LMFDB - Embedded newform 375.2.g.b.301.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [375,2,Mod(76,375)]

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, 2]))

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

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

chi := DirichletCharacter("375.76");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.99439007580$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.26265625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 2x^{6} + x^{4} + 8x^{2} - 24x + 16 $ x^8 - 3x^7 + 2x^6 + x^4 + 8x^2 - 24x + 16
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 5 $
Twist minimal:	no (minimal twist has level 75)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			301.2
Root			$1.33631 - 0.462894i$ of defining polynomial
Character	$\chi$	$=$	375.301
Dual form			375.2.g.b.76.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.18949 - 1.59076i) q^{2} +(-0.309017 + 0.951057i) q^{3} +(1.64533 - 5.06380i) q^{4} +(0.836312 + 2.57390i) q^{6} -0.470294 q^{7} +(-2.78023 - 8.55667i) q^{8} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})$	\(q+(2.18949 - 1.59076i) q^{2} +(-0.309017 + 0.951057i) q^{3} +(1.64533 - 5.06380i) q^{4} +(0.836312 + 2.57390i) q^{6} -0.470294 q^{7} +(-2.78023 - 8.55667i) q^{8} +(-0.809017 - 0.587785i) q^{9} +(2.57387 - 1.87003i) q^{11} +(4.30753 + 3.12960i) q^{12} +(0.455836 + 0.331184i) q^{13} +(-1.02971 + 0.748125i) q^{14} +(-11.0839 - 8.05289i) q^{16} +(0.527295 + 1.62285i) q^{17} -2.70636 q^{18} +(1.15575 + 3.55705i) q^{19} +(0.145329 - 0.447276i) q^{21} +(2.66071 - 8.18882i) q^{22} +(-1.83631 + 1.33416i) q^{23} +8.99702 q^{24} +1.52488 q^{26} +(0.809017 - 0.587785i) q^{27} +(-0.773789 + 2.38148i) q^{28} +(-2.57238 + 7.91697i) q^{29} +(1.67999 + 5.17047i) q^{31} -19.0842 q^{32} +(0.983131 + 3.02577i) q^{33} +(3.73607 + 2.71441i) q^{34} +(-4.30753 + 3.12960i) q^{36} +(0.825886 + 0.600041i) q^{37} +(8.18892 + 5.94960i) q^{38} +(-0.455836 + 0.331184i) q^{39} +(-1.19098 - 0.865300i) q^{41} +(-0.393313 - 1.21049i) q^{42} -6.72721 q^{43} +(-5.23458 - 16.1104i) q^{44} +(-1.89827 + 5.84226i) q^{46} +(1.37005 - 4.21658i) q^{47} +(11.0839 - 8.05289i) q^{48} -6.77882 q^{49} -1.70636 q^{51} +(2.42705 - 1.76336i) q^{52} +(2.17907 - 6.70648i) q^{53} +(0.836312 - 2.57390i) q^{54} +(1.30753 + 4.02415i) q^{56} -3.74010 q^{57} +(6.96179 + 21.4262i) q^{58} +(10.4136 + 7.56596i) q^{59} +(-0.102655 + 0.0745831i) q^{61} +(11.9033 + 8.64825i) q^{62} +(0.380476 + 0.276432i) q^{63} +(-19.6170 + 14.2526i) q^{64} +(6.96582 + 5.06097i) q^{66} +(0.863607 + 2.65791i) q^{67} +9.08535 q^{68} +(-0.701409 - 2.15871i) q^{69} +(4.95838 - 15.2603i) q^{71} +(-2.78023 + 8.55667i) q^{72} +(-7.91925 + 5.75367i) q^{73} +2.76279 q^{74} +19.9138 q^{76} +(-1.21048 + 0.879462i) q^{77} +(-0.471215 + 1.45025i) q^{78} +(-1.46937 + 4.52227i) q^{79} +(0.309017 + 0.951057i) q^{81} -3.98413 q^{82} +(-3.61256 - 11.1183i) q^{83} +(-2.02580 - 1.47183i) q^{84} +(-14.7292 + 10.7014i) q^{86} +(-6.73458 - 4.89296i) q^{87} +(-23.1572 - 16.8247i) q^{88} +(5.01630 - 3.64456i) q^{89} +(-0.214377 - 0.155754i) q^{91} +(3.73458 + 11.4938i) q^{92} -5.43656 q^{93} +(-3.70785 - 11.4116i) q^{94} +(5.89735 - 18.1502i) q^{96} +(-2.61256 + 8.04064i) q^{97} +(-14.8422 + 10.7835i) q^{98} -3.18148 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + q^{2} + 2 q^{3} + q^{4} - q^{6} - 4 q^{7} - 2 q^{9}+O(q^{10}) $ 8 * q + q^2 + 2 * q^3 + q^4 - q^6 - 4 * q^7 - 2 * q^9	$ 8 q + q^{2} + 2 q^{3} + q^{4} - q^{6} - 4 q^{7} - 2 q^{9} + 16 q^{11} + 9 q^{12} + 8 q^{13} - 8 q^{14} - 17 q^{16} + q^{17} - 4 q^{18} - 5 q^{19} - 11 q^{21} - 13 q^{22} - 7 q^{23} + 30 q^{24} + 6 q^{26} + 2 q^{27} + 17 q^{28} + 5 q^{29} - 19 q^{31} - 24 q^{32} + 9 q^{33} + 12 q^{34} - 9 q^{36} + q^{37} + 10 q^{38} - 8 q^{39} - 14 q^{41} + 8 q^{42} - 32 q^{43} - 3 q^{44} + 16 q^{46} + q^{47} + 17 q^{48} + 16 q^{49} + 4 q^{51} + 6 q^{52} + 3 q^{53} - q^{54} - 15 q^{56} - 10 q^{57} - 5 q^{58} + 30 q^{59} - 14 q^{61} + 17 q^{62} - 9 q^{63} - 44 q^{64} - 7 q^{66} - 4 q^{67} + 22 q^{68} - 8 q^{69} + 21 q^{71} - 2 q^{73} - 38 q^{74} + 80 q^{76} + 37 q^{77} + 14 q^{78} - 30 q^{79} - 2 q^{81} + 12 q^{82} - 2 q^{83} + 8 q^{84} - 34 q^{86} - 15 q^{87} - 70 q^{88} + 21 q^{91} - 9 q^{92} - 46 q^{93} - 33 q^{94} + 34 q^{96} + 6 q^{97} - 73 q^{98} - 14 q^{99}+O(q^{100}) $ 8 * q + q^2 + 2 * q^3 + q^4 - q^6 - 4 * q^7 - 2 * q^9 + 16 * q^11 + 9 * q^12 + 8 * q^13 - 8 * q^14 - 17 * q^16 + q^17 - 4 * q^18 - 5 * q^19 - 11 * q^21 - 13 * q^22 - 7 * q^23 + 30 * q^24 + 6 * q^26 + 2 * q^27 + 17 * q^28 + 5 * q^29 - 19 * q^31 - 24 * q^32 + 9 * q^33 + 12 * q^34 - 9 * q^36 + q^37 + 10 * q^38 - 8 * q^39 - 14 * q^41 + 8 * q^42 - 32 * q^43 - 3 * q^44 + 16 * q^46 + q^47 + 17 * q^48 + 16 * q^49 + 4 * q^51 + 6 * q^52 + 3 * q^53 - q^54 - 15 * q^56 - 10 * q^57 - 5 * q^58 + 30 * q^59 - 14 * q^61 + 17 * q^62 - 9 * q^63 - 44 * q^64 - 7 * q^66 - 4 * q^67 + 22 * q^68 - 8 * q^69 + 21 * q^71 - 2 * q^73 - 38 * q^74 + 80 * q^76 + 37 * q^77 + 14 * q^78 - 30 * q^79 - 2 * q^81 + 12 * q^82 - 2 * q^83 + 8 * q^84 - 34 * q^86 - 15 * q^87 - 70 * q^88 + 21 * q^91 - 9 * q^92 - 46 * q^93 - 33 * q^94 + 34 * q^96 + 6 * q^97 - 73 * q^98 - 14 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$251$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$

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 $

$2$	2.18949	−	1.59076i	1.54821	−	1.12484i	0.603290	−	0.797522i	$-0.293856\pi$
$2$	2.18949	−	1.59076i	1.54821	−	1.12484i	0.944915	−	0.327315i	$-0.106144\pi$
$3$	−0.309017	+	0.951057i	−0.178411	+	0.549093i
$3$	−0.309017	+	0.951057i	−0.178411	+	0.549093i
$4$	1.64533	−	5.06380i	0.822664	−	2.53190i
$5$		0			0
$5$		0			0
$6$	0.836312	+	2.57390i	0.341423	+	1.05079i
$7$	−0.470294			−0.177754			−0.0888772	−	0.996043i	$-0.528328\pi$
$7$	−0.470294			−0.177754			−0.0888772	+	0.996043i	$0.528328\pi$
$8$	−2.78023	−	8.55667i	−0.982960	−	3.02524i
$9$	−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	$0.140772\pi$
$12$	4.30753	+	3.12960i	1.24348	+	0.903438i
$13$	0.455836	+	0.331184i	0.126426	+	0.0918540i	0.649201	−	0.760617i	$-0.275103\pi$
$13$	0.455836	+	0.331184i	0.126426	+	0.0918540i	−0.522775	+	0.852471i	$0.675103\pi$
$14$	−1.02971	+	0.748125i	−0.275200	+	0.199945i
$15$		0			0
$16$	−11.0839	−	8.05289i	−2.77096	−	2.01322i
$17$	0.527295	+	1.62285i	0.127888	+	0.393598i	0.994416	−	0.105530i	$-0.0336538\pi$
$17$	0.527295	+	1.62285i	0.127888	+	0.393598i	−0.866528	+	0.499128i	$0.833654\pi$
$18$	−2.70636			−0.637896
$19$	1.15575	+	3.55705i	0.265148	+	0.816043i	0.991659	+	0.128888i	$0.0411406\pi$
$19$	1.15575	+	3.55705i	0.265148	+	0.816043i	−0.726511	+	0.687155i	$0.758859\pi$
$20$		0			0
$21$	0.145329	−	0.447276i	0.0317134	−	0.0976037i
$22$	2.66071	−	8.18882i	0.567265	−	1.74586i
$23$	−1.83631	+	1.33416i	−0.382898	+	0.278191i	−0.762539	−	0.646942i	$-0.776047\pi$
$23$	−1.83631	+	1.33416i	−0.382898	+	0.278191i	0.379641	+	0.925134i	$0.376047\pi$
$24$	8.99702			1.83651
$25$		0			0
$26$	1.52488			0.299054
$27$	0.809017	−	0.587785i	0.155695	−	0.113119i
$28$	−0.773789	+	2.38148i	−0.146232	+	0.450057i
$29$	−2.57238	+	7.91697i	−0.477679	+	1.47014i	0.364631	+	0.931152i	$0.381195\pi$
$29$	−2.57238	+	7.91697i	−0.477679	+	1.47014i	−0.842310	+	0.538993i	$0.818805\pi$
$30$		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	$0.737647\pi$
$32$	−19.0842			−3.37364
$33$	0.983131	+	3.02577i	0.171141	+	0.526718i
$34$	3.73607	+	2.71441i	0.640730	+	0.465518i
$35$		0			0
$36$	−4.30753	+	3.12960i	−0.717921	+	0.521600i
$37$	0.825886	+	0.600041i	0.135775	+	0.0986462i	0.653600	−	0.756841i	$-0.273258\pi$
$37$	0.825886	+	0.600041i	0.135775	+	0.0986462i	−0.517825	+	0.855487i	$0.673258\pi$
$38$	8.18892	+	5.94960i	1.32842	+	0.965153i
