LMFDB - Embedded newform 375.2.i.b.199.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [375,2,Mod(49,375)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(375, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 7]))

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

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

chi := DirichletCharacter("375.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 375 = 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	375.i (of order $10$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.99439007580$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 5x^{14} + 6x^{12} - 20x^{10} - 79x^{8} - 80x^{6} + 96x^{4} + 320x^{2} + 256 $ x^16 + 5x^14 + 6x^12 - 20x^10 - 79x^8 - 80x^6 + 96x^4 + 320*x^2 + 256
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 5^{2} $
Twist minimal:	no (minimal twist has level 75)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			199.1
Root			$-1.41395 - 0.0272949i$ of defining polynomial
Character	$\chi$	$=$	375.199
Dual form			375.2.i.b.49.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.59076 - 2.18949i) q^{2} +(-0.951057 - 0.309017i) q^{3} +(-1.64533 + 5.06380i) q^{4} +(0.836312 + 2.57390i) q^{6} +0.470294i q^{7} +(8.55667 - 2.78023i) q^{8} +(0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(-1.59076 - 2.18949i) q^{2} +(-0.951057 - 0.309017i) q^{3} +(-1.64533 + 5.06380i) q^{4} +(0.836312 + 2.57390i) q^{6} +0.470294i q^{7} +(8.55667 - 2.78023i) q^{8} +(0.809017 + 0.587785i) q^{9} +(2.57387 - 1.87003i) q^{11} +(3.12960 - 4.30753i) q^{12} +(-0.331184 + 0.455836i) q^{13} +(1.02971 - 0.748125i) q^{14} +(-11.0839 - 8.05289i) q^{16} +(1.62285 - 0.527295i) q^{17} -2.70636i q^{18} +(-1.15575 - 3.55705i) q^{19} +(0.145329 - 0.447276i) q^{21} +(-8.18882 - 2.66071i) q^{22} +(-1.33416 - 1.83631i) q^{23} -8.99702 q^{24} +1.52488 q^{26} +(-0.587785 - 0.809017i) q^{27} +(-2.38148 - 0.773789i) q^{28} +(2.57238 - 7.91697i) q^{29} +(1.67999 + 5.17047i) q^{31} +19.0842i q^{32} +(-3.02577 + 0.983131i) q^{33} +(-3.73607 - 2.71441i) q^{34} +(-4.30753 + 3.12960i) q^{36} +(0.600041 - 0.825886i) q^{37} +(-5.94960 + 8.18892i) q^{38} +(0.455836 - 0.331184i) q^{39} +(-1.19098 - 0.865300i) q^{41} +(-1.21049 + 0.393313i) q^{42} -6.72721i q^{43} +(5.23458 + 16.1104i) q^{44} +(-1.89827 + 5.84226i) q^{46} +(-4.21658 - 1.37005i) q^{47} +(8.05289 + 11.0839i) q^{48} +6.77882 q^{49} -1.70636 q^{51} +(-1.76336 - 2.42705i) q^{52} +(6.70648 + 2.17907i) q^{53} +(-0.836312 + 2.57390i) q^{54} +(1.30753 + 4.02415i) q^{56} +3.74010i q^{57} +(-21.4262 + 6.96179i) q^{58} +(-10.4136 - 7.56596i) q^{59} +(-0.102655 + 0.0745831i) q^{61} +(8.64825 - 11.9033i) q^{62} +(-0.276432 + 0.380476i) q^{63} +(19.6170 - 14.2526i) q^{64} +(6.96582 + 5.06097i) q^{66} +(2.65791 - 0.863607i) q^{67} +9.08535i q^{68} +(0.701409 + 2.15871i) q^{69} +(4.95838 - 15.2603i) q^{71} +(8.55667 + 2.78023i) q^{72} +(-5.75367 - 7.91925i) q^{73} -2.76279 q^{74} +19.9138 q^{76} +(0.879462 + 1.21048i) q^{77} +(-1.45025 - 0.471215i) q^{78} +(1.46937 - 4.52227i) q^{79} +(0.309017 + 0.951057i) q^{81} +3.98413i q^{82} +(11.1183 - 3.61256i) q^{83} +(2.02580 + 1.47183i) q^{84} +(-14.7292 + 10.7014i) q^{86} +(-4.89296 + 6.73458i) q^{87} +(16.8247 - 23.1572i) q^{88} +(-5.01630 + 3.64456i) q^{89} +(-0.214377 - 0.155754i) q^{91} +(11.4938 - 3.73458i) q^{92} -5.43656i q^{93} +(3.70785 + 11.4116i) q^{94} +(5.89735 - 18.1502i) q^{96} +(8.04064 + 2.61256i) q^{97} +(-10.7835 - 14.8422i) q^{98} +3.18148 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{4} - 2 q^{6} + 4 q^{9}+O(q^{10}) $ 16 * q - 2 * q^4 - 2 * q^6 + 4 * q^9	$ 16 q - 2 q^{4} - 2 q^{6} + 4 q^{9} + 32 q^{11} + 16 q^{14} - 34 q^{16} + 10 q^{19} - 22 q^{21} - 60 q^{24} + 12 q^{26} - 10 q^{29} - 38 q^{31} - 24 q^{34} - 18 q^{36} + 16 q^{39} - 28 q^{41} + 6 q^{44} + 32 q^{46} - 32 q^{49} + 8 q^{51} + 2 q^{54} - 30 q^{56} - 60 q^{59} - 28 q^{61} + 88 q^{64} - 14 q^{66} + 16 q^{69} + 42 q^{71} + 76 q^{74} + 160 q^{76} + 60 q^{79} - 4 q^{81} - 16 q^{84} - 68 q^{86} + 42 q^{91} + 66 q^{94} + 68 q^{96} + 28 q^{99}+O(q^{100}) $ 16 * q - 2 * q^4 - 2 * q^6 + 4 * q^9 + 32 * q^11 + 16 * q^14 - 34 * q^16 + 10 * q^19 - 22 * q^21 - 60 * q^24 + 12 * q^26 - 10 * q^29 - 38 * q^31 - 24 * q^34 - 18 * q^36 + 16 * q^39 - 28 * q^41 + 6 * q^44 + 32 * q^46 - 32 * q^49 + 8 * q^51 + 2 * q^54 - 30 * q^56 - 60 * q^59 - 28 * q^61 + 88 * q^64 - 14 * q^66 + 16 * q^69 + 42 * q^71 + 76 * q^74 + 160 * q^76 + 60 * q^79 - 4 * q^81 - 16 * q^84 - 68 * q^86 + 42 * q^91 + 66 * q^94 + 68 * q^96 + 28 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/375\mathbb{Z}\right)^\times$.

$n$	$127$	$251$
$\chi(n)$	$e\left(\frac{3}{10}\right)$	$1$

Coefficient data

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

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

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

$2$	−1.59076	−	2.18949i	−1.12484	−	1.54821i	−0.797522	−	0.603290i	$-0.793856\pi$
$2$	−1.59076	−	2.18949i	−1.12484	−	1.54821i	−0.327315	−	0.944915i	$-0.606144\pi$
$3$	−0.951057	−	0.309017i	−0.549093	−	0.178411i
$3$	−0.951057	−	0.309017i	−0.549093	−	0.178411i
$4$	−1.64533	+	5.06380i	−0.822664	+	2.53190i
$5$		0			0
$5$		0			0
$6$	0.836312	+	2.57390i	0.341423	+	1.05079i
$7$			0.470294i			0.177754i	0.996043	+	0.0888772i	$0.0283279\pi$
$7$			0.470294i			0.177754i	−0.996043	+	0.0888772i	$0.971672\pi$
$8$	8.55667	−	2.78023i	3.02524	−	0.982960i
$9$	0.809017	+	0.587785i	0.269672	+	0.195928i
$10$		0			0
$11$	2.57387	−	1.87003i	0.776051	−	0.563834i	−0.127740	−	0.991808i	$-0.540772\pi$
$11$	2.57387	−	1.87003i	0.776051	−	0.563834i	0.903791	+	0.427974i	$0.140772\pi$
$12$	3.12960	−	4.30753i	0.903438	−	1.24348i
$13$	−0.331184	+	0.455836i	−0.0918540	+	0.126426i	−0.852471	−	0.522775i	$-0.824897\pi$
$13$	−0.331184	+	0.455836i	−0.0918540	+	0.126426i	0.760617	+	0.649201i	$0.224897\pi$
$14$	1.02971	−	0.748125i	0.275200	−	0.199945i
$15$		0			0
$16$	−11.0839	−	8.05289i	−2.77096	−	2.01322i
$17$	1.62285	−	0.527295i	0.393598	−	0.127888i	−0.105530	−	0.994416i	$-0.533654\pi$
$17$	1.62285	−	0.527295i	0.393598	−	0.127888i	0.499128	+	0.866528i	$0.333654\pi$
$18$		−	2.70636i		−	0.637896i
$19$	−1.15575	−	3.55705i	−0.265148	−	0.816043i	−0.991659	−	0.128888i	$-0.958859\pi$
$19$	−1.15575	−	3.55705i	−0.265148	−	0.816043i	0.726511	−	0.687155i	$-0.241141\pi$
$20$		0			0
$21$	0.145329	−	0.447276i	0.0317134	−	0.0976037i
$22$	−8.18882	−	2.66071i	−1.74586	−	0.567265i
$23$	−1.33416	−	1.83631i	−0.278191	−	0.382898i	0.646942	−	0.762539i	$-0.276047\pi$
$23$	−1.33416	−	1.83631i	−0.278191	−	0.382898i	−0.925134	+	0.379641i	$0.876047\pi$
$24$	−8.99702			−1.83651
$25$		0			0
$26$	1.52488			0.299054
$27$	−0.587785	−	0.809017i	−0.113119	−	0.155695i
$28$	−2.38148	−	0.773789i	−0.450057	−	0.146232i
$29$	2.57238	−	7.91697i	0.477679	−	1.47014i	−0.364631	−	0.931152i	$-0.618805\pi$
$29$	2.57238	−	7.91697i	0.477679	−	1.47014i	0.842310	−	0.538993i	$-0.181195\pi$
$30$		0			0
$31$	1.67999	+	5.17047i	0.301735	+	0.928644i	0.980876	+	0.194636i	$0.0623526\pi$
$31$	1.67999	+	5.17047i	0.301735	+	0.928644i	−0.679141	+	0.734008i	$0.737647\pi$
$32$			19.0842i			3.37364i
$33$	−3.02577	+	0.983131i	−0.526718	+	0.171141i
$34$	−3.73607	−	2.71441i	−0.640730	−	0.465518i
$35$		0			0
$36$	−4.30753	+	3.12960i	−0.717921	+	0.521600i
$37$	0.600041	−	0.825886i	0.0986462	−	0.135775i	−0.756841	−	0.653600i	$-0.773258\pi$
$37$	0.600041	−	0.825886i	0.0986462	−	0.135775i	0.855487	+	0.517825i	$0.173258\pi$
$38$	−5.94960	+	8.18892i	−0.965153	+	1.32842i
$39$	0.455836	−	0.331184i	0.0729922	−	0.0530319i
$40$		0			0
$41$	−1.19098	−	0.865300i	−0.186000	−	0.135137i	0.490889	−	0.871222i	$-0.336672\pi$
$41$	−1.19098	−	0.865300i	−0.186000	−	0.135137i	−0.676889	+	0.736085i	$0.736672\pi$
$42$	−1.21049	+	0.393313i	−0.186783	+	0.0606895i
$43$		−	6.72721i		−	1.02589i	−0.858421	−	0.512945i	$-0.828554\pi$
$43$		−	6.72721i		−	1.02589i	0.858421	−	0.512945i	$-0.171446\pi$
$44$	5.23458	+	16.1104i	0.789142	+	2.42873i
$45$		0			0
$46$	−1.89827	+	5.84226i	−0.279884	+	0.861395i
$47$	−4.21658	−	1.37005i	−0.615052	−	0.199842i	−0.0151095	−	0.999886i	$-0.504810\pi$
$47$	−4.21658	−	1.37005i	−0.615052	−	0.199842i	−0.599942	+	0.800043i	$0.704810\pi$
$48$	8.05289	+	11.0839i	1.16234	+	1.59982i
$49$	6.77882			0.968403
$50$		0			0
$51$	−1.70636			−0.238938
$52$	−1.76336	−	2.42705i	−0.244533	−	0.336571i
