LMFDB - Embedded newform 927.2.f.f.46.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [927,2,Mod(46,927)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(927, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("927.46");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 927 = 3^{2} \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	927.f (of order $3$, 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:	$7.40213226737$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			46.4
Character	$\chi$	$=$	927.46
Dual form			927.2.f.f.262.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.959463 - 1.66184i) q^{2} +(-0.841140 + 1.45690i) q^{4} +(1.43954 - 2.49335i) q^{5} +(2.39836 - 4.15408i) q^{7} -0.609683 q^{8} +O(q^{10})$	\(q+(-0.959463 - 1.66184i) q^{2} +(-0.841140 + 1.45690i) q^{4} +(1.43954 - 2.49335i) q^{5} +(2.39836 - 4.15408i) q^{7} -0.609683 q^{8} -5.52473 q^{10} +(2.29446 - 3.97412i) q^{11} -5.61480 q^{13} -9.20456 q^{14} +(2.26725 + 3.92699i) q^{16} +(2.90046 - 5.02374i) q^{17} +(4.10171 + 7.10437i) q^{19} +(2.42170 + 4.19451i) q^{20} -8.80580 q^{22} +1.59859 q^{23} +(-1.64453 - 2.84842i) q^{25} +(5.38720 + 9.33090i) q^{26} +(4.03471 + 6.98833i) q^{28} +(-1.07775 - 1.86672i) q^{29} -0.283590 q^{31} +(3.74100 - 6.47960i) q^{32} -11.1315 q^{34} +(-6.90506 - 11.9599i) q^{35} +9.23862 q^{37} +(7.87089 - 13.6328i) q^{38} +(-0.877661 + 1.52015i) q^{40} +(3.46058 + 5.99390i) q^{41} +(3.04290 + 5.27045i) q^{43} +(3.85992 + 6.68558i) q^{44} +(-1.53379 - 2.65660i) q^{46} +(-1.34836 + 2.33542i) q^{47} +(-8.00428 - 13.8638i) q^{49} +(-3.15574 + 5.46590i) q^{50} +(4.72283 - 8.18018i) q^{52} +(-2.95608 + 5.12009i) q^{53} +(-6.60592 - 11.4418i) q^{55} +(-1.46224 + 2.53267i) q^{56} +(-2.06812 + 3.58209i) q^{58} +(1.59728 + 2.76657i) q^{59} -5.23380 q^{61} +(0.272094 + 0.471281i) q^{62} -5.28841 q^{64} +(-8.08271 + 13.9997i) q^{65} +(-0.395058 + 0.684260i) q^{67} +(4.87938 + 8.45133i) q^{68} +(-13.2503 + 22.9502i) q^{70} +(-6.80294 + 11.7830i) q^{71} +4.36788 q^{73} +(-8.86412 - 15.3531i) q^{74} -13.8005 q^{76} +(-11.0059 - 19.0628i) q^{77} -0.555227 q^{79} +13.0551 q^{80} +(6.64060 - 11.5019i) q^{82} +(-0.116246 - 0.201345i) q^{83} +(-8.35063 - 14.4637i) q^{85} +(5.83909 - 10.1136i) q^{86} +(-1.39889 + 2.42295i) q^{88} -6.40526 q^{89} +(-13.4663 + 23.3244i) q^{91} +(-1.34464 + 2.32898i) q^{92} +5.17480 q^{94} +23.6183 q^{95} +(1.62601 + 2.81634i) q^{97} +(-15.3596 + 26.6037i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 18 q^{4} + 8 q^{7}+O(q^{10}) $ 32 * q - 18 * q^4 + 8 * q^7	$ 32 q - 18 q^{4} + 8 q^{7} - 32 q^{10} - 4 q^{13} - 18 q^{16} + 4 q^{19} - 40 q^{22} - 26 q^{25} + 8 q^{28} + 32 q^{31} + 8 q^{34} - 48 q^{37} + 22 q^{40} + 2 q^{43} + 18 q^{46} - 8 q^{49} - 68 q^{52} - 32 q^{55} - 24 q^{58} - 20 q^{61} + 68 q^{64} + 8 q^{67} + 38 q^{70} - 64 q^{73} - 188 q^{76} - 20 q^{79} + 60 q^{82} + 8 q^{85} + 6 q^{88} - 30 q^{91} - 92 q^{94} + 32 q^{97}+O(q^{100}) $ 32 * q - 18 * q^4 + 8 * q^7 - 32 * q^10 - 4 * q^13 - 18 * q^16 + 4 * q^19 - 40 * q^22 - 26 * q^25 + 8 * q^28 + 32 * q^31 + 8 * q^34 - 48 * q^37 + 22 * q^40 + 2 * q^43 + 18 * q^46 - 8 * q^49 - 68 * q^52 - 32 * q^55 - 24 * q^58 - 20 * q^61 + 68 * q^64 + 8 * q^67 + 38 * q^70 - 64 * q^73 - 188 * q^76 - 20 * q^79 + 60 * q^82 + 8 * q^85 + 6 * q^88 - 30 * q^91 - 92 * q^94 + 32 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/927\mathbb{Z}\right)^\times$.

$n$	$722$	$829$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.959463	−	1.66184i	−0.678443	−	1.17510i	−0.975450	−	0.220222i	$-0.929322\pi$
$2$	−0.959463	−	1.66184i	−0.678443	−	1.17510i	0.297007	−	0.954875i	$-0.404012\pi$
$3$		0			0
$3$		0			0
$4$	−0.841140	+	1.45690i	−0.420570	+	0.728448i
$5$	1.43954	−	2.49335i	0.643781	−	1.11506i	−0.340801	−	0.940135i	$-0.610698\pi$
$5$	1.43954	−	2.49335i	0.643781	−	1.11506i	0.984582	−	0.174925i	$-0.0559684\pi$
$6$		0			0
$7$	2.39836	−	4.15408i	0.906496	−	1.57010i	0.0875986	−	0.996156i	$-0.472081\pi$
$7$	2.39836	−	4.15408i	0.906496	−	1.57010i	0.818897	−	0.573941i	$-0.194586\pi$
$8$	−0.609683			−0.215555
$9$		0			0
$10$	−5.52473			−1.74707
$11$	2.29446	−	3.97412i	0.691805	−	1.19824i	−0.279440	−	0.960163i	$-0.590149\pi$
$11$	2.29446	−	3.97412i	0.691805	−	1.19824i	0.971246	−	0.238079i	$-0.0765177\pi$
$12$		0			0
$13$	−5.61480			−1.55727			−0.778633	−	0.627480i	$-0.784086\pi$
$13$	−5.61480			−1.55727			−0.778633	+	0.627480i	$0.784086\pi$
$14$	−9.20456			−2.46002
$15$		0			0
$16$	2.26725	+	3.92699i	0.566812	+	0.981747i
$17$	2.90046	−	5.02374i	0.703464	−	1.21844i	−0.263779	−	0.964583i	$-0.584969\pi$
$17$	2.90046	−	5.02374i	0.703464	−	1.21844i	0.967243	−	0.253853i	$-0.0816978\pi$
$18$		0			0
$19$	4.10171	+	7.10437i	0.940997	+	1.62986i	0.763574	+	0.645721i	$0.223443\pi$
$19$	4.10171	+	7.10437i	0.940997	+	1.62986i	0.177424	+	0.984135i	$0.443224\pi$
$20$	2.42170	+	4.19451i	0.541509	+	0.937922i
$21$		0			0
$22$	−8.80580			−1.87740
$23$	1.59859			0.333329			0.166665	−	0.986014i	$-0.446700\pi$
$23$	1.59859			0.333329			0.166665	+	0.986014i	$0.446700\pi$
$24$		0			0
$25$	−1.64453	−	2.84842i	−0.328907	−	0.569683i
$26$	5.38720	+	9.33090i	1.05652	+	1.82994i
$27$		0			0
$28$	4.03471	+	6.98833i	0.762489	+	1.32067i
$29$	−1.07775	−	1.86672i	−0.200133	−	0.346641i	0.748438	−	0.663205i	$-0.230804\pi$
$29$	−1.07775	−	1.86672i	−0.200133	−	0.346641i	−0.948571	+	0.316564i	$0.897471\pi$
$30$		0			0
$31$	−0.283590			−0.0509342			−0.0254671	−	0.999676i	$-0.508107\pi$
$31$	−0.283590			−0.0509342			−0.0254671	+	0.999676i	$0.508107\pi$
$32$	3.74100	−	6.47960i	0.661321	−	1.14544i
$33$		0			0
$34$	−11.1315			−1.90904
$35$	−6.90506	−	11.9599i	−1.16717	−	2.02160i
$36$		0			0
$37$	9.23862			1.51882			0.759410	−	0.650612i	$-0.225488\pi$
$37$	9.23862			1.51882			0.759410	+	0.650612i	$0.225488\pi$
$38$	7.87089	−	13.6328i	1.27683	−	2.21153i
$39$		0			0
$40$	−0.877661	+	1.52015i	−0.138770	+	0.240357i
$41$	3.46058	+	5.99390i	0.540452	+	0.936091i	0.998878	+	0.0473579i	$0.0150801\pi$
$41$	3.46058	+	5.99390i	0.540452	+	0.936091i	−0.458426	+	0.888733i	$0.651587\pi$
$42$		0			0
$43$	3.04290	+	5.27045i	0.464037	+	0.803736i	0.999158	−	0.0410397i	$-0.0130670\pi$
$43$	3.04290	+	5.27045i	0.464037	+	0.803736i	−0.535120	+	0.844776i	$0.679734\pi$
$44$	3.85992	+	6.68558i	0.581905	+	1.00789i
$45$		0			0
$46$	−1.53379	−	2.65660i	−0.226145	−	0.391694i
$47$	−1.34836	+	2.33542i	−0.196678	+	0.340657i	−0.947449	−	0.319906i	$-0.896349\pi$
$47$	−1.34836	+	2.33542i	−0.196678	+	0.340657i	0.750771	+	0.660562i	$0.229682\pi$
$48$		0			0
$49$	−8.00428	−	13.8638i	−1.14347	−	1.98055i
$50$	−3.15574	+	5.46590i	−0.446289	+	0.772995i
$51$		0			0
$52$	4.72283	−	8.18018i	0.654939	−	1.13439i
$53$	−2.95608	+	5.12009i	−0.406049	+	0.703298i	−0.994443	−	0.105277i	$-0.966427\pi$
$53$	−2.95608	+	5.12009i	−0.406049	+	0.703298i	0.588394	+	0.808575i	$0.299761\pi$
$54$		0			0
$55$	−6.60592	−	11.4418i	−0.890742	−	1.54281i
$56$	−1.46224	+	2.53267i	−0.195400	+	0.338443i
$57$		0			0
$58$	−2.06812	+	3.58209i	−0.271558	+	0.470352i
$59$	1.59728	+	2.76657i	0.207948	+	0.360177i	0.951068	−	0.308981i	$-0.0999881\pi$
$59$	1.59728	+	2.76657i	0.207948	+	0.360177i	−0.743120	+	0.669158i	$0.766655\pi$
