LMFDB - Embedded newform 115.3.c.c.114.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [115,3,Mod(114,115)]

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, 1]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("115.114");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 115 = 5 \cdot 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	115.c (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.13352304014$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 6 x^{18} - 827 x^{16} - 12720 x^{14} + 346250 x^{12} + 9668500 x^{10} + 216406250 x^{8} + \cdots + 95367431640625 $ x^20 + 6x^18 - 827x^16 - 12720x^14 + 346250x^12 + 9668500x^10 + 216406250x^8 - 4968750000x^6 - 201904296875x^4 + 915527343750*x^2 + 95367431640625
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4}\cdot 5 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			114.13
Root			$0.993286 + 4.90035i$ of defining polynomial
Character	$\chi$	$=$	115.114
Dual form			115.3.c.c.114.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.10506i q^{2} -1.12745i q^{3} -0.431264 q^{4} +(-0.993286 + 4.90035i) q^{5} +2.37335 q^{6} -4.72229 q^{7} +7.51239i q^{8} +7.72885 q^{9} +O(q^{10})$	\(q+2.10506i q^{2} -1.12745i q^{3} -0.431264 q^{4} +(-0.993286 + 4.90035i) q^{5} +2.37335 q^{6} -4.72229 q^{7} +7.51239i q^{8} +7.72885 q^{9} +(-10.3155 - 2.09092i) q^{10} +8.84323i q^{11} +0.486229i q^{12} +8.75729i q^{13} -9.94069i q^{14} +(5.52490 + 1.11988i) q^{15} -17.5391 q^{16} -1.51883 q^{17} +16.2697i q^{18} -19.7862i q^{19} +(0.428369 - 2.11334i) q^{20} +5.32415i q^{21} -18.6155 q^{22} +(17.3122 - 15.1422i) q^{23} +8.46985 q^{24} +(-23.0268 - 9.73489i) q^{25} -18.4346 q^{26} -18.8610i q^{27} +2.03655 q^{28} +27.8949 q^{29} +(-2.35741 + 11.6302i) q^{30} +4.05824 q^{31} -6.87117i q^{32} +9.97030 q^{33} -3.19723i q^{34} +(4.69059 - 23.1408i) q^{35} -3.33318 q^{36} +49.6342 q^{37} +41.6511 q^{38} +9.87341 q^{39} +(-36.8133 - 7.46196i) q^{40} +15.8908 q^{41} -11.2076 q^{42} +35.4812 q^{43} -3.81377i q^{44} +(-7.67697 + 37.8741i) q^{45} +(31.8752 + 36.4432i) q^{46} -33.6286i q^{47} +19.7744i q^{48} -26.7000 q^{49} +(20.4925 - 48.4726i) q^{50} +1.71241i q^{51} -3.77670i q^{52} +29.2104 q^{53} +39.7034 q^{54} +(-43.3349 - 8.78386i) q^{55} -35.4757i q^{56} -22.3080 q^{57} +58.7203i q^{58} -57.1959 q^{59} +(-2.38269 - 0.482965i) q^{60} -96.2173i q^{61} +8.54282i q^{62} -36.4979 q^{63} -55.6921 q^{64} +(-42.9137 - 8.69849i) q^{65} +20.9881i q^{66} -89.7866 q^{67} +0.655018 q^{68} +(-17.0721 - 19.5187i) q^{69} +(48.7128 + 9.87395i) q^{70} -36.1309 q^{71} +58.0622i q^{72} +117.869i q^{73} +104.483i q^{74} +(-10.9756 + 25.9615i) q^{75} +8.53309i q^{76} -41.7603i q^{77} +20.7841i q^{78} -46.4212i q^{79} +(17.4213 - 85.9475i) q^{80} +48.2949 q^{81} +33.4510i q^{82} +114.118 q^{83} -2.29612i q^{84} +(1.50864 - 7.44280i) q^{85} +74.6899i q^{86} -31.4501i q^{87} -66.4338 q^{88} +65.0727i q^{89} +(-79.7270 - 16.1604i) q^{90} -41.3544i q^{91} +(-7.46614 + 6.53030i) q^{92} -4.57546i q^{93} +70.7901 q^{94} +(96.9593 + 19.6534i) q^{95} -7.74691 q^{96} -138.315 q^{97} -56.2050i q^{98} +68.3480i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 56 q^{4} - 8 q^{6} - 72 q^{9}+O(q^{10}) $ 20 * q - 56 * q^4 - 8 * q^6 - 72 * q^9	$ 20 q - 56 q^{4} - 8 q^{6} - 72 q^{9} + 88 q^{16} + 44 q^{24} - 12 q^{25} - 56 q^{26} + 236 q^{31} + 92 q^{35} - 32 q^{36} - 168 q^{39} + 124 q^{41} - 248 q^{46} + 88 q^{49} + 200 q^{50} - 196 q^{54} + 268 q^{55} + 56 q^{59} - 28 q^{64} + 376 q^{69} - 636 q^{70} - 196 q^{71} + 428 q^{75} - 988 q^{81} - 284 q^{85} + 276 q^{94} + 184 q^{95} - 264 q^{96}+O(q^{100}) $ 20 * q - 56 * q^4 - 8 * q^6 - 72 * q^9 + 88 * q^16 + 44 * q^24 - 12 * q^25 - 56 * q^26 + 236 * q^31 + 92 * q^35 - 32 * q^36 - 168 * q^39 + 124 * q^41 - 248 * q^46 + 88 * q^49 + 200 * q^50 - 196 * q^54 + 268 * q^55 + 56 * q^59 - 28 * q^64 + 376 * q^69 - 636 * q^70 - 196 * q^71 + 428 * q^75 - 988 * q^81 - 284 * q^85 + 276 * q^94 + 184 * q^95 - 264 * q^96

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 $

$2$			2.10506i			1.05253i	0.850321	+	0.526264i	$0.176408\pi$
$2$			2.10506i			1.05253i	−0.850321	+	0.526264i	$0.823592\pi$
$3$		−	1.12745i		−	0.375817i	−0.982187	−	0.187909i	$-0.939829\pi$
$3$		−	1.12745i		−	0.375817i	0.982187	−	0.187909i	$-0.0601708\pi$
$4$	−0.431264			−0.107816
$5$	−0.993286	+	4.90035i	−0.198657	+	0.980069i
$5$	−0.993286	+	4.90035i	−0.198657	+	0.980069i
$6$	2.37335			0.395558
$7$	−4.72229			−0.674613			−0.337306	−	0.941395i	$-0.609516\pi$
$7$	−4.72229			−0.674613			−0.337306	+	0.941395i	$0.609516\pi$
$8$			7.51239i			0.939049i
$9$	7.72885			0.858762
$10$	−10.3155	−	2.09092i	−1.03155	−	0.209092i
$11$			8.84323i			0.803930i	0.915655	+	0.401965i	$0.131673\pi$
$11$			8.84323i			0.803930i	−0.915655	+	0.401965i	$0.868327\pi$
$12$			0.486229i			0.0405191i
$13$			8.75729i			0.673637i	0.941570	+	0.336819i	$0.109351\pi$
$13$			8.75729i			0.673637i	−0.941570	+	0.336819i	$0.890649\pi$
$14$		−	9.94069i		−	0.710049i
$15$	5.52490	+	1.11988i	0.368327	+	0.0746588i
$16$	−17.5391			−1.09619
$17$	−1.51883			−0.0893431			−0.0446715	−	0.999002i	$-0.514224\pi$
$17$	−1.51883			−0.0893431			−0.0446715	+	0.999002i	$0.514224\pi$
$18$			16.2697i			0.903871i
$19$		−	19.7862i		−	1.04138i	−0.853746	−	0.520690i	$-0.825675\pi$
$19$		−	19.7862i		−	1.04138i	0.853746	−	0.520690i	$-0.174325\pi$
$20$	0.428369	−	2.11334i	0.0214184	−	0.105667i
$21$			5.32415i			0.253531i
$22$	−18.6155			−0.846159
$23$	17.3122	−	15.1422i	0.752705	−	0.658358i
$23$	17.3122	−	15.1422i	0.752705	−	0.658358i
$24$	8.46985			0.352911
$25$	−23.0268	−	9.73489i	−0.921071	−	0.389396i
$26$	−18.4346			−0.709022
$27$		−	18.8610i		−	0.698554i
$28$	2.03655			0.0727341
$29$	27.8949			0.961893			0.480946	−	0.876750i	$-0.340293\pi$
$29$	27.8949			0.961893			0.480946	+	0.876750i	$0.340293\pi$
$30$	−2.35741	+	11.6302i	−0.0785805	+	0.387674i
$31$	4.05824			0.130911			0.0654554	−	0.997855i	$-0.479150\pi$
$31$	4.05824			0.130911			0.0654554	+	0.997855i	$0.479150\pi$
$32$		−	6.87117i		−	0.214724i
$33$	9.97030			0.302130
$34$		−	3.19723i		−	0.0940361i
$35$	4.69059	−	23.1408i	0.134017	−	0.661167i
$36$	−3.33318			−0.0925883
$37$	49.6342			1.34147			0.670733	−	0.741699i	$-0.265980\pi$
$37$	49.6342			1.34147			0.670733	+	0.741699i	$0.265980\pi$
$38$	41.6511			1.09608
$39$	9.87341			0.253164
$40$	−36.8133	−	7.46196i	−0.920333	−	0.186549i
$41$	15.8908			0.387580			0.193790	−	0.981043i	$-0.437922\pi$
$41$	15.8908			0.387580			0.193790	+	0.981043i	$0.437922\pi$
$42$	−11.2076			−0.266849
$43$	35.4812			0.825144			0.412572	−	0.910925i	$-0.364631\pi$
$43$	35.4812			0.825144			0.412572	+	0.910925i	$0.364631\pi$
$44$		−	3.81377i		−	0.0866765i
$45$	−7.67697	+	37.8741i	−0.170599	+	0.841646i
$46$	31.8752	+	36.4432i	0.692940	+	0.792244i
$47$		−	33.6286i		−	0.715502i	−0.933817	−	0.357751i	$-0.883544\pi$
$47$		−	33.6286i		−	0.715502i	0.933817	−	0.357751i	$-0.116456\pi$
$48$			19.7744i			0.411968i
$49$	−26.7000			−0.544898
$50$	20.4925	−	48.4726i	0.409850	−	0.969453i
$51$			1.71241i			0.0335766i
$52$		−	3.77670i		−	0.0726289i
$53$	29.2104			0.551141			0.275570	−	0.961281i	$-0.411133\pi$
$53$	29.2104			0.551141			0.275570	+	0.961281i	$0.411133\pi$
$54$	39.7034			0.735248
