LMFDB - Embedded newform 275.3.q.f.24.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [275,3,Mod(24,275)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

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

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(275, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([5, 1])) N = Newforms(chi, 3, names="a")

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

Newform invariants

comment:select newform

sage:traces = [24,0,0,-26,0,40] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)

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

Self dual:	no
Analytic conductor:	$7.49320726991$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{10})$
Twist minimal:	no (minimal twist has level 55)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			24.4
Character	$\chi$	$=$	275.24
Dual form			275.3.q.f.149.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.0941972 - 0.289909i) q^{2} +(-3.03467 - 4.17687i) q^{3} +(3.16089 + 2.29652i) q^{4} +(-1.49677 + 0.486330i) q^{6} +(8.17974 + 5.94293i) q^{7} +(1.94998 - 1.41674i) q^{8} +(-5.45583 + 16.7913i) q^{9} +(-1.50807 + 10.8961i) q^{11} -20.1718i q^{12} +(-1.49891 + 4.61316i) q^{13} +(2.49342 - 1.81157i) q^{14} +(4.60237 + 14.1646i) q^{16} +(0.883556 + 2.71930i) q^{17} +(4.35403 + 3.16339i) q^{18} +(12.5616 + 17.2895i) q^{19} -52.2005i q^{21} +(3.01683 + 1.46359i) q^{22} -12.1155i q^{23} +(-11.8351 - 3.84545i) q^{24} +(1.19620 + 0.869094i) q^{26} +(42.4999 - 13.8091i) q^{27} +(12.2072 + 37.5699i) q^{28} +(28.0610 - 38.6227i) q^{29} +(9.63737 - 29.6608i) q^{31} +14.1812 q^{32} +(50.0882 - 26.7672i) q^{33} +0.871580 q^{34} +(-55.8070 + 40.5461i) q^{36} +(-11.6773 + 16.0724i) q^{37} +(6.19566 - 2.01309i) q^{38} +(23.8172 - 7.73869i) q^{39} +(23.5474 + 32.4102i) q^{41} +(-15.1334 - 4.91714i) q^{42} -28.7133 q^{43} +(-29.7901 + 30.9782i) q^{44} +(-3.51240 - 1.14125i) q^{46} +(-2.31141 - 3.18139i) q^{47} +(45.1971 - 62.2085i) q^{48} +(16.4479 + 50.6214i) q^{49} +(8.67687 - 11.9427i) q^{51} +(-15.3321 + 11.1394i) q^{52} +(-59.9100 - 19.4659i) q^{53} -13.6219i q^{54} +24.3699 q^{56} +(34.0958 - 104.936i) q^{57} +(-8.55381 - 11.7733i) q^{58} +(-41.4758 - 30.1339i) q^{59} +(31.6001 - 10.2675i) q^{61} +(-7.69112 - 5.58793i) q^{62} +(-144.417 + 104.925i) q^{63} +(-17.0737 + 52.5473i) q^{64} +(-3.04189 - 17.0424i) q^{66} +90.1298i q^{67} +(-3.45212 + 10.6245i) q^{68} +(-50.6049 + 36.7666i) q^{69} +(1.85591 + 5.71191i) q^{71} +(13.1502 + 40.4722i) q^{72} +(105.902 + 76.9424i) q^{73} +(3.55957 + 4.89933i) q^{74} +83.4983i q^{76} +(-77.0905 + 80.1652i) q^{77} -7.63380i q^{78} +(-85.4604 - 27.7678i) q^{79} +(-58.1000 - 42.2121i) q^{81} +(11.6141 - 3.77365i) q^{82} +(-27.3155 - 84.0686i) q^{83} +(119.880 - 165.000i) q^{84} +(-2.70472 + 8.32426i) q^{86} -246.478 q^{87} +(12.4963 + 23.3837i) q^{88} +118.531 q^{89} +(-39.6764 + 28.8266i) q^{91} +(27.8236 - 38.2959i) q^{92} +(-153.135 + 49.7567i) q^{93} +(-1.14004 + 0.370422i) q^{94} +(-43.0353 - 59.2330i) q^{96} +(63.5544 + 20.6501i) q^{97} +16.2250 q^{98} +(-174.733 - 84.7699i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 26 q^{4} + 40 q^{6} - 8 q^{9} + 24 q^{11} + 120 q^{14} - 86 q^{16} + 160 q^{19} - 420 q^{24} - 240 q^{26} - 10 q^{29} - 92 q^{31} - 20 q^{34} - 78 q^{36} + 570 q^{39} + 460 q^{41} - 976 q^{44} + 410 q^{46}+ \cdots - 1338 q^{99}+O(q^{100}) $ 24 * q - 26 * q^4 + 40 * q^6 - 8 * q^9 + 24 * q^11 + 120 * q^14 - 86 * q^16 + 160 * q^19 - 420 * q^24 - 240 * q^26 - 10 * q^29 - 92 * q^31 - 20 * q^34 - 78 * q^36 + 570 * q^39 + 460 * q^41 - 976 * q^44 + 410 * q^46 + 424 * q^49 + 720 * q^51 - 820 * q^56 + 148 * q^59 - 580 * q^61 + 14 * q^64 + 370 * q^66 + 146 * q^69 - 552 * q^71 + 200 * q^74 - 470 * q^79 - 60 * q^81 + 1160 * q^84 - 960 * q^86 + 228 * q^89 + 320 * q^91 - 750 * q^94 + 530 * q^96 - 1338 * 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 $

$2$	0.0941972	−	0.289909i	0.0470986	−	0.144955i	−0.924742	−	0.380596i	$-0.875719\pi$
$2$	0.0941972	−	0.289909i	0.0470986	−	0.144955i	0.971840	+	0.235641i	$0.0757190\pi$
$3$	−3.03467	−	4.17687i	−1.01156	−	1.39229i	−0.917957	−	0.396679i	$-0.870163\pi$
$3$	−3.03467	−	4.17687i	−1.01156	−	1.39229i	−0.0935994	−	0.995610i	$-0.529837\pi$
$4$	3.16089	+	2.29652i	0.790223	+	0.574131i
$5$		0			0
$5$		0			0
$6$	−1.49677	+	0.486330i	−0.249462	+	0.0810550i
$7$	8.17974	+	5.94293i	1.16853	+	0.848990i	0.990833	−	0.135095i	$-0.0431339\pi$
$7$	8.17974	+	5.94293i	1.16853	+	0.848990i	0.177701	+	0.984084i	$0.443134\pi$
$8$	1.94998	−	1.41674i	0.243747	−	0.177093i
$9$	−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
$12$		−	20.1718i		−	1.68099i
$13$	−1.49891	+	4.61316i	−0.115301	+	0.354859i	−0.992010	−	0.126162i	$-0.959734\pi$
$13$	−1.49891	+	4.61316i	−0.115301	+	0.354859i	0.876709	+	0.481021i	$0.159734\pi$
$14$	2.49342	−	1.81157i	0.178101	−	0.129398i
$15$		0			0
$16$	4.60237	+	14.1646i	0.287648	+	0.885290i
$17$	0.883556	+	2.71930i	0.0519739	+	0.159959i	0.973675	−	0.227943i	$-0.0731999\pi$
$17$	0.883556	+	2.71930i	0.0519739	+	0.159959i	−0.921701	+	0.387902i	$0.873200\pi$
$18$	4.35403	+	3.16339i	0.241891	+	0.175744i
$19$	12.5616	+	17.2895i	0.661136	+	0.909975i	0.999518	−	0.0310333i	$-0.00987978\pi$
$19$	12.5616	+	17.2895i	0.661136	+	0.909975i	−0.338383	+	0.941009i	$0.609880\pi$
$20$		0			0
$21$		−	52.2005i		−	2.48574i
$22$	3.01683	+	1.46359i	0.137129	+	0.0665267i
$23$		−	12.1155i		−	0.526762i	−0.964692	−	0.263381i	$-0.915162\pi$
$23$		−	12.1155i		−	0.526762i	0.964692	−	0.263381i	$-0.0848376\pi$
$24$	−11.8351	−	3.84545i	−0.493128	−	0.160227i
$25$		0			0
$26$	1.19620	+	0.869094i	0.0460079	+	0.0334267i
$27$	42.4999	−	13.8091i	1.57407	−	0.511447i
$28$	12.2072	+	37.5699i	0.435972	+	1.34178i
$29$	28.0610	−	38.6227i	0.967622	−	1.33182i	0.0243833	−	0.999703i	$-0.492238\pi$
$29$	28.0610	−	38.6227i	0.967622	−	1.33182i	0.943239	−	0.332115i	$-0.107762\pi$
$30$		0			0
$31$	9.63737	−	29.6608i	0.310883	−	0.956800i	−0.666533	−	0.745476i	$-0.732222\pi$
$31$	9.63737	−	29.6608i	0.310883	−	0.956800i	0.977416	−	0.211324i	$-0.0677776\pi$
$32$	14.1812			0.443163
$33$	50.0882	−	26.7672i	1.51782	−	0.811127i
$34$	0.871580			0.0256347
$35$		0			0
$36$	−55.8070	+	40.5461i	−1.55019	+	1.12628i
$37$	−11.6773	+	16.0724i	−0.315602	+	0.434389i	−0.937118	−	0.349012i	$-0.886517\pi$
$37$	−11.6773	+	16.0724i	−0.315602	+	0.434389i	0.621516	+	0.783402i	$0.286517\pi$
$38$	6.19566	−	2.01309i	0.163044	−	0.0529761i
$39$	23.8172	−	7.73869i	0.610699	−	0.198428i
$40$		0			0
$41$	23.5474	+	32.4102i	0.574326	+	0.790493i	0.993059	−	0.117617i	$-0.0375255\pi$
$41$	23.5474	+	32.4102i	0.574326	+	0.790493i	−0.418733	+	0.908110i	$0.637526\pi$
$42$	−15.1334	−	4.91714i	−0.360319	−	0.117075i
$43$	−28.7133			−0.667752			−0.333876	−	0.942617i	$-0.608357\pi$
$43$	−28.7133			−0.667752			−0.333876	+	0.942617i	$0.608357\pi$
$44$	−29.7901	+	30.9782i	−0.677047	+	0.704050i
$45$		0			0
$46$	−3.51240	−	1.14125i	−0.0763566	−	0.0248098i
$47$	−2.31141	−	3.18139i	−0.0491790	−	0.0676891i	0.783719	−	0.621115i	$-0.213320\pi$
$47$	−2.31141	−	3.18139i	−0.0491790	−	0.0676891i	−0.832898	+	0.553426i	$0.813320\pi$
$48$	45.1971	−	62.2085i	0.941607	−	1.29601i
$49$	16.4479	+	50.6214i	0.335671	+	1.03309i
$50$		0			0
$51$	8.67687	−	11.9427i	0.170135	−	0.234170i
$52$	−15.3321	+	11.1394i	−0.294848	+	0.214220i
$53$	−59.9100	−	19.4659i	−1.13038	−	0.367282i	−0.316658	−	0.948540i	$-0.602561\pi$
$53$	−59.9100	−	19.4659i	−1.13038	−	0.367282i	−0.813719	+	0.581258i	$0.802561\pi$
$54$		−	13.6219i		−	0.252257i
$55$		0			0
$56$	24.3699			0.435177
$57$	34.0958	−	104.936i	0.598172	−	1.84098i
$58$	−8.55381	−	11.7733i	−0.147479	−	0.202988i
$59$	−41.4758	−	30.1339i	−0.702979	−	0.510744i	0.177922	−	0.984045i	$-0.443063\pi$
$59$	−41.4758	−	30.1339i	−0.702979	−	0.510744i	−0.880901	+	0.473300i	$0.843063\pi$
$60$		0			0
$61$	31.6001	−	10.2675i	0.518035	−	0.168320i	−0.0383184	−	0.999266i	$-0.512200\pi$
$61$	31.6001	−	10.2675i	0.518035	−	0.168320i	0.556353	+	0.830946i	$0.312200\pi$
$62$	−7.69112	−	5.58793i	−0.124050	−	0.0901279i
