LMFDB - Embedded newform 121.4.c.f.27.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [121,4,Mod(3,121)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(121, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([8]))

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

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

chi := DirichletCharacter("121.3");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 121 = 11^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	121.c (of order $5$, degree $4$, not 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:	$7.13923111069$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.324000000.3
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 3x^{6} + 9x^{4} + 27x^{2} + 81 $ x^8 + 3x^6 + 9x^4 + 27*x^2 + 81
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 11)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			27.1
Root			$1.40126 + 1.01807i$ of defining polynomial
Character	$\chi$	$=$	121.27
Dual form			121.4.c.f.9.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.844250 - 2.59833i) q^{2} +(6.41405 + 4.66008i) q^{3} +(0.433551 - 0.314993i) q^{4} +(4.59088 - 14.1293i) q^{5} +(6.69339 - 20.6001i) q^{6} +(2.48514 - 1.80556i) q^{7} +(-18.8667 - 13.7075i) q^{8} +(11.0802 + 34.1015i) q^{9} +O(q^{10})$	\(q+(-0.844250 - 2.59833i) q^{2} +(6.41405 + 4.66008i) q^{3} +(0.433551 - 0.314993i) q^{4} +(4.59088 - 14.1293i) q^{5} +(6.69339 - 20.6001i) q^{6} +(2.48514 - 1.80556i) q^{7} +(-18.8667 - 13.7075i) q^{8} +(11.0802 + 34.1015i) q^{9} -40.5885 q^{10} +4.24871 q^{12} +(-1.65602 - 5.09670i) q^{13} +(-6.78952 - 4.93287i) q^{14} +(95.2898 - 69.2321i) q^{15} +(-18.3635 + 56.5171i) q^{16} +(12.7363 - 39.1982i) q^{17} +(79.2525 - 57.5803i) q^{18} +(113.200 + 82.2447i) q^{19} +(-2.46025 - 7.57186i) q^{20} +24.3538 q^{21} -111.354 q^{23} +(-57.1341 - 175.841i) q^{24} +(-77.4333 - 56.2586i) q^{25} +(-11.8448 + 8.60577i) q^{26} +(-21.6977 + 66.7788i) q^{27} +(0.508695 - 1.56560i) q^{28} +(-20.2213 + 14.6916i) q^{29} +(-260.336 - 189.145i) q^{30} +(9.73324 + 29.9558i) q^{31} -24.2102 q^{32} -112.603 q^{34} +(-14.1023 - 43.4023i) q^{35} +(15.5456 + 11.2945i) q^{36} +(-10.6334 + 7.72561i) q^{37} +(118.130 - 363.567i) q^{38} +(13.1292 - 40.4076i) q^{39} +(-280.291 + 203.643i) q^{40} +(211.212 + 153.454i) q^{41} +(-20.5607 - 63.2794i) q^{42} +57.7128 q^{43} +532.697 q^{45} +(94.0105 + 289.335i) q^{46} +(278.177 + 202.108i) q^{47} +(-381.159 + 276.928i) q^{48} +(-103.077 + 317.238i) q^{49} +(-80.8056 + 248.694i) q^{50} +(264.358 - 192.067i) q^{51} +(-2.32339 - 1.68804i) q^{52} +(-105.991 - 326.207i) q^{53} +191.832 q^{54} -71.6359 q^{56} +(342.804 + 1055.04i) q^{57} +(55.2455 + 40.1382i) q^{58} +(-71.4923 + 51.9422i) q^{59} +(19.5053 - 60.0312i) q^{60} +(-228.270 + 702.543i) q^{61} +(69.6180 - 50.5804i) q^{62} +(89.1080 + 64.7408i) q^{63} +(167.348 + 515.043i) q^{64} -79.6152 q^{65} +342.359 q^{67} +(-6.82534 - 21.0062i) q^{68} +(-714.229 - 518.918i) q^{69} +(-100.868 + 73.2848i) q^{70} +(-64.0790 + 197.215i) q^{71} +(258.397 - 795.264i) q^{72} +(-817.592 + 594.016i) q^{73} +(29.0510 + 21.1068i) q^{74} +(-234.492 - 721.691i) q^{75} +74.9845 q^{76} -116.077 q^{78} +(-399.938 - 1230.88i) q^{79} +(714.242 + 518.927i) q^{80} +(332.863 - 241.839i) q^{81} +(220.410 - 678.352i) q^{82} +(-136.538 + 420.221i) q^{83} +(10.5586 - 7.67129i) q^{84} +(-495.371 - 359.908i) q^{85} +(-48.7240 - 149.957i) q^{86} -198.164 q^{87} -1489.11 q^{89} +(-449.730 - 1384.13i) q^{90} +(-13.3178 - 9.67595i) q^{91} +(-48.2776 + 35.0757i) q^{92} +(-77.1671 + 237.496i) q^{93} +(290.292 - 893.427i) q^{94} +(1681.75 - 1221.86i) q^{95} +(-155.286 - 112.822i) q^{96} +(416.065 + 1280.52i) q^{97} +911.314 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{2} + 2 q^{3} + 8 q^{4} - 2 q^{5} - 26 q^{6} + 20 q^{7} - 12 q^{8} - 44 q^{9}+O(q^{10}) $ 8 * q + 2 * q^2 + 2 * q^3 + 8 * q^4 - 2 * q^5 - 26 * q^6 + 20 * q^7 - 12 * q^8 - 44 * q^9	\( 8 q + 2 q^{2} + 2 q^{3} + 8 q^{4} - 2 q^{5} - 26 q^{6} + 20 q^{7} - 12 q^{8} - 44 q^{9} - 200 q^{10} - 160 q^{12} + 80 q^{13} + 4 q^{14} + 194 q^{15} + 8 q^{16} - 124 q^{17} + 92 q^{18} + 72 q^{19} - 88 q^{20} - 304 q^{21} - 392 q^{23} + 252 q^{24} - 136 q^{25} + 40 q^{26} + 182 q^{27} - 128 q^{28} + 144 q^{29} - 266 q^{30} + 34 q^{31} + 416 q^{32} - 208 q^{34} - 172 q^{35} + 80 q^{36} - 54 q^{37} - 432 q^{38} + 400 q^{39} - 492 q^{40} + 536 q^{41} + 140 q^{42} + 240 q^{43} + 1712 q^{45} - 314 q^{46} + 272 q^{47} - 776 q^{48} + 390 q^{49} + 232 q^{50} - 164 q^{51} - 560 q^{52} + 492 q^{53} + 440 q^{54} + 480 q^{56} - 1512 q^{57} + 192 q^{58} - 634 q^{59} - 632 q^{60} + 840 q^{61} + 134 q^{62} + 248 q^{63} - 224 q^{64} + 3520 q^{65} + 3016 q^{67} + 640 q^{68} - 962 q^{69} - 284 q^{70} + 678 q^{71} - 744 q^{72} - 400 q^{73} + 6 q^{74} + 520 q^{75} - 1728 q^{76} - 1760 q^{78} + 316 q^{79} + 1544 q^{80} + 1294 q^{81} - 512 q^{82} + 468 q^{83} - 736 q^{84} + 452 q^{85} + 156 q^{86} - 4800 q^{87} - 7368 q^{89} + 1532 q^{90} - 1280 q^{91} + 40 q^{92} + 638 q^{93} - 992 q^{94} + 2952 q^{95} - 952 q^{96} - 2194 q^{97} + 3480 q^{98}+O(q^{100}) \) 8 * q + 2 * q^2 + 2 * q^3 + 8 * q^4 - 2 * q^5 - 26 * q^6 + 20 * q^7 - 12 * q^8 - 44 * q^9 - 200 * q^10 - 160 * q^12 + 80 * q^13 + 4 * q^14 + 194 * q^15 + 8 * q^16 - 124 * q^17 + 92 * q^18 + 72 * q^19 - 88 * q^20 - 304 * q^21 - 392 * q^23 + 252 * q^24 - 136 * q^25 + 40 * q^26 + 182 * q^27 - 128 * q^28 + 144 * q^29 - 266 * q^30 + 34 * q^31 + 416 * q^32 - 208 * q^34 - 172 * q^35 + 80 * q^36 - 54 * q^37 - 432 * q^38 + 400 * q^39 - 492 * q^40 + 536 * q^41 + 140 * q^42 + 240 * q^43 + 1712 * q^45 - 314 * q^46 + 272 * q^47 - 776 * q^48 + 390 * q^49 + 232 * q^50 - 164 * q^51 - 560 * q^52 + 492 * q^53 + 440 * q^54 + 480 * q^56 - 1512 * q^57 + 192 * q^58 - 634 * q^59 - 632 * q^60 + 840 * q^61 + 134 * q^62 + 248 * q^63 - 224 * q^64 + 3520 * q^65 + 3016 * q^67 + 640 * q^68 - 962 * q^69 - 284 * q^70 + 678 * q^71 - 744 * q^72 - 400 * q^73 + 6 * q^74 + 520 * q^75 - 1728 * q^76 - 1760 * q^78 + 316 * q^79 + 1544 * q^80 + 1294 * q^81 - 512 * q^82 + 468 * q^83 - 736 * q^84 + 452 * q^85 + 156 * q^86 - 4800 * q^87 - 7368 * q^89 + 1532 * q^90 - 1280 * q^91 + 40 * q^92 + 638 * q^93 - 992 * q^94 + 2952 * q^95 - 952 * q^96 - 2194 * q^97 + 3480 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/121\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{2}{5}\right)$

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 $

$2$	−0.844250	−	2.59833i	−0.298487	−	0.918650i	−0.982028	−	0.188737i	$-0.939561\pi$
$2$	−0.844250	−	2.59833i	−0.298487	−	0.918650i	0.683540	−	0.729913i	$-0.260439\pi$
$3$	6.41405	+	4.66008i	1.23438	+	0.896833i	0.997211	−	0.0746343i	$-0.0237789\pi$
$3$	6.41405	+	4.66008i	1.23438	+	0.896833i	0.237174	+	0.971467i	$0.423779\pi$
$4$	0.433551	−	0.314993i	0.0541939	−	0.0393741i
$5$	4.59088	−	14.1293i	0.410621	−	1.26376i	−0.505489	−	0.862833i	$-0.668688\pi$
$5$	4.59088	−	14.1293i	0.410621	−	1.26376i	0.916110	−	0.400928i	$-0.131312\pi$
$6$	6.69339	−	20.6001i	0.455427	−	1.40166i
$7$	2.48514	−	1.80556i	0.134185	−	0.0974909i	−0.518668	−	0.854976i	$-0.673572\pi$
$7$	2.48514	−	1.80556i	0.134185	−	0.0974909i	0.652853	+	0.757485i	$0.273572\pi$
$8$	−18.8667	−	13.7075i	−0.833798	−	0.605789i
$9$	11.0802	+	34.1015i	0.410379	+	1.26302i
$10$	−40.5885			−1.28352
$11$		0			0
$11$		0			0
$12$	4.24871			0.102208
