LMFDB - Embedded newform 121.4.c.f.81.1

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			81.1
Root			$0.535233 - 1.64728i$ of defining polynomial
Character	$\chi$	$=$	121.81
Dual form			121.4.c.f.3.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.592242 - 0.430289i) q^{2} +(1.83192 - 5.63806i) q^{3} +(-2.30653 - 7.09878i) q^{4} +(10.4011 - 7.55681i) q^{5} +(-3.51093 + 2.55084i) q^{6} +(-5.23110 - 16.0997i) q^{7} +(-3.49823 + 10.7664i) q^{8} +(-6.58831 - 4.78668i) q^{9} +O(q^{10})$	\(q+(-0.592242 - 0.430289i) q^{2} +(1.83192 - 5.63806i) q^{3} +(-2.30653 - 7.09878i) q^{4} +(10.4011 - 7.55681i) q^{5} +(-3.51093 + 2.55084i) q^{6} +(-5.23110 - 16.0997i) q^{7} +(-3.49823 + 10.7664i) q^{8} +(-6.58831 - 4.78668i) q^{9} -9.41154 q^{10} -44.2487 q^{12} +(60.3859 + 43.8729i) q^{13} +(-3.82943 + 11.7858i) q^{14} +(-23.5519 - 72.4851i) q^{15} +(-41.6042 + 30.2272i) q^{16} +(-66.9742 + 48.6596i) q^{17} +(1.84221 + 5.66975i) q^{18} +(20.9894 - 64.5987i) q^{19} +(-77.6345 - 56.4048i) q^{20} -100.354 q^{21} +13.3538 q^{23} +(54.2934 + 39.4464i) q^{24} +(12.4494 - 38.3154i) q^{25} +(-16.8850 - 51.9667i) q^{26} +(90.4356 - 65.7053i) q^{27} +(-102.222 + 74.2689i) q^{28} +(-52.2223 - 160.724i) q^{29} +(-17.2412 + 53.0628i) q^{30} +(52.9885 + 38.4984i) q^{31} +128.210 q^{32} +60.6025 q^{34} +(-176.071 - 127.923i) q^{35} +(-18.7835 + 57.8096i) q^{36} +(12.6253 + 38.8568i) q^{37} +(-40.2269 + 29.2265i) q^{38} +(357.980 - 260.087i) q^{39} +(44.9747 + 138.418i) q^{40} +(-84.9575 + 261.472i) q^{41} +(59.4337 + 43.1811i) q^{42} +2.28719 q^{43} -104.697 q^{45} +(-7.90869 - 5.74600i) q^{46} +(22.2017 - 68.3297i) q^{47} +(94.2074 + 289.941i) q^{48} +(45.6576 - 33.1722i) q^{49} +(-23.8597 + 17.3351i) q^{50} +(151.654 + 466.744i) q^{51} +(172.162 - 529.860i) q^{52} +(120.548 + 87.5830i) q^{53} -81.8320 q^{54} +191.636 q^{56} +(-325.760 - 236.679i) q^{57} +(-38.2294 + 117.658i) q^{58} +(168.609 + 518.926i) q^{59} +(-460.233 + 334.379i) q^{60} +(81.9556 - 59.5442i) q^{61} +(-14.8166 - 45.6007i) q^{62} +(-42.6000 + 131.109i) q^{63} +(256.902 + 186.650i) q^{64} +959.615 q^{65} +411.641 q^{67} +(499.902 + 363.200i) q^{68} +(24.4631 - 75.2896i) q^{69} +(49.2327 + 151.523i) q^{70} +(380.752 - 276.633i) q^{71} +(74.5830 - 54.1877i) q^{72} +(-188.686 - 580.715i) q^{73} +(9.24238 - 28.4451i) q^{74} +(-193.218 - 140.381i) q^{75} -506.985 q^{76} -323.923 q^{78} +(-791.401 - 574.986i) q^{79} +(-204.306 + 628.790i) q^{80} +(-272.726 - 839.363i) q^{81} +(162.824 - 118.298i) q^{82} +(21.1590 - 15.3729i) q^{83} +(231.470 + 712.390i) q^{84} +(-328.891 + 1012.22i) q^{85} +(-1.35457 - 0.984151i) q^{86} -1001.84 q^{87} -352.887 q^{89} +(62.0061 + 45.0501i) q^{90} +(390.455 - 1201.70i) q^{91} +(-30.8011 - 94.7959i) q^{92} +(314.127 - 228.226i) q^{93} +(-42.5502 + 30.9146i) q^{94} +(-269.848 - 830.507i) q^{95} +(234.870 - 722.857i) q^{96} +(-685.710 - 498.198i) q^{97} -41.3140 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 $\left(\mathbb{Z}/121\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{5}\right)$

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 $

$2$	−0.592242	−	0.430289i	−0.209389	−	0.152130i	0.478148	−	0.878279i	$-0.341308\pi$
$2$	−0.592242	−	0.430289i	−0.209389	−	0.152130i	−0.687537	+	0.726149i	$0.741308\pi$
$3$	1.83192	−	5.63806i	0.352552	−	1.08504i	−0.604863	−	0.796330i	$-0.706772\pi$
$3$	1.83192	−	5.63806i	0.352552	−	1.08504i	0.957415	−	0.288715i	$-0.0932279\pi$
$4$	−2.30653	−	7.09878i	−0.288317	−	0.887348i
$5$	10.4011	−	7.55681i	0.930298	−	0.675901i	−0.0157675	−	0.999876i	$-0.505019\pi$
$5$	10.4011	−	7.55681i	0.930298	−	0.675901i	0.946066	+	0.323974i	$0.105019\pi$
$6$	−3.51093	+	2.55084i	−0.238888	+	0.173563i
$7$	−5.23110	−	16.0997i	−0.282453	−	0.869301i	−0.987151	−	0.159793i	$-0.948917\pi$
$7$	−5.23110	−	16.0997i	−0.282453	−	0.869301i	0.704698	−	0.709508i	$-0.251083\pi$
$8$	−3.49823	+	10.7664i	−0.154601	+	0.475814i
$9$	−6.58831	−	4.78668i	−0.244011	−	0.177285i
$10$	−9.41154			−0.297619
$11$		0			0
$11$		0			0
$12$	−44.2487			−1.06446
$13$	60.3859	+	43.8729i	1.28831	+	0.936012i	0.999770	−	0.0214564i	$-0.00683032\pi$
$13$	60.3859	+	43.8729i	1.28831	+	0.936012i	0.288540	+	0.957468i	$0.406830\pi$
$14$	−3.82943	+	11.7858i	−0.0731042	+	0.224992i
$15$	−23.5519	−	72.4851i	−0.405404	−	1.24771i
$16$	−41.6042	+	30.2272i	−0.650066	+	0.472300i
$17$	−66.9742	+	48.6596i	−0.955507	+	0.694216i	−0.952103	−	0.305778i	$-0.901084\pi$
$17$	−66.9742	+	48.6596i	−0.955507	+	0.694216i	−0.00340407	+	0.999994i	$0.501084\pi$
$18$	1.84221	+	5.66975i	0.0241230	+	0.0742429i
$19$	20.9894	−	64.5987i	0.253436	−	0.779997i	−0.740697	−	0.671839i	$-0.765505\pi$
$19$	20.9894	−	64.5987i	0.253436	−	0.779997i	0.994134	−	0.108158i	$-0.0344953\pi$
$20$	−77.6345	−	56.4048i	−0.867980	−	0.630624i
$21$	−100.354			−1.04281
$22$		0			0
$23$	13.3538			0.121064			0.0605319	−	0.998166i	$-0.480720\pi$
$23$	13.3538			0.121064			0.0605319	+	0.998166i	$0.480720\pi$
$24$	54.2934	+	39.4464i	0.461774	+	0.335499i
$25$	12.4494	−	38.3154i	0.0995954	−	0.306523i
$26$	−16.8850	−	51.9667i	−0.127362	−	0.391981i
$27$	90.4356	−	65.7053i	0.644606	−	0.468333i
$28$	−102.222	+	74.2689i	−0.689936	+	0.501268i
$29$	−52.2223	−	160.724i	−0.334394	−	1.02916i	−0.967020	−	0.254702i	$-0.918023\pi$
$29$	−52.2223	−	160.724i	−0.334394	−	1.02916i	0.632625	−	0.774458i	$-0.281977\pi$
$30$	−17.2412	+	53.0628i	−0.104926	+	0.322930i
$31$	52.9885	+	38.4984i	0.307001	+	0.223049i	0.730608	−	0.682797i	$-0.239237\pi$
$31$	52.9885	+	38.4984i	0.307001	+	0.223049i	−0.423608	+	0.905846i	$0.639237\pi$
$32$	128.210			0.708268
$33$		0			0
$34$	60.6025			0.305684
$35$	−176.071	−	127.923i	−0.850327	−	0.617799i
$36$	−18.7835	+	57.8096i	−0.0869605	+	0.267637i
$37$	12.6253	+	38.8568i	0.0560970	+	0.172649i	0.975179	−	0.221417i	$-0.0710682\pi$
$37$	12.6253	+	38.8568i	0.0560970	+	0.172649i	−0.919082	+	0.394066i	$0.871068\pi$
$38$	−40.2269	+	29.2265i	−0.171728	+	0.124768i
$39$	357.980	−	260.087i	1.46981	−	1.06788i
$40$	44.9747	+	138.418i	0.177778	+	0.547144i
$41$	−84.9575	+	261.472i	−0.323613	+	0.995978i	0.648450	+	0.761257i	$0.275418\pi$
$41$	−84.9575	+	261.472i	−0.323613	+	0.995978i	−0.972063	+	0.234721i	$0.924582\pi$
$42$	59.4337	+	43.1811i	0.218353	+	0.158643i
$43$	2.28719			0.00811146			0.00405573	−	0.999992i	$-0.498709\pi$
$43$	2.28719			0.00811146			0.00405573	+	0.999992i	$0.498709\pi$
$44$		0			0
$45$	−104.697			−0.346830
$46$	−7.90869	−	5.74600i	−0.0253494	−	0.0184174i
$47$	22.2017	−	68.3297i	0.0689031	−	0.212062i	−0.910676	−	0.413121i	$-0.864438\pi$
$47$	22.2017	−	68.3297i	0.0689031	−	0.212062i	0.979579	+	0.201060i	$0.0644385\pi$
