LMFDB - Embedded newform 121.4.c.c.3.2

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			3.2
Root			$-0.535233 - 1.64728i$ of defining polynomial
Character	$\chi$	$=$	121.3
Dual form			121.4.c.c.81.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.592242 - 0.430289i) q^{2} +(1.83192 + 5.63806i) q^{3} +(-2.30653 + 7.09878i) q^{4} +(10.4011 + 7.55681i) q^{5} +(3.51093 + 2.55084i) q^{6} +(5.23110 - 16.0997i) q^{7} +(3.49823 + 10.7664i) q^{8} +(-6.58831 + 4.78668i) q^{9} +O(q^{10})$	\(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 $\left(\mathbb{Z}/121\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{4}{5}\right)$

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	$-0.658692\pi$
$2$	0.592242	−	0.430289i	0.209389	−	0.152130i	0.687537	+	0.726149i	$0.258692\pi$
$3$	1.83192	+	5.63806i	0.352552	+	1.08504i	0.957415	+	0.288715i	$0.0932279\pi$
$3$	1.83192	+	5.63806i	0.352552	+	1.08504i	−0.604863	+	0.796330i	$0.706772\pi$
$4$	−2.30653	+	7.09878i	−0.288317	+	0.887348i
$5$	10.4011	+	7.55681i	0.930298	+	0.675901i	0.946066	−	0.323974i	$-0.105019\pi$
$5$	10.4011	+	7.55681i	0.930298	+	0.675901i	−0.0157675	+	0.999876i	$0.505019\pi$
$6$	3.51093	+	2.55084i	0.238888	+	0.173563i
$7$	5.23110	−	16.0997i	0.282453	−	0.869301i	−0.704698	−	0.709508i	$-0.748917\pi$
$7$	5.23110	−	16.0997i	0.282453	−	0.869301i	0.987151	−	0.159793i	$-0.0510827\pi$
$8$	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	$-0.993170\pi$
$13$	−60.3859	+	43.8729i	−1.28831	+	0.936012i	−0.288540	+	0.957468i	$0.593170\pi$
$14$	−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	$-0.0989164\pi$
$17$	66.9742	+	48.6596i	0.955507	+	0.694216i	0.00340407	+	0.999994i	$0.498916\pi$
$18$	−1.84221	+	5.66975i	−0.0241230	+	0.0742429i
$19$	−20.9894	−	64.5987i	−0.253436	−	0.779997i	−0.994134	−	0.108158i	$-0.965505\pi$
$19$	−20.9894	−	64.5987i	−0.253436	−	0.779997i	0.740697	−	0.671839i	$-0.234495\pi$
$20$	−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	−0.632625	−	0.774458i	$-0.718023\pi$
$29$	52.2223	−	160.724i	0.334394	−	1.02916i	0.967020	−	0.254702i	$-0.0819773\pi$
$30$	17.2412	+	53.0628i	0.104926	+	0.322930i
$31$	52.9885	−	38.4984i	0.307001	−	0.223049i	−0.423608	−	0.905846i	$-0.639237\pi$
$31$	52.9885	−	38.4984i	0.307001	−	0.223049i	0.730608	+	0.682797i	$0.239237\pi$
$32$	−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	−0.919082	−	0.394066i	$-0.871068\pi$
$37$	12.6253	−	38.8568i	0.0560970	−	0.172649i	0.975179	+	0.221417i	$0.0710682\pi$
$38$	−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	0.972063	+	0.234721i	$0.0754176\pi$
$41$	84.9575	+	261.472i	0.323613	+	0.995978i	−0.648450	+	0.761257i	$0.724582\pi$
$42$	59.4337	−	43.1811i	0.218353	−	0.158643i
$43$	−2.28719			−0.00811146			−0.00405573	−	0.999992i	$-0.501291\pi$
$43$	−2.28719			−0.00811146			−0.00405573	+	0.999992i	$0.501291\pi$
$44$		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	0.979579	−	0.201060i	$-0.0644385\pi$
$47$	22.2017	+	68.3297i	0.0689031	+	0.212062i	−0.910676	+	0.413121i	$0.864438\pi$
$48$	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	−0.420512	−	0.907287i	$-0.638149\pi$
$53$	120.548	−	87.5830i	0.312425	−	0.226990i	0.732936	+	0.680297i	$0.238149\pi$
