LMFDB - Embedded newform 253.3.c.a.208.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [253,3,Mod(208,253)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://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);

sage: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")

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:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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			208.6
Character	$\chi$	$=$	253.208
Dual form			253.3.c.a.208.39

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-3.08733i q^{2} -3.11851 q^{3} -5.53163 q^{4} +8.57758 q^{5} +9.62787i q^{6} -4.55083i q^{7} +4.72864i q^{8} +0.725091 q^{9} -26.4818i q^{10} +(-9.41847 - 5.68264i) q^{11} +17.2504 q^{12} -5.40393i q^{13} -14.0499 q^{14} -26.7492 q^{15} -7.52762 q^{16} -30.3632i q^{17} -2.23860i q^{18} +32.2837i q^{19} -47.4479 q^{20} +14.1918i q^{21} +(-17.5442 + 29.0780i) q^{22} +4.79583 q^{23} -14.7463i q^{24} +48.5748 q^{25} -16.6837 q^{26} +25.8054 q^{27} +25.1735i q^{28} +3.47506i q^{29} +82.5838i q^{30} -51.2579 q^{31} +42.1548i q^{32} +(29.3716 + 17.7213i) q^{33} -93.7412 q^{34} -39.0351i q^{35} -4.01093 q^{36} -47.7165 q^{37} +99.6706 q^{38} +16.8522i q^{39} +40.5603i q^{40} -68.9006i q^{41} +43.8148 q^{42} +3.80031i q^{43} +(52.0995 + 31.4342i) q^{44} +6.21952 q^{45} -14.8063i q^{46} -55.3907 q^{47} +23.4749 q^{48} +28.2900 q^{49} -149.967i q^{50} +94.6877i q^{51} +29.8925i q^{52} +45.7406 q^{53} -79.6698i q^{54} +(-80.7877 - 48.7432i) q^{55} +21.5192 q^{56} -100.677i q^{57} +10.7287 q^{58} +43.9724 q^{59} +147.967 q^{60} +17.4561i q^{61} +158.250i q^{62} -3.29976i q^{63} +100.036 q^{64} -46.3527i q^{65} +(54.7117 - 90.6799i) q^{66} +78.2581 q^{67} +167.958i q^{68} -14.9558 q^{69} -120.514 q^{70} +15.7894 q^{71} +3.42869i q^{72} -66.2206i q^{73} +147.317i q^{74} -151.481 q^{75} -178.582i q^{76} +(-25.8607 + 42.8618i) q^{77} +52.0284 q^{78} -66.9926i q^{79} -64.5687 q^{80} -87.0001 q^{81} -212.719 q^{82} +38.9831i q^{83} -78.5037i q^{84} -260.442i q^{85} +11.7328 q^{86} -10.8370i q^{87} +(26.8711 - 44.5366i) q^{88} +70.6051 q^{89} -19.2017i q^{90} -24.5924 q^{91} -26.5287 q^{92} +159.848 q^{93} +171.009i q^{94} +276.916i q^{95} -131.460i q^{96} +18.9107 q^{97} -87.3406i q^{98} +(-6.82925 - 4.12043i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$		−	3.08733i		−	1.54367i	−0.635825	−	0.771833i	$-0.719340\pi$
$2$		−	3.08733i		−	1.54367i	0.635825	−	0.771833i	$-0.280660\pi$
$3$	−3.11851			−1.03950			−0.519751	−	0.854318i	$-0.673975\pi$
$3$	−3.11851			−1.03950			−0.519751	+	0.854318i	$0.673975\pi$
$4$	−5.53163			−1.38291
$5$	8.57758			1.71552			0.857758	−	0.514054i	$-0.171857\pi$
$5$	8.57758			1.71552			0.857758	+	0.514054i	$0.171857\pi$
$6$			9.62787i			1.60465i
$7$		−	4.55083i		−	0.650118i	−0.945694	−	0.325059i	$-0.894616\pi$
$7$		−	4.55083i		−	0.650118i	0.945694	−	0.325059i	$-0.105384\pi$
$8$			4.72864i			0.591080i
$9$	0.725091			0.0805656
$10$		−	26.4818i		−	2.64818i
$11$	−9.41847	−	5.68264i	−0.856225	−	0.516603i
$11$	−9.41847	−	5.68264i	−0.856225	−	0.516603i
$12$	17.2504			1.43753
$13$		−	5.40393i		−	0.415687i	−0.978162	−	0.207844i	$-0.933355\pi$
$13$		−	5.40393i		−	0.415687i	0.978162	−	0.207844i	$-0.0666445\pi$
$14$	−14.0499			−1.00357
$15$	−26.7492			−1.78328
$16$	−7.52762			−0.470476
$17$		−	30.3632i		−	1.78607i	−0.449989	−	0.893034i	$-0.648572\pi$
$17$		−	30.3632i		−	1.78607i	0.449989	−	0.893034i	$-0.351428\pi$
$18$		−	2.23860i		−	0.124366i
$19$			32.2837i			1.69914i	0.527473	+	0.849572i	$0.323140\pi$
$19$			32.2837i			1.69914i	−0.527473	+	0.849572i	$0.676860\pi$
$20$	−47.4479			−2.37240
$21$			14.1918i			0.675799i
$22$	−17.5442	+	29.0780i	−0.797463	+	1.32173i
$23$	4.79583			0.208514
$23$	4.79583			0.208514
$24$		−	14.7463i		−	0.614429i
$25$	48.5748			1.94299
$26$	−16.6837			−0.641682
$27$	25.8054			0.955754
$28$			25.1735i			0.899052i
$29$			3.47506i			0.119830i	0.998203	+	0.0599148i	$0.0190829\pi$
$29$			3.47506i			0.119830i	−0.998203	+	0.0599148i	$0.980917\pi$
$30$			82.5838i			2.75279i
$31$	−51.2579			−1.65348			−0.826741	−	0.562583i	$-0.809808\pi$
$31$	−51.2579			−1.65348			−0.826741	+	0.562583i	$0.809808\pi$
$32$			42.1548i			1.31734i
$33$	29.3716	+	17.7213i	0.890048	+	0.537010i
$34$	−93.7412			−2.75709
$35$		−	39.0351i		−	1.11529i
$36$	−4.01093			−0.111415
$37$	−47.7165			−1.28964			−0.644818	−	0.764336i	$-0.723067\pi$
$37$	−47.7165			−1.28964			−0.644818	+	0.764336i	$0.723067\pi$
$38$	99.6706			2.62291
$39$			16.8522i			0.432108i
$40$			40.5603i			1.01401i
$41$		−	68.9006i		−	1.68050i	−0.542198	−	0.840251i	$-0.682408\pi$
$41$		−	68.9006i		−	1.68050i	0.542198	−	0.840251i	$-0.317592\pi$
$42$	43.8148			1.04321
$43$			3.80031i			0.0883793i	0.999023	+	0.0441897i	$0.0140706\pi$
$43$			3.80031i			0.0883793i	−0.999023	+	0.0441897i	$0.985929\pi$
$44$	52.0995	+	31.4342i	1.18408	+	0.714414i
$45$	6.21952			0.138212
$46$		−	14.8063i		−	0.321877i
$47$	−55.3907			−1.17852			−0.589262	−	0.807942i	$-0.700582\pi$
$47$	−55.3907			−1.17852			−0.589262	+	0.807942i	$0.700582\pi$
$48$	23.4749			0.489061
$49$	28.2900			0.577347
$50$		−	149.967i		−	2.99933i
$51$			94.6877i			1.85662i
$52$			29.8925i			0.574856i
$53$	45.7406			0.863030			0.431515	−	0.902106i	$-0.357979\pi$
$53$	45.7406			0.863030			0.431515	+	0.902106i	$0.357979\pi$
$54$		−	79.6698i		−	1.47537i
$55$	−80.7877	−	48.7432i	−1.46887	−	0.886241i
$56$	21.5192			0.384272
$57$		−	100.677i		−	1.76626i
$58$	10.7287			0.184977
$59$	43.9724			0.745295			0.372647	−	0.927973i	$-0.378450\pi$
$59$	43.9724			0.745295			0.372647	+	0.927973i	$0.378450\pi$
$60$	147.967			2.46611
$61$			17.4561i			0.286165i	0.989711	+	0.143083i	$0.0457015\pi$
$61$			17.4561i			0.286165i	−0.989711	+	0.143083i	$0.954299\pi$
$62$			158.250i			2.55242i
$63$		−	3.29976i		−	0.0523772i
$64$	100.036			1.56305
$65$		−	46.3527i		−	0.713118i
$66$	54.7117	−	90.6799i	0.828965	−	1.37394i
$67$	78.2581			1.16803			0.584016	−	0.811742i	$-0.301481\pi$
$67$	78.2581			1.16803			0.584016	+	0.811742i	$0.301481\pi$
$68$			167.958i			2.46997i
$69$	−14.9558			−0.216751
$70$	−120.514			−1.72163
$71$	15.7894			0.222386			0.111193	−	0.993799i	$-0.464533\pi$
$71$	15.7894			0.222386			0.111193	+	0.993799i	$0.464533\pi$
$72$			3.42869i			0.0476207i
$73$		−	66.2206i		−	0.907132i	−0.891223	−	0.453566i	$-0.850152\pi$
$73$		−	66.2206i		−	0.907132i	0.891223	−	0.453566i	$-0.149848\pi$
$74$			147.317i			1.99077i
$75$	−151.481			−2.01975
