LMFDB - Embedded newform 143.4.g.a.21.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [143,4,Mod(21,143)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(143, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1]))

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

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

chi := DirichletCharacter("143.21");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 143 = 11 \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	143.g (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.43727313082$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$40$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			21.11
Character	$\chi$	$=$	143.21
Dual form			143.4.g.a.109.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.06691 + 2.06691i) q^{2} +5.96848 q^{3} -0.544246i q^{4} +(12.2628 + 12.2628i) q^{5} +(-12.3363 + 12.3363i) q^{6} +(19.3939 + 19.3939i) q^{7} +(-15.4104 - 15.4104i) q^{8} +8.62277 q^{9} +O(q^{10})$	\(q+(-2.06691 + 2.06691i) q^{2} +5.96848 q^{3} -0.544246i q^{4} +(12.2628 + 12.2628i) q^{5} +(-12.3363 + 12.3363i) q^{6} +(19.3939 + 19.3939i) q^{7} +(-15.4104 - 15.4104i) q^{8} +8.62277 q^{9} -50.6922 q^{10} +(34.3555 - 12.2759i) q^{11} -3.24832i q^{12} +(-13.1465 - 44.9908i) q^{13} -80.1708 q^{14} +(73.1903 + 73.1903i) q^{15} +68.0578 q^{16} -25.5042 q^{17} +(-17.8225 + 17.8225i) q^{18} +(23.2393 - 23.2393i) q^{19} +(6.67398 - 6.67398i) q^{20} +(115.752 + 115.752i) q^{21} +(-45.6367 + 96.3830i) q^{22} -108.744i q^{23} +(-91.9766 - 91.9766i) q^{24} +175.753i q^{25} +(120.165 + 65.8193i) q^{26} -109.684 q^{27} +(10.5550 - 10.5550i) q^{28} +138.391i q^{29} -302.556 q^{30} +(-194.683 - 194.683i) q^{31} +(-17.3863 + 17.3863i) q^{32} +(205.050 - 73.2684i) q^{33} +(52.7148 - 52.7148i) q^{34} +475.646i q^{35} -4.69291i q^{36} +(-290.380 + 290.380i) q^{37} +96.0673i q^{38} +(-78.4647 - 268.527i) q^{39} -377.949i q^{40} +(17.7813 - 17.7813i) q^{41} -478.498 q^{42} +190.703 q^{43} +(-6.68110 - 18.6979i) q^{44} +(105.739 + 105.739i) q^{45} +(224.764 + 224.764i) q^{46} +(137.246 - 137.246i) q^{47} +406.202 q^{48} +409.244i q^{49} +(-363.265 - 363.265i) q^{50} -152.221 q^{51} +(-24.4860 + 7.15493i) q^{52} +237.523 q^{53} +(226.707 - 226.707i) q^{54} +(571.832 + 270.758i) q^{55} -597.734i q^{56} +(138.704 - 138.704i) q^{57} +(-286.042 - 286.042i) q^{58} +(225.726 - 225.726i) q^{59} +(39.8335 - 39.8335i) q^{60} -377.526i q^{61} +804.787 q^{62} +(167.229 + 167.229i) q^{63} +472.590i q^{64} +(390.500 - 712.926i) q^{65} +(-272.382 + 575.260i) q^{66} +(-255.027 - 255.027i) q^{67} +13.8805i q^{68} -649.036i q^{69} +(-983.119 - 983.119i) q^{70} +(-9.58861 - 9.58861i) q^{71} +(-132.880 - 132.880i) q^{72} +(-514.810 - 514.810i) q^{73} -1200.38i q^{74} +1048.98i q^{75} +(-12.6479 - 12.6479i) q^{76} +(904.364 + 428.210i) q^{77} +(717.200 + 392.841i) q^{78} +769.644i q^{79} +(834.579 + 834.579i) q^{80} -887.463 q^{81} +73.5047i q^{82} +(983.204 - 983.204i) q^{83} +(62.9975 - 62.9975i) q^{84} +(-312.752 - 312.752i) q^{85} +(-394.166 + 394.166i) q^{86} +825.985i q^{87} +(-718.608 - 340.256i) q^{88} +(280.040 - 280.040i) q^{89} -437.108 q^{90} +(617.584 - 1127.51i) q^{91} -59.1834 q^{92} +(-1161.96 - 1161.96i) q^{93} +567.352i q^{94} +569.959 q^{95} +(-103.770 + 103.770i) q^{96} +(204.800 + 204.800i) q^{97} +(-845.872 - 845.872i) q^{98} +(296.240 - 105.852i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 8 q^{3} - 4 q^{5} + 640 q^{9}+O(q^{10}) $ 80 * q - 8 * q^3 - 4 * q^5 + 640 * q^9	$ 80 q - 8 q^{3} - 4 q^{5} + 640 q^{9} + 14 q^{11} + 280 q^{14} - 80 q^{15} - 952 q^{16} - 200 q^{20} - 424 q^{22} - 508 q^{26} - 848 q^{27} + 208 q^{31} + 860 q^{33} - 232 q^{34} - 340 q^{37} + 1308 q^{42} - 644 q^{44} - 1148 q^{45} - 280 q^{47} + 2420 q^{48} + 2976 q^{53} + 1652 q^{55} - 1972 q^{58} - 84 q^{59} + 1484 q^{60} - 4924 q^{66} + 2468 q^{67} - 3540 q^{70} + 1704 q^{71} + 2368 q^{78} - 3544 q^{80} + 6160 q^{81} + 32 q^{86} + 424 q^{89} - 5868 q^{91} - 164 q^{92} + 3944 q^{93} - 4936 q^{97} - 3750 q^{99}+O(q^{100}) $ 80 * q - 8 * q^3 - 4 * q^5 + 640 * q^9 + 14 * q^11 + 280 * q^14 - 80 * q^15 - 952 * q^16 - 200 * q^20 - 424 * q^22 - 508 * q^26 - 848 * q^27 + 208 * q^31 + 860 * q^33 - 232 * q^34 - 340 * q^37 + 1308 * q^42 - 644 * q^44 - 1148 * q^45 - 280 * q^47 + 2420 * q^48 + 2976 * q^53 + 1652 * q^55 - 1972 * q^58 - 84 * q^59 + 1484 * q^60 - 4924 * q^66 + 2468 * q^67 - 3540 * q^70 + 1704 * q^71 + 2368 * q^78 - 3544 * q^80 + 6160 * q^81 + 32 * q^86 + 424 * q^89 - 5868 * q^91 - 164 * q^92 + 3944 * q^93 - 4936 * q^97 - 3750 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/143\mathbb{Z}\right)^\times$.

$n$	$67$	$79$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$

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 $

$2$	−2.06691	+	2.06691i	−0.730764	+	0.730764i	−0.970771	−	0.240007i	$-0.922850\pi$
$2$	−2.06691	+	2.06691i	−0.730764	+	0.730764i	0.240007	+	0.970771i	$0.422850\pi$
$3$	5.96848			1.14863			0.574317	−	0.818633i	$-0.305268\pi$
$3$	5.96848			1.14863			0.574317	+	0.818633i	$0.305268\pi$
$4$		−	0.544246i		−	0.0680307i
$5$	12.2628	+	12.2628i	1.09682	+	1.09682i	0.994781	+	0.102038i	$0.0325362\pi$
$5$	12.2628	+	12.2628i	1.09682	+	1.09682i	0.102038	+	0.994781i	$0.467464\pi$
$6$	−12.3363	+	12.3363i	−0.839380	+	0.839380i
$7$	19.3939	+	19.3939i	1.04717	+	1.04717i	0.998831	+	0.0483395i	$0.0153929\pi$
$7$	19.3939	+	19.3939i	1.04717	+	1.04717i	0.0483395	+	0.998831i	$0.484607\pi$
$8$	−15.4104	−	15.4104i	−0.681049	−	0.681049i
$9$	8.62277			0.319362
$10$	−50.6922			−1.60303
$11$	34.3555	−	12.2759i	0.941689	−	0.336484i
$11$	34.3555	−	12.2759i	0.941689	−	0.336484i
$12$		−	3.24832i		−	0.0781425i
$13$	−13.1465	−	44.9908i	−0.280476	−	0.959861i
$13$	−13.1465	−	44.9908i	−0.280476	−	0.959861i
$14$	−80.1708			−1.53047
$15$	73.1903	+	73.1903i	1.25984	+	1.25984i
$16$	68.0578			1.06340
$17$	−25.5042			−0.363863			−0.181931	−	0.983311i	$-0.558235\pi$
$17$	−25.5042			−0.363863			−0.181931	+	0.983311i	$0.558235\pi$
$18$	−17.8225	+	17.8225i	−0.233378	+	0.233378i
$19$	23.2393	−	23.2393i	0.280604	−	0.280604i	−0.552746	−	0.833350i	$-0.686420\pi$
$19$	23.2393	−	23.2393i	0.280604	−	0.280604i	0.833350	+	0.552746i	$0.186420\pi$
$20$	6.67398	−	6.67398i	0.0746174	−	0.0746174i
$21$	115.752	+	115.752i	1.20282	+	1.20282i
$22$	−45.6367	+	96.3830i	−0.442262	+	0.934042i
$23$		−	108.744i		−	0.985855i	−0.870070	−	0.492928i	$-0.835927\pi$
$23$		−	108.744i		−	0.985855i	0.870070	−	0.492928i	$-0.164073\pi$
$24$	−91.9766	−	91.9766i	−0.782277	−	0.782277i
$25$			175.753i			1.40602i
$26$	120.165	+	65.8193i	0.906393	+	0.496470i
$27$	−109.684			−0.781805
$28$	10.5550	−	10.5550i	0.0712398	−	0.0712398i
$29$			138.391i			0.886158i	0.896482	+	0.443079i	$0.146114\pi$
$29$			138.391i			0.886158i	−0.896482	+	0.443079i	$0.853886\pi$
$30$	−302.556			−1.84130
$31$	−194.683	−	194.683i	−1.12794	−	1.12794i	−0.990512	−	0.137429i	$-0.956116\pi$
$31$	−194.683	−	194.683i	−1.12794	−	1.12794i	−0.137429	−	0.990512i	$-0.543884\pi$
$32$	−17.3863	+	17.3863i	−0.0960467	+	0.0960467i
$33$	205.050	−	73.2684i	1.08166	−	0.386497i
$34$	52.7148	−	52.7148i	0.265898	−	0.265898i
$35$			475.646i			2.29711i
$36$		−	4.69291i		−	0.0217264i
$37$	−290.380	+	290.380i	−1.29022	+	1.29022i	−0.355572	+	0.934649i	$0.615714\pi$
$37$	−290.380	+	290.380i	−1.29022	+	1.29022i	−0.934649	+	0.355572i	$0.884286\pi$
$38$			96.0673i			0.410110i
$39$	−78.4647	−	268.527i	−0.322164	−	1.10253i
$40$		−	377.949i		−	1.49397i
$41$	17.7813	−	17.7813i	0.0677310	−	0.0677310i	−0.672430	−	0.740161i	$-0.734749\pi$
$41$	17.7813	−	17.7813i	0.0677310	−	0.0677310i	0.740161	+	0.672430i	$0.234749\pi$
$42$	−478.498			−1.75795
$43$	190.703			0.676324			0.338162	−	0.941088i	$-0.390195\pi$
$43$	190.703			0.676324			0.338162	+	0.941088i	$0.390195\pi$
$44$	−6.68110	−	18.6979i	−0.0228912	−	0.0640638i
$45$	105.739	+	105.739i	0.350282	+	0.350282i
$46$	224.764	+	224.764i	0.720427	+	0.720427i
$47$	137.246	−	137.246i	0.425945	−	0.425945i	−0.461299	−	0.887245i	$-0.652617\pi$
$47$	137.246	−	137.246i	0.425945	−	0.425945i	0.887245	+	0.461299i	$0.152617\pi$
$48$	406.202			1.22146
$49$			409.244i			1.19313i
$50$	−363.265	−	363.265i	−1.02747	−	1.02747i
$51$	−152.221			−0.417945
$52$	−24.4860	+	7.15493i	−0.0653001	+	0.0190810i
$53$	237.523			0.615591			0.307795	−	0.951453i	$-0.400409\pi$
$53$	237.523			0.615591			0.307795	+	0.951453i	$0.400409\pi$
