LMFDB - Embedded newform 52.4.h.a.17.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [52,4,Mod(17,52)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(52, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 1]))

N = Newforms(chi, 4, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("52.17");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 52 = 2^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	52.h (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$3.06809932030$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 51x^{6} - 224x^{5} + 2520x^{4} - 5712x^{3} + 16675x^{2} + 9072x + 6561 $ x^8 + 51x^6 - 224x^5 + 2520x^4 - 5712x^3 + 16675x^2 + 9072x + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{6}\cdot 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			17.4
Root			$-0.287051 + 0.497187i$ of defining polynomial
Character	$\chi$	$=$	52.17
Dual form			52.4.h.a.49.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(4.89420 - 8.47701i) q^{3} -2.49640i q^{5} +(-15.5619 + 8.98467i) q^{7} +(-34.4065 - 59.5937i) q^{9} +O(q^{10})$	\(q+(4.89420 - 8.47701i) q^{3} -2.49640i q^{5} +(-15.5619 + 8.98467i) q^{7} +(-34.4065 - 59.5937i) q^{9} +(49.6032 + 28.6384i) q^{11} +(46.6395 - 4.66469i) q^{13} +(-21.1620 - 12.2179i) q^{15} +(-8.75292 - 15.1605i) q^{17} +(19.1586 - 11.0612i) q^{19} +175.891i q^{21} +(-65.5963 + 113.616i) q^{23} +118.768 q^{25} -409.282 q^{27} +(-37.1264 + 64.3048i) q^{29} +110.463i q^{31} +(485.537 - 280.325i) q^{33} +(22.4294 + 38.8488i) q^{35} +(209.104 + 120.726i) q^{37} +(188.720 - 418.193i) q^{39} +(-369.537 - 213.352i) q^{41} +(-104.148 - 180.390i) q^{43} +(-148.770 + 85.8924i) q^{45} +158.624i q^{47} +(-10.0516 + 17.4098i) q^{49} -171.354 q^{51} +47.9103 q^{53} +(71.4931 - 123.830i) q^{55} -216.544i q^{57} +(-382.291 + 220.716i) q^{59} +(-434.699 - 752.921i) q^{61} +(1070.86 + 618.261i) q^{63} +(-11.6449 - 116.431i) q^{65} +(693.726 + 400.523i) q^{67} +(642.084 + 1112.12i) q^{69} +(-773.901 + 446.812i) q^{71} -413.180i q^{73} +(581.275 - 1006.80i) q^{75} -1029.23 q^{77} -246.527 q^{79} +(-1074.13 + 1860.46i) q^{81} -333.857i q^{83} +(-37.8467 + 21.8508i) q^{85} +(363.408 + 629.441i) q^{87} +(-328.376 - 189.588i) q^{89} +(-683.888 + 491.632i) q^{91} +(936.399 + 540.630i) q^{93} +(-27.6133 - 47.8276i) q^{95} +(815.158 - 470.632i) q^{97} -3941.39i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 36 q^{7} - 70 q^{9}+O(q^{10}) $ 8 * q - 36 * q^7 - 70 * q^9	$ 8 q - 36 q^{7} - 70 q^{9} + 72 q^{11} + 62 q^{13} + 96 q^{15} + 88 q^{17} - 144 q^{19} - 20 q^{23} - 84 q^{25} - 432 q^{27} - 484 q^{29} + 1038 q^{33} + 40 q^{35} + 996 q^{37} - 236 q^{39} + 156 q^{41} + 504 q^{43} - 1530 q^{45} + 922 q^{49} - 1808 q^{51} - 1164 q^{53} - 1128 q^{55} + 600 q^{59} - 1224 q^{61} + 6480 q^{63} + 670 q^{65} + 960 q^{67} + 1738 q^{69} - 2964 q^{71} + 1448 q^{75} - 3972 q^{77} - 3968 q^{79} - 4132 q^{81} + 3870 q^{85} - 1660 q^{87} + 5430 q^{89} - 1720 q^{91} + 3324 q^{93} + 2400 q^{95} - 3042 q^{97}+O(q^{100}) $ 8 * q - 36 * q^7 - 70 * q^9 + 72 * q^11 + 62 * q^13 + 96 * q^15 + 88 * q^17 - 144 * q^19 - 20 * q^23 - 84 * q^25 - 432 * q^27 - 484 * q^29 + 1038 * q^33 + 40 * q^35 + 996 * q^37 - 236 * q^39 + 156 * q^41 + 504 * q^43 - 1530 * q^45 + 922 * q^49 - 1808 * q^51 - 1164 * q^53 - 1128 * q^55 + 600 * q^59 - 1224 * q^61 + 6480 * q^63 + 670 * q^65 + 960 * q^67 + 1738 * q^69 - 2964 * q^71 + 1448 * q^75 - 3972 * q^77 - 3968 * q^79 - 4132 * q^81 + 3870 * q^85 - 1660 * q^87 + 5430 * q^89 - 1720 * q^91 + 3324 * q^93 + 2400 * q^95 - 3042 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/52\mathbb{Z}\right)^\times$.

$n$	$27$	$41$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$

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			0
$2$		0			0
$3$	4.89420	−	8.47701i	0.941890	−	1.63140i	0.180028	−	0.983661i	$-0.442381\pi$
$3$	4.89420	−	8.47701i	0.941890	−	1.63140i	0.761862	−	0.647740i	$-0.224286\pi$
$4$		0			0
$5$		−	2.49640i		−	0.223285i	−0.993748	−	0.111643i	$-0.964389\pi$
$5$		−	2.49640i		−	0.223285i	0.993748	−	0.111643i	$-0.0356112\pi$
$6$		0			0
$7$	−15.5619	+	8.98467i	−0.840264	+	0.485126i	−0.857354	−	0.514728i	$-0.827893\pi$
$7$	−15.5619	+	8.98467i	−0.840264	+	0.485126i	0.0170903	+	0.999854i	$0.494560\pi$
$8$		0			0
$9$	−34.4065	−	59.5937i	−1.27431	−	2.20718i
$10$		0			0
$11$	49.6032	+	28.6384i	1.35963	+	0.784983i	0.989574	−	0.144026i	$-0.0460050\pi$
$11$	49.6032	+	28.6384i	1.35963	+	0.784983i	0.370057	+	0.929009i	$0.379338\pi$
$12$		0			0
$13$	46.6395	−	4.66469i	0.995036	−	0.0995194i
$13$	46.6395	−	4.66469i	0.995036	−	0.0995194i
$14$		0			0
$15$	−21.1620	−	12.2179i	−0.364268	−	0.210310i
$16$		0			0
$17$	−8.75292	−	15.1605i	−0.124876	−	0.216292i	0.796808	−	0.604232i	$-0.206520\pi$
$17$	−8.75292	−	15.1605i	−0.124876	−	0.216292i	−0.921685	+	0.387940i	$0.873187\pi$
$18$		0			0
$19$	19.1586	−	11.0612i	0.231331	−	0.133559i	−0.379855	−	0.925046i	$-0.624026\pi$
$19$	19.1586	−	11.0612i	0.231331	−	0.133559i	0.611186	+	0.791487i	$0.290693\pi$
$20$		0			0
$21$			175.891i			1.82774i
$22$		0			0
$23$	−65.5963	+	113.616i	−0.594686	+	1.03003i	0.398905	+	0.916992i	$0.369390\pi$
$23$	−65.5963	+	113.616i	−0.594686	+	1.03003i	−0.993591	+	0.113034i	$0.963943\pi$
$24$		0			0
$25$	118.768			0.950144
$26$		0			0
$27$	−409.282			−2.91727
$28$		0			0
$29$	−37.1264	+	64.3048i	−0.237731	+	0.411762i	−0.960063	−	0.279785i	$-0.909737\pi$
$29$	−37.1264	+	64.3048i	−0.237731	+	0.411762i	0.722332	+	0.691546i	$0.243070\pi$
$30$		0			0
$31$			110.463i			0.639994i	0.947419	+	0.319997i	$0.103682\pi$
$31$			110.463i			0.639994i	−0.947419	+	0.319997i	$0.896318\pi$
$32$		0			0
$33$	485.537	−	280.325i	2.56124	−	1.47874i
$34$		0			0
$35$	22.4294	+	38.8488i	0.108322	+	0.187618i
$36$		0			0
$37$	209.104	+	120.726i	0.929093	+	0.536412i	0.886525	−	0.462681i	$-0.153113\pi$
$37$	209.104	+	120.726i	0.929093	+	0.536412i	0.0425684	+	0.999094i	$0.486446\pi$
$38$		0			0
$39$	188.720	−	418.193i	0.774858	−	1.71704i
$40$		0			0
$41$	−369.537	−	213.352i	−1.40761	−	0.812683i	−0.412451	−	0.910980i	$-0.635327\pi$
$41$	−369.537	−	213.352i	−1.40761	−	0.812683i	−0.995157	+	0.0982971i	$0.968660\pi$
$42$		0			0
$43$	−104.148	−	180.390i	−0.369359	−	0.639749i	0.620106	−	0.784518i	$-0.287089\pi$
$43$	−104.148	−	180.390i	−0.369359	−	0.639749i	−0.989465	+	0.144769i	$0.953756\pi$
$44$		0			0
$45$	−148.770	+	85.8924i	−0.492829	+	0.284535i
$46$		0			0
$47$			158.624i			0.492292i	0.969233	+	0.246146i	$0.0791642\pi$
$47$			158.624i			0.492292i	−0.969233	+	0.246146i	$0.920836\pi$
$48$		0			0
$49$	−10.0516	+	17.4098i	−0.0293048	+	0.0507574i
$50$		0			0
$51$	−171.354			−0.470478
$52$		0			0
$53$	47.9103			0.124170			0.0620848	−	0.998071i	$-0.480225\pi$
$53$	47.9103			0.124170			0.0620848	+	0.998071i	$0.480225\pi$
