	+	0.283986i	0.894261	+	0.447546i	$0.147702\pi$
$644$		0			0
$645$	−2.62266	+	1.90547i	−0.103267	+	0.0750279i
$646$		0			0
$647$	−27.1595			−1.06775			−0.533875	−	0.845563i	$-0.679265\pi$
$647$	−27.1595			−1.06775			−0.533875	+	0.845563i	$0.679265\pi$
$648$		0			0
$649$	−0.340923	−	1.04925i	−0.0133824	−	0.0411868i
$650$		0			0
$651$	59.1346	+	42.9638i	2.31767	+	1.68388i
$652$		0			0
$653$	−25.1297			−0.983400			−0.491700	−	0.870765i	$-0.663624\pi$
$653$	−25.1297			−0.983400			−0.491700	+	0.870765i	$0.663624\pi$
$654$		0			0
$655$	17.7164			0.692235
$656$		0			0
$657$	−2.49349			−0.0972803
$658$		0			0
$659$	−9.02522			−0.351573			−0.175786	−	0.984428i	$-0.556247\pi$
$659$	−9.02522			−0.351573			−0.175786	+	0.984428i	$0.556247\pi$
$660$		0			0
$661$	−24.7600	−	17.9892i	−0.963052	−	0.699698i	−0.00919459	−	0.999958i	$-0.502927\pi$
$661$	−24.7600	−	17.9892i	−0.963052	−	0.699698i	−0.953858	+	0.300259i	$0.902927\pi$
$662$		0			0
$663$	−8.07650	−	24.8569i	−0.313665	−	0.965363i
$664$		0			0
$665$	−36.5723			−1.41821
$666$		0			0
$667$	−6.26926	+	4.55489i	−0.242747	+	0.176366i
$668$		0			0
$669$	−2.96983	+	9.14018i	−0.114820	+	0.353380i
$670$		0			0
$671$	−3.22555	−	2.34350i	−0.124521	−	0.0904698i
$672$		0			0
$673$	−18.8126	+	13.6682i	−0.725174	+	0.526870i	−0.888033	−	0.459780i	$-0.847928\pi$
$673$	−18.8126	+	13.6682i	−0.725174	+	0.526870i	0.162859	+	0.986649i	$0.447928\pi$
$674$		0			0
$675$	5.08959	+	15.6641i	0.195898	+	0.602913i
$676$		0			0
$677$	−11.8210	−	36.3812i	−0.454316	−	1.39824i	−0.871936	−	0.489620i	$-0.837136\pi$
$677$	−11.8210	−	36.3812i	−0.454316	−	1.39824i	0.417620	−	0.908622i	$-0.362864\pi$
$678$		0			0
$679$	−4.75303	+	14.6283i	−0.182404	+	0.561383i
$680$		0			0
$681$	8.17220	+	25.1515i	0.313159	+	0.963806i
$682$		0			0
$683$	3.06575			0.117308			0.0586538	−	0.998278i	$-0.481319\pi$
$683$	3.06575			0.117308			0.0586538	+	0.998278i	$0.481319\pi$
$684$		0			0
$685$	41.9259	+	30.4610i	1.60191	+	1.16385i
$686$		0			0
$687$	43.6483	−	31.7124i	1.66529	−	1.20990i
$688$		0			0
$689$	17.6538	−	12.8262i	0.672555	−	0.488640i
$690$		0			0
$691$	−9.39011	+	28.8998i	−0.357216	+	1.09940i	0.597497	+	0.801871i	$0.296162\pi$
$691$	−9.39011	+	28.8998i	−0.357216	+	1.09940i	−0.954713	+	0.297528i	$0.903838\pi$
$692$		0			0
$693$	3.24412	+	2.35699i	0.123234	+	0.0895348i
$694$		0			0
$695$	14.4210	−	44.3832i	0.547018	−	1.68355i
$696$		0			0
$697$	8.00133	−	42.6286i	0.303072	−	1.61467i
