LMFDB - Embedded newform 684.3.b.a.683.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [684,3,Mod(683,684)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(684, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("684.683");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 684 = 2^{2} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	684.b (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:	$18.6376500822$
Analytic rank:	$0$
Dimension:	$80$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			683.19
Character	$\chi$	$=$	684.683
Dual form			684.3.b.a.683.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.45112 + 1.37632i) q^{2} +(0.211495 - 3.99440i) q^{4} -4.00161i q^{5} -12.0281i q^{7} +(5.19067 + 6.08744i) q^{8} +O(q^{10})$	\(q+(-1.45112 + 1.37632i) q^{2} +(0.211495 - 3.99440i) q^{4} -4.00161i q^{5} -12.0281i q^{7} +(5.19067 + 6.08744i) q^{8} +(5.50748 + 5.80681i) q^{10} +15.7569 q^{11} -4.74430i q^{13} +(16.5544 + 17.4542i) q^{14} +(-15.9105 - 1.68959i) q^{16} -7.81502i q^{17} +(13.2190 + 13.6476i) q^{19} +(-15.9840 - 0.846319i) q^{20} +(-22.8651 + 21.6865i) q^{22} +3.71703 q^{23} +8.98715 q^{25} +(6.52966 + 6.88454i) q^{26} +(-48.0450 - 2.54387i) q^{28} +46.8191 q^{29} -56.2449 q^{31} +(25.4135 - 19.4462i) q^{32} +(10.7560 + 11.3405i) q^{34} -48.1316 q^{35} -52.6460i q^{37} +(-37.9658 - 1.61075i) q^{38} +(24.3595 - 20.7710i) q^{40} -31.8316 q^{41} -30.9062i q^{43} +(3.33249 - 62.9393i) q^{44} +(-5.39385 + 5.11582i) q^{46} -35.5329 q^{47} -95.6743 q^{49} +(-13.0414 + 12.3692i) q^{50} +(-18.9506 - 1.00339i) q^{52} +64.9036 q^{53} -63.0527i q^{55} +(73.2201 - 62.4337i) q^{56} +(-67.9401 + 64.4380i) q^{58} +31.1080i q^{59} +6.13439 q^{61} +(81.6180 - 77.4108i) q^{62} +(-10.1139 + 63.1958i) q^{64} -18.9848 q^{65} -102.779 q^{67} +(-31.2163 - 1.65284i) q^{68} +(69.8447 - 66.2444i) q^{70} +89.2964i q^{71} +101.964 q^{73} +(72.4577 + 76.3957i) q^{74} +(57.3099 - 49.9157i) q^{76} -189.524i q^{77} +26.6868 q^{79} +(-6.76108 + 63.6677i) q^{80} +(46.1914 - 43.8104i) q^{82} -62.4230 q^{83} -31.2726 q^{85} +(42.5367 + 44.8485i) q^{86} +(81.7886 + 95.9190i) q^{88} -17.0849 q^{89} -57.0647 q^{91} +(0.786132 - 14.8473i) q^{92} +(51.5625 - 48.9046i) q^{94} +(54.6124 - 52.8973i) q^{95} -134.344i q^{97} +(138.835 - 131.678i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 8 q^{4}+O(q^{10}) $ 80 * q - 8 * q^4	$ 80 q - 8 q^{4} - 56 q^{16} - 400 q^{25} - 464 q^{49} - 272 q^{58} - 352 q^{61} - 200 q^{64} + 480 q^{73} + 152 q^{76} + 32 q^{82} + 704 q^{85}+O(q^{100}) $ 80 * q - 8 * q^4 - 56 * q^16 - 400 * q^25 - 464 * q^49 - 272 * q^58 - 352 * q^61 - 200 * q^64 + 480 * q^73 + 152 * q^76 + 32 * q^82 + 704 * q^85

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/684\mathbb{Z}\right)^\times$.

$n$	$325$	$343$	$533$
$\chi(n)$	$-1$	$-1$	$-1$

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 $

$2$	−1.45112	+	1.37632i	−0.725560	+	0.688159i
$2$	−1.45112	+	1.37632i	−0.725560	+	0.688159i
$3$		0			0
$3$		0			0
$4$	0.211495	−	3.99440i	0.0528737	−	0.998601i
$5$		−	4.00161i		−	0.800321i	−0.916445	−	0.400161i	$-0.868954\pi$
$5$		−	4.00161i		−	0.800321i	0.916445	−	0.400161i	$-0.131046\pi$
$6$		0			0
$7$		−	12.0281i		−	1.71829i	−0.511728	−	0.859147i	$-0.670995\pi$
$7$		−	12.0281i		−	1.71829i	0.511728	−	0.859147i	$-0.329005\pi$
$8$	5.19067	+	6.08744i	0.648834	+	0.760930i
$9$		0			0
$10$	5.50748	+	5.80681i	0.550748	+	0.580681i
$11$	15.7569			1.43244			0.716221	−	0.697874i	$-0.245870\pi$
$11$	15.7569			1.43244			0.716221	+	0.697874i	$0.245870\pi$
$12$		0			0
$13$		−	4.74430i		−	0.364946i	−0.983211	−	0.182473i	$-0.941590\pi$
$13$		−	4.74430i		−	0.364946i	0.983211	−	0.182473i	$-0.0584102\pi$
$14$	16.5544	+	17.4542i	1.18246	+	1.24673i
$15$		0			0
$16$	−15.9105	−	1.68959i	−0.994409	−	0.105599i
$17$		−	7.81502i		−	0.459707i	−0.973225	−	0.229853i	$-0.926175\pi$
$17$		−	7.81502i		−	0.459707i	0.973225	−	0.229853i	$-0.0738247\pi$
$18$		0			0
$19$	13.2190	+	13.6476i	0.695738	+	0.718296i
$19$	13.2190	+	13.6476i	0.695738	+	0.718296i
$20$	−15.9840	−	0.846319i	−0.799202	−	0.0423159i
$21$		0			0
$22$	−22.8651	+	21.6865i	−1.03932	+	0.985748i
$23$	3.71703			0.161610			0.0808050	−	0.996730i	$-0.474251\pi$
$23$	3.71703			0.161610			0.0808050	+	0.996730i	$0.474251\pi$
$24$		0			0
$25$	8.98715			0.359486
$26$	6.52966	+	6.88454i	0.251141	+	0.264790i
$27$		0			0
$28$	−48.0450	−	2.54387i	−1.71589	−	0.0908526i
$29$	46.8191			1.61445			0.807226	−	0.590243i	$-0.200968\pi$
$29$	46.8191			1.61445			0.807226	+	0.590243i	$0.200968\pi$
$30$		0			0
$31$	−56.2449			−1.81435			−0.907175	−	0.420753i	$-0.861766\pi$
$31$	−56.2449			−1.81435			−0.907175	+	0.420753i	$0.861766\pi$
$32$	25.4135	−	19.4462i	0.794172	−	0.607693i
$33$		0			0
$34$	10.7560	+	11.3405i	0.316352	+	0.333545i
$35$	−48.1316			−1.37519
$36$		0			0
$37$		−	52.6460i		−	1.42287i	−0.702754	−	0.711433i	$-0.748047\pi$
$37$		−	52.6460i		−	1.42287i	0.702754	−	0.711433i	$-0.251953\pi$
$38$	−37.9658	−	1.61075i	−0.999101	−	0.0423882i
$39$		0			0
$40$	24.3595	−	20.7710i	0.608989	−	0.519275i
$41$	−31.8316			−0.776380			−0.388190	−	0.921579i	$-0.626899\pi$
$41$	−31.8316			−0.776380			−0.388190	+	0.921579i	$0.626899\pi$
$42$		0			0
$43$		−	30.9062i		−	0.718748i	−0.933194	−	0.359374i	$-0.882990\pi$
$43$		−	30.9062i		−	0.718748i	0.933194	−	0.359374i	$-0.117010\pi$
$44$	3.33249	−	62.9393i	0.0757385	−	1.43044i
$45$		0			0
$46$	−5.39385	+	5.11582i	−0.117258	+	0.111213i
$47$	−35.5329			−0.756020			−0.378010	−	0.925802i	$-0.623391\pi$
$47$	−35.5329			−0.756020			−0.378010	+	0.925802i	$0.623391\pi$
$48$		0			0
$49$	−95.6743			−1.95254
$50$	−13.0414	+	12.3692i	−0.260828	+	0.247384i
$51$		0			0
$52$	−18.9506	−	1.00339i	−0.364435	−	0.0192960i
$53$	64.9036			1.22460			0.612298	−	0.790627i	$-0.290245\pi$
$53$	64.9036			1.22460			0.612298	+	0.790627i	$0.290245\pi$
$54$		0			0
$55$		−	63.0527i		−	1.14641i
$56$	73.2201	−	62.4337i	1.30750	−	1.11489i
$57$		0			0
$58$	−67.9401	+	64.4380i	−1.17138	+	1.11100i
$59$			31.1080i			0.527255i	0.964625	+	0.263627i	$0.0849190\pi$
$59$			31.1080i			0.527255i	−0.964625	+	0.263627i	$0.915081\pi$
$60$		0			0
$61$	6.13439			0.100564			0.0502819	−	0.998735i	$-0.483988\pi$
$61$	6.13439			0.100564			0.0502819	+	0.998735i	$0.483988\pi$
$62$	81.6180	−	77.4108i	1.31642	−	1.24856i
$63$		0			0
$64$	−10.1139	+	63.1958i	−0.158030	+	0.987434i
$65$	−18.9848			−0.292074
$66$		0			0
$67$	−102.779			−1.53401			−0.767004	−	0.641642i	$-0.778254\pi$
$67$	−102.779			−1.53401			−0.767004	+	0.641642i	$0.778254\pi$
$68$	−31.2163	−	1.65284i	−0.459064	−	0.0243064i
$69$		0			0
$70$	69.8447	−	66.2444i	0.997781	−	0.946348i
