LMFDB - Embedded newform 143.4.b.a.12.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [143,4,Mod(12,143)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(143, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("143.12");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 143 = 11 \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	143.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$8.43727313082$
Analytic rank:	$0$
Dimension:	$36$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			12.15
Character	$\chi$	$=$	143.12
Dual form			143.4.b.a.12.22

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.26989i q^{2} +3.96847 q^{3} +6.38737 q^{4} +4.99906i q^{5} -5.03953i q^{6} -32.3730i q^{7} -18.2704i q^{8} -11.2513 q^{9} +O(q^{10})$	\(q-1.26989i q^{2} +3.96847 q^{3} +6.38737 q^{4} +4.99906i q^{5} -5.03953i q^{6} -32.3730i q^{7} -18.2704i q^{8} -11.2513 q^{9} +6.34827 q^{10} +11.0000i q^{11} +25.3481 q^{12} +(41.9782 - 20.8525i) q^{13} -41.1102 q^{14} +19.8386i q^{15} +27.8975 q^{16} +65.4417 q^{17} +14.2879i q^{18} +66.3251i q^{19} +31.9309i q^{20} -128.471i q^{21} +13.9688 q^{22} -25.5111 q^{23} -72.5055i q^{24} +100.009 q^{25} +(-26.4805 - 53.3078i) q^{26} -151.799 q^{27} -206.778i q^{28} -195.053 q^{29} +25.1929 q^{30} +23.5247i q^{31} -181.590i q^{32} +43.6531i q^{33} -83.1040i q^{34} +161.834 q^{35} -71.8661 q^{36} +95.7674i q^{37} +84.2257 q^{38} +(166.589 - 82.7526i) q^{39} +91.3350 q^{40} +245.497i q^{41} -163.144 q^{42} +397.276 q^{43} +70.2611i q^{44} -56.2458i q^{45} +32.3963i q^{46} +139.763i q^{47} +110.710 q^{48} -705.008 q^{49} -127.001i q^{50} +259.703 q^{51} +(268.131 - 133.193i) q^{52} -224.488 q^{53} +192.768i q^{54} -54.9897 q^{55} -591.467 q^{56} +263.209i q^{57} +247.696i q^{58} +584.190i q^{59} +126.717i q^{60} -732.958 q^{61} +29.8738 q^{62} +364.237i q^{63} -7.41971 q^{64} +(104.243 + 209.852i) q^{65} +55.4348 q^{66} -211.980i q^{67} +418.001 q^{68} -101.240 q^{69} -205.512i q^{70} -59.0998i q^{71} +205.565i q^{72} -19.3785i q^{73} +121.614 q^{74} +396.884 q^{75} +423.643i q^{76} +356.102 q^{77} +(-105.087 - 211.550i) q^{78} +282.957 q^{79} +139.462i q^{80} -298.625 q^{81} +311.754 q^{82} +1356.44i q^{83} -820.592i q^{84} +327.148i q^{85} -504.497i q^{86} -774.062 q^{87} +200.975 q^{88} +856.502i q^{89} -71.4261 q^{90} +(-675.058 - 1358.96i) q^{91} -162.949 q^{92} +93.3570i q^{93} +177.484 q^{94} -331.563 q^{95} -720.635i q^{96} -1013.29i q^{97} +895.284i q^{98} -123.764i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 152 q^{4} + 360 q^{9}+O(q^{10}) $ 36 * q - 152 * q^4 + 360 * q^9	$ 36 q - 152 q^{4} + 360 q^{9} - 112 q^{10} - 108 q^{12} - 50 q^{13} + 8 q^{14} + 728 q^{16} + 276 q^{17} + 44 q^{22} - 472 q^{23} - 1172 q^{25} + 152 q^{26} - 12 q^{27} - 572 q^{29} + 712 q^{30} + 68 q^{35} - 430 q^{36} - 50 q^{38} + 640 q^{39} - 216 q^{40} + 1126 q^{42} + 920 q^{43} + 1674 q^{48} - 2164 q^{49} - 340 q^{51} - 800 q^{52} + 2432 q^{53} + 440 q^{55} - 2274 q^{56} - 1844 q^{61} + 2796 q^{62} - 2592 q^{64} + 2264 q^{65} + 1078 q^{66} - 4548 q^{68} - 3288 q^{69} - 4036 q^{74} + 820 q^{75} - 616 q^{77} + 2222 q^{78} + 360 q^{79} + 852 q^{81} + 1948 q^{82} - 2480 q^{87} + 264 q^{88} - 496 q^{90} + 4600 q^{91} + 454 q^{92} - 488 q^{94} + 952 q^{95}+O(q^{100}) $ 36 * q - 152 * q^4 + 360 * q^9 - 112 * q^10 - 108 * q^12 - 50 * q^13 + 8 * q^14 + 728 * q^16 + 276 * q^17 + 44 * q^22 - 472 * q^23 - 1172 * q^25 + 152 * q^26 - 12 * q^27 - 572 * q^29 + 712 * q^30 + 68 * q^35 - 430 * q^36 - 50 * q^38 + 640 * q^39 - 216 * q^40 + 1126 * q^42 + 920 * q^43 + 1674 * q^48 - 2164 * q^49 - 340 * q^51 - 800 * q^52 + 2432 * q^53 + 440 * q^55 - 2274 * q^56 - 1844 * q^61 + 2796 * q^62 - 2592 * q^64 + 2264 * q^65 + 1078 * q^66 - 4548 * q^68 - 3288 * q^69 - 4036 * q^74 + 820 * q^75 - 616 * q^77 + 2222 * q^78 + 360 * q^79 + 852 * q^81 + 1948 * q^82 - 2480 * q^87 + 264 * q^88 - 496 * q^90 + 4600 * q^91 + 454 * q^92 - 488 * q^94 + 952 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/143\mathbb{Z}\right)^\times$.

$n$	$67$	$79$
$\chi(n)$	$-1$	$1$

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 $

$2$		−	1.26989i		−	0.448975i	−0.974477	−	0.224487i	$-0.927929\pi$
$2$		−	1.26989i		−	0.448975i	0.974477	−	0.224487i	$-0.0720707\pi$
$3$	3.96847			0.763732			0.381866	−	0.924218i	$-0.375282\pi$
$3$	3.96847			0.763732			0.381866	+	0.924218i	$0.375282\pi$
$4$	6.38737			0.798422
$5$			4.99906i			0.447130i	0.974689	+	0.223565i	$0.0717695\pi$
$5$			4.99906i			0.447130i	−0.974689	+	0.223565i	$0.928231\pi$
$6$		−	5.03953i		−	0.342896i
$7$		−	32.3730i		−	1.74798i	−0.485948	−	0.873988i	$-0.661526\pi$
$7$		−	32.3730i		−	1.74798i	0.485948	−	0.873988i	$-0.338474\pi$
$8$		−	18.2704i		−	0.807446i
$9$	−11.2513			−0.416714
$10$	6.34827			0.200750
$11$			11.0000i			0.301511i
$11$			11.0000i			0.301511i
$12$	25.3481			0.609780
$13$	41.9782	−	20.8525i	0.895590	−	0.444881i
$13$	41.9782	−	20.8525i	0.895590	−	0.444881i
$14$	−41.1102			−0.784797
$15$			19.8386i			0.341487i
$16$	27.8975			0.435899
$17$	65.4417			0.933644			0.466822	−	0.884351i	$-0.345399\pi$
$17$	65.4417			0.933644			0.466822	+	0.884351i	$0.345399\pi$
$18$			14.2879i			0.187094i
$19$			66.3251i			0.800843i	0.916331	+	0.400421i	$0.131136\pi$
$19$			66.3251i			0.800843i	−0.916331	+	0.400421i	$0.868864\pi$
$20$			31.9309i			0.356998i
$21$		−	128.471i		−	1.33498i
$22$	13.9688			0.135371
$23$	−25.5111			−0.231279			−0.115640	−	0.993291i	$-0.536892\pi$
$23$	−25.5111			−0.231279			−0.115640	+	0.993291i	$0.536892\pi$
$24$		−	72.5055i		−	0.616672i
$25$	100.009			0.800075
$26$	−26.4805	−	53.3078i	−0.199740	−	0.402097i
$27$	−151.799			−1.08199
$28$		−	206.778i		−	1.39562i
$29$	−195.053			−1.24898			−0.624490	−	0.781032i	$-0.714693\pi$
$29$	−195.053			−1.24898			−0.624490	+	0.781032i	$0.714693\pi$
$30$	25.1929			0.153319
$31$			23.5247i			0.136296i	0.997675	+	0.0681478i	$0.0217089\pi$
$31$			23.5247i			0.136296i	−0.997675	+	0.0681478i	$0.978291\pi$
$32$		−	181.590i		−	1.00315i
$33$			43.6531i			0.230274i
$34$		−	83.1040i		−	0.419183i
$35$	161.834			0.781572
$36$	−71.8661			−0.332713
$37$			95.7674i			0.425515i	0.977105	+	0.212758i	$0.0682445\pi$
$37$			95.7674i			0.425515i	−0.977105	+	0.212758i	$0.931756\pi$
$38$	84.2257			0.359558
$39$	166.589	−	82.7526i	0.683990	−	0.339770i
$40$	91.3350			0.361033
$41$			245.497i			0.935126i	0.883960	+	0.467563i	$0.154868\pi$
$41$			245.497i			0.935126i	−0.883960	+	0.467563i	$0.845132\pi$
$42$	−163.144			−0.599374
$43$	397.276			1.40893			0.704465	−	0.709739i	$-0.251187\pi$
$43$	397.276			1.40893			0.704465	+	0.709739i	$0.251187\pi$
$44$			70.2611i			0.240733i
$45$		−	56.2458i		−	0.186325i
$46$			32.3963i			0.103839i
$47$			139.763i			0.433755i	0.976199	+	0.216878i	$0.0695873\pi$
$47$			139.763i			0.433755i	−0.976199	+	0.216878i	$0.930413\pi$
$48$	110.710			0.332910
$49$	−705.008			−2.05542
