LMFDB - Embedded newform 275.3.q.d.74.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [275,3,Mod(24,275)] 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([5, 1])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("275.24"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 275 = 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	275.q (of order $10$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,0,18,0,30] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)

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

Self dual:	no
Analytic conductor:	$7.49320726991$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{10})$
Coefficient field:	$\Q(\zeta_{20})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{6} + x^{4} - x^{2} + 1 $ x^8 - x^6 + x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 5 $
Twist minimal:	no (minimal twist has level 11)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			74.2
Root			$-0.951057 + 0.309017i$ of defining polynomial
Character	$\chi$	$=$	275.74
Dual form			275.3.q.d.249.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.48990 - 1.80902i) q^{2} +(3.44095 - 1.11803i) q^{3} +(1.69098 - 5.20431i) q^{4} +(6.54508 - 9.00854i) q^{6} +(0.277515 - 0.854102i) q^{7} +(-1.40008 - 4.30902i) q^{8} +(3.30902 - 2.40414i) q^{9} +(10.8713 - 1.67760i) q^{11} -19.7984i q^{12} +(-6.88191 + 5.00000i) q^{13} +(-0.854102 - 2.62866i) q^{14} +(6.42705 + 4.66953i) q^{16} +(-20.0049 - 14.5344i) q^{17} +(3.88998 - 11.9721i) q^{18} +(-11.2812 + 3.66547i) q^{19} -3.24920i q^{21} +(24.0337 - 23.8435i) q^{22} +7.23607i q^{23} +(-9.63525 - 13.2618i) q^{24} +(-8.09017 + 24.8990i) q^{26} +(-10.4414 + 14.3713i) q^{27} +(-3.97574 - 2.88854i) q^{28} +(3.29180 + 1.06957i) q^{29} +(-26.7984 + 19.4702i) q^{31} +42.5730 q^{32} +(35.5321 - 17.9271i) q^{33} -76.1033 q^{34} +(-6.91641 - 21.2865i) q^{36} +(38.2793 + 12.4377i) q^{37} +(-21.4580 + 29.5344i) q^{38} +(-18.0902 + 24.8990i) q^{39} +(1.24265 - 0.403760i) q^{41} +(-5.87785 - 8.09017i) q^{42} +33.0625 q^{43} +(9.65248 - 59.4145i) q^{44} +(13.0902 + 18.0171i) q^{46} +(-21.6498 + 7.03444i) q^{47} +(27.3359 + 8.88197i) q^{48} +(38.9894 + 28.3274i) q^{49} +(-85.0861 - 27.6462i) q^{51} +(14.3844 + 44.2705i) q^{52} +(-46.1653 - 63.5410i) q^{53} +54.6718i q^{54} -4.06888 q^{56} +(-34.7198 + 25.2254i) q^{57} +(10.1311 - 3.29180i) q^{58} +(-9.66312 + 29.7400i) q^{59} +(-16.5066 + 22.7194i) q^{61} +(-31.5034 + 96.9574i) q^{62} +(-1.13508 - 3.49342i) q^{63} +(80.2943 - 58.3372i) q^{64} +(56.0410 - 108.915i) q^{66} -76.5066i q^{67} +(-109.470 + 79.5344i) q^{68} +(8.09017 + 24.8990i) q^{69} +(50.4164 + 36.6297i) q^{71} +(-14.9924 - 10.8926i) q^{72} +(29.0915 - 89.5344i) q^{73} +(117.812 - 38.2793i) q^{74} +64.9089i q^{76} +(1.58411 - 9.75078i) q^{77} +94.7214i q^{78} +(-38.7426 - 53.3247i) q^{79} +(-31.2361 + 96.1347i) q^{81} +(2.36365 - 3.25329i) q^{82} +(-45.8752 - 33.3303i) q^{83} +(-16.9098 - 5.49434i) q^{84} +(82.3222 - 59.8106i) q^{86} +12.5227 q^{87} +(-22.4496 - 44.4959i) q^{88} +62.2968 q^{89} +(2.36068 + 7.26543i) q^{91} +(37.6587 + 12.2361i) q^{92} +(-70.4437 + 96.9574i) q^{93} +(-41.1803 + 56.6799i) q^{94} +(146.492 - 47.5981i) q^{96} +(-42.5605 - 58.5795i) q^{97} +148.324 q^{98} +(31.9402 - 31.6874i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 18 q^{4} + 30 q^{6} + 22 q^{9} + 2 q^{11} + 20 q^{14} + 38 q^{16} - 50 q^{19} - 10 q^{24} - 20 q^{26} + 80 q^{29} - 116 q^{31} - 260 q^{34} + 52 q^{36} - 100 q^{39} - 160 q^{41} - 48 q^{44} + 60 q^{46}+ \cdots - 62 q^{99}+O(q^{100}) $ 8 * q + 18 * q^4 + 30 * q^6 + 22 * q^9 + 2 * q^11 + 20 * q^14 + 38 * q^16 - 50 * q^19 - 10 * q^24 - 20 * q^26 + 80 * q^29 - 116 * q^31 - 260 * q^34 + 52 * q^36 - 100 * q^39 - 160 * q^41 - 48 * q^44 + 60 * q^46 + 218 * q^49 - 390 * q^51 + 200 * q^56 - 46 * q^59 + 20 * q^61 + 298 * q^64 + 180 * q^66 + 20 * q^69 + 296 * q^71 + 540 * q^74 - 140 * q^79 - 232 * q^81 - 180 * q^84 + 350 * q^86 - 244 * q^89 - 160 * q^91 - 240 * q^94 + 680 * q^96 - 62 * q^99

Character values

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

$n$	$101$	$177$
$\chi(n)$	$e\left(\frac{3}{10}\right)$	$-1$

Coefficient data

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

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

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

$2$	2.48990	−	1.80902i	1.24495	−	0.904508i	0.247031	−	0.969007i	$-0.420545\pi$
$2$	2.48990	−	1.80902i	1.24495	−	0.904508i	0.997918	+	0.0644990i	$0.0205449\pi$
$3$	3.44095	−	1.11803i	1.14698	−	0.372678i	0.326978	−	0.945032i	$-0.393970\pi$
$3$	3.44095	−	1.11803i	1.14698	−	0.372678i	0.820007	+	0.572354i	$0.193970\pi$
$4$	1.69098	−	5.20431i	0.422746	−	1.30108i
$5$		0			0
$5$		0			0
$6$	6.54508	−	9.00854i	1.09085	−	1.50142i
$7$	0.277515	−	0.854102i	0.0396449	−	0.122015i	−0.929275	−	0.369388i	$-0.879567\pi$
$7$	0.277515	−	0.854102i	0.0396449	−	0.122015i	0.968920	+	0.247373i	$0.0795674\pi$
$8$	−1.40008	−	4.30902i	−0.175011	−	0.538627i
$9$	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
$12$		−	19.7984i		−	1.64986i
$13$	−6.88191	+	5.00000i	−0.529378	+	0.384615i	−0.820125	−	0.572185i	$-0.806096\pi$
$13$	−6.88191	+	5.00000i	−0.529378	+	0.384615i	0.290747	+	0.956800i	$0.406096\pi$
$14$	−0.854102	−	2.62866i	−0.0610073	−	0.187761i
$15$		0			0
$16$	6.42705	+	4.66953i	0.401691	+	0.291845i
$17$	−20.0049	−	14.5344i	−1.17676	−	0.854967i	−0.184959	−	0.982746i	$-0.559215\pi$
$17$	−20.0049	−	14.5344i	−1.17676	−	0.854967i	−0.991803	+	0.127779i	$0.959215\pi$
$18$	3.88998	−	11.9721i	0.216110	−	0.665119i
$19$	−11.2812	+	3.66547i	−0.593745	+	0.192919i	−0.590449	−	0.807075i	$-0.701049\pi$
$19$	−11.2812	+	3.66547i	−0.593745	+	0.192919i	−0.00329617	+	0.999995i	$0.501049\pi$
$20$		0			0
$21$		−	3.24920i		−	0.154724i
$22$	24.0337	−	23.8435i	1.09244	−	1.08379i
$23$			7.23607i			0.314612i	0.987550	+	0.157306i	$0.0502808\pi$
$23$			7.23607i			0.314612i	−0.987550	+	0.157306i	$0.949719\pi$
$24$	−9.63525	−	13.2618i	−0.401469	−	0.552575i
$25$		0			0
$26$	−8.09017	+	24.8990i	−0.311160	+	0.957653i
$27$	−10.4414	+	14.3713i	−0.386718	+	0.532271i
$28$	−3.97574	−	2.88854i	−0.141991	−	0.103162i
$29$	3.29180	+	1.06957i	0.113510	+	0.0368817i	0.365221	−	0.930921i	$-0.380993\pi$
$29$	3.29180	+	1.06957i	0.113510	+	0.0368817i	−0.251711	+	0.967802i	$0.580993\pi$
$30$		0			0
$31$	−26.7984	+	19.4702i	−0.864464	+	0.628070i	−0.929096	−	0.369840i	$-0.879413\pi$
$31$	−26.7984	+	19.4702i	−0.864464	+	0.628070i	0.0646320	+	0.997909i	$0.479413\pi$
$32$	42.5730			1.33041
$33$	35.5321	−	17.9271i	1.07673	−	0.543244i
$34$	−76.1033			−2.23833
$35$		0			0
$36$	−6.91641	−	21.2865i	−0.192122	−	0.591292i
$37$	38.2793	+	12.4377i	1.03458	+	0.336154i	0.776598	−	0.629997i	$-0.216944\pi$
$37$	38.2793	+	12.4377i	1.03458	+	0.336154i	0.257978	+	0.966151i	$0.416944\pi$
$38$	−21.4580	+	29.5344i	−0.564685	+	0.777222i
$39$	−18.0902	+	24.8990i	−0.463851	+	0.638435i
$40$		0			0
$41$	1.24265	−	0.403760i	0.0303084	−	0.00984781i	−0.293824	−	0.955860i	$-0.594928\pi$
$41$	1.24265	−	0.403760i	0.0303084	−	0.00984781i	0.324132	+	0.946012i	$0.394928\pi$
$42$	−5.87785	−	8.09017i	−0.139949	−	0.192623i
$43$	33.0625			0.768895			0.384447	−	0.923147i	$-0.374392\pi$
$43$	33.0625			0.768895			0.384447	+	0.923147i	$0.374392\pi$
$44$	9.65248	−	59.4145i	0.219374	−	1.35033i
$45$		0			0
$46$	13.0902	+	18.0171i	0.284569	+	0.391676i
$47$	−21.6498	+	7.03444i	−0.460634	+	0.149669i	−0.530136	−	0.847913i	$-0.677859\pi$
$47$	−21.6498	+	7.03444i	−0.460634	+	0.149669i	0.0695019	+	0.997582i	$0.477859\pi$
$48$	27.3359	+	8.88197i	0.569498	+	0.185041i
$49$	38.9894	+	28.3274i	0.795701	+	0.578111i
$50$		0			0
$51$	−85.0861	−	27.6462i	−1.66835	−	0.542081i
$52$	14.3844	+	44.2705i	0.276622	+	0.851356i
$53$	−46.1653	−	63.5410i	−0.871043	−	1.19889i	−0.978822	−	0.204712i	$-0.934374\pi$
$53$	−46.1653	−	63.5410i	−0.871043	−	1.19889i	0.107780	−	0.994175i	$-0.465626\pi$
$54$			54.6718i			1.01244i
$55$		0			0
$56$	−4.06888			−0.0726586
$57$	−34.7198	+	25.2254i	−0.609120	+	0.442551i
$58$	10.1311	−	3.29180i	0.174674	−	0.0567551i
$59$	−9.66312	+	29.7400i	−0.163782	+	0.504068i	−0.998944	−	0.0459347i	$-0.985373\pi$
