LMFDB - Embedded newform 287.3.b.a.83.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [287,3,Mod(83,287)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(287, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

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

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

chi := DirichletCharacter("287.83");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 287 = 7 \cdot 41 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	287.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:	$7.82018358714$
Analytic rank:	$0$
Dimension:	$52$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			83.3
Character	$\chi$	$=$	287.83
Dual form			287.3.b.a.83.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.56913 q^{2} -1.37648i q^{3} +8.73868 q^{4} -6.83538i q^{5} +4.91282i q^{6} +(-2.60551 + 6.49702i) q^{7} -16.9130 q^{8} +7.10532 q^{9} +O(q^{10})$	\(q-3.56913 q^{2} -1.37648i q^{3} +8.73868 q^{4} -6.83538i q^{5} +4.91282i q^{6} +(-2.60551 + 6.49702i) q^{7} -16.9130 q^{8} +7.10532 q^{9} +24.3964i q^{10} +17.8532 q^{11} -12.0286i q^{12} +8.43498i q^{13} +(9.29940 - 23.1887i) q^{14} -9.40874 q^{15} +25.4098 q^{16} +22.4953i q^{17} -25.3598 q^{18} +8.11318i q^{19} -59.7322i q^{20} +(8.94299 + 3.58642i) q^{21} -63.7202 q^{22} -20.6094 q^{23} +23.2803i q^{24} -21.7225 q^{25} -30.1055i q^{26} -22.1686i q^{27} +(-22.7687 + 56.7754i) q^{28} +43.6810 q^{29} +33.5810 q^{30} +14.9300i q^{31} -23.0390 q^{32} -24.5744i q^{33} -80.2885i q^{34} +(44.4096 + 17.8097i) q^{35} +62.0911 q^{36} +35.7776 q^{37} -28.9570i q^{38} +11.6105 q^{39} +115.607i q^{40} +6.40312i q^{41} +(-31.9187 - 12.8004i) q^{42} +12.7324 q^{43} +156.013 q^{44} -48.5675i q^{45} +73.5578 q^{46} +1.72414i q^{47} -34.9760i q^{48} +(-35.4226 - 33.8561i) q^{49} +77.5302 q^{50} +30.9642 q^{51} +73.7106i q^{52} +69.3404 q^{53} +79.1225i q^{54} -122.033i q^{55} +(44.0669 - 109.884i) q^{56} +11.1676 q^{57} -155.903 q^{58} -86.8227i q^{59} -82.2199 q^{60} +5.22390i q^{61} -53.2871i q^{62} +(-18.5130 + 46.1634i) q^{63} -19.4099 q^{64} +57.6563 q^{65} +87.7093i q^{66} +63.7697 q^{67} +196.579i q^{68} +28.3684i q^{69} +(-158.504 - 63.5650i) q^{70} -5.78584 q^{71} -120.172 q^{72} +95.1040i q^{73} -127.695 q^{74} +29.9004i q^{75} +70.8985i q^{76} +(-46.5166 + 115.992i) q^{77} -41.4395 q^{78} -95.0672 q^{79} -173.686i q^{80} +33.4333 q^{81} -22.8536i q^{82} -148.948i q^{83} +(78.1500 + 31.3406i) q^{84} +153.764 q^{85} -45.4436 q^{86} -60.1258i q^{87} -301.950 q^{88} +81.8312i q^{89} +173.344i q^{90} +(-54.8023 - 21.9774i) q^{91} -180.099 q^{92} +20.5508 q^{93} -6.15368i q^{94} +55.4567 q^{95} +31.7127i q^{96} -140.927i q^{97} +(126.428 + 120.837i) q^{98} +126.852 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q + 2 q^{2} + 90 q^{4} + 12 q^{7} - 2 q^{8} - 140 q^{9}+O(q^{10}) $ 52 * q + 2 * q^2 + 90 * q^4 + 12 * q^7 - 2 * q^8 - 140 * q^9	$ 52 q + 2 q^{2} + 90 q^{4} + 12 q^{7} - 2 q^{8} - 140 q^{9} + 24 q^{11} - 14 q^{14} + 44 q^{15} + 194 q^{16} + 70 q^{18} - 16 q^{21} - 48 q^{22} - 80 q^{23} - 304 q^{25} + 64 q^{28} - 12 q^{29} + 64 q^{30} - 166 q^{32} + 30 q^{35} - 70 q^{36} + 36 q^{37} - 68 q^{39} + 164 q^{42} - 172 q^{43} + 72 q^{44} + 68 q^{46} - 172 q^{49} - 234 q^{50} + 156 q^{51} + 64 q^{53} - 234 q^{56} + 140 q^{57} - 556 q^{58} + 152 q^{60} - 130 q^{63} + 334 q^{64} - 76 q^{65} + 160 q^{67} + 202 q^{70} - 408 q^{71} - 40 q^{72} + 398 q^{74} - 248 q^{77} + 390 q^{78} + 264 q^{79} - 116 q^{81} - 418 q^{84} + 232 q^{85} + 368 q^{86} - 220 q^{88} + 32 q^{91} - 74 q^{92} + 240 q^{93} - 44 q^{95} + 838 q^{98} - 24 q^{99}+O(q^{100}) $ 52 * q + 2 * q^2 + 90 * q^4 + 12 * q^7 - 2 * q^8 - 140 * q^9 + 24 * q^11 - 14 * q^14 + 44 * q^15 + 194 * q^16 + 70 * q^18 - 16 * q^21 - 48 * q^22 - 80 * q^23 - 304 * q^25 + 64 * q^28 - 12 * q^29 + 64 * q^30 - 166 * q^32 + 30 * q^35 - 70 * q^36 + 36 * q^37 - 68 * q^39 + 164 * q^42 - 172 * q^43 + 72 * q^44 + 68 * q^46 - 172 * q^49 - 234 * q^50 + 156 * q^51 + 64 * q^53 - 234 * q^56 + 140 * q^57 - 556 * q^58 + 152 * q^60 - 130 * q^63 + 334 * q^64 - 76 * q^65 + 160 * q^67 + 202 * q^70 - 408 * q^71 - 40 * q^72 + 398 * q^74 - 248 * q^77 + 390 * q^78 + 264 * q^79 - 116 * q^81 - 418 * q^84 + 232 * q^85 + 368 * q^86 - 220 * q^88 + 32 * q^91 - 74 * q^92 + 240 * q^93 - 44 * q^95 + 838 * q^98 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/287\mathbb{Z}\right)^\times$.

$n$	$206$	$211$
$\chi(n)$	$-1$	$1$

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 $

$2$	−3.56913			−1.78456			−0.892282	−	0.451478i	$-0.850897\pi$
$2$	−3.56913			−1.78456			−0.892282	+	0.451478i	$0.850897\pi$
$3$		−	1.37648i		−	0.458825i	−0.973329	−	0.229413i	$-0.926319\pi$
$3$		−	1.37648i		−	0.458825i	0.973329	−	0.229413i	$-0.0736805\pi$
$4$	8.73868			2.18467
$5$		−	6.83538i		−	1.36708i	−0.729915	−	0.683538i	$-0.760440\pi$
$5$		−	6.83538i		−	1.36708i	0.729915	−	0.683538i	$-0.239560\pi$
$6$			4.91282i			0.818803i
$7$	−2.60551	+	6.49702i	−0.372216	+	0.928146i
$7$	−2.60551	+	6.49702i	−0.372216	+	0.928146i
$8$	−16.9130			−2.11412
$9$	7.10532			0.789479
$10$			24.3964i			2.43964i
$11$	17.8532			1.62301			0.811507	−	0.584342i	$-0.198648\pi$
$11$	17.8532			1.62301			0.811507	+	0.584342i	$0.198648\pi$
$12$		−	12.0286i		−	1.00238i
$13$			8.43498i			0.648845i	0.945912	+	0.324422i	$0.105170\pi$
$13$			8.43498i			0.648845i	−0.945912	+	0.324422i	$0.894830\pi$
$14$	9.29940	−	23.1887i	0.664243	−	1.65634i
$15$	−9.40874			−0.627249
$16$	25.4098			1.58811
$17$			22.4953i			1.32325i	0.749834	+	0.661626i	$0.230133\pi$
$17$			22.4953i			1.32325i	−0.749834	+	0.661626i	$0.769867\pi$
$18$	−25.3598			−1.40888
$19$			8.11318i			0.427010i	0.976942	+	0.213505i	$0.0684879\pi$
$19$			8.11318i			0.427010i	−0.976942	+	0.213505i	$0.931512\pi$
$20$		−	59.7322i		−	2.98661i
$21$	8.94299	+	3.58642i	0.425857	+	0.170782i
$22$	−63.7202			−2.89637
$23$	−20.6094			−0.896063			−0.448031	−	0.894018i	$-0.647875\pi$
$23$	−20.6094			−0.896063			−0.448031	+	0.894018i	$0.647875\pi$
$24$			23.2803i			0.970011i
$25$	−21.7225			−0.868898
$26$		−	30.1055i		−	1.15791i
$27$		−	22.1686i		−	0.821058i
$28$	−22.7687	+	56.7754i	−0.813169	+	2.02769i
$29$	43.6810			1.50624			0.753120	−	0.657883i	$-0.228548\pi$
$29$	43.6810			1.50624			0.753120	+	0.657883i	$0.228548\pi$
$30$	33.5810			1.11937
$31$			14.9300i			0.481613i	0.970573	+	0.240806i	$0.0774118\pi$
$31$			14.9300i			0.481613i	−0.970573	+	0.240806i	$0.922588\pi$
$32$	−23.0390			−0.719970
$33$		−	24.5744i		−	0.744680i
$34$		−	80.2885i		−	2.36143i
$35$	44.4096	+	17.8097i	1.26885	+	0.508847i
$36$	62.0911			1.72475
$37$	35.7776			0.966962			0.483481	−	0.875355i	$-0.339372\pi$
$37$	35.7776			0.966962			0.483481	+	0.875355i	$0.339372\pi$
$38$		−	28.9570i		−	0.762026i
$39$	11.6105			0.297706
$40$			115.607i			2.89016i
$41$			6.40312i			0.156174i
$41$			6.40312i			0.156174i
$42$	−31.9187	−	12.8004i	−0.759969	−	0.304771i
$43$	12.7324			0.296103			0.148051	−	0.988980i	$-0.452700\pi$
$43$	12.7324			0.296103			0.148051	+	0.988980i	$0.452700\pi$
