LMFDB - Embedded newform 121.4.c.c.9.2

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			9.2
Root			$-1.40126 + 1.01807i$ of defining polynomial
Character	$\chi$	$=$	121.9
Dual form			121.4.c.c.27.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.844250 - 2.59833i) q^{2} +(6.41405 - 4.66008i) q^{3} +(0.433551 + 0.314993i) q^{4} +(4.59088 + 14.1293i) q^{5} +(-6.69339 - 20.6001i) q^{6} +(-2.48514 - 1.80556i) q^{7} +(18.8667 - 13.7075i) q^{8} +(11.0802 - 34.1015i) q^{9} +O(q^{10})$	\(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 $\left(\mathbb{Z}/121\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{3}{5}\right)$

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	−0.683540	−	0.729913i	$-0.739561\pi$
$2$	0.844250	−	2.59833i	0.298487	−	0.918650i	0.982028	−	0.188737i	$-0.0604394\pi$
$3$	6.41405	−	4.66008i	1.23438	−	0.896833i	0.237174	−	0.971467i	$-0.423779\pi$
$3$	6.41405	−	4.66008i	1.23438	−	0.896833i	0.997211	+	0.0746343i	$0.0237789\pi$
$4$	0.433551	+	0.314993i	0.0541939	+	0.0393741i
$5$	4.59088	+	14.1293i	0.410621	+	1.26376i	0.916110	+	0.400928i	$0.131312\pi$
$5$	4.59088	+	14.1293i	0.410621	+	1.26376i	−0.505489	+	0.862833i	$0.668688\pi$
$6$	−6.69339	−	20.6001i	−0.455427	−	1.40166i
$7$	−2.48514	−	1.80556i	−0.134185	−	0.0974909i	0.518668	−	0.854976i	$-0.326428\pi$
$7$	−2.48514	−	1.80556i	−0.134185	−	0.0974909i	−0.652853	+	0.757485i	$0.726428\pi$
$8$	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	$-0.881794\pi$
$13$	1.65602	−	5.09670i	0.0353305	−	0.108736i	0.967166	+	0.254144i	$0.0817936\pi$
$14$	−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	$-0.194989\pi$
$17$	−12.7363	−	39.1982i	−0.181706	−	0.559232i	−0.999876	+	0.0157433i	$0.994989\pi$
$18$	−79.2525	−	57.5803i	−1.03778	−	0.753990i
$19$	−113.200	+	82.2447i	−1.36684	+	0.993065i	−0.368860	+	0.929485i	$0.620252\pi$
$19$	−113.200	+	82.2447i	−1.36684	+	0.993065i	−0.997977	+	0.0635795i	$0.979748\pi$
$20$	−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	$-0.274500\pi$
$29$	20.2213	+	14.6916i	0.129483	+	0.0940745i	−0.521159	+	0.853460i	$0.674500\pi$
$30$	260.336	−	189.145i	1.58436	−	1.15110i
$31$	9.73324	−	29.9558i	0.0563917	−	0.173556i	−0.918893	−	0.394506i	$-0.870916\pi$
$31$	9.73324	−	29.9558i	0.0563917	−	0.173556i	0.975285	+	0.220950i	$0.0709158\pi$
$32$	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	0.563911	−	0.825835i	$-0.309296\pi$
$37$	−10.6334	−	7.72561i	−0.0472464	−	0.0343266i	−0.611158	+	0.791509i	$0.709296\pi$
$38$	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	$-0.865648\pi$
$41$	−211.212	+	153.454i	−0.804529	+	0.584525i	0.107710	+	0.994182i	$0.465648\pi$
$42$	−20.5607	+	63.2794i	−0.0755378	+	0.232482i
$43$	−57.7128			−0.204677			−0.102339	−	0.994750i	$-0.532633\pi$
$43$	−57.7128			−0.204677			−0.102339	+	0.994750i	$0.532633\pi$
$44$		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	−0.0654616	−	0.997855i	$-0.520852\pi$
$47$	278.177	−	202.108i	0.863326	−	0.627243i	0.928788	+	0.370612i	$0.120852\pi$
$48$	−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	0.714601	+	0.699533i	$0.246608\pi$
$53$	−105.991	+	326.207i	−0.274698	+	0.845435i	−0.989299	+	0.145902i	$0.953392\pi$