$54$	226.707	−	226.707i	0.571314	−	0.571314i
$55$	571.832	+	270.758i	1.40192	+	0.663801i
$56$		−	597.734i		−	1.42635i
$57$	138.704	−	138.704i	0.322311	−	0.322311i
$58$	−286.042	−	286.042i	−0.647572	−	0.647572i
$59$	225.726	−	225.726i	0.498085	−	0.498085i	−0.412756	−	0.910842i	$-0.635434\pi$
$59$	225.726	−	225.726i	0.498085	−	0.498085i	0.910842	+	0.412756i	$0.135434\pi$
$60$	39.8335	−	39.8335i	0.0857081	−	0.0857081i
$61$		−	377.526i		−	0.792414i	−0.918161	−	0.396207i	$-0.870326\pi$
$61$		−	377.526i		−	0.792414i	0.918161	−	0.396207i	$-0.129674\pi$
$62$	804.787			1.64852
$63$	167.229	+	167.229i	0.334426	+	0.334426i
$64$			472.590i			0.923028i
$65$	390.500	−	712.926i	0.745162	−	1.36042i
$66$	−272.382	+	575.260i	−0.507998	+	1.07287i
$67$	−255.027	−	255.027i	−0.465022	−	0.465022i	0.435276	−	0.900297i	$-0.356651\pi$
$67$	−255.027	−	255.027i	−0.465022	−	0.465022i	−0.900297	+	0.435276i	$0.856651\pi$
$68$			13.8805i			0.0247539i
$69$		−	649.036i		−	1.13239i
$70$	−983.119	−	983.119i	−1.67865	−	1.67865i
$71$	−9.58861	−	9.58861i	−0.0160276	−	0.0160276i	0.699048	−	0.715075i	$-0.253608\pi$
$71$	−9.58861	−	9.58861i	−0.0160276	−	0.0160276i	−0.715075	+	0.699048i	$0.753608\pi$
$72$	−132.880	−	132.880i	−0.217501	−	0.217501i
$73$	−514.810	−	514.810i	−0.825396	−	0.825396i	0.161480	−	0.986876i	$-0.448373\pi$
$73$	−514.810	−	514.810i	−0.825396	−	0.825396i	−0.986876	+	0.161480i	$0.948373\pi$
$74$		−	1200.38i		−	1.88569i
$75$			1048.98i			1.61500i
$76$	−12.6479	−	12.6479i	−0.0190897	−	0.0190897i
$77$	904.364	+	428.210i	1.33846	+	0.633754i
$78$	717.200	+	392.841i	1.04111	+	0.570263i
$79$			769.644i			1.09610i	0.836446	+	0.548049i	$0.184629\pi$
$79$			769.644i			1.09610i	−0.836446	+	0.548049i	$0.815371\pi$
$80$	834.579	+	834.579i	1.16636	+	1.16636i
$81$	−887.463			−1.21737
$82$			73.5047i			0.0989907i
$83$	983.204	−	983.204i	1.30025	−	1.30025i	0.372027	−	0.928222i	$-0.378663\pi$
$83$	983.204	−	983.204i	1.30025	−	1.30025i	0.928222	−	0.372027i	$-0.121337\pi$
$84$	62.9975	−	62.9975i	0.0818285	−	0.0818285i
$85$	−312.752	−	312.752i	−0.399091	−	0.399091i
$86$	−394.166	+	394.166i	−0.494233	+	0.494233i
$87$			825.985i			1.01787i
$88$	−718.608	−	340.256i	−0.870499	−	0.412175i
$89$	280.040	−	280.040i	0.333531	−	0.333531i	−0.520395	−	0.853926i	$-0.674215\pi$
$89$	280.040	−	280.040i	0.333531	−	0.333531i	0.853926	+	0.520395i	$0.174215\pi$
$90$	−437.108			−0.511947
$91$	617.584	−	1127.51i	0.711432	−	1.29884i
$92$	−59.1834			−0.0670685
$93$	−1161.96	−	1161.96i	−1.29559	−	1.29559i
$94$			567.352i			0.622531i
$95$	569.959			0.615543
$96$	−103.770	+	103.770i	−0.110323	+	0.110323i
$97$	204.800	+	204.800i	0.214375	+	0.214375i	0.806123	−	0.591748i	$-0.201562\pi$
$97$	204.800	+	204.800i	0.214375	+	0.214375i	−0.591748	+	0.806123i	$0.701562\pi$
$98$	−845.872	−	845.872i	−0.871897	−	0.871897i
$99$	296.240	−	105.852i	0.300740	−	0.107460i
$100$	95.6526			0.0956526
$101$	−1118.12			−1.10156			−0.550780	−	0.834650i	$-0.685670\pi$
$101$	−1118.12			−1.10156			−0.550780	+	0.834650i	$0.685670\pi$
$102$	314.627	−	314.627i	0.305419	−	0.305419i
$103$			1416.53i			1.35509i	0.735481	+	0.677546i	$0.236956\pi$
$103$			1416.53i			1.35509i	−0.735481	+	0.677546i	$0.763044\pi$
$104$	−490.732	+	895.918i	−0.462695	+	0.844730i
$105$			2838.89i			2.63854i
$106$	−490.939	+	490.939i	−0.449851	+	0.449851i
$107$			742.346i			0.670704i	0.942093	+	0.335352i	$0.108855\pi$
$107$			742.346i			0.670704i	−0.942093	+	0.335352i	$0.891145\pi$
$108$			59.6952i			0.0531868i
$109$	−1103.39	+	1103.39i	−0.969590	+	0.969590i	−0.999551	−	0.0299607i	$-0.990462\pi$
$109$	−1103.39	+	1103.39i	−0.969590	+	0.969590i	0.0299607	+	0.999551i	$0.490462\pi$
$110$	−1741.56	+	622.292i	−1.50956	+	0.539393i
$111$	−1733.13	+	1733.13i	−1.48199	+	1.48199i
$112$	1319.90	+	1319.90i	1.11356	+	1.11356i
$113$	1134.65			0.944591			0.472295	−	0.881440i	$-0.343426\pi$
$113$	1134.65			0.944591			0.472295	+	0.881440i	$0.343426\pi$
$114$			573.376i			0.471067i
$115$	1333.50	−	1333.50i	1.08130	−	1.08130i
$116$	75.3188			0.0602860
$117$	−113.359	−	387.945i	−0.0895732	−	0.306543i
$118$			933.112i			0.727965i
$119$	−494.624	−	494.624i	−0.381026	−	0.381026i
$120$		−	2255.78i		−	1.71603i
$121$	1029.61	−	843.489i	0.773558	−	0.633726i
$122$	780.313	+	780.313i	0.579067	+	0.579067i
$123$	106.127	−	106.127i	0.0777982	−	0.0777982i
$124$	−105.956	+	105.956i	−0.0767347	+	0.0767347i
$125$	−622.369	+	622.369i	−0.445331	+	0.445331i
$126$	−691.295			−0.488773
$127$	−1476.39			−1.03156			−0.515781	−	0.856720i	$-0.672498\pi$
$127$	−1476.39			−1.03156			−0.515781	+	0.856720i	$0.672498\pi$
$128$	−1115.89	−	1115.89i	−0.770562	−	0.770562i
$129$	1138.21			0.776849
$130$	666.426	+	2280.68i	0.449611	+	1.53869i
$131$		−	1794.10i		−	1.19657i	−0.801282	−	0.598287i	$-0.795848\pi$
$131$		−	1794.10i		−	1.19657i	0.801282	−	0.598287i	$-0.204152\pi$
$132$	−39.8760	−	111.598i	−0.0262937	−	0.0735859i
$133$	901.401			0.587680
$134$	1054.23			0.679642
$135$	−1345.03	−	1345.03i	−0.857498	−	0.857498i
$136$	393.029	+	393.029i	0.247808	+	0.247808i
$137$	875.356	−	875.356i	0.545888	−	0.545888i	−0.379361	−	0.925249i	$-0.623856\pi$
$137$	875.356	−	875.356i	0.545888	−	0.545888i	0.925249	+	0.379361i	$0.123856\pi$
$138$	1341.50	+	1341.50i	0.827508	+	0.827508i
$139$		−	2050.48i		−	1.25122i	−0.780136	−	0.625610i	$-0.784850\pi$
$139$		−	2050.48i		−	1.25122i	0.780136	−	0.625610i	$-0.215150\pi$
$140$	258.869			0.156274
$141$	819.152	−	819.152i	0.489256	−	0.489256i
$142$	39.6376			0.0234248
$143$	−1003.96	−	1384.30i	−0.587099	−	0.809516i
$144$	586.847			0.339610
$145$	−1697.06	+	1697.06i	−0.971955	+	0.971955i
$146$	2128.13			1.20634
$147$			2442.57i			1.37047i
$148$	158.038	+	158.038i	0.0877747	+	0.0877747i
$149$	−69.8526	+	69.8526i	−0.0384063	+	0.0384063i	−0.726049	−	0.687643i	$-0.758646\pi$
$149$	−69.8526	+	69.8526i	−0.0384063	+	0.0384063i	0.687643	+	0.726049i	$0.258646\pi$
$150$	−2168.14	−	2168.14i	−1.18019	−	1.18019i
$151$	1664.74	+	1664.74i	0.897184	+	0.897184i	0.995186	−	0.0980019i	$-0.0312451\pi$
$151$	1664.74	+	1664.74i	0.897184	+	0.897184i	−0.0980019	+	0.995186i	$0.531245\pi$
$152$	−716.254			−0.382210
$153$	−219.916			−0.116204
$154$	−2754.31	+	984.168i	−1.44123	+	0.514977i
$155$		−	4774.73i		−	2.47429i
$156$	−146.145	+	42.7041i	−0.0750059	+	0.0219171i
$157$	1756.50			0.892892			0.446446	−	0.894811i	$-0.352690\pi$
$157$	1756.50			0.892892			0.446446	+	0.894811i	$0.352690\pi$
$158$	−1590.79	−	1590.79i	−0.800989	−	0.800989i
$159$	1417.65			0.707089
$160$	−426.410			−0.210691
$161$	2108.97	−	2108.97i	1.03236	−	1.03236i
$162$	1834.31	−	1834.31i	0.889610	−	0.889610i
$163$	−753.894	+	753.894i	−0.362267	+	0.362267i	−0.864647	−	0.502380i	$-0.832458\pi$
$163$	−753.894	+	753.894i	−0.362267	+	0.362267i	0.502380	+	0.864647i	$0.332458\pi$
$164$	−9.67740	−	9.67740i	−0.00460779	−	0.00460779i
$165$	3412.97	+	1616.02i	1.61030	+	0.762465i
$166$			4064.39i			1.90035i
$167$	1527.41	+	1527.41i	0.707751	+	0.707751i	0.966062	−	0.258311i	$-0.0831658\pi$
$167$	1527.41	+	1527.41i	0.707751	+	0.707751i	−0.258311	+	0.966062i	$0.583166\pi$
$168$		−	3567.56i		−	1.63835i
$169$	−1851.34	+	1182.94i	−0.842667	+	0.538435i
$170$	1292.86			0.583283
$171$	200.388	−	200.388i	0.0896141	−	0.0896141i
$172$		−	103.789i		−	0.0460108i
$173$	−2102.49			−0.923986			−0.461993	−	0.886884i	$-0.652865\pi$
$173$	−2102.49			−0.923986			−0.461993	+	0.886884i	$0.652865\pi$
$174$	−1707.24	−	1707.24i	−0.743824	−	0.743824i
$175$	−3408.52	+	3408.52i	−1.47234	+	1.47234i
$176$	2338.16	−	835.470i	1.00139	−	0.357818i
$177$	1347.24	−	1347.24i	0.572118	−	0.572118i
$178$			1157.64i			0.487464i
$179$			4277.34i			1.78605i	0.450007	+	0.893025i	$0.351422\pi$
$179$			4277.34i			1.78605i	−0.450007	+	0.893025i	$0.648578\pi$
$180$	57.5482	−	57.5482i	0.0238299	−	0.0238299i
$181$			1466.58i			0.602267i	0.953582	+	0.301134i	$0.0973650\pi$
$181$			1466.58i			0.602267i	−0.953582	+	0.301134i	$0.902635\pi$
$182$	1053.97	+	3606.95i	0.429259	+	1.46904i
$183$		−	2253.26i		−	0.910194i
$184$	−1675.79	+	1675.79i	−0.671416	+	0.671416i
$185$	−7121.74			−2.83028
$186$	4803.35			1.89354
$187$	−876.209	+	313.086i	−0.342646	+	0.122434i
$188$	−74.6957	−	74.6957i	−0.0289774	−	0.0289774i
$189$	−2127.20	−	2127.20i	−0.818683	−	0.818683i
$190$	−1178.05	+	1178.05i	−0.449816	+	0.449816i
$191$	3006.82			1.13909			0.569543	−	0.821961i	$-0.307120\pi$
$191$	3006.82			1.13909			0.569543	+	0.821961i	$0.307120\pi$