$76$		−	178.582i		−	2.34976i
$77$	−25.8607	+	42.8618i	−0.335853	+	0.556647i
$78$	52.0284			0.667031
$79$		−	66.9926i		−	0.848008i	−0.905660	−	0.424004i	$-0.860624\pi$
$79$		−	66.9926i		−	0.848008i	0.905660	−	0.424004i	$-0.139376\pi$
$80$	−64.5687			−0.807109
$81$	−87.0001			−1.07407
$82$	−212.719			−2.59413
$83$			38.9831i			0.469676i	0.972034	+	0.234838i	$0.0754560\pi$
$83$			38.9831i			0.469676i	−0.972034	+	0.234838i	$0.924544\pi$
$84$		−	78.5037i		−	0.934567i
$85$		−	260.442i		−	3.06403i
$86$	11.7328			0.136428
$87$		−	10.8370i		−	0.124563i
$88$	26.8711	−	44.5366i	0.305354	−	0.506097i
$89$	70.6051			0.793316			0.396658	−	0.917966i	$-0.370170\pi$
$89$	70.6051			0.793316			0.396658	+	0.917966i	$0.370170\pi$
$90$		−	19.2017i		−	0.213353i
$91$	−24.5924			−0.270246
$92$	−26.5287			−0.288356
$93$	159.848			1.71880
$94$			171.009i			1.81925i
$95$			276.916i			2.91491i
$96$		−	131.460i		−	1.36938i
$97$	18.9107			0.194956			0.0974778	−	0.995238i	$-0.468922\pi$
$97$	18.9107			0.194956			0.0974778	+	0.995238i	$0.468922\pi$
$98$		−	87.3406i		−	0.891231i
$99$	−6.82925	−	4.12043i	−0.0689823	−	0.0416205i
$100$	−268.698			−2.68698
$101$		−	90.7089i		−	0.898107i	−0.893505	−	0.449054i	$-0.851761\pi$
$101$		−	90.7089i		−	0.898107i	0.893505	−	0.449054i	$-0.148239\pi$
$102$	292.333			2.86601
$103$	141.637			1.37512			0.687559	−	0.726128i	$-0.258682\pi$
$103$	141.637			1.37512			0.687559	+	0.726128i	$0.258682\pi$
$104$	25.5533			0.245704
$105$			121.731i			1.15934i
$106$		−	141.216i		−	1.33223i
$107$		−	185.704i		−	1.73555i	−0.496955	−	0.867777i	$-0.665548\pi$
$107$		−	185.704i		−	1.73555i	0.496955	−	0.867777i	$-0.334452\pi$
$108$	−142.746			−1.32172
$109$			10.8768i			0.0997869i	0.998755	+	0.0498934i	$0.0158882\pi$
$109$			10.8768i			0.0997869i	−0.998755	+	0.0498934i	$0.984112\pi$
$110$	−150.487	+	249.418i	−1.36806	+	2.26744i
$111$	148.804			1.34058
$112$			34.2569i			0.305865i
$113$	42.5593			0.376631			0.188316	−	0.982109i	$-0.439697\pi$
$113$	42.5593			0.376631			0.188316	+	0.982109i	$0.439697\pi$
$114$	−310.824			−2.72652
$115$	41.1366			0.357710
$116$		−	19.2227i		−	0.165713i
$117$		−	3.91834i		−	0.0334901i
$118$		−	135.757i		−	1.15049i
$119$	−138.177			−1.16116
$120$		−	126.488i		−	1.05406i
$121$	56.4153	+	107.044i	0.466242	+	0.884657i
$122$	53.8927			0.441744
$123$			214.867i			1.74689i
$124$	283.540			2.28661
$125$	202.215			1.61772
$126$	−10.1875			−0.0808529
$127$		−	28.0371i		−	0.220764i	−0.993889	−	0.110382i	$-0.964792\pi$
$127$		−	28.0371i		−	0.220764i	0.993889	−	0.110382i	$-0.0352075\pi$
$128$		−	140.224i		−	1.09550i
$129$		−	11.8513i		−	0.0918705i
$130$	−143.106			−1.10082
$131$			31.1135i			0.237507i	0.992924	+	0.118754i	$0.0378899\pi$
$131$			31.1135i			0.237507i	−0.992924	+	0.118754i	$0.962110\pi$
$132$	−162.473	−	98.0279i	−1.23085	−	0.742635i
$133$	146.918			1.10464
$134$		−	241.609i		−	1.80305i
$135$	221.348			1.63961
$136$	143.576			1.05571
$137$	159.064			1.16105			0.580526	−	0.814242i	$-0.302847\pi$
$137$	159.064			1.16105			0.580526	+	0.814242i	$0.302847\pi$
$138$			46.1737i			0.334592i
$139$			21.2491i			0.152871i	0.997075	+	0.0764355i	$0.0243539\pi$
$139$			21.2491i			0.152871i	−0.997075	+	0.0764355i	$0.975646\pi$
$140$			215.927i			1.54234i
$141$	172.736			1.22508
$142$		−	48.7471i		−	0.343290i
$143$	−30.7086	+	50.8968i	−0.214745	+	0.355922i
$144$	−5.45821			−0.0379042
$145$			29.8076i			0.205570i
$146$	−204.445			−1.40031
$147$	−88.2225			−0.600153
$148$	263.950			1.78344
$149$			199.750i			1.34060i	0.742089	+	0.670301i	$0.233835\pi$
$149$			199.750i			1.34060i	−0.742089	+	0.670301i	$0.766165\pi$
$150$			467.672i			3.11782i
$151$		−	196.482i		−	1.30120i	−0.759420	−	0.650601i	$-0.774517\pi$
$151$		−	196.482i		−	1.30120i	0.759420	−	0.650601i	$-0.225483\pi$
$152$	−152.658			−1.00433
$153$		−	22.0160i		−	0.143896i
$154$	132.329	+	79.8406i	0.859278	+	0.518445i
$155$	−439.669			−2.83657
$156$		−	93.2201i		−	0.597565i
$157$	38.5450			0.245509			0.122755	−	0.992437i	$-0.460827\pi$
$157$	38.5450			0.245509			0.122755	+	0.992437i	$0.460827\pi$
$158$	−206.829			−1.30904
$159$	−142.642			−0.897122
$160$			361.586i			2.25991i
$161$		−	21.8250i		−	0.135559i
$162$			268.598i			1.65801i
$163$	−98.7328			−0.605723			−0.302861	−	0.953035i	$-0.597942\pi$
$163$	−98.7328			−0.605723			−0.302861	+	0.953035i	$0.597942\pi$
$164$			381.132i			2.32398i
$165$	251.937	+	152.006i	1.52689	+	0.921250i
$166$	120.354			0.725024
$167$		−	140.960i		−	0.844075i	−0.906578	−	0.422037i	$-0.861315\pi$
$167$		−	140.960i		−	0.844075i	0.906578	−	0.422037i	$-0.138685\pi$
$168$	−67.1078			−0.399451
$169$	139.798			0.827204
$170$	−804.072			−4.72984
$171$			23.4086i			0.136893i
$172$		−	21.0219i		−	0.122220i
$173$			220.835i			1.27650i	0.769828	+	0.638252i	$0.220342\pi$
$173$			220.835i			1.27650i	−0.769828	+	0.638252i	$0.779658\pi$
$174$	−33.4574			−0.192284
$175$		−	221.056i		−	1.26317i
$176$	70.8987	+	42.7767i	0.402833	+	0.243050i
$177$	−137.128			−0.774736
$178$		−	217.982i		−	1.22462i
$179$	175.763			0.981915			0.490958	−	0.871184i	$-0.336647\pi$
$179$	175.763			0.981915			0.490958	+	0.871184i	$0.336647\pi$
$180$	−34.4041			−0.191134
$181$	−79.1478			−0.437281			−0.218640	−	0.975805i	$-0.570162\pi$
$181$	−79.1478			−0.437281			−0.218640	+	0.975805i	$0.570162\pi$
$182$			75.9248i			0.417169i
$183$		−	54.4369i		−	0.297469i
$184$			22.6778i			0.123249i
$185$	−409.292			−2.21239
$186$		−	493.505i		−	2.65325i
$187$	−172.543	+	285.975i	−0.922689	+	1.52928i
$188$	306.400			1.62979
$189$		−	117.436i		−	0.621353i
$190$	854.933			4.49965
$191$	168.727			0.883388			0.441694	−	0.897166i	$-0.354378\pi$
$191$	168.727			0.883388			0.441694	+	0.897166i	$0.354378\pi$
$192$	−311.962			−1.62480
$193$		−	96.4351i		−	0.499664i	−0.968289	−	0.249832i	$-0.919625\pi$
$193$		−	96.4351i		−	0.499664i	0.968289	−	0.249832i	$-0.0803754\pi$
$194$		−	58.3836i		−	0.300947i
$195$			144.551i			0.741288i
$196$	−156.490			−0.798416
$197$			220.963i			1.12164i	0.827938	+	0.560820i	$0.189514\pi$
$197$			220.963i			1.12164i	−0.827938	+	0.560820i	$0.810486\pi$
$198$	−12.7211	+	21.0842i	−0.0642481	+	0.106486i
$199$	−186.161			−0.935482			−0.467741	−	0.883866i	$-0.654932\pi$
$199$	−186.161			−0.935482			−0.467741	+	0.883866i	$0.654932\pi$
$200$			229.693i			1.14846i
$201$	−244.049			−1.21417
$202$	−280.048			−1.38638
$203$	15.8144			0.0779034
$204$		−	523.777i		−	2.56754i
$205$		−	591.000i		−	2.88293i
$206$		−	437.281i		−	2.12272i
