LMFDB - Embedded newform 275.3.x.f.226.2

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)

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);

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")

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 = [12,-5,13] 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:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 25x^{10} + 235x^{8} + 1025x^{6} + 2090x^{4} + 1880x^{2} + 605 $ x^12 + 25x^10 + 235x^8 + 1025x^6 + 2090x^4 + 1880*x^2 + 605
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 55)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			226.2
Root			$-0.914937i$ of defining polynomial
Character	$\chi$	$=$	275.226
Dual form			275.3.x.f.101.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.289909 + 0.0941972i) q^{2} +(4.17687 + 3.03467i) q^{3} +(-3.16089 + 2.29652i) q^{4} +(-1.49677 - 0.486330i) q^{6} +(5.94293 + 8.17974i) q^{7} +(1.41674 - 1.94998i) q^{8} +(5.45583 + 16.7913i) q^{9} +(-1.50807 - 10.8961i) q^{11} -20.1718 q^{12} +(-4.61316 + 1.49891i) q^{13} +(-2.49342 - 1.81157i) q^{14} +(4.60237 - 14.1646i) q^{16} +(2.71930 + 0.883556i) q^{17} +(-3.16339 - 4.35403i) q^{18} +(-12.5616 + 17.2895i) q^{19} +52.2005i q^{21} +(1.46359 + 3.01683i) q^{22} +12.1155 q^{23} +(11.8351 - 3.84545i) q^{24} +(1.19620 - 0.869094i) q^{26} +(-13.8091 + 42.4999i) q^{27} +(-37.5699 - 12.2072i) q^{28} +(-28.0610 - 38.6227i) q^{29} +(9.63737 + 29.6608i) q^{31} +14.1812i q^{32} +(26.7672 - 50.0882i) q^{33} -0.871580 q^{34} +(-55.8070 - 40.5461i) q^{36} +(16.0724 - 11.6773i) q^{37} +(2.01309 - 6.19566i) q^{38} +(-23.8172 - 7.73869i) q^{39} +(23.5474 - 32.4102i) q^{41} +(-4.91714 - 15.1334i) q^{42} +28.7133i q^{43} +(29.7901 + 30.9782i) q^{44} +(-3.51240 + 1.14125i) q^{46} +(-3.18139 - 2.31141i) q^{47} +(62.2085 - 45.1971i) q^{48} +(-16.4479 + 50.6214i) q^{49} +(8.67687 + 11.9427i) q^{51} +(11.1394 - 15.3321i) q^{52} +(19.4659 + 59.9100i) q^{53} -13.6219i q^{54} +24.3699 q^{56} +(-104.936 + 34.0958i) q^{57} +(11.7733 + 8.55381i) q^{58} +(41.4758 - 30.1339i) q^{59} +(31.6001 + 10.2675i) q^{61} +(-5.58793 - 7.69112i) q^{62} +(-104.925 + 144.417i) q^{63} +(17.0737 + 52.5473i) q^{64} +(-3.04189 + 17.0424i) q^{66} +90.1298 q^{67} +(-10.6245 + 3.45212i) q^{68} +(50.6049 + 36.7666i) q^{69} +(1.85591 - 5.71191i) q^{71} +(40.4722 + 13.1502i) q^{72} +(-76.9424 - 105.902i) q^{73} +(-3.55957 + 4.89933i) q^{74} -83.4983i q^{76} +(80.1652 - 77.0905i) q^{77} +7.63380 q^{78} +(85.4604 - 27.7678i) q^{79} +(-58.1000 + 42.2121i) q^{81} +(-3.77365 + 11.6141i) q^{82} +(84.0686 + 27.3155i) q^{83} +(-119.880 - 165.000i) q^{84} +(-2.70472 - 8.32426i) q^{86} -246.478i q^{87} +(-23.3837 - 12.4963i) q^{88} -118.531 q^{89} +(-39.6764 - 28.8266i) q^{91} +(-38.2959 + 27.8236i) q^{92} +(-49.7567 + 153.135i) q^{93} +(1.14004 + 0.370422i) q^{94} +(-43.0353 + 59.2330i) q^{96} +(20.6501 + 63.5544i) q^{97} -16.2250i q^{98} +(174.733 - 84.7699i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 5 q^{2} + 13 q^{3} + 13 q^{4} + 20 q^{6} + 5 q^{7} + 35 q^{8} + 4 q^{9} + 12 q^{11} + 2 q^{12} - 70 q^{13} - 60 q^{14} - 43 q^{16} + 15 q^{17} + 30 q^{18} - 80 q^{19} + 10 q^{22} - 42 q^{23} + 210 q^{24}+ \cdots + 669 q^{99}+O(q^{100}) $ 12 * q - 5 * q^2 + 13 * q^3 + 13 * q^4 + 20 * q^6 + 5 * q^7 + 35 * q^8 + 4 * q^9 + 12 * q^11 + 2 * q^12 - 70 * q^13 - 60 * q^14 - 43 * q^16 + 15 * q^17 + 30 * q^18 - 80 * q^19 + 10 * q^22 - 42 * q^23 + 210 * q^24 - 120 * q^26 + 109 * q^27 - 140 * q^28 + 5 * q^29 - 46 * q^31 - 42 * q^33 + 10 * q^34 - 39 * q^36 + 42 * q^37 + 130 * q^38 - 285 * q^39 + 230 * q^41 - 135 * q^42 + 488 * q^44 + 205 * q^46 - 58 * q^47 + 323 * q^48 - 212 * q^49 + 360 * q^51 - 410 * q^52 + 43 * q^53 - 410 * q^56 - 270 * q^57 + 450 * q^58 - 74 * q^59 - 290 * q^61 + 350 * q^62 - 295 * q^63 - 7 * q^64 + 185 * q^66 + 212 * q^67 - 55 * q^68 - 73 * q^69 - 276 * q^71 + 555 * q^72 - 645 * q^73 - 100 * q^74 + 140 * q^77 - 360 * q^78 + 235 * q^79 - 30 * q^81 - 215 * q^82 - 60 * q^83 - 580 * q^84 - 480 * q^86 + 165 * q^88 - 114 * q^89 + 160 * q^91 - 33 * q^92 - 129 * q^93 + 375 * q^94 + 265 * q^96 - 63 * q^97 + 669 * q^99

Character values

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

$n$	$101$	$177$
$\chi(n)$	$e\left(\frac{9}{10}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.289909	+	0.0941972i	−0.144955	+	0.0470986i	−0.380596	−	0.924742i	$-0.624281\pi$
$2$	−0.289909	+	0.0941972i	−0.144955	+	0.0470986i	0.235641	+	0.971840i	$0.424281\pi$
$3$	4.17687	+	3.03467i	1.39229	+	1.01156i	0.995610	+	0.0935994i	$0.0298373\pi$
$3$	4.17687	+	3.03467i	1.39229	+	1.01156i	0.396679	+	0.917957i	$0.370163\pi$
$4$	−3.16089	+	2.29652i	−0.790223	+	0.574131i
$5$		0			0
$5$		0			0
$6$	−1.49677	−	0.486330i	−0.249462	−	0.0810550i
$7$	5.94293	+	8.17974i	0.848990	+	1.16853i	0.984084	+	0.177701i	$0.0568661\pi$
$7$	5.94293	+	8.17974i	0.848990	+	1.16853i	−0.135095	+	0.990833i	$0.543134\pi$
$8$	1.41674	−	1.94998i	0.177093	−	0.243747i
$9$	5.45583	+	16.7913i	0.606203	+	1.86570i
$10$		0			0
$11$	−1.50807	−	10.8961i	−0.137097	−	0.990558i
$11$	−1.50807	−	10.8961i	−0.137097	−	0.990558i
$12$	−20.1718			−1.68099
$13$	−4.61316	+	1.49891i	−0.354859	+	0.115301i	−0.481021	−	0.876709i	$-0.659734\pi$
$13$	−4.61316	+	1.49891i	−0.354859	+	0.115301i	0.126162	+	0.992010i	$0.459734\pi$
$14$	−2.49342	−	1.81157i	−0.178101	−	0.129398i
$15$		0			0
$16$	4.60237	−	14.1646i	0.287648	−	0.885290i
$17$	2.71930	+	0.883556i	0.159959	+	0.0519739i	0.387902	−	0.921701i	$-0.373200\pi$
$17$	2.71930	+	0.883556i	0.159959	+	0.0519739i	−0.227943	+	0.973675i	$0.573200\pi$
$18$	−3.16339	−	4.35403i	−0.175744	−	0.241891i
$19$	−12.5616	+	17.2895i	−0.661136	+	0.909975i	−0.999518	−	0.0310333i	$-0.990120\pi$
$19$	−12.5616	+	17.2895i	−0.661136	+	0.909975i	0.338383	+	0.941009i	$0.390120\pi$
$20$		0			0
$21$			52.2005i			2.48574i
$22$	1.46359	+	3.01683i	0.0665267	+	0.137129i
$23$	12.1155			0.526762			0.263381	−	0.964692i	$-0.415162\pi$
$23$	12.1155			0.526762			0.263381	+	0.964692i	$0.415162\pi$
$24$	11.8351	−	3.84545i	0.493128	−	0.160227i
$25$		0			0
$26$	1.19620	−	0.869094i	0.0460079	−	0.0334267i
$27$	−13.8091	+	42.4999i	−0.511447	+	1.57407i
$28$	−37.5699	−	12.2072i	−1.34178	−	0.435972i
$29$	−28.0610	−	38.6227i	−0.967622	−	1.33182i	−0.943239	−	0.332115i	$-0.892238\pi$
$29$	−28.0610	−	38.6227i	−0.967622	−	1.33182i	−0.0243833	−	0.999703i	$-0.507762\pi$
$30$		0			0
$31$	9.63737	+	29.6608i	0.310883	+	0.956800i	0.977416	+	0.211324i	$0.0677776\pi$
$31$	9.63737	+	29.6608i	0.310883	+	0.956800i	−0.666533	+	0.745476i	$0.732222\pi$
$32$			14.1812i			0.443163i
$33$	26.7672	−	50.0882i	0.811127	−	1.51782i
$34$	−0.871580			−0.0256347
$35$		0			0
$36$	−55.8070	−	40.5461i	−1.55019	−	1.12628i
$37$	16.0724	−	11.6773i	0.434389	−	0.315602i	−0.349012	−	0.937118i	$-0.613483\pi$
$37$	16.0724	−	11.6773i	0.434389	−	0.315602i	0.783402	+	0.621516i	$0.213483\pi$
$38$	2.01309	−	6.19566i	0.0529761	−	0.163044i
$39$	−23.8172	−	7.73869i	−0.610699	−	0.198428i
$40$		0			0
$41$	23.5474	−	32.4102i	0.574326	−	0.790493i	−0.418733	−	0.908110i	$-0.637526\pi$
$41$	23.5474	−	32.4102i	0.574326	−	0.790493i	0.993059	+	0.117617i	$0.0375255\pi$
$42$	−4.91714	−	15.1334i	−0.117075	−	0.360319i
$43$			28.7133i			0.667752i	0.942617	+	0.333876i	$0.108357\pi$
$43$			28.7133i			0.667752i	−0.942617	+	0.333876i	$0.891643\pi$
$44$	29.7901	+	30.9782i	0.677047	+	0.704050i
$45$		0			0
$46$	−3.51240	+	1.14125i	−0.0763566	+	0.0248098i
$47$	−3.18139	−	2.31141i	−0.0676891	−	0.0491790i	0.553426	−	0.832898i	$-0.313320\pi$
$47$	−3.18139	−	2.31141i	−0.0676891	−	0.0491790i	−0.621115	+	0.783719i	$0.713320\pi$
$48$	62.2085	−	45.1971i	1.29601	−	0.941607i
$49$	−16.4479	+	50.6214i	−0.335671	+	1.03309i
$50$		0			0
$51$	8.67687	+	11.9427i	0.170135	+	0.234170i
$52$	11.1394	−	15.3321i	0.214220	−	0.294848i
$53$	19.4659	+	59.9100i	0.367282	+	1.13038i	0.948540	+	0.316658i	$0.102561\pi$
$53$	19.4659	+	59.9100i	0.367282	+	1.13038i	−0.581258	+	0.813719i	$0.697439\pi$
$54$		−	13.6219i		−	0.252257i
$55$		0			0
$56$	24.3699			0.435177
$57$	−104.936	+	34.0958i	−1.84098	+	0.598172i
$58$	11.7733	+	8.55381i	0.202988	+	0.147479i
$59$	41.4758	−	30.1339i	0.702979	−	0.510744i	−0.177922	−	0.984045i	$-0.556937\pi$
