LMFDB - Embedded newform 275.3.x.i.101.4

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 = [28,5,-14] 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:	$28$
Relative dimension:	$7$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			101.4
Character	$\chi$	$=$	275.101
Dual form			275.3.x.i.226.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.101311 - 0.0329179i) q^{2} +(0.121004 - 0.0879149i) q^{3} +(-3.22689 - 2.34447i) q^{4} +(-0.0151531 + 0.00492353i) q^{6} +(-2.91426 + 4.01113i) q^{7} +(0.500198 + 0.688464i) q^{8} +(-2.77424 + 8.53823i) q^{9} +(9.59279 - 5.38315i) q^{11} -0.596582 q^{12} +(17.6682 + 5.74075i) q^{13} +(0.427284 - 0.310440i) q^{14} +(4.90223 + 15.0875i) q^{16} +(27.1482 - 8.82097i) q^{17} +(0.562122 - 0.773694i) q^{18} +(-15.5974 - 21.4680i) q^{19} +0.741571i q^{21} +(-1.14906 + 0.229597i) q^{22} +25.8328 q^{23} +(0.121052 + 0.0393323i) q^{24} +(-1.60101 - 1.16320i) q^{26} +(0.830919 + 2.55730i) q^{27} +(18.8080 - 6.11108i) q^{28} +(-6.29400 + 8.66295i) q^{29} +(0.964986 - 2.96992i) q^{31} -5.09386i q^{32} +(0.687512 - 1.49473i) q^{33} -3.04077 q^{34} +(28.9698 - 21.0478i) q^{36} +(28.2855 + 20.5506i) q^{37} +(0.873507 + 2.68838i) q^{38} +(2.64263 - 0.858642i) q^{39} +(18.9383 + 26.0664i) q^{41} +(0.0244110 - 0.0751293i) q^{42} +42.8073i q^{43} +(-43.5755 - 5.11920i) q^{44} +(-2.61714 - 0.850361i) q^{46} +(-50.2380 + 36.5001i) q^{47} +(1.91961 + 1.39468i) q^{48} +(7.54556 + 23.2228i) q^{49} +(2.50955 - 3.45410i) q^{51} +(-43.5543 - 59.9474i) q^{52} +(8.54679 - 26.3043i) q^{53} -0.286435i q^{54} -4.21923 q^{56} +(-3.77471 - 1.22648i) q^{57} +(0.922817 - 0.670466i) q^{58} +(41.7010 + 30.2976i) q^{59} +(-36.7117 + 11.9283i) q^{61} +(-0.195527 + 0.269120i) q^{62} +(-26.1631 - 36.0104i) q^{63} +(19.4413 - 59.8340i) q^{64} +(-0.118856 + 0.128802i) q^{66} +81.7051 q^{67} +(-108.285 - 35.1838i) q^{68} +(3.12588 - 2.27108i) q^{69} +(-33.2581 - 102.358i) q^{71} +(-7.26594 + 2.36085i) q^{72} +(-34.7613 + 47.8449i) q^{73} +(-2.18915 - 3.01311i) q^{74} +105.842i q^{76} +(-6.36334 + 54.1658i) q^{77} -0.295992 q^{78} +(63.1470 + 20.5177i) q^{79} +(-65.0421 - 47.2559i) q^{81} +(-1.06061 - 3.26422i) q^{82} +(12.8655 - 4.18025i) q^{83} +(1.73859 - 2.39297i) q^{84} +(1.40913 - 4.33685i) q^{86} +1.60159i q^{87} +(8.50441 + 3.91165i) q^{88} +69.3575 q^{89} +(-74.5166 + 54.1395i) q^{91} +(-83.3594 - 60.5641i) q^{92} +(-0.144333 - 0.444211i) q^{93} +(6.29117 - 2.04412i) q^{94} +(-0.447826 - 0.616379i) q^{96} +(31.7379 - 97.6793i) q^{97} -2.60111i q^{98} +(19.3499 + 96.8397i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 5 q^{2} - 14 q^{3} + 9 q^{4} + 30 q^{6} - 5 q^{7} - 15 q^{8} - 31 q^{9} - 5 q^{11} + 4 q^{12} + 45 q^{13} + 37 q^{14} - 35 q^{16} - 5 q^{17} - 35 q^{18} + 80 q^{19} + 50 q^{22} - 34 q^{23} - 13 q^{26}+ \cdots - 609 q^{99}+O(q^{100}) $ 28 * q + 5 * q^2 - 14 * q^3 + 9 * q^4 + 30 * q^6 - 5 * q^7 - 15 * q^8 - 31 * q^9 - 5 * q^11 + 4 * q^12 + 45 * q^13 + 37 * q^14 - 35 * q^16 - 5 * q^17 - 35 * q^18 + 80 * q^19 + 50 * q^22 - 34 * q^23 - 13 * q^26 + 118 * q^27 + 145 * q^28 - 95 * q^29 + 95 * q^31 + 381 * q^33 - 148 * q^34 - 347 * q^36 - 146 * q^37 + 10 * q^38 - 65 * q^39 - 290 * q^41 - 615 * q^42 - 253 * q^44 - 110 * q^46 + 179 * q^47 - 364 * q^48 + 224 * q^49 + 400 * q^51 + 185 * q^52 - 344 * q^53 + 884 * q^56 + 430 * q^57 - 265 * q^58 + 67 * q^59 + 135 * q^61 - 155 * q^62 - 220 * q^63 - 119 * q^64 + 250 * q^66 + 204 * q^67 - 45 * q^68 + 311 * q^69 - 189 * q^71 + 235 * q^72 + 5 * q^73 + 940 * q^74 + 215 * q^77 - 290 * q^78 + 565 * q^79 - 583 * q^81 + 195 * q^82 + 530 * q^83 - 1050 * q^84 + 207 * q^86 + 1930 * q^88 + 146 * q^89 - 783 * q^91 - 521 * q^92 + 57 * q^93 - 845 * q^94 - 1210 * q^96 - 506 * q^97 - 609 * q^99

Character values

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

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

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 $

$2$	−0.101311	−	0.0329179i	−0.0506555	−	0.0164590i	0.283580	−	0.958949i	$-0.408478\pi$
$2$	−0.101311	−	0.0329179i	−0.0506555	−	0.0164590i	−0.334235	+	0.942490i	$0.608478\pi$
$3$	0.121004	−	0.0879149i	0.0403348	−	0.0293050i	−0.567435	−	0.823418i	$-0.692064\pi$
$3$	0.121004	−	0.0879149i	0.0403348	−	0.0293050i	0.607770	+	0.794113i	$0.292064\pi$
$4$	−3.22689	−	2.34447i	−0.806722	−	0.586118i
$5$		0			0
$5$		0			0
$6$	−0.0151531	+	0.00492353i	−0.00252551	+	0.000820588i
$7$	−2.91426	+	4.01113i	−0.416322	+	0.573019i	−0.964746	−	0.263182i	$-0.915228\pi$
$7$	−2.91426	+	4.01113i	−0.416322	+	0.573019i	0.548424	+	0.836201i	$0.315228\pi$
$8$	0.500198	+	0.688464i	0.0625248	+	0.0860580i
$9$	−2.77424	+	8.53823i	−0.308249	+	0.948692i
$10$		0			0
$11$	9.59279	−	5.38315i	0.872072	−	0.489377i
$11$	9.59279	−	5.38315i	0.872072	−	0.489377i
$12$	−0.596582			−0.0497151
$13$	17.6682	+	5.74075i	1.35909	+	0.441596i	0.895740	−	0.444578i	$-0.146646\pi$
$13$	17.6682	+	5.74075i	1.35909	+	0.441596i	0.463353	+	0.886174i	$0.346646\pi$
$14$	0.427284	−	0.310440i	0.0305203	−	0.0221743i
$15$		0			0
$16$	4.90223	+	15.0875i	0.306390	+	0.942970i
$17$	27.1482	−	8.82097i	1.59695	−	0.518881i	0.630600	−	0.776108i	$-0.282809\pi$
$17$	27.1482	−	8.82097i	1.59695	−	0.518881i	0.966351	+	0.257228i	$0.0828090\pi$
$18$	0.562122	−	0.773694i	0.0312290	−	0.0429830i
$19$	−15.5974	−	21.4680i	−0.820916	−	1.12989i	−0.989546	−	0.144215i	$-0.953934\pi$
$19$	−15.5974	−	21.4680i	−0.820916	−	1.12989i	0.168630	−	0.985679i	$-0.446066\pi$
$20$		0			0
$21$			0.741571i			0.0353129i
$22$	−1.14906	+	0.229597i	−0.0522299	+	0.0104362i
$23$	25.8328			1.12316			0.561582	−	0.827421i	$-0.310193\pi$
$23$	25.8328			1.12316			0.561582	+	0.827421i	$0.310193\pi$
$24$	0.121052	+	0.0393323i	0.00504385	+	0.00163885i
$25$		0			0
$26$	−1.60101	−	1.16320i	−0.0615773	−	0.0447385i
$27$	0.830919	+	2.55730i	0.0307748	+	0.0947150i
$28$	18.8080	−	6.11108i	0.671713	−	0.218253i
$29$	−6.29400	+	8.66295i	−0.217034	+	0.298722i	−0.903627	−	0.428320i	$-0.859106\pi$
$29$	−6.29400	+	8.66295i	−0.217034	+	0.298722i	0.686593	+	0.727042i	$0.259106\pi$
$30$		0			0
$31$	0.964986	−	2.96992i	0.0311286	−	0.0958040i	−0.934285	−	0.356527i	$-0.883961\pi$
$31$	0.964986	−	2.96992i	0.0311286	−	0.0958040i	0.965414	+	0.260723i	$0.0839609\pi$
$32$		−	5.09386i		−	0.159183i
$33$	0.687512	−	1.49473i	0.0208337	−	0.0452950i
$34$	−3.04077			−0.0894345
$35$		0			0
$36$	28.9698	−	21.0478i	0.804717	−	0.584661i
$37$	28.2855	+	20.5506i	0.764474	+	0.555423i	0.900279	−	0.435313i	$-0.143362\pi$
$37$	28.2855	+	20.5506i	0.764474	+	0.555423i	−0.135805	+	0.990736i	$0.543362\pi$
$38$	0.873507	+	2.68838i	0.0229870	+	0.0707468i
$39$	2.64263	−	0.858642i	0.0677597	−	0.0220165i
$40$		0			0
$41$	18.9383	+	26.0664i	0.461910	+	0.635765i	0.974904	−	0.222627i	$-0.0714634\pi$
$41$	18.9383	+	26.0664i	0.461910	+	0.635765i	−0.512993	+	0.858393i	$0.671463\pi$
$42$	0.0244110	−	0.0751293i	0.000581214	−	0.00178879i
$43$			42.8073i			0.995519i	0.867315	+	0.497759i	$0.165844\pi$
$43$			42.8073i			0.995519i	−0.867315	+	0.497759i	$0.834156\pi$
$44$	−43.5755	−	5.11920i	−0.990352	−	0.116346i
$45$		0			0
$46$	−2.61714	−	0.850361i	−0.0568944	−	0.0184861i
$47$	−50.2380	+	36.5001i	−1.06889	+	0.776597i	−0.975713	−	0.219052i	$-0.929703\pi$
$47$	−50.2380	+	36.5001i	−1.06889	+	0.776597i	−0.0931809	+	0.995649i	$0.529703\pi$
$48$	1.91961	+	1.39468i	0.0399919	+	0.0290558i
$49$	7.54556	+	23.2228i	0.153991	+	0.473935i
$50$		0			0
$51$	2.50955	−	3.45410i	0.0492069	−	0.0677275i
$52$	−43.5543	−	59.9474i	−0.837583	−	1.15283i
$53$	8.54679	−	26.3043i	0.161260	−	0.496308i	−0.837481	−	0.546466i	$-0.815973\pi$
$53$	8.54679	−	26.3043i	0.161260	−	0.496308i	0.998741	+	0.0501585i	$0.0159726\pi$
$54$		−	0.286435i		−	0.00530435i
$55$		0			0
$56$	−4.21923			−0.0753433
$57$	−3.77471	−	1.22648i	−0.0662230	−	0.0215172i
$58$	0.922817	−	0.670466i	0.0159106	−	0.0115598i
$59$	41.7010	+	30.2976i	0.706797	+	0.513518i	0.882139	−	0.470990i	$-0.156103\pi$
$59$	41.7010	+	30.2976i	0.706797	+	0.513518i	−0.175342	+	0.984508i	$0.556103\pi$
$60$		0			0
$61$	−36.7117	+	11.9283i	−0.601831	+	0.195547i	−0.594057	−	0.804423i	$-0.702475\pi$
$61$	−36.7117	+	11.9283i	−0.601831	+	0.195547i	−0.00777386	+	0.999970i	$0.502475\pi$
$62$	−0.195527	+	0.269120i	−0.00315367	+	0.00434065i
$63$	−26.1631	−	36.0104i	−0.415288	−	0.571594i