$54$	−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	0.506108	−	0.862470i	$-0.331084\pi$
$59$	−71.4923	−	51.9422i	−0.157754	−	0.114615i	−0.663862	+	0.747855i	$0.731084\pi$
$60$	19.5053	+	60.0312i	0.0419688	+	0.129167i
$61$	228.270	+	702.543i	0.479131	+	1.47461i	0.840305	+	0.542115i	$0.182376\pi$
$61$	228.270	+	702.543i	0.479131	+	1.47461i	−0.361174	+	0.932499i	$0.617624\pi$
$62$	−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	0.883110	−	0.469166i	$-0.155445\pi$
$71$	−64.0790	−	197.215i	−0.107110	−	0.329650i	−0.990220	+	0.139516i	$0.955445\pi$
$72$	−258.397	−	795.264i	−0.422949	−	1.30170i
$73$	817.592	+	594.016i	1.31085	+	0.952387i	0.999998	+	0.00192848i	$0.000613855\pi$
$73$	817.592	+	594.016i	1.31085	+	0.952387i	0.310851	+	0.950459i	$0.399386\pi$
$74$	−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	−0.0843714	−	0.996434i	$-0.526888\pi$
$79$	399.938	−	1230.88i	0.569576	−	1.75297i	0.653947	−	0.756540i	$-0.273112\pi$
$80$	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	$-0.00562532\pi$
$83$	136.538	+	420.221i	0.180566	+	0.555725i	−0.819278	+	0.573397i	$0.805625\pi$
$84$	−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	−0.457042	−	0.889445i	$-0.651091\pi$
$97$	416.065	−	1280.52i	0.435516	−	1.34038i	0.892557	−	0.450934i	$-0.148909\pi$
$98$	−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	$-0.925343\pi$
$101$	−49.8943	+	153.559i	−0.0491551	+	0.151284i	0.923466	+	0.383680i	$0.125343\pi$
$102$	−722.238	+	524.737i	−0.701101	+	0.509379i
$103$	28.1208	+	20.4309i	0.0269012	+	0.0195449i	0.601155	−	0.799133i	$-0.294708\pi$
$103$	28.1208	+	20.4309i	0.0269012	+	0.0195449i	−0.574253	+	0.818678i	$0.694708\pi$
$104$	−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	$-0.822678\pi$
$107$	−673.247	+	489.143i	−0.608273	+	0.441937i	0.240532	+	0.970641i	$0.422678\pi$
$108$	11.6278	−	35.7867i	0.0103600	−	0.0318849i
$109$	1044.26			0.917629			0.458815	−	0.888532i	$-0.348274\pi$
$109$	1044.26			0.917629			0.458815	+	0.888532i	$0.348274\pi$
$110$		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	−0.682704	−	0.730695i	$-0.739196\pi$
$113$	−238.726	+	173.445i	−0.198739	+	0.144392i	0.483965	+	0.875087i	$0.339196\pi$
$114$	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	−0.986552	−	0.163448i	$-0.947739\pi$
$127$	−407.162	−	1253.12i	−0.284487	−	0.875560i	0.702065	−	0.712113i	$-0.252261\pi$
$128$	−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	$-0.679235\pi$
$131$	−1600.71			−1.06759			−0.533797	+	0.845612i	$0.679235\pi$
$132$		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	0.977534	+	0.210777i	$0.0675995\pi$
$137$	498.035	+	1532.80i	0.310584	+	0.955880i	−0.666950	+	0.745103i	$0.732400\pi$
$138$	745.334	+	2293.90i	0.459761	+	1.41500i
$139$	25.7768	+	18.7280i	0.0157292	+	0.0114280i	0.595622	−	0.803265i	$-0.296906\pi$
$139$	25.7768	+	18.7280i	0.0157292	+	0.0114280i	−0.579893	+	0.814693i	$0.696906\pi$
$140$	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	−0.914394	−	0.404826i	$-0.867332\pi$
$149$	−750.399	−	2309.49i	−0.412585	−	1.26980i	0.501809	−	0.864978i	$-0.332668\pi$
$150$	1677.22	+	1218.58i	0.912966	+	0.663308i
$151$	2084.58	−	1514.53i	1.12345	−	0.816231i	0.138718	−	0.990332i	$-0.455702\pi$