$59$	41.4758	−	30.1339i	0.702979	−	0.510744i	0.880901	+	0.473300i	$0.156937\pi$
$60$		0			0
$61$	31.6001	+	10.2675i	0.518035	+	0.168320i	0.556353	−	0.830946i	$-0.312200\pi$
$61$	31.6001	+	10.2675i	0.518035	+	0.168320i	−0.0383184	+	0.999266i	$0.512200\pi$
$62$	−5.58793	−	7.69112i	−0.0901279	−	0.124050i
$63$	−104.925	+	144.417i	−1.66548	+	2.29233i
$64$	17.0737	+	52.5473i	0.266776	+	0.821052i
$65$		0			0
$66$	−3.04189	+	17.0424i	−0.0460892	+	0.258218i
$67$	90.1298			1.34522			0.672611	−	0.739997i	$-0.265173\pi$
$67$	90.1298			1.34522			0.672611	+	0.739997i	$0.265173\pi$
$68$	−10.6245	+	3.45212i	−0.156243	+	0.0507665i
$69$	50.6049	+	36.7666i	0.733405	+	0.532850i
$70$		0			0
$71$	1.85591	−	5.71191i	0.0261396	−	0.0804494i	−0.937136	−	0.348965i	$-0.886533\pi$
$71$	1.85591	−	5.71191i	0.0261396	−	0.0804494i	0.963275	+	0.268516i	$0.0865331\pi$
$72$	40.4722	+	13.1502i	0.562114	+	0.182642i
$73$	−76.9424	−	105.902i	−1.05401	−	1.45071i	−0.885284	−	0.465051i	$-0.846036\pi$
$73$	−76.9424	−	105.902i	−1.05401	−	1.45071i	−0.168722	−	0.985664i	$-0.553964\pi$
$74$	−3.55957	+	4.89933i	−0.0481023	+	0.0662072i
$75$		0			0
$76$		−	83.4983i		−	1.09866i
$77$	80.1652	−	77.0905i	1.04111	−	1.00118i
$78$	7.63380			0.0978693
$79$	85.4604	−	27.7678i	1.08178	−	0.351491i	0.286714	−	0.958016i	$-0.407437\pi$
$79$	85.4604	−	27.7678i	1.08178	−	0.351491i	0.795064	+	0.606525i	$0.207437\pi$
$80$		0			0
$81$	−58.1000	+	42.2121i	−0.717284	+	0.521137i
$82$	−3.77365	+	11.6141i	−0.0460202	+	0.141636i
$83$	84.0686	+	27.3155i	1.01287	+	0.329103i	0.767999	−	0.640451i	$-0.221253\pi$
$83$	84.0686	+	27.3155i	1.01287	+	0.329103i	0.244876	+	0.969554i	$0.421253\pi$
$84$	−119.880	−	165.000i	−1.42714	−	1.96429i
$85$		0			0
$86$	−2.70472	−	8.32426i	−0.0314502	−	0.0967937i
$87$		−	246.478i		−	2.83308i
$88$	−23.3837	−	12.4963i	−0.265724	−	0.142003i
$89$	−118.531			−1.33180			−0.665902	−	0.746039i	$-0.731953\pi$
$89$	−118.531			−1.33180			−0.665902	+	0.746039i	$0.731953\pi$
$90$		0			0
$91$	−39.6764	−	28.8266i	−0.436004	−	0.316775i
$92$	−38.2959	+	27.8236i	−0.416260	+	0.302430i
$93$	−49.7567	+	153.135i	−0.535018	+	1.64662i
$94$	1.14004	+	0.370422i	0.0121281	+	0.00394066i
$95$		0			0
$96$	−43.0353	+	59.2330i	−0.448284	+	0.617010i
$97$	20.6501	+	63.5544i	0.212887	+	0.655200i	0.999297	+	0.0374942i	$0.0119376\pi$
$97$	20.6501	+	63.5544i	0.212887	+	0.655200i	−0.786410	+	0.617705i	$0.788062\pi$
$98$		−	16.2250i		−	0.165561i
$99$	174.733	−	84.7699i	1.76498	−	0.856262i
$100$		0			0
$101$	12.3073	−	3.99890i	0.121855	−	0.0395931i	−0.247455	−	0.968899i	$-0.579594\pi$
$101$	12.3073	−	3.99890i	0.121855	−	0.0395931i	0.369310	+	0.929306i	$0.379594\pi$
$102$	−3.64047	−	2.64496i	−0.0356909	−	0.0259310i
$103$	91.4263	−	66.4251i	0.887634	−	0.644904i	−0.0476260	−	0.998865i	$-0.515166\pi$
$103$	91.4263	−	66.4251i	0.887634	−	0.644904i	0.935260	+	0.353961i	$0.115166\pi$
$104$	−3.61282	+	11.1191i	−0.0347387	+	0.106915i
$105$		0			0
$106$	−11.2867	−	15.5348i	−0.106478	−	0.146555i
$107$	9.42241	−	12.9688i	0.0880599	−	0.121204i	−0.762714	−	0.646736i	$-0.776134\pi$
$107$	9.42241	−	12.9688i	0.0880599	−	0.121204i	0.850774	+	0.525532i	$0.176134\pi$
$108$	−53.9531	−	166.051i	−0.499566	−	1.53751i
$109$		−	156.813i		−	1.43865i	−0.694671	−	0.719327i	$-0.744450\pi$
$109$		−	156.813i		−	1.43865i	0.694671	−	0.719327i	$-0.255550\pi$
$110$		0			0
$111$	102.569			0.924045
$112$	143.215	−	46.5333i	1.27870	−	0.415476i
$113$	25.8896	+	18.8099i	0.229112	+	0.166459i	0.696419	−	0.717636i	$-0.254776\pi$
$113$	25.8896	+	18.8099i	0.229112	+	0.166459i	−0.467307	+	0.884095i	$0.654776\pi$
$114$	27.2102	−	19.7694i	0.238686	−	0.173416i
$115$		0			0
$116$	177.396	+	57.6394i	1.52928	+	0.496892i
$117$	−50.3372	−	69.2833i	−0.430233	−	0.592165i
$118$	−9.18568	+	12.6430i	−0.0778447	+	0.107144i
$119$	8.93338	+	27.4941i	0.0750704	+	0.231043i
$120$		0			0
$121$	−116.451	+	32.8642i	−0.962409	+	0.271605i
$122$	−10.1283			−0.0830192
$123$	196.709	−	63.9145i	1.59926	−	0.519630i
$124$	−98.5794	−	71.6221i	−0.794995	−	0.577598i
$125$		0			0
$126$	16.8151	−	51.7514i	0.133453	−	0.410726i
$127$	−102.574	−	33.3284i	−0.807671	−	0.262428i	−0.124060	−	0.992275i	$-0.539592\pi$
$127$	−102.574	−	33.3284i	−0.807671	−	0.262428i	−0.683611	+	0.729846i	$0.739592\pi$
$128$	−43.2416	−	59.5170i	−0.337825	−	0.464977i
$129$	−87.1355	+	119.932i	−0.675469	+	0.929703i
$130$		0			0
$131$		−	48.6741i		−	0.371558i	−0.982592	−	0.185779i	$-0.940519\pi$
$131$		−	48.6741i		−	0.371558i	0.982592	−	0.185779i	$-0.0594808\pi$
$132$	30.4205	+	219.795i	0.230458	+	1.66511i
$133$	−216.076			−1.62463
$134$	−26.1295	+	8.48998i	−0.194996	+	0.0633580i
$135$		0			0
$136$	5.57546	−	4.05081i	0.0409961	−	0.0297854i
$137$	23.2157	−	71.4507i	0.169458	−	0.521538i	−0.829879	−	0.557943i	$-0.811591\pi$
$137$	23.2157	−	71.4507i	0.169458	−	0.521538i	0.999337	+	0.0364052i	$0.0115907\pi$
$138$	−18.1341	−	5.89214i	−0.131407	−	0.0426967i
$139$	−28.3745	−	39.0542i	−0.204133	−	0.280965i	0.694660	−	0.719338i	$-0.255555\pi$
$139$	−28.3745	−	39.0542i	−0.204133	−	0.280965i	−0.898793	+	0.438373i	$0.855555\pi$
$140$		0			0
$141$	−6.27385	−	19.3089i	−0.0444954	−	0.136943i
$142$			1.83076i			0.0128926i
$143$	23.2892	+	48.0052i	0.162862	+	0.335700i
$144$	262.953			1.82606
$145$		0			0
$146$	32.2820	+	23.4542i	0.221110	+	0.160646i
$147$	−222.320	+	161.525i	−1.51238	+	1.09881i
$148$	−23.9860	+	73.8213i	−0.162068	+	0.498793i
$149$	114.600	+	37.2357i	0.769126	+	0.249904i	0.667191	−	0.744887i	$-0.267497\pi$
$149$	114.600	+	37.2357i	0.769126	+	0.249904i	0.101935	+	0.994791i	$0.467497\pi$
$150$		0			0
$151$	−45.4102	+	62.5018i	−0.300730	+	0.413919i	−0.932462	−	0.361268i	$-0.882344\pi$
$151$	−45.4102	+	62.5018i	−0.300730	+	0.413919i	0.631733	+	0.775186i	$0.282344\pi$
$152$	15.9177	+	48.9896i	0.104722	+	0.322300i
$153$			50.4812i			0.329943i
$154$	−15.9789	+	29.9006i	−0.103759	+	0.194160i
$155$		0			0
$156$	93.0559	−	30.2357i	0.596512	−	0.193819i
$157$	43.8515	+	31.8599i	0.279309	+	0.202930i	0.718616	−	0.695407i	$-0.244776\pi$
$157$	43.8515	+	31.8599i	0.279309	+	0.202930i	−0.439307	+	0.898337i	$0.644776\pi$
$158$	−22.1601	+	16.1003i	−0.140254	+	0.101900i
$159$	−100.501	+	309.309i	−0.632079	+	1.94534i
$160$		0			0
$161$	72.0017	+	99.1018i	0.447215	+	0.615539i
$162$	12.8675	−	17.7105i	0.0794287	−	0.109324i
$163$	62.7761	+	193.205i	0.385129	+	1.18531i	0.936386	+	0.350971i	$0.114148\pi$
$163$	62.7761	+	193.205i	0.385129	+	1.18531i	−0.551257	+	0.834336i	$0.685852\pi$
$164$			156.522i			0.954404i
$165$		0			0
$166$	−26.9453			−0.162321
$167$	−126.214	+	41.0093i	−0.755771	+	0.245565i	−0.661462	−	0.749978i	$-0.730064\pi$
$167$	−126.214	+	41.0093i	−0.755771	+	0.245565i	−0.0943081	+	0.995543i	$0.530064\pi$
$168$	101.790	+	73.9546i	0.605891	+	0.440206i
$169$	−117.689	+	85.5063i	−0.696387	+	0.505954i
$170$		0			0
$171$	−358.848	−	116.597i	−2.09853	−	0.681852i
$172$	−65.9408	−	90.7598i	−0.383377	−	0.527673i
$173$	65.7416	−	90.4855i	0.380009	−	0.523037i	−0.575578	−	0.817747i	$-0.695223\pi$
$173$	65.7416	−	90.4855i	0.380009	−	0.523037i	0.955587	+	0.294709i	$0.0952229\pi$
$174$	23.2175	+	71.4562i	0.133434	+	0.410668i
$175$		0			0
$176$	−161.281	−	28.7868i	−0.916367	−	0.163562i
$177$	264.685			1.49540
$178$	34.3631	−	11.1652i	0.193051	−	0.0627261i
$179$	38.7619	+	28.1621i	0.216547	+	0.157330i	0.690771	−	0.723074i	$-0.257271\pi$
$179$	38.7619	+	28.1621i	0.216547	+	0.157330i	−0.474224	+	0.880404i	$0.657271\pi$
$180$		0			0
$181$	2.09873	−	6.45923i	0.0115952	−	0.0356864i	−0.945092	−	0.326806i	$-0.894028\pi$
$181$	2.09873	−	6.45923i	0.0115952	−	0.0356864i	0.956687	+	0.291119i	$0.0940277\pi$
$182$	14.2179	+	4.61968i	0.0781204	+	0.0253829i
$183$	100.831	+	138.782i	0.550989	+	0.758371i
$184$	17.1646	−	23.6250i	0.0932857	−	0.128397i
$185$		0			0
$186$		−	49.0823i		−	0.263883i
$187$	5.52645	−	30.9624i	0.0295532	−	0.165574i
$188$	15.3642			0.0817246
$189$	−429.705	+	139.619i	−2.27357	+	0.738728i
$190$		0			0
$191$	60.7195	−	44.1153i	0.317903	−	0.230970i	−0.417377	−	0.908733i	$-0.637051\pi$
$191$	60.7195	−	44.1153i	0.317903	−	0.230970i	0.735280	+	0.677763i	$0.237051\pi$
$192$	−88.1494	+	271.296i	−0.459112	+	1.41300i
$193$	−360.857	−	117.250i	−1.86973	−	0.607511i	−0.991645	−	0.128998i	$-0.958824\pi$
$193$	−360.857	−	117.250i	−1.86973	−	0.607511i	−0.878081	−	0.478513i	$-0.841176\pi$
