LMFDB - Embedded newform 968.2.i.t.81.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [968,2,Mod(9,968)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(968, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 6]))

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

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

chi := DirichletCharacter("968.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 968 = 2^{3} \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	968.i (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:	$7.72951891566$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.682515625.5
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 5x^{6} + 2x^{5} + 19x^{4} + 28x^{3} + 100x^{2} + 88x + 121 $ x^8 - 3x^7 + 5x^6 + 2x^5 + 19x^4 + 28x^3 + 100x^2 + 88*x + 121
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 88)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			81.1
Root			$-1.20316 + 0.874145i$ of defining polynomial
Character	$\chi$	$=$	968.81
Dual form			968.2.i.t.729.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.284027 + 0.874145i) q^{3} +(3.25577 - 2.36545i) q^{5} +(1.15055 + 3.54102i) q^{7} +(1.74359 + 1.26679i) q^{9} +O(q^{10})$	\(q+(-0.284027 + 0.874145i) q^{3} +(3.25577 - 2.36545i) q^{5} +(1.15055 + 3.54102i) q^{7} +(1.74359 + 1.26679i) q^{9} +(0.849452 + 0.617163i) q^{13} +(1.14302 + 3.51787i) q^{15} +(-0.764328 + 0.555317i) q^{17} +(-0.736068 + 2.26538i) q^{19} -3.42216 q^{21} -1.73830 q^{23} +(3.45957 - 10.6474i) q^{25} +(-3.83337 + 2.78510i) q^{27} +(0.849452 + 2.61434i) q^{29} +(-3.87380 - 2.81448i) q^{31} +(12.1220 + 8.80718i) q^{35} +(0.653574 + 2.01149i) q^{37} +(-0.780757 + 0.567253i) q^{39} +(2.82119 - 8.68274i) q^{41} -0.431946 q^{43} +8.67327 q^{45} +(1.95467 - 6.01586i) q^{47} +(-5.55197 + 4.03374i) q^{49} +(-0.268338 - 0.825859i) q^{51} +(-0.255767 - 0.185826i) q^{53} +(-1.77121 - 1.28686i) q^{57} +(2.50000 + 7.69421i) q^{59} +(-11.0290 + 8.01304i) q^{61} +(-2.47966 + 7.63161i) q^{63} +4.22549 q^{65} +5.68178 q^{67} +(0.493725 - 1.51953i) q^{69} +(10.4110 - 7.56401i) q^{71} +(1.08815 + 3.34898i) q^{73} +(8.32481 + 6.04833i) q^{75} +(-7.14927 - 5.19425i) q^{79} +(0.652173 + 2.00718i) q^{81} +(11.8656 - 8.62089i) q^{83} +(-1.17490 + 3.61596i) q^{85} -2.52658 q^{87} +2.43195 q^{89} +(-1.20805 + 3.71800i) q^{91} +(3.56053 - 2.58688i) q^{93} +(2.96219 + 9.11670i) q^{95} +(-1.19890 - 0.871054i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - q^{3} + 2 q^{5} + 8 q^{7} + 7 q^{9}+O(q^{10}) $ 8 * q - q^3 + 2 * q^5 + 8 * q^7 + 7 * q^9	$ 8 q - q^{3} + 2 q^{5} + 8 q^{7} + 7 q^{9} + 8 q^{13} - 3 q^{15} - 11 q^{17} + 12 q^{19} + 2 q^{21} - 4 q^{23} + 22 q^{25} + 8 q^{27} + 8 q^{29} + 2 q^{31} + 29 q^{35} - 14 q^{37} + 21 q^{39} + q^{41} - 6 q^{43} + 44 q^{45} - 6 q^{47} - 2 q^{49} + 52 q^{51} + 22 q^{53} + q^{57} + 20 q^{59} - 26 q^{61} + 5 q^{63} + 10 q^{65} - 10 q^{67} + 42 q^{69} + 30 q^{71} - 13 q^{73} - q^{75} + 6 q^{79} - 6 q^{81} + 20 q^{83} + 26 q^{85} + 6 q^{87} + 22 q^{89} - 13 q^{91} + 15 q^{93} + 13 q^{95} - 12 q^{97}+O(q^{100}) $ 8 * q - q^3 + 2 * q^5 + 8 * q^7 + 7 * q^9 + 8 * q^13 - 3 * q^15 - 11 * q^17 + 12 * q^19 + 2 * q^21 - 4 * q^23 + 22 * q^25 + 8 * q^27 + 8 * q^29 + 2 * q^31 + 29 * q^35 - 14 * q^37 + 21 * q^39 + q^41 - 6 * q^43 + 44 * q^45 - 6 * q^47 - 2 * q^49 + 52 * q^51 + 22 * q^53 + q^57 + 20 * q^59 - 26 * q^61 + 5 * q^63 + 10 * q^65 - 10 * q^67 + 42 * q^69 + 30 * q^71 - 13 * q^73 - q^75 + 6 * q^79 - 6 * q^81 + 20 * q^83 + 26 * q^85 + 6 * q^87 + 22 * q^89 - 13 * q^91 + 15 * q^93 + 13 * q^95 - 12 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/968\mathbb{Z}\right)^\times$.

$n$	$485$	$727$	$849$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{5}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.284027	+	0.874145i	−0.163983	+	0.504688i	−0.998960	−	0.0455971i	$-0.985481\pi$
$3$	−0.284027	+	0.874145i	−0.163983	+	0.504688i	0.834977	+	0.550285i	$0.185481\pi$
$4$		0			0
$5$	3.25577	−	2.36545i	1.45602	−	1.05786i	0.471647	−	0.881788i	$-0.343660\pi$
$5$	3.25577	−	2.36545i	1.45602	−	1.05786i	0.984377	−	0.176075i	$-0.0563402\pi$
$6$		0			0
$7$	1.15055	+	3.54102i	0.434866	+	1.33838i	0.893223	+	0.449613i	$0.148438\pi$
$7$	1.15055	+	3.54102i	0.434866	+	1.33838i	−0.458357	+	0.888768i	$0.651562\pi$
$8$		0			0
$9$	1.74359	+	1.26679i	0.581197	+	0.422265i
$10$		0			0
$11$		0			0
$11$		0			0
$12$		0			0
$13$	0.849452	+	0.617163i	0.235595	+	0.171170i	0.699319	−	0.714810i	$-0.253487\pi$
$13$	0.849452	+	0.617163i	0.235595	+	0.171170i	−0.463723	+	0.885980i	$0.653487\pi$
$14$		0			0
$15$	1.14302	+	3.51787i	0.295128	+	0.908309i
$16$		0			0
$17$	−0.764328	+	0.555317i	−0.185377	+	0.134684i	−0.676603	−	0.736348i	$-0.736549\pi$
$17$	−0.764328	+	0.555317i	−0.185377	+	0.134684i	0.491226	+	0.871032i	$0.336549\pi$
$18$		0			0
$19$	−0.736068	+	2.26538i	−0.168866	+	0.519715i	−0.999300	−	0.0374011i	$-0.988092\pi$
$19$	−0.736068	+	2.26538i	−0.168866	+	0.519715i	0.830435	+	0.557116i	$0.188092\pi$
$20$		0			0
$21$	−3.42216			−0.746776
$22$		0			0
$23$	−1.73830			−0.362461			−0.181230	−	0.983441i	$-0.558008\pi$
$23$	−1.73830			−0.362461			−0.181230	+	0.983441i	$0.558008\pi$
$24$		0			0
$25$	3.45957	−	10.6474i	0.691913	−	2.12949i
$26$		0			0
$27$	−3.83337	+	2.78510i	−0.737732	+	0.535993i
$28$		0			0
$29$	0.849452	+	2.61434i	0.157739	+	0.485471i	0.998428	−	0.0560470i	$-0.0178497\pi$
$29$	0.849452	+	2.61434i	0.157739	+	0.485471i	−0.840689	+	0.541518i	$0.817850\pi$
$30$		0			0
$31$	−3.87380	−	2.81448i	−0.695755	−	0.505496i	0.182792	−	0.983152i	$-0.441487\pi$
$31$	−3.87380	−	2.81448i	−0.695755	−	0.505496i	−0.878547	+	0.477656i	$0.841487\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	12.1220	+	8.80718i	2.04900	+	1.48869i
$36$		0			0
$37$	0.653574	+	2.01149i	0.107447	+	0.330687i	0.990297	−	0.138967i	$-0.0443784\pi$
$37$	0.653574	+	2.01149i	0.107447	+	0.330687i	−0.882850	+	0.469655i	$0.844378\pi$
$38$		0			0
$39$	−0.780757	+	0.567253i	−0.125021	+	0.0908332i
$40$		0			0
$41$	2.82119	−	8.68274i	0.440596	−	1.35602i	−0.446646	−	0.894711i	$-0.647382\pi$
$41$	2.82119	−	8.68274i	0.440596	−	1.35602i	0.887242	−	0.461305i	$-0.152618\pi$
$42$		0			0
$43$	−0.431946			−0.0658711			−0.0329356	−	0.999457i	$-0.510486\pi$
$43$	−0.431946			−0.0658711			−0.0329356	+	0.999457i	$0.510486\pi$
$44$		0			0
$45$	8.67327			1.29294
$46$		0			0
$47$	1.95467	−	6.01586i	0.285118	−	0.877503i	−0.701245	−	0.712920i	$-0.747372\pi$
$47$	1.95467	−	6.01586i	0.285118	−	0.877503i	0.986363	−	0.164583i	$-0.0526278\pi$
$48$		0			0
$49$	−5.55197	+	4.03374i	−0.793138	+	0.576249i
$50$		0			0
$51$	−0.268338	−	0.825859i	−0.0375748	−	0.115643i
$52$		0			0
$53$	−0.255767	−	0.185826i	−0.0351323	−	0.0255251i	0.570081	−	0.821589i	$-0.306912\pi$
$53$	−0.255767	−	0.185826i	−0.0351323	−	0.0255251i	−0.605213	+	0.796064i	$0.706912\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−1.77121	−	1.28686i	−0.234603	−	0.170449i
