LMFDB - Embedded newform 476.3.s.a.341.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [476,3,Mod(341,476)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(476, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5, 0]))

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

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

chi := DirichletCharacter("476.341");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 476 = 2^{2} \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	476.s (of order $6$, degree $2$, 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:	$12.9700605836$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			341.18
Character	$\chi$	$=$	476.341
Dual form			476.3.s.a.409.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.95906 - 1.70841i) q^{3} +(6.58749 + 3.80329i) q^{5} +(6.95862 - 0.760040i) q^{7} +(1.33734 - 2.31634i) q^{9} +O(q^{10})$	\(q+(2.95906 - 1.70841i) q^{3} +(6.58749 + 3.80329i) q^{5} +(6.95862 - 0.760040i) q^{7} +(1.33734 - 2.31634i) q^{9} +(-10.0039 - 17.3272i) q^{11} -21.2973i q^{13} +25.9903 q^{15} +(3.57071 - 2.06155i) q^{17} +(9.70722 + 5.60447i) q^{19} +(19.2925 - 14.1372i) q^{21} +(-18.0966 + 31.3442i) q^{23} +(16.4300 + 28.4576i) q^{25} +21.6125i q^{27} +35.0270 q^{29} +(-41.9103 + 24.1969i) q^{31} +(-59.2040 - 34.1814i) q^{33} +(48.7305 + 21.4589i) q^{35} +(21.6323 - 37.4682i) q^{37} +(-36.3846 - 63.0199i) q^{39} +44.5491i q^{41} +24.5666 q^{43} +(17.6194 - 10.1726i) q^{45} +(-5.60192 - 3.23427i) q^{47} +(47.8447 - 10.5776i) q^{49} +(7.04396 - 12.2005i) q^{51} +(-16.5592 - 28.6814i) q^{53} -152.190i q^{55} +38.2989 q^{57} +(-40.6548 + 23.4720i) q^{59} +(5.98184 + 3.45362i) q^{61} +(7.54552 - 17.1349i) q^{63} +(80.9998 - 140.296i) q^{65} +(43.5007 + 75.3453i) q^{67} +123.666i q^{69} -100.452 q^{71} +(-69.4304 + 40.0857i) q^{73} +(97.2346 + 56.1384i) q^{75} +(-82.7824 - 112.970i) q^{77} +(-29.5905 + 51.2523i) q^{79} +(48.9591 + 84.7996i) q^{81} +63.0422i q^{83} +31.3627 q^{85} +(103.647 - 59.8405i) q^{87} +(-121.923 - 70.3924i) q^{89} +(-16.1868 - 148.200i) q^{91} +(-82.6767 + 143.200i) q^{93} +(42.6308 + 73.8388i) q^{95} -21.0852i q^{97} -53.5142 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 6 q^{3} + 22 q^{7} + 88 q^{9}+O(q^{10}) $ 44 * q - 6 * q^3 + 22 * q^7 + 88 * q^9	$ 44 q - 6 q^{3} + 22 q^{7} + 88 q^{9} + 8 q^{11} + 16 q^{15} - 54 q^{19} - 16 q^{21} - 52 q^{23} + 150 q^{25} + 8 q^{29} + 78 q^{31} - 6 q^{33} + 10 q^{35} - 34 q^{37} - 60 q^{39} - 76 q^{43} - 72 q^{45} - 6 q^{47} - 56 q^{49} - 172 q^{53} - 64 q^{57} + 30 q^{59} + 444 q^{61} + 206 q^{63} - 54 q^{65} - 56 q^{67} + 204 q^{71} - 48 q^{73} + 132 q^{75} - 494 q^{77} - 16 q^{79} - 342 q^{81} + 594 q^{87} - 252 q^{89} + 284 q^{91} - 146 q^{93} + 148 q^{95} - 180 q^{99}+O(q^{100}) $ 44 * q - 6 * q^3 + 22 * q^7 + 88 * q^9 + 8 * q^11 + 16 * q^15 - 54 * q^19 - 16 * q^21 - 52 * q^23 + 150 * q^25 + 8 * q^29 + 78 * q^31 - 6 * q^33 + 10 * q^35 - 34 * q^37 - 60 * q^39 - 76 * q^43 - 72 * q^45 - 6 * q^47 - 56 * q^49 - 172 * q^53 - 64 * q^57 + 30 * q^59 + 444 * q^61 + 206 * q^63 - 54 * q^65 - 56 * q^67 + 204 * q^71 - 48 * q^73 + 132 * q^75 - 494 * q^77 - 16 * q^79 - 342 * q^81 + 594 * q^87 - 252 * q^89 + 284 * q^91 - 146 * q^93 + 148 * q^95 - 180 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/476\mathbb{Z}\right)^\times$.

$n$	$239$	$309$	$409$
$\chi(n)$	$1$	$1$	$e\left(\frac{5}{6}\right)$

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
$3$	2.95906	−	1.70841i	0.986352	−	0.569470i	0.0821700	−	0.996618i	$-0.473815\pi$
$3$	2.95906	−	1.70841i	0.986352	−	0.569470i	0.904182	+	0.427148i	$0.140482\pi$
$4$		0			0
$5$	6.58749	+	3.80329i	1.31750	+	0.760658i	0.983326	−	0.181854i	$-0.0582099\pi$
$5$	6.58749	+	3.80329i	1.31750	+	0.760658i	0.334172	+	0.942512i	$0.391543\pi$
$6$		0			0
$7$	6.95862	−	0.760040i	0.994088	−	0.108577i
$7$	6.95862	−	0.760040i	0.994088	−	0.108577i
$8$		0			0
$9$	1.33734	−	2.31634i	0.148593	−	0.257371i
$10$		0			0
$11$	−10.0039	−	17.3272i	−0.909442	−	1.57520i	−0.814841	−	0.579685i	$-0.803176\pi$
$11$	−10.0039	−	17.3272i	−0.909442	−	1.57520i	−0.0946017	−	0.995515i	$-0.530158\pi$
$12$		0			0
$13$		−	21.2973i		−	1.63825i	−0.573612	−	0.819127i	$-0.694458\pi$
$13$		−	21.2973i		−	1.63825i	0.573612	−	0.819127i	$-0.305542\pi$
$14$		0			0
$15$	25.9903			1.73269
$16$		0			0
$17$	3.57071	−	2.06155i	0.210042	−	0.121268i
$17$	3.57071	−	2.06155i	0.210042	−	0.121268i
$18$		0			0
$19$	9.70722	+	5.60447i	0.510907	+	0.294972i	0.733206	−	0.680006i	$-0.238023\pi$
$19$	9.70722	+	5.60447i	0.510907	+	0.294972i	−0.222300	+	0.974978i	$0.571356\pi$
$20$		0			0
$21$	19.2925	−	14.1372i	0.918689	−	0.673199i
$22$		0			0
$23$	−18.0966	+	31.3442i	−0.786808	+	1.36279i	0.141106	+	0.989995i	$0.454934\pi$
$23$	−18.0966	+	31.3442i	−0.786808	+	1.36279i	−0.927913	+	0.372796i	$0.878399\pi$
$24$		0			0
$25$	16.4300	+	28.4576i	0.657201	+	1.13830i
$26$		0			0
$27$			21.6125i			0.800463i
$28$		0			0
$29$	35.0270			1.20783			0.603913	−	0.797050i	$-0.293607\pi$
$29$	35.0270			1.20783			0.603913	+	0.797050i	$0.293607\pi$
$30$		0			0
$31$	−41.9103	+	24.1969i	−1.35195	+	0.780546i	−0.988522	−	0.151077i	$-0.951726\pi$
$31$	−41.9103	+	24.1969i	−1.35195	+	0.780546i	−0.363424	+	0.931624i	$0.618392\pi$
$32$		0			0
$33$	−59.2040	−	34.1814i	−1.79406	−	1.03580i
$34$		0			0
$35$	48.7305	+	21.4589i	1.39230	+	0.613111i
$36$		0			0
$37$	21.6323	−	37.4682i	0.584656	−	1.01265i	−0.410262	−	0.911968i	$-0.634563\pi$
$37$	21.6323	−	37.4682i	0.584656	−	1.01265i	0.994918	−	0.100687i	$-0.0321040\pi$
$38$		0			0
$39$	−36.3846	−	63.0199i	−0.932937	−	1.61589i
$40$		0			0
$41$			44.5491i			1.08656i	0.839550	+	0.543282i	$0.182819\pi$
$41$			44.5491i			1.08656i	−0.839550	+	0.543282i	$0.817181\pi$
$42$		0			0
$43$	24.5666			0.571317			0.285658	−	0.958332i	$-0.407788\pi$
$43$	24.5666			0.571317			0.285658	+	0.958332i	$0.407788\pi$
$44$		0			0
$45$	17.6194	−	10.1726i	0.391543	−	0.226057i
$46$		0			0
$47$	−5.60192	−	3.23427i	−0.119190	−	0.0688142i	0.439220	−	0.898380i	$-0.355255\pi$
$47$	−5.60192	−	3.23427i	−0.119190	−	0.0688142i	−0.558410	+	0.829565i	$0.688588\pi$
$48$		0			0
$49$	47.8447	−	10.5776i	0.976422	−	0.215870i
$50$		0			0
$51$	7.04396	−	12.2005i	0.138117	−	0.239225i
$52$		0			0
$53$	−16.5592	−	28.6814i	−0.312439	−	0.541159i	0.666451	−	0.745549i	$-0.267812\pi$
$53$	−16.5592	−	28.6814i	−0.312439	−	0.541159i	−0.978890	+	0.204389i	$0.934479\pi$
$54$		0			0
$55$		−	152.190i		−	2.76710i
$56$		0			0
$57$	38.2989			0.671911
$58$		0			0
$59$	−40.6548	+	23.4720i	−0.689064	+	0.397831i	−0.803261	−	0.595627i	$-0.796904\pi$