$64$	19.4413	−	59.8340i	0.303770	−	0.934907i
$65$		0			0
$66$	−0.118856	+	0.128802i	−0.00180085	+	0.00195154i
$67$	81.7051			1.21948			0.609740	−	0.792602i	$-0.291274\pi$
$67$	81.7051			1.21948			0.609740	+	0.792602i	$0.291274\pi$
$68$	−108.285	−	35.1838i	−1.59242	−	0.517409i
$69$	3.12588	−	2.27108i	0.0453026	−	0.0329143i
$70$		0			0
$71$	−33.2581	−	102.358i	−0.468424	−	1.44166i	−0.854625	−	0.519246i	$-0.826213\pi$
$71$	−33.2581	−	102.358i	−0.468424	−	1.44166i	0.386201	−	0.922415i	$-0.373787\pi$
$72$	−7.26594	+	2.36085i	−0.100916	+	0.0327895i
$73$	−34.7613	+	47.8449i	−0.476183	+	0.655409i	−0.977766	−	0.209700i	$-0.932751\pi$
$73$	−34.7613	+	47.8449i	−0.476183	+	0.655409i	0.501583	+	0.865110i	$0.332751\pi$
$74$	−2.18915	−	3.01311i	−0.0295831	−	0.0407177i
$75$		0			0
$76$			105.842i			1.39266i
$77$	−6.36334	+	54.1658i	−0.0826408	+	0.703452i
$78$	−0.295992			−0.00379477
$79$	63.1470	+	20.5177i	0.799329	+	0.259718i	0.680072	−	0.733145i	$-0.261949\pi$
$79$	63.1470	+	20.5177i	0.799329	+	0.259718i	0.119258	+	0.992863i	$0.461949\pi$
$80$		0			0
$81$	−65.0421	−	47.2559i	−0.802989	−	0.583406i
$82$	−1.06061	−	3.26422i	−0.0129343	−	0.0398076i
$83$	12.8655	−	4.18025i	0.155006	−	0.0503644i	−0.230486	−	0.973076i	$-0.574032\pi$
$83$	12.8655	−	4.18025i	0.155006	−	0.0503644i	0.385492	+	0.922711i	$0.374032\pi$
$84$	1.73859	−	2.39297i	0.0206975	−	0.0284877i
$85$		0			0
$86$	1.40913	−	4.33685i	0.0163852	−	0.0504285i
$87$			1.60159i			0.0184091i
$88$	8.50441	+	3.91165i	0.0966410	+	0.0444506i
$89$	69.3575			0.779297			0.389649	−	0.920964i	$-0.372596\pi$
$89$	69.3575			0.779297			0.389649	+	0.920964i	$0.372596\pi$
$90$		0			0
$91$	−74.5166	+	54.1395i	−0.818864	+	0.594939i
$92$	−83.3594	−	60.5641i	−0.906080	−	0.658306i
$93$	−0.144333	−	0.444211i	−0.00155197	−	0.00477646i
$94$	6.29117	−	2.04412i	0.0669273	−	0.0217460i
$95$		0			0
$96$	−0.447826	−	0.616379i	−0.00466485	−	0.00642062i
$97$	31.7379	−	97.6793i	0.327195	−	1.00700i	−0.643245	−	0.765661i	$-0.722412\pi$
$97$	31.7379	−	97.6793i	0.327195	−	1.00700i	0.970440	−	0.241343i	$-0.0775877\pi$
$98$		−	2.60111i		−	0.0265420i
$99$	19.3499	+	96.8397i	0.195453	+	0.978178i
$100$		0			0
$101$	−41.1989	−	13.3863i	−0.407910	−	0.132538i	0.0978725	−	0.995199i	$-0.468796\pi$
$101$	−41.1989	−	13.3863i	−0.407910	−	0.132538i	−0.505783	+	0.862661i	$0.668796\pi$
$102$	−0.367947	+	0.267329i	−0.00360733	+	0.00262088i
$103$	−142.199	−	103.314i	−1.38058	−	1.00305i	−0.996826	−	0.0796093i	$-0.974633\pi$
$103$	−142.199	−	103.314i	−1.38058	−	1.00305i	−0.383749	−	0.923437i	$-0.625367\pi$
$104$	4.88531	+	15.0354i	0.0469741	+	0.144572i
$105$		0			0
$106$	−1.73177	+	2.38357i	−0.0163374	+	0.0224865i
$107$	17.7189	+	24.3879i	0.165597	+	0.227925i	0.883749	−	0.467962i	$-0.155012\pi$
$107$	17.7189	+	24.3879i	0.165597	+	0.227925i	−0.718152	+	0.695887i	$0.755012\pi$
$108$	3.31425	−	10.2002i	0.0306875	−	0.0944463i
$109$		−	162.867i		−	1.49420i	−0.664714	−	0.747098i	$-0.731446\pi$
$109$		−	162.867i		−	1.49420i	0.664714	−	0.747098i	$-0.268554\pi$
$110$		0			0
$111$	5.22938			0.0471116
$112$	−74.8044	−	24.3054i	−0.667896	−	0.217013i
$113$	−146.189	+	106.213i	−1.29371	+	0.939934i	−0.999873	−	0.0159217i	$-0.994932\pi$
$113$	−146.189	+	106.213i	−1.29371	+	0.939934i	−0.293835	+	0.955856i	$0.594932\pi$
$114$	0.342046	+	0.248511i	0.00300041	+	0.00217992i
$115$		0			0
$116$	40.6201	−	13.1983i	0.350173	−	0.113778i
$117$	−98.0317	+	134.929i	−0.837878	+	1.15324i
$118$	−3.22744	−	4.44219i	−0.0273512	−	0.0376456i
$119$	−43.7346	+	134.601i	−0.367518	+	1.13110i
$120$		0			0
$121$	63.0434	−	103.279i	0.521020	−	0.853545i
$122$	4.11195			0.0337045
$123$	4.58324	+	1.48919i	0.0372622	+	0.0121072i
$124$	−10.0768	+	7.32122i	−0.0812645	+	0.0590421i
$125$		0			0
$126$	1.46522	+	4.50949i	0.0116287	+	0.0357896i
$127$	22.6358	−	7.35483i	0.178235	−	0.0579120i	−0.218540	−	0.975828i	$-0.570129\pi$
$127$	22.6358	−	7.35483i	0.178235	−	0.0579120i	0.396775	+	0.917916i	$0.370129\pi$
$128$	−15.9156	+	21.9059i	−0.124341	+	0.171140i
$129$	3.76340	+	5.17988i	0.0291736	+	0.0401541i
$130$		0			0
$131$			20.0018i			0.152685i	0.997082	+	0.0763426i	$0.0243243\pi$
$131$			20.0018i			0.152685i	−0.997082	+	0.0763426i	$0.975676\pi$
$132$	−5.72288	+	3.21149i	−0.0433552	+	0.0243295i
$133$	131.566			0.989216
$134$	−8.27762	−	2.68956i	−0.0617733	−	0.0200714i
$135$		0			0
$136$	19.6524	+	14.2783i	0.144503	+	0.104987i
$137$	27.2731	+	83.9379i	0.199074	+	0.612686i	0.999905	+	0.0137956i	$0.00439140\pi$
$137$	27.2731	+	83.9379i	0.199074	+	0.612686i	−0.800831	+	0.598890i	$0.795609\pi$
$138$	−0.391445	+	0.127188i	−0.00283656	+	0.000921654i
$139$	67.3531	−	92.7036i	0.484555	−	0.666932i	−0.494818	−	0.868997i	$-0.664765\pi$
$139$	67.3531	−	92.7036i	0.484555	−	0.666932i	0.979372	+	0.202065i	$0.0647651\pi$
$140$		0			0
$141$	−2.87013	+	8.83334i	−0.0203555	+	0.0626478i
$142$			11.4648i			0.0807378i
$143$	200.391	−	40.0408i	1.40133	−	0.280006i
$144$	−142.421			−0.989033
$145$		0			0
$146$	5.09666	−	3.70294i	0.0349086	−	0.0253626i
$147$	2.95468	+	2.14670i	0.0200999	+	0.0146034i
$148$	−43.0939	−	132.629i	−0.291175	−	0.896143i
$149$	−110.403	+	35.8722i	−0.740962	+	0.240753i	−0.655088	−	0.755553i	$-0.727368\pi$
$149$	−110.403	+	35.8722i	−0.740962	+	0.240753i	−0.0858741	+	0.996306i	$0.527368\pi$
$150$		0			0
$151$	−5.47261	−	7.53241i	−0.0362425	−	0.0498835i	0.790511	−	0.612448i	$-0.209815\pi$
$151$	−5.47261	−	7.53241i	−0.0362425	−	0.0498835i	−0.826754	+	0.562564i	$0.809815\pi$
$152$	6.97814	−	21.4765i	0.0459088	−	0.141293i
$153$			256.269i			1.67496i
$154$	2.42770	−	5.27812i	0.0157643	−	0.0342735i
$155$		0			0
$156$	−10.5405	−	3.42483i	−0.0675675	−	0.0219540i
$157$	102.228	−	74.2729i	0.651133	−	0.473076i	−0.212524	−	0.977156i	$-0.568168\pi$
$157$	102.228	−	74.2729i	0.651133	−	0.473076i	0.863657	+	0.504080i	$0.168168\pi$
$158$	−5.72208	−	4.15734i	−0.0362157	−	0.0263123i
$159$	−1.27834	−	3.93433i	−0.00803988	−	0.0247442i
$160$		0			0
$161$	−75.2833	+	103.619i	−0.467598	+	0.643594i
$162$	5.03391	+	6.92859i	0.0310735	+	0.0427691i
$163$	61.6337	−	189.689i	0.378121	−	1.16374i	−0.563228	−	0.826301i	$-0.690441\pi$
$163$	61.6337	−	189.689i	0.378121	−	1.16374i	0.941349	−	0.337435i	$-0.109559\pi$
$164$		−	128.514i		−	0.783620i
$165$		0			0
$166$	−1.44102			−0.00868084
$167$	20.2380	+	6.57572i	0.121186	+	0.0393756i	0.368982	−	0.929437i	$-0.379706\pi$
$167$	20.2380	+	6.57572i	0.121186	+	0.0393756i	−0.247796	+	0.968812i	$0.579706\pi$
$168$	−0.510545	+	0.370933i	−0.00303896	+	0.00220793i
$169$	142.486	+	103.522i	0.843110	+	0.612555i
$170$		0			0
$171$	226.570	−	73.6169i	1.32497	−	0.430508i
$172$	100.360	−	138.134i	0.583491	−	0.803107i
$173$	122.377	+	168.437i	0.707379	+	0.973624i	0.999849	+	0.0173494i	$0.00552275\pi$
$173$	122.377	+	168.437i	0.707379	+	0.973624i	−0.292470	+	0.956275i	$0.594477\pi$
$174$	0.0527211	−	0.162259i	0.000302995	−	0.000932521i
$175$		0			0
$176$	128.245	+	118.342i	0.728662	+	0.672398i
$177$	7.70962			0.0435571
$178$	−7.02667	−	2.28310i	−0.0394757	−	0.0128264i
$179$	39.4489	−	28.6613i	0.220385	−	0.160119i	−0.472115	−	0.881537i	$-0.656509\pi$
$179$	39.4489	−	28.6613i	0.220385	−	0.160119i	0.692500	+	0.721418i	$0.256509\pi$
$180$		0			0
$181$	47.9638	+	147.617i	0.264993	+	0.815565i	0.991695	+	0.128612i	$0.0410522\pi$
$181$	47.9638	+	147.617i	0.264993	+	0.815565i	−0.726702	+	0.686953i	$0.758948\pi$
$182$	9.33151	−	3.03199i	0.0512720	−	0.0166593i
$183$	−3.39360	+	4.67088i	−0.0185442	+	0.0255240i
$184$	12.9215	+	17.7849i	0.0702256	+	0.0966572i
$185$		0			0
$186$			0.0497545i			0.000267497i
$187$	212.942	−	230.760i	1.13873	−	1.23401i
$188$	247.686			1.31748
$189$	−12.6792	−	4.11972i	−0.0670857	−	0.0217975i
$190$		0			0
$191$	−114.165	−	82.9456i	−0.597722	−	0.434270i	0.247348	−	0.968927i	$-0.420441\pi$
$191$	−114.165	−	82.9456i	−0.597722	−	0.434270i	−0.845069	+	0.534657i	$0.820441\pi$
$192$	−2.90782	−	8.94936i	−0.0151449	−	0.0466112i
$193$	290.300	−	94.3242i	1.50415	−	0.488727i	0.562922	−	0.826510i	$-0.309677\pi$
$193$	290.300	−	94.3242i	1.50415	−	0.488727i	0.941224	+	0.337783i	$0.109677\pi$
$194$	−6.43080	+	8.85124i	−0.0331485	+	0.0456249i
$195$		0			0
$196$	30.0966	−	92.6278i	0.153554	−	0.472591i
$197$			300.287i			1.52430i	0.647400	+	0.762151i	$0.275856\pi$
$197$			300.287i			1.52430i	−0.647400	+	0.762151i	$0.724144\pi$
