LMFDB - Embedded newform 375.2.i.c.349.1

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} + 20x^{14} + 156x^{12} + 610x^{10} + 1286x^{8} + 1440x^{6} + 761x^{4} + 130x^{2} + 1 $ x^16 + 20x^14 + 156x^12 + 610x^10 + 1286x^8 + 1440x^6 + 761x^4 + 130*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 75)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			349.1
Root			$-1.53655i$ of defining polynomial
Character	$\chi$	$=$	375.349
Dual form			375.2.i.c.274.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.46134 + 0.474819i) q^{2} +(-0.587785 - 0.809017i) q^{3} +(0.292036 - 0.212177i) q^{4} +(1.24309 + 0.903160i) q^{6} +1.49550i q^{7} +(1.48030 - 2.03746i) q^{8} +(-0.309017 + 0.951057i) q^{9} +O(q^{10})$	\(q+(-1.46134 + 0.474819i) q^{2} +(-0.587785 - 0.809017i) q^{3} +(0.292036 - 0.212177i) q^{4} +(1.24309 + 0.903160i) q^{6} +1.49550i q^{7} +(1.48030 - 2.03746i) q^{8} +(-0.309017 + 0.951057i) q^{9} +(-0.728123 - 2.24093i) q^{11} +(-0.343309 - 0.111548i) q^{12} +(-1.28346 - 0.417020i) q^{13} +(-0.710090 - 2.18543i) q^{14} +(-1.41890 + 4.36692i) q^{16} +(-1.28963 + 1.77502i) q^{17} -1.53655i q^{18} +(4.62004 + 3.35666i) q^{19} +(1.20988 - 0.879031i) q^{21} +(2.12807 + 2.92904i) q^{22} +(8.36455 - 2.71781i) q^{23} -2.51844 q^{24} +2.07358 q^{26} +(0.951057 - 0.309017i) q^{27} +(0.317309 + 0.436739i) q^{28} +(6.39137 - 4.64360i) q^{29} +(2.99107 + 2.17314i) q^{31} -2.01841i q^{32} +(-1.38497 + 1.90625i) q^{33} +(1.04178 - 3.20626i) q^{34} +(0.111548 + 0.343309i) q^{36} +(9.27372 + 3.01321i) q^{37} +(-8.34527 - 2.71154i) q^{38} +(0.417020 + 1.28346i) q^{39} +(0.573380 - 1.76468i) q^{41} +(-1.35067 + 1.85904i) q^{42} +8.01874i q^{43} +(-0.688111 - 0.499942i) q^{44} +(-10.9330 + 7.94330i) q^{46} +(-3.91640 - 5.39046i) q^{47} +(4.36692 - 1.41890i) q^{48} +4.76349 q^{49} +2.19405 q^{51} +(-0.463298 + 0.150535i) q^{52} +(2.45196 + 3.37484i) q^{53} +(-1.24309 + 0.903160i) q^{54} +(3.04701 + 2.21378i) q^{56} -5.71069i q^{57} +(-7.13511 + 9.82064i) q^{58} +(-3.41917 + 10.5231i) q^{59} +(-3.78151 - 11.6383i) q^{61} +(-5.40283 - 1.75549i) q^{62} +(-1.42230 - 0.462134i) q^{63} +(-1.87942 - 5.78425i) q^{64} +(1.11879 - 3.44330i) q^{66} +(2.53546 - 3.48976i) q^{67} +0.792000i q^{68} +(-7.11531 - 5.16958i) q^{69} +(-4.67410 + 3.39593i) q^{71} +(1.48030 + 2.03746i) q^{72} +(6.58781 - 2.14051i) q^{73} -14.9828 q^{74} +2.06142 q^{76} +(3.35130 - 1.08890i) q^{77} +(-1.21882 - 1.67756i) q^{78} +(-8.63118 + 6.27092i) q^{79} +(-0.809017 - 0.587785i) q^{81} +2.85106i q^{82} +(-0.131666 + 0.181222i) q^{83} +(0.166819 - 0.513417i) q^{84} +(-3.80745 - 11.7181i) q^{86} +(-7.51351 - 2.44129i) q^{87} +(-5.64364 - 1.83373i) q^{88} +(-0.132620 - 0.408162i) q^{89} +(0.623652 - 1.91940i) q^{91} +(1.86610 - 2.56846i) q^{92} -3.69717i q^{93} +(8.28270 + 6.01773i) q^{94} +(-1.63293 + 1.18639i) q^{96} +(-7.34411 - 10.1083i) q^{97} +(-6.96109 + 2.26180i) q^{98} +2.35626 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 2 q^{4} + 2 q^{6} + 30 q^{8} + 4 q^{9}+O(q^{10}) $ 16 * q + 2 * q^4 + 2 * q^6 + 30 * q^8 + 4 * q^9	$ 16 q + 2 q^{4} + 2 q^{6} + 30 q^{8} + 4 q^{9} - 6 q^{11} - 12 q^{14} - 10 q^{16} - 10 q^{17} - 2 q^{19} + 4 q^{21} + 30 q^{22} + 20 q^{23} + 24 q^{24} + 12 q^{26} - 30 q^{28} + 16 q^{29} + 6 q^{31} - 10 q^{33} - 36 q^{34} - 2 q^{36} + 10 q^{37} - 30 q^{38} - 8 q^{39} - 14 q^{41} + 10 q^{42} + 26 q^{44} + 16 q^{46} - 40 q^{47} - 32 q^{51} - 40 q^{52} - 10 q^{53} - 2 q^{54} - 10 q^{58} + 12 q^{59} + 10 q^{62} + 10 q^{63} + 8 q^{64} + 16 q^{66} + 40 q^{67} - 12 q^{69} - 8 q^{71} + 30 q^{72} + 20 q^{73} - 52 q^{74} - 32 q^{76} + 40 q^{77} - 20 q^{79} - 4 q^{81} - 10 q^{83} + 12 q^{84} - 36 q^{86} - 40 q^{87} + 40 q^{88} + 18 q^{89} + 26 q^{91} - 10 q^{92} - 38 q^{94} - 26 q^{96} - 40 q^{97} - 60 q^{98} - 4 q^{99}+O(q^{100}) $ 16 * q + 2 * q^4 + 2 * q^6 + 30 * q^8 + 4 * q^9 - 6 * q^11 - 12 * q^14 - 10 * q^16 - 10 * q^17 - 2 * q^19 + 4 * q^21 + 30 * q^22 + 20 * q^23 + 24 * q^24 + 12 * q^26 - 30 * q^28 + 16 * q^29 + 6 * q^31 - 10 * q^33 - 36 * q^34 - 2 * q^36 + 10 * q^37 - 30 * q^38 - 8 * q^39 - 14 * q^41 + 10 * q^42 + 26 * q^44 + 16 * q^46 - 40 * q^47 - 32 * q^51 - 40 * q^52 - 10 * q^53 - 2 * q^54 - 10 * q^58 + 12 * q^59 + 10 * q^62 + 10 * q^63 + 8 * q^64 + 16 * q^66 + 40 * q^67 - 12 * q^69 - 8 * q^71 + 30 * q^72 + 20 * q^73 - 52 * q^74 - 32 * q^76 + 40 * q^77 - 20 * q^79 - 4 * q^81 - 10 * q^83 + 12 * q^84 - 36 * q^86 - 40 * q^87 + 40 * q^88 + 18 * q^89 + 26 * q^91 - 10 * q^92 - 38 * q^94 - 26 * q^96 - 40 * q^97 - 60 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$251$
$\chi(n)$	$e\left(\frac{9}{10}\right)$	$1$

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 $

$2$	−1.46134	+	0.474819i	−1.03333	+	0.335748i	−0.776104	−	0.630605i	$-0.782807\pi$
$2$	−1.46134	+	0.474819i	−1.03333	+	0.335748i	−0.257221	+	0.966353i	$0.582807\pi$
$3$	−0.587785	−	0.809017i	−0.339358	−	0.467086i
$3$	−0.587785	−	0.809017i	−0.339358	−	0.467086i
$4$	0.292036	−	0.212177i	0.146018	−	0.106088i
$5$		0			0
$5$		0			0
$6$	1.24309	+	0.903160i	0.507490	+	0.368713i
$7$			1.49550i			0.565244i	0.959231	+	0.282622i	$0.0912043\pi$
$7$			1.49550i			0.565244i	−0.959231	+	0.282622i	$0.908796\pi$
$8$	1.48030	−	2.03746i	0.523365	−	0.720350i
$9$	−0.309017	+	0.951057i	−0.103006	+	0.317019i
$10$		0			0
$11$	−0.728123	−	2.24093i	−0.219537	−	0.675666i	−0.998800	−	0.0489693i	$-0.984406\pi$
$11$	−0.728123	−	2.24093i	−0.219537	−	0.675666i	0.779263	−	0.626697i	$-0.215594\pi$
$12$	−0.343309	−	0.111548i	−0.0991048	−	0.0322011i
$13$	−1.28346	−	0.417020i	−0.355967	−	0.115661i	0.125574	−	0.992084i	$-0.459923\pi$
$13$	−1.28346	−	0.417020i	−0.355967	−	0.115661i	−0.481541	+	0.876424i	$0.659923\pi$
$14$	−0.710090	−	2.18543i	−0.189780	−	0.584081i
$15$		0			0
$16$	−1.41890	+	4.36692i	−0.354724	+	1.09173i
$17$	−1.28963	+	1.77502i	−0.312781	+	0.430507i	−0.936246	−	0.351345i	$-0.885724\pi$
$17$	−1.28963	+	1.77502i	−0.312781	+	0.430507i	0.623465	+	0.781851i	$0.285724\pi$
$18$		−	1.53655i		−	0.362168i
$19$	4.62004	+	3.35666i	1.05991	+	0.770070i	0.974072	−	0.226239i	$-0.0726431\pi$
$19$	4.62004	+	3.35666i	1.05991	+	0.770070i	0.0858386	+	0.996309i	$0.472643\pi$
$20$		0			0
$21$	1.20988	−	0.879031i	0.264018	−	0.191820i
$22$	2.12807	+	2.92904i	0.453707	+	0.624474i
$23$	8.36455	−	2.71781i	1.74413	−	0.566702i	0.748762	−	0.662840i	$-0.230649\pi$
$23$	8.36455	−	2.71781i	1.74413	−	0.566702i	0.995368	+	0.0961375i	$0.0306488\pi$
$24$	−2.51844			−0.514074
$25$		0			0
$26$	2.07358			0.406662
$27$	0.951057	−	0.309017i	0.183031	−	0.0594703i
$28$	0.317309	+	0.436739i	0.0599658	+	0.0825359i
$29$	6.39137	−	4.64360i	1.18685	−	0.862296i	0.193920	−	0.981017i	$-0.437880\pi$
$29$	6.39137	−	4.64360i	1.18685	−	0.862296i	0.992928	+	0.118722i	$0.0378796\pi$
$30$		0			0
$31$	2.99107	+	2.17314i	0.537213	+	0.390308i	0.823049	−	0.567971i	$-0.192271\pi$
$31$	2.99107	+	2.17314i	0.537213	+	0.390308i	−0.285836	+	0.958279i	$0.592271\pi$
$32$		−	2.01841i		−	0.356808i
$33$	−1.38497	+	1.90625i	−0.241093	+	0.331836i
$34$	1.04178	−	3.20626i	0.178663	−	0.549869i
$35$		0			0
$36$	0.111548	+	0.343309i	0.0185913	+	0.0572182i
$37$	9.27372	+	3.01321i	1.52459	+	0.495369i	0.947076	−	0.321011i	$-0.104023\pi$
$37$	9.27372	+	3.01321i	1.52459	+	0.495369i	0.577515	+	0.816380i	$0.304023\pi$
$38$	−8.34527	−	2.71154i	−1.35378	−	0.439870i
$39$	0.417020	+	1.28346i	0.0667767	+	0.205518i
$40$		0			0
$41$	0.573380	−	1.76468i	0.0895468	−	0.275597i	−0.896247	−	0.443555i	$-0.853717\pi$
$41$	0.573380	−	1.76468i	0.0895468	−	0.275597i	0.985794	+	0.167958i	$0.0537172\pi$
$42$	−1.35067	+	1.85904i	−0.208413	+	0.286856i
$43$			8.01874i			1.22285i	0.791304	+	0.611423i	$0.209403\pi$
$43$			8.01874i			1.22285i	−0.791304	+	0.611423i	$0.790597\pi$
$44$	−0.688111	−	0.499942i	−0.103737	−	0.0753691i
$45$		0			0
$46$	−10.9330	+	7.94330i	−1.61198	+	1.17118i
$47$	−3.91640	−	5.39046i	−0.571266	−	0.786280i	0.421438	−	0.906857i	$-0.361525\pi$
$47$	−3.91640	−	5.39046i	−0.571266	−	0.786280i	−0.992704	+	0.120577i	$0.961525\pi$
$48$	4.36692	−	1.41890i	0.630310	−	0.204800i
$49$	4.76349			0.680499
$50$		0			0
$51$	2.19405			0.307228
$52$	−0.463298	+	0.150535i	−0.0642478	+	0.0208754i
$53$	2.45196	+	3.37484i	0.336803	+	0.463569i	0.943504	−	0.331360i	$-0.107508\pi$
$53$	2.45196	+	3.37484i	0.336803	+	0.463569i	−0.606701	+	0.794930i	$0.707508\pi$
$54$	−1.24309	+	0.903160i	−0.169163	+	0.122904i
$55$		0			0
$56$	3.04701	+	2.21378i	0.407174	+	0.295829i
