LMFDB - Embedded newform 275.3.x.e.51.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [275,3,Mod(51,275)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(275, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 7])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("275.51"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 275 = 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	275.x (of order $10$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,5,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$7.49320726991$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 11)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			51.1
Root			$-0.309017 - 0.951057i$ of defining polynomial
Character	$\chi$	$=$	275.51
Dual form			275.3.x.e.151.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.80902 - 2.48990i) q^{2} +(-1.11803 + 3.44095i) q^{3} +(-1.69098 - 5.20431i) q^{4} +(6.54508 + 9.00854i) q^{6} +(0.854102 - 0.277515i) q^{7} +(-4.30902 - 1.40008i) q^{8} +(-3.30902 - 2.40414i) q^{9} +(10.8713 + 1.67760i) q^{11} +19.7984 q^{12} +(5.00000 - 6.88191i) q^{13} +(0.854102 - 2.62866i) q^{14} +(6.42705 - 4.66953i) q^{16} +(14.5344 + 20.0049i) q^{17} +(-11.9721 + 3.88998i) q^{18} +(11.2812 + 3.66547i) q^{19} +3.24920i q^{21} +(23.8435 - 24.0337i) q^{22} +7.23607 q^{23} +(9.63525 - 13.2618i) q^{24} +(-8.09017 - 24.8990i) q^{26} +(-14.3713 + 10.4414i) q^{27} +(-2.88854 - 3.97574i) q^{28} +(-3.29180 + 1.06957i) q^{29} +(-26.7984 - 19.4702i) q^{31} -42.5730i q^{32} +(-17.9271 + 35.5321i) q^{33} +76.1033 q^{34} +(-6.91641 + 21.2865i) q^{36} +(-12.4377 - 38.2793i) q^{37} +(29.5344 - 21.4580i) q^{38} +(18.0902 + 24.8990i) q^{39} +(1.24265 + 0.403760i) q^{41} +(8.09017 + 5.87785i) q^{42} +33.0625i q^{43} +(-9.65248 - 59.4145i) q^{44} +(13.0902 - 18.0171i) q^{46} +(-7.03444 + 21.6498i) q^{47} +(8.88197 + 27.3359i) q^{48} +(-38.9894 + 28.3274i) q^{49} +(-85.0861 + 27.6462i) q^{51} +(-44.2705 - 14.3844i) q^{52} +(-63.5410 - 46.1653i) q^{53} +54.6718i q^{54} -4.06888 q^{56} +(-25.2254 + 34.7198i) q^{57} +(-3.29180 + 10.1311i) q^{58} +(9.66312 + 29.7400i) q^{59} +(-16.5066 - 22.7194i) q^{61} +(-96.9574 + 31.5034i) q^{62} +(-3.49342 - 1.13508i) q^{63} +(-80.2943 - 58.3372i) q^{64} +(56.0410 + 108.915i) q^{66} +76.5066 q^{67} +(79.5344 - 109.470i) q^{68} +(-8.09017 + 24.8990i) q^{69} +(50.4164 - 36.6297i) q^{71} +(10.8926 + 14.9924i) q^{72} +(-89.5344 + 29.0915i) q^{73} +(-117.812 - 38.2793i) q^{74} -64.9089i q^{76} +(9.75078 - 1.58411i) q^{77} +94.7214 q^{78} +(38.7426 - 53.3247i) q^{79} +(-31.2361 - 96.1347i) q^{81} +(3.25329 - 2.36365i) q^{82} +(-33.3303 - 45.8752i) q^{83} +(16.9098 - 5.49434i) q^{84} +(82.3222 + 59.8106i) q^{86} -12.5227i q^{87} +(-44.4959 - 22.4496i) q^{88} -62.2968 q^{89} +(2.36068 - 7.26543i) q^{91} +(-12.2361 - 37.6587i) q^{92} +(96.9574 - 70.4437i) q^{93} +(41.1803 + 56.6799i) q^{94} +(146.492 + 47.5981i) q^{96} +(58.5795 + 42.5605i) q^{97} +148.324i q^{98} +(-31.9402 - 31.6874i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 5 q^{2} - 9 q^{4} + 15 q^{6} - 10 q^{7} - 15 q^{8} - 11 q^{9} + q^{11} + 30 q^{12} + 20 q^{13} - 10 q^{14} + 19 q^{16} - 30 q^{18} + 25 q^{19} + 35 q^{22} + 20 q^{23} + 5 q^{24} - 10 q^{26} - 15 q^{27}+ \cdots + 31 q^{99}+O(q^{100}) $ 4 * q + 5 * q^2 - 9 * q^4 + 15 * q^6 - 10 * q^7 - 15 * q^8 - 11 * q^9 + q^11 + 30 * q^12 + 20 * q^13 - 10 * q^14 + 19 * q^16 - 30 * q^18 + 25 * q^19 + 35 * q^22 + 20 * q^23 + 5 * q^24 - 10 * q^26 - 15 * q^27 + 60 * q^28 - 40 * q^29 - 58 * q^31 - 65 * q^33 + 130 * q^34 + 26 * q^36 - 90 * q^37 + 60 * q^38 + 50 * q^39 - 80 * q^41 + 10 * q^42 + 24 * q^44 + 30 * q^46 + 30 * q^47 + 40 * q^48 - 109 * q^49 - 195 * q^51 - 110 * q^52 - 120 * q^53 + 100 * q^56 - 45 * q^57 - 40 * q^58 + 23 * q^59 + 10 * q^61 - 200 * q^62 - 90 * q^63 - 149 * q^64 + 90 * q^66 + 230 * q^67 + 260 * q^68 - 10 * q^69 + 148 * q^71 + 95 * q^72 - 300 * q^73 - 270 * q^74 + 200 * q^77 + 200 * q^78 + 70 * q^79 - 116 * q^81 - 25 * q^82 - 225 * q^83 + 90 * q^84 + 175 * q^86 - 55 * q^88 + 122 * q^89 - 80 * q^91 - 40 * q^92 + 200 * q^93 + 120 * q^94 + 340 * q^96 + 165 * q^97 + 31 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/275\mathbb{Z}\right)^\times$.

$n$	$101$	$177$
$\chi(n)$	$e\left(\frac{7}{10}\right)$	$1$

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 $

$2$	1.80902	−	2.48990i	0.904508	−	1.24495i	−0.0644990	−	0.997918i	$-0.520545\pi$
$2$	1.80902	−	2.48990i	0.904508	−	1.24495i	0.969007	−	0.247031i	$-0.0794551\pi$
$3$	−1.11803	+	3.44095i	−0.372678	+	1.14698i	0.572354	+	0.820007i	$0.306030\pi$
$3$	−1.11803	+	3.44095i	−0.372678	+	1.14698i	−0.945032	+	0.326978i	$0.893970\pi$
$4$	−1.69098	−	5.20431i	−0.422746	−	1.30108i
$5$		0			0
$5$		0			0
$6$	6.54508	+	9.00854i	1.09085	+	1.50142i
$7$	0.854102	−	0.277515i	0.122015	−	0.0396449i	−0.247373	−	0.968920i	$-0.579567\pi$
$7$	0.854102	−	0.277515i	0.122015	−	0.0396449i	0.369388	+	0.929275i	$0.379567\pi$
$8$	−4.30902	−	1.40008i	−0.538627	−	0.175011i
$9$	−3.30902	−	2.40414i	−0.367669	−	0.267127i
$10$		0			0
$11$	10.8713	+	1.67760i	0.988302	+	0.152509i
$11$	10.8713	+	1.67760i	0.988302	+	0.152509i
$12$	19.7984			1.64986
$13$	5.00000	−	6.88191i	0.384615	−	0.529378i	−0.572185	−	0.820125i	$-0.693904\pi$
$13$	5.00000	−	6.88191i	0.384615	−	0.529378i	0.956800	+	0.290747i	$0.0939039\pi$
$14$	0.854102	−	2.62866i	0.0610073	−	0.187761i
$15$		0			0
$16$	6.42705	−	4.66953i	0.401691	−	0.291845i
$17$	14.5344	+	20.0049i	0.854967	+	1.17676i	0.982746	+	0.184959i	$0.0592151\pi$
$17$	14.5344	+	20.0049i	0.854967	+	1.17676i	−0.127779	+	0.991803i	$0.540785\pi$
$18$	−11.9721	+	3.88998i	−0.665119	+	0.216110i
$19$	11.2812	+	3.66547i	0.593745	+	0.192919i	0.590449	−	0.807075i	$-0.298951\pi$
$19$	11.2812	+	3.66547i	0.593745	+	0.192919i	0.00329617	+	0.999995i	$0.498951\pi$
$20$		0			0
$21$			3.24920i			0.154724i
$22$	23.8435	−	24.0337i	1.08379	−	1.09244i
$23$	7.23607			0.314612			0.157306	−	0.987550i	$-0.449719\pi$
$23$	7.23607			0.314612			0.157306	+	0.987550i	$0.449719\pi$
$24$	9.63525	−	13.2618i	0.401469	−	0.552575i
$25$		0			0
$26$	−8.09017	−	24.8990i	−0.311160	−	0.957653i
$27$	−14.3713	+	10.4414i	−0.532271	+	0.386718i
$28$	−2.88854	−	3.97574i	−0.103162	−	0.141991i
$29$	−3.29180	+	1.06957i	−0.113510	+	0.0368817i	−0.365221	−	0.930921i	$-0.619007\pi$
$29$	−3.29180	+	1.06957i	−0.113510	+	0.0368817i	0.251711	+	0.967802i	$0.419007\pi$
$30$		0			0
$31$	−26.7984	−	19.4702i	−0.864464	−	0.628070i	0.0646320	−	0.997909i	$-0.479413\pi$
$31$	−26.7984	−	19.4702i	−0.864464	−	0.628070i	−0.929096	+	0.369840i	$0.879413\pi$
$32$		−	42.5730i		−	1.33041i
$33$	−17.9271	+	35.5321i	−0.543244	+	1.07673i
$34$	76.1033			2.23833
$35$		0			0
$36$	−6.91641	+	21.2865i	−0.192122	+	0.591292i
$37$	−12.4377	−	38.2793i	−0.336154	−	1.03458i	−0.966151	−	0.257978i	$-0.916944\pi$
$37$	−12.4377	−	38.2793i	−0.336154	−	1.03458i	0.629997	−	0.776598i	$-0.283056\pi$
$38$	29.5344	−	21.4580i	0.777222	−	0.564685i
$39$	18.0902	+	24.8990i	0.463851	+	0.638435i
$40$		0			0
$41$	1.24265	+	0.403760i	0.0303084	+	0.00984781i	0.324132	−	0.946012i	$-0.394928\pi$
$41$	1.24265	+	0.403760i	0.0303084	+	0.00984781i	−0.293824	+	0.955860i	$0.594928\pi$
$42$	8.09017	+	5.87785i	0.192623	+	0.139949i
$43$			33.0625i			0.768895i	0.923147	+	0.384447i	$0.125608\pi$
$43$			33.0625i			0.768895i	−0.923147	+	0.384447i	$0.874392\pi$
$44$	−9.65248	−	59.4145i	−0.219374	−	1.35033i
$45$		0			0
$46$	13.0902	−	18.0171i	0.284569	−	0.391676i
$47$	−7.03444	+	21.6498i	−0.149669	+	0.460634i	−0.997582	−	0.0695019i	$-0.977859\pi$
$47$	−7.03444	+	21.6498i	−0.149669	+	0.460634i	0.847913	+	0.530136i	$0.177859\pi$
$48$	8.88197	+	27.3359i	0.185041	+	0.569498i
$49$	−38.9894	+	28.3274i	−0.795701	+	0.578111i
$50$		0			0
$51$	−85.0861	+	27.6462i	−1.66835	+	0.542081i
$52$	−44.2705	−	14.3844i	−0.851356	−	0.276622i
$53$	−63.5410	−	46.1653i	−1.19889	−	0.871043i	−0.204712	−	0.978822i	$-0.565626\pi$
$53$	−63.5410	−	46.1653i	−1.19889	−	0.871043i	−0.994175	+	0.107780i	$0.965626\pi$
$54$			54.6718i			1.01244i
$55$		0			0
$56$	−4.06888			−0.0726586
$57$	−25.2254	+	34.7198i	−0.442551	+	0.609120i
$58$	−3.29180	+	10.1311i	−0.0567551	+	0.174674i
$59$	9.66312	+	29.7400i	0.163782	+	0.504068i	0.998944	−	0.0459347i	$-0.0146266\pi$
$59$	9.66312	+	29.7400i	0.163782	+	0.504068i	−0.835163	+	0.550003i	$0.814627\pi$
$60$		0			0