$59$	−40.6548	+	23.4720i	−0.689064	+	0.397831i	0.114197	+	0.993458i	$0.463570\pi$
$60$		0			0
$61$	5.98184	+	3.45362i	0.0980630	+	0.0566167i	0.548229	−	0.836328i	$-0.315302\pi$
$61$	5.98184	+	3.45362i	0.0980630	+	0.0566167i	−0.450167	+	0.892945i	$0.648635\pi$
$62$		0			0
$63$	7.54552	−	17.1349i	0.119770	−	0.271983i
$64$		0			0
$65$	80.9998	−	140.296i	1.24615	−	2.15840i
$66$		0			0
$67$	43.5007	+	75.3453i	0.649264	+	1.12456i	0.983299	+	0.181997i	$0.0582561\pi$
$67$	43.5007	+	75.3453i	0.649264	+	1.12456i	−0.334036	+	0.942560i	$0.608411\pi$
$68$		0			0
$69$			123.666i			1.79225i
$70$		0			0
$71$	−100.452			−1.41481			−0.707406	−	0.706807i	$-0.750135\pi$
$71$	−100.452			−1.41481			−0.707406	+	0.706807i	$0.750135\pi$
$72$		0			0
$73$	−69.4304	+	40.0857i	−0.951102	+	0.549119i	−0.893423	−	0.449216i	$-0.851703\pi$
$73$	−69.4304	+	40.0857i	−0.951102	+	0.549119i	−0.0576788	+	0.998335i	$0.518370\pi$
$74$		0			0
$75$	97.2346	+	56.1384i	1.29646	+	0.748513i
$76$		0			0
$77$	−82.7824	−	112.970i	−1.07510	−	1.46714i
$78$		0			0
$79$	−29.5905	+	51.2523i	−0.374564	+	0.648763i	−0.990262	−	0.139219i	$-0.955541\pi$
$79$	−29.5905	+	51.2523i	−0.374564	+	0.648763i	0.615698	+	0.787982i	$0.288874\pi$
$80$		0			0
$81$	48.9591	+	84.7996i	0.604433	+	1.04691i
$82$		0			0
$83$			63.0422i			0.759545i	0.925080	+	0.379772i	$0.123998\pi$
$83$			63.0422i			0.759545i	−0.925080	+	0.379772i	$0.876002\pi$
$84$		0			0
$85$	31.3627			0.368973
$86$		0			0
$87$	103.647	−	59.8405i	1.19134	−	0.687822i
$88$		0			0
$89$	−121.923	−	70.3924i	−1.36992	−	0.790926i	−0.379006	−	0.925394i	$-0.623734\pi$
$89$	−121.923	−	70.3924i	−1.36992	−	0.790926i	−0.990918	+	0.134469i	$0.957067\pi$
$90$		0			0
$91$	−16.1868	−	148.200i	−0.177877	−	1.62857i
$92$		0			0
$93$	−82.6767	+	143.200i	−0.888996	+	1.53979i
$94$		0			0
$95$	42.6308	+	73.8388i	0.448746	+	0.777250i
$96$		0			0
$97$		−	21.0852i		−	0.217373i	−0.994076	−	0.108687i	$-0.965335\pi$
$97$		−	21.0852i		−	0.217373i	0.994076	−	0.108687i	$-0.0346645\pi$
$98$		0			0
$99$	−53.5142			−0.540548
$100$		0			0
$101$	46.7701	−	27.0027i	0.463070	−	0.267354i	−0.250264	−	0.968178i	$-0.580517\pi$
$101$	46.7701	−	27.0027i	0.463070	−	0.267354i	0.713334	+	0.700824i	$0.247184\pi$
$102$		0			0
$103$	47.7132	+	27.5472i	0.463235	+	0.267449i	0.713403	−	0.700754i	$-0.247153\pi$
$103$	47.7132	+	27.5472i	0.463235	+	0.267449i	−0.250169	+	0.968202i	$0.580486\pi$
$104$		0			0
$105$	180.857	−	19.7537i	1.72244	−	0.188130i
$106$		0			0
$107$	34.4907	−	59.7397i	0.322343	−	0.558315i	−0.658628	−	0.752469i	$-0.728863\pi$
$107$	34.4907	−	59.7397i	0.322343	−	0.558315i	0.980971	+	0.194154i	$0.0621961\pi$
$108$		0			0
$109$	4.35944	+	7.55078i	0.0399949	+	0.0692732i	0.885330	−	0.464963i	$-0.153932\pi$
$109$	4.35944	+	7.55078i	0.0399949	+	0.0692732i	−0.845335	+	0.534237i	$0.820599\pi$
$110$		0			0
$111$		−	147.827i		−	1.33178i
$112$		0			0
$113$	85.7638			0.758972			0.379486	−	0.925198i	$-0.376101\pi$
$113$	85.7638			0.758972			0.379486	+	0.925198i	$0.376101\pi$
$114$		0			0
$115$	−238.422	+	137.653i	−2.07323	+	1.19698i
$116$		0			0
$117$	−49.3318	−	28.4817i	−0.421639	−	0.243433i
$118$		0			0
$119$	23.2804	−	17.0594i	0.195633	−	0.143357i
$120$		0			0
$121$	−139.655	+	241.889i	−1.15417	+	1.99908i
$122$		0			0
$123$	76.1083	+	131.823i	0.618766	+	1.07173i
$124$		0			0
$125$			59.7879i			0.478303i
$126$		0			0
$127$	15.5397			0.122360			0.0611798	−	0.998127i	$-0.480514\pi$
$127$	15.5397			0.122360			0.0611798	+	0.998127i	$0.480514\pi$
$128$		0			0
$129$	72.6940	−	41.9699i	0.563519	−	0.325348i
$130$		0			0
$131$	−15.5848	−	8.99788i	−0.118968	−	0.0686861i	0.439335	−	0.898323i	$-0.355214\pi$
$131$	−15.5848	−	8.99788i	−0.118968	−	0.0686861i	−0.558303	+	0.829637i	$0.688547\pi$
$132$		0			0
$133$	71.8085	+	31.6215i	0.539913	+	0.237755i
$134$		0			0
$135$	−82.1986	+	142.372i	−0.608878	+	1.05461i
$136$		0			0
$137$	50.5752	+	87.5988i	0.369162	+	0.639407i	0.989435	−	0.144979i	$-0.0463114\pi$
$137$	50.5752	+	87.5988i	0.369162	+	0.639407i	−0.620273	+	0.784386i	$0.712978\pi$
$138$		0			0
$139$		−	224.942i		−	1.61829i	−0.587609	−	0.809145i	$-0.699931\pi$
$139$		−	224.942i		−	1.61829i	0.587609	−	0.809145i	$-0.300069\pi$
$140$		0			0
$141$	−22.1019			−0.156751
$142$		0			0
$143$	−369.023	+	213.055i	−2.58058	+	1.48990i
$144$		0			0
$145$	230.740	+	133.218i	1.59131	+	0.918743i
$146$		0			0
$147$	123.504	−	113.038i	0.840164	−	0.768968i
$148$		0			0
$149$	3.10963	−	5.38604i	0.0208700	−	0.0361479i	−0.855402	−	0.517965i	$-0.826690\pi$
$149$	3.10963	−	5.38604i	0.0208700	−	0.0361479i	0.876272	+	0.481817i	$0.160023\pi$
$150$		0			0
$151$	−92.1875	−	159.673i	−0.610513	−	1.05744i	−0.991154	−	0.132717i	$-0.957630\pi$
$151$	−92.1875	−	159.673i	−0.610513	−	1.05744i	0.380641	−	0.924723i	$-0.375703\pi$
$152$		0			0
$153$		−	11.0280i		−	0.0720783i
$154$		0			0
$155$	−368.112			−2.37491
$156$		0			0
$157$	−48.5597	+	28.0359i	−0.309297	+	0.178573i	−0.646612	−	0.762819i	$-0.723815\pi$
$157$	−48.5597	+	28.0359i	−0.309297	+	0.178573i	0.337315	+	0.941392i	$0.390481\pi$
$158$		0			0
$159$	−97.9994	−	56.5800i	−0.616349	−	0.355849i
$160$		0			0
$161$	−102.104	+	231.866i	−0.634188	+	1.44016i
$162$		0			0
$163$	132.024	−	228.673i	0.809966	−	1.40290i	−0.102921	−	0.994690i	$-0.532819\pi$
$163$	132.024	−	228.673i	0.809966	−	1.40290i	0.912887	−	0.408213i	$-0.133848\pi$
$164$		0			0
$165$	−260.004	−	450.340i	−1.57578	−	2.72933i
$166$		0			0
$167$			239.740i			1.43557i	0.696265	+	0.717785i	$0.254844\pi$
$167$			239.740i			1.43557i	−0.696265	+	0.717785i	$0.745156\pi$
$168$		0			0
$169$	−284.575			−1.68388
$170$		0			0
$171$	25.9637	−	14.9901i	0.151834	−	0.0876617i
$172$		0			0
$173$	140.301	+	81.0026i	0.810986	+	0.468223i	0.847298	−	0.531117i	$-0.178228\pi$
$173$	140.301	+	81.0026i	0.810986	+	0.468223i	−0.0363120	+	0.999341i	$0.511561\pi$
$174$		0			0
$175$	135.959	+	185.538i	0.776909	+	1.06022i
$176$		0			0
$177$	−80.1998	+	138.910i	−0.453106	+	0.784803i
$178$		0			0
$179$	−107.153	−	185.594i	−0.598620	−	1.03684i	−0.993025	−	0.117903i	$-0.962383\pi$
$179$	−107.153	−	185.594i	−0.598620	−	1.03684i	0.394405	−	0.918937i	$-0.370951\pi$
$180$		0			0
$181$		−	112.423i		−	0.621123i	−0.950553	−	0.310562i	$-0.899483\pi$
$181$		−	112.423i		−	0.621123i	0.950553	−	0.310562i	$-0.100517\pi$
$182$		0			0
$183$	23.6008			0.128966
$184$		0			0
$185$	285.005	−	164.548i	1.54057	−	0.889447i
$186$		0			0
$187$	−71.4419	−	41.2470i	−0.382042	−	0.220572i
$188$		0			0
$189$	16.4264	+	150.393i	0.0869120	+	0.795731i
$190$		0			0
$191$	−152.302	+	263.795i	−0.797392	+	1.38112i	0.123916	+	0.992293i	$0.460455\pi$