$194$	−11.9733	−	16.4798i	−0.0617180	−	0.0849475i
$195$		0			0
$196$	−64.2633	−	197.782i	−0.327874	−	1.00909i
$197$			91.4898i			0.464415i	0.972666	+	0.232208i	$0.0745949\pi$
$197$			91.4898i			0.464415i	−0.972666	+	0.232208i	$0.925405\pi$
$198$	−42.6715	+	41.0349i	−0.215513	+	0.207247i
$199$	24.0213			0.120710			0.0603551	−	0.998177i	$-0.480777\pi$
$199$	24.0213			0.120710			0.0603551	+	0.998177i	$0.480777\pi$
$200$		0			0
$201$	376.460	+	273.514i	1.87294	+	1.36077i
$202$	−3.19133	+	2.31864i	−0.0157987	+	0.0114784i
$203$	149.159	−	459.064i	0.734773	−	2.26140i
$204$	−54.8533	−	17.8229i	−0.268889	−	0.0873673i
$205$		0			0
$206$	−20.2483	+	27.8693i	−0.0982926	+	0.135288i
$207$	66.1002	+	203.436i	0.319325	+	0.982781i
$208$			72.2423i			0.347319i
$209$	207.333	+	110.799i	0.992023	+	0.530138i
$210$		0			0
$211$	−349.688	+	113.620i	−1.65729	+	0.538486i	−0.980301	−	0.197509i	$-0.936715\pi$
$211$	−349.688	+	113.620i	−1.65729	+	0.538486i	−0.676987	+	0.735995i	$0.736715\pi$
$212$	−199.115	−	144.665i	−0.939219	−	0.682383i
$213$	25.0856	−	18.2258i	0.117773	−	0.0855671i
$214$	−1.51002	+	4.64735i	−0.00705615	+	0.0217166i
$215$		0			0
$216$	63.3100	+	87.1387i	0.293102	+	0.403420i
$217$	−185.343	+	255.103i	−0.854117	+	1.17559i
$218$	14.7714	+	45.4616i	0.0677586	+	0.208540i
$219$		−	675.834i		−	3.08600i
$220$		0			0
$221$	−13.8690			−0.0627555
$222$	−29.7357	+	9.66172i	−0.133945	+	0.0435212i
$223$	−143.396	−	104.183i	−0.643032	−	0.467190i	0.217858	−	0.975980i	$-0.430093\pi$
$223$	−143.396	−	104.183i	−0.643032	−	0.467190i	−0.860891	+	0.508790i	$0.830093\pi$
$224$	−115.999	+	84.2779i	−0.517851	+	0.376241i
$225$		0			0
$226$	−9.27747	−	3.01443i	−0.0410508	−	0.0133382i
$227$	−10.8732	−	14.9656i	−0.0478994	−	0.0659279i	0.784395	−	0.620261i	$-0.212973\pi$
$227$	−10.8732	−	14.9656i	−0.0478994	−	0.0659279i	−0.832295	+	0.554333i	$0.812973\pi$
$228$	253.390	−	348.761i	1.11136	−	1.52966i
$229$	−41.3284	−	127.196i	−0.180473	−	0.555440i	0.819368	−	0.573268i	$-0.194325\pi$
$229$	−41.3284	−	127.196i	−0.180473	−	0.555440i	−0.999841	+	0.0178283i	$0.994325\pi$
$230$		0			0
$231$	568.784	−	78.7219i	2.46227	−	0.340787i
$232$	−115.069			−0.495985
$233$	41.8780	−	13.6070i	0.179734	−	0.0583991i	−0.217767	−	0.976001i	$-0.569877\pi$
$233$	41.8780	−	13.6070i	0.179734	−	0.0583991i	0.397501	+	0.917602i	$0.369877\pi$
$234$	21.1195	+	15.3442i	0.0902544	+	0.0655736i
$235$		0			0
$236$	−61.8973	+	190.500i	−0.262277	+	0.807204i
$237$	441.223	+	143.362i	1.86170	+	0.604903i
$238$	−5.17974	−	7.12930i	−0.0217636	−	0.0299550i
$239$	97.2433	−	133.844i	0.406876	−	0.560017i	−0.555577	−	0.831465i	$-0.687503\pi$
$239$	97.2433	−	133.844i	0.406876	−	0.560017i	0.962453	+	0.271448i	$0.0875026\pi$
$240$		0			0
$241$			68.3979i			0.283809i	0.989880	+	0.141904i	$0.0453225\pi$
$241$			68.3979i			0.283809i	−0.989880	+	0.141904i	$0.954677\pi$
$242$	30.6646	−	20.4970i	0.126713	−	0.0846985i
$243$	31.4080			0.129251
$244$	−123.464	+	40.1160i	−0.506001	+	0.164410i
$245$		0			0
$246$	−51.0071	+	37.0588i	−0.207346	+	0.150645i
$247$	32.0332	−	98.5880i	0.129689	−	0.399142i
$248$	71.4915	+	23.2290i	0.288272	+	0.0936653i
$249$	268.250	+	369.214i	1.07731	+	1.48279i
$250$		0			0
$251$	104.767	+	322.440i	0.417399	+	1.28462i	0.910087	+	0.414417i	$0.136014\pi$
$251$	104.767	+	322.440i	0.417399	+	1.28462i	−0.492688	+	0.870206i	$0.663986\pi$
$252$		−	697.449i		−	2.76766i
$253$	−18.2710	−	132.012i	−0.0722175	−	0.521788i
$254$	32.8767			0.129436
$255$		0			0
$256$	−160.655	−	116.723i	−0.627559	−	0.455949i
$257$	−203.807	+	148.075i	−0.793025	+	0.576167i	−0.908860	−	0.417102i	$-0.863046\pi$
$257$	−203.807	+	148.075i	−0.793025	+	0.576167i	0.115835	+	0.993269i	$0.463046\pi$
$258$	13.9641	−	42.9772i	0.0541246	−	0.166578i
$259$	191.034	+	62.0708i	0.737584	+	0.239656i
$260$		0			0
$261$	495.430	−	681.901i	1.89820	−	2.61265i
$262$	4.58496	+	14.1111i	0.0174999	+	0.0538590i
$263$			424.803i			1.61522i	0.589717	+	0.807610i	$0.299239\pi$
$263$			424.803i			1.61522i	−0.589717	+	0.807610i	$0.700761\pi$
$264$	−59.7486	−	123.157i	−0.226320	−	0.466505i
$265$		0			0
$266$	62.6425	−	20.3538i	0.235498	−	0.0765180i
$267$	−495.086	−	359.701i	−1.85426	−	1.34720i
$268$	−284.891	+	206.985i	−1.06303	+	0.772333i
$269$	154.300	−	474.888i	0.573608	−	1.76538i	−0.0672640	−	0.997735i	$-0.521427\pi$
$269$	154.300	−	474.888i	0.573608	−	1.76538i	0.640872	−	0.767648i	$-0.278573\pi$
$270$		0			0
$271$	−138.031	−	189.983i	−0.509339	−	0.701045i	0.474468	−	0.880273i	$-0.342640\pi$
$271$	−138.031	−	189.983i	−0.509339	−	0.701045i	−0.983808	+	0.179227i	$0.942640\pi$
$272$	25.0305	−	34.4515i	0.0920239	−	0.126660i
$273$	−78.2437	−	240.809i	−0.286607	−	0.882086i
$274$			22.9011i			0.0835806i
$275$		0			0
$276$	−244.392			−0.885479
$277$	−129.339	+	42.0248i	−0.466928	+	0.151714i	−0.533026	−	0.846099i	$-0.678945\pi$
$277$	−129.339	+	42.0248i	−0.466928	+	0.151714i	0.0660976	+	0.997813i	$0.478945\pi$
$278$	11.9048	+	8.64937i	0.0428232	+	0.0311128i
$279$	−445.464	+	323.648i	−1.59664	+	1.16003i
$280$		0			0
$281$	−287.964	−	93.5652i	−1.02478	−	0.332972i	−0.252057	−	0.967712i	$-0.581107\pi$
$281$	−287.964	−	93.5652i	−1.02478	−	0.332972i	−0.772726	+	0.634740i	$0.781107\pi$
$282$	3.63769	+	5.00685i	0.0128996	+	0.0177548i
$283$	6.25933	−	8.61523i	0.0221178	−	0.0304425i	−0.797815	−	0.602902i	$-0.794011\pi$
$283$	6.25933	−	8.61523i	0.0221178	−	0.0304425i	0.819933	+	0.572460i	$0.194011\pi$
$284$	7.25119	+	22.3169i	0.0255324	+	0.0785805i
$285$		0			0
$286$	−11.2737	−	11.7234i	−0.0394186	−	0.0409908i
$287$	405.047			1.41131
$288$	−238.121	+	77.3703i	−0.826810	+	0.268647i
$289$	−227.192	−	165.065i	−0.786131	−	0.571158i
$290$		0			0
$291$	−106.614	+	328.124i	−0.366371	+	1.12757i
$292$	486.414	+	158.045i	1.66580	+	0.541251i
$293$	193.994	+	267.010i	0.662095	+	0.911296i	0.999549	−	0.0300463i	$-0.00956549\pi$
$293$	193.994	+	267.010i	0.662095	+	0.911296i	−0.337453	+	0.941342i	$0.609565\pi$
$294$	49.2374	−	67.7695i	0.167474	−	0.230509i
$295$		0			0
$296$		−	47.8845i		−	0.161772i
$297$	483.910	+	86.3727i	1.62933	+	0.290817i
$298$	−36.7310			−0.123259
$299$	−55.8909	+	18.1600i	−0.186926	+	0.0607359i
$300$		0			0
$301$	−234.868	+	170.641i	−0.780291	+	0.566914i
$302$	7.27734	−	22.3973i	0.0240971	−	0.0741634i
$303$	63.5415	+	20.6459i	0.209708	+	0.0681382i
$304$	187.087	+	257.503i	0.615418	+	0.847050i
$305$		0			0
$306$	−4.75519	−	14.6350i	−0.0155398	−	0.0478267i
$307$		−	111.473i		−	0.363104i	−0.983381	−	0.181552i	$-0.941888\pi$
$307$		−	111.473i		−	0.363104i	0.983381	−	0.181552i	$-0.0581121\pi$
$308$	−76.3534	+	427.776i	−0.247901	+	1.38888i
$309$	583.454			1.88820
$310$		0			0
$311$	−327.747	−	238.122i	−1.05385	−	0.765665i	−0.0809071	−	0.996722i	$-0.525782\pi$
$311$	−327.747	−	238.122i	−1.05385	−	0.765665i	−0.972940	+	0.231057i	$0.925782\pi$
$312$	−48.8331	+	35.4794i	−0.156516	+	0.113716i
$313$	−52.4582	+	161.450i	−0.167598	+	0.515814i	−0.999218	−	0.0395307i	$-0.987414\pi$
$313$	−52.4582	+	161.450i	−0.167598	+	0.515814i	0.831620	+	0.555345i	$0.187414\pi$
$314$	−15.7141	−	5.10581i	−0.0500448	−	0.0162605i
$315$		0			0
$316$	−206.362	+	284.033i	−0.653044	+	0.898838i
$317$	119.372	+	367.389i	0.376567	+	1.15895i	0.942415	+	0.334445i	$0.108549\pi$
$317$	119.372	+	367.389i	0.376567	+	1.15895i	−0.565848	+	0.824510i	$0.691451\pi$
$318$		−	99.1383i		−	0.311756i
$319$	−378.520	+	364.003i	−1.18658	+	1.14107i
$320$		0			0
$321$	78.7123	−	25.5752i	0.245210	−	0.0796735i
$322$	−30.2091	−	21.9482i	−0.0938170	−	0.0681620i
$323$	−49.4350	+	35.9167i	−0.153050	+	0.111197i
$324$	86.7068	−	266.856i	0.267613	−	0.823630i
$325$		0			0
$326$	−36.3987	−	50.0986i	−0.111653	−	0.153677i
$327$	475.877	−	654.988i	1.45528	−	2.00302i
$328$	−29.8386	−	91.8337i	−0.0909713	−	0.279981i
$329$		−	39.7595i		−	0.120849i
$330$		0			0
$331$	118.966			0.359413			0.179706	−	0.983720i	$-0.442485\pi$
$331$	118.966			0.359413			0.179706	+	0.983720i	$0.442485\pi$
$332$	−328.463	+	106.724i	−0.989346	+	0.321458i
$333$	283.765	+	206.168i	0.852148	+	0.619122i
$334$	32.7275	−	23.7780i	0.0979867	−	0.0711915i
$335$		0			0
$336$	739.402	+	240.246i	2.20060	+	0.715018i
$337$	−260.717	−	358.847i	−0.773642	−	1.06483i	−0.995955	−	0.0898516i	$-0.971361\pi$