$55$	−43.3349	−	8.78386i	−0.787906	−	0.159706i
$56$		−	35.4757i		−	0.633494i
$57$	−22.3080			−0.391368
$58$			58.7203i			1.01242i
$59$	−57.1959			−0.969422			−0.484711	−	0.874674i	$-0.661075\pi$
$59$	−57.1959			−0.969422			−0.484711	+	0.874674i	$0.661075\pi$
$60$	−2.38269	−	0.482965i	−0.0397115	−	0.00804942i
$61$		−	96.2173i		−	1.57733i	−0.614822	−	0.788666i	$-0.710772\pi$
$61$		−	96.2173i		−	1.57733i	0.614822	−	0.788666i	$-0.289228\pi$
$62$			8.54282i			0.137787i
$63$	−36.4979			−0.579332
$64$	−55.6921			−0.870189
$65$	−42.9137	−	8.69849i	−0.660211	−	0.133823i
$66$			20.9881i			0.318001i
$67$	−89.7866			−1.34010			−0.670050	−	0.742316i	$-0.733727\pi$
$67$	−89.7866			−1.34010			−0.670050	+	0.742316i	$0.733727\pi$
$68$	0.655018			0.00963262
$69$	−17.0721	−	19.5187i	−0.247422	−	0.282879i
$70$	48.7128	+	9.87395i	0.695897	+	0.141056i
$71$	−36.1309			−0.508885			−0.254443	−	0.967088i	$-0.581892\pi$
$71$	−36.1309			−0.508885			−0.254443	+	0.967088i	$0.581892\pi$
$72$			58.0622i			0.806419i
$73$			117.869i			1.61464i	0.590113	+	0.807321i	$0.299083\pi$
$73$			117.869i			1.61464i	−0.590113	+	0.807321i	$0.700917\pi$
$74$			104.483i			1.41193i
$75$	−10.9756	+	25.9615i	−0.146342	+	0.346154i
$76$			8.53309i			0.112277i
$77$		−	41.7603i		−	0.542341i
$78$			20.7841i			0.266463i
$79$		−	46.4212i		−	0.587610i	−0.955865	−	0.293805i	$-0.905078\pi$
$79$		−	46.4212i		−	0.587610i	0.955865	−	0.293805i	$-0.0949216\pi$
$80$	17.4213	−	85.9475i	0.217766	−	1.07434i
$81$	48.2949			0.596233
$82$			33.4510i			0.407939i
$83$	114.118			1.37491			0.687456	−	0.726226i	$-0.258727\pi$
$83$	114.118			1.37491			0.687456	+	0.726226i	$0.258727\pi$
$84$		−	2.29612i		−	0.0273347i
$85$	1.50864	−	7.44280i	0.0177487	−	0.0875624i
$86$			74.6899i			0.868487i
$87$		−	31.4501i		−	0.361496i
$88$	−66.4338			−0.754929
$89$			65.0727i			0.731153i	0.930781	+	0.365577i	$0.119128\pi$
$89$			65.0727i			0.731153i	−0.930781	+	0.365577i	$0.880872\pi$
$90$	−79.7270	−	16.1604i	−0.885856	−	0.179561i
$91$		−	41.3544i		−	0.454444i
$92$	−7.46614	+	6.53030i	−0.0811537	+	0.0709815i
$93$		−	4.57546i		−	0.0491985i
$94$	70.7901			0.753086
$95$	96.9593	+	19.6534i	1.02062	+	0.206878i
$96$	−7.74691			−0.0806970
$97$	−138.315			−1.42592			−0.712962	−	0.701202i	$-0.752647\pi$
$97$	−138.315			−1.42592			−0.712962	+	0.701202i	$0.752647\pi$
$98$		−	56.2050i		−	0.573520i
$99$			68.3480i			0.690384i
$100$	9.93062	+	4.19831i	0.0993062	+	0.0419831i
$101$	51.7472			0.512348			0.256174	−	0.966631i	$-0.417538\pi$
$101$	51.7472			0.512348			0.256174	+	0.966631i	$0.417538\pi$
$102$	−3.60472			−0.0353404
$103$	77.7604			0.754955			0.377478	−	0.926019i	$-0.376791\pi$
$103$	77.7604			0.754955			0.377478	+	0.926019i	$0.376791\pi$
$104$	−65.7882			−0.632578
$105$	−26.0902	−	5.28841i	−0.248478	−	0.0503658i
$106$			61.4897i			0.580091i
$107$	107.650			1.00607			0.503036	−	0.864266i	$-0.332216\pi$
$107$	107.650			1.00607			0.503036	+	0.864266i	$0.332216\pi$
$108$			8.13406i			0.0753154i
$109$			179.496i			1.64675i	0.567495	+	0.823377i	$0.307913\pi$
$109$			179.496i			1.64675i	−0.567495	+	0.823377i	$0.692087\pi$
$110$	18.4905	−	91.2223i	0.168096	−	0.829294i
$111$		−	55.9601i		−	0.504145i
$112$	82.8246			0.739505
$113$	−179.992			−1.59285			−0.796424	−	0.604739i	$-0.793278\pi$
$113$	−179.992			−1.59285			−0.796424	+	0.604739i	$0.793278\pi$
$114$		−	46.9596i		−	0.411926i
$115$	57.0061	+	99.8764i	0.495706	+	0.868491i
$116$	−12.0301			−0.103708
$117$			67.6838i			0.578494i
$118$		−	120.401i		−	1.02034i
$119$	7.17237			0.0602720
$120$	−8.41299	+	41.5052i	−0.0701082	+	0.345877i
$121$	42.7974			0.353697
$122$	202.543			1.66019
$123$		−	17.9161i		−	0.145659i
$124$	−1.75017			−0.0141143
$125$	70.5765	−	103.170i	0.564612	−	0.825356i
$126$		−	76.8301i		−	0.609763i
$127$		−	94.7208i		−	0.745833i	−0.927865	−	0.372916i	$-0.878358\pi$
$127$		−	94.7208i		−	0.745833i	0.927865	−	0.372916i	$-0.121642\pi$
$128$		−	144.720i		−	1.13062i
$129$		−	40.0033i		−	0.310103i
$130$	18.3108	−	90.3358i	0.140852	−	0.694891i
$131$	−47.3062			−0.361116			−0.180558	−	0.983564i	$-0.557790\pi$
$131$	−47.3062			−0.361116			−0.180558	+	0.983564i	$0.557790\pi$
$132$	−4.29984			−0.0325745
$133$			93.4362i			0.702528i
$134$		−	189.006i		−	1.41049i
$135$	92.4252	+	18.7343i	0.684631	+	0.138773i
$136$		−	11.4101i		−	0.0838975i
$137$	−89.9096			−0.656275			−0.328137	−	0.944630i	$-0.606421\pi$
$137$	−89.9096			−0.656275			−0.328137	+	0.944630i	$0.606421\pi$
$138$	41.0879	−	35.9378i	0.297739	−	0.260419i
$139$	−130.784			−0.940889			−0.470445	−	0.882430i	$-0.655906\pi$
$139$	−130.784			−0.940889			−0.470445	+	0.882430i	$0.655906\pi$
$140$	−2.02288	+	9.97982i	−0.0144492	+	0.0712844i
$141$	−37.9146			−0.268898
$142$		−	76.0575i		−	0.535616i
$143$	−77.4427			−0.541557
$144$	−135.557			−0.941367
$145$	−27.7076	+	136.695i	−0.191087	+	0.942721i
$146$	−248.121			−1.69946
$147$			30.1029i			0.204782i
$148$	−21.4055			−0.144631
$149$		−	92.4289i		−	0.620328i	−0.950683	−	0.310164i	$-0.899616\pi$
$149$		−	92.4289i		−	0.620328i	0.950683	−	0.310164i	$-0.100384\pi$
$150$	−54.6505	−	23.1043i	−0.364337	−	0.154029i
$151$	244.122			1.61670			0.808350	−	0.588703i	$-0.200361\pi$
$151$	244.122			1.61670			0.808350	+	0.588703i	$0.200361\pi$
$152$	148.642			0.977907
$153$	−11.7388			−0.0767244
$154$	87.9077			0.570829
$155$	−4.03099	+	19.8868i	−0.0260064	+	0.128302i
$156$	−4.25805			−0.0272952
$157$	−166.858			−1.06279			−0.531393	−	0.847125i	$-0.678331\pi$
$157$	−166.858			−1.06279			−0.531393	+	0.847125i	$0.678331\pi$
$158$	97.7192			0.618476
$159$		−	32.9334i		−	0.207128i
$160$	33.6711	+	6.82504i	0.210444	+	0.0426565i
$161$	−81.7533	+	71.5060i	−0.507785	+	0.444136i
$162$			101.663i			0.627552i
$163$		−	232.097i		−	1.42391i	−0.702225	−	0.711955i	$-0.747810\pi$
$163$		−	232.097i		−	1.42391i	0.702225	−	0.711955i	$-0.252190\pi$
$164$	−6.85312			−0.0417873
$165$	−9.90337	+	48.8579i	−0.0600204	+	0.296109i
$166$			240.224i			1.44713i
$167$		−	101.651i		−	0.608689i	−0.952562	−	0.304344i	$-0.901563\pi$
$167$		−	101.651i		−	0.608689i	0.952562	−	0.304344i	$-0.0984374\pi$
$168$	−39.9971			−0.238078
$169$	92.3099			0.546213
$170$	15.6675	+	3.17576i	0.0921619	+	0.0186810i
$171$		−	152.925i		−	0.894297i
$172$	−15.3018			−0.0889638
$173$			17.7428i			0.102559i	0.998684	+	0.0512797i	$0.0163300\pi$
$173$			17.7428i			0.102559i	−0.998684	+	0.0512797i	$0.983670\pi$
$174$	66.2043			0.380485
$175$	108.739	+	45.9710i	0.621366	+	0.262691i
$176$		−	155.102i		−	0.881261i
$177$			64.4856i			0.364325i
$178$	−136.982			−0.769560
$179$	207.961			1.16179			0.580895	−	0.813978i	$-0.302703\pi$
$179$	207.961			1.16179			0.580895	+	0.813978i	$0.302703\pi$
$180$	3.31080	−	16.3337i	0.0183933	−	0.0907429i
$181$		−	59.8275i		−	0.330539i	−0.986248	−	0.165269i	$-0.947151\pi$
$181$		−	59.8275i		−	0.330539i	0.986248	−	0.165269i	$-0.0528493\pi$
$182$	87.0534			0.478316
$183$	−108.480			−0.592788
$184$	113.754	+	130.056i	0.618230	+	0.706827i
$185$	−49.3010	+	243.225i	−0.266492	+	1.31473i
$186$	9.63161			0.0517828
$187$		−	13.4314i		−	0.0718255i
$188$			14.5028i			0.0771426i
$189$			89.0669i			0.471254i
$190$	−41.3715	+	204.105i	−0.217745	+	1.07424i
$191$			368.981i			1.93184i	0.258840	+	0.965920i	$0.416660\pi$