$191$	−152.302	+	263.795i	−0.797392	+	1.38112i	−0.921309	+	0.388831i	$0.872879\pi$
$192$		0			0
$193$	−16.5220	−	28.6170i	−0.0856065	−	0.148275i	0.820043	−	0.572302i	$-0.193949\pi$
$193$	−16.5220	−	28.6170i	−0.0856065	−	0.148275i	−0.905649	+	0.424027i	$0.860616\pi$
$194$		0			0
$195$		−	553.524i		−	2.83858i
$196$		0			0
$197$	−198.693			−1.00859			−0.504296	−	0.863531i	$-0.668248\pi$
$197$	−198.693			−1.00859			−0.504296	+	0.863531i	$0.668248\pi$
$198$		0			0
$199$	82.0740	−	47.3854i	0.412432	−	0.238118i	−0.279402	−	0.960174i	$-0.590136\pi$
$199$	82.0740	−	47.3854i	0.412432	−	0.238118i	0.691834	+	0.722056i	$0.256803\pi$
$200$		0			0
$201$	257.442	+	148.634i	1.28080	+	0.739473i
$202$		0			0
$203$	243.739	−	26.6219i	1.20069	−	0.131142i
$204$		0			0
$205$	−169.433	+	293.467i	−0.826504	+	1.43155i
$206$		0			0
$207$	48.4025	+	83.8356i	0.233829	+	0.405003i
$208$		0			0
$209$		−	224.265i		−	1.07304i
$210$		0			0
$211$	−254.261			−1.20503			−0.602515	−	0.798108i	$-0.705834\pi$
$211$	−254.261			−1.20503			−0.602515	+	0.798108i	$0.705834\pi$
$212$		0			0
$213$	−297.242	+	171.613i	−1.39550	+	0.805694i
$214$		0			0
$215$	161.832	+	93.4339i	0.752709	+	0.434577i
$216$		0			0
$217$	−273.247	+	200.231i	−1.25920	+	0.922722i
$218$		0			0
$219$	−136.966	+	237.232i	−0.625414	+	1.08325i
$220$		0			0
$221$	−43.9055	−	76.0466i	−0.198667	−	0.344102i
$222$		0			0
$223$			20.5180i			0.0920088i	0.998941	+	0.0460044i	$0.0146488\pi$
$223$			20.5180i			0.0920088i	−0.998941	+	0.0460044i	$0.985351\pi$
$224$		0			0
$225$	87.8900			0.390622
$226$		0			0
$227$	−139.038	+	80.2737i	−0.612503	+	0.353629i	−0.773944	−	0.633254i	$-0.781719\pi$
$227$	−139.038	+	80.2737i	−0.612503	+	0.353629i	0.161442	+	0.986882i	$0.448386\pi$
$228$		0			0
$229$	37.4066	+	21.5967i	0.163348	+	0.0943088i	0.579445	−	0.815011i	$-0.303269\pi$
$229$	37.4066	+	21.5967i	0.163348	+	0.0943088i	−0.416098	+	0.909320i	$0.636603\pi$
$230$		0			0
$231$	−437.957	−	192.858i	−1.89592	−	0.834884i
$232$		0			0
$233$	23.5906	−	40.8602i	0.101247	−	0.175366i	−0.810951	−	0.585113i	$-0.801050\pi$
$233$	23.5906	−	40.8602i	0.101247	−	0.175366i	0.912199	+	0.409748i	$0.134383\pi$
$234$		0			0
$235$	−24.6017	−	42.6114i	−0.104688	−	0.181325i
$236$		0			0
$237$			202.211i			0.853212i
$238$		0			0
$239$	12.9231			0.0540717			0.0270359	−	0.999634i	$-0.491393\pi$
$239$	12.9231			0.0540717			0.0270359	+	0.999634i	$0.491393\pi$
$240$		0			0
$241$	289.801	−	167.316i	1.20249	−	0.694259i	0.241383	−	0.970430i	$-0.422399\pi$
$241$	289.801	−	167.316i	1.20249	−	0.694259i	0.961109	+	0.276171i	$0.0890656\pi$
$242$		0			0
$243$	121.293	+	70.0283i	0.499146	+	0.288182i
$244$		0			0
$245$	355.406	+	112.287i	1.45064	+	0.458314i
$246$		0			0
$247$	119.360	−	206.738i	0.483239	−	0.836995i
$248$		0			0
$249$	107.702	+	186.545i	0.432538	+	0.749178i
$250$		0			0
$251$			359.431i			1.43199i	0.698103	+	0.715997i	$0.254028\pi$
$251$			359.431i			1.43199i	−0.698103	+	0.715997i	$0.745972\pi$
$252$		0			0
$253$	724.143			2.86222
$254$		0			0
$255$	92.8040	−	53.5804i	0.363937	−	0.210119i
$256$		0			0
$257$	252.252	+	145.638i	0.981524	+	0.566683i	0.902730	−	0.430208i	$-0.141560\pi$
$257$	252.252	+	145.638i	0.981524	+	0.566683i	0.0787943	+	0.996891i	$0.474893\pi$
$258$		0			0
$259$	122.053	−	277.168i	0.471249	−	1.07015i
$260$		0			0
$261$	46.8429	−	81.1344i	0.179475	−	0.310860i
$262$		0			0
$263$	−31.6563	−	54.8304i	−0.120366	−	0.208481i	0.799546	−	0.600605i	$-0.205074\pi$
$263$	−31.6563	−	54.8304i	−0.120366	−	0.208481i	−0.919912	+	0.392125i	$0.871740\pi$
$264$		0			0
$265$		−	251.918i		−	0.950635i
$266$		0			0
$267$	−481.037			−1.80164
$268$		0			0
$269$	−119.188	+	68.8132i	−0.443078	+	0.255811i	−0.704902	−	0.709304i	$-0.749009\pi$
$269$	−119.188	+	68.8132i	−0.443078	+	0.255811i	0.261824	+	0.965116i	$0.415676\pi$
$270$		0			0
$271$	−114.023	−	65.8313i	−0.420750	−	0.242920i	0.274648	−	0.961545i	$-0.411439\pi$
$271$	−114.023	−	65.8313i	−0.420750	−	0.242920i	−0.695398	+	0.718625i	$0.744772\pi$
$272$		0			0
$273$	−301.084	−	410.878i	−1.10287	−	1.50505i
$274$		0			0
$275$	328.727	−	569.372i	1.19537	−	2.07044i
$276$		0			0
$277$	72.5157	+	125.601i	0.261789	+	0.453433i	0.966718	−	0.255846i	$-0.0823540\pi$
$277$	72.5157	+	125.601i	0.261789	+	0.453433i	−0.704928	+	0.709279i	$0.749021\pi$
$278$		0			0
$279$			129.438i			0.463936i
$280$		0			0
$281$	264.645			0.941796			0.470898	−	0.882188i	$-0.343930\pi$
$281$	264.645			0.941796			0.470898	+	0.882188i	$0.343930\pi$
$282$		0			0
$283$	−225.238	+	130.041i	−0.795894	+	0.459510i	−0.842034	−	0.539425i	$-0.818642\pi$
$283$	−225.238	+	130.041i	−0.795894	+	0.459510i	0.0461391	+	0.998935i	$0.485308\pi$
$284$		0			0
$285$	252.294	+	145.662i	0.885242	+	0.511095i
$286$		0			0
$287$	33.8591	+	310.000i	0.117976	+	1.08014i
$288$		0			0
$289$	8.50000	−	14.7224i	0.0294118	−	0.0509427i
$290$		0			0
$291$	−36.0222	−	62.3923i	−0.123788	−	0.214407i
$292$		0			0
$293$			185.750i			0.633960i	0.948432	+	0.316980i	$0.102669\pi$
$293$			185.750i			0.633960i	−0.948432	+	0.316980i	$0.897331\pi$
$294$		0			0
$295$	−357.084			−1.21045
$296$		0			0
$297$	374.484	−	216.209i	1.26089	−	0.727975i
$298$		0			0
$299$	667.547	+	385.408i	2.23260	+	1.28899i
$300$		0			0
$301$	170.950	−	18.6716i	0.567939	−	0.0620319i
$302$		0			0
$303$	92.2635	−	159.805i	0.304500	−	0.527410i
$304$		0			0
$305$	26.2702	+	45.5013i	0.0861318	+	0.149185i
$306$		0			0
$307$		−	601.788i		−	1.96022i	−0.198452	−	0.980111i	$-0.563591\pi$
$307$		−	601.788i		−	1.96022i	0.198452	−	0.980111i	$-0.436409\pi$
$308$		0			0
$309$	188.248			0.609216
$310$		0			0
$311$	99.7522	−	57.5919i	0.320746	−	0.185183i	−0.330979	−	0.943638i	$-0.607379\pi$
$311$	99.7522	−	57.5919i	0.320746	−	0.185183i	0.651725	+	0.758455i	$0.274046\pi$
$312$		0			0
$313$	−318.699	−	184.001i	−1.01821	−	0.587862i	−0.104622	−	0.994512i	$-0.533363\pi$
$313$	−318.699	−	184.001i	−1.01821	−	0.587862i	−0.913584	+	0.406650i	$0.866697\pi$
$314$		0			0
$315$	114.875	−	84.1785i	0.364683	−	0.267233i
$316$		0			0
$317$	−151.261	+	261.993i	−0.477166	+	0.826475i	−0.999658	−	0.0261692i	$-0.991669\pi$
$317$	−151.261	+	261.993i	−0.477166	+	0.826475i	0.522492	+	0.852644i	$0.325002\pi$
$318$		0			0
$319$	−350.405	−	606.920i	−1.09845	−	1.90257i
$320$		0			0
$321$		−	235.697i		−	0.734260i
$322$		0			0
$323$	46.2156			0.143082
$324$		0			0
$325$	606.071	−	349.915i	1.86483	−	1.07666i
$326$		0			0
$327$	25.7997	+	14.8954i	0.0788981	+	0.0455518i
$328$		0			0
$329$	−41.4398	−	18.2484i	−0.125957	−	0.0554661i
$330$		0			0
$331$	42.3286	−	73.3152i	0.127881	−	0.221496i	−0.794974	−	0.606643i	$-0.792516\pi$