$57$		−	5.71069i		−	0.756399i
$58$	−7.13511	+	9.82064i	−0.936886	+	1.28951i
$59$	−3.41917	+	10.5231i	−0.445138	+	1.36999i	0.437195	+	0.899367i	$0.355972\pi$
$59$	−3.41917	+	10.5231i	−0.445138	+	1.36999i	−0.882332	+	0.470627i	$0.844028\pi$
$60$		0			0
$61$	−3.78151	−	11.6383i	−0.484173	−	1.49013i	−0.833175	−	0.553009i	$-0.813480\pi$
$61$	−3.78151	−	11.6383i	−0.484173	−	1.49013i	0.349003	−	0.937122i	$-0.386520\pi$
$62$	−5.40283	−	1.75549i	−0.686161	−	0.222947i
$63$	−1.42230	−	0.462134i	−0.179193	−	0.0582234i
$64$	−1.87942	−	5.78425i	−0.234927	−	0.723031i
$65$		0			0
$66$	1.11879	−	3.44330i	0.137714	−	0.423841i
$67$	2.53546	−	3.48976i	0.309756	−	0.426342i	−0.625549	−	0.780185i	$-0.715125\pi$
$67$	2.53546	−	3.48976i	0.309756	−	0.426342i	0.935305	+	0.353842i	$0.115125\pi$
$68$			0.792000i			0.0960442i
$69$	−7.11531	−	5.16958i	−0.856583	−	0.622344i
$70$		0			0
$71$	−4.67410	+	3.39593i	−0.554713	+	0.403023i	−0.829520	−	0.558477i	$-0.811386\pi$
$71$	−4.67410	+	3.39593i	−0.554713	+	0.403023i	0.274807	+	0.961499i	$0.411386\pi$
$72$	1.48030	+	2.03746i	0.174455	+	0.240117i
$73$	6.58781	−	2.14051i	0.771045	−	0.250528i	0.103033	−	0.994678i	$-0.467145\pi$
$73$	6.58781	−	2.14051i	0.771045	−	0.250528i	0.668012	+	0.744150i	$0.267145\pi$
$74$	−14.9828			−1.74172
$75$		0			0
$76$	2.06142			0.236461
$77$	3.35130	−	1.08890i	0.381917	−	0.124092i
$78$	−1.21882	−	1.67756i	−0.138004	−	0.189946i
$79$	−8.63118	+	6.27092i	−0.971084	+	0.705534i	−0.955698	−	0.294348i	$-0.904898\pi$
$79$	−8.63118	+	6.27092i	−0.971084	+	0.705534i	−0.0153858	+	0.999882i	$0.504898\pi$
$80$		0			0
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$			2.85106i			0.314846i
$83$	−0.131666	+	0.181222i	−0.0144522	+	0.0198917i	−0.816182	−	0.577795i	$-0.803913\pi$
$83$	−0.131666	+	0.181222i	−0.0144522	+	0.0198917i	0.801730	+	0.597687i	$0.203913\pi$
$84$	0.166819	−	0.513417i	0.0182015	−	0.0560184i
$85$		0			0
$86$	−3.80745	−	11.7181i	−0.410568	−	1.26360i
$87$	−7.51351	−	2.44129i	−0.805533	−	0.261733i
$88$	−5.64364	−	1.83373i	−0.601615	−	0.195476i
$89$	−0.132620	−	0.408162i	−0.0140577	−	0.0432651i	0.943782	−	0.330570i	$-0.107241\pi$
$89$	−0.132620	−	0.408162i	−0.0140577	−	0.0432651i	−0.957839	+	0.287304i	$0.907241\pi$
$90$		0			0
$91$	0.623652	−	1.91940i	0.0653765	−	0.201208i
$92$	1.86610	−	2.56846i	0.194554	−	0.267780i
$93$		−	3.69717i		−	0.383379i
$94$	8.28270	+	6.01773i	0.854295	+	0.620682i
$95$		0			0
$96$	−1.63293	+	1.18639i	−0.166660	+	0.121086i
$97$	−7.34411	−	10.1083i	−0.745682	−	1.02634i	−0.998272	−	0.0587692i	$-0.981282\pi$
$97$	−7.34411	−	10.1083i	−0.745682	−	1.02634i	0.252590	−	0.967573i	$-0.418718\pi$
$98$	−6.96109	+	2.26180i	−0.703177	+	0.228476i
$99$	2.35626			0.236813
$100$		0			0
$101$	8.19767			0.815698			0.407849	−	0.913049i	$-0.366279\pi$
$101$	8.19767			0.815698			0.407849	+	0.913049i	$0.366279\pi$
$102$	−3.20626	+	1.04178i	−0.317467	+	0.103151i
$103$	1.46949	+	2.02258i	0.144794	+	0.199291i	0.875254	−	0.483664i	$-0.160694\pi$
$103$	1.46949	+	2.02258i	0.144794	+	0.199291i	−0.730460	+	0.682955i	$0.760694\pi$
$104$	−2.74956	+	1.99767i	−0.269617	+	0.195888i
$105$		0			0
$106$	−5.18559	−	3.76755i	−0.503669	−	0.365937i
$107$		−	1.81004i		−	0.174983i	−0.996165	−	0.0874914i	$-0.972115\pi$
$107$		−	1.81004i		−	0.174983i	0.996165	−	0.0874914i	$-0.0278850\pi$
$108$	0.212177	−	0.292036i	0.0204167	−	0.0281012i
$109$	0.910913	−	2.80350i	0.0872496	−	0.268527i	−0.897907	−	0.440186i	$-0.854913\pi$
$109$	0.910913	−	2.80350i	0.0872496	−	0.268527i	0.985156	+	0.171659i	$0.0549127\pi$
$110$		0			0
$111$	−3.01321	−	9.27372i	−0.286002	−	0.880223i
$112$	−6.53071	−	2.12196i	−0.617094	−	0.200506i
$113$	−13.1593	−	4.27571i	−1.23792	−	0.402225i	−0.384342	−	0.923191i	$-0.625572\pi$
$113$	−13.1593	−	4.27571i	−1.23792	−	0.402225i	−0.853577	+	0.520966i	$0.825572\pi$
$114$	2.71154	+	8.34527i	0.253959	+	0.781606i
$115$		0			0
$116$	0.881247	−	2.71220i	0.0818217	−	0.251821i
$117$	0.793220	−	1.09177i	0.0733332	−	0.100934i
$118$		−	17.0014i		−	1.56510i
$119$	−2.65454	−	1.92864i	−0.243341	−	0.176798i
$120$		0			0
$121$	4.40757	−	3.20229i	0.400689	−	0.291117i
$122$	11.0522	+	15.2120i	1.00062	+	1.37723i
$123$	−1.76468	+	0.573380i	−0.159116	+	0.0516999i
$124$	1.33459			0.119850
$125$		0			0
$126$	2.29790			0.204713
$127$	−5.45902	+	1.77374i	−0.484410	+	0.157394i	−0.541033	−	0.841001i	$-0.681967\pi$
$127$	−5.45902	+	1.77374i	−0.484410	+	0.157394i	0.0566233	+	0.998396i	$0.481967\pi$
$128$	7.86572	+	10.8262i	0.695238	+	0.956914i
$129$	6.48730	−	4.71330i	0.571175	−	0.414983i
$130$		0			0
$131$	3.52534	+	2.56131i	0.308010	+	0.223783i	0.731042	−	0.682332i	$-0.239034\pi$
$131$	3.52534	+	2.56131i	0.308010	+	0.223783i	−0.423032	+	0.906115i	$0.639034\pi$
$132$			0.850553i			0.0740311i
$133$	−5.01987	+	6.90926i	−0.435278	+	0.599108i
$134$	−2.04817	+	6.30363i	−0.176935	+	0.544550i
$135$		0			0
$136$	1.70750	+	5.25514i	0.146417	+	0.450624i
$137$	1.87796	+	0.610187i	0.160445	+	0.0521318i	0.388138	−	0.921601i	$-0.373118\pi$
$137$	1.87796	+	0.610187i	0.160445	+	0.0521318i	−0.227693	+	0.973733i	$0.573118\pi$
$138$	12.8525	+	4.17604i	1.09408	+	0.355488i
$139$	−0.518869	−	1.59692i	−0.0440099	−	0.135449i	0.926637	−	0.375957i	$-0.122686\pi$
$139$	−0.518869	−	1.59692i	−0.0440099	−	0.135449i	−0.970647	+	0.240508i	$0.922686\pi$
$140$		0			0
$141$	−2.05897	+	6.33687i	−0.173397	+	0.533661i
$142$	5.21801	−	7.18197i	0.437885	−	0.602698i
$143$			3.17978i			0.265907i
$144$	−3.71472	−	2.69890i	−0.309560	−	0.224909i
$145$		0			0
$146$	−8.61070	+	6.25604i	−0.712627	+	0.517754i
$147$	−2.79991	−	3.85375i	−0.230933	−	0.317852i
$148$	3.34759	−	1.08770i	0.275171	−	0.0894083i
$149$	7.38524			0.605023			0.302511	−	0.953146i	$-0.402175\pi$
$149$	7.38524			0.605023			0.302511	+	0.953146i	$0.402175\pi$
$150$		0			0
$151$	−4.26137			−0.346785			−0.173393	−	0.984853i	$-0.555473\pi$
$151$	−4.26137			−0.346785			−0.173393	+	0.984853i	$0.555473\pi$
$152$	13.6781	−	4.44428i	1.10944	−	0.360479i
$153$	−1.28963	−	1.77502i	−0.104260	−	0.143502i
$154$	−4.38037	+	3.18253i	−0.352980	+	0.256455i
$155$		0			0
$156$	0.394104	+	0.286334i	0.0315536	+	0.0229250i
$157$			16.0573i			1.28152i	0.767743	+	0.640758i	$0.221380\pi$
$157$			16.0573i			1.28152i	−0.767743	+	0.640758i	$0.778620\pi$
$158$	9.63557	−	13.2622i	0.766565	−	1.05509i
$159$	1.28907	−	3.96736i	0.102230	−	0.314632i
$160$		0			0
$161$	4.06447	+	12.5092i	0.320325	+	0.985859i
$162$	1.46134	+	0.474819i	0.114814	+	0.0373053i
$163$	21.2026	+	6.88916i	1.66072	+	0.539600i	0.981023	−	0.193893i	$-0.0621114\pi$
$163$	21.2026	+	6.88916i	1.66072	+	0.539600i	0.679697	+	0.733493i	$0.262111\pi$
$164$	−0.206976	−	0.637008i	−0.0161621	−	0.0497420i
$165$		0			0
$166$	0.106361	−	0.327345i	0.00825520	−	0.0254069i
$167$	−3.80062	+	5.23111i	−0.294101	+	0.404795i	−0.930341	−	0.366696i	$-0.880489\pi$
$167$	−3.80062	+	5.23111i	−0.294101	+	0.404795i	0.636240	+	0.771491i	$0.280489\pi$
$168$		−	3.76631i		−	0.290577i
$169$	−9.04387	−	6.57075i	−0.695682	−	0.505443i
$170$		0			0
$171$	−4.62004	+	3.35666i	−0.353303	+	0.256690i
$172$	1.70139	+	2.34176i	0.129730	+	0.178558i
$173$	−11.2396	+	3.65198i	−0.854533	+	0.277655i	−0.703344	−	0.710850i	$-0.748310\pi$
$173$	−11.2396	+	3.65198i	−0.854533	+	0.277655i	−0.151190	+	0.988505i	$0.548310\pi$
$174$	12.1390			0.920254
$175$		0			0
$176$	10.8191			0.815520
$177$	10.5231	−	3.41917i	0.790966	−	0.257000i
$178$	0.387606	+	0.533494i	0.0290523	+	0.0399871i
$179$	12.6001	−	9.15450i	0.941775	−	0.684240i	−0.00707213	−	0.999975i	$-0.502251\pi$
$179$	12.6001	−	9.15450i	0.941775	−	0.684240i	0.948847	+	0.315735i	$0.102251\pi$
$180$		0			0
$181$	11.7952	+	8.56974i	0.876733	+	0.636984i	0.932385	−	0.361466i	$-0.117724\pi$
$181$	11.7952	+	8.56974i	0.876733	+	0.636984i	−0.0556522	+	0.998450i	$0.517724\pi$
$182$			3.10103i			0.229864i
$183$	−7.19286	+	9.90012i	−0.531711	+	0.731838i
$184$	6.84463	−	21.0656i	0.504593	−	1.55298i
$185$		0			0
$186$	1.75549	+	5.40283i	0.128719	+	0.396155i
$187$	4.91672	+	1.59754i	0.359546	+	0.116824i
$188$	−2.28746	−	0.743241i	−0.166830	−	0.0542064i
$189$	0.462134	+	1.42230i	0.0336153	+	0.103457i
$190$		0			0
$191$	−6.48577	+	19.9611i	−0.469294	+	1.44434i	0.384207	+	0.923247i	$0.374475\pi$
$191$	−6.48577	+	19.9611i	−0.469294	+	1.44434i	−0.853501	+	0.521091i	$0.825525\pi$
$192$	−3.57486	+	4.92037i	−0.257993	+	0.355097i
$193$		−	22.7094i		−	1.63466i	−0.576173	−	0.817328i	$-0.695454\pi$
$193$		−	22.7094i		−	1.63466i	0.576173	−	0.817328i	$-0.304546\pi$