$59$	−9.66312	+	29.7400i	−0.163782	+	0.504068i	0.835163	+	0.550003i	$0.185373\pi$
$60$		0			0
$61$	−16.5066	+	22.7194i	−0.270600	+	0.372448i	−0.922592	−	0.385777i	$-0.873933\pi$
$61$	−16.5066	+	22.7194i	−0.270600	+	0.372448i	0.651992	+	0.758226i	$0.273933\pi$
$62$	−31.5034	+	96.9574i	−0.508119	+	1.56383i
$63$	−1.13508	−	3.49342i	−0.0180172	−	0.0554511i
$64$	80.2943	−	58.3372i	1.25460	−	0.911519i
$65$		0			0
$66$	56.0410	−	108.915i	0.849106	−	1.65022i
$67$		−	76.5066i		−	1.14189i	−0.820989	−	0.570945i	$-0.806577\pi$
$67$		−	76.5066i		−	1.14189i	0.820989	−	0.570945i	$-0.193423\pi$
$68$	−109.470	+	79.5344i	−1.60985	+	1.16962i
$69$	8.09017	+	24.8990i	0.117249	+	0.360855i
$70$		0			0
$71$	50.4164	+	36.6297i	0.710090	+	0.515911i	0.883203	−	0.468991i	$-0.155382\pi$
$71$	50.4164	+	36.6297i	0.710090	+	0.515911i	−0.173113	+	0.984902i	$0.555382\pi$
$72$	−14.9924	−	10.8926i	−0.208228	−	0.151286i
$73$	29.0915	−	89.5344i	0.398514	−	1.22650i	−0.527677	−	0.849445i	$-0.676937\pi$
$73$	29.0915	−	89.5344i	0.398514	−	1.22650i	0.926191	−	0.377054i	$-0.123063\pi$
$74$	117.812	−	38.2793i	1.59205	−	0.517288i
$75$		0			0
$76$			64.9089i			0.854064i
$77$	1.58411	−	9.75078i	0.0205729	−	0.126633i
$78$			94.7214i			1.21438i
$79$	−38.7426	−	53.3247i	−0.490413	−	0.674996i	0.490051	−	0.871694i	$-0.336978\pi$
$79$	−38.7426	−	53.3247i	−0.490413	−	0.674996i	−0.980464	+	0.196698i	$0.936978\pi$
$80$		0			0
$81$	−31.2361	+	96.1347i	−0.385630	+	1.18685i
$82$	2.36365	−	3.25329i	0.0288250	−	0.0396743i
$83$	−45.8752	−	33.3303i	−0.552714	−	0.401570i	0.276071	−	0.961137i	$-0.410967\pi$
$83$	−45.8752	−	33.3303i	−0.552714	−	0.401570i	−0.828785	+	0.559567i	$0.810967\pi$
$84$	−16.9098	−	5.49434i	−0.201308	−	0.0654088i
$85$		0			0
$86$	82.3222	−	59.8106i	0.957235	−	0.695472i
$87$	12.5227			0.143939
$88$	−22.4496	−	44.4959i	−0.255109	−	0.505636i
$89$	62.2968			0.699964			0.349982	−	0.936756i	$-0.386188\pi$
$89$	62.2968			0.699964			0.349982	+	0.936756i	$0.386188\pi$
$90$		0			0
$91$	2.36068	+	7.26543i	0.0259415	+	0.0798398i
$92$	37.6587	+	12.2361i	0.409334	+	0.133001i
$93$	−70.4437	+	96.9574i	−0.757459	+	1.04255i
$94$	−41.1803	+	56.6799i	−0.438089	+	0.602977i
$95$		0			0
$96$	146.492	−	47.5981i	1.52596	−	0.495813i
$97$	−42.5605	−	58.5795i	−0.438768	−	0.603913i	0.531170	−	0.847266i	$-0.321753\pi$
$97$	−42.5605	−	58.5795i	−0.438768	−	0.603913i	−0.969938	+	0.243353i	$0.921753\pi$
$98$	148.324			1.51351
$99$	31.9402	−	31.6874i	0.322628	−	0.320075i
$100$		0			0
$101$	−37.8409	−	52.0836i	−0.374663	−	0.515679i	0.579498	−	0.814974i	$-0.303249\pi$
$101$	−37.8409	−	52.0836i	−0.374663	−	0.515679i	−0.954161	+	0.299295i	$0.903249\pi$
$102$	−261.868	+	85.0861i	−2.56733	+	0.834177i
$103$	31.0139	+	10.0770i	0.301105	+	0.0978351i	0.455673	−	0.890147i	$-0.349399\pi$
$103$	31.0139	+	10.0770i	0.301105	+	0.0978351i	−0.154568	+	0.987982i	$0.549399\pi$
$104$	31.1803	+	22.6538i	0.299811	+	0.217825i
$105$		0			0
$106$	−229.894	−	74.6969i	−2.16881	−	0.704688i
$107$	−1.66987	−	5.13932i	−0.0156062	−	0.0480310i	0.942950	−	0.332934i	$-0.108039\pi$
$107$	−1.66987	−	5.13932i	−0.0156062	−	0.0480310i	−0.958556	+	0.284903i	$0.908039\pi$
$108$	57.1366	+	78.6418i	0.529043	+	0.728165i
$109$			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
$112$	5.77185	−	4.19350i	0.0515344	−	0.0374419i
$113$	−44.2304	+	14.3713i	−0.391419	+	0.127180i	−0.498113	−	0.867112i	$-0.665974\pi$
$113$	−44.2304	+	14.3713i	−0.391419	+	0.127180i	0.106694	+	0.994292i	$0.465974\pi$
$114$	−40.8156	+	125.617i	−0.358032	+	1.10191i
$115$		0			0
$116$	11.1327	−	15.3229i	0.0959719	−	0.132094i
$117$	−10.7516	+	33.0902i	−0.0918944	+	0.282822i
$118$	29.7400	+	91.5304i	0.252034	+	0.775681i
$119$	−17.9656	+	13.0527i	−0.150971	+	0.109687i
$120$		0			0
$121$	115.371	−	36.4754i	0.953482	−	0.301450i
$122$			86.4296i			0.708439i
$123$	3.82447	−	2.77864i	0.0310933	−	0.0225906i
$124$	56.0132	+	172.391i	0.451719	+	1.39025i
$125$		0			0
$126$	−9.14590	−	6.64488i	−0.0725865	−	0.0527372i
$127$	67.4970	+	49.0395i	0.531473	+	0.386138i	0.820908	−	0.571060i	$-0.193468\pi$
$127$	67.4970	+	49.0395i	0.531473	+	0.386138i	−0.289436	+	0.957197i	$0.593468\pi$
$128$	41.7685	−	128.550i	0.326316	−	1.00430i
$129$	113.766	−	36.9650i	0.881910	−	0.286550i
$130$		0			0
$131$			85.0901i			0.649543i	0.945793	+	0.324771i	$0.105287\pi$
$131$			85.0901i			0.649543i	−0.945793	+	0.324771i	$0.894713\pi$
$132$	−33.2137	−	215.235i	−0.251619	−	1.63056i
$133$			10.6525i			0.0800938i
$134$	−138.402	−	190.494i	−1.03285	−	1.42159i
$135$		0			0
$136$	−34.6205	+	106.551i	−0.254563	+	0.783464i
$137$	34.5281	−	47.5238i	0.252030	−	0.346889i	−0.664191	−	0.747563i	$-0.731224\pi$
$137$	34.5281	−	47.5238i	0.252030	−	0.346889i	0.916221	+	0.400674i	$0.131224\pi$
$138$	65.1864	+	47.3607i	0.472365	+	0.343193i
$139$	−153.108	−	49.7479i	−1.10150	−	0.357899i	−0.298820	−	0.954310i	$-0.596593\pi$
$139$	−153.108	−	49.7479i	−1.10150	−	0.357899i	−0.802679	+	0.596411i	$0.796593\pi$
$140$		0			0
$141$	−66.6312	+	48.4104i	−0.472562	+	0.343336i
$142$	191.795			1.35067
$143$	−66.4275	+	65.9017i	−0.464528	+	0.460851i
$144$	32.4934			0.225649
$145$		0			0
$146$	−89.5344	−	275.559i	−0.613250	−	1.88739i
$147$	165.832	+	53.8820i	1.12811	+	0.366544i
$148$	129.459	−	178.185i	0.874725	−	1.20396i
$149$	151.103	−	207.976i	1.01412	−	1.39581i	0.0978685	−	0.995199i	$-0.468798\pi$
$149$	151.103	−	207.976i	1.01412	−	1.39581i	0.916248	−	0.400612i	$-0.131202\pi$
$150$		0			0
$151$	−274.087	+	89.0563i	−1.81515	+	0.589777i	−0.815202	+	0.579176i	$0.803374\pi$
$151$	−274.087	+	89.0563i	−1.81515	+	0.589777i	−0.999944	+	0.0106004i	$0.996626\pi$
$152$	31.5891	+	43.4787i	0.207823	+	0.286044i
$153$	−101.140			−0.661043
$154$	−13.6950	−	27.1441i	−0.0889289	−	0.176261i
$155$		0			0
$156$	98.9919	+	136.251i	0.634563	+	0.873401i
$157$	−263.081	+	85.4803i	−1.67568	+	0.544460i	−0.984065	−	0.177809i	$-0.943099\pi$
$157$	−263.081	+	85.4803i	−1.67568	+	0.544460i	−0.691612	+	0.722270i	$0.743099\pi$
$158$	−192.930	−	62.6869i	−1.22108	−	0.396753i
$159$	−229.894	−	167.027i	−1.44587	−	1.05049i
$160$		0			0
$161$	6.18034	+	2.00811i	0.0383872	+	0.0124728i
$162$	96.1347	+	295.872i	0.593424	+	1.82637i
$163$	−40.7721	−	56.1180i	−0.250136	−	0.344282i	0.665423	−	0.746466i	$-0.268251\pi$
$163$	−40.7721	−	56.1180i	−0.250136	−	0.344282i	−0.915559	+	0.402184i	$0.868251\pi$
$164$		−	7.14987i		−	0.0435967i
$165$		0			0
$166$	−174.520			−1.05132
$167$	233.798	−	169.864i	1.39999	−	1.01715i	0.405303	−	0.914182i	$-0.367166\pi$
$167$	233.798	−	169.864i	1.39999	−	1.01715i	0.994685	−	0.102968i	$-0.0328340\pi$
$168$	−14.0008	+	4.54915i	−0.0833384	+	0.0270783i
$169$	−29.8632	+	91.9095i	−0.176705	+	0.543843i
$170$		0			0
$171$	−28.5172	+	39.2506i	−0.166767	+	0.229536i
$172$	55.9081	−	172.067i	0.325047	−	1.00039i
$173$	−56.6144	−	174.241i	−0.327251	−	1.00717i	−0.970414	−	0.241445i	$-0.922379\pi$
$173$	−56.6144	−	174.241i	−0.327251	−	1.00717i	0.643164	−	0.765729i	$-0.277621\pi$
$174$	31.1803	−	22.6538i	0.179197	−	0.130194i
$175$		0			0
$176$	77.7041	+	39.9819i	0.441501	+	0.227170i
$177$			113.138i			0.639196i
$178$	155.113	−	112.696i	0.871420	−	0.633124i
$179$	−0.633702	−	1.95033i	−0.00354024	−	0.0108957i	0.949271	−	0.314460i	$-0.101823\pi$
$179$	−0.633702	−	1.95033i	−0.00354024	−	0.0108957i	−0.952811	+	0.303564i	$0.901823\pi$
$180$		0			0
$181$	58.9787	+	42.8505i	0.325849	+	0.236743i	0.738667	−	0.674070i	$-0.235455\pi$
$181$	58.9787	+	42.8505i	0.325849	+	0.236743i	−0.412818	+	0.910814i	$0.635455\pi$
$182$	19.0211	+	13.8197i	0.104512	+	0.0759322i
$183$	−31.3974	+	96.6312i	−0.171570	+	0.528039i
$184$	31.1803	−	10.1311i	0.169458	−	0.0550604i
$185$		0			0
$186$			368.848i			1.98305i
$187$	−241.863	−	124.448i	−1.29339	−	0.665499i
$188$			124.567i			0.662592i
$189$	9.37694	+	12.9063i	0.0496134	+	0.0682870i
$190$		0			0
$191$	−32.0770	+	98.7229i	−0.167942	+	0.516874i	−0.999241	−	0.0389523i	$-0.987598\pi$
$191$	−32.0770	+	98.7229i	−0.167942	+	0.516874i	0.831299	+	0.555826i	$0.187598\pi$
$192$	211.066	−	290.508i	1.09930	−	1.51306i
$193$	−278.314	−	202.207i	−1.44204	−	1.04770i	−0.987611	−	0.156919i	$-0.949844\pi$
$193$	−278.314	−	202.207i	−1.44204	−	1.04770i	−0.454428	−	0.890784i	$-0.650156\pi$
$194$	−211.943	−	68.8644i	−1.09249	−	0.354971i