$60$		0			0
$61$	−5.23380			−0.670119			−0.335060	−	0.942197i	$-0.608757\pi$
$61$	−5.23380			−0.670119			−0.335060	+	0.942197i	$0.608757\pi$
$62$	0.272094	+	0.471281i	0.0345560	+	0.0598527i
$63$		0			0
$64$	−5.28841			−0.661052
$65$	−8.08271	+	13.9997i	−1.00254	+	1.73645i
$66$		0			0
$67$	−0.395058	+	0.684260i	−0.0482640	+	0.0835957i	−0.889148	−	0.457619i	$-0.848702\pi$
$67$	−0.395058	+	0.684260i	−0.0482640	+	0.0835957i	0.840884	+	0.541215i	$0.182036\pi$
$68$	4.87938	+	8.45133i	0.591712	+	1.02487i
$69$		0			0
$70$	−13.2503	+	22.9502i	−1.58371	+	2.74307i
$71$	−6.80294	+	11.7830i	−0.807361	+	1.39839i	0.107325	+	0.994224i	$0.465772\pi$
$71$	−6.80294	+	11.7830i	−0.807361	+	1.39839i	−0.914686	+	0.404166i	$0.867562\pi$
$72$		0			0
$73$	4.36788			0.511221			0.255611	−	0.966780i	$-0.417724\pi$
$73$	4.36788			0.511221			0.255611	+	0.966780i	$0.417724\pi$
$74$	−8.86412	−	15.3531i	−1.03043	−	1.78476i
$75$		0			0
$76$	−13.8005			−1.58302
$77$	−11.0059	−	19.0628i	−1.25424	−	2.17240i
$78$		0			0
$79$	−0.555227			−0.0624679			−0.0312339	−	0.999512i	$-0.509944\pi$
$79$	−0.555227			−0.0624679			−0.0312339	+	0.999512i	$0.509944\pi$
$80$	13.0551			1.45961
$81$		0			0
$82$	6.64060	−	11.5019i	0.733332	−	1.27017i
$83$	−0.116246	−	0.201345i	−0.0127597	−	0.0221005i	0.859575	−	0.511010i	$-0.170728\pi$
$83$	−0.116246	−	0.201345i	−0.0127597	−	0.0221005i	−0.872335	+	0.488909i	$0.837395\pi$
$84$		0			0
$85$	−8.35063	−	14.4637i	−0.905753	−	1.56881i
$86$	5.83909	−	10.1136i	0.629646	−	1.09058i
$87$		0			0
$88$	−1.39889	+	2.42295i	−0.149122	+	0.258288i
$89$	−6.40526			−0.678957			−0.339478	−	0.940614i	$-0.610251\pi$
$89$	−6.40526			−0.678957			−0.339478	+	0.940614i	$0.610251\pi$
$90$		0			0
$91$	−13.4663	+	23.3244i	−1.41165	+	2.44506i
$92$	−1.34464	+	2.32898i	−0.140188	+	0.242813i
$93$		0			0
$94$	5.17480			0.533740
$95$	23.6183			2.42318
$96$		0			0
$97$	1.62601	+	2.81634i	0.165097	+	0.285956i	0.936690	−	0.350161i	$-0.113873\pi$
$97$	1.62601	+	2.81634i	0.165097	+	0.285956i	−0.771593	+	0.636117i	$0.780540\pi$
$98$	−15.3596	+	26.6037i	−1.55156	+	2.68737i
$99$		0			0
$100$	5.53313			0.553313
$101$	5.64036	+	9.76940i	0.561237	+	0.972091i	0.997389	+	0.0722182i	$0.0230078\pi$
$101$	5.64036	+	9.76940i	0.561237	+	0.972091i	−0.436152	+	0.899873i	$0.643659\pi$
$102$		0			0
$103$	10.1482	−	0.116389i	0.999934	−	0.0114682i
$103$	10.1482	−	0.116389i	0.999934	−	0.0114682i
$104$	3.42325			0.335677
$105$		0			0
$106$	11.3450			1.10193
$107$	3.73119	−	6.46261i	0.360708	−	0.624764i	−0.627370	−	0.778722i	$-0.715868\pi$
$107$	3.73119	−	6.46261i	0.360708	−	0.624764i	0.988078	+	0.153957i	$0.0492018\pi$
$108$		0			0
$109$	4.96953	+	8.60749i	0.475995	+	0.824448i	0.999622	−	0.0275001i	$-0.00875467\pi$
$109$	4.96953	+	8.60749i	0.475995	+	0.824448i	−0.523627	+	0.851948i	$0.675421\pi$
$110$	−12.6763	+	21.9559i	−1.20863	+	2.09342i
$111$		0			0
$112$	21.7507			2.05525
$113$	−13.7774			−1.29607			−0.648036	−	0.761610i	$-0.724409\pi$
$113$	−13.7774			−1.29607			−0.648036	+	0.761610i	$0.724409\pi$
$114$		0			0
$115$	2.30123	−	3.98585i	0.214591	−	0.371682i
$116$	3.62615			0.336680
$117$		0			0
$118$	3.06507	−	5.30885i	0.282162	−	0.488719i
$119$	−13.9127	−	24.0975i	−1.27537	−	2.20901i
$120$		0			0
$121$	−5.02908	−	8.71063i	−0.457189	−	0.791875i
$122$	5.02164	+	8.69773i	0.454638	+	0.787456i
$123$		0			0
$124$	0.238539	−	0.413161i	0.0214214	−	0.0371030i
$125$	4.92590			0.440586
$126$		0			0
$127$	−13.4729			−1.19553			−0.597765	−	0.801671i	$-0.703944\pi$
$127$	−13.4729			−1.19553			−0.597765	+	0.801671i	$0.703944\pi$
$128$	−2.40796	−	4.17071i	−0.212835	−	0.368642i
$129$		0			0
$130$	31.0203			2.72066
$131$	−7.80058	−	13.5110i	−0.681540	−	1.18046i	−0.974511	−	0.224340i	$-0.927977\pi$
$131$	−7.80058	−	13.5110i	−0.681540	−	1.18046i	0.292971	−	0.956121i	$-0.405356\pi$
$132$		0			0
$133$	39.3496			3.41204
$134$	1.51617			0.130977
$135$		0			0
$136$	−1.76836	+	3.06289i	−0.151636	+	0.262640i
$137$	−17.3874			−1.48551			−0.742753	−	0.669566i	$-0.766480\pi$
$137$	−17.3874			−1.48551			−0.742753	+	0.669566i	$0.766480\pi$
$138$		0			0
$139$	−0.969930	+	1.67997i	−0.0822684	+	0.142493i	−0.904224	−	0.427059i	$-0.859550\pi$
$139$	−0.969930	+	1.67997i	−0.0822684	+	0.142493i	0.821956	+	0.569552i	$0.192883\pi$
$140$	23.2325			1.96350
$141$		0			0
$142$	26.1087			2.19099
$143$	−12.8829	+	22.3139i	−1.07732	+	1.86598i
$144$		0			0
$145$	−6.20584			−0.515367
$146$	−4.19082	−	7.25871i	−0.346834	−	0.600735i
$147$		0			0
$148$	−7.77097	+	13.4597i	−0.638770	+	1.10638i
$149$	11.8042	+	20.4454i	0.967034	+	1.67495i	0.704048	+	0.710152i	$0.251374\pi$
$149$	11.8042	+	20.4454i	0.967034	+	1.67495i	0.262986	+	0.964800i	$0.415293\pi$
$150$		0			0
$151$	−4.88764	−	8.46565i	−0.397751	−	0.688925i	0.595697	−	0.803209i	$-0.296876\pi$
$151$	−4.88764	−	8.46565i	−0.397751	−	0.688925i	−0.993448	+	0.114284i	$0.963543\pi$
$152$	−2.50074	−	4.33142i	−0.202837	−	0.351324i
$153$		0			0
$154$	−21.1195	+	36.5800i	−1.70186	+	2.94770i
$155$	−0.408238	+	0.707089i	−0.0327905	+	0.0567948i
$156$		0			0
$157$	−3.76307	−	6.51782i	−0.300326	−	0.520179i	0.675884	−	0.737008i	$-0.263762\pi$
$157$	−3.76307	−	6.51782i	−0.300326	−	0.520179i	−0.976210	+	0.216829i	$0.930429\pi$
$158$	0.532720	+	0.922697i	0.0423809	+	0.0734059i
$159$		0			0
$160$	−10.7706	−	18.6552i	−0.851492	−	1.47483i
$161$	3.83400	−	6.64068i	0.302162	−	0.523359i
$162$		0			0
$163$	3.90110	+	6.75691i	0.305558	+	0.529242i	0.977385	−	0.211466i	$-0.0678237\pi$
$163$	3.90110	+	6.75691i	0.305558	+	0.529242i	−0.671828	+	0.740708i	$0.734490\pi$
$164$	−11.6433			−0.909191
$165$		0			0
$166$	−0.223068	+	0.386366i	−0.0173135	+	0.0299878i
$167$	2.36535			0.183036			0.0915180	−	0.995803i	$-0.470828\pi$
$167$	2.36535			0.183036			0.0915180	+	0.995803i	$0.470828\pi$
$168$		0			0
$169$	18.5260			1.42508
$170$	−16.0242	+	27.7548i	−1.22900	+	2.12870i
$171$		0			0
$172$	−10.2380			−0.780640
$173$	7.45646	−	12.9150i	0.566904	−	0.981907i	−0.429965	−	0.902845i	$-0.641474\pi$
$173$	7.45646	−	12.9150i	0.566904	−	0.981907i	0.996870	−	0.0790617i	$-0.0251924\pi$
$174$		0			0
$175$	−15.7768			−1.19261
$176$	20.8084			1.56849
$177$		0			0
$178$	6.14562	+	10.6445i	0.460633	+	0.797840i
$179$	−6.96966			−0.520937			−0.260468	−	0.965482i	$-0.583877\pi$
$179$	−6.96966			−0.520937			−0.260468	+	0.965482i	$0.583877\pi$
$180$		0			0
$181$	−0.705311	−	1.22163i	−0.0524253	−	0.0908033i	0.838622	−	0.544714i	$-0.183362\pi$
$181$	−0.705311	−	1.22163i	−0.0524253	−	0.0908033i	−0.891047	+	0.453911i	$0.850028\pi$
$182$	51.6818			3.83091
$183$		0			0
$184$	−0.974634			−0.0718509
$185$	13.2993	−	23.0351i	0.977787	−	1.69358i
$186$		0			0
$187$	−13.3100	−	23.0535i	−0.973321	−	1.68584i
$188$	−2.26831	−	3.92884i	−0.165434	−	0.286540i
$189$		0			0
$190$	−22.6609	−	39.2498i	−1.64399	−	2.84748i
$191$	−6.51183	+	11.2788i	−0.471180	+	0.816107i	−0.999457	−	0.0329652i	$-0.989505\pi$
$191$	−6.51183	+	11.2788i	−0.471180	+	0.816107i	0.528277	+	0.849072i	$0.322838\pi$
$192$		0			0
$193$	3.80102			0.273604			0.136802	−	0.990598i	$-0.456318\pi$
$193$	3.80102			0.273604			0.136802	+	0.990598i	$0.456318\pi$
$194$	3.12020	−	5.40435i	0.224017	−	0.388009i
$195$		0			0
$196$	26.9309			1.92363