$71$			89.2964i			1.25770i	0.777528	+	0.628848i	$0.216473\pi$
$71$			89.2964i			1.25770i	−0.777528	+	0.628848i	$0.783527\pi$
$72$		0			0
$73$	101.964			1.39676			0.698382	−	0.715725i	$-0.253904\pi$
$73$	101.964			1.39676			0.698382	+	0.715725i	$0.253904\pi$
$74$	72.4577	+	76.3957i	0.979158	+	1.03237i
$75$		0			0
$76$	57.3099	−	49.9157i	0.754077	−	0.656786i
$77$		−	189.524i		−	2.46136i
$78$		0			0
$79$	26.6868			0.337808			0.168904	−	0.985633i	$-0.445977\pi$
$79$	26.6868			0.337808			0.168904	+	0.985633i	$0.445977\pi$
$80$	−6.76108	+	63.6677i	−0.0845135	+	0.795846i
$81$		0			0
$82$	46.1914	−	43.8104i	0.563310	−	0.534273i
$83$	−62.4230			−0.752084			−0.376042	−	0.926603i	$-0.622715\pi$
$83$	−62.4230			−0.752084			−0.376042	+	0.926603i	$0.622715\pi$
$84$		0			0
$85$	−31.2726			−0.367913
$86$	42.5367	+	44.8485i	0.494613	+	0.521494i
$87$		0			0
$88$	81.7886	+	95.9190i	0.929416	+	1.08999i
$89$	−17.0849			−0.191965			−0.0959826	−	0.995383i	$-0.530599\pi$
$89$	−17.0849			−0.191965			−0.0959826	+	0.995383i	$0.530599\pi$
$90$		0			0
$91$	−57.0647			−0.627084
$92$	0.786132	−	14.8473i	0.00854492	−	0.161384i
$93$		0			0
$94$	51.5625	−	48.9046i	0.548537	−	0.520262i
$95$	54.6124	−	52.8973i	0.574867	−	0.556814i
$96$		0			0
$97$		−	134.344i		−	1.38499i	−0.721423	−	0.692494i	$-0.756512\pi$
$97$		−	134.344i		−	1.38499i	0.721423	−	0.692494i	$-0.243488\pi$
$98$	138.835	−	131.678i	1.41668	−	1.34366i
$99$		0			0
$100$	1.90073	−	35.8983i	0.0190073	−	0.358983i
$101$		−	113.622i		−	1.12497i	−0.826809	−	0.562483i	$-0.809846\pi$
$101$		−	113.622i		−	1.12497i	0.826809	−	0.562483i	$-0.190154\pi$
$102$		0			0
$103$	92.7894			0.900868			0.450434	−	0.892810i	$-0.351269\pi$
$103$	92.7894			0.900868			0.450434	+	0.892810i	$0.351269\pi$
$104$	28.8806	−	24.6261i	0.277698	−	0.236789i
$105$		0			0
$106$	−94.1829	+	89.3280i	−0.888518	+	0.842717i
$107$			9.75736i			0.0911903i	0.998960	+	0.0455951i	$0.0145184\pi$
$107$			9.75736i			0.0911903i	−0.998960	+	0.0455951i	$0.985482\pi$
$108$		0			0
$109$			6.03824i			0.0553967i	0.999616	+	0.0276984i	$0.00881779\pi$
$109$			6.03824i			0.0553967i	−0.999616	+	0.0276984i	$0.991182\pi$
$110$	86.7807	+	91.4971i	0.788915	+	0.831791i
$111$		0			0
$112$	−20.3225	+	191.373i	−0.181451	+	1.70869i
$113$	−203.980			−1.80513			−0.902565	−	0.430554i	$-0.858318\pi$
$113$	−203.980			−1.80513			−0.902565	+	0.430554i	$0.858318\pi$
$114$		0			0
$115$		−	14.8741i		−	0.129340i
$116$	9.90200	−	187.014i	0.0853620	−	1.61219i
$117$		0			0
$118$	−42.8146	−	45.1415i	−0.362835	−	0.382555i
$119$	−93.9995			−0.789912
$120$		0			0
$121$	127.279			1.05189
$122$	−8.90174	+	8.44288i	−0.0729651	+	0.0692039i
$123$		0			0
$124$	−11.8955	+	224.665i	−0.0959314	+	1.81181i
$125$		−	136.003i		−	1.08803i
$126$		0			0
$127$	112.456			0.885482			0.442741	−	0.896649i	$-0.354006\pi$
$127$	112.456			0.885482			0.442741	+	0.896649i	$0.354006\pi$
$128$	−72.3011	−	105.625i	−0.564852	−	0.825192i
$129$		0			0
$130$	27.5492	−	26.1291i	0.211917	−	0.200993i
$131$	82.4318			0.629250			0.314625	−	0.949216i	$-0.398121\pi$
$131$	82.4318			0.629250			0.314625	+	0.949216i	$0.398121\pi$
$132$		0			0
$133$	164.154	−	158.999i	1.23424	−	1.19548i
$134$	149.144	−	141.456i	1.11301	−	1.05564i
$135$		0			0
$136$	47.5735	−	40.5652i	0.349805	−	0.298273i
$137$			249.682i			1.82250i	0.411854	+	0.911250i	$0.364881\pi$
$137$			249.682i			1.82250i	−0.411854	+	0.911250i	$0.635119\pi$
$138$		0			0
$139$		−	3.28561i		−	0.0236375i	−0.999930	−	0.0118188i	$-0.996238\pi$
$139$		−	3.28561i		−	0.0236375i	0.999930	−	0.0118188i	$-0.00376211\pi$
$140$	−10.1796	+	192.257i	−0.0727113	+	1.37326i
$141$		0			0
$142$	−122.900	−	129.580i	−0.865495	−	0.912533i
$143$		−	74.7552i		−	0.522764i
$144$		0			0
$145$		−	187.352i		−	1.29208i
$146$	−147.962	+	140.335i	−1.01344	+	0.961196i
$147$		0			0
$148$	−210.290	−	11.1344i	−1.42088	−	0.0752322i
$149$		−	40.7940i		−	0.273785i	−0.990586	−	0.136893i	$-0.956288\pi$
$149$		−	40.7940i		−	0.273785i	0.990586	−	0.136893i	$-0.0437115\pi$
$150$		0			0
$151$	−240.053			−1.58975			−0.794876	−	0.606772i	$-0.792464\pi$
$151$	−240.053			−1.58975			−0.794876	+	0.606772i	$0.792464\pi$
$152$	−14.4636	+	151.310i	−0.0951551	+	0.995462i
$153$		0			0
$154$	260.846	+	275.023i	1.69381	+	1.78586i
$155$			225.070i			1.45206i
$156$		0			0
$157$	72.1857			0.459782			0.229891	−	0.973216i	$-0.426163\pi$
$157$	72.1857			0.459782			0.229891	+	0.973216i	$0.426163\pi$
$158$	−38.7257	+	36.7295i	−0.245100	+	0.232465i
$159$		0			0
$160$	−77.8159	−	101.695i	−0.486350	−	0.635593i
$161$		−	44.7087i		−	0.277694i
$162$		0			0
$163$			98.5895i			0.604844i	0.953174	+	0.302422i	$0.0977951\pi$
$163$			98.5895i			0.604844i	−0.953174	+	0.302422i	$0.902205\pi$
$164$	−6.73221	+	127.148i	−0.0410501	+	0.775294i
$165$		0			0
$166$	90.5832	−	85.9139i	0.545682	−	0.517553i
$167$			53.8093i			0.322211i	0.986937	+	0.161106i	$0.0515060\pi$
$167$			53.8093i			0.322211i	−0.986937	+	0.161106i	$0.948494\pi$
$168$		0			0
$169$	146.492			0.866815
$170$	45.3803	−	43.0411i	0.266943	−	0.253183i
$171$		0			0
$172$	−123.452	−	6.53649i	−0.717742	−	0.0380029i
$173$	−66.0323			−0.381690			−0.190845	−	0.981620i	$-0.561123\pi$
$173$	−66.0323			−0.381690			−0.190845	+	0.981620i	$0.561123\pi$
$174$		0			0
$175$		−	108.098i		−	0.617703i
$176$	−250.700	−	26.6227i	−1.42443	−	0.151265i
$177$		0			0
$178$	24.7922	−	23.5143i	0.139282	−	0.132103i
$179$			154.451i			0.862856i	0.902147	+	0.431428i	$0.141990\pi$
$179$			154.451i			0.862856i	−0.902147	+	0.431428i	$0.858010\pi$
$180$		0			0
$181$		−	36.0989i		−	0.199441i	−0.995015	−	0.0997206i	$-0.968205\pi$
$181$		−	36.0989i		−	0.199441i	0.995015	−	0.0997206i	$-0.0317949\pi$
$182$	82.8077	−	78.5392i	0.454987	−	0.431534i
$183$		0			0
$184$	19.2939	+	22.6272i	0.104858	+	0.122974i
$185$	−210.669			−1.13875
$186$		0			0
$187$		−	123.140i		−	0.658503i
$188$	−7.51503	+	141.933i	−0.0399736	+	0.754962i
$189$		0			0
$190$	−6.44559	+	151.924i	−0.0339242	+	0.799602i
$191$	−47.0762			−0.246472			−0.123236	−	0.992377i	$-0.539327\pi$
$191$	−47.0762			−0.246472			−0.123236	+	0.992377i	$0.539327\pi$
$192$		0			0
$193$		−	45.0791i		−	0.233570i	−0.993157	−	0.116785i	$-0.962741\pi$
$193$		−	45.0791i		−	0.233570i	0.993157	−	0.116785i	$-0.0372589\pi$
$194$	184.900	+	194.949i	0.953092	+	1.00489i
$195$		0			0
$196$	−20.2346	+	382.162i	−0.103238	+	1.94981i
$197$			290.498i			1.47461i	0.675560	+	0.737305i	$0.263902\pi$
$197$			290.498i			1.47461i	−0.675560	+	0.737305i	$0.736098\pi$
$198$		0			0
$199$		−	311.638i		−	1.56602i	−0.622008	−	0.783011i	$-0.713683\pi$
$199$		−	311.638i		−	1.56602i	0.622008	−	0.783011i	$-0.286317\pi$