$54$	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	−0.573395	−	0.819279i	$-0.694374\pi$
$59$	168.609	−	518.926i	0.372052	−	1.14506i	0.945446	−	0.325778i	$-0.105626\pi$
$60$	−460.233	−	334.379i	−0.990264	−	0.719469i
$61$	−81.9556	−	59.5442i	−0.172022	−	0.124981i	0.498443	−	0.866922i	$-0.333905\pi$
$61$	−81.9556	−	59.5442i	−0.172022	−	0.124981i	−0.670465	+	0.741941i	$0.733905\pi$
$62$	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	0.858624	−	0.512606i	$-0.171320\pi$
$71$	380.752	+	276.633i	0.636437	+	0.462398i	−0.222188	+	0.975004i	$0.571320\pi$
$72$	−74.5830	−	54.1877i	−0.122079	−	0.0886956i
$73$	188.686	−	580.715i	0.302520	−	0.931062i	−0.678070	−	0.734997i	$-0.737184\pi$
$73$	188.686	−	580.715i	0.302520	−	0.931062i	0.980591	−	0.196065i	$-0.0628164\pi$
$74$	−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	$-0.454706\pi$
$79$	791.401	−	574.986i	1.12708	−	0.818874i	0.985268	+	0.171019i	$0.0547061\pi$
$80$	−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	$-0.305505\pi$
$83$	−21.1590	−	15.3729i	−0.0279819	−	0.0203300i	−0.601688	+	0.798731i	$0.705505\pi$
$84$	−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	−0.885670	−	0.464316i	$-0.846300\pi$
$97$	−685.710	+	498.198i	−0.717766	+	0.521488i	0.167903	+	0.985803i	$0.446300\pi$
$98$	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	$-0.919887\pi$
$101$	−1046.43	+	760.277i	−1.03093	+	0.749014i	−0.0624351	+	0.998049i	$0.519887\pi$
$102$	111.019	+	341.681i	0.107770	+	0.331681i
$103$	−533.129	+	1640.80i	−0.510007	+	1.56964i	0.282179	+	0.959362i	$0.408943\pi$
$103$	−533.129	+	1640.80i	−0.510007	+	1.56964i	−0.792187	+	0.610279i	$0.791057\pi$
$104$	−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	$-0.170190\pi$
$107$	−149.620	−	460.482i	−0.135180	−	0.416042i	−0.995618	+	0.0935137i	$0.970190\pi$
$108$	−675.021	+	490.431i	−0.601425	+	0.436961i
$109$	−64.2563			−0.0564645			−0.0282323	−	0.999601i	$-0.508988\pi$
$109$	−64.2563			−0.0564645			−0.0282323	+	0.999601i	$0.508988\pi$
$110$		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	−0.781788	−	0.623544i	$-0.785692\pi$
$113$	−619.604	−	1906.95i	−0.515818	−	1.58753i	0.265970	−	0.963981i	$-0.414308\pi$
$114$	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	$-0.312191\pi$
$127$	−88.6723	−	64.4242i	−0.0619558	−	0.0450135i	−0.618332	+	0.785917i	$0.712191\pi$
$128$	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	$-0.373948\pi$
$131$	1156.71			0.771469			0.385734	+	0.922610i	$0.373948\pi$
$132$		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	0.536631	−	0.843817i	$-0.319697\pi$
$137$	−160.447	−	116.571i	−0.100058	−	0.0726962i	−0.636689	+	0.771121i	$0.719697\pi$
$138$	46.8843	+	34.0635i	0.0289207	+	0.0210121i
$139$	−896.192	+	2758.20i	−0.546863	+	1.68307i	0.169654	+	0.985504i	$0.445735\pi$
$139$	−896.192	+	2758.20i	−0.546863	+	1.68307i	−0.716518	+	0.697569i	$0.754265\pi$
$140$	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	−0.942452	−	0.334341i	$-0.891486\pi$
$149$	−2822.13	−	2050.40i	−1.55166	−	1.12735i	−0.609211	−	0.793008i	$-0.708514\pi$
$150$	−54.0273	+	166.279i	−0.0294088	+	0.0905109i
$151$	−359.487	−	1106.39i	−0.193739	−	0.596268i	−0.999989	−	0.00469259i	$-0.998506\pi$
