LMFDB - Embedded newform 121.4.c.g.9.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [121,4,Mod(3,121)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(121, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([8])) N = Newforms(chi, 4, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("121.3"); S:= CuspForms(chi, 4); N := Newforms(S);

Level:	$ N $	$=$	$ 121 = 11^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	121.c (of order $5$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,2,8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$7.13923111069$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.324000000.3
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 3x^{6} + 9x^{4} + 27x^{2} + 81 $ x^8 + 3x^6 + 9x^4 + 27*x^2 + 81
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			9.1
Root			$1.40126 - 1.01807i$ of defining polynomial
Character	$\chi$	$=$	121.9
Dual form			121.4.c.g.27.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.37948 + 4.24561i) q^{2} +(6.03859 - 4.38729i) q^{3} +(-9.65012 - 7.01122i) q^{4} +(-2.61555 - 8.04984i) q^{5} +(10.2966 + 31.6897i) q^{6} +(-16.3816 - 11.9019i) q^{7} +(14.1868 - 10.3073i) q^{8} +(8.87275 - 27.3075i) q^{9} +37.7846 q^{10} -89.0333 q^{12} +(19.0156 - 58.5241i) q^{13} +(73.1289 - 53.1313i) q^{14} +(-51.1112 - 37.1345i) q^{15} +(-5.29766 - 16.3045i) q^{16} +(-21.4315 - 65.9594i) q^{17} +(103.697 + 75.3405i) q^{18} +(-5.80625 + 4.21848i) q^{19} +(-31.1988 + 96.0201i) q^{20} -151.138 q^{21} +50.3154 q^{23} +(40.4472 - 124.484i) q^{24} +(43.1683 - 31.3636i) q^{25} +(222.239 + 161.466i) q^{26} +(-3.95066 - 12.1589i) q^{27} +(74.6371 + 229.709i) q^{28} +(115.828 + 84.1542i) q^{29} +(228.166 - 165.772i) q^{30} +(-78.7415 + 242.341i) q^{31} +216.818 q^{32} +309.603 q^{34} +(-52.9615 + 162.999i) q^{35} +(-277.082 + 201.312i) q^{36} +(-272.367 - 197.886i) q^{37} +(-9.90043 - 30.4704i) q^{38} +(-141.935 - 436.830i) q^{39} +(-120.079 - 87.2424i) q^{40} +(-144.063 + 104.668i) q^{41} +(208.493 - 641.675i) q^{42} -55.7898 q^{43} -243.028 q^{45} +(-69.4092 + 213.620i) q^{46} +(207.525 - 150.776i) q^{47} +(-103.523 - 75.2139i) q^{48} +(20.7073 + 63.7306i) q^{49} +(73.6078 + 226.542i) q^{50} +(-418.799 - 304.275i) q^{51} +(-593.829 + 431.442i) q^{52} +(65.9593 - 203.002i) q^{53} +57.0718 q^{54} -355.079 q^{56} +(-16.5538 + 50.9474i) q^{57} +(-517.070 + 375.673i) q^{58} +(645.185 + 468.754i) q^{59} +(232.871 + 716.704i) q^{60} +(52.1303 + 160.441i) q^{61} +(-920.265 - 668.612i) q^{62} +(-470.360 + 341.737i) q^{63} +(-256.715 + 790.089i) q^{64} -520.846 q^{65} -366.105 q^{67} +(-255.639 + 786.777i) q^{68} +(303.834 - 220.748i) q^{69} +(-618.971 - 449.708i) q^{70} +(-241.648 - 743.716i) q^{71} +(-155.592 - 478.862i) q^{72} +(774.665 + 562.827i) q^{73} +(1215.87 - 883.384i) q^{74} +(123.074 - 378.784i) q^{75} +85.6077 q^{76} +2050.41 q^{78} +(180.956 - 556.926i) q^{79} +(-117.393 + 85.2906i) q^{80} +(549.986 + 399.588i) q^{81} +(-245.647 - 756.024i) q^{82} +(-202.922 - 624.530i) q^{83} +(1458.50 + 1059.67i) q^{84} +(-474.907 + 345.040i) q^{85} +(76.9610 - 236.862i) q^{86} +1068.65 q^{87} +72.6819 q^{89} +(335.253 - 1031.80i) q^{90} +(-1008.05 + 732.394i) q^{91} +(-485.549 - 352.772i) q^{92} +(587.734 + 1808.86i) q^{93} +(353.859 + 1089.06i) q^{94} +(49.1447 + 35.7057i) q^{95} +(1309.27 - 951.243i) q^{96} +(-302.713 + 931.655i) q^{97} -299.141 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{2} + 8 q^{3} - 10 q^{4} + 10 q^{5} - 32 q^{6} + 8 q^{7} + 42 q^{8} - 2 q^{9} + 136 q^{10} - 352 q^{12} - 130 q^{13} + 160 q^{14} - 64 q^{15} + 62 q^{16} + 14 q^{17} + 194 q^{18} + 48 q^{19} + 98 q^{20}+ \cdots + 3288 q^{98}+O(q^{100}) $ 8 * q + 2 * q^2 + 8 * q^3 - 10 * q^4 + 10 * q^5 - 32 * q^6 + 8 * q^7 + 42 * q^8 - 2 * q^9 + 136 * q^10 - 352 * q^12 - 130 * q^13 + 160 * q^14 - 64 * q^15 + 62 * q^16 + 14 * q^17 + 194 * q^18 + 48 * q^19 + 98 * q^20 - 544 * q^21 - 512 * q^23 - 144 * q^24 + 176 * q^25 + 106 * q^26 - 16 * q^27 - 296 * q^28 + 30 * q^29 + 280 * q^30 + 184 * q^31 + 1208 * q^32 + 1784 * q^34 + 128 * q^35 - 394 * q^36 - 126 * q^37 + 168 * q^38 + 496 * q^39 - 186 * q^40 - 370 * q^41 - 712 * q^42 - 1056 * q^43 - 808 * q^45 + 664 * q^46 - 256 * q^47 - 152 * q^48 - 522 * q^49 + 64 * q^50 - 488 * q^51 - 602 * q^52 + 162 * q^53 + 512 * q^54 + 1344 * q^56 + 24 * q^57 - 918 * q^58 + 1304 * q^59 - 752 * q^60 + 300 * q^61 - 1312 * q^62 - 1336 * q^63 + 262 * q^64 - 2504 * q^65 - 2624 * q^67 + 934 * q^68 + 280 * q^69 - 872 * q^70 + 1176 * q^71 - 150 * q^72 + 668 * q^73 + 2022 * q^74 - 464 * q^75 + 768 * q^76 + 7840 * q^78 - 416 * q^79 - 214 * q^80 - 26 * q^81 + 322 * q^82 + 960 * q^83 + 1832 * q^84 - 502 * q^85 + 264 * q^86 + 4032 * q^87 - 4296 * q^89 - 1186 * q^90 + 688 * q^91 - 944 * q^92 - 1864 * q^93 - 2408 * q^94 - 24 * q^95 + 1664 * q^96 + 338 * q^97 + 3288 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/121\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{3}{5}\right)$

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 $

$2$	−1.37948	+	4.24561i	−0.487721	+	1.50105i	0.340280	+	0.940324i	$0.389478\pi$
$2$	−1.37948	+	4.24561i	−0.487721	+	1.50105i	−0.828001	+	0.560727i	$0.810522\pi$
$3$	6.03859	−	4.38729i	1.16213	−	0.844334i	0.172081	−	0.985083i	$-0.444951\pi$
$3$	6.03859	−	4.38729i	1.16213	−	0.844334i	0.990045	+	0.140749i	$0.0449510\pi$
$4$	−9.65012	−	7.01122i	−1.20626	−	0.876403i
$5$	−2.61555	−	8.04984i	−0.233942	−	0.719999i	−0.997260	−	0.0739765i	$-0.976431\pi$
$5$	−2.61555	−	8.04984i	−0.233942	−	0.719999i	0.763318	−	0.646023i	$-0.223569\pi$
$6$	10.2966	+	31.6897i	0.700595	+	2.15621i
$7$	−16.3816	−	11.9019i	−0.884521	−	0.642642i	0.0499229	−	0.998753i	$-0.484102\pi$
$7$	−16.3816	−	11.9019i	−0.884521	−	0.642642i	−0.934444	+	0.356111i	$0.884102\pi$
$8$	14.1868	−	10.3073i	0.626976	−	0.455524i
$9$	8.87275	−	27.3075i	0.328620	−	1.01139i
$10$	37.7846			1.19485
$11$		0			0
$11$		0			0
$12$	−89.0333			−2.14181
$13$	19.0156	−	58.5241i	0.405691	−	1.24859i	−0.514625	−	0.857415i	$-0.672069\pi$
$13$	19.0156	−	58.5241i	0.405691	−	1.24859i	0.920316	−	0.391175i	$-0.127931\pi$
$14$	73.1289	−	53.1313i	1.39604	−	1.01428i
$15$	−51.1112	−	37.1345i	−0.879790	−	0.639205i
$16$	−5.29766	−	16.3045i	−0.0827760	−	0.254758i
$17$	−21.4315	−	65.9594i	−0.305759	−	0.941030i	−0.979393	−	0.201964i	$-0.935267\pi$
$17$	−21.4315	−	65.9594i	−0.305759	−	0.941030i	0.673634	−	0.739065i	$-0.264733\pi$
$18$	103.697	+	75.3405i	1.35787	+	0.986551i
$19$	−5.80625	+	4.21848i	−0.0701076	+	0.0509361i	−0.622287	−	0.782789i	$-0.713796\pi$
$19$	−5.80625	+	4.21848i	−0.0701076	+	0.0509361i	0.552179	+	0.833725i	$0.313796\pi$
$20$	−31.1988	+	96.0201i	−0.348813	+	1.07354i
$21$	−151.138			−1.57053
$22$		0			0
$23$	50.3154			0.456151			0.228076	−	0.973643i	$-0.426757\pi$
$23$	50.3154			0.456151			0.228076	+	0.973643i	$0.426757\pi$
$24$	40.4472	−	124.484i	0.344010	−	1.05875i
$25$	43.1683	−	31.3636i	0.345347	−	0.250909i
$26$	222.239	+	161.466i	1.67633	+	1.21793i
$27$	−3.95066	−	12.1589i	−0.0281595	−	0.0866659i
$28$	74.6371	+	229.709i	0.503753	+	1.55039i
$29$	115.828	+	84.1542i	0.741682	+	0.538864i	0.893238	−	0.449585i	$-0.148428\pi$
$29$	115.828	+	84.1542i	0.741682	+	0.538864i	−0.151555	+	0.988449i	$0.548428\pi$
$30$	228.166	−	165.772i	1.38857	−	1.00886i
$31$	−78.7415	+	242.341i	−0.456206	+	1.40406i	0.413507	+	0.910501i	$0.364304\pi$
$31$	−78.7415	+	242.341i	−0.456206	+	1.40406i	−0.869713	+	0.493557i	$0.835696\pi$
$32$	216.818			1.19776
$33$		0			0
$34$	309.603			1.56166
$35$	−52.9615	+	162.999i	−0.255775	+	0.787195i
$36$	−277.082	+	201.312i	−1.28279	+	0.932000i
$37$	−272.367	−	197.886i	−1.21019	−	0.879251i	−0.214937	−	0.976628i	$-0.568955\pi$
$37$	−272.367	−	197.886i	−1.21019	−	0.879251i	−0.995248	+	0.0973769i	$0.968955\pi$
$38$	−9.90043	−	30.4704i	−0.0422648	−	0.130078i
$39$	−141.935	−	436.830i	−0.582762	−	1.79356i
$40$	−120.079	−	87.2424i	−0.474653	−	0.344856i
$41$	−144.063	+	104.668i	−0.548753	+	0.398692i	−0.827326	−	0.561723i	$-0.810139\pi$
$41$	−144.063	+	104.668i	−0.548753	+	0.398692i	0.278572	+	0.960415i	$0.410139\pi$
$42$	208.493	−	641.675i	0.765980	−	2.35744i
$43$	−55.7898			−0.197857			−0.0989286	−	0.995095i	$-0.531542\pi$
$43$	−55.7898			−0.197857			−0.0989286	+	0.995095i	$0.531542\pi$
$44$		0			0
$45$	−243.028			−0.805078
$46$	−69.4092	+	213.620i	−0.222474	+	0.684706i
$47$	207.525	−	150.776i	0.644057	−	0.467935i	−0.217185	−	0.976131i	$-0.569687\pi$
$47$	207.525	−	150.776i	0.644057	−	0.467935i	0.861241	+	0.508196i	$0.169687\pi$
$48$	−103.523	−	75.2139i	−0.311297	−	0.226171i
$49$	20.7073	+	63.7306i	0.0603712	+	0.185803i
$50$	73.6078	+	226.542i	0.208194	+	0.640756i
$51$	−418.799	−	304.275i	−1.14987	−	0.835433i
$52$	−593.829	+	431.442i	−1.58364	+	1.15058i
