LMFDB - Embedded newform 684.3.b.a.683.5

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			683.5
Character	$\chi$	$=$	684.683
Dual form			684.3.b.a.683.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.90361 - 0.613402i) q^{2} +(3.24748 + 2.33536i) q^{4} -6.64226i q^{5} +0.470842i q^{7} +(-4.74942 - 6.43762i) q^{8} +O(q^{10})$	\(q+(-1.90361 - 0.613402i) q^{2} +(3.24748 + 2.33536i) q^{4} -6.64226i q^{5} +0.470842i q^{7} +(-4.74942 - 6.43762i) q^{8} +(-4.07438 + 12.6443i) q^{10} +10.1736 q^{11} +3.45114i q^{13} +(0.288815 - 0.896300i) q^{14} +(5.09220 + 15.1680i) q^{16} -14.2737i q^{17} +(13.6293 - 13.2379i) q^{19} +(15.5121 - 21.5706i) q^{20} +(-19.3666 - 6.24052i) q^{22} +25.5501 q^{23} -19.1197 q^{25} +(2.11694 - 6.56963i) q^{26} +(-1.09958 + 1.52905i) q^{28} -14.1589 q^{29} -19.3243 q^{31} +(-0.389466 - 31.9976i) q^{32} +(-8.75551 + 27.1716i) q^{34} +3.12746 q^{35} +30.0832i q^{37} +(-34.0651 + 16.8396i) q^{38} +(-42.7604 + 31.5469i) q^{40} +25.6549 q^{41} -38.5869i q^{43} +(33.0386 + 23.7591i) q^{44} +(-48.6375 - 15.6725i) q^{46} -16.5047 q^{47} +48.7783 q^{49} +(36.3964 + 11.7280i) q^{50} +(-8.05965 + 11.2075i) q^{52} -41.6477 q^{53} -67.5759i q^{55} +(3.03110 - 2.23623i) q^{56} +(26.9530 + 8.68510i) q^{58} -31.3349i q^{59} -3.53469 q^{61} +(36.7859 + 11.8535i) q^{62} +(-18.8860 + 61.1500i) q^{64} +22.9234 q^{65} -13.9620 q^{67} +(33.3342 - 46.3535i) q^{68} +(-5.95346 - 1.91839i) q^{70} -128.352i q^{71} -71.6376 q^{73} +(18.4531 - 57.2667i) q^{74} +(75.1761 - 11.1604i) q^{76} +4.79017i q^{77} +100.177 q^{79} +(100.750 - 33.8237i) q^{80} +(-48.8369 - 15.7367i) q^{82} -58.6257 q^{83} -94.8096 q^{85} +(-23.6693 + 73.4545i) q^{86} +(-48.3188 - 65.4940i) q^{88} -108.060 q^{89} -1.62494 q^{91} +(82.9734 + 59.6687i) q^{92} +(31.4186 + 10.1240i) q^{94} +(-87.9296 - 90.5295i) q^{95} -124.227i q^{97} +(-92.8550 - 29.9207i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.90361	−	0.613402i	−0.951806	−	0.306701i
$2$	−1.90361	−	0.613402i	−0.951806	−	0.306701i
$3$		0			0
$3$		0			0
$4$	3.24748	+	2.33536i	0.811869	+	0.583840i
$5$		−	6.64226i		−	1.32845i	−0.747531	−	0.664226i	$-0.768761\pi$
$5$		−	6.64226i		−	1.32845i	0.747531	−	0.664226i	$-0.231239\pi$
$6$		0			0
$7$			0.470842i			0.0672631i	0.999434	+	0.0336316i	$0.0107073\pi$
$7$			0.470842i			0.0672631i	−0.999434	+	0.0336316i	$0.989293\pi$
$8$	−4.74942	−	6.43762i	−0.593678	−	0.804703i
$9$		0			0
$10$	−4.07438	+	12.6443i	−0.407438	+	1.26443i
$11$	10.1736			0.924875			0.462437	−	0.886652i	$-0.346975\pi$
$11$	10.1736			0.924875			0.462437	+	0.886652i	$0.346975\pi$
$12$		0			0
$13$			3.45114i			0.265472i	0.991151	+	0.132736i	$0.0423763\pi$
$13$			3.45114i			0.265472i	−0.991151	+	0.132736i	$0.957624\pi$
$14$	0.288815	−	0.896300i	0.0206297	−	0.0640214i
$15$		0			0
$16$	5.09220	+	15.1680i	0.318263	+	0.948003i
$17$		−	14.2737i		−	0.839629i	−0.907610	−	0.419814i	$-0.862095\pi$
$17$		−	14.2737i		−	0.839629i	0.907610	−	0.419814i	$-0.137905\pi$
$18$		0			0
$19$	13.6293	−	13.2379i	0.717332	−	0.696731i
$19$	13.6293	−	13.2379i	0.717332	−	0.696731i
$20$	15.5121	−	21.5706i	0.775603	−	1.07853i
$21$		0			0
$22$	−19.3666	−	6.24052i	−0.880301	−	0.283660i
$23$	25.5501			1.11087			0.555437	−	0.831558i	$-0.312551\pi$
$23$	25.5501			1.11087			0.555437	+	0.831558i	$0.312551\pi$
$24$		0			0
$25$	−19.1197			−0.764787
$26$	2.11694	−	6.56963i	0.0814206	−	0.252678i
$27$		0			0
$28$	−1.09958	+	1.52905i	−0.0392709	+	0.0546088i
$29$	−14.1589			−0.488238			−0.244119	−	0.969745i	$-0.578499\pi$
$29$	−14.1589			−0.488238			−0.244119	+	0.969745i	$0.578499\pi$
$30$		0			0
$31$	−19.3243			−0.623364			−0.311682	−	0.950187i	$-0.600892\pi$
$31$	−19.3243			−0.623364			−0.311682	+	0.950187i	$0.600892\pi$
$32$	−0.389466	−	31.9976i	−0.0121708	−	0.999926i
$33$		0			0
$34$	−8.75551	+	27.1716i	−0.257515	+	0.799164i
$35$	3.12746			0.0893559
$36$		0			0
$37$			30.0832i			0.813059i	0.913638	+	0.406529i	$0.133261\pi$
$37$			30.0832i			0.813059i	−0.913638	+	0.406529i	$0.866739\pi$
$38$	−34.0651	+	16.8396i	−0.896449	+	0.443147i
$39$		0			0
$40$	−42.7604	+	31.5469i	−1.06901	+	0.788673i
$41$	25.6549			0.625728			0.312864	−	0.949798i	$-0.398712\pi$
$41$	25.6549			0.625728			0.312864	+	0.949798i	$0.398712\pi$
$42$		0			0
$43$		−	38.5869i		−	0.897370i	−0.893690	−	0.448685i	$-0.851893\pi$
$43$		−	38.5869i		−	0.897370i	0.893690	−	0.448685i	$-0.148107\pi$
$44$	33.0386	+	23.7591i	0.750877	+	0.539979i
$45$		0			0
$46$	−48.6375	−	15.6725i	−1.05734	−	0.340706i
$47$	−16.5047			−0.351164			−0.175582	−	0.984465i	$-0.556181\pi$
$47$	−16.5047			−0.351164			−0.175582	+	0.984465i	$0.556181\pi$
$48$		0			0
$49$	48.7783			0.995476
$50$	36.3964	+	11.7280i	0.727929	+	0.234561i
$51$		0			0
$52$	−8.05965	+	11.2075i	−0.154993	+	0.215529i
$53$	−41.6477			−0.785805			−0.392903	−	0.919580i	$-0.628529\pi$
$53$	−41.6477			−0.785805			−0.392903	+	0.919580i	$0.628529\pi$
$54$		0			0
$55$		−	67.5759i		−	1.22865i
$56$	3.03110	−	2.23623i	0.0541268	−	0.0399326i
$57$		0			0
$58$	26.9530	+	8.68510i	0.464708	+	0.149743i
$59$		−	31.3349i		−	0.531099i	−0.964097	−	0.265550i	$-0.914447\pi$
$59$		−	31.3349i		−	0.531099i	0.964097	−	0.265550i	$-0.0855534\pi$
$60$		0			0
$61$	−3.53469			−0.0579457			−0.0289728	−	0.999580i	$-0.509224\pi$
$61$	−3.53469			−0.0579457			−0.0289728	+	0.999580i	$0.509224\pi$
$62$	36.7859	+	11.8535i	0.593321	+	0.191186i
$63$		0			0
$64$	−18.8860	+	61.1500i	−0.295094	+	0.955468i
$65$	22.9234			0.352667
$66$		0			0
$67$	−13.9620			−0.208388			−0.104194	−	0.994557i	$-0.533226\pi$
$67$	−13.9620			−0.208388			−0.104194	+	0.994557i	$0.533226\pi$
$68$	33.3342	−	46.3535i	0.490209	−	0.681669i
$69$		0			0
$70$	−5.95346	−	1.91839i	−0.0850494	−	0.0274055i
$71$		−	128.352i		−	1.80777i	−0.427773	−	0.903886i	$-0.640702\pi$
$71$		−	128.352i		−	1.80777i	0.427773	−	0.903886i	$-0.359298\pi$
$72$		0			0
$73$	−71.6376			−0.981337			−0.490668	−	0.871346i	$-0.663247\pi$
$73$	−71.6376			−0.981337			−0.490668	+	0.871346i	$0.663247\pi$
$74$	18.4531	−	57.2667i	0.249366	−	0.773874i
$75$		0			0
$76$	75.1761	−	11.1604i	0.989159	−	0.146848i
$77$			4.79017i			0.0622100i
$78$		0			0
$79$	100.177			1.26807			0.634034	−	0.773305i	$-0.281398\pi$
$79$	100.177			1.26807			0.634034	+	0.773305i	$0.281398\pi$
$80$	100.750	−	33.8237i	1.25938	−	0.422797i
$81$		0			0
$82$	−48.8369	−	15.7367i	−0.595572	−	0.191912i
$83$	−58.6257			−0.706333			−0.353167	−	0.935560i	$-0.614895\pi$
$83$	−58.6257			−0.706333			−0.353167	+	0.935560i	$0.614895\pi$