$151$	2084.58	−	1514.53i	1.12345	−	0.816231i	0.984728	+	0.174101i	$0.0557018\pi$
$152$	−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	−0.965921	−	0.258838i	$-0.916660\pi$
$157$	−2003.08	+	1455.32i	−1.01824	+	0.739792i	−0.0523162	+	0.998631i	$0.516660\pi$
$158$	−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	0.516529	+	0.856270i	$0.327224\pi$
$163$	−842.105	+	2591.73i	−0.404655	+	1.24540i	−0.921183	+	0.389129i	$0.872776\pi$
$164$	−139.908			−0.0666157
$165$		0			0
$166$	1207.15			0.564414
$167$	845.871	−	2603.32i	0.391949	−	1.20630i	−0.539363	−	0.842073i	$-0.681335\pi$
$167$	845.871	−	2603.32i	0.391949	−	1.20630i	0.931312	−	0.364222i	$-0.118665\pi$
$168$	−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	$-0.869254\pi$
$173$	−1866.74	+	1356.26i	−0.820378	+	0.596040i	0.0964424	+	0.995339i	$0.469254\pi$
$174$	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	−0.343666	−	0.939092i	$-0.611669\pi$
$179$	1061.56	−	771.265i	0.443265	−	0.322051i	0.786931	+	0.617041i	$0.211669\pi$
$180$	230.951	+	167.796i	0.0956339	+	0.0694821i
$181$	−248.194	−	763.864i	−0.101923	−	0.313688i	0.887073	−	0.461630i	$-0.152735\pi$
$181$	−248.194	−	763.864i	−0.101923	−	0.313688i	−0.988996	+	0.147942i	$0.952735\pi$
$182$	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	0.292475	−	0.956273i	$-0.405521\pi$
$191$	−1390.09	−	1009.96i	−0.526615	−	0.382608i	−0.819090	+	0.573665i	$0.805521\pi$
$192$	−1326.77	−	4083.37i	−0.498704	−	1.53485i
$193$	414.140	+	1274.59i	0.154458	+	0.475373i	0.998106	−	0.0615242i	$-0.0195962\pi$
$193$	414.140	+	1274.59i	0.154458	+	0.475373i	−0.843647	+	0.536898i	$0.819596\pi$
$194$	−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	$-0.719503\pi$
$197$	−3518.33			−1.27244			−0.636220	+	0.771508i	$0.719503\pi$
$198$		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	$-0.905574\pi$
$211$	−33.1709	+	102.089i	−0.0108226	+	0.0333086i	0.945499	+	0.325624i	$0.105574\pi$
$212$	−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	0.00351474	−	0.999994i	$-0.498881\pi$
$223$	3182.42	−	2312.16i	0.955651	−	0.694321i	0.952137	+	0.305672i	$0.0988812\pi$
$224$	−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	$-0.216593\pi$
$227$	1433.50	+	1041.50i	0.419139	+	0.304523i	−0.358152	+	0.933663i	$0.616593\pi$
$228$	−480.955	+	349.434i	−0.139702	+	0.101499i
$229$	591.882	−	1821.62i	0.170798	−	0.525661i	−0.828619	−	0.559813i	$-0.810873\pi$
$229$	591.882	−	1821.62i	0.170798	−	0.525661i	0.999417	+	0.0341519i	$0.0108730\pi$
$230$	−4519.68			−1.29573
$231$		0			0
$232$	582.892			0.164952
$233$	1358.54	−	4181.15i	0.381977	−	1.17561i	−0.556672	−	0.830732i	$-0.687922\pi$
$233$	1358.54	−	4181.15i	0.381977	−	1.17561i	0.938649	−	0.344873i	$-0.112078\pi$
$234$	−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	$-0.513587\pi$
$239$	3304.42	−	2400.80i	0.894332	−	0.649770i	0.937004	+	0.349319i	$0.113587\pi$
$240$	2162.94	−	6656.85i	0.581739	−	1.79041i
$241$	3908.58			1.04471			0.522353	−	0.852730i	$-0.325054\pi$
$241$	3908.58			1.04471			0.522353	+	0.852730i	$0.325054\pi$
$242$		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	−0.899460	−	0.437004i	$-0.856040\pi$
$251$	338.340	−	1041.30i	0.0850831	−	0.261859i	0.984543	+	0.175145i	$0.0560395\pi$