$50$		−	127.001i		−	0.359213i
$51$	259.703			0.713054
$52$	268.131	−	133.193i	0.715058	−	0.355203i
$53$	−224.488			−0.581808			−0.290904	−	0.956752i	$-0.593956\pi$
$53$	−224.488			−0.581808			−0.290904	+	0.956752i	$0.593956\pi$
$54$			192.768i			0.485786i
$55$	−54.9897			−0.134815
$56$	−591.467			−1.41140
$57$			263.209i			0.611629i
$58$			247.696i			0.560761i
$59$			584.190i			1.28907i	0.764576	+	0.644534i	$0.222949\pi$
$59$			584.190i			1.28907i	−0.764576	+	0.644534i	$0.777051\pi$
$60$			126.717i			0.272651i
$61$	−732.958			−1.53845			−0.769226	−	0.638977i	$-0.779358\pi$
$61$	−732.958			−1.53845			−0.769226	+	0.638977i	$0.779358\pi$
$62$	29.8738			0.0611933
$63$			364.237i			0.728405i
$64$	−7.41971			−0.0144916
$65$	104.243	+	209.852i	0.198920	+	0.400445i
$66$	55.4348			0.103387
$67$		−	211.980i		−	0.386529i	−0.981147	−	0.193264i	$-0.938092\pi$
$67$		−	211.980i		−	0.386529i	0.981147	−	0.193264i	$-0.0619075\pi$
$68$	418.001			0.745442
$69$	−101.240			−0.176635
$70$		−	205.512i		−	0.350906i
$71$		−	59.0998i		−	0.0987867i	−0.998779	−	0.0493934i	$-0.984271\pi$
$71$		−	59.0998i		−	0.0987867i	0.998779	−	0.0493934i	$-0.0157288\pi$
$72$			205.565i			0.336474i
$73$		−	19.3785i		−	0.0310696i	−0.999879	−	0.0155348i	$-0.995055\pi$
$73$		−	19.3785i		−	0.0310696i	0.999879	−	0.0155348i	$-0.00494509\pi$
$74$	121.614			0.191046
$75$	396.884			0.611043
$76$			423.643i			0.639410i
$77$	356.102			0.527034
$78$	−105.087	−	211.550i	−0.152548	−	0.307094i
$79$	282.957			0.402976			0.201488	−	0.979491i	$-0.435422\pi$
$79$	282.957			0.402976			0.201488	+	0.979491i	$0.435422\pi$
$80$			139.462i			0.194903i
$81$	−298.625			−0.409636
$82$	311.754			0.419848
$83$			1356.44i			1.79384i	0.442190	+	0.896921i	$0.354202\pi$
$83$			1356.44i			1.79384i	−0.442190	+	0.896921i	$0.645798\pi$
$84$		−	820.592i		−	1.06588i
$85$			327.148i			0.417460i
$86$		−	504.497i		−	0.632574i
$87$	−774.062			−0.953887
$88$	200.975			0.243454
$89$			856.502i			1.02010i	0.860144	+	0.510051i	$0.170373\pi$
$89$			856.502i			1.02010i	−0.860144	+	0.510051i	$0.829627\pi$
$90$	−71.4261			−0.0836553
$91$	−675.058	−	1358.96i	−0.777641	−	1.56547i
$92$	−162.949			−0.184658
$93$			93.3570i			0.104093i
$94$	177.484			0.194745
$95$	−331.563			−0.358081
$96$		−	720.635i		−	0.766140i
$97$		−	1013.29i		−	1.06066i	−0.847792	−	0.530330i	$-0.822068\pi$
$97$		−	1013.29i		−	1.06066i	0.847792	−	0.530330i	$-0.177932\pi$
$98$			895.284i			0.922830i
$99$		−	123.764i		−	0.125644i
$100$	638.797			0.638797
$101$	45.1645			0.0444954			0.0222477	−	0.999752i	$-0.492918\pi$
$101$	45.1645			0.0444954			0.0222477	+	0.999752i	$0.492918\pi$
$102$		−	329.795i		−	0.320143i
$103$	−683.159			−0.653530			−0.326765	−	0.945106i	$-0.605959\pi$
$103$	−683.159			−0.653530			−0.326765	+	0.945106i	$0.605959\pi$
$104$	−380.984	−	766.960i	−0.359217	−	0.723140i
$105$	642.235			0.596911
$106$			285.076i			0.261217i
$107$	1202.00			1.08600			0.542999	−	0.839733i	$-0.317289\pi$
$107$	1202.00			1.08600			0.542999	+	0.839733i	$0.317289\pi$
$108$	−969.596			−0.863884
$109$		−	981.385i		−	0.862382i	−0.902261	−	0.431191i	$-0.858094\pi$
$109$		−	981.385i		−	0.862382i	0.902261	−	0.431191i	$-0.141906\pi$
$110$			69.8310i			0.0605284i
$111$			380.050i			0.324980i
$112$		−	903.125i		−	0.761940i
$113$	252.546			0.210244			0.105122	−	0.994459i	$-0.466477\pi$
$113$	252.546			0.210244			0.105122	+	0.994459i	$0.466477\pi$
$114$	334.247			0.274606
$115$		−	127.532i		−	0.103412i
$116$	−1245.88			−0.997213
$117$	−472.308	+	234.617i	−0.373204	+	0.185388i
$118$	741.858			0.578759
$119$		−	2118.54i		−	1.63199i
$120$	362.460			0.275733
$121$	−121.000			−0.0909091
$122$			930.777i			0.690726i
$123$			974.246i			0.714185i
$124$			150.261i			0.108821i
$125$			1124.84i			0.804867i
$126$	462.541			0.327035
$127$	−1513.45			−1.05745			−0.528727	−	0.848792i	$-0.677330\pi$
$127$	−1513.45			−1.05745			−0.528727	+	0.848792i	$0.677330\pi$
$128$		−	1443.30i		−	0.996647i
$129$	1576.58			1.07604
$130$	266.489	−	132.378i	0.179790	−	0.0893099i
$131$	2795.84			1.86468			0.932341	−	0.361579i	$-0.117762\pi$
$131$	2795.84			1.86468			0.932341	+	0.361579i	$0.117762\pi$
$132$			278.829i			0.183856i
$133$	2147.14			1.39985
$134$	−269.191			−0.173542
$135$		−	758.853i		−	0.483790i
$136$		−	1195.65i		−	0.753867i
$137$		−	1651.30i		−	1.02978i	−0.857255	−	0.514892i	$-0.827832\pi$
$137$		−	1651.30i		−	1.02978i	0.857255	−	0.514892i	$-0.172168\pi$
$138$			128.564i			0.0793049i
$139$	−1429.39			−0.872223			−0.436112	−	0.899893i	$-0.643645\pi$
$139$	−1429.39			−0.872223			−0.436112	+	0.899893i	$0.643645\pi$
$140$	1033.70			0.624024
$141$			554.644i			0.331273i
$142$	−75.0504			−0.0443527
$143$	229.378	+	461.761i	0.134137	+	0.270030i
$144$	−313.883			−0.181645
$145$		−	975.083i		−	0.558457i
$146$	−24.6086			−0.0139495
$147$	−2797.80			−1.56979
$148$			611.702i			0.339741i
$149$			514.352i			0.282801i	0.989952	+	0.141401i	$0.0451605\pi$
$149$			514.352i			0.282801i	−0.989952	+	0.141401i	$0.954839\pi$
$150$		−	504.000i		−	0.274343i
$151$			1547.44i			0.833963i	0.908915	+	0.416982i	$0.136912\pi$
$151$			1547.44i			0.833963i	−0.908915	+	0.416982i	$0.863088\pi$
$152$	1211.79			0.646637
$153$	−736.303			−0.389062
$154$		−	452.212i		−	0.236625i
$155$	−117.602			−0.0609418
$156$	1064.07	−	528.572i	0.546113	−	0.271280i
$157$	−1704.15			−0.866278			−0.433139	−	0.901327i	$-0.642594\pi$
$157$	−1704.15			−0.866278			−0.433139	+	0.901327i	$0.642594\pi$
$158$		−	359.325i		−	0.180926i
$159$	−890.874			−0.444346
$160$	907.781			0.448540
$161$			825.869i			0.404271i
$162$			379.221i			0.183916i
$163$			3437.52i			1.65182i	0.563799	+	0.825912i	$0.309339\pi$
$163$			3437.52i			1.65182i	−0.563799	+	0.825912i	$0.690661\pi$
$164$			1568.08i			0.746625i
$165$	−218.225			−0.102962
$166$	1722.54			0.805390
$167$		−	2060.63i		−	0.954828i	−0.878679	−	0.477414i	$-0.841574\pi$
$167$		−	2060.63i		−	0.954828i	0.878679	−	0.477414i	$-0.158426\pi$
$168$	−2347.22			−1.07793
$169$	1327.34	−	1750.70i	0.604162	−	0.796862i
$170$	415.442			0.187429
$171$		−	746.241i		−	0.333722i
$172$	2537.55			1.12492
$173$	−522.234			−0.229507			−0.114754	−	0.993394i	$-0.536608\pi$
$173$	−522.234			−0.229507			−0.114754	+	0.993394i	$0.536608\pi$
$174$			982.975i			0.428271i
$175$		−	3237.60i		−	1.39851i
$176$			306.873i			0.131428i
$177$			2318.34i			0.984502i
$178$	1087.67			0.458000
$179$	−181.450			−0.0757667			−0.0378833	−	0.999282i	$-0.512062\pi$
$179$	−181.450			−0.0757667			−0.0378833	+	0.999282i	$0.512062\pi$
$180$		−	359.263i		−	0.148766i
$181$	2845.40			1.16849			0.584246	−	0.811576i	$-0.301390\pi$
$181$	2845.40			1.16849			0.584246	+	0.811576i	$0.301390\pi$
$182$	−1725.73	+	857.251i	−0.702856	+	0.349141i
$183$	−2908.72			−1.17497
$184$			466.098i			0.186746i
$185$	−478.747			−0.190261
$186$	118.553			0.0467352
$187$			719.859i			0.281504i
$188$			892.717i			0.346320i
