LMFDB - Embedded newform 1050.3.e.e.701.17

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			701.17
Character	$\chi$	$=$	1050.701
Dual form			1050.3.e.e.701.19

$q$-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	$-0.761142\pi$
$13$	−19.0169			−1.46284			−0.731421	+	0.681926i	$0.761142\pi$
$14$		−	3.74166i		−	0.267261i
$15$		0			0
$16$	4.00000			0.250000
$17$			2.02915i			0.119362i	0.998218	+	0.0596809i	$0.0190083\pi$
$17$			2.02915i			0.119362i	−0.998218	+	0.0596809i	$0.980992\pi$
$18$	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	$0.247511\pi$
$23$			32.2716i			1.40311i	−0.712615	+	0.701555i	$0.752489\pi$
$24$	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	$-0.411438\pi$
$37$	20.3241			0.549301			0.274650	+	0.961544i	$0.411438\pi$
$38$		−	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	$-0.344628\pi$
$43$	40.3307			0.937924			0.468962	+	0.883218i	$0.344628\pi$
$44$			11.9715i			0.272080i
$45$		0			0
$46$	45.6389			0.992149
$47$		−	72.4398i		−	1.54127i	−0.637275	−	0.770636i	$-0.719939\pi$
$47$		−	72.4398i		−	1.54127i	0.637275	−	0.770636i	$-0.280061\pi$
$48$	−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	$-0.817193\pi$
$53$		−	57.5848i		−	1.08651i	0.839569	−	0.543253i	$-0.182807\pi$
$54$	−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	$-0.708750\pi$
$67$	−81.7131			−1.21960			−0.609799	+	0.792556i	$0.708750\pi$
$68$		−	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	$-0.526344\pi$
$73$	−12.0694			−0.165334			−0.0826671	+	0.996577i	$0.526344\pi$
$74$		−	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	$-0.754083\pi$
$83$		−	115.864i		−	1.39596i	0.716119	−	0.697978i	$-0.245917\pi$
$84$	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	$-0.513447\pi$
$97$	−8.19281			−0.0844619			−0.0422310	+	0.999108i	$0.513447\pi$
$98$		−	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	$-0.715776\pi$
$103$	−129.191			−1.25428			−0.627142	+	0.778905i	$0.715776\pi$
$104$		−	53.7880i		−	0.517193i
$105$		0			0
$106$	−81.4372			−0.768275
$107$		−	20.2629i		−	0.189373i	−0.995507	−	0.0946866i	$-0.969815\pi$
$107$		−	20.2629i		−	0.189373i	0.995507	−	0.0946866i	$-0.0301849\pi$
$108$	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	$0.00920944\pi$
$113$			6.53779i			0.0578565i	−0.999581	+	0.0289283i	$0.990791\pi$
$114$	−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	$-0.481140\pi$
$127$	15.0411			0.118434			0.0592170	+	0.998245i	$0.481140\pi$
$128$			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	$0.0555664\pi$
$137$			47.5888i			0.347364i	−0.984802	+	0.173682i	$0.944434\pi$
$138$	−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	$-0.180457\pi$
$157$	264.877			1.68712			0.843558	+	0.537038i	$0.180457\pi$
$158$			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	$-0.270924\pi$
$163$	214.877			1.31826			0.659132	+	0.752027i	$0.270924\pi$
$164$			69.4366i			0.423394i
$165$		0			0
$166$	−163.857			−0.987090
$167$			54.5954i			0.326919i	0.986550	+	0.163459i	$0.0522653\pi$
$167$			54.5954i			0.326919i	−0.986550	+	0.163459i	$0.947735\pi$
$168$	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	$-0.645140\pi$
$173$		−	310.651i		−	1.79567i	0.440334	−	0.897834i	$-0.354860\pi$
$174$	−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	$-0.286564\pi$
$193$	239.861			1.24280			0.621401	+	0.783493i	$0.286564\pi$
$194$			11.5864i			0.0597236i
$195$		0			0
$196$	−14.0000			−0.0714286
$197$		−	184.116i		−	0.934599i	−0.884099	−	0.467300i	$-0.845227\pi$