$207$	3.47741			0.0167991
$208$			40.6787i			0.195571i
$209$	183.457	−	304.063i	0.877783	−	1.45485i
$210$	375.825			1.78964
$211$		−	216.846i		−	1.02771i	−0.857878	−	0.513854i	$-0.828217\pi$
$211$		−	216.846i		−	1.02771i	0.857878	−	0.513854i	$-0.171783\pi$
$212$	−253.020			−1.19349
$213$	−49.2394			−0.231171
$214$	−573.331			−2.67912
$215$			32.5975i			0.151616i
$216$			122.024i			0.564927i
$217$			233.266i			1.07496i
$218$	33.5802			0.154038
$219$			206.509i			0.942966i
$220$	446.887	+	269.629i	2.03131	+	1.22559i
$221$	−164.080			−0.742446
$222$		−	459.408i		−	2.06941i
$223$	−61.4239			−0.275444			−0.137722	−	0.990471i	$-0.543978\pi$
$223$	−61.4239			−0.275444			−0.137722	+	0.990471i	$0.543978\pi$
$224$	191.839			0.856425
$225$	35.2212			0.156538
$226$		−	131.395i		−	0.581393i
$227$			110.064i			0.484864i	0.970168	+	0.242432i	$0.0779451\pi$
$227$			110.064i			0.484864i	−0.970168	+	0.242432i	$0.922055\pi$
$228$			556.908i			2.44258i
$229$	100.135			0.437273			0.218636	−	0.975806i	$-0.429839\pi$
$229$	100.135			0.437273			0.218636	+	0.975806i	$0.429839\pi$
$230$		−	127.002i		−	0.552184i
$231$	80.6468	−	133.665i	0.349120	−	0.578636i
$232$	−16.4323			−0.0708289
$233$			162.034i			0.695426i	0.937601	+	0.347713i	$0.113042\pi$
$233$			162.034i			0.695426i	−0.937601	+	0.347713i	$0.886958\pi$
$234$	−12.0972			−0.0516975
$235$	−475.118			−2.02178
$236$	−243.239			−1.03067
$237$			208.917i			0.881507i
$238$			426.600i			1.79244i
$239$		−	182.769i		−	0.764725i	−0.924012	−	0.382363i	$-0.875111\pi$
$239$		−	182.769i		−	0.764725i	0.924012	−	0.382363i	$-0.124889\pi$
$240$	201.358			0.838992
$241$			35.0424i			0.145404i	0.997354	+	0.0727020i	$0.0231622\pi$
$241$			35.0424i			0.145404i	−0.997354	+	0.0727020i	$0.976838\pi$
$242$	330.479	−	174.173i	1.36562	−	0.719722i
$243$	39.0620			0.160749
$244$		−	96.5605i		−	0.395740i
$245$	242.660			0.990447
$246$	663.366			2.69661
$247$	174.459			0.706312
$248$		−	242.380i		−	0.977340i
$249$		−	121.569i		−	0.488230i
$250$		−	624.305i		−	2.49722i
$251$	137.664			0.548460			0.274230	−	0.961664i	$-0.411577\pi$
$251$	137.664			0.548460			0.274230	+	0.961664i	$0.411577\pi$
$252$			18.2530i			0.0724327i
$253$	−45.1694	−	27.2530i	−0.178535	−	0.107719i
$254$	−86.5598			−0.340787
$255$			812.191i			3.18506i
$256$	−32.7751			−0.128028
$257$	−140.243			−0.545693			−0.272847	−	0.962058i	$-0.587965\pi$
$257$	−140.243			−0.545693			−0.272847	+	0.962058i	$0.587965\pi$
$258$	−36.5889			−0.141817
$259$			217.150i			0.838415i
$260$			256.406i			0.986175i
$261$			2.51973i			0.00965415i
$262$	96.0576			0.366632
$263$			426.828i			1.62292i	0.584407	+	0.811461i	$0.301327\pi$
$263$			426.828i			1.62292i	−0.584407	+	0.811461i	$0.698673\pi$
$264$	−83.7978	+	138.888i	−0.317416	+	0.526089i
$265$	392.343			1.48054
$266$		−	453.584i		−	1.70520i
$267$	−220.183			−0.824654
$268$	−432.895			−1.61528
$269$	−223.004			−0.829010			−0.414505	−	0.910047i	$-0.636045\pi$
$269$	−223.004			−0.829010			−0.414505	+	0.910047i	$0.636045\pi$
$270$		−	683.374i		−	2.53101i
$271$		−	3.60362i		−	0.0132975i	−0.999978	−	0.00664875i	$-0.997884\pi$
$271$		−	3.60362i		−	0.0132975i	0.999978	−	0.00664875i	$-0.00211638\pi$
$272$			228.562i			0.840302i
$273$	76.6915			0.280921
$274$		−	491.084i		−	1.79228i
$275$	−457.501	−	276.033i	−1.66364	−	1.00376i
$276$	82.7301			0.299747
$277$			48.9346i			0.176659i	0.996091	+	0.0883296i	$0.0281529\pi$
$277$			48.9346i			0.176659i	−0.996091	+	0.0883296i	$0.971847\pi$
$278$	65.6030			0.235982
$279$	−37.1667			−0.133214
$280$	184.583			0.659224
$281$			351.503i			1.25090i	0.780264	+	0.625450i	$0.215085\pi$
$281$			351.503i			1.25090i	−0.780264	+	0.625450i	$0.784915\pi$
$282$		−	533.294i		−	1.89111i
$283$			3.54558i			0.0125285i	0.999980	+	0.00626427i	$0.00199399\pi$
$283$			3.54558i			0.0125285i	−0.999980	+	0.00626427i	$0.998006\pi$
$284$	−87.3411			−0.307539
$285$		−	863.565i		−	3.03005i
$286$	157.135	+	94.8076i	0.549424	+	0.331495i
$287$	−313.554			−1.09252
$288$			30.5661i			0.106132i
$289$	−632.921			−2.19004
$290$	92.0259			0.317331
$291$	−58.9732			−0.202657
$292$			366.308i			1.25448i
$293$		−	30.7033i		−	0.104789i	−0.998626	−	0.0523946i	$-0.983315\pi$
$293$		−	30.7033i		−	0.104789i	0.998626	−	0.0523946i	$-0.0166854\pi$
$294$			272.372i			0.926437i
$295$	377.177			1.27856
$296$		−	225.634i		−	0.762278i
$297$	−243.047	−	146.643i	−0.818341	−	0.493746i
$298$	616.694			2.06944
$299$		−	25.9164i		−	0.0866768i
$300$	837.936			2.79312
$301$	17.2945			0.0574570
$302$	−606.604			−2.00862
$303$			282.876i			0.933585i
$304$		−	243.020i		−	0.799407i
$305$			149.731i			0.490921i
$306$	−67.9709			−0.222127
$307$		−	355.660i		−	1.15850i	−0.815149	−	0.579251i	$-0.803345\pi$
$307$		−	355.660i		−	1.15850i	0.815149	−	0.579251i	$-0.196655\pi$
$308$	143.052	−	237.096i	0.464453	−	0.769791i
$309$	−441.697			−1.42944
$310$			1357.40i			4.37872i
$311$	255.425			0.821304			0.410652	−	0.911792i	$-0.365301\pi$
$311$	255.425			0.821304			0.410652	+	0.911792i	$0.365301\pi$
$312$	−79.6880			−0.255410
$313$	179.478			0.573411			0.286705	−	0.958019i	$-0.407440\pi$
$313$	179.478			0.573411			0.286705	+	0.958019i	$0.407440\pi$
$314$		−	119.001i		−	0.378984i
$315$		−	28.3040i		−	0.0898538i
$316$			370.578i			1.17272i
$317$	−59.9143			−0.189004			−0.0945021	−	0.995525i	$-0.530126\pi$
$317$	−59.9143			−0.189004			−0.0945021	+	0.995525i	$0.530126\pi$
$318$			440.385i			1.38486i
$319$	19.7475	−	32.7298i	0.0619044	−	0.102601i
$320$	858.062			2.68144
$321$			579.120i			1.80411i
$322$	−67.3810			−0.209258
$323$	980.236			3.03479
$324$	481.252			1.48535
$325$		−	262.495i		−	0.807677i
$326$			304.821i			0.935034i
$327$		−	33.9193i		−	0.103729i
$328$	325.806			0.993311
$329$			252.073i			0.766180i
$330$	469.294	−	777.814i	1.42210	−	2.35701i
$331$	−116.779			−0.352808			−0.176404	−	0.984318i	$-0.556446\pi$
$331$	−116.779			−0.352808			−0.176404	+	0.984318i	$0.556446\pi$
$332$		−	215.640i		−	0.649518i
$333$	−34.5988			−0.103900
$334$	−435.192			−1.30297
$335$	671.265			2.00378
$336$		−	106.830i		−	0.317947i
$337$			93.9769i			0.278863i	0.990232	+	0.139432i	$0.0445275\pi$
$337$			93.9769i			0.278863i	−0.990232	+	0.139432i	$0.955472\pi$
$338$		−	431.601i		−	1.27693i
$339$	−132.722			−0.391509
$340$			1440.67i			4.23726i
$341$	482.772	+	291.280i	1.41575	+	0.854194i
$342$	72.2702			0.211317
$343$		−	351.733i		−	1.02546i
$344$	−17.9703			−0.0522392
$345$	−128.285			−0.371840
$346$	681.792			1.97050