$53$	6.70648	+	2.17907i	0.921206	+	0.299318i	0.730961	−	0.682419i	$-0.239072\pi$
$53$	6.70648	+	2.17907i	0.921206	+	0.299318i	0.190244	+	0.981737i	$0.439072\pi$
$54$	−0.836312	+	2.57390i	−0.113808	+	0.350264i
$55$		0			0
$56$	1.30753	+	4.02415i	0.174726	+	0.537750i
$57$			3.74010i			0.495388i
$58$	−21.4262	+	6.96179i	−2.81340	+	0.914128i
$59$	−10.4136	−	7.56596i	−1.35574	−	0.985004i	−0.998703	−	0.0509138i	$-0.983787\pi$
$59$	−10.4136	−	7.56596i	−1.35574	−	0.985004i	−0.357038	−	0.934090i	$-0.616213\pi$
$60$		0			0
$61$	−0.102655	+	0.0745831i	−0.0131436	+	0.00954939i	−0.594338	−	0.804216i	$-0.702586\pi$
$61$	−0.102655	+	0.0745831i	−0.0131436	+	0.00954939i	0.581194	+	0.813765i	$0.302586\pi$
$62$	8.64825	−	11.9033i	1.09833	−	1.51172i
$63$	−0.276432	+	0.380476i	−0.0348272	+	0.0479355i
$64$	19.6170	−	14.2526i	2.45213	−	1.78158i
$65$		0			0
$66$	6.96582	+	5.06097i	0.857434	+	0.622962i
$67$	2.65791	−	0.863607i	0.324715	−	0.105506i	−0.142123	−	0.989849i	$-0.545393\pi$
$67$	2.65791	−	0.863607i	0.324715	−	0.105506i	0.466838	+	0.884343i	$0.345393\pi$
$68$			9.08535i			1.10176i
$69$	0.701409	+	2.15871i	0.0844397	+	0.259879i
$70$		0			0
$71$	4.95838	−	15.2603i	0.588451	−	1.81107i	0.00350617	−	0.999994i	$-0.498884\pi$
$71$	4.95838	−	15.2603i	0.588451	−	1.81107i	0.584945	−	0.811073i	$-0.301116\pi$
$72$	8.55667	+	2.78023i	1.00841	+	0.327653i
$73$	−5.75367	−	7.91925i	−0.673416	−	0.926878i	0.326415	−	0.945226i	$-0.394159\pi$
$73$	−5.75367	−	7.91925i	−0.673416	−	0.926878i	−0.999832	+	0.0183484i	$0.994159\pi$
$74$	−2.76279			−0.321168
$75$		0			0
$76$	19.9138			2.28427
$77$	0.879462	+	1.21048i	0.100224	+	0.137947i
$78$	−1.45025	−	0.471215i	−0.164209	−	0.0533546i
$79$	1.46937	−	4.52227i	0.165317	−	0.508795i	−0.833742	−	0.552154i	$-0.813806\pi$
$79$	1.46937	−	4.52227i	0.165317	−	0.508795i	0.999060	+	0.0433593i	$0.0138060\pi$
$80$		0			0
$81$	0.309017	+	0.951057i	0.0343352	+	0.105673i
$82$			3.98413i			0.439974i
$83$	11.1183	−	3.61256i	1.22039	−	0.396530i	0.373169	−	0.927763i	$-0.378271\pi$
$83$	11.1183	−	3.61256i	1.22039	−	0.396530i	0.847226	+	0.531233i	$0.178271\pi$
$84$	2.02580	+	1.47183i	0.221033	+	0.160590i
$85$		0			0
$86$	−14.7292	+	10.7014i	−1.58829	+	1.15396i
$87$	−4.89296	+	6.73458i	−0.524580	+	0.722023i
$88$	16.8247	−	23.1572i	1.79351	−	2.46856i
$89$	−5.01630	+	3.64456i	−0.531727	+	0.386322i	−0.821003	−	0.570923i	$-0.806585\pi$
$89$	−5.01630	+	3.64456i	−0.531727	+	0.386322i	0.289277	+	0.957246i	$0.406585\pi$
$90$		0			0
$91$	−0.214377	−	0.155754i	−0.0224728	−	0.0163275i
$92$	11.4938	−	3.73458i	1.19832	−	0.389357i
$93$		−	5.43656i		−	0.563745i
$94$	3.70785	+	11.4116i	0.382436	+	1.17702i
$95$		0			0
$96$	5.89735	−	18.1502i	0.601895	−	1.85244i
$97$	8.04064	+	2.61256i	0.816403	+	0.265265i	0.687307	−	0.726367i	$-0.258793\pi$
$97$	8.04064	+	2.61256i	0.816403	+	0.265265i	0.129096	+	0.991632i	$0.458793\pi$
$98$	−10.7835	−	14.8422i	−1.08930	−	1.49929i
$99$	3.18148			0.319751
$100$		0			0
$101$	−5.83325			−0.580430			−0.290215	−	0.956961i	$-0.593727\pi$
$101$	−5.83325			−0.580430			−0.290215	+	0.956961i	$0.593727\pi$
$102$	2.71441	+	3.73607i	0.268767	+	0.369926i
$103$	13.3903	+	4.35077i	1.31938	+	0.428694i	0.882284	−	0.470718i	$-0.156005\pi$
$103$	13.3903	+	4.35077i	1.31938	+	0.428694i	0.437101	+	0.899412i	$0.356005\pi$
$104$	−1.56651	+	4.82121i	−0.153609	+	0.472758i
$105$		0			0
$106$	−5.89735	−	18.1502i	−0.572801	−	1.76290i
$107$		−	8.61207i		−	0.832561i	−0.909236	−	0.416280i	$-0.863334\pi$
$107$		−	8.61207i		−	0.832561i	0.909236	−	0.416280i	$-0.136666\pi$
$108$	5.06380	−	1.64533i	0.487265	−	0.158322i
$109$	13.5005	+	9.80868i	1.29311	+	0.939501i	0.999863	−	0.0165355i	$-0.00526367\pi$
$109$	13.5005	+	9.80868i	1.29311	+	0.939501i	0.293249	+	0.956036i	$0.405264\pi$
$110$		0			0
$111$	−0.825886	+	0.600041i	−0.0783896	+	0.0569534i
$112$	3.78723	−	5.21267i	0.357860	−	0.492551i
$113$	−6.92167	+	9.52686i	−0.651136	+	0.896211i	−0.999148	−	0.0412787i	$-0.986857\pi$
$113$	−6.92167	+	9.52686i	−0.651136	+	0.896211i	0.348012	+	0.937490i	$0.386857\pi$
$114$	8.18892	−	5.94960i	0.766963	−	0.557231i
$115$		0			0
$116$	35.8576	+	26.0520i	3.32929	+	2.41887i
$117$	−0.535867	+	0.174114i	−0.0495409	+	0.0160968i
$118$			34.8362i			3.20693i
$119$	0.247984	+	0.763215i	0.0227326	+	0.0699638i
$120$		0			0
$121$	−0.271378	+	0.835215i	−0.0246707	+	0.0759286i
$122$	0.326598	+	0.106118i	0.0295688	+	0.00960749i
$123$	0.865300	+	1.19098i	0.0780215	+	0.107387i
$124$	−28.9464			−2.59946
$125$		0			0
$126$	1.27279			0.113389
$127$	−1.04557	−	1.43910i	−0.0927790	−	0.127699i	0.760104	−	0.649801i	$-0.225148\pi$
$127$	−1.04557	−	1.43910i	−0.0927790	−	0.127699i	−0.852883	+	0.522102i	$0.825148\pi$
$128$	−26.1116	−	8.48418i	−2.30796	−	0.749903i
$129$	−2.07882	+	6.39796i	−0.183030	+	0.563309i
$130$		0			0
$131$	−1.82895	−	5.62892i	−0.159796	−	0.491801i	0.838819	−	0.544410i	$-0.183246\pi$
$131$	−1.82895	−	5.62892i	−0.159796	−	0.491801i	−0.998615	+	0.0526087i	$0.983246\pi$
$132$		−	16.9395i		−	1.47439i
$133$	1.67286	−	0.543545i	0.145055	−	0.0471313i
$134$	−6.11895	−	4.44568i	−0.528597	−	0.384048i
$135$		0			0
$136$	12.4202	−	9.02378i	1.06502	−	0.773783i
$137$	−3.00717	+	4.13902i	−0.256920	+	0.353620i	−0.917920	−	0.396766i	$-0.870132\pi$
$137$	−3.00717	+	4.13902i	−0.256920	+	0.353620i	0.661000	+	0.750386i	$0.270132\pi$
$138$	3.61072	−	4.96973i	0.307365	−	0.423051i
$139$	−6.66482	+	4.84228i	−0.565303	+	0.410717i	−0.833396	−	0.552676i	$-0.813607\pi$
$139$	−6.66482	+	4.84228i	−0.565303	+	0.410717i	0.268093	+	0.963393i	$0.413607\pi$
$140$		0			0
$141$	3.58684	+	2.60599i	0.302066	+	0.219464i
$142$	−41.3000	+	13.4192i	−3.46581	+	1.12611i
$143$			1.79259i			0.149904i
$144$	−4.23366	−	13.0299i	−0.352805	−	1.08582i
$145$		0			0
$146$	−8.18643	+	25.1952i	−0.677514	+	2.08517i
$147$	−6.44704	−	2.09477i	−0.531743	−	0.172774i
$148$	3.19486	+	4.39735i	0.262616	+	0.361460i
$149$	10.0585			0.824027			0.412014	−	0.911178i	$-0.364826\pi$
$149$	10.0585			0.824027			0.412014	+	0.911178i	$0.364826\pi$
$150$		0			0
$151$	−11.9810			−0.974999			−0.487500	−	0.873123i	$-0.662091\pi$
$151$	−11.9810			−0.974999			−0.487500	+	0.873123i	$0.662091\pi$
$152$	−19.7788	−	27.2232i	−1.60428	−	2.20810i
$153$	1.62285	+	0.527295i	0.131199	+	0.0426293i
$154$	1.25132	−	3.85115i	0.100834	−	0.310335i
$155$		0			0
$156$	0.927051	+	2.85317i	0.0742235	+	0.228436i
$157$			19.5960i			1.56393i	0.623319	+	0.781967i	$0.285784\pi$
$157$			19.5960i			1.56393i	−0.623319	+	0.781967i	$0.714216\pi$
$158$	−12.2389	+	3.97666i	−0.973674	+	0.316366i
$159$	−5.70487	−	4.14483i	−0.452426	−	0.328707i
$160$		0			0
$161$	0.863607	−	0.627447i	0.0680618	−	0.0494498i
$162$	1.59076	−	2.18949i	0.124982	−	0.172023i
$163$	−6.99033	+	9.62137i	−0.547525	+	0.753604i	−0.989674	−	0.143338i	$-0.954216\pi$
$163$	−6.99033	+	9.62137i	−0.547525	+	0.753604i	0.442149	+	0.896942i	$0.354216\pi$
$164$	6.34127	−	4.60720i	0.495170	−	0.359762i
$165$		0			0
$166$	−25.5963	−	18.5968i	−1.98665	−	1.44339i
$167$	5.70042	−	1.85218i	0.441112	−	0.143326i	−0.0800367	−	0.996792i	$-0.525504\pi$
$167$	5.70042	−	1.85218i	0.441112	−	0.143326i	0.521149	+	0.853466i	$0.325504\pi$
$168$		−	4.23125i		−	0.326448i
$169$	3.91912	+	12.0618i	0.301471	+	0.927831i
$170$		0			0
$171$	1.15575	−	3.55705i	0.0883828	−	0.272014i
$172$	34.0653	+	11.0685i	2.59745	+	0.843964i
$173$	10.1830	+	14.0157i	0.774201	+	1.06560i	0.995898	+	0.0904807i	$0.0288404\pi$
$173$	10.1830	+	14.0157i	0.774201	+	1.06560i	−0.221697	+	0.975116i	$0.571160\pi$
$174$	22.5288			1.70791
$175$		0			0
$176$	−43.5875			−3.28553
$177$	7.56596	+	10.4136i	0.568692	+	0.782738i
$178$	15.9595	+	5.18554i	1.19621	+	0.388673i
$179$	−3.26832	+	10.0588i	−0.244285	+	0.751833i	0.751468	+	0.659770i	$0.229346\pi$
$179$	−3.26832	+	10.0588i	−0.244285	+	0.751833i	−0.995753	+	0.0920634i	$0.970654\pi$
$180$		0			0
$181$	3.70198	+	11.3935i	0.275166	+	0.846873i	0.989175	+	0.146738i	$0.0468773\pi$
$181$	3.70198	+	11.3935i	0.275166	+	0.846873i	−0.714010	+	0.700136i	$0.753123\pi$
$182$			0.717144i			0.0531583i
$183$	0.120678	−	0.0392107i	0.00892077	−	0.00289854i
$184$	−16.5213	−	12.0035i	−1.21797	−	0.884906i
$185$		0			0
$186$	−11.9033	+	8.64825i	−0.872792	+	0.634121i
$187$	3.19094	−	4.39195i	0.233345	−	0.321172i
$188$	13.8753	−	19.0977i	1.01196	−	1.39285i
$189$	0.380476	−	0.276432i	0.0276756	−	0.0201075i
$190$		0			0
$191$	−14.7773	−	10.7363i	−1.06924	−	0.776852i	−0.0934681	−	0.995622i	$-0.529795\pi$