$195$		0			0
$196$	213.355	−	155.012i	1.08855	−	0.790875i
$197$	99.0718			0.502903			0.251451	−	0.967870i	$-0.419092\pi$
$197$	99.0718			0.502903			0.251451	+	0.967870i	$0.419092\pi$
$198$	22.2048	−	136.679i	0.112146	−	0.690297i
$199$	153.469			0.771201			0.385601	−	0.922666i	$-0.373994\pi$
$199$	153.469			0.771201			0.385601	+	0.922666i	$0.373994\pi$
$200$		0			0
$201$	−85.5370	−	263.256i	−0.425557	−	1.30973i
$202$	−188.440	−	61.2279i	−0.932872	−	0.303109i
$203$	1.82704	−	2.51471i	0.00900021	−	0.0123877i
$204$	−287.758	+	396.065i	−1.41058	+	1.94150i
$205$		0			0
$206$	95.4508	−	31.0139i	0.463354	−	0.150553i
$207$	17.3965	+	23.9443i	0.0840412	+	0.115673i
$208$	−67.5780			−0.324894
$209$	−116.492	+	58.7737i	−0.557377	+	0.281214i
$210$		0			0
$211$	−196.035	−	269.820i	−0.929078	−	1.27877i	−0.960218	−	0.279251i	$-0.909914\pi$
$211$	−196.035	−	269.820i	−0.929078	−	1.27877i	0.0311405	−	0.999515i	$-0.490086\pi$
$212$	−408.752	+	132.812i	−1.92807	+	0.626469i
$213$	214.434	+	69.6738i	1.00673	+	0.327107i
$214$	−13.4549	−	9.77557i	−0.0628734	−	0.0456802i
$215$		0			0
$216$	76.5451	+	24.8710i	0.354375	+	0.115144i
$217$	9.19256	+	28.2918i	0.0423620	+	0.130377i
$218$	247.839	+	341.122i	1.13688	+	1.56478i
$219$		−	340.609i		−	1.55529i
$220$		0			0
$221$	210.344			0.951785
$222$	362.587	−	263.435i	1.63327	−	1.18664i
$223$	108.395	−	35.2198i	0.486078	−	0.157936i	−0.0557176	−	0.998447i	$-0.517745\pi$
$223$	108.395	−	35.2198i	0.486078	−	0.157936i	0.541796	+	0.840510i	$0.317745\pi$
$224$	11.8146	−	36.3617i	0.0527439	−	0.162329i
$225$		0			0
$226$	−84.1312	+	115.797i	−0.372262	+	0.512375i
$227$	12.0564	−	37.1058i	0.0531120	−	0.163462i	−0.920982	−	0.389605i	$-0.872612\pi$
$227$	12.0564	−	37.1058i	0.0531120	−	0.163462i	0.974094	+	0.226143i	$0.0726116\pi$
$228$	72.5703	+	223.348i	0.318291	+	0.979599i
$229$	108.575	−	78.8847i	0.474129	−	0.344475i	−0.324919	−	0.945742i	$-0.605337\pi$
$229$	108.575	−	78.8847i	0.474129	−	0.344475i	0.799048	+	0.601267i	$0.205337\pi$
$230$		0			0
$231$	−5.45085	−	35.3231i	−0.0235968	−	0.152914i
$232$		−	15.6819i		−	0.0675944i
$233$	216.283	−	157.139i	0.928253	−	0.674415i	−0.0173116	−	0.999850i	$-0.505511\pi$
$233$	216.283	−	157.139i	0.928253	−	0.674415i	0.945564	+	0.325435i	$0.105511\pi$
$234$	33.0902	+	101.841i	0.141411	+	0.435218i
$235$		0			0
$236$	138.436	+	100.580i	0.586594	+	0.426185i
$237$	−192.930	−	140.172i	−0.814053	−	0.591444i
$238$	−21.1198	+	65.0000i	−0.0887386	+	0.273109i
$239$	−104.751	+	34.0356i	−0.438288	+	0.142408i	−0.519846	−	0.854260i	$-0.674010\pi$
$239$	−104.751	+	34.0356i	−0.438288	+	0.142408i	0.0815577	+	0.996669i	$0.474010\pi$
$240$		0			0
$241$		−	191.103i		−	0.792960i	−0.918043	−	0.396480i	$-0.870232\pi$
$241$		−	191.103i		−	0.792960i	0.918043	−	0.396480i	$-0.129768\pi$
$242$	221.278	−	299.529i	0.914373	−	1.23772i
$243$			205.843i			0.847090i
$244$	90.3262	+	124.323i	0.370189	+	0.509522i
$245$		0			0
$246$	4.49593	−	13.8371i	0.0182762	−	0.0562482i
$247$	59.3085	−	81.6312i	0.240116	−	0.330491i
$248$	121.417	+	88.2148i	0.489586	+	0.355705i
$249$	−195.119	−	63.3980i	−0.783610	−	0.254610i
$250$		0			0
$251$	345.559	−	251.063i	1.37673	−	1.00025i	0.379553	−	0.925170i	$-0.376078\pi$
$251$	345.559	−	251.063i	1.37673	−	1.00025i	0.997177	−	0.0750826i	$-0.0239221\pi$
$252$	−20.1003			−0.0797629
$253$	12.1392	+	78.6656i	0.0479811	+	0.310931i
$254$	256.774			1.01092
$255$		0			0
$256$	−5.87132	−	18.0701i	−0.0229349	−	0.0705862i
$257$	26.8964	+	8.73917i	0.104655	+	0.0340046i	0.360877	−	0.932614i	$-0.382478\pi$
$257$	26.8964	+	8.73917i	0.104655	+	0.0340046i	−0.256221	+	0.966618i	$0.582478\pi$
$258$	216.397	−	297.844i	0.838747	−	1.15444i
$259$	21.2461	−	29.2428i	0.0820313	−	0.112906i
$260$		0			0
$261$	13.4640	−	4.37472i	0.0515862	−	0.0167614i
$262$	153.929	+	211.866i	0.587517	+	0.808648i
$263$	94.5506			0.359508			0.179754	−	0.983712i	$-0.442470\pi$
$263$	94.5506			0.359508			0.179754	+	0.983712i	$0.442470\pi$
$264$	−126.996	−	128.009i	−0.481045	−	0.484883i
$265$		0			0
$266$	19.2705	+	26.5236i	0.0724455	+	0.0997127i
$267$	214.361	−	69.6500i	0.802848	−	0.260861i
$268$	−398.164	−	129.371i	−1.48569	−	0.482729i
$269$	189.305	+	137.538i	0.703736	+	0.511294i	0.881147	−	0.472843i	$-0.156772\pi$
$269$	189.305	+	137.538i	0.703736	+	0.511294i	−0.177411	+	0.984137i	$0.556772\pi$
$270$		0			0
$271$	136.400	+	44.3191i	0.503322	+	0.163539i	0.549663	−	0.835387i	$-0.314756\pi$
$271$	136.400	+	44.3191i	0.503322	+	0.163539i	−0.0463413	+	0.998926i	$0.514756\pi$
$272$	−60.7038	−	186.827i	−0.223176	−	0.686865i
$273$	16.2460	+	22.3607i	0.0595091	+	0.0819073i
$274$		−	180.791i		−	0.659822i
$275$		0			0
$276$	143.262			0.519067
$277$	−314.772	+	228.695i	−1.13636	+	0.825614i	−0.986608	−	0.163110i	$-0.947848\pi$
$277$	−314.772	+	228.695i	−1.13636	+	0.825614i	−0.149752	+	0.988724i	$0.547848\pi$
$278$	−471.219	+	153.108i	−1.69503	+	0.550749i
$279$	−41.8673	+	128.854i	−0.150062	+	0.461843i
$280$		0			0
$281$	−59.3860	+	81.7379i	−0.211338	+	0.290882i	−0.901505	−	0.432768i	$-0.857537\pi$
$281$	−59.3860	+	81.7379i	−0.211338	+	0.290882i	0.690167	+	0.723650i	$0.257537\pi$
$282$	−78.3297	+	241.074i	−0.277765	+	0.854872i
$283$	0.655123	+	2.01626i	0.00231492	+	0.00712460i	0.952207	−	0.305453i	$-0.0988077\pi$
$283$	0.655123	+	2.01626i	0.00231492	+	0.00712460i	−0.949892	+	0.312577i	$0.898808\pi$
$284$	275.885	−	200.443i	0.971428	−	0.705783i
$285$		0			0
$286$	−46.1803	+	284.257i	−0.161470	+	0.993905i
$287$		−	1.17340i		−	0.00408849i
$288$	140.875	−	102.352i	0.489149	−	0.355387i
$289$	99.6418	+	306.666i	0.344781	+	1.06113i
$290$		0			0
$291$	−211.943	−	153.985i	−0.728325	−	0.529159i
$292$	−416.772	−	302.802i	−1.42730	−	1.03699i
$293$	−145.272	+	447.100i	−0.495808	+	1.52594i	0.319886	+	0.947456i	$0.396355\pi$
$293$	−145.272	+	447.100i	−0.495808	+	1.52594i	−0.815694	+	0.578483i	$0.803645\pi$
$294$	510.377	−	165.832i	1.73598	−	0.564053i
$295$		0			0
$296$		−	182.360i		−	0.616081i
$297$	−89.4023	+	173.752i	−0.301018	+	0.585023i
$298$		−	791.187i		−	2.65499i
$299$	−36.1803	−	49.7980i	−0.121004	−	0.166548i
$300$		0			0
$301$	9.17531	−	28.2387i	0.0304828	−	0.0938163i
$302$	−521.345	+	717.569i	−1.72631	+	2.37606i
$303$	−188.440	−	136.910i	−0.621915	−	0.451848i
$304$	−89.6205	−	29.1195i	−0.294804	−	0.0957878i
$305$		0			0
$306$	−251.827	+	182.963i	−0.822965	+	0.597919i
$307$	−99.4185			−0.323839			−0.161919	−	0.986804i	$-0.551768\pi$
$307$	−99.4185			−0.323839			−0.161919	+	0.986804i	$0.551768\pi$
$308$	−48.0674	−	24.7326i	−0.156063	−	0.0803006i
$309$	117.984			0.381824
$310$		0			0
$311$	104.823	+	322.611i	0.337051	+	1.03734i	0.965703	+	0.259649i	$0.0836068\pi$
$311$	104.823	+	322.611i	0.337051	+	1.03734i	−0.628652	+	0.777686i	$0.716393\pi$
$312$	132.618	+	43.0902i	0.425057	+	0.138110i
$313$	−227.114	+	312.595i	−0.725603	+	0.998707i	0.273716	+	0.961810i	$0.411747\pi$
$313$	−227.114	+	312.595i	−0.725603	+	0.998707i	−0.999319	+	0.0368962i	$0.988253\pi$
$314$	−500.410	+	688.756i	−1.59366	+	2.19349i
$315$		0			0
$316$	−343.031	+	111.458i	−1.08554	+	0.352714i
$317$	148.752	+	204.740i	0.469249	+	0.645866i	0.976395	−	0.215994i	$-0.0692993\pi$
$317$	148.752	+	204.740i	0.469249	+	0.645866i	−0.507145	+	0.861860i	$0.669299\pi$
$318$	−874.567			−2.75021
$319$	37.5805	+	6.10532i	0.117807	+	0.0191389i
$320$		0			0
$321$	−11.4919	−	15.8172i	−0.0358002	−	0.0492748i
$322$	19.0211	−	6.18034i	0.0590718	−	0.0191936i
$323$	278.954	+	90.6378i	0.863636	+	0.280612i
$324$	447.495	+	325.124i	1.38116	+	1.00347i
$325$		0			0
$326$	−203.037	−	65.9707i	−0.622813	−	0.202364i
$327$	153.173	+	471.418i	0.468419	+	1.44165i
$328$	−3.47962	−	4.78928i	−0.0106086	−	0.0146015i
$329$			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	$0.309990\pi$
$332$	−251.035	+	182.388i	−0.756131	+	0.549361i
$333$	156.569	−	50.8723i	0.470177	−	0.152770i
$334$	274.846	−	845.889i	0.822892	−	2.53260i
$335$		0			0
$336$	15.1722	−	20.8828i	0.0451554	−	0.0621511i
$337$	25.4058	−	78.1910i	0.0753881	−	0.232021i	−0.906260	−	0.422720i	$-0.861075\pi$
$337$	25.4058	−	78.1910i	0.0753881	−	0.232021i	0.981649	+	0.190699i	$0.0610755\pi$
$338$	91.9095	+	282.868i	0.271921	+	0.836888i
