LMFDB - Embedded newform 253.3.c.a.208.31

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [253,3,Mod(208,253)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(253, 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("253.208");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 253 = 11 \cdot 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	253.c (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:	$6.89375068832$
Analytic rank:	$0$
Dimension:	$44$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			208.31
Character	$\chi$	$=$	253.208
Dual form			253.3.c.a.208.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.81287i q^{2} -2.41374 q^{3} +0.713501 q^{4} +4.05365 q^{5} -4.37579i q^{6} -13.5027i q^{7} +8.54497i q^{8} -3.17387 q^{9} +7.34874i q^{10} +(-8.89372 - 6.47315i) q^{11} -1.72220 q^{12} -22.1899i q^{13} +24.4787 q^{14} -9.78444 q^{15} -12.6369 q^{16} +2.51854i q^{17} -5.75382i q^{18} -18.9423i q^{19} +2.89228 q^{20} +32.5921i q^{21} +(11.7350 - 16.1232i) q^{22} -4.79583 q^{23} -20.6253i q^{24} -8.56793 q^{25} +40.2274 q^{26} +29.3845 q^{27} -9.63421i q^{28} +44.4146i q^{29} -17.7379i q^{30} +58.9192 q^{31} +11.2708i q^{32} +(21.4671 + 15.6245i) q^{33} -4.56579 q^{34} -54.7354i q^{35} -2.26456 q^{36} +27.8878 q^{37} +34.3400 q^{38} +53.5605i q^{39} +34.6383i q^{40} -35.5308i q^{41} -59.0852 q^{42} -23.8456i q^{43} +(-6.34568 - 4.61860i) q^{44} -12.8658 q^{45} -8.69422i q^{46} -18.3044 q^{47} +30.5022 q^{48} -133.324 q^{49} -15.5325i q^{50} -6.07910i q^{51} -15.8325i q^{52} -10.6548 q^{53} +53.2703i q^{54} +(-36.0520 - 26.2399i) q^{55} +115.380 q^{56} +45.7218i q^{57} -80.5180 q^{58} +12.3620 q^{59} -6.98121 q^{60} +33.3369i q^{61} +106.813i q^{62} +42.8560i q^{63} -70.9801 q^{64} -89.9500i q^{65} +(-28.3252 + 38.9171i) q^{66} +97.8030 q^{67} +1.79698i q^{68} +11.5759 q^{69} +99.2281 q^{70} -92.8328 q^{71} -27.1206i q^{72} +59.0459i q^{73} +50.5570i q^{74} +20.6807 q^{75} -13.5154i q^{76} +(-87.4053 + 120.090i) q^{77} -97.0983 q^{78} -82.0385i q^{79} -51.2256 q^{80} -42.3617 q^{81} +64.4127 q^{82} +26.5309i q^{83} +23.2545i q^{84} +10.2093i q^{85} +43.2289 q^{86} -107.205i q^{87} +(55.3129 - 75.9966i) q^{88} +28.0260 q^{89} -23.3240i q^{90} -299.624 q^{91} -3.42183 q^{92} -142.216 q^{93} -33.1835i q^{94} -76.7855i q^{95} -27.2047i q^{96} +54.0964 q^{97} -241.699i q^{98} +(28.2275 + 20.5450i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 8 q^{3} - 88 q^{4} + 100 q^{9} + 8 q^{14} - 8 q^{15} + 72 q^{16} - 40 q^{20} - 76 q^{22} + 268 q^{25} - 40 q^{26} + 32 q^{27} + 72 q^{31} - 90 q^{33} + 60 q^{34} - 312 q^{36} + 4 q^{37} + 40 q^{38}+ \cdots + 494 q^{99}+O(q^{100}) $ 44 * q + 8 * q^3 - 88 * q^4 + 100 * q^9 + 8 * q^14 - 8 * q^15 + 72 * q^16 - 40 * q^20 - 76 * q^22 + 268 * q^25 - 40 * q^26 + 32 * q^27 + 72 * q^31 - 90 * q^33 + 60 * q^34 - 312 * q^36 + 4 * q^37 + 40 * q^38 + 12 * q^42 + 186 * q^44 - 180 * q^45 - 72 * q^47 + 252 * q^48 - 464 * q^49 + 100 * q^53 - 48 * q^55 + 208 * q^56 - 148 * q^58 - 144 * q^59 - 324 * q^60 - 416 * q^64 - 238 * q^66 + 292 * q^67 + 540 * q^70 + 544 * q^71 - 236 * q^75 + 64 * q^77 - 344 * q^78 + 156 * q^80 - 404 * q^81 + 72 * q^82 - 136 * q^86 + 608 * q^88 - 80 * q^89 - 4 * q^91 - 372 * q^93 + 68 * q^97 + 494 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/253\mathbb{Z}\right)^\times$.

$n$	$24$	$166$
$\chi(n)$	$-1$	$1$

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 $

$2$			1.81287i			0.906435i	0.891400	+	0.453218i	$0.149724\pi$
$2$			1.81287i			0.906435i	−0.891400	+	0.453218i	$0.850276\pi$
$3$	−2.41374			−0.804579			−0.402290	−	0.915512i	$-0.631785\pi$
$3$	−2.41374			−0.804579			−0.402290	+	0.915512i	$0.631785\pi$
$4$	0.713501			0.178375
$5$	4.05365			0.810730			0.405365	−	0.914155i	$-0.367144\pi$
$5$	4.05365			0.810730			0.405365	+	0.914155i	$0.367144\pi$
$6$		−	4.37579i		−	0.729299i
$7$		−	13.5027i		−	1.92896i	−0.264151	−	0.964481i	$-0.585092\pi$
$7$		−	13.5027i		−	1.92896i	0.264151	−	0.964481i	$-0.414908\pi$
$8$			8.54497i			1.06812i
$9$	−3.17387			−0.352653
$10$			7.34874i			0.734874i
$11$	−8.89372	−	6.47315i	−0.808520	−	0.588468i
$11$	−8.89372	−	6.47315i	−0.808520	−	0.588468i
$12$	−1.72220			−0.143517
$13$		−	22.1899i		−	1.70691i	−0.521164	−	0.853457i	$-0.674502\pi$
$13$		−	22.1899i		−	1.70691i	0.521164	−	0.853457i	$-0.325498\pi$
$14$	24.4787			1.74848
$15$	−9.78444			−0.652296
$16$	−12.6369			−0.789807
$17$			2.51854i			0.148150i	0.997253	+	0.0740748i	$0.0236004\pi$
$17$			2.51854i			0.148150i	−0.997253	+	0.0740748i	$0.976400\pi$
$18$		−	5.75382i		−	0.319657i
$19$		−	18.9423i		−	0.996964i	−0.866900	−	0.498482i	$-0.833891\pi$
$19$		−	18.9423i		−	0.996964i	0.866900	−	0.498482i	$-0.166109\pi$
$20$	2.89228			0.144614
$21$			32.5921i			1.55200i
$22$	11.7350	−	16.1232i	0.533408	−	0.732871i
$23$	−4.79583			−0.208514
$23$	−4.79583			−0.208514
$24$		−	20.6253i		−	0.859388i
$25$	−8.56793			−0.342717
$26$	40.2274			1.54721
$27$	29.3845			1.08832
$28$		−	9.63421i		−	0.344079i
$29$			44.4146i			1.53154i	0.643115	+	0.765769i	$0.277642\pi$
$29$			44.4146i			1.53154i	−0.643115	+	0.765769i	$0.722358\pi$
$30$		−	17.7379i		−	0.591264i
$31$	58.9192			1.90062			0.950310	−	0.311305i	$-0.100766\pi$
$31$	58.9192			1.90062			0.950310	+	0.311305i	$0.100766\pi$
$32$			11.2708i			0.352212i
$33$	21.4671	+	15.6245i	0.650518	+	0.473469i
$34$	−4.56579			−0.134288
$35$		−	54.7354i		−	1.56387i
$36$	−2.26456			−0.0629045
$37$	27.8878			0.753725			0.376863	−	0.926269i	$-0.377003\pi$
$37$	27.8878			0.753725			0.376863	+	0.926269i	$0.377003\pi$
$38$	34.3400			0.903683
$39$			53.5605i			1.37335i
$40$			34.6383i			0.865957i
$41$		−	35.5308i		−	0.866604i	−0.901249	−	0.433302i	$-0.857348\pi$
$41$		−	35.5308i		−	0.866604i	0.901249	−	0.433302i	$-0.142652\pi$
$42$	−59.0852			−1.40679
$43$		−	23.8456i		−	0.554548i	−0.960791	−	0.277274i	$-0.910569\pi$
$43$		−	23.8456i		−	0.554548i	0.960791	−	0.277274i	$-0.0894309\pi$
$44$	−6.34568	−	4.61860i	−0.144220	−	0.104968i
$45$	−12.8658			−0.285906
$46$		−	8.69422i		−	0.189005i
$47$	−18.3044			−0.389455			−0.194727	−	0.980857i	$-0.562382\pi$
$47$	−18.3044			−0.389455			−0.194727	+	0.980857i	$0.562382\pi$
$48$	30.5022			0.635462
$49$	−133.324			−2.72090
$50$		−	15.5325i		−	0.310651i
$51$		−	6.07910i		−	0.119198i
$52$		−	15.8325i		−	0.304471i
$53$	−10.6548			−0.201034			−0.100517	−	0.994935i	$-0.532050\pi$
$53$	−10.6548			−0.201034			−0.100517	+	0.994935i	$0.532050\pi$
$54$			53.2703i			0.986488i
$55$	−36.0520	−	26.2399i	−0.655492	−	0.477089i
$56$	115.380			2.06037
$57$			45.7218i			0.802136i
$58$	−80.5180			−1.38824
$59$	12.3620			0.209526			0.104763	−	0.994497i	$-0.466592\pi$
$59$	12.3620			0.209526			0.104763	+	0.994497i	$0.466592\pi$