$61$	−16.5066	−	22.7194i	−0.270600	−	0.372448i	0.651992	−	0.758226i	$-0.273933\pi$
$61$	−16.5066	−	22.7194i	−0.270600	−	0.372448i	−0.922592	+	0.385777i	$0.873933\pi$
$62$	−96.9574	+	31.5034i	−1.56383	+	0.508119i
$63$	−3.49342	−	1.13508i	−0.0554511	−	0.0180172i
$64$	−80.2943	−	58.3372i	−1.25460	−	0.911519i
$65$		0			0
$66$	56.0410	+	108.915i	0.849106	+	1.65022i
$67$	76.5066			1.14189			0.570945	−	0.820989i	$-0.306577\pi$
$67$	76.5066			1.14189			0.570945	+	0.820989i	$0.306577\pi$
$68$	79.5344	−	109.470i	1.16962	−	1.60985i
$69$	−8.09017	+	24.8990i	−0.117249	+	0.360855i
$70$		0			0
$71$	50.4164	−	36.6297i	0.710090	−	0.515911i	−0.173113	−	0.984902i	$-0.555382\pi$
$71$	50.4164	−	36.6297i	0.710090	−	0.515911i	0.883203	+	0.468991i	$0.155382\pi$
$72$	10.8926	+	14.9924i	0.151286	+	0.208228i
$73$	−89.5344	+	29.0915i	−1.22650	+	0.398514i	−0.849445	−	0.527677i	$-0.823063\pi$
$73$	−89.5344	+	29.0915i	−1.22650	+	0.398514i	−0.377054	+	0.926191i	$0.623063\pi$
$74$	−117.812	−	38.2793i	−1.59205	−	0.517288i
$75$		0			0
$76$		−	64.9089i		−	0.854064i
$77$	9.75078	−	1.58411i	0.126633	−	0.0205729i
$78$	94.7214			1.21438
$79$	38.7426	−	53.3247i	0.490413	−	0.674996i	−0.490051	−	0.871694i	$-0.663022\pi$
$79$	38.7426	−	53.3247i	0.490413	−	0.674996i	0.980464	+	0.196698i	$0.0630218\pi$
$80$		0			0
$81$	−31.2361	−	96.1347i	−0.385630	−	1.18685i
$82$	3.25329	−	2.36365i	0.0396743	−	0.0288250i
$83$	−33.3303	−	45.8752i	−0.401570	−	0.552714i	0.559567	−	0.828785i	$-0.310967\pi$
$83$	−33.3303	−	45.8752i	−0.401570	−	0.552714i	−0.961137	+	0.276071i	$0.910967\pi$
$84$	16.9098	−	5.49434i	0.201308	−	0.0654088i
$85$		0			0
$86$	82.3222	+	59.8106i	0.957235	+	0.695472i
$87$		−	12.5227i		−	0.143939i
$88$	−44.4959	−	22.4496i	−0.505636	−	0.255109i
$89$	−62.2968			−0.699964			−0.349982	−	0.936756i	$-0.613812\pi$
$89$	−62.2968			−0.699964			−0.349982	+	0.936756i	$0.613812\pi$
$90$		0			0
$91$	2.36068	−	7.26543i	0.0259415	−	0.0798398i
$92$	−12.2361	−	37.6587i	−0.133001	−	0.409334i
$93$	96.9574	−	70.4437i	1.04255	−	0.757459i
$94$	41.1803	+	56.6799i	0.438089	+	0.602977i
$95$		0			0
$96$	146.492	+	47.5981i	1.52596	+	0.495813i
$97$	58.5795	+	42.5605i	0.603913	+	0.438768i	0.847266	−	0.531170i	$-0.178247\pi$
$97$	58.5795	+	42.5605i	0.603913	+	0.438768i	−0.243353	+	0.969938i	$0.578247\pi$
$98$			148.324i			1.51351i
$99$	−31.9402	−	31.6874i	−0.322628	−	0.320075i
$100$		0			0
$101$	−37.8409	+	52.0836i	−0.374663	+	0.515679i	−0.954161	−	0.299295i	$-0.903249\pi$
$101$	−37.8409	+	52.0836i	−0.374663	+	0.515679i	0.579498	+	0.814974i	$0.303249\pi$
$102$	−85.0861	+	261.868i	−0.834177	+	2.56733i
$103$	10.0770	+	31.0139i	0.0978351	+	0.301105i	0.987982	−	0.154568i	$-0.0493985\pi$
$103$	10.0770	+	31.0139i	0.0978351	+	0.301105i	−0.890147	+	0.455673i	$0.849399\pi$
$104$	−31.1803	+	22.6538i	−0.299811	+	0.217825i
$105$		0			0
$106$	−229.894	+	74.6969i	−2.16881	+	0.704688i
$107$	5.13932	+	1.66987i	0.0480310	+	0.0156062i	0.332934	−	0.942950i	$-0.391961\pi$
$107$	5.13932	+	1.66987i	0.0480310	+	0.0156062i	−0.284903	+	0.958556i	$0.591961\pi$
$108$	78.6418	+	57.1366i	0.728165	+	0.529043i
$109$			137.002i			1.25690i	0.777850	+	0.628450i	$0.216310\pi$
$109$			137.002i			1.25690i	−0.777850	+	0.628450i	$0.783690\pi$
$110$		0			0
$111$	145.623			1.31192
$112$	4.19350	−	5.77185i	0.0374419	−	0.0515344i
$113$	14.3713	−	44.2304i	0.127180	−	0.391419i	−0.867112	−	0.498113i	$-0.834026\pi$
$113$	14.3713	−	44.2304i	0.127180	−	0.391419i	0.994292	+	0.106694i	$0.0340264\pi$
$114$	40.8156	+	125.617i	0.358032	+	1.10191i
$115$		0			0
$116$	11.1327	+	15.3229i	0.0959719	+	0.132094i
$117$	−33.0902	+	10.7516i	−0.282822	+	0.0918944i
$118$	91.5304	+	29.7400i	0.775681	+	0.252034i
$119$	17.9656	+	13.0527i	0.150971	+	0.109687i
$120$		0			0
$121$	115.371	+	36.4754i	0.953482	+	0.301450i
$122$	−86.4296			−0.708439
$123$	−2.77864	+	3.82447i	−0.0225906	+	0.0310933i
$124$	−56.0132	+	172.391i	−0.451719	+	1.39025i
$125$		0			0
$126$	−9.14590	+	6.64488i	−0.0725865	+	0.0527372i
$127$	−49.0395	−	67.4970i	−0.386138	−	0.531473i	0.571060	−	0.820908i	$-0.306532\pi$
$127$	−49.0395	−	67.4970i	−0.386138	−	0.531473i	−0.957197	+	0.289436i	$0.906532\pi$
$128$	−128.550	+	41.7685i	−1.00430	+	0.326316i
$129$	−113.766	−	36.9650i	−0.881910	−	0.286550i
$130$		0			0
$131$		−	85.0901i		−	0.649543i	−0.945793	−	0.324771i	$-0.894713\pi$
$131$		−	85.0901i		−	0.649543i	0.945793	−	0.324771i	$-0.105287\pi$
$132$	215.235	+	33.2137i	1.63056	+	0.251619i
$133$	10.6525			0.0800938
$134$	138.402	−	190.494i	1.03285	−	1.42159i
$135$		0			0
$136$	−34.6205	−	106.551i	−0.254563	−	0.783464i
$137$	47.5238	−	34.5281i	0.346889	−	0.252030i	−0.400674	−	0.916221i	$-0.631224\pi$
$137$	47.5238	−	34.5281i	0.346889	−	0.252030i	0.747563	+	0.664191i	$0.231224\pi$
$138$	47.3607	+	65.1864i	0.343193	+	0.472365i
$139$	153.108	−	49.7479i	1.10150	−	0.357899i	0.298820	−	0.954310i	$-0.403407\pi$
$139$	153.108	−	49.7479i	1.10150	−	0.357899i	0.802679	+	0.596411i	$0.203407\pi$
$140$		0			0
$141$	−66.6312	−	48.4104i	−0.472562	−	0.343336i
$142$		−	191.795i		−	1.35067i
$143$	65.9017	−	66.4275i	0.460851	−	0.464528i
$144$	−32.4934			−0.225649
$145$		0			0
$146$	−89.5344	+	275.559i	−0.613250	+	1.88739i
$147$	−53.8820	−	165.832i	−0.366544	−	1.12811i
$148$	−178.185	+	129.459i	−1.20396	+	0.874725i
$149$	−151.103	−	207.976i	−1.01412	−	1.39581i	−0.916248	−	0.400612i	$-0.868798\pi$
$149$	−151.103	−	207.976i	−1.01412	−	1.39581i	−0.0978685	−	0.995199i	$-0.531202\pi$
$150$		0			0
$151$	−274.087	−	89.0563i	−1.81515	−	0.589777i	−0.999944	−	0.0106004i	$-0.996626\pi$
$151$	−274.087	−	89.0563i	−1.81515	−	0.589777i	−0.815202	−	0.579176i	$-0.803374\pi$
$152$	−43.4787	−	31.5891i	−0.286044	−	0.207823i
$153$		−	101.140i		−	0.661043i
$154$	13.6950	−	27.1441i	0.0889289	−	0.176261i
$155$		0			0
$156$	98.9919	−	136.251i	0.634563	−	0.873401i
$157$	−85.4803	+	263.081i	−0.544460	+	1.67568i	0.177809	+	0.984065i	$0.443099\pi$
$157$	−85.4803	+	263.081i	−0.544460	+	1.67568i	−0.722270	+	0.691612i	$0.756901\pi$
$158$	−62.6869	−	192.930i	−0.396753	−	1.22108i
$159$	229.894	−	167.027i	1.44587	−	1.05049i
$160$		0			0
$161$	6.18034	−	2.00811i	0.0383872	−	0.0124728i
$162$	−295.872	−	96.1347i	−1.82637	−	0.593424i
$163$	−56.1180	−	40.7721i	−0.344282	−	0.250136i	0.402184	−	0.915559i	$-0.368251\pi$
$163$	−56.1180	−	40.7721i	−0.344282	−	0.250136i	−0.746466	+	0.665423i	$0.768251\pi$
$164$		−	7.14987i		−	0.0435967i
$165$		0			0
$166$	−174.520			−1.05132
$167$	169.864	−	233.798i	1.01715	−	1.39999i	0.102968	−	0.994685i	$-0.467166\pi$
$167$	169.864	−	233.798i	1.01715	−	1.39999i	0.914182	−	0.405303i	$-0.132834\pi$
$168$	4.54915	−	14.0008i	0.0270783	−	0.0833384i
$169$	29.8632	+	91.9095i	0.176705	+	0.543843i
$170$		0			0
$171$	−28.5172	−	39.2506i	−0.166767	−	0.229536i
$172$	172.067	−	55.9081i	1.00039	−	0.325047i
$173$	−174.241	−	56.6144i	−1.00717	−	0.327251i	−0.241445	−	0.970414i	$-0.577621\pi$
$173$	−174.241	−	56.6144i	−1.00717	−	0.327251i	−0.765729	+	0.643164i	$0.777621\pi$
$174$	−31.1803	−	22.6538i	−0.179197	−	0.130194i
$175$		0			0
$176$	77.7041	−	39.9819i	0.441501	−	0.227170i
$177$	−113.138			−0.639196
$178$	−112.696	+	155.113i	−0.633124	+	0.871420i
$179$	0.633702	−	1.95033i	0.00354024	−	0.0108957i	−0.949271	−	0.314460i	$-0.898177\pi$
$179$	0.633702	−	1.95033i	0.00354024	−	0.0108957i	0.952811	+	0.303564i	$0.0981766\pi$
$180$		0			0
$181$	58.9787	−	42.8505i	0.325849	−	0.236743i	−0.412818	−	0.910814i	$-0.635455\pi$
$181$	58.9787	−	42.8505i	0.325849	−	0.236743i	0.738667	+	0.674070i	$0.235455\pi$
$182$	−13.8197	−	19.0211i	−0.0759322	−	0.104512i
$183$	96.6312	−	31.3974i	0.528039	−	0.171570i
$184$	−31.1803	−	10.1311i	−0.169458	−	0.0550604i
$185$		0			0
$186$		−	368.848i		−	1.98305i
$187$	124.448	+	241.863i	0.665499	+	1.29339i
$188$	124.567			0.662592
$189$	−9.37694	+	12.9063i	−0.0496134	+	0.0682870i
$190$		0			0
$191$	−32.0770	−	98.7229i	−0.167942	−	0.516874i	0.831299	−	0.555826i	$-0.187598\pi$
$191$	−32.0770	−	98.7229i	−0.167942	−	0.516874i	−0.999241	+	0.0389523i	$0.987598\pi$
$192$	290.508	−	211.066i	1.51306	−	1.09930i
$193$	−202.207	−	278.314i	−1.04770	−	1.44204i	−0.890784	−	0.454428i	$-0.849844\pi$
$193$	−202.207	−	278.314i	−1.04770	−	1.44204i	−0.156919	−	0.987611i	$-0.550156\pi$
$194$	211.943	−	68.8644i	1.09249	−	0.354971i
$195$		0			0
$196$	213.355	+	155.012i	1.08855	+	0.790875i
$197$		−	99.0718i		−	0.502903i	−0.967870	−	0.251451i	$-0.919092\pi$