$192$			2820.65i			1.06022i
$193$	2381.08	+	2381.08i	0.888051	+	0.888051i	0.994336	−	0.106284i	$-0.0338954\pi$
$193$	2381.08	+	2381.08i	0.888051	+	0.888051i	−0.106284	+	0.994336i	$0.533895\pi$
$194$	−846.608			−0.313314
$195$	2330.69	−	4255.08i	0.855919	−	1.56263i
$196$	222.730			0.0811697
$197$	828.404	−	828.404i	0.299601	−	0.299601i	−0.541257	−	0.840857i	$-0.682051\pi$
$197$	828.404	−	828.404i	0.299601	−	0.299601i	0.840857	+	0.541257i	$0.182051\pi$
$198$	−393.515	+	831.089i	−0.141242	+	0.298297i
$199$			777.035i			0.276797i	0.990377	+	0.138398i	$0.0441955\pi$
$199$			777.035i			0.276797i	−0.990377	+	0.138398i	$0.955805\pi$
$200$	2708.41	−	2708.41i	0.957569	−	0.957569i
$201$	−1522.12	−	1522.12i	−0.534140	−	0.534140i
$202$	2311.06	−	2311.06i	0.804980	−	0.804980i
$203$	−2683.94	+	2683.94i	−0.927959	+	0.927959i
$204$			82.8457i			0.0284331i
$205$	436.097			0.148577
$206$	−2927.83	−	2927.83i	−0.990251	−	0.990251i
$207$		−	937.674i		−	0.314845i
$208$	−894.722	−	3061.97i	−0.298259	−	1.02072i
$209$	513.116	−	1083.68i	0.169823	−	0.358660i
$210$	−5867.73	−	5867.73i	−1.92815	−	1.92815i
$211$			2563.75i			0.836473i	0.908338	+	0.418236i	$0.137352\pi$
$211$			2563.75i			0.836473i	−0.908338	+	0.418236i	$0.862648\pi$
$212$		−	129.271i		−	0.0418791i
$213$	−57.2295	−	57.2295i	−0.0184099	−	0.0184099i
$214$	−1534.36	−	1534.36i	−0.490126	−	0.490126i
$215$	2338.55	+	2338.55i	0.741805	+	0.741805i
$216$	1690.27	+	1690.27i	0.532447	+	0.532447i
$217$		−	7551.33i		−	2.36229i
$218$		−	4561.21i		−	1.41708i
$219$	−3072.63	−	3072.63i	−0.948079	−	0.948079i
$220$	147.359	−	311.217i	0.0451589	−	0.0953739i
$221$	335.290	+	1147.45i	0.102055	+	0.349258i
$222$		−	7164.44i		−	2.16597i
$223$	−3951.40	−	3951.40i	−1.18657	−	1.18657i	−0.978009	−	0.208562i	$-0.933122\pi$
$223$	−3951.40	−	3951.40i	−1.18657	−	1.18657i	−0.208562	−	0.978009i	$-0.566878\pi$
$224$	−674.375			−0.201154
$225$			1515.47i			0.449029i
$226$	−2345.22	+	2345.22i	−0.690273	+	0.690273i
$227$	−877.486	+	877.486i	−0.256567	+	0.256567i	−0.823656	−	0.567089i	$-0.808069\pi$
$227$	−877.486	+	877.486i	−0.256567	+	0.256567i	0.567089	+	0.823656i	$0.308069\pi$
$228$	−75.4889	−	75.4889i	−0.0219271	−	0.0219271i
$229$	1416.04	−	1416.04i	0.408622	−	0.408622i	−0.472636	−	0.881258i	$-0.656697\pi$
$229$	1416.04	−	1416.04i	0.408622	−	0.408622i	0.881258	+	0.472636i	$0.156697\pi$
$230$			5512.47i			1.58036i
$231$	5397.68	+	2555.76i	1.53741	+	0.727951i
$232$	2132.66	−	2132.66i	0.603517	−	0.603517i
$233$	−129.158			−0.0363150			−0.0181575	−	0.999835i	$-0.505780\pi$
$233$	−129.158			−0.0363150			−0.0181575	+	0.999835i	$0.505780\pi$
$234$	1036.15	+	567.545i	0.289467	+	0.158554i
$235$	3366.05			0.934369
$236$	−122.851	−	122.851i	−0.0338851	−	0.0338851i
$237$			4593.61i			1.25902i
$238$	2044.69			0.556880
$239$	3167.55	−	3167.55i	0.857289	−	0.857289i	−0.133729	−	0.991018i	$-0.542695\pi$
$239$	3167.55	−	3167.55i	0.857289	−	0.857289i	0.991018	+	0.133729i	$0.0426952\pi$
$240$	4981.17	+	4981.17i	1.33972	+	1.33972i
$241$	2413.00	+	2413.00i	0.644958	+	0.644958i	0.951770	−	0.306812i	$-0.0992623\pi$
$241$	2413.00	+	2413.00i	0.644958	+	0.644958i	−0.306812	+	0.951770i	$0.599262\pi$
$242$	−384.685	+	3871.52i	−0.102184	+	1.02839i
$243$	−2335.33			−0.616509
$244$	−205.467			−0.0539085
$245$	−5018.48	+	5018.48i	−1.30865	+	1.30865i
$246$			438.712i			0.113704i
$247$	−1351.07	−	740.040i	−0.348043	−	0.190638i
$248$			6000.29i			1.53637i
$249$	5868.24	−	5868.24i	1.49351	−	1.49351i
$250$		−	2572.76i		−	0.650863i
$251$			6493.55i			1.63294i	0.577385	+	0.816472i	$0.304073\pi$
$251$			6493.55i			1.63294i	−0.577385	+	0.816472i	$0.695927\pi$
$252$	91.0137	−	91.0137i	0.0227513	−	0.0227513i
$253$	−1334.93	−	3735.95i	−0.331724	−	0.928369i
$254$	3051.57	−	3051.57i	0.753828	−	0.753828i
$255$	−1866.66	−	1866.66i	−0.458410	−	0.458410i
$256$	832.181			0.203169
$257$		−	3581.02i		−	0.869175i	−0.900630	−	0.434587i	$-0.856894\pi$
$257$		−	3581.02i		−	0.869175i	0.900630	−	0.434587i	$-0.143106\pi$
$258$	−2352.57	+	2352.57i	−0.567693	+	0.567693i
$259$	−11263.2			−2.70216
$260$	−388.007	−	212.528i	−0.0925507	−	0.0506940i
$261$			1193.32i			0.283005i
$262$	3708.25	+	3708.25i	0.874413	+	0.874413i
$263$			6276.67i			1.47162i	0.677188	+	0.735810i	$0.263198\pi$
$263$			6276.67i			1.47162i	−0.677188	+	0.735810i	$0.736802\pi$
$264$	−4289.00	−	2030.81i	−0.999885	−	0.473438i
$265$	2912.70	+	2912.70i	0.675191	+	0.675191i
$266$	−1863.12	+	1863.12i	−0.429455	+	0.429455i
$267$	1671.42	−	1671.42i	0.383105	−	0.383105i
$268$	−138.797	+	138.797i	−0.0316358	+	0.0316358i
$269$	288.929			0.0654882			0.0327441	−	0.999464i	$-0.489575\pi$
$269$	288.929			0.0654882			0.0327441	+	0.999464i	$0.489575\pi$
$270$	5560.14			1.25326
$271$	−3241.63	−	3241.63i	−0.726623	−	0.726623i	0.243322	−	0.969945i	$-0.421763\pi$
$271$	−3241.63	−	3241.63i	−0.726623	−	0.726623i	−0.969945	+	0.243322i	$0.921763\pi$
$272$	−1735.76			−0.386933
$273$	3686.04	−	6729.50i	0.817176	−	1.49190i
$274$			3618.57i			0.797830i
$275$	2157.52	+	6038.07i	0.473103	+	1.32403i
$276$	−353.235			−0.0770372
$277$	20.5845			0.00446499			0.00223250	−	0.999998i	$-0.499289\pi$
$277$	20.5845			0.00446499			0.00223250	+	0.999998i	$0.499289\pi$
$278$	4238.17	+	4238.17i	0.914346	+	0.914346i
$279$	−1678.71	−	1678.71i	−0.360221	−	0.360221i
$280$	7329.89	−	7329.89i	1.56445	−	1.56445i
$281$	−799.146	−	799.146i	−0.169655	−	0.169655i	0.617173	−	0.786828i	$-0.288278\pi$
$281$	−799.146	−	799.146i	−0.169655	−	0.169655i	−0.786828	+	0.617173i	$0.788278\pi$
$282$			3386.23i			0.715060i
$283$	−8881.16			−1.86548			−0.932739	−	0.360551i	$-0.882589\pi$
$283$	−8881.16			−1.86548			−0.932739	+	0.360551i	$0.882589\pi$
$284$	−5.21856	+	5.21856i	−0.00109037	+	0.00109037i
$285$	3401.79			0.707034
$286$	4936.31	+	786.129i	1.02059	+	0.162534i
$287$	689.696			0.141852
$288$	−149.918	+	149.918i	−0.0306736	+	0.0306736i
$289$	−4262.54			−0.867604
$290$		−	7015.36i		−	1.42054i
$291$	1222.35	+	1222.35i	0.246238	+	0.246238i
$292$	−280.183	+	280.183i	−0.0561523	+	0.0561523i
$293$	−5928.87	−	5928.87i	−1.18214	−	1.18214i	−0.979188	−	0.202956i	$-0.934945\pi$
$293$	−5928.87	−	5928.87i	−1.18214	−	1.18214i	−0.202956	−	0.979188i	$-0.565055\pi$
$294$	−5048.57	−	5048.57i	−1.00149	−	1.00149i
$295$	5536.07			1.09262
$296$	8949.73			1.75741
$297$	−3768.26	+	1346.47i	−0.736217	+	0.263064i
$298$		−	288.758i		−	0.0561319i
$299$	−4892.47	+	1429.60i	−0.946284	+	0.276508i
$300$	570.901			0.109870
$301$	3698.47	+	3698.47i	0.708227	+	0.708227i
$302$	−6881.75			−1.31126
$303$	−6673.51			−1.26529
$304$	1581.62	−	1581.62i	0.298395	−	0.298395i
$305$	4629.53	−	4629.53i	0.869134	−	0.869134i
$306$	454.548	−	454.548i	0.0849176	−	0.0849176i
$307$	−4984.31	−	4984.31i	−0.926611	−	0.926611i	0.0708741	−	0.997485i	$-0.477421\pi$
$307$	−4984.31	−	4984.31i	−0.926611	−	0.926611i	−0.997485	+	0.0708741i	$0.977421\pi$
$308$	233.051	−	492.196i	0.0431147	−	0.0910568i
$309$			8454.51i			1.55651i
$310$	9868.94	+	9868.94i	1.80812	+	1.80812i
$311$			1680.74i			0.306451i	0.988191	+	0.153225i	$0.0489660\pi$
$311$			1680.74i			0.306451i	−0.988191	+	0.153225i	$0.951034\pi$
$312$	−2928.93	+	5347.27i	−0.531467	+	0.970287i
$313$	573.659			0.103595			0.0517973	−	0.998658i	$-0.483505\pi$
$313$	573.659			0.103595			0.0517973	+	0.998658i	$0.483505\pi$
$314$	−3630.53	+	3630.53i	−0.652493	+	0.652493i
$315$			4101.39i			0.733610i
$316$	418.876			0.0745684
$317$	−3617.50	−	3617.50i	−0.640944	−	0.640944i	0.309844	−	0.950788i	$-0.399723\pi$
$317$	−3617.50	−	3617.50i	−0.640944	−	0.640944i	−0.950788	+	0.309844i	$0.899723\pi$
$318$	−2930.16	+	2930.16i	−0.516715	+	0.516715i
$319$	1698.87	+	4754.50i	0.298178	+	0.834486i
$320$	−5795.28	+	5795.28i	−1.01239	+	1.01239i
$321$			4430.68i			0.770394i
$322$			8718.09i			1.50882i
$323$	−592.700	+	592.700i	−0.102101	+	0.102101i
$324$			482.998i			0.0828186i
$325$	7907.24	−	2310.53i	1.34958	−	0.394355i
$326$		−	3116.47i		−	0.529463i
$327$	−6585.55	+	6585.55i	−1.11371	+	1.11371i
$328$	−548.033			−0.0922563
$329$	5323.47			0.892075
$330$	−10394.5	+	3714.14i	−1.73393	+	0.619566i
$331$	4329.22	+	4329.22i	0.718899	+	0.718899i	0.968380	−	0.249481i	$-0.0802599\pi$
$331$	4329.22	+	4329.22i	0.718899	+	0.718899i	−0.249481	+	0.968380i	$0.580260\pi$
$332$	−535.105	−	535.105i	−0.0884569	−	0.0884569i
$333$	−2503.88	+	2503.88i	−0.412047	+	0.412047i
$334$	−6314.04			−1.03440
$335$		−	6254.68i		−	1.02009i
$336$	7877.82	+	7877.82i	1.27908	+	1.27908i