$60$	−6.98121			−0.116353
$61$			33.3369i			0.546507i	0.961942	+	0.273253i	$0.0880998\pi$
$61$			33.3369i			0.546507i	−0.961942	+	0.273253i	$0.911900\pi$
$62$			106.813i			1.72279i
$63$			42.8560i			0.680254i
$64$	−70.9801			−1.10906
$65$		−	89.9500i		−	1.38385i
$66$	−28.3252	+	38.9171i	−0.429169	+	0.589653i
$67$	97.8030			1.45975			0.729873	−	0.683582i	$-0.239579\pi$
$67$	97.8030			1.45975			0.729873	+	0.683582i	$0.239579\pi$
$68$			1.79698i			0.0264262i
$69$	11.5759			0.167766
$70$	99.2281			1.41754
$71$	−92.8328			−1.30750			−0.653752	−	0.756709i	$-0.726806\pi$
$71$	−92.8328			−1.30750			−0.653752	+	0.756709i	$0.726806\pi$
$72$		−	27.1206i		−	0.376676i
$73$			59.0459i			0.808848i	0.914572	+	0.404424i	$0.132528\pi$
$73$			59.0459i			0.808848i	−0.914572	+	0.404424i	$0.867472\pi$
$74$			50.5570i			0.683203i
$75$	20.6807			0.275743
$76$		−	13.5154i		−	0.177834i
$77$	−87.4053	+	120.090i	−1.13513	+	1.55961i
$78$	−97.0983			−1.24485
$79$		−	82.0385i		−	1.03846i	−0.854634	−	0.519231i	$-0.826218\pi$
$79$		−	82.0385i		−	1.03846i	0.854634	−	0.519231i	$-0.173782\pi$
$80$	−51.2256			−0.640320
$81$	−42.3617			−0.522984
$82$	64.4127			0.785521
$83$			26.5309i			0.319649i	0.987145	+	0.159824i	$0.0510928\pi$
$83$			26.5309i			0.319649i	−0.987145	+	0.159824i	$0.948907\pi$
$84$			23.2545i			0.276839i
$85$			10.2093i			0.120109i
$86$	43.2289			0.502662
$87$		−	107.205i		−	1.23224i
$88$	55.3129	−	75.9966i	0.628555	−	0.863597i
$89$	28.0260			0.314899			0.157450	−	0.987527i	$-0.449673\pi$
$89$	28.0260			0.314899			0.157450	+	0.987527i	$0.449673\pi$
$90$		−	23.3240i		−	0.259155i
$91$	−299.624			−3.29257
$92$	−3.42183			−0.0371938
$93$	−142.216			−1.52920
$94$		−	33.1835i		−	0.353016i
$95$		−	76.7855i		−	0.808268i
$96$		−	27.2047i		−	0.283382i
$97$	54.0964			0.557694			0.278847	−	0.960335i	$-0.410048\pi$
$97$	54.0964			0.557694			0.278847	+	0.960335i	$0.410048\pi$
$98$		−	241.699i		−	2.46632i
$99$	28.2275	+	20.5450i	0.285127	+	0.207525i
$100$	−6.11322			−0.0611322
$101$		−	133.004i		−	1.31687i	−0.752638	−	0.658435i	$-0.771219\pi$
$101$		−	133.004i		−	1.31687i	0.752638	−	0.658435i	$-0.228781\pi$
$102$	11.0206			0.108045
$103$	79.4892			0.771740			0.385870	−	0.922553i	$-0.373901\pi$
$103$	79.4892			0.771740			0.385870	+	0.922553i	$0.373901\pi$
$104$	189.612			1.82319
$105$			132.117i			1.25826i
$106$		−	19.3158i		−	0.182225i
$107$			56.2129i			0.525354i	0.964884	+	0.262677i	$0.0846054\pi$
$107$			56.2129i			0.525354i	−0.964884	+	0.262677i	$0.915395\pi$
$108$	20.9659			0.194129
$109$			85.6467i			0.785750i	0.919592	+	0.392875i	$0.128519\pi$
$109$			85.6467i			0.785750i	−0.919592	+	0.392875i	$0.871481\pi$
$110$	47.5695	−	65.3577i	0.432450	−	0.594161i
$111$	−67.3139			−0.606432
$112$			170.633i			1.52351i
$113$	60.9071			0.539001			0.269500	−	0.963000i	$-0.413141\pi$
$113$	60.9071			0.539001			0.269500	+	0.963000i	$0.413141\pi$
$114$	−82.8876			−0.727084
$115$	−19.4406			−0.169049
$116$			31.6899i			0.273189i
$117$			70.4278i			0.601947i
$118$			22.4107i			0.189921i
$119$	34.0072			0.285775
$120$		−	83.6077i		−	0.696731i
$121$	37.1966	+	115.141i	0.307410	+	0.951577i
$122$	−60.4355			−0.495373
$123$			85.7620i			0.697252i
$124$	42.0389			0.339023
$125$	−136.073			−1.08858
$126$	−77.6923			−0.616606
$127$			0.909716i			0.00716312i	0.999994	+	0.00358156i	$0.00114005\pi$
$127$			0.909716i			0.00716312i	−0.999994	+	0.00358156i	$0.998860\pi$
$128$		−	83.5946i		−	0.653083i
$129$			57.5569i			0.446177i
$130$	163.068			1.25437
$131$			31.2111i			0.238253i	0.992879	+	0.119126i	$0.0380093\pi$
$131$			31.2111i			0.238253i	−0.992879	+	0.119126i	$0.961991\pi$
$132$	15.3168	+	11.1481i	0.116036	+	0.0844552i
$133$	−255.773			−1.92311
$134$			177.304i			1.32317i
$135$	119.115			0.882330
$136$	−21.5209			−0.158242
$137$	200.413			1.46287			0.731433	−	0.681914i	$-0.238852\pi$
$137$	200.413			1.46287			0.731433	+	0.681914i	$0.238852\pi$
$138$			20.9856i			0.152069i
$139$		−	116.474i		−	0.837939i	−0.908000	−	0.418969i	$-0.862391\pi$
$139$		−	116.474i		−	0.837939i	0.908000	−	0.418969i	$-0.137609\pi$
$140$		−	39.0537i		−	0.278955i
$141$	44.1820			0.313347
$142$		−	168.294i		−	1.18517i
$143$	−143.638	+	197.351i	−1.00446	+	1.38007i
$144$	40.1080			0.278527
$145$			180.041i			1.24166i
$146$	−107.043			−0.733168
$147$	321.809			2.18918
$148$	19.8980			0.134446
$149$		−	218.936i		−	1.46937i	−0.678409	−	0.734685i	$-0.737330\pi$
$149$		−	218.936i		−	1.46937i	0.678409	−	0.734685i	$-0.262670\pi$
$150$			37.4915i			0.249943i
$151$			3.91292i			0.0259134i	0.999916	+	0.0129567i	$0.00412436\pi$
$151$			3.91292i			0.0259134i	−0.999916	+	0.0129567i	$0.995876\pi$
$152$	161.861			1.06488
$153$		−	7.99354i		−	0.0522454i
$154$	−217.707	−	158.454i	−1.41368	−	1.02893i
$155$	238.838			1.54089
$156$			38.2155i			0.244971i
$157$	−14.2337			−0.0906603			−0.0453301	−	0.998972i	$-0.514434\pi$
$157$	−14.2337			−0.0906603			−0.0453301	+	0.998972i	$0.514434\pi$
$158$	148.725			0.941298
$159$	25.7179			0.161748
$160$			45.6878i			0.285549i
$161$			64.7569i			0.402217i
$162$		−	76.7962i		−	0.474051i
$163$	117.514			0.720947			0.360474	−	0.932769i	$-0.382615\pi$
$163$	117.514			0.720947			0.360474	+	0.932769i	$0.382615\pi$
$164$		−	25.3512i		−	0.154581i
$165$	87.0201	+	63.3362i	0.527395	+	0.383856i
$166$	−48.0970			−0.289741
$167$		−	154.210i		−	0.923411i	−0.887033	−	0.461705i	$-0.847238\pi$
$167$		−	154.210i		−	0.923411i	0.887033	−	0.461705i	$-0.152762\pi$
$168$	−278.498			−1.65773
$169$	−323.390			−1.91355
$170$	−18.5081			−0.108871
$171$			60.1205i			0.351582i
$172$		−	17.0138i		−	0.0989176i
$173$		−	34.9790i		−	0.202191i	−0.994877	−	0.101095i	$-0.967765\pi$
$173$		−	34.9790i		−	0.202191i	0.994877	−	0.101095i	$-0.0322347\pi$
$174$	194.349			1.11695
$175$			115.690i			0.661088i
$176$	112.389	+	81.8007i	0.638575	+	0.464777i
$177$	−29.8386			−0.168580
$178$			50.8076i			0.285436i
$179$	21.6631			0.121023			0.0605116	−	0.998167i	$-0.480727\pi$
$179$	21.6631			0.121023			0.0605116	+	0.998167i	$0.480727\pi$
$180$	−9.17974			−0.0509985
$181$	−185.090			−1.02259			−0.511297	−	0.859404i	$-0.670835\pi$
$181$	−185.090			−1.02259			−0.511297	+	0.859404i	$0.670835\pi$
$182$		−	543.180i		−	2.98450i
$183$		−	80.4666i		−	0.439708i
$184$		−	40.9802i		−	0.222719i
$185$	113.048			0.611068
$186$		−	257.818i		−	1.38612i
$187$	16.3029	−	22.3992i	0.0871814	−	0.119782i
$188$	−13.0602			−0.0694691
$189$		−	396.772i		−	2.09932i
$190$	139.202			0.732643
$191$	49.3509			0.258382			0.129191	−	0.991620i	$-0.458762\pi$
$191$	49.3509			0.258382			0.129191	+	0.991620i	$0.458762\pi$
$192$	171.327			0.892330
$193$			334.290i			1.73207i	0.499981	+	0.866036i	$0.333340\pi$
