LMFDB - Embedded newform 1050.3.e.e.701.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1050,3,Mod(701,1050)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1050, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 0]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("1050.701");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	1050.e (of order $2$, degree $1$, 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:	$28.6104277578$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	no (minimal twist has level 210)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			701.20
Character	$\chi$	$=$	1050.701
Dual form			1050.3.e.e.701.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.41421i q^{2} +(2.79991 + 1.07726i) q^{3} -2.00000 q^{4} +(-1.52347 + 3.95968i) q^{6} -2.64575 q^{7} -2.82843i q^{8} +(6.67904 + 6.03245i) q^{9} +O(q^{10})$	\(q+1.41421i q^{2} +(2.79991 + 1.07726i) q^{3} -2.00000 q^{4} +(-1.52347 + 3.95968i) q^{6} -2.64575 q^{7} -2.82843i q^{8} +(6.67904 + 6.03245i) q^{9} -5.98577i q^{11} +(-5.59983 - 2.15451i) q^{12} +19.0169 q^{13} -3.74166i q^{14} +4.00000 q^{16} -2.02915i q^{17} +(-8.53117 + 9.44559i) q^{18} +21.1068 q^{19} +(-7.40788 - 2.85015i) q^{21} +8.46515 q^{22} -32.2716i q^{23} +(3.04694 - 7.91935i) q^{24} +26.8940i q^{26} +(12.2023 + 24.0854i) q^{27} +5.29150 q^{28} +12.2603i q^{29} +39.3082 q^{31} +5.65685i q^{32} +(6.44820 - 16.7596i) q^{33} +2.86965 q^{34} +(-13.3581 - 12.0649i) q^{36} -20.3241 q^{37} +29.8495i q^{38} +(53.2458 + 20.4861i) q^{39} -34.7183i q^{41} +(4.03072 - 10.4763i) q^{42} -40.3307 q^{43} +11.9715i q^{44} +45.6389 q^{46} +72.4398i q^{47} +(11.1997 + 4.30902i) q^{48} +7.00000 q^{49} +(2.18591 - 5.68144i) q^{51} -38.0339 q^{52} +57.5848i q^{53} +(-34.0619 + 17.2566i) q^{54} +7.48331i q^{56} +(59.0972 + 22.7374i) q^{57} -17.3387 q^{58} +71.7934i q^{59} +81.7294 q^{61} +55.5902i q^{62} +(-17.6711 - 15.9604i) q^{63} -8.00000 q^{64} +(23.7017 + 9.11913i) q^{66} +81.7131 q^{67} +4.05830i q^{68} +(34.7647 - 90.3576i) q^{69} +7.70229i q^{71} +(17.0623 - 18.8912i) q^{72} +12.0694 q^{73} -28.7427i q^{74} -42.2136 q^{76} +15.8369i q^{77} +(-28.9717 + 75.3009i) q^{78} -131.622 q^{79} +(8.21915 + 80.5819i) q^{81} +49.0991 q^{82} +115.864i q^{83} +(14.8158 + 5.70030i) q^{84} -57.0363i q^{86} +(-13.2075 + 34.3277i) q^{87} -16.9303 q^{88} -101.939i q^{89} -50.3141 q^{91} +64.5431i q^{92} +(110.060 + 42.3450i) q^{93} -102.445 q^{94} +(-6.09388 + 15.8387i) q^{96} +8.19281 q^{97} +9.89949i q^{98} +(36.1088 - 39.9792i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 48 q^{4} - 44 q^{9}+O(q^{10}) $ 24 * q - 48 * q^4 - 44 * q^9	$ 24 q - 48 q^{4} - 44 q^{9} + 96 q^{16} + 80 q^{19} - 28 q^{21} + 224 q^{31} - 128 q^{34} + 88 q^{36} + 92 q^{39} - 144 q^{46} + 168 q^{49} - 284 q^{51} + 144 q^{54} - 192 q^{64} + 224 q^{66} + 152 q^{69} - 160 q^{76} + 72 q^{79} - 212 q^{81} + 56 q^{84} + 168 q^{91} + 128 q^{94} + 876 q^{99}+O(q^{100}) $ 24 * q - 48 * q^4 - 44 * q^9 + 96 * q^16 + 80 * q^19 - 28 * q^21 + 224 * q^31 - 128 * q^34 + 88 * q^36 + 92 * q^39 - 144 * q^46 + 168 * q^49 - 284 * q^51 + 144 * q^54 - 192 * q^64 + 224 * q^66 + 152 * q^69 - 160 * q^76 + 72 * q^79 - 212 * q^81 + 56 * q^84 + 168 * q^91 + 128 * q^94 + 876 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times$.

$n$	$127$	$451$	$701$
$\chi(n)$	$1$	$1$	$-1$

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 $

$2$			1.41421i			0.707107i
$2$			1.41421i			0.707107i
$3$	2.79991	+	1.07726i	0.933305	+	0.359085i
$3$	2.79991	+	1.07726i	0.933305	+	0.359085i
$4$	−2.00000			−0.500000
$5$		0			0
$5$		0			0
$6$	−1.52347	+	3.95968i	−0.253912	+	0.659946i
$7$	−2.64575			−0.377964
$7$	−2.64575			−0.377964
$8$		−	2.82843i		−	0.353553i
$9$	6.67904	+	6.03245i	0.742116	+	0.670272i
$10$		0			0
$11$		−	5.98577i		−	0.544161i	−0.962275	−	0.272080i	$-0.912288\pi$
$11$		−	5.98577i		−	0.544161i	0.962275	−	0.272080i	$-0.0877116\pi$
$12$	−5.59983	−	2.15451i	−0.466652	−	0.179543i
$13$	19.0169			1.46284			0.731421	−	0.681926i	$-0.238858\pi$
$13$	19.0169			1.46284			0.731421	+	0.681926i	$0.238858\pi$
$14$		−	3.74166i		−	0.267261i
$15$		0			0
$16$	4.00000			0.250000
$17$		−	2.02915i		−	0.119362i	−0.998218	−	0.0596809i	$-0.980992\pi$
$17$		−	2.02915i		−	0.119362i	0.998218	−	0.0596809i	$-0.0190083\pi$
$18$	−8.53117	+	9.44559i	−0.473954	+	0.524755i
$19$	21.1068			1.11088			0.555442	−	0.831556i	$-0.312549\pi$
$19$	21.1068			1.11088			0.555442	+	0.831556i	$0.312549\pi$
$20$		0			0
$21$	−7.40788	−	2.85015i	−0.352756	−	0.135721i
$22$	8.46515			0.384780
$23$		−	32.2716i		−	1.40311i	−0.712615	−	0.701555i	$-0.752489\pi$
$23$		−	32.2716i		−	1.40311i	0.712615	−	0.701555i	$-0.247511\pi$
$24$	3.04694	−	7.91935i	0.126956	−	0.329973i
$25$		0			0
$26$			26.8940i			1.03439i
$27$	12.2023	+	24.0854i	0.451935	+	0.892051i
$28$	5.29150			0.188982
$29$			12.2603i			0.422768i	0.977403	+	0.211384i	$0.0677971\pi$
$29$			12.2603i			0.422768i	−0.977403	+	0.211384i	$0.932203\pi$
$30$		0			0
$31$	39.3082			1.26801			0.634004	−	0.773330i	$-0.281410\pi$
$31$	39.3082			1.26801			0.634004	+	0.773330i	$0.281410\pi$
$32$			5.65685i			0.176777i
$33$	6.44820	−	16.7596i	0.195400	−	0.507868i
$34$	2.86965			0.0844015
$35$		0			0
$36$	−13.3581	−	12.0649i	−0.371058	−	0.335136i
$37$	−20.3241			−0.549301			−0.274650	−	0.961544i	$-0.588562\pi$
$37$	−20.3241			−0.549301			−0.274650	+	0.961544i	$0.588562\pi$
$38$			29.8495i			0.785513i
$39$	53.2458	+	20.4861i	1.36528	+	0.525285i
$40$		0			0
$41$		−	34.7183i		−	0.846788i	−0.905946	−	0.423394i	$-0.860839\pi$
$41$		−	34.7183i		−	0.846788i	0.905946	−	0.423394i	$-0.139161\pi$
$42$	4.03072	−	10.4763i	0.0959696	−	0.249436i
$43$	−40.3307			−0.937924			−0.468962	−	0.883218i	$-0.655372\pi$
$43$	−40.3307			−0.937924			−0.468962	+	0.883218i	$0.655372\pi$
$44$			11.9715i			0.272080i
$45$		0			0
$46$	45.6389			0.992149
$47$			72.4398i			1.54127i	0.637275	+	0.770636i	$0.280061\pi$
$47$			72.4398i			1.54127i	−0.637275	+	0.770636i	$0.719939\pi$
$48$	11.1997	+	4.30902i	0.233326	+	0.0897713i
$49$	7.00000			0.142857
$50$		0			0
$51$	2.18591	−	5.68144i	0.0428610	−	0.111401i
$52$	−38.0339			−0.731421
$53$			57.5848i			1.08651i	0.839569	+	0.543253i	$0.182807\pi$
$53$			57.5848i			1.08651i	−0.839569	+	0.543253i	$0.817193\pi$
$54$	−34.0619	+	17.2566i	−0.630775	+	0.319566i
$55$		0			0
$56$			7.48331i			0.133631i
$57$	59.0972	+	22.7374i	1.03679	+	0.398902i
$58$	−17.3387			−0.298942
$59$			71.7934i			1.21684i	0.793616	+	0.608419i	$0.208196\pi$
$59$			71.7934i			1.21684i	−0.793616	+	0.608419i	$0.791804\pi$
$60$		0			0
$61$	81.7294			1.33983			0.669913	−	0.742439i	$-0.266331\pi$
$61$	81.7294			1.33983			0.669913	+	0.742439i	$0.266331\pi$
$62$			55.5902i			0.896617i
$63$	−17.6711	−	15.9604i	−0.280493	−	0.253339i