$44$	156.013			3.54575
$45$		−	48.5675i		−	1.07928i
$46$	73.5578			1.59908
$47$			1.72414i			0.0366838i	0.999832	+	0.0183419i	$0.00583874\pi$
$47$			1.72414i			0.0366838i	−0.999832	+	0.0183419i	$0.994161\pi$
$48$		−	34.9760i		−	0.728666i
$49$	−35.4226	−	33.8561i	−0.722911	−	0.690941i
$50$	77.5302			1.55060
$51$	30.9642			0.607141
$52$			73.7106i			1.41751i
$53$	69.3404			1.30831			0.654155	−	0.756361i	$-0.273025\pi$
$53$	69.3404			1.30831			0.654155	+	0.756361i	$0.273025\pi$
$54$			79.1225i			1.46523i
$55$		−	122.033i		−	2.21878i
$56$	44.0669	−	109.884i	0.786909	−	1.96221i
$57$	11.1676			0.195923
$58$	−155.903			−2.68798
$59$		−	86.8227i		−	1.47157i	−0.677215	−	0.735786i	$-0.736813\pi$
$59$		−	86.8227i		−	1.47157i	0.677215	−	0.735786i	$-0.263187\pi$
$60$	−82.2199			−1.37033
$61$			5.22390i			0.0856377i	0.999083	+	0.0428188i	$0.0136338\pi$
$61$			5.22390i			0.0856377i	−0.999083	+	0.0428188i	$0.986366\pi$
$62$		−	53.2871i		−	0.859469i
$63$	−18.5130	+	46.1634i	−0.293857	+	0.732752i
$64$	−19.4099			−0.303280
$65$	57.6563			0.887020
$66$			87.7093i			1.32893i
$67$	63.7697			0.951787			0.475894	−	0.879503i	$-0.342125\pi$
$67$	63.7697			0.951787			0.475894	+	0.879503i	$0.342125\pi$
$68$			196.579i			2.89087i
$69$			28.3684i			0.411136i
$70$	−158.504	−	63.5650i	−2.26434	−	0.908071i
$71$	−5.78584			−0.0814908			−0.0407454	−	0.999170i	$-0.512973\pi$
$71$	−5.78584			−0.0814908			−0.0407454	+	0.999170i	$0.512973\pi$
$72$	−120.172			−1.66905
$73$			95.1040i			1.30279i	0.758737	+	0.651397i	$0.225817\pi$
$73$			95.1040i			1.30279i	−0.758737	+	0.651397i	$0.774183\pi$
$74$	−127.695			−1.72561
$75$			29.9004i			0.398672i
$76$			70.8985i			0.932875i
$77$	−46.5166	+	115.992i	−0.604112	+	1.50639i
$78$	−41.4395			−0.531276
$79$	−95.0672			−1.20338			−0.601691	−	0.798729i	$-0.705506\pi$
$79$	−95.0672			−1.20338			−0.601691	+	0.798729i	$0.705506\pi$
$80$		−	173.686i		−	2.17107i
$81$	33.4333			0.412757
$82$		−	22.8536i		−	0.278702i
$83$		−	148.948i		−	1.79455i	−0.441469	−	0.897277i	$-0.645542\pi$
$83$		−	148.948i		−	1.79455i	0.441469	−	0.897277i	$-0.354458\pi$
$84$	78.1500	+	31.3406i	0.930357	+	0.373102i
$85$	153.764			1.80899
$86$	−45.4436			−0.528414
$87$		−	60.1258i		−	0.691101i
$88$	−301.950			−3.43125
$89$			81.8312i			0.919451i	0.888061	+	0.459726i	$0.152052\pi$
$89$			81.8312i			0.919451i	−0.888061	+	0.459726i	$0.847948\pi$
$90$			173.344i			1.92604i
$91$	−54.8023	−	21.9774i	−0.602223	−	0.241510i
$92$	−180.099			−1.95760
$93$	20.5508			0.220976
$94$		−	6.15368i		−	0.0654647i
$95$	55.4567			0.583755
$96$			31.7127i			0.330340i
$97$		−	140.927i		−	1.45286i	−0.687240	−	0.726430i	$-0.741178\pi$
$97$		−	140.927i		−	1.45286i	0.687240	−	0.726430i	$-0.258822\pi$
$98$	126.428	+	120.837i	1.29008	+	1.23303i
$99$	126.852			1.28134
$100$	−189.826			−1.89826
$101$		−	53.8121i		−	0.532793i	−0.963864	−	0.266396i	$-0.914167\pi$
$101$		−	53.8121i		−	0.532793i	0.963864	−	0.266396i	$-0.0858330\pi$
$102$	−110.515			−1.08348
$103$			44.0318i			0.427493i	0.976889	+	0.213747i	$0.0685667\pi$
$103$			44.0318i			0.427493i	−0.976889	+	0.213747i	$0.931433\pi$
$104$		−	142.660i		−	1.37174i
$105$	24.5146	−	61.1288i	0.233472	−	0.582179i
$106$	−247.485			−2.33476
$107$	−32.4436			−0.303211			−0.151605	−	0.988441i	$-0.548444\pi$
$107$	−32.4436			−0.303211			−0.151605	+	0.988441i	$0.548444\pi$
$108$		−	193.724i		−	1.79374i
$109$	−38.1938			−0.350402			−0.175201	−	0.984533i	$-0.556057\pi$
$109$	−38.1938			−0.350402			−0.175201	+	0.984533i	$0.556057\pi$
$110$			435.552i			3.95956i
$111$		−	49.2470i		−	0.443667i
$112$	−66.2055	+	165.088i	−0.591121	+	1.47400i
$113$	6.30129			0.0557636			0.0278818	−	0.999611i	$-0.491124\pi$
$113$	6.30129			0.0557636			0.0278818	+	0.999611i	$0.491124\pi$
$114$	−39.8586			−0.349637
$115$			140.873i			1.22499i
$116$	381.714			3.29064
$117$			59.9332i			0.512250i
$118$			309.881i			2.62611i
$119$	−146.152	−	58.6117i	−1.22817	−	0.492535i
$120$	159.130			1.32608
$121$	197.735			1.63418
$122$		−	18.6448i		−	0.152826i
$123$	8.81374			0.0716565
$124$			130.468i			1.05216i
$125$		−	22.4033i		−	0.179226i
$126$	66.0752	−	164.763i	0.524406	−	1.30764i
$127$	−231.724			−1.82460			−0.912298	−	0.409526i	$-0.865694\pi$
$127$	−231.724			−1.82460			−0.912298	+	0.409526i	$0.865694\pi$
$128$	161.433			1.26119
$129$		−	17.5259i		−	0.135859i
$130$	−205.783			−1.58295
$131$			111.179i			0.848695i	0.905499	+	0.424347i	$0.139496\pi$
$131$			111.179i			0.848695i	−0.905499	+	0.424347i	$0.860504\pi$
$132$		−	214.748i		−	1.62688i
$133$	−52.7115	−	21.1390i	−0.396327	−	0.158940i
$134$	−227.602			−1.69853
$135$	−151.531			−1.12245
$136$		−	380.462i		−	2.79751i
$137$	−65.8699			−0.480802			−0.240401	−	0.970674i	$-0.577279\pi$
$137$	−65.8699			−0.480802			−0.240401	+	0.970674i	$0.577279\pi$
$138$		−	101.250i		−	0.733699i
$139$		−	136.620i		−	0.982881i	−0.870911	−	0.491440i	$-0.836471\pi$
$139$		−	136.620i		−	0.982881i	0.870911	−	0.491440i	$-0.163529\pi$
$140$	388.082	+	155.633i	2.77201	+	1.11166i
$141$	2.37324			0.0168315
$142$	20.6504			0.145426
$143$			150.591i			1.05308i
$144$	180.545			1.25378
$145$		−	298.576i		−	2.05915i
$146$		−	339.438i		−	2.32492i
$147$	−46.6021	+	48.7584i	−0.317021	+	0.331690i
$148$	312.649			2.11249
$149$	−35.2593			−0.236640			−0.118320	−	0.992976i	$-0.537751\pi$
$149$	−35.2593			−0.236640			−0.118320	+	0.992976i	$0.537751\pi$
$150$		−	106.718i		−	0.711456i
$151$	158.861			1.05206			0.526028	−	0.850467i	$-0.323681\pi$
$151$	158.861			1.05206			0.526028	+	0.850467i	$0.323681\pi$
$152$		−	137.218i		−	0.902749i
$153$			159.836i			1.04468i
$154$	166.024	−	413.992i	1.07808	−	2.68826i
$155$	102.052			0.658401
$156$	101.461			0.650390
$157$			226.044i			1.43977i	0.694094	+	0.719884i	$0.255805\pi$
$157$			226.044i			1.43977i	−0.694094	+	0.719884i	$0.744195\pi$
$158$	339.307			2.14751
$159$		−	95.4453i		−	0.600285i
$160$			157.481i			0.984254i
$161$	53.6981	−	133.900i	0.333529	−	0.831677i
$162$	−119.328			−0.736592
$163$	119.445			0.732793			0.366396	−	0.930459i	$-0.380591\pi$
$163$	119.445			0.732793			0.366396	+	0.930459i	$0.380591\pi$
$164$			55.9549i			0.341188i
$165$	−167.976			−1.01803
$166$			531.614i			3.20250i
$167$			219.332i			1.31337i	0.754167	+	0.656683i	$0.228041\pi$
$167$			219.332i			1.31337i	−0.754167	+	0.656683i	$0.771959\pi$
$168$	−151.252	−	60.6570i	−0.900312	−	0.361054i
$169$	97.8511			0.579000
$170$	−548.803			−3.22825
$171$			57.6467i			0.337115i
$172$	111.265			0.646887
$173$		−	319.785i		−	1.84847i	−0.381824	−	0.924235i	$-0.624704\pi$
$173$		−	319.785i		−	1.84847i	0.381824	−	0.924235i	$-0.375296\pi$
$174$			214.597i			1.23331i
$175$	56.5981	−	141.131i	0.323418	−	0.806465i
$176$	453.645			2.57753
$177$	−119.509			−0.675194
$178$		−	292.066i		−	1.64082i
$179$	−180.103			−1.00616			−0.503082	−	0.864239i	$-0.667801\pi$
$179$	−180.103			−1.00616			−0.503082	+	0.864239i	$0.667801\pi$
$180$		−	424.416i		−	2.35787i
$181$			356.390i			1.96901i	0.175369	+	0.984503i	$0.443888\pi$
$181$			356.390i			1.96901i	−0.175369	+	0.984503i	$0.556112\pi$