$58$		0			0
$59$	2.50000	+	7.69421i	0.325472	+	1.00170i	0.971227	+	0.238156i	$0.0765429\pi$
$59$	2.50000	+	7.69421i	0.325472	+	1.00170i	−0.645755	+	0.763545i	$0.723457\pi$
$60$		0			0
$61$	−11.0290	+	8.01304i	−1.41212	+	1.02596i	−0.419108	+	0.907936i	$0.637657\pi$
$61$	−11.0290	+	8.01304i	−1.41212	+	1.02596i	−0.993010	+	0.118028i	$0.962343\pi$
$62$		0			0
$63$	−2.47966	+	7.63161i	−0.312408	+	0.961492i
$64$		0			0
$65$	4.22549			0.524107
$66$		0			0
$67$	5.68178			0.694140			0.347070	−	0.937839i	$-0.387177\pi$
$67$	5.68178			0.694140			0.347070	+	0.937839i	$0.387177\pi$
$68$		0			0
$69$	0.493725	−	1.51953i	0.0594375	−	0.182930i
$70$		0			0
$71$	10.4110	−	7.56401i	1.23555	−	0.897683i	0.238260	−	0.971201i	$-0.423423\pi$
$71$	10.4110	−	7.56401i	1.23555	−	0.897683i	0.997294	+	0.0735185i	$0.0234228\pi$
$72$		0			0
$73$	1.08815	+	3.34898i	0.127358	+	0.391968i	0.994323	−	0.106401i	$-0.0339326\pi$
$73$	1.08815	+	3.34898i	0.127358	+	0.391968i	−0.866965	+	0.498369i	$0.833933\pi$
$74$		0			0
$75$	8.32481	+	6.04833i	0.961266	+	0.698400i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−7.14927	−	5.19425i	−0.804355	−	0.584398i	0.107833	−	0.994169i	$-0.465609\pi$
$79$	−7.14927	−	5.19425i	−0.804355	−	0.584398i	−0.912189	+	0.409771i	$0.865609\pi$
$80$		0			0
$81$	0.652173	+	2.00718i	0.0724637	+	0.223020i
$82$		0			0
$83$	11.8656	−	8.62089i	1.30242	−	0.946266i	0.302447	−	0.953166i	$-0.402197\pi$
$83$	11.8656	−	8.62089i	1.30242	−	0.946266i	0.999976	+	0.00690080i	$0.00219661\pi$
$84$		0			0
$85$	−1.17490	+	3.61596i	−0.127436	+	0.392206i
$86$		0			0
$87$	−2.52658			−0.270878
$88$		0			0
$89$	2.43195			0.257786			0.128893	−	0.991659i	$-0.458858\pi$
$89$	2.43195			0.257786			0.128893	+	0.991659i	$0.458858\pi$
$90$		0			0
$91$	−1.20805	+	3.71800i	−0.126638	+	0.389753i
$92$		0			0
$93$	3.56053	−	2.58688i	0.369210	−	0.268247i
$94$		0			0
$95$	2.96219	+	9.11670i	0.303915	+	0.935353i
$96$		0			0
$97$	−1.19890	−	0.871054i	−0.121730	−	0.0884422i	0.525254	−	0.850945i	$-0.323970\pi$
$97$	−1.19890	−	0.871054i	−0.121730	−	0.0884422i	−0.646985	+	0.762503i	$0.723970\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−3.51747	−	2.55559i	−0.350001	−	0.254291i	0.398869	−	0.917008i	$-0.369403\pi$
$101$	−3.51747	−	2.55559i	−0.350001	−	0.254291i	−0.748869	+	0.662718i	$0.769403\pi$
$102$		0			0
$103$	3.42681	+	10.5466i	0.337653	+	1.03919i	0.965400	+	0.260772i	$0.0839772\pi$
$103$	3.42681	+	10.5466i	0.337653	+	1.03919i	−0.627747	+	0.778417i	$0.716023\pi$
$104$		0			0
$105$	−11.1417	+	8.09495i	−1.08732	+	0.789986i
$106$		0			0
$107$	−2.95204	+	9.08545i	−0.285385	+	0.878323i	0.700899	+	0.713261i	$0.252783\pi$
$107$	−2.95204	+	9.08545i	−0.285385	+	0.878323i	−0.986283	+	0.165062i	$0.947217\pi$
$108$		0			0
$109$	−4.14866			−0.397369			−0.198685	−	0.980063i	$-0.563667\pi$
$109$	−4.14866			−0.397369			−0.198685	+	0.980063i	$0.563667\pi$
$110$		0			0
$111$	−1.94397			−0.184513
$112$		0			0
$113$	−2.87218	+	8.83965i	−0.270192	+	0.831564i	0.720260	+	0.693704i	$0.244022\pi$
$113$	−2.87218	+	8.83965i	−0.270192	+	0.831564i	−0.990452	+	0.137860i	$0.955978\pi$
$114$		0			0
$115$	−5.65950	+	4.11187i	−0.527752	+	0.383434i
$116$		0			0
$117$	0.699279	+	2.15216i	0.0646484	+	0.198967i
$118$		0			0
$119$	−2.84579	−	2.06758i	−0.260873	−	0.189535i
$120$		0			0
$121$		0			0
$122$		0			0
$123$	6.78868	+	4.93226i	0.612114	+	0.444727i
$124$		0			0
$125$	−7.70454	−	23.7121i	−0.689115	−	2.12088i
$126$		0			0
$127$	6.43660	−	4.67646i	0.571156	−	0.414969i	−0.264369	−	0.964422i	$-0.585164\pi$
$127$	6.43660	−	4.67646i	0.571156	−	0.414969i	0.835525	+	0.549453i	$0.185164\pi$
$128$		0			0
$129$	0.122684	−	0.377584i	0.0108018	−	0.0332444i
$130$		0			0
$131$	−12.2670			−1.07177			−0.535885	−	0.844291i	$-0.680022\pi$
$131$	−12.2670			−1.07177			−0.535885	+	0.844291i	$0.680022\pi$
$132$		0			0
$133$	−8.86866			−0.769010
$134$		0			0
$135$	−5.89252	+	18.1353i	−0.507147	+	1.56084i
$136$		0			0
$137$	2.03716	−	1.48009i	0.174047	−	0.126452i	−0.497351	−	0.867549i	$-0.665694\pi$
$137$	2.03716	−	1.48009i	0.174047	−	0.126452i	0.671398	+	0.741097i	$0.265694\pi$
$138$		0			0
$139$	−4.35573	−	13.4055i	−0.369448	−	1.13704i	−0.947149	−	0.320795i	$-0.896050\pi$
$139$	−4.35573	−	13.4055i	−0.369448	−	1.13704i	0.577701	−	0.816249i	$-0.303950\pi$
$140$		0			0
$141$	4.70355	+	3.41733i	0.396111	+	0.287791i
$142$		0			0
$143$		0			0
$144$		0			0
$145$	8.94972	+	6.50235i	0.743234	+	0.539991i
$146$		0			0
$147$	−1.94917	−	5.99892i	−0.160765	−	0.494782i
$148$		0			0
$149$	8.63645	−	6.27475i	0.707526	−	0.514048i	−0.174849	−	0.984595i	$-0.555944\pi$
$149$	8.63645	−	6.27475i	0.707526	−	0.514048i	0.882375	+	0.470548i	$0.155944\pi$
$150$		0			0
$151$	6.25577	−	19.2533i	0.509087	−	1.56681i	−0.284702	−	0.958616i	$-0.591895\pi$
$151$	6.25577	−	19.2533i	0.509087	−	1.56681i	0.793789	−	0.608193i	$-0.208105\pi$
$152$		0			0
$153$	−2.03615			−0.164613
$154$		0			0
$155$	−19.2697			−1.54778
$156$		0			0
$157$	5.99811	−	18.4603i	0.478701	−	1.47329i	−0.362199	−	0.932101i	$-0.617974\pi$
$157$	5.99811	−	18.4603i	0.478701	−	1.47329i	0.840900	−	0.541190i	$-0.182026\pi$
$158$		0			0
$159$	0.235083	−	0.170798i	0.0186433	−	0.0135452i
$160$		0			0
$161$	−2.00000	−	6.15537i	−0.157622	−	0.485111i
$162$		0			0
$163$	−15.2693	−	11.0938i	−1.19599	−	0.868934i	−0.202102	−	0.979365i	$-0.564777\pi$
$163$	−15.2693	−	11.0938i	−1.19599	−	0.868934i	−0.993884	+	0.110430i	$0.964777\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−14.3716	−	10.4416i	−1.11211	−	0.807992i	−0.129111	−	0.991630i	$-0.541212\pi$
$167$	−14.3716	−	10.4416i	−1.11211	−	0.807992i	−0.982994	+	0.183638i	$0.941212\pi$
$168$		0			0
$169$	−3.67654	−	11.3152i	−0.282811	−	0.870403i
$170$		0			0
$171$	−4.15318	+	3.01746i	−0.317601	+	0.230751i
$172$		0			0
$173$	1.96397	−	6.04448i	0.149318	−	0.459553i	−0.848223	−	0.529639i	$-0.822327\pi$
$173$	1.96397	−	6.04448i	0.149318	−	0.459553i	0.997541	+	0.0700858i	$0.0223273\pi$
$174$		0			0
$175$	41.6833			3.15096
$176$		0			0
$177$	−7.43592			−0.558918
$178$		0			0
$179$	−0.434971	+	1.33870i	−0.0325113	+	0.100059i	−0.965995	−	0.258559i	$-0.916752\pi$
$179$	−0.434971	+	1.33870i	−0.0325113	+	0.100059i	0.933484	+	0.358619i	$0.116752\pi$
$180$		0			0
$181$	−14.0290	+	10.1927i	−1.04277	+	0.757615i	−0.970824	−	0.239794i	$-0.922920\pi$
$181$	−14.0290	+	10.1927i	−1.04277	+	0.757615i	−0.0719435	+	0.997409i	$0.522920\pi$
$182$		0			0
$183$	−3.87202	−	11.9169i	−0.286228	−	0.880920i
$184$		0			0
$185$	6.88598	+	5.00295i	0.506267	+	0.367825i
$186$		0			0
$187$		0			0
$188$		0			0
$189$	−14.2726	−	10.3696i	−1.03818	−	0.754281i
$190$		0			0
$191$	−2.15985	−	6.64733i	−0.156281	−	0.480984i	0.842007	−	0.539466i	$-0.181374\pi$
$191$	−2.15985	−	6.64733i	−0.156281	−	0.480984i	−0.998288	+	0.0584821i	$0.981374\pi$
$192$		0			0