$197$		−	184.116i		−	0.934599i	0.884099	−	0.467300i	$-0.154773\pi$
$198$	−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	$-0.449739\pi$
$223$	70.1315			0.314491			0.157245	+	0.987560i	$0.449739\pi$
$224$		−	14.9666i		−	0.0668153i
$225$		0			0
$226$	9.24583			0.0409108
$227$		−	31.4277i		−	0.138448i	−0.997601	−	0.0692240i	$-0.977948\pi$
$227$		−	31.4277i		−	0.138448i	0.997601	−	0.0692240i	$-0.0220523\pi$
$228$	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	$0.245235\pi$
$233$			324.542i			1.39288i	−0.717613	+	0.696442i	$0.754765\pi$
$234$	−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	$0.129785\pi$
$257$			203.815i			0.793055i	−0.918023	+	0.396528i	$0.870215\pi$
$258$	−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	$0.0597778\pi$
$263$			98.2019i			0.373391i	−0.982418	+	0.186696i	$0.940222\pi$
$264$	−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	$-0.454036\pi$
$277$	79.7207			0.287800			0.143900	+	0.989592i	$0.454036\pi$
$278$		−	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	$-0.346213\pi$
$283$	262.941			0.929120			0.464560	+	0.885542i	$0.346213\pi$
$284$		−	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	$-0.791094\pi$
$293$		−	357.570i		−	1.22037i	0.792257	−	0.610187i	$-0.208906\pi$
$294$	−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	$-0.341413\pi$
$307$	293.405			0.955717			0.477858	+	0.878437i	$0.341413\pi$
$308$			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	$-0.755761\pi$
$313$	−450.587			−1.43957			−0.719787	+	0.694195i	$0.755761\pi$
$314$		−	374.593i		−	1.19297i
$315$		0			0
$316$	263.243			0.833049
$317$			277.454i			0.875249i	0.899158	+	0.437624i	$0.144180\pi$
$317$			277.454i			0.875249i	−0.899158	+	0.437624i	$0.855820\pi$
$318$	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	$-0.451261\pi$
$337$	102.798			0.305038			0.152519	+	0.988301i	$0.451261\pi$
$338$		−	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	$0.228559\pi$
$347$			456.590i			1.31582i	−0.753096	+	0.657910i	$0.771441\pi$
$348$	−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	$-0.997861\pi$
$353$		−	4.74525i		−	0.0134426i	0.999977	−	0.00672132i	$-0.00213948\pi$
$354$	−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	$-0.226000\pi$
$367$	556.637			1.51672			0.758361	+	0.651834i	$0.226000\pi$
$368$			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	$-0.466989\pi$
$373$	77.2267			0.207042			0.103521	+	0.994627i	$0.466989\pi$
$374$		−	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	$0.286710\pi$
$383$			600.374i			1.56756i	−0.621041	+	0.783778i	$0.713290\pi$
$384$	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	$-0.380329\pi$
$397$	291.527			0.734325			0.367163	+	0.930157i	$0.380329\pi$
$398$		−	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	$-0.563794\pi$
$433$	−172.401			−0.398155			−0.199077	+	0.979984i	$0.563794\pi$
$434$		−	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	$0.144865\pi$
$443$			389.448i			0.879115i	−0.898214	+	0.439558i	$0.855135\pi$
$444$	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	$-0.575784\pi$
$457$	−215.558			−0.471681			−0.235840	+	0.971792i	$0.575784\pi$
$458$			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	$-0.499768\pi$
$463$	0.675303			0.00145854			0.000729269		1.00000i	$0.499768\pi$
$464$			49.0411i			0.105692i
$465$		0			0
$466$	458.972			0.984918
$467$			90.1341i			0.193007i	0.995333	+	0.0965033i	$0.0307658\pi$
$467$			90.1341i			0.193007i	−0.995333	+	0.0965033i	$0.969234\pi$