$698$		0			0
$699$	−0.0457047	+	0.140665i	−0.00172871	+	0.00532042i
$700$		0			0
$701$	−31.9175	−	23.1894i	−1.20551	−	0.875852i	−0.210692	−	0.977552i	$-0.567572\pi$
$701$	−31.9175	−	23.1894i	−1.20551	−	0.875852i	−0.994815	+	0.101700i	$0.967572\pi$
$702$		0			0
$703$	−1.22164	+	3.75984i	−0.0460752	+	0.141805i
$704$		0			0
$705$	75.4341	−	54.8061i	2.84101	−	2.06412i
$706$		0			0
$707$	20.7225	−	15.0558i	0.779351	−	0.566232i
$708$		0			0
$709$	−7.54290	−	5.48024i	−0.283280	−	0.205815i	0.437067	−	0.899429i	$-0.356017\pi$
$709$	−7.54290	−	5.48024i	−0.283280	−	0.205815i	−0.720347	+	0.693614i	$0.756017\pi$
$710$		0			0
$711$	0.272306			0.0102123
$712$		0			0
$713$	21.8017	+	67.0988i	0.816481	+	2.51287i
$714$		0			0
$715$	0.909728	−	2.79986i	0.0340219	−	0.104709i
$716$		0			0
$717$	16.6429	+	51.2216i	0.621541	+	1.91291i
$718$		0			0
$719$	9.12517	+	28.0844i	0.340312	+	1.04737i	0.964046	+	0.265735i	$0.0856146\pi$
$719$	9.12517	+	28.0844i	0.340312	+	1.04737i	−0.623735	+	0.781636i	$0.714385\pi$
$720$		0			0
$721$	−4.39803	+	3.19536i	−0.163791	+	0.119001i
$722$		0			0
$723$	7.94254	+	5.77060i	0.295386	+	0.214611i
$724$		0			0
$725$	1.90329	−	5.85771i	0.0706863	−	0.217550i
$726$		0			0
$727$	−7.40015	+	5.37653i	−0.274456	+	0.199404i	−0.716496	−	0.697591i	$-0.754255\pi$
$727$	−7.40015	+	5.37653i	−0.274456	+	0.199404i	0.442039	+	0.896996i	$0.354255\pi$
$728$		0			0
$729$	−6.28608			−0.232818
$730$		0			0
$731$	0.873657	+	2.68884i	0.0323134	+	0.0994503i
$732$		0			0
$733$	0.660100	+	0.479591i	0.0243813	+	0.0177141i	0.599909	−	0.800068i	$-0.295203\pi$
$733$	0.660100	+	0.479591i	0.0243813	+	0.0177141i	−0.575528	+	0.817782i	$0.695203\pi$
$734$		0			0
$735$	81.4079			3.00278
$736$		0			0
$737$	2.70574			0.0996673
$738$		0			0
$739$	0.196762			0.00723800			0.00361900	−	0.999993i	$-0.498848\pi$
$739$	0.196762			0.00723800			0.00361900	+	0.999993i	$0.498848\pi$
$740$		0			0
$741$	−9.68343			−0.355730
$742$		0			0
$743$	13.2018	+	9.59166i	0.484327	+	0.351884i	0.802998	−	0.595981i	$-0.203237\pi$
$743$	13.2018	+	9.59166i	0.484327	+	0.351884i	−0.318672	+	0.947865i	$0.603237\pi$
$744$		0			0
$745$	−22.8789	−	70.4139i	−0.838216	−	2.57976i
$746$		0			0
$747$	−8.97084			−0.328226
$748$		0			0
$749$	−0.966106	+	0.701917i	−0.0353007	+	0.0256475i
$750$		0			0
$751$	−3.82397	+	11.7690i	−0.139539	+	0.429455i	−0.996268	−	0.0863101i	$-0.972492\pi$
