LMFDB - Embedded newform 684.3.b.a.683.6

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			683.6
Character	$\chi$	$=$	684.683
Dual form			684.3.b.a.683.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.90361 - 0.613402i) q^{2} +(3.24748 + 2.33536i) q^{4} +6.64226i q^{5} +0.470842i q^{7} +(-4.74942 - 6.43762i) q^{8} +O(q^{10})$	\(q+(-1.90361 - 0.613402i) q^{2} +(3.24748 + 2.33536i) q^{4} +6.64226i q^{5} +0.470842i q^{7} +(-4.74942 - 6.43762i) q^{8} +(4.07438 - 12.6443i) q^{10} -10.1736 q^{11} -3.45114i q^{13} +(0.288815 - 0.896300i) q^{14} +(5.09220 + 15.1680i) q^{16} +14.2737i q^{17} +(-13.6293 - 13.2379i) q^{19} +(-15.5121 + 21.5706i) q^{20} +(19.3666 + 6.24052i) q^{22} -25.5501 q^{23} -19.1197 q^{25} +(-2.11694 + 6.56963i) q^{26} +(-1.09958 + 1.52905i) q^{28} -14.1589 q^{29} +19.3243 q^{31} +(-0.389466 - 31.9976i) q^{32} +(8.75551 - 27.1716i) q^{34} -3.12746 q^{35} -30.0832i q^{37} +(17.8248 + 33.5601i) q^{38} +(42.7604 - 31.5469i) q^{40} +25.6549 q^{41} -38.5869i q^{43} +(-33.0386 - 23.7591i) q^{44} +(48.6375 + 15.6725i) q^{46} +16.5047 q^{47} +48.7783 q^{49} +(36.3964 + 11.7280i) q^{50} +(8.05965 - 11.2075i) q^{52} -41.6477 q^{53} -67.5759i q^{55} +(3.03110 - 2.23623i) q^{56} +(26.9530 + 8.68510i) q^{58} -31.3349i q^{59} -3.53469 q^{61} +(-36.7859 - 11.8535i) q^{62} +(-18.8860 + 61.1500i) q^{64} +22.9234 q^{65} +13.9620 q^{67} +(-33.3342 + 46.3535i) q^{68} +(5.95346 + 1.91839i) q^{70} -128.352i q^{71} -71.6376 q^{73} +(-18.4531 + 57.2667i) q^{74} +(-13.3456 - 74.8191i) q^{76} -4.79017i q^{77} -100.177 q^{79} +(-100.750 + 33.8237i) q^{80} +(-48.8369 - 15.7367i) q^{82} +58.6257 q^{83} -94.8096 q^{85} +(-23.6693 + 73.4545i) q^{86} +(48.3188 + 65.4940i) q^{88} -108.060 q^{89} +1.62494 q^{91} +(-82.9734 - 59.6687i) q^{92} +(-31.4186 - 10.1240i) q^{94} +(87.9296 - 90.5295i) q^{95} +124.227i q^{97} +(-92.8550 - 29.9207i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	$0.231239\pi$
$5$			6.64226i			1.32845i	−0.747531	+	0.664226i	$0.768761\pi$
$6$		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	$-0.653025\pi$
$11$	−10.1736			−0.924875			−0.462437	+	0.886652i	$0.653025\pi$
$12$		0			0
$13$		−	3.45114i		−	0.265472i	−0.991151	−	0.132736i	$-0.957624\pi$
$13$		−	3.45114i		−	0.265472i	0.991151	−	0.132736i	$-0.0423763\pi$
$14$	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	$0.137905\pi$
$17$			14.2737i			0.839629i	−0.907610	+	0.419814i	$0.862095\pi$
$18$		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	$-0.687449\pi$
$23$	−25.5501			−1.11087			−0.555437	+	0.831558i	$0.687449\pi$
$24$		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	$-0.399108\pi$
$31$	19.3243			0.623364			0.311682	+	0.950187i	$0.399108\pi$
$32$	−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	$-0.866739\pi$
$37$		−	30.0832i		−	0.813059i	0.913638	−	0.406529i	$-0.133261\pi$
$38$	17.8248	+	33.5601i	0.469073	+	0.883160i
$39$		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	$-0.443819\pi$
$47$	16.5047			0.351164			0.175582	+	0.984465i	$0.443819\pi$
$48$		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	$-0.466774\pi$
$67$	13.9620			0.208388			0.104194	+	0.994557i	$0.466774\pi$
$68$	−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
$76$	−13.3456	−	74.8191i	−0.175600	−	0.984462i
$77$		−	4.79017i		−	0.0622100i
$78$		0			0
$79$	−100.177			−1.26807			−0.634034	−	0.773305i	$-0.718602\pi$
$79$	−100.177			−1.26807			−0.634034	+	0.773305i	$0.718602\pi$