$339$	−136.127	+	98.9021i	−0.401555	+	0.291747i
$340$		0			0
$341$	−258.671	+	256.623i	−0.758565	+	0.752561i
$342$			149.318i			0.436603i
$343$	70.6152	−	51.3050i	0.205875	−	0.149577i
$344$	−46.2902	−	142.467i	−0.134565	−	0.414147i
$345$		0			0
$346$	−456.169	−	331.426i	−1.31841	−	0.957879i
$347$	−185.620	−	134.861i	−0.534927	−	0.388647i	0.287270	−	0.957850i	$-0.407252\pi$
$347$	−185.620	−	134.861i	−0.534927	−	0.388647i	−0.822198	+	0.569202i	$0.807252\pi$
$348$	21.1757	−	65.1722i	0.0608498	−	0.187276i
$349$	−220.997	+	71.8062i	−0.633229	+	0.205749i	−0.608005	−	0.793933i	$-0.708030\pi$
$349$	−220.997	+	71.8062i	−0.633229	+	0.205749i	−0.0252240	+	0.999682i	$0.508030\pi$
$350$		0			0
$351$		−	151.109i		−	0.430510i
$352$	462.825	−	71.4205i	1.31484	−	0.202899i
$353$		−	34.6443i		−	0.0981426i	−0.998795	−	0.0490713i	$-0.984374\pi$
$353$		−	34.6443i		−	0.0981426i	0.998795	−	0.0490713i	$-0.0156262\pi$
$354$	204.668	+	281.702i	0.578159	+	0.795767i
$355$		0			0
$356$	105.343	−	324.212i	0.295907	−	0.910708i
$357$	−47.2253	+	65.0000i	−0.132284	+	0.182073i
$358$	−5.10604	−	3.70976i	−0.0142627	−	0.0103624i
$359$	429.681	+	139.612i	1.19688	+	0.388891i	0.838613	−	0.544728i	$-0.183367\pi$
$359$	429.681	+	139.612i	1.19688	+	0.388891i	0.358269	+	0.933618i	$0.383367\pi$
$360$		0			0
$361$	−178.226	+	129.489i	−0.493702	+	0.358695i
$362$	224.368			0.619802
$363$	356.207	−	254.499i	0.981286	−	0.701100i
$364$	41.8034			0.114845
$365$		0			0
$366$	96.6312	+	297.400i	0.264020	+	0.812569i
$367$	350.775	+	113.974i	0.955790	+	0.310555i	0.745066	−	0.666991i	$-0.232418\pi$
$367$	350.775	+	113.974i	0.955790	+	0.310555i	0.210724	+	0.977546i	$0.432418\pi$
$368$	−33.7890	+	46.5066i	−0.0918180	+	0.126377i
$369$	3.14124	−	4.32355i	0.00851284	−	0.0117169i
$370$		0			0
$371$	−67.0820	+	21.7963i	−0.180814	+	0.0587501i
$372$	385.477	+	530.564i	1.03623	+	1.42625i
$373$	593.166			1.59026			0.795129	−	0.606440i	$-0.207403\pi$
$373$	593.166			1.59026			0.795129	+	0.606440i	$0.207403\pi$
$374$	−827.344	+	127.671i	−2.21215	+	0.341366i
$375$		0			0
$376$	60.6231	+	83.4405i	0.161232	+	0.221916i
$377$	−28.0017	+	9.09830i	−0.0742750	+	0.0241334i
$378$	46.6953	+	15.1722i	0.123532	+	0.0401381i
$379$	−227.537	−	165.315i	−0.600361	−	0.436188i	0.245646	−	0.969360i	$-0.421000\pi$
$379$	−227.537	−	165.315i	−0.600361	−	0.436188i	−0.846007	+	0.533172i	$0.821000\pi$
$380$		0			0
$381$	287.082	+	93.2786i	0.753496	+	0.244826i
$382$	98.7229	+	303.838i	0.258437	+	0.795387i
$383$	374.747	+	515.795i	0.978452	+	1.34672i	0.937659	+	0.347556i	$0.112988\pi$
$383$	374.747	+	515.795i	0.978452	+	1.34672i	0.0407931	+	0.999168i	$0.487012\pi$
$384$		−	489.034i		−	1.27353i
$385$		0			0
$386$	−1058.77			−2.74292
$387$	109.404	−	79.4868i	0.282698	−	0.205392i
$388$	−376.835	+	122.441i	−0.971225	+	0.315570i
$389$	−206.259	+	634.801i	−0.530229	+	1.63188i	0.223507	+	0.974702i	$0.428249\pi$
$389$	−206.259	+	634.801i	−0.530229	+	1.63188i	−0.753737	+	0.657176i	$0.771751\pi$
$390$		0			0
$391$	105.172	−	144.757i	0.268983	−	0.370223i
$392$	67.4750	−	207.667i	0.172130	−	0.529762i
$393$	95.1336	+	292.791i	0.242070	+	0.745016i
$394$	246.679	−	179.223i	0.626088	−	0.454880i
$395$		0			0
$396$	−110.901	−	219.810i	−0.280052	−	0.555075i
$397$		−	5.37384i		−	0.0135361i	−0.999977	−	0.00676805i	$-0.997846\pi$
$397$		−	5.37384i		−	0.0135361i	0.999977	−	0.00676805i	$-0.00215436\pi$
$398$	382.122	−	277.628i	0.960106	−	0.697558i
$399$	11.9098	+	36.6547i	0.0298492	+	0.0918664i
$400$		0			0
$401$	228.786	+	166.223i	0.570539	+	0.414521i	0.835301	−	0.549793i	$-0.185293\pi$
$401$	228.786	+	166.223i	0.570539	+	0.414521i	−0.264762	+	0.964314i	$0.585293\pi$
$402$	−689.212	−	500.742i	−1.71446	−	1.24563i
$403$	87.0732	−	267.984i	0.216063	−	0.664972i
$404$	−335.048	+	108.864i	−0.829326	+	0.269464i
$405$		0			0
$406$		−	9.56652i		−	0.0235629i
$407$	437.012	+	70.9969i	1.07374	+	0.174440i
$408$			405.344i			0.993491i
$409$	18.2554	+	25.1265i	0.0446343	+	0.0614339i	0.830751	−	0.556644i	$-0.187911\pi$
$409$	18.2554	+	25.1265i	0.0446343	+	0.0614339i	−0.786116	+	0.618078i	$0.787911\pi$
$410$		0			0
$411$	65.6763	−	202.131i	0.159796	−	0.491802i
$412$	104.888	−	144.366i	0.254582	−	0.350402i
$413$	22.7194	+	16.5066i	0.0550105	+	0.0399675i
$414$	86.6312	+	28.1482i	0.209254	+	0.0679908i
$415$		0			0
$416$	−292.984	+	212.865i	−0.704288	+	0.511695i
$417$	−582.459			−1.39678
$418$	−183.730	+	357.076i	−0.439546	+	0.854250i
$419$	245.156			0.585098			0.292549	−	0.956251i	$-0.405497\pi$
$419$	245.156			0.585098			0.292549	+	0.956251i	$0.405497\pi$
$420$		0			0
$421$	−23.9211	−	73.6215i	−0.0568196	−	0.174873i	0.918619	−	0.395145i	$-0.129306\pi$
$421$	−23.9211	−	73.6215i	−0.0568196	−	0.174873i	−0.975439	+	0.220272i	$0.929306\pi$
$422$	−976.216	−	317.192i	−2.31331	−	0.751640i
$423$	−54.7277	+	75.3262i	−0.129380	+	0.178076i
$424$	−209.164	+	287.890i	−0.493312	+	0.678985i
$425$		0			0
$426$	659.959	−	214.434i	1.54920	−	0.503366i
$427$	14.8238	+	20.4033i	0.0347162	+	0.0477828i
$428$	−29.5703			−0.0690896
$429$	−154.894	+	301.033i	−0.361057	+	0.701708i
$430$		0			0
$431$	264.193	+	363.631i	0.612978	+	0.843692i	0.996818	−	0.0797077i	$-0.0253987\pi$
$431$	264.193	+	363.631i	0.612978	+	0.843692i	−0.383840	+	0.923399i	$0.625399\pi$
$432$	−134.215	+	43.6089i	−0.310682	+	0.100947i
$433$	−137.293	−	44.6093i	−0.317075	−	0.103024i	0.146156	−	0.989262i	$-0.453310\pi$
$433$	−137.293	−	44.6093i	−0.317075	−	0.103024i	−0.463231	+	0.886238i	$0.653310\pi$
$434$	74.0689	+	53.8142i	0.170666	+	0.123996i
$435$		0			0
$436$	713.002	+	231.668i	1.63533	+	0.531349i
$437$	−26.5236	−	81.6312i	−0.0606947	−	0.186799i
$438$	−616.168	−	848.082i	−1.40678	−	1.93626i
$439$			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
$442$	523.736	−	380.517i	1.18492	−	0.860897i
$443$	308.434	−	100.216i	0.696240	−	0.226222i	0.0605483	−	0.998165i	$-0.480715\pi$
$443$	308.434	−	100.216i	0.696240	−	0.226222i	0.635691	+	0.771943i	$0.280715\pi$
$444$	246.246	−	757.868i	0.554608	−	1.70691i
$445$		0			0
$446$	206.180	−	283.783i	0.462288	−	0.636285i
$447$	287.416	−	884.574i	0.642988	−	1.97891i
$448$	−27.5431	−	84.7690i	−0.0614801	−	0.189216i
$449$	−316.651	+	230.060i	−0.705236	+	0.512384i	−0.881633	−	0.471935i	$-0.843556\pi$
$449$	−316.651	+	230.060i	−0.705236	+	0.512384i	0.176397	+	0.984319i	$0.443556\pi$
$450$		0			0
$451$	12.8319	−	6.47407i	0.0284520	−	0.0143549i
$452$			254.490i			0.563032i
$453$	−843.553	+	612.877i	−1.86215	+	1.35293i
$454$	−37.1058	−	114.200i	−0.0817309	−	0.251542i
$455$		0			0
$456$	157.307	+	114.291i	0.344973	+	0.250637i
$457$	−42.2675	−	30.7092i	−0.0924891	−	0.0671973i	0.540580	−	0.841293i	$-0.318205\pi$
$457$	−42.2675	−	30.7092i	−0.0924891	−	0.0671973i	−0.633069	+	0.774096i	$0.718205\pi$
$458$	127.638	−	392.830i	0.278686	−	0.857707i
$459$	417.758	−	135.738i	0.910149	−	0.295725i
$460$		0			0
$461$		−	339.293i		−	0.735994i	−0.929827	−	0.367997i	$-0.880044\pi$
$461$		−	339.293i		−	0.735994i	0.929827	−	0.367997i	$-0.119956\pi$
$462$	−77.4721	−	78.0902i	−0.167689	−	0.169026i
$463$		−	676.869i		−	1.46192i	−0.682420	−	0.730960i	$-0.739072\pi$
$463$		−	676.869i		−	1.46192i	0.682420	−	0.730960i	$-0.260928\pi$
$464$	16.1622	+	22.2453i	0.0348322	+	0.0479425i
$465$		0			0
$466$	254.256	−	782.519i	0.545613	−	1.67923i
$467$	216.825	−	298.435i	0.464294	−	0.639046i	−0.511098	−	0.859522i	$-0.670761\pi$
$467$	216.825	−	298.435i	0.464294	−	0.639046i	0.975392	+	0.220476i	$0.0707611\pi$
$468$	154.031	+	111.910i	0.329125	+	0.239124i
$469$	−65.3444	−	21.2317i	−0.139327	−	0.0452701i
$470$		0			0
$471$	−809.681	+	588.267i	−1.71907	+	1.24898i
$472$	141.679			0.300168
$473$	359.433	−	55.4656i	0.759900	−	0.117263i
$474$	−733.951			−1.54842
$475$		0			0
$476$	37.5511	+	115.570i	0.0788888	+	0.242795i
$477$	−305.523	−	99.2705i	−0.640510	−	0.208114i
$478$	−199.248	+	274.241i	−0.416836	+	0.573726i
$479$	279.454	−	384.635i	0.583411	−	0.802997i	−0.410653	−	0.911792i	$-0.634699\pi$
$479$	279.454	−	384.635i	0.583411	−	0.802997i	0.994064	+	0.108795i	$0.0346992\pi$
$480$		0			0
$481$	−325.623	+	105.801i	−0.676971	+	0.219961i
$482$	−345.709	−	475.828i	−0.717239	−	0.987195i
$483$	23.5114			0.0486779
$484$	5.26142	−	662.108i	0.0108707	−	1.36799i