$182$	195.596	+	78.4403i	1.07471	+	0.430991i
$183$	7.19057			0.0392927
$184$	348.567			1.89438
$185$		−	244.554i		−	1.32191i
$186$	−73.3483			−0.394346
$187$			401.612i			2.14766i
$188$			15.0667i			0.0801421i
$189$	144.030	+	57.7604i	0.762062	+	0.305611i
$190$	−197.932			−1.04175
$191$	−114.410			−0.599004			−0.299502	−	0.954096i	$-0.596821\pi$
$191$	−114.410			−0.599004			−0.299502	+	0.954096i	$0.596821\pi$
$192$			26.7173i			0.139153i
$193$	333.354			1.72722			0.863612	−	0.504158i	$-0.168197\pi$
$193$	333.354			1.72722			0.863612	+	0.504158i	$0.168197\pi$
$194$			502.988i			2.59272i
$195$		−	79.3625i		−	0.406987i
$196$	−309.547	−	295.858i	−1.57932	−	1.50948i
$197$	−172.865			−0.877486			−0.438743	−	0.898613i	$-0.644576\pi$
$197$	−172.865			−0.877486			−0.438743	+	0.898613i	$0.644576\pi$
$198$	−452.752			−2.28663
$199$			220.849i			1.10979i	0.831919	+	0.554897i	$0.187242\pi$
$199$			220.849i			1.10979i	−0.831919	+	0.554897i	$0.812758\pi$
$200$	367.391			1.83695
$201$		−	87.7775i		−	0.436704i
$202$			192.062i			0.950803i
$203$	−113.811	+	283.796i	−0.560646	+	1.39801i
$204$	270.586			1.32640
$205$	43.7678			0.213501
$206$		−	157.155i		−	0.762889i
$207$	−146.437			−0.707423
$208$			214.331i			1.03044i
$209$			144.846i			0.693043i
$210$	−87.4956	+	218.177i	−0.416646	+	1.03894i
$211$	328.165			1.55528			0.777642	−	0.628708i	$-0.216416\pi$
$211$	328.165			1.55528			0.777642	+	0.628708i	$0.216416\pi$
$212$	605.943			2.85822
$213$			7.96407i			0.0373900i
$214$	115.795			0.541099
$215$		−	87.0310i		−	0.404795i
$216$			374.936i			1.73582i
$217$	−97.0005	−	38.9002i	−0.447007	−	0.179264i
$218$	136.318			0.625314
$219$	130.908			0.597755
$220$		−	1066.41i		−	4.84731i
$221$	−189.747			−0.858585
$222$			175.769i			0.791752i
$223$			78.3541i			0.351364i	0.984447	+	0.175682i	$0.0562130\pi$
$223$			78.3541i			0.351364i	−0.984447	+	0.175682i	$0.943787\pi$
$224$	60.0284	−	149.685i	0.267984	−	0.668237i
$225$	−154.345			−0.685977
$226$	−22.4901			−0.0995137
$227$		−	35.3919i		−	0.155912i	−0.996957	−	0.0779558i	$-0.975161\pi$
$227$		−	35.3919i		−	0.155912i	0.996957	−	0.0779558i	$-0.0248393\pi$
$228$	97.5900			0.428027
$229$		−	340.538i		−	1.48706i	−0.668701	−	0.743532i	$-0.733149\pi$
$229$		−	340.538i		−	1.48706i	0.668701	−	0.743532i	$-0.266851\pi$
$230$		−	502.795i		−	2.18607i
$231$	159.661	+	64.0289i	0.691172	+	0.277182i
$232$	−738.775			−3.18437
$233$	283.387			1.21625			0.608126	−	0.793841i	$-0.291922\pi$
$233$	283.387			1.21625			0.608126	+	0.793841i	$0.291922\pi$
$234$		−	213.909i		−	0.914142i
$235$	11.7852			0.0501496
$236$		−	758.716i		−	3.21490i
$237$			130.858i			0.552142i
$238$	521.636	+	209.193i	2.19175	+	0.878960i
$239$	−67.5405			−0.282596			−0.141298	−	0.989967i	$-0.545128\pi$
$239$	−67.5405			−0.282596			−0.141298	+	0.989967i	$0.545128\pi$
$240$	−239.074			−0.996142
$241$			96.6618i			0.401086i	0.979685	+	0.200543i	$0.0642707\pi$
$241$			96.6618i			0.401086i	−0.979685	+	0.200543i	$0.935729\pi$
$242$	−705.743			−2.91629
$243$		−	245.537i		−	1.01044i
$244$			45.6500i			0.187090i
$245$	−231.420	+	242.127i	−0.944570	+	0.988274i
$246$	−31.4574			−0.127876
$247$	−68.4345			−0.277063
$248$		−	252.510i		−	1.01819i
$249$	−205.023			−0.823386
$250$			79.9602i			0.319841i
$251$		−	114.867i		−	0.457637i	−0.973469	−	0.228818i	$-0.926514\pi$
$251$		−	114.867i		−	0.457637i	0.973469	−	0.228818i	$-0.0734862\pi$
$252$	−161.779	+	403.407i	−0.641980	+	1.60082i
$253$	−367.944			−1.45432
$254$	827.052			3.25611
$255$		−	211.652i		−	0.830008i
$256$	−498.534			−1.94740
$257$		−	461.142i		−	1.79433i	−0.441698	−	0.897164i	$-0.645624\pi$
$257$		−	461.142i		−	1.79433i	0.441698	−	0.897164i	$-0.354376\pi$
$258$			62.5521i			0.242450i
$259$	−93.2189	+	232.448i	−0.359919	+	0.897482i
$260$	503.840			1.93785
$261$	310.367			1.18915
$262$		−	396.812i		−	1.51455i
$263$	−288.683			−1.09765			−0.548827	−	0.835936i	$-0.684925\pi$
$263$	−288.683			−1.09765			−0.548827	+	0.835936i	$0.684925\pi$
$264$			415.626i			1.57434i
$265$		−	473.968i		−	1.78856i
$266$	188.134	+	75.4477i	0.707272	+	0.283638i
$267$	112.639			0.421867
$268$	557.263			2.07934
$269$			257.281i			0.956434i	0.878242	+	0.478217i	$0.158717\pi$
$269$			257.281i			0.956434i	−0.878242	+	0.478217i	$0.841283\pi$
$270$	540.832			2.00308
$271$			236.001i			0.870852i	0.900224	+	0.435426i	$0.143402\pi$
$271$			236.001i			0.870852i	−0.900224	+	0.435426i	$0.856598\pi$
$272$			571.601i			2.10147i
$273$	−30.2514	+	75.4340i	−0.110811	+	0.276315i
$274$	235.098			0.858023
$275$	−387.814			−1.41023
$276$			247.902i			0.898197i
$277$	−372.455			−1.34460			−0.672302	−	0.740277i	$-0.734694\pi$
$277$	−372.455			−1.34460			−0.672302	+	0.740277i	$0.734694\pi$
$278$			487.616i			1.75401i
$279$			106.082i			0.380223i
$280$	−751.098	−	301.214i	−2.68249	−	1.07576i
$281$	173.312			0.616768			0.308384	−	0.951262i	$-0.400212\pi$
$281$	173.312			0.616768			0.308384	+	0.951262i	$0.400212\pi$
$282$	−8.47039			−0.0300368
$283$			200.954i			0.710084i	0.934850	+	0.355042i	$0.115533\pi$
$283$			200.954i			0.710084i	−0.934850	+	0.355042i	$0.884467\pi$
$284$	−50.5606			−0.178030
$285$		−	76.3348i		−	0.267841i
$286$		−	537.479i		−	1.87930i
$287$	−41.6012	−	16.6834i	−0.144952	−	0.0581303i
$288$	−163.700			−0.568401
$289$	−217.037			−0.750994
$290$			1065.66i			3.67468i
$291$	−193.983			−0.666609
$292$			831.083i			2.84617i
$293$		−	537.694i		−	1.83513i	−0.397582	−	0.917566i	$-0.630151\pi$
$293$		−	537.694i		−	1.83513i	0.397582	−	0.917566i	$-0.369849\pi$
$294$	166.329	−	174.025i	0.565745	−	0.591922i
$295$	−593.466			−2.01175
$296$	−605.105			−2.04427
$297$		−	395.779i		−	1.33259i
$298$	125.845			0.422299
$299$		−	173.840i		−	0.581406i
$300$			261.290i			0.870968i
$301$	−33.1744	+	82.7228i	−0.110214	+	0.274827i
$302$	−566.994			−1.87746
$303$	−74.0710			−0.244459
$304$			206.154i			0.678139i
$305$	35.7073			0.117073
$306$		−	570.475i		−	1.86430i
$307$			229.876i			0.748782i	0.927271	+	0.374391i	$0.122148\pi$
$307$			229.876i			0.748782i	−0.927271	+	0.374391i	$0.877852\pi$
$308$	−406.494	+	1013.62i	−1.31978	+	3.29098i
$309$	60.6087			0.196145
$310$	−364.237			−1.17496
$311$			359.611i			1.15631i	0.815928	+	0.578153i	$0.196226\pi$
$311$			359.611i			1.15631i	−0.815928	+	0.578153i	$0.803774\pi$
$312$	−196.369			−0.629387
$313$			85.4839i			0.273111i	0.990632	+	0.136556i	$0.0436033\pi$
$313$			85.4839i			0.273111i	−0.990632	+	0.136556i	$0.956397\pi$
$314$		−	806.779i		−	2.56936i
$315$	315.545	+	126.543i	1.00173	+	0.401725i
$316$	−830.762			−2.62899
$317$	513.015			1.61834			0.809172	−	0.587571i	$-0.199916\pi$
$317$	513.015			1.61834			0.809172	+	0.587571i	$0.199916\pi$
$318$			340.657i			1.07125i
$319$	779.843			2.44465
$320$			132.674i			0.414608i
$321$			44.6578i			0.139121i
$322$	−191.655	+	477.906i	−0.595203	+	1.48418i
$323$	−182.508			−0.565041
$324$	292.163			0.901738
$325$		−	183.229i		−	0.563780i
$326$	−426.315			−1.30772
$327$			52.5728i			0.160773i
$328$		−	108.296i		−	0.330170i
$329$	−11.2018	−	4.49226i	−0.0340480	−	0.0136543i
$330$	599.527			1.81675