$197$	10.7237			0.764030			0.382015	−	0.924156i	$-0.375230\pi$
$197$	10.7237			0.764030			0.382015	+	0.924156i	$0.375230\pi$
$198$		0			0
$199$	9.84292	−	17.0484i	0.697746	−	1.20853i	−0.271500	−	0.962439i	$-0.587520\pi$
$199$	9.84292	−	17.0484i	0.697746	−	1.20853i	0.969246	−	0.246094i	$-0.0791471\pi$
$200$	1.00264	+	1.73663i	0.0708977	+	0.122798i
$201$		0			0
$202$	10.8234	−	18.7468i	0.761535	−	1.31902i
$203$	−10.3393			−0.725679
$204$		0			0
$205$	19.9265			1.39173
$206$	−9.93027	−	16.7530i	−0.691875	−	1.16724i
$207$		0			0
$208$	−12.7301	−	22.0493i	−0.882677	−	1.52884i
$209$	37.6448			2.60395
$210$		0			0
$211$	−0.654572	+	1.13375i	−0.0450626	+	0.0780507i	−0.887677	−	0.460467i	$-0.847682\pi$
$211$	−0.654572	+	1.13375i	−0.0450626	+	0.0780507i	0.842614	+	0.538517i	$0.181015\pi$
$212$	−4.97296	−	8.61342i	−0.341544	−	0.591572i
$213$		0			0
$214$	−14.3198			−0.978879
$215$	17.5214			1.19495
$216$		0			0
$217$	−0.680151	+	1.17806i	−0.0461717	+	0.0799717i
$218$	9.53617	−	16.5171i	0.645871	−	1.11868i
$219$		0			0
$220$	22.2260			1.49848
$221$	−16.2855	+	28.2073i	−1.09548	+	1.89743i
$222$		0			0
$223$	1.15268	−	1.99650i	0.0771892	−	0.133696i	−0.824847	−	0.565356i	$-0.808739\pi$
$223$	1.15268	−	1.99650i	0.0771892	−	0.133696i	0.902036	+	0.431660i	$0.142072\pi$
$224$	−17.9445	−	31.0809i	−1.19897	−	2.07668i
$225$		0			0
$226$	13.2189	+	22.8959i	0.879311	+	1.52301i
$227$	2.10574	−	3.64725i	0.139763	−	0.242076i	−0.787644	−	0.616131i	$-0.788699\pi$
$227$	2.10574	−	3.64725i	0.139763	−	0.242076i	0.927407	+	0.374054i	$0.122033\pi$
$228$		0			0
$229$	1.33200			0.0880214			0.0440107	−	0.999031i	$-0.485986\pi$
$229$	1.33200			0.0880214			0.0440107	+	0.999031i	$0.485986\pi$
$230$	−8.83179			−0.582351
$231$		0			0
$232$	0.657085	+	1.13811i	0.0431398	+	0.0747203i
$233$	−1.34549			−0.0881461			−0.0440731	−	0.999028i	$-0.514033\pi$
$233$	−1.34549			−0.0881461			−0.0440731	+	0.999028i	$0.514033\pi$
$234$		0			0
$235$	3.88202	+	6.72386i	0.253235	+	0.438616i
$236$	−5.37415			−0.349827
$237$		0			0
$238$	−26.6974	+	46.2413i	−1.73054	+	2.99738i
$239$	10.0757	−	17.4517i	0.651744	−	1.12885i	−0.330955	−	0.943647i	$-0.607371\pi$
$239$	10.0757	−	17.4517i	0.651744	−	1.12885i	0.982699	−	0.185208i	$-0.0592959\pi$
$240$		0			0
$241$	5.91364	+	10.2427i	0.380931	+	0.659792i	0.991196	−	0.132406i	$-0.0422702\pi$
$241$	5.91364	+	10.2427i	0.380931	+	0.659792i	−0.610265	+	0.792198i	$0.708937\pi$
$242$	−9.65044	+	16.7151i	−0.620354	+	1.07448i
$243$		0			0
$244$	4.40236	−	7.62511i	0.281832	−	0.488147i
$245$	−46.0898			−2.94457
$246$		0			0
$247$	−23.0303	−	39.8896i	−1.46538	−	2.53812i
$248$	0.172900			0.0109792
$249$		0			0
$250$	−4.72622	−	8.18605i	−0.298912	−	0.517731i
$251$	0.385996	−	0.668564i	0.0243638	−	0.0421994i	−0.853586	−	0.520951i	$-0.825577\pi$
$251$	0.385996	−	0.668564i	0.0243638	−	0.0421994i	0.877950	+	0.478752i	$0.158911\pi$
$252$		0			0
$253$	3.66790	−	6.35299i	0.230599	−	0.399409i
$254$	12.9268	+	22.3899i	0.811099	+	1.40486i
$255$		0			0
$256$	−9.90911	+	17.1631i	−0.619319	+	1.07269i
$257$	−2.39918	+	4.15549i	−0.149656	+	0.259213i	−0.931101	−	0.364763i	$-0.881150\pi$
$257$	−2.39918	+	4.15549i	−0.149656	+	0.259213i	0.781444	+	0.623975i	$0.214483\pi$
$258$		0			0
$259$	22.1576	−	38.3780i	1.37680	−	2.38469i
$260$	−13.5974	−	23.5514i	−0.843274	−	1.46059i
$261$		0			0
$262$	−14.9687	+	25.9266i	−0.924771	+	1.60175i
$263$	−13.5533	−	23.4749i	−0.835730	−	1.44753i	−0.893435	−	0.449193i	$-0.851712\pi$
$263$	−13.5533	−	23.4749i	−0.835730	−	1.44753i	0.0577050	−	0.998334i	$-0.481622\pi$
$264$		0			0
$265$	8.51078	+	14.7411i	0.522813	+	0.905539i
$266$	−37.7545	−	65.3926i	−2.31487	−	4.00948i
$267$		0			0
$268$	−0.664598	−	1.15112i	−0.0405968	−	0.0703156i
$269$	−2.56926	+	4.45009i	−0.156651	+	0.271327i	−0.933659	−	0.358164i	$-0.883403\pi$
$269$	−2.56926	+	4.45009i	−0.156651	+	0.271327i	0.777008	+	0.629490i	$0.216736\pi$
$270$		0			0
$271$	3.88589	−	6.73056i	0.236051	−	0.408853i	−0.723526	−	0.690297i	$-0.757480\pi$
$271$	3.88589	−	6.73056i	0.236051	−	0.408853i	0.959578	+	0.281444i	$0.0908134\pi$
$272$	26.3042			1.59493
$273$		0			0
$274$	16.6826	+	28.8950i	1.00783	+	1.74561i
$275$	−15.0933			−0.910158
$276$		0			0
$277$	3.04118	−	5.26747i	0.182727	−	0.316492i	−0.760082	−	0.649828i	$-0.774841\pi$
$277$	3.04118	−	5.26747i	0.182727	−	0.316492i	0.942808	+	0.333336i	$0.108174\pi$
$278$	3.72245			0.223258
$279$		0			0
$280$	4.20990	+	7.29176i	0.251590	+	0.435766i
$281$	1.46826	+	2.54309i	0.0875888	+	0.151708i	0.906491	−	0.422224i	$-0.138751\pi$
$281$	1.46826	+	2.54309i	0.0875888	+	0.151708i	−0.818903	+	0.573932i	$0.805417\pi$
$282$		0			0
$283$	8.03765	+	13.9216i	0.477789	+	0.827555i	0.999676	−	0.0254601i	$-0.00810507\pi$
$283$	8.03765	+	13.9216i	0.477789	+	0.827555i	−0.521887	+	0.853015i	$0.674772\pi$
$284$	−11.4445	−	19.8224i	−0.679103	−	1.17624i
$285$		0			0
$286$	49.4428			2.92361
$287$	33.1989			1.95967
$288$		0			0
$289$	−8.32530	−	14.4198i	−0.489724	−	0.848226i
$290$	5.95428	+	10.3131i	0.349647	+	0.605607i
$291$		0			0
$292$	−3.67399	+	6.36354i	−0.215004	+	0.372398i
$293$	−9.18121	−	15.9023i	−0.536372	−	0.929023i	−0.999096	−	0.0425207i	$-0.986461\pi$
$293$	−9.18121	−	15.9023i	−0.536372	−	0.929023i	0.462724	−	0.886502i	$-0.346872\pi$
$294$		0			0
$295$	9.19738			0.535492
$296$	−5.63263			−0.327390
$297$		0			0
$298$	22.6513	−	39.2332i	1.31215	−	2.27272i
$299$	−8.97577			−0.519082
$300$		0			0
$301$	29.1919			1.68259
$302$	−9.37903	+	16.2450i	−0.539703	+	0.934792i
$303$		0			0
$304$	−18.5992	+	32.2148i	−1.06674	+	1.84764i
$305$	−7.53425	+	13.0497i	−0.431410	+	0.747224i
$306$		0			0
$307$	−12.9398	−	22.4124i	−0.738513	−	1.27914i	−0.953165	−	0.302451i	$-0.902195\pi$
$307$	−12.9398	−	22.4124i	−0.738513	−	1.27914i	0.214652	−	0.976691i	$-0.431138\pi$
$308$	37.0299			2.10998
$309$		0			0
$310$	1.56676			0.0889859
$311$	2.38478	+	4.13056i	0.135228	+	0.234222i	0.925685	−	0.378296i	$-0.123490\pi$
$311$	2.38478	+	4.13056i	0.135228	+	0.234222i	−0.790456	+	0.612518i	$0.790157\pi$
$312$		0			0
$313$	−10.9015	+	18.8819i	−0.616187	+	1.06727i	0.373988	+	0.927434i	$0.377990\pi$
$313$	−10.9015	+	18.8819i	−0.616187	+	1.06727i	−0.990175	+	0.139834i	$0.955343\pi$
$314$	−7.22105	+	12.5072i	−0.407507	+	0.705824i
$315$		0			0
$316$	0.467023	−	0.808908i	0.0262721	−	0.0455046i
$317$	19.9853			1.12249			0.561244	−	0.827650i	$-0.310323\pi$
$317$	19.9853			1.12249			0.561244	+	0.827650i	$0.310323\pi$
$318$		0			0
$319$	−9.89141			−0.553813
$320$	−7.61287	+	13.1859i	−0.425572	+	0.737113i
$321$		0			0
$322$	−14.7143			−0.819997
$323$	47.5874			2.64783
$324$		0			0
$325$	9.23373	+	15.9933i	0.512195	+	0.887148i
$326$	7.48593	−	12.9660i	0.414607	−	0.718121i
$327$		0			0
$328$	−2.10986	−	3.65438i	−0.116497	−	0.201779i
$329$	6.46770	+	11.2024i	0.356576	+	0.617608i
$330$		0			0
$331$	16.2059			0.890756			0.445378	−	0.895343i	$-0.353069\pi$
$331$	16.2059			0.890756			0.445378	+	0.895343i	$0.353069\pi$
$332$	0.391118			0.0214654
$333$		0			0
$334$	−2.26946	−	3.93082i	−0.124179	−	0.215085i
$335$	1.13740	+	1.97004i	0.0621428	+	0.107635i
$336$		0			0
$337$	13.5492	+	23.4680i	0.738074	+	1.27838i	0.953362	+	0.301831i	$0.0975977\pi$