$468$	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	$-0.420688\pi$
$487$	240.184			0.493191			0.246595	+	0.969119i	$0.420688\pi$
$488$			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	$-0.964202\pi$
$503$		−	112.900i		−	0.224453i	0.993683	−	0.112226i	$-0.0357982\pi$
$504$	−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	$-0.334552\pi$
$523$	519.528			0.993362			0.496681	+	0.867933i	$0.334552\pi$
$524$			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	$-0.359218\pi$
$547$	468.232			0.855999			0.428000	+	0.903779i	$0.359218\pi$
$548$		−	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	$-0.924902\pi$
$557$		−	260.390i		−	0.467487i	0.972298	−	0.233744i	$-0.0750976\pi$
$558$	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	$-0.982274\pi$
$563$		−	62.6717i		−	0.111317i	0.998450	−	0.0556587i	$-0.0177259\pi$
$564$	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	$-0.478238\pi$
$577$	78.8359			0.136631			0.0683154	+	0.997664i	$0.478238\pi$
$578$		−	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	$-0.960187\pi$
$587$		−	146.455i		−	0.249498i	0.992188	−	0.124749i	$-0.0398125\pi$
$588$	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	$-0.935133\pi$
$593$		−	240.021i		−	0.404758i	0.979307	−	0.202379i	$-0.0648672\pi$
$594$	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	$-0.679605\pi$
$607$	−649.221			−1.06956			−0.534779	+	0.844992i	$0.679605\pi$
$608$		−	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	$-0.471441\pi$
$613$	109.849			0.179199			0.0895994	+	0.995978i	$0.471441\pi$
$614$		−	414.937i		−	0.675794i
$615$		0			0
$616$	44.7934			0.0727165
$617$		−	871.161i		−	1.41193i	−0.708246	−	0.705966i	$-0.750513\pi$
$617$		−	871.161i		−	1.41193i	0.708246	−	0.705966i	$-0.249487\pi$
$618$	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	$-0.540780\pi$
$643$	−164.305			−0.255529			−0.127765	+	0.991805i	$0.540780\pi$
$644$		−	170.765i		−	0.265163i
$645$		0			0
$646$	60.5691			0.0937602
$647$		−	1171.84i		−	1.81119i	−0.424146	−	0.905594i	$-0.639426\pi$
$647$		−	1171.84i		−	1.81119i	0.424146	−	0.905594i	$-0.360574\pi$
$648$	−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	$-0.788744\pi$
$653$		−	804.521i		−	1.23204i	0.787731	−	0.616019i	$-0.211256\pi$
$654$	−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	$-0.535483\pi$
$673$	−149.734			−0.222487			−0.111244	+	0.993793i	$0.535483\pi$
$674$		−	145.378i		−	0.215694i
$675$		0			0
$676$	−385.288			−0.569953
$677$		−	325.257i		−	0.480439i	−0.970719	−	0.240219i	$-0.922781\pi$
$677$		−	325.257i		−	0.480439i	0.970719	−	0.240219i	$-0.0772194\pi$
$678$	−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	$-0.867694\pi$
$683$		−	551.573i		−	0.807575i	0.914853	−	0.403787i	$-0.132306\pi$
$684$	−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	$-0.289526\pi$
$727$	892.878			1.22817			0.614084	+	0.789241i	$0.289526\pi$
$728$		−	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	$-0.298106\pi$
$733$	868.737			1.18518			0.592590	+	0.805504i	$0.298106\pi$
$734$		−	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	$-0.770183\pi$
$743$		−	982.069i		−	1.32176i	0.750491	−	0.660881i	$-0.229817\pi$
$744$	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	$-0.573470\pi$
$757$	−346.357			−0.457540			−0.228770	+	0.973481i	$0.573470\pi$
$758$			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	$-0.702010\pi$
$773$		−	1244.98i		−	1.61058i	0.592881	−	0.805290i	$-0.297990\pi$
$774$	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	$-0.567963\pi$