$189$			4914.18i			1.89129i
$190$			421.050i			0.160769i
$191$	−4825.05			−1.82790			−0.913948	−	0.405831i	$-0.866982\pi$
$191$	−4825.05			−1.82790			−0.913948	+	0.405831i	$0.866982\pi$
$192$	−29.4449			−0.0110677
$193$		−	4662.94i		−	1.73910i	−0.493847	−	0.869549i	$-0.664410\pi$
$193$		−	4662.94i		−	1.73910i	0.493847	−	0.869549i	$-0.335590\pi$
$194$	−1286.77			−0.476209
$195$	413.686	+	832.790i	0.151921	+	0.305833i
$196$	−4503.15			−1.64109
$197$		−	415.981i		−	0.150444i	−0.997167	−	0.0752218i	$-0.976034\pi$
$197$		−	415.981i		−	0.150444i	0.997167	−	0.0752218i	$-0.0239665\pi$
$198$	−157.167			−0.0564109
$199$	4372.09			1.55743			0.778717	−	0.627376i	$-0.215871\pi$
$199$	4372.09			1.55743			0.778717	+	0.627376i	$0.215871\pi$
$200$		−	1827.21i		−	0.646017i
$201$		−	841.234i		−	0.295205i
$202$		−	57.3540i		−	0.0199773i
$203$			6314.44i			2.18319i
$204$	1658.82			0.569318
$205$	−1227.25			−0.418123
$206$			867.538i			0.293419i
$207$	287.032			0.0963773
$208$	1171.09	−	581.734i	0.390387	−	0.193923i
$209$	−729.576			−0.241463
$210$		−	815.569i		−	0.267998i
$211$	−294.344			−0.0960354			−0.0480177	−	0.998846i	$-0.515290\pi$
$211$	−294.344			−0.0960354			−0.0480177	+	0.998846i	$0.515290\pi$
$212$	−1433.89			−0.464528
$213$		−	234.536i		−	0.0754466i
$214$		−	1526.41i		−	0.487586i
$215$			1986.01i			0.629975i
$216$			2773.43i			0.873648i
$217$	761.564			0.238241
$218$	−1246.25			−0.387188
$219$		−	76.9030i		−	0.0237289i
$220$	−351.240			−0.107639
$221$	2747.13	−	1364.63i	0.836162	−	0.415361i
$222$	482.622			0.145908
$223$		−	1064.30i		−	0.319601i	−0.987149	−	0.159800i	$-0.948915\pi$
$223$		−	1064.30i		−	0.319601i	0.987149	−	0.159800i	$-0.0510851\pi$
$224$	−5878.61			−1.75349
$225$	−1125.23			−0.333402
$226$		−	320.707i		−	0.0943942i
$227$		−	5384.86i		−	1.57447i	−0.616650	−	0.787237i	$-0.711511\pi$
$227$		−	5384.86i		−	1.57447i	0.616650	−	0.787237i	$-0.288489\pi$
$228$			1681.21i			0.488338i
$229$			732.853i			0.211477i	0.994394	+	0.105739i	$0.0337207\pi$
$229$			732.853i			0.211477i	−0.994394	+	0.105739i	$0.966279\pi$
$230$	−161.951			−0.0464293
$231$	1413.18			0.402513
$232$			3563.70i			1.00848i
$233$	2754.99			0.774616			0.387308	−	0.921950i	$-0.373405\pi$
$233$	2754.99			0.774616			0.387308	+	0.921950i	$0.373405\pi$
$234$	297.939	+	599.781i	0.0832345	+	0.167559i
$235$	−698.683			−0.193945
$236$			3731.44i			1.02922i
$237$	1122.90			0.307766
$238$	−2690.32			−0.732721
$239$			2395.98i			0.648464i	0.945978	+	0.324232i	$0.105106\pi$
$239$			2395.98i			0.648464i	−0.945978	+	0.324232i	$0.894894\pi$
$240$			553.449i			0.148854i
$241$		−	3961.59i		−	1.05887i	−0.848349	−	0.529437i	$-0.822403\pi$
$241$		−	3961.59i		−	1.05887i	0.848349	−	0.529437i	$-0.177597\pi$
$242$			153.657i			0.0408159i
$243$	2913.49			0.769137
$244$	−4681.67			−1.22833
$245$		−	3524.38i		−	0.919038i
$246$	1237.19			0.320651
$247$	1383.05	+	2784.21i	0.356280	+	0.717227i
$248$	429.806			0.110051
$249$			5383.00i			1.37001i
$250$	1428.42			0.361365
$251$	−146.537			−0.0368498			−0.0184249	−	0.999830i	$-0.505865\pi$
$251$	−146.537			−0.0368498			−0.0184249	+	0.999830i	$0.505865\pi$
$252$			2326.52i			0.581574i
$253$		−	280.622i		−	0.0697334i
$254$			1921.91i			0.474770i
$255$			1298.27i			0.318828i
$256$	−1892.19			−0.461961
$257$	−3590.96			−0.871586			−0.435793	−	0.900047i	$-0.643532\pi$
$257$	−3590.96			−0.871586			−0.435793	+	0.900047i	$0.643532\pi$
$258$		−	2002.08i		−	0.483117i
$259$	3100.27			0.743790
$260$	665.840	+	1340.40i	0.158822	+	0.319724i
$261$	2194.59			0.520467
$262$		−	3550.41i		−	0.837195i
$263$	−6675.46			−1.56512			−0.782559	−	0.622576i	$-0.786086\pi$
$263$	−6675.46			−1.56512			−0.782559	+	0.622576i	$0.786086\pi$
$264$	797.561			0.185934
$265$		−	1122.23i		−	0.260144i
$266$		−	2726.63i		−	0.628499i
$267$			3399.00i			0.779084i
$268$		−	1353.99i		−	0.308613i
$269$	4613.40			1.04567			0.522833	−	0.852435i	$-0.324875\pi$
$269$	4613.40			1.04567			0.522833	+	0.852435i	$0.324875\pi$
$270$	−963.661			−0.217209
$271$		−	7795.95i		−	1.74749i	−0.486383	−	0.873746i	$-0.661684\pi$
$271$		−	7795.95i		−	1.74749i	0.486383	−	0.873746i	$-0.338316\pi$
$272$	1825.66			0.406975
$273$	−2678.95	−	5392.98i	−0.593909	−	1.19560i
$274$	−2096.98			−0.462347
$275$			1100.10i			0.241232i
$276$	−646.657			−0.141030
$277$	5527.75			1.19903			0.599513	−	0.800365i	$-0.295361\pi$
$277$	5527.75			1.19903			0.599513	+	0.800365i	$0.295361\pi$
$278$			1815.17i			0.391606i
$279$		−	264.683i		−	0.0567962i
$280$		−	2956.78i		−	0.631077i
$281$			2142.52i			0.454846i	0.973796	+	0.227423i	$0.0730300\pi$
$281$			2142.52i			0.454846i	−0.973796	+	0.227423i	$0.926970\pi$
$282$	704.338			0.148733
$283$	8790.28			1.84639			0.923194	−	0.384335i	$-0.125569\pi$
$283$	8790.28			1.84639			0.923194	+	0.384335i	$0.125569\pi$
$284$		−	377.493i		−	0.0788735i
$285$	−1315.80			−0.273478
$286$	586.386	−	291.285i	0.121237	−	0.0602240i
$287$	7947.46			1.63458
$288$			2043.12i			0.418028i
$289$	−630.378			−0.128308
$290$	−1238.25			−0.250733
$291$		−	4021.20i		−	0.810059i
$292$		−	123.778i		−	0.0248067i
$293$		−	9469.04i		−	1.88801i	−0.329930	−	0.944005i	$-0.607025\pi$
$293$		−	9469.04i		−	1.88801i	0.329930	−	0.944005i	$-0.392975\pi$
$294$			3552.91i			0.704795i
$295$	−2920.40			−0.576381
$296$	1749.71			0.343581
$297$		−	1669.79i		−	0.326232i
$298$	653.172			0.126971
$299$	−1070.91	+	531.971i	−0.207131	+	0.102892i
$300$	2535.05			0.487870
$301$		−	12861.0i		−	2.46277i
$302$	1965.08			0.374428
$303$	179.234			0.0339825
$304$			1850.31i			0.349087i
$305$		−	3664.10i		−	0.687888i
$306$			935.025i			0.174679i
$307$			10120.2i			1.88140i	0.339234	+	0.940702i	$0.389832\pi$
$307$			10120.2i			1.88140i	−0.339234	+	0.940702i	$0.610168\pi$
$308$	2274.56			0.420796
$309$	−2711.09			−0.499122
$310$			149.341i			0.0273613i
$311$	−292.541			−0.0533392			−0.0266696	−	0.999644i	$-0.508490\pi$
$311$	−292.541			−0.0533392			−0.0266696	+	0.999644i	$0.508490\pi$
$312$	−1511.92	−	3043.65i	−0.274346	−	0.552285i
$313$	−6584.75			−1.18911			−0.594556	−	0.804054i	$-0.702672\pi$
$313$	−6584.75			−1.18911			−0.594556	+	0.804054i	$0.702672\pi$
$314$			2164.08i			0.388937i
$315$	−1820.84			−0.325692
$316$	1807.35			0.321745
$317$		−	7401.38i		−	1.31137i	−0.755037	−	0.655683i	$-0.772381\pi$
$317$		−	7401.38i		−	1.31137i	0.755037	−	0.655683i	$-0.227619\pi$
$318$			1131.31i			0.199500i
$319$		−	2145.58i		−	0.376582i
$320$		−	37.0916i		−	0.00647964i
$321$	4770.10			0.829411
$322$	1048.76			0.181507
$323$			4340.43i			0.747702i
$324$	−1907.43			−0.327062
$325$	4198.22	−	2085.45i	0.716539	−	0.355938i
$326$	4365.28			0.741627
$327$		−	3894.59i		−	0.658629i
$328$	4485.33			0.755064
$329$	4524.53			0.758193
$330$			277.122i			0.0462275i
$331$		−	5504.40i		−	0.914046i	−0.889455	−	0.457023i	$-0.848916\pi$
$331$		−	5504.40i		−	0.914046i	0.889455	−	0.457023i	$-0.151084\pi$
$332$			8664.11i			1.43224i