$347$		−	84.3932i		−	0.243208i	−0.992579	−	0.121604i	$-0.961196\pi$
$347$		−	84.3932i		−	0.243208i	0.992579	−	0.121604i	$-0.0388038\pi$
$348$			59.9462i			0.172259i
$349$		−	365.606i		−	1.04758i	−0.851847	−	0.523791i	$-0.824517\pi$
$349$		−	365.606i		−	1.04758i	0.851847	−	0.523791i	$-0.175483\pi$
$350$	−682.472			−1.94992
$351$		−	139.450i		−	0.397295i
$352$	239.551	−	397.034i	0.680541	−	1.12794i
$353$	323.926			0.917638			0.458819	−	0.888530i	$-0.348273\pi$
$353$	323.926			0.917638			0.458819	+	0.888530i	$0.348273\pi$
$354$			423.361i			1.19593i
$355$	135.435			0.381507
$356$	−390.561			−1.09708
$357$	430.907			1.20702
$358$		−	542.638i		−	1.51575i
$359$		−	121.369i		−	0.338075i	−0.985610	−	0.169038i	$-0.945934\pi$
$359$		−	121.369i		−	0.338075i	0.985610	−	0.169038i	$-0.0540659\pi$
$360$			29.4099i			0.0816941i
$361$	−681.239			−1.88709
$362$			244.356i			0.675016i
$363$	−175.932	−	333.816i	−0.484660	−	0.919603i
$364$	136.036			0.373725
$365$		−	568.012i		−	1.55620i
$366$	−168.065			−0.459194
$367$	86.3340			0.235243			0.117621	−	0.993059i	$-0.462473\pi$
$367$	86.3340			0.235243			0.117621	+	0.993059i	$0.462473\pi$
$368$	−36.1012			−0.0981011
$369$		−	49.9592i		−	0.135391i
$370$			1263.62i			3.41519i
$371$		−	208.157i		−	0.561071i
$372$	−884.221			−2.37694
$373$			339.832i			0.911079i	0.890216	+	0.455539i	$0.150554\pi$
$373$			339.832i			0.911079i	−0.890216	+	0.455539i	$0.849446\pi$
$374$	882.899	+	532.697i	2.36069	+	1.42432i
$375$	−630.609			−1.68162
$376$		−	261.922i		−	0.696602i
$377$	18.7790			0.0498116
$378$	−362.563			−0.959162
$379$	−231.363			−0.610457			−0.305228	−	0.952279i	$-0.598733\pi$
$379$	−231.363			−0.610457			−0.305228	+	0.952279i	$0.598733\pi$
$380$		−	1531.80i		−	4.03104i
$381$			87.4339i			0.229485i
$382$		−	520.917i		−	1.36366i
$383$	−519.802			−1.35719			−0.678593	−	0.734515i	$-0.737410\pi$
$383$	−519.802			−1.35719			−0.678593	+	0.734515i	$0.737410\pi$
$384$			437.289i			1.13877i
$385$	−221.822	+	367.651i	−0.576161	+	0.954937i
$386$	−297.727			−0.771314
$387$			2.75557i			0.00712033i
$388$	−104.607			−0.269605
$389$	−218.841			−0.562572			−0.281286	−	0.959624i	$-0.590761\pi$
$389$	−218.841			−0.562572			−0.281286	+	0.959624i	$0.590761\pi$
$390$	446.277			1.14430
$391$		−	145.617i		−	0.372421i
$392$			133.773i			0.341258i
$393$		−	97.0276i		−	0.246889i
$394$	682.187			1.73144
$395$		−	574.635i		−	1.45477i
$396$	37.7768	+	22.7927i	0.0953961	+	0.0575572i
$397$	437.512			1.10204			0.551022	−	0.834491i	$-0.314238\pi$
$397$	437.512			1.10204			0.551022	+	0.834491i	$0.314238\pi$
$398$			574.741i			1.44407i
$399$	−458.164			−1.14828
$400$	−365.653			−0.914132
$401$	−610.664			−1.52285			−0.761427	−	0.648251i	$-0.775501\pi$
$401$	−610.664			−1.52285			−0.761427	+	0.648251i	$0.775501\pi$
$402$			753.459i			1.87428i
$403$			276.994i			0.687331i
$404$			501.767i			1.24200i
$405$	−746.250			−1.84259
$406$		−	48.8243i		−	0.120257i
$407$	449.417	+	271.156i	1.10422	+	0.666230i
$408$	−447.744			−1.09741
$409$		−	448.266i		−	1.09600i	−0.836477	−	0.548002i	$-0.815388\pi$
$409$		−	448.266i		−	1.09600i	0.836477	−	0.548002i	$-0.184612\pi$
$410$	−1824.61			−4.45028
$411$	−496.042			−1.20692
$412$	−783.484			−1.90166
$413$		−	200.111i		−	0.484529i
$414$		−	10.7359i		−	0.0259322i
$415$			334.381i			0.805737i
$416$	227.802			0.547601
$417$		−	66.2654i		−	0.158910i
$418$	−938.745	−	566.392i	−2.24580	−	1.35500i
$419$	778.121			1.85709			0.928546	−	0.371218i	$-0.121060\pi$
$419$	778.121			1.85709			0.928546	+	0.371218i	$0.121060\pi$
$420$		−	673.371i		−	1.60326i
$421$	238.509			0.566529			0.283265	−	0.959042i	$-0.408583\pi$
$421$	238.509			0.566529			0.283265	+	0.959042i	$0.408583\pi$
$422$	−669.476			−1.58644
$423$	−40.1633			−0.0949486
$424$			216.291i			0.510120i
$425$		−	1474.89i		−	3.47032i
$426$			152.018i			0.356851i
$427$	79.4396			0.186041
$428$			1027.25i			2.40011i
$429$	95.7650	−	158.722i	0.223228	−	0.369982i
$430$	100.639			0.234045
$431$		−	655.794i		−	1.52156i	−0.649008	−	0.760781i	$-0.724816\pi$
$431$		−	655.794i		−	1.52156i	0.649008	−	0.760781i	$-0.275184\pi$
$432$	−194.253			−0.449660
$433$	349.972			0.808249			0.404125	−	0.914704i	$-0.367576\pi$
$433$	349.972			0.808249			0.404125	+	0.914704i	$0.367576\pi$
$434$	720.170			1.65938
$435$		−	92.9552i		−	0.213690i
$436$		−	60.1662i		−	0.137996i
$437$			154.827i			0.354296i
$438$	637.563			1.45562
$439$			511.576i			1.16532i	0.812716	+	0.582660i	$0.197988\pi$
$439$			511.576i			1.16532i	−0.812716	+	0.582660i	$0.802012\pi$
$440$	230.489	−	382.016i	0.523839	−	0.868218i
$441$	20.5128			0.0465143
$442$			506.571i			1.14609i
$443$	5.47559			0.0123603			0.00618013	−	0.999981i	$-0.498033\pi$
$443$	5.47559			0.0123603			0.00618013	+	0.999981i	$0.498033\pi$
$444$	−823.130			−1.85390
$445$	605.621			1.36095
$446$			189.636i			0.425193i
$447$		−	622.921i		−	1.39356i
$448$		−	455.244i		−	1.01617i
$449$	−223.082			−0.496841			−0.248421	−	0.968652i	$-0.579911\pi$
$449$	−223.082			−0.496841			−0.248421	+	0.968652i	$0.579911\pi$
$450$		−	108.739i		−	0.241643i
$451$	−391.537	+	648.938i	−0.868153	+	1.43889i
$452$	−235.422			−0.520846
$453$			612.729i			1.35260i
$454$	339.804			0.748468
$455$	−210.943			−0.463611
$456$	476.066			1.04400
$457$			526.851i			1.15285i	0.817151	+	0.576423i	$0.195552\pi$
$457$			526.851i			1.15285i	−0.817151	+	0.576423i	$0.804448\pi$
$458$		−	309.152i		−	0.675004i
$459$		−	783.533i		−	1.70704i
$460$	−227.552			−0.494679
$461$			262.848i			0.570169i	0.958502	+	0.285085i	$0.0920217\pi$
$461$			262.848i			0.570169i	−0.958502	+	0.285085i	$0.907978\pi$
$462$	−412.668	−	248.983i	−0.893221	−	0.538925i
$463$	−608.646			−1.31457			−0.657285	−	0.753642i	$-0.728295\pi$
$463$	−608.646			−1.31457			−0.657285	+	0.753642i	$0.728295\pi$
$464$		−	26.1589i		−	0.0563770i
$465$	1371.11			2.94863
$466$	500.254			1.07351
$467$	−261.094			−0.559087			−0.279543	−	0.960133i	$-0.590183\pi$
$467$	−261.094			−0.559087			−0.279543	+	0.960133i	$0.590183\pi$
$468$			21.6748i			0.0463137i
$469$		−	356.139i		−	0.759358i
$470$			1466.85i			3.12095i
$471$	−120.203			−0.255208
$472$			207.930i			0.440529i
$473$	21.5958	−	35.7931i	0.0456570	−	0.0756726i
$474$	644.997			1.36075
$475$			1568.18i			3.30142i
$476$	764.346			1.60577
$477$	33.1661			0.0695305
$478$	−564.270			−1.18048
$479$			605.207i			1.26348i	0.775180	+	0.631741i	$0.217659\pi$
$479$			605.207i			1.26348i	−0.775180	+	0.631741i	$0.782341\pi$
$480$		−	1127.61i		−	2.34919i