$751$	−3.82397	+	11.7690i	−0.139539	+	0.429455i	0.856730	+	0.515765i	$0.172492\pi$
$752$		0			0
$753$	−44.0753	−	32.0226i	−1.60619	−	1.16697i
$754$		0			0
$755$	−54.1156	+	39.3173i	−1.96947	+	1.43090i
$756$		0			0
$757$	−12.9490	−	39.8528i	−0.470638	−	1.44848i	−0.851751	−	0.523947i	$-0.824459\pi$
$757$	−12.9490	−	39.8528i	−0.470638	−	1.44848i	0.381112	−	0.924529i	$-0.375541\pi$
$758$		0			0
$759$	3.02113	+	9.29809i	0.109660	+	0.337499i
$760$		0			0
$761$	−6.79733	+	20.9200i	−0.246403	+	0.758350i	0.749000	+	0.662571i	$0.230535\pi$
$761$	−6.79733	+	20.9200i	−0.246403	+	0.758350i	−0.995403	+	0.0957799i	$0.969465\pi$
$762$		0			0
$763$	9.75136	+	30.0116i	0.353023	+	1.08649i
$764$		0			0
$765$	−46.4154			−1.67815
$766$		0			0
$767$	−3.16790	−	2.30161i	−0.114386	−	0.0831065i
$768$		0			0
$769$	−0.949440	+	0.689809i	−0.0342377	+	0.0248751i	−0.604772	−	0.796398i	$-0.706736\pi$
$769$	−0.949440	+	0.689809i	−0.0342377	+	0.0248751i	0.570535	+	0.821273i	$0.306736\pi$
$770$		0			0
$771$	−23.6200	+	17.1610i	−0.850655	+	0.618037i
$772$		0			0
$773$	−11.6799	+	35.9472i	−0.420098	+	1.29293i	0.487512	+	0.873116i	$0.337905\pi$
$773$	−11.6799	+	35.9472i	−0.420098	+	1.29293i	−0.907610	+	0.419814i	$0.862095\pi$
$774$		0			0
$775$	−45.3658	−	32.9602i	−1.62959	−	1.18397i
$776$		0			0
$777$	4.53543	−	13.9586i	0.162708	−	0.500763i
$778$		0			0
$779$	−14.1048	−	7.69998i	−0.505357	−	0.275881i
$780$		0			0
$781$	1.13818	−	3.50296i	0.0407273	−	0.125346i
$782$		0			0
$783$	−1.60630	−	1.16704i	−0.0574043	−	0.0417067i
$784$		0			0
$785$	−18.4445	+	56.7663i	−0.658312	+	2.02607i
$786$		0			0
$787$	−25.6991	+	18.6715i	−0.916075	+	0.665568i	−0.942544	−	0.334082i	$-0.891574\pi$
$787$	−25.6991	+	18.6715i	−0.916075	+	0.665568i	0.0264689	+	0.999650i	$0.491574\pi$
$788$		0			0
$789$	−57.2960	+	41.6280i	−2.03979	+	1.48199i
$790$		0			0
$791$	27.5521	+	20.0177i	0.979639	+	0.711749i
$792$		0			0
$793$	−14.1510			−0.502515
$794$		0			0
$795$	−30.2487	−	93.0958i	−1.07281	−	3.30177i
$796$		0			0
$797$	5.25313	−	16.1675i	0.186075	−	0.572681i	−0.813890	−	0.581019i	$-0.802654\pi$
$797$	5.25313	−	16.1675i	0.186075	−	0.572681i	0.999965	+	0.00833795i	$0.00265408\pi$
$798$		0			0
$799$	−25.1285	−	77.3376i	−0.888983	−	2.73601i
$800$		0			0
$801$	−7.01512	−	21.5903i	−0.247867	−	0.762856i
$802$		0			0
$803$	−0.500554	+	0.363674i	−0.0176642	+	0.0128338i
$804$		0			0
$805$	106.025	+	77.0317i	3.73689	+	2.71501i
$806$		0			0