$337$	−9396.94			−1.51894			−0.759471	−	0.650541i	$-0.774542\pi$
$337$	−9396.94			−1.51894			−0.759471	+	0.650541i	$0.774542\pi$
$338$	1381.52	−	6271.59i	0.222321	−	1.00926i
$339$	6772.13			1.08499
$340$	−170.214	+	170.214i	−0.0271505	+	0.0271505i
$341$	−9078.36	−	4298.54i	−1.44170	−	0.682636i
$342$			828.366i			0.130973i
$343$	−1284.73	+	1284.73i	−0.202242	+	0.202242i
$344$	−2938.81	−	2938.81i	−0.460610	−	0.460610i
$345$	7959.00	−	7959.00i	1.24202	−	1.24202i
$346$	4345.67	−	4345.67i	0.675215	−	0.675215i
$347$		−	4834.74i		−	0.747960i	−0.927437	−	0.373980i	$-0.877993\pi$
$347$		−	4834.74i		−	0.747960i	0.927437	−	0.373980i	$-0.122007\pi$
$348$	449.539			0.0692466
$349$	7047.76	+	7047.76i	1.08097	+	1.08097i	0.996419	+	0.0845495i	$0.0269451\pi$
$349$	7047.76	+	7047.76i	1.08097	+	1.08097i	0.0845495	+	0.996419i	$0.473055\pi$
$350$		−	14090.2i		−	2.15187i
$351$	1441.96	+	4934.77i	0.219277	+	0.750424i
$352$	−383.883	+	810.748i	−0.0581280	+	0.122764i
$353$	−361.947	−	361.947i	−0.0545737	−	0.0545737i	0.679293	−	0.733867i	$-0.262286\pi$
$353$	−361.947	−	361.947i	−0.0545737	−	0.0545737i	−0.733867	+	0.679293i	$0.762286\pi$
$354$			5569.26i			0.836166i
$355$		−	235.167i		−	0.0351587i
$356$	−152.411	−	152.411i	−0.0226903	−	0.0226903i
$357$	−2952.16	−	2952.16i	−0.437660	−	0.437660i
$358$	−8840.87	−	8840.87i	−1.30518	−	1.30518i
$359$	4780.81	+	4780.81i	0.702846	+	0.702846i	0.965021	−	0.262174i	$-0.0844396\pi$
$359$	4780.81	+	4780.81i	0.702846	+	0.702846i	−0.262174	+	0.965021i	$0.584440\pi$
$360$		−	3258.97i		−	0.477118i
$361$			5778.87i			0.842523i
$362$	−3031.30	−	3031.30i	−0.440115	−	0.440115i
$363$	6145.18	−	5034.35i	0.888535	−	0.727920i
$364$	−613.641	−	336.117i	−0.0883613	−	0.0483993i
$365$		−	12626.0i		−	1.81062i
$366$	4657.28	+	4657.28i	0.665137	+	0.665137i
$367$	−11441.6			−1.62737			−0.813684	−	0.581307i	$-0.802541\pi$
$367$	−11441.6			−1.62737			−0.813684	+	0.581307i	$0.802541\pi$
$368$		−	7400.87i		−	1.04836i
$369$	153.324	−	153.324i	0.0216307	−	0.0216307i
$370$	14720.0	−	14720.0i	2.06826	−	2.06826i
$371$	4606.49	+	4606.49i	0.644629	+	0.644629i
$372$	−632.394	+	632.394i	−0.0881401	+	0.0881401i
$373$		−	7964.64i		−	1.10561i	−0.833310	−	0.552806i	$-0.813557\pi$
$373$		−	7964.64i		−	1.10561i	0.833310	−	0.552806i	$-0.186443\pi$
$374$	1163.92	−	2458.17i	0.160923	−	0.339863i
$375$	−3714.60	+	3714.60i	−0.511522	+	0.511522i
$376$	−4230.04			−0.580179
$377$	6226.33	−	1819.36i	0.850589	−	0.248546i
$378$	8793.47			1.19653
$379$	−5087.71	−	5087.71i	−0.689546	−	0.689546i	0.272585	−	0.962132i	$-0.412121\pi$
$379$	−5087.71	−	5087.71i	−0.689546	−	0.689546i	−0.962132	+	0.272585i	$0.912121\pi$
$380$		−	310.198i		−	0.0418758i
$381$	−8811.81			−1.18489
$382$	−6214.82	+	6214.82i	−0.832403	+	0.832403i
$383$	−1010.64	−	1010.64i	−0.134833	−	0.134833i	0.636469	−	0.771302i	$-0.280394\pi$
$383$	−1010.64	−	1010.64i	−0.134833	−	0.134833i	−0.771302	+	0.636469i	$0.780394\pi$
$384$	−6660.18	−	6660.18i	−0.885094	−	0.885094i
$385$	5838.98	+	16341.1i	0.772940	+	2.16317i
$386$	−9842.96			−1.29791
$387$	1644.39			0.215992
$388$	111.462	−	111.462i	0.0145841	−	0.0145841i
$389$			5189.33i			0.676374i	0.941079	+	0.338187i	$0.109814\pi$
$389$			5189.33i			0.676374i	−0.941079	+	0.338187i	$0.890186\pi$
$390$	3977.55	+	13612.2i	0.516439	+	1.76739i
$391$			2773.42i			0.358716i
$392$	6306.61	−	6306.61i	0.812582	−	0.812582i
$393$		−	10708.1i		−	1.37443i
$394$			3424.48i			0.437875i
$395$	−9438.00	+	9438.00i	−1.20222	+	1.20222i
$396$	−57.6096	−	161.227i	−0.00731059	−	0.0204595i
$397$	4408.53	−	4408.53i	0.557324	−	0.557324i	−0.371221	−	0.928545i	$-0.621061\pi$
$397$	4408.53	−	4408.53i	0.557324	−	0.557324i	0.928545	+	0.371221i	$0.121061\pi$
$398$	−1606.06	−	1606.06i	−0.202273	−	0.202273i
$399$	5380.00			0.675030
$400$			11961.3i			1.49517i
$401$	1251.05	−	1251.05i	0.155797	−	0.155797i	−0.624904	−	0.780701i	$-0.714862\pi$
$401$	1251.05	−	1251.05i	0.155797	−	0.155797i	0.780701	+	0.624904i	$0.214862\pi$
$402$	6292.18			0.780660
$403$	−6199.55	+	11318.4i	−0.766307	+	1.39903i
$404$			608.535i			0.0749400i
$405$	−10882.8	−	10882.8i	−1.33523	−	1.33523i
$406$		−	11094.9i		−	1.35624i
$407$	−6411.48	+	13540.8i	−0.780849	+	1.64913i
$408$	2345.79	+	2345.79i	0.284641	+	0.284641i
$409$	7189.82	−	7189.82i	0.869227	−	0.869227i	−0.123160	−	0.992387i	$-0.539303\pi$
$409$	7189.82	−	7189.82i	0.869227	−	0.869227i	0.992387	+	0.123160i	$0.0393027\pi$
$410$	−901.374	+	901.374i	−0.108575	+	0.108575i
$411$	5224.54	−	5224.54i	0.627026	−	0.627026i
$412$	770.938			0.0921879
$413$	8755.40			1.04316
$414$	1938.09	+	1938.09i	0.230077	+	0.230077i
$415$	24113.7			2.85227
$416$	1010.79	+	553.654i	0.119130	+	0.0652527i
$417$		−	12238.3i		−	1.43720i
$418$	1179.31	+	3300.44i	0.137995	+	0.386196i
$419$	8015.54			0.934570			0.467285	−	0.884107i	$-0.345232\pi$
$419$	8015.54			0.934570			0.467285	+	0.884107i	$0.345232\pi$
$420$	1545.05			0.179502
$421$	−11105.2	−	11105.2i	−1.28559	−	1.28559i	−0.937435	−	0.348160i	$-0.886807\pi$
$421$	−11105.2	−	11105.2i	−1.28559	−	1.28559i	−0.348160	−	0.937435i	$-0.613193\pi$
$422$	−5299.04	−	5299.04i	−0.611264	−	0.611264i
$423$	1183.44	−	1183.44i	0.136031	−	0.136031i
$424$	−3660.32	−	3660.32i	−0.419248	−	0.419248i
$425$		−	4482.42i		−	0.511598i
$426$	236.576			0.0269065
$427$	7321.69	−	7321.69i	0.829792	−	0.829792i
$428$	404.019			0.0456285
$429$	−5992.10	−	8262.15i	−0.674362	−	0.929838i
$430$	−9667.17			−1.08417
$431$	−8176.11	+	8176.11i	−0.913758	+	0.913758i	−0.996566	−	0.0828078i	$-0.973611\pi$
$431$	−8176.11	+	8176.11i	−0.913758	+	0.913758i	0.0828078	+	0.996566i	$0.473611\pi$
$432$	−7464.86			−0.831373
$433$		−	12643.4i		−	1.40324i	−0.712551	−	0.701621i	$-0.752460\pi$
$433$		−	12643.4i		−	1.40324i	0.712551	−	0.701621i	$-0.247540\pi$
$434$	15607.9	+	15607.9i	1.72628	+	1.72628i
$435$	−10128.9	+	10128.9i	−1.11642	+	1.11642i
$436$	600.514	+	600.514i	0.0659620	+	0.0659620i
$437$	−2527.14	−	2527.14i	−0.276635	−	0.276635i
$438$	12701.7			1.38564
$439$	10640.6			1.15683			0.578414	−	0.815743i	$-0.303672\pi$
$439$	10640.6			1.15683			0.578414	+	0.815743i	$0.303672\pi$
$440$	−4639.66	−	12984.6i	−0.502698	−	1.40686i
$441$			3528.82i			0.381041i
$442$	−3064.70	−	1678.67i	−0.329803	−	0.180647i
$443$	−12580.4			−1.34923			−0.674617	−	0.738168i	$-0.735691\pi$
$443$	−12580.4			−1.34923			−0.674617	+	0.738168i	$0.735691\pi$
$444$	943.248	+	943.248i	0.100821	+	0.100821i
$445$	6868.16			0.731645
$446$	16334.4			1.73421
$447$	−416.914	+	416.914i	−0.0441149	+	0.0441149i
$448$	−9165.35	+	9165.35i	−0.966567	+	0.966567i
$449$	−1093.63	+	1093.63i	−0.114948	+	0.114948i	−0.762241	−	0.647293i	$-0.775901\pi$
$449$	−1093.63	+	1093.63i	−0.114948	+	0.114948i	0.647293	+	0.762241i	$0.275901\pi$
$450$	−3132.35	−	3132.35i	−0.328134	−	0.328134i
$451$	392.605	−	829.167i	0.0409912	−	0.0865719i
$452$		−	617.528i		−	0.0642612i
$453$	9935.99	+	9935.99i	1.03054	+	1.03054i
$454$		−	3627.37i		−	0.374980i
$455$	21399.7	−	6253.09i	2.20491	−	0.644284i
$456$	−4274.95			−0.439020
$457$	4006.22	−	4006.22i	0.410073	−	0.410073i	−0.471691	−	0.881764i	$-0.656356\pi$
$457$	4006.22	−	4006.22i	0.410073	−	0.410073i	0.881764	+	0.471691i	$0.156356\pi$
$458$			5853.65i			0.597212i
$459$	2797.40			0.284470
$460$	−725.755	−	725.755i	−0.0735619	−	0.0735619i
$461$	−6635.56	+	6635.56i	−0.670388	+	0.670388i	−0.957805	−	0.287417i	$-0.907203\pi$
$461$	−6635.56	+	6635.56i	−0.670388	+	0.670388i	0.287417	+	0.957805i	$0.407203\pi$
$462$	−16439.1	+	5873.99i	−1.65544	+	0.591521i
$463$	979.353	−	979.353i	0.0983032	−	0.0983032i	−0.656245	−	0.754548i	$-0.727856\pi$
$463$	979.353	−	979.353i	0.0983032	−	0.0983032i	0.754548	+	0.656245i	$0.227856\pi$
$464$			9418.59i			0.942343i
$465$		−	28497.9i		−	2.84206i
$466$	266.957	−	266.957i	0.0265377	−	0.0265377i
$467$			10625.3i			1.05285i	0.850222	+	0.526424i	$0.176468\pi$
$467$			10625.3i			1.05285i	−0.850222	+	0.526424i	$0.823532\pi$
$468$	−211.138	+	61.6953i	−0.0208544	+	0.00609373i
$469$		−	9891.90i		−	0.973914i
$470$	−6957.32	+	6957.32i	−0.682803	+	0.682803i
$471$	10483.6			1.02561
$472$	−6957.05			−0.678441
$473$	6551.70	−	2341.05i	0.636887	−	0.227572i
$474$	−9494.58	−	9494.58i	−0.920043	−	0.920043i
$475$	4084.37	+	4084.37i	0.394535	+	0.394535i
$476$	−269.197	+	269.197i	−0.0259215	+	0.0259215i
$477$	2048.11			0.196596
$478$			13094.1i			1.25295i
$479$	−6420.52	−	6420.52i	−0.612445	−	0.612445i	0.331138	−	0.943582i	$-0.392568\pi$