$80$	−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	$-0.385105\pi$
$83$	58.6257			0.706333			0.353167	+	0.935560i	$0.385105\pi$
$84$		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	$0.221209\pi$
$97$			124.227i			1.28069i	−0.768087	+	0.640346i	$0.778791\pi$
$98$	−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	$-0.974498\pi$
$101$		−	16.1661i		−	0.160060i	0.996792	−	0.0800301i	$-0.0255016\pi$
$102$		0			0
$103$	8.61325			0.0836238			0.0418119	−	0.999126i	$-0.486687\pi$
$103$	8.61325			0.0836238			0.0418119	+	0.999126i	$0.486687\pi$
$104$	−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	$0.0465495\pi$
$109$			31.7667i			0.291438i	−0.989326	+	0.145719i	$0.953450\pi$
$110$	−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	$-0.654099\pi$
$127$	−118.218			−0.930851			−0.465425	+	0.885087i	$0.654099\pi$
$128$	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	$-0.339307\pi$
$131$	126.719			0.967322			0.483661	+	0.875255i	$0.339307\pi$
$132$		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	$-0.976277\pi$
$137$		−	20.4018i		−	0.148918i	0.997224	−	0.0744590i	$-0.0237230\pi$
$138$		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	$-0.784006\pi$
$149$		−	187.048i		−	1.25535i	0.778474	−	0.627677i	$-0.215994\pi$
$150$		0			0
$151$	−280.997			−1.86091			−0.930454	−	0.366409i	$-0.880587\pi$
$151$	−280.997			−1.86091			−0.930454	+	0.366409i	$0.880587\pi$
$152$	−20.4893	+	150.613i	−0.134798	+	0.990873i
$153$		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	$-0.964676\pi$
$181$		−	40.0902i		−	0.221493i	0.993849	−	0.110746i	$-0.0353242\pi$
$182$	−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
$190$	−222.915	+	118.397i	−1.17324	+	0.623141i
$191$	−12.1725			−0.0637301			−0.0318651	−	0.999492i	$-0.510145\pi$
$191$	−12.1725			−0.0637301			−0.0318651	+	0.999492i	$0.510145\pi$
$192$		0			0
$193$			268.517i			1.39128i	0.718390	+	0.695641i	$0.244879\pi$
$193$			268.517i			1.39128i	−0.718390	+	0.695641i	$0.755121\pi$
$194$	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	$-0.945313\pi$
$197$		−	67.3589i		−	0.341923i	0.985278	−	0.170962i	$-0.0546874\pi$
$198$		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	$-0.400173\pi$
$211$	130.187			0.616998			0.308499	+	0.951225i	$0.400173\pi$
$212$	−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	$-0.818309\pi$
$223$	−375.296			−1.68294			−0.841470	+	0.540303i	$0.818309\pi$
$224$	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	$-0.790358\pi$
$233$		−	285.201i		−	1.22404i	0.790844	−	0.612018i	$-0.209642\pi$
$234$		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	$-0.520610\pi$
$239$	−30.9287			−0.129409			−0.0647045	+	0.997904i	$0.520610\pi$
$240$		0			0
$241$		−	81.9792i		−	0.340162i	−0.985430	−	0.170081i	$-0.945597\pi$
$241$		−	81.9792i		−	0.340162i	0.985430	−	0.170081i	$-0.0544030\pi$
$242$	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	$-0.456172\pi$
$251$	68.9014			0.274508			0.137254	+	0.990536i	$0.456172\pi$
$252$		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	$-0.815415\pi$
$263$	−440.010			−1.67304			−0.836522	+	0.547934i	$0.815415\pi$
$264$		0			0
$265$		−	276.635i		−	1.04391i
$266$	−15.8015	+	8.39264i	−0.0594041	+	0.0315513i
$267$		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
$304$	131.390	−	274.140i	0.432203	−	0.901776i
$305$		−	23.4783i		−	0.0769781i
$306$		0			0
$307$	368.613			1.20070			0.600348	−	0.799739i	$-0.295029\pi$