$191$	−14.7773	−	10.7363i	−1.06924	−	0.776852i	−0.975776	+	0.218771i	$0.929795\pi$
$192$	−23.0612	+	7.49304i	−1.66430	+	0.540763i
$193$		−	25.2063i		−	1.81439i	−0.420713	−	0.907194i	$-0.638220\pi$
$193$		−	25.2063i		−	1.81439i	0.420713	−	0.907194i	$-0.361780\pi$
$194$	−7.07054	−	21.7609i	−0.507635	−	1.56234i
$195$		0			0
$196$	−11.1534	+	34.3266i	−0.796671	+	2.45190i
$197$	11.5004	+	3.73672i	0.819372	+	0.266230i	0.688562	−	0.725177i	$-0.258242\pi$
$197$	11.5004	+	3.73672i	0.819372	+	0.266230i	0.130810	+	0.991407i	$0.458242\pi$
$198$	−5.06097	−	6.96582i	−0.359667	−	0.495040i
$199$	0.544434			0.0385939			0.0192970	−	0.999814i	$-0.493857\pi$
$199$	0.544434			0.0385939			0.0192970	+	0.999814i	$0.493857\pi$
$200$		0			0
$201$	−2.79469			−0.197122
$202$	9.27930	+	12.7719i	0.652889	+	0.898625i
$203$	3.72331	+	1.20978i	0.261325	+	0.0849096i
$204$	2.80753	−	8.64068i	0.196566	−	0.604969i
$205$		0			0
$206$	−11.7748	−	36.2390i	−0.820386	−	2.52489i
$207$		−	2.26981i		−	0.157762i
$208$	7.34160	−	2.38543i	0.509048	−	0.165400i
$209$	−9.62653	−	6.99409i	−0.665881	−	0.483791i
$210$		0			0
$211$	2.52580	−	1.83510i	0.173884	−	0.126334i	−0.497439	−	0.867499i	$-0.665726\pi$
$211$	2.52580	−	1.83510i	0.173884	−	0.126334i	0.671323	+	0.741165i	$0.265726\pi$
$212$	−22.0687	+	30.3750i	−1.51569	+	2.08616i
$213$	−9.43140	+	12.9812i	−0.646229	+	0.889457i
$214$	−18.8561	+	13.6997i	−1.28897	+	0.936495i
$215$		0			0
$216$	−7.27874	−	5.28832i	−0.495256	−	0.359824i
$217$	−2.43164	+	0.790089i	−0.165071	+	0.0536347i
$218$		−	45.1625i		−	3.05879i
$219$	3.02488	+	9.30964i	0.204403	+	0.629087i
$220$		0			0
$221$	−0.297101	+	0.914384i	−0.0199852	+	0.0615081i
$222$	2.62757	+	0.853750i	0.176351	+	0.0573000i
$223$	0.199333	+	0.274358i	0.0133483	+	0.0183724i	0.815639	−	0.578561i	$-0.196386\pi$
$223$	0.199333	+	0.274358i	0.0133483	+	0.0183724i	−0.802291	+	0.596934i	$0.796386\pi$
$224$	−8.97519			−0.599680
$225$		0			0
$226$	31.8697			2.11994
$227$	1.05123	+	1.44690i	0.0697729	+	0.0960341i	0.842477	−	0.538732i	$-0.181096\pi$
$227$	1.05123	+	1.44690i	0.0697729	+	0.0960341i	−0.772704	+	0.634766i	$0.781096\pi$
$228$	−18.9391	−	6.15370i	−1.25427	−	0.407538i
$229$	8.64730	−	26.6137i	0.571430	−	1.75868i	−0.0765965	−	0.997062i	$-0.524405\pi$
$229$	8.64730	−	26.6137i	0.571430	−	1.75868i	0.648026	−	0.761618i	$-0.275595\pi$
$230$		0			0
$231$	−0.462361	−	1.42300i	−0.0304211	−	0.0936265i
$232$		−	74.8948i		−	4.91708i
$233$	−6.44246	+	2.09328i	−0.422059	+	0.137135i	−0.512343	−	0.858781i	$-0.671223\pi$
$233$	−6.44246	+	2.09328i	−0.422059	+	0.137135i	0.0902840	+	0.995916i	$0.471223\pi$
$234$	1.23366	+	0.896304i	0.0806467	+	0.0585932i
$235$		0			0
$236$	55.4464	−	40.2841i	3.60925	−	2.62227i
$237$	−2.79491	+	3.84687i	−0.181549	+	0.249881i
$238$	1.27657	−	1.75705i	0.0827479	−	0.113893i
$239$	−5.24514	+	3.81081i	−0.339280	+	0.246501i	−0.744358	−	0.667781i	$-0.767244\pi$
$239$	−5.24514	+	3.81081i	−0.339280	+	0.246501i	0.405078	+	0.914282i	$0.367244\pi$
$240$		0			0
$241$	6.02602	+	4.37816i	0.388170	+	0.282022i	0.764705	−	0.644380i	$-0.222885\pi$
$241$	6.02602	+	4.37816i	0.388170	+	0.282022i	−0.376535	+	0.926402i	$0.622885\pi$
$242$	2.26039	−	0.734446i	0.145304	−	0.0472120i
$243$		−	1.00000i		−	0.0641500i
$244$	−0.208773	−	0.642537i	−0.0133653	−	0.0411342i
$245$		0			0
$246$	1.23116	−	3.78914i	0.0784962	−	0.241586i
$247$	2.00420	+	0.651203i	0.127524	+	0.0414351i
$248$	28.7502	+	39.5713i	1.82564	+	2.51278i
$249$	−11.6905			−0.740855
$250$		0			0
$251$	−4.60217			−0.290486			−0.145243	−	0.989396i	$-0.546396\pi$
$251$	−4.60217			−0.290486			−0.145243	+	0.989396i	$0.546396\pi$
$252$	−1.47183	−	2.02580i	−0.0927168	−	0.127614i
$253$	−6.86790	−	2.23152i	−0.431781	−	0.140294i
$254$	−1.48765	+	4.57852i	−0.0933435	+	0.287282i
$255$		0			0
$256$	7.97520	+	24.5451i	0.498450	+	1.53407i
$257$		−	5.79485i		−	0.361473i	−0.983532	−	0.180736i	$-0.942152\pi$
$257$		−	5.79485i		−	0.361473i	0.983532	−	0.180736i	$-0.0578481\pi$
$258$	17.3152	−	5.62605i	1.07800	−	0.350262i
$259$	0.388409	+	0.282196i	0.0241346	+	0.0175348i
$260$		0			0
$261$	6.73458	−	4.89296i	0.416860	−	0.302866i
$262$	−9.41507	+	12.9587i	−0.581665	+	0.800593i
$263$	−8.40467	+	11.5680i	−0.518254	+	0.713316i	−0.985284	−	0.170926i	$-0.945324\pi$
$263$	−8.40467	+	11.5680i	−0.518254	+	0.713316i	0.467030	+	0.884242i	$0.345324\pi$
$264$	−23.1572	+	16.8247i	−1.42522	+	1.03549i
$265$		0			0
$266$	−3.85120	−	2.79806i	−0.236132	−	0.171560i
$267$	5.89701	−	1.91606i	0.360891	−	0.117261i
$268$			14.8800i			0.908943i
$269$	5.93945	+	18.2797i	0.362135	+	1.11454i	0.951756	+	0.306856i	$0.0992770\pi$
$269$	5.93945	+	18.2797i	0.362135	+	1.11454i	−0.589621	+	0.807680i	$0.700723\pi$
$270$		0			0
$271$	−7.18256	+	22.1057i	−0.436310	+	1.34282i	0.455429	+	0.890272i	$0.349486\pi$
$271$	−7.18256	+	22.1057i	−0.436310	+	1.34282i	−0.891739	+	0.452551i	$0.850514\pi$
$272$	−22.2337	−	7.22415i	−1.34811	−	0.438029i
$273$	0.155754	+	0.214377i	0.00942666	+	0.0129747i
$274$	13.8460			0.836470
$275$		0			0
$276$	−12.0853			−0.727452
$277$	−12.8672	−	17.7102i	−0.773115	−	1.06410i	−0.996008	−	0.0892586i	$-0.971550\pi$
$277$	−12.8672	−	17.7102i	−0.773115	−	1.06410i	0.222894	−	0.974843i	$-0.428450\pi$
$278$	21.2043	+	6.88968i	1.27175	+	0.413216i
$279$	−1.67999	+	5.17047i	−0.100578	+	0.309548i
$280$		0			0
$281$	8.37863	+	25.7868i	0.499827	+	1.53831i	0.809296	+	0.587401i	$0.199849\pi$
$281$	8.37863	+	25.7868i	0.499827	+	1.53831i	−0.309469	+	0.950910i	$0.600151\pi$
$282$		−	11.9989i		−	0.714522i
$283$	15.5093	−	5.03926i	0.921929	−	0.299553i	0.190671	−	0.981654i	$-0.438934\pi$
$283$	15.5093	−	5.03926i	0.921929	−	0.299553i	0.731258	+	0.682101i	$0.238934\pi$
$284$	69.1171	+	50.2165i	4.10134	+	2.97980i
$285$		0			0
$286$	3.92485	−	2.85157i	0.232081	−	0.168617i
$287$	0.406945	−	0.560112i	0.0240212	−	0.0330624i
$288$	−11.2174	+	15.4395i	−0.660993	+	0.909778i
$289$	−11.3977	+	8.28091i	−0.670453	+	0.487112i
$290$		0			0
$291$	−6.83978	−	4.96939i	−0.400955	−	0.291311i
$292$	49.5682	−	16.1057i	2.90076	−	0.942514i
$293$		−	5.46407i		−	0.319214i	−0.987181	−	0.159607i	$-0.948977\pi$
$293$		−	5.46407i		−	0.319214i	0.987181	−	0.159607i	$-0.0510228\pi$
$294$	5.66921	+	17.4480i	0.330635	+	1.01759i
$295$		0			0
$296$	2.83820	−	8.73509i	0.164967	−	0.507717i
$297$	−3.02577	−	0.983131i	−0.175573	−	0.0570470i
$298$	−16.0007	−	22.0231i	−0.926897	−	1.27576i
$299$	1.27891			0.0739612
$300$		0			0
$301$	3.16377			0.182357
$302$	19.0589	+	26.2323i	1.09672	+	1.50950i
$303$	5.54775	+	1.80257i	0.318710	+	0.103555i
$304$	−15.8343	+	48.7330i	−0.908160	+	2.79503i
$305$		0			0
$306$	−1.42705	−	4.39201i	−0.0815791	−	0.251075i
$307$		−	21.4194i		−	1.22247i	−0.791450	−	0.611235i	$-0.790673\pi$
$307$		−	21.4194i		−	1.22247i	0.791450	−	0.611235i	$-0.209327\pi$
$308$	−7.57662	+	2.46179i	−0.431718	+	0.140274i
$309$	−11.3905	−	8.27566i	−0.647981	−	0.470786i
$310$		0			0
$311$	2.30731	−	1.67636i	0.130836	−	0.0950578i	−0.520443	−	0.853897i	$-0.674233\pi$
$311$	2.30731	−	1.67636i	0.130836	−	0.0950578i	0.651278	+	0.758839i	$0.274233\pi$
$312$	2.97967	−	4.10116i	0.168691	−	0.232183i
$313$	−8.48616	+	11.6802i	−0.479666	+	0.660204i	−0.978441	−	0.206528i	$-0.933784\pi$
$313$	−8.48616	+	11.6802i	−0.479666	+	0.660204i	0.498774	+	0.866732i	$0.333784\pi$
$314$	42.9054	−	31.1726i	2.42129	−	1.75917i
$315$		0			0
$316$	20.4823	+	14.8812i	1.15222	+	0.837135i
$317$	−21.5036	+	6.98695i	−1.20776	+	0.392426i	−0.842611	−	0.538522i	$-0.818983\pi$
$317$	−21.5036	+	6.98695i	−1.20776	+	0.392426i	−0.365152	+	0.930948i	$0.618983\pi$
$318$			19.0842i			1.07019i
$319$	−8.18397	−	25.1877i	−0.458214	−	1.41024i
$320$		0			0
$321$	−2.66128	+	8.19057i	−0.148538	+	0.457153i
$322$	−2.74758	−	0.892743i	−0.153117	−	0.0497506i
$323$	−3.75123	−	5.16312i	−0.208724	−	0.287284i
$324$	−5.32440			−0.295800
$325$		0			0
$326$	32.1859			1.78261
$327$	−9.80868	−	13.5005i	−0.542421	−	0.746578i
$328$	−12.5966	−	4.09288i	−0.695530	−	0.225991i
$329$	0.644327	−	1.98303i	0.0355229	−	0.109328i
$330$		0			0
$331$	1.19480	+	3.67721i	0.0656720	+	0.202118i	0.978508	−	0.206209i	$-0.0661125\pi$
$331$	1.19480	+	3.67721i	0.0656720	+	0.202118i	−0.912836	+	0.408326i	$0.866113\pi$
$332$			62.2448i			3.41613i
$333$	0.970887	−	0.315460i	0.0532043	−	0.0172871i
$334$	−13.1233	−	9.53466i	−0.718077	−	0.521713i
$335$		0			0
$336$	−5.21267	+	3.78723i	−0.284375	+	0.206610i