$84$		0			0
$85$	−94.8096			−1.11541
$86$	−23.6693	+	73.4545i	−0.275224	+	0.854122i
$87$		0			0
$88$	−48.3188	−	65.4940i	−0.549077	−	0.744250i
$89$	−108.060			−1.21415			−0.607077	−	0.794643i	$-0.707658\pi$
$89$	−108.060			−1.21415			−0.607077	+	0.794643i	$0.707658\pi$
$90$		0			0
$91$	−1.62494			−0.0178565
$92$	82.9734	+	59.6687i	0.901885	+	0.648573i
$93$		0			0
$94$	31.4186	+	10.1240i	0.334240	+	0.107702i
$95$	−87.9296	−	90.5295i	−0.925575	−	0.952942i
$96$		0			0
$97$		−	124.227i		−	1.28069i	−0.768087	−	0.640346i	$-0.778791\pi$
$97$		−	124.227i		−	1.28069i	0.768087	−	0.640346i	$-0.221209\pi$
$98$	−92.8550	−	29.9207i	−0.947500	−	0.305313i
$99$		0			0
$100$	−62.0907	−	44.6513i	−0.620907	−	0.446513i
$101$			16.1661i			0.160060i	0.996792	+	0.0800301i	$0.0255016\pi$
$101$			16.1661i			0.160060i	−0.996792	+	0.0800301i	$0.974498\pi$
$102$		0			0
$103$	−8.61325			−0.0836238			−0.0418119	−	0.999126i	$-0.513313\pi$
$103$	−8.61325			−0.0836238			−0.0418119	+	0.999126i	$0.513313\pi$
$104$	22.2171	−	16.3909i	0.213626	−	0.157605i
$105$		0			0
$106$	79.2810	+	25.5468i	0.747934	+	0.241007i
$107$		−	192.384i		−	1.79798i	−0.437972	−	0.898989i	$-0.644303\pi$
$107$		−	192.384i		−	1.79798i	0.437972	−	0.898989i	$-0.355697\pi$
$108$		0			0
$109$		−	31.7667i		−	0.291438i	−0.989326	−	0.145719i	$-0.953450\pi$
$109$		−	31.7667i		−	0.291438i	0.989326	−	0.145719i	$-0.0465495\pi$
$110$	−41.4512	+	128.638i	−0.376829	+	1.16944i
$111$		0			0
$112$	−7.14175	+	2.39762i	−0.0637656	+	0.0214073i
$113$	−157.215			−1.39128			−0.695640	−	0.718391i	$-0.744879\pi$
$113$	−157.215			−1.39128			−0.695640	+	0.718391i	$0.744879\pi$
$114$		0			0
$115$		−	169.711i		−	1.47574i
$116$	−45.9807	−	33.0661i	−0.396385	−	0.285053i
$117$		0			0
$118$	−19.2209	+	59.6494i	−0.162889	+	0.505504i
$119$	6.72065			0.0564761
$120$		0			0
$121$	−17.4974			−0.144607
$122$	6.72867	+	2.16818i	0.0551530	+	0.0177720i
$123$		0			0
$124$	−62.7551	−	45.1291i	−0.506090	−	0.363944i
$125$		−	39.0587i		−	0.312470i
$126$		0			0
$127$	118.218			0.930851			0.465425	−	0.885087i	$-0.345901\pi$
$127$	118.218			0.930851			0.465425	+	0.885087i	$0.345901\pi$
$128$	73.4612	−	104.821i	0.573915	−	0.818915i
$129$		0			0
$130$	−43.6372	−	14.0612i	−0.335671	−	0.108163i
$131$	−126.719			−0.967322			−0.483661	−	0.875255i	$-0.660693\pi$
$131$	−126.719			−0.967322			−0.483661	+	0.875255i	$0.660693\pi$
$132$		0			0
$133$	6.23295	+	6.41725i	0.0468643	+	0.0482500i
$134$	26.5783	+	8.56433i	0.198345	+	0.0639129i
$135$		0			0
$136$	−91.8887	+	67.7918i	−0.675652	+	0.498469i
$137$			20.4018i			0.148918i	0.997224	+	0.0744590i	$0.0237230\pi$
$137$			20.4018i			0.148918i	−0.997224	+	0.0744590i	$0.976277\pi$
$138$		0			0
$139$		−	106.578i		−	0.766746i	−0.923594	−	0.383373i	$-0.874762\pi$
$139$		−	106.578i		−	0.766746i	0.923594	−	0.383373i	$-0.125238\pi$
$140$	10.1563	+	7.30373i	0.0725453	+	0.0521695i
$141$		0			0
$142$	−78.7313	+	244.332i	−0.554446	+	1.72065i
$143$			35.1106i			0.245529i
$144$		0			0
$145$			94.0471i			0.648601i
$146$	136.370	+	43.9426i	0.934042	+	0.300977i
$147$		0			0
$148$	−70.2550	+	97.6944i	−0.474696	+	0.660097i
$149$			187.048i			1.25535i	0.778474	+	0.627677i	$0.215994\pi$
$149$			187.048i			1.25535i	−0.778474	+	0.627677i	$0.784006\pi$
$150$		0			0
$151$	280.997			1.86091			0.930454	−	0.366409i	$-0.119413\pi$
$151$	280.997			1.86091			0.930454	+	0.366409i	$0.119413\pi$
$152$	−149.952	−	24.8681i	−0.986526	−	0.163606i
$153$		0			0
$154$	2.93830	−	9.11862i	0.0190799	−	0.0592118i
$155$			128.357i			0.828109i
$156$		0			0
$157$	−191.202			−1.21785			−0.608923	−	0.793230i	$-0.708398\pi$
$157$	−191.202			−1.21785			−0.608923	+	0.793230i	$0.708398\pi$
$158$	−190.699	−	61.4490i	−1.20695	−	0.388918i
$159$		0			0
$160$	−212.537	+	2.58693i	−1.32835	+	0.0161683i
$161$			12.0301i			0.0747209i
$162$		0			0
$163$		−	177.569i		−	1.08938i	−0.838637	−	0.544691i	$-0.816647\pi$
$163$		−	177.569i		−	1.08938i	0.838637	−	0.544691i	$-0.183353\pi$
$164$	83.3136	+	59.9133i	0.508009	+	0.365325i
$165$		0			0
$166$	111.601	+	35.9611i	0.672292	+	0.216633i
$167$			101.127i			0.605550i	0.953062	+	0.302775i	$0.0979131\pi$
$167$			101.127i			0.605550i	−0.953062	+	0.302775i	$0.902087\pi$
$168$		0			0
$169$	157.090			0.929525
$170$	180.481	+	58.1564i	1.06165	+	0.342097i
$171$		0			0
$172$	90.1143	−	125.310i	0.523920	−	0.728547i
$173$	178.731			1.03313			0.516565	−	0.856248i	$-0.327211\pi$
$173$	178.731			1.03313			0.516565	+	0.856248i	$0.327211\pi$
$174$		0			0
$175$		−	9.00234i		−	0.0514419i
$176$	51.8061	+	154.314i	0.294353	+	0.876784i
$177$		0			0
$178$	205.704	+	66.2840i	1.15564	+	0.372382i
$179$			149.034i			0.832591i	0.909229	+	0.416296i	$0.136672\pi$
$179$			149.034i			0.832591i	−0.909229	+	0.416296i	$0.863328\pi$
$180$		0			0
$181$			40.0902i			0.221493i	0.993849	+	0.110746i	$0.0353242\pi$
$181$			40.0902i			0.221493i	−0.993849	+	0.110746i	$0.964676\pi$
$182$	3.09326	+	0.996742i	0.0169959	+	0.00547660i
$183$		0			0
$184$	−121.348	−	164.482i	−0.659501	−	0.893924i
$185$	199.820			1.08011
$186$		0			0
$187$		−	145.215i		−	0.776552i
$188$	−53.5987	−	38.5444i	−0.285099	−	0.205024i
$189$		0			0
$190$	111.853	+	226.269i	0.588699	+	1.19089i
$191$	12.1725			0.0637301			0.0318651	−	0.999492i	$-0.489855\pi$
$191$	12.1725			0.0637301			0.0318651	+	0.999492i	$0.489855\pi$
$192$		0			0
$193$		−	268.517i		−	1.39128i	−0.718390	−	0.695641i	$-0.755121\pi$
$193$		−	268.517i		−	1.39128i	0.718390	−	0.695641i	$-0.244879\pi$
$194$	−76.2012	+	236.480i	−0.392790	+	1.21897i
$195$		0			0
$196$	158.406	+	113.915i	0.808196	+	0.581198i
$197$			67.3589i			0.341923i	0.985278	+	0.170962i	$0.0546874\pi$
$197$			67.3589i			0.341923i	−0.985278	+	0.170962i	$0.945313\pi$
$198$		0			0
$199$			347.506i			1.74626i	0.487485	+	0.873131i	$0.337914\pi$
$199$			347.506i			1.74626i	−0.487485	+	0.873131i	$0.662086\pi$
$200$	90.8073	+	123.085i	0.454037	+	0.615426i
$201$		0			0
$202$	9.91630	−	30.7739i	0.0490906	−	0.152346i
$203$		−	6.66660i		−	0.0328404i
$204$		0			0
$205$		−	170.406i		−	0.831251i
$206$	16.3963	+	5.28338i	0.0795936	+	0.0256475i
$207$		0			0
$208$	−52.3470	+	17.5739i	−0.251668	+	0.0844899i
$209$	138.659	−	134.677i	0.663442	−	0.644389i
$210$		0			0
$211$	−130.187			−0.616998			−0.308499	−	0.951225i	$-0.599827\pi$
$211$	−130.187			−0.616998			−0.308499	+	0.951225i	$0.599827\pi$
$212$	−135.250	−	97.2623i	−0.637971	−	0.458784i
$213$		0			0
$214$	−118.008	+	366.224i	−0.551442	+	1.71133i
