LMFDB - Embedded newform 740.4.i.b.121.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [740,4,Mod(121,740)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(740, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

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

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

chi := DirichletCharacter("740.121");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 740 = 2^{2} \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	740.i (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$43.6614134042$
Analytic rank:	$0$
Dimension:	$38$
Relative dimension:	$19$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			121.15
Character	$\chi$	$=$	740.121
Dual form			740.4.i.b.581.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.83527 + 4.91084i) q^{3} +(2.50000 + 4.33013i) q^{5} +(-6.77514 - 11.7349i) q^{7} +(-2.57754 + 4.46443i) q^{9} -43.5452 q^{11} +(2.82036 + 4.88500i) q^{13} +(-14.1764 + 24.5542i) q^{15} +(21.8636 - 37.8689i) q^{17} +(-70.7788 - 122.592i) q^{19} +(38.4188 - 66.5432i) q^{21} +198.737 q^{23} +(-12.5000 + 21.6506i) q^{25} +123.873 q^{27} -55.1373 q^{29} +257.316 q^{31} +(-123.462 - 213.843i) q^{33} +(33.8757 - 58.6745i) q^{35} +(200.126 + 102.968i) q^{37} +(-15.9930 + 27.7006i) q^{39} +(-195.691 - 338.947i) q^{41} -139.455 q^{43} -25.7754 q^{45} +269.584 q^{47} +(79.6948 - 138.036i) q^{49} +247.957 q^{51} +(-174.639 + 302.483i) q^{53} +(-108.863 - 188.556i) q^{55} +(401.354 - 695.166i) q^{57} +(124.593 - 215.802i) q^{59} +(-460.357 - 797.362i) q^{61} +69.8528 q^{63} +(-14.1018 + 24.4250i) q^{65} +(56.1834 + 97.3126i) q^{67} +(563.473 + 975.964i) q^{69} +(278.129 + 481.734i) q^{71} -154.111 q^{73} -141.764 q^{75} +(295.025 + 510.998i) q^{77} +(172.461 + 298.710i) q^{79} +(420.806 + 728.858i) q^{81} +(138.719 - 240.268i) q^{83} +218.636 q^{85} +(-156.329 - 270.770i) q^{87} +(145.889 - 252.688i) q^{89} +(38.2167 - 66.1932i) q^{91} +(729.560 + 1263.63i) q^{93} +(353.894 - 612.962i) q^{95} -226.298 q^{97} +(112.239 - 194.404i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 38 q - 6 q^{3} + 95 q^{5} - 32 q^{7} - 187 q^{9} - 2 q^{11} + 93 q^{13} + 30 q^{15} + 38 q^{17} - 91 q^{19} - 230 q^{21} - 306 q^{23} - 475 q^{25} + 552 q^{27} + 156 q^{29} - 144 q^{31} - 484 q^{33} + 160 q^{35}+ \cdots + 721 q^{99}+O(q^{100}) $ 38 * q - 6 * q^3 + 95 * q^5 - 32 * q^7 - 187 * q^9 - 2 * q^11 + 93 * q^13 + 30 * q^15 + 38 * q^17 - 91 * q^19 - 230 * q^21 - 306 * q^23 - 475 * q^25 + 552 * q^27 + 156 * q^29 - 144 * q^31 - 484 * q^33 + 160 * q^35 - 231 * q^37 - 590 * q^39 - 236 * q^41 + 228 * q^43 - 1870 * q^45 - 1082 * q^47 - 655 * q^49 - 1560 * q^51 + 2 * q^53 - 5 * q^55 + 598 * q^57 - 285 * q^59 + 1290 * q^61 + 2992 * q^63 - 465 * q^65 + 664 * q^67 - 240 * q^69 + 1614 * q^71 - 400 * q^73 + 300 * q^75 - 1334 * q^77 + 2236 * q^79 - 1759 * q^81 - 922 * q^83 + 380 * q^85 - 1968 * q^87 + 1107 * q^89 + 2456 * q^91 + 2986 * q^93 + 455 * q^95 - 5328 * q^97 + 721 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/740\mathbb{Z}\right)^\times$.

$n$	$261$	$297$	$371$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	2.83527	+	4.91084i	0.545648	+	0.945091i	0.998566	+	0.0535383i	$0.0170499\pi$
$3$	2.83527	+	4.91084i	0.545648	+	0.945091i	−0.452917	+	0.891552i	$0.649617\pi$
$4$		0			0
$5$	2.50000	+	4.33013i	0.223607	+	0.387298i
$5$	2.50000	+	4.33013i	0.223607	+	0.387298i
$6$		0			0
$7$	−6.77514	−	11.7349i	−0.365823	−	0.633625i	0.623085	−	0.782155i	$-0.285879\pi$
$7$	−6.77514	−	11.7349i	−0.365823	−	0.633625i	−0.988908	+	0.148530i	$0.952546\pi$
$8$		0			0
$9$	−2.57754	+	4.46443i	−0.0954644	+	0.165349i
$10$		0			0
$11$	−43.5452			−1.19358			−0.596789	−	0.802398i	$-0.703557\pi$
$11$	−43.5452			−1.19358			−0.596789	+	0.802398i	$0.703557\pi$
$12$		0			0
$13$	2.82036	+	4.88500i	0.0601713	+	0.104220i	0.894542	−	0.446984i	$-0.147502\pi$
$13$	2.82036	+	4.88500i	0.0601713	+	0.104220i	−0.834371	+	0.551204i	$0.814169\pi$
$14$		0			0
$15$	−14.1764	+	24.5542i	−0.244021	+	0.422657i
$16$		0			0
$17$	21.8636	−	37.8689i	0.311924	−	0.540268i	−0.666855	−	0.745188i	$-0.732360\pi$
$17$	21.8636	−	37.8689i	0.311924	−	0.540268i	0.978779	+	0.204920i	$0.0656933\pi$
$18$		0			0
$19$	−70.7788	−	122.592i	−0.854619	−	1.48024i	−0.876998	−	0.480495i	$-0.840457\pi$
$19$	−70.7788	−	122.592i	−0.854619	−	1.48024i	0.0223782	−	0.999750i	$-0.492876\pi$
$20$		0			0
$21$	38.4188	−	66.5432i	0.399222	−	0.691473i
$22$		0			0
$23$	198.737			1.80172			0.900858	−	0.434113i	$-0.142938\pi$
$23$	198.737			1.80172			0.900858	+	0.434113i	$0.142938\pi$
$24$		0			0
$25$	−12.5000	+	21.6506i	−0.100000	+	0.173205i
$26$		0			0
$27$	123.873			0.882937
$28$		0			0
$29$	−55.1373			−0.353060			−0.176530	−	0.984295i	$-0.556487\pi$
$29$	−55.1373			−0.353060			−0.176530	+	0.984295i	$0.556487\pi$
$30$		0			0
$31$	257.316			1.49081			0.745407	−	0.666609i	$-0.232255\pi$
$31$	257.316			1.49081			0.745407	+	0.666609i	$0.232255\pi$
$32$		0			0
$33$	−123.462	−	213.843i	−0.651274	−	1.12804i
$34$		0			0
$35$	33.8757	−	58.6745i	0.163601	−	0.283366i
$36$		0			0
$37$	200.126	+	102.968i	0.889204	+	0.457510i
$37$	200.126	+	102.968i	0.889204	+	0.457510i
$38$		0			0
$39$	−15.9930	+	27.7006i	−0.0656647	+	0.113735i
$40$		0			0
$41$	−195.691	−	338.947i	−0.745410	−	1.29109i	−0.950003	−	0.312241i	$-0.898920\pi$
$41$	−195.691	−	338.947i	−0.745410	−	1.29109i	0.204593	−	0.978847i	$-0.434413\pi$
$42$		0			0
$43$	−139.455			−0.494575			−0.247288	−	0.968942i	$-0.579539\pi$
$43$	−139.455			−0.494575			−0.247288	+	0.968942i	$0.579539\pi$
$44$		0			0
$45$	−25.7754			−0.0853859
$46$		0			0
$47$	269.584			0.836657			0.418328	−	0.908296i	$-0.362616\pi$
$47$	269.584			0.836657			0.418328	+	0.908296i	$0.362616\pi$
$48$		0			0
$49$	79.6948	−	138.036i	0.232346	−	0.402436i
$50$		0			0
$51$	247.957			0.680803
$52$		0			0
$53$	−174.639	+	302.483i	−0.452613	+	0.783948i	−0.998547	−	0.0538797i	$-0.982841\pi$
$53$	−174.639	+	302.483i	−0.452613	+	0.783948i	0.545935	+	0.837828i	$0.316175\pi$
$54$		0			0
$55$	−108.863	−	188.556i	−0.266892	−	0.462271i
$56$		0			0
$57$	401.354	−	695.166i	0.932643	−	1.61539i
$58$		0			0
$59$	124.593	−	215.802i	0.274926	−	0.476187i	−0.695190	−	0.718826i	$-0.744680\pi$
$59$	124.593	−	215.802i	0.274926	−	0.476187i	0.970117	+	0.242639i	$0.0780132\pi$
$60$		0			0
$61$	−460.357	−	797.362i	−0.966273	−	1.67363i	−0.706154	−	0.708058i	$-0.749572\pi$
$61$	−460.357	−	797.362i	−0.966273	−	1.67363i	−0.260119	−	0.965577i	$-0.583762\pi$