$337$	10.2776	−	14.1459i	0.559856	−	0.770576i	−0.431452	−	0.902136i	$-0.641999\pi$
$337$	10.2776	−	14.1459i	0.559856	−	0.770576i	0.991308	+	0.131560i	$0.0419986\pi$
$338$	20.1749	−	27.7683i	1.09737	−	1.51040i
$339$	9.52686	−	6.92167i	0.517428	−	0.375933i
$340$		0			0
$341$	13.9930	+	10.1665i	0.757763	+	0.550547i
$342$	−9.62666	+	3.12789i	−0.520550	+	0.169137i
$343$			6.48010i			0.349893i
$344$	−18.7032	−	57.5626i	−1.00841	−	3.10357i
$345$		0			0
$346$	14.4886	−	44.5913i	0.778912	−	2.39724i
$347$	−21.9638	−	7.13647i	−1.17908	−	0.383106i	−0.347055	−	0.937845i	$-0.612818\pi$
$347$	−21.9638	−	7.13647i	−1.17908	−	0.383106i	−0.832024	+	0.554739i	$0.812818\pi$
$348$	−26.0520	−	35.8576i	−1.39654	−	1.92217i
$349$	9.32650			0.499236			0.249618	−	0.968344i	$-0.419695\pi$
$349$	9.32650			0.499236			0.249618	+	0.968344i	$0.419695\pi$
$350$		0			0
$351$	0.563444			0.0300744
$352$	35.6880	+	49.1203i	1.90218	+	2.61812i
$353$	−30.3835	−	9.87219i	−1.61715	−	0.525444i	−0.645883	−	0.763437i	$-0.723510\pi$
$353$	−30.3835	−	9.87219i	−1.61715	−	0.525444i	−0.971267	+	0.237993i	$0.923510\pi$
$354$	10.7650	−	33.1312i	0.572152	−	1.76090i
$355$		0			0
$356$	−10.2018	−	31.3980i	−0.540697	−	1.66409i
$357$		−	0.802492i		−	0.0424724i
$358$	27.2229	−	8.84525i	1.43877	−	0.467486i
$359$	−7.75810	−	5.63659i	−0.409457	−	0.297488i	0.363925	−	0.931428i	$-0.381436\pi$
$359$	−7.75810	−	5.63659i	−0.409457	−	0.297488i	−0.773382	+	0.633940i	$0.781436\pi$
$360$		0			0
$361$	4.05451	−	2.94577i	0.213395	−	0.155041i
$362$	19.0571	−	26.2298i	1.00162	−	1.37861i
$363$	0.516191	−	0.710476i	0.0270930	−	0.0372903i
$364$	1.14143	−	0.829296i	0.0598271	−	0.0434669i
$365$		0			0
$366$	−0.277821	−	0.201849i	−0.0145219	−	0.0105508i
$367$	−1.01215	+	0.328866i	−0.0528336	+	0.0171667i	−0.335315	−	0.942106i	$-0.608843\pi$
$367$	−1.01215	+	0.328866i	−0.0528336	+	0.0171667i	0.282481	+	0.959273i	$0.408843\pi$
$368$			31.0973i			1.62106i
$369$	−0.454915	−	1.40008i	−0.0236819	−	0.0728855i
$370$		0			0
$371$	−1.02480	+	3.15402i	−0.0532051	+	0.163748i
$372$	27.5296	+	8.94492i	1.42735	+	0.463773i
$373$	−2.42181	−	3.33333i	−0.125396	−	0.172593i	0.741703	−	0.670728i	$-0.234018\pi$
$373$	−2.42181	−	3.33333i	−0.125396	−	0.172593i	−0.867099	+	0.498135i	$0.834018\pi$
$374$	−14.6922			−0.759714
$375$		0			0
$376$	−39.8890			−2.05712
$377$	2.75691	+	3.79456i	0.141988	+	0.195430i
$378$	−1.21049	−	0.393313i	−0.0622610	−	0.0202298i
$379$	−3.20027	+	9.84942i	−0.164387	+	0.505931i	−0.998991	−	0.0449201i	$-0.985697\pi$
$379$	−3.20027	+	9.84942i	−0.164387	+	0.505931i	0.834604	+	0.550851i	$0.185697\pi$
$380$		0			0
$381$	0.549687	+	1.69176i	0.0281613	+	0.0866716i
$382$			49.4336i			2.52924i
$383$	1.14065	−	0.370619i	0.0582845	−	0.0189378i	−0.279730	−	0.960079i	$-0.590245\pi$
$383$	1.14065	−	0.370619i	0.0582845	−	0.0189378i	0.338014	+	0.941141i	$0.390245\pi$
$384$	22.2119	+	16.1379i	1.13350	+	0.823533i
$385$		0			0
$386$	−55.1890	+	40.0971i	−2.80904	+	2.04089i
$387$	3.95416	−	5.44243i	0.201001	−	0.276654i
$388$	−26.4590	+	36.4177i	−1.34325	+	1.84883i
$389$	10.1971	−	7.40861i	0.517012	−	0.375631i	−0.298465	−	0.954421i	$-0.596475\pi$
$389$	10.1971	−	7.40861i	0.517012	−	0.375631i	0.815477	+	0.578789i	$0.196475\pi$
$390$		0			0
$391$	−3.13341	−	2.27656i	−0.158464	−	0.115130i
$392$	58.0042	−	18.8467i	2.92965	−	0.951902i
$393$			5.91860i			0.298554i
$394$	−10.1129	−	31.1243i	−0.509481	−	1.56802i
$395$		0			0
$396$	−5.23458	+	16.1104i	−0.263047	+	0.809577i
$397$	−1.24907	−	0.405848i	−0.0626891	−	0.0203689i	0.277505	−	0.960724i	$-0.410493\pi$
$397$	−1.24907	−	0.405848i	−0.0626891	−	0.0203689i	−0.340194	+	0.940355i	$0.610493\pi$
$398$	−0.866064	−	1.19204i	−0.0434119	−	0.0597513i
$399$	−1.75895			−0.0880575
$400$		0			0
$401$	16.1042			0.804205			0.402102	−	0.915595i	$-0.368280\pi$
$401$	16.1042			0.804205			0.402102	+	0.915595i	$0.368280\pi$
$402$	4.44568	+	6.11895i	0.221730	+	0.305186i
$403$	−2.91327	−	0.946580i	−0.145120	−	0.0471525i
$404$	9.59762	−	29.5384i	0.477499	−	1.46959i
$405$		0			0
$406$	−3.27409	−	10.0766i	−0.162490	−	0.500094i
$407$		−	3.24782i		−	0.160988i
$408$	−14.6008	+	4.74408i	−0.722847	+	0.234867i
$409$	17.1188	+	12.4375i	0.846471	+	0.614997i	0.924171	−	0.381980i	$-0.124758\pi$
$409$	17.1188	+	12.4375i	0.846471	+	0.614997i	−0.0776999	+	0.996977i	$0.524758\pi$
$410$		0			0
$411$	4.13902	−	3.00717i	0.204163	−	0.148333i
$412$	−44.0629	+	60.6473i	−2.17082	+	2.98788i
$413$	3.55823	−	4.89748i	0.175089	−	0.240989i
$414$	−4.96973	+	3.61072i	−0.244249	+	0.177457i
$415$		0			0
$416$	−8.69927	−	6.32039i	−0.426517	−	0.309883i
$417$	7.83497	−	2.54574i	0.383680	−	0.124665i
$418$			32.2031i			1.57511i
$419$	2.06144	+	6.34445i	0.100708	+	0.309946i	0.988699	−	0.149914i	$-0.0478996\pi$
$419$	2.06144	+	6.34445i	0.100708	+	0.309946i	−0.887991	+	0.459860i	$0.847900\pi$
$420$		0			0
$421$	8.43555	−	25.9620i	0.411124	−	1.26531i	−0.504549	−	0.863383i	$-0.668341\pi$
$421$	8.43555	−	25.9620i	0.411124	−	1.26531i	0.915673	−	0.401925i	$-0.131659\pi$
$422$	−8.03590	−	2.61102i	−0.391181	−	0.127103i
$423$	−2.60599	−	3.58684i	−0.126708	−	0.174398i
$424$	63.4435			3.08109
$425$		0			0
$426$	43.4253			2.10396
$427$	−0.0350760	−	0.0482780i	−0.00169745	−	0.00233633i
$428$	43.6098	+	14.1697i	2.10796	+	0.684918i
$429$	0.553939	−	1.70485i	0.0267444	−	0.0823109i
$430$		0			0
$431$	3.80011	+	11.6955i	0.183045	+	0.563354i	0.999909	−	0.0134755i	$-0.00428951\pi$
$431$	3.80011	+	11.6955i	0.183045	+	0.563354i	−0.816864	+	0.576830i	$0.804290\pi$
$432$			13.7004i			0.659161i
$433$	−32.1887	+	10.4587i	−1.54689	+	0.502614i	−0.953267	−	0.302130i	$-0.902302\pi$
$433$	−32.1887	+	10.4587i	−1.54689	+	0.502614i	−0.593622	+	0.804744i	$0.702302\pi$
$434$	5.59805	+	4.06722i	0.268715	+	0.195233i
$435$		0			0
$436$	−71.8819	+	52.2253i	−3.44252	+	2.50114i
$437$	−4.98989	+	6.86799i	−0.238699	+	0.328541i
$438$	15.5715	−	21.4324i	0.744036	−	1.02408i
$439$	−16.9614	+	12.3231i	−0.809521	+	0.588152i	−0.913692	−	0.406408i	$-0.866781\pi$
$439$	−16.9614	+	12.3231i	−0.809521	+	0.588152i	0.104171	+	0.994559i	$0.466781\pi$
$440$		0			0
$441$	5.48418	+	3.98449i	0.261152	+	0.189738i
$442$	2.47465	−	0.804064i	0.117707	−	0.0382454i
$443$		−	6.04847i		−	0.287371i	−0.989623	−	0.143686i	$-0.954105\pi$
$443$		−	6.04847i		−	0.287371i	0.989623	−	0.143686i	$-0.0458954\pi$
$444$	−1.67964	−	5.16939i	−0.0797120	−	0.245328i
$445$		0			0
$446$	0.283614	−	0.872875i	0.0134295	−	0.0413318i
$447$	−9.56624	−	3.10826i	−0.452467	−	0.147016i
$448$	6.70292	+	9.22577i	0.316683	+	0.435877i
$449$	−15.5896			−0.735721			−0.367860	−	0.929881i	$-0.619910\pi$
$449$	−15.5896			−0.735721			−0.367860	+	0.929881i	$0.619910\pi$
$450$		0			0
$451$	−4.68357			−0.220541
$452$	−36.8537	−	50.7248i	−1.73345	−	2.38589i
$453$	11.3946	+	3.70233i	0.535365	+	0.173951i
$454$	1.49572	−	4.60334i	0.0701974	−	0.216046i
$455$		0			0
$456$	10.3983	+	32.0028i	0.486947	+	1.49867i
$457$		−	2.50193i		−	0.117035i	−0.998286	−	0.0585176i	$-0.981363\pi$
$457$		−	2.50193i		−	0.117035i	0.998286	−	0.0585176i	$-0.0186374\pi$
$458$	−72.0262	+	23.4027i	−3.36556	+	1.09354i
$459$	−1.38048	−	1.00297i	−0.0644351	−	0.0468148i
$460$		0			0
$461$	0.124559	−	0.0904973i	0.00580128	−	0.00421488i	−0.584881	−	0.811119i	$-0.698859\pi$
$461$	0.124559	−	0.0904973i	0.00580128	−	0.00421488i	0.590682	+	0.806904i	$0.298859\pi$
$462$	−2.38014	+	3.27599i	−0.110734	+	0.152413i
$463$	6.83751	−	9.41102i	0.317766	−	0.437367i	−0.620018	−	0.784588i	$-0.712875\pi$
$463$	6.83751	−	9.41102i	0.317766	−	0.437367i	0.937783	+	0.347221i	$0.112875\pi$
$464$	−92.2664	+	67.0355i	−4.28336	+	3.11204i
$465$		0			0
$466$	14.8316	+	10.7758i	0.687062	+	0.499180i
$467$	−0.447276	+	0.145329i	−0.0206975	+	0.00672502i	−0.319347	−	0.947638i	$-0.603464\pi$
$467$	−0.447276	+	0.145329i	−0.0206975	+	0.00672502i	0.298650	+	0.954363i	$0.403464\pi$
$468$		−	3.00000i		−	0.138675i
$469$	0.406149	+	1.25000i	0.0187542	+	0.0577196i
$470$		0			0
$471$	6.05551	−	18.6369i	0.279023	−	0.858745i
$472$	−110.141	−	35.7871i	−5.06966	−	1.64723i
$473$	−12.5801	−	17.3150i	−0.578432	−	0.796143i
$474$	12.8687			0.591080
$475$		0			0
$476$	−4.27279			−0.195843
$477$	4.14483	+	5.70487i	0.189779	+	0.261208i
$478$	16.6875	+	5.42210i	0.763269	+	0.248001i
$479$	−3.83534	+	11.8040i	−0.175241	+	0.539337i	−0.999644	−	0.0266660i	$-0.991511\pi$
$479$	−3.83534	+	11.8040i	−0.175241	+	0.539337i	0.824403	+	0.566003i	$0.191511\pi$