$54$		0			0
$55$	71.4931	−	123.830i	0.175275	−	0.303585i
$56$		0			0
$57$		−	216.544i		−	0.503191i
$58$		0			0
$59$	−382.291	+	220.716i	−0.843561	+	0.487030i	−0.858473	−	0.512859i	$-0.828586\pi$
$59$	−382.291	+	220.716i	−0.843561	+	0.487030i	0.0149121	+	0.999889i	$0.495253\pi$
$60$		0			0
$61$	−434.699	−	752.921i	−0.912419	−	1.58036i	−0.810637	−	0.585549i	$-0.800879\pi$
$61$	−434.699	−	752.921i	−0.912419	−	1.58036i	−0.101781	−	0.994807i	$-0.532454\pi$
$62$		0			0
$63$	1070.86	+	618.261i	2.14152	+	1.23641i
$64$		0			0
$65$	−11.6449	−	116.431i	−0.0222212	−	0.222177i
$66$		0			0
$67$	693.726	+	400.523i	1.26496	+	0.730323i	0.974029	−	0.226422i	$-0.0727029\pi$
$67$	693.726	+	400.523i	1.26496	+	0.730323i	0.290927	+	0.956745i	$0.406036\pi$
$68$		0			0
$69$	642.084	+	1112.12i	1.12026	+	1.94034i
$70$		0			0
$71$	−773.901	+	446.812i	−1.29359	+	0.746857i	−0.979289	−	0.202465i	$-0.935105\pi$
$71$	−773.901	+	446.812i	−1.29359	+	0.746857i	−0.314305	+	0.949322i	$0.601771\pi$
$72$		0			0
$73$		−	413.180i		−	0.662452i	−0.943551	−	0.331226i	$-0.892538\pi$
$73$		−	413.180i		−	0.662452i	0.943551	−	0.331226i	$-0.107462\pi$
$74$		0			0
$75$	581.275	−	1006.80i	0.894931	−	1.55007i
$76$		0			0
$77$	−1029.23			−1.52326
$78$		0			0
$79$	−246.527			−0.351094			−0.175547	−	0.984471i	$-0.556169\pi$
$79$	−246.527			−0.351094			−0.175547	+	0.984471i	$0.556169\pi$
$80$		0			0
$81$	−1074.13	+	1860.46i	−1.47344	+	2.55206i
$82$		0			0
$83$		−	333.857i		−	0.441513i	−0.975329	−	0.220756i	$-0.929147\pi$
$83$		−	333.857i		−	0.441513i	0.975329	−	0.220756i	$-0.0708526\pi$
$84$		0			0
$85$	−37.8467	+	21.8508i	−0.0482947	+	0.0278830i
$86$		0			0
$87$	363.408	+	629.441i	0.447833	+	0.775669i
$88$		0			0
$89$	−328.376	−	189.588i	−0.391098	−	0.225801i	0.291538	−	0.956559i	$-0.405833\pi$
$89$	−328.376	−	189.588i	−0.391098	−	0.225801i	−0.682636	+	0.730759i	$0.739166\pi$
$90$		0			0
$91$	−683.888	+	491.632i	−0.787813	+	0.566341i
$92$		0			0
$93$	936.399	+	540.630i	1.04409	+	0.602804i
$94$		0			0
$95$	−27.6133	−	47.8276i	−0.0298217	−	0.0516527i
$96$		0			0
$97$	815.158	−	470.632i	0.853265	−	0.492633i	−0.00848590	−	0.999964i	$-0.502701\pi$
$97$	815.158	−	470.632i	0.853265	−	0.492633i	0.861751	+	0.507331i	$0.169368\pi$
$98$		0			0
$99$		−	3941.39i		−	4.00126i
$100$		0			0
$101$	192.975	−	334.242i	0.190116	−	0.329290i	−0.755173	−	0.655526i	$-0.772447\pi$
$101$	192.975	−	334.242i	0.190116	−	0.329290i	0.945288	+	0.326236i	$0.105780\pi$
$102$		0			0
$103$	395.674			0.378514			0.189257	−	0.981928i	$-0.439392\pi$
$103$	395.674			0.378514			0.189257	+	0.981928i	$0.439392\pi$
$104$		0			0
$105$	439.095			0.408108
$106$		0			0
$107$	−614.070	+	1063.60i	−0.554807	+	0.960955i	0.443111	+	0.896467i	$0.353875\pi$
$107$	−614.070	+	1063.60i	−0.554807	+	0.960955i	−0.997918	+	0.0644880i	$0.979459\pi$
$108$		0			0
$109$		−	542.176i		−	0.476431i	−0.971212	−	0.238216i	$-0.923438\pi$
$109$		−	542.176i		−	0.476431i	0.971212	−	0.238216i	$-0.0765625\pi$
$110$		0			0
$111$	2046.79	−	1181.72i	1.75021	−	1.01048i
$112$		0			0
$113$	338.706	+	586.655i	0.281971	+	0.488388i	0.971870	−	0.235517i	$-0.0756784\pi$
$113$	338.706	+	586.655i	0.281971	+	0.488388i	−0.689899	+	0.723906i	$0.742345\pi$
$114$		0			0
$115$	283.632	+	163.755i	0.229990	+	0.132785i
$116$		0			0
$117$	−1882.69	−	2618.93i	−1.48764	−	2.06940i
$118$		0			0
$119$	272.424	+	157.284i	0.209858	+	0.121161i
$120$		0			0
$121$	974.820	+	1688.44i	0.732397	+	1.26855i
$122$		0			0
$123$	−3617.17	+	2088.38i	−2.65162	+	1.53092i
$124$		0			0
$125$		−	608.543i		−	0.435438i
$126$		0			0
$127$	635.930	−	1101.46i	0.444328	−	0.769599i	−0.553677	−	0.832731i	$-0.686776\pi$
$127$	635.930	−	1101.46i	0.444328	−	0.769599i	0.998005	+	0.0631327i	$0.0201091\pi$
$128$		0			0
$129$	−2038.89			−1.39158
$130$		0			0
$131$	1249.24			0.833179			0.416589	−	0.909095i	$-0.363225\pi$
$131$	1249.24			0.833179			0.416589	+	0.909095i	$0.363225\pi$
$132$		0			0
$133$	−198.763	+	344.267i	−0.129586	+	0.224449i
$134$		0			0
$135$			1021.73i			0.651383i
$136$		0			0
$137$	−1509.40	+	871.453i	−0.941290	+	0.543454i	−0.890365	−	0.455248i	$-0.849550\pi$
$137$	−1509.40	+	871.453i	−0.941290	+	0.543454i	−0.0509257	+	0.998702i	$0.516217\pi$
$138$		0			0
$139$	−494.442	−	856.398i	−0.301712	−	0.522581i	0.674812	−	0.737990i	$-0.264225\pi$
$139$	−494.442	−	856.398i	−0.301712	−	0.522581i	−0.976524	+	0.215409i	$0.930891\pi$
$140$		0			0
$141$	1344.66	+	776.339i	0.803125	+	0.463685i
$142$		0			0
$143$	2447.06	+	1104.30i	1.43100	+	0.645776i
$144$		0			0
$145$	160.531	+	92.6824i	0.0919403	+	0.0530818i
$146$		0			0
$147$	98.3887	+	170.414i	0.0552038	+	0.0956158i
$148$		0			0
$149$	1469.28	−	848.291i	0.807842	−	0.466408i	−0.0383642	−	0.999264i	$-0.512215\pi$
$149$	1469.28	−	848.291i	0.807842	−	0.466408i	0.846206	+	0.532856i	$0.178881\pi$
$150$		0			0
$151$			2603.11i			1.40290i	0.712719	+	0.701449i	$0.247463\pi$
$151$			2603.11i			1.40290i	−0.712719	+	0.701449i	$0.752537\pi$
$152$		0			0
$153$	−602.314	+	1043.24i	−0.318263	+	0.551247i
$154$		0			0
$155$	275.761			0.142901
$156$		0			0
$157$	−178.988			−0.0909859			−0.0454930	−	0.998965i	$-0.514486\pi$
$157$	−178.988			−0.0909859			−0.0454930	+	0.998965i	$0.514486\pi$
$158$		0			0
$159$	234.483	−	406.136i	0.116954	−	0.202571i
$160$		0			0
$161$		−	2357.44i		−	1.15399i
$162$		0			0
$163$	−1801.51	+	1040.10i	−0.865678	+	0.499799i	−0.865910	−	0.500201i	$-0.833260\pi$
$163$	−1801.51	+	1040.10i	−0.865678	+	0.499799i	0.000231624		1.00000i	$0.499926\pi$
$164$		0			0
$165$	−699.803	−	1212.10i	−0.330180	−	0.571888i
$166$		0			0
$167$	2632.63	+	1519.95i	1.21987	+	0.704295i	0.964891	−	0.262650i	$-0.0845965\pi$
$167$	2632.63	+	1519.95i	1.21987	+	0.704295i	0.254984	+	0.966945i	$0.417930\pi$
$168$		0			0
$169$	2153.48	−	435.117i	0.980192	−	0.198051i
$170$		0			0
$171$	−1318.36	−	761.155i	−0.589576	−	0.340392i
$172$		0			0
$173$	25.8677	+	44.8042i	0.0113681	+	0.0196902i	0.871654	−	0.490123i	$-0.163048\pi$
$173$	25.8677	+	44.8042i	0.0113681	+	0.0196902i	−0.860285	+	0.509813i	$0.829715\pi$
$174$		0			0
$175$	−1848.26	+	1067.09i	−0.798371	+	0.460940i
$176$		0			0
$177$			4320.92i			1.83492i
$178$		0			0
$179$	314.447	−	544.638i	0.131301	−	0.227420i	−0.792877	−	0.609381i	$-0.791418\pi$
$179$	314.447	−	544.638i	0.131301	−	0.227420i	0.924178	+	0.381961i	$0.124751\pi$
$180$		0			0
$181$	−1661.09			−0.682145			−0.341072	−	0.940037i	$-0.610790\pi$
$181$	−1661.09			−0.682145			−0.341072	+	0.940037i	$0.610790\pi$
$182$		0			0
$183$	−8510.03			−3.43759
$184$		0			0
$185$	301.381	−	522.007i	0.119773	−	0.207453i
$186$		0			0
$187$		−	1002.68i		−	0.392103i
$188$		0			0
$189$	6369.20	−	3677.26i	2.45128	−	1.41525i
$190$		0			0
$191$	−958.968	−	1660.98i	−0.363291	−	0.629238i	0.625210	−	0.780457i	$-0.285013\pi$