$63$	−144.417	+	104.925i	−2.29233	+	1.66548i
$64$	−17.0737	+	52.5473i	−0.266776	+	0.821052i
$65$		0			0
$66$	−3.04189	−	17.0424i	−0.0460892	−	0.258218i
$67$			90.1298i			1.34522i	0.739997	+	0.672611i	$0.234827\pi$
$67$			90.1298i			1.34522i	−0.739997	+	0.672611i	$0.765173\pi$
$68$	−3.45212	+	10.6245i	−0.0507665	+	0.156243i
$69$	−50.6049	+	36.7666i	−0.733405	+	0.532850i
$70$		0			0
$71$	1.85591	+	5.71191i	0.0261396	+	0.0804494i	0.963275	−	0.268516i	$-0.0865331\pi$
$71$	1.85591	+	5.71191i	0.0261396	+	0.0804494i	−0.937136	+	0.348965i	$0.886533\pi$
$72$	13.1502	+	40.4722i	0.182642	+	0.562114i
$73$	105.902	+	76.9424i	1.45071	+	1.05401i	0.985664	+	0.168722i	$0.0539639\pi$
$73$	105.902	+	76.9424i	1.45071	+	1.05401i	0.465051	+	0.885284i	$0.346036\pi$
$74$	3.55957	+	4.89933i	0.0481023	+	0.0662072i
$75$		0			0
$76$			83.4983i			1.09866i
$77$	−77.0905	+	80.1652i	−1.00118	+	1.04111i
$78$		−	7.63380i		−	0.0978693i
$79$	−85.4604	−	27.7678i	−1.08178	−	0.351491i	−0.286714	−	0.958016i	$-0.592563\pi$
$79$	−85.4604	−	27.7678i	−1.08178	−	0.351491i	−0.795064	+	0.606525i	$0.792563\pi$
$80$		0			0
$81$	−58.1000	−	42.2121i	−0.717284	−	0.521137i
$82$	11.6141	−	3.77365i	0.141636	−	0.0460202i
$83$	−27.3155	−	84.0686i	−0.329103	−	1.01287i	−0.969554	−	0.244876i	$-0.921253\pi$
$83$	−27.3155	−	84.0686i	−0.329103	−	1.01287i	0.640451	−	0.767999i	$-0.278747\pi$
$84$	119.880	−	165.000i	1.42714	−	1.96429i
$85$		0			0
$86$	−2.70472	+	8.32426i	−0.0314502	+	0.0967937i
$87$	−246.478			−2.83308
$88$	12.4963	+	23.3837i	0.142003	+	0.265724i
$89$	118.531			1.33180			0.665902	−	0.746039i	$-0.268047\pi$
$89$	118.531			1.33180			0.665902	+	0.746039i	$0.268047\pi$
$90$		0			0
$91$	−39.6764	+	28.8266i	−0.436004	+	0.316775i
$92$	27.8236	−	38.2959i	0.302430	−	0.416260i
$93$	−153.135	+	49.7567i	−1.64662	+	0.535018i
$94$	−1.14004	+	0.370422i	−0.0121281	+	0.00394066i
$95$		0			0
$96$	−43.0353	−	59.2330i	−0.448284	−	0.617010i
$97$	63.5544	+	20.6501i	0.655200	+	0.212887i	0.617705	−	0.786410i	$-0.288062\pi$
$97$	63.5544	+	20.6501i	0.655200	+	0.212887i	0.0374942	+	0.999297i	$0.488062\pi$
$98$	16.2250			0.165561
$99$	−174.733	−	84.7699i	−1.76498	−	0.856262i
$100$		0			0
$101$	12.3073	+	3.99890i	0.121855	+	0.0395931i	0.369310	−	0.929306i	$-0.379594\pi$
$101$	12.3073	+	3.99890i	0.121855	+	0.0395931i	−0.247455	+	0.968899i	$0.579594\pi$
$102$	−2.64496	−	3.64047i	−0.0259310	−	0.0356909i
$103$	66.4251	−	91.4263i	0.644904	−	0.887634i	−0.353961	−	0.935260i	$-0.615166\pi$
$103$	66.4251	−	91.4263i	0.644904	−	0.887634i	0.998865	+	0.0476260i	$0.0151656\pi$
$104$	3.61282	+	11.1191i	0.0347387	+	0.106915i
$105$		0			0
$106$	−11.2867	+	15.5348i	−0.106478	+	0.146555i
$107$	−12.9688	+	9.42241i	−0.121204	+	0.0880599i	−0.646736	−	0.762714i	$-0.723866\pi$
$107$	−12.9688	+	9.42241i	−0.121204	+	0.0880599i	0.525532	+	0.850774i	$0.323866\pi$
$108$	166.051	+	53.9531i	1.53751	+	0.499566i
$109$		−	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
$112$	−46.5333	+	143.215i	−0.415476	+	1.27870i
$113$	−18.8099	−	25.8896i	−0.166459	−	0.229112i	0.717636	−	0.696419i	$-0.245224\pi$
$113$	−18.8099	−	25.8896i	−0.166459	−	0.229112i	−0.884095	+	0.467307i	$0.845224\pi$
$114$	−27.2102	−	19.7694i	−0.238686	−	0.173416i
$115$		0			0
$116$	177.396	−	57.6394i	1.52928	−	0.496892i
$117$	−69.2833	−	50.3372i	−0.592165	−	0.430233i
$118$	−12.6430	+	9.18568i	−0.107144	+	0.0778447i
$119$	−8.93338	+	27.4941i	−0.0750704	+	0.231043i
$120$		0			0
$121$	−116.451	−	32.8642i	−0.962409	−	0.271605i
$122$		−	10.1283i		−	0.0830192i
$123$	63.9145	−	196.709i	0.519630	−	1.59926i
$124$	98.5794	−	71.6221i	0.794995	−	0.577598i
$125$		0			0
$126$	16.8151	+	51.7514i	0.133453	+	0.410726i
$127$	−33.3284	−	102.574i	−0.262428	−	0.807671i	−0.992275	−	0.124060i	$-0.960408\pi$
$127$	−33.3284	−	102.574i	−0.262428	−	0.807671i	0.729846	−	0.683611i	$-0.239592\pi$
$128$	59.5170	+	43.2416i	0.464977	+	0.337825i
$129$	87.1355	+	119.932i	0.675469	+	0.929703i
$130$		0			0
$131$			48.6741i			0.371558i	0.982592	+	0.185779i	$0.0594808\pi$
$131$			48.6741i			0.371558i	−0.982592	+	0.185779i	$0.940519\pi$
$132$	219.795	+	30.4205i	1.66511	+	0.230458i
$133$			216.076i			1.62463i
$134$	26.1295	+	8.48998i	0.194996	+	0.0633580i
$135$		0			0
$136$	5.57546	+	4.05081i	0.0409961	+	0.0297854i
$137$	−71.4507	+	23.2157i	−0.521538	+	0.169458i	−0.557943	−	0.829879i	$-0.688409\pi$
$137$	−71.4507	+	23.2157i	−0.521538	+	0.169458i	0.0364052	+	0.999337i	$0.488409\pi$
$138$	5.89214	+	18.1341i	0.0426967	+	0.131407i
$139$	28.3745	−	39.0542i	0.204133	−	0.280965i	−0.694660	−	0.719338i	$-0.744445\pi$
$139$	28.3745	−	39.0542i	0.204133	−	0.280965i	0.898793	+	0.438373i	$0.144445\pi$
$140$		0			0
$141$	−6.27385	+	19.3089i	−0.0444954	+	0.136943i
$142$	1.83076			0.0128926
$143$	−48.0052	−	23.2892i	−0.335700	−	0.162862i
$144$	−262.953			−1.82606
$145$		0			0
$146$	32.2820	−	23.4542i	0.221110	−	0.160646i
$147$	161.525	−	222.320i	1.09881	−	1.51238i
$148$	−73.8213	+	23.9860i	−0.498793	+	0.162068i
$149$	−114.600	+	37.2357i	−0.769126	+	0.249904i	−0.667191	−	0.744887i	$-0.732503\pi$
$149$	−114.600	+	37.2357i	−0.769126	+	0.249904i	−0.101935	+	0.994791i	$0.532503\pi$
$150$		0			0
$151$	−45.4102	−	62.5018i	−0.300730	−	0.413919i	0.631733	−	0.775186i	$-0.282344\pi$
$151$	−45.4102	−	62.5018i	−0.300730	−	0.413919i	−0.932462	+	0.361268i	$0.882344\pi$
$152$	48.9896	+	15.9177i	0.322300	+	0.104722i
$153$	−50.4812			−0.329943
$154$	15.9789	+	29.9006i	0.103759	+	0.194160i
$155$		0			0
$156$	93.0559	+	30.2357i	0.596512	+	0.193819i
$157$	31.8599	+	43.8515i	0.202930	+	0.279309i	0.898337	−	0.439307i	$-0.144776\pi$
$157$	31.8599	+	43.8515i	0.202930	+	0.279309i	−0.695407	+	0.718616i	$0.744776\pi$
$158$	−16.1003	+	22.1601i	−0.101900	+	0.140254i
$159$	100.501	+	309.309i	0.632079	+	1.94534i
$160$		0			0
$161$	72.0017	−	99.1018i	0.447215	−	0.615539i
$162$	−17.7105	+	12.8675i	−0.109324	+	0.0794287i
$163$	−193.205	−	62.7761i	−1.18531	−	0.385129i	−0.350971	−	0.936386i	$-0.614148\pi$
$163$	−193.205	−	62.7761i	−1.18531	−	0.385129i	−0.834336	+	0.551257i	$0.814148\pi$
$164$			156.522i			0.954404i
$165$		0			0
$166$	−26.9453			−0.162321
$167$	41.0093	−	126.214i	0.245565	−	0.755771i	−0.749978	−	0.661462i	$-0.769936\pi$
$167$	41.0093	−	126.214i	0.245565	−	0.755771i	0.995543	−	0.0943081i	$-0.0300639\pi$
$168$	−73.9546	−	101.790i	−0.440206	−	0.605891i
$169$	117.689	+	85.5063i	0.696387	+	0.505954i
$170$		0			0
$171$	−358.848	+	116.597i	−2.09853	+	0.681852i
$172$	−90.7598	−	65.9408i	−0.527673	−	0.383377i
$173$	90.4855	−	65.7416i	0.523037	−	0.380009i	−0.294709	−	0.955587i	$-0.595223\pi$
$173$	90.4855	−	65.7416i	0.523037	−	0.380009i	0.817747	+	0.575578i	$0.195223\pi$
$174$	−23.2175	+	71.4562i	−0.133434	+	0.410668i
$175$		0			0
$176$	−161.281	+	28.7868i	−0.916367	+	0.163562i
$177$			264.685i			1.49540i
$178$	11.1652	−	34.3631i	0.0627261	−	0.193051i
$179$	−38.7619	+	28.1621i	−0.216547	+	0.157330i	−0.690771	−	0.723074i	$-0.742729\pi$
$179$	−38.7619	+	28.1621i	−0.216547	+	0.157330i	0.474224	+	0.880404i	$0.342729\pi$
$180$		0			0
$181$	2.09873	+	6.45923i	0.0115952	+	0.0356864i	0.956687	−	0.291119i	$-0.0940277\pi$
$181$	2.09873	+	6.45923i	0.0115952	+	0.0356864i	−0.945092	+	0.326806i	$0.894028\pi$
$182$	4.61968	+	14.2179i	0.0253829	+	0.0781204i
$183$	−138.782	−	100.831i	−0.758371	−	0.550989i
$184$	−17.1646	−	23.6250i	−0.0932857	−	0.128397i
$185$		0			0
$186$			49.0823i			0.263883i
$187$	−30.9624	+	5.52645i	−0.165574	+	0.0295532i
$188$		−	15.3642i		−	0.0817246i
$189$	429.705	+	139.619i	2.27357	+	0.738728i
$190$		0			0
$191$	60.7195	+	44.1153i	0.317903	+	0.230970i	0.735280	−	0.677763i	$-0.237051\pi$
$191$	60.7195	+	44.1153i	0.317903	+	0.230970i	−0.417377	+	0.908733i	$0.637051\pi$
$192$	271.296	−	88.1494i	1.41300	−	0.459112i
$193$	117.250	+	360.857i	0.607511	+	1.86973i	0.478513	+	0.878081i	$0.341176\pi$
$193$	117.250	+	360.857i	0.607511	+	1.86973i	0.128998	+	0.991645i	$0.458824\pi$
$194$	11.9733	−	16.4798i	0.0617180	−	0.0849475i
$195$		0			0
$196$	−64.2633	+	197.782i	−0.327874	+	1.00909i