$331$	42.3286	−	73.3152i	0.127881	−	0.221496i	0.922855	+	0.385147i	$0.125849\pi$
$332$		0			0
$333$	−57.8594	−	100.215i	−0.173752	−	0.300947i
$334$		0			0
$335$			661.782i			1.97547i
$336$		0			0
$337$	40.5304			0.120268			0.0601341	−	0.998190i	$-0.480847\pi$
$337$	40.5304			0.120268			0.0601341	+	0.998190i	$0.480847\pi$
$338$		0			0
$339$	253.780	−	146.520i	0.748613	−	0.432212i
$340$		0			0
$341$	838.531	+	484.126i	2.45903	+	1.41972i
$342$		0			0
$343$	324.893	−	109.970i	0.947211	−	0.320611i
$344$		0			0
$345$	−470.336	+	814.646i	−1.36329	+	2.36129i
$346$		0			0
$347$	−317.699	−	550.271i	−0.915559	−	1.58580i	−0.806080	−	0.591806i	$-0.798415\pi$
$347$	−317.699	−	550.271i	−0.915559	−	1.58580i	−0.109479	−	0.993989i	$-0.534918\pi$
$348$		0			0
$349$		−	358.525i		−	1.02729i	−0.858002	−	0.513646i	$-0.828295\pi$
$349$		−	358.525i		−	1.02729i	0.858002	−	0.513646i	$-0.171705\pi$
$350$		0			0
$351$	460.288			1.31136
$352$		0			0
$353$	420.428	−	242.734i	1.19101	−	0.687632i	0.232477	−	0.972602i	$-0.425317\pi$
$353$	420.428	−	242.734i	1.19101	−	0.687632i	0.958537	+	0.284970i	$0.0919835\pi$
$354$		0			0
$355$	−661.725	−	382.047i	−1.86401	−	1.07619i
$356$		0			0
$357$	39.7434	−	90.2523i	0.111326	−	0.252807i
$358$		0			0
$359$	−102.809	+	178.070i	−0.286375	+	0.496017i	−0.972942	−	0.231050i	$-0.925784\pi$
$359$	−102.809	+	178.070i	−0.286375	+	0.496017i	0.686566	+	0.727067i	$0.259117\pi$
$360$		0			0
$361$	−117.680	−	203.828i	−0.325983	−	0.564619i
$362$		0			0
$363$			954.350i			2.62906i
$364$		0			0
$365$	−609.830			−1.67077
$366$		0			0
$367$	85.9298	−	49.6116i	0.234141	−	0.135181i	−0.378340	−	0.925667i	$-0.623505\pi$
$367$	85.9298	−	49.6116i	0.234141	−	0.135181i	0.612481	+	0.790485i	$0.290172\pi$
$368$		0			0
$369$	103.191	+	59.5773i	0.279650	+	0.161456i
$370$		0			0
$371$	−137.028	−	186.998i	−0.369349	−	0.504036i
$372$		0			0
$373$	210.497	−	364.592i	0.564335	−	0.977458i	−0.432776	−	0.901502i	$-0.642466\pi$
$373$	210.497	−	364.592i	0.564335	−	0.977458i	0.997111	−	0.0759560i	$-0.0242009\pi$
$374$		0			0
$375$	102.142	+	176.916i	0.272380	+	0.471775i
$376$		0			0
$377$		−	745.980i		−	1.97873i
$378$		0			0
$379$	164.079			0.432925			0.216463	−	0.976291i	$-0.430548\pi$
$379$	164.079			0.432925			0.216463	+	0.976291i	$0.430548\pi$
$380$		0			0
$381$	45.9827	−	26.5481i	0.120690	−	0.0696802i
$382$		0			0
$383$	349.637	+	201.863i	0.912891	+	0.527058i	0.881360	−	0.472445i	$-0.156628\pi$
$383$	349.637	+	201.863i	0.912891	+	0.527058i	0.0315306	+	0.999503i	$0.489962\pi$
$384$		0			0
$385$	−115.671	−	1059.03i	−0.300443	−	2.75074i
$386$		0			0
$387$	32.8539	−	56.9046i	0.0848938	−	0.147040i
$388$		0			0
$389$	−211.133	−	365.693i	−0.542759	−	0.940086i	−0.998744	−	0.0500984i	$-0.984047\pi$
$389$	−211.133	−	365.693i	−0.542759	−	0.940086i	0.455986	−	0.889987i	$-0.349287\pi$
$390$		0			0
$391$			149.228i			0.381658i
$392$		0			0
$393$	−61.4883			−0.156459
$394$		0			0
$395$	−389.855	+	225.083i	−0.986974	+	0.569830i
$396$		0			0
$397$	−7.05169	−	4.07129i	−0.0177624	−	0.0102552i	0.491092	−	0.871107i	$-0.336598\pi$
$397$	−7.05169	−	4.07129i	−0.0177624	−	0.0102552i	−0.508855	+	0.860852i	$0.669931\pi$
$398$		0			0
$399$	266.508	−	29.1087i	0.667939	−	0.0729542i
$400$		0			0
$401$	−275.045	+	476.392i	−0.685897	+	1.18801i	0.287256	+	0.957854i	$0.407257\pi$
$401$	−275.045	+	476.392i	−0.685897	+	1.18801i	−0.973154	+	0.230156i	$0.926077\pi$
$402$		0			0
$403$	515.330	+	892.577i	1.27873	+	2.21483i
$404$		0			0
$405$			744.822i			1.83907i
$406$		0			0
$407$	−865.626			−2.12685
$408$		0			0
$409$	−175.687	+	101.433i	−0.429554	+	0.248003i	−0.699156	−	0.714969i	$-0.746441\pi$
$409$	−175.687	+	101.433i	−0.429554	+	0.248003i	0.269603	+	0.962972i	$0.413108\pi$
$410$		0			0
$411$	299.310	+	172.806i	0.728247	+	0.420454i
$412$		0			0
$413$	−265.061	+	194.232i	−0.641795	+	0.470296i
$414$		0			0
$415$	−239.768	+	415.290i	−0.577753	+	1.00070i
$416$		0			0
$417$	−384.294	−	665.617i	−0.921568	−	1.59620i
$418$		0			0
$419$			181.721i			0.433703i	0.976205	+	0.216851i	$0.0695787\pi$
$419$			181.721i			0.433703i	−0.976205	+	0.216851i	$0.930421\pi$
$420$		0			0
$421$	−702.525			−1.66871			−0.834353	−	0.551231i	$-0.814158\pi$
$421$	−702.525			−1.66871			−0.834353	+	0.551231i	$0.814158\pi$
$422$		0			0
$423$	−14.9833	+	8.65063i	−0.0354216	+	0.0204507i
$424$		0			0
$425$	117.334	+	67.7427i	0.276079	+	0.159395i
$426$		0			0
$427$	44.2502	+	19.4860i	0.103630	+	0.0456346i
$428$		0			0
$429$	−727.972	+	1260.89i	−1.69691	+	2.93913i
$430$		0			0
$431$	28.1679	+	48.7882i	0.0653547	+	0.113198i	0.896851	−	0.442332i	$-0.145849\pi$
$431$	28.1679	+	48.7882i	0.0653547	+	0.113198i	−0.831497	+	0.555530i	$0.812515\pi$
$432$		0			0
$433$		−	116.101i		−	0.268133i	−0.990972	−	0.134066i	$-0.957196\pi$
$433$		−	116.101i		−	0.268133i	0.990972	−	0.134066i	$-0.0428035\pi$
$434$		0			0
$435$	910.363			2.09279
$436$		0			0
$437$	−351.335	+	202.843i	−0.803970	+	0.464172i
$438$		0			0
$439$	169.759	+	98.0105i	0.386695	+	0.223259i	0.680727	−	0.732537i	$-0.261664\pi$
$439$	169.759	+	98.0105i	0.386695	+	0.223259i	−0.294032	+	0.955796i	$0.594997\pi$
$440$		0			0
$441$	39.4831	−	124.970i	0.0895309	−	0.283380i
$442$		0			0
$443$	268.247	−	464.617i	0.605523	−	1.04880i	−0.386445	−	0.922312i	$-0.626297\pi$
$443$	268.247	−	464.617i	0.605523	−	1.04880i	0.991969	−	0.126485i	$-0.0403694\pi$
$444$		0			0
$445$	−535.445	−	927.418i	−1.20325	−	2.08409i
$446$		0			0
$447$		−	21.2501i		−	0.0475394i
$448$		0			0
$449$	313.837			0.698968			0.349484	−	0.936942i	$-0.386357\pi$
$449$	313.837			0.698968			0.349484	+	0.936942i	$0.386357\pi$
$450$		0			0
$451$	771.912	−	445.664i	1.71156	−	0.988168i
$452$		0			0
$453$	−545.576	−	314.988i	−1.20436	−	0.695338i
$454$		0			0
$455$	457.016	−	1037.83i	1.00443	−	2.28094i
$456$		0			0
$457$	−293.482	+	508.327i	−0.642194	+	1.11231i	0.342749	+	0.939427i	$0.388642\pi$
$457$	−293.482	+	508.327i	−0.642194	+	1.11231i	−0.984942	+	0.172885i	$0.944691\pi$
$458$		0			0
$459$	44.5553	+	77.1721i	0.0970704	+	0.168131i
$460$		0			0
$461$			292.959i			0.635485i	0.948177	+	0.317743i	$0.102925\pi$
$461$			292.959i			0.635485i	−0.948177	+	0.317743i	$0.897075\pi$
$462$		0			0
$463$	608.464			1.31418			0.657088	−	0.753814i	$-0.271788\pi$
$463$	608.464			1.31418			0.657088	+	0.753814i	$0.271788\pi$
$464$		0			0
$465$	−1089.26	+	628.886i	−2.34250	+	1.35244i
$466$		0			0
$467$	−174.342	−	100.656i	−0.373323	−	0.215538i	0.301586	−	0.953439i	$-0.402484\pi$
$467$	−174.342	−	100.656i	−0.373323	−	0.215538i	−0.674909	+	0.737901i	$0.735817\pi$
$468$		0			0
$469$	359.970	+	491.237i	0.767526	+	1.04741i
$470$		0			0