$13$	−1.65602	−	5.09670i	−0.0353305	−	0.108736i	0.931836	−	0.362880i	$-0.118206\pi$
$13$	−1.65602	−	5.09670i	−0.0353305	−	0.108736i	−0.967166	+	0.254144i	$0.918206\pi$
$14$	−6.78952	−	4.93287i	−0.129612	−	0.0941690i
$15$	95.2898	−	69.2321i	1.64025	−	1.19171i
$16$	−18.3635	+	56.5171i	−0.286930	+	0.883080i
$17$	12.7363	−	39.1982i	0.181706	−	0.559232i	−0.818170	−	0.574976i	$-0.805011\pi$
$17$	12.7363	−	39.1982i	0.181706	−	0.559232i	0.999876	+	0.0157433i	$0.00501147\pi$
$18$	79.2525	−	57.5803i	1.03778	−	0.753990i
$19$	113.200	+	82.2447i	1.36684	+	0.993065i	0.997977	+	0.0635795i	$0.0202517\pi$
$19$	113.200	+	82.2447i	1.36684	+	0.993065i	0.368860	+	0.929485i	$0.379748\pi$
$20$	−2.46025	−	7.57186i	−0.0275064	−	0.0846560i
$21$	24.3538			0.253069
$22$		0			0
$23$	−111.354			−1.00952			−0.504758	−	0.863261i	$-0.668418\pi$
$23$	−111.354			−1.00952			−0.504758	+	0.863261i	$0.668418\pi$
$24$	−57.1341	−	175.841i	−0.485935	−	1.49555i
$25$	−77.4333	−	56.2586i	−0.619466	−	0.450069i
$26$	−11.8448	+	8.60577i	−0.0893447	+	0.0649127i
$27$	−21.6977	+	66.7788i	−0.154657	+	0.475985i
$28$	0.508695	−	1.56560i	0.00343337	−	0.0105668i
$29$	−20.2213	+	14.6916i	−0.129483	+	0.0940745i	−0.650641	−	0.759385i	$-0.725500\pi$
$29$	−20.2213	+	14.6916i	−0.129483	+	0.0940745i	0.521159	+	0.853460i	$0.325500\pi$
$30$	−260.336	−	189.145i	−1.58436	−	1.15110i
$31$	9.73324	+	29.9558i	0.0563917	+	0.173556i	0.975285	−	0.220950i	$-0.0709158\pi$
$31$	9.73324	+	29.9558i	0.0563917	+	0.173556i	−0.918893	+	0.394506i	$0.870916\pi$
$32$	−24.2102			−0.133744
$33$		0			0
$34$	−112.603			−0.567976
$35$	−14.1023	−	43.4023i	−0.0681062	−	0.209609i
$36$	15.5456	+	11.2945i	0.0719703	+	0.0522895i
$37$	−10.6334	+	7.72561i	−0.0472464	+	0.0343266i	−0.611158	−	0.791509i	$-0.709296\pi$
$37$	−10.6334	+	7.72561i	−0.0472464	+	0.0343266i	0.563911	+	0.825835i	$0.309296\pi$
$38$	118.130	−	363.567i	0.504295	−	1.55206i
$39$	13.1292	−	40.4076i	0.0539067	−	0.165908i
$40$	−280.291	+	203.643i	−1.10795	+	0.804971i
$41$	211.212	+	153.454i	0.804529	+	0.584525i	0.912239	−	0.409658i	$-0.134352\pi$
$41$	211.212	+	153.454i	0.804529	+	0.584525i	−0.107710	+	0.994182i	$0.534352\pi$
$42$	−20.5607	−	63.2794i	−0.0755378	−	0.232482i
$43$	57.7128			0.204677			0.102339	−	0.994750i	$-0.467367\pi$
$43$	57.7128			0.204677			0.102339	+	0.994750i	$0.467367\pi$
$44$		0			0
$45$	532.697			1.76466
$46$	94.0105	+	289.335i	0.301328	+	0.927392i
$47$	278.177	+	202.108i	0.863326	+	0.627243i	0.928788	−	0.370612i	$-0.120852\pi$
$47$	278.177	+	202.108i	0.863326	+	0.627243i	−0.0654616	+	0.997855i	$0.520852\pi$
$48$	−381.159	+	276.928i	−1.14616	+	0.832732i
$49$	−103.077	+	317.238i	−0.300516	+	0.924893i
$50$	−80.8056	+	248.694i	−0.228553	+	0.703413i
$51$	264.358	−	192.067i	0.725833	−	0.527348i
$52$	−2.32339	−	1.68804i	−0.00619609	−	0.00450172i
$53$	−105.991	−	326.207i	−0.274698	−	0.845435i	−0.989299	−	0.145902i	$-0.953392\pi$
$53$	−105.991	−	326.207i	−0.274698	−	0.845435i	0.714601	−	0.699533i	$-0.246608\pi$
$54$	191.832			0.483426
$55$		0			0
$56$	−71.6359			−0.170942
$57$	342.804	+	1055.04i	0.796589	+	2.45165i
$58$	55.2455	+	40.1382i	0.125070	+	0.0908690i
$59$	−71.4923	+	51.9422i	−0.157754	+	0.114615i	−0.663862	−	0.747855i	$-0.731084\pi$
$59$	−71.4923	+	51.9422i	−0.157754	+	0.114615i	0.506108	+	0.862470i	$0.331084\pi$
$60$	19.5053	−	60.0312i	0.0419688	−	0.129167i
$61$	−228.270	+	702.543i	−0.479131	+	1.47461i	0.361174	+	0.932499i	$0.382376\pi$
$61$	−228.270	+	702.543i	−0.479131	+	1.47461i	−0.840305	+	0.542115i	$0.817624\pi$
$62$	69.6180	−	50.5804i	0.142605	−	0.103608i
$63$	89.1080	+	64.7408i	0.178199	+	0.129469i
$64$	167.348	+	515.043i	0.326851	+	1.00594i
$65$	−79.6152			−0.151924
$66$		0			0
$67$	342.359			0.624266			0.312133	−	0.950038i	$-0.398957\pi$
$67$	342.359			0.624266			0.312133	+	0.950038i	$0.398957\pi$
$68$	−6.82534	−	21.0062i	−0.0121720	−	0.0374615i
$69$	−714.229	−	518.918i	−1.24613	−	0.905368i
$70$	−100.868	+	73.2848i	−0.172229	+	0.125131i
$71$	−64.0790	+	197.215i	−0.107110	+	0.329650i	−0.990220	−	0.139516i	$-0.955445\pi$
$71$	−64.0790	+	197.215i	−0.107110	+	0.329650i	0.883110	+	0.469166i	$0.155445\pi$
$72$	258.397	−	795.264i	0.422949	−	1.30170i
$73$	−817.592	+	594.016i	−1.31085	+	0.952387i	−0.310851	+	0.950459i	$0.600614\pi$
$73$	−817.592	+	594.016i	−1.31085	+	0.952387i	−0.999998	+	0.00192848i	$0.999386\pi$
$74$	29.0510	+	21.1068i	0.0456366	+	0.0331569i
$75$	−234.492	−	721.691i	−0.361023	−	1.11112i
$76$	74.9845			0.113175
$77$		0			0
$78$	−116.077			−0.168502
$79$	−399.938	−	1230.88i	−0.569576	−	1.75297i	−0.653947	−	0.756540i	$-0.726888\pi$
$79$	−399.938	−	1230.88i	−0.569576	−	1.75297i	0.0843714	−	0.996434i	$-0.473112\pi$
$80$	714.242	+	518.927i	0.998183	+	0.725222i
$81$	332.863	−	241.839i	0.456602	−	0.331741i
$82$	220.410	−	678.352i	0.296832	−	0.913554i
$83$	−136.538	+	420.221i	−0.180566	+	0.555725i	−0.999844	−	0.0176715i	$-0.994375\pi$
$83$	−136.538	+	420.221i	−0.180566	+	0.555725i	0.819278	+	0.573397i	$0.194375\pi$
$84$	10.5586	−	7.67129i	0.0137148	−	0.00996436i
$85$	−495.371	−	359.908i	−0.632124	−	0.459265i
$86$	−48.7240	−	149.957i	−0.0610936	−	0.188027i
$87$	−198.164			−0.244200
$88$		0			0
$89$	−1489.11			−1.77355			−0.886773	−	0.462205i	$-0.847058\pi$
$89$	−1489.11			−1.77355			−0.886773	+	0.462205i	$0.847058\pi$
$90$	−449.730	−	1384.13i	−0.526730	−	1.62111i
$91$	−13.3178	−	9.67595i	−0.0153416	−	0.0111463i
$92$	−48.2776	+	35.0757i	−0.0547096	+	0.0397488i
$93$	−77.1671	+	237.496i	−0.0860415	+	0.264808i
$94$	290.292	−	893.427i	0.318525	−	0.980319i
$95$	1681.75	−	1221.86i	1.81625	−	1.31958i
$96$	−155.286	−	112.822i	−0.165091	−	0.119946i
$97$	416.065	+	1280.52i	0.435516	+	1.34038i	0.892557	+	0.450934i	$0.148909\pi$
$97$	416.065	+	1280.52i	0.435516	+	1.34038i	−0.457042	+	0.889445i	$0.651091\pi$
$98$	911.314			0.939353
$99$		0			0
$100$	−51.2923			−0.0512923
$101$	49.8943	+	153.559i	0.0491551	+	0.151284i	0.972621	−	0.232396i	$-0.0746566\pi$
$101$	49.8943	+	153.559i	0.0491551	+	0.151284i	−0.923466	+	0.383680i	$0.874657\pi$
$102$	−722.238	−	524.737i	−0.701101	−	0.509379i
$103$	28.1208	−	20.4309i	0.0269012	−	0.0195449i	−0.574253	−	0.818678i	$-0.694708\pi$
$103$	28.1208	−	20.4309i	0.0269012	−	0.0195449i	0.601155	+	0.799133i	$0.294708\pi$
$104$	−38.6192	+	118.858i	−0.0364127	+	0.112067i
$105$	111.806	−	344.102i	0.103915	−	0.319818i
$106$	−758.113	+	550.801i	−0.694665	+	0.504703i
$107$	673.247	+	489.143i	0.608273	+	0.441937i	0.848806	−	0.528705i	$-0.177322\pi$
$107$	673.247	+	489.143i	0.608273	+	0.441937i	−0.240532	+	0.970641i	$0.577322\pi$
$108$	11.6278	+	35.7867i	0.0103600	+	0.0318849i
$109$	−1044.26			−0.917629			−0.458815	−	0.888532i	$-0.651726\pi$
$109$	−1044.26			−0.917629			−0.458815	+	0.888532i	$0.651726\pi$
$110$		0			0
$111$	−104.205			−0.0891055
$112$	56.4090	+	173.609i	0.0475906	+	0.146469i
$113$	−238.726	−	173.445i	−0.198739	−	0.144392i	0.483965	−	0.875087i	$-0.339196\pi$
$113$	−238.726	−	173.445i	−0.198739	−	0.144392i	−0.682704	+	0.730695i	$0.739196\pi$
$114$	2451.94	−	1781.44i	2.01443	−	1.46357i
$115$	−511.212	+	1573.35i	−0.414529	+	1.27579i
$116$	−4.13919	+	12.7391i	−0.00331305	+	0.0101965i
$117$	155.456	−	112.945i	0.122837	−	0.0892461i
$118$	195.320	+	141.909i	0.152379	+	0.110710i
$119$	−39.1232	−	120.409i	−0.0301380	−	0.0927551i
$120$	−2746.80			−2.08956
$121$		0			0
$122$	2018.16			1.49767
$123$	639.613	+	1968.53i	0.468878	+	1.44306i