$807$	20.5365	−	63.2050i	0.722920	−	2.22492i
$808$		0			0
$809$	8.77631	−	6.37636i	0.308559	−	0.224181i	−0.422719	−	0.906261i	$-0.638924\pi$
$809$	8.77631	−	6.37636i	0.308559	−	0.224181i	0.731278	+	0.682080i	$0.238924\pi$
$810$		0			0
$811$	33.9766			1.19308			0.596539	−	0.802584i	$-0.296542\pi$
$811$	33.9766			1.19308			0.596539	+	0.802584i	$0.296542\pi$
$812$		0			0
$813$	0.806165	+	2.48112i	0.0282734	+	0.0870167i
$814$		0			0
$815$	−14.6178	−	10.6205i	−0.512041	−	0.372020i
$816$		0			0
$817$	1.04748			0.0366467
$818$		0			0
$819$	14.2325			0.497322
$820$		0			0
$821$	−18.5195			−0.646335			−0.323168	−	0.946342i	$-0.604748\pi$
$821$	−18.5195			−0.646335			−0.323168	+	0.946342i	$0.604748\pi$
$822$		0			0
$823$	−48.8249			−1.70193			−0.850964	−	0.525224i	$-0.823982\pi$
$823$	−48.8249			−1.70193			−0.850964	+	0.525224i	$0.823982\pi$
$824$		0			0
$825$	−6.28648	−	4.56740i	−0.218867	−	0.159016i
$826$		0			0
$827$	7.78235	+	23.9516i	0.270619	+	0.832879i	0.990345	+	0.138622i	$0.0442672\pi$
$827$	7.78235	+	23.9516i	0.270619	+	0.832879i	−0.719727	+	0.694258i	$0.755733\pi$
$828$		0			0
$829$	12.9272			0.448981			0.224490	−	0.974476i	$-0.427928\pi$
$829$	12.9272			0.448981			0.224490	+	0.974476i	$0.427928\pi$
$830$		0			0
$831$	−8.16022	+	5.92875i	−0.283075	+	0.205666i
$832$		0			0
$833$	21.9393	−	67.5223i	0.760152	−	2.33951i
$834$		0			0
$835$	26.3001	+	19.1081i	0.910151	+	0.661263i
$836$		0			0
$837$	−14.6243	+	10.6252i	−0.505490	+	0.367260i
$838$		0			0
$839$	11.4493	+	35.2372i	0.395272	+	1.21652i	0.928749	+	0.370709i	$0.120885\pi$
$839$	11.4493	+	35.2372i	0.395272	+	1.21652i	−0.533477	+	0.845815i	$0.679115\pi$
$840$		0			0
$841$	−8.73205	−	26.8745i	−0.301105	−	0.926707i
$842$		0			0
$843$	−9.23482	+	28.4219i	−0.318064	+	0.978901i
$844$		0			0
$845$	10.7727	+	33.1549i	0.370591	+	1.14056i
$846$		0			0
$847$	−44.9966			−1.54610
$848$		0			0
$849$	−21.4864	−	15.6108i	−0.737410	−	0.535760i
$850$		0			0
$851$	11.4609	−	8.32683i	0.392874	−	0.285440i
$852$		0			0
$853$	−15.9117	+	11.5605i	−0.544805	+	0.395824i	−0.825866	−	0.563866i	$-0.809313\pi$
$853$	−15.9117	+	11.5605i	−0.544805	+	0.395824i	0.281062	+	0.959690i	$0.409313\pi$
$854$		0			0
$855$	−5.31413	+	16.3552i	−0.181740	+	0.559337i
$856$		0			0
$857$	−14.1086	−	10.2505i	−0.481941	−	0.350150i	0.320136	−	0.947372i	$-0.396271\pi$
$857$	−14.1086	−	10.2505i	−0.481941	−	0.350150i	−0.802076	+	0.597221i	$0.796271\pi$
$858$		0			0