$62$		0			0
$63$	69.8528			0.139692
$64$		0			0
$65$	−14.1018	+	24.4250i	−0.0269094	+	0.0466085i
$66$		0			0
$67$	56.1834	+	97.3126i	0.102446	+	0.177442i	0.912692	−	0.408648i	$-0.134000\pi$
$67$	56.1834	+	97.3126i	0.102446	+	0.177442i	−0.810246	+	0.586090i	$0.800666\pi$
$68$		0			0
$69$	563.473	+	975.964i	0.983104	+	1.70279i
$70$		0			0
$71$	278.129	+	481.734i	0.464899	+	0.805229i	0.999197	−	0.0400671i	$-0.0127572\pi$
$71$	278.129	+	481.734i	0.464899	+	0.805229i	−0.534298	+	0.845296i	$0.679424\pi$
$72$		0			0
$73$	−154.111			−0.247087			−0.123543	−	0.992339i	$-0.539426\pi$
$73$	−154.111			−0.247087			−0.123543	+	0.992339i	$0.539426\pi$
$74$		0			0
$75$	−141.764			−0.218259
$76$		0			0
$77$	295.025	+	510.998i	0.436639	+	0.756281i
$78$		0			0
$79$	172.461	+	298.710i	0.245612	+	0.425412i	0.962303	−	0.271978i	$-0.0876778\pi$
$79$	172.461	+	298.710i	0.245612	+	0.425412i	−0.716692	+	0.697390i	$0.754345\pi$
$80$		0			0
$81$	420.806	+	728.858i	0.577237	+	0.999805i
$82$		0			0
$83$	138.719	−	240.268i	0.183451	−	0.317746i	−0.759603	−	0.650387i	$-0.774607\pi$
$83$	138.719	−	240.268i	0.183451	−	0.317746i	0.943053	+	0.332642i	$0.107940\pi$
$84$		0			0
$85$	218.636			0.278993
$86$		0			0
$87$	−156.329	−	270.770i	−0.192647	−	0.333674i
$88$		0			0
$89$	145.889	−	252.688i	0.173755	−	0.300953i	−0.765974	−	0.642871i	$-0.777743\pi$
$89$	145.889	−	252.688i	0.173755	−	0.300953i	0.939730	+	0.341918i	$0.111076\pi$
$90$		0			0
$91$	38.2167	−	66.1932i	0.0440241	−	0.0762520i
$92$		0			0
$93$	729.560	+	1263.63i	0.813461	+	1.40896i
$94$		0			0
$95$	353.894	−	612.962i	0.382197	−	0.661985i
$96$		0			0
$97$	−226.298			−0.236877			−0.118439	−	0.992961i	$-0.537789\pi$
$97$	−226.298			−0.236877			−0.118439	+	0.992961i	$0.537789\pi$
$98$		0			0
$99$	112.239	−	194.404i	0.113944	−	0.197357i
$100$		0			0
$101$	880.505			0.867461			0.433730	−	0.901043i	$-0.357197\pi$
$101$	880.505			0.867461			0.433730	+	0.901043i	$0.357197\pi$
$102$		0			0
$103$	−1593.14			−1.52405			−0.762024	−	0.647549i	$-0.775794\pi$
$103$	−1593.14			−1.52405			−0.762024	+	0.647549i	$0.775794\pi$
$104$		0			0
$105$	384.188			0.357075
$106$		0			0
$107$	299.092	+	518.043i	0.270227	+	0.468047i	0.968920	−	0.247375i	$-0.0795678\pi$
$107$	299.092	+	518.043i	0.270227	+	0.468047i	−0.698693	+	0.715422i	$0.746234\pi$
$108$		0			0
$109$	890.024	−	1541.57i	0.782099	−	1.35464i	−0.148618	−	0.988895i	$-0.547482\pi$
$109$	890.024	−	1541.57i	0.782099	−	1.35464i	0.930717	−	0.365741i	$-0.119184\pi$
$110$		0			0
$111$	61.7523	+	1274.73i	0.0528042	+	1.09002i
$112$		0			0
$113$	219.799	−	380.703i	0.182982	−	0.316934i	−0.759913	−	0.650025i	$-0.774758\pi$
$113$	219.799	−	380.703i	0.182982	−	0.316934i	0.942895	+	0.333091i	$0.108092\pi$
$114$		0			0
$115$	496.842	+	860.556i	0.402876	+	0.697802i
$116$		0			0
$117$	−29.0783			−0.0229769
$118$		0			0
$119$	−592.517			−0.456436
$120$		0			0
$121$	565.182			0.424630
$122$		0			0
$123$	1109.68	−	1922.01i	0.813464	−	1.40896i
$124$		0			0
$125$	−125.000			−0.0894427
$126$		0			0
$127$	953.168	−	1650.94i	0.665984	−	1.15352i	−0.313033	−	0.949742i	$-0.601345\pi$
$127$	953.168	−	1650.94i	0.665984	−	1.15352i	0.979017	−	0.203776i	$-0.0653216\pi$
$128$		0			0
$129$	−395.394	−	684.842i	−0.269864	−	0.467419i
$130$		0			0
$131$	1011.86	−	1752.59i	0.674858	−	1.16889i	−0.301652	−	0.953418i	$-0.597538\pi$
$131$	1011.86	−	1752.59i	0.674858	−	1.16889i	0.976510	−	0.215470i	$-0.0691284\pi$
$132$		0			0
$133$	−959.073	+	1661.16i	−0.625280	+	1.08302i
$134$		0			0
$135$	309.682	+	536.384i	0.197431	+	0.341960i
$136$		0			0
$137$	1914.67			1.19402			0.597012	−	0.802232i	$-0.296354\pi$
$137$	1914.67			1.19402			0.597012	+	0.802232i	$0.296354\pi$
$138$		0			0
$139$	−1633.06	+	2828.53i	−0.996503	+	1.72599i	−0.425890	+	0.904775i	$0.640039\pi$
$139$	−1633.06	+	2828.53i	−0.996503	+	1.72599i	−0.570613	+	0.821219i	$0.693294\pi$
$140$		0			0
$141$	764.344	+	1323.88i	0.456520	+	0.790717i
$142$		0			0
$143$	−122.813	−	212.718i	−0.0718192	−	0.124394i
$144$		0			0
$145$	−137.843	−	238.752i	−0.0789466	−	0.136740i
$146$		0			0
$147$	903.826			0.507118
$148$		0			0
$149$	−3250.63			−1.78726			−0.893631	−	0.448803i	$-0.851850\pi$
$149$	−3250.63			−1.78726			−0.893631	+	0.448803i	$0.851850\pi$
$150$		0			0
$151$	1574.77	+	2727.58i	0.848694	+	1.46998i	0.882374	+	0.470549i	$0.155944\pi$
$151$	1574.77	+	2727.58i	0.848694	+	1.46998i	−0.0336797	+	0.999433i	$0.510723\pi$
$152$		0			0
$153$	112.709	+	195.217i	0.0595552	+	0.103153i
$154$		0			0
$155$	643.289	+	1114.21i	0.333356	+	0.577390i
$156$		0			0
$157$	1661.64	−	2878.05i	0.844672	−	1.46302i	−0.0412334	−	0.999150i	$-0.513129\pi$
$157$	1661.64	−	2878.05i	0.844672	−	1.46302i	0.885906	−	0.463866i	$-0.153538\pi$
$158$		0			0
$159$	−1980.59			−0.987869
$160$		0			0
$161$	−1346.47	−	2332.16i	−0.659110	−	1.14161i
$162$		0			0
$163$	−1308.78	+	2266.87i	−0.628903	+	1.08929i	0.358869	+	0.933388i	$0.383162\pi$
$163$	−1308.78	+	2266.87i	−0.628903	+	1.08929i	−0.987772	+	0.155904i	$0.950171\pi$
$164$		0			0
$165$	617.312	−	1069.22i	0.291259	−	0.504475i
$166$		0			0
$167$	−671.021	−	1162.24i	−0.310929	−	0.538545i	0.667635	−	0.744489i	$-0.267307\pi$
$167$	−671.021	−	1162.24i	−0.310929	−	0.538545i	−0.978564	+	0.205944i	$0.933974\pi$
$168$		0			0
$169$	1082.59	−	1875.10i	0.492759	−	0.853483i
$170$		0			0
$171$	729.740			0.326343
$172$		0			0
$173$	1601.02	−	2773.05i	0.703603	−	1.21868i	−0.263590	−	0.964635i	$-0.584907\pi$
$173$	1601.02	−	2773.05i	0.703603	−	1.21868i	0.967193	−	0.254041i	$-0.0817599\pi$
$174$		0			0
$175$	338.757			0.146329
$176$		0			0
$177$	1413.02			0.600053
$178$		0			0
$179$	−1377.59			−0.575227			−0.287613	−	0.957747i	$-0.592862\pi$
$179$	−1377.59			−0.575227			−0.287613	+	0.957747i	$0.592862\pi$
$180$		0			0
$181$	132.228	+	229.026i	0.0543008	+	0.0940518i	0.891898	−	0.452236i	$-0.149374\pi$
$181$	132.228	+	229.026i	0.0543008	+	0.0940518i	−0.837597	+	0.546288i	$0.816040\pi$
$182$		0			0
$183$	2610.47	−	4521.47i	1.05449	−	1.82643i
$184$		0			0
$185$	54.4500	+	1123.99i	0.0216392	+	0.446690i
$186$		0			0
$187$	−952.055	+	1649.01i	−0.372306	+	0.644852i
$188$		0			0
$189$	−839.255	−	1453.63i	−0.322999	−	0.559451i
$190$		0			0
$191$	1884.08			0.713757			0.356878	−	0.934151i	$-0.383841\pi$
$191$	1884.08			0.713757			0.356878	+	0.934151i	$0.383841\pi$
$192$		0			0
$193$	49.8591			0.0185955			0.00929777	−	0.999957i	$-0.497040\pi$
$193$	49.8591			0.0185955			0.00929777	+	0.999957i	$0.497040\pi$