$215$	−256.304			−1.19211
$216$		0			0
$217$		−	9.09867i		−	0.0419294i
$218$	−19.4858	+	60.4715i	−0.0893843	+	0.277392i
$219$		0			0
$220$	157.814	−	219.451i	0.717336	−	0.997505i
$221$	49.2605			0.222898
$222$		0			0
$223$	375.296			1.68294			0.841470	−	0.540303i	$-0.181691\pi$
$223$	375.296			1.68294			0.841470	+	0.540303i	$0.181691\pi$
$224$	15.0658	−	0.183377i	0.0672581	−	0.000818646i
$225$		0			0
$226$	299.275	+	96.4357i	1.32423	+	0.426707i
$227$			151.029i			0.665326i	0.943046	+	0.332663i	$0.107947\pi$
$227$			151.029i			0.665326i	−0.943046	+	0.332663i	$0.892053\pi$
$228$		0			0
$229$	239.645			1.04649			0.523243	−	0.852183i	$-0.324722\pi$
$229$	239.645			1.04649			0.523243	+	0.852183i	$0.324722\pi$
$230$	−104.101	+	323.063i	−0.452612	+	1.40462i
$231$		0			0
$232$	67.2466	+	91.1497i	0.289856	+	0.392887i
$233$			285.201i			1.22404i	0.790844	+	0.612018i	$0.209642\pi$
$233$			285.201i			1.22404i	−0.790844	+	0.612018i	$0.790358\pi$
$234$		0			0
$235$			109.629i			0.466505i
$236$	73.1781	−	101.759i	0.310077	−	0.431183i
$237$		0			0
$238$	−12.7935	−	4.12246i	−0.0537542	−	0.0173213i
$239$	30.9287			0.129409			0.0647045	−	0.997904i	$-0.479390\pi$
$239$	30.9287			0.129409			0.0647045	+	0.997904i	$0.479390\pi$
$240$		0			0
$241$			81.9792i			0.340162i	0.985430	+	0.170081i	$0.0544030\pi$
$241$			81.9792i			0.340162i	−0.985430	+	0.170081i	$0.945597\pi$
$242$	33.3082	+	10.7329i	0.137637	+	0.0443510i
$243$		0			0
$244$	−11.4788	−	8.25476i	−0.0470443	−	0.0338310i
$245$		−	323.998i		−	1.32244i
$246$		0			0
$247$	45.6858	+	47.0366i	0.184963	+	0.190432i
$248$	91.7791	+	124.402i	0.370077	+	0.501623i
$249$		0			0
$250$	−23.9587	+	74.3526i	−0.0958347	+	0.297410i
$251$	−68.9014			−0.274508			−0.137254	−	0.990536i	$-0.543828\pi$
$251$	−68.9014			−0.274508			−0.137254	+	0.990536i	$0.543828\pi$
$252$		0			0
$253$	259.937			1.02742
$254$	−225.041	−	72.5152i	−0.885989	−	0.285493i
$255$		0			0
$256$	−204.139	+	154.477i	−0.797418	+	0.603427i
$257$	−432.173			−1.68161			−0.840803	−	0.541342i	$-0.817917\pi$
$257$	−432.173			−1.68161			−0.840803	+	0.541342i	$0.817917\pi$
$258$		0			0
$259$	−14.1644			−0.0546889
$260$	74.4431	+	53.5343i	0.286320	+	0.205901i
$261$		0			0
$262$	241.224	+	77.7298i	0.920703	+	0.296679i
$263$	440.010			1.67304			0.836522	−	0.547934i	$-0.184585\pi$
$263$	440.010			1.67304			0.836522	+	0.547934i	$0.184585\pi$
$264$		0			0
$265$			276.635i			1.04391i
$266$	−7.92877	−	16.0393i	−0.0298074	−	0.0602980i
$267$		0			0
$268$	−45.3413	−	32.6063i	−0.169184	−	0.121665i
$269$	217.732			0.809413			0.404706	−	0.914447i	$-0.367374\pi$
$269$	217.732			0.809413			0.404706	+	0.914447i	$0.367374\pi$
$270$		0			0
$271$			301.510i			1.11258i	0.830987	+	0.556291i	$0.187776\pi$
$271$			301.510i			1.11258i	−0.830987	+	0.556291i	$0.812224\pi$
$272$	216.504	−	72.6845i	0.795970	−	0.267222i
$273$		0			0
$274$	12.5145	−	38.8370i	0.0456733	−	0.141741i
$275$	−194.516			−0.707332
$276$		0			0
$277$	99.8731			0.360553			0.180276	−	0.983616i	$-0.442301\pi$
$277$	99.8731			0.360553			0.180276	+	0.983616i	$0.442301\pi$
$278$	−65.3750	+	202.883i	−0.235162	+	0.729794i
$279$		0			0
$280$	−14.8536	−	20.1334i	−0.0530486	−	0.0719049i
$281$	530.591			1.88822			0.944112	−	0.329625i	$-0.106922\pi$
$281$	530.591			1.88822			0.944112	+	0.329625i	$0.106922\pi$
$282$		0			0
$283$			135.855i			0.480052i	0.970766	+	0.240026i	$0.0771560\pi$
$283$			135.855i			0.480052i	−0.970766	+	0.240026i	$0.922844\pi$
$284$	299.748	−	416.819i	1.05545	−	1.46767i
$285$		0			0
$286$	21.5369	−	66.8369i	0.0753039	−	0.233696i
$287$			12.0794i			0.0420884i
$288$		0			0
$289$	85.2617			0.295023
$290$	57.6887	−	179.029i	0.198927	−	0.617342i
$291$		0			0
$292$	−232.641	−	167.299i	−0.796717	−	0.572943i
$293$	−96.2009			−0.328331			−0.164165	−	0.986433i	$-0.552493\pi$
$293$	−96.2009			−0.328331			−0.164165	+	0.986433i	$0.552493\pi$
$294$		0			0
$295$	−208.134			−0.705540
$296$	193.664	−	142.878i	0.654271	−	0.482695i
$297$		0			0
$298$	114.735	−	356.066i	0.385018	−	1.19485i
$299$			88.1770i			0.294906i
$300$		0			0
$301$	18.1683			0.0603599
$302$	−534.909	−	172.364i	−1.77122	−	0.570742i
$303$		0			0
$304$	270.196	+	139.320i	0.888803	+	0.458289i
$305$			23.4783i			0.0769781i
$306$		0			0
$307$	−368.613			−1.20070			−0.600348	−	0.799739i	$-0.704971\pi$
$307$	−368.613			−1.20070			−0.600348	+	0.799739i	$0.704971\pi$
$308$	−11.1868	+	15.5560i	−0.0363206	+	0.0505063i
$309$		0			0
$310$	78.7344	−	244.342i	0.253982	−	0.788199i
$311$	−69.9477			−0.224912			−0.112456	−	0.993657i	$-0.535872\pi$
$311$	−69.9477			−0.224912			−0.112456	+	0.993657i	$0.535872\pi$
$312$		0			0
$313$	−465.161			−1.48614			−0.743068	−	0.669216i	$-0.766630\pi$
$313$	−465.161			−1.48614			−0.743068	+	0.669216i	$0.766630\pi$
$314$	363.974	+	117.284i	1.15915	+	0.373514i
$315$		0			0
$316$	325.323	+	233.950i	1.02950	+	0.740348i
$317$	−477.532			−1.50641			−0.753205	−	0.657786i	$-0.771493\pi$
$317$	−477.532			−1.50641			−0.753205	+	0.657786i	$0.771493\pi$
$318$		0			0
$319$	−144.047			−0.451559
$320$	406.174	+	125.446i	1.26929	+	0.392019i
$321$		0			0
$322$	7.37927	−	22.9006i	0.0229170	−	0.0711198i
$323$	−188.954	−	194.541i	−0.584996	−	0.602293i
$324$		0			0
$325$		−	65.9846i		−	0.203030i
$326$	−108.921	+	338.023i	−0.334115	+	1.03688i
$327$		0			0
$328$	−121.846	−	165.156i	−0.371481	−	0.503526i
$329$		−	7.77111i		−	0.0236204i
$330$		0			0
$331$	158.883			0.480009			0.240004	−	0.970772i	$-0.422851\pi$
$331$	158.883			0.480009			0.240004	+	0.970772i	$0.422851\pi$
$332$	−190.385	−	136.912i	−0.573450	−	0.412385i
$333$		0			0
$334$	62.0315	−	192.506i	0.185723	−	0.576366i
$335$			92.7395i			0.276834i
$336$		0			0
$337$			611.695i			1.81512i	0.419922	+	0.907560i	$0.362057\pi$
$337$			611.695i			1.81512i	−0.419922	+	0.907560i	$0.637943\pi$
$338$	−299.038	−	96.3591i	−0.884727	−	0.285086i
$339$		0			0
$340$	−307.892	−	221.414i	−0.905565	−	0.651219i
$341$	−196.598			−0.576533
$342$		0			0
$343$			46.0381i			0.134222i
$344$	−248.408	+	183.265i	−0.722116	+	0.532748i
$345$		0			0
$346$	−340.235	−	109.634i	−0.983339	−	0.316862i
$347$	332.664			0.958685			0.479343	−	0.877628i	$-0.340875\pi$
$347$	332.664			0.958685			0.479343	+	0.877628i	$0.340875\pi$
$348$		0			0
$349$	−34.3612			−0.0984562			−0.0492281	−	0.998788i	$-0.515676\pi$
$349$	−34.3612			−0.0984562			−0.0492281	+	0.998788i	$0.515676\pi$
$350$	−5.52205	+	17.1370i	−0.0157773	+	0.0489627i
$351$		0			0