$64$	−8.00000			−0.125000
$65$		0			0
$66$	23.7017	+	9.11913i	0.359117	+	0.138169i
$67$	81.7131			1.21960			0.609799	−	0.792556i	$-0.291250\pi$
$67$	81.7131			1.21960			0.609799	+	0.792556i	$0.291250\pi$
$68$			4.05830i			0.0596809i
$69$	34.7647	−	90.3576i	0.503836	−	1.30953i
$70$		0			0
$71$			7.70229i			0.108483i	0.998528	+	0.0542415i	$0.0172741\pi$
$71$			7.70229i			0.108483i	−0.998528	+	0.0542415i	$0.982726\pi$
$72$	17.0623	−	18.8912i	0.236977	−	0.262377i
$73$	12.0694			0.165334			0.0826671	−	0.996577i	$-0.473656\pi$
$73$	12.0694			0.165334			0.0826671	+	0.996577i	$0.473656\pi$
$74$		−	28.7427i		−	0.388414i
$75$		0			0
$76$	−42.2136			−0.555442
$77$			15.8369i			0.205673i
$78$	−28.9717	+	75.3009i	−0.371433	+	0.965397i
$79$	−131.622			−1.66610			−0.833049	−	0.553199i	$-0.813407\pi$
$79$	−131.622			−1.66610			−0.833049	+	0.553199i	$0.813407\pi$
$80$		0			0
$81$	8.21915	+	80.5819i	0.101471	+	0.994838i
$82$	49.0991			0.598769
$83$			115.864i			1.39596i	0.716119	+	0.697978i	$0.245917\pi$
$83$			115.864i			1.39596i	−0.716119	+	0.697978i	$0.754083\pi$
$84$	14.8158	+	5.70030i	0.176378	+	0.0678607i
$85$		0			0
$86$		−	57.0363i		−	0.663212i
$87$	−13.2075	+	34.3277i	−0.151810	+	0.394572i
$88$	−16.9303			−0.192390
$89$		−	101.939i		−	1.14538i	−0.819771	−	0.572692i	$-0.805899\pi$
$89$		−	101.939i		−	1.14538i	0.819771	−	0.572692i	$-0.194101\pi$
$90$		0			0
$91$	−50.3141			−0.552902
$92$			64.5431i			0.701555i
$93$	110.060	+	42.3450i	1.18344	+	0.455323i
$94$	−102.445			−1.08984
$95$		0			0
$96$	−6.09388	+	15.8387i	−0.0634779	+	0.164987i
$97$	8.19281			0.0844619			0.0422310	−	0.999108i	$-0.486553\pi$
$97$	8.19281			0.0844619			0.0422310	+	0.999108i	$0.486553\pi$
$98$			9.89949i			0.101015i
$99$	36.1088	−	39.9792i	0.364736	−	0.403830i
$100$		0			0
$101$		−	136.484i		−	1.35133i	−0.737208	−	0.675665i	$-0.763856\pi$
$101$		−	136.484i		−	1.35133i	0.737208	−	0.675665i	$-0.236144\pi$
$102$	8.03477	+	3.09135i	0.0787723	+	0.0303073i
$103$	129.191			1.25428			0.627142	−	0.778905i	$-0.284224\pi$
$103$	129.191			1.25428			0.627142	+	0.778905i	$0.284224\pi$
$104$		−	53.7880i		−	0.517193i
$105$		0			0
$106$	−81.4372			−0.768275
$107$			20.2629i			0.189373i	0.995507	+	0.0946866i	$0.0301849\pi$
$107$			20.2629i			0.189373i	−0.995507	+	0.0946866i	$0.969815\pi$
$108$	−24.4045	−	48.1707i	−0.225968	−	0.446025i
$109$	112.569			1.03275			0.516373	−	0.856364i	$-0.327282\pi$
$109$	112.569			1.03275			0.516373	+	0.856364i	$0.327282\pi$
$110$		0			0
$111$	−56.9058	−	21.8943i	−0.512665	−	0.197246i
$112$	−10.5830			−0.0944911
$113$		−	6.53779i		−	0.0578565i	−0.999581	−	0.0289283i	$-0.990791\pi$
$113$		−	6.53779i		−	0.0578565i	0.999581	−	0.0289283i	$-0.00920944\pi$
$114$	−32.1555	+	83.5760i	−0.282066	+	0.733123i
$115$		0			0
$116$		−	24.5206i		−	0.211384i
$117$	127.015	+	114.719i	1.08560	+	0.980502i
$118$	−101.531			−0.860434
$119$			5.36862i			0.0451145i
$120$		0			0
$121$	85.1706			0.703889
$122$			115.583i			0.947400i
$123$	37.4005	−	97.2082i	0.304069	−	0.790311i
$124$	−78.6165			−0.634004
$125$		0			0
$126$	22.5714	−	24.9907i	0.179138	−	0.198339i
$127$	−15.0411			−0.118434			−0.0592170	−	0.998245i	$-0.518860\pi$
$127$	−15.0411			−0.118434			−0.0592170	+	0.998245i	$0.518860\pi$
$128$		−	11.3137i		−	0.0883883i
$129$	−112.923	−	43.4465i	−0.875369	−	0.336795i
$130$		0			0
$131$		−	51.5923i		−	0.393834i	−0.980420	−	0.196917i	$-0.936907\pi$
$131$		−	51.5923i		−	0.393834i	0.980420	−	0.196917i	$-0.0630930\pi$
$132$	−12.8964	+	33.5193i	−0.0977000	+	0.253934i
$133$	−55.8433			−0.419874
$134$			115.560i			0.862386i
$135$		0			0
$136$	−5.73930			−0.0422007
$137$		−	47.5888i		−	0.347364i	−0.984802	−	0.173682i	$-0.944434\pi$
$137$		−	47.5888i		−	0.347364i	0.984802	−	0.173682i	$-0.0555664\pi$
$138$	127.785	+	49.1647i	0.925978	+	0.356266i
$139$	117.730			0.846975			0.423488	−	0.905902i	$-0.360806\pi$
$139$	117.730			0.846975			0.423488	+	0.905902i	$0.360806\pi$
$140$		0			0
$141$	−78.0362	+	202.825i	−0.553448	+	1.43848i
$142$	−10.8927			−0.0767091
$143$		−	113.831i		−	0.796021i
$144$	26.7162	+	24.1298i	0.185529	+	0.167568i
$145$		0			0
$146$			17.0687i			0.116909i
$147$	19.5994	+	7.54079i	0.133329	+	0.0512979i
$148$	40.6483			0.274650
$149$		−	186.336i		−	1.25057i	−0.780395	−	0.625287i	$-0.784982\pi$
$149$		−	186.336i		−	1.25057i	0.780395	−	0.625287i	$-0.215018\pi$
$150$		0			0
$151$	−183.560			−1.21563			−0.607816	−	0.794078i	$-0.707954\pi$
$151$	−183.560			−1.21563			−0.607816	+	0.794078i	$0.707954\pi$
$152$		−	59.6990i		−	0.392756i
$153$	12.2407	−	13.5528i	0.0800048	−	0.0885802i
$154$	−22.3967			−0.145433
$155$		0			0
$156$	−106.492	−	40.9722i	−0.682639	−	0.262642i
$157$	−264.877			−1.68712			−0.843558	−	0.537038i	$-0.819543\pi$
$157$	−264.877			−1.68712			−0.843558	+	0.537038i	$0.819543\pi$
$158$		−	186.141i		−	1.17811i
$159$	−62.0335	+	161.232i	−0.390148	+	1.01404i
$160$		0			0
$161$			85.3825i			0.530326i
$162$	−113.960	+	11.6236i	−0.703457	+	0.0717508i
$163$	−214.877			−1.31826			−0.659132	−	0.752027i	$-0.729076\pi$
$163$	−214.877			−1.31826			−0.659132	+	0.752027i	$0.729076\pi$
$164$			69.4366i			0.423394i
$165$		0			0
$166$	−163.857			−0.987090
$167$		−	54.5954i		−	0.326919i	−0.986550	−	0.163459i	$-0.947735\pi$
$167$		−	54.5954i		−	0.326919i	0.986550	−	0.163459i	$-0.0522653\pi$
$168$	−8.06144	+	20.9526i	−0.0479848	+	0.124718i
$169$	192.644			1.13991
$170$		0			0
$171$	140.973	+	127.326i	0.824404	+	0.744594i
$172$	80.6615			0.468962
$173$			310.651i			1.79567i	0.440334	+	0.897834i	$0.354860\pi$
$173$			310.651i			1.79567i	−0.440334	+	0.897834i	$0.645140\pi$
$174$	−48.5468	−	18.6782i	−0.279004	−	0.107346i
$175$		0			0
$176$		−	23.9431i		−	0.136040i
$177$	−77.3399	+	201.015i	−0.436949	+	1.13568i
$178$	144.164			0.809909
$179$		−	162.922i		−	0.910181i	−0.890445	−	0.455090i	$-0.849607\pi$
$179$		−	162.922i		−	0.910181i	0.890445	−	0.455090i	$-0.150393\pi$
$180$		0			0
$181$	−51.5088			−0.284579			−0.142289	−	0.989825i	$-0.545446\pi$
$181$	−51.5088			−0.284579			−0.142289	+	0.989825i	$0.545446\pi$
$182$		−	71.1549i		−	0.390961i
$183$	228.835	+	88.0435i	1.25047	+	0.481112i
$184$	−91.2777			−0.496075
$185$		0			0
$186$	−59.8849	+	155.648i	−0.321962	+	0.836817i
$187$	−12.1460			−0.0649519
$188$		−	144.880i		−	0.770636i
$189$	−32.2841	−	63.7239i	−0.170815	−	0.337163i
$190$		0			0
$191$		−	227.310i		−	1.19011i	−0.803687	−	0.595053i	$-0.797131\pi$
$191$		−	227.310i		−	1.19011i	0.803687	−	0.595053i	$-0.202869\pi$
$192$	−22.3993	−	8.61805i	−0.116663	−	0.0448857i
$193$	−239.861			−1.24280			−0.621401	−	0.783493i	$-0.713436\pi$
$193$	−239.861			−1.24280			−0.621401	+	0.783493i	$0.713436\pi$
$194$			11.5864i			0.0597236i
$195$		0			0
$196$	−14.0000			−0.0714286
$197$			184.116i			0.934599i	0.884099	+	0.467300i	$0.154773\pi$