$191$			368.981i			1.93184i	−0.258840	+	0.965920i	$0.583340\pi$
$192$			62.7901i			0.327032i
$193$			0.810039i			0.00419709i	0.999998	+	0.00209855i	$0.000667988\pi$
$193$			0.810039i			0.00419709i	−0.999998	+	0.00209855i	$0.999332\pi$
$194$		−	291.160i		−	1.50083i
$195$	−9.80712	+	48.3831i	−0.0502929	+	0.248119i
$196$	11.5148			0.0587487
$197$			267.632i			1.35854i	0.733889	+	0.679269i	$0.237703\pi$
$197$			267.632i			1.35854i	−0.733889	+	0.679269i	$0.762297\pi$
$198$	−143.876			−0.726649
$199$		−	194.373i		−	0.976751i	−0.872634	−	0.488376i	$-0.837590\pi$
$199$		−	194.373i		−	0.976751i	0.872634	−	0.488376i	$-0.162410\pi$
$200$	73.1323	−	172.986i	0.365662	−	0.864930i
$201$			101.230i			0.503632i
$202$			108.931i			0.539261i
$203$	−131.728			−0.648905
$204$		−	0.738501i		−	0.00362010i
$205$	−15.7841	+	77.8703i	−0.0769956	+	0.379855i
$206$			163.690i			0.794612i
$207$	133.804	−	117.032i	0.646394	−	0.565372i
$208$		−	153.595i		−	0.738436i
$209$	174.974			0.837196
$210$	11.1324	−	54.9213i	0.0530114	−	0.261530i
$211$	−133.911			−0.634651			−0.317326	−	0.948317i	$-0.602785\pi$
$211$	−133.911			−0.634651			−0.317326	+	0.948317i	$0.602785\pi$
$212$	−12.5974			−0.0594218
$213$			40.7358i			0.191248i
$214$			226.609i			1.05892i
$215$	−35.2430	+	173.870i	−0.163921	+	0.808698i
$216$	141.691			0.655977
$217$	−19.1642			−0.0883141
$218$	−377.850			−1.73326
$219$	132.891			0.606810
$220$	18.6888	+	3.78816i	0.0849490	+	0.0172189i
$221$		−	13.3008i		−	0.0601848i
$222$	117.799			0.530627
$223$			81.8416i			0.367003i	0.983019	+	0.183501i	$0.0587432\pi$
$223$			81.8416i			0.367003i	−0.983019	+	0.183501i	$0.941257\pi$
$224$			32.4477i			0.144856i
$225$	−177.971	−	75.2396i	−0.790980	−	0.334398i
$226$		−	378.893i		−	1.67652i
$227$	−310.923			−1.36970			−0.684852	−	0.728683i	$-0.740133\pi$
$227$	−310.923			−1.36970			−0.684852	+	0.728683i	$0.740133\pi$
$228$	9.62064			0.0421958
$229$		−	83.2629i		−	0.363594i	−0.983336	−	0.181797i	$-0.941809\pi$
$229$		−	83.2629i		−	0.363594i	0.983336	−	0.181797i	$-0.0581913\pi$
$230$	−210.246	+	120.001i	−0.914111	+	0.521744i
$231$	−47.0827			−0.203821
$232$			209.557i			0.903265i
$233$		−	28.3926i		−	0.121857i	−0.998142	−	0.0609283i	$-0.980594\pi$
$233$		−	28.3926i		−	0.121857i	0.998142	−	0.0609283i	$-0.0194061\pi$
$234$	−142.478			−0.608881
$235$	164.792	+	33.4028i	0.701241	+	0.142140i
$236$	24.6666			0.104519
$237$	−52.3376			−0.220834
$238$			15.0982i			0.0634380i
$239$	−218.778			−0.915390			−0.457695	−	0.889109i	$-0.651325\pi$
$239$	−218.778			−0.915390			−0.457695	+	0.889109i	$0.651325\pi$
$240$	−96.9016	−	19.6417i	−0.403757	−	0.0818403i
$241$		−	271.370i		−	1.12602i	−0.826451	−	0.563009i	$-0.809644\pi$
$241$		−	271.370i		−	1.12602i	0.826451	−	0.563009i	$-0.190356\pi$
$242$			90.0909i			0.372276i
$243$		−	224.199i		−	0.922629i
$244$			41.4951i			0.170062i
$245$	26.5207	−	130.839i	0.108248	−	0.534037i
$246$	37.7144			0.153310
$247$	173.274			0.701512
$248$			30.4871i			0.122932i
$249$		−	128.662i		−	0.516715i
$250$	217.178	+	148.568i	0.868711	+	0.594270i
$251$		−	150.800i		−	0.600798i	−0.953814	−	0.300399i	$-0.902880\pi$
$251$		−	150.800i		−	0.600798i	0.953814	−	0.300399i	$-0.0971198\pi$
$252$	15.7402			0.0624613
$253$	133.906	+	153.096i	0.529273	+	0.605122i
$254$	199.393			0.785010
$255$	−8.39139	−	1.70091i	−0.0329074	−	0.00667024i
$256$	81.8748			0.319823
$257$		−	124.821i		−	0.485684i	−0.970066	−	0.242842i	$-0.921920\pi$
$257$		−	124.821i		−	0.485684i	0.970066	−	0.242842i	$-0.0780797\pi$
$258$	84.2092			0.326392
$259$	−234.387			−0.904969
$260$	18.5072	+	3.75135i	0.0711814	+	0.0144283i
$261$	215.596			0.826037
$262$		−	99.5822i		−	0.380085i
$263$	52.8302			0.200875			0.100438	−	0.994943i	$-0.467976\pi$
$263$	52.8302			0.200875			0.100438	+	0.994943i	$0.467976\pi$
$264$			74.9008i			0.283715i
$265$	−29.0143	+	143.141i	−0.109488	+	0.540156i
$266$	−196.689			−0.739431
$267$	73.3662			0.274780
$268$	38.7218			0.144484
$269$	−143.238			−0.532483			−0.266242	−	0.963906i	$-0.585782\pi$
$269$	−143.238			−0.532483			−0.266242	+	0.963906i	$0.585782\pi$
$270$	−39.4368	+	194.560i	−0.146062	+	0.720594i
$271$	9.21196			0.0339925			0.0169962	−	0.999856i	$-0.494590\pi$
$271$	9.21196			0.0339925			0.0169962	+	0.999856i	$0.494590\pi$
$272$	26.6389			0.0979371
$273$	−46.6251			−0.170788
$274$		−	189.265i		−	0.690748i
$275$	86.0878	−	203.631i	0.313047	−	0.740476i
$276$	7.36260	+	8.41771i	0.0266761	+	0.0304990i
$277$		−	475.243i		−	1.71568i	−0.513918	−	0.857839i	$-0.671806\pi$
$277$		−	475.243i		−	1.71568i	0.513918	−	0.857839i	$-0.328194\pi$
$278$		−	275.307i		−	0.990312i
$279$	31.3655			0.112421
$280$	173.843	+	35.2375i	0.620868	+	0.125848i
$281$			242.778i			0.863979i	0.901879	+	0.431990i	$0.142188\pi$
$281$			242.778i			0.863979i	−0.901879	+	0.431990i	$0.857812\pi$
$282$		−	79.8123i		−	0.283023i
$283$	−73.1111			−0.258343			−0.129172	−	0.991622i	$-0.541232\pi$
$283$	−73.1111			−0.258343			−0.129172	+	0.991622i	$0.541232\pi$
$284$	15.5820			0.0548660
$285$	22.1582	−	109.317i	0.0777481	−	0.383568i
$286$		−	163.021i		−	0.570004i
$287$	−75.0408			−0.261466
$288$		−	53.1063i		−	0.184397i
$289$	−286.693			−0.992018
$290$	−287.750	−	58.3261i	−0.992241	−	0.201125i
$291$			155.943i			0.535887i
$292$		−	50.8326i		−	0.174084i
$293$	374.244			1.27728			0.638642	−	0.769504i	$-0.279497\pi$
$293$	374.244			1.27728			0.638642	+	0.769504i	$0.279497\pi$
$294$	−63.3684			−0.215539
$295$	56.8119	−	280.280i	0.192583	−	0.950101i
$296$			372.872i			1.25970i
$297$	166.792			0.561588
$298$	194.568			0.652913
$299$	132.605	+	151.608i	0.443494	+	0.507050i
$300$	4.73339	−	11.1963i	0.0157780	−	0.0373210i
$301$	−167.552			−0.556652
$302$			513.890i			1.70162i
$303$		−	58.3424i		−	0.192549i
$304$			347.032i			1.14155i
$305$	471.498	+	95.5713i	1.54589	+	0.313349i
$306$		−	24.7109i		−	0.0807546i
$307$		−	516.100i		−	1.68111i	−0.541729	−	0.840553i	$-0.682230\pi$
$307$		−	516.100i		−	1.68111i	0.541729	−	0.840553i	$-0.317770\pi$
$308$			18.0097i			0.0584731i
$309$		−	87.6710i		−	0.283725i
$310$	−41.8628	−	8.48546i	−0.135041	−	0.0273725i
$311$	−273.791			−0.880358			−0.440179	−	0.897910i	$-0.645085\pi$
$311$	−273.791			−0.880358			−0.440179	+	0.897910i	$0.645085\pi$
$312$			74.1729i			0.237734i
$313$	−72.3728			−0.231223			−0.115612	−	0.993295i	$-0.536883\pi$
$313$	−72.3728			−0.231223			−0.115612	+	0.993295i	$0.536883\pi$
$314$		−	351.245i		−	1.11861i
$315$	36.2529	−	178.852i	0.115088	−	0.567785i
$316$			20.0198i			0.0633538i
$317$		−	108.562i		−	0.342466i	−0.985231	−	0.171233i	$-0.945225\pi$
$317$		−	108.562i		−	0.342466i	0.985231	−	0.171233i	$-0.0547751\pi$
$318$	69.3266			0.218008
$319$			246.681i			0.773294i
$320$	55.3182	−	272.910i	0.172869	−	0.852845i
$321$		−	121.370i		−	0.378099i
$322$	−150.524	−	172.095i	−0.467466	−	0.534458i
$323$			30.0519i			0.0930401i
$324$	−20.8279			−0.0642835
$325$	85.2512	−	201.652i	0.262311	−	0.620468i
$326$	488.578			1.49871
$327$	202.373			0.618878
$328$			119.378i			0.363957i
$329$			158.804i			0.482687i
$330$	−102.849	−	20.8471i	−0.311663	−	0.0631732i
$331$	−114.739			−0.346643			−0.173322	−	0.984865i	$-0.555450\pi$
$331$	−114.739			−0.346643			−0.173322	+	0.984865i	$0.555450\pi$
$332$	−49.2149			−0.148238
$333$	383.616			1.15200