$200$	46.6493	+	54.7087i	0.233247	+	0.273544i
$201$		0			0
$202$	156.380	+	164.879i	0.774156	+	0.816230i
$203$		−	563.143i		−	2.77410i
$204$		0			0
$205$			127.377i			0.621353i
$206$	−134.648	+	127.708i	−0.653633	+	0.619940i
$207$		0			0
$208$	−8.01592	+	75.4843i	−0.0385381	+	0.362905i
$209$	208.290	+	215.044i	0.996604	+	1.02892i
$210$		0			0
$211$	−274.975			−1.30320			−0.651600	−	0.758563i	$-0.725902\pi$
$211$	−274.975			−1.30320			−0.651600	+	0.758563i	$0.725902\pi$
$212$	13.7268	−	259.251i	0.0647489	−	1.22288i
$213$		0			0
$214$	−13.4292	−	14.1591i	−0.0627534	−	0.0661640i
$215$	−123.674			−0.575229
$216$		0			0
$217$			676.517i			3.11759i
$218$	−8.31054	−	8.76221i	−0.0381218	−	0.0401936i
$219$		0			0
$220$	−251.858	−	13.3353i	−1.14481	−	0.0606151i
$221$	−37.0768			−0.167768
$222$		0			0
$223$	−16.0992			−0.0721935			−0.0360968	−	0.999348i	$-0.511492\pi$
$223$	−16.0992			−0.0721935			−0.0360968	+	0.999348i	$0.511492\pi$
$224$	−233.900	−	305.675i	−1.04420	−	1.36462i
$225$		0			0
$226$	295.999	−	280.741i	1.30973	−	1.24222i
$227$			259.732i			1.14419i	0.820186	+	0.572096i	$0.193870\pi$
$227$			259.732i			1.14419i	−0.820186	+	0.572096i	$0.806130\pi$
$228$		0			0
$229$	−367.921			−1.60664			−0.803322	−	0.595545i	$-0.796936\pi$
$229$	−367.921			−1.60664			−0.803322	+	0.595545i	$0.796936\pi$
$230$	20.4715	+	21.5841i	0.0890064	+	0.0938438i
$231$		0			0
$232$	243.022	+	285.009i	1.04751	+	1.22849i
$233$		−	249.444i		−	1.07057i	−0.844670	−	0.535287i	$-0.820203\pi$
$233$		−	249.444i		−	1.07057i	0.844670	−	0.535287i	$-0.179797\pi$
$234$		0			0
$235$			142.189i			0.605059i
$236$	124.258	+	6.57919i	0.526517	+	0.0278779i
$237$		0			0
$238$	136.405	−	129.373i	0.573128	−	0.543585i
$239$	47.0788			0.196982			0.0984912	−	0.995138i	$-0.468598\pi$
$239$	47.0788			0.196982			0.0984912	+	0.995138i	$0.468598\pi$
$240$		0			0
$241$			316.682i			1.31403i	0.753877	+	0.657016i	$0.228182\pi$
$241$			316.682i			1.31403i	−0.753877	+	0.657016i	$0.771818\pi$
$242$	−184.696	+	175.176i	−0.763208	+	0.723867i
$243$		0			0
$244$	1.29739	−	24.5032i	0.00531718	−	0.100423i
$245$			382.851i			1.56266i
$246$		0			0
$247$	64.7483	−	62.7149i	0.262139	−	0.253907i
$248$	−291.948	−	342.387i	−1.17721	−	1.38059i
$249$		0			0
$250$	187.184	+	197.357i	0.748735	+	0.789427i
$251$	−399.629			−1.59215			−0.796074	−	0.605199i	$-0.793093\pi$
$251$	−399.629			−1.59215			−0.796074	+	0.605199i	$0.793093\pi$
$252$		0			0
$253$	58.5687			0.231497
$254$	−163.187	+	154.776i	−0.642470	+	0.609353i
$255$		0			0
$256$	250.291	+	53.7646i	0.977698	+	0.210018i
$257$	−36.1991			−0.140853			−0.0704263	−	0.997517i	$-0.522436\pi$
$257$	−36.1991			−0.140853			−0.0704263	+	0.997517i	$0.522436\pi$
$258$		0			0
$259$	−633.230			−2.44490
$260$	−4.01519	+	75.8330i	−0.0154430	+	0.291665i
$261$		0			0
$262$	−119.618	+	113.452i	−0.456559	+	0.433024i
$263$	96.8904			0.368405			0.184202	−	0.982888i	$-0.441030\pi$
$263$	96.8904			0.368405			0.184202	+	0.982888i	$0.441030\pi$
$264$		0			0
$265$		−	259.719i		−	0.980071i
$266$	−19.3742	+	456.656i	−0.0728354	+	1.71675i
$267$		0			0
$268$	−21.7371	+	410.539i	−0.0811087	+	1.53186i
$269$	−193.082			−0.717777			−0.358889	−	0.933380i	$-0.616844\pi$
$269$	−193.082			−0.717777			−0.358889	+	0.933380i	$0.616844\pi$
$270$		0			0
$271$		−	388.111i		−	1.43215i	−0.698026	−	0.716073i	$-0.745938\pi$
$271$		−	388.111i		−	1.43215i	0.698026	−	0.716073i	$-0.254062\pi$
$272$	−13.2042	+	124.341i	−0.0485448	+	0.457137i
$273$		0			0
$274$	−343.643	−	362.319i	−1.25417	−	1.32233i
$275$	141.609			0.514943
$276$		0			0
$277$	152.205			0.549477			0.274738	−	0.961519i	$-0.411409\pi$
$277$	152.205			0.549477			0.274738	+	0.961519i	$0.411409\pi$
$278$	4.52205	+	4.76782i	0.0162664	+	0.0171504i
$279$		0			0
$280$	−249.835	−	292.998i	−0.892268	−	1.04642i
$281$	−25.3220			−0.0901137			−0.0450569	−	0.998984i	$-0.514347\pi$
$281$	−25.3220			−0.0901137			−0.0450569	+	0.998984i	$0.514347\pi$
$282$		0			0
$283$			459.492i			1.62365i	0.583903	+	0.811823i	$0.301525\pi$
$283$			459.492i			1.62365i	−0.583903	+	0.811823i	$0.698475\pi$
$284$	356.686	+	18.8857i	1.25594	+	0.0664990i
$285$		0			0
$286$	102.887	+	108.479i	0.359745	+	0.379296i
$287$			382.872i			1.33405i
$288$		0			0
$289$	227.925			0.788669
$290$	257.855	+	271.870i	0.889157	+	0.937481i
$291$		0			0
$292$	21.5648	−	407.284i	0.0738521	−	1.39481i
$293$	122.228			0.417159			0.208579	−	0.978005i	$-0.433116\pi$
$293$	122.228			0.417159			0.208579	+	0.978005i	$0.433116\pi$
$294$		0			0
$295$	124.482			0.421973
$296$	320.480	−	273.268i	1.08270	−	0.923203i
$297$		0			0
$298$	56.1456	+	59.1970i	0.188408	+	0.198648i
$299$		−	17.6347i		−	0.0589789i
$300$		0			0
$301$	−371.741			−1.23502
$302$	348.345	−	330.389i	1.15346	−	1.09400i
$303$		0			0
$304$	−187.263	−	239.476i	−0.615996	−	0.787749i
$305$		−	24.5474i		−	0.0804834i
$306$		0			0
$307$	515.721			1.67987			0.839937	−	0.542685i	$-0.182592\pi$
$307$	515.721			1.67987			0.839937	+	0.542685i	$0.182592\pi$
$308$	−757.037	−	40.0834i	−2.45791	−	0.130141i
$309$		0			0
$310$	−309.768	−	326.603i	−0.999251	−	1.05356i
$311$	127.010			0.408393			0.204196	−	0.978930i	$-0.434542\pi$
$311$	127.010			0.408393			0.204196	+	0.978930i	$0.434542\pi$
$312$		0			0
$313$	88.0936			0.281449			0.140725	−	0.990049i	$-0.455057\pi$
$313$	88.0936			0.281449			0.140725	+	0.990049i	$0.455057\pi$
$314$	−104.750	+	99.3506i	−0.333599	+	0.316403i
$315$		0			0
$316$	5.64412	−	106.598i	0.0178611	−	0.337335i
$317$	581.946			1.83579			0.917896	−	0.396821i	$-0.129887\pi$
$317$	581.946			1.83579			0.917896	+	0.396821i	$0.129887\pi$
$318$		0			0
$319$	737.722			2.31261
$320$	252.885	+	40.4719i	0.790265	+	0.126475i
$321$		0			0
$322$	61.5333	+	64.8776i	0.191097	+	0.201483i
$323$	106.656	−	103.307i	0.330206	−	0.319835i
$324$		0			0
$325$		−	42.6377i		−	0.131193i
$326$	−135.691	−	143.065i	−0.416229	−	0.438850i
$327$		0			0
$328$	−165.227	−	193.773i	−0.503741	−	0.590771i
$329$			427.392i			1.29906i
$330$		0			0
$331$	382.665			1.15609			0.578044	−	0.816006i	$-0.303816\pi$
$331$	382.665			1.15609			0.578044	+	0.816006i	$0.303816\pi$
$332$	−13.2021	+	249.343i	−0.0397654	+	0.751032i
$333$		0			0
$334$	−74.0588	−	78.0837i	−0.221733	−	0.233784i
$335$			411.279i			1.22770i
$336$		0			0
$337$		−	188.264i		−	0.558645i	−0.960197	−	0.279323i	$-0.909890\pi$
$337$		−	188.264i		−	0.558645i	0.960197	−	0.279323i	$-0.0901099\pi$
$338$	−212.577	+	201.619i	−0.628926	+	0.596506i
$339$		0			0
$340$	−6.61400	+	124.916i	−0.0194529	+	0.367399i
$341$	−886.242			−2.59895
$342$		0			0
$343$			561.401i			1.63674i