$333$		−	1077.50i		−	0.177318i
$334$	−2616.78			−0.428694
$335$	1059.70			0.172829
$336$		−	3584.02i		−	0.581918i
$337$	−6284.71			−1.01587			−0.507937	−	0.861394i	$-0.669592\pi$
$337$	−6284.71			−1.01587			−0.507937	+	0.861394i	$0.669592\pi$
$338$	−2223.21	−	1685.58i	−0.357771	−	0.271253i
$339$	1002.22			0.160570
$340$			2089.61i			0.333309i
$341$	−258.772			−0.0410947
$342$	−947.646			−0.149833
$343$			11719.3i			1.84484i
$344$		−	7258.39i		−	1.13763i
$345$		−	506.105i		−	0.0789790i
$346$			663.181i			0.103043i
$347$	−11558.0			−1.78809			−0.894046	−	0.447974i	$-0.852146\pi$
$347$	−11558.0			−1.78809			−0.894046	+	0.447974i	$0.852146\pi$
$348$	−4944.22			−0.761604
$349$		−	4235.53i		−	0.649636i	−0.945777	−	0.324818i	$-0.894697\pi$
$349$		−	4235.53i		−	0.649636i	0.945777	−	0.324818i	$-0.105303\pi$
$350$	−4111.40			−0.627896
$351$	−6372.25	+	3165.39i	−0.969019	+	0.481356i
$352$	1997.49			0.302462
$353$			5559.11i			0.838191i	0.907942	+	0.419096i	$0.137653\pi$
$353$			5559.11i			0.838191i	−0.907942	+	0.419096i	$0.862347\pi$
$354$	2944.04			0.442017
$355$	295.444			0.0441705
$356$			5470.80i			0.814471i
$357$		−	8407.37i		−	1.24640i
$358$			230.422i			0.0340173i
$359$			7592.61i			1.11622i	0.829767	+	0.558109i	$0.188473\pi$
$359$			7592.61i			1.11622i	−0.829767	+	0.558109i	$0.811527\pi$
$360$	−1027.63			−0.150447
$361$	2459.98			0.358651
$362$		−	3613.36i		−	0.524624i
$363$	−480.185			−0.0694302
$364$	−4311.85	−	8680.18i	−0.620885	−	1.24990i
$365$	96.8745			0.0138922
$366$			3693.76i			0.527530i
$367$	1655.86			0.235518			0.117759	−	0.993042i	$-0.462429\pi$
$367$	1655.86			0.235518			0.117759	+	0.993042i	$0.462429\pi$
$368$	−711.696			−0.100814
$369$		−	2762.15i		−	0.389680i
$370$			607.958i			0.0854222i
$371$			7267.35i			1.01699i
$372$			596.306i			0.0831103i
$373$	1380.23			0.191597			0.0957983	−	0.995401i	$-0.469460\pi$
$373$	1380.23			0.191597			0.0957983	+	0.995401i	$0.469460\pi$
$374$	914.144			0.126388
$375$			4463.88i			0.614703i
$376$	2553.52			0.350234
$377$	−8187.98	+	4067.35i	−1.11857	+	0.555648i
$378$	6240.48			0.849142
$379$			11001.2i			1.49101i	0.666501	+	0.745504i	$0.267791\pi$
$379$			11001.2i			1.49101i	−0.666501	+	0.745504i	$0.732209\pi$
$380$	−2117.82			−0.285900
$381$	−6006.06			−0.807611
$382$			6127.29i			0.820679i
$383$			2205.60i			0.294259i	0.989117	+	0.147129i	$0.0470034\pi$
$383$			2205.60i			0.294259i	−0.989117	+	0.147129i	$0.952997\pi$
$384$		−	5727.69i		−	0.761171i
$385$			1780.18i			0.235653i
$386$	−5921.43			−0.780811
$387$	−4469.86			−0.587120
$388$		−	6472.26i		−	0.846853i
$389$	−2689.14			−0.350501			−0.175250	−	0.984524i	$-0.556074\pi$
$389$	−2689.14			−0.350501			−0.175250	+	0.984524i	$0.556074\pi$
$390$	1057.55	−	525.336i	0.137311	−	0.0682088i
$391$	−1669.49			−0.215933
$392$			12880.8i			1.65964i
$393$	11095.2			1.42412
$394$	−528.251			−0.0675454
$395$			1414.52i			0.180183i
$396$		−	790.527i		−	0.100317i
$397$			14239.4i			1.80013i	0.435753	+	0.900066i	$0.356482\pi$
$397$			14239.4i			1.80013i	−0.435753	+	0.900066i	$0.643518\pi$
$398$		−	5552.08i		−	0.699248i
$399$	8520.85			1.06911
$400$	2790.01			0.348752
$401$		−	13243.5i		−	1.64925i	−0.565680	−	0.824625i	$-0.691386\pi$
$401$		−	13243.5i		−	1.64925i	0.565680	−	0.824625i	$-0.308614\pi$
$402$	−1068.28			−0.132539
$403$	490.550	+	987.526i	0.0606353	+	0.122065i
$404$	288.482			0.0355261
$405$		−	1492.84i		−	0.183161i
$406$	8018.66			0.980196
$407$	−1053.44			−0.128298
$408$		−	4744.89i		−	0.575752i
$409$			3291.46i			0.397928i	0.980007	+	0.198964i	$0.0637576\pi$
$409$			3291.46i			0.397928i	−0.980007	+	0.198964i	$0.936242\pi$
$410$			1558.48i			0.187727i
$411$		−	6553.15i		−	0.786479i
$412$	−4363.59			−0.521793
$413$	18911.9			2.25326
$414$		−	364.500i		−	0.0432710i
$415$	−6780.95			−0.802081
$416$	−3786.62	−	7622.83i	−0.446284	−	0.898414i
$417$	−5672.47			−0.666145
$418$			926.483i			0.108411i
$419$	−10279.4			−1.19853			−0.599263	−	0.800552i	$-0.704540\pi$
$419$	−10279.4			−1.19853			−0.599263	+	0.800552i	$0.704540\pi$
$420$	4102.19			0.476587
$421$			13466.6i			1.55896i	0.626427	+	0.779480i	$0.284517\pi$
$421$			13466.6i			1.55896i	−0.626427	+	0.779480i	$0.715483\pi$
$422$			373.785i			0.0431175i
$423$		−	1572.51i		−	0.180752i
$424$			4101.49i			0.469779i
$425$	6544.79			0.746985
$426$	−297.835			−0.0338736
$427$			23728.0i			2.68918i
$428$	7677.63			0.867084
$429$	910.279	+	1832.48i	0.102444	+	0.206231i
$430$	2522.02			0.282843
$431$		−	17756.1i		−	1.98441i	−0.124598	−	0.992207i	$-0.539764\pi$
$431$		−	17756.1i		−	1.98441i	0.124598	−	0.992207i	$-0.460236\pi$
$432$	−4234.81			−0.471638
$433$	1858.88			0.206310			0.103155	−	0.994665i	$-0.467106\pi$
$433$	1858.88			0.206310			0.103155	+	0.994665i	$0.467106\pi$
$434$		−	967.105i		−	0.106964i
$435$		−	3869.58i		−	0.426511i
$436$		−	6268.47i		−	0.688545i
$437$		−	1692.02i		−	0.185218i
$438$	−97.6585			−0.0106537
$439$	−8311.97			−0.903664			−0.451832	−	0.892103i	$-0.649229\pi$
$439$	−8311.97			−0.903664			−0.451832	+	0.892103i	$0.649229\pi$
$440$			1004.68i			0.108856i
$441$	7932.23			0.856520
$442$	−1732.93	−	3488.56i	−0.186486	−	0.375416i
$443$	−63.6070			−0.00682181			−0.00341090	−	0.999994i	$-0.501086\pi$
$443$	−63.6070			−0.00682181			−0.00341090	+	0.999994i	$0.501086\pi$
$444$			2427.52i			0.259471i
$445$	−4281.71			−0.456118
$446$	−1351.55			−0.143493
$447$			2041.19i			0.215984i
$448$			240.198i			0.0253310i
$449$			12006.5i			1.26196i	0.775799	+	0.630980i	$0.217347\pi$
$449$			12006.5i			1.26196i	−0.775799	+	0.630980i	$0.782653\pi$
$450$			1428.92i			0.149689i
$451$	−2700.46			−0.281951
$452$	1613.11			0.167863
$453$			6140.95i			0.636924i
$454$	−6838.19			−0.706899
$455$	6793.52	−	3374.66i	0.699968	−	0.347706i
$456$	4808.94			0.493858
$457$		−	2723.61i		−	0.278786i	−0.990237	−	0.139393i	$-0.955485\pi$
$457$		−	2723.61i		−	0.278786i	0.990237	−	0.139393i	$-0.0445151\pi$
$458$	930.645			0.0949480
$459$	−9933.99			−1.01019
$460$		−	814.591i		−	0.0825663i
$461$		−	8513.80i		−	0.860146i	−0.902794	−	0.430073i	$-0.858488\pi$
$461$		−	8513.80i		−	0.860146i	0.902794	−	0.430073i	$-0.141512\pi$
$462$		−	1794.59i		−	0.180718i
$463$		−	7667.09i		−	0.769590i	−0.923002	−	0.384795i	$-0.874272\pi$
$463$		−	7667.09i		−	0.769590i	0.923002	−	0.384795i	$-0.125728\pi$
$464$	−5441.50			−0.544429
$465$	−466.698			−0.0465432
$466$		−	3498.54i		−	0.347783i
$467$	−9955.18			−0.986447			−0.493223	−	0.869903i	$-0.664181\pi$
$467$	−9955.18			−0.986447			−0.493223	+	0.869903i	$0.664181\pi$
$468$	−3016.81	+	1498.59i	−0.297975	+	0.148018i
$469$	−6862.41			−0.675643
$470$			887.252i			0.0870764i
$471$	−6762.85			−0.661604
$472$	10673.4			1.04085
$473$			4370.03i			0.424808i
$474$		−	1425.97i		−	0.138179i
$475$			6633.13i			0.640734i
$476$		−	13531.9i		−	1.30301i
$477$	2525.78			0.242447
$478$	3042.63			0.291144
$479$			5955.09i			0.568048i	0.958817	+	0.284024i	$0.0916696\pi$