$197$		−	99.0718i		−	0.502903i	0.967870	−	0.251451i	$-0.0809078\pi$
$198$	−136.679	+	22.2048i	−0.690297	+	0.112146i
$199$	−153.469			−0.771201			−0.385601	−	0.922666i	$-0.626006\pi$
$199$	−153.469			−0.771201			−0.385601	+	0.922666i	$0.626006\pi$
$200$		0			0
$201$	−85.5370	+	263.256i	−0.425557	+	1.30973i
$202$	61.2279	+	188.440i	0.303109	+	0.932872i
$203$	−2.51471	+	1.82704i	−0.0123877	+	0.00900021i
$204$	287.758	+	396.065i	1.41058	+	1.94150i
$205$		0			0
$206$	95.4508	+	31.0139i	0.463354	+	0.150553i
$207$	−23.9443	−	17.3965i	−0.115673	−	0.0840412i
$208$		−	67.5780i		−	0.324894i
$209$	116.492	+	58.7737i	0.557377	+	0.281214i
$210$		0			0
$211$	−196.035	+	269.820i	−0.929078	+	1.27877i	0.0311405	+	0.999515i	$0.490086\pi$
$211$	−196.035	+	269.820i	−0.929078	+	1.27877i	−0.960218	+	0.279251i	$0.909914\pi$
$212$	−132.812	+	408.752i	−0.626469	+	1.92807i
$213$	69.6738	+	214.434i	0.327107	+	1.00673i
$214$	13.4549	−	9.77557i	0.0628734	−	0.0456802i
$215$		0			0
$216$	76.5451	−	24.8710i	0.354375	−	0.115144i
$217$	−28.2918	−	9.19256i	−0.130377	−	0.0423620i
$218$	341.122	+	247.839i	1.56478	+	1.13688i
$219$		−	340.609i		−	1.55529i
$220$		0			0
$221$	210.344			0.951785
$222$	263.435	−	362.587i	1.18664	−	1.63327i
$223$	−35.2198	+	108.395i	−0.157936	+	0.486078i	−0.998447	−	0.0557176i	$-0.982255\pi$
$223$	−35.2198	+	108.395i	−0.157936	+	0.486078i	0.840510	+	0.541796i	$0.182255\pi$
$224$	−11.8146	−	36.3617i	−0.0527439	−	0.162329i
$225$		0			0
$226$	−84.1312	−	115.797i	−0.372262	−	0.512375i
$227$	37.1058	−	12.0564i	0.163462	−	0.0531120i	−0.226143	−	0.974094i	$-0.572612\pi$
$227$	37.1058	−	12.0564i	0.163462	−	0.0531120i	0.389605	+	0.920982i	$0.372612\pi$
$228$	223.348	+	72.5703i	0.979599	+	0.318291i
$229$	−108.575	−	78.8847i	−0.474129	−	0.344475i	0.324919	−	0.945742i	$-0.394663\pi$
$229$	−108.575	−	78.8847i	−0.474129	−	0.344475i	−0.799048	+	0.601267i	$0.794663\pi$
$230$		0			0
$231$	−5.45085	+	35.3231i	−0.0235968	+	0.152914i
$232$	15.6819			0.0675944
$233$	−157.139	+	216.283i	−0.674415	+	0.928253i	−0.999850	−	0.0173116i	$-0.994489\pi$
$233$	−157.139	+	216.283i	−0.674415	+	0.928253i	0.325435	+	0.945564i	$0.394489\pi$
$234$	−33.0902	+	101.841i	−0.141411	+	0.435218i
$235$		0			0
$236$	138.436	−	100.580i	0.586594	−	0.426185i
$237$	140.172	+	192.930i	0.591444	+	0.814053i
$238$	65.0000	−	21.1198i	0.273109	−	0.0887386i
$239$	104.751	+	34.0356i	0.438288	+	0.142408i	0.519846	−	0.854260i	$-0.325990\pi$
$239$	104.751	+	34.0356i	0.438288	+	0.142408i	−0.0815577	+	0.996669i	$0.525990\pi$
$240$		0			0
$241$			191.103i			0.792960i	0.918043	+	0.396480i	$0.129768\pi$
$241$			191.103i			0.792960i	−0.918043	+	0.396480i	$0.870232\pi$
$242$	299.529	−	221.278i	1.23772	−	0.914373i
$243$	205.843			0.847090
$244$	−90.3262	+	124.323i	−0.370189	+	0.509522i
$245$		0			0
$246$	4.49593	+	13.8371i	0.0182762	+	0.0562482i
$247$	81.6312	−	59.3085i	0.330491	−	0.240116i
$248$	88.2148	+	121.417i	0.355705	+	0.489586i
$249$	195.119	−	63.3980i	0.783610	−	0.254610i
$250$		0			0
$251$	345.559	+	251.063i	1.37673	+	1.00025i	0.997177	+	0.0750826i	$0.0239221\pi$
$251$	345.559	+	251.063i	1.37673	+	1.00025i	0.379553	+	0.925170i	$0.376078\pi$
$252$			20.1003i			0.0797629i
$253$	78.6656	+	12.1392i	0.310931	+	0.0479811i
$254$	−256.774			−1.01092
$255$		0			0
$256$	−5.87132	+	18.0701i	−0.0229349	+	0.0705862i
$257$	−8.73917	−	26.8964i	−0.0340046	−	0.104655i	0.932614	−	0.360877i	$-0.117522\pi$
$257$	−8.73917	−	26.8964i	−0.0340046	−	0.104655i	−0.966618	+	0.256221i	$0.917522\pi$
$258$	−297.844	+	216.397i	−1.15444	+	0.838747i
$259$	−21.2461	−	29.2428i	−0.0820313	−	0.112906i
$260$		0			0
$261$	13.4640	+	4.37472i	0.0515862	+	0.0167614i
$262$	−211.866	−	153.929i	−0.808648	−	0.587517i
$263$			94.5506i			0.359508i	0.983712	+	0.179754i	$0.0575302\pi$
$263$			94.5506i			0.359508i	−0.983712	+	0.179754i	$0.942470\pi$
$264$	126.996	−	128.009i	0.481045	−	0.484883i
$265$		0			0
$266$	19.2705	−	26.5236i	0.0724455	−	0.0997127i
$267$	69.6500	−	214.361i	0.260861	−	0.802848i
$268$	−129.371	−	398.164i	−0.482729	−	1.48569i
$269$	−189.305	+	137.538i	−0.703736	+	0.511294i	−0.881147	−	0.472843i	$-0.843228\pi$
$269$	−189.305	+	137.538i	−0.703736	+	0.511294i	0.177411	+	0.984137i	$0.443228\pi$
$270$		0			0
$271$	136.400	−	44.3191i	0.503322	−	0.163539i	−0.0463413	−	0.998926i	$-0.514756\pi$
$271$	136.400	−	44.3191i	0.503322	−	0.163539i	0.549663	+	0.835387i	$0.314756\pi$
$272$	186.827	+	60.7038i	0.686865	+	0.223176i
$273$	22.3607	+	16.2460i	0.0819073	+	0.0595091i
$274$		−	180.791i		−	0.659822i
$275$		0			0
$276$	143.262			0.519067
$277$	−228.695	+	314.772i	−0.825614	+	1.13636i	0.163110	+	0.986608i	$0.447848\pi$
$277$	−228.695	+	314.772i	−0.825614	+	1.13636i	−0.988724	+	0.149752i	$0.952152\pi$
$278$	153.108	−	471.219i	0.550749	−	1.69503i
$279$	41.8673	+	128.854i	0.150062	+	0.461843i
$280$		0			0
$281$	−59.3860	−	81.7379i	−0.211338	−	0.290882i	0.690167	−	0.723650i	$-0.257537\pi$
$281$	−59.3860	−	81.7379i	−0.211338	−	0.290882i	−0.901505	+	0.432768i	$0.857537\pi$
$282$	−241.074	+	78.3297i	−0.854872	+	0.277765i
$283$	2.01626	+	0.655123i	0.00712460	+	0.00231492i	0.312577	−	0.949892i	$-0.398808\pi$
$283$	2.01626	+	0.655123i	0.00712460	+	0.00231492i	−0.305453	+	0.952207i	$0.598808\pi$
$284$	−275.885	−	200.443i	−0.971428	−	0.705783i
$285$		0			0
$286$	−46.1803	−	284.257i	−0.161470	−	0.993905i
$287$	1.17340			0.00408849
$288$	−102.352	+	140.875i	−0.355387	+	0.489149i
$289$	−99.6418	+	306.666i	−0.344781	+	1.06113i
$290$		0			0
$291$	−211.943	+	153.985i	−0.728325	+	0.529159i
$292$	302.802	+	416.772i	1.03699	+	1.42730i
$293$	447.100	−	145.272i	1.52594	−	0.495808i	0.578483	−	0.815694i	$-0.303645\pi$
$293$	447.100	−	145.272i	1.52594	−	0.495808i	0.947456	+	0.319886i	$0.103645\pi$
$294$	−510.377	−	165.832i	−1.73598	−	0.564053i
$295$		0			0
$296$			182.360i			0.616081i
$297$	−173.752	+	89.4023i	−0.585023	+	0.301018i
$298$	−791.187			−2.65499
$299$	36.1803	−	49.7980i	0.121004	−	0.166548i
$300$		0			0
$301$	9.17531	+	28.2387i	0.0304828	+	0.0938163i
$302$	−717.569	+	521.345i	−2.37606	+	1.72631i
$303$	−136.910	−	188.440i	−0.451848	−	0.621915i
$304$	89.6205	−	29.1195i	0.294804	−	0.0957878i
$305$		0			0
$306$	−251.827	−	182.963i	−0.822965	−	0.597919i
$307$			99.4185i			0.323839i	0.986804	+	0.161919i	$0.0517685\pi$
$307$			99.4185i			0.323839i	−0.986804	+	0.161919i	$0.948232\pi$
$308$	−24.7326	−	48.0674i	−0.0803006	−	0.156063i
$309$	−117.984			−0.381824
$310$		0			0
$311$	104.823	−	322.611i	0.337051	−	1.03734i	−0.628652	−	0.777686i	$-0.716393\pi$
$311$	104.823	−	322.611i	0.337051	−	1.03734i	0.965703	−	0.259649i	$-0.0836068\pi$
$312$	−43.0902	−	132.618i	−0.138110	−	0.425057i
$313$	312.595	−	227.114i	0.998707	−	0.725603i	0.0368962	−	0.999319i	$-0.488253\pi$
$313$	312.595	−	227.114i	0.998707	−	0.725603i	0.961810	+	0.273716i	$0.0882529\pi$
$314$	500.410	+	688.756i	1.59366	+	2.19349i
$315$		0			0
$316$	−343.031	−	111.458i	−1.08554	−	0.352714i
$317$	−204.740	−	148.752i	−0.645866	−	0.469249i	0.215994	−	0.976395i	$-0.430701\pi$
$317$	−204.740	−	148.752i	−0.645866	−	0.469249i	−0.861860	+	0.507145i	$0.830701\pi$
$318$		−	874.567i		−	2.75021i
$319$	−37.5805	+	6.10532i	−0.117807	+	0.0191389i
$320$		0			0
$321$	−11.4919	+	15.8172i	−0.0358002	+	0.0492748i
$322$	6.18034	−	19.0211i	0.0191936	−	0.0590718i
$323$	90.6378	+	278.954i	0.280612	+	0.863636i
$324$	−447.495	+	325.124i	−1.38116	+	1.00347i
$325$		0			0
$326$	−203.037	+	65.9707i	−0.622813	+	0.202364i
$327$	−471.418	−	153.173i	−1.44165	−	0.468419i
$328$	−4.78928	−	3.47962i	−0.0146015	−	0.0106086i
$329$			20.4433i			0.0621376i
$330$		0			0
$331$	372.116			1.12422			0.562109	−	0.827063i	$-0.309990\pi$
$331$	372.116			1.12422			0.562109	+	0.827063i	$0.309990\pi$
$332$	−182.388	+	251.035i	−0.549361	+	0.756131i
$333$	−50.8723	+	156.569i	−0.152770	+	0.470177i
$334$	−274.846	−	845.889i	−0.822892	−	2.53260i
$335$		0			0
$336$	15.1722	+	20.8828i	0.0451554	+	0.0621511i
$337$	78.1910	−	25.4058i	0.232021	−	0.0753881i	−0.190699	−	0.981649i	$-0.561075\pi$
$337$	78.1910	−	25.4058i	0.232021	−	0.0753881i	0.422720	+	0.906260i	$0.361075\pi$
$338$	282.868	+	91.9095i	0.836888	+	0.271921i
$339$	136.127	+	98.9021i	0.401555	+	0.291747i
$340$		0			0
$341$	−258.671	−	256.623i	−0.758565	−	0.752561i
$342$	−149.318			−0.436603
$343$	−51.3050	+	70.6152i	−0.149577	+	0.205875i