$194$	15.5319	+	11.2846i	1.11512	+	0.810185i
$195$		0			0
$196$	1.39111	−	1.01070i	0.0993651	−	0.0721930i
$197$	−0.795517	−	1.09494i	−0.0566782	−	0.0780109i	0.779737	−	0.626107i	$-0.215353\pi$
$197$	−0.795517	−	1.09494i	−0.0566782	−	0.0780109i	−0.836415	+	0.548096i	$0.815353\pi$
$198$	−3.44330	+	1.11879i	−0.244704	+	0.0795093i
$199$	8.96061			0.635201			0.317600	−	0.948225i	$-0.397123\pi$
$199$	8.96061			0.635201			0.317600	+	0.948225i	$0.397123\pi$
$200$		0			0
$201$	−4.31358			−0.304257
$202$	−11.9796	+	3.89241i	−0.842882	+	0.273869i
$203$	6.94449	+	9.55827i	0.487408	+	0.670859i
$204$	0.640742	−	0.465526i	0.0448609	−	0.0325933i
$205$		0			0
$206$	−3.10780	−	2.25795i	−0.216530	−	0.157319i
$207$			8.79501i			0.611295i
$208$	3.64219	−	5.01304i	0.252540	−	0.347592i
$209$	4.15808	−	12.7973i	0.287621	−	0.885205i
$210$		0			0
$211$	1.80461	+	5.55401i	0.124234	+	0.382354i	0.993761	−	0.111532i	$-0.0355759\pi$
$211$	1.80461	+	5.55401i	0.124234	+	0.382354i	−0.869527	+	0.493886i	$0.835576\pi$
$212$	1.43212	+	0.465325i	0.0983586	+	0.0319586i
$213$	5.49473	+	1.78535i	0.376493	+	0.122330i
$214$	0.859440	+	2.64508i	0.0587501	+	0.180814i
$215$		0			0
$216$	0.778240	−	2.39518i	0.0529525	−	0.162971i
$217$	−3.24993	+	4.47314i	−0.220619	+	0.303656i
$218$			4.52939i			0.306769i
$219$	−5.60393	−	4.07149i	−0.378678	−	0.275126i
$220$		0			0
$221$	2.39541	−	1.74036i	0.161132	−	0.117070i
$222$	8.80668	+	12.1214i	0.591066	+	0.813532i
$223$	−7.43818	+	2.41681i	−0.498098	+	0.161842i	−0.547283	−	0.836948i	$-0.684338\pi$
$223$	−7.43818	+	2.41681i	−0.498098	+	0.161842i	0.0491848	+	0.998790i	$0.484338\pi$
$224$	3.01853			0.201684
$225$		0			0
$226$	21.2604			1.41422
$227$	−15.5107	+	5.03975i	−1.02948	+	0.334500i	−0.774586	−	0.632468i	$-0.782042\pi$
$227$	−15.5107	+	5.03975i	−1.02948	+	0.334500i	−0.254898	+	0.966968i	$0.582042\pi$
$228$	−1.21167	−	1.66773i	−0.0802451	−	0.110448i
$229$	−17.5628	+	12.7601i	−1.16058	+	0.843211i	−0.989851	−	0.142107i	$-0.954612\pi$
$229$	−17.5628	+	12.7601i	−1.16058	+	0.843211i	−0.170729	+	0.985318i	$0.554612\pi$
$230$		0			0
$231$	−2.85079	−	2.07122i	−0.187568	−	0.136276i
$232$		−	19.8961i		−	1.30624i
$233$	7.95512	−	10.9493i	0.521157	−	0.717312i	−0.464593	−	0.885524i	$-0.653799\pi$
$233$	7.95512	−	10.9493i	0.521157	−	0.717312i	0.985751	+	0.168213i	$0.0537995\pi$
$234$	−0.640771	+	1.97209i	−0.0418885	+	0.128920i
$235$		0			0
$236$	1.23424	+	3.79860i	0.0803421	+	0.247268i
$237$	10.1466	+	3.29682i	0.659090	+	0.214151i
$238$	4.79495	+	1.55797i	0.310810	+	0.100988i
$239$	3.25514	+	10.0183i	0.210557	+	0.648028i	0.999439	+	0.0334838i	$0.0106602\pi$
$239$	3.25514	+	10.0183i	0.210557	+	0.648028i	−0.788882	+	0.614545i	$0.789340\pi$
$240$		0			0
$241$	6.02082	−	18.5302i	0.387835	−	1.19363i	−0.546567	−	0.837415i	$-0.684066\pi$
$241$	6.02082	−	18.5302i	0.387835	−	1.19363i	0.934403	−	0.356219i	$-0.115934\pi$
$242$	−4.92047	+	6.77244i	−0.316300	+	0.435349i
$243$			1.00000i			0.0641500i
$244$	−3.57371	−	2.59645i	−0.228783	−	0.166221i
$245$		0			0
$246$	2.30655	−	1.67581i	0.147060	−	0.106846i
$247$	−4.52983	−	6.23478i	−0.288226	−	0.396709i
$248$	8.85537	−	2.87728i	0.562317	−	0.182708i
$249$	0.224003			0.0141956
$250$		0			0
$251$	−20.9446			−1.32201			−0.661007	−	0.750380i	$-0.729871\pi$
$251$	−20.9446			−1.32201			−0.661007	+	0.750380i	$0.729871\pi$
$252$	−0.513417	+	0.166819i	−0.0323422	+	0.0105086i
$253$	−12.1808	−	16.7655i	−0.765803	−	1.05404i
$254$	7.13529	−	5.18409i	0.447708	−	0.325279i
$255$		0			0
$256$	−6.79428	−	4.93633i	−0.424643	−	0.308521i
$257$		−	1.67121i		−	0.104247i	−0.998641	−	0.0521237i	$-0.983401\pi$
$257$		−	1.67121i		−	0.104247i	0.998641	−	0.0521237i	$-0.0165990\pi$
$258$	−7.24220	+	9.96804i	−0.450880	+	0.620583i
$259$	−4.50625	+	13.8688i	−0.280005	+	0.861766i
$260$		0			0
$261$	2.44129	+	7.51351i	0.151112	+	0.465074i
$262$	−6.36789	−	2.06905i	−0.393409	−	0.127826i
$263$	−7.18682	−	2.33514i	−0.443158	−	0.143991i	0.0789341	−	0.996880i	$-0.474848\pi$
$263$	−7.18682	−	2.33514i	−0.443158	−	0.143991i	−0.522092	+	0.852889i	$0.674848\pi$
$264$	1.83373	+	5.64364i	0.112858	+	0.347342i
$265$		0			0
$266$	4.05510	−	12.4803i	0.248634	−	0.765218i
$267$	−0.252258	+	0.347203i	−0.0154379	+	0.0212485i
$268$		−	1.55710i		−	0.0951151i
$269$	−9.12904	−	6.63264i	−0.556608	−	0.404399i	0.273608	−	0.961841i	$-0.411783\pi$
$269$	−9.12904	−	6.63264i	−0.556608	−	0.404399i	−0.830216	+	0.557442i	$0.811783\pi$
$270$		0			0
$271$	8.87912	−	6.45106i	0.539368	−	0.391874i	−0.284482	−	0.958681i	$-0.591822\pi$
$271$	8.87912	−	6.45106i	0.539368	−	0.391874i	0.823850	+	0.566808i	$0.191822\pi$
$272$	−5.92153	−	8.15029i	−0.359045	−	0.494184i
$273$	−1.91940	+	0.623652i	−0.116168	+	0.0377452i
$274$	−3.03407			−0.183295
$275$		0			0
$276$	−3.17479			−0.191100
$277$	5.46964	−	1.77719i	0.328639	−	0.106781i	−0.140050	−	0.990144i	$-0.544726\pi$
$277$	5.46964	−	1.77719i	0.328639	−	0.106781i	0.468689	+	0.883363i	$0.344726\pi$
$278$	1.51649	+	2.08727i	0.0909531	+	0.125186i
$279$	−2.99107	+	2.17314i	−0.179071	+	0.130103i
$280$		0			0
$281$	−6.87633	−	4.99595i	−0.410208	−	0.298033i	0.363478	−	0.931603i	$-0.381589\pi$
$281$	−6.87633	−	4.99595i	−0.410208	−	0.298033i	−0.773686	+	0.633569i	$0.781589\pi$
$282$		−	10.2380i		−	0.609663i
$283$	10.1245	−	13.9352i	0.601839	−	0.828360i	−0.394036	−	0.919095i	$-0.628922\pi$
$283$	10.1245	−	13.9352i	0.601839	−	0.828360i	0.995875	+	0.0907350i	$0.0289216\pi$
$284$	−0.644468	+	1.98347i	−0.0382421	+	0.117697i
$285$		0			0
$286$	−1.50982	−	4.64675i	−0.0892776	−	0.274768i
$287$	2.63907	+	0.857487i	0.155780	+	0.0506158i
$288$	1.91962	+	0.623723i	0.113115	+	0.0367532i
$289$	3.76573	+	11.5897i	0.221513	+	0.681748i
$290$		0			0
$291$	−3.86103	+	11.8830i	−0.226337	+	0.696595i
$292$	1.46971	−	2.02289i	0.0860084	−	0.118380i
$293$		−	9.38764i		−	0.548432i	−0.961668	−	0.274216i	$-0.911582\pi$
$293$		−	9.38764i		−	0.548432i	0.961668	−	0.274216i	$-0.0884183\pi$
$294$	5.92146	+	4.30219i	0.345347	+	0.250909i
$295$		0			0
$296$	19.8672	−	14.4344i	1.15476	−	0.838980i
$297$	−1.38497	−	1.90625i	−0.0803642	−	0.110612i
$298$	−10.7924	+	3.50665i	−0.625185	+	0.203135i
$299$	−11.8689			−0.686397
$300$		0			0
$301$	−11.9920			−0.691207
$302$	6.22732	−	2.02338i	0.358342	−	0.116432i
$303$	−4.81847	−	6.63205i	−0.276814	−	0.381001i
$304$	−21.2136	+	15.4126i	−1.21668	+	0.883973i
$305$		0			0
$306$	2.72741	+	1.98158i	0.155916	+	0.113279i
$307$			10.6465i			0.607627i	0.952731	+	0.303814i	$0.0982600\pi$
$307$			10.6465i			0.607627i	−0.952731	+	0.303814i	$0.901740\pi$
$308$	0.747662	−	1.02907i	0.0426020	−	0.0586366i
$309$	0.772559	−	2.37769i	0.0439493	−	0.135262i
$310$		0			0
$311$	−8.45383	−	26.0182i	−0.479373	−	1.47536i	−0.839969	−	0.542635i	$-0.817427\pi$
$311$	−8.45383	−	26.0182i	−0.479373	−	1.47536i	0.360596	−	0.932722i	$-0.382573\pi$
$312$	3.23230	+	1.05024i	0.182993	+	0.0594581i
$313$	1.89744	+	0.616517i	0.107250	+	0.0348476i	0.362150	−	0.932120i	$-0.382043\pi$
$313$	1.89744	+	0.616517i	0.107250	+	0.0348476i	−0.254900	+	0.966967i	$0.582043\pi$
$314$	−7.62433	−	23.4653i	−0.430266	−	1.32422i
$315$		0			0
$316$	−1.19007	+	3.66267i	−0.0669469	+	0.206041i
$317$	5.08361	−	6.99699i	0.285524	−	0.392990i	−0.642030	−	0.766680i	$-0.721907\pi$
$317$	5.08361	−	6.99699i	0.285524	−	0.392990i	0.927554	+	0.373690i	$0.121907\pi$
$318$			6.40975i			0.359441i
$319$	−15.0597	−	10.9415i	−0.843182	−	0.612607i
$320$		0			0
$321$	−1.46435	+	1.06391i	−0.0817321	+	0.0593818i
$322$	−11.8792	−	16.3503i	−0.662000	−	0.911165i
$323$	−11.9163	+	3.87184i	−0.663040	+	0.215435i
$324$	−0.360976			−0.0200542
$325$		0			0
$326$	−34.2554			−1.89723
$327$	−2.80350	+	0.910913i	−0.155034	+	0.0503736i
$328$	−2.74669	−	3.78049i	−0.151661	−	0.208743i
$329$	8.06141	−	5.85696i	0.444440	−	0.322905i
$330$		0			0
$331$	3.19020	+	2.31782i	0.175349	+	0.127399i	0.671998	−	0.740553i	$-0.265436\pi$
$331$	3.19020	+	2.31782i	0.175349	+	0.127399i	−0.496649	+	0.867952i	$0.665436\pi$
$332$			0.0808598i			0.00443776i
$333$	−5.73148	+	7.88870i	−0.314083	+	0.432298i
$334$	3.07018	−	9.44905i	0.167993	−	0.517029i
$335$		0			0
$336$	2.12196	+	6.53071i	0.115762	+	0.356279i
$337$	3.76115	+	1.22207i	0.204883	+	0.0665706i	0.409661	−	0.912238i	$-0.365647\pi$
$337$	3.76115	+	1.22207i	0.204883	+	0.0665706i	−0.204778	+	0.978809i	$0.565647\pi$
$338$	16.3361	+	5.30792i	0.888567	+	0.288713i
$339$	4.27571	+	13.1593i	0.232224	+	0.714713i
$340$		0			0
$341$	2.69199	−	8.28511i	0.145780	−	0.448664i