$479$	−6420.52	−	6420.52i	−0.612445	−	0.612445i	−0.943582	+	0.331138i	$0.892568\pi$
$480$	−2545.02			−0.242008
$481$	16881.9	+	9246.94i	1.60031	+	0.876557i
$482$	−9974.91			−0.942624
$483$	12587.3	−	12587.3i	1.18580	−	1.18580i
$484$	−459.066	−	560.358i	−0.0431129	−	0.0526257i
$485$			5022.85i			0.470260i
$486$	4826.92	−	4826.92i	0.450522	−	0.450522i
$487$	13021.5	+	13021.5i	1.21162	+	1.21162i	0.970493	+	0.241131i	$0.0775184\pi$
$487$	13021.5	+	13021.5i	1.21162	+	1.21162i	0.241131	+	0.970493i	$0.422482\pi$
$488$	−5817.82	+	5817.82i	−0.539673	+	0.539673i
$489$	−4499.60	+	4499.60i	−0.416113	+	0.416113i
$490$		−	20745.5i		−	1.91263i
$491$	2507.05			0.230431			0.115216	−	0.993341i	$-0.463244\pi$
$491$	2507.05			0.230431			0.115216	+	0.993341i	$0.463244\pi$
$492$	−57.7594	−	57.7594i	−0.00529267	−	0.00529267i
$493$		−	3529.55i		−	0.322440i
$494$	4322.14	−	1262.95i	0.393649	−	0.115026i
$495$	4930.77	+	2334.69i	0.447721	+	0.211993i
$496$	−13249.7	−	13249.7i	−1.19946	−	1.19946i
$497$		−	371.921i		−	0.0335672i
$498$			24258.2i			2.18281i
$499$	−35.0934	−	35.0934i	−0.00314829	−	0.00314829i	0.705531	−	0.708679i	$-0.250709\pi$
$499$	−35.0934	−	35.0934i	−0.00314829	−	0.00314829i	−0.708679	+	0.705531i	$0.750709\pi$
$500$	338.722	+	338.722i	0.0302962	+	0.0302962i
$501$	9116.31	+	9116.31i	0.812948	+	0.812948i
$502$	−13421.6	−	13421.6i	−1.19330	−	1.19330i
$503$			9938.73i			0.881006i	0.897751	+	0.440503i	$0.145200\pi$
$503$			9938.73i			0.881006i	−0.897751	+	0.440503i	$0.854800\pi$
$504$		−	5154.12i		−	0.455522i
$505$	−13711.3	−	13711.3i	−1.20821	−	1.20821i
$506$	10481.1	+	4962.71i	0.920831	+	0.436007i
$507$	−11049.7	+	7060.37i	−0.967916	+	0.618466i
$508$			803.519i			0.0701780i
$509$	−1751.37	−	1751.37i	−0.152511	−	0.152511i	0.626727	−	0.779239i	$-0.284394\pi$
$509$	−1751.37	−	1751.37i	−0.152511	−	0.152511i	−0.779239	+	0.626727i	$0.784394\pi$
$510$	7716.43			0.669979
$511$		−	19968.3i		−	1.72866i
$512$	7207.10	−	7207.10i	0.622093	−	0.622093i
$513$	−2548.99	+	2548.99i	−0.219377	+	0.219377i
$514$	7401.65	+	7401.65i	0.635161	+	0.635161i
$515$	−17370.6	+	17370.6i	−1.48629	+	1.48629i
$516$		−	619.465i		−	0.0528497i
$517$	3030.35	−	6399.99i	0.257785	−	0.544432i
$518$	23280.0	−	23280.0i	1.97464	−	1.97464i
$519$	−12548.7			−1.06132
$520$	−17004.2	+	4968.71i	−1.43401	+	0.419023i
$521$	−15707.7			−1.32086			−0.660428	−	0.750889i	$-0.729625\pi$
$521$	−15707.7			−1.32086			−0.660428	+	0.750889i	$0.729625\pi$
$522$	−2466.48	−	2466.48i	−0.206810	−	0.206810i
$523$		−	7637.76i		−	0.638577i	−0.947657	−	0.319289i	$-0.896556\pi$
$523$		−	7637.76i		−	0.638577i	0.947657	−	0.319289i	$-0.103444\pi$
$524$	−976.432			−0.0814038
$525$	−20343.7	+	20343.7i	−1.69118	+	1.69118i
$526$	−12973.3	−	12973.3i	−1.07541	−	1.07541i
$527$	4965.23	+	4965.23i	0.410416	+	0.410416i
$528$	13955.3	−	4986.48i	1.15024	−	0.411002i
$529$	341.761			0.0280892
$530$	−12040.6			−0.986810
$531$	1946.38	−	1946.38i	0.159069	−	0.159069i
$532$		−	490.584i		−	0.0399803i
$533$	−1033.76	−	566.232i	−0.0840093	−	0.0460155i
$534$			6909.34i			0.559918i
$535$	−9103.24	+	9103.24i	−0.735640	+	0.735640i
$536$			7860.11i			0.633405i
$537$			25529.2i			2.05152i
$538$	−597.192	+	597.192i	−0.0478564	+	0.0478564i
$539$	5023.84	+	14059.8i	0.401469	+	1.12356i
$540$	−732.030	+	732.030i	−0.0583362	+	0.0583362i
$541$	15255.2	+	15255.2i	1.21233	+	1.21233i	0.970258	+	0.242073i	$0.0778274\pi$
$541$	15255.2	+	15255.2i	1.21233	+	1.21233i	0.242073	+	0.970258i	$0.422173\pi$
$542$	13400.3			1.06198
$543$			8753.28i			0.691785i
$544$	443.423	−	443.423i	0.0349478	−	0.0349478i
$545$	−27061.2			−2.12693
$546$	6290.58	+	21528.0i	0.493062	+	1.68739i
$547$		−	13354.3i		−	1.04386i	−0.852990	−	0.521928i	$-0.825213\pi$
$547$		−	13354.3i		−	1.04386i	0.852990	−	0.521928i	$-0.174787\pi$
$548$	−476.409	−	476.409i	−0.0371372	−	0.0371372i
$549$		−	3255.32i		−	0.253067i
$550$	−16939.6	−	8020.76i	−1.31328	−	0.621830i
$551$	3216.12	+	3216.12i	0.248659	+	0.248659i
$552$	−10001.9	+	10001.9i	−0.771212	+	0.771212i
$553$	−14926.4	+	14926.4i	−1.14780	+	1.14780i
$554$	−42.5463	+	42.5463i	−0.00326285	+	0.00326285i
$555$	−42506.0			−3.25095
$556$	−1115.97			−0.0851215
$557$	−1489.90	−	1489.90i	−0.113338	−	0.113338i	0.648164	−	0.761501i	$-0.275537\pi$
$557$	−1489.90	−	1489.90i	−0.113338	−	0.113338i	−0.761501	+	0.648164i	$0.775537\pi$
$558$	6939.49			0.526473
$559$	−2507.08	−	8579.88i	−0.189692	−	0.649177i
$560$			32371.4i			2.44275i
$561$	−5229.64	+	1868.65i	−0.393575	+	0.140632i
$562$	3303.53			0.247956
$563$	10112.5			0.757000			0.378500	−	0.925601i	$-0.376440\pi$
$563$	10112.5			0.757000			0.378500	+	0.925601i	$0.376440\pi$
$564$	−445.820	−	445.820i	−0.0332844	−	0.0332844i
$565$	13914.0	+	13914.0i	1.03604	+	1.03604i
$566$	18356.6	−	18356.6i	1.36322	−	1.36322i
$567$	−17211.3	−	17211.3i	−1.27479	−	1.27479i
$568$			295.528i			0.0218312i
$569$	−1056.47			−0.0778373			−0.0389187	−	0.999242i	$-0.512391\pi$
$569$	−1056.47			−0.0778373			−0.0389187	+	0.999242i	$0.512391\pi$
$570$	−7031.20	+	7031.20i	−0.516674	+	0.516674i
$571$	−7374.45			−0.540475			−0.270237	−	0.962794i	$-0.587102\pi$
$571$	−7374.45			−0.540475			−0.270237	+	0.962794i	$0.587102\pi$
$572$	−753.398	+	546.399i	−0.0550719	+	0.0399407i
$573$	17946.1			1.30839
$574$	−1425.54	+	1425.54i	−0.103660	+	0.103660i
$575$	19112.0			1.38613
$576$			4075.04i			0.294780i
$577$	−3690.40	−	3690.40i	−0.266262	−	0.266262i	0.561330	−	0.827592i	$-0.310290\pi$
$577$	−3690.40	−	3690.40i	−0.266262	−	0.266262i	−0.827592	+	0.561330i	$0.810290\pi$
$578$	8810.29	−	8810.29i	0.634013	−	0.634013i
$579$	14211.4	+	14211.4i	1.02005	+	1.02005i
$580$	923.620	+	923.620i	0.0661228	+	0.0661228i
$581$	38136.3			2.72317
$582$	−5052.97			−0.359884
$583$	8160.24	−	2915.81i	0.579695	−	0.207136i
$584$			15866.8i			1.12427i
$585$	3367.19	−	6147.40i	0.237976	−	0.434468i
$586$	24508.9			1.72774
$587$	−1425.50	−	1425.50i	−0.100233	−	0.100233i	0.655212	−	0.755445i	$-0.272579\pi$
$587$	−1425.50	−	1425.50i	−0.100233	−	0.100233i	−0.755445	+	0.655212i	$0.772579\pi$
$588$	1329.36			0.0932343
$589$	−9048.63			−0.633009
$590$	−11442.6	+	11442.6i	−0.798445	+	0.798445i
$591$	4944.31	−	4944.31i	0.344132	−	0.344132i
$592$	−19762.6	+	19762.6i	−1.37202	+	1.37202i
$593$	−1877.02	−	1877.02i	−0.129983	−	0.129983i	0.639122	−	0.769105i	$-0.279298\pi$
$593$	−1877.02	−	1877.02i	−0.129983	−	0.129983i	−0.769105	+	0.639122i	$0.779298\pi$
$594$	5005.62	−	10571.7i	0.345763	−	0.730239i
$595$		−	12131.0i		−	0.835833i
$596$	38.0170	+	38.0170i	0.00261281	+	0.00261281i
$597$			4637.72i			0.317939i
$598$	7157.45	−	13067.2i	0.489448	−	0.893572i
$599$	−11835.4			−0.807317			−0.403658	−	0.914910i	$-0.632262\pi$
$599$	−11835.4			−0.807317			−0.403658	+	0.914910i	$0.632262\pi$
$600$	16165.1	−	16165.1i	1.09990	−	1.09990i
$601$			21676.7i			1.47123i	0.677398	+	0.735616i	$0.263107\pi$
$601$			21676.7i			1.47123i	−0.677398	+	0.735616i	$0.736893\pi$
$602$	−15288.8			−1.03509
$603$	−2199.04	−	2199.04i	−0.148510	−	0.148510i
$604$	906.029	−	906.029i	0.0610361	−	0.0610361i
$605$	22969.4	+	2282.30i	1.54353	+	0.153370i
$606$	13793.5	−	13793.5i	0.924628	−	0.924628i
$607$			8503.65i			0.568620i	0.958732	+	0.284310i	$0.0917645\pi$
$607$			8503.65i			0.568620i	−0.958732	+	0.284310i	$0.908235\pi$
$608$			808.093i			0.0539021i
$609$	−16019.0	+	16019.0i	−1.06589	+	1.06589i
$610$			19137.6i			1.27026i
$611$	−7979.13	−	4370.51i	−0.528316	−	0.289381i
$612$			119.689i			0.00790544i
$613$	151.870	−	151.870i	0.0100065	−	0.0100065i	−0.702086	−	0.712092i	$-0.747748\pi$
$613$	151.870	−	151.870i	0.0100065	−	0.0100065i	0.712092	+	0.702086i	$0.247748\pi$
$614$	20604.3			1.35427
$615$	2602.84			0.170661
$616$	−7337.72	−	20535.5i	−0.479943	−	1.34318i
$617$	5603.92	+	5603.92i	0.365649	+	0.365649i	0.865888	−	0.500239i	$-0.166754\pi$
$617$	5603.92	+	5603.92i	0.365649	+	0.365649i	−0.500239	+	0.865888i	$0.666754\pi$
$618$	−17474.7	−	17474.7i	−1.13744	−	1.13744i
$619$	−9658.22	+	9658.22i	−0.627135	+	0.627135i	−0.947346	−	0.320211i	$-0.896246\pi$
$619$	−9658.22	+	9658.22i	−0.627135	+	0.627135i	0.320211	+	0.947346i	$0.396246\pi$
$620$	−2598.63			−0.168328
$621$			11927.5i			0.770746i
$622$	−3473.95	−	3473.95i	−0.223943	−	0.223943i
$623$	10862.1			0.698527
$624$	−5340.13	−	18275.3i	−0.342590	−	1.17243i
$625$	6705.11			0.429127
$626$	−1185.70	+	1185.70i	−0.0757032	+	0.0757032i
$627$	3062.53	−	6467.94i	0.195065	−	0.411969i