$479$			5955.09i			0.568048i	−0.958817	+	0.284024i	$0.908330\pi$
$480$	3602.50			0.342564
$481$	1996.99	+	4020.15i	0.189304	+	0.381087i
$482$	−5030.79			−0.475407
$483$			3277.43i			0.308754i
$484$	−772.872			−0.0725838
$485$	5065.50			0.474252
$486$		−	3699.82i		−	0.345323i
$487$			12295.1i			1.14404i	0.820241	+	0.572019i	$0.193839\pi$
$487$			12295.1i			1.14404i	−0.820241	+	0.572019i	$0.806161\pi$
$488$			13391.4i			1.24222i
$489$			13641.7i			1.26155i
$490$	−4475.58			−0.412625
$491$	3476.04			0.319494			0.159747	−	0.987158i	$-0.448932\pi$
$491$	3476.04			0.319494			0.159747	+	0.987158i	$0.448932\pi$
$492$			6222.87i			0.570221i
$493$	−12764.6			−1.16610
$494$	3535.65	−	1756.32i	0.322017	−	0.159961i
$495$	618.704			0.0561791
$496$			656.281i			0.0594111i
$497$	−1913.24			−0.172677
$498$	6835.83			0.615102
$499$			5515.09i			0.494768i	0.968918	+	0.247384i	$0.0795709\pi$
$499$			5515.09i			0.494768i	−0.968918	+	0.247384i	$0.920429\pi$
$500$			7184.75i			0.642624i
$501$		−	8177.54i		−	0.729232i
$502$			186.086i			0.0165446i
$503$	14285.6			1.26633			0.633164	−	0.774018i	$-0.281756\pi$
$503$	14285.6			1.26633			0.633164	+	0.774018i	$0.281756\pi$
$504$	6654.76			0.588148
$505$			225.780i			0.0198952i
$506$	−356.359			−0.0313085
$507$	5267.52	−	6947.62i	0.461418	−	0.608589i
$508$	−9666.94			−0.844293
$509$		−	13326.9i		−	1.16052i	−0.814433	−	0.580258i	$-0.802952\pi$
$509$		−	13326.9i		−	1.16052i	0.814433	−	0.580258i	$-0.197048\pi$
$510$	1648.67			0.143146
$511$	−627.340			−0.0543090
$512$		−	9143.51i		−	0.789238i
$513$		−	10068.1i		−	0.866503i
$514$			4560.13i			0.391320i
$515$		−	3415.16i		−	0.292213i
$516$	10070.2			0.859137
$517$	−1537.39			−0.130782
$518$		−	3937.01i		−	0.333943i
$519$	−2072.47			−0.175282
$520$	3834.08	−	1904.57i	0.323338	−	0.160617i
$521$	−5713.55			−0.480451			−0.240226	−	0.970717i	$-0.577221\pi$
$521$	−5713.55			−0.480451			−0.240226	+	0.970717i	$0.577221\pi$
$522$		−	2786.90i		−	0.233677i
$523$	−15307.5			−1.27983			−0.639913	−	0.768448i	$-0.721029\pi$
$523$	−15307.5			−1.27983			−0.639913	+	0.768448i	$0.721029\pi$
$524$	17858.1			1.48880
$525$		−	12848.3i		−	1.06809i
$526$			8477.11i			0.702699i
$527$			1539.50i			0.127252i
$528$			1217.81i			0.100376i
$529$	−11516.2			−0.946510
$530$	−1425.11			−0.116798
$531$		−	6572.88i		−	0.537172i
$532$	13714.6			1.11767
$533$	5119.23	+	10305.5i	0.416020	+	0.837489i
$534$	4316.36			0.349789
$535$			6008.88i			0.485582i
$536$	−3872.96			−0.312101
$537$	−720.079			−0.0578654
$538$		−	5858.52i		−	0.469477i
$539$		−	7755.09i		−	0.619731i
$540$		−	4847.07i		−	0.386268i
$541$		−	14533.6i		−	1.15498i	−0.816396	−	0.577492i	$-0.804031\pi$
$541$		−	14533.6i		−	1.15498i	0.816396	−	0.577492i	$-0.195969\pi$
$542$	−9900.01			−0.784579
$543$	11291.9			0.892415
$544$		−	11883.6i		−	0.936589i
$545$	4906.01			0.385597
$546$	−6848.51	+	3401.97i	−0.536793	+	0.266650i
$547$	−12963.6			−1.01332			−0.506658	−	0.862147i	$-0.669119\pi$
$547$	−12963.6			−1.01332			−0.506658	+	0.862147i	$0.669119\pi$
$548$		−	10547.5i		−	0.822202i
$549$	8246.70			0.641094
$550$	1397.01			0.108307
$551$		−	12936.9i		−	1.00024i
$552$			1849.69i			0.142624i
$553$		−	9160.14i		−	0.704392i
$554$		−	7019.64i		−	0.538332i
$555$	−1899.89			−0.145308
$556$	−9130.03			−0.696402
$557$			4755.08i			0.361722i	0.983509	+	0.180861i	$0.0578885\pi$
$557$			4755.08i			0.361722i	−0.983509	+	0.180861i	$0.942112\pi$
$558$	−336.119			−0.0255001
$559$	16676.9	−	8284.21i	1.26182	−	0.626806i
$560$	4514.78			0.340686
$561$			2856.74i			0.214994i
$562$	2720.76			0.204214
$563$	−8702.18			−0.651426			−0.325713	−	0.945469i	$-0.605604\pi$
$563$	−8702.18			−0.651426			−0.325713	+	0.945469i	$0.605604\pi$
$564$			3542.72i			0.264495i
$565$			1262.50i			0.0940063i
$566$		−	11162.7i		−	0.828981i
$567$			9667.36i			0.716034i
$568$	−1079.78			−0.0797649
$569$	−18691.1			−1.37710			−0.688552	−	0.725187i	$-0.741753\pi$
$569$	−18691.1			−1.37710			−0.688552	+	0.725187i	$0.741753\pi$
$570$			1670.92i			0.122785i
$571$	6006.57			0.440223			0.220111	−	0.975475i	$-0.429358\pi$
$571$	6006.57			0.440223			0.220111	+	0.975475i	$0.429358\pi$
$572$	1465.12	+	2949.44i	0.107098	+	0.215598i
$573$	−19148.0			−1.39602
$574$		−	10092.4i		−	0.733884i
$575$	−2551.35			−0.185041
$576$	83.4811			0.00603886
$577$		−	1612.72i		−	0.116358i	−0.998306	−	0.0581789i	$-0.981471\pi$
$577$		−	1612.72i		−	0.116358i	0.998306	−	0.0581789i	$-0.0185294\pi$
$578$			800.512i			0.0576071i
$579$		−	18504.7i		−	1.32820i
$580$		−	6228.22i		−	0.445884i
$581$	43912.1			3.13559
$582$	−5106.50			−0.363696
$583$		−	2469.37i		−	0.175422i
$584$	−354.054			−0.0250871
$585$	−1172.87	−	2361.10i	−0.0828925	−	0.166871i
$586$	−12024.7			−0.847669
$587$		−	7095.81i		−	0.498936i	−0.968383	−	0.249468i	$-0.919744\pi$
$587$		−	7095.81i		−	0.498936i	0.968383	−	0.249468i	$-0.0802558\pi$
$588$	−17870.6			−1.25335
$589$	−1560.28			−0.109151
$590$			3708.60i			0.258780i
$591$		−	1650.81i		−	0.114899i
$592$			2671.67i			0.185482i
$593$			2171.66i			0.150387i	0.997169	+	0.0751934i	$0.0239574\pi$
$593$			2171.66i			0.150387i	−0.997169	+	0.0751934i	$0.976043\pi$
$594$	−2120.45			−0.146470
$595$	10590.7			0.729710
$596$			3285.36i			0.225794i
$597$	17350.5			1.18946
$598$	675.545	+	1359.94i	0.0461958	+	0.0929968i
$599$	24227.4			1.65260			0.826299	−	0.563232i	$-0.190442\pi$
$599$	24227.4			1.65260			0.826299	+	0.563232i	$0.190442\pi$
$600$		−	7251.23i		−	0.493384i
$601$	20675.9			1.40331			0.701654	−	0.712518i	$-0.252445\pi$
$601$	20675.9			1.40331			0.701654	+	0.712518i	$0.252445\pi$
$602$	−16332.1			−1.10572
$603$			2385.04i			0.161072i
$604$			9884.05i			0.665854i
$605$		−	604.887i		−	0.0406482i
$606$		−	227.607i		−	0.0152573i
$607$	3796.10			0.253837			0.126918	−	0.991913i	$-0.459491\pi$
$607$	3796.10			0.253837			0.126918	+	0.991913i	$0.459491\pi$
$608$	12044.0			0.803368
$609$			25058.7i			1.66737i
$610$	−4653.02			−0.308844
$611$	2914.41	+	5866.99i	0.192969	+	0.388467i
$612$	−4703.04			−0.310636
$613$		−	23062.2i		−	1.51954i	−0.650195	−	0.759768i	$-0.725313\pi$
$613$		−	23062.2i		−	1.51954i	0.650195	−	0.759768i	$-0.274687\pi$
$614$	12851.6			0.844703
$615$	−4870.32			−0.319334
$616$		−	6506.14i		−	0.425552i
$617$			13799.9i			0.900428i	0.892921	+	0.450214i	$0.148652\pi$
$617$			13799.9i			0.900428i	−0.892921	+	0.450214i	$0.851348\pi$
$618$			3442.80i			0.224093i
$619$			7474.39i			0.485333i	0.970110	+	0.242666i	$0.0780220\pi$
$619$			7474.39i			0.485333i	−0.970110	+	0.242666i	$0.921978\pi$
$620$	−751.165			−0.0486573
$621$	3872.55			0.250242
$622$			371.496i			0.0239480i
$623$	27727.5			1.78311
$624$	4647.43	−	2308.59i	0.298151	−	0.148105i
$625$	6878.04			0.440195
$626$			8361.92i			0.533881i
$627$	−2895.30			−0.184413
$628$	−10885.0			−0.691655
$629$			6267.19i			0.397280i
$630$			2312.27i			0.146227i