$485$		0			0
$486$	372.373	+	512.528i	0.766200	+	1.05458i
$487$	170.389	−	55.3626i	0.349874	−	0.113681i	−0.128807	−	0.991670i	$-0.541115\pi$
$487$	170.389	−	55.3626i	0.349874	−	0.113681i	0.478681	+	0.877989i	$0.341115\pi$
$488$	121.009	+	39.3181i	0.247969	+	0.0805699i
$489$	−203.037	−	147.515i	−0.415208	−	0.301667i
$490$		0			0
$491$	611.297	+	198.622i	1.24500	+	0.404526i	0.856128	−	0.516764i	$-0.172863\pi$
$491$	611.297	+	198.622i	1.24500	+	0.404526i	0.388876	+	0.921290i	$0.372863\pi$
$492$	−7.99379	−	24.6024i	−0.0162475	−	0.0500048i
$493$	−50.3066	−	69.2411i	−0.102042	−	0.140448i
$494$		−	310.543i		−	0.628631i
$495$		0			0
$496$	−263.151			−0.530546
$497$	45.2768	−	32.8955i	0.0911001	−	0.0661881i
$498$	−600.515	+	195.119i	−1.20585	+	0.391805i
$499$	162.446	−	499.958i	0.325543	−	1.00192i	−0.645651	−	0.763632i	$-0.723414\pi$
$499$	162.446	−	499.958i	0.325543	−	1.00192i	0.971195	−	0.238287i	$-0.0765860\pi$
$500$		0			0
$501$	614.574	−	845.889i	1.22670	−	1.68840i
$502$	406.229	−	1250.24i	0.809222	−	2.49053i
$503$	−198.182	−	609.941i	−0.394000	−	1.21261i	−0.929738	−	0.368222i	$-0.879967\pi$
$503$	−198.182	−	609.941i	−0.394000	−	1.21261i	0.535738	−	0.844384i	$-0.320033\pi$
$504$	−13.4640	+	9.78217i	−0.0267143	+	0.0194091i
$505$		0			0
$506$	172.533	+	173.909i	0.340974	+	0.343694i
$507$			349.644i			0.689634i
$508$	369.353	−	268.351i	0.727073	−	0.528249i
$509$	140.705	+	433.046i	0.276434	+	0.850778i	0.988836	+	0.149006i	$0.0476073\pi$
$509$	140.705	+	433.046i	0.276434	+	0.850778i	−0.712402	+	0.701772i	$0.752393\pi$
$510$		0			0
$511$	−68.3982	−	49.6942i	−0.133852	−	0.0972490i
$512$	390.097	+	283.422i	0.761908	+	0.553559i
$513$	65.1131	−	200.398i	0.126926	−	0.390639i
$514$	82.7786	−	26.8964i	0.161048	−	0.0523276i
$515$		0			0
$516$		−	654.583i		−	1.26857i
$517$	−223.561	+	112.793i	−0.432419	+	0.218169i
$518$		−	111.246i		−	0.214761i
$519$	−389.615	−	536.259i	−0.750703	−	1.03325i
$520$		0			0
$521$	−56.0044	+	172.364i	−0.107494	+	0.330833i	−0.990308	−	0.138891i	$-0.955646\pi$
$521$	−56.0044	+	172.364i	−0.107494	+	0.330833i	0.882814	+	0.469723i	$0.155646\pi$
$522$	25.6101	−	35.2492i	0.0490614	−	0.0675272i
$523$	277.305	+	201.474i	0.530219	+	0.385227i	0.820440	−	0.571733i	$-0.193729\pi$
$523$	277.305	+	201.474i	0.530219	+	0.385227i	−0.290220	+	0.956960i	$0.593729\pi$
$524$	442.835	+	143.886i	0.845106	+	0.274591i
$525$		0			0
$526$	235.421	−	171.044i	0.447569	−	0.325178i
$527$	819.088			1.55425
$528$	312.078	+	50.7001i	0.591056	+	0.0960229i
$529$	476.639			0.901020
$530$		0			0
$531$	39.5238	+	121.642i	0.0744328	+	0.229080i
$532$	55.4388	+	18.0132i	0.104208	+	0.0338593i
$533$	−6.53298	+	8.99187i	−0.0122570	+	0.0168703i
$534$	407.738	−	561.203i	0.763554	−	1.05094i
$535$		0			0
$536$	−329.668	+	107.116i	−0.615053	+	0.199843i
$537$	−4.36108	−	6.00251i	−0.00812119	−	0.0111779i
$538$	720.159			1.33859
$539$	471.388	+	242.548i	0.874560	+	0.449996i
$540$		0			0
$541$	179.366	+	246.876i	0.331545	+	0.456332i	0.941948	−	0.335759i	$-0.108993\pi$
$541$	179.366	+	246.876i	0.331545	+	0.456332i	−0.610403	+	0.792091i	$0.708993\pi$
$542$	419.796	−	136.400i	0.774532	−	0.251661i
$543$	250.851	+	81.5066i	0.461973	+	0.150104i
$544$	−851.671	−	618.775i	−1.56557	−	1.13745i
$545$		0			0
$546$	80.9017	+	26.2866i	0.148172	+	0.0481439i
$547$	46.7494	+	143.880i	0.0854651	+	0.263034i	0.984652	−	0.174531i	$-0.0558409\pi$
$547$	46.7494	+	143.880i	0.0854651	+	0.263034i	−0.899187	+	0.437565i	$0.855841\pi$
$548$	−188.942	−	260.057i	−0.344785	−	0.474556i
$549$			114.863i			0.209222i
$550$		0			0
$551$	−41.0557			−0.0745113
$552$	95.9632	−	69.7214i	0.173846	−	0.126307i
$553$	−56.2964	+	18.2918i	−0.101802	+	0.0330774i
$554$	−370.036	+	1138.85i	−0.667936	+	2.05569i
$555$		0			0
$556$	−517.807	+	712.701i	−0.931308	+	1.28184i
$557$	33.6867	−	103.677i	0.0604787	−	0.186134i	−0.916253	−	0.400601i	$-0.868801\pi$
$557$	33.6867	−	103.677i	0.0604787	−	0.186134i	0.976731	+	0.214467i	$0.0688013\pi$
$558$	128.854	+	396.572i	0.230921	+	0.710703i
$559$	−227.533	+	165.312i	−0.407036	+	0.295729i
$560$		0			0
$561$	−971.378	−	157.810i	−1.73151	−	0.281301i
$562$			310.949i			0.553291i
$563$	−806.321	+	585.827i	−1.43219	+	1.04054i	−0.442583	+	0.896728i	$0.645938\pi$
$563$	−806.321	+	585.827i	−1.43219	+	1.04054i	−0.989604	+	0.143817i	$0.954062\pi$
$564$	139.271	+	428.631i	0.246934	+	0.759983i
$565$		0			0
$566$	5.27864	+	3.83516i	0.00932622	+	0.00677590i
$567$	73.4404	+	53.3576i	0.129525	+	0.0941051i
$568$	87.2506	−	268.530i	0.153610	−	0.472764i
$569$	−94.4665	+	30.6940i	−0.166022	+	0.0539438i	−0.390849	−	0.920455i	$-0.627818\pi$
$569$	−94.4665	+	30.6940i	−0.166022	+	0.0539438i	0.224827	+	0.974399i	$0.427818\pi$
$570$		0			0
$571$		−	930.127i		−	1.62894i	−0.580202	−	0.814472i	$-0.697027\pi$
$571$		−	930.127i		−	1.62894i	0.580202	−	0.814472i	$-0.302973\pi$
$572$	230.645	+	457.148i	0.403226	+	0.799209i
$573$			375.564i			0.655435i
$574$	−2.12269	−	2.92164i	−0.00369807	−	0.00508996i
$575$		0			0
$576$	125.444	−	386.078i	0.217785	−	0.670274i
$577$	−204.167	+	281.012i	−0.353842	+	0.487022i	−0.948420	−	0.317016i	$-0.897319\pi$
$577$	−204.167	+	281.012i	−0.353842	+	0.487022i	0.594578	+	0.804038i	$0.297319\pi$
$578$	802.862	+	583.313i	1.38903	+	1.00919i
$579$	−1183.74	−	384.620i	−2.04445	−	0.664283i
$580$		0			0
$581$	−41.1985	+	29.9325i	−0.0709097	+	0.0515189i
$582$	−806.278			−1.38536
$583$	−608.474	−	613.328i	−1.04369	−	1.05202i
$584$	−426.536			−0.730370
$585$		0			0
$586$	447.100	+	1376.03i	0.762970	+	2.34818i
$587$	−604.294	−	196.347i	−1.02946	−	0.334492i	−0.254884	−	0.966972i	$-0.582037\pi$
$587$	−604.294	−	196.347i	−1.02946	−	0.334492i	−0.774577	+	0.632479i	$0.782037\pi$
$588$	560.837	−	771.926i	0.953804	−	1.31280i
$589$	230.949	−	317.874i	0.392104	−	0.539685i
$590$		0			0
$591$	340.902	−	110.766i	0.576822	−	0.187421i
$592$	187.945	+	258.684i	0.317474	+	0.436966i
$593$	341.152			0.575299			0.287650	−	0.957736i	$-0.407126\pi$
$593$	341.152			0.575299			0.287650	+	0.957736i	$0.407126\pi$
$594$	91.7173	+	594.354i	0.154406	+	1.00060i
$595$		0			0
$596$	−826.858	−	1138.07i	−1.38735	−	1.90952i
$597$	528.080	−	171.584i	0.884556	−	0.287410i
$598$	−180.171	−	58.5410i	−0.301289	−	0.0978947i
$599$	−362.164	−	263.128i	−0.604614	−	0.439278i	0.242899	−	0.970052i	$-0.421902\pi$
$599$	−362.164	−	263.128i	−0.604614	−	0.439278i	−0.847514	+	0.530773i	$0.821902\pi$
$600$		0			0
$601$	−762.584	−	247.779i	−1.26886	−	0.412277i	−0.404215	−	0.914664i	$-0.632455\pi$
$601$	−762.584	−	247.779i	−1.26886	−	0.412277i	−0.864643	+	0.502387i	$0.832455\pi$
$602$	−28.2387	−	86.9098i	−0.0469082	−	0.144368i
$603$	−183.933	−	253.162i	−0.305029	−	0.419837i
$604$			1577.03i			2.61097i
$605$		0			0
$606$	−716.869			−1.18295
$607$	−824.779	+	599.237i	−1.35878	+	0.987211i	−0.360257	+	0.932853i	$0.617311\pi$
$607$	−824.779	+	599.237i	−1.35878	+	0.987211i	−0.998522	+	0.0543575i	$0.982689\pi$
$608$	−480.273	+	156.050i	−0.789922	+	0.256661i
$609$	3.47524	−	10.6957i	0.00570647	−	0.0175627i
$610$		0			0
$611$	113.820	−	156.659i	0.186284	−	0.256398i
$612$	−171.025	+	526.362i	−0.279453	+	0.860068i
$613$	231.212	+	711.597i	0.377181	+	1.16084i	0.941995	+	0.335626i	$0.108948\pi$
$613$	231.212	+	711.597i	0.377181	+	1.16084i	−0.564814	+	0.825218i	$0.691052\pi$
$614$	−247.542	+	179.850i	−0.403163	+	0.292915i
$615$		0			0
$616$	−44.2341	+	6.82596i	−0.0718087	+	0.0110811i
$617$			517.100i			0.838088i	0.907966	+	0.419044i	$0.137635\pi$
$617$			517.100i			0.838088i	−0.907966	+	0.419044i	$0.862365\pi$
$618$	293.768	−	213.435i	0.475352	−	0.345363i
$619$	214.219	+	659.299i	0.346073	+	1.06510i	0.961007	+	0.276525i	$0.0891827\pi$
$619$	214.219	+	659.299i	0.346073	+	1.06510i	−0.614934	+	0.788579i	$0.710817\pi$
$620$		0			0
$621$	−103.992	−	75.5545i	−0.167459	−	0.121666i
$622$	844.607	+	613.643i	1.35789	+	0.986565i
$623$	17.2883	−	53.2078i	0.0277500	−	0.0854058i
$624$	−232.533	+	75.5545i	−0.372649	+	0.121081i
$625$		0			0
$626$			1189.18i			1.89965i
$627$	−335.132	+	332.480i	−0.534501	+	0.530271i
$628$			1513.70i			2.41035i
$629$	−585.000	−	805.183i	−0.930048	−	1.28010i
$630$		0			0
$631$	−277.128	+	852.911i	−0.439188	+	1.35168i	0.449545	+	0.893258i	$0.351586\pi$