$628$		−	955.968i		−	0.0607441i
$629$	7405.89	−	7405.89i	0.469463	−	0.469463i
$630$	−8477.21	−	8477.21i	−0.536095	−	0.536095i
$631$	−12454.3	+	12454.3i	−0.785731	+	0.785731i	−0.980791	−	0.195060i	$-0.937510\pi$
$631$	−12454.3	+	12454.3i	−0.785731	+	0.785731i	0.195060	+	0.980791i	$0.437510\pi$
$632$	11860.5	−	11860.5i	0.746497	−	0.746497i
$633$			15301.7i			0.960802i
$634$	14954.1			0.936757
$635$	−18104.7	−	18104.7i	−1.13144	−	1.13144i
$636$		−	771.552i		−	0.0481038i
$637$	18412.2	−	5380.13i	1.14524	−	0.334645i
$638$	−13338.6	−	6315.71i	−0.827709	−	0.391914i
$639$	−82.6804	−	82.6804i	−0.00511860	−	0.00511860i
$640$		−	27367.9i		−	1.69033i
$641$		−	17871.4i		−	1.10121i	−0.834765	−	0.550607i	$-0.814396\pi$
$641$		−	17871.4i		−	1.10121i	0.834765	−	0.550607i	$-0.185604\pi$
$642$	−9157.82	−	9157.82i	−0.562976	−	0.562976i
$643$	1658.11	+	1658.11i	0.101695	+	0.101695i	0.756124	−	0.654429i	$-0.227091\pi$
$643$	1658.11	+	1658.11i	0.101695	+	0.101695i	−0.654429	+	0.756124i	$0.727091\pi$
$644$	−1147.80	−	1147.80i	−0.0702321	−	0.0702321i
$645$	13957.6	+	13957.6i	0.852063	+	0.852063i
$646$		−	2450.12i		−	0.149224i
$647$		−	2443.18i		−	0.148456i	−0.997241	−	0.0742281i	$-0.976351\pi$
$647$		−	2443.18i		−	0.148456i	0.997241	−	0.0742281i	$-0.0236493\pi$
$648$	13676.1	+	13676.1i	0.829089	+	0.829089i
$649$	4983.95	−	10525.9i	0.301444	−	0.636639i
$650$	−11567.9	+	21119.2i	−0.698047	+	1.27441i
$651$		−	45070.0i		−	2.71341i
$652$	410.304	+	410.304i	0.0246453	+	0.0246453i
$653$	−6311.02			−0.378207			−0.189104	−	0.981957i	$-0.560558\pi$
$653$	−6311.02			−0.378207			−0.189104	+	0.981957i	$0.560558\pi$
$654$		−	27223.5i		−	1.62771i
$655$	22000.7	−	22000.7i	1.31242	−	1.31242i
$656$	1210.15	−	1210.15i	0.0720253	−	0.0720253i
$657$	−4439.09	−	4439.09i	−0.263600	−	0.263600i
$658$	−11003.1	+	11003.1i	−0.651896	+	0.651896i
$659$			11742.8i			0.694137i	0.937840	+	0.347069i	$0.112823\pi$
$659$			11742.8i			0.694137i	−0.937840	+	0.347069i	$0.887177\pi$
$660$	879.510	−	1857.49i	0.0518710	−	0.109550i
$661$	−1333.15	+	1333.15i	−0.0784472	+	0.0784472i	−0.745242	−	0.666794i	$-0.767666\pi$
$661$	−1333.15	+	1333.15i	−0.0784472	+	0.0784472i	0.666794	+	0.745242i	$0.267666\pi$
$662$	−17896.2			−1.05069
$663$	2001.17	+	6848.54i	0.117224	+	0.401170i
$664$	−30303.1			−1.77107
$665$	11053.7	+	11053.7i	0.644578	+	0.644578i
$666$		−	10350.6i		−	0.602218i
$667$	15049.2			0.873624
$668$	831.286	−	831.286i	0.0481488	−	0.0481488i
$669$	−23583.9	−	23583.9i	−1.36294	−	1.36294i
$670$	12927.9	+	12927.9i	0.745443	+	0.745443i
$671$	−4634.47	−	12970.1i	−0.266634	−	0.746208i
$672$	−4025.00			−0.231053
$673$	−6652.48			−0.381032			−0.190516	−	0.981684i	$-0.561016\pi$
$673$	−6652.48			−0.381032			−0.190516	+	0.981684i	$0.561016\pi$
$674$	19422.6	−	19422.6i	1.10999	−	1.10999i
$675$		−	19277.3i		−	1.09923i
$676$	643.812	+	1007.58i	0.0366302	+	0.0573273i
$677$			13653.5i			0.775105i	0.921848	+	0.387553i	$0.126679\pi$
$677$			13653.5i			0.775105i	−0.921848	+	0.387553i	$0.873321\pi$
$678$	−13997.4	+	13997.4i	−0.792871	+	0.792871i
$679$			7943.74i			0.448973i
$680$			9639.27i			0.543602i
$681$	−5237.26	+	5237.26i	−0.294702	+	0.294702i
$682$	27648.9	−	9879.47i	1.55239	−	0.554699i
$683$	2377.67	−	2377.67i	0.133205	−	0.133205i	−0.637361	−	0.770566i	$-0.719974\pi$
$683$	2377.67	−	2377.67i	0.133205	−	0.133205i	0.770566	+	0.637361i	$0.219974\pi$
$684$	−109.060	−	109.060i	−0.00609652	−	0.00609652i
$685$	21468.6			1.19748
$686$		−	5310.86i		−	0.295582i
$687$	8451.60	−	8451.60i	0.469357	−	0.469357i
$688$	12978.8			0.719205
$689$	−3122.60	−	10686.4i	−0.172658	−	0.590882i
$690$			32901.1i			1.81525i
$691$	9025.14	+	9025.14i	0.496863	+	0.496863i	0.910460	−	0.413597i	$-0.135728\pi$
$691$	9025.14	+	9025.14i	0.496863	+	0.496863i	−0.413597	+	0.910460i	$0.635728\pi$
$692$			1144.27i			0.0628594i
$693$	7798.12	+	3692.35i	0.427455	+	0.202397i
$694$	9992.97	+	9992.97i	0.546582	+	0.546582i
$695$	25144.7	−	25144.7i	1.37236	−	1.37236i
$696$	12728.7	−	12728.7i	0.693221	−	0.693221i
$697$	−453.497	+	453.497i	−0.0246448	+	0.0246448i
$698$	−29134.2			−1.57987
$699$	−770.874			−0.0417126
$700$	1855.07	+	1855.07i	0.100165	+	0.100165i
$701$	−764.666			−0.0411998			−0.0205999	−	0.999788i	$-0.506558\pi$
$701$	−764.666			−0.0411998			−0.0205999	+	0.999788i	$0.506558\pi$
$702$	−13180.2	−	7219.33i	−0.708622	−	0.388143i
$703$			13496.5i			0.724081i
$704$	5801.47	+	16236.1i	0.310584	+	0.869205i
$705$	20090.2			1.07325
$706$	1496.23			0.0797609
$707$	−21684.8	−	21684.8i	−1.15352	−	1.15352i
$708$	−733.231	−	733.231i	−0.0389216	−	0.0389216i
$709$	7271.52	−	7271.52i	0.385173	−	0.385173i	−0.487789	−	0.872962i	$-0.662196\pi$
$709$	7271.52	−	7271.52i	0.385173	−	0.385173i	0.872962	+	0.487789i	$0.162196\pi$
$710$	486.068	+	486.068i	0.0256927	+	0.0256927i
$711$			6636.47i			0.350052i
$712$	−8631.06			−0.454302
$713$	−21170.6	+	21170.6i	−1.11199	+	1.11199i
$714$	12203.7			0.639652
$715$	4664.03	−	29286.7i	0.243951	−	1.53183i
$716$	2327.92			0.121506
$717$	18905.5	−	18905.5i	0.984712	−	0.984712i
$718$	−19763.0			−1.02723
$719$		−	6257.13i		−	0.324550i	−0.986746	−	0.162275i	$-0.948117\pi$
$719$		−	6257.13i		−	0.324550i	0.986746	−	0.162275i	$-0.0518832\pi$
$720$	7196.38	+	7196.38i	0.372491	+	0.372491i
$721$	−27471.9	+	27471.9i	−1.41901	+	1.41901i
$722$	−11944.4	−	11944.4i	−0.615685	−	0.615685i
$723$	14401.9	+	14401.9i	0.740821	+	0.740821i
$724$	798.183			0.0409727
$725$	−24322.6			−1.24596
$726$	−2295.98	+	23107.1i	−0.117372	+	1.18125i
$727$		−	5034.30i		−	0.256825i	−0.991721	−	0.128413i	$-0.959012\pi$
$727$		−	5034.30i		−	0.256825i	0.991721	−	0.128413i	$-0.0409881\pi$
$728$	−26892.5	+	7858.11i	−1.36910	+	0.400056i
$729$	10023.1			0.509226
$730$	26096.9	+	26096.9i	1.32313	+	1.32313i
$731$	−4863.72			−0.246089
$732$	−1226.33			−0.0619212
$733$	10241.4	−	10241.4i	0.516066	−	0.516066i	−0.400313	−	0.916379i	$-0.631098\pi$
$733$	10241.4	−	10241.4i	0.516066	−	0.516066i	0.916379	+	0.400313i	$0.131098\pi$
$734$	23648.7	−	23648.7i	1.18922	−	1.18922i
$735$	−29952.7	+	29952.7i	−1.50316	+	1.50316i
$736$	1890.65	+	1890.65i	0.0946881	+	0.0946881i
$737$	−11892.2	−	5630.89i	−0.594378	−	0.281434i
$738$			633.814i			0.0316139i
$739$	85.3600	+	85.3600i	0.00424901	+	0.00424901i	0.709228	−	0.704979i	$-0.249044\pi$
$739$	85.3600	+	85.3600i	0.00424901	+	0.00424901i	−0.704979	+	0.709228i	$0.749044\pi$
$740$			3875.98i			0.192546i
$741$	−8063.85	−	4416.91i	−0.399774	−	0.218974i
$742$	−19042.4			−0.942142
$743$	9705.27	−	9705.27i	0.479208	−	0.479208i	−0.425670	−	0.904878i	$-0.639962\pi$
$743$	9705.27	−	9705.27i	0.479208	−	0.479208i	0.904878	+	0.425670i	$0.139962\pi$
$744$			35812.6i			1.76472i
$745$	−1713.18			−0.0842496
$746$	16462.2	+	16462.2i	0.807941	+	0.807941i
$747$	8477.94	−	8477.94i	0.415250	−	0.415250i
$748$	170.396	+	476.873i	0.00832927	+	0.0233104i
$749$	−14397.0	+	14397.0i	−0.702341	+	0.702341i
$750$		−	15355.5i		−	0.747604i
$751$		−	29953.3i		−	1.45541i	−0.685891	−	0.727704i	$-0.740587\pi$
$751$		−	29953.3i		−	1.45541i	0.685891	−	0.727704i	$-0.259413\pi$
$752$	9340.68	−	9340.68i	0.452951	−	0.452951i
$753$			38756.6i			1.87566i
$754$	−9108.81	+	16629.7i	−0.439951	+	0.803208i
$755$			40828.8i			1.96810i
$756$	−1157.72	+	1157.72i	−0.0556956	+	0.0556956i
$757$	11075.0			0.531739			0.265869	−	0.964009i	$-0.414341\pi$
$757$	11075.0			0.531739			0.265869	+	0.964009i	$0.414341\pi$
$758$	21031.7			1.00779
$759$	−7967.49	−	22298.0i	−0.381030	−	1.06636i
$760$	−8783.28	−	8783.28i	−0.419215	−	0.419215i
$761$	20389.0	+	20389.0i	0.971225	+	0.971225i	0.999597	−	0.0283725i	$-0.00903245\pi$
$761$	20389.0	+	20389.0i	0.971225	+	0.971225i	−0.0283725	+	0.999597i	$0.509032\pi$
$762$	18213.2	−	18213.2i	0.865873	−	0.865873i
$763$	−42797.9			−2.03065
$764$		−	1636.45i		−	0.0774929i
$765$	−2696.79	−	2696.79i	−0.127455	−	0.127455i
$766$	4177.79			0.197062
$767$	−13123.1	−	7188.08i	−0.617793	−	0.338392i
$768$	4966.85			0.233367
$769$	−17503.5	+	17503.5i	−0.820794	+	0.820794i	−0.986222	−	0.165428i	$-0.947099\pi$
$769$	−17503.5	+	17503.5i	−0.820794	+	0.820794i	0.165428	+	0.986222i	$0.447099\pi$
$770$	−45844.2	−	21706.9i	−2.14560	−	1.01593i
$771$		−	21373.3i		−	0.998364i
$772$	1295.89	−	1295.89i	0.0604148	−	0.0604148i
$773$	−14691.5	−	14691.5i	−0.683590	−	0.683590i	0.277217	−	0.960807i	$-0.410588\pi$
$773$	−14691.5	−	14691.5i	−0.683590	−	0.683590i	−0.960807	+	0.277217i	$0.910588\pi$
$774$	−3398.81	+	3398.81i	−0.157839	+	0.157839i