$342$	5.15766	−	7.09891i	0.278894	−	0.383865i
$343$			17.5923i			0.949893i
$344$	16.3379	+	11.8701i	0.880878	+	0.639995i
$345$		0			0
$346$	14.6909	−	10.6736i	0.789789	−	0.573815i
$347$	5.87548	+	8.08690i	0.315412	+	0.434127i	0.937060	−	0.349170i	$-0.113536\pi$
$347$	5.87548	+	8.08690i	0.315412	+	0.434127i	−0.621647	+	0.783297i	$0.713536\pi$
$348$	−2.71220	+	0.881247i	−0.145389	+	0.0472398i
$349$	−18.4534			−0.987789			−0.493895	−	0.869522i	$-0.664427\pi$
$349$	−18.4534			−0.987789			−0.493895	+	0.869522i	$0.664427\pi$
$350$		0			0
$351$	−1.34951			−0.0720313
$352$	−4.52312	+	1.46965i	−0.241083	+	0.0783327i
$353$	5.48050	+	7.54326i	0.291697	+	0.401487i	0.929565	−	0.368659i	$-0.120183\pi$
$353$	5.48050	+	7.54326i	0.291697	+	0.401487i	−0.637867	+	0.770146i	$0.720183\pi$
$354$	−13.7544	+	9.99316i	−0.731038	+	0.531130i
$355$		0			0
$356$	−0.125332	−	0.0910592i	−0.00664260	−	0.00482613i
$357$			3.28119i			0.173659i
$358$	−14.0663	+	19.3606i	−0.743428	+	1.02324i
$359$	−8.94412	+	27.5272i	−0.472052	+	1.45283i	0.377839	+	0.925871i	$0.376667\pi$
$359$	−8.94412	+	27.5272i	−0.472052	+	1.45283i	−0.849892	+	0.526957i	$0.823333\pi$
$360$		0			0
$361$	4.20632	+	12.9457i	0.221385	+	0.681354i
$362$	−21.3060	−	6.92273i	−1.11982	−	0.363850i
$363$	−5.18141	−	1.68354i	−0.271954	−	0.0883631i
$364$	−0.225124	−	0.692860i	−0.0117997	−	0.0363157i
$365$		0			0
$366$	5.81047	−	17.8828i	0.303718	−	0.934748i
$367$	−2.35037	+	3.23501i	−0.122688	+	0.168866i	−0.865943	−	0.500142i	$-0.833281\pi$
$367$	−2.35037	+	3.23501i	−0.122688	+	0.168866i	0.743255	+	0.669008i	$0.233281\pi$
$368$			40.3836i			2.10514i
$369$	1.50113	+	1.09063i	0.0781456	+	0.0567761i
$370$		0			0
$371$	−5.04705	+	3.66690i	−0.262030	+	0.190376i
$372$	−0.784453	−	1.07971i	−0.0406720	−	0.0559802i
$373$	−3.01732	+	0.980386i	−0.156231	+	0.0507625i	−0.386088	−	0.922462i	$-0.626174\pi$
$373$	−3.01732	+	0.980386i	−0.156231	+	0.0507625i	0.229857	+	0.973224i	$0.426174\pi$
$374$	−7.94355			−0.410751
$375$		0			0
$376$	−16.7803			−0.865377
$377$	−10.1395	+	3.29453i	−0.522212	+	0.169677i
$378$	−1.35067	−	1.85904i	−0.0694711	−	0.0956187i
$379$	23.0736	−	16.7640i	1.18521	−	0.861107i	0.192462	−	0.981304i	$-0.438353\pi$
$379$	23.0736	−	16.7640i	1.18521	−	0.861107i	0.992750	+	0.120198i	$0.0383528\pi$
$380$		0			0
$381$	4.64372	+	3.37386i	0.237905	+	0.172848i
$382$		−	32.2497i		−	1.65004i
$383$	6.73667	−	9.27224i	0.344228	−	0.473789i	−0.601442	−	0.798916i	$-0.705407\pi$
$383$	6.73667	−	9.27224i	0.344228	−	0.473789i	0.945670	+	0.325127i	$0.105407\pi$
$384$	4.13526	−	12.7270i	0.211026	−	0.649472i
$385$		0			0
$386$	10.7828	+	33.1862i	0.548832	+	1.68913i
$387$	−7.62628	−	2.47793i	−0.387665	−	0.125960i
$388$	−4.28949	−	1.39374i	−0.217766	−	0.0707564i
$389$	−10.5827	−	32.5702i	−0.536564	−	1.65137i	−0.740245	−	0.672337i	$-0.765291\pi$
$389$	−10.5827	−	32.5702i	−0.536564	−	1.65137i	0.203681	−	0.979037i	$-0.434709\pi$
$390$		0			0
$391$	−5.96301	+	18.3522i	−0.301562	+	0.928113i
$392$	7.05140	−	9.70541i	0.356149	−	0.490197i
$393$		−	4.35756i		−	0.219810i
$394$	1.68242	+	1.22235i	0.0847591	+	0.0615811i
$395$		0			0
$396$	0.688111	−	0.499942i	0.0345789	−	0.0251230i
$397$	11.7753	+	16.2073i	0.590986	+	0.813422i	0.994846	−	0.101399i	$-0.0323318\pi$
$397$	11.7753	+	16.2073i	0.590986	+	0.813422i	−0.403860	+	0.914821i	$0.632332\pi$
$398$	−13.0945	+	4.25467i	−0.656369	+	0.213267i
$399$	8.54031			0.427550
$400$		0			0
$401$	4.98200			0.248789			0.124395	−	0.992233i	$-0.460301\pi$
$401$	4.98200			0.248789			0.124395	+	0.992233i	$0.460301\pi$
$402$	6.30363	−	2.04817i	0.314396	−	0.102154i
$403$	−2.93267	−	4.03647i	−0.146087	−	0.201071i
$404$	2.39401	−	1.73935i	0.119107	−	0.0865361i
$405$		0			0
$406$	−14.6867	−	10.6705i	−0.728890	−	0.529570i
$407$		−	22.9758i		−	1.13887i
$408$	3.24785	−	4.47029i	0.160793	−	0.221312i
$409$	−7.37286	+	22.6913i	−0.364565	+	1.12201i	0.585689	+	0.810536i	$0.300824\pi$
$409$	−7.37286	+	22.6913i	−0.364565	+	1.12201i	−0.950253	+	0.311478i	$0.899176\pi$
$410$		0			0
$411$	−0.610187	−	1.87796i	−0.0300983	−	0.0926330i
$412$	0.858290	+	0.278875i	0.0422849	+	0.0137392i
$413$	−15.7373	−	5.11335i	−0.774381	−	0.251612i
$414$	−4.17604	−	12.8525i	−0.205241	−	0.631667i
$415$		0			0
$416$	−0.841718	+	2.59054i	−0.0412686	+	0.127012i
$417$	−0.986948	+	1.35842i	−0.0483311	+	0.0665220i
$418$			20.6755i			1.01127i
$419$	0.390391	+	0.283636i	0.0190719	+	0.0138565i	0.597280	−	0.802033i	$-0.296248\pi$
$419$	0.390391	+	0.283636i	0.0190719	+	0.0138565i	−0.578208	+	0.815889i	$0.696248\pi$
$420$		0			0
$421$	14.3344	−	10.4146i	0.698616	−	0.507575i	−0.180865	−	0.983508i	$-0.557890\pi$
$421$	14.3344	−	10.4146i	0.698616	−	0.507575i	0.879481	+	0.475933i	$0.157890\pi$
$422$	−5.27430	−	7.25945i	−0.256749	−	0.353385i
$423$	6.33687	−	2.05897i	0.308109	−	0.100111i
$424$	10.5057			0.510203
$425$		0			0
$426$	−8.87740			−0.430112
$427$	17.4050	−	5.65523i	0.842288	−	0.273676i
$428$	−0.384047	−	0.528596i	−0.0185636	−	0.0255506i
$429$	2.57250	−	1.86903i	0.124201	−	0.0902375i
$430$		0			0
$431$	−21.6866	−	15.7562i	−1.04461	−	0.758952i	−0.0734279	−	0.997301i	$-0.523394\pi$
$431$	−21.6866	−	15.7562i	−1.04461	−	0.758952i	−0.971180	+	0.238349i	$0.923394\pi$
$432$			4.59165i			0.220916i
$433$	5.42593	−	7.46816i	0.260754	−	0.358897i	−0.658487	−	0.752592i	$-0.728803\pi$
$433$	5.42593	−	7.46816i	0.260754	−	0.358897i	0.919241	+	0.393695i	$0.128803\pi$
$434$	2.62532	−	8.07992i	0.126020	−	0.387848i
$435$		0			0
$436$	−0.328818	−	1.01200i	−0.0157475	−	0.0484659i
$437$	47.7673	+	15.5205i	2.28502	+	0.742448i
$438$	10.1225	+	3.28899i	0.483671	+	0.157154i
$439$	−0.309760	−	0.953343i	−0.0147840	−	0.0455006i	0.943392	−	0.331679i	$-0.107615\pi$
$439$	−0.309760	−	0.953343i	−0.0147840	−	0.0455006i	−0.958176	+	0.286178i	$0.907615\pi$
$440$		0			0
$441$	−1.47200	+	4.53035i	−0.0700952	+	0.215731i
$442$	−2.67415	+	3.68065i	−0.127196	+	0.175071i
$443$			26.2872i			1.24894i	0.781048	+	0.624471i	$0.214685\pi$
$443$			26.2872i			1.24894i	−0.781048	+	0.624471i	$0.785315\pi$
$444$	−2.84763	−	2.06893i	−0.135143	−	0.0981869i
$445$		0			0
$446$	9.72219	−	7.06358i	0.460359	−	0.334470i
$447$	−4.34094	−	5.97479i	−0.205319	−	0.282598i
$448$	8.65032	−	2.81066i	0.408689	−	0.132791i
$449$	−4.75449			−0.224378			−0.112189	−	0.993687i	$-0.535786\pi$
$449$	−4.75449			−0.224378			−0.112189	+	0.993687i	$0.535786\pi$
$450$		0			0
$451$	−4.37202			−0.205870
$452$	−4.75019	+	1.54343i	−0.223430	+	0.0725968i
$453$	2.50477	+	3.44752i	0.117684	+	0.161979i
$454$	20.2736	−	14.7296i	0.951485	−	0.691294i
$455$		0			0
$456$	−11.6353	−	8.45353i	−0.544872	−	0.395873i
$457$			15.9703i			0.747059i	0.927618	+	0.373529i	$0.121852\pi$
$457$			15.9703i			0.747059i	−0.927618	+	0.373529i	$0.878148\pi$
$458$	19.6065	−	26.9860i	0.916151	−	1.26097i
$459$	−0.677999	+	2.08667i	−0.0316463	+	0.0973972i
$460$		0			0
$461$	12.2852	+	37.8100i	0.572180	+	1.76099i	0.645588	+	0.763686i	$0.276613\pi$
$461$	12.2852	+	37.8100i	0.572180	+	1.76099i	−0.0734077	+	0.997302i	$0.523387\pi$
$462$	5.14944	+	1.67315i	0.239573	+	0.0778421i
$463$	24.8425	+	8.07181i	1.15453	+	0.375129i	0.822847	−	0.568263i	$-0.192384\pi$
$463$	24.8425	+	8.07181i	1.15453	+	0.375129i	0.331681	+	0.943392i	$0.392384\pi$
$464$	11.2095	+	34.4994i	0.520389	+	1.60159i
$465$		0			0
$466$	−6.42623	+	19.7779i	−0.297689	+	0.916194i
$467$	2.26417	−	3.11637i	0.104773	−	0.144208i	−0.753411	−	0.657550i	$-0.771593\pi$
$467$	2.26417	−	3.11637i	0.104773	−	0.144208i	0.858184	+	0.513342i	$0.171593\pi$
$468$		−	0.487140i		−	0.0225181i
$469$	5.21893	+	3.79177i	0.240988	+	0.175088i
$470$		0			0
$471$	12.9907	−	9.43827i	0.598578	−	0.434893i
$472$	16.3790	+	22.5438i	0.753906	+	1.03766i
$473$	17.9695	−	5.83863i	0.826236	−	0.268460i
$474$	−16.3930			−0.752956
$475$		0			0
$476$	−1.18443			−0.0542884
$477$	−3.96736	+	1.28907i	−0.181653	+	0.0590226i
$478$	−9.51374	−	13.0945i	−0.435148	−	0.598930i
$479$	−11.5445	+	8.38758i	−0.527483	+	0.383239i	−0.819415	−	0.573200i	$-0.805702\pi$
$479$	−11.5445	+	8.38758i	−0.527483	+	0.383239i	0.291933	+	0.956439i	$0.405702\pi$
$480$		0			0
$481$	−10.6458	−	7.73466i	−0.485409	−	0.352670i
$482$			29.9377i			1.36363i
$483$	7.73108	−	10.6409i	0.351776	−	0.484179i
$484$	0.607720	−	1.87037i	0.0276236	−	0.0850167i
$485$		0			0
$486$	−0.474819	−	1.46134i	−0.0215382	−	0.0662879i
$487$	−23.6073	−	7.67049i	−1.06975	−	0.347583i	−0.279360	−	0.960186i	$-0.590122\pi$
$487$	−23.6073	−	7.67049i	−1.06975	−	0.347583i	−0.790390	+	0.612604i	$0.790122\pi$