$631$	−277.128	+	852.911i	−0.439188	+	1.35168i	−0.888733	+	0.458425i	$0.848414\pi$
$632$	−175.534	+	241.602i	−0.277744	+	0.382281i
$633$	−976.216	−	709.263i	−1.54221	−	1.12048i
$634$	740.755	+	240.686i	1.16838	+	0.379631i
$635$		0			0
$636$	−1258.01	+	913.997i	−1.97800	+	1.43710i
$637$	−409.958			−0.643577
$638$	104.616	−	52.7821i	0.163975	−	0.0827306i
$639$	254.892			0.398891
$640$		0			0
$641$	175.756	+	540.922i	0.274191	+	0.843872i	0.989432	+	0.144995i	$0.0463165\pi$
$641$	175.756	+	540.922i	0.274191	+	0.843872i	−0.715242	+	0.698877i	$0.753683\pi$
$642$	−57.2272	−	18.5942i	−0.0891389	−	0.0289630i
$643$	−388.238	+	534.364i	−0.603791	+	0.831048i	−0.996049	−	0.0888080i	$-0.971694\pi$
$643$	−388.238	+	534.364i	−0.603791	+	0.831048i	0.392257	+	0.919855i	$0.371694\pi$
$644$	20.9017	−	28.7687i	0.0324561	−	0.0446719i
$645$		0			0
$646$	858.533	−	278.954i	1.32900	−	0.431818i
$647$	−20.7790	−	28.5999i	−0.0321159	−	0.0442038i	0.792657	−	0.609668i	$-0.208697\pi$
$647$	−20.7790	−	28.5999i	−0.0321159	−	0.0442038i	−0.824773	+	0.565464i	$0.808697\pi$
$648$	457.979			0.706758
$649$	−55.1591	+	339.524i	−0.0849908	+	0.523150i
$650$		0			0
$651$	63.2624	+	87.0732i	0.0971772	+	0.133753i
$652$	−361.001	+	117.296i	−0.553682	+	0.179902i
$653$	−398.914	−	129.615i	−0.610894	−	0.198491i	−0.0128008	−	0.999918i	$-0.504075\pi$
$653$	−398.914	−	129.615i	−0.610894	−	0.198491i	−0.598093	+	0.801427i	$0.704075\pi$
$654$	1234.19	+	896.691i	1.88714	+	1.37109i
$655$		0			0
$656$	9.87192	+	3.20758i	0.0150487	+	0.00488960i
$657$	−118.989	−	366.211i	−0.181110	−	0.557399i
$658$	36.9822	+	50.9017i	0.0562040	+	0.0773582i
$659$		−	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	$0.482970\pi$
$662$	926.532	−	673.165i	1.39960	−	1.01687i
$663$	723.786	−	235.172i	1.09168	−	0.354709i
$664$	−79.3916	+	244.342i	−0.119566	+	0.367986i
$665$		0			0
$666$	297.812	−	409.902i	0.447164	−	0.615469i
$667$	−7.73948	+	23.8197i	−0.0116034	+	0.0357116i
$668$	−488.677	−	1503.99i	−0.731553	−	2.25149i
$669$	333.607	−	242.380i	0.498665	−	0.362301i
$670$		0			0
$671$	−141.334	+	274.681i	−0.210632	+	0.409360i
$672$		−	138.328i		−	0.205845i
$673$	−647.216	+	470.230i	−0.961689	+	0.698708i	−0.953542	−	0.301259i	$-0.902593\pi$
$673$	−647.216	+	470.230i	−0.961689	+	0.698708i	−0.00814624	+	0.999967i	$0.502593\pi$
$674$	−78.1910	−	240.647i	−0.116010	−	0.357043i
$675$		0			0
$676$	427.827	+	310.835i	0.632880	+	0.459815i
$677$	757.288	+	550.202i	1.11859	+	0.812706i	0.983995	−	0.178195i	$-0.0570257\pi$
$677$	757.288	+	550.202i	1.11859	+	0.812706i	0.134598	+	0.990900i	$0.457026\pi$
$678$	−160.027	+	492.513i	−0.236028	+	0.726420i
$679$	−61.8441	+	20.0944i	−0.0910811	+	0.0295940i
$680$		0			0
$681$		−	141.159i		−	0.207282i
$682$	−179.828	+	1106.91i	−0.263677	+	1.62303i
$683$			241.319i			0.353322i	0.984272	+	0.176661i	$0.0565296\pi$
$683$			241.319i			0.353322i	−0.984272	+	0.176661i	$0.943470\pi$
$684$	156.050	+	214.785i	0.228143	+	0.314013i
$685$		0			0
$686$	83.0132	−	255.488i	0.121010	−	0.372432i
$687$	285.407	−	392.830i	0.415440	−	0.571805i
$688$	212.494	+	154.386i	0.308858	+	0.224398i
$689$	635.410	+	206.457i	0.922221	+	0.299648i
$690$		0			0
$691$	736.915	−	535.400i	1.06645	−	0.774819i	0.0911771	−	0.995835i	$-0.470937\pi$
$691$	736.915	−	535.400i	1.06645	−	0.774819i	0.975270	+	0.221015i	$0.0709371\pi$
$692$	−1002.54			−1.44876
$693$	−18.2004	−	36.0739i	−0.0262632	−	0.0520547i
$694$	−706.140			−1.01749
$695$		0			0
$696$	−17.5329	−	53.9607i	−0.0251909	−	0.0775297i
$697$	−30.7275	−	9.98397i	−0.0440853	−	0.0143242i
$698$	−420.361	+	578.577i	−0.602236	+	0.828907i
$699$	568.533	−	782.519i	0.813352	−	1.11948i
$700$		0			0
$701$	−410.902	+	133.510i	−0.586165	+	0.190457i	−0.587061	−	0.809543i	$-0.699715\pi$
$701$	−410.902	+	133.510i	−0.586165	+	0.190457i	0.000895496		1.00000i	$0.499715\pi$
$702$	−273.359	−	376.246i	−0.389400	−	0.535963i
$703$	−477.424			−0.679124
$704$	775.039	−	768.905i	1.10091	−	1.09219i
$705$		0			0
$706$	−62.6722	−	86.2609i	−0.0887708	−	0.122183i
$707$	−54.9861	+	17.8661i	−0.0777739	+	0.0252703i
$708$	588.804	+	191.314i	0.831644	+	0.270218i
$709$	−708.956	−	515.087i	−0.999938	−	0.726498i	−0.0378633	−	0.999283i	$-0.512055\pi$
$709$	−708.956	−	515.087i	−0.999938	−	0.726498i	−0.962075	+	0.272785i	$0.912055\pi$
$710$		0			0
$711$	−256.400	−	83.3095i	−0.360619	−	0.117172i
$712$	−87.2208	−	268.438i	−0.122501	−	0.377020i
$713$	−140.887	−	193.915i	−0.197598	−	0.271970i
$714$			247.275i			0.346323i
$715$		0			0
$716$	−11.2217			−0.0156728
$717$	−322.390	+	234.230i	−0.449637	+	0.326680i
$718$	1322.42	−	429.681i	1.84181	−	0.598441i
$719$	−155.218	+	477.712i	−0.215880	+	0.664411i	0.783210	+	0.621758i	$0.213581\pi$
$719$	−155.218	+	477.712i	−0.215880	+	0.664411i	−0.999090	+	0.0426534i	$0.986419\pi$
$720$		0			0
$721$	17.2136	−	23.6925i	0.0238746	−	0.0328606i
$722$	−209.518	+	644.829i	−0.290191	+	0.893115i
$723$	−213.660	−	657.578i	−0.295519	−	0.909514i
$724$	322.740	−	234.484i	0.445773	−	0.323873i
$725$		0			0
$726$	426.525	−	1278.06i	0.587500	−	1.76042i
$727$		−	393.878i		−	0.541786i	−0.962609	−	0.270893i	$-0.912681\pi$
$727$		−	393.878i		−	0.541786i	0.962609	−	0.270893i	$-0.0873190\pi$
$728$	28.0017	−	20.3444i	0.0384639	−	0.0279456i
$729$	−50.9853	−	156.917i	−0.0699387	−	0.215249i
$730$		0			0
$731$	−661.413	−	480.544i	−0.904805	−	0.657380i
$732$	449.806	+	326.803i	0.614489	+	0.446453i
$733$	−191.826	+	590.381i	−0.261700	+	0.805431i	0.730735	+	0.682661i	$0.239178\pi$
$733$	−191.826	+	590.381i	−0.261700	+	0.805431i	−0.992435	+	0.122769i	$0.960822\pi$
$734$	1079.57	−	350.775i	1.47081	−	0.477895i
$735$		0			0
$736$			308.061i			0.418562i
$737$	−128.347	−	831.728i	−0.174148	−	1.12853i
$738$		−	16.4477i		−	0.0222869i
$739$	499.618	+	687.666i	0.676074	+	0.930535i	0.999878	−	0.0155884i	$-0.00496214\pi$
$739$	499.618	+	687.666i	0.676074	+	0.930535i	−0.323805	+	0.946124i	$0.604962\pi$
$740$		0			0
$741$	112.812	−	347.198i	0.152242	−	0.468554i
$742$	−127.598	+	175.623i	−0.171964	+	0.236689i
$743$	−328.152	−	238.416i	−0.441658	−	0.320883i	0.344635	−	0.938737i	$-0.388003\pi$
$743$	−328.152	−	238.416i	−0.441658	−	0.320883i	−0.786293	+	0.617853i	$0.788003\pi$
$744$	516.418	+	167.794i	0.694111	+	0.225530i
$745$		0			0
$746$	1476.92	−	1073.05i	1.97979	−	1.43840i
$747$	−231.933			−0.310486
$748$	−1056.65	+	1048.29i	−1.41264	+	1.40146i
$749$	−4.85292			−0.00647919
$750$		0			0
$751$	−262.486	−	807.849i	−0.349515	−	1.07570i	−0.959122	−	0.282993i	$-0.908673\pi$
$751$	−262.486	−	807.849i	−0.349515	−	1.07570i	0.609606	−	0.792704i	$-0.291327\pi$
$752$	−171.992	−	55.8835i	−0.228712	−	0.0743132i
$753$	908.356	−	1250.24i	1.20632	−	1.66035i
$754$	−53.2624	+	73.3094i	−0.0706398	+	0.0972273i
$755$		0			0
$756$	83.0244	−	26.9763i	0.109821	−	0.0356829i
$757$	−352.977	−	485.832i	−0.466284	−	0.641786i	0.509513	−	0.860463i	$-0.329826\pi$
$757$	−352.977	−	485.832i	−0.466284	−	0.641786i	−0.975797	+	0.218678i	$0.929826\pi$
$758$	−865.602			−1.14196
$759$	129.721	+	257.113i	0.170911	+	0.338752i
$760$		0			0
$761$	205.275	+	282.537i	0.269744	+	0.371271i	0.922303	−	0.386467i	$-0.126305\pi$
$761$	205.275	+	282.537i	0.269744	+	0.371271i	−0.652559	+	0.757738i	$0.726305\pi$
$762$	883.548	−	287.082i	1.15951	−	0.376748i
$763$	117.014	+	38.0201i	0.153360	+	0.0498298i
$764$	459.543	+	333.877i	0.601496	+	0.437012i
$765$		0			0
$766$	1866.16	+	606.354i	2.43625	+	0.791584i
$767$	−82.1994	−	252.984i	−0.107170	−	0.329835i
$768$	−40.4059	−	55.6140i	−0.0526119	−	0.0724140i
$769$			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
$772$	−1522.97	+	1106.50i	−1.97276	+	1.43329i
$773$	6.64488	−	2.15905i	0.00859623	−	0.00279308i	−0.304716	−	0.952443i	$-0.598561\pi$
$773$	6.64488	−	2.15905i	0.00859623	−	0.00279308i	0.313312	+	0.949650i	$0.398561\pi$
$774$	128.612	−	395.828i	0.166166	−	0.511406i
$775$		0			0
$776$	−192.832	+	265.410i	−0.248495	+	0.342024i
$777$	40.4125	−	124.377i	0.0520110	−	0.160073i
$778$	634.801	+	1953.72i	0.815939	+	2.51120i
$779$	−12.5385	+	9.10976i	−0.0160956	+	0.0116942i
$780$		0			0
$781$	609.543	+	313.634i	0.780465	+	0.401581i
$782$		−	550.689i		−	0.704206i
$783$	−49.7420	+	36.1397i	−0.0635275	+	0.0461554i