$352$	−3.96228	−	325.532i	−0.0112565	−	0.924806i
$353$		−	66.4096i		−	0.188129i	−0.995566	−	0.0940646i	$-0.970014\pi$
$353$		−	66.4096i		−	0.188129i	0.995566	−	0.0940646i	$-0.0299860\pi$
$354$		0			0
$355$	−852.547			−2.40154
$356$	−350.921	−	252.358i	−0.985733	−	0.708871i
$357$		0			0
$358$	91.4177	−	283.703i	0.255357	−	0.792465i
$359$	−423.674			−1.18015			−0.590076	−	0.807348i	$-0.700902\pi$
$359$	−423.674			−1.18015			−0.590076	+	0.807348i	$0.700902\pi$
$360$		0			0
$361$	10.5162	−	360.847i	0.0291308	−	0.999576i
$362$	24.5914	−	76.3162i	0.0679321	−	0.210818i
$363$		0			0
$364$	−5.27695	−	3.79482i	−0.0144971	−	0.0104253i
$365$			475.836i			1.30366i
$366$		0			0
$367$			280.945i			0.765517i	0.923848	+	0.382759i	$0.125026\pi$
$367$			280.945i			0.765517i	−0.923848	+	0.382759i	$0.874974\pi$
$368$	130.106	+	387.545i	0.353550	+	1.05311i
$369$		0			0
$370$	−380.380	−	122.570i	−1.02806	−	0.331271i
$371$		−	19.6095i		−	0.0528557i
$372$		0			0
$373$			72.2157i			0.193608i	0.995303	+	0.0968038i	$0.0308619\pi$
$373$			72.2157i			0.193608i	−0.995303	+	0.0968038i	$0.969138\pi$
$374$	−89.0753	+	276.433i	−0.238169	+	0.739126i
$375$		0			0
$376$	78.3878	+	106.251i	0.208478	+	0.282583i
$377$		−	48.8643i		−	0.129614i
$378$		0			0
$379$	84.5932			0.223201			0.111601	−	0.993753i	$-0.464402\pi$
$379$	84.5932			0.223201			0.111601	+	0.993753i	$0.464402\pi$
$380$	−74.1305	−	499.339i	−0.195080	−	1.31405i
$381$		0			0
$382$	−23.1716	−	7.46661i	−0.0606587	−	0.0195461i
$383$			60.9941i			0.159254i	0.996825	+	0.0796268i	$0.0253729\pi$
$383$			60.9941i			0.159254i	−0.996825	+	0.0796268i	$0.974627\pi$
$384$		0			0
$385$	31.8176			0.0826430
$386$	−164.709	+	511.153i	−0.426707	+	1.32423i
$387$		0			0
$388$	290.115	−	403.425i	0.747719	−	1.03975i
$389$		−	147.820i		−	0.380001i	−0.981784	−	0.190001i	$-0.939151\pi$
$389$		−	147.820i		−	0.380001i	0.981784	−	0.190001i	$-0.0608490\pi$
$390$		0			0
$391$		−	364.695i		−	0.932723i
$392$	−231.669	−	314.016i	−0.590992	−	0.801062i
$393$		0			0
$394$	41.3181	−	128.225i	0.104868	−	0.325445i
$395$		−	665.404i		−	1.68457i
$396$		0			0
$397$	−116.017			−0.292234			−0.146117	−	0.989267i	$-0.546678\pi$
$397$	−116.017			−0.292234			−0.146117	+	0.989267i	$0.546678\pi$
$398$	213.161	−	661.517i	0.535580	−	1.66210i
$399$		0			0
$400$	−97.3612	−	290.008i	−0.243403	−	0.725020i
$401$	−145.033			−0.361678			−0.180839	−	0.983513i	$-0.557881\pi$
$401$	−145.033			−0.361678			−0.180839	+	0.983513i	$0.557881\pi$
$402$		0			0
$403$		−	66.6907i		−	0.165486i
$404$	−37.7536	+	52.4989i	−0.0934495	+	0.129948i
$405$		0			0
$406$	−4.08931	+	12.6906i	−0.0100722	+	0.0312577i
$407$			306.055i			0.751978i
$408$		0			0
$409$			197.143i			0.482012i	0.970524	+	0.241006i	$0.0774773\pi$
$409$			197.143i			0.482012i	−0.970524	+	0.241006i	$0.922523\pi$
$410$	−104.528	+	324.388i	−0.254945	+	0.791189i
$411$		0			0
$412$	−27.9713	−	20.1150i	−0.0678915	−	0.0488229i
$413$	14.7538			0.0357234
$414$		0			0
$415$			389.407i			0.938331i
$416$	110.428	−	1.34410i	0.265453	−	0.00323101i
$417$		0			0
$418$	−346.565	+	171.319i	−0.829103	+	0.409855i
$419$	659.596			1.57421			0.787107	−	0.616816i	$-0.211578\pi$
$419$	659.596			1.57421			0.787107	+	0.616816i	$0.211578\pi$
$420$		0			0
$421$		−	714.982i		−	1.69830i	−0.528155	−	0.849148i	$-0.677116\pi$
$421$		−	714.982i		−	1.69830i	0.528155	−	0.849148i	$-0.322884\pi$
$422$	247.825	+	79.8568i	0.587263	+	0.189234i
$423$		0			0
$424$	197.802	+	268.112i	0.466515	+	0.632340i
$425$			272.908i			0.642137i
$426$		0			0
$427$		−	1.66428i		−	0.00389761i
$428$	449.285	−	624.761i	1.04973	−	1.45972i
$429$		0			0
$430$	487.904	+	157.218i	1.13466	+	0.365622i
$431$			534.659i			1.24051i	0.784401	+	0.620255i	$0.212971\pi$
$431$			534.659i			1.24051i	−0.784401	+	0.620255i	$0.787029\pi$
$432$		0			0
$433$		−	482.402i		−	1.11409i	−0.830482	−	0.557046i	$-0.811935\pi$
$433$		−	482.402i		−	1.11409i	0.830482	−	0.557046i	$-0.188065\pi$
$434$	−5.58115	+	17.3203i	−0.0128598	+	0.0399086i
$435$		0			0
$436$	74.1867	−	103.162i	0.170153	−	0.236609i
$437$	348.231	−	338.230i	0.796866	−	0.773981i
$438$		0			0
$439$	−376.488			−0.857603			−0.428802	−	0.903399i	$-0.641064\pi$
$439$	−376.488			−0.857603			−0.428802	+	0.903399i	$0.641064\pi$
$440$	−435.028	+	320.946i	−0.988701	+	0.729423i
$441$		0			0
$442$	−93.7729	−	30.2165i	−0.212156	−	0.0683631i
$443$	828.172			1.86946			0.934731	−	0.355356i	$-0.115640\pi$
$443$	828.172			1.86946			0.934731	+	0.355356i	$0.115640\pi$
$444$		0			0
$445$			717.761i			1.61295i
$446$	−714.417	−	230.207i	−1.60183	−	0.516160i
$447$		0			0
$448$	−28.7920	−	8.89233i	−0.0642678	−	0.0198489i
$449$	484.547			1.07917			0.539585	−	0.841931i	$-0.318581\pi$
$449$	484.547			1.07917			0.539585	+	0.841931i	$0.318581\pi$
$450$		0			0
$451$	261.003			0.578720
$452$	−510.551	−	367.152i	−1.12954	−	0.812284i
$453$		0			0
$454$	92.6415	−	287.501i	0.204056	−	0.633261i
$455$			10.7933i			0.0237215i
$456$		0			0
$457$	14.5377			0.0318113			0.0159056	−	0.999873i	$-0.494937\pi$
$457$	14.5377			0.0318113			0.0159056	+	0.999873i	$0.494937\pi$
$458$	−456.192	−	146.999i	−0.996052	−	0.320958i
$459$		0			0
$460$	396.335	−	551.131i	0.861598	−	1.19811i
$461$		−	822.917i		−	1.78507i	−0.450979	−	0.892534i	$-0.648925\pi$
$461$		−	822.917i		−	1.78507i	0.450979	−	0.892534i	$-0.351075\pi$
$462$		0			0
$463$			13.5543i			0.0292750i	0.999893	+	0.0146375i	$0.00465943\pi$
$463$			13.5543i			0.0292750i	−0.999893	+	0.0146375i	$0.995341\pi$
$464$	−72.1000	−	214.763i	−0.155388	−	0.462851i
$465$		0			0
$466$	174.943	−	542.911i	0.375413	−	1.16505i
$467$	335.258			0.717897			0.358948	−	0.933357i	$-0.383135\pi$
$467$	335.258			0.717897			0.358948	+	0.933357i	$0.383135\pi$
$468$		0			0
$469$		−	6.57390i		−	0.0140169i
$470$	67.2465	−	208.690i	0.143078	−	0.444022i
$471$		0			0
$472$	−201.722	+	148.822i	−0.427377	+	0.315302i
$473$		−	392.569i		−	0.829955i
$474$		0			0
$475$	−260.588	+	253.104i	−0.548606	+	0.532851i
$476$	21.8252	+	15.6951i	0.0458512	+	0.0329730i
$477$		0			0
$478$	−58.8763	−	18.9717i	−0.123172	−	0.0396899i
$479$	760.782			1.58827			0.794136	−	0.607740i	$-0.207924\pi$
$479$	760.782			1.58827			0.794136	+	0.607740i	$0.207924\pi$
$480$		0			0
$481$	−103.821			−0.215845
$482$	50.2862	−	156.057i	0.104328	−	0.323769i
$483$		0			0
$484$	−56.8223	−	40.8627i	−0.117402	−	0.0844270i
$485$	−825.149			−1.70134
$486$		0			0
$487$	687.736			1.41219			0.706095	−	0.708117i	$-0.250455\pi$
$487$	687.736			1.41219			0.706095	+	0.708117i	$0.250455\pi$