$191$	−958.968	−	1660.98i	−0.363291	−	0.629238i	−0.988500	+	0.151219i	$0.951680\pi$
$192$		0			0
$193$	200.131	+	115.546i	0.0746413	+	0.0430942i	0.536856	−	0.843674i	$-0.319612\pi$
$193$	200.131	+	115.546i	0.0746413	+	0.0430942i	−0.462215	+	0.886768i	$0.652945\pi$
$194$		0			0
$195$	−1043.98	−	471.123i	−0.383389	−	0.173014i
$196$		0			0
$197$	−1411.98	−	815.208i	−0.510657	−	0.294828i	0.222447	−	0.974945i	$-0.428596\pi$
$197$	−1411.98	−	815.208i	−0.510657	−	0.294828i	−0.733104	+	0.680117i	$0.761929\pi$
$198$		0			0
$199$	−1532.79	−	2654.86i	−0.546011	−	0.945720i	−0.998543	−	0.0539709i	$-0.982812\pi$
$199$	−1532.79	−	2654.86i	−0.546011	−	0.945720i	0.452531	−	0.891749i	$-0.350521\pi$
$200$		0			0
$201$	6790.47	−	3920.48i	2.38290	−	1.37577i
$202$		0			0
$203$		−	1334.27i		−	0.461318i
$204$		0			0
$205$	−532.613	+	922.513i	−0.181460	+	0.314298i
$206$		0			0
$207$	9027.75			3.03127
$208$		0			0
$209$	1267.11			0.419366
$210$		0			0
$211$	1724.90	−	2987.61i	0.562780	−	0.974764i	−0.434472	−	0.900685i	$-0.643065\pi$
$211$	1724.90	−	2987.61i	0.562780	−	0.974764i	0.997252	−	0.0740789i	$-0.0236017\pi$
$212$		0			0
$213$			8747.16i			2.81383i
$214$		0			0
$215$	−450.326	+	259.996i	−0.142846	+	0.0824724i
$216$		0			0
$217$	−992.476	−	1719.02i	−0.310478	−	0.537763i
$218$		0			0
$219$	−3502.53	−	2022.19i	−1.08073	−	0.623957i
$220$		0			0
$221$	−478.950	−	666.248i	−0.145781	−	0.202790i
$222$		0			0
$223$	−2186.26	−	1262.24i	−0.656516	−	0.379040i	0.134432	−	0.990923i	$-0.457079\pi$
$223$	−2186.26	−	1262.24i	−0.656516	−	0.379040i	−0.790948	+	0.611883i	$0.790412\pi$
$224$		0			0
$225$	−4086.39	−	7077.83i	−1.21078	−	2.09713i
$226$		0			0
$227$	998.580	−	576.530i	0.291974	−	0.168571i	−0.346858	−	0.937918i	$-0.612751\pi$
$227$	998.580	−	576.530i	0.291974	−	0.168571i	0.638832	+	0.769347i	$0.279418\pi$
$228$		0			0
$229$			3857.53i			1.11316i	0.830795	+	0.556578i	$0.187886\pi$
$229$			3857.53i			1.11316i	−0.830795	+	0.556578i	$0.812114\pi$
$230$		0			0
$231$	−5037.25	+	8724.77i	−1.43475	+	2.48505i
$232$		0			0
$233$	1018.55			0.286385			0.143192	−	0.989695i	$-0.454263\pi$
$233$	1018.55			0.286385			0.143192	+	0.989695i	$0.454263\pi$
$234$		0			0
$235$	395.990			0.109921
$236$		0			0
$237$	−1206.55	+	2089.81i	−0.330692	+	0.572776i
$238$		0			0
$239$		−	1263.24i		−	0.341893i	−0.985280	−	0.170947i	$-0.945317\pi$
$239$		−	1263.24i		−	0.341893i	0.985280	−	0.170947i	$-0.0546825\pi$
$240$		0			0
$241$	−1790.89	+	1033.97i	−0.478677	+	0.276365i	−0.719865	−	0.694114i	$-0.755796\pi$
$241$	−1790.89	+	1033.97i	−0.478677	+	0.276365i	0.241188	+	0.970478i	$0.422463\pi$
$242$		0			0
$243$	4988.76	+	8640.78i	1.31699	+	2.28110i
$244$		0			0
$245$	43.4619	+	25.0927i	0.0113334	+	0.00654333i
$246$		0			0
$247$	841.950	−	605.259i	0.216891	−	0.155918i
$248$		0			0
$249$	−2830.11	−	1633.96i	−0.720285	−	0.415857i
$250$		0			0
$251$	2563.19	+	4439.58i	0.644570	+	1.11643i	0.984401	+	0.175942i	$0.0562971\pi$
$251$	2563.19	+	4439.58i	0.644570	+	1.11643i	−0.339830	+	0.940487i	$0.610370\pi$
$252$		0			0
$253$	−6507.58	+	3757.15i	−1.61711	+	0.933637i
$254$		0			0
$255$			427.769i			0.105051i
$256$		0			0
$257$	1980.76	−	3430.77i	0.480764	−	0.832707i	−0.518993	−	0.854779i	$-0.673693\pi$
$257$	1980.76	−	3430.77i	0.480764	−	0.832707i	0.999756	+	0.0220714i	$0.00702613\pi$
$258$		0			0
$259$	−4338.73			−1.04091
$260$		0			0
$261$	5109.55			1.21177
$262$		0			0
$263$	3552.31	−	6152.79i	0.832871	−	1.44257i	−0.0628817	−	0.998021i	$-0.520029\pi$
$263$	3552.31	−	6152.79i	0.832871	−	1.44257i	0.895752	−	0.444553i	$-0.146638\pi$
$264$		0			0
$265$		−	119.604i		−	0.0277252i
$266$		0			0
$267$	−3214.28	+	1855.76i	−0.736743	+	0.425359i
$268$		0			0
$269$	−2806.94	−	4861.76i	−0.636216	−	1.10196i	−0.986256	−	0.165223i	$-0.947165\pi$
$269$	−2806.94	−	4861.76i	−0.636216	−	1.10196i	0.350040	−	0.936735i	$-0.386168\pi$
$270$		0			0
$271$	382.095	+	220.603i	0.0856480	+	0.0494489i	0.542212	−	0.840242i	$-0.317587\pi$
$271$	382.095	+	220.603i	0.0856480	+	0.0494489i	−0.456564	+	0.889690i	$0.650920\pi$
$272$		0			0
$273$	820.477	+	8203.47i	0.181896	+	1.81867i
$274$		0			0
$275$	5891.27	+	3401.33i	1.29184	+	0.745847i
$276$		0			0
$277$	2338.44	+	4050.29i	0.507231	+	0.878550i	0.999965	+	0.00837023i	$0.00266436\pi$
$277$	2338.44	+	4050.29i	0.507231	+	0.878550i	−0.492734	+	0.870180i	$0.664002\pi$
$278$		0			0
$279$	6582.92	−	3800.65i	1.41258	−	0.815552i
$280$		0			0
$281$			1253.34i			0.266079i	0.991111	+	0.133040i	$0.0424737\pi$
$281$			1253.34i			0.266079i	−0.991111	+	0.133040i	$0.957526\pi$
$282$		0			0
$283$	2086.08	−	3613.19i	0.438178	−	0.758947i	−0.559371	−	0.828917i	$-0.688957\pi$
$283$	2086.08	−	3613.19i	0.438178	−	0.758947i	0.997549	+	0.0699707i	$0.0222906\pi$
$284$		0			0
$285$	−540.580			−0.112355
$286$		0			0
$287$	7667.59			1.57702
$288$		0			0
$289$	2303.27	−	3989.39i	0.468812	−	0.812006i
$290$		0			0
$291$		−	9213.47i		−	1.85602i
$292$		0			0
$293$	−8468.92	+	4889.53i	−1.68860	+	0.974913i	−0.733007	+	0.680221i	$0.761884\pi$
$293$	−8468.92	+	4889.53i	−1.68860	+	0.974913i	−0.955592	+	0.294692i	$0.904783\pi$
$294$		0			0
$295$	550.996	+	954.354i	0.108747	+	0.188355i
$296$		0			0
$297$	−20301.7	−	11721.2i	−3.96641	−	2.29001i
$298$		0			0
$299$	−2529.39	+	5604.99i	−0.489226	+	1.08410i
$300$		0			0
$301$	3241.48	+	1871.47i	0.620718	+	0.358372i
$302$		0			0
$303$	−1888.91	−	3271.70i	−0.358136	−	0.620310i
$304$		0			0
$305$	−1879.60	+	1085.18i	−0.352870	+	0.203729i
$306$		0			0
$307$			1641.63i			0.305187i	0.988289	+	0.152594i	$0.0487626\pi$
$307$			1641.63i			0.305187i	−0.988289	+	0.152594i	$0.951237\pi$
$308$		0			0
$309$	1936.51	−	3354.13i	0.356519	−	0.617508i
$310$		0			0
$311$	−5900.48			−1.07584			−0.537919	−	0.842996i	$-0.680789\pi$
$311$	−5900.48			−1.07584			−0.537919	+	0.842996i	$0.680789\pi$
$312$		0			0
$313$	5268.10			0.951344			0.475672	−	0.879623i	$-0.342205\pi$
$313$	5268.10			0.951344			0.475672	+	0.879623i	$0.342205\pi$
$314$		0			0
$315$	1543.43	−	2673.30i	0.276071	−	0.478169i
$316$		0			0
$317$		−	20.4536i		−	0.00362395i	−0.999998	−	0.00181197i	$-0.999423\pi$
$317$		−	20.4536i		−	0.00362395i	0.999998	−	0.00181197i	$-0.000576769\pi$
$318$		0			0
$319$	−3683.18	+	2126.48i	−0.646452	+	0.373229i
$320$		0			0
$321$	6010.77	+	10411.0i	1.04514	+	1.81023i
$322$		0			0
$323$	−335.387	−	193.636i	−0.0577754	−	0.0333566i
$324$		0			0
$325$	5539.28	−	554.016i	0.945427	−	0.0945577i
$326$		0			0
$327$	−4596.03	−	2653.52i	−0.777250	−	0.448746i
$328$		0			0
$329$	−1425.19	−	2468.49i	−0.238824	−	0.413655i
$330$		0			0
$331$	5458.06	−	3151.21i	0.906351	−	0.523282i	0.0270955	−	0.999633i	$-0.491374\pi$
$331$	5458.06	−	3151.21i	0.906351	−	0.523282i	0.879255	+	0.476351i	$0.158041\pi$
$332$		0			0
$333$		−	16615.0i		−	2.73423i