$197$	91.4898			0.464415			0.232208	−	0.972666i	$-0.425405\pi$
$197$	91.4898			0.464415			0.232208	+	0.972666i	$0.425405\pi$
$198$	−41.0349	+	42.6715i	−0.207247	+	0.215513i
$199$	−24.0213			−0.120710			−0.0603551	−	0.998177i	$-0.519223\pi$
$199$	−24.0213			−0.120710			−0.0603551	+	0.998177i	$0.519223\pi$
$200$		0			0
$201$	376.460	−	273.514i	1.87294	−	1.36077i
$202$	2.31864	−	3.19133i	0.0114784	−	0.0157987i
$203$	459.064	−	149.159i	2.26140	−	0.734773i
$204$	54.8533	−	17.8229i	0.268889	−	0.0873673i
$205$		0			0
$206$	−20.2483	−	27.8693i	−0.0982926	−	0.135288i
$207$	203.436	+	66.1002i	0.982781	+	0.319325i
$208$	−72.2423			−0.347319
$209$	−207.333	+	110.799i	−0.992023	+	0.530138i
$210$		0			0
$211$	−349.688	−	113.620i	−1.65729	−	0.538486i	−0.676987	−	0.735995i	$-0.736715\pi$
$211$	−349.688	−	113.620i	−1.65729	−	0.538486i	−0.980301	+	0.197509i	$0.936715\pi$
$212$	−144.665	−	199.115i	−0.682383	−	0.939219i
$213$	18.2258	−	25.0856i	0.0855671	−	0.117773i
$214$	1.51002	+	4.64735i	0.00705615	+	0.0217166i
$215$		0			0
$216$	63.3100	−	87.1387i	0.293102	−	0.403420i
$217$	255.103	−	185.343i	1.17559	−	0.854117i
$218$	−45.4616	−	14.7714i	−0.208540	−	0.0677586i
$219$		−	675.834i		−	3.08600i
$220$		0			0
$221$	−13.8690			−0.0627555
$222$	9.66172	−	29.7357i	0.0435212	−	0.133945i
$223$	104.183	+	143.396i	0.467190	+	0.643032i	0.975980	−	0.217858i	$-0.0699071\pi$
$223$	104.183	+	143.396i	0.467190	+	0.643032i	−0.508790	+	0.860891i	$0.669907\pi$
$224$	115.999	+	84.2779i	0.517851	+	0.376241i
$225$		0			0
$226$	−9.27747	+	3.01443i	−0.0410508	+	0.0133382i
$227$	−14.9656	−	10.8732i	−0.0659279	−	0.0478994i	0.554333	−	0.832295i	$-0.312973\pi$
$227$	−14.9656	−	10.8732i	−0.0659279	−	0.0478994i	−0.620261	+	0.784395i	$0.712973\pi$
$228$	348.761	−	253.390i	1.52966	−	1.11136i
$229$	41.3284	−	127.196i	0.180473	−	0.555440i	−0.819368	−	0.573268i	$-0.805675\pi$
$229$	41.3284	−	127.196i	0.180473	−	0.555440i	0.999841	+	0.0178283i	$0.00567522\pi$
$230$		0			0
$231$	568.784	+	78.7219i	2.46227	+	0.340787i
$232$		−	115.069i		−	0.495985i
$233$	13.6070	−	41.8780i	0.0583991	−	0.179734i	−0.917602	−	0.397501i	$-0.869877\pi$
$233$	13.6070	−	41.8780i	0.0583991	−	0.179734i	0.976001	+	0.217767i	$0.0698774\pi$
$234$	−21.1195	+	15.3442i	−0.0902544	+	0.0655736i
$235$		0			0
$236$	−61.8973	−	190.500i	−0.262277	−	0.807204i
$237$	143.362	+	441.223i	0.604903	+	1.86170i
$238$	7.12930	+	5.17974i	0.0299550	+	0.0217636i
$239$	−97.2433	−	133.844i	−0.406876	−	0.560017i	0.555577	−	0.831465i	$-0.312497\pi$
$239$	−97.2433	−	133.844i	−0.406876	−	0.560017i	−0.962453	+	0.271448i	$0.912497\pi$
$240$		0			0
$241$		−	68.3979i		−	0.283809i	−0.989880	−	0.141904i	$-0.954677\pi$
$241$		−	68.3979i		−	0.283809i	0.989880	−	0.141904i	$-0.0453225\pi$
$242$	−20.4970	+	30.6646i	−0.0846985	+	0.126713i
$243$		−	31.4080i		−	0.129251i
$244$	123.464	+	40.1160i	0.506001	+	0.164410i
$245$		0			0
$246$	−51.0071	−	37.0588i	−0.207346	−	0.150645i
$247$	−98.5880	+	32.0332i	−0.399142	+	0.129689i
$248$	−23.2290	−	71.4915i	−0.0936653	−	0.288272i
$249$	−268.250	+	369.214i	−1.07731	+	1.48279i
$250$		0			0
$251$	104.767	−	322.440i	0.417399	−	1.28462i	−0.492688	−	0.870206i	$-0.663986\pi$
$251$	104.767	−	322.440i	0.417399	−	1.28462i	0.910087	−	0.414417i	$-0.136014\pi$
$252$	−697.449			−2.76766
$253$	132.012	+	18.2710i	0.521788	+	0.0722175i
$254$	−32.8767			−0.129436
$255$		0			0
$256$	−160.655	+	116.723i	−0.627559	+	0.455949i
$257$	148.075	−	203.807i	0.576167	−	0.793025i	−0.417102	−	0.908860i	$-0.636954\pi$
$257$	148.075	−	203.807i	0.576167	−	0.793025i	0.993269	+	0.115835i	$0.0369542\pi$
$258$	42.9772	−	13.9641i	0.166578	−	0.0541246i
$259$	−191.034	+	62.0708i	−0.737584	+	0.239656i
$260$		0			0
$261$	495.430	+	681.901i	1.89820	+	2.61265i
$262$	14.1111	+	4.58496i	0.0538590	+	0.0174999i
$263$	−424.803			−1.61522			−0.807610	−	0.589717i	$-0.799239\pi$
$263$	−424.803			−1.61522			−0.807610	+	0.589717i	$0.799239\pi$
$264$	59.7486	−	123.157i	0.226320	−	0.466505i
$265$		0			0
$266$	62.6425	+	20.3538i	0.235498	+	0.0765180i
$267$	−359.701	−	495.086i	−1.34720	−	1.85426i
$268$	−206.985	+	284.891i	−0.772333	+	1.06303i
$269$	−154.300	−	474.888i	−0.573608	−	1.76538i	−0.640872	−	0.767648i	$-0.721427\pi$
$269$	−154.300	−	474.888i	−0.573608	−	1.76538i	0.0672640	−	0.997735i	$-0.478573\pi$
$270$		0			0
$271$	−138.031	+	189.983i	−0.509339	+	0.701045i	−0.983808	−	0.179227i	$-0.942640\pi$
$271$	−138.031	+	189.983i	−0.509339	+	0.701045i	0.474468	+	0.880273i	$0.342640\pi$
$272$	−34.4515	+	25.0305i	−0.126660	+	0.0920239i
$273$	240.809	+	78.2437i	0.882086	+	0.286607i
$274$			22.9011i			0.0835806i
$275$		0			0
$276$	−244.392			−0.885479
$277$	42.0248	−	129.339i	0.151714	−	0.466928i	−0.846099	−	0.533026i	$-0.821055\pi$
$277$	42.0248	−	129.339i	0.151714	−	0.466928i	0.997813	+	0.0660976i	$0.0210549\pi$
$278$	−8.64937	−	11.9048i	−0.0311128	−	0.0428232i
$279$	445.464	+	323.648i	1.59664	+	1.16003i
$280$		0			0
$281$	−287.964	+	93.5652i	−1.02478	+	0.332972i	−0.772726	−	0.634740i	$-0.781107\pi$
$281$	−287.964	+	93.5652i	−1.02478	+	0.332972i	−0.252057	+	0.967712i	$0.581107\pi$
$282$	5.00685	+	3.63769i	0.0177548	+	0.0128996i
$283$	8.61523	−	6.25933i	0.0304425	−	0.0221178i	−0.572460	−	0.819933i	$-0.694011\pi$
$283$	8.61523	−	6.25933i	0.0304425	−	0.0221178i	0.602902	+	0.797815i	$0.294011\pi$
$284$	−7.25119	+	22.3169i	−0.0255324	+	0.0785805i
$285$		0			0
$286$	−11.2737	+	11.7234i	−0.0394186	+	0.0409908i
$287$			405.047i			1.41131i
$288$	−77.3703	+	238.121i	−0.268647	+	0.826810i
$289$	227.192	−	165.065i	0.786131	−	0.571158i
$290$		0			0
$291$	−106.614	−	328.124i	−0.366371	−	1.12757i
$292$	158.045	+	486.414i	0.541251	+	1.66580i
$293$	−267.010	−	193.994i	−0.911296	−	0.662095i	0.0300463	−	0.999549i	$-0.490435\pi$
$293$	−267.010	−	193.994i	−0.911296	−	0.662095i	−0.941342	+	0.337453i	$0.890435\pi$
$294$	−49.2374	−	67.7695i	−0.167474	−	0.230509i
$295$		0			0
$296$			47.8845i			0.161772i
$297$	86.3727	+	483.910i	0.290817	+	1.62933i
$298$			36.7310i			0.123259i
$299$	55.8909	+	18.1600i	0.186926	+	0.0607359i
$300$		0			0
$301$	−234.868	−	170.641i	−0.780291	−	0.566914i
$302$	−22.3973	+	7.27734i	−0.0741634	+	0.0240971i
$303$	−20.6459	−	63.5415i	−0.0681382	−	0.209708i
$304$	−187.087	+	257.503i	−0.615418	+	0.847050i
$305$		0			0
$306$	−4.75519	+	14.6350i	−0.0155398	+	0.0478267i
$307$	−111.473			−0.363104			−0.181552	−	0.983381i	$-0.558112\pi$
$307$	−111.473			−0.363104			−0.181552	+	0.983381i	$0.558112\pi$
$308$	−427.776	+	76.3534i	−1.38888	+	0.247901i
$309$	−583.454			−1.88820
$310$		0			0
$311$	−327.747	+	238.122i	−1.05385	+	0.765665i	−0.972940	−	0.231057i	$-0.925782\pi$
$311$	−327.747	+	238.122i	−1.05385	+	0.765665i	−0.0809071	+	0.996722i	$0.525782\pi$
$312$	35.4794	−	48.8331i	0.113716	−	0.156516i
$313$	−161.450	+	52.4582i	−0.515814	+	0.167598i	−0.555345	−	0.831620i	$-0.687414\pi$
$313$	−161.450	+	52.4582i	−0.515814	+	0.167598i	0.0395307	+	0.999218i	$0.487414\pi$
$314$	15.7141	−	5.10581i	0.0500448	−	0.0162605i
$315$		0			0
$316$	−206.362	−	284.033i	−0.653044	−	0.898838i
$317$	367.389	+	119.372i	1.15895	+	0.376567i	0.824510	−	0.565848i	$-0.191451\pi$
$317$	367.389	+	119.372i	1.15895	+	0.376567i	0.334445	+	0.942415i	$0.391451\pi$
$318$	99.1383			0.311756
$319$	378.520	+	364.003i	1.18658	+	1.14107i
$320$		0			0
$321$	78.7123	+	25.5752i	0.245210	+	0.0796735i
$322$	−21.9482	−	30.2091i	−0.0681620	−	0.0938170i
$323$	−35.9167	+	49.4350i	−0.111197	+	0.153050i
$324$	−86.7068	−	266.856i	−0.267613	−	0.823630i
$325$		0			0
$326$	−36.3987	+	50.0986i	−0.111653	+	0.153677i
$327$	−654.988	+	475.877i	−2.00302	+	1.45528i
$328$	91.8337	+	29.8386i	0.279981	+	0.0909713i
$329$		−	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	$0.442485\pi$
$332$	106.724	−	328.463i	0.321458	−	0.989346i
$333$	−206.168	−	283.765i	−0.619122	−	0.852148i
$334$	−32.7275	−	23.7780i	−0.0979867	−	0.0711915i
$335$		0			0
$336$	739.402	−	240.246i	2.20060	−	0.715018i
$337$	−358.847	−	260.717i	−1.06483	−	0.773642i	−0.0898516	−	0.995955i	$-0.528639\pi$
$337$	−358.847	−	260.717i	−1.06483	−	0.773642i	−0.974975	+	0.222313i	$0.928639\pi$