$39$	−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	$0.736672\pi$
$42$	−0.393313	−	1.21049i	−0.0606895	−	0.186783i
$43$	−6.72721			−1.02589			−0.512945	−	0.858421i	$-0.671446\pi$
$43$	−6.72721			−1.02589			−0.512945	+	0.858421i	$0.671446\pi$
$44$	−5.23458	−	16.1104i	−0.789142	−	2.42873i
$45$		0			0
$46$	−1.89827	+	5.84226i	−0.279884	+	0.861395i
$47$	1.37005	−	4.21658i	0.199842	−	0.615052i	−0.800043	−	0.599942i	$-0.795190\pi$
$47$	1.37005	−	4.21658i	0.199842	−	0.615052i	0.999886	−	0.0151095i	$-0.00480970\pi$
$48$	11.0839	−	8.05289i	1.59982	−	1.16234i
$49$	−6.77882			−0.968403
$50$		0			0
$51$	−1.70636			−0.238938
$52$	2.42705	−	1.76336i	0.336571	−	0.244533i
$53$	2.17907	−	6.70648i	0.299318	−	0.921206i	−0.682419	−	0.730961i	$-0.739072\pi$
$53$	2.17907	−	6.70648i	0.299318	−	0.921206i	0.981737	−	0.190244i	$-0.0609281\pi$
$54$	0.836312	−	2.57390i	0.113808	−	0.350264i
$55$		0			0
$56$	1.30753	+	4.02415i	0.174726	+	0.537750i
$57$	−3.74010			−0.495388
$58$	6.96179	+	21.4262i	0.914128	+	2.81340i
$59$	10.4136	+	7.56596i	1.35574	+	0.985004i	0.998703	+	0.0509138i	$0.0162134\pi$
$59$	10.4136	+	7.56596i	1.35574	+	0.985004i	0.357038	+	0.934090i	$0.383787\pi$
$60$		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	$0.302586\pi$
$62$	11.9033	+	8.64825i	1.51172	+	1.09833i
$63$	0.380476	+	0.276432i	0.0479355	+	0.0348272i
$64$	−19.6170	+	14.2526i	−2.45213	+	1.78158i
$65$		0			0
$66$	6.96582	+	5.06097i	0.857434	+	0.622962i
$67$	0.863607	+	2.65791i	0.105506	+	0.324715i	0.989849	−	0.142123i	$-0.0453929\pi$
$67$	0.863607	+	2.65791i	0.105506	+	0.324715i	−0.884343	+	0.466838i	$0.845393\pi$
$68$	9.08535			1.10176
$69$	−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	$-0.301116\pi$
$72$	−2.78023	+	8.55667i	−0.327653	+	1.00841i
$73$	−7.91925	+	5.75367i	−0.926878	+	0.673416i	−0.945226	−	0.326415i	$-0.894159\pi$
$73$	−7.91925	+	5.75367i	−0.926878	+	0.673416i	0.0183484	+	0.999832i	$0.494159\pi$
$74$	2.76279			0.321168
$75$		0			0
$76$	19.9138			2.28427
$77$	−1.21048	+	0.879462i	−0.137947	+	0.100224i
$78$	−0.471215	+	1.45025i	−0.0533546	+	0.164209i
$79$	−1.46937	+	4.52227i	−0.165317	+	0.508795i	−0.999060	−	0.0433593i	$-0.986194\pi$
$79$	−1.46937	+	4.52227i	−0.165317	+	0.508795i	0.833742	+	0.552154i	$0.186194\pi$
$80$		0			0
$81$	0.309017	+	0.951057i	0.0343352	+	0.105673i
$82$	−3.98413			−0.439974
$83$	−3.61256	−	11.1183i	−0.396530	−	1.22039i	−0.927763	−	0.373169i	$-0.878271\pi$
$83$	−3.61256	−	11.1183i	−0.396530	−	1.22039i	0.531233	−	0.847226i	$-0.321729\pi$
$84$	−2.02580	−	1.47183i	−0.221033	−	0.160590i
$85$		0			0
$86$	−14.7292	+	10.7014i	−1.58829	+	1.15396i
$87$	−6.73458	−	4.89296i	−0.722023	−	0.524580i
$88$	−23.1572	−	16.8247i	−2.46856	−	1.79351i
$89$	5.01630	−	3.64456i	0.531727	−	0.386322i	−0.289277	−	0.957246i	$-0.593415\pi$
$89$	5.01630	−	3.64456i	0.531727	−	0.386322i	0.821003	+	0.570923i	$0.193415\pi$
$90$		0			0
$91$	−0.214377	−	0.155754i	−0.0224728	−	0.0163275i
$92$	3.73458	+	11.4938i	0.389357	+	1.19832i
$93$	−5.43656			−0.563745
$94$	−3.70785	−	11.4116i	−0.382436	−	1.17702i
$95$		0			0
$96$	5.89735	−	18.1502i	0.601895	−	1.85244i
$97$	−2.61256	+	8.04064i	−0.265265	+	0.816403i	0.726367	+	0.687307i	$0.241207\pi$
$97$	−2.61256	+	8.04064i	−0.265265	+	0.816403i	−0.991632	+	0.129096i	$0.958793\pi$
$98$	−14.8422	+	10.7835i	−1.49929	+	1.08930i
$99$	−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	$0.593727\pi$
$102$	−3.73607	+	2.71441i	−0.369926	+	0.268767i
$103$	4.35077	−	13.3903i	0.428694	−	1.31938i	−0.470718	−	0.882284i	$-0.656005\pi$
$103$	4.35077	−	13.3903i	0.428694	−	1.31938i	0.899412	−	0.437101i	$-0.143995\pi$
$104$	1.56651	−	4.82121i	0.153609	−	0.472758i
$105$		0			0
$106$	−5.89735	−	18.1502i	−0.572801	−	1.76290i
$107$	8.61207			0.832561			0.416280	−	0.909236i	$-0.363334\pi$
$107$	8.61207			0.832561			0.416280	+	0.909236i	$0.363334\pi$
$108$	−1.64533	−	5.06380i	−0.158322	−	0.487265i
$109$	−13.5005	−	9.80868i	−1.29311	−	0.939501i	−0.293249	−	0.956036i	$-0.594736\pi$
$109$	−13.5005	−	9.80868i	−1.29311	−	0.939501i	−0.999863	+	0.0165355i	$0.994736\pi$
$110$		0			0
$111$	−0.825886	+	0.600041i	−0.0783896	+	0.0569534i
$112$	5.21267	+	3.78723i	0.492551	+	0.357860i
$113$	9.52686	+	6.92167i	0.896211	+	0.651136i	0.937490	−	0.348012i	$-0.113143\pi$
$113$	9.52686	+	6.92167i	0.896211	+	0.651136i	−0.0412787	+	0.999148i	$0.513143\pi$
$114$	−8.18892	+	5.94960i	−0.766963	+	0.557231i
$115$		0			0
$116$	35.8576	+	26.0520i	3.32929	+	2.41887i
$117$	−0.174114	−	0.535867i	−0.0160968	−	0.0495409i
$118$	34.8362			3.20693
$119$	−0.247984	−	0.763215i	−0.0227326	−	0.0699638i
$120$		0			0
$121$	−0.271378	+	0.835215i	−0.0246707	+	0.0759286i
$122$	−0.106118	+	0.326598i	−0.00960749	+	0.0295688i
$123$	1.19098	−	0.865300i	0.107387	−	0.0780215i
$124$	28.9464			2.59946
$125$		0			0
$126$	1.27279			0.113389
$127$	1.43910	−	1.04557i	0.127699	−	0.0927790i	−0.522102	−	0.852883i	$-0.674852\pi$
$127$	1.43910	−	1.04557i	0.127699	−	0.0927790i	0.649801	+	0.760104i	$0.274852\pi$
$128$	−8.48418	+	26.1116i	−0.749903	+	2.30796i
$129$	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	$0.983246\pi$
$132$	16.9395			1.47439
$133$	−0.543545	−	1.67286i	−0.0471313	−	0.145055i
$134$	6.11895	+	4.44568i	0.528597	+	0.384048i
$135$		0			0
$136$	12.4202	−	9.02378i	1.06502	−	0.773783i
$137$	−4.13902	−	3.00717i	−0.353620	−	0.256920i	0.396766	−	0.917920i	$-0.370132\pi$
$137$	−4.13902	−	3.00717i	−0.353620	−	0.256920i	−0.750386	+	0.661000i	$0.770132\pi$
$138$	−4.96973	−	3.61072i	−0.423051	−	0.307365i
$139$	6.66482	−	4.84228i	0.565303	−	0.410717i	−0.268093	−	0.963393i	$-0.586393\pi$
$139$	6.66482	−	4.84228i	0.565303	−	0.410717i	0.833396	+	0.552676i	$0.186393\pi$
$140$		0			0
$141$	3.58684	+	2.60599i	0.302066	+	0.219464i
$142$	−13.4192	−	41.3000i	−1.12611	−	3.46581i
$143$	1.79259			0.149904
$144$	4.23366	+	13.0299i	0.352805	+	1.08582i
$145$		0			0
$146$	−8.18643	+	25.1952i	−0.677514	+	2.08517i
$147$	2.09477	−	6.44704i	0.172774	−	0.531743i
$148$	4.39735	−	3.19486i	0.361460	−	0.262616i
$149$	−10.0585			−0.824027			−0.412014	−	0.911178i	$-0.635174\pi$
$149$	−10.0585			−0.824027			−0.412014	+	0.911178i	$0.635174\pi$
$150$		0			0
$151$	−11.9810			−0.974999			−0.487500	−	0.873123i	$-0.662091\pi$
$151$	−11.9810			−0.974999			−0.487500	+	0.873123i	$0.662091\pi$
$152$	27.2232	−	19.7788i	2.20810	−	1.60428i
$153$	0.527295	−	1.62285i	0.0426293	−	0.131199i
$154$	−1.25132	+	3.85115i	−0.100834	+	0.310335i
$155$		0			0
$156$	0.927051	+	2.85317i	0.0742235	+	0.228436i
$157$	−19.5960			−1.56393			−0.781967	−	0.623319i	$-0.785784\pi$
$157$	−19.5960			−1.56393			−0.781967	+	0.623319i	$0.785784\pi$
$158$	3.97666	+	12.2389i	0.316366	+	0.973674i
$159$	5.70487	+	4.14483i	0.452426	+	0.328707i
$160$		0			0
$161$	0.863607	−	0.627447i	0.0680618	−	0.0494498i
$162$	2.18949	+	1.59076i	0.172023	+	0.124982i
$163$	9.62137	+	6.99033i	0.753604	+	0.547525i	0.896942	−	0.442149i	$-0.145784\pi$
$163$	9.62137	+	6.99033i	0.753604	+	0.547525i	−0.143338	+	0.989674i	$0.545784\pi$
$164$	−6.34127	+	4.60720i	−0.495170	+	0.359762i
$165$		0			0
$166$	−25.5963	−	18.5968i	−1.98665	−	1.44339i
$167$	1.85218	+	5.70042i	0.143326	+	0.441112i	0.996792	−	0.0800367i	$-0.0255038\pi$
$167$	1.85218	+	5.70042i	0.143326	+	0.441112i	−0.853466	+	0.521149i	$0.825504\pi$
$168$	−4.23125			−0.326448
$169$	−3.91912	−	12.0618i	−0.301471	−	0.927831i
$170$		0			0
$171$	1.15575	−	3.55705i	0.0883828	−	0.272014i
$172$	−11.0685	+	34.0653i	−0.843964	+	2.59745i
$173$	14.0157	−	10.1830i	1.06560	−	0.774201i	0.0904807	−	0.995898i	$-0.471160\pi$
$173$	14.0157	−	10.1830i	1.06560	−	0.774201i	0.975116	+	0.221697i	$0.0711596\pi$
$174$	−22.5288			−1.70791
$175$		0			0
$176$	−43.5875			−3.28553
$177$	−10.4136	+	7.56596i	−0.782738	+	0.568692i
$178$	5.18554	−	15.9595i	0.388673	−	1.19621i