$334$		0			0
$335$	999.866	−	1731.82i	0.163070	−	0.282446i
$336$		0			0
$337$	3060.14			0.494648			0.247324	−	0.968933i	$-0.420449\pi$
$337$	3060.14			0.494648			0.247324	+	0.968933i	$0.420449\pi$
$338$		0			0
$339$	6630.78			1.06234
$340$		0			0
$341$	−3163.50	+	5479.34i	−0.502384	+	0.870155i
$342$		0			0
$343$		−	6524.72i		−	1.02712i
$344$		0			0
$345$	2776.30	−	1602.90i	0.433250	−	0.250137i
$346$		0			0
$347$	101.809	+	176.338i	0.0157504	+	0.0272805i	0.873793	−	0.486298i	$-0.161653\pi$
$347$	101.809	+	176.338i	0.0157504	+	0.0272805i	−0.858043	+	0.513578i	$0.828320\pi$
$348$		0			0
$349$	1303.90	+	752.806i	0.199989	+	0.115464i	0.596650	−	0.802501i	$-0.296498\pi$
$349$	1303.90	+	752.806i	0.199989	+	0.115464i	−0.396661	+	0.917965i	$0.629831\pi$
$350$		0			0
$351$	−19088.7	+	1909.17i	−2.90279	+	0.290325i
$352$		0			0
$353$	9641.82	+	5566.71i	1.45377	+	0.839337i	0.998693	−	0.0511134i	$-0.0162770\pi$
$353$	9641.82	+	5566.71i	1.45377	+	0.839337i	0.455081	+	0.890450i	$0.349610\pi$
$354$		0			0
$355$	1115.42	+	1931.97i	0.166762	+	0.288840i
$356$		0			0
$357$	2666.60	−	1539.56i	0.395326	−	0.228241i
$358$		0			0
$359$		−	4176.37i		−	0.613985i	−0.951712	−	0.306992i	$-0.900677\pi$
$359$		−	4176.37i		−	0.613985i	0.951712	−	0.306992i	$-0.0993226\pi$
$360$		0			0
$361$	−3184.80	+	5516.23i	−0.464324	+	0.804233i
$362$		0			0
$363$	19083.9			2.75935
$364$		0			0
$365$	−1031.46			−0.147916
$366$		0			0
$367$	−2240.40	+	3880.49i	−0.318659	+	0.551934i	−0.980209	−	0.197968i	$-0.936566\pi$
$367$	−2240.40	+	3880.49i	−0.318659	+	0.551934i	0.661549	+	0.749902i	$0.269899\pi$
$368$		0			0
$369$			29362.8i			4.14245i
$370$		0			0
$371$	−745.576	+	430.458i	−0.104335	+	0.0602380i
$372$		0			0
$373$	181.930	+	315.111i	0.0252546	+	0.0437422i	0.878376	−	0.477969i	$-0.158627\pi$
$373$	181.930	+	315.111i	0.0252546	+	0.0437422i	−0.853122	+	0.521712i	$0.825294\pi$
$374$		0			0
$375$	−5158.63	−	2978.33i	−0.710374	−	0.410135i
$376$		0			0
$377$	−1431.59	+	3172.32i	−0.195572	+	0.433377i
$378$		0			0
$379$	−8448.46	−	4877.72i	−1.14503	−	0.661086i	−0.197362	−	0.980331i	$-0.563238\pi$
$379$	−8448.46	−	4877.72i	−1.14503	−	0.661086i	−0.947672	+	0.319245i	$0.896571\pi$
$380$		0			0
$381$	−6224.74	−	10781.6i	−0.837016	−	1.44975i
$382$		0			0
$383$	−4548.66	+	2626.17i	−0.606856	+	0.350368i	−0.771734	−	0.635946i	$-0.780610\pi$
$383$	−4548.66	+	2626.17i	−0.606856	+	0.350368i	0.164878	+	0.986314i	$0.447277\pi$
$384$		0			0
$385$			2569.37i			0.340122i
$386$		0			0
$387$	−7166.73	+	12413.1i	−0.941358	+	1.63048i
$388$		0			0
$389$	−11266.0			−1.46841			−0.734205	−	0.678928i	$-0.762445\pi$
$389$	−11266.0			−1.46841			−0.734205	+	0.678928i	$0.762445\pi$
$390$		0			0
$391$	2296.64			0.297048
$392$		0			0
$393$	6114.03	−	10589.8i	0.784763	−	1.35925i
$394$		0			0
$395$			615.431i			0.0783941i
$396$		0			0
$397$	−2599.10	+	1500.59i	−0.328576	+	0.189704i	−0.655209	−	0.755448i	$-0.727419\pi$
$397$	−2599.10	+	1500.59i	−0.328576	+	0.189704i	0.326632	+	0.945151i	$0.394086\pi$
$398$		0			0
$399$	1945.57	+	3369.83i	0.244111	+	0.422813i
$400$		0			0
$401$	−6927.02	−	3999.31i	−0.862640	−	0.498045i	0.00225548	−	0.999997i	$-0.499282\pi$
$401$	−6927.02	−	3999.31i	−0.862640	−	0.498045i	−0.864895	+	0.501952i	$0.832615\pi$
$402$		0			0
$403$	515.277	+	5151.95i	0.0636918	+	0.636817i
$404$		0			0
$405$	4644.45	+	2681.47i	0.569838	+	0.328996i
$406$		0			0
$407$	6914.81	+	11976.8i	0.842149	+	1.45864i
$408$		0			0
$409$	9207.67	−	5316.05i	1.11318	−	0.642694i	0.173528	−	0.984829i	$-0.444483\pi$
$409$	9207.67	−	5316.05i	1.11318	−	0.642694i	0.939651	+	0.342135i	$0.111150\pi$
$410$		0			0
$411$			17060.3i			2.04750i
$412$		0			0
$413$	3966.12	−	6869.52i	0.472542	−	0.818467i
$414$		0			0
$415$	−833.442			−0.0985833
$416$		0			0
$417$	−9679.59			−1.13672
$418$		0			0
$419$	164.769	−	285.389i	0.0192112	−	0.0332748i	−0.856260	−	0.516545i	$-0.827218\pi$
$419$	164.769	−	285.389i	0.0192112	−	0.0332748i	0.875471	+	0.483270i	$0.160551\pi$
$420$		0			0
$421$		−	10594.7i		−	1.22649i	−0.789891	−	0.613247i	$-0.789863\pi$
$421$		−	10594.7i		−	1.22649i	0.789891	−	0.613247i	$-0.210137\pi$
$422$		0			0
$423$	9453.01	−	5457.70i	1.08657	−	0.627334i
$424$		0			0
$425$	−1039.57	−	1800.58i	−0.118650	−	0.205508i
$426$		0			0
$427$	13529.5	+	7811.25i	1.53334	+	0.885277i
$428$		0			0
$429$	21337.5	−	15339.1i	2.40137	−	1.72629i
$430$		0			0
$431$	−11044.8	−	6376.69i	−1.23436	−	0.712655i	−0.266421	−	0.963857i	$-0.585841\pi$
$431$	−11044.8	−	6376.69i	−1.23436	−	0.712655i	−0.967935	+	0.251202i	$0.919174\pi$
$432$		0			0
$433$	−7004.92	−	12132.9i	−0.777448	−	1.34658i	−0.933408	−	0.358816i	$-0.883181\pi$
$433$	−7004.92	−	12132.9i	−0.777448	−	1.34658i	0.155961	−	0.987763i	$-0.450153\pi$
$434$		0			0
$435$	1571.34	−	907.213i	0.173195	−	0.0999943i
$436$		0			0
$437$			2902.30i			0.317703i
$438$		0			0
$439$	3648.09	−	6318.68i	0.396615	−	0.686957i	−0.596691	−	0.802471i	$-0.703518\pi$
$439$	3648.09	−	6318.68i	0.396615	−	0.686957i	0.993306	+	0.115514i	$0.0368515\pi$
$440$		0			0
$441$	1383.35			0.149374
$442$		0			0
$443$	−6098.72			−0.654084			−0.327042	−	0.945010i	$-0.606052\pi$
$443$	−6098.72			−0.654084			−0.327042	+	0.945010i	$0.606052\pi$
$444$		0			0
$445$	−473.288	+	819.758i	−0.0504179	+	0.0873265i
$446$		0			0
$447$		−	16606.8i		−	1.75722i
$448$		0			0
$449$	−9393.12	+	5423.12i	−0.987280	+	0.570006i	−0.904460	−	0.426558i	$-0.859726\pi$
$449$	−9393.12	+	5423.12i	−0.987280	+	0.570006i	−0.0828196	+	0.996565i	$0.526393\pi$
$450$		0			0
$451$	−12220.1	−	21165.9i	−1.27588	−	2.20990i
$452$		0			0
$453$	22066.5	+	12740.1i	2.28869	+	1.32138i
$454$		0			0
$455$	1227.31	+	1707.26i	0.126455	+	0.175907i
$456$		0			0
$457$	4636.57	+	2676.92i	0.474594	+	0.274007i	0.718161	−	0.695877i	$-0.244984\pi$
$457$	4636.57	+	2676.92i	0.474594	+	0.274007i	−0.243567	+	0.969884i	$0.578317\pi$
$458$		0			0
$459$	3582.41	+	6204.92i	0.364298	+	0.630982i
$460$		0			0
$461$	−13074.6	+	7548.65i	−1.32093	+	0.762637i	−0.983876	−	0.178850i	$-0.942762\pi$
$461$	−13074.6	+	7548.65i	−1.32093	+	0.762637i	−0.337050	+	0.941487i	$0.609429\pi$
$462$		0			0
$463$			9543.47i			0.957932i	0.877833	+	0.478966i	$0.158988\pi$
$463$			9543.47i			0.957932i	−0.877833	+	0.478966i	$0.841012\pi$
$464$		0			0
$465$	1349.63	−	2337.63i	0.134597	−	0.233129i
$466$		0			0
$467$	−4319.08			−0.427972			−0.213986	−	0.976837i	$-0.568645\pi$
$467$	−4319.08			−0.427972			−0.213986	+	0.976837i	$0.568645\pi$
$468$		0			0
$469$	−14394.3			−1.41720
$470$		0			0
$471$	−876.003	+	1517.28i	−0.0856987	+	0.148435i
$472$		0			0
$473$		−	11930.6i		−	1.15976i
$474$		0			0
$475$	2275.43	−	1313.72i	0.219798	−	0.126900i
$476$		0			0
$477$	−1648.43	−	2855.16i	−0.158231	−	0.274064i
$478$		0			0