$334$	213.981			0.640662
$335$	89.1838	−	439.986i	0.266220	−	1.31339i
$336$		−	93.3806i		−	0.277919i
$337$	−629.335			−1.86746			−0.933732	−	0.357973i	$-0.883468\pi$
$337$	−629.335			−1.86746			−0.933732	+	0.357973i	$0.883468\pi$
$338$			194.318i			0.574904i
$339$			202.932i			0.598619i
$340$	−0.650621	+	3.20981i	−0.00191359	+	0.00944063i
$341$			35.8879i			0.105243i
$342$	321.915			0.941273
$343$	357.477			1.04221
$344$			266.549i			0.774850i
$345$	112.606	−	64.2716i	0.326394	−	0.186295i
$346$	−37.3496			−0.107947
$347$			601.525i			1.73350i	0.498741	+	0.866751i	$0.333796\pi$
$347$			601.525i			1.73350i	−0.498741	+	0.866751i	$0.666204\pi$
$348$			13.5633i			0.0389750i
$349$	−188.680			−0.540631			−0.270315	−	0.962772i	$-0.587128\pi$
$349$	−188.680			−0.540631			−0.270315	+	0.962772i	$0.587128\pi$
$350$	−96.7715	+	228.902i	−0.276490	+	0.654005i
$351$	165.171			0.470572
$352$	60.7633			0.172623
$353$			454.678i			1.28804i	0.765009	+	0.644020i	$0.222735\pi$
$353$			454.678i			1.28804i	−0.765009	+	0.644020i	$0.777265\pi$
$354$	−135.746			−0.383463
$355$	35.8883	−	177.054i	0.101094	−	0.498743i
$356$		−	28.0635i		−	0.0788301i
$357$		−	8.08649i		−	0.0226512i
$358$			437.769i			1.22282i
$359$			432.967i			1.20604i	0.797728	+	0.603018i	$0.206035\pi$
$359$			432.967i			1.20604i	−0.797728	+	0.603018i	$0.793965\pi$
$360$	−284.525	−	57.6724i	−0.790346	−	0.160201i
$361$	−30.4944			−0.0844720
$362$	125.940			0.347901
$363$		−	48.2519i		−	0.132925i
$364$			17.8347i			0.0489964i
$365$	−577.598	−	117.077i	−1.58246	−	0.320760i
$366$		−	228.357i		−	0.623927i
$367$	−18.9820			−0.0517222			−0.0258611	−	0.999666i	$-0.508233\pi$
$367$	−18.9820			−0.0517222			−0.0258611	+	0.999666i	$0.508233\pi$
$368$	−303.640	+	265.581i	−0.825109	+	0.721686i
$369$	122.817			0.332839
$370$	−512.002	−	103.781i	−1.38379	−	0.280490i
$371$	−137.940			−0.371806
$372$			1.97323i			0.00530439i
$373$	187.416			0.502455			0.251228	−	0.967928i	$-0.419166\pi$
$373$	187.416			0.502455			0.251228	+	0.967928i	$0.419166\pi$
$374$	28.2738			0.0755984
$375$	−116.319	−	79.5715i	−0.310183	−	0.212191i
$376$	252.631			0.671891
$377$			244.284i			0.647967i
$378$	−187.491			−0.496008
$379$		−	654.337i		−	1.72648i	−0.504792	−	0.863241i	$-0.668431\pi$
$379$		−	654.337i		−	1.72648i	0.504792	−	0.863241i	$-0.331569\pi$
$380$	−41.8151	−	8.47580i	−0.110040	−	0.0223047i
$381$	−106.793			−0.280297
$382$	−776.727			−2.03332
$383$	−587.972			−1.53517			−0.767587	−	0.640944i	$-0.778543\pi$
$383$	−587.972			−1.53517			−0.767587	+	0.640944i	$0.778543\pi$
$384$	−163.164			−0.424907
$385$	204.640	+	41.4799i	0.531532	+	0.107740i
$386$	−1.70518			−0.00441756
$387$	274.229			0.708602
$388$	59.6502			0.153738
$389$			176.707i			0.454259i	0.973865	+	0.227130i	$0.0729341\pi$
$389$			176.707i			0.454259i	−0.973865	+	0.227130i	$0.927066\pi$
$390$	−101.849	−	20.6446i	−0.261152	−	0.0529348i
$391$	−26.2944	+	22.9985i	−0.0672490	+	0.0588197i
$392$		−	200.581i		−	0.511686i
$393$			53.3354i			0.135713i
$394$	−563.381			−1.42990
$395$	227.480	+	46.1095i	0.575898	+	0.116733i
$396$		−	29.4761i		−	0.0744345i
$397$		−	783.097i		−	1.97254i	−0.165148	−	0.986269i	$-0.552810\pi$
$397$		−	783.097i		−	1.97254i	0.165148	−	0.986269i	$-0.447190\pi$
$398$	409.167			1.02806
$399$	105.345			0.264022
$400$	403.868	+	170.741i	1.00967	+	0.426852i
$401$		−	325.446i		−	0.811586i	−0.913965	−	0.405793i	$-0.866995\pi$
$401$		−	325.446i		−	0.811586i	0.913965	−	0.405793i	$-0.133005\pi$
$402$	−213.095			−0.530087
$403$			35.5391i			0.0881864i
$404$	−22.3167			−0.0552394
$405$	−47.9706	+	236.662i	−0.118446	+	0.584350i
$406$		−	277.294i		−	0.682991i
$407$			438.926i			1.07844i
$408$	−12.8643			−0.0315301
$409$	−155.743			−0.380790			−0.190395	−	0.981708i	$-0.560977\pi$
$409$	−155.743			−0.380790			−0.190395	+	0.981708i	$0.560977\pi$
$410$	−163.921	−	33.2264i	−0.399808	−	0.0810400i
$411$			101.369i			0.246639i
$412$	−33.5353			−0.0813963
$413$	270.096			0.653984
$414$	246.359	+	281.664i	0.595070	+	0.680348i
$415$	−113.352	+	559.216i	−0.273136	+	1.34751i
$416$	60.1728			0.144646
$417$			147.452i			0.353602i
$418$			368.330i			0.881173i
$419$		−	461.518i		−	1.10148i	−0.834678	−	0.550738i	$-0.814346\pi$
$419$		−	461.518i		−	1.10148i	0.834678	−	0.550738i	$-0.185654\pi$
$420$	11.2518	+	2.28070i	0.0267899	+	0.00543024i
$421$			376.842i			0.895112i	0.894256	+	0.447556i	$0.147705\pi$
$421$			376.842i			0.895112i	−0.894256	+	0.447556i	$0.852295\pi$
$422$		−	281.891i		−	0.667988i
$423$		−	259.910i		−	0.614445i
$424$			219.440i			0.517548i
$425$	34.9738	+	14.7857i	0.0822913	+	0.0347898i
$426$	−85.7511			−0.201294
$427$			454.366i			1.06409i
$428$	−46.4254			−0.108471
$429$			87.3128i			0.203526i
$430$	−366.006	−	74.1885i	−0.851177	−	0.172531i
$431$			244.334i			0.566901i	0.958987	+	0.283450i	$0.0914791\pi$
$431$			244.334i			0.566901i	−0.958987	+	0.283450i	$0.908521\pi$
$432$			330.804i			0.765749i
$433$	440.925			1.01830			0.509152	−	0.860677i	$-0.329959\pi$
$433$	440.925			1.01830			0.509152	+	0.860677i	$0.329959\pi$
$434$		−	40.3417i		−	0.0929531i
$435$	154.116	+	31.2390i	0.354291	+	0.0718138i
$436$		−	77.4103i		−	0.177547i
$437$	−299.607	−	342.543i	−0.685600	−	0.783852i
$438$			279.744i			0.638684i
$439$	208.579			0.475122			0.237561	−	0.971373i	$-0.423652\pi$
$439$	208.579			0.475122			0.237561	+	0.971373i	$0.423652\pi$
$440$	65.9878	−	325.548i	0.149972	−	0.739883i
$441$	−206.360			−0.467937
$442$	27.9990			0.0633462
$443$			297.634i			0.671859i	0.941887	+	0.335929i	$0.109050\pi$
$443$			297.634i			0.671859i	−0.941887	+	0.335929i	$0.890950\pi$
$444$			24.1336i			0.0543550i
$445$	−318.878	−	64.6358i	−0.716581	−	0.145249i
$446$	−172.281			−0.386281
$447$	−104.209			−0.233130
$448$	262.994			0.587040
$449$	662.734			1.47602			0.738012	−	0.674788i	$-0.235765\pi$
$449$	662.734			1.47602			0.738012	+	0.674788i	$0.235765\pi$
$450$	158.384	−	374.638i	0.351963	−	0.832529i
$451$			140.526i			0.311587i
$452$	77.6241			0.171735
$453$		−	275.235i		−	0.607583i
$454$		−	654.510i		−	1.44165i
$455$	202.651	+	41.0768i	0.445387	+	0.0902787i
$456$		−	167.586i		−	0.367514i
$457$	−210.475			−0.460559			−0.230279	−	0.973125i	$-0.573964\pi$
$457$	−210.475			−0.460559			−0.230279	+	0.973125i	$0.573964\pi$
$458$	175.273			0.382693
$459$			28.6466i			0.0624110i
$460$	−24.5847	−	43.0731i	−0.0534450	−	0.0936373i
$461$	663.470			1.43920			0.719598	−	0.694391i	$-0.244326\pi$
$461$	663.470			1.43920			0.719598	+	0.694391i	$0.244326\pi$
$462$		−	99.1117i		−	0.214527i
$463$		−	130.126i		−	0.281050i	−0.990077	−	0.140525i	$-0.955121\pi$
$463$		−	130.126i		−	0.281050i	0.990077	−	0.140525i	$-0.0448791\pi$
$464$	−489.250			−1.05442
$465$	22.4213	+	4.54474i	0.0482179	+	0.00977364i
$466$	59.7681			0.128258
$467$	−316.631			−0.678010			−0.339005	−	0.940785i	$-0.610090\pi$
$467$	−316.631			−0.678010			−0.339005	+	0.940785i	$0.610090\pi$
$468$		−	29.1896i		−	0.0623709i
$469$	423.999			0.904048
$470$	−70.3148	+	346.896i	−0.149606	+	0.738076i
$471$			188.124i			0.399413i
$472$		−	429.678i		−	0.910335i
$473$			313.768i			0.663357i
$474$		−	110.174i		−	0.232434i
$475$	−192.617	+	455.613i	−0.405509	+	0.959184i
$476$	−3.09319			−0.00649829
$477$	225.763			0.473298
$478$		−	460.541i		−	0.963474i