$179$	3.26832	−	10.0588i	0.244285	−	0.751833i	−0.751468	−	0.659770i	$-0.770654\pi$
$179$	3.26832	−	10.0588i	0.244285	−	0.751833i	0.995753	−	0.0920634i	$-0.0293462\pi$
$180$		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	$0.753123\pi$
$182$	−0.717144			−0.0531583
$183$	−0.0392107	−	0.120678i	−0.00289854	−	0.00892077i
$184$	16.5213	+	12.0035i	1.21797	+	0.884906i
$185$		0			0
$186$	−11.9033	+	8.64825i	−0.872792	+	0.634121i
$187$	4.39195	+	3.19094i	0.321172	+	0.233345i
$188$	−19.0977	−	13.8753i	−1.39285	−	1.01196i
$189$	−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	$0.929795\pi$
$192$	−7.49304	−	23.0612i	−0.540763	−	1.66430i
$193$	−25.2063			−1.81439			−0.907194	−	0.420713i	$-0.861780\pi$
$193$	−25.2063			−1.81439			−0.907194	+	0.420713i	$0.861780\pi$
$194$	7.07054	+	21.7609i	0.507635	+	1.56234i
$195$		0			0
$196$	−11.1534	+	34.3266i	−0.796671	+	2.45190i
$197$	−3.73672	+	11.5004i	−0.266230	+	0.819372i	0.725177	+	0.688562i	$0.241758\pi$
$197$	−3.73672	+	11.5004i	−0.266230	+	0.819372i	−0.991407	+	0.130810i	$0.958242\pi$
$198$	−6.96582	+	5.06097i	−0.495040	+	0.359667i
$199$	−0.544434			−0.0385939			−0.0192970	−	0.999814i	$-0.506143\pi$
$199$	−0.544434			−0.0385939			−0.0192970	+	0.999814i	$0.506143\pi$
$200$		0			0
$201$	−2.79469			−0.197122
$202$	−12.7719	+	9.27930i	−0.898625	+	0.652889i
$203$	1.20978	−	3.72331i	0.0849096	−	0.261325i
$204$	−2.80753	+	8.64068i	−0.196566	+	0.604969i
$205$		0			0
$206$	−11.7748	−	36.2390i	−0.820386	−	2.52489i
$207$	2.26981			0.157762
$208$	−2.38543	−	7.34160i	−0.165400	−	0.509048i
$209$	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	$0.265726\pi$
$212$	−30.3750	−	22.0687i	−2.08616	−	1.51569i
$213$	12.9812	+	9.43140i	0.889457	+	0.646229i
$214$	18.8561	−	13.6997i	1.28897	−	0.936495i
$215$		0			0
$216$	−7.27874	−	5.28832i	−0.495256	−	0.359824i
$217$	−0.790089	−	2.43164i	−0.0536347	−	0.165071i
$218$	−45.1625			−3.05879
$219$	−3.02488	−	9.30964i	−0.204403	−	0.629087i
$220$		0			0
$221$	−0.297101	+	0.914384i	−0.0199852	+	0.0615081i
$222$	−0.853750	+	2.62757i	−0.0573000	+	0.176351i
$223$	0.274358	−	0.199333i	0.0183724	−	0.0133483i	−0.578561	−	0.815639i	$-0.696386\pi$
$223$	0.274358	−	0.199333i	0.0183724	−	0.0133483i	0.596934	+	0.802291i	$0.296386\pi$
$224$	8.97519			0.599680
$225$		0			0
$226$	31.8697			2.11994
$227$	−1.44690	+	1.05123i	−0.0960341	+	0.0697729i	−0.634766	−	0.772704i	$-0.718904\pi$
$227$	−1.44690	+	1.05123i	−0.0960341	+	0.0697729i	0.538732	+	0.842477i	$0.318904\pi$
$228$	−6.15370	+	18.9391i	−0.407538	+	1.25427i
$229$	−8.64730	+	26.6137i	−0.571430	+	1.75868i	0.0765965	+	0.997062i	$0.475595\pi$
$229$	−8.64730	+	26.6137i	−0.571430	+	1.75868i	−0.648026	+	0.761618i	$0.724405\pi$
$230$		0			0
$231$	−0.462361	−	1.42300i	−0.0304211	−	0.0936265i
$232$	74.8948			4.91708
$233$	2.09328	+	6.44246i	0.137135	+	0.422059i	0.995916	−	0.0902840i	$-0.0287775\pi$
$233$	2.09328	+	6.44246i	0.137135	+	0.422059i	−0.858781	+	0.512343i	$0.828777\pi$
$234$	−1.23366	−	0.896304i	−0.0806467	−	0.0585932i
$235$		0			0
$236$	55.4464	−	40.2841i	3.60925	−	2.62227i
$237$	−3.84687	−	2.79491i	−0.249881	−	0.181549i
$238$	−1.75705	−	1.27657i	−0.113893	−	0.0827479i
$239$	5.24514	−	3.81081i	0.339280	−	0.246501i	−0.405078	−	0.914282i	$-0.632756\pi$
$239$	5.24514	−	3.81081i	0.339280	−	0.246501i	0.744358	+	0.667781i	$0.232756\pi$
$240$		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	$0.622885\pi$
$242$	0.734446	+	2.26039i	0.0472120	+	0.145304i
$243$	−1.00000			−0.0641500
$244$	0.208773	+	0.642537i	0.0133653	+	0.0411342i
$245$		0			0
$246$	1.23116	−	3.78914i	0.0784962	−	0.241586i
$247$	−0.651203	+	2.00420i	−0.0414351	+	0.127524i
$248$	39.5713	−	28.7502i	2.51278	−	1.82564i
$249$	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	$0.546396\pi$
$252$	2.02580	−	1.47183i	0.127614	−	0.0927168i
$253$	−2.23152	+	6.86790i	−0.140294	+	0.431781i
$254$	1.48765	−	4.57852i	0.0933435	−	0.287282i
$255$		0			0
$256$	7.97520	+	24.5451i	0.498450	+	1.53407i
$257$	5.79485			0.361473			0.180736	−	0.983532i	$-0.442152\pi$
$257$	5.79485			0.361473			0.180736	+	0.983532i	$0.442152\pi$
$258$	−5.62605	−	17.3152i	−0.350262	−	1.07800i
$259$	−0.388409	−	0.282196i	−0.0241346	−	0.0175348i
$260$		0			0
$261$	6.73458	−	4.89296i	0.416860	−	0.302866i
$262$	−12.9587	−	9.41507i	−0.800593	−	0.581665i
$263$	11.5680	+	8.40467i	0.713316	+	0.518254i	0.884242	−	0.467030i	$-0.154676\pi$
$263$	11.5680	+	8.40467i	0.713316	+	0.518254i	−0.170926	+	0.985284i	$0.554676\pi$
$264$	23.1572	−	16.8247i	1.42522	−	1.03549i
$265$		0			0
$266$	−3.85120	−	2.79806i	−0.236132	−	0.171560i
$267$	1.91606	+	5.89701i	0.117261	+	0.360891i
$268$	14.8800			0.908943
$269$	−5.93945	−	18.2797i	−0.362135	−	1.11454i	−0.951756	−	0.306856i	$-0.900723\pi$
$269$	−5.93945	−	18.2797i	−0.362135	−	1.11454i	0.589621	−	0.807680i	$-0.299277\pi$
$270$		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	$0.850514\pi$
$272$	7.22415	−	22.2337i	0.438029	−	1.34811i
$273$	0.214377	−	0.155754i	0.0129747	−	0.00942666i
$274$	−13.8460			−0.836470
$275$		0			0
$276$	−12.0853			−0.727452
$277$	17.7102	−	12.8672i	1.06410	−	0.773115i	0.0892586	−	0.996008i	$-0.471550\pi$
$277$	17.7102	−	12.8672i	1.06410	−	0.773115i	0.974843	+	0.222894i	$0.0715502\pi$
$278$	6.88968	−	21.2043i	0.413216	−	1.27175i
$279$	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	$0.600151\pi$
$282$	11.9989			0.714522
$283$	−5.03926	−	15.5093i	−0.299553	−	0.921929i	−0.981654	−	0.190671i	$-0.938934\pi$
$283$	−5.03926	−	15.5093i	−0.299553	−	0.921929i	0.682101	−	0.731258i	$-0.261066\pi$
$284$	−69.1171	−	50.2165i	−4.10134	−	2.97980i
$285$		0			0
$286$	3.92485	−	2.85157i	0.232081	−	0.168617i
$287$	0.560112	+	0.406945i	0.0330624	+	0.0240212i
$288$	15.4395	+	11.2174i	0.909778	+	0.660993i
$289$	11.3977	−	8.28091i	0.670453	−	0.487112i
$290$		0			0
$291$	−6.83978	−	4.96939i	−0.400955	−	0.291311i
$292$	16.1057	+	49.5682i	0.942514	+	2.90076i
$293$	−5.46407			−0.319214			−0.159607	−	0.987181i	$-0.551023\pi$
$293$	−5.46407			−0.319214			−0.159607	+	0.987181i	$0.551023\pi$
$294$	−5.66921	−	17.4480i	−0.330635	−	1.01759i
$295$		0			0
$296$	2.83820	−	8.73509i	0.164967	−	0.507717i
$297$	0.983131	−	3.02577i	0.0570470	−	0.175573i
$298$	−22.0231	+	16.0007i	−1.27576	+	0.926897i
$299$	−1.27891			−0.0739612
$300$		0			0
$301$	3.16377			0.182357
$302$	−26.2323	+	19.0589i	−1.50950	+	1.09672i
$303$	1.80257	−	5.54775i	0.103555	−	0.318710i
$304$	15.8343	−	48.7330i	0.908160	−	2.79503i
$305$		0			0
$306$	−1.42705	−	4.39201i	−0.0815791	−	0.251075i
$307$	21.4194			1.22247			0.611235	−	0.791450i	$-0.290673\pi$
$307$	21.4194			1.22247			0.611235	+	0.791450i	$0.290673\pi$
$308$	2.46179	+	7.57662i	0.140274	+	0.431718i
$309$	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	$0.274233\pi$
$312$	4.10116	+	2.97967i	0.232183	+	0.168691i
$313$	11.6802	+	8.48616i	0.660204	+	0.479666i	0.866732	−	0.498774i	$-0.166216\pi$
$313$	11.6802	+	8.48616i	0.660204	+	0.479666i	−0.206528	+	0.978441i	$0.566216\pi$
$314$	−42.9054	+	31.1726i	−2.42129	+	1.75917i
$315$		0			0
$316$	20.4823	+	14.8812i	1.15222	+	0.837135i
$317$	−6.98695	−	21.5036i	−0.392426	−	1.20776i	−0.930948	−	0.365152i	$-0.881017\pi$
$317$	−6.98695	−	21.5036i	−0.392426	−	1.20776i	0.538522	−	0.842611i	$-0.318983\pi$
$318$	19.0842			1.07019
$319$	8.18397	+	25.1877i	0.458214	+	1.41024i
$320$		0			0
$321$	−2.66128	+	8.19057i	−0.148538	+	0.457153i
$322$	0.892743	−	2.74758i	0.0497506	−	0.153117i
$323$	−5.16312	+	3.75123i	−0.287284	+	0.208724i
$324$	5.32440			0.295800
$325$		0			0
$326$	32.1859			1.78261
$327$	13.5005	−	9.80868i	0.746578	−	0.542421i
$328$	−4.09288	+	12.5966i	−0.225991	+	0.695530i
$329$	−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	$0.866113\pi$
$332$	−62.2448			−3.41613
$333$	−0.315460	−	0.970887i	−0.0172871	−	0.0532043i