$344$	46.2902	−	142.467i	0.134565	−	0.414147i
$345$		0			0
$346$	−456.169	+	331.426i	−1.31841	+	0.957879i
$347$	134.861	+	185.620i	0.388647	+	0.534927i	0.957850	−	0.287270i	$-0.0927478\pi$
$347$	134.861	+	185.620i	0.388647	+	0.534927i	−0.569202	+	0.822198i	$0.692748\pi$
$348$	−65.1722	+	21.1757i	−0.187276	+	0.0608498i
$349$	220.997	+	71.8062i	0.633229	+	0.205749i	0.608005	−	0.793933i	$-0.291970\pi$
$349$	220.997	+	71.8062i	0.633229	+	0.205749i	0.0252240	+	0.999682i	$0.491970\pi$
$350$		0			0
$351$			151.109i			0.430510i
$352$	71.4205	−	462.825i	0.202899	−	1.31484i
$353$	−34.6443			−0.0981426			−0.0490713	−	0.998795i	$-0.515626\pi$
$353$	−34.6443			−0.0981426			−0.0490713	+	0.998795i	$0.515626\pi$
$354$	−204.668	+	281.702i	−0.578159	+	0.795767i
$355$		0			0
$356$	105.343	+	324.212i	0.295907	+	0.910708i
$357$	−65.0000	+	47.2253i	−0.182073	+	0.132284i
$358$	−3.70976	−	5.10604i	−0.0103624	−	0.0142627i
$359$	−429.681	+	139.612i	−1.19688	+	0.388891i	−0.838613	−	0.544728i	$-0.816633\pi$
$359$	−429.681	+	139.612i	−1.19688	+	0.388891i	−0.358269	+	0.933618i	$0.616633\pi$
$360$		0			0
$361$	−178.226	−	129.489i	−0.493702	−	0.358695i
$362$		−	224.368i		−	0.619802i
$363$	−254.499	+	356.207i	−0.701100	+	0.981286i
$364$	−41.8034			−0.114845
$365$		0			0
$366$	96.6312	−	297.400i	0.264020	−	0.812569i
$367$	−113.974	−	350.775i	−0.310555	−	0.955790i	−0.977546	−	0.210724i	$-0.932418\pi$
$367$	−113.974	−	350.775i	−0.310555	−	0.955790i	0.666991	−	0.745066i	$-0.267582\pi$
$368$	46.5066	−	33.7890i	0.126377	−	0.0918180i
$369$	−3.14124	−	4.32355i	−0.00851284	−	0.0117169i
$370$		0			0
$371$	−67.0820	−	21.7963i	−0.180814	−	0.0587501i
$372$	−530.564	−	385.477i	−1.42625	−	1.03623i
$373$			593.166i			1.59026i	0.606440	+	0.795129i	$0.292597\pi$
$373$			593.166i			1.59026i	−0.606440	+	0.795129i	$0.707403\pi$
$374$	827.344	+	127.671i	2.21215	+	0.341366i
$375$		0			0
$376$	60.6231	−	83.4405i	0.161232	−	0.221916i
$377$	−9.09830	+	28.0017i	−0.0241334	+	0.0742750i
$378$	15.1722	+	46.6953i	0.0401381	+	0.123532i
$379$	227.537	−	165.315i	0.600361	−	0.436188i	−0.245646	−	0.969360i	$-0.579000\pi$
$379$	227.537	−	165.315i	0.600361	−	0.436188i	0.846007	+	0.533172i	$0.179000\pi$
$380$		0			0
$381$	287.082	−	93.2786i	0.753496	−	0.244826i
$382$	−303.838	−	98.7229i	−0.795387	−	0.258437i
$383$	515.795	+	374.747i	1.34672	+	0.978452i	0.999168	+	0.0407931i	$0.0129885\pi$
$383$	515.795	+	374.747i	1.34672	+	0.978452i	0.347556	+	0.937659i	$0.387012\pi$
$384$		−	489.034i		−	1.27353i
$385$		0			0
$386$	−1058.77			−2.74292
$387$	79.4868	−	109.404i	0.205392	−	0.282698i
$388$	122.441	−	376.835i	0.315570	−	0.971225i
$389$	206.259	+	634.801i	0.530229	+	1.63188i	0.753737	+	0.657176i	$0.228249\pi$
$389$	206.259	+	634.801i	0.530229	+	1.63188i	−0.223507	+	0.974702i	$0.571751\pi$
$390$		0			0
$391$	105.172	+	144.757i	0.268983	+	0.370223i
$392$	207.667	−	67.4750i	0.529762	−	0.172130i
$393$	292.791	+	95.1336i	0.745016	+	0.242070i
$394$	−246.679	−	179.223i	−0.626088	−	0.454880i
$395$		0			0
$396$	−110.901	+	219.810i	−0.280052	+	0.555075i
$397$	5.37384			0.0135361			0.00676805	−	0.999977i	$-0.497846\pi$
$397$	5.37384			0.0135361			0.00676805	+	0.999977i	$0.497846\pi$
$398$	−277.628	+	382.122i	−0.697558	+	0.960106i
$399$	−11.9098	+	36.6547i	−0.0298492	+	0.0918664i
$400$		0			0
$401$	228.786	−	166.223i	0.570539	−	0.414521i	−0.264762	−	0.964314i	$-0.585293\pi$
$401$	228.786	−	166.223i	0.570539	−	0.414521i	0.835301	+	0.549793i	$0.185293\pi$
$402$	500.742	+	689.212i	1.24563	+	1.71446i
$403$	−267.984	+	87.0732i	−0.664972	+	0.216063i
$404$	335.048	+	108.864i	0.829326	+	0.269464i
$405$		0			0
$406$			9.56652i			0.0235629i
$407$	−70.9969	−	437.012i	−0.174440	−	1.07374i
$408$	405.344			0.993491
$409$	−18.2554	+	25.1265i	−0.0446343	+	0.0614339i	−0.830751	−	0.556644i	$-0.812089\pi$
$409$	−18.2554	+	25.1265i	−0.0446343	+	0.0614339i	0.786116	+	0.618078i	$0.212089\pi$
$410$		0			0
$411$	65.6763	+	202.131i	0.159796	+	0.491802i
$412$	144.366	−	104.888i	0.350402	−	0.254582i
$413$	16.5066	+	22.7194i	0.0399675	+	0.0550105i
$414$	−86.6312	+	28.1482i	−0.209254	+	0.0679908i
$415$		0			0
$416$	−292.984	−	212.865i	−0.704288	−	0.511695i
$417$			582.459i			1.39678i
$418$	357.076	−	183.730i	0.854250	−	0.439546i
$419$	−245.156			−0.585098			−0.292549	−	0.956251i	$-0.594503\pi$
$419$	−245.156			−0.585098			−0.292549	+	0.956251i	$0.594503\pi$
$420$		0			0
$421$	−23.9211	+	73.6215i	−0.0568196	+	0.174873i	−0.975439	−	0.220272i	$-0.929306\pi$
$421$	−23.9211	+	73.6215i	−0.0568196	+	0.174873i	0.918619	+	0.395145i	$0.129306\pi$
$422$	317.192	+	976.216i	0.751640	+	2.31331i
$423$	75.3262	−	54.7277i	0.178076	−	0.129380i
$424$	209.164	+	287.890i	0.493312	+	0.678985i
$425$		0			0
$426$	659.959	+	214.434i	1.54920	+	0.503366i
$427$	−20.4033	−	14.8238i	−0.0477828	−	0.0347162i
$428$		−	29.5703i		−	0.0690896i
$429$	154.894	+	301.033i	0.361057	+	0.701708i
$430$		0			0
$431$	264.193	−	363.631i	0.612978	−	0.843692i	−0.383840	−	0.923399i	$-0.625399\pi$
$431$	264.193	−	363.631i	0.612978	−	0.843692i	0.996818	+	0.0797077i	$0.0253987\pi$
$432$	−43.6089	+	134.215i	−0.100947	+	0.310682i
$433$	−44.6093	−	137.293i	−0.103024	−	0.317075i	0.886238	−	0.463231i	$-0.153310\pi$
$433$	−44.6093	−	137.293i	−0.103024	−	0.317075i	−0.989262	+	0.146156i	$0.953310\pi$
$434$	−74.0689	+	53.8142i	−0.170666	+	0.123996i
$435$		0			0
$436$	713.002	−	231.668i	1.63533	−	0.531349i
$437$	81.6312	+	26.5236i	0.186799	+	0.0606947i
$438$	−848.082	−	616.168i	−1.93626	−	1.40678i
$439$			155.406i			0.354001i	0.984211	+	0.177000i	$0.0566394\pi$
$439$			155.406i			0.354001i	−0.984211	+	0.177000i	$0.943361\pi$
$440$		0			0
$441$	197.120			0.446983
$442$	380.517	−	523.736i	0.860897	−	1.18492i
$443$	−100.216	+	308.434i	−0.226222	+	0.696240i	0.771943	+	0.635691i	$0.219285\pi$
$443$	−100.216	+	308.434i	−0.226222	+	0.696240i	−0.998165	+	0.0605483i	$0.980715\pi$
$444$	−246.246	−	757.868i	−0.554608	−	1.70691i
$445$		0			0
$446$	206.180	+	283.783i	0.462288	+	0.636285i
$447$	884.574	−	287.416i	1.97891	−	0.642988i
$448$	−84.7690	−	27.5431i	−0.189216	−	0.0614801i
$449$	316.651	+	230.060i	0.705236	+	0.512384i	0.881633	−	0.471935i	$-0.156444\pi$
$449$	316.651	+	230.060i	0.705236	+	0.512384i	−0.176397	+	0.984319i	$0.556444\pi$
$450$		0			0
$451$	12.8319	+	6.47407i	0.0284520	+	0.0143549i
$452$	−254.490			−0.563032
$453$	612.877	−	843.553i	1.35293	−	1.86215i
$454$	37.1058	−	114.200i	0.0817309	−	0.251542i
$455$		0			0
$456$	157.307	−	114.291i	0.344973	−	0.250637i
$457$	30.7092	+	42.2675i	0.0671973	+	0.0924891i	0.841293	−	0.540580i	$-0.181795\pi$
$457$	30.7092	+	42.2675i	0.0671973	+	0.0924891i	−0.774096	+	0.633069i	$0.781795\pi$
$458$	−392.830	+	127.638i	−0.857707	+	0.278686i
$459$	−417.758	−	135.738i	−0.910149	−	0.295725i
$460$		0			0
$461$			339.293i			0.735994i	0.929827	+	0.367997i	$0.119956\pi$
$461$			339.293i			0.735994i	−0.929827	+	0.367997i	$0.880044\pi$
$462$	78.0902	+	77.4721i	0.169026	+	0.167689i
$463$	−676.869			−1.46192			−0.730960	−	0.682420i	$-0.760928\pi$
$463$	−676.869			−1.46192			−0.730960	+	0.682420i	$0.760928\pi$
$464$	−16.1622	+	22.2453i	−0.0348322	+	0.0479425i
$465$		0			0
$466$	254.256	+	782.519i	0.545613	+	1.67923i
$467$	298.435	−	216.825i	0.639046	−	0.464294i	−0.220476	−	0.975392i	$-0.570761\pi$
$467$	298.435	−	216.825i	0.639046	−	0.464294i	0.859522	+	0.511098i	$0.170761\pi$
$468$	111.910	+	154.031i	0.239124	+	0.329125i
$469$	65.3444	−	21.2317i	0.139327	−	0.0452701i
$470$		0			0
$471$	−809.681	−	588.267i	−1.71907	−	1.24898i
$472$		−	141.679i		−	0.300168i
$473$	−55.4656	+	359.433i	−0.117263	+	0.759900i
$474$	733.951			1.54842
$475$		0			0
$476$	37.5511	−	115.570i	0.0788888	−	0.242795i
$477$	99.2705	+	305.523i	0.208114	+	0.640510i
$478$	274.241	−	199.248i	0.573726	−	0.416836i
$479$	−279.454	−	384.635i	−0.583411	−	0.802997i	0.410653	−	0.911792i	$-0.365301\pi$
$479$	−279.454	−	384.635i	−0.583411	−	0.802997i	−0.994064	+	0.108795i	$0.965301\pi$
$480$		0			0
$481$	−325.623	−	105.801i	−0.676971	−	0.219961i
$482$	475.828	+	345.709i	0.987195	+	0.717239i
$483$			23.5114i			0.0486779i
$484$	−5.26142	−	662.108i	−0.0108707	−	1.36799i
$485$		0			0
$486$	372.373	−	512.528i	0.766200	−	1.05458i
$487$	55.3626	−	170.389i	0.113681	−	0.349874i	−0.877989	−	0.478681i	$-0.841115\pi$
$487$	55.3626	−	170.389i	0.113681	−	0.349874i	0.991670	+	0.128807i	$0.0411149\pi$