$784$	118.311	+	364.124i	0.150907	+	0.464443i
$785$		0			0
$786$	766.537	+	556.922i	0.975238	+	0.708552i
$787$	−892.115	−	648.159i	−1.13356	−	0.823582i	−0.147354	−	0.989084i	$-0.547076\pi$
$787$	−892.115	−	648.159i	−1.13356	−	0.823582i	−0.986210	+	0.165501i	$0.947076\pi$
$788$	167.529	−	515.601i	0.212600	−	0.654315i
$789$	325.344	−	105.711i	0.412350	−	0.133981i
$790$		0			0
$791$			41.7655i			0.0528009i
$792$	−181.261	−	93.2659i	−0.228864	−	0.117760i
$793$		−	238.885i		−	0.301243i
$794$	−9.72136	−	13.3803i	−0.0122435	−	0.0168518i
$795$		0			0
$796$	259.514	−	798.700i	0.326022	−	1.00339i
$797$	−424.007	+	583.596i	−0.532004	+	0.732240i	−0.987434	−	0.158031i	$-0.949485\pi$
$797$	−424.007	+	583.596i	−0.532004	+	0.732240i	0.455430	+	0.890271i	$0.349485\pi$
$798$	95.9632	+	69.7214i	0.120255	+	0.0873701i
$799$	535.344	+	173.944i	0.670018	+	0.217702i
$800$		0			0
$801$	206.141	−	149.770i	0.257355	−	0.186979i
$802$	870.354			1.08523
$803$	166.060	−	1022.16i	0.206800	−	1.27293i
$804$	−1514.71			−1.88396
$805$		0			0
$806$	−267.984	−	824.769i	−0.332486	−	1.02329i
$807$	805.162	+	261.613i	0.997722	+	0.324180i
$808$	−171.449	+	235.979i	−0.212189	+	0.292053i
$809$	471.682	−	649.215i	0.583044	−	0.802491i	−0.410981	−	0.911644i	$-0.634814\pi$
$809$	471.682	−	649.215i	0.583044	−	0.802491i	0.994025	+	0.109153i	$0.0348139\pi$
$810$		0			0
$811$	−471.598	+	153.232i	−0.581502	+	0.188942i	−0.584973	−	0.811052i	$-0.698895\pi$
$811$	−471.598	+	153.232i	−0.581502	+	0.188942i	0.00347122	+	0.999994i	$0.498895\pi$
$812$	−9.99783	−	13.7608i	−0.0123126	−	0.0169468i
$813$	518.897			0.638250
$814$	1216.55	−	613.787i	1.49453	−	0.754038i
$815$		0			0
$816$	−417.758	−	574.995i	−0.511959	−	0.704651i
$817$	−372.983	+	121.189i	−0.456527	+	0.148335i
$818$	90.9084	+	29.5379i	0.111135	+	0.0361099i
$819$	25.2786	+	18.3660i	0.0308653	+	0.0224249i
$820$		0			0
$821$	−276.921	−	89.9771i	−0.337297	−	0.109595i	0.135471	−	0.990781i	$-0.456745\pi$
$821$	−276.921	−	89.9771i	−0.337297	−	0.109595i	−0.472768	+	0.881187i	$0.656745\pi$
$822$	−202.131	−	622.095i	−0.245901	−	0.756806i
$823$	631.860	+	869.681i	0.767752	+	1.05672i	0.996529	+	0.0832414i	$0.0265273\pi$
$823$	631.860	+	869.681i	0.767752	+	1.05672i	−0.228777	+	0.973479i	$0.573473\pi$
$824$		−	147.748i		−	0.179306i
$825$		0			0
$826$	86.4296			0.104636
$827$	369.554	−	268.497i	0.446861	−	0.324664i	−0.341494	−	0.939884i	$-0.610933\pi$
$827$	369.554	−	268.497i	0.446861	−	0.324664i	0.788355	+	0.615220i	$0.210933\pi$
$828$	154.031	−	50.0476i	0.186027	−	0.0604440i
$829$	−0.679973	+	2.09274i	−0.000820233	+	0.00252442i	−0.951466	−	0.307755i	$-0.900422\pi$
$829$	−0.679973	+	2.09274i	−0.000820233	+	0.00252442i	0.950646	+	0.310279i	$0.100422\pi$
$830$		0			0
$831$	−827.426	+	1138.85i	−0.995700	+	1.37046i
$832$	−260.892	+	802.943i	−0.313572	+	0.965076i
$833$	−368.257	−	1133.38i	−0.442085	−	1.36060i
$834$	−1450.26	+	1053.68i	−1.73892	+	1.26340i
$835$		0			0
$836$	108.891	+	705.645i	0.130252	+	0.844073i
$837$		−	588.423i		−	0.703015i
$838$	610.413	−	443.491i	0.728417	−	0.529226i
$839$	−448.822	−	1381.33i	−0.534948	−	1.64640i	−0.743761	−	0.668446i	$-0.766960\pi$
$839$	−448.822	−	1381.33i	−0.534948	−	1.64640i	0.208813	−	0.977956i	$-0.433040\pi$
$840$		0			0
$841$	−670.691	−	487.286i	−0.797493	−	0.579412i
$842$	−192.744	−	140.036i	−0.228912	−	0.166314i
$843$	−112.959	+	347.652i	−0.133996	+	0.412398i
$844$	−1735.72	+	563.969i	−2.05654	+	0.668209i
$845$		0			0
$846$			286.558i			0.338721i
$847$	0.863474	−	108.661i	0.00101945	−	0.128290i
$848$		−	623.951i		−	0.735792i
$849$	4.50850	+	6.20541i	0.00531036	+	0.00730909i
$850$		0			0
$851$	−90.0000	+	276.992i	−0.105758	+	0.325489i
$852$	725.208	−	998.163i	0.851183	−	1.17155i
$853$	−857.151	−	622.757i	−1.00487	−	0.730079i	−0.0417407	−	0.999128i	$-0.513290\pi$
$853$	−857.151	−	622.757i	−1.00487	−	0.730079i	−0.963126	+	0.269050i	$0.913290\pi$
$854$	73.8197	+	23.9855i	0.0864399	+	0.0280860i
$855$		0			0
$856$	−19.8075	+	14.3910i	−0.0231396	+	0.0168119i
$857$	951.067			1.10976			0.554882	−	0.831929i	$-0.312763\pi$
$857$	951.067			1.10976			0.554882	+	0.831929i	$0.312763\pi$
$858$	158.904	+	1029.75i	0.185203	+	1.20017i
$859$	−1146.23			−1.33438			−0.667188	−	0.744890i	$-0.732502\pi$
$859$	−1146.23			−1.33438			−0.667188	+	0.744890i	$0.732502\pi$
$860$		0			0
$861$	−1.31190	−	4.03760i	−0.00152369	−	0.00468943i
$862$	1315.63	+	427.474i	1.52625	+	0.495910i
$863$	−555.629	+	764.758i	−0.643834	+	0.886162i	−0.998813	−	0.0487126i	$-0.984488\pi$
$863$	−555.629	+	764.758i	−0.643834	+	0.886162i	0.354979	+	0.934874i	$0.384488\pi$
$864$	−444.521	+	611.831i	−0.514492	+	0.708137i
$865$		0			0
$866$	−422.545	+	137.293i	−0.487928	+	0.158537i
$867$	685.726	+	943.821i	0.790918	+	1.08861i
$868$	162.784			0.187539
$869$	−510.641	−	514.715i	−0.587619	−	0.592307i
$870$		0			0
$871$	382.533	+	526.511i	0.439188	+	0.604491i
$872$	590.345	−	191.815i	0.677001	−	0.219971i
$873$	−281.667	−	91.5191i	−0.322643	−	0.104833i
$874$	−213.713	−	155.272i	−0.244523	−	0.177656i
$875$		0			0
$876$	−1772.64	−	575.964i	−2.02356	−	0.657494i
$877$	49.0405	+	150.931i	0.0559185	+	0.172099i	0.975115	−	0.221700i	$-0.0711605\pi$
$877$	49.0405	+	150.931i	0.0559185	+	0.172099i	−0.919196	+	0.393799i	$0.871161\pi$
$878$	281.133	+	386.946i	0.320197	+	0.440713i
$879$			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	$0.426664\pi$
$882$	490.808	−	356.593i	0.556471	−	0.404300i
$883$	752.530	−	244.512i	0.852243	−	0.276910i	0.149858	−	0.988708i	$-0.452118\pi$
$883$	752.530	−	244.512i	0.852243	−	0.276910i	0.702385	+	0.711797i	$0.252118\pi$
$884$	355.689	−	1094.70i	0.402363	−	1.23835i
$885$		0			0
$886$	586.677	−	807.491i	0.662163	−	0.911390i
$887$	−261.775	+	805.659i	−0.295124	+	0.908297i	0.688056	+	0.725657i	$0.258464\pi$
$887$	−261.775	+	805.659i	−0.295124	+	0.908297i	−0.983180	+	0.182640i	$0.941536\pi$
$888$	−203.885	−	627.492i	−0.229600	−	0.706635i
$889$	60.6161	−	44.0402i	0.0681846	−	0.0495390i
$890$		0			0
$891$	−178.302	+	1097.51i	−0.200114	+	1.23178i
$892$		−	623.680i		−	0.699192i
$893$	218.450	−	158.713i	0.244625	−	0.177730i
$894$	−884.574	−	2722.44i	−0.989457	−	3.04523i
$895$		0			0
$896$	−98.2035	−	71.3491i	−0.109602	−	0.0796306i
$897$	−180.171	−	130.902i	−0.200859	−	0.145933i
$898$	−372.245	+	1145.65i	−0.414527	+	1.27578i
$899$	−109.039	+	35.4291i	−0.121290	+	0.0394094i
$900$		0			0
$901$			1942.12i			2.15552i
$902$	20.2383	−	39.3328i	0.0224372	−	0.0436062i
$903$		−	107.426i		−	0.118966i
$904$	123.853	+	170.468i	0.137005	+	0.188571i
$905$		0			0
$906$	−991.656	+	3052.00i	−1.09454	+	3.36866i
$907$	250.814	−	345.216i	0.276532	−	0.380613i	−0.648049	−	0.761598i	$-0.724415\pi$
$907$	250.814	−	345.216i	0.276532	−	0.380613i	0.924581	+	0.380985i	$0.124415\pi$
$908$	−172.723	−	125.491i	−0.190224	−	0.138206i
$909$	−250.433	−	81.3705i	−0.275503	−	0.0895165i
$910$		0			0
$911$	−113.353	+	82.3554i	−0.124427	+	0.0904011i	−0.648258	−	0.761421i	$-0.724502\pi$
$911$	−113.353	+	82.3554i	−0.124427	+	0.0904011i	0.523831	+	0.851822i	$0.324502\pi$
$912$	−340.937			−0.373834
$913$	−554.639	−	285.384i	−0.607491	−	0.312579i
$914$	−160.795			−0.175925
$915$		0			0
$916$	−226.941	−	698.453i	−0.247752	−	0.762503i
$917$	72.6756	+	23.6137i	0.0792537	+	0.0257511i
$918$	794.624	−	1093.71i	0.865603	−	1.19140i
$919$	−611.124	+	841.140i	−0.664988	+	0.915278i	−0.999634	−	0.0270664i	$-0.991383\pi$
$919$	−611.124	+	841.140i	−0.664988	+	0.915278i	0.334645	+	0.942344i	$0.391383\pi$
$920$		0			0
$921$	−342.095	+	111.153i	−0.371438	+	0.120688i
$922$	−613.787	−	844.805i	−0.665713	−	0.916275i
$923$	−530.109			−0.574333
$924$	−193.050	−	31.3628i	−0.208928	−	0.0339424i
$925$		0			0
$926$	−1224.47	−	1685.34i	−1.32232	−	1.82002i
$927$	126.852	−	41.2167i	0.136841	−	0.0444625i
$928$	140.142	+	45.5348i	0.151015	+	0.0490677i
$929$	1329.96	+	966.270i	1.43160	+	1.04012i	0.989716	+	0.143046i	$0.0456898\pi$
$929$	1329.96	+	966.270i	1.43160	+	1.04012i	0.441884	+	0.897072i	$0.354310\pi$
$930$		0			0
$931$	−543.678	−	176.652i	−0.583972	−	0.189744i
$932$	−452.068	−	1391.32i	−0.485052	−	1.49284i
$933$	721.381	+	992.895i	0.773184	+	1.06420i
$934$		−	1135.31i		−	1.21554i
$935$		0			0
$936$	157.639			0.168418