$331$	−161.181			−0.486950			−0.243475	−	0.969907i	$-0.578287\pi$
$331$	−161.181			−0.486950			−0.243475	+	0.969907i	$0.578287\pi$
$332$		−	1301.61i		−	3.92051i
$333$	254.211			0.763397
$334$		−	782.824i		−	2.34379i
$335$		−	435.891i		−	1.30117i
$336$	227.240	+	91.1303i	0.676309	+	0.271221i
$337$	−392.714			−1.16532			−0.582662	−	0.812715i	$-0.697989\pi$
$337$	−392.714			−1.16532			−0.582662	+	0.812715i	$0.697989\pi$
$338$	−349.243			−1.03326
$339$		−	8.67357i		−	0.0255857i
$340$	1343.69			3.95204
$341$			266.547i			0.781664i
$342$		−	205.749i		−	0.601604i
$343$	312.258	−	141.929i	0.910373	−	0.413788i
$344$	−215.343			−0.625997
$345$	193.909			0.562055
$346$			1141.36i			3.29871i
$347$	−132.235			−0.381082			−0.190541	−	0.981679i	$-0.561024\pi$
$347$	−132.235			−0.381082			−0.190541	+	0.981679i	$0.561024\pi$
$348$		−	525.420i		−	1.50983i
$349$			103.072i			0.295336i	0.989037	+	0.147668i	$0.0471767\pi$
$349$			103.072i			0.295336i	−0.989037	+	0.147668i	$0.952823\pi$
$350$	−202.006	+	503.716i	−0.577160	+	1.43919i
$351$	186.991			0.532739
$352$	−411.319			−1.16852
$353$			51.3283i			0.145406i	0.997354	+	0.0727029i	$0.0231625\pi$
$353$			51.3283i			0.145406i	−0.997354	+	0.0727029i	$0.976838\pi$
$354$	426.544			1.20493
$355$			39.5485i			0.111404i
$356$			715.096i			2.00870i
$357$	−80.6775	+	201.175i	−0.225987	+	0.563516i
$358$	642.812			1.79556
$359$	−284.674			−0.792963			−0.396481	−	0.918043i	$-0.629769\pi$
$359$	−284.674			−0.792963			−0.396481	+	0.918043i	$0.629769\pi$
$360$			821.421i			2.28172i
$361$	295.176			0.817663
$362$		−	1272.00i		−	3.51382i
$363$		−	272.178i		−	0.749801i
$364$	−478.900	−	192.054i	−1.31566	−	0.527620i
$365$	650.072			1.78102
$366$	−25.6641			−0.0701204
$367$		−	279.000i		−	0.760219i	−0.924942	−	0.380109i	$-0.875886\pi$
$367$		−	279.000i		−	0.760219i	0.924942	−	0.380109i	$-0.124114\pi$
$368$	−523.682			−1.42305
$369$			45.4962i			0.123296i
$370$			872.843i			2.35904i
$371$	−180.667	+	450.506i	−0.486973	+	1.21430i
$372$	179.587			0.482760
$373$	−42.8760			−0.114949			−0.0574745	−	0.998347i	$-0.518305\pi$
$373$	−42.8760			−0.114949			−0.0574745	+	0.998347i	$0.518305\pi$
$374$		−	1433.40i		−	3.83263i
$375$	−30.8376			−0.0822335
$376$		−	29.1603i		−	0.0775540i
$377$			368.448i			0.977316i
$378$	−514.061	−	206.154i	−1.35995	−	0.545382i
$379$	393.335			1.03782			0.518911	−	0.854828i	$-0.326337\pi$
$379$	393.335			1.03782			0.518911	+	0.854828i	$0.326337\pi$
$380$	484.618			1.27531
$381$			318.962i			0.837171i
$382$	408.343			1.06896
$383$		−	245.288i		−	0.640440i	−0.947343	−	0.320220i	$-0.896243\pi$
$383$		−	245.288i		−	0.640440i	0.947343	−	0.320220i	$-0.103757\pi$
$384$		−	222.208i		−	0.578667i
$385$	792.852	+	317.959i	2.05936	+	0.825867i
$386$	−1189.78			−3.08234
$387$	90.4678			0.233767
$388$		−	1231.52i		−	3.17402i
$389$	−419.477			−1.07835			−0.539174	−	0.842194i	$-0.681263\pi$
$389$	−419.477			−1.07835			−0.539174	+	0.842194i	$0.681263\pi$
$390$			283.255i			0.726295i
$391$		−	463.615i		−	1.18572i
$392$	599.102	+	572.607i	1.52832	+	1.46073i
$393$	153.035			0.389403
$394$	616.977			1.56593
$395$			649.821i			1.64512i
$396$	1108.52			2.79930
$397$		−	155.485i		−	0.391649i	−0.980639	−	0.195825i	$-0.937262\pi$
$397$		−	155.485i		−	0.391649i	0.980639	−	0.195825i	$-0.0627384\pi$
$398$		−	788.238i		−	1.98050i
$399$	−29.0973	+	72.5561i	−0.0729255	+	0.181845i
$400$	−551.963			−1.37991
$401$	195.911			0.488557			0.244278	−	0.969705i	$-0.421449\pi$
$401$	195.911			0.488557			0.244278	+	0.969705i	$0.421449\pi$
$402$			313.289i			0.779326i
$403$	−125.934			−0.312492
$404$		−	470.247i		−	1.16398i
$405$		−	228.530i		−	0.564271i
$406$	406.207	−	1012.91i	1.00051	−	2.49484i
$407$	638.743			1.56939
$408$	−523.696			−1.28357
$409$			334.253i			0.817244i	0.912704	+	0.408622i	$0.133991\pi$
$409$			334.253i			0.817244i	−0.912704	+	0.408622i	$0.866009\pi$
$410$	−156.213			−0.381007
$411$			90.6683i			0.220604i
$412$			384.780i			0.933931i
$413$	564.089	+	226.217i	1.36583	+	0.547742i
$414$	522.651			1.26244
$415$	−1018.12			−2.45329
$416$		−	194.334i		−	0.467149i
$417$	−188.055			−0.450970
$418$		−	516.974i		−	1.23678i
$419$			464.254i			1.10801i	0.832515	+	0.554003i	$0.186900\pi$
$419$			464.254i			1.10801i	−0.832515	+	0.554003i	$0.813100\pi$
$420$	214.225	−	534.185i	0.510059	−	1.27187i
$421$	281.034			0.667540			0.333770	−	0.942655i	$-0.391679\pi$
$421$	281.034			0.667540			0.333770	+	0.942655i	$0.391679\pi$
$422$	−1171.26			−2.77550
$423$			12.2506i			0.0289611i
$424$	−1172.75			−2.76592
$425$		−	488.653i		−	1.14977i
$426$		−	28.4248i		−	0.0667249i
$427$	−33.9398	−	13.6109i	−0.0794843	−	0.0318757i
$428$	−283.514			−0.662416
$429$	207.285			0.483182
$430$			310.625i			0.722383i
$431$	−227.657			−0.528206			−0.264103	−	0.964494i	$-0.585076\pi$
$431$	−227.657			−0.528206			−0.264103	+	0.964494i	$0.585076\pi$
$432$		−	563.299i		−	1.30393i
$433$		−	464.690i		−	1.07319i	−0.843841	−	0.536593i	$-0.819711\pi$
$433$		−	464.690i		−	1.07319i	0.843841	−	0.536593i	$-0.180289\pi$
$434$	346.207	+	138.840i	0.797712	+	0.319908i
$435$	−410.983			−0.944788
$436$	−333.763			−0.765512
$437$		−	167.208i		−	0.382627i
$438$	−467.228			−1.06673
$439$		−	39.7946i		−	0.0906483i	−0.998972	−	0.0453242i	$-0.985568\pi$
$439$		−	39.7946i		−	0.0906483i	0.998972	−	0.0453242i	$-0.0144321\pi$
$440$			2063.94i			4.69078i
$441$	−251.689	−	240.558i	−0.570723	−	0.545484i
$442$	677.232			1.53220
$443$	−574.027			−1.29577			−0.647887	−	0.761737i	$-0.724347\pi$
$443$	−574.027			−1.29577			−0.647887	+	0.761737i	$0.724347\pi$
$444$		−	430.354i		−	0.969265i
$445$	559.347			1.25696
$446$		−	279.656i		−	0.627031i
$447$			48.5336i			0.108576i
$448$	50.5728	−	126.107i	0.112886	−	0.281489i
$449$	−14.2372			−0.0317086			−0.0158543	−	0.999874i	$-0.505047\pi$
$449$	−14.2372			−0.0317086			−0.0158543	+	0.999874i	$0.505047\pi$
$450$	550.877			1.22417
$451$			114.316i			0.253472i
$452$	55.0649			0.121825
$453$		−	218.668i		−	0.482710i
$454$			126.318i			0.278234i
$455$	−150.224	+	374.595i	−0.330163	+	0.823285i
$456$	−188.877			−0.414204
$457$	141.167			0.308899			0.154449	−	0.988001i	$-0.450640\pi$
$457$	141.167			0.308899			0.154449	+	0.988001i	$0.450640\pi$
$458$			1215.42i			2.65376i
$459$	498.688			1.08647
$460$			1231.05i			2.67619i
$461$		−	221.015i		−	0.479425i	−0.970844	−	0.239712i	$-0.922947\pi$
$461$		−	221.015i		−	0.479425i	0.970844	−	0.239712i	$-0.0770532\pi$
$462$	−569.850	−	228.528i	−1.23344	−	0.494648i
$463$	−653.162			−1.41072			−0.705358	−	0.708851i	$-0.749214\pi$
$463$	−653.162			−1.41072			−0.705358	+	0.708851i	$0.749214\pi$
$464$	1109.93			2.39208
$465$		−	140.472i		−	0.302091i
$466$	−1011.44			−2.17048
$467$			413.469i			0.885373i	0.896676	+	0.442687i	$0.145975\pi$
$467$			413.469i			0.885373i	−0.896676	+	0.442687i	$0.854025\pi$
$468$			523.737i			1.11910i
$469$	−166.153	+	414.313i	−0.354270	+	0.883398i
$470$	−42.0627			−0.0894952
$471$	311.143			0.660602
$472$			1468.43i			3.11108i
$473$	227.314			0.480579
$474$		−	467.048i		−	0.985333i
$475$		−	176.238i		−	0.371028i