$193$			334.290i			1.73207i	−0.499981	+	0.866036i	$0.666660\pi$
$194$			98.0697i			0.505514i
$195$			217.116i			1.11341i
$196$	−95.1267			−0.485341
$197$			94.5191i			0.479792i	0.970799	+	0.239896i	$0.0771134\pi$
$197$			94.5191i			0.479792i	−0.970799	+	0.239896i	$0.922887\pi$
$198$	−37.2454	+	51.1729i	−0.188108	+	0.258449i
$199$	232.703			1.16936			0.584680	−	0.811264i	$-0.301220\pi$
$199$	232.703			1.16936			0.584680	+	0.811264i	$0.301220\pi$
$200$		−	73.2126i		−	0.366063i
$201$	−236.071			−1.17448
$202$	241.119			1.19366
$203$	599.719			2.95428
$204$		−	4.33745i		−	0.0212620i
$205$		−	144.029i		−	0.702582i
$206$			144.104i			0.699532i
$207$	15.2214			0.0735331
$208$			280.412i			1.34813i
$209$	−122.616	+	168.468i	−0.586682	+	0.806065i
$210$	−239.511			−1.14053
$211$			24.8409i			0.117729i	0.998266	+	0.0588647i	$0.0187481\pi$
$211$			24.8409i			0.117729i	−0.998266	+	0.0588647i	$0.981252\pi$
$212$	−7.60222			−0.0358595
$213$	224.074			1.05199
$214$	−101.907			−0.476200
$215$		−	96.6615i		−	0.449588i
$216$			251.090i			1.16245i
$217$		−	795.571i		−	3.66623i
$218$	−155.266			−0.712231
$219$		−	142.521i		−	0.650782i
$220$	−25.7232	−	18.7222i	−0.116923	−	0.0851008i
$221$	55.8862			0.252879
$222$		−	122.031i		−	0.549691i
$223$	45.9524			0.206065			0.103032	−	0.994678i	$-0.467145\pi$
$223$	45.9524			0.206065			0.103032	+	0.994678i	$0.467145\pi$
$224$	152.186			0.679403
$225$	27.1935			0.120860
$226$			110.417i			0.488569i
$227$		−	31.3188i		−	0.137968i	−0.997618	−	0.0689841i	$-0.978024\pi$
$227$		−	31.3188i		−	0.137968i	0.997618	−	0.0689841i	$-0.0219758\pi$
$228$			32.6225i			0.143081i
$229$	−133.525			−0.583080			−0.291540	−	0.956559i	$-0.594168\pi$
$229$	−133.525			−0.583080			−0.291540	+	0.956559i	$0.594168\pi$
$230$		−	35.2433i		−	0.153232i
$231$	210.973	−	289.865i	0.913305	−	1.25483i
$232$	−379.521			−1.63587
$233$		−	249.308i		−	1.06999i	−0.844855	−	0.534995i	$-0.820314\pi$
$233$		−	249.308i		−	1.06999i	0.844855	−	0.534995i	$-0.179686\pi$
$234$	−127.677			−0.545626
$235$	−74.1995			−0.315743
$236$	8.82030			0.0373742
$237$			198.019i			0.835525i
$238$			61.6507i			0.259037i
$239$			306.906i			1.28413i	0.766652	+	0.642063i	$0.221921\pi$
$239$			306.906i			1.28413i	−0.766652	+	0.642063i	$0.778079\pi$
$240$	123.645			0.515188
$241$			78.8990i			0.327382i	0.986512	+	0.163691i	$0.0523400\pi$
$241$			78.8990i			0.327382i	−0.986512	+	0.163691i	$0.947660\pi$
$242$	−208.735	+	67.4326i	−0.862543	+	0.278647i
$243$	−162.211			−0.667534
$244$			23.7859i			0.0974833i
$245$	−540.449			−2.20591
$246$	−155.475			−0.632014
$247$	−420.327			−1.70173
$248$			503.463i			2.03009i
$249$		−	64.0385i		−	0.257183i
$250$		−	246.682i		−	0.986728i
$251$	209.252			0.833671			0.416836	−	0.908982i	$-0.363139\pi$
$251$	209.252			0.833671			0.416836	+	0.908982i	$0.363139\pi$
$252$			30.5778i			0.121340i
$253$	42.6528	+	31.0441i	0.168588	+	0.122704i
$254$	−1.64920			−0.00649290
$255$		−	24.6426i		−	0.0966375i
$256$	−132.374			−0.517087
$257$	463.573			1.80379			0.901893	−	0.431960i	$-0.142178\pi$
$257$	463.573			1.80379			0.901893	+	0.431960i	$0.142178\pi$
$258$	−104.343			−0.404431
$259$		−	376.562i		−	1.45391i
$260$		−	64.1794i		−	0.246844i
$261$		−	140.966i		−	0.540101i
$262$	−56.5817			−0.215961
$263$		−	167.850i		−	0.638214i	−0.947719	−	0.319107i	$-0.896617\pi$
$263$		−	167.850i		−	0.638214i	0.947719	−	0.319107i	$-0.103383\pi$
$264$	−133.511	+	183.436i	−0.505722	+	0.694832i
$265$	−43.1909			−0.162984
$266$		−	463.683i		−	1.74317i
$267$	−67.6475			−0.253361
$268$	69.7825			0.260383
$269$	−341.773			−1.27053			−0.635265	−	0.772294i	$-0.719109\pi$
$269$	−341.773			−1.27053			−0.635265	+	0.772294i	$0.719109\pi$
$270$			215.939i			0.799775i
$271$			96.2045i			0.354998i	0.984121	+	0.177499i	$0.0568007\pi$
$271$			96.2045i			0.354998i	−0.984121	+	0.177499i	$0.943199\pi$
$272$		−	31.8266i		−	0.117010i
$273$	723.214			2.64913
$274$			363.322i			1.32599i
$275$	76.2008	+	55.4615i	0.277094	+	0.201678i
$276$	8.25940			0.0299254
$277$		−	177.374i		−	0.640341i	−0.947360	−	0.320170i	$-0.896260\pi$
$277$		−	177.374i		−	0.640341i	0.947360	−	0.320170i	$-0.103740\pi$
$278$	211.151			0.759537
$279$	−187.002			−0.670259
$280$	467.712			1.67040
$281$			160.955i			0.572795i	0.958111	+	0.286397i	$0.0924577\pi$
$281$			160.955i			0.572795i	−0.958111	+	0.286397i	$0.907542\pi$
$282$			80.0962i			0.284029i
$283$			53.6629i			0.189622i	0.995495	+	0.0948108i	$0.0302246\pi$
$283$			53.6629i			0.189622i	−0.995495	+	0.0948108i	$0.969775\pi$
$284$	−66.2363			−0.233226
$285$			185.340i			0.650316i
$286$	−357.771	−	260.398i	−1.25095	−	0.910482i
$287$	−479.763			−1.67165
$288$		−	35.7720i		−	0.124208i
$289$	282.657			0.978052
$290$	−326.392			−1.12549
$291$	−130.574			−0.448709
$292$			42.1293i			0.144278i
$293$			308.858i			1.05412i	0.849827	+	0.527062i	$0.176706\pi$
$293$			308.858i			1.05412i	−0.849827	+	0.527062i	$0.823294\pi$
$294$			583.398i			1.98435i
$295$	50.1112			0.169869
$296$			238.301i			0.805070i
$297$	−261.338	−	190.211i	−0.879925	−	0.640440i
$298$	396.903			1.33189
$299$			106.419i			0.355916i
$300$	14.7557			0.0491857
$301$	−321.980			−1.06970
$302$	−7.09361			−0.0234888
$303$			321.036i			1.05953i
$304$			239.372i			0.787409i
$305$			135.136i			0.443069i
$306$	14.4913			0.0473570
$307$			167.497i			0.545594i	0.962072	+	0.272797i	$0.0879488\pi$
$307$			167.497i			0.545594i	−0.962072	+	0.272797i	$0.912051\pi$
$308$	−62.3637	+	85.6840i	−0.202480	+	0.278195i
$309$	−191.866			−0.620926
$310$			432.982i			1.39672i
$311$	−26.0234			−0.0836764			−0.0418382	−	0.999124i	$-0.513321\pi$
$311$	−26.0234			−0.0836764			−0.0418382	+	0.999124i	$0.513321\pi$
$312$	−457.673			−1.46690
$313$	290.728			0.928845			0.464422	−	0.885614i	$-0.346262\pi$
$313$	290.728			0.928845			0.464422	+	0.885614i	$0.346262\pi$
$314$		−	25.8038i		−	0.0821777i
$315$			173.723i			0.551502i
$316$		−	58.5345i		−	0.185236i
$317$	390.940			1.23325			0.616625	−	0.787257i	$-0.288500\pi$
$317$	390.940			1.23325			0.616625	+	0.787257i	$0.288500\pi$
$318$			46.6233i			0.146614i
$319$	287.503	−	395.011i	0.901262	−	1.23828i
$320$	−287.729			−0.899152
$321$		−	135.683i		−	0.422689i
$322$	−117.396			−0.364583
$323$	47.7070			0.147700
$324$	−30.2251			−0.0932873
$325$			190.121i			0.584988i
$326$			213.038i			0.653492i
$327$		−	206.729i		−	0.632198i
$328$	303.609			0.925638
$329$			247.159i			0.751244i
$330$	−114.820	+	157.756i	−0.347940	+	0.478049i
$331$	28.1447			0.0850292			0.0425146	−	0.999096i	$-0.486463\pi$
$331$	28.1447			0.0850292			0.0425146	+	0.999096i	$0.486463\pi$
$332$			18.9298i			0.0570174i
$333$	−88.5125			−0.265803
$334$	279.562			0.837012
$335$	396.459			1.18346
$336$		−	411.863i		−	1.22578i