$787$	−333.519			−0.423785			−0.211892	+	0.977293i	$0.567963\pi$
$788$			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	$-0.889690\pi$
$797$		−	541.407i		−	0.679306i	0.940551	−	0.339653i	$-0.110310\pi$
$798$	−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	$-0.311593\pi$
$823$	918.365			1.11588			0.557938	+	0.829883i	$0.311593\pi$
$824$		−	365.408i		−	0.443457i
$825$		0			0
$826$	268.626			0.325214
$827$			973.601i			1.17727i	0.808400	+	0.588634i	$0.200334\pi$
$827$			973.601i			1.17727i	−0.808400	+	0.588634i	$0.799666\pi$
$828$	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	$-0.412024\pi$
$853$	465.533			0.545760			0.272880	+	0.962048i	$0.412024\pi$
$854$		−	305.803i		−	0.358084i
$855$		0			0
$856$	57.3122			0.0669535
$857$			1612.01i			1.88099i	0.339811	+	0.940494i	$0.389637\pi$
$857$			1612.01i			1.88099i	−0.339811	+	0.940494i	$0.610363\pi$
$858$	−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	$0.129274\pi$
$863$			681.862i			0.790106i	−0.918658	+	0.395053i	$0.870726\pi$
$864$	−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	$-0.537471\pi$
$877$	−206.003			−0.234896			−0.117448	+	0.993079i	$0.537471\pi$
$878$			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	$-0.354995\pi$
$883$	776.956			0.879905			0.439952	+	0.898021i	$0.354995\pi$
$884$			77.1764i			0.0873036i
$885$		0			0
$886$	550.763			0.621628
$887$			1228.23i			1.38470i	0.721562	+	0.692350i	$0.243425\pi$
$887$			1228.23i			1.38470i	−0.721562	+	0.692350i	$0.756575\pi$
$888$	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	$-0.544793\pi$
$907$	−254.429			−0.280517			−0.140259	+	0.990115i	$0.544793\pi$
$908$			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	$-0.769144\pi$
$937$	−1402.37			−1.49666			−0.748329	+	0.663328i	$0.769144\pi$
$938$			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	$-0.978042\pi$
$947$		−	130.552i		−	0.137858i	0.997622	−	0.0689290i	$-0.0219582\pi$
$948$	−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	$0.0257480\pi$
$953$			154.008i			0.161603i	−0.996730	+	0.0808016i	$0.974252\pi$
$954$	−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	$-0.602858\pi$
$967$	−614.131			−0.635089			−0.317544	+	0.948243i	$0.602858\pi$
$968$			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	$-0.920876\pi$
$977$		−	480.732i		−	0.492049i	0.969264	−	0.246025i	$-0.0791244\pi$
$978$	−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	$0.255641\pi$
$983$			1414.59i			1.43905i	−0.694465	+	0.719526i	$0.744359\pi$
$984$	−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	$-0.415267\pi$
$997$	524.552			0.526130			0.263065	+	0.964778i	$0.415267\pi$
$998$			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.701.17		24
3.2	odd	2	inner	1050.3.e.e.701.19		24
5.2	odd	4		210.3.c.a.29.18	yes	24
5.3	odd	4		210.3.c.a.29.7	✓	24
5.4	even	2	inner	1050.3.e.e.701.20		24
15.2	even	4		210.3.c.a.29.8	yes	24
15.8	even	4		210.3.c.a.29.17	yes	24
15.14	odd	2	inner	1050.3.e.e.701.18		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.3.c.a.29.7	✓	24	5.3	odd	4
210.3.c.a.29.8	yes	24	15.2	even	4
210.3.c.a.29.17	yes	24	15.8	even	4
210.3.c.a.29.18	yes	24	5.2	odd	4
1050.3.e.e.701.17		24	1.1	even	1	trivial
1050.3.e.e.701.18		24	15.14	odd	2	inner
1050.3.e.e.701.19		24	3.2	odd	2	inner
1050.3.e.e.701.20		24	5.4	even	2	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:	\( N \)	\(=\)	\( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
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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