$193$	18.8818	−	13.7184i	1.35914	−	0.987475i	0.360644	−	0.932703i	$-0.382557\pi$
$193$	18.8818	−	13.7184i	1.35914	−	0.987475i	0.998499	−	0.0547719i	$-0.0174432\pi$
$194$		0			0
$195$	−1.20015	+	3.69369i	−0.0859447	+	0.264511i
$196$		0			0
$197$	10.8142			0.770481			0.385240	−	0.922816i	$-0.374119\pi$
$197$	10.8142			0.770481			0.385240	+	0.922816i	$0.374119\pi$
$198$		0			0
$199$	9.07433			0.643262			0.321631	−	0.946865i	$-0.395769\pi$
$199$	9.07433			0.643262			0.321631	+	0.946865i	$0.395769\pi$
$200$		0			0
$201$	−1.61378	+	4.96670i	−0.113827	+	0.350324i
$202$		0			0
$203$	−8.28012	+	6.01586i	−0.581150	+	0.422230i
$204$		0			0
$205$	−11.3535	−	34.9424i	−0.792960	−	2.44048i
$206$		0			0
$207$	−3.03089	−	2.20207i	−0.210661	−	0.153054i
$208$		0			0
$209$		0			0
$210$		0			0
$211$	−1.93066	−	1.40271i	−0.132912	−	0.0965666i	0.519343	−	0.854566i	$-0.326177\pi$
$211$	−1.93066	−	1.40271i	−0.132912	−	0.0965666i	−0.652255	+	0.758000i	$0.726177\pi$
$212$		0			0
$213$	3.65505	+	11.2491i	0.250440	+	0.770774i
$214$		0			0
$215$	−1.40632	+	1.02175i	−0.0959099	+	0.0696826i
$216$		0			0
$217$	5.50915	−	16.9554i	0.373985	−	1.15101i
$218$		0			0
$219$	−3.23656			−0.218706
$220$		0			0
$221$	−0.991980			−0.0667278
$222$		0			0
$223$	−4.75274	+	14.6274i	−0.318267	+	0.979526i	0.656122	+	0.754655i	$0.272196\pi$
$223$	−4.75274	+	14.6274i	−0.318267	+	0.979526i	−0.974389	+	0.224870i	$0.927804\pi$
$224$		0			0
$225$	19.5202	−	14.1823i	1.30135	−	0.945483i
$226$		0			0
$227$	3.87543	+	11.9273i	0.257221	+	0.791645i	0.993384	+	0.114841i	$0.0366357\pi$
$227$	3.87543	+	11.9273i	0.257221	+	0.791645i	−0.736163	+	0.676804i	$0.763364\pi$
$228$		0			0
$229$	−10.7929	−	7.84152i	−0.713217	−	0.518182i	0.170993	−	0.985272i	$-0.445302\pi$
$229$	−10.7929	−	7.84152i	−0.713217	−	0.518182i	−0.884210	+	0.467090i	$0.845302\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−18.9952	−	13.8008i	−1.24442	−	0.904122i	−0.246533	−	0.969134i	$-0.579291\pi$
$233$	−18.9952	−	13.8008i	−1.24442	−	0.904122i	−0.997884	+	0.0650124i	$0.979291\pi$
$234$		0			0
$235$	−7.86628	−	24.2099i	−0.513139	−	1.57928i
$236$		0			0
$237$	6.57111	−	4.77419i	0.426840	−	0.310117i
$238$		0			0
$239$	−1.15380	+	3.55103i	−0.0746330	+	0.229697i	−0.981413	−	0.191907i	$-0.938533\pi$
$239$	−1.15380	+	3.55103i	−0.0746330	+	0.229697i	0.906780	+	0.421604i	$0.138533\pi$
$240$		0			0
$241$	−15.9621			−1.02821			−0.514104	−	0.857728i	$-0.671875\pi$
$241$	−15.9621			−1.02821			−0.514104	+	0.857728i	$0.671875\pi$
$242$		0			0
$243$	−16.1547			−1.03633
$244$		0			0
$245$	−8.53429	+	26.2658i	−0.545236	+	1.67806i
$246$		0			0
$247$	−2.02336	+	1.47006i	−0.128744	+	0.0935377i
$248$		0			0
$249$	4.16575	+	12.8209i	0.263994	+	0.812489i
$250$		0			0
$251$	8.96525	+	6.51364i	0.565882	+	0.411137i	0.833607	−	0.552358i	$-0.186272\pi$
$251$	8.96525	+	6.51364i	0.565882	+	0.411137i	−0.267725	+	0.963495i	$0.586272\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$	−2.82717	−	2.05406i	−0.177045	−	0.128630i
$256$		0			0
$257$	4.63057	+	14.2514i	0.288847	+	0.888980i	0.985219	+	0.171299i	$0.0547964\pi$
$257$	4.63057	+	14.2514i	0.288847	+	0.888980i	−0.696372	+	0.717681i	$0.745204\pi$
$258$		0			0
$259$	−6.37078	+	4.62864i	−0.395861	+	0.287610i
$260$		0			0
$261$	−1.83074	+	5.63443i	−0.113320	+	0.348762i
$262$		0			0
$263$	−8.96129			−0.552577			−0.276288	−	0.961075i	$-0.589104\pi$
$263$	−8.96129			−0.552577			−0.276288	+	0.961075i	$0.589104\pi$
$264$		0			0
$265$	−1.27228			−0.0781555
$266$		0			0
$267$	−0.690738	+	2.12587i	−0.0422725	+	0.130101i
$268$		0			0
$269$	−0.849452	+	0.617163i	−0.0517920	+	0.0376291i	−0.613380	−	0.789788i	$-0.710191\pi$
$269$	−0.849452	+	0.617163i	−0.0517920	+	0.0376291i	0.561588	+	0.827417i	$0.310191\pi$
$270$		0			0
$271$	−5.61338	−	17.2762i	−0.340989	−	1.04946i	−0.963696	−	0.267001i	$-0.913967\pi$
$271$	−5.61338	−	17.2762i	−0.340989	−	1.04946i	0.622708	−	0.782455i	$-0.286033\pi$
$272$		0			0
$273$	−2.90696	−	2.11203i	−0.175937	−	0.127826i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	16.1342	+	11.7222i	0.969411	+	0.704318i	0.955317	−	0.295582i	$-0.0955136\pi$
$277$	16.1342	+	11.7222i	0.969411	+	0.704318i	0.0140939	+	0.999901i	$0.495514\pi$
$278$		0			0
$279$	−3.18896	−	9.81462i	−0.190918	−	0.587586i
$280$		0			0
$281$	−16.9952	+	12.3477i	−1.01385	+	0.736604i	−0.965013	−	0.262202i	$-0.915551\pi$
$281$	−16.9952	+	12.3477i	−1.01385	+	0.736604i	−0.0488360	+	0.998807i	$0.515551\pi$
$282$		0			0
$283$	−2.02295	+	6.22600i	−0.120252	+	0.370097i	−0.993006	−	0.118063i	$-0.962332\pi$
$283$	−2.02295	+	6.22600i	−0.120252	+	0.370097i	0.872754	+	0.488160i	$0.162332\pi$
$284$		0			0
$285$	−8.81066			−0.521899
$286$		0			0
$287$	33.9917			2.00647
$288$		0			0
$289$	−4.97747	+	15.3191i	−0.292792	+	0.901122i
$290$		0			0
$291$	1.10195	−	0.800613i	0.0645974	−	0.0469327i
$292$		0			0
$293$	4.95142	+	15.2389i	0.289265	+	0.890266i	0.985088	+	0.172053i	$0.0550399\pi$
$293$	4.95142	+	15.2389i	0.289265	+	0.890266i	−0.695823	+	0.718214i	$0.744960\pi$
$294$		0			0
$295$	26.3397	+	19.1369i	1.53356	+	1.11419i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−1.47660	−	1.07281i	−0.0853942	−	0.0620425i
$300$		0			0
$301$	−0.496975	−	1.52953i	−0.0286451	−	0.0881607i
$302$		0			0
$303$	3.23301	−	2.34892i	0.185732	−	0.134942i
$304$		0			0
$305$	−16.9534	+	52.1772i	−0.970748	+	2.98766i
$306$		0			0
$307$	−10.8016			−0.616478			−0.308239	−	0.951309i	$-0.599740\pi$
$307$	−10.8016			−0.616478			−0.308239	+	0.951309i	$0.599740\pi$
$308$		0			0
$309$	−10.1926			−0.579836
$310$		0			0
$311$	0.985560	−	3.03324i	0.0558860	−	0.171999i	−0.919217	−	0.393751i	$-0.871177\pi$
$311$	0.985560	−	3.03324i	0.0558860	−	0.171999i	0.975103	+	0.221751i	$0.0711773\pi$
$312$		0			0
$313$	−12.1799	+	8.84925i	−0.688451	+	0.500189i	−0.876151	−	0.482037i	$-0.839897\pi$
$313$	−12.1799	+	8.84925i	−0.688451	+	0.500189i	0.187699	+	0.982227i	$0.439897\pi$
$314$		0			0
$315$	9.97902	+	30.7123i	0.562254	+	1.73044i
$316$		0			0
$317$	−10.7194	−	7.78810i	−0.602061	−	0.437423i	0.244549	−	0.969637i	$-0.421360\pi$
$317$	−10.7194	−	7.78810i	−0.602061	−	0.437423i	−0.846610	+	0.532214i	$0.821360\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	−7.10354	−	5.16103i	−0.396481	−	0.288060i
$322$		0			0
$323$	−0.695408	−	2.14025i	−0.0386936	−	0.119087i
$324$		0			0
$325$	9.50994	−	6.90938i	0.527517	−	0.383263i
$326$		0			0
$327$	1.17833	−	3.62653i	0.0651619	−	0.200548i
$328$		0			0
$329$	23.5512			1.29842
$330$		0			0
$331$	−33.5540			−1.84429			−0.922147	−	0.386839i	$-0.873567\pi$
$331$	−33.5540			−1.84429			−0.922147	+	0.386839i	$0.873567\pi$
$332$		0			0
$333$	−1.40858	+	4.33517i	−0.0771898	+	0.237566i
$334$		0			0
$335$	18.4986	−	13.4400i	1.01068	−	0.734305i
$336$		0			0
$337$	−2.13387	−	6.56739i	−0.116240	−	0.357749i	0.875964	−	0.482376i	$-0.160226\pi$
$337$	−2.13387	−	6.56739i	−0.116240	−	0.357749i	−0.992204	+	0.124628i	$0.960226\pi$