$334$	13.1233	+	9.53466i	0.718077	+	0.521713i
$335$		0			0
$336$	−5.21267	+	3.78723i	−0.284375	+	0.206610i
$337$	14.1459	+	10.2776i	0.770576	+	0.559856i	0.902136	−	0.431452i	$-0.141999\pi$
$337$	14.1459	+	10.2776i	0.770576	+	0.559856i	−0.131560	+	0.991308i	$0.541999\pi$
$338$	−27.7683	−	20.1749i	−1.51040	−	1.09737i
$339$	−9.52686	+	6.92167i	−0.517428	+	0.375933i
$340$		0			0
$341$	13.9930	+	10.1665i	0.757763	+	0.550547i
$342$	−3.12789	−	9.62666i	−0.169137	−	0.520550i
$343$	6.48010			0.349893
$344$	18.7032	+	57.5626i	1.00841	+	3.10357i
$345$		0			0
$346$	14.4886	−	44.5913i	0.778912	−	2.39724i
$347$	7.13647	−	21.9638i	0.383106	−	1.17908i	−0.554739	−	0.832024i	$-0.687182\pi$
$347$	7.13647	−	21.9638i	0.383106	−	1.17908i	0.937845	−	0.347055i	$-0.112818\pi$
$348$	−35.8576	+	26.0520i	−1.92217	+	1.39654i
$349$	−9.32650			−0.499236			−0.249618	−	0.968344i	$-0.580305\pi$
$349$	−9.32650			−0.499236			−0.249618	+	0.968344i	$0.580305\pi$
$350$		0			0
$351$	0.563444			0.0300744
$352$	−49.1203	+	35.6880i	−2.61812	+	1.90218i
$353$	−9.87219	+	30.3835i	−0.525444	+	1.61715i	0.237993	+	0.971267i	$0.423510\pi$
$353$	−9.87219	+	30.3835i	−0.525444	+	1.61715i	−0.763437	+	0.645883i	$0.776490\pi$
$354$	−10.7650	+	33.1312i	−0.572152	+	1.76090i
$355$		0			0
$356$	−10.2018	−	31.3980i	−0.540697	−	1.66409i
$357$	0.802492			0.0424724
$358$	−8.84525	−	27.2229i	−0.467486	−	1.43877i
$359$	7.75810	+	5.63659i	0.409457	+	0.297488i	0.773382	−	0.633940i	$-0.218564\pi$
$359$	7.75810	+	5.63659i	0.409457	+	0.297488i	−0.363925	+	0.931428i	$0.618564\pi$
$360$		0			0
$361$	4.05451	−	2.94577i	0.213395	−	0.155041i
$362$	26.2298	+	19.0571i	1.37861	+	1.00162i
$363$	−0.710476	−	0.516191i	−0.0372903	−	0.0270930i
$364$	−1.14143	+	0.829296i	−0.0598271	+	0.0434669i
$365$		0			0
$366$	−0.277821	−	0.201849i	−0.0145219	−	0.0105508i
$367$	−0.328866	−	1.01215i	−0.0171667	−	0.0528336i	0.942106	−	0.335315i	$-0.108843\pi$
$367$	−0.328866	−	1.01215i	−0.0171667	−	0.0528336i	−0.959273	+	0.282481i	$0.908843\pi$
$368$	31.0973			1.62106
$369$	0.454915	+	1.40008i	0.0236819	+	0.0728855i
$370$		0			0
$371$	−1.02480	+	3.15402i	−0.0532051	+	0.163748i
$372$	−8.94492	+	27.5296i	−0.463773	+	1.42735i
$373$	−3.33333	+	2.42181i	−0.172593	+	0.125396i	−0.670728	−	0.741703i	$-0.734018\pi$
$373$	−3.33333	+	2.42181i	−0.172593	+	0.125396i	0.498135	+	0.867099i	$0.334018\pi$
$374$	14.6922			0.759714
$375$		0			0
$376$	−39.8890			−2.05712
$377$	−3.79456	+	2.75691i	−0.195430	+	0.141988i
$378$	−0.393313	+	1.21049i	−0.0202298	+	0.0622610i
$379$	3.20027	−	9.84942i	0.164387	−	0.505931i	−0.834604	−	0.550851i	$-0.814303\pi$
$379$	3.20027	−	9.84942i	0.164387	−	0.505931i	0.998991	+	0.0449201i	$0.0143033\pi$
$380$		0			0
$381$	0.549687	+	1.69176i	0.0281613	+	0.0866716i
$382$	−49.4336			−2.52924
$383$	−0.370619	−	1.14065i	−0.0189378	−	0.0582845i	0.941141	−	0.338014i	$-0.109755\pi$
$383$	−0.370619	−	1.14065i	−0.0189378	−	0.0582845i	−0.960079	+	0.279730i	$0.909755\pi$
$384$	−22.2119	−	16.1379i	−1.13350	−	0.823533i
$385$		0			0
$386$	−55.1890	+	40.0971i	−2.80904	+	2.04089i
$387$	5.44243	+	3.95416i	0.276654	+	0.201001i
$388$	36.4177	+	26.4590i	1.84883	+	1.34325i
$389$	−10.1971	+	7.40861i	−0.517012	+	0.375631i	−0.815477	−	0.578789i	$-0.803525\pi$
$389$	−10.1971	+	7.40861i	−0.517012	+	0.375631i	0.298465	+	0.954421i	$0.403525\pi$
$390$		0			0
$391$	−3.13341	−	2.27656i	−0.158464	−	0.115130i
$392$	18.8467	+	58.0042i	0.951902	+	2.92965i
$393$	5.91860			0.298554
$394$	10.1129	+	31.1243i	0.509481	+	1.56802i
$395$		0			0
$396$	−5.23458	+	16.1104i	−0.263047	+	0.809577i
$397$	0.405848	−	1.24907i	0.0203689	−	0.0626891i	−0.940355	−	0.340194i	$-0.889507\pi$
$397$	0.405848	−	1.24907i	0.0203689	−	0.0626891i	0.960724	+	0.277505i	$0.0895074\pi$
$398$	−1.19204	+	0.866064i	−0.0597513	+	0.0434119i
$399$	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	$0.368280\pi$
$402$	−6.11895	+	4.44568i	−0.305186	+	0.221730i
$403$	−0.946580	+	2.91327i	−0.0471525	+	0.145120i
$404$	−9.59762	+	29.5384i	−0.477499	+	1.46959i
$405$		0			0
$406$	−3.27409	−	10.0766i	−0.162490	−	0.500094i
$407$	3.24782			0.160988
$408$	4.74408	+	14.6008i	0.234867	+	0.722847i
$409$	−17.1188	−	12.4375i	−0.846471	−	0.614997i	0.0776999	−	0.996977i	$-0.475242\pi$
$409$	−17.1188	−	12.4375i	−0.846471	−	0.614997i	−0.924171	+	0.381980i	$0.875242\pi$
$410$		0			0
$411$	4.13902	−	3.00717i	0.204163	−	0.148333i
$412$	−60.6473	−	44.0629i	−2.98788	−	2.17082i
$413$	−4.89748	−	3.55823i	−0.240989	−	0.175089i
$414$	4.96973	−	3.61072i	0.244249	−	0.177457i
$415$		0			0
$416$	−8.69927	−	6.32039i	−0.426517	−	0.309883i
$417$	2.54574	+	7.83497i	0.124665	+	0.383680i
$418$	32.2031			1.57511
$419$	−2.06144	−	6.34445i	−0.100708	−	0.309946i	0.887991	−	0.459860i	$-0.152100\pi$
$419$	−2.06144	−	6.34445i	−0.100708	−	0.309946i	−0.988699	+	0.149914i	$0.952100\pi$
$420$		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	$-0.131659\pi$
$422$	2.61102	−	8.03590i	0.127103	−	0.391181i
$423$	−3.58684	+	2.60599i	−0.174398	+	0.126708i
$424$	−63.4435			−3.08109
$425$		0			0
$426$	43.4253			2.10396
$427$	0.0482780	−	0.0350760i	0.00233633	−	0.00169745i
$428$	14.1697	−	43.6098i	0.684918	−	2.10796i
$429$	−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	$0.804290\pi$
$432$	−13.7004			−0.659161
$433$	10.4587	+	32.1887i	0.502614	+	1.54689i	0.804744	+	0.593622i	$0.202302\pi$
$433$	10.4587	+	32.1887i	0.502614	+	1.54689i	−0.302130	+	0.953267i	$0.597698\pi$
$434$	−5.59805	−	4.06722i	−0.268715	−	0.195233i
$435$		0			0
$436$	−71.8819	+	52.2253i	−3.44252	+	2.50114i
$437$	−6.86799	−	4.98989i	−0.328541	−	0.238699i
$438$	−21.4324	−	15.5715i	−1.02408	−	0.744036i
$439$	16.9614	−	12.3231i	0.809521	−	0.588152i	−0.104171	−	0.994559i	$-0.533219\pi$
$439$	16.9614	−	12.3231i	0.809521	−	0.588152i	0.913692	+	0.406408i	$0.133219\pi$
$440$		0			0
$441$	5.48418	+	3.98449i	0.261152	+	0.189738i
$442$	0.804064	+	2.47465i	0.0382454	+	0.117707i
$443$	−6.04847			−0.287371			−0.143686	−	0.989623i	$-0.545895\pi$
$443$	−6.04847			−0.287371			−0.143686	+	0.989623i	$0.545895\pi$
$444$	1.67964	+	5.16939i	0.0797120	+	0.245328i
$445$		0			0
$446$	0.283614	−	0.872875i	0.0134295	−	0.0413318i
$447$	3.10826	−	9.56624i	0.147016	−	0.452467i
$448$	9.22577	−	6.70292i	0.435877	−	0.316683i
$449$	15.5896			0.735721			0.367860	−	0.929881i	$-0.380090\pi$
$449$	15.5896			0.735721			0.367860	+	0.929881i	$0.380090\pi$
$450$		0			0
$451$	−4.68357			−0.220541
$452$	50.7248	−	36.8537i	2.38589	−	1.73345i
$453$	3.70233	−	11.3946i	0.173951	−	0.535365i
$454$	−1.49572	+	4.60334i	−0.0701974	+	0.216046i
$455$		0			0
$456$	10.3983	+	32.0028i	0.486947	+	1.49867i
$457$	2.50193			0.117035			0.0585176	−	0.998286i	$-0.481363\pi$
$457$	2.50193			0.117035			0.0585176	+	0.998286i	$0.481363\pi$
$458$	23.4027	+	72.0262i	1.09354	+	3.36556i
$459$	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	$0.298859\pi$
$462$	−3.27599	−	2.38014i	−0.152413	−	0.110734i
$463$	−9.41102	−	6.83751i	−0.437367	−	0.317766i	0.347221	−	0.937783i	$-0.387125\pi$
$463$	−9.41102	−	6.83751i	−0.437367	−	0.317766i	−0.784588	+	0.620018i	$0.787125\pi$
$464$	92.2664	−	67.0355i	4.28336	−	3.11204i
$465$		0			0
$466$	14.8316	+	10.7758i	0.687062	+	0.499180i
$467$	−0.145329	−	0.447276i	−0.00672502	−	0.0206975i	0.947638	−	0.319347i	$-0.103464\pi$
$467$	−0.145329	−	0.447276i	−0.00672502	−	0.0206975i	−0.954363	+	0.298650i	$0.903464\pi$
$468$	−3.00000			−0.138675
$469$	−0.406149	−	1.25000i	−0.0187542	−	0.0577196i
$470$		0			0
$471$	6.05551	−	18.6369i	0.279023	−	0.858745i
$472$	35.7871	−	110.141i	1.64723	−	5.06966i
$473$	−17.3150	+	12.5801i	−0.796143	+	0.578432i
$474$	−12.8687			−0.591080
$475$		0			0
$476$	−4.27279			−0.195843
$477$	−5.70487	+	4.14483i	−0.261208	+	0.189779i
$478$	5.42210	−	16.6875i	0.248001	−	0.763269i