$479$		−	223.544i		−	0.466689i	−0.972394	−	0.233344i	$-0.925033\pi$
$479$		−	223.544i		−	0.466689i	0.972394	−	0.233344i	$-0.0749669\pi$
$480$	7.69490	−	37.9625i	0.0160310	−	0.0790886i
$481$			434.661i			0.903661i
$482$	571.250			1.18517
$483$	80.6195	+	92.1729i	0.166914	+	0.190834i
$484$	−18.4570			−0.0381342
$485$	137.386	−	677.790i	0.283270	−	1.39750i
$486$	471.951			0.971093
$487$		−	507.679i		−	1.04246i	−0.853416	−	0.521231i	$-0.825473\pi$
$487$		−	507.679i		−	1.04246i	0.853416	−	0.521231i	$-0.174527\pi$
$488$	722.822			1.48119
$489$	−261.679			−0.535130
$490$	275.424	+	55.8276i	0.562089	+	0.113934i
$491$	−241.993			−0.492857			−0.246429	−	0.969161i	$-0.579257\pi$
$491$	−241.993			−0.492857			−0.246429	+	0.969161i	$0.579257\pi$
$492$			7.72656i			0.0157044i
$493$	−42.3677			−0.0859385
$494$			364.751i			0.738362i
$495$	−334.929	−	67.8891i	−0.676624	−	0.137150i
$496$	−71.1777			−0.143503
$497$	170.620			0.343301
$498$	270.841			0.543858
$499$	903.334			1.81029			0.905144	−	0.425105i	$-0.139763\pi$
$499$	903.334			1.81029			0.905144	+	0.425105i	$0.139763\pi$
$500$	−30.4371	+	44.4933i	−0.0608743	+	0.0889867i
$501$	−114.607			−0.228756
$502$	317.443			0.632357
$503$	−784.248			−1.55914			−0.779570	−	0.626315i	$-0.784562\pi$
$503$	−784.248			−1.55914			−0.779570	+	0.626315i	$0.784562\pi$
$504$		−	274.186i		−	0.544021i
$505$	−51.3997	+	253.579i	−0.101782	+	0.502137i
$506$	−322.276	+	281.880i	−0.636908	+	0.557075i
$507$		−	104.075i		−	0.205276i
$508$			40.8497i			0.0804128i
$509$	−771.140			−1.51501			−0.757505	−	0.652829i	$-0.773582\pi$
$509$	−771.140			−1.51501			−0.757505	+	0.652829i	$0.773582\pi$
$510$	3.58052	−	17.6644i	0.00702062	−	0.0346360i
$511$		−	556.611i		−	1.08926i
$512$		−	406.527i		−	0.793999i
$513$	−373.187			−0.727460
$514$	262.755			0.511196
$515$	−77.2383	+	381.053i	−0.149977	+	0.739908i
$516$			17.2520i			0.0334341i
$517$	297.385			0.575213
$518$		−	493.398i		−	0.952506i
$519$	20.0041			0.0385436
$520$	65.3465	−	322.385i	0.125666	−	0.619971i
$521$			355.019i			0.681418i	0.940169	+	0.340709i	$0.110667\pi$
$521$			355.019i			0.681418i	−0.940169	+	0.340709i	$0.889333\pi$
$522$			453.841i			0.869427i
$523$	349.799			0.668832			0.334416	−	0.942426i	$-0.391461\pi$
$523$	349.799			0.668832			0.334416	+	0.942426i	$0.391461\pi$
$524$	20.4015			0.0389341
$525$	51.8300	−	122.598i	0.0987239	−	0.233520i
$526$			111.211i			0.211427i
$527$	−6.16378			−0.0116960
$528$	−174.870			−0.331193
$529$	70.4260	−	524.291i	0.133130	−	0.991099i
$530$	−301.321	−	61.0768i	−0.568529	−	0.115239i
$531$	−442.059			−0.832502
$532$		−	40.2957i		−	0.0757438i
$533$			139.160i			0.261088i
$534$			154.440i			0.289214i
$535$	−106.927	+	527.520i	−0.199863	+	0.986019i
$536$		−	674.512i		−	1.25842i
$537$		−	234.465i		−	0.436621i
$538$		−	301.524i		−	0.560454i
$539$		−	236.114i		−	0.438059i
$540$	−39.8597	−	8.07945i	−0.0738143	−	0.0149619i
$541$	−345.367			−0.638387			−0.319194	−	0.947690i	$-0.603412\pi$
$541$	−345.367			−0.638387			−0.319194	+	0.947690i	$0.603412\pi$
$542$			19.3917i			0.0357780i
$543$	−67.4525			−0.124222
$544$			10.4362i			0.0191841i
$545$	−879.593	−	178.291i	−1.61393	−	0.327140i
$546$		−	98.1485i		−	0.179759i
$547$			526.178i			0.961935i	0.876739	+	0.480967i	$0.159714\pi$
$547$			526.178i			0.961935i	−0.876739	+	0.480967i	$0.840286\pi$
$548$	38.7748			0.0707570
$549$		−	743.649i		−	1.35455i
$550$	428.655	+	181.220i	0.779372	+	0.329491i
$551$		−	551.934i		−	1.00170i
$552$	146.632	−	128.252i	0.265638	−	0.232341i
$553$			219.214i			0.396409i
$554$	1000.41			1.80580
$555$	274.224	+	55.5844i	0.494097	+	0.100152i
$556$	56.4023			0.101443
$557$	945.958			1.69831			0.849155	−	0.528144i	$-0.177112\pi$
$557$	945.958			1.69831			0.849155	+	0.528144i	$0.177112\pi$
$558$			66.0262i			0.118327i
$559$			310.719i			0.555848i
$560$	−82.2685	+	405.869i	−0.146908	+	0.724766i
$561$	−15.1432			−0.0269933
$562$	−511.062			−0.909363
$563$	−522.991			−0.928936			−0.464468	−	0.885590i	$-0.653754\pi$
$563$	−522.991			−0.928936			−0.464468	+	0.885590i	$0.653754\pi$
$564$	16.3512			0.0289915
$565$	178.783	−	882.022i	0.316431	−	1.56110i
$566$		−	153.903i		−	0.271914i
$567$	−228.062			−0.402226
$568$		−	271.429i		−	0.477868i
$569$			140.348i			0.246658i	0.992366	+	0.123329i	$0.0393570\pi$
$569$			140.348i			0.246658i	−0.992366	+	0.123329i	$0.960643\pi$
$570$	230.118	+	46.6443i	0.403716	+	0.0818321i
$571$			171.380i			0.300141i	0.988675	+	0.150070i	$0.0479500\pi$
$571$			171.380i			0.300141i	−0.988675	+	0.150070i	$0.952050\pi$
$572$	33.3983			0.0583886
$573$	416.009			0.726018
$574$		−	157.965i		−	0.275201i
$575$	−546.052	+	180.144i	−0.949656	+	0.313294i
$576$	−430.436			−0.747285
$577$			787.037i			1.36401i	0.731345	+	0.682007i	$0.238893\pi$
$577$			787.037i			1.36401i	−0.731345	+	0.682007i	$0.761107\pi$
$578$		−	603.505i		−	1.04413i
$579$	0.913279			0.00157734
$580$	11.9493	−	58.9515i	0.0206023	−	0.101641i
$581$	−538.897			−0.927533
$582$	−328.269			−0.564036
$583$			258.315i			0.443078i
$584$	−885.477			−1.51623
$585$	−331.674	−	67.2294i	−0.566964	−	0.114922i
$586$			787.805i			1.34438i
$587$			322.491i			0.549388i	0.961532	+	0.274694i	$0.0885765\pi$
$587$			322.491i			0.549388i	−0.961532	+	0.274694i	$0.911423\pi$
$588$		−	12.9823i		−	0.0220788i
$589$		−	80.2971i		−	0.136328i
$590$	590.005	+	119.592i	1.00001	+	0.202699i
$591$	301.742			0.510562
$592$	−870.538			−1.47050
$593$		−	207.526i		−	0.349959i	−0.984572	−	0.174980i	$-0.944014\pi$
$593$		−	207.526i		−	0.349959i	0.984572	−	0.174980i	$-0.0559859\pi$
$594$			351.106i			0.591088i
$595$	−7.12421	+	35.1471i	−0.0119735	+	0.0590707i
$596$			39.8613i			0.0668814i
$597$	−219.147			−0.367080
$598$	−319.144	+	279.141i	−0.533685	+	0.466790i
$599$	−507.894			−0.847904			−0.423952	−	0.905685i	$-0.639357\pi$
$599$	−507.894			−0.847904			−0.423952	+	0.905685i	$0.639357\pi$
$600$	−195.033	−	82.4531i	−0.325056	−	0.137422i
$601$	1137.17			1.89213			0.946063	−	0.323982i	$-0.105022\pi$
$601$	1137.17			1.89213			0.946063	+	0.323982i	$0.105022\pi$
$602$		−	352.707i		−	0.585893i
$603$	−693.948			−1.15083
$604$	−105.281			−0.174306
$605$	−42.5100	+	209.722i	−0.0702645	+	0.346648i
$606$	122.814			0.202663
$607$			460.047i			0.757902i	0.925417	+	0.378951i	$0.123715\pi$
$607$			460.047i			0.757902i	−0.925417	+	0.378951i	$0.876285\pi$
$608$	−135.954			−0.223609
$609$			148.517i			0.243870i
$610$	−201.183	+	992.530i	−0.329808	+	1.62710i
$611$	294.495			0.481989
$612$	5.06254			0.00827212
$613$	−75.2299			−0.122724			−0.0613621	−	0.998116i	$-0.519544\pi$
$613$	−75.2299			−0.122724			−0.0613621	+	0.998116i	$0.519544\pi$
$614$	1086.42			1.76941
$615$	87.7949	+	17.7958i	0.142756	+	0.0289362i
$616$	313.719			0.509285
$617$	−305.214			−0.494674			−0.247337	−	0.968930i	$-0.579555\pi$
$617$	−305.214			−0.494674			−0.247337	+	0.968930i	$0.579555\pi$
$618$	184.553			0.298629
$619$			456.404i			0.737325i	0.929563	+	0.368662i	$0.120184\pi$
$619$			456.404i			0.737325i	−0.929563	+	0.368662i	$0.879816\pi$
$620$	1.73842	−	8.57645i	0.00280391	−	0.0138330i
$621$	−285.597	−	326.525i	−0.459899	−	0.525805i
$622$		−	576.346i		−	0.926601i
$623$		−	307.292i		−	0.493245i
$624$	−173.170			−0.277517
$625$	435.464	+	448.326i	0.696742	+	0.717322i
$626$		−	152.349i		−	0.243369i
