LMFDB - Embedded newform 115.4.b.a.24.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [115,4,Mod(24,115)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(115, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("115.24");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 115 = 5 \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	115.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:	$6.78521965066$
Analytic rank:	$0$
Dimension:	$34$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			24.4
Character	$\chi$	$=$	115.24
Dual form			115.4.b.a.24.31

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.94561i q^{2} +5.42743i q^{3} -16.4591 q^{4} +(9.51102 + 5.87712i) q^{5} +26.8419 q^{6} -28.7748i q^{7} +41.8353i q^{8} -2.45696 q^{9} +O(q^{10})$	\(q-4.94561i q^{2} +5.42743i q^{3} -16.4591 q^{4} +(9.51102 + 5.87712i) q^{5} +26.8419 q^{6} -28.7748i q^{7} +41.8353i q^{8} -2.45696 q^{9} +(29.0660 - 47.0378i) q^{10} +16.7210 q^{11} -89.3304i q^{12} -65.8600i q^{13} -142.309 q^{14} +(-31.8976 + 51.6204i) q^{15} +75.2286 q^{16} -73.6189i q^{17} +12.1512i q^{18} +76.3128 q^{19} +(-156.543 - 96.7320i) q^{20} +156.173 q^{21} -82.6955i q^{22} +23.0000i q^{23} -227.058 q^{24} +(55.9189 + 111.795i) q^{25} -325.718 q^{26} +133.206i q^{27} +473.606i q^{28} -36.8512 q^{29} +(255.294 + 157.753i) q^{30} +25.8215 q^{31} -37.3689i q^{32} +90.7519i q^{33} -364.090 q^{34} +(169.113 - 273.677i) q^{35} +40.4393 q^{36} -95.0278i q^{37} -377.413i q^{38} +357.450 q^{39} +(-245.871 + 397.896i) q^{40} +159.298 q^{41} -772.371i q^{42} -492.347i q^{43} -275.212 q^{44} +(-23.3682 - 14.4398i) q^{45} +113.749 q^{46} +421.614i q^{47} +408.298i q^{48} -484.988 q^{49} +(552.894 - 276.553i) q^{50} +399.561 q^{51} +1084.00i q^{52} +40.8194i q^{53} +658.783 q^{54} +(159.034 + 98.2712i) q^{55} +1203.80 q^{56} +414.182i q^{57} +182.252i q^{58} -495.047 q^{59} +(525.006 - 849.623i) q^{60} -653.531 q^{61} -127.703i q^{62} +70.6985i q^{63} +417.017 q^{64} +(387.067 - 626.396i) q^{65} +448.824 q^{66} +859.860i q^{67} +1211.70i q^{68} -124.831 q^{69} +(-1353.50 - 836.366i) q^{70} +1171.37 q^{71} -102.788i q^{72} +842.104i q^{73} -469.970 q^{74} +(-606.758 + 303.496i) q^{75} -1256.04 q^{76} -481.143i q^{77} -1767.81i q^{78} -497.161 q^{79} +(715.500 + 442.127i) q^{80} -789.301 q^{81} -787.825i q^{82} +1187.34i q^{83} -2570.46 q^{84} +(432.667 - 700.190i) q^{85} -2434.96 q^{86} -200.007i q^{87} +699.528i q^{88} +540.814 q^{89} +(-71.4139 + 115.570i) q^{90} -1895.11 q^{91} -378.559i q^{92} +140.144i q^{93} +2085.14 q^{94} +(725.812 + 448.499i) q^{95} +202.817 q^{96} -641.210i q^{97} +2398.56i q^{98} -41.0828 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q - 144 q^{4} + 14 q^{5} + 24 q^{6} - 310 q^{9}+O(q^{10}) $ 34 * q - 144 * q^4 + 14 * q^5 + 24 * q^6 - 310 * q^9	$ 34 q - 144 q^{4} + 14 q^{5} + 24 q^{6} - 310 q^{9} + 14 q^{10} - 8 q^{11} + 236 q^{14} + 440 q^{16} + 144 q^{19} - 180 q^{20} - 32 q^{21} + 108 q^{24} + 134 q^{25} - 144 q^{26} + 56 q^{29} - 294 q^{30} - 80 q^{31} + 264 q^{34} + 116 q^{35} + 1864 q^{36} - 1200 q^{39} + 650 q^{40} + 268 q^{41} - 1612 q^{44} - 1346 q^{45} + 184 q^{46} - 1474 q^{49} + 120 q^{50} - 1104 q^{51} + 1564 q^{54} + 1160 q^{55} - 2300 q^{56} - 708 q^{59} - 516 q^{60} + 1100 q^{61} + 100 q^{64} + 1164 q^{65} - 1416 q^{66} - 552 q^{69} + 1144 q^{70} + 1360 q^{71} + 1588 q^{74} - 2064 q^{75} + 108 q^{76} + 3968 q^{79} + 2542 q^{80} + 4914 q^{81} - 1948 q^{84} + 124 q^{85} - 6148 q^{86} + 1196 q^{89} + 2760 q^{90} - 544 q^{91} - 2340 q^{94} + 3920 q^{95} + 2960 q^{96} - 3816 q^{99}+O(q^{100}) $ 34 * q - 144 * q^4 + 14 * q^5 + 24 * q^6 - 310 * q^9 + 14 * q^10 - 8 * q^11 + 236 * q^14 + 440 * q^16 + 144 * q^19 - 180 * q^20 - 32 * q^21 + 108 * q^24 + 134 * q^25 - 144 * q^26 + 56 * q^29 - 294 * q^30 - 80 * q^31 + 264 * q^34 + 116 * q^35 + 1864 * q^36 - 1200 * q^39 + 650 * q^40 + 268 * q^41 - 1612 * q^44 - 1346 * q^45 + 184 * q^46 - 1474 * q^49 + 120 * q^50 - 1104 * q^51 + 1564 * q^54 + 1160 * q^55 - 2300 * q^56 - 708 * q^59 - 516 * q^60 + 1100 * q^61 + 100 * q^64 + 1164 * q^65 - 1416 * q^66 - 552 * q^69 + 1144 * q^70 + 1360 * q^71 + 1588 * q^74 - 2064 * q^75 + 108 * q^76 + 3968 * q^79 + 2542 * q^80 + 4914 * q^81 - 1948 * q^84 + 124 * q^85 - 6148 * q^86 + 1196 * q^89 + 2760 * q^90 - 544 * q^91 - 2340 * q^94 + 3920 * q^95 + 2960 * q^96 - 3816 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/115\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$-1$	$1$

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 $

$2$		−	4.94561i		−	1.74854i	−0.485442	−	0.874269i	$-0.661341\pi$
$2$		−	4.94561i		−	1.74854i	0.485442	−	0.874269i	$-0.338659\pi$
$3$			5.42743i			1.04451i	0.852790	+	0.522254i	$0.174909\pi$
$3$			5.42743i			1.04451i	−0.852790	+	0.522254i	$0.825091\pi$
$4$	−16.4591			−2.05738
$5$	9.51102	+	5.87712i	0.850691	+	0.525666i
$5$	9.51102	+	5.87712i	0.850691	+	0.525666i
$6$	26.8419			1.82636
$7$		−	28.7748i		−	1.55369i	−0.629691	−	0.776846i	$-0.716818\pi$
$7$		−	28.7748i		−	1.55369i	0.629691	−	0.776846i	$-0.283182\pi$
$8$			41.8353i			1.84888i
$9$	−2.45696			−0.0909985
$10$	29.0660	−	47.0378i	0.919146	−	1.48747i
$11$	16.7210			0.458324			0.229162	−	0.973388i	$-0.426401\pi$
$11$	16.7210			0.458324			0.229162	+	0.973388i	$0.426401\pi$
$12$		−	89.3304i		−	2.14896i
$13$		−	65.8600i		−	1.40510i	−0.711635	−	0.702549i	$-0.752045\pi$
$13$		−	65.8600i		−	1.40510i	0.711635	−	0.702549i	$-0.247955\pi$
$14$	−142.309			−2.71669
$15$	−31.8976	+	51.6204i	−0.549062	+	0.888555i
$16$	75.2286			1.17545
$17$		−	73.6189i		−	1.05031i	−0.851008	−	0.525153i	$-0.824008\pi$
$17$		−	73.6189i		−	1.05031i	0.851008	−	0.525153i	$-0.175992\pi$
$18$			12.1512i			0.159114i
$19$	76.3128			0.921439			0.460720	−	0.887546i	$-0.347591\pi$
$19$	76.3128			0.921439			0.460720	+	0.887546i	$0.347591\pi$
$20$	−156.543	−	96.7320i	−1.75020	−	1.08150i
$21$	156.173			1.62284
$22$		−	82.6955i		−	0.801397i
$23$			23.0000i			0.208514i
$23$			23.0000i			0.208514i
$24$	−227.058			−1.93117
$25$	55.9189	+	111.795i	0.447351	+	0.894358i
$26$	−325.718			−2.45687
$27$			133.206i			0.949460i
$28$			473.606i			3.19654i
$29$	−36.8512			−0.235969			−0.117984	−	0.993015i	$-0.537643\pi$
$29$	−36.8512			−0.235969			−0.117984	+	0.993015i	$0.537643\pi$
$30$	255.294	+	157.753i	1.55367	+	0.960056i
$31$	25.8215			0.149602			0.0748012	−	0.997198i	$-0.476168\pi$
$31$	25.8215			0.149602			0.0748012	+	0.997198i	$0.476168\pi$
$32$		−	37.3689i		−	0.206436i
$33$			90.7519i			0.478724i
$34$	−364.090			−1.83650
$35$	169.113	−	273.677i	0.816722	−	1.32171i
$36$	40.4393			0.187219
$37$		−	95.0278i		−	0.422229i	−0.977461	−	0.211114i	$-0.932291\pi$
$37$		−	95.0278i		−	0.422229i	0.977461	−	0.211114i	$-0.0677093\pi$
$38$		−	377.413i		−	1.61117i
$39$	357.450			1.46764
$40$	−245.871	+	397.896i	−0.971891	+	1.57282i
$41$	159.298			0.606783			0.303392	−	0.952866i	$-0.401881\pi$
$41$	159.298			0.606783			0.303392	+	0.952866i	$0.401881\pi$
$42$		−	772.371i		−	2.83761i
$43$		−	492.347i		−	1.74610i	−0.487633	−	0.873049i	$-0.662139\pi$
$43$		−	492.347i		−	1.74610i	0.487633	−	0.873049i	$-0.337861\pi$
$44$	−275.212			−0.942949
$45$	−23.3682	−	14.4398i	−0.0774116	−	0.0478348i