$252$	−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	0.508231	−	0.861221i	$-0.330300\pi$
$257$	−633.605	−	460.341i	−0.153787	−	0.111733i	−0.662018	+	0.749488i	$0.730300\pi$
$258$	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	$-0.242078\pi$
$263$	6180.06			1.44897			0.724484	+	0.689292i	$0.242078\pi$
$264$		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	0.979653	−	0.200700i	$-0.0643218\pi$
$269$	304.989	+	938.659i	0.0691282	+	0.212755i	−0.910524	+	0.413455i	$0.864322\pi$
$270$	−880.678	−	2710.45i	−0.198505	−	0.610936i
$271$	−3702.86	−	2690.29i	−0.830011	−	0.603038i	0.0895518	−	0.995982i	$-0.471457\pi$
$271$	−3702.86	−	2690.29i	−0.830011	−	0.603038i	−0.919562	+	0.392944i	$0.871457\pi$
$272$	−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	$-0.880385\pi$
$277$	175.471	−	540.044i	0.0380615	−	0.117141i	0.968282	+	0.249860i	$0.0803846\pi$
$278$	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	0.959729	+	0.280929i	$0.0906426\pi$
$281$	1641.19	+	5051.07i	0.348418	+	1.07232i	−0.611311	+	0.791391i	$0.709357\pi$
$282$	−6025.39	−	4377.70i	−1.27236	−	0.924427i
$283$	3825.39	−	2779.31i	0.803519	−	0.583790i	−0.108426	−	0.994105i	$-0.534581\pi$
$283$	3825.39	−	2779.31i	0.803519	−	0.583790i	0.911944	+	0.410314i	$0.134581\pi$
$284$	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	$-0.374585\pi$
$293$	−1884.13	−	1368.90i	−0.375673	−	0.272942i	−0.759559	+	0.650438i	$0.774585\pi$
$294$	−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	$-0.549854\pi$
$307$	−1678.07			−0.311962			−0.155981	+	0.987760i	$0.549854\pi$
$308$		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	−0.819236	−	0.573456i	$-0.805602\pi$
$311$	−2890.38	+	2099.98i	−0.527005	+	0.382891i	0.292232	+	0.956348i	$0.405602\pi$
$312$	−801.591	−	582.390i	−0.145452	−	0.105677i
$313$	2220.09	+	6832.74i	0.400917	+	1.23389i	0.924257	+	0.381771i	$0.124686\pi$
$313$	2220.09	+	6832.74i	0.400917	+	1.23389i	−0.523340	+	0.852124i	$0.675314\pi$
$314$	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	−0.951486	−	0.307693i	$-0.900443\pi$
$317$	−4.85393	+	14.9389i	−0.000860013	+	0.00264685i	0.950626	+	0.310340i	$0.100443\pi$
$318$	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	$-0.293846\pi$
$337$	193.503	+	140.588i	0.0312783	+	0.0227250i	−0.572036	+	0.820228i	$0.693846\pi$
$338$	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	−0.987774	−	0.155894i	$-0.950174\pi$
$347$	−1811.70	−	5575.85i	−0.280280	−	0.862614i	0.707493	−	0.706720i	$-0.249826\pi$
$348$	85.9143	+	62.4204i	0.0132342	+	0.00961518i
$349$	−2824.87	+	2052.39i	−0.433271	+	0.314790i	−0.782956	−	0.622078i	$-0.786289\pi$
$349$	−2824.87	+	2052.39i	−0.433271	+	0.314790i	0.349684	+	0.936868i	$0.386289\pi$
$350$	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	0.997901	+	0.0647598i	$0.0206281\pi$
$359$	9304.29	+	6759.96i	1.36786	+	0.993808i	0.369959	+	0.929048i	$0.379372\pi$
$360$	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	0.125908	−	0.992042i	$-0.459816\pi$
$367$	−5474.62	−	3977.55i	−0.778673	−	0.565739i	−0.904580	+	0.426303i	$0.859816\pi$
$368$	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	$-0.620152\pi$
$373$	−5310.22			−0.737139			−0.368569	+	0.929600i	$0.620152\pi$