$488$	16.7877	+	22.7550i	0.0344010	+	0.0466291i
$489$		0			0
$490$	−198.741	+	616.767i	−0.405594	+	1.25871i
$491$	276.744			0.563634			0.281817	−	0.959468i	$-0.409063\pi$
$491$	276.744			0.563634			0.281817	+	0.959468i	$0.409063\pi$
$492$		0			0
$493$			202.100i			0.409939i
$494$	−58.1157	−	117.563i	−0.117643	−	0.237982i
$495$		0			0
$496$	−98.4031	−	293.111i	−0.198393	−	0.590950i
$497$	60.4334			0.121596
$498$		0			0
$499$		−	75.2973i		−	0.150896i	−0.997150	−	0.0754482i	$-0.975961\pi$
$499$		−	75.2973i		−	0.150896i	0.997150	−	0.0754482i	$-0.0240388\pi$
$500$	91.2161	−	126.842i	0.182432	−	0.253684i
$501$		0			0
$502$	131.162	+	42.2643i	0.261278	+	0.0841917i
$503$	−379.172			−0.753820			−0.376910	−	0.926250i	$-0.623013\pi$
$503$	−379.172			−0.753820			−0.376910	+	0.926250i	$0.623013\pi$
$504$		0			0
$505$	107.379			0.212632
$506$	−494.820	−	159.446i	−0.977905	−	0.315111i
$507$		0			0
$508$	383.910	+	276.081i	0.755729	+	0.543467i
$509$	565.844			1.11168			0.555839	−	0.831290i	$-0.312397\pi$
$509$	565.844			1.11168			0.555839	+	0.831290i	$0.312397\pi$
$510$		0			0
$511$		−	33.7300i		−	0.0660078i
$512$	483.358	−	168.846i	0.944059	−	0.329777i
$513$		0			0
$514$	822.689	+	265.096i	1.60056	+	0.515750i
$515$			57.2115i			0.111090i
$516$		0			0
$517$	−167.913			−0.324783
$518$	26.9636	+	8.68848i	0.0520532	+	0.0167731i
$519$		0			0
$520$	−108.873	−	147.572i	−0.209371	−	0.283792i
$521$	−324.637			−0.623103			−0.311552	−	0.950229i	$-0.600849\pi$
$521$	−324.637			−0.623103			−0.311552	+	0.950229i	$0.600849\pi$
$522$		0			0
$523$	−271.054			−0.518268			−0.259134	−	0.965841i	$-0.583437\pi$
$523$	−271.054			−0.518268			−0.259134	+	0.965841i	$0.583437\pi$
$524$	−411.518	−	295.935i	−0.785339	−	0.564761i
$525$		0			0
$526$	−837.609	−	269.903i	−1.59241	−	0.513124i
$527$			275.829i			0.523394i
$528$		0			0
$529$	123.809			0.234043
$530$	169.688	−	526.605i	0.320167	−	0.993595i
$531$		0			0
$532$	5.25479	+	35.3960i	0.00987743	+	0.0665339i
$533$			88.5385i			0.166113i
$534$		0			0
$535$	−1277.86			−2.38853
$536$	66.3115	+	89.8823i	0.123716	+	0.167691i
$537$		0			0
$538$	−414.477	−	133.557i	−0.770404	−	0.248248i
$539$	496.252			0.920690
$540$		0			0
$541$	4.97150			0.00918947			0.00459473	−	0.999989i	$-0.498537\pi$
$541$	4.97150			0.00918947			0.00459473	+	0.999989i	$0.498537\pi$
$542$	184.947	−	573.958i	0.341230	−	1.05896i
$543$		0			0
$544$	−456.724	+	5.55911i	−0.839567	+	0.0102190i
$545$	−211.003			−0.387161
$546$		0			0
$547$	−148.968			−0.272337			−0.136168	−	0.990686i	$-0.543479\pi$
$547$	−148.968			−0.272337			−0.136168	+	0.990686i	$0.543479\pi$
$548$	−47.6454	+	66.2542i	−0.0869442	+	0.120902i
$549$		0			0
$550$	370.284	+	119.317i	0.673243	+	0.216939i
$551$	−192.976	+	187.434i	−0.350229	+	0.340171i
$552$		0			0
$553$			47.1677i			0.0852942i
$554$	−190.120	−	61.2624i	−0.343176	−	0.110582i
$555$		0			0
$556$	248.897	−	346.109i	0.447657	−	0.622498i
$557$			507.393i			0.910940i	0.890251	+	0.455470i	$0.150529\pi$
$557$			507.393i			0.910940i	−0.890251	+	0.455470i	$0.849471\pi$
$558$		0			0
$559$	133.169			0.238227
$560$	15.9256	+	47.4374i	0.0284386	+	0.0847096i
$561$		0			0
$562$	−1010.04	−	325.466i	−1.79722	−	0.579120i
$563$		−	430.982i		−	0.765510i	−0.923850	−	0.382755i	$-0.874975\pi$
$563$		−	430.982i		−	0.765510i	0.923850	−	0.382755i	$-0.125025\pi$
$564$		0			0
$565$			1044.26i			1.84825i
$566$	83.3336	−	258.615i	0.147232	−	0.456917i
$567$		0			0
$568$	−826.281	+	609.597i	−1.45472	+	1.07323i
$569$	−607.193			−1.06712			−0.533561	−	0.845761i	$-0.679147\pi$
$569$	−607.193			−1.06712			−0.533561	+	0.845761i	$0.679147\pi$
$570$		0			0
$571$		−	248.126i		−	0.434547i	−0.976111	−	0.217274i	$-0.930284\pi$
$571$		−	248.126i		−	0.434547i	0.976111	−	0.217274i	$-0.0697164\pi$
$572$	−81.9958	+	114.021i	−0.143349	+	0.199337i
$573$		0			0
$574$	7.40952	−	22.9945i	0.0129086	−	0.0400600i
$575$	−488.510			−0.849582
$576$		0			0
$577$	958.765			1.66164			0.830818	−	0.556543i	$-0.187873\pi$
$577$	958.765			1.66164			0.830818	+	0.556543i	$0.187873\pi$
$578$	−162.305	−	52.2997i	−0.280805	−	0.0904839i
$579$		0			0
$580$	−219.634	+	305.416i	−0.378679	+	0.526579i
$581$		−	27.6034i		−	0.0475102i
$582$		0			0
$583$	−423.708			−0.726772
$584$	340.237	+	461.176i	0.582597	+	0.789685i
$585$		0			0
$586$	183.129	+	59.0098i	0.312507	+	0.100699i
$587$	702.884			1.19742			0.598708	−	0.800967i	$-0.295681\pi$
$587$	702.884			1.19742			0.598708	+	0.800967i	$0.295681\pi$
$588$		0			0
$589$	−263.377	+	255.813i	−0.447159	+	0.434317i
$590$	396.207	+	127.670i	0.671538	+	0.216390i
$591$		0			0
$592$	−456.303	+	153.190i	−0.770782	+	0.258766i
$593$		−	266.340i		−	0.449141i	−0.974458	−	0.224570i	$-0.927902\pi$
$593$		−	266.340i		−	0.449141i	0.974458	−	0.224570i	$-0.0720979\pi$
$594$		0			0
$595$		−	44.6403i		−	0.0750258i
$596$	−436.824	+	607.433i	−0.732926	+	1.01918i
$597$		0			0
$598$	54.0880	−	167.855i	0.0904481	−	0.280694i
$599$			929.881i			1.55239i	0.630493	+	0.776195i	$0.282853\pi$
$599$			929.881i			1.55239i	−0.630493	+	0.776195i	$0.717147\pi$
$600$		0			0
$601$			666.868i			1.10960i	0.831985	+	0.554798i	$0.187205\pi$
$601$			666.868i			1.10960i	−0.831985	+	0.554798i	$0.812795\pi$
$602$	−34.5854	−	11.1445i	−0.0574509	−	0.0185124i
$603$		0			0
$604$	912.531	+	656.229i	1.51081	+	1.08647i
$605$			116.222i			0.192103i
$606$		0			0
$607$	−146.368			−0.241134			−0.120567	−	0.992705i	$-0.538471\pi$
$607$	−146.368			−0.241134			−0.120567	+	0.992705i	$0.538471\pi$
$608$	−428.889	−	430.950i	−0.705410	−	0.708799i
$609$		0			0
$610$	14.4016	−	44.6936i	0.0236093	−	0.0732682i
$611$		−	56.9601i		−	0.0932243i
$612$		0			0
$613$	8.51007			0.0138827			0.00694133	−	0.999976i	$-0.497790\pi$
$613$	8.51007			0.0138827			0.00694133	+	0.999976i	$0.497790\pi$
$614$	701.697	+	226.108i	1.14283	+	0.368254i
$615$		0			0
$616$	30.8373	−	22.7505i	0.0500605	−	0.0369327i
$617$		−	1036.99i		−	1.68069i	−0.542052	−	0.840345i	$-0.682352\pi$
$617$		−	1036.99i		−	1.68069i	0.542052	−	0.840345i	$-0.317648\pi$
$618$		0			0
$619$			1128.03i			1.82234i	0.412035	+	0.911168i	$0.364818\pi$
$619$			1128.03i			1.82234i	−0.412035	+	0.911168i	$0.635182\pi$
$620$	−299.759	+	416.836i	−0.483483	+	0.672316i
$621$		0			0
$622$	133.153	+	42.9061i	0.214073	+	0.0689808i
$623$		−	50.8790i		−	0.0816677i
$624$		0			0
$625$	−737.430			−1.17989
$626$	885.485	+	285.330i	1.41451	+	0.455799i
$627$		0			0
$628$	−620.923	−	446.525i	−0.988731	−	0.711026i