$151$	−359.487	−	1106.39i	−0.193739	−	0.596268i	0.806250	−	0.591575i	$-0.201494\pi$
$152$	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	0.974321	−	0.225162i	$-0.0722912\pi$
$157$	105.701	+	325.315i	0.0537318	+	0.165369i	−0.920590	+	0.390532i	$0.872291\pi$
$158$	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	−0.282656	−	0.959221i	$-0.591216\pi$
$163$	1128.49	−	819.897i	0.542272	−	0.393983i	0.824928	+	0.565238i	$0.191216\pi$
$164$	−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	$-0.735376\pi$
$167$	−387.279	+	281.374i	−0.179452	+	0.130380i	0.494433	+	0.869216i	$0.335376\pi$
$168$	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	0.995535	+	0.0943936i	$0.0300912\pi$
$173$	558.883	+	1720.07i	0.245613	+	0.755920i	−0.749922	+	0.661527i	$0.769909\pi$
$174$	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	−0.647479	−	0.762084i	$-0.724176\pi$
$179$	−1368.90	−	4213.03i	−0.571599	−	1.75920i	0.0758796	−	0.997117i	$-0.475824\pi$
$180$	241.488	−	743.224i	0.0999970	−	0.307759i
$181$	−2758.08	−	2003.86i	−1.13263	−	0.822905i	−0.146557	−	0.989202i	$-0.546819\pi$
$181$	−2758.08	−	2003.86i	−1.13263	−	0.822905i	−0.986076	+	0.166297i	$0.946819\pi$
$182$	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	−0.620754	−	0.784005i	$-0.713173\pi$
$191$	903.490	−	2780.65i	0.342273	−	1.05341i	0.963027	−	0.269404i	$-0.0868266\pi$
$192$	1522.97	+	1106.50i	0.572452	+	0.415911i
$193$	2009.75	+	1460.17i	0.749558	+	0.544586i	0.895690	−	0.444679i	$-0.146682\pi$
$193$	2009.75	+	1460.17i	0.749558	+	0.544586i	−0.146132	+	0.989265i	$0.546682\pi$
$194$	−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	$-0.877516\pi$
$197$	−5125.67			−1.85375			−0.926876	+	0.375369i	$0.877516\pi$
$198$		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	$-0.869214\pi$
$211$	−2513.89	+	1826.45i	−0.820206	+	0.595915i	0.0965652	+	0.995327i	$0.469214\pi$
$212$	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	0.950483	−	0.310776i	$-0.100589\pi$
$223$	−3.80662	−	11.7156i	−0.00114310	−	0.00351809i	−0.951626	+	0.307257i	$0.900589\pi$
$224$	−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	−0.493332	−	0.869841i	$-0.664221\pi$
$227$	1426.39	−	4389.98i	0.417062	−	1.28358i	0.910394	−	0.413743i	$-0.135779\pi$
$228$	928.753	+	2858.41i	0.269773	+	0.830275i
$229$	−4105.46	+	2982.79i	−1.18470	+	0.860736i	−0.992694	−	0.120658i	$-0.961500\pi$
$229$	−4105.46	+	2982.79i	−1.18470	+	0.860736i	−0.192007	+	0.981394i	$0.561500\pi$
$230$	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	$-0.709474\pi$
$233$	−171.255	+	124.424i	−0.0481514	+	0.0349840i	0.563449	+	0.826151i	$0.309474\pi$
$234$	−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	0.952646	+	0.304080i	$0.0983490\pi$
$239$	1332.63	+	4101.42i	0.360673	+	1.11004i	−0.591973	+	0.805958i	$0.701651\pi$
$240$	3170.88	−	2303.78i	0.852831	−	0.619618i
$241$	−996.584			−0.266372			−0.133186	−	0.991091i	$-0.542521\pi$
$241$	−996.584			−0.266372			−0.133186	+	0.991091i	$0.542521\pi$
$242$		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	−0.559263	−	0.828990i	$-0.688916\pi$
$251$	224.010	−	162.753i	0.0563323	−	0.0409278i	0.615595	+	0.788063i	$0.288916\pi$
$252$	−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	0.753364	+	0.657604i	$0.228430\pi$