$374$		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	0.931967	−	0.362544i	$-0.118092\pi$
$379$	−259.039	−	797.239i	−0.0351080	−	0.108051i	−0.967075	+	0.254492i	$0.918092\pi$
$380$	−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	−0.992311	−	0.123773i	$-0.960500\pi$
$383$	−875.187	+	2693.55i	−0.116762	+	0.359357i	0.875548	+	0.483131i	$0.160500\pi$
$384$	−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	0.411540	−	0.911392i	$-0.364991\pi$
$389$	−2517.06	−	1828.75i	−0.328072	−	0.238358i	−0.739612	+	0.673034i	$0.764991\pi$
$390$	−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	−0.996274	−	0.0862478i	$-0.972512\pi$
$401$	−1934.97	−	5955.21i	−0.240967	−	0.741619i	0.755307	−	0.655371i	$-0.227488\pi$
$402$	−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	$-0.981559\pi$
$409$	−1295.55	+	3987.31i	−0.156628	+	0.482053i	0.841694	+	0.539955i	$0.181559\pi$
$410$	−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	−0.996980	−	0.0776651i	$-0.975254\pi$
$421$	−10635.3	+	7727.03i	−1.23120	+	0.894519i	−0.234220	+	0.972184i	$0.575254\pi$
$422$	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	$-0.811537\pi$
$431$	1517.17	−	4669.37i	0.169558	−	0.521846i	0.999343	+	0.0362369i	$0.0115371\pi$
$432$	−3375.70	+	2452.59i	−0.375957	+	0.273149i
$433$	9500.53	+	6902.54i	1.05443	+	0.766085i	0.973049	−	0.230598i	$-0.0740682\pi$
$433$	9500.53	+	6902.54i	1.05443	+	0.766085i	0.0813771	+	0.996683i	$0.474068\pi$
$434$	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	$-0.722208\pi$
$439$	−11824.2			−1.28551			−0.642754	+	0.766073i	$0.722208\pi$
$440$		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	−0.932330	−	0.361609i	$-0.882228\pi$
$443$	−8172.78	+	5937.87i	−0.876525	+	0.636833i	0.0558049	+	0.998442i	$0.482228\pi$
$444$	−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	−0.956507	−	0.291710i	$-0.905776\pi$
$449$	−106.689	+	328.356i	−0.0112138	+	0.0345124i	0.945293	+	0.326222i	$0.105776\pi$
$450$	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	−0.967092	−	0.254426i	$-0.918114\pi$
$457$	−3265.43	−	10050.0i	−0.334246	−	1.02870i	0.632847	−	0.774277i	$-0.281886\pi$
$458$	−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	$-0.423136\pi$
$461$	4733.96			0.478270			0.239135	+	0.970986i	$0.423136\pi$
$462$		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	0.998327	−	0.0578129i	$-0.0184127\pi$
$467$	1581.23	+	4866.52i	0.156682	+	0.482218i	−0.841645	+	0.540031i	$0.818413\pi$
$468$	−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	0.963714	+	0.266936i	$0.0860111\pi$
$479$	3574.36	+	11000.8i	0.340954	+	1.04935i	−0.622761	+	0.782412i	$0.713989\pi$
$480$	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	0.382653	−	0.923892i	$-0.375010\pi$
$487$	14826.5	−	10772.1i	1.37957	−	1.00232i	0.996920	−	0.0784263i	$-0.0249895\pi$
$488$	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	$-0.186155\pi$
$491$	6162.75	+	4477.50i	0.566438	+	0.411541i	−0.267371	+	0.963594i	$0.586155\pi$
$492$	−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	0.0107555	−	0.999942i	$-0.496576\pi$
$499$	−10443.7	−	7587.79i	−0.936922	−	0.680714i	−0.947678	+	0.319228i	$0.896576\pi$
$500$	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	$-0.848776\pi$