$198$	1.22740	−	10.4479i	0.00619901	−	0.0527671i
$199$	−328.028			−1.64838			−0.824190	−	0.566313i	$-0.808369\pi$
$199$	−328.028			−1.64838			−0.824190	+	0.566313i	$0.808369\pi$
$200$		0			0
$201$	9.88668	−	7.18309i	0.0491875	−	0.0357368i
$202$	3.73325	+	2.71237i	0.0184815	+	0.0134276i
$203$	−16.4059	−	50.4921i	−0.0808171	−	0.248730i
$204$	−16.1961	+	5.26243i	−0.0793926	+	0.0257962i
$205$		0			0
$206$	11.0055	+	15.1477i	0.0534246	+	0.0735326i
$207$	−71.6663	+	220.566i	−0.346214	+	1.06554i
$208$			294.712i			1.41688i
$209$	−265.188	−	121.975i	−1.26884	−	0.583611i
$210$		0			0
$211$	−198.717	−	64.5672i	−0.941789	−	0.306006i	−0.202414	−	0.979300i	$-0.564879\pi$
$211$	−198.717	−	64.5672i	−0.941789	−	0.306006i	−0.739375	+	0.673294i	$0.764879\pi$
$212$	−89.2492	+	64.8434i	−0.420987	+	0.305865i
$213$	−13.0232	−	9.46188i	−0.0611416	−	0.0444220i
$214$	−0.992316	−	3.05403i	−0.00463699	−	0.0142712i
$215$		0			0
$216$	−1.34499	+	1.85122i	−0.00622680	+	0.00857045i
$217$	9.10053	+	12.5258i	0.0419379	+	0.0577226i
$218$	−5.36126	+	16.5003i	−0.0245929	+	0.0756892i
$219$			8.84548i			0.0403903i
$220$		0			0
$221$	530.298			2.39954
$222$	−0.529794	−	0.172140i	−0.00238646	−	0.000775407i
$223$	52.7495	−	38.3248i	0.236545	−	0.171860i	−0.463198	−	0.886255i	$-0.653298\pi$
$223$	52.7495	−	38.3248i	0.236545	−	0.171860i	0.699743	+	0.714395i	$0.253298\pi$
$224$	20.4321	+	14.8448i	0.0912148	+	0.0662715i
$225$		0			0
$226$	18.3069	−	5.94826i	0.0810038	−	0.0263197i
$227$	14.5146	−	19.9777i	0.0639410	−	0.0880073i	−0.775849	−	0.630919i	$-0.782678\pi$
$227$	14.5146	−	19.9777i	0.0639410	−	0.0880073i	0.839790	+	0.542912i	$0.182678\pi$
$228$	9.30513	+	12.8074i	0.0408120	+	0.0561728i
$229$	12.9100	−	39.7328i	0.0563754	−	0.173506i	−0.918904	−	0.394481i	$-0.870924\pi$
$229$	12.9100	−	39.7328i	0.0563754	−	0.173506i	0.975279	+	0.220976i	$0.0709242\pi$
$230$		0			0
$231$	3.99199	+	7.11374i	0.0172813	+	0.0307954i
$232$	−9.11237			−0.0392775
$233$	−341.939	−	111.103i	−1.46755	−	0.476836i	−0.537183	−	0.843466i	$-0.680511\pi$
$233$	−341.939	−	111.103i	−1.46755	−	0.476836i	−0.930367	+	0.366630i	$0.880511\pi$
$234$	14.3733	−	10.4428i	0.0614242	−	0.0446273i
$235$		0			0
$236$	−63.5327	−	195.534i	−0.269207	−	0.828532i
$237$	9.44488	−	3.06883i	0.0398518	−	0.0129486i
$238$	8.86160	−	12.1969i	0.0372336	−	0.0512477i
$239$	89.9081	+	123.748i	0.376184	+	0.517773i	0.954569	−	0.297991i	$-0.0963165\pi$
$239$	89.9081	+	123.748i	0.376184	+	0.517773i	−0.578384	+	0.815764i	$0.696317\pi$
$240$		0			0
$241$			411.766i			1.70857i	0.519801	+	0.854287i	$0.326006\pi$
$241$			411.766i			1.70857i	−0.519801	+	0.854287i	$0.673994\pi$
$242$	−9.78671	+	8.38803i	−0.0404410	+	0.0346613i
$243$	−36.2251			−0.149074
$244$	146.430	+	47.5780i	0.600123	+	0.194992i
$245$		0			0
$246$	−0.415312	−	0.301742i	−0.00168826	−	0.00122659i
$247$	−152.336	−	468.842i	−0.616745	−	1.89814i
$248$	2.52737	−	0.821192i	0.0101910	−	0.00331126i
$249$	1.18927	−	1.63690i	0.00477620	−	0.00657388i
$250$		0			0
$251$	108.491	−	333.902i	0.432237	−	1.33029i	−0.463655	−	0.886016i	$-0.653462\pi$
$251$	108.491	−	333.902i	0.432237	−	1.33029i	0.895892	−	0.444272i	$-0.146538\pi$
$252$			177.540i			0.704525i
$253$	247.808	−	139.062i	0.979479	−	0.549651i
$254$	−2.53536			−0.00998174
$255$		0			0
$256$	−201.258	+	146.222i	−0.786164	+	0.571181i
$257$	−210.588	−	153.001i	−0.819408	−	0.595335i	0.0971345	−	0.995271i	$-0.469032\pi$
$257$	−210.588	−	153.001i	−0.819408	−	0.595335i	−0.916543	+	0.399936i	$0.869032\pi$
$258$	−0.210763	−	0.648661i	−0.000816910	−	0.00251419i
$259$	−164.863	+	53.5671i	−0.636535	+	0.206823i
$260$		0			0
$261$	−56.5052	−	77.7727i	−0.216495	−	0.297980i
$262$	0.658416	−	2.02640i	0.00251304	−	0.00773434i
$263$			342.750i			1.30323i	0.758549	+	0.651616i	$0.225909\pi$
$263$			342.750i			1.30323i	−0.758549	+	0.651616i	$0.774091\pi$
$264$	1.37296	−	0.274337i	0.00520062	−	0.00103915i
$265$		0			0
$266$	−13.3291	−	4.33087i	−0.0501092	−	0.0162815i
$267$	8.39256	−	6.09755i	0.0314328	−	0.0228373i
$268$	−263.653	−	191.555i	−0.983781	−	0.714758i
$269$	−40.8387	−	125.688i	−0.151817	−	0.467243i	0.846008	−	0.533170i	$-0.179000\pi$
$269$	−40.8387	−	125.688i	−0.151817	−	0.467243i	−0.997824	+	0.0659271i	$0.979000\pi$
$270$		0			0
$271$	−68.2898	+	93.9929i	−0.251992	+	0.346837i	−0.916208	−	0.400704i	$-0.868766\pi$
$271$	−68.2898	+	93.9929i	−0.251992	+	0.346837i	0.664216	+	0.747541i	$0.268766\pi$
$272$	266.173	+	366.356i	0.978578	+	1.34690i
$273$	−4.25717	+	13.1022i	−0.0155940	+	0.0479935i
$274$		−	9.40161i		−	0.0343124i
$275$		0			0
$276$	−15.4113			−0.0558382
$277$	−62.1400	−	20.1905i	−0.224332	−	0.0728899i	0.194694	−	0.980864i	$-0.437629\pi$
$277$	−62.1400	−	20.1905i	−0.224332	−	0.0728899i	−0.419026	+	0.907974i	$0.637629\pi$
$278$	−9.87522	+	7.17477i	−0.0355224	+	0.0258085i
$279$	22.6808	+	16.4786i	0.0812931	+	0.0590629i
$280$		0			0
$281$	−208.088	+	67.6118i	−0.740526	+	0.240611i	−0.654900	−	0.755716i	$-0.727289\pi$
$281$	−208.088	+	67.6118i	−0.740526	+	0.240611i	−0.0856263	+	0.996327i	$0.527289\pi$
$282$	0.581550	−	0.800435i	0.00206224	−	0.00283842i
$283$	−110.353	−	151.887i	−0.389938	−	0.536704i	0.568245	−	0.822860i	$-0.307623\pi$
$283$	−110.353	−	151.887i	−0.389938	−	0.536704i	−0.958183	+	0.286155i	$0.907623\pi$
$284$	−132.655	+	408.270i	−0.467095	+	1.43757i
$285$		0			0
$286$	−21.6198	−	2.53988i	−0.0755939	−	0.00888068i
$287$	−159.747			−0.556609
$288$	43.4925	+	14.1316i	0.151016	+	0.0490680i
$289$	425.407	−	309.076i	1.47200	−	1.06947i
$290$		0			0
$291$	−4.74703	−	14.6099i	−0.0163128	−	0.0502057i
$292$	224.342	−	72.8931i	0.768294	−	0.249634i
$293$	−284.095	+	391.023i	−0.969607	+	1.33455i	−0.0273613	+	0.999626i	$0.508710\pi$
$293$	−284.095	+	391.023i	−0.969607	+	1.33455i	−0.942245	+	0.334923i	$0.891290\pi$
$294$	−0.228676	−	0.314746i	−0.000777811	−	0.00107056i
$295$		0			0
$296$			29.7530i			0.100517i
$297$	21.7372	+	20.0587i	0.0731892	+	0.0675378i
$298$	12.3659			0.0414963
$299$	456.419	+	148.299i	1.52648	+	0.495984i
$300$		0			0
$301$	−171.706	−	124.752i	−0.570451	−	0.414457i
$302$	0.306485	+	0.943262i	0.00101485	+	0.00312339i
$303$	−6.16211	+	2.00219i	−0.0203370	+	0.00660790i
$304$	247.437	−	340.567i	0.813936	−	1.12029i
$305$		0			0
$306$	8.43584	−	25.9628i	0.0275681	−	0.0848459i
$307$		−	42.8858i		−	0.139693i	−0.997558	−	0.0698466i	$-0.977749\pi$
$307$		−	42.8858i		−	0.139693i	0.997558	−	0.0698466i	$-0.0222510\pi$
$308$	147.524	−	159.868i	0.478974	−	0.519053i
$309$	−26.2896			−0.0850795
$310$		0			0
$311$	−190.665	+	138.527i	−0.613072	+	0.445423i	−0.850495	−	0.525983i	$-0.823697\pi$
$311$	−190.665	+	138.527i	−0.613072	+	0.445423i	0.237423	+	0.971406i	$0.423697\pi$
$312$	1.91298	+	1.38986i	0.00613136	+	0.00445469i
$313$	−95.7292	−	294.624i	−0.305844	−	0.941291i	−0.979361	−	0.202119i	$-0.935217\pi$
$313$	−95.7292	−	294.624i	−0.305844	−	0.941291i	0.673517	−	0.739172i	$-0.264783\pi$
$314$	−12.8017	+	4.15953i	−0.0407698	+	0.0132469i
$315$		0			0
$316$	−155.665	−	214.255i	−0.492611	−	0.678021i
$317$	83.4626	−	256.871i	0.263289	−	0.810320i	−0.728794	−	0.684733i	$-0.759919\pi$
$317$	83.4626	−	256.871i	0.263289	−	0.810320i	0.992083	−	0.125587i	$-0.0400813\pi$
$318$			0.440671i			0.00138576i
$319$	−13.7431	+	116.983i	−0.0430818	+	0.366719i
$320$		0			0
$321$	4.28813	+	1.39330i	0.0133587	+	0.00434049i
$322$	11.0379	−	8.01953i	0.0342793	−	0.0249054i
$323$	−612.809	−	445.232i	−1.89724	−	1.37843i
$324$	99.0936	+	304.979i	0.305844	+	0.941292i
$325$		0			0
$326$	−12.4883	+	17.1887i	−0.0383078	+	0.0527261i
$327$	−14.3185	−	19.7077i	−0.0437874	−	0.0602681i
$328$	−8.47284	+	26.0767i	−0.0258318	+	0.0795022i
$329$		−	307.882i		−	0.935811i
$330$		0			0
$331$	20.4547			0.0617967			0.0308983	−	0.999523i	$-0.490163\pi$
$331$	20.4547			0.0617967			0.0308983	+	0.999523i	$0.490163\pi$
$332$	−51.3159	−	16.6736i	−0.154566	−	0.0502216i
$333$	−253.937	+	184.496i	−0.762574	+	0.554042i
$334$	−1.83387	−	1.33239i	−0.00549063	−	0.00398918i
$335$		0			0
$336$	−11.1885	+	3.63536i	−0.0332990	+	0.0108195i
$337$	−74.0571	+	101.931i	−0.219754	+	0.302466i	−0.904633	−	0.426191i	$-0.859855\pi$
$337$	−74.0571	+	101.931i	−0.219754	+	0.302466i	0.684879	+	0.728657i	$0.259855\pi$
$338$	−11.0276	−	15.1782i	−0.0326261	−	0.0449060i
$339$	−8.35186	+	25.7044i	−0.0246368	+	0.0758242i
$340$		0			0
$341$	−6.73063	−	33.6845i	−0.0197379	−	0.0987816i