$307$	368.613			1.20070			0.600348	+	0.799739i	$0.295029\pi$
$308$	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	$-0.464128\pi$
$311$	69.9477			0.224912			0.112456	+	0.993657i	$0.464128\pi$
$312$		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	$-0.577149\pi$
$331$	−158.883			−0.480009			−0.240004	+	0.970772i	$0.577149\pi$
$332$	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	$-0.637943\pi$
$337$		−	611.695i		−	1.81512i	0.419922	−	0.907560i	$-0.362057\pi$
$338$	−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	$-0.659125\pi$
$347$	−332.664			−0.958685			−0.479343	+	0.877628i	$0.659125\pi$
$348$		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	$0.0299860\pi$
$353$			66.4096i			0.188129i	−0.995566	+	0.0940646i	$0.970014\pi$
$354$		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	$-0.299098\pi$
$359$	423.674			1.18015			0.590076	+	0.807348i	$0.299098\pi$
$360$		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	$-0.969138\pi$
$373$		−	72.2157i		−	0.193608i	0.995303	−	0.0968038i	$-0.0308619\pi$
$374$	−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	$-0.535598\pi$
$379$	−84.5932			−0.223201			−0.111601	+	0.993753i	$0.535598\pi$
$380$	496.968	−	88.6452i	1.30781	−	0.233277i
$381$		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	$0.0608490\pi$
$389$			147.820i			0.380001i	−0.981784	+	0.190001i	$0.939151\pi$
$390$		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	$-0.922523\pi$
$409$		−	197.143i		−	0.482012i	0.970524	−	0.241006i	$-0.0774773\pi$
$410$	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
$418$	−181.342	−	341.427i	−0.433834	−	0.816812i
$419$	−659.596			−1.57421			−0.787107	−	0.616816i	$-0.788422\pi$
$419$	−659.596			−1.57421			−0.787107	+	0.616816i	$0.788422\pi$
$420$		0			0
$421$			714.982i			1.69830i	0.528155	+	0.849148i	$0.322884\pi$
$421$			714.982i			1.69830i	−0.528155	+	0.849148i	$0.677116\pi$
$422$	−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	$0.188065\pi$
$433$			482.402i			1.11409i	−0.830482	+	0.557046i	$0.811935\pi$
$434$	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	$-0.358936\pi$
$439$	376.488			0.857603			0.428802	+	0.903399i	$0.358936\pi$
$440$	−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	$-0.884360\pi$
$443$	−828.172			−1.86946			−0.934731	+	0.355356i	$0.884360\pi$
$444$		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	$0.351075\pi$
$461$			822.917i			1.78507i	−0.450979	+	0.892534i	$0.648925\pi$
$462$		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	$-0.616865\pi$
$467$	−335.258			−0.717897			−0.358948	+	0.933357i	$0.616865\pi$
$468$		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	$-0.792076\pi$
$479$	−760.782			−1.58827			−0.794136	+	0.607740i	$0.792076\pi$
$480$		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	$-0.749545\pi$
$487$	−687.736			−1.41219			−0.706095	+	0.708117i	$0.749545\pi$
$488$	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	$-0.590937\pi$
$491$	−276.744			−0.563634			−0.281817	+	0.959468i	$0.590937\pi$
$492$		0			0
$493$		−	202.100i		−	0.409939i
$494$	115.820	−	61.5157i	0.234454	−	0.124526i
$495$		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	$-0.376987\pi$
$503$	379.172			0.753820			0.376910	+	0.926250i	$0.376987\pi$
$504$		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	$-0.416563\pi$
$523$	271.054			0.518268			0.259134	+	0.965841i	$0.416563\pi$