$476$	−1277.18	−	512.189i	−2.68315	−	1.07603i
$477$	492.685			1.03288
$478$	241.061			0.504312
$479$		−	786.057i		−	1.64104i	−0.571620	−	0.820518i	$-0.693685\pi$
$479$		−	786.057i		−	1.64104i	0.571620	−	0.820518i	$-0.306315\pi$
$480$	216.768			0.451600
$481$			301.783i			0.627408i
$482$		−	344.998i		−	0.715764i
$483$	−184.310	−	73.9141i	−0.381594	−	0.153031i
$484$	1727.95			3.57013
$485$	−963.293			−1.98617
$486$			876.354i			1.80320i
$487$	−373.312			−0.766555			−0.383278	−	0.923633i	$-0.625205\pi$
$487$	−373.312			−0.766555			−0.383278	+	0.923633i	$0.625205\pi$
$488$		−	88.3516i		−	0.181048i
$489$		−	164.413i		−	0.336224i
$490$	825.966	−	864.183i	1.68565	−	1.76364i
$491$	−841.374			−1.71359			−0.856797	−	0.515655i	$-0.827549\pi$
$491$	−841.374			−1.71359			−0.856797	+	0.515655i	$0.827549\pi$
$492$	77.0205			0.156546
$493$			982.616i			1.99314i
$494$	244.252			0.494437
$495$		−	867.084i		−	1.75169i
$496$			379.368i			0.764855i
$497$	15.0751	−	37.5908i	0.0303321	−	0.0756353i
$498$	731.754			1.46939
$499$	244.444			0.489867			0.244934	−	0.969540i	$-0.421234\pi$
$499$	244.444			0.489867			0.244934	+	0.969540i	$0.421234\pi$
$500$		−	195.775i		−	0.391550i
$501$	301.905			0.602605
$502$			409.974i			0.816682i
$503$			408.227i			0.811585i	0.913965	+	0.405793i	$0.133004\pi$
$503$			408.227i			0.811585i	−0.913965	+	0.405793i	$0.866996\pi$
$504$	313.109	−	780.760i	0.621248	−	1.54913i
$505$	−367.826			−0.728369
$506$	1313.24			2.59533
$507$		−	134.690i		−	0.265660i
$508$	−2024.96			−3.98614
$509$		−	261.276i		−	0.513312i	−0.966503	−	0.256656i	$-0.917379\pi$
$509$		−	261.276i		−	0.513312i	0.966503	−	0.256656i	$-0.0826207\pi$
$510$			755.414i			1.48120i
$511$	−617.893	−	247.794i	−1.20918	−	0.484920i
$512$	1133.60			2.21407
$513$	179.858			0.350600
$514$			1645.88i			3.20209i
$515$	300.974			0.584416
$516$		−	153.153i		−	0.296808i
$517$			30.7813i			0.0595384i
$518$	332.710	−	829.637i	0.642298	−	1.60161i
$519$	−440.177			−0.848125
$520$	−975.139			−1.87527
$521$		−	384.464i		−	0.737935i	−0.929442	−	0.368968i	$-0.879711\pi$
$521$		−	384.464i		−	0.737935i	0.929442	−	0.368968i	$-0.120289\pi$
$522$	−1107.74			−2.12211
$523$		−	789.085i		−	1.50877i	−0.656434	−	0.754383i	$-0.727936\pi$
$523$		−	789.085i		−	1.50877i	0.656434	−	0.754383i	$-0.272064\pi$
$524$			971.558i			1.85412i
$525$	−194.264	−	77.9059i	−0.370026	−	0.148392i
$526$	1030.35			1.95883
$527$	−335.854			−0.637294
$528$		−	624.432i		−	1.18264i
$529$	−104.251			−0.197072
$530$			1691.65i			3.19180i
$531$		−	616.903i		−	1.16178i
$532$	−460.629	−	184.727i	−0.865844	−	0.347231i
$533$	−54.0102			−0.101333
$534$	−402.022			−0.752849
$535$			221.764i			0.414513i
$536$	−1078.53			−2.01219
$537$			247.908i			0.461653i
$538$		−	918.268i		−	1.70682i
$539$	−632.406	−	604.439i	−1.17329	−	1.12141i
$540$	−1324.18			−2.45218
$541$	−655.254			−1.21119			−0.605595	−	0.795773i	$-0.707065\pi$
$541$	−655.254			−1.21119			−0.605595	+	0.795773i	$0.707065\pi$
$542$		−	842.318i		−	1.55409i
$543$	490.562			0.903429
$544$		−	518.269i		−	0.952701i
$545$			261.069i			0.479026i
$546$	107.971	−	269.234i	0.197749	−	0.493102i
$547$	−189.122			−0.345744			−0.172872	−	0.984944i	$-0.555305\pi$
$547$	−189.122			−0.345744			−0.172872	+	0.984944i	$0.555305\pi$
$548$	−575.616			−1.05039
$549$			37.1174i			0.0676092i
$550$	1384.16			2.51665
$551$			354.392i			0.643179i
$552$		−	479.793i		−	0.869191i
$553$	247.699	−	617.654i	0.447918	−	1.11691i
$554$	1329.34			2.39953
$555$	−336.622			−0.606526
$556$		−	1193.88i		−	2.14727i
$557$	65.0551			0.116796			0.0583978	−	0.998293i	$-0.481401\pi$
$557$	65.0551			0.116796			0.0583978	+	0.998293i	$0.481401\pi$
$558$		−	378.621i		−	0.678533i
$559$			107.398i			0.192125i
$560$	1128.44	+	452.540i	2.01507	+	0.808107i
$561$	552.809			0.985399
$562$	−618.572			−1.10066
$563$			42.9791i			0.0763394i	0.999271	+	0.0381697i	$0.0121527\pi$
$563$			42.9791i			0.0763394i	−0.999271	+	0.0381697i	$0.987847\pi$
$564$	20.7390			0.0367712
$565$		−	43.0717i		−	0.0762331i
$566$		−	717.229i		−	1.26719i
$567$	−87.1109	+	217.217i	−0.153635	+	0.383099i
$568$	97.8557			0.172281
$569$	566.032			0.994783			0.497392	−	0.867526i	$-0.334291\pi$
$569$	566.032			0.994783			0.497392	+	0.867526i	$0.334291\pi$
$570$			272.449i			0.477980i
$571$	−636.913			−1.11543			−0.557717	−	0.830031i	$-0.688323\pi$
$571$	−636.913			−1.11543			−0.557717	+	0.830031i	$0.688323\pi$
$572$			1315.97i			2.30064i
$573$			157.482i			0.274838i
$574$	148.480	+	59.5452i	0.258676	+	0.103737i
$575$	447.688			0.778587
$576$	−137.914			−0.239434
$577$			95.6010i			0.165686i	0.996563	+	0.0828431i	$0.0264000\pi$
$577$			95.6010i			0.165686i	−0.996563	+	0.0828431i	$0.973600\pi$
$578$	774.634			1.34020
$579$		−	458.854i		−	0.792493i
$580$		−	2609.16i		−	4.49855i
$581$	967.718	+	388.085i	1.66561	+	0.667961i
$582$	692.351			1.18961
$583$	1237.94			2.12340
$584$		−	1608.49i		−	2.75426i
$585$	409.666			0.700284
$586$			1919.10i			3.27491i
$587$			917.498i			1.56303i	0.623887	+	0.781515i	$0.285553\pi$
$587$			917.498i			1.56303i	−0.623887	+	0.781515i	$0.714447\pi$
$588$	−407.241	+	426.084i	−0.692587	+	0.724633i
$589$	−121.130			−0.205653
$590$	2118.16			3.59010
$591$			237.944i			0.402613i
$592$	909.102			1.53564
$593$			888.504i			1.49832i	0.662389	+	0.749161i	$0.269543\pi$
$593$			888.504i			1.49832i	−0.662389	+	0.749161i	$0.730457\pi$
$594$			1412.59i			2.37809i
$595$	−400.633	+	999.007i	−0.673333	+	1.67900i
$596$	−308.120			−0.516979
$597$	303.993			0.509201
$598$			620.458i			1.03756i
$599$	680.423			1.13593			0.567966	−	0.823052i	$-0.307730\pi$
$599$	680.423			1.13593			0.567966	+	0.823052i	$0.307730\pi$
$600$		−	505.705i		−	0.842841i
$601$		−	225.543i		−	0.375279i	−0.982238	−	0.187640i	$-0.939916\pi$
$601$		−	225.543i		−	0.375279i	0.982238	−	0.187640i	$-0.0600837\pi$
$602$	118.404	−	295.248i	0.196684	−	0.490446i
$603$	453.104			0.751416
$604$	1388.23			2.29840
$605$		−	1351.60i		−	2.23404i
$606$	264.369			0.436252
$607$		−	714.354i		−	1.17686i	−0.808548	−	0.588430i	$-0.799746\pi$
$607$		−	714.354i		−	1.17686i	0.808548	−	0.588430i	$-0.200254\pi$
$608$		−	186.920i		−	0.307434i
$609$	390.639	+	156.658i	0.641443	+	0.257239i
$610$	−127.444			−0.208925
$611$	−14.5431			−0.0238021
$612$			1396.76i			2.28228i
$613$	460.583			0.751359			0.375680	−	0.926750i	$-0.377409\pi$
$613$	460.583			0.751359			0.375680	+	0.926750i	$0.377409\pi$
$614$		−	820.458i		−	1.33625i
$615$		−	60.2453i		−	0.0979599i
$616$	786.733	−	1961.77i	1.27716	−	3.18470i
$617$	−575.598			−0.932898			−0.466449	−	0.884548i	$-0.654467\pi$
$617$	−575.598			−0.932898			−0.466449	+	0.884548i	$0.654467\pi$
$618$	−216.320			−0.350033
$619$		−	1145.56i		−	1.85066i	−0.379157	−	0.925332i	$-0.623786\pi$
$619$		−	1145.56i		−	1.85066i	0.379157	−	0.925332i	$-0.376214\pi$
$620$	891.801			1.43839
$621$			456.882i			0.735720i
$622$		−	1283.50i		−	2.06350i
$623$	−531.659	−	213.212i	−0.853385	−	0.342234i
$624$	295.022			0.472791
$625$	−696.196			−1.11391
$626$		−	305.103i		−	0.487385i
$627$	199.377			0.317985