$342$	−25.3773			−0.0742026
$343$	−346.193	−	112.485i	−1.00931	−	0.327944i
$344$	−29.4713	+	21.4121i	−0.0856724	+	0.0622446i
$345$		0			0
$346$	−6.85350	−	21.0929i	−0.0198078	−	0.0609621i
$347$	−451.079	+	146.564i	−1.29994	+	0.422376i	−0.875560	−	0.483109i	$-0.839508\pi$
$347$	−451.079	+	146.564i	−1.29994	+	0.422376i	−0.424379	+	0.905485i	$0.639508\pi$
$348$	3.75488	−	5.16815i	0.0107899	−	0.0148510i
$349$	−164.395	−	226.270i	−0.471046	−	0.648339i	0.505707	−	0.862705i	$-0.331232\pi$
$349$	−164.395	−	226.270i	−0.471046	−	0.648339i	−0.976753	+	0.214366i	$0.931232\pi$
$350$		0			0
$351$			49.9531i			0.142316i
$352$	−27.4210	−	48.8643i	−0.0779006	−	0.138819i
$353$	292.911			0.829775			0.414888	−	0.909873i	$-0.363821\pi$
$353$	292.911			0.829775			0.414888	+	0.909873i	$0.363821\pi$
$354$	−0.781069	−	0.253785i	−0.00220641	−	0.000716905i
$355$		0			0
$356$	−223.809	−	162.607i	−0.628676	−	0.456760i
$357$	6.54138	+	20.1323i	0.0183232	+	0.0563930i
$358$	−4.94007	+	1.60513i	−0.0137991	+	0.00448360i
$359$	−76.3495	+	105.086i	−0.212673	+	0.292719i	−0.902004	−	0.431727i	$-0.857904\pi$
$359$	−76.3495	+	105.086i	−0.212673	+	0.292719i	0.689332	+	0.724446i	$0.257904\pi$
$360$		0			0
$361$	−106.040	+	326.358i	−0.293740	+	0.904040i
$362$		−	16.5341i		−	0.0456744i
$363$	−1.45123	−	18.0397i	−0.00399787	−	0.0496960i
$364$	367.385			1.00930
$365$		0			0
$366$	0.497564	−	0.361502i	0.00135947	−	0.000987709i
$367$	−121.593	−	88.3422i	−0.331315	−	0.240715i	0.409673	−	0.912232i	$-0.365643\pi$
$367$	−121.593	−	88.3422i	−0.331315	−	0.240715i	−0.740988	+	0.671518i	$0.765643\pi$
$368$	126.638	+	389.752i	0.344125	+	1.05911i
$369$	−275.100	+	89.3855i	−0.745529	+	0.242237i
$370$		0			0
$371$	80.6025	+	110.940i	0.217257	+	0.299029i
$372$	−0.575693	+	1.77180i	−0.00154756	+	0.00476291i
$373$			563.298i			1.51018i	0.655620	+	0.755091i	$0.272407\pi$
$373$			563.298i			1.51018i	−0.655620	+	0.755091i	$0.727593\pi$
$374$	−29.1695	+	16.3689i	−0.0779934	+	0.0437672i
$375$		0			0
$376$	−50.2580	−	16.3298i	−0.133665	−	0.0434303i
$377$	−160.935	+	116.926i	−0.426885	+	0.310150i
$378$	1.14893	+	0.834746i	0.00303949	+	0.00220832i
$379$	71.0636	+	218.711i	0.187503	+	0.577075i	0.999983	−	0.00591490i	$-0.00188278\pi$
$379$	71.0636	+	218.711i	0.187503	+	0.577075i	−0.812480	+	0.582990i	$0.801883\pi$
$380$		0			0
$381$	2.09244	−	2.87999i	0.00549196	−	0.00755904i
$382$	8.83575	+	12.1614i	0.0231302	+	0.0318360i
$383$	200.665	−	617.582i	0.523928	−	1.61249i	−0.242497	−	0.970152i	$-0.577966\pi$
$383$	200.665	−	617.582i	0.523928	−	1.61249i	0.766425	−	0.642333i	$-0.222034\pi$
$384$			4.04993i			0.0105467i
$385$		0			0
$386$	−32.5155			−0.0842372
$387$	−365.499	−	118.758i	−0.944441	−	0.306868i
$388$	−331.421	+	240.791i	−0.854178	+	0.620597i
$389$	365.035	+	265.214i	0.938394	+	0.681783i	0.948034	−	0.318170i	$-0.103068\pi$
$389$	365.035	+	265.214i	0.938394	+	0.681783i	−0.00963935	+	0.999954i	$0.503068\pi$
$390$		0			0
$391$	701.312	−	227.870i	1.79364	−	0.582788i
$392$	−12.2138	+	16.8109i	−0.0311577	+	0.0428849i
$393$	1.75845	+	2.42030i	0.00447443	+	0.00615853i
$394$	9.88484	−	30.4224i	0.0250884	−	0.0772142i
$395$		0			0
$396$	164.598	−	357.856i	0.415651	−	0.903677i
$397$	193.392			0.487133			0.243567	−	0.969884i	$-0.421683\pi$
$397$	193.392			0.487133			0.243567	+	0.969884i	$0.421683\pi$
$398$	33.2328	+	10.7980i	0.0834995	+	0.0271306i
$399$	15.9200	−	11.5666i	0.0398999	−	0.0289889i
$400$		0			0
$401$	16.6678	+	51.2982i	0.0415655	+	0.127926i	0.969686	−	0.244355i	$-0.0785761\pi$
$401$	16.6678	+	51.2982i	0.0415655	+	0.127926i	−0.928120	+	0.372280i	$0.878576\pi$
$402$	−1.23808	+	0.402277i	−0.00307981	+	0.00100069i
$403$	34.0992	−	46.9335i	0.0846133	−	0.116460i
$404$	101.560	+	139.786i	0.251387	+	0.346005i
$405$		0			0
$406$			5.65545i			0.0139297i
$407$	381.965	+	44.8728i	0.938488	+	0.110252i
$408$	3.63330			0.00890515
$409$	−376.937	−	122.474i	−0.921605	−	0.299448i	−0.190480	−	0.981691i	$-0.561004\pi$
$409$	−376.937	−	122.474i	−0.921605	−	0.299448i	−0.731125	+	0.682243i	$0.761004\pi$
$410$		0			0
$411$	10.6796	+	7.75915i	0.0259843	+	0.0188787i
$412$	216.645	+	666.764i	0.525837	+	1.61836i
$413$	−243.055	+	78.9733i	−0.588511	+	0.191219i
$414$	14.5212	−	19.9867i	0.0350753	−	0.0482769i
$415$		0			0
$416$	29.2425	−	89.9993i	0.0702946	−	0.216345i
$417$		−	17.1389i		−	0.0411004i
$418$	22.8513	+	21.0868i	0.0546682	+	0.0504469i
$419$	−689.397			−1.64534			−0.822669	−	0.568520i	$-0.807516\pi$
$419$	−689.397			−1.64534			−0.822669	+	0.568520i	$0.807516\pi$
$420$		0			0
$421$	139.546	−	101.386i	0.331463	−	0.240822i	−0.409588	−	0.912270i	$-0.634328\pi$
$421$	139.546	−	101.386i	0.331463	−	0.240822i	0.741051	+	0.671449i	$0.234328\pi$
$422$	18.0068	+	13.0827i	0.0426702	+	0.0310017i
$423$	−172.274	−	530.204i	−0.407266	−	1.25344i
$424$	22.3847	−	7.27322i	0.0527940	−	0.0171538i
$425$		0			0
$426$	1.00792	+	1.38729i	0.00236602	+	0.00325654i
$427$	59.1411	−	182.018i	0.138504	−	0.426271i
$428$		−	120.239i		−	0.280931i
$429$	20.7280	−	22.4625i	0.0483170	−	0.0523600i
$430$		0			0
$431$	−426.191	−	138.478i	−0.988842	−	0.321294i	−0.230444	−	0.973086i	$-0.574018\pi$
$431$	−426.191	−	138.478i	−0.988842	−	0.321294i	−0.758398	+	0.651791i	$0.774018\pi$
$432$	−34.5100	+	25.0730i	−0.0798843	+	0.0580394i
$433$	538.217	+	391.038i	1.24300	+	0.903090i	0.997794	−	0.0663824i	$-0.0211457\pi$
$433$	538.217	+	391.038i	1.24300	+	0.903090i	0.245202	+	0.969472i	$0.421146\pi$
$434$	−0.509660	−	1.56857i	−0.00117433	−	0.00361422i
$435$		0			0
$436$	−381.838	+	525.555i	−0.875775	+	1.20540i
$437$	−402.924	−	554.577i	−0.922023	−	1.26906i
$438$	0.291175	−	0.896145i	0.000664783	−	0.00204599i
$439$		−	498.050i		−	1.13451i	−0.823542	−	0.567255i	$-0.808006\pi$
$439$		−	498.050i		−	1.13451i	0.823542	−	0.567255i	$-0.191994\pi$
$440$		0			0
$441$	−219.215			−0.497086
$442$	−53.7250	−	17.4563i	−0.121550	−	0.0394939i
$443$	409.429	−	297.467i	0.924219	−	0.671484i	−0.0203518	−	0.999793i	$-0.506479\pi$
$443$	409.429	−	297.467i	0.924219	−	0.671484i	0.944570	+	0.328309i	$0.106479\pi$
$444$	−16.8746	−	12.2601i	−0.0380059	−	0.0276129i
$445$		0			0
$446$	−6.60568	+	2.14631i	−0.0148109	+	0.00481237i
$447$	−10.2056	+	14.0468i	−0.0228313	+	0.0314246i
$448$	183.345	+	252.353i	0.409253	+	0.563288i
$449$	182.166	−	560.649i	0.405715	−	1.24866i	−0.514582	−	0.857441i	$-0.672053\pi$
$449$	182.166	−	560.649i	0.405715	−	1.24866i	0.920297	−	0.391221i	$-0.127947\pi$
$450$		0			0
$451$	321.991	+	148.101i	0.713948	+	0.328385i
$452$	720.748			1.59458
$453$	−1.32442	−	0.430331i	−0.00292367	−	0.000949957i
$454$	−2.12811	+	1.54616i	−0.00468747	+	0.00340565i
$455$		0			0
$456$	−1.04372	−	3.21224i	−0.00228886	−	0.00704438i
$457$	432.905	−	140.659i	0.947276	−	0.307789i	0.205668	−	0.978622i	$-0.434063\pi$
$457$	432.905	−	140.659i	0.947276	−	0.307789i	0.741608	+	0.670833i	$0.234063\pi$
$458$	−2.61584	+	3.60040i	−0.00571144	+	0.00786113i
$459$	45.1158	+	62.0966i	0.0982916	+	0.135287i
$460$		0			0
$461$			627.429i			1.36102i	0.732740	+	0.680509i	$0.238241\pi$
$461$			627.429i			1.36102i	−0.732740	+	0.680509i	$0.761759\pi$
$462$	−0.170263	−	0.852108i	−0.000368534	−	0.00184439i
$463$	546.399			1.18013			0.590064	−	0.807357i	$-0.299103\pi$
$463$	546.399			1.18013			0.590064	+	0.807357i	$0.299103\pi$
$464$	−161.557	−	52.4931i	−0.348183	−	0.113132i
$465$		0			0
$466$	30.9849	+	22.5118i	0.0664912	+	0.0483087i
$467$	−44.7840	−	137.831i	−0.0958972	−	0.295141i	0.891589	−	0.452845i	$-0.149591\pi$
$467$	−44.7840	−	137.831i	−0.0958972	−	0.295141i	−0.987486	+	0.157704i	$0.949591\pi$
$468$	632.675	−	205.568i	1.35187	−	0.439249i
$469$	−238.110	+	327.730i	−0.507697	+	0.698784i
$470$		0			0
$471$	5.84034	−	17.9747i	0.0123999	−	0.0381629i
$472$			43.8644i			0.0929331i
$473$	230.438	+	410.642i	0.487184	+	0.868164i
$474$	−1.05789			−0.00223183
$475$		0			0
$476$	456.696	−	331.809i	0.959445	−	0.697078i
$477$	200.882	+	145.949i	0.421135	+	0.305973i
$478$	−5.03515	−	15.4966i	−0.0105338	−	0.0324197i
$479$	451.686	−	146.762i	0.942977	−	0.306392i	0.203119	−	0.979154i	$-0.434892\pi$
$479$	451.686	−	146.762i	0.942977	−	0.306392i	0.739859	+	0.672762i	$0.234892\pi$
$480$		0			0
$481$	381.779	+	525.473i	0.793719	+	1.09246i
$482$	13.5545	−	41.7165i	0.0281214	−	0.0865487i
$483$			19.1568i			0.0396622i