$337$			92.6692i			0.274983i	0.990503	+	0.137491i	$0.0439039\pi$
$337$			92.6692i			0.274983i	−0.990503	+	0.137491i	$0.956096\pi$
$338$		−	586.265i		−	1.73451i
$339$	−147.014			−0.433669
$340$			7.28434i			0.0214245i
$341$	−524.011	−	381.393i	−1.53669	−	1.11845i
$342$	−108.991			−0.318686
$343$			1138.60i			3.31955i
$344$	203.759			0.592324
$345$	46.9245			0.136013
$346$	63.4123			0.183273
$347$		−	684.490i		−	1.97259i	−0.164978	−	0.986297i	$-0.552755\pi$
$347$		−	684.490i		−	1.97259i	0.164978	−	0.986297i	$-0.447245\pi$
$348$		−	76.4910i		−	0.219802i
$349$			423.915i			1.21466i	0.794451	+	0.607328i	$0.207759\pi$
$349$			423.915i			1.21466i	−0.794451	+	0.607328i	$0.792241\pi$
$350$	−209.732			−0.599234
$351$		−	652.039i		−	1.85766i
$352$	72.9575	−	100.239i	0.207266	−	0.284770i
$353$	−408.890			−1.15833			−0.579164	−	0.815211i	$-0.696621\pi$
$353$	−408.890			−1.15833			−0.579164	+	0.815211i	$0.696621\pi$
$354$		−	54.0936i		−	0.152807i
$355$	−376.312			−1.06003
$356$	19.9966			0.0561702
$357$	−82.0846			−0.229929
$358$			39.2725i			0.109700i
$359$		−	289.903i		−	0.807528i	−0.914863	−	0.403764i	$-0.867702\pi$
$359$		−	289.903i		−	0.807528i	0.914863	−	0.403764i	$-0.132298\pi$
$360$		−	109.938i		−	0.305382i
$361$	2.18893			0.00606353
$362$		−	335.544i		−	0.926916i
$363$	−89.7828	−	277.920i	−0.247336	−	0.765619i
$364$	−213.782			−0.587313
$365$			239.351i			0.655757i
$366$	145.875			0.398567
$367$	492.366			1.34160			0.670799	−	0.741639i	$-0.265951\pi$
$367$	492.366			1.34160			0.670799	+	0.741639i	$0.265951\pi$
$368$	60.6045			0.164686
$369$			112.770i			0.305610i
$370$			204.941i			0.553893i
$371$			143.869i			0.387788i
$372$	−101.471			−0.272771
$373$			453.359i			1.21544i	0.794151	+	0.607721i	$0.207916\pi$
$373$			453.359i			1.21544i	−0.794151	+	0.607721i	$0.792084\pi$
$374$	40.6069	+	29.5551i	0.108575	+	0.0790243i
$375$	328.444			0.875849
$376$		−	156.410i		−	0.415985i
$377$	985.555			2.61420
$378$	719.296			1.90290
$379$	−296.860			−0.783272			−0.391636	−	0.920120i	$-0.628091\pi$
$379$	−296.860			−0.783272			−0.391636	+	0.920120i	$0.628091\pi$
$380$		−	54.7865i		−	0.144175i
$381$		−	2.19582i		−	0.00576330i
$382$			89.4667i			0.234206i
$383$	−225.597			−0.589025			−0.294513	−	0.955648i	$-0.595157\pi$
$383$	−225.597			−0.589025			−0.294513	+	0.955648i	$0.595157\pi$
$384$			201.775i			0.525457i
$385$	−354.310	+	486.801i	−0.920287	+	1.26442i
$386$	−606.024			−1.57001
$387$			75.6828i			0.195563i
$388$	38.5978			0.0994789
$389$	758.261			1.94926			0.974629	−	0.223826i	$-0.0718547\pi$
$389$	758.261			1.94926			0.974629	+	0.223826i	$0.0718547\pi$
$390$	−393.602			−1.00924
$391$		−	12.0785i		−	0.0308913i
$392$		−	1139.25i		−	2.90625i
$393$		−	75.3354i		−	0.191693i
$394$	−171.351			−0.434901
$395$		−	332.555i		−	0.841912i
$396$	20.1404	+	14.6588i	0.0508595	+	0.0370173i
$397$	742.992			1.87152			0.935758	−	0.352642i	$-0.114717\pi$
$397$	742.992			1.87152			0.935758	+	0.352642i	$0.114717\pi$
$398$			421.860i			1.05995i
$399$	617.369			1.54729
$400$	108.272			0.270680
$401$	−156.339			−0.389873			−0.194937	−	0.980816i	$-0.562450\pi$
$401$	−156.339			−0.389873			−0.194937	+	0.980816i	$0.562450\pi$
$402$		−	427.966i		−	1.06459i
$403$		−	1307.41i		−	3.24419i
$404$		−	94.8984i		−	0.234897i
$405$	−171.719			−0.423998
$406$			1087.21i			2.67786i
$407$	−248.027	−	180.522i	−0.609402	−	0.443544i
$408$	51.9457			0.127318
$409$		−	51.2499i		−	0.125305i	−0.998035	−	0.0626527i	$-0.980044\pi$
$409$		−	51.2499i		−	0.125305i	0.998035	−	0.0626527i	$-0.0199560\pi$
$410$	261.107			0.636845
$411$	−483.743			−1.17699
$412$	56.7156			0.137659
$413$		−	166.921i		−	0.404167i
$414$			27.5944i			0.0666530i
$415$			107.547i			0.259149i
$416$	250.097			0.601195
$417$			281.136i			0.674188i
$418$	−305.410	−	222.288i	−0.730646	−	0.531789i
$419$	−363.522			−0.867595			−0.433797	−	0.901010i	$-0.642827\pi$
$419$	−363.522			−0.867595			−0.433797	+	0.901010i	$0.642827\pi$
$420$			94.2654i			0.224442i
$421$	−742.486			−1.76363			−0.881813	−	0.471600i	$-0.843677\pi$
$421$	−742.486			−1.76363			−0.881813	+	0.471600i	$0.843677\pi$
$422$	−45.0334			−0.106714
$423$	58.0958			0.137342
$424$		−	91.0450i		−	0.214729i
$425$		−	21.5787i		−	0.0507734i
$426$			406.217i			0.953562i
$427$	450.140			1.05419
$428$			40.1080i			0.0937102i
$429$	346.705	−	476.352i	0.808171	−	1.11038i
$430$	175.235			0.407523
$431$		−	302.522i		−	0.701908i	−0.936393	−	0.350954i	$-0.885857\pi$
$431$		−	302.522i		−	0.701908i	0.936393	−	0.350954i	$-0.114143\pi$
$432$	−371.330			−0.859560
$433$	103.173			0.238275			0.119137	−	0.992878i	$-0.461987\pi$
$433$	103.173			0.238275			0.119137	+	0.992878i	$0.461987\pi$
$434$	1442.27			3.32320
$435$		−	434.572i		−	0.999017i
$436$			61.1090i			0.140158i
$437$			90.8441i			0.207881i
$438$	258.373			0.589892
$439$		−	779.429i		−	1.77546i	−0.460360	−	0.887732i	$-0.652280\pi$
$439$		−	779.429i		−	1.77546i	0.460360	−	0.887732i	$-0.347720\pi$
$440$	224.219	−	308.063i	0.509589	−	0.700144i
$441$	423.153			0.959531
$442$			101.314i			0.229218i
$443$	−561.689			−1.26792			−0.633960	−	0.773366i	$-0.718572\pi$
$443$	−561.689			−1.26792			−0.633960	+	0.773366i	$0.718572\pi$
$444$	−48.0285			−0.108172
$445$	113.608			0.255298
$446$			83.3058i			0.186784i
$447$			528.454i			1.18222i
$448$			958.426i			2.13934i
$449$	−104.903			−0.233637			−0.116818	−	0.993153i	$-0.537270\pi$
$449$	−104.903			−0.233637			−0.116818	+	0.993153i	$0.537270\pi$
$450$			49.2983i			0.109552i
$451$	−229.996	+	316.001i	−0.509969	+	0.700667i
$452$	43.4573			0.0961444
$453$		−	9.44476i		−	0.0208494i
$454$	56.7769			0.125059
$455$	−1214.57			−2.66939
$456$	−390.691			−0.856778
$457$		−	366.064i		−	0.801015i	−0.916294	−	0.400507i	$-0.868834\pi$
$457$		−	366.064i		−	0.801015i	0.916294	−	0.400507i	$-0.131166\pi$
$458$		−	242.064i		−	0.528524i
$459$			74.0062i			0.161234i
$460$	−13.8709			−0.0301541
$461$			189.513i			0.411092i	0.978647	+	0.205546i	$0.0658970\pi$
$461$			189.513i			0.411092i	−0.978647	+	0.205546i	$0.934103\pi$
$462$	525.487	+	382.467i	1.13742	+	0.827852i
$463$	574.273			1.24033			0.620165	−	0.784471i	$-0.287066\pi$
$463$	574.273			1.24033			0.620165	+	0.784471i	$0.287066\pi$
$464$		−	561.264i		−	1.20962i
$465$	−576.492			−1.23977
$466$	451.962			0.969877
$467$	−756.087			−1.61903			−0.809515	−	0.587099i	$-0.800270\pi$
$467$	−756.087			−1.61903			−0.809515	+	0.587099i	$0.800270\pi$
$468$			50.2503i			0.107372i
$469$		−	1320.61i		−	2.81580i
$470$		−	134.514i		−	0.286200i
$471$	34.3563			0.0729434
$472$			105.633i			0.223799i
$473$	−154.356	+	212.076i	−0.326334	+	0.448363i
$474$	−358.983			−0.757349
$475$			162.296i			0.341676i
$476$	24.2642			0.0509752