$471$	−95.7938	+	165.920i	−0.203384	+	0.352271i
$472$		0			0
$473$	−245.761	−	425.671i	−0.519580	−	0.899938i
$474$		0			0
$475$			368.326i			0.775423i
$476$		0			0
$477$	−88.5813			−0.185705
$478$		0			0
$479$	−49.3706	+	28.5041i	−0.103070	+	0.0595075i	−0.550649	−	0.834737i	$-0.685620\pi$
$479$	−49.3706	+	28.5041i	−0.103070	+	0.0595075i	0.447579	+	0.894244i	$0.352286\pi$
$480$		0			0
$481$	−797.972	−	460.709i	−1.65899	−	0.957816i
$482$		0			0
$483$	93.9907	+	860.541i	0.194598	+	1.78166i
$484$		0			0
$485$	80.1932	−	138.899i	0.165347	−	0.286389i
$486$		0			0
$487$	−54.2551	−	93.9727i	−0.111407	−	0.192962i	0.804931	−	0.593369i	$-0.202202\pi$
$487$	−54.2551	−	93.9727i	−0.111407	−	0.192962i	−0.916338	+	0.400406i	$0.868869\pi$
$488$		0			0
$489$		−	902.208i		−	1.84501i
$490$		0			0
$491$	640.110			1.30369			0.651844	−	0.758353i	$-0.273996\pi$
$491$	640.110			1.30369			0.651844	+	0.758353i	$0.273996\pi$
$492$		0			0
$493$	125.071	−	72.2100i	0.253694	−	0.146471i
$494$		0			0
$495$	−352.525	−	203.530i	−0.712171	−	0.411172i
$496$		0			0
$497$	−699.005	+	76.3473i	−1.40645	+	0.153616i
$498$		0			0
$499$	12.5914	−	21.8090i	0.0252333	−	0.0437054i	−0.853133	−	0.521693i	$-0.825300\pi$
$499$	12.5914	−	21.8090i	0.0252333	−	0.0437054i	0.878366	+	0.477988i	$0.158634\pi$
$500$		0			0
$501$	409.575	+	709.405i	0.817515	+	1.41598i
$502$		0			0
$503$		−	13.0731i		−	0.0259903i	−0.999916	−	0.0129952i	$-0.995863\pi$
$503$		−	13.0731i		−	0.0259903i	0.999916	−	0.0129952i	$-0.00413661\pi$
$504$		0			0
$505$	410.797			0.813459
$506$		0			0
$507$	−842.074	+	486.171i	−1.66089	+	0.958918i
$508$		0			0
$509$	−229.264	−	132.366i	−0.450421	−	0.260051i	0.257587	−	0.966255i	$-0.417073\pi$
$509$	−229.264	−	132.366i	−0.450421	−	0.260051i	−0.708008	+	0.706204i	$0.750406\pi$
$510$		0			0
$511$	−452.673	+	331.711i	−0.885857	+	0.649140i
$512$		0			0
$513$	−121.127	+	209.797i	−0.236114	+	0.408962i
$514$		0			0
$515$	209.540	+	362.934i	0.406874	+	0.704726i
$516$		0			0
$517$			129.421i			0.250330i
$518$		0			0
$519$	553.543			1.06656
$520$		0			0
$521$	713.894	−	412.167i	1.37024	−	0.791107i	0.379279	−	0.925282i	$-0.376172\pi$
$521$	713.894	−	412.167i	1.37024	−	0.791107i	0.990958	+	0.134175i	$0.0428386\pi$
$522$		0			0
$523$	716.557	+	413.705i	1.37009	+	0.791022i	0.990939	−	0.134313i	$-0.0428826\pi$
$523$	716.557	+	413.705i	1.37009	+	0.791022i	0.379151	+	0.925335i	$0.376216\pi$
$524$		0			0
$525$	719.286	+	316.744i	1.37007	+	0.603321i
$526$		0			0
$527$	−99.7665	+	172.801i	−0.189310	+	0.327895i
$528$		0			0
$529$	−390.472	−	676.317i	−0.738132	−	1.27848i
$530$		0			0
$531$			125.560i			0.236460i
$532$		0			0
$533$	948.776			1.78007
$534$		0			0
$535$	454.415	−	262.356i	0.849373	−	0.490386i
$536$		0			0
$537$	−634.143	−	366.123i	−1.18090	−	0.681793i
$538$		0			0
$539$	−661.913	−	723.197i	−1.22804	−	1.34174i
$540$		0			0
$541$	295.679	−	512.130i	0.546541	−	0.946637i	−0.451967	−	0.892035i	$-0.649278\pi$
$541$	295.679	−	512.130i	0.546541	−	0.946637i	0.998508	−	0.0546021i	$-0.0173891\pi$
$542$		0			0
$543$	−192.065	−	332.667i	−0.353711	−	0.612646i
$544$		0			0
$545$			66.3209i			0.121690i
$546$		0			0
$547$	−243.528			−0.445207			−0.222603	−	0.974909i	$-0.571456\pi$
$547$	−243.528			−0.445207			−0.222603	+	0.974909i	$0.571456\pi$
$548$		0			0
$549$	15.9995	−	9.23731i	0.0291430	−	0.0168257i
$550$		0			0
$551$	340.015	+	196.308i	0.617087	+	0.356275i
$552$		0			0
$553$	−166.955	+	379.135i	−0.301908	+	0.685597i
$554$		0			0
$555$	562.230	−	973.811i	1.01303	−	1.75461i
$556$		0			0
$557$	182.185	+	315.554i	0.327083	+	0.566524i	0.981932	−	0.189236i	$-0.0606011\pi$
$557$	182.185	+	315.554i	0.327083	+	0.566524i	−0.654849	+	0.755760i	$0.727268\pi$
$558$		0			0
$559$		−	523.203i		−	0.935962i
$560$		0			0
$561$	−281.867			−0.502437
$562$		0			0
$563$	−368.988	+	213.036i	−0.655397	+	0.378393i	−0.790521	−	0.612435i	$-0.790190\pi$
$563$	−368.988	+	213.036i	−0.655397	+	0.378393i	0.135124	+	0.990829i	$0.456857\pi$
$564$		0			0
$565$	564.968	+	326.185i	0.999944	+	0.577318i
$566$		0			0
$567$	405.139	+	552.877i	0.714530	+	0.975092i
$568$		0			0
$569$	465.109	−	805.592i	0.817414	−	1.41580i	−0.0901674	−	0.995927i	$-0.528740\pi$
$569$	465.109	−	805.592i	0.817414	−	1.41580i	0.907581	−	0.419876i	$-0.137926\pi$
$570$		0			0
$571$	188.368	+	326.263i	0.329892	+	0.571390i	0.982490	−	0.186315i	$-0.0596543\pi$
$571$	188.368	+	326.263i	0.329892	+	0.571390i	−0.652598	+	0.757704i	$0.726321\pi$
$572$		0			0
$573$			1040.78i			1.81637i
$574$		0			0
$575$	−1189.31			−2.06836
$576$		0			0
$577$	739.734	−	427.085i	1.28203	−	0.740183i	0.304814	−	0.952412i	$-0.401406\pi$
$577$	739.734	−	427.085i	1.28203	−	0.740183i	0.977220	+	0.212229i	$0.0680724\pi$
$578$		0			0
$579$	−97.7793	−	56.4529i	−0.168876	−	0.0975007i
$580$		0			0
$581$	47.9146	+	438.686i	0.0824691	+	0.755054i
$582$		0			0
$583$	−331.313	+	573.851i	−0.568290	+	0.984307i
$584$		0			0
$585$	−216.648	−	375.246i	−0.370339	−	0.641446i
$586$		0			0
$587$		−	75.7980i		−	0.129128i	−0.997914	−	0.0645639i	$-0.979434\pi$
$587$		−	75.7980i		−	0.129128i	0.997914	−	0.0645639i	$-0.0205656\pi$
$588$		0			0
$589$	−542.444			−0.920957
$590$		0			0
$591$	−587.943	+	339.449i	−0.994827	+	0.574364i
$592$		0			0
$593$	−479.612	−	276.904i	−0.808790	−	0.466955i	0.0377456	−	0.999287i	$-0.487982\pi$
$593$	−479.612	−	276.904i	−0.808790	−	0.466955i	−0.846535	+	0.532332i	$0.821316\pi$
$594$		0			0
$595$	218.241	−	23.8369i	0.366792	−	0.0400620i
$596$		0			0
$597$	161.908	−	280.432i	0.271202	−	0.469736i
$598$		0			0
$599$	142.479	+	246.781i	0.237861	+	0.411988i	0.960100	−	0.279656i	$-0.0902202\pi$
$599$	142.479	+	246.781i	0.237861	+	0.411988i	−0.722239	+	0.691644i	$0.756887\pi$
$600$		0			0
$601$		−	955.549i		−	1.58993i	−0.606654	−	0.794966i	$-0.707489\pi$
$601$		−	955.549i		−	1.58993i	0.606654	−	0.794966i	$-0.292511\pi$
$602$		0			0
$603$	232.701			0.385905
$604$		0			0
$605$	−1839.95	+	1062.29i	−3.04123	+	1.75586i
$606$		0			0
$607$	620.164	+	358.052i	1.02169	+	0.589871i	0.914592	−	0.404378i	$-0.132512\pi$
$607$	620.164	+	358.052i	1.02169	+	0.589871i	0.107095	+	0.994249i	$0.465845\pi$
$608$		0			0
$609$	675.757	−	495.183i	1.10962	−	0.813108i
$610$		0			0
$611$	−68.8812	+	119.306i	−0.112735	+	0.195263i
$612$		0			0
$613$	205.328	+	355.638i	0.334955	+	0.580159i	0.983476	−	0.181037i	$-0.0579455\pi$
$613$	205.328	+	355.638i	0.334955	+	0.580159i	−0.648521	+	0.761197i	$0.724612\pi$
$614$		0			0
$615$			1157.85i			1.88268i
$616$		0			0
$617$	−495.122			−0.802467			−0.401234	−	0.915976i	$-0.631418\pi$
$617$	−495.122			−0.802467			−0.401234	+	0.915976i	$0.631418\pi$
$618$		0			0