$53$	65.9593	−	203.002i	0.170947	−	0.526121i	−0.828478	−	0.560022i	$-0.810793\pi$
$53$	65.9593	−	203.002i	0.170947	−	0.526121i	0.999425	+	0.0339002i	$0.0107928\pi$
$54$	57.0718			0.143824
$55$		0			0
$56$	−355.079			−0.847312
$57$	−16.5538	+	50.9474i	−0.0384667	+	0.118388i
$58$	−517.070	+	375.673i	−1.17060	+	0.850488i
$59$	645.185	+	468.754i	1.42366	+	1.03435i	0.991154	+	0.132718i	$0.0423704\pi$
$59$	645.185	+	468.754i	1.42366	+	1.03435i	0.432506	+	0.901631i	$0.357630\pi$
$60$	232.871	+	716.704i	0.501059	+	1.54210i
$61$	52.1303	+	160.441i	0.109420	+	0.336759i	0.990742	−	0.135756i	$-0.0433462\pi$
$61$	52.1303	+	160.441i	0.109420	+	0.336759i	−0.881323	+	0.472515i	$0.843346\pi$
$62$	−920.265	−	668.612i	−1.88506	−	1.36958i
$63$	−470.360	+	341.737i	−0.940632	+	0.683409i
$64$	−256.715	+	790.089i	−0.501397	+	1.54314i
$65$	−520.846			−0.993892
$66$		0			0
$67$	−366.105			−0.667565			−0.333783	−	0.942650i	$-0.608325\pi$
$67$	−366.105			−0.667565			−0.333783	+	0.942650i	$0.608325\pi$
$68$	−255.639	+	786.777i	−0.455895	+	1.40310i
$69$	303.834	−	220.748i	0.530105	−	0.385144i
$70$	−618.971	−	449.708i	−1.05687	−	0.767863i
$71$	−241.648	−	743.716i	−0.403920	−	1.24314i	−0.921793	−	0.387682i	$-0.873276\pi$
$71$	−241.648	−	743.716i	−0.403920	−	1.24314i	0.517873	−	0.855458i	$-0.326724\pi$
$72$	−155.592	−	478.862i	−0.254676	−	0.783811i
$73$	774.665	+	562.827i	1.24202	+	0.902382i	0.997731	−	0.0673197i	$-0.0214447\pi$
$73$	774.665	+	562.827i	1.24202	+	0.902382i	0.244291	+	0.969702i	$0.421445\pi$
$74$	1215.87	−	883.384i	1.91003	−	1.38772i
$75$	123.074	−	378.784i	0.189485	−	0.583176i
$76$	85.6077			0.129209
$77$		0			0
$78$	2050.41			2.97645
$79$	180.956	−	556.926i	0.257711	−	0.793153i	−0.735572	−	0.677446i	$-0.763087\pi$
$79$	180.956	−	556.926i	0.257711	−	0.793153i	0.993283	−	0.115707i	$-0.0369134\pi$
$80$	−117.393	+	85.2906i	−0.164061	+	0.119197i
$81$	549.986	+	399.588i	0.754439	+	0.548132i
$82$	−245.647	−	756.024i	−0.330819	−	1.01816i
$83$	−202.922	−	624.530i	−0.268356	−	0.825916i	−0.990901	−	0.134592i	$-0.957028\pi$
$83$	−202.922	−	624.530i	−0.268356	−	0.825916i	0.722545	−	0.691324i	$-0.242972\pi$
$84$	1458.50	+	1059.67i	1.89447	+	1.37642i
$85$	−474.907	+	345.040i	−0.606011	+	0.440293i
$86$	76.9610	−	236.862i	0.0964991	−	0.296994i
$87$	1068.65			1.31691
$88$		0			0
$89$	72.6819			0.0865648			0.0432824	−	0.999063i	$-0.486218\pi$
$89$	72.6819			0.0865648			0.0432824	+	0.999063i	$0.486218\pi$
$90$	335.253	−	1031.80i	0.392653	−	1.20846i
$91$	−1008.05	+	732.394i	−1.16124	+	0.843689i
$92$	−485.549	−	352.772i	−0.550239	−	0.399772i
$93$	587.734	+	1808.86i	0.655325	+	2.01688i
$94$	353.859	+	1089.06i	0.388274	+	1.19498i
$95$	49.1447	+	35.7057i	0.0530751	+	0.0385613i
$96$	1309.27	−	951.243i	1.39195	−	1.01131i
$97$	−302.713	+	931.655i	−0.316864	+	0.975208i	0.658116	+	0.752917i	$0.271354\pi$
$97$	−302.713	+	931.655i	−0.316864	+	0.975208i	−0.974980	+	0.222292i	$0.928646\pi$
$98$	−299.141			−0.308345
$99$		0			0
$100$	−636.477			−0.636477
$101$	316.567	−	974.292i	0.311877	−	0.959858i	−0.665144	−	0.746715i	$-0.731630\pi$
$101$	316.567	−	974.292i	0.311877	−	0.959858i	0.977021	−	0.213143i	$-0.0683700\pi$
$102$	1869.56	−	1358.32i	1.81484	−	1.31856i
$103$	600.050	+	435.962i	0.574026	+	0.417054i	0.836565	−	0.547867i	$-0.184560\pi$
$103$	600.050	+	435.962i	0.574026	+	0.417054i	−0.262539	+	0.964921i	$0.584560\pi$
$104$	−333.456	−	1026.27i	−0.314405	−	0.967638i
$105$	395.310	+	1216.64i	0.367413	+	1.13078i
$106$	770.877	+	560.075i	0.706360	+	0.513201i
$107$	1050.00	−	762.871i	0.948669	−	0.689248i	−0.00182288	−	0.999998i	$-0.500580\pi$
$107$	1050.00	−	762.871i	0.948669	−	0.689248i	0.950492	+	0.310750i	$0.100580\pi$
$108$	−47.1243	+	145.034i	−0.0419865	+	0.129221i
$109$	−691.844			−0.607951			−0.303975	−	0.952680i	$-0.598314\pi$
$109$	−691.844			−0.607951			−0.303975	+	0.952680i	$0.598314\pi$
$110$		0			0
$111$	−2512.89			−2.14877
$112$	−107.271	+	330.146i	−0.0905013	+	0.278534i
$113$	436.052	−	316.810i	0.363012	−	0.263743i	−0.391296	−	0.920265i	$-0.627973\pi$
$113$	436.052	−	316.810i	0.363012	−	0.263743i	0.754307	+	0.656522i	$0.227973\pi$
$114$	−193.467	−	140.562i	−0.158946	−	0.115481i
$115$	−131.602	−	405.030i	−0.106713	−	0.328429i
$116$	−527.734	−	1624.20i	−0.422404	−	1.30003i
$117$	−1429.43	−	1038.54i	−1.12949	−	0.820624i
$118$	−2880.17	+	2092.57i	−2.24696	+	1.63251i
$119$	−433.960	+	1335.59i	−0.334295	+	1.02885i
$120$	−1107.86			−0.842781
$121$		0			0
$122$	−753.082			−0.558859
$123$	−410.729	+	1264.09i	−0.301091	+	0.926662i
$124$	2458.97	−	1786.55i	1.78083	−	1.29385i
$125$	−1221.33	−	887.349i	−0.873914	−	0.634935i
$126$	−802.028	−	2468.39i	−0.567066	−	1.74525i
$127$	217.470	+	669.305i	0.151948	+	0.467647i	0.997839	−	0.0657085i	$-0.0209308\pi$
$127$	217.470	+	669.305i	0.151948	+	0.467647i	−0.845891	+	0.533356i	$0.820931\pi$
$128$	−1597.00	−	1160.29i	−1.10278	−	0.801219i
$129$	−336.891	+	244.766i	−0.229935	+	0.167058i
$130$	718.498	−	2211.31i	0.484742	−	1.49188i
$131$	446.318			0.297672			0.148836	−	0.988862i	$-0.452447\pi$
$131$	446.318			0.297672			0.148836	+	0.988862i	$0.452447\pi$
$132$		0			0
$133$	145.323			0.0947453
$134$	505.036	−	1554.34i	0.325585	−	1.00205i
$135$	−87.5439	+	63.6044i	−0.0558117	+	0.0405496i
$136$	−983.912	−	714.854i	−0.620366	−	0.450722i
$137$	608.602	+	1873.08i	0.379535	+	1.16809i	0.940367	+	0.340160i	$0.110481\pi$
$137$	608.602	+	1873.08i	0.379535	+	1.16809i	−0.560832	+	0.827930i	$0.689519\pi$
$138$	518.077	+	1594.48i	0.319577	+	0.983558i
$139$	209.293	+	152.060i	0.127712	+	0.0927883i	0.649807	−	0.760099i	$-0.274850\pi$
$139$	209.293	+	152.060i	0.127712	+	0.0927883i	−0.522095	+	0.852887i	$0.674850\pi$
$140$	1653.91	−	1201.63i	0.998433	−	0.725404i
$141$	591.661	−	1820.95i	0.353382	−	1.08760i
$142$	3490.88			2.06302
$143$		0			0
$144$	−492.241			−0.284862
$145$	374.473	−	1152.51i	0.214471	−	0.660074i
$146$	−3458.18	+	2512.52i	−1.96028	+	1.42423i
$147$	404.647	+	293.994i	0.227039	+	0.164954i
$148$	1240.95	+	3819.25i	0.689226	+	2.12122i
$149$	−30.5396	−	93.9912i	−0.0167913	−	0.0516783i	0.942310	−	0.334742i	$-0.108649\pi$
$149$	−30.5396	−	93.9912i	−0.0167913	−	0.0516783i	−0.959101	+	0.283064i	$0.908649\pi$
$150$	1438.39	+	1045.05i	0.782961	+	0.568854i
$151$	1203.46	−	874.362i	0.648582	−	0.471222i	−0.214206	−	0.976789i	$-0.568716\pi$
$151$	1203.46	−	874.362i	0.648582	−	0.471222i	0.862788	+	0.505566i	$0.168716\pi$
$152$	−38.8909	+	119.694i	−0.0207531	+	0.0638714i
$153$	−1991.34			−1.05223
$154$		0			0
$155$	2156.76			1.11765
$156$	−1693.03	+	5210.60i	−0.868914	+	2.67424i
$157$	−1708.65	+	1241.41i	−0.868569	+	0.631052i	−0.930203	−	0.367047i	$-0.880369\pi$
$157$	−1708.65	+	1241.41i	−0.868569	+	0.631052i	0.0616338	+	0.998099i	$0.480369\pi$
$158$	2114.87	+	1536.54i	1.06487	+	0.773675i
$159$	−492.327	−	1515.23i	−0.245560	−	0.755756i
$160$	−567.098	−	1745.35i	−0.280207	−	0.862387i
$161$	−824.244	−	598.848i	−0.403475	−	0.293142i
$162$	−2455.19	+	1783.80i	−1.19073	+	0.865116i
$163$	427.981	−	1317.19i	0.205657	−	0.632947i	−0.794029	−	0.607880i	$-0.792020\pi$
$163$	427.981	−	1317.19i	0.205657	−	0.632947i	0.999686	−	0.0250670i	$-0.00797991\pi$
$164$	2124.08			1.01136
$165$		0			0
$166$	2931.44			1.37062
$167$	239.570	−	737.322i	0.111009	−	0.341651i	−0.880085	−	0.474817i	$-0.842514\pi$
$167$	239.570	−	737.322i	0.111009	−	0.341651i	0.991094	+	0.133166i	$0.0425143\pi$
$168$	−2144.18	+	1557.84i	−0.984684	+	0.715414i
$169$	−1286.07	−	934.383i	−0.585374	−	0.425299i
$170$	−809.781	−	2492.25i	−0.365338	−	1.12439i
$171$	63.6789	+	195.984i	0.0284775	+	0.0876447i
$172$	538.378	+	391.154i	0.238668	+	0.173403i
$173$	361.320	−	262.514i	0.158790	−	0.115367i	−0.505553	−	0.862796i	$-0.668712\pi$
$173$	361.320	−	262.514i	0.158790	−	0.115367i	0.664343	+	0.747428i	$0.268712\pi$
$174$	−1474.18	+	4537.07i	−0.642285	+	1.97675i
$175$	−1080.45			−0.466711
$176$		0			0
$177$	5952.56			2.52781
$178$	−100.263	+	308.579i	−0.0422195	+	0.129938i
$179$	2271.11	−	1650.06i	0.948328	−	0.689001i	−0.00208294	−	0.999998i	$-0.500663\pi$
$179$	2271.11	−	1650.06i	0.948328	−	0.689001i	0.950411	+	0.310997i	$0.100663\pi$
$180$	2345.25	+	1703.92i	0.971137	+	0.705572i
$181$	−412.662	−	1270.04i	−0.169464	−	0.521555i	0.829874	−	0.557951i	$-0.188412\pi$
$181$	−412.662	−	1270.04i	−0.169464	−	0.521555i	−0.999337	+	0.0363957i	$0.988412\pi$
$182$	−1718.87	−	5290.13i	−0.700060	−	2.15456i
$183$	1018.69	+	740.124i	0.411497	+	0.298970i
$184$	713.816	−	518.618i	0.285996	−	0.207788i
$185$	−880.562	+	2710.09i	−0.349947	+	1.07703i
$186$	−8490.49			−3.34706
$187$		0			0
$188$	−3059.77			−1.18700
$189$	−79.9958	+	246.202i	−0.0307875	+	0.0947542i
$190$	−219.387	+	159.394i	−0.0837683	+	0.0608613i
$191$	1613.96	+	1172.61i	0.611426	+	0.444227i	0.849916	−	0.526918i	$-0.176652\pi$