$194$		0			0
$195$	−159.930			−0.0587323
$196$		0			0
$197$	1284.90	−	2225.52i	0.464699	−	0.804882i	−0.534489	−	0.845175i	$-0.679496\pi$
$197$	1284.90	−	2225.52i	0.464699	−	0.804882i	0.999188	+	0.0402933i	$0.0128292\pi$
$198$		0			0
$199$	1434.33			0.510941			0.255471	−	0.966817i	$-0.417770\pi$
$199$	1434.33			0.510941			0.255471	+	0.966817i	$0.417770\pi$
$200$		0			0
$201$	−318.591	+	551.815i	−0.111799	+	0.193642i
$202$		0			0
$203$	373.563	+	647.031i	0.129158	+	0.223708i
$204$		0			0
$205$	978.456	−	1694.73i	0.333358	−	0.577392i
$206$		0			0
$207$	−512.252	+	887.246i	−0.172000	+	0.297912i
$208$		0			0
$209$	3082.08	+	5338.31i	1.02006	+	1.76679i
$210$		0			0
$211$	−1915.18			−0.624865			−0.312432	−	0.949940i	$-0.601144\pi$
$211$	−1915.18			−0.624865			−0.312432	+	0.949940i	$0.601144\pi$
$212$		0			0
$213$	−1577.14	+	2731.69i	−0.507343	+	0.878744i
$214$		0			0
$215$	−348.638	−	603.859i	−0.110590	−	0.191548i
$216$		0			0
$217$	−1743.35	−	3019.57i	−0.545375	−	0.944617i
$218$		0			0
$219$	−436.947	−	756.814i	−0.134823	−	0.233520i
$220$		0			0
$221$	246.653			0.0750754
$222$		0			0
$223$	−1627.58			−0.488749			−0.244375	−	0.969681i	$-0.578583\pi$
$223$	−1627.58			−0.488749			−0.244375	+	0.969681i	$0.578583\pi$
$224$		0			0
$225$	−64.4385	−	111.611i	−0.0190929	−	0.0330698i
$226$		0			0
$227$	−1779.89	−	3082.87i	−0.520421	−	0.901396i	−0.999718	−	0.0237435i	$-0.992442\pi$
$227$	−1779.89	−	3082.87i	−0.520421	−	0.901396i	0.479297	−	0.877653i	$-0.340892\pi$
$228$		0			0
$229$	−2643.68	−	4578.99i	−0.762879	−	1.32135i	−0.941360	−	0.337403i	$-0.890452\pi$
$229$	−2643.68	−	4578.99i	−0.762879	−	1.32135i	0.178481	−	0.983943i	$-0.442882\pi$
$230$		0			0
$231$	−1672.95	+	2897.64i	−0.476503	+	0.825327i
$232$		0			0
$233$	4843.72			1.36190			0.680949	−	0.732331i	$-0.261567\pi$
$233$	4843.72			1.36190			0.680949	+	0.732331i	$0.261567\pi$
$234$		0			0
$235$	673.960	+	1167.33i	0.187082	+	0.324036i
$236$		0			0
$237$	−977.945	+	1693.85i	−0.268035	+	0.464251i
$238$		0			0
$239$	−3044.54	+	5273.30i	−0.823995	+	1.42720i	0.0786895	+	0.996899i	$0.474926\pi$
$239$	−3044.54	+	5273.30i	−0.823995	+	1.42720i	−0.902685	+	0.430302i	$0.858407\pi$
$240$		0			0
$241$	1077.14	+	1865.66i	0.287903	+	0.498662i	0.973309	−	0.229499i	$-0.0737087\pi$
$241$	1077.14	+	1865.66i	0.287903	+	0.498662i	−0.685406	+	0.728161i	$0.740375\pi$
$242$		0			0
$243$	−713.920	+	1236.55i	−0.188469	+	0.326438i
$244$		0			0
$245$	796.948			0.207817
$246$		0			0
$247$	399.243	−	691.509i	0.102847	−	0.178136i
$248$		0			0
$249$	1573.22			0.400398
$250$		0			0
$251$	−808.738			−0.203375			−0.101687	−	0.994816i	$-0.532424\pi$
$251$	−808.738			−0.203375			−0.101687	+	0.994816i	$0.532424\pi$
$252$		0			0
$253$	−8654.03			−2.15049
$254$		0			0
$255$	619.893	+	1073.69i	0.152232	+	0.263674i
$256$		0			0
$257$	−1141.60	+	1977.32i	−0.277087	+	0.479929i	−0.970660	−	0.240458i	$-0.922702\pi$
$257$	−1141.60	+	1977.32i	−0.277087	+	0.479929i	0.693573	+	0.720387i	$0.256036\pi$
$258$		0			0
$259$	−147.563	−	3046.09i	−0.0354019	−	0.730790i
$260$		0			0
$261$	142.119	−	246.157i	0.0337047	−	0.0583782i
$262$		0			0
$263$	1776.59	+	3077.15i	0.416538	+	0.721465i	0.995589	−	0.0938268i	$-0.0299100\pi$
$263$	1776.59	+	3077.15i	0.416538	+	0.721465i	−0.579051	+	0.815292i	$0.696577\pi$
$264$		0			0
$265$	−1746.39			−0.404829
$266$		0			0
$267$	1654.54			0.379238
$268$		0			0
$269$	−5187.40			−1.17577			−0.587883	−	0.808946i	$-0.700038\pi$
$269$	−5187.40			−1.17577			−0.587883	+	0.808946i	$0.700038\pi$
$270$		0			0
$271$	2645.70	−	4582.49i	0.593044	−	1.02718i	−0.400775	−	0.916176i	$-0.631259\pi$
$271$	2645.70	−	4582.49i	0.593044	−	1.02718i	0.993820	−	0.111006i	$-0.0354074\pi$
$272$		0			0
$273$	433.419			0.0960868
$274$		0			0
$275$	544.315	−	942.781i	0.119358	−	0.206734i
$276$		0			0
$277$	−3750.08	−	6495.32i	−0.813430	−	1.40890i	−0.910449	−	0.413620i	$-0.864264\pi$
$277$	−3750.08	−	6495.32i	−0.813430	−	1.40890i	0.0970191	−	0.995283i	$-0.469069\pi$
$278$		0			0
$279$	−663.241	+	1148.77i	−0.142320	+	0.246505i
$280$		0			0
$281$	−1304.50	+	2259.47i	−0.276940	+	0.479674i	−0.970623	−	0.240607i	$-0.922654\pi$
$281$	−1304.50	+	2259.47i	−0.276940	+	0.479674i	0.693683	+	0.720281i	$0.255987\pi$
$282$		0			0
$283$	−1921.18	−	3327.59i	−0.403542	−	0.698956i	0.590608	−	0.806958i	$-0.298888\pi$
$283$	−1921.18	−	3327.59i	−0.403542	−	0.698956i	−0.994151	+	0.108003i	$0.965554\pi$
$284$		0			0
$285$	4013.54			0.834182
$286$		0			0
$287$	−2651.67	+	4592.83i	−0.545377	+	0.944621i
$288$		0			0
$289$	1500.46	+	2598.88i	0.305407	+	0.528981i
$290$		0			0
$291$	−641.617	−	1111.31i	−0.129252	−	0.223870i
$292$		0			0
$293$	−1493.25	−	2586.38i	−0.297735	−	0.515693i	0.677882	−	0.735171i	$-0.262898\pi$
$293$	−1493.25	−	2586.38i	−0.297735	−	0.515693i	−0.975618	+	0.219478i	$0.929565\pi$
$294$		0			0
$295$	1245.93			0.245902
$296$		0			0
$297$	−5394.05			−1.05385
$298$		0			0
$299$	560.509	+	970.830i	0.108412	+	0.187774i
$300$		0			0
$301$	944.830	+	1636.49i	0.180927	+	0.313375i
$302$		0			0
$303$	2496.47	+	4324.02i	0.473329	+	0.819829i
$304$		0			0
$305$	2301.78	−	3986.81i	0.432131	−	0.748472i
$306$		0			0
$307$	921.454			0.171303			0.0856517	−	0.996325i	$-0.472703\pi$
$307$	921.454			0.171303			0.0856517	+	0.996325i	$0.472703\pi$
$308$		0			0
$309$	−4516.99	−	7823.65i	−0.831594	−	1.44036i
$310$		0			0
$311$	276.466	−	478.853i	0.0504082	−	0.0873095i	−0.839720	−	0.543019i	$-0.817281\pi$
$311$	276.466	−	478.853i	0.0504082	−	0.0873095i	0.890129	+	0.455710i	$0.150614\pi$
$312$		0			0
$313$	2759.60	−	4779.78i	0.498345	−	0.863159i	−0.501653	−	0.865069i	$-0.667275\pi$
$313$	2759.60	−	4779.78i	0.498345	−	0.863159i	0.999998	+	0.00190961i	$0.000607848\pi$
$314$		0			0
$315$	174.632	+	302.471i	0.0312362	+	0.0541026i
$316$		0			0
$317$	−3389.97	+	5871.60i	−0.600629	+	1.04032i	0.392096	+	0.919924i	$0.371750\pi$
$317$	−3389.97	+	5871.60i	−0.600629	+	1.04032i	−0.992726	+	0.120397i	$0.961583\pi$
$318$		0			0
$319$	2400.96			0.421405
$320$		0			0
$321$	−1696.01	+	2937.58i	−0.294898	+	0.510779i
$322$		0			0
$323$	−6189.92			−1.06630
$324$		0			0
$325$	−141.018			−0.0240685
$326$		0			0
$327$	10093.8			1.70700
$328$		0			0
$329$	−1826.47	−	3163.54i	−0.306069	−	0.530126i
$330$		0			0
$331$	−4637.80	+	8032.90i	−0.770141	+	1.33392i	0.167345	+	0.985898i	$0.446481\pi$
$331$	−4637.80	+	8032.90i	−0.770141	+	1.33392i	−0.937486	+	0.348024i	$0.886853\pi$
$332$		0			0
$333$	−975.528	+	628.045i	−0.160536	+	0.103353i