$124$	13.6557	+	9.92147i	0.00988969	+	0.00718528i
$125$	352.005	−	255.747i	0.251874	−	0.182997i
$126$	92.9887	−	286.190i	0.0657468	−	0.202348i
$127$	407.162	−	1253.12i	0.284487	−	0.875560i	−0.702065	−	0.712113i	$-0.747739\pi$
$127$	407.162	−	1253.12i	0.284487	−	0.875560i	0.986552	−	0.163448i	$-0.0522614\pi$
$128$	1040.28	−	755.807i	0.718348	−	0.521911i
$129$	370.173	+	268.946i	0.252650	+	0.183561i
$130$	67.2152	+	206.867i	0.0453474	+	0.139565i
$131$	1600.71			1.06759			0.533797	−	0.845612i	$-0.320765\pi$
$131$	1600.71			1.06759			0.533797	+	0.845612i	$0.320765\pi$
$132$		0			0
$133$	429.815			0.280223
$134$	−289.037	−	889.563i	−0.186336	−	0.573482i
$135$	843.925	+	613.147i	0.538026	+	0.390899i
$136$	−777.598	+	564.958i	−0.490283	+	0.356211i
$137$	498.035	−	1532.80i	0.310584	−	0.955880i	−0.666950	−	0.745103i	$-0.732400\pi$
$137$	498.035	−	1532.80i	0.310584	−	0.955880i	0.977534	−	0.210777i	$-0.0675995\pi$
$138$	−745.334	+	2293.90i	−0.459761	+	1.41500i
$139$	−25.7768	+	18.7280i	−0.0157292	+	0.0114280i	−0.595622	−	0.803265i	$-0.703094\pi$
$139$	−25.7768	+	18.7280i	−0.0157292	+	0.0114280i	0.579893	+	0.814693i	$0.303094\pi$
$140$	−19.7855	−	14.3750i	−0.0119441	−	0.00867791i
$141$	842.406	+	2592.66i	0.503144	+	1.54852i
$142$	566.529			0.334803
$143$		0			0
$144$	−2130.79			−1.23310
$145$	114.748	+	353.159i	0.0657196	+	0.202264i
$146$	2233.70	+	1622.88i	1.26618	+	0.919935i
$147$	−2139.50	+	1554.44i	−1.20043	+	0.872161i
$148$	−2.17660	+	6.69889i	−0.00120889	+	0.00372058i
$149$	750.399	−	2309.49i	0.412585	−	1.26980i	−0.501809	−	0.864978i	$-0.667332\pi$
$149$	750.399	−	2309.49i	0.412585	−	1.26980i	0.914394	−	0.404826i	$-0.132668\pi$
$150$	−1677.22	+	1218.58i	−0.912966	+	0.663308i
$151$	−2084.58	−	1514.53i	−1.12345	−	0.816231i	−0.138718	−	0.990332i	$-0.544298\pi$
$151$	−2084.58	−	1514.53i	−1.12345	−	0.816231i	−0.984728	+	0.174101i	$0.944298\pi$
$152$	−1008.35	−	3103.37i	−0.538077	−	1.65603i
$153$	1477.84			0.780889
$154$		0			0
$155$	467.939			0.242489
$156$	−7.03594	−	21.6544i	−0.00361106	−	0.0111137i
$157$	−2003.08	−	1455.32i	−1.01824	−	0.739792i	−0.0523162	−	0.998631i	$-0.516660\pi$
$157$	−2003.08	−	1455.32i	−1.01824	−	0.739792i	−0.965921	+	0.258838i	$0.916660\pi$
$158$	−2860.59	+	2078.34i	−1.44036	+	1.04648i
$159$	840.320	−	2586.24i	0.419130	−	1.28995i
$160$	−111.146	+	342.073i	−0.0549181	+	0.169020i
$161$	−276.729	+	201.056i	−0.135462	+	0.0984187i
$162$	−909.398	−	660.716i	−0.441044	−	0.320437i
$163$	−842.105	−	2591.73i	−0.404655	−	1.24540i	−0.921183	−	0.389129i	$-0.872776\pi$
$163$	−842.105	−	2591.73i	−0.404655	−	1.24540i	0.516529	−	0.856270i	$-0.327224\pi$
$164$	139.908			0.0666157
$165$		0			0
$166$	1207.15			0.564414
$167$	−845.871	−	2603.32i	−0.391949	−	1.20630i	−0.931312	−	0.364222i	$-0.881335\pi$
$167$	−845.871	−	2603.32i	−0.391949	−	1.20630i	0.539363	−	0.842073i	$-0.318665\pi$
$168$	−459.476	−	333.829i	−0.211008	−	0.153306i
$169$	1754.18	−	1274.48i	0.798442	−	0.580102i
$170$	−516.945	+	1590.99i	−0.233223	+	0.717786i
$171$	−1550.38	+	4771.58i	−0.693337	+	2.13387i
$172$	25.0214	−	18.1791i	0.0110923	−	0.00805899i
$173$	1866.74	+	1356.26i	0.820378	+	0.596040i	0.916821	−	0.399299i	$-0.130746\pi$
$173$	1866.74	+	1356.26i	0.820378	+	0.596040i	−0.0964424	+	0.995339i	$0.530746\pi$
$174$	167.300	+	514.897i	0.0728908	+	0.224335i
$175$	−294.010			−0.127001
$176$		0			0
$177$	−700.610			−0.297520
$178$	1257.18	+	3869.21i	0.529381	+	1.62927i
$179$	1061.56	+	771.265i	0.443265	+	0.322051i	0.786931	−	0.617041i	$-0.211669\pi$
$179$	1061.56	+	771.265i	0.443265	+	0.322051i	−0.343666	+	0.939092i	$0.611669\pi$
$180$	230.951	−	167.796i	0.0956339	−	0.0694821i
$181$	−248.194	+	763.864i	−0.101923	+	0.313688i	−0.988996	−	0.147942i	$-0.952735\pi$
$181$	−248.194	+	763.864i	−0.101923	+	0.313688i	0.887073	+	0.461630i	$0.152735\pi$
$182$	−13.8978	+	42.7730i	−0.00566029	+	0.0174206i
$183$	−4738.04	+	3442.39i	−1.91391	+	1.39054i
$184$	2100.88	+	1526.38i	0.841732	+	0.611554i
$185$	60.3407	+	185.710i	0.0239802	+	0.0738034i
$186$	682.242			0.268949
$187$		0			0
$188$	184.267			0.0714842
$189$	66.6511	+	205.131i	0.0256516	+	0.0789475i
$190$	−4594.62	−	3338.19i	−1.75436	−	1.27462i
$191$	−1390.09	+	1009.96i	−0.526615	+	0.382608i	−0.819090	−	0.573665i	$-0.805521\pi$
$191$	−1390.09	+	1009.96i	−0.526615	+	0.382608i	0.292475	+	0.956273i	$0.405521\pi$
$192$	−1326.77	+	4083.37i	−0.498704	+	1.53485i
$193$	−414.140	+	1274.59i	−0.154458	+	0.475373i	−0.998106	−	0.0615242i	$-0.980404\pi$
$193$	−414.140	+	1274.59i	−0.154458	+	0.475373i	0.843647	+	0.536898i	$0.180404\pi$
$194$	2975.95	−	2162.15i	1.10134	−	0.800173i
$195$	−510.656	−	371.013i	−0.187533	−	0.136250i
$196$	55.2388	+	170.007i	0.0201308	+	0.0619561i
$197$	3518.33			1.27244			0.636220	−	0.771508i	$-0.280497\pi$
$197$	3518.33			1.27244			0.636220	+	0.771508i	$0.280497\pi$
$198$		0			0
$199$	823.692			0.293417			0.146709	−	0.989180i	$-0.453132\pi$
$199$	823.692			0.293417			0.146709	+	0.989180i	$0.453132\pi$
$200$	689.748	+	2122.83i	0.243863	+	0.750532i
$201$	2195.91	+	1595.42i	0.770584	+	0.559862i
$202$	356.874	−	259.284i	0.124305	−	0.0903127i
$203$	−23.7260	+	73.0212i	−0.00820316	+	0.0252467i
$204$	54.1127	−	166.542i	0.0185718	−	0.0571581i
$205$	3137.84	−	2279.78i	1.06906	−	0.776715i
$206$	−76.8274	−	55.8184i	−0.0259846	−	0.0188789i
$207$	−1233.83	−	3797.33i	−0.414285	−	1.27504i
$208$	318.461			0.106160
$209$		0			0
$210$	−988.484			−0.324819
$211$	33.1709	+	102.089i	0.0108226	+	0.0333086i	0.956322	−	0.292315i	$-0.0944257\pi$
$211$	33.1709	+	102.089i	0.0108226	+	0.0333086i	−0.945499	+	0.325624i	$0.894426\pi$
$212$	−148.706	−	108.041i	−0.0481752	−	0.0350014i
$213$	−1330.04	+	966.334i	−0.427855	+	0.310855i
$214$	702.567	−	2162.28i	0.224423	−	0.690703i
$215$	264.953	−	815.441i	0.0840448	−	0.258663i
$216$	1324.73	−	962.474i	0.417299	−	0.303185i
$217$	78.2754	+	56.8704i	0.0244870	+	0.0177908i
$218$	881.613	+	2713.33i	0.273901	+	0.842980i
$219$	−8012.24			−2.47222
$220$		0			0
$221$	−220.873			−0.0672285
$222$	87.9752	+	270.760i	0.0265969	+	0.0818568i
$223$	3182.42	+	2312.16i	0.955651	+	0.694321i	0.952137	−	0.305672i	$-0.0988812\pi$
$223$	3182.42	+	2312.16i	0.955651	+	0.694321i	0.00351474	+	0.999994i	$0.498881\pi$
$224$	−60.1657	+	43.7130i	−0.0179464	+	0.0130388i
$225$	1060.52	−	3263.95i	0.314228	−	0.967096i
$226$	−249.123	+	766.721i	−0.0733248	+	0.225670i
$227$	−1433.50	+	1041.50i	−0.419139	+	0.304523i	−0.777291	−	0.629141i	$-0.783407\pi$
$227$	−1433.50	+	1041.50i	−0.419139	+	0.304523i	0.358152	+	0.933663i	$0.383407\pi$
$228$	480.955	+	349.434i	0.139702	+	0.101499i
$229$	591.882	+	1821.62i	0.170798	+	0.525661i	0.999417	−	0.0341519i	$-0.0108730\pi$
$229$	591.882	+	1821.62i	0.170798	+	0.525661i	−0.828619	+	0.559813i	$0.810873\pi$
$230$	4519.68			1.29573
$231$		0			0
$232$	582.892			0.164952
$233$	−1358.54	−	4181.15i	−0.381977	−	1.17561i	−0.938649	−	0.344873i	$-0.887922\pi$
$233$	−1358.54	−	4181.15i	−0.381977	−	1.17561i	0.556672	−	0.830732i	$-0.312078\pi$
$234$	−424.713	−	308.572i	−0.118651	−	0.0862051i
$235$	4132.72	−	3002.59i	1.14719	−	0.833479i
$236$	−14.6341	+	45.0391i	−0.00403644	+	0.0124229i
$237$	3170.79	−	9758.68i	0.869050	−	2.67466i
$238$	−279.833	+	203.310i	−0.0762137	+	0.0553725i
$239$	−3304.42	−	2400.80i	−0.894332	−	0.649770i	0.0426719	−	0.999089i	$-0.486413\pi$
$239$	−3304.42	−	2400.80i	−0.894332	−	0.649770i	−0.937004	+	0.349319i	$0.886413\pi$