$197$			184.116i			0.934599i	−0.884099	+	0.467300i	$0.845227\pi$
$198$	56.5391	+	51.0656i	0.285551	+	0.257907i
$199$	215.792			1.08438			0.542190	−	0.840256i	$-0.317595\pi$
$199$	215.792			1.08438			0.542190	+	0.840256i	$0.317595\pi$
$200$		0			0
$201$	228.790	+	88.0259i	1.13826	+	0.437940i
$202$	193.018			0.955535
$203$		−	32.4377i		−	0.159791i
$204$	−4.37182	+	11.3629i	−0.0214305	+	0.0557004i
$205$		0			0
$206$			182.704i			0.886913i
$207$	194.676	−	215.543i	0.940466	−	1.04127i
$208$	76.0678			0.365710
$209$		−	126.340i		−	0.604499i
$210$		0			0
$211$	−122.387			−0.580031			−0.290015	−	0.957022i	$-0.593660\pi$
$211$	−122.387			−0.580031			−0.290015	+	0.957022i	$0.593660\pi$
$212$		−	115.170i		−	0.543253i
$213$	−8.29734	+	21.5658i	−0.0389546	+	0.101248i
$214$	−28.6561			−0.133907
$215$		0			0
$216$	68.1237	−	34.5132i	0.315388	−	0.159783i
$217$	−104.000			−0.479262
$218$			159.197i			0.730262i
$219$	33.7933	+	13.0018i	0.154307	+	0.0593690i
$220$		0			0
$221$		−	38.5882i		−	0.174607i
$222$	30.9632	−	80.4770i	0.139474	−	0.362509i
$223$	−70.1315			−0.314491			−0.157245	−	0.987560i	$-0.550261\pi$
$223$	−70.1315			−0.314491			−0.157245	+	0.987560i	$0.550261\pi$
$224$		−	14.9666i		−	0.0668153i
$225$		0			0
$226$	9.24583			0.0409108
$227$			31.4277i			0.138448i	0.997601	+	0.0692240i	$0.0220523\pi$
$227$			31.4277i			0.138448i	−0.997601	+	0.0692240i	$0.977948\pi$
$228$	−118.194	−	45.4748i	−0.518396	−	0.199451i
$229$	−35.7207			−0.155986			−0.0779928	−	0.996954i	$-0.524851\pi$
$229$	−35.7207			−0.155986			−0.0779928	+	0.996954i	$0.524851\pi$
$230$		0			0
$231$	−17.0603	+	44.3418i	−0.0738543	+	0.191956i
$232$	34.6773			0.149471
$233$		−	324.542i		−	1.39288i	−0.717613	−	0.696442i	$-0.754765\pi$
$233$		−	324.542i		−	1.39288i	0.717613	−	0.696442i	$-0.245235\pi$
$234$	−162.237	+	179.626i	−0.693319	+	0.767633i
$235$		0			0
$236$		−	143.587i		−	0.608419i
$237$	−368.530	−	141.790i	−1.55498	−	0.598271i
$238$	−7.59238			−0.0319008
$239$			400.039i			1.67380i	0.547353	+	0.836902i	$0.315636\pi$
$239$			400.039i			1.67380i	−0.547353	+	0.836902i	$0.684364\pi$
$240$		0			0
$241$	396.305			1.64442			0.822209	−	0.569185i	$-0.192741\pi$
$241$	396.305			1.64442			0.822209	+	0.569185i	$0.192741\pi$
$242$			120.449i			0.497725i
$243$	−63.7944	+	234.477i	−0.262528	+	0.964924i
$244$	−163.459			−0.669913
$245$		0			0
$246$	137.473	+	52.8923i	0.558834	+	0.215009i
$247$	401.386			1.62505
$248$		−	111.180i		−	0.448308i
$249$	−124.816	+	324.410i	−0.501267	+	1.30285i
$250$		0			0
$251$		−	221.226i		−	0.881377i	−0.897660	−	0.440688i	$-0.854734\pi$
$251$		−	221.226i		−	0.881377i	0.897660	−	0.440688i	$-0.145266\pi$
$252$	35.3422	+	31.9207i	0.140247	+	0.126669i
$253$	−193.170			−0.763518
$254$		−	21.2714i		−	0.0837455i
$255$		0			0
$256$	16.0000			0.0625000
$257$		−	203.815i		−	0.793055i	−0.918023	−	0.396528i	$-0.870215\pi$
$257$		−	203.815i		−	0.793055i	0.918023	−	0.396528i	$-0.129785\pi$
$258$	61.4426	−	159.697i	0.238150	−	0.618979i
$259$	53.7726			0.207616
$260$		0			0
$261$	−73.9595	+	81.8869i	−0.283370	+	0.313743i
$262$	72.9625			0.278483
$263$		−	98.2019i		−	0.373391i	−0.982418	−	0.186696i	$-0.940222\pi$
$263$		−	98.2019i		−	0.373391i	0.982418	−	0.186696i	$-0.0597778\pi$
$264$	−47.4034	−	18.2383i	−0.179558	−	0.0690844i
$265$		0			0
$266$		−	78.9743i		−	0.296896i
$267$	109.815	−	285.421i	0.411290	−	1.06899i
$268$	−163.426			−0.609799
$269$			308.644i			1.14738i	0.819074	+	0.573688i	$0.194488\pi$
$269$			308.644i			1.14738i	−0.819074	+	0.573688i	$0.805512\pi$
$270$		0			0
$271$	−398.841			−1.47174			−0.735870	−	0.677123i	$-0.763226\pi$
$271$	−398.841			−1.47174			−0.735870	+	0.677123i	$0.763226\pi$
$272$		−	8.11660i		−	0.0298404i
$273$	−140.875	−	54.2012i	−0.516026	−	0.198539i
$274$	67.3007			0.245623
$275$		0			0
$276$	−69.5294	+	180.715i	−0.251918	+	0.654765i
$277$	−79.7207			−0.287800			−0.143900	−	0.989592i	$-0.545964\pi$
$277$	−79.7207			−0.287800			−0.143900	+	0.989592i	$0.545964\pi$
$278$			166.495i			0.598902i
$279$	262.541	+	237.125i	0.941008	+	0.849910i
$280$		0			0
$281$		−	210.169i		−	0.747934i	−0.927442	−	0.373967i	$-0.877997\pi$
$281$		−	210.169i		−	0.747934i	0.927442	−	0.373967i	$-0.122003\pi$
$282$	−286.838	−	110.360i	−1.01716	−	0.391347i
$283$	−262.941			−0.929120			−0.464560	−	0.885542i	$-0.653787\pi$
$283$	−262.941			−0.929120			−0.464560	+	0.885542i	$0.653787\pi$
$284$		−	15.4046i		−	0.0542415i
$285$		0			0
$286$	160.981			0.562872
$287$			91.8560i			0.320056i
$288$	−34.1247	+	37.7824i	−0.118488	+	0.131189i
$289$	284.883			0.985753
$290$		0			0
$291$	22.9392	+	8.82575i	0.0788287	+	0.0303290i
$292$	−24.1388			−0.0826671
$293$			357.570i			1.22037i	0.792257	+	0.610187i	$0.208906\pi$
$293$			357.570i			1.22037i	−0.792257	+	0.610187i	$0.791094\pi$
$294$	−10.6643	+	27.7177i	−0.0362731	+	0.0942780i
$295$		0			0
$296$			57.4853i			0.194207i
$297$	144.169	−	73.0398i	0.485419	−	0.245925i
$298$	263.518			0.884290
$299$		−	613.706i		−	2.05253i
$300$		0			0
$301$	106.705			0.354502
$302$		−	259.593i		−	0.859581i
$303$	147.029	−	382.145i	0.485243	−	1.26120i
$304$	84.4271			0.277721
$305$		0			0
$306$	19.1665	+	17.3110i	0.0626356	+	0.0565719i
$307$	−293.405			−0.955717			−0.477858	−	0.878437i	$-0.658587\pi$
$307$	−293.405			−0.955717			−0.477858	+	0.878437i	$0.658587\pi$
$308$		−	31.6737i		−	0.102837i
$309$	361.725	+	139.172i	1.17063	+	0.450395i
$310$		0			0
$311$		−	59.2465i		−	0.190503i	−0.995453	−	0.0952517i	$-0.969634\pi$
$311$		−	59.2465i		−	0.190503i	0.995453	−	0.0952517i	$-0.0303656\pi$
$312$	57.9435	−	150.602i	0.185716	−	0.482698i
$313$	450.587			1.43957			0.719787	−	0.694195i	$-0.244239\pi$
$313$	450.587			1.43957			0.719787	+	0.694195i	$0.244239\pi$
$314$		−	374.593i		−	1.19297i
$315$		0			0
$316$	263.243			0.833049
$317$		−	277.454i		−	0.875249i	−0.899158	−	0.437624i	$-0.855820\pi$
$317$		−	277.454i		−	0.875249i	0.899158	−	0.437624i	$-0.144180\pi$
$318$	−228.017	−	87.7287i	−0.717035	−	0.275876i
$319$	73.3872			0.230054
$320$		0			0
$321$	−21.8284	+	56.7345i	−0.0680011	+	0.176743i
$322$	−120.749			−0.374997
$323$		−	42.8288i		−	0.132597i
$324$	−16.4383	−	161.164i	−0.0507355	−	0.497419i
$325$		0			0
$326$		−	303.882i		−	0.932153i
$327$	315.185	+	121.266i	0.963867	+	0.370844i
$328$	−98.1982			−0.299385
$329$		−	191.658i		−	0.582546i
$330$		0			0
$331$	275.898			0.833529			0.416764	−	0.909015i	$-0.363164\pi$
$331$	275.898			0.833529			0.416764	+	0.909015i	$0.363164\pi$
$332$		−	231.729i		−	0.697978i
$333$	−135.746	−	122.604i	−0.407645	−	0.368181i
$334$	77.2096			0.231166
$335$		0			0
$336$	−29.6315	−	11.4006i	−0.0881890	−	0.0339304i
$337$	−102.798			−0.305038			−0.152519	−	0.988301i	$-0.548739\pi$
$337$	−102.798			−0.305038			−0.152519	+	0.988301i	$0.548739\pi$
$338$			272.440i			0.806035i