$481$			257.857i			0.536085i
$482$	108.187			0.224455
$483$			68.0614i			0.140914i
$484$	−312.068	−	592.125i	−0.644769	−	1.22340i
$485$	162.208			0.334449
$486$		−	120.598i		−	0.248143i
$487$	−215.688			−0.442892			−0.221446	−	0.975173i	$-0.571078\pi$
$487$	−215.688			−0.442892			−0.221446	+	0.975173i	$0.571078\pi$
$488$	−82.5435			−0.169146
$489$	307.899			0.629650
$490$		−	749.171i		−	1.52892i
$491$		−	91.3882i		−	0.186127i	−0.995660	−	0.0930633i	$-0.970334\pi$
$491$		−	91.3882i		−	0.186127i	0.995660	−	0.0930633i	$-0.0296659\pi$
$492$		−	1188.56i		−	2.41578i
$493$	105.514			0.214024
$494$		−	538.613i		−	1.09031i
$495$	−58.5784	−	35.3433i	−0.118340	−	0.0714006i
$496$	385.850			0.777924
$497$		−	71.8548i		−	0.144577i
$498$	−375.325			−0.753664
$499$	−721.156			−1.44520			−0.722601	−	0.691266i	$-0.757053\pi$
$499$	−721.156			−1.44520			−0.722601	+	0.691266i	$0.757053\pi$
$500$	−1118.58			−2.23715
$501$			439.586i			0.877418i
$502$		−	425.013i		−	0.846640i
$503$			358.812i			0.713345i	0.934230	+	0.356672i	$0.116089\pi$
$503$			358.812i			0.713345i	−0.934230	+	0.356672i	$0.883911\pi$
$504$	15.6034			0.0309591
$505$		−	778.062i		−	1.54072i
$506$	−84.1390	+	139.453i	−0.166283	+	0.275599i
$507$	−435.960			−0.859881
$508$			155.091i			0.305297i
$509$	112.771			0.221553			0.110777	−	0.993845i	$-0.464666\pi$
$509$	112.771			0.221553			0.110777	+	0.993845i	$0.464666\pi$
$510$	2507.51			4.91668
$511$	−301.358			−0.589743
$512$		−	459.707i		−	0.897865i
$513$			833.094i			1.62396i
$514$			432.977i			0.842369i
$515$	1214.90			2.35904
$516$			65.5569i			0.127048i
$517$	521.696	+	314.765i	1.00908	+	0.608830i
$518$	670.413			1.29423
$519$		−	688.676i		−	1.32693i
$520$	219.185			0.421510
$521$	−762.917			−1.46433			−0.732166	−	0.681126i	$-0.761490\pi$
$521$	−762.917			−1.46433			−0.732166	+	0.681126i	$0.761490\pi$
$522$	7.77925			0.0149028
$523$			396.267i			0.757680i	0.925462	+	0.378840i	$0.123677\pi$
$523$			396.267i			0.757680i	−0.925462	+	0.378840i	$0.876323\pi$
$524$		−	172.108i		−	0.328450i
$525$			689.364i			1.31307i
$526$	1317.76			2.50525
$527$			1556.35i			2.95323i
$528$	−221.098	−	133.400i	−0.418746	−	0.252651i
$529$	23.0000			0.0434783
$530$		−	1211.29i		−	2.28546i
$531$	31.8840			0.0600451
$532$	−812.693			−1.52762
$533$	−372.334			−0.698563
$534$			679.777i			1.27299i
$535$		−	1592.89i		−	2.97737i
$536$			370.054i			0.690400i
$537$	−548.118			−1.02070
$538$			688.487i			1.27972i
$539$	−266.448	−	160.762i	−0.494339	−	0.298259i
$540$	−1224.41			−2.26743
$541$			419.347i			0.775134i	0.921842	+	0.387567i	$0.126684\pi$
$541$			419.347i			0.775134i	−0.921842	+	0.387567i	$0.873316\pi$
$542$	−11.1256			−0.0205269
$543$	246.823			0.454555
$544$	1279.95			2.35286
$545$			93.2963i			0.171186i
$546$		−	236.772i		−	0.433649i
$547$			795.866i			1.45497i	0.686126	+	0.727483i	$0.259310\pi$
$547$			795.866i			1.45497i	−0.686126	+	0.727483i	$0.740690\pi$
$548$	−879.882			−1.60562
$549$			12.6572i			0.0230551i
$550$	−852.206	+	1412.46i	−1.54947	+	2.56810i
$551$	−112.188			−0.203608
$552$		−	70.7208i		−	0.128117i
$553$	−304.872			−0.551305
$554$	151.077			0.272703
$555$	1276.38			2.29978
$556$		−	117.542i		−	0.211406i
$557$		−	651.681i		−	1.16998i	−0.811039	−	0.584992i	$-0.801098\pi$
$557$		−	651.681i		−	1.16998i	0.811039	−	0.584992i	$-0.198902\pi$
$558$			114.746i			0.205638i
$559$	20.5366			0.0367381
$560$			293.841i			0.524716i
$561$	538.076	−	891.814i	0.959137	−	1.58969i
$562$	1085.21			1.93097
$563$			484.108i			0.859871i	0.902860	+	0.429936i	$0.141464\pi$
$563$			484.108i			0.859871i	−0.902860	+	0.429936i	$0.858536\pi$
$564$	−955.512			−1.69417
$565$	365.056			0.646117
$566$	10.9464			0.0193399
$567$			395.922i			0.698275i
$568$			74.6624i			0.131448i
$569$			17.7336i			0.0311662i	0.999879	+	0.0155831i	$0.00496045\pi$
$569$			17.7336i			0.0311662i	−0.999879	+	0.0155831i	$0.995040\pi$
$570$	−2666.11			−4.67739
$571$		−	734.976i		−	1.28717i	−0.765373	−	0.643586i	$-0.777446\pi$
$571$		−	734.976i		−	1.28717i	0.765373	−	0.643586i	$-0.222554\pi$
$572$	169.868	−	281.542i	0.296973	−	0.492206i
$573$	−526.177			−0.918284
$574$			968.047i			1.68649i
$575$	232.957			0.405142
$576$	72.5348			0.125928
$577$	63.1118			0.109379			0.0546896	−	0.998503i	$-0.482583\pi$
$577$	63.1118			0.109379			0.0546896	+	0.998503i	$0.482583\pi$
$578$			1954.04i			3.38069i
$579$			300.734i			0.519402i
$580$		−	164.884i		−	0.284283i
$581$	177.405			0.305345
$582$			182.070i			0.312835i
$583$	−430.807	−	259.927i	−0.738948	−	0.445844i
$584$	313.133			0.536187
$585$		−	33.6099i		−	0.0574528i
$586$	−94.7912			−0.161760
$587$	440.955			0.751201			0.375601	−	0.926782i	$-0.377436\pi$
$587$	440.955			0.751201			0.375601	+	0.926782i	$0.377436\pi$
$588$	488.014			0.829956
$589$		−	1654.80i		−	2.80950i
$590$		−	1164.47i		−	1.97368i
$591$		−	689.075i		−	1.16595i
$592$	359.192			0.606743
$593$		−	646.534i		−	1.09028i	−0.838346	−	0.545138i	$-0.816477\pi$
$593$		−	646.534i		−	1.09028i	0.838346	−	0.545138i	$-0.183523\pi$
$594$	−452.734	+	750.368i	−0.762179	+	1.26325i
$595$	−1185.23			−1.99198
$596$		−	1104.94i		−	1.85393i
$597$	580.544			0.972436
$598$	−80.0124			−0.133800
$599$	−323.342			−0.539804			−0.269902	−	0.962888i	$-0.586991\pi$
$599$	−323.342			−0.539804			−0.269902	+	0.962888i	$0.586991\pi$
$600$		−	716.299i		−	1.19383i
$601$			738.670i			1.22907i	0.788890	+	0.614535i	$0.210656\pi$
$601$			738.670i			1.22907i	−0.788890	+	0.614535i	$0.789344\pi$
$602$		−	53.3940i		−	0.0886944i
$603$	56.7442			0.0941032
$604$			1086.86i			1.79944i
$605$	483.907	+	918.174i	0.799846	+	1.51764i
$606$	873.333			1.44114
$607$			704.658i			1.16089i	0.814301	+	0.580443i	$0.197121\pi$
$607$			704.658i			1.16089i	−0.814301	+	0.580443i	$0.802879\pi$
$608$	−1360.92			−2.23835
$609$	−49.3173			−0.0809808
$610$	462.269			0.757818
$611$			299.327i			0.489898i
$612$			121.785i			0.198994i
$613$		−	703.847i		−	1.14820i	−0.818785	−	0.574100i	$-0.805352\pi$
$613$		−	703.847i		−	1.14820i	0.818785	−	0.574100i	$-0.194648\pi$
$614$	−1098.04			−1.78834
$615$			1843.04i			2.99681i
$616$	−202.678	−	122.286i	−0.329023	−	0.198516i
$617$	−475.675			−0.770948			−0.385474	−	0.922719i	$-0.625962\pi$
$617$	−475.675			−0.770948			−0.385474	+	0.922719i	$0.625962\pi$
$618$			1363.67i			2.20658i
$619$	381.583			0.616451			0.308226	−	0.951313i	$-0.400265\pi$
$619$	381.583			0.616451			0.308226	+	0.951313i	$0.400265\pi$
$620$	2432.08			3.92272
$621$	123.758			0.199289