$240$	2162.94	+	6656.85i	0.581739	+	1.79041i
$241$	−3908.58			−1.04471			−0.522353	−	0.852730i	$-0.674946\pi$
$241$	−3908.58			−1.04471			−0.522353	+	0.852730i	$0.674946\pi$
$242$		0			0
$243$	5157.80			1.36162
$244$	122.330	+	376.492i	0.0320957	+	0.0987804i
$245$	4009.13	+	2912.81i	1.04545	+	0.759561i
$246$	4574.90	−	3323.86i	1.18571	−	0.861469i
$247$	231.715	−	713.145i	0.0596910	−	0.183710i
$248$	226.984	−	698.585i	0.0581190	−	0.178872i
$249$	−2834.02	+	2059.04i	−0.721281	+	0.524041i
$250$	−961.696	−	698.713i	−0.243292	−	0.176762i
$251$	338.340	+	1041.30i	0.0850831	+	0.261859i	0.984543	−	0.175145i	$-0.0560395\pi$
$251$	338.340	+	1041.30i	0.0850831	+	0.261859i	−0.899460	+	0.437004i	$0.856040\pi$
$252$	59.0258			0.0147551
$253$		0			0
$254$	−3599.76			−0.889249
$255$	−1500.13	−	4616.94i	−0.368400	−	1.13382i
$256$	662.879	+	481.610i	0.161836	+	0.117581i
$257$	−633.605	+	460.341i	−0.153787	+	0.111733i	−0.662018	−	0.749488i	$-0.730300\pi$
$257$	−633.605	+	460.341i	−0.153787	+	0.111733i	0.508231	+	0.861221i	$0.330300\pi$
$258$	386.294	−	1188.89i	0.0932156	−	0.286888i
$259$	−12.4764	+	38.3984i	−0.00299322	+	0.00921220i
$260$	−34.5173	+	25.0783i	−0.00823334	+	0.00598187i
$261$	−725.062	−	526.788i	−0.171955	−	0.124932i
$262$	−1351.40	−	4159.19i	−0.318664	−	0.980746i
$263$	−6180.06			−1.44897			−0.724484	−	0.689292i	$-0.757922\pi$
$263$	−6180.06			−1.44897			−0.724484	+	0.689292i	$0.757922\pi$
$264$		0			0
$265$	−5095.67			−1.18122
$266$	−362.872	−	1116.80i	−0.0836432	−	0.257427i
$267$	−9551.24	−	6939.39i	−2.18924	−	1.59057i
$268$	148.430	−	107.841i	0.0338314	−	0.0245799i
$269$	304.989	−	938.659i	0.0691282	−	0.212755i	−0.910524	−	0.413455i	$-0.864322\pi$
$269$	304.989	−	938.659i	0.0691282	−	0.212755i	0.979653	+	0.200700i	$0.0643218\pi$
$270$	880.678	−	2710.45i	0.198505	−	0.610936i
$271$	3702.86	−	2690.29i	0.830011	−	0.603038i	−0.0895518	−	0.995982i	$-0.528543\pi$
$271$	3702.86	−	2690.29i	0.830011	−	0.603038i	0.919562	+	0.392944i	$0.128543\pi$
$272$	1981.49	+	1439.63i	0.441710	+	0.320921i
$273$	−40.3304	−	124.124i	−0.00894104	−	0.0275177i
$274$	−4403.18			−0.970825
$275$		0			0
$276$	−473.110			−0.103181
$277$	−175.471	−	540.044i	−0.0380615	−	0.117141i	0.930221	−	0.367001i	$-0.119615\pi$
$277$	−175.471	−	540.044i	−0.0380615	−	0.117141i	−0.968282	+	0.249860i	$0.919615\pi$
$278$	70.4236	+	51.1658i	0.0151933	+	0.0110386i
$279$	−913.691	+	663.835i	−0.196062	+	0.142447i
$280$	−328.872	+	1012.16i	−0.0701923	+	0.216030i
$281$	−1641.19	+	5051.07i	−0.348418	+	1.07232i	0.611311	+	0.791391i	$0.290643\pi$
$281$	−1641.19	+	5051.07i	−0.348418	+	1.07232i	−0.959729	+	0.280929i	$0.909357\pi$
$282$	6025.39	−	4377.70i	1.27236	−	0.924427i
$283$	−3825.39	−	2779.31i	−0.803519	−	0.583790i	0.108426	−	0.994105i	$-0.465419\pi$
$283$	−3825.39	−	2779.31i	−0.803519	−	0.583790i	−0.911944	+	0.410314i	$0.865419\pi$
$284$	34.3399	+	105.687i	0.00717498	+	0.0220823i
$285$	16480.8			3.42539
$286$		0			0
$287$	801.960			0.164941
$288$	−268.255	−	825.605i	−0.0548857	−	0.168921i
$289$	2600.42	+	1889.31i	0.529293	+	0.384554i
$290$	820.750	−	596.309i	0.166193	−	0.120747i
$291$	−3298.65	+	10152.2i	−0.664503	+	2.04513i
$292$	−167.357	+	515.072i	−0.0335405	+	0.103227i
$293$	1884.13	−	1368.90i	0.375673	−	0.272942i	−0.383886	−	0.923380i	$-0.625415\pi$
$293$	1884.13	−	1368.90i	0.375673	−	0.272942i	0.759559	+	0.650438i	$0.225415\pi$
$294$	5845.21	+	4246.80i	1.15952	+	0.842443i
$295$	405.693	+	1248.59i	0.0800690	+	0.246427i
$296$	306.515			0.0601886
$297$		0			0
$298$	−6634.36			−1.28966
$299$	184.404	+	567.537i	0.0356667	+	0.109771i
$300$	−328.992	−	239.026i	−0.0633145	−	0.0460007i
$301$	143.424	−	104.204i	0.0274646	−	0.0199542i
$302$	−2175.36	+	6695.07i	−0.414496	+	1.27569i
$303$	−395.572	+	1217.45i	−0.0750001	+	0.230827i
$304$	−6726.99	+	4887.44i	−1.26914	+	0.922086i
$305$	8878.47	+	6450.58i	1.66682	+	1.21101i
$306$	−1247.66	−	3839.91i	−0.233085	−	0.717363i
$307$	1678.07			0.311962			0.155981	−	0.987760i	$-0.450146\pi$
$307$	1678.07			0.311962			0.155981	+	0.987760i	$0.450146\pi$
$308$		0			0
$309$	275.578			0.0507349
$310$	−395.057	−	1215.86i	−0.0723798	−	0.222762i
$311$	−2890.38	−	2099.98i	−0.527005	−	0.382891i	0.292232	−	0.956348i	$-0.405602\pi$
$311$	−2890.38	−	2099.98i	−0.527005	−	0.382891i	−0.819236	+	0.573456i	$0.805602\pi$
$312$	−801.591	+	582.390i	−0.145452	+	0.105677i
$313$	2220.09	−	6832.74i	0.400917	−	1.23389i	−0.523340	−	0.852124i	$-0.675314\pi$
$313$	2220.09	−	6832.74i	0.400917	−	1.23389i	0.924257	−	0.381771i	$-0.124686\pi$
$314$	−2090.32	+	6433.33i	−0.375679	+	1.15622i
$315$	1323.83	−	961.815i	0.236791	−	0.172039i
$316$	−561.113	−	407.672i	−0.0998894	−	0.0725739i
$317$	−4.85393	−	14.9389i	−0.000860013	−	0.00264685i	0.950626	−	0.310340i	$-0.100443\pi$
$317$	−4.85393	−	14.9389i	−0.000860013	−	0.00264685i	−0.951486	+	0.307693i	$0.900443\pi$
$318$	−7429.36			−1.31012
$319$		0			0
$320$	8045.47			1.40549
$321$	2038.80	+	6274.77i	0.354500	+	1.09104i
$322$	756.039	+	549.294i	0.130846	+	0.0950651i
$323$	4665.59	−	3389.75i	0.803716	−	0.583934i
$324$	68.1353	−	209.699i	0.0116830	−	0.0359566i
$325$	−158.502	+	487.819i	−0.0270527	+	0.0832595i
$326$	−6023.24	+	4376.14i	−1.02330	+	0.743472i
$327$	−6697.91	−	4866.32i	−1.13271	−	0.822960i
$328$	−1881.40	−	5790.34i	−0.316716	−	0.974751i
$329$	1056.23			0.176996
$330$		0			0
$331$	−1318.95			−0.219022			−0.109511	−	0.993986i	$-0.534928\pi$
$331$	−1318.95			−0.219022			−0.109511	+	0.993986i	$0.534928\pi$
$332$	73.1705	+	225.196i	0.0120956	+	0.0372265i
$333$	−381.275	−	277.013i	−0.0627440	−	0.0455862i
$334$	−6050.18	+	4395.71i	−0.991171	+	0.720128i
$335$	1571.73	−	4837.29i	0.256337	−	0.788923i
$336$	−447.222	+	1376.41i	−0.0726130	+	0.223480i
$337$	−193.503	+	140.588i	−0.0312783	+	0.0227250i	−0.603315	−	0.797503i	$-0.706154\pi$
$337$	−193.503	+	140.588i	−0.0312783	+	0.0227250i	0.572036	+	0.820228i	$0.306154\pi$
$338$	−4792.50	−	3481.95i	−0.771235	−	0.560335i
$339$	−722.935	−	2224.97i	−0.115824	−	0.356471i
$340$	−328.137			−0.0523404
$341$		0			0
$342$	13707.1			2.16723
$343$	642.220	+	1976.55i	0.101098	+	0.311148i
$344$	−1088.85	−	791.096i	−0.170659	−	0.123991i
$345$	−10610.9	+	7709.25i	−1.65586	+	1.20305i
$346$	1948.04	−	5995.44i	0.302679	−	0.931551i
$347$	1811.70	−	5575.85i	0.280280	−	0.862614i	−0.707493	−	0.706720i	$-0.750174\pi$
$347$	1811.70	−	5575.85i	0.280280	−	0.862614i	0.987774	−	0.155894i	$-0.0498259\pi$
$348$	−85.9143	+	62.4204i	−0.0132342	+	0.00961518i
$349$	2824.87	+	2052.39i	0.433271	+	0.314790i	0.782956	−	0.622078i	$-0.213711\pi$
$349$	2824.87	+	2052.39i	0.433271	+	0.314790i	−0.349684	+	0.936868i	$0.613711\pi$
$350$	248.218	+	763.937i	0.0379081	+	0.116669i
$351$	376.283			0.0572208
$352$		0			0
$353$	−10916.7			−1.64600			−0.822999	−	0.568043i	$-0.807701\pi$
$353$	−10916.7			−1.64600			−0.822999	+	0.568043i	$0.807701\pi$
$354$	591.490	+	1820.42i	0.0888060	+	0.273317i
$355$	2492.33	+	1810.78i	0.372617	+	0.270722i
$356$	−645.606	+	469.060i	−0.0961153	+	0.0698319i
$357$	310.177	−	954.625i	0.0459840	−	0.141524i
$358$	1107.79	−	3409.42i	0.163543	−	0.503333i
$359$	−9304.29	+	6759.96i	−1.36786	+	0.993808i	−0.369959	+	0.929048i	$0.620628\pi$
$359$	−9304.29	+	6759.96i	−1.36786	+	0.993808i	−0.997901	+	0.0647598i	$0.979372\pi$
$360$	−10050.2	−	7301.92i	−1.47137	−	1.06901i
$361$	3930.53	+	12096.9i	0.573047	+	1.76366i
$362$	2194.31			0.318592