$339$	7.04287	−	18.3053i	0.0207754	−	0.0539978i
$340$		0			0
$341$		−	235.290i		−	0.690000i
$342$	−180.066	+	199.366i	−0.526507	+	0.582941i
$343$	−18.5203			−0.0539949
$344$			114.073i			0.331606i
$345$		0			0
$346$	−439.326			−1.26973
$347$		−	456.590i		−	1.31582i	−0.753096	−	0.657910i	$-0.771441\pi$
$347$		−	456.590i		−	1.31582i	0.753096	−	0.657910i	$-0.228559\pi$
$348$	26.4149	−	68.6555i	0.0759049	−	0.197286i
$349$	−570.605			−1.63497			−0.817486	−	0.575948i	$-0.804633\pi$
$349$	−570.605			−1.63497			−0.817486	+	0.575948i	$0.804633\pi$
$350$		0			0
$351$	232.050	+	458.030i	0.661110	+	1.30493i
$352$	33.8606			0.0961949
$353$			4.74525i			0.0134426i	0.999977	+	0.00672132i	$0.00213948\pi$
$353$			4.74525i			0.0134426i	−0.999977	+	0.00672132i	$0.997861\pi$
$354$	−284.279	−	109.375i	−0.803048	−	0.308969i
$355$		0			0
$356$			203.878i			0.572692i
$357$	−5.78338	+	15.0317i	−0.0161999	+	0.0421056i
$358$	230.407			0.643595
$359$		−	457.086i		−	1.27322i	−0.771186	−	0.636610i	$-0.780336\pi$
$359$		−	457.086i		−	1.27322i	0.771186	−	0.636610i	$-0.219664\pi$
$360$		0			0
$361$	84.4961			0.234061
$362$		−	72.8444i		−	0.201228i
$363$	238.470	+	91.7505i	0.656943	+	0.252756i
$364$	100.628			0.276451
$365$		0			0
$366$	−124.512	+	323.622i	−0.340198	+	0.884213i
$367$	−556.637			−1.51672			−0.758361	−	0.651834i	$-0.774000\pi$
$367$	−556.637			−1.51672			−0.758361	+	0.651834i	$0.774000\pi$
$368$		−	129.086i		−	0.350778i
$369$	209.436	−	231.885i	0.567578	−	0.628414i
$370$		0			0
$371$		−	152.355i		−	0.410660i
$372$	−220.119	−	84.6900i	−0.591719	−	0.227661i
$373$	−77.2267			−0.207042			−0.103521	−	0.994627i	$-0.533011\pi$
$373$	−77.2267			−0.207042			−0.103521	+	0.994627i	$0.533011\pi$
$374$		−	17.1771i		−	0.0459280i
$375$		0			0
$376$	204.891			0.544922
$377$			233.153i			0.618443i
$378$	90.1192	−	45.6566i	0.238411	−	0.120785i
$379$	−476.133			−1.25629			−0.628143	−	0.778098i	$-0.716185\pi$
$379$	−476.133			−1.25629			−0.628143	+	0.778098i	$0.716185\pi$
$380$		0			0
$381$	−42.1138	−	16.2031i	−0.110535	−	0.0425279i
$382$	321.465			0.841532
$383$		−	600.374i		−	1.56756i	−0.621041	−	0.783778i	$-0.713290\pi$
$383$		−	600.374i		−	1.56756i	0.621041	−	0.783778i	$-0.286710\pi$
$384$	12.1878	−	31.6774i	0.0317390	−	0.0824933i
$385$		0			0
$386$		−	339.214i		−	0.878794i
$387$	−269.371	−	243.293i	−0.696048	−	0.628664i
$388$	−16.3856			−0.0422310
$389$			315.387i			0.810763i	0.914148	+	0.405382i	$0.132861\pi$
$389$			315.387i			0.810763i	−0.914148	+	0.405382i	$0.867139\pi$
$390$		0			0
$391$	−65.4838			−0.167478
$392$		−	19.7990i		−	0.0505076i
$393$	55.5781	−	144.454i	0.141420	−	0.367567i
$394$	−260.379			−0.660861
$395$		0			0
$396$	−72.2176	+	79.9584i	−0.182368	+	0.201915i
$397$	−291.527			−0.734325			−0.367163	−	0.930157i	$-0.619671\pi$
$397$	−291.527			−0.734325			−0.367163	+	0.930157i	$0.619671\pi$
$398$			305.176i			0.766773i
$399$	−156.356	−	60.1575i	−0.391871	−	0.150771i
$400$		0			0
$401$		−	312.203i		−	0.778560i	−0.921119	−	0.389280i	$-0.872724\pi$
$401$		−	312.203i		−	0.778560i	0.921119	−	0.389280i	$-0.127276\pi$
$402$	−124.487	+	323.557i	−0.309670	+	0.804869i
$403$	747.522			1.85489
$404$			272.969i			0.675665i
$405$		0			0
$406$	45.8738			0.112990
$407$			121.655i			0.298908i
$408$	−16.0695	−	6.18269i	−0.0393861	−	0.0151537i
$409$	602.689			1.47357			0.736784	−	0.676128i	$-0.236343\pi$
$409$	602.689			1.47357			0.736784	+	0.676128i	$0.236343\pi$
$410$		0			0
$411$	51.2653	−	133.245i	0.124733	−	0.324196i
$412$	−258.383			−0.627142
$413$		−	189.948i		−	0.459922i
$414$	304.824	+	275.314i	0.736289	+	0.665010i
$415$		0			0
$416$			107.576i			0.258596i
$417$	329.633	+	126.825i	0.790486	+	0.304136i
$418$	178.672			0.427445
$419$		−	179.970i		−	0.429522i	−0.976667	−	0.214761i	$-0.931103\pi$
$419$		−	179.970i		−	0.429522i	0.976667	−	0.214761i	$-0.0688972\pi$
$420$		0			0
$421$	454.959			1.08066			0.540331	−	0.841453i	$-0.318299\pi$
$421$	454.959			1.08066			0.540331	+	0.841453i	$0.318299\pi$
$422$		−	173.081i		−	0.410144i
$423$	−436.989	+	483.828i	−1.03307	+	1.14380i
$424$	162.874			0.384138
$425$		0			0
$426$	−30.4986	−	11.7342i	−0.0715929	−	0.0275451i
$427$	−216.236			−0.506407
$428$		−	40.5259i		−	0.0946866i
$429$	122.625	−	318.717i	0.285839	−	0.742930i
$430$		0			0
$431$			280.437i			0.650665i	0.945600	+	0.325333i	$0.105476\pi$
$431$			280.437i			0.650665i	−0.945600	+	0.325333i	$0.894524\pi$
$432$	48.8090	+	96.3415i	0.112984	+	0.223013i
$433$	172.401			0.398155			0.199077	−	0.979984i	$-0.436206\pi$
$433$	172.401			0.398155			0.199077	+	0.979984i	$0.436206\pi$
$434$		−	147.078i		−	0.338889i
$435$		0			0
$436$	−225.139			−0.516373
$437$		−	681.149i		−	1.55869i
$438$	−18.3874	+	47.7909i	−0.0419803	+	0.109112i
$439$	−299.659			−0.682594			−0.341297	−	0.939955i	$-0.610866\pi$
$439$	−299.659			−0.682594			−0.341297	+	0.939955i	$0.610866\pi$
$440$		0			0
$441$	46.7533	+	42.2271i	0.106017	+	0.0957531i
$442$	54.5720			0.123466
$443$		−	389.448i		−	0.879115i	−0.898214	−	0.439558i	$-0.855135\pi$
$443$		−	389.448i		−	0.879115i	0.898214	−	0.439558i	$-0.144865\pi$
$444$	113.812	+	43.7886i	0.256332	+	0.0986229i
$445$		0			0
$446$		−	99.1809i		−	0.222379i
$447$	200.731	−	521.724i	0.449063	−	1.16717i
$448$	21.1660			0.0472456
$449$			614.023i			1.36753i	0.729700	+	0.683767i	$0.239660\pi$
$449$			614.023i			1.36753i	−0.729700	+	0.683767i	$0.760340\pi$
$450$		0			0
$451$	−207.816			−0.460788
$452$			13.0756i			0.0289283i
$453$	−513.953	−	197.741i	−1.13455	−	0.436515i
$454$	−44.4455			−0.0978975
$455$		0			0
$456$	64.3111	−	167.152i	0.141033	−	0.366562i
$457$	215.558			0.471681			0.235840	−	0.971792i	$-0.424216\pi$
$457$	215.558			0.471681			0.235840	+	0.971792i	$0.424216\pi$
$458$		−	50.5167i		−	0.110299i
$459$	48.8728	−	24.7602i	0.106477	−	0.0539438i
$460$		0			0
$461$		−	369.603i		−	0.801743i	−0.916134	−	0.400871i	$-0.868707\pi$
$461$		−	369.603i		−	0.801743i	0.916134	−	0.400871i	$-0.131293\pi$
$462$	−62.7088	−	24.1270i	−0.135733	−	0.0522229i
$463$	−0.675303			−0.00145854			−0.000729269	−	1.00000i	$-0.500232\pi$
$463$	−0.675303			−0.00145854			−0.000729269		1.00000i	$0.500232\pi$
$464$			49.0411i			0.105692i
$465$		0			0
$466$	458.972			0.984918
$467$		−	90.1341i		−	0.193007i	−0.995333	−	0.0965033i	$-0.969234\pi$
$467$		−	90.1341i		−	0.193007i	0.995333	−	0.0965033i	$-0.0307658\pi$
$468$	−254.030	−	229.437i	−0.542799	−	0.490251i
$469$	−216.193			−0.460965
$470$		0			0
$471$	−741.634	−	285.341i	−1.57459	−	0.605819i
$472$	203.063			0.430217
$473$			241.410i			0.510381i
$474$	200.522	−	521.179i	0.423042	−	1.09953i
$475$		0			0
$476$		−	10.7372i		−	0.0225572i
$477$	−347.377	+	384.611i	−0.728254	+	0.806313i
$478$	−565.741			−1.18356
$479$		−	422.277i		−	0.881579i	−0.897610	−	0.440790i	$-0.854698\pi$