$631$			12919.7i			0.815092i	0.913185	+	0.407546i	$0.133615\pi$
$631$			12919.7i			0.815092i	−0.913185	+	0.407546i	$0.866385\pi$
$632$		−	5169.74i		−	0.325381i
$633$	−1168.09			−0.0733453
$634$	−9398.95			−0.588770
$635$		−	7565.81i		−	0.472819i
$636$	−5690.35			−0.354775
$637$	−29595.0	+	14701.2i	−1.84081	+	0.914416i
$638$	−2724.66			−0.169076
$639$			664.948i			0.0411658i
$640$	7215.15			0.445631
$641$	294.282			0.0181333			0.00906666	−	0.999959i	$-0.497114\pi$
$641$	294.282			0.0181333			0.00906666	+	0.999959i	$0.497114\pi$
$642$		−	6057.51i		−	0.372385i
$643$			28745.1i			1.76298i	0.472205	+	0.881489i	$0.343458\pi$
$643$			28745.1i			1.76298i	−0.472205	+	0.881489i	$0.656542\pi$
$644$			5275.13i			0.322778i
$645$			7881.40i			0.481132i
$646$	5511.88			0.335700
$647$	−19531.3			−1.18680			−0.593398	−	0.804909i	$-0.702214\pi$
$647$	−19531.3			−1.18680			−0.593398	+	0.804909i	$0.702214\pi$
$648$			5456.00i			0.330759i
$649$	−6426.09			−0.388669
$650$	−2648.29	−	5331.28i	−0.159807	−	0.321708i
$651$	3022.24			0.181952
$652$			21956.7i			1.31885i
$653$	−19077.8			−1.14330			−0.571648	−	0.820499i	$-0.693696\pi$
$653$	−19077.8			−1.14330			−0.571648	+	0.820499i	$0.693696\pi$
$654$	−4945.72			−0.295708
$655$			13976.6i			0.833756i
$656$			6848.75i			0.407620i
$657$			218.033i			0.0129471i
$658$		−	5745.67i		−	0.340410i
$659$	−7668.16			−0.453276			−0.226638	−	0.973979i	$-0.572774\pi$
$659$	−7668.16			−0.453276			−0.226638	+	0.973979i	$0.572774\pi$
$660$	−1393.88			−0.0822074
$661$			25112.0i			1.47767i	0.673885	+	0.738837i	$0.264625\pi$
$661$			25112.0i			1.47767i	−0.673885	+	0.738837i	$0.735375\pi$
$662$	−6990.00			−0.410383
$663$	10901.9	−	5415.47i	0.638604	−	0.317224i
$664$	24782.8			1.44843
$665$			10733.7i			0.625916i
$666$	−1368.32			−0.0796113
$667$	4976.01			0.288864
$668$		−	13162.0i		−	0.762355i
$669$		−	4223.65i		−	0.244089i
$670$		−	1345.71i		−	0.0775957i
$671$		−	8062.53i		−	0.463861i
$672$	−23329.1			−1.33919
$673$	−28940.0			−1.65759			−0.828793	−	0.559555i	$-0.810972\pi$
$673$	−28940.0			−1.65759			−0.828793	+	0.559555i	$0.810972\pi$
$674$			7980.90i			0.456102i
$675$	−15181.3			−0.865672
$676$	8478.24	−	11182.4i	0.482376	−	0.636232i
$677$	15694.4			0.890969			0.445484	−	0.895290i	$-0.353032\pi$
$677$	15694.4			0.890969			0.445484	+	0.895290i	$0.353032\pi$
$678$		−	1272.71i		−	0.0720918i
$679$	−32803.2			−1.85401
$680$	5977.12			0.337077
$681$		−	21369.6i		−	1.20248i
$682$			328.612i			0.0184505i
$683$			2250.42i			0.126076i	0.998011	+	0.0630380i	$0.0200789\pi$
$683$			2250.42i			0.126076i	−0.998011	+	0.0630380i	$0.979921\pi$
$684$		−	4766.52i		−	0.266451i
$685$	8254.98			0.460447
$686$	14882.2			0.828287
$687$			2908.30i			0.161512i
$688$	11083.0			0.614151
$689$	−9423.62	+	4681.15i	−0.521062	+	0.258835i
$690$	−642.698			−0.0354596
$691$		−	17919.9i		−	0.986546i	−0.869874	−	0.493273i	$-0.835800\pi$
$691$		−	17919.9i		−	0.986546i	0.869874	−	0.493273i	$-0.164200\pi$
$692$	−3335.71			−0.183243
$693$	−4006.60			−0.219622
$694$			14677.5i			0.802808i
$695$		−	7145.60i		−	0.389997i
$696$			14142.4i			0.770212i
$697$			16065.7i			0.873075i
$698$	−5378.67			−0.291670
$699$	10933.1			0.591599
$700$		−	20679.7i		−	1.11660i
$701$	−28053.5			−1.51151			−0.755753	−	0.654857i	$-0.772729\pi$
$701$	−28053.5			−1.51151			−0.755753	+	0.654857i	$0.772729\pi$
$702$	4019.71	+	8092.07i	0.216117	+	0.435065i
$703$	−6351.78			−0.340771
$704$		−	81.6168i		−	0.00436939i
$705$	−2772.70			−0.148122
$706$	7059.47			0.376327
$707$		−	1462.11i		−	0.0777768i
$708$			14808.1i			0.786048i
$709$		−	15166.0i		−	0.803342i	−0.915784	−	0.401671i	$-0.868430\pi$
$709$		−	15166.0i		−	0.803342i	0.915784	−	0.401671i	$-0.131570\pi$
$710$		−	375.182i		−	0.0198314i
$711$	−3183.62			−0.167926
$712$	15648.6			0.823677
$713$		−	600.141i		−	0.0315224i
$714$	−10676.4			−0.559602
$715$	−2308.37	+	1146.67i	−0.120739	+	0.0599765i
$716$	−1158.99			−0.0604937
$717$			9508.36i			0.495253i
$718$	9641.79			0.501154
$719$	12995.0			0.674036			0.337018	−	0.941498i	$-0.390582\pi$
$719$	12995.0			0.674036			0.337018	+	0.941498i	$0.390582\pi$
$720$		−	1569.12i		−	0.0812189i
$721$			22115.9i			1.14235i
$722$		−	3123.92i		−	0.161025i
$723$		−	15721.4i		−	0.808695i
$724$	18174.7			0.932950
$725$	−19507.1			−0.999278
$726$			609.783i			0.0311724i
$727$	11214.2			0.572091			0.286046	−	0.958216i	$-0.407659\pi$
$727$	11214.2			0.572091			0.286046	+	0.958216i	$0.407659\pi$
$728$	−24828.7	+	12333.6i	−1.26403	+	0.627903i
$729$	19624.9			0.997051
$730$		−	123.020i		−	0.00623723i
$731$	25998.4			1.31544
$732$	−18579.1			−0.938118
$733$			14541.3i			0.732736i	0.930470	+	0.366368i	$0.119399\pi$
$733$			14541.3i			0.732736i	−0.930470	+	0.366368i	$0.880601\pi$
$734$		−	2102.77i		−	0.105742i
$735$		−	13986.4i		−	0.701899i
$736$			4632.56i			0.232009i
$737$	2331.78			0.116543
$738$	−3507.63			−0.174956
$739$		−	3802.12i		−	0.189260i	−0.995513	−	0.0946300i	$-0.969833\pi$
$739$		−	3802.12i		−	0.189260i	0.995513	−	0.0946300i	$-0.0301668\pi$
$740$	−3057.94			−0.151908
$741$	5488.57	+	11049.0i	0.272102	+	0.547769i
$742$	9228.75			0.456601
$743$		−	1717.74i		−	0.0848155i	−0.999100	−	0.0424077i	$-0.986497\pi$
$743$		−	1717.74i		−	0.0848155i	0.999100	−	0.0424077i	$-0.0135029\pi$
$744$	1705.67			0.0840497
$745$	−2571.28			−0.126449
$746$		−	1752.74i		−	0.0860221i
$747$		−	15261.7i		−	0.747519i
$748$			4598.01i			0.224759i
$749$		−	38912.3i		−	1.89830i
$750$	5668.64			0.275986
$751$	11166.2			0.542559			0.271280	−	0.962501i	$-0.412553\pi$
$751$	11166.2			0.542559			0.271280	+	0.962501i	$0.412553\pi$
$752$			3899.04i			0.189073i
$753$	−581.525			−0.0281434
$754$	5165.10	+	10397.9i	0.249472	+	0.502212i
$755$	−7735.73			−0.372890
$756$			31388.7i			1.51005i
$757$	15801.8			0.758689			0.379345	−	0.925255i	$-0.376150\pi$
$757$	15801.8			0.758689			0.379345	+	0.925255i	$0.376150\pi$
$758$	13970.3			0.669425
$759$		−	1113.64i		−	0.0532576i
$760$			6057.80i			0.289131i
$761$		−	17664.7i		−	0.841450i	−0.907188	−	0.420725i	$-0.861776\pi$
$761$		−	17664.7i		−	0.841450i	0.907188	−	0.420725i	$-0.138224\pi$
$762$			7627.05i			0.362597i
$763$	−31770.3			−1.50742
$764$	−30819.4			−1.45943
$765$		−	3680.82i		−	0.173961i
$766$	2800.88			0.132115
$767$	12181.8	+	24523.3i	0.573482	+	1.15448i
$768$	−7509.10			−0.352814
$769$		−	31530.9i		−	1.47859i	−0.673382	−	0.739295i	$-0.735159\pi$
$769$		−	31530.9i		−	1.47859i	0.673382	−	0.739295i	$-0.264841\pi$
$770$	2260.64			0.105802
$771$	−14250.6			−0.665658
$772$		−	29784.0i		−	1.38853i
$773$			7958.36i			0.370300i	0.982710	+	0.185150i	$0.0592772\pi$
$773$			7958.36i			0.370300i	−0.982710	+	0.185150i	$0.940723\pi$
$774$			5676.24i			0.263602i
$775$			2352.69i			0.109047i
$776$	−18513.2			−0.856425
$777$	12303.3			0.568056
$778$			3414.92i			0.157366i
$779$	−16282.6			−0.748889
$780$	2642.36	+	5319.34i	0.121297	+	0.244183i
$781$	650.098			0.0297853