$479$	3.83534	−	11.8040i	0.175241	−	0.539337i	−0.824403	−	0.566003i	$-0.808489\pi$
$479$	3.83534	−	11.8040i	0.175241	−	0.539337i	0.999644	+	0.0266660i	$0.00848907\pi$
$480$		0			0
$481$	0.177744	+	0.547041i	0.00810444	+	0.0249429i
$482$	20.1585			0.918196
$483$	0.329868	+	1.01523i	0.0150095	+	0.0461946i
$484$	3.78286	+	2.74841i	0.171948	+	0.124928i
$485$		0			0
$486$	−2.18949	+	1.59076i	−0.0993174	+	0.0721583i
$487$	27.9633	+	20.3165i	1.26714	+	0.920631i	0.999085	−	0.0427731i	$-0.0136193\pi$
$487$	27.9633	+	20.3165i	1.26714	+	0.920631i	0.268055	+	0.963404i	$0.413619\pi$
$488$	0.923588	+	0.671026i	0.0418088	+	0.0303759i
$489$	−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	$0.510383\pi$
$492$	−2.42215	−	7.45460i	−0.109199	−	0.336080i
$493$	−14.2044			−0.639736
$494$	1.76239	+	5.42408i	0.0792938	+	0.244041i
$495$		0			0
$496$	23.0165	−	70.8375i	1.03347	−	3.18070i
$497$	−2.33190	+	7.17684i	−0.104600	+	0.321925i
$498$	25.5963	−	18.5968i	1.14700	−	0.833341i
$499$	12.6037			0.564220			0.282110	−	0.959382i	$-0.408966\pi$
$499$	12.6037			0.564220			0.282110	+	0.959382i	$0.408966\pi$
$500$		0			0
$501$	−5.99378			−0.267782
$502$	−10.0764	+	7.32094i	−0.449732	+	0.326750i
$503$	−9.26827	+	28.5248i	−0.413252	+	1.27186i	0.500554	+	0.865705i	$0.333130\pi$
$503$	−9.26827	+	28.5248i	−0.413252	+	1.27186i	−0.913805	+	0.406152i	$0.866870\pi$
$504$	1.30753	−	4.02415i	0.0582419	−	0.179250i
$505$		0			0
$506$	6.03929	+	18.5870i	0.268479	+	0.826294i
$507$	12.6825			0.563251
$508$	−2.92675	−	9.00761i	−0.129854	−	0.399648i
$509$	0.377802	+	0.274489i	0.0167458	+	0.0121665i	0.596127	−	0.802890i	$-0.296706\pi$
$509$	0.377802	+	0.274489i	0.0167458	+	0.0121665i	−0.579381	+	0.815057i	$0.696706\pi$
$510$		0			0
$511$	3.72438	−	2.70592i	0.164757	−	0.119703i
$512$	12.0833	+	8.77902i	0.534011	+	0.387982i
$513$	3.02580	+	2.19838i	0.133593	+	0.0970607i
$514$	12.6878	−	9.21822i	0.559634	−	0.406598i
$515$		0			0
$516$	−28.9777	−	21.0535i	−1.27567	−	0.926829i
$517$	−4.35878	−	13.4150i	−0.191699	−	0.589989i
$518$	−1.29933			−0.0570891
$519$	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	$0.976417\pi$
$522$	6.96179	−	21.4262i	0.304709	−	0.937799i
$523$	32.8849	−	23.8922i	1.43795	−	1.04473i	0.449489	−	0.893286i	$-0.351606\pi$
$523$	32.8849	−	23.8922i	1.43795	−	1.04473i	0.988465	−	0.151449i	$-0.0483940\pi$
$524$	−31.5130			−1.37665
$525$		0			0
$526$	38.6980			1.68731
$527$	−7.50503	+	5.45273i	−0.326924	+	0.237525i
$528$	13.4693	−	41.4542i	0.586175	−	1.80406i
$529$	−5.51533	+	16.9744i	−0.239797	+	0.738019i
$530$		0			0
$531$	−3.97766	−	12.2420i	−0.172616	−	0.531256i
$532$	−9.36533			−0.406039
$533$	−0.256319	−	0.788869i	−0.0111024	−	0.0341697i
$534$	13.5759	+	9.86349i	0.587488	+	0.426835i
$535$		0			0
$536$	20.3418	−	14.7792i	0.878633	−	0.638364i
$537$	8.55656	+	6.21671i	0.369243	+	0.268271i
$538$	−42.0831	−	30.5751i	−1.81433	−	1.31819i
$539$	−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	$0.686441\pi$
$542$	19.4386	+	59.8259i	0.834960	+	2.56974i
$543$	−11.9799			−0.514105
$544$	−10.0630	−	30.9707i	−0.431448	−	1.32786i
$545$		0			0
$546$	0.221610	−	0.682045i	0.00948402	−	0.0291888i
$547$	−10.8324	+	33.3386i	−0.463158	+	1.42545i	0.398126	+	0.917331i	$0.369661\pi$
$547$	−10.8324	+	33.3386i	−0.463158	+	1.42545i	−0.861284	+	0.508124i	$0.830339\pi$
$548$	−22.0378	+	16.0114i	−0.941407	+	0.683972i
$549$	0.126888			0.00541546
$550$		0			0
$551$	−31.1341			−1.32636
$552$	−16.5213	+	12.0035i	−0.703195	+	0.510901i
$553$	0.691038	−	2.12680i	0.0293859	−	0.0904405i
$554$	18.3077	−	56.3453i	0.777819	−	2.39388i
$555$		0			0
$556$	−13.5545	−	41.7165i	−0.574839	−	1.76917i
$557$	−19.2383			−0.815154			−0.407577	−	0.913171i	$-0.633626\pi$
$557$	−19.2383			−0.815154			−0.407577	+	0.913171i	$0.633626\pi$
$558$	−4.54666	−	13.9932i	−0.192475	−	0.592378i
$559$	−3.06651	−	2.22795i	−0.129699	−	0.0942321i
$560$		0			0
$561$	−4.39195	+	3.19094i	−0.185428	+	0.134722i
$562$	59.3655	+	43.1316i	2.50418	+	1.81940i
$563$	−23.6023	−	17.1481i	−0.994720	−	0.722707i	−0.0337705	−	0.999430i	$-0.510752\pi$
$563$	−23.6023	−	17.1481i	−0.994720	−	0.722707i	−0.960950	+	0.276723i	$0.910752\pi$
$564$	19.0977	−	13.8753i	0.804160	−	0.584257i
$565$		0			0
$566$	−35.7049	−	25.9411i	−1.50079	−	1.09039i
$567$	−0.145329	−	0.447276i	−0.00610324	−	0.0187838i
$568$	−144.363			−6.05734
$569$	−10.1701	−	31.3004i	−0.426354	−	1.31218i	−0.901692	−	0.432380i	$-0.857674\pi$
$569$	−10.1701	−	31.3004i	−0.426354	−	1.31218i	0.475338	−	0.879803i	$-0.342326\pi$
$570$		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	$-0.0881698\pi$
$572$	2.94939	−	9.07730i	0.123320	−	0.379541i
$573$	14.7773	−	10.7363i	0.617329	−	0.448515i
$574$	1.87371			0.0782073
$575$		0			0
$576$	24.2480			1.01033
$577$	27.9237	−	20.2878i	1.16248	−	0.844591i	0.172390	−	0.985029i	$-0.444851\pi$
$577$	27.9237	−	20.2878i	1.16248	−	0.844591i	0.990089	+	0.140438i	$0.0448511\pi$
$578$	11.7822	−	36.2620i	0.490076	−	1.50830i
$579$	7.78917	−	23.9726i	0.323707	−	0.996267i
$580$		0			0
$581$	1.69897	+	5.22888i	0.0704850	+	0.216931i
$582$	−22.8807			−0.948437
$583$	−6.93265	−	21.3365i	−0.287121	−	0.883668i
$584$	71.2496	+	51.7659i	2.94833	+	2.14209i
$585$		0			0
$586$	−11.9635	+	8.69202i	−0.494209	+	0.359064i
$587$	−18.0213	−	13.0932i	−0.743817	−	0.540414i	0.150087	−	0.988673i	$-0.452045\pi$
$587$	−18.0213	−	13.0932i	−0.743817	−	0.540414i	−0.893904	+	0.448258i	$0.852045\pi$
$588$	−29.2000	−	21.2150i	−1.20419	−	0.874893i
$589$	−16.4500	+	11.9516i	−0.677809	+	0.492457i
$590$		0			0
$591$	−9.78286	−	7.10766i	−0.402413	−	0.292370i
$592$	−4.32193	−	13.3015i	−0.177630	−	0.546690i
$593$	30.9158			1.26956			0.634779	−	0.772693i	$-0.281091\pi$
$593$	30.9158			1.26956			0.634779	+	0.772693i	$0.281091\pi$
$594$	−2.66071	−	8.18882i	−0.109170	−	0.335991i
$595$		0			0
$596$	−16.5496	+	50.9344i	−0.677898	+	2.08636i
$597$	0.168240	−	0.517788i	0.00688558	−	0.0211917i
$598$	−2.80016	+	2.03444i	−0.114507	+	0.0831943i
$599$	−24.0276			−0.981742			−0.490871	−	0.871232i	$-0.663321\pi$
$599$	−24.0276			−0.981742			−0.490871	+	0.871232i	$0.663321\pi$
$600$		0			0
$601$	−32.0387			−1.30688			−0.653442	−	0.756977i	$-0.726676\pi$
$601$	−32.0387			−1.30688			−0.653442	+	0.756977i	$0.726676\pi$
$602$	6.92705	−	5.03280i	0.282326	−	0.205121i
$603$	0.863607	−	2.65791i	0.0351688	−	0.108238i
$604$	−19.7127	+	60.6694i	−0.802097	+	2.46860i
$605$		0			0
$606$	−4.87842	−	15.0142i	−0.198172	−	0.609911i
$607$	−45.5915			−1.85050			−0.925251	−	0.379356i	$-0.876145\pi$
$607$	−45.5915			−1.85050			−0.925251	+	0.379356i	$0.876145\pi$
$608$	−22.0567	−	67.8834i	−0.894516	−	2.75304i
$609$	3.16723	+	2.30113i	0.128343	+	0.0932465i
$610$		0			0
$611$	2.02098	−	1.46833i	0.0817602	−	0.0594023i
$612$	−7.35020	−	5.34023i	−0.297114	−	0.215866i
$613$	−8.78299	−	6.38121i	−0.354742	−	0.257735i	0.396114	−	0.918201i	$-0.370359\pi$
$613$	−8.78299	−	6.38121i	−0.354742	−	0.257735i	−0.750855	+	0.660467i	$0.770359\pi$
$614$	46.8976	−	34.0731i	1.89263	−	1.37508i
$615$		0			0
$616$	10.8907	+	7.91254i	0.438798	+	0.318805i
$617$	4.97685	+	15.3172i	0.200360	+	0.616646i	0.999872	+	0.0159954i	$0.00509171\pi$
$617$	4.97685	+	15.3172i	0.200360	+	0.616646i	−0.799512	+	0.600651i	$0.794908\pi$
$618$	38.1039			1.53276
$619$	11.8533	+	36.4807i	0.476425	+	1.46628i	0.844026	+	0.536302i	$0.180179\pi$
$619$	11.8533	+	36.4807i	0.476425	+	1.46628i	−0.367602	+	0.929983i	$0.619821\pi$
$620$		0			0
$621$	−0.701409	+	2.15871i	−0.0281466	+	0.0866262i
$622$	2.38516	−	7.34076i	0.0956362	−	0.294338i
$623$	−2.35914	+	1.71401i	−0.0945168	+	0.0686705i
$624$	7.71941			0.309024
$625$		0			0
$626$	39.0732			1.56168
$627$	−9.62653	+	6.99409i	−0.384447	+	0.279317i
$628$	−32.2419	+	99.2305i	−1.28659	+	3.95973i
$629$	−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	$0.750562\pi$