$337$	−260.717	−	358.847i	−0.773642	−	1.06483i	0.222313	−	0.974975i	$-0.428639\pi$
$338$	26.0648	−	35.8751i	0.0771147	−	0.106139i
$339$	51.0556	+	157.133i	0.150606	+	0.463519i
$340$		0			0
$341$	308.654	−	149.741i	0.905144	−	0.439122i
$342$	115.016			0.336305
$343$	−40.6417	+	13.2053i	−0.118489	+	0.0384993i
$344$	55.9903	+	40.6793i	0.162763	+	0.118254i
$345$		0			0
$346$	−10.5356	+	32.4252i	−0.0304497	+	0.0937146i
$347$	−501.898	−	163.076i	−1.44639	−	0.469961i	−0.522507	−	0.852635i	$-0.675003\pi$
$347$	−501.898	−	163.076i	−1.44639	−	0.469961i	−0.923883	+	0.382674i	$0.875003\pi$
$348$	566.042	+	779.091i	1.62656	+	2.23877i
$349$	318.255	−	438.040i	0.911905	−	1.25513i	−0.0546065	−	0.998508i	$-0.517390\pi$
$349$	318.255	−	438.040i	0.911905	−	1.25513i	0.966512	−	0.256622i	$-0.0826096\pi$
$350$		0			0
$351$		−	216.758i		−	0.617543i
$352$	154.520	−	21.3862i	0.438978	−	0.0607563i
$353$	−216.813			−0.614201			−0.307101	−	0.951677i	$-0.599359\pi$
$353$	−216.813			−0.614201			−0.307101	+	0.951677i	$0.599359\pi$
$354$	−76.7347	+	24.9326i	−0.216765	+	0.0704311i
$355$		0			0
$356$	374.662	−	272.208i	1.05242	−	0.764630i
$357$	−46.1221	+	141.949i	−0.129193	+	0.397616i
$358$	−13.8902	−	4.51321i	−0.0387995	−	0.0126067i
$359$	−329.315	−	453.263i	−0.917311	−	1.26257i	−0.964608	−	0.263689i	$-0.915061\pi$
$359$	−329.315	−	453.263i	−0.917311	−	1.26257i	0.0472967	−	0.998881i	$-0.484939\pi$
$360$		0			0
$361$	−29.5795	−	91.0363i	−0.0819376	−	0.252178i
$362$			2.07029i			0.00571902i
$363$	−586.134	−	216.123i	−1.61469	−	0.595379i
$364$	191.614			0.526411
$365$		0			0
$366$	−42.3047	−	30.7362i	−0.115587	−	0.0839786i
$367$	25.0380	−	18.1911i	0.0682233	−	0.0495671i	−0.553151	−	0.833081i	$-0.686575\pi$
$367$	25.0380	−	18.1911i	0.0682233	−	0.0495671i	0.621374	+	0.783514i	$0.286575\pi$
$368$	55.7602	−	171.612i	0.151522	−	0.466337i
$369$	672.680	+	218.567i	1.82298	+	0.592323i
$370$		0			0
$371$	−374.364	+	515.267i	−1.00907	+	1.38886i
$372$	−194.403	−	598.312i	−0.522590	−	1.60837i
$373$		−	483.806i		−	1.29707i	−0.761186	−	0.648534i	$-0.775383\pi$
$373$		−	483.806i		−	1.29707i	0.761186	−	0.648534i	$-0.224617\pi$
$374$	1.31440	+	9.49685i	0.00351444	+	0.0253927i
$375$		0			0
$376$	−9.01440	+	2.92896i	−0.0239745	+	0.00778977i
$377$	187.342	+	136.112i	0.496928	+	0.361040i
$378$	111.424	−	80.9540i	0.294771	−	0.214164i
$379$	25.3368	−	77.9786i	0.0668517	−	0.205748i	−0.912050	−	0.410078i	$-0.865501\pi$
$379$	25.3368	−	77.9786i	0.0668517	−	0.205748i	0.978902	+	0.204330i	$0.0655015\pi$
$380$		0			0
$381$	−327.298	−	450.487i	−0.859050	−	1.18238i
$382$	−13.4476	+	18.5090i	−0.0352031	+	0.0484530i
$383$	−225.261	−	693.283i	−0.588150	−	1.81014i	−0.586234	−	0.810141i	$-0.699390\pi$
$383$	−225.261	−	693.283i	−0.588150	−	1.81014i	−0.00191562	−	0.999998i	$-0.500610\pi$
$384$		−	379.819i		−	0.989111i
$385$		0			0
$386$	115.660			0.299638
$387$	−482.135	+	156.655i	−1.24583	+	0.404793i
$388$	−211.227	−	153.465i	−0.544399	−	0.395529i
$389$	−193.321	+	140.456i	−0.496969	+	0.361069i	−0.807858	−	0.589377i	$-0.799373\pi$
$389$	−193.321	+	140.456i	−0.496969	+	0.361069i	0.310889	+	0.950446i	$0.399373\pi$
$390$		0			0
$391$	32.9458	+	10.7047i	0.0842604	+	0.0273779i
$392$	75.4082	+	103.790i	0.192368	+	0.264772i
$393$	147.710	−	203.305i	0.375852	−	0.517316i
$394$	−8.61808	−	26.5237i	−0.0218733	−	0.0673191i
$395$		0			0
$396$	−357.635	+	669.226i	−0.903120	+	1.68997i
$397$	354.733			0.893535			0.446768	−	0.894650i	$-0.352575\pi$
$397$	354.733			0.893535			0.446768	+	0.894650i	$0.352575\pi$
$398$	−6.96401	+	2.26274i	−0.0174975	+	0.00568528i
$399$	−902.522	−	655.721i	−2.26196	−	1.64341i
$400$		0			0
$401$	79.1417	−	243.573i	0.197361	−	0.607414i	−0.802580	−	0.596545i	$-0.796540\pi$
$401$	79.1417	−	243.573i	0.197361	−	0.607414i	0.999941	−	0.0108700i	$-0.00346008\pi$
$402$	−134.904	−	43.8328i	−0.335581	−	0.109037i
$403$	−88.9175	−	122.384i	−0.220639	−	0.303684i
$404$	−29.7187	+	40.9042i	−0.0735610	+	0.101248i
$405$		0			0
$406$			147.137i			0.362407i
$407$	−151.476	−	157.517i	−0.372176	−	0.387020i
$408$	35.5808			0.0872079
$409$	261.500	−	84.9666i	0.639365	−	0.207742i	0.0286458	−	0.999590i	$-0.490881\pi$
$409$	261.500	−	84.9666i	0.639365	−	0.207742i	0.610719	+	0.791847i	$0.290881\pi$
$410$		0			0
$411$	313.798	−	227.988i	0.763500	−	0.554715i
$412$	−136.442	+	419.925i	−0.331170	+	1.01924i
$413$	492.975	+	160.177i	1.19364	+	0.387839i
$414$	−38.3261	−	52.7514i	−0.0925752	−	0.127419i
$415$		0			0
$416$	−21.2563	−	65.4202i	−0.0510969	−	0.157260i
$417$		−	249.232i		−	0.597678i
$418$	−70.5446	−	12.5914i	−0.168767	−	0.0301231i
$419$	44.0757			0.105193			0.0525963	−	0.998616i	$-0.483250\pi$
$419$	44.0757			0.105193			0.0525963	+	0.998616i	$0.483250\pi$
$420$		0			0
$421$	65.8608	+	47.8507i	0.156439	+	0.113660i	0.663251	−	0.748397i	$-0.269176\pi$
$421$	65.8608	+	47.8507i	0.156439	+	0.113660i	−0.506812	+	0.862057i	$0.669176\pi$
$422$	90.6750	−	65.8792i	0.214870	−	0.156112i
$423$	21.4546	−	66.0303i	0.0507200	−	0.156100i
$424$	144.401	+	46.9188i	0.340569	+	0.110658i
$425$		0			0
$426$	−5.55574	+	7.64682i	−0.0130416	+	0.0179503i
$427$	103.812	+	319.500i	0.243119	+	0.748243i
$428$			62.6319i			0.146336i
$429$	−48.4038	+	271.186i	−0.112829	+	0.632136i
$430$		0			0
$431$	690.547	−	224.372i	1.60220	−	0.520585i	0.634547	−	0.772884i	$-0.281187\pi$
$431$	690.547	−	224.372i	1.60220	−	0.520585i	0.967649	+	0.252299i	$0.0811866\pi$
$432$	538.442	+	391.201i	1.24639	+	0.905558i
$433$	280.828	−	204.033i	0.648563	−	0.471208i	−0.214218	−	0.976786i	$-0.568720\pi$
$433$	280.828	−	204.033i	0.648563	−	0.471208i	0.862781	+	0.505577i	$0.168720\pi$
$434$	29.7027	−	91.4156i	0.0684394	−	0.210635i
$435$		0			0
$436$	360.126	+	495.670i	0.825976	+	1.13686i
$437$	−152.190	+	209.472i	−0.348261	+	0.479340i
$438$	63.6617	+	195.930i	0.145346	+	0.447330i
$439$			72.1914i			0.164445i	0.996614	+	0.0822226i	$0.0262018\pi$
$439$			72.1914i			0.164445i	−0.996614	+	0.0822226i	$0.973798\pi$
$440$		0			0
$441$	−939.738			−2.13092
$442$	4.02074	−	1.30642i	0.00909669	−	0.00295569i
$443$	−304.024	−	220.886i	−0.686284	−	0.498614i	0.189153	−	0.981948i	$-0.439426\pi$
$443$	−304.024	−	220.886i	−0.686284	−	0.498614i	−0.875436	+	0.483333i	$0.839426\pi$
$444$	−324.210	+	235.552i	−0.730202	+	0.530523i
$445$		0			0
$446$	51.3857	+	16.6962i	0.115214	+	0.0374355i
$447$	365.670	+	503.301i	0.818053	+	1.12595i
$448$	−328.356	+	451.943i	−0.732937	+	1.00880i
$449$	34.6764	+	106.723i	0.0772302	+	0.237690i	0.982217	−	0.187750i	$-0.0601194\pi$
$449$	34.6764	+	106.723i	0.0772302	+	0.237690i	−0.904987	+	0.425440i	$0.860119\pi$
$450$		0			0
$451$	−388.657	−	207.699i	−0.861767	−	0.460529i
$452$	−125.032			−0.276619
$453$	−379.344	+	123.256i	−0.837405	+	0.272089i
$454$	4.56195	+	3.31445i	0.0100483	+	0.00730055i
$455$		0			0
$456$	−82.1812	+	252.928i	−0.180222	+	0.554666i
$457$	177.567	+	57.6949i	0.388549	+	0.126247i	0.496775	−	0.867879i	$-0.334517\pi$
$457$	177.567	+	57.6949i	0.388549	+	0.126247i	−0.108227	+	0.994126i	$0.534517\pi$
$458$	23.9630	+	32.9822i	0.0523209	+	0.0720136i
$459$	−75.1021	+	103.369i	−0.163621	+	0.225205i
$460$		0			0
$461$			559.922i			1.21458i	0.794479	+	0.607291i	$0.207744\pi$
$461$			559.922i			1.21458i	−0.794479	+	0.607291i	$0.792256\pi$
$462$	−157.480	+	76.4000i	−0.340866	+	0.165368i
$463$	648.611			1.40089			0.700444	−	0.713708i	$-0.252986\pi$
$463$	648.611			1.40089			0.700444	+	0.713708i	$0.252986\pi$
$464$	−676.224	+	219.719i	−1.45738	+	0.473532i
$465$		0			0
$466$	−10.8591	+	7.88958i	−0.0233028	+	0.0169304i
$467$	278.242	−	856.339i	0.595806	−	1.83370i	0.0451348	−	0.998981i	$-0.485628\pi$
$467$	278.242	−	856.339i	0.595806	−	1.83370i	0.550671	−	0.834722i	$-0.314372\pi$
$468$	318.221	+	103.396i	0.679960	+	0.220932i
$469$	535.635	+	737.238i	1.14208	+	1.57194i
$470$		0			0
$471$	86.4772	+	266.149i	0.183603	+	0.565073i
$472$		−	123.569i		−	0.261798i
$473$	312.864	−	43.3016i	0.661447	−	0.0915468i
$474$	−141.419			−0.298352
$475$		0			0
$476$	−91.3783	−	66.3902i	−0.191971	−	0.139475i
$477$	−899.765	+	653.718i	−1.88630	+	1.37048i
$478$	−15.5840	+	47.9626i	−0.0326025	+	0.100340i
$479$	−441.790	−	143.546i	−0.922317	−	0.299679i	−0.190900	−	0.981609i	$-0.561141\pi$
$479$	−441.790	−	143.546i	−0.922317	−	0.299679i	−0.731417	+	0.681930i	$0.761141\pi$
$480$		0			0