$619$	−67.8957	+	39.1996i	−0.109686	+	0.0633273i	−0.553839	−	0.832623i	$-0.686838\pi$
$619$	−67.8957	+	39.1996i	−0.109686	+	0.0633273i	0.444153	+	0.895951i	$0.353505\pi$
$620$		0			0
$621$	−677.426	−	391.112i	−1.09086	−	0.629810i
$622$		0			0
$623$	−901.918	−	397.167i	−1.44770	−	0.637507i
$624$		0			0
$625$	183.360	−	317.588i	0.293375	−	0.508141i
$626$		0			0
$627$	−383.138	−	663.614i	−0.611065	−	1.05840i
$628$		0			0
$629$		−	178.384i		−	0.283600i
$630$		0			0
$631$	−636.712			−1.00905			−0.504526	−	0.863396i	$-0.668333\pi$
$631$	−636.712			−1.00905			−0.504526	+	0.863396i	$0.668333\pi$
$632$		0			0
$633$	−752.373	+	434.383i	−1.18858	+	0.686229i
$634$		0			0
$635$	102.367	+	59.1018i	0.161209	+	0.0930738i
$636$		0			0
$637$	−225.275	−	1018.96i	−0.353651	−	1.59963i
$638$		0			0
$639$	−134.338	+	232.680i	−0.210232	+	0.364132i
$640$		0			0
$641$	530.318	+	918.537i	0.827329	+	1.43298i	0.900127	+	0.435629i	$0.143474\pi$
$641$	530.318	+	918.537i	0.827329	+	1.43298i	−0.0727979	+	0.997347i	$0.523193\pi$
$642$		0			0
$643$			937.642i			1.45823i	0.684391	+	0.729115i	$0.260068\pi$
$643$			937.642i			1.45823i	−0.684391	+	0.729115i	$0.739932\pi$
$644$		0			0
$645$	638.495			0.989914
$646$		0			0
$647$	−63.9153	+	36.9015i	−0.0987872	+	0.0570348i	−0.548580	−	0.836098i	$-0.684831\pi$
$647$	−63.9153	+	36.9015i	−0.0987872	+	0.0570348i	0.449792	+	0.893133i	$0.351498\pi$
$648$		0			0
$649$	813.410	+	469.622i	1.25333	+	0.723609i
$650$		0			0
$651$	−466.477	+	1059.31i	−0.716555	+	1.62721i
$652$		0			0
$653$	−455.335	+	788.663i	−0.697297	+	1.20775i	0.272103	+	0.962268i	$0.412281\pi$
$653$	−455.335	+	788.663i	−0.697297	+	1.20775i	−0.969400	+	0.245486i	$0.921052\pi$
$654$		0			0
$655$	−68.4430	−	118.547i	−0.104493	−	0.180988i
$656$		0			0
$657$			214.433i			0.326381i
$658$		0			0
$659$	176.839			0.268345			0.134172	−	0.990958i	$-0.457162\pi$
$659$	176.839			0.268345			0.134172	+	0.990958i	$0.457162\pi$
$660$		0			0
$661$	73.9455	−	42.6925i	0.111869	−	0.0645877i	−0.443021	−	0.896511i	$-0.646093\pi$
$661$	73.9455	−	42.6925i	0.111869	−	0.0645877i	0.554891	+	0.831923i	$0.312760\pi$
$662$		0			0
$663$	−259.838	−	150.017i	−0.391912	−	0.226271i
$664$		0			0
$665$	352.772	+	481.414i	0.530484	+	0.723931i
$666$		0			0
$667$	−633.868	+	1097.89i	−0.950327	+	1.64601i
$668$		0			0
$669$	35.0531	+	60.7138i	0.0523963	+	0.0907530i
$670$		0			0
$671$		−	138.198i		−	0.205958i
$672$		0			0
$673$	103.211			0.153359			0.0766796	−	0.997056i	$-0.475568\pi$
$673$	103.211			0.153359			0.0766796	+	0.997056i	$0.475568\pi$
$674$		0			0
$675$	−615.040	+	355.094i	−0.911171	+	0.526065i
$676$		0			0
$677$	−124.496	−	71.8780i	−0.183894	−	0.106171i	0.405227	−	0.914216i	$-0.367193\pi$
$677$	−124.496	−	71.8780i	−0.183894	−	0.106171i	−0.589121	+	0.808045i	$0.700526\pi$
$678$		0			0
$679$	−16.0256	−	146.724i	−0.0236018	−	0.216088i
$680$		0			0
$681$	−274.281	+	475.068i	−0.402762	+	0.697604i
$682$		0			0
$683$	−93.4824	−	161.916i	−0.136870	−	0.237066i	0.789440	−	0.613828i	$-0.210371\pi$
$683$	−93.4824	−	161.916i	−0.136870	−	0.237066i	−0.926310	+	0.376761i	$0.877038\pi$
$684$		0			0
$685$			769.408i			1.12322i
$686$		0			0
$687$	147.584			0.214824
$688$		0			0
$689$	−610.838	+	352.667i	−0.886557	+	0.511854i
$690$		0			0
$691$	−718.379	−	414.756i	−1.03962	−	0.600226i	−0.119896	−	0.992787i	$-0.538256\pi$
$691$	−718.379	−	414.756i	−1.03962	−	0.600226i	−0.919726	+	0.392561i	$0.871589\pi$
$692$		0			0
$693$	−372.385	+	40.6729i	−0.537352	+	0.0586911i
$694$		0			0
$695$	855.520	−	1481.80i	1.23096	−	2.13209i
$696$		0			0
$697$	91.8404	+	159.072i	0.131765	+	0.228224i
$698$		0			0
$699$		−	161.210i		−	0.230629i
$700$		0			0
$701$	−657.446			−0.937869			−0.468934	−	0.883233i	$-0.655362\pi$
$701$	−657.446			−0.937869			−0.468934	+	0.883233i	$0.655362\pi$
$702$		0			0
$703$	419.979	−	242.475i	0.597410	−	0.344915i
$704$		0			0
$705$	−145.596	−	84.0597i	−0.206519	−	0.119234i
$706$		0			0
$707$	304.932	−	223.449i	0.431304	−	0.316052i
$708$		0			0
$709$	56.0666	−	97.1101i	0.0790784	−	0.136968i	−0.823774	−	0.566918i	$-0.808136\pi$
$709$	56.0666	−	97.1101i	0.0790784	−	0.136968i	0.902853	+	0.429950i	$0.141469\pi$
$710$		0			0
$711$	79.1451	+	137.083i	0.111315	+	0.192804i
$712$		0			0
$713$		−	1751.53i		−	2.45656i
$714$		0			0
$715$	−3241.24			−4.53321
$716$		0			0
$717$	38.2403	−	22.0780i	0.0533337	−	0.0307922i
$718$		0			0
$719$	525.686	+	303.505i	0.731135	+	0.422121i	0.818837	−	0.574026i	$-0.194619\pi$
$719$	525.686	+	303.505i	0.731135	+	0.422121i	−0.0877022	+	0.996147i	$0.527952\pi$
$720$		0			0
$721$	352.954	+	155.427i	0.489535	+	0.215571i
$722$		0			0
$723$	571.691	−	990.197i	0.790720	−	1.36957i
$724$		0			0
$725$	575.494	+	996.784i	0.793784	+	1.37487i
$726$		0			0
$727$		−	1330.13i		−	1.82962i	−0.403884	−	0.914810i	$-0.632340\pi$
$727$		−	1330.13i		−	1.82962i	0.403884	−	0.914810i	$-0.367660\pi$
$728$		0			0
$729$	−402.715			−0.552421
$730$		0			0
$731$	87.7204	−	50.6454i	0.120001	−	0.0692823i
$732$		0			0
$733$	−349.057	−	201.528i	−0.476203	−	0.274936i	0.242630	−	0.970119i	$-0.421990\pi$
$733$	−349.057	−	201.528i	−0.476203	−	0.274936i	−0.718833	+	0.695183i	$0.755323\pi$
$734$		0			0
$735$	1243.50	−	274.917i	1.69184	−	0.374036i
$736$		0			0
$737$	870.349	−	1507.49i	1.18094	−	2.04544i
$738$		0			0
$739$	75.3128	+	130.446i	0.101912	+	0.176516i	0.912472	−	0.409139i	$-0.134171\pi$
$739$	75.3128	+	130.446i	0.101912	+	0.176516i	−0.810560	+	0.585655i	$0.800837\pi$
$740$		0			0
$741$		−	815.664i		−	1.10076i
$742$		0			0
$743$	−617.366			−0.830910			−0.415455	−	0.909614i	$-0.636378\pi$
$743$	−617.366			−0.830910			−0.415455	+	0.909614i	$0.636378\pi$
$744$		0			0
$745$	40.9693	−	23.6537i	0.0549924	−	0.0317499i
$746$		0			0
$747$	146.027	+	84.3088i	0.195485	+	0.112863i
$748$		0			0
$749$	194.603	−	441.920i	0.259817	−	0.590013i
$750$		0			0
$751$	603.585	−	1045.44i	0.803708	−	1.39206i	−0.113452	−	0.993544i	$-0.536191\pi$
$751$	603.585	−	1045.44i	0.803708	−	1.39206i	0.917160	−	0.398520i	$-0.130476\pi$
$752$		0			0
$753$	614.055	+	1063.58i	0.815479	+	1.41245i
$754$		0			0
$755$		−	1402.46i		−	1.85757i
$756$		0			0
$757$	975.902			1.28917			0.644585	−	0.764533i	$-0.277030\pi$
$757$	975.902			1.28917			0.644585	+	0.764533i	$0.277030\pi$
$758$		0			0
$759$	2142.78	−	1237.13i	2.82316	−	1.62995i
$760$		0			0
$761$	716.239	+	413.521i	0.941181	+	0.543391i	0.890330	−	0.455315i	$-0.150473\pi$
$761$	716.239	+	413.521i	0.941181	+	0.543391i	0.0508507	+	0.998706i	$0.483807\pi$
$762$		0			0
$763$	36.0746	+	49.2296i	0.0472799	+	0.0645211i
$764$		0			0
$765$	41.9426	−	72.6467i	0.0548269	−	0.0949630i
$766$		0			0