$363$		0			0
$364$	−8.82180			−0.00127030
$365$	4639.54	+	14279.0i	0.665328	+	2.04767i
$366$	12944.6	+	9404.78i	1.84870	+	1.34316i
$367$	−5474.62	+	3977.55i	−0.778673	+	0.565739i	−0.904580	−	0.426303i	$-0.859816\pi$
$367$	−5474.62	+	3977.55i	−0.778673	+	0.565739i	0.125908	+	0.992042i	$0.459816\pi$
$368$	2044.85	−	6293.40i	0.289661	−	0.891484i
$369$	−2892.74	+	8902.93i	−0.408103	+	1.25601i
$370$	431.593	−	313.571i	0.0606417	−	0.0440588i
$371$	−852.389	−	619.297i	−0.119283	−	0.0866638i
$372$	41.3537	+	127.274i	0.00576368	+	0.0177388i
$373$	5310.22			0.737139			0.368569	−	0.929600i	$-0.379848\pi$
$373$	5310.22			0.737139			0.368569	+	0.929600i	$0.379848\pi$
$374$		0			0
$375$	3449.58			0.475028
$376$	−2477.90	−	7626.20i	−0.339862	−	1.04599i
$377$	108.365	+	78.7321i	0.0148040	+	0.0107557i
$378$	476.729	−	346.364i	0.0648684	−	0.0471297i
$379$	−259.039	+	797.239i	−0.0351080	+	0.108051i	−0.967075	−	0.254492i	$-0.918092\pi$
$379$	−259.039	+	797.239i	−0.0351080	+	0.108051i	0.931967	+	0.362544i	$0.118092\pi$
$380$	344.245	−	1059.48i	0.0464721	−	0.143026i
$381$	8451.19	−	6140.15i	1.13640	−	0.825641i
$382$	3797.80	+	2759.26i	0.508671	+	0.369571i
$383$	−875.187	−	2693.55i	−0.116762	−	0.359357i	0.875548	−	0.483131i	$-0.160500\pi$
$383$	−875.187	−	2693.55i	−0.116762	−	0.359357i	−0.992311	+	0.123773i	$0.960500\pi$
$384$	10194.5			1.35479
$385$		0			0
$386$	3661.45			0.482806
$387$	639.472	+	1968.09i	0.0839953	+	0.258511i
$388$	583.740	+	424.112i	0.0763786	+	0.0554923i
$389$	−2517.06	+	1828.75i	−0.328072	+	0.238358i	−0.739612	−	0.673034i	$-0.764991\pi$
$389$	−2517.06	+	1828.75i	−0.328072	+	0.238358i	0.411540	+	0.911392i	$0.364991\pi$
$390$	−532.896	+	1640.08i	−0.0691903	+	0.212946i
$391$	−1418.23	+	4364.87i	−0.183435	+	0.564554i
$392$	6293.25	−	4572.31i	0.810860	−	0.589124i
$393$	10267.1	+	7459.45i	1.31782	+	0.957454i
$394$	−2970.35	−	9141.79i	−0.379807	−	1.16893i
$395$	−19227.5			−2.44922
$396$		0			0
$397$	14208.7			1.79626			0.898131	−	0.439728i	$-0.144925\pi$
$397$	14208.7			1.79626			0.898131	+	0.439728i	$0.144925\pi$
$398$	−695.402	−	2140.23i	−0.0875813	−	0.269548i
$399$	2756.86	+	2002.97i	0.345903	+	0.251314i
$400$	4601.52	−	3343.20i	0.575190	−	0.417900i
$401$	−1934.97	+	5955.21i	−0.240967	+	0.741619i	0.755307	+	0.655371i	$0.227488\pi$
$401$	−1934.97	+	5955.21i	−0.240967	+	0.741619i	−0.996274	+	0.0862478i	$0.972512\pi$
$402$	2291.54	−	7052.64i	0.284308	−	0.875009i
$403$	136.557	−	99.2147i	0.0168794	−	0.0122636i
$404$	70.0017	+	50.8592i	0.00862058	+	0.00626322i
$405$	−1888.88	−	5813.37i	−0.231751	−	0.713256i
$406$	209.764			0.0256415
$407$		0			0
$408$	−7620.30			−0.924660
$409$	1295.55	+	3987.31i	0.156628	+	0.482053i	0.998322	−	0.0579024i	$-0.0184412\pi$
$409$	1295.55	+	3987.31i	0.156628	+	0.482053i	−0.841694	+	0.539955i	$0.818441\pi$
$410$	−8572.75	−	6228.47i	−1.03263	−	0.750249i
$411$	10337.4	−	7510.54i	1.24065	−	0.901382i
$412$	5.75618	−	17.7157i	0.000688318	−	0.00211842i
$413$	−83.8834	+	258.167i	−0.00999427	+	0.0307592i
$414$	−8825.07	+	6411.79i	−1.04765	+	0.761165i
$415$	5310.59	+	3858.37i	0.628160	+	0.456385i
$416$	40.0926	+	123.392i	0.00472524	+	0.0145428i
$417$	−252.608			−0.0296649
$418$		0			0
$419$	−9287.15			−1.08283			−0.541416	−	0.840755i	$-0.682112\pi$
$419$	−9287.15			−1.08283			−0.541416	+	0.840755i	$0.682112\pi$
$420$	−59.9164	−	184.404i	−0.00696100	−	0.0214238i
$421$	−10635.3	−	7727.03i	−1.23120	−	0.894519i	−0.234220	−	0.972184i	$-0.575254\pi$
$421$	−10635.3	−	7727.03i	−1.23120	−	0.894519i	−0.996980	+	0.0776651i	$0.975254\pi$
$422$	237.258	−	172.378i	0.0273686	−	0.0198844i
$423$	−3809.90	+	11725.7i	−0.437928	+	1.34780i
$424$	−2471.77	+	7607.32i	−0.283113	+	0.871331i
$425$	−3191.44	+	2318.72i	−0.364254	+	0.264646i
$426$	3633.75	+	2640.07i	0.413276	+	0.300263i
$427$	701.199	+	2158.07i	0.0794693	+	0.244581i
$428$	445.964			0.0503656
$429$		0			0
$430$	−2342.47			−0.262707
$431$	−1517.17	−	4669.37i	−0.169558	−	0.521846i	0.829785	−	0.558083i	$-0.188463\pi$
$431$	−1517.17	−	4669.37i	−0.169558	−	0.521846i	−0.999343	+	0.0362369i	$0.988463\pi$
$432$	−3375.70	−	2452.59i	−0.375957	−	0.273149i
$433$	9500.53	−	6902.54i	1.05443	−	0.766085i	0.0813771	−	0.996683i	$-0.474068\pi$
$433$	9500.53	−	6902.54i	1.05443	−	0.766085i	0.973049	+	0.230598i	$0.0740682\pi$
$434$	81.6843	−	251.398i	0.00903450	−	0.0278053i
$435$	−909.749	+	2799.92i	−0.100274	+	0.308611i
$436$	−452.738	+	328.934i	−0.0497299	+	0.0361309i
$437$	−12605.3	−	9158.26i	−1.37984	−	1.00252i
$438$	6764.34	+	20818.5i	0.737928	+	2.27111i
$439$	11824.2			1.28551			0.642754	−	0.766073i	$-0.277792\pi$
$439$	11824.2			1.28551			0.642754	+	0.766073i	$0.277792\pi$
$440$		0			0
$441$	−11960.4			−1.29148
$442$	186.472	+	573.901i	0.0200669	+	0.0617595i
$443$	−8172.78	−	5937.87i	−0.876525	−	0.636833i	0.0558049	−	0.998442i	$-0.482228\pi$
$443$	−8172.78	−	5937.87i	−0.876525	−	0.636833i	−0.932330	+	0.361609i	$0.882228\pi$
$444$	−45.1782	+	32.8239i	−0.00482897	+	0.00350845i
$445$	−6836.34	+	21040.1i	−0.728255	+	2.24134i
$446$	3321.01	−	10221.0i	0.352588	−	1.08516i
$447$	15575.5	−	11316.3i	1.64809	−	1.19741i
$448$	1345.82	+	977.797i	0.141929	+	0.103117i
$449$	−106.689	−	328.356i	−0.0112138	−	0.0345124i	0.945293	−	0.326222i	$-0.105776\pi$
$449$	−106.689	−	328.356i	−0.0112138	−	0.0345124i	−0.956507	+	0.291710i	$0.905776\pi$
$450$	−9376.17			−0.982216
$451$		0			0
$452$	−158.134			−0.0164557
$453$	−6312.73	−	19428.6i	−0.654741	−	2.01509i
$454$	3916.39	+	2845.42i	0.404858	+	0.294146i
$455$	−197.855	+	143.750i	−0.0203859	+	0.0148112i
$456$	7994.37	−	24604.2i	0.820989	−	2.52674i
$457$	3265.43	−	10050.0i	0.334246	−	1.02870i	−0.632847	−	0.774277i	$-0.718114\pi$
$457$	3265.43	−	10050.0i	0.334246	−	1.02870i	0.967092	−	0.254426i	$-0.0818864\pi$
$458$	4233.49	−	3075.81i	0.431918	−	0.313806i
$459$	2341.26	+	1701.02i	0.238084	+	0.172978i
$460$	273.958	+	843.156i	0.0277682	+	0.0854616i
$461$	−4733.96			−0.478270			−0.239135	−	0.970986i	$-0.576864\pi$
$461$	−4733.96			−0.478270			−0.239135	+	0.970986i	$0.576864\pi$
$462$		0			0
$463$	3431.20			0.344409			0.172204	−	0.985061i	$-0.444911\pi$
$463$	3431.20			0.344409			0.172204	+	0.985061i	$0.444911\pi$
$464$	−458.994	−	1412.64i	−0.0459229	−	0.141336i
$465$	3001.38	+	2180.63i	0.299324	+	0.217472i
$466$	−9717.07	+	7059.87i	−0.965954	+	0.701807i
$467$	1581.23	−	4866.52i	0.156682	−	0.482218i	−0.841645	−	0.540031i	$-0.818413\pi$
$467$	1581.23	−	4866.52i	0.156682	−	0.482218i	0.998327	+	0.0578129i	$0.0184127\pi$
$468$	31.8210	−	97.9350i	0.00314301	−	0.00967318i
$469$	850.809	−	618.149i	0.0837669	−	0.0608602i
$470$	−11290.8	−	8203.24i	−1.10810	−	0.805079i
$471$	−6065.94	−	18669.0i	−0.593426	−	1.82638i
$472$	2060.82			0.200968
$473$		0			0
$474$	−28033.2			−2.71648
$475$	−4138.49	−	12737.0i	−0.399762	−	1.23034i
$476$	−54.8898	−	39.8798i	−0.00528545	−	0.00384010i
$477$	9949.75	−	7228.91i	0.955068	−	0.693898i
$478$	−3448.33	+	10612.9i	−0.329965	+	1.01553i
$479$	−3574.36	+	11000.8i	−0.340954	+	1.04935i	0.622761	+	0.782412i	$0.286011\pi$
$479$	−3574.36	+	11000.8i	−0.340954	+	1.04935i	−0.963714	+	0.266936i	$0.913989\pi$
$480$	−2306.99	+	1676.12i	−0.219373	+	0.159384i
$481$	56.9842	+	41.4014i	0.00540178	+	0.00392462i
$482$	3299.82	+	10155.8i	0.311832	+	0.959719i
$483$	−2711.89			−0.255477
$484$		0			0
$485$	20002.9			1.87275
$486$	−4354.48	−	13401.7i	−0.406426	−	1.25085i