$481$	−56.6415	+	77.9603i	−0.117758	+	0.162080i
$482$	−6.44289	−	19.8292i	−0.0133670	−	0.0411394i
$483$			632.437i			1.30939i
$484$	292.617	−	371.314i	0.604581	−	0.767177i
$485$		0			0
$486$	−9.10546	+	2.95854i	−0.0187355	+	0.00608753i
$487$	26.6567	+	19.3672i	0.0547366	+	0.0397685i	0.614817	−	0.788670i	$-0.289230\pi$
$487$	26.6567	+	19.3672i	0.0547366	+	0.0397685i	−0.560081	+	0.828438i	$0.689230\pi$
$488$	64.7906	−	47.0731i	0.132768	−	0.0964613i
$489$	−324.106	+	997.496i	−0.662794	+	2.03987i
$490$		0			0
$491$	−469.003	−	645.528i	−0.955200	−	1.31472i	−0.949179	−	0.314738i	$-0.898083\pi$
$491$	−469.003	−	645.528i	−0.955200	−	1.31472i	−0.00602158	−	0.999982i	$-0.501917\pi$
$492$	−474.994	+	653.773i	−0.965434	+	1.32881i
$493$	−42.1812	−	129.820i	−0.0855603	−	0.263327i
$494$			31.5990i			0.0639656i
$495$		0			0
$496$	464.489			0.936470
$497$	57.7514	−	18.7646i	0.116200	−	0.0377557i
$498$	−112.547	−	81.7701i	−0.225998	−	0.164197i
$499$	−479.816	+	348.607i	−0.961555	+	0.698611i	−0.953511	−	0.301357i	$-0.902560\pi$
$499$	−479.816	+	348.607i	−0.961555	+	0.698611i	−0.00804363	+	0.999968i	$0.502560\pi$
$500$		0			0
$501$	−651.627	−	211.727i	−1.30065	−	0.422608i
$502$	−60.7459	−	83.6096i	−0.121008	−	0.166553i
$503$	−461.015	+	634.532i	−0.916530	+	1.26150i	0.0483569	+	0.998830i	$0.484602\pi$
$503$	−461.015	+	634.532i	−0.916530	+	1.26150i	−0.964887	+	0.262665i	$0.915398\pi$
$504$	132.958	+	409.203i	0.263806	+	0.811910i
$505$		0			0
$506$	17.7321	+	36.5505i	0.0350437	+	0.0722342i
$507$	−751.056			−1.48137
$508$	400.766	−	130.217i	0.788909	−	0.256332i
$509$	639.768	+	464.819i	1.25691	+	0.913200i	0.998602	−	0.0528625i	$-0.0168345\pi$
$509$	639.768	+	464.819i	1.25691	+	0.913200i	0.258310	+	0.966062i	$0.416835\pi$
$510$		0			0
$511$	408.989	−	1258.74i	0.800369	−	2.46328i
$512$	337.436	+	109.640i	0.659055	+	0.214140i
$513$	−561.340	−	772.619i	−1.09423	−	1.50608i
$514$	45.1374	−	62.1263i	0.0878160	−	0.120868i
$515$		0			0
$516$		−	579.200i		−	1.12248i
$517$	−20.3877	+	38.1506i	−0.0394346	+	0.0737922i
$518$	−61.2295			−0.118204
$519$	549.187	−	178.442i	1.05816	−	0.343818i
$520$		0			0
$521$	−514.280	+	373.646i	−0.987101	+	0.717171i	−0.959284	−	0.282442i	$-0.908856\pi$
$521$	−514.280	+	373.646i	−0.987101	+	0.717171i	−0.0278170	+	0.999613i	$0.508856\pi$
$522$	−79.3966	+	244.357i	−0.152101	+	0.468118i
$523$	−180.831	−	58.7556i	−0.345757	−	0.112343i	0.130990	−	0.991384i	$-0.458184\pi$
$523$	−180.831	−	58.7556i	−0.345757	−	0.112343i	−0.476747	+	0.879040i	$0.658184\pi$
$524$	111.781	+	153.854i	0.213323	+	0.293614i
$525$		0			0
$526$	−40.0152	−	123.154i	−0.0760746	−	0.234134i
$527$			89.1719i			0.169207i
$528$	−586.289	−	609.672i	−1.11040	−	1.15468i
$529$	−382.214			−0.722522
$530$		0			0
$531$	732.273	+	532.027i	1.37905	+	1.00193i
$532$	682.995	−	496.225i	1.28382	−	0.932753i
$533$	−60.0480	+	184.809i	−0.112660	+	0.346733i
$534$	177.413	+	57.6449i	0.332234	+	0.107949i
$535$		0			0
$536$	127.691	−	175.751i	0.238229	−	0.327894i
$537$	76.4403	+	235.259i	0.142347	+	0.438099i
$538$			152.209i			0.282917i
$539$	576.382	+	102.878i	1.06936	+	0.190868i
$540$		0			0
$541$	37.6026	−	12.2178i	0.0695058	−	0.0225838i	−0.274058	−	0.961713i	$-0.588366\pi$
$541$	37.6026	−	12.2178i	0.0695058	−	0.0225838i	0.343563	+	0.939129i	$0.388366\pi$
$542$	57.9123	+	42.0758i	0.106849	+	0.0776306i
$543$	28.3678	−	20.6104i	0.0522427	−	0.0379565i
$544$	−12.5299	+	38.5630i	−0.0230329	+	0.0708879i
$545$		0			0
$546$	45.3671	+	62.4425i	0.0830900	+	0.114364i
$547$	−347.554	+	478.368i	−0.635383	+	0.874529i	−0.998359	−	0.0572690i	$-0.981761\pi$
$547$	−347.554	+	478.368i	−0.635383	+	0.874529i	0.362976	+	0.931799i	$0.381761\pi$
$548$	90.7057	+	279.164i	0.165521	+	0.509423i
$549$			586.626i			1.06853i
$550$		0			0
$551$	1020.26			1.85165
$552$	143.388	−	46.5896i	0.259761	−	0.0844015i
$553$	735.018	+	534.022i	1.32915	+	0.965682i
$554$	33.5380	−	24.3668i	0.0605379	−	0.0439833i
$555$		0			0
$556$	179.378	+	58.2834i	0.322622	+	0.104826i
$557$	−128.305	−	176.596i	−0.230350	−	0.317049i	0.678159	−	0.734915i	$-0.262778\pi$
$557$	−128.305	−	176.596i	−0.230350	−	0.317049i	−0.908509	+	0.417866i	$0.862778\pi$
$558$	98.6573	−	135.790i	0.176805	−	0.243351i
$559$	−43.0386	−	132.459i	−0.0769921	−	0.236957i
$560$		0			0
$561$	117.044	−	112.555i	0.208634	−	0.200632i
$562$	92.2970			0.164229
$563$	356.595	−	115.865i	0.633383	−	0.205799i	0.0253101	−	0.999680i	$-0.491943\pi$
$563$	356.595	−	115.865i	0.633383	−	0.205799i	0.608073	+	0.793881i	$0.291943\pi$
$564$	64.1743	+	46.6254i	0.113784	+	0.0826691i
$565$		0			0
$566$	−1.00311	+	3.08725i	−0.00177227	+	0.00545450i
$567$	−690.568	−	224.379i	−1.21793	−	0.395730i
$568$	−8.50874	−	11.7113i	−0.0149802	−	0.0206184i
$569$	−131.674	+	181.234i	−0.231413	+	0.318513i	−0.908894	−	0.417028i	$-0.863072\pi$
$569$	−131.674	+	181.234i	−0.231413	+	0.318513i	0.677480	+	0.735541i	$0.263072\pi$
$570$		0			0
$571$			176.017i			0.308262i	0.988050	+	0.154131i	$0.0492577\pi$
$571$			176.017i			0.308262i	−0.988050	+	0.154131i	$0.950742\pi$
$572$	−183.860	−	98.2549i	−0.321433	−	0.171774i
$573$	387.492			0.676252
$574$	−117.427	+	38.1543i	−0.204577	+	0.0664710i
$575$		0			0
$576$	−789.188	+	573.378i	−1.37012	+	0.995449i
$577$	−206.377	+	635.162i	−0.357672	+	1.10080i	0.596772	+	0.802411i	$0.296450\pi$
$577$	−206.377	+	635.162i	−0.357672	+	1.10080i	−0.954444	+	0.298391i	$0.903550\pi$
$578$	81.4137	+	26.4529i	0.140854	+	0.0457663i
$579$	−1151.44	−	1584.82i	−1.98867	−	2.73716i
$580$		0			0
$581$	276.180	+	849.994i	0.475352	+	1.46298i
$582$		−	105.169i		−	0.180703i
$583$	623.432	−	302.452i	1.06935	−	0.518785i
$584$	−315.514			−0.540264
$585$		0			0
$586$	−81.3922	−	59.1349i	−0.138895	−	0.100913i
$587$	−79.0311	+	57.4195i	−0.134636	+	0.0978185i	−0.653065	−	0.757302i	$-0.726517\pi$
$587$	−79.0311	+	57.4195i	−0.134636	+	0.0978185i	0.518429	+	0.855121i	$0.326517\pi$
$588$	331.784	−	1021.13i	0.564259	−	1.73661i
$589$	−633.882	−	205.961i	−1.07620	−	0.349679i
$590$		0			0
$591$	−277.641	+	382.141i	−0.469782	+	0.646600i
$592$	−91.4335	−	281.403i	−0.154448	−	0.475343i
$593$		−	479.081i		−	0.807893i	−0.914783	−	0.403947i	$-0.867638\pi$
$593$		−	479.081i		−	0.807893i	0.914783	−	0.403947i	$-0.132362\pi$
$594$	−148.426	+	20.5427i	−0.249875	+	0.0345837i
$595$		0			0
$596$	−447.751	+	145.483i	−0.751259	+	0.244099i
$597$	100.334	+	72.8968i	0.168063	+	0.122105i
$598$	14.4927	−	10.5295i	0.0242352	−	0.0176079i
$599$	146.829	−	451.894i	0.245124	−	0.754414i	−0.750492	−	0.660879i	$-0.770183\pi$
$599$	146.829	−	451.894i	0.245124	−	0.754414i	0.995616	−	0.0935345i	$-0.0298165\pi$
$600$		0			0
$601$	316.409	+	435.499i	0.526470	+	0.724624i	0.986587	−	0.163234i	$-0.0521926\pi$
$601$	316.409	+	435.499i	0.526470	+	0.724624i	−0.460117	+	0.887858i	$0.652193\pi$
$602$	52.0163	−	71.5943i	0.0864059	−	0.118927i
$603$	491.733	+	1513.40i	0.815477	+	2.50978i
$604$		−	301.847i		−	0.499747i
$605$		0			0
$606$	−20.3660			−0.0336073
$607$	391.027	−	127.052i	0.644196	−	0.209312i	0.0313426	−	0.999509i	$-0.490022\pi$
$607$	391.027	−	127.052i	0.644196	−	0.209312i	0.612853	+	0.790197i	$0.290022\pi$
$608$	−245.186	−	178.138i	−0.403267	−	0.292991i
$609$	2016.13	−	1464.80i	3.31055	−	2.40526i
$610$		0			0
$611$	18.1408	+	5.89431i	0.0296904	+	0.00964700i
$612$	−115.931	−	159.566i	−0.189430	−	0.260728i
$613$	−146.092	+	201.079i	−0.238324	+	0.328025i	−0.911379	−	0.411567i	$-0.864981\pi$
$613$	−146.092	+	201.079i	−0.238324	+	0.328025i	0.673056	+	0.739592i	$0.264981\pi$
$614$	10.5004	+	32.3170i	0.0171017	+	0.0526336i
$615$		0			0
$616$	−36.7514	−	265.538i	−0.0596614	−	0.431067i
$617$	1141.96			1.85082			0.925411	−	0.378964i	$-0.123720\pi$
$617$	1141.96			1.85082			0.925411	+	0.378964i	$0.123720\pi$
$618$	−169.149	+	54.9597i	−0.273703	+	0.0889316i
$619$	−4.57281	−	3.32234i	−0.00738742	−	0.00536727i	0.584085	−	0.811692i	$-0.301453\pi$
$619$	−4.57281	−	3.32234i	−0.00738742	−	0.00536727i	−0.591473	+	0.806325i	$0.701453\pi$
$620$		0			0
$621$	−167.304	+	514.909i	−0.269411	+	0.829161i
$622$	117.447	+	38.1609i	0.188822	+	0.0613519i
$623$	−704.418	−	969.549i	−1.13069	−	1.55626i
$624$	−219.232	+	301.746i	−0.351333	+	0.483568i
$625$		0			0
$626$		−	51.7472i		−	0.0826633i
$627$	529.763	+	1091.98i	0.844917	+	1.74159i
$628$	−211.777			−0.337224