$775$	34216.1	−	34216.1i	1.58591	−	1.58591i
$776$		−	6312.10i		−	0.291999i
$777$	−67224.1			−3.10380
$778$	−10725.9	−	10725.9i	−0.494269	−	0.494269i
$779$		−	826.451i		−	0.0380111i
$780$	−2315.81	−	1268.47i	−0.106307	−	0.0582288i
$781$	−447.131	−	211.713i	−0.0204860	−	0.00969999i
$782$	−5732.42	−	5732.42i	−0.262137	−	0.262137i
$783$		−	15179.3i		−	0.692803i
$784$			27852.3i			1.26878i
$785$	21539.6	+	21539.6i	0.979340	+	0.979340i
$786$	22132.6	+	22132.6i	1.00438	+	1.00438i
$787$	−25073.1	−	25073.1i	−1.13565	−	1.13565i	−0.989221	−	0.146433i	$-0.953221\pi$
$787$	−25073.1	−	25073.1i	−1.13565	−	1.13565i	−0.146433	−	0.989221i	$-0.546779\pi$
$788$	−450.856	−	450.856i	−0.0203821	−	0.0203821i
$789$			37462.2i			1.69035i
$790$		−	39015.0i		−	1.75708i
$791$	22005.2	+	22005.2i	0.989148	+	0.989148i
$792$	−6196.39	−	2933.95i	−0.278004	−	0.131633i
$793$	−16985.2	+	4963.15i	−0.760607	+	0.222253i
$794$			18224.1i			0.814544i
$795$	17384.4	+	17384.4i	0.775548	+	0.775548i
$796$	422.898			0.0188307
$797$		−	14620.0i		−	0.649770i	−0.945753	−	0.324885i	$-0.894674\pi$
$797$		−	14620.0i		−	0.649770i	0.945753	−	0.324885i	$-0.105326\pi$
$798$	−11120.0	+	11120.0i	−0.493287	+	0.493287i
$799$	−3500.35	+	3500.35i	−0.154986	+	0.154986i
$800$	−3055.69	−	3055.69i	−0.135044	−	0.135044i
$801$	2414.72	−	2414.72i	0.106517	−	0.106517i
$802$			5171.62i			0.227701i
$803$	−24006.3	−	11366.8i	−1.05500	−	0.499534i
$804$	−828.408	+	828.408i	−0.0363379	+	0.0363379i
$805$	51723.6			2.26462
$806$	−10580.1	−	36208.0i	−0.462369	−	1.58235i
$807$	1724.47			0.0752221
$808$	17230.7	+	17230.7i	0.750217	+	0.750217i
$809$		−	43462.8i		−	1.88884i	−0.328740	−	0.944421i	$-0.606624\pi$
$809$		−	43462.8i		−	1.88884i	0.328740	−	0.944421i	$-0.393376\pi$
$810$	44987.5			1.95148
$811$	7430.12	−	7430.12i	0.321710	−	0.321710i	−0.527713	−	0.849423i	$-0.676950\pi$
$811$	7430.12	−	7430.12i	0.321710	−	0.321710i	0.849423	+	0.527713i	$0.176950\pi$
$812$	1460.72	+	1460.72i	0.0631297	+	0.0631297i
$813$	−19347.6	−	19347.6i	−0.834624	−	0.834624i
$814$	−14735.7	−	41239.7i	−0.634505	−	1.77574i
$815$	−18489.7			−0.794683
$816$	−10359.8			−0.444444
$817$	4431.81	−	4431.81i	0.189779	−	0.189779i
$818$			29721.5i			1.27040i
$819$	5325.28	−	9722.23i	0.227204	−	0.414801i
$820$		−	237.344i		−	0.0101078i
$821$	9879.72	−	9879.72i	0.419981	−	0.419981i	−0.465216	−	0.885197i	$-0.654023\pi$
$821$	9879.72	−	9879.72i	0.419981	−	0.419981i	0.885197	+	0.465216i	$0.154023\pi$
$822$			21597.3i			0.916416i
$823$		−	21037.4i		−	0.891028i	−0.895275	−	0.445514i	$-0.853021\pi$
$823$		−	21037.4i		−	0.891028i	0.895275	−	0.445514i	$-0.146979\pi$
$824$	21829.2	−	21829.2i	0.922884	−	0.922884i
$825$	12877.1	+	36038.1i	0.543422	+	1.52083i
$826$	−18096.6	+	18096.6i	−0.762304	+	0.762304i
$827$	−3925.23	−	3925.23i	−0.165047	−	0.165047i	0.619751	−	0.784798i	$-0.287233\pi$
$827$	−3925.23	−	3925.23i	−0.165047	−	0.165047i	−0.784798	+	0.619751i	$0.787233\pi$
$828$	−510.325			−0.0214191
$829$			9954.70i			0.417058i	0.978016	+	0.208529i	$0.0668675\pi$
$829$			9954.70i			0.417058i	−0.978016	+	0.208529i	$0.933132\pi$
$830$	−49840.8	+	49840.8i	−2.08434	+	2.08434i
$831$	122.858			0.00512865
$832$	21262.2	−	6212.91i	0.885978	−	0.258887i
$833$		−	10437.4i		−	0.434136i
$834$	25295.4	+	25295.4i	1.05025	+	1.05025i
$835$			37460.6i			1.55255i
$836$	−589.790	−	279.261i	−0.0243999	−	0.0115532i
$837$	21353.7	+	21353.7i	0.881829	+	0.881829i
$838$	−16567.4	+	16567.4i	−0.682950	+	0.682950i
$839$	4322.46	−	4322.46i	0.177864	−	0.177864i	−0.612560	−	0.790424i	$-0.709860\pi$
$839$	4322.46	−	4322.46i	0.177864	−	0.177864i	0.790424	+	0.612560i	$0.209860\pi$
$840$	43748.3	−	43748.3i	1.79698	−	1.79698i
$841$	5236.88			0.214723
$842$	45907.0			1.87893
$843$	−4769.69	−	4769.69i	−0.194872	−	0.194872i
$844$	1395.31			0.0569059
$845$	−37208.8	−	8196.41i	−1.51482	−	0.333687i
$846$			4892.15i			0.198813i
$847$	36326.5	+	3609.50i	1.47367	+	0.146427i
$848$	16165.3			0.654621
$849$	−53007.1			−2.14275
$850$	9264.77	+	9264.77i	0.373857	+	0.373857i
$851$	31577.0	+	31577.0i	1.27197	+	1.27197i
$852$	−31.1469	+	31.1469i	−0.00125244	+	0.00125244i
$853$	21005.3	+	21005.3i	0.843150	+	0.843150i	0.989267	−	0.146117i	$-0.0466777\pi$
$853$	21005.3	+	21005.3i	0.843150	+	0.843150i	−0.146117	+	0.989267i	$0.546678\pi$
$854$			30266.6i			1.21276i
$855$	4914.62			0.196581
$856$	11439.8	−	11439.8i	0.456782	−	0.456782i
$857$	−25882.6			−1.03166			−0.515829	−	0.856691i	$-0.672516\pi$
$857$	−25882.6			−1.03166			−0.515829	+	0.856691i	$0.672516\pi$
$858$	29462.3	+	4692.00i	1.17229	+	0.186692i
$859$	3330.83			0.132301			0.0661505	−	0.997810i	$-0.478928\pi$
$859$	3330.83			0.132301			0.0661505	+	0.997810i	$0.478928\pi$
$860$	1272.75	−	1272.75i	0.0504655	−	0.0504655i
$861$	4116.44			0.162936
$862$		−	33798.6i		−	1.33548i
$863$	12501.8	+	12501.8i	0.493126	+	0.493126i	0.909290	−	0.416164i	$-0.136626\pi$
$863$	12501.8	+	12501.8i	0.493126	+	0.493126i	−0.416164	+	0.909290i	$0.636626\pi$
$864$	1907.00	−	1907.00i	0.0750897	−	0.0750897i
$865$	−25782.4	−	25782.4i	−1.01344	−	1.01344i
$866$	26132.8	+	26132.8i	1.02544	+	1.02544i
$867$	−25440.9			−0.996560
$868$	−4109.78			−0.160709
$869$	9448.07	+	26441.5i	0.368819	+	1.03218i
$870$		−	41871.0i		−	1.63168i
$871$	−8121.13	+	14826.5i	−0.315929	+	0.576783i
$872$	34007.2			1.32068
$873$	1765.95	+	1765.95i	0.0684630	+	0.0684630i
$874$	10446.7			0.404309
$875$	−24140.3			−0.932674
$876$	−1672.27	+	1672.27i	−0.0644985	+	0.0644985i
$877$	−23851.4	+	23851.4i	−0.918365	+	0.918365i	−0.996911	−	0.0785458i	$-0.974972\pi$
$877$	−23851.4	+	23851.4i	−0.918365	+	0.918365i	0.0785458	+	0.996911i	$0.474972\pi$
$878$	−21993.1	+	21993.1i	−0.845368	+	0.845368i
$879$	−35386.3	−	35386.3i	−1.35785	−	1.35785i
$880$	38917.6	+	18427.2i	1.49081	+	0.705887i
$881$		−	28494.8i		−	1.08969i	−0.838537	−	0.544844i	$-0.816589\pi$
$881$		−	28494.8i		−	1.08969i	0.838537	−	0.544844i	$-0.183411\pi$
$882$	−7293.76	−	7293.76i	−0.278451	−	0.278451i
$883$			3366.04i			0.128286i	0.997941	+	0.0641428i	$0.0204313\pi$
$883$			3366.04i			0.128286i	−0.997941	+	0.0641428i	$0.979569\pi$
$884$	624.496	−	182.480i	0.0237603	−	0.00694285i
$885$	33041.9			1.25502
$886$	26002.5	−	26002.5i	0.985971	−	0.985971i
$887$			34501.9i			1.30604i	0.757339	+	0.653022i	$0.226499\pi$
$887$			34501.9i			1.30604i	−0.757339	+	0.653022i	$0.773501\pi$
$888$	53416.3			2.01862
$889$	−28632.9	−	28632.9i	−1.08022	−	1.08022i
$890$	−14195.9	+	14195.9i	−0.534660	+	0.534660i
$891$	−30489.3	+	10894.4i	−1.14638	+	0.409625i
$892$	−2150.53	+	2150.53i	−0.0807233	+	0.0807233i
$893$		−	6379.03i		−	0.239044i
$894$		−	1723.45i		−	0.0644751i
$895$	−52452.1	+	52452.1i	−1.95897	+	1.95897i
$896$		−	43282.9i		−	1.61382i
$897$	−29200.6	+	8532.55i	−1.08694	+	0.317607i
$898$		−	4520.89i		−	0.168000i
$899$	26942.5	−	26942.5i	0.999534	−	0.999534i
$900$	824.791			0.0305478
$901$	−6057.83			−0.223991
$902$	902.336	+	2525.29i	0.0333088	+	0.0932185i
$903$	22074.2	+	22074.2i	0.813494	+	0.813494i
$904$	−17485.4	−	17485.4i	−0.643313	−	0.643313i
$905$	−17984.4	+	17984.4i	−0.660578	+	0.660578i
$906$	−41073.6			−1.50616
$907$			8014.50i			0.293404i	0.989181	+	0.146702i	$0.0468658\pi$
$907$			8014.50i			0.293404i	−0.989181	+	0.146702i	$0.953134\pi$
$908$	477.568	+	477.568i	0.0174545	+	0.0174545i
$909$	−9641.33			−0.351796
$910$	−31306.7	+	57155.8i	−1.14045	+	2.08209i
$911$	29347.8			1.06733			0.533664	−	0.845696i	$-0.320815\pi$
$911$	29347.8			1.06733			0.533664	+	0.845696i	$0.320815\pi$
$912$	9439.86	−	9439.86i	0.342747	−	0.342747i
$913$	21708.8	−	45848.2i	0.786918	−	1.66194i
$914$			16561.0i			0.599332i
$915$	27631.2	−	27631.2i	0.998317	−	0.998317i
$916$	−770.673	−	770.673i	−0.0277989	−	0.0277989i
$917$	34794.5	−	34794.5i	1.25302	−	1.25302i
$918$	−5781.98	+	5781.98i	−0.207880	+	0.207880i
$919$			3243.61i			0.116427i	0.998304	+	0.0582137i	$0.0185405\pi$
$919$			3243.61i			0.116427i	−0.998304	+	0.0582137i	$0.981460\pi$
$920$	−41099.6			−1.47284
$921$	−29748.8	−	29748.8i	−1.06434	−	1.06434i
$922$		−	27430.2i		−	0.979790i
$923$	−305.342	+	557.456i	−0.0108889	+	0.0198796i
$924$	1390.96	−	2937.66i	0.0495231	−	0.104591i
$925$	−51035.0	−	51035.0i	−1.81408	−	1.81408i
$926$			4048.47i			0.143673i
$927$			12214.4i			0.432765i
$928$	−2406.11	−	2406.11i	−0.0851126	−	0.0851126i
$929$	−25868.5	−	25868.5i	−0.913582	−	0.913582i	0.0829697	−	0.996552i	$-0.473560\pi$