$46$	113.749			0.364595
$47$			421.614i			1.30848i	0.756286	+	0.654241i	$0.227012\pi$
$47$			421.614i			1.30848i	−0.756286	+	0.654241i	$0.772988\pi$
$48$			408.298i			1.22776i
$49$	−484.988			−1.41396
$50$	552.894	−	276.553i	1.56382	−	0.782211i
$51$	399.561			1.09705
$52$			1084.00i			2.89083i
$53$			40.8194i			0.105792i	0.998600	+	0.0528959i	$0.0168452\pi$
$53$			40.8194i			0.105792i	−0.998600	+	0.0528959i	$0.983155\pi$
$54$	658.783			1.66017
$55$	159.034	+	98.2712i	0.389892	+	0.240925i
$56$	1203.80			2.87259
$57$			414.182i			0.962451i
$58$			182.252i			0.412601i
$59$	−495.047			−1.09237			−0.546183	−	0.837666i	$-0.683920\pi$
$59$	−495.047			−1.09237			−0.546183	+	0.837666i	$0.683920\pi$
$60$	525.006	−	849.623i	1.12963	−	1.82810i
$61$	−653.531			−1.37174			−0.685870	−	0.727724i	$-0.740578\pi$
$61$	−653.531			−1.37174			−0.685870	+	0.727724i	$0.740578\pi$
$62$		−	127.703i		−	0.261585i
$63$			70.6985i			0.141384i
$64$	417.017			0.814486
$65$	387.067	−	626.396i	0.738612	−	1.19531i
$66$	448.824			0.837066
$67$			859.860i			1.56789i	0.620831	+	0.783945i	$0.286795\pi$
$67$			859.860i			1.56789i	−0.620831	+	0.783945i	$0.713205\pi$
$68$			1211.70i			2.16088i
$69$	−124.831			−0.217795
$70$	−1353.50	−	836.366i	−2.31106	−	1.42807i
$71$	1171.37			1.95798			0.978990	−	0.203906i	$-0.0653638\pi$
$71$	1171.37			1.95798			0.978990	+	0.203906i	$0.0653638\pi$
$72$		−	102.788i		−	0.168245i
$73$			842.104i			1.35015i	0.737750	+	0.675074i	$0.235888\pi$
$73$			842.104i			1.35015i	−0.737750	+	0.675074i	$0.764112\pi$
$74$	−469.970			−0.738283
$75$	−606.758	+	303.496i	−0.934165	+	0.467262i
$76$	−1256.04			−1.89575
$77$		−	481.143i		−	0.712095i
$78$		−	1767.81i		−	2.56622i
$79$	−497.161			−0.708037			−0.354019	−	0.935238i	$-0.615185\pi$
$79$	−497.161			−0.708037			−0.354019	+	0.935238i	$0.615185\pi$
$80$	715.500	+	442.127i	0.999942	+	0.617892i
$81$	−789.301			−1.08272
$82$		−	787.825i		−	1.06098i
$83$			1187.34i			1.57021i	0.619362	+	0.785106i	$0.287391\pi$
$83$			1187.34i			1.57021i	−0.619362	+	0.785106i	$0.712609\pi$
$84$	−2570.46			−3.33882
$85$	432.667	−	700.190i	0.552109	−	0.893486i
$86$	−2434.96			−3.05312
$87$		−	200.007i		−	0.246472i
$88$			699.528i			0.847385i
$89$	540.814			0.644114			0.322057	−	0.946720i	$-0.395626\pi$
$89$	540.814			0.644114			0.322057	+	0.946720i	$0.395626\pi$
$90$	−71.4139	+	115.570i	−0.0836409	+	0.135357i
$91$	−1895.11			−2.18309
$92$		−	378.559i		−	0.428994i
$93$			140.144i			0.156261i
$94$	2085.14			2.28793
$95$	725.812	+	448.499i	0.783860	+	0.484369i
$96$	202.817			0.215624
$97$		−	641.210i		−	0.671186i	−0.942007	−	0.335593i	$-0.891063\pi$
$97$		−	641.210i		−	0.671186i	0.942007	−	0.335593i	$-0.108937\pi$
$98$			2398.56i			2.47236i
$99$	−41.0828			−0.0417068
$100$	−920.374	−	1840.04i	−0.920374	−	1.84004i
$101$	205.740			0.202692			0.101346	−	0.994851i	$-0.467685\pi$
$101$	205.740			0.202692			0.101346	+	0.994851i	$0.467685\pi$
$102$		−	1976.07i		−	1.91824i
$103$			790.392i			0.756113i	0.925783	+	0.378056i	$0.123407\pi$
$103$			790.392i			0.756113i	−0.925783	+	0.378056i	$0.876593\pi$
$104$	2755.27			2.59785
$105$	1485.36	+	917.847i	1.38054	+	0.853074i
$106$	201.877			0.184981
$107$			192.007i			0.173476i	0.996231	+	0.0867382i	$0.0276444\pi$
$107$			192.007i			0.173476i	−0.996231	+	0.0867382i	$0.972356\pi$
$108$		−	2192.44i		−	1.95340i
$109$	1238.31			1.08815			0.544074	−	0.839037i	$-0.316881\pi$
$109$	1238.31			1.08815			0.544074	+	0.839037i	$0.316881\pi$
$110$	486.011	−	786.518i	0.421267	−	0.681742i
$111$	515.756			0.441022
$112$		−	2164.69i		−	1.82628i
$113$		−	1829.76i		−	1.52327i	−0.648009	−	0.761633i	$-0.724398\pi$
$113$		−	1829.76i		−	1.52327i	0.648009	−	0.761633i	$-0.275602\pi$
$114$	2048.38			1.68288
$115$	−135.174	+	218.753i	−0.109609	+	0.177381i
$116$	606.537			0.485479
$117$			161.815i			0.127862i
$118$			2448.31i			1.91004i
$119$	−2118.37			−1.63185
$120$	−2159.55	−	1334.45i	−1.64283	−	1.01515i
$121$	−1051.41			−0.789939
$122$			3232.11i			2.39854i
$123$			864.577i			0.633791i
$124$	−424.998			−0.307790
$125$	−125.185	+	1391.92i	−0.0895754	+	0.995980i
$126$	349.647			0.247215
$127$			1177.03i			0.822399i	0.911545	+	0.411199i	$0.134890\pi$
$127$			1177.03i			0.822399i	−0.911545	+	0.411199i	$0.865110\pi$
$128$		−	2361.35i		−	1.63059i
$129$	2672.18			1.82381
$130$	−3097.91	−	1914.28i	−2.09004	−	1.29149i
$131$	−1118.17			−0.745763			−0.372881	−	0.927879i	$-0.621630\pi$
$131$	−1118.17			−0.745763			−0.372881	+	0.927879i	$0.621630\pi$
$132$		−	1493.69i		−	0.984919i
$133$		−	2195.88i		−	1.43163i
$134$	4252.53			2.74151
$135$	−782.865	+	1266.92i	−0.499098	+	0.807697i
$136$	3079.87			1.94189
$137$		−	174.022i		−	0.108523i	−0.998527	−	0.0542616i	$-0.982720\pi$
$137$		−	174.022i		−	0.108523i	0.998527	−	0.0542616i	$-0.0172805\pi$
$138$			617.365i			0.380823i
$139$	−871.055			−0.531524			−0.265762	−	0.964039i	$-0.585624\pi$
$139$	−871.055			−0.531524			−0.265762	+	0.964039i	$0.585624\pi$
$140$	−2783.44	+	4504.48i	−1.68031	+	2.71927i
$141$	−2288.28			−1.36672
$142$		−	5793.17i		−	3.42360i
$143$		−	1101.24i		−	0.643991i
$144$	−184.834			−0.106964
$145$	−350.493	−	216.579i	−0.200737	−	0.124041i
$146$	4164.72			2.36078
$147$		−	2632.24i		−	1.47689i
$148$			1564.07i			0.868687i
$149$	1163.23			0.639565			0.319782	−	0.947491i	$-0.396390\pi$
$149$	1163.23			0.639565			0.319782	+	0.947491i	$0.396390\pi$
$150$	1500.97	+	3000.79i	0.817026	+	1.63342i
$151$	−133.547			−0.0719730			−0.0359865	−	0.999352i	$-0.511457\pi$
$151$	−133.547			−0.0719730			−0.0359865	+	0.999352i	$0.511457\pi$
$152$			3192.57i			1.70363i
$153$			180.879i			0.0955762i
$154$	−2379.54			−1.24512
$155$	245.588	+	151.756i	0.127265	+	0.0786408i
$156$	−5883.30			−3.01950
$157$		−	1356.69i		−	0.689653i	−0.938666	−	0.344826i	$-0.887938\pi$
$157$		−	1356.69i		−	0.689653i	0.938666	−	0.344826i	$-0.112062\pi$
$158$			2458.76i			1.23803i
$159$	−221.544			−0.110501
$160$	219.621	−	355.416i	0.108516	−	0.175613i
$161$	661.820			0.323967
$162$			3903.58i			1.89317i
$163$			3579.07i			1.71984i	0.510425	+	0.859922i	$0.329488\pi$
$163$			3579.07i			1.71984i	−0.510425	+	0.859922i	$0.670512\pi$
$164$	−2621.89			−1.24839
$165$	−533.360	+	863.143i	−0.251649	+	0.407246i
$166$	5872.12			2.74557
$167$		−	1903.72i		−	0.882123i	−0.897477	−	0.441062i	$-0.854602\pi$
$167$		−	1903.72i		−	0.882123i	0.897477	−	0.441062i	$-0.145398\pi$
$168$			6533.55i			3.00044i
$169$	−2140.54			−0.974302
$170$	−3462.87	−	2139.80i	−1.56229	−	0.965384i
$171$	−187.497			−0.0838496
$172$			8103.58i			3.59239i
$173$		−	2700.03i		−	1.18659i	−0.804986	−	0.593293i	$-0.797827\pi$
$173$		−	2700.03i		−	1.18659i	0.804986	−	0.593293i	$-0.202173\pi$
$174$	−989.158			−0.430965
$175$	3216.87	−	1609.05i	1.38956	−	0.695046i
$176$	1257.90			0.538736
$177$		−	2686.83i		−	1.14099i
$178$		−	2674.66i		−	1.12626i
$179$	754.312			0.314972			0.157486	−	0.987521i	$-0.449661\pi$
$179$	754.312			0.314972			0.157486	+	0.987521i	$0.449661\pi$
$180$	384.619	+	237.667i	0.159265	+	0.0984145i
$181$	−3006.53			−1.23466			−0.617330	−	0.786705i	$-0.711786\pi$
$181$	−3006.53			−1.23466			−0.617330	+	0.786705i	$0.711786\pi$
$182$			9372.47i			3.81722i
$183$		−	3546.99i		−	1.43279i
$184$	−962.212			−0.385517
