LMFDB - Embedded newform 975.2.i.n.601.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [975,2,Mod(451,975)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(975, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("975.451");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$975 = 3 \cdot 5^{2} \cdot 13$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	975.i (of order $3$ , degree $2$ , minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.78541419707$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$x^{12} + 10x^{10} - 4x^{9} + 79x^{8} - 24x^{7} + 210x^{6} - 38x^{5} + 429x^{4} - 76x^{3} + 58x^{2} + 8x + 4$ x^12 + 10x^10 - 4x^9 + 79x^8 - 24x^7 + 210x^6 - 38x^5 + 429x^4 - 76x^3 + 58x^2 + 8x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$1$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			601.6
Root			$1.22736 - 2.12585i$ of defining polynomial
Character	$\chi$	$=$	975.601
Dual form			975.2.i.n.451.6

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.22736 + 2.12585i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-2.01283 + 3.48633i) q^{4} +(1.22736 - 2.12585i) q^{6} +(2.09272 - 3.62470i) q^{7} -4.97244 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-2.69817 - 4.67337i) q^{11} +4.02566 q^{12} +(1.80423 - 3.12166i) q^{13} +10.2741 q^{14} +(-2.07731 - 3.59801i) q^{16} +(-1.04734 + 1.81405i) q^{17} -2.45472 q^{18} +(2.08635 - 3.61366i) q^{19} -4.18544 q^{21} +(6.62326 - 11.4718i) q^{22} +(-1.17897 - 2.04203i) q^{23} +(2.48622 + 4.30626i) q^{24} +(8.85063 + 0.00413129i) q^{26} +1.00000 q^{27} +(8.42458 + 14.5918i) q^{28} +(-3.58220 - 6.20455i) q^{29} +6.72862 q^{31} +(0.126792 - 0.219610i) q^{32} +(-2.69817 + 4.67337i) q^{33} -5.14188 q^{34} +(-2.01283 - 3.48633i) q^{36} +(3.82956 + 6.63298i) q^{37} +10.2428 q^{38} +(-3.60555 - 0.00168300i) q^{39} +(-1.04734 - 1.81405i) q^{41} +(-5.13705 - 8.89763i) q^{42} +(-4.38766 + 7.59966i) q^{43} +21.7239 q^{44} +(2.89404 - 5.01262i) q^{46} +6.99206 q^{47} +(-2.07731 + 3.59801i) q^{48} +(-5.25896 - 9.10878i) q^{49} +2.09469 q^{51} +(7.25150 + 12.5735i) q^{52} -5.85317 q^{53} +(1.22736 + 2.12585i) q^{54} +(-10.4059 + 18.0236i) q^{56} -4.17269 q^{57} +(8.79330 - 15.2304i) q^{58} +(2.66624 - 4.61805i) q^{59} +(-2.34951 + 4.06947i) q^{61} +(8.25845 + 14.3040i) q^{62} +(2.09272 + 3.62470i) q^{63} -7.68678 q^{64} -13.2465 q^{66} +(6.61043 + 11.4496i) q^{67} +(-4.21625 - 7.30276i) q^{68} +(-1.17897 + 2.04203i) q^{69} +(-0.698173 + 1.20927i) q^{71} +(2.48622 - 4.30626i) q^{72} +1.12598 q^{73} +(-9.40049 + 16.2821i) q^{74} +(8.39892 + 14.5474i) q^{76} -22.5861 q^{77} +(-4.42174 - 7.66693i) q^{78} +2.90483 q^{79} +(-0.500000 - 0.866025i) q^{81} +(2.57094 - 4.45300i) q^{82} -2.28874 q^{83} +(8.42458 - 14.5918i) q^{84} -21.5410 q^{86} +(-3.58220 + 6.20455i) q^{87} +(13.4165 + 23.2380i) q^{88} +(-6.98684 - 12.1016i) q^{89} +(-7.53931 - 13.0726i) q^{91} +9.49225 q^{92} +(-3.36431 - 5.82716i) q^{93} +(8.58179 + 14.8641i) q^{94} -0.253584 q^{96} +(-2.07351 + 3.59143i) q^{97} +(12.9093 - 22.3595i) q^{98} +5.39635 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$12 q - 6 q^{3} - 8 q^{4} + q^{7} + 12 q^{8} - 6 q^{9} - q^{11} + 16 q^{12} - 3 q^{13} + 30 q^{14} - 20 q^{16} + 8 q^{17} + 3 q^{19} - 2 q^{21} - 3 q^{22} - q^{23} - 6 q^{24} + 9 q^{26} + 12 q^{27} + 3 q^{28}+ \cdots + 2 q^{99}+O(q^{100})$ 12 * q - 6 * q^3 - 8 * q^4 + q^7 + 12 * q^8 - 6 * q^9 - q^11 + 16 * q^12 - 3 * q^13 + 30 * q^14 - 20 * q^16 + 8 * q^17 + 3 * q^19 - 2 * q^21 - 3 * q^22 - q^23 - 6 * q^24 + 9 * q^26 + 12 * q^27 + 3 * q^28 - 12 * q^29 + 24 * q^31 - 32 * q^32 - q^33 - 56 * q^34 - 8 * q^36 - 5 * q^37 + 14 * q^38 - 3 * q^39 + 8 * q^41 - 15 * q^42 - 15 * q^43 + 78 * q^44 - 5 * q^46 - 24 * q^47 - 20 * q^48 - 9 * q^49 - 16 * q^51 + 62 * q^52 - 16 * q^53 - 17 * q^56 - 6 * q^57 - 6 * q^58 + 2 * q^59 - 33 * q^61 - 2 * q^62 + q^63 + 72 * q^64 + 6 * q^66 + 13 * q^67 + 36 * q^68 - q^69 + 23 * q^71 - 6 * q^72 - 12 * q^73 - 59 * q^74 + 35 * q^76 - 36 * q^77 - 6 * q^78 + 22 * q^79 - 6 * q^81 + 28 * q^82 - 34 * q^83 + 3 * q^84 - 26 * q^86 - 12 * q^87 - 7 * q^88 - 8 * q^89 + 5 * q^91 + 38 * q^92 - 12 * q^93 - 8 * q^94 + 64 * q^96 - 19 * q^97 + 43 * q^98 + 2 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/975\mathbb{Z}\right)^\times$ .

$n$	$301$	$326$	$352$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$

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

)

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

$2$	1.22736	+	2.12585i	0.867875	+	1.50320i	0.864163	+	0.503211i	$0.167848\pi$
$2$	1.22736	+	2.12585i	0.867875	+	1.50320i	0.00371189	+	0.999993i	$0.498818\pi$
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	−2.01283	+	3.48633i	−1.00642	+	1.74316i
$5$		0			0
$5$		0			0
$6$	1.22736	−	2.12585i	0.501068	−	0.867875i
$7$	2.09272	−	3.62470i	0.790974	−	1.37001i	−0.134391	−	0.990928i	$-0.542908\pi$
$7$	2.09272	−	3.62470i	0.790974	−	1.37001i	0.925365	−	0.379078i	$-0.123759\pi$
$8$	−4.97244			−1.75802
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$		0			0
$11$	−2.69817	−	4.67337i	−0.813530	−	1.40907i	−0.910379	−	0.413776i	$-0.864210\pi$
$11$	−2.69817	−	4.67337i	−0.813530	−	1.40907i	0.0968491	−	0.995299i	$-0.469124\pi$
$12$	4.02566			1.16211
$13$	1.80423	−	3.12166i	0.500404	−	0.865792i
$13$	1.80423	−	3.12166i	0.500404	−	0.865792i
$14$	10.2741			2.74587
$15$		0			0
$16$	−2.07731	−	3.59801i	−0.519328	−	0.899503i
$17$	−1.04734	+	1.81405i	−0.254018	+	0.439973i	−0.964628	−	0.263613i	$-0.915086\pi$
$17$	−1.04734	+	1.81405i	−0.254018	+	0.439973i	0.710610	+	0.703586i	$0.248419\pi$
$18$	−2.45472			−0.578584
$19$	2.08635	−	3.61366i	0.478641	−	0.829030i	−0.521060	−	0.853520i	$-0.674463\pi$
$19$	2.08635	−	3.61366i	0.478641	−	0.829030i	0.999700	+	0.0244906i	$0.00779639\pi$
$20$		0			0
$21$	−4.18544			−0.913338
$22$	6.62326	−	11.4718i	1.41208	−	2.44580i
$23$	−1.17897	−	2.04203i	−0.245832	−	0.425793i	0.716533	−	0.697553i	$-0.245728\pi$
$23$	−1.17897	−	2.04203i	−0.245832	−	0.425793i	−0.962365	+	0.271760i	$0.912394\pi$
$24$	2.48622	+	4.30626i	0.507497	+	0.879011i
$25$		0			0
$26$	8.85063	+	0.00413129i	1.73575	+	0.000810212i
$27$	1.00000			0.192450
$28$	8.42458	+	14.5918i	1.59210	+	2.75759i
$29$	−3.58220	−	6.20455i	−0.665197	−	1.15216i	−0.979232	−	0.202744i	$-0.935014\pi$
$29$	−3.58220	−	6.20455i	−0.665197	−	1.15216i	0.314035	−	0.949412i	$-0.398319\pi$
$30$		0			0
$31$	6.72862			1.20850			0.604248	−	0.796796i	$-0.293474\pi$
$31$	6.72862			1.20850			0.604248	+	0.796796i	$0.293474\pi$
$32$	0.126792	−	0.219610i	0.0224138	−	0.0388219i
$33$	−2.69817	+	4.67337i	−0.469692	+	0.813530i
$34$	−5.14188			−0.881825
$35$		0			0
$36$	−2.01283	−	3.48633i	−0.335472	−	0.581054i
$37$	3.82956	+	6.63298i	0.629575	+	1.09046i	0.987637	+	0.156758i	$0.0501043\pi$
$37$	3.82956	+	6.63298i	0.629575	+	1.09046i	−0.358062	+	0.933698i	$0.616562\pi$
$38$	10.2428			1.66160
$39$	−3.60555	−	0.00168300i	−0.577350	−	0.000269495i
$40$		0			0
$41$	−1.04734	−	1.81405i	−0.163568	−	0.283308i	0.772578	−	0.634920i	$-0.218967\pi$
$41$	−1.04734	−	1.81405i	−0.163568	−	0.283308i	−0.936146	+	0.351612i	$0.885634\pi$
$42$	−5.13705	−	8.89763i	−0.792664	−	1.37293i
$43$	−4.38766	+	7.59966i	−0.669112	+	1.15894i	0.309040	+	0.951049i	$0.399992\pi$
$43$	−4.38766	+	7.59966i	−0.669112	+	1.15894i	−0.978153	+	0.207888i	$0.933341\pi$
$44$	21.7239			3.27500
$45$		0			0
$46$	2.89404	−	5.01262i	0.426703	−	0.739071i
$47$	6.99206			1.01990			0.509949	−	0.860205i	$-0.329664\pi$