$479$		−	422.277i		−	0.881579i	0.897610	−	0.440790i	$-0.145302\pi$
$480$		0			0
$481$	−386.503			−0.803540
$482$			560.460i			1.16278i
$483$	−91.9788	+	239.064i	−0.190432	+	0.494956i
$484$	−170.341			−0.351945
$485$		0			0
$486$	−331.600	−	90.2189i	−0.682304	−	0.185636i
$487$	−240.184			−0.493191			−0.246595	−	0.969119i	$-0.579312\pi$
$487$	−240.184			−0.493191			−0.246595	+	0.969119i	$0.579312\pi$
$488$		−	231.166i		−	0.473700i
$489$	−601.637	−	231.478i	−1.23034	−	0.473369i
$490$		0			0
$491$			961.188i			1.95761i	0.204788	+	0.978806i	$0.434349\pi$
$491$			961.188i			1.95761i	−0.204788	+	0.978806i	$0.565651\pi$
$492$	−74.8010	+	194.416i	−0.152034	+	0.395155i
$493$	24.8779			0.0504624
$494$			567.646i			1.14908i
$495$		0			0
$496$	157.233			0.317002
$497$		−	20.3783i		−	0.0410027i
$498$	−458.785	−	176.516i	−0.921256	−	0.354450i
$499$	−203.222			−0.407259			−0.203629	−	0.979048i	$-0.565274\pi$
$499$	−203.222			−0.407259			−0.203629	+	0.979048i	$0.565274\pi$
$500$		0			0
$501$	58.8132	−	152.862i	0.117392	−	0.305115i
$502$	312.860			0.623228
$503$			112.900i			0.224453i	0.993683	+	0.112226i	$0.0357982\pi$
$503$			112.900i			0.224453i	−0.993683	+	0.112226i	$0.964202\pi$
$504$	−45.1427	+	49.9814i	−0.0895689	+	0.0991694i
$505$		0			0
$506$		−	273.184i		−	0.539889i
$507$	539.387	+	207.527i	1.06388	+	0.409323i
$508$	30.0822			0.0592170
$509$		−	876.657i		−	1.72231i	−0.508341	−	0.861156i	$-0.669741\pi$
$509$		−	876.657i		−	1.72231i	0.508341	−	0.861156i	$-0.330259\pi$
$510$		0			0
$511$	−31.9326			−0.0624904
$512$			22.6274i			0.0441942i
$513$	257.550	+	508.365i	0.502047	+	0.990964i
$514$	288.238			0.560775
$515$		0			0
$516$	225.845	+	86.8930i	0.437684	+	0.168397i
$517$	433.608			0.838700
$518$			76.0459i			0.146807i
$519$	−334.650	+	869.795i	−0.644798	+	1.67591i
$520$		0			0
$521$		−	497.586i		−	0.955060i	−0.878616	−	0.477530i	$-0.841532\pi$
$521$		−	497.586i		−	0.955060i	0.878616	−	0.477530i	$-0.158468\pi$
$522$	−115.806	−	104.595i	−0.221850	−	0.200373i
$523$	−519.528			−0.993362			−0.496681	−	0.867933i	$-0.665448\pi$
$523$	−519.528			−0.993362			−0.496681	+	0.867933i	$0.665448\pi$
$524$			103.185i			0.196917i
$525$		0			0
$526$	138.878			0.264027
$527$		−	79.7623i		−	0.151352i
$528$	25.7928	−	67.0385i	0.0488500	−	0.126967i
$529$	−512.453			−0.968720
$530$		0			0
$531$	−433.090	+	479.511i	−0.815612	+	0.903034i
$532$	111.687			0.209937
$533$		−	660.236i		−	1.23872i
$534$	403.646	+	155.301i	0.755892	+	0.290826i
$535$		0			0
$536$		−	231.120i		−	0.431193i
$537$	175.509	−	456.169i	0.326832	−	0.849476i
$538$	−436.488			−0.811317
$539$		−	41.9004i		−	0.0777372i
$540$		0			0
$541$	853.843			1.57827			0.789134	−	0.614220i	$-0.210529\pi$
$541$	853.843			1.57827			0.789134	+	0.614220i	$0.210529\pi$
$542$		−	564.047i		−	1.04068i
$543$	−144.220	−	55.4881i	−0.265599	−	0.102188i
$544$	11.4786			0.0211004
$545$		0			0
$546$	76.6520	−	199.228i	0.140388	−	0.364886i
$547$	−468.232			−0.855999			−0.428000	−	0.903779i	$-0.640782\pi$
$547$	−468.232			−0.855999			−0.428000	+	0.903779i	$0.640782\pi$
$548$			95.1776i			0.173682i
$549$	545.874	+	493.028i	0.994306	+	0.898048i
$550$		0			0
$551$			258.775i			0.469646i
$552$	−255.570	−	98.3295i	−0.462989	−	0.178133i
$553$	348.238			0.629726
$554$		−	112.742i		−	0.203506i
$555$		0			0
$556$	−235.459			−0.423488
$557$			260.390i			0.467487i	0.972298	+	0.233744i	$0.0750976\pi$
$557$			260.390i			0.467487i	−0.972298	+	0.233744i	$0.924902\pi$
$558$	−335.345	+	371.289i	−0.600977	+	0.665393i
$559$	−766.967			−1.37203
$560$		0			0
$561$	−34.0078	−	13.0844i	−0.0606200	−	0.0233233i
$562$	297.224			0.528869
$563$			62.6717i			0.111317i	0.998450	+	0.0556587i	$0.0177259\pi$
$563$			62.6717i			0.111317i	−0.998450	+	0.0556587i	$0.982274\pi$
$564$	156.072	−	405.650i	0.276724	−	0.719238i
$565$		0			0
$566$		−	371.855i		−	0.656987i
$567$	−21.7458	−	213.200i	−0.0383524	−	0.376014i
$568$	21.7854			0.0383545
$569$			221.137i			0.388641i	0.980938	+	0.194320i	$0.0622501\pi$
$569$			221.137i			0.388641i	−0.980938	+	0.194320i	$0.937750\pi$
$570$		0			0
$571$	520.798			0.912080			0.456040	−	0.889959i	$-0.349267\pi$
$571$	520.798			0.912080			0.456040	+	0.889959i	$0.349267\pi$
$572$			227.662i			0.398010i
$573$	244.871	−	636.449i	0.427349	−	1.11073i
$574$	−129.904			−0.226314
$575$		0			0
$576$	−53.4323	−	48.2596i	−0.0927644	−	0.0837840i
$577$	−78.8359			−0.136631			−0.0683154	−	0.997664i	$-0.521762\pi$
$577$	−78.8359			−0.136631			−0.0683154	+	0.997664i	$0.521762\pi$
$578$			402.885i			0.697032i
$579$	−671.590	−	258.391i	−1.15991	−	0.446272i
$580$		0			0
$581$		−	306.548i		−	0.527622i
$582$	−12.4815	+	32.4409i	−0.0214459	+	0.0557403i
$583$	344.689			0.591234
$584$		−	34.1374i		−	0.0584544i
$585$		0			0
$586$	−505.680			−0.862935
$587$			146.455i			0.249498i	0.992188	+	0.124749i	$0.0398125\pi$
$587$			146.455i			0.249498i	−0.992188	+	0.124749i	$0.960187\pi$
$588$	−39.1988	−	15.0816i	−0.0666646	−	0.0256489i
$589$	829.670			1.40861
$590$		0			0
$591$	−198.340	+	515.509i	−0.335601	+	0.872266i
$592$	−81.2965			−0.137325
$593$			240.021i			0.404758i	0.979307	+	0.202379i	$0.0648672\pi$
$593$			240.021i			0.404758i	−0.979307	+	0.202379i	$0.935133\pi$
$594$	103.294	+	203.886i	0.173895	+	0.343243i
$595$		0			0
$596$			372.671i			0.625287i
$597$	604.198	+	232.463i	1.01206	+	0.389385i
$598$	867.912			1.45136
$599$			886.239i			1.47953i	0.672865	+	0.739766i	$0.265064\pi$
$599$			886.239i			1.47953i	−0.672865	+	0.739766i	$0.734936\pi$
$600$		0			0
$601$	−162.944			−0.271121			−0.135561	−	0.990769i	$-0.543284\pi$
$601$	−162.944			−0.271121			−0.135561	+	0.990769i	$0.543284\pi$
$602$			150.904i			0.250671i
$603$	545.765	+	492.930i	0.905083	+	0.817463i
$604$	367.121			0.607816
$605$		0			0
$606$	540.434	+	207.930i	0.891805	+	0.343119i
$607$	649.221			1.06956			0.534779	−	0.844992i	$-0.320395\pi$
$607$	649.221			1.06956			0.534779	+	0.844992i	$0.320395\pi$
$608$			119.398i			0.196378i
$609$	34.9437	−	90.8227i	0.0573787	−	0.149134i
$610$		0			0
$611$			1377.58i			2.25464i
$612$	−24.4815	+	27.1055i	−0.0400024	+	0.0442901i
$613$	−109.849			−0.179199			−0.0895994	−	0.995978i	$-0.528559\pi$
$613$	−109.849			−0.179199			−0.0895994	+	0.995978i	$0.528559\pi$
$614$		−	414.937i		−	0.675794i
$615$		0			0
$616$	44.7934			0.0727165
$617$			871.161i			1.41193i	0.708246	+	0.705966i	$0.249487\pi$
$617$			871.161i			1.41193i	−0.708246	+	0.705966i	$0.750513\pi$
$618$	−196.819	+	511.556i	−0.318477	+	0.827760i
$619$	153.281			0.247627			0.123814	−	0.992305i	$-0.460487\pi$
$619$	153.281			0.247627			0.123814	+	0.992305i	$0.460487\pi$
$620$		0			0
$621$	777.272	−	393.786i	1.25165	−	0.634115i
$622$	83.7873			0.134706
$623$			269.706i			0.432914i
$624$	212.983	+	81.9444i	0.341319	+	0.131321i
$625$		0			0
$626$			637.226i			1.01793i