$334$		0			0
$335$	−280.917	+	486.563i	−0.0458154	+	0.0793545i
$336$		0			0
$337$	−2573.19	−	4456.89i	−0.415936	−	0.720422i	0.579590	−	0.814908i	$-0.303213\pi$
$337$	−2573.19	−	4456.89i	−0.415936	−	0.720422i	−0.995526	+	0.0944857i	$0.969879\pi$
$338$		0			0
$339$	2492.76			0.399375
$340$		0			0
$341$	−11204.9			−1.77940
$342$		0			0
$343$	−6807.53			−1.07164
$344$		0			0
$345$	−2817.36	+	4879.82i	−0.439657	+	0.761509i
$346$		0			0
$347$	7202.20			1.11422			0.557110	−	0.830438i	$-0.311910\pi$
$347$	7202.20			1.11422			0.557110	+	0.830438i	$0.311910\pi$
$348$		0			0
$349$	−6112.15	+	10586.6i	−0.937467	+	1.62374i	−0.167293	+	0.985907i	$0.553503\pi$
$349$	−6112.15	+	10586.6i	−0.937467	+	1.62374i	−0.770174	+	0.637834i	$0.779831\pi$
$350$		0			0
$351$	349.365	+	605.118i	0.0531274	+	0.0920194i
$352$		0			0
$353$	−3415.96	+	5916.61i	−0.515051	+	0.892095i	0.484796	+	0.874627i	$0.338894\pi$
$353$	−3415.96	+	5916.61i	−0.515051	+	0.892095i	−0.999847	+	0.0174678i	$0.994440\pi$
$354$		0			0
$355$	−1390.65	+	2408.67i	−0.207909	+	0.360110i
$356$		0			0
$357$	−1679.95	−	2909.75i	−0.249054	−	0.431374i
$358$		0			0
$359$	−5531.33			−0.813183			−0.406591	−	0.913610i	$-0.633283\pi$
$359$	−5531.33			−0.813183			−0.406591	+	0.913610i	$0.633283\pi$
$360$		0			0
$361$	−6589.78	+	11413.8i	−0.960749	+	1.66407i
$362$		0			0
$363$	1602.45	+	2775.52i	0.231699	+	0.401314i
$364$		0			0
$365$	−385.278	−	667.321i	−0.0552503	−	0.0956963i
$366$		0			0
$367$	6683.32	+	11575.8i	0.950589	+	1.64647i	0.744154	+	0.668009i	$0.232853\pi$
$367$	6683.32	+	11575.8i	0.950589	+	1.64647i	0.206436	+	0.978460i	$0.433814\pi$
$368$		0			0
$369$	2017.61			0.284640
$370$		0			0
$371$	4732.81			0.662305
$372$		0			0
$373$	473.794	+	820.634i	0.0657697	+	0.113916i	0.897035	−	0.441959i	$-0.145716\pi$
$373$	473.794	+	820.634i	0.0657697	+	0.113916i	−0.831265	+	0.555876i	$0.812383\pi$
$374$		0			0
$375$	−354.409	−	613.854i	−0.0488043	−	0.0845315i
$376$		0			0
$377$	−155.507	−	269.346i	−0.0212441	−	0.0367958i
$378$		0			0
$379$	3444.60	−	5966.23i	0.466853	−	0.808613i	−0.532430	−	0.846474i	$-0.678721\pi$
$379$	3444.60	−	5966.23i	0.466853	−	0.808613i	0.999283	+	0.0378608i	$0.0120543\pi$
$380$		0			0
$381$	10810.0			1.45357
$382$		0			0
$383$	−3327.53	−	5763.45i	−0.443939	−	0.768925i	0.554038	−	0.832491i	$-0.313086\pi$
$383$	−3327.53	−	5763.45i	−0.443939	−	0.768925i	−0.997978	+	0.0635658i	$0.979753\pi$
$384$		0			0
$385$	−1475.12	+	2554.99i	−0.195271	+	0.338219i
$386$		0			0
$387$	359.452	−	622.588i	0.0472143	−	0.0817776i
$388$		0			0
$389$	−3077.18	−	5329.83i	−0.401078	−	0.694687i	0.592778	−	0.805366i	$-0.298031\pi$
$389$	−3077.18	−	5329.83i	−0.401078	−	0.694687i	−0.993856	+	0.110678i	$0.964698\pi$
$390$		0			0
$391$	4345.10	−	7525.94i	0.561998	−	0.973410i
$392$		0			0
$393$	11475.6			1.47294
$394$		0			0
$395$	−862.303	+	1493.55i	−0.109841	+	0.190250i
$396$		0			0
$397$	−14366.5			−1.81621			−0.908104	−	0.418744i	$-0.862471\pi$
$397$	−14366.5			−1.81621			−0.908104	+	0.418744i	$0.862471\pi$
$398$		0			0
$399$	−10876.9			−1.36473
$400$		0			0
$401$	7823.08			0.974229			0.487115	−	0.873338i	$-0.338049\pi$
$401$	7823.08			0.974229			0.487115	+	0.873338i	$0.338049\pi$
$402$		0			0
$403$	725.722	+	1256.99i	0.0897042	+	0.155372i
$404$		0			0
$405$	−2104.03	+	3644.29i	−0.258148	+	0.447126i
$406$		0			0
$407$	−8714.54	−	4483.77i	−1.06134	−	0.546074i
$408$		0			0
$409$	−2350.84	+	4071.77i	−0.284209	+	0.492264i	−0.972417	−	0.233249i	$-0.925064\pi$
$409$	−2350.84	+	4071.77i	−0.284209	+	0.492264i	0.688208	+	0.725513i	$0.258398\pi$
$410$		0			0
$411$	5428.61	+	9402.63i	0.651517	+	1.12846i
$412$		0			0
$413$	−3376.55			−0.402298
$414$		0			0
$415$	1387.19			0.164083
$416$		0			0
$417$	−18520.6			−2.17496
$418$		0			0
$419$	−2005.76	+	3474.08i	−0.233861	+	0.405059i	−0.958941	−	0.283605i	$-0.908469\pi$
$419$	−2005.76	+	3474.08i	−0.233861	+	0.405059i	0.725080	+	0.688665i	$0.241803\pi$
$420$		0			0
$421$	2879.82			0.333382			0.166691	−	0.986009i	$-0.446692\pi$
$421$	2879.82			0.333382			0.166691	+	0.986009i	$0.446692\pi$
$422$		0			0
$423$	−694.863	+	1203.54i	−0.0798709	+	0.138341i
$424$		0			0
$425$	546.590	+	946.722i	0.0623848	+	0.108054i
$426$		0			0
$427$	−6237.97	+	10804.5i	−0.706971	+	1.22451i
$428$		0			0
$429$	696.417	−	1206.23i	0.0783760	−	0.135751i
$430$		0			0
$431$	7063.65	+	12234.6i	0.789429	+	1.36733i	0.926317	+	0.376745i	$0.122957\pi$
$431$	7063.65	+	12234.6i	0.789429	+	1.36733i	−0.136887	+	0.990587i	$0.543710\pi$
$432$		0			0
$433$	2640.68			0.293079			0.146539	−	0.989205i	$-0.453186\pi$
$433$	2640.68			0.293079			0.146539	+	0.989205i	$0.453186\pi$
$434$		0			0
$435$	781.647	−	1353.85i	0.0861542	−	0.149223i
$436$		0			0
$437$	−14066.4	−	24363.6i	−1.53978	−	2.66698i
$438$		0			0
$439$	7824.99	+	13553.3i	0.850721	+	1.47349i	0.880559	+	0.473937i	$0.157168\pi$
$439$	7824.99	+	13553.3i	0.850721	+	1.47349i	−0.0298377	+	0.999555i	$0.509499\pi$
$440$		0			0
$441$	410.833	+	711.584i	0.0443616	+	0.0768366i
$442$		0			0
$443$	−6233.20			−0.668507			−0.334253	−	0.942483i	$-0.608484\pi$
$443$	−6233.20			−0.668507			−0.334253	+	0.942483i	$0.608484\pi$
$444$		0			0
$445$	1458.89			0.155412
$446$		0			0
$447$	−9216.42	−	15963.3i	−0.975216	−	1.68912i
$448$		0			0
$449$	−1635.30	−	2832.43i	−0.171881	−	0.297707i	0.767196	−	0.641412i	$-0.221651\pi$
$449$	−1635.30	−	2832.43i	−0.171881	−	0.297707i	−0.939078	+	0.343705i	$0.888318\pi$
$450$		0			0
$451$	8521.40	+	14759.5i	0.889706	+	1.54102i
$452$		0			0
$453$	−8929.79	+	15466.9i	−0.926177	+	1.60419i
$454$		0			0
$455$	382.167			0.0393764
$456$		0			0
$457$	2924.05	+	5064.61i	0.299303	+	0.518408i	0.975977	−	0.217875i	$-0.0699126\pi$
$457$	2924.05	+	5064.61i	0.299303	+	0.518408i	−0.676674	+	0.736283i	$0.736579\pi$
$458$		0			0
$459$	2708.30	−	4690.92i	0.275409	−	0.477022i
$460$		0			0
$461$	5768.22	−	9990.85i	0.582761	−	1.00937i	−0.412389	−	0.911008i	$-0.635306\pi$
$461$	5768.22	−	9990.85i	0.582761	−	1.00937i	0.995150	−	0.0983642i	$-0.0313610\pi$
$462$		0			0
$463$	−2250.79	−	3898.49i	−0.225925	−	0.391314i	0.730672	−	0.682729i	$-0.239207\pi$
$463$	−2250.79	−	3898.49i	−0.225925	−	0.391314i	−0.956597	+	0.291416i	$0.905874\pi$
$464$		0			0
$465$	−3647.80	+	6318.17i	−0.363791	+	0.630104i
$466$		0			0
$467$	−6511.26			−0.645193			−0.322596	−	0.946537i	$-0.604556\pi$
$467$	−6511.26			−0.645193			−0.322596	+	0.946537i	$0.604556\pi$
$468$		0			0
$469$	761.302	−	1318.61i	0.0749545	−	0.129825i
$470$		0			0