$344$	188.139	−	160.424i	0.546917	−	0.466348i
$345$		0			0
$346$	95.8207	−	90.8815i	0.276939	−	0.262663i
$347$	306.142			0.882253			0.441127	−	0.897445i	$-0.354579\pi$
$347$	306.142			0.882253			0.441127	+	0.897445i	$0.354579\pi$
$348$		0			0
$349$	192.206			0.550734			0.275367	−	0.961339i	$-0.411201\pi$
$349$	192.206			0.550734			0.275367	+	0.961339i	$0.411201\pi$
$350$	148.777	+	156.863i	0.425078	+	0.448180i
$351$		0			0
$352$	400.437	−	306.411i	1.13761	−	0.870485i
$353$		−	455.473i		−	1.29029i	−0.764060	−	0.645145i	$-0.776797\pi$
$353$		−	455.473i		−	1.29029i	0.764060	−	0.645145i	$-0.223203\pi$
$354$		0			0
$355$	357.329			1.00656
$356$	−3.61337	+	68.2440i	−0.0101499	+	0.191697i
$357$		0			0
$358$	−212.574	−	224.127i	−0.593782	−	0.626054i
$359$	290.476			0.809125			0.404562	−	0.914510i	$-0.367424\pi$
$359$	290.476			0.809125			0.404562	+	0.914510i	$0.367424\pi$
$360$		0			0
$361$	−11.5152	+	360.816i	−0.0318980	+	0.999491i
$362$	49.6835	+	52.3838i	0.137247	+	0.144707i
$363$		0			0
$364$	−12.0689	+	227.939i	−0.0331563	+	0.626207i
$365$		−	408.019i		−	1.11786i
$366$		0			0
$367$			380.381i			1.03646i	0.855241	+	0.518230i	$0.173409\pi$
$367$			380.381i			1.03646i	−0.855241	+	0.518230i	$0.826591\pi$
$368$	−59.1399	−	6.28026i	−0.160706	−	0.0170659i
$369$		0			0
$370$	305.705	−	289.947i	0.826231	−	0.783641i
$371$		−	780.665i		−	2.10422i
$372$		0			0
$373$		−	381.277i		−	1.02219i	−0.859524	−	0.511095i	$-0.829240\pi$
$373$		−	381.277i		−	1.02219i	0.859524	−	0.511095i	$-0.170760\pi$
$374$	169.480	+	178.691i	0.453155	+	0.477784i
$375$		0			0
$376$	−184.440	−	216.305i	−0.490531	−	0.575278i
$377$		−	222.124i		−	0.589187i
$378$		0			0
$379$	−388.600			−1.02533			−0.512665	−	0.858589i	$-0.671342\pi$
$379$	−388.600			−1.02533			−0.512665	+	0.858589i	$0.671342\pi$
$380$	−199.743	−	229.332i	−0.525639	−	0.603504i
$381$		0			0
$382$	68.3132	−	64.7918i	0.178830	−	0.169612i
$383$		−	147.201i		−	0.384337i	−0.981362	−	0.192168i	$-0.938448\pi$
$383$		−	147.201i		−	0.384337i	0.981362	−	0.192168i	$-0.0615520\pi$
$384$		0			0
$385$	−758.402			−1.96988
$386$	62.0432	+	65.4151i	0.160734	+	0.169469i
$387$		0			0
$388$	−536.624	−	28.4130i	−1.38305	−	0.0732295i
$389$			105.479i			0.271153i	0.990767	+	0.135577i	$0.0432887\pi$
$389$			105.479i			0.271153i	−0.990767	+	0.135577i	$0.956711\pi$
$390$		0			0
$391$		−	29.0486i		−	0.0742932i
$392$	−496.614	−	582.412i	−1.26687	−	1.48574i
$393$		0			0
$394$	−399.818	−	421.548i	−1.01477	−	1.06992i
$395$		−	106.790i		−	0.270355i
$396$		0			0
$397$	−218.614			−0.550665			−0.275332	−	0.961349i	$-0.588788\pi$
$397$	−218.614			−0.550665			−0.275332	+	0.961349i	$0.588788\pi$
$398$	428.914	+	452.225i	1.07767	+	1.13624i
$399$		0			0
$400$	−142.990	−	15.1846i	−0.357476	−	0.0379615i
$401$	479.946			1.19687			0.598437	−	0.801170i	$-0.295789\pi$
$401$	479.946			1.19687			0.598437	+	0.801170i	$0.295789\pi$
$402$		0			0
$403$			266.842i			0.662139i
$404$	−453.851	−	24.0304i	−1.12339	−	0.0594811i
$405$		0			0
$406$	775.064	+	817.188i	1.90903	+	2.01278i
$407$		−	829.536i		−	2.03817i
$408$		0			0
$409$			138.535i			0.338716i	0.985555	+	0.169358i	$0.0541694\pi$
$409$			138.535i			0.338716i	−0.985555	+	0.169358i	$0.945831\pi$
$410$	−175.312	−	184.840i	−0.427590	−	0.450829i
$411$		0			0
$412$	19.6245	−	370.638i	0.0476322	−	0.899607i
$413$	374.169			0.905979
$414$		0			0
$415$			249.792i			0.601909i
$416$	−92.2584	−	120.569i	−0.221775	−	0.289830i
$417$		0			0
$418$	−598.222	−	25.3804i	−1.43115	−	0.0607186i
$419$	−67.4631			−0.161010			−0.0805049	−	0.996754i	$-0.525653\pi$
$419$	−67.4631			−0.161010			−0.0805049	+	0.996754i	$0.525653\pi$
$420$		0			0
$421$			86.5279i			0.205529i	0.994706	+	0.102765i	$0.0327689\pi$
$421$			86.5279i			0.205529i	−0.994706	+	0.102765i	$0.967231\pi$
$422$	399.022	−	378.453i	0.945549	−	0.896809i
$423$		0			0
$424$	336.893	+	395.097i	0.794559	+	0.931833i
$425$		−	70.2347i		−	0.165258i
$426$		0			0
$427$		−	73.7849i		−	0.172798i
$428$	38.9748	+	2.06363i	0.0910627	+	0.00482157i
$429$		0			0
$430$	179.466	−	170.215i	0.417363	−	0.395849i
$431$		−	223.844i		−	0.519359i	−0.965695	−	0.259680i	$-0.916383\pi$
$431$		−	223.844i		−	0.519359i	0.965695	−	0.259680i	$-0.0836169\pi$
$432$		0			0
$433$		−	659.844i		−	1.52389i	−0.647642	−	0.761945i	$-0.724245\pi$
$433$		−	659.844i		−	1.52389i	0.647642	−	0.761945i	$-0.275755\pi$
$434$	−931.102	−	981.706i	−2.14540	−	2.26200i
$435$		0			0
$436$	24.1192	+	1.27706i	0.0553192	+	0.00292903i
$437$	49.1355	+	50.7286i	0.112438	+	0.116084i
$438$		0			0
$439$	206.969			0.471455			0.235728	−	0.971819i	$-0.424253\pi$
$439$	206.969			0.471455			0.235728	+	0.971819i	$0.424253\pi$
$440$	383.830	−	327.286i	0.872341	−	0.743832i
$441$		0			0
$442$	53.8028	−	51.0294i	0.121726	−	0.115451i
$443$	−384.066			−0.866966			−0.433483	−	0.901162i	$-0.642716\pi$
$443$	−384.066			−0.866966			−0.433483	+	0.901162i	$0.642716\pi$
$444$		0			0
$445$			68.3671i			0.153634i
$446$	23.3618	−	22.1576i	0.0523807	−	0.0496807i
$447$		0			0
$448$	760.123	+	121.651i	1.69670	+	0.271542i
$449$	345.980			0.770558			0.385279	−	0.922800i	$-0.374105\pi$
$449$	345.980			0.770558			0.385279	+	0.922800i	$0.374105\pi$
$450$		0			0
$451$	−501.565			−1.11212
$452$	−43.1406	+	814.777i	−0.0954439	+	1.80260i
$453$		0			0
$454$	−357.474	−	376.902i	−0.787387	−	0.830180i
$455$			228.350i			0.501869i
$456$		0			0
$457$	268.260			0.587003			0.293502	−	0.955959i	$-0.405179\pi$
$457$	268.260			0.587003			0.293502	+	0.955959i	$0.405179\pi$
$458$	533.898	−	506.377i	1.16572	−	1.10563i
$459$		0			0
$460$	−59.4131	−	3.14579i	−0.129159	−	0.00683868i
$461$			548.763i			1.19037i	0.803587	+	0.595187i	$0.202922\pi$
$461$			548.763i			1.19037i	−0.803587	+	0.595187i	$0.797078\pi$
$462$		0			0
$463$			226.387i			0.488957i	0.969655	+	0.244478i	$0.0786167\pi$
$463$			226.387i			0.488957i	−0.969655	+	0.244478i	$0.921383\pi$
$464$	−744.917	−	79.1052i	−1.60542	−	0.170485i
$465$		0			0
$466$	343.314	+	361.973i	0.736725	+	0.776765i
$467$	230.126			0.492774			0.246387	−	0.969171i	$-0.420757\pi$
$467$	230.126			0.492774			0.246387	+	0.969171i	$0.420757\pi$
$468$		0			0
$469$			1236.23i			2.63588i
$470$	−195.697	−	206.333i	−0.416377	−	0.439006i
$471$		0			0
$472$	−189.368	+	161.472i	−0.401204	+	0.342101i
$473$		−	486.984i		−	1.02956i
$474$		0			0
$475$	118.801	+	122.653i	0.250108	+	0.258217i
$476$	−19.8804	+	375.472i	−0.0417656	+	0.788807i
$477$		0			0
$478$	−68.3169	+	64.7954i	−0.142922	+	0.135555i
$479$	496.609			1.03676			0.518381	−	0.855150i	$-0.326535\pi$
$479$	496.609			1.03676			0.518381	+	0.855150i	$0.326535\pi$
$480$		0			0
$481$	−249.768			−0.519269