$48$	94.2074	+	289.941i	0.283285	+	0.871861i
$49$	45.6576	−	33.1722i	0.133113	−	0.0967120i
$50$	−23.8597	+	17.3351i	−0.0674856	+	0.0490311i
$51$	151.654	+	466.744i	0.416390	+	1.28152i
$52$	172.162	−	529.860i	0.459127	−	1.41305i
$53$	120.548	+	87.5830i	0.312425	+	0.226990i	0.732936	−	0.680297i	$-0.238149\pi$
$53$	120.548	+	87.5830i	0.312425	+	0.226990i	−0.420512	+	0.907287i	$0.638149\pi$
$54$	−81.8320			−0.206221
$55$		0			0
$56$	191.636			0.457293
$57$	−325.760	−	236.679i	−0.756982	−	0.549980i
$58$	−38.2294	+	117.658i	−0.0865476	+	0.266366i
$59$	168.609	+	518.926i	0.372052	+	1.14506i	0.945446	+	0.325778i	$0.105626\pi$
$59$	168.609	+	518.926i	0.372052	+	1.14506i	−0.573395	+	0.819279i	$0.694374\pi$
$60$	−460.233	+	334.379i	−0.990264	+	0.719469i
$61$	81.9556	−	59.5442i	0.172022	−	0.124981i	−0.498443	−	0.866922i	$-0.666095\pi$
$61$	81.9556	−	59.5442i	0.172022	−	0.124981i	0.670465	+	0.741941i	$0.266095\pi$
$62$	−14.8166	−	45.6007i	−0.0303501	−	0.0934080i
$63$	−42.6000	+	131.109i	−0.0851919	+	0.262194i
$64$	256.902	+	186.650i	0.501762	+	0.364552i
$65$	959.615			1.83116
$66$		0			0
$67$	411.641			0.750596			0.375298	−	0.926904i	$-0.377540\pi$
$67$	411.641			0.750596			0.375298	+	0.926904i	$0.377540\pi$
$68$	499.902	+	363.200i	0.891500	+	0.647713i
$69$	24.4631	−	75.2896i	0.0426813	−	0.131360i
$70$	49.2327	+	151.523i	0.0840634	+	0.258721i
$71$	380.752	−	276.633i	0.636437	−	0.462398i	−0.222188	−	0.975004i	$-0.571320\pi$
$71$	380.752	−	276.633i	0.636437	−	0.462398i	0.858624	+	0.512606i	$0.171320\pi$
$72$	74.5830	−	54.1877i	0.122079	−	0.0886956i
$73$	−188.686	−	580.715i	−0.302520	−	0.931062i	−0.980591	−	0.196065i	$-0.937184\pi$
$73$	−188.686	−	580.715i	−0.302520	−	0.931062i	0.678070	−	0.734997i	$-0.262816\pi$
$74$	9.24238	−	28.4451i	0.0145190	−	0.0446848i
$75$	−193.218	−	140.381i	−0.297479	−	0.216131i
$76$	−506.985			−0.765199
$77$		0			0
$78$	−323.923			−0.470219
$79$	−791.401	−	574.986i	−1.12708	−	0.818874i	−0.141815	−	0.989893i	$-0.545294\pi$
$79$	−791.401	−	574.986i	−1.12708	−	0.818874i	−0.985268	+	0.171019i	$0.945294\pi$
$80$	−204.306	+	628.790i	−0.285527	+	0.878760i
$81$	−272.726	−	839.363i	−0.374109	−	1.15139i
$82$	162.824	−	118.298i	0.219279	−	0.159316i
$83$	21.1590	−	15.3729i	0.0279819	−	0.0203300i	−0.573706	−	0.819061i	$-0.694495\pi$
$83$	21.1590	−	15.3729i	0.0279819	−	0.0203300i	0.601688	+	0.798731i	$0.294495\pi$
$84$	231.470	+	712.390i	0.300659	+	0.925335i
$85$	−328.891	+	1012.22i	−0.419685	+	1.29166i
$86$	−1.35457	−	0.984151i	−0.00169845	−	0.00123400i
$87$	−1001.84			−1.23458
$88$		0			0
$89$	−352.887			−0.420292			−0.210146	−	0.977670i	$-0.567394\pi$
$89$	−352.887			−0.420292			−0.210146	+	0.977670i	$0.567394\pi$
$90$	62.0061	+	45.0501i	0.0726224	+	0.0527633i
$91$	390.455	−	1201.70i	0.449789	−	1.38431i
$92$	−30.8011	−	94.7959i	−0.0349047	−	0.107426i
$93$	314.127	−	228.226i	0.350252	−	0.254473i
$94$	−42.5502	+	30.9146i	−0.0466885	+	0.0339212i
$95$	−269.848	−	830.507i	−0.291430	−	0.896928i
$96$	234.870	−	722.857i	0.249702	−	0.768502i
$97$	−685.710	−	498.198i	−0.717766	−	0.521488i	0.167903	−	0.985803i	$-0.446300\pi$
$97$	−685.710	−	498.198i	−0.717766	−	0.521488i	−0.885670	+	0.464316i	$0.846300\pi$
$98$	−41.3140			−0.0425851
$99$		0			0
$100$	−300.708			−0.300708
$101$	1046.43	+	760.277i	1.03093	+	0.749014i	0.968495	−	0.249035i	$-0.0801133\pi$
$101$	1046.43	+	760.277i	1.03093	+	0.749014i	0.0624351	+	0.998049i	$0.480113\pi$
$102$	111.019	−	341.681i	0.107770	−	0.331681i
$103$	−533.129	−	1640.80i	−0.510007	−	1.56964i	−0.792187	−	0.610279i	$-0.791057\pi$
$103$	−533.129	−	1640.80i	−0.510007	−	1.56964i	0.282179	−	0.959362i	$-0.408943\pi$
$104$	−683.599	+	496.663i	−0.644542	+	0.468287i
$105$	−1043.79	+	758.354i	−0.970124	+	0.704836i
$106$	−33.7074	−	103.741i	−0.0308863	−	0.0950583i
$107$	149.620	−	460.482i	0.135180	−	0.416042i	−0.860438	−	0.509555i	$-0.829810\pi$
$107$	149.620	−	460.482i	0.135180	−	0.416042i	0.995618	+	0.0935137i	$0.0298099\pi$
$108$	−675.021	−	490.431i	−0.601425	−	0.436961i
$109$	64.2563			0.0564645			0.0282323	−	0.999601i	$-0.491012\pi$
$109$	64.2563			0.0564645			0.0282323	+	0.999601i	$0.491012\pi$
$110$		0			0
$111$	242.205			0.207109
$112$	704.284	+	511.693i	0.594184	+	0.431700i
$113$	−619.604	+	1906.95i	−0.515818	+	1.58753i	0.265970	+	0.963981i	$0.414308\pi$
$113$	−619.604	+	1906.95i	−0.515818	+	1.58753i	−0.781788	+	0.623544i	$0.785692\pi$
$114$	91.0886	+	280.342i	0.0748353	+	0.230319i
$115$	138.894	−	100.912i	0.112625	−	0.0818271i
$116$	−1020.49	+	741.429i	−0.816811	+	0.593448i
$117$	−187.835	−	578.096i	−0.148422	−	0.456795i
$118$	123.430	−	379.880i	0.0962940	−	0.296363i
$119$	1133.75	+	823.719i	0.873369	+	0.634540i
$120$	862.797			0.656352
$121$		0			0
$122$	−74.1587			−0.0550329
$123$	1318.56	+	957.990i	0.966590	+	0.702269i
$124$	151.072	−	464.952i	0.109409	−	0.336725i
$125$	336.551	+	1035.80i	0.240816	+	0.741157i
$126$	81.6443	−	59.3180i	0.0577258	−	0.0419403i
$127$	88.6723	−	64.4242i	0.0619558	−	0.0450135i	−0.556376	−	0.830930i	$-0.687809\pi$
$127$	88.6723	−	64.4242i	0.0619558	−	0.0450135i	0.618332	+	0.785917i	$0.287809\pi$
$128$	−388.788	−	1196.57i	−0.268471	−	0.826269i
$129$	4.18993	−	12.8953i	0.00285971	−	0.00880129i
$130$	−568.324	−	412.912i	−0.383425	−	0.278575i
$131$	−1156.71			−0.771469			−0.385734	−	0.922610i	$-0.626052\pi$
$131$	−1156.71			−0.771469			−0.385734	+	0.922610i	$0.626052\pi$
$132$		0			0
$133$	−1149.82			−0.749636
$134$	−243.791	−	177.124i	−0.157167	−	0.114188i
$135$	444.103	−	1366.81i	0.283128	−	0.871379i
$136$	−289.600	−	891.296i	−0.182595	−	0.561970i
$137$	−160.447	+	116.571i	−0.100058	+	0.0726962i	−0.636689	−	0.771121i	$-0.719697\pi$
$137$	−160.447	+	116.571i	−0.100058	+	0.0726962i	0.536631	+	0.843817i	$0.319697\pi$
$138$	−46.8843	+	34.0635i	−0.0289207	+	0.0210121i
$139$	896.192	+	2758.20i	0.546863	+	1.68307i	0.716518	+	0.697569i	$0.245735\pi$
$139$	896.192	+	2758.20i	0.546863	+	1.68307i	−0.169654	+	0.985504i	$0.554265\pi$
$140$	−501.985	+	1544.95i	−0.303039	+	0.932658i
$141$	−344.575	−	250.348i	−0.205805	−	0.149526i
$142$	−344.529			−0.203607
$143$		0			0
$144$	418.789			0.242355
$145$	−1757.72	−	1277.06i	−1.00670	−	0.731408i
$146$	−138.128	+	425.113i	−0.0782981	+	0.240977i
$147$	−103.386	−	318.189i	−0.0580076	−	0.178529i
$148$	246.715	−	179.249i	0.137026	−	0.0995552i
$149$	2822.13	−	2050.40i	1.55166	−	1.12735i	0.609211	−	0.793008i	$-0.291486\pi$
$149$	2822.13	−	2050.40i	1.55166	−	1.12735i	0.942452	−	0.334341i	$-0.108514\pi$
$150$	54.0273	+	166.279i	0.0294088	+	0.0905109i
$151$	359.487	−	1106.39i	0.193739	−	0.596268i	−0.806250	−	0.591575i	$-0.798506\pi$
$151$	359.487	−	1106.39i	0.193739	−	0.596268i	0.999989	−	0.00469259i	$-0.00149370\pi$