$185$	558.489	−	903.811i	0.221951	−	0.359186i
$186$	693.099			0.273228
$187$		−	1230.98i		−	0.481381i
$188$		−	6939.37i		−	2.69205i
$189$	3832.96			1.47517
$190$	2218.10	−	3589.58i	0.846937	−	1.37061i
$191$	2145.54			0.812806			0.406403	−	0.913694i	$-0.366783\pi$
$191$	2145.54			0.812806			0.406403	+	0.913694i	$0.366783\pi$
$192$			2263.33i			0.850737i
$193$			3612.08i			1.34717i	0.739111	+	0.673584i	$0.235246\pi$
$193$			3612.08i			1.34717i	−0.739111	+	0.673584i	$0.764754\pi$
$194$	−3171.18			−1.17359
$195$	3399.72	+	2100.78i	1.24851	+	0.771487i
$196$	7982.45			2.90906
$197$		−	2155.29i		−	0.779483i	−0.920924	−	0.389742i	$-0.872564\pi$
$197$		−	2155.29i		−	0.779483i	0.920924	−	0.389742i	$-0.127436\pi$
$198$			203.179i			0.0729260i
$199$	4366.37			1.55539			0.777697	−	0.628639i	$-0.216388\pi$
$199$	4366.37			1.55539			0.777697	+	0.628639i	$0.216388\pi$
$200$	−4676.97	+	2339.39i	−1.65356	+	0.827098i
$201$	−4666.83			−1.63767
$202$		−	1017.51i		−	0.354414i
$203$			1060.39i			0.366623i
$204$	−6576.40			−2.25706
$205$	1515.08	+	936.212i	0.516185	+	0.318965i
$206$	3908.97			1.32209
$207$		−	56.5101i		−	0.0189745i
$208$		−	4954.56i		−	1.65162i
$209$	1276.02			0.422318
$210$	4539.32	−	7346.04i	1.49163	−	2.41393i
$211$	−1373.27			−0.448057			−0.224028	−	0.974583i	$-0.571921\pi$
$211$	−1373.27			−0.448057			−0.224028	+	0.974583i	$0.571921\pi$
$212$		−	671.849i		−	0.217655i
$213$			6357.55i			2.04513i
$214$	949.590			0.303330
$215$	2893.58	−	4682.72i	0.917864	−	1.48539i
$216$	−5572.69			−1.75543
$217$		−	743.007i		−	0.232436i
$218$		−	6124.18i		−	1.90267i
$219$	−4570.46			−1.41024
$220$	−2617.55	−	1617.45i	−0.802159	−	0.495676i
$221$	−4848.54			−1.47578
$222$		−	2550.73i		−	0.771143i
$223$		−	1005.22i		−	0.301859i	−0.988545	−	0.150929i	$-0.951773\pi$
$223$		−	1005.22i		−	0.301859i	0.988545	−	0.150929i	$-0.0482266\pi$
$224$	−1075.28			−0.320738
$225$	−137.391	−	274.675i	−0.0407083	−	0.0813853i
$226$	−9049.26			−2.66349
$227$			2971.43i			0.868813i	0.900717	+	0.434407i	$0.143042\pi$
$227$			2971.43i			0.868813i	−0.900717	+	0.434407i	$0.856958\pi$
$228$		−	6817.05i		−	1.98013i
$229$	−291.005			−0.0839744			−0.0419872	−	0.999118i	$-0.513369\pi$
$229$	−291.005			−0.0839744			−0.0419872	+	0.999118i	$0.513369\pi$
$230$	1081.87	+	668.517i	0.310158	+	0.191655i
$231$	2611.37			0.743789
$232$		−	1541.68i		−	0.436277i
$233$		−	4215.49i		−	1.18526i	−0.805474	−	0.592631i	$-0.798089\pi$
$233$		−	4215.49i		−	1.18526i	0.805474	−	0.592631i	$-0.201911\pi$
$234$	800.276			0.223571
$235$	−2477.87	+	4009.97i	−0.687824	+	1.11311i
$236$	8148.02			2.24742
$237$		−	2698.30i		−	0.739551i
$238$			10476.6i			2.85335i
$239$	234.318			0.0634176			0.0317088	−	0.999497i	$-0.489905\pi$
$239$	234.318			0.0634176			0.0317088	+	0.999497i	$0.489905\pi$
$240$	−2399.61	+	3883.33i	−0.645393	+	1.04445i
$241$	4644.28			1.24135			0.620673	−	0.784070i	$-0.286860\pi$
$241$	4644.28			1.24135			0.620673	+	0.784070i	$0.286860\pi$
$242$			5199.86i			1.38124i
$243$		−	687.325i		−	0.181448i
$244$	10756.5			2.82220
$245$	−4612.73	−	2850.33i	−1.20284	−	0.743270i
$246$	4275.86			1.10821
$247$		−	5025.96i		−	1.29471i
$248$			1080.25i			0.276596i
$249$	−6444.20			−1.64010
$250$	6883.92	+	619.118i	1.74151	+	0.156626i
$251$	−961.417			−0.241769			−0.120885	−	0.992667i	$-0.538573\pi$
$251$	−961.417			−0.241769			−0.120885	+	0.992667i	$0.538573\pi$
$252$		−	1163.63i		−	0.290881i
$253$			384.583i			0.0955672i
$254$	5821.14			1.43800
$255$	3800.23	+	2348.27i	0.933254	+	0.576683i
$256$	−8342.20			−2.03667
$257$			2800.34i			0.679689i	0.940482	+	0.339845i	$0.110375\pi$
$257$			2800.34i			0.679689i	−0.940482	+	0.339845i	$0.889625\pi$
$258$		−	13215.5i		−	3.18901i
$259$	−2734.40			−0.656014
$260$	−6370.77	+	10309.9i	−1.51961	+	2.45920i
$261$	90.5419			0.0214728
$262$			5530.03i			1.30399i
$263$			7316.97i			1.71553i	0.514045	+	0.857763i	$0.328147\pi$
$263$			7316.97i			1.71553i	−0.514045	+	0.857763i	$0.671853\pi$
$264$	−3796.63			−0.885101
$265$	−239.900	+	388.234i	−0.0556111	+	0.0899962i
$266$	−10860.0			−2.50326
$267$			2935.23i			0.672783i
$268$		−	14152.5i		−	3.22575i
$269$	−3429.15			−0.777244			−0.388622	−	0.921397i	$-0.627049\pi$
$269$	−3429.15			−0.777244			−0.388622	+	0.921397i	$0.627049\pi$
$270$	6265.70	+	3871.75i	1.41229	+	0.872692i
$271$	7608.53			1.70548			0.852740	−	0.522336i	$-0.174939\pi$
$271$	7608.53			1.70548			0.852740	+	0.522336i	$0.174939\pi$
$272$		−	5538.24i		−	1.23458i
$273$		−	10285.6i		−	2.28026i
$274$	−860.644			−0.189757
$275$	935.020	+	1869.32i	0.205032	+	0.409906i
$276$	2054.60			0.448088
$277$		−	3156.98i		−	0.684782i	−0.939558	−	0.342391i	$-0.888763\pi$
$277$		−	3156.98i		−	0.684782i	0.939558	−	0.342391i	$-0.111237\pi$
$278$			4307.90i			0.929391i
$279$	−63.4423			−0.0136136
$280$	11449.4	+	7074.89i	2.44368	+	1.51002i
$281$	2217.02			0.470663			0.235331	−	0.971915i	$-0.424382\pi$
$281$	2217.02			0.470663			0.235331	+	0.971915i	$0.424382\pi$
$282$			11316.9i			2.38976i
$283$			2162.68i			0.454268i	0.973864	+	0.227134i	$0.0729355\pi$
$283$			2162.68i			0.454268i	−0.973864	+	0.227134i	$0.927065\pi$
$284$	−19279.7			−4.02832
$285$	−2434.20	+	3939.29i	−0.505928	+	0.818749i
$286$	−5446.33			−1.12604
$287$		−	4583.76i		−	0.942755i
$288$			91.8138i			0.0187853i
$289$	−506.736			−0.103142
$290$	−1071.12	+	1733.40i	−0.216890	+	0.350996i
$291$	3480.12			0.701059
$292$		−	13860.3i		−	2.77777i
$293$		−	2576.23i		−	0.513669i	−0.966455	−	0.256835i	$-0.917320\pi$
$293$		−	2576.23i		−	0.513669i	0.966455	−	0.256835i	$-0.0826795\pi$
$294$	−13018.0			−2.58240
$295$	−4708.40	−	2909.45i	−0.929267	−	0.574220i
$296$	3975.51			0.780649
$297$			2227.33i			0.435161i
$298$		−	5752.86i		−	1.11830i
$299$	1514.78			0.292983
$300$	9986.68	−	4995.26i	1.92194	−	0.961339i
$301$	−14167.2			−2.71290
$302$			660.473i			0.125848i
$303$			1116.64i			0.211713i
$304$	5740.90			1.08310
$305$	−6215.75	−	3840.88i	−1.16693	−	0.721076i
$306$	894.555			0.167119
$307$		−	3252.03i		−	0.604571i	−0.953217	−	0.302286i	$-0.902250\pi$
$307$		−	3252.03i		−	0.604571i	0.953217	−	0.302286i	$-0.0977497\pi$
$308$			7919.16i			1.46505i
$309$	−4289.79			−0.789766
$310$	750.526	−	1214.59i	0.137506	−	0.222528i
$311$	3954.42			0.721012			0.360506	−	0.932757i	$-0.382604\pi$
$311$	3954.42			0.721012			0.360506	+	0.932757i	$0.382604\pi$
$312$			14954.0i			2.71348i
$313$			6423.16i			1.15993i	0.814641	+	0.579966i	$0.196934\pi$
$313$			6423.16i			1.15993i	−0.814641	+	0.579966i	$0.803066\pi$
$314$	−6709.65			−1.20588
$315$	−415.503	+	672.414i	−0.0743205	+	0.120274i
$316$	8182.80			1.45670
$317$		−	2582.98i		−	0.457649i	−0.973468	−	0.228825i	$-0.926512\pi$
$317$		−	2582.98i		−	0.457649i	0.973468	−	0.228825i	$-0.0734882\pi$
$318$			1095.67i			0.193214i
$319$	−616.189			−0.108150
$320$	3966.25	+	2450.86i	0.692876	+	0.428147i
$321$	−1042.10			−0.181198
$322$		−	3273.10i		−	0.566469i
$323$		−	5618.06i		−	0.967793i
$324$	12991.2			2.22757
$325$	7362.81	−	3682.82i	1.25666	−	0.628573i
$326$	17700.7			3.00721
$327$			6720.81i			1.13658i
$328$			6664.27i			1.12187i
$329$	12131.8			2.03298
$330$	4268.77	+	2637.79i	0.712085	+	0.440017i
$331$	−7154.87			−1.18812			−0.594059	−	0.804421i	$-0.702475\pi$