$627$		−	197.275i		−	0.314633i
$628$	71.9597			0.114586
$629$	−75.3860			−0.119851
$630$	376.494	+	76.3143i	0.597610	+	0.121134i
$631$			1133.73i			1.79672i	0.439260	+	0.898360i	$0.355241\pi$
$631$			1133.73i			1.79672i	−0.439260	+	0.898360i	$0.644759\pi$
$632$	348.734			0.551794
$633$			150.979i			0.238513i
$634$	228.529			0.360455
$635$	464.164	+	94.0848i	0.730968	+	0.148165i
$636$			14.2030i			0.0223317i
$637$		−	233.819i		−	0.367063i
$638$	−519.277			−0.813914
$639$	−279.250			−0.437011
$640$	709.176	+	143.748i	1.10809	+	0.224606i
$641$		−	904.020i		−	1.41033i	−0.709044	−	0.705164i	$-0.750873\pi$
$641$		−	904.020i		−	1.41033i	0.709044	−	0.705164i	$-0.249127\pi$
$642$	255.490			0.397960
$643$	−1049.41			−1.63206			−0.816028	−	0.578013i	$-0.803828\pi$
$643$	−1049.41			−1.63206			−0.816028	+	0.578013i	$0.803828\pi$
$644$	35.2573	−	30.8380i	0.0547473	−	0.0478851i
$645$	196.030	+	39.7347i	0.303922	+	0.0616042i
$646$	−63.2611			−0.0979273
$647$			1279.12i			1.97700i	0.151208	+	0.988502i	$0.451684\pi$
$647$			1279.12i			1.97700i	−0.151208	+	0.988502i	$0.548316\pi$
$648$			362.810i			0.559892i
$649$		−	505.796i		−	0.779347i
$650$	424.489	+	179.459i	0.653060	+	0.276090i
$651$			21.6067i			0.0331900i
$652$			100.095i			0.153520i
$653$		−	1020.82i		−	1.56328i	−0.623731	−	0.781639i	$-0.714384\pi$
$653$		−	1020.82i		−	1.56328i	0.623731	−	0.781639i	$-0.285616\pi$
$654$			426.007i			0.651387i
$655$	46.9886	−	231.817i	0.0717383	−	0.353918i
$656$	−278.709			−0.424862
$657$			910.991i			1.38659i
$658$	−334.291			−0.508041
$659$			791.953i			1.20175i	0.799343	+	0.600875i	$0.205181\pi$
$659$			791.953i			1.20175i	−0.799343	+	0.600875i	$0.794819\pi$
$660$	4.27097	−	21.0707i	0.00647116	−	0.0319253i
$661$		−	197.840i		−	0.299304i	−0.988739	−	0.149652i	$-0.952185\pi$
$661$		−	197.840i		−	0.299304i	0.988739	−	0.149652i	$-0.0478153\pi$
$662$		−	241.532i		−	0.364852i
$663$	−14.9961			−0.0226185
$664$			857.297i			1.29111i
$665$	−457.870	−	92.8089i	−0.688526	−	0.139562i
$666$			807.533i			1.21251i
$667$	482.923	−	422.391i	0.724022	−	0.633270i
$668$			43.8385i			0.0656265i
$669$	92.2724			0.137926
$670$	926.195	+	187.737i	1.38238	+	0.280205i
$671$	850.871			1.26806
$672$	36.5831			0.0544392
$673$			1067.06i			1.58552i	0.609534	+	0.792760i	$0.291357\pi$
$673$			1067.06i			1.58552i	−0.609534	+	0.792760i	$0.708643\pi$
$674$		−	1324.79i		−	1.96556i
$675$	−183.609	+	434.307i	−0.272014	+	0.643418i
$676$	−39.8100			−0.0588905
$677$	1197.09			1.76823			0.884115	−	0.467269i	$-0.154762\pi$
$677$	1197.09			1.76823			0.884115	+	0.467269i	$0.154762\pi$
$678$	−427.183			−0.630064
$679$	653.162			0.961947
$680$	55.9132	+	11.3335i	0.0822254	+	0.0166669i
$681$			350.550i			0.514758i
$682$	−75.5461			−0.110771
$683$		−	550.536i		−	0.806056i	−0.915188	−	0.403028i	$-0.867958\pi$
$683$		−	550.536i		−	0.806056i	0.915188	−	0.403028i	$-0.132042\pi$
$684$			65.9510i			0.0964196i
$685$	89.3060	−	440.588i	0.130374	−	0.643194i
$686$			752.510i			1.09695i
$687$	−93.8749			−0.136645
$688$	−622.307			−0.904516
$689$			255.804i			0.371269i
$690$	135.295	+	237.042i	0.196080	+	0.343538i
$691$	−337.110			−0.487858			−0.243929	−	0.969793i	$-0.578436\pi$
$691$	−337.110			−0.487858			−0.243929	+	0.969793i	$0.578436\pi$
$692$		−	7.65183i		−	0.0110576i
$693$		−	322.759i		−	0.465742i
$694$	−1266.24			−1.82456
$695$	129.906	−	640.885i	0.186914	−	0.922136i
$696$	236.266			0.339462
$697$	−24.1354			−0.0346276
$698$		−	397.182i		−	0.569029i
$699$	−32.0113			−0.0457958
$700$	−46.8953	−	19.8256i	−0.0669932	−	0.0283223i
$701$		−	592.555i		−	0.845300i	−0.906293	−	0.422650i	$-0.861100\pi$
$701$		−	592.555i		−	0.845300i	0.906293	−	0.422650i	$-0.138900\pi$
$702$			347.694i			0.495291i
$703$		−	982.073i		−	1.39697i
$704$		−	492.498i		−	0.699570i
$705$	37.6600	−	185.795i	0.0534185	−	0.263538i
$706$	−957.123			−1.35570
$707$	−244.365			−0.345637
$708$		−	27.8103i		−	0.0392801i
$709$			665.746i			0.938993i	0.882934	+	0.469496i	$0.155565\pi$
$709$			665.746i			0.938993i	−0.882934	+	0.469496i	$0.844435\pi$
$710$	372.708	+	75.5469i	0.524941	+	0.106404i
$711$		−	358.782i		−	0.504617i
$712$	−488.851			−0.686589
$713$	70.2571	−	61.4507i	0.0985373	−	0.0861862i
$714$	17.0225			0.0238411
$715$	76.9227	−	379.496i	0.107584	−	0.530763i
$716$	−89.6860			−0.125260
$717$			246.662i			0.344019i
$718$	−911.420			−1.26939
$719$	−950.921			−1.32256			−0.661280	−	0.750139i	$-0.729987\pi$
$719$	−950.921			−1.32256			−0.661280	+	0.750139i	$0.729987\pi$
$720$	134.647	−	664.276i	0.187009	−	0.922605i
$721$	−367.207			−0.509302
$722$		−	64.1924i		−	0.0889092i
$723$	−305.957			−0.423177
$724$			25.8015i			0.0356374i
$725$	−642.329	−	271.554i	−0.885971	−	0.374557i
$726$	101.573			0.139908
$727$	447.443			0.615465			0.307732	−	0.951473i	$-0.400430\pi$
$727$	447.443			0.615465			0.307732	+	0.951473i	$0.400430\pi$
$728$	310.671			0.426746
$729$	181.881			0.249493
$730$	246.455	−	1215.88i	0.337609	−	1.66558i
$731$	−53.8900			−0.0737209
$732$	46.7837			0.0639121
$733$	581.960			0.793942			0.396971	−	0.917831i	$-0.370061\pi$
$733$	581.960			0.793942			0.396971	+	0.917831i	$0.370061\pi$
$734$		−	39.9583i		−	0.0544391i
$735$	−147.515	−	29.9008i	−0.200700	−	0.0406814i
$736$	−104.045	−	118.955i	−0.141365	−	0.161624i
$737$		−	794.004i		−	1.07735i
$738$			258.538i			0.350322i
$739$	−878.311			−1.18851			−0.594257	−	0.804276i	$-0.702554\pi$
$739$	−878.311			−1.18851			−0.594257	+	0.804276i	$0.702554\pi$
$740$	21.2618	−	104.894i	0.0287321	−	0.141749i
$741$		−	195.357i		−	0.263640i
$742$		−	290.372i		−	0.391337i
$743$	−101.796			−0.137006			−0.0685032	−	0.997651i	$-0.521822\pi$
$743$	−101.796			−0.137006			−0.0685032	+	0.997651i	$0.521822\pi$
$744$	34.3727			0.0461998
$745$	452.934	+	91.8084i	0.607964	+	0.123233i
$746$			394.521i			0.528849i
$747$	881.999			1.18072
$748$			5.79247i			0.00774395i
$749$	−508.353			−0.678709
$750$	167.503	−	244.857i	0.223337	−	0.326476i
$751$		−	377.197i		−	0.502260i	−0.967953	−	0.251130i	$-0.919198\pi$
$751$		−	377.197i		−	0.502260i	0.967953	−	0.251130i	$-0.0808022\pi$
$752$			589.814i			0.784327i
$753$	−170.020			−0.225790
$754$	−514.231			−0.682004
$755$	−242.483	+	1196.28i	−0.321169	+	1.58448i
$756$		−	38.4114i		−	0.0508087i
$757$	−347.543			−0.459106			−0.229553	−	0.973296i	$-0.573726\pi$
$757$	−347.543			−0.459106			−0.229553	+	0.973296i	$0.573726\pi$
$758$	1377.42			1.81717
$759$	172.608	−	150.973i	0.227415	−	0.198910i
$760$	−147.644	+	728.396i	−0.194268	+	0.958416i
$761$	369.308			0.485292			0.242646	−	0.970115i	$-0.421985\pi$
$761$	369.308			0.485292			0.242646	+	0.970115i	$0.421985\pi$
$762$		−	224.805i		−	0.295020i
$763$		−	847.633i		−	1.11092i
$764$		−	159.129i		−	0.208283i
$765$	11.6600	−	57.5243i	0.0152419	−	0.0751952i
$766$		−	1237.71i		−	1.61581i
$767$		−	500.881i		−	0.653039i
$768$		−	92.3098i		−	0.120195i
$769$			1049.11i			1.36426i	0.731233	+	0.682128i	$0.238945\pi$
$769$			1049.11i			1.36426i	−0.731233	+	0.682128i	$0.761055\pi$
$770$	−87.3176	+	430.778i	−0.113399	+	0.559452i
$771$	−140.729			−0.182528
$772$		−	0.349341i		−	0.000452514i
$773$	1056.22			1.36639			0.683195	−	0.730236i	$-0.260590\pi$
$773$	1056.22			1.36639			0.683195	+	0.730236i	$0.260590\pi$
$774$			577.267i			0.745823i