$152$	622.072	+	451.962i	0.331952	+	0.241177i
$153$	674.164			0.356228
$154$		0			0
$155$	842.061			0.436361
$156$	−2672.00	−	1941.32i	−1.37135	−	0.996345i
$157$	105.701	−	325.315i	0.0537318	−	0.165369i	−0.920590	−	0.390532i	$-0.872291\pi$
$157$	105.701	−	325.315i	0.0537318	−	0.165369i	0.974321	+	0.225162i	$0.0722912\pi$
$158$	221.290	+	681.062i	0.111424	+	0.342926i
$159$	714.631	−	519.210i	0.356440	−	0.258969i
$160$	1333.52	−	968.860i	0.658901	−	0.478719i
$161$	−69.8552	−	214.992i	−0.0341948	−	0.105241i
$162$	−199.649	+	614.457i	−0.0968266	+	0.298002i
$163$	1128.49	+	819.897i	0.542272	+	0.393983i	0.824928	−	0.565238i	$-0.191216\pi$
$163$	1128.49	+	819.897i	0.542272	+	0.393983i	−0.282656	+	0.959221i	$0.591216\pi$
$164$	2052.09			0.977082
$165$		0			0
$166$	−19.1460			−0.00895191
$167$	387.279	+	281.374i	0.179452	+	0.130380i	0.673885	−	0.738836i	$-0.264624\pi$
$167$	387.279	+	281.374i	0.179452	+	0.130380i	−0.494433	+	0.869216i	$0.664624\pi$
$168$	351.061	−	1080.45i	0.161220	−	0.496183i
$169$	1042.71	+	3209.13i	0.474606	+	1.46069i
$170$	630.330	−	457.962i	0.284377	−	0.206612i
$171$	−447.498	+	325.126i	−0.200123	+	0.145398i
$172$	−5.27548	−	16.2362i	−0.00233867	−	0.00719769i
$173$	−558.883	+	1720.07i	−0.245613	+	0.755920i	0.749922	+	0.661527i	$0.230091\pi$
$173$	−558.883	+	1720.07i	−0.245613	+	0.755920i	−0.995535	+	0.0943936i	$0.969909\pi$
$174$	593.329	+	431.079i	0.258507	+	0.187816i
$175$	−681.990			−0.294592
$176$		0			0
$177$	3234.61			1.37361
$178$	208.995	+	151.843i	0.0880045	+	0.0639390i
$179$	−1368.90	+	4213.03i	−0.571599	+	1.75920i	0.0758796	+	0.997117i	$0.475824\pi$
$179$	−1368.90	+	4213.03i	−0.571599	+	1.75920i	−0.647479	+	0.762084i	$0.724176\pi$
$180$	241.488	+	743.224i	0.0999970	+	0.307759i
$181$	−2758.08	+	2003.86i	−1.13263	+	0.822905i	−0.986076	−	0.166297i	$-0.946819\pi$
$181$	−2758.08	+	2003.86i	−1.13263	+	0.822905i	−0.146557	+	0.989202i	$0.546819\pi$
$182$	−748.320	+	543.686i	−0.304776	+	0.221432i
$183$	−185.578	−	571.150i	−0.0749635	−	0.230714i
$184$	−46.7148	+	143.773i	−0.0187166	+	0.0576038i
$185$	424.950	+	308.744i	0.168881	+	0.122699i
$186$	−284.242			−0.112052
$187$		0			0
$188$	−536.267			−0.208039
$189$	−1530.91	−	1112.27i	−0.589193	−	0.428074i
$190$	−197.542	+	607.973i	−0.0754275	+	0.232142i
$191$	903.490	+	2780.65i	0.342273	+	1.05341i	0.963027	+	0.269404i	$0.0868266\pi$
$191$	903.490	+	2780.65i	0.342273	+	1.05341i	−0.620754	+	0.784005i	$0.713173\pi$
$192$	1522.97	−	1106.50i	0.572452	−	0.415911i
$193$	−2009.75	+	1460.17i	−0.749558	+	0.544586i	−0.895690	−	0.444679i	$-0.853318\pi$
$193$	−2009.75	+	1460.17i	−0.749558	+	0.544586i	0.146132	+	0.989265i	$0.453318\pi$
$194$	191.737	+	590.107i	0.0709584	+	0.218388i
$195$	1757.93	−	5410.36i	0.645581	−	1.98689i
$196$	−340.793	−	247.601i	−0.124196	−	0.0902335i
$197$	5125.67			1.85375			0.926876	−	0.375369i	$-0.122484\pi$
$197$	5125.67			1.85375			0.926876	+	0.375369i	$0.122484\pi$
$198$		0			0
$199$	−7.69219			−0.00274013			−0.00137006	−	0.999999i	$-0.500436\pi$
$199$	−7.69219			−0.00274013			−0.00137006	+	0.999999i	$0.500436\pi$
$200$	368.970	+	268.072i	0.130450	+	0.0947778i
$201$	754.092	−	2320.86i	0.264624	−	0.814430i
$202$	−292.602	−	900.536i	−0.101918	−	0.313671i
$203$	−2314.42	+	1681.52i	−0.800199	+	0.581378i
$204$	2963.52	−	2153.12i	1.01710	−	0.738965i
$205$	1092.25	+	3361.59i	0.372126	+	1.14529i
$206$	−390.277	+	1201.15i	−0.132000	+	0.406253i
$207$	−87.9791	−	63.9206i	−0.0295409	−	0.0214627i
$208$	−3838.46			−1.27956
$209$		0			0
$210$	944.484			0.310360
$211$	2513.89	+	1826.45i	0.820206	+	0.595915i	0.916772	−	0.399412i	$-0.130786\pi$
$211$	2513.89	+	1826.45i	0.820206	+	0.595915i	−0.0965652	+	0.995327i	$0.530786\pi$
$212$	343.685	−	1057.76i	0.111342	−	0.342674i
$213$	−862.165	−	2653.47i	−0.277345	−	0.853582i
$214$	−286.751	+	208.337i	−0.0915977	+	0.0665496i
$215$	23.7892	−	17.2838i	0.00754608	−	0.00548255i
$216$	391.048	+	1203.52i	0.123183	+	0.379117i
$217$	342.624	−	1054.49i	0.107183	−	0.329877i
$218$	−38.0552	−	27.6487i	−0.0118231	−	0.00858995i
$219$	−3619.76			−1.11690
$220$		0			0
$221$	−6179.13			−1.88078
$222$	−143.444	−	104.218i	−0.0433663	−	0.0315075i
$223$	−3.80662	+	11.7156i	−0.00114310	+	0.00351809i	−0.951626	−	0.307257i	$-0.900589\pi$
$223$	−3.80662	+	11.7156i	−0.00114310	+	0.00351809i	0.950483	+	0.310776i	$0.100589\pi$
$224$	−670.681	−	2064.14i	−0.200052	−	0.615698i
$225$	−265.424	+	192.842i	−0.0786442	+	0.0571384i
$226$	1187.49	−	862.764i	0.349517	−	0.253939i
$227$	−1426.39	−	4389.98i	−0.417062	−	1.28358i	−0.910394	−	0.413743i	$-0.864221\pi$
$227$	−1426.39	−	4389.98i	−0.417062	−	1.28358i	0.493332	−	0.869841i	$-0.335779\pi$
$228$	−928.753	+	2858.41i	−0.269773	+	0.830275i
$229$	−4105.46	−	2982.79i	−1.18470	−	0.860736i	−0.192007	−	0.981394i	$-0.561500\pi$
$229$	−4105.46	−	2982.79i	−1.18470	−	0.860736i	−0.992694	+	0.120658i	$0.961500\pi$
$230$	−125.680			−0.0360309
$231$		0			0
$232$	1913.11			0.541386
$233$	171.255	+	124.424i	0.0481514	+	0.0349840i	0.611601	−	0.791167i	$-0.290526\pi$
$233$	171.255	+	124.424i	0.0481514	+	0.0349840i	−0.563449	+	0.826151i	$0.690526\pi$
$234$	−137.505	+	423.196i	−0.0384143	+	0.118227i
$235$	−285.434	−	878.474i	−0.0792325	−	0.243853i
$236$	3294.84	−	2393.84i	0.908795	−	0.660278i
$237$	−4691.59	+	3408.64i	−1.28587	+	0.934239i
$238$	−317.018	−	975.681i	−0.0863413	−	0.265731i
$239$	−1332.63	+	4101.42i	−0.360673	+	1.11004i	0.591973	+	0.805958i	$0.298349\pi$
$239$	−1332.63	+	4101.42i	−0.360673	+	1.11004i	−0.952646	+	0.304080i	$0.901651\pi$
$240$	3170.88	+	2303.78i	0.852831	+	0.619618i
$241$	996.584			0.266372			0.133186	−	0.991091i	$-0.457479\pi$
$241$	996.584			0.266372			0.133186	+	0.991091i	$0.457479\pi$
$242$		0			0
$243$	−2213.80			−0.584426
$244$	−611.725	−	444.444i	−0.160499	−	0.116609i
$245$	224.211	−	690.052i	0.0584667	−	0.179942i
$246$	−368.694	−	1134.72i	−0.0955572	−	0.294095i
$247$	4101.59	−	2979.98i	1.05659	−	0.767658i
$248$	−599.857	+	435.822i	−0.153593	+	0.111592i
$249$	−47.9117	−	147.457i	−0.0121939	−	0.0375290i
$250$	246.373	−	758.257i	0.0623279	−	0.191825i
$251$	224.010	+	162.753i	0.0563323	+	0.0409278i	0.615595	−	0.788063i	$-0.288916\pi$
$251$	224.010	+	162.753i	0.0563323	+	0.0409278i	−0.559263	+	0.828990i	$0.688916\pi$
$252$	1028.97			0.257219
$253$		0			0
$254$	−80.2364			−0.0198208
$255$	5104.46	+	3708.61i	1.25354	+	0.910753i
$256$	500.411	−	1540.11i	0.122171	−	0.376003i
$257$	−999.725	−	3076.84i	−0.242650	−	0.746801i	−0.996014	−	0.0891969i	$-0.971570\pi$
$257$	−999.725	−	3076.84i	−0.242650	−	0.746801i	0.753364	−	0.657604i	$-0.228430\pi$
$258$	−8.03015	+	5.83425i	−0.00193773	+	0.00140785i