$937$	586.966	−	426.456i	0.626431	−	0.455129i	−0.228731	−	0.973490i	$-0.573458\pi$
$937$	586.966	−	426.456i	0.626431	−	0.455129i	0.855162	+	0.518361i	$0.173458\pi$
$938$	−201.109	+	65.3444i	−0.214402	+	0.0696636i
$939$	−431.996	+	1329.55i	−0.460060	+	1.41592i
$940$		0			0
$941$	−107.800	+	148.374i	−0.114559	+	0.157677i	−0.862446	−	0.506149i	$-0.831069\pi$
$941$	−107.800	+	148.374i	−0.114559	+	0.157677i	0.747887	+	0.663826i	$0.231069\pi$
$942$	−951.837	+	2929.45i	−1.01044	+	3.10982i
$943$	2.92164	+	8.99187i	0.00309823	+	0.00953539i
$944$	−200.977	+	146.018i	−0.212900	+	0.154681i
$945$		0			0
$946$	794.613	−	788.324i	0.839971	−	0.833323i
$947$		−	926.439i		−	0.978288i	−0.872203	−	0.489144i	$-0.837309\pi$
$947$		−	926.439i		−	0.978288i	0.872203	−	0.489144i	$-0.162691\pi$
$948$	−1055.74	+	767.041i	−1.11365	+	0.809115i
$949$	247.467	+	761.625i	0.260766	+	0.802556i
$950$		0			0
$951$	740.755	+	538.190i	0.778922	+	0.565920i
$952$	81.3978	+	59.1390i	0.0855019	+	0.0621207i
$953$	77.2030	−	237.606i	0.0810105	−	0.249325i	−0.902346	−	0.431013i	$-0.858156\pi$
$953$	77.2030	−	237.606i	0.0810105	−	0.249325i	0.983356	+	0.181688i	$0.0581562\pi$
$954$	−940.304	+	305.523i	−0.985643	+	0.320255i
$955$		0			0
$956$			602.709i			0.630449i
$957$	136.139	−	21.0081i	0.142256	−	0.0219521i
$958$		−	1463.24i		−	1.52739i
$959$	−31.0081	−	42.6790i	−0.0323338	−	0.0445037i
$960$		0			0
$961$	42.1004	−	129.572i	0.0438090	−	0.134830i
$962$	−619.372	+	852.492i	−0.643838	+	0.886167i
$963$	−17.8813	−	12.9915i	−0.0185683	−	0.0134907i
$964$	−994.562	−	323.153i	−1.03170	−	0.335221i
$965$		0			0
$966$	58.5410	−	42.5325i	0.0606015	−	0.0440295i
$967$	−554.026			−0.572933			−0.286466	−	0.958090i	$-0.592481\pi$
$967$	−554.026			−0.572933			−0.286466	+	0.958090i	$0.592481\pi$
$968$	−318.703	−	446.068i	−0.329239	−	0.460814i
$969$	1061.21			1.09516
$970$		0			0
$971$	−352.634	−	1085.30i	−0.363166	−	1.11771i	−0.951121	−	0.308817i	$-0.900067\pi$
$971$	−352.634	−	1085.30i	−0.363166	−	1.11771i	0.587955	−	0.808893i	$-0.299933\pi$
$972$	1071.27	+	348.077i	1.10213	+	0.358104i
$973$	−84.9796	+	116.964i	−0.0873377	+	0.120210i
$974$	324.098	−	446.083i	0.332750	−	0.457991i
$975$		0			0
$976$	−212.177	+	68.9406i	−0.217395	+	0.0706358i
$977$	−75.6451	−	104.116i	−0.0774258	−	0.106568i	0.768547	−	0.639793i	$-0.220980\pi$
$977$	−75.6451	−	104.116i	−0.0774258	−	0.106568i	−0.845973	+	0.533225i	$0.820980\pi$
$978$	−772.398			−0.789773
$979$	677.249	−	104.509i	0.691776	−	0.106751i
$980$		0			0
$981$	329.373	+	453.343i	0.335752	+	0.462123i
$982$	1881.38	−	611.297i	1.91586	−	0.622502i
$983$	1269.53	+	412.497i	1.29149	+	0.419630i	0.872613	−	0.488413i	$-0.162424\pi$
$983$	1269.53	+	412.497i	1.29149	+	0.419630i	0.418876	+	0.908043i	$0.362424\pi$
$984$	−17.3278	−	12.5894i	−0.0176095	−	0.0127941i
$985$		0			0
$986$	−250.517	−	81.3978i	−0.254074	−	0.0825535i
$987$	22.8563	+	70.3444i	0.0231573	+	0.0712709i
$988$	−324.544	−	446.697i	−0.328486	−	0.452122i
$989$			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	$0.374383\pi$
$992$	−1140.89	+	828.904i	−1.15009	+	0.835588i
$993$	1280.44	−	416.039i	1.28946	−	0.418972i
$994$	53.2260	−	163.813i	0.0535473	−	0.164802i
$995$		0			0
$996$	−659.886	+	908.255i	−0.662536	+	0.911903i
$997$	−372.540	+	1146.56i	−0.373661	+	1.15001i	0.570716	+	0.821147i	$0.306666\pi$
$997$	−372.540	+	1146.56i	−0.373661	+	1.15001i	−0.944377	+	0.328864i	$0.893334\pi$
$998$	−499.958	−	1538.71i	−0.500960	−	1.54180i
$999$	−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.q.d.74.2		8
5.2	odd	4		275.3.x.e.151.1		4
5.3	odd	4		11.3.d.a.8.1	yes	4
5.4	even	2	inner	275.3.q.d.74.1		8
11.7	odd	10	inner	275.3.q.d.249.1		8
15.8	even	4		99.3.k.a.19.1		4
20.3	even	4		176.3.n.a.129.1		4
55.3	odd	20		121.3.d.a.94.1		4
55.7	even	20		275.3.x.e.51.1		4
55.8	even	20		121.3.d.c.94.1		4
55.13	even	20		121.3.b.b.120.1		4
55.18	even	20		11.3.d.a.7.1	✓	4
55.28	even	20		121.3.d.a.112.1		4
55.29	odd	10	inner	275.3.q.d.249.2		8
55.38	odd	20		121.3.d.c.112.1		4
55.43	even	4		121.3.d.d.118.1		4
55.48	odd	20		121.3.d.d.40.1		4
55.53	odd	20		121.3.b.b.120.4		4
165.53	even	20		1089.3.c.e.604.1		4
165.68	odd	20		1089.3.c.e.604.4		4
165.128	odd	20		99.3.k.a.73.1		4
220.183	odd	20		176.3.n.a.161.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
11.3.d.a.7.1	✓	4	55.18	even	20
11.3.d.a.8.1	yes	4	5.3	odd	4
99.3.k.a.19.1		4	15.8	even	4
99.3.k.a.73.1		4	165.128	odd	20
121.3.b.b.120.1		4	55.13	even	20
121.3.b.b.120.4		4	55.53	odd	20
121.3.d.a.94.1		4	55.3	odd	20
121.3.d.a.112.1		4	55.28	even	20
121.3.d.c.94.1		4	55.8	even	20
121.3.d.c.112.1		4	55.38	odd	20
121.3.d.d.40.1		4	55.48	odd	20
121.3.d.d.118.1		4	55.43	even	4
176.3.n.a.129.1		4	20.3	even	4
176.3.n.a.161.1		4	220.183	odd	20
275.3.q.d.74.1		8	5.4	even	2	inner
275.3.q.d.74.2		8	1.1	even	1	trivial
275.3.q.d.249.1		8	11.7	odd	10	inner
275.3.q.d.249.2		8	55.29	odd	10	inner
275.3.x.e.51.1		4	55.7	even	20
275.3.x.e.151.1		4	5.2	odd	4
1089.3.c.e.604.1		4	165.53	even	20
1089.3.c.e.604.4		4	165.68	odd	20

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 275 = 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	275.q (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.48990 - 1.80902i) q^{2} +(3.44095 - 1.11803i) q^{3} +(1.69098 - 5.20431i) q^{4} +(6.54508 - 9.00854i) q^{6} +(0.277515 - 0.854102i) q^{7} +(-1.40008 - 4.30902i) q^{8} +(3.30902 - 2.40414i) q^{9} +(10.8713 - 1.67760i) q^{11} -19.7984i q^{12} +(-6.88191 + 5.00000i) q^{13} +(-0.854102 - 2.62866i) q^{14} +(6.42705 + 4.66953i) q^{16} +(-20.0049 - 14.5344i) q^{17} +(3.88998 - 11.9721i) q^{18} +(-11.2812 + 3.66547i) q^{19} -3.24920i q^{21} +(24.0337 - 23.8435i) q^{22} +7.23607i q^{23} +(-9.63525 - 13.2618i) q^{24} +(-8.09017 + 24.8990i) q^{26} +(-10.4414 + 14.3713i) q^{27} +(-3.97574 - 2.88854i) q^{28} +(3.29180 + 1.06957i) q^{29} +(-26.7984 + 19.4702i) q^{31} +42.5730 q^{32} +(35.5321 - 17.9271i) q^{33} -76.1033 q^{34} +(-6.91641 - 21.2865i) q^{36} +(38.2793 + 12.4377i) q^{37} +(-21.4580 + 29.5344i) q^{38} +(-18.0902 + 24.8990i) q^{39} +(1.24265 - 0.403760i) q^{41} +(-5.87785 - 8.09017i) q^{42} +33.0625 q^{43} +(9.65248 - 59.4145i) q^{44} +(13.0902 + 18.0171i) q^{46} +(-21.6498 + 7.03444i) q^{47} +(27.3359 + 8.88197i) q^{48} +(38.9894 + 28.3274i) q^{49} +(-85.0861 - 27.6462i) q^{51} +(14.3844 + 44.2705i) q^{52} +(-46.1653 - 63.5410i) q^{53} +54.6718i q^{54} -4.06888 q^{56} +(-34.7198 + 25.2254i) q^{57} +(10.1311 - 3.29180i) q^{58} +(-9.66312 + 29.7400i) q^{59} +(-16.5066 + 22.7194i) q^{61} +(-31.5034 + 96.9574i) q^{62} +(-1.13508 - 3.49342i) q^{63} +(80.2943 - 58.3372i) q^{64} +(56.0410 - 108.915i) q^{66} -76.5066i q^{67} +(-109.470 + 79.5344i) q^{68} +(8.09017 + 24.8990i) q^{69} +(50.4164 + 36.6297i) q^{71} +(-14.9924 - 10.8926i) q^{72} +(29.0915 - 89.5344i) q^{73} +(117.812 - 38.2793i) q^{74} +64.9089i q^{76} +(1.58411 - 9.75078i) q^{77} +94.7214i q^{78} +(-38.7426 - 53.3247i) q^{79} +(-31.2361 + 96.1347i) q^{81} +(2.36365 - 3.25329i) q^{82} +(-45.8752 - 33.3303i) q^{83} +(-16.9098 - 5.49434i) q^{84} +(82.3222 - 59.8106i) q^{86} +12.5227 q^{87} +(-22.4496 - 44.4959i) q^{88} +62.2968 q^{89} +(2.36068 + 7.26543i) q^{91} +(37.6587 + 12.2361i) q^{92} +(-70.4437 + 96.9574i) q^{93} +(-41.1803 + 56.6799i) q^{94} +(146.492 - 47.5981i) q^{96} +(-42.5605 - 58.5795i) q^{97} +148.324 q^{98} +(31.9402 - 31.6874i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 18 q^{4} + 30 q^{6} + 22 q^{9} + 2 q^{11} + 20 q^{14} + 38 q^{16} - 50 q^{19} - 10 q^{24} - 20 q^{26} + 80 q^{29} - 116 q^{31} - 260 q^{34} + 52 q^{36} - 100 q^{39} - 160 q^{41} - 48 q^{44} + 60 q^{46}+ \cdots - 62 q^{99}+O(q^{100}) \) 8 * q + 18 * q^4 + 30 * q^6 + 22 * q^9 + 2 * q^11 + 20 * q^14 + 38 * q^16 - 50 * q^19 - 10 * q^24 - 20 * q^26 + 80 * q^29 - 116 * q^31 - 260 * q^34 + 52 * q^36 - 100 * q^39 - 160 * q^41 - 48 * q^44 + 60 * q^46 + 218 * q^49 - 390 * q^51 + 200 * q^56 - 46 * q^59 + 20 * q^61 + 298 * q^64 + 180 * q^66 + 20 * q^69 + 296 * q^71 + 540 * q^74 - 140 * q^79 - 232 * q^81 - 180 * q^84 + 350 * q^86 - 244 * q^89 - 160 * q^91 - 240 * q^94 + 680 * q^96 - 62 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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