$47$	6.99206			1.01990			0.509949	+	0.860205i	$0.329664\pi$
$48$	−2.07731	+	3.59801i	−0.299834	+	0.519328i
$49$	−5.25896	−	9.10878i	−0.751279	−	1.30125i
$50$		0			0
$51$	2.09469			0.293315
$52$	7.25150	+	12.5735i	1.00560	+	1.74363i
$53$	−5.85317			−0.803994			−0.401997	−	0.915641i	$-0.631684\pi$
$53$	−5.85317			−0.803994			−0.401997	+	0.915641i	$0.631684\pi$
$54$	1.22736	+	2.12585i	0.167023	+	0.289292i
$55$		0			0
$56$	−10.4059	+	18.0236i	−1.39055	+	2.40850i
$57$	−4.17269			−0.552686
$58$	8.79330	−	15.2304i	1.15462	−	1.99985i
$59$	2.66624	−	4.61805i	0.347114	−	0.601220i	−0.638621	−	0.769521i	$-0.720495\pi$
$59$	2.66624	−	4.61805i	0.347114	−	0.601220i	0.985736	+	0.168302i	$0.0538283\pi$
$60$		0			0
$61$	−2.34951	+	4.06947i	−0.300824	+	0.521042i	−0.976323	−	0.216319i	$-0.930595\pi$
$61$	−2.34951	+	4.06947i	−0.300824	+	0.521042i	0.675499	+	0.737361i	$0.263928\pi$
$62$	8.25845	+	14.3040i	1.04882	+	1.81662i
$63$	2.09272	+	3.62470i	0.263658	+	0.456669i
$64$	−7.68678			−0.960847
$65$		0			0
$66$	−13.2465			−1.63054
$67$	6.61043	+	11.4496i	0.807593	+	1.39879i	0.914526	+	0.404526i	$0.132564\pi$
$67$	6.61043	+	11.4496i	0.807593	+	1.39879i	−0.106933	+	0.994266i	$0.534103\pi$
$68$	−4.21625	−	7.30276i	−0.511296	−	0.885590i
$69$	−1.17897	+	2.04203i	−0.141931	+	0.245832i
$70$		0			0
$71$	−0.698173	+	1.20927i	−0.0828579	+	0.143514i	−0.904476	−	0.426524i	$-0.859738\pi$
$71$	−0.698173	+	1.20927i	−0.0828579	+	0.143514i	0.821619	+	0.570038i	$0.193071\pi$
$72$	2.48622	−	4.30626i	0.293004	−	0.507497i
$73$	1.12598			0.131786			0.0658932	−	0.997827i	$-0.479010\pi$
$73$	1.12598			0.131786			0.0658932	+	0.997827i	$0.479010\pi$
$74$	−9.40049	+	16.2821i	−1.09279	+	1.89276i
$75$		0			0
$76$	8.39892	+	14.5474i	0.963422	+	1.66870i
$77$	−22.5861			−2.57392
$78$	−4.42174	−	7.66693i	−0.500663	−	0.868109i
$79$	2.90483			0.326819			0.163409	−	0.986558i	$-0.447751\pi$
$79$	2.90483			0.326819			0.163409	+	0.986558i	$0.447751\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	2.57094	−	4.45300i	0.283913	−	0.491751i
$83$	−2.28874			−0.251222			−0.125611	−	0.992080i	$-0.540089\pi$
$83$	−2.28874			−0.251222			−0.125611	+	0.992080i	$0.540089\pi$
$84$	8.42458	−	14.5918i	0.919197	−	1.59210i
$85$		0			0
$86$	−21.5410			−2.32282
$87$	−3.58220	+	6.20455i	−0.384052	+	0.665197i
$88$	13.4165	+	23.2380i	1.43020	+	2.47718i
$89$	−6.98684	−	12.1016i	−0.740604	−	1.28276i	−0.952221	−	0.305410i	$-0.901206\pi$
$89$	−6.98684	−	12.1016i	−0.740604	−	1.28276i	0.211617	−	0.977353i	$-0.432127\pi$
$90$		0			0
$91$	−7.53931	−	13.0726i	−0.790334	−	1.37038i
$92$	9.49225			0.989635
$93$	−3.36431	−	5.82716i	−0.348863	−	0.604248i
$94$	8.58179	+	14.8641i	0.885144	+	1.53311i
$95$		0			0
$96$	−0.253584			−0.0258813
$97$	−2.07351	+	3.59143i	−0.210534	+	0.364655i	−0.951882	−	0.306466i	$-0.900853\pi$
$97$	−2.07351	+	3.59143i	−0.210534	+	0.364655i	0.741348	+	0.671121i	$0.234187\pi$
$98$	12.9093	−	22.3595i	1.30403	−	2.25865i
$99$	5.39635			0.542353
$100$		0			0
$101$	7.62974	+	13.2151i	0.759187	+	1.31495i	0.943266	+	0.332039i	$0.107737\pi$
$101$	7.62974	+	13.2151i	0.759187	+	1.31495i	−0.184078	+	0.982912i	$0.558930\pi$
$102$	2.57094	+	4.45300i	0.254561	+	0.440912i
$103$	18.7116			1.84371			0.921857	−	0.387531i	$-0.126672\pi$
$103$	18.7116			1.84371			0.921857	+	0.387531i	$0.126672\pi$
$104$	−8.97143	+	15.5222i	−0.879721	+	1.52208i
$105$		0			0
$106$	−7.18395	−	12.4430i	−0.697767	−	1.20857i
$107$	0.497522	+	0.861734i	0.0480973	+	0.0833070i	0.889072	−	0.457768i	$-0.151351\pi$
$107$	0.497522	+	0.861734i	0.0480973	+	0.0833070i	−0.840974	+	0.541075i	$0.818018\pi$
$108$	−2.01283	+	3.48633i	−0.193685	+	0.335472i
$109$	14.3877			1.37809			0.689047	−	0.724716i	$-0.258029\pi$
$109$	14.3877			1.37809			0.689047	+	0.724716i	$0.258029\pi$
$110$		0			0
$111$	3.82956	−	6.63298i	0.363485	−	0.629575i
$112$	−17.3889			−1.64310
$113$	3.41341	−	5.91221i	0.321107	−	0.556173i	−0.659610	−	0.751608i	$-0.729278\pi$
$113$	3.41341	−	5.91221i	0.321107	−	0.556173i	0.980717	+	0.195435i	$0.0626118\pi$
$114$	−5.12140	−	8.87052i	−0.479663	−	0.830801i
$115$		0			0
$116$	28.8414			2.67786
$117$	1.80132	+	3.12334i	0.166532	+	0.288753i
$118$	13.0897			1.20501
$119$	4.38360	+	7.59261i	0.401844	+	0.696014i
$120$		0			0
$121$	−9.06027	+	15.6929i	−0.823661	+	1.42662i
$122$	−11.5348			−1.04431
$123$	−1.04734	+	1.81405i	−0.0944358	+	0.163568i
$124$	−13.5436	+	23.4582i	−1.21625	+	2.10660i
$125$		0			0
$126$	−5.13705	+	8.89763i	−0.457645	+	0.792664i
$127$	−10.3665	−	17.9553i	−0.919876	−	1.59327i	−0.799601	−	0.600531i	$-0.794956\pi$
$127$	−10.3665	−	17.9553i	−0.919876	−	1.59327i	−0.120274	−	0.992741i	$-0.538377\pi$
$128$	−9.68804	−	16.7802i	−0.856309	−	1.48317i
$129$	8.77533			0.772624
$130$		0			0
$131$	−11.1331			−0.972703			−0.486352	−	0.873763i	$-0.661673\pi$
$131$	−11.1331			−0.972703			−0.486352	+	0.873763i	$0.661673\pi$
$132$	−10.8619	−	18.8134i	−0.945410	−	1.63750i
$133$	−8.73228	−	15.1247i	−0.757184	−	1.31148i
$134$	−16.2268	+	28.1056i	−1.40178	+	2.42795i
$135$		0			0
$136$	5.20785	−	9.02027i	0.446570	−	0.773481i
$137$	9.31018	−	16.1257i	0.795422	−	1.37771i	−0.127148	−	0.991884i	$-0.540582\pi$
$137$	9.31018	−	16.1257i	0.795422	−	1.37771i	0.922571	−	0.385828i	$-0.126084\pi$
$138$	−5.78808			−0.492714
$139$	4.88006	−	8.45250i	0.413921	−	0.716932i	−0.581394	−	0.813622i	$-0.697492\pi$
$139$	4.88006	−	8.45250i	0.413921	−	0.716932i	0.995315	+	0.0966904i	$0.0308257\pi$
$140$		0			0
$141$	−3.49603	−	6.05530i	−0.294419	−	0.509949i
$142$	−3.42764			−0.287641
$143$	−19.4568	−	0.00908203i	−1.62706	−	0.000759477i
$144$	4.15463			0.346219
$145$		0			0
$146$	1.38199	+	2.39367i	0.114374	+	0.198102i
$147$	−5.25896	+	9.10878i	−0.433751	+	0.751279i
$148$	−30.8330			−2.53446
$149$	−1.37129	+	2.37515i	−0.112341	+	0.194580i	−0.916714	−	0.399545i	$-0.869168\pi$
$149$	−1.37129	+	2.37515i	−0.112341	+	0.194580i	0.804373	+	0.594125i	$0.202501\pi$
$150$		0			0
$151$	−5.81427			−0.473159			−0.236579	−	0.971612i	$-0.576026\pi$
$151$	−5.81427			−0.473159			−0.236579	+	0.971612i	$0.576026\pi$
$152$	−10.3742	+	17.9687i	−0.841460	+	1.45745i
$153$	−1.04734	−	1.81405i	−0.0846728	−	0.146658i
$154$	−27.7213	−	48.0147i	−2.23384	−	3.86913i
$155$		0			0
$156$	7.26323	−	12.5667i	0.581524	−	1.00614i
$157$	−5.24558			−0.418643			−0.209321	−	0.977847i	$-0.567125\pi$
$157$	−5.24558			−0.418643			−0.209321	+	0.977847i	$0.567125\pi$
$158$	3.56527	+	6.17524i	0.283638	+	0.491275i
$159$	2.92658	+	5.06899i	0.232093	+	0.401997i
$160$		0			0
$161$	−9.86900			−0.777786
$162$	1.22736	−	2.12585i	0.0964306	−	0.167023i
$163$	−2.68701	+	4.65404i	−0.210463	+	0.364533i	−0.951860	−	0.306534i	$-0.900831\pi$
$163$	−2.68701	+	4.65404i	−0.210463	+	0.364533i	0.741396	+	0.671067i	$0.234164\pi$
$164$	8.43251			0.658468
$165$		0			0
$166$	−2.80912	−	4.86553i	−0.218030	−	0.377639i
$167$	9.54985	+	16.5408i	0.738989	+	1.27997i	0.952951	+	0.303125i	$0.0980300\pi$
$167$	9.54985	+	16.5408i	0.738989	+	1.27997i	−0.213961	+	0.976842i	$0.568637\pi$
$168$	20.8118			1.60567
$169$	−6.48949	−	11.2644i	−0.499191	−	0.866492i
$170$		0			0
$171$	2.08635	+	3.61366i	0.159547	+	0.276343i
$172$	−17.6632	−	30.5936i	−1.34681	−	2.33274i
$173$	−6.25905	+	10.8410i	−0.475867	+	0.824226i	−0.999618	−	0.0276457i	$-0.991199\pi$
$173$	−6.25905	+	10.8410i	−0.475867	+	0.824226i	0.523751	+	0.851872i	$0.324532\pi$
$174$	−17.5866			−1.33324
$175$		0			0
$176$	−11.2099	+	19.4161i	−0.844978	+	1.46355i
$177$	−5.33247			−0.400813