$479$	−11469.8	−	6622.10i	−1.09409	−	0.631673i	−0.159428	−	0.987210i	$-0.550965\pi$
$479$	−11469.8	−	6622.10i	−1.09409	−	0.631673i	−0.934662	+	0.355536i	$0.884298\pi$
$480$		0			0
$481$	10315.6	+	4655.20i	0.977864	+	0.441286i
$482$		0			0
$483$	−19984.1	−	11537.8i	−1.88262	−	1.08693i
$484$		0			0
$485$	−1174.89	−	2034.96i	−0.109998	−	0.190521i
$486$		0			0
$487$	536.591	−	309.801i	0.0499286	−	0.0288263i	−0.474828	−	0.880079i	$-0.657490\pi$
$487$	536.591	−	309.801i	0.0499286	−	0.0288263i	0.524757	+	0.851252i	$0.324156\pi$
$488$		0			0
$489$			20361.9i			1.88302i
$490$		0			0
$491$	−2731.07	+	4730.35i	−0.251021	+	0.434781i	−0.963807	−	0.266600i	$-0.914100\pi$
$491$	−2731.07	+	4730.35i	−0.251021	+	0.434781i	0.712786	+	0.701382i	$0.247433\pi$
$492$		0			0
$493$	1299.86			0.118748
$494$		0			0
$495$	−9839.30			−0.893421
$496$		0			0
$497$	8028.91	−	13906.5i	0.724640	−	1.25511i
$498$		0			0
$499$			16005.2i			1.43585i	0.696119	+	0.717926i	$0.254908\pi$
$499$			16005.2i			1.43585i	−0.696119	+	0.717926i	$0.745092\pi$
$500$		0			0
$501$	25769.3	−	14877.9i	2.29798	−	1.32674i
$502$		0			0
$503$	5027.91	+	8708.60i	0.445693	+	0.771963i	0.998100	−	0.0616117i	$-0.0196240\pi$
$503$	5027.91	+	8708.60i	0.445693	+	0.771963i	−0.552407	+	0.833574i	$0.686291\pi$
$504$		0			0
$505$	−834.403	−	481.743i	−0.0735256	−	0.0424500i
$506$		0			0
$507$	6851.08	−	20384.6i	0.600133	−	1.78563i
$508$		0			0
$509$	12620.1	+	7286.21i	1.09897	+	0.634490i	0.935950	−	0.352133i	$-0.114543\pi$
$509$	12620.1	+	7286.21i	1.09897	+	0.634490i	0.163019	+	0.986623i	$0.447877\pi$
$510$		0			0
$511$	3712.28	+	6429.86i	0.321373	+	0.556635i
$512$		0			0
$513$	−7841.27	+	4527.16i	−0.674855	+	0.389628i
$514$		0			0
$515$		−	987.763i		−	0.0845166i
$516$		0			0
$517$	−4542.75	+	7868.27i	−0.386441	+	0.669335i
$518$		0			0
$519$	506.408			0.0428301
$520$		0			0
$521$	14409.9			1.21172			0.605862	−	0.795570i	$-0.292828\pi$
$521$	14409.9			1.21172			0.605862	+	0.795570i	$0.292828\pi$
$522$		0			0
$523$	2124.16	−	3679.15i	0.177597	−	0.307606i	−0.763460	−	0.645855i	$-0.776501\pi$
$523$	2124.16	−	3679.15i	0.177597	−	0.307606i	0.941057	+	0.338249i	$0.109834\pi$
$524$		0			0
$525$			20890.2i			1.73662i
$526$		0			0
$527$	1674.68	−	966.877i	0.138425	−	0.0799199i
$528$		0			0
$529$	−2522.26	−	4368.68i	−0.207303	−	0.359060i
$530$		0			0
$531$	26306.6	+	15188.1i	2.14992	+	1.24126i
$532$		0			0
$533$	−18230.2	−	8226.86i	−1.48150	−	0.668564i
$534$		0			0
$535$	2655.18	+	1532.97i	0.214567	+	0.123880i
$536$		0			0
$537$	−3077.93	−	5331.14i	−0.247342	−	0.428409i
$538$		0			0
$539$	−997.179	+	575.721i	−0.0796874	+	0.0460076i
$540$		0			0
$541$		−	14369.4i		−	1.14194i	−0.820970	−	0.570971i	$-0.806567\pi$
$541$		−	14369.4i		−	1.14194i	0.820970	−	0.570971i	$-0.193433\pi$
$542$		0			0
$543$	−8129.74	+	14081.1i	−0.642505	+	1.11285i
$544$		0			0
$545$	−1353.49			−0.106380
$546$		0			0
$547$	−18950.8			−1.48131			−0.740657	−	0.671884i	$-0.765485\pi$
$547$	−18950.8			−1.48131			−0.740657	+	0.671884i	$0.765485\pi$
$548$		0			0
$549$	−29912.9	+	51810.7i	−2.32541	+	4.02774i
$550$		0			0
$551$			1642.65i			0.127004i
$552$		0			0
$553$	3836.43	−	2214.96i	0.295012	−	0.170325i
$554$		0			0
$555$	−2950.04	−	5109.62i	−0.225626	−	0.390795i
$556$		0			0
$557$	10264.9	+	5926.42i	0.780855	+	0.450827i	0.836733	−	0.547611i	$-0.184462\pi$
$557$	10264.9	+	5926.42i	0.780855	+	0.450827i	−0.0558780	+	0.998438i	$0.517796\pi$
$558$		0			0
$559$	−5698.88	−	7927.47i	−0.431193	−	0.599814i
$560$		0			0
$561$	−8499.72	−	4907.32i	−0.639677	−	0.369317i
$562$		0			0
$563$	5792.65	+	10033.2i	0.433625	+	0.751061i	0.997182	−	0.0750161i	$-0.0239008\pi$
$563$	5792.65	+	10033.2i	0.433625	+	0.751061i	−0.563557	+	0.826077i	$0.690567\pi$
$564$		0			0
$565$	1464.53	−	845.546i	0.109050	−	0.0629600i
$566$		0			0
$567$		−	38603.0i		−	2.85921i
$568$		0			0
$569$	4621.17	−	8004.10i	0.340474	−	0.589718i	−0.644047	−	0.764986i	$-0.722746\pi$
$569$	4621.17	−	8004.10i	0.340474	−	0.589718i	0.984521	+	0.175268i	$0.0560792\pi$
$570$		0			0
$571$	20877.1			1.53009			0.765043	−	0.643979i	$-0.222718\pi$
$571$	20877.1			1.53009			0.765043	+	0.643979i	$0.222718\pi$
$572$		0			0
$573$	−18773.5			−1.36872
$574$		0			0
$575$	−7790.74	+	13494.0i	−0.565037	+	0.978673i
$576$		0			0
$577$			19966.8i			1.44060i	0.693661	+	0.720302i	$0.255997\pi$
$577$			19966.8i			1.44060i	−0.693661	+	0.720302i	$0.744003\pi$
$578$		0			0
$579$	1958.97	−	1131.01i	0.140608	−	0.0811799i
$580$		0			0
$581$	2999.59	+	5195.45i	0.214190	+	0.370987i
$582$		0			0
$583$	2376.51	+	1372.08i	0.168825	+	0.0974711i
$584$		0			0
$585$	−6537.89	+	4699.94i	−0.462066	+	0.332169i
$586$		0			0
$587$	16811.2	+	9705.96i	1.18207	+	0.682466i	0.956492	−	0.291760i	$-0.0942408\pi$
$587$	16811.2	+	9705.96i	1.18207	+	0.682466i	0.225575	+	0.974226i	$0.427574\pi$
$588$		0			0
$589$	1221.86	+	2116.32i	0.0854769	+	0.148050i
$590$		0			0
$591$	−13821.0	+	7979.58i	−0.961966	+	0.555391i
$592$		0			0
$593$		−	19259.0i		−	1.33368i	−0.745200	−	0.666841i	$-0.767646\pi$
$593$		−	19259.0i		−	1.33368i	0.745200	−	0.666841i	$-0.232354\pi$
$594$		0			0
$595$	392.645	−	680.080i	0.0270535	−	0.0468581i
$596$		0			0
$597$	−30007.1			−2.05713
$598$		0			0
$599$	27804.6			1.89660			0.948301	−	0.317372i	$-0.102800\pi$
$599$	27804.6			1.89660			0.948301	+	0.317372i	$0.102800\pi$
$600$		0			0
$601$	4963.55	−	8597.12i	0.336884	−	0.583501i	−0.646961	−	0.762523i	$-0.723960\pi$
$601$	4963.55	−	8597.12i	0.336884	−	0.583501i	0.983845	+	0.179023i	$0.0572935\pi$
$602$		0			0
$603$		−	55122.3i		−	3.72264i
$604$		0			0
$605$	4215.02	−	2433.54i	0.283248	−	0.163533i
$606$		0			0
$607$	7201.01	+	12472.5i	0.481516	+	0.834010i	0.999775	−	0.0212137i	$-0.00675305\pi$
$607$	7201.01	+	12472.5i	0.481516	+	0.834010i	−0.518259	+	0.855224i	$0.673420\pi$
$608$		0			0
$609$	−11310.6	−	6530.20i	−0.752595	−	0.434511i
$610$		0			0
$611$	739.932	+	7398.15i	0.0489926	+	0.489848i
$612$		0			0
$613$	−12798.3	−	7389.10i	−0.843260	−	0.486856i	0.0151111	−	0.999886i	$-0.495190\pi$
$613$	−12798.3	−	7389.10i	−0.843260	−	0.486856i	−0.858371	+	0.513029i	$0.828523\pi$
$614$		0			0
$615$	5213.43	+	9029.93i	0.341831	+	0.592068i
$616$		0			0
$617$	14862.7	−	8580.96i	0.969770	−	0.559897i	0.0706037	−	0.997504i	$-0.477507\pi$
$617$	14862.7	−	8580.96i	0.969770	−	0.559897i	0.899166	+	0.437608i	$0.144174\pi$
$618$		0			0
$619$			7592.09i			0.492975i	0.969146	+	0.246488i	$0.0792765\pi$
$619$			7592.09i			0.492975i	−0.969146	+	0.246488i	$0.920724\pi$
$620$		0			0
$621$	26847.4	−	46501.0i	1.73486	−	3.00487i
$622$		0			0
$623$	6813.53			0.438168
$624$		0			0
$625$	13326.8			0.852917
$626$		0			0
$627$	6201.47	−	10741.3i	0.394997	−	0.684154i
$628$		0			0
$629$		−	4226.82i		−	0.267940i
$630$		0			0
$631$	−5852.36	+	3378.86i	−0.369222	+	0.213170i	−0.673118	−	0.739535i	$-0.735046\pi$