$487$	14826.5	+	10772.1i	1.37957	+	1.00232i	0.996920	+	0.0784263i	$0.0249895\pi$
$487$	14826.5	+	10772.1i	1.37957	+	1.00232i	0.382653	+	0.923892i	$0.375010\pi$
$488$	13936.8	−	10125.7i	1.29280	−	0.939277i
$489$	6676.38	−	20547.8i	0.617415	−	1.90021i
$490$	4183.73	−	12876.2i	0.385718	−	1.18712i
$491$	−6162.75	+	4477.50i	−0.566438	+	0.411541i	−0.833810	−	0.552052i	$-0.813845\pi$
$491$	−6162.75	+	4477.50i	−0.566438	+	0.411541i	0.267371	+	0.963594i	$0.413845\pi$
$492$	897.377	+	651.982i	0.0822294	+	0.0597432i
$493$	318.341	+	979.752i	0.0290818	+	0.0895047i
$494$	−2048.62			−0.186582
$495$		0			0
$496$	−1871.75			−0.169444
$497$	196.838	+	605.804i	0.0177654	+	0.0546761i
$498$	7742.70	+	5625.40i	0.696704	+	0.506185i
$499$	−10443.7	+	7587.79i	−0.936922	+	0.680714i	−0.947678	−	0.319228i	$-0.896576\pi$
$499$	−10443.7	+	7587.79i	−0.936922	+	0.680714i	0.0107555	+	0.999942i	$0.496576\pi$
$500$	72.0537	−	221.758i	0.00644468	−	0.0198347i
$501$	6706.24	−	20639.7i	0.598029	−	1.84055i
$502$	2420.01	−	1758.24i	0.215160	−	0.156323i
$503$	8224.18	+	5975.22i	0.729022	+	0.529666i	0.889254	−	0.457414i	$-0.151224\pi$
$503$	8224.18	+	5975.22i	0.729022	+	0.529666i	−0.160232	+	0.987079i	$0.551224\pi$
$504$	−793.742	−	2442.89i	−0.0701510	−	0.215903i
$505$	2398.74			0.211371
$506$		0			0
$507$	17190.6			1.50584
$508$	−218.198	−	671.543i	−0.0190570	−	0.0586514i
$509$	−5218.10	−	3791.18i	−0.454398	−	0.330139i	0.336932	−	0.941529i	$-0.390611\pi$
$509$	−5218.10	−	3791.18i	−0.454398	−	0.330139i	−0.791330	+	0.611390i	$0.790611\pi$
$510$	−10729.9	+	7795.71i	−0.931621	+	0.676862i
$511$	−959.299	+	2952.42i	−0.0830468	+	0.255592i
$512$	3870.56	−	11912.4i	0.334094	−	1.02824i
$513$	−7948.39	+	5774.84i	−0.684074	+	0.497009i
$514$	1731.04	+	1257.68i	0.148547	+	0.107925i
$515$	−159.575	−	491.123i	−0.0136539	−	0.0420222i
$516$	245.205			0.0209197
$517$		0			0
$518$	110.305			0.00935623
$519$	5653.05	+	17398.3i	0.478114	+	1.47148i
$520$	1502.08	+	1091.32i	0.126674	+	0.0920339i
$521$	15636.2	−	11360.4i	1.31485	−	0.955292i	0.314866	−	0.949136i	$-0.398041\pi$
$521$	15636.2	−	11360.4i	1.31485	−	0.955292i	0.999981	−	0.00615574i	$-0.00195944\pi$
$522$	−756.638	+	2328.69i	−0.0634428	+	0.195257i
$523$	−1934.17	+	5952.75i	−0.161712	+	0.497697i	−0.998779	−	0.0494027i	$-0.984268\pi$
$523$	−1934.17	+	5952.75i	−0.161712	+	0.497697i	0.837067	+	0.547100i	$0.184268\pi$
$524$	693.990	−	504.213i	0.0578571	−	0.0420356i
$525$	−1885.80	−	1370.11i	−0.156767	−	0.113898i
$526$	5217.51	+	16057.9i	0.432499	+	1.33109i
$527$	1298.18			0.107305
$528$		0			0
$529$	232.675			0.0191235
$530$	4302.02	+	13240.3i	0.352581	+	1.08513i
$531$	−2563.46	−	1862.46i	−0.209500	−	0.152211i
$532$	186.347	−	135.389i	0.0151864	−	0.0110336i
$533$	432.339	−	1330.60i	0.0351345	−	0.108133i
$534$	−9967.21	+	30675.9i	−0.807721	+	2.48591i
$535$	10002.0	−	7266.90i	0.808272	−	0.587244i
$536$	−6459.18	−	4692.87i	−0.520511	−	0.378174i
$537$	3214.71	+	9893.87i	0.258333	+	0.795069i
$538$	−2696.44			−0.216081
$539$		0			0
$540$	559.022			0.0445490
$541$	4328.76	+	13322.6i	0.344007	+	1.05875i	0.962113	+	0.272651i	$0.0879004\pi$
$541$	4328.76	+	13322.6i	0.344007	+	1.05875i	−0.618106	+	0.786095i	$0.712100\pi$
$542$	−10116.4	−	7350.00i	−0.801729	−	0.582490i
$543$	−5151.60	+	3742.85i	−0.407139	+	0.295803i
$544$	−308.348	+	948.997i	−0.0243020	+	0.0747939i
$545$	−4794.06	+	14754.6i	−0.376798	+	1.15966i
$546$	−288.467	+	209.584i	−0.0226103	+	0.0164274i
$547$	−4004.19	−	2909.21i	−0.312992	−	0.227402i	0.420187	−	0.907437i	$-0.361964\pi$
$547$	−4004.19	−	2909.21i	−0.312992	−	0.227402i	−0.733179	+	0.680035i	$0.761964\pi$
$548$	−266.896	−	821.423i	−0.0208052	−	0.0640318i
$549$	−26487.0			−2.05909
$550$		0			0
$551$	−3497.35			−0.270404
$552$	6362.10	+	19580.5i	0.490559	+	1.50979i
$553$	−3216.33	−	2336.80i	−0.247327	−	0.179694i
$554$	−1255.07	+	911.864i	−0.0962508	+	0.0699303i
$555$	−478.393	+	1472.34i	−0.0365886	+	0.112608i
$556$	−5.27639	+	16.2391i	−0.000402462	+	0.00123865i
$557$	−3075.54	+	2234.51i	−0.233958	+	0.169981i	−0.698587	−	0.715525i	$-0.746188\pi$
$557$	−3075.54	+	2234.51i	−0.233958	+	0.169981i	0.464629	+	0.885505i	$0.346188\pi$
$558$	2496.25	+	1813.63i	0.189381	+	0.137594i
$559$	−95.5734	−	294.145i	−0.00723135	−	0.0222558i
$560$	2711.94			0.204644
$561$		0			0
$562$	14510.0			1.08908
$563$	3059.30	+	9415.57i	0.229013	+	0.704829i	0.997859	+	0.0653958i	$0.0208310\pi$
$563$	3059.30	+	9415.57i	0.229013	+	0.704829i	−0.768847	+	0.639433i	$0.779169\pi$
$564$	1181.90	+	858.697i	0.0882389	+	0.0641093i
$565$	−3546.61	+	2576.76i	−0.264083	+	0.191868i
$566$	−3991.99	+	12286.1i	−0.296459	+	0.912407i
$567$	390.555	−	1202.01i	0.0289273	−	0.0890291i
$568$	3912.27	−	2842.43i	0.289006	−	0.209975i
$569$	4311.38	+	3132.40i	0.317649	+	0.230786i	0.735172	−	0.677881i	$-0.237102\pi$
$569$	4311.38	+	3132.40i	0.317649	+	0.230786i	−0.417523	+	0.908667i	$0.637102\pi$
$570$	−13913.9	−	42822.6i	−1.02244	−	3.14674i
$571$	16962.6			1.24319			0.621597	−	0.783337i	$-0.286484\pi$
$571$	16962.6			1.24319			0.621597	+	0.783337i	$0.286484\pi$
$572$		0			0
$573$	−13622.6			−0.993181
$574$	−677.054	−	2083.76i	−0.0492329	−	0.151523i
$575$	8622.49	+	6264.61i	0.625361	+	0.454352i
$576$	−15709.5	+	11413.6i	−1.13639	+	0.825637i
$577$	−4785.74	+	14729.0i	−0.345291	+	1.06270i	0.616137	+	0.787639i	$0.288697\pi$
$577$	−4785.74	+	14729.0i	−0.345291	+	1.06270i	−0.961428	+	0.275057i	$0.911303\pi$
$578$	2713.67	−	8351.81i	0.195283	−	0.601020i
$579$	−8596.01	+	6245.37i	−0.616991	+	0.448270i
$580$	160.992	+	116.968i	0.0115256	+	0.00837382i
$581$	419.417	+	1290.83i	0.0299490	+	0.0921734i
$582$	29163.7			2.07710
$583$		0			0
$584$	23567.7			1.66993
$585$	−882.156	−	2715.00i	−0.0623464	−	0.191883i
$586$	−5147.55	−	3739.91i	−0.362872	−	0.263642i
$587$	−8967.27	+	6515.10i	−0.630526	+	0.458104i	−0.856582	−	0.516010i	$-0.827417\pi$
$587$	−8967.27	+	6515.10i	−0.630526	+	0.458104i	0.226056	+	0.974114i	$0.427417\pi$
$588$	−437.944	+	1347.85i	−0.0307152	+	0.0945316i
$589$	−1361.90	+	4191.51i	−0.0952738	+	0.293223i
$590$	2901.76	−	2108.25i	0.202481	−	0.147111i
$591$	22566.7	+	16395.7i	1.57068	+	1.14117i
$592$	−241.363	−	742.838i	−0.0167567	−	0.0515717i
$593$	−4349.68			−0.301214			−0.150607	−	0.988594i	$-0.548123\pi$
$593$	−4349.68			−0.301214			−0.150607	+	0.988594i	$0.548123\pi$
$594$		0			0
$595$	−1880.90			−0.129596
$596$	−402.138	−	1237.65i	−0.0276379	−	0.0850608i
$597$	5283.20	+	3838.47i	0.362190	+	0.263146i
$598$	1318.97	−	958.286i	0.0901950	−	0.0655305i
$599$	4074.05	−	12538.7i	0.277899	−	0.855284i	−0.710539	−	0.703658i	$-0.751549\pi$
$599$	4074.05	−	12538.7i	0.277899	−	0.855284i	0.988438	−	0.151627i	$-0.0484512\pi$
$600$	−5468.46	+	16830.2i	−0.372082	+	1.14515i
$601$	−15181.2	+	11029.8i	−1.03037	+	0.748611i	−0.968384	−	0.249466i	$-0.919745\pi$
$601$	−15181.2	+	11029.8i	−1.03037	+	0.748611i	−0.0619905	+	0.998077i	$0.519745\pi$
$602$	−391.842	−	284.690i	−0.0265287	−	0.0192742i
$603$	3793.42	+	11674.9i	0.256186	+	0.788459i
$604$	−1380.84			−0.0930223
$605$		0			0
$606$	3497.29			0.234435
$607$	−6758.62	−	20800.9i	−0.451934	−	1.39091i	−0.874697	−	0.484669i	$-0.838940\pi$
$607$	−6758.62	−	20800.9i	−0.451934	−	1.39091i	0.422763	−	0.906240i	$-0.361060\pi$
$608$	−2740.60	−	1991.16i	−0.182806	−	0.132816i
$609$	−492.465	+	357.797i	−0.0327680	+	0.0238073i
$610$	9265.13	−	28515.1i	0.614974	−	1.89270i
$611$	569.415	−	1752.48i	0.0377022	−	0.116036i