$338$	35.8751	−	26.0648i	0.106139	−	0.0771147i
$339$	−51.0556	+	157.133i	−0.150606	+	0.463519i
$340$		0			0
$341$	308.654	+	149.741i	0.905144	+	0.439122i
$342$			115.016i			0.336305i
$343$	−13.2053	+	40.6417i	−0.0384993	+	0.118489i
$344$	−55.9903	+	40.6793i	−0.162763	+	0.118254i
$345$		0			0
$346$	−10.5356	−	32.4252i	−0.0304497	−	0.0937146i
$347$	−163.076	−	501.898i	−0.469961	−	1.44639i	−0.852635	−	0.522507i	$-0.824997\pi$
$347$	−163.076	−	501.898i	−0.469961	−	1.44639i	0.382674	−	0.923883i	$-0.375003\pi$
$348$	−779.091	−	566.042i	−2.23877	−	1.62656i
$349$	−318.255	−	438.040i	−0.911905	−	1.25513i	−0.966512	−	0.256622i	$-0.917390\pi$
$349$	−318.255	−	438.040i	−0.911905	−	1.25513i	0.0546065	−	0.998508i	$-0.482610\pi$
$350$		0			0
$351$			216.758i			0.617543i
$352$	−21.3862	+	154.520i	−0.0607563	+	0.438978i
$353$			216.813i			0.614201i	0.951677	+	0.307101i	$0.0993588\pi$
$353$			216.813i			0.614201i	−0.951677	+	0.307101i	$0.900641\pi$
$354$	76.7347	+	24.9326i	0.216765	+	0.0704311i
$355$		0			0
$356$	374.662	+	272.208i	1.05242	+	0.764630i
$357$	141.949	−	46.1221i	0.397616	−	0.129193i
$358$	4.51321	+	13.8902i	0.0126067	+	0.0387995i
$359$	329.315	−	453.263i	0.917311	−	1.26257i	−0.0472967	−	0.998881i	$-0.515061\pi$
$359$	329.315	−	453.263i	0.917311	−	1.26257i	0.964608	−	0.263689i	$-0.0849394\pi$
$360$		0			0
$361$	−29.5795	+	91.0363i	−0.0819376	+	0.252178i
$362$	2.07029			0.00571902
$363$	216.123	+	586.134i	0.595379	+	1.61469i
$364$	−191.614			−0.526411
$365$		0			0
$366$	−42.3047	+	30.7362i	−0.115587	+	0.0839786i
$367$	−18.1911	+	25.0380i	−0.0495671	+	0.0682233i	−0.833081	−	0.553151i	$-0.813425\pi$
$367$	−18.1911	+	25.0380i	−0.0495671	+	0.0682233i	0.783514	+	0.621374i	$0.213425\pi$
$368$	171.612	−	55.7602i	0.466337	−	0.151522i
$369$	−672.680	+	218.567i	−1.82298	+	0.592323i
$370$		0			0
$371$	−374.364	−	515.267i	−1.00907	−	1.38886i
$372$	−598.312	−	194.403i	−1.60837	−	0.522590i
$373$	483.806			1.29707			0.648534	−	0.761186i	$-0.275383\pi$
$373$	483.806			1.29707			0.648534	+	0.761186i	$0.275383\pi$
$374$	−1.31440	+	9.49685i	−0.00351444	+	0.0253927i
$375$		0			0
$376$	−9.01440	−	2.92896i	−0.0239745	−	0.00778977i
$377$	136.112	+	187.342i	0.361040	+	0.496928i
$378$	80.9540	−	111.424i	0.214164	−	0.294771i
$379$	−25.3368	−	77.9786i	−0.0668517	−	0.205748i	0.912050	−	0.410078i	$-0.134499\pi$
$379$	−25.3368	−	77.9786i	−0.0668517	−	0.205748i	−0.978902	+	0.204330i	$0.934499\pi$
$380$		0			0
$381$	−327.298	+	450.487i	−0.859050	+	1.18238i
$382$	18.5090	−	13.4476i	0.0484530	−	0.0352031i
$383$	693.283	+	225.261i	1.81014	+	0.588150i	0.999998	+	0.00191562i	$0.000609760\pi$
$383$	693.283	+	225.261i	1.81014	+	0.588150i	0.810141	+	0.586234i	$0.199390\pi$
$384$		−	379.819i		−	0.989111i
$385$		0			0
$386$	115.660			0.299638
$387$	156.655	−	482.135i	0.404793	−	1.24583i
$388$	153.465	+	211.227i	0.395529	+	0.544399i
$389$	193.321	+	140.456i	0.496969	+	0.361069i	0.807858	−	0.589377i	$-0.200627\pi$
$389$	193.321	+	140.456i	0.496969	+	0.361069i	−0.310889	+	0.950446i	$0.600627\pi$
$390$		0			0
$391$	32.9458	−	10.7047i	0.0842604	−	0.0273779i
$392$	103.790	+	75.4082i	0.264772	+	0.192368i
$393$	203.305	−	147.710i	0.517316	−	0.375852i
$394$	8.61808	−	26.5237i	0.0218733	−	0.0673191i
$395$		0			0
$396$	−357.635	−	669.226i	−0.903120	−	1.68997i
$397$			354.733i			0.893535i	0.894650	+	0.446768i	$0.147425\pi$
$397$			354.733i			0.893535i	−0.894650	+	0.446768i	$0.852575\pi$
$398$	−2.26274	+	6.96401i	−0.00568528	+	0.0174975i
$399$	902.522	−	655.721i	2.26196	−	1.64341i
$400$		0			0
$401$	79.1417	+	243.573i	0.197361	+	0.607414i	0.999941	+	0.0108700i	$0.00346008\pi$
$401$	79.1417	+	243.573i	0.197361	+	0.607414i	−0.802580	+	0.596545i	$0.796540\pi$
$402$	−43.8328	−	134.904i	−0.109037	−	0.335581i
$403$	122.384	+	88.9175i	0.303684	+	0.220639i
$404$	29.7187	+	40.9042i	0.0735610	+	0.101248i
$405$		0			0
$406$		−	147.137i		−	0.362407i
$407$	−157.517	−	151.476i	−0.387020	−	0.372176i
$408$		−	35.5808i		−	0.0872079i
$409$	−261.500	−	84.9666i	−0.639365	−	0.207742i	−0.0286458	−	0.999590i	$-0.509119\pi$
$409$	−261.500	−	84.9666i	−0.639365	−	0.207742i	−0.610719	+	0.791847i	$0.709119\pi$
$410$		0			0
$411$	313.798	+	227.988i	0.763500	+	0.554715i
$412$	419.925	−	136.442i	1.01924	−	0.331170i
$413$	−160.177	−	492.975i	−0.387839	−	1.19364i
$414$	38.3261	−	52.7514i	0.0925752	−	0.127419i
$415$		0			0
$416$	−21.2563	+	65.4202i	−0.0510969	+	0.157260i
$417$	−249.232			−0.597678
$418$	12.5914	+	70.5446i	0.0301231	+	0.168767i
$419$	−44.0757			−0.105193			−0.0525963	−	0.998616i	$-0.516750\pi$
$419$	−44.0757			−0.105193			−0.0525963	+	0.998616i	$0.516750\pi$
$420$		0			0
$421$	65.8608	−	47.8507i	0.156439	−	0.113660i	−0.506812	−	0.862057i	$-0.669176\pi$
$421$	65.8608	−	47.8507i	0.156439	−	0.113660i	0.663251	+	0.748397i	$0.269176\pi$
$422$	−65.8792	+	90.6750i	−0.156112	+	0.214870i
$423$	66.0303	−	21.4546i	0.156100	−	0.0507200i
$424$	−144.401	+	46.9188i	−0.340569	+	0.110658i
$425$		0			0
$426$	−5.55574	−	7.64682i	−0.0130416	−	0.0179503i
$427$	319.500	+	103.812i	0.748243	+	0.243119i
$428$	−62.6319			−0.146336
$429$	48.4038	+	271.186i	0.112829	+	0.632136i
$430$		0			0
$431$	690.547	+	224.372i	1.60220	+	0.520585i	0.967649	−	0.252299i	$-0.0811866\pi$
$431$	690.547	+	224.372i	1.60220	+	0.520585i	0.634547	+	0.772884i	$0.281187\pi$
$432$	391.201	+	538.442i	0.905558	+	1.24639i
$433$	204.033	−	280.828i	0.471208	−	0.648563i	−0.505577	−	0.862781i	$-0.668720\pi$
$433$	204.033	−	280.828i	0.471208	−	0.648563i	0.976786	+	0.214218i	$0.0687205\pi$
$434$	−29.7027	−	91.4156i	−0.0684394	−	0.210635i
$435$		0			0
$436$	360.126	−	495.670i	0.825976	−	1.13686i
$437$	209.472	−	152.190i	0.479340	−	0.348261i
$438$	−195.930	−	63.6617i	−0.447330	−	0.145346i
$439$			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
$442$	−1.30642	+	4.02074i	−0.00295569	+	0.00909669i
$443$	220.886	+	304.024i	0.498614	+	0.686284i	0.981948	−	0.189153i	$-0.0605741\pi$
$443$	220.886	+	304.024i	0.498614	+	0.686284i	−0.483333	+	0.875436i	$0.660574\pi$
$444$	324.210	+	235.552i	0.730202	+	0.530523i
$445$		0			0
$446$	51.3857	−	16.6962i	0.115214	−	0.0374355i
$447$	503.301	+	365.670i	1.12595	+	0.818053i
$448$	−451.943	+	328.356i	−1.00880	+	0.732937i
$449$	−34.6764	+	106.723i	−0.0772302	+	0.237690i	−0.982217	−	0.187750i	$-0.939881\pi$
$449$	−34.6764	+	106.723i	−0.0772302	+	0.237690i	0.904987	+	0.425440i	$0.139881\pi$
$450$		0			0
$451$	−388.657	+	207.699i	−0.861767	+	0.460529i
$452$		−	125.032i		−	0.276619i
$453$	−123.256	+	379.344i	−0.272089	+	0.837405i
$454$	−4.56195	+	3.31445i	−0.0100483	+	0.00730055i
$455$		0			0
$456$	−82.1812	−	252.928i	−0.180222	−	0.554666i
$457$	57.6949	+	177.567i	0.126247	+	0.388549i	0.994126	−	0.108227i	$-0.0345173\pi$
$457$	57.6949	+	177.567i	0.126247	+	0.388549i	−0.867879	+	0.496775i	$0.834517\pi$
$458$	−32.9822	−	23.9630i	−0.0720136	−	0.0523209i
$459$	75.1021	+	103.369i	0.163621	+	0.225205i
$460$		0			0
$461$		−	559.922i		−	1.21458i	−0.794479	−	0.607291i	$-0.792256\pi$
$461$		−	559.922i		−	1.21458i	0.794479	−	0.607291i	$-0.207744\pi$
$462$	76.4000	−	157.480i	0.165368	−	0.340866i
$463$		−	648.611i		−	1.40089i	−0.713708	−	0.700444i	$-0.752986\pi$
$463$		−	648.611i		−	1.40089i	0.713708	−	0.700444i	$-0.247014\pi$
$464$	676.224	+	219.719i	1.45738	+	0.473532i
$465$		0			0
$466$	−10.8591	−	7.88958i	−0.0233028	−	0.0169304i
$467$	−856.339	+	278.242i	−1.83370	+	0.595806i	−0.834722	+	0.550671i	$0.814372\pi$
$467$	−856.339	+	278.242i	−1.83370	+	0.595806i	−0.998981	+	0.0451348i	$0.985628\pi$
$468$	−103.396	−	318.221i	−0.220932	−	0.679960i
$469$	−535.635	+	737.238i	−1.14208	+	1.57194i
$470$		0			0
$471$	86.4772	−	266.149i	0.183603	−	0.565073i
$472$	−123.569			−0.261798
$473$	43.3016	−	312.864i	0.0915468	−	0.661447i
$474$	141.419			0.298352
$475$		0			0
$476$	−91.3783	+	66.3902i	−0.191971	+	0.139475i
$477$	653.718	−	899.765i	1.37048	−	1.88630i
$478$	−47.9626	+	15.5840i	−0.100340	+	0.0326025i
$479$	441.790	−	143.546i	0.922317	−	0.299679i	0.190900	−	0.981609i	$-0.438859\pi$