$191$	1613.96	+	1172.61i	0.611426	+	0.444227i	−0.238490	+	0.971145i	$0.576652\pi$
$192$	1916.15	+	5897.30i	0.720241	+	2.21667i
$193$	−646.359	−	1989.29i	−0.241067	−	0.741928i	−0.996258	−	0.0864236i	$-0.972456\pi$
$193$	−646.359	−	1989.29i	−0.241067	−	0.741928i	0.755192	−	0.655504i	$-0.227544\pi$
$194$	−3537.86	−	2570.40i	−1.30930	−	0.951259i
$195$	−3145.17	+	2285.10i	−1.15503	+	0.839177i
$196$	247.001	−	760.191i	0.0900150	−	0.277038i
$197$	3777.20			1.36606			0.683032	−	0.730389i	$-0.260661\pi$
$197$	3777.20			1.36606			0.683032	+	0.730389i	$0.260661\pi$
$198$		0			0
$199$	−1251.15			−0.445688			−0.222844	−	0.974854i	$-0.571534\pi$
$199$	−1251.15			−0.445688			−0.222844	+	0.974854i	$0.571534\pi$
$200$	289.146	−	889.901i	0.102229	−	0.314628i
$201$	−2210.76	+	1606.21i	−0.775795	+	0.563648i
$202$	3699.77	+	2688.04i	1.28869	+	0.936286i
$203$	−895.854	−	2757.15i	−0.309737	−	0.953272i
$204$	1908.12	+	5872.59i	0.654878	+	2.01551i
$205$	1219.36	+	885.920i	0.415435	+	0.301831i
$206$	−2678.68	+	1946.18i	−0.905984	+	0.658236i
$207$	446.435	−	1373.99i	0.149901	−	0.461346i
$208$	−1054.95			−0.351670
$209$		0			0
$210$	−5710.71			−1.87655
$211$	−1422.81	+	4378.95i	−0.464218	+	1.42872i	0.395745	+	0.918360i	$0.370486\pi$
$211$	−1422.81	+	4378.95i	−0.464218	+	1.42872i	−0.859963	+	0.510356i	$0.829514\pi$
$212$	−2059.80	+	1496.54i	−0.667302	+	0.484823i
$213$	−4722.11	−	3430.81i	−1.51903	−	1.10364i
$214$	1790.40	+	5510.27i	0.571911	+	1.76016i
$215$	145.921	+	449.099i	0.0462871	+	0.142457i
$216$	−181.373	−	131.775i	−0.0571337	−	0.0415101i
$217$	4174.23	−	3032.75i	1.30583	−	0.948741i
$218$	954.387	−	2937.30i	0.296510	−	0.912565i
$219$	7147.16			2.20530
$220$		0			0
$221$	−4267.75			−1.29900
$222$	3466.50	−	10668.8i	1.04800	−	3.22541i
$223$	3756.63	−	2729.35i	1.12808	−	0.819601i	0.142670	−	0.989770i	$-0.454431\pi$
$223$	3756.63	−	2729.35i	1.12808	−	0.819601i	0.985415	+	0.170169i	$0.0544313\pi$
$224$	−3551.81	−	2580.54i	−1.05944	−	0.769731i
$225$	−473.441	−	1457.10i	−0.140279	−	0.431734i
$226$	743.527	+	2288.34i	0.218844	+	0.673532i
$227$	3446.38	+	2503.94i	1.00769	+	0.732126i	0.963722	−	0.266907i	$-0.0860017\pi$
$227$	3446.38	+	2503.94i	1.00769	+	0.732126i	0.0439628	+	0.999033i	$0.486002\pi$
$228$	516.949	−	375.586i	0.150157	−	0.109095i
$229$	1778.82	−	5474.64i	0.513308	−	1.57980i	−0.273031	−	0.962005i	$-0.588026\pi$
$229$	1778.82	−	5474.64i	0.513308	−	1.57980i	0.786339	−	0.617795i	$-0.211974\pi$
$230$	1901.15			0.545034
$231$		0			0
$232$	2510.65			0.710483
$233$	−1591.77	+	4898.97i	−0.447555	+	1.37743i	0.432101	+	0.901825i	$0.357772\pi$
$233$	−1591.77	+	4898.97i	−0.447555	+	1.37743i	−0.879657	+	0.475609i	$0.842228\pi$
$234$	6381.11	−	4636.15i	1.78268	−	1.29519i
$235$	−1756.51	−	1276.18i	−0.487585	−	0.354251i
$236$	−2939.57	−	9047.07i	−0.810804	−	2.49540i
$237$	−1350.68	−	4156.96i	−0.370194	−	1.13934i
$238$	−5071.77	−	3684.86i	−1.38132	−	1.00359i
$239$	−1683.78	+	1223.34i	−0.455710	+	0.331093i	−0.791846	−	0.610721i	$-0.790880\pi$
$239$	−1683.78	+	1223.34i	−0.455710	+	0.331093i	0.336136	+	0.941814i	$0.390880\pi$
$240$	−334.690	+	1030.07i	−0.0900173	+	0.277045i
$241$	−6829.14			−1.82533			−0.912663	−	0.408714i	$-0.865977\pi$
$241$	−6829.14			−1.82533			−0.912663	+	0.408714i	$0.865977\pi$
$242$		0			0
$243$	5419.43			1.43069
$244$	621.821	−	1913.77i	0.163148	−	0.502117i
$245$	458.860	−	333.381i	0.119655	−	0.0869345i
$246$	−4800.26	−	3487.59i	−1.24412	−	0.903905i
$247$	136.474	+	420.023i	0.0351563	+	0.108200i
$248$	1380.80	+	4249.67i	0.353553	+	1.08812i
$249$	−3965.35	−	2881.00i	−1.00921	−	0.733236i
$250$	5452.15	−	3961.22i	1.37930	−	1.00212i
$251$	6.22067	−	19.1453i	0.00156432	−	0.00481450i	−0.950271	−	0.311423i	$-0.899194\pi$
$251$	6.22067	−	19.1453i	0.00156432	−	0.00481450i	0.951836	+	0.306609i	$0.0991943\pi$
$252$	6935.03			1.73359
$253$		0			0
$254$	−3141.60			−0.776070
$255$	−1353.98	+	4167.11i	−0.332507	+	1.02335i
$256$	1752.46	−	1273.24i	0.427847	−	0.310849i
$257$	−122.154	−	88.7499i	−0.0296488	−	0.0215411i	0.572862	−	0.819652i	$-0.305833\pi$
$257$	−122.154	−	88.7499i	−0.0296488	−	0.0215411i	−0.602511	+	0.798111i	$0.705833\pi$
$258$	−574.445	−	1767.96i	−0.138618	−	0.426622i
$259$	2106.57	+	6483.36i	0.505390	+	1.55543i
$260$	5026.23	+	3651.77i	1.19890	+	0.871050i
$261$	3325.76	−	2416.31i	0.788733	−	0.573048i
$262$	−615.688	+	1894.89i	−0.145181	+	0.446820i
$263$	2609.68			0.611862			0.305931	−	0.952054i	$-0.401032\pi$
$263$	2609.68			0.611862			0.305931	+	0.952054i	$0.401032\pi$
$264$		0			0
$265$	−1806.65			−0.418799
$266$	−200.471	+	616.986i	−0.0462093	+	0.142218i
$267$	438.896	−	318.876i	0.100599	−	0.0730896i
$268$	3532.96	+	2566.84i	0.805260	+	0.585056i
$269$	−372.656	−	1146.92i	−0.0844656	−	0.259959i	0.899900	−	0.436097i	$-0.143639\pi$
$269$	−372.656	−	1146.92i	−0.0844656	−	0.259959i	−0.984365	+	0.176138i	$0.943639\pi$
$270$	−149.274	−	459.419i	−0.0336464	−	0.103553i
$271$	4925.43	+	3578.53i	1.10405	+	0.802142i	0.981717	−	0.190347i	$-0.0609613\pi$
$271$	4925.43	+	3578.53i	1.10405	+	0.802142i	0.122336	+	0.992489i	$0.460961\pi$
$272$	−961.900	+	698.861i	−0.214426	+	0.155789i
$273$	−2873.99	+	8845.24i	−0.637150	+	1.96095i
$274$	−8791.94			−1.93847
$275$		0			0
$276$	−4479.74			−0.976989
$277$	2303.27	−	7088.73i	0.499603	−	1.53762i	−0.310055	−	0.950719i	$-0.600348\pi$
$277$	2303.27	−	7088.73i	0.499603	−	1.53762i	0.809658	−	0.586901i	$-0.199652\pi$
$278$	−934.304	+	678.812i	−0.201568	+	0.146448i
$279$	5919.09	+	4300.47i	1.27013	+	0.922804i
$280$	928.728	+	2858.33i	0.198222	+	0.610064i
$281$	2076.55	+	6390.95i	0.440841	+	1.35677i	0.886981	+	0.461806i	$0.152798\pi$
$281$	2076.55	+	6390.95i	0.440841	+	1.35677i	−0.446140	+	0.894963i	$0.647202\pi$
$282$	6914.85	+	5023.93i	1.46019	+	1.06089i
$283$	−551.008	+	400.330i	−0.115739	+	0.0840890i	−0.644149	−	0.764900i	$-0.722788\pi$
$283$	−551.008	+	400.330i	−0.115739	+	0.0840890i	0.528410	+	0.848989i	$0.322788\pi$
$284$	−2882.43	+	8871.20i	−0.602256	+	1.85355i
$285$	453.415			0.0942386
$286$		0			0
$287$	3605.72			0.741600
$288$	1923.77	−	5920.76i	0.393609	−	1.21140i
$289$	83.3663	−	60.5692i	0.0169685	−	0.0123283i
$290$	4376.53	+	3179.74i	0.886202	+	0.643864i
$291$	2259.48	+	6953.97i	0.455165	+	1.40085i
$292$	−3529.50	−	10862.7i	−0.707358	−	2.17702i
$293$	−4628.08	−	3362.49i	−0.922782	−	0.670440i	0.0214328	−	0.999770i	$-0.493177\pi$
$293$	−4628.08	−	3362.49i	−0.922782	−	0.670440i	−0.944215	+	0.329330i	$0.893177\pi$
$294$	−1806.39	+	1312.42i	−0.358336	+	0.260346i
$295$	2085.88	−	6419.68i	0.411677	−	1.26701i
$296$	−5903.71			−1.15928
$297$		0			0
$298$	441.179			0.0857612
$299$	956.779	−	2944.66i	0.185057	−	0.569546i
$300$	−3843.42	+	2792.41i	−0.739666	+	0.537399i
$301$	913.923	+	664.004i	0.175009	+	0.127151i
$302$	2052.05	+	6315.58i	0.391002	+	1.20338i
$303$	−2362.88	−	7272.21i	−0.448001	−	1.37880i
$304$	99.5399	+	72.3200i	0.0187796	+	0.0136442i
$305$	1155.17	−	839.282i	0.216869	−	0.157564i
$306$	2747.03	−	8454.47i	0.513193	−	1.57944i
$307$	−185.674			−0.0345178			−0.0172589	−	0.999851i	$-0.505494\pi$
$307$	−185.674			−0.0345178			−0.0172589	+	0.999851i	$0.505494\pi$
$308$		0			0
$309$	5536.14			1.01922
$310$	−2975.22	+	9156.77i	−0.545100	+	1.67764i
$311$	−2053.62	+	1492.04i	−0.374438	+	0.272045i	−0.759049	−	0.651034i	$-0.774336\pi$
$311$	−2053.62	+	1492.04i	−0.374438	+	0.272045i	0.384611	+	0.923079i	$0.374336\pi$
$312$	−6516.16	−	4734.27i	−1.18239	−	0.859055i
$313$	−2745.05	−	8448.40i	−0.495717	−	1.52566i	−0.815836	−	0.578284i	$-0.803723\pi$
$313$	−2745.05	−	8448.40i	−0.495717	−	1.52566i	0.320118	−	0.947378i	$-0.396277\pi$
$314$	−2913.48	−	8966.78i	−0.523622	−	1.61154i
$315$	3981.18	+	2892.50i	0.712108	+	0.517377i
$316$	−5650.99	+	4105.68i	−1.00599	+	0.730894i
$317$	−888.523	+	2734.59i	−0.157427	+	0.484511i	−0.998399	−	0.0565682i	$-0.981984\pi$
$317$	−888.523	+	2734.59i	−0.157427	+	0.484511i	0.840971	+	0.541079i	$0.181984\pi$
$318$	7112.22			1.25419
$319$		0			0
$320$	7031.54			1.22836
$321$	2993.59	−	9213.33i	0.520517	−	1.60199i
$322$	3679.51	−	2673.32i	0.636804	−	0.462665i
$323$	402.685	+	292.568i	0.0693685	+	0.0503991i
$324$	−2505.83	−	7712.15i	−0.429669	−	1.32239i
$325$	−1014.66	−	3122.79i	−0.173178	−	0.532988i
$326$	5001.89	+	3634.09i	0.849783	+	0.617403i
$327$	−4177.76	+	3035.32i	−0.706515	+	0.513313i
$328$	−964.952	+	2969.82i	−0.162441	+	0.499941i
$329$	−5194.10			−0.870396
$330$		0			0
$331$	−8295.55			−1.37754			−0.688769	−	0.724981i	$-0.741848\pi$
$331$	−8295.55			−1.37754			−0.688769	+	0.724981i	$0.741848\pi$
$332$	−2420.49	+	7449.51i	−0.400126	+	1.23146i
$333$	−7820.42	+	5681.87i	−1.28696	+	0.935028i
$334$	2799.90	+	2034.25i	0.458694	+	0.333261i
$335$	957.567	+	2947.09i	0.156172	+	0.480646i
$336$	800.680	+	2464.24i	0.130002	+	0.400105i
$337$	−8215.84	−	5969.16i	−1.32803	−	0.964869i	−0.999795	−	0.0202719i	$-0.993547\pi$