$628$			1975.32i			3.14542i
$629$			804.827i			1.27953i
$630$	−1126.22	−	451.649i	−1.78765	−	0.716903i
$631$	−19.6528			−0.0311455			−0.0155727	−	0.999879i	$-0.504957\pi$
$631$	−19.6528			−0.0311455			−0.0155727	+	0.999879i	$0.504957\pi$
$632$	1607.87			2.54409
$633$		−	451.711i		−	0.713603i
$634$	−1831.02			−2.88804
$635$			1583.92i			2.49436i
$636$		−	834.066i		−	1.31143i
$637$	285.576	−	298.789i	0.448314	−	0.469057i
$638$	−2783.36			−4.36264
$639$	−41.1102			−0.0643353
$640$		−	1103.45i		−	1.72415i
$641$	−514.965			−0.803377			−0.401689	−	0.915776i	$-0.631577\pi$
$641$	−514.965			−0.803377			−0.401689	+	0.915776i	$0.631577\pi$
$642$		−	159.389i		−	0.248270i
$643$			84.1930i			0.130938i	0.997855	+	0.0654689i	$0.0208543\pi$
$643$			84.1930i			0.130938i	−0.997855	+	0.0654689i	$0.979146\pi$
$644$	469.251	−	1170.11i	0.728650	−	1.81694i
$645$	−119.796			−0.185730
$646$	651.395			1.00835
$647$		−	113.442i		−	0.175336i	−0.996150	−	0.0876681i	$-0.972059\pi$
$647$		−	113.442i		−	0.175336i	0.996150	−	0.0876681i	$-0.0279415\pi$
$648$	−565.457			−0.872618
$649$		−	1550.06i		−	2.38838i
$650$			653.966i			1.00610i
$651$	−53.5452	+	133.519i	−0.0822507	+	0.205098i
$652$	1043.79			1.60091
$653$	−550.682			−0.843311			−0.421656	−	0.906756i	$-0.638551\pi$
$653$	−550.682			−0.843311			−0.421656	+	0.906756i	$0.638551\pi$
$654$		−	187.639i		−	0.286910i
$655$	759.951			1.16023
$656$			162.702i			0.248022i
$657$			675.744i			1.02853i
$658$	39.9806	+	16.0335i	0.0607608	+	0.0243670i
$659$	−598.779			−0.908618			−0.454309	−	0.890844i	$-0.650114\pi$
$659$	−598.779			−0.908618			−0.454309	+	0.890844i	$0.650114\pi$
$660$	−1467.89			−2.22407
$661$			477.598i			0.722539i	0.932461	+	0.361269i	$0.117657\pi$
$661$			477.598i			0.722539i	−0.932461	+	0.361269i	$0.882343\pi$
$662$	575.274			0.868994
$663$			261.182i			0.393940i
$664$			2519.15i			3.79390i
$665$	−144.493	+	360.303i	−0.217283	+	0.541810i
$666$	−907.312			−1.36233
$667$	−900.241			−1.34969
$668$			1916.67i			2.86927i
$669$	107.852			0.161214
$670$			1555.75i			2.32201i
$671$			93.2631i			0.138991i
$672$	−206.038	−	82.6277i	−0.306604	−	0.122958i
$673$	−1006.09			−1.49493			−0.747465	−	0.664301i	$-0.768729\pi$
$673$	−1006.09			−1.49493			−0.747465	+	0.664301i	$0.768729\pi$
$674$	1401.65			2.07960
$675$			481.556i			0.713416i
$676$	855.089			1.26492
$677$			129.897i			0.191872i	0.995387	+	0.0959361i	$0.0305844\pi$
$677$			129.897i			0.191872i	−0.995387	+	0.0959361i	$0.969416\pi$
$678$			30.9571i			0.0456594i
$679$	915.609	+	367.188i	1.34847	+	0.540778i
$680$	−2600.60			−3.82441
$681$	−48.7161			−0.0715362
$682$		−	951.342i		−	1.39493i
$683$	−262.282			−0.384015			−0.192007	−	0.981393i	$-0.561500\pi$
$683$	−262.282			−0.384015			−0.192007	+	0.981393i	$0.561500\pi$
$684$			503.756i			0.736486i
$685$			450.246i			0.657294i
$686$	−1114.49	+	506.564i	−1.62462	+	0.738431i
$687$	−468.742			−0.682302
$688$	323.528			0.470245
$689$			584.885i			0.848890i
$690$	−692.086			−1.00302
$691$		−	956.437i		−	1.38414i	−0.721833	−	0.692068i	$-0.756700\pi$
$691$		−	956.437i		−	1.38414i	0.721833	−	0.692068i	$-0.243300\pi$
$692$		−	2794.50i		−	4.03830i
$693$	−330.515	+	824.162i	−0.476934	+	1.18927i
$694$	471.965			0.680065
$695$	−933.853			−1.34367
$696$			1016.91i			1.46107i
$697$	−144.040			−0.206657
$698$		−	367.878i		−	0.527046i
$699$		−	390.075i		−	0.558047i
$700$	494.592	−	1233.30i	0.706561	−	1.76186i
$701$	−611.307			−0.872050			−0.436025	−	0.899934i	$-0.643614\pi$
$701$	−611.307			−0.872050			−0.436025	+	0.899934i	$0.643614\pi$
$702$	−667.397			−0.950708
$703$			290.270i			0.412902i
$704$	−346.529			−0.492228
$705$		−	16.2220i		−	0.0230099i
$706$		−	183.197i		−	0.259486i
$707$	349.618	+	140.208i	0.494510	+	0.198314i
$708$	−1044.35			−1.47508
$709$	724.770			1.02224			0.511121	−	0.859509i	$-0.329230\pi$
$709$	724.770			1.02224			0.511121	+	0.859509i	$0.329230\pi$
$710$		−	141.154i		−	0.198808i
$711$	−675.482			−0.950046
$712$		−	1384.01i		−	1.94383i
$713$		−	307.699i		−	0.431555i
$714$	287.948	−	718.020i	0.403289	−	1.00563i
$715$	1029.35			1.43965
$716$	−1573.86			−2.19813
$717$			92.9679i			0.129662i
$718$	1016.04			1.41509
$719$		−	274.377i		−	0.381609i	−0.981628	−	0.190804i	$-0.938890\pi$
$719$		−	274.377i		−	0.381609i	0.981628	−	0.190804i	$-0.0611096\pi$
$720$		−	1234.09i		−	1.71402i
$721$	−286.076	−	114.725i	−0.396776	−	0.159120i
$722$	−1053.52			−1.45917
$723$	133.053			0.184028
$724$			3114.38i			4.30163i
$725$	−948.858			−1.30877
$726$			971.437i			1.33807i
$727$		−	272.099i		−	0.374277i	−0.982334	−	0.187138i	$-0.940079\pi$
$727$		−	272.099i		−	0.374277i	0.982334	−	0.187138i	$-0.0599213\pi$
$728$	926.869	+	371.703i	1.27317	+	0.510582i
$729$	−37.0761			−0.0508588
$730$	−2320.19			−3.17834
$731$			286.419i			0.391818i
$732$	62.8361			0.0858416
$733$			641.043i			0.874547i	0.899329	+	0.437274i	$0.144056\pi$
$733$			641.043i			0.874547i	−0.899329	+	0.437274i	$0.855944\pi$
$734$			995.788i			1.35666i
$735$	333.282	+	318.543i	0.453445	+	0.433392i
$736$	474.822			0.645138
$737$	1138.49			1.54476
$738$		−	162.382i		−	0.220030i
$739$	991.093			1.34113			0.670564	−	0.741852i	$-0.266052\pi$
$739$	991.093			1.34113			0.670564	+	0.741852i	$0.266052\pi$
$740$		−	2137.08i		−	2.88794i
$741$			94.1985i			0.127123i
$742$	644.824	−	1607.91i	0.869035	−	2.16700i
$743$	1212.55			1.63196			0.815981	−	0.578078i	$-0.196197\pi$
$743$	1212.55			1.63196			0.815981	+	0.578078i	$0.196197\pi$
$744$	−347.574			−0.467170
$745$			241.011i			0.323504i
$746$	153.030			0.205134
$747$		−	1058.32i		−	1.41676i
$748$			3509.56i			4.69192i
$749$	84.5320	−	210.787i	0.112860	−	0.281424i
$750$	110.063			0.146751
$751$	−44.2669			−0.0589439			−0.0294720	−	0.999566i	$-0.509383\pi$
$751$	−44.2669			−0.0589439			−0.0294720	+	0.999566i	$0.509383\pi$
$752$			43.8101i			0.0582581i
$753$	−158.111			−0.209975
$754$		−	1315.04i		−	1.74408i
$755$		−	1085.87i		−	1.43824i
$756$	1258.63	+	504.750i	1.66485	+	0.667659i
$757$	−362.989			−0.479510			−0.239755	−	0.970833i	$-0.577067\pi$
$757$	−362.989			−0.479510			−0.239755	+	0.970833i	$0.577067\pi$
$758$	−1403.86			−1.85206
$759$			506.465i			0.667280i
$760$	−937.937			−1.23413
$761$		−	483.200i		−	0.634954i	−0.948266	−	0.317477i	$-0.897164\pi$
$761$		−	483.200i		−	0.634954i	0.948266	−	0.317477i	$-0.102836\pi$
$762$		−	1138.42i		−	1.49399i
$763$	99.5142	−	248.146i	0.130425	−	0.325224i
$764$	−999.791			−1.30863
$765$	1092.54			1.42816
$766$			875.466i			1.14291i
$767$	732.348			0.954821
$768$			686.220i			0.893516i
$769$			681.276i			0.885925i	0.896540	+	0.442962i	$0.146072\pi$
$769$			681.276i			0.885925i	−0.896540	+	0.442962i	$0.853928\pi$
$770$	−2829.79	−	1134.84i	−3.67505	−	1.47381i
$771$	−634.751			−0.823282
$772$	2913.07			3.77341
$773$		−	524.201i		−	0.678138i	−0.940761	−	0.339069i	$-0.889888\pi$
$773$		−	524.201i		−	0.678138i	0.940761	−	0.339069i	$-0.110112\pi$
$774$	−322.891			−0.417172
$775$		−	324.316i		−	0.418472i
$776$			2383.50i			3.07152i
$777$	319.959	+	128.314i	0.411787	+	0.165140i
$778$	1497.17			1.92438