$331$	−7154.87			−1.18812			−0.594059	+	0.804421i	$0.702475\pi$
$332$		−	19542.5i		−	3.23053i
$333$			233.479i			0.0384222i
$334$	−9415.08			−1.54243
$335$	−5053.50	+	8178.14i	−0.824185	+	1.33379i
$336$	11748.7			1.90757
$337$			3151.02i			0.509338i	0.967028	+	0.254669i	$0.0819665\pi$
$337$			3151.02i			0.509338i	−0.967028	+	0.254669i	$0.918033\pi$
$338$			10586.3i			1.70360i
$339$	9930.87			1.59106
$340$	−7121.30	+	11524.5i	−1.13590	+	1.83824i
$341$	431.760			0.0685664
$342$			927.289i			0.146614i
$343$			4085.67i			0.643165i
$344$	20597.5			3.22832
$345$	−1187.27	−	733.646i	−0.185276	−	0.114487i
$346$	−13353.3			−2.07479
$347$			8874.67i			1.37296i	0.727148	+	0.686480i	$0.240845\pi$
$347$			8874.67i			1.37296i	−0.727148	+	0.686480i	$0.759155\pi$
$348$			3291.93i			0.507087i
$349$	3484.70			0.534475			0.267238	−	0.963631i	$-0.413889\pi$
$349$	3484.70			0.534475			0.267238	+	0.963631i	$0.413889\pi$
$350$	−7957.76	−	15909.4i	−1.21531	−	2.42969i
$351$	8772.92			1.33409
$352$		−	624.844i		−	0.0946145i
$353$			3409.79i			0.514121i	0.966395	+	0.257060i	$0.0827539\pi$
$353$			3409.79i			0.514121i	−0.966395	+	0.257060i	$0.917246\pi$
$354$	−13288.0			−1.99506
$355$	11141.0	+	6884.31i	1.66564	+	1.02924i
$356$	−8901.30			−1.32519
$357$		−	11497.3i		−	1.70448i
$358$		−	3730.54i		−	0.550740i
$359$	2191.51			0.322183			0.161091	−	0.986940i	$-0.448499\pi$
$359$	2191.51			0.322183			0.161091	+	0.986940i	$0.448499\pi$
$360$	604.095	−	977.615i	0.0884406	−	0.143125i
$361$	−1035.36			−0.150950
$362$			14869.1i			2.15885i
$363$		−	5706.44i		−	0.825098i
$364$	31191.7			4.49146
$365$	−4949.14	+	8009.26i	−0.709726	+	1.14856i
$366$	−17542.1			−2.50529
$367$			1446.01i			0.205670i	0.994698	+	0.102835i	$0.0327914\pi$
$367$			1446.01i			0.205670i	−0.994698	+	0.102835i	$0.967209\pi$
$368$			1730.26i			0.245098i
$369$	−391.388			−0.0552164
$370$	−4469.90	−	2762.07i	−0.628051	−	0.388090i
$371$	1174.57			0.164368
$372$		−	2306.64i		−	0.321489i
$373$			9909.59i			1.37560i	0.725900	+	0.687801i	$0.241424\pi$
$373$			9909.59i			1.37560i	−0.725900	+	0.687801i	$0.758576\pi$
$374$	−6087.95			−0.841712
$375$	−7554.57	−	679.434i	−1.04031	−	0.0935622i
$376$	−17638.3			−2.41922
$377$			2427.02i			0.331560i
$378$		−	18956.3i		−	2.57939i
$379$	−6430.45			−0.871531			−0.435765	−	0.900060i	$-0.643522\pi$
$379$	−6430.45			−0.871531			−0.435765	+	0.900060i	$0.643522\pi$
$380$	−11946.2	−	7381.88i	−1.61270	−	0.996533i
$381$	−6388.25			−0.859003
$382$		−	10611.0i		−	1.42122i
$383$			881.749i			0.117638i	0.998269	+	0.0588189i	$0.0187334\pi$
$383$			881.749i			0.117638i	−0.998269	+	0.0588189i	$0.981267\pi$
$384$	12816.1			1.70317
$385$	2827.73	−	4576.16i	0.374324	−	0.605773i
$386$	17864.0			2.35557
$387$			1209.68i			0.158892i
$388$			10553.7i			1.38089i
$389$	8893.90			1.15923			0.579613	−	0.814892i	$-0.303204\pi$
$389$	8893.90			1.15923			0.579613	+	0.814892i	$0.303204\pi$
$390$	10389.6	−	16813.7i	1.34897	−	2.18306i
$391$	1693.23			0.219004
$392$		−	20289.6i		−	2.61424i
$393$		−	6068.78i		−	0.778956i
$394$	−10659.2			−1.36296
$395$	−4728.50	−	2921.87i	−0.602321	−	0.372191i
$396$	676.185			0.0858070
$397$			3537.94i			0.447265i	0.974674	+	0.223633i	$0.0717916\pi$
$397$			3537.94i			0.447265i	−0.974674	+	0.223633i	$0.928208\pi$
$398$		−	21594.4i		−	2.71967i
$399$	11918.0			1.49535
$400$	4206.70	+	8410.16i	0.525838	+	1.05127i
$401$	8308.81			1.03472			0.517360	−	0.855768i	$-0.326915\pi$
$401$	8308.81			1.03472			0.517360	+	0.855768i	$0.326915\pi$
$402$			23080.3i			2.86354i
$403$		−	1700.60i		−	0.210206i
$404$	−3386.28			−0.417015
$405$	−7507.06	−	4638.82i	−0.921059	−	0.569147i
$406$	5244.26			0.641054
$407$		−	1588.96i		−	0.193518i
$408$			16715.8i			2.02832i
$409$	−15235.6			−1.84194			−0.920969	−	0.389637i	$-0.872600\pi$
$409$	−15235.6			−1.84194			−0.920969	+	0.389637i	$0.872600\pi$
$410$	4630.14	−	7493.01i	0.557723	−	0.902570i
$411$	944.490			0.113353
$412$		−	13009.1i		−	1.55561i
$413$			14244.9i			1.69720i
$414$	−279.477			−0.0331776
$415$	−6978.14	+	11292.8i	−0.825406	+	1.33577i
$416$	−2461.11			−0.290063
$417$		−	4727.59i		−	0.555182i
$418$		−	6310.72i		−	0.738439i
$419$	−2610.62			−0.304385			−0.152193	−	0.988351i	$-0.548633\pi$
$419$	−2610.62			−0.304385			−0.152193	+	0.988351i	$0.548633\pi$
$420$	−24447.7	−	15106.9i	−2.84030	−	1.75510i
$421$	5889.61			0.681810			0.340905	−	0.940098i	$-0.389267\pi$
$421$	5889.61			0.681810			0.340905	+	0.940098i	$0.389267\pi$
$422$			6791.67i			0.783444i
$423$		−	1035.89i		−	0.119070i
$424$	−1707.69			−0.195596
$425$	8230.20	−	4116.69i	0.939349	−	0.469856i
$426$	31442.0			3.57598
$427$			18805.2i			2.13126i
$428$		−	3160.25i		−	0.356908i
$429$	5976.92			0.672654
$430$	−23158.9	−	14310.5i	−2.59726	−	1.60492i
$431$	−15351.4			−1.71567			−0.857833	−	0.513929i	$-0.828189\pi$
$431$	−15351.4			−1.71567			−0.857833	+	0.513929i	$0.828189\pi$
$432$			10020.9i			1.11604i
$433$			2875.39i			0.319128i	0.987188	+	0.159564i	$0.0510088\pi$
$433$			2875.39i			0.319128i	−0.987188	+	0.159564i	$0.948991\pi$
$434$	−3674.63			−0.406423
$435$	1175.47	−	1902.27i	0.129562	−	0.209671i
$436$	−20381.4			−2.23874
$437$			1755.19i			0.192133i
$438$			22603.7i			2.46586i
$439$	−13824.2			−1.50294			−0.751471	−	0.659766i	$-0.770655\pi$
$439$	−13824.2			−1.50294			−0.751471	+	0.659766i	$0.770655\pi$
$440$	−4111.21	+	6653.22i	−0.445441	+	0.720863i
$441$	1191.60			0.128668
$442$			23979.0i			2.58046i
$443$		−	10229.0i		−	1.09705i	−0.836133	−	0.548526i	$-0.815189\pi$
$443$		−	10229.0i		−	1.09705i	0.836133	−	0.548526i	$-0.184811\pi$
$444$	−8488.87			−0.907351
$445$	5143.69	+	3178.43i	0.547942	+	0.338589i
$446$	−4971.43			−0.527812
$447$			6313.32i			0.668031i
$448$		−	11999.6i		−	1.26546i
$449$	−8117.62			−0.853216			−0.426608	−	0.904437i	$-0.640292\pi$
$449$	−8117.62			−0.853216			−0.426608	+	0.904437i	$0.640292\pi$
$450$	−1358.44	+	679.480i	−0.142305	+	0.0711800i
$451$	2663.61			0.278104
$452$			30116.1i			3.13394i
$453$		−	724.818i		−	0.0751764i
$454$	14695.5			1.51915
$455$	−18024.4	−	11137.8i	−1.85714	−	1.14758i
$456$	−17327.4			−1.77945
$457$		−	11728.0i		−	1.20047i	−0.799824	−	0.600235i	$-0.795074\pi$
$457$		−	11728.0i		−	1.20047i	0.799824	−	0.600235i	$-0.204926\pi$
$458$			1439.20i			0.146832i
$459$	9806.44			0.997223
$460$	2224.84	−	3600.48i	0.225508	−	0.364942i
$461$	1557.75			0.157379			0.0786897	−	0.996899i	$-0.474926\pi$
$461$	1557.75			0.157379			0.0786897	+	0.996899i	$0.474926\pi$
$462$		−	12914.8i		−	1.30054i
$463$			1824.04i			0.183089i	0.995801	+	0.0915446i	$0.0291804\pi$
$463$			1824.04i			0.183089i	−0.995801	+	0.0915446i	$0.970820\pi$
$464$	−2772.26			−0.277369
$465$	−823.644	+	1332.91i	−0.0821410	+	0.132930i
$466$	−20848.2			−2.07247
$467$		−	13059.8i		−	1.29408i	−0.762456	−	0.647040i	$-0.776007\pi$
$467$		−	13059.8i		−	1.29408i	0.762456	−	0.647040i	$-0.223993\pi$
$468$		−	2663.33i		−	0.263061i
$469$	24742.3			2.43602
$470$	19831.8	+	12254.6i	1.94632	+	1.20269i
$471$	7363.32			0.720348
$472$		−	20710.4i		−	2.01965i
$473$		−	8232.53i		−	0.800279i
$474$	−13344.8			−1.29313
$475$	4267.33	+	8531.37i	0.412207	+	0.824097i
$476$	34866.4			3.35735
$477$		−	100.291i		−	0.00962690i
$478$		−	1158.85i		−	0.110888i
$479$	18106.1			1.72712			0.863559	−	0.504247i	$-0.168230\pi$