$178$	17.1508	−	29.7060i	1.28550	−	2.22656i
$179$	−2.78825	−	4.82938i	−0.208403	−	0.360965i	0.742808	−	0.669504i	$-0.233493\pi$
$179$	−2.78825	−	4.82938i	−0.208403	−	0.360965i	−0.951212	+	0.308539i	$0.900160\pi$
$180$		0			0
$181$	−15.9187			−1.18323			−0.591613	−	0.806222i	$-0.701509\pi$
$181$	−15.9187			−1.18323			−0.591613	+	0.806222i	$0.701509\pi$
$182$	18.5369	−	32.0722i	1.37404	−	2.37735i
$183$	4.69902			0.347362
$184$	5.86234	+	10.1539i	0.432178	+	0.748553i
$185$		0			0
$186$	8.25845	−	14.3040i	0.605539	−	1.04882i
$187$	11.3037			0.826606
$188$	−14.0738	+	24.3766i	−1.02644	+	1.77785i
$189$	2.09272	−	3.62470i	0.152223	−	0.263658i
$190$		0			0
$191$	3.46558	−	6.00257i	0.250761	−	0.434331i	−0.712975	−	0.701190i	$-0.752653\pi$
$191$	3.46558	−	6.00257i	0.250761	−	0.434331i	0.963736	+	0.266859i	$0.0859859\pi$
$192$	3.84339	+	6.65694i	0.277373	+	0.480424i
$193$	−2.03890	−	3.53148i	−0.146763	−	0.254202i	0.783266	−	0.621687i	$-0.213552\pi$
$193$	−2.03890	−	3.53148i	−0.146763	−	0.254202i	−0.930029	+	0.367485i	$0.880219\pi$
$194$	−10.1798			−0.730868
$195$		0			0
$196$	42.3415			3.02440
$197$	5.13810	+	8.89944i	0.366074	+	0.634059i	0.988948	−	0.148263i	$-0.0473683\pi$
$197$	5.13810	+	8.89944i	0.366074	+	0.634059i	−0.622874	+	0.782322i	$0.714035\pi$
$198$	6.62326	+	11.4718i	0.470695	+	0.815268i
$199$	3.16846	−	5.48794i	0.224606	−	0.389029i	−0.731595	−	0.681740i	$-0.761224\pi$
$199$	3.16846	−	5.48794i	0.224606	−	0.389029i	0.956201	+	0.292710i	$0.0945571\pi$
$200$		0			0
$201$	6.61043	−	11.4496i	0.466264	−	0.807593i
$202$	−18.7289	+	32.4394i	−1.31776	+	2.28243i
$203$	−29.9861			−2.10461
$204$	−4.21625	+	7.30276i	−0.295197	+	0.511296i
$205$		0			0
$206$	22.9659	+	39.7782i	1.60011	+	2.77148i
$207$	2.35794			0.163888
$208$	−14.9797	−	0.00699222i	−1.03866	−	0.000484823i
$209$	−22.5173			−1.55755
$210$		0			0
$211$	5.57541	+	9.65690i	0.383827	+	0.664808i	0.991606	−	0.129298i	$-0.0412725\pi$
$211$	5.57541	+	9.65690i	0.383827	+	0.664808i	−0.607779	+	0.794107i	$0.707939\pi$
$212$	11.7814	−	20.4060i	0.809152	−	1.40149i
$213$	1.39635			0.0956760
$214$	−1.22128	+	2.11532i	−0.0834849	+	0.144600i
$215$		0			0
$216$	−4.97244			−0.338331
$217$	14.0811	−	24.3892i	0.955889	−	1.65565i
$218$	17.6589	+	30.5862i	1.19601	+	2.07156i
$219$	−0.562992	−	0.975130i	−0.0380435	−	0.0658932i
$220$		0			0
$221$	3.77320	+	6.54242i	0.253813	+	0.440091i
$222$	18.8010			1.26184
$223$	4.46374	+	7.73143i	0.298914	+	0.517735i	0.975888	−	0.218273i	$-0.0700422\pi$
$223$	4.46374	+	7.73143i	0.298914	+	0.517735i	−0.676973	+	0.736007i	$0.736709\pi$
$224$	−0.530679	−	0.919164i	−0.0354575	−	0.0614142i
$225$		0			0
$226$	16.7580			1.11472
$227$	−12.9762	+	22.4754i	−0.861259	+	1.49174i	0.00945554	+	0.999955i	$0.496990\pi$
$227$	−12.9762	+	22.4754i	−0.861259	+	1.49174i	−0.870714	+	0.491789i	$0.836343\pi$
$228$	8.39892	−	14.5474i	0.556232	−	0.963422i
$229$	4.37335			0.288999			0.144499	−	0.989505i	$-0.453843\pi$
$229$	4.37335			0.288999			0.144499	+	0.989505i	$0.453843\pi$
$230$		0			0
$231$	11.2930	+	19.5601i	0.743028	+	1.28696i
$232$	17.8122	+	30.8517i	1.16943	+	2.02551i
$233$	22.1372			1.45026			0.725129	−	0.688613i	$-0.241780\pi$
$233$	22.1372			1.45026			0.725129	+	0.688613i	$0.241780\pi$
$234$	−4.42889	+	7.66280i	−0.289526	+	0.500933i
$235$		0			0
$236$	10.7334	+	18.5907i	0.698682	+	1.21015i
$237$	−1.45241	−	2.51566i	−0.0943445	−	0.163409i
$238$	−10.7605	+	18.6378i	−0.697500	+	1.20811i
$239$	8.14973			0.527162			0.263581	−	0.964637i	$-0.415096\pi$
$239$	8.14973			0.527162			0.263581	+	0.964637i	$0.415096\pi$
$240$		0			0
$241$	0.868798	−	1.50480i	0.0559642	−	0.0969328i	−0.836686	−	0.547683i	$-0.815510\pi$
$241$	0.868798	−	1.50480i	0.0559642	−	0.0969328i	0.892650	+	0.450750i	$0.148843\pi$
$242$	−44.4809			−2.85934
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	−9.45833	−	16.3823i	−0.605508	−	1.04877i
$245$		0			0
$246$	−5.14188			−0.327834
$247$	−7.51634	−	13.0327i	−0.478253	−	0.829253i
$248$	−33.4576			−2.12456
$249$	1.14437	+	1.98211i	0.0725217	+	0.125611i
$250$		0			0
$251$	8.41637	−	14.5776i	0.531236	−	0.920128i	−0.468099	−	0.883676i	$-0.655061\pi$
$251$	8.41637	−	14.5776i	0.531236	−	0.920128i	0.999335	−	0.0364524i	$-0.0116057\pi$
$252$	−16.8492			−1.06140
$253$	−6.36212	+	11.0195i	−0.399983	+	0.692791i
$254$	25.4468	−	44.0752i	1.59668	−	2.76552i
$255$		0			0
$256$	16.0947	−	27.8768i	1.00592	−	1.74230i
$257$	8.03857	+	13.9232i	0.501432	+	0.868507i	0.999999	+	0.00165486i	$0.000526760\pi$
$257$	8.03857	+	13.9232i	0.501432	+	0.868507i	−0.498566	+	0.866852i	$0.666140\pi$
$258$	10.7705	+	18.6550i	0.670542	+	1.16141i
$259$	32.0567			1.99191
$260$		0			0
$261$	7.16439			0.443465
$262$	−13.6643	−	23.6673i	−0.844185	−	1.46217i
$263$	11.4754	+	19.8759i	0.707600	+	1.22560i	0.965745	+	0.259494i	$0.0835557\pi$
$263$	11.4754	+	19.8759i	0.707600	+	1.22560i	−0.258144	+	0.966106i	$0.583111\pi$
$264$	13.4165	−	23.2380i	0.825728	−	1.43020i
$265$		0			0
$266$	21.4353	−	37.1270i	1.31428	−	2.27641i
$267$	−6.98684	+	12.1016i	−0.427588	+	0.740604i
$268$	−53.2227			−3.25110
$269$	−14.2893	+	24.7497i	−0.871231	+	1.50902i	−0.0105078	+	0.999945i	$0.503345\pi$
$269$	−14.2893	+	24.7497i	−0.871231	+	1.50902i	−0.860724	+	0.509072i	$0.829989\pi$
$270$		0			0
$271$	−8.96308	−	15.5245i	−0.544468	−	0.943046i	−0.998640	−	0.0521324i	$-0.983398\pi$
$271$	−8.96308	−	15.5245i	−0.544468	−	0.943046i	0.454172	−	0.890914i	$-0.349935\pi$
$272$	8.70265			0.527676
$273$	−7.55151	+	13.0655i	−0.457038	+	0.790761i
$274$	45.7078			2.76131
$275$		0			0
$276$	−4.74612	−	8.22053i	−0.285683	−	0.494818i
$277$	1.67873	−	2.90764i	0.100865	−	0.174703i	−0.811176	−	0.584802i	$-0.801172\pi$
$277$	1.67873	−	2.90764i	0.100865	−	0.174703i	0.912041	+	0.410098i	$0.134506\pi$
$278$	23.9584			1.43693
$279$	−3.36431	+	5.82716i	−0.201416	+	0.348863i
$280$		0			0
$281$	1.73465			0.103480			0.0517401	−	0.998661i	$-0.483523\pi$
$281$	1.73465			0.103480			0.0517401	+	0.998661i	$0.483523\pi$
$282$	8.58179	−	14.8641i	0.511038	−	0.885144i
$283$	0.454383	+	0.787014i	0.0270103	+	0.0467832i	0.879215	−	0.476426i	$-0.158068\pi$
$283$	0.454383	+	0.787014i	0.0270103	+	0.0467832i	−0.852204	+	0.523209i	$0.824735\pi$
$284$	−2.81061	−	4.86811i	−0.166779	−	0.288869i
$285$		0			0
$286$	−23.8612	−	41.3734i	−1.41094	−	2.44646i
$287$	−8.76719			−0.517511
$288$	0.126792	+	0.219610i	0.00747128	+	0.0129406i
$289$	6.30614	+	10.9226i	0.370949	+	0.642503i
$290$		0			0
$291$	4.14703			0.243103
$292$	−2.26641	+	3.92554i	−0.132632	+	0.229725i
$293$	−6.70818	+	11.6189i	−0.391896	+	0.678784i	−0.992700	−	0.120613i	$-0.961514\pi$
$293$	−6.70818	+	11.6189i	−0.391896	+	0.678784i	0.600804	+	0.799397i	$0.294847\pi$
$294$	−25.8185			−1.50577
$295$		0			0
$296$	−19.0422	−	32.9821i	−1.10681	−	1.91705i
$297$	−2.69817	−	4.67337i	−0.156564	−	0.271177i
$298$	−6.73228			−0.389991
$299$	−8.50166	−	0.00396839i	−0.491663	−	0.000229498i
$300$		0			0
$301$	18.3643	+	31.8079i	1.05850	+	1.83338i
$302$	−7.13621	−	12.3603i	−0.410643	−	0.711254i
$303$	7.62974	−	13.2151i	0.438317	−	0.759187i
$304$	−17.3360			−0.994287
$305$		0			0
$306$	2.57094	−	4.45300i	0.146971	−	0.254561i
$307$	−19.4208			−1.10841			−0.554203	−	0.832382i	$-0.686977\pi$
$307$	−19.4208			−1.10841			−0.554203	+	0.832382i	$0.686977\pi$
$308$	45.4620	−	78.7424i	2.59044	−	4.48677i
$309$	−9.35582	−	16.2048i	−0.532234	−	0.921857i
$310$		0			0
$311$	20.3980			1.15666			0.578332	−	0.815802i	$-0.303704\pi$
$311$	20.3980			1.15666			0.578332	+	0.815802i	$0.303704\pi$