$480$		0			0
$481$	0.177744	+	0.547041i	0.00810444	+	0.0249429i
$482$		−	20.1585i		−	0.918196i
$483$	−1.01523	+	0.329868i	−0.0461946	+	0.0150095i
$484$	−3.78286	−	2.74841i	−0.171948	−	0.124928i
$485$		0			0
$486$	−2.18949	+	1.59076i	−0.0993174	+	0.0721583i
$487$	20.3165	−	27.9633i	0.920631	−	1.26714i	−0.0427731	−	0.999085i	$-0.513619\pi$
$487$	20.3165	−	27.9633i	0.920631	−	1.26714i	0.963404	−	0.268055i	$-0.0863807\pi$
$488$	−0.671026	+	0.923588i	−0.0303759	+	0.0418088i
$489$	9.62137	−	6.99033i	0.435093	−	0.316114i
$490$		0			0
$491$	20.1168	+	14.6157i	0.907859	+	0.659598i	0.940473	−	0.339870i	$-0.110383\pi$
$491$	20.1168	+	14.6157i	0.907859	+	0.659598i	−0.0326134	+	0.999468i	$0.510383\pi$
$492$	−7.45460	+	2.42215i	−0.336080	+	0.109199i
$493$		−	14.2044i		−	0.639736i
$494$	−1.76239	−	5.42408i	−0.0792938	−	0.244041i
$495$		0			0
$496$	23.0165	−	70.8375i	1.03347	−	3.18070i
$497$	7.17684	+	2.33190i	0.321925	+	0.104600i
$498$	18.5968	+	25.5963i	0.833341	+	1.14700i
$499$	−12.6037			−0.564220			−0.282110	−	0.959382i	$-0.591034\pi$
$499$	−12.6037			−0.564220			−0.282110	+	0.959382i	$0.591034\pi$
$500$		0			0
$501$	−5.99378			−0.267782
$502$	7.32094	+	10.0764i	0.326750	+	0.449732i
$503$	−28.5248	−	9.26827i	−1.27186	−	0.413252i	−0.406152	−	0.913805i	$-0.633130\pi$
$503$	−28.5248	−	9.26827i	−1.27186	−	0.413252i	−0.865705	+	0.500554i	$0.833130\pi$
$504$	−1.30753	+	4.02415i	−0.0582419	+	0.179250i
$505$		0			0
$506$	6.03929	+	18.5870i	0.268479	+	0.826294i
$507$		−	12.6825i		−	0.563251i
$508$	9.00761	−	2.92675i	0.399648	−	0.129854i
$509$	−0.377802	−	0.274489i	−0.0167458	−	0.0121665i	0.579381	−	0.815057i	$-0.303294\pi$
$509$	−0.377802	−	0.274489i	−0.0167458	−	0.0121665i	−0.596127	+	0.802890i	$0.703294\pi$
$510$		0			0
$511$	3.72438	−	2.70592i	0.164757	−	0.119703i
$512$	8.77902	−	12.0833i	0.387982	−	0.534011i
$513$	−2.19838	+	3.02580i	−0.0970607	+	0.133593i
$514$	−12.6878	+	9.21822i	−0.559634	+	0.406598i
$515$		0			0
$516$	−28.9777	−	21.0535i	−1.27567	−	0.926829i
$517$	−13.4150	+	4.35878i	−0.589989	+	0.191699i
$518$		−	1.29933i		−	0.0570891i
$519$	−5.35353	−	16.4765i	−0.234994	−	0.723237i
$520$		0			0
$521$	−5.34039	+	16.4360i	−0.233967	+	0.720076i	0.763290	+	0.646056i	$0.223583\pi$
$521$	−5.34039	+	16.4360i	−0.233967	+	0.720076i	−0.997257	+	0.0740200i	$0.976417\pi$
$522$	−21.4262	−	6.96179i	−0.937799	−	0.304709i
$523$	23.8922	+	32.8849i	1.04473	+	1.43795i	0.893286	+	0.449489i	$0.148394\pi$
$523$	23.8922	+	32.8849i	1.04473	+	1.43795i	0.151449	+	0.988465i	$0.451606\pi$
$524$	31.5130			1.37665
$525$		0			0
$526$	38.6980			1.68731
$527$	5.45273	+	7.50503i	0.237525	+	0.326924i
$528$	41.4542	+	13.4693i	1.80406	+	0.586175i
$529$	5.51533	−	16.9744i	0.239797	−	0.738019i
$530$		0			0
$531$	−3.97766	−	12.2420i	−0.172616	−	0.531256i
$532$			9.36533i			0.406039i
$533$	0.788869	−	0.256319i	0.0341697	−	0.0111024i
$534$	−13.5759	−	9.86349i	−0.587488	−	0.426835i
$535$		0			0
$536$	20.3418	−	14.7792i	0.878633	−	0.638364i
$537$	6.21671	−	8.55656i	0.268271	−	0.369243i
$538$	30.5751	−	42.0831i	1.31819	−	1.81433i
$539$	17.4478	−	12.6766i	0.751530	−	0.546019i
$540$		0			0
$541$	1.60265	+	1.16440i	0.0689035	+	0.0500613i	0.621704	−	0.783252i	$-0.286441\pi$
$541$	1.60265	+	1.16440i	0.0689035	+	0.0500613i	−0.552800	+	0.833314i	$0.686441\pi$
$542$	59.8259	−	19.4386i	2.56974	−	0.834960i
$543$		−	11.9799i		−	0.514105i
$544$	10.0630	+	30.9707i	0.431448	+	1.32786i
$545$		0			0
$546$	0.221610	−	0.682045i	0.00948402	−	0.0291888i
$547$	33.3386	+	10.8324i	1.42545	+	0.463158i	0.917331	−	0.398126i	$-0.130339\pi$
$547$	33.3386	+	10.8324i	1.42545	+	0.463158i	0.508124	+	0.861284i	$0.330339\pi$
$548$	−16.0114	−	22.0378i	−0.683972	−	0.941407i
$549$	−0.126888			−0.00541546
$550$		0			0
$551$	−31.1341			−1.32636
$552$	12.0035	+	16.5213i	0.510901	+	0.703195i
$553$	2.12680	+	0.691038i	0.0904405	+	0.0293859i
$554$	−18.3077	+	56.3453i	−0.777819	+	2.39388i
$555$		0			0
$556$	−13.5545	−	41.7165i	−0.574839	−	1.76917i
$557$			19.2383i			0.815154i	0.913171	+	0.407577i	$0.133626\pi$
$557$			19.2383i			0.815154i	−0.913171	+	0.407577i	$0.866374\pi$
$558$	13.9932	−	4.54666i	0.592378	−	0.192475i
$559$	3.06651	+	2.22795i	0.129699	+	0.0942321i
$560$		0			0
$561$	−4.39195	+	3.19094i	−0.185428	+	0.134722i
$562$	43.1316	−	59.3655i	1.81940	−	2.50418i
$563$	17.1481	−	23.6023i	0.722707	−	0.994720i	−0.276723	−	0.960950i	$-0.589248\pi$
$563$	17.1481	−	23.6023i	0.722707	−	0.994720i	0.999430	−	0.0337705i	$-0.0107515\pi$
$564$	−19.0977	+	13.8753i	−0.804160	+	0.584257i
$565$		0			0
$566$	−35.7049	−	25.9411i	−1.50079	−	1.09039i
$567$	−0.447276	+	0.145329i	−0.0187838	+	0.00610324i
$568$		−	144.363i		−	6.05734i
$569$	10.1701	+	31.3004i	0.426354	+	1.31218i	0.901692	+	0.432380i	$0.142326\pi$
$569$	10.1701	+	31.3004i	0.426354	+	1.31218i	−0.475338	+	0.879803i	$0.657674\pi$
$570$		0			0
$571$	8.23065	−	25.3313i	0.344442	−	1.06008i	−0.617440	−	0.786618i	$-0.711830\pi$
$571$	8.23065	−	25.3313i	0.344442	−	1.06008i	0.961882	−	0.273465i	$-0.0881698\pi$
$572$	−9.07730	−	2.94939i	−0.379541	−	0.123320i
$573$	10.7363	+	14.7773i	0.448515	+	0.617329i
$574$	−1.87371			−0.0782073
$575$		0			0
$576$	24.2480			1.01033
$577$	−20.2878	−	27.9237i	−0.844591	−	1.16248i	−0.985029	−	0.172390i	$-0.944851\pi$
$577$	−20.2878	−	27.9237i	−0.844591	−	1.16248i	0.140438	−	0.990089i	$-0.455149\pi$
$578$	36.2620	+	11.7822i	1.50830	+	0.490076i
$579$	−7.78917	+	23.9726i	−0.323707	+	0.996267i
$580$		0			0
$581$	1.69897	+	5.22888i	0.0704850	+	0.216931i
$582$			22.8807i			0.948437i
$583$	21.3365	−	6.93265i	0.883668	−	0.287121i
$584$	−71.2496	−	51.7659i	−2.94833	−	2.14209i
$585$		0			0
$586$	−11.9635	+	8.69202i	−0.494209	+	0.359064i
$587$	−13.0932	+	18.0213i	−0.540414	+	0.743817i	−0.988673	−	0.150087i	$-0.952045\pi$
$587$	−13.0932	+	18.0213i	−0.540414	+	0.743817i	0.448258	+	0.893904i	$0.352045\pi$
$588$	21.2150	−	29.2000i	0.874893	−	1.20419i
$589$	16.4500	−	11.9516i	0.677809	−	0.492457i
$590$		0			0
$591$	−9.78286	−	7.10766i	−0.402413	−	0.292370i
$592$	−13.3015	+	4.32193i	−0.546690	+	0.177630i
$593$			30.9158i			1.26956i	0.772693	+	0.634779i	$0.218909\pi$
$593$			30.9158i			1.26956i	−0.772693	+	0.634779i	$0.781091\pi$
$594$	2.66071	+	8.18882i	0.109170	+	0.335991i
$595$		0			0
$596$	−16.5496	+	50.9344i	−0.677898	+	2.08636i
$597$	−0.517788	−	0.168240i	−0.0211917	−	0.00688558i
$598$	−2.03444	−	2.80016i	−0.0831943	−	0.114507i
$599$	24.0276			0.981742			0.490871	−	0.871232i	$-0.336679\pi$
$599$	24.0276			0.981742			0.490871	+	0.871232i	$0.336679\pi$
$600$		0			0
$601$	−32.0387			−1.30688			−0.653442	−	0.756977i	$-0.726676\pi$
$601$	−32.0387			−1.30688			−0.653442	+	0.756977i	$0.726676\pi$
$602$	−5.03280	−	6.92705i	−0.205121	−	0.282326i
$603$	2.65791	+	0.863607i	0.108238	+	0.0351688i
$604$	19.7127	−	60.6694i	0.802097	−	2.46860i
$605$		0			0
$606$	−4.87842	−	15.0142i	−0.198172	−	0.609911i
$607$			45.5915i			1.85050i	0.379356	+	0.925251i	$0.376145\pi$
$607$			45.5915i			1.85050i	−0.379356	+	0.925251i	$0.623855\pi$
$608$	67.8834	−	22.0567i	2.75304	−	0.894516i
$609$	−3.16723	−	2.30113i	−0.128343	−	0.0932465i
$610$		0			0
$611$	2.02098	−	1.46833i	0.0817602	−	0.0594023i
$612$	−5.34023	+	7.35020i	−0.215866	+	0.297114i
$613$	6.38121	−	8.78299i	0.257735	−	0.354742i	−0.660467	−	0.750855i	$-0.729641\pi$
$613$	6.38121	−	8.78299i	0.257735	−	0.354742i	0.918201	+	0.396114i	$0.129641\pi$
$614$	−46.8976	+	34.0731i	−1.89263	+	1.37508i
$615$		0			0
$616$	10.8907	+	7.91254i	0.438798	+	0.318805i
$617$	15.3172	−	4.97685i	0.616646	−	0.200360i	0.0159954	−	0.999872i	$-0.494908\pi$
$617$	15.3172	−	4.97685i	0.616646	−	0.200360i	0.600651	+	0.799512i	$0.294908\pi$
$618$			38.1039i			1.53276i
$619$	−11.8533	−	36.4807i	−0.476425	−	1.46628i	−0.844026	−	0.536302i	$-0.819821\pi$
$619$	−11.8533	−	36.4807i	−0.476425	−	1.46628i	0.367602	−	0.929983i	$-0.380179\pi$
$620$		0			0
$621$	−0.701409	+	2.15871i	−0.0281466	+	0.0866262i
$622$	−7.34076	−	2.38516i	−0.294338	−	0.0956362i
$623$	−1.71401	−	2.35914i	−0.0686705	−	0.0945168i
$624$	−7.71941			−0.309024
$625$		0			0
$626$	39.0732			1.56168
$627$	6.99409	+	9.62653i	0.279317	+	0.384447i
$628$	−99.2305	−	32.2419i	−3.95973	−	1.28659i
$629$	0.538290	−	1.65669i	0.0214630	−	0.0660564i
$630$		0			0
$631$	7.02370	+	21.6167i	0.279609	+	0.860548i	0.987963	+	0.154690i	$0.0494380\pi$
$631$	7.02370	+	21.6167i	0.279609	+	0.860548i	−0.708354	+	0.705857i	$0.750562\pi$