$484$	−445.568	+	185.466i	−0.920596	+	0.383194i
$485$		0			0
$486$	3.67000	+	1.19245i	0.00755143	+	0.00245361i
$487$	61.4734	−	44.6630i	0.126229	−	0.0917105i	−0.522879	−	0.852407i	$-0.675142\pi$
$487$	61.4734	−	44.6630i	0.126229	−	0.0917105i	0.649108	+	0.760696i	$0.275142\pi$
$488$	−26.5754	−	19.3081i	−0.0544577	−	0.0395658i
$489$	−9.21853	−	28.3717i	−0.0188518	−	0.0580199i
$490$		0			0
$491$	521.848	−	718.262i	1.06283	−	1.46286i	0.185694	−	0.982608i	$-0.440547\pi$
$491$	521.848	−	718.262i	1.06283	−	1.46286i	0.877133	−	0.480248i	$-0.159453\pi$
$492$	−11.2983	−	15.5507i	−0.0229639	−	0.0316072i
$493$	−94.4549	+	290.702i	−0.191592	+	0.589660i
$494$			52.5134i			0.106302i
$495$		0			0
$496$	49.5394			0.0998777
$497$	507.494	+	164.895i	1.02111	+	0.331780i
$498$	−0.174370	+	0.126687i	−0.000350140	+	0.000254392i
$499$	−116.418	−	84.5823i	−0.233302	−	0.169504i	0.464992	−	0.885315i	$-0.346057\pi$
$499$	−116.418	−	84.5823i	−0.233302	−	0.169504i	−0.698294	+	0.715811i	$0.746057\pi$
$500$		0			0
$501$	3.02699	−	0.983529i	0.00604190	−	0.00196313i
$502$	−21.9827	+	30.2566i	−0.0437903	+	0.0602722i
$503$	−47.7249	−	65.6877i	−0.0948805	−	0.130592i	0.758937	−	0.651164i	$-0.225719\pi$
$503$	−47.7249	−	65.6877i	−0.0948805	−	0.130592i	−0.853818	+	0.520572i	$0.825719\pi$
$504$	11.7051	−	36.0247i	0.0232245	−	0.0714777i
$505$		0			0
$506$	−29.6833	+	5.93113i	−0.0586627	+	0.0117216i
$507$	26.3425			0.0519576
$508$	−90.2864	−	29.3358i	−0.177729	−	0.0577477i
$509$	−743.157	+	539.935i	−1.46003	+	1.06078i	−0.476679	+	0.879077i	$0.658160\pi$
$509$	−743.157	+	539.935i	−1.46003	+	1.06078i	−0.983354	+	0.181699i	$0.941840\pi$
$510$		0			0
$511$	−90.6086	−	278.865i	−0.177316	−	0.545723i
$512$	128.211	−	41.6582i	0.250412	−	0.0813638i
$513$	41.9400	−	57.7255i	0.0817544	−	0.112525i
$514$	16.2984	+	22.4328i	0.0317089	+	0.0436436i
$515$		0			0
$516$		−	25.5381i		−	0.0494924i
$517$	−285.438	+	620.576i	−0.552104	+	1.20034i
$518$	18.4657			0.0356481
$519$	29.6162	+	9.62290i	0.0570640	+	0.0185412i
$520$		0			0
$521$	118.489	+	86.0876i	0.227427	+	0.165235i	0.695663	−	0.718368i	$-0.255110\pi$
$521$	118.489	+	86.0876i	0.227427	+	0.165235i	−0.468237	+	0.883603i	$0.655110\pi$
$522$	3.16448	+	9.73926i	0.00606222	+	0.0186576i
$523$	417.876	−	135.776i	0.798998	−	0.259610i	0.119067	−	0.992886i	$-0.462010\pi$
$523$	417.876	−	135.776i	0.798998	−	0.259610i	0.679931	+	0.733276i	$0.262010\pi$
$524$	46.8935	−	64.5434i	0.0894915	−	0.123174i
$525$		0			0
$526$	11.2826	−	34.7243i	0.0214499	−	0.0660159i
$527$		−	89.1400i		−	0.169146i
$528$	25.9222	+	3.04531i	0.0490950	+	0.00576763i
$529$	138.331			0.261496
$530$		0			0
$531$	−374.376	+	272.000i	−0.705040	+	0.512242i
$532$	−424.548	−	308.452i	−0.798022	−	0.579797i
$533$	184.966	+	569.266i	0.347028	+	1.06804i
$534$	−1.05098	+	0.341483i	−0.00196812	+	0.000639482i
$535$		0			0
$536$	40.8688	+	56.2510i	0.0762477	+	0.104946i
$537$	2.25374	−	6.93629i	0.00419690	−	0.0129167i
$538$			14.0779i			0.0261672i
$539$	197.395	+	182.153i	0.366224	+	0.337946i
$540$		0			0
$541$	366.080	+	118.946i	0.676672	+	0.219864i	0.627138	−	0.778908i	$-0.284226\pi$
$541$	366.080	+	118.946i	0.676672	+	0.219864i	0.0495344	+	0.998772i	$0.484226\pi$
$542$	10.0126	−	7.27455i	0.0184734	−	0.0134217i
$543$	18.7816	+	13.6456i	0.0345886	+	0.0251301i
$544$	−44.9328	−	138.289i	−0.0825970	−	0.254207i
$545$		0			0
$546$	0.862597	−	1.18726i	0.00157985	−	0.00217447i
$547$	−117.808	−	162.149i	−0.215372	−	0.296434i	0.687638	−	0.726054i	$-0.258648\pi$
$547$	−117.808	−	162.149i	−0.215372	−	0.296434i	−0.903010	+	0.429620i	$0.858648\pi$
$548$	108.783	−	334.799i	0.198509	−	0.610948i
$549$		−	346.545i		−	0.631229i
$550$		0			0
$551$	284.146			0.515692
$552$	3.12712	+	1.01606i	0.00566507	+	0.00184069i
$553$	−266.326	+	193.497i	−0.481602	+	0.349904i
$554$	5.63083	+	4.09104i	0.0101640	+	0.00738455i
$555$		0			0
$556$	−434.682	+	141.237i	−0.781802	+	0.254023i
$557$	−529.229	+	728.421i	−0.950142	+	1.30776i	0.00132234	+	0.999999i	$0.499579\pi$
$557$	−529.229	+	728.421i	−0.950142	+	1.30776i	−0.951464	+	0.307759i	$0.900421\pi$
$558$	−1.75537	−	2.41606i	−0.00314583	−	0.00432986i
$559$	−245.746	+	756.328i	−0.439617	+	1.35300i
$560$		0			0
$561$	5.47966	−	46.6438i	0.00976767	−	0.0831441i
$562$	23.3072			0.0414719
$563$	139.504	+	45.3275i	0.247786	+	0.0805106i	0.430277	−	0.902697i	$-0.358416\pi$
$563$	139.504	+	45.3275i	0.247786	+	0.0805106i	−0.182491	+	0.983208i	$0.558416\pi$
$564$	29.9711	−	21.7753i	0.0531402	−	0.0386086i
$565$		0			0
$566$	6.18011	+	19.0204i	0.0109189	+	0.0336050i
$567$	379.099	−	123.177i	0.668605	−	0.217243i
$568$	53.8341	−	74.0963i	0.0947783	−	0.130451i
$569$	−566.352	−	779.517i	−0.995347	−	1.36998i	−0.928137	−	0.372238i	$-0.878590\pi$
$569$	−566.352	−	779.517i	−0.995347	−	1.36998i	−0.0672092	−	0.997739i	$-0.521410\pi$
$570$		0			0
$571$		−	706.490i		−	1.23729i	−0.785672	−	0.618643i	$-0.787683\pi$
$571$		−	706.490i		−	1.23729i	0.785672	−	0.618643i	$-0.212317\pi$
$572$	−740.513	−	340.603i	−1.29460	−	0.595460i
$573$	−21.1066			−0.0368353
$574$	16.1841	+	5.25853i	0.0281953	+	0.00916121i
$575$		0			0
$576$	456.942	+	331.988i	0.793302	+	0.576368i
$577$	−124.587	−	383.441i	−0.215923	−	0.664542i	−0.999087	−	0.0427267i	$-0.986396\pi$
$577$	−124.587	−	383.441i	−0.215923	−	0.664542i	0.783164	−	0.621815i	$-0.213604\pi$
$578$	−53.2726	+	17.3093i	−0.0921671	+	0.0299469i
$579$	26.8351	−	36.9354i	0.0463473	−	0.0637916i
$580$		0			0
$581$	−20.7258	+	63.7875i	−0.0356726	+	0.109789i
$582$			1.63640i			0.00281169i
$583$	−59.6125	−	298.341i	−0.102251	−	0.511733i
$584$	−50.3271			−0.0861765
$585$		0			0
$586$	41.6536	−	30.2631i	0.0710812	−	0.0516435i
$587$	565.400	+	410.787i	0.963203	+	0.699808i	0.953892	−	0.300149i	$-0.0970364\pi$
$587$	565.400	+	410.787i	0.963203	+	0.699808i	0.00931024	+	0.999957i	$0.497036\pi$
$588$	−4.50154	−	13.8543i	−0.00765568	−	0.0235618i
$589$	−78.8095	+	25.6068i	−0.133802	+	0.0434750i
$590$		0			0
$591$	26.3997	+	36.3361i	0.0446696	+	0.0614824i
$592$	−171.396	+	527.503i	−0.289520	+	0.891052i
$593$		−	531.446i		−	0.896198i	−0.893984	−	0.448099i	$-0.852101\pi$
$593$		−	531.446i		−	0.896198i	0.893984	−	0.448099i	$-0.147899\pi$
$594$	−1.54192	−	2.74771i	−0.00259583	−	0.00462578i
$595$		0			0
$596$	440.360	+	143.082i	0.738860	+	0.240070i
$597$	−39.6928	+	28.8385i	−0.0664871	+	0.0483057i
$598$	−41.3585	−	30.0487i	−0.0691614	−	0.0502487i
$599$	−133.793	−	411.773i	−0.223361	−	0.687434i	−0.998454	−	0.0555866i	$-0.982297\pi$
$599$	−133.793	−	411.773i	−0.223361	−	0.687434i	0.775093	−	0.631847i	$-0.217703\pi$
$600$		0			0
$601$	335.144	−	461.286i	0.557644	−	0.767531i	−0.433381	−	0.901211i	$-0.642679\pi$
$601$	335.144	−	461.286i	0.557644	−	0.767531i	0.991025	+	0.133680i	$0.0426794\pi$
$602$	13.2891	+	18.2909i	0.0220749	+	0.0303835i
$603$	−226.670	+	697.617i	−0.375903	+	1.15691i
$604$			37.1366i			0.0614845i
$605$		0			0
$606$	0.690198			0.00113894
$607$	215.125	+	69.8984i	0.354407	+	0.115154i	0.480809	−	0.876825i	$-0.340343\pi$
$607$	215.125	+	69.8984i	0.354407	+	0.115154i	−0.126402	+	0.991979i	$0.540343\pi$
$608$	−109.355	+	79.4509i	−0.179860	+	0.130676i
$609$	−6.42419	−	4.66745i	−0.0105488	−	0.00766412i
$610$		0			0
$611$	−1097.15	+	356.487i	−1.79567	+	0.583448i
$612$	600.815	−	826.951i	0.981724	−	1.35123i
$613$	−359.606	−	494.956i	−0.586634	−	0.807432i	0.407769	−	0.913085i	$-0.366307\pi$
$613$	−359.606	−	494.956i	−0.586634	−	0.807432i	−0.994403	+	0.105653i	$0.966307\pi$
$614$	−1.41171	+	4.34480i	−0.00229920	+	0.00707622i
$615$		0			0
$616$	−40.4742	+	22.7127i	−0.0657048	+	0.0368713i
$617$	−155.555			−0.252116			−0.126058	−	0.992023i	$-0.540232\pi$
$617$	−155.555			−0.252116			−0.126058	+	0.992023i	$0.540232\pi$
$618$	2.66342	+	0.865398i	0.00430974	+	0.00140032i
$619$	4.15106	−	3.01592i	0.00670607	−	0.00487225i	−0.584427	−	0.811446i	$-0.698681\pi$
$619$	4.15106	−	3.01592i	0.00670607	−	0.00487225i	0.591133	+	0.806574i	$0.298681\pi$
$620$		0			0
$621$	21.4649	+	66.0622i	0.0345651	+	0.106380i
$622$	23.8765	−	7.75795i	0.0383867	−	0.0124726i
$623$	−202.125	+	278.202i	−0.324439	+	0.446552i
$624$	25.9096	+	35.6615i	0.0415217	+	0.0571498i
$625$		0			0
$626$			32.9999i			0.0527154i
$627$	−42.8123	+	8.55449i	−0.0682812	+	0.0136435i
$628$	−504.009			−0.802562
$629$	949.177	+	308.406i	1.50903	+	0.490312i
$630$		0			0