$859$	12.9989	−	40.0065i	0.443517	−	1.36500i	−0.440586	−	0.897711i	$-0.645229\pi$
$859$	12.9989	−	40.0065i	0.443517	−	1.36500i	0.884102	−	0.467293i	$-0.154771\pi$
$860$		0			0
$861$	52.3650	+	28.5867i	1.78459	+	0.974231i
$862$		0			0
$863$	−10.8766	+	33.4748i	−0.370245	+	1.13950i	0.576386	+	0.817177i	$0.304462\pi$
$863$	−10.8766	+	33.4748i	−0.370245	+	1.13950i	−0.946631	+	0.322319i	$0.895538\pi$
$864$		0			0
$865$	44.3632	+	32.2317i	1.50839	+	1.09591i
$866$		0			0
$867$	−19.8900	+	61.2151i	−0.675500	+	2.07897i
$868$		0			0
$869$	0.0546639	−	0.0397156i	0.00185435	−	0.00134726i
$870$		0			0
$871$	7.76934	−	5.64475i	0.263254	−	0.191265i
$872$		0			0
$873$	5.85118	+	4.25113i	0.198032	+	0.143879i
$874$		0			0
$875$	−31.3001			−1.05814
$876$		0			0
$877$	1.67438	+	5.15320i	0.0565397	+	0.174011i	0.975338	−	0.220716i	$-0.0708392\pi$
$877$	1.67438	+	5.15320i	0.0565397	+	0.174011i	−0.918799	+	0.394727i	$0.870839\pi$
$878$		0			0
$879$	−4.02244	+	12.3798i	−0.135674	+	0.417561i
$880$		0			0
$881$	−8.43466	−	25.9592i	−0.284171	−	0.874588i	−0.986646	−	0.162880i	$-0.947922\pi$
$881$	−8.43466	−	25.9592i	−0.284171	−	0.874588i	0.702475	−	0.711708i	$-0.252078\pi$
$882$		0			0
$883$	−4.84546	−	14.9128i	−0.163063	−	0.501855i	0.835826	−	0.548995i	$-0.184989\pi$
$883$	−4.84546	−	14.9128i	−0.163063	−	0.501855i	−0.998888	+	0.0471397i	$0.984989\pi$
$884$		0			0
$885$	−14.2107	+	10.3247i	−0.477688	+	0.347060i
$886$		0			0
$887$	−5.51007	−	4.00330i	−0.185010	−	0.134418i	0.491425	−	0.870920i	$-0.336476\pi$
$887$	−5.51007	−	4.00330i	−0.185010	−	0.134418i	−0.676435	+	0.736502i	$0.736476\pi$
$888$		0			0
$889$	0.624339	−	1.92152i	0.0209396	−	0.0644456i
$890$		0			0
$891$	−4.35426	+	3.16356i	−0.145873	+	0.105983i
$892$		0			0
$893$	−30.1282			−1.00820
$894$		0			0
$895$	10.8841	+	33.4978i	0.363816	+	1.11971i
$896$		0			0
$897$	28.0728	+	20.3961i	0.937322	+	0.681004i
$898$		0			0
$899$	6.75988			0.225455
$900$		0			0
$901$	−85.3686			−2.84404
$902$		0			0
$903$	−3.88884			−0.129412
$904$		0			0
$905$	81.6281			2.71341
$906$		0			0
$907$	−7.34685	−	5.33780i	−0.243948	−	0.177239i	0.459092	−	0.888389i	$-0.348175\pi$
$907$	−7.34685	−	5.33780i	−0.243948	−	0.177239i	−0.703040	+	0.711150i	$0.748175\pi$
$908$		0			0
$909$	−3.72191	−	11.4549i	−0.123448	−	0.379933i
$910$		0			0
$911$	−7.03099			−0.232947			−0.116474	−	0.993194i	$-0.537159\pi$
$911$	−7.03099			−0.232947			−0.116474	+	0.993194i	$0.537159\pi$