$312$	17.9284	+	0.00836859i	1.01499	+	0.000473778i
$313$	−13.3674			−0.755568			−0.377784	−	0.925894i	$-0.623314\pi$
$313$	−13.3674			−0.755568			−0.377784	+	0.925894i	$0.623314\pi$
$314$	−6.43822	−	11.1513i	−0.363330	−	0.629305i
$315$		0			0
$316$	−5.84693	+	10.1272i	−0.328916	+	0.569698i
$317$	31.7412			1.78277			0.891383	−	0.453251i	$-0.149736\pi$
$317$	31.7412			1.78277			0.891383	+	0.453251i	$0.149736\pi$
$318$	−7.18395	+	12.4430i	−0.402856	+	0.697767i
$319$	−19.3308	+	33.4819i	−1.08232	+	1.87463i
$320$		0			0
$321$	0.497522	−	0.861734i	0.0277690	−	0.0480973i
$322$	−12.1128	−	20.9800i	−0.675021	−	1.16917i
$323$	4.37024	+	7.56948i	0.243167	+	0.421177i
$324$	4.02566			0.223648
$325$		0			0
$326$	−13.1917			−0.730623
$327$	−7.19386	−	12.4601i	−0.397822	−	0.689047i
$328$	5.20785	+	9.02027i	0.287556	+	0.498061i
$329$	14.6324	−	25.3441i	0.806712	−	1.39727i
$330$		0			0
$331$	−14.4245	+	24.9840i	−0.792843	+	1.37324i	0.131357	+	0.991335i	$0.458067\pi$
$331$	−14.4245	+	24.9840i	−0.792843	+	1.37324i	−0.924200	+	0.381909i	$0.875267\pi$
$332$	4.60686	−	7.97931i	0.252834	−	0.437921i
$333$	−7.65911			−0.419717
$334$	−23.4422	+	40.6031i	−1.28270	+	2.22170i
$335$		0			0
$336$	8.69447	+	15.0593i	0.474322	+	0.821550i
$337$	19.6071			1.06807			0.534034	−	0.845463i	$-0.320675\pi$
$337$	19.6071			1.06807			0.534034	+	0.845463i	$0.320675\pi$
$338$	15.9815	−	27.6212i	0.869278	−	1.50239i
$339$	−6.82683			−0.370782
$340$		0			0
$341$	−18.1550	−	31.4453i	−0.983147	−	1.70286i
$342$	−5.12140	+	8.87052i	−0.276934	+	0.479663i
$343$	−14.7240			−0.795022
$344$	21.8174	−	37.7888i	1.17631	−	2.03744i
$345$		0			0
$346$	−30.7285			−1.65197
$347$	−8.23242	+	14.2590i	−0.441939	+	0.765461i	−0.997833	−	0.0657918i	$-0.979043\pi$
$347$	−8.23242	+	14.2590i	−0.441939	+	0.765461i	0.555894	+	0.831253i	$0.312376\pi$
$348$	−14.4207	−	24.9774i	−0.773031	−	1.33893i
$349$	3.65816	+	6.33612i	0.195817	+	0.339165i	0.947168	−	0.320738i	$-0.103931\pi$
$349$	3.65816	+	6.33612i	0.195817	+	0.339165i	−0.751351	+	0.659903i	$0.770597\pi$
$350$		0			0
$351$	1.80423	−	3.12166i	0.0963028	−	0.166622i
$352$	−1.36842			−0.0729373
$353$	−4.46102	−	7.72672i	−0.237436	−	0.411252i	0.722542	−	0.691327i	$-0.242974\pi$
$353$	−4.46102	−	7.72672i	−0.237436	−	0.411252i	−0.959978	+	0.280076i	$0.909640\pi$
$354$	−6.54487	−	11.3360i	−0.347856	−	0.602504i
$355$		0			0
$356$	56.2533			2.98142
$357$	4.38360	−	7.59261i	0.232005	−	0.401844i
$358$	6.84437	−	11.8548i	0.361736	−	0.626545i
$359$	13.2099			0.697193			0.348596	−	0.937273i	$-0.386658\pi$
$359$	13.2099			0.697193			0.348596	+	0.937273i	$0.386658\pi$
$360$		0			0
$361$	0.794323	+	1.37581i	0.0418065	+	0.0724110i
$362$	−19.5380	−	33.8407i	−1.02689	−	1.77863i
$363$	18.1205			0.951082
$364$	60.7505	+	0.0283571i	3.18419	+	0.00148631i
$365$		0			0
$366$	5.76740	+	9.98942i	0.301467	+	0.522156i
$367$	8.57120	+	14.8458i	0.447413	+	0.774942i	0.998217	−	0.0596926i	$-0.0190120\pi$
$367$	8.57120	+	14.8458i	0.447413	+	0.774942i	−0.550804	+	0.834635i	$0.685679\pi$
$368$	−4.89817	+	8.48388i	−0.255335	+	0.442253i
$369$	2.09469			0.109045
$370$		0			0
$371$	−12.2490	+	21.2160i	−0.635938	+	1.10148i
$372$	27.0871			1.40440
$373$	−0.106510	+	0.184481i	−0.00551489	+	0.00955207i	−0.868770	−	0.495216i	$-0.835089\pi$
$373$	−0.106510	+	0.184481i	−0.00551489	+	0.00955207i	0.863255	+	0.504768i	$0.168422\pi$
$374$	13.8737	+	24.0299i	0.717391	+	1.24256i
$375$		0			0
$376$	−34.7676			−1.79300
$377$	−25.8316	−	0.0120576i	−1.33039	−	0.000621000i
$378$	10.2741			0.528442
$379$	−15.8405	−	27.4365i	−0.813671	−	1.40932i	−0.910278	−	0.413997i	$-0.864132\pi$
$379$	−15.8405	−	27.4365i	−0.813671	−	1.40932i	0.0966073	−	0.995323i	$-0.469201\pi$
$380$		0			0
$381$	−10.3665	+	17.9553i	−0.531091	+	0.919876i
$382$	17.0141			0.870517
$383$	0.573308	−	0.992998i	0.0292947	−	0.0507398i	−0.851006	−	0.525155i	$-0.824007\pi$
$383$	0.573308	−	0.992998i	0.0292947	−	0.0507398i	0.880301	+	0.474415i	$0.157341\pi$
$384$	−9.68804	+	16.7802i	−0.494390	+	0.856309i
$385$		0			0
$386$	5.00494	−	8.66881i	0.254745	−	0.441231i
$387$	−4.38766	−	7.59966i	−0.223037	−	0.386312i
$388$	−8.34727	−	14.4579i	−0.423768	−	0.733988i
$389$	−21.8539			−1.10804			−0.554019	−	0.832504i	$-0.686907\pi$
$389$	−21.8539			−1.10804			−0.554019	+	0.832504i	$0.686907\pi$
$390$		0			0
$391$	4.93914			0.249783
$392$	26.1498	+	45.2928i	1.32077	+	2.28763i
$393$	5.56655	+	9.64155i	0.280795	+	0.486352i
$394$	−12.6126	+	21.8457i	−0.635414	+	1.10057i
$395$		0			0
$396$	−10.8619	+	18.8134i	−0.545833	+	0.945410i
$397$	18.4697	−	31.9905i	0.926968	−	1.60556i	0.138603	−	0.990348i	$-0.455739\pi$
$397$	18.4697	−	31.9905i	0.926968	−	1.60556i	0.788365	−	0.615208i	$-0.210928\pi$
$398$	15.5554			0.779721
$399$	−8.73228	+	15.1247i	−0.437161	+	0.757184i
$400$		0			0
$401$	16.3844	+	28.3787i	0.818199	+	1.41716i	0.907008	+	0.421114i	$0.138361\pi$
$401$	16.3844	+	28.3787i	0.818199	+	1.41716i	−0.0888083	+	0.996049i	$0.528306\pi$
$402$	32.4536			1.61864
$403$	12.1400	−	21.0044i	0.604736	−	1.04631i
$404$	−61.4295			−3.05623
$405$		0			0
$406$	−36.8038	−	63.7461i	−1.82654	−	3.16367i
$407$	20.6656	−	35.7939i	1.02436	−	1.77424i
$408$	−10.4157			−0.515654
$409$	−2.47333	+	4.28393i	−0.122298	+	0.211827i	−0.920674	−	0.390333i	$-0.872360\pi$
$409$	−2.47333	+	4.28393i	−0.122298	+	0.211827i	0.798375	+	0.602160i	$0.205693\pi$
$410$		0			0
$411$	−18.6204			−0.918475
$412$	−37.6634	+	65.2349i	−1.85554	+	3.21389i
$413$	−11.1594	−	19.3286i	−0.549117	−	0.951098i
$414$	2.89404	+	5.01262i	0.142234	+	0.246357i
$415$		0			0
$416$	−0.456785	−	0.792028i	−0.0223957	−	0.0388324i
$417$	−9.76011			−0.477955
$418$	−27.6368	−	47.8684i	−1.35176	−	2.34132i
$419$	6.48476	+	11.2319i	0.316801	+	0.548716i	0.979819	−	0.199888i	$-0.0640579\pi$
$419$	6.48476	+	11.2319i	0.316801	+	0.548716i	−0.663018	+	0.748604i	$0.730725\pi$
$420$		0			0
$421$	−25.3303			−1.23452			−0.617262	−	0.786758i	$-0.711758\pi$
$421$	−25.3303			−1.23452			−0.617262	+	0.786758i	$0.711758\pi$
$422$	−13.6861	+	23.7050i	−0.666228	+	1.15394i
$423$	−3.49603	+	6.05530i	−0.169983	+	0.294419i
$424$	29.1045			1.41344
$425$		0			0
$426$	1.71382	+	2.96842i	0.0830349	+	0.143821i
$427$	9.83374	+	17.0325i	0.475888	+	0.824262i
$428$	−4.00571			−0.193623
$429$	9.72053	+	16.8546i	0.469312	+	0.813749i
$430$		0			0
$431$	−10.9118	−	18.8997i	−0.525601	−	0.910368i	−0.999555	−	0.0298183i	$-0.990507\pi$
$431$	−10.9118	−	18.8997i	−0.525601	−	0.910368i	0.473954	−	0.880549i	$-0.342826\pi$
$432$	−2.07731	−	3.59801i	−0.0999448	−	0.173109i
$433$	−8.20200	+	14.2063i	−0.394163	+	0.682710i	−0.992994	−	0.118165i	$-0.962299\pi$
$433$	−8.20200	+	14.2063i	−0.394163	+	0.682710i	0.598831	+	0.800875i	$0.295632\pi$
$434$	69.1305			3.31837
$435$		0			0
$436$	−28.9601	+	50.1603i	−1.38694	+	2.40224i
$437$	−9.83894			−0.470660
$438$	1.38199	−	2.39367i	0.0660340	−	0.114374i
$439$	8.32948	+	14.4271i	0.397545	+	0.688567i	0.993422	−	0.114508i	$-0.0365291\pi$
$439$	8.32948	+	14.4271i	0.397545	+	0.688567i	−0.595878	+	0.803075i	$0.703196\pi$
$440$		0			0
$441$	10.5179			0.500853
$442$	−9.27715	+	16.0512i	−0.441269	+	0.763477i
$443$	10.6646			0.506690			0.253345	−	0.967376i	$-0.418469\pi$
$443$	10.6646			0.506690			0.253345	+	0.967376i	$0.418469\pi$
$444$	15.4165	+	26.7021i	0.731634	+	1.26723i
$445$		0			0
$446$	−10.9573	+	18.9785i	−0.518841	+	0.898659i
$447$	2.74258			0.129720
$448$	−16.0863	+	27.8622i	−0.760005	+	1.31637i
$449$	−7.63537	+	13.2249i	−0.360335	+	0.624119i	−0.988016	−	0.154352i	$-0.950671\pi$