$471$	18844.8			1.84358
$472$		0			0
$473$	6072.61			0.590315
$474$		0			0
$475$	3538.94			0.341848
$476$		0			0
$477$	−900.276	−	1559.32i	−0.0864168	−	0.149678i
$478$		0			0
$479$	10169.1	−	17613.5i	0.970020	−	1.68012i	0.274543	−	0.961575i	$-0.411473\pi$
$479$	10169.1	−	17613.5i	0.970020	−	1.68012i	0.695477	−	0.718549i	$-0.255193\pi$
$480$		0			0
$481$	61.4275	+	1268.03i	0.00582297	+	0.120202i
$482$		0			0
$483$	7635.22	−	13224.6i	0.719285	−	1.24584i
$484$		0			0
$485$	−565.745	−	979.900i	−0.0529674	−	0.0917422i
$486$		0			0
$487$	−12506.8			−1.16373			−0.581864	−	0.813286i	$-0.697676\pi$
$487$	−12506.8			−1.16373			−0.581864	+	0.813286i	$0.697676\pi$
$488$		0			0
$489$	−14842.9			−1.37264
$490$		0			0
$491$	15564.8			1.43061			0.715306	−	0.698811i	$-0.246287\pi$
$491$	15564.8			1.43061			0.715306	+	0.698811i	$0.246287\pi$
$492$		0			0
$493$	−1205.50	+	2087.99i	−0.110128	+	0.190747i
$494$		0			0
$495$	1122.39			0.101915
$496$		0			0
$497$	3768.73	−	6527.63i	0.340142	−	0.589143i
$498$		0			0
$499$	−5638.13	−	9765.53i	−0.505806	−	0.876082i	−0.999977	−	0.00671771i	$-0.997862\pi$
$499$	−5638.13	−	9765.53i	−0.505806	−	0.876082i	0.494171	−	0.869365i	$-0.335472\pi$
$500$		0			0
$501$	3805.06	−	6590.55i	0.339316	−	0.587713i
$502$		0			0
$503$	5350.30	−	9267.00i	0.474271	−	0.821461i	−0.525295	−	0.850920i	$-0.676045\pi$
$503$	5350.30	−	9267.00i	0.474271	−	0.821461i	0.999566	+	0.0294588i	$0.00937840\pi$
$504$		0			0
$505$	2201.26	+	3812.70i	0.193970	+	0.335966i
$506$		0			0
$507$	12277.8			1.07549
$508$		0			0
$509$	7085.49	−	12272.4i	0.617011	−	1.06869i	−0.373017	−	0.927824i	$-0.621677\pi$
$509$	7085.49	−	12272.4i	0.617011	−	1.06869i	0.990028	−	0.140870i	$-0.0449899\pi$
$510$		0			0
$511$	1044.13	+	1808.48i	0.0903902	+	0.156560i
$512$		0			0
$513$	−8767.55	−	15185.8i	−0.754575	−	1.30696i
$514$		0			0
$515$	−3982.85	−	6898.50i	−0.340787	−	0.590261i
$516$		0			0
$517$	−11739.1			−0.998616
$518$		0			0
$519$	18157.3			1.53568
$520$		0			0
$521$	−6169.75	−	10686.3i	−0.518814	−	0.898611i	−0.999761	−	0.0218620i	$-0.993041\pi$
$521$	−6169.75	−	10686.3i	−0.518814	−	0.898611i	0.480947	−	0.876749i	$-0.340293\pi$
$522$		0			0
$523$	9324.76	+	16151.0i	0.779624	+	1.35035i	0.932159	+	0.362050i	$0.117923\pi$
$523$	9324.76	+	16151.0i	0.779624	+	1.35035i	−0.152535	+	0.988298i	$0.548744\pi$
$524$		0			0
$525$	960.469	+	1663.58i	0.0798444	+	0.138295i
$526$		0			0
$527$	5625.85	−	9744.26i	0.465021	−	0.805439i
$528$		0			0
$529$	27329.3			2.24618
$530$		0			0
$531$	642.288	+	1112.48i	0.0524914	+	0.0909177i
$532$		0			0
$533$	1103.84	−	1911.90i	0.0897046	−	0.155373i
$534$		0			0
$535$	−1495.46	+	2590.21i	−0.120849	+	0.209317i
$536$		0			0
$537$	−3905.83	−	6765.10i	−0.313872	−	0.543642i
$538$		0			0
$539$	−3470.33	+	6010.78i	−0.277324	+	0.480339i
$540$		0			0
$541$	−2167.59			−0.172259			−0.0861293	−	0.996284i	$-0.527450\pi$
$541$	−2167.59			−0.172259			−0.0861293	+	0.996284i	$0.527450\pi$
$542$		0			0
$543$	−749.806	+	1298.70i	−0.0592583	+	0.102638i
$544$		0			0
$545$	8900.24			0.699531
$546$		0			0
$547$	3440.27			0.268912			0.134456	−	0.990920i	$-0.457071\pi$
$547$	3440.27			0.268912			0.134456	+	0.990920i	$0.457071\pi$
$548$		0			0
$549$	4746.35			0.368979
$550$		0			0
$551$	3902.55	+	6759.42i	0.301732	+	0.522615i
$552$		0			0
$553$	2336.89	−	4047.61i	0.179701	−	0.311251i
$554$		0			0
$555$	−5365.36	+	3454.22i	−0.410355	+	0.264187i
$556$		0			0
$557$	−3414.75	+	5914.52i	−0.259762	+	0.449922i	−0.966178	−	0.257875i	$-0.916978\pi$
$557$	−3414.75	+	5914.52i	−0.259762	+	0.449922i	0.706416	+	0.707797i	$0.250311\pi$
$558$		0			0
$559$	−393.314	−	681.240i	−0.0297592	−	0.0515445i
$560$		0			0
$561$	−10797.3			−0.812592
$562$		0			0
$563$	−5874.63			−0.439763			−0.219881	−	0.975527i	$-0.570567\pi$
$563$	−5874.63			−0.439763			−0.219881	+	0.975527i	$0.570567\pi$
$564$		0			0
$565$	2197.99			0.163664
$566$		0			0
$567$	5702.04	−	9876.23i	0.422334	−	0.731504i
$568$		0			0
$569$	−4327.74			−0.318855			−0.159427	−	0.987210i	$-0.550965\pi$
$569$	−4327.74			−0.318855			−0.159427	+	0.987210i	$0.550965\pi$
$570$		0			0
$571$	3088.31	−	5349.12i	0.226343	−	0.392038i	−0.730378	−	0.683043i	$-0.760656\pi$
$571$	3088.31	−	5349.12i	0.226343	−	0.392038i	0.956722	+	0.291005i	$0.0939896\pi$
$572$		0			0
$573$	5341.89	+	9252.43i	0.389460	+	0.674565i
$574$		0			0
$575$	−2484.21	+	4302.78i	−0.180172	+	0.312067i
$576$		0			0
$577$	5012.23	−	8681.43i	0.361632	−	0.626365i	−0.626598	−	0.779343i	$-0.715553\pi$
$577$	5012.23	−	8681.43i	0.361632	−	0.626365i	0.988230	+	0.152978i	$0.0488863\pi$
$578$		0			0
$579$	141.364	+	244.850i	0.0101466	+	0.0175745i
$580$		0			0
$581$	−3759.37			−0.268442
$582$		0			0
$583$	7604.67	−	13171.7i	0.540229	−	0.935704i
$584$		0			0
$585$	−72.6958	−	125.913i	−0.00513778	−	0.00889890i
$586$		0			0
$587$	−9167.44	−	15878.5i	−0.644601	−	1.11648i	−0.984393	−	0.175981i	$-0.943690\pi$
$587$	−9167.44	−	15878.5i	−0.644601	−	1.11648i	0.339792	−	0.940500i	$-0.389643\pi$
$588$		0			0
$589$	−18212.5	−	31545.0i	−1.27408	−	2.20677i
$590$		0			0
$591$	14572.2			1.01425
$592$		0			0
$593$	−11408.7			−0.790051			−0.395026	−	0.918670i	$-0.629264\pi$
$593$	−11408.7			−0.790051			−0.395026	+	0.918670i	$0.629264\pi$
$594$		0			0
$595$	−1481.29	−	2565.67i	−0.102062	−	0.176777i
$596$		0			0
$597$	4066.73	+	7043.78i	0.278794	+	0.482886i
$598$		0			0
$599$	2027.99	+	3512.59i	0.138333	+	0.239600i	0.926866	−	0.375393i	$-0.122492\pi$
$599$	2027.99	+	3512.59i	0.138333	+	0.239600i	−0.788533	+	0.614993i	$0.789159\pi$
$600$		0			0
$601$	−2020.30	+	3499.27i	−0.137121	+	0.237501i	−0.926406	−	0.376527i	$-0.877118\pi$
$601$	−2020.30	+	3499.27i	−0.137121	+	0.237501i	0.789284	+	0.614028i	$0.210452\pi$
$602$		0			0
$603$	−579.260			−0.0391199
$604$		0			0
$605$	1412.96	+	2447.31i	0.0949501	+	0.164458i
$606$		0			0
$607$	−8383.36	+	14520.4i	−0.560576	+	0.970947i	0.436870	+	0.899525i	$0.356087\pi$
$607$	−8383.36	+	14520.4i	−0.560576	+	0.970947i	−0.997446	+	0.0714221i	$0.977246\pi$
$608$		0			0
$609$	−2118.31	+	3669.02i	−0.140949	+	0.244131i
$610$		0			0
$611$	760.323	+	1316.92i	0.0503427	+	0.0871961i
$612$		0			0
$613$	507.788	−	879.514i	0.0334574	−	0.0579498i	−0.848812	−	0.528695i	$-0.822682\pi$
$613$	507.788	−	879.514i	0.0334574	−	0.0579498i	0.882269	+	0.470745i	$0.156015\pi$
$614$		0			0
$615$	11096.8			0.727584
$616$		0			0
$617$	−2926.26	+	5068.43i	−0.190935	+	0.330708i	−0.945560	−	0.325447i	$-0.894485\pi$