$259$	559.537	−	406.527i	0.134239	−	0.0975304i
$260$	−2213.39	−	6812.10i	−0.527955	−	1.62488i
$261$	−425.277	+	1308.87i	−0.100858	+	0.310410i
$262$	685.053	+	497.720i	0.161537	+	0.117364i
$263$	−207.944			−0.0487544			−0.0243772	−	0.999703i	$-0.507760\pi$
$263$	−207.944			−0.0487544			−0.0243772	+	0.999703i	$0.507760\pi$
$264$		0			0
$265$	1915.67			0.444071
$266$	680.968	+	494.752i	0.156966	+	0.114042i
$267$	−646.460	+	1989.60i	−0.148175	+	0.456035i
$268$	−949.464	−	2922.15i	−0.216410	−	0.666040i
$269$	−4071.81	+	2958.34i	−0.922910	+	0.670533i	−0.944247	−	0.329239i	$-0.893208\pi$
$269$	−4071.81	+	2958.34i	−0.922910	+	0.670533i	0.0213369	+	0.999772i	$0.493208\pi$
$270$	−851.139	+	618.389i	−0.191847	+	0.139385i
$271$	−459.512	−	1414.23i	−0.103001	−	0.317005i	0.886255	−	0.463198i	$-0.153298\pi$
$271$	−459.512	−	1414.23i	−0.103001	−	0.317005i	−0.989256	+	0.146193i	$0.953298\pi$
$272$	1315.56	−	4048.89i	0.293264	−	0.902573i
$273$	−6059.95	−	4402.81i	−1.34346	−	0.976082i
$274$	145.183			0.0320102
$275$		0			0
$276$	−590.890			−0.128867
$277$	−190.795	−	138.621i	−0.0413855	−	0.0300683i	0.566900	−	0.823786i	$-0.308142\pi$
$277$	−190.795	−	138.621i	−0.0413855	−	0.0300683i	−0.608286	+	0.793718i	$0.708142\pi$
$278$	656.058	−	2019.14i	0.141539	−	0.435611i
$279$	−164.825	−	507.279i	−0.0353685	−	0.108853i
$280$	1993.21	−	1448.16i	0.425419	−	0.309085i
$281$	−3976.33	+	2888.97i	−0.844156	+	0.613316i	−0.923529	−	0.383530i	$-0.874708\pi$
$281$	−3976.33	+	2888.97i	−0.844156	+	0.613316i	0.0793722	+	0.996845i	$0.474708\pi$
$282$	96.3496	+	296.534i	0.0203459	+	0.0626181i
$283$	1606.75	−	4945.07i	0.337496	−	1.03871i	−0.627983	−	0.778227i	$-0.716119\pi$
$283$	1606.75	−	4945.07i	0.337496	−	1.03871i	0.965479	−	0.260480i	$-0.0838808\pi$
$284$	−2841.97	−	2064.82i	−0.593803	−	0.431423i
$285$	−5176.78			−1.07595
$286$		0			0
$287$	4654.04			0.957210
$288$	−844.688	−	613.702i	−0.172825	−	0.125565i
$289$	599.583	−	1845.33i	0.122040	−	0.375601i
$290$	491.492	+	1512.66i	0.0995221	+	0.306298i
$291$	−4065.03	+	2953.42i	−0.818888	+	0.594957i
$292$	−3687.16	+	2678.88i	−0.738954	+	0.536882i
$293$	2744.35	+	8446.25i	0.547191	+	1.68408i	0.715723	+	0.698384i	$0.246097\pi$
$293$	2744.35	+	8446.25i	0.547191	+	1.68408i	−0.168533	+	0.985696i	$0.553903\pi$
$294$	−75.6837	+	232.931i	−0.0150135	+	0.0462067i
$295$	5675.13	+	4123.23i	1.12006	+	0.813774i
$296$	−462.515			−0.0908215
$297$		0			0
$298$	−2553.64			−0.496405
$299$	806.382	+	585.871i	0.155968	+	0.113317i
$300$	−550.871	+	1695.41i	−0.106015	+	0.326281i
$301$	−11.9645	−	36.8230i	−0.00229111	−	0.00705130i
$302$	−688.968	+	500.565i	−0.131277	+	0.0953784i
$303$	6203.46	−	4507.08i	1.17617	−	0.854538i
$304$	1079.39	+	3322.03i	0.203643	+	0.626748i
$305$	402.460	−	1238.64i	0.0755567	−	0.232540i
$306$	−399.268	−	290.085i	−0.0745903	−	0.0541930i
$307$	1497.93			0.278474			0.139237	−	0.990259i	$-0.455535\pi$
$307$	1497.93			0.278474			0.139237	+	0.990259i	$0.455535\pi$
$308$		0			0
$309$	−10227.6			−1.88293
$310$	−498.704	−	362.330i	−0.0913693	−	0.0663837i
$311$	−2312.90	+	7118.38i	−0.421713	+	1.29790i	0.484395	+	0.874850i	$0.339040\pi$
$311$	−2312.90	+	7118.38i	−0.421713	+	1.29790i	−0.906107	+	0.423048i	$0.860960\pi$
$312$	1547.92	+	4764.01i	0.280878	+	0.864452i
$313$	532.627	−	386.976i	0.0961848	−	0.0698824i	−0.538653	−	0.842527i	$-0.681067\pi$
$313$	532.627	−	386.976i	0.0961848	−	0.0698824i	0.634838	+	0.772645i	$0.281067\pi$
$314$	−202.580	+	147.183i	−0.0364085	+	0.0264523i
$315$	547.683	+	1685.59i	0.0979632	+	0.301500i
$316$	−2256.31	+	6944.21i	−0.401669	+	1.23621i
$317$	−189.073	−	137.370i	−0.0334998	−	0.0243390i	0.570909	−	0.821013i	$-0.306591\pi$
$317$	−189.073	−	137.370i	−0.0334998	−	0.0243390i	−0.604409	+	0.796674i	$0.706591\pi$
$318$	−646.645			−0.114032
$319$		0			0
$320$	4082.53			0.713189
$321$	−2322.13	−	1687.13i	−0.403766	−	0.293353i
$322$	−51.1376	+	157.385i	−0.00885027	+	0.0272383i
$323$	1737.60	+	5347.77i	0.299327	+	0.921233i
$324$	−5329.41	+	3872.04i	−0.913822	+	0.663930i
$325$	2432.78	−	1767.52i	0.415219	−	0.301674i
$326$	−315.547	−	971.154i	−0.0536090	−	0.164992i
$327$	117.712	−	362.280i	0.0199067	−	0.0612665i
$328$	−2517.93	−	1829.38i	−0.423869	−	0.307959i
$329$	−1216.23			−0.203808
$330$		0			0
$331$	8532.95			1.41696			0.708480	−	0.705731i	$-0.249381\pi$
$331$	8532.95			1.41696			0.708480	+	0.705731i	$0.249381\pi$
$332$	−157.933	−	114.745i	−0.0261075	−	0.0189682i
$333$	102.816	−	316.434i	0.0169197	−	0.0520734i
$334$	−108.290	−	333.283i	−0.0177407	−	0.0546002i
$335$	4281.50	−	3110.69i	0.698278	−	0.507329i
$336$	4175.14	−	3033.42i	0.677895	−	0.492519i
$337$	−3612.77	−	11119.0i	−0.583977	−	1.79730i	−0.603339	−	0.797485i	$-0.706163\pi$
$337$	−3612.77	−	11119.0i	−0.583977	−	1.79730i	0.0193617	−	0.999813i	$-0.493837\pi$
$338$	763.317	−	2349.25i	0.122837	−	0.378054i
$339$	9616.41	+	6986.73i	1.54068	+	1.11937i
$340$	7944.14			1.26715
$341$		0			0
$342$	404.925			0.0640229
$343$	−5470.36	−	3974.45i	−0.861141	−	0.625656i
$344$	−8.00111	+	24.6249i	−0.00125404	+	0.00385955i
$345$	−314.507	−	967.954i	−0.0490797	−	0.151052i
$346$	1071.12	−	778.213i	0.166427	−	0.120916i
$347$	3720.50	−	2703.10i	0.575582	−	0.418185i	−0.261547	−	0.965191i	$-0.584232\pi$
$347$	3720.50	−	2703.10i	0.575582	−	0.418185i	0.837129	+	0.547006i	$0.184232\pi$
$348$	2310.77	+	7111.81i	0.355949	+	1.09550i
$349$	−2076.68	+	6391.36i	−0.318516	+	0.980291i	0.655767	+	0.754963i	$0.272345\pi$
$349$	−2076.68	+	6391.36i	−0.318516	+	0.980291i	−0.974283	+	0.225328i	$0.927655\pi$
$350$	403.903	+	293.452i	0.0616843	+	0.0448163i
$351$	8343.72			1.26882
$352$		0			0
$353$	5738.70			0.865270			0.432635	−	0.901569i	$-0.357584\pi$
$353$	5738.70			0.865270			0.432635	+	0.901569i	$0.357584\pi$
$354$	−1915.67	−	1391.82i	−0.287618	−	0.208967i
$355$	1869.76	−	5754.54i	0.279540	−	0.860337i
$356$	813.947	+	2505.07i	0.121177	+	0.372945i
$357$	6721.11	−	4883.17i	0.996412	−	0.723936i
$358$	2623.54	−	1906.11i	0.387314	−	0.281400i
$359$	1271.69	+	3913.85i	0.186956	+	0.575391i	0.999977	−	0.00684400i	$-0.00217853\pi$
$359$	1271.69	+	3913.85i	0.186956	+	0.575391i	−0.813021	+	0.582235i	$0.802179\pi$
$360$	366.255	−	1127.22i	0.0536204	−	0.165027i
$361$	1816.61	+	1319.85i	0.264851	+	0.192426i
$362$	2495.69			0.362349
$363$		0			0
$364$	−9431.18			−1.35804
$365$	−6350.88	−	4614.18i	−0.910740	−	0.661692i
$366$	−135.852	+	418.111i	−0.0194020	+	0.0597131i
$367$	2986.03	+	9190.05i	0.424712	+	1.30713i	0.903269	+	0.429074i	$0.141160\pi$
$367$	2986.03	+	9190.05i	0.424712	+	1.30713i	−0.478557	+	0.878057i	$0.658840\pi$
$368$	−555.575	+	403.649i	−0.0786994	+	0.0571784i