$337$	13.5492	+	23.4680i	0.738074	+	1.27838i	−0.215288	+	0.976551i	$0.569069\pi$
$338$	−17.7750	−	30.7872i	−0.966833	−	1.67460i
$339$		0			0
$340$	28.0962			1.52373
$341$	−0.650685	+	1.12702i	−0.0352366	+	0.0610315i
$342$		0			0
$343$	−43.2116			−2.33321
$344$	−1.85520	−	3.21330i	−0.100026	−	0.173250i
$345$		0			0
$346$	−28.6168			−1.53845
$347$	6.80577	−	11.7879i	0.365353	−	0.632810i	−0.623480	−	0.781839i	$-0.714282\pi$
$347$	6.80577	−	11.7879i	0.365353	−	0.632810i	0.988833	+	0.149030i	$0.0476150\pi$
$348$		0			0
$349$	4.00916	−	6.94407i	0.214606	−	0.371708i	−0.738545	−	0.674204i	$-0.764487\pi$
$349$	4.00916	−	6.94407i	0.214606	−	0.371708i	0.953150	+	0.302497i	$0.0978201\pi$
$350$	15.1372	+	26.2184i	0.809118	+	1.40143i
$351$		0			0
$352$	−17.1671	−	29.7344i	−0.915011	−	1.58485i
$353$	17.3950	+	30.1291i	0.925845	+	1.60361i	0.790197	+	0.612853i	$0.209978\pi$
$353$	17.3950	+	30.1291i	0.925845	+	1.60361i	0.135647	+	0.990757i	$0.456689\pi$
$354$		0			0
$355$	19.5862	+	33.9243i	1.03953	+	1.80051i
$356$	5.38772	−	9.33181i	0.285549	−	0.494585i
$357$		0			0
$358$	6.68713	+	11.5825i	0.353426	+	0.612152i
$359$	−11.6205	+	20.1272i	−0.613304	+	1.06227i	0.377375	+	0.926060i	$0.376827\pi$
$359$	−11.6205	+	20.1272i	−0.613304	+	1.06227i	−0.990679	+	0.136214i	$0.956507\pi$
$360$		0			0
$361$	−24.1481	+	41.8257i	−1.27095	+	2.20135i
$362$	−1.35344	+	2.34423i	−0.0711352	+	0.123210i
$363$		0			0
$364$	−22.6541	−	39.2381i	−1.18740	−	2.05663i
$365$	6.28772	−	10.8906i	0.329114	−	0.570043i
$366$		0			0
$367$	−0.908305	+	1.57323i	−0.0474131	+	0.0821219i	−0.888758	−	0.458377i	$-0.848431\pi$
$367$	−0.908305	+	1.57323i	−0.0474131	+	0.0821219i	0.841345	+	0.540499i	$0.181764\pi$
$368$	3.62440	+	6.27765i	0.188935	+	0.327245i
$369$		0			0
$370$	−51.0409			−2.65349
$371$	14.1795	+	24.5596i	0.736164	+	1.27507i
$372$		0			0
$373$	32.7799			1.69728			0.848639	−	0.528973i	$-0.177423\pi$
$373$	32.7799			1.69728			0.848639	+	0.528973i	$0.177423\pi$
$374$	−25.5408	+	44.2380i	−1.32069	+	2.28749i
$375$		0			0
$376$	0.822071	−	1.42387i	0.0423951	−	0.0734304i
$377$	6.05135	+	10.4812i	0.311660	+	0.539812i
$378$		0			0
$379$	−0.306078	+	0.530142i	−0.0157222	+	0.0272316i	−0.873779	−	0.486322i	$-0.838338\pi$
$379$	−0.306078	+	0.530142i	−0.0157222	+	0.0272316i	0.858057	+	0.513554i	$0.171671\pi$
$380$	−19.8663	+	34.4094i	−1.01912	+	1.76516i
$381$		0			0
$382$	24.9915			1.27867
$383$	−8.85762	−	15.3418i	−0.452603	−	0.783932i	0.545944	−	0.837822i	$-0.316171\pi$
$383$	−8.85762	−	15.3418i	−0.452603	−	0.783932i	−0.998547	+	0.0538901i	$0.982838\pi$
$384$		0			0
$385$	−63.3735			−3.22981
$386$	−3.64694	−	6.31669i	−0.185624	−	0.321511i
$387$		0			0
$388$	−5.47082			−0.277739
$389$	−6.11815			−0.310203			−0.155101	−	0.987899i	$-0.549570\pi$
$389$	−6.11815			−0.310203			−0.155101	+	0.987899i	$0.549570\pi$
$390$		0			0
$391$	4.63665	−	8.03090i	0.234485	−	0.406140i
$392$	4.88007	+	8.45253i	0.246481	+	0.426917i
$393$		0			0
$394$	−10.2890	−	17.8210i	−0.518351	−	0.897810i
$395$	−0.799269	+	1.38438i	−0.0402156	+	0.0696555i
$396$		0			0
$397$	3.20571	−	5.55246i	0.160890	−	0.278670i	−0.774298	−	0.632821i	$-0.781897\pi$
$397$	3.20571	−	5.55246i	0.160890	−	0.278670i	0.935188	+	0.354151i	$0.115230\pi$
$398$	−37.7757			−1.89352
$399$		0			0
$400$	7.45713	−	12.9161i	0.372857	−	0.645807i
$401$	3.50123	−	6.06431i	0.174843	−	0.302837i	−0.765264	−	0.643717i	$-0.777392\pi$
$401$	3.50123	−	6.06431i	0.174843	−	0.302837i	0.940107	+	0.340880i	$0.110725\pi$
$402$		0			0
$403$	1.59230			0.0793181
$404$	−18.9773			−0.944158
$405$		0			0
$406$	9.92021	+	17.1823i	0.492332	+	0.852744i
$407$	21.1976	−	36.7154i	1.05073	−	1.81991i
$408$		0			0
$409$	11.8650			0.586689			0.293344	−	0.956007i	$-0.405232\pi$
$409$	11.8650			0.586689			0.293344	+	0.956007i	$0.405232\pi$
$410$	−19.1188	−	33.1147i	−0.944210	−	1.63542i
$411$		0			0
$412$	−8.36651	+	14.8828i	−0.412188	+	0.733224i
$413$	15.3234			0.754017
$414$		0			0
$415$	−0.669364			−0.0328578
$416$	−21.0050	+	36.3817i	−1.02985	+	1.78376i
$417$		0			0
$418$	−36.1188	−	62.5597i	−1.76663	−	3.05989i
$419$	−7.23695	+	12.5348i	−0.353548	+	0.612363i	−0.986868	−	0.161527i	$-0.948358\pi$
$419$	−7.23695	+	12.5348i	−0.353548	+	0.612363i	0.633320	+	0.773890i	$0.281692\pi$
$420$		0			0
$421$	−11.2530			−0.548437			−0.274218	−	0.961667i	$-0.588419\pi$
$421$	−11.2530			−0.548437			−0.274218	+	0.961667i	$0.588419\pi$
$422$	2.51215			0.122290
$423$		0			0
$424$	1.80227	−	3.12163i	0.0875261	−	0.151600i
$425$	−19.0796			−0.925497
$426$		0			0
$427$	−12.5525	+	21.7416i	−0.607460	+	1.05215i
$428$	6.27690	+	10.8719i	0.303406	+	0.525514i
$429$		0			0
$430$	−16.8112	−	29.1178i	−0.810707	−	1.40419i
$431$	−0.748327	−	1.29614i	−0.0360456	−	0.0624329i	0.847440	−	0.530892i	$-0.178143\pi$
$431$	−0.748327	−	1.29614i	−0.0360456	−	0.0624329i	−0.883485	+	0.468459i	$0.844810\pi$
$432$		0			0
$433$	−15.5656	+	26.9604i	−0.748034	+	1.29563i	0.200730	+	0.979647i	$0.435669\pi$
$433$	−15.5656	+	26.9604i	−0.748034	+	1.29563i	−0.948764	+	0.315986i	$0.897665\pi$
$434$	2.61032			0.125299
$435$		0			0
$436$	−16.7203			−0.800757
$437$	6.55696	+	11.3570i	0.313662	+	0.543278i
$438$		0			0
$439$	−24.5270			−1.17061			−0.585306	−	0.810813i	$-0.699025\pi$
$439$	−24.5270			−1.17061			−0.585306	+	0.810813i	$0.699025\pi$
$440$	4.02751	+	6.97586i	0.192004	+	0.332561i
$441$		0			0
$442$	62.5013			2.97288
$443$	−32.4322			−1.54090			−0.770449	−	0.637501i	$-0.779968\pi$
$443$	−32.4322			−1.54090			−0.770449	+	0.637501i	$0.779968\pi$
$444$		0			0
$445$	−9.22061	+	15.9706i	−0.437099	+	0.757078i
$446$	−4.42382			−0.209474
$447$		0			0
$448$	−12.6835	+	21.9685i	−0.599240	+	1.03791i
$449$	−27.8198			−1.31290			−0.656449	−	0.754370i	$-0.727942\pi$
$449$	−27.8198			−1.31290			−0.656449	+	0.754370i	$0.727942\pi$
$450$		0			0
$451$	31.7607			1.49555
$452$	11.5887	−	20.0723i	0.545089	−	0.944122i
$453$		0			0
$454$	−8.08152			−0.379284
$455$	38.7706	+	67.1526i	1.81759	+	3.14816i
$456$		0			0
$457$	−8.97858	+	15.5513i	−0.420000	+	0.727461i	−0.995939	−	0.0900313i	$-0.971303\pi$
$457$	−8.97858	+	15.5513i	−0.420000	+	0.727461i	0.575939	+	0.817493i	$0.304637\pi$
$458$	−1.27801	−	2.21358i	−0.0597175	−	0.103434i
$459$		0			0
$460$	3.87131	+	6.70531i	0.180501	+	0.312637i
$461$	−18.0609	−	31.2823i	−0.841178	−	1.45696i	−0.888900	−	0.458102i	$-0.848529\pi$
$461$	−18.0609	−	31.2823i	−0.841178	−	1.45696i	0.0477218	−	0.998861i	$-0.484804\pi$
$462$		0			0
$463$	8.74568	−	15.1480i	0.406446	−	0.703986i	−0.588042	−	0.808830i	$-0.700101\pi$
$463$	8.74568	−	15.1480i	0.406446	−	0.703986i	0.994489	+	0.104844i	$0.0334345\pi$
$464$	4.88705	−	8.46462i	0.226876	−	0.392960i
$465$		0			0
$466$	1.29095	+	2.23599i	0.0598021	+	0.103580i
$467$	17.6585	+	30.5854i	0.817138	+	1.41532i	0.907782	+	0.419441i	$0.137774\pi$
$467$	17.6585	+	30.5854i	0.817138	+	1.41532i	−0.0906442	+	0.995883i	$0.528893\pi$
$468$		0			0
$469$	1.89498	+	3.28221i	0.0875022	+	0.151558i
$470$	7.44932	−	12.9026i	0.343611	−	0.595152i
$471$		0			0
$472$	−0.973835	−	1.68673i	−0.0448244	−	0.0776381i
$473$	27.9272			1.28409
$474$		0			0
$475$	13.4908	−	23.3668i	0.619001	−	1.07214i
$476$	46.8101			2.14554
$477$		0			0
$478$	−38.6692			−1.76869