$482$	−435.855	−	459.543i	−0.904263	−	0.953409i
$483$		0			0
$484$	26.9188	−	508.402i	0.0556173	−	1.05042i
$485$	−537.591			−1.10844
$486$		0			0
$487$	−14.9943			−0.0307892			−0.0153946	−	0.999881i	$-0.504900\pi$
$487$	−14.9943			−0.0307892			−0.0153946	+	0.999881i	$0.504900\pi$
$488$	31.8416	+	37.3428i	0.0652492	+	0.0765221i
$489$		0			0
$490$	−526.925	−	555.562i	−1.07536	−	1.13380i
$491$	−319.685			−0.651090			−0.325545	−	0.945526i	$-0.605548\pi$
$491$	−319.685			−0.651090			−0.325545	+	0.945526i	$0.605548\pi$
$492$		0			0
$493$		−	365.892i		−	0.742175i
$494$	−7.64188	+	180.121i	−0.0154694	+	0.364618i
$495$		0			0
$496$	894.886	+	95.0308i	1.80421	+	0.191594i
$497$	1074.06			2.16109
$498$		0			0
$499$			488.538i			0.979033i	0.871994	+	0.489517i	$0.162827\pi$
$499$			488.538i			0.979033i	−0.871994	+	0.489517i	$0.837173\pi$
$500$	−543.252	−	28.7640i	−1.08650	−	0.0575279i
$501$		0			0
$502$	579.910	−	550.017i	1.15520	−	1.09565i
$503$	887.019			1.76346			0.881729	−	0.471757i	$-0.156380\pi$
$503$	887.019			1.76346			0.881729	+	0.471757i	$0.156380\pi$
$504$		0			0
$505$	−454.669			−0.900335
$506$	−84.9902	+	80.6092i	−0.167965	+	0.159307i
$507$		0			0
$508$	23.7839	−	449.196i	0.0468187	−	0.884244i
$509$	908.075			1.78404			0.892018	−	0.451999i	$-0.149289\pi$
$509$	908.075			1.78404			0.892018	+	0.451999i	$0.149289\pi$
$510$		0			0
$511$		−	1226.43i		−	2.40005i
$512$	−437.199	+	266.461i	−0.853904	+	0.520431i
$513$		0			0
$514$	52.5293	−	49.8215i	0.102197	−	0.0969291i
$515$		−	371.306i		−	0.720983i
$516$		0			0
$517$	−559.887			−1.08295
$518$	918.892	−	871.526i	1.77392	−	1.68248i
$519$		0			0
$520$	−98.5438	−	115.569i	−0.189507	−	0.222248i
$521$	481.619			0.924413			0.462207	−	0.886772i	$-0.347058\pi$
$521$	481.619			0.924413			0.462207	+	0.886772i	$0.347058\pi$
$522$		0			0
$523$	31.0148			0.0593017			0.0296509	−	0.999560i	$-0.490560\pi$
$523$	31.0148			0.0593017			0.0296509	+	0.999560i	$0.490560\pi$
$524$	17.4339	−	329.266i	0.0332708	−	0.628370i
$525$		0			0
$526$	−140.600	+	133.352i	−0.267299	+	0.253521i
$527$			439.555i			0.834069i
$528$		0			0
$529$	−515.184			−0.973882
$530$	357.456	+	376.883i	0.674445	+	0.711100i
$531$		0			0
$532$	−600.389	−	689.327i	−1.12855	−	1.29573i
$533$			151.018i			0.283336i
$534$		0			0
$535$	39.0451			0.0729815
$536$	−533.490	−	625.659i	−0.995316	−	1.16727i
$537$		0			0
$538$	280.185	−	265.743i	0.520790	−	0.493945i
$539$	−1507.53			−2.79689
$540$		0			0
$541$	437.142			0.808025			0.404013	−	0.914753i	$-0.367615\pi$
$541$	437.142			0.808025			0.404013	+	0.914753i	$0.367615\pi$
$542$	534.165	+	563.196i	0.985544	+	1.03911i
$543$		0			0
$544$	−151.972	−	198.607i	−0.279361	−	0.365086i
$545$	24.1627			0.0443352
$546$		0			0
$547$	413.515			0.755968			0.377984	−	0.925812i	$-0.376617\pi$
$547$	413.515			0.755968			0.377984	+	0.925812i	$0.376617\pi$
$548$	997.333	+	52.8065i	1.81995	+	0.0963623i
$549$		0			0
$550$	−205.492	+	194.899i	−0.373622	+	0.354363i
$551$	618.902	+	638.969i	1.12323	+	1.15965i
$552$		0			0
$553$		−	320.991i		−	0.580453i
$554$	−220.868	+	209.483i	−0.398678	+	0.378128i
$555$		0			0
$556$	−13.1241	−	0.694890i	−0.0236044	−	0.00124980i
$557$			363.687i			0.652939i	0.945208	+	0.326469i	$0.105859\pi$
$557$			363.687i			0.652939i	−0.945208	+	0.326469i	$0.894141\pi$
$558$		0			0
$559$	−146.628			−0.262304
$560$	765.799	+	81.3227i	1.36750	+	0.145219i
$561$		0			0
$562$	36.7452	−	34.8511i	0.0653829	−	0.0620126i
$563$		−	35.5312i		−	0.0631105i	−0.999502	−	0.0315552i	$-0.989954\pi$
$563$		−	35.5312i		−	0.0631105i	0.999502	−	0.0315552i	$-0.0100460\pi$
$564$		0			0
$565$			816.246i			1.44468i
$566$	−632.407	−	666.778i	−1.11733	−	1.17805i
$567$		0			0
$568$	−543.587	+	463.508i	−0.957019	+	0.816035i
$569$	−162.235			−0.285123			−0.142561	−	0.989786i	$-0.545534\pi$
$569$	−162.235			−0.285123			−0.142561	+	0.989786i	$0.545534\pi$
$570$		0			0
$571$		−	585.417i		−	1.02525i	−0.858613	−	0.512625i	$-0.828673\pi$
$571$		−	585.417i		−	1.02525i	0.858613	−	0.512625i	$-0.171327\pi$
$572$	−298.602	−	15.8103i	−0.522032	−	0.0276404i
$573$		0			0
$574$	−526.954	−	555.593i	−0.918038	−	0.967932i
$575$	33.4055			0.0580965
$576$		0			0
$577$	−333.812			−0.578530			−0.289265	−	0.957249i	$-0.593411\pi$
$577$	−333.812			−0.578530			−0.289265	+	0.957249i	$0.593411\pi$
$578$	−330.747	+	313.698i	−0.572227	+	0.542730i
$579$		0			0
$580$	−748.358	−	39.6239i	−1.29027	−	0.0683170i
$581$			750.827i			1.29230i
$582$		0			0
$583$	1022.68			1.75416
$584$	529.260	+	620.698i	0.906267	+	1.06284i
$585$		0			0
$586$	−177.367	+	168.224i	−0.302674	+	0.287072i
$587$	691.627			1.17824			0.589120	−	0.808046i	$-0.299475\pi$
$587$	691.627			1.17824			0.589120	+	0.808046i	$0.299475\pi$
$588$		0			0
$589$	−743.502	−	767.609i	−1.26231	−	1.30324i
$590$	−180.638	+	171.327i	−0.306167	+	0.290385i
$591$		0			0
$592$	−88.9503	+	837.627i	−0.150254	+	1.41491i
$593$		−	665.716i		−	1.12262i	−0.827604	−	0.561312i	$-0.810297\pi$
$593$		−	665.716i		−	1.12262i	0.827604	−	0.561312i	$-0.189703\pi$
$594$		0			0
$595$			376.149i			0.632183i
$596$	−162.948	−	8.62772i	−0.273402	−	0.0144760i
$597$		0			0
$598$	24.2709	+	25.5900i	0.0405869	+	0.0427927i
$599$			384.914i			0.642595i	0.946978	+	0.321297i	$0.104119\pi$
$599$			384.914i			0.642595i	−0.946978	+	0.321297i	$0.895881\pi$
$600$		0			0
$601$			50.3020i			0.0836972i	0.999124	+	0.0418486i	$0.0133247\pi$
$601$			50.3020i			0.0836972i	−0.999124	+	0.0418486i	$0.986675\pi$
$602$	539.441	−	511.634i	0.896081	−	0.849891i
$603$		0			0
$604$	−50.7699	+	958.867i	−0.0840561	+	1.58753i
$605$		−	509.319i		−	0.841849i
$606$		0			0
$607$	−481.565			−0.793353			−0.396677	−	0.917958i	$-0.629837\pi$
$607$	−481.565			−0.793353			−0.396677	+	0.917958i	$0.629837\pi$
$608$	601.336	+	89.7747i	0.989039	+	0.147656i
$609$		0			0
$610$	33.7851	+	35.6212i	0.0553854	+	0.0583955i
$611$			168.579i			0.275906i
$612$		0			0
$613$	736.995			1.20228			0.601138	−	0.799146i	$-0.294714\pi$
$613$	736.995			1.20228			0.601138	+	0.799146i	$0.294714\pi$
$614$	−748.373	+	709.796i	−1.21885	+	1.15602i
$615$		0			0
$616$	1153.72	−	983.759i	1.87292	−	1.59701i
$617$			1144.65i			1.85518i	0.373594	+	0.927592i	$0.378125\pi$
$617$			1144.65i			1.85518i	−0.373594	+	0.927592i	$0.621875\pi$
$618$		0			0
$619$			95.5720i			0.154397i	0.997016	+	0.0771987i	$0.0245976\pi$
$619$			95.5720i			0.154397i	−0.997016	+	0.0771987i	$0.975402\pi$
$620$	899.020	+	47.6011i	1.45003	+	0.0767759i
$621$		0			0
$622$	−184.307	+	174.806i	−0.296313	+	0.281039i
$623$			205.498i			0.329853i
$624$		0			0
$625$	−319.552			−0.511284
$626$	−127.834	+	121.245i	−0.204208	+	0.193682i
$627$		0			0