$369$	1811.31	−	1315.99i	0.255537	−	0.185658i
$370$	−118.824	−	365.702i	−0.0166956	−	0.0513836i
$371$	779.461	−	2398.94i	0.109077	−	0.335705i
$372$	−2344.67	−	1703.51i	−0.326789	−	0.237426i
$373$	141.780			0.0196812			0.00984062	−	0.999952i	$-0.496868\pi$
$373$	141.780			0.0196812			0.00984062	+	0.999952i	$0.496868\pi$
$374$		0			0
$375$	6456.42			0.889088
$376$	658.001	+	478.066i	0.0902495	+	0.0655701i
$377$	3897.92	−	11996.6i	0.532502	−	1.63887i
$378$	428.072	+	1317.47i	0.0582477	+	0.179268i
$379$	2281.21	−	1657.40i	0.309177	−	0.224630i	−0.422366	−	0.906425i	$-0.638800\pi$
$379$	2281.21	−	1657.40i	0.309177	−	0.224630i	0.731543	+	0.681795i	$0.238800\pi$
$380$	−5273.17	+	3831.18i	−0.711863	+	0.517199i
$381$	−200.787	−	617.959i	−0.0269990	−	0.0830945i
$382$	661.400	−	2035.58i	0.0885869	−	0.272642i
$383$	5127.42	+	3725.29i	0.684070	+	0.497006i	0.874705	−	0.484655i	$-0.161055\pi$
$383$	5127.42	+	3725.29i	0.684070	+	0.497006i	−0.190636	+	0.981661i	$0.561055\pi$
$384$	−7458.53			−0.991189
$385$		0			0
$386$	1818.55			0.239797
$387$	−15.0687	−	10.9480i	−0.00197929	−	0.00143804i
$388$	−1954.98	+	6016.82i	−0.255797	+	0.787262i
$389$	−2720.97	−	8374.29i	−0.354650	−	1.09150i	−0.956212	−	0.292674i	$-0.905455\pi$
$389$	−2720.97	−	8374.29i	−0.354650	−	1.09150i	0.601562	−	0.798826i	$-0.294545\pi$
$390$	−3369.14	+	2447.82i	−0.437444	+	0.317821i
$391$	−894.361	+	649.792i	−0.115677	+	0.0840444i
$392$	197.426	+	607.614i	0.0254375	+	0.0782887i
$393$	−2119.00	+	6521.61i	−0.271983	+	0.837078i
$394$	−3035.64	−	2205.52i	−0.388155	−	0.282011i
$395$	−12576.5			−1.60200
$396$		0			0
$397$	4315.26			0.545534			0.272767	−	0.962080i	$-0.412061\pi$
$397$	4315.26			0.545534			0.272767	+	0.962080i	$0.412061\pi$
$398$	4.55564	+	3.30986i	0.000573752	+	0.000416855i
$399$	−2106.36	+	6482.72i	−0.264286	+	0.813389i
$400$	640.219	+	1970.39i	0.0800274	+	0.246299i
$401$	−292.606	+	212.591i	−0.0364390	+	0.0264745i	−0.605856	−	0.795575i	$-0.707169\pi$
$401$	−292.606	+	212.591i	−0.0364390	+	0.0264745i	0.569417	+	0.822049i	$0.307169\pi$
$402$	−1445.24	+	1050.03i	−0.179309	+	0.130275i
$403$	1510.72	+	4649.52i	0.186735	+	0.574712i
$404$	2983.41	−	9182.00i	0.367402	−	1.13075i
$405$	−9179.54	−	6669.33i	−1.12626	−	0.818275i
$406$	2094.24			0.255998
$407$		0			0
$408$	−5555.70			−0.674137
$409$	7459.54	+	5419.67i	0.901835	+	0.655222i	0.938937	−	0.344090i	$-0.111812\pi$
$409$	7459.54	+	5419.67i	0.901835	+	0.655222i	−0.0371015	+	0.999312i	$0.511812\pi$
$410$	799.581	−	2460.86i	0.0963134	−	0.296422i
$411$	363.311	+	1118.16i	0.0436030	+	0.134196i
$412$	−10418.0	+	7569.13i	−1.24577	+	0.905107i
$413$	7472.52	−	5429.11i	0.890312	−	0.646850i
$414$	24.6006	+	75.7128i	0.00292042	+	0.00898812i
$415$	103.905	−	319.788i	0.0122904	−	0.0378260i
$416$	7742.08	+	5624.95i	0.912469	+	0.662947i
$417$	17192.6			2.01901
$418$		0			0
$419$	−14912.9			−1.73876			−0.869380	−	0.494144i	$-0.835481\pi$
$419$	−14912.9			−1.73876			−0.869380	+	0.494144i	$0.835481\pi$
$420$	7790.92	+	5660.43i	0.905138	+	0.657621i
$421$	−4167.41	+	12826.0i	−0.482439	+	1.48480i	0.353217	+	0.935542i	$0.385088\pi$
$421$	−4167.41	+	12826.0i	−0.482439	+	1.48480i	−0.835656	+	0.549254i	$0.814912\pi$
$422$	−702.931	−	2163.40i	−0.0810857	−	0.249556i
$423$	−473.344	+	343.905i	−0.0544085	+	0.0395301i
$424$	−1364.66	+	991.484i	−0.156306	+	0.113563i
$425$	1030.62	+	3171.92i	0.117629	+	0.362026i
$426$	−631.149	+	1942.48i	−0.0717823	+	0.220923i
$427$	−1387.36	−	1007.98i	−0.157234	−	0.114237i
$428$	−3613.96			−0.408148
$429$		0			0
$430$	−21.5260			−0.00241413
$431$	328.731	+	238.837i	0.0367388	+	0.0266923i	0.606003	−	0.795462i	$-0.292772\pi$
$431$	328.731	+	238.837i	0.0367388	+	0.0266923i	−0.569264	+	0.822155i	$0.692772\pi$
$432$	−1776.41	+	5467.24i	−0.197842	+	0.608895i
$433$	−545.938	−	1680.23i	−0.0605915	−	0.186481i	0.916179	−	0.400769i	$-0.131257\pi$
$433$	−545.938	−	1680.23i	−0.0605915	−	0.186481i	−0.976771	+	0.214288i	$0.931257\pi$
$434$	−656.650	+	477.084i	−0.0726272	+	0.0527668i
$435$	−10420.1	+	7570.68i	−1.14852	+	0.834451i
$436$	−148.209	−	456.141i	−0.0162797	−	0.0501037i
$437$	280.289	−	862.639i	0.0306820	−	0.0944294i
$438$	2143.77	+	1557.54i	0.233866	+	0.169914i
$439$	−7824.19			−0.850634			−0.425317	−	0.905044i	$-0.639837\pi$
$439$	−7824.19			−0.850634			−0.425317	+	0.905044i	$0.639837\pi$
$440$		0			0
$441$	−459.591			−0.0496265
$442$	3659.54	+	2658.81i	0.393815	+	0.286124i
$443$	3605.58	−	11096.8i	0.386695	−	1.19013i	−0.548548	−	0.836119i	$-0.684819\pi$
$443$	3605.58	−	11096.8i	0.386695	−	1.19013i	0.935243	−	0.354007i	$-0.115181\pi$
$444$	−558.654	−	1719.36i	−0.0597130	−	0.183778i
$445$	−3670.40	+	2666.70i	−0.390997	+	0.284076i
$446$	7.29552	−	5.30050i	0.000774558	−	0.000562749i
$447$	−6390.35	−	19667.5i	−0.676182	−	2.08107i
$448$	1661.13	−	5112.43i	0.175181	−	0.539151i
$449$	−13733.3	−	9977.80i	−1.44346	−	1.04873i	−0.987305	−	0.158833i	$-0.949227\pi$
$449$	−13733.3	−	9977.80i	−1.44346	−	1.04873i	−0.456153	−	0.889901i	$-0.650773\pi$
$450$	240.173			0.0251597
$451$		0			0
$452$	14966.1			1.55741
$453$	−5579.32	−	4053.61i	−0.578674	−	0.420431i
$454$	−1044.19	+	3213.69i	−0.107943	+	0.332216i
$455$	−5019.85	−	15449.5i	−0.517218	−	1.59183i
$456$	3687.77	−	2679.32i	0.378719	−	0.275155i
$457$	−13100.3	+	9517.92i	−1.34093	+	0.974244i	−0.341523	+	0.939874i	$0.610943\pi$
$457$	−13100.3	+	9517.92i	−1.34093	+	0.974244i	−0.999409	+	0.0343703i	$0.989057\pi$
$458$	1147.96	+	3533.07i	0.117120	+	0.360457i
$459$	−2859.66	+	8801.12i	−0.290800	+	0.894992i
$460$	−1036.72	−	753.220i	−0.105081	−	0.0763458i
$461$	−8586.04			−0.867444			−0.433722	−	0.901047i	$-0.642800\pi$
$461$	−8586.04			−0.867444			−0.433722	+	0.901047i	$0.642800\pi$
$462$		0			0
$463$	−7917.20			−0.794694			−0.397347	−	0.917668i	$-0.630069\pi$
$463$	−7917.20			−0.794694			−0.397347	+	0.917668i	$0.630069\pi$
$464$	7030.90	+	5108.25i	0.703451	+	0.511087i
$465$	1542.59	−	4747.59i	0.153840	−	0.473471i
$466$	−47.8860	−	147.378i	−0.00476025	−	0.0146505i
$467$	12260.6	−	8907.86i	1.21489	−	0.882670i	0.219225	−	0.975674i	$-0.429647\pi$
$467$	12260.6	−	8907.86i	1.21489	−	0.882670i	0.995666	+	0.0930047i	$0.0296472\pi$
$468$	−3670.53	+	2666.80i	−0.362543	+	0.263403i
$469$	−2153.34	−	6627.29i	−0.212008	−	0.652494i
$470$	−208.952	+	643.088i	−0.0205069	+	0.0631137i
$471$	−1640.51	−	1191.90i	−0.160490	−	0.116603i
$472$	−6176.82			−0.602354
$473$		0			0
$474$	4245.25			0.411373
$475$	−2213.82	−	1608.43i	−0.213846	−	0.155368i
$476$	3232.36	−	9948.20i	0.311250	−	0.957930i
$477$	−374.973	−	1154.05i	−0.0359933	−	0.110776i
$478$	2554.04	−	1855.62i	0.244391	−	0.177560i
$479$	8091.07	−	5878.51i	0.771796	−	0.560743i	−0.130709	−	0.991421i	$-0.541725\pi$