$479$	2.63746	−	4.56822i	0.120509	−	0.208727i	−0.799460	−	0.600720i	$-0.794881\pi$
$479$	2.63746	−	4.56822i	0.120509	−	0.208727i	0.919968	+	0.391992i	$0.128214\pi$
$480$		0			0
$481$	−51.8730			−2.36521
$482$	11.3478	−	19.6550i	0.516880	−	0.895262i
$483$		0			0
$484$	16.9206			0.769120
$485$	9.36283			0.425144
$486$		0			0
$487$	−3.72137	−	6.44561i	−0.168632	−	0.292078i	0.769307	−	0.638879i	$-0.220601\pi$
$487$	−3.72137	−	6.44561i	−0.168632	−	0.292078i	−0.937939	+	0.346800i	$0.887268\pi$
$488$	3.19096			0.144448
$489$		0			0
$490$	44.2215	+	76.5939i	1.99772	+	3.46016i
$491$	16.2930			0.735292			0.367646	−	0.929966i	$-0.380164\pi$
$491$	16.2930			0.735292			0.367646	+	0.929966i	$0.380164\pi$
$492$		0			0
$493$	−12.5039			−0.563146
$494$	−44.1935	+	76.5453i	−1.98836	+	3.44394i
$495$		0			0
$496$	−0.642968	−	1.11365i	−0.0288701	−	0.0500045i
$497$	32.6318	+	56.5200i	1.46374	+	2.53527i
$498$		0			0
$499$	−21.0576	−	36.4728i	−0.942666	−	1.63275i	−0.760358	−	0.649504i	$-0.774976\pi$
$499$	−21.0576	−	36.4728i	−0.942666	−	1.63275i	−0.182308	−	0.983241i	$-0.558357\pi$
$500$	−4.14337	+	7.17652i	−0.185297	+	0.320944i
$501$		0			0
$502$	−1.48139			−0.0661179
$503$	−8.04802	+	13.9396i	−0.358844	+	0.621536i	−0.987768	−	0.155931i	$-0.950162\pi$
$503$	−8.04802	+	13.9396i	−0.358844	+	0.621536i	0.628924	+	0.777467i	$0.283496\pi$
$504$		0			0
$505$	32.4781			1.44525
$506$	−14.0769			−0.625793
$507$		0			0
$508$	11.3326	−	19.6287i	0.502804	−	0.870882i
$509$	4.06987	+	7.04922i	0.180394	+	0.312451i	0.942015	−	0.335572i	$-0.108929\pi$
$509$	4.06987	+	7.04922i	0.180394	+	0.312451i	−0.761621	+	0.648023i	$0.775596\pi$
$510$		0			0
$511$	10.4757	−	18.1445i	0.463420	−	0.802666i
$512$	28.3979			1.25502
$513$		0			0
$514$	9.20768			0.406134
$515$	14.3185	−	25.4706i	0.630951	−	1.12237i
$516$		0			0
$517$	6.18750	+	10.7171i	0.272126	+	0.471336i
$518$	−85.0375			−3.73633
$519$		0			0
$520$	4.92789	−	8.53536i	0.216102	−	0.374300i
$521$	−6.90824	−	11.9654i	−0.302655	−	0.524214i	0.674081	−	0.738657i	$-0.264540\pi$
$521$	−6.90824	−	11.9654i	−0.302655	−	0.524214i	−0.976737	+	0.214443i	$0.931206\pi$
$522$		0			0
$523$	6.90150			0.301782			0.150891	−	0.988550i	$-0.451786\pi$
$523$	6.90150			0.301782			0.150891	+	0.988550i	$0.451786\pi$
$524$	26.2455			1.14654
$525$		0			0
$526$	−26.0077	+	45.0467i	−1.13399	+	1.96413i
$527$	−0.822540	+	1.42468i	−0.0358304	+	0.0620601i
$528$		0			0
$529$	−20.4445			−0.888892
$530$	16.3316	−	28.2871i	0.709398	−	1.22871i
$531$		0			0
$532$	−33.0985	+	57.3282i	−1.43500	+	2.48549i
$533$	−19.4305	−	33.6546i	−0.841628	−	1.45774i
$534$		0			0
$535$	−10.7424	−	18.6063i	−0.464433	−	0.804422i
$536$	0.240860	−	0.417182i	0.0104036	−	0.0180195i
$537$		0			0
$538$	9.86045			0.425114
$539$	−73.4620			−3.16423
$540$		0			0
$541$	−3.19320	−	5.53078i	−0.137286	−	0.237787i	0.789182	−	0.614159i	$-0.210505\pi$
$541$	−3.19320	−	5.53078i	−0.137286	−	0.237787i	−0.926468	+	0.376372i	$0.877171\pi$
$542$	−14.9135			−0.640589
$543$		0			0
$544$	−21.7012	−	37.5876i	−0.930432	−	1.61156i
$545$	28.6153			1.22575
$546$		0			0
$547$	16.5866	−	28.7288i	0.709191	−	1.22836i	−0.255966	−	0.966686i	$-0.582394\pi$
$547$	16.5866	−	28.7288i	0.709191	−	1.22836i	0.965158	−	0.261669i	$-0.0842730\pi$
$548$	14.6252	−	25.3316i	0.624759	−	1.08211i
$549$		0			0
$550$	14.4814	+	25.0826i	0.617490	+	1.06952i
$551$	8.84124	−	15.3135i	0.376649	−	0.652376i
$552$		0			0
$553$	−1.33163	+	2.30646i	−0.0566269	+	0.0980806i
$554$	−11.6716			−0.495878
$555$		0			0
$556$	−1.63169	−	2.82618i	−0.0691992	−	0.119857i
$557$	−23.4458			−0.993431			−0.496716	−	0.867913i	$-0.665461\pi$
$557$	−23.4458			−0.993431			−0.496716	+	0.867913i	$0.665461\pi$
$558$		0			0
$559$	−17.0853	−	29.5925i	−0.722629	−	1.25163i
$560$	31.3110	−	54.2322i	1.32313	−	2.29173i
$561$		0			0
$562$	2.81748	−	4.88001i	0.118848	−	0.205851i
$563$	−2.33806	−	4.04963i	−0.0985373	−	0.170672i	0.812542	−	0.582902i	$-0.198083\pi$
$563$	−2.33806	−	4.04963i	−0.0985373	−	0.170672i	−0.911079	+	0.412231i	$0.864750\pi$
$564$		0			0
$565$	−19.8331	+	34.3520i	−0.834386	+	1.44520i
$566$	15.4237	−	26.7146i	0.648305	−	1.12290i
$567$		0			0
$568$	4.14764	−	7.18392i	0.174031	−	0.301431i
$569$	13.8160	+	23.9300i	0.579196	+	1.00320i	0.995572	+	0.0940041i	$0.0299667\pi$
$569$	13.8160	+	23.9300i	0.579196	+	1.00320i	−0.416376	+	0.909193i	$0.636700\pi$
$570$		0			0
$571$	−13.7464	+	23.8094i	−0.575268	+	0.996393i	0.420745	+	0.907179i	$0.361769\pi$
$571$	−13.7464	+	23.8094i	−0.575268	+	0.996393i	−0.996012	+	0.0892139i	$0.971565\pi$
$572$	−21.6727	−	37.5382i	−0.906181	−	1.56955i
$573$		0			0
$574$	−31.8531	−	55.1713i	−1.32952	−	2.30280i
$575$	−2.62894	−	4.55345i	−0.109634	−	0.189892i
$576$		0			0
$577$	11.2941	+	19.5620i	0.470181	+	0.814377i	0.999419	−	0.0340963i	$-0.0108553\pi$
$577$	11.2941	+	19.5620i	0.470181	+	0.814377i	−0.529238	+	0.848474i	$0.677522\pi$
$578$	−15.9756	+	27.6706i	−0.664499	+	1.15095i
$579$		0			0
$580$	5.21998	−	9.04127i	0.216748	−	0.375418i
$581$	−1.11520			−0.0462665
$582$		0			0
$583$	13.5652	+	23.4957i	0.561814	+	0.973091i
$584$	−2.66302			−0.110196
$585$		0			0
$586$	−17.6181	+	30.5154i	−0.727795	+	1.26058i
$587$	−29.7551			−1.22812			−0.614061	−	0.789258i	$-0.710465\pi$
$587$	−29.7551			−1.22812			−0.614061	+	0.789258i	$0.710465\pi$
$588$		0			0
$589$	−1.16320	−	2.01473i	−0.0479290	−	0.0830154i
$590$	−8.82455	−	15.2846i	−0.363301	−	0.629256i
$591$		0			0
$592$	20.9462	+	36.2800i	0.860885	+	1.49110i
$593$	3.30279	+	5.72060i	0.135629	+	0.234917i	0.925838	−	0.377921i	$-0.123361\pi$
$593$	3.30279	+	5.72060i	0.135629	+	0.234917i	−0.790208	+	0.612838i	$0.790028\pi$
$594$		0			0
$595$	−80.1113			−3.28425
$596$	−39.7158			−1.62682
$597$		0			0
$598$	8.61192	+	14.9163i	0.352168	+	0.609972i
$599$	4.12365	+	7.14238i	0.168488	+	0.291830i	0.937888	−	0.346937i	$-0.112778\pi$
$599$	4.12365	+	7.14238i	0.168488	+	0.291830i	−0.769400	+	0.638767i	$0.779445\pi$
$600$		0			0
$601$	15.2424	−	26.4006i	0.621750	−	1.07690i	−0.367410	−	0.930059i	$-0.619756\pi$
$601$	15.2424	−	26.4006i	0.621750	−	1.07690i	0.989160	−	0.146843i	$-0.0469111\pi$
$602$	−28.0085	−	48.5122i	−1.14154	−	1.97721i
$603$		0			0
$604$	16.4448			0.669128
$605$	−28.9582			−1.17732
$606$		0			0
$607$	−11.4524	+	19.8362i	−0.464839	+	0.805125i	−0.999194	−	0.0401349i	$-0.987221\pi$
$607$	−11.4524	+	19.8362i	−0.464839	+	0.805125i	0.534355	+	0.845260i	$0.320555\pi$
$608$	61.3780			2.48921
$609$		0			0
$610$	28.9153			1.17075
$611$	7.57076	−	13.1129i	0.306280	−	0.530493i
$612$		0			0
$613$	17.2924	−	29.9514i	0.698435	−	1.20972i	−0.270574	−	0.962699i	$-0.587214\pi$
$613$	17.2924	−	29.9514i	0.698435	−	1.20972i	0.969009	−	0.247025i	$-0.0794531\pi$
$614$	−24.8305	+	43.0077i	−1.00208	+	1.73565i
$615$		0			0
$616$	6.71010	+	11.6222i	0.270358	+	0.468273i
$617$	29.0302			1.16871			0.584355	−	0.811498i	$-0.301348\pi$
$617$	29.0302			1.16871			0.584355	+	0.811498i	$0.301348\pi$
$618$		0			0
$619$	−31.1286			−1.25116			−0.625582	−	0.780159i	$-0.715138\pi$
$619$	−31.1286			−1.25116			−0.625582	+	0.780159i	$0.715138\pi$
$620$	−0.686770	−	1.18952i	−0.0275814	−	0.0477723i
$621$		0			0
$622$	4.57621	−	7.92624i	0.183489	−	0.317813i
$623$	−15.3621	+	26.6080i	−0.615471	+	1.06603i