$617$	−2926.26	+	5068.43i	−0.190935	+	0.330708i	0.754626	+	0.656156i	$0.227819\pi$
$618$		0			0
$619$	26585.2			1.72625			0.863124	−	0.504991i	$-0.168504\pi$
$619$	26585.2			1.72625			0.863124	+	0.504991i	$0.168504\pi$
$620$		0			0
$621$	24618.0			1.59080
$622$		0			0
$623$	−3953.68			−0.254255
$624$		0			0
$625$	−312.500	−	541.266i	−0.0200000	−	0.0346410i
$626$		0			0
$627$	−17477.0	+	30271.1i	−1.11318	+	1.92809i
$628$		0			0
$629$	8274.78	−	5327.30i	0.524542	−	0.337700i
$630$		0			0
$631$	−14809.3	+	25650.4i	−0.934307	+	1.61827i	−0.158442	+	0.987368i	$0.550647\pi$
$631$	−14809.3	+	25650.4i	−0.934307	+	1.61827i	−0.775865	+	0.630899i	$0.782686\pi$
$632$		0			0
$633$	−5430.06	−	9405.14i	−0.340957	−	0.590554i
$634$		0			0
$635$	9531.68			0.595674
$636$		0			0
$637$	899.072			0.0559223
$638$		0			0
$639$	−2867.55			−0.177525
$640$		0			0
$641$	−3191.84	+	5528.43i	−0.196677	+	0.340655i	−0.947449	−	0.319907i	$-0.896348\pi$
$641$	−3191.84	+	5528.43i	−0.196677	+	0.340655i	0.750772	+	0.660562i	$0.229682\pi$
$642$		0			0
$643$	14918.2			0.914958			0.457479	−	0.889221i	$-0.348753\pi$
$643$	14918.2			0.914958			0.457479	+	0.889221i	$0.348753\pi$
$644$		0			0
$645$	1976.97	−	3424.21i	0.120687	−	0.209036i
$646$		0			0
$647$	4392.18	+	7607.48i	0.266885	+	0.462258i	0.968056	−	0.250735i	$-0.0806723\pi$
$647$	4392.18	+	7607.48i	0.266885	+	0.462258i	−0.701171	+	0.712993i	$0.747339\pi$
$648$		0			0
$649$	−5425.44	+	9397.13i	−0.328146	+	0.568366i
$650$		0			0
$651$	9885.75	−	17122.6i	0.595166	−	1.03086i
$652$		0			0
$653$	−6930.86	−	12004.6i	−0.415353	−	0.719413i	0.580112	−	0.814536i	$-0.303009\pi$
$653$	−6930.86	−	12004.6i	−0.415353	−	0.719413i	−0.995465	+	0.0951238i	$0.969675\pi$
$654$		0			0
$655$	10118.6			0.603611
$656$		0			0
$657$	397.227	−	688.018i	0.0235880	−	0.0408556i
$658$		0			0
$659$	1494.02	+	2587.72i	0.0883137	+	0.152964i	0.906798	−	0.421564i	$-0.138519\pi$
$659$	1494.02	+	2587.72i	0.0883137	+	0.152964i	−0.818485	+	0.574528i	$0.805186\pi$
$660$		0			0
$661$	5506.42	+	9537.41i	0.324017	+	0.561214i	0.981313	−	0.192419i	$-0.0616332\pi$
$661$	5506.42	+	9537.41i	0.324017	+	0.561214i	−0.657296	+	0.753632i	$0.728300\pi$
$662$		0			0
$663$	699.328	+	1211.27i	0.0409648	+	0.0709531i
$664$		0			0
$665$	−9590.73			−0.559267
$666$		0			0
$667$	−10957.8			−0.636114
$668$		0			0
$669$	−4614.64	−	7992.80i	−0.266685	−	0.461912i
$670$		0			0
$671$	20046.3	+	34721.3i	1.15332	+	1.99761i
$672$		0			0
$673$	15561.6	+	26953.4i	0.891314	+	1.54380i	0.838301	+	0.545208i	$0.183549\pi$
$673$	15561.6	+	26953.4i	0.891314	+	1.54380i	0.0530136	+	0.998594i	$0.483117\pi$
$674$		0			0
$675$	−1548.41	+	2681.92i	−0.0882937	+	0.152929i
$676$		0			0
$677$	19357.4			1.09891			0.549457	−	0.835522i	$-0.314835\pi$
$677$	19357.4			1.09891			0.549457	+	0.835522i	$0.314835\pi$
$678$		0			0
$679$	1533.20	+	2655.58i	0.0866552	+	0.150091i
$680$		0			0
$681$	10093.0	−	17481.5i	0.567934	−	0.983691i
$682$		0			0
$683$	17285.8	−	29939.9i	0.968409	−	1.67733i	0.268248	−	0.963350i	$-0.413555\pi$
$683$	17285.8	−	29939.9i	0.968409	−	1.67733i	0.700161	−	0.713985i	$-0.253111\pi$
$684$		0			0
$685$	4786.68	+	8290.76i	0.266992	+	0.462444i
$686$		0			0
$687$	14991.1	−	25965.4i	0.832528	−	1.44198i
$688$		0			0
$689$	−1970.17			−0.108937
$690$		0			0
$691$	−5427.98	+	9401.53i	−0.298828	+	0.517585i	−0.975868	−	0.218361i	$-0.929929\pi$
$691$	−5427.98	+	9401.53i	−0.298828	+	0.517585i	0.677040	+	0.735946i	$0.263262\pi$
$692$		0			0
$693$	−3041.75			−0.166734
$694$		0			0
$695$	−16330.6			−0.891299
$696$		0			0
$697$	−17114.1			−0.930045
$698$		0			0
$699$	13733.3	+	23786.7i	0.743118	+	1.28712i
$700$		0			0
$701$	4958.72	−	8588.76i	0.267173	−	0.462758i	−0.700957	−	0.713203i	$-0.747244\pi$
$701$	4958.72	−	8588.76i	0.267173	−	0.462758i	0.968131	+	0.250445i	$0.0805771\pi$
$702$		0			0
$703$	−1541.56	−	31821.9i	−0.0827044	−	1.70724i
$704$		0			0
$705$	−3821.72	+	6619.41i	−0.204162	+	0.353619i
$706$		0			0
$707$	−5965.55	−	10332.6i	−0.317337	−	0.549644i
$708$		0			0
$709$	13733.2			0.727450			0.363725	−	0.931506i	$-0.381505\pi$
$709$	13733.2			0.727450			0.363725	+	0.931506i	$0.381505\pi$
$710$		0			0
$711$	−1778.09			−0.0937887
$712$		0			0
$713$	51138.1			2.68603
$714$		0			0
$715$	614.065	−	1063.59i	0.0321185	−	0.0556309i
$716$		0			0
$717$	−34528.4			−1.79845
$718$		0			0
$719$	4301.12	−	7449.75i	0.223094	−	0.386410i	−0.732652	−	0.680604i	$-0.761718\pi$
$719$	4301.12	−	7449.75i	0.223094	−	0.386410i	0.955746	+	0.294193i	$0.0950510\pi$
$720$		0			0
$721$	10793.8	+	18695.3i	0.557532	+	0.965674i
$722$		0			0
$723$	−6107.96	+	10579.3i	−0.314187	+	0.544188i
$724$		0			0
$725$	689.216	−	1193.76i	0.0353060	−	0.0611518i
$726$		0			0
$727$	9066.43	+	15703.5i	0.462524	+	0.801115i	0.999086	−	0.0427456i	$-0.0136105\pi$
$727$	9066.43	+	15703.5i	0.462524	+	0.801115i	−0.536562	+	0.843861i	$0.680277\pi$
$728$		0			0
$729$	14626.9			0.743124
$730$		0			0
$731$	−3049.00	+	5281.02i	−0.154270	+	0.267203i
$732$		0			0
$733$	7846.08	+	13589.8i	0.395364	+	0.684790i	0.993148	−	0.116867i	$-0.0372852\pi$
$733$	7846.08	+	13589.8i	0.395364	+	0.684790i	−0.597784	+	0.801657i	$0.703952\pi$
$734$		0			0
$735$	2259.57	+	3913.68i	0.113395	+	0.196406i
$736$		0			0
$737$	−2446.52	−	4237.49i	−0.122278	−	0.211791i
$738$		0			0
$739$	−29761.8			−1.48147			−0.740734	−	0.671798i	$-0.765522\pi$
$739$	−29761.8			−1.48147			−0.740734	+	0.671798i	$0.765522\pi$
$740$		0			0
$741$	4527.85			0.224473
$742$		0			0
$743$	8828.92	+	15292.1i	0.435938	+	0.755066i	0.997372	−	0.0724553i	$-0.0230835\pi$
$743$	8828.92	+	15292.1i	0.435938	+	0.755066i	−0.561434	+	0.827522i	$0.689750\pi$
$744$		0			0
$745$	−8126.57	−	14075.6i	−0.399644	−	0.692203i
$746$		0			0
$747$	715.107	+	1238.60i	0.0350260	+	0.0606668i
$748$		0			0
$749$	4052.78	−	7019.63i	0.197711	−	0.342445i
$750$		0			0
$751$	8427.28			0.409475			0.204738	−	0.978817i	$-0.434366\pi$
$751$	8427.28			0.409475			0.204738	+	0.978817i	$0.434366\pi$
$752$		0			0
$753$	−2292.99	−	3971.58i	−0.110971	−	0.192208i
$754$		0			0
$755$	−7873.84	+	13637.9i	−0.379548	+	0.657396i
$756$		0			0
$757$	−7680.99	+	13303.9i	−0.368785	+	0.638755i	−0.989376	−	0.145380i	$-0.953560\pi$
$757$	−7680.99	+	13303.9i	−0.368785	+	0.638755i	0.620591	+	0.784135i	$0.286893\pi$
$758$		0			0
$759$	−24536.5	−	42498.5i	−1.17341	−	2.03241i
$760$		0			0
$761$	−8056.00	+	13953.4i	−0.383745	+	0.664666i	−0.991594	−	0.129387i	$-0.958699\pi$
$761$	−8056.00	+	13953.4i	−0.383745	+	0.664666i	0.607849	+	0.794052i	$0.292032\pi$