$488$	−29.3103	−	9.52349i	−1.32681	−	0.431108i
$489$	−6.88916	−	21.2026i	−0.311538	−	0.958817i
$490$		0			0
$491$	3.55040	−	10.9270i	0.160227	−	0.493129i	−0.838426	−	0.545016i	$-0.816524\pi$
$491$	3.55040	−	10.9270i	0.160227	−	0.493129i	0.998653	+	0.0518868i	$0.0165235\pi$
$492$	−0.393693	+	0.541871i	−0.0177490	+	0.0244295i
$493$			17.3334i			0.780656i
$494$	9.58003	+	6.96030i	0.431026	+	0.313159i
$495$		0			0
$496$	−13.7340	+	9.97831i	−0.616673	+	0.448039i
$497$	−5.07860	−	6.99010i	−0.227806	−	0.313549i
$498$	−0.327345	+	0.106361i	−0.0146687	+	0.00476614i
$499$	4.17487			0.186893			0.0934465	−	0.995624i	$-0.470212\pi$
$499$	4.17487			0.186893			0.0934465	+	0.995624i	$0.470212\pi$
$500$		0			0
$501$	6.46601			0.288880
$502$	30.6073	−	9.94491i	1.36607	−	0.443863i
$503$	−22.7569	−	31.3221i	−1.01468	−	1.39658i	−0.915869	−	0.401478i	$-0.868497\pi$
$503$	−22.7569	−	31.3221i	−1.01468	−	1.39658i	−0.0988094	−	0.995106i	$-0.531503\pi$
$504$	−3.04701	+	2.21378i	−0.135725	+	0.0986097i
$505$		0			0
$506$	25.7610	+	18.7164i	1.14521	+	0.832047i
$507$			11.1788i			0.496469i
$508$	−1.21788	+	1.67627i	−0.0540349	+	0.0743726i
$509$	−9.32603	+	28.7026i	−0.413369	+	1.27222i	0.500333	+	0.865833i	$0.333211\pi$
$509$	−9.32603	+	28.7026i	−0.413369	+	1.27222i	−0.913702	+	0.406385i	$0.866789\pi$
$510$		0			0
$511$	3.20112	+	9.85205i	0.141609	+	0.435829i
$512$	−13.1814	−	4.28289i	−0.582540	−	0.189279i
$513$	5.43119	+	1.76470i	0.239793	+	0.0779134i
$514$	0.793523	+	2.44221i	0.0350008	+	0.107721i
$515$		0			0
$516$	0.894473	−	2.75291i	0.0393770	−	0.121190i
$517$	−9.22804	+	12.7013i	−0.405849	+	0.558603i
$518$		−	22.4067i		−	0.984496i
$519$	9.56100	+	6.94647i	0.419681	+	0.304916i
$520$		0			0
$521$	20.6183	−	14.9801i	0.903304	−	0.656288i	−0.0360088	−	0.999351i	$-0.511464\pi$
$521$	20.6183	−	14.9801i	0.903304	−	0.656288i	0.939312	+	0.343063i	$0.111464\pi$
$522$	−7.13511	−	9.82064i	−0.312295	−	0.429838i
$523$	3.70132	−	1.20263i	0.161847	−	0.0525874i	−0.226973	−	0.973901i	$-0.572883\pi$
$523$	3.70132	−	1.20263i	0.161847	−	0.0525874i	0.388820	+	0.921314i	$0.372883\pi$
$524$	1.57298			0.0687158
$525$		0			0
$526$	11.6112			0.506271
$527$	−7.71476	+	2.50668i	−0.336060	+	0.109193i
$528$	−6.35931	−	8.75283i	−0.276753	−	0.380918i
$529$	43.9719	−	31.9474i	1.91182	−	1.38902i
$530$		0			0
$531$	−8.95150	−	6.50365i	−0.388462	−	0.282234i
$532$			3.08285i			0.133659i
$533$	−1.47182	+	2.02578i	−0.0637514	+	0.0877463i
$534$	0.203777	−	0.627160i	0.00881828	−	0.0271399i
$535$		0			0
$536$	−3.35700	−	10.3318i	−0.145000	−	0.446265i
$537$	−14.8123	−	4.81281i	−0.639198	−	0.207688i
$538$	16.4900	+	5.35792i	0.710933	+	0.230996i
$539$	−3.46841	−	10.6747i	−0.149395	−	0.459790i
$540$		0			0
$541$	12.4270	−	38.2465i	0.534280	−	1.64435i	−0.210919	−	0.977504i	$-0.567646\pi$
$541$	12.4270	−	38.2465i	0.534280	−	1.64435i	0.745199	−	0.666842i	$-0.232354\pi$
$542$	−9.91235	+	13.6432i	−0.425772	+	0.586025i
$543$		−	14.5797i		−	0.625675i
$544$	3.58273	+	2.60300i	0.153608	+	0.111603i
$545$		0			0
$546$	2.50879	−	1.82274i	0.107366	−	0.0780061i
$547$	−4.33740	−	5.96992i	−0.185454	−	0.255255i	0.706160	−	0.708053i	$-0.250426\pi$
$547$	−4.33740	−	5.96992i	−0.185454	−	0.255255i	−0.891613	+	0.452797i	$0.850426\pi$
$548$	0.677900	−	0.220263i	0.0289584	−	0.00940917i
$549$	12.2372			0.522272
$550$		0			0
$551$	45.1154			1.92198
$552$	−21.0656	+	6.84463i	−0.896611	+	0.291327i
$553$	−9.37814	−	12.9079i	−0.398799	−	0.548900i
$554$	−7.14917	+	5.19418i	−0.303739	+	0.220679i
$555$		0			0
$556$	−0.490357	−	0.356265i	−0.0207958	−	0.0151090i
$557$			1.52499i			0.0646160i	0.999478	+	0.0323080i	$0.0102857\pi$
$557$			1.52499i			0.0646160i	−0.999478	+	0.0323080i	$0.989714\pi$
$558$	3.33913	−	4.59592i	0.141357	−	0.194561i
$559$	3.34398	−	10.2917i	0.141435	−	0.435293i
$560$		0			0
$561$	−1.59754	−	4.91672i	−0.0674481	−	0.207584i
$562$	12.4209	+	4.03578i	0.523942	+	0.170239i
$563$	−13.1203	−	4.26305i	−0.552955	−	0.179666i	0.0191938	−	0.999816i	$-0.493890\pi$
$563$	−13.1203	−	4.26305i	−0.552955	−	0.179666i	−0.572149	+	0.820150i	$0.693890\pi$
$564$	0.743241	+	2.28746i	0.0312961	+	0.0963194i
$565$		0			0
$566$	−8.17867	+	25.1714i	−0.343775	+	1.05803i
$567$	0.879031	−	1.20988i	0.0369158	−	0.0508103i
$568$			14.5503i			0.610516i
$569$	−6.87586	−	4.99561i	−0.288251	−	0.209427i	0.434257	−	0.900789i	$-0.357011\pi$
$569$	−6.87586	−	4.99561i	−0.288251	−	0.209427i	−0.722508	+	0.691362i	$0.757011\pi$
$570$		0			0
$571$	−31.8130	+	23.1135i	−1.33133	+	0.967269i	−0.331617	+	0.943414i	$0.607594\pi$
$571$	−31.8130	+	23.1135i	−1.33133	+	0.967269i	−0.999715	+	0.0238553i	$0.992406\pi$
$572$	0.674675	+	0.928611i	0.0282096	+	0.0388272i
$573$	19.9611	−	6.48577i	0.833889	−	0.270947i
$574$	−4.26374			−0.177965
$575$		0			0
$576$	6.08192			0.253413
$577$	−23.3800	+	7.59664i	−0.973324	+	0.316252i	−0.752157	−	0.658984i	$-0.770987\pi$
$577$	−23.3800	+	7.59664i	−0.973324	+	0.316252i	−0.221167	+	0.975236i	$0.570987\pi$
$578$	−11.0060	−	15.1485i	−0.457791	−	0.630095i
$579$	−18.3723	+	13.3482i	−0.763525	+	0.554734i
$580$		0			0
$581$	−0.271017	−	0.196905i	−0.0112437	−	0.00816901i
$582$		−	19.1985i		−	0.795802i
$583$	5.77745	−	7.95197i	0.239277	−	0.329337i
$584$	5.39074	−	16.5910i	0.223070	−	0.686540i
$585$		0			0
$586$	4.45743	+	13.7186i	0.184135	+	0.566708i
$587$	−8.79033	−	2.85615i	−0.362816	−	0.117886i	0.121936	−	0.992538i	$-0.461090\pi$
$587$	−8.79033	−	2.85615i	−0.362816	−	0.117886i	−0.484751	+	0.874652i	$0.661090\pi$
$588$	−1.63535	−	0.531357i	−0.0674407	−	0.0219128i
$589$	6.52439	+	20.0800i	0.268833	+	0.827383i
$590$		0			0
$591$	−0.418228	+	1.28717i	−0.0172036	+	0.0529472i
$592$	−26.3169	+	36.2221i	−1.08162	+	1.48872i
$593$			6.07888i			0.249630i	0.992180	+	0.124815i	$0.0398337\pi$
$593$			6.07888i			0.249630i	−0.992180	+	0.124815i	$0.960166\pi$
$594$	2.92904	+	2.12807i	0.120180	+	0.0873160i
$595$		0			0
$596$	2.15676	−	1.56698i	0.0883442	−	0.0641858i
$597$	−5.26692	−	7.24929i	−0.215560	−	0.296694i
$598$	17.3446	−	5.63559i	0.709272	−	0.230456i
$599$	−6.40129			−0.261550			−0.130775	−	0.991412i	$-0.541746\pi$
$599$	−6.40129			−0.261550			−0.130775	+	0.991412i	$0.541746\pi$
$600$		0			0
$601$	−38.4675			−1.56912			−0.784560	−	0.620052i	$-0.787111\pi$
$601$	−38.4675			−1.56912			−0.784560	+	0.620052i	$0.787111\pi$
$602$	17.5244	−	5.69403i	0.714242	−	0.232071i
$603$	2.53546	+	3.48976i	0.103252	+	0.142114i
$604$	−1.24447	+	0.904162i	−0.0506369	+	0.0367898i
$605$		0			0
$606$	10.1905	+	7.40380i	0.413959	+	0.300759i
$607$			5.22464i			0.212062i	0.994363	+	0.106031i	$0.0338142\pi$
$607$			5.22464i			0.212062i	−0.994363	+	0.106031i	$0.966186\pi$
$608$	6.77511	−	9.32514i	0.274767	−	0.378184i
$609$	3.65093	−	11.2364i	0.147943	−	0.455323i
$610$		0			0
$611$	2.77860	+	8.55164i	0.112410	+	0.345962i
$612$	−0.753237	−	0.244742i	−0.0304478	−	0.00989309i
$613$	−28.3560	−	9.21343i	−1.14529	−	0.372127i	−0.325922	−	0.945397i	$-0.605675\pi$
$613$	−28.3560	−	9.21343i	−1.14529	−	0.372127i	−0.819367	+	0.573270i	$0.805675\pi$
$614$	−5.05516	−	15.5582i	−0.204010	−	0.627877i
$615$		0			0
$616$	2.74234	−	8.44005i	0.110492	−	0.340059i
$617$	13.6969	−	18.8521i	0.551415	−	0.758958i	−0.438788	−	0.898591i	$-0.644592\pi$
$617$	13.6969	−	18.8521i	0.551415	−	0.758958i	0.990203	+	0.139633i	$0.0445921\pi$
$618$			3.84145i			0.154526i
$619$	−0.191326	−	0.139007i	−0.00769006	−	0.00558715i	0.583934	−	0.811801i	$-0.301513\pi$
$619$	−0.191326	−	0.139007i	−0.00769006	−	0.00558715i	−0.591624	+	0.806214i	$0.701513\pi$
$620$		0			0
$621$	7.11531	−	5.16958i	0.285528	−	0.207448i
$622$	24.7079	+	34.0075i	0.990696	+	1.36358i
$623$	0.610405	−	0.198333i	0.0244554	−	0.00794603i
$624$	−6.19646			−0.248057
$625$		0			0
$626$	−3.06555			−0.122524
$627$	−12.7973	+	4.15808i	−0.511073	+	0.166058i
$628$	3.40699	+	4.68932i	0.135954	+	0.187124i
$629$	−17.3082	+	12.5751i	−0.690123	+	0.501404i
$630$		0			0
$631$	14.4643	+	10.5090i	0.575816	+	0.418355i	0.837213	−	0.546876i	$-0.184183\pi$
$631$	14.4643	+	10.5090i	0.575816	+	0.418355i	−0.261397	+	0.965231i	$0.584183\pi$
$632$			26.8685i			1.06877i
$633$	3.43257	−	4.72452i	0.136432	−	0.187783i
$634$	−4.10659	+	12.6388i	−0.163094	+	0.501951i
$635$		0			0
$636$	−0.465325	−	1.43212i	−0.0184513	−	0.0567873i
$637$	−6.11374	−	1.98647i	−0.242235	−	0.0787069i
$638$	27.2026	+	8.83867i	1.07696	+	0.349926i
$639$	−1.78535	−	5.49473i	−0.0706272	−	0.217368i
$640$		0			0
$641$	3.35839	−	10.3361i	0.132648	−	0.408250i	−0.862568	−	0.505940i	$-0.831146\pi$