$338$		0			0
$339$	−6.91136	−	5.02140i	−0.375374	−	0.272725i
$340$		0			0
$341$		0			0
$342$		0			0
$343$	0.413840	+	0.300672i	0.0223453	+	0.0162348i
$344$		0			0
$345$	−1.98692	−	6.11511i	−0.106972	−	0.329227i
$346$		0			0
$347$	−16.7459	+	12.1666i	−0.898968	+	0.653139i	−0.938201	−	0.346091i	$-0.887509\pi$
$347$	−16.7459	+	12.1666i	−0.898968	+	0.653139i	0.0392324	+	0.999230i	$0.487509\pi$
$348$		0			0
$349$	3.41671	−	10.5156i	0.182893	−	0.562885i	−0.817013	−	0.576619i	$-0.804372\pi$
$349$	3.41671	−	10.5156i	0.182893	−	0.562885i	0.999906	+	0.0137337i	$0.00437172\pi$
$350$		0			0
$351$	−4.97512			−0.265552
$352$		0			0
$353$	13.5005			0.718557			0.359279	−	0.933230i	$-0.383023\pi$
$353$	13.5005			0.718557			0.359279	+	0.933230i	$0.383023\pi$
$354$		0			0
$355$	16.0034	−	49.2533i	0.849371	−	2.61409i
$356$		0			0
$357$	2.61565	−	1.90038i	0.138435	−	0.100579i
$358$		0			0
$359$	−10.3293	−	31.7903i	−0.545160	−	1.67783i	−0.720610	−	0.693341i	$-0.756138\pi$
$359$	−10.3293	−	31.7903i	−0.545160	−	1.67783i	0.175450	−	0.984488i	$-0.443862\pi$
$360$		0			0
$361$	10.7812	+	7.83297i	0.567429	+	0.412261i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	11.4646	+	8.32953i	0.600085	+	0.435987i
$366$		0			0
$367$	6.20934	+	19.1104i	0.324125	+	0.997554i	0.971834	+	0.235666i	$0.0757272\pi$
$367$	6.20934	+	19.1104i	0.324125	+	0.997554i	−0.647709	+	0.761888i	$0.724273\pi$
$368$		0			0
$369$	15.9182	−	11.5653i	0.828671	−	0.602065i
$370$		0			0
$371$	0.363741	−	1.11948i	0.0188845	−	0.0581204i
$372$		0			0
$373$	26.4379			1.36890			0.684451	−	0.729059i	$-0.260042\pi$
$373$	26.4379			1.36890			0.684451	+	0.729059i	$0.260042\pi$
$374$		0			0
$375$	22.9161			1.18338
$376$		0			0
$377$	−0.891907	+	2.74501i	−0.0459356	+	0.141375i
$378$		0			0
$379$	−16.3890	+	11.9073i	−0.841848	+	0.611638i	−0.922886	−	0.385073i	$-0.874176\pi$
$379$	−16.3890	+	11.9073i	−0.841848	+	0.611638i	0.0810382	+	0.996711i	$0.474176\pi$
$380$		0			0
$381$	2.25974	+	6.95476i	0.115770	+	0.356303i
$382$		0			0
$383$	3.72918	+	2.70941i	0.190552	+	0.138444i	0.678971	−	0.734165i	$-0.262426\pi$
$383$	3.72918	+	2.70941i	0.190552	+	0.138444i	−0.488419	+	0.872609i	$0.662426\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−0.753138	−	0.547187i	−0.0382841	−	0.0278151i
$388$		0			0
$389$	9.52597	+	29.3179i	0.482986	+	1.48648i	0.834877	+	0.550437i	$0.185539\pi$
$389$	9.52597	+	29.3179i	0.482986	+	1.48648i	−0.351891	+	0.936041i	$0.614461\pi$
$390$		0			0
$391$	1.32863	−	0.965308i	0.0671918	−	0.0488177i
$392$		0			0
$393$	3.48415	−	10.7231i	0.175752	−	0.540909i
$394$		0			0
$395$	−35.5631			−1.78937
$396$		0			0
$397$	15.9382			0.799916			0.399958	−	0.916533i	$-0.369025\pi$
$397$	15.9382			0.799916			0.399958	+	0.916533i	$0.369025\pi$
$398$		0			0
$399$	2.51894	−	7.75250i	0.126105	−	0.388110i
$400$		0			0
$401$	−18.6624	+	13.5590i	−0.931957	+	0.677106i	−0.946471	−	0.322788i	$-0.895380\pi$
$401$	−18.6624	+	13.5590i	−0.931957	+	0.677106i	0.0145141	+	0.999895i	$0.495380\pi$
$402$		0			0
$403$	−1.55361	−	4.78153i	−0.0773910	−	0.238185i
$404$		0			0
$405$	6.87122	+	4.99224i	0.341434	+	0.248066i
$406$		0			0
$407$		0			0
$408$		0			0
$409$	11.7588	+	8.54326i	0.581435	+	0.422437i	0.839241	−	0.543759i	$-0.183000\pi$
$409$	11.7588	+	8.54326i	0.581435	+	0.422437i	−0.257806	+	0.966197i	$0.583000\pi$
$410$		0			0
$411$	0.715201	+	2.20116i	0.0352783	+	0.108575i
$412$		0			0
$413$	−24.3690	+	17.7051i	−1.19912	+	0.871212i
$414$		0			0
$415$	18.2394	−	56.1352i	0.895339	−	2.75557i
$416$		0			0
$417$	12.9555			0.634436
$418$		0			0
$419$	7.34710			0.358929			0.179465	−	0.983764i	$-0.442563\pi$
$419$	7.34710			0.358929			0.179465	+	0.983764i	$0.442563\pi$
$420$		0			0
$421$	0.546346	−	1.68148i	0.0266273	−	0.0819504i	−0.936860	−	0.349705i	$-0.886282\pi$
$421$	0.546346	−	1.68148i	0.0266273	−	0.0819504i	0.963487	+	0.267755i	$0.0862817\pi$
$422$		0			0
$423$	11.0290	−	8.01304i	0.536248	−	0.389607i
$424$		0			0
$425$	3.26846	+	10.0593i	0.158544	+	0.487947i
$426$		0			0
$427$	−41.0638	−	29.8346i	−1.98721	−	1.44380i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−13.1757	−	9.57270i	−0.634651	−	0.461101i	0.223358	−	0.974737i	$-0.428298\pi$
$431$	−13.1757	−	9.57270i	−0.634651	−	0.461101i	−0.858008	+	0.513636i	$0.828298\pi$
$432$		0			0
$433$	−0.695086	−	2.13926i	−0.0334037	−	0.102806i	0.932965	−	0.359968i	$-0.117213\pi$
$433$	−0.695086	−	2.13926i	−0.0334037	−	0.102806i	−0.966368	+	0.257162i	$0.917213\pi$
$434$		0			0
$435$	−8.22597	+	5.97651i	−0.394405	+	0.286552i
$436$		0			0
$437$	1.27951	−	3.93792i	0.0612072	−	0.188376i
$438$		0			0
$439$	8.85337			0.422549			0.211274	−	0.977427i	$-0.432239\pi$
$439$	8.85337			0.422549			0.211274	+	0.977427i	$0.432239\pi$
$440$		0			0
$441$	−14.7903			−0.704300
$442$		0			0
$443$	4.93344	−	15.1836i	0.234395	−	0.721393i	−0.762806	−	0.646627i	$-0.776179\pi$
$443$	4.93344	−	15.1836i	0.234395	−	0.721393i	0.997201	−	0.0747660i	$-0.0238210\pi$
$444$		0			0
$445$	7.91785	−	5.75265i	0.375342	−	0.272702i
$446$		0			0
$447$	3.03206	+	9.33171i	0.143411	+	0.441375i
$448$		0			0
$449$	−19.2543	−	13.9890i	−0.908665	−	0.660184i	0.0320116	−	0.999487i	$-0.489809\pi$
$449$	−19.2543	−	13.9890i	−0.908665	−	0.660184i	−0.940677	+	0.339303i	$0.889809\pi$
$450$		0			0
$451$		0			0
$452$		0			0
$453$	15.0533	+	10.9369i	0.707268	+	0.513860i
$454$		0			0
$455$	4.86163	+	14.9625i	0.227917	+	0.701455i
$456$		0			0
$457$	23.9814	−	17.4235i	1.12180	−	0.815039i	0.137323	−	0.990526i	$-0.456150\pi$
$457$	23.9814	−	17.4235i	1.12180	−	0.815039i	0.984482	+	0.175488i	$0.0561503\pi$
$458$		0			0
$459$	1.38333	−	4.25746i	0.0645685	−	0.198721i
$460$		0			0
$461$	−9.00605			−0.419454			−0.209727	−	0.977760i	$-0.567257\pi$
$461$	−9.00605			−0.419454			−0.209727	+	0.977760i	$0.567257\pi$
$462$		0			0
$463$	16.0634			0.746528			0.373264	−	0.927725i	$-0.378239\pi$
$463$	16.0634			0.746528			0.373264	+	0.927725i	$0.378239\pi$
$464$		0			0
$465$	5.47312	−	16.8445i	0.253810	−	0.781147i
$466$		0			0
$467$	3.29645	−	2.39501i	0.152541	−	0.110828i	−0.508897	−	0.860828i	$-0.669946\pi$
$467$	3.29645	−	2.39501i	0.152541	−	0.110828i	0.661438	+	0.750000i	$0.269946\pi$
$468$		0			0
$469$	6.53716	+	20.1193i	0.301858	+	0.929024i
$470$		0			0
$471$	14.4333	+	10.4864i	0.665053	+	0.483190i
$472$		0			0
$473$		0			0
$474$		0			0
$475$	21.5741	+	15.6745i	0.989887	+	0.719195i
$476$		0			0
$477$	−0.210551	−	0.648009i	−0.00964046	−	0.0296703i
$478$		0			0
$479$	0.282679	−	0.205378i	0.0129159	−	0.00938396i	−0.581309	−	0.813683i	$-0.697459\pi$
$479$	0.282679	−	0.205378i	0.0129159	−	0.00938396i	0.594224	+	0.804299i	$0.297459\pi$
$480$		0			0
$481$	−0.686239	+	2.11203i	−0.0312898	+	0.0963001i
$482$		0			0
$483$	5.94874			0.270677
$484$		0			0
$485$	−5.96379			−0.270802
$486$		0			0
$487$	12.0981	−	37.2340i	0.548216	−	1.68724i	−0.165002	−	0.986293i	$-0.552763\pi$