$782$			2120.07i			0.0969483i
$783$	29608.8			1.35138
$784$	−19668.0			−0.895954
$785$		−	8519.14i		−	0.387339i
$786$		−	14089.7i		−	0.639393i
$787$			5185.08i			0.234852i	0.993082	+	0.117426i	$0.0374642\pi$
$787$			5185.08i			0.234852i	−0.993082	+	0.117426i	$0.962536\pi$
$788$		−	2657.02i		−	0.120117i
$789$	−26491.3			−1.19533
$790$	1796.29			0.0808975
$791$		−	8175.67i		−	0.367501i
$792$	−2261.22			−0.101451
$793$	−30768.3	+	15284.0i	−1.37782	+	0.684428i
$794$	18082.4			0.808214
$795$		−	4453.54i		−	0.198680i
$796$	27926.2			1.24349
$797$	13511.3			0.600494			0.300247	−	0.953861i	$-0.402931\pi$
$797$	13511.3			0.600494			0.300247	+	0.953861i	$0.402931\pi$
$798$		−	10820.6i		−	0.480005i
$799$			9146.32i			0.404973i
$800$		−	18160.7i		−	0.802598i
$801$		−	9636.73i		−	0.425090i
$802$	−16817.8			−0.740471
$803$	213.164			0.00936785
$804$		−	5373.28i		−	0.235698i
$805$	−4128.57			−0.180761
$806$	1254.05	−	622.945i	0.0548041	−	0.0272237i
$807$	18308.1			0.798608
$808$		−	825.173i		−	0.0359276i
$809$	18939.2			0.823072			0.411536	−	0.911393i	$-0.364992\pi$
$809$	18939.2			0.823072			0.411536	+	0.911393i	$0.364992\pi$
$810$	−1895.75			−0.0822345
$811$		−	27498.0i		−	1.19061i	−0.803499	−	0.595306i	$-0.797031\pi$
$811$		−	27498.0i		−	1.19061i	0.803499	−	0.595306i	$-0.202969\pi$
$812$			40332.7i			1.74310i
$813$		−	30938.0i		−	1.33461i
$814$			1337.76i			0.0576024i
$815$	−17184.4			−0.738580
$816$	7245.08			0.310819
$817$			26349.3i			1.12833i
$818$	4179.80			0.178659
$819$	7595.26	+	15290.0i	0.324054	+	0.652352i
$820$	−7838.93			−0.333838
$821$			23049.9i			0.979840i	0.871767	+	0.489920i	$0.162974\pi$
$821$			23049.9i			0.979840i	−0.871767	+	0.489920i	$0.837026\pi$
$822$	−8321.79			−0.353109
$823$	−24031.4			−1.01784			−0.508920	−	0.860814i	$-0.669955\pi$
$823$	−24031.4			−1.01784			−0.508920	+	0.860814i	$0.669955\pi$
$824$			12481.6i			0.527690i
$825$			4365.72i			0.184236i
$826$		−	24016.1i		−	1.01166i
$827$			4449.75i			0.187102i	0.995615	+	0.0935508i	$0.0298218\pi$
$827$			4449.75i			0.187102i	−0.995615	+	0.0935508i	$0.970178\pi$
$828$	1833.38			0.0769497
$829$	−4554.87			−0.190829			−0.0954145	−	0.995438i	$-0.530418\pi$
$829$	−4554.87			−0.190829			−0.0954145	+	0.995438i	$0.530418\pi$
$830$			8611.07i			0.360114i
$831$	21936.7			0.915734
$832$	−311.466	+	154.720i	−0.0129785	+	0.00644705i
$833$	−46136.9			−1.91903
$834$			7203.43i			0.299082i
$835$	10301.2			0.426932
$836$	−4660.07			−0.192789
$837$		−	3571.03i		−	0.147470i
$838$			13053.7i			0.538108i
$839$		−	31846.2i		−	1.31043i	−0.755441	−	0.655217i	$-0.772577\pi$
$839$		−	31846.2i		−	1.31043i	0.755441	−	0.655217i	$-0.227423\pi$
$840$		−	11733.9i		−	0.481974i
$841$	13656.7			0.559953
$842$	17101.1			0.699934
$843$			8502.51i			0.347381i
$844$	−1880.08			−0.0766768
$845$	8751.89	+	6635.48i	0.356301	+	0.270139i
$846$	−1996.92			−0.0811530
$847$			3917.13i			0.158907i
$848$	−6262.67			−0.253610
$849$	34883.9			1.41015
$850$		−	8311.17i		−	0.335378i
$851$		−	2443.13i		−	0.0984129i
$852$		−	1498.07i		−	0.0602382i
$853$		−	43935.5i		−	1.76357i	−0.471656	−	0.881783i	$-0.656343\pi$
$853$		−	43935.5i		−	1.76357i	0.471656	−	0.881783i	$-0.343657\pi$
$854$	30132.0			1.20737
$855$	3730.51			0.149217
$856$		−	21961.0i		−	0.876885i
$857$	33734.8			1.34464			0.672322	−	0.740259i	$-0.265297\pi$
$857$	33734.8			1.34464			0.672322	+	0.740259i	$0.265297\pi$
$858$	2327.05	−	1155.96i	0.0925924	−	0.0459950i
$859$	30499.0			1.21142			0.605711	−	0.795685i	$-0.292889\pi$
$859$	30499.0			1.21142			0.605711	+	0.795685i	$0.292889\pi$
$860$			12685.4i			0.502986i
$861$	31539.2			1.24838
$862$	−22548.4			−0.890952
$863$		−	5677.31i		−	0.223937i	−0.993712	−	0.111969i	$-0.964284\pi$
$863$		−	5677.31i		−	0.223937i	0.993712	−	0.111969i	$-0.0357156\pi$
$864$			27565.2i			1.08540i
$865$		−	2610.68i		−	0.102620i
$866$		−	2360.58i		−	0.0926278i
$867$	−2501.63			−0.0979930
$868$	4864.40			0.190217
$869$			3112.52i			0.121502i
$870$	−4913.96			−0.191493
$871$	−4420.31	−	8898.53i	−0.171959	−	0.346171i
$872$	−17930.3			−0.696327
$873$			11400.8i			0.441991i
$874$	−2148.69			−0.0831584
$875$	36414.3			1.40689
$876$		−	491.208i		−	0.0189457i
$877$		−	6490.42i		−	0.249904i	−0.992163	−	0.124952i	$-0.960122\pi$
$877$		−	6490.42i		−	0.249904i	0.992163	−	0.124952i	$-0.0398777\pi$
$878$			10555.3i			0.405722i
$879$		−	37577.6i		−	1.44193i
$880$	−1534.08			−0.0587656
$881$	−3334.19			−0.127505			−0.0637525	−	0.997966i	$-0.520307\pi$
$881$	−3334.19			−0.127505			−0.0637525	+	0.997966i	$0.520307\pi$
$882$		−	10073.1i		−	0.384556i
$883$	40609.4			1.54769			0.773847	−	0.633372i	$-0.218330\pi$
$883$	40609.4			1.54769			0.773847	+	0.633372i	$0.218330\pi$
$884$	17546.9	−	8716.38i	0.667610	−	0.331633i
$885$	−11589.5			−0.440201
$886$			80.7741i			0.00306282i
$887$	−5984.16			−0.226526			−0.113263	−	0.993565i	$-0.536130\pi$
$887$	−5984.16			−0.226526			−0.113263	+	0.993565i	$0.536130\pi$
$888$	6943.67			0.262403
$889$			48994.7i			1.84840i
$890$			5437.31i			0.204785i
$891$		−	3284.87i		−	0.123510i
$892$		−	6798.10i		−	0.255176i
$893$	−9269.78			−0.347370
$894$	2592.09			0.0969714
$895$		−	907.082i		−	0.0338775i
$896$	−46723.9			−1.74211
$897$	−4249.87	+	2111.11i	−0.158193	+	0.0785817i
$898$	15246.9			0.566588
$899$		−	4588.57i		−	0.170231i
$900$	−7187.28			−0.266195
$901$	−14690.9			−0.543202
$902$			3429.30i			0.126589i
$903$		−	51038.4i		−	1.88090i
$904$		−	4614.12i		−	0.169761i
$905$			14224.4i			0.522468i
$906$	7798.34			0.285963
$907$	18581.3			0.680246			0.340123	−	0.940381i	$-0.389531\pi$
$907$	18581.3			0.680246			0.340123	+	0.940381i	$0.389531\pi$
$908$		−	34395.1i		−	1.25709i
$909$	−508.157			−0.0185418
$910$	−4285.45	−	8627.04i	−0.156111	−	0.314268i
$911$	−2418.57			−0.0879592			−0.0439796	−	0.999032i	$-0.514004\pi$
$911$	−2418.57			−0.0879592			−0.0439796	+	0.999032i	$0.514004\pi$
$912$			7342.88i			0.266609i
$913$	−14920.9			−0.540864
$914$	−3458.69			−0.125168
$915$		−	14540.9i		−	0.525362i
$916$			4681.01i			0.168848i
$917$		−	90509.5i		−	3.25942i
$918$			12615.1i			0.453551i
$919$	−25585.2			−0.918364			−0.459182	−	0.888342i	$-0.651857\pi$
$919$	−25585.2			−0.918364			−0.459182	+	0.888342i	$0.651857\pi$
$920$	−2330.05			−0.0834995
$921$			40161.7i			1.43689i
$922$	−10811.6			−0.386184
$923$	−1232.38	−	2480.91i	−0.0439483	−	0.0884724i
$924$	9026.51			0.321375
$925$			9577.64i			0.340444i
$926$	−9736.38			−0.345526
$927$	7686.40			0.272335
$928$			35419.7i			1.25292i
$929$		−	12091.4i		−	0.427026i	−0.976940	−	0.213513i	$-0.931509\pi$
$929$		−	12091.4i		−	0.427026i	0.976940	−	0.213513i	$-0.0684905\pi$
$930$			592.656i			0.0208967i
$931$		−	46759.7i		−	1.64607i
$932$	17597.2			0.618470
$933$	−1160.94			−0.0407369
$934$			12642.0i			0.442890i
$935$	−3598.62			−0.125869
$936$	4286.56	+	8629.27i	0.149691	+	0.301342i
$937$	4975.34			0.173466			0.0867329	−	0.996232i	$-0.472357\pi$