$631$	−810.728	−	589.028i	−1.28483	−	0.933484i	−0.285143	−	0.958485i	$-0.592041\pi$
$631$	−810.728	−	589.028i	−1.28483	−	0.933484i	−0.999687	+	0.0250010i	$0.992041\pi$
$632$	17.4603	+	53.7374i	0.0276271	+	0.0850275i
$633$	−29.7221	+	9.65730i	−0.0469544	+	0.0152564i
$634$	−16.9114	+	23.2765i	−0.0266741	+	0.0367137i
$635$		0			0
$636$	−5.09886	+	15.6927i	−0.00801707	+	0.0246740i
$637$			453.623i			0.712124i
$638$	5.24318	−	11.3993i	0.00821814	−	0.0178673i
$639$	966.221			1.51208
$640$		0			0
$641$	−88.7231	+	64.4611i	−0.138414	+	0.100563i	−0.654837	−	0.755770i	$-0.727263\pi$
$641$	−88.7231	+	64.4611i	−0.138414	+	0.100563i	0.516424	+	0.856333i	$0.327263\pi$
$642$	−0.388570	−	0.282312i	−0.000605249	−	0.000439739i
$643$	−0.444667	−	1.36855i	−0.000691551	−	0.00212838i	0.950710	−	0.310081i	$-0.100356\pi$
$643$	−0.444667	−	1.36855i	−0.000691551	−	0.00212838i	−0.951402	+	0.307953i	$0.900356\pi$
$644$	485.861	−	157.866i	0.754443	−	0.245133i
$645$		0			0
$646$	47.4282	+	65.2793i	0.0734182	+	0.101052i
$647$	312.650	−	962.237i	0.483230	−	1.48723i	−0.351298	−	0.936264i	$-0.614260\pi$
$647$	312.650	−	962.237i	0.483230	−	1.48723i	0.834528	−	0.550966i	$-0.185740\pi$
$648$		−	68.4165i		−	0.105581i
$649$	563.126	+	66.1554i	0.867682	+	0.101934i
$650$		0			0
$651$	2.20241	+	0.715606i	0.00338312	+	0.00109924i
$652$	−643.605	+	467.607i	−0.987125	+	0.717188i
$653$	−51.7809	−	37.6210i	−0.0792969	−	0.0576126i	0.547431	−	0.836851i	$-0.315606\pi$
$653$	−51.7809	−	37.6210i	−0.0792969	−	0.0576126i	−0.626727	+	0.779239i	$0.715606\pi$
$654$	0.801882	+	2.46794i	0.00122612	+	0.00377361i
$655$		0			0
$656$	−300.437	+	413.516i	−0.457983	+	0.630360i
$657$	−312.074	−	429.534i	−0.474999	−	0.653780i
$658$	−10.1348	+	31.1918i	−0.0154025	+	0.0474040i
$659$			1088.54i			1.65180i	0.563816	+	0.825900i	$0.309333\pi$
$659$			1088.54i			1.65180i	−0.563816	+	0.825900i	$0.690667\pi$
$660$		0			0
$661$	−730.366			−1.10494			−0.552471	−	0.833532i	$-0.686315\pi$
$661$	−730.366			−1.10494			−0.552471	+	0.833532i	$0.686315\pi$
$662$	−2.07229	−	0.673326i	−0.00313034	−	0.00101711i
$663$	64.1685	−	46.6211i	0.0967850	−	0.0703184i
$664$	9.31324	+	6.76647i	0.0140260	+	0.0101905i
$665$		0			0
$666$	31.7998	−	10.3324i	0.0477475	−	0.0155141i
$667$	−162.591	+	223.788i	−0.243765	+	0.335514i
$668$	−49.8891	−	68.6665i	−0.0746843	−	0.102794i
$669$	3.01361	−	9.27494i	0.00450465	−	0.0138639i
$670$		0			0
$671$	−287.955	+	312.051i	−0.429144	+	0.465053i
$672$	3.77746			0.00562122
$673$	457.745	+	148.730i	0.680156	+	0.220996i	0.628664	−	0.777677i	$-0.283602\pi$
$673$	457.745	+	148.730i	0.680156	+	0.220996i	0.0514924	+	0.998673i	$0.483602\pi$
$674$	10.8582	−	7.88891i	0.0161100	−	0.0117046i
$675$		0			0
$676$	−217.081	−	668.106i	−0.321126	−	0.988323i
$677$	−343.772	+	111.698i	−0.507787	+	0.164990i	−0.551695	−	0.834046i	$-0.686019\pi$
$677$	−343.772	+	111.698i	−0.507787	+	0.164990i	0.0439087	+	0.999036i	$0.486019\pi$
$678$	1.69227	−	2.32921i	0.00249597	−	0.00343541i
$679$	299.312	+	411.968i	0.440813	+	0.606727i
$680$		0			0
$681$		−	3.69344i		−	0.00542355i
$682$	−0.426938	+	3.63417i	−0.000626009	+	0.00532869i
$683$	−886.073			−1.29732			−0.648662	−	0.761076i	$-0.724671\pi$
$683$	−886.073			−1.29732			−0.648662	+	0.761076i	$0.724671\pi$
$684$	−903.707	−	293.632i	−1.32121	−	0.429287i
$685$		0			0
$686$	31.3703	+	22.7919i	0.0457293	+	0.0332243i
$687$	−1.93094	−	5.94282i	−0.00281068	−	0.00865039i
$688$	−645.856	+	209.851i	−0.938744	+	0.305017i
$689$	302.013	−	415.685i	0.438335	−	0.603317i
$690$		0			0
$691$	18.7077	−	57.5762i	0.0270733	−	0.0833231i	−0.936607	−	0.350382i	$-0.886052\pi$
$691$	18.7077	−	57.5762i	0.0270733	−	0.0833231i	0.963680	+	0.267059i	$0.0860518\pi$
$692$		−	830.436i		−	1.20005i
$693$	−444.827	−	204.601i	−0.641886	−	0.295239i
$694$	50.5238			0.0728009
$695$		0			0
$696$	−1.10264	+	0.801113i	−0.00158425	+	0.00115102i
$697$	744.072	+	540.600i	1.06753	+	0.775609i
$698$	9.20667	+	28.3352i	0.0131901	+	0.0405949i
$699$	−51.1437	+	16.6176i	−0.0731670	+	0.0237734i
$700$		0			0
$701$	−260.778	−	358.930i	−0.372009	−	0.512026i	0.581437	−	0.813592i	$-0.302491\pi$
$701$	−260.778	−	358.930i	−0.372009	−	0.512026i	−0.953445	+	0.301565i	$0.902491\pi$
$702$	1.64435	−	5.06080i	0.00234238	−	0.00720911i
$703$		−	927.770i		−	1.31973i
$704$	−135.600	−	678.631i	−0.192613	−	0.963964i
$705$		0			0
$706$	−29.6751	−	9.64201i	−0.0420327	−	0.0136572i
$707$	173.759	−	126.243i	0.245769	−	0.178562i
$708$	−24.8781	−	18.0750i	−0.0351385	−	0.0255296i
$709$	152.584	+	469.605i	0.215210	+	0.662349i	0.999139	+	0.0414975i	$0.0132129\pi$
$709$	152.584	+	469.605i	0.215210	+	0.662349i	−0.783928	+	0.620851i	$0.786787\pi$
$710$		0			0
$711$	−350.370	+	482.243i	−0.492785	+	0.678260i
$712$	34.6925	+	47.7501i	0.0487254	+	0.0670648i
$713$	24.9283	−	76.7213i	0.0349625	−	0.107603i
$714$		−	2.25495i		−	0.00315819i
$715$		0			0
$716$	−194.493			−0.271638
$717$	21.7586	+	7.06978i	0.0303467	+	0.00986023i
$718$	11.1943	−	8.13311i	0.0155909	−	0.0113274i
$719$	38.7270	+	28.1368i	0.0538623	+	0.0391332i	0.614391	−	0.789002i	$-0.289402\pi$
$719$	38.7270	+	28.1368i	0.0538623	+	0.0391332i	−0.560528	+	0.828135i	$0.689402\pi$
$720$		0			0
$721$	828.810	−	269.297i	1.14953	−	0.373505i
$722$	21.4861	−	29.5731i	0.0297591	−	0.0409599i
$723$	36.2004	+	49.8256i	0.0500697	+	0.0689150i
$724$	191.311	−	588.794i	0.264241	−	0.813251i
$725$		0			0
$726$	−0.446803	+	1.87539i	−0.000615431	+	0.00258318i
$727$	−988.659			−1.35992			−0.679958	−	0.733251i	$-0.738002\pi$
$727$	−988.659			−1.35992			−0.679958	+	0.733251i	$0.738002\pi$
$728$	−74.5462	−	24.2215i	−0.102399	−	0.0332713i
$729$	580.996	−	422.118i	0.796976	−	0.579037i
$730$		0			0
$731$	377.602	+	1162.14i	0.516555	+	1.58979i
$732$	21.9015	−	7.11623i	0.0299201	−	0.00972163i
$733$	32.5550	−	44.8081i	0.0444134	−	0.0611297i	−0.786233	−	0.617930i	$-0.787971\pi$
$733$	32.5550	−	44.8081i	0.0444134	−	0.0611297i	0.830646	+	0.556801i	$0.187971\pi$
$734$	9.41063	+	12.9526i	0.0128210	+	0.0176466i
$735$		0			0
$736$		−	131.588i		−	0.178788i
$737$	783.780	−	439.831i	1.06347	−	0.596785i
$738$	30.8131			0.0417521
$739$	−364.147	−	118.319i	−0.492757	−	0.160106i	0.0520894	−	0.998642i	$-0.483412\pi$
$739$	−364.147	−	118.319i	−0.492757	−	0.160106i	−0.544846	+	0.838536i	$0.683412\pi$
$740$		0			0
$741$	−59.6515	−	43.3393i	−0.0805013	−	0.0584876i
$742$	−4.51401	−	13.8927i	−0.00608357	−	0.0187233i
$743$	−1137.86	+	369.712i	−1.53144	+	0.497594i	−0.948999	−	0.315280i	$-0.897901\pi$
$743$	−1137.86	+	369.712i	−1.53144	+	0.497594i	−0.582439	+	0.812875i	$0.697901\pi$
$744$	0.233628	−	0.321561i	0.000314016	−	0.000432206i
$745$		0			0
$746$	18.5426	−	57.0682i	0.0248560	−	0.0764990i
$747$			121.445i			0.162578i
$748$	−1228.15	+	245.401i	−1.64191	+	0.328077i
$749$	−149.461			−0.199547
$750$		0			0
$751$	614.130	−	446.192i	0.817750	−	0.594130i	−0.0983169	−	0.995155i	$-0.531346\pi$
$751$	614.130	−	446.192i	0.817750	−	0.594130i	0.916067	+	0.401025i	$0.131346\pi$
$752$	−796.974	−	579.035i	−1.05981	−	0.769994i
$753$	−16.2270	−	49.9417i	−0.0215498	−	0.0663236i
$754$	20.1535	−	6.54827i	0.0267288	−	0.00868471i
$755$		0			0
$756$	31.2558	+	43.0199i	0.0413436	+	0.0569046i
$757$	−411.505	+	1266.48i	−0.543600	+	1.67303i	0.180697	+	0.983539i	$0.442165\pi$
$757$	−411.505	+	1266.48i	−0.543600	+	1.67303i	−0.724296	+	0.689489i	$0.757835\pi$
$758$		−	24.4971i		−	0.0323181i
$759$	17.7603	−	38.6131i	0.0233996	−	0.0508737i
$760$		0			0
$761$	−921.263	−	299.337i	−1.21060	−	0.393346i	−0.366947	−	0.930242i	$-0.619597\pi$
$761$	−921.263	−	299.337i	−1.21060	−	0.393346i	−0.843649	+	0.536896i	$0.819597\pi$
$762$	−0.306790	+	0.222896i	−0.000402612	+	0.000292515i
$763$	653.283	+	474.638i	0.856203	+	0.622068i
$764$	173.933	+	535.312i	0.227662	+	0.700671i
$765$		0			0
$766$	−40.6590	+	55.9624i	−0.0530797	+	0.0730579i
$767$	562.852	+	774.699i	0.733835	+	1.01004i
$768$	−11.4980	+	35.3871i	−0.0149713	+	0.0460770i
$769$			1183.94i			1.53958i	0.638296	+	0.769791i	$0.279640\pi$
$769$			1183.94i			1.53958i	−0.638296	+	0.769791i	$0.720360\pi$
$770$		0			0
$771$	−38.9332			−0.0504970
$772$	−1157.91	−	376.227i	−1.49988	−	0.487340i
$773$	394.318	−	286.489i	0.510114	−	0.370619i	−0.302753	−	0.953069i	$-0.597906\pi$
$773$	394.318	−	286.489i	0.510114	−	0.370619i	0.812867	+	0.582450i	$0.197906\pi$
$774$	33.1198	+	24.0629i	0.0427904	+	0.0310890i