$632$	42.7808			1.70173
$633$	0.964772	+	2.96926i	0.0383462	+	0.118018i
$634$	−49.5049	−	35.9674i	−1.96609	−	1.42845i
$635$		0			0
$636$	30.3750	−	22.0687i	1.20445	−	0.875082i
$637$	−3.09003	−	2.24504i	−0.122431	−	0.0889517i
$638$	57.9863	+	42.1295i	2.29570	+	1.66792i
$639$	−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	$0.878965\pi$
$642$	7.20238	+	22.1666i	0.284255	+	0.874848i
$643$	25.9062			1.02164			0.510821	−	0.859687i	$-0.329341\pi$
$643$	25.9062			1.02164			0.510821	+	0.859687i	$0.329341\pi$
$644$	−1.75635	−	5.40549i	−0.0692099	−	0.213006i
$645$		0			0
$646$	−5.33731	+	16.4266i	−0.209994	+	0.646295i
$647$	6.69401	−	20.6021i	0.263169	−	0.809950i	−0.728941	−	0.684577i	$-0.759987\pi$
$647$	6.69401	−	20.6021i	0.263169	−	0.809950i	0.992110	−	0.125374i	$-0.0400129\pi$
$648$	7.27874	−	5.28832i	0.285936	−	0.207745i
$649$	40.9519			1.60750
$650$		0			0
$651$	2.55678			0.100208
$652$	51.2280	−	37.2193i	2.00624	−	1.45762i
$653$	−3.45405	+	10.6305i	−0.135167	+	0.416002i	−0.995616	−	0.0935349i	$-0.970183\pi$
$653$	−3.45405	+	10.6305i	−0.135167	+	0.416002i	0.860449	+	0.509537i	$0.170183\pi$
$654$	13.9560	−	42.9521i	0.545722	−	1.67956i
$655$		0			0
$656$	6.23252	+	19.1817i	0.243339	+	0.748920i
$657$	9.78873			0.381895
$658$	1.74378	+	5.36681i	0.0679797	+	0.209220i
$659$	−10.9010	−	7.92006i	−0.424644	−	0.308522i	0.354860	−	0.934919i	$-0.384529\pi$
$659$	−10.9010	−	7.92006i	−0.424644	−	0.308522i	−0.779503	+	0.626398i	$0.784529\pi$
$660$		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	$0.150569\pi$
$662$	8.46556	+	6.15059i	0.329023	+	0.239049i
$663$	−0.777821	−	0.565120i	−0.0302081	−	0.0219474i
$664$	−85.0921	+	61.8230i	−3.30221	+	2.39920i
$665$		0			0
$666$	−2.23515	−	1.62393i	−0.0866102	−	0.0629260i
$667$	−5.83880	−	17.9700i	−0.226079	−	0.695801i
$668$	31.9132			1.23476
$669$	0.104795	+	0.322527i	0.00405162	+	0.0124696i
$670$		0			0
$671$	−0.124748	+	0.383934i	−0.00481584	+	0.0148216i
$672$	−2.77349	+	8.53592i	−0.106990	+	0.329280i
$673$	15.2412	−	11.0734i	0.587507	−	0.426849i	−0.253916	−	0.967226i	$-0.581719\pi$
$673$	15.2412	−	11.0734i	0.587507	−	0.426849i	0.841423	+	0.540378i	$0.181719\pi$
$674$	47.3215			1.82276
$675$		0			0
$676$	−67.5268			−2.59719
$677$	−34.1761	+	24.8304i	−1.31350	+	0.954310i	−0.313507	+	0.949586i	$0.601504\pi$
$677$	−34.1761	+	24.8304i	−1.31350	+	0.954310i	−0.999989	+	0.00472433i	$0.998496\pi$
$678$	−9.84828	+	30.3099i	−0.378221	+	1.16404i
$679$	1.22867	−	3.78147i	0.0471521	−	0.145119i
$680$		0			0
$681$	−0.552667	−	1.70093i	−0.0211782	−	0.0651799i
$682$	46.8100			1.79245
$683$	−15.1264	−	46.5544i	−0.578797	−	1.78135i	−0.622870	−	0.782325i	$-0.714034\pi$
$683$	−15.1264	−	46.5544i	−0.578797	−	1.78135i	0.0440734	−	0.999028i	$-0.485966\pi$
$684$	−16.1106	−	11.7050i	−0.616004	−	0.447553i
$685$		0			0
$686$	14.1881	−	10.3083i	0.541705	−	0.393572i
$687$	−22.6389	−	16.4481i	−0.863729	−	0.627536i
$688$	74.5635	+	54.1735i	2.84271	+	2.06535i
$689$	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	$0.612996\pi$
$692$	−28.5043	−	87.7273i	−1.08357	−	3.33489i
$693$	1.49623			0.0568371
$694$	−19.3139	−	59.4420i	−0.733145	−	2.25639i
$695$		0			0
$696$	−23.1438	+	71.2291i	−0.877262	+	2.69993i
$697$	0.776250	−	2.38905i	0.0294026	−	0.0904918i
$698$	−20.4203	+	14.8362i	−0.772920	+	0.561559i
$699$	−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	$0.554413\pi$
$702$	1.23366	−	0.896304i	0.0465614	−	0.0338288i
$703$	−1.17985	+	3.63122i	−0.0444990	+	0.136954i
$704$	−23.8389	+	73.3687i	−0.898464	+	2.76519i
$705$		0			0
$706$	26.7177	+	82.2287i	1.00553	+	3.09472i
$707$	2.74334			0.103174
$708$	21.1786	+	65.1811i	0.795942	+	2.44966i
$709$	−40.2076	−	29.2126i	−1.51003	−	1.09710i	−0.966164	−	0.257928i	$-0.916960\pi$
$709$	−40.2076	−	29.2126i	−1.51003	−	1.09710i	−0.543865	−	0.839173i	$-0.683040\pi$
$710$		0			0
$711$	3.84687	−	2.79491i	0.144269	−	0.104817i
$712$	−45.1318	−	32.7901i	−1.69138	−	1.22886i
$713$	−9.98321	−	7.25323i	−0.373874	−	0.271636i
$714$	1.75705	−	1.27657i	0.0657560	−	0.0477745i
$715$		0			0
$716$	−45.5585	−	33.1002i	−1.70260	−	1.23701i
$717$	2.00346	+	6.16603i	0.0748207	+	0.230274i
$718$	25.9528			0.968549
$719$	−0.660387	−	2.03246i	−0.0246283	−	0.0757981i	0.937987	−	0.346671i	$-0.112688\pi$
$719$	−0.660387	−	2.03246i	−0.0246283	−	0.0757981i	−0.962615	+	0.270872i	$0.912688\pi$
$720$		0			0
$721$	−2.04614	+	6.29738i	−0.0762023	+	0.234527i
$722$	4.19130	−	12.8995i	0.155984	−	0.480070i
$723$	−6.02602	+	4.37816i	−0.224110	+	0.162825i
$724$	63.7855			2.37057
$725$		0			0
$726$	−2.37672			−0.0882083
$727$	−33.5446	+	24.3716i	−1.24410	+	0.903891i	−0.997864	−	0.0653195i	$-0.979193\pi$
$727$	−33.5446	+	24.3716i	−1.24410	+	0.903891i	−0.246235	+	0.969210i	$0.579193\pi$
$728$	−0.736718	+	2.26739i	−0.0273046	+	0.0840349i
$729$	0.309017	−	0.951057i	0.0114451	−	0.0352243i
$730$		0			0
$731$	−3.54723	−	10.9172i	−0.131199	−	0.403789i
$732$	−0.675604			−0.0249710
$733$	−10.0496	−	30.9293i	−0.371189	−	1.14240i	−0.946014	−	0.324125i	$-0.894930\pi$
$733$	−10.0496	−	30.9293i	−0.371189	−	1.14240i	0.574826	−	0.818276i	$-0.305070\pi$
$734$	−2.33013	−	1.69294i	−0.0860067	−	0.0624875i
$735$		0			0
$736$	35.0446	−	25.4614i	1.29176	−	0.938518i
$737$	7.19317	+	5.22614i	0.264964	+	0.192507i
$738$	3.22323	+	2.34181i	0.118649	+	0.0862034i
$739$	28.5724	−	20.7591i	1.05105	−	0.763635i	0.0786411	−	0.996903i	$-0.474942\pi$
$739$	28.5724	−	20.7591i	1.05105	−	0.763635i	0.972413	+	0.233268i	$0.0749419\pi$
$740$		0			0
$741$	−1.70487	−	1.23866i	−0.0626300	−	0.0455034i
$742$	2.77349	+	8.53592i	0.101818	+	0.313363i
$743$	36.0897			1.32400			0.662001	−	0.749503i	$-0.269708\pi$
$743$	36.0897			1.32400			0.662001	+	0.749503i	$0.269708\pi$
$744$	15.1149	+	46.5188i	0.554139	+	1.70546i
$745$		0			0
$746$	−3.44579	+	10.6051i	−0.126159	+	0.388279i
$747$	−3.61256	+	11.1183i	−0.132177	+	0.406798i
$748$	23.3845	−	16.9898i	0.855022	−	0.621210i
$749$	−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	$0.526910\pi$
$752$	−49.1411	+	35.7031i	−1.79199	+	1.30196i
$753$	1.42215	−	4.37692i	0.0518259	−	0.159504i
$754$	−3.92258	+	12.0725i	−0.142852	+	0.439653i
$755$		0			0
$756$	0.773789	+	2.38148i	0.0281424	+	0.0866135i
$757$	−14.6243			−0.531530			−0.265765	−	0.964038i	$-0.585625\pi$
$757$	−14.6243			−0.531530			−0.265765	+	0.964038i	$0.585625\pi$
$758$	−8.66109	−	26.6561i	−0.314585	−	0.968193i
$759$	−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	$0.370909\pi$
$762$	3.89472	+	2.82968i	0.141091	+	0.102509i
$763$	6.34920	+	4.61296i	0.229856	+	0.167000i
$764$	−78.6799	+	57.1643i	−2.84654	+	2.06813i
$765$		0			0
$766$	−2.62597	−	1.90788i	−0.0948801	−	0.0689344i
$767$	2.24119	+	6.89767i	0.0809246	+	0.249060i
$768$	−25.8083			−0.931276
$769$	4.26323	+	13.1209i	0.153736	+	0.473150i	0.998031	−	0.0627287i	$-0.0199803\pi$
$769$	4.26323	+	13.1209i	0.153736	+	0.473150i	−0.844295	+	0.535879i	$0.819980\pi$
$770$		0			0
$771$	−1.79071	+	5.51123i	−0.0644908	+	0.198482i
$772$	−41.4726	+	127.640i	−1.49263	+	4.59385i
$773$	18.3274	−	13.3156i	0.659190	−	0.478929i	−0.207199	−	0.978299i	$-0.566435\pi$
$773$	18.3274	−	13.3156i	0.659190	−	0.478929i	0.866389	+	0.499369i	$0.166435\pi$
$774$	18.2063			0.654411
$775$		0			0
$776$	76.0647			2.73056
$777$	0.388409	−	0.282196i	0.0139341	−	0.0101237i
$778$	−10.5411	+	32.4422i	−0.377917	+	1.16311i
$779$	1.70143	−	5.23646i	0.0609600	−	0.187616i
$780$		0			0
$781$	−15.7750	−	48.5504i	−0.564473	−	1.73727i
$782$	−10.4820			−0.374837
$783$	2.57238	+	7.91697i	0.0919294	+	0.282929i
$784$	75.1355	+	54.5891i	2.68341	+	1.94961i
$785$		0			0
$786$	12.9587	−	9.41507i	0.462223	−	0.335824i
$787$	−38.5785	−	28.0289i	−1.37518	−	0.999123i	−0.997313	−	0.0732618i	$-0.976659\pi$
$787$	−38.5785	−	28.0289i	−1.37518	−	0.999123i	−0.377863	−	0.925862i	$-0.623341\pi$