$912$		0			0
$913$	−1.80084	+	1.30839i	−0.0595993	+	0.0433014i
$914$		0			0
$915$	−19.6161	+	60.3721i	−0.648488	+	1.99584i
$916$		0			0
$917$	17.1936	+	12.4919i	0.567784	+	0.412519i
$918$		0			0
$919$	−4.15841	+	3.02127i	−0.137173	+	0.0996623i	−0.654256	−	0.756273i	$-0.727018\pi$
$919$	−4.15841	+	3.02127i	−0.137173	+	0.0996623i	0.517082	+	0.855936i	$0.327018\pi$
$920$		0			0
$921$	19.8477	+	61.0848i	0.654003	+	2.01281i
$922$		0			0
$923$	−4.03972	−	12.4330i	−0.132969	−	0.409237i
$924$		0			0
$925$	−3.47941	+	10.7085i	−0.114402	+	0.352094i
$926$		0			0
$927$	0.789916	+	2.43111i	0.0259443	+	0.0798482i
$928$		0			0
$929$	−16.6151			−0.545123			−0.272561	−	0.962138i	$-0.587871\pi$
$929$	−16.6151			−0.545123			−0.272561	+	0.962138i	$0.587871\pi$
$930$		0			0
$931$	−21.2807	−	15.4614i	−0.697448	−	0.506725i
$932$		0			0
$933$	−13.6862	+	9.94364i	−0.448068	+	0.325540i
$934$		0			0
$935$	−9.31763	+	6.76965i	−0.304719	+	0.221391i
$936$		0			0
$937$	9.48299	−	29.1856i	0.309796	−	0.953453i	−0.668048	−	0.744118i	$-0.732870\pi$
$937$	9.48299	−	29.1856i	0.309796	−	0.953453i	0.977844	−	0.209335i	$-0.0671300\pi$
$938$		0			0
$939$	8.60415	+	6.25128i	0.280786	+	0.204003i
$940$		0			0
$941$	6.92165	−	21.3026i	0.225639	−	0.694446i	−0.772587	−	0.634909i	$-0.781038\pi$
$941$	6.92165	−	21.3026i	0.225639	−	0.694446i	0.998226	−	0.0595371i	$-0.0189624\pi$
$942$		0			0
$943$	24.6722	+	52.0314i	0.803438	+	1.69438i
$944$		0			0
$945$	−10.3763	+	31.9349i	−0.337541	+	1.03884i
$946$		0			0
$947$	12.7654	+	9.27462i	0.414820	+	0.301385i	0.775550	−	0.631286i	$-0.217472\pi$
$947$	12.7654	+	9.27462i	0.414820	+	0.301385i	−0.360730	+	0.932670i	$0.617472\pi$
$948$		0			0
$949$	−0.678603	+	2.08852i	−0.0220284	+	0.0677964i
$950$		0			0
$951$	−7.34112	+	5.33364i	−0.238052	+	0.172955i
$952$		0			0
$953$	−38.7814	+	28.1763i	−1.25625	+	0.912721i	−0.998567	−	0.0535074i	$-0.982960\pi$
$953$	−38.7814	+	28.1763i	−1.25625	+	0.912721i	−0.257686	+	0.966229i	$0.582960\pi$
$954$		0			0
$955$	2.74249	+	1.99254i	0.0887450	+	0.0644770i
$956$		0			0
$957$	0.936737			0.0302804
$958$		0			0
$959$	19.2107	+	59.1245i	0.620346	+	1.90923i
$960$		0			0
$961$	9.43874	−	29.0495i	0.304476	−	0.937079i
$962$		0			0
$963$	0.173519	+	0.534037i	0.00559157	+	0.0172091i
$964$		0			0
$965$	11.5699	+	35.6084i	0.372447	+	1.14627i
$966$		0			0
$967$	−30.0762	+	21.8516i	−0.967185	+	0.702701i	−0.954808	−	0.297222i	$-0.903940\pi$