$641$	3.35839	−	10.3361i	0.132648	−	0.408250i	0.995217	+	0.0976905i	$0.0311455\pi$
$642$	1.63475	−	2.25004i	0.0645185	−	0.0888021i
$643$		−	3.09039i		−	0.121873i	−0.998142	−	0.0609366i	$-0.980591\pi$
$643$		−	3.09039i		−	0.121873i	0.998142	−	0.0609366i	$-0.0194088\pi$
$644$	3.84112	+	2.79074i	0.151361	+	0.109970i
$645$		0			0
$646$	15.5754	−	11.3162i	0.612805	−	0.445229i
$647$	3.25460	+	4.47957i	0.127951	+	0.176110i	0.868186	−	0.496238i	$-0.165286\pi$
$647$	3.25460	+	4.47957i	0.127951	+	0.176110i	−0.740235	+	0.672348i	$0.765286\pi$
$648$	−2.39518	+	0.778240i	−0.0940914	+	0.0305721i
$649$	26.0712			1.02338
$650$		0			0
$651$	5.52910			0.216703
$652$	7.65366	−	2.48682i	0.299740	−	0.0973915i
$653$	22.8504	+	31.4509i	0.894206	+	1.23077i	0.972280	+	0.233821i	$0.0751230\pi$
$653$	22.8504	+	31.4509i	0.894206	+	1.23077i	−0.0780738	+	0.996948i	$0.524877\pi$
$654$	3.66436	−	2.66231i	0.143288	−	0.104105i
$655$		0			0
$656$	6.89265	+	5.00780i	0.269113	+	0.195522i
$657$			6.92684i			0.270242i
$658$	−8.99949	+	12.3867i	−0.350837	+	0.482885i
$659$	6.34687	−	19.5337i	0.247239	−	0.760923i	−0.748021	−	0.663675i	$-0.768996\pi$
$659$	6.34687	−	19.5337i	0.247239	−	0.760923i	0.995260	−	0.0972484i	$-0.0310041\pi$
$660$		0			0
$661$	11.8741	+	36.5447i	0.461848	+	1.42142i	0.862903	+	0.505369i	$0.168644\pi$
$661$	11.8741	+	36.5447i	0.461848	+	1.42142i	−0.401055	+	0.916054i	$0.631356\pi$
$662$	−5.76252	−	1.87236i	−0.223967	−	0.0727712i
$663$	−2.81597	−	0.914964i	−0.109363	−	0.0355342i
$664$	0.174328	+	0.536526i	0.00676524	+	0.0208213i
$665$		0			0
$666$	4.62995	−	14.2495i	0.179407	−	0.552157i
$667$	40.8405	−	56.2122i	1.58135	−	2.17654i
$668$			2.33408i			0.0903081i
$669$	6.32730	+	4.59705i	0.244627	+	0.177732i
$670$		0			0
$671$	−23.3272	+	16.9482i	−0.900537	+	0.654278i
$672$	−1.77424	−	2.44204i	−0.0684430	−	0.0942037i
$673$	−12.3466	+	4.01164i	−0.475925	+	0.154637i	−0.537150	−	0.843487i	$-0.680499\pi$
$673$	−12.3466	+	4.01164i	−0.475925	+	0.154637i	0.0612254	+	0.998124i	$0.480499\pi$
$674$	−6.07660			−0.234062
$675$		0			0
$676$	−4.03529			−0.155204
$677$	−6.88524	+	2.23715i	−0.264621	+	0.0859807i	−0.438323	−	0.898818i	$-0.644427\pi$
$677$	−6.88524	+	2.23715i	−0.264621	+	0.0859807i	0.173701	+	0.984798i	$0.444427\pi$
$678$	−12.4965	−	17.2000i	−0.479927	−	0.660563i
$679$	15.1169	−	10.9831i	0.580134	−	0.421492i
$680$		0			0
$681$	13.1942	+	9.58617i	0.505604	+	0.367343i
$682$			13.3856i			0.512561i
$683$	−14.6241	+	20.1283i	−0.559575	+	0.770188i	−0.991272	−	0.131830i	$-0.957915\pi$
$683$	−14.6241	+	20.1283i	−0.559575	+	0.770188i	0.431698	+	0.902018i	$0.357915\pi$
$684$	−0.637015	+	1.96053i	−0.0243569	+	0.0749627i
$685$		0			0
$686$	−8.35314	−	25.7083i	−0.318924	−	0.981548i
$687$	20.6463	+	6.70838i	0.787704	+	0.255941i
$688$	−35.0172	−	11.3778i	−1.33502	−	0.433774i
$689$	−1.73961	−	5.35397i	−0.0662739	−	0.203970i
$690$		0			0
$691$	−10.2812	+	31.6422i	−0.391114	+	1.20373i	0.540832	+	0.841130i	$0.318109\pi$
$691$	−10.2812	+	31.6422i	−0.391114	+	1.20373i	−0.931947	+	0.362595i	$0.881891\pi$
$692$	−2.50751	+	3.45130i	−0.0953213	+	0.131199i
$693$			3.52377i			0.133857i
$694$	−12.4259	−	9.02794i	−0.471681	−	0.342696i
$695$		0			0
$696$	−16.0963	+	11.6946i	−0.610127	+	0.443283i
$697$	2.39290	+	3.29355i	0.0906377	+	0.124752i
$698$	26.9668	−	8.76204i	1.02071	−	0.331648i
$699$	−13.5341			−0.511905
$700$		0			0
$701$	−13.2163			−0.499173			−0.249586	−	0.968353i	$-0.580295\pi$
$701$	−13.2163			−0.499173			−0.249586	+	0.968353i	$0.580295\pi$
$702$	1.97209	−	0.640771i	0.0744318	−	0.0241844i
$703$	32.7307	+	45.0499i	1.23446	+	1.69909i
$704$	−11.5937	+	8.42328i	−0.436952	+	0.317464i
$705$		0			0
$706$	−11.5906	−	8.42104i	−0.436217	−	0.316930i
$707$			12.2596i			0.461069i
$708$	2.34766	−	3.23128i	0.0882306	−	0.121439i
$709$	−1.93157	+	5.94475i	−0.0725415	+	0.223260i	−0.980753	−	0.195251i	$-0.937448\pi$
$709$	−1.93157	+	5.94475i	−0.0725415	+	0.223260i	0.908212	+	0.418511i	$0.137448\pi$
$710$		0			0
$711$	−3.29682	−	10.1466i	−0.123640	−	0.380526i
$712$	−1.02793	−	0.333995i	−0.0385233	−	0.0125170i
$713$	30.9252	+	10.0482i	1.15816	+	0.376308i
$714$	−1.55797	−	4.79495i	−0.0583057	−	0.179446i
$715$		0			0
$716$	1.73731	−	5.34689i	0.0649263	−	0.199823i
$717$	6.19164	−	8.52206i	0.231231	−	0.318262i
$718$		−	44.4735i		−	1.65973i
$719$	22.2492	+	16.1650i	0.829757	+	0.602854i	0.919491	−	0.393112i	$-0.128602\pi$
$719$	22.2492	+	16.1650i	0.829757	+	0.602854i	−0.0897336	+	0.995966i	$0.528602\pi$
$720$		0			0
$721$	−3.02477	+	2.19762i	−0.112648	+	0.0818437i
$722$	−12.2938	−	16.9209i	−0.457526	−	0.629731i
$723$	−18.5302	+	6.02082i	−0.689145	+	0.223917i
$724$	5.26293			0.195595
$725$		0			0
$726$	8.37120			0.310684
$727$	20.9610	−	6.81063i	0.777399	−	0.252592i	0.106670	−	0.994295i	$-0.465981\pi$
$727$	20.9610	−	6.81063i	0.777399	−	0.252592i	0.670729	+	0.741702i	$0.265981\pi$
$728$	−2.98751	−	4.11196i	−0.110725	−	0.152399i
$729$	0.809017	−	0.587785i	0.0299636	−	0.0217698i
$730$		0			0
$731$	−14.2335	−	10.3412i	−0.526443	−	0.382484i
$732$			4.41735i			0.163270i
$733$	−20.4041	+	28.0838i	−0.753641	+	1.03730i	0.244076	+	0.969756i	$0.421515\pi$
$733$	−20.4041	+	28.0838i	−0.753641	+	1.03730i	−0.997716	+	0.0675414i	$0.978485\pi$
$734$	1.89865	−	5.84345i	0.0700806	−	0.215686i
$735$		0			0
$736$	−5.48565	−	16.8831i	−0.202204	−	0.622319i
$737$	−9.66645	−	3.14082i	−0.356068	−	0.115694i
$738$	−2.71151	−	0.881025i	−0.0998122	−	0.0324310i
$739$	2.34418	+	7.21465i	0.0862321	+	0.265395i	0.984870	−	0.173297i	$-0.0554420\pi$
$739$	2.34418	+	7.21465i	0.0862321	+	0.265395i	−0.898638	+	0.438692i	$0.855442\pi$
$740$		0			0
$741$	−2.38147	+	7.32942i	−0.0874856	+	0.269253i
$742$	5.63436	−	7.75503i	0.206844	−	0.284696i
$743$		−	27.5328i		−	1.01008i	−0.863096	−	0.505040i	$-0.831478\pi$
$743$		−	27.5328i		−	1.01008i	0.863096	−	0.505040i	$-0.168522\pi$
$744$	−7.53283	−	5.47292i	−0.276167	−	0.200647i
$745$		0			0
$746$	3.94383	−	2.86536i	0.144394	−	0.104908i
$747$	−0.131666	−	0.181222i	−0.00481739	−	0.00663057i
$748$	1.77482	−	0.576674i	0.0648938	−	0.0210853i
$749$	2.70690			0.0989081
$750$		0			0
$751$	4.24930			0.155059			0.0775296	−	0.996990i	$-0.475297\pi$
$751$	4.24930			0.155059			0.0775296	+	0.996990i	$0.475297\pi$
$752$	29.0967	−	9.45408i	1.06105	−	0.344755i
$753$	12.3109	+	16.9446i	0.448636	+	0.617494i
$754$	13.2530	−	9.62888i	0.482646	−	0.350663i
$755$		0			0
$756$	0.436739	+	0.317309i	0.0158840	+	0.0115404i
$757$		−	45.6609i		−	1.65957i	−0.558081	−	0.829787i	$-0.688462\pi$
$757$		−	45.6609i		−	1.65957i	0.558081	−	0.829787i	$-0.311538\pi$
$758$	−25.7586	+	35.4537i	−0.935595	+	1.28774i
$759$	−6.40385	+	19.7090i	−0.232445	+	0.715392i
$760$		0			0
$761$	−12.3999	−	38.1628i	−0.449495	−	1.38340i	−0.877479	−	0.479616i	$-0.840776\pi$
$761$	−12.3999	−	38.1628i	−0.449495	−	1.38340i	0.427984	−	0.903786i	$-0.359224\pi$
$762$	−8.38804	−	2.72544i	−0.303867	−	0.0987323i
$763$	4.19262	+	1.36227i	0.151783	+	0.0493173i
$764$	2.34121	+	7.20550i	0.0847020	+	0.260686i
$765$		0			0
$766$	−5.44196	+	16.7486i	−0.196626	+	0.605152i
$767$	8.77671	−	12.0801i	0.316909	−	0.436187i
$768$			8.39819i			0.303044i
$769$	−30.6092	−	22.2389i	−1.10380	−	0.801954i	−0.122120	−	0.992515i	$-0.538969\pi$
$769$	−30.6092	−	22.2389i	−1.10380	−	0.801954i	−0.981675	+	0.190561i	$0.938969\pi$
$770$		0			0
$771$	−1.35204	+	0.982314i	−0.0486925	+	0.0353772i
$772$	−4.81840	−	6.63195i	−0.173418	−	0.238689i
$773$	−24.9318	+	8.10082i	−0.896733	+	0.291366i	−0.720888	−	0.693052i	$-0.756266\pi$
$773$	−24.9318	+	8.10082i	−0.896733	+	0.291366i	−0.175845	+	0.984418i	$0.556266\pi$
$774$	12.3212			0.442875
$775$		0			0
$776$	−31.4667			−1.12959
$777$	13.8688	−	4.50625i	0.497541	−	0.161661i
$778$	30.9299	+	42.5713i	1.10889	+	1.52626i
$779$	8.57247	−	6.22826i	0.307140	−	0.223151i
$780$		0			0
$781$	11.0134	+	8.00168i	0.394089	+	0.286323i
$782$		−	29.6503i		−	1.06029i
$783$	4.64360	−	6.39137i	0.165949	−	0.228409i
$784$	−6.75891	+	20.8018i	−0.241390	+	0.742921i
$785$		0			0
$786$	2.06905	+	6.36789i	0.0738007	+	0.227135i
$787$	−2.29446	−	0.745515i	−0.0817887	−	0.0265747i	0.267837	−	0.963464i	$-0.413691\pi$
$787$	−2.29446	−	0.745515i	−0.0817887	−	0.0265747i	−0.349626	+	0.936890i	$0.613691\pi$
$788$	−0.464639	−	0.150970i	−0.0165521	−	0.00537810i
$789$	2.33514	+	7.18682i	0.0831331	+	0.255858i
$790$		0			0
$791$	6.39430	−	19.6796i	0.227355	−	0.699727i
$792$	3.48796	−	4.80077i	0.123939	−	0.170588i
$793$			16.5142i			0.586437i