$762$		0			0
$763$	−24120.2			−1.14444
$764$		0			0
$765$	−563.543	+	976.085i	−0.0266339	+	0.0461313i
$766$		0			0
$767$	1405.59			0.0661707
$768$		0			0
$769$	6513.89			0.305458			0.152729	−	0.988268i	$-0.451194\pi$
$769$	6513.89			0.305458			0.152729	+	0.988268i	$0.451194\pi$
$770$		0			0
$771$	−12947.0			−0.604768
$772$		0			0
$773$	9322.26	+	16146.6i	0.433762	+	0.751298i	0.997194	−	0.0748646i	$-0.0238524\pi$
$773$	9322.26	+	16146.6i	0.433762	+	0.751298i	−0.563431	+	0.826163i	$0.690519\pi$
$774$		0			0
$775$	−3216.45	+	5571.05i	−0.149081	+	0.258217i
$776$		0			0
$777$	14540.4	−	9361.14i	0.671346	−	0.432212i
$778$		0			0
$779$	−27701.6	+	47980.5i	−1.27408	+	2.20678i
$780$		0			0
$781$	−12111.2	−	20977.2i	−0.554894	−	0.961105i
$782$		0			0
$783$	−6830.00			−0.311730
$784$		0			0
$785$	16616.4			0.755498
$786$		0			0
$787$	−12379.1			−0.560696			−0.280348	−	0.959898i	$-0.590450\pi$
$787$	−12379.1			−0.560696			−0.280348	+	0.959898i	$0.590450\pi$
$788$		0			0
$789$	−10074.3	+	17449.1i	−0.454566	+	0.787332i
$790$		0			0
$791$	−5956.68			−0.267756
$792$		0			0
$793$	2596.74	−	4497.69i	0.116284	−	0.201409i
$794$		0			0
$795$	−4951.48	−	8576.22i	−0.220894	−	0.382600i
$796$		0			0
$797$	17401.7	−	30140.7i	0.773401	−	1.33957i	−0.162288	−	0.986743i	$-0.551887\pi$
$797$	17401.7	−	30140.7i	0.773401	−	1.33957i	0.935689	−	0.352826i	$-0.114779\pi$
$798$		0			0
$799$	5894.08	−	10208.8i	0.260973	−	0.452019i
$800$		0			0
$801$	752.070	+	1302.62i	0.0331749	+	0.0574606i
$802$		0			0
$803$	6710.80			0.294918
$804$		0			0
$805$	6732.35	−	11660.8i	0.294763	−	0.510545i
$806$		0			0
$807$	−14707.7	−	25474.4i	−0.641555	−	1.11121i
$808$		0			0
$809$	15754.7	+	27287.9i	0.684678	+	1.18590i	0.973538	+	0.228525i	$0.0733903\pi$
$809$	15754.7	+	27287.9i	0.684678	+	1.18590i	−0.288860	+	0.957371i	$0.593276\pi$
$810$		0			0
$811$	12948.7	+	22427.9i	0.560656	+	0.971084i	0.997439	+	0.0715174i	$0.0227841\pi$
$811$	12948.7	+	22427.9i	0.560656	+	0.971084i	−0.436784	+	0.899567i	$0.643883\pi$
$812$		0			0
$813$	30005.1			1.29437
$814$		0			0
$815$	−13087.8			−0.562508
$816$		0			0
$817$	9870.48	+	17096.2i	0.422674	+	0.732092i
$818$		0			0
$819$	197.010	+	341.231i	0.00840547	+	0.0145587i
$820$		0			0
$821$	−12499.9	−	21650.4i	−0.531362	−	0.920346i	−0.999330	−	0.0366006i	$-0.988347\pi$
$821$	−12499.9	−	21650.4i	−0.531362	−	0.920346i	0.467968	−	0.883745i	$-0.344986\pi$
$822$		0			0
$823$	−21348.5	+	36976.6i	−0.904204	+	1.56613i	−0.0822228	+	0.996614i	$0.526202\pi$
$823$	−21348.5	+	36976.6i	−0.904204	+	1.56613i	−0.821982	+	0.569514i	$0.807131\pi$
$824$		0			0
$825$	6173.12			0.260510
$826$		0			0
$827$	−16091.7	−	27871.6i	−0.676617	−	1.17193i	−0.975994	−	0.217800i	$-0.930112\pi$
$827$	−16091.7	−	27871.6i	−0.676617	−	1.17193i	0.299377	−	0.954135i	$-0.403221\pi$
$828$		0			0
$829$	972.795	−	1684.93i	0.0407558	−	0.0705911i	−0.844928	−	0.534880i	$-0.820357\pi$
$829$	972.795	−	1684.93i	0.0407558	−	0.0705911i	0.885684	+	0.464289i	$0.153690\pi$
$830$		0			0
$831$	21265.0	−	36832.0i	0.887694	−	1.53753i
$832$		0			0
$833$	−3484.83	−	6035.91i	−0.144949	−	0.251059i
$834$		0			0
$835$	3355.11	−	5811.21i	0.139052	−	0.240845i
$836$		0			0
$837$	31874.4			1.31630
$838$		0			0
$839$	867.634	−	1502.79i	0.0357021	−	0.0618379i	−0.847622	−	0.530600i	$-0.821967\pi$
$839$	867.634	−	1502.79i	0.0357021	−	0.0618379i	0.883324	+	0.468762i	$0.155300\pi$
$840$		0			0
$841$	−21348.9			−0.875349
$842$		0			0
$843$	−14794.5			−0.604447
$844$		0			0
$845$	10825.9			0.440737
$846$		0			0
$847$	−3829.19	−	6632.36i	−0.155340	−	0.269056i
$848$		0			0
$849$	10894.2	−	18869.2i	0.440384	−	0.762768i
$850$		0			0
$851$	39772.5	+	20463.6i	1.60209	+	0.824304i
$852$		0			0
$853$	−11260.5	+	19503.7i	−0.451994	+	0.782877i	−0.998510	−	0.0545722i	$-0.982621\pi$
$853$	−11260.5	+	19503.7i	−0.451994	+	0.782877i	0.546516	+	0.837449i	$0.315954\pi$
$854$		0			0
$855$	1824.35	+	3159.87i	0.0729725	+	0.126392i
$856$		0			0
$857$	6366.07			0.253747			0.126873	−	0.991919i	$-0.459506\pi$
$857$	6366.07			0.253747			0.126873	+	0.991919i	$0.459506\pi$
$858$		0			0
$859$	−5085.94			−0.202014			−0.101007	−	0.994886i	$-0.532206\pi$
$859$	−5085.94			−0.202014			−0.101007	+	0.994886i	$0.532206\pi$
$860$		0			0
$861$	−30072.8			−1.19034
$862$		0			0
$863$	19285.4	−	33403.2i	0.760696	−	1.31756i	−0.181796	−	0.983336i	$-0.558191\pi$
$863$	19285.4	−	33403.2i	0.760696	−	1.31756i	0.942492	−	0.334229i	$-0.108476\pi$
$864$		0			0
$865$	16010.2			0.629322
$866$		0			0
$867$	−8508.45	+	14737.1i	−0.333290	+	0.577275i
$868$		0			0
$869$	−7509.83	−	13007.4i	−0.293157	−	0.507763i
$870$		0			0
$871$	−316.915	+	548.913i	−0.0123286	+	0.0213538i
$872$		0			0
$873$	583.292	−	1010.29i	0.0226133	−	0.0391675i
$874$		0			0
$875$	846.893	+	1466.86i	0.0327202	+	0.0566731i
$876$		0			0
$877$	−12201.6			−0.469805			−0.234902	−	0.972019i	$-0.575477\pi$
$877$	−12201.6			−0.469805			−0.234902	+	0.972019i	$0.575477\pi$
$878$		0			0
$879$	8467.53	−	14666.2i	0.324918	−	0.562774i
$880$		0			0
$881$	2286.81	+	3960.87i	0.0874513	+	0.151470i	0.906433	−	0.422349i	$-0.138794\pi$
$881$	2286.81	+	3960.87i	0.0874513	+	0.151470i	−0.818982	+	0.573819i	$0.805461\pi$
$882$		0			0
$883$	9056.89	+	15687.0i	0.345174	+	0.597859i	0.985385	−	0.170340i	$-0.0544866\pi$
$883$	9056.89	+	15687.0i	0.345174	+	0.597859i	−0.640211	+	0.768199i	$0.721153\pi$
$884$		0			0
$885$	3532.56	+	6118.57i	0.134176	+	0.232399i
$886$		0			0
$887$	−35187.6			−1.33200			−0.666000	−	0.745952i	$-0.731995\pi$
$887$	−35187.6			−1.33200			−0.666000	+	0.745952i	$0.731995\pi$
$888$		0			0
$889$	−25831.4			−0.974531
$890$		0			0
$891$	−18324.1	−	31738.2i	−0.688978	−	1.19335i
$892$		0			0
$893$	−19080.8	−	33049.0i	−0.715023	−	1.23846i
$894$		0			0
$895$	−3443.96	−	5965.12i	−0.128625	−	0.222784i
$896$		0			0
$897$	−3178.39	+	5505.14i	−0.118309	+	0.204918i
$898$		0			0
$899$	−14187.7			−0.526347
$900$		0			0
$901$	7636.46	+	13226.7i	0.282361	+	0.489064i
$902$		0			0
$903$	−5357.70	+	9279.81i	−0.197445	+	0.341985i
$904$		0			0
$905$	−661.141	+	1145.13i	−0.0242841	+	0.0420612i
$906$		0			0
$907$	24767.4	+	42898.4i	0.906713	+	1.57047i	0.818601	+	0.574363i	$0.194750\pi$
$907$	24767.4	+	42898.4i	0.906713	+	1.57047i	0.0881126	+	0.996111i	$0.471916\pi$
$908$		0			0
$909$	−2269.54	+	3930.95i	−0.0828116	+	0.143434i
$910$		0			0
$911$	40173.5			1.46104			0.730521	−	0.682890i	$-0.239277\pi$
$911$	40173.5			1.46104			0.730521	+	0.682890i	$0.239277\pi$
$912$		0			0