$632$		−	42.7808i		−	1.70173i
$633$	−2.96926	+	0.964772i	−0.118018	+	0.0383462i
$634$	49.5049	+	35.9674i	1.96609	+	1.42845i
$635$		0			0
$636$	30.3750	−	22.0687i	1.20445	−	0.875082i
$637$	−2.24504	+	3.09003i	−0.0889517	+	0.122431i
$638$	−42.1295	+	57.9863i	−1.66792	+	2.29570i
$639$	12.9812	−	9.43140i	0.513528	−	0.373100i
$640$		0			0
$641$	−21.8378	−	15.8661i	−0.862541	−	0.626673i	0.0660340	−	0.997817i	$-0.478965\pi$
$641$	−21.8378	−	15.8661i	−0.862541	−	0.626673i	−0.928575	+	0.371145i	$0.878965\pi$
$642$	22.1666	−	7.20238i	0.874848	−	0.284255i
$643$			25.9062i			1.02164i	0.859687	+	0.510821i	$0.170659\pi$
$643$			25.9062i			1.02164i	−0.859687	+	0.510821i	$0.829341\pi$
$644$	1.75635	+	5.40549i	0.0692099	+	0.213006i
$645$		0			0
$646$	−5.33731	+	16.4266i	−0.209994	+	0.646295i
$647$	−20.6021	−	6.69401i	−0.809950	−	0.263169i	−0.125374	−	0.992110i	$-0.540013\pi$
$647$	−20.6021	−	6.69401i	−0.809950	−	0.263169i	−0.684577	+	0.728941i	$0.740013\pi$
$648$	5.28832	+	7.27874i	0.207745	+	0.285936i
$649$	−40.9519			−1.60750
$650$		0			0
$651$	2.55678			0.100208
$652$	−37.2193	−	51.2280i	−1.45762	−	2.00624i
$653$	−10.6305	−	3.45405i	−0.416002	−	0.135167i	0.0935349	−	0.995616i	$-0.470183\pi$
$653$	−10.6305	−	3.45405i	−0.416002	−	0.135167i	−0.509537	+	0.860449i	$0.670183\pi$
$654$	−13.9560	+	42.9521i	−0.545722	+	1.67956i
$655$		0			0
$656$	6.23252	+	19.1817i	0.243339	+	0.748920i
$657$		−	9.78873i		−	0.381895i
$658$	−5.36681	+	1.74378i	−0.209220	+	0.0679797i
$659$	10.9010	+	7.92006i	0.424644	+	0.308522i	0.779503	−	0.626398i	$-0.215471\pi$
$659$	10.9010	+	7.92006i	0.424644	+	0.308522i	−0.354860	+	0.934919i	$0.615471\pi$
$660$		0			0
$661$	18.8195	−	13.6732i	0.731993	−	0.531824i	−0.158200	−	0.987407i	$-0.550569\pi$
$661$	18.8195	−	13.6732i	0.731993	−	0.531824i	0.890193	+	0.455583i	$0.150569\pi$
$662$	6.15059	−	8.46556i	0.239049	−	0.329023i
$663$	0.565120	−	0.777821i	0.0219474	−	0.0302081i
$664$	85.0921	−	61.8230i	3.30221	−	2.39920i
$665$		0			0
$666$	−2.23515	−	1.62393i	−0.0866102	−	0.0629260i
$667$	−17.9700	+	5.83880i	−0.695801	+	0.226079i
$668$			31.9132i			1.23476i
$669$	−0.104795	−	0.322527i	−0.00405162	−	0.0124696i
$670$		0			0
$671$	−0.124748	+	0.383934i	−0.00481584	+	0.0148216i
$672$	8.53592	+	2.77349i	0.329280	+	0.106990i
$673$	11.0734	+	15.2412i	0.426849	+	0.587507i	0.967226	−	0.253916i	$-0.0817186\pi$
$673$	11.0734	+	15.2412i	0.426849	+	0.587507i	−0.540378	+	0.841423i	$0.681719\pi$
$674$	−47.3215			−1.82276
$675$		0			0
$676$	−67.5268			−2.59719
$677$	24.8304	+	34.1761i	0.954310	+	1.31350i	0.949586	+	0.313507i	$0.101504\pi$
$677$	24.8304	+	34.1761i	0.954310	+	1.31350i	0.00472433	+	0.999989i	$0.498496\pi$
$678$	−30.3099	−	9.84828i	−1.16404	−	0.378221i
$679$	−1.22867	+	3.78147i	−0.0471521	+	0.145119i
$680$		0			0
$681$	−0.552667	−	1.70093i	−0.0211782	−	0.0651799i
$682$		−	46.8100i		−	1.79245i
$683$	46.5544	−	15.1264i	1.78135	−	0.578797i	0.782325	−	0.622870i	$-0.214034\pi$
$683$	46.5544	−	15.1264i	1.78135	−	0.578797i	0.999028	+	0.0440734i	$0.0140336\pi$
$684$	16.1106	+	11.7050i	0.616004	+	0.447553i
$685$		0			0
$686$	14.1881	−	10.3083i	0.541705	−	0.393572i
$687$	−16.4481	+	22.6389i	−0.627536	+	0.863729i
$688$	−54.1735	+	74.5635i	−2.06535	+	2.84271i
$689$	−3.21438	+	2.33538i	−0.122458	+	0.0889710i
$690$		0			0
$691$	11.4813	+	8.34168i	0.436771	+	0.317332i	0.784350	−	0.620318i	$-0.212996\pi$
$691$	11.4813	+	8.34168i	0.436771	+	0.317332i	−0.347580	+	0.937650i	$0.612996\pi$
$692$	−87.7273	+	28.5043i	−3.33489	+	1.08357i
$693$			1.49623i			0.0568371i
$694$	19.3139	+	59.4420i	0.733145	+	2.25639i
$695$		0			0
$696$	−23.1438	+	71.2291i	−0.877262	+	2.69993i
$697$	−2.38905	−	0.776250i	−0.0904918	−	0.0294026i
$698$	−14.8362	−	20.4203i	−0.561559	−	0.772920i
$699$	6.77400			0.256216
$700$		0			0
$701$	−9.00786			−0.340222			−0.170111	−	0.985425i	$-0.554413\pi$
$701$	−9.00786			−0.340222			−0.170111	+	0.985425i	$0.554413\pi$
$702$	−0.896304	−	1.23366i	−0.0338288	−	0.0465614i
$703$	−3.63122	−	1.17985i	−0.136954	−	0.0444990i
$704$	23.8389	−	73.3687i	0.898464	−	2.76519i
$705$		0			0
$706$	26.7177	+	82.2287i	1.00553	+	3.09472i
$707$		−	2.74334i		−	0.103174i
$708$	−65.1811	+	21.1786i	−2.44966	+	0.795942i
$709$	40.2076	+	29.2126i	1.51003	+	1.09710i	0.966164	+	0.257928i	$0.0830397\pi$
$709$	40.2076	+	29.2126i	1.51003	+	1.09710i	0.543865	+	0.839173i	$0.316960\pi$
$710$		0			0
$711$	3.84687	−	2.79491i	0.144269	−	0.104817i
$712$	−32.7901	+	45.1318i	−1.22886	+	1.69138i
$713$	7.25323	−	9.98321i	0.271636	−	0.373874i
$714$	−1.75705	+	1.27657i	−0.0657560	+	0.0477745i
$715$		0			0
$716$	−45.5585	−	33.1002i	−1.70260	−	1.23701i
$717$	6.16603	−	2.00346i	0.230274	−	0.0748207i
$718$			25.9528i			0.968549i
$719$	0.660387	+	2.03246i	0.0246283	+	0.0757981i	0.962615	−	0.270872i	$-0.0873122\pi$
$719$	0.660387	+	2.03246i	0.0246283	+	0.0757981i	−0.937987	+	0.346671i	$0.887312\pi$
$720$		0			0
$721$	−2.04614	+	6.29738i	−0.0762023	+	0.234527i
$722$	−12.8995	−	4.19130i	−0.480070	−	0.155984i
$723$	−4.37816	−	6.02602i	−0.162825	−	0.224110i
$724$	−63.7855			−2.37057
$725$		0			0
$726$	−2.37672			−0.0882083
$727$	24.3716	+	33.5446i	0.903891	+	1.24410i	0.969210	+	0.246235i	$0.0791933\pi$
$727$	24.3716	+	33.5446i	0.903891	+	1.24410i	−0.0653195	+	0.997864i	$0.520807\pi$
$728$	−2.26739	−	0.736718i	−0.0840349	−	0.0273046i
$729$	−0.309017	+	0.951057i	−0.0114451	+	0.0352243i
$730$		0			0
$731$	−3.54723	−	10.9172i	−0.131199	−	0.403789i
$732$			0.675604i			0.0249710i
$733$	30.9293	−	10.0496i	1.14240	−	0.371189i	0.324125	−	0.946014i	$-0.394930\pi$
$733$	30.9293	−	10.0496i	1.14240	−	0.371189i	0.818276	+	0.574826i	$0.194930\pi$
$734$	2.33013	+	1.69294i	0.0860067	+	0.0624875i
$735$		0			0
$736$	35.0446	−	25.4614i	1.29176	−	0.938518i
$737$	5.22614	−	7.19317i	0.192507	−	0.264964i
$738$	−2.34181	+	3.22323i	−0.0862034	+	0.118649i
$739$	−28.5724	+	20.7591i	−1.05105	+	0.763635i	−0.972413	−	0.233268i	$-0.925058\pi$
$739$	−28.5724	+	20.7591i	−1.05105	+	0.763635i	−0.0786411	+	0.996903i	$0.525058\pi$
$740$		0			0
$741$	−1.70487	−	1.23866i	−0.0626300	−	0.0455034i
$742$	8.53592	−	2.77349i	0.313363	−	0.101818i
$743$			36.0897i			1.32400i	0.749503	+	0.662001i	$0.230292\pi$
$743$			36.0897i			1.32400i	−0.749503	+	0.662001i	$0.769708\pi$
$744$	−15.1149	−	46.5188i	−0.554139	−	1.70546i
$745$		0			0
$746$	−3.44579	+	10.6051i	−0.126159	+	0.388279i
$747$	11.1183	+	3.61256i	0.406798	+	0.132177i
$748$	16.9898	+	23.3845i	0.621210	+	0.855022i
$749$	4.05021			0.147991
$750$		0			0
$751$	−4.62810			−0.168882			−0.0844409	−	0.996428i	$-0.526910\pi$
$751$	−4.62810			−0.168882			−0.0844409	+	0.996428i	$0.526910\pi$
$752$	35.7031	+	49.1411i	1.30196	+	1.79199i
$753$	4.37692	+	1.42215i	0.159504	+	0.0518259i
$754$	3.92258	−	12.0725i	0.142852	−	0.439653i
$755$		0			0
$756$	0.773789	+	2.38148i	0.0281424	+	0.0866135i
$757$			14.6243i			0.531530i	0.964038	+	0.265765i	$0.0856245\pi$
$757$			14.6243i			0.531530i	−0.964038	+	0.265765i	$0.914375\pi$
$758$	26.6561	−	8.66109i	0.968193	−	0.314585i
$759$	5.84219	+	4.24460i	0.212058	+	0.154069i
$760$		0			0
$761$	−9.86133	+	7.16467i	−0.357473	+	0.259719i	−0.751997	−	0.659166i	$-0.770909\pi$
$761$	−9.86133	+	7.16467i	−0.357473	+	0.259719i	0.394524	+	0.918885i	$0.370909\pi$
$762$	2.82968	−	3.89472i	0.102509	−	0.141091i
$763$	−4.61296	+	6.34920i	−0.167000	+	0.229856i
$764$	78.6799	−	57.1643i	2.84654	−	2.06813i
$765$		0			0
$766$	−2.62597	−	1.90788i	−0.0948801	−	0.0689344i
$767$	6.89767	−	2.24119i	0.249060	−	0.0809246i
$768$		−	25.8083i		−	0.931276i
$769$	−4.26323	−	13.1209i	−0.153736	−	0.473150i	0.844295	−	0.535879i	$-0.180020\pi$
$769$	−4.26323	−	13.1209i	−0.153736	−	0.473150i	−0.998031	+	0.0627287i	$0.980020\pi$
$770$		0			0
$771$	−1.79071	+	5.51123i	−0.0644908	+	0.198482i
$772$	127.640	+	41.4726i	4.59385	+	1.49263i
$773$	13.3156	+	18.3274i	0.478929	+	0.659190i	0.978299	−	0.207199i	$-0.0664349\pi$
$773$	13.3156	+	18.3274i	0.478929	+	0.659190i	−0.499369	+	0.866389i	$0.666435\pi$
$774$	−18.2063			−0.654411
$775$		0			0
$776$	76.0647			2.73056
$777$	−0.282196	−	0.388409i	−0.0101237	−	0.0139341i
$778$	−32.4422	−	10.5411i	−1.16311	−	0.377917i
$779$	−1.70143	+	5.23646i	−0.0609600	+	0.187616i
$780$		0			0
$781$	−15.7750	−	48.5504i	−0.564473	−	1.73727i
$782$			10.4820i			0.374837i
$783$	−7.91697	+	2.57238i	−0.282929	+	0.0919294i
$784$	−75.1355	−	54.5891i	−2.68341	−	1.94961i
$785$		0			0