$779$	−51.9497			−0.0666877
$780$		−	693.524i		−	0.889133i
$781$	−103.296			−0.132261
$782$			1654.70i			2.11599i
$783$		−	968.345i		−	1.23671i
$784$	−900.082	−	860.277i	−1.14806	−	1.09729i
$785$	1545.09			1.96827
$786$	−546.202			−0.694914
$787$		−	179.306i		−	0.227835i	−0.993490	−	0.113917i	$-0.963660\pi$
$787$		−	179.306i		−	0.227835i	0.993490	−	0.113917i	$-0.0363399\pi$
$788$	−1510.61			−1.91702
$789$			397.365i			0.503631i
$790$		−	2319.29i		−	2.93581i
$791$	−16.4181	+	40.9396i	−0.0207561	+	0.0517568i
$792$	−2145.45			−2.70890
$793$	−44.0635			−0.0555656
$794$			554.945i			0.698924i
$795$	−652.405			−0.820636
$796$			1929.93i			2.42453i
$797$			21.6890i			0.0272133i	0.999907	+	0.0136067i	$0.00433127\pi$
$797$			21.6890i			0.0272133i	−0.999907	+	0.0136067i	$0.995669\pi$
$798$	103.852	−	258.962i	0.130140	−	0.324514i
$799$	−38.7850			−0.0485419
$800$	500.464			0.625580
$801$			581.436i			0.725888i
$802$	−699.232			−0.871861
$803$			1697.91i			2.11445i
$804$		−	767.059i		−	0.954054i
$805$	−915.258	−	367.047i	−1.13697	−	0.455959i
$806$	449.475			0.557662
$807$	354.141			0.438836
$808$			910.121i			1.12639i
$809$	−350.172			−0.432845			−0.216423	−	0.976300i	$-0.569439\pi$
$809$	−350.172			−0.432845			−0.216423	+	0.976300i	$0.569439\pi$
$810$			815.652i			1.00698i
$811$		−	1399.06i		−	1.72511i	−0.505963	−	0.862555i	$-0.668863\pi$
$811$		−	1399.06i		−	1.72511i	0.505963	−	0.862555i	$-0.331137\pi$
$812$	−994.560	+	2480.01i	−1.22483	+	3.05419i
$813$	324.850			0.399569
$814$	−2279.76			−2.80068
$815$		−	816.454i		−	1.00178i
$816$	786.794			0.964209
$817$			103.300i			0.126439i
$818$		−	1192.99i		−	1.45842i
$819$	−389.387	−	156.157i	−0.475443	−	0.190667i
$820$	382.473			0.466430
$821$	−567.159			−0.690815			−0.345407	−	0.938453i	$-0.612259\pi$
$821$	−567.159			−0.690815			−0.345407	+	0.938453i	$0.612259\pi$
$822$		−	323.607i		−	0.393682i
$823$	−569.433			−0.691899			−0.345949	−	0.938253i	$-0.612443\pi$
$823$	−569.433			−0.691899			−0.345949	+	0.938253i	$0.612443\pi$
$824$		−	744.708i		−	0.903771i
$825$			533.817i			0.647051i
$826$	−2013.31	−	807.399i	−2.43742	−	0.977481i
$827$	388.718			0.470034			0.235017	−	0.971991i	$-0.424485\pi$
$827$	388.718			0.470034			0.235017	+	0.971991i	$0.424485\pi$
$828$	−1279.66			−1.54549
$829$			565.579i			0.682242i	0.940019	+	0.341121i	$0.110807\pi$
$829$			565.579i			0.682242i	−0.940019	+	0.341121i	$0.889193\pi$
$830$	3633.79			4.37806
$831$			512.676i			0.616938i
$832$		−	163.723i		−	0.196782i
$833$	761.603	−	796.842i	0.914289	−	0.956593i
$834$	671.191			0.804786
$835$	1499.22			1.79547
$836$			1265.76i			1.51407i
$837$	330.977			0.395432
$838$		−	1656.98i		−	1.97731i
$839$			1293.71i			1.54197i	0.636856	+	0.770983i	$0.280235\pi$
$839$			1293.71i			1.54197i	−0.636856	+	0.770983i	$0.719765\pi$
$840$	−414.614	+	1033.87i	−0.493588	+	1.23080i
$841$	1067.03			1.26876
$842$	−1003.05			−1.19127
$843$		−	238.559i		−	0.282989i
$844$	2867.73			3.39778
$845$		−	668.850i		−	0.791538i
$846$		−	43.7238i		−	0.0516830i
$847$	−515.201	+	1284.69i	−0.608266	+	1.51675i
$848$	1761.93			2.07774
$849$	276.608			0.325804
$850$			1744.06i			2.05184i
$851$	−737.356			−0.866459
$852$			69.5955i			0.0816848i
$853$		−	968.279i		−	1.13515i	−0.823323	−	0.567573i	$-0.807883\pi$
$853$		−	968.279i		−	1.13515i	0.823323	−	0.567573i	$-0.192117\pi$
$854$	121.135	+	48.5791i	0.141845	+	0.0568842i
$855$	394.037			0.460862
$856$	548.717			0.641024
$857$		−	232.918i		−	0.271783i	−0.990724	−	0.135891i	$-0.956610\pi$
$857$		−	232.918i		−	0.271783i	0.990724	−	0.135891i	$-0.0433898\pi$
$858$	−739.827			−0.862269
$859$		−	565.423i		−	0.658234i	−0.944289	−	0.329117i	$-0.893249\pi$
$859$		−	565.423i		−	0.658234i	0.944289	−	0.329117i	$-0.106751\pi$
$860$		−	760.536i		−	0.884344i
$861$	−22.9643	+	57.2631i	−0.0266717	+	0.0665077i
$862$	812.537			0.942618
$863$	−198.963			−0.230548			−0.115274	−	0.993334i	$-0.536775\pi$
$863$	−198.963			−0.230548			−0.115274	+	0.993334i	$0.536775\pi$
$864$			510.742i			0.591137i
$865$	−2185.86			−2.52700
$866$			1658.54i			1.91517i
$867$			298.747i			0.344575i
$868$	−847.656	−	339.937i	−0.976562	−	0.391632i
$869$	−1697.25			−1.95311
$870$	1466.85			1.68604
$871$			537.897i			0.617562i
$872$	645.970			0.740791
$873$		−	1001.33i		−	1.14700i
$874$			596.787i			0.682823i
$875$	145.555	+	58.3720i	0.166348	+	0.0667108i
$876$	1143.97			1.30590
$877$	−773.145			−0.881580			−0.440790	−	0.897610i	$-0.645302\pi$
$877$	−773.145			−0.881580			−0.440790	+	0.897610i	$0.645302\pi$
$878$			142.032i			0.161768i
$879$	−740.123			−0.842005
$880$		−	3100.84i		−	3.52368i
$881$			390.043i			0.442727i	0.975191	+	0.221364i	$0.0710508\pi$
$881$			390.043i			0.442727i	−0.975191	+	0.221364i	$0.928949\pi$
$882$	898.310	+	858.584i	1.01849	+	0.973451i
$883$	−273.027			−0.309204			−0.154602	−	0.987977i	$-0.549409\pi$
$883$	−273.027			−0.309204			−0.154602	+	0.987977i	$0.549409\pi$
$884$	−1658.14			−1.87572
$885$			816.892i			0.923042i
$886$	2048.78			2.31239
$887$		−	495.523i		−	0.558651i	−0.960196	−	0.279325i	$-0.909889\pi$
$887$		−	495.523i		−	0.558651i	0.960196	−	0.279325i	$-0.0901108\pi$
$888$			832.912i			0.937964i
$889$	603.759	−	1505.52i	0.679144	−	1.69349i
$890$	−1996.38			−2.24313
$891$	596.891			0.669911
$892$			684.711i			0.767613i
$893$	−13.9883			−0.0156643
$894$		−	173.223i		−	0.193761i
$895$			1231.07i			1.37550i
$896$	−420.615	+	1048.83i	−0.469436	+	1.17057i
$897$	−239.287			−0.266764
$898$	50.8143			0.0565861
$899$			652.156i			0.725424i
$900$	−1348.77			−1.49863
$901$			1559.83i			1.73122i
$902$		−	408.008i		−	0.452338i
$903$	113.866	+	45.6638i	0.126097	+	0.0505690i
$904$	−106.573			−0.117891
$905$	2436.06			2.69178
$906$			780.453i			0.861427i
$907$	15.9087			0.0175399			0.00876997	−	0.999962i	$-0.497208\pi$
$907$	15.9087			0.0175399			0.00876997	+	0.999962i	$0.497208\pi$
$908$		−	309.279i		−	0.340615i
$909$		−	382.352i		−	0.420629i
$910$	536.169	−	1336.98i	0.589197	−	1.46920i
$911$	236.418			0.259515			0.129757	−	0.991546i	$-0.458580\pi$
$911$	236.418			0.259515			0.129757	+	0.991546i	$0.458580\pi$
$912$	283.766			0.311147
$913$		−	2659.19i		−	2.91259i
$914$	−503.842			−0.551250
$915$		−	49.1503i		−	0.0537162i
$916$		−	2975.85i		−	3.24874i
$917$	−722.333	−	289.678i	−0.787713	−	0.315898i
$918$	−1779.88			−1.93887
$919$	−1059.13			−1.15248			−0.576238	−	0.817282i	$-0.695480\pi$
$919$	−1059.13			−1.15248			−0.576238	+	0.817282i	$0.695480\pi$
$920$		−	2382.59i		−	2.58977i
$921$	316.419			0.343560
$922$			788.831i			0.855565i
$923$		−	48.8035i		−	0.0528749i
$924$	1395.22	+	559.528i	1.50998	+	0.605550i
$925$	−777.177			−0.840192
$926$	2331.22			2.51751
$927$			312.860i			0.337497i
$928$	−1006.37			−1.08445
$929$			217.826i			0.234474i	0.993104	+	0.117237i	$0.0374036\pi$
$929$			217.826i			0.234474i	−0.993104	+	0.117237i	$0.962596\pi$
$930$			501.364i			0.539101i
$931$	274.681	−	287.390i	0.295039	−	0.308690i
$932$	2476.42			2.65711
$933$	494.996			0.530542
$934$		−	1475.73i		−	1.58001i
$935$	2745.17			2.93601
$936$		−	1013.65i		−	1.08296i