$487$	12.0981	−	37.2340i	0.548216	−	1.68724i	0.713218	−	0.700942i	$-0.247237\pi$
$488$		0			0
$489$	14.0345	−	10.1967i	0.634662	−	0.461109i
$490$		0			0
$491$	2.71518	+	8.35647i	0.122534	+	0.377122i	0.993444	−	0.114321i	$-0.0364694\pi$
$491$	2.71518	+	8.35647i	0.122534	+	0.377122i	−0.870909	+	0.491444i	$0.836469\pi$
$492$		0			0
$493$	−2.10105	−	1.52650i	−0.0946264	−	0.0687501i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	38.7627	+	28.1627i	1.73874	+	1.26327i
$498$		0			0
$499$	−7.95651	−	24.4876i	−0.356182	−	1.09622i	−0.955321	−	0.295571i	$-0.904490\pi$
$499$	−7.95651	−	24.4876i	−0.356182	−	1.09622i	0.599139	−	0.800645i	$-0.295510\pi$
$500$		0			0
$501$	13.2093	−	9.59715i	0.590150	−	0.428769i
$502$		0			0
$503$	−4.59380	+	14.1383i	−0.204828	+	0.630394i	0.794893	+	0.606750i	$0.207527\pi$
$503$	−4.59380	+	14.1383i	−0.204828	+	0.630394i	−0.999720	+	0.0236446i	$0.992473\pi$
$504$		0			0
$505$	−17.4972			−0.778614
$506$		0			0
$507$	10.9354			0.485658
$508$		0			0
$509$	1.06393	−	3.27444i	0.0471579	−	0.145137i	−0.924705	−	0.380685i	$-0.875688\pi$
$509$	1.06393	−	3.27444i	0.0471579	−	0.145137i	0.971863	+	0.235548i	$0.0756883\pi$
$510$		0			0
$511$	−10.6068	+	7.70632i	−0.469219	+	0.340908i
$512$		0			0
$513$	−3.48771	−	10.7341i	−0.153986	−	0.473921i
$514$		0			0
$515$	36.1044	+	26.2314i	1.59095	+	1.15589i
$516$		0			0
$517$		0			0
$518$		0			0
$519$	4.72593	+	3.43359i	0.207445	+	0.150718i
$520$		0			0
$521$	12.4289	+	38.2523i	0.544521	+	1.67586i	0.722126	+	0.691761i	$0.243165\pi$
$521$	12.4289	+	38.2523i	0.544521	+	1.67586i	−0.177605	+	0.984102i	$0.556835\pi$
$522$		0			0
$523$	−27.8519	+	20.2356i	−1.21788	+	0.884842i	−0.995922	−	0.0902146i	$-0.971245\pi$
$523$	−27.8519	+	20.2356i	−1.21788	+	0.884842i	−0.221958	+	0.975056i	$0.571245\pi$
$524$		0			0
$525$	−11.8392	+	36.4372i	−0.516704	+	1.59025i
$526$		0			0
$527$	4.52378			0.197059
$528$		0			0
$529$	−19.9783			−0.868622
$530$		0			0
$531$	−5.38800	+	16.5825i	−0.233819	+	0.719621i
$532$		0			0
$533$	7.75513	−	5.63443i	0.335912	−	0.244054i
$534$		0			0
$535$	11.8800	+	36.5630i	0.513619	+	1.58076i
$536$		0			0
$537$	−1.04668	−	0.760456i	−0.0451675	−	0.0328161i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	−15.3097	−	11.1232i	−0.658216	−	0.478222i	0.207844	−	0.978162i	$-0.433355\pi$
$541$	−15.3097	−	11.1232i	−0.658216	−	0.478222i	−0.866060	+	0.499940i	$0.833355\pi$
$542$		0			0
$543$	−4.92525	−	15.1584i	−0.211363	−	0.650508i
$544$		0			0
$545$	−13.5071	+	9.81346i	−0.578579	+	0.420362i
$546$		0			0
$547$	−10.1476	+	31.2312i	−0.433882	+	1.33535i	0.460346	+	0.887739i	$0.347725\pi$
$547$	−10.1476	+	31.2312i	−0.433882	+	1.33535i	−0.894228	+	0.447612i	$0.852275\pi$
$548$		0			0
$549$	−29.3809			−1.25395
$550$		0			0
$551$	−6.54775			−0.278943
$552$		0			0
$553$	10.1674	−	31.2920i	0.432361	−	1.33067i
$554$		0			0
$555$	−6.32911	+	4.59837i	−0.268656	+	0.195190i
$556$		0			0
$557$	9.90745	+	30.4920i	0.419792	+	1.29199i	0.907894	+	0.419201i	$0.137690\pi$
$557$	9.90745	+	30.4920i	0.419792	+	1.29199i	−0.488101	+	0.872787i	$0.662310\pi$
$558$		0			0
$559$	−0.366917	−	0.266581i	−0.0155189	−	0.0112752i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	1.01361	+	0.736429i	0.0427184	+	0.0310368i	0.608940	−	0.793217i	$-0.291595\pi$
$563$	1.01361	+	0.736429i	0.0427184	+	0.0310368i	−0.566221	+	0.824253i	$0.691595\pi$
$564$		0			0
$565$	11.5586	+	35.5738i	0.486276	+	1.49660i
$566$		0			0
$567$	−6.35713	+	4.61872i	−0.266974	+	0.193968i
$568$		0			0
$569$	−1.59513	+	4.90929i	−0.0668712	+	0.205808i	−0.978909	−	0.204299i	$-0.934509\pi$
$569$	−1.59513	+	4.90929i	−0.0668712	+	0.205808i	0.912037	+	0.410107i	$0.134509\pi$
$570$		0			0
$571$	−1.46767			−0.0614200			−0.0307100	−	0.999528i	$-0.509777\pi$
$571$	−1.46767			−0.0614200			−0.0307100	+	0.999528i	$0.509777\pi$
$572$		0			0
$573$	6.42419			0.268374
$574$		0			0
$575$	−6.01377	+	18.5085i	−0.250791	+	0.771857i
$576$		0			0
$577$	15.5342	−	11.2863i	0.646697	−	0.469853i	−0.215447	−	0.976516i	$-0.569121\pi$
$577$	15.5342	−	11.2863i	0.646697	−	0.469853i	0.862145	+	0.506662i	$0.169121\pi$
$578$		0			0
$579$	6.62897	+	20.4019i	0.275490	+	0.847873i
$580$		0			0
$581$	44.1788	+	32.0977i	1.83284	+	1.33164i
$582$		0			0
$583$		0			0
$584$		0			0
$585$	7.36753	+	5.35282i	0.304610	+	0.221312i
$586$		0			0
$587$	−1.76495	−	5.43195i	−0.0728472	−	0.224201i	0.908003	−	0.418963i	$-0.137606\pi$
$587$	−1.76495	−	5.43195i	−0.0728472	−	0.224201i	−0.980850	+	0.194763i	$0.937606\pi$
$588$		0			0
$589$	9.22726	−	6.70400i	0.380203	−	0.276233i
$590$		0			0
$591$	−3.07153	+	9.45319i	−0.126346	+	0.388852i
$592$		0			0
$593$	−36.3301			−1.49190			−0.745949	−	0.666003i	$-0.768004\pi$
$593$	−36.3301			−1.49190			−0.745949	+	0.666003i	$0.768004\pi$
$594$		0			0
$595$	−14.1560			−0.580339
$596$		0			0
$597$	−2.57735	+	7.93228i	−0.105484	+	0.324647i
$598$		0			0
$599$	33.3690	−	24.2440i	1.36342	−	0.990583i	0.365202	−	0.930928i	$-0.381000\pi$
$599$	33.3690	−	24.2440i	1.36342	−	0.990583i	0.998219	−	0.0596546i	$-0.0189999\pi$
$600$		0			0
$601$	−6.63057	−	20.4068i	−0.270467	−	0.832411i	−0.990383	−	0.138350i	$-0.955820\pi$
$601$	−6.63057	−	20.4068i	−0.270467	−	0.832411i	0.719917	−	0.694061i	$-0.244180\pi$
$602$		0			0
$603$	9.90671	+	7.19765i	0.403432	+	0.293111i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	3.01316	+	2.18919i	0.122300	+	0.0888564i	0.647254	−	0.762274i	$-0.275917\pi$
$607$	3.01316	+	2.18919i	0.122300	+	0.0888564i	−0.524954	+	0.851131i	$0.675917\pi$
$608$		0			0
$609$	−2.90696	−	8.94669i	−0.117796	−	0.362538i
$610$		0			0
$611$	5.37316	−	3.90383i	0.217375	−	0.157932i
$612$		0			0
$613$	4.40215	−	13.5484i	0.177801	−	0.547216i	−0.821949	−	0.569561i	$-0.807113\pi$
$613$	4.40215	−	13.5484i	0.177801	−	0.547216i	0.999750	+	0.0223449i	$0.00711318\pi$
$614$		0			0
$615$	33.7694			1.36171
$616$		0			0
$617$	33.2403			1.33821			0.669103	−	0.743170i	$-0.266678\pi$
$617$	33.2403			1.33821			0.669103	+	0.743170i	$0.266678\pi$
$618$		0			0
$619$	−4.84050	+	14.8975i	−0.194556	+	0.598782i	0.805426	+	0.592697i	$0.201937\pi$
$619$	−4.84050	+	14.8975i	−0.194556	+	0.598782i	−0.999981	+	0.00608462i	$0.998063\pi$
$620$		0			0
$621$	6.66355	−	4.84135i	0.267399	−	0.194277i
$622$		0			0
$623$	2.79807	+	8.61158i	0.112102	+	0.345016i
$624$		0			0
$625$	−35.8878	−	26.0740i	−1.43551	−	1.04296i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−1.61656	−	1.17450i	−0.0644565	−	0.0468304i
$630$		0			0
$631$	2.35898	+	7.26019i	0.0939094	+	0.289023i	0.986968	−	0.160917i	$-0.0514452\pi$
$631$	2.35898	+	7.26019i	0.0939094	+	0.289023i	−0.893059	+	0.449941i	$0.851445\pi$
$632$		0			0
$633$	1.77453	−	1.28927i	0.0705314	−	0.0512440i
$634$		0			0
$635$	9.89411	−	30.4509i	0.392636	−	1.20841i
$636$		0			0
$637$	−7.20560			−0.285496
$638$		0			0
$639$	27.7345			1.09716
$640$		0			0