$786$	12.9587	−	9.41507i	0.462223	−	0.335824i
$787$	−28.0289	+	38.5785i	−0.999123	+	1.37518i	−0.0732618	+	0.997313i	$0.523341\pi$
$787$	−28.0289	+	38.5785i	−0.999123	+	1.37518i	−0.925862	+	0.377863i	$0.876659\pi$
$788$	−37.8440	+	52.0878i	−1.34814	+	1.85555i
$789$	11.5680	−	8.40467i	0.411833	−	0.299214i
$790$		0			0
$791$	−4.48043	−	3.25522i	−0.159306	−	0.115742i
$792$	27.2229	−	8.84525i	0.967323	−	0.314302i
$793$		−	0.0714945i		−	0.00253884i
$794$	1.09837	+	3.38044i	0.0389797	+	0.119967i
$795$		0			0
$796$	−0.895774	+	2.75691i	−0.0317499	+	0.0977160i
$797$	25.8812	+	8.40931i	0.916759	+	0.297873i	0.729137	−	0.684368i	$-0.239922\pi$
$797$	25.8812	+	8.40931i	0.916759	+	0.297873i	0.187622	+	0.982241i	$0.439922\pi$
$798$	2.79806	+	3.85120i	0.0990504	+	0.136331i
$799$	−7.56529			−0.267641
$800$		0			0
$801$	−6.20049			−0.219083
$802$	−25.6179	−	35.2600i	−0.904599	−	1.24507i
$803$	−29.6184	−	9.62360i	−1.04521	−	0.339610i
$804$	4.59818	−	14.1518i	0.162165	−	0.499094i
$805$		0			0
$806$	2.56179	+	7.88437i	0.0902351	+	0.277715i
$807$		−	19.2205i		−	0.676592i
$808$	−49.9132	+	16.2178i	−1.75594	+	0.570540i
$809$	−15.8693	−	11.5297i	−0.557933	−	0.405362i	0.272769	−	0.962080i	$-0.412061\pi$
$809$	−15.8693	−	11.5297i	−0.557933	−	0.405362i	−0.830702	+	0.556717i	$0.812061\pi$
$810$		0			0
$811$	−17.0468	+	12.3852i	−0.598594	+	0.434904i	−0.845380	−	0.534166i	$-0.820626\pi$
$811$	−17.0468	+	12.3852i	−0.598594	+	0.434904i	0.246786	+	0.969070i	$0.420626\pi$
$812$	−12.2521	+	16.8636i	−0.429965	+	0.591796i
$813$	13.6620	−	18.8042i	0.479149	−	0.659492i
$814$	−7.11107	+	5.16650i	−0.249243	+	0.181086i
$815$		0			0
$816$	18.9131	+	13.7412i	0.662090	+	0.481037i
$817$	−23.9290	+	7.77501i	−0.837170	+	0.272013i
$818$		−	57.2667i		−	2.00228i
$819$	−0.0818847	−	0.252015i	−0.00286128	−	0.00880613i
$820$		0			0
$821$	12.8039	−	39.4062i	0.446858	−	1.37529i	−0.433575	−	0.901117i	$-0.642748\pi$
$821$	12.8039	−	39.4062i	0.446858	−	1.37529i	0.880433	−	0.474170i	$-0.157252\pi$
$822$	−13.1684	−	4.27866i	−0.459299	−	0.149235i
$823$	3.55077	+	4.88721i	0.123772	+	0.170358i	0.866406	−	0.499340i	$-0.166424\pi$
$823$	3.55077	+	4.88721i	0.123772	+	0.170358i	−0.742634	+	0.669697i	$0.766424\pi$
$824$	126.673			4.41285
$825$		0			0
$826$	−16.3833			−0.570047
$827$	1.75960	+	2.42188i	0.0611874	+	0.0842172i	0.838514	−	0.544880i	$-0.183425\pi$
$827$	1.75960	+	2.42188i	0.0611874	+	0.0842172i	−0.777327	+	0.629097i	$0.783425\pi$
$828$	11.4938	+	3.73458i	0.399439	+	0.129786i
$829$	−8.29802	+	25.5387i	−0.288202	+	0.886995i	0.697218	+	0.716859i	$0.254421\pi$
$829$	−8.29802	+	25.5387i	−0.288202	+	0.886995i	−0.985421	+	0.170136i	$0.945579\pi$
$830$		0			0
$831$	6.76469	+	20.8196i	0.234664	+	0.722223i
$832$			13.6624i			0.473658i
$833$	11.0010	−	3.57444i	0.381162	−	0.123847i
$834$	−18.0374	−	13.1050i	−0.624585	−	0.453787i
$835$		0			0
$836$	51.2555	−	37.2393i	1.77271	−	1.28795i
$837$	3.19553	−	4.39827i	0.110454	−	0.152026i
$838$	10.6119	−	14.6060i	0.366581	−	0.504555i
$839$	10.0800	−	7.32352i	0.347999	−	0.252836i	−0.400030	−	0.916502i	$-0.631000\pi$
$839$	10.0800	−	7.32352i	0.347999	−	0.252836i	0.748029	+	0.663666i	$0.231000\pi$
$840$		0			0
$841$	−32.5998	−	23.6851i	−1.12413	−	0.816729i
$842$	−70.2624	+	22.8297i	−2.42140	+	0.786762i
$843$		−	27.1138i		−	0.933850i
$844$	5.13683	+	15.8095i	0.176817	+	0.544186i
$845$		0			0
$846$	−3.70785	+	11.4116i	−0.127479	+	0.392339i
$847$	−0.392797	−	0.127627i	−0.0134967	−	0.00438533i
$848$	−56.7859	−	78.1590i	−1.95003	−	2.68399i
$849$	−16.3074			−0.559668
$850$		0			0
$851$	−2.31714			−0.0794304
$852$	−50.2165	−	69.1171i	−1.72039	−	2.36791i
$853$	5.41851	+	1.76058i	0.185526	+	0.0602811i	0.400307	−	0.916381i	$-0.368904\pi$
$853$	5.41851	+	1.76058i	0.185526	+	0.0602811i	−0.214780	+	0.976662i	$0.568904\pi$
$854$	−0.0499068	+	0.153597i	−0.00170778	+	0.00525599i
$855$		0			0
$856$	−23.9436	−	73.6907i	−0.818374	−	2.51870i
$857$		−	7.41982i		−	0.253456i	−0.991937	−	0.126728i	$-0.959552\pi$
$857$		−	7.41982i		−	0.253456i	0.991937	−	0.126728i	$-0.0404476\pi$
$858$	−4.61394	+	1.49916i	−0.157517	+	0.0511805i
$859$	−4.59726	−	3.34011i	−0.156857	−	0.113963i	0.506588	−	0.862188i	$-0.330906\pi$
$859$	−4.59726	−	3.34011i	−0.156857	−	0.113963i	−0.663445	+	0.748225i	$0.730906\pi$
$860$		0			0
$861$	−0.560112	+	0.406945i	−0.0190886	+	0.0138687i
$862$	19.5622	−	26.9251i	0.666293	−	0.917073i
$863$	20.3225	−	27.9715i	0.691785	−	0.952160i	−0.308215	−	0.951317i	$-0.599732\pi$
$863$	20.3225	−	27.9715i	0.691785	−	0.952160i	1.00000		0.000843465i	$-0.000268483\pi$
$864$	15.4395	−	11.2174i	0.525261	−	0.381624i
$865$		0			0
$866$	74.1037	+	53.8395i	2.51815	+	1.82954i
$867$	13.3988	−	4.35353i	0.455047	−	0.147854i
$868$		−	13.6133i		−	0.462066i
$869$	−4.67478	−	14.3875i	−0.158581	−	0.488062i
$870$		0			0
$871$	−0.486594	+	1.49758i	−0.0164876	+	0.0507437i
$872$	142.790	+	46.3952i	4.83547	+	1.57114i
$873$	4.96939	+	6.83978i	0.168188	+	0.231491i
$874$	22.9751			0.777145
$875$		0			0
$876$	−52.1191			−1.76094
$877$	3.11534	+	4.28790i	0.105197	+	0.144792i	0.858370	−	0.513031i	$-0.171477\pi$
$877$	3.11534	+	4.28790i	0.105197	+	0.144792i	−0.753173	+	0.657823i	$0.771477\pi$
$878$	53.9629	+	17.5336i	1.82116	+	0.591730i
$879$	−1.68849	+	5.19664i	−0.0569514	+	0.175278i
$880$		0			0
$881$	2.35251	+	7.24028i	0.0792580	+	0.243931i	0.982833	−	0.184500i	$-0.0590665\pi$
$881$	2.35251	+	7.24028i	0.0792580	+	0.243931i	−0.903575	+	0.428431i	$0.859067\pi$
$882$		−	18.3460i		−	0.617740i
$883$	−50.2476	+	16.3264i	−1.69096	+	0.549428i	−0.986988	−	0.160795i	$-0.948594\pi$
$883$	−50.2476	+	16.3264i	−1.69096	+	0.549428i	−0.703977	+	0.710223i	$0.748594\pi$
$884$	−4.14143	−	3.00892i	−0.139291	−	0.101201i
$885$		0			0
$886$	−13.2431	+	9.62166i	−0.444910	+	0.323246i
$887$	4.53052	−	6.23572i	0.152120	−	0.209375i	−0.726155	−	0.687531i	$-0.758695\pi$
$887$	4.53052	−	6.23572i	0.152120	−	0.209375i	0.878275	+	0.478156i	$0.158695\pi$
$888$	−5.39858	+	7.43051i	−0.181165	+	0.249352i
$889$	0.676800	−	0.491724i	0.0226991	−	0.0164919i
$890$		0			0
$891$	2.57387	+	1.87003i	0.0862279	+	0.0626482i
$892$	−1.71726	+	0.557972i	−0.0574981	+	0.0186823i
$893$			16.5820i			0.554896i
$894$	8.41207	+	25.8897i	0.281342	+	0.865881i
$895$		0			0
$896$	3.99006	−	12.2801i	0.133299	−	0.410251i
$897$	−1.21631	−	0.395205i	−0.0406116	−	0.0131955i
$898$	24.7994	+	34.1334i	0.827566	+	1.13905i
$899$	45.2560			1.50937
$900$		0			0
$901$	12.0326			0.400864
$902$	7.45043	+	10.2546i	0.248072	+	0.341442i
$903$	−3.00892	−	0.977659i	−0.100131	−	0.0325344i
$904$	−32.7396	+	100.762i	−1.08890	+	3.35130i
$905$		0			0
$906$	−10.0198	−	30.8379i	−0.332887	−	1.02452i
$907$		−	11.3735i		−	0.377650i	−0.982011	−	0.188825i	$-0.939532\pi$
$907$		−	11.3735i		−	0.377650i	0.982011	−	0.188825i	$-0.0604678\pi$
$908$	−9.05644	+	2.94262i	−0.300549	+	0.0976542i
$909$	−4.71920	−	3.42870i	−0.156526	−	0.113723i
$910$		0			0
$911$	15.0393	−	10.9267i	0.498275	−	0.362018i	−0.310082	−	0.950710i	$-0.600357\pi$
$911$	15.0393	−	10.9267i	0.498275	−	0.362018i	0.808358	+	0.588691i	$0.200357\pi$
$912$	30.1186	−	41.4547i	0.997328	−	1.37270i
$913$	21.8615	−	30.0898i	0.723511	−	0.995827i
$914$	−5.47795	+	3.97997i	−0.181195	+	0.131646i
$915$		0			0
$916$	120.539	+	87.5764i	3.98271	+	2.89361i
$917$	2.64725	−	0.860143i	0.0874199	−	0.0284044i
$918$			4.61803i			0.152418i
$919$	−2.36336	−	7.27367i	−0.0779600	−	0.239936i	0.904480	−	0.426517i	$-0.140259\pi$
$919$	−2.36336	−	7.27367i	−0.0779600	−	0.239936i	−0.982440	+	0.186581i	$0.940259\pi$
$920$		0			0
$921$	−6.61895	+	20.3710i	−0.218102	+	0.671249i
$922$	−0.396286	−	0.128761i	−0.0130510	−	0.00424052i
$923$	5.31407	+	7.31418i	0.174915	+	0.240749i
$924$	7.96652			0.262079
$925$		0			0
$926$	−31.4822			−1.03457
$927$	8.27566	+	11.3905i	0.271808	+	0.374112i
$928$	151.089	+	49.0918i	4.95974	+	1.61152i
$929$	9.56366	−	29.4339i	0.313774	−	0.965696i	−0.662483	−	0.749077i	$-0.730497\pi$
$929$	9.56366	−	29.4339i	0.313774	−	0.965696i	0.976256	−	0.216619i	$-0.0695028\pi$
$930$		0			0
$931$	−7.83466	−	24.1126i	−0.256770	−	0.790258i
$932$		−	36.0675i		−	1.18143i
$933$	−2.71241	+	0.881316i	−0.0888003	+	0.0288530i
$934$	1.02971	+	0.748125i	0.0336930	+	0.0244794i
$935$		0			0
$936$	−4.10116	+	2.97967i	−0.134051	+	0.0973936i
$937$	18.4385	−	25.3784i	0.602360	−	0.829077i	−0.393562	−	0.919298i	$-0.628757\pi$
$937$	18.4385	−	25.3784i	0.602360	−	0.829077i	0.995922	+	0.0902212i	$0.0287574\pi$