$488$	39.3181	+	121.009i	0.0805699	+	0.247969i
$489$	203.037	−	147.515i	0.415208	−	0.301667i
$490$		0			0
$491$	611.297	−	198.622i	1.24500	−	0.404526i	0.388876	−	0.921290i	$-0.372863\pi$
$491$	611.297	−	198.622i	1.24500	−	0.404526i	0.856128	+	0.516764i	$0.172863\pi$
$492$	24.6024	+	7.99379i	0.0500048	+	0.0162475i
$493$	−69.2411	−	50.3066i	−0.140448	−	0.102042i
$494$		−	310.543i		−	0.628631i
$495$		0			0
$496$	−263.151			−0.530546
$497$	32.8955	−	45.2768i	0.0661881	−	0.0911001i
$498$	195.119	−	600.515i	0.391805	−	1.20585i
$499$	−162.446	−	499.958i	−0.325543	−	1.00192i	−0.971195	−	0.238287i	$-0.923414\pi$
$499$	−162.446	−	499.958i	−0.325543	−	1.00192i	0.645651	−	0.763632i	$-0.276586\pi$
$500$		0			0
$501$	614.574	+	845.889i	1.22670	+	1.68840i
$502$	1250.24	−	406.229i	2.49053	−	0.809222i
$503$	−609.941	−	198.182i	−1.21261	−	0.394000i	−0.368222	−	0.929738i	$-0.620033\pi$
$503$	−609.941	−	198.182i	−1.21261	−	0.394000i	−0.844384	+	0.535738i	$0.820033\pi$
$504$	13.4640	+	9.78217i	0.0267143	+	0.0194091i
$505$		0			0
$506$	172.533	−	173.909i	0.340974	−	0.343694i
$507$	−349.644			−0.689634
$508$	−268.351	+	369.353i	−0.528249	+	0.727073i
$509$	−140.705	+	433.046i	−0.276434	+	0.850778i	0.712402	+	0.701772i	$0.247607\pi$
$509$	−140.705	+	433.046i	−0.276434	+	0.850778i	−0.988836	+	0.149006i	$0.952393\pi$
$510$		0			0
$511$	−68.3982	+	49.6942i	−0.133852	+	0.0972490i
$512$	−283.422	−	390.097i	−0.553559	−	0.761908i
$513$	−200.398	+	65.1131i	−0.390639	+	0.126926i
$514$	−82.7786	−	26.8964i	−0.161048	−	0.0523276i
$515$		0			0
$516$			654.583i			1.26857i
$517$	−112.793	+	223.561i	−0.218169	+	0.432419i
$518$	−111.246			−0.214761
$519$	389.615	−	536.259i	0.750703	−	1.03325i
$520$		0			0
$521$	−56.0044	−	172.364i	−0.107494	−	0.330833i	0.882814	−	0.469723i	$-0.155646\pi$
$521$	−56.0044	−	172.364i	−0.107494	−	0.330833i	−0.990308	+	0.138891i	$0.955646\pi$
$522$	35.2492	−	25.6101i	0.0675272	−	0.0490614i
$523$	201.474	+	277.305i	0.385227	+	0.530219i	0.956960	−	0.290220i	$-0.0937286\pi$
$523$	201.474	+	277.305i	0.385227	+	0.530219i	−0.571733	+	0.820440i	$0.693729\pi$
$524$	−442.835	+	143.886i	−0.845106	+	0.274591i
$525$		0			0
$526$	235.421	+	171.044i	0.447569	+	0.325178i
$527$		−	819.088i		−	1.55425i
$528$	50.7001	+	312.078i	0.0960229	+	0.591056i
$529$	−476.639			−0.901020
$530$		0			0
$531$	39.5238	−	121.642i	0.0744328	−	0.229080i
$532$	−18.0132	−	55.4388i	−0.0338593	−	0.104208i
$533$	8.99187	−	6.53298i	0.0168703	−	0.0122570i
$534$	−407.738	−	561.203i	−0.763554	−	1.05094i
$535$		0			0
$536$	−329.668	−	107.116i	−0.615053	−	0.199843i
$537$	6.00251	+	4.36108i	0.0111779	+	0.00812119i
$538$			720.159i			1.33859i
$539$	−471.388	+	242.548i	−0.874560	+	0.449996i
$540$		0			0
$541$	179.366	−	246.876i	0.331545	−	0.456332i	−0.610403	−	0.792091i	$-0.708993\pi$
$541$	179.366	−	246.876i	0.331545	−	0.456332i	0.941948	+	0.335759i	$0.108993\pi$
$542$	136.400	−	419.796i	0.251661	−	0.774532i
$543$	81.5066	+	250.851i	0.150104	+	0.461973i
$544$	851.671	−	618.775i	1.56557	−	1.13745i
$545$		0			0
$546$	80.9017	−	26.2866i	0.148172	−	0.0481439i
$547$	−143.880	−	46.7494i	−0.263034	−	0.0854651i	0.174531	−	0.984652i	$-0.444159\pi$
$547$	−143.880	−	46.7494i	−0.263034	−	0.0854651i	−0.437565	+	0.899187i	$0.644159\pi$
$548$	−260.057	−	188.942i	−0.474556	−	0.344785i
$549$			114.863i			0.209222i
$550$		0			0
$551$	−41.0557			−0.0745113
$552$	69.7214	−	95.9632i	0.126307	−	0.173846i
$553$	18.2918	−	56.2964i	0.0330774	−	0.101802i
$554$	370.036	+	1138.85i	0.667936	+	2.05569i
$555$		0			0
$556$	−517.807	−	712.701i	−0.931308	−	1.28184i
$557$	103.677	−	33.6867i	0.186134	−	0.0604787i	−0.214467	−	0.976731i	$-0.568801\pi$
$557$	103.677	−	33.6867i	0.186134	−	0.0604787i	0.400601	+	0.916253i	$0.368801\pi$
$558$	396.572	+	128.854i	0.710703	+	0.230921i
$559$	227.533	+	165.312i	0.407036	+	0.295729i
$560$		0			0
$561$	−971.378	+	157.810i	−1.73151	+	0.281301i
$562$	−310.949			−0.553291
$563$	585.827	−	806.321i	1.04054	−	1.43219i	0.143817	−	0.989604i	$-0.454062\pi$
$563$	585.827	−	806.321i	1.04054	−	1.43219i	0.896728	−	0.442583i	$-0.145938\pi$
$564$	−139.271	+	428.631i	−0.246934	+	0.759983i
$565$		0			0
$566$	5.27864	−	3.83516i	0.00932622	−	0.00677590i
$567$	−53.3576	−	73.4404i	−0.0941051	−	0.129525i
$568$	−268.530	+	87.2506i	−0.472764	+	0.153610i
$569$	94.4665	+	30.6940i	0.166022	+	0.0539438i	0.390849	−	0.920455i	$-0.372182\pi$
$569$	94.4665	+	30.6940i	0.166022	+	0.0539438i	−0.224827	+	0.974399i	$0.572182\pi$
$570$		0			0
$571$			930.127i			1.62894i	0.580202	+	0.814472i	$0.302973\pi$
$571$			930.127i			1.62894i	−0.580202	+	0.814472i	$0.697027\pi$
$572$	−457.148	−	230.645i	−0.799209	−	0.403226i
$573$	375.564			0.655435
$574$	2.12269	−	2.92164i	0.00369807	−	0.00508996i
$575$		0			0
$576$	125.444	+	386.078i	0.217785	+	0.670274i
$577$	−281.012	+	204.167i	−0.487022	+	0.353842i	−0.804038	−	0.594578i	$-0.797319\pi$
$577$	−281.012	+	204.167i	−0.487022	+	0.353842i	0.317016	+	0.948420i	$0.397319\pi$
$578$	583.313	+	802.862i	1.00919	+	1.38903i
$579$	1183.74	−	384.620i	2.04445	−	0.664283i
$580$		0			0
$581$	−41.1985	−	29.9325i	−0.0709097	−	0.0515189i
$582$			806.278i			1.38536i
$583$	−613.328	−	608.474i	−1.05202	−	1.04369i
$584$	426.536			0.730370
$585$		0			0
$586$	447.100	−	1376.03i	0.762970	−	2.34818i
$587$	196.347	+	604.294i	0.334492	+	1.02946i	0.966972	+	0.254884i	$0.0820373\pi$
$587$	196.347	+	604.294i	0.334492	+	1.02946i	−0.632479	+	0.774577i	$0.717963\pi$
$588$	−771.926	+	560.837i	−1.31280	+	0.953804i
$589$	−230.949	−	317.874i	−0.392104	−	0.539685i
$590$		0			0
$591$	340.902	+	110.766i	0.576822	+	0.187421i
$592$	−258.684	−	187.945i	−0.436966	−	0.317474i
$593$			341.152i			0.575299i	0.957736	+	0.287650i	$0.0928739\pi$
$593$			341.152i			0.575299i	−0.957736	+	0.287650i	$0.907126\pi$
$594$	−91.7173	+	594.354i	−0.154406	+	1.00060i
$595$		0			0
$596$	−826.858	+	1138.07i	−1.38735	+	1.90952i
$597$	171.584	−	528.080i	0.287410	−	0.884556i
$598$	−58.5410	−	180.171i	−0.0978947	−	0.301289i
$599$	362.164	−	263.128i	0.604614	−	0.439278i	−0.242899	−	0.970052i	$-0.578098\pi$
$599$	362.164	−	263.128i	0.604614	−	0.439278i	0.847514	+	0.530773i	$0.178098\pi$
$600$		0			0
$601$	−762.584	+	247.779i	−1.26886	+	0.412277i	−0.864643	−	0.502387i	$-0.832455\pi$
$601$	−762.584	+	247.779i	−1.26886	+	0.412277i	−0.404215	+	0.914664i	$0.632455\pi$
$602$	86.9098	+	28.2387i	0.144368	+	0.0469082i
$603$	−253.162	−	183.933i	−0.419837	−	0.305029i
$604$			1577.03i			2.61097i
$605$		0			0
$606$	−716.869			−1.18295
$607$	−599.237	+	824.779i	−0.987211	+	1.35878i	−0.0543575	+	0.998522i	$0.517311\pi$
$607$	−599.237	+	824.779i	−0.987211	+	1.35878i	−0.932853	+	0.360257i	$0.882689\pi$
$608$	156.050	−	480.273i	0.256661	−	0.789922i
$609$	−3.47524	−	10.6957i	−0.00570647	−	0.0175627i
$610$		0			0
$611$	113.820	+	156.659i	0.186284	+	0.256398i
$612$	−526.362	+	171.025i	−0.860068	+	0.279453i
$613$	711.597	+	231.212i	1.16084	+	0.377181i	0.825218	−	0.564814i	$-0.191052\pi$
$613$	711.597	+	231.212i	1.16084	+	0.377181i	0.335626	+	0.941995i	$0.391052\pi$
$614$	247.542	+	179.850i	0.403163	+	0.292915i
$615$		0			0
$616$	−44.2341	−	6.82596i	−0.0718087	−	0.0110811i
$617$	−517.100			−0.838088			−0.419044	−	0.907966i	$-0.637635\pi$
$617$	−517.100			−0.838088			−0.419044	+	0.907966i	$0.637635\pi$
$618$	−213.435	+	293.768i	−0.345363	+	0.475352i
$619$	−214.219	+	659.299i	−0.346073	+	1.06510i	0.614934	+	0.788579i	$0.289183\pi$
$619$	−214.219	+	659.299i	−0.346073	+	1.06510i	−0.961007	+	0.276525i	$0.910817\pi$
$620$		0			0
$621$	−103.992	+	75.5545i	−0.167459	+	0.121666i
$622$	−613.643	−	844.607i	−0.986565	−	1.35789i
$623$	−53.2078	+	17.2883i	−0.0854058	+	0.0277500i
$624$	232.533	+	75.5545i	0.372649	+	0.121081i
$625$		0			0
$626$		−	1189.18i		−	1.89965i
$627$	−332.480	+	335.132i	−0.530271	+	0.534501i
$628$	1513.70			2.41035
$629$	585.000	−	805.183i	0.930048	−	1.28010i
$630$		0			0
$631$	−277.128	−	852.911i	−0.439188	−	1.35168i	−0.888733	−	0.458425i	$-0.848414\pi$
$631$	−277.128	−	852.911i	−0.439188	−	1.35168i	0.449545	−	0.893258i	$-0.351586\pi$
$632$	−241.602	+	175.534i	−0.382281	+	0.277744i
$633$	−709.263	−	976.216i	−1.12048	−	1.54221i
$634$	−740.755	+	240.686i	−1.16838	+	0.379631i
$635$		0			0
$636$	−1258.01	−	913.997i	−1.97800	−	1.43710i
$637$			409.958i			0.643577i
$638$	−52.7821	+	104.616i	−0.0827306	+	0.163975i