$479$	18106.1			1.72712			0.863559	+	0.504247i	$0.168230\pi$
$480$	1928.99	+	1191.98i	0.183429	+	0.113346i
$481$	−6258.53			−0.593273
$482$		−	22968.8i		−	2.17054i
$483$			3591.98i			0.338387i
$484$	17305.2			1.62521
$485$	3768.47	−	6098.56i	0.352819	−	0.570972i
$486$	−3399.24			−0.317269
$487$		−	5675.51i		−	0.528095i	−0.964510	−	0.264047i	$-0.914942\pi$
$487$		−	5675.51i		−	0.528095i	0.964510	−	0.264047i	$-0.0850575\pi$
$488$		−	27340.7i		−	2.53618i
$489$	−19425.2			−1.79639
$490$	−14096.6	+	22812.8i	−1.29963	+	2.10322i
$491$	−2.76101			−0.000253773			−0.000126887	−	1.00000i	$-0.500040\pi$
$491$	−2.76101			−0.000253773			−0.000126887		1.00000i	$0.500040\pi$
$492$		−	14230.1i		−	1.30395i
$493$			2712.94i			0.247839i
$494$	−24856.4			−2.26385
$495$	−390.739	−	241.448i	−0.0354796	−	0.0219238i
$496$	1942.51			0.175850
$497$		−	33706.1i		−	3.04210i
$498$			31870.5i			2.86778i
$499$	−1240.62			−0.111299			−0.0556493	−	0.998450i	$-0.517723\pi$
$499$	−1240.62			−0.111299			−0.0556493	+	0.998450i	$0.517723\pi$
$500$	2060.44	−	22909.8i	0.184291	−	2.04911i
$501$	10332.3			0.921385
$502$			4754.80i			0.422743i
$503$			11807.7i			1.04668i	0.852124	+	0.523340i	$0.175314\pi$
$503$			11807.7i			1.04668i	−0.852124	+	0.523340i	$0.824686\pi$
$504$	−2957.69			−0.261401
$505$	1956.79	+	1209.16i	0.172428	+	0.106548i
$506$	1902.00			0.167103
$507$		−	11617.6i		−	1.01767i
$508$		−	19372.8i		−	1.69199i
$509$	−8573.55			−0.746593			−0.373296	−	0.927712i	$-0.621773\pi$
$509$	−8573.55			−0.746593			−0.373296	+	0.927712i	$0.621773\pi$
$510$	11613.6	−	18794.5i	1.00835	−	1.63183i
$511$	24231.4			2.09771
$512$			22366.5i			1.93060i
$513$			10165.3i			0.874870i
$514$	13849.4			1.18846
$515$	−4645.23	+	7517.43i	−0.397462	+	0.643219i
$516$	−43981.6			−3.75229
$517$			7049.80i			0.599709i
$518$			13523.3i			1.14706i
$519$	14654.2			1.23940
$520$	26205.5	+	16193.1i	2.20997	+	1.36560i
$521$	1036.56			0.0871638			0.0435819	−	0.999050i	$-0.486123\pi$
$521$	1036.56			0.0871638			0.0435819	+	0.999050i	$0.486123\pi$
$522$		−	447.785i		−	0.0375460i
$523$			4294.28i			0.359036i	0.983755	+	0.179518i	$0.0574538\pi$
$523$			4294.28i			0.359036i	−0.983755	+	0.179518i	$0.942546\pi$
$524$	18404.0			1.53432
$525$	8733.03	+	17459.3i	0.725982	+	1.45140i
$526$	36186.9			2.99966
$527$		−	1900.95i		−	0.157128i
$528$			6827.14i			0.562714i
$529$	−529.000			−0.0434783
$530$	1920.05	+	1186.45i	0.157362	+	0.0972382i
$531$	1216.31			0.0994037
$532$			36142.2i			2.94542i
$533$		−	10491.4i		−	0.852591i
$534$	14516.5			1.17639
$535$	−1128.45	+	1826.18i	−0.0911906	+	0.147575i
$536$	−35972.5			−2.89883
$537$			4093.97i			0.328991i
$538$			16959.2i			1.35904i
$539$	−8109.48			−0.648052
$540$	12885.2	−	20852.3i	1.02684	−	1.66174i
$541$	5428.80			0.431427			0.215714	−	0.976457i	$-0.430792\pi$
$541$	5428.80			0.431427			0.215714	+	0.976457i	$0.430792\pi$
$542$		−	37628.8i		−	2.98210i
$543$		−	16317.7i		−	1.28961i
$544$	−2751.05			−0.216821
$545$	11777.5	+	7277.67i	0.925678	+	0.572002i
$546$	−50868.4			−3.98712
$547$		−	10768.0i		−	0.841694i	−0.907132	−	0.420847i	$-0.861733\pi$
$547$		−	10768.0i		−	0.841694i	0.907132	−	0.420847i	$-0.138267\pi$
$548$			2864.24i			0.223274i
$549$	1605.70			0.124826
$550$	9244.93	−	4624.24i	0.716736	−	0.358506i
$551$	−2812.22			−0.217431
$552$		−	5222.34i		−	0.402676i
$553$			14305.7i			1.10007i
$554$	−15613.2			−1.19737
$555$	4905.37	+	3031.16i	0.375173	+	0.231830i
$556$	14336.8			1.09355
$557$		−	16061.8i		−	1.22183i	−0.791695	−	0.610916i	$-0.790801\pi$
$557$		−	16061.8i		−	1.22183i	0.791695	−	0.610916i	$-0.209199\pi$
$558$			313.761i			0.0238039i
$559$	−32426.0			−2.45344
$560$	12722.1	−	20588.4i	0.960013	−	1.55360i
$561$	6681.05			0.502806
$562$		−	10964.5i		−	0.822972i
$563$			7755.76i			0.580580i	0.956939	+	0.290290i	$0.0937517\pi$
$563$			7755.76i			0.580580i	−0.956939	+	0.290290i	$0.906248\pi$
$564$	37662.9			2.81187
$565$	10753.7	−	17402.8i	0.800728	−	1.29583i
$566$	10695.8			0.794304
$567$			22712.0i			1.68221i
$568$			49004.8i			3.62007i
$569$	−3993.21			−0.294207			−0.147104	−	0.989121i	$-0.546995\pi$
$569$	−3993.21			−0.294207			−0.147104	+	0.989121i	$0.546995\pi$
$570$	19482.2	+	12038.6i	1.43161	+	0.884633i
$571$	−16239.2			−1.19017			−0.595087	−	0.803662i	$-0.702882\pi$
$571$	−16239.2			−1.19017			−0.595087	+	0.803662i	$0.702882\pi$
$572$			18125.5i			1.32494i
$573$			11644.8i			0.848983i
$574$	−22669.5			−1.64844
$575$	−2571.28	+	1286.14i	−0.186487	+	0.0932792i
$576$	−1024.59			−0.0741170
$577$			6260.37i			0.451685i	0.974164	+	0.225843i	$0.0725135\pi$
$577$			6260.37i			0.451685i	−0.974164	+	0.225843i	$0.927486\pi$
$578$			2506.12i			0.180347i
$579$	−19604.3			−1.40713
$580$	5768.78	+	3564.69i	0.412993	+	0.255200i
$581$	34165.5			2.43962
$582$		−	17211.3i		−	1.22583i
$583$			682.540i			0.0484870i
$584$	−35229.7			−2.49626
$585$	−951.008	+	1539.03i	−0.0672126	+	0.108771i
$586$	−12741.0			−0.898170
$587$		−	24332.7i		−	1.71093i	−0.517859	−	0.855466i	$-0.673271\pi$
$587$		−	24332.7i		−	1.71093i	0.517859	−	0.855466i	$-0.326729\pi$
$588$			43324.2i			3.03854i
$589$	1970.51			0.137849
$590$	−14389.0	+	23285.9i	−1.00404	+	1.62486i
$591$	11697.7			0.814177
$592$		−	7148.80i		−	0.496307i
$593$			6503.42i			0.450360i	0.974317	+	0.225180i	$0.0722970\pi$
$593$			6503.42i			0.450360i	−0.974317	+	0.225180i	$0.927703\pi$
$594$	11015.5			0.760895
$595$	−20147.8	−	12449.9i	−1.38820	−	0.857808i
$596$	−19145.6			−1.31583
$597$			23698.1i			1.62462i
$598$		−	7491.52i		−	0.512292i
$599$	−8996.68			−0.613680			−0.306840	−	0.951761i	$-0.599272\pi$
$599$	−8996.68			−0.613680			−0.306840	+	0.951761i	$0.599272\pi$
$600$	−12696.8	−	25383.9i	−0.863911	−	1.72716i
$601$	−24207.6			−1.64301			−0.821504	−	0.570203i	$-0.806864\pi$
$601$	−24207.6			−1.64301			−0.821504	+	0.570203i	$0.806864\pi$
$602$			70065.3i			4.74361i
$603$		−	2112.64i		−	0.142676i
$604$	2198.06			0.148076
$605$	−9999.97	−	6179.25i	−0.671994	−	0.415244i
$606$	5522.45			0.370189
$607$		−	24601.9i		−	1.64507i	−0.568712	−	0.822536i	$-0.692558\pi$
$607$		−	24601.9i		−	1.64507i	0.568712	−	0.822536i	$-0.307442\pi$
$608$		−	2851.72i		−	0.190218i
$609$	−5755.17			−0.382941
$610$	−18995.5	+	30740.7i	−1.26083	+	2.04042i
$611$	27767.5			1.83855
$612$		−	2977.09i		−	0.196637i
$613$		−	17927.6i		−	1.18122i	−0.806956	−	0.590612i	$-0.798886\pi$
$613$		−	17927.6i		−	1.18122i	0.806956	−	0.590612i	$-0.201114\pi$
$614$	−16083.3			−1.05712
$615$	−5081.22	+	8223.00i	−0.333162	+	0.539160i
$616$	20128.7			1.31658
$617$		−	11105.0i		−	0.724589i	−0.932064	−	0.362295i	$-0.881993\pi$
$617$		−	11105.0i		−	0.724589i	0.932064	−	0.362295i	$-0.118007\pi$
$618$			21215.7i			1.38094i
$619$	9846.80			0.639380			0.319690	−	0.947522i	$-0.396421\pi$
$619$	9846.80			0.639380			0.319690	+	0.947522i	$0.396421\pi$
$620$	−4042.16	−	2497.76i	−0.261834	−	0.161794i
$621$	−3063.73			−0.197976
$622$		−	19557.0i		−	1.26072i
$623$		−	15561.8i		−	1.00076i
$624$	26890.5			1.72513
$625$	−9371.15	+	12502.9i	−0.599753	+	0.800185i
$626$	31766.5			2.02818
$627$			6925.53i			0.441115i
$628$			22329.8i			1.41888i
$629$	−6995.83			−0.443469
$630$	3325.50	+	2054.92i	0.210303	+	0.129952i