$624$		0			0
$625$	15.3137	−	26.5241i	0.612547	−	1.06096i
$626$	41.8382			1.67219
$627$		0			0
$628$	12.6611			0.505231
$629$	26.7962	−	46.4124i	1.06844	−	1.85059i
$630$		0			0
$631$	9.60433			0.382342			0.191171	−	0.981557i	$-0.438771\pi$
$631$	9.60433			0.382342			0.191171	+	0.981557i	$0.438771\pi$
$632$	0.338512			0.0134653
$633$		0			0
$634$	−19.1752	−	33.2124i	−0.761545	−	1.31903i
$635$	−19.3948	+	33.5928i	−0.769659	+	1.33309i
$636$		0			0
$637$	44.9424	+	77.8426i	1.78068	+	3.08424i
$638$	9.49044	+	16.4379i	0.375730	+	0.650784i
$639$		0			0
$640$	−13.8654			−0.548077
$641$	−41.4060			−1.63544			−0.817718	−	0.575618i	$-0.804761\pi$
$641$	−41.4060			−1.63544			−0.817718	+	0.575618i	$0.804761\pi$
$642$		0			0
$643$	−0.482002	−	0.834852i	−0.0190083	−	0.0329234i	0.856365	−	0.516371i	$-0.172718\pi$
$643$	−0.482002	−	0.834852i	−0.0190083	−	0.0329234i	−0.875373	+	0.483448i	$0.839384\pi$
$644$	6.44986	+	11.1715i	0.254160	+	0.440218i
$645$		0			0
$646$	−45.6583	−	79.0825i	−1.79640	−	3.11146i
$647$	−2.79514	−	4.84133i	−0.109888	−	0.190332i	0.805836	−	0.592138i	$-0.201716\pi$
$647$	−2.79514	−	4.84133i	−0.109888	−	0.190332i	−0.915725	+	0.401806i	$0.868383\pi$
$648$		0			0
$649$	14.6596			0.575439
$650$	17.7189	−	30.6900i	0.694991	−	1.20376i
$651$		0			0
$652$	−13.1255			−0.514034
$653$	11.7680	+	20.3828i	0.460519	+	0.797642i	0.998987	−	0.0450038i	$-0.0143300\pi$
$653$	11.7680	+	20.3828i	0.460519	+	0.797642i	−0.538468	+	0.842646i	$0.680997\pi$
$654$		0			0
$655$	−44.9169			−1.75505
$656$	−15.6920	+	27.1793i	−0.612669	+	1.06117i
$657$		0			0
$658$	12.4110	−	21.4966i	0.483833	−	0.838023i
$659$	3.68407	+	6.38099i	0.143511	+	0.248568i	0.928816	−	0.370540i	$-0.120827\pi$
$659$	3.68407	+	6.38099i	0.143511	+	0.248568i	−0.785305	+	0.619108i	$0.787494\pi$
$660$		0			0
$661$	−16.0230	−	27.7526i	−0.623221	−	1.07945i	−0.988882	−	0.148703i	$-0.952490\pi$
$661$	−16.0230	−	27.7526i	−0.623221	−	1.07945i	0.365661	−	0.930748i	$-0.380843\pi$
$662$	−15.5490	−	26.9316i	−0.604327	−	1.04673i
$663$		0			0
$664$	0.0708735	+	0.122756i	0.00275042	+	0.00476387i
$665$	56.6452	−	98.1123i	2.19660	−	3.80463i
$666$		0			0
$667$	−1.72288	−	2.98412i	−0.0667102	−	0.115545i
$668$	−1.98959	+	3.44606i	−0.0769794	+	0.133332i
$669$		0			0
$670$	2.18259	−	3.78035i	0.0843208	−	0.146048i
$671$	−12.0087	+	20.7997i	−0.463592	+	0.802965i
$672$		0			0
$673$	−0.688535	−	1.19258i	−0.0265411	−	0.0459705i	0.852450	−	0.522809i	$-0.175116\pi$
$673$	−0.688535	−	1.19258i	−0.0265411	−	0.0459705i	−0.878991	+	0.476839i	$0.841783\pi$
$674$	26.0000	−	45.0333i	1.00148	−	1.73462i
$675$		0			0
$676$	−15.5829	+	26.9905i	−0.599344	+	1.03809i
$677$	−17.4445	−	30.2148i	−0.670447	−	1.16125i	−0.977777	−	0.209646i	$-0.932769\pi$
$677$	−17.4445	−	30.2148i	−0.670447	−	1.16125i	0.307330	−	0.951603i	$-0.400564\pi$
$678$		0			0
$679$	15.5991			0.598638
$680$	5.09124	+	8.81828i	0.195240	+	0.338166i
$681$		0			0
$682$	2.49723			0.0956240
$683$	−14.8620	+	25.7417i	−0.568678	+	0.984980i	0.428019	+	0.903770i	$0.359212\pi$
$683$	−14.8620	+	25.7417i	−0.568678	+	0.984980i	−0.996697	+	0.0812101i	$0.974122\pi$
$684$		0			0
$685$	−25.0298	+	43.3529i	−0.956339	+	1.65643i
$686$	41.4599	+	71.8107i	1.58295	+	2.74174i
$687$		0			0
$688$	−13.7980	+	23.8988i	−0.526044	+	0.911134i
$689$	16.5978	−	28.7483i	0.632327	−	1.09522i
$690$		0			0
$691$	22.4939			0.855707			0.427854	−	0.903848i	$-0.359270\pi$
$691$	22.4939			0.855707			0.427854	+	0.903848i	$0.359270\pi$
$692$	12.5439	+	21.7266i	0.476846	+	0.825921i
$693$		0			0
$694$	−26.1195			−0.991484
$695$	2.79250	+	4.83675i	0.105926	+	0.183469i
$696$		0			0
$697$	40.1491			1.52075
$698$	−15.3866			−0.582391
$699$		0			0
$700$	13.2705	−	22.9851i	0.501576	−	0.868755i
$701$	−4.21242	−	7.29613i	−0.159101	−	0.275571i	0.775444	−	0.631417i	$-0.217526\pi$
$701$	−4.21242	−	7.29613i	−0.159101	−	0.275571i	−0.934545	+	0.355846i	$0.884193\pi$
$702$		0			0
$703$	37.8942	+	65.6346i	1.42921	+	2.47546i
$704$	−12.1340	+	21.0168i	−0.457319	+	0.792100i
$705$		0			0
$706$	33.3798	−	57.8155i	1.25627	−	2.17592i
$707$	54.1105			2.03504
$708$		0			0
$709$	−5.84828	+	10.1295i	−0.219637	+	0.380422i	−0.954697	−	0.297580i	$-0.903821\pi$
$709$	−5.84828	+	10.1295i	−0.219637	+	0.380422i	0.735060	+	0.678002i	$0.237154\pi$
$710$	37.5844	−	65.0982i	1.41052	−	2.44309i
$711$		0			0
$712$	3.90518			0.146353
$713$	−0.453344			−0.0169779
$714$		0			0
$715$	37.0909	+	64.2433i	1.38712	+	2.40256i
$716$	5.86246	−	10.1541i	0.219090	−	0.379475i
$717$		0			0
$718$	44.5976			1.66437
$719$	−18.6207	−	32.2520i	−0.694435	−	1.20280i	−0.970371	−	0.241621i	$-0.922321\pi$
$719$	−18.6207	−	32.2520i	−0.694435	−	1.20280i	0.275935	−	0.961176i	$-0.411012\pi$
$720$		0			0
$721$	23.8556	−	42.4357i	0.888430	−	1.58039i
$722$	92.6768			3.44907
$723$		0			0
$724$	2.37306			0.0881941
$725$	−3.54479	+	6.13976i	−0.131650	+	0.228025i
$726$		0			0
$727$	−14.6235	−	25.3287i	−0.542356	−	0.939389i	−0.998768	−	0.0496199i	$-0.984199\pi$
$727$	−14.6235	−	25.3287i	−0.542356	−	0.939389i	0.456412	−	0.889769i	$-0.349134\pi$
$728$	8.21019	−	14.2205i	0.304290	−	0.527045i
$729$		0			0
$730$	−24.1313			−0.893141
$731$	35.3032			1.30573
$732$		0			0
$733$	14.1834	−	24.5663i	0.523874	−	0.907377i	−0.475739	−	0.879586i	$-0.657819\pi$
$733$	14.1834	−	24.5663i	0.523874	−	0.907377i	0.999614	−	0.0277907i	$-0.00884720\pi$
$734$	3.48594			0.128668
$735$		0			0
$736$	5.98033	−	10.3582i	0.220438	−	0.381809i
$737$	1.81289	+	3.14001i	0.0667786	+	0.115664i
$738$		0			0
$739$	−5.94742	−	10.3012i	−0.218780	−	0.378937i	0.735656	−	0.677356i	$-0.236874\pi$
$739$	−5.94742	−	10.3012i	−0.218780	−	0.378937i	−0.954435	+	0.298419i	$0.903541\pi$
$740$	22.3732	+	38.7515i	0.822455	+	1.42453i
$741$		0			0
$742$	27.2094	−	47.1281i	0.998890	−	1.73013i
$743$	−42.1806			−1.54746			−0.773728	−	0.633518i	$-0.781610\pi$
$743$	−42.1806			−1.54746			−0.773728	+	0.633518i	$0.781610\pi$
$744$		0			0
$745$	67.9701			2.49023
$746$	−31.4511	−	54.4749i	−1.15151	−	1.99447i
$747$		0			0
$748$	44.7821			1.63740
$749$	−17.8975	−	30.9994i	−0.653960	−	1.13269i
$750$		0			0
$751$	−11.4076			−0.416270			−0.208135	−	0.978100i	$-0.566739\pi$
$751$	−11.4076			−0.416270			−0.208135	+	0.978100i	$0.566739\pi$
$752$	−12.2282			−0.445918
$753$		0			0
$754$	11.6121	−	20.1127i	0.422888	−	0.732463i
$755$	−28.1438			−1.02426
$756$		0			0
$757$	−3.01855	+	5.22827i	−0.109711	+	0.190025i	−0.915653	−	0.401969i	$-0.868326\pi$
$757$	−3.01855	+	5.22827i	−0.109711	+	0.190025i	0.805942	+	0.591994i	$0.201659\pi$
$758$	1.17468			0.0426664
$759$		0			0
$760$	−14.3997			−0.522330
$761$	−5.06703	+	8.77635i	−0.183680	+	0.318143i	−0.943131	−	0.332422i	$-0.892134\pi$
$761$	−5.06703	+	8.77635i	−0.183680	+	0.318143i	0.759451	+	0.650564i	$0.225468\pi$
$762$		0			0
$763$	47.6750			1.72595
$764$	−10.9547	−	18.9741i	−0.396328	−	0.686460i
$765$		0			0
$766$	−16.9971	+	29.4399i	−0.614131	+	1.06371i
$767$	−8.96842	−	15.5338i	−0.323831	−	0.560891i
$768$		0			0
$769$	15.7710	+	27.3161i	0.568716	+	0.985044i	0.996693	+	0.0812549i	$0.0258928\pi$
$769$	15.7710	+	27.3161i	0.568716	+	0.985044i	−0.427978	+	0.903789i	$0.640774\pi$
$770$	60.8046	+	105.317i	2.19124	+	3.79535i
$771$		0			0