$767$	499.891	+	865.837i	0.651749	+	1.12886i
$768$		0			0
$769$			915.196i			1.19011i	0.803684	+	0.595056i	$0.202870\pi$
$769$			915.196i			1.19011i	−0.803684	+	0.595056i	$0.797130\pi$
$770$		0			0
$771$	995.236			1.29084
$772$		0			0
$773$	771.019	−	445.148i	0.997438	−	0.575871i	0.0899487	−	0.995946i	$-0.471330\pi$
$773$	771.019	−	445.148i	0.997438	−	0.575871i	0.907489	+	0.420075i	$0.137996\pi$
$774$		0			0
$775$	−1377.17	−	795.112i	−1.77700	−	1.02595i
$776$		0			0
$777$	−112.355	−	1028.67i	−0.144601	−	1.32390i
$778$		0			0
$779$	−249.674	+	432.448i	−0.320506	+	0.555133i
$780$		0			0
$781$	1004.91	+	1740.55i	1.28669	+	2.22861i
$782$		0			0
$783$			757.021i			0.966821i
$784$		0			0
$785$	−426.515			−0.543331
$786$		0			0
$787$	76.0033	−	43.8805i	0.0965735	−	0.0557567i	−0.450935	−	0.892557i	$-0.648910\pi$
$787$	76.0033	−	43.8805i	0.0965735	−	0.0557567i	0.547509	+	0.836800i	$0.315576\pi$
$788$		0			0
$789$	−187.346	−	108.164i	−0.237447	−	0.137090i
$790$		0			0
$791$	596.797	−	65.1839i	0.754485	−	0.0824069i
$792$		0			0
$793$	73.5527	−	127.397i	0.0927525	−	0.160652i
$794$		0			0
$795$	−430.380	−	745.440i	−0.541359	−	0.937661i
$796$		0			0
$797$		−	963.149i		−	1.20847i	−0.796807	−	0.604234i	$-0.793479\pi$
$797$		−	963.149i		−	1.20847i	0.796807	−	0.604234i	$-0.206521\pi$
$798$		0			0
$799$	−26.6705			−0.0333798
$800$		0			0
$801$	−326.105	+	188.277i	−0.407123	+	0.235052i
$802$		0			0
$803$	1389.15	+	802.024i	1.72994	+	0.998784i
$804$		0			0
$805$	−1554.47	+	1139.08i	−1.93101	+	1.41501i
$806$		0			0
$807$	−235.123	+	407.244i	−0.291354	+	0.504640i
$808$		0			0
$809$	272.037	+	471.182i	0.336264	+	0.582426i	0.983727	−	0.179671i	$-0.0575033\pi$
$809$	272.037	+	471.182i	0.336264	+	0.582426i	−0.647463	+	0.762097i	$0.724170\pi$
$810$		0			0
$811$		−	1098.68i		−	1.35473i	−0.735648	−	0.677364i	$-0.763122\pi$
$811$		−	1098.68i		−	1.35473i	0.735648	−	0.677364i	$-0.236878\pi$
$812$		0			0
$813$	−449.868			−0.553343
$814$		0			0
$815$	1739.42	−	1004.25i	2.13426	−	1.23221i
$816$		0			0
$817$	238.474	+	137.683i	0.291889	+	0.168522i
$818$		0			0
$819$	−364.928	−	160.699i	−0.445578	−	0.196214i
$820$		0			0
$821$	−533.679	+	924.359i	−0.650035	+	1.12589i	0.333078	+	0.942899i	$0.391913\pi$
$821$	−533.679	+	924.359i	−0.650035	+	1.12589i	−0.983114	+	0.182995i	$0.941421\pi$
$822$		0			0
$823$	−260.473	−	451.153i	−0.316492	−	0.548181i	0.663261	−	0.748388i	$-0.269172\pi$
$823$	−260.473	−	451.153i	−0.316492	−	0.548181i	−0.979754	+	0.200207i	$0.935839\pi$
$824$		0			0
$825$		−	2246.41i		−	2.72292i
$826$		0			0
$827$	623.675			0.754142			0.377071	−	0.926184i	$-0.376931\pi$
$827$	623.675			0.754142			0.377071	+	0.926184i	$0.376931\pi$
$828$		0			0
$829$	599.432	−	346.082i	0.723078	−	0.417469i	−0.0928064	−	0.995684i	$-0.529584\pi$
$829$	599.432	−	346.082i	0.723078	−	0.417469i	0.815885	+	0.578215i	$0.196250\pi$
$830$		0			0
$831$	429.156	+	247.773i	0.516433	+	0.298163i
$832$		0			0
$833$	149.033	−	136.404i	0.178912	−	0.163750i
$834$		0			0
$835$	−911.801	+	1579.29i	−1.09198	+	1.89136i
$836$		0			0
$837$	−522.956	−	905.787i	−0.624799	−	1.08218i
$838$		0			0
$839$			516.302i			0.615377i	0.951487	+	0.307689i	$0.0995555\pi$
$839$			516.302i			0.615377i	−0.951487	+	0.307689i	$0.900444\pi$
$840$		0			0
$841$	385.889			0.458845
$842$		0			0
$843$	783.098	−	452.122i	0.928942	−	0.536325i
$844$		0			0
$845$	−1874.64	−	1082.32i	−2.21850	−	1.28085i
$846$		0			0
$847$	−787.958	+	1789.36i	−0.930293	+	2.11258i
$848$		0			0
$849$	−444.328	+	769.599i	−0.523355	+	0.906477i
$850$		0			0
$851$	782.941	+	1356.09i	0.920024	+	1.59353i
$852$		0			0
$853$		−	134.154i		−	0.157273i	−0.996903	−	0.0786365i	$-0.974943\pi$
$853$		−	134.154i		−	0.157273i	0.996903	−	0.0786365i	$-0.0250567\pi$
$854$		0			0
$855$	228.047			0.266722
$856$		0			0
$857$	−973.094	+	561.816i	−1.13547	+	0.655562i	−0.945304	−	0.326191i	$-0.894235\pi$
$857$	−973.094	+	561.816i	−1.13547	+	0.655562i	−0.190162	+	0.981753i	$0.560901\pi$
$858$		0			0
$859$	1081.68	+	624.506i	1.25923	+	0.727015i	0.972924	−	0.231124i	$-0.0742403\pi$
$859$	1081.68	+	624.506i	1.25923	+	0.727015i	0.286303	+	0.958139i	$0.407574\pi$
$860$		0			0
$861$	629.799	+	859.463i	0.731474	+	0.998215i
$862$		0			0
$863$	282.719	−	489.683i	0.327600	−	0.567419i	−0.654435	−	0.756118i	$-0.727094\pi$
$863$	282.719	−	489.683i	0.327600	−	0.567419i	0.982035	+	0.188699i	$0.0604269\pi$
$864$		0			0
$865$	616.153	+	1067.21i	0.712315	+	1.23377i
$866$		0			0
$867$		−	58.0860i		−	0.0669965i
$868$		0			0
$869$	1184.08			1.36258
$870$		0			0
$871$	1604.65	−	926.447i	1.84231	−	1.06366i
$872$		0			0
$873$	−48.8405	−	28.1981i	−0.0559456	−	0.0323002i
$874$		0			0
$875$	45.4412	+	416.041i	0.0519328	+	0.475475i
$876$		0			0
$877$	511.456	−	885.868i	0.583188	−	1.01011i	−0.411911	−	0.911224i	$-0.635138\pi$
$877$	511.456	−	885.868i	0.583188	−	1.01011i	0.995099	−	0.0988871i	$-0.0315283\pi$
$878$		0			0
$879$	317.338	+	549.646i	0.361022	+	0.625308i
$880$		0			0
$881$			463.166i			0.525728i	0.964833	+	0.262864i	$0.0846670\pi$
$881$			463.166i			0.525728i	−0.964833	+	0.262864i	$0.915333\pi$
$882$		0			0
$883$	−375.351			−0.425086			−0.212543	−	0.977152i	$-0.568175\pi$
$883$	−375.351			−0.425086			−0.212543	+	0.977152i	$0.568175\pi$
$884$		0			0
$885$	−1056.63	+	610.046i	−1.19393	+	0.689318i
$886$		0			0
$887$	−901.930	−	520.729i	−1.01683	−	0.587068i	−0.103647	−	0.994614i	$-0.533051\pi$
$887$	−901.930	−	520.729i	−1.01683	−	0.587068i	−0.913185	+	0.407546i	$0.866385\pi$
$888$		0			0
$889$	108.135	−	11.8108i	0.121636	−	0.0132854i
$890$		0			0
$891$	979.560	−	1696.65i	1.09939	−	1.90421i
$892$		0			0
$893$	−36.2527	−	62.7916i	−0.0405966	−	0.0703153i
$894$		0			0
$895$		−	1630.13i		−	1.82138i
$896$		0			0
$897$	2633.74			2.93617
$898$		0			0
$899$	−1467.99	+	847.546i	−1.63292	+	0.942765i
$900$		0			0
$901$	−118.257	−	68.2755i	−0.131250	−	0.0757775i
$902$		0			0
$903$	473.951	−	347.303i	0.524862	−	0.384610i
$904$		0			0
$905$	427.578	−	740.587i	0.472462	−	0.818328i
$906$		0			0
$907$	−223.052	−	386.337i	−0.245922	−	0.425950i	0.716468	−	0.697620i	$-0.245757\pi$
$907$	−223.052	−	386.337i	−0.245922	−	0.425950i	−0.962391	+	0.271670i	$0.912424\pi$
$908$		0			0
$909$		−	144.447i		−	0.158908i
$910$		0			0
$911$	−654.905			−0.718885			−0.359443	−	0.933167i	$-0.617033\pi$
$911$	−654.905			−0.718885			−0.359443	+	0.933167i	$0.617033\pi$
$912$		0			0
$913$	1092.34	−	630.666i	1.19643	−	0.690762i
$914$		0			0
$915$	155.470	+	89.7607i	0.169913	+	0.0980991i
$916$		0			0
$917$	−115.287	−	50.7677i	−0.125722	−	0.0553628i
$918$		0			0
$919$	−382.775	+	662.986i	−0.416513	+	0.721422i	−0.995586	−	0.0938541i	$-0.970081\pi$