$627$	136.101	−	353.742i	0.217067	−	0.564182i
$628$	529.755			0.843558
$629$			41.2407i			0.0655655i
$630$		0			0
$631$	−959.345			−1.52036			−0.760178	−	0.649715i	$-0.774888\pi$
$631$	−959.345			−1.52036			−0.760178	+	0.649715i	$0.774888\pi$
$632$			372.282i			0.589055i
$633$	−342.672	−	131.842i	−0.541346	−	0.208281i
$634$	392.379			0.618894
$635$		0			0
$636$	124.067	−	322.465i	0.195074	−	0.507020i
$637$	133.119			0.208977
$638$			103.785i			0.162673i
$639$	−46.4637	+	51.4439i	−0.0727131	+	0.0805069i
$640$		0			0
$641$			733.758i			1.14471i	0.820007	+	0.572354i	$0.193970\pi$
$641$			733.758i			1.14471i	−0.820007	+	0.572354i	$0.806030\pi$
$642$	−80.2346	−	30.8700i	−0.124976	−	0.0480840i
$643$	164.305			0.255529			0.127765	−	0.991805i	$-0.459220\pi$
$643$	164.305			0.255529			0.127765	+	0.991805i	$0.459220\pi$
$644$		−	170.765i		−	0.265163i
$645$		0			0
$646$	60.5691			0.0937602
$647$			1171.84i			1.81119i	0.424146	+	0.905594i	$0.360574\pi$
$647$			1171.84i			1.81119i	−0.424146	+	0.905594i	$0.639426\pi$
$648$	227.920	−	23.2473i	0.351729	−	0.0358754i
$649$	429.739			0.662155
$650$		0			0
$651$	−291.191	−	112.034i	−0.447297	−	0.172096i
$652$	429.754			0.659132
$653$			804.521i			1.23204i	0.787731	+	0.616019i	$0.211256\pi$
$653$			804.521i			1.23204i	−0.787731	+	0.616019i	$0.788744\pi$
$654$	−171.496	+	445.738i	−0.262226	+	0.681557i
$655$		0			0
$656$		−	138.873i		−	0.211697i
$657$	80.6119	+	72.8080i	0.122697	+	0.110819i
$658$	271.045			0.411922
$659$			864.248i			1.31145i	0.754999	+	0.655727i	$0.227638\pi$
$659$			864.248i			1.31145i	−0.754999	+	0.655727i	$0.772362\pi$
$660$		0			0
$661$	−963.638			−1.45785			−0.728924	−	0.684595i	$-0.759979\pi$
$661$	−963.638			−1.45785			−0.728924	+	0.684595i	$0.759979\pi$
$662$			390.179i			0.589394i
$663$	41.5694	−	108.044i	0.0626989	−	0.162962i
$664$	327.714			0.493545
$665$		0			0
$666$	173.389	−	191.973i	0.260343	−	0.288248i
$667$	395.658			0.593191
$668$			109.191i			0.163459i
$669$	−196.362	−	75.5496i	−0.293516	−	0.112929i
$670$		0			0
$671$		−	489.213i		−	0.729081i
$672$	16.1229	−	41.9053i	0.0239924	−	0.0623590i
$673$	149.734			0.222487			0.111244	−	0.993793i	$-0.464517\pi$
$673$	149.734			0.222487			0.111244	+	0.993793i	$0.464517\pi$
$674$		−	145.378i		−	0.215694i
$675$		0			0
$676$	−385.288			−0.569953
$677$			325.257i			0.480439i	0.970719	+	0.240219i	$0.0772194\pi$
$677$			325.257i			0.480439i	−0.970719	+	0.240219i	$0.922781\pi$
$678$	25.8875	+	9.96012i	0.0381822	+	0.0146904i
$679$	−21.6761			−0.0319236
$680$		0			0
$681$	−33.8557	+	87.9949i	−0.0497146	+	0.129214i
$682$	332.750			0.487904
$683$			551.573i			0.807575i	0.914853	+	0.403787i	$0.132306\pi$
$683$			551.573i			0.807575i	−0.914853	+	0.403787i	$0.867694\pi$
$684$	−281.946	−	254.651i	−0.412202	−	0.372297i
$685$		0			0
$686$		−	26.1916i		−	0.0381802i
$687$	−100.015	−	38.4803i	−0.145582	−	0.0560121i
$688$	−161.323			−0.234481
$689$			1095.09i			1.58939i
$690$		0			0
$691$	−495.558			−0.717161			−0.358580	−	0.933499i	$-0.616739\pi$
$691$	−495.558			−0.717161			−0.358580	+	0.933499i	$0.616739\pi$
$692$		−	621.301i		−	0.897834i
$693$	−95.5350	+	105.775i	−0.137857	+	0.152633i
$694$	645.715			0.930426
$695$		0			0
$696$	97.0935	+	37.3563i	0.139502	+	0.0536729i
$697$	−70.4486			−0.101074
$698$		−	806.958i		−	1.15610i
$699$	349.615	−	908.690i	0.500164	−	1.29999i
$700$		0			0
$701$			377.346i			0.538297i	0.963099	+	0.269149i	$0.0867423\pi$
$701$			377.346i			0.538297i	−0.963099	+	0.269149i	$0.913258\pi$
$702$	−647.752	+	328.168i	−0.922724	+	0.467475i
$703$	−428.977			−0.610209
$704$			47.8861i			0.0680201i
$705$		0			0
$706$	−6.71080			−0.00950539
$707$			361.104i			0.510755i
$708$	154.680	−	402.031i	0.218474	−	0.567840i
$709$	−517.276			−0.729585			−0.364792	−	0.931089i	$-0.618860\pi$
$709$	−517.276			−0.729585			−0.364792	+	0.931089i	$0.618860\pi$
$710$		0			0
$711$	−879.107	−	794.001i	−1.23644	−	1.11674i
$712$	−288.327			−0.404954
$713$		−	1268.54i		−	1.77916i
$714$	−21.2580	−	8.17894i	−0.0297731	−	0.0114551i
$715$		0			0
$716$			325.845i			0.455090i
$717$	−430.944	+	1120.08i	−0.601038	+	1.56217i
$718$	646.418			0.900303
$719$			1187.74i			1.65193i	0.563720	+	0.825966i	$0.309370\pi$
$719$			1187.74i			1.65193i	−0.563720	+	0.825966i	$0.690630\pi$
$720$		0			0
$721$	−341.808			−0.474075
$722$			119.496i			0.165506i
$723$	1109.62	+	426.922i	1.53474	+	0.590487i
$724$	103.018			0.142289
$725$		0			0
$726$	−129.755	+	337.248i	−0.178726	+	0.464529i
$727$	−892.878			−1.22817			−0.614084	−	0.789241i	$-0.710474\pi$
$727$	−892.878			−1.22817			−0.614084	+	0.789241i	$0.710474\pi$
$728$			142.310i			0.195480i
$729$	−431.210	+	587.791i	−0.591509	+	0.806298i
$730$		0			0
$731$			81.8371i			0.111952i
$732$	−457.671	−	176.087i	−0.625233	−	0.240556i
$733$	−868.737			−1.18518			−0.592590	−	0.805504i	$-0.701894\pi$
$733$	−868.737			−1.18518			−0.592590	+	0.805504i	$0.701894\pi$
$734$		−	787.204i		−	1.07248i
$735$		0			0
$736$	182.555			0.248037
$737$		−	489.116i		−	0.663657i
$738$	327.935	+	296.188i	0.444356	+	0.401338i
$739$	356.963			0.483035			0.241517	−	0.970396i	$-0.422355\pi$
$739$	356.963			0.483035			0.241517	+	0.970396i	$0.422355\pi$
$740$		0			0
$741$	1123.85	+	432.396i	1.51666	+	0.583530i
$742$	215.463			0.290381
$743$			982.069i			1.32176i	0.750491	+	0.660881i	$0.229817\pi$
$743$			982.069i			1.32176i	−0.750491	+	0.660881i	$0.770183\pi$
$744$	119.770	−	311.296i	0.160981	−	0.418408i
$745$		0			0
$746$		−	109.215i		−	0.146401i
$747$	−698.946	+	773.863i	−0.935670	+	1.03596i
$748$	24.2920			0.0324760
$749$		−	53.6107i		−	0.0715763i
$750$		0			0
$751$	−710.167			−0.945628			−0.472814	−	0.881162i	$-0.656762\pi$
$751$	−710.167			−0.945628			−0.472814	+	0.881162i	$0.656762\pi$
$752$			289.759i			0.385318i
$753$	238.317	−	619.413i	0.316489	−	0.822593i
$754$	−329.728			−0.437305
$755$		0			0
$756$	64.5682	+	127.448i	0.0854077	+	0.168582i
$757$	346.357			0.457540			0.228770	−	0.973481i	$-0.426530\pi$
$757$	346.357			0.457540			0.228770	+	0.973481i	$0.426530\pi$
$758$		−	673.353i		−	0.888329i
$759$	−540.859	−	208.093i	−0.712595	−	0.274168i
$760$		0			0
$761$		−	1138.06i		−	1.49548i	−0.663994	−	0.747738i	$-0.731140\pi$
$761$		−	1138.06i		−	1.49548i	0.663994	−	0.747738i	$-0.268860\pi$
$762$	22.9147	−	59.5580i	0.0300718	−	0.0781600i
$763$	−297.830			−0.390341
$764$			454.620i			0.595053i
$765$		0			0
$766$	849.057			1.10843
$767$			1365.29i			1.78004i
$768$	44.7986	+	17.2361i	0.0583315	+	0.0224428i
$769$	395.138			0.513833			0.256917	−	0.966434i	$-0.417293\pi$
$769$	395.138			0.513833			0.256917	+	0.966434i	$0.417293\pi$
$770$		0			0
$771$	219.561	−	570.665i	0.284774	−	0.740162i
$772$	479.722			0.621401
$773$			1244.98i			1.61058i	0.592881	+	0.805290i	$0.297990\pi$
$773$			1244.98i			1.61058i	−0.592881	+	0.805290i	$0.702010\pi$