$631$	5127.98			0.323521			0.161760	−	0.986830i	$-0.448283\pi$
$631$	5127.98			0.323521			0.161760	+	0.986830i	$0.448283\pi$
$632$		−	20798.9i		−	1.30907i
$633$		−	7453.34i		−	0.467999i
$634$	−12774.4			−0.800217
$635$	−6917.55	+	11194.8i	−0.432307	+	0.699607i
$636$	3646.41			0.227342
$637$			31941.3i			1.98675i
$638$			3047.43i			0.189105i
$639$	−2878.02			−0.178173
$640$	13878.0	−	22458.9i	0.857148	−	1.38713i
$641$	−16730.1			−1.03089			−0.515445	−	0.856922i	$-0.672373\pi$
$641$	−16730.1			−1.03089			−0.515445	+	0.856922i	$0.672373\pi$
$642$			5153.83i			0.316831i
$643$		−	8215.70i		−	0.503881i	−0.967743	−	0.251941i	$-0.918931\pi$
$643$		−	8215.70i		−	0.503881i	0.967743	−	0.251941i	$-0.0810688\pi$
$644$	−10892.9			−0.666525
$645$	25415.1	+	15704.7i	1.55150	+	0.958716i
$646$	−27784.7			−1.69222
$647$		−	2755.97i		−	0.167462i	−0.996488	−	0.0837312i	$-0.973316\pi$
$647$		−	2755.97i		−	0.167462i	0.996488	−	0.0837312i	$-0.0266837\pi$
$648$		−	33020.7i		−	2.00181i
$649$	−8277.67			−0.500658
$650$	−18213.8	−	36413.6i	−1.09908	−	2.19732i
$651$	4032.62			0.242781
$652$		−	58908.2i		−	3.53838i
$653$			17413.8i			1.04357i	0.853076	+	0.521787i	$0.174735\pi$
$653$			17413.8i			1.04357i	−0.853076	+	0.521787i	$0.825265\pi$
$654$	33238.5			1.98735
$655$	−10634.9	−	6571.61i	−0.634414	−	0.392022i
$656$	11983.7			0.713241
$657$		−	2069.02i		−	0.122861i
$658$		−	59999.4i		−	3.55474i
$659$	−10288.6			−0.608175			−0.304088	−	0.952644i	$-0.598352\pi$
$659$	−10288.6			−0.608175			−0.304088	+	0.952644i	$0.598352\pi$
$660$	8778.61	−	14206.5i	0.517738	−	0.837862i
$661$	−6418.58			−0.377691			−0.188846	−	0.982007i	$-0.560475\pi$
$661$	−6418.58			−0.377691			−0.188846	+	0.982007i	$0.560475\pi$
$662$			35385.2i			2.07747i
$663$		−	26315.1i		−	1.54147i
$664$	−49672.7			−2.90313
$665$	12905.5	−	20885.1i	0.752560	−	1.21788i
$666$	1154.70			0.0671827
$667$		−	847.578i		−	0.0492029i
$668$			31333.5i			1.81487i
$669$	5455.76			0.315294
$670$	40445.9	+	24992.6i	2.33218	+	1.44112i
$671$	−10927.7			−0.628702
$672$		−	5836.01i		−	0.335013i
$673$		−	27817.4i		−	1.59329i	−0.604448	−	0.796645i	$-0.706606\pi$
$673$		−	27817.4i		−	1.59329i	0.604448	−	0.796645i	$-0.293394\pi$
$674$	15583.7			0.890597
$675$	−14891.7	+	7448.71i	−0.849157	+	0.424742i
$676$	35231.3			2.00451
$677$			12716.6i			0.721921i	0.932581	+	0.360960i	$0.117551\pi$
$677$			12716.6i			0.721921i	−0.932581	+	0.360960i	$0.882449\pi$
$678$		−	49114.2i		−	2.78204i
$679$	−18450.7			−1.04282
$680$	29292.7	+	18100.7i	1.65195	+	1.02078i
$681$	−16127.2			−0.907483
$682$		−	2135.32i		−	0.119891i
$683$			14735.9i			0.825557i	0.910831	+	0.412778i	$0.135442\pi$
$683$			14735.9i			0.825557i	−0.910831	+	0.412778i	$0.864558\pi$
$684$	3086.03			0.172511
$685$	1022.75	−	1655.12i	0.0570469	−	0.0923198i
$686$	20206.1			1.12460
$687$		−	1579.41i		−	0.0877120i
$688$		−	37038.6i		−	2.05244i
$689$	2688.36			0.148648
$690$	−3628.33	+	5871.77i	−0.200186	+	0.323963i
$691$	20890.4			1.15008			0.575041	−	0.818125i	$-0.304986\pi$
$691$	20890.4			1.15008			0.575041	+	0.818125i	$0.304986\pi$
$692$			44440.0i			2.44127i
$693$			1182.15i			0.0647996i
$694$	43890.7			2.40067
$695$	−8284.62	−	5119.29i	−0.452163	−	0.279404i
$696$	8367.37			0.455696
$697$		−	11727.3i		−	0.637308i
$698$		−	17234.0i		−	0.934551i
$699$	22879.3			1.23802
$700$	−52946.7	+	26483.6i	−2.85885	+	1.42998i
$701$	−31086.0			−1.67490			−0.837448	−	0.546517i	$-0.815953\pi$
$701$	−31086.0			−1.67490			−0.837448	+	0.546517i	$0.815953\pi$
$702$		−	43387.5i		−	2.33270i
$703$		−	7251.83i		−	0.389058i
$704$	6972.93			0.373299
$705$	−21763.8	−	13448.5i	−1.16266	−	0.718438i
$706$	16863.5			0.898960
$707$		−	5920.11i		−	0.314920i
$708$			44222.8i			2.34745i
$709$	−4701.78			−0.249054			−0.124527	−	0.992216i	$-0.539741\pi$
$709$	−4701.78			−0.249054			−0.124527	+	0.992216i	$0.539741\pi$
$710$	34047.1	−	55098.9i	1.79967	−	2.91243i
$711$	1221.50			0.0644303
$712$			22625.1i			1.19089i
$713$			593.894i			0.0311942i
$714$	−56861.1			−2.98035
$715$	6472.15	−	10474.0i	0.338524	−	0.547837i
$716$	−12415.3			−0.648018
$717$			1271.75i			0.0662402i
$718$		−	10838.4i		−	0.563348i
$719$	631.878			0.0327748			0.0163874	−	0.999866i	$-0.494783\pi$
$719$	631.878			0.0327748			0.0163874	+	0.999866i	$0.494783\pi$
$720$	−1757.96	−	1086.29i	−0.0909932	−	0.0562272i
$721$	22743.4			1.17477
$722$			5120.51i			0.263941i
$723$			25206.5i			1.29660i
$724$	49484.6			2.54017
$725$	−2060.68	−	4119.77i	−0.105561	−	0.211041i
$726$	−28221.9			−1.44272
$727$			22570.8i			1.15145i	0.817644	+	0.575724i	$0.195280\pi$
$727$			22570.8i			1.15145i	−0.817644	+	0.575724i	$0.804720\pi$
$728$		−	79282.4i		−	4.03627i
$729$	−17580.7			−0.893194
$730$	39610.7	+	24476.5i	2.00830	+	1.24098i
$731$	−36246.0			−1.83394
$732$			58380.2i			2.94781i
$733$		−	4267.53i		−	0.215041i	−0.994203	−	0.107520i	$-0.965709\pi$
$733$		−	4267.53i		−	0.215041i	0.994203	−	0.107520i	$-0.0342911\pi$
$734$	7151.39			0.359622
$735$	15470.0	−	25035.2i	0.776352	−	1.25638i
$736$	859.484			0.0430448
$737$			14377.7i			0.718602i
$738$			1935.65i			0.0965479i
$739$	−35877.7			−1.78590			−0.892951	−	0.450154i	$-0.851369\pi$
$739$	−35877.7			−1.78590			−0.892951	+	0.450154i	$0.851369\pi$
$740$	−9192.22	+	14875.9i	−0.456639	+	0.738985i
$741$	27278.0			1.35234
$742$		−	5808.96i		−	0.287404i
$743$			6006.44i			0.296575i	0.988944	+	0.148287i	$0.0473760\pi$
$743$			6006.44i			0.296575i	−0.988944	+	0.148287i	$0.952624\pi$
$744$	−5862.97			−0.288907
$745$	11063.5	+	6836.41i	0.544072	+	0.336197i
$746$	49009.0			2.40529
$747$		−	2917.25i		−	0.142887i
$748$			20260.8i			0.990385i
$749$	5524.95			0.269529
$750$	−3360.22	+	37362.0i	−0.163597	+	1.81902i
$751$	29115.9			1.41472			0.707359	−	0.706855i	$-0.249887\pi$
$751$	29115.9			1.41472			0.707359	+	0.706855i	$0.249887\pi$
$752$			31717.4i			1.53805i
$753$		−	5218.02i		−	0.252530i
$754$	12003.1			0.579745
$755$	−1270.17	−	784.873i	−0.0612268	−	0.0378337i
$756$	−63087.0			−3.03499
$757$			16513.9i			0.792875i	0.918062	+	0.396438i	$0.129754\pi$
$757$			16513.9i			0.792875i	−0.918062	+	0.396438i	$0.870246\pi$
$758$			31802.5i			1.52390i
$759$	−2087.29			−0.0998208
$760$	−18763.1	+	30364.6i	−0.895538	+	1.44926i
$761$	7596.54			0.361859			0.180929	−	0.983496i	$-0.442089\pi$
$761$	7596.54			0.361859			0.180929	+	0.983496i	$0.442089\pi$
$762$			31593.8i			1.50200i
$763$		−	35632.0i		−	1.69065i
$764$	−35313.6			−1.67225
$765$	−1063.04	+	1720.34i	−0.0502411	+	0.0813059i
$766$	4360.79			0.205694
$767$			32603.8i			1.53488i
$768$		−	45276.7i		−	2.12732i
$769$	−10360.9			−0.485858			−0.242929	−	0.970044i	$-0.578108\pi$
$769$	−10360.9			−0.485858			−0.242929	+	0.970044i	$0.578108\pi$
$770$	−22631.9	−	13984.9i	−1.05922	−	0.654519i
$771$	−15198.6			−0.709942
$772$		−	59451.5i		−	2.77164i
$773$		−	28121.4i		−	1.30848i	−0.756286	−	0.654241i	$-0.772988\pi$
$773$		−	28121.4i		−	1.30848i	0.756286	−	0.654241i	$-0.227012\pi$
$774$	5982.59			0.277829
$775$	1443.91	+	2886.71i	0.0669248	+	0.133798i
$776$	26825.2			1.24094
$777$		−	14840.8i		−	0.685212i
$778$		−	43985.8i		−	2.02695i
$779$	12156.4			0.559114
$780$	−55956.2	−	34576.9i	−2.56866	−	1.58724i
$781$	19586.5			0.897390
$782$		−	8374.08i		−	0.382937i
$783$		−	4908.79i		−	0.224043i