$257$	−999.725	+	3076.84i	−0.242650	+	0.746801i	−0.996014	+	0.0891969i	$0.971570\pi$
$258$	−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	$-0.492240\pi$
$263$	207.944			0.0487544			0.0243772	+	0.999703i	$0.492240\pi$
$264$		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	0.0213369	−	0.999772i	$-0.493208\pi$
$269$	−4071.81	−	2958.34i	−0.922910	−	0.670533i	−0.944247	+	0.329239i	$0.893208\pi$
$270$	851.139	+	618.389i	0.191847	+	0.139385i
$271$	459.512	−	1414.23i	0.103001	−	0.317005i	−0.886255	−	0.463198i	$-0.846702\pi$
$271$	459.512	−	1414.23i	0.103001	−	0.317005i	0.989256	+	0.146193i	$0.0467019\pi$
$272$	−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	$-0.691858\pi$
$277$	190.795	−	138.621i	0.0413855	−	0.0300683i	0.608286	+	0.793718i	$0.291858\pi$
$278$	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	$-0.125292\pi$
$281$	3976.33	+	2888.97i	0.844156	+	0.613316i	−0.0793722	+	0.996845i	$0.525292\pi$
$282$	−96.3496	+	296.534i	−0.0203459	+	0.0626181i
$283$	−1606.75	−	4945.07i	−0.337496	−	1.03871i	−0.965479	−	0.260480i	$-0.916119\pi$
$283$	−1606.75	−	4945.07i	−0.337496	−	1.03871i	0.627983	−	0.778227i	$-0.283881\pi$
$284$	−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	0.168533	+	0.985696i	$0.446097\pi$
$293$	−2744.35	+	8446.25i	−0.547191	+	1.68408i	−0.715723	+	0.698384i	$0.753903\pi$
$294$	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	$-0.544465\pi$
$307$	−1497.93			−0.278474			−0.139237	+	0.990259i	$0.544465\pi$
$308$		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	−0.906107	−	0.423048i	$-0.860960\pi$
$311$	−2312.90	−	7118.38i	−0.421713	−	1.29790i	0.484395	−	0.874850i	$-0.339040\pi$
$312$	1547.92	−	4764.01i	0.280878	−	0.864452i
$313$	532.627	+	386.976i	0.0961848	+	0.0698824i	0.634838	−	0.772645i	$-0.281067\pi$
$313$	532.627	+	386.976i	0.0961848	+	0.0698824i	−0.538653	+	0.842527i	$0.681067\pi$
$314$	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	−0.604409	−	0.796674i	$-0.706591\pi$
$317$	−189.073	+	137.370i	−0.0334998	+	0.0243390i	0.570909	+	0.821013i	$0.306591\pi$
$318$	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	−0.0193617	−	0.999813i	$-0.506163\pi$
$337$	3612.77	−	11119.0i	0.583977	−	1.79730i	0.603339	−	0.797485i	$-0.293837\pi$
$338$	−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	$-0.415768\pi$
$347$	−3720.50	−	2703.10i	−0.575582	−	0.418185i	−0.837129	+	0.547006i	$0.815768\pi$
$348$	−2310.77	+	7111.81i	−0.355949	+	1.09550i
$349$	2076.68	+	6391.36i	0.318516	+	0.980291i	0.974283	+	0.225328i	$0.0723453\pi$
$349$	2076.68	+	6391.36i	0.318516	+	0.980291i	−0.655767	+	0.754963i	$0.727655\pi$
$350$	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	$-0.997821\pi$
$359$	−1271.69	+	3913.85i	−0.186956	+	0.575391i	0.813021	+	0.582235i	$0.197821\pi$
$360$	−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	−0.478557	−	0.878057i	$-0.658840\pi$
$367$	2986.03	−	9190.05i	0.424712	−	1.30713i	0.903269	−	0.429074i	$-0.141160\pi$
$368$	−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	$-0.503132\pi$
$373$	−141.780			−0.0196812			−0.00984062	+	0.999952i	$0.503132\pi$
$374$		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	0.731543	−	0.681795i	$-0.238800\pi$