$337$	−8215.84	−	5969.16i	−1.32803	−	0.964869i	−0.328233	−	0.944597i	$-0.606453\pi$
$338$	5741.14	−	4171.18i	0.923895	−	0.671249i
$339$	1243.20	−	3826.17i	0.199178	−	0.613006i
$340$	7002.07			1.11688
$341$		0			0
$342$	−919.915			−0.145448
$343$	−1726.92	+	5314.92i	−0.271851	+	0.836672i
$344$	−791.480	+	575.044i	−0.124052	+	0.0901288i
$345$	−2571.68	−	1868.43i	−0.401317	−	0.291574i
$346$	616.099	+	1896.16i	0.0957274	+	0.294619i
$347$	3679.17	+	11323.3i	0.569187	+	1.75178i	0.655170	+	0.755482i	$0.272597\pi$
$347$	3679.17	+	11323.3i	0.569187	+	1.75178i	−0.0859821	+	0.996297i	$0.527403\pi$
$348$	−10312.6	−	7492.53i	−1.58854	−	1.15414i
$349$	3673.30	−	2668.81i	0.563402	−	0.409335i	−0.269301	−	0.963056i	$-0.586793\pi$
$349$	3673.30	−	2668.81i	0.563402	−	0.409335i	0.832702	+	0.553721i	$0.186793\pi$
$350$	1490.46	−	4587.18i	0.227625	−	0.700557i
$351$	−786.712			−0.119634
$352$		0			0
$353$	−722.250			−0.108899			−0.0544497	−	0.998517i	$-0.517340\pi$
$353$	−722.250			−0.108899			−0.0544497	+	0.998517i	$0.517340\pi$
$354$	−8211.46	+	25272.3i	−1.23287	+	3.79437i
$355$	−5354.75	+	3890.46i	−0.800566	+	0.581645i
$356$	−701.389	−	509.589i	−0.104420	−	0.0758656i
$357$	3239.13	+	9969.00i	0.480204	+	1.47791i
$358$	3872.55	+	11918.5i	0.571705	+	1.75953i
$359$	−9870.02	−	7170.99i	−1.45103	−	1.05423i	−0.985589	−	0.169155i	$-0.945896\pi$
$359$	−9870.02	−	7170.99i	−1.45103	−	1.05423i	−0.465440	−	0.885080i	$-0.654104\pi$
$360$	−3447.80	+	2504.97i	−0.504764	+	0.366733i
$361$	−2103.63	+	6474.31i	−0.306696	+	0.943914i
$362$	5961.37			0.865532
$363$		0			0
$364$	14862.8			2.14017
$365$	2504.49	−	7708.03i	0.359153	−	1.10536i
$366$	−4547.55	+	3303.99i	−0.649465	+	0.471864i
$367$	116.186	+	84.4142i	0.0165255	+	0.0120065i	0.596017	−	0.802972i	$-0.296749\pi$
$367$	116.186	+	84.4142i	0.0165255	+	0.0120065i	−0.579492	+	0.814978i	$0.696749\pi$
$368$	−266.554	−	820.368i	−0.0377584	−	0.116208i
$369$	1579.99	+	4862.70i	0.222902	+	0.686021i
$370$	−10291.3	−	7477.05i	−1.44599	−	1.05058i
$371$	−3496.62	+	2540.44i	−0.489314	+	0.355507i
$372$	7010.62	−	21576.5i	0.977106	−	3.00722i
$373$	3676.93			0.510414			0.255207	−	0.966886i	$-0.417856\pi$
$373$	3676.93			0.510414			0.255207	+	0.966886i	$0.417856\pi$
$374$		0			0
$375$	−11268.2			−1.55170
$376$	1390.03	−	4278.07i	0.190652	−	0.586767i
$377$	7127.60	−	5178.51i	0.973714	−	0.707445i
$378$	−934.925	−	679.262i	−0.127215	−	0.0924272i
$379$	720.339	+	2216.98i	0.0976289	+	0.300471i	0.987930	−	0.154902i	$-0.0495061\pi$
$379$	720.339	+	2216.98i	0.0976289	+	0.300471i	−0.890301	+	0.455373i	$0.849506\pi$
$380$	−223.911	−	689.128i	−0.0302274	−	0.0930303i
$381$	4249.65	+	3087.55i	0.571433	+	0.415170i
$382$	−7204.90	+	5234.67i	−0.965012	+	0.701123i
$383$	−1145.28	+	3524.80i	−0.152796	+	0.470258i	−0.997931	−	0.0642954i	$-0.979520\pi$
$383$	−1145.28	+	3524.80i	−0.152796	+	0.470258i	0.845135	+	0.534553i	$0.179520\pi$
$384$	−14734.2			−1.95807
$385$		0			0
$386$	9337.39			1.23124
$387$	−495.008	+	1523.48i	−0.0650199	+	0.200111i
$388$	9453.25	−	6868.19i	1.23690	−	0.898659i
$389$	−5280.60	−	3836.58i	−0.688270	−	0.500058i	0.187821	−	0.982203i	$-0.439858\pi$
$389$	−5280.60	−	3836.58i	−0.688270	−	0.500058i	−0.876091	+	0.482146i	$0.839858\pi$
$390$	−5362.95	−	16505.4i	−0.696316	−	2.14304i
$391$	−1078.33	−	3318.77i	−0.139472	−	0.429252i
$392$	950.665	+	690.698i	0.122489	+	0.0889937i
$393$	2695.13	−	1958.13i	0.345932	−	0.251334i
$394$	−5210.59	+	16036.5i	−0.666258	+	2.05053i
$395$	−4956.47			−0.631359
$396$		0			0
$397$	−11290.7			−1.42736			−0.713682	−	0.700470i	$-0.752974\pi$
$397$	−11290.7			−1.42736			−0.713682	+	0.700470i	$0.752974\pi$
$398$	1725.95	−	5311.91i	0.217371	−	0.669000i
$399$	877.547	−	637.575i	0.110106	−	0.0799967i
$400$	−740.060	−	537.685i	−0.0925075	−	0.0672107i
$401$	4267.73	+	13134.7i	0.531472	+	1.63570i	0.751151	+	0.660130i	$0.229499\pi$
$401$	4267.73	+	13134.7i	0.531472	+	1.63570i	−0.219679	+	0.975572i	$0.570501\pi$
$402$	−3769.64	−	11601.8i	−0.467693	−	1.43941i
$403$	12685.5	+	9216.55i	1.56801	+	1.13923i
$404$	−9885.88	+	7182.51i	−1.21743	+	0.884513i
$405$	1778.10	−	5472.44i	0.218160	−	0.671427i
$406$	12941.6			1.58198
$407$		0			0
$408$	−9077.70			−1.10150
$409$	−2870.58	+	8834.74i	−0.347044	+	1.06809i	0.613436	+	0.789744i	$0.289787\pi$
$409$	−2870.58	+	8834.74i	−0.347044	+	1.06809i	−0.960480	+	0.278348i	$0.910213\pi$
$410$	−5443.37	+	3954.84i	−0.655680	+	0.476379i
$411$	11892.9	+	8640.66i	1.42733	+	1.03701i
$412$	−2733.93	−	8414.17i	−0.326920	−	1.00616i
$413$	−4990.07	−	15357.8i	−0.594540	−	1.82981i
$414$	5217.57	+	3790.78i	0.619395	+	0.450017i
$415$	−4496.61	+	3266.98i	−0.531879	+	0.386433i
$416$	4122.93	−	12689.1i	0.485921	−	1.49551i
$417$	1930.96			0.226762
$418$		0			0
$419$	3072.83			0.358276			0.179138	−	0.983824i	$-0.442669\pi$
$419$	3072.83			0.358276			0.179138	+	0.983824i	$0.442669\pi$
$420$	4715.34	−	14512.3i	0.547822	−	1.68602i
$421$	−4832.93	+	3511.33i	−0.559483	+	0.406488i	−0.831270	−	0.555869i	$-0.812386\pi$
$421$	−4832.93	+	3511.33i	−0.559483	+	0.406488i	0.271787	+	0.962358i	$0.412386\pi$
$422$	−16628.6	−	12081.4i	−1.91817	−	1.39363i
$423$	−2276.00	−	7004.79i	−0.261614	−	0.805165i
$424$	−1156.65	−	3559.82i	−0.132481	−	0.407736i
$425$	−2993.89	−	2175.19i	−0.341706	−	0.248264i
$426$	21080.0	−	15315.5i	2.39748	−	1.74187i
$427$	1055.57	−	3248.72i	0.119632	−	0.368188i
$428$	−15481.3			−1.74840
$429$		0			0
$430$	−2107.99			−0.236411
$431$	72.1217	−	221.968i	0.00806028	−	0.0248070i	−0.946945	−	0.321394i	$-0.895849\pi$
$431$	72.1217	−	221.968i	0.00806028	−	0.0248070i	0.955006	+	0.296587i	$0.0958485\pi$
$432$	−177.316	+	128.827i	−0.0197479	+	0.0143477i
$433$	4507.29	+	3274.74i	0.500247	+	0.363450i	0.809111	−	0.587656i	$-0.199949\pi$
$433$	4507.29	+	3274.74i	0.500247	+	0.363450i	−0.308865	+	0.951106i	$0.599949\pi$
$434$	7117.62	+	21905.8i	0.787228	+	2.42284i
$435$	−2795.11	−	8602.45i	−0.308081	−	0.948174i
$436$	6676.37	+	4850.67i	0.733349	+	0.532810i
$437$	−292.143	+	212.255i	−0.0319797	+	0.0232346i
$438$	−9859.39	+	30344.1i	−1.07557	+	3.31027i
$439$	3533.06			0.384109			0.192054	−	0.981384i	$-0.438485\pi$
$439$	3533.06			0.384109			0.192054	+	0.981384i	$0.438485\pi$
$440$		0			0
$441$	1924.05			0.207759
$442$	5887.29	−	18119.2i	0.633552	−	1.94987i
$443$	12056.5	−	8759.54i	1.29305	−	0.939454i	0.293186	−	0.956055i	$-0.405284\pi$
$443$	12056.5	−	8759.54i	1.29305	−	0.939454i	0.999862	+	0.0166010i	$0.00528450\pi$
$444$	24249.7	+	17618.5i	2.59198	+	1.88319i
$445$	−190.103	−	585.077i	−0.0202511	−	0.0623266i
$446$	6405.57	+	19714.3i	0.680073	+	2.09305i
$447$	−596.783	−	433.588i	−0.0631473	−	0.0458792i
$448$	13608.9	−	9887.48i	1.43518	−	1.04272i
$449$	−2221.88	+	6838.23i	−0.233534	+	0.718744i	0.763778	+	0.645479i	$0.223342\pi$
$449$	−2221.88	+	6838.23i	−0.233534	+	0.718744i	−0.997312	+	0.0732656i	$0.976658\pi$
$450$	6839.39			0.716471
$451$		0			0
$452$	−6429.18			−0.669033
$453$	3431.09	−	10559.8i	0.355865	−	1.09524i
$454$	−15385.0	+	11177.9i	−1.59043	+	1.15551i
$455$	8532.27	+	6199.05i	0.879118	+	0.638717i
$456$	290.286	+	893.408i	0.0298111	+	0.0917492i
$457$	1218.21	+	3749.26i	0.124694	+	0.383770i	0.993845	−	0.110777i	$-0.0353339\pi$
$457$	1218.21	+	3749.26i	0.124694	+	0.383770i	−0.869151	+	0.494547i	$0.835334\pi$
$458$	20789.3	+	15104.3i	2.12101	+	1.54100i
$459$	−717.324	+	521.167i	−0.0729452	+	0.0529978i
$460$	−1569.78	+	4831.29i	−0.159112	+	0.489695i
$461$	−8254.37			−0.833936			−0.416968	−	0.908921i	$-0.636907\pi$
$461$	−8254.37			−0.833936			−0.416968	+	0.908921i	$0.636907\pi$
$462$		0			0
$463$	7083.97			0.711058			0.355529	−	0.934665i	$-0.384301\pi$
$463$	7083.97			0.711058			0.355529	+	0.934665i	$0.384301\pi$
$464$	758.476	−	2334.35i	0.0758865	−	0.233555i
$465$	13023.8	−	9462.33i	1.29885	−	0.943667i
$466$	−18603.3	−	13516.1i	−1.84932	−	1.34361i
$467$	−5524.91	−	17003.9i	−0.547457	−	1.68490i	−0.715076	−	0.699046i	$-0.753608\pi$
$467$	−5524.91	−	17003.9i	−0.547457	−	1.68490i	0.167620	−	0.985852i	$-0.446392\pi$
$468$	6512.71	+	20044.1i	0.643269	+	1.97978i
$469$	5997.37	+	4357.34i	0.590475	+	0.429005i
$470$	7841.26	−	5697.01i	0.769554	−	0.559114i
$471$	−4871.42	+	14992.7i	−0.476568	+	1.46672i
$472$	13984.7			1.36377
$473$		0			0
$474$	19512.1			1.89076
$475$	−118.339	+	364.210i	−0.0114311	+	0.0351812i
$476$	13551.9	−	9846.04i	1.30494	−	0.948093i
$477$	−4958.23	−	3602.37i	−0.475937	−	0.345788i
$478$	−2871.07	−	8836.26i	−0.274728	−	0.845525i
$479$	1331.31	+	4097.34i	0.126991	+	0.390840i	0.994259	−	0.107003i	$-0.0341256\pi$
$479$	1331.31	+	4097.34i	0.126991	+	0.390840i	−0.867267	+	0.497843i	$0.834126\pi$
$480$	−11081.8	−	8051.42i	−1.05378	−	0.765615i
$481$	−16760.3	+	12177.1i	−1.58879	+	1.15432i
$482$	9420.68	−	28993.9i	0.890249	−	2.73991i