$477$	33.8170			0.0708952
$478$	−556.381			−1.16398
$479$			492.353i			1.02788i	0.857827	+	0.513939i	$0.171814\pi$
$479$			492.353i			1.02788i	−0.857827	+	0.513939i	$0.828186\pi$
$480$		−	110.278i		−	0.229746i
$481$		−	618.828i		−	1.28654i
$482$	−143.034			−0.296750
$483$		−	156.306i		−	0.323615i
$484$	26.5398	+	82.1531i	0.0548343	+	0.169738i
$485$	219.288			0.452140
$486$		−	294.067i		−	0.605077i
$487$	564.566			1.15927			0.579636	−	0.814875i	$-0.303195\pi$
$487$	564.566			1.15927			0.579636	+	0.814875i	$0.303195\pi$
$488$	−284.863			−0.583735
$489$	−283.649			−0.580059
$490$		−	979.763i		−	1.99952i
$491$			207.819i			0.423257i	0.977350	+	0.211628i	$0.0678767\pi$
$491$			207.819i			0.423257i	−0.977350	+	0.211628i	$0.932123\pi$
$492$			61.1912i			0.124372i
$493$	−111.860			−0.226897
$494$		−	761.999i		−	1.54251i
$495$	114.425	+	83.2821i	0.231161	+	0.168247i
$496$	−744.557			−1.50112
$497$			1253.50i			2.52213i
$498$	116.094			0.233119
$499$	595.088			1.19256			0.596281	−	0.802776i	$-0.296644\pi$
$499$	595.088			1.19256			0.596281	+	0.802776i	$0.296644\pi$
$500$	−97.0879			−0.194176
$501$			372.221i			0.742957i
$502$			379.346i			0.755669i
$503$			53.6203i			0.106601i	0.998579	+	0.0533005i	$0.0169741\pi$
$503$			53.6203i			0.106601i	−0.998579	+	0.0533005i	$0.983026\pi$
$504$	−366.203			−0.726593
$505$		−	539.151i		−	1.06763i
$506$	−56.2790	+	77.3240i	−0.111223	+	0.152814i
$507$	780.580			1.53960
$508$			0.649083i			0.00127772i
$509$	−411.867			−0.809168			−0.404584	−	0.914501i	$-0.632584\pi$
$509$	−411.867			−0.809168			−0.404584	+	0.914501i	$0.632584\pi$
$510$	44.6738			0.0875956
$511$	797.281			1.56024
$512$		−	574.356i		−	1.12179i
$513$		−	556.611i		−	1.08501i
$514$			840.397i			1.63501i
$515$	322.221			0.625672
$516$			41.0669i			0.0795870i
$517$	162.794	+	118.487i	0.314882	+	0.229182i
$518$	682.659			1.31787
$519$			84.4300i			0.162678i
$520$	768.619			1.47811
$521$	448.231			0.860328			0.430164	−	0.902751i	$-0.358456\pi$
$521$	448.231			0.860328			0.430164	+	0.902751i	$0.358456\pi$
$522$	255.554			0.489567
$523$			733.316i			1.40213i	0.713096	+	0.701067i	$0.247293\pi$
$523$			733.316i			1.40213i	−0.713096	+	0.701067i	$0.752707\pi$
$524$			22.2691i			0.0424983i
$525$		−	279.246i		−	0.531898i
$526$	304.291			0.578500
$527$			148.391i			0.281576i
$528$	−271.278	−	197.445i	−0.513784	−	0.373949i
$529$	23.0000			0.0434783
$530$		−	78.2995i		−	0.147735i
$531$	−39.2354			−0.0738897
$532$	−182.494			−0.343034
$533$	−788.424			−1.47922
$534$		−	122.636i		−	0.229656i
$535$			227.867i			0.425921i
$536$			835.724i			1.55919i
$537$	−52.2891			−0.0973727
$538$		−	619.590i		−	1.15165i
$539$	1185.75	+	863.026i	2.19990	+	1.60116i
$540$	84.9883			0.157386
$541$			565.900i			1.04603i	0.852325	+	0.523013i	$0.175192\pi$
$541$			565.900i			1.04603i	−0.852325	+	0.523013i	$0.824808\pi$
$542$	−174.406			−0.321783
$543$	446.758			0.822758
$544$	−28.3860			−0.0521801
$545$			347.182i			0.637031i
$546$			1311.09i			2.40127i
$547$		−	500.147i		−	0.914345i	−0.889378	−	0.457173i	$-0.848862\pi$
$547$		−	500.147i		−	0.914345i	0.889378	−	0.457173i	$-0.151138\pi$
$548$	142.995			0.260939
$549$		−	105.807i		−	0.192727i
$550$	−100.544	+	138.142i	−0.182808	+	0.251167i
$551$	841.316			1.52689
$552$			98.9155i			0.179195i
$553$	−1107.74			−2.00315
$554$	321.557			0.580427
$555$	−272.867			−0.491652
$556$		−	83.1039i		−	0.149468i
$557$			651.935i			1.17044i	0.810874	+	0.585220i	$0.198992\pi$
$557$			651.935i			1.17044i	−0.810874	+	0.585220i	$0.801008\pi$
$558$		−	339.011i		−	0.607546i
$559$	−529.130			−0.946565
$560$			691.686i			1.23515i
$561$	−39.3510	+	54.0659i	−0.0701443	+	0.0963741i
$562$	−291.791			−0.519201
$563$			190.474i			0.338320i	0.985589	+	0.169160i	$0.0541054\pi$
$563$			190.474i			0.338320i	−0.985589	+	0.169160i	$0.945895\pi$
$564$	31.5239			0.0558934
$565$	246.896			0.436984
$566$	−97.2839			−0.171880
$567$			571.999i			1.00882i
$568$		−	793.253i		−	1.39657i
$569$		−	609.233i		−	1.07071i	−0.844627	−	0.535354i	$-0.820178\pi$
$569$		−	609.233i		−	1.07071i	0.844627	−	0.535354i	$-0.179822\pi$
$570$	−335.997			−0.589469
$571$		−	317.980i		−	0.556883i	−0.960453	−	0.278442i	$-0.910182\pi$
$571$		−	317.980i		−	0.556883i	0.960453	−	0.278442i	$-0.0898179\pi$
$572$	−102.486	+	140.810i	−0.179172	+	0.246171i
$573$	−119.120			−0.207888
$574$		−	869.748i		−	1.51524i
$575$	41.0903			0.0714614
$576$	225.282			0.391114
$577$	1030.26			1.78554			0.892771	−	0.450511i	$-0.148758\pi$
$577$	1030.26			1.78554			0.892771	+	0.450511i	$0.148758\pi$
$578$			512.420i			0.886540i
$579$		−	806.888i		−	1.39359i
$580$			128.460i			0.221482i
$581$	358.239			0.616591
$582$		−	236.714i		−	0.406726i
$583$	94.7610	+	68.9702i	0.162540	+	0.118302i
$584$	−504.545			−0.863947
$585$			285.490i			0.488017i
$586$	−559.920			−0.955494
$587$	11.5022			0.0195949			0.00979747	−	0.999952i	$-0.496881\pi$
$587$	11.5022			0.0195949			0.00979747	+	0.999952i	$0.496881\pi$
$588$	229.611			0.390495
$589$		−	1116.07i		−	1.89485i
$590$			90.8452i			0.153975i
$591$		−	228.144i		−	0.386031i
$592$	−352.416			−0.595298
$593$			110.209i			0.185851i	0.995673	+	0.0929254i	$0.0296218\pi$
$593$			110.209i			0.185851i	−0.995673	+	0.0929254i	$0.970378\pi$
$594$	344.827	−	473.772i	0.580517	−	0.797595i
$595$	137.853			0.231686
$596$		−	156.211i		−	0.262099i
$597$	−561.683			−0.940843
$598$	−192.924			−0.322615
$599$	318.539			0.531784			0.265892	−	0.964003i	$-0.414334\pi$
$599$	318.539			0.531784			0.265892	+	0.964003i	$0.414334\pi$
$600$			176.716i			0.294527i
$601$			106.752i			0.177623i	0.996048	+	0.0888117i	$0.0283069\pi$
$601$			106.752i			0.177623i	−0.996048	+	0.0888117i	$0.971693\pi$
$602$		−	583.708i		−	0.969615i
$603$	−310.414			−0.514783
$604$			2.79187i			0.00462230i
$605$	150.782	+	466.741i	0.249226	+	0.771472i
$606$	−581.997			−0.960392
$607$		−	224.285i		−	0.369498i	−0.982786	−	0.184749i	$-0.940853\pi$
$607$		−	224.285i		−	0.369498i	0.982786	−	0.184749i	$-0.0591471\pi$
$608$	213.495			0.351142
$609$	−1447.56			−2.37695
$610$	−244.984			−0.401614
$611$			406.172i			0.664766i
$612$		−	5.70340i		−	0.00931928i
$613$		−	581.363i		−	0.948390i	−0.880420	−	0.474195i	$-0.842739\pi$
$613$		−	581.363i		−	0.948390i	0.880420	−	0.474195i	$-0.157261\pi$
$614$	−303.651			−0.494546
$615$			347.649i			0.565283i
$616$	−1026.16	−	746.875i	−1.66585	−	1.21246i
$617$	128.671			0.208543			0.104272	−	0.994549i	$-0.466749\pi$
$617$	128.671			0.208543			0.104272	+	0.994549i	$0.466749\pi$
$618$		−	347.828i		−	0.562829i
$619$	566.715			0.915533			0.457767	−	0.889072i	$-0.348650\pi$
$619$	566.715			0.915533			0.457767	+	0.889072i	$0.348650\pi$
$620$	170.411			0.274856
$621$	−140.923			−0.226930