$937$	4975.34			0.173466			0.0867329	+	0.996232i	$0.472357\pi$
$938$			8714.52i			0.303347i
$939$	−26131.4			−0.908163
$940$	−4462.75			−0.154850
$941$			16314.0i			0.565166i	0.959243	+	0.282583i	$0.0911913\pi$
$941$			16314.0i			0.565166i	−0.959243	+	0.282583i	$0.908809\pi$
$942$			8588.09i			0.297044i
$943$		−	6262.89i		−	0.216275i
$944$			16297.5i			0.561903i
$945$	−24566.3			−0.845653
$946$	5549.47			0.190728
$947$		−	29901.2i		−	1.02604i	−0.858378	−	0.513019i	$-0.828527\pi$
$947$		−	29901.2i		−	1.02604i	0.858378	−	0.513019i	$-0.171473\pi$
$948$	7172.41			0.245727
$949$	−404.091	−	813.476i	−0.0138223	−	0.0278257i
$950$	8423.36			0.287673
$951$		−	29372.1i		−	1.00153i
$952$	−38706.6			−1.31774
$953$	−19450.0			−0.661120			−0.330560	−	0.943785i	$-0.607238\pi$
$953$	−19450.0			−0.661120			−0.330560	+	0.943785i	$0.607238\pi$
$954$		−	3207.47i		−	0.108853i
$955$		−	24120.7i		−	0.817307i
$956$			15304.0i			0.517748i
$957$		−	8514.68i		−	0.287608i
$958$	7562.33			0.255039
$959$	−53457.6			−1.80004
$960$		−	147.197i		−	0.00494871i
$961$	29237.6			0.981424
$962$	5105.15	−	2535.97i	0.171098	−	0.0849925i
$963$	−13524.0			−0.452550
$964$		−	25304.2i		−	0.845427i
$965$	23310.3			0.777603
$966$	4161.99			0.138623
$967$			22015.8i			0.732141i	0.930587	+	0.366070i	$0.119297\pi$
$967$			22015.8i			0.732141i	−0.930587	+	0.366070i	$0.880703\pi$
$968$			2210.72i			0.0734042i
$969$			17224.8i			0.571044i
$970$		−	6432.64i		−	0.212927i
$971$	25479.9			0.842110			0.421055	−	0.907035i	$-0.361660\pi$
$971$	25479.9			0.842110			0.421055	+	0.907035i	$0.361660\pi$
$972$	18609.5			0.614096
$973$			46273.5i			1.52462i
$974$	15613.5			0.513644
$975$	16660.5	−	8276.03i	0.547243	−	0.271841i
$976$	−20447.7			−0.670610
$977$			36655.5i			1.20032i	0.799880	+	0.600160i	$0.204896\pi$
$977$			36655.5i			1.20032i	−0.799880	+	0.600160i	$0.795104\pi$
$978$	17323.5			0.566404
$979$	−9421.52			−0.307572
$980$		−	22511.5i		−	0.733780i
$981$			11041.8i			0.359366i
$982$		−	4414.20i		−	0.143445i
$983$			23339.6i			0.757293i	0.925541	+	0.378647i	$0.123610\pi$
$983$			23339.6i			0.757293i	−0.925541	+	0.378647i	$0.876390\pi$
$984$	17799.9			0.576666
$985$	2079.51			0.0672678
$986$			16209.7i			0.523551i
$987$	17955.5			0.579056
$988$	8834.03	+	17783.8i	0.284461	+	0.572649i
$989$	−10134.9			−0.325856
$990$		−	785.687i		−	0.0252230i
$991$	−32249.8			−1.03375			−0.516877	−	0.856060i	$-0.672905\pi$
$991$	−32249.8			−1.03375			−0.516877	+	0.856060i	$0.672905\pi$
$992$	4271.86			0.136725
$993$		−	21844.0i		−	0.698086i
$994$			2429.60i			0.0775275i
$995$			21856.4i			0.696375i
$996$			34383.2i			1.09385i
$997$	38605.4			1.22632			0.613162	−	0.789957i	$-0.289897\pi$
$997$	38605.4			1.22632			0.613162	+	0.789957i	$0.289897\pi$
$998$	7003.56			0.222138
$999$		−	14537.4i		−	0.460403i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	143.4.b.a.12.15	✓	36
13.5	odd	4		1859.4.a.j.1.8		18
13.8	odd	4		1859.4.a.k.1.11		18
13.12	even	2	inner	143.4.b.a.12.22	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.b.a.12.15	✓	36	1.1	even	1	trivial
143.4.b.a.12.22	yes	36	13.12	even	2	inner
1859.4.a.j.1.8		18	13.5	odd	4
1859.4.a.k.1.11		18	13.8	odd	4

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:	\( N \)	\(=\)	\( 143 = 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	143.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.26989i q^{2} +3.96847 q^{3} +6.38737 q^{4} +4.99906i q^{5} -5.03953i q^{6} -32.3730i q^{7} -18.2704i q^{8} -11.2513 q^{9} +O(q^{10})\)	\(q-1.26989i q^{2} +3.96847 q^{3} +6.38737 q^{4} +4.99906i q^{5} -5.03953i q^{6} -32.3730i q^{7} -18.2704i q^{8} -11.2513 q^{9} +6.34827 q^{10} +11.0000i q^{11} +25.3481 q^{12} +(41.9782 - 20.8525i) q^{13} -41.1102 q^{14} +19.8386i q^{15} +27.8975 q^{16} +65.4417 q^{17} +14.2879i q^{18} +66.3251i q^{19} +31.9309i q^{20} -128.471i q^{21} +13.9688 q^{22} -25.5111 q^{23} -72.5055i q^{24} +100.009 q^{25} +(-26.4805 - 53.3078i) q^{26} -151.799 q^{27} -206.778i q^{28} -195.053 q^{29} +25.1929 q^{30} +23.5247i q^{31} -181.590i q^{32} +43.6531i q^{33} -83.1040i q^{34} +161.834 q^{35} -71.8661 q^{36} +95.7674i q^{37} +84.2257 q^{38} +(166.589 - 82.7526i) q^{39} +91.3350 q^{40} +245.497i q^{41} -163.144 q^{42} +397.276 q^{43} +70.2611i q^{44} -56.2458i q^{45} +32.3963i q^{46} +139.763i q^{47} +110.710 q^{48} -705.008 q^{49} -127.001i q^{50} +259.703 q^{51} +(268.131 - 133.193i) q^{52} -224.488 q^{53} +192.768i q^{54} -54.9897 q^{55} -591.467 q^{56} +263.209i q^{57} +247.696i q^{58} +584.190i q^{59} +126.717i q^{60} -732.958 q^{61} +29.8738 q^{62} +364.237i q^{63} -7.41971 q^{64} +(104.243 + 209.852i) q^{65} +55.4348 q^{66} -211.980i q^{67} +418.001 q^{68} -101.240 q^{69} -205.512i q^{70} -59.0998i q^{71} +205.565i q^{72} -19.3785i q^{73} +121.614 q^{74} +396.884 q^{75} +423.643i q^{76} +356.102 q^{77} +(-105.087 - 211.550i) q^{78} +282.957 q^{79} +139.462i q^{80} -298.625 q^{81} +311.754 q^{82} +1356.44i q^{83} -820.592i q^{84} +327.148i q^{85} -504.497i q^{86} -774.062 q^{87} +200.975 q^{88} +856.502i q^{89} -71.4261 q^{90} +(-675.058 - 1358.96i) q^{91} -162.949 q^{92} +93.3570i q^{93} +177.484 q^{94} -331.563 q^{95} -720.635i q^{96} -1013.29i q^{97} +895.284i q^{98} -123.764i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 152 q^{4} + 360 q^{9}+O(q^{10}) \) 36 * q - 152 * q^4 + 360 * q^9	\( 36 q - 152 q^{4} + 360 q^{9} - 112 q^{10} - 108 q^{12} - 50 q^{13} + 8 q^{14} + 728 q^{16} + 276 q^{17} + 44 q^{22} - 472 q^{23} - 1172 q^{25} + 152 q^{26} - 12 q^{27} - 572 q^{29} + 712 q^{30} + 68 q^{35} - 430 q^{36} - 50 q^{38} + 640 q^{39} - 216 q^{40} + 1126 q^{42} + 920 q^{43} + 1674 q^{48} - 2164 q^{49} - 340 q^{51} - 800 q^{52} + 2432 q^{53} + 440 q^{55} - 2274 q^{56} - 1844 q^{61} + 2796 q^{62} - 2592 q^{64} + 2264 q^{65} + 1078 q^{66} - 4548 q^{68} - 3288 q^{69} - 4036 q^{74} + 820 q^{75} - 616 q^{77} + 2222 q^{78} + 360 q^{79} + 852 q^{81} + 1948 q^{82} - 2480 q^{87} + 264 q^{88} - 496 q^{90} + 4600 q^{91} + 454 q^{92} - 488 q^{94} + 952 q^{95}+O(q^{100}) \) 36 * q - 152 * q^4 + 360 * q^9 - 112 * q^10 - 108 * q^12 - 50 * q^13 + 8 * q^14 + 728 * q^16 + 276 * q^17 + 44 * q^22 - 472 * q^23 - 1172 * q^25 + 152 * q^26 - 12 * q^27 - 572 * q^29 + 712 * q^30 + 68 * q^35 - 430 * q^36 - 50 * q^38 + 640 * q^39 - 216 * q^40 + 1126 * q^42 + 920 * q^43 + 1674 * q^48 - 2164 * q^49 - 340 * q^51 - 800 * q^52 + 2432 * q^53 + 440 * q^55 - 2274 * q^56 - 1844 * q^61 + 2796 * q^62 - 2592 * q^64 + 2264 * q^65 + 1078 * q^66 - 4548 * q^68 - 3288 * q^69 - 4036 * q^74 + 820 * q^75 - 616 * q^77 + 2222 * q^78 + 360 * q^79 + 852 * q^81 + 1948 * q^82 - 2480 * q^87 + 264 * q^88 - 496 * q^90 + 4600 * q^91 + 454 * q^92 - 488 * q^94 + 952 * q^95

Introduction

L-functions

Modular forms

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Database

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