$775$	−93.4480	−	39.5065i	−0.120578	−	0.0509761i
$776$		−	1039.07i		−	1.33901i
$777$			264.260i			0.340103i
$778$	−371.978			−0.478121
$779$		−	314.418i		−	0.403618i
$780$	4.22946	−	20.8659i	0.00542239	−	0.0267512i
$781$		−	319.513i		−	0.409108i
$782$	−48.4132	−	55.3511i	−0.0619094	−	0.0707815i
$783$		−	526.125i		−	0.671934i
$784$	468.293			0.597312
$785$	165.737	−	817.659i	0.211130	−	1.04160i
$786$	−112.274			−0.142842
$787$	−1082.10			−1.37497			−0.687485	−	0.726199i	$-0.741285\pi$
$787$	−1082.10			−1.37497			−0.687485	+	0.726199i	$0.741285\pi$
$788$		−	115.420i		−	0.146472i
$789$		−	59.5635i		−	0.0754924i
$790$	−97.0631	+	478.858i	−0.122865	+	0.606149i
$791$	849.974			1.07456
$792$	−513.457			−0.648304
$793$	842.602			1.06255
$794$	1648.46			2.07615
$795$	161.385	+	32.7122i	0.203000	+	0.0411475i
$796$			83.8263i			0.105309i
$797$	1182.29			1.48343			0.741715	−	0.670715i	$-0.234013\pi$
$797$	1182.29			1.48343			0.741715	+	0.670715i	$0.234013\pi$
$798$			221.757i			0.277891i
$799$			51.0762i			0.0639251i
$800$	−66.8901	+	158.221i	−0.0836126	+	0.197776i
$801$			502.937i			0.627886i
$802$	685.082			0.854217
$803$	−1042.34			−1.29806
$804$		−	43.6569i		−	0.0542996i
$805$	−269.199	−	471.645i	−0.334409	−	0.585895i
$806$	−74.8119			−0.0928187
$807$			161.494i			0.200116i
$808$			388.745i			0.481120i
$809$	−874.487			−1.08095			−0.540474	−	0.841361i	$-0.681755\pi$
$809$	−874.487			−1.08095			−0.540474	+	0.841361i	$0.681755\pi$
$810$	−498.186	−	100.981i	−0.615044	−	0.124668i
$811$	1052.55			1.29784			0.648920	−	0.760856i	$-0.275221\pi$
$811$	1052.55			1.29784			0.648920	+	0.760856i	$0.275221\pi$
$812$	56.8095			0.0699624
$813$		−	10.3860i		−	0.0127749i
$814$	−923.965			−1.13509
$815$	1137.36	+	230.539i	1.39553	+	0.282870i
$816$		−	30.0341i		−	0.0368064i
$817$		−	702.038i		−	0.859288i
$818$		−	327.848i		−	0.400793i
$819$		−	319.622i		−	0.390259i
$820$	6.80712	−	33.5827i	0.00830136	−	0.0409545i
$821$	−210.260			−0.256103			−0.128051	−	0.991768i	$-0.540872\pi$
$821$	−210.260			−0.256103			−0.128051	+	0.991768i	$0.540872\pi$
$822$	−213.387			−0.259595
$823$			451.771i			0.548932i	0.961597	+	0.274466i	$0.0885011\pi$
$823$			451.771i			0.548932i	−0.961597	+	0.274466i	$0.911499\pi$
$824$			584.167i			0.708940i
$825$	−229.584	−	97.0598i	−0.278283	−	0.117648i
$826$			568.567i			0.688337i
$827$	1133.04			1.37006			0.685031	−	0.728514i	$-0.259789\pi$
$827$	1133.04			1.37006			0.685031	+	0.728514i	$0.259789\pi$
$828$	−57.7047	+	50.4718i	−0.0696917	+	0.0609562i
$829$	1452.30			1.75187			0.875937	−	0.482426i	$-0.160244\pi$
$829$	1452.30			1.75187			0.875937	+	0.482426i	$0.160244\pi$
$830$	−1177.18	−	238.611i	−1.41829	−	0.287484i
$831$	−535.813			−0.644781
$832$		−	487.711i		−	0.586192i
$833$	40.5528			0.0486828
$834$	−310.395			−0.372176
$835$	498.125	+	100.969i	0.596557	+	0.120920i
$836$	−75.4600			−0.0902632
$837$		−	76.5422i		−	0.0914483i
$838$	971.523			1.15933
$839$			1361.07i			1.62225i	0.584871	+	0.811126i	$0.301145\pi$
$839$			1361.07i			1.62225i	−0.584871	+	0.811126i	$0.698855\pi$
$840$	39.7286	−	196.000i	0.0472959	−	0.233333i
$841$	−62.8749			−0.0747620
$842$	−793.274			−0.942130
$843$	273.720			0.324698
$844$	57.7512			0.0684256
$845$	−91.6902	+	452.351i	−0.108509	+	0.535326i
$846$	547.126			0.646721
$847$	−202.102			−0.238609
$848$	−512.324			−0.604156
$849$			82.4292i			0.0970898i
$850$	−31.1247	+	73.6218i	−0.0366173	+	0.0866139i
$851$	859.278	−	751.572i	1.00973	−	0.883164i
$852$		−	17.5679i		−	0.0206196i
$853$		−	728.789i		−	0.854383i	−0.904161	−	0.427192i	$-0.859503\pi$
$853$		−	728.789i		−	0.854383i	0.904161	−	0.427192i	$-0.140497\pi$
$854$	−956.466			−1.11998
$855$	749.384	+	151.898i	0.876473	+	0.177659i
$856$			808.706i			0.944750i
$857$		−	1056.75i		−	1.23308i	−0.787324	−	0.616539i	$-0.788534\pi$
$857$		−	1056.75i		−	1.23308i	0.787324	−	0.616539i	$-0.211466\pi$
$858$	−183.798			−0.214217
$859$	459.265			0.534651			0.267326	−	0.963606i	$-0.413860\pi$
$859$	459.265			0.534651			0.267326	+	0.963606i	$0.413860\pi$
$860$	15.1990	−	74.9839i	0.0176733	−	0.0871906i
$861$			84.6049i			0.0982635i
$862$	−514.337			−0.596679
$863$		−	66.7126i		−	0.0773032i	−0.999253	−	0.0386516i	$-0.987694\pi$
$863$		−	66.7126i		−	0.0773032i	0.999253	−	0.0386516i	$-0.0123062\pi$
$864$	−129.597			−0.149996
$865$	−86.9457	−	17.6237i	−0.100515	−	0.0203742i
$866$			928.173i			1.07179i
$867$			323.232i			0.372817i
$868$	8.26482			0.00952168
$869$	410.513			0.472397
$870$	−65.7598	+	324.424i	−0.0755860	+	0.372901i
$871$		−	786.287i		−	0.902741i
$872$	−1348.45			−1.54638
$873$	−1069.01			−1.22453
$874$	721.073	−	630.691i	0.825027	−	0.721614i
$875$	−333.283	+	487.196i	−0.380894	+	0.556796i
$876$	−57.3113			−0.0654238
$877$			536.457i			0.611696i	0.952080	+	0.305848i	$0.0989399\pi$
$877$			536.457i			0.611696i	−0.952080	+	0.305848i	$0.901060\pi$
$878$			439.070i			0.500079i
$879$		−	421.942i		−	0.480025i
$880$	760.053	+	154.061i	0.863697	+	0.175069i
$881$		−	222.229i		−	0.252246i	−0.992015	−	0.126123i	$-0.959747\pi$
$881$		−	222.229i		−	0.252246i	0.992015	−	0.126123i	$-0.0402534\pi$
$882$		−	434.400i		−	0.492517i
$883$			780.490i			0.883908i	0.897038	+	0.441954i	$0.145714\pi$
$883$			780.490i			0.883908i	−0.897038	+	0.441954i	$0.854286\pi$
$884$			5.73618i			0.00648889i
$885$	−316.002	−	64.0526i	−0.357064	−	0.0723759i
$886$	−626.535			−0.707151
$887$			1303.18i			1.46920i	0.678498	+	0.734602i	$0.262631\pi$
$887$			1303.18i			1.46920i	−0.678498	+	0.734602i	$0.737369\pi$
$888$	420.394			0.473417
$889$			447.299i			0.503148i
$890$	136.062	−	671.257i	0.152879	−	0.754222i
$891$			427.082i			0.479329i
$892$		−	35.2954i		−	0.0395688i
$893$	−665.382			−0.745109
$894$		−	219.366i		−	0.245376i
$895$	−206.564	+	1019.08i	−0.230798	+	1.13864i
$896$			683.408i			0.762732i
$897$	170.931	−	149.505i	0.190558	−	0.166673i
$898$			1395.09i			1.55356i
$899$	113.204			0.125922
$900$	76.7523	+	32.4481i	0.0852804	+	0.0360535i
$901$	−44.3658			−0.0492406
$902$	−295.815			−0.327954
$903$			188.907i			0.209199i
$904$		−	1352.17i		−	1.49576i
$905$	293.175	+	59.4258i	0.323951	+	0.0656639i
$906$	579.386			0.639499
$907$	297.121			0.327586			0.163793	−	0.986495i	$-0.447627\pi$
$907$	297.121			0.327586			0.163793	+	0.986495i	$0.447627\pi$
$908$	134.090			0.147676
$909$	399.946			0.439985
$910$	−86.4690	+	426.592i	−0.0950209	+	0.468782i
$911$		−	608.455i		−	0.667898i	−0.942591	−	0.333949i	$-0.891619\pi$
$911$		−	608.455i		−	0.667898i	0.942591	−	0.333949i	$-0.108381\pi$
$912$	391.261			0.429015
$913$			1009.17i			1.10533i
$914$		−	443.063i		−	0.484751i
$915$	107.752	−	531.591i	0.117762	−	0.580973i
$916$			35.9083i			0.0392012i
$917$	223.393			0.243613
$918$	−60.3028			−0.0656893
$919$		−	1425.50i		−	1.55114i	−0.631261	−	0.775570i	$-0.717462\pi$
$919$		−	1425.50i		−	1.55114i	0.631261	−	0.775570i	$-0.282538\pi$
$920$	−750.311	+	428.252i	−0.815555	+	0.465492i
$921$	−581.877			−0.631789
$922$			1396.64i			1.51480i
$923$		−	316.408i		−	0.342804i
$924$	20.3051			0.0219752
$925$	−1142.92	−	483.184i	−1.23558	−	0.522361i
$926$	273.923			0.295814
$927$	600.999			0.648327
$928$		−	191.671i		−	0.206542i
$929$	−779.527			−0.839104			−0.419552	−	0.907731i	$-0.637813\pi$
$929$	−779.527			−0.839104			−0.419552	+	0.907731i	$0.637813\pi$