$929$	−25868.5	−	25868.5i	−0.913582	−	0.913582i	−0.996552	+	0.0829697i	$0.973560\pi$
$930$	58902.6	+	58902.6i	2.07687	+	2.07687i
$931$	9510.57	+	9510.57i	0.334797	+	0.334797i
$932$			70.2935i			0.00247054i
$933$			10031.5i			0.352000i
$934$	−21961.5	−	21961.5i	−0.769383	−	0.769383i
$935$	−14584.1	−	6905.46i	−0.510108	−	0.241532i
$936$	−4231.47	+	7725.29i	−0.147767	+	0.269775i
$937$			26096.5i			0.909856i	0.890528	+	0.454928i	$0.150335\pi$
$937$			26096.5i			0.909856i	−0.890528	+	0.454928i	$0.849665\pi$
$938$	20445.7	+	20445.7i	0.711701	+	0.711701i
$939$	3423.87			0.118992
$940$		−	1831.96i		−	0.0635658i
$941$	−1391.64	+	1391.64i	−0.0482105	+	0.0482105i	−0.730801	−	0.682591i	$-0.760853\pi$
$941$	−1391.64	+	1391.64i	−0.0482105	+	0.0482105i	0.682591	+	0.730801i	$0.260853\pi$
$942$	−21668.8	+	21668.8i	−0.749476	+	0.749476i
$943$	−1933.61	−	1933.61i	−0.0667730	−	0.0667730i
$944$	15362.4	−	15362.4i	0.529665	−	0.529665i
$945$		−	52170.9i		−	1.79589i
$946$	−8703.05	+	18380.5i	−0.299113	+	0.631715i
$947$	9173.54	−	9173.54i	0.314784	−	0.314784i	−0.531976	−	0.846759i	$-0.678550\pi$
$947$	9173.54	−	9173.54i	0.314784	−	0.314784i	0.846759	+	0.531976i	$0.178550\pi$
$948$	2500.05			0.0856518
$949$	−16393.7	+	29929.6i	−0.560762	+	1.02377i
$950$	−16884.1			−0.576623
$951$	−21591.0	−	21591.0i	−0.736210	−	0.736210i
$952$			15244.7i			0.518995i
$953$	3491.04			0.118663			0.0593315	−	0.998238i	$-0.481103\pi$
$953$	3491.04			0.118663			0.0593315	+	0.998238i	$0.481103\pi$
$954$	−4233.26	+	4233.26i	−0.143665	+	0.143665i
$955$	36872.0	+	36872.0i	1.24937	+	1.24937i
$956$	−1723.93	−	1723.93i	−0.0583220	−	0.0583220i
$957$	10139.7	+	28377.2i	0.342497	+	0.958520i
$958$	26541.3			0.895105
$959$	33953.1			1.14328
$960$	−34589.0	+	34589.0i	−1.16287	+	1.16287i
$961$			46012.2i			1.54450i
$962$	−54006.0	+	15780.8i	−1.81000	+	0.528891i
$963$			6401.08i			0.214197i
$964$	1313.26	−	1313.26i	0.0438770	−	0.0438770i
$965$			58397.4i			1.94806i
$966$			52033.8i			1.73308i
$967$	−13184.0	+	13184.0i	−0.438438	+	0.438438i	−0.891486	−	0.453048i	$-0.850337\pi$
$967$	−13184.0	+	13184.0i	−0.438438	+	0.438438i	0.453048	+	0.891486i	$0.350337\pi$
$968$	−28865.1	−	2868.11i	−0.958429	−	0.0952321i
$969$	−3537.52	+	3537.52i	−0.117277	+	0.117277i
$970$	−10381.8	−	10381.8i	−0.343649	−	0.343649i
$971$	−37948.3			−1.25419			−0.627095	−	0.778943i	$-0.715756\pi$
$971$	−37948.3			−1.25419			−0.627095	+	0.778943i	$0.715756\pi$
$972$			1271.00i			0.0419416i
$973$	39766.8	−	39766.8i	1.31024	−	1.31024i
$974$	−53828.6			−1.77082
$975$	47194.2	−	13790.4i	1.55018	−	0.452969i
$976$		−	25693.6i		−	0.842655i
$977$	−26225.8	−	26225.8i	−0.858788	−	0.858788i	0.132407	−	0.991195i	$-0.457729\pi$
$977$	−26225.8	−	26225.8i	−0.858788	−	0.858788i	−0.991195	+	0.132407i	$0.957729\pi$
$978$		−	18600.6i		−	0.608160i
$979$	6183.19	−	13058.7i	0.201855	−	0.426310i
$980$	2731.29	+	2731.29i	0.0890284	+	0.0890284i
$981$	−9514.26	+	9514.26i	−0.309650	+	0.309650i
$982$	−5181.85	+	5181.85i	−0.168391	+	0.168391i
$983$	11589.1	−	11589.1i	0.376026	−	0.376026i	−0.493640	−	0.869666i	$-0.664334\pi$
$983$	11589.1	−	11589.1i	0.376026	−	0.376026i	0.869666	+	0.493640i	$0.164334\pi$
$984$	−3270.93			−0.105969
$985$	20317.1			0.657215
$986$	7295.27	+	7295.27i	0.235627	+	0.235627i
$987$	31773.1			1.02467
$988$	−402.764	+	735.315i	−0.0129693	+	0.0236776i
$989$		−	20737.8i		−	0.666758i
$990$	−15017.1	+	5365.89i	−0.482095	+	0.172262i
$991$	22744.8			0.729074			0.364537	−	0.931189i	$-0.381227\pi$
$991$	22744.8			0.729074			0.364537	+	0.931189i	$0.381227\pi$
$992$	6769.65			0.216670
$993$	25838.9	+	25838.9i	0.825753	+	0.825753i
$994$	768.727	+	768.727i	0.0245297	+	0.0245297i
$995$	−9528.63	+	9528.63i	−0.303596	+	0.303596i
$996$	−3193.76	−	3193.76i	−0.101605	−	0.101605i
$997$			12089.1i			0.384019i	0.981393	+	0.192010i	$0.0615005\pi$
$997$			12089.1i			0.384019i	−0.981393	+	0.192010i	$0.938500\pi$
$998$	145.070			0.00460130
$999$	31850.1	−	31850.1i	1.00870	−	1.00870i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	143.4.g.a.21.11	✓	80
11.10	odd	2	inner	143.4.g.a.21.30	yes	80
13.5	odd	4	inner	143.4.g.a.109.30	yes	80
143.109	even	4	inner	143.4.g.a.109.11	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.g.a.21.11	✓	80	1.1	even	1	trivial
143.4.g.a.21.30	yes	80	11.10	odd	2	inner
143.4.g.a.109.11	yes	80	143.109	even	4	inner
143.4.g.a.109.30	yes	80	13.5	odd	4	inner

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:	\( N \)	\(=\)	\( 143 = 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	143.g (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.06691 + 2.06691i) q^{2} +5.96848 q^{3} -0.544246i q^{4} +(12.2628 + 12.2628i) q^{5} +(-12.3363 + 12.3363i) q^{6} +(19.3939 + 19.3939i) q^{7} +(-15.4104 - 15.4104i) q^{8} +8.62277 q^{9} +O(q^{10})\)	\(q+(-2.06691 + 2.06691i) q^{2} +5.96848 q^{3} -0.544246i q^{4} +(12.2628 + 12.2628i) q^{5} +(-12.3363 + 12.3363i) q^{6} +(19.3939 + 19.3939i) q^{7} +(-15.4104 - 15.4104i) q^{8} +8.62277 q^{9} -50.6922 q^{10} +(34.3555 - 12.2759i) q^{11} -3.24832i q^{12} +(-13.1465 - 44.9908i) q^{13} -80.1708 q^{14} +(73.1903 + 73.1903i) q^{15} +68.0578 q^{16} -25.5042 q^{17} +(-17.8225 + 17.8225i) q^{18} +(23.2393 - 23.2393i) q^{19} +(6.67398 - 6.67398i) q^{20} +(115.752 + 115.752i) q^{21} +(-45.6367 + 96.3830i) q^{22} -108.744i q^{23} +(-91.9766 - 91.9766i) q^{24} +175.753i q^{25} +(120.165 + 65.8193i) q^{26} -109.684 q^{27} +(10.5550 - 10.5550i) q^{28} +138.391i q^{29} -302.556 q^{30} +(-194.683 - 194.683i) q^{31} +(-17.3863 + 17.3863i) q^{32} +(205.050 - 73.2684i) q^{33} +(52.7148 - 52.7148i) q^{34} +475.646i q^{35} -4.69291i q^{36} +(-290.380 + 290.380i) q^{37} +96.0673i q^{38} +(-78.4647 - 268.527i) q^{39} -377.949i q^{40} +(17.7813 - 17.7813i) q^{41} -478.498 q^{42} +190.703 q^{43} +(-6.68110 - 18.6979i) q^{44} +(105.739 + 105.739i) q^{45} +(224.764 + 224.764i) q^{46} +(137.246 - 137.246i) q^{47} +406.202 q^{48} +409.244i q^{49} +(-363.265 - 363.265i) q^{50} -152.221 q^{51} +(-24.4860 + 7.15493i) q^{52} +237.523 q^{53} +(226.707 - 226.707i) q^{54} +(571.832 + 270.758i) q^{55} -597.734i q^{56} +(138.704 - 138.704i) q^{57} +(-286.042 - 286.042i) q^{58} +(225.726 - 225.726i) q^{59} +(39.8335 - 39.8335i) q^{60} -377.526i q^{61} +804.787 q^{62} +(167.229 + 167.229i) q^{63} +472.590i q^{64} +(390.500 - 712.926i) q^{65} +(-272.382 + 575.260i) q^{66} +(-255.027 - 255.027i) q^{67} +13.8805i q^{68} -649.036i q^{69} +(-983.119 - 983.119i) q^{70} +(-9.58861 - 9.58861i) q^{71} +(-132.880 - 132.880i) q^{72} +(-514.810 - 514.810i) q^{73} -1200.38i q^{74} +1048.98i q^{75} +(-12.6479 - 12.6479i) q^{76} +(904.364 + 428.210i) q^{77} +(717.200 + 392.841i) q^{78} +769.644i q^{79} +(834.579 + 834.579i) q^{80} -887.463 q^{81} +73.5047i q^{82} +(983.204 - 983.204i) q^{83} +(62.9975 - 62.9975i) q^{84} +(-312.752 - 312.752i) q^{85} +(-394.166 + 394.166i) q^{86} +825.985i q^{87} +(-718.608 - 340.256i) q^{88} +(280.040 - 280.040i) q^{89} -437.108 q^{90} +(617.584 - 1127.51i) q^{91} -59.1834 q^{92} +(-1161.96 - 1161.96i) q^{93} +567.352i q^{94} +569.959 q^{95} +(-103.770 + 103.770i) q^{96} +(204.800 + 204.800i) q^{97} +(-845.872 - 845.872i) q^{98} +(296.240 - 105.852i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 8 q^{3} - 4 q^{5} + 640 q^{9}+O(q^{10}) \) 80 * q - 8 * q^3 - 4 * q^5 + 640 * q^9	\( 80 q - 8 q^{3} - 4 q^{5} + 640 q^{9} + 14 q^{11} + 280 q^{14} - 80 q^{15} - 952 q^{16} - 200 q^{20} - 424 q^{22} - 508 q^{26} - 848 q^{27} + 208 q^{31} + 860 q^{33} - 232 q^{34} - 340 q^{37} + 1308 q^{42} - 644 q^{44} - 1148 q^{45} - 280 q^{47} + 2420 q^{48} + 2976 q^{53} + 1652 q^{55} - 1972 q^{58} - 84 q^{59} + 1484 q^{60} - 4924 q^{66} + 2468 q^{67} - 3540 q^{70} + 1704 q^{71} + 2368 q^{78} - 3544 q^{80} + 6160 q^{81} + 32 q^{86} + 424 q^{89} - 5868 q^{91} - 164 q^{92} + 3944 q^{93} - 4936 q^{97} - 3750 q^{99}+O(q^{100}) \) 80 * q - 8 * q^3 - 4 * q^5 + 640 * q^9 + 14 * q^11 + 280 * q^14 - 80 * q^15 - 952 * q^16 - 200 * q^20 - 424 * q^22 - 508 * q^26 - 848 * q^27 + 208 * q^31 + 860 * q^33 - 232 * q^34 - 340 * q^37 + 1308 * q^42 - 644 * q^44 - 1148 * q^45 - 280 * q^47 + 2420 * q^48 + 2976 * q^53 + 1652 * q^55 - 1972 * q^58 - 84 * q^59 + 1484 * q^60 - 4924 * q^66 + 2468 * q^67 - 3540 * q^70 + 1704 * q^71 + 2368 * q^78 - 3544 * q^80 + 6160 * q^81 + 32 * q^86 + 424 * q^89 - 5868 * q^91 - 164 * q^92 + 3944 * q^93 - 4936 * q^97 - 3750 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more