$629$	54.0233	−	17.5532i	0.0858876	−	0.0279066i
$630$		0			0
$631$	601.402	−	436.944i	0.953094	−	0.692463i	0.00155713	−	0.999999i	$-0.499504\pi$
$631$	601.402	−	436.944i	0.953094	−	0.692463i	0.951537	+	0.307536i	$0.0995043\pi$
$632$	66.9288	−	205.986i	0.105900	−	0.325927i
$633$	−1805.40	−	586.610i	−2.85213	−	0.926714i
$634$	−69.2140	−	95.2649i	−0.109170	−	0.150260i
$635$		0			0
$636$	−392.664	−	1208.49i	−0.617396	−	1.90015i
$637$		−	258.179i		−	0.405304i
$638$	75.4485	−	141.183i	0.118258	−	0.221290i
$639$	106.036			0.165940
$640$		0			0
$641$	−292.789	−	212.724i	−0.456769	−	0.331862i	0.335493	−	0.942043i	$-0.391097\pi$
$641$	−292.789	−	212.724i	−0.456769	−	0.331862i	−0.792263	+	0.610180i	$0.791097\pi$
$642$	−20.4103	+	14.8290i	−0.0317918	+	0.0230981i
$643$	−200.009	+	615.565i	−0.311056	+	0.957333i	0.666291	+	0.745692i	$0.267881\pi$
$643$	−200.009	+	615.565i	−0.311056	+	0.957333i	−0.977347	+	0.211641i	$0.932119\pi$
$644$	−455.179	−	147.897i	−0.706800	−	0.229653i
$645$		0			0
$646$	10.9484	−	15.0692i	0.0169480	−	0.0233269i
$647$	−225.784	−	694.892i	−0.348971	−	1.07402i	−0.959423	−	0.281969i	$-0.909012\pi$
$647$	−225.784	−	694.892i	−0.348971	−	1.07402i	0.610453	−	0.792053i	$-0.290988\pi$
$648$			173.097i			0.267125i
$649$	−390.891	−	406.482i	−0.602298	−	0.626320i
$650$		0			0
$651$	−1548.31	+	503.076i	−2.37835	+	0.772774i
$652$	−642.128	−	466.534i	−0.984859	−	0.715542i
$653$	243.570	−	176.964i	0.373001	−	0.271001i	−0.385453	−	0.922727i	$-0.625955\pi$
$653$	243.570	−	176.964i	0.373001	−	0.271001i	0.758454	+	0.651726i	$0.225955\pi$
$654$	−76.2630	+	234.713i	−0.116610	+	0.358889i
$655$		0			0
$656$	−350.705	−	482.704i	−0.534611	−	0.735829i
$657$	1358.45	−	1869.75i	2.06766	−	2.84589i
$658$	3.74523	+	11.5266i	0.00569184	+	0.0175177i
$659$			596.433i			0.905057i	0.891750	+	0.452529i	$0.149478\pi$
$659$			596.433i			0.905057i	−0.891750	+	0.452529i	$0.850522\pi$
$660$		0			0
$661$	882.175			1.33461			0.667303	−	0.744786i	$-0.267449\pi$
$661$	882.175			1.33461			0.667303	+	0.744786i	$0.267449\pi$
$662$	−34.4892	+	11.2062i	−0.0520985	+	0.0169278i
$663$	−57.9288	−	42.0877i	−0.0873737	−	0.0634807i
$664$	172.368	−	125.233i	0.259591	−	0.188604i
$665$		0			0
$666$	−101.687	−	33.0400i	−0.152683	−	0.0496096i
$667$	−339.974	−	467.934i	−0.509707	−	0.701551i
$668$	304.769	−	419.479i	0.456241	−	0.627962i
$669$	−282.784	−	870.320i	−0.422697	−	1.30093i
$670$		0			0
$671$	64.2210	−	359.803i	0.0957094	−	0.536220i
$672$	−740.266			−1.10159
$673$	−383.533	+	124.617i	−0.569886	+	0.185167i	−0.579764	−	0.814784i	$-0.696855\pi$
$673$	−383.533	+	124.617i	−0.569886	+	0.185167i	0.00987877	+	0.999951i	$0.496855\pi$
$674$	109.387	+	79.4741i	0.162295	+	0.117914i
$675$		0			0
$676$	175.636	−	540.553i	0.259817	−	0.799634i
$677$	595.604	+	193.523i	0.879769	+	0.285854i	0.713861	−	0.700287i	$-0.246945\pi$
$677$	595.604	+	193.523i	0.879769	+	0.285854i	0.165908	+	0.986141i	$0.446945\pi$
$678$	−29.6029	−	40.7450i	−0.0436622	−	0.0600958i
$679$	−397.136	+	546.611i	−0.584884	+	0.805024i
$680$		0			0
$681$		−	95.5059i		−	0.140244i
$682$	−75.3765	+	72.4855i	−0.110523	+	0.106284i
$683$	−935.585			−1.36982			−0.684909	−	0.728629i	$-0.740158\pi$
$683$	−935.585			−1.36982			−0.684909	+	0.728629i	$0.740158\pi$
$684$	1402.05	−	455.553i	2.04978	−	0.666013i
$685$		0			0
$686$	10.5385	−	7.65666i	0.0153622	−	0.0111613i
$687$	213.374	−	656.698i	0.310588	−	0.955892i
$688$	406.714	+	132.149i	0.591154	+	0.192078i
$689$	−179.599	−	247.197i	−0.260666	−	0.358776i
$690$		0			0
$691$	255.366	+	785.937i	0.369561	+	1.13739i	0.947076	+	0.321011i	$0.104023\pi$
$691$	255.366	+	785.937i	0.369561	+	1.13739i	−0.577515	+	0.816380i	$0.695977\pi$
$692$			436.992i			0.631491i
$693$	1731.82	+	925.486i	2.49902	+	1.33548i
$694$	160.866			0.231795
$695$		0			0
$696$	−480.626	−	349.195i	−0.690555	−	0.501718i
$697$	92.6687	−	67.3278i	0.132954	−	0.0965965i
$698$	−51.0029	+	156.971i	−0.0730700	+	0.224886i
$699$	216.212	+	70.2514i	0.309316	+	0.100503i
$700$		0			0
$701$	−139.111	+	191.469i	−0.198446	+	0.273138i	−0.896630	−	0.442781i	$-0.853992\pi$
$701$	−139.111	+	191.469i	−0.198446	+	0.273138i	0.698184	+	0.715919i	$0.253992\pi$
$702$	20.4180	+	62.8400i	0.0290854	+	0.0895157i
$703$			424.570i			0.603940i
$704$	546.814	−	265.282i	0.776725	−	0.376821i
$705$		0			0
$706$	62.8561	−	20.4232i	0.0890313	−	0.0289280i
$707$	105.852	+	76.9057i	0.149719	+	0.108778i
$708$	−836.642	+	607.856i	−1.18170	+	0.858554i
$709$	−278.848	+	858.205i	−0.393297	+	1.21044i	0.536982	+	0.843593i	$0.319564\pi$
$709$	−278.848	+	858.205i	−0.393297	+	1.21044i	−0.930280	+	0.366851i	$0.880436\pi$
$710$		0			0
$711$	932.515	+	1283.50i	1.31155	+	1.80520i
$712$	−167.927	+	231.132i	−0.235853	+	0.324623i
$713$	116.762	+	359.356i	0.163761	+	0.504006i
$714$		−	45.4969i		−	0.0637212i
$715$		0			0
$716$	−187.197			−0.261449
$717$	812.345	−	263.947i	1.13298	−	0.368127i
$718$	138.167	+	100.385i	0.192434	+	0.139811i
$719$	318.157	−	231.154i	0.442499	−	0.321494i	−0.344128	−	0.938923i	$-0.611826\pi$
$719$	318.157	−	231.154i	0.442499	−	0.321494i	0.786627	+	0.617428i	$0.211826\pi$
$720$		0			0
$721$	1086.68	+	353.084i	1.50718	+	0.489714i
$722$	17.1507	+	23.6060i	0.0237545	+	0.0326952i
$723$	−207.565	+	285.689i	−0.287089	+	0.395144i
$724$	8.19991	+	25.2367i	0.0113258	+	0.0348574i
$725$		0			0
$726$	190.284	+	7.44370i	0.262099	+	0.0102530i
$727$	−1284.55			−1.76691			−0.883456	−	0.468514i	$-0.844790\pi$
$727$	−1284.55			−1.76691			−0.883456	+	0.468514i	$0.844790\pi$
$728$	−112.422	+	36.5282i	−0.154426	+	0.0501761i
$729$	654.087	+	475.222i	0.897238	+	0.651882i
$730$		0			0
$731$	−25.3698	+	78.0803i	−0.0347056	+	0.106813i
$732$	−637.432	−	207.114i	−0.870809	−	0.282943i
$733$	246.425	+	339.175i	0.336187	+	0.462722i	0.943323	−	0.331876i	$-0.107682\pi$
$733$	246.425	+	339.175i	0.336187	+	0.462722i	−0.607136	+	0.794598i	$0.707682\pi$
$734$	−5.54518	+	7.63228i	−0.00755474	+	0.0103982i
$735$		0			0
$736$			171.813i			0.233441i
$737$	−135.922	−	982.066i	−0.184426	−	1.33252i
$738$	−215.605			−0.292147
$739$	−269.243	+	87.4823i	−0.364334	+	0.118379i	−0.485462	−	0.874258i	$-0.661349\pi$
$739$	−269.243	+	87.4823i	−0.364334	+	0.118379i	0.121128	+	0.992637i	$0.461349\pi$
$740$		0			0
$741$	432.981	−	314.579i	0.584319	−	0.424533i
$742$	59.9947	−	184.645i	0.0808554	−	0.248847i
$743$	10.6813	+	3.47057i	0.0143759	+	0.00467102i	0.316196	−	0.948694i	$-0.397594\pi$
$743$	10.6813	+	3.47057i	0.0143759	+	0.00467102i	−0.301820	+	0.953365i	$0.597594\pi$
$744$	228.118	+	313.978i	0.306610	+	0.422013i
$745$		0			0
$746$	45.5732	+	140.260i	0.0610901	+	0.188016i
$747$			1560.65i			2.08923i
$748$	53.6373	+	110.560i	0.0717076	+	0.147808i
$749$	162.078			0.216393
$750$		0			0
$751$	−700.813	−	509.171i	−0.933174	−	0.677990i	0.0135942	−	0.999908i	$-0.495673\pi$
$751$	−700.813	−	509.171i	−0.933174	−	0.677990i	−0.946768	+	0.321917i	$0.895673\pi$
$752$	−47.3822	+	34.4252i	−0.0630083	+	0.0457782i
$753$	−540.902	+	1664.72i	−0.718329	+	2.21079i
$754$	−67.1335	−	21.8130i	−0.0890365	−	0.0289297i
$755$		0			0
$756$	1037.61	−	1428.15i	1.37250	−	1.88909i
$757$	−38.2121	−	117.605i	−0.0504783	−	0.155356i	0.922640	−	0.385663i	$-0.126027\pi$
$757$	−38.2121	−	117.605i	−0.0504783	−	0.155356i	−0.973118	+	0.230306i	$0.926027\pi$
$758$			24.9934i			0.0329728i
$759$	324.299	−	606.845i	0.427271	−	0.799532i
$760$		0			0
$761$	627.999	−	204.049i	0.825228	−	0.268133i	0.134194	−	0.990955i	$-0.457155\pi$
$761$	627.999	−	204.049i	0.825228	−	0.268133i	0.691034	+	0.722822i	$0.257155\pi$
$762$	137.321	+	99.7698i	0.180212	+	0.130932i
$763$	1282.69	−	931.931i	1.68112	−	1.22140i
$764$	−90.6160	+	278.887i	−0.118607	+	0.365036i
$765$		0			0
$766$	130.611	+	179.770i	0.170510	+	0.234687i
$767$	−146.167	+	201.181i	−0.190569	+	0.262296i
$768$	−316.820	−	975.071i	−0.412526	−	1.26962i
$769$		−	753.219i		−	0.979479i	−0.871869	−	0.489739i	$-0.837092\pi$
$769$		−	753.219i		−	0.979479i	0.871869	−	0.489739i	$-0.162908\pi$
$770$		0			0
$771$	−1300.63			−1.68695
$772$	1409.90	−	458.103i	1.82629	−	0.593398i
$773$	−134.737	−	97.8922i	−0.174304	−	0.126639i	0.497213	−	0.867629i	$-0.334357\pi$
$773$	−134.737	−	97.8922i	−0.174304	−	0.126639i	−0.671517	+	0.740989i	$0.734357\pi$
$774$	125.019	−	90.8315i	0.161523	−	0.117353i