$479$	8091.07	−	5878.51i	0.771796	−	0.560743i	0.902506	+	0.430678i	$0.141725\pi$
$480$	−3019.59	−	9293.34i	−0.287135	−	0.883710i
$481$	−942.367	+	2900.31i	−0.0893311	+	0.274933i
$482$	−590.218	−	428.819i	−0.0557753	−	0.0405232i
$483$	−1340.11			−0.126246
$484$		0			0
$485$	−10896.9			−1.02021
$486$	1311.11	+	952.575i	0.122372	+	0.0889088i
$487$	2176.88	−	6699.76i	0.202554	−	0.623398i	−0.797251	−	0.603648i	$-0.793713\pi$
$487$	2176.88	−	6699.76i	0.202554	−	0.623398i	0.999805	−	0.0197497i	$-0.00628694\pi$
$488$	354.380	+	1090.67i	0.0328730	+	0.101173i
$489$	6689.93	−	4860.52i	0.618669	−	0.449489i
$490$	−429.709	+	312.202i	−0.0396169	+	0.0287833i
$491$	4118.09	+	12674.2i	0.378507	+	1.16492i	0.941082	+	0.338178i	$0.109811\pi$
$491$	4118.09	+	12674.2i	0.378507	+	1.16492i	−0.562575	+	0.826746i	$0.690189\pi$
$492$	3759.26	−	11569.8i	0.344473	−	1.06018i
$493$	11318.3	+	8223.22i	1.03398	+	0.751227i
$494$	−3711.38			−0.338022
$495$		0			0
$496$	−3368.25			−0.304917
$497$	−6445.45	−	4682.90i	−0.581727	−	0.422649i
$498$	−35.0738	+	107.946i	−0.00315602	+	0.00971322i
$499$	−6201.70	−	19086.9i	−0.556365	−	1.71232i	−0.692311	−	0.721600i	$-0.743407\pi$
$499$	−6201.70	−	19086.9i	−0.556365	−	1.71232i	0.135945	−	0.990716i	$-0.456593\pi$
$500$	6576.64	−	4778.21i	0.588232	−	0.427376i
$501$	2295.87	−	1668.05i	0.204734	−	0.148748i
$502$	−62.6375	−	192.778i	−0.00556902	−	0.0171397i
$503$	−2404.88	+	7401.45i	−0.213177	+	0.656092i	0.786101	+	0.618099i	$0.212097\pi$
$503$	−2404.88	+	7401.45i	−0.213177	+	0.656092i	−0.999278	+	0.0379939i	$0.987903\pi$
$504$	−1262.56	−	917.300i	−0.111585	−	0.0810710i
$505$	16629.3			1.46533
$506$		0			0
$507$	20003.4			1.75224
$508$	−661.859	−	480.868i	−0.0578056	−	0.0419982i
$509$	−456.088	+	1403.69i	−0.0397166	+	0.122235i	−0.968949	−	0.247261i	$-0.920470\pi$
$509$	−456.088	+	1403.69i	−0.0397166	+	0.122235i	0.929232	+	0.369496i	$0.120470\pi$
$510$	−1427.30	−	4392.78i	−0.123925	−	0.381403i
$511$	−8362.29	+	6075.56i	−0.723925	+	0.525963i
$512$	−9101.93	+	6612.94i	−0.785649	+	0.570807i
$513$	−2346.29	−	7221.14i	−0.201932	−	0.621483i
$514$	−731.850	+	2252.40i	−0.0628025	+	0.193286i
$515$	−17944.3	−	13037.3i	−1.53538	−	1.11552i
$516$	−101.205			−0.00863431
$517$		0			0
$518$	−506.305			−0.0429455
$519$	8674.00	+	6302.03i	0.733616	+	0.533003i
$520$	−3356.95	+	10331.6i	−0.283100	+	0.871293i
$521$	2351.44	+	7237.00i	0.197732	+	0.608558i	0.999934	+	0.0115042i	$0.00366198\pi$
$521$	2351.44	+	7237.00i	0.197732	+	0.608558i	−0.802201	+	0.597053i	$0.796338\pi$
$522$	815.058	−	592.174i	0.0683412	−	0.0496528i
$523$	10074.6	−	7319.63i	0.842318	−	0.611980i	−0.0806995	−	0.996738i	$-0.525715\pi$
$523$	10074.6	−	7319.63i	0.842318	−	0.611980i	0.923017	+	0.384759i	$0.125715\pi$
$524$	2668.00	+	8211.25i	0.222427	+	0.684561i
$525$	−1249.35	+	3845.10i	−0.103859	+	0.319645i
$526$	123.153	+	89.4761i	0.0102086	+	0.00741700i
$527$	−5422.18			−0.448186
$528$		0			0
$529$	−11988.7			−0.985344
$530$	−1134.54	−	824.291i	−0.0929835	−	0.0675565i
$531$	1373.08	−	4225.92i	0.112216	−	0.345366i
$532$	2652.09	+	8162.29i	0.216133	+	0.665188i
$533$	−16601.8	+	12061.9i	−1.34916	+	0.980223i
$534$	1238.96	−	900.159i	0.100403	−	0.0729470i
$535$	−1923.57	−	5920.14i	−0.155445	−	0.478411i
$536$	−1440.01	+	4431.91i	−0.116043	+	0.357144i
$537$	21245.6	+	15435.8i	1.70729	+	1.24042i
$538$	3684.44			0.295255
$539$		0			0
$540$	−10727.0			−0.854847
$541$	7533.70	+	5473.55i	0.598704	+	0.434984i	0.845419	−	0.534104i	$-0.179351\pi$
$541$	7533.70	+	5473.55i	0.598704	+	0.434984i	−0.246714	+	0.969088i	$0.579351\pi$
$542$	−336.386	+	1035.29i	−0.0266587	+	0.0820470i
$543$	6245.32	+	19221.1i	0.493577	+	1.51907i
$544$	−8586.77	+	6238.66i	−0.676755	+	0.491691i
$545$	668.333	−	485.572i	0.0525289	−	0.0381644i
$546$	1694.47	+	5215.06i	0.132815	+	0.408762i
$547$	3404.92	−	10479.3i	0.266150	−	0.819124i	−0.725277	−	0.688458i	$-0.758288\pi$
$547$	3404.92	−	10479.3i	0.266150	−	0.819124i	0.991426	−	0.130667i	$-0.0417119\pi$
$548$	1197.59	+	870.101i	0.0933551	+	0.0678264i
$549$	−824.968			−0.0641325
$550$		0			0
$551$	−11478.6			−0.887490
$552$	725.024	+	526.761i	0.0559041	+	0.0406167i
$553$	−5117.20	+	15749.1i	−0.393500	+	1.21107i
$554$	53.3499	+	164.194i	0.00409137	+	0.0125919i
$555$	2519.19	−	1830.30i	0.192673	−	0.139985i
$556$	17512.7	−	12723.7i	1.33580	−	0.970516i
$557$	3713.90	+	11430.2i	0.282519	+	0.869503i	0.987131	+	0.159911i	$0.0511207\pi$
$557$	3713.90	+	11430.2i	0.282519	+	0.869503i	−0.704613	+	0.709592i	$0.748879\pi$
$558$	−120.660	+	371.354i	−0.00915404	+	0.0281732i
$559$	138.114	+	100.346i	0.0104501	+	0.00759242i
$560$	11192.1			0.844555
$561$		0			0
$562$	3598.04			0.270061
$563$	−7090.13	−	5151.28i	−0.530752	−	0.385614i	0.289887	−	0.957061i	$-0.406382\pi$
$563$	−7090.13	−	5151.28i	−0.530752	−	0.385614i	−0.820639	+	0.571447i	$0.806382\pi$
$564$	−982.395	+	3023.50i	−0.0733445	+	0.225731i
$565$	7965.89	+	24516.5i	0.593146	+	1.82551i
$566$	−3079.39	+	2237.31i	−0.228687	+	0.166151i
$567$	−12086.8	+	8781.59i	−0.895236	+	0.650427i
$568$	1646.39	+	5067.07i	0.121622	+	0.374313i
$569$	3174.58	−	9770.35i	0.233893	−	0.719850i	−0.763373	−	0.645958i	$-0.776458\pi$
$569$	3174.58	−	9770.35i	0.233893	−	0.719850i	0.997266	−	0.0738917i	$-0.0235419\pi$
$570$	3065.91	+	2227.51i	0.225292	+	0.163684i
$571$	−2602.62			−0.190747			−0.0953734	−	0.995442i	$-0.530404\pi$
$571$	−2602.62			−0.190747			−0.0953734	+	0.995442i	$0.530404\pi$
$572$		0			0
$573$	17332.6			1.26366
$574$	−2756.32	−	2002.58i	−0.200429	−	0.145620i
$575$	166.247	−	511.657i	0.0120574	−	0.0371088i
$576$	−799.114	−	2459.42i	−0.0578063	−	0.177909i
$577$	15959.5	−	11595.3i	1.15148	−	0.836598i	0.162801	−	0.986659i	$-0.447947\pi$
$577$	15959.5	−	11595.3i	1.15148	−	0.836598i	0.988677	+	0.150061i	$0.0479471\pi$
$578$	−1149.12	+	834.885i	−0.0826940	+	0.0600807i
$579$	4550.82	+	14006.0i	0.326642	+	1.00530i
$580$	−5011.33	+	15423.3i	−0.358766	+	1.10417i
$581$	−358.183	−	260.235i	−0.0255765	−	0.0185824i
$582$	3678.30			0.261977
$583$		0			0
$584$	6912.30			0.489783
$585$	−6322.24	−	4593.38i	−0.446825	−	0.324637i
$586$	2009.01	−	6183.09i	0.141623	−	0.435872i
$587$	−3126.06	−	9621.03i	−0.219806	−	0.676495i	−0.998777	−	0.0494347i	$-0.984258\pi$
$587$	−3126.06	−	9621.03i	−0.219806	−	0.676495i	0.778971	−	0.627060i	$-0.215742\pi$
$588$	−2020.29	+	1467.83i	−0.141693	+	0.102946i
$589$	3599.14	−	2614.93i	0.251783	−	0.182931i
$590$	−1586.87	−	4883.89i	−0.110730	−	0.340791i
$591$	9389.80	−	28898.8i	0.653544	−	2.01140i
$592$	−1699.80	−	1234.98i	−0.118009	−	0.0857385i
$593$	−3130.32			−0.216774			−0.108387	−	0.994109i	$-0.534569\pi$