$641$	−5.86542	+	18.0519i	−0.231670	+	0.713008i	0.765875	+	0.642989i	$0.222306\pi$
$641$	−5.86542	+	18.0519i	−0.231670	+	0.713008i	−0.997546	+	0.0700188i	$0.977694\pi$
$642$		0			0
$643$	−13.3285	+	9.68370i	−0.525624	+	0.381888i	−0.818718	−	0.574196i	$-0.805315\pi$
$643$	−13.3285	+	9.68370i	−0.525624	+	0.381888i	0.293095	+	0.956083i	$0.405315\pi$
$644$		0			0
$645$	−0.493725	−	1.51953i	−0.0194404	−	0.0598314i
$646$		0			0
$647$	−32.2159	−	23.4062i	−1.26654	−	0.920193i	−0.267478	−	0.963564i	$-0.586190\pi$
$647$	−32.2159	−	23.4062i	−1.26654	−	0.920193i	−0.999059	+	0.0433711i	$0.986190\pi$
$648$		0			0
$649$		0			0
$650$		0			0
$651$	13.2568	+	9.63159i	0.519573	+	0.377492i
$652$		0			0
$653$	−7.61864	−	23.4478i	−0.298141	−	0.917582i	−0.982148	−	0.188108i	$-0.939765\pi$
$653$	−7.61864	−	23.4478i	−0.298141	−	0.917582i	0.684008	−	0.729475i	$-0.260235\pi$
$654$		0			0
$655$	−39.9384	+	29.0169i	−1.56052	+	1.13378i
$656$		0			0
$657$	−2.34518	+	7.21771i	−0.0914941	+	0.281590i
$658$		0			0
$659$	11.3599			0.442518			0.221259	−	0.975215i	$-0.428983\pi$
$659$	11.3599			0.442518			0.221259	+	0.975215i	$0.428983\pi$
$660$		0			0
$661$	−5.05889			−0.196768			−0.0983841	−	0.995149i	$-0.531367\pi$
$661$	−5.05889			−0.196768			−0.0983841	+	0.995149i	$0.531367\pi$
$662$		0			0
$663$	0.281749	−	0.867135i	0.0109422	−	0.0336767i
$664$		0			0
$665$	−28.8743	+	20.9784i	−1.11970	+	0.813508i
$666$		0			0
$667$	−1.47660	−	4.54452i	−0.0571743	−	0.175964i
$668$		0			0
$669$	−11.4366	−	8.30917i	−0.442164	−	0.321251i
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−32.6487	−	23.7207i	−1.25852	−	0.914365i	−0.259832	−	0.965654i	$-0.583667\pi$
$673$	−32.6487	−	23.7207i	−1.25852	−	0.914365i	−0.998684	+	0.0512885i	$0.983667\pi$
$674$		0			0
$675$	16.3925	+	50.4508i	0.630946	+	1.94185i
$676$		0			0
$677$	25.4670	−	18.5029i	0.978776	−	0.711123i	0.0213414	−	0.999772i	$-0.493206\pi$
$677$	25.4670	−	18.5029i	0.978776	−	0.711123i	0.957435	+	0.288650i	$0.0932063\pi$
$678$		0			0
$679$	1.70503	−	5.24753i	0.0654329	−	0.201382i
$680$		0			0
$681$	−11.5269			−0.441714
$682$		0			0
$683$	40.0582			1.53279			0.766393	−	0.642372i	$-0.222050\pi$
$683$	40.0582			1.53279			0.766393	+	0.642372i	$0.222050\pi$
$684$		0			0
$685$	3.13146	−	9.63764i	0.119647	−	0.368235i
$686$		0			0
$687$	9.92012	−	7.20739i	0.378476	−	0.274979i
$688$		0			0
$689$	−0.102577	−	0.315700i	−0.00390788	−	0.0120272i
$690$		0			0
$691$	10.4961	+	7.62586i	0.399290	+	0.290101i	0.769252	−	0.638946i	$-0.220629\pi$
$691$	10.4961	+	7.62586i	0.399290	+	0.290101i	−0.369962	+	0.929047i	$0.620629\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−45.8914	−	33.3421i	−1.74076	−	1.26474i
$696$		0			0
$697$	2.66535	+	8.20311i	0.100957	+	0.310715i
$698$		0			0
$699$	17.4591	−	12.6848i	0.660363	−	0.479782i
$700$		0			0
$701$	−4.07421	+	12.5391i	−0.153881	+	0.473596i	−0.998046	−	0.0624871i	$-0.980097\pi$
$701$	−4.07421	+	12.5391i	−0.153881	+	0.473596i	0.844165	+	0.536083i	$0.180097\pi$
$702$		0			0
$703$	−5.03788			−0.190007
$704$		0			0
$705$	23.3972			0.881190
$706$		0			0
$707$	5.00238	−	15.3958i	0.188134	−	0.579017i
$708$		0			0
$709$	−13.2223	+	9.60657i	−0.496574	+	0.360782i	−0.807707	−	0.589584i	$-0.799292\pi$
$709$	−13.2223	+	9.60657i	−0.496574	+	0.360782i	0.311133	+	0.950367i	$0.399292\pi$
$710$		0			0
$711$	−5.88537	−	18.1133i	−0.220719	−	0.679302i
$712$		0			0
$713$	6.73383	+	4.89242i	0.252184	+	0.183222i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−2.77640	−	2.01718i	−0.103687	−	0.0753328i
$718$		0			0
$719$	−1.73115	−	5.32794i	−0.0645611	−	0.198699i	0.913573	−	0.406676i	$-0.133312\pi$
$719$	−1.73115	−	5.32794i	−0.0645611	−	0.198699i	−0.978134	+	0.207977i	$0.933312\pi$
$720$		0			0
$721$	−33.4031	+	24.2688i	−1.24400	+	0.903818i
$722$		0			0
$723$	4.53366	−	13.9532i	0.168609	−	0.518924i
$724$		0			0
$725$	30.7748			1.14295
$726$		0			0
$727$	−29.1822			−1.08231			−0.541155	−	0.840923i	$-0.682013\pi$
$727$	−29.1822			−1.08231			−0.541155	+	0.840923i	$0.682013\pi$
$728$		0			0
$729$	2.63185	−	8.10001i	0.0974761	−	0.300000i
$730$		0			0
$731$	0.330148	−	0.239867i	0.0122110	−	0.00887179i
$732$		0			0
$733$	−7.66087	−	23.5777i	−0.282961	−	0.870863i	−0.987003	−	0.160705i	$-0.948623\pi$
$733$	−7.66087	−	23.5777i	−0.282961	−	0.870863i	0.704042	−	0.710158i	$-0.251377\pi$
$734$		0			0
$735$	−20.5362	−	14.9204i	−0.757489	−	0.550348i
$736$		0			0
$737$		0			0
$738$		0			0
$739$	21.6415	+	15.7235i	0.796095	+	0.578397i	0.909766	−	0.415121i	$-0.136261\pi$
$739$	21.6415	+	15.7235i	0.796095	+	0.578397i	−0.113671	+	0.993518i	$0.536261\pi$
$740$		0			0
$741$	−0.710356	−	2.18625i	−0.0260956	−	0.0803140i
$742$		0			0
$743$	29.7103	−	21.5858i	1.08996	−	0.791906i	0.110572	−	0.993868i	$-0.464732\pi$
$743$	29.7103	−	21.5858i	1.08996	−	0.791906i	0.979393	+	0.201962i	$0.0647318\pi$
$744$		0			0
$745$	13.2756	−	40.8582i	0.486382	−	1.49693i
$746$		0			0
$747$	31.6097			1.15654
$748$		0			0
$749$	−35.5683			−1.29964
$750$		0			0
$751$	−7.04937	+	21.6957i	−0.257235	+	0.791689i	0.736146	+	0.676823i	$0.236644\pi$
$751$	−7.04937	+	21.6957i	−0.257235	+	0.791689i	−0.993381	+	0.114866i	$0.963356\pi$
$752$		0			0
$753$	−8.24024	+	5.98688i	−0.300291	+	0.218174i
$754$		0			0
$755$	−25.1754	−	77.4819i	−0.916226	−	2.81985i
$756$		0			0
$757$	21.6149	+	15.7041i	0.785606	+	0.570776i	0.906656	−	0.421870i	$-0.138626\pi$
$757$	21.6149	+	15.7041i	0.785606	+	0.570776i	−0.121051	+	0.992646i	$0.538626\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	17.5736	+	12.7680i	0.637043	+	0.462839i	0.858833	−	0.512256i	$-0.171190\pi$
$761$	17.5736	+	12.7680i	0.637043	+	0.462839i	−0.221790	+	0.975094i	$0.571190\pi$
$762$		0			0
$763$	−4.77323	−	14.6905i	−0.172803	−	0.531832i
$764$		0			0
$765$	−6.62922	+	4.81641i	−0.239680	+	0.174138i
$766$		0			0
$767$	−2.62495	+	8.07877i	−0.0947814	+	0.291707i
$768$		0			0
$769$	53.7688			1.93895			0.969476	−	0.245185i	$-0.0788488\pi$
$769$	53.7688			1.93895			0.969476	+	0.245185i	$0.0788488\pi$
$770$		0			0
$771$	−13.7730			−0.496024
$772$		0			0
$773$	3.00741	−	9.25586i	0.108169	−	0.332910i	−0.882292	−	0.470702i	$-0.844001\pi$
$773$	3.00741	−	9.25586i	0.108169	−	0.332910i	0.990461	+	0.137792i	$0.0440006\pi$
$774$		0			0
$775$	−43.3687	+	31.5092i	−1.55785	+	1.13184i
$776$		0			0
$777$	−2.23663	−	6.88364i	−0.0802387	−	0.246949i
$778$		0			0
$779$	17.5931	+	12.7822i	0.630340	+	0.457969i
$780$		0			0
$781$		0			0
$782$		0			0
$783$	−10.5375	−	7.65593i	−0.376579	−	0.273600i
$784$		0			0
$785$	−24.1385	−	74.2906i	−0.861540	−	2.65155i
$786$		0			0
$787$	30.9170	−	22.4625i	1.10207	−	0.800701i	0.120674	−	0.992692i	$-0.461494\pi$
$787$	30.9170	−	22.4625i	1.10207	−	0.800701i	0.981397	+	0.191991i	$0.0614944\pi$
$788$		0			0
$789$	2.54525	−	7.83347i	0.0906132	−	0.278879i
$790$		0			0
$791$	−34.6060			−1.23045
$792$		0			0
$793$	−14.3139			−0.508303
$794$		0			0