$622$		−	47.1770i		−	0.0758473i
$623$		−	378.428i		−	0.607429i
$624$		−	676.840i		−	1.08468i
$625$	−337.392			−0.539828
$626$			527.053i			0.841938i
$627$	295.964	−	406.637i	0.472032	−	0.648543i
$628$	−10.1557			−0.0161715
$629$			70.2368i			0.111664i
$630$	−314.937			−0.499901
$631$	−625.667			−0.991548			−0.495774	−	0.868452i	$-0.665116\pi$
$631$	−625.667			−0.991548			−0.495774	+	0.868452i	$0.665116\pi$
$632$	701.016			1.10920
$633$		−	59.9594i		−	0.0947227i
$634$			708.724i			1.11786i
$635$			3.68767i			0.00580736i
$636$	18.3498			0.0288518
$637$			2958.44i			4.64434i
$638$	716.104	+	521.205i	1.12242	+	0.816936i
$639$	294.640			0.461095
$640$		−	338.863i		−	0.529474i
$641$	172.633			0.269318			0.134659	−	0.990892i	$-0.457006\pi$
$641$	172.633			0.269318			0.134659	+	0.990892i	$0.457006\pi$
$642$	245.976			0.383140
$643$	−413.921			−0.643735			−0.321867	−	0.946785i	$-0.604311\pi$
$643$	−413.921			−0.643735			−0.321867	+	0.946785i	$0.604311\pi$
$644$			46.2041i			0.0717454i
$645$			233.315i			0.361729i
$646$			86.4867i			0.133880i
$647$	−119.849			−0.185237			−0.0926187	−	0.995702i	$-0.529524\pi$
$647$	−119.849			−0.185237			−0.0926187	+	0.995702i	$0.529524\pi$
$648$		−	361.979i		−	0.558610i
$649$	−109.944	−	80.0212i	−0.169406	−	0.123299i
$650$	−344.665			−0.530254
$651$			1920.30i			2.94977i
$652$	83.8466			0.128599
$653$	−785.724			−1.20325			−0.601626	−	0.798778i	$-0.705480\pi$
$653$	−785.724			−1.20325			−0.601626	+	0.798778i	$0.705480\pi$
$654$	374.772			0.573046
$655$			126.519i			0.193158i
$656$			448.999i			0.684450i
$657$		−	187.404i		−	0.285242i
$658$	−448.068			−0.680954
$659$			1034.86i			1.57035i	0.619275	+	0.785174i	$0.287427\pi$
$659$			1034.86i			1.57035i	−0.619275	+	0.785174i	$0.712573\pi$
$660$	62.0889	+	45.1904i	0.0940741	+	0.0684703i
$661$	−519.935			−0.786589			−0.393294	−	0.919413i	$-0.628665\pi$
$661$	−519.935			−0.786589			−0.393294	+	0.919413i	$0.628665\pi$
$662$			51.0226i			0.0770734i
$663$	−134.895			−0.203461
$664$	−226.705			−0.341424
$665$	−1036.81			−1.55912
$666$		−	160.462i		−	0.240933i
$667$		−	213.005i		−	0.319348i
$668$		−	110.029i		−	0.164714i
$669$	−110.917			−0.165795
$670$			718.729i			1.07273i
$671$	215.795	−	296.489i	0.321602	−	0.441862i
$672$	−367.338			−0.546634
$673$			478.298i			0.710696i	0.934734	+	0.355348i	$0.115638\pi$
$673$			478.298i			0.710696i	−0.934734	+	0.355348i	$0.884362\pi$
$674$	−167.997			−0.249254
$675$	−251.764			−0.372984
$676$	−230.739			−0.341330
$677$			837.879i			1.23764i	0.785535	+	0.618818i	$0.212388\pi$
$677$			837.879i			1.23764i	−0.785535	+	0.618818i	$0.787612\pi$
$678$		−	266.517i		−	0.393093i
$679$		−	730.449i		−	1.07577i
$680$	−87.2381			−0.128291
$681$			75.5953i			0.111006i
$682$	691.416	−	949.964i	1.01381	−	1.39291i
$683$	−442.274			−0.647546			−0.323773	−	0.946135i	$-0.604951\pi$
$683$	−442.274			−0.647546			−0.323773	+	0.946135i	$0.604951\pi$
$684$			42.8960i			0.0627135i
$685$	812.402			1.18599
$686$	−2064.14			−3.00895
$687$	322.295			0.469134
$688$			301.334i			0.437986i
$689$			236.429i			0.343148i
$690$			85.0681i			0.123287i
$691$	−492.175			−0.712265			−0.356133	−	0.934435i	$-0.615905\pi$
$691$	−492.175			−0.712265			−0.356133	+	0.934435i	$0.615905\pi$
$692$		−	24.9575i		−	0.0360658i
$693$	277.413	−	381.149i	0.400308	−	0.549999i
$694$	1240.89			1.78803
$695$		−	472.143i		−	0.679342i
$696$	916.065			1.31619
$697$	89.4858			0.128387
$698$	−768.503			−1.10101
$699$			601.763i			0.860891i
$700$			82.5452i			0.117922i
$701$			915.854i			1.30650i	0.757144	+	0.653248i	$0.226594\pi$
$701$			915.854i			1.30650i	−0.757144	+	0.653248i	$0.773406\pi$
$702$	1182.06			1.68385
$703$		−	528.260i		−	0.751437i
$704$	631.277	+	459.465i	0.896701	+	0.652649i
$705$	179.098			0.254040
$706$		−	741.265i		−	1.04995i
$707$	−1795.92			−2.54019
$708$	−21.2899			−0.0300705
$709$	−310.817			−0.438389			−0.219194	−	0.975681i	$-0.570343\pi$
$709$	−310.817			−0.438389			−0.219194	+	0.975681i	$0.570343\pi$
$710$		−	682.204i		−	0.960851i
$711$			260.380i			0.366216i
$712$			239.481i			0.336350i
$713$	−282.567			−0.396307
$714$		−	148.809i		−	0.208415i
$715$	−582.260	+	799.990i	−0.814349	+	1.11887i
$716$	15.4567			0.0215875
$717$		−	740.791i		−	1.03318i
$718$	525.556			0.731972
$719$	−974.552			−1.35543			−0.677713	−	0.735326i	$-0.737029\pi$
$719$	−974.552			−1.35543			−0.677713	+	0.735326i	$0.737029\pi$
$720$	162.584			0.225811
$721$		−	1073.32i		−	1.48866i
$722$			3.96825i			0.00549620i
$723$		−	190.441i		−	0.263404i
$724$	−132.062			−0.182406
$725$		−	380.541i		−	0.524884i
$726$	503.832	−	162.765i	0.693984	−	0.224194i
$727$	−32.3511			−0.0444995			−0.0222498	−	0.999752i	$-0.507083\pi$
$727$	−32.3511			−0.0444995			−0.0222498	+	0.999752i	$0.507083\pi$
$728$		−	2560.28i		−	3.51686i
$729$	772.789			1.06007
$730$	−433.913			−0.594401
$731$	60.0561			0.0821561
$732$		−	57.4129i		−	0.0784330i
$733$			174.275i			0.237756i	0.992909	+	0.118878i	$0.0379298\pi$
$733$			174.275i			0.237756i	−0.992909	+	0.118878i	$0.962070\pi$
$734$			892.597i			1.21607i
$735$	1304.50			1.77483
$736$		−	54.0528i		−	0.0734412i
$737$	−869.833	−	633.094i	−1.18023	−	0.859015i
$738$	−204.438			−0.277016
$739$		−	839.164i		−	1.13554i	−0.823187	−	0.567770i	$-0.807806\pi$
$739$		−	839.164i		−	1.13554i	0.823187	−	0.567770i	$-0.192194\pi$
$740$	80.6595			0.108999
$741$	1014.56			1.36918
$742$	−260.816			−0.351504
$743$		−	928.544i		−	1.24972i	−0.780736	−	0.624861i	$-0.785156\pi$
$743$		−	928.544i		−	1.24972i	0.780736	−	0.624861i	$-0.214844\pi$
$744$		−	1215.23i		−	1.63337i
$745$		−	887.490i		−	1.19126i
$746$	−821.882			−1.10172
$747$		−	84.2056i		−	0.112725i
$748$	11.6321	−	15.9819i	0.0155510	−	0.0213661i
$749$	759.028			1.01339
$750$			595.426i			0.793901i
$751$	−632.961			−0.842825			−0.421412	−	0.906869i	$-0.638465\pi$
$751$	−632.961			−0.842825			−0.421412	+	0.906869i	$0.638465\pi$
$752$	231.311			0.307594
$753$	−505.078			−0.670755
$754$			1786.68i			2.36961i
$755$			15.8616i			0.0210087i
$756$		−	283.097i		−	0.374467i
$757$	−721.693			−0.953360			−0.476680	−	0.879077i	$-0.658160\pi$
$757$	−721.693			−0.953360			−0.476680	+	0.879077i	$0.658160\pi$
$758$		−	538.169i		−	0.709986i
$759$	−102.953	−	74.9324i	−0.135642	−	0.0987252i
$760$	656.129			0.863328
$761$		−	696.480i		−	0.915217i	−0.889154	−	0.457608i	$-0.848706\pi$
$761$		−	696.480i		−	0.915217i	0.889154	−	0.457608i	$-0.151294\pi$
$762$	3.98073			0.00522405
$763$	1156.47			1.51568
$764$	35.2119			0.0460889
$765$		−	32.4030i		−	0.0423569i
$766$		−	408.978i		−	0.533913i
$767$		−	274.311i		−	0.357642i
$768$	319.517			0.416037
$769$		−	1108.76i		−	1.44183i	−0.693026	−	0.720913i	$-0.743723\pi$