$775$		0			0
$776$	153.185	+	49.7729i	0.197404	+	0.0641404i
$777$	609.560	+	838.988i	0.784505	+	1.07978i
$778$	42.8149	−	58.9297i	0.0550320	−	0.0757451i
$779$	264.565	+	814.247i	0.339621	+	1.04525i
$780$		0			0
$781$	−65.0365	−	11.6083i	−0.0832734	−	0.0148634i
$782$	−10.5596			−0.0135034
$783$	2028.96	−	659.249i	2.59126	−	0.841953i
$784$	641.335	+	465.957i	0.818030	+	0.594333i
$785$		0			0
$786$	−23.6717	+	72.8539i	−0.0301166	+	0.0926894i
$787$	−329.445	−	107.043i	−0.418609	−	0.136014i	0.0921365	−	0.995746i	$-0.470630\pi$
$787$	−329.445	−	107.043i	−0.418609	−	0.136014i	−0.510745	+	0.859732i	$0.670630\pi$
$788$	−210.108	−	289.190i	−0.266635	−	0.366992i
$789$	−1289.14	+	1774.34i	−1.63389	+	2.24885i
$790$		0			0
$791$			323.556i			0.409047i
$792$	82.2517	−	460.822i	0.103853	−	0.581846i
$793$	−161.167			−0.203236
$794$	−102.840	+	33.4149i	−0.129522	+	0.0420843i
$795$		0			0
$796$	−75.9289	+	55.1656i	−0.0953880	+	0.0693035i
$797$	−13.9224	+	42.8487i	−0.0174685	+	0.0537625i	−0.959411	−	0.282012i	$-0.908998\pi$
$797$	−13.9224	+	42.8487i	−0.0174685	+	0.0537625i	0.941942	+	0.335775i	$0.108998\pi$
$798$	323.417	+	105.084i	0.405284	+	0.131685i
$799$	−6.60890	−	9.09636i	−0.00827146	−	0.0113847i
$800$		0			0
$801$	−646.683	−	1990.28i	−0.807344	−	2.48475i
$802$			78.0690i			0.0973429i
$803$	−1037.89	+	998.082i	−1.29252	+	1.24294i
$804$	−1818.08			−2.26130
$805$		0			0
$806$	37.3063	+	27.1046i	0.0462857	+	0.0336285i
$807$	2085.62	−	1515.29i	2.58441	−	1.87769i
$808$	9.63856	−	29.6644i	0.0119289	−	0.0367134i
$809$	−1187.16	−	385.731i	−1.46744	−	0.476800i	−0.537106	−	0.843515i	$-0.680482\pi$
$809$	−1187.16	−	385.731i	−1.46744	−	0.476800i	−0.930333	+	0.366715i	$0.880482\pi$
$810$		0			0
$811$	−62.7425	+	86.3577i	−0.0773644	+	0.106483i	−0.845945	−	0.533270i	$-0.820963\pi$
$811$	−62.7425	+	86.3577i	−0.0773644	+	0.106483i	0.768581	+	0.639753i	$0.220963\pi$
$812$	582.776	+	1793.60i	0.717704	+	2.20887i
$813$		−	1212.41i		−	1.49128i
$814$	58.7518	+	31.3971i	0.0721767	+	0.0385713i
$815$		0			0
$816$	209.098	−	67.9401i	0.256248	−	0.0832599i
$817$	−496.440	−	360.685i	−0.607638	−	0.441475i
$818$	−67.8077	+	49.2652i	−0.0828945	+	0.0602264i
$819$	267.568	−	823.491i	0.326701	−	1.00548i
$820$		0			0
$821$	−361.534	−	497.608i	−0.440358	−	0.606100i	0.529934	−	0.848039i	$-0.322217\pi$
$821$	−361.534	−	497.608i	−0.440358	−	0.606100i	−0.970292	+	0.241939i	$0.922217\pi$
$822$	−69.4972	+	95.6547i	−0.0845465	+	0.116368i
$823$	118.117	+	363.528i	0.143521	+	0.441711i	0.996818	−	0.0797139i	$-0.0254007\pi$
$823$	118.117	+	363.528i	0.143521	+	0.441711i	−0.853297	+	0.521425i	$0.825401\pi$
$824$		−	272.386i		−	0.330566i
$825$		0			0
$826$	−158.006			−0.191291
$827$	−909.438	+	295.494i	−1.09968	+	0.357309i	−0.801981	−	0.597350i	$-0.796220\pi$
$827$	−909.438	+	295.494i	−1.09968	+	0.357309i	−0.297703	+	0.954659i	$0.596220\pi$
$828$	−676.131	−	491.238i	−0.816583	−	0.593282i
$829$	591.020	−	429.401i	0.712931	−	0.517975i	−0.171187	−	0.985239i	$-0.554760\pi$
$829$	591.020	−	429.401i	0.712931	−	0.517975i	0.884118	+	0.467264i	$0.154760\pi$
$830$		0			0
$831$	−667.764	−	216.970i	−0.803566	−	0.261095i
$832$	−157.527	−	216.817i	−0.189335	−	0.260598i
$833$	−89.4537	+	123.122i	−0.107387	+	0.147806i
$834$	23.4769	+	72.2545i	0.0281498	+	0.0866361i
$835$		0			0
$836$	−909.809	+	125.921i	−1.08829	+	0.150623i
$837$	−1393.66			−1.66507
$838$	−12.7780	+	4.15181i	−0.0152482	+	0.00495443i
$839$	739.591	+	537.345i	0.881515	+	0.640458i	0.933652	−	0.358182i	$-0.116603\pi$
$839$	739.591	+	537.345i	0.881515	+	0.640458i	−0.0521367	+	0.998640i	$0.516603\pi$
$840$		0			0
$841$	−444.409	+	1367.75i	−0.528429	+	1.62634i
$842$	−23.6010	−	7.66845i	−0.0280297	−	0.00910742i
$843$	−918.847	−	1264.68i	−1.08997	−	1.50022i
$844$	844.394	−	1162.21i	1.00047	−	1.37702i
$845$		0			0
$846$			21.1638i			0.0250163i
$847$	−960.883	−	757.233i	−1.13445	−	0.894018i
$848$	938.193			1.10636
$849$	52.2888	−	16.9896i	0.0615887	−	0.0200114i
$850$		0			0
$851$	194.726	−	141.476i	0.228820	−	0.166247i
$852$	−37.4371	+	115.220i	−0.0439403	+	0.135234i
$853$	1041.09	+	338.270i	1.22050	+	0.396565i	0.847265	−	0.531171i	$-0.178248\pi$
$853$	1041.09	+	338.270i	1.22050	+	0.396565i	0.373237	+	0.927736i	$0.378248\pi$
$854$	−60.1920	−	82.8472i	−0.0704824	−	0.0970107i
$855$		0			0
$856$	−11.9398	−	36.7470i	−0.0139484	−	0.0429287i
$857$			1161.22i			1.35499i	0.735528	+	0.677494i	$0.236934\pi$
$857$			1161.22i			1.35499i	−0.735528	+	0.677494i	$0.763066\pi$
$858$	−11.5123	−	83.1789i	−0.0134176	−	0.0969451i
$859$	−465.631			−0.542061			−0.271031	−	0.962571i	$-0.587364\pi$
$859$	−465.631			−0.542061			−0.271031	+	0.962571i	$0.587364\pi$
$860$		0			0
$861$	1691.83	+	1229.19i	1.96496	+	1.42763i
$862$	−179.061	+	130.095i	−0.207727	+	0.150922i
$863$	−240.025	+	738.720i	−0.278128	+	0.855990i	0.710247	+	0.703953i	$0.248583\pi$
$863$	−240.025	+	738.720i	−0.278128	+	0.855990i	−0.988375	+	0.152037i	$0.951417\pi$
$864$	−602.700	−	195.829i	−0.697570	−	0.226654i
$865$		0			0
$866$	−62.1952	+	85.6043i	−0.0718189	+	0.0988502i
$867$	−448.034	−	1378.91i	−0.516763	−	1.59043i
$868$		−	1232.00i		−	1.41935i
$869$	−431.442	−	889.313i	−0.496480	−	1.02337i
$870$		0			0
$871$	−415.783	+	135.096i	−0.477363	+	0.155105i
$872$	−305.782	−	222.164i	−0.350668	−	0.254775i
$873$	−954.498	+	693.484i	−1.09335	+	0.794368i
$874$	24.3897	−	75.0637i	0.0279058	−	0.0858852i
$875$		0			0
$876$	1552.07	+	2136.24i	1.77177	+	2.43863i
$877$	−814.144	+	1120.57i	−0.928329	+	1.27773i	0.0321793	+	0.999482i	$0.489755\pi$
$877$	−814.144	+	1120.57i	−0.928329	+	1.27773i	−0.960508	+	0.278253i	$0.910245\pi$
$878$	−6.80023	−	20.9290i	−0.00774514	−	0.0238371i
$879$			1703.97i			1.93853i
$880$		0			0
$881$	−1570.42			−1.78255			−0.891273	−	0.453467i	$-0.850187\pi$
$881$	−1570.42			−1.78255			−0.891273	+	0.453467i	$0.850187\pi$
$882$	272.439	−	88.5206i	0.308887	−	0.100364i
$883$	885.963	+	643.690i	1.00336	+	0.728981i	0.962805	−	0.270197i	$-0.0870888\pi$
$883$	885.963	+	643.690i	1.00336	+	0.728981i	0.0405507	+	0.999177i	$0.487089\pi$
$884$	43.8383	−	31.8504i	0.0495908	−	0.0360299i
$885$		0			0
$886$	108.946	+	35.3987i	0.122964	+	0.0399534i
$887$	520.530	+	716.448i	0.586843	+	0.807720i	0.994425	−	0.105449i	$-0.0336279\pi$
$887$	520.530	+	716.448i	0.586843	+	0.807720i	−0.407582	+	0.913169i	$0.633628\pi$
$888$	145.314	−	200.007i	0.163642	−	0.225233i
$889$	−336.974	−	1037.10i	−0.379048	−	1.16659i
$890$		0			0
$891$	547.567	+	569.407i	0.614554	+	0.639065i
$892$	692.520			0.776368
$893$	79.9265	−	25.9697i	0.0895033	−	0.0290814i
$894$	−153.421	−	111.467i	−0.171611	−	0.124683i
$895$		0			0
$896$	229.852	−	707.411i	0.256531	−	0.789521i
$897$	−288.558	−	93.7583i	−0.321693	−	0.104524i
$898$	−20.1060	−	27.6735i	−0.0223897	−	0.0308168i
$899$	875.145	−	1204.53i	0.973465	−	1.33986i
$900$		0			0
$901$			180.113i			0.199903i
$902$	132.240	+	23.6034i	0.146607	+	0.0261678i
$903$	−1498.85			−1.65986
$904$	73.3577	−	23.8354i	0.0811479	−	0.0263666i
$905$		0			0
$906$	98.3650	−	71.4664i	0.108571	−	0.0788812i
$907$	96.6622	−	297.496i	0.106573	−	0.327999i	−0.883523	−	0.468388i	$-0.844835\pi$
$907$	96.6622	−	297.496i	0.106573	−	0.327999i	0.990097	+	0.140388i	$0.0448351\pi$
$908$	68.7378	+	22.3343i	0.0757025	+	0.0245972i
$909$	134.294	+	184.839i	0.147738	+	0.203344i
$910$		0			0
$911$	−140.671	−	432.942i	−0.154414	−	0.475238i	0.843687	−	0.536836i	$-0.180380\pi$
$911$	−140.671	−	432.942i	−0.154414	−	0.475238i	−0.998101	+	0.0615976i	$0.980380\pi$
$912$			1643.30i			1.80187i
$913$	170.853	−	957.216i	0.187133	−	1.04843i
$914$	−56.9129			−0.0622680
$915$		0			0
$916$	422.743	+	307.141i	0.461510	+	0.335306i
$917$	398.141	−	289.267i	0.434178	−	0.315449i
$918$	12.0357	−	37.0421i	0.0131108	−	0.0403509i
$919$	981.783	+	319.001i	1.06832	+	0.347117i	0.789832	−	0.613324i	$-0.210168\pi$
$919$	981.783	+	319.001i	1.06832	+	0.347117i	0.278485	+	0.960441i	$0.410168\pi$
$920$		0			0
$921$	338.284	−	465.607i	0.367300	−	0.505545i
$922$	−52.7431	−	162.327i	−0.0572051	−	0.176059i
$923$			29.1318i			0.0315621i
$924$	−1617.08	+	1555.06i	−1.75008	+	1.68296i
$925$		0			0
$926$	−188.038	+	61.0973i	−0.203065	+	0.0659798i
$927$	1614.17	+	1172.76i	1.74129	+	1.26512i
$928$	547.717	−	397.939i	0.590212	−	0.428814i