$524$	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
$532$	35.2279	−	6.28368i	0.0662179	−	0.0118114i
$533$		−	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	$-0.456521\pi$
$547$	148.968			0.272337			0.136168	+	0.990686i	$0.456521\pi$
$548$	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	$-0.849471\pi$
$557$		−	507.393i		−	0.910940i	0.890251	−	0.455470i	$-0.150529\pi$
$558$		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	$-0.704319\pi$
$587$	−702.884			−1.19742			−0.598708	+	0.800967i	$0.704319\pi$
$588$		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	$0.0720979\pi$
$593$			266.340i			0.449141i	−0.974458	+	0.224570i	$0.927902\pi$
$594$		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	$-0.812795\pi$
$601$		−	666.868i		−	1.10960i	0.831985	−	0.554798i	$-0.187205\pi$
$602$	−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	$-0.461529\pi$
$607$	146.368			0.241134			0.120567	+	0.992705i	$0.461529\pi$
$608$	−418.273	+	441.261i	−0.687949	+	0.725759i
$609$		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	$0.317648\pi$
$617$			1036.99i			1.68069i	−0.542052	+	0.840345i	$0.682352\pi$
$618$		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
$646$	−479.026	+	254.425i	−0.741526	+	0.393847i
$647$	504.684			0.780037			0.390018	−	0.920807i	$-0.372469\pi$
$647$	504.684			0.780037			0.390018	+	0.920807i	$0.372469\pi$
$648$		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	$-0.938408\pi$
$653$		−	251.132i		−	0.384581i	0.981338	−	0.192291i	$-0.0615916\pi$
$654$		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	$0.329477\pi$
$661$			1136.79i			1.71981i	−0.510455	+	0.859905i	$0.670523\pi$
$662$	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	$-0.953280\pi$
$673$		−	196.852i		−	0.292499i	0.989248	−	0.146250i	$-0.0467202\pi$
$674$	−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	$-0.856752\pi$
$701$		−	609.856i		−	0.869980i	0.900435	−	0.434990i	$-0.143248\pi$
$702$		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	$-0.193466\pi$
$719$	1180.47			1.64182			0.820910	+	0.571057i	$0.193466\pi$
$720$		0			0
$721$			4.05548i			0.00562479i
$722$	201.325	−	693.363i	0.278844	−	0.960336i
$723$		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	$-0.897689\pi$
$751$	−1425.08			−1.89758			−0.948788	+	0.315915i	$0.897689\pi$
$752$	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
$760$	−1000.41	−	136.095i	−1.31633	−	0.179073i
$761$		−	1284.03i		−	1.68729i	−0.536899	−	0.843647i	$-0.680404\pi$
$761$		−	1284.03i		−	1.68729i	0.536899	−	0.843647i	$-0.319596\pi$
$762$		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	$-0.501943\pi$
$787$	−9.60697			−0.0122071			−0.00610354	+	0.999981i	$0.501943\pi$
$788$	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	$0.000587334\pi$
$809$			2.98547i			0.00369032i	−0.999998	+	0.00184516i	$0.999413\pi$
$810$		0			0
$811$	−1009.04			−1.24419			−0.622094	−	0.782942i	$-0.713718\pi$
$811$	−1009.04			−1.24419			−0.622094	+	0.782942i	$0.713718\pi$
$812$	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	$-0.834608\pi$
$821$		−	815.300i		−	0.993057i	0.868020	−	0.496528i	$-0.165392\pi$
$822$		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	$-0.864766\pi$
$829$		−	683.402i		−	0.824369i	0.911100	−	0.412185i	$-0.135234\pi$
$830$	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
$836$	135.773	+	761.181i	0.162408	+	0.910504i
$837$		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