$479$	441.790	−	143.546i	0.922317	−	0.299679i	0.731417	+	0.681930i	$0.238859\pi$
$480$		0			0
$481$	−56.6415	−	77.9603i	−0.117758	−	0.162080i
$482$	−19.8292	−	6.44289i	−0.0411394	−	0.0133670i
$483$	−632.437			−1.30939
$484$	−292.617	−	371.314i	−0.604581	−	0.767177i
$485$		0			0
$486$	−9.10546	−	2.95854i	−0.0187355	−	0.00608753i
$487$	19.3672	+	26.6567i	0.0397685	+	0.0547366i	0.828438	−	0.560081i	$-0.189230\pi$
$487$	19.3672	+	26.6567i	0.0397685	+	0.0547366i	−0.788670	+	0.614817i	$0.789230\pi$
$488$	47.0731	−	64.7906i	0.0964613	−	0.132768i
$489$	324.106	+	997.496i	0.662794	+	2.03987i
$490$		0			0
$491$	−469.003	+	645.528i	−0.955200	+	1.31472i	−0.00602158	+	0.999982i	$0.501917\pi$
$491$	−469.003	+	645.528i	−0.955200	+	1.31472i	−0.949179	+	0.314738i	$0.898083\pi$
$492$	653.773	−	474.994i	1.32881	−	0.965434i
$493$	129.820	+	42.1812i	0.263327	+	0.0855603i
$494$			31.5990i			0.0639656i
$495$		0			0
$496$	464.489			0.936470
$497$	−18.7646	+	57.7514i	−0.0377557	+	0.116200i
$498$	81.7701	+	112.547i	0.164197	+	0.225998i
$499$	479.816	+	348.607i	0.961555	+	0.698611i	0.953511	−	0.301357i	$-0.0974396\pi$
$499$	479.816	+	348.607i	0.961555	+	0.698611i	0.00804363	+	0.999968i	$0.497440\pi$
$500$		0			0
$501$	−651.627	+	211.727i	−1.30065	+	0.422608i
$502$	−83.6096	−	60.7459i	−0.166553	−	0.121008i
$503$	−634.532	+	461.015i	−1.26150	+	0.916530i	−0.998830	−	0.0483569i	$-0.984602\pi$
$503$	−634.532	+	461.015i	−1.26150	+	0.916530i	−0.262665	+	0.964887i	$0.584602\pi$
$504$	−132.958	+	409.203i	−0.263806	+	0.811910i
$505$		0			0
$506$	17.7321	−	36.5505i	0.0350437	−	0.0722342i
$507$		−	751.056i		−	1.48137i
$508$	130.217	−	400.766i	0.256332	−	0.788909i
$509$	−639.768	+	464.819i	−1.25691	+	0.913200i	−0.998602	−	0.0528625i	$-0.983165\pi$
$509$	−639.768	+	464.819i	−1.25691	+	0.913200i	−0.258310	+	0.966062i	$0.583165\pi$
$510$		0			0
$511$	408.989	+	1258.74i	0.800369	+	2.46328i
$512$	109.640	+	337.436i	0.214140	+	0.659055i
$513$	772.619	+	561.340i	1.50608	+	1.09423i
$514$	−45.1374	−	62.1263i	−0.0878160	−	0.120868i
$515$		0			0
$516$			579.200i			1.12248i
$517$	38.1506	−	20.3877i	0.0737922	−	0.0394346i
$518$			61.2295i			0.118204i
$519$	−549.187	−	178.442i	−1.05816	−	0.343818i
$520$		0			0
$521$	−514.280	−	373.646i	−0.987101	−	0.717171i	−0.0278170	−	0.999613i	$-0.508856\pi$
$521$	−514.280	−	373.646i	−0.987101	−	0.717171i	−0.959284	+	0.282442i	$0.908856\pi$
$522$	244.357	−	79.3966i	0.468118	−	0.152101i
$523$	58.7556	+	180.831i	0.112343	+	0.345757i	0.991384	−	0.130990i	$-0.0418156\pi$
$523$	58.7556	+	180.831i	0.112343	+	0.345757i	−0.879040	+	0.476747i	$0.841816\pi$
$524$	−111.781	+	153.854i	−0.213323	+	0.293614i
$525$		0			0
$526$	−40.0152	+	123.154i	−0.0760746	+	0.234134i
$527$	89.1719			0.169207
$528$	609.672	+	586.289i	1.15468	+	1.11040i
$529$	382.214			0.722522
$530$		0			0
$531$	732.273	−	532.027i	1.37905	−	1.00193i
$532$	−496.225	+	682.995i	−0.932753	+	1.28382i
$533$	−184.809	+	60.0480i	−0.346733	+	0.112660i
$534$	−177.413	+	57.6449i	−0.332234	+	0.107949i
$535$		0			0
$536$	127.691	+	175.751i	0.238229	+	0.327894i
$537$	235.259	+	76.4403i	0.438099	+	0.142347i
$538$	−152.209			−0.282917
$539$	−576.382	+	102.878i	−1.06936	+	0.190868i
$540$		0			0
$541$	37.6026	+	12.2178i	0.0695058	+	0.0225838i	0.343563	−	0.939129i	$-0.388366\pi$
$541$	37.6026	+	12.2178i	0.0695058	+	0.0225838i	−0.274058	+	0.961713i	$0.588366\pi$
$542$	42.0758	+	57.9123i	0.0776306	+	0.106849i
$543$	20.6104	−	28.3678i	0.0379565	−	0.0522427i
$544$	12.5299	+	38.5630i	0.0230329	+	0.0708879i
$545$		0			0
$546$	45.3671	−	62.4425i	0.0830900	−	0.114364i
$547$	478.368	−	347.554i	0.874529	−	0.635383i	−0.0572690	−	0.998359i	$-0.518239\pi$
$547$	478.368	−	347.554i	0.874529	−	0.635383i	0.931799	+	0.362976i	$0.118239\pi$
$548$	−279.164	−	90.7057i	−0.509423	−	0.165521i
$549$			586.626i			1.06853i
$550$		0			0
$551$	1020.26			1.85165
$552$	−46.5896	+	143.388i	−0.0844015	+	0.259761i
$553$	−534.022	−	735.018i	−0.965682	−	1.32915i
$554$	−33.5380	−	24.3668i	−0.0605379	−	0.0439833i
$555$		0			0
$556$	179.378	−	58.2834i	0.322622	−	0.104826i
$557$	−176.596	−	128.305i	−0.317049	−	0.230350i	0.417866	−	0.908509i	$-0.362778\pi$
$557$	−176.596	−	128.305i	−0.317049	−	0.230350i	−0.734915	+	0.678159i	$0.762778\pi$
$558$	135.790	−	98.6573i	0.243351	−	0.176805i
$559$	43.0386	−	132.459i	0.0769921	−	0.236957i
$560$		0			0
$561$	117.044	+	112.555i	0.208634	+	0.200632i
$562$			92.2970i			0.164229i
$563$	115.865	−	356.595i	0.205799	−	0.633383i	−0.793881	−	0.608073i	$-0.791943\pi$
$563$	115.865	−	356.595i	0.205799	−	0.633383i	0.999680	−	0.0253101i	$-0.00805730\pi$
$564$	−64.1743	+	46.6254i	−0.113784	+	0.0826691i
$565$		0			0
$566$	−1.00311	−	3.08725i	−0.00177227	−	0.00545450i
$567$	−224.379	−	690.568i	−0.395730	−	1.21793i
$568$	11.7113	+	8.50874i	0.0206184	+	0.0149802i
$569$	131.674	+	181.234i	0.231413	+	0.318513i	0.908894	−	0.417028i	$-0.136928\pi$
$569$	131.674	+	181.234i	0.231413	+	0.318513i	−0.677480	+	0.735541i	$0.736928\pi$
$570$		0			0
$571$		−	176.017i		−	0.308262i	−0.988050	−	0.154131i	$-0.950742\pi$
$571$		−	176.017i		−	0.308262i	0.988050	−	0.154131i	$-0.0492577\pi$
$572$	−98.2549	−	183.860i	−0.171774	−	0.321433i
$573$		−	387.492i		−	0.676252i
$574$	117.427	+	38.1543i	0.204577	+	0.0664710i
$575$		0			0
$576$	−789.188	−	573.378i	−1.37012	−	0.995449i
$577$	635.162	−	206.377i	1.10080	−	0.357672i	0.298391	−	0.954444i	$-0.403550\pi$
$577$	635.162	−	206.377i	1.10080	−	0.357672i	0.802411	+	0.596772i	$0.203550\pi$
$578$	−26.4529	−	81.4137i	−0.0457663	−	0.140854i
$579$	1151.44	−	1584.82i	1.98867	−	2.73716i
$580$		0			0
$581$	276.180	−	849.994i	0.475352	−	1.46298i
$582$	−105.169			−0.180703
$583$	302.452	−	623.432i	0.518785	−	1.06935i
$584$	315.514			0.540264
$585$		0			0
$586$	−81.3922	+	59.1349i	−0.138895	+	0.100913i
$587$	57.4195	−	79.0311i	0.0978185	−	0.134636i	−0.757302	−	0.653065i	$-0.773483\pi$
$587$	57.4195	−	79.0311i	0.0978185	−	0.134636i	0.855121	+	0.518429i	$0.173483\pi$
$588$	1021.13	−	331.784i	1.73661	−	0.564259i
$589$	633.882	−	205.961i	1.07620	−	0.349679i
$590$		0			0
$591$	−277.641	−	382.141i	−0.469782	−	0.646600i
$592$	−281.403	−	91.4335i	−0.475343	−	0.154448i
$593$	479.081			0.807893			0.403947	−	0.914783i	$-0.367638\pi$
$593$	479.081			0.807893			0.403947	+	0.914783i	$0.367638\pi$
$594$	148.426	+	20.5427i	0.249875	+	0.0345837i
$595$		0			0
$596$	−447.751	−	145.483i	−0.751259	−	0.244099i
$597$	72.8968	+	100.334i	0.122105	+	0.168063i
$598$	10.5295	−	14.4927i	0.0176079	−	0.0242352i
$599$	−146.829	−	451.894i	−0.245124	−	0.754414i	−0.995616	−	0.0935345i	$-0.970183\pi$
$599$	−146.829	−	451.894i	−0.245124	−	0.754414i	0.750492	−	0.660879i	$-0.229817\pi$
$600$		0			0
$601$	316.409	−	435.499i	0.526470	−	0.724624i	−0.460117	−	0.887858i	$-0.652193\pi$
$601$	316.409	−	435.499i	0.526470	−	0.724624i	0.986587	+	0.163234i	$0.0521926\pi$
$602$	−71.5943	+	52.0163i	−0.118927	+	0.0864059i
$603$	−1513.40	−	491.733i	−2.50978	−	0.815477i
$604$		−	301.847i		−	0.499747i
$605$		0			0
$606$	−20.3660			−0.0336073
$607$	−127.052	+	391.027i	−0.209312	+	0.644196i	0.790197	+	0.612853i	$0.209978\pi$
$607$	−127.052	+	391.027i	−0.209312	+	0.644196i	−0.999509	+	0.0313426i	$0.990022\pi$
$608$	178.138	+	245.186i	0.292991	+	0.403267i
$609$	−2016.13	−	1464.80i	−3.31055	−	2.40526i
$610$		0			0
$611$	18.1408	−	5.89431i	0.0296904	−	0.00964700i
$612$	−159.566	−	115.931i	−0.260728	−	0.189430i
$613$	−201.079	+	146.092i	−0.328025	+	0.238324i	−0.739592	−	0.673056i	$-0.764981\pi$
$613$	−201.079	+	146.092i	−0.328025	+	0.238324i	0.411567	+	0.911379i	$0.364981\pi$
$614$	−10.5004	+	32.3170i	−0.0171017	+	0.0526336i
$615$		0			0
$616$	−36.7514	+	265.538i	−0.0596614	+	0.431067i
$617$			1141.96i			1.85082i	0.378964	+	0.925411i	$0.376280\pi$
$617$			1141.96i			1.85082i	−0.378964	+	0.925411i	$0.623720\pi$
$618$	−54.9597	+	169.149i	−0.0889316	+	0.273703i
$619$	4.57281	−	3.32234i	0.00738742	−	0.00536727i	−0.584085	−	0.811692i	$-0.698547\pi$
$619$	4.57281	−	3.32234i	0.00738742	−	0.00536727i	0.591473	+	0.806325i	$0.298547\pi$
$620$		0			0