$628$	15.2669	−	288.339i	0.0243104	−	0.459139i
$629$	−411.430			−0.654101
$630$		0			0
$631$			1050.08i			1.66414i	0.554667	+	0.832072i	$0.312846\pi$
$631$			1050.08i			1.66414i	−0.554667	+	0.832072i	$0.687154\pi$
$632$	138.522	+	162.454i	0.219181	+	0.257048i
$633$		0			0
$634$	−844.473	+	800.943i	−1.33198	+	1.26332i
$635$		−	450.006i		−	0.708670i
$636$		0			0
$637$			453.907i			0.712570i
$638$	−1070.52	+	1015.34i	−1.67794	+	1.59144i
$639$		0			0
$640$	−422.668	+	289.320i	−0.660419	+	0.452063i
$641$	−7.10871			−0.0110900			−0.00554502	−	0.999985i	$-0.501765\pi$
$641$	−7.10871			−0.0110900			−0.00554502	+	0.999985i	$0.501765\pi$
$642$		0			0
$643$		−	65.3645i		−	0.101655i	−0.998707	−	0.0508277i	$-0.983814\pi$
$643$		−	65.3645i		−	0.101655i	0.998707	−	0.0508277i	$-0.0161859\pi$
$644$	−178.584	−	9.45565i	−0.277305	−	0.0146827i
$645$		0			0
$646$	−12.5881	+	296.704i	−0.0194861	+	0.459294i
$647$	−43.8513			−0.0677764			−0.0338882	−	0.999426i	$-0.510789\pi$
$647$	−43.8513			−0.0677764			−0.0338882	+	0.999426i	$0.510789\pi$
$648$		0			0
$649$			490.165i			0.755262i
$650$	58.6830	+	61.8724i	0.0902816	+	0.0951882i
$651$		0			0
$652$	393.807	+	20.8512i	0.603998	+	0.0319803i
$653$			143.120i			0.219173i	0.993977	+	0.109587i	$0.0349527\pi$
$653$			143.120i			0.219173i	−0.993977	+	0.109587i	$0.965047\pi$
$654$		0			0
$655$		−	329.860i		−	0.503602i
$656$	506.457	+	53.7823i	0.772039	+	0.0819853i
$657$		0			0
$658$	−588.228	−	620.197i	−0.893963	−	0.942549i
$659$		−	461.885i		−	0.700888i	−0.936584	−	0.350444i	$-0.886031\pi$
$659$		−	461.885i		−	0.700888i	0.936584	−	0.350444i	$-0.113969\pi$
$660$		0			0
$661$		−	4.75146i		−	0.00718830i	−0.999994	−	0.00359415i	$-0.998856\pi$
$661$		−	4.75146i		−	0.00718830i	0.999994	−	0.00359415i	$-0.00114406\pi$
$662$	−555.293	+	526.669i	−0.838811	+	0.795573i
$663$		0			0
$664$	−324.017	−	379.996i	−0.487977	−	0.572283i
$665$	−636.252	−	656.881i	−0.956770	−	0.987792i
$666$		0			0
$667$	174.028			0.260911
$668$	214.936	+	11.3804i	0.321761	+	0.0170365i
$669$		0			0
$670$	−566.051	−	596.815i	−0.844853	−	0.890769i
$671$	96.6588			0.144052
$672$		0			0
$673$		−	98.2320i		−	0.145961i	−0.997333	−	0.0729807i	$-0.976749\pi$
$673$		−	98.2320i		−	0.145961i	0.997333	−	0.0729807i	$-0.0232511\pi$
$674$	259.111	+	273.193i	0.384437	+	0.405331i
$675$		0			0
$676$	30.9822	−	585.147i	0.0458317	−	0.865602i
$677$	−794.006			−1.17283			−0.586415	−	0.810011i	$-0.699461\pi$
$677$	−794.006			−1.17283			−0.586415	+	0.810011i	$0.699461\pi$
$678$		0			0
$679$	−1615.90			−2.37982
$680$	−162.326	−	190.370i	−0.238715	−	0.279956i
$681$		0			0
$682$	1286.04	−	1219.75i	1.88569	−	1.78849i
$683$		−	1074.63i		−	1.57340i	−0.617333	−	0.786702i	$-0.711787\pi$
$683$		−	1074.63i		−	1.57340i	0.617333	−	0.786702i	$-0.288213\pi$
$684$		0			0
$685$	999.131			1.45859
$686$	−772.667	−	814.660i	−1.12634	−	1.18755i
$687$		0			0
$688$	−52.2188	+	491.734i	−0.0758994	+	0.714729i
$689$		−	307.922i		−	0.446911i
$690$		0			0
$691$			880.983i			1.27494i	0.770475	+	0.637470i	$0.220019\pi$
$691$			880.983i			1.27494i	−0.770475	+	0.637470i	$0.779981\pi$
$692$	−13.9655	+	263.760i	−0.0201813	+	0.381156i
$693$		0			0
$694$	−444.248	+	421.349i	−0.640127	+	0.607131i
$695$	−13.1477			−0.0189176
$696$		0			0
$697$			248.764i			0.356907i
$698$	−278.914	+	264.537i	−0.399590	+	0.378993i
$699$		0			0
$700$	−431.787	−	22.8622i	−0.616839	−	0.0326602i
$701$		−	1176.49i		−	1.67831i	−0.543893	−	0.839154i	$-0.683050\pi$
$701$		−	1176.49i		−	1.67831i	0.543893	−	0.839154i	$-0.316950\pi$
$702$		0			0
$703$	718.493	−	695.929i	1.02204	−	0.989941i
$704$	−159.363	+	995.767i	−0.226369	+	1.41444i
$705$		0			0
$706$	626.875	+	660.945i	0.887926	+	0.936183i
$707$	−1366.65			−1.93302
$708$		0			0
$709$	694.414			0.979427			0.489714	−	0.871883i	$-0.337101\pi$
$709$	694.414			0.979427			0.489714	+	0.871883i	$0.337101\pi$
$710$	−518.527	+	491.799i	−0.730320	+	0.692674i
$711$		0			0
$712$	−88.6821	−	104.003i	−0.124553	−	0.146072i
$713$	−209.064			−0.293217
$714$		0			0
$715$	−299.141			−0.418379
$716$	616.941	+	32.6656i	0.861649	+	0.0456224i
$717$		0			0
$718$	−421.515	+	399.787i	−0.587068	+	0.556807i
$719$	−268.127			−0.372917			−0.186458	−	0.982463i	$-0.559701\pi$
$719$	−268.127			−0.372917			−0.186458	+	0.982463i	$0.559701\pi$
$720$		0			0
$721$		−	1116.08i		−	1.54796i
$722$	−479.888	−	539.436i	−0.664665	−	0.747141i
$723$		0			0
$724$	−144.193	−	7.63472i	−0.199162	−	0.0105452i
$725$	420.770			0.580373
$726$		0			0
$727$		−	509.724i		−	0.701134i	−0.936538	−	0.350567i	$-0.885989\pi$
$727$		−	509.724i		−	0.701134i	0.936538	−	0.350567i	$-0.114011\pi$
$728$	−296.204	−	347.378i	−0.406873	−	0.477167i
$729$		0			0
$730$	561.564	+	592.084i	0.769265	+	0.811074i
$731$	−241.532			−0.330413
$732$		0			0
$733$	−186.307			−0.254170			−0.127085	−	0.991892i	$-0.540562\pi$
$733$	−186.307			−0.254170			−0.127085	+	0.991892i	$0.540562\pi$
$734$	−523.525	−	551.978i	−0.713250	−	0.752014i
$735$		0			0
$736$	94.4627	−	72.2820i	0.128346	−	0.0982092i
$737$	−1619.47			−2.19738
$738$		0			0
$739$		−	225.185i		−	0.304715i	−0.988325	−	0.152358i	$-0.951313\pi$
$739$		−	225.185i		−	0.304715i	0.988325	−	0.152358i	$-0.0486866\pi$
$740$	−44.5553	+	841.496i	−0.0602099	+	1.13716i
$741$		0			0
$742$	1074.44	+	1132.84i	1.44804	+	1.52674i
$743$			182.940i			0.246218i	0.992393	+	0.123109i	$0.0392865\pi$
$743$			182.940i			0.246218i	−0.992393	+	0.123109i	$0.960713\pi$
$744$		0			0
$745$	−163.242			−0.219116
$746$	524.759	+	553.279i	0.703430	+	0.741660i
$747$		0			0
$748$	−491.872	−	26.0435i	−0.657582	−	0.0348175i
$749$	117.362			0.156692
$750$		0			0
$751$	1130.62			1.50549			0.752746	−	0.658311i	$-0.228729\pi$
$751$	1130.62			1.50549			0.752746	+	0.658311i	$0.228729\pi$
$752$	565.348	+	60.0361i	0.751793	+	0.0798353i
$753$		0			0
$754$	305.713	+	322.328i	0.405455	+	0.427491i
$755$			960.596i			1.27231i
$756$		0			0
$757$	714.219			0.943486			0.471743	−	0.881736i	$-0.343625\pi$
$757$	714.219			0.943486			0.471743	+	0.881736i	$0.343625\pi$
$758$	563.905	−	534.837i	0.743937	−	0.705590i
$759$		0			0
$760$	605.484	+	57.8775i	0.796690	+	0.0761546i
$761$			1081.23i			1.42080i	0.703799	+	0.710399i	$0.251486\pi$
$761$			1081.23i			1.42080i	−0.703799	+	0.710399i	$0.748514\pi$
$762$		0			0
$763$	72.6284			0.0951879
$764$	−9.95637	+	188.041i	−0.0130319	+	0.246127i
$765$		0			0
$766$	202.596	+	213.606i	0.264485	+	0.278859i
$767$	147.586			0.192419
$768$		0			0
$769$	204.176			0.265508			0.132754	−	0.991149i	$-0.457618\pi$
$769$	204.176			0.265508			0.132754	+	0.991149i	$0.457618\pi$
$770$	1100.53	−	1043.80i	1.42926	−	1.35559i