$788$	52.0878	+	37.8440i	1.85555	+	1.34814i
$789$	−11.5680	+	8.40467i	−0.411833	+	0.299214i
$790$		0			0
$791$	−4.48043	−	3.25522i	−0.159306	−	0.115742i
$792$	8.84525	+	27.2229i	0.314302	+	0.967323i
$793$	−0.0714945			−0.00253884
$794$	−1.09837	−	3.38044i	−0.0389797	−	0.119967i
$795$		0			0
$796$	−0.895774	+	2.75691i	−0.0317499	+	0.0977160i
$797$	−8.40931	+	25.8812i	−0.297873	+	0.916759i	0.684368	+	0.729137i	$0.260078\pi$
$797$	−8.40931	+	25.8812i	−0.297873	+	0.916759i	−0.982241	+	0.187622i	$0.939922\pi$
$798$	3.85120	−	2.79806i	0.136331	−	0.0990504i
$799$	7.56529			0.267641
$800$		0			0
$801$	−6.20049			−0.219083
$802$	35.2600	−	25.6179i	1.24507	−	0.904599i
$803$	−9.62360	+	29.6184i	−0.339610	+	1.04521i
$804$	−4.59818	+	14.1518i	−0.162165	+	0.499094i
$805$		0			0
$806$	2.56179	+	7.88437i	0.0902351	+	0.277715i
$807$	19.2205			0.676592
$808$	16.2178	+	49.9132i	0.570540	+	1.75594i
$809$	15.8693	+	11.5297i	0.557933	+	0.405362i	0.830702	−	0.556717i	$-0.187939\pi$
$809$	15.8693	+	11.5297i	0.557933	+	0.405362i	−0.272769	+	0.962080i	$0.587939\pi$
$810$		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	$0.420626\pi$
$812$	−16.8636	−	12.2521i	−0.591796	−	0.429965i
$813$	−18.8042	−	13.6620i	−0.659492	−	0.479149i
$814$	7.11107	−	5.16650i	0.249243	−	0.181086i
$815$		0			0
$816$	18.9131	+	13.7412i	0.662090	+	0.481037i
$817$	−7.77501	−	23.9290i	−0.272013	−	0.837170i
$818$	−57.2667			−2.00228
$819$	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	$-0.157252\pi$
$822$	4.27866	−	13.1684i	0.149235	−	0.459299i
$823$	4.88721	−	3.55077i	0.170358	−	0.123772i	−0.499340	−	0.866406i	$-0.666424\pi$
$823$	4.88721	−	3.55077i	0.170358	−	0.123772i	0.669697	+	0.742634i	$0.266424\pi$
$824$	−126.673			−4.41285
$825$		0			0
$826$	−16.3833			−0.570047
$827$	−2.42188	+	1.75960i	−0.0842172	+	0.0611874i	−0.629097	−	0.777327i	$-0.716575\pi$
$827$	−2.42188	+	1.75960i	−0.0842172	+	0.0611874i	0.544880	+	0.838514i	$0.316575\pi$
$828$	3.73458	−	11.4938i	0.129786	−	0.399439i
$829$	8.29802	−	25.5387i	0.288202	−	0.886995i	−0.697218	−	0.716859i	$-0.745579\pi$
$829$	8.29802	−	25.5387i	0.288202	−	0.886995i	0.985421	−	0.170136i	$-0.0544208\pi$
$830$		0			0
$831$	6.76469	+	20.8196i	0.234664	+	0.722223i
$832$	−13.6624			−0.473658
$833$	−3.57444	−	11.0010i	−0.123847	−	0.381162i
$834$	18.0374	+	13.1050i	0.624585	+	0.453787i
$835$		0			0
$836$	51.2555	−	37.2393i	1.77271	−	1.28795i
$837$	4.39827	+	3.19553i	0.152026	+	0.110454i
$838$	−14.6060	−	10.6119i	−0.504555	−	0.366581i
$839$	−10.0800	+	7.32352i	−0.347999	+	0.252836i	−0.748029	−	0.663666i	$-0.769000\pi$
$839$	−10.0800	+	7.32352i	−0.347999	+	0.252836i	0.400030	+	0.916502i	$0.369000\pi$
$840$		0			0
$841$	−32.5998	−	23.6851i	−1.12413	−	0.816729i
$842$	−22.8297	−	70.2624i	−0.786762	−	2.42140i
$843$	−27.1138			−0.933850
$844$	−5.13683	−	15.8095i	−0.176817	−	0.544186i
$845$		0			0
$846$	−3.70785	+	11.4116i	−0.127479	+	0.392339i
$847$	0.127627	−	0.392797i	0.00438533	−	0.0134967i
$848$	−78.1590	+	56.7859i	−2.68399	+	1.95003i
$849$	16.3074			0.559668
$850$		0			0
$851$	−2.31714			−0.0794304
$852$	69.1171	−	50.2165i	2.36791	−	1.72039i
$853$	1.76058	−	5.41851i	0.0602811	−	0.185526i	−0.916381	−	0.400307i	$-0.868904\pi$
$853$	1.76058	−	5.41851i	0.0602811	−	0.185526i	0.976662	+	0.214780i	$0.0689036\pi$
$854$	0.0499068	−	0.153597i	0.00170778	−	0.00525599i
$855$		0			0
$856$	−23.9436	−	73.6907i	−0.818374	−	2.51870i
$857$	7.41982			0.253456			0.126728	−	0.991937i	$-0.459552\pi$
$857$	7.41982			0.253456			0.126728	+	0.991937i	$0.459552\pi$
$858$	1.49916	+	4.61394i	0.0511805	+	0.157517i
$859$	4.59726	+	3.34011i	0.156857	+	0.113963i	0.663445	−	0.748225i	$-0.269094\pi$
$859$	4.59726	+	3.34011i	0.156857	+	0.113963i	−0.506588	+	0.862188i	$0.669094\pi$
$860$		0			0
$861$	−0.560112	+	0.406945i	−0.0190886	+	0.0138687i
$862$	26.9251	+	19.5622i	0.917073	+	0.666293i
$863$	−27.9715	−	20.3225i	−0.952160	−	0.691785i	−0.000843465	−	1.00000i	$-0.500268\pi$
$863$	−27.9715	−	20.3225i	−0.952160	−	0.691785i	−0.951317	+	0.308215i	$0.900268\pi$
$864$	−15.4395	+	11.2174i	−0.525261	+	0.381624i
$865$		0			0
$866$	74.1037	+	53.8395i	2.51815	+	1.82954i
$867$	4.35353	+	13.3988i	0.147854	+	0.455047i
$868$	−13.6133			−0.462066
$869$	4.67478	+	14.3875i	0.158581	+	0.488062i
$870$		0			0
$871$	−0.486594	+	1.49758i	−0.0164876	+	0.0507437i
$872$	−46.3952	+	142.790i	−1.57114	+	4.83547i
$873$	6.83978	−	4.96939i	0.231491	−	0.168188i
$874$	−22.9751			−0.777145
$875$		0			0
$876$	−52.1191			−1.76094
$877$	−4.28790	+	3.11534i	−0.144792	+	0.105197i	−0.657823	−	0.753173i	$-0.728523\pi$
$877$	−4.28790	+	3.11534i	−0.144792	+	0.105197i	0.513031	+	0.858370i	$0.328523\pi$
$878$	17.5336	−	53.9629i	0.591730	−	1.82116i
$879$	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	$0.859067\pi$
$882$	18.3460			0.617740
$883$	16.3264	+	50.2476i	0.549428	+	1.69096i	0.710223	+	0.703977i	$0.248594\pi$
$883$	16.3264	+	50.2476i	0.549428	+	1.69096i	−0.160795	+	0.986988i	$0.551406\pi$
$884$	4.14143	+	3.00892i	0.139291	+	0.101201i
$885$		0			0
$886$	−13.2431	+	9.62166i	−0.444910	+	0.323246i
$887$	6.23572	+	4.53052i	0.209375	+	0.152120i	0.687531	−	0.726155i	$-0.258695\pi$
$887$	6.23572	+	4.53052i	0.209375	+	0.152120i	−0.478156	+	0.878275i	$0.658695\pi$
$888$	7.43051	+	5.39858i	0.249352	+	0.181165i
$889$	−0.676800	+	0.491724i	−0.0226991	+	0.0164919i
$890$		0			0
$891$	2.57387	+	1.87003i	0.0862279	+	0.0626482i
$892$	−0.557972	−	1.71726i	−0.0186823	−	0.0574981i
$893$	16.5820			0.554896
$894$	−8.41207	−	25.8897i	−0.281342	−	0.865881i
$895$		0			0
$896$	3.99006	−	12.2801i	0.133299	−	0.410251i
$897$	0.395205	−	1.21631i	0.0131955	−	0.0406116i
$898$	34.1334	−	24.7994i	1.13905	−	0.827566i
$899$	−45.2560			−1.50937
$900$		0			0
$901$	12.0326			0.400864
$902$	−10.2546	+	7.45043i	−0.341442	+	0.248072i
$903$	−0.977659	+	3.00892i	−0.0325344	+	0.100131i
$904$	32.7396	−	100.762i	1.08890	−	3.35130i
$905$		0			0
$906$	−10.0198	−	30.8379i	−0.332887	−	1.02452i
$907$	11.3735			0.377650			0.188825	−	0.982011i	$-0.439532\pi$
$907$	11.3735			0.377650			0.188825	+	0.982011i	$0.439532\pi$
$908$	2.94262	+	9.05644i	0.0976542	+	0.300549i
$909$	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	$0.200357\pi$
$912$	41.4547	+	30.1186i	1.37270	+	0.997328i
$913$	−30.0898	−	21.8615i	−0.995827	−	0.723511i
$914$	5.47795	−	3.97997i	0.181195	−	0.131646i
$915$		0			0
$916$	120.539	+	87.5764i	3.98271	+	2.89361i
$917$	0.860143	+	2.64725i	0.0284044	+	0.0874199i
$918$	4.61803			0.152418
$919$	2.36336	+	7.27367i	0.0779600	+	0.239936i	0.982440	−	0.186581i	$-0.0597405\pi$
$919$	2.36336	+	7.27367i	0.0779600	+	0.239936i	−0.904480	+	0.426517i	$0.859741\pi$
$920$		0			0
$921$	−6.61895	+	20.3710i	−0.218102	+	0.671249i
$922$	0.128761	−	0.396286i	0.00424052	−	0.0130510i
$923$	7.31418	−	5.31407i	0.240749	−	0.174915i
$924$	−7.96652			−0.262079
$925$		0			0
$926$	−31.4822			−1.03457
$927$	−11.3905	+	8.27566i	−0.374112	+	0.271808i
$928$	49.0918	−	151.089i	1.61152	−	4.95974i
$929$	−9.56366	+	29.4339i	−0.313774	+	0.965696i	0.662483	+	0.749077i	$0.269503\pi$
$929$	−9.56366	+	29.4339i	−0.313774	+	0.965696i	−0.976256	+	0.216619i	$0.930497\pi$
$930$		0			0
$931$	−7.83466	−	24.1126i	−0.256770	−	0.790258i
$932$	36.0675			1.18143
$933$	0.881316	+	2.71241i	0.0288530	+	0.0888003i
$934$	−1.02971	−	0.748125i	−0.0336930	−	0.0244794i
$935$		0			0
$936$	−4.10116	+	2.97967i	−0.134051	+	0.0973936i
$937$	25.3784	+	18.4385i	0.829077	+	0.602360i	0.919298	−	0.393562i	$-0.128757\pi$
$937$	25.3784	+	18.4385i	0.829077	+	0.602360i	−0.0902212	+	0.995922i	$0.528757\pi$
$938$	−2.87771	−	2.09078i	−0.0939605	−	0.0682663i
$939$	−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	$0.681217\pi$
$942$	−16.3884	−	50.4383i	−0.533963	−	1.64337i