$449$	−7.63537	+	13.2249i	−0.360335	+	0.624119i	0.627681	+	0.778471i	$0.284004\pi$
$450$		0			0
$451$	−5.65183	+	9.78926i	−0.266134	+	0.460958i
$452$	13.7412	+	23.8005i	0.646334	+	1.11948i
$453$	2.90714	+	5.03531i	0.136589	+	0.236579i
$454$	−63.7058			−2.98986
$455$		0			0
$456$	20.7484			0.971635
$457$	−11.9908	−	20.7687i	−0.560907	−	0.971520i	−0.997418	−	0.0718207i	$-0.977119\pi$
$457$	−11.9908	−	20.7687i	−0.560907	−	0.971520i	0.436510	−	0.899699i	$-0.356214\pi$
$458$	5.36768	+	9.29709i	0.250815	+	0.434424i
$459$	−1.04734	+	1.81405i	−0.0488858	+	0.0846728i
$460$		0			0
$461$	−1.69922	+	2.94313i	−0.0791405	+	0.137075i	−0.902879	−	0.429894i	$-0.858551\pi$
$461$	−1.69922	+	2.94313i	−0.0791405	+	0.137075i	0.823739	+	0.566969i	$0.191884\pi$
$462$	−27.7213	+	48.0147i	−1.28971	+	2.23384i
$463$	25.2215			1.17214			0.586072	−	0.810259i	$-0.300673\pi$
$463$	25.2215			1.17214			0.586072	+	0.810259i	$0.300673\pi$
$464$	−14.8827	+	25.7776i	−0.690912	+	1.19669i
$465$		0			0
$466$	27.1704	+	47.0605i	1.25864	+	2.18003i
$467$	−14.8622			−0.687742			−0.343871	−	0.939017i	$-0.611738\pi$
$467$	−14.8622			−0.687742			−0.343871	+	0.939017i	$0.611738\pi$
$468$	−14.5147	−	0.00677517i	−0.670944	−	0.000313182i
$469$	55.3352			2.55514
$470$		0			0
$471$	2.62279	+	4.54280i	0.120852	+	0.209321i
$472$	−13.2577	+	22.9630i	−0.610234	+	1.05696i
$473$	47.3547			2.17737
$474$	3.56527	−	6.17524i	0.163758	−	0.283638i
$475$		0			0
$476$	−35.2938			−1.61769
$477$	2.92658	−	5.06899i	0.133999	−	0.232093i
$478$	10.0027	+	17.3251i	0.457511	+	0.792432i
$479$	19.1931	+	33.2434i	0.876954	+	1.51893i	0.854666	+	0.519178i	$0.173762\pi$
$479$	19.1931	+	33.2434i	0.876954	+	1.51893i	0.0222878	+	0.999752i	$0.492905\pi$
$480$		0			0
$481$	27.6153	+	0.0128902i	1.25915	+	0.000587745i
$482$	4.26531			0.194280
$483$	4.93450	+	8.54680i	0.224527	+	0.388893i
$484$	−36.4736	−	63.1741i	−1.65789	−	2.87155i
$485$		0			0
$486$	−2.45472			−0.111348
$487$	−10.7380	+	18.5988i	−0.486587	+	0.842794i	−0.999881	−	0.0154192i	$-0.995092\pi$
$487$	−10.7380	+	18.5988i	−0.486587	+	0.842794i	0.513294	+	0.858213i	$0.328425\pi$
$488$	11.6828	−	20.2352i	0.528855	−	0.916004i
$489$	5.37403			0.243022
$490$		0			0
$491$	−6.70317	−	11.6102i	−0.302510	−	0.523962i	0.674194	−	0.738554i	$-0.264491\pi$
$491$	−6.70317	−	11.6102i	−0.302510	−	0.523962i	−0.976704	+	0.214592i	$0.931158\pi$
$492$	−4.21625	−	7.30276i	−0.190083	−	0.329234i
$493$	15.0072			0.675889
$494$	18.4804	−	31.9745i	0.831472	−	1.43860i
$495$		0			0
$496$	−13.9775	−	24.2097i	−0.627606	−	1.08705i
$497$	2.92216	+	5.06133i	0.131077	+	0.227032i
$498$	−2.80912	+	4.86553i	−0.125880	+	0.218030i
$499$	1.06797			0.0478089			0.0239045	−	0.999714i	$-0.492390\pi$
$499$	1.06797			0.0478089			0.0239045	+	0.999714i	$0.492390\pi$
$500$		0			0
$501$	9.54985	−	16.5408i	0.426656	−	0.738989i
$502$	41.3197			1.84419
$503$	−7.66505	+	13.2763i	−0.341768	+	0.591959i	−0.984761	−	0.173913i	$-0.944359\pi$
$503$	−7.66505	+	13.2763i	−0.341768	+	0.591959i	0.642994	+	0.765872i	$0.277692\pi$
$504$	−10.4059	−	18.0236i	−0.463516	−	0.802834i
$505$		0			0
$506$	−31.2345			−1.38854
$507$	−6.51051	+	11.2523i	−0.289142	+	0.499730i
$508$	83.4638			3.70311
$509$	−13.6334	−	23.6138i	−0.604292	−	1.04666i	−0.992163	−	0.124951i	$-0.960123\pi$
$509$	−13.6334	−	23.6138i	−0.604292	−	1.04666i	0.387871	−	0.921714i	$-0.373211\pi$
$510$		0			0
$511$	2.35637	−	4.08135i	0.104240	−	0.180548i
$512$	40.2637			1.77942
$513$	2.08635	−	3.61366i	0.0921144	−	0.159547i
$514$	−19.7325	+	34.1776i	−0.870362	+	1.50751i
$515$		0			0
$516$	−17.6632	+	30.5936i	−0.777581	+	1.34681i
$517$	−18.8658	−	32.6765i	−0.829717	−	1.43711i
$518$	39.3452	+	68.1479i	1.72873	+	2.99425i
$519$	12.5181			0.549484
$520$		0			0
$521$	−0.508877			−0.0222943			−0.0111471	−	0.999938i	$-0.503548\pi$
$521$	−0.508877			−0.0222943			−0.0111471	+	0.999938i	$0.503548\pi$
$522$	8.79330	+	15.2304i	0.384872	+	0.666618i
$523$	2.45015	+	4.24379i	0.107138	+	0.185568i	0.914610	−	0.404338i	$-0.132498\pi$
$523$	2.45015	+	4.24379i	0.107138	+	0.185568i	−0.807472	+	0.589906i	$0.799165\pi$
$524$	22.4090	−	38.8136i	0.978944	−	1.69558i
$525$		0			0
$526$	−28.1688	+	48.7898i	−1.22822	+	2.12734i
$527$	−7.04718	+	12.2061i	−0.306980	+	0.531705i
$528$	22.4198			0.975697
$529$	8.72007	−	15.1036i	0.379134	−	0.656679i
$530$		0			0
$531$	2.66624	+	4.61805i	0.115705	+	0.200407i
$532$	70.3064			3.04817
$533$	−7.55251	−	0.00352535i	−0.327135	−	0.000152700i
$534$	−34.3015			−1.48437
$535$		0			0
$536$	−32.8700	−	56.9324i	−1.41977	−	2.45911i
$537$	−2.78825	+	4.82938i	−0.120322	+	0.208403i
$538$	−70.1523			−3.02448
$539$	−28.3791	+	49.1541i	−1.22238	+	2.11722i
$540$		0			0
$541$	25.6457			1.10259			0.551297	−	0.834309i	$-0.314133\pi$
$541$	25.6457			1.10259			0.551297	+	0.834309i	$0.314133\pi$
$542$	22.0019	−	38.1083i	0.945061	−	1.63689i
$543$	7.95934	+	13.7860i	0.341568	+	0.591613i
$544$	0.265589	+	0.460014i	0.0113870	+	0.0197229i
$545$		0			0
$546$	−37.0438	−	0.0172913i	−1.58533	−	0.000739997i
$547$	22.3486			0.955558			0.477779	−	0.878480i	$-0.341442\pi$
$547$	22.3486			0.955558			0.477779	+	0.878480i	$0.341442\pi$
$548$	37.4796	+	64.9166i	1.60105	+	2.77310i
$549$	−2.34951	−	4.06947i	−0.100275	−	0.173681i
$550$		0			0
$551$	−29.8948			−1.27356
$552$	5.86234	−	10.1539i	0.249518	−	0.432178i
$553$	6.07900	−	10.5291i	0.258505	−	0.447744i
$554$	8.24161			0.350153
$555$		0			0
$556$	19.6455	+	34.0269i	0.833153	+	1.44306i
$557$	−10.1767	−	17.6265i	−0.431199	−	0.746859i	0.565778	−	0.824558i	$-0.308576\pi$
$557$	−10.1767	−	17.6265i	−0.431199	−	0.746859i	−0.996977	+	0.0776988i	$0.975243\pi$
$558$	−16.5169			−0.699216
$559$	15.8072	+	27.4083i	0.668571	+	1.15925i
$560$		0			0
$561$	−5.65183	−	9.78926i	−0.238621	−	0.413303i
$562$	2.12904	+	3.68760i	0.0898080	+	0.155552i
$563$	6.28428	−	10.8847i	0.264851	−	0.458735i	−0.702674	−	0.711512i	$-0.748011\pi$
$563$	6.28428	−	10.8847i	0.264851	−	0.458735i	0.967524	+	0.252777i	$0.0813440\pi$
$564$	28.1477			1.18523
$565$		0			0
$566$	−1.11538	+	1.93190i	−0.0468831	+	0.0812039i
$567$	−4.18544			−0.175772
$568$	3.47162	−	6.01302i	0.145666	−	0.252301i
$569$	−6.60706	−	11.4438i	−0.276982	−	0.479747i	0.693651	−	0.720311i	$-0.256001\pi$
$569$	−6.60706	−	11.4438i	−0.276982	−	0.479747i	−0.970633	+	0.240564i	$0.922668\pi$
$570$		0			0
$571$	29.1427			1.21958			0.609792	−	0.792562i	$-0.291253\pi$
$571$	29.1427			1.21958			0.609792	+	0.792562i	$0.291253\pi$
$572$	39.1949	−	67.8144i	1.63882	−	2.83546i
$573$	−6.93117			−0.289554
$574$	−10.7605	−	18.6378i	−0.449135	−	0.777925i
$575$		0			0
$576$	3.84339	−	6.65694i	0.160141	−	0.277373i
$577$	−19.3680			−0.806302			−0.403151	−	0.915133i	$-0.632085\pi$
$577$	−19.3680			−0.806302			−0.403151	+	0.915133i	$0.632085\pi$
$578$	−15.4798	+	26.8118i	−0.643876	+	1.11523i
$579$	−2.03890	+	3.53148i	−0.0847339	+	0.146763i
$580$		0			0
$581$	−4.78970	+	8.29601i	−0.198710	+	0.344176i
$582$	5.08990	+	8.81597i	0.210983	+	0.365434i
$583$	15.7929	+	27.3540i	0.654073	+	1.13289i
$584$	−5.59888			−0.231683
$585$		0			0
$586$	−32.9334			−1.36047
$587$	2.37400	+	4.11189i	0.0979855	+	0.169716i	0.910851	−	0.412736i	$-0.135427\pi$
$587$	2.37400	+	4.11189i	0.0979855	+	0.169716i	−0.812865	+	0.582452i	$0.802093\pi$
$588$	−21.1708	−	36.6689i	−0.873068	−	1.51220i
$589$	14.0382	−	24.3149i	0.578435	−	1.00188i
$590$		0			0
$591$	5.13810	−	8.89944i	0.211353	−	0.366074i
$592$	15.9104	−	27.5576i	0.653912	−	1.13261i