$771$		0			0
$772$	−180.064	−	9.53399i	−0.233244	−	0.0123497i
$773$	−278.794			−0.360665			−0.180333	−	0.983606i	$-0.557717\pi$
$773$	−278.794			−0.360665			−0.180333	+	0.983606i	$0.557717\pi$
$774$		0			0
$775$	−505.481			−0.652233
$776$	817.811	−	697.335i	1.05388	−	0.898627i
$777$		0			0
$778$	−145.172	−	153.062i	−0.186596	−	0.196738i
$779$	−420.782	−	434.425i	−0.540157	−	0.557670i
$780$		0			0
$781$			1407.03i			1.80158i
$782$	39.9802	+	42.1531i	0.0511256	+	0.0539042i
$783$		0			0
$784$	1522.23	+	161.650i	1.94162	+	0.206187i
$785$		−	288.859i		−	0.367973i
$786$		0			0
$787$	−525.124			−0.667247			−0.333624	−	0.942706i	$-0.608271\pi$
$787$	−525.124			−0.667247			−0.333624	+	0.942706i	$0.608271\pi$
$788$	1160.37	+	61.4389i	1.47255	+	0.0779681i
$789$		0			0
$790$	146.977	+	154.965i	0.186047	+	0.196158i
$791$			2453.48i			3.10174i
$792$		0			0
$793$		−	29.1034i		−	0.0367003i
$794$	317.235	−	300.882i	0.399540	−	0.378945i
$795$		0			0
$796$	−1244.81	−	65.9099i	−1.56383	−	0.0828014i
$797$	−253.195			−0.317685			−0.158842	−	0.987304i	$-0.550776\pi$
$797$	−253.195			−0.317685			−0.158842	+	0.987304i	$0.550776\pi$
$798$		0			0
$799$			277.691i			0.347548i
$800$	228.395	−	174.766i	0.285494	−	0.218457i
$801$		0			0
$802$	−696.459	+	660.559i	−0.868403	+	0.823639i
$803$	1606.63			2.00078
$804$		0			0
$805$	−178.906			−0.222244
$806$	−367.260	−	387.220i	−0.455657	−	0.480422i
$807$		0			0
$808$	691.665	−	589.772i	0.856021	−	0.729916i
$809$			606.601i			0.749815i	0.927062	+	0.374908i	$0.122326\pi$
$809$			606.601i			0.749815i	−0.927062	+	0.374908i	$0.877674\pi$
$810$		0			0
$811$	−798.123			−0.984122			−0.492061	−	0.870561i	$-0.663756\pi$
$811$	−798.123			−0.984122			−0.492061	+	0.870561i	$0.663756\pi$
$812$	−2249.42	−	119.102i	−2.77022	−	0.146677i
$813$		0			0
$814$	1141.71	+	1203.76i	1.40259	+	1.47882i
$815$	394.516			0.484069
$816$		0			0
$817$	421.796	−	408.549i	0.516274	−	0.500060i
$818$	−190.668	−	201.031i	−0.233090	−	0.245759i
$819$		0			0
$820$	508.797	+	26.9397i	0.620484	+	0.0328532i
$821$			1391.89i			1.69536i	0.530507	+	0.847681i	$0.322002\pi$
$821$			1391.89i			1.69536i	−0.530507	+	0.847681i	$0.677998\pi$
$822$		0			0
$823$			187.191i			0.227449i	0.993512	+	0.113725i	$0.0362781\pi$
$823$			187.191i			0.227449i	−0.993512	+	0.113725i	$0.963722\pi$
$824$	481.639	+	564.850i	0.584513	+	0.685497i
$825$		0			0
$826$	−542.965	+	514.976i	−0.657342	+	0.623458i
$827$		−	641.991i		−	0.776289i	−0.921599	−	0.388144i	$-0.873116\pi$
$827$		−	641.991i		−	0.776289i	0.921599	−	0.388144i	$-0.126884\pi$
$828$		0			0
$829$			865.303i			1.04379i	0.853009	+	0.521895i	$0.174775\pi$
$829$			865.303i			1.04379i	−0.853009	+	0.521895i	$0.825225\pi$
$830$	−343.793	−	362.478i	−0.414209	−	0.436721i
$831$		0			0
$832$	299.820	+	47.9834i	0.360360	+	0.0576723i
$833$			747.696i			0.897595i
$834$		0			0
$835$	215.324			0.257873
$836$	903.024	−	786.515i	1.08017	−	0.940807i
$837$		0			0
$838$	97.8971	−	92.8508i	0.116822	−	0.110800i
$839$		−	1338.12i		−	1.59490i	−0.603388	−	0.797448i	$-0.706183\pi$
$839$		−	1338.12i		−	1.59490i	0.603388	−	0.797448i	$-0.293817\pi$
$840$		0			0
$841$	1351.03			1.60645
$842$	−119.090	−	125.562i	−0.141437	−	0.149124i
$843$		0			0
$844$	−58.1558	+	1098.36i	−0.0689050	+	1.30138i
$845$		−	586.202i		−	0.693730i
$846$		0			0
$847$		−	1530.91i		−	1.80746i
$848$	−1032.65	−	109.661i	−1.21775	−	0.129317i
$849$		0			0
$850$	96.6654	+	101.919i	0.113724	+	0.119905i
$851$		−	195.687i		−	0.229949i
$852$		0			0
$853$	618.514			0.725105			0.362552	−	0.931963i	$-0.381905\pi$
$853$	618.514			0.725105			0.362552	+	0.931963i	$0.381905\pi$
$854$	101.551	+	107.071i	0.118913	+	0.125375i
$855$		0			0
$856$	−59.3974	+	50.6472i	−0.0693894	+	0.0591673i
$857$	287.229			0.335156			0.167578	−	0.985859i	$-0.446405\pi$
$857$	287.229			0.335156			0.167578	+	0.985859i	$0.446405\pi$
$858$		0			0
$859$		−	422.771i		−	0.492167i	−0.969249	−	0.246083i	$-0.920856\pi$
$859$		−	422.771i		−	0.492167i	0.969249	−	0.246083i	$-0.0791437\pi$
$860$	−26.1565	+	494.005i	−0.0304145	+	0.574425i
$861$		0			0
$862$	308.080	+	324.824i	0.357402	+	0.376826i
$863$			1490.14i			1.72670i	0.504606	+	0.863350i	$0.331638\pi$
$863$			1490.14i			1.72670i	−0.504606	+	0.863350i	$0.668362\pi$
$864$		0			0
$865$			264.235i			0.305474i
$866$	908.156	+	957.513i	1.04868	+	1.10567i
$867$		0			0
$868$	2702.28	+	143.080i	3.11323	+	0.164838i
$869$	420.500			0.483890
$870$		0			0
$871$			487.612i			0.559830i
$872$	−36.7574	+	31.3425i	−0.0421530	+	0.0359433i
$873$		0			0
$874$	−141.120	−	5.98721i	−0.161465	−	0.00685035i
$875$	−1635.85			−1.86955
$876$		0			0
$877$		−	1425.21i		−	1.62509i	−0.582897	−	0.812546i	$-0.698081\pi$
$877$		−	1425.21i		−	1.62509i	0.582897	−	0.812546i	$-0.301919\pi$
$878$	−300.336	+	284.855i	−0.342069	+	0.324436i
$879$		0			0
$880$	−106.533	+	1003.20i	−0.121061	+	1.14000i
$881$		−	611.690i		−	0.694313i	−0.937807	−	0.347157i	$-0.887147\pi$
$881$		−	611.690i		−	0.694313i	0.937807	−	0.347157i	$-0.112853\pi$
$882$		0			0
$883$			24.2111i			0.0274192i	0.999906	+	0.0137096i	$0.00436403\pi$
$883$			24.2111i			0.0274192i	−0.999906	+	0.0137096i	$0.995636\pi$
$884$	−7.84154	+	148.100i	−0.00887052	+	0.167533i
$885$		0			0
$886$	557.326	−	528.597i	0.629036	−	0.596611i
$887$			1105.34i			1.24616i	0.782158	+	0.623080i	$0.214119\pi$
$887$			1105.34i			1.24616i	−0.782158	+	0.623080i	$0.785881\pi$
$888$		0			0
$889$		−	1352.63i		−	1.52152i
$890$	−94.0948	−	99.2088i	−0.105725	−	0.111471i
$891$		0			0
$892$	−3.40489	+	64.3066i	−0.00381714	+	0.0720926i
$893$	−469.710	−	484.940i	−0.525991	−	0.543046i
$894$		0			0
$895$	618.053			0.690562
$896$	−1270.46	+	869.642i	−1.41792	+	0.970582i
$897$		0			0
$898$	−502.059	+	476.179i	−0.559086	+	0.530266i
$899$	−2633.33			−2.92918
$900$		0			0
$901$		−	507.223i		−	0.562956i
$902$	727.831	−	690.314i	0.806908	−	0.765315i
$903$		0			0
$904$	−1058.79	−	1241.71i	−1.17123	−	1.37358i
$905$	−144.453			−0.159617
$906$		0			0
$907$	−981.815			−1.08249			−0.541243	−	0.840866i	$-0.682046\pi$
$907$	−981.815			−1.08249			−0.541243	+	0.840866i	$0.682046\pi$
$908$	1037.47	+	54.9319i	1.14259	+	0.0604977i
$909$		0			0
$910$	−314.283	−	331.364i	−0.345366	−	0.364136i
$911$		−	1541.03i		−	1.69158i	−0.533518	−	0.845789i	$-0.679130\pi$
$911$		−	1541.03i		−	1.69158i	0.533518	−	0.845789i	$-0.320870\pi$
$912$		0			0
$913$	−983.590			−1.07732
$914$	−389.278	+	369.212i	−0.425906	+	0.403952i
$915$		0			0
$916$	−77.8134	+	1469.63i	−0.0849492	+	1.60440i
$917$		−	991.495i		−	1.08124i
$918$		0			0
$919$		−	399.591i		−	0.434811i	−0.976081	−	0.217406i	$-0.930241\pi$