$483$	−7604.58			−0.716399
$484$		0			0
$485$	8291.43			0.776277
$486$	−7476.02	+	23008.8i	−0.697776	+	2.14753i
$487$	−10726.1	+	7792.97i	−0.998042	+	0.725120i	−0.961667	−	0.274219i	$-0.911581\pi$
$487$	−10726.1	+	7792.97i	−0.998042	+	0.725120i	−0.0363742	+	0.999338i	$0.511581\pi$
$488$	2393.28	+	1738.82i	0.222006	+	0.161297i
$489$	−3194.50	−	9831.65i	−0.295420	−	0.909208i
$490$	782.418	+	2408.04i	0.0721348	+	0.222008i
$491$	−743.284	−	540.027i	−0.0683176	−	0.0496356i	0.553102	−	0.833113i	$-0.313444\pi$
$491$	−743.284	−	540.027i	−0.0683176	−	0.0496356i	−0.621420	+	0.783478i	$0.713444\pi$
$492$	12826.4	−	9318.94i	1.17532	−	0.853923i
$493$	3068.39	−	9443.52i	0.280311	−	0.862708i
$494$	−1971.52			−0.179560
$495$		0			0
$496$	4368.41			0.395458
$497$	−4893.06	+	15059.3i	−0.441617	+	1.35916i
$498$	17701.7	−	12861.1i	1.59284	−	1.15727i
$499$	−9886.98	−	7183.31i	−0.886978	−	0.644427i	0.0481105	−	0.998842i	$-0.484680\pi$
$499$	−9886.98	−	7183.31i	−0.886978	−	0.644427i	−0.935088	+	0.354415i	$0.884680\pi$
$500$	5564.59	+	17126.1i	0.497712	+	1.53180i
$501$	−1788.18	−	5503.45i	−0.159461	−	0.490770i
$502$	72.7021	+	52.8211i	0.00646385	+	0.00469626i
$503$	4440.55	−	3226.25i	0.393627	−	0.285986i	−0.373313	−	0.927705i	$-0.621778\pi$
$503$	4440.55	−	3226.25i	0.393627	−	0.285986i	0.766940	+	0.641719i	$0.221778\pi$
$504$	−3150.53	+	9696.33i	−0.278444	+	0.856962i
$505$	−8670.89			−0.764058
$506$		0			0
$507$	−11865.4			−1.03937
$508$	2594.03	−	7983.60i	0.226558	−	0.697274i
$509$	75.1105	−	54.5710i	0.00654070	−	0.00475209i	−0.584510	−	0.811386i	$-0.698713\pi$
$509$	75.1105	−	54.5710i	0.00654070	−	0.00475209i	0.591051	+	0.806634i	$0.298713\pi$
$510$	−15824.2	−	11496.9i	−1.37393	−	0.998220i
$511$	−5991.50	−	18440.0i	−0.518686	−	1.59635i
$512$	−1891.82	−	5822.43i	−0.163296	−	0.502573i
$513$	74.2306	+	53.9317i	0.00638862	+	0.00464160i
$514$	545.307	−	396.189i	0.0467947	−	0.0339983i
$515$	1939.96	−	5970.59i	0.165990	−	0.510865i
$516$	4967.15			0.423772
$517$		0			0
$518$	−30431.8			−2.58127
$519$	1030.13	−	3170.43i	0.0871250	−	0.268143i
$520$	−7389.16	+	5368.54i	−0.623146	+	0.452742i
$521$	3558.78	+	2585.61i	0.299257	+	0.217423i	0.727273	−	0.686348i	$-0.240787\pi$
$521$	3558.78	+	2585.61i	0.299257	+	0.217423i	−0.428016	+	0.903771i	$0.640787\pi$
$522$	5670.87	+	17453.1i	0.475493	+	1.46342i
$523$	−1782.94	−	5487.33i	−0.149068	−	0.458785i	0.848444	−	0.529286i	$-0.177540\pi$
$523$	−1782.94	−	5487.33i	−0.149068	−	0.458785i	−0.997512	+	0.0705013i	$0.977540\pi$
$524$	−4307.02	−	3129.24i	−0.359071	−	0.260880i
$525$	−6524.39	+	4740.25i	−0.542377	+	0.394060i
$526$	−3600.01	+	11079.7i	−0.298418	+	0.918436i
$527$	17672.2			1.46075
$528$		0			0
$529$	−9635.37			−0.791926
$530$	2492.24	−	7670.34i	0.204257	−	0.628638i
$531$	18525.1	−	13459.3i	1.51397	−	1.09997i
$532$	−1402.39	−	1018.89i	−0.114288	−	0.0830350i
$533$	3386.15	+	10421.5i	0.275179	+	0.846914i
$534$	748.377	+	2303.27i	0.0606469	+	0.186652i
$535$	−8887.33	−	6457.02i	−0.718192	−	0.521797i
$536$	−5193.87	+	3773.57i	−0.418547	+	0.304092i
$537$	6475.01	−	19928.0i	0.520330	−	1.60141i
$538$	5383.44			0.431407
$539$		0			0
$540$	1290.75			0.102861
$541$	3564.62	−	10970.8i	0.283281	−	0.871849i	−0.703628	−	0.710569i	$-0.748438\pi$
$541$	3564.62	−	10970.8i	0.283281	−	0.871849i	0.986909	−	0.161280i	$-0.0515623\pi$
$542$	−21987.6	+	15974.9i	−1.74253	+	1.26602i
$543$	−8063.94	−	5858.79i	−0.637305	−	0.463029i
$544$	−4646.74	−	14301.2i	−0.366226	−	1.12713i
$545$	1809.55	+	5569.23i	0.142225	+	0.437724i
$546$	−33588.9	−	24403.7i	−2.63273	−	1.91279i
$547$	2630.07	−	1910.85i	0.205582	−	0.149364i	−0.480230	−	0.877142i	$-0.659447\pi$
$547$	2630.07	−	1910.85i	0.205582	−	0.149364i	0.685813	+	0.727778i	$0.259447\pi$
$548$	7259.52	−	22342.5i	0.565897	−	1.74165i
$549$	4843.78			0.376552
$550$		0			0
$551$	−1027.53			−0.0794452
$552$	2035.11	−	6263.43i	0.156921	−	0.482952i
$553$	−9592.82	+	6969.60i	−0.737664	+	0.535945i
$554$	26918.7	+	19557.6i	2.06438	+	1.49986i
$555$	6572.60	+	20228.4i	0.502687	+	1.54711i
$556$	−953.573	−	2934.80i	−0.0727347	−	0.223854i
$557$	16324.8	+	11860.6i	1.24184	+	0.902247i	0.997719	−	0.0674983i	$-0.0215017\pi$
$557$	16324.8	+	11860.6i	1.24184	+	0.902247i	0.244118	+	0.969746i	$0.421502\pi$
$558$	−26423.4	+	19197.7i	−2.00464	+	1.45646i
$559$	−1060.88	+	3265.05i	−0.0802690	+	0.247043i
$560$	2938.19			0.221717
$561$		0			0
$562$	−29998.1			−2.25159
$563$	−3996.96	+	12301.4i	−0.299204	+	0.920854i	0.682573	+	0.730817i	$0.260861\pi$
$563$	−3996.96	+	12301.4i	−0.299204	+	0.920854i	−0.981777	+	0.190037i	$0.939139\pi$
$564$	−18476.7	+	13424.1i	−1.37945	+	1.00223i
$565$	−3690.79	−	2681.51i	−0.274819	−	0.199667i
$566$	−939.542	−	2891.61i	−0.0697737	−	0.214741i
$567$	−4253.77	−	13091.8i	−0.315064	−	0.969668i
$568$	−11094.0	−	8060.24i	−0.819529	−	0.595422i
$569$	−11581.5	+	8414.44i	−0.853288	+	0.619950i	−0.926051	−	0.377399i	$-0.876818\pi$
$569$	−11581.5	+	8414.44i	−0.853288	+	0.619950i	0.0727626	+	0.997349i	$0.476818\pi$
$570$	−625.479	+	1925.03i	−0.0459622	+	0.141457i
$571$	2503.96			0.183516			0.0917580	−	0.995781i	$-0.470751\pi$
$571$	2503.96			0.183516			0.0917580	+	0.995781i	$0.470751\pi$
$572$		0			0
$573$	14890.7			1.08563
$574$	−4974.04	+	15308.5i	−0.361694	+	1.11318i
$575$	2172.03	−	1578.07i	0.157530	−	0.114452i
$576$	19297.6	+	14020.5i	1.39595	+	1.01422i
$577$	1643.89	+	5059.37i	0.118607	+	0.365034i	0.992682	−	0.120756i	$-0.0385320\pi$
$577$	1643.89	+	5059.37i	0.118607	+	0.365034i	−0.874076	+	0.485790i	$0.838532\pi$
$578$	142.151	+	437.495i	0.0102296	+	0.0314834i
$579$	−12630.7	−	9176.72i	−0.906585	−	0.658673i
$580$	−11694.2	+	8496.34i	−0.837199	+	0.608261i
$581$	−4108.91	+	12645.9i	−0.293401	+	0.902997i
$582$	−32640.8			−2.32475
$583$		0			0
$584$	16791.3			1.18978
$585$	−4621.34	+	14223.0i	−0.326613	+	1.00521i
$586$	20660.2	−	15010.5i	1.45643	−	1.05815i
$587$	−5844.86	−	4246.54i	−0.410976	−	0.298592i	0.363021	−	0.931781i	$-0.381745\pi$
$587$	−5844.86	−	4246.54i	−0.410976	−	0.298592i	−0.773997	+	0.633189i	$0.781745\pi$
$588$	−1843.64	−	5674.15i	−0.129304	−	0.397956i
$589$	−565.121	−	1739.26i	−0.0395338	−	0.121672i
$590$	24378.1	+	17711.7i	1.70107	+	1.23590i
$591$	22809.0	−	16571.7i	1.58754	−	1.15341i
$592$	−1783.53	+	5489.15i	−0.123822	+	0.381085i
$593$	−26210.5			−1.81507			−0.907535	−	0.419976i	$-0.862038\pi$
$593$	−26210.5			−1.81507			−0.907535	+	0.419976i	$0.862038\pi$
$594$		0			0
$595$	11886.4			0.818980
$596$	−364.283	+	1121.15i	−0.0250362	+	0.0770536i
$597$	−7555.20	+	5489.17i	−0.517946	+	0.376310i
$598$	11182.0	+	8124.22i	0.764661	+	0.555559i
$599$	−1257.70	−	3870.80i	−0.0857900	−	0.264035i	0.898954	−	0.438043i	$-0.144328\pi$
$599$	−1257.70	−	3870.80i	−0.0857900	−	0.264035i	−0.984744	+	0.174008i	$0.944328\pi$
$600$	−2158.22	−	6642.31i	−0.146848	−	0.451952i
$601$	−1345.85	−	977.818i	−0.0913451	−	0.0663661i	0.541175	−	0.840910i	$-0.317980\pi$
$601$	−1345.85	−	977.818i	−0.0913451	−	0.0663661i	−0.632520	+	0.774544i	$0.717980\pi$
$602$	−4079.84	+	2964.18i	−0.276216	+	0.200683i
$603$	−3248.36	+	9997.42i	−0.219375	+	0.675168i
$604$	−17743.8			−1.19534
$605$		0			0
$606$	34134.6			2.28815
$607$	3421.98	−	10531.8i	0.228821	−	0.704237i	−0.769061	−	0.639176i	$-0.779276\pi$
$607$	3421.98	−	10531.8i	0.228821	−	0.704237i	0.997881	−	0.0650615i	$-0.0207244\pi$
$608$	−1258.90	+	914.643i	−0.0839721	+	0.0610093i
$609$	−17506.1	−	12718.9i	−1.16483	−	0.846301i
$610$	1969.72	+	6062.19i	0.130741	+	0.402379i
$611$	−4877.80	−	15012.3i	−0.322970	−	0.994000i
$612$	19216.7	+	13961.8i	1.26926	+	0.922174i
$613$	12749.2	−	9262.86i	0.840027	−	0.610316i	−0.0823510	−	0.996603i	$-0.526243\pi$
$613$	12749.2	−	9262.86i	0.840027	−	0.610316i	0.922378	+	0.386288i	$0.126243\pi$
$614$	256.134	−	788.298i	0.0168350	−	0.0518129i
$615$	11250.0			0.737634
$616$		0			0
$617$	19132.5			1.24837			0.624185	−	0.781277i	$-0.285431\pi$
$617$	19132.5			1.24837			0.624185	+	0.781277i	$0.285431\pi$
$618$	−7637.02	+	23504.3i	−0.497097	+	1.52991i
$619$	−8298.54	+	6029.25i	−0.538848	+	0.391496i	−0.823657	−	0.567089i	$-0.808070\pi$
$619$	−8298.54	+	6029.25i	−0.538848	+	0.391496i	0.284809	+	0.958584i	$0.408070\pi$
$620$	−20813.0	−	15121.5i	−1.34818	−	0.979509i
$621$	−198.779	−	611.779i	−0.0128450	−	0.0395327i
$622$	−3501.70	−	10777.1i	−0.225732	−	0.694732i
$623$	−1190.64	−	865.052i	−0.0765683	−	0.0556301i
$624$	−6370.38	+	4628.35i	−0.408685	+	0.296927i
$625$	−1887.46	+	5809.00i	−0.120797	+	0.371776i
$626$	39655.4			2.53187
$627$		0			0
$628$	25192.5			1.60078
$629$	−7215.22	+	22206.2i	−0.457376	+	1.40766i
$630$	−17772.4	+	12912.4i	−1.12392	+	0.816575i
$631$	2188.92	+	1590.34i	0.138097	+	0.100334i	0.654689	−	0.755898i	$-0.272800\pi$
$631$	2188.92	+	1590.34i	0.138097	+	0.100334i	−0.516592	+	0.856232i	$0.672800\pi$