$593$	−35.2607			−1.44799			−0.723993	−	0.689808i	$-0.757695\pi$
$593$	−35.2607			−1.44799			−0.723993	+	0.689808i	$0.757695\pi$
$594$	6.62326	−	11.4718i	0.271756	−	0.470695i
$595$		0			0
$596$	−5.52036	−	9.56154i	−0.226123	−	0.391656i
$597$	−6.33692			−0.259353
$598$	−10.4262	−	18.0781i	−0.426358	−	0.739270i
$599$	−21.1497			−0.864155			−0.432078	−	0.901836i	$-0.642219\pi$
$599$	−21.1497			−0.864155			−0.432078	+	0.901836i	$0.642219\pi$
$600$		0			0
$601$	1.01691	+	1.76134i	0.0414805	+	0.0718464i	0.886020	−	0.463646i	$-0.153459\pi$
$601$	1.01691	+	1.76134i	0.0414805	+	0.0718464i	−0.844540	+	0.535493i	$0.820126\pi$
$602$	−45.0793	+	78.0796i	−1.83729	+	3.18229i
$603$	−13.2209			−0.538395
$604$	11.7031	−	20.2704i	0.476194	−	0.824793i
$605$		0			0
$606$	37.4578			1.52162
$607$	4.02150	−	6.96544i	0.163228	−	0.282718i	−0.772797	−	0.634653i	$-0.781143\pi$
$607$	4.02150	−	6.96544i	0.163228	−	0.282718i	0.936024	+	0.351935i	$0.114476\pi$
$608$	−0.529063	−	0.916364i	−0.0214563	−	0.0371635i
$609$	14.9931	+	25.9688i	0.607550	+	1.05231i
$610$		0			0
$611$	12.6153	−	21.8268i	0.510361	−	0.883019i
$612$	8.43251			0.340864
$613$	−11.0515	−	19.1417i	−0.446366	−	0.773128i	0.551781	−	0.833989i	$-0.313949\pi$
$613$	−11.0515	−	19.1417i	−0.446366	−	0.773128i	−0.998146	+	0.0608614i	$0.980615\pi$
$614$	−23.8364	−	41.2858i	−0.961957	−	1.66616i
$615$		0			0
$616$	112.308			4.52501
$617$	5.31943	−	9.21353i	0.214152	−	0.370923i	−0.738858	−	0.673861i	$-0.764634\pi$
$617$	5.31943	−	9.21353i	0.214152	−	0.370923i	0.953010	+	0.302939i	$0.0979678\pi$
$618$	22.9659	−	39.7782i	0.923826	−	1.60011i
$619$	−15.9640			−0.641648			−0.320824	−	0.947139i	$-0.603960\pi$
$619$	−15.9640			−0.641648			−0.320824	+	0.947139i	$0.603960\pi$
$620$		0			0
$621$	−1.17897	−	2.04203i	−0.0473103	−	0.0819439i
$622$	25.0357	+	43.3631i	1.00384	+	1.73870i
$623$	−58.4860			−2.34319
$624$	7.48380	+	12.9763i	0.299592	+	0.519468i
$625$		0			0
$626$	−16.4066	−	28.4170i	−0.655739	−	1.13577i
$627$	11.2586	+	19.5005i	0.449627	+	0.778777i
$628$	10.5585	−	18.2878i	0.421328	−	0.729762i
$629$	−16.0434			−0.639694
$630$		0			0
$631$	−7.00197	+	12.1278i	−0.278744	+	0.482799i	−0.971073	−	0.238783i	$-0.923251\pi$
$631$	−7.00197	+	12.1278i	−0.278744	+	0.482799i	0.692329	+	0.721582i	$0.256585\pi$
$632$	−14.4441			−0.574555
$633$	5.57541	−	9.65690i	0.221603	−	0.383827i
$634$	38.9580	+	67.4772i	1.54722	+	2.67986i
$635$		0			0
$636$	−23.5629			−0.934328
$637$	−37.9229	−	0.0177016i	−1.50256	−	0.000701363i
$638$	−94.9034			−3.75726
$639$	−0.698173	−	1.20927i	−0.0276193	−	0.0478380i
$640$		0			0
$641$	−10.3747	+	17.9695i	−0.409776	+	0.709752i	−0.994864	−	0.101217i	$-0.967726\pi$
$641$	−10.3747	+	17.9695i	−0.409776	+	0.709752i	0.585089	+	0.810969i	$0.301060\pi$
$642$	2.44256			0.0964001
$643$	−4.30119	+	7.44988i	−0.169622	+	0.293794i	−0.938287	−	0.345857i	$-0.887588\pi$
$643$	−4.30119	+	7.44988i	−0.169622	+	0.293794i	0.768665	+	0.639652i	$0.220921\pi$
$644$	19.8646	−	34.4065i	0.782776	−	1.35581i
$645$		0			0
$646$	−10.7277	+	18.5810i	−0.422077	+	0.731059i
$647$	5.34964	+	9.26586i	0.210316	+	0.364278i	0.951813	−	0.306678i	$-0.0992173\pi$
$647$	5.34964	+	9.26586i	0.210316	+	0.364278i	−0.741497	+	0.670956i	$0.765884\pi$
$648$	2.48622	+	4.30626i	0.0976679	+	0.169166i
$649$	−28.7759			−1.12955
$650$		0			0
$651$	−28.1622			−1.10377
$652$	−10.8170	−	18.7356i	−0.423627	−	0.733743i
$653$	−0.590565	−	1.02289i	−0.0231106	−	0.0400288i	0.854239	−	0.519881i	$-0.174024\pi$
$653$	−0.590565	−	1.02289i	−0.0231106	−	0.0400288i	−0.877349	+	0.479852i	$0.840690\pi$
$654$	17.6589	−	30.5862i	0.690519	−	1.19601i
$655$		0			0
$656$	−4.35132	+	7.53672i	−0.169891	+	0.294259i
$657$	−0.562992	+	0.975130i	−0.0219644	+	0.0380435i
$658$	71.8371			2.80050
$659$	17.0861	−	29.5940i	0.665580	−	1.15282i	−0.313548	−	0.949572i	$-0.601518\pi$
$659$	17.0861	−	29.5940i	0.665580	−	1.15282i	0.979128	−	0.203246i	$-0.0651491\pi$
$660$		0			0
$661$	−13.8148	−	23.9278i	−0.537332	−	0.930685i	−0.999047	−	0.0436572i	$-0.986099\pi$
$661$	−13.8148	−	23.9278i	−0.537332	−	0.930685i	0.461715	−	0.887028i	$-0.347234\pi$
$662$	−70.8163			−2.75236
$663$	3.77931	−	6.53890i	0.146776	−	0.253950i
$664$	11.3806			0.441654
$665$		0			0
$666$	−9.40049	−	16.2821i	−0.364262	−	0.630920i
$667$	−8.44659	+	14.6299i	−0.327053	+	0.566473i
$668$	−76.8889			−2.97492
$669$	4.46374	−	7.73143i	0.172578	−	0.298914i
$670$		0			0
$671$	25.3575			0.978917
$672$	−0.530679	+	0.919164i	−0.0204714	+	0.0354575i
$673$	−2.06796	−	3.58181i	−0.0797139	−	0.138068i	0.823413	−	0.567443i	$-0.192067\pi$
$673$	−2.06796	−	3.58181i	−0.0797139	−	0.138068i	−0.903126	+	0.429375i	$0.858734\pi$
$674$	24.0650	+	41.6819i	0.926950	+	1.60552i
$675$		0			0
$676$	52.3336	+	0.0488564i	2.01283	+	0.00187909i
$677$	20.1697			0.775183			0.387591	−	0.921831i	$-0.373307\pi$
$677$	20.1697			0.775183			0.387591	+	0.921831i	$0.373307\pi$
$678$	−8.37898	−	14.5128i	−0.321793	−	0.557362i
$679$	8.67857	+	15.0317i	0.333053	+	0.576865i
$680$		0			0
$681$	25.9523			0.994496
$682$	44.5654	−	77.1896i	1.70650	−	2.95574i
$683$	9.98079	−	17.2872i	0.381904	−	0.661478i	−0.609430	−	0.792840i	$-0.708602\pi$
$683$	9.98079	−	17.2872i	0.381904	−	0.661478i	0.991334	+	0.131362i	$0.0419351\pi$
$684$	−16.7978			−0.642282
$685$		0			0
$686$	−18.0717	−	31.3011i	−0.689980	−	1.19508i
$687$	−2.18667	−	3.78743i	−0.0834268	−	0.144499i
$688$	36.4582			1.38996
$689$	−10.5605	+	18.2716i	−0.402322	+	0.696092i
$690$		0			0
$691$	−6.43083	−	11.1385i	−0.244640	−	0.423730i	0.717390	−	0.696672i	$-0.245337\pi$
$691$	−6.43083	−	11.1385i	−0.244640	−	0.423730i	−0.962030	+	0.272942i	$0.912003\pi$
$692$	−25.1968	−	43.6422i	−0.957840	−	1.65903i
$693$	11.2930	−	19.5601i	0.428987	−	0.743028i
$694$	−40.4166			−1.53419
$695$		0			0
$696$	17.8122	−	30.8517i	0.675171	−	1.16943i
$697$	4.38772			0.166197
$698$	−8.97977	+	15.5534i	−0.339889	+	0.588706i
$699$	−11.0686	−	19.1714i	−0.418654	−	0.725129i
$700$		0			0
$701$	35.9501			1.35782			0.678908	−	0.734223i	$-0.262453\pi$
$701$	35.9501			1.35782			0.678908	+	0.734223i	$0.262453\pi$
$702$	8.85063	+	0.00413129i	0.334045	+	0.000155925i
$703$	31.9591			1.20536
$704$	20.7403	+	35.9232i	0.781678	+	1.35391i
$705$		0			0
$706$	10.9506	−	18.9670i	0.412130	−	0.713831i
$707$	63.8676			2.40199
$708$	10.7334	−	18.5907i	0.403384	−	0.698682i
$709$	−0.575147	+	0.996184i	−0.0216001	+	0.0374125i	−0.876623	−	0.481177i	$-0.840209\pi$
$709$	−0.575147	+	0.996184i	−0.0216001	+	0.0374125i	0.855023	+	0.518590i	$0.173543\pi$
$710$		0			0
$711$	−1.45241	+	2.51566i	−0.0544698	+	0.0943445i
$712$	34.7416	+	60.1742i	1.30200	+	2.25513i
$713$	−7.93282	−	13.7401i	−0.297087	−	0.514569i
$714$	21.5210			0.805404
$715$		0			0
$716$	22.4491			0.838961
$717$	−4.07486	−	7.05787i	−0.152179	−	0.263581i
$718$	16.2133	+	28.0823i	0.605077	+	1.04802i
$719$	0.0185524	−	0.0321336i	0.000691886	−	0.00119838i	−0.865679	−	0.500599i	$-0.833113\pi$
$719$	0.0185524	−	0.0321336i	0.000691886	−	0.00119838i	0.866371	+	0.499401i	$0.166446\pi$
$720$		0			0
$721$	39.1582	−	67.8241i	1.45833	−	2.52590i
$722$	−1.94984	+	3.37723i	−0.0725657	+	0.125687i
$723$	−1.73760			−0.0646219
$724$	32.0416	−	55.4977i	1.19082	−	2.06255i
$725$		0			0
$726$	22.2405	+	38.5216i	0.825421	+	1.42967i
$727$	15.9912			0.593080			0.296540	−	0.955020i	$-0.404167\pi$
$727$	15.9912			0.593080			0.296540	+	0.955020i	$0.404167\pi$
$728$	37.4887	+	65.0024i	1.38942	+	2.40915i
$729$	1.00000			0.0370370
$730$		0			0