$639$	−254.892			−0.398891
$640$		0			0
$641$	175.756	−	540.922i	0.274191	−	0.843872i	−0.715242	−	0.698877i	$-0.753683\pi$
$641$	175.756	−	540.922i	0.274191	−	0.843872i	0.989432	−	0.144995i	$-0.0463165\pi$
$642$	18.5942	+	57.2272i	0.0289630	+	0.0891389i
$643$	534.364	−	388.238i	0.831048	−	0.603791i	−0.0888080	−	0.996049i	$-0.528306\pi$
$643$	534.364	−	388.238i	0.831048	−	0.603791i	0.919855	+	0.392257i	$0.128306\pi$
$644$	−20.9017	−	28.7687i	−0.0324561	−	0.0446719i
$645$		0			0
$646$	858.533	+	278.954i	1.32900	+	0.431818i
$647$	28.5999	+	20.7790i	0.0442038	+	0.0321159i	0.609668	−	0.792657i	$-0.291303\pi$
$647$	28.5999	+	20.7790i	0.0442038	+	0.0321159i	−0.565464	+	0.824773i	$0.691303\pi$
$648$			457.979i			0.706758i
$649$	55.1591	+	339.524i	0.0849908	+	0.523150i
$650$		0			0
$651$	63.2624	−	87.0732i	0.0971772	−	0.133753i
$652$	−117.296	+	361.001i	−0.179902	+	0.553682i
$653$	−129.615	−	398.914i	−0.198491	−	0.610894i	−0.999918	−	0.0128008i	$-0.995925\pi$
$653$	−129.615	−	398.914i	−0.198491	−	0.610894i	0.801427	−	0.598093i	$-0.204075\pi$
$654$	−1234.19	+	896.691i	−1.88714	+	1.37109i
$655$		0			0
$656$	9.87192	−	3.20758i	0.0150487	−	0.00488960i
$657$	366.211	+	118.989i	0.557399	+	0.181110i
$658$	50.9017	+	36.9822i	0.0773582	+	0.0562040i
$659$		−	1281.39i		−	1.94445i	−0.234058	−	0.972223i	$-0.575200\pi$
$659$		−	1281.39i		−	1.94445i	0.234058	−	0.972223i	$-0.424800\pi$
$660$		0			0
$661$	70.6950			0.106952			0.0534758	−	0.998569i	$-0.482970\pi$
$661$	70.6950			0.106952			0.0534758	+	0.998569i	$0.482970\pi$
$662$	673.165	−	926.532i	1.01687	−	1.39960i
$663$	−235.172	+	723.786i	−0.354709	+	1.09168i
$664$	79.3916	+	244.342i	0.119566	+	0.367986i
$665$		0			0
$666$	297.812	+	409.902i	0.447164	+	0.615469i
$667$	−23.8197	+	7.73948i	−0.0357116	+	0.0116034i
$668$	−1503.99	−	488.677i	−2.25149	−	0.731553i
$669$	−333.607	−	242.380i	−0.498665	−	0.362301i
$670$		0			0
$671$	−141.334	−	274.681i	−0.210632	−	0.409360i
$672$	138.328			0.205845
$673$	470.230	−	647.216i	0.698708	−	0.961689i	−0.301259	−	0.953542i	$-0.597407\pi$
$673$	470.230	−	647.216i	0.698708	−	0.961689i	0.999967	−	0.00814624i	$-0.00259306\pi$
$674$	78.1910	−	240.647i	0.116010	−	0.357043i
$675$		0			0
$676$	427.827	−	310.835i	0.632880	−	0.459815i
$677$	−550.202	−	757.288i	−0.812706	−	1.11859i	−0.990900	−	0.134598i	$-0.957026\pi$
$677$	−550.202	−	757.288i	−0.812706	−	1.11859i	0.178195	−	0.983995i	$-0.442974\pi$
$678$	492.513	−	160.027i	0.726420	−	0.236028i
$679$	61.8441	+	20.0944i	0.0910811	+	0.0295940i
$680$		0			0
$681$			141.159i			0.207282i
$682$	−1106.91	+	179.828i	−1.62303	+	0.263677i
$683$	241.319			0.353322			0.176661	−	0.984272i	$-0.443470\pi$
$683$	241.319			0.353322			0.176661	+	0.984272i	$0.443470\pi$
$684$	−156.050	+	214.785i	−0.228143	+	0.314013i
$685$		0			0
$686$	83.0132	+	255.488i	0.121010	+	0.372432i
$687$	392.830	−	285.407i	0.571805	−	0.415440i
$688$	154.386	+	212.494i	0.224398	+	0.308858i
$689$	−635.410	+	206.457i	−0.922221	+	0.299648i
$690$		0			0
$691$	736.915	+	535.400i	1.06645	+	0.774819i	0.975270	−	0.221015i	$-0.0709371\pi$
$691$	736.915	+	535.400i	1.06645	+	0.774819i	0.0911771	+	0.995835i	$0.470937\pi$
$692$			1002.54i			1.44876i
$693$	−36.0739	−	18.2004i	−0.0520547	−	0.0262632i
$694$	706.140			1.01749
$695$		0			0
$696$	−17.5329	+	53.9607i	−0.0251909	+	0.0775297i
$697$	9.98397	+	30.7275i	0.0143242	+	0.0440853i
$698$	578.577	−	420.361i	0.828907	−	0.602236i
$699$	−568.533	−	782.519i	−0.813352	−	1.11948i
$700$		0			0
$701$	−410.902	−	133.510i	−0.586165	−	0.190457i	0.000895496	−	1.00000i	$-0.499715\pi$
$701$	−410.902	−	133.510i	−0.586165	−	0.190457i	−0.587061	+	0.809543i	$0.699715\pi$
$702$	376.246	+	273.359i	0.535963	+	0.389400i
$703$		−	477.424i		−	0.679124i
$704$	−775.039	−	768.905i	−1.10091	−	1.09219i
$705$		0			0
$706$	−62.6722	+	86.2609i	−0.0887708	+	0.122183i
$707$	−17.8661	+	54.9861i	−0.0252703	+	0.0777739i
$708$	191.314	+	588.804i	0.270218	+	0.831644i
$709$	708.956	−	515.087i	0.999938	−	0.726498i	0.0378633	−	0.999283i	$-0.487945\pi$
$709$	708.956	−	515.087i	0.999938	−	0.726498i	0.962075	+	0.272785i	$0.0879448\pi$
$710$		0			0
$711$	−256.400	+	83.3095i	−0.360619	+	0.117172i
$712$	268.438	+	87.2208i	0.377020	+	0.122501i
$713$	−193.915	−	140.887i	−0.271970	−	0.197598i
$714$			247.275i			0.346323i
$715$		0			0
$716$	−11.2217			−0.0156728
$717$	−234.230	+	322.390i	−0.326680	+	0.449637i
$718$	−429.681	+	1322.42i	−0.598441	+	1.84181i
$719$	155.218	+	477.712i	0.215880	+	0.664411i	0.999090	+	0.0426534i	$0.0135811\pi$
$719$	155.218	+	477.712i	0.215880	+	0.664411i	−0.783210	+	0.621758i	$0.786419\pi$
$720$		0			0
$721$	17.2136	+	23.6925i	0.0238746	+	0.0328606i
$722$	−644.829	+	209.518i	−0.893115	+	0.290191i
$723$	−657.578	−	213.660i	−0.909514	−	0.295519i
$724$	−322.740	−	234.484i	−0.445773	−	0.323873i
$725$		0			0
$726$	426.525	+	1278.06i	0.587500	+	1.76042i
$727$	393.878			0.541786			0.270893	−	0.962609i	$-0.412681\pi$
$727$	393.878			0.541786			0.270893	+	0.962609i	$0.412681\pi$
$728$	−20.3444	+	28.0017i	−0.0279456	+	0.0384639i
$729$	50.9853	−	156.917i	0.0699387	−	0.215249i
$730$		0			0
$731$	−661.413	+	480.544i	−0.904805	+	0.657380i
$732$	−326.803	−	449.806i	−0.446453	−	0.614489i
$733$	590.381	−	191.826i	0.805431	−	0.261700i	0.122769	−	0.992435i	$-0.460822\pi$
$733$	590.381	−	191.826i	0.805431	−	0.261700i	0.682661	+	0.730735i	$0.260822\pi$
$734$	−1079.57	−	350.775i	−1.47081	−	0.477895i
$735$		0			0
$736$		−	308.061i		−	0.418562i
$737$	831.728	+	128.347i	1.12853	+	0.174148i
$738$	−16.4477			−0.0222869
$739$	−499.618	+	687.666i	−0.676074	+	0.930535i	−0.999878	−	0.0155884i	$-0.995038\pi$
$739$	−499.618	+	687.666i	−0.676074	+	0.930535i	0.323805	+	0.946124i	$0.395038\pi$
$740$		0			0
$741$	112.812	+	347.198i	0.152242	+	0.468554i
$742$	−175.623	+	127.598i	−0.236689	+	0.171964i
$743$	−238.416	−	328.152i	−0.320883	−	0.441658i	0.617853	−	0.786293i	$-0.288003\pi$
$743$	−238.416	−	328.152i	−0.320883	−	0.441658i	−0.938737	+	0.344635i	$0.888003\pi$
$744$	−516.418	+	167.794i	−0.694111	+	0.225530i
$745$		0			0
$746$	1476.92	+	1073.05i	1.97979	+	1.43840i
$747$			231.933i			0.310486i
$748$	1048.29	−	1056.65i	1.40146	−	1.41264i
$749$	4.85292			0.00647919
$750$		0			0
$751$	−262.486	+	807.849i	−0.349515	+	1.07570i	0.609606	+	0.792704i	$0.291327\pi$
$751$	−262.486	+	807.849i	−0.349515	+	1.07570i	−0.959122	+	0.282993i	$0.908673\pi$
$752$	55.8835	+	171.992i	0.0743132	+	0.228712i
$753$	−1250.24	+	908.356i	−1.66035	+	1.20632i
$754$	53.2624	+	73.3094i	0.0706398	+	0.0972273i
$755$		0			0
$756$	83.0244	+	26.9763i	0.109821	+	0.0356829i
$757$	485.832	+	352.977i	0.641786	+	0.466284i	0.860463	−	0.509513i	$-0.170174\pi$
$757$	485.832	+	352.977i	0.641786	+	0.466284i	−0.218678	+	0.975797i	$0.570174\pi$
$758$		−	865.602i		−	1.14196i
$759$	−129.721	+	257.113i	−0.170911	+	0.338752i
$760$		0			0
$761$	205.275	−	282.537i	0.269744	−	0.371271i	−0.652559	−	0.757738i	$-0.726305\pi$
$761$	205.275	−	282.537i	0.269744	−	0.371271i	0.922303	+	0.386467i	$0.126305\pi$
$762$	287.082	−	883.548i	0.376748	−	1.15951i
$763$	38.0201	+	117.014i	0.0498298	+	0.153360i
$764$	−459.543	+	333.877i	−0.601496	+	0.437012i
$765$		0			0
$766$	1866.16	−	606.354i	2.43625	−	0.791584i
$767$	252.984	+	82.1994i	0.329835	+	0.107170i
$768$	−55.6140	−	40.4059i	−0.0724140	−	0.0526119i
$769$			768.616i			0.999500i	0.866170	+	0.499750i	$0.166575\pi$
$769$			768.616i			0.999500i	−0.866170	+	0.499750i	$0.833425\pi$
$770$		0			0
$771$	102.320			0.132711
$772$	−1106.50	+	1522.97i	−1.43329	+	1.97276i
$773$	−2.15905	+	6.64488i	−0.00279308	+	0.00859623i	−0.952443	−	0.304716i	$-0.901439\pi$
$773$	−2.15905	+	6.64488i	−0.00279308	+	0.00859623i	0.949650	+	0.313312i	$0.101439\pi$
$774$	−128.612	−	395.828i	−0.166166	−	0.511406i
$775$		0			0
$776$	−192.832	−	265.410i	−0.248495	−	0.342024i
$777$	124.377	−	40.4125i	0.160073	−	0.0520110i
$778$	1953.72	+	634.801i	2.51120	+	0.815939i
$779$	12.5385	+	9.10976i	0.0160956	+	0.0116942i
$780$		0			0
$781$	609.543	−	313.634i	0.780465	−	0.401581i
$782$	550.689			0.704206
$783$	36.1397	−	49.7420i	0.0461554	−	0.0635275i
$784$	−118.311	+	364.124i	−0.150907	+	0.464443i
$785$		0			0
$786$	766.537	−	556.922i	0.975238	−	0.708552i
$787$	648.159	+	892.115i	0.823582	+	1.13356i	0.989084	+	0.147354i	$0.0470758\pi$
$787$	648.159	+	892.115i	0.823582	+	1.13356i	−0.165501	+	0.986210i	$0.552924\pi$