$632$	−3173.23	−	9766.20i	−0.199722	−	0.614682i
$633$	10620.0	+	32684.9i	0.666834	+	2.05230i
$634$	−10384.3	−	7544.65i	−0.650495	−	0.472613i
$635$	4818.99	−	3501.20i	0.301159	−	0.218805i
$636$	−5872.57	+	18073.9i	−0.366136	+	1.12685i
$637$	4123.54			0.256484
$638$		0			0
$639$	−22453.1			−1.39003
$640$	−5163.10	+	15890.4i	−0.318890	+	0.981443i
$641$	−4343.27	+	3155.57i	−0.267627	+	0.194442i	−0.713503	−	0.700653i	$-0.752892\pi$
$641$	−4343.27	+	3155.57i	−0.267627	+	0.194442i	0.445876	+	0.895095i	$0.352892\pi$
$642$	34986.6	+	25419.3i	2.15080	+	1.56265i
$643$	9538.24	+	29355.7i	0.584994	+	1.80043i	0.599293	+	0.800530i	$0.295449\pi$
$643$	9538.24	+	29355.7i	0.584994	+	1.80043i	−0.0142983	+	0.999898i	$0.504551\pi$
$644$	3755.39	+	11557.9i	0.229788	+	0.707213i
$645$	2851.48	+	2071.72i	0.174073	+	0.126471i
$646$	−1797.63	+	1306.05i	−0.109484	+	0.0795449i
$647$	−2710.98	+	8343.52i	−0.164729	+	0.506983i	−0.999016	−	0.0443469i	$-0.985879\pi$
$647$	−2710.98	+	8343.52i	−0.164729	+	0.506983i	0.834288	+	0.551330i	$0.185879\pi$
$648$	11921.3			0.722703
$649$		0			0
$650$	14657.8			0.884505
$651$	11900.9	−	36627.1i	0.716485	−	2.20511i
$652$	−13365.2	+	9710.38i	−0.802793	+	0.583264i
$653$	24151.9	+	17547.4i	1.44737	+	1.05158i	0.986436	+	0.164147i	$0.0524870\pi$
$653$	24151.9	+	17547.4i	1.44737	+	1.05158i	0.460938	+	0.887432i	$0.347513\pi$
$654$	−7123.64	−	21924.3i	−0.425927	−	1.31087i
$655$	−1167.37	−	3592.79i	−0.0696379	−	0.214323i
$656$	2469.76	+	1794.39i	0.146994	+	0.106797i
$657$	22242.8	−	16160.3i	1.32081	−	0.959627i
$658$	7165.18	−	22052.2i	0.424510	−	1.30651i
$659$	−9304.45			−0.550000			−0.275000	−	0.961444i	$-0.588678\pi$
$659$	−9304.45			−0.550000			−0.275000	+	0.961444i	$0.588678\pi$
$660$		0			0
$661$	2078.54			0.122309			0.0611543	−	0.998128i	$-0.480522\pi$
$661$	2078.54			0.122309			0.0611543	+	0.998128i	$0.480522\pi$
$662$	11443.6	−	35219.7i	0.671854	−	2.06775i
$663$	−25771.2	+	18723.9i	−1.50961	+	1.09679i
$664$	−9316.06	−	6768.51i	−0.544478	−	0.395586i
$665$	−380.100	−	1169.83i	−0.0221649	−	0.0682166i
$666$	−13334.9	−	41040.5i	−0.775850	−	2.38782i
$667$	5827.95	+	4234.25i	0.338319	+	0.245803i
$668$	−7481.41	+	5435.56i	−0.433330	+	0.314833i
$669$	10710.3	−	32962.9i	0.618959	−	1.90496i
$670$	−13833.1			−0.797643
$671$		0			0
$672$	−32769.5			−1.88112
$673$	4624.57	−	14233.0i	0.264880	−	0.815217i	−0.726841	−	0.686806i	$-0.759012\pi$
$673$	4624.57	−	14233.0i	0.264880	−	0.815217i	0.991721	−	0.128411i	$-0.0409876\pi$
$674$	36676.3	−	26646.9i	2.09602	−	1.52285i
$675$	−551.890	−	400.972i	−0.0314700	−	0.0228643i
$676$	5859.54	+	18033.8i	0.333383	+	1.02605i
$677$	7121.14	+	21916.6i	0.404265	+	1.24420i	0.921507	+	0.388361i	$0.126959\pi$
$677$	7121.14	+	21916.6i	0.404265	+	1.24420i	−0.517242	+	0.855839i	$0.673041\pi$
$678$	14529.5	+	10556.3i	0.823010	+	0.597952i
$679$	16047.4	−	11659.1i	0.906983	−	0.658962i
$680$	−3180.99	+	9790.07i	−0.179390	+	0.552106i
$681$	31796.8			1.78922
$682$		0			0
$683$	17860.8			1.00062			0.500312	−	0.865845i	$-0.333219\pi$
$683$	17860.8			1.00062			0.500312	+	0.865845i	$0.333219\pi$
$684$	759.575	−	2337.73i	0.0424607	−	0.130680i
$685$	13486.2	−	9798.29i	0.752235	−	0.546531i
$686$	−20182.8	−	14663.7i	−1.12330	−	0.816125i
$687$	−13277.3	−	40863.3i	−0.737350	−	2.26933i
$688$	295.555	+	909.626i	0.0163778	+	0.0504057i
$689$	−10626.2	−	7720.41i	−0.587558	−	0.426886i
$690$	11480.2	−	8340.88i	0.633398	−	0.460191i
$691$	3627.64	−	11164.7i	0.199713	−	0.614654i	−0.800176	−	0.599765i	$-0.795261\pi$
$691$	3627.64	−	11164.7i	0.199713	−	0.614654i	0.999889	−	0.0148886i	$-0.00473936\pi$
$692$	−5327.32			−0.292651
$693$		0			0
$694$	−53149.7			−2.90711
$695$	676.643	−	2082.49i	0.0369303	−	0.113660i
$696$	15160.7	−	11014.9i	0.825670	−	0.599885i
$697$	9991.33	+	7259.12i	0.542968	+	0.394489i
$698$	6263.47	+	19277.0i	0.339650	+	1.04534i
$699$	11881.1	+	36566.4i	0.642899	+	1.97864i
$700$	10426.5	+	7575.28i	0.562977	+	0.409027i
$701$	−24671.2	+	17924.6i	−1.32927	+	0.965769i	−0.329501	+	0.944155i	$0.606881\pi$
$701$	−24671.2	+	17924.6i	−1.32927	+	0.965769i	−0.999766	+	0.0216142i	$0.993119\pi$
$702$	1085.26	−	3340.08i	0.0583481	−	0.179577i
$703$	2416.21			0.129629
$704$		0			0
$705$	−16205.8			−0.865741
$706$	996.332	−	3066.40i	0.0531126	−	0.163464i
$707$	−16781.8	+	12192.7i	−0.892706	+	0.648589i
$708$	−57442.9	−	41734.7i	−3.04921	−	2.21538i
$709$	187.415	+	576.805i	0.00992741	+	0.0305534i	0.955898	−	0.293700i	$-0.0948868\pi$
$709$	187.415	+	576.805i	0.00992741	+	0.0305534i	−0.945970	+	0.324254i	$0.894887\pi$
$710$	−9130.58	−	28101.0i	−0.482626	−	1.48537i
$711$	−13602.7	−	9882.93i	−0.717498	−	0.521293i
$712$	1031.13	−	749.157i	0.0542740	−	0.0394324i
$713$	−3961.91	+	12193.5i	−0.208099	+	0.640463i
$714$	−46792.8			−2.45263
$715$		0			0
$716$	−33485.4			−1.74778
$717$	−4800.52	+	14774.5i	−0.250040	+	0.769544i
$718$	44060.8	−	32012.0i	2.29016	−	1.66390i
$719$	−18371.8	−	13347.9i	−0.952922	−	0.692338i	−0.00142584	−	0.999999i	$-0.500454\pi$
$719$	−18371.8	−	13347.9i	−0.952922	−	0.692338i	−0.951496	+	0.307661i	$0.900454\pi$
$720$	1287.48	+	3962.46i	0.0666411	+	0.205100i
$721$	−4640.98	−	14283.5i	−0.239721	−	0.737786i
$722$	−24585.5	−	17862.4i	−1.26728	−	0.920734i
$723$	−41238.3	+	29961.4i	−2.12126	+	1.54118i
$724$	−4922.31	+	15149.3i	−0.252675	+	0.777652i
$725$	7639.50			0.391343
$726$		0			0
$727$	34351.1			1.75243			0.876213	−	0.481925i	$-0.160062\pi$
$727$	34351.1			1.75243			0.876213	+	0.481925i	$0.160062\pi$
$728$	−6752.06	+	20780.7i	−0.343747	+	1.05795i
$729$	17876.1	−	12987.7i	0.908199	−	0.659845i
$730$	29270.4	+	21266.2i	1.48404	+	1.07822i
$731$	1195.66	+	3679.86i	0.0604966	+	0.186190i
$732$	−4641.34	−	14284.6i	−0.234356	−	0.721274i
$733$	−1292.84	−	939.304i	−0.0651462	−	0.0473315i	0.554736	−	0.832027i	$-0.312819\pi$
$733$	−1292.84	−	939.304i	−0.0651462	−	0.0473315i	−0.619882	+	0.784695i	$0.712819\pi$
$734$	−518.667	+	376.833i	−0.0260822	+	0.0189498i
$735$	1308.22	−	4026.30i	0.0656525	−	0.202058i
$736$	10909.3			0.546360
$737$		0			0
$738$	−22824.7			−1.13847
$739$	−4382.51	+	13488.0i	−0.218151	+	0.671398i	0.780764	+	0.624826i	$0.214830\pi$
$739$	−4382.51	+	13488.0i	−0.218151	+	0.671398i	−0.998915	+	0.0465728i	$0.985170\pi$
$740$	27498.6	−	19978.9i	1.36604	−	0.992484i
$741$	2666.87	+	1937.59i	0.132213	+	0.0960584i
$742$	−5962.21	−	18349.8i	−0.294986	−	0.907873i
$743$	10738.3	+	33049.2i	0.530217	+	1.63184i	0.753763	+	0.657146i	$0.228236\pi$
$743$	10738.3	+	33049.2i	0.530217	+	1.63184i	−0.223547	+	0.974693i	$0.571764\pi$
$744$	26982.6	+	19604.0i	1.32961	+	0.966020i
$745$	−676.736	+	491.678i	−0.0332801	+	0.0241794i
$746$	−5072.27	+	15610.8i	−0.248940	+	0.766157i
$747$	−18854.8			−0.923510
$748$		0			0
$749$	−26280.3			−1.28206
$750$	15544.3	−	47840.3i	0.756794	−	2.32917i
$751$	22554.7	−	16387.0i	1.09592	−	0.796230i	0.115528	−	0.993304i	$-0.463144\pi$
$751$	22554.7	−	16387.0i	1.09592	−	0.796230i	0.980389	+	0.197074i	$0.0631439\pi$
$752$	−3557.73	−	2584.84i	−0.172523	−	0.125345i
$753$	−46.4317	−	142.902i	−0.00224710	−	0.00691586i
$754$	12153.5	+	37404.7i	0.587010	+	1.80663i
$755$	−10186.2	−	7400.69i	−0.491010	−	0.356740i
$756$	2498.14	−	1815.01i	0.120181	−	0.0873164i
$757$	−2449.44	+	7538.60i	−0.117604	+	0.361949i	−0.992481	−	0.122397i	$-0.960942\pi$
$757$	−2449.44	+	7538.60i	−0.117604	+	0.361949i	0.874877	+	0.484345i	$0.160942\pi$
$758$	−10406.1			−0.498638
$759$		0			0
$760$	1065.24			0.0508424
$761$	2861.49	−	8806.77i	0.136306	−	0.419507i	−0.859485	−	0.511161i	$-0.829215\pi$
$761$	2861.49	−	8806.77i	0.136306	−	0.419507i	0.995791	+	0.0916541i	$0.0292154\pi$
$762$	−18970.8	+	13783.1i	−0.901892	+	0.655263i
$763$	11333.5	+	8234.25i	0.537745	+	0.390694i
$764$	−7353.49	−	22631.7i	−0.348220	−	1.07171i
$765$	5208.46	+	16030.0i	0.246160	+	0.757602i
$766$	−13385.0	−	9724.80i	−0.631359	−	0.458709i
$767$	39702.0	−	28845.2i	1.86904	−	1.35794i
$768$	4996.32	−	15377.1i	0.234752	−	0.722491i
$769$	30944.5			1.45109			0.725545	−	0.688175i	$-0.241588\pi$
$769$	30944.5			1.45109			0.725545	+	0.688175i	$0.241588\pi$
$770$		0			0
$771$	−1127.01			−0.0526436
$772$	−7709.90	+	23728.6i	−0.359437	+	1.10623i
$773$	−12161.0	+	8835.45i	−0.565846	+	0.411111i	−0.833594	−	0.552378i	$-0.813721\pi$
$773$	−12161.0	+	8835.45i	−0.565846	+	0.411111i	0.267748	+	0.963489i	$0.413721\pi$
$774$	−5785.25	−	4203.23i	−0.268665	−	0.195196i
$775$	4201.57	+	12931.1i	0.194742	+	0.599353i
$776$	5308.34	+	16337.4i	0.245565	+	0.755771i
$777$	41165.1	+	29908.2i	1.90063	+	1.38089i
$778$	23573.1	−	17126.9i	1.08630	−	0.789240i
$779$	394.926	−	1215.46i	0.0181639	−	0.0559027i
$780$	46372.7			2.12873
$781$		0			0
$782$	15577.8			0.712352
$783$	565.623	−	1740.81i	0.0258157	−	0.0794527i
$784$	929.397	−	675.246i	0.0423377	−	0.0307601i
$785$	14462.2	+	10507.4i	0.657552	+	0.477739i