$967$	−30.0762	+	21.8516i	−0.967185	+	0.702701i	−0.0123769	+	0.999923i	$0.503940\pi$
$968$		0			0
$969$	30.6482	+	22.2672i	0.984562	+	0.715326i
$970$		0			0
$971$	11.6985	−	36.0042i	0.375422	−	1.15543i	−0.567771	−	0.823186i	$-0.692194\pi$
$971$	11.6985	−	36.0042i	0.375422	−	1.15543i	0.943193	−	0.332244i	$-0.107806\pi$
$972$		0			0
$973$	45.2903	−	32.9053i	1.45194	−	1.05490i
$974$		0			0
$975$	−27.5797			−0.883258
$976$		0			0
$977$	8.78221	+	27.0288i	0.280968	+	0.864730i	0.987578	+	0.157127i	$0.0502232\pi$
$977$	8.78221	+	27.0288i	0.280968	+	0.864730i	−0.706611	+	0.707602i	$0.749777\pi$
$978$		0			0
$979$	−4.55718	−	3.31098i	−0.145648	−	0.105820i
$980$		0			0
$981$	14.8382			0.473747
$982$		0			0
$983$	−35.6604			−1.13739			−0.568695	−	0.822549i	$-0.692551\pi$
$983$	−35.6604			−1.13739			−0.568695	+	0.822549i	$0.692551\pi$
$984$		0			0
$985$	67.0560			2.13658
$986$		0			0
$987$	111.853			3.56031
$988$		0			0
$989$	−3.03670	−	2.20629i	−0.0965616	−	0.0701561i
$990$		0			0
$991$	0.662613	+	2.03931i	0.0210486	+	0.0647809i	0.961029	−	0.276447i	$-0.0891571\pi$
$991$	0.662613	+	2.03931i	0.0210486	+	0.0647809i	−0.939980	+	0.341228i	$0.889157\pi$
$992$		0			0
$993$	−51.3547			−1.62969
$994$		0			0
$995$	−37.0684	+	26.9317i	−1.17515	+	0.853794i
$996$		0			0
$997$	−3.10406	+	9.55333i	−0.0983067	+	0.302557i	−0.988101	−	0.153804i	$-0.950847\pi$
$997$	−3.10406	+	9.55333i	−0.0983067	+	0.302557i	0.889795	+	0.456361i	$0.150847\pi$
$998$		0			0
$999$	2.93648	+	2.13348i	0.0929062	+	0.0675003i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	656.2.u.h.385.1		20
4.3	odd	2		328.2.m.c.57.5	✓	20
41.18	even	5	inner	656.2.u.h.305.1		20
164.59	odd	10		328.2.m.c.305.5	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
328.2.m.c.57.5	✓	20	4.3	odd	2
328.2.m.c.305.5	yes	20	164.59	odd	10
656.2.u.h.305.1		20	41.18	even	5	inner
656.2.u.h.385.1		20	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 656 = 2^{4} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	656.u (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q-2.22845 q^{3} +(2.81973 + 2.04866i) q^{5} +(1.29202 + 3.97642i) q^{7} +1.96600 q^{9} +O(q^{10})\)	\(q-2.22845 q^{3} +(2.81973 + 2.04866i) q^{5} +(1.29202 + 3.97642i) q^{7} +1.96600 q^{9} +(0.394664 - 0.286740i) q^{11} +(0.535047 - 1.64671i) q^{13} +(-6.28364 - 4.56533i) q^{15} +(-5.48006 + 3.98150i) q^{17} +(0.775530 + 2.38683i) q^{19} +(-2.87920 - 