$731$	−9.19079	−	15.9189i	−0.339934	−	0.588782i
$732$	−9.45833	+	16.3823i	−0.349590	+	0.605508i
$733$	9.99906			0.369324			0.184662	−	0.982802i	$-0.440881\pi$
$733$	9.99906			0.369324			0.184662	+	0.982802i	$0.440881\pi$
$734$	−21.0399	+	36.4422i	−0.776598	+	1.34511i
$735$		0			0
$736$	−0.597934			−0.0220401
$737$	35.6722	−	61.7860i	1.31400	−	2.27592i
$738$	2.57094	+	4.45300i	0.0946376	+	0.163917i
$739$	4.89718	+	8.48216i	0.180146	+	0.312021i	0.941930	−	0.335809i	$-0.109010\pi$
$739$	4.89718	+	8.48216i	0.180146	+	0.312021i	−0.761784	+	0.647831i	$0.775676\pi$
$740$		0			0
$741$	−7.52851	+	13.0257i	−0.276567	+	0.478511i
$742$	−60.1360			−2.20766
$743$	9.08281	+	15.7319i	0.333216	+	0.577147i	0.983140	−	0.182852i	$-0.0585329\pi$
$743$	9.08281	+	15.7319i	0.333216	+	0.577147i	−0.649925	+	0.759999i	$0.725200\pi$
$744$	16.7288	+	28.9752i	0.613308	+	1.06228i
$745$		0			0
$746$	−0.522906			−0.0191449
$747$	1.14437	−	1.98211i	0.0418704	−	0.0725217i
$748$	−22.7524	+	39.4082i	−0.831909	+	1.44091i
$749$	4.16470			0.152175
$750$		0			0
$751$	−12.1148	−	20.9835i	−0.442076	−	0.765699i	0.555767	−	0.831338i	$-0.312425\pi$
$751$	−12.1148	−	20.9835i	−0.442076	−	0.765699i	−0.997843	+	0.0656393i	$0.979091\pi$
$752$	−14.5247	−	25.1575i	−0.529662	−	0.917401i
$753$	−16.8327			−0.613419
$754$	−31.6791	−	54.9289i	−1.15368	−	2.00039i
$755$		0			0
$756$	8.42458	+	14.5918i	0.306399	+	0.530699i
$757$	−16.1859	−	28.0348i	−0.588287	−	1.01894i	−0.994457	−	0.105146i	$-0.966469\pi$
$757$	−16.1859	−	28.0348i	−0.588287	−	1.01894i	0.406170	−	0.913798i	$-0.366864\pi$
$758$	38.8840	−	67.3490i	1.41233	−	2.44623i
$759$	12.7242			0.461860
$760$		0			0
$761$	−20.1172	+	34.8441i	−0.729250	+	1.26310i	0.227951	+	0.973673i	$0.426797\pi$
$761$	−20.1172	+	34.8441i	−0.729250	+	1.26310i	−0.957201	+	0.289425i	$0.906536\pi$
$762$	−50.8936			−1.84368
$763$	30.1095	−	52.1512i	1.09004	−	1.88800i
$764$	13.9513	+	24.1643i	0.504739	+	0.874234i
$765$		0			0
$766$	2.81462			0.101696
$767$	−9.60547	−	16.6551i	−0.346834	−	0.601381i
$768$	−32.1893			−1.16153
$769$	−15.0436	−	26.0563i	−0.542486	−	0.939613i	−0.998761	−	0.0497738i	$-0.984150\pi$
$769$	−15.0436	−	26.0563i	−0.542486	−	0.939613i	0.456275	−	0.889839i	$-0.349183\pi$
$770$		0			0
$771$	8.03857	−	13.9232i	0.289502	−	0.501432i
$772$	16.4159			0.590820
$773$	−6.45330	+	11.1774i	−0.232109	+	0.402025i	−0.958429	−	0.285332i	$-0.907896\pi$
$773$	−6.45330	+	11.1774i	−0.232109	+	0.402025i	0.726319	+	0.687357i	$0.241229\pi$
$774$	10.7705	−	18.6550i	0.387137	−	0.670542i
$775$		0			0
$776$	10.3104	−	17.8582i	0.370123	−	0.641071i
$777$	−16.0284	−	27.7620i	−0.575015	−	0.995955i
$778$	−26.8227	−	46.4582i	−0.961640	−	1.66561i
$779$	−8.74049			−0.313160
$780$		0			0
$781$	7.53516			0.269629
$782$	6.06211	+	10.4999i	0.216781	+	0.375475i
$783$	−3.58220	−	6.20455i	−0.128017	−	0.221732i
$784$	−21.8490	+	37.8436i	−0.780321	+	1.35156i
$785$		0			0
$786$	−13.6643	+	23.6673i	−0.487391	+	0.844185i
$787$	−17.8178	+	30.8613i	−0.635136	+	1.10009i	0.351350	+	0.936244i	$0.385723\pi$
$787$	−17.8178	+	30.8613i	−0.635136	+	1.10009i	−0.986486	+	0.163844i	$0.947611\pi$
$788$	−41.3685			−1.47369
$789$	11.4754	−	19.8759i	0.408533	−	0.707600i
$790$		0			0
$791$	−14.2866	−	24.7452i	−0.507974	−	0.879837i
$792$	−26.8330			−0.953469
$793$	8.46443	+	14.6766i	0.300581	+	0.521183i
$794$	90.6760			3.21797
$795$		0			0
$796$	12.7552	+	22.0926i	0.452094	+	0.783050i
$797$	−9.71289	+	16.8232i	−0.344048	+	0.595909i	−0.985180	−	0.171521i	$-0.945132\pi$
$797$	−9.71289	+	16.8232i	−0.344048	+	0.595909i	0.641132	+	0.767431i	$0.278465\pi$
$798$	−42.8706			−1.51760
$799$	−7.32310	+	12.6840i	−0.259073	+	0.448727i
$800$		0			0
$801$	13.9737			0.493736
$802$	−40.2192	+	69.6617i	−1.42019	+	2.45984i
$803$	−3.03810	−	5.26214i	−0.107212	−	0.185697i
$804$	26.6114	+	46.0922i	0.938511	+	1.62555i
$805$		0			0
$806$	59.5525	+	0.0277979i	2.09765	+	0.000979138i
$807$	28.5785			1.00601
$808$	−37.9384	−	65.7112i	−1.33467	−	2.31171i
$809$	−1.90800	−	3.30476i	−0.0670819	−	0.116189i	0.830534	−	0.556968i	$-0.188036\pi$
$809$	−1.90800	−	3.30476i	−0.0670819	−	0.116189i	−0.897616	+	0.440779i	$0.854702\pi$
$810$		0			0
$811$	−51.4748			−1.80753			−0.903763	−	0.428034i	$-0.859206\pi$
$811$	−51.4748			−1.80753			−0.903763	+	0.428034i	$0.859206\pi$
$812$	60.3570	−	104.541i	2.11812	−	3.66869i
$813$	−8.96308	+	15.5245i	−0.314349	+	0.544468i
$814$	101.457			3.55605
$815$		0			0
$816$	−4.35132	−	7.53672i	−0.152327	−	0.263838i
$817$	18.3084	+	31.7110i	0.640529	+	1.10943i
$818$	−12.1427			−0.424559
$819$	15.0908	+	0.00704408i	0.527316	+	0.000246140i
$820$		0			0
$821$	−11.5513	−	20.0074i	−0.403142	−	0.698262i	0.590961	−	0.806700i	$-0.298749\pi$
$821$	−11.5513	−	20.0074i	−0.403142	−	0.698262i	−0.994103	+	0.108438i	$0.965415\pi$
$822$	−22.8539	−	39.5841i	−0.797122	−	1.38065i
$823$	−13.2905	+	23.0199i	−0.463279	+	0.802423i	−0.999122	−	0.0418949i	$-0.986661\pi$
$823$	−13.2905	+	23.0199i	−0.463279	+	0.802423i	0.535843	+	0.844318i	$0.319994\pi$
$824$	−93.0425			−3.24129
$825$		0			0
$826$	27.3931	−	47.4463i	0.953130	−	1.65087i
$827$	25.7927			0.896899			0.448450	−	0.893808i	$-0.351976\pi$
$827$	25.7927			0.896899			0.448450	+	0.893808i	$0.351976\pi$
$828$	−4.74612	+	8.22053i	−0.164939	+	0.285683i
$829$	−8.11655	−	14.0583i	−0.281899	−	0.488264i	0.689953	−	0.723854i	$-0.257631\pi$
$829$	−8.11655	−	14.0583i	−0.281899	−	0.488264i	−0.971853	+	0.235590i	$0.924298\pi$
$830$		0			0
$831$	−3.35745			−0.116469
$832$	−13.8687	+	23.9955i	−0.480812	+	0.831894i
$833$	22.0317			0.763355
$834$	−11.9792	−	20.7485i	−0.414805	−	0.718464i
$835$		0			0
$836$	45.3235	−	78.5026i	1.56755	−	2.71507i
$837$	6.72862			0.232575
$838$	−15.9183	+	27.5713i	−0.549888	+	0.952434i
$839$	3.01057	−	5.21447i	0.103937	−	0.180023i	−0.809367	−	0.587304i	$-0.800189\pi$
$839$	3.01057	−	5.21447i	0.103937	−	0.180023i	0.913303	+	0.407280i	$0.133523\pi$
$840$		0			0
$841$	−11.1643	+	19.3371i	−0.384975	+	0.666796i
$842$	−31.0894	−	53.8485i	−1.07141	−	1.85574i
$843$	−0.867323	−	1.50225i	−0.0298722	−	0.0517401i
$844$	−44.8894			−1.54516
$845$		0			0
$846$	−17.1636			−0.590096
$847$	37.9212	+	65.6815i	1.30299	+	2.25684i
$848$	12.1589	+	21.0598i	0.417537	+	0.723195i
$849$	0.454383	−	0.787014i	0.0155944	−	0.0270103i
$850$		0			0
$851$	9.02984	−	15.6401i	0.309539	−	0.536137i
$852$	−2.81061	+	4.86811i	−0.0962898	+	0.166779i
$853$	44.4656			1.52247			0.761236	−	0.648474i	$-0.224593\pi$
$853$	44.4656			1.52247			0.761236	+	0.648474i	$0.224593\pi$
$854$	−24.1391	+	41.8101i	−0.826023	+	1.43071i
$855$		0			0
$856$	−2.47390	−	4.28492i	−0.0845561	−	0.146455i
$857$	−17.2845			−0.590428			−0.295214	−	0.955431i	$-0.595391\pi$
$857$	−17.2845			−0.590428			−0.295214	+	0.955431i	$0.595391\pi$
$858$	−23.8998	+	41.3511i	−0.815927	+	1.41170i
$859$	−10.8850			−0.371391			−0.185696	−	0.982607i	$-0.559454\pi$
$859$	−10.8850			−0.371391			−0.185696	+	0.982607i	$0.559454\pi$
$860$		0			0
$861$	4.38360	+	7.59261i	0.149393	+	0.258756i
$862$	26.7853	−	46.3936i	0.912312	−	1.58017i
$863$	−33.7945			−1.15038			−0.575189	−	0.818021i	$-0.695071\pi$
$863$	−33.7945			−1.15038			−0.575189	+	0.818021i	$0.695071\pi$
$864$	0.126792	−	0.219610i	0.00431354	−	0.00747128i
$865$		0			0
$866$	−40.2673			−1.36834
$867$	6.30614	−	10.9226i	0.214168	−	0.370949i
$868$	56.6858	+	98.1827i	1.92404	+	3.33254i
$869$	−7.83773	−	13.5753i	−0.265877	−	0.460512i
$870$		0			0
$871$	47.6685	+	0.0222507i	1.61519	+	0.000753935i
$872$	−71.5421			−2.42272