$919$	−382.775	+	662.986i	−0.416513	+	0.721422i	0.579073	+	0.815276i	$0.303415\pi$
$920$		0			0
$921$	−1028.10	−	1780.72i	−1.11629	−	1.93347i
$922$		0			0
$923$			2139.35i			2.31782i
$924$		0			0
$925$	1421.67			1.53695
$926$		0			0
$927$	127.617	−	73.6799i	0.137667	−	0.0794821i
$928$		0			0
$929$	1447.87	+	835.926i	1.55852	+	0.899812i	0.997399	+	0.0720789i	$0.0229633\pi$
$929$	1447.87	+	835.926i	1.55852	+	0.899812i	0.561122	+	0.827733i	$0.310370\pi$
$930$		0			0
$931$	523.721	+	165.464i	0.562536	+	0.177728i
$932$		0			0
$933$	196.781	−	340.835i	0.210913	−	0.365311i
$934$		0			0
$935$	−313.748	−	543.428i	−0.335560	−	0.581207i
$936$		0			0
$937$		−	166.200i		−	0.177375i	−0.996060	−	0.0886874i	$-0.971733\pi$
$937$		−	166.200i		−	0.177375i	0.996060	−	0.0886874i	$-0.0282672\pi$
$938$		0			0
$939$	−1257.40			−1.33908
$940$		0			0
$941$	−230.170	+	132.889i	−0.244601	+	0.141221i	−0.617290	−	0.786736i	$-0.711769\pi$
$941$	−230.170	+	132.889i	−0.244601	+	0.141221i	0.372688	+	0.927957i	$0.378436\pi$
$942$		0			0
$943$	−1396.36	−	806.187i	−1.48076	−	0.854917i
$944$		0			0
$945$	−463.780	+	1053.19i	−0.490772	+	1.11448i
$946$		0			0
$947$	705.462	−	1221.90i	0.744944	−	1.29028i	−0.205277	−	0.978704i	$-0.565809\pi$
$947$	705.462	−	1221.90i	0.744944	−	1.29028i	0.950221	−	0.311577i	$-0.100857\pi$
$948$		0			0
$949$	853.717	+	1478.68i	0.899596	+	1.55815i
$950$		0			0
$951$			1033.67i			1.08693i
$952$		0			0
$953$	606.016			0.635903			0.317952	−	0.948107i	$-0.397005\pi$
$953$	606.016			0.635903			0.317952	+	0.948107i	$0.397005\pi$
$954$		0			0
$955$	−2006.58	+	1158.50i	−2.10113	+	1.21309i
$956$		0			0
$957$	−2073.74	−	1197.27i	−2.16691	−	1.25107i
$958$		0			0
$959$	418.512	+	571.127i	0.436404	+	0.595545i
$960$		0			0
$961$	690.484	−	1195.95i	0.718505	−	1.24449i
$962$		0			0
$963$	−92.2516	−	159.785i	−0.0957961	−	0.165924i
$964$		0			0
$965$		−	251.352i		−	0.260469i
$966$		0			0
$967$	−893.289			−0.923773			−0.461887	−	0.886939i	$-0.652827\pi$
$967$	−893.289			−0.923773			−0.461887	+	0.886939i	$0.652827\pi$
$968$		0			0
$969$	136.755	−	78.9553i	0.141130	−	0.0814812i
$970$		0			0
$971$	−418.257	−	241.481i	−0.430749	−	0.248693i	0.268917	−	0.963163i	$-0.413334\pi$
$971$	−418.257	−	241.481i	−0.430749	−	0.248693i	−0.699665	+	0.714471i	$0.746668\pi$
$972$		0			0
$973$	−170.965	−	1565.29i	−0.175709	−	1.60872i
$974$		0			0
$975$	1195.60	−	2070.84i	1.22625	−	2.12393i
$976$		0			0
$977$	−131.948	−	228.541i	−0.135055	−	0.233922i	0.790564	−	0.612380i	$-0.209788\pi$
$977$	−131.948	−	228.541i	−0.135055	−	0.233922i	−0.925618	+	0.378458i	$0.876454\pi$
$978$		0			0
$979$			2816.78i			2.87721i
$980$		0			0
$981$	23.3202			0.0237719
$982$		0			0
$983$	803.540	−	463.924i	0.817437	−	0.471947i	−0.0320950	−	0.999485i	$-0.510218\pi$
$983$	803.540	−	463.924i	0.817437	−	0.471947i	0.849532	+	0.527538i	$0.176885\pi$
$984$		0			0
$985$	−1308.89	−	755.686i	−1.32882	−	0.767194i
$986$		0			0
$987$	−153.798	+	16.7983i	−0.155824	+	0.0170195i
$988$		0			0
$989$	−444.572	+	770.021i	−0.449516	+	0.778585i
$990$		0			0
$991$	−826.546	−	1431.62i	−0.834052	−	1.44462i	−0.894800	−	0.446468i	$-0.852682\pi$
$991$	−826.546	−	1431.62i	−0.834052	−	1.44462i	0.0607476	−	0.998153i	$-0.480652\pi$
$992$		0			0
$993$		−	289.258i		−	0.291298i
$994$		0			0
$995$	720.882			0.724505
$996$		0			0
$997$	−820.589	+	473.767i	−0.823058	+	0.475193i	−0.851470	−	0.524404i	$-0.824288\pi$
$997$	−820.589	+	473.767i	−0.823058	+	0.475193i	0.0284120	+	0.999596i	$0.490955\pi$
$998$		0			0
$999$	809.782	+	467.528i	0.810593	+	0.467996i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	476.3.s.a.341.18	✓	44
7.3	odd	6	inner	476.3.s.a.409.18	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
476.3.s.a.341.18	✓	44	1.1	even	1	trivial
476.3.s.a.409.18	yes	44	7.3	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 476 = 2^{2} \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	476.s (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.95906 - 1.70841i) q^{3} +(6.58749 + 3.80329i) q^{5} +(6.95862 - 0.760040i) q^{7} +(1.33734 - 2.31634i) q^{9} +O(q^{10})\)	\(q+(2.95906 - 1.70841i) q^{3} +(6.58749 + 3.80329i) q^{5} +(6.95862 - 0.760040i) q^{7} +(1.33734 - 2.31634i) q^{9} +(-10.0039 - 17.3272i) q^{11} -21.2973i q^{13} +25.9903 q^{15} +(3.57071 - 2.06155i) q^{17} +(9.70722 + 5.60447i) q^{19} +(19.2925 - 14.1372i) q^{21} +(-18.0966 + 31.3442i) q^{23} +(16.4300 + 28.4576i) q^{25} +21.6125i q^{27} +35.0270 q^{29} +(-41.9103 + 24.1969i) q^{31} +(-59.2040 - 34.1814i) q^{33} +(48.7305 + 21.4589i) q^{35} +(21.6323 - 37.4682i) q^{37} +(-36.3846 - 63.0199i) q^{39} +44.5491i q^{41} +24.5666 q^{43} +(17.6194 - 10.1726i) q^{45} +(-5.60192 - 3.23427i) q^{47} +(47.8447 - 10.5776i) q^{49} +(7.04396 - 12.2005i) q^{51} +(-16.5592 - 28.6814i) q^{53} -152.190i q^{55} +38.2989 q^{57} +(-40.6548 + 23.4720i) q^{59} +(5.98184 + 3.45362i) q^{61} +(7.54552 - 17.1349i) q^{63} +(80.9998 - 140.296i) q^{65} +(43.5007 + 75.3453i) q^{67} +123.666i q^{69} -100.452 q^{71} +(-69.4304 + 40.0857i) q^{73} +(97.2346 + 56.1384i) q^{75} +(-82.7824 - 112.970i) q^{77} +(-29.5905 + 51.2523i) q^{79} +(48.9591 + 84.7996i) q^{81} +63.0422i q^{83} +31.3627 q^{85} +(103.647 - 59.8405i) q^{87} +(-121.923 - 70.3924i) q^{89} +(-16.1868 - 148.200i) q^{91} +(-82.6767 + 143.200i) q^{93} +(42.6308 + 73.8388i) q^{95} -21.0852i q^{97} -53.5142 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 6 q^{3} + 22 q^{7} + 88 q^{9}+O(q^{10}) \) 44 * q - 6 * q^3 + 22 * q^7 + 88 * q^9	\( 44 q - 6 q^{3} + 22 q^{7} + 88 q^{9} + 8 q^{11} + 16 q^{15} - 54 q^{19} - 16 q^{21} - 52 q^{23} + 150 q^{25} + 8 q^{29} + 78 q^{31} - 6 q^{33} + 10 q^{35} - 34 q^{37} - 60 q^{39} - 76 q^{43} - 72 q^{45} - 6 q^{47} - 56 q^{49} - 172 q^{53} - 64 q^{57} + 30 q^{59} + 444 q^{61} + 206 q^{63} - 54 q^{65} - 56 q^{67} + 204 q^{71} - 48 q^{73} + 132 q^{75} - 494 q^{77} - 16 q^{79} - 342 q^{81} + 594 q^{87} - 252 q^{89} + 284 q^{91} - 146 q^{93} + 148 q^{95} - 180 q^{99}+O(q^{100}) \) 44 * q - 6 * q^3 + 22 * q^7 + 88 * q^9 + 8 * q^11 + 16 * q^15 - 54 * q^19 - 16 * q^21 - 52 * q^23 + 150 * q^25 + 8 * q^29 + 78 * q^31 - 6 * q^33 + 10 * q^35 - 34 * q^37 - 60 * q^39 - 76 * q^43 - 72 * q^45 - 6 * q^47 - 56 * q^49 - 172 * q^53 - 64 * q^57 + 30 * q^59 + 444 * q^61 + 206 * q^63 - 54 * q^65 - 56 * q^67 + 204 * q^71 - 48 * q^73 + 132 * q^75 - 494 * q^77 - 16 * q^79 - 342 * q^81 + 594 * q^87 - 252 * q^89 + 284 * q^91 - 146 * q^93 + 148 * q^95 - 180 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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