$621$	−167.304	−	514.909i	−0.269411	−	0.829161i
$622$	38.1609	+	117.447i	0.0613519	+	0.188822i
$623$	969.549	+	704.418i	1.55626	+	1.13069i
$624$	219.232	+	301.746i	0.351333	+	0.483568i
$625$		0			0
$626$			51.7472i			0.0826633i
$627$	1091.98	+	529.763i	1.74159	+	0.844917i
$628$			211.777i			0.337224i
$629$	−54.0233	−	17.5532i	−0.0858876	−	0.0279066i
$630$		0			0
$631$	601.402	+	436.944i	0.953094	+	0.692463i	0.951537	−	0.307536i	$-0.0995043\pi$
$631$	601.402	+	436.944i	0.953094	+	0.692463i	0.00155713	+	0.999999i	$0.499504\pi$
$632$	−205.986	+	66.9288i	−0.325927	+	0.105900i
$633$	586.610	+	1805.40i	0.926714	+	2.85213i
$634$	69.2140	−	95.2649i	0.109170	−	0.150260i
$635$		0			0
$636$	−392.664	+	1208.49i	−0.617396	+	1.90015i
$637$	−258.179			−0.405304
$638$	141.183	−	75.4485i	0.221290	−	0.118258i
$639$	−106.036			−0.165940
$640$		0			0
$641$	−292.789	+	212.724i	−0.456769	+	0.331862i	−0.792263	−	0.610180i	$-0.791097\pi$
$641$	−292.789	+	212.724i	−0.456769	+	0.331862i	0.335493	+	0.942043i	$0.391097\pi$
$642$	14.8290	−	20.4103i	0.0230981	−	0.0317918i
$643$	−615.565	+	200.009i	−0.957333	+	0.311056i	−0.745692	−	0.666291i	$-0.767881\pi$
$643$	−615.565	+	200.009i	−0.957333	+	0.311056i	−0.211641	+	0.977347i	$0.567881\pi$
$644$	455.179	−	147.897i	0.706800	−	0.229653i
$645$		0			0
$646$	10.9484	+	15.0692i	0.0169480	+	0.0233269i
$647$	−694.892	−	225.784i	−1.07402	−	0.348971i	−0.281969	−	0.959423i	$-0.590988\pi$
$647$	−694.892	−	225.784i	−1.07402	−	0.348971i	−0.792053	+	0.610453i	$0.790988\pi$
$648$	−173.097			−0.267125
$649$	390.891	−	406.482i	0.602298	−	0.626320i
$650$		0			0
$651$	−1548.31	−	503.076i	−2.37835	−	0.772774i
$652$	−466.534	−	642.128i	−0.715542	−	0.984859i
$653$	176.964	−	243.570i	0.271001	−	0.373001i	−0.651726	−	0.758454i	$-0.725955\pi$
$653$	176.964	−	243.570i	0.271001	−	0.373001i	0.922727	+	0.385453i	$0.125955\pi$
$654$	76.2630	+	234.713i	0.116610	+	0.358889i
$655$		0			0
$656$	−350.705	+	482.704i	−0.534611	+	0.735829i
$657$	−1869.75	+	1358.45i	−2.84589	+	2.06766i
$658$	−11.5266	−	3.74523i	−0.0175177	−	0.00569184i
$659$			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	$0.267449\pi$
$662$	11.2062	−	34.4892i	0.0169278	−	0.0520985i
$663$	42.0877	+	57.9288i	0.0634807	+	0.0873737i
$664$	−172.368	−	125.233i	−0.259591	−	0.188604i
$665$		0			0
$666$	−101.687	+	33.0400i	−0.152683	+	0.0496096i
$667$	−467.934	−	339.974i	−0.701551	−	0.509707i
$668$	419.479	−	304.769i	0.627962	−	0.456241i
$669$	282.784	−	870.320i	0.422697	−	1.30093i
$670$		0			0
$671$	64.2210	+	359.803i	0.0957094	+	0.536220i
$672$		−	740.266i		−	1.10159i
$673$	−124.617	+	383.533i	−0.185167	+	0.569886i	−0.999951	−	0.00987877i	$-0.996855\pi$
$673$	−124.617	+	383.533i	−0.185167	+	0.569886i	0.814784	+	0.579764i	$0.196855\pi$
$674$	−109.387	+	79.4741i	−0.162295	+	0.117914i
$675$		0			0
$676$	175.636	+	540.553i	0.259817	+	0.799634i
$677$	193.523	+	595.604i	0.285854	+	0.879769i	0.986141	+	0.165908i	$0.0530554\pi$
$677$	193.523	+	595.604i	0.285854	+	0.879769i	−0.700287	+	0.713861i	$0.746945\pi$
$678$	40.7450	+	29.6029i	0.0600958	+	0.0436622i
$679$	397.136	+	546.611i	0.584884	+	0.805024i
$680$		0			0
$681$			95.5059i			0.140244i
$682$	72.4855	−	75.3765i	0.106284	−	0.110523i
$683$			935.585i			1.36982i	0.728629	+	0.684909i	$0.240158\pi$
$683$			935.585i			1.36982i	−0.728629	+	0.684909i	$0.759842\pi$
$684$	−1402.05	−	455.553i	−2.04978	−	0.666013i
$685$		0			0
$686$	10.5385	+	7.65666i	0.0153622	+	0.0111613i
$687$	−656.698	+	213.374i	−0.955892	+	0.310588i
$688$	−132.149	−	406.714i	−0.192078	−	0.591154i
$689$	179.599	−	247.197i	0.260666	−	0.358776i
$690$		0			0
$691$	255.366	−	785.937i	0.369561	−	1.13739i	−0.577515	−	0.816380i	$-0.695977\pi$
$691$	255.366	−	785.937i	0.369561	−	1.13739i	0.947076	−	0.321011i	$-0.104023\pi$
$692$	436.992			0.631491
$693$	−925.486	−	1731.82i	−1.33548	−	2.49902i
$694$	−160.866			−0.231795
$695$		0			0
$696$	−480.626	+	349.195i	−0.690555	+	0.501718i
$697$	−67.3278	+	92.6687i	−0.0965965	+	0.132954i
$698$	−156.971	+	51.0029i	−0.224886	+	0.0730700i
$699$	−216.212	+	70.2514i	−0.309316	+	0.100503i
$700$		0			0
$701$	−139.111	−	191.469i	−0.198446	−	0.273138i	0.698184	−	0.715919i	$-0.253992\pi$
$701$	−139.111	−	191.469i	−0.198446	−	0.273138i	−0.896630	+	0.442781i	$0.853992\pi$
$702$	62.8400	+	20.4180i	0.0895157	+	0.0290854i
$703$	−424.570			−0.603940
$704$	−546.814	−	265.282i	−0.776725	−	0.376821i
$705$		0			0
$706$	62.8561	+	20.4232i	0.0890313	+	0.0289280i
$707$	76.9057	+	105.852i	0.108778	+	0.149719i
$708$	−607.856	+	836.642i	−0.858554	+	1.18170i
$709$	278.848	+	858.205i	0.393297	+	1.21044i	0.930280	+	0.366851i	$0.119564\pi$
$709$	278.848	+	858.205i	0.393297	+	1.21044i	−0.536982	+	0.843593i	$0.680436\pi$
$710$		0			0
$711$	932.515	−	1283.50i	1.31155	−	1.80520i
$712$	231.132	−	167.927i	0.324623	−	0.235853i
$713$	−359.356	−	116.762i	−0.504006	−	0.163761i
$714$		−	45.4969i		−	0.0637212i
$715$		0			0
$716$	−187.197			−0.261449
$717$	−263.947	+	812.345i	−0.368127	+	1.13298i
$718$	−100.385	−	138.167i	−0.139811	−	0.192434i
$719$	−318.157	−	231.154i	−0.442499	−	0.321494i	0.344128	−	0.938923i	$-0.388174\pi$
$719$	−318.157	−	231.154i	−0.442499	−	0.321494i	−0.786627	+	0.617428i	$0.788174\pi$
$720$		0			0
$721$	1086.68	−	353.084i	1.50718	−	0.489714i
$722$	23.6060	+	17.1507i	0.0326952	+	0.0237545i
$723$	−285.689	+	207.565i	−0.395144	+	0.287089i
$724$	−8.19991	+	25.2367i	−0.0113258	+	0.0348574i
$725$		0			0
$726$	190.284	−	7.44370i	0.262099	−	0.0102530i
$727$		−	1284.55i		−	1.76691i	−0.468514	−	0.883456i	$-0.655210\pi$
$727$		−	1284.55i		−	1.76691i	0.468514	−	0.883456i	$-0.344790\pi$
$728$	−36.5282	+	112.422i	−0.0501761	+	0.154426i
$729$	−654.087	+	475.222i	−0.897238	+	0.651882i
$730$		0			0
$731$	−25.3698	−	78.0803i	−0.0347056	−	0.106813i
$732$	−207.114	−	637.432i	−0.282943	−	0.870809i
$733$	−339.175	−	246.425i	−0.462722	−	0.336187i	0.331876	−	0.943323i	$-0.392318\pi$
$733$	−339.175	−	246.425i	−0.462722	−	0.336187i	−0.794598	+	0.607136i	$0.792318\pi$
$734$	5.54518	+	7.63228i	0.00755474	+	0.0103982i
$735$		0			0
$736$		−	171.813i		−	0.233441i
$737$	−982.066	−	135.922i	−1.33252	−	0.184426i
$738$			215.605i			0.292147i
$739$	269.243	+	87.4823i	0.364334	+	0.118379i	0.485462	−	0.874258i	$-0.338651\pi$
$739$	269.243	+	87.4823i	0.364334	+	0.118379i	−0.121128	+	0.992637i	$0.538651\pi$
$740$		0			0
$741$	432.981	+	314.579i	0.584319	+	0.424533i
$742$	−184.645	+	59.9947i	−0.248847	+	0.0808554i
$743$	−3.47057	−	10.6813i	−0.00467102	−	0.0143759i	0.948694	−	0.316196i	$-0.102406\pi$
$743$	−3.47057	−	10.6813i	−0.00467102	−	0.0143759i	−0.953365	+	0.301820i	$0.902406\pi$
$744$	−228.118	+	313.978i	−0.306610	+	0.422013i
$745$		0			0
$746$	45.5732	−	140.260i	0.0610901	−	0.188016i
$747$	1560.65			2.08923
$748$	−110.560	−	53.6373i	−0.147808	−	0.0717076i
$749$	−162.078			−0.216393
$750$		0			0
$751$	−700.813	+	509.171i	−0.933174	+	0.677990i	−0.946768	−	0.321917i	$-0.895673\pi$
$751$	−700.813	+	509.171i	−0.933174	+	0.677990i	0.0135942	+	0.999908i	$0.495673\pi$
$752$	34.4252	−	47.3822i	0.0457782	−	0.0630083i
$753$	−1664.72	+	540.902i	−2.21079	+	0.718329i
$754$	67.1335	−	21.8130i	0.0890365	−	0.0289297i
$755$		0			0
$756$	1037.61	+	1428.15i	1.37250	+	1.88909i
$757$	−117.605	−	38.2121i	−0.155356	−	0.0504783i	0.230306	−	0.973118i	$-0.426027\pi$
$757$	−117.605	−	38.2121i	−0.155356	−	0.0504783i	−0.385663	+	0.922640i	$0.626027\pi$
$758$	−24.9934			−0.0329728
$759$	−324.299	−	606.845i	−0.427271	−	0.799532i
$760$		0			0
$761$	627.999	+	204.049i	0.825228	+	0.268133i	0.691034	−	0.722822i	$-0.257155\pi$
$761$	627.999	+	204.049i	0.825228	+	0.268133i	0.134194	+	0.990955i	$0.457155\pi$
$762$	99.7698	+	137.321i	0.130932	+	0.180212i
$763$	931.931	−	1282.69i	1.22140	−	1.68112i
$764$	90.6160	+	278.887i	0.118607	+	0.365036i
$765$		0			0
$766$	130.611	−	179.770i	0.170510	−	0.234687i
$767$	201.181	−	146.167i	0.262296	−	0.190569i
$768$	975.071	+	316.820i	1.26962	+	0.412526i
$769$		−	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
$772$	−458.103	+	1409.90i	−0.593398	+	1.82629i