$943$	3.34146			0.108813
$944$	−54.4955	−	167.720i	−1.77368	−	5.45882i
$945$		0			0
$946$	−17.8992	+	55.0879i	−0.581952	+	1.79106i
$947$	3.49856	−	10.7675i	0.113688	−	0.349896i	−0.877983	−	0.478692i	$-0.841111\pi$
$947$	3.49856	−	10.7675i	0.113688	−	0.349896i	0.991671	+	0.128796i	$0.0411112\pi$
$948$	−20.4823	+	14.8812i	−0.665233	+	0.483320i
$949$	−5.51540			−0.179038
$950$		0			0
$951$	22.6102			0.733187
$952$	−5.84113	+	4.24383i	−0.189312	+	0.137543i
$953$	5.32071	−	16.3755i	0.172355	−	0.530453i	−0.827148	−	0.561984i	$-0.810038\pi$
$953$	5.32071	−	16.3755i	0.172355	−	0.530453i	0.999503	+	0.0315307i	$0.0100382\pi$
$954$	−5.89735	+	18.1502i	−0.190934	+	0.587633i
$955$		0			0
$956$	−10.6672	−	32.8304i	−0.345003	−	1.06181i
$957$	−26.4839			−0.856102
$958$	−10.3798	−	31.9458i	−0.335357	−	1.03212i
$959$	1.94656	+	1.41426i	0.0628576	+	0.0456687i
$960$		0			0
$961$	1.16811	−	0.848680i	0.0376809	−	0.0273768i
$962$	1.25938	+	0.914994i	0.0406041	+	0.0295006i
$963$	−6.96731	−	5.06205i	−0.224519	−	0.163122i
$964$	32.0849	−	23.3110i	1.03339	−	0.750798i
$965$		0			0
$966$	2.33723	+	1.69810i	0.0751992	+	0.0546354i
$967$	9.24157	+	28.4426i	0.297189	+	0.914653i	0.982477	+	0.186382i	$0.0596761\pi$
$967$	9.24157	+	28.4426i	0.297189	+	0.914653i	−0.685289	+	0.728272i	$0.740324\pi$
$968$	7.90115			0.253953
$969$	−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	$0.967537\pi$
$972$	−1.64533	+	5.06380i	−0.0527739	+	0.162422i
$973$	−3.13443	+	2.27729i	−0.100485	+	0.0730067i
$974$	93.5443			2.99735
$975$		0			0
$976$	1.73842			0.0556455
$977$	46.1907	−	33.5595i	1.47777	−	1.07366i	0.499504	−	0.866311i	$-0.333515\pi$
$977$	46.1907	−	33.5595i	1.47777	−	1.07366i	0.978266	−	0.207352i	$-0.0664845\pi$
$978$	−9.94597	+	30.6106i	−0.318037	+	0.978818i
$979$	6.09589	−	18.7612i	0.194826	−	0.599611i
$980$		0			0
$981$	5.15673	+	15.8708i	0.164642	+	0.506715i
$982$	67.2957			2.14749
$983$	8.16325	+	25.1239i	0.260367	+	0.801328i	0.992725	+	0.120407i	$0.0384201\pi$
$983$	8.16325	+	25.1239i	0.260367	+	0.801328i	−0.732357	+	0.680921i	$0.761580\pi$
$984$	−10.7153	−	7.78512i	−0.341591	−	0.248181i
$985$		0			0
$986$	−31.1005	+	22.5958i	−0.990442	+	0.719598i
$987$	−1.68687	−	1.22558i	−0.0536936	−	0.0390107i
$988$	9.07741	+	6.59513i	0.288791	+	0.209819i
$989$	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	$0.583525\pi$
$992$	−32.0612	−	98.6744i	−1.01795	−	3.13291i
$993$	−3.86645			−0.122698
$994$	6.31096	+	19.4231i	0.200171	+	0.616064i
$995$		0			0
$996$	19.2347	−	59.1983i	0.609475	−	1.87577i
$997$	7.44865	−	22.9246i	0.235901	−	0.726029i	−0.761099	−	0.648635i	$-0.775340\pi$
$997$	7.44865	−	22.9246i	0.235901	−	0.726029i	0.997001	−	0.0773940i	$-0.0246599\pi$
$998$	27.5958	−	20.0495i	0.873529	−	0.634656i
$999$	1.02085			0.0322983

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.2.g.b.16.1	✓	8	25.9	even	10
75.2.g.b.61.1	yes	8	5.4	even	2
225.2.h.c.91.2		8	75.59	odd	10
225.2.h.c.136.2		8	15.14	odd	2
375.2.g.b.76.2		8	25.16	even	5	inner
375.2.g.b.301.2		8	1.1	even	1	trivial
375.2.i.b.49.1		16	25.12	odd	20
375.2.i.b.49.4		16	25.13	odd	20
375.2.i.b.199.1		16	5.3	odd	4
375.2.i.b.199.4		16	5.2	odd	4
1875.2.a.e.1.1		4	25.21	even	5
1875.2.a.h.1.4		4	25.4	even	10
1875.2.b.c.1249.1		8	25.22	odd	20
1875.2.b.c.1249.8		8	25.3	odd	20
5625.2.a.i.1.1		4	75.29	odd	10
5625.2.a.n.1.4		4	75.71	odd	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(2.18949 - 1.59076i) q^{2} +(-0.309017 + 0.951057i) q^{3} +(1.64533 - 5.06380i) q^{4} +(0.836312 + 2.57390i) q^{6} -0.470294 q^{7} +(-2.78023 - 8.55667i) q^{8} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})\)	\(q+(2.18949 - 1.59076i) q^{2} +(-0.309017 + 0.951057i) q^{3} +(1.64533 - 5.06380i) q^{4} +(0.836312 + 2.57390i) q^{6} -0.470294 q^{7} +(-2.78023 - 8.55667i) q^{8} +(-0.809017 - 0.587785i) q^{9} +(2.57387 - 1.87003i) q^{11} +(4.30753 + 3.12960i) q^{12} +(0.455836 + 0.331184i) q^{13} +(-1.02971 + 0.748125i) q^{14} +(-11.0839 - 8.05289i) q^{16} +(0.527295 + 1.62285i) q^{17} -2.70636 q^{18} +(1.15575 + 3.55705i) q^{19} +(0.145329 - 0.447276i) q^{21} +(2.66071 - 8.18882i) q^{22} +(-1.83631 + 1.33416i) q^{23} +8.99702 q^{24} +1.52488 q^{26} +(0.809017 - 0.587785i) q^{27} +(-0.773789 + 2.38148i) q^{28} +(-2.57238 + 7.91697i) q^{29} +(1.67999 + 5.17047i) q^{31} -19.0842 q^{32} +(0.983131 + 3.02577i) q^{33} +(3.73607 + 2.71441i) q^{34} +(-4.30753 + 3.12960i) q^{36} +(0.825886 + 0.600041i) q^{37} +(8.18892 + 5.94960i) q^{38} +(-0.455836 + 0.331184i) q^{39} +(-1.19098 - 0.865300i) q^{41} +(-0.393313 - 1.21049i) q^{42} -6.72721 q^{43} +(-5.23458 - 16.1104i) q^{44} +(-1.89827 + 5.84226i) q^{46} +(1.37005 - 4.21658i) q^{47} +(11.0839 - 8.05289i) q^{48} -6.77882 q^{49} -1.70636 q^{51} +(2.42705 - 1.76336i) q^{52} +(2.17907 - 6.70648i) q^{53} +(0.836312 - 2.57390i) q^{54} +(1.30753 + 4.02415i) q^{56} -3.74010 q^{57} +(6.96179 + 21.4262i) q^{58} +(10.4136 + 7.56596i) q^{59} +(-0.102655 + 0.0745831i) q^{61} +(11.9033 + 8.64825i) q^{62} +(0.380476 + 0.276432i) q^{63} +(-19.6170 + 14.2526i) q^{64} +(6.96582 + 5.06097i) q^{66} +(0.863607 + 2.65791i) q^{67} +9.08535 q^{68} +(-0.701409 - 2.15871i) q^{69} +(4.95838 - 15.2603i) q^{71} +(-2.78023 + 8.55667i) q^{72} +(-7.91925 + 5.75367i) q^{73} +2.76279 q^{74} +19.9138 q^{76} +(-1.21048 + 0.879462i) q^{77} +(-0.471215 + 1.45025i) q^{78} +(-1.46937 + 4.52227i) q^{79} +(0.309017 + 0.951057i) q^{81} -3.98413 q^{82} +(-3.61256 - 11.1183i) q^{83} +(-2.02580 - 1.47183i) q^{84} +(-14.7292 + 10.7014i) q^{86} +(-6.73458 - 4.89296i) q^{87} +(-23.1572 - 16.8247i) q^{88} +(5.01630 - 3.64456i) q^{89} +(-0.214377 - 0.155754i) q^{91} +(3.73458 + 11.4938i) q^{92} -5.43656 q^{93} +(-3.70785 - 11.4116i) q^{94} +(5.89735 - 18.1502i) q^{96} +(-2.61256 + 8.04064i) q^{97} +(-14.8422 + 10.7835i) q^{98} -3.18148 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + q^{2} + 2 q^{3} + q^{4} - q^{6} - 4 q^{7} - 2 q^{9}+O(q^{10}) \) 8 * q + q^2 + 2 * q^3 + q^4 - q^6 - 4 * q^7 - 2 * q^9	\( 8 q + q^{2} + 2 q^{3} + q^{4} - q^{6} - 4 q^{7} - 2 q^{9} + 16 q^{11} + 9 q^{12} + 8 q^{13} - 8 q^{14} - 17 q^{16} + q^{17} - 4 q^{18} - 5 q^{19} - 11 q^{21} - 13 q^{22} - 7 q^{23} + 30 q^{24} + 6 q^{26} + 2 q^{27} + 17 q^{28} + 5 q^{29} - 19 q^{31} - 24 q^{32} + 9 q^{33} + 12 q^{34} - 9 q^{36} + q^{37} + 10 q^{38} - 8 q^{39} - 14 q^{41} + 8 q^{42} - 32 q^{43} - 3 q^{44} + 16 q^{46} + q^{47} + 17 q^{48} + 16 q^{49} + 4 q^{51} + 6 q^{52} + 3 q^{53} - q^{54} - 15 q^{56} - 10 q^{57} - 5 q^{58} + 30 q^{59} - 14 q^{61} + 17 q^{62} - 9 q^{63} - 44 q^{64} - 7 q^{66} - 4 q^{67} + 22 q^{68} - 8 q^{69} + 21 q^{71} - 2 q^{73} - 38 q^{74} + 80 q^{76} + 37 q^{77} + 14 q^{78} - 30 q^{79} - 2 q^{81} + 12 q^{82} - 2 q^{83} + 8 q^{84} - 34 q^{86} - 15 q^{87} - 70 q^{88} + 21 q^{91} - 9 q^{92} - 46 q^{93} - 33 q^{94} + 34 q^{96} + 6 q^{97} - 73 q^{98} - 14 q^{99}+O(q^{100}) \) 8 * q + q^2 + 2 * q^3 + q^4 - q^6 - 4 * q^7 - 2 * q^9 + 16 * q^11 + 9 * q^12 + 8 * q^13 - 8 * q^14 - 17 * q^16 + q^17 - 4 * q^18 - 5 * q^19 - 11 * q^21 - 13 * q^22 - 7 * q^23 + 30 * q^24 + 6 * q^26 + 2 * q^27 + 17 * q^28 + 5 * q^29 - 19 * q^31 - 24 * q^32 + 9 * q^33 + 12 * q^34 - 9 * q^36 + q^37 + 10 * q^38 - 8 * q^39 - 14 * q^41 + 8 * q^42 - 32 * q^43 - 3 * q^44 + 16 * q^46 + q^47 + 17 * q^48 + 16 * q^49 + 4 * q^51 + 6 * q^52 + 3 * q^53 - q^54 - 15 * q^56 - 10 * q^57 - 5 * q^58 + 30 * q^59 - 14 * q^61 + 17 * q^62 - 9 * q^63 - 44 * q^64 - 7 * q^66 - 4 * q^67 + 22 * q^68 - 8 * q^69 + 21 * q^71 - 2 * q^73 - 38 * q^74 + 80 * q^76 + 37 * q^77 + 14 * q^78 - 30 * q^79 - 2 * q^81 + 12 * q^82 - 2 * q^83 + 8 * q^84 - 34 * q^86 - 15 * q^87 - 70 * q^88 + 21 * q^91 - 9 * q^92 - 46 * q^93 - 33 * q^94 + 34 * q^96 + 6 * q^97 - 73 * q^98 - 14 * q^99

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