$913$	−6040.55	+	10462.5i	−0.218963	+	0.379254i
$914$		0			0
$915$	26104.7			0.943165
$916$		0			0
$917$	−27421.9			−0.987515
$918$		0			0
$919$	1476.18			0.0529867			0.0264933	−	0.999649i	$-0.491566\pi$
$919$	1476.18			0.0529867			0.0264933	+	0.999649i	$0.491566\pi$
$920$		0			0
$921$	2612.57	+	4525.11i	0.0934714	+	0.161897i
$922$		0			0
$923$	−1568.85	+	2717.32i	−0.0559472	+	0.0969034i
$924$		0			0
$925$	−4730.91	+	3045.76i	−0.168164	+	0.108264i
$926$		0			0
$927$	4106.38	−	7112.46i	0.145492	−	0.252000i
$928$		0			0
$929$	−5551.97	−	9616.29i	−0.196076	−	0.339613i	0.751177	−	0.660101i	$-0.229486\pi$
$929$	−5551.97	−	9616.29i	−0.196076	−	0.339613i	−0.947253	+	0.320488i	$0.896153\pi$
$930$		0			0
$931$	−22562.8			−0.794271
$932$		0			0
$933$	3135.43			0.110021
$934$		0			0
$935$	−9520.55			−0.333000
$936$		0			0
$937$	13963.1	−	24184.7i	0.486823	−	0.843202i	−0.513062	−	0.858351i	$-0.671489\pi$
$937$	13963.1	−	24184.7i	0.486823	−	0.843202i	0.999885	+	0.0151492i	$0.00482232\pi$
$938$		0			0
$939$	31296.9			1.08769
$940$		0			0
$941$	−15181.0	+	26294.2i	−0.525915	+	0.910912i	0.473629	+	0.880724i	$0.342944\pi$
$941$	−15181.0	+	26294.2i	−0.525915	+	0.910912i	−0.999544	+	0.0301872i	$0.990390\pi$
$942$		0			0
$943$	−38891.0	−	67361.2i	−1.34302	−	2.32618i
$944$		0			0
$945$	4196.27	−	7268.16i	0.144450	−	0.250194i
$946$		0			0
$947$	8343.78	−	14451.9i	0.286311	−	0.495905i	−0.686615	−	0.727021i	$-0.740904\pi$
$947$	8343.78	−	14451.9i	0.286311	−	0.495905i	0.972926	+	0.231116i	$0.0742376\pi$
$948$		0			0
$949$	−434.649	−	752.833i	−0.0148675	−	0.0257513i
$950$		0			0
$951$	−38445.9			−1.31093
$952$		0			0
$953$	−14481.3	+	25082.3i	−0.492229	+	0.852566i	−0.999960	−	0.00895002i	$-0.997151\pi$
$953$	−14481.3	+	25082.3i	−0.492229	+	0.852566i	0.507731	+	0.861516i	$0.330484\pi$
$954$		0			0
$955$	4710.21	+	8158.32i	0.159601	+	0.276437i
$956$		0			0
$957$	6807.39	+	11790.7i	0.229939	+	0.398266i
$958$		0			0
$959$	−12972.2	−	22468.5i	−0.436802	−	0.756563i
$960$		0			0
$961$	36420.4			1.22253
$962$		0			0
$963$	−3083.68			−0.103188
$964$		0			0
$965$	124.648	+	215.896i	0.00415809	+	0.00720202i
$966$		0			0
$967$	10173.8	+	17621.6i	0.338333	+	0.586010i	0.984119	−	0.177508i	$-0.0568036\pi$
$967$	10173.8	+	17621.6i	0.338333	+	0.586010i	−0.645786	+	0.763518i	$0.723470\pi$
$968$		0			0
$969$	−17550.1	−	30397.7i	−0.581827	−	1.00775i
$970$		0			0
$971$	−4406.76	+	7632.73i	−0.145643	+	0.252262i	−0.929613	−	0.368538i	$-0.879859\pi$
$971$	−4406.76	+	7632.73i	−0.145643	+	0.252262i	0.783969	+	0.620799i	$0.213192\pi$
$972$		0			0
$973$	44256.7			1.45818
$974$		0			0
$975$	−399.824	−	692.516i	−0.0131329	−	0.0227469i
$976$		0			0
$977$	24596.3	−	42602.0i	0.805429	−	1.39504i	−0.110572	−	0.993868i	$-0.535268\pi$
$977$	24596.3	−	42602.0i	0.805429	−	1.39504i	0.916001	−	0.401176i	$-0.131398\pi$
$978$		0			0
$979$	−6352.77	+	11003.3i	−0.207391	+	0.359211i
$980$		0			0
$981$	4588.14	+	7946.89i	0.149325	+	0.258639i
$982$		0			0
$983$	−23361.8	+	40463.9i	−0.758012	+	1.31292i	0.185850	+	0.982578i	$0.440496\pi$
$983$	−23361.8	+	40463.9i	−0.758012	+	1.31292i	−0.943863	+	0.330338i	$0.892837\pi$
$984$		0			0
$985$	12849.0			0.415639
$986$		0			0
$987$	10357.1	−	17939.0i	0.334012	−	0.578525i
$988$		0			0
$989$	−27714.9			−0.891085
$990$		0			0
$991$	−22656.2			−0.726233			−0.363116	−	0.931744i	$-0.618287\pi$
$991$	−22656.2			−0.726233			−0.363116	+	0.931744i	$0.618287\pi$
$992$		0			0
$993$	−52597.7			−1.68090
$994$		0			0
$995$	3585.84	+	6210.85i	0.114250	+	0.197887i
$996$		0			0
$997$	−13763.4	+	23838.9i	−0.437203	+	0.757258i	−0.997473	−	0.0710523i	$-0.977364\pi$
$997$	−13763.4	+	23838.9i	−0.437203	+	0.757258i	0.560269	+	0.828310i	$0.310698\pi$
$998$		0			0
$999$	24790.2	+	12754.9i	0.785111	+	0.403953i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	740.4.i.b.121.15	✓	38
37.26	even	3	inner	740.4.i.b.581.15	yes	38

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
740.4.i.b.121.15	✓	38	1.1	even	1	trivial
740.4.i.b.581.15	yes	38	37.26	even	3	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:	\( N \)	\(=\)	\( 740 = 2^{2} \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	740.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.83527 + 4.91084i) q^{3} +(2.50000 + 4.33013i) q^{5} +(-6.77514 - 11.7349i) q^{7} +(-2.57754 + 4.46443i) q^{9} -43.5452 q^{11} +(2.82036 + 4.88500i) q^{13} +(-14.1764 + 24.5542i) q^{15} +(21.8636 - 37.8689i) q^{17} +(-70.7788 - 122.592i) q^{19} +(38.4188 - 66.5432i) q^{21} +198.737 q^{23} +(-12.5000 + 21.6506i) q^{25} +123.873 q^{27} -55.1373 q^{29} +257.316 q^{31} +(-123.462 - 213.843i) q^{33} +(33.8757 - 58.6745i) q^{35} +(200.126 + 102.968i) q^{37} +(-15.9930 + 27.7006i) q^{39} +(-195.691 - 338.947i) q^{41} -139.455 q^{43} -25.7754 q^{45} +269.584 q^{47} +(79.6948 - 138.036i) q^{49} +247.957 q^{51} +(-174.639 + 302.483i) q^{53} +(-108.863 - 188.556i) q^{55} +(401.354 - 695.166i) q^{57} +(124.593 - 215.802i) q^{59} +(-460.357 - 797.362i) q^{61} +69.8528 q^{63} +(-14.1018 + 24.4250i) q^{65} +(56.1834 + 97.3126i) q^{67} +(563.473 + 975.964i) q^{69} +(278.129 + 481.734i) q^{71} -154.111 q^{73} -141.764 q^{75} +(295.025 + 510.998i) q^{77} +(172.461 + 298.710i) q^{79} +(420.806 + 728.858i) q^{81} +(138.719 - 240.268i) q^{83} +218.636 q^{85} +(-156.329 - 270.770i) q^{87} +(145.889 - 252.688i) q^{89} +(38.2167 - 66.1932i) q^{91} +(729.560 + 1263.63i) q^{93} +(353.894 - 612.962i) q^{95} -226.298 q^{97} +(112.239 - 194.404i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 38 q - 6 q^{3} + 95 q^{5} - 32 q^{7} - 187 q^{9} - 2 q^{11} + 93 q^{13} + 30 q^{15} + 38 q^{17} - 91 q^{19} - 230 q^{21} - 306 q^{23} - 475 q^{25} + 552 q^{27} + 156 q^{29} - 144 q^{31} - 484 q^{33} + 160 q^{35}+ \cdots + 721 q^{99}+O(q^{100}) \) 38 * q - 6 * q^3 + 95 * q^5 - 32 * q^7 - 187 * q^9 - 2 * q^11 + 93 * q^13 + 30 * q^15 + 38 * q^17 - 91 * q^19 - 230 * q^21 - 306 * q^23 - 475 * q^25 + 552 * q^27 + 156 * q^29 - 144 * q^31 - 484 * q^33 + 160 * q^35 - 231 * q^37 - 590 * q^39 - 236 * q^41 + 228 * q^43 - 1870 * q^45 - 1082 * q^47 - 655 * q^49 - 1560 * q^51 + 2 * q^53 - 5 * q^55 + 598 * q^57 - 285 * q^59 + 1290 * q^61 + 2992 * q^63 - 465 * q^65 + 664 * q^67 - 240 * q^69 + 1614 * q^71 - 400 * q^73 + 300 * q^75 - 1334 * q^77 + 2236 * q^79 - 1759 * q^81 - 922 * q^83 + 380 * q^85 - 1968 * q^87 + 1107 * q^89 + 2456 * q^91 + 2986 * q^93 + 455 * q^95 - 5328 * q^97 + 721 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more