$937$			967.357i			1.03240i	0.856469	+	0.516199i	$0.172653\pi$
$937$			967.357i			1.03240i	−0.856469	+	0.516199i	$0.827347\pi$
$938$	593.020	−	1478.74i	0.632218	−	1.57648i
$939$	117.666			0.125310
$940$	102.987			0.109560
$941$		−	1195.57i		−	1.27054i	−0.772292	−	0.635268i	$-0.780890\pi$
$941$		−	1195.57i		−	1.27054i	0.772292	−	0.635268i	$-0.219110\pi$
$942$	−1110.51			−1.17889
$943$		−	131.965i		−	0.139941i
$944$		−	2206.15i		−	2.33702i
$945$	394.815	−	984.498i	0.417793	−	1.04180i
$946$	−811.312			−0.857624
$947$	638.755			0.674504			0.337252	−	0.941414i	$-0.390503\pi$
$947$	638.755			0.674504			0.337252	+	0.941414i	$0.390503\pi$
$948$			1143.52i			1.20625i
$949$	−802.200			−0.845311
$950$			629.017i			0.662123i
$951$		−	706.153i		−	0.742537i
$952$	2471.87	+	991.297i	2.59650	+	1.04128i
$953$	1696.95			1.78064			0.890319	−	0.455337i	$-0.150481\pi$
$953$	1696.95			1.78064			0.890319	+	0.455337i	$0.150481\pi$
$954$	−1758.46			−1.84325
$955$			782.035i			0.818885i
$956$	−590.215			−0.617380
$957$		−	1073.44i		−	1.12167i
$958$			2805.54i			2.92854i
$959$	171.625	−	427.958i	0.178962	−	0.446255i
$960$	182.623			0.190232
$961$	738.095			0.768049
$962$		−	1077.10i		−	1.11965i
$963$	−230.522			−0.239379
$964$			844.696i			0.876241i
$965$		−	2278.60i		−	2.36125i
$966$	657.827	+	263.809i	0.680980	+	0.273094i
$967$	−481.888			−0.498333			−0.249167	−	0.968461i	$-0.580157\pi$
$967$	−481.888			−0.498333			−0.249167	+	0.968461i	$0.580157\pi$
$968$	−3344.29			−3.45484
$969$			251.218i			0.259255i
$970$	3438.12			3.54445
$971$		−	84.6967i		−	0.0872262i	−0.999048	−	0.0436131i	$-0.986113\pi$
$971$		−	84.6967i		−	0.0872262i	0.999048	−	0.0436131i	$-0.0138869\pi$
$972$		−	2145.67i		−	2.20748i
$973$	887.626	+	355.966i	0.912257	+	0.365844i
$974$	1332.40			1.36797
$975$	−252.210			−0.258676
$976$			132.738i			0.136002i
$977$	−56.2662			−0.0575908			−0.0287954	−	0.999585i	$-0.509167\pi$
$977$	−56.2662			−0.0575908			−0.0287954	+	0.999585i	$0.509167\pi$
$978$			586.813i			0.600013i
$979$			1460.94i			1.49228i
$980$	−2022.30	+	2115.87i	−2.06357	+	2.15905i
$981$	−271.379			−0.276635
$982$	3002.97			3.05802
$983$			151.363i			0.153980i	0.997032	+	0.0769901i	$0.0245310\pi$
$983$			151.363i			0.153980i	−0.997032	+	0.0769901i	$0.975469\pi$
$984$	−149.066			−0.151490
$985$			1181.60i			1.19959i
$986$		−	3507.08i		−	3.55688i
$987$	−6.18349	+	15.4190i	−0.00626494	+	0.0156221i
$988$	−598.028			−0.605291
$989$	−262.408			−0.265327
$990$			3094.73i			3.12599i
$991$	−1100.83			−1.11082			−0.555412	−	0.831575i	$-0.687439\pi$
$991$	−1100.83			−1.11082			−0.555412	+	0.831575i	$0.687439\pi$
$992$		−	343.972i		−	0.346746i
$993$			221.861i			0.223425i
$994$	−53.8049	+	134.166i	−0.0541297	+	0.134976i
$995$	1509.59			1.51717
$996$	−1791.63			−1.79883
$997$		−	249.863i		−	0.250615i	−0.992118	−	0.125308i	$-0.960008\pi$
$997$		−	249.863i		−	0.250615i	0.992118	−	0.125308i	$-0.0399918\pi$
$998$	−872.451			−0.874200
$999$		−	793.138i		−	0.793932i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	287.3.b.a.83.3	✓	52
7.6	odd	2	inner	287.3.b.a.83.4	yes	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.3.b.a.83.3	✓	52	1.1	even	1	trivial
287.3.b.a.83.4	yes	52	7.6	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:	\( N \)	\(=\)	\( 287 = 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	287.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-3.56913 q^{2} -1.37648i q^{3} +8.73868 q^{4} -6.83538i q^{5} +4.91282i q^{6} +(-2.60551 + 6.49702i) q^{7} -16.9130 q^{8} +7.10532 q^{9} +O(q^{10})\)	\(q-3.56913 q^{2} -1.37648i q^{3} +8.73868 q^{4} -6.83538i q^{5} +4.91282i q^{6} +(-2.60551 + 6.49702i) q^{7} -16.9130 q^{8} +7.10532 q^{9} +24.3964i q^{10} +17.8532 q^{11} -12.0286i q^{12} +8.43498i q^{13} +(9.29940 - 23.1887i) q^{14} -9.40874 q^{15} +25.4098 q^{16} +22.4953i q^{17} -25.3598 q^{18} +8.11318i q^{19} -59.7322i q^{20} +(8.94299 + 3.58642i) q^{21} -63.7202 q^{22} -20.6094 q^{23} +23.2803i q^{24} -21.7225 q^{25} -30.1055i q^{26} -22.1686i q^{27} +(-22.7687 + 56.7754i) q^{28} +43.6810 q^{29} +33.5810 q^{30} +14.9300i q^{31} -23.0390 q^{32} -24.5744i q^{33} -80.2885i q^{34} +(44.4096 + 17.8097i) q^{35} +62.0911 q^{36} +35.7776 q^{37} -28.9570i q^{38} +11.6105 q^{39} +115.607i q^{40} +6.40312i q^{41} +(-31.9187 - 12.8004i) q^{42} +12.7324 q^{43} +156.013 q^{44} -48.5675i q^{45} +73.5578 q^{46} +1.72414i q^{47} -34.9760i q^{48} +(-35.4226 - 33.8561i) q^{49} +77.5302 q^{50} +30.9642 q^{51} +73.7106i q^{52} +69.3404 q^{53} +79.1225i q^{54} -122.033i q^{55} +(44.0669 - 109.884i) q^{56} +11.1676 q^{57} -155.903 q^{58} -86.8227i q^{59} -82.2199 q^{60} +5.22390i q^{61} -53.2871i q^{62} +(-18.5130 + 46.1634i) q^{63} -19.4099 q^{64} +57.6563 q^{65} +87.7093i q^{66} +63.7697 q^{67} +196.579i q^{68} +28.3684i q^{69} +(-158.504 - 63.5650i) q^{70} -5.78584 q^{71} -120.172 q^{72} +95.1040i q^{73} -127.695 q^{74} +29.9004i q^{75} +70.8985i q^{76} +(-46.5166 + 115.992i) q^{77} -41.4395 q^{78} -95.0672 q^{79} -173.686i q^{80} +33.4333 q^{81} -22.8536i q^{82} -148.948i q^{83} +(78.1500 + 31.3406i) q^{84} +153.764 q^{85} -45.4436 q^{86} -60.1258i q^{87} -301.950 q^{88} +81.8312i q^{89} +173.344i q^{90} +(-54.8023 - 21.9774i) q^{91} -180.099 q^{92} +20.5508 q^{93} -6.15368i q^{94} +55.4567 q^{95} +31.7127i q^{96} -140.927i q^{97} +(126.428 + 120.837i) q^{98} +126.852 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q + 2 q^{2} + 90 q^{4} + 12 q^{7} - 2 q^{8} - 140 q^{9}+O(q^{10}) \) 52 * q + 2 * q^2 + 90 * q^4 + 12 * q^7 - 2 * q^8 - 140 * q^9	\( 52 q + 2 q^{2} + 90 q^{4} + 12 q^{7} - 2 q^{8} - 140 q^{9} + 24 q^{11} - 14 q^{14} + 44 q^{15} + 194 q^{16} + 70 q^{18} - 16 q^{21} - 48 q^{22} - 80 q^{23} - 304 q^{25} + 64 q^{28} - 12 q^{29} + 64 q^{30} - 166 q^{32} + 30 q^{35} - 70 q^{36} + 36 q^{37} - 68 q^{39} + 164 q^{42} - 172 q^{43} + 72 q^{44} + 68 q^{46} - 172 q^{49} - 234 q^{50} + 156 q^{51} + 64 q^{53} - 234 q^{56} + 140 q^{57} - 556 q^{58} + 152 q^{60} - 130 q^{63} + 334 q^{64} - 76 q^{65} + 160 q^{67} + 202 q^{70} - 408 q^{71} - 40 q^{72} + 398 q^{74} - 248 q^{77} + 390 q^{78} + 264 q^{79} - 116 q^{81} - 418 q^{84} + 232 q^{85} + 368 q^{86} - 220 q^{88} + 32 q^{91} - 74 q^{92} + 240 q^{93} - 44 q^{95} + 838 q^{98} - 24 q^{99}+O(q^{100}) \) 52 * q + 2 * q^2 + 90 * q^4 + 12 * q^7 - 2 * q^8 - 140 * q^9 + 24 * q^11 - 14 * q^14 + 44 * q^15 + 194 * q^16 + 70 * q^18 - 16 * q^21 - 48 * q^22 - 80 * q^23 - 304 * q^25 + 64 * q^28 - 12 * q^29 + 64 * q^30 - 166 * q^32 + 30 * q^35 - 70 * q^36 + 36 * q^37 - 68 * q^39 + 164 * q^42 - 172 * q^43 + 72 * q^44 + 68 * q^46 - 172 * q^49 - 234 * q^50 + 156 * q^51 + 64 * q^53 - 234 * q^56 + 140 * q^57 - 556 * q^58 + 152 * q^60 - 130 * q^63 + 334 * q^64 - 76 * q^65 + 160 * q^67 + 202 * q^70 - 408 * q^71 - 40 * q^72 + 398 * q^74 - 248 * q^77 + 390 * q^78 + 264 * q^79 - 116 * q^81 - 418 * q^84 + 232 * q^85 + 368 * q^86 - 220 * q^88 + 32 * q^91 - 74 * q^92 + 240 * q^93 - 44 * q^95 + 838 * q^98 - 24 * q^99

Introduction

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