$775$		0			0
$776$	83.1239	−	27.0086i	0.107118	−	0.0348049i
$777$	−15.2398	+	20.9757i	−0.0196136	+	0.0269958i
$778$	−28.2518	−	38.8853i	−0.0363134	−	0.0499811i
$779$	264.204	−	813.136i	0.339158	−	1.04382i
$780$		0			0
$781$	−870.046	−	802.865i	−1.11402	−	1.02800i
$782$	−78.5516			−0.100450
$783$	−27.3836	−	8.89747i	−0.0349727	−	0.0113633i
$784$	−313.385	+	227.687i	−0.399726	+	0.290418i
$785$		0			0
$786$	−0.0984791	−	0.303088i	−0.000125292	−	0.000385608i
$787$	−1125.42	+	365.670i	−1.43001	+	0.464638i	−0.918767	−	0.394800i	$-0.870814\pi$
$787$	−1125.42	+	365.670i	−1.43001	+	0.464638i	−0.511240	+	0.859438i	$0.670814\pi$
$788$	704.015	−	968.994i	0.893420	−	1.22969i
$789$	30.1328	+	41.4743i	0.0381912	+	0.0525656i
$790$		0			0
$791$		−	895.914i		−	1.13264i
$792$	−56.9918	+	61.7607i	−0.0719594	+	0.0779807i
$793$	−717.107			−0.904296
$794$	−19.5927	−	6.36606i	−0.0246760	−	0.00801771i
$795$		0			0
$796$	1058.51	+	769.052i	1.32979	+	0.966145i
$797$	116.700	+	359.167i	0.146425	+	0.450649i	0.997191	−	0.0748947i	$-0.0238621\pi$
$797$	116.700	+	359.167i	0.146425	+	0.450649i	−0.850767	+	0.525543i	$0.823862\pi$
$798$	−1.99362	+	0.647767i	−0.00249827	+	0.000811739i
$799$	−1041.90	+	1434.06i	−1.30401	+	1.79482i
$800$		0			0
$801$	−192.414	+	592.190i	−0.240217	+	0.739313i
$802$		−	5.74574i		−	0.00716426i
$803$	−75.9021	+	646.092i	−0.0945232	+	0.804597i
$804$	−48.7438			−0.0606266
$805$		0			0
$806$	−4.99957	+	3.63240i	−0.00620294	+	0.00450670i
$807$	−15.9915	−	11.6185i	−0.0198160	−	0.0143972i
$808$	−11.3916	−	35.0598i	−0.0140985	−	0.0433909i
$809$	−26.8844	+	8.73528i	−0.0332317	+	0.0107976i	−0.325586	−	0.945513i	$-0.605561\pi$
$809$	−26.8844	+	8.73528i	−0.0332317	+	0.0107976i	0.292354	+	0.956310i	$0.405561\pi$
$810$		0			0
$811$	−649.305	−	893.692i	−0.800623	−	1.10196i	−0.992703	−	0.120584i	$-0.961523\pi$
$811$	−649.305	−	893.692i	−0.800623	−	1.10196i	0.192080	−	0.981379i	$-0.438477\pi$
$812$	−65.4374	+	201.395i	−0.0805879	+	0.248024i
$813$			17.3772i			0.0213742i
$814$	−37.2201	−	17.1196i	−0.0457249	−	0.0210314i
$815$		0			0
$816$	64.4163	+	20.9301i	0.0789415	+	0.0256497i
$817$	918.987	−	667.683i	1.12483	−	0.817237i
$818$	34.1562	+	24.8159i	0.0417558	+	0.0303373i
$819$	−255.529	−	786.436i	−0.312001	−	0.960239i
$820$		0			0
$821$	370.247	−	509.601i	0.450971	−	0.620708i	−0.521635	−	0.853169i	$-0.674678\pi$
$821$	370.247	−	509.601i	0.450971	−	0.620708i	0.972606	+	0.232461i	$0.0746777\pi$
$822$	−0.826541	−	1.13764i	−0.00100552	−	0.00138399i
$823$	−130.777	+	402.491i	−0.158903	+	0.489054i	−0.998535	−	0.0541017i	$-0.982770\pi$
$823$	−130.777	+	402.491i	−0.158903	+	0.489054i	0.839632	+	0.543155i	$0.182770\pi$
$824$		−	149.576i		−	0.181525i
$825$		0			0
$826$	27.2238			0.0329586
$827$	998.161	+	324.322i	1.20697	+	0.392167i	0.842319	−	0.538979i	$-0.181190\pi$
$827$	998.161	+	324.322i	1.20697	+	0.392167i	0.364647	+	0.931146i	$0.381190\pi$
$828$	748.370	−	543.722i	0.903828	−	0.656670i
$829$	−510.030	−	370.559i	−0.615236	−	0.446995i	0.236019	−	0.971749i	$-0.424157\pi$
$829$	−510.030	−	370.559i	−0.615236	−	0.446995i	−0.851254	+	0.524754i	$0.824157\pi$
$830$		0			0
$831$	−9.29426	+	3.01989i	−0.0111844	+	0.00363404i
$832$	686.984	−	945.553i	0.825702	−	1.13648i
$833$	409.696	+	563.898i	0.491832	+	0.676948i
$834$	−0.564177	+	1.73636i	−0.000676471	+	0.00208196i
$835$		0			0
$836$	569.766	+	1015.32i	0.681538	+	1.21450i
$837$	8.39682			0.0100320
$838$	69.8435	+	22.6935i	0.0833454	+	0.0270806i
$839$	864.090	−	627.798i	1.02991	−	0.748270i	0.0616154	−	0.998100i	$-0.480375\pi$
$839$	864.090	−	627.798i	1.02991	−	0.748270i	0.968290	+	0.249830i	$0.0803748\pi$
$840$		0			0
$841$	224.451	+	690.789i	0.266886	+	0.821390i
$842$	−17.4749	+	5.67795i	−0.0207541	+	0.00674341i
$843$	−19.2355	+	26.4753i	−0.0228179	+	0.0314061i
$844$	489.863	+	674.239i	0.580406	+	0.798861i
$845$		0			0
$846$			59.3863i			0.0701966i
$847$	230.541	+	553.857i	0.272185	+	0.653904i
$848$	438.765			0.517412
$849$	−26.7063	−	8.67741i	−0.0314562	−	0.0102207i
$850$		0			0
$851$	730.693	+	530.880i	0.858629	+	0.623830i
$852$	19.8412	+	61.0648i	0.0232878	+	0.0716724i
$853$	−18.6827	+	6.07037i	−0.0219023	+	0.00711649i	−0.319948	−	0.947435i	$-0.603665\pi$
$853$	−18.6827	+	6.07037i	−0.0219023	+	0.00711649i	0.298045	+	0.954552i	$0.403665\pi$
$854$	−11.9833	+	16.4936i	−0.0140319	+	0.0193133i
$855$		0			0
$856$	−7.92727	+	24.3976i	−0.00926083	+	0.0285019i
$857$		−	1638.89i		−	1.91236i	−0.292785	−	0.956178i	$-0.594582\pi$
$857$		−	1638.89i		−	1.91236i	0.292785	−	0.956178i	$-0.405418\pi$
$858$	−2.83939	+	1.59337i	−0.00330931	+	0.00185707i
$859$	108.616			0.126445			0.0632223	−	0.997999i	$-0.479862\pi$
$859$	108.616			0.126445			0.0632223	+	0.997999i	$0.479862\pi$
$860$		0			0
$861$	−19.3301	+	14.0441i	−0.0224507	+	0.0163114i
$862$	38.6194	+	28.0586i	0.0448021	+	0.0325506i
$863$	123.617	+	380.453i	0.143241	+	0.440849i	0.996781	−	0.0801782i	$-0.0255489\pi$
$863$	123.617	+	380.453i	0.143241	+	0.440849i	−0.853540	+	0.521027i	$0.825549\pi$
$864$	13.0265	−	4.23258i	0.0150770	−	0.00489882i
$865$		0			0
$866$	−41.6552	−	57.3334i	−0.0481007	−	0.0662049i
$867$	24.3037	−	74.7992i	0.0280320	−	0.0862736i
$868$		−	61.7553i		−	0.0711467i
$869$	716.206	−	143.108i	0.824173	−	0.164681i
$870$		0			0
$871$	1443.58	+	469.048i	1.65739	+	0.538517i
$872$	112.128	−	81.4660i	0.128588	−	0.0934243i
$873$	745.960	+	541.972i	0.854479	+	0.620815i
$874$	22.5651	+	69.4482i	0.0258182	+	0.0794602i
$875$		0			0
$876$	20.7380	−	28.5434i	0.0236735	−	0.0325838i
$877$	323.764	+	445.623i	0.369172	+	0.508122i	0.952676	−	0.303989i	$-0.0983185\pi$
$877$	323.764	+	445.623i	0.369172	+	0.508122i	−0.583503	+	0.812111i	$0.698319\pi$
$878$	−16.3948	+	50.4579i	−0.0186728	+	0.0574691i
$879$			72.2917i			0.0822431i
$880$		0			0
$881$	−546.029			−0.619784			−0.309892	−	0.950772i	$-0.600293\pi$
$881$	−546.029			−0.619784			−0.309892	+	0.950772i	$0.600293\pi$
$882$	22.2089	+	7.21611i	0.0251802	+	0.00818153i
$883$	897.053	−	651.747i	1.01592	−	0.738106i	0.0504738	−	0.998725i	$-0.483927\pi$
$883$	897.053	−	651.747i	1.01592	−	0.738106i	0.965442	+	0.260620i	$0.0839269\pi$
$884$	−1711.21	−	1243.27i	−1.93576	−	1.40641i
$885$		0			0
$886$	−51.2716	+	16.6592i	−0.0578687	+	0.0188027i
$887$	−166.275	+	228.858i	−0.187458	+	0.258013i	−0.892394	−	0.451257i	$-0.850976\pi$
$887$	−166.275	+	228.858i	−0.187458	+	0.258013i	0.704936	+	0.709271i	$0.250976\pi$
$888$	2.61573	+	3.60024i	0.00294564	+	0.00405433i
$889$	−36.4655	+	112.229i	−0.0410185	+	0.126242i
$890$		0			0
$891$	−878.321	−	103.184i	−0.985770	−	0.115807i
$892$	−260.068			−0.291556
$893$	1567.17	+	509.203i	1.75494	+	0.570216i
$894$	1.49633	−	1.08715i	0.00167375	−	0.00121605i
$895$		0			0
$896$	−41.4855	−	127.679i	−0.0463007	−	0.142499i
$897$	68.2664	−	22.1811i	0.0761052	−	0.0247281i
$898$	−36.9108	+	50.8034i	−0.0411034	+	0.0565739i
$899$	19.6547	+	27.0523i	0.0218628	+	0.0300916i
$900$		0			0
$901$		−	789.505i		−	0.876254i
$902$	−27.7460	−	25.6036i	−0.0307605	−	0.0283853i
$903$	−31.7447			−0.0351547
$904$	−146.247	−	47.5186i	−0.161778	−	0.0525648i
$905$		0			0
$906$	0.120013	+	0.0871944i	0.000132464	+	9.62411e-5i
$907$	41.2383	+	126.918i	0.0454666	+	0.139932i	0.971213	−	0.238214i	$-0.0765619\pi$
$907$	41.2383	+	126.918i	0.0454666	+	0.139932i	−0.925746	+	0.378146i	$0.876562\pi$
$908$	−93.6740	+	30.4365i	−0.103165	+	0.0335204i
$909$	228.591	−	314.629i	0.251476	−	0.346127i
$910$		0			0
$911$	−235.346	+	724.320i	−0.258338	+	0.795082i	0.734816	+	0.678267i	$0.237269\pi$
$911$	−235.346	+	724.320i	−0.258338	+	0.795082i	−0.993154	+	0.116815i	$0.962731\pi$
$912$		−	62.9635i		−	0.0690389i
$913$	100.913	−	109.357i	0.110529	−	0.119778i
$914$	−48.4882			−0.0530506
$915$		0			0
$916$	−134.811	+	97.9462i	−0.147174	+	0.106928i
$917$	−80.2296	−	58.2903i	−0.0874914	−	0.0635662i
$918$	−2.52664	−	7.77619i	−0.00275233	−	0.00847079i
$919$	−871.649	+	283.216i	−0.948476	+	0.308179i	−0.742096	−	0.670293i	$-0.766168\pi$
$919$	−871.649	+	283.216i	−0.948476	+	0.308179i	−0.206380	+	0.978472i	$0.566168\pi$
$920$		0			0
$921$	−3.77030	−	5.18937i	−0.00409370	−	0.00563450i
$922$	20.6537	−	63.5654i	0.0224009	−	0.0689430i
$923$		−	1999.41i		−	2.16620i
$924$	3.79625	−	32.3143i	0.00410850	−	0.0349722i
$925$		0			0
$926$	−55.3562	−	17.9863i	−0.0597799	−	0.0194237i