$773$	97.8922	+	134.737i	0.126639	+	0.174304i	0.867629	−	0.497213i	$-0.165643\pi$
$773$	97.8922	+	134.737i	0.126639	+	0.174304i	−0.740989	+	0.671517i	$0.765643\pi$
$774$	−125.019	−	90.8315i	−0.161523	−	0.117353i
$775$		0			0
$776$	153.185	−	49.7729i	0.197404	−	0.0641404i
$777$	838.988	+	609.560i	1.07978	+	0.784505i
$778$	58.9297	−	42.8149i	0.0757451	−	0.0550320i
$779$	−264.565	+	814.247i	−0.339621	+	1.04525i
$780$		0			0
$781$	−65.0365	+	11.6083i	−0.0832734	+	0.0148634i
$782$		−	10.5596i		−	0.0135034i
$783$	659.249	−	2028.96i	0.841953	−	2.59126i
$784$	−641.335	+	465.957i	−0.818030	+	0.594333i
$785$		0			0
$786$	−23.6717	−	72.8539i	−0.0301166	−	0.0926894i
$787$	−107.043	−	329.445i	−0.136014	−	0.418609i	0.859732	−	0.510745i	$-0.170630\pi$
$787$	−107.043	−	329.445i	−0.136014	−	0.418609i	−0.995746	+	0.0921365i	$0.970630\pi$
$788$	289.190	+	210.108i	0.366992	+	0.266635i
$789$	1289.14	+	1774.34i	1.63389	+	2.24885i
$790$		0			0
$791$		−	323.556i		−	0.409047i
$792$	−460.822	+	82.2517i	−0.581846	+	0.103853i
$793$			161.167i			0.203236i
$794$	102.840	+	33.4149i	0.129522	+	0.0420843i
$795$		0			0
$796$	−75.9289	−	55.1656i	−0.0953880	−	0.0693035i
$797$	42.8487	−	13.9224i	0.0537625	−	0.0174685i	−0.282012	−	0.959411i	$-0.591002\pi$
$797$	42.8487	−	13.9224i	0.0537625	−	0.0174685i	0.335775	+	0.941942i	$0.391002\pi$
$798$	−105.084	−	323.417i	−0.131685	−	0.405284i
$799$	6.60890	−	9.09636i	0.00827146	−	0.0113847i
$800$		0			0
$801$	−646.683	+	1990.28i	−0.807344	+	2.48475i
$802$	78.0690			0.0973429
$803$	−998.082	+	1037.89i	−1.24294	+	1.29252i
$804$	1818.08			2.26130
$805$		0			0
$806$	37.3063	−	27.1046i	0.0462857	−	0.0336285i
$807$	−1515.29	+	2085.62i	−1.87769	+	2.58441i
$808$	29.6644	−	9.63856i	0.0367134	−	0.0119289i
$809$	1187.16	−	385.731i	1.46744	−	0.476800i	0.537106	−	0.843515i	$-0.319518\pi$
$809$	1187.16	−	385.731i	1.46744	−	0.476800i	0.930333	+	0.366715i	$0.119518\pi$
$810$		0			0
$811$	−62.7425	−	86.3577i	−0.0773644	−	0.106483i	0.768581	−	0.639753i	$-0.220963\pi$
$811$	−62.7425	−	86.3577i	−0.0773644	−	0.106483i	−0.845945	+	0.533270i	$0.820963\pi$
$812$	1793.60	+	582.776i	2.20887	+	0.717704i
$813$	1212.41			1.49128
$814$	−58.7518	+	31.3971i	−0.0721767	+	0.0385713i
$815$		0			0
$816$	209.098	+	67.9401i	0.256248	+	0.0832599i
$817$	−360.685	−	496.440i	−0.441475	−	0.607638i
$818$	−49.2652	+	67.8077i	−0.0602264	+	0.0828945i
$819$	−267.568	−	823.491i	−0.326701	−	1.00548i
$820$		0			0
$821$	−361.534	+	497.608i	−0.440358	+	0.606100i	−0.970292	−	0.241939i	$-0.922217\pi$
$821$	−361.534	+	497.608i	−0.440358	+	0.606100i	0.529934	+	0.848039i	$0.322217\pi$
$822$	95.6547	−	69.4972i	0.116368	−	0.0845465i
$823$	−363.528	−	118.117i	−0.441711	−	0.143521i	0.0797139	−	0.996818i	$-0.474599\pi$
$823$	−363.528	−	118.117i	−0.441711	−	0.143521i	−0.521425	+	0.853297i	$0.674599\pi$
$824$		−	272.386i		−	0.330566i
$825$		0			0
$826$	−158.006			−0.191291
$827$	295.494	−	909.438i	0.357309	−	1.09968i	−0.597350	−	0.801981i	$-0.703780\pi$
$827$	295.494	−	909.438i	0.357309	−	1.09968i	0.954659	−	0.297703i	$-0.0962205\pi$
$828$	491.238	+	676.131i	0.593282	+	0.816583i
$829$	−591.020	−	429.401i	−0.712931	−	0.517975i	0.171187	−	0.985239i	$-0.445240\pi$
$829$	−591.020	−	429.401i	−0.712931	−	0.517975i	−0.884118	+	0.467264i	$0.845240\pi$
$830$		0			0
$831$	−667.764	+	216.970i	−0.803566	+	0.261095i
$832$	−216.817	−	157.527i	−0.260598	−	0.189335i
$833$	−123.122	+	89.4537i	−0.147806	+	0.107387i
$834$	−23.4769	+	72.2545i	−0.0281498	+	0.0866361i
$835$		0			0
$836$	−909.809	−	125.921i	−1.08829	−	0.150623i
$837$		−	1393.66i		−	1.66507i
$838$	−4.15181	+	12.7780i	−0.00495443	+	0.0152482i
$839$	−739.591	+	537.345i	−0.881515	+	0.640458i	−0.933652	−	0.358182i	$-0.883397\pi$
$839$	−739.591	+	537.345i	−0.881515	+	0.640458i	0.0521367	+	0.998640i	$0.483397\pi$
$840$		0			0
$841$	−444.409	−	1367.75i	−0.528429	−	1.62634i
$842$	−7.66845	−	23.6010i	−0.00910742	−	0.0280297i
$843$	1264.68	+	918.847i	1.50022	+	1.08997i
$844$	−844.394	−	1162.21i	−1.00047	−	1.37702i
$845$		0			0
$846$		−	21.1638i		−	0.0250163i
$847$	−757.233	−	960.883i	−0.894018	−	1.13445i
$848$		−	938.193i		−	1.10636i
$849$	−52.2888	−	16.9896i	−0.0615887	−	0.0200114i
$850$		0			0
$851$	194.726	+	141.476i	0.228820	+	0.166247i
$852$	115.220	−	37.4371i	0.135234	−	0.0439403i
$853$	−338.270	−	1041.09i	−0.396565	−	1.22050i	−0.927736	−	0.373237i	$-0.878248\pi$
$853$	−338.270	−	1041.09i	−0.396565	−	1.22050i	0.531171	−	0.847265i	$-0.321752\pi$
$854$	60.1920	−	82.8472i	0.0704824	−	0.0970107i
$855$		0			0
$856$	−11.9398	+	36.7470i	−0.0139484	+	0.0429287i
$857$	1161.22			1.35499			0.677494	−	0.735528i	$-0.263066\pi$
$857$	1161.22			1.35499			0.677494	+	0.735528i	$0.263066\pi$
$858$	83.1789	+	11.5123i	0.0969451	+	0.0134176i
$859$	465.631			0.542061			0.271031	−	0.962571i	$-0.412636\pi$
$859$	465.631			0.542061			0.271031	+	0.962571i	$0.412636\pi$
$860$		0			0
$861$	1691.83	−	1229.19i	1.96496	−	1.42763i
$862$	130.095	−	179.061i	0.150922	−	0.207727i
$863$	−738.720	+	240.025i	−0.855990	+	0.278128i	−0.703953	−	0.710247i	$-0.748583\pi$
$863$	−738.720	+	240.025i	−0.855990	+	0.278128i	−0.152037	+	0.988375i	$0.548583\pi$
$864$	602.700	−	195.829i	0.697570	−	0.226654i
$865$		0			0
$866$	−62.1952	−	85.6043i	−0.0718189	−	0.0988502i
$867$	−1378.91	−	448.034i	−1.59043	−	0.516763i
$868$	1232.00			1.41935
$869$	431.442	−	889.313i	0.496480	−	1.02337i
$870$		0			0
$871$	−415.783	−	135.096i	−0.477363	−	0.155105i
$872$	−222.164	−	305.782i	−0.254775	−	0.350668i
$873$	−693.484	+	954.498i	−0.794368	+	1.09335i
$874$	−24.3897	−	75.0637i	−0.0279058	−	0.0858852i
$875$		0			0
$876$	1552.07	−	2136.24i	1.77177	−	2.43863i
$877$	1120.57	−	814.144i	1.27773	−	0.928329i	0.278253	−	0.960508i	$-0.410245\pi$
$877$	1120.57	−	814.144i	1.27773	−	0.928329i	0.999482	+	0.0321793i	$0.0102447\pi$
$878$	20.9290	+	6.80023i	0.0238371	+	0.00774514i
$879$			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	$0.850187\pi$
$882$	−88.5206	+	272.439i	−0.100364	+	0.308887i
$883$	−643.690	−	885.963i	−0.728981	−	1.00336i	−0.999177	−	0.0405507i	$-0.987089\pi$
$883$	−643.690	−	885.963i	−0.728981	−	1.00336i	0.270197	−	0.962805i	$-0.412911\pi$
$884$	−43.8383	−	31.8504i	−0.0495908	−	0.0360299i
$885$		0			0
$886$	108.946	−	35.3987i	0.122964	−	0.0399534i
$887$	716.448	+	520.530i	0.807720	+	0.586843i	0.913169	−	0.407582i	$-0.133628\pi$
$887$	716.448	+	520.530i	0.807720	+	0.586843i	−0.105449	+	0.994425i	$0.533628\pi$
$888$	200.007	−	145.314i	0.225233	−	0.163642i
$889$	336.974	−	1037.10i	0.379048	−	1.16659i
$890$		0			0
$891$	547.567	−	569.407i	0.614554	−	0.639065i
$892$			692.520i			0.776368i
$893$	25.9697	−	79.9265i	0.0290814	−	0.0895033i
$894$	153.421	−	111.467i	0.171611	−	0.124683i
$895$		0			0
$896$	229.852	+	707.411i	0.256531	+	0.789521i
$897$	−93.7583	−	288.558i	−0.104524	−	0.321693i
$898$	27.6735	+	20.1060i	0.0308168	+	0.0223897i
$899$	−875.145	−	1204.53i	−0.973465	−	1.33986i
$900$		0			0
$901$		−	180.113i		−	0.199903i
$902$	23.6034	+	132.240i	0.0261678	+	0.146607i
$903$			1498.85i			1.65986i
$904$	−73.3577	−	23.8354i	−0.0811479	−	0.0263666i
$905$		0			0
$906$	98.3650	+	71.4664i	0.108571	+	0.0788812i
$907$	−297.496	+	96.6622i	−0.327999	+	0.106573i	−0.468388	−	0.883523i	$-0.655165\pi$
$907$	−297.496	+	96.6622i	−0.327999	+	0.106573i	0.140388	+	0.990097i	$0.455165\pi$
$908$	−22.3343	−	68.7378i	−0.0245972	−	0.0757025i
$909$	−134.294	+	184.839i	−0.147738	+	0.203344i
$910$		0			0
$911$	−140.671	+	432.942i	−0.154414	+	0.475238i	−0.998101	−	0.0615976i	$-0.980380\pi$
$911$	−140.671	+	432.942i	−0.154414	+	0.475238i	0.843687	+	0.536836i	$0.180380\pi$
$912$	1643.30			1.80187
$913$	957.216	−	170.853i	1.04843	−	0.187133i
$914$	56.9129			0.0622680
$915$		0			0
$916$	422.743	−	307.141i	0.461510	−	0.335306i
$917$	−289.267	+	398.141i	−0.315449	+	0.434178i
$918$	37.0421	−	12.0357i	0.0403509	−	0.0131108i
$919$	−981.783	+	319.001i	−1.06832	+	0.347117i	−0.789832	−	0.613324i	$-0.789832\pi$
$919$	−981.783	+	319.001i	−1.06832	+	0.347117i	−0.278485	+	0.960441i	$0.589832\pi$
$920$		0			0