$788$	−515.601	+	167.529i	−0.654315	+	0.212600i
$789$	−325.344	−	105.711i	−0.412350	−	0.133981i
$790$		0			0
$791$		−	41.7655i		−	0.0528009i
$792$	93.2659	+	181.261i	0.117760	+	0.228864i
$793$	−238.885			−0.301243
$794$	9.72136	−	13.3803i	0.0122435	−	0.0168518i
$795$		0			0
$796$	259.514	+	798.700i	0.326022	+	1.00339i
$797$	−583.596	+	424.007i	−0.732240	+	0.532004i	−0.890271	−	0.455430i	$-0.849485\pi$
$797$	−583.596	+	424.007i	−0.732240	+	0.532004i	0.158031	+	0.987434i	$0.449485\pi$
$798$	69.7214	+	95.9632i	0.0873701	+	0.120255i
$799$	−535.344	+	173.944i	−0.670018	+	0.217702i
$800$		0			0
$801$	206.141	+	149.770i	0.257355	+	0.186979i
$802$		−	870.354i		−	1.08523i
$803$	−1022.16	+	166.060i	−1.27293	+	0.206800i
$804$	1514.71			1.88396
$805$		0			0
$806$	−267.984	+	824.769i	−0.332486	+	1.02329i
$807$	−261.613	−	805.162i	−0.324180	−	0.997722i
$808$	235.979	−	171.449i	0.292053	−	0.212189i
$809$	−471.682	−	649.215i	−0.583044	−	0.802491i	0.410981	−	0.911644i	$-0.365186\pi$
$809$	−471.682	−	649.215i	−0.583044	−	0.802491i	−0.994025	+	0.109153i	$0.965186\pi$
$810$		0			0
$811$	−471.598	−	153.232i	−0.581502	−	0.188942i	0.00347122	−	0.999994i	$-0.498895\pi$
$811$	−471.598	−	153.232i	−0.581502	−	0.188942i	−0.584973	+	0.811052i	$0.698895\pi$
$812$	13.7608	+	9.99783i	0.0169468	+	0.0123126i
$813$			518.897i			0.638250i
$814$	−1216.55	−	613.787i	−1.49453	−	0.754038i
$815$		0			0
$816$	−417.758	+	574.995i	−0.511959	+	0.704651i
$817$	−121.189	+	372.983i	−0.148335	+	0.456527i
$818$	29.5379	+	90.9084i	0.0361099	+	0.111135i
$819$	−25.2786	+	18.3660i	−0.0308653	+	0.0224249i
$820$		0			0
$821$	−276.921	+	89.9771i	−0.337297	+	0.109595i	−0.472768	−	0.881187i	$-0.656745\pi$
$821$	−276.921	+	89.9771i	−0.337297	+	0.109595i	0.135471	+	0.990781i	$0.456745\pi$
$822$	622.095	+	202.131i	0.756806	+	0.245901i
$823$	869.681	+	631.860i	1.05672	+	0.767752i	0.973479	−	0.228777i	$-0.0734727\pi$
$823$	869.681	+	631.860i	1.05672	+	0.767752i	0.0832414	+	0.996529i	$0.473473\pi$
$824$		−	147.748i		−	0.179306i
$825$		0			0
$826$	86.4296			0.104636
$827$	268.497	−	369.554i	0.324664	−	0.446861i	−0.615220	−	0.788355i	$-0.710933\pi$
$827$	268.497	−	369.554i	0.324664	−	0.446861i	0.939884	+	0.341494i	$0.110933\pi$
$828$	−50.0476	+	154.031i	−0.0604440	+	0.186027i
$829$	0.679973	+	2.09274i	0.000820233	+	0.00252442i	0.951466	−	0.307755i	$-0.0995776\pi$
$829$	0.679973	+	2.09274i	0.000820233	+	0.00252442i	−0.950646	+	0.310279i	$0.899578\pi$
$830$		0			0
$831$	−827.426	−	1138.85i	−0.995700	−	1.37046i
$832$	−802.943	+	260.892i	−0.965076	+	0.313572i
$833$	−1133.38	−	368.257i	−1.36060	−	0.442085i
$834$	1450.26	+	1053.68i	1.73892	+	1.26340i
$835$		0			0
$836$	108.891	−	705.645i	0.130252	−	0.844073i
$837$	588.423			0.703015
$838$	−443.491	+	610.413i	−0.529226	+	0.728417i
$839$	448.822	−	1381.33i	0.534948	−	1.64640i	−0.208813	−	0.977956i	$-0.566960\pi$
$839$	448.822	−	1381.33i	0.534948	−	1.64640i	0.743761	−	0.668446i	$-0.233040\pi$
$840$		0			0
$841$	−670.691	+	487.286i	−0.797493	+	0.579412i
$842$	140.036	+	192.744i	0.166314	+	0.228912i
$843$	347.652	−	112.959i	0.412398	−	0.133996i
$844$	1735.72	+	563.969i	2.05654	+	0.668209i
$845$		0			0
$846$		−	286.558i		−	0.338721i
$847$	108.661	−	0.863474i	0.128290	−	0.00101945i
$848$	−623.951			−0.735792
$849$	−4.50850	+	6.20541i	−0.00531036	+	0.00730909i
$850$		0			0
$851$	−90.0000	−	276.992i	−0.105758	−	0.325489i
$852$	998.163	−	725.208i	1.17155	−	0.851183i
$853$	−622.757	−	857.151i	−0.730079	−	1.00487i	−0.999128	−	0.0417407i	$-0.986710\pi$
$853$	−622.757	−	857.151i	−0.730079	−	1.00487i	0.269050	−	0.963126i	$-0.413290\pi$
$854$	−73.8197	+	23.9855i	−0.0864399	+	0.0280860i
$855$		0			0
$856$	−19.8075	−	14.3910i	−0.0231396	−	0.0168119i
$857$		−	951.067i		−	1.10976i	−0.831929	−	0.554882i	$-0.812763\pi$
$857$		−	951.067i		−	1.10976i	0.831929	−	0.554882i	$-0.187237\pi$
$858$	1029.75	+	158.904i	1.20017	+	0.185203i
$859$	1146.23			1.33438			0.667188	−	0.744890i	$-0.267498\pi$
$859$	1146.23			1.33438			0.667188	+	0.744890i	$0.267498\pi$
$860$		0			0
$861$	−1.31190	+	4.03760i	−0.00152369	+	0.00468943i
$862$	−427.474	−	1315.63i	−0.495910	−	1.52625i
$863$	764.758	−	555.629i	0.886162	−	0.643834i	−0.0487126	−	0.998813i	$-0.515512\pi$
$863$	764.758	−	555.629i	0.886162	−	0.643834i	0.934874	+	0.354979i	$0.115512\pi$
$864$	444.521	+	611.831i	0.514492	+	0.708137i
$865$		0			0
$866$	−422.545	−	137.293i	−0.487928	−	0.158537i
$867$	−943.821	−	685.726i	−1.08861	−	0.790918i
$868$			162.784i			0.187539i
$869$	510.641	−	514.715i	0.587619	−	0.592307i
$870$		0			0
$871$	382.533	−	526.511i	0.439188	−	0.604491i
$872$	191.815	−	590.345i	0.219971	−	0.677001i
$873$	−91.5191	−	281.667i	−0.104833	−	0.322643i
$874$	213.713	−	155.272i	0.244523	−	0.177656i
$875$		0			0
$876$	−1772.64	+	575.964i	−2.02356	+	0.657494i
$877$	−150.931	−	49.0405i	−0.172099	−	0.0559185i	0.221700	−	0.975115i	$-0.428839\pi$
$877$	−150.931	−	49.0405i	−0.172099	−	0.0559185i	−0.393799	+	0.919196i	$0.628839\pi$
$878$	386.946	+	281.133i	0.440713	+	0.320197i
$879$			1700.87i			1.93501i
$880$		0			0
$881$	402.370			0.456719			0.228360	−	0.973577i	$-0.426664\pi$
$881$	402.370			0.456719			0.228360	+	0.973577i	$0.426664\pi$
$882$	356.593	−	490.808i	0.404300	−	0.556471i
$883$	−244.512	+	752.530i	−0.276910	+	0.852243i	0.711797	+	0.702385i	$0.247882\pi$
$883$	−244.512	+	752.530i	−0.276910	+	0.852243i	−0.988708	+	0.149858i	$0.952118\pi$
$884$	−355.689	−	1094.70i	−0.402363	−	1.23835i
$885$		0			0
$886$	586.677	+	807.491i	0.662163	+	0.911390i
$887$	−805.659	+	261.775i	−0.908297	+	0.295124i	−0.725657	−	0.688056i	$-0.758464\pi$
$887$	−805.659	+	261.775i	−0.908297	+	0.295124i	−0.182640	+	0.983180i	$0.558464\pi$
$888$	−627.492	−	203.885i	−0.706635	−	0.229600i
$889$	−60.6161	−	44.0402i	−0.0681846	−	0.0495390i
$890$		0			0
$891$	−178.302	−	1097.51i	−0.200114	−	1.23178i
$892$	623.680			0.699192
$893$	−158.713	+	218.450i	−0.177730	+	0.244625i
$894$	884.574	−	2722.44i	0.989457	−	3.04523i
$895$		0			0
$896$	−98.2035	+	71.3491i	−0.109602	+	0.0796306i
$897$	130.902	+	180.171i	0.145933	+	0.200859i
$898$	1145.65	−	372.245i	1.27578	−	0.414527i
$899$	109.039	+	35.4291i	0.121290	+	0.0394094i
$900$		0			0
$901$		−	1942.12i		−	2.15552i
$902$	39.3328	−	20.2383i	0.0436062	−	0.0224372i
$903$	−107.426			−0.118966
$904$	−123.853	+	170.468i	−0.137005	+	0.188571i
$905$		0			0
$906$	−991.656	−	3052.00i	−1.09454	−	3.36866i
$907$	345.216	−	250.814i	0.380613	−	0.276532i	−0.380985	−	0.924581i	$-0.624415\pi$
$907$	345.216	−	250.814i	0.380613	−	0.276532i	0.761598	+	0.648049i	$0.224415\pi$
$908$	−125.491	−	172.723i	−0.138206	−	0.190224i
$909$	250.433	−	81.3705i	0.275503	−	0.0895165i
$910$		0			0
$911$	−113.353	−	82.3554i	−0.124427	−	0.0904011i	0.523831	−	0.851822i	$-0.324502\pi$
$911$	−113.353	−	82.3554i	−0.124427	−	0.0904011i	−0.648258	+	0.761421i	$0.724502\pi$
$912$			340.937i			0.373834i
$913$	−285.384	−	554.639i	−0.312579	−	0.607491i
$914$	160.795			0.175925
$915$		0			0
$916$	−226.941	+	698.453i	−0.247752	+	0.762503i
$917$	−23.6137	−	72.6756i	−0.0257511	−	0.0792537i
$918$	−1093.71	+	794.624i	−1.19140	+	0.865603i
$919$	611.124	+	841.140i	0.664988	+	0.915278i	0.999634	−	0.0270664i	$-0.00861655\pi$
$919$	611.124	+	841.140i	0.664988	+	0.915278i	−0.334645	+	0.942344i	$0.608617\pi$
$920$		0			0
$921$	−342.095	−	111.153i	−0.371438	−	0.120688i
$922$	844.805	+	613.787i	0.916275	+	0.665713i
$923$		−	530.109i		−	0.574333i
$924$	193.050	−	31.3628i	0.208928	−	0.0339424i
$925$		0			0
$926$	−1224.47	+	1685.34i	−1.32232	+	1.82002i
$927$	41.2167	−	126.852i	0.0444625	−	0.136841i
$928$	45.5348	+	140.142i	0.0490677	+	0.151015i
$929$	−1329.96	+	966.270i	−1.43160	+	1.04012i	−0.441884	+	0.897072i	$0.645690\pi$
$929$	−1329.96	+	966.270i	−1.43160	+	1.04012i	−0.989716	+	0.143046i	$0.954310\pi$
$930$		0			0
$931$	−543.678	+	176.652i	−0.583972	+	0.189744i
$932$	1391.32	+	452.068i	1.49284	+	0.485052i
$933$	992.895	+	721.381i	1.06420	+	0.773184i
$934$		−	1135.31i		−	1.21554i
$935$		0			0
$936$	157.639			0.168418
$937$	426.456	−	586.966i	0.455129	−	0.626431i	−0.518361	−	0.855162i	$-0.673458\pi$
$937$	426.456	−	586.966i	0.455129	−	0.626431i	0.973490	+	0.228731i	$0.0734577\pi$
$938$	65.3444	−	201.109i	0.0696636	−	0.214402i
$939$	431.996	+	1329.55i	0.460060	+	1.41592i
$940$		0			0
$941$	−107.800	−	148.374i	−0.114559	−	0.157677i	0.747887	−	0.663826i	$-0.231069\pi$