$593$	−3130.32			−0.216774			−0.108387	+	0.994109i	$0.534569\pi$
$594$		0			0
$595$	18016.9			1.24138
$596$	−21064.7	−	15304.4i	−1.44772	−	1.05183i
$597$	−14.0914	+	43.3690i	−0.000966038	+	0.00297316i
$598$	−225.479	−	693.954i	−0.0154190	−	0.0474547i
$599$	−8154.96	+	5924.92i	−0.556265	+	0.404150i	−0.830090	−	0.557629i	$-0.811711\pi$
$599$	−8154.96	+	5924.92i	−0.556265	+	0.404150i	0.273825	+	0.961779i	$0.411711\pi$
$600$	2187.33	−	1589.19i	0.148829	−	0.108130i
$601$	−1476.18	−	4543.21i	−0.100191	−	0.308355i	0.888381	−	0.459107i	$-0.151831\pi$
$601$	−1476.18	−	4543.21i	−0.100191	−	0.308355i	−0.988572	+	0.150752i	$0.951831\pi$
$602$	−8.75863	+	26.9563i	−0.000592982	+	0.00182501i
$603$	−2712.02	−	1970.40i	−0.183154	−	0.133069i
$604$	−8683.16			−0.584955
$605$		0			0
$606$	−5613.29			−0.376278
$607$	−2080.27	−	1511.40i	−0.139103	−	0.101064i	0.516058	−	0.856554i	$-0.327399\pi$
$607$	−2080.27	−	1511.40i	−0.139103	−	0.101064i	−0.655160	+	0.755490i	$0.727399\pi$
$608$	2691.05	−	8282.21i	0.179501	−	0.552447i
$609$	5240.71	+	16129.2i	0.348710	+	1.07322i
$610$	−771.328	+	560.403i	−0.0511970	+	0.0371968i
$611$	4338.49	−	3152.10i	0.287261	−	0.208707i
$612$	−1554.98	−	4785.75i	−0.102707	−	0.316098i
$613$	−3928.18	+	12089.7i	−0.258822	+	0.796571i	0.734231	+	0.678900i	$0.237543\pi$
$613$	−3928.18	+	12089.7i	−0.258822	+	0.796571i	−0.993053	+	0.117671i	$0.962457\pi$
$614$	−887.138	−	644.544i	−0.0583094	−	0.0423643i
$615$	20953.8			1.37388
$616$		0			0
$617$	16236.1			1.05939			0.529693	−	0.848189i	$-0.322307\pi$
$617$	16236.1			1.05939			0.529693	+	0.848189i	$0.322307\pi$
$618$	6057.20	+	4400.81i	0.394266	+	0.286451i
$619$	3911.32	−	12037.8i	0.253973	−	0.781649i	−0.740057	−	0.672544i	$-0.765202\pi$
$619$	3911.32	−	12037.8i	0.253973	−	0.781649i	0.994030	−	0.109105i	$-0.0347984\pi$
$620$	−1942.24	−	5977.61i	−0.125810	−	0.387204i
$621$	1207.66	−	877.418i	0.0780383	−	0.0566982i
$622$	4432.75	−	3220.58i	0.285751	−	0.207610i
$623$	1845.99	+	5681.37i	0.118713	+	0.365360i
$624$	−7031.74	+	21641.5i	−0.451113	+	1.38838i
$625$	15401.9	+	11190.2i	0.985724	+	0.716170i
$626$	−481.955			−0.0307713
$627$		0			0
$628$	−2553.15			−0.162232
$629$	−2736.32	−	1988.06i	−0.173457	−	0.126024i
$630$	400.931	−	1233.94i	0.0253547	−	0.0780339i
$631$	−1220.61	−	3756.64i	−0.0770073	−	0.237004i	0.905141	−	0.425111i	$-0.139765\pi$
$631$	−1220.61	−	3756.64i	−0.0770073	−	0.237004i	−0.982149	+	0.188107i	$0.939765\pi$
$632$	8959.06	−	6509.14i	0.563880	−	0.409683i
$633$	14902.9	−	10827.6i	0.935760	−	0.679869i
$634$	52.8684	+	162.712i	0.00331179	+	0.0101926i
$635$	435.444	−	1340.16i	0.0272127	−	0.0837520i
$636$	−5334.08	−	3875.44i	−0.332563	−	0.241621i
$637$	4212.44			0.262014
$638$		0			0
$639$	−3832.67			−0.237274
$640$	−13086.0	−	9507.55i	−0.808235	−	0.587217i
$641$	−2286.19	+	7036.17i	−0.140872	+	0.433560i	−0.996457	−	0.0841024i	$-0.973198\pi$
$641$	−2286.19	+	7036.17i	−0.140872	+	0.433560i	0.855585	+	0.517663i	$0.173198\pi$
$642$	649.311	+	1998.37i	0.0399163	+	0.122850i
$643$	10106.0	−	7342.43i	0.619815	−	0.450322i	−0.233042	−	0.972467i	$-0.574868\pi$
$643$	10106.0	−	7342.43i	0.619815	−	0.450322i	0.852857	+	0.522145i	$0.174868\pi$
$644$	−1365.06	+	991.774i	−0.0835263	+	0.0606854i
$645$	−53.8675	−	165.787i	−0.00328842	−	0.0101207i
$646$	1272.01	−	3914.84i	0.0774714	−	0.238433i
$647$	8472.01	+	6155.27i	0.514790	+	0.374017i	0.814638	−	0.579970i	$-0.196936\pi$
$647$	8472.01	+	6155.27i	0.514790	+	0.374017i	−0.299848	+	0.953987i	$0.596936\pi$
$648$	9991.02			0.605685
$649$		0			0
$650$	−2201.33			−0.132836
$651$	−5317.60	−	3863.46i	−0.320143	−	0.232598i
$652$	3217.37	−	9902.04i	0.193254	−	0.594776i
$653$	1958.53	+	6027.73i	0.117371	+	0.361230i	0.992434	−	0.122778i	$-0.0391804\pi$
$653$	1958.53	+	6027.73i	0.117371	+	0.361230i	−0.875063	+	0.484009i	$0.839180\pi$
$654$	−225.599	+	163.907i	−0.0134887	+	0.00980013i
$655$	−12031.0	+	8741.05i	−0.717696	+	0.521437i
$656$	−4368.99	−	13446.4i	−0.260031	−	0.800294i
$657$	−1536.58	+	4729.11i	−0.0912446	+	0.280822i
$658$	720.299	+	523.328i	0.0426751	+	0.0310052i
$659$	−15196.7			−0.898302			−0.449151	−	0.893456i	$-0.648274\pi$
$659$	−15196.7			−0.898302			−0.449151	+	0.893456i	$0.648274\pi$
$660$		0			0
$661$	2298.17			0.135232			0.0676161	−	0.997711i	$-0.478461\pi$
$661$	2298.17			0.135232			0.0676161	+	0.997711i	$0.478461\pi$
$662$	−5053.57	−	3671.63i	−0.296696	−	0.215562i
$663$	−11319.6	+	34838.3i	−0.663074	+	2.04073i
$664$	91.4924	+	281.585i	0.00534728	+	0.0164572i
$665$	−11959.3	+	8688.93i	−0.697385	+	0.506680i
$666$	−197.049	+	143.165i	−0.0114647	+	0.00832961i
$667$	−697.367	−	2146.28i	−0.0404830	−	0.124594i
$668$	1104.14	−	3398.21i	0.0639530	−	0.196827i
$669$	59.0797	+	42.9239i	0.00341428	+	0.00248062i
$670$	−3874.18			−0.223392
$671$		0			0
$672$	−12866.4			−0.738589
$673$	18768.9	+	13636.4i	1.07502	+	0.781047i	0.976808	−	0.214118i	$-0.0686878\pi$
$673$	18768.9	+	13636.4i	1.07502	+	0.781047i	0.0982115	+	0.995166i	$0.468688\pi$
$674$	−2644.73	+	8139.66i	−0.151144	+	0.465175i
$675$	−1391.65	−	4283.07i	−0.0793553	−	0.244230i
$676$	20375.9	−	14803.9i	1.15930	−	0.842282i
$677$	−1735.65	+	1261.02i	−0.0985322	+	0.0715879i	−0.635960	−	0.771722i	$-0.719396\pi$
$677$	−1735.65	+	1261.02i	−0.0985322	+	0.0715879i	0.537428	+	0.843309i	$0.319396\pi$
$678$	−2688.93	−	8275.66i	−0.152312	−	0.468768i
$679$	−4433.80	+	13645.8i	−0.250595	+	0.771251i
$680$	−9747.49	−	7081.97i	−0.549705	−	0.399384i
$681$	−27364.0			−1.53978
$682$		0			0
$683$	−29544.6			−1.65519			−0.827593	−	0.561329i	$-0.810290\pi$
$683$	−29544.6			−1.65519			−0.827593	+	0.561329i	$0.810290\pi$
$684$	3340.17	+	2426.77i	0.186717	+	0.135658i
$685$	−787.908	+	2424.93i	−0.0439481	+	0.135258i
$686$	1529.61	+	4707.66i	0.0851325	+	0.262011i
$687$	−24338.0	+	17682.6i	−1.35161	+	0.981999i
$688$	−95.1566	+	69.1353i	−0.00527298	+	0.00383105i
$689$	3436.85	+	10577.6i	0.190034	+	0.584866i
$690$	−230.235	+	708.592i	−0.0127028	+	0.0390951i
$691$	−22493.2	−	16342.2i	−1.23832	−	0.899693i	−0.240836	−	0.970566i	$-0.577422\pi$
$691$	−22493.2	−	16342.2i	−1.23832	−	0.899693i	−0.997485	+	0.0708727i	$0.977422\pi$
$692$	13499.5			0.741579
$693$		0			0
$694$	−3366.55			−0.184139
$695$	30164.5	+	21915.8i	1.64634	+	1.19613i
$696$	3504.65	−	10786.2i	0.190867	−	0.587428i
$697$	−7033.17	−	21645.9i	−0.382210	−	1.17632i
$698$	3980.02	−	2891.66i	0.215825	−	0.156806i
$699$	1015.23	−	737.610i	0.0549351	−	0.0399127i
$700$	1573.03	+	4841.30i	0.0849358	+	0.261405i
$701$	6086.94	−	18733.7i	0.327961	−	1.00936i	−0.642125	−	0.766600i	$-0.721947\pi$
$701$	6086.94	−	18733.7i	0.327961	−	1.00936i	0.970086	−	0.242760i	$-0.0780528\pi$