$622$		−	788.583i		−	1.26782i
$623$		−	321.312i		−	0.515749i
$624$		−	126.857i		−	0.203296i
$625$	520.143			0.832229
$626$		−	554.107i		−	0.885155i
$627$	−572.111	+	948.224i	−0.912458	+	1.51232i
$628$	−213.216			−0.339516
$629$			1448.82i			2.30338i
$630$	−87.3837			−0.138704
$631$	−61.8786			−0.0980644			−0.0490322	−	0.998797i	$-0.515614\pi$
$631$	−61.8786			−0.0980644			−0.0490322	+	0.998797i	$0.515614\pi$
$632$	316.784			0.501241
$633$			676.237i			1.06830i
$634$			184.976i			0.291760i
$635$		−	240.490i		−	0.378725i
$636$	789.044			1.24064
$637$		−	152.877i		−	0.239996i
$638$	−101.048	−	60.9671i	−0.158382	−	0.0955597i
$639$	11.4487			0.0179167
$640$		−	1202.78i		−	1.87934i
$641$	451.782			0.704808			0.352404	−	0.935848i	$-0.385364\pi$
$641$	451.782			0.704808			0.352404	+	0.935848i	$0.385364\pi$
$642$	1787.94			2.78495
$643$	−195.516			−0.304068			−0.152034	−	0.988375i	$-0.548582\pi$
$643$	−195.516			−0.304068			−0.152034	+	0.988375i	$0.548582\pi$
$644$			120.728i			0.187465i
$645$		−	101.655i		−	0.157605i
$646$		−	3026.32i		−	4.68470i
$647$	567.650			0.877357			0.438679	−	0.898644i	$-0.355447\pi$
$647$	567.650			0.877357			0.438679	+	0.898644i	$0.355447\pi$
$648$		−	411.392i		−	0.634864i
$649$	−414.153	−	249.879i	−0.638140	−	0.385022i
$650$	−810.410			−1.24678
$651$		−	727.442i		−	1.11742i
$652$	546.153			0.837658
$653$	1223.01			1.87291			0.936454	−	0.350792i	$-0.114087\pi$
$653$	1223.01			1.87291			0.936454	+	0.350792i	$0.114087\pi$
$654$	−104.720			−0.160123
$655$			266.878i			0.407447i
$656$			518.657i			0.790636i
$657$		−	48.0159i		−	0.0730836i
$658$	778.234			1.18273
$659$		−	61.2330i		−	0.0929180i	−0.998920	−	0.0464590i	$-0.985206\pi$
$659$		−	61.2330i		−	0.0929180i	0.998920	−	0.0464590i	$-0.0147937\pi$
$660$	−1393.62	−	840.841i	−2.11155	−	1.27400i
$661$	−492.520			−0.745113			−0.372556	−	0.928010i	$-0.621519\pi$
$661$	−492.520			−0.745113			−0.372556	+	0.928010i	$0.621519\pi$
$662$			360.537i			0.544618i
$663$	511.686			0.771774
$664$	−184.337			−0.277616
$665$	1260.20			1.89503
$666$			106.818i			0.160387i
$667$			16.6658i			0.0249862i
$668$			779.741i			1.16728i
$669$	191.551			0.286324
$670$		−	2072.42i		−	3.09316i
$671$	99.1965	−	164.410i	0.147834	−	0.245022i
$672$	−598.252			−0.890256
$673$		−	834.108i		−	1.23939i	−0.784844	−	0.619694i	$-0.787257\pi$
$673$		−	834.108i		−	1.23939i	0.784844	−	0.619694i	$-0.212743\pi$
$674$	290.138			0.430472
$675$	1253.49			1.85702
$676$	−773.308			−1.14395
$677$		−	975.616i		−	1.44109i	−0.693410	−	0.720543i	$-0.743892\pi$
$677$		−	975.616i		−	1.44109i	0.693410	−	0.720543i	$-0.256108\pi$
$678$			409.756i			0.604360i
$679$		−	86.0593i		−	0.126744i
$680$	1231.54			1.81109
$681$		−	343.236i		−	0.504017i
$682$	899.279	−	1490.48i	1.31859	−	2.18545i
$683$	312.097			0.456951			0.228475	−	0.973550i	$-0.426626\pi$
$683$	312.097			0.456951			0.228475	+	0.973550i	$0.426626\pi$
$684$		−	129.488i		−	0.189310i
$685$	1364.38			1.99180
$686$	−1085.92			−1.58297
$687$	−312.273			−0.454546
$688$		−	28.6073i		−	0.0415804i
$689$		−	247.179i		−	0.358750i
$690$			396.058i			0.573997i
$691$	959.653			1.38879			0.694394	−	0.719595i	$-0.255672\pi$
$691$	959.653			1.38879			0.694394	+	0.719595i	$0.255672\pi$
$692$		−	1221.58i		−	1.76529i
$693$	−18.7513	+	31.0787i	−0.0270582	+	0.0448466i
$694$	−260.550			−0.375432
$695$			182.266i			0.262253i
$696$	51.2443			0.0736268
$697$	−2092.04			−3.00149
$698$	−1128.75			−1.61712
$699$		−	505.305i		−	0.722897i
$700$			1222.80i			1.74685i
$701$		−	1074.84i		−	1.53330i	−0.642066	−	0.766650i	$-0.721922\pi$
$701$		−	1074.84i		−	1.53330i	0.642066	−	0.766650i	$-0.278078\pi$
$702$	−430.530			−0.613291
$703$		−	1540.47i		−	2.19128i
$704$	−942.182	−	568.465i	−1.33833	−	0.807479i
$705$	1481.66			2.10164
$706$		−	1000.07i		−	1.41653i
$707$	−412.800			−0.583876
$708$	758.542			1.07139
$709$	−221.296			−0.312124			−0.156062	−	0.987747i	$-0.549880\pi$
$709$	−221.296			−0.312124			−0.156062	+	0.987747i	$0.549880\pi$
$710$		−	418.132i		−	0.588919i
$711$		−	48.5757i		−	0.0683203i
$712$			333.866i			0.468913i
$713$	−245.824			−0.344775
$714$		−	1330.35i		−	1.86324i
$715$	−263.405	+	436.571i	−0.368399	+	0.610589i
$716$	−972.254			−1.35790
$717$			569.968i			0.794934i
$718$	−374.706			−0.521875
$719$	−355.387			−0.494279			−0.247140	−	0.968980i	$-0.579491\pi$
$719$	−355.387			−0.494279			−0.247140	+	0.968980i	$0.579491\pi$
$720$	−46.8182			−0.0650253
$721$		−	644.566i		−	0.893989i
$722$			2103.21i			2.91304i
$723$		−	109.280i		−	0.151148i
$724$	437.816			0.604719
$725$			168.800i			0.232828i
$726$	−1030.60	+	543.159i	−1.41956	+	0.748153i
$727$	547.274			0.752785			0.376392	−	0.926460i	$-0.377165\pi$
$727$	547.274			0.752785			0.376392	+	0.926460i	$0.377165\pi$
$728$		−	116.288i		−	0.159737i
$729$	661.185			0.906976
$730$	−1753.64			−2.40225
$731$	115.389			0.157851
$732$			301.125i			0.411372i
$733$			697.757i			0.951919i	0.879467	+	0.475960i	$0.157899\pi$
$733$			697.757i			0.951919i	−0.879467	+	0.475960i	$0.842101\pi$
$734$		−	266.542i		−	0.363136i
$735$	−756.736			−1.02957
$736$			202.167i			0.274684i
$737$	−737.072	−	444.712i	−1.00010	−	0.603409i
$738$	−154.241			−0.208998
$739$			508.859i			0.688577i	0.938864	+	0.344289i	$0.111880\pi$
$739$			508.859i			0.688577i	−0.938864	+	0.344289i	$0.888120\pi$
$740$	2264.05			3.05953
$741$	−544.052			−0.734213
$742$	−642.651			−0.866107
$743$		−	1219.41i		−	1.64120i	−0.571502	−	0.820601i	$-0.693639\pi$
$743$		−	1219.41i		−	1.64120i	0.571502	−	0.820601i	$-0.306361\pi$
$744$			755.865i			1.01595i
$745$			1713.37i			2.29982i
$746$	1049.18			1.40640
$747$			28.2663i			0.0378398i
$748$	954.442	−	1581.90i	1.27599	−	2.11485i
$749$	−845.107			−1.12831
$750$			1946.90i			2.59587i
$751$	−577.056			−0.768383			−0.384191	−	0.923253i	$-0.625520\pi$
$751$	−577.056			−0.768383			−0.384191	+	0.923253i	$0.625520\pi$
$752$	416.960			0.554468
$753$	−429.305			−0.570126
$754$		−	57.9770i		−	0.0768926i
$755$		−	1685.34i		−	2.23223i
$756$			649.611i			0.859273i
$757$	135.068			0.178425			0.0892126	−	0.996013i	$-0.471565\pi$
$757$	135.068			0.178425			0.0892126	+	0.996013i	$0.471565\pi$
$758$			714.295i			0.942341i
$759$	140.861	+	84.9886i	0.185588	+	0.111974i
$760$	−1309.44			−1.72294
$761$			526.290i			0.691576i	0.938313	+	0.345788i	$0.112388\pi$
$761$			526.290i			0.691576i	−0.938313	+	0.345788i	$0.887612\pi$
$762$	269.938			0.354249
$763$	49.4983			0.0648732
$764$	−933.336			−1.22164