$938$	2.09078	−	2.87771i	0.0682663	−	0.0939605i
$939$	11.6802	−	8.48616i	0.381169	−	0.276935i
$940$		0			0
$941$	2.92710	+	2.12666i	0.0954208	+	0.0693273i	0.634473	−	0.772945i	$-0.281217\pi$
$941$	2.92710	+	2.12666i	0.0954208	+	0.0693273i	−0.539052	+	0.842273i	$0.681217\pi$
$942$	−50.4383	+	16.3884i	−1.64337	+	0.533963i
$943$			3.34146i			0.108813i
$944$	54.4955	+	167.720i	1.77368	+	5.45882i
$945$		0			0
$946$	−17.8992	+	55.0879i	−0.581952	+	1.79106i
$947$	−10.7675	−	3.49856i	−0.349896	−	0.113688i	0.128796	−	0.991671i	$-0.458889\pi$
$947$	−10.7675	−	3.49856i	−0.349896	−	0.113688i	−0.478692	+	0.877983i	$0.658889\pi$
$948$	−14.8812	−	20.4823i	−0.483320	−	0.665233i
$949$	5.51540			0.179038
$950$		0			0
$951$	22.6102			0.733187
$952$	4.24383	+	5.84113i	0.137543	+	0.189312i
$953$	16.3755	+	5.32071i	0.530453	+	0.172355i	0.561984	−	0.827148i	$-0.310038\pi$
$953$	16.3755	+	5.32071i	0.530453	+	0.172355i	−0.0315307	+	0.999503i	$0.510038\pi$
$954$	5.89735	−	18.1502i	0.190934	−	0.587633i
$955$		0			0
$956$	−10.6672	−	32.8304i	−0.345003	−	1.06181i
$957$			26.4839i			0.856102i
$958$	31.9458	−	10.3798i	1.03212	−	0.335357i
$959$	−1.94656	−	1.41426i	−0.0628576	−	0.0456687i
$960$		0			0
$961$	1.16811	−	0.848680i	0.0376809	−	0.0273768i
$962$	0.914994	−	1.25938i	0.0295006	−	0.0406041i
$963$	5.06205	−	6.96731i	0.163122	−	0.224519i
$964$	−32.0849	+	23.3110i	−1.03339	+	0.750798i
$965$		0			0
$966$	2.33723	+	1.69810i	0.0751992	+	0.0546354i
$967$	28.4426	−	9.24157i	0.914653	−	0.297189i	0.186382	−	0.982477i	$-0.440324\pi$
$967$	28.4426	−	9.24157i	0.914653	−	0.297189i	0.728272	+	0.685289i	$0.240324\pi$
$968$			7.90115i			0.253953i
$969$	1.97214	+	6.06961i	0.0633541	+	0.194984i
$970$		0			0
$971$	−7.78497	+	23.9597i	−0.249832	+	0.768902i	0.744973	+	0.667095i	$0.232463\pi$
$971$	−7.78497	+	23.9597i	−0.249832	+	0.768902i	−0.994804	+	0.101807i	$0.967537\pi$
$972$	5.06380	+	1.64533i	0.162422	+	0.0527739i
$973$	−2.27729	−	3.13443i	−0.0730067	−	0.100485i
$974$	−93.5443			−2.99735
$975$		0			0
$976$	1.73842			0.0556455
$977$	−33.5595	−	46.1907i	−1.07366	−	1.47777i	−0.866311	−	0.499504i	$-0.833515\pi$
$977$	−33.5595	−	46.1907i	−1.07366	−	1.47777i	−0.207352	−	0.978266i	$-0.566485\pi$
$978$	−30.6106	−	9.94597i	−0.978818	−	0.318037i
$979$	−6.09589	+	18.7612i	−0.194826	+	0.599611i
$980$		0			0
$981$	5.15673	+	15.8708i	0.164642	+	0.506715i
$982$		−	67.2957i		−	2.14749i
$983$	−25.1239	+	8.16325i	−0.801328	+	0.260367i	−0.680921	−	0.732357i	$-0.738420\pi$
$983$	−25.1239	+	8.16325i	−0.801328	+	0.260367i	−0.120407	+	0.992725i	$0.538420\pi$
$984$	10.7153	+	7.78512i	0.341591	+	0.248181i
$985$		0			0
$986$	−31.1005	+	22.5958i	−0.990442	+	0.719598i
$987$	−1.22558	+	1.68687i	−0.0390107	+	0.0536936i
$988$	−6.59513	+	9.07741i	−0.209819	+	0.288791i
$989$	−12.3533	+	8.97517i	−0.392811	+	0.285394i
$990$		0			0
$991$	18.2252	+	13.2414i	0.578943	+	0.420626i	0.838343	−	0.545144i	$-0.183525\pi$
$991$	18.2252	+	13.2414i	0.578943	+	0.420626i	−0.259400	+	0.965770i	$0.583525\pi$
$992$	−98.6744	+	32.0612i	−3.13291	+	1.01795i
$993$		−	3.86645i		−	0.122698i
$994$	−6.31096	−	19.4231i	−0.200171	−	0.616064i
$995$		0			0
$996$	19.2347	−	59.1983i	0.609475	−	1.87577i
$997$	−22.9246	−	7.44865i	−0.726029	−	0.235901i	−0.0773940	−	0.997001i	$-0.524660\pi$
$997$	−22.9246	−	7.44865i	−0.726029	−	0.235901i	−0.648635	+	0.761099i	$0.724660\pi$
$998$	20.0495	+	27.5958i	0.634656	+	0.873529i
$999$	−1.02085			−0.0322983

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	375.2.i.b.199.1		16
5.2	odd	4		375.2.g.b.301.2		8
5.3	odd	4		75.2.g.b.61.1	yes	8
5.4	even	2	inner	375.2.i.b.199.4		16
15.8	even	4		225.2.h.c.136.2		8
25.3	odd	20		1875.2.a.h.1.4		4
25.4	even	10		1875.2.b.c.1249.1		8
25.9	even	10	inner	375.2.i.b.49.1		16
25.12	odd	20		375.2.g.b.76.2		8
25.13	odd	20		75.2.g.b.16.1	✓	8
25.16	even	5	inner	375.2.i.b.49.4		16
25.21	even	5		1875.2.b.c.1249.8		8
25.22	odd	20		1875.2.a.e.1.1		4
75.38	even	20		225.2.h.c.91.2		8
75.47	even	20		5625.2.a.n.1.4		4
75.53	even	20		5625.2.a.i.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.2.g.b.16.1	✓	8	25.13	odd	20
75.2.g.b.61.1	yes	8	5.3	odd	4
225.2.h.c.91.2		8	75.38	even	20
225.2.h.c.136.2		8	15.8	even	4
375.2.g.b.76.2		8	25.12	odd	20
375.2.g.b.301.2		8	5.2	odd	4
375.2.i.b.49.1		16	25.9	even	10	inner
375.2.i.b.49.4		16	25.16	even	5	inner
375.2.i.b.199.1		16	1.1	even	1	trivial
375.2.i.b.199.4		16	5.4	even	2	inner
1875.2.a.e.1.1		4	25.22	odd	20
1875.2.a.h.1.4		4	25.3	odd	20
1875.2.b.c.1249.1		8	25.4	even	10
1875.2.b.c.1249.8		8	25.21	even	5
5625.2.a.i.1.1		4	75.53	even	20
5625.2.a.n.1.4		4	75.47	even	20

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:	\( N \)	\(=\)	\( 375 = 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	375.i (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.59076 - 2.18949i) q^{2} +(-0.951057 - 0.309017i) q^{3} +(-1.64533 + 5.06380i) q^{4} +(0.836312 + 2.57390i) q^{6} +0.470294i q^{7} +(8.55667 - 2.78023i) q^{8} +(0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(-1.59076 - 2.18949i) q^{2} +(-0.951057 - 0.309017i) q^{3} +(-1.64533 + 5.06380i) q^{4} +(0.836312 + 2.57390i) q^{6} +0.470294i q^{7} +(8.55667 - 2.78023i) q^{8} +(0.809017 + 0.587785i) q^{9} +(2.57387 - 1.87003i) q^{11} +(3.12960 - 4.30753i) q^{12} +(-0.331184 + 0.455836i) q^{13} +(1.02971 - 0.748125i) q^{14} +(-11.0839 - 8.05289i) q^{16} +(1.62285 - 0.527295i) q^{17} -2.70636i q^{18} +(-1.15575 - 3.55705i) q^{19} +(0.145329 - 0.447276i) q^{21} +(-8.18882 - 2.66071i) q^{22} +(-1.33416 - 1.83631i) q^{23} -8.99702 q^{24} +1.52488 q^{26} +(-0.587785 - 0.809017i) q^{27} +(-2.38148 - 0.773789i) q^{28} +(2.57238 - 7.91697i) q^{29} +(1.67999 + 5.17047i) q^{31} +19.0842i q^{32} +(-3.02577 + 0.983131i) q^{33} +(-3.73607 - 2.71441i) q^{34} +(-4.30753 + 3.12960i) q^{36} +(0.600041 - 0.825886i) q^{37} +(-5.94960 + 8.18892i) q^{38} +(0.455836 - 0.331184i) q^{39} +(-1.19098 - 0.865300i) q^{41} +(-1.21049 + 0.393313i) q^{42} -6.72721i q^{43} +(5.23458 + 16.1104i) q^{44} +(-1.89827 + 5.84226i) q^{46} +(-4.21658 - 1.37005i) q^{47} +(8.05289 + 11.0839i) q^{48} +6.77882 q^{49} -1.70636 q^{51} +(-1.76336 - 2.42705i) q^{52} +(6.70648 + 2.17907i) q^{53} +(-0.836312 + 2.57390i) q^{54} +(1.30753 + 4.02415i) q^{56} +3.74010i q^{57} +(-21.4262 + 6.96179i) q^{58} +(-10.4136 - 7.56596i) q^{59} +(-0.102655 + 0.0745831i) q^{61} +(8.64825 - 11.9033i) q^{62} +(-0.276432 + 0.380476i) q^{63} +(19.6170 - 14.2526i) q^{64} +(6.96582 + 5.06097i) q^{66} +(2.65791 - 0.863607i) q^{67} +9.08535i q^{68} +(0.701409 + 2.15871i) q^{69} +(4.95838 - 15.2603i) q^{71} +(8.55667 + 2.78023i) q^{72} +(-5.75367 - 7.91925i) q^{73} -2.76279 q^{74} +19.9138 q^{76} +(0.879462 + 1.21048i) q^{77} +(-1.45025 - 0.471215i) q^{78} +(1.46937 - 4.52227i) q^{79} +(0.309017 + 0.951057i) q^{81} +3.98413i q^{82} +(11.1183 - 3.61256i) q^{83} +(2.02580 + 1.47183i) q^{84} +(-14.7292 + 10.7014i) q^{86} +(-4.89296 + 6.73458i) q^{87} +(16.8247 - 23.1572i) q^{88} +(-5.01630 + 3.64456i) q^{89} +(-0.214377 - 0.155754i) q^{91} +(11.4938 - 3.73458i) q^{92} -5.43656i q^{93} +(3.70785 + 11.4116i) q^{94} +(5.89735 - 18.1502i) q^{96} +(8.04064 + 2.61256i) q^{97} +(-10.7835 - 14.8422i) q^{98} +3.18148 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{4} - 2 q^{6} + 4 q^{9}+O(q^{10}) \) 16 * q - 2 * q^4 - 2 * q^6 + 4 * q^9	\( 16 q - 2 q^{4} - 2 q^{6} + 4 q^{9} + 32 q^{11} + 16 q^{14} - 34 q^{16} + 10 q^{19} - 22 q^{21} - 60 q^{24} + 12 q^{26} - 10 q^{29} - 38 q^{31} - 24 q^{34} - 18 q^{36} + 16 q^{39} - 28 q^{41} + 6 q^{44} + 32 q^{46} - 32 q^{49} + 8 q^{51} + 2 q^{54} - 30 q^{56} - 60 q^{59} - 28 q^{61} + 88 q^{64} - 14 q^{66} + 16 q^{69} + 42 q^{71} + 76 q^{74} + 160 q^{76} + 60 q^{79} - 4 q^{81} - 16 q^{84} - 68 q^{86} + 42 q^{91} + 66 q^{94} + 68 q^{96} + 28 q^{99}+O(q^{100}) \) 16 * q - 2 * q^4 - 2 * q^6 + 4 * q^9 + 32 * q^11 + 16 * q^14 - 34 * q^16 + 10 * q^19 - 22 * q^21 - 60 * q^24 + 12 * q^26 - 10 * q^29 - 38 * q^31 - 24 * q^34 - 18 * q^36 + 16 * q^39 - 28 * q^41 + 6 * q^44 + 32 * q^46 - 32 * q^49 + 8 * q^51 + 2 * q^54 - 30 * q^56 - 60 * q^59 - 28 * q^61 + 88 * q^64 - 14 * q^66 + 16 * q^69 + 42 * q^71 + 76 * q^74 + 160 * q^76 + 60 * q^79 - 4 * q^81 - 16 * q^84 - 68 * q^86 + 42 * q^91 + 66 * q^94 + 68 * q^96 + 28 * q^99

Introduction

L-functions

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