$769$		−	1108.76i		−	1.44183i	0.693026	−	0.720913i	$-0.256277\pi$
$770$	−882.507	−	642.319i	−1.14611	−	0.834180i
$771$	−1118.94			−1.45129
$772$			238.516i			0.308959i
$773$	−217.553			−0.281439			−0.140720	−	0.990049i	$-0.544942\pi$
$773$	−217.553			−0.281439			−0.140720	+	0.990049i	$0.544942\pi$
$774$	−137.203			−0.177265
$775$	−504.816			−0.651375
$776$			462.252i			0.595685i
$777$			908.922i			1.16978i
$778$			1374.63i			1.76688i
$779$	−673.035			−0.863973
$780$			154.912i			0.198605i
$781$	825.629	+	600.921i	1.05714	+	0.769425i
$782$	21.8968			0.0280010
$783$			1305.10i			1.66680i
$784$	1684.80			2.14898
$785$	−57.6983			−0.0735010
$786$	136.573			0.173757
$787$		−	11.2866i		−	0.0143413i	−0.999974	−	0.00717066i	$-0.997717\pi$
$787$		−	11.2866i		−	0.0143413i	0.999974	−	0.00717066i	$-0.00228251\pi$
$788$			67.4394i			0.0855830i
$789$			405.147i			0.513494i
$790$	602.880			0.763139
$791$		−	822.413i		−	1.03971i
$792$	−175.556	+	241.203i	−0.221662	+	0.304550i
$793$	739.742			0.932840
$794$			1346.95i			1.69641i
$795$	104.251			0.131134
$796$	166.034			0.208585
$797$	−90.7566			−0.113873			−0.0569364	−	0.998378i	$-0.518133\pi$
$797$	−90.7566			−0.113873			−0.0569364	+	0.998378i	$0.518133\pi$
$798$			1119.21i			1.40252i
$799$		−	46.1004i		−	0.0576976i
$800$		−	96.5672i		−	0.120709i
$801$	−88.9511			−0.111050
$802$		−	283.423i		−	0.353395i
$803$	382.213	−	525.138i	0.475981	−	0.653970i
$804$	−168.437			−0.209498
$805$			262.502i			0.326089i
$806$	2370.17			2.94065
$807$	824.950			1.02224
$808$	1136.51			1.40658
$809$			236.018i			0.291741i	0.989304	+	0.145870i	$0.0465982\pi$
$809$			236.018i			0.291741i	−0.989304	+	0.145870i	$0.953402\pi$
$810$		−	311.305i		−	0.384327i
$811$			1251.91i			1.54367i	0.635826	+	0.771833i	$0.280660\pi$
$811$			1251.91i			1.54367i	−0.635826	+	0.771833i	$0.719340\pi$
$812$	427.900			0.526970
$813$		−	232.212i		−	0.285624i
$814$	327.263	−	449.640i	0.402044	−	0.552384i
$815$	476.362			0.584493
$816$			76.8211i			0.0941435i
$817$	−451.690			−0.552864
$818$	92.9095			0.113581
$819$	950.969			1.16113
$820$		−	102.765i		−	0.125323i
$821$			739.921i			0.901244i	0.892715	+	0.450622i	$0.148798\pi$
$821$			739.921i			0.901244i	−0.892715	+	0.450622i	$0.851202\pi$
$822$		−	876.964i		−	1.06687i
$823$	−1316.90			−1.60012			−0.800062	−	0.599917i	$-0.795200\pi$
$823$	−1316.90			−1.60012			−0.800062	+	0.599917i	$0.795200\pi$
$824$			679.232i			0.824311i
$825$	−183.929	−	133.869i	−0.222944	−	0.162266i
$826$	302.606			0.366351
$827$		−	612.865i		−	0.741071i	−0.928818	−	0.370535i	$-0.879174\pi$
$827$		−	612.865i		−	0.741071i	0.928818	−	0.370535i	$-0.120826\pi$
$828$	10.8605			0.0131165
$829$	213.437			0.257464			0.128732	−	0.991679i	$-0.458909\pi$
$829$	213.437			0.257464			0.128732	+	0.991679i	$0.458909\pi$
$830$	−194.968			−0.234902
$831$			428.135i			0.515205i
$832$			1575.04i			1.89308i
$833$		−	335.782i		−	0.403100i
$834$	−509.664			−0.611108
$835$		−	625.112i		−	0.748637i
$836$	−87.4869	+	120.202i	−0.104649	+	0.143782i
$837$	1731.31			2.06848
$838$		−	659.019i		−	0.786418i
$839$	−234.972			−0.280062			−0.140031	−	0.990147i	$-0.544720\pi$
$839$	−234.972			−0.280062			−0.140031	+	0.990147i	$0.544720\pi$
$840$	−1128.93			−1.34397
$841$	−1131.66			−1.34561
$842$		−	1346.03i		−	1.59861i
$843$		−	388.504i		−	0.460859i
$844$			17.7240i			0.0210000i
$845$	−1310.91			−1.55137
$846$			105.320i			0.124492i
$847$	1554.72	−	502.256i	1.83556	−	0.592982i
$848$	134.644			0.158778
$849$		−	129.528i		−	0.152566i
$850$	39.1194			0.0460228
$851$	−133.745			−0.157163
$852$	159.877			0.187649
$853$		−	989.590i		−	1.16013i	−0.814570	−	0.580065i	$-0.803027\pi$
$853$		−	989.590i		−	1.16013i	0.814570	−	0.580065i	$-0.196973\pi$
$854$			816.045i			0.955556i
$855$			243.707i			0.285038i
$856$	−480.338			−0.561142
$857$		−	407.343i		−	0.475312i	−0.971349	−	0.237656i	$-0.923621\pi$
$857$		−	407.343i		−	0.475312i	0.971349	−	0.237656i	$-0.0763791\pi$
$858$	863.565	+	628.532i	1.00649	+	0.732555i
$859$	651.382			0.758303			0.379151	−	0.925335i	$-0.376216\pi$
$859$	651.382			0.758303			0.379151	+	0.925335i	$0.376216\pi$
$860$		−	68.9681i		−	0.0801954i
$861$	1158.02			1.34497
$862$	548.433			0.636234
$863$	1257.43			1.45704			0.728520	−	0.685025i	$-0.240209\pi$
$863$	1257.43			1.45704			0.728520	+	0.685025i	$0.240209\pi$
$864$			331.187i			0.383318i
$865$		−	141.792i		−	0.163922i
$866$			187.039i			0.215981i
$867$	−682.260			−0.786920
$868$		−	567.640i		−	0.653964i
$869$	−531.048	+	729.627i	−0.611102	+	0.839617i
$870$	787.824			0.905544
$871$		−	2170.24i		−	2.49166i
$872$	−731.848			−0.839276
$873$	−171.695			−0.196672
$874$	−164.689			−0.188431
$875$			1837.35i			2.09983i
$876$		−	101.689i		−	0.116083i
$877$		−	245.688i		−	0.280146i	−0.990141	−	0.140073i	$-0.955266\pi$
$877$		−	245.688i		−	0.280146i	0.990141	−	0.140073i	$-0.0447338\pi$
$878$	1413.00			1.60934
$879$		−	745.502i		−	0.848125i
$880$	455.586	+	331.591i	0.517712	+	0.376808i
$881$	270.265			0.306771			0.153385	−	0.988166i	$-0.450982\pi$
$881$	270.265			0.306771			0.153385	+	0.988166i	$0.450982\pi$
$882$			767.122i			0.869753i
$883$	−622.208			−0.704652			−0.352326	−	0.935877i	$-0.614609\pi$
$883$	−622.208			−0.704652			−0.352326	+	0.935877i	$0.614609\pi$
$884$	39.8748			0.0451073
$885$	−120.955			−0.136673
$886$		−	1018.27i		−	1.14929i
$887$		−	583.315i		−	0.657627i	−0.944395	−	0.328813i	$-0.893351\pi$
$887$		−	583.315i		−	0.657627i	0.944395	−	0.328813i	$-0.106649\pi$
$888$		−	575.195i		−	0.647742i
$889$	12.2837			0.0138174
$890$			205.956i			0.231411i
$891$	376.753	+	274.214i	0.422843	+	0.307759i
$892$	32.7871			0.0367568
$893$			346.727i			0.388272i
$894$	−958.019			−1.07161
$895$	87.8148			0.0981171
$896$	−1128.76			−1.25977
$897$		−	256.867i		−	0.286363i
$898$		−	190.175i		−	0.211776i
$899$			2616.88i			2.91087i
$900$	19.4026			0.0215584
$901$		−	26.8346i		−	0.0297832i
$902$	−572.869	−	416.953i	−0.635109	−	0.462254i
$903$	777.176			0.860660
$904$			520.449i			0.575718i
$905$	−750.289			−0.829048
$906$	17.1221			0.0188986
$907$	464.554			0.512187			0.256094	−	0.966652i	$-0.417564\pi$
$907$	464.554			0.512187			0.256094	+	0.966652i	$0.417564\pi$
$908$		−	22.3460i		−	0.0246101i
$909$			422.137i			0.464398i
$910$		−	2201.86i		−	2.41963i
$911$	−1766.64			−1.93923			−0.969615	−	0.244637i	$-0.921331\pi$
$911$	−1766.64			−1.93923			−0.969615	+	0.244637i	$0.921331\pi$
$912$		−	577.782i		−	0.633533i
$913$	171.738	−	235.958i	0.188103	−	0.258443i
$914$	663.626			0.726068
$915$		−	326.183i		−	0.356484i
$916$	−95.2705			−0.104007
$917$	421.435			0.459580
$918$	−134.164			−0.146148
$919$			1381.68i			1.50346i	0.659468	+	0.751732i	$0.270782\pi$
$919$			1381.68i			1.50346i	−0.659468	+	0.751732i	$0.729218\pi$