$784$	−36484.9			−1.66203
$785$	7973.42	−	12903.5i	0.362527	−	0.586682i
$786$	−30013.8			−1.36203
$787$			23907.1i			1.08284i	0.840751	+	0.541421i	$0.182114\pi$
$787$			23907.1i			1.08284i	−0.840751	+	0.541421i	$0.817886\pi$
$788$			35474.1i			1.60370i
$789$	−39712.3			−1.79188
$790$	−14450.4	+	23385.3i	−0.650790	+	1.05318i
$791$	−52650.8			−2.36668
$792$		−	1718.71i		−	0.0771108i
$793$			43041.6i			1.92743i
$794$	17497.3			0.782060
$795$	−2107.11	−	1302.04i	−0.0940018	−	0.0580863i
$796$	−71866.4			−3.20004
$797$			25272.2i			1.12320i	0.827410	+	0.561598i	$0.189813\pi$
$797$			25272.2i			1.12320i	−0.827410	+	0.561598i	$0.810187\pi$
$798$		−	58941.8i		−	2.61468i
$799$	31038.7			1.37431
$800$	4177.64	−	2089.63i	0.184628	−	0.0923493i
$801$	−1328.76			−0.0586134
$802$		−	41092.2i		−	1.80925i
$803$			14080.8i			0.618806i
$804$	76811.6			3.36933
$805$	6294.58	+	3889.59i	0.275596	+	0.170298i
$806$	−8410.52			−0.367553
$807$		−	18611.4i		−	0.811838i
$808$			8607.18i			0.374752i
$809$	36235.2			1.57474			0.787368	−	0.616484i	$-0.211443\pi$
$809$	36235.2			1.57474			0.787368	+	0.616484i	$0.211443\pi$
$810$	−22941.8	+	37127.0i	−0.995176	+	1.61051i
$811$	−4007.44			−0.173514			−0.0867572	−	0.996229i	$-0.527650\pi$
$811$	−4007.44			−0.173514			−0.0867572	+	0.996229i	$0.527650\pi$
$812$		−	17453.0i		−	0.754285i
$813$			41294.7i			1.78139i
$814$	−7858.37			−0.338373
$815$	−21034.6	+	34040.6i	−0.904063	+	1.46306i
$816$	30058.4			1.28953
$817$		−	37572.4i		−	1.60892i
$818$			75349.4i			3.22070i
$819$	4656.20			0.198658
$820$	−24936.9	−	15409.2i	−1.06199	−	0.656234i
$821$	−18085.0			−0.768785			−0.384392	−	0.923170i	$-0.625589\pi$
$821$	−18085.0			−0.768785			−0.384392	+	0.923170i	$0.625589\pi$
$822$		−	4671.08i		−	0.198203i
$823$		−	5589.80i		−	0.236753i	−0.992969	−	0.118377i	$-0.962231\pi$
$823$		−	5589.80i		−	0.236753i	0.992969	−	0.118377i	$-0.0377690\pi$
$824$	−33066.3			−1.39796
$825$	−10145.6	+	5074.75i	−0.428150	+	0.214158i
$826$	70449.6			2.96762
$827$		−	9001.00i		−	0.378471i	−0.981932	−	0.189235i	$-0.939399\pi$
$827$		−	9001.00i		−	0.378471i	0.981932	−	0.189235i	$-0.0606010\pi$
$828$			930.104i			0.0390378i
$829$	35846.4			1.50181			0.750904	−	0.660412i	$-0.229618\pi$
$829$	35846.4			1.50181			0.750904	+	0.660412i	$0.229618\pi$
$830$	55849.9	+	34511.2i	2.33564	+	1.44325i
$831$	17134.3			0.715261
$832$		−	27464.7i		−	1.14443i
$833$			35704.3i			1.48509i
$834$	−23380.8			−0.970757
$835$	11188.4	−	18106.4i	0.463702	−	0.750414i
$836$	−21002.2			−0.868870
$837$			3439.56i			0.142041i
$838$			12911.1i			0.532229i
$839$	24753.9			1.01859			0.509296	−	0.860592i	$-0.329906\pi$
$839$	24753.9			1.01859			0.509296	+	0.860592i	$0.329906\pi$
$840$	−38398.4	+	62140.7i	−1.57723	+	2.55245i
$841$	−23031.0			−0.944319
$842$		−	29127.7i		−	1.19217i
$843$			12032.7i			0.491612i
$844$	22602.8			0.921825
$845$	−20358.7	−	12580.2i	−0.828831	−	0.512157i
$846$	−5123.10			−0.208198
$847$			30254.1i			1.22732i
$848$			3070.78i			0.124353i
$849$	−11737.8			−0.474486
$850$	−20359.5	−	40703.4i	−0.821560	−	1.64249i
$851$	2185.64			0.0880408
$852$		−	104639.i		−	4.20761i
$853$			17445.9i			0.700278i	0.936698	+	0.350139i	$0.113866\pi$
$853$			17445.9i			0.700278i	−0.936698	+	0.350139i	$0.886134\pi$
$854$	93003.3			3.72659
$855$	−1783.29	−	1101.94i	−0.0713301	−	0.0440768i
$856$	−8032.65			−0.320737
$857$			10455.3i			0.416738i	0.978050	+	0.208369i	$0.0668155\pi$
$857$			10455.3i			0.416738i	−0.978050	+	0.208369i	$0.933184\pi$
$858$		−	29559.5i		−	1.17616i
$859$	22362.5			0.888240			0.444120	−	0.895967i	$-0.353516\pi$
$859$	22362.5			0.888240			0.444120	+	0.895967i	$0.353516\pi$
$860$	−47625.7	+	77073.3i	−1.88840	+	3.05602i
$861$	24878.0			0.984715
$862$			75922.1i			2.99991i
$863$		−	17633.2i		−	0.695527i	−0.937582	−	0.347763i	$-0.886941\pi$
$863$		−	17633.2i		−	0.695527i	0.937582	−	0.347763i	$-0.113059\pi$
$864$	4977.74			0.196002
$865$	15868.4	−	25680.0i	0.623748	−	1.00942i
$866$	14220.5			0.558007
$867$		−	2750.27i		−	0.107733i
$868$			12229.2i			0.478210i
$869$	−8313.01			−0.324511
$870$	−9407.90	−	5813.40i	−0.366618	−	0.226543i
$871$	56630.4			2.20304
$872$			51804.9i			2.01185i
$873$			1575.43i			0.0610769i
$874$	8680.50			0.335952
$875$	40052.3	+	3602.18i	1.54745	+	0.139173i
$876$	75225.5			2.90141
$877$		−	3700.88i		−	0.142497i	−0.997459	−	0.0712486i	$-0.977302\pi$
$877$		−	3700.88i		−	0.142497i	0.997459	−	0.0712486i	$-0.0226984\pi$
$878$			68369.0i			2.62795i
$879$	13982.3			0.536532
$880$	11963.9	+	7392.80i	0.458298	+	0.283195i
$881$	7648.64			0.292496			0.146248	−	0.989248i	$-0.453280\pi$
$881$	7648.64			0.292496			0.146248	+	0.989248i	$0.453280\pi$
$882$		−	5893.17i		−	0.224981i
$883$		−	40610.2i		−	1.54772i	−0.633354	−	0.773862i	$-0.718322\pi$
$883$		−	40610.2i		−	1.54772i	0.633354	−	0.773862i	$-0.281678\pi$
$884$	79802.5			3.03625
$885$	15790.8	−	25554.5i	0.599777	−	0.970627i
$886$	−50588.6			−1.91824
$887$		−	27976.1i		−	1.05901i	−0.848305	−	0.529507i	$-0.822377\pi$
$887$		−	27976.1i		−	1.05901i	0.848305	−	0.529507i	$-0.177623\pi$
$888$			21576.8i			0.815395i
$889$	33868.8			1.27775
$890$	15719.3	−	25438.7i	0.592035	−	0.958098i
$891$	−13197.9			−0.496236
$892$			16545.0i			0.621040i
$893$			32174.5i			1.20569i
$894$	31223.2			1.16808
$895$	7174.28	+	4433.18i	0.267944	+	0.165570i
$896$	−67947.4			−2.53344
$897$			8221.36i			0.306024i
$898$			40146.6i			1.49188i
$899$	−951.553			−0.0353015
$900$	2261.32	+	4520.90i	0.0837526	+	0.167441i
$901$	3005.07			0.111114
$902$		−	13173.2i		−	0.486275i
$903$		−	76891.3i		−	2.83365i
$904$	76548.4			2.81633
$905$	−28595.1	−	17669.7i	−1.05031	−	0.649018i
$906$	−3584.67			−0.131449
$907$			4.67623i			0.000171192i	1.00000		8.55962e-5i	$2.72461e-5\pi$
$907$			4.67623i			0.000171192i	−1.00000		8.55962e-5i	$0.999973\pi$
$908$		−	48907.0i		−	1.78748i
$909$	−505.494			−0.0184446
$910$	−55083.1	+	89141.7i	−2.00658	+	3.24727i
$911$	−27794.1			−1.01082			−0.505411	−	0.862879i	$-0.668659\pi$
$911$	−27794.1			−1.01082			−0.505411	+	0.862879i	$0.668659\pi$
$912$			31158.3i			1.13131i
$913$			19853.5i			0.719666i
$914$	−58002.4			−2.09907
$915$	20846.1	−	33735.5i	0.753170	−	1.21887i
$916$	4789.67			0.172768
$917$			32175.1i			1.15869i
$918$		−	48498.8i		−	1.74368i
$919$	−29644.0			−1.06405			−0.532027	−	0.846727i	$-0.678570\pi$
$919$	−29644.0			−1.06405			−0.532027	+	0.846727i	$0.678570\pi$
$920$	−9151.62	−	5655.04i	−0.327956	−	0.202653i
$921$	17650.2			0.631480
$922$		−	7704.05i		−	0.275184i
$923$		−	77146.8i		−	2.75116i
$924$	−42980.7			−1.53026
$925$	10623.6	−	5313.85i	0.377624	−	0.188885i
$926$	9020.99			0.320139
$927$		−	1941.96i		−	0.0688051i
$928$			1377.09i			0.0487124i
$929$	10032.8			0.354324			0.177162	−	0.984182i	$-0.443308\pi$
$929$	10032.8			0.354324			0.177162	+	0.984182i	$0.443308\pi$
$930$	6592.07	+	4073.42i	0.232433	+	0.143627i
$931$	−37010.8			−1.30288
$932$			69383.0i			2.43854i
$933$			21462.3i			0.753103i
$934$	−64588.7			−2.26275
$935$	7234.62	−	11707.9i	0.253045	−	0.409506i
$936$	−6769.60			−0.236401
$937$		−	50301.8i		−	1.75377i	−0.480696	−	0.876887i	$-0.659616\pi$
$937$		−	50301.8i		−	1.75377i	0.480696	−	0.876887i	$-0.340384\pi$
$938$		−	122366.i		−	4.25947i