$612$	640.717	−	465.508i	0.0423194	−	0.0307468i
$613$	−2854.09	−	2073.62i	−0.188052	−	0.136628i	0.489776	−	0.871848i	$-0.337079\pi$
$613$	−2854.09	−	2073.62i	−0.188052	−	0.136628i	−0.677828	+	0.735221i	$0.737079\pi$
$614$	−1416.71	−	4360.18i	−0.0931167	−	0.286584i
$615$	30750.2			2.01621
$616$		0			0
$617$	−22728.1			−1.48298			−0.741490	−	0.670963i	$-0.765881\pi$
$617$	−22728.1			−1.48298			−0.741490	+	0.670963i	$0.765881\pi$
$618$	−232.657	−	716.044i	−0.0151437	−	0.0466076i
$619$	17348.0	+	12604.1i	1.12645	+	0.818417i	0.985175	−	0.171553i	$-0.0548785\pi$
$619$	17348.0	+	12604.1i	1.12645	+	0.818417i	0.141279	+	0.989970i	$0.454879\pi$
$620$	202.875	−	147.397i	0.0131414	−	0.00954778i
$621$	2416.13	−	7436.08i	0.156129	−	0.480514i
$622$	−3016.26	+	9283.09i	−0.194439	+	0.598421i
$623$	−3700.65	+	2688.68i	−0.237983	+	0.172905i
$624$	2042.62	+	1484.05i	0.131042	+	0.0952079i
$625$	−5694.61	−	17526.2i	−0.364455	−	1.12168i
$626$	−19628.0			−1.25319
$627$		0			0
$628$	−1326.85			−0.0843109
$629$	167.400	+	515.205i	0.0106116	+	0.0326591i
$630$	−3616.76	−	2627.73i	−0.228722	−	0.166177i
$631$	−17419.7	+	12656.2i	−1.09900	+	0.798469i	−0.980896	−	0.194532i	$-0.937681\pi$
$631$	−17419.7	+	12656.2i	−1.09900	+	0.798469i	−0.118103	+	0.993001i	$0.537681\pi$
$632$	−9326.75	+	28704.8i	−0.587022	+	1.80667i
$633$	−262.985	+	809.386i	−0.0165130	+	0.0508218i
$634$	−34.7183	+	25.2243i	−0.00217482	+	0.00158010i
$635$	−15836.4	−	11505.8i	−0.989683	−	0.719047i
$636$	−450.326	−	1385.96i	−0.0280764	−	0.0864103i
$637$	1787.56			0.111187
$638$		0			0
$639$	−7435.33			−0.460309
$640$	−5903.22	−	18168.2i	−0.364602	−	1.12213i
$641$	−16300.3	−	11842.9i	−1.00440	−	0.729742i	−0.0413758	−	0.999144i	$-0.513174\pi$
$641$	−16300.3	−	11842.9i	−1.00440	−	0.729742i	−0.963028	+	0.269402i	$0.913174\pi$
$642$	14582.7	−	10595.0i	0.896470	−	0.651323i
$643$	8921.22	−	27456.7i	0.547152	−	1.68396i	−0.168666	−	0.985673i	$-0.553946\pi$
$643$	8921.22	−	27456.7i	0.547152	−	1.68396i	0.715818	−	0.698287i	$-0.246054\pi$
$644$	−56.6451	+	174.336i	−0.00346604	+	0.0106674i
$645$	5499.44	−	3995.58i	0.335721	−	0.243916i
$646$	−12746.6	−	9260.96i	−0.776330	−	0.564037i
$647$	−491.344	−	1512.20i	−0.0298558	−	0.0918868i	0.935018	−	0.354600i	$-0.115383\pi$
$647$	−491.344	−	1512.20i	−0.0298558	−	0.0918868i	−0.964874	+	0.262713i	$0.915383\pi$
$648$	−9595.02			−0.581679
$649$		0			0
$650$	1401.33			0.0845612
$651$	237.042	+	729.539i	0.0142710	+	0.0439215i
$652$	−1181.47	−	858.390i	−0.0709663	−	0.0515601i
$653$	−16203.0	+	11772.2i	−0.971017	+	0.705485i	−0.955683	−	0.294397i	$-0.904881\pi$
$653$	−16203.0	+	11772.2i	−0.971017	+	0.705485i	−0.0153339	+	0.999882i	$0.504881\pi$
$654$	−6989.61	+	21511.8i	−0.417913	+	1.28621i
$655$	7348.68	−	22616.9i	0.438377	−	1.34918i
$656$	−12551.4	+	9119.11i	−0.747026	+	0.542746i
$657$	−29315.9	−	21299.3i	−1.74083	−	1.26478i
$658$	−891.718	−	2744.43i	−0.0528310	−	0.162597i
$659$	10520.7			0.621897			0.310948	−	0.950427i	$-0.399353\pi$
$659$	10520.7			0.621897			0.310948	+	0.950427i	$0.399353\pi$
$660$		0			0
$661$	3295.83			0.193938			0.0969690	−	0.995287i	$-0.469085\pi$
$661$	3295.83			0.193938			0.0969690	+	0.995287i	$0.469085\pi$
$662$	1113.53	+	3427.08i	0.0653752	+	0.201204i
$663$	−1416.69	−	1029.28i	−0.0829858	−	0.0602927i
$664$	8336.17	−	6056.58i	0.487208	−	0.353977i
$665$	1973.23	−	6072.98i	0.115066	−	0.354135i
$666$	−397.880	+	1224.55i	−0.0231494	+	0.0712467i
$667$	2251.71	−	1635.97i	0.130715	−	0.0949698i
$668$	−1186.76	−	862.230i	−0.0687381	−	0.0499411i
$669$	9637.32	+	29660.6i	0.556951	+	1.71412i
$670$	−13895.8			−0.801257
$671$		0			0
$672$	−589.612			−0.0338464
$673$	367.000	+	1129.51i	0.0210205	+	0.0646946i	0.961017	−	0.276491i	$-0.0891716\pi$
$673$	367.000	+	1129.51i	0.0210205	+	0.0646946i	−0.939996	+	0.341185i	$0.889172\pi$
$674$	528.660	+	384.094i	0.0302125	+	0.0219507i
$675$	5437.01	−	3950.22i	0.310030	−	0.225250i
$676$	359.071	−	1105.11i	0.0204296	−	0.0628759i
$677$	−4085.63	+	12574.3i	−0.231940	+	0.713839i	0.765572	+	0.643350i	$0.222456\pi$
$677$	−4085.63	+	12574.3i	−0.231940	+	0.713839i	−0.997513	+	0.0704888i	$0.977544\pi$
$678$	−5170.87	+	3756.86i	−0.292900	+	0.212804i
$679$	3346.02	+	2431.03i	0.189114	+	0.137400i
$680$	4412.59	+	13580.6i	0.248846	+	0.765868i
$681$	−14048.0			−0.790485
$682$		0			0
$683$	−13831.4			−0.774882			−0.387441	−	0.921894i	$-0.626641\pi$
$683$	−13831.4			−0.774882			−0.387441	+	0.921894i	$0.626641\pi$
$684$	830.847	+	2557.08i	0.0464448	+	0.142942i
$685$	−19370.9	−	14073.8i	−1.08047	−	0.785009i
$686$	4593.54	−	3337.40i	0.255659	−	0.185747i
$687$	−4692.56	+	14442.2i	−0.260600	+	0.802045i
$688$	−1059.81	+	3261.76i	−0.0587281	+	0.180746i
$689$	−1487.06	+	1080.41i	−0.0822240	+	0.0597393i
$690$	28989.5	+	21062.1i	1.59943	+	1.16206i
$691$	−3033.64	−	9336.59i	−0.167012	−	0.514010i	0.832167	−	0.554525i	$-0.187100\pi$
$691$	−3033.64	−	9336.59i	−0.167012	−	0.514010i	−0.999179	+	0.0405154i	$0.987100\pi$
$692$	1236.54			0.0679280
$693$		0			0
$694$	−16017.4			−0.876101
$695$	146.274	+	450.186i	0.00798346	+	0.0245706i
$696$	3738.70	+	2716.33i	0.203614	+	0.147934i
$697$	8705.17	−	6324.67i	0.473073	−	0.343707i
$698$	2947.89	−	9072.68i	0.159856	−	0.491986i
$699$	10770.8	−	33149.0i	0.582815	−	1.79372i
$700$	−127.468	+	92.6112i	−0.00688265	+	0.00500054i
$701$	24229.9	+	17604.0i	1.30549	+	0.948495i	0.999993	−	0.00369814i	$-0.00117716\pi$
$701$	24229.9	+	17604.0i	1.30549	+	0.948495i	0.305498	+	0.952193i	$0.401177\pi$
$702$	−317.677	−	977.710i	−0.0170797	−	0.0525659i
$703$	−1839.09			−0.0986667
$704$		0			0
$705$	40499.8			2.16356
$706$	9216.43	+	28365.2i	0.491310	+	1.51210i
$707$	401.253	+	291.528i	0.0213447	+	0.0155078i
$708$	−303.750	+	220.687i	−0.0161238	+	0.0117146i
$709$	3494.21	−	10754.1i	0.185088	−	0.569644i	−0.814861	−	0.579656i	$-0.803187\pi$
$709$	3494.21	−	10754.1i	0.185088	−	0.569644i	0.999950	+	0.0100121i	$0.00318701\pi$
$710$	2600.87	−	8004.65i	0.137477	−	0.423112i
$711$	37543.5	−	27276.9i	1.98030	−	1.43877i
$712$	28094.6	+	20411.9i	1.47878	+	1.07440i
$713$	−1083.83	−	3335.70i	−0.0569283	−	0.175207i
$714$	−2742.30			−0.143737
$715$		0			0
$716$	703.181			0.0367027
$717$	−10006.8	−	30797.8i	−0.521214	−	1.60413i
$718$	25419.8	+	18468.6i	1.32125	+	0.959945i
$719$	26392.9	−	19175.6i	1.36897	−	0.994615i	0.371154	−	0.928571i	$-0.378962\pi$
$719$	26392.9	−	19175.6i	1.36897	−	0.994615i	0.997817	−	0.0660438i	$-0.0210377\pi$
$720$	−9782.20	+	30106.5i	−0.506335	+	1.55834i
$721$	32.9947	−	101.547i	0.00170428	−	0.00524524i
$722$	28113.5	−	20425.7i	1.44914	−	1.05286i
$723$	−25069.9	−	18214.3i	−1.28957	−	0.936926i
$724$	133.007	+	409.353i	0.00682758	+	0.0210131i
$725$	2392.33			0.122550
$726$		0			0
$727$	−502.545			−0.0256373			−0.0128187	−	0.999918i	$-0.504080\pi$
$727$	−502.545			−0.0256373			−0.0128187	+	0.999918i	$0.504080\pi$
$728$	118.630	+	365.106i	0.00603946	+	0.0185876i
$729$	24095.1	+	17506.1i	1.22416	+	0.889404i
$730$	33184.8	−	24110.2i	1.68250	−	1.22241i
$731$	735.045	−	2262.24i	0.0371910	−	0.114462i
$732$	−969.853	+	2984.90i	−0.0489711	+	0.150717i
$733$	6982.93	−	5073.39i	0.351870	−	0.255648i	−0.397783	−	0.917479i	$-0.630220\pi$
$733$	6982.93	−	5073.39i	0.351870	−	0.255648i	0.749653	+	0.661831i	$0.230220\pi$
$734$	14956.9	+	10866.9i	0.752140	+	0.546462i
$735$	12140.9	+	37365.8i	0.609283	+	1.87518i
$736$	2695.90			0.135017
$737$		0			0
$738$	25575.0			1.27565