$379$	2281.21	+	1657.40i	0.309177	+	0.224630i	−0.422366	+	0.906425i	$0.638800\pi$
$380$	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	−0.190636	−	0.981661i	$-0.561055\pi$
$383$	5127.42	−	3725.29i	0.684070	−	0.497006i	0.874705	+	0.484655i	$0.161055\pi$
$384$	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	0.601562	+	0.798826i	$0.294545\pi$
$389$	−2720.97	+	8374.29i	−0.354650	+	1.09150i	−0.956212	+	0.292674i	$0.905455\pi$
$390$	−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	0.569417	−	0.822049i	$-0.307169\pi$
$401$	−292.606	−	212.591i	−0.0364390	−	0.0264745i	−0.605856	+	0.795575i	$0.707169\pi$
$402$	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	$-0.888188\pi$
$409$	−7459.54	+	5419.67i	−0.901835	+	0.655222i	0.0371015	+	0.999312i	$0.488188\pi$
$410$	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	−0.835656	−	0.549254i	$-0.814912\pi$
$421$	−4167.41	−	12826.0i	−0.482439	−	1.48480i	0.353217	−	0.935542i	$-0.385088\pi$
$422$	−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	$-0.707228\pi$
$431$	−328.731	+	238.837i	−0.0367388	+	0.0266923i	0.569264	+	0.822155i	$0.307228\pi$
$432$	−1776.41	−	5467.24i	−0.197842	−	0.608895i
$433$	−545.938	+	1680.23i	−0.0605915	+	0.186481i	−0.976771	−	0.214288i	$-0.931257\pi$
$433$	−545.938	+	1680.23i	−0.0605915	+	0.186481i	0.916179	+	0.400769i	$0.131257\pi$
$434$	−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	$-0.360163\pi$
$439$	7824.19			0.850634			0.425317	+	0.905044i	$0.360163\pi$
$440$		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	0.935243	+	0.354007i	$0.115181\pi$
$443$	3605.58	+	11096.8i	0.386695	+	1.19013i	−0.548548	+	0.836119i	$0.684819\pi$
$444$	−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	−0.456153	+	0.889901i	$0.650773\pi$
$449$	−13733.3	+	9977.80i	−1.44346	+	1.04873i	−0.987305	+	0.158833i	$0.949227\pi$
$450$	−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	0.999409	+	0.0343703i	$0.0109426\pi$
$457$	13100.3	+	9517.92i	1.34093	+	0.974244i	0.341523	+	0.939874i	$0.389057\pi$
$458$	−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	$-0.357200\pi$
$461$	8586.04			0.867444			0.433722	+	0.901047i	$0.357200\pi$
$462$		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	0.995666	−	0.0930047i	$-0.0296472\pi$
$467$	12260.6	+	8907.86i	1.21489	+	0.882670i	0.219225	+	0.975674i	$0.429647\pi$
$468$	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	$-0.458275\pi$
$479$	−8091.07	−	5878.51i	−0.771796	−	0.560743i	−0.902506	+	0.430678i	$0.858275\pi$
$480$	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	0.999805	+	0.0197497i	$0.00628694\pi$
$487$	2176.88	+	6699.76i	0.202554	+	0.623398i	−0.797251	+	0.603648i	$0.793713\pi$
$488$	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	0.562575	+	0.826746i	$0.309811\pi$
$491$	−4118.09	+	12674.2i	−0.378507	+	1.16492i	−0.941082	+	0.338178i	$0.890189\pi$
$492$	−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	0.135945	+	0.990716i	$0.456593\pi$
$499$	−6201.70	+	19086.9i	−0.556365	+	1.71232i	−0.692311	+	0.721600i	$0.743407\pi$
$500$	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	0.999278	+	0.0379939i	$0.0120967\pi$
$503$	2404.88	+	7401.45i	0.213177	+	0.656092i	−0.786101	+	0.618099i	$0.787903\pi$