$629$	429.398			0.682668
$630$		0			0
$631$		−	73.3862i		−	0.116301i	−0.998308	−	0.0581507i	$-0.981480\pi$
$631$		−	73.3862i		−	0.116301i	0.998308	−	0.0581507i	$-0.0185204\pi$
$632$	−475.784	−	644.904i	−0.752823	−	1.02042i
$633$		0			0
$634$	909.036	+	292.919i	1.43381	+	0.462017i
$635$		−	785.235i		−	1.23659i
$636$		0			0
$637$			168.341i			0.264271i
$638$	274.210	+	88.3589i	0.429796	+	0.138494i
$639$		0			0
$640$	−696.249	−	487.948i	−1.08789	−	0.762419i
$641$	458.489			0.715271			0.357635	−	0.933861i	$-0.383583\pi$
$641$	458.489			0.715271			0.357635	+	0.933861i	$0.383583\pi$
$642$		0			0
$643$		−	691.411i		−	1.07529i	−0.843172	−	0.537645i	$-0.819314\pi$
$643$		−	691.411i		−	1.07529i	0.843172	−	0.537645i	$-0.180686\pi$
$644$	−28.0945	+	39.0673i	−0.0436250	+	0.0606636i
$645$		0			0
$646$	240.363	+	486.234i	0.372079	+	0.752685i
$647$	−504.684			−0.780037			−0.390018	−	0.920807i	$-0.627531\pi$
$647$	−504.684			−0.780037			−0.390018	+	0.920807i	$0.627531\pi$
$648$		0			0
$649$		−	318.789i		−	0.491200i
$650$	−40.4751	+	125.609i	−0.0622694	+	0.193245i
$651$		0			0
$652$	414.688	−	576.652i	0.636025	−	0.884436i
$653$			251.132i			0.384581i	0.981338	+	0.192291i	$0.0615916\pi$
$653$			251.132i			0.384581i	−0.981338	+	0.192291i	$0.938408\pi$
$654$		0			0
$655$			841.702i			1.28504i
$656$	130.640	+	389.134i	0.199146	+	0.593192i
$657$		0			0
$658$	−4.76682	+	14.7932i	−0.00724440	+	0.0224820i
$659$			785.619i			1.19214i	0.802933	+	0.596069i	$0.203271\pi$
$659$			785.619i			1.19214i	−0.802933	+	0.596069i	$0.796729\pi$
$660$		0			0
$661$		−	1136.79i		−	1.71981i	−0.510455	−	0.859905i	$-0.670523\pi$
$661$		−	1136.79i		−	1.71981i	0.510455	−	0.859905i	$-0.329477\pi$
$662$	−302.451	−	97.4591i	−0.456875	−	0.147219i
$663$		0			0
$664$	278.438	+	377.410i	0.419334	+	0.568389i
$665$	42.6251	−	41.4009i	0.0640978	−	0.0622570i
$666$		0			0
$667$	−361.762			−0.542371
$668$	−236.168	+	328.407i	−0.353544	+	0.491628i
$669$		0			0
$670$	56.8866	−	176.540i	0.0849053	−	0.263492i
$671$	−35.9606			−0.0535925
$672$		0			0
$673$			196.852i			0.292499i	0.989248	+	0.146250i	$0.0467202\pi$
$673$			196.852i			0.292499i	−0.989248	+	0.146250i	$0.953280\pi$
$674$	375.215	−	1164.43i	0.556699	−	1.72764i
$675$		0			0
$676$	510.145	+	366.861i	0.754652	+	0.542693i
$677$	1186.26			1.75223			0.876117	−	0.482099i	$-0.160125\pi$
$677$	1186.26			1.75223			0.876117	+	0.482099i	$0.160125\pi$
$678$		0			0
$679$	58.4913			0.0861433
$680$	450.291	+	610.349i	0.662192	+	0.897572i
$681$		0			0
$682$	374.246	+	120.594i	0.548748	+	0.176823i
$683$		−	777.354i		−	1.13815i	−0.822287	−	0.569073i	$-0.807302\pi$
$683$		−	777.354i		−	1.13815i	0.822287	−	0.569073i	$-0.192698\pi$
$684$		0			0
$685$	135.514			0.197831
$686$	28.2399	−	87.6387i	0.0411660	−	0.127753i
$687$		0			0
$688$	585.288	−	196.492i	0.850709	−	0.285599i
$689$		−	143.732i		−	0.208609i
$690$		0			0
$691$		−	531.659i		−	0.769405i	−0.923041	−	0.384702i	$-0.874304\pi$
$691$		−	531.659i		−	0.769405i	0.923041	−	0.384702i	$-0.125696\pi$
$692$	580.426	+	417.402i	0.838766	+	0.603182i
$693$		0			0
$694$	−633.263	−	204.057i	−0.912482	−	0.294030i
$695$	−707.918			−1.01859
$696$		0			0
$697$		−	366.190i		−	0.525380i
$698$	65.4104	+	21.0772i	0.0937112	+	0.0301966i
$699$		0			0
$700$	21.0237	−	29.2349i	0.0300338	−	0.0417641i
$701$			609.856i			0.869980i	0.900435	+	0.434990i	$0.143248\pi$
$701$			609.856i			0.869980i	−0.900435	+	0.434990i	$0.856752\pi$
$702$		0			0
$703$	398.238	+	410.013i	0.566484	+	0.583233i
$704$	−192.139	+	622.117i	−0.272925	+	0.883689i
$705$		0			0
$706$	−40.7358	+	126.418i	−0.0576994	+	0.179063i
$707$	−7.61166			−0.0107661
$708$		0			0
$709$	963.066			1.35834			0.679172	−	0.733979i	$-0.262339\pi$
$709$	963.066			1.35834			0.679172	+	0.733979i	$0.262339\pi$
$710$	1622.92	+	522.954i	2.28580	+	0.736555i
$711$		0			0
$712$	513.221	+	695.647i	0.720816	+	0.977033i
$713$	−493.737			−0.692479
$714$		0			0
$715$	233.214			0.326173
$716$	−348.048	+	483.984i	−0.486100	+	0.675955i
$717$		0			0
$718$	806.511	+	259.883i	1.12327	+	0.361954i
$719$	−1180.47			−1.64182			−0.820910	−	0.571057i	$-0.806534\pi$
$719$	−1180.47			−1.64182			−0.820910	+	0.571057i	$0.806534\pi$
$720$		0			0
$721$		−	4.05548i		−	0.00562479i
$722$	−241.363	+	680.462i	−0.334298	+	0.942468i
$723$		0			0
$724$	−93.6250	+	130.192i	−0.129316	+	0.179823i
$725$	270.713			0.373398
$726$		0			0
$727$		−	86.0390i		−	0.118348i	−0.998248	−	0.0591740i	$-0.981153\pi$
$727$		−	86.0390i		−	0.118348i	0.998248	−	0.0591740i	$-0.0188467\pi$
$728$	7.71752	+	10.4608i	0.0106010	+	0.0143692i
$729$		0			0
$730$	291.879	−	905.806i	0.399834	−	1.24083i
$731$	−550.778			−0.753458
$732$		0			0
$733$	−824.526			−1.12486			−0.562432	−	0.826843i	$-0.690134\pi$
$733$	−824.526			−1.12486			−0.562432	+	0.826843i	$0.690134\pi$
$734$	172.332	−	534.810i	0.234785	−	0.728624i
$735$		0			0
$736$	−9.95089	−	817.543i	−0.0135202	−	1.11079i
$737$	−142.044			−0.192733
$738$		0			0
$739$			1108.68i			1.50024i	0.661300	+	0.750121i	$0.270005\pi$
$739$			1108.68i			1.50024i	−0.661300	+	0.750121i	$0.729995\pi$
$740$	648.912	+	466.652i	0.876908	+	0.630611i
$741$		0			0
$742$	−12.0285	+	37.3288i	−0.0162109	+	0.0503084i
$743$			1014.11i			1.36488i	0.730941	+	0.682441i	$0.239081\pi$
$743$			1014.11i			1.36488i	−0.730941	+	0.682441i	$0.760919\pi$
$744$		0			0
$745$	1242.42			1.66768
$746$	44.2972	−	137.471i	0.0593797	−	0.184277i
$747$		0			0
$748$	339.129	−	471.583i	0.453382	−	0.630458i
$749$	90.5822			0.120938
$750$		0			0
$751$	1425.08			1.89758			0.948788	−	0.315915i	$-0.102311\pi$
$751$	1425.08			1.89758			0.948788	+	0.315915i	$0.102311\pi$
$752$	−84.0453	−	250.344i	−0.111762	−	0.332905i
$753$		0			0
$754$	−29.9735	+	93.0187i	−0.0397526	+	0.123367i
$755$		−	1866.46i		−	2.47213i
$756$		0			0
$757$	354.171			0.467861			0.233931	−	0.972253i	$-0.424841\pi$
$757$	354.171			0.467861			0.233931	+	0.972253i	$0.424841\pi$
$758$	−161.033	−	51.8896i	−0.212444	−	0.0684560i
$759$		0			0
$760$	−165.180	+	996.020i	−0.217342	+	1.31055i
$761$			1284.03i			1.68729i	0.536899	+	0.843647i	$0.319596\pi$
$761$			1284.03i			1.68729i	−0.536899	+	0.843647i	$0.680404\pi$
$762$		0			0
$763$	14.9571			0.0196030
$764$	39.5298	+	28.4270i	0.0517405	+	0.0372082i
$765$		0			0
$766$	37.4139	−	116.109i	0.0488432	−	0.151578i
$767$	108.141			0.140992
$768$		0			0
$769$	203.965			0.265233			0.132617	−	0.991167i	$-0.457662\pi$
$769$	203.965			0.265233			0.132617	+	0.991167i	$0.457662\pi$