$794$	−24.9033	−	18.0933i	−0.883785	−	0.642108i
$795$		0			0
$796$	2.61682	−	1.90123i	0.0927508	−	0.0673874i
$797$	−4.76829	−	6.56299i	−0.168902	−	0.232473i	0.716172	−	0.697923i	$-0.245892\pi$
$797$	−4.76829	−	6.56299i	−0.168902	−	0.232473i	−0.885074	+	0.465450i	$0.845892\pi$
$798$	−12.4803	+	4.05510i	−0.441799	+	0.143549i
$799$	14.6189			0.517180
$800$		0			0
$801$	0.429167			0.0151639
$802$	−7.28041	+	2.36555i	−0.257080	+	0.0835304i
$803$	−9.59348	−	13.2043i	−0.338546	−	0.465969i
$804$	−1.25972	+	0.915242i	−0.0444270	+	0.0322781i
$805$		0			0
$806$	6.20223	+	4.50618i	0.218464	+	0.158724i
$807$			11.2841i			0.397220i
$808$	12.1350	−	16.7024i	0.426908	−	0.587589i
$809$	12.5798	−	38.7166i	0.442282	−	1.36120i	−0.443155	−	0.896445i	$-0.646141\pi$
$809$	12.5798	−	38.7166i	0.442282	−	1.36120i	0.885437	−	0.464759i	$-0.153859\pi$
$810$		0			0
$811$	−15.2960	−	47.0763i	−0.537116	−	1.65307i	−0.739032	−	0.673671i	$-0.764717\pi$
$811$	−15.2960	−	47.0763i	−0.537116	−	1.65307i	0.201915	−	0.979403i	$-0.435283\pi$
$812$	4.05608	+	1.31790i	0.142341	+	0.0462493i
$813$	−10.4380	−	3.39152i	−0.366078	−	0.118946i
$814$	10.9093	+	33.5755i	0.382372	+	1.17682i
$815$		0			0
$816$	−3.11313	+	9.58124i	−0.108981	+	0.335410i
$817$	−26.9162	+	37.0469i	−0.941678	+	1.29611i
$818$		−	36.6606i		−	1.28181i
$819$	1.63274	+	1.18626i	0.0570527	+	0.0414512i
$820$		0			0
$821$	−34.1498	+	24.8113i	−1.19183	+	0.865919i	−0.993457	−	0.114207i	$-0.963567\pi$
$821$	−34.1498	+	24.8113i	−1.19183	+	0.865919i	−0.198378	+	0.980126i	$0.563567\pi$
$822$	1.78338	+	2.45462i	0.0622027	+	0.0856146i
$823$	−46.8252	+	15.2144i	−1.63222	+	0.530342i	−0.974781	−	0.223162i	$-0.928362\pi$
$823$	−46.8252	+	15.2144i	−1.63222	+	0.530342i	−0.657443	+	0.753504i	$0.728362\pi$
$824$	6.29622			0.219339
$825$		0			0
$826$	25.4255			0.884666
$827$	−48.5050	+	15.7602i	−1.68668	+	0.548036i	−0.986189	−	0.165623i	$-0.947037\pi$
$827$	−48.5050	+	15.7602i	−1.68668	+	0.548036i	−0.700493	+	0.713659i	$0.747037\pi$
$828$	1.86610	+	2.56846i	0.0648513	+	0.0892602i
$829$	−30.9321	+	22.4735i	−1.07432	+	0.780537i	−0.976683	−	0.214686i	$-0.931127\pi$
$829$	−30.9321	+	22.4735i	−1.07432	+	0.780537i	−0.0976336	+	0.995222i	$0.531127\pi$
$830$		0			0
$831$	−4.65275	−	3.38042i	−0.161402	−	0.117266i
$832$			8.20758i			0.284547i
$833$	−6.14314	+	8.45531i	−0.212847	+	0.292959i
$834$	0.797267	−	2.45374i	0.0276071	−	0.0849659i
$835$		0			0
$836$	−1.50097	−	4.61951i	−0.0519121	−	0.159769i
$837$	3.51622	+	1.14249i	0.121538	+	0.0394902i
$838$	−0.705171	−	0.229124i	−0.0243597	−	0.00791496i
$839$	5.16324	+	15.8908i	0.178255	+	0.548612i	0.999767	−	0.0215787i	$-0.00686926\pi$
$839$	5.16324	+	15.8908i	0.178255	+	0.548612i	−0.821512	+	0.570191i	$0.806869\pi$
$840$		0			0
$841$	10.3251	−	31.7774i	0.356038	−	1.09577i
$842$	−16.0025	+	22.0255i	−0.551481	+	0.759049i
$843$			8.49962i			0.292742i
$844$	1.70544	+	1.23908i	0.0587037	+	0.0426507i
$845$		0			0
$846$	−8.28270	+	6.01773i	−0.284765	+	0.206894i
$847$	4.78901	+	6.59151i	0.164552	+	0.226487i
$848$	−18.2167	+	5.91897i	−0.625564	+	0.203258i
$849$	−17.2248			−0.591154
$850$		0			0
$851$	85.7599			2.93981
$852$	1.98347	−	0.644468i	0.0679525	−	0.0220791i
$853$	−10.7355	−	14.7762i	−0.367578	−	0.505928i	0.584662	−	0.811277i	$-0.301227\pi$
$853$	−10.7355	−	14.7762i	−0.367578	−	0.505928i	−0.952241	+	0.305349i	$0.901227\pi$
$854$	−22.7495	+	16.5285i	−0.778471	+	0.565593i
$855$		0			0
$856$	−3.68787	−	2.67940i	−0.126049	−	0.0915799i
$857$		−	53.4773i		−	1.82675i	−0.407119	−	0.913375i	$-0.633466\pi$
$857$		−	53.4773i		−	1.82675i	0.407119	−	0.913375i	$-0.366534\pi$
$858$	−2.87185	+	3.95276i	−0.0980433	+	0.134945i
$859$	5.79639	−	17.8395i	0.197770	−	0.608674i	−0.802163	−	0.597105i	$-0.796317\pi$
$859$	5.79639	−	17.8395i	0.197770	−	0.608674i	0.999933	−	0.0115690i	$-0.00368259\pi$
$860$		0			0
$861$	−0.857487	−	2.63907i	−0.0292231	−	0.0899394i
$862$	39.1730	+	12.7281i	1.33424	+	0.433520i
$863$	48.7286	+	15.8329i	1.65874	+	0.538957i	0.980607	−	0.195982i	$-0.0627894\pi$
$863$	48.7286	+	15.8329i	1.65874	+	0.538957i	0.678133	+	0.734939i	$0.262789\pi$
$864$	−0.623723	−	1.91962i	−0.0212195	−	0.0653069i
$865$		0			0
$866$	−4.38313	+	13.4899i	−0.148945	+	0.458405i
$867$	7.16284	−	9.85880i	0.243263	−	0.334822i
$868$			1.99588i			0.0677444i
$869$	20.3373	+	14.7759i	0.689895	+	0.501238i
$870$		0			0
$871$	−4.70946	+	3.42162i	−0.159574	+	0.115937i
$872$	−4.36359	−	6.00597i	−0.147770	−	0.203388i
$873$	11.8830	−	3.86103i	0.402179	−	0.130676i
$874$	−77.1739			−2.61045
$875$		0			0
$876$	−2.50042			−0.0844815
$877$	5.76631	−	1.87359i	0.194715	−	0.0632666i	−0.210036	−	0.977694i	$-0.567358\pi$
$877$	5.76631	−	1.87359i	0.194715	−	0.0632666i	0.404751	+	0.914427i	$0.367358\pi$
$878$	0.905331	+	1.24608i	0.0305534	+	0.0420532i
$879$	−7.59476	+	5.51791i	−0.256165	+	0.186115i
$880$		0			0
$881$	−18.3403	−	13.3250i	−0.617899	−	0.448930i	0.234288	−	0.972167i	$-0.424724\pi$
$881$	−18.3403	−	13.3250i	−0.617899	−	0.448930i	−0.852187	+	0.523237i	$0.824724\pi$
$882$		−	7.31933i		−	0.246455i
$883$	3.25574	−	4.48114i	0.109564	−	0.150802i	−0.750713	−	0.660628i	$-0.770290\pi$
$883$	3.25574	−	4.48114i	0.109564	−	0.150802i	0.860278	+	0.509826i	$0.170290\pi$
$884$	0.330280	−	1.01650i	0.0111085	−	0.0341885i
$885$		0			0
$886$	−12.4817	−	38.4146i	−0.419329	−	1.29056i
$887$	−10.4346	−	3.39041i	−0.350360	−	0.113839i	0.128550	−	0.991703i	$-0.458968\pi$
$887$	−10.4346	−	3.39041i	−0.350360	−	0.113839i	−0.478909	+	0.877864i	$0.658968\pi$
$888$	−23.3553	−	7.58859i	−0.783752	−	0.254656i
$889$	−2.65263	−	8.16394i	−0.0889662	−	0.273810i
$890$		0			0
$891$	−0.728123	+	2.24093i	−0.0243930	+	0.0750740i
$892$	−1.65943	+	2.28401i	−0.0555617	+	0.0764742i
$893$		−	38.0502i		−	1.27330i
$894$	9.18054	+	6.67005i	0.307043	+	0.223080i
$895$		0			0
$896$	−16.1906	+	11.7632i	−0.540890	+	0.392980i
$897$	6.97638	+	9.60216i	0.232934	+	0.320607i
$898$	6.94794	−	2.25752i	0.231856	−	0.0753345i
$899$	29.2083			0.974151
$900$		0			0
$901$	−9.15254			−0.304915
$902$	6.38902	−	2.07592i	0.212731	−	0.0691205i
$903$	7.04872	+	9.70173i	0.234567	+	0.322853i
$904$	−28.1912	+	20.4821i	−0.937627	+	0.681226i
$905$		0			0
$906$	−5.29727	−	3.84869i	−0.175990	−	0.127864i
$907$		−	19.3907i		−	0.643856i	−0.946764	−	0.321928i	$-0.895669\pi$
$907$		−	19.3907i		−	0.643856i	0.946764	−	0.321928i	$-0.104331\pi$
$908$	−3.46038	+	4.76281i	−0.114837	+	0.158059i
$909$	−2.53322	+	7.79645i	−0.0840216	+	0.258592i
$910$		0			0
$911$	−4.23940	−	13.0475i	−0.140458	−	0.432284i	0.855941	−	0.517073i	$-0.172978\pi$
$911$	−4.23940	−	13.0475i	−0.140458	−	0.432284i	−0.996399	+	0.0847888i	$0.972978\pi$
$912$	24.9381	+	8.10288i	0.825783	+	0.268313i
$913$	0.501975	+	0.163102i	0.0166130	+	0.00539788i
$914$	−7.58300	−	23.3381i	−0.250823	−	0.771955i
$915$		0			0
$916$	−2.42157	+	7.45282i	−0.0800108	+	0.246248i
$917$	−3.83043	+	5.27213i	−0.126492	+	0.174101i
$918$		−	3.37126i		−	0.111268i
$919$	−26.2209	−	19.0506i	−0.864947	−	0.628421i	0.0642792	−	0.997932i	$-0.479525\pi$
$919$	−26.2209	−	19.0506i	−0.864947	−	0.628421i	−0.929226	+	0.369511i	$0.879525\pi$
$920$		0			0
$921$	8.61319	−	6.25785i	0.283814	−	0.206203i
$922$	−35.9058	−	49.4202i	−1.18250	−	1.62757i
$923$	7.41518	−	2.40934i	0.244073	−	0.0793043i
$924$	−1.27200			−0.0418457
$925$		0			0
$926$	−40.1360			−1.31895
$927$	−2.37769	+	0.772559i	−0.0780936	+	0.0253742i
$928$	−9.37270	−	12.9004i	−0.307674	−	0.423477i
$929$	−3.50664	+	2.54772i	−0.115049	+	0.0835880i	−0.643822	−	0.765175i	$-0.722652\pi$
$929$	−3.50664	+	2.54772i	−0.115049	+	0.0835880i	0.528773	+	0.848763i	$0.322652\pi$
$930$		0			0
$931$	22.0075	+	15.9894i	0.721268	+	0.524032i
$932$		−	4.88548i		−	0.160029i
$933$	−16.0801	+	22.1324i	−0.526440	+	0.724582i
$934$	−1.82902	+	5.62915i	−0.0598474	+	0.184192i
$935$		0			0
$936$	−1.05024	−	3.23230i	−0.0343281	−	0.105651i
$937$	−51.9206	−	16.8700i	−1.69617	−	0.551120i	−0.708235	−	0.705977i	$-0.750508\pi$
$937$	−51.9206	−	16.8700i	−1.69617	−	0.551120i	−0.987937	+	0.154857i	$0.950508\pi$
$938$	−9.42705	−	3.06303i	−0.307804	−	0.100012i
$939$	−0.616517	−	1.89744i	−0.0201193	−	0.0619208i
$940$		0			0
$941$	1.30978	−	4.03108i	0.0426975	−	0.131409i	−0.927435	−	0.373983i	$-0.877992\pi$
$941$	1.30978	−	4.03108i	0.0426975	−	0.131409i	0.970133	+	0.242574i	$0.0779917\pi$
$942$	−14.5023	+	19.9608i	−0.472512	+	0.650357i
$943$		−	16.3191i		−	0.531423i
$944$	−41.1022	−	29.8625i	−1.33776	−	0.971940i
$945$		0			0
$946$	−23.4872	+	17.0645i	−0.763636	+	0.554814i