$786$	4595.56	+	14143.7i	0.208547	+	0.641843i
$787$	2079.65	+	6400.51i	0.0941951	+	0.289903i	0.987043	−	0.160456i	$-0.0512963\pi$
$787$	2079.65	+	6400.51i	0.0941951	+	0.289903i	−0.892848	+	0.450358i	$0.851296\pi$
$788$	−36450.4	−	26482.8i	−1.64783	−	1.19722i
$789$	15758.8	−	11449.4i	0.711061	−	0.516616i
$790$	6837.37	−	21043.2i	0.307927	−	0.947703i
$791$	−10913.8			−0.490584
$792$		0			0
$793$	10380.9			0.464865
$794$	15575.3	−	47935.9i	0.696155	−	2.14254i
$795$	−10909.6	+	7926.30i	−0.486697	+	0.353606i
$796$	12073.8	+	8772.12i	0.537618	+	0.390602i
$797$	−5607.52	−	17258.2i	−0.249220	−	0.767021i	−0.994914	−	0.100732i	$-0.967882\pi$
$797$	−5607.52	−	17258.2i	−0.249220	−	0.767021i	0.745693	−	0.666289i	$-0.232118\pi$
$798$	1496.34	+	4605.25i	0.0663781	+	0.204291i
$799$	−14392.7	−	10456.9i	−0.637267	−	0.463001i
$800$	9359.67	−	6800.20i	0.413643	−	0.300529i
$801$	644.888	−	1984.76i	0.0284469	−	0.0875507i
$802$	−61652.2			−2.71448
$803$		0			0
$804$	32595.6			1.42980
$805$	−2664.78	+	8201.35i	−0.116672	+	0.359080i
$806$	−56629.3	+	41143.6i	−2.47479	+	1.79804i
$807$	−7282.18	−	5290.81i	−0.317652	−	0.230787i
$808$	−5551.28	−	17085.1i	−0.241700	−	0.743875i
$809$	−8948.11	−	27539.5i	−0.388874	−	1.19683i	−0.933631	−	0.358237i	$-0.883378\pi$
$809$	−8948.11	−	27539.5i	−0.388874	−	1.19683i	0.544757	−	0.838594i	$-0.316622\pi$
$810$	20781.0	+	15098.3i	0.901445	+	0.654938i
$811$	−2159.89	+	1569.25i	−0.0935192	+	0.0679457i	−0.633562	−	0.773692i	$-0.718408\pi$
$811$	−2159.89	+	1569.25i	−0.0935192	+	0.0679457i	0.540043	+	0.841637i	$0.318408\pi$
$812$	−10685.9	+	32887.9i	−0.461826	+	1.42135i
$813$	45442.7			1.96032
$814$		0			0
$815$	−11722.6			−0.503833
$816$	−2742.41	+	8440.27i	−0.117651	+	0.362094i
$817$	323.929	−	235.348i	0.0138713	−	0.0100781i
$818$	−33549.0	−	24374.7i	−1.43400	−	1.04186i
$819$	11055.6	+	34025.8i	0.471692	+	1.45172i
$820$	−5555.63	−	17098.5i	−0.236599	−	0.728176i
$821$	6651.69	+	4832.73i	0.282759	+	0.205437i	0.720120	−	0.693849i	$-0.244087\pi$
$821$	6651.69	+	4832.73i	0.282759	+	0.205437i	−0.437361	+	0.899286i	$0.644087\pi$
$822$	−53090.9	+	38572.8i	−2.25275	+	1.63672i
$823$	5067.39	−	15595.8i	0.214627	−	0.660555i	−0.784553	−	0.620062i	$-0.787107\pi$
$823$	5067.39	−	15595.8i	0.214627	−	0.660555i	0.999180	−	0.0404924i	$-0.0128926\pi$
$824$	13006.4			0.549879
$825$		0			0
$826$	72087.2			3.03660
$827$	−6962.32	+	21427.8i	−0.292749	+	0.900989i	0.691219	+	0.722645i	$0.257074\pi$
$827$	−6962.32	+	21427.8i	−0.292749	+	0.900989i	−0.983968	+	0.178344i	$0.942926\pi$
$828$	−13941.5	+	10129.1i	−0.585145	+	0.425133i
$829$	10702.7	+	7775.97i	0.448396	+	0.325779i	0.788962	−	0.614442i	$-0.210619\pi$
$829$	10702.7	+	7775.97i	0.448396	+	0.325779i	−0.340566	+	0.940221i	$0.610619\pi$
$830$	−7667.33	−	23597.6i	−0.320647	−	0.986849i
$831$	−17191.8	−	52911.0i	−0.717663	−	2.20874i
$832$	41357.6	+	30048.1i	1.72334	+	1.25208i
$833$	3759.84	−	2731.69i	0.156388	−	0.113622i
$834$	−2663.73	+	8198.13i	−0.110597	+	0.340381i
$835$	−6561.93			−0.271958
$836$		0			0
$837$	3257.68			0.134530
$838$	−4238.92	+	13046.1i	−0.174739	+	0.537791i
$839$	−2652.99	+	1927.51i	−0.109167	+	0.0793148i	−0.641030	−	0.767516i	$-0.721492\pi$
$839$	−2652.99	+	1927.51i	−0.109167	+	0.0793148i	0.531862	+	0.846831i	$0.321492\pi$
$840$	18148.5	+	13185.7i	0.745457	+	0.541606i
$841$	−1202.34	−	3700.42i	−0.0492984	−	0.151725i
$842$	−8240.79	−	25362.6i	−0.337288	−	1.03807i
$843$	40578.4	+	29481.9i	1.65788	+	1.20452i
$844$	44432.0	−	32281.7i	1.81210	−	1.31657i
$845$	−4157.85	+	12796.6i	−0.169272	+	0.520965i
$846$	32879.3			1.33619
$847$		0			0
$848$	−3659.28			−0.148184
$849$	−1570.94	+	4834.86i	−0.0635036	+	0.195444i
$850$	13365.0	−	9710.26i	0.539314	−	0.391834i
$851$	−13704.2	−	9956.71i	−0.552027	−	0.401071i
$852$	21514.7	+	66215.5i	0.865120	+	2.66257i
$853$	−10542.3	−	32445.8i	−0.423167	−	1.30237i	−0.904739	−	0.425966i	$-0.859934\pi$
$853$	−10542.3	−	32445.8i	−0.423167	−	1.30237i	0.481572	−	0.876406i	$-0.340066\pi$
$854$	12336.7	+	8963.10i	0.494323	+	0.359146i
$855$	1411.08	−	1025.21i	0.0564421	−	0.0410076i
$856$	7033.04	−	21645.5i	0.280823	−	0.864284i
$857$	5029.20			0.200460			0.100230	−	0.994964i	$-0.468042\pi$
$857$	5029.20			0.200460			0.100230	+	0.994964i	$0.468042\pi$
$858$		0			0
$859$	−3540.39			−0.140625			−0.0703124	−	0.997525i	$-0.522400\pi$
$859$	−3540.39			−0.140625			−0.0703124	+	0.997525i	$0.522400\pi$
$860$	1740.58	−	5356.94i	0.0690153	−	0.212407i
$861$	21773.5	−	15819.4i	0.861833	−	0.626158i
$862$	842.898	+	612.401i	0.0333054	+	0.0241978i
$863$	−3227.40	−	9932.91i	−0.127302	−	0.391796i	0.867011	−	0.498289i	$-0.166038\pi$
$863$	−3227.40	−	9932.91i	−0.127302	−	0.391796i	−0.994314	+	0.106492i	$0.966038\pi$
$864$	−856.574	−	2636.26i	−0.0337283	−	0.103805i
$865$	−3058.25	−	2221.95i	−0.120212	−	0.0873392i
$866$	−20121.0	+	14618.8i	−0.789538	+	0.573633i
$867$	237.680	−	731.504i	0.00931031	−	0.0286542i
$868$	−61545.1			−2.40666
$869$		0			0
$870$	40378.5			1.57352
$871$	−6961.72	+	21426.0i	−0.270825	+	0.833515i
$872$	−9815.08	+	7131.07i	−0.381170	+	0.276936i
$873$	22755.3	+	16532.7i	0.882187	+	0.640946i
$874$	−498.144	−	1533.13i	−0.0192791	−	0.0593351i
$875$	9446.17	+	29072.3i	0.364959	+	1.12323i
$876$	−68971.0	−	50110.3i	−2.66018	−	1.93273i
$877$	−13982.2	+	10158.7i	−0.538364	+	0.391144i	−0.823477	−	0.567350i	$-0.807969\pi$
$877$	−13982.2	+	10158.7i	−0.538364	+	0.391144i	0.285113	+	0.958494i	$0.407969\pi$
$878$	−4873.80	+	15000.0i	−0.187338	+	0.576567i
$879$	−42699.3			−1.63847
$880$		0			0
$881$	−6262.31			−0.239481			−0.119740	−	0.992805i	$-0.538206\pi$
$881$	−6262.31			−0.239481			−0.119740	+	0.992805i	$0.538206\pi$
$882$	−2654.20	+	8168.79i	−0.101328	+	0.311857i
$883$	−23792.9	+	17286.5i	−0.906788	+	0.658820i	−0.940201	−	0.340621i	$-0.889363\pi$
$883$	−23792.9	+	17286.5i	−0.906788	+	0.658820i	0.0334123	+	0.999442i	$0.489363\pi$
$884$	41184.3	+	29922.1i	1.56694	+	1.13845i
$885$	−15569.2	−	47917.2i	−0.591361	−	1.82002i
$886$	20557.9	+	63270.8i	0.779522	+	2.39912i
$887$	−9614.96	−	6985.68i	−0.363967	−	0.264437i	0.390738	−	0.920502i	$-0.372220\pi$
$887$	−9614.96	−	6985.68i	−0.363967	−	0.264437i	−0.754705	+	0.656065i	$0.772220\pi$
$888$	−35650.0	+	25901.3i	−1.34723	+	0.978817i
$889$	4403.49	−	13552.6i	0.166129	−	0.511291i
$890$	2746.26			0.103432
$891$		0			0
$892$	−55388.1			−2.07907
$893$	−568.897	+	1750.88i	−0.0213185	+	0.0656115i
$894$	2664.10	−	1935.58i	0.0996653	−	0.0724111i
$895$	−19222.9	−	13966.3i	−0.717934	−	0.521609i
$896$	12351.7	+	38014.7i	0.460538	+	1.41739i
$897$	−7141.49	−	21979.3i	−0.265828	−	0.818134i
$898$	−25967.5	−	18866.5i	−0.964972	−	0.701093i
$899$	−29514.6	+	21443.6i	−1.09496	+	0.795532i
$900$	−5647.30	+	17380.6i	−0.209159	+	0.643726i
$901$	−14803.5			−0.547365
$902$		0			0
$903$	8431.98			0.310740
$904$	2920.73	−	8989.07i	0.107458	−	0.330721i
$905$	−9144.30	+	6643.72i	−0.335875	+	0.244027i
$906$	40099.8	+	29134.2i	1.47045	+	1.06834i
$907$	13613.5	+	41898.1i	0.498378	+	1.53385i	0.811625	+	0.584179i	$0.198583\pi$
$907$	13613.5	+	41898.1i	0.498378	+	1.53385i	−0.313247	+	0.949672i	$0.601417\pi$
$908$	−15702.3	−	48326.7i	−0.573898	−	1.76628i
$909$	−23796.7	−	17289.3i	−0.868301	−	0.630857i
$910$	−38088.9	+	27673.2i	−1.38751	+	1.00809i
$911$	−11026.4	+	33935.8i	−0.401011	+	1.23418i	0.523170	+	0.852229i	$0.324749\pi$
$911$	−11026.4	+	33935.8i	−0.401011	+	1.23418i	−0.924181	+	0.381956i	$0.875251\pi$
$912$	918.369			0.0333446
$913$		0			0
$914$	−17598.4			−0.636874
$915$	3293.43	−	10136.1i	0.118992	−	0.366219i
$916$	−55549.7	+	40359.2i	−2.00373	+	1.45579i
$917$	−7311.38	−	5312.03i	−0.263297	−	0.191296i
$918$	−1223.13	−	3764.42i	−0.0439755	−	0.135343i
$919$	−1790.77	−	5511.43i	−0.0642787	−	0.197829i	0.913759	−	0.406256i	$-0.133166\pi$
$919$	−1790.77	−	5511.43i	−0.0642787	−	0.197829i	−0.978038	+	0.208426i	$0.933166\pi$
$920$	−6041.81	−	4389.63i	−0.216514	−	0.157306i
$921$	−1121.21	+	814.604i	−0.0401140	+	0.0291445i
$922$	11386.8	−	35044.9i	0.406728	−	1.25178i
$923$	−48120.4			−1.71604
$924$		0			0
$925$	−17964.1			−0.638545
$926$	−9772.21	+	30075.8i	−0.346798	+	1.06733i
$927$	17229.1	−	12517.7i	0.610441	−	0.443511i
$928$	25113.7	+	18246.2i	0.888358	+	0.645430i
$929$	−10791.4	−	33212.5i	−0.381113	−	1.17295i	−0.939261	−	0.343204i	$-0.888488\pi$
$929$	−10791.4	−	33212.5i	−0.381113	−	1.17295i	0.558147	−	0.829742i	$-0.311512\pi$
$930$	22207.3	+	68347.1i	0.783018	+	2.40988i
$931$	−389.078	−	282.682i	−0.0136966	−	0.00995116i
$932$	49708.5	−	36115.4i	1.74706	−	1.26931i
$933$	−5854.94	+	18019.7i	−0.205447	+	0.632301i
$934$	79813.6			2.79612
$935$		0			0
$936$	−30983.6			−1.08198
$937$	6114.59	−	18818.8i	0.213185	−	0.656117i	−0.786092	−	0.618110i	$-0.787899\pi$
$937$	6114.59	−	18818.8i	0.213185	−	0.656117i	0.999277	−	0.0380079i	$-0.0121012\pi$