$921$	338.284	+	465.607i	0.367300	+	0.505545i
$922$	−162.327	−	52.7431i	−0.176059	−	0.0572051i
$923$	−29.1318			−0.0315621
$924$	1617.08	+	1555.06i	1.75008	+	1.68296i
$925$		0			0
$926$	−188.038	−	61.0973i	−0.203065	−	0.0659798i
$927$	1172.76	+	1614.17i	1.26512	+	1.74129i
$928$	397.939	−	547.717i	0.428814	−	0.590212i
$929$	431.640	+	1328.45i	0.464629	+	1.42998i	0.859449	+	0.511222i	$0.170807\pi$
$929$	431.640	+	1328.45i	0.464629	+	1.42998i	−0.394820	+	0.918758i	$0.629193\pi$
$930$		0			0
$931$	−668.609	+	920.262i	−0.718162	+	0.988466i
$932$	139.184	−	101.123i	0.149339	−	0.108501i
$933$	1989.21	+	646.332i	2.13205	+	0.692746i
$934$			274.470i			0.293865i
$935$		0			0
$936$	−206.416			−0.220530
$937$	370.868	−	1141.42i	0.395804	−	1.21816i	−0.532530	−	0.846411i	$-0.678759\pi$
$937$	370.868	−	1141.42i	0.395804	−	1.21816i	0.928334	−	0.371748i	$-0.121241\pi$
$938$	163.277	+	224.731i	0.174069	+	0.239586i
$939$	709.058	+	515.161i	0.755120	+	0.548627i
$940$		0			0
$941$	29.9217	−	9.72215i	0.0317978	−	0.0103317i	−0.293075	−	0.956089i	$-0.594679\pi$
$941$	29.9217	−	9.72215i	0.0317978	−	0.0103317i	0.324873	+	0.945758i	$0.394679\pi$
$942$	−69.0133	−	50.1411i	−0.0732625	−	0.0532283i
$943$	392.667	−	285.289i	0.416401	−	0.302533i
$944$	235.949	−	726.177i	0.249946	−	0.769255i
$945$		0			0
$946$	−86.6233	−	42.0245i	−0.0915680	−	0.0444233i
$947$			540.682i			0.570942i	0.958387	+	0.285471i	$0.0921501\pi$
$947$			540.682i			0.570942i	−0.958387	+	0.285471i	$0.907850\pi$
$948$	−560.127	+	1723.89i	−0.590851	+	1.81845i
$949$	−513.685	+	373.214i	−0.541291	+	0.393271i
$950$		0			0
$951$	−616.304	−	1896.79i	−0.648059	−	1.99452i
$952$	21.5322	+	66.2692i	0.0226178	+	0.0696105i
$953$	−462.279	−	335.865i	−0.485077	−	0.352429i	0.318211	−	0.948020i	$-0.396918\pi$
$953$	−462.279	−	335.865i	−0.485077	−	0.352429i	−0.803288	+	0.595591i	$0.796918\pi$
$954$	−199.272	−	274.274i	−0.208880	−	0.287499i
$955$		0			0
$956$		−	646.388i		−	0.676138i
$957$	371.705	−	2685.66i	0.388407	−	2.80633i
$958$		−	141.601i		−	0.147809i
$959$	−722.418	−	234.728i	−0.753303	−	0.244763i
$960$		0			0
$961$	−9.41808	−	6.84263i	−0.00980029	−	0.00712033i
$962$	−27.9369	+	9.07724i	−0.0290404	+	0.00943580i
$963$	−87.4590	−	269.171i	−0.0908193	−	0.279513i
$964$	157.077	−	216.198i	0.162943	−	0.224272i
$965$		0			0
$966$	−59.5738	+	183.349i	−0.0616705	+	0.189802i
$967$	1228.33			1.27025			0.635125	−	0.772410i	$-0.280949\pi$
$967$	1228.33			1.27025			0.635125	+	0.772410i	$0.280949\pi$
$968$	−273.638	+	100.897i	−0.282684	+	0.104233i
$969$	315.479			0.325571
$970$		0			0
$971$	−1282.98	+	932.137i	−1.32129	+	0.959976i	−0.321379	+	0.946951i	$0.604146\pi$
$971$	−1282.98	+	932.137i	−1.32129	+	0.959976i	−0.999915	+	0.0130253i	$0.995854\pi$
$972$	72.1291	−	99.2772i	0.0742069	−	0.102137i
$973$	464.193	−	150.825i	0.477074	−	0.155011i
$974$	9.55237	−	3.10375i	0.00980736	−	0.00318660i
$975$		0			0
$976$	290.871	+	400.350i	0.298024	+	0.410194i
$977$	−895.345	−	290.915i	−0.916422	−	0.297764i	−0.187424	−	0.982279i	$-0.560014\pi$
$977$	−895.345	−	290.915i	−0.916422	−	0.297764i	−0.728998	+	0.684515i	$0.760014\pi$
$978$	319.713			0.326905
$979$	−178.752	+	1291.52i	−0.182586	+	1.31923i
$980$		0			0
$981$	2633.10	+	855.547i	2.68410	+	0.872117i
$982$	142.966	+	196.775i	0.145586	+	0.200382i
$983$	−410.154	+	564.528i	−0.417247	+	0.574291i	−0.964967	−	0.262370i	$-0.915496\pi$
$983$	−410.154	+	564.528i	−0.417247	+	0.574291i	0.547720	+	0.836662i	$0.315496\pi$
$984$	−154.053	−	474.127i	−0.156558	−	0.481837i
$985$		0			0
$986$	24.4574	−	33.6628i	0.0248047	−	0.0341408i
$987$	−166.070	+	120.657i	−0.168257	+	0.122246i
$988$	−385.191	−	125.156i	−0.389870	−	0.126676i
$989$			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	$0.292542\pi$
$992$	136.670	−	420.626i	0.137772	−	0.424018i
$993$	−361.021	−	496.903i	−0.363566	−	0.500406i
$994$	14.9751	+	10.8800i	0.0150655	+	0.0109457i
$995$		0			0
$996$	−1695.82	+	551.004i	−1.70263	+	0.553217i
$997$	655.602	+	476.323i	0.657575	+	0.477756i	0.865843	−	0.500316i	$-0.166783\pi$
$997$	655.602	+	476.323i	0.657575	+	0.477756i	−0.208268	+	0.978072i	$0.566783\pi$
$998$	146.262	−	106.265i	0.146555	−	0.106478i
$999$	−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.q.f.24.4		24
5.2	odd	4		55.3.i.d.46.2	yes	12
5.3	odd	4		275.3.x.f.101.2		12
5.4	even	2	inner	275.3.q.f.24.3		24
11.6	odd	10	inner	275.3.q.f.149.3		24
55.7	even	20		605.3.c.d.241.5		12
55.17	even	20		55.3.i.d.6.2	✓	12
55.28	even	20		275.3.x.f.226.2		12
55.37	odd	20		605.3.c.d.241.8		12
55.39	odd	10	inner	275.3.q.f.149.4		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.3.i.d.6.2	✓	12	55.17	even	20
55.3.i.d.46.2	yes	12	5.2	odd	4
275.3.q.f.24.3		24	5.4	even	2	inner
275.3.q.f.24.4		24	1.1	even	1	trivial
275.3.q.f.149.3		24	11.6	odd	10	inner
275.3.q.f.149.4		24	55.39	odd	10	inner
275.3.x.f.101.2		12	5.3	odd	4
275.3.x.f.226.2		12	55.28	even	20
605.3.c.d.241.5		12	55.7	even	20
605.3.c.d.241.8		12	55.37	odd	20

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.0941972 - 0.289909i) q^{2} +(-3.03467 - 4.17687i) q^{3} +(3.16089 + 2.29652i) q^{4} +(-1.49677 + 0.486330i) q^{6} +(8.17974 + 5.94293i) q^{7} +(1.94998 - 1.41674i) q^{8} +(-5.45583 + 16.7913i) q^{9} +(-1.50807 + 10.8961i) q^{11} -20.1718i q^{12} +(-1.49891 + 4.61316i) q^{13} +(2.49342 - 1.81157i) q^{14} +(4.60237 + 14.1646i) q^{16} +(0.883556 + 2.71930i) q^{17} +(4.35403 + 3.16339i) q^{18} +(12.5616 + 17.2895i) q^{19} -52.2005i q^{21} +(3.01683 + 1.46359i) q^{22} -12.1155i q^{23} +(-11.8351 - 3.84545i) q^{24} +(1.19620 + 0.869094i) q^{26} +(42.4999 - 13.8091i) q^{27} +(12.2072 + 37.5699i) q^{28} +(28.0610 - 38.6227i) q^{29} +(9.63737 - 29.6608i) q^{31} +14.1812 q^{32} +(50.0882 - 26.7672i) q^{33} +0.871580 q^{34} +(-55.8070 + 40.5461i) q^{36} +(-11.6773 + 16.0724i) q^{37} +(6.19566 - 2.01309i) q^{38} +(23.8172 - 7.73869i) q^{39} +(23.5474 + 32.4102i) q^{41} +(-15.1334 - 4.91714i) q^{42} -28.7133 q^{43} +(-29.7901 + 30.9782i) q^{44} +(-3.51240 - 1.14125i) q^{46} +(-2.31141 - 3.18139i) q^{47} +(45.1971 - 62.2085i) q^{48} +(16.4479 + 50.6214i) q^{49} +(8.67687 - 11.9427i) q^{51} +(-15.3321 + 11.1394i) q^{52} +(-59.9100 - 19.4659i) q^{53} -13.6219i q^{54} +24.3699 q^{56} +(34.0958 - 104.936i) q^{57} +(-8.55381 - 11.7733i) q^{58} +(-41.4758 - 30.1339i) q^{59} +(31.6001 - 10.2675i) q^{61} +(-7.69112 - 5.58793i) q^{62} +(-144.417 + 104.925i) q^{63} +(-17.0737 + 52.5473i) q^{64} +(-3.04189 - 17.0424i) q^{66} +90.1298i q^{67} +(-3.45212 + 10.6245i) q^{68} +(-50.6049 + 36.7666i) q^{69} +(1.85591 + 5.71191i) q^{71} +(13.1502 + 40.4722i) q^{72} +(105.902 + 76.9424i) q^{73} +(3.55957 + 4.89933i) q^{74} +83.4983i q^{76} +(-77.0905 + 80.1652i) q^{77} -7.63380i q^{78} +(-85.4604 - 27.7678i) q^{79} +(-58.1000 - 42.2121i) q^{81} +(11.6141 - 3.77365i) q^{82} +(-27.3155 - 84.0686i) q^{83} +(119.880 - 165.000i) q^{84} +(-2.70472 + 8.32426i) q^{86} -246.478 q^{87} +(12.4963 + 23.3837i) q^{88} +118.531 q^{89} +(-39.6764 + 28.8266i) q^{91} +(27.8236 - 38.2959i) q^{92} +(-153.135 + 49.7567i) q^{93} +(-1.14004 + 0.370422i) q^{94} +(-43.0353 - 59.2330i) q^{96} +(63.5544 + 20.6501i) q^{97} +16.2250 q^{98} +(-174.733 - 84.7699i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 26 q^{4} + 40 q^{6} - 8 q^{9} + 24 q^{11} + 120 q^{14} - 86 q^{16} + 160 q^{19} - 420 q^{24} - 240 q^{26} - 10 q^{29} - 92 q^{31} - 20 q^{34} - 78 q^{36} + 570 q^{39} + 460 q^{41} - 976 q^{44} + 410 q^{46}+ \cdots - 1338 q^{99}+O(q^{100}) \) 24 * q - 26 * q^4 + 40 * q^6 - 8 * q^9 + 24 * q^11 + 120 * q^14 - 86 * q^16 + 160 * q^19 - 420 * q^24 - 240 * q^26 - 10 * q^29 - 92 * q^31 - 20 * q^34 - 78 * q^36 + 570 * q^39 + 460 * q^41 - 976 * q^44 + 410 * q^46 + 424 * q^49 + 720 * q^51 - 820 * q^56 + 148 * q^59 - 580 * q^61 + 14 * q^64 + 370 * q^66 + 146 * q^69 - 552 * q^71 + 200 * q^74 - 470 * q^79 - 60 * q^81 + 1160 * q^84 - 960 * q^86 + 228 * q^89 + 320 * q^91 - 750 * q^94 + 530 * q^96 - 1338 * q^99

Introduction

L-functions

Modular forms

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