$631$	−5852.36	+	3378.86i	−0.369222	+	0.213170i	0.303897	+	0.952705i	$0.401712\pi$
$632$		0			0
$633$	−16884.0	−	29243.9i	−1.06015	−	1.83624i
$634$		0			0
$635$	−2749.70	−	1587.54i	−0.171840	−	0.0992118i
$636$		0			0
$637$	−387.588	+	858.871i	−0.0241080	+	0.0534218i
$638$		0			0
$639$	53254.4	+	30746.4i	3.29689	+	1.90346i
$640$		0			0
$641$	7126.36	+	12343.2i	0.439117	+	0.760574i	0.997622	−	0.0689281i	$-0.0219579\pi$
$641$	7126.36	+	12343.2i	0.439117	+	0.760574i	−0.558504	+	0.829502i	$0.688625\pi$
$642$		0			0
$643$	−11160.5	+	6443.54i	−0.684492	+	0.395192i	−0.801545	−	0.597934i	$-0.795988\pi$
$643$	−11160.5	+	6443.54i	−0.684492	+	0.395192i	0.117053	+	0.993126i	$0.462655\pi$
$644$		0			0
$645$			5089.89i			0.310720i
$646$		0			0
$647$	14176.2	−	24553.9i	0.861398	−	1.49199i	−0.00918183	−	0.999958i	$-0.502923\pi$
$647$	14176.2	−	24553.9i	0.861398	−	1.49199i	0.870580	−	0.492027i	$-0.163744\pi$
$648$		0			0
$649$	−25283.8			−1.52924
$650$		0			0
$651$	−19429.5			−1.16974
$652$		0			0
$653$	−12008.1	+	20798.7i	−0.719623	+	1.24642i	0.241526	+	0.970394i	$0.422352\pi$
$653$	−12008.1	+	20798.7i	−0.719623	+	1.24642i	−0.961149	+	0.276030i	$0.910981\pi$
$654$		0			0
$655$		−	3118.60i		−	0.186036i
$656$		0			0
$657$	−24622.9	+	14216.0i	−1.46215	+	0.844172i
$658$		0			0
$659$	183.020	+	317.000i	0.0108186	+	0.0187383i	0.871384	−	0.490602i	$-0.163223\pi$
$659$	183.020	+	317.000i	0.0108186	+	0.0187383i	−0.860565	+	0.509340i	$0.829890\pi$
$660$		0			0
$661$	6329.00	+	3654.05i	0.372420	+	0.215017i	0.674515	−	0.738261i	$-0.264353\pi$
$661$	6329.00	+	3654.05i	0.372420	+	0.215017i	−0.302095	+	0.953278i	$0.597686\pi$
$662$		0			0
$663$	−7991.87	+	799.314i	−0.468143	+	0.0468217i
$664$		0			0
$665$	859.430	+	496.192i	0.0501162	+	0.0289346i
$666$		0			0
$667$	−4870.71	−	8436.31i	−0.282750	−	0.489738i
$668$		0			0
$669$	−21400.0	+	12355.3i	−1.23673	+	0.714028i
$670$		0			0
$671$		−	49796.4i		−	2.86493i
$672$		0			0
$673$	−6947.01	+	12032.6i	−0.397901	+	0.689186i	−0.993467	−	0.114121i	$-0.963595\pi$
$673$	−6947.01	+	12032.6i	−0.397901	+	0.689186i	0.595565	+	0.803307i	$0.296928\pi$
$674$		0			0
$675$	−48609.6			−2.77183
$676$		0			0
$677$	23804.6			1.35138			0.675691	−	0.737185i	$-0.263845\pi$
$677$	23804.6			1.35138			0.675691	+	0.737185i	$0.263845\pi$
$678$		0			0
$679$	−8456.94	+	14647.8i	−0.477979	+	0.827883i
$680$		0			0
$681$		−	11286.6i		−	0.635102i
$682$		0			0
$683$	−18071.0	+	10433.3i	−1.01240	+	0.584508i	−0.911893	−	0.410429i	$-0.865379\pi$
$683$	−18071.0	+	10433.3i	−1.01240	+	0.584508i	−0.100505	+	0.994937i	$0.532046\pi$
$684$		0			0
$685$	2175.50	+	3768.07i	0.121345	+	0.210176i
$686$		0			0
$687$	32700.3	+	18879.5i	1.81600	+	1.04847i
$688$		0			0
$689$	2234.51	−	223.487i	0.123553	−	0.0123573i
$690$		0			0
$691$	−4453.31	−	2571.12i	−0.245169	−	0.141549i	0.372381	−	0.928080i	$-0.378541\pi$
$691$	−4453.31	−	2571.12i	−0.245169	−	0.141549i	−0.617550	+	0.786531i	$0.711875\pi$
$692$		0			0
$693$	35412.1	+	61335.5i	1.94112	+	3.36211i
$694$		0			0
$695$	−2137.91	+	1234.33i	−0.116685	+	0.0673678i
$696$		0			0
$697$			7469.81i			0.405939i
$698$		0			0
$699$	4985.01	−	8634.29i	0.269743	−	0.467209i
$700$		0			0
$701$	8584.99			0.462554			0.231277	−	0.972888i	$-0.425710\pi$
$701$	8584.99			0.462554			0.231277	+	0.972888i	$0.425710\pi$
$702$		0			0
$703$	5341.52			0.286571
$704$		0			0
$705$	1938.06	−	3356.81i	0.103534	−	0.179326i
$706$		0			0
$707$			6935.25i			0.368921i
$708$		0			0
$709$	18679.2	−	10784.4i	0.989437	−	0.571252i	0.0843311	−	0.996438i	$-0.473125\pi$
$709$	18679.2	−	10784.4i	0.989437	−	0.571252i	0.905106	+	0.425186i	$0.139791\pi$
$710$		0			0
$711$	8482.12	+	14691.5i	0.447404	+	0.774926i
$712$		0			0
$713$	−12550.4	−	7245.99i	−0.659211	−	0.380595i
$714$		0			0
$715$	2756.77	−	6108.84i	0.144192	−	0.319521i
$716$		0			0
$717$	−10708.5	−	6182.57i	−0.557765	−	0.322026i
$718$		0			0
$719$	−16317.7	−	28263.0i	−0.846379	−	1.46597i	−0.884418	−	0.466695i	$-0.845444\pi$
$719$	−16317.7	−	28263.0i	−0.846379	−	1.46597i	0.0380391	−	0.999276i	$-0.487889\pi$
$720$		0			0
$721$	−6157.44	+	3555.00i	−0.318052	+	0.183627i
$722$		0			0
$723$			20241.8i			1.04122i
$724$		0			0
$725$	−4409.42	+	7637.35i	−0.225878	+	0.391233i
$726$		0			0
$727$	6636.77			0.338575			0.169288	−	0.985567i	$-0.445853\pi$
$727$	6636.77			0.338575			0.169288	+	0.985567i	$0.445853\pi$
$728$		0			0
$729$	39660.8			2.01498
$730$		0			0
$731$	−1823.20	+	3157.87i	−0.0922482	+	0.159779i
$732$		0			0
$733$		−	18221.6i		−	0.918188i	−0.888388	−	0.459094i	$-0.848174\pi$
$733$		−	18221.6i		−	0.918188i	0.888388	−	0.459094i	$-0.151826\pi$
$734$		0			0
$735$	425.423	−	245.618i	0.0213496	−	0.0123262i
$736$		0			0
$737$	22940.7	+	39734.4i	1.14658	+	1.98594i
$738$		0			0
$739$	−22048.9	−	12729.9i	−1.09754	−	0.633665i	−0.161967	−	0.986796i	$-0.551784\pi$
$739$	−22048.9	−	12729.9i	−1.09754	−	0.633665i	−0.935574	+	0.353131i	$0.885117\pi$
$740$		0			0
$741$	−1010.11	−	10099.5i	−0.0500773	−	0.500693i
$742$		0			0
$743$	−19536.8	−	11279.6i	−0.964651	−	0.556942i	−0.0670498	−	0.997750i	$-0.521359\pi$
$743$	−19536.8	−	11279.6i	−0.964651	−	0.556942i	−0.897601	+	0.440808i	$0.854692\pi$
$744$		0			0
$745$	−2117.68	−	3667.92i	−0.104142	−	0.180379i
$746$		0			0
$747$	−19895.8	+	11486.8i	−0.974496	+	0.562626i
$748$		0			0
$749$		−	22068.9i		−	1.07661i
$750$		0			0
$751$	−10904.3	+	18886.8i	−0.529830	+	0.917693i	0.469564	+	0.882898i	$0.344411\pi$
$751$	−10904.3	+	18886.8i	−0.529830	+	0.917693i	−0.999394	+	0.0347948i	$0.988922\pi$
$752$		0			0
$753$	50179.1			2.42846
$754$		0			0
$755$	6498.40			0.313246
$756$		0			0
$757$	6401.86	−	11088.4i	0.307371	−	0.532382i	−0.670416	−	0.741986i	$-0.733884\pi$
$757$	6401.86	−	11088.4i	0.307371	−	0.532382i	0.977786	+	0.209604i	$0.0672175\pi$
$758$		0			0
$759$			73553.1i			3.51753i
$760$		0			0
$761$	3597.82	−	2077.20i	0.171381	−	0.0989467i	−0.411856	−	0.911249i	$-0.635119\pi$
$761$	3597.82	−	2077.20i	0.171381	−	0.0989467i	0.583237	+	0.812302i	$0.301786\pi$
$762$		0			0
$763$	4871.27	+	8437.28i	0.231129	+	0.400328i
$764$		0			0
$765$	2604.34	+	1503.62i	0.123085	+	0.0710633i
$766$		0			0
$767$	−16800.3	+	12077.3i	−0.790904	+	0.568563i
$768$		0			0
$769$	−3570.43	−	2061.39i	−0.167429	−	0.0966652i	0.413944	−	0.910302i	$-0.364151\pi$
$769$	−3570.43	−	2061.39i	−0.167429	−	0.0966652i	−0.581373	+	0.813637i	$0.697484\pi$
$770$		0			0
$771$	−19388.5	−	33581.8i	−0.905653	−	1.56864i
$772$		0			0
$773$	29533.8	−	17051.3i	1.37420	−	0.793394i	0.382745	−	0.923854i	$-0.374979\pi$
$773$	29533.8	−	17051.3i	1.37420	−	0.793394i	0.991454	+	0.130460i	$0.0416453\pi$
$774$		0			0
$775$			13119.5i			0.608086i
$776$		0			0
$777$	−21234.7	+	36779.5i	−0.980423	+	1.69814i
$778$		0			0
$779$	−9439.74			−0.434164