$938$	−26772.9	+	19451.6i	−0.931946	+	0.677098i
$939$	−53641.8	−	38973.1i	−1.86425	−	1.35446i
$940$	8002.98	+	24630.6i	0.277690	+	0.854641i
$941$	5740.04	+	17666.0i	0.198852	+	0.612004i	0.999910	+	0.0134172i	$0.00427094\pi$
$941$	5740.04	+	17666.0i	0.198852	+	0.612004i	−0.801058	+	0.598587i	$0.795729\pi$
$942$	−56933.2	−	41364.4i	−1.96920	−	1.43070i
$943$	−7248.59	+	5266.41i	−0.250314	+	0.181864i
$944$	4224.84	−	13002.7i	0.145664	−	0.448308i
$945$	2191.12			0.0754255
$946$		0			0
$947$	24620.0			0.844817			0.422408	−	0.906406i	$-0.361185\pi$
$947$	24620.0			0.844817			0.422408	+	0.906406i	$0.361185\pi$
$948$	−16111.1	+	49585.0i	−0.551968	+	1.69878i
$949$	47669.7	−	34634.1i	1.63058	−	1.18469i
$950$	−1383.05	−	1004.84i	−0.0472337	−	0.0343173i
$951$	6632.03	+	20411.3i	0.226139	+	0.695984i
$952$	7609.89	+	23420.8i	0.259073	+	0.797346i
$953$	−21545.8	−	15653.9i	−0.732357	−	0.532088i	0.157951	−	0.987447i	$-0.449511\pi$
$953$	−21545.8	−	15653.9i	−0.732357	−	0.532088i	−0.890308	+	0.455358i	$0.849511\pi$
$954$	22134.0	−	16081.3i	0.751170	−	0.545757i
$955$	5217.94	−	16059.2i	0.176805	−	0.544150i
$956$	24825.8			0.839878
$957$		0			0
$958$	−19232.2			−0.648607
$959$	12323.4	−	37927.5i	0.414957	−	1.27710i
$960$	42460.6	−	30849.4i	1.42751	−	1.03715i
$961$	−28427.7	−	20653.9i	−0.954237	−	0.693294i
$962$	−28578.6	−	87956.0i	−0.957809	−	2.94783i
$963$	−11515.7	−	35441.7i	−0.385346	−	1.18597i
$964$	65902.0	+	47880.6i	2.20183	+	1.59972i
$965$	−14322.9	+	10406.2i	−0.477792	+	0.347136i
$966$	10490.4	−	32286.1i	0.349403	−	1.07535i
$967$	20484.3			0.681210			0.340605	−	0.940207i	$-0.389368\pi$
$967$	20484.3			0.681210			0.340605	+	0.940207i	$0.389368\pi$
$968$		0			0
$969$	3715.23			0.123169
$970$	−11437.9	+	35202.2i	−0.378607	+	1.16523i
$971$	44853.0	−	32587.6i	1.48239	−	1.07702i	0.505612	−	0.862761i	$-0.331267\pi$
$971$	44853.0	−	32587.6i	1.48239	−	1.07702i	0.976777	−	0.214258i	$-0.0687334\pi$
$972$	−52298.2	−	37996.8i	−1.72579	−	1.25386i
$973$	−1618.74	−	4981.96i	−0.0533344	−	0.164146i
$974$	−18289.5	−	56289.2i	−0.601676	−	1.85177i
$975$	−19827.7	−	14405.6i	−0.651275	−	0.473179i
$976$	2339.74	−	1699.92i	0.0767349	−	0.0557512i
$977$	18112.4	−	55744.1i	0.593108	−	1.82540i	0.0291781	−	0.999574i	$-0.490711\pi$
$977$	18112.4	−	55744.1i	0.593108	−	1.82540i	0.563929	−	0.825823i	$-0.309289\pi$
$978$	46148.1			1.50885
$979$		0			0
$980$	−6765.46			−0.220525
$981$	−6138.55	+	18892.5i	−0.199785	+	0.614875i
$982$	3318.09	−	2410.74i	0.107826	−	0.0783398i
$983$	25100.7	+	18236.7i	0.814432	+	0.591719i	0.915112	−	0.403199i	$-0.132102\pi$
$983$	25100.7	+	18236.7i	0.814432	+	0.591719i	−0.100680	+	0.994919i	$0.532102\pi$
$984$	7202.50	+	22167.0i	0.233341	+	0.718149i
$985$	−9879.47	−	30405.9i	−0.319580	−	0.983565i
$986$	35860.8	+	26054.4i	1.15825	+	0.841521i
$987$	−31365.0	+	22788.0i	−1.01151	+	0.734905i
$988$	1627.88	−	5010.11i	0.0524189	−	0.161329i
$989$	−2807.08			−0.0902528
$990$		0			0
$991$	11965.1			0.383537			0.191769	−	0.981440i	$-0.438578\pi$
$991$	11965.1			0.383537			0.191769	+	0.981440i	$0.438578\pi$
$992$	−17072.6	+	52544.0i	−0.546426	+	1.68173i
$993$	−50093.4	+	36395.0i	−1.60087	+	1.16310i
$994$	−57186.1	−	41548.1i	−1.82478	−	1.32578i
$995$	3272.46	+	10071.6i	0.104265	+	0.320895i
$996$	18066.8	+	55603.9i	0.574768	+	1.76895i
$997$	−26897.0	−	19541.8i	−0.854401	−	0.620758i	0.0719552	−	0.997408i	$-0.477076\pi$
$997$	−26897.0	−	19541.8i	−0.854401	−	0.620758i	−0.926356	+	0.376649i	$0.877076\pi$
$998$	44136.5	−	32067.0i	1.39992	−	1.01710i
$999$	−1330.05	+	4093.46i	−0.0421229	+	0.129641i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	121.4.c.g.9.1		8
11.2	odd	10		121.4.c.d.3.1		8
11.3	even	5	inner	121.4.c.g.81.2		8
11.4	even	5		121.4.a.b.1.1	✓	2
11.5	even	5	inner	121.4.c.g.27.1		8
11.6	odd	10		121.4.c.d.27.2		8
11.7	odd	10		121.4.a.e.1.2	yes	2
11.8	odd	10		121.4.c.d.81.1		8
11.9	even	5	inner	121.4.c.g.3.2		8
11.10	odd	2		121.4.c.d.9.2		8
33.26	odd	10		1089.4.a.x.1.2		2
33.29	even	10		1089.4.a.k.1.1		2
44.7	even	10		1936.4.a.y.1.2		2
44.15	odd	10		1936.4.a.z.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
121.4.a.b.1.1	✓	2	11.4	even	5
121.4.a.e.1.2	yes	2	11.7	odd	10
121.4.c.d.3.1		8	11.2	odd	10
121.4.c.d.9.2		8	11.10	odd	2
121.4.c.d.27.2		8	11.6	odd	10
121.4.c.d.81.1		8	11.8	odd	10
121.4.c.g.3.2		8	11.9	even	5	inner
121.4.c.g.9.1		8	1.1	even	1	trivial
121.4.c.g.27.1		8	11.5	even	5	inner
121.4.c.g.81.2		8	11.3	even	5	inner
1089.4.a.k.1.1		2	33.29	even	10
1089.4.a.x.1.2		2	33.26	odd	10
1936.4.a.y.1.2		2	44.7	even	10
1936.4.a.z.1.2		2	44.15	odd	10

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:	\( N \)	\(=\)	\( 121 = 11^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	121.c (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.37948 + 4.24561i) q^{2} +(6.03859 - 4.38729i) q^{3} +(-9.65012 - 7.01122i) q^{4} +(-2.61555 - 8.04984i) q^{5} +(10.2966 + 31.6897i) q^{6} +(-16.3816 - 11.9019i) q^{7} +(14.1868 - 10.3073i) q^{8} +(8.87275 - 27.3075i) q^{9} +37.7846 q^{10} -89.0333 q^{12} +(19.0156 - 58.5241i) q^{13} +(73.1289 - 53.1313i) q^{14} +(-51.1112 - 37.1345i) q^{15} +(-5.29766 - 16.3045i) q^{16} +(-21.4315 - 65.9594i) q^{17} +(103.697 + 75.3405i) q^{18} +(-5.80625 + 4.21848i) q^{19} +(-31.1988 + 96.0201i) q^{20} -151.138 q^{21} +50.3154 q^{23} +(40.4472 - 124.484i) q^{24} +(43.1683 - 31.3636i) q^{25} +(222.239 + 161.466i) q^{26} +(-3.95066 - 12.1589i) q^{27} +(74.6371 + 229.709i) q^{28} +(115.828 + 84.1542i) q^{29} +(228.166 - 165.772i) q^{30} +(-78.7415 + 242.341i) q^{31} +216.818 q^{32} +309.603 q^{34} +(-52.9615 + 162.999i) q^{35} +(-277.082 + 201.312i) q^{36} +(-272.367 - 197.886i) q^{37} +(-9.90043 - 30.4704i) q^{38} +(-141.935 - 436.830i) q^{39} +(-120.079 - 87.2424i) q^{40} +(-144.063 + 104.668i) q^{41} +(208.493 - 641.675i) q^{42} -55.7898 q^{43} -243.028 q^{45} +(-69.4092 + 213.620i) q^{46} +(207.525 - 150.776i) q^{47} +(-103.523 - 75.2139i) q^{48} +(20.7073 + 63.7306i) q^{49} +(73.6078 + 226.542i) q^{50} +(-418.799 - 304.275i) q^{51} +(-593.829 + 431.442i) q^{52} +(65.9593 - 203.002i) q^{53} +57.0718 q^{54} -355.079 q^{56} +(-16.5538 + 50.9474i) q^{57} +(-517.070 + 375.673i) q^{58} +(645.185 + 468.754i) q^{59} +(232.871 + 716.704i) q^{60} +(52.1303 + 160.441i) q^{61} +(-920.265 - 668.612i) q^{62} +(-470.360 + 341.737i) q^{63} +(-256.715 + 790.089i) q^{64} -520.846 q^{65} -366.105 q^{67} +(-255.639 + 786.777i) q^{68} +(303.834 - 220.748i) q^{69} +(-618.971 - 449.708i) q^{70} +(-241.648 - 743.716i) q^{71} +(-155.592 - 478.862i) q^{72} +(774.665 + 562.827i) q^{73} +(1215.87 - 883.384i) q^{74} +(123.074 - 378.784i) q^{75} +85.6077 q^{76} +2050.41 q^{78} +(180.956 - 556.926i) q^{79} +(-117.393 + 85.2906i) q^{80} +(549.986 + 399.588i) q^{81} +(-245.647 - 756.024i) q^{82} +(-202.922 - 624.530i) q^{83} +(1458.50 + 1059.67i) q^{84} +(-474.907 + 345.040i) q^{85} +(76.9610 - 236.862i) q^{86} +1068.65 q^{87} +72.6819 q^{89} +(335.253 - 1031.80i) q^{90} +(-1008.05 + 732.394i) q^{91} +(-485.549 - 352.772i) q^{92} +(587.734 + 1808.86i) q^{93} +(353.859 + 1089.06i) q^{94} +(49.1447 + 35.7057i) q^{95} +(1309.27 - 951.243i) q^{96} +(-302.713 + 931.655i) q^{97} -299.141 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{2} + 8 q^{3} - 10 q^{4} + 10 q^{5} - 32 q^{6} + 8 q^{7} + 42 q^{8} - 2 q^{9} + 136 q^{10} - 352 q^{12} - 130 q^{13} + 160 q^{14} - 64 q^{15} + 62 q^{16} + 14 q^{17} + 194 q^{18} + 48 q^{19} + 98 q^{20}+ \cdots + 3288 q^{98}+O(q^{100}) \) 8 * q + 2 * q^2 + 8 * q^3 - 10 * q^4 + 10 * q^5 - 32 * q^6 + 8 * q^7 + 42 * q^8 - 2 * q^9 + 136 * q^10 - 352 * q^12 - 130 * q^13 + 160 * q^14 - 64 * q^15 + 62 * q^16 + 14 * q^17 + 194 * q^18 + 48 * q^19 + 98 * q^20 - 544 * q^21 - 512 * q^23 - 144 * q^24 + 176 * q^25 + 106 * q^26 - 16 * q^27 - 296 * q^28 + 30 * q^29 + 280 * q^30 + 184 * q^31 + 1208 * q^32 + 1784 * q^34 + 128 * q^35 - 394 * q^36 - 126 * q^37 + 168 * q^38 + 496 * q^39 - 186 * q^40 - 370 * q^41 - 712 * q^42 - 1056 * q^43 - 808 * q^45 + 664 * q^46 - 256 * q^47 - 152 * q^48 - 522 * q^49 + 64 * q^50 - 488 * q^51 - 602 * q^52 + 162 * q^53 + 512 * q^54 + 1344 * q^56 + 24 * q^57 - 918 * q^58 + 1304 * q^59 - 752 * q^60 + 300 * q^61 - 1312 * q^62 - 1336 * q^63 + 262 * q^64 - 2504 * q^65 - 2624 * q^67 + 934 * q^68 + 280 * q^69 - 872 * q^70 + 1176 * q^71 - 150 * q^72 + 668 * q^73 + 2022 * q^74 - 464 * q^75 + 768 * q^76 + 7840 * q^78 - 416 * q^79 - 214 * q^80 - 26 * q^81 + 322 * q^82 + 960 * q^83 + 1832 * q^84 - 502 * q^85 + 264 * q^86 + 4032 * q^87 - 4296 * q^89 - 1186 * q^90 + 688 * q^91 - 944 * q^92 - 1864 * q^93 - 2408 * q^94 - 24 * q^95 + 1664 * q^96 + 338 * q^97 + 3288 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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