$774$	344.068	−	380.947i	0.444533	−	0.492180i
$775$		0			0
$776$		−	23.1728i		−	0.0298618i
$777$	150.559	+	57.9268i	0.193769	+	0.0745519i
$778$	−446.024			−0.573296
$779$		−	732.791i		−	0.940682i
$780$		0			0
$781$	46.1041			0.0590322
$782$		−	92.6081i		−	0.118425i
$783$	−295.293	+	149.603i	−0.377131	+	0.191064i
$784$	28.0000			0.0357143
$785$		0			0
$786$	204.289	+	78.5992i	0.259909	+	0.0999990i
$787$	333.519			0.423785			0.211892	−	0.977293i	$-0.432037\pi$
$787$	333.519			0.423785			0.211892	+	0.977293i	$0.432037\pi$
$788$		−	368.232i		−	0.467300i
$789$	105.789	−	274.957i	0.134079	−	0.348488i
$790$		0			0
$791$			17.2974i			0.0218677i
$792$	−113.078	−	102.131i	−0.142775	−	0.128954i
$793$	1554.24			1.95995
$794$		−	412.281i		−	0.519246i
$795$		0			0
$796$	−431.583			−0.542190
$797$			541.407i			0.679306i	0.940551	+	0.339653i	$0.110310\pi$
$797$			541.407i			0.679306i	−0.940551	+	0.339653i	$0.889690\pi$
$798$	85.0756	−	221.121i	0.106611	−	0.277094i
$799$	146.991			0.183969
$800$		0			0
$801$	614.943	−	680.856i	0.767719	−	0.850007i
$802$	441.521			0.550525
$803$		−	72.2446i		−	0.0899683i
$804$	−457.579	−	176.052i	−0.569128	−	0.218970i
$805$		0			0
$806$			1057.16i			1.31161i
$807$	−332.488	+	864.176i	−0.412005	+	1.07085i
$808$	−386.036			−0.477768
$809$		−	812.942i		−	1.00487i	−0.864614	−	0.502436i	$-0.832437\pi$
$809$		−	812.942i		−	1.00487i	0.864614	−	0.502436i	$-0.167563\pi$
$810$		0			0
$811$	−750.662			−0.925600			−0.462800	−	0.886463i	$-0.653155\pi$
$811$	−750.662			−0.925600			−0.462800	+	0.886463i	$0.653155\pi$
$812$			64.8753i			0.0798957i
$813$	−1116.72	−	429.654i	−1.37358	−	0.528480i
$814$	−172.047			−0.211360
$815$		0			0
$816$	8.74365	−	22.7258i	0.0107153	−	0.0278502i
$817$	−851.252			−1.04192
$818$			852.331i			1.04197i
$819$	−336.050	−	303.517i	−0.410317	−	0.370595i
$820$		0			0
$821$		−	1216.71i		−	1.48199i	−0.671513	−	0.740993i	$-0.734355\pi$
$821$		−	1216.71i		−	1.48199i	0.671513	−	0.740993i	$-0.265645\pi$
$822$	188.436	+	72.5001i	0.229241	+	0.0881996i
$823$	−918.365			−1.11588			−0.557938	−	0.829883i	$-0.688407\pi$
$823$	−918.365			−1.11588			−0.557938	+	0.829883i	$0.688407\pi$
$824$		−	365.408i		−	0.443457i
$825$		0			0
$826$	268.626			0.325214
$827$		−	973.601i		−	1.17727i	−0.808400	−	0.588634i	$-0.799666\pi$
$827$		−	973.601i		−	1.17727i	0.808400	−	0.588634i	$-0.200334\pi$
$828$	−389.353	+	431.086i	−0.470233	+	0.520635i
$829$	−759.447			−0.916100			−0.458050	−	0.888926i	$-0.651452\pi$
$829$	−759.447			−0.916100			−0.458050	+	0.888926i	$0.651452\pi$
$830$		0			0
$831$	−223.211	−	85.8796i	−0.268606	−	0.103345i
$832$	−152.136			−0.182855
$833$		−	14.2040i		−	0.0170517i
$834$	−179.357	+	466.171i	−0.215057	+	0.558958i
$835$		0			0
$836$			252.681i			0.302249i
$837$	479.649	+	946.753i	0.573057	+	1.13113i
$838$	254.515			0.303718
$839$		−	937.182i		−	1.11702i	−0.829497	−	0.558512i	$-0.811373\pi$
$839$		−	937.182i		−	1.11702i	0.829497	−	0.558512i	$-0.188627\pi$
$840$		0			0
$841$	690.685			0.821267
$842$			643.409i			0.764144i
$843$	226.406	−	588.456i	0.268572	−	0.698050i
$844$	244.773			0.290015
$845$		0			0
$846$	−684.237	−	617.996i	−0.808790	−	0.730492i
$847$	−225.340			−0.266045
$848$			230.339i			0.271626i
$849$	−736.212	−	283.255i	−0.867152	−	0.333633i
$850$		0			0
$851$			655.891i			0.770730i
$852$	16.5947	−	43.1315i	0.0194773	−	0.0506238i
$853$	−465.533			−0.545760			−0.272880	−	0.962048i	$-0.587976\pi$
$853$	−465.533			−0.545760			−0.272880	+	0.962048i	$0.587976\pi$
$854$		−	305.803i		−	0.358084i
$855$		0			0
$856$	57.3122			0.0669535
$857$		−	1612.01i		−	1.88099i	−0.339811	−	0.940494i	$-0.610363\pi$
$857$		−	1612.01i		−	1.88099i	0.339811	−	0.940494i	$-0.389637\pi$
$858$	450.734	+	173.418i	0.525331	+	0.202119i
$859$	−1111.27			−1.29368			−0.646842	−	0.762624i	$-0.723911\pi$
$859$	−1111.27			−1.29368			−0.646842	+	0.762624i	$0.723911\pi$
$860$		0			0
$861$	−98.9524	+	257.189i	−0.114927	+	0.298709i
$862$	−396.597			−0.460090
$863$		−	681.862i		−	0.790106i	−0.918658	−	0.395053i	$-0.870726\pi$
$863$		−	681.862i		−	0.790106i	0.918658	−	0.395053i	$-0.129274\pi$
$864$	−136.247	+	69.0264i	−0.157694	+	0.0798916i
$865$		0			0
$866$			243.812i			0.281538i
$867$	797.647	+	306.891i	0.920008	+	0.353969i
$868$	208.000			0.239631
$869$			787.857i			0.906625i
$870$		0			0
$871$	1553.93			1.78408
$872$		−	318.394i		−	0.365131i
$873$	54.7201	+	49.4227i	0.0626805	+	0.0566125i
$874$	963.289			1.10216
$875$		0			0
$876$	−67.5865	−	26.0036i	−0.0771536	−	0.0296845i
$877$	206.003			0.234896			0.117448	−	0.993079i	$-0.462529\pi$
$877$	206.003			0.234896			0.117448	+	0.993079i	$0.462529\pi$
$878$		−	423.782i		−	0.482667i
$879$	−385.194	+	1001.16i	−0.438219	+	1.13898i
$880$		0			0
$881$			909.333i			1.03216i	0.856540	+	0.516080i	$0.172609\pi$
$881$			909.333i			1.03216i	−0.856540	+	0.516080i	$0.827391\pi$
$882$	−59.7182	+	66.1191i	−0.0677077	+	0.0749650i
$883$	−776.956			−0.879905			−0.439952	−	0.898021i	$-0.645005\pi$
$883$	−776.956			−0.879905			−0.439952	+	0.898021i	$0.645005\pi$
$884$			77.1764i			0.0873036i
$885$		0			0
$886$	550.763			0.621628
$887$		−	1228.23i		−	1.38470i	−0.721562	−	0.692350i	$-0.756575\pi$
$887$		−	1228.23i		−	1.38470i	0.721562	−	0.692350i	$-0.243425\pi$
$888$	−61.9264	+	160.954i	−0.0697369	+	0.181254i
$889$	39.7951			0.0447638
$890$		0			0
$891$	482.345	−	49.1979i	0.541352	−	0.0552165i
$892$	140.263			0.157245
$893$			1528.97i			1.71217i
$894$	737.829	+	283.877i	0.825312	+	0.317535i
$895$		0			0
$896$			29.9333i			0.0334077i
$897$	661.119	−	1718.32i	0.737033	−	1.91564i
$898$	−868.359			−0.966993
$899$			481.930i			0.536074i
$900$		0			0
$901$	116.848			0.129687
$902$		−	293.896i		−	0.325827i
$903$	298.765	+	114.949i	0.330858	+	0.127296i
$904$	−18.4917			−0.0204554
$905$		0			0
$906$	279.649	−	726.840i	0.308663	−	0.802251i
$907$	254.429			0.280517			0.140259	−	0.990115i	$-0.455207\pi$
$907$	254.429			0.280517			0.140259	+	0.990115i	$0.455207\pi$
$908$		−	62.8554i		−	0.0692240i
$909$	823.335	−	911.585i	0.905759	−	1.00284i
$910$		0			0
$911$		−	231.235i		−	0.253825i	−0.991914	−	0.126913i	$-0.959493\pi$
$911$		−	231.235i		−	0.253825i	0.991914	−	0.126913i	$-0.0405068\pi$
$912$	236.389	+	90.9496i	0.259198	+	0.0997254i
$913$	693.537			0.759624
$914$			304.845i			0.333529i
$915$		0			0
$916$	71.4414			0.0779928
$917$			136.500i			0.148855i
$918$	35.0162	+	69.1166i	0.0381440	+	0.0752904i
$919$	−279.584			−0.304226			−0.152113	−	0.988363i	$-0.548608\pi$
$919$	−279.584			−0.304226			−0.152113	+	0.988363i	$0.548608\pi$
$920$		0			0
$921$	−821.509	−	316.072i	−0.891975	−	0.343184i
$922$	522.698			0.566918
$923$			146.474i			0.158693i
$924$	34.1207	−	88.6836i	0.0369271	−	0.0959780i
$925$		0			0
$926$		−	0.955022i		−	0.00103134i