$765$		−	188.844i		−	0.246855i
$766$			1604.80i			2.09504i
$767$		−	237.624i		−	0.309809i
$768$	102.209			0.133085
$769$			838.578i			1.09048i	0.838281	+	0.545239i	$0.183561\pi$
$769$			838.578i			1.09048i	−0.838281	+	0.545239i	$0.816439\pi$
$770$	1135.06	+	684.839i	1.47410	+	0.889401i
$771$	437.349			0.567250
$772$			533.443i			0.690988i
$773$	420.471			0.543947			0.271974	−	0.962305i	$-0.412324\pi$
$773$	420.471			0.543947			0.271974	+	0.962305i	$0.412324\pi$
$774$	8.50736			0.0109914
$775$	−2489.85			−3.21270
$776$			89.4219i			0.115234i
$777$		−	677.182i		−	0.871535i
$778$			675.634i			0.868424i
$779$	2224.37			2.85541
$780$		−	799.603i		−	1.02513i
$781$	−148.712	−	89.7254i	−0.190412	−	0.114885i
$782$	−449.567			−0.574894
$783$			89.6752i			0.114528i
$784$	−212.956			−0.271628
$785$	330.622			0.421175
$786$	−299.556			−0.381115
$787$		−	1101.35i		−	1.39943i	−0.714421	−	0.699717i	$-0.753310\pi$
$787$		−	1101.35i		−	1.39943i	0.714421	−	0.699717i	$-0.246690\pi$
$788$		−	1222.29i		−	1.55112i
$789$		−	1331.07i		−	1.68703i
$790$	−1774.09			−2.24568
$791$		−	193.680i		−	0.244855i
$792$	19.4840	−	32.2930i	0.0246010	−	0.0407740i
$793$	94.3315			0.118955
$794$		−	1350.74i		−	1.70119i
$795$	−1223.53			−1.53903
$796$	1029.77			1.29368
$797$	631.199			0.791968			0.395984	−	0.918257i	$-0.370404\pi$
$797$	631.199			0.791968			0.395984	+	0.918257i	$0.370404\pi$
$798$			1414.50i			1.77256i
$799$			1681.84i			2.10493i
$800$			2047.66i			2.55958i
$801$	51.1951			0.0639140
$802$			1885.32i			2.35078i
$803$	−376.308	+	623.697i	−0.468627	+	0.776709i
$804$	1349.99			1.67909
$805$		−	187.206i		−	0.232554i
$806$	855.174			1.06101
$807$	695.439			0.861758
$808$	428.929			0.530853
$809$			965.150i			1.19302i	0.802607	+	0.596508i	$0.203446\pi$
$809$			965.150i			1.19302i	−0.802607	+	0.596508i	$0.796554\pi$
$810$			2303.92i			2.84435i
$811$		−	8.87104i		−	0.0109384i	−0.999985	−	0.00546920i	$-0.998259\pi$
$811$		−	8.87104i		−	0.0109384i	0.999985	−	0.00546920i	$-0.00174091\pi$
$812$	−87.4793			−0.107733
$813$			11.2379i			0.0138228i
$814$	837.147	−	1387.50i	1.02844	−	1.70454i
$815$	−846.888			−1.03913
$816$		−	712.773i		−	0.873497i
$817$	−122.688			−0.150169
$818$	−1383.95			−1.69187
$819$	−17.8317			−0.0217725
$820$			3269.19i			3.98682i
$821$			439.482i			0.535301i	0.963516	+	0.267650i	$0.0862472\pi$
$821$			439.482i			0.535301i	−0.963516	+	0.267650i	$0.913753\pi$
$822$			1531.45i			1.86308i
$823$	−658.887			−0.800592			−0.400296	−	0.916386i	$-0.631093\pi$
$823$	−658.887			−0.800592			−0.400296	+	0.916386i	$0.631093\pi$
$824$			669.751i			0.812805i
$825$	1426.72	+	860.811i	1.72936	+	1.04341i
$826$	−617.808			−0.747952
$827$		−	122.771i		−	0.148453i	−0.997241	−	0.0742265i	$-0.976351\pi$
$827$		−	122.771i		−	0.148453i	0.997241	−	0.0742265i	$-0.0236488\pi$
$828$	−19.2357			−0.0232316
$829$	−1558.02			−1.87939			−0.939696	−	0.342011i	$-0.888892\pi$
$829$	−1558.02			−1.87939			−0.939696	+	0.342011i	$0.888892\pi$
$830$	1032.35			1.24379
$831$		−	152.603i		−	0.183638i
$832$		−	540.585i		−	0.649742i
$833$		−	858.973i		−	1.03118i
$834$	−204.583			−0.245304
$835$		−	1209.10i		−	1.44802i
$836$	−1014.81	+	1681.97i	−1.21389	+	2.01192i
$837$	−1322.73			−1.58032
$838$		−	2402.32i		−	2.86673i
$839$	−1125.17			−1.34108			−0.670540	−	0.741874i	$-0.733937\pi$
$839$	−1125.17			−1.34108			−0.670540	+	0.741874i	$0.733937\pi$
$840$	−575.623			−0.685265
$841$	828.924			0.985641
$842$		−	736.356i		−	0.874532i
$843$		−	1096.17i		−	1.30031i
$844$			1199.51i			1.42122i
$845$	1199.12			1.41908
$846$			123.997i			0.146569i
$847$	487.136	−	256.736i	0.575132	−	0.303112i
$848$	−344.318			−0.406035
$849$		−	11.0569i		−	0.0130235i
$850$	−4553.46			−5.35701
$851$	−228.840			−0.268908
$852$	272.374			0.319688
$853$		−	199.354i		−	0.233709i	−0.993149	−	0.116855i	$-0.962719\pi$
$853$		−	199.354i		−	0.233709i	0.993149	−	0.116855i	$-0.0372812\pi$
$854$		−	245.256i		−	0.287185i
$855$			200.789i			0.234841i
$856$	878.128			1.02585
$857$			1392.60i			1.62498i	0.582977	+	0.812488i	$0.301888\pi$
$857$			1392.60i			1.62498i	−0.582977	+	0.812488i	$0.698112\pi$
$858$	−490.028	−	295.658i	−0.571128	−	0.344590i
$859$	38.5364			0.0448619			0.0224310	−	0.999748i	$-0.492859\pi$
$859$	38.5364			0.0448619			0.0224310	+	0.999748i	$0.492859\pi$
$860$		−	180.317i		−	0.209671i
$861$	977.822			1.13568
$862$	−2024.65			−2.34879
$863$	−38.1809			−0.0442421			−0.0221210	−	0.999755i	$-0.507042\pi$
$863$	−38.1809			−0.0442421			−0.0221210	+	0.999755i	$0.507042\pi$
$864$			1087.82i			1.25905i
$865$			1894.23i			2.18986i
$866$		−	1080.48i		−	1.24767i
$867$	1973.77			2.27655
$868$		−	1290.34i		−	1.48657i
$869$	−380.695	+	630.968i	−0.438084	+	0.726086i
$870$	−286.984			−0.329866
$871$		−	422.902i		−	0.485536i
$872$	−51.4323			−0.0589820
$873$	13.7120			0.0157067
$874$	478.004			0.546915
$875$		−	920.245i		−	1.05171i
$876$		−	1142.33i		−	1.30403i
$877$		−	930.199i		−	1.06066i	−0.847791	−	0.530330i	$-0.822068\pi$
$877$		−	930.199i		−	1.06066i	0.847791	−	0.530330i	$-0.177932\pi$
$878$	1579.40			1.79887
$879$			95.7484i			0.108929i
$880$	608.139	+	366.921i	0.691067	+	0.416955i
$881$	−36.0069			−0.0408705			−0.0204352	−	0.999791i	$-0.506505\pi$
$881$	−36.0069			−0.0408705			−0.0204352	+	0.999791i	$0.506505\pi$
$882$		−	63.3299i		−	0.0718026i
$883$	1427.10			1.61620			0.808099	−	0.589047i	$-0.200497\pi$
$883$	1427.10			1.61620			0.808099	+	0.589047i	$0.200497\pi$
$884$	907.632			1.02673
$885$	−1176.23			−1.32907
$886$		−	16.9050i		−	0.0190801i
$887$			529.743i			0.597230i	0.954374	+	0.298615i	$0.0965246\pi$
$887$			529.743i			0.597230i	−0.954374	+	0.298615i	$0.903475\pi$
$888$			703.642i			0.792389i
$889$	−127.592			−0.143523
$890$		−	1869.75i		−	2.10085i
$891$	819.408	+	494.390i	0.919650	+	0.554871i
$892$	339.774			0.380913
$893$		−	1788.22i		−	2.00248i
$894$	−1923.17			−2.15119
$895$	1507.62			1.68449
$896$	−638.133			−0.712202
$897$			80.8203i			0.0901007i
$898$			688.727i			0.766957i
$899$		−	178.124i		−	0.198136i
$900$	−194.830			−0.216478
$901$		−	1388.83i		−	1.54143i
$902$	2003.49	+	1208.80i	2.22116	+	1.34014i
$903$	−53.9332			−0.0597267
$904$			201.248i			0.222619i
$905$	−678.897			−0.750162
$906$	1891.70			2.08797
$907$	−957.437			−1.05561			−0.527805	−	0.849366i	$-0.676985\pi$
$907$	−957.437			−1.05561			−0.527805	+	0.849366i	$0.676985\pi$
$908$		−	608.833i		−	0.670521i
$909$		−	65.7721i		−	0.0723566i
$910$			651.251i			0.715660i