$941$	−107.800	−	148.374i	−0.114559	−	0.157677i	−0.862446	+	0.506149i	$0.831069\pi$
$942$	−2929.45	+	951.837i	−3.10982	+	1.01044i
$943$	8.99187	+	2.92164i	0.00953539	+	0.00309823i
$944$	200.977	+	146.018i	0.212900	+	0.154681i
$945$		0			0
$946$	794.613	+	788.324i	0.839971	+	0.833323i
$947$	926.439			0.978288			0.489144	−	0.872203i	$-0.337309\pi$
$947$	926.439			0.978288			0.489144	+	0.872203i	$0.337309\pi$
$948$	767.041	−	1055.74i	0.809115	−	1.11365i
$949$	−247.467	+	761.625i	−0.260766	+	0.802556i
$950$		0			0
$951$	740.755	−	538.190i	0.778922	−	0.565920i
$952$	−59.1390	−	81.3978i	−0.0621207	−	0.0855019i
$953$	−237.606	+	77.2030i	−0.249325	+	0.0810105i	−0.431013	−	0.902346i	$-0.641844\pi$
$953$	−237.606	+	77.2030i	−0.249325	+	0.0810105i	0.181688	+	0.983356i	$0.441844\pi$
$954$	940.304	+	305.523i	0.985643	+	0.320255i
$955$		0			0
$956$		−	602.709i		−	0.630449i
$957$	21.0081	−	136.139i	0.0219521	−	0.142256i
$958$	−1463.24			−1.52739
$959$	31.0081	−	42.6790i	0.0323338	−	0.0445037i
$960$		0			0
$961$	42.1004	+	129.572i	0.0438090	+	0.134830i
$962$	−852.492	+	619.372i	−0.886167	+	0.643838i
$963$	−12.9915	−	17.8813i	−0.0134907	−	0.0185683i
$964$	994.562	−	323.153i	1.03170	−	0.335221i
$965$		0			0
$966$	58.5410	+	42.5325i	0.0606015	+	0.0440295i
$967$			554.026i			0.572933i	0.958090	+	0.286466i	$0.0924806\pi$
$967$			554.026i			0.572933i	−0.958090	+	0.286466i	$0.907519\pi$
$968$	−446.068	−	318.703i	−0.460814	−	0.329239i
$969$	−1061.21			−1.09516
$970$		0			0
$971$	−352.634	+	1085.30i	−0.363166	+	1.11771i	0.587955	+	0.808893i	$0.299933\pi$
$971$	−352.634	+	1085.30i	−0.363166	+	1.11771i	−0.951121	+	0.308817i	$0.900067\pi$
$972$	−348.077	−	1071.27i	−0.358104	−	1.10213i
$973$	116.964	−	84.9796i	0.120210	−	0.0873377i
$974$	−324.098	−	446.083i	−0.332750	−	0.457991i
$975$		0			0
$976$	−212.177	−	68.9406i	−0.217395	−	0.0706358i
$977$	104.116	+	75.6451i	0.106568	+	0.0774258i	0.639793	−	0.768547i	$-0.279020\pi$
$977$	104.116	+	75.6451i	0.106568	+	0.0774258i	−0.533225	+	0.845973i	$0.679020\pi$
$978$		−	772.398i		−	0.789773i
$979$	−677.249	−	104.509i	−0.691776	−	0.106751i
$980$		0			0
$981$	329.373	−	453.343i	0.335752	−	0.462123i
$982$	611.297	−	1881.38i	0.622502	−	1.91586i
$983$	412.497	+	1269.53i	0.419630	+	1.29149i	0.908043	+	0.418876i	$0.137576\pi$
$983$	412.497	+	1269.53i	0.419630	+	1.29149i	−0.488413	+	0.872613i	$0.662424\pi$
$984$	17.3278	−	12.5894i	0.0176095	−	0.0127941i
$985$		0			0
$986$	−250.517	+	81.3978i	−0.254074	+	0.0825535i
$987$	−70.3444	−	22.8563i	−0.0712709	−	0.0231573i
$988$	−446.697	−	324.544i	−0.452122	−	0.328486i
$989$			239.242i			0.241903i
$990$		0			0
$991$	762.024			0.768944			0.384472	−	0.923137i	$-0.374383\pi$
$991$	762.024			0.768944			0.384472	+	0.923137i	$0.374383\pi$
$992$	−828.904	+	1140.89i	−0.835588	+	1.15009i
$993$	−416.039	+	1280.44i	−0.418972	+	1.28946i
$994$	−53.2260	−	163.813i	−0.0535473	−	0.164802i
$995$		0			0
$996$	−659.886	−	908.255i	−0.662536	−	0.911903i
$997$	−1146.56	+	372.540i	−1.15001	+	0.373661i	−0.821147	−	0.570716i	$-0.806666\pi$
$997$	−1146.56	+	372.540i	−1.15001	+	0.373661i	−0.328864	+	0.944377i	$0.606666\pi$
$998$	−1538.71	−	499.958i	−1.54180	−	0.500960i
$999$	578.435	+	420.257i	0.579014	+	0.420678i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	275.3.x.e.51.1		4
5.2	odd	4		275.3.q.d.249.2		8
5.3	odd	4		275.3.q.d.249.1		8
5.4	even	2		11.3.d.a.7.1	✓	4
11.8	odd	10	inner	275.3.x.e.151.1		4
15.14	odd	2		99.3.k.a.73.1		4
20.19	odd	2		176.3.n.a.161.1		4
55.4	even	10		121.3.d.a.112.1		4
55.8	even	20		275.3.q.d.74.2		8
55.9	even	10		121.3.d.c.94.1		4
55.14	even	10		121.3.d.d.118.1		4
55.19	odd	10		11.3.d.a.8.1	yes	4
55.24	odd	10		121.3.d.a.94.1		4
55.29	odd	10		121.3.d.c.112.1		4
55.39	odd	10		121.3.b.b.120.4		4
55.49	even	10		121.3.b.b.120.1		4
55.52	even	20		275.3.q.d.74.1		8
55.54	odd	2		121.3.d.d.40.1		4
165.74	even	10		99.3.k.a.19.1		4
165.104	odd	10		1089.3.c.e.604.4		4
165.149	even	10		1089.3.c.e.604.1		4
220.19	even	10		176.3.n.a.129.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
11.3.d.a.7.1	✓	4	5.4	even	2
11.3.d.a.8.1	yes	4	55.19	odd	10
99.3.k.a.19.1		4	165.74	even	10
99.3.k.a.73.1		4	15.14	odd	2
121.3.b.b.120.1		4	55.49	even	10
121.3.b.b.120.4		4	55.39	odd	10
121.3.d.a.94.1		4	55.24	odd	10
121.3.d.a.112.1		4	55.4	even	10
121.3.d.c.94.1		4	55.9	even	10
121.3.d.c.112.1		4	55.29	odd	10
121.3.d.d.40.1		4	55.54	odd	2
121.3.d.d.118.1		4	55.14	even	10
176.3.n.a.129.1		4	220.19	even	10
176.3.n.a.161.1		4	20.19	odd	2
275.3.q.d.74.1		8	55.52	even	20
275.3.q.d.74.2		8	55.8	even	20
275.3.q.d.249.1		8	5.3	odd	4
275.3.q.d.249.2		8	5.2	odd	4
275.3.x.e.51.1		4	1.1	even	1	trivial
275.3.x.e.151.1		4	11.8	odd	10	inner
1089.3.c.e.604.1		4	165.149	even	10
1089.3.c.e.604.4		4	165.104	odd	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 275 = 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	275.x (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.80902 - 2.48990i) q^{2} +(-1.11803 + 3.44095i) q^{3} +(-1.69098 - 5.20431i) q^{4} +(6.54508 + 9.00854i) q^{6} +(0.854102 - 0.277515i) q^{7} +(-4.30902 - 1.40008i) q^{8} +(-3.30902 - 2.40414i) q^{9} +(10.8713 + 1.67760i) q^{11} +19.7984 q^{12} +(5.00000 - 6.88191i) q^{13} +(0.854102 - 2.62866i) q^{14} +(6.42705 - 4.66953i) q^{16} +(14.5344 + 20.0049i) q^{17} +(-11.9721 + 3.88998i) q^{18} +(11.2812 + 3.66547i) q^{19} +3.24920i q^{21} +(23.8435 - 24.0337i) q^{22} +7.23607 q^{23} +(9.63525 - 13.2618i) q^{24} +(-8.09017 - 24.8990i) q^{26} +(-14.3713 + 10.4414i) q^{27} +(-2.88854 - 3.97574i) q^{28} +(-3.29180 + 1.06957i) q^{29} +(-26.7984 - 19.4702i) q^{31} -42.5730i q^{32} +(-17.9271 + 35.5321i) q^{33} +76.1033 q^{34} +(-6.91641 + 21.2865i) q^{36} +(-12.4377 - 38.2793i) q^{37} +(29.5344 - 21.4580i) q^{38} +(18.0902 + 24.8990i) q^{39} +(1.24265 + 0.403760i) q^{41} +(8.09017 + 5.87785i) q^{42} +33.0625i q^{43} +(-9.65248 - 59.4145i) q^{44} +(13.0902 - 18.0171i) q^{46} +(-7.03444 + 21.6498i) q^{47} +(8.88197 + 27.3359i) q^{48} +(-38.9894 + 28.3274i) q^{49} +(-85.0861 + 27.6462i) q^{51} +(-44.2705 - 14.3844i) q^{52} +(-63.5410 - 46.1653i) q^{53} +54.6718i q^{54} -4.06888 q^{56} +(-25.2254 + 34.7198i) q^{57} +(-3.29180 + 10.1311i) q^{58} +(9.66312 + 29.7400i) q^{59} +(-16.5066 - 22.7194i) q^{61} +(-96.9574 + 31.5034i) q^{62} +(-3.49342 - 1.13508i) q^{63} +(-80.2943 - 58.3372i) q^{64} +(56.0410 + 108.915i) q^{66} +76.5066 q^{67} +(79.5344 - 109.470i) q^{68} +(-8.09017 + 24.8990i) q^{69} +(50.4164 - 36.6297i) q^{71} +(10.8926 + 14.9924i) q^{72} +(-89.5344 + 29.0915i) q^{73} +(-117.812 - 38.2793i) q^{74} -64.9089i q^{76} +(9.75078 - 1.58411i) q^{77} +94.7214 q^{78} +(38.7426 - 53.3247i) q^{79} +(-31.2361 - 96.1347i) q^{81} +(3.25329 - 2.36365i) q^{82} +(-33.3303 - 45.8752i) q^{83} +(16.9098 - 5.49434i) q^{84} +(82.3222 + 59.8106i) q^{86} -12.5227i q^{87} +(-44.4959 - 22.4496i) q^{88} -62.2968 q^{89} +(2.36068 - 7.26543i) q^{91} +(-12.2361 - 37.6587i) q^{92} +(96.9574 - 70.4437i) q^{93} +(41.1803 + 56.6799i) q^{94} +(146.492 + 47.5981i) q^{96} +(58.5795 + 42.5605i) q^{97} +148.324i q^{98} +(-31.9402 - 31.6874i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 5 q^{2} - 9 q^{4} + 15 q^{6} - 10 q^{7} - 15 q^{8} - 11 q^{9} + q^{11} + 30 q^{12} + 20 q^{13} - 10 q^{14} + 19 q^{16} - 30 q^{18} + 25 q^{19} + 35 q^{22} + 20 q^{23} + 5 q^{24} - 10 q^{26} - 15 q^{27}+ \cdots + 31 q^{99}+O(q^{100}) \) 4 * q + 5 * q^2 - 9 * q^4 + 15 * q^6 - 10 * q^7 - 15 * q^8 - 11 * q^9 + q^11 + 30 * q^12 + 20 * q^13 - 10 * q^14 + 19 * q^16 - 30 * q^18 + 25 * q^19 + 35 * q^22 + 20 * q^23 + 5 * q^24 - 10 * q^26 - 15 * q^27 + 60 * q^28 - 40 * q^29 - 58 * q^31 - 65 * q^33 + 130 * q^34 + 26 * q^36 - 90 * q^37 + 60 * q^38 + 50 * q^39 - 80 * q^41 + 10 * q^42 + 24 * q^44 + 30 * q^46 + 30 * q^47 + 40 * q^48 - 109 * q^49 - 195 * q^51 - 110 * q^52 - 120 * q^53 + 100 * q^56 - 45 * q^57 - 40 * q^58 + 23 * q^59 + 10 * q^61 - 200 * q^62 - 90 * q^63 - 149 * q^64 + 90 * q^66 + 230 * q^67 + 260 * q^68 - 10 * q^69 + 148 * q^71 + 95 * q^72 - 300 * q^73 - 270 * q^74 + 200 * q^77 + 200 * q^78 + 70 * q^79 - 116 * q^81 - 25 * q^82 - 225 * q^83 + 90 * q^84 + 175 * q^86 - 55 * q^88 + 122 * q^89 - 80 * q^91 - 40 * q^92 + 200 * q^93 + 120 * q^94 + 340 * q^96 + 165 * q^97 + 31 * q^99

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