$927$	862.874	+	779.340i	0.930824	+	0.840712i
$928$	−69.3546			−0.0747356
$929$		−	1522.35i		−	1.63870i	−0.573294	−	0.819350i	$-0.694335\pi$
$929$		−	1522.35i		−	1.63870i	0.573294	−	0.819350i	$-0.305665\pi$
$930$		0			0
$931$	147.747			0.158698
$932$			649.084i			0.696442i
$933$	63.8237	−	165.885i	0.0684069	−	0.177798i
$934$	127.469			0.136476
$935$		0			0
$936$	324.474	−	359.252i	0.346660	−	0.383817i
$937$	1402.37			1.49666			0.748329	−	0.663328i	$-0.230856\pi$
$937$	1402.37			1.49666			0.748329	+	0.663328i	$0.230856\pi$
$938$		−	305.742i		−	0.325951i
$939$	1261.60	+	485.397i	1.34356	+	0.516930i
$940$		0			0
$941$			569.377i			0.605077i	0.953137	+	0.302538i	$0.0978340\pi$
$941$			569.377i			0.605077i	−0.953137	+	0.302538i	$0.902166\pi$
$942$	403.533	−	1048.83i	0.428379	−	1.11341i
$943$	−1120.41			−1.18814
$944$			287.174i			0.304210i
$945$		0			0
$946$	−341.406			−0.360894
$947$			130.552i			0.137858i	0.997622	+	0.0689290i	$0.0219582\pi$
$947$			130.552i			0.137858i	−0.997622	+	0.0689290i	$0.978042\pi$
$948$	737.059	+	283.581i	0.777488	+	0.299136i
$949$	229.523			0.241858
$950$		0			0
$951$	298.889	−	776.847i	0.314289	−	0.816874i
$952$	15.1848			0.0159504
$953$		−	154.008i		−	0.161603i	−0.996730	−	0.0808016i	$-0.974252\pi$
$953$		−	154.008i		−	0.161603i	0.996730	−	0.0808016i	$-0.0257480\pi$
$954$	−543.922	−	491.266i	−0.570149	−	0.514953i
$955$		0			0
$956$		−	800.078i		−	0.836902i
$957$	205.478	+	79.0568i	0.214710	+	0.0826090i
$958$	597.189			0.623371
$959$			125.908i			0.131291i
$960$		0			0
$961$	584.137			0.607843
$962$		−	546.597i		−	0.568189i
$963$	−122.235	+	135.337i	−0.126932	+	0.140537i
$964$	−792.610			−0.822209
$965$		0			0
$966$	−338.087	−	130.078i	−0.349987	−	0.134656i
$967$	614.131			0.635089			0.317544	−	0.948243i	$-0.397142\pi$
$967$	614.131			0.635089			0.317544	+	0.948243i	$0.397142\pi$
$968$		−	240.899i		−	0.248862i
$969$	46.1376	−	119.917i	0.0476136	−	0.123753i
$970$		0			0
$971$			288.285i			0.296895i	0.988920	+	0.148448i	$0.0474277\pi$
$971$			288.285i			0.296895i	−0.988920	+	0.148448i	$0.952572\pi$
$972$	127.589	−	468.953i	0.131264	−	0.482462i
$973$	−311.483			−0.320127
$974$		−	339.671i		−	0.348739i
$975$		0			0
$976$	326.918			0.334957
$977$			480.732i			0.492049i	0.969264	+	0.246025i	$0.0791244\pi$
$977$			480.732i			0.492049i	−0.969264	+	0.246025i	$0.920876\pi$
$978$	327.359	−	850.844i	0.334723	−	0.869983i
$979$	−610.184			−0.623273
$980$		0			0
$981$	751.855	+	679.069i	0.766417	+	0.692221i
$982$	−1359.32			−1.38424
$983$		−	1414.59i		−	1.43905i	−0.694465	−	0.719526i	$-0.744359\pi$
$983$		−	1414.59i		−	1.43905i	0.694465	−	0.719526i	$-0.255641\pi$
$984$	−274.946	−	105.785i	−0.279417	−	0.107505i
$985$		0			0
$986$			35.1827i			0.0356823i
$987$	206.464	−	536.625i	0.209184	−	0.543693i
$988$	−802.773			−0.812523
$989$			1301.54i			1.31601i
$990$		0			0
$991$	−549.944			−0.554939			−0.277469	−	0.960735i	$-0.589496\pi$
$991$	−549.944			−0.554939			−0.277469	+	0.960735i	$0.589496\pi$
$992$			222.361i			0.224154i
$993$	772.491	+	297.213i	0.777937	+	0.299308i
$994$	28.8193			0.0289933
$995$		0			0
$996$	249.631	−	648.821i	0.250634	−	0.651426i
$997$	−524.552			−0.526130			−0.263065	−	0.964778i	$-0.584733\pi$
$997$	−524.552			−0.526130			−0.263065	+	0.964778i	$0.584733\pi$
$998$		−	287.399i		−	0.287975i
$999$	−248.000	−	489.514i	−0.248248	−	0.490004i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.3.e.e.701.20		24
3.2	odd	2	inner	1050.3.e.e.701.18		24
5.2	odd	4		210.3.c.a.29.7	✓	24
5.3	odd	4		210.3.c.a.29.18	yes	24
5.4	even	2	inner	1050.3.e.e.701.17		24
15.2	even	4		210.3.c.a.29.17	yes	24
15.8	even	4		210.3.c.a.29.8	yes	24
15.14	odd	2	inner	1050.3.e.e.701.19		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.3.c.a.29.7	✓	24	5.2	odd	4
210.3.c.a.29.8	yes	24	15.8	even	4
210.3.c.a.29.17	yes	24	15.2	even	4
210.3.c.a.29.18	yes	24	5.3	odd	4
1050.3.e.e.701.17		24	5.4	even	2	inner
1050.3.e.e.701.18		24	3.2	odd	2	inner
1050.3.e.e.701.19		24	15.14	odd	2	inner
1050.3.e.e.701.20		24	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1050.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.41421i q^{2} +(2.79991 + 1.07726i) q^{3} -2.00000 q^{4} +(-1.52347 + 3.95968i) q^{6} -2.64575 q^{7} -2.82843i q^{8} +(6.67904 + 6.03245i) q^{9} +O(q^{10})\)	\(q+1.41421i q^{2} +(2.79991 + 1.07726i) q^{3} -2.00000 q^{4} +(-1.52347 + 3.95968i) q^{6} -2.64575 q^{7} -2.82843i q^{8} +(6.67904 + 6.03245i) q^{9} -5.98577i q^{11} +(-5.59983 - 2.15451i) q^{12} +19.0169 q^{13} -3.74166i q^{14} +4.00000 q^{16} -2.02915i q^{17} +(-8.53117 + 9.44559i) q^{18} +21.1068 q^{19} +(-7.40788 - 2.85015i) q^{21} +8.46515 q^{22} -32.2716i q^{23} +(3.04694 - 7.91935i) q^{24} +26.8940i q^{26} +(12.2023 + 24.0854i) q^{27} +5.29150 q^{28} +12.2603i q^{29} +39.3082 q^{31} +5.65685i q^{32} +(6.44820 - 16.7596i) q^{33} +2.86965 q^{34} +(-13.3581 - 12.0649i) q^{36} -20.3241 q^{37} +29.8495i q^{38} +(53.2458 + 20.4861i) q^{39} -34.7183i q^{41} +(4.03072 - 10.4763i) q^{42} -40.3307 q^{43} +11.9715i q^{44} +45.6389 q^{46} +72.4398i q^{47} +(11.1997 + 4.30902i) q^{48} +7.00000 q^{49} +(2.18591 - 5.68144i) q^{51} -38.0339 q^{52} +57.5848i q^{53} +(-34.0619 + 17.2566i) q^{54} +7.48331i q^{56} +(59.0972 + 22.7374i) q^{57} -17.3387 q^{58} +71.7934i q^{59} +81.7294 q^{61} +55.5902i q^{62} +(-17.6711 - 15.9604i) q^{63} -8.00000 q^{64} +(23.7017 + 9.11913i) q^{66} +81.7131 q^{67} +4.05830i q^{68} +(34.7647 - 90.3576i) q^{69} +7.70229i q^{71} +(17.0623 - 18.8912i) q^{72} +12.0694 q^{73} -28.7427i q^{74} -42.2136 q^{76} +15.8369i q^{77} +(-28.9717 + 75.3009i) q^{78} -131.622 q^{79} +(8.21915 + 80.5819i) q^{81} +49.0991 q^{82} +115.864i q^{83} +(14.8158 + 5.70030i) q^{84} -57.0363i q^{86} +(-13.2075 + 34.3277i) q^{87} -16.9303 q^{88} -101.939i q^{89} -50.3141 q^{91} +64.5431i q^{92} +(110.060 + 42.3450i) q^{93} -102.445 q^{94} +(-6.09388 + 15.8387i) q^{96} +8.19281 q^{97} +9.89949i q^{98} +(36.1088 - 39.9792i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 48 q^{4} - 44 q^{9}+O(q^{10}) \) 24 * q - 48 * q^4 - 44 * q^9	\( 24 q - 48 q^{4} - 44 q^{9} + 96 q^{16} + 80 q^{19} - 28 q^{21} + 224 q^{31} - 128 q^{34} + 88 q^{36} + 92 q^{39} - 144 q^{46} + 168 q^{49} - 284 q^{51} + 144 q^{54} - 192 q^{64} + 224 q^{66} + 152 q^{69} - 160 q^{76} + 72 q^{79} - 212 q^{81} + 56 q^{84} + 168 q^{91} + 128 q^{94} + 876 q^{99}+O(q^{100}) \) 24 * q - 48 * q^4 - 44 * q^9 + 96 * q^16 + 80 * q^19 - 28 * q^21 + 224 * q^31 - 128 * q^34 + 88 * q^36 + 92 * q^39 - 144 * q^46 + 168 * q^49 - 284 * q^51 + 144 * q^54 - 192 * q^64 + 224 * q^66 + 152 * q^69 - 160 * q^76 + 72 * q^79 - 212 * q^81 + 56 * q^84 + 168 * q^91 + 128 * q^94 + 876 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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