$873$	−2.07351	−	3.59143i	−0.0701778	−	0.121552i
$874$	−12.0759	−	20.9161i	−0.408474	−	0.707498i
$875$		0			0
$876$	4.53283			0.153150
$877$	13.8321	−	23.9580i	0.467078	−	0.809003i	−0.532214	−	0.846610i	$-0.678640\pi$
$877$	13.8321	−	23.9580i	0.467078	−	0.809003i	0.999293	+	0.0376065i	$0.0119733\pi$
$878$	−20.4466	+	35.4145i	−0.690038	+	1.19518i
$879$	13.4164			0.452523
$880$		0			0
$881$	10.6504	+	18.4470i	0.358820	+	0.621495i	0.987764	−	0.155956i	$-0.0498458\pi$
$881$	10.6504	+	18.4470i	0.358820	+	0.621495i	−0.628944	+	0.777451i	$0.716512\pi$
$882$	12.9093	+	22.3595i	0.434678	+	0.752884i
$883$	−13.7397			−0.462379			−0.231190	−	0.972909i	$-0.574262\pi$
$883$	−13.7397			−0.462379			−0.231190	+	0.972909i	$0.574262\pi$
$884$	−30.4038	−	0.0141919i	−1.02259	−	0.000477324i
$885$		0			0
$886$	13.0893	+	22.6714i	0.439744	+	0.761659i
$887$	12.2511	+	21.2196i	0.411353	+	0.712483i	0.995038	−	0.0994964i	$-0.0317232\pi$
$887$	12.2511	+	21.2196i	0.411353	+	0.712483i	−0.583685	+	0.811980i	$0.698390\pi$
$888$	−19.0422	+	32.9821i	−0.639015	+	1.10681i
$889$	−86.7765			−2.91039
$890$		0			0
$891$	−2.69817	+	4.67337i	−0.0903922	+	0.156564i
$892$	−35.9390			−1.20333
$893$	14.5879	−	25.2669i	0.488164	−	0.845525i
$894$	3.36614	+	5.83033i	0.112581	+	0.194995i
$895$		0			0
$896$	−81.0974			−2.70927
$897$	4.24739	+	7.36463i	0.141816	+	0.245898i
$898$	−37.4854			−1.25091
$899$	−24.1032	−	41.7480i	−0.803888	−	1.39237i
$900$		0			0
$901$	6.13028	−	10.6180i	0.204229	−	0.353735i
$902$	−27.7474			−0.923886
$903$	18.3643	−	31.8079i	0.611126	−	1.05850i
$904$	−16.9730	+	29.3981i	−0.564513	+	0.977765i
$905$		0			0
$906$	−7.13621	+	12.3603i	−0.237085	+	0.410643i
$907$	−16.1004	−	27.8868i	−0.534606	−	0.925965i	−0.999182	−	0.0404320i	$-0.987127\pi$
$907$	−16.1004	−	27.8868i	−0.534606	−	0.925965i	0.464576	−	0.885533i	$-0.346207\pi$
$908$	−52.2377	−	90.4783i	−1.73357	−	3.00263i
$909$	−15.2595			−0.506125
$910$		0			0
$911$	5.94165			0.196856			0.0984279	−	0.995144i	$-0.468619\pi$
$911$	5.94165			0.196856			0.0984279	+	0.995144i	$0.468619\pi$
$912$	8.66799	+	15.0134i	0.287026	+	0.497143i
$913$	6.17543	+	10.6962i	0.204377	+	0.353991i
$914$	29.4342	−	50.9815i	0.973595	−	1.68632i
$915$		0			0
$916$	−8.80281	+	15.2469i	−0.290853	+	0.503772i
$917$	−23.2985	+	40.3541i	−0.769383	+	1.33261i
$918$	−5.14188			−0.169707
$919$	18.1234	−	31.3906i	0.597835	−	1.03548i	−0.395305	−	0.918550i	$-0.629361\pi$
$919$	18.1234	−	31.3906i	0.597835	−	1.03548i	0.993140	−	0.116931i	$-0.0373057\pi$
$920$		0			0
$921$	9.71041	+	16.8189i	0.319969	+	0.554203i
$922$	−8.34222			−0.274736
$923$	2.51526	+	4.36126i	0.0827909	+	0.143553i
$924$	−90.9239			−2.99118
$925$		0			0
$926$	30.9559	+	53.6173i	1.01728	+	1.76197i
$927$	−9.35582	+	16.2048i	−0.307286	+	0.532234i
$928$	−1.81677			−0.0596385
$929$	10.2148	−	17.6926i	0.335138	−	0.580476i	−0.648373	−	0.761323i	$-0.724550\pi$
$929$	10.2148	−	17.6926i	0.335138	−	0.580476i	0.983511	+	0.180846i	$0.0578837\pi$
$930$		0			0
$931$	−43.8880			−1.43837
$932$	−44.5585	+	77.1776i	−1.45956	+	2.52804i
$933$	−10.1990	−	17.6652i	−0.333900	−	0.578332i
$934$	−18.2413	−	31.5949i	−0.596874	−	1.03382i
$935$		0			0
$936$	−8.95694	−	15.5306i	−0.292767	−	0.507634i
$937$	5.03650			0.164535			0.0822676	−	0.996610i	$-0.473784\pi$
$937$	5.03650			0.164535			0.0822676	+	0.996610i	$0.473784\pi$
$938$	67.9162	+	117.634i	2.21754	+	3.84090i
$939$	6.68368	+	11.5765i	0.218114	+	0.377784i
$940$		0			0
$941$	16.7621			0.546429			0.273215	−	0.961953i	$-0.411913\pi$
$941$	16.7621			0.546429			0.273215	+	0.961953i	$0.411913\pi$
$942$	−6.43822	+	11.1513i	−0.209768	+	0.363330i
$943$	−2.46957	+	4.27742i	−0.0804203	+	0.139292i
$944$	−22.1544			−0.721065
$945$		0			0
$946$	58.1213	+	100.669i	1.88969	+	3.27303i
$947$	−19.0207	−	32.9448i	−0.618089	−	1.07056i	−0.989834	−	0.142227i	$-0.954574\pi$
$947$	−19.0207	−	32.9448i	−0.618089	−	1.07056i	0.371745	−	0.928335i	$-0.378760\pi$
$948$	11.6939			0.379799
$949$	2.03154	−	3.51493i	0.0659465	−	0.114100i
$950$		0			0
$951$	−15.8706	−	27.4887i	−0.514640	−	0.891383i
$952$	−21.7972	−	37.7538i	−0.706450	−	1.22361i
$953$	17.6171	−	30.5137i	0.570674	−	0.988437i	−0.425823	−	0.904807i	$-0.640015\pi$
$953$	17.6171	−	30.5137i	0.570674	−	0.988437i	0.996497	−	0.0836302i	$-0.0266514\pi$
$954$	14.3679			0.465178
$955$		0			0
$956$	−16.4040	+	28.4126i	−0.530544	+	0.918929i
$957$	38.6615			1.24975
$958$	−47.1137	+	81.6033i	−1.52217	+	2.63648i
$959$	−38.9672	−	67.4932i	−1.25832	−	2.17947i
$960$		0			0
$961$	14.2743			0.460462
$962$	33.8666	+	58.7219i	1.09190	+	1.89327i
$963$	−0.995045			−0.0320649
$964$	3.49749	+	6.05782i	0.112646	+	0.195109i
$965$		0			0
$966$	−12.1128	+	20.9800i	−0.389724	+	0.675021i
$967$	12.5190			0.402585			0.201292	−	0.979531i	$-0.435486\pi$
$967$	12.5190			0.402585			0.201292	+	0.979531i	$0.435486\pi$
$968$	45.0516	−	78.0317i	1.44801	−	2.50803i
$969$	4.37024	−	7.56948i	0.140392	−	0.243167i
$970$		0			0
$971$	16.3558	−	28.3291i	0.524883	−	0.909124i	−0.474697	−	0.880149i	$-0.657442\pi$
$971$	16.3558	−	28.3291i	0.524883	−	0.909124i	0.999580	−	0.0289746i	$-0.00922420\pi$
$972$	−2.01283	−	3.48633i	−0.0645616	−	0.111824i
$973$	−20.4252	−	35.3775i	−0.654801	−	1.13415i
$974$	−52.7178			−1.68919
$975$		0			0
$976$	19.5227			0.624906
$977$	−4.80950	−	8.33031i	−0.153870	−	0.266510i	0.778777	−	0.627301i	$-0.215840\pi$
$977$	−4.80950	−	8.33031i	−0.153870	−	0.266510i	−0.932647	+	0.360791i	$0.882507\pi$
$978$	6.59587	+	11.4244i	0.210913	+	0.365312i
$979$	−37.7034	+	65.3042i	−1.20501	+	2.08713i
$980$		0			0
$981$	−7.19386	+	12.4601i	−0.229682	+	0.397822i
$982$	16.4544	−	28.4999i	0.525082	−	0.909468i
$983$	37.0370			1.18130			0.590649	−	0.806929i	$-0.298872\pi$
$983$	37.0370			1.18130			0.590649	+	0.806929i	$0.298872\pi$
$984$	5.20785	−	9.02027i	0.166020	−	0.287556i
$985$		0			0
$986$	18.4192	+	31.9030i	0.586588	+	1.01600i
$987$	−29.2649			−0.931511
$988$	60.5655	+	0.0282707i	1.92684	+	0.000899411i
$989$	20.6917			0.657956
$990$		0			0
$991$	24.0884	+	41.7224i	0.765195	+	1.32536i	0.940144	+	0.340778i	$0.110691\pi$
$991$	24.0884	+	41.7224i	0.765195	+	1.32536i	−0.174949	+	0.984577i	$0.555976\pi$
$992$	0.853134	−	1.47767i	0.0270870	−	0.0469161i
$993$	28.8490			0.915496
$994$	−7.17309	+	12.4242i	−0.227517	+	0.394070i
$995$		0			0
$996$	−9.21371			−0.291948
$997$	−18.9666	+	32.8511i	−0.600677	+	1.04040i	0.392041	+	0.919948i	$0.371769\pi$
$997$	−18.9666	+	32.8511i	−0.600677	+	1.04040i	−0.992719	+	0.120456i	$0.961564\pi$
$998$	1.31079	+	2.27035i	0.0414922	+	0.0718666i
$999$	3.82956	+	6.63298i	0.121162	+	0.209858i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	975.2.i.n.601.6	yes	12
5.2	odd	4		975.2.bb.l.874.2		24
5.3	odd	4		975.2.bb.l.874.11		24
5.4	even	2		975.2.i.p.601.1	yes	12
13.9	even	3	inner	975.2.i.n.451.6	✓	12
65.9	even	6		975.2.i.p.451.1	yes	12
65.22	odd	12		975.2.bb.l.724.11		24
65.48	odd	12		975.2.bb.l.724.2		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
975.2.i.n.451.6	✓	12	13.9	even	3	inner
975.2.i.n.601.6	yes	12	1.1	even	1	trivial
975.2.i.p.451.1	yes	12	65.9	even	6
975.2.i.p.601.1	yes	12	5.4	even	2
975.2.bb.l.724.2		24	65.48	odd	12
975.2.bb.l.724.11		24	65.22	odd	12
975.2.bb.l.874.2		24	5.2	odd	4
975.2.bb.l.874.11		24	5.3	odd	4

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Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	975.2.i.n.601.6

Level	$975$
Weight	$2$
Character	975.601
Analytic conductor	$7.785$
Analytic rank	$0$
Dimension	$12$
Inner twists	$2$