$795$	0.361362	−	1.11216i	0.0128162	−	0.0394442i
$796$		0			0
$797$	−17.6056	+	12.7912i	−0.623621	+	0.453087i	−0.854184	−	0.519970i	$-0.825943\pi$
$797$	−17.6056	+	12.7912i	−0.623621	+	0.453087i	0.230563	+	0.973057i	$0.425943\pi$
$798$		0			0
$799$	1.84670	+	5.68355i	0.0653314	+	0.201069i
$800$		0			0
$801$	4.24032	+	3.08077i	0.149824	+	0.108854i
$802$		0			0
$803$		0			0
$804$		0			0
$805$	−21.0718	−	15.3095i	−0.742682	−	0.539590i
$806$		0			0
$807$	−0.298223	−	0.917835i	−0.0104979	−	0.0323093i
$808$		0			0
$809$	−11.0577	+	8.03389i	−0.388768	+	0.282457i	−0.764951	−	0.644089i	$-0.777237\pi$
$809$	−11.0577	+	8.03389i	−0.388768	+	0.282457i	0.376182	+	0.926546i	$0.377237\pi$
$810$		0			0
$811$	−10.9626	+	33.7393i	−0.384947	+	1.18475i	0.551571	+	0.834128i	$0.314029\pi$
$811$	−10.9626	+	33.7393i	−0.384947	+	1.18475i	−0.936518	+	0.350619i	$0.885971\pi$
$812$		0			0
$813$	16.6963			0.585564
$814$		0			0
$815$	−75.9553			−2.66060
$816$		0			0
$817$	0.317942	−	0.978524i	0.0111234	−	0.0342342i
$818$		0			0
$819$	−6.81630	+	4.95233i	−0.238181	+	0.173048i
$820$		0			0
$821$	4.62469	+	14.2333i	0.161403	+	0.496747i	0.998753	−	0.0499196i	$-0.0158965\pi$
$821$	4.62469	+	14.2333i	0.161403	+	0.496747i	−0.837350	+	0.546667i	$0.815897\pi$
$822$		0			0
$823$	−9.88231	−	7.17992i	−0.344476	−	0.250276i	0.402072	−	0.915608i	$-0.368290\pi$
$823$	−9.88231	−	7.17992i	−0.344476	−	0.250276i	−0.746548	+	0.665332i	$0.768290\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	11.2482	+	8.17227i	0.391137	+	0.284178i	0.765921	−	0.642934i	$-0.222283\pi$
$827$	11.2482	+	8.17227i	0.391137	+	0.284178i	−0.374784	+	0.927112i	$0.622283\pi$
$828$		0			0
$829$	−3.81531	−	11.7423i	−0.132511	−	0.407828i	0.862683	−	0.505744i	$-0.168782\pi$
$829$	−3.81531	−	11.7423i	−0.132511	−	0.407828i	−0.995195	+	0.0979167i	$0.968782\pi$
$830$		0			0
$831$	−14.8295	+	10.7742i	−0.514428	+	0.373754i
$832$		0			0
$833$	2.00352	−	6.16620i	0.0694179	−	0.213646i
$834$		0			0
$835$	−71.4895			−2.47400
$836$		0			0
$837$	22.6883			0.784223
$838$		0			0
$839$	6.29316	−	19.3683i	0.217264	−	0.668670i	−0.781721	−	0.623628i	$-0.785658\pi$
$839$	6.29316	−	19.3683i	0.217264	−	0.668670i	0.998985	−	0.0450415i	$-0.0143420\pi$
$840$		0			0
$841$	17.3483	−	12.6043i	0.598216	−	0.434630i
$842$		0			0
$843$	−5.96662	−	18.3634i	−0.205501	−	0.632468i
$844$		0			0
$845$	−38.7356	−	28.1431i	−1.33255	−	0.968151i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−4.86785	−	3.53670i	−0.167064	−	0.121379i
$850$		0			0
$851$	−1.13611	−	3.49658i	−0.0389453	−	0.119861i
$852$		0			0
$853$	−42.2599	+	30.7036i	−1.44695	+	1.05127i	−0.460422	+	0.887700i	$0.652302\pi$
$853$	−42.2599	+	30.7036i	−1.44695	+	1.05127i	−0.986531	+	0.163572i	$0.947698\pi$
$854$		0			0
$855$	−6.38412	+	19.6483i	−0.218332	+	0.671958i
$856$		0			0
$857$	38.4691			1.31408			0.657041	−	0.753855i	$-0.271808\pi$
$857$	38.4691			1.31408			0.657041	+	0.753855i	$0.271808\pi$
$858$		0			0
$859$	33.3955			1.13944			0.569720	−	0.821839i	$-0.307052\pi$
$859$	33.3955			1.13944			0.569720	+	0.821839i	$0.307052\pi$
$860$		0			0
$861$	−9.65456	+	29.7137i	−0.329026	+	1.01264i
$862$		0			0
$863$	12.2281	−	8.88421i	0.416248	−	0.302422i	−0.359878	−	0.932999i	$-0.617182\pi$
$863$	12.2281	−	8.88421i	0.416248	−	0.302422i	0.776126	+	0.630577i	$0.217182\pi$
$864$		0			0
$865$	−7.90371	−	24.3251i	−0.268734	−	0.827078i
$866$		0			0
$867$	−11.9774	−	8.70206i	−0.406772	−	0.295537i
$868$		0			0
$869$		0			0
$870$		0			0
$871$	4.82640	+	3.50658i	0.163536	+	0.118816i
$872$		0			0
$873$	−0.986952	−	3.03753i	−0.0334033	−	0.102805i
$874$		0			0
$875$	75.1008	−	54.5639i	2.53887	−	1.84460i
$876$		0			0
$877$	−4.94336	+	15.2141i	−0.166925	+	0.513744i	−0.999173	−	0.0406605i	$-0.987054\pi$
$877$	−4.94336	+	15.2141i	−0.166925	+	0.513744i	0.832248	+	0.554404i	$0.187054\pi$
$878$		0			0
$879$	−14.7274			−0.496741
$880$		0			0
$881$	−43.0908			−1.45177			−0.725883	−	0.687818i	$-0.758569\pi$
$881$	−43.0908			−1.45177			−0.725883	+	0.687818i	$0.758569\pi$
$882$		0			0
$883$	−13.8975	+	42.7722i	−0.467689	+	1.43940i	0.387880	+	0.921710i	$0.373208\pi$
$883$	−13.8975	+	42.7722i	−0.467689	+	1.43940i	−0.855569	+	0.517689i	$0.826792\pi$
$884$		0			0
$885$	−24.2096	+	17.5893i	−0.813798	+	0.591259i
$886$		0			0
$887$	14.0014	+	43.0918i	0.470120	+	1.44688i	0.852428	+	0.522845i	$0.175129\pi$
$887$	14.0014	+	43.0918i	0.470120	+	1.44688i	−0.382308	+	0.924035i	$0.624871\pi$
$888$		0			0
$889$	23.9651	+	17.4116i	0.803763	+	0.583968i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	12.1895	+	8.85616i	0.407905	+	0.296360i
$894$		0			0
$895$	1.75048	+	5.38741i	0.0585120	+	0.180081i
$896$		0			0
$897$	1.35719	−	0.986057i	0.0453153	−	0.0329235i
$898$		0			0
$899$	4.06741	−	12.5182i	0.135656	−	0.417506i
$900$		0			0
$901$	0.298682			0.00995054
$902$		0			0
$903$	1.47819			0.0491910
$904$		0			0
$905$	−21.5649	+	66.3699i	−0.716841	+	2.20621i
$906$		0			0
$907$	17.1609	−	12.4681i	0.569817	−	0.413996i	−0.265222	−	0.964187i	$-0.585445\pi$
$907$	17.1609	−	12.4681i	0.569817	−	0.413996i	0.835039	+	0.550191i	$0.185445\pi$
$908$		0			0
$909$	−2.89562	−	8.91181i	−0.0960417	−	0.295586i
$910$		0			0
$911$	15.4776	+	11.2451i	0.512795	+	0.372567i	0.813883	−	0.581029i	$-0.197350\pi$
$911$	15.4776	+	11.2451i	0.512795	+	0.372567i	−0.301088	+	0.953596i	$0.597350\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$	−40.7952	−	29.6395i	−1.34865	−	0.979850i
$916$		0			0
$917$	−14.1137	−	43.4376i	−0.466076	−	1.43444i
$918$		0			0
$919$	33.2561	−	24.1619i	1.09702	−	0.797029i	0.116446	−	0.993197i	$-0.462850\pi$
$919$	33.2561	−	24.1619i	1.09702	−	0.797029i	0.980570	+	0.196168i	$0.0628497\pi$
$920$		0			0
$921$	3.06793	−	9.44213i	0.101092	−	0.311129i
$922$		0			0
$923$	13.5118			0.444748
$924$		0			0
$925$	23.6783			0.778539
$926$		0			0
$927$	−7.38545	+	22.7301i	−0.242570	+	0.746554i
$928$		0			0
$929$	38.4056	−	27.9033i	1.26005	−	0.915478i	0.261288	−	0.965261i	$-0.415853\pi$
$929$	38.4056	−	27.9033i	1.26005	−	0.915478i	0.998760	+	0.0497826i	$0.0158529\pi$
$930$		0			0
$931$	−5.05135	−	15.5465i	−0.165551	−	0.509514i
$932$		0			0
$933$	2.37157	+	1.72304i	0.0776416	+	0.0564100i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−22.2168	−	16.1414i	−0.725791	−	0.527318i	0.162438	−	0.986719i	$-0.448064\pi$
$937$	−22.2168	−	16.1414i	−0.725791	−	0.527318i	−0.888229	+	0.459401i	$0.848064\pi$
$938$		0			0
$939$	−4.27609	−	13.1605i	−0.139545	−	0.429476i
$940$		0			0
$941$	−13.0770	+	9.50100i	−0.426298	+	0.309724i	−0.780167	−	0.625571i	$-0.784866\pi$
$941$	−13.0770	+	9.50100i	−0.426298	+	0.309724i	0.353869	+	0.935295i	$0.384866\pi$
$942$		0			0
$943$	−4.90408	+	15.0932i	−0.159699	+	0.491503i
$944$		0			0
$945$	−70.9971			−2.30954
$946$		0			0
$947$	−28.3252			−0.920445			−0.460223	−	0.887804i	$-0.652230\pi$
$947$	−28.3252			−0.920445			−0.460223	+	0.887804i	$0.652230\pi$
$948$		0			0