$780$		0			0
$781$	−51184.0			−2.34508
$782$		0			0
$783$	15195.1	−	26318.8i	0.693525	−	1.20122i
$784$		0			0
$785$			446.826i			0.0203158i
$786$		0			0
$787$	36869.4	−	21286.6i	1.66995	−	0.964147i	0.702292	−	0.711889i	$-0.252160\pi$
$787$	36869.4	−	21286.6i	1.66995	−	0.964147i	0.967660	−	0.252258i	$-0.0811732\pi$
$788$		0			0
$789$	−34771.5	−	60226.0i	−1.56895	−	2.71749i
$790$		0			0
$791$	−10541.8	−	6086.31i	−0.473860	−	0.273583i
$792$		0			0
$793$	−23786.3	−	33088.1i	−1.06516	−	1.48171i
$794$		0			0
$795$	−1013.88	−	585.364i	−0.0452310	−	0.0261141i
$796$		0			0
$797$	−3027.38	−	5243.57i	−0.134549	−	0.233045i	0.790876	−	0.611976i	$-0.209625\pi$
$797$	−3027.38	−	5243.57i	−0.134549	−	0.233045i	−0.925425	+	0.378931i	$0.876292\pi$
$798$		0			0
$799$	2404.82	−	1388.42i	0.106479	−	0.0614755i
$800$		0			0
$801$			26092.2i			1.15096i
$802$		0			0
$803$	11832.8	−	20495.0i	0.520014	−	0.900690i
$804$		0			0
$805$	−5885.13			−0.257669
$806$		0			0
$807$	−54950.9			−2.39698
$808$		0			0
$809$	−18951.3	+	32824.7i	−0.823601	+	1.42652i	0.0793826	+	0.996844i	$0.474705\pi$
$809$	−18951.3	+	32824.7i	−0.823601	+	1.42652i	−0.902984	+	0.429675i	$0.858628\pi$
$810$		0			0
$811$			2418.43i			0.104714i	0.998628	+	0.0523568i	$0.0166733\pi$
$811$			2418.43i			0.104714i	−0.998628	+	0.0523568i	$0.983327\pi$
$812$		0			0
$813$	3740.10	−	2159.35i	0.161342	−	0.0931508i
$814$		0			0
$815$	2596.52	+	4497.31i	0.111598	+	0.193293i
$816$		0			0
$817$	−3990.67	−	2304.01i	−0.170888	−	0.0986624i
$818$		0			0
$819$	52828.3	+	23840.1i	2.25393	+	1.01715i
$820$		0			0
$821$	35364.7	+	20417.8i	1.50333	+	0.867950i	0.999993	+	0.00386148i	$0.00122915\pi$
$821$	35364.7	+	20417.8i	1.50333	+	0.867950i	0.503340	+	0.864088i	$0.332104\pi$
$822$		0			0
$823$	849.678	+	1471.69i	0.0359877	+	0.0623326i	0.883458	−	0.468510i	$-0.155209\pi$
$823$	849.678	+	1471.69i	0.0359877	+	0.0623326i	−0.847471	+	0.530842i	$0.821876\pi$
$824$		0			0
$825$	57666.2	−	33293.6i	2.43355	−	1.40501i
$826$		0			0
$827$		−	28148.2i		−	1.18357i	−0.806097	−	0.591784i	$-0.798424\pi$
$827$		−	28148.2i		−	1.18357i	0.806097	−	0.591784i	$-0.201576\pi$
$828$		0			0
$829$	889.754	−	1541.10i	0.0372768	−	0.0645653i	−0.846785	−	0.531935i	$-0.821465\pi$
$829$	889.754	−	1541.10i	0.0372768	−	0.0645653i	0.884062	+	0.467370i	$0.154798\pi$
$830$		0			0
$831$	45779.2			1.91102
$832$		0			0
$833$	351.922			0.0146379
$834$		0			0
$835$	3794.41	−	6572.11i	0.157259	−	0.272380i
$836$		0			0
$837$		−	45210.6i		−	1.86704i
$838$		0			0
$839$	23734.4	−	13703.1i	0.976643	−	0.563865i	0.0753879	−	0.997154i	$-0.475980\pi$
$839$	23734.4	−	13703.1i	0.976643	−	0.563865i	0.901255	+	0.433289i	$0.142647\pi$
$840$		0			0
$841$	9437.77	+	16346.7i	0.386968	+	0.670248i
$842$		0			0
$843$	10624.6	+	6134.12i	0.434082	+	0.250617i
$844$		0			0
$845$	−1086.23	−	5375.96i	−0.0442218	−	0.218862i
$846$		0			0
$847$	−30340.1	−	17516.9i	−1.23081	−	0.710610i
$848$		0			0
$849$	−20419.4	−	35367.4i	−0.825431	−	1.42969i
$850$		0			0
$851$	−27432.9	+	15838.4i	−1.10504	+	0.637994i
$852$		0			0
$853$			49349.2i			1.98087i	0.137964	+	0.990437i	$0.455944\pi$
$853$			49349.2i			1.98087i	−0.137964	+	0.990437i	$0.544056\pi$
$854$		0			0
$855$	−1900.15	+	3291.16i	−0.0760044	+	0.131644i
$856$		0			0
$857$	657.558			0.0262098			0.0131049	−	0.999914i	$-0.495828\pi$
$857$	657.558			0.0262098			0.0131049	+	0.999914i	$0.495828\pi$
$858$		0			0
$859$	2866.78			0.113869			0.0569343	−	0.998378i	$-0.481867\pi$
$859$	2866.78			0.113869			0.0569343	+	0.998378i	$0.481867\pi$
$860$		0			0
$861$	37526.7	−	64998.2i	1.48537	−	2.57274i
$862$		0			0
$863$		−	18625.8i		−	0.734683i	−0.930086	−	0.367341i	$-0.880268\pi$
$863$		−	18625.8i		−	0.734683i	0.930086	−	0.367341i	$-0.119732\pi$
$864$		0			0
$865$	111.849	−	64.5763i	0.00439652	−	0.00253833i
$866$		0			0
$867$	−22545.4	−	39049.7i	−0.883138	−	1.52964i
$868$		0			0
$869$	−12228.5	−	7060.14i	−0.477358	−	0.275603i
$870$		0			0
$871$	34223.3	+	15444.2i	1.33136	+	0.600810i
$872$		0			0
$873$	−56093.4	−	32385.5i	−2.17465	−	1.25554i
$874$		0			0
$875$	5467.56	+	9470.09i	0.211242	+	0.365883i
$876$		0			0
$877$	17084.9	−	9863.97i	0.657829	−	0.379798i	−0.133620	−	0.991033i	$-0.542660\pi$
$877$	17084.9	−	9863.97i	0.657829	−	0.379798i	0.791449	+	0.611235i	$0.209327\pi$
$878$		0			0
$879$			95721.5i			3.67304i
$880$		0			0
$881$	−25212.2	+	43668.8i	−0.964156	+	1.66997i	−0.252290	+	0.967652i	$0.581184\pi$
$881$	−25212.2	+	43668.8i	−0.964156	+	1.66997i	−0.711866	+	0.702315i	$0.752150\pi$
$882$		0			0
$883$	27255.8			1.03877			0.519384	−	0.854541i	$-0.326162\pi$
$883$	27255.8			1.03877			0.519384	+	0.854541i	$0.326162\pi$
$884$		0			0
$885$	10786.8			0.409709
$886$		0			0
$887$	−5869.03	+	10165.5i	−0.222168	+	0.384806i	−0.955466	−	0.295101i	$-0.904647\pi$
$887$	−5869.03	+	10165.5i	−0.222168	+	0.384806i	0.733298	+	0.679907i	$0.237980\pi$
$888$		0			0
$889$			22854.5i			0.862221i
$890$		0			0
$891$	−106561.	+	61523.0i	−4.00665	+	2.31324i
$892$		0			0
$893$	1754.58	+	3039.02i	0.0657500	+	0.113882i
$894$		0			0
$895$	−1359.64	−	784.986i	−0.0507795	−	0.0293175i
$896$		0			0
$897$	35134.1	+	48873.6i	1.30780	+	1.81922i
$898$		0			0
$899$	−7103.32	−	4101.10i	−0.263525	−	0.152146i
$900$		0			0
$901$	−419.355	−	726.345i	−0.0155058	−	0.0268569i
$902$		0			0
$903$	31729.0	−	18318.7i	1.16930	−	0.675093i
$904$		0			0
$905$			4146.76i			0.152313i
$906$		0			0
$907$	7717.36	−	13366.9i	0.282526	−	0.489349i	−0.689481	−	0.724304i	$-0.742161\pi$
$907$	7717.36	−	13366.9i	0.282526	−	0.489349i	0.972006	+	0.234956i	$0.0754945\pi$
$908$		0			0
$909$	−26558.3			−0.969069
$910$		0			0
$911$	−24957.2			−0.907649			−0.453825	−	0.891091i	$-0.649941\pi$
$911$	−24957.2			−0.907649			−0.453825	+	0.891091i	$0.649941\pi$
$912$		0			0
$913$	9561.14	−	16560.4i	0.346580	−	0.600294i
$914$		0			0
$915$			21244.5i			0.767563i
$916$		0			0
$917$	−19440.5	+	11224.0i	−0.700090	+	0.404197i
$918$		0			0
$919$	−8291.17	−	14360.7i	−0.297606	−	0.515469i	0.677981	−	0.735079i	$-0.262855\pi$
$919$	−8291.17	−	14360.7i	−0.297606	−	0.515469i	−0.975588	+	0.219610i	$0.929522\pi$
$920$		0			0
$921$	13916.1	+	8034.45i	0.497883	+	0.287453i
$922$		0			0
$923$	−34010.1	+	24449.1i	−1.21285	+	0.871887i
$924$		0			0
$925$	24834.8	+	14338.4i	0.882772	+	0.509669i
$926$		0			0
$927$	−13613.8	−	23579.7i	−0.482345	−	0.835447i
$928$		0			0
$929$	−5118.69	+	2955.28i	−0.180774	+	0.104370i	−0.587656	−	0.809111i	$-0.699949\pi$
$929$	−5118.69	+	2955.28i	−0.180774	+	0.104370i	0.406882	+	0.913481i	$0.366616\pi$
$930$		0			0
$931$			444.730i			0.0156557i
$932$		0			0
$933$	−28878.2	+	50018.5i	−1.01332	+	1.75512i
$934$		0			0
$935$	−2503.09			−0.0875507
$936$		0			0
$937$	−7798.93			−0.271910			−0.135955	−	0.990715i	$-0.543410\pi$