$929$	−431.640	+	1328.45i	−0.464629	+	1.42998i	0.394820	+	0.918758i	$0.370807\pi$
$929$	−431.640	+	1328.45i	−0.464629	+	1.42998i	−0.859449	+	0.511222i	$0.829193\pi$
$930$		0			0
$931$	−668.609	−	920.262i	−0.718162	−	0.988466i
$932$	−101.123	+	139.184i	−0.108501	+	0.149339i
$933$	−646.332	−	1989.21i	−0.692746	−	2.13205i
$934$			274.470i			0.293865i
$935$		0			0
$936$	−206.416			−0.220530
$937$	−1141.42	+	370.868i	−1.21816	+	0.395804i	−0.846411	−	0.532530i	$-0.821241\pi$
$937$	−1141.42	+	370.868i	−1.21816	+	0.395804i	−0.371748	+	0.928334i	$0.621241\pi$
$938$	−224.731	−	163.277i	−0.239586	−	0.174069i
$939$	−709.058	+	515.161i	−0.755120	+	0.548627i
$940$		0			0
$941$	29.9217	+	9.72215i	0.0317978	+	0.0103317i	0.324873	−	0.945758i	$-0.394679\pi$
$941$	29.9217	+	9.72215i	0.0317978	+	0.0103317i	−0.293075	+	0.956089i	$0.594679\pi$
$942$	−50.1411	−	69.0133i	−0.0532283	−	0.0732625i
$943$	285.289	−	392.667i	0.302533	−	0.416401i
$944$	−235.949	−	726.177i	−0.249946	−	0.769255i
$945$		0			0
$946$	−86.6233	+	42.0245i	−0.0915680	+	0.0444233i
$947$	540.682			0.570942			0.285471	−	0.958387i	$-0.407850\pi$
$947$	540.682			0.570942			0.285471	+	0.958387i	$0.407850\pi$
$948$	−1723.89	+	560.127i	−1.81845	+	0.590851i
$949$	513.685	+	373.214i	0.541291	+	0.393271i
$950$		0			0
$951$	−616.304	+	1896.79i	−0.648059	+	1.99452i
$952$	66.2692	+	21.5322i	0.0696105	+	0.0226178i
$953$	335.865	+	462.279i	0.352429	+	0.485077i	0.948020	−	0.318211i	$-0.103082\pi$
$953$	335.865	+	462.279i	0.352429	+	0.485077i	−0.595591	+	0.803288i	$0.703082\pi$
$954$	199.272	−	274.274i	0.208880	−	0.287499i
$955$		0			0
$956$			646.388i			0.676138i
$957$	−2685.66	+	371.705i	−2.80633	+	0.388407i
$958$	141.601			0.147809
$959$	722.418	−	234.728i	0.753303	−	0.244763i
$960$		0			0
$961$	−9.41808	+	6.84263i	−0.00980029	+	0.00712033i
$962$	9.07724	−	27.9369i	0.00943580	−	0.0290404i
$963$	269.171	+	87.4590i	0.279513	+	0.0908193i
$964$	−157.077	−	216.198i	−0.162943	−	0.224272i
$965$		0			0
$966$	−59.5738	−	183.349i	−0.0616705	−	0.189802i
$967$			1228.33i			1.27025i	0.772410	+	0.635125i	$0.219051\pi$
$967$			1228.33i			1.27025i	−0.772410	+	0.635125i	$0.780949\pi$
$968$	−100.897	+	273.638i	−0.104233	+	0.282684i
$969$	−315.479			−0.325571
$970$		0			0
$971$	−1282.98	−	932.137i	−1.32129	−	0.959976i	−0.999915	−	0.0130253i	$-0.995854\pi$
$971$	−1282.98	−	932.137i	−1.32129	−	0.959976i	−0.321379	−	0.946951i	$-0.604146\pi$
$972$	−99.2772	+	72.1291i	−0.102137	+	0.0742069i
$973$	150.825	−	464.193i	0.155011	−	0.477074i
$974$	−9.55237	−	3.10375i	−0.00980736	−	0.00318660i
$975$		0			0
$976$	290.871	−	400.350i	0.298024	−	0.410194i
$977$	−290.915	−	895.345i	−0.297764	−	0.916422i	−0.982279	−	0.187424i	$-0.939986\pi$
$977$	−290.915	−	895.345i	−0.297764	−	0.916422i	0.684515	−	0.728998i	$-0.260014\pi$
$978$		−	319.713i		−	0.326905i
$979$	178.752	+	1291.52i	0.182586	+	1.31923i
$980$		0			0
$981$	2633.10	−	855.547i	2.68410	−	0.872117i
$982$	196.775	+	142.966i	0.200382	+	0.145586i
$983$	−564.528	+	410.154i	−0.574291	+	0.417247i	−0.836662	−	0.547720i	$-0.815496\pi$
$983$	−564.528	+	410.154i	−0.574291	+	0.417247i	0.262370	+	0.964967i	$0.415496\pi$
$984$	154.053	−	474.127i	0.156558	−	0.481837i
$985$		0			0
$986$	24.4574	+	33.6628i	0.0248047	+	0.0341408i
$987$	120.657	−	166.070i	0.122246	−	0.168257i
$988$	125.156	+	385.191i	0.126676	+	0.389870i
$989$			347.877i			0.351746i
$990$		0			0
$991$	1202.24			1.21315			0.606577	−	0.795025i	$-0.292542\pi$
$991$	1202.24			1.21315			0.606577	+	0.795025i	$0.292542\pi$
$992$	−420.626	+	136.670i	−0.424018	+	0.137772i
$993$	496.903	+	361.021i	0.500406	+	0.363566i
$994$	−14.9751	+	10.8800i	−0.0150655	+	0.0109457i
$995$		0			0
$996$	−1695.82	−	551.004i	−1.70263	−	0.553217i
$997$	476.323	+	655.602i	0.477756	+	0.657575i	0.978072	−	0.208268i	$-0.0667827\pi$
$997$	476.323	+	655.602i	0.477756	+	0.657575i	−0.500316	+	0.865843i	$0.666783\pi$
$998$	106.265	−	146.262i	0.106478	−	0.146555i
$999$	274.339	+	844.329i	0.274614	+	0.845174i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	275.3.x.f.226.2		12
5.2	odd	4		275.3.q.f.149.3		24
5.3	odd	4		275.3.q.f.149.4		24
5.4	even	2		55.3.i.d.6.2	✓	12
11.2	odd	10	inner	275.3.x.f.101.2		12
55.2	even	20		275.3.q.f.24.4		24
55.13	even	20		275.3.q.f.24.3		24
55.14	even	10		605.3.c.d.241.5		12
55.19	odd	10		605.3.c.d.241.8		12
55.24	odd	10		55.3.i.d.46.2	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.3.i.d.6.2	✓	12	5.4	even	2
55.3.i.d.46.2	yes	12	55.24	odd	10
275.3.q.f.24.3		24	55.13	even	20
275.3.q.f.24.4		24	55.2	even	20
275.3.q.f.149.3		24	5.2	odd	4
275.3.q.f.149.4		24	5.3	odd	4
275.3.x.f.101.2		12	11.2	odd	10	inner
275.3.x.f.226.2		12	1.1	even	1	trivial
605.3.c.d.241.5		12	55.14	even	10
605.3.c.d.241.8		12	55.19	odd	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.289909 + 0.0941972i) q^{2} +(4.17687 + 3.03467i) q^{3} +(-3.16089 + 2.29652i) q^{4} +(-1.49677 - 0.486330i) q^{6} +(5.94293 + 8.17974i) q^{7} +(1.41674 - 1.94998i) q^{8} +(5.45583 + 16.7913i) q^{9} +(-1.50807 - 10.8961i) q^{11} -20.1718 q^{12} +(-4.61316 + 1.49891i) q^{13} +(-2.49342 - 1.81157i) q^{14} +(4.60237 - 14.1646i) q^{16} +(2.71930 + 0.883556i) q^{17} +(-3.16339 - 4.35403i) q^{18} +(-12.5616 + 17.2895i) q^{19} +52.2005i q^{21} +(1.46359 + 3.01683i) q^{22} +12.1155 q^{23} +(11.8351 - 3.84545i) q^{24} +(1.19620 - 0.869094i) q^{26} +(-13.8091 + 42.4999i) q^{27} +(-37.5699 - 12.2072i) q^{28} +(-28.0610 - 38.6227i) q^{29} +(9.63737 + 29.6608i) q^{31} +14.1812i q^{32} +(26.7672 - 50.0882i) q^{33} -0.871580 q^{34} +(-55.8070 - 40.5461i) q^{36} +(16.0724 - 11.6773i) q^{37} +(2.01309 - 6.19566i) q^{38} +(-23.8172 - 7.73869i) q^{39} +(23.5474 - 32.4102i) q^{41} +(-4.91714 - 15.1334i) q^{42} +28.7133i q^{43} +(29.7901 + 30.9782i) q^{44} +(-3.51240 + 1.14125i) q^{46} +(-3.18139 - 2.31141i) q^{47} +(62.2085 - 45.1971i) q^{48} +(-16.4479 + 50.6214i) q^{49} +(8.67687 + 11.9427i) q^{51} +(11.1394 - 15.3321i) q^{52} +(19.4659 + 59.9100i) q^{53} -13.6219i q^{54} +24.3699 q^{56} +(-104.936 + 34.0958i) q^{57} +(11.7733 + 8.55381i) q^{58} +(41.4758 - 30.1339i) q^{59} +(31.6001 + 10.2675i) q^{61} +(-5.58793 - 7.69112i) q^{62} +(-104.925 + 144.417i) q^{63} +(17.0737 + 52.5473i) q^{64} +(-3.04189 + 17.0424i) q^{66} +90.1298 q^{67} +(-10.6245 + 3.45212i) q^{68} +(50.6049 + 36.7666i) q^{69} +(1.85591 - 5.71191i) q^{71} +(40.4722 + 13.1502i) q^{72} +(-76.9424 - 105.902i) q^{73} +(-3.55957 + 4.89933i) q^{74} -83.4983i q^{76} +(80.1652 - 77.0905i) q^{77} +7.63380 q^{78} +(85.4604 - 27.7678i) q^{79} +(-58.1000 + 42.2121i) q^{81} +(-3.77365 + 11.6141i) q^{82} +(84.0686 + 27.3155i) q^{83} +(-119.880 - 165.000i) q^{84} +(-2.70472 - 8.32426i) q^{86} -246.478i q^{87} +(-23.3837 - 12.4963i) q^{88} -118.531 q^{89} +(-39.6764 - 28.8266i) q^{91} +(-38.2959 + 27.8236i) q^{92} +(-49.7567 + 153.135i) q^{93} +(1.14004 + 0.370422i) q^{94} +(-43.0353 + 59.2330i) q^{96} +(20.6501 + 63.5544i) q^{97} -16.2250i q^{98} +(174.733 - 84.7699i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 5 q^{2} + 13 q^{3} + 13 q^{4} + 20 q^{6} + 5 q^{7} + 35 q^{8} + 4 q^{9} + 12 q^{11} + 2 q^{12} - 70 q^{13} - 60 q^{14} - 43 q^{16} + 15 q^{17} + 30 q^{18} - 80 q^{19} + 10 q^{22} - 42 q^{23} + 210 q^{24}+ \cdots + 669 q^{99}+O(q^{100}) \) 12 * q - 5 * q^2 + 13 * q^3 + 13 * q^4 + 20 * q^6 + 5 * q^7 + 35 * q^8 + 4 * q^9 + 12 * q^11 + 2 * q^12 - 70 * q^13 - 60 * q^14 - 43 * q^16 + 15 * q^17 + 30 * q^18 - 80 * q^19 + 10 * q^22 - 42 * q^23 + 210 * q^24 - 120 * q^26 + 109 * q^27 - 140 * q^28 + 5 * q^29 - 46 * q^31 - 42 * q^33 + 10 * q^34 - 39 * q^36 + 42 * q^37 + 130 * q^38 - 285 * q^39 + 230 * q^41 - 135 * q^42 + 488 * q^44 + 205 * q^46 - 58 * q^47 + 323 * q^48 - 212 * q^49 + 360 * q^51 - 410 * q^52 + 43 * q^53 - 410 * q^56 - 270 * q^57 + 450 * q^58 - 74 * q^59 - 290 * q^61 + 350 * q^62 - 295 * q^63 - 7 * q^64 + 185 * q^66 + 212 * q^67 - 55 * q^68 - 73 * q^69 - 276 * q^71 + 555 * q^72 - 645 * q^73 - 100 * q^74 + 140 * q^77 - 360 * q^78 + 235 * q^79 - 30 * q^81 - 215 * q^82 - 60 * q^83 - 580 * q^84 - 480 * q^86 + 165 * q^88 - 114 * q^89 + 160 * q^91 - 33 * q^92 - 129 * q^93 + 375 * q^94 + 265 * q^96 - 63 * q^97 + 669 * q^99

Introduction

L-functions

Modular forms

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