$504$	−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	0.929232	−	0.369496i	$-0.120470\pi$
$509$	−456.088	−	1403.69i	−0.0397166	−	0.122235i	−0.968949	+	0.247261i	$0.920470\pi$
$510$	−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	−0.802201	−	0.597053i	$-0.796338\pi$
$521$	2351.44	−	7237.00i	0.197732	−	0.608558i	0.999934	−	0.0115042i	$-0.00366198\pi$
$522$	815.058	+	592.174i	0.0683412	+	0.0496528i
$523$	−10074.6	−	7319.63i	−0.842318	−	0.611980i	0.0806995	−	0.996738i	$-0.474285\pi$
$523$	−10074.6	−	7319.63i	−0.842318	−	0.611980i	−0.923017	+	0.384759i	$0.874285\pi$
$524$	−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	$-0.820649\pi$
$541$	−7533.70	+	5473.55i	−0.598704	+	0.434984i	0.246714	+	0.969088i	$0.420649\pi$
$542$	−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	−0.991426	−	0.130667i	$-0.958288\pi$
$547$	−3404.92	−	10479.3i	−0.266150	−	0.819124i	0.725277	−	0.688458i	$-0.241712\pi$
$548$	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	0.704613	+	0.709592i	$0.251121\pi$
$557$	−3713.90	+	11430.2i	−0.282519	+	0.869503i	−0.987131	+	0.159911i	$0.948879\pi$
$558$	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	$-0.593618\pi$
$563$	7090.13	−	5151.28i	0.530752	−	0.385614i	0.820639	+	0.571447i	$0.193618\pi$
$564$	−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	−0.997266	−	0.0738917i	$-0.976458\pi$
$569$	−3174.58	−	9770.35i	−0.233893	−	0.719850i	0.763373	−	0.645958i	$-0.223542\pi$
$570$	3065.91	−	2227.51i	0.225292	−	0.163684i
$571$	2602.62			0.190747			0.0953734	−	0.995442i	$-0.469596\pi$
$571$	2602.62			0.190747			0.0953734	+	0.995442i	$0.469596\pi$
$572$		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	0.988677	−	0.150061i	$-0.0479471\pi$
$577$	15959.5	+	11595.3i	1.15148	+	0.836598i	0.162801	+	0.986659i	$0.447947\pi$
$578$	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	0.778971	+	0.627060i	$0.215742\pi$
$587$	−3126.06	+	9621.03i	−0.219806	+	0.676495i	−0.998777	+	0.0494347i	$0.984258\pi$
$588$	−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	$-0.465431\pi$
$593$	3130.32			0.216774			0.108387	+	0.994109i	$0.465431\pi$
$594$		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	0.273825	−	0.961779i	$-0.411711\pi$
$599$	−8154.96	−	5924.92i	−0.556265	−	0.404150i	−0.830090	+	0.557629i	$0.811711\pi$
$600$	−2187.33	−	1589.19i	−0.148829	−	0.108130i
$601$	1476.18	−	4543.21i	0.100191	−	0.308355i	−0.888381	−	0.459107i	$-0.848169\pi$
$601$	1476.18	−	4543.21i	0.100191	−	0.308355i	0.988572	+	0.150752i	$0.0481694\pi$
$602$	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	$-0.672601\pi$
$607$	2080.27	−	1511.40i	0.139103	−	0.101064i	0.655160	+	0.755490i	$0.272601\pi$
$608$	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	0.993053	+	0.117671i	$0.0375429\pi$
$613$	3928.18	+	12089.7i	0.258822	+	0.796571i	−0.734231	+	0.678900i	$0.762457\pi$
$614$	−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	0.994030	+	0.109105i	$0.0347984\pi$
$619$	3911.32	+	12037.8i	0.253973	+	0.781649i	−0.740057	+	0.672544i	$0.765202\pi$
$620$	−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	−0.982149	−	0.188107i	$-0.939765\pi$
$631$	−1220.61	+	3756.64i	−0.0770073	+	0.237004i	0.905141	+	0.425111i	$0.139765\pi$