$770$	−60.5683	−	19.5170i	−0.0786601	−	0.0253467i
$771$		0			0
$772$	627.084	−	872.004i	0.812285	−	1.12954i
$773$	−528.359			−0.683518			−0.341759	−	0.939788i	$-0.611023\pi$
$773$	−528.359			−0.683518			−0.341759	+	0.939788i	$0.611023\pi$
$774$		0			0
$775$	369.474			0.476740
$776$	−799.728	+	590.007i	−1.03058	+	0.760318i
$777$		0			0
$778$	−90.6734	+	281.393i	−0.116547	+	0.361687i
$779$	349.658	−	339.616i	0.448855	−	0.435965i
$780$		0			0
$781$		−	1305.80i		−	1.67196i
$782$	−223.704	+	694.237i	−0.286067	+	0.887771i
$783$		0			0
$784$	248.389	+	739.871i	0.316823	+	0.943714i
$785$			1270.01i			1.61785i
$786$		0			0
$787$	9.60697			0.0122071			0.00610354	−	0.999981i	$-0.498057\pi$
$787$	9.60697			0.0122071			0.00610354	+	0.999981i	$0.498057\pi$
$788$	−157.307	+	218.746i	−0.199628	+	0.277597i
$789$		0			0
$790$	−408.160	+	1266.67i	−0.516659	+	1.60338i
$791$		−	74.0232i		−	0.0935818i
$792$		0			0
$793$		−	12.1987i		−	0.0153830i
$794$	220.852	+	71.1651i	0.278151	+	0.0896286i
$795$		0			0
$796$	−811.552	+	1128.52i	−1.01954	+	1.41774i
$797$	−1086.28			−1.36296			−0.681481	−	0.731836i	$-0.738664\pi$
$797$	−1086.28			−1.36296			−0.681481	+	0.731836i	$0.738664\pi$
$798$		0			0
$799$			235.583i			0.294848i
$800$	7.44646	+	611.784i	0.00930807	+	0.764730i
$801$		0			0
$802$	276.087	+	88.9636i	0.344248	+	0.110927i
$803$	−728.814			−0.907614
$804$		0			0
$805$	79.9069			0.0992632
$806$	−40.9082	+	126.953i	−0.0507546	+	0.157510i
$807$		0			0
$808$	104.071	−	76.7795i	0.128801	−	0.0950241i
$809$		−	2.98547i		−	0.00369032i	−0.999998	−	0.00184516i	$-0.999413\pi$
$809$		−	2.98547i		−	0.00369032i	0.999998	−	0.00184516i	$-0.000587334\pi$
$810$		0			0
$811$	1009.04			1.24419			0.622094	−	0.782942i	$-0.286282\pi$
$811$	1009.04			1.24419			0.622094	+	0.782942i	$0.286282\pi$
$812$	15.5689	−	21.6496i	0.0191735	−	0.0266621i
$813$		0			0
$814$	187.735	−	582.610i	0.230632	−	0.715737i
$815$	−1179.46			−1.44719
$816$		0			0
$817$	−510.809	−	525.913i	−0.625226	−	0.643712i
$818$	120.928	−	375.284i	0.147834	−	0.458782i
$819$		0			0
$820$	397.960	−	553.391i	0.485317	−	0.674867i
$821$			815.300i			0.993057i	0.868020	+	0.496528i	$0.165392\pi$
$821$			815.300i			0.993057i	−0.868020	+	0.496528i	$0.834608\pi$
$822$		0			0
$823$		−	1406.52i		−	1.70901i	−0.519442	−	0.854505i	$-0.673860\pi$
$823$		−	1406.52i		−	1.70901i	0.519442	−	0.854505i	$-0.326140\pi$
$824$	40.9079	+	55.4489i	0.0496455	+	0.0672923i
$825$		0			0
$826$	−28.0854	−	9.04999i	−0.0340017	−	0.0109564i
$827$			212.808i			0.257326i	0.991688	+	0.128663i	$0.0410685\pi$
$827$			212.808i			0.257326i	−0.991688	+	0.128663i	$0.958932\pi$
$828$		0			0
$829$			683.402i			0.824369i	0.911100	+	0.412185i	$0.135234\pi$
$829$			683.402i			0.824369i	−0.911100	+	0.412185i	$0.864766\pi$
$830$	238.863	−	741.280i	0.287787	−	0.893109i
$831$		0			0
$832$	−211.037	−	65.1783i	−0.253650	−	0.0783393i
$833$		−	696.247i		−	0.835830i
$834$		0			0
$835$	671.712			0.804445
$836$	764.813	−	113.542i	0.914848	−	0.135816i
$837$		0			0
$838$	−1255.61	−	404.597i	−1.49835	−	0.482813i
$839$			629.634i			0.750458i	0.926932	+	0.375229i	$0.122436\pi$
$839$			629.634i			0.750458i	−0.926932	+	0.375229i	$0.877564\pi$
$840$		0			0
$841$	−640.526			−0.761624
$842$	−438.572	+	1361.05i	−0.520869	+	1.61645i
$843$		0			0
$844$	−422.778	−	304.033i	−0.500922	−	0.360228i
$845$		−	1043.43i		−	1.23483i
$846$		0			0
$847$		−	8.23850i		−	0.00972668i
$848$	−212.078	−	631.714i	−0.250092	−	0.744946i
$849$		0			0
$850$	167.402	−	519.511i	0.196944	−	0.611190i
$851$			768.629i			0.903207i
$852$		0			0
$853$	−1223.56			−1.43443			−0.717213	−	0.696854i	$-0.754582\pi$
$853$	−1223.56			−1.43443			−0.717213	+	0.696854i	$0.754582\pi$
$854$	−1.02087	+	3.16814i	−0.00119540	+	0.00370976i
$855$		0			0
$856$	−1238.49	+	913.711i	−1.44684	+	1.06742i
$857$	549.572			0.641274			0.320637	−	0.947202i	$-0.396103\pi$
$857$	549.572			0.641274			0.320637	+	0.947202i	$0.396103\pi$
$858$		0			0
$859$		−	1063.96i		−	1.23861i	−0.785151	−	0.619304i	$-0.787415\pi$
$859$		−	1063.96i		−	1.23861i	0.785151	−	0.619304i	$-0.212585\pi$
$860$	−832.342	−	598.563i	−0.967840	−	0.696003i
$861$		0			0
$862$	327.961	−	1017.78i	0.380465	−	1.18072i
$863$		−	696.514i		−	0.807084i	−0.914961	−	0.403542i	$-0.867779\pi$
$863$		−	696.514i		−	0.807084i	0.914961	−	0.403542i	$-0.132221\pi$
$864$		0			0
$865$		−	1187.18i		−	1.37246i
$866$	−295.906	+	918.305i	−0.341693	+	1.06040i
$867$		0			0
$868$	21.2487	−	29.5477i	0.0244800	−	0.0340412i
$869$	1019.17			1.17280
$870$		0			0
$871$		−	48.1849i		−	0.0553213i
$872$	−204.502	+	150.874i	−0.234521	+	0.173020i
$873$		0			0
$874$	−870.367	+	430.253i	−0.995843	+	0.492280i
$875$	18.3905			0.0210177
$876$		0			0
$877$		−	372.892i		−	0.425190i	−0.977140	−	0.212595i	$-0.931808\pi$
$877$		−	372.892i		−	0.425190i	0.977140	−	0.212595i	$-0.0681915\pi$
$878$	716.687	+	230.938i	0.816272	+	0.263028i
$879$		0			0
$880$	1024.99	−	344.110i	1.16477	−	0.391034i
$881$			1643.37i			1.86534i	0.360725	+	0.932672i	$0.382529\pi$
$881$			1643.37i			1.86534i	−0.360725	+	0.932672i	$0.617471\pi$
$882$		0			0
$883$		−	1613.97i		−	1.82783i	−0.405911	−	0.913913i	$-0.633046\pi$
$883$		−	1613.97i		−	1.82783i	0.405911	−	0.913913i	$-0.366954\pi$
$884$	159.972	+	115.041i	0.180964	+	0.130137i
$885$		0			0
$886$	−1576.52	−	508.002i	−1.77937	−	0.573366i
$887$			1163.22i			1.31141i	0.755019	+	0.655703i	$0.227628\pi$
$887$			1163.22i			1.31141i	−0.755019	+	0.655703i	$0.772372\pi$
$888$		0			0
$889$			55.6620i			0.0626119i
$890$	440.276	−	1366.34i	0.494692	−	1.53521i
$891$		0			0
$892$	1218.76	+	876.450i	1.36633	+	0.982567i
$893$	−224.948	+	218.488i	−0.251901	+	0.244667i
$894$		0			0
$895$	989.922			1.10606
$896$	49.3541	+	34.5886i	0.0550828	+	0.0386033i
$897$		0			0
$898$	−922.390	−	297.222i	−1.02716	−	0.330983i
$899$	273.610			0.304350
$900$		0			0
$901$			594.466i			0.659785i
$902$	−496.848	−	160.100i	−0.550830	−	0.177494i
$903$		0			0
$904$	746.678	+	1012.09i	0.825971	+	1.11957i
$905$	266.290			0.294243
$906$		0			0
$907$	798.239			0.880087			0.440043	−	0.897976i	$-0.354963\pi$
$907$	798.239			0.880087			0.440043	+	0.897976i	$0.354963\pi$
$908$	−352.707	+	490.463i	−0.388444	+	0.540158i
$909$		0			0
$910$	6.62062	−	20.5462i	0.00727541	−	0.0225783i
$911$			509.410i			0.559177i	0.960120	+	0.279588i	$0.0901980\pi$
$911$			509.410i			0.559177i	−0.960120	+	0.279588i	$0.909802\pi$
$912$		0			0
$913$	−596.435			−0.653270
$914$	−27.6742	−	8.91748i	−0.0302781	−	0.00975655i