$939$	−34861.2			−1.21156
$940$	40783.5	−	66000.5i	1.41512	−	2.29010i
$941$	−35772.6			−1.23927			−0.619635	−	0.784890i	$-0.712720\pi$
$941$	−35772.6			−1.23927			−0.619635	+	0.784890i	$0.712720\pi$
$942$		−	36416.1i		−	1.25956i
$943$			3663.85i			0.126523i
$944$	−37241.7			−1.28402
$945$	36455.4	+	22526.8i	1.25491	+	0.775445i
$946$	−40714.9			−1.39932
$947$		−	22482.0i		−	0.771456i	−0.922613	−	0.385728i	$-0.873950\pi$
$947$		−	22482.0i		−	0.771456i	0.922613	−	0.385728i	$-0.126050\pi$
$948$			44411.6i			1.52154i
$949$	55461.0			1.89709
$950$	42192.8	−	21104.5i	1.44096	−	0.720760i
$951$	14018.9			0.478018
$952$		−	88622.5i		−	3.01709i
$953$		−	43503.4i		−	1.47871i	−0.673314	−	0.739357i	$-0.735130\pi$
$953$		−	43503.4i		−	1.47871i	0.673314	−	0.739357i	$-0.264870\pi$
$954$	−496.003			−0.0168330
$955$	20406.3	+	12609.6i	0.691447	+	0.427264i
$956$	−3856.66			−0.130474
$957$		−	3344.32i		−	0.112964i
$958$		−	89545.8i		−	3.01993i
$959$	−5007.44			−0.168612
$960$	−13301.8	+	21526.5i	−0.447203	+	0.723715i
$961$	−29124.3			−0.977619
$962$			30952.3i			1.03736i
$963$		−	471.752i		−	0.0157861i
$964$	−76440.5			−2.55392
$965$	−21228.6	+	34354.6i	−0.708160	+	1.14602i
$966$	17764.5			0.591682
$967$		−	22419.0i		−	0.745548i	−0.927922	−	0.372774i	$-0.878407\pi$
$967$		−	22419.0i		−	0.745548i	0.927922	−	0.372774i	$-0.121593\pi$
$968$		−	43986.0i		−	1.46050i
$969$	30491.6			1.01087
$970$	−30161.1	−	18637.4i	−0.998366	−	0.616918i
$971$	14978.2			0.495031			0.247515	−	0.968884i	$-0.420386\pi$
$971$	14978.2			0.495031			0.247515	+	0.968884i	$0.420386\pi$
$972$			11312.7i			0.373309i
$973$			25064.4i			0.825825i
$974$	−28068.9			−0.923393
$975$	19988.2	+	39961.1i	0.656550	+	1.31259i
$976$	−49164.2			−1.61241
$977$			31907.0i			1.04483i	0.852692	+	0.522413i	$0.174968\pi$
$977$			31907.0i			1.04483i	−0.852692	+	0.522413i	$0.825032\pi$
$978$			96069.3i			3.14106i
$979$	9042.94			0.295213
$980$	75921.3	+	46913.8i	2.47471	+	1.52919i
$981$	−3042.47			−0.0990198
$982$			13.6549i			0.000443732i
$983$			11156.9i			0.362005i	0.983483	+	0.181002i	$0.0579341\pi$
$983$			11156.9i			0.362005i	−0.983483	+	0.181002i	$0.942066\pi$
$984$	−36169.8			−1.17180
$985$	12666.9	−	20499.0i	0.409748	−	0.663100i
$986$	13417.2			0.433357
$987$			65844.7i			2.12346i
$988$			82722.6i			2.66372i
$989$	11324.0			0.364087
$990$	−1194.11	+	1932.44i	−0.0383347	+	0.0620375i
$991$	−18389.7			−0.589473			−0.294737	−	0.955579i	$-0.595232\pi$
$991$	−18389.7			−0.589473			−0.294737	+	0.955579i	$0.595232\pi$
$992$		−	964.919i		−	0.0308833i
$993$		−	38832.5i		−	1.24100i
$994$	−166697.			−5.31923
$995$	41528.6	+	25661.7i	1.32316	+	0.817617i
$996$	106066.			3.37432
$997$			49492.0i			1.57214i	0.618135	+	0.786072i	$0.287889\pi$
$997$			49492.0i			1.57214i	−0.618135	+	0.786072i	$0.712111\pi$
$998$			6135.64i			0.194610i
$999$	12658.2			0.400889

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	115.4.b.a.24.4	✓	34
5.2	odd	4		575.4.a.r.1.15		17
5.3	odd	4		575.4.a.q.1.3		17
5.4	even	2	inner	115.4.b.a.24.31	yes	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.4.b.a.24.4	✓	34	1.1	even	1	trivial
115.4.b.a.24.31	yes	34	5.4	even	2	inner
575.4.a.q.1.3		17	5.3	odd	4
575.4.a.r.1.15		17	5.2	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:	\( N \)	\(=\)	\( 115 = 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	115.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-4.94561i q^{2} +5.42743i q^{3} -16.4591 q^{4} +(9.51102 + 5.87712i) q^{5} +26.8419 q^{6} -28.7748i q^{7} +41.8353i q^{8} -2.45696 q^{9} +O(q^{10})\)	\(q-4.94561i q^{2} +5.42743i q^{3} -16.4591 q^{4} +(9.51102 + 5.87712i) q^{5} +26.8419 q^{6} -28.7748i q^{7} +41.8353i q^{8} -2.45696 q^{9} +(29.0660 - 47.0378i) q^{10} +16.7210 q^{11} -89.3304i q^{12} -65.8600i q^{13} -142.309 q^{14} +(-31.8976 + 51.6204i) q^{15} +75.2286 q^{16} -73.6189i q^{17} +12.1512i q^{18} +76.3128 q^{19} +(-156.543 - 96.7320i) q^{20} +156.173 q^{21} -82.6955i q^{22} +23.0000i q^{23} -227.058 q^{24} +(55.9189 + 111.795i) q^{25} -325.718 q^{26} +133.206i q^{27} +473.606i q^{28} -36.8512 q^{29} +(255.294 + 157.753i) q^{30} +25.8215 q^{31} -37.3689i q^{32} +90.7519i q^{33} -364.090 q^{34} +(169.113 - 273.677i) q^{35} +40.4393 q^{36} -95.0278i q^{37} -377.413i q^{38} +357.450 q^{39} +(-245.871 + 397.896i) q^{40} +159.298 q^{41} -772.371i q^{42} -492.347i q^{43} -275.212 q^{44} +(-23.3682 - 14.4398i) q^{45} +113.749 q^{46} +421.614i q^{47} +408.298i q^{48} -484.988 q^{49} +(552.894 - 276.553i) q^{50} +399.561 q^{51} +1084.00i q^{52} +40.8194i q^{53} +658.783 q^{54} +(159.034 + 98.2712i) q^{55} +1203.80 q^{56} +414.182i q^{57} +182.252i q^{58} -495.047 q^{59} +(525.006 - 849.623i) q^{60} -653.531 q^{61} -127.703i q^{62} +70.6985i q^{63} +417.017 q^{64} +(387.067 - 626.396i) q^{65} +448.824 q^{66} +859.860i q^{67} +1211.70i q^{68} -124.831 q^{69} +(-1353.50 - 836.366i) q^{70} +1171.37 q^{71} -102.788i q^{72} +842.104i q^{73} -469.970 q^{74} +(-606.758 + 303.496i) q^{75} -1256.04 q^{76} -481.143i q^{77} -1767.81i q^{78} -497.161 q^{79} +(715.500 + 442.127i) q^{80} -789.301 q^{81} -787.825i q^{82} +1187.34i q^{83} -2570.46 q^{84} +(432.667 - 700.190i) q^{85} -2434.96 q^{86} -200.007i q^{87} +699.528i q^{88} +540.814 q^{89} +(-71.4139 + 115.570i) q^{90} -1895.11 q^{91} -378.559i q^{92} +140.144i q^{93} +2085.14 q^{94} +(725.812 + 448.499i) q^{95} +202.817 q^{96} -641.210i q^{97} +2398.56i q^{98} -41.0828 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q - 144 q^{4} + 14 q^{5} + 24 q^{6} - 310 q^{9}+O(q^{10}) \) 34 * q - 144 * q^4 + 14 * q^5 + 24 * q^6 - 310 * q^9	\( 34 q - 144 q^{4} + 14 q^{5} + 24 q^{6} - 310 q^{9} + 14 q^{10} - 8 q^{11} + 236 q^{14} + 440 q^{16} + 144 q^{19} - 180 q^{20} - 32 q^{21} + 108 q^{24} + 134 q^{25} - 144 q^{26} + 56 q^{29} - 294 q^{30} - 80 q^{31} + 264 q^{34} + 116 q^{35} + 1864 q^{36} - 1200 q^{39} + 650 q^{40} + 268 q^{41} - 1612 q^{44} - 1346 q^{45} + 184 q^{46} - 1474 q^{49} + 120 q^{50} - 1104 q^{51} + 1564 q^{54} + 1160 q^{55} - 2300 q^{56} - 708 q^{59} - 516 q^{60} + 1100 q^{61} + 100 q^{64} + 1164 q^{65} - 1416 q^{66} - 552 q^{69} + 1144 q^{70} + 1360 q^{71} + 1588 q^{74} - 2064 q^{75} + 108 q^{76} + 3968 q^{79} + 2542 q^{80} + 4914 q^{81} - 1948 q^{84} + 124 q^{85} - 6148 q^{86} + 1196 q^{89} + 2760 q^{90} - 544 q^{91} - 2340 q^{94} + 3920 q^{95} + 2960 q^{96} - 3816 q^{99}+O(q^{100}) \) 34 * q - 144 * q^4 + 14 * q^5 + 24 * q^6 - 310 * q^9 + 14 * q^10 - 8 * q^11 + 236 * q^14 + 440 * q^16 + 144 * q^19 - 180 * q^20 - 32 * q^21 + 108 * q^24 + 134 * q^25 - 144 * q^26 + 56 * q^29 - 294 * q^30 - 80 * q^31 + 264 * q^34 + 116 * q^35 + 1864 * q^36 - 1200 * q^39 + 650 * q^40 + 268 * q^41 - 1612 * q^44 - 1346 * q^45 + 184 * q^46 - 1474 * q^49 + 120 * q^50 - 1104 * q^51 + 1564 * q^54 + 1160 * q^55 - 2300 * q^56 - 708 * q^59 - 516 * q^60 + 1100 * q^61 + 100 * q^64 + 1164 * q^65 - 1416 * q^66 - 552 * q^69 + 1144 * q^70 + 1360 * q^71 + 1588 * q^74 - 2064 * q^75 + 108 * q^76 + 3968 * q^79 + 2542 * q^80 + 4914 * q^81 - 1948 * q^84 + 124 * q^85 - 6148 * q^86 + 1196 * q^89 + 2760 * q^90 - 544 * q^91 - 2340 * q^94 + 3920 * q^95 + 2960 * q^96 - 3816 * q^99

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