$947$	7.41018	+	10.1992i	0.240798	+	0.331431i	0.912262	−	0.409607i	$-0.134334\pi$
$947$	7.41018	+	10.1992i	0.240798	+	0.331431i	−0.671464	+	0.741037i	$0.734334\pi$
$948$	3.66267	−	1.19007i	0.118958	−	0.0386518i
$949$	−9.34781			−0.303443
$950$		0			0
$951$	−8.64876			−0.280455
$952$	−7.85903	+	2.55356i	−0.254713	+	0.0827612i
$953$	18.3174	+	25.2118i	0.593360	+	0.816690i	0.995080	−	0.0990725i	$-0.0315876\pi$
$953$	18.3174	+	25.2118i	0.593360	+	0.816690i	−0.401720	+	0.915762i	$0.631588\pi$
$954$	5.18559	−	3.76755i	0.167890	−	0.121979i
$955$		0			0
$956$	3.07626	+	2.23503i	0.0994934	+	0.0722862i
$957$			18.6148i			0.601732i
$958$	12.8879	−	17.7387i	0.416390	−	0.573111i
$959$	−0.912532	+	2.80848i	−0.0294672	+	0.0906907i
$960$		0			0
$961$	−5.35555	−	16.4827i	−0.172760	−	0.531700i
$962$	19.2298	+	6.24814i	0.619994	+	0.201448i
$963$	1.72145	+	0.559332i	0.0554729	+	0.0180242i
$964$	−2.17337	−	6.68896i	−0.0699997	−	0.215437i
$965$		0			0
$966$	−6.24525	+	19.2209i	−0.200938	+	0.618422i
$967$	−0.912880	+	1.25647i	−0.0293562	+	0.0404054i	−0.823443	−	0.567399i	$-0.807950\pi$
$967$	−0.912880	+	1.25647i	−0.0293562	+	0.0404054i	0.794087	+	0.607805i	$0.207950\pi$
$968$		−	13.7206i		−	0.440997i
$969$	10.1366	+	7.36467i	0.325635	+	0.236587i
$970$		0			0
$971$	30.9548	−	22.4900i	0.993388	−	0.721739i	0.0327278	−	0.999464i	$-0.489581\pi$
$971$	30.9548	−	22.4900i	0.993388	−	0.721739i	0.960660	+	0.277725i	$0.0895806\pi$
$972$	0.212177	+	0.292036i	0.00680557	+	0.00936706i
$973$	2.38818	−	0.775967i	0.0765616	−	0.0248764i
$974$	38.1405			1.22210
$975$		0			0
$976$	56.1890			1.79857
$977$	−19.3693	+	6.29348i	−0.619680	+	0.201346i	−0.601998	−	0.798497i	$-0.705629\pi$
$977$	−19.3693	+	6.29348i	−0.619680	+	0.201346i	−0.0176817	+	0.999844i	$0.505629\pi$
$978$	20.1348	+	27.7132i	0.643841	+	0.886172i
$979$	−0.818100	+	0.594384i	−0.0261466	+	0.0189966i
$980$		0			0
$981$	2.38480	+	1.73266i	0.0761408	+	0.0553195i
$982$			17.6539i			0.563359i
$983$	−7.79150	+	10.7241i	−0.248510	+	0.342045i	−0.914989	−	0.403479i	$-0.867801\pi$
$983$	−7.79150	+	10.7241i	−0.248510	+	0.342045i	0.666479	+	0.745524i	$0.267801\pi$
$984$	−1.44402	+	4.44424i	−0.0460337	+	0.141677i
$985$		0			0
$986$	−8.23022	−	25.3300i	−0.262103	−	0.806671i
$987$	−9.47676	−	3.07919i	−0.301649	−	0.0980116i
$988$	−2.64575	−	0.859655i	−0.0841724	−	0.0273493i
$989$	21.7934	+	67.0732i	0.692990	+	2.13280i
$990$		0			0
$991$	−0.692448	+	2.13113i	−0.0219963	+	0.0676977i	−0.961452	−	0.274972i	$-0.911331\pi$
$991$	−0.692448	+	2.13113i	−0.0219963	+	0.0676977i	0.939456	+	0.342670i	$0.111331\pi$
$992$	4.38629	−	6.03721i	0.139265	−	0.191682i
$993$		−	3.94331i		−	0.125137i
$994$	10.7406	+	7.80351i	0.340671	+	0.247512i
$995$		0			0
$996$	0.0654169	−	0.0475282i	0.00207281	−	0.00150599i
$997$	−8.25272	−	11.3589i	−0.261366	−	0.359740i	0.658085	−	0.752943i	$-0.271367\pi$
$997$	−8.25272	−	11.3589i	−0.261366	−	0.359740i	−0.919451	+	0.393204i	$0.871367\pi$
$998$	−6.10092	+	1.98231i	−0.193121	+	0.0627489i
$999$	9.75097			0.308507

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	375.2.i.c.349.1		16
5.2	odd	4		375.2.g.e.151.2		16
5.3	odd	4		375.2.g.d.151.3		16
5.4	even	2		75.2.i.a.19.4	yes	16
15.14	odd	2		225.2.m.b.19.1		16
25.2	odd	20		1875.2.a.m.1.3		8
25.3	odd	20		375.2.g.d.226.3		16
25.4	even	10	inner	375.2.i.c.274.1		16
25.11	even	5		1875.2.b.h.1249.13		16
25.14	even	10		1875.2.b.h.1249.4		16
25.21	even	5		75.2.i.a.4.4	✓	16
25.22	odd	20		375.2.g.e.226.2		16
25.23	odd	20		1875.2.a.p.1.6		8
75.2	even	20		5625.2.a.bd.1.6		8
75.23	even	20		5625.2.a.t.1.3		8
75.71	odd	10		225.2.m.b.154.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.2.i.a.4.4	✓	16	25.21	even	5
75.2.i.a.19.4	yes	16	5.4	even	2
225.2.m.b.19.1		16	15.14	odd	2
225.2.m.b.154.1		16	75.71	odd	10
375.2.g.d.151.3		16	5.3	odd	4
375.2.g.d.226.3		16	25.3	odd	20
375.2.g.e.151.2		16	5.2	odd	4
375.2.g.e.226.2		16	25.22	odd	20
375.2.i.c.274.1		16	25.4	even	10	inner
375.2.i.c.349.1		16	1.1	even	1	trivial
1875.2.a.m.1.3		8	25.2	odd	20
1875.2.a.p.1.6		8	25.23	odd	20
1875.2.b.h.1249.4		16	25.14	even	10
1875.2.b.h.1249.13		16	25.11	even	5
5625.2.a.t.1.3		8	75.23	even	20
5625.2.a.bd.1.6		8	75.2	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)

\(f(q)\)	\(=\)	\(q+(-1.46134 + 0.474819i) q^{2} +(-0.587785 - 0.809017i) q^{3} +(0.292036 - 0.212177i) q^{4} +(1.24309 + 0.903160i) q^{6} +1.49550i q^{7} +(1.48030 - 2.03746i) q^{8} +(-0.309017 + 0.951057i) q^{9} +O(q^{10})\)	\(q+(-1.46134 + 0.474819i) q^{2} +(-0.587785 - 0.809017i) q^{3} +(0.292036 - 0.212177i) q^{4} +(1.24309 + 0.903160i) q^{6} +1.49550i q^{7} +(1.48030 - 2.03746i) q^{8} +(-0.309017 + 0.951057i) q^{9} +(-0.728123 - 2.24093i) q^{11} +(-0.343309 - 0.111548i) q^{12} +(-1.28346 - 0.417020i) q^{13} +(-0.710090 - 2.18543i) q^{14} +(-1.41890 + 4.36692i) q^{16} +(-1.28963 + 1.77502i) q^{17} -1.53655i q^{18} +(4.62004 + 3.35666i) q^{19} +(1.20988 - 0.879031i) q^{21} +(2.12807 + 2.92904i) q^{22} +(8.36455 - 2.71781i) q^{23} -2.51844 q^{24} +2.07358 q^{26} +(0.951057 - 0.309017i) q^{27} +(0.317309 + 0.436739i) q^{28} +(6.39137 - 4.64360i) q^{29} +(2.99107 + 2.17314i) q^{31} -2.01841i q^{32} +(-1.38497 + 1.90625i) q^{33} +(1.04178 - 3.20626i) q^{34} +(0.111548 + 0.343309i) q^{36} +(9.27372 + 3.01321i) q^{37} +(-8.34527 - 2.71154i) q^{38} +(0.417020 + 1.28346i) q^{39} +(0.573380 - 1.76468i) q^{41} +(-1.35067 + 1.85904i) q^{42} +8.01874i q^{43} +(-0.688111 - 0.499942i) q^{44} +(-10.9330 + 7.94330i) q^{46} +(-3.91640 - 5.39046i) q^{47} +(4.36692 - 1.41890i) q^{48} +4.76349 q^{49} +2.19405 q^{51} +(-0.463298 + 0.150535i) q^{52} +(2.45196 + 3.37484i) q^{53} +(-1.24309 + 0.903160i) q^{54} +(3.04701 + 2.21378i) q^{56} -5.71069i q^{57} +(-7.13511 + 9.82064i) q^{58} +(-3.41917 + 10.5231i) q^{59} +(-3.78151 - 11.6383i) q^{61} +(-5.40283 - 1.75549i) q^{62} +(-1.42230 - 0.462134i) q^{63} +(-1.87942 - 5.78425i) q^{64} +(1.11879 - 3.44330i) q^{66} +(2.53546 - 3.48976i) q^{67} +0.792000i q^{68} +(-7.11531 - 5.16958i) q^{69} +(-4.67410 + 3.39593i) q^{71} +(1.48030 + 2.03746i) q^{72} +(6.58781 - 2.14051i) q^{73} -14.9828 q^{74} +2.06142 q^{76} +(3.35130 - 1.08890i) q^{77} +(-1.21882 - 1.67756i) q^{78} +(-8.63118 + 6.27092i) q^{79} +(-0.809017 - 0.587785i) q^{81} +2.85106i q^{82} +(-0.131666 + 0.181222i) q^{83} +(0.166819 - 0.513417i) q^{84} +(-3.80745 - 11.7181i) q^{86} +(-7.51351 - 2.44129i) q^{87} +(-5.64364 - 1.83373i) q^{88} +(-0.132620 - 0.408162i) q^{89} +(0.623652 - 1.91940i) q^{91} +(1.86610 - 2.56846i) q^{92} -3.69717i q^{93} +(8.28270 + 6.01773i) q^{94} +(-1.63293 + 1.18639i) q^{96} +(-7.34411 - 10.1083i) q^{97} +(-6.96109 + 2.26180i) q^{98} +2.35626 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 2 q^{4} + 2 q^{6} + 30 q^{8} + 4 q^{9}+O(q^{10}) \) 16 * q + 2 * q^4 + 2 * q^6 + 30 * q^8 + 4 * q^9	\( 16 q + 2 q^{4} + 2 q^{6} + 30 q^{8} + 4 q^{9} - 6 q^{11} - 12 q^{14} - 10 q^{16} - 10 q^{17} - 2 q^{19} + 4 q^{21} + 30 q^{22} + 20 q^{23} + 24 q^{24} + 12 q^{26} - 30 q^{28} + 16 q^{29} + 6 q^{31} - 10 q^{33} - 36 q^{34} - 2 q^{36} + 10 q^{37} - 30 q^{38} - 8 q^{39} - 14 q^{41} + 10 q^{42} + 26 q^{44} + 16 q^{46} - 40 q^{47} - 32 q^{51} - 40 q^{52} - 10 q^{53} - 2 q^{54} - 10 q^{58} + 12 q^{59} + 10 q^{62} + 10 q^{63} + 8 q^{64} + 16 q^{66} + 40 q^{67} - 12 q^{69} - 8 q^{71} + 30 q^{72} + 20 q^{73} - 52 q^{74} - 32 q^{76} + 40 q^{77} - 20 q^{79} - 4 q^{81} - 10 q^{83} + 12 q^{84} - 36 q^{86} - 40 q^{87} + 40 q^{88} + 18 q^{89} + 26 q^{91} - 10 q^{92} - 38 q^{94} - 26 q^{96} - 40 q^{97} - 60 q^{98} - 4 q^{99}+O(q^{100}) \) 16 * q + 2 * q^4 + 2 * q^6 + 30 * q^8 + 4 * q^9 - 6 * q^11 - 12 * q^14 - 10 * q^16 - 10 * q^17 - 2 * q^19 + 4 * q^21 + 30 * q^22 + 20 * q^23 + 24 * q^24 + 12 * q^26 - 30 * q^28 + 16 * q^29 + 6 * q^31 - 10 * q^33 - 36 * q^34 - 2 * q^36 + 10 * q^37 - 30 * q^38 - 8 * q^39 - 14 * q^41 + 10 * q^42 + 26 * q^44 + 16 * q^46 - 40 * q^47 - 32 * q^51 - 40 * q^52 - 10 * q^53 - 2 * q^54 - 10 * q^58 + 12 * q^59 + 10 * q^62 + 10 * q^63 + 8 * q^64 + 16 * q^66 + 40 * q^67 - 12 * q^69 - 8 * q^71 + 30 * q^72 + 20 * q^73 - 52 * q^74 - 32 * q^76 + 40 * q^77 - 20 * q^79 - 4 * q^81 - 10 * q^83 + 12 * q^84 - 36 * q^86 - 40 * q^87 + 40 * q^88 + 18 * q^89 + 26 * q^91 - 10 * q^92 - 38 * q^94 - 26 * q^96 - 40 * q^97 - 60 * q^98 - 4 * q^99

Introduction

L-functions

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Database

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