$920$		−	166.119i		−	0.180565i
$921$		−	404.295i		−	0.438974i
$922$	−343.563			−0.372628
$923$			2059.95i			2.23180i
$924$	150.530	−	206.819i	0.162911	−	0.223830i
$925$	−238.941			−0.258315
$926$			1041.08i			1.12428i
$927$	−252.289			−0.272156
$928$	−500.587			−0.539426
$929$	394.410			0.424553			0.212276	−	0.977210i	$-0.431912\pi$
$929$	394.410			0.424553			0.212276	+	0.977210i	$0.431912\pi$
$930$		−	1045.11i		−	1.12377i
$931$			2525.46i			2.71264i
$932$		−	177.881i		−	0.190860i
$933$	62.8136			0.0673243
$934$		−	1370.69i		−	1.46755i
$935$	66.0863	−	90.7986i	0.0706806	−	0.0971108i
$936$	−601.804			−0.642952
$937$		−	729.277i		−	0.778310i	−0.921172	−	0.389155i	$-0.872767\pi$
$937$		−	729.277i		−	0.778310i	0.921172	−	0.389155i	$-0.127233\pi$
$938$	2394.09			2.55234
$939$	−701.742			−0.747329
$940$	−52.9414			−0.0563207
$941$		−	1359.29i		−	1.44452i	−0.691621	−	0.722261i	$-0.743103\pi$
$941$		−	1359.29i		−	1.44452i	0.691621	−	0.722261i	$-0.256897\pi$
$942$			62.2836i			0.0661184i
$943$			170.400i			0.180700i
$944$	−156.218			−0.165485
$945$		−	1608.37i		−	1.70198i
$946$	−384.466	−	279.827i	−0.406412	−	0.295800i
$947$	−1686.32			−1.78070			−0.890351	−	0.455275i	$-0.849541\pi$
$947$	−1686.32			−1.78070			−0.890351	+	0.455275i	$0.849541\pi$
$948$			141.287i			0.149037i
$949$	1310.22			1.38063
$950$	−294.222			−0.309708
$951$	−943.627			−0.992247
$952$			290.591i			0.305242i
$953$		−	586.820i		−	0.615761i	−0.951425	−	0.307880i	$-0.900380\pi$
$953$		−	586.820i		−	0.615761i	0.951425	−	0.307880i	$-0.0996196\pi$
$954$			61.3059i			0.0642619i
$955$	200.051			0.209478
$956$			218.978i			0.229056i
$957$	−693.956	+	953.454i	−0.725137	+	0.996294i
$958$	−892.573			−0.931704
$959$		−	2706.12i		−	2.82181i
$960$	694.501			0.723439
$961$	2510.47			2.61236
$962$	1121.85			1.16617
$963$		−	178.413i		−	0.185268i
$964$			56.2945i			0.0583968i
$965$			1355.09i			1.40424i
$966$	283.363			0.293336
$967$		−	1811.88i		−	1.87371i	−0.349717	−	0.936855i	$-0.613722\pi$
$967$		−	1811.88i		−	1.87371i	0.349717	−	0.936855i	$-0.386278\pi$
$968$	−983.875	+	317.844i	−1.01640	+	0.328351i
$969$	−115.152			−0.118836
$970$			397.540i			0.409835i
$971$	192.734			0.198490			0.0992452	−	0.995063i	$-0.468357\pi$
$971$	192.734			0.198490			0.0992452	+	0.995063i	$0.468357\pi$
$972$	−115.738			−0.119072
$973$	−1572.71			−1.61635
$974$			1023.48i			1.05081i
$975$		−	458.903i		−	0.470669i
$976$		−	421.276i		−	0.431635i
$977$	857.182			0.877361			0.438681	−	0.898643i	$-0.355446\pi$
$977$	857.182			0.877361			0.438681	+	0.898643i	$0.355446\pi$
$978$		−	514.219i		−	0.525786i
$979$	−249.256	−	181.417i	−0.254602	−	0.185308i
$980$	−385.610			−0.393480
$981$		−	271.832i		−	0.277097i
$982$	−376.749			−0.383655
$983$	−432.837			−0.440323			−0.220161	−	0.975463i	$-0.570658\pi$
$983$	−432.837			−0.440323			−0.220161	+	0.975463i	$0.570658\pi$
$984$	−732.833			−0.744749
$985$			383.147i			0.388982i
$986$		−	202.788i		−	0.205667i
$987$		−	596.577i		−	0.604435i
$988$	−299.904			−0.303547
$989$			114.359i			0.115631i
$990$	−150.980	+	207.437i	−0.152505	+	0.209532i
$991$	173.645			0.175222			0.0876110	−	0.996155i	$-0.472077\pi$
$991$	173.645			0.175222			0.0876110	+	0.996155i	$0.472077\pi$
$992$			664.065i			0.669421i
$993$	−67.9338			−0.0684127
$994$	−2272.43			−2.28615
$995$	943.295			0.948035
$996$		−	45.6915i		−	0.0458750i
$997$			1200.96i			1.20458i	0.798279	+	0.602288i	$0.205744\pi$
$997$			1200.96i			1.20458i	−0.798279	+	0.602288i	$0.794256\pi$
$998$			1078.82i			1.08098i
$999$	819.471			0.820291

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	253.3.c.a.208.31	yes	44
11.10	odd	2	inner	253.3.c.a.208.14	✓	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
253.3.c.a.208.14	✓	44	11.10	odd	2	inner
253.3.c.a.208.31	yes	44	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 253 = 11 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	253.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.81287i q^{2} -2.41374 q^{3} +0.713501 q^{4} +4.05365 q^{5} -4.37579i q^{6} -13.5027i q^{7} +8.54497i q^{8} -3.17387 q^{9} +7.34874i q^{10} +(-8.89372 - 6.47315i) q^{11} -1.72220 q^{12} -22.1899i q^{13} +24.4787 q^{14} -9.78444 q^{15} -12.6369 q^{16} +2.51854i q^{17} -5.75382i q^{18} -18.9423i q^{19} +2.89228 q^{20} +32.5921i q^{21} +(11.7350 - 16.1232i) q^{22} -4.79583 q^{23} -20.6253i q^{24} -8.56793 q^{25} +40.2274 q^{26} +29.3845 q^{27} -9.63421i q^{28} +44.4146i q^{29} -17.7379i q^{30} +58.9192 q^{31} +11.2708i q^{32} +(21.4671 + 15.6245i) q^{33} -4.56579 q^{34} -54.7354i q^{35} -2.26456 q^{36} +27.8878 q^{37} +34.3400 q^{38} +53.5605i q^{39} +34.6383i q^{40} -35.5308i q^{41} -59.0852 q^{42} -23.8456i q^{43} +(-6.34568 - 4.61860i) q^{44} -12.8658 q^{45} -8.69422i q^{46} -18.3044 q^{47} +30.5022 q^{48} -133.324 q^{49} -15.5325i q^{50} -6.07910i q^{51} -15.8325i q^{52} -10.6548 q^{53} +53.2703i q^{54} +(-36.0520 - 26.2399i) q^{55} +115.380 q^{56} +45.7218i q^{57} -80.5180 q^{58} +12.3620 q^{59} -6.98121 q^{60} +33.3369i q^{61} +106.813i q^{62} +42.8560i q^{63} -70.9801 q^{64} -89.9500i q^{65} +(-28.3252 + 38.9171i) q^{66} +97.8030 q^{67} +1.79698i q^{68} +11.5759 q^{69} +99.2281 q^{70} -92.8328 q^{71} -27.1206i q^{72} +59.0459i q^{73} +50.5570i q^{74} +20.6807 q^{75} -13.5154i q^{76} +(-87.4053 + 120.090i) q^{77} -97.0983 q^{78} -82.0385i q^{79} -51.2256 q^{80} -42.3617 q^{81} +64.4127 q^{82} +26.5309i q^{83} +23.2545i q^{84} +10.2093i q^{85} +43.2289 q^{86} -107.205i q^{87} +(55.3129 - 75.9966i) q^{88} +28.0260 q^{89} -23.3240i q^{90} -299.624 q^{91} -3.42183 q^{92} -142.216 q^{93} -33.1835i q^{94} -76.7855i q^{95} -27.2047i q^{96} +54.0964 q^{97} -241.699i q^{98} +(28.2275 + 20.5450i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 8 q^{3} - 88 q^{4} + 100 q^{9} + 8 q^{14} - 8 q^{15} + 72 q^{16} - 40 q^{20} - 76 q^{22} + 268 q^{25} - 40 q^{26} + 32 q^{27} + 72 q^{31} - 90 q^{33} + 60 q^{34} - 312 q^{36} + 4 q^{37} + 40 q^{38}+ \cdots + 494 q^{99}+O(q^{100}) \) 44 * q + 8 * q^3 - 88 * q^4 + 100 * q^9 + 8 * q^14 - 8 * q^15 + 72 * q^16 - 40 * q^20 - 76 * q^22 + 268 * q^25 - 40 * q^26 + 32 * q^27 + 72 * q^31 - 90 * q^33 + 60 * q^34 - 312 * q^36 + 4 * q^37 + 40 * q^38 + 12 * q^42 + 186 * q^44 - 180 * q^45 - 72 * q^47 + 252 * q^48 - 464 * q^49 + 100 * q^53 - 48 * q^55 + 208 * q^56 - 148 * q^58 - 144 * q^59 - 324 * q^60 - 416 * q^64 - 238 * q^66 + 292 * q^67 + 540 * q^70 + 544 * q^71 - 236 * q^75 + 64 * q^77 - 344 * q^78 + 156 * q^80 - 404 * q^81 + 72 * q^82 - 136 * q^86 + 608 * q^88 - 80 * q^89 - 4 * q^91 - 372 * q^93 + 68 * q^97 + 494 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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