$911$	−47.3903			−0.0520201			−0.0260101	−	0.999662i	$-0.508280\pi$
$911$	−47.3903			−0.0520201			−0.0260101	+	0.999662i	$0.508280\pi$
$912$			757.859i			0.830985i
$913$	221.527	−	367.162i	0.242636	−	0.402149i
$914$	1626.56			1.77961
$915$		−	466.937i		−	0.510313i
$916$	−553.912			−0.604708
$917$	141.592			0.154408
$918$	−2419.03			−2.63510
$919$			472.252i			0.513876i	0.966428	+	0.256938i	$0.0827135\pi$
$919$			472.252i			0.513876i	−0.966428	+	0.256938i	$0.917286\pi$
$920$			194.520i			0.211435i
$921$			1109.13i			1.20427i
$922$	811.499			0.880151
$923$		−	85.3249i		−	0.0924430i
$924$	−446.108	+	739.385i	−0.482801	+	0.800200i
$925$	−2317.82			−2.50575
$926$			1879.09i			2.02926i
$927$	102.700			0.110787
$928$	−146.490			−0.157856
$929$	934.122			1.00551			0.502757	−	0.864428i	$-0.332319\pi$
$929$	934.122			1.00551			0.502757	+	0.864428i	$0.332319\pi$
$930$		−	4233.08i		−	4.55169i
$931$			913.306i			0.980995i
$932$		−	896.313i		−	0.961709i
$933$	−796.546			−0.853747
$934$			806.083i			0.863043i
$935$	−1480.00	+	2452.97i	−1.58289	+	2.62350i
$936$	18.5284			0.0197953
$937$			240.278i			0.256433i	0.991746	+	0.128217i	$0.0409253\pi$
$937$			240.278i			0.256433i	−0.991746	+	0.128217i	$0.959075\pi$
$938$	−1099.52			−1.17220
$939$	−559.702			−0.596062
$940$	2628.17			2.79593
$941$			1176.41i			1.25017i	0.780555	+	0.625087i	$0.214937\pi$
$941$			1176.41i			1.25017i	−0.780555	+	0.625087i	$0.785063\pi$
$942$			371.106i			0.393955i
$943$		−	330.435i		−	0.350409i
$944$	−331.007			−0.350643
$945$		−	1007.31i		−	1.06594i
$946$	−110.505	−	66.6734i	−0.116813	−	0.0704792i
$947$	1342.61			1.41775			0.708874	−	0.705335i	$-0.249203\pi$
$947$	1342.61			1.41775			0.708874	+	0.705335i	$0.249203\pi$
$948$		−	1155.65i		−	1.21904i
$949$	−357.852			−0.377083
$950$	4841.48			5.09630
$951$	186.843			0.196470
$952$		−	653.391i		−	0.686335i
$953$		−	1412.09i		−	1.48173i	−0.671653	−	0.740866i	$-0.734415\pi$
$953$		−	1412.09i		−	1.48173i	0.671653	−	0.740866i	$-0.265585\pi$
$954$		−	102.395i		−	0.107332i
$955$	1447.27			1.51547
$956$			1011.01i			1.05754i
$957$	−61.5827	+	102.068i	−0.0643498	+	0.106654i
$958$	1868.48			1.95039
$959$		−	723.873i		−	0.754820i
$960$	−2675.87			−2.78737
$961$	1666.38			1.73400
$962$	796.090			0.827536
$963$		−	134.652i		−	0.139826i
$964$		−	193.841i		−	0.201080i
$965$		−	827.180i		−	0.857181i
$966$	210.128			0.217524
$967$			1803.09i			1.86462i	0.361660	+	0.932310i	$0.382210\pi$
$967$			1803.09i			1.86462i	−0.361660	+	0.932310i	$0.617790\pi$
$968$	−506.170	+	266.768i	−0.522903	+	0.275586i
$969$	−3056.87			−3.15467
$970$		−	500.790i		−	0.516278i
$971$	−105.210			−0.108352			−0.0541759	−	0.998531i	$-0.517253\pi$
$971$	−105.210			−0.108352			−0.0541759	+	0.998531i	$0.517253\pi$
$972$	−216.077			−0.222301
$973$	96.7009			0.0993842
$974$			665.901i			0.683677i
$975$			818.593i			0.839583i
$976$		−	131.403i		−	0.134634i
$977$	1159.08			1.18636			0.593181	−	0.805069i	$-0.297872\pi$
$977$	1159.08			1.18636			0.593181	+	0.805069i	$0.297872\pi$
$978$		−	950.587i		−	0.971970i
$979$	−664.992	−	401.223i	−0.679257	−	0.409830i
$980$	−1342.30			−1.36970
$981$			7.88664i			0.00803939i
$982$	−282.146			−0.287317
$983$	1365.47			1.38909			0.694545	−	0.719450i	$-0.255606\pi$
$983$	1365.47			1.38909			0.694545	+	0.719450i	$0.255606\pi$
$984$	−1016.03			−1.03255
$985$			1895.33i			1.92419i
$986$		−	325.756i		−	0.330381i
$987$		−	786.092i		−	0.796446i
$988$	−965.043			−0.976764
$989$			18.2256i			0.0184284i
$990$	−109.116	+	180.851i	−0.110219	+	0.182678i
$991$	323.509			0.326447			0.163223	−	0.986589i	$-0.447811\pi$
$991$	323.509			0.326447			0.163223	+	0.986589i	$0.447811\pi$
$992$		−	2160.77i		−	2.17819i
$993$	364.177			0.366745
$994$	−221.840			−0.223179
$995$	−1596.81			−1.60483
$996$			672.475i			0.675176i
$997$			859.879i			0.862467i	0.902240	+	0.431233i	$0.141921\pi$
$997$			859.879i			0.862467i	−0.902240	+	0.431233i	$0.858079\pi$
$998$			2226.45i			2.23091i
$999$	−1231.34			−1.23257

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	253.3.c.a.208.6	✓	44
11.10	odd	2	inner	253.3.c.a.208.39	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
253.3.c.a.208.6	✓	44	1.1	even	1	trivial
253.3.c.a.208.39	yes	44	11.10	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 $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q-3.08733i q^{2} -3.11851 q^{3} -5.53163 q^{4} +8.57758 q^{5} +9.62787i q^{6} -4.55083i q^{7} +4.72864i q^{8} +0.725091 q^{9} -26.4818i q^{10} +(-9.41847 - 5.68264i) q^{11} +17.2504 q^{12} -5.40393i q^{13} -14.0499 q^{14} -26.7492 q^{15} -7.52762 q^{16} -30.3632i q^{17} -2.23860i q^{18} +32.2837i q^{19} -47.4479 q^{20} +14.1918i q^{21} +(-17.5442 + 29.0780i) q^{22} +4.79583 q^{23} -14.7463i q^{24} +48.5748 q^{25} -16.6837 q^{26} +25.8054 q^{27} +25.1735i q^{28} +3.47506i q^{29} +82.5838i q^{30} -51.2579 q^{31} +42.1548i q^{32} +(29.3716 + 17.7213i) q^{33} -93.7412 q^{34} -39.0351i q^{35} -4.01093 q^{36} -47.7165 q^{37} +99.6706 q^{38} +16.8522i q^{39} +40.5603i q^{40} -68.9006i q^{41} +43.8148 q^{42} +3.80031i q^{43} +(52.0995 + 31.4342i) q^{44} +6.21952 q^{45} -14.8063i q^{46} -55.3907 q^{47} +23.4749 q^{48} +28.2900 q^{49} -149.967i q^{50} +94.6877i q^{51} +29.8925i q^{52} +45.7406 q^{53} -79.6698i q^{54} +(-80.7877 - 48.7432i) q^{55} +21.5192 q^{56} -100.677i q^{57} +10.7287 q^{58} +43.9724 q^{59} +147.967 q^{60} +17.4561i q^{61} +158.250i q^{62} -3.29976i q^{63} +100.036 q^{64} -46.3527i q^{65} +(54.7117 - 90.6799i) q^{66} +78.2581 q^{67} +167.958i q^{68} -14.9558 q^{69} -120.514 q^{70} +15.7894 q^{71} +3.42869i q^{72} -66.2206i q^{73} +147.317i q^{74} -151.481 q^{75} -178.582i q^{76} +(-25.8607 + 42.8618i) q^{77} +52.0284 q^{78} -66.9926i q^{79} -64.5687 q^{80} -87.0001 q^{81} -212.719 q^{82} +38.9831i q^{83} -78.5037i q^{84} -260.442i q^{85} +11.7328 q^{86} -10.8370i q^{87} +(26.8711 - 44.5366i) q^{88} +70.6051 q^{89} -19.2017i q^{90} -24.5924 q^{91} -26.5287 q^{92} +159.848 q^{93} +171.009i q^{94} +276.916i q^{95} -131.460i q^{96} +18.9107 q^{97} -87.3406i q^{98} +(-6.82925 - 4.12043i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 8 q^{3} - 88 q^{4} + 100 q^{9} + 8 q^{14} - 8 q^{15} + 72 q^{16} - 40 q^{20} - 76 q^{22} + 268 q^{25} - 40 q^{26} + 32 q^{27} + 72 q^{31} - 90 q^{33} + 60 q^{34} - 312 q^{36} + 4 q^{37} + 40 q^{38}+ \cdots + 494 q^{99}+O(q^{100}) \) 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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