$632$	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	0.855585	−	0.517663i	$-0.173198\pi$
$641$	−2286.19	−	7036.17i	−0.140872	−	0.433560i	−0.996457	+	0.0841024i	$0.973198\pi$
$642$	649.311	−	1998.37i	0.0399163	−	0.122850i
$643$	10106.0	+	7342.43i	0.619815	+	0.450322i	0.852857	−	0.522145i	$-0.174868\pi$
$643$	10106.0	+	7342.43i	0.619815	+	0.450322i	−0.233042	+	0.972467i	$0.574868\pi$
$644$	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	−0.299848	−	0.953987i	$-0.596936\pi$
$647$	8472.01	−	6155.27i	0.514790	−	0.374017i	0.814638	+	0.579970i	$0.196936\pi$
$648$	−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	−0.875063	−	0.484009i	$-0.839180\pi$
$653$	1958.53	−	6027.73i	0.117371	−	0.361230i	0.992434	+	0.122778i	$0.0391804\pi$
$654$	−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	$-0.351726\pi$
$659$	15196.7			0.898302			0.449151	+	0.893456i	$0.351726\pi$
$660$		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	$-0.931312\pi$
$673$	−18768.9	+	13636.4i	−1.07502	+	0.781047i	−0.0982115	+	0.995166i	$0.531312\pi$
$674$	−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	$-0.280604\pi$
$677$	1735.65	+	1261.02i	0.0985322	+	0.0715879i	−0.537428	+	0.843309i	$0.680604\pi$
$678$	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	−0.997485	−	0.0708727i	$-0.977422\pi$
$691$	−22493.2	+	16342.2i	−1.23832	+	0.899693i	−0.240836	+	0.970566i	$0.577422\pi$
$692$	−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	−0.970086	−	0.242760i	$-0.921947\pi$
$701$	−6086.94	−	18733.7i	−0.327961	−	1.00936i	0.642125	−	0.766600i	$-0.278053\pi$
$702$	−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	0.0970906	−	0.995276i	$-0.469046\pi$
$709$	−15470.4	−	11239.9i	−0.819470	−	0.595380i	−0.916561	+	0.399896i	$0.869046\pi$
$710$	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	−0.935250	−	0.353987i	$-0.884826\pi$
$719$	567.801	−	1747.51i	0.0294512	−	0.0906414i	0.964702	+	0.263345i	$0.0848258\pi$
$720$	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	$-0.802362\pi$
$733$	3703.45	−	11398.1i	0.186617	−	0.574348i	0.999972	+	0.00741920i	$0.00236163\pi$
$734$	−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	$-0.463909\pi$
$739$	21958.7	−	15953.9i	1.09305	−	0.794148i	0.979912	+	0.199431i	$0.0639093\pi$
$740$	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	$-0.0434760\pi$
$743$	23641.6	+	17176.6i	1.16733	+	0.848115i	0.176644	+	0.984275i	$0.443476\pi$
$744$	−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	0.862254	−	0.506475i	$-0.169052\pi$
$751$	−2737.70	−	8425.78i	−0.133023	−	0.409402i	−0.995277	+	0.0970731i	$0.969052\pi$
$752$	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	−0.391957	+	0.919984i	$0.628202\pi$
$757$	−28909.7	+	21004.2i	−1.38803	+	1.00847i	−0.996078	+	0.0884828i	$0.971798\pi$
$758$	2064.19			0.0989112
$759$		0			0
$760$	9885.59			0.471826
$761$	−27825.9	+	20216.7i	−1.32548	+	0.963014i	−0.325629	+	0.945498i	$0.605576\pi$
$761$	−27825.9	+	20216.7i	−1.32548	+	0.963014i	−0.999847	+	0.0175169i	$0.994424\pi$
$762$	−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
$768$	−7766.50	+	5642.69i

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

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