$702$	−4941.50	−	3590.21i	−0.265676	−	0.193025i
$703$	2775.09			0.148883
$704$		0			0
$705$	−5475.78			−0.292524
$706$	−3398.70	−	2469.30i	−0.181178	−	0.131633i
$707$	6766.23	−	20824.3i	0.359930	−	1.10775i
$708$	−7460.74	−	22961.8i	−0.396033	−	1.21887i
$709$	−15470.4	+	11239.9i	−0.819470	+	0.595380i	−0.916561	−	0.399896i	$-0.869046\pi$
$709$	−15470.4	+	11239.9i	−0.819470	+	0.595380i	0.0970906	+	0.995276i	$0.469046\pi$
$710$	−3583.47	+	2603.54i	−0.189416	+	0.137619i
$711$	2461.71	+	7576.37i	0.129847	+	0.399629i
$712$	1234.48	−	3799.34i	0.0649777	−	0.199981i
$713$	707.600	+	514.101i	0.0371666	+	0.0270031i
$714$	−6081.70			−0.318770
$715$		0			0
$716$	33064.8			1.72582
$717$	20682.8	+	15026.9i	1.07728	+	0.782693i
$718$	930.940	−	2865.14i	0.0483877	−	0.148922i
$719$	567.801	+	1747.51i	0.0294512	+	0.0906414i	0.964702	−	0.263345i	$-0.0848258\pi$
$719$	567.801	+	1747.51i	0.0294512	+	0.0906414i	−0.935250	+	0.353987i	$0.884826\pi$
$720$	4355.85	−	3164.71i	0.225462	−	0.163808i
$721$	−23627.5	+	17166.4i	−1.22044	+	0.886699i
$722$	−507.959	−	1563.34i	−0.0261832	−	0.0805837i
$723$	1825.66	−	5618.80i	0.0939100	−	0.289025i
$724$	20586.6	+	14957.0i	1.05676	+	0.767781i
$725$	−6808.33			−0.348765
$726$		0			0
$727$	−7555.46			−0.385442			−0.192721	−	0.981254i	$-0.561731\pi$
$727$	−7555.46			−0.385442			−0.192721	+	0.981254i	$0.561731\pi$
$728$	11572.1	+	8407.62i	0.589135	+	0.428032i
$729$	3308.09	−	10181.3i	0.168068	−	0.517262i
$730$	1775.82	+	5465.42i	0.0900359	+	0.277102i
$731$	−153.182	+	111.294i	−0.00775056	+	0.00563111i
$732$	−3626.43	+	2634.75i	−0.183110	+	0.133037i
$733$	−3703.45	−	11398.1i	−0.186617	−	0.574348i	0.813356	−	0.581767i	$-0.197638\pi$
$733$	−3703.45	−	11398.1i	−0.186617	−	0.574348i	−0.999972	+	0.00741920i	$0.997638\pi$
$734$	2185.93	−	6727.59i	0.109924	−	0.338310i
$735$	−3479.81	−	2528.23i	−0.174632	−	0.126878i
$736$	1712.10			0.0857456
$737$		0			0
$738$	−1638.99			−0.0817508
$739$	−21958.7	−	15953.9i	−1.09305	−	0.794148i	−0.113139	−	0.993579i	$-0.536091\pi$
$739$	−21958.7	−	15953.9i	−1.09305	−	0.794148i	−0.979912	+	0.199431i	$0.936091\pi$
$740$	1211.55	−	3728.75i	0.0601855	−	0.185232i
$741$	−9287.53	−	28584.1i	−0.460440	−	1.41709i
$742$	−1493.86	+	1085.36i	−0.0739103	+	0.0536990i
$743$	−23641.6	+	17176.6i	−1.16733	+	0.848115i	−0.990687	−	0.136160i	$-0.956524\pi$
$743$	−23641.6	+	17176.6i	−1.16733	+	0.848115i	−0.176644	+	0.984275i	$0.556524\pi$
$744$	1358.30	+	4180.42i	0.0669324	+	0.205997i
$745$	13858.7	−	42652.6i	0.681533	−	2.09754i
$746$	−83.9681	−	61.0064i	−0.00412103	−	0.00299411i
$747$	−212.987			−0.0104321
$748$		0			0
$749$	−8196.29			−0.399847
$750$	−3823.76	−	2778.12i	−0.186165	−	0.135257i
$751$	−2737.70	+	8425.78i	−0.133023	+	0.409402i	−0.995277	−	0.0970731i	$-0.969052\pi$
$751$	−2737.70	+	8425.78i	−0.133023	+	0.409402i	0.862254	+	0.506475i	$0.169052\pi$
$752$	1141.73	+	3513.90i	0.0553654	+	0.170397i
$753$	1327.98	−	964.833i	0.0642686	−	0.0466939i
$754$	−7470.50	+	5427.64i	−0.360822	+	0.262152i
$755$	−4621.71	−	14224.2i	−0.222783	−	0.685655i
$756$	−4364.68	+	13433.1i	−0.209976	+	0.646240i
$757$	−28909.7	−	21004.2i	−1.38803	−	1.00847i	−0.996078	−	0.0884828i	$-0.971798\pi$
$757$	−28909.7	−	21004.2i	−1.38803	−	1.00847i	−0.391957	−	0.919984i	$-0.628202\pi$
$758$	−2064.19			−0.0989112
$759$		0			0
$760$	9885.59			0.471826
$761$	27825.9	+	20216.7i	1.32548	+	0.963014i	0.999847	+	0.0175169i	$0.00557610\pi$
$761$	27825.9	+	20216.7i	1.32548	+	0.963014i	0.325629	+	0.945498i	$0.394424\pi$
$762$	−146.986	+	452.377i	−0.00698786	+	0.0215064i
$763$	−336.131	−	1034.51i	−0.0159486	−	0.0490847i
$764$	17655.3	−	12827.4i	0.836057	−	0.607431i
$765$	7012.02	−	5094.53i	0.331399	−	0.240775i
$766$	−1433.72	−	4412.54i	−0.0676272	−	0.208135i
$767$	−12585.2	+	38733.1i	−0.592469	+	1.82343i

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)

\(f(q)\)	\(=\)	\(q+(-0.592242 - 0.430289i) q^{2} +(1.83192 - 5.63806i) q^{3} +(-2.30653 - 7.09878i) q^{4} +(10.4011 - 7.55681i) q^{5} +(-3.51093 + 2.55084i) q^{6} +(-5.23110 - 16.0997i) q^{7} +(-3.49823 + 10.7664i) q^{8} +(-6.58831 - 4.78668i) q^{9} +O(q^{10})\)	\(q+(-0.592242 - 0.430289i) q^{2} +(1.83192 - 5.63806i) q^{3} +(-2.30653 - 7.09878i) q^{4} +(10.4011 - 7.55681i) q^{5} +(-3.51093 + 2.55084i) q^{6} +(-5.23110 - 16.0997i) q^{7} +(-3.49823 + 10.7664i) q^{8} +(-6.58831 - 4.78668i) q^{9} -9.41154 q^{10} -44.2487 q^{12} +(60.3859 + 43.8729i) q^{13} +(-3.82943 + 11.7858i) q^{14} +(-23.5519 - 72.4851i) q^{15} +(-41.6042 + 30.2272i) q^{16} +(-66.9742 + 48.6596i) q^{17} +(1.84221 + 5.66975i) q^{18} +(20.9894 - 64.5987i) q^{19} +(-77.6345 - 56.4048i) q^{20} -100.354 q^{21} +13.3538 q^{23} +(54.2934 + 39.4464i) q^{24} +(12.4494 - 38.3154i) q^{25} +(-16.8850 - 51.9667i) q^{26} +(90.4356 - 65.7053i) q^{27} +(-102.222 + 74.2689i) q^{28} +(-52.2223 - 160.724i) q^{29} +(-17.2412 + 53.0628i) q^{30} +(52.9885 + 38.4984i) q^{31} +128.210 q^{32} +60.6025 q^{34} +(-176.071 - 127.923i) q^{35} +(-18.7835 + 57.8096i) q^{36} +(12.6253 + 38.8568i) q^{37} +(-40.2269 + 29.2265i) q^{38} +(357.980 - 260.087i) q^{39} +(44.9747 + 138.418i) q^{40} +(-84.9575 + 261.472i) q^{41} +(59.4337 + 43.1811i) q^{42} +2.28719 q^{43} -104.697 q^{45} +(-7.90869 - 5.74600i) q^{46} +(22.2017 - 68.3297i) q^{47} +(94.2074 + 289.941i) q^{48} +(45.6576 - 33.1722i) q^{49} +(-23.8597 + 17.3351i) q^{50} +(151.654 + 466.744i) q^{51} +(172.162 - 529.860i) q^{52} +(120.548 + 87.5830i) q^{53} -81.8320 q^{54} +191.636 q^{56} +(-325.760 - 236.679i) q^{57} +(-38.2294 + 117.658i) q^{58} +(168.609 + 518.926i) q^{59} +(-460.233 + 334.379i) q^{60} +(81.9556 - 59.5442i) q^{61} +(-14.8166 - 45.6007i) q^{62} +(-42.6000 + 131.109i) q^{63} +(256.902 + 186.650i) q^{64} +959.615 q^{65} +411.641 q^{67} +(499.902 + 363.200i) q^{68} +(24.4631 - 75.2896i) q^{69} +(49.2327 + 151.523i) q^{70} +(380.752 - 276.633i) q^{71} +(74.5830 - 54.1877i) q^{72} +(-188.686 - 580.715i) q^{73} +(9.24238 - 28.4451i) q^{74} +(-193.218 - 140.381i) q^{75} -506.985 q^{76} -323.923 q^{78} +(-791.401 - 574.986i) q^{79} +(-204.306 + 628.790i) q^{80} +(-272.726 - 839.363i) q^{81} +(162.824 - 118.298i) q^{82} +(21.1590 - 15.3729i) q^{83} +(231.470 + 712.390i) q^{84} +(-328.891 + 1012.22i) q^{85} +(-1.35457 - 0.984151i) q^{86} -1001.84 q^{87} -352.887 q^{89} +(62.0061 + 45.0501i) q^{90} +(390.455 - 1201.70i) q^{91} +(-30.8011 - 94.7959i) q^{92} +(314.127 - 228.226i) q^{93} +(-42.5502 + 30.9146i) q^{94} +(-269.848 - 830.507i) q^{95} +(234.870 - 722.857i) q^{96} +(-685.710 - 498.198i) q^{97} -41.3140 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

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more