8.86127i) q^{21} +(2.77905 - 8.55304i) q^{23} +(2.20882 + 6.79803i) q^{25} +2.30422 q^{27} +(-0.697111 - 0.506481i) q^{29} +(-6.34676 + 4.61119i) q^{31} +(-0.879490 + 0.638987i) q^{33} +(-4.50317 + 13.8593i) q^{35} +(1.27440 + 0.925902i) q^{37} +(-1.19233 + 3.66961i) q^{39} +(-4.65470 + 4.39702i) q^{41} +(0.128977 - 0.396951i) q^{43} +(5.54360 + 4.02766i) q^{45} +(-3.70970 + 11.4173i) q^{47} +(-8.47950 + 6.16072i) q^{49} +(12.2121 - 8.87258i) q^{51} +(10.1959 + 7.40779i) q^{53} +1.70028 q^{55} +(-1.72823 - 5.31895i) q^{57} +(0.698854 - 2.15085i) q^{59} +(-2.52557 - 7.77289i) q^{61} +(2.54011 + 7.81765i) q^{63} +(4.88222 - 3.54714i) q^{65} +(4.48719 + 3.26013i) q^{67} +(-6.19299 + 19.0601i) q^{69} +(6.10826 - 4.43791i) q^{71} -1.26830 q^{73} +(-4.92224 - 15.1491i) q^{75} +(1.65011 + 1.19888i) q^{77} +0.138508 q^{79} -11.0328 q^{81} -4.56299 q^{83} -23.6090 q^{85} +(1.55348 + 1.12867i) q^{87} +(-3.56822 - 10.9818i) q^{89} +7.23929 q^{91} +(14.1435 - 10.2758i) q^{93} +(-2.70302 + 8.31903i) q^{95} +(2.97618 + 2.16232i) q^{97} +(0.775910 - 0.563731i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 2 q^{3} + 2 q^{5} + 10 q^{9}+O(q^{10}) \) 20 * q - 2 * q^3 + 2 * q^5 + 10 * q^9	\( 20 q - 2 q^{3} + 2 q^{5} + 10 q^{9} - 9 q^{11} + 7 q^{13} - q^{15} - 8 q^{17} - q^{19} - 6 q^{21} + 11 q^{23} + 15 q^{25} - 2 q^{27} + 21 q^{29} + 5 q^{31} + 19 q^{33} - 4 q^{37} - 4 q^{39} + 9 q^{41} + 17 q^{43} + 11 q^{45} - 15 q^{47} - 25 q^{49} + 22 q^{51} + 10 q^{53} + 28 q^{55} - 20 q^{57} + 24 q^{59} + 15 q^{61} + 65 q^{63} - 29 q^{65} + 26 q^{67} - 47 q^{69} - 16 q^{71} + 14 q^{73} - 11 q^{75} + 12 q^{77} + 26 q^{79} - 60 q^{81} - 20 q^{83} - 94 q^{85} - 57 q^{87} + 5 q^{89} + 46 q^{91} + 43 q^{93} - 71 q^{95} - 22 q^{97} - 8 q^{99}+O(q^{100}) \) 20 * q - 2 * q^3 + 2 * q^5 + 10 * q^9 - 9 * q^11 + 7 * q^13 - q^15 - 8 * q^17 - q^19 - 6 * q^21 + 11 * q^23 + 15 * q^25 - 2 * q^27 + 21 * q^29 + 5 * q^31 + 19 * q^33 - 4 * q^37 - 4 * q^39 + 9 * q^41 + 17 * q^43 + 11 * q^45 - 15 * q^47 - 25 * q^49 + 22 * q^51 + 10 * q^53 + 28 * q^55 - 20 * q^57 + 24 * q^59 + 15 * q^61 + 65 * q^63 - 29 * q^65 + 26 * q^67 - 47 * q^69 - 16 * q^71 + 14 * q^73 - 11 * q^75 + 12 * q^77 + 26 * q^79 - 60 * q^81 - 20 * q^83 - 94 * q^85 - 57 * q^87 + 5 * q^89 + 46 * q^91 + 43 * q^93 - 71 * q^95 - 22 * q^97 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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