$930$	−9.56695	+	47.1982i	−0.0102870	+	0.0507508i
$931$			528.292i			0.567445i
$932$			12.2447i			0.0131381i
$933$			308.686i			0.330853i
$934$		−	666.525i		−	0.713625i
$935$	65.8184	+	13.3412i	0.0703940	+	0.0142687i
$936$	−508.467			−0.543234
$937$	−123.699			−0.132016			−0.0660082	−	0.997819i	$-0.521026\pi$
$937$	−123.699			−0.132016			−0.0660082	+	0.997819i	$0.521026\pi$
$938$			892.541i			0.951536i
$939$			81.5968i			0.0868976i
$940$	−71.0688	−	14.4054i	−0.0756051	−	0.0153249i
$941$			294.870i			0.313359i	0.987650	+	0.156679i	$0.0500789\pi$
$941$			294.870i			0.313359i	−0.987650	+	0.156679i	$0.949921\pi$
$942$	−396.011			−0.420394
$943$	275.105	−	240.622i	0.291733	−	0.255166i
$944$	1003.16			1.06267
$945$	−436.459	−	88.4690i	−0.461861	−	0.0936179i
$946$	−660.500			−0.698203
$947$			372.050i			0.392872i	0.980517	+	0.196436i	$0.0629368\pi$
$947$			372.050i			0.392872i	−0.980517	+	0.196436i	$0.937063\pi$
$948$	22.5713			0.0238094
$949$	−1032.21			−1.08768
$950$	−959.090	−	405.469i	−1.00957	−	0.426810i
$951$	−122.398			−0.128705
$952$			53.8816i			0.0565983i
$953$	798.182			0.837547			0.418774	−	0.908091i	$-0.362460\pi$
$953$	798.182			0.837547			0.418774	+	0.908091i	$0.362460\pi$
$954$			475.245i			0.498160i
$955$	−1808.14	−	366.504i	−1.89334	−	0.383774i
$956$	94.3513			0.0986938
$957$	278.121			0.290617
$958$	470.572			0.491203
$959$	424.579			0.442731
$960$	−307.693	−	62.3685i	−0.320514	−	0.0649672i
$961$	−944.531			−0.982862
$962$	−914.986			−0.951129
$963$	832.008			0.863975
$964$			117.032i			0.121403i
$965$	−3.96947	−	0.804600i	−0.00411344	−	0.000833783i
$966$	−194.029	+	169.709i	−0.200858	+	0.175682i
$967$			19.5986i			0.0202674i	0.999949	+	0.0101337i	$0.00322571\pi$
$967$			19.5986i			0.0202674i	−0.999949	+	0.0101337i	$0.996774\pi$
$968$			321.511i			0.332139i
$969$	33.8821			0.0349660
$970$	1426.79	+	289.206i	1.47091	+	0.298150i
$971$		−	1818.61i		−	1.87292i	−0.350768	−	0.936462i	$-0.614080\pi$
$971$		−	1818.61i		−	1.87292i	0.350768	−	0.936462i	$-0.385920\pi$
$972$			96.6889i			0.0994742i
$973$	617.598			0.634736
$974$	1068.69			1.09722
$975$	−227.353	−	96.1166i	−0.233182	−	0.0985811i
$976$			1687.56i			1.72906i
$977$	−1389.80			−1.42252			−0.711258	−	0.702931i	$-0.751874\pi$
$977$	−1389.80			−1.42252			−0.711258	+	0.702931i	$0.751874\pi$
$978$		−	550.848i		−	0.563239i
$979$	−575.452			−0.587796
$980$	−11.4374	+	56.4262i	−0.0116709	+	0.0575778i
$981$			1387.30i			1.41417i
$982$		−	509.409i		−	0.518746i
$983$	−1204.31			−1.22514			−0.612568	−	0.790418i	$-0.709863\pi$
$983$	−1204.31			−1.22514			−0.612568	+	0.790418i	$0.709863\pi$
$984$	134.593			0.136781
$985$	−1311.49	−	265.835i	−1.33146	−	0.269884i
$986$		−	89.1863i		−	0.0904527i
$987$	179.044			0.181402
$988$	−74.7267			−0.0756343
$989$	614.258	−	537.264i	0.621090	−	0.543240i
$990$	142.910	−	705.044i	0.144354	−	0.712166i
$991$	−1412.01			−1.42483			−0.712417	−	0.701756i	$-0.752399\pi$
$991$	−1412.01			−1.42483			−0.712417	+	0.701756i	$0.752399\pi$
$992$		−	27.8848i		−	0.0281097i
$993$			129.363i			0.130274i
$994$			359.166i			0.361334i
$995$	952.497	+	193.069i	0.957284	+	0.194039i
$996$			55.4874i			0.0557102i
$997$			247.030i			0.247773i	0.992296	+	0.123887i	$0.0395359\pi$
$997$			247.030i			0.247773i	−0.992296	+	0.123887i	$0.960464\pi$
$998$			1901.57i			1.90538i
$999$		−	936.149i		−	0.937086i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	115.3.c.c.114.13	yes	20
5.2	odd	4		575.3.d.i.551.7		20
5.3	odd	4		575.3.d.i.551.14		20
5.4	even	2	inner	115.3.c.c.114.8	yes	20
23.22	odd	2	inner	115.3.c.c.114.14	yes	20
115.22	even	4		575.3.d.i.551.8		20
115.68	even	4		575.3.d.i.551.13		20
115.114	odd	2	inner	115.3.c.c.114.7	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.3.c.c.114.7	✓	20	115.114	odd	2	inner
115.3.c.c.114.8	yes	20	5.4	even	2	inner
115.3.c.c.114.13	yes	20	1.1	even	1	trivial
115.3.c.c.114.14	yes	20	23.22	odd	2	inner
575.3.d.i.551.7		20	5.2	odd	4
575.3.d.i.551.8		20	115.22	even	4
575.3.d.i.551.13		20	115.68	even	4
575.3.d.i.551.14		20	5.3	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:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	115.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+2.10506i q^{2} -1.12745i q^{3} -0.431264 q^{4} +(-0.993286 + 4.90035i) q^{5} +2.37335 q^{6} -4.72229 q^{7} +7.51239i q^{8} +7.72885 q^{9} +O(q^{10})\)	\(q+2.10506i q^{2} -1.12745i q^{3} -0.431264 q^{4} +(-0.993286 + 4.90035i) q^{5} +2.37335 q^{6} -4.72229 q^{7} +7.51239i q^{8} +7.72885 q^{9} +(-10.3155 - 2.09092i) q^{10} +8.84323i q^{11} +0.486229i q^{12} +8.75729i q^{13} -9.94069i q^{14} +(5.52490 + 1.11988i) q^{15} -17.5391 q^{16} -1.51883 q^{17} +16.2697i q^{18} -19.7862i q^{19} +(0.428369 - 2.11334i) q^{20} +5.32415i q^{21} -18.6155 q^{22} +(17.3122 - 15.1422i) q^{23} +8.46985 q^{24} +(-23.0268 - 9.73489i) q^{25} -18.4346 q^{26} -18.8610i q^{27} +2.03655 q^{28} +27.8949 q^{29} +(-2.35741 + 11.6302i) q^{30} +4.05824 q^{31} -6.87117i q^{32} +9.97030 q^{33} -3.19723i q^{34} +(4.69059 - 23.1408i) q^{35} -3.33318 q^{36} +49.6342 q^{37} +41.6511 q^{38} +9.87341 q^{39} +(-36.8133 - 7.46196i) q^{40} +15.8908 q^{41} -11.2076 q^{42} +35.4812 q^{43} -3.81377i q^{44} +(-7.67697 + 37.8741i) q^{45} +(31.8752 + 36.4432i) q^{46} -33.6286i q^{47} +19.7744i q^{48} -26.7000 q^{49} +(20.4925 - 48.4726i) q^{50} +1.71241i q^{51} -3.77670i q^{52} +29.2104 q^{53} +39.7034 q^{54} +(-43.3349 - 8.78386i) q^{55} -35.4757i q^{56} -22.3080 q^{57} +58.7203i q^{58} -57.1959 q^{59} +(-2.38269 - 0.482965i) q^{60} -96.2173i q^{61} +8.54282i q^{62} -36.4979 q^{63} -55.6921 q^{64} +(-42.9137 - 8.69849i) q^{65} +20.9881i q^{66} -89.7866 q^{67} +0.655018 q^{68} +(-17.0721 - 19.5187i) q^{69} +(48.7128 + 9.87395i) q^{70} -36.1309 q^{71} +58.0622i q^{72} +117.869i q^{73} +104.483i q^{74} +(-10.9756 + 25.9615i) q^{75} +8.53309i q^{76} -41.7603i q^{77} +20.7841i q^{78} -46.4212i q^{79} +(17.4213 - 85.9475i) q^{80} +48.2949 q^{81} +33.4510i q^{82} +114.118 q^{83} -2.29612i q^{84} +(1.50864 - 7.44280i) q^{85} +74.6899i q^{86} -31.4501i q^{87} -66.4338 q^{88} +65.0727i q^{89} +(-79.7270 - 16.1604i) q^{90} -41.3544i q^{91} +(-7.46614 + 6.53030i) q^{92} -4.57546i q^{93} +70.7901 q^{94} +(96.9593 + 19.6534i) q^{95} -7.74691 q^{96} -138.315 q^{97} -56.2050i q^{98} +68.3480i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 56 q^{4} - 8 q^{6} - 72 q^{9}+O(q^{10}) \) 20 * q - 56 * q^4 - 8 * q^6 - 72 * q^9	\( 20 q - 56 q^{4} - 8 q^{6} - 72 q^{9} + 88 q^{16} + 44 q^{24} - 12 q^{25} - 56 q^{26} + 236 q^{31} + 92 q^{35} - 32 q^{36} - 168 q^{39} + 124 q^{41} - 248 q^{46} + 88 q^{49} + 200 q^{50} - 196 q^{54} + 268 q^{55} + 56 q^{59} - 28 q^{64} + 376 q^{69} - 636 q^{70} - 196 q^{71} + 428 q^{75} - 988 q^{81} - 284 q^{85} + 276 q^{94} + 184 q^{95} - 264 q^{96}+O(q^{100}) \) 20 * q - 56 * q^4 - 8 * q^6 - 72 * q^9 + 88 * q^16 + 44 * q^24 - 12 * q^25 - 56 * q^26 + 236 * q^31 + 92 * q^35 - 32 * q^36 - 168 * q^39 + 124 * q^41 - 248 * q^46 + 88 * q^49 + 200 * q^50 - 196 * q^54 + 268 * q^55 + 56 * q^59 - 28 * q^64 + 376 * q^69 - 636 * q^70 - 196 * q^71 + 428 * q^75 - 988 * q^81 - 284 * q^85 + 276 * q^94 + 184 * q^95 - 264 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more