$919$		−	399.591i		−	0.434811i	0.976081	−	0.217406i	$-0.0697594\pi$
$920$	90.5451	−	77.2065i	0.0984186	−	0.0839201i
$921$		0			0
$922$	−755.272	−	796.320i	−0.819167	−	0.863688i
$923$	423.648			0.458991
$924$		0			0
$925$		−	473.138i		−	0.511500i
$926$	−311.581	−	328.515i	−0.336480	−	0.354767i
$927$		0			0
$928$	1189.84	−	910.452i	1.28215	−	0.981091i
$929$			1640.90i			1.76631i	0.469081	+	0.883155i	$0.344585\pi$
$929$			1640.90i			1.76631i	−0.469081	+	0.883155i	$0.655415\pi$
$930$		0			0
$931$	−1264.72	−	1305.73i	−1.35845	−	1.40250i
$932$	−996.379	−	52.7561i	−1.06908	−	0.0566052i
$933$		0			0
$934$	−333.940	+	316.726i	−0.357537	+	0.339107i
$935$	−492.758			−0.527014
$936$		0			0
$937$	756.518			0.807383			0.403692	−	0.914895i	$-0.367727\pi$
$937$	756.518			0.807383			0.403692	+	0.914895i	$0.367727\pi$
$938$	−1701.44	−	1793.91i	−1.81390	−	1.91249i
$939$		0			0
$940$	567.960	+	30.0722i	0.604212	+	0.0319917i
$941$	−974.395			−1.03549			−0.517744	−	0.855535i	$-0.673228\pi$
$941$	−974.395			−1.03549			−0.517744	+	0.855535i	$0.673228\pi$
$942$		0			0
$943$	−118.319			−0.125471
$944$	52.5599	−	494.946i	0.0556778	−	0.524307i
$945$		0			0
$946$	670.245	+	706.672i	0.708504	+	0.747010i
$947$	1226.50			1.29514			0.647569	−	0.762006i	$-0.275786\pi$
$947$	1226.50			1.29514			0.647569	+	0.762006i	$0.275786\pi$
$948$		0			0
$949$		−	483.746i		−	0.509743i
$950$	−341.205	−	14.4761i	−0.359163	−	0.0152380i
$951$		0			0
$952$	−487.920	−	572.217i	−0.512521	−	0.601068i
$953$	132.903			0.139457			0.0697287	−	0.997566i	$-0.477787\pi$
$953$	132.903			0.139457			0.0697287	+	0.997566i	$0.477787\pi$
$954$		0			0
$955$			188.380i			0.197257i
$956$	9.95692	−	188.052i	0.0104152	−	0.196707i
$957$		0			0
$958$	−720.638	+	683.492i	−0.752232	+	0.713457i
$959$	3003.20			3.13159
$960$		0			0
$961$	2202.48			2.29187
$962$	362.444	−	343.761i	0.376760	−	0.357340i
$963$		0			0
$964$	1264.96	+	66.9765i	1.31219	+	0.0694777i
$965$	−180.389			−0.186931
$966$		0			0
$967$		−	710.932i		−	0.735193i	−0.929985	−	0.367597i	$-0.880181\pi$
$967$		−	710.932i		−	0.735193i	0.929985	−	0.367597i	$-0.119819\pi$
$968$	660.661	+	774.801i	0.682501	+	0.800414i
$969$		0			0
$970$	780.109	−	739.897i	0.804236	−	0.762780i
$971$			273.889i			0.282069i	0.990005	+	0.141035i	$0.0450429\pi$
$971$			273.889i			0.282069i	−0.990005	+	0.141035i	$0.954957\pi$
$972$		0			0
$973$	−39.5196			−0.0406162
$974$	21.7586	−	20.6370i	0.0223394	−	0.0211879i
$975$		0			0
$976$	−97.6015	−	10.3646i	−0.100002	−	0.0106195i
$977$	−815.931			−0.835139			−0.417570	−	0.908645i	$-0.637118\pi$
$977$	−815.931			−0.835139			−0.417570	+	0.908645i	$0.637118\pi$
$978$		0			0
$979$	−269.204			−0.274979
$980$	1529.26	+	80.9710i	1.56047	+	0.0826234i
$981$		0			0
$982$	463.902	−	439.989i	0.472405	−	0.448054i
$983$		−	0.404692i		−	0.000411691i	−1.00000		0.000205845i	$-0.999934\pi$
$983$		−	0.404692i		−	0.000411691i	1.00000		0.000205845i	$-6.55226e-5\pi$
$984$		0			0
$985$	1162.46			1.18016
$986$	503.584	+	530.953i	0.510734	+	0.538492i
$987$		0			0
$988$	−236.815	−	271.895i	−0.239691	−	0.275197i
$989$		−	114.879i		−	0.116157i
$990$		0			0
$991$	914.945			0.923254			0.461627	−	0.887074i	$-0.347266\pi$
$991$	914.945			0.923254			0.461627	+	0.887074i	$0.347266\pi$
$992$	−1429.38	+	1093.75i	−1.44091	+	1.10257i
$993$		0			0
$994$	−1558.59	+	1478.25i	−1.56800	+	1.48718i
$995$	−1247.05			−1.25332
$996$		0			0
$997$	−1931.46			−1.93727			−0.968634	−	0.248491i	$-0.920065\pi$
$997$	−1931.46			−1.93727			−0.968634	+	0.248491i	$0.920065\pi$
$998$	−672.383	−	708.926i	−0.673731	−	0.710347i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.3.b.a.683.19	yes	80
3.2	odd	2	inner	684.3.b.a.683.61	yes	80
4.3	odd	2	inner	684.3.b.a.683.18	yes	80
12.11	even	2	inner	684.3.b.a.683.64	yes	80
19.18	odd	2	inner	684.3.b.a.683.62	yes	80
57.56	even	2	inner	684.3.b.a.683.20	yes	80
76.75	even	2	inner	684.3.b.a.683.63	yes	80
228.227	odd	2	inner	684.3.b.a.683.17	✓	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
684.3.b.a.683.17	✓	80	228.227	odd	2	inner
684.3.b.a.683.18	yes	80	4.3	odd	2	inner
684.3.b.a.683.19	yes	80	1.1	even	1	trivial
684.3.b.a.683.20	yes	80	57.56	even	2	inner
684.3.b.a.683.61	yes	80	3.2	odd	2	inner
684.3.b.a.683.62	yes	80	19.18	odd	2	inner
684.3.b.a.683.63	yes	80	76.75	even	2	inner
684.3.b.a.683.64	yes	80	12.11	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:	\( N \)	\(=\)	\( 684 = 2^{2} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	684.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.45112 + 1.37632i) q^{2} +(0.211495 - 3.99440i) q^{4} -4.00161i q^{5} -12.0281i q^{7} +(5.19067 + 6.08744i) q^{8} +O(q^{10})\)	\(q+(-1.45112 + 1.37632i) q^{2} +(0.211495 - 3.99440i) q^{4} -4.00161i q^{5} -12.0281i q^{7} +(5.19067 + 6.08744i) q^{8} +(5.50748 + 5.80681i) q^{10} +15.7569 q^{11} -4.74430i q^{13} +(16.5544 + 17.4542i) q^{14} +(-15.9105 - 1.68959i) q^{16} -7.81502i q^{17} +(13.2190 + 13.6476i) q^{19} +(-15.9840 - 0.846319i) q^{20} +(-22.8651 + 21.6865i) q^{22} +3.71703 q^{23} +8.98715 q^{25} +(6.52966 + 6.88454i) q^{26} +(-48.0450 - 2.54387i) q^{28} +46.8191 q^{29} -56.2449 q^{31} +(25.4135 - 19.4462i) q^{32} +(10.7560 + 11.3405i) q^{34} -48.1316 q^{35} -52.6460i q^{37} +(-37.9658 - 1.61075i) q^{38} +(24.3595 - 20.7710i) q^{40} -31.8316 q^{41} -30.9062i q^{43} +(3.33249 - 62.9393i) q^{44} +(-5.39385 + 5.11582i) q^{46} -35.5329 q^{47} -95.6743 q^{49} +(-13.0414 + 12.3692i) q^{50} +(-18.9506 - 1.00339i) q^{52} +64.9036 q^{53} -63.0527i q^{55} +(73.2201 - 62.4337i) q^{56} +(-67.9401 + 64.4380i) q^{58} +31.1080i q^{59} +6.13439 q^{61} +(81.6180 - 77.4108i) q^{62} +(-10.1139 + 63.1958i) q^{64} -18.9848 q^{65} -102.779 q^{67} +(-31.2163 - 1.65284i) q^{68} +(69.8447 - 66.2444i) q^{70} +89.2964i q^{71} +101.964 q^{73} +(72.4577 + 76.3957i) q^{74} +(57.3099 - 49.9157i) q^{76} -189.524i q^{77} +26.6868 q^{79} +(-6.76108 + 63.6677i) q^{80} +(46.1914 - 43.8104i) q^{82} -62.4230 q^{83} -31.2726 q^{85} +(42.5367 + 44.8485i) q^{86} +(81.7886 + 95.9190i) q^{88} -17.0849 q^{89} -57.0647 q^{91} +(0.786132 - 14.8473i) q^{92} +(51.5625 - 48.9046i) q^{94} +(54.6124 - 52.8973i) q^{95} -134.344i q^{97} +(138.835 - 131.678i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 8 q^{4}+O(q^{10}) \) 80 * q - 8 * q^4	\( 80 q - 8 q^{4} - 56 q^{16} - 400 q^{25} - 464 q^{49} - 272 q^{58} - 352 q^{61} - 200 q^{64} + 480 q^{73} + 152 q^{76} + 32 q^{82} + 704 q^{85}+O(q^{100}) \) 80 * q - 8 * q^4 - 56 * q^16 - 400 * q^25 - 464 * q^49 - 272 * q^58 - 352 * q^61 - 200 * q^64 + 480 * q^73 + 152 * q^76 + 32 * q^82 + 704 * q^85

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more