$937$	−7798.93			−0.271910			−0.135955	+	0.990715i	$0.543410\pi$
$938$		0			0
$939$	25783.2	−	44657.8i	0.896062	−	1.55202i
$940$		0			0
$941$			9738.22i			0.337361i	0.985671	+	0.168681i	$0.0539507\pi$
$941$			9738.22i			0.337361i	−0.985671	+	0.168681i	$0.946049\pi$
$942$		0			0
$943$	48480.5	−	27990.2i	1.67417	−	0.966582i
$944$		0			0
$945$	−9179.93	−	15900.1i	−0.316003	−	0.547334i
$946$		0			0
$947$	−11928.9	−	6887.17i	−0.409332	−	0.236328i	0.281170	−	0.959658i	$-0.409277\pi$
$947$	−11928.9	−	6887.17i	−0.409332	−	0.236328i	−0.690503	+	0.723330i	$0.742611\pi$
$948$		0			0
$949$	−1927.35	−	19270.5i	−0.0659268	−	0.659164i
$950$		0			0
$951$	−173.386	−	100.104i	−0.00591211	−	0.00341336i
$952$		0			0
$953$	15302.3	+	26504.3i	0.520135	+	0.900901i	0.999726	+	0.0234084i	$0.00745179\pi$
$953$	15302.3	+	26504.3i	0.520135	+	0.900901i	−0.479591	+	0.877492i	$0.659215\pi$
$954$		0			0
$955$	−4146.48	+	2393.97i	−0.140499	+	0.0811174i
$956$		0			0
$957$			41629.7i			1.40616i
$958$		0			0
$959$	15659.4	−	27122.9i	0.527288	−	0.913289i
$960$		0			0
$961$	17588.8			0.590408
$962$		0			0
$963$	84511.9			2.82799
$964$		0			0
$965$	288.449	−	499.608i	0.00962228	−	0.0166663i
$966$		0			0
$967$			48790.3i			1.62253i	0.584677	+	0.811266i	$0.301221\pi$
$967$			48790.3i			1.62253i	−0.584677	+	0.811266i	$0.698779\pi$
$968$		0			0
$969$	−3282.91	+	1895.39i	−0.108836	+	0.0628366i
$970$		0			0
$971$	16538.8	+	28646.0i	0.546607	+	0.946751i	0.998504	+	0.0546805i	$0.0174140\pi$
$971$	16538.8	+	28646.0i	0.546607	+	0.946751i	−0.451897	+	0.892070i	$0.649253\pi$
$972$		0			0
$973$	15388.9	+	8884.79i	0.507035	+	0.292737i
$974$		0			0
$975$	22413.9	−	49668.0i	0.736227	−	1.63143i
$976$		0			0
$977$	11795.8	+	6810.30i	0.386265	+	0.223010i	0.680540	−	0.732711i	$-0.261745\pi$
$977$	11795.8	+	6810.30i	0.386265	+	0.223010i	−0.294276	+	0.955721i	$0.595078\pi$
$978$		0			0
$979$	−10859.0	−	18808.3i	−0.354499	−	0.614011i
$980$		0			0
$981$	−32310.3	+	18654.3i	−1.05157	+	0.607123i
$982$		0			0
$983$		−	23886.5i		−	0.775037i	−0.921862	−	0.387519i	$-0.873332\pi$
$983$		−	23886.5i		−	0.775037i	0.921862	−	0.387519i	$-0.126668\pi$
$984$		0			0
$985$	−2035.09	+	3524.87i	−0.0658307	+	0.114022i
$986$		0			0
$987$	−27900.6			−0.899783
$988$		0			0
$989$	27326.9			0.878611
$990$		0			0
$991$	1590.09	−	2754.11i	0.0509695	−	0.0882818i	−0.839415	−	0.543491i	$-0.817102\pi$
$991$	1590.09	−	2754.11i	0.0509695	−	0.0882818i	0.890385	+	0.455209i	$0.150436\pi$
$992$		0			0
$993$		−	61690.7i		−	1.97150i
$994$		0			0
$995$	−6627.61	+	3826.45i	−0.211165	+	0.121916i
$996$		0			0
$997$	26513.7	+	45923.0i	0.842223	+	1.45877i	0.888011	+	0.459822i	$0.152087\pi$
$997$	26513.7	+	45923.0i	0.842223	+	1.45877i	−0.0457876	+	0.998951i	$0.514580\pi$
$998$		0			0
$999$	−85582.4	−	49411.0i	−2.71042	−	1.56486i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	52.4.h.a.17.4	✓	8
3.2	odd	2		468.4.t.g.433.2		8
4.3	odd	2		208.4.w.c.17.1		8
13.2	odd	12		676.4.e.h.653.7		16
13.3	even	3		676.4.h.e.361.4		8
13.4	even	6		676.4.d.d.337.2		8
13.5	odd	4		676.4.e.h.529.7		16
13.6	odd	12		676.4.a.g.1.1		8
13.7	odd	12		676.4.a.g.1.2		8
13.8	odd	4		676.4.e.h.529.8		16
13.9	even	3		676.4.d.d.337.1		8
13.10	even	6	inner	52.4.h.a.49.4	yes	8
13.11	odd	12		676.4.e.h.653.8		16
13.12	even	2		676.4.h.e.485.4		8
39.23	odd	6		468.4.t.g.361.3		8
52.23	odd	6		208.4.w.c.49.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
52.4.h.a.17.4	✓	8	1.1	even	1	trivial
52.4.h.a.49.4	yes	8	13.10	even	6	inner
208.4.w.c.17.1		8	4.3	odd	2
208.4.w.c.49.1		8	52.23	odd	6
468.4.t.g.361.3		8	39.23	odd	6
468.4.t.g.433.2		8	3.2	odd	2
676.4.a.g.1.1		8	13.6	odd	12
676.4.a.g.1.2		8	13.7	odd	12
676.4.d.d.337.1		8	13.9	even	3
676.4.d.d.337.2		8	13.4	even	6
676.4.e.h.529.7		16	13.5	odd	4
676.4.e.h.529.8		16	13.8	odd	4
676.4.e.h.653.7		16	13.2	odd	12
676.4.e.h.653.8		16	13.11	odd	12
676.4.h.e.361.4		8	13.3	even	3
676.4.h.e.485.4		8	13.12	even	2

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 52 = 2^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	52.h (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(4.89420 - 8.47701i) q^{3} -2.49640i q^{5} +(-15.5619 + 8.98467i) q^{7} +(-34.4065 - 59.5937i) q^{9} +O(q^{10})\)	\(q+(4.89420 - 8.47701i) q^{3} -2.49640i q^{5} +(-15.5619 + 8.98467i) q^{7} +(-34.4065 - 59.5937i) q^{9} +(49.6032 + 28.6384i) q^{11} +(46.6395 - 4.66469i) q^{13} +(-21.1620 - 12.2179i) q^{15} +(-8.75292 - 15.1605i) q^{17} +(19.1586 - 11.0612i) q^{19} +175.891i q^{21} +(-65.5963 + 113.616i) q^{23} +118.768 q^{25} -409.282 q^{27} +(-37.1264 + 64.3048i) q^{29} +110.463i q^{31} +(485.537 - 280.325i) q^{33} +(22.4294 + 38.8488i) q^{35} +(209.104 + 120.726i) q^{37} +(188.720 - 418.193i) q^{39} +(-369.537 - 213.352i) q^{41} +(-104.148 - 180.390i) q^{43} +(-148.770 + 85.8924i) q^{45} +158.624i q^{47} +(-10.0516 + 17.4098i) q^{49} -171.354 q^{51} +47.9103 q^{53} +(71.4931 - 123.830i) q^{55} -216.544i q^{57} +(-382.291 + 220.716i) q^{59} +(-434.699 - 752.921i) q^{61} +(1070.86 + 618.261i) q^{63} +(-11.6449 - 116.431i) q^{65} +(693.726 + 400.523i) q^{67} +(642.084 + 1112.12i) q^{69} +(-773.901 + 446.812i) q^{71} -413.180i q^{73} +(581.275 - 1006.80i) q^{75} -1029.23 q^{77} -246.527 q^{79} +(-1074.13 + 1860.46i) q^{81} -333.857i q^{83} +(-37.8467 + 21.8508i) q^{85} +(363.408 + 629.441i) q^{87} +(-328.376 - 189.588i) q^{89} +(-683.888 + 491.632i) q^{91} +(936.399 + 540.630i) q^{93} +(-27.6133 - 47.8276i) q^{95} +(815.158 - 470.632i) q^{97} -3941.39i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 36 q^{7} - 70 q^{9}+O(q^{10}) \) 8 * q - 36 * q^7 - 70 * q^9	\( 8 q - 36 q^{7} - 70 q^{9} + 72 q^{11} + 62 q^{13} + 96 q^{15} + 88 q^{17} - 144 q^{19} - 20 q^{23} - 84 q^{25} - 432 q^{27} - 484 q^{29} + 1038 q^{33} + 40 q^{35} + 996 q^{37} - 236 q^{39} + 156 q^{41} + 504 q^{43} - 1530 q^{45} + 922 q^{49} - 1808 q^{51} - 1164 q^{53} - 1128 q^{55} + 600 q^{59} - 1224 q^{61} + 6480 q^{63} + 670 q^{65} + 960 q^{67} + 1738 q^{69} - 2964 q^{71} + 1448 q^{75} - 3972 q^{77} - 3968 q^{79} - 4132 q^{81} + 3870 q^{85} - 1660 q^{87} + 5430 q^{89} - 1720 q^{91} + 3324 q^{93} + 2400 q^{95} - 3042 q^{97}+O(q^{100}) \) 8 * q - 36 * q^7 - 70 * q^9 + 72 * q^11 + 62 * q^13 + 96 * q^15 + 88 * q^17 - 144 * q^19 - 20 * q^23 - 84 * q^25 - 432 * q^27 - 484 * q^29 + 1038 * q^33 + 40 * q^35 + 996 * q^37 - 236 * q^39 + 156 * q^41 + 504 * q^43 - 1530 * q^45 + 922 * q^49 - 1808 * q^51 - 1164 * q^53 - 1128 * q^55 + 600 * q^59 - 1224 * q^61 + 6480 * q^63 + 670 * q^65 + 960 * q^67 + 1738 * q^69 - 2964 * q^71 + 1448 * q^75 - 3972 * q^77 - 3968 * q^79 - 4132 * q^81 + 3870 * q^85 - 1660 * q^87 + 5430 * q^89 - 1720 * q^91 + 3324 * q^93 + 2400 * q^95 - 3042 * q^97

Introduction

L-functions

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