$927$	1276.61	−	927.513i	1.37714	−	1.00055i
$928$	44.1278	+	32.0607i	0.0475515	+	0.0345482i
$929$	−129.241	−	397.763i	−0.139118	−	0.428162i	0.857089	−	0.515168i	$-0.172270\pi$
$929$	−129.241	−	397.763i	−0.139118	−	0.428162i	−0.996208	+	0.0870052i	$0.972270\pi$
$930$		0			0
$931$	380.856	−	524.204i	0.409083	−	0.563055i
$932$	842.922	+	1160.18i	0.904422	+	1.24483i
$933$	−10.8928	+	33.5247i	−0.0116751	+	0.0359321i
$934$			15.4380i			0.0165289i
$935$		0			0
$936$	−141.929			−0.151634
$937$	723.691	+	235.141i	0.772349	+	0.250951i	0.668570	−	0.743649i	$-0.266907\pi$
$937$	723.691	+	235.141i	0.772349	+	0.250951i	0.103779	+	0.994600i	$0.466907\pi$
$938$	34.9113	−	25.3645i	0.0372189	−	0.0270411i
$939$	−37.4855	−	27.2348i	−0.0399207	−	0.0290041i
$940$		0			0
$941$	129.727	−	42.1508i	0.137861	−	0.0447936i	−0.239274	−	0.970952i	$-0.576909\pi$
$941$	129.727	−	42.1508i	0.137861	−	0.0447936i	0.377135	+	0.926158i	$0.376909\pi$
$942$	−1.18338	+	1.62878i	−0.00125624	+	0.00172907i
$943$	489.229	+	673.366i	0.518801	+	0.714068i
$944$	−252.687	+	777.691i	−0.267677	+	0.823825i
$945$		0			0
$946$	−9.82844	−	49.1880i	−0.0103895	−	0.0519958i
$947$	−873.748			−0.922648			−0.461324	−	0.887232i	$-0.652625\pi$
$947$	−873.748			−0.922648			−0.461324	+	0.887232i	$0.652625\pi$
$948$	−37.6724	−	12.2405i	−0.0397388	−	0.0129119i
$949$	−888.836	+	645.777i	−0.936603	+	0.680482i
$950$		0			0
$951$	−12.4835	−	38.4202i	−0.0131267	−	0.0403998i
$952$	−114.544	+	37.2177i	−0.120320	+	0.0390942i
$953$	471.312	−	648.705i	0.494556	−	0.680698i	−0.486664	−	0.873589i	$-0.661786\pi$
$953$	471.312	−	648.705i	0.494556	−	0.680698i	0.981220	+	0.192891i	$0.0617864\pi$
$954$	−15.5472	−	21.3988i	−0.0162968	−	0.0224306i
$955$		0			0
$956$		−	610.107i		−	0.638188i
$957$	8.62161	+	15.3637i	0.00900899	+	0.0160541i
$958$	−50.5918			−0.0528099
$959$	−416.167	−	135.221i	−0.433959	−	0.141002i
$960$		0			0
$961$	769.576	+	559.130i	0.800808	+	0.581821i
$962$	−21.3809	−	65.8036i	−0.0222254	−	0.0684029i
$963$	−257.386	+	83.6299i	−0.267276	+	0.0868431i
$964$	965.375	−	1328.72i	1.00143	−	1.37834i
$965$		0			0
$966$	0.630603	−	1.94080i	0.000652798	−	0.00200911i
$967$			1090.91i			1.12813i	0.825729	+	0.564067i	$0.190764\pi$
$967$			1090.91i			1.12813i	−0.825729	+	0.564067i	$0.809236\pi$
$968$	102.638	−	8.25686i	0.106031	−	0.00852981i
$969$	−113.295			−0.116920
$970$		0			0
$971$	250.955	−	182.330i	0.258450	−	0.187775i	−0.451013	−	0.892517i	$-0.648937\pi$
$971$	250.955	−	182.330i	0.258450	−	0.187775i	0.709464	+	0.704742i	$0.248937\pi$
$972$	116.894	+	84.9286i	0.120262	+	0.0873751i
$973$	175.562	+	540.324i	0.180434	+	0.555318i
$974$	−7.69814	+	2.50128i	−0.00790364	+	0.00256805i
$975$		0			0
$976$	−359.938	−	495.412i	−0.368789	−	0.507595i
$977$	67.8062	−	208.686i	0.0694024	−	0.213599i	−0.910340	−	0.413862i	$-0.864180\pi$
$977$	67.8062	−	208.686i	0.0694024	−	0.213599i	0.979742	+	0.200263i	$0.0641797\pi$
$978$			3.17782i			0.00324931i
$979$	665.332	−	373.362i	0.679603	−	0.381370i
$980$		0			0
$981$	1390.60	+	451.833i	1.41753	+	0.460584i
$982$	−76.5126	+	55.5897i	−0.0779151	+	0.0566086i
$983$	1050.44	+	763.188i	1.06860	+	0.776386i	0.975661	−	0.219285i	$-0.0703725\pi$
$983$	1050.44	+	763.188i	1.06860	+	0.776386i	0.0929433	+	0.995671i	$0.470372\pi$
$984$	1.26728	+	3.90029i	0.00128789	+	0.00396371i
$985$		0			0
$986$	19.1386	−	26.3421i	0.0194104	−	0.0267161i
$987$	−27.0674	−	37.2551i	−0.0274239	−	0.0377458i
$988$	−607.615	+	1870.05i	−0.614995	+	1.89276i
$989$			1105.83i			1.11813i
$990$		0			0
$991$	1411.24			1.42406			0.712030	−	0.702149i	$-0.247776\pi$
$991$	1411.24			1.42406			0.712030	+	0.702149i	$0.247776\pi$
$992$	−15.1284	−	4.91550i	−0.0152504	−	0.00495514i
$993$	2.47511	−	1.79827i	0.00249256	−	0.00181095i
$994$	−45.9867	−	33.4113i	−0.0462643	−	0.0336129i
$995$		0			0
$996$	−7.67531	+	2.49386i	−0.00770614	+	0.00250388i
$997$	−221.858	+	305.362i	−0.222526	+	0.306280i	−0.905654	−	0.424018i	$-0.860619\pi$
$997$	−221.858	+	305.362i	−0.222526	+	0.306280i	0.683128	+	0.730299i	$0.260619\pi$
$998$	9.01010	+	12.4013i	0.00902815	+	0.0124262i
$999$	−29.0513	+	89.4106i	−0.0290804	+	0.0895001i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	275.3.x.i.101.4	yes	28
5.2	odd	4		275.3.q.g.24.8		56
5.3	odd	4		275.3.q.g.24.7		56
5.4	even	2		275.3.x.h.101.4	✓	28
11.6	odd	10	inner	275.3.x.i.226.4	yes	28
55.17	even	20		275.3.q.g.149.7		56
55.28	even	20		275.3.q.g.149.8		56
55.39	odd	10		275.3.x.h.226.4	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
275.3.q.g.24.7		56	5.3	odd	4
275.3.q.g.24.8		56	5.2	odd	4
275.3.q.g.149.7		56	55.17	even	20
275.3.q.g.149.8		56	55.28	even	20
275.3.x.h.101.4	✓	28	5.4	even	2
275.3.x.h.226.4	yes	28	55.39	odd	10
275.3.x.i.101.4	yes	28	1.1	even	1	trivial
275.3.x.i.226.4	yes	28	11.6	odd	10	inner

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+(-0.101311 - 0.0329179i) q^{2} +(0.121004 - 0.0879149i) q^{3} +(-3.22689 - 2.34447i) q^{4} +(-0.0151531 + 0.00492353i) q^{6} +(-2.91426 + 4.01113i) q^{7} +(0.500198 + 0.688464i) q^{8} +(-2.77424 + 8.53823i) q^{9} +(9.59279 - 5.38315i) q^{11} -0.596582 q^{12} +(17.6682 + 5.74075i) q^{13} +(0.427284 - 0.310440i) q^{14} +(4.90223 + 15.0875i) q^{16} +(27.1482 - 8.82097i) q^{17} +(0.562122 - 0.773694i) q^{18} +(-15.5974 - 21.4680i) q^{19} +0.741571i q^{21} +(-1.14906 + 0.229597i) q^{22} +25.8328 q^{23} +(0.121052 + 0.0393323i) q^{24} +(-1.60101 - 1.16320i) q^{26} +(0.830919 + 2.55730i) q^{27} +(18.8080 - 6.11108i) q^{28} +(-6.29400 + 8.66295i) q^{29} +(0.964986 - 2.96992i) q^{31} -5.09386i q^{32} +(0.687512 - 1.49473i) q^{33} -3.04077 q^{34} +(28.9698 - 21.0478i) q^{36} +(28.2855 + 20.5506i) q^{37} +(0.873507 + 2.68838i) q^{38} +(2.64263 - 0.858642i) q^{39} +(18.9383 + 26.0664i) q^{41} +(0.0244110 - 0.0751293i) q^{42} +42.8073i q^{43} +(-43.5755 - 5.11920i) q^{44} +(-2.61714 - 0.850361i) q^{46} +(-50.2380 + 36.5001i) q^{47} +(1.91961 + 1.39468i) q^{48} +(7.54556 + 23.2228i) q^{49} +(2.50955 - 3.45410i) q^{51} +(-43.5543 - 59.9474i) q^{52} +(8.54679 - 26.3043i) q^{53} -0.286435i q^{54} -4.21923 q^{56} +(-3.77471 - 1.22648i) q^{57} +(0.922817 - 0.670466i) q^{58} +(41.7010 + 30.2976i) q^{59} +(-36.7117 + 11.9283i) q^{61} +(-0.195527 + 0.269120i) q^{62} +(-26.1631 - 36.0104i) q^{63} +(19.4413 - 59.8340i) q^{64} +(-0.118856 + 0.128802i) q^{66} +81.7051 q^{67} +(-108.285 - 35.1838i) q^{68} +(3.12588 - 2.27108i) q^{69} +(-33.2581 - 102.358i) q^{71} +(-7.26594 + 2.36085i) q^{72} +(-34.7613 + 47.8449i) q^{73} +(-2.18915 - 3.01311i) q^{74} +105.842i q^{76} +(-6.36334 + 54.1658i) q^{77} -0.295992 q^{78} +(63.1470 + 20.5177i) q^{79} +(-65.0421 - 47.2559i) q^{81} +(-1.06061 - 3.26422i) q^{82} +(12.8655 - 4.18025i) q^{83} +(1.73859 - 2.39297i) q^{84} +(1.40913 - 4.33685i) q^{86} +1.60159i q^{87} +(8.50441 + 3.91165i) q^{88} +69.3575 q^{89} +(-74.5166 + 54.1395i) q^{91} +(-83.3594 - 60.5641i) q^{92} +(-0.144333 - 0.444211i) q^{93} +(6.29117 - 2.04412i) q^{94} +(-0.447826 - 0.616379i) q^{96} +(31.7379 - 97.6793i) q^{97} -2.60111i q^{98} +(19.3499 + 96.8397i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 5 q^{2} - 14 q^{3} + 9 q^{4} + 30 q^{6} - 5 q^{7} - 15 q^{8} - 31 q^{9} - 5 q^{11} + 4 q^{12} + 45 q^{13} + 37 q^{14} - 35 q^{16} - 5 q^{17} - 35 q^{18} + 80 q^{19} + 50 q^{22} - 34 q^{23} - 13 q^{26}+ \cdots - 609 q^{99}+O(q^{100}) \) 28 * q + 5 * q^2 - 14 * q^3 + 9 * q^4 + 30 * q^6 - 5 * q^7 - 15 * q^8 - 31 * q^9 - 5 * q^11 + 4 * q^12 + 45 * q^13 + 37 * q^14 - 35 * q^16 - 5 * q^17 - 35 * q^18 + 80 * q^19 + 50 * q^22 - 34 * q^23 - 13 * q^26 + 118 * q^27 + 145 * q^28 - 95 * q^29 + 95 * q^31 + 381 * q^33 - 148 * q^34 - 347 * q^36 - 146 * q^37 + 10 * q^38 - 65 * q^39 - 290 * q^41 - 615 * q^42 - 253 * q^44 - 110 * q^46 + 179 * q^47 - 364 * q^48 + 224 * q^49 + 400 * q^51 + 185 * q^52 - 344 * q^53 + 884 * q^56 + 430 * q^57 - 265 * q^58 + 67 * q^59 + 135 * q^61 - 155 * q^62 - 220 * q^63 - 119 * q^64 + 250 * q^66 + 204 * q^67 - 45 * q^68 + 311 * q^69 - 189 * q^71 + 235 * q^72 + 5 * q^73 + 940 * q^74 + 215 * q^77 - 290 * q^78 + 565 * q^79 - 583 * q^81 + 195 * q^82 + 530 * q^83 - 1050 * q^84 + 207 * q^86 + 1930 * q^88 + 146 * q^89 - 783 * q^91 - 521 * q^92 + 57 * q^93 - 845 * q^94 - 1210 * q^96 - 506 * q^97 - 609 * q^99

Introduction

L-functions

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