$503$	−8224.18	+	5975.22i	−0.729022	+	0.529666i	0.160232	+	0.987079i	$0.448776\pi$
$504$	−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	−0.791330	−	0.611390i	$-0.790611\pi$
$509$	−5218.10	+	3791.18i	−0.454398	+	0.330139i	0.336932	+	0.941529i	$0.390611\pi$
$510$	−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	0.999981	+	0.00615574i	$0.00195944\pi$
$521$	15636.2	+	11360.4i	1.31485	+	0.955292i	0.314866	+	0.949136i	$0.398041\pi$
$522$	−756.638	−	2328.69i	−0.0634428	−	0.195257i
$523$	1934.17	+	5952.75i	0.161712	+	0.497697i	0.998779	−	0.0494027i	$-0.0157318\pi$
$523$	1934.17	+	5952.75i	0.161712	+	0.497697i	−0.837067	+	0.547100i	$0.815732\pi$
$524$	−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	0.618106	+	0.786095i	$0.287900\pi$
$541$	−4328.76	+	13322.6i	−0.344007	+	1.05875i	−0.962113	+	0.272651i	$0.912100\pi$
$542$	−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	$-0.638036\pi$
$547$	4004.19	−	2909.21i	0.312992	−	0.227402i	0.733179	+	0.680035i	$0.238036\pi$
$548$	−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	$-0.253812\pi$
$557$	3075.54	+	2234.51i	0.233958	+	0.169981i	−0.464629	+	0.885505i	$0.653812\pi$
$558$	−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	0.768847	+	0.639433i	$0.220831\pi$
$563$	−3059.30	+	9415.57i	−0.229013	+	0.704829i	−0.997859	+	0.0653958i	$0.979169\pi$
$564$	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	$-0.762898\pi$
$569$	−4311.38	+	3132.40i	−0.317649	+	0.230786i	0.417523	+	0.908667i	$0.362898\pi$
$570$	−13913.9	+	42822.6i	−1.02244	+	3.14674i
$571$	−16962.6			−1.24319			−0.621597	−	0.783337i	$-0.713516\pi$
$571$	−16962.6			−1.24319			−0.621597	+	0.783337i	$0.713516\pi$
$572$		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	−0.961428	−	0.275057i	$-0.911303\pi$
$577$	−4785.74	−	14729.0i	−0.345291	−	1.06270i	0.616137	−	0.787639i	$-0.288697\pi$
$578$	−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	0.226056	−	0.974114i	$-0.427417\pi$
$587$	−8967.27	−	6515.10i	−0.630526	−	0.458104i	−0.856582	+	0.516010i	$0.827417\pi$
$588$	−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	$-0.451877\pi$
$593$	4349.68			0.301214			0.150607	+	0.988594i	$0.451877\pi$
$594$		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	0.988438	+	0.151627i	$0.0484512\pi$
$599$	4074.05	+	12538.7i	0.277899	+	0.855284i	−0.710539	+	0.703658i	$0.751549\pi$
$600$	5468.46	+	16830.2i	0.372082	+	1.14515i
$601$	15181.2	+	11029.8i	1.03037	+	0.748611i	0.968384	−	0.249466i	$-0.0802551\pi$
$601$	15181.2	+	11029.8i	1.03037	+	0.748611i	0.0619905	+	0.998077i	$0.480255\pi$
$602$	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	−0.422763	−	0.906240i	$-0.638940\pi$
$607$	6758.62	−	20800.9i	0.451934	−	1.39091i	0.874697	−	0.484669i	$-0.161060\pi$
$608$	−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	$-0.662921\pi$
$613$	2854.09	−	2073.62i	0.188052	−	0.136628i	0.677828	+	0.735221i	$0.262921\pi$
$614$	−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	0.141279	−	0.989970i	$-0.454879\pi$
$619$	17348.0	−	12604.1i	1.12645	−	0.818417i	0.985175	+	0.171553i	$0.0548785\pi$
$620$	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	−0.118103	−	0.993001i	$-0.537681\pi$