$915$		0			0
$916$	778.243	+	559.658i	0.849610	+	0.610980i
$917$		−	59.6647i		−	0.0650651i
$918$		0			0
$919$		−	1415.52i		−	1.54028i	−0.637873	−	0.770141i	$-0.720186\pi$
$919$		−	1415.52i		−	1.54028i	0.637873	−	0.770141i	$-0.279814\pi$
$920$	−1092.53	+	806.027i	−1.18754	+	0.876116i
$921$		0			0
$922$	−504.779	+	1566.51i	−0.547482	+	1.69904i
$923$	442.960			0.479913
$924$		0			0
$925$		−	575.180i		−	0.621817i
$926$	8.31425	−	25.8022i	0.00897867	−	0.0278641i
$927$		0			0
$928$	5.51441	+	453.051i	0.00594225	+	0.488202i
$929$		−	1201.56i		−	1.29339i	−0.762749	−	0.646695i	$-0.776151\pi$
$929$		−	1201.56i		−	1.29339i	0.762749	−	0.646695i	$-0.223849\pi$
$930$		0			0
$931$	664.815	−	645.722i	0.714087	−	0.693579i
$932$	−666.046	+	926.182i	−0.714641	+	0.993758i
$933$		0			0
$934$	−638.201	−	205.648i	−0.683298	−	0.220180i
$935$	−964.557			−1.03161
$936$		0			0
$937$	−834.064			−0.890143			−0.445071	−	0.895495i	$-0.646822\pi$
$937$	−834.064			−0.890143			−0.445071	+	0.895495i	$0.646822\pi$
$938$	−4.03245	+	12.5142i	−0.00429898	+	0.0133413i
$939$		0			0
$940$	−256.022	+	356.017i	−0.272364	+	0.378741i
$941$	104.743			0.111310			0.0556551	−	0.998450i	$-0.482275\pi$
$941$	104.743			0.111310			0.0556551	+	0.998450i	$0.482275\pi$
$942$		0			0
$943$	655.485			0.695106
$944$	475.289	−	159.563i	0.503484	−	0.169029i
$945$		0			0
$946$	−240.802	+	747.298i	−0.254548	+	0.789956i
$947$	−659.420			−0.696325			−0.348162	−	0.937434i	$-0.613194\pi$
$947$	−659.420			−0.696325			−0.348162	+	0.937434i	$0.613194\pi$
$948$		0			0
$949$		−	247.231i		−	0.260518i
$950$	651.313	−	321.967i	0.685593	−	0.338913i
$951$		0			0
$952$	−31.9192	−	43.2650i	−0.0335286	−	0.0454465i
$953$	−840.251			−0.881690			−0.440845	−	0.897583i	$-0.645321\pi$
$953$	−840.251			−0.881690			−0.440845	+	0.897583i	$0.645321\pi$
$954$		0			0
$955$		−	80.8526i		−	0.0846625i
$956$	100.440	+	72.2297i	0.105063	+	0.0755541i
$957$		0			0
$958$	−1448.23	−	466.665i	−1.51173	−	0.487124i
$959$	−9.60600			−0.0100167
$960$		0			0
$961$	−587.573			−0.611418
$962$	197.635	+	63.6841i	0.205442	+	0.0661997i
$963$		0			0
$964$	−191.451	+	266.225i	−0.198600	+	0.276167i
$965$	−1783.56			−1.84825
$966$		0			0
$967$			247.792i			0.256249i	0.991758	+	0.128124i	$0.0408956\pi$
$967$			247.792i			0.256249i	−0.991758	+	0.128124i	$0.959104\pi$
$968$	83.1024	+	112.642i	0.0858496	+	0.116365i
$969$		0			0
$970$	1570.76	+	506.148i	1.61934	+	0.521802i
$971$		−	1373.60i		−	1.41463i	−0.706900	−	0.707314i	$-0.749907\pi$
$971$		−	1373.60i		−	1.41463i	0.706900	−	0.707314i	$-0.250093\pi$
$972$		0			0
$973$	50.1813			0.0515738
$974$	−1309.18	−	421.859i	−1.34413	−	0.433120i
$975$		0			0
$976$	−17.9993	−	53.6143i	−0.0184419	−	0.0549326i
$977$	1414.12			1.44741			0.723704	−	0.690111i	$-0.242438\pi$
$977$	1414.12			1.44741			0.723704	+	0.690111i	$0.242438\pi$
$978$		0			0
$979$	−1099.36			−1.12294
$980$	756.652	−	1052.18i	0.772094	−	1.07365i
$981$		0			0
$982$	−526.813	−	169.755i	−0.536470	−	0.172867i
$983$		−	1125.03i		−	1.14448i	−0.820085	−	0.572242i	$-0.806074\pi$
$983$		−	1125.03i		−	1.14448i	0.820085	−	0.572242i	$-0.193926\pi$
$984$		0			0
$985$	447.416			0.454229
$986$	123.968	−	384.719i	0.125729	−	0.390182i
$987$		0			0
$988$	38.5162	+	259.443i	0.0389840	+	0.262594i
$989$		−	985.900i		−	0.996865i
$990$		0			0
$991$	975.022			0.983877			0.491939	−	0.870630i	$-0.336288\pi$
$991$	975.022			0.983877			0.491939	+	0.870630i	$0.336288\pi$
$992$	7.52614	+	618.331i	0.00758684	+	0.623317i
$993$		0			0
$994$	−115.042	−	37.0700i	−0.115736	−	0.0372937i
$995$	2308.23			2.31983
$996$		0			0
$997$	200.568			0.201172			0.100586	−	0.994928i	$-0.467928\pi$
$997$	200.568			0.201172			0.100586	+	0.994928i	$0.467928\pi$
$998$	−46.1875	+	143.337i	−0.0462801	+	0.143624i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.3.b.a.683.5	✓	80
3.2	odd	2	inner	684.3.b.a.683.76	yes	80
4.3	odd	2	inner	684.3.b.a.683.8	yes	80
12.11	even	2	inner	684.3.b.a.683.73	yes	80
19.18	odd	2	inner	684.3.b.a.683.75	yes	80
57.56	even	2	inner	684.3.b.a.683.6	yes	80
76.75	even	2	inner	684.3.b.a.683.74	yes	80
228.227	odd	2	inner	684.3.b.a.683.7	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
684.3.b.a.683.5	✓	80	1.1	even	1	trivial
684.3.b.a.683.6	yes	80	57.56	even	2	inner
684.3.b.a.683.7	yes	80	228.227	odd	2	inner
684.3.b.a.683.8	yes	80	4.3	odd	2	inner
684.3.b.a.683.73	yes	80	12.11	even	2	inner
684.3.b.a.683.74	yes	80	76.75	even	2	inner
684.3.b.a.683.75	yes	80	19.18	odd	2	inner
684.3.b.a.683.76	yes	80	3.2	odd	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)

\(f(q)\)	\(=\)	\(q+(-1.90361 - 0.613402i) q^{2} +(3.24748 + 2.33536i) q^{4} -6.64226i q^{5} +0.470842i q^{7} +(-4.74942 - 6.43762i) q^{8} +O(q^{10})\)	\(q+(-1.90361 - 0.613402i) q^{2} +(3.24748 + 2.33536i) q^{4} -6.64226i q^{5} +0.470842i q^{7} +(-4.74942 - 6.43762i) q^{8} +(-4.07438 + 12.6443i) q^{10} +10.1736 q^{11} +3.45114i q^{13} +(0.288815 - 0.896300i) q^{14} +(5.09220 + 15.1680i) q^{16} -14.2737i q^{17} +(13.6293 - 13.2379i) q^{19} +(15.5121 - 21.5706i) q^{20} +(-19.3666 - 6.24052i) q^{22} +25.5501 q^{23} -19.1197 q^{25} +(2.11694 - 6.56963i) q^{26} +(-1.09958 + 1.52905i) q^{28} -14.1589 q^{29} -19.3243 q^{31} +(-0.389466 - 31.9976i) q^{32} +(-8.75551 + 27.1716i) q^{34} +3.12746 q^{35} +30.0832i q^{37} +(-34.0651 + 16.8396i) q^{38} +(-42.7604 + 31.5469i) q^{40} +25.6549 q^{41} -38.5869i q^{43} +(33.0386 + 23.7591i) q^{44} +(-48.6375 - 15.6725i) q^{46} -16.5047 q^{47} +48.7783 q^{49} +(36.3964 + 11.7280i) q^{50} +(-8.05965 + 11.2075i) q^{52} -41.6477 q^{53} -67.5759i q^{55} +(3.03110 - 2.23623i) q^{56} +(26.9530 + 8.68510i) q^{58} -31.3349i q^{59} -3.53469 q^{61} +(36.7859 + 11.8535i) q^{62} +(-18.8860 + 61.1500i) q^{64} +22.9234 q^{65} -13.9620 q^{67} +(33.3342 - 46.3535i) q^{68} +(-5.95346 - 1.91839i) q^{70} -128.352i q^{71} -71.6376 q^{73} +(18.4531 - 57.2667i) q^{74} +(75.1761 - 11.1604i) q^{76} +4.79017i q^{77} +100.177 q^{79} +(100.750 - 33.8237i) q^{80} +(-48.8369 - 15.7367i) q^{82} -58.6257 q^{83} -94.8096 q^{85} +(-23.6693 + 73.4545i) q^{86} +(-48.3188 - 65.4940i) q^{88} -108.060 q^{89} -1.62494 q^{91} +(82.9734 + 59.6687i) q^{92} +(31.4186 + 10.1240i) q^{94} +(-87.9296 - 90.5295i) q^{95} -124.227i q^{97} +(-92.8550 - 29.9207i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 8 q^{4}+O(q^{10}) \) 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

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