$949$	−1.14253	+	3.51636i	−0.0370882	+	0.114146i
$950$		0			0
$951$	9.85252	−	7.15828i	0.319490	−	0.232123i
$952$		0			0
$953$	16.4967	+	50.7717i	0.534382	+	1.64466i	0.744981	+	0.667085i	$0.232458\pi$
$953$	16.4967	+	50.7717i	0.534382	+	1.64466i	−0.210600	+	0.977572i	$0.567542\pi$
$954$		0			0
$955$	−22.7559	−	16.5331i	−0.736364	−	0.535000i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	7.58488	+	5.51074i	0.244929	+	0.177951i
$960$		0			0
$961$	−2.49450	−	7.67727i	−0.0804676	−	0.247654i
$962$		0			0
$963$	−16.6565	+	12.1017i	−0.536750	+	0.389972i
$964$		0			0
$965$	29.0245	−	89.3281i	0.934331	−	2.87557i
$966$		0			0
$967$	45.0985			1.45027			0.725136	−	0.688606i	$-0.241777\pi$
$967$	45.0985			1.45027			0.725136	+	0.688606i	$0.241777\pi$
$968$		0			0
$969$	2.06840			0.0664466
$970$		0			0
$971$	−14.6897	+	45.2103i	−0.471416	+	1.45087i	0.379316	+	0.925267i	$0.376159\pi$
$971$	−14.6897	+	45.2103i	−0.471416	+	1.45087i	−0.850731	+	0.525601i	$0.823841\pi$
$972$		0			0
$973$	42.4579	−	30.8475i	1.36114	−	0.988924i
$974$		0			0
$975$	3.33872	+	10.2755i	0.106925	+	0.329080i
$976$		0			0
$977$	4.30042	+	3.12444i	0.137583	+	0.0999597i	0.654448	−	0.756107i	$-0.272901\pi$
$977$	4.30042	+	3.12444i	0.137583	+	0.0999597i	−0.516865	+	0.856067i	$0.672901\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	−7.23357	−	5.25550i	−0.230950	−	0.167795i
$982$		0			0
$983$	1.09905	+	3.38253i	0.0350542	+	0.107886i	0.967053	−	0.254577i	$-0.0819361\pi$
$983$	1.09905	+	3.38253i	0.0350542	+	0.107886i	−0.931998	+	0.362462i	$0.881936\pi$
$984$		0			0
$985$	35.2086	−	25.5805i	1.12184	−	0.815063i
$986$		0			0
$987$	−6.68919	+	20.5872i	−0.212919	+	0.655298i
$988$		0			0
$989$	0.750852			0.0238757
$990$		0			0
$991$	−38.1592			−1.21217			−0.606083	−	0.795401i	$-0.707260\pi$
$991$	−38.1592			−1.21217			−0.606083	+	0.795401i	$0.707260\pi$
$992$		0			0
$993$	9.53024	−	29.3311i	0.302433	−	0.930793i
$994$		0			0
$995$	29.5439	−	21.4649i	0.936605	−	0.680483i
$996$		0			0
$997$	−9.01365	−	27.7412i	−0.285465	−	0.878571i	−0.986259	−	0.165207i	$-0.947171\pi$
$997$	−9.01365	−	27.7412i	−0.285465	−	0.878571i	0.700794	−	0.713364i	$-0.252829\pi$
$998$		0			0
$999$	−8.10760	−	5.89052i	−0.256513	−	0.186368i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	968.2.i.t.81.1		8
11.2	odd	10		88.2.i.b.49.2	yes	8
11.3	even	5	inner	968.2.i.t.729.1		8
11.4	even	5		968.2.i.p.9.2		8
11.5	even	5		968.2.a.m.1.2		4
11.6	odd	10		968.2.a.n.1.2		4
11.7	odd	10		88.2.i.b.9.2	✓	8
11.8	odd	10		968.2.i.s.729.1		8
11.9	even	5		968.2.i.p.753.2		8
11.10	odd	2		968.2.i.s.81.1		8
33.2	even	10		792.2.r.g.577.2		8
33.5	odd	10		8712.2.a.cd.1.4		4
33.17	even	10		8712.2.a.ce.1.4		4
33.29	even	10		792.2.r.g.361.2		8
44.7	even	10		176.2.m.d.97.1		8
44.27	odd	10		1936.2.a.bc.1.3		4
44.35	even	10		176.2.m.d.49.1		8
44.39	even	10		1936.2.a.bb.1.3		4
88.5	even	10		7744.2.a.dh.1.3		4
88.13	odd	10		704.2.m.l.577.1		8
88.27	odd	10		7744.2.a.ds.1.2		4
88.29	odd	10		704.2.m.l.449.1		8
88.35	even	10		704.2.m.i.577.2		8
88.51	even	10		704.2.m.i.449.2		8
88.61	odd	10		7744.2.a.di.1.3		4
88.83	even	10		7744.2.a.dr.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
88.2.i.b.9.2	✓	8	11.7	odd	10
88.2.i.b.49.2	yes	8	11.2	odd	10
176.2.m.d.49.1		8	44.35	even	10
176.2.m.d.97.1		8	44.7	even	10
704.2.m.i.449.2		8	88.51	even	10
704.2.m.i.577.2		8	88.35	even	10
704.2.m.l.449.1		8	88.29	odd	10
704.2.m.l.577.1		8	88.13	odd	10
792.2.r.g.361.2		8	33.29	even	10
792.2.r.g.577.2		8	33.2	even	10
968.2.a.m.1.2		4	11.5	even	5
968.2.a.n.1.2		4	11.6	odd	10
968.2.i.p.9.2		8	11.4	even	5
968.2.i.p.753.2		8	11.9	even	5
968.2.i.s.81.1		8	11.10	odd	2
968.2.i.s.729.1		8	11.8	odd	10
968.2.i.t.81.1		8	1.1	even	1	trivial
968.2.i.t.729.1		8	11.3	even	5	inner
1936.2.a.bb.1.3		4	44.39	even	10
1936.2.a.bc.1.3		4	44.27	odd	10
7744.2.a.dh.1.3		4	88.5	even	10
7744.2.a.di.1.3		4	88.61	odd	10
7744.2.a.dr.1.2		4	88.83	even	10
7744.2.a.ds.1.2		4	88.27	odd	10
8712.2.a.cd.1.4		4	33.5	odd	10
8712.2.a.ce.1.4		4	33.17	even	10

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:	\( N \)	\(=\)	\( 968 = 2^{3} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	968.i (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.284027 + 0.874145i) q^{3} +(3.25577 - 2.36545i) q^{5} +(1.15055 + 3.54102i) q^{7} +(1.74359 + 1.26679i) q^{9} +O(q^{10})\)	\(q+(-0.284027 + 0.874145i) q^{3} +(3.25577 - 2.36545i) q^{5} +(1.15055 + 3.54102i) q^{7} +(1.74359 + 1.26679i) q^{9} +(0.849452 + 0.617163i) q^{13} +(1.14302 + 3.51787i) q^{15} +(-0.764328 + 0.555317i) q^{17} +(-0.736068 + 2.26538i) q^{19} -3.42216 q^{21} -1.73830 q^{23} +(3.45957 - 10.6474i) q^{25} +(-3.83337 + 2.78510i) q^{27} +(0.849452 + 2.61434i) q^{29} +(-3.87380 - 2.81448i) q^{31} +(12.1220 + 8.80718i) q^{35} +(0.653574 + 2.01149i) q^{37} +(-0.780757 + 0.567253i) q^{39} +(2.82119 - 8.68274i) q^{41} -0.431946 q^{43} +8.67327 q^{45} +(1.95467 - 6.01586i) q^{47} +(-5.55197 + 4.03374i) q^{49} +(-0.268338 - 0.825859i) q^{51} +(-0.255767 - 0.185826i) q^{53} +(-1.77121 - 1.28686i) q^{57} +(2.50000 + 7.69421i) q^{59} +(-11.0290 + 8.01304i) q^{61} +(-2.47966 + 7.63161i) q^{63} +4.22549 q^{65} +5.68178 q^{67} +(0.493725 - 1.51953i) q^{69} +(10.4110 - 7.56401i) q^{71} +(1.08815 + 3.34898i) q^{73} +(8.32481 + 6.04833i) q^{75} +(-7.14927 - 5.19425i) q^{79} +(0.652173 + 2.00718i) q^{81} +(11.8656 - 8.62089i) q^{83} +(-1.17490 + 3.61596i) q^{85} -2.52658 q^{87} +2.43195 q^{89} +(-1.20805 + 3.71800i) q^{91} +(3.56053 - 2.58688i) q^{93} +(2.96219 + 9.11670i) q^{95} +(-1.19890 - 0.871054i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - q^{3} + 2 q^{5} + 8 q^{7} + 7 q^{9}+O(q^{10}) \) 8 * q - q^3 + 2 * q^5 + 8 * q^7 + 7 * q^9	\( 8 q - q^{3} + 2 q^{5} + 8 q^{7} + 7 q^{9} + 8 q^{13} - 3 q^{15} - 11 q^{17} + 12 q^{19} + 2 q^{21} - 4 q^{23} + 22 q^{25} + 8 q^{27} + 8 q^{29} + 2 q^{31} + 29 q^{35} - 14 q^{37} + 21 q^{39} + q^{41} - 6 q^{43} + 44 q^{45} - 6 q^{47} - 2 q^{49} + 52 q^{51} + 22 q^{53} + q^{57} + 20 q^{59} - 26 q^{61} + 5 q^{63} + 10 q^{65} - 10 q^{67} + 42 q^{69} + 30 q^{71} - 13 q^{73} - q^{75} + 6 q^{79} - 6 q^{81} + 20 q^{83} + 26 q^{85} + 6 q^{87} + 22 q^{89} - 13 q^{91} + 15 q^{93} + 13 q^{95} - 12 q^{97}+O(q^{100}) \) 8 * q - q^3 + 2 * q^5 + 8 * q^7 + 7 * q^9 + 8 * q^13 - 3 * q^15 - 11 * q^17 + 12 * q^19 + 2 * q^21 - 4 * q^23 + 22 * q^25 + 8 * q^27 + 8 * q^29 + 2 * q^31 + 29 * q^35 - 14 * q^37 + 21 * q^39 + q^41 - 6 * q^43 + 44 * q^45 - 6 * q^47 - 2 * q^49 + 52 * q^51 + 22 * q^53 + q^57 + 20 * q^59 - 26 * q^61 + 5 * q^63 + 10 * q^65 - 10 * q^67 + 42 * q^69 + 30 * q^71 - 13 * q^73 - q^75 + 6 * q^79 - 6 * q^81 + 20 * q^83 + 26 * q^85 + 6 * q^87 + 22 * q^89 - 13 * q^91 + 15 * q^93 + 13 * q^95 - 12 * q^97

Introduction

L-functions

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Database

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