$739$	5672.79	+	17459.0i	0.282377	+	0.869068i	0.987173	+	0.159657i	$0.0510388\pi$
$739$	5672.79	+	17459.0i	0.282377	+	0.869068i	−0.704795	+	0.709411i	$0.748961\pi$
$740$	84.6580	+	61.5076i	0.00420553	+	0.00305549i
$741$	4809.55	−	3494.34i	0.238439	−	0.173236i
$742$	−889.511	+	2737.63i	−0.0440094	+	0.135447i
$743$	−3455.63	+	10635.3i	−0.170625	+	0.525131i	−0.999407	−	0.0344418i	$-0.989035\pi$
$743$	−3455.63	+	10635.3i	−0.170625	+	0.525131i	0.828781	+	0.559573i	$0.189035\pi$
$744$	4711.35	−	3423.00i	0.232159	−	0.168674i
$745$	−29186.5	−	21205.2i	−1.43531	−	1.04282i
$746$	−4483.15	−	13797.7i	−0.220027	−	0.677173i
$747$	−15843.0			−0.775991
$748$		0			0
$749$	2556.29			0.124706
$750$	−2912.31	−	8963.16i	−0.141790	−	0.436385i
$751$	−13537.6	−	9835.64i	−0.657782	−	0.477906i	0.208131	−	0.978101i	$-0.433262\pi$
$751$	−13537.6	−	9835.64i	−0.657782	−	0.477906i	−0.865913	+	0.500195i	$0.833262\pi$
$752$	−16530.9	+	12010.4i	−0.801620	+	0.582411i
$753$	−2682.43	+	8255.67i	−0.129818	+	0.399540i
$754$	113.085	−	348.039i	0.00546194	−	0.0168101i
$755$	−30969.3	+	22500.5i	−1.49283	+	1.08461i
$756$	93.5115	+	67.9401i	0.00449865	+	0.00326846i
$757$	−7540.76	−	23208.1i	−0.362052	−	1.11428i	−0.951806	−	0.306699i	$-0.900775\pi$
$757$	−7540.76	−	23208.1i	−0.362052	−	1.11428i	0.589754	−	0.807583i	$-0.299225\pi$
$758$	2290.19			0.109741
$759$		0			0
$760$	−48477.6			−2.31377
$761$	−2617.17	−	8054.81i	−0.124668	−	0.383688i	0.869173	−	0.494509i	$-0.164652\pi$
$761$	−2617.17	−	8054.81i	−0.124668	−	0.383688i	−0.993840	+	0.110821i	$0.964652\pi$
$762$	−23089.1	−	16775.2i	−1.09768	−	0.797508i
$763$	−2595.12	+	1885.46i	−0.123132	+	0.0894605i
$764$	−284.545	+	875.738i	−0.0134744	+	0.0414700i
$765$	6784.57	−	20880.8i	0.320649	−	0.986857i
$766$	−6259.86	+	4548.06i	−0.295272	+	0.214527i
$767$	383.126	+	278.357i	0.0180363	+	0.0131042i
$768$	2007.40	+	6178.14i	0.0943175

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:	\( N \)	\(=\)	\( 121 = 11^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	121.c (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.844250 - 2.59833i) q^{2} +(6.41405 + 4.66008i) q^{3} +(0.433551 - 0.314993i) q^{4} +(4.59088 - 14.1293i) q^{5} +(6.69339 - 20.6001i) q^{6} +(2.48514 - 1.80556i) q^{7} +(-18.8667 - 13.7075i) q^{8} +(11.0802 + 34.1015i) q^{9} +O(q^{10})\)	\(q+(-0.844250 - 2.59833i) q^{2} +(6.41405 + 4.66008i) q^{3} +(0.433551 - 0.314993i) q^{4} +(4.59088 - 14.1293i) q^{5} +(6.69339 - 20.6001i) q^{6} +(2.48514 - 1.80556i) q^{7} +(-18.8667 - 13.7075i) q^{8} +(11.0802 + 34.1015i) q^{9} -40.5885 q^{10} +4.24871 q^{12} +(-1.65602 - 5.09670i) q^{13} +(-6.78952 - 4.93287i) q^{14} +(95.2898 - 69.2321i) q^{15} +(-18.3635 + 56.5171i) q^{16} +(12.7363 - 39.1982i) q^{17} +(79.2525 - 57.5803i) q^{18} +(113.200 + 82.2447i) q^{19} +(-2.46025 - 7.57186i) q^{20} +24.3538 q^{21} -111.354 q^{23} +(-57.1341 - 175.841i) q^{24} +(-77.4333 - 56.2586i) q^{25} +(-11.8448 + 8.60577i) q^{26} +(-21.6977 + 66.7788i) q^{27} +(0.508695 - 1.56560i) q^{28} +(-20.2213 + 14.6916i) q^{29} +(-260.336 - 189.145i) q^{30} +(9.73324 + 29.9558i) q^{31} -24.2102 q^{32} -112.603 q^{34} +(-14.1023 - 43.4023i) q^{35} +(15.5456 + 11.2945i) q^{36} +(-10.6334 + 7.72561i) q^{37} +(118.130 - 363.567i) q^{38} +(13.1292 - 40.4076i) q^{39} +(-280.291 + 203.643i) q^{40} +(211.212 + 153.454i) q^{41} +(-20.5607 - 63.2794i) q^{42} +57.7128 q^{43} +532.697 q^{45} +(94.0105 + 289.335i) q^{46} +(278.177 + 202.108i) q^{47} +(-381.159 + 276.928i) q^{48} +(-103.077 + 317.238i) q^{49} +(-80.8056 + 248.694i) q^{50} +(264.358 - 192.067i) q^{51} +(-2.32339 - 1.68804i) q^{52} +(-105.991 - 326.207i) q^{53} +191.832 q^{54} -71.6359 q^{56} +(342.804 + 1055.04i) q^{57} +(55.2455 + 40.1382i) q^{58} +(-71.4923 + 51.9422i) q^{59} +(19.5053 - 60.0312i) q^{60} +(-228.270 + 702.543i) q^{61} +(69.6180 - 50.5804i) q^{62} +(89.1080 + 64.7408i) q^{63} +(167.348 + 515.043i) q^{64} -79.6152 q^{65} +342.359 q^{67} +(-6.82534 - 21.0062i) q^{68} +(-714.229 - 518.918i) q^{69} +(-100.868 + 73.2848i) q^{70} +(-64.0790 + 197.215i) q^{71} +(258.397 - 795.264i) q^{72} +(-817.592 + 594.016i) q^{73} +(29.0510 + 21.1068i) q^{74} +(-234.492 - 721.691i) q^{75} +74.9845 q^{76} -116.077 q^{78} +(-399.938 - 1230.88i) q^{79} +(714.242 + 518.927i) q^{80} +(332.863 - 241.839i) q^{81} +(220.410 - 678.352i) q^{82} +(-136.538 + 420.221i) q^{83} +(10.5586 - 7.67129i) q^{84} +(-495.371 - 359.908i) q^{85} +(-48.7240 - 149.957i) q^{86} -198.164 q^{87} -1489.11 q^{89} +(-449.730 - 1384.13i) q^{90} +(-13.3178 - 9.67595i) q^{91} +(-48.2776 + 35.0757i) q^{92} +(-77.1671 + 237.496i) q^{93} +(290.292 - 893.427i) q^{94} +(1681.75 - 1221.86i) q^{95} +(-155.286 - 112.822i) q^{96} +(416.065 + 1280.52i) q^{97} +911.314 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{2} + 2 q^{3} + 8 q^{4} - 2 q^{5} - 26 q^{6} + 20 q^{7} - 12 q^{8} - 44 q^{9}+O(q^{10}) \) 8 * q + 2 * q^2 + 2 * q^3 + 8 * q^4 - 2 * q^5 - 26 * q^6 + 20 * q^7 - 12 * q^8 - 44 * q^9	\( 8 q + 2 q^{2} + 2 q^{3} + 8 q^{4} - 2 q^{5} - 26 q^{6} + 20 q^{7} - 12 q^{8} - 44 q^{9} - 200 q^{10} - 160 q^{12} + 80 q^{13} + 4 q^{14} + 194 q^{15} + 8 q^{16} - 124 q^{17} + 92 q^{18} + 72 q^{19} - 88 q^{20} - 304 q^{21} - 392 q^{23} + 252 q^{24} - 136 q^{25} + 40 q^{26} + 182 q^{27} - 128 q^{28} + 144 q^{29} - 266 q^{30} + 34 q^{31} + 416 q^{32} - 208 q^{34} - 172 q^{35} + 80 q^{36} - 54 q^{37} - 432 q^{38} + 400 q^{39} - 492 q^{40} + 536 q^{41} + 140 q^{42} + 240 q^{43} + 1712 q^{45} - 314 q^{46} + 272 q^{47} - 776 q^{48} + 390 q^{49} + 232 q^{50} - 164 q^{51} - 560 q^{52} + 492 q^{53} + 440 q^{54} + 480 q^{56} - 1512 q^{57} + 192 q^{58} - 634 q^{59} - 632 q^{60} + 840 q^{61} + 134 q^{62} + 248 q^{63} - 224 q^{64} + 3520 q^{65} + 3016 q^{67} + 640 q^{68} - 962 q^{69} - 284 q^{70} + 678 q^{71} - 744 q^{72} - 400 q^{73} + 6 q^{74} + 520 q^{75} - 1728 q^{76} - 1760 q^{78} + 316 q^{79} + 1544 q^{80} + 1294 q^{81} - 512 q^{82} + 468 q^{83} - 736 q^{84} + 452 q^{85} + 156 q^{86} - 4800 q^{87} - 7368 q^{89} + 1532 q^{90} - 1280 q^{91} + 40 q^{92} + 638 q^{93} - 992 q^{94} + 2952 q^{95} - 952 q^{96} - 2194 q^{97} + 3480 q^{98}+O(q^{100}) \) 8 * q + 2 * q^2 + 2 * q^3 + 8 * q^4 - 2 * q^5 - 26 * q^6 + 20 * q^7 - 12 * q^8 - 44 * q^9 - 200 * q^10 - 160 * q^12 + 80 * q^13 + 4 * q^14 + 194 * q^15 + 8 * q^16 - 124 * q^17 + 92 * q^18 + 72 * q^19 - 88 * q^20 - 304 * q^21 - 392 * q^23 + 252 * q^24 - 136 * q^25 + 40 * q^26 + 182 * q^27 - 128 * q^28 + 144 * q^29 - 266 * q^30 + 34 * q^31 + 416 * q^32 - 208 * q^34 - 172 * q^35 + 80 * q^36 - 54 * q^37 - 432 * q^38 + 400 * q^39 - 492 * q^40 + 536 * q^41 + 140 * q^42 + 240 * q^43 + 1712 * q^45 - 314 * q^46 + 272 * q^47 - 776 * q^48 + 390 * q^49 + 232 * q^50 - 164 * q^51 - 560 * q^52 + 492 * q^53 + 440 * q^54 + 480 * q^56 - 1512 * q^57 + 192 * q^58 - 634 * q^59 - 632 * q^60 + 840 * q^61 + 134 * q^62 + 248 * q^63 - 224 * q^64 + 3520 * q^65 + 3016 * q^67 + 640 * q^68 - 962 * q^69 - 284 * q^70 + 678 * q^71 - 744 * q^72 - 400 * q^73 + 6 * q^74 + 520 * q^75 - 1728 * q^76 - 1760 * q^78 + 316 * q^79 + 1544 * q^80 + 1294 * q^81 - 512 * q^82 + 468 * q^83 - 736 * q^84 + 452 * q^85 + 156 * q^86 - 4800 * q^87 - 7368 * q^89 + 1532 * q^90 - 1280 * q^91 + 40 * q^92 + 638 * q^93 - 992 * q^94 + 2952 * q^95 - 952 * q^96 - 2194 * q^97 + 3480 * q^98

Introduction

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