$772$	−3.19719	+	5.53770i	−0.115069	+	0.199306i
$773$	15.8587	−	27.4680i	0.570397	−	0.987956i	−0.426128	−	0.904663i	$-0.640123\pi$
$773$	15.8587	−	27.4680i	0.570397	−	0.987956i	0.996525	−	0.0832934i	$-0.0265439\pi$
$774$		0			0
$775$	0.466373	+	0.807782i	0.0167526	+	0.0290164i
$776$	−0.991353	−	1.71707i	−0.0355875	−	0.0616393i
$777$		0			0
$778$	5.87014	+	10.1674i	0.210455	+	0.364518i
$779$	−28.3886	+	49.1705i	−1.01713	+	1.76172i
$780$		0			0
$781$	31.2181	+	54.0714i	1.11707	+	1.93483i
$782$	−17.7948			−0.636339
$783$		0			0
$784$	36.2954	−	62.8654i	1.29626	−	2.24519i
$785$	−21.6683			−0.773375
$786$		0			0
$787$	−45.7949			−1.63241			−0.816205	−	0.577762i	$-0.803926\pi$
$787$	−45.7949			−1.63241			−0.816205	+	0.577762i	$0.803926\pi$
$788$	−9.02011	+	15.6233i	−0.321328	+	0.556556i
$789$		0			0
$790$	3.06748			0.109136
$791$	−33.0433	+	57.2326i	−1.17488	+	2.03496i
$792$		0			0
$793$	29.3867			1.04355
$794$	−12.3031			−0.436619
$795$		0			0
$796$	16.5585	+	28.6802i	0.586902	+	1.01654i
$797$	−5.99922			−0.212503			−0.106252	−	0.994339i	$-0.533885\pi$
$797$	−5.99922			−0.212503			−0.106252	+	0.994339i	$0.533885\pi$
$798$		0			0
$799$	7.82171	+	13.5476i	0.276712	+	0.479280i
$800$	−24.6088			−0.870053
$801$		0			0
$802$	−13.4372			−0.474484
$803$	10.0219	−	17.3585i	0.353666	−	0.612567i
$804$		0			0
$805$	−11.0384	−	19.1190i	−0.389051	−	0.673857i
$806$	−1.52775	−	2.64615i	−0.0538128	−	0.0932066i
$807$		0			0
$808$	−3.43883	−	5.95623i	−0.120978	−	0.209540i
$809$	6.68623	−	11.5809i	0.235075	−	0.407162i	−0.724219	−	0.689570i	$-0.757800\pi$
$809$	6.68623	−	11.5809i	0.235075	−	0.407162i	0.959295	+	0.282408i	$0.0911330\pi$
$810$		0			0
$811$	−24.0974			−0.846174			−0.423087	−	0.906089i	$-0.639054\pi$
$811$	−24.0974			−0.846174			−0.423087	+	0.906089i	$0.639054\pi$
$812$	8.69682	−	15.0633i	0.305199	−	0.528620i
$813$		0			0
$814$	−81.3534			−2.85144
$815$	22.4631			0.786849
$816$		0			0
$817$	−24.9622	+	43.2357i	−0.873316	+	1.51263i
$818$	−11.3841	−	19.7178i	−0.398035	−	0.689416i
$819$		0			0
$820$	−16.7610	+	29.0309i	−0.585320	+	1.01380i
$821$	−20.7057			−0.722632			−0.361316	−	0.932443i	$-0.617672\pi$
$821$	−20.7057			−0.722632			−0.361316	+	0.932443i	$0.617672\pi$
$822$		0			0
$823$	−24.0998			−0.840065			−0.420033	−	0.907509i	$-0.637981\pi$
$823$	−24.0998			−0.840065			−0.420033	+	0.907509i	$0.637981\pi$
$824$	−6.18720	+	0.0709604i	−0.215541	+	0.00247202i
$825$		0			0
$826$	−14.7023	−	25.4651i	−0.511558	−	0.886044i
$827$	−4.73851			−0.164774			−0.0823871	−	0.996600i	$-0.526254\pi$
$827$	−4.73851			−0.164774			−0.0823871	+	0.996600i	$0.526254\pi$
$828$		0			0
$829$	−12.5861	+	21.7998i	−0.437135	+	0.757140i	−0.997467	−	0.0711281i	$-0.977340\pi$
$829$	−12.5861	+	21.7998i	−0.437135	+	0.757140i	0.560332	+	0.828268i	$0.310673\pi$
$830$	0.642230	+	1.11238i	0.0222921	+	0.0386111i
$831$		0			0
$832$	29.6934			1.02943
$833$	−92.8643			−3.21756
$834$		0			0
$835$	3.40500	−	5.89764i	0.117835	−	0.204096i
$836$	−31.6646	+	54.8446i	−1.09514	+	1.89684i
$837$		0			0
$838$	27.7743			0.959449
$839$	13.4344	−	23.2690i	0.463806	−	0.803335i	−0.535341	−	0.844636i	$-0.679817\pi$
$839$	13.4344	−	23.2690i	0.463806	−	0.803335i	0.999147	+	0.0413009i	$0.0131502\pi$
$840$		0			0
$841$	12.1769	−	21.0910i	0.419894	−	0.727277i
$842$	10.7968	+	18.7006i	0.372083	+	0.644467i
$843$		0			0
$844$	−1.10117	−	1.90729i	−0.0379039	−	0.0656516i
$845$	26.6689	−	46.1918i	0.917436	−	1.58905i
$846$		0			0
$847$	−48.2462			−1.65776
$848$	−26.8087			−0.920614
$849$		0			0
$850$	18.3062	+	31.7072i	0.627897	+	1.08755i
$851$	14.7688			0.506267
$852$		0			0
$853$	−8.98692	−	15.5658i	−0.307706	−	0.532963i	0.670154	−	0.742222i	$-0.266228\pi$
$853$	−8.98692	−	15.5658i	−0.307706	−	0.532963i	−0.977860	+	0.209259i	$0.932895\pi$
$854$	48.1748			1.64851
$855$		0			0
$856$	−2.27484	+	3.94014i	−0.0777525	+	0.134671i
$857$	11.8587	−	20.5399i	0.405087	−	0.701631i	−0.589245	−	0.807955i	$-0.700575\pi$
$857$	11.8587	−	20.5399i	0.405087	−	0.701631i	0.994332	+	0.106324i	$0.0339079\pi$
$858$		0			0
$859$	7.42192	+	12.8551i	0.253233	+	0.438612i	0.964414	−	0.264397i	$-0.0851729\pi$
$859$	7.42192	+	12.8551i	0.253233	+	0.438612i	−0.711181	+	0.703009i	$0.751840\pi$
$860$	−14.7380	+	25.5269i	−0.502561	+	0.870461i
$861$		0			0
$862$	−1.43598	+	2.48720i	−0.0489098	+	0.0847143i
$863$	37.4350			1.27430			0.637151	−	0.770739i	$-0.280113\pi$
$863$	37.4350			1.27430			0.637151	+	0.770739i	$0.280113\pi$
$864$		0			0
$865$	−21.4677	−	37.1832i	−0.729924	−	1.26427i
$866$	59.7384			2.02999
$867$		0			0
$868$	−1.14420	−	1.98182i	−0.0388368	−	0.0672673i
$869$	−1.27394	+	2.20654i	−0.0432156	+	0.0748516i
$870$		0			0
$871$	2.21817	−	3.84198i	0.0751599	−	0.130181i
$872$	−3.02984	−	5.24784i	−0.102603	−	0.177714i
$873$		0			0
$874$	12.5823	−	21.7932i	0.425604	−	0.737167i
$875$	11.8141	−	20.4626i	0.399389	−	0.691762i
$876$		0			0
$877$	2.87629	−	4.98188i	0.0971255	−	0.168226i	−0.813368	−	0.581749i	$-0.802369\pi$
$877$	2.87629	−	4.98188i	0.0971255	−	0.168226i	0.910494	+	0.413523i	$0.135702\pi$
$878$	23.5328	+	40.7600i	0.794193	+	1.37558i
$879$		0			0
$880$	29.9545	−	51.8827i	1.00977	−	1.74897i
$881$	18.7875	+	32.5408i	0.632965	+	1.09633i	0.986942	+	0.161074i	$0.0514958\pi$
$881$	18.7875	+	32.5408i	0.632965	+	1.09633i	−0.353977	+	0.935254i	$0.615171\pi$
$882$		0			0
$883$	0.718036	+	1.24368i	0.0241638	+	0.0418530i	0.877854	−	0.478928i	$-0.158974\pi$
$883$	0.718036	+	1.24368i	0.0241638	+	0.0418530i	−0.853691	+	0.520781i	$0.825641\pi$
$884$	−27.3967	−	47.4526i	−0.921452	−	1.59600i
$885$		0			0
$886$	31.1175	+	53.8970i	1.04541	+	1.81071i
$887$	4.58583	−	7.94289i	0.153977	−	0.266696i	−0.778709	−	0.627385i	$-0.784125\pi$
$887$	4.58583	−	7.94289i	0.153977	−	0.266696i	0.932686	+	0.360689i	$0.117458\pi$
$888$		0			0
$889$	−32.3130	+	55.9677i	−1.08374	+	1.87710i
$890$	35.3874			1.18619
$891$		0			0
$892$	1.93913	+	3.35867i	0.0649269	+	0.112457i
$893$	−22.1223			−0.740295
$894$		0			0
$895$	−10.0331	+	17.3778i	−0.335369	+	0.580876i
$896$	−23.1006			−0.771738
$897$		0			0
$898$	26.6921	+	46.2321i	0.890727	+	1.54278i
$899$	0.305639	+	0.529382i	0.0101936	+	0.0176559i
$900$		0			0
$901$	17.1480	+	29.7012i	0.571282	+	0.989490i
$902$	−30.4732	−	52.7811i	−1.01465	−	1.75742i
$903$		0			0
$904$	8.39987			0.279375
$905$	−4.06128			−0.135002
$906$		0			0
$907$	−18.5670	−	32.1589i	−0.616506	−	1.06782i	−0.990118	−	0.140234i	$-0.955214\pi$
$907$	−18.5670	−	32.1589i	−0.616506	−	1.06782i	0.373613	−	0.927585i	$-0.378119\pi$
$908$	3.54244	+	6.13569i	0.117560	+	0.203620i
$909$		0			0
$910$	74.3978	−	128.861i	2.46626	−	4.27170i
$911$	−1.49357	−	2.58695i	−0.0494843	−	0.0857094i	0.840222	−	0.542242i	$-0.182424\pi$
$911$	−1.49357	−	2.58695i	−0.0494843	−	0.0857094i	−0.889707	+	0.456533i	$0.849091\pi$
$912$		0			0
$913$	−1.06689			−0.0353089
$914$	34.4585			1.13978
$915$		0			0
$916$	−1.12040	+	1.94059i	−0.0370191	+	0.0641190i
$917$	−74.8344			−2.47125
$918$		0			0
$919$	48.1885			1.58959			0.794795	−	0.606877i	$-0.207578\pi$
$919$	48.1885			1.58959			0.794795	+	0.606877i	$0.207578\pi$
$920$	−1.40302	+	2.43010i	−0.0462562	+	0.0801182i
$921$		0			0
$922$	−34.6575	+	60.0285i	−1.14138	+	1.97693i