$631$	−17419.7	−	12656.2i	−1.09900	−	0.798469i	−0.980896	+	0.194532i	$0.937681\pi$
$632$	−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	−0.963028	−	0.269402i	$-0.913174\pi$
$641$	−16300.3	+	11842.9i	−1.00440	+	0.729742i	−0.0413758	+	0.999144i	$0.513174\pi$
$642$	14582.7	+	10595.0i	0.896470	+	0.651323i
$643$	8921.22	+	27456.7i	0.547152	+	1.68396i	0.715818	+	0.698287i	$0.246054\pi$
$643$	8921.22	+	27456.7i	0.547152	+	1.68396i	−0.168666	+	0.985673i	$0.553946\pi$
$644$	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	−0.964874	−	0.262713i	$-0.915383\pi$
$647$	−491.344	+	1512.20i	−0.0298558	+	0.0918868i	0.935018	+	0.354600i	$0.115383\pi$
$648$	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	−0.0153339	−	0.999882i	$-0.504881\pi$
$653$	−16203.0	−	11772.2i	−0.971017	−	0.705485i	−0.955683	+	0.294397i	$0.904881\pi$
$654$	−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	$-0.600647\pi$
$659$	−10520.7			−0.621897			−0.310948	+	0.950427i	$0.600647\pi$
$660$		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	$-0.910828\pi$
$673$	−367.000	+	1129.51i	−0.0210205	+	0.0646946i	0.939996	+	0.341185i	$0.110828\pi$
$674$	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	0.997513	+	0.0704888i	$0.0224559\pi$
$677$	4085.63	+	12574.3i	0.231940	+	0.713839i	−0.765572	+	0.643350i	$0.777544\pi$
$678$	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	−0.999179	−	0.0405154i	$-0.987100\pi$
$691$	−3033.64	+	9336.59i	−0.167012	+	0.514010i	0.832167	+	0.554525i	$0.187100\pi$
$692$	−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	$-0.998823\pi$
$701$	−24229.9	+	17604.0i	−1.30549	+	0.948495i	−0.305498	+	0.952193i	$0.598823\pi$
$702$	−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	0.999950	−	0.0100121i	$-0.00318701\pi$
$709$	3494.21	+	10754.1i	0.185088	+	0.569644i	−0.814861	+	0.579656i	$0.803187\pi$
$710$	−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	0.997817	+	0.0660438i	$0.0210377\pi$
$719$	26392.9	+	19175.6i	1.36897	+	0.994615i	0.371154	+	0.928571i	$0.378962\pi$
$720$	−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	$-0.369780\pi$
$733$	−6982.93	−	5073.39i	−0.351870	−	0.255648i	−0.749653	+	0.661831i	$0.769780\pi$
$734$	−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	0.704795	+	0.709411i	$0.251039\pi$
$739$	−5672.79	+	17459.0i	−0.282377	+	0.869068i	−0.987173	+	0.159657i	$0.948961\pi$
$740$	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	$-0.0109653\pi$
$743$	3455.63	+	10635.3i	0.170625	+	0.525131i	−0.828781	+	0.559573i	$0.810965\pi$
$744$	−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	−0.865913	−	0.500195i	$-0.833262\pi$
$751$	−13537.6	+	9835.64i	−0.657782	+	0.477906i	0.208131	+	0.978101i	$0.433262\pi$
$752$	−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	0.589754	+	0.807583i	$0.299225\pi$
$757$	−7540.76	+	23208.1i	−0.362052	+	1.11428i	−0.951806	+	0.306699i	$0.900775\pi$
$758$	−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	$-0.835348\pi$
$761$	2617.17	−	8054.81i	0.124668	−	0.383688i	0.993840	+	0.110821i	$0.0353479\pi$
$762$	−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

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

L-functions

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