$874$	−455.425	−	857.464i	−0.521081	−	0.981080i
$875$	−18.3905			−0.0210177
$876$		0			0
$877$			372.892i			0.425190i	0.977140	+	0.212595i	$0.0681915\pi$
$877$			372.892i			0.425190i	−0.977140	+	0.212595i	$0.931808\pi$
$878$	−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	$-0.617471\pi$
$881$		−	1643.37i		−	1.86534i	0.360725	−	0.932672i	$-0.382529\pi$
$882$		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	$-0.645037\pi$
$907$	−798.239			−0.880087			−0.440043	+	0.897976i	$0.645037\pi$
$908$	−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	$0.223849\pi$
$929$			1201.56i			1.29339i	−0.762749	+	0.646695i	$0.776151\pi$
$930$		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	$-0.386806\pi$
$947$	659.420			0.696325			0.348162	+	0.937434i	$0.386806\pi$
$948$		0			0
$949$			247.231i			0.260518i
$950$	−340.804	−	641.657i	−0.358741	−	0.675429i
$951$		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
$988$	−258.211	+	46.0576i	−0.261347	+	0.0466170i
$989$			985.900i			0.996865i
$990$		0			0
$991$	−975.022			−0.983877			−0.491939	−	0.870630i	$-0.663712\pi$
$991$	−975.022			−0.983877			−0.491939	+	0.870630i	$0.663712\pi$
$992$	−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.683.6	yes	80
3.2	odd	2	inner	684.3.b.a.683.75	yes	80
4.3	odd	2	inner	684.3.b.a.683.7	yes	80
12.11	even	2	inner	684.3.b.a.683.74	yes	80
19.18	odd	2	inner	684.3.b.a.683.76	yes	80
57.56	even	2	inner	684.3.b.a.683.5	✓	80
76.75	even	2	inner	684.3.b.a.683.73	yes	80
228.227	odd	2	inner	684.3.b.a.683.8	yes	80

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

\(f(q)\)	\(=\)	\(q+(-1.90361 - 0.613402i) q^{2} +(3.24748 + 2.33536i) q^{4} +6.64226i q^{5} +0.470842i q^{7} +(-4.74942 - 6.43762i) q^{8} +O(q^{10})\)	\(q+(-1.90361 - 0.613402i) q^{2} +(3.24748 + 2.33536i) q^{4} +6.64226i q^{5} +0.470842i q^{7} +(-4.74942 - 6.43762i) q^{8} +(4.07438 - 12.6443i) q^{10} -10.1736 q^{11} -3.45114i q^{13} +(0.288815 - 0.896300i) q^{14} +(5.09220 + 15.1680i) q^{16} +14.2737i q^{17} +(-13.6293 - 13.2379i) q^{19} +(-15.5121 + 21.5706i) q^{20} +(19.3666 + 6.24052i) q^{22} -25.5501 q^{23} -19.1197 q^{25} +(-2.11694 + 6.56963i) q^{26} +(-1.09958 + 1.52905i) q^{28} -14.1589 q^{29} +19.3243 q^{31} +(-0.389466 - 31.9976i) q^{32} +(8.75551 - 27.1716i) q^{34} -3.12746 q^{35} -30.0832i q^{37} +(17.8248 + 33.5601i) q^{38} +(42.7604 - 31.5469i) q^{40} +25.6549 q^{41} -38.5869i q^{43} +(-33.0386 - 23.7591i) q^{44} +(48.6375 + 15.6725i) q^{46} +16.5047 q^{47} +48.7783 q^{49} +(36.3964 + 11.7280i) q^{50} +(8.05965 - 11.2075i) q^{52} -41.6477 q^{53} -67.5759i q^{55} +(3.03110 - 2.23623i) q^{56} +(26.9530 + 8.68510i) q^{58} -31.3349i q^{59} -3.53469 q^{61} +(-36.7859 - 11.8535i) q^{62} +(-18.8860 + 61.1500i) q^{64} +22.9234 q^{65} +13.9620 q^{67} +(-33.3342 + 46.3535i) q^{68} +(5.95346 + 1.91839i) q^{70} -128.352i q^{71} -71.6376 q^{73} +(-18.4531 + 57.2667i) q^{74} +(-13.3456 - 74.8191i) q^{76} -4.79017i q^{77} -100.177 q^{79} +(-100.750 + 33.8237i) q^{80} +(-48.8369 - 15.7367i) q^{82} +58.6257 q^{83} -94.8096 q^{85} +(-23.6693 + 73.4545i) q^{86} +(48.3188 + 65.4940i) q^{88} -108.060 q^{89} +1.62494 q^{91} +(-82.9734 - 59.6687i) q^{92} +(-31.4186 - 10.1240i) q^{94} +(87.9296 - 90.5295i) q^{95} +124.227i q^{97} +(-92.8550 - 29.9207i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 8 q^{4}+O(q^{10}) \) 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

Related objects

Downloads

Learn more