$923$	38.1972	−	66.1594i	1.25728	−	2.17766i
$924$		0			0
$925$	−15.1932	−	26.3155i	−0.499550	−	0.865247i
$926$	−33.5646			−1.10300
$927$		0			0
$928$	−16.1274			−0.529409
$929$	−5.91698	−	10.2485i	−0.194130	−	0.336243i	0.752485	−	0.658609i	$-0.228855\pi$
$929$	−5.91698	−	10.2485i	−0.194130	−	0.336243i	−0.946615	+	0.322366i	$0.895522\pi$
$930$		0			0
$931$	65.6625	−	113.731i	2.15200	−	3.72738i
$932$	1.13175	−	1.96024i	0.0370716	−	0.0642099i
$933$		0			0
$934$	33.8854	−	58.6912i	1.10876	−	1.92043i
$935$	−76.6407			−2.50642
$936$		0			0
$937$	11.3060			0.369349			0.184675	−	0.982800i	$-0.440877\pi$
$937$	11.3060			0.369349			0.184675	+	0.982800i	$0.440877\pi$
$938$	3.63633	−	6.29831i	0.118730	−	0.205647i
$939$		0			0
$940$	−13.0613			−0.426012
$941$	28.2558			0.921111			0.460556	−	0.887631i	$-0.347650\pi$
$941$	28.2558			0.921111			0.460556	+	0.887631i	$0.347650\pi$
$942$		0			0
$943$	5.53206	+	9.58180i	0.180149	+	0.312026i
$944$	−7.24287	+	12.5450i	−0.235735	+	0.408305i
$945$		0			0
$946$	−26.7951	−	46.4105i	−0.871185	−	1.50894i
$947$	3.12730	+	5.41664i	0.101624	+	0.176017i	0.912354	−	0.409403i	$-0.134263\pi$
$947$	3.12730	+	5.41664i	0.101624	+	0.176017i	−0.810730	+	0.585420i	$0.800930\pi$
$948$		0			0
$949$	−24.5248			−0.796107
$950$	−51.7758			−1.67983
$951$		0			0
$952$	8.48233	+	14.6918i	0.274914	+	0.476165i
$953$	−9.14825	−	15.8452i	−0.296341	−	0.513277i	0.678955	−	0.734180i	$-0.262433\pi$
$953$	−9.14825	−	15.8452i	−0.296341	−	0.513277i	−0.975296	+	0.220902i	$0.929100\pi$
$954$		0			0
$955$	18.7480	+	32.4726i	0.606673	+	1.05079i
$956$	16.9502	+	29.3586i	0.548208	+	0.949524i
$957$		0			0
$958$	−10.1222			−0.327034
$959$	−41.7013	+	72.2287i	−1.34660	+	2.33239i
$960$		0			0
$961$	−30.9196			−0.997406
$962$	49.7703	+	86.2046i	1.60466	+	2.77935i
$963$		0			0
$964$	−19.8968			−0.640832
$965$	5.47171	−	9.47729i	0.176141	−	0.305085i
$966$		0			0
$967$	−10.7490	+	18.6178i	−0.345664	+	0.598708i	−0.985474	−	0.169825i	$-0.945680\pi$
$967$	−10.7490	+	18.6178i	−0.345664	+	0.598708i	0.639810	+	0.768533i	$0.279013\pi$
$968$	3.06615	+	5.31072i	0.0985497	+	0.170693i
$969$		0			0
$970$	−8.98329	−	15.5595i	−0.288436	−	0.499586i
$971$	15.0009	+	25.9823i	0.481401	+	0.833811i	0.999772	−	0.0213448i	$-0.00679477\pi$
$971$	15.0009	+	25.9823i	0.481401	+	0.833811i	−0.518371	+	0.855156i	$0.673461\pi$
$972$		0			0
$973$	4.65249	+	8.05835i	0.149152	+	0.258339i
$974$	−7.14104	+	12.3686i	−0.228814	+	0.396317i
$975$		0			0
$976$	−11.8663	−	20.5531i	−0.379832	−	0.657888i
$977$	−2.22445	+	3.85286i	−0.0711665	+	0.123264i	−0.899413	−	0.437100i	$-0.856006\pi$
$977$	−2.22445	+	3.85286i	−0.0711665	+	0.123264i	0.828246	+	0.560364i	$0.189339\pi$
$978$		0			0
$979$	−14.6966	+	25.4553i	−0.469706	+	0.813554i
$980$	38.7680	−	67.1481i	1.23840	−	2.14497i
$981$		0			0
$982$	−15.6325	−	27.0763i	−0.498854	−	0.864040i
$983$	12.2411	−	21.2022i	0.390430	−	0.676244i	−0.602077	−	0.798438i	$-0.705660\pi$
$983$	12.2411	−	21.2022i	0.390430	−	0.676244i	0.992506	+	0.122194i	$0.0389932\pi$
$984$		0			0
$985$	15.4371	−	26.7379i	0.491868	−	0.851940i
$986$	11.9970	+	20.7794i	0.382062	+	0.661751i
$987$		0			0
$988$	77.4868			2.46518
$989$	4.86435	+	8.42530i	0.154677	+	0.267909i
$990$		0			0
$991$	−21.1163			−0.670781			−0.335391	−	0.942079i	$-0.608868\pi$
$991$	−21.1163			−0.670781			−0.335391	+	0.942079i	$0.608868\pi$
$992$	−1.06091	+	1.83755i	−0.0336839	+	0.0583422i
$993$		0			0
$994$	62.6181	−	108.458i	1.98613	−	3.44007i
$995$	−28.3385	−	49.0837i	−0.898391	−	1.55606i
$996$		0			0
$997$	25.8951	−	44.8517i	0.820107	−	1.42047i	−0.0854943	−	0.996339i	$-0.527247\pi$
$997$	25.8951	−	44.8517i	0.820107	−	1.42047i	0.905602	−	0.424129i	$-0.139420\pi$
$998$	−40.4079	+	69.9886i	−1.27909	+	2.21545i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	927.2.f.f.46.4	✓	32
3.2	odd	2	inner	927.2.f.f.46.13	yes	32
103.56	even	3	inner	927.2.f.f.262.4	yes	32
309.56	odd	6	inner	927.2.f.f.262.13	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
927.2.f.f.46.4	✓	32	1.1	even	1	trivial
927.2.f.f.46.13	yes	32	3.2	odd	2	inner
927.2.f.f.262.4	yes	32	103.56	even	3	inner
927.2.f.f.262.13	yes	32	309.56	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:	\( N \)	\(=\)	\( 927 = 3^{2} \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	927.f (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.959463 - 1.66184i) q^{2} +(-0.841140 + 1.45690i) q^{4} +(1.43954 - 2.49335i) q^{5} +(2.39836 - 4.15408i) q^{7} -0.609683 q^{8} +O(q^{10})\)	\(q+(-0.959463 - 1.66184i) q^{2} +(-0.841140 + 1.45690i) q^{4} +(1.43954 - 2.49335i) q^{5} +(2.39836 - 4.15408i) q^{7} -0.609683 q^{8} -5.52473 q^{10} +(2.29446 - 3.97412i) q^{11} -5.61480 q^{13} -9.20456 q^{14} +(2.26725 + 3.92699i) q^{16} +(2.90046 - 5.02374i) q^{17} +(4.10171 + 7.10437i) q^{19} +(2.42170 + 4.19451i) q^{20} -8.80580 q^{22} +1.59859 q^{23} +(-1.64453 - 2.84842i) q^{25} +(5.38720 + 9.33090i) q^{26} +(4.03471 + 6.98833i) q^{28} +(-1.07775 - 1.86672i) q^{29} -0.283590 q^{31} +(3.74100 - 6.47960i) q^{32} -11.1315 q^{34} +(-6.90506 - 11.9599i) q^{35} +9.23862 q^{37} +(7.87089 - 13.6328i) q^{38} +(-0.877661 + 1.52015i) q^{40} +(3.46058 + 5.99390i) q^{41} +(3.04290 + 5.27045i) q^{43} +(3.85992 + 6.68558i) q^{44} +(-1.53379 - 2.65660i) q^{46} +(-1.34836 + 2.33542i) q^{47} +(-8.00428 - 13.8638i) q^{49} +(-3.15574 + 5.46590i) q^{50} +(4.72283 - 8.18018i) q^{52} +(-2.95608 + 5.12009i) q^{53} +(-6.60592 - 11.4418i) q^{55} +(-1.46224 + 2.53267i) q^{56} +(-2.06812 + 3.58209i) q^{58} +(1.59728 + 2.76657i) q^{59} -5.23380 q^{61} +(0.272094 + 0.471281i) q^{62} -5.28841 q^{64} +(-8.08271 + 13.9997i) q^{65} +(-0.395058 + 0.684260i) q^{67} +(4.87938 + 8.45133i) q^{68} +(-13.2503 + 22.9502i) q^{70} +(-6.80294 + 11.7830i) q^{71} +4.36788 q^{73} +(-8.86412 - 15.3531i) q^{74} -13.8005 q^{76} +(-11.0059 - 19.0628i) q^{77} -0.555227 q^{79} +13.0551 q^{80} +(6.64060 - 11.5019i) q^{82} +(-0.116246 - 0.201345i) q^{83} +(-8.35063 - 14.4637i) q^{85} +(5.83909 - 10.1136i) q^{86} +(-1.39889 + 2.42295i) q^{88} -6.40526 q^{89} +(-13.4663 + 23.3244i) q^{91} +(-1.34464 + 2.32898i) q^{92} +5.17480 q^{94} +23.6183 q^{95} +(1.62601 + 2.81634i) q^{97} +(-15.3596 + 26.6037i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 18 q^{4} + 8 q^{7}+O(q^{10}) \) 32 * q - 18 * q^4 + 8 * q^7	\( 32 q - 18 q^{4} + 8 q^{7} - 32 q^{10} - 4 q^{13} - 18 q^{16} + 4 q^{19} - 40 q^{22} - 26 q^{25} + 8 q^{28} + 32 q^{31} + 8 q^{34} - 48 q^{37} + 22 q^{40} + 2 q^{43} + 18 q^{46} - 8 q^{49} - 68 q^{52} - 32 q^{55} - 24 q^{58} - 20 q^{61} + 68 q^{64} + 8 q^{67} + 38 q^{70} - 64 q^{73} - 188 q^{76} - 20 q^{79} + 60 q^{82} + 8 q^{85} + 6 q^{88} - 30 q^{91} - 92 q^{94} + 32 q^{97}+O(q^{100}) \) 32 * q - 18 * q^4 + 8 * q^7 - 32 * q^10 - 4 * q^13 - 18 * q^16 + 4 * q^19 - 40 * q^22 - 26 * q^25 + 8 * q^28 + 32 * q^31 + 8 * q^34 - 48 * q^37 + 22 * q^40 + 2 * q^43 + 18 * q^46 - 8 * q^49 - 68 * q^52 - 32 * q^55 - 24 * q^58 - 20 * q^61 + 68 * q^64 + 8 * q^67 + 38 * q^70 - 64 * q^73 - 188 * q^76 - 20 * q^79 + 60 * q^82 + 8 * q^85 + 6 * q^88 - 30 * q^91 - 92 * q^94 + 32 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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