LMFDB - Embedded newform 115.3.c.c.114.14

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			114.14
Root			$-0.993286 - 4.90035i$ of defining polynomial
Character	$\chi$	$=$	115.114
Dual form			115.3.c.c.114.8

$q$-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	$-0.390484\pi$
$7$	4.72229			0.674613			0.337306	+	0.941395i	$0.390484\pi$
$8$			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	$-0.868327\pi$
$11$		−	8.84323i		−	0.803930i	0.915655	−	0.401965i	$-0.131673\pi$
$12$			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	$-0.485776\pi$
$17$	1.51883			0.0893431			0.0446715	+	0.999002i	$0.485776\pi$
$18$			16.2697i			0.903871i
$19$			19.7862i			1.04138i	0.853746	+	0.520690i	$0.174325\pi$
$19$			19.7862i			1.04138i	−0.853746	+	0.520690i	$0.825675\pi$
$20$	−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	$-0.734020\pi$
$37$	−49.6342			−1.34147			−0.670733	+	0.741699i	$0.734020\pi$
$38$	−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	$-0.635369\pi$
$43$	−35.4812			−0.825144			−0.412572	+	0.910925i	$0.635369\pi$
$44$			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	$-0.588867\pi$
$53$	−29.2104			−0.551141			−0.275570	+	0.961281i	$0.588867\pi$
$54$	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	$0.289228\pi$
$61$			96.2173i			1.57733i	−0.614822	+	0.788666i	$0.710772\pi$
$62$			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	$-0.266273\pi$
$67$	89.7866			1.34010			0.670050	+	0.742316i	$0.266273\pi$
$68$	−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	$0.0949216\pi$
$79$			46.4212i			0.587610i	−0.955865	+	0.293805i	$0.905078\pi$
$80$	−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	$-0.741273\pi$
$83$	−114.118			−1.37491			−0.687456	+	0.726226i	$0.741273\pi$
$84$			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	$-0.880872\pi$
$89$		−	65.0727i		−	0.731153i	0.930781	−	0.365577i	$-0.119128\pi$
$90$	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	$-0.247353\pi$
$97$	138.315			1.42592			0.712962	+	0.701202i	$0.247353\pi$
$98$		−	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	$-0.623209\pi$
$103$	−77.7604			−0.754955			−0.377478	+	0.926019i	$0.623209\pi$
$104$	−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	$-0.667784\pi$
$107$	−107.650			−1.00607			−0.503036	+	0.864266i	$0.667784\pi$
$108$			8.13406i			0.0753154i
$109$		−	179.496i		−	1.64675i	−0.567495	−	0.823377i	$-0.692087\pi$
$109$		−	179.496i		−	1.64675i	0.567495	−	0.823377i	$-0.307913\pi$
$110$	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	$-0.206722\pi$
$113$	179.992			1.59285			0.796424	+	0.604739i	$0.206722\pi$
$114$			46.9596i			0.411926i
$115$	−91.3981	+	69.7953i	−0.794766	+	0.606916i
$116$	−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	$-0.393579\pi$
$137$	89.9096			0.656275			0.328137	+	0.944630i	$0.393579\pi$
$138$	−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	$0.100384\pi$
$149$			92.4289i			0.620328i	−0.950683	+	0.310164i	$0.899616\pi$
$150$	−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	$-0.321669\pi$
$157$	166.858			1.06279			0.531393	+	0.847125i	$0.321669\pi$
$158$	−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	$0.0528493\pi$
$181$			59.8275i			0.330539i	−0.986248	+	0.165269i	$0.947151\pi$
$182$	−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	$-0.583340\pi$
$191$		−	368.981i		−	1.93184i	0.258840	−	0.965920i	$-0.416660\pi$
$192$			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	$0.162410\pi$
$199$			194.373i			0.976751i	−0.872634	+	0.488376i	$0.837590\pi$
$200$	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	$-0.259867\pi$
$227$	310.923			1.36970			0.684852	+	0.728683i	$0.259867\pi$
$228$	−9.62064			−0.0421958
$229$			83.2629i			0.363594i	0.983336	+	0.181797i	$0.0581913\pi$
$229$			83.2629i			0.363594i	−0.983336	+	0.181797i	$0.941809\pi$
$230$	−146.923	−	192.398i	−0.638796	−	0.836514i
$231$	−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	$0.190356\pi$
$241$			271.370i			1.12602i	−0.826451	+	0.563009i	$0.809644\pi$
$242$			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	$0.0971198\pi$
$251$			150.800i			0.600798i	−0.953814	+	0.300399i	$0.902880\pi$
$252$	−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	$-0.532024\pi$
$263$	−52.8302			−0.200875			−0.100438	+	0.994943i	$0.532024\pi$
$264$		−	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	$-0.857812\pi$
$281$		−	242.778i		−	0.863979i	0.901879	−	0.431990i	$-0.142188\pi$
$282$		−	79.8123i		−	0.283023i
$283$	73.1111			0.258343			0.129172	−	0.991622i	$-0.458768\pi$
$283$	73.1111			0.258343			0.129172	+	0.991622i	$0.458768\pi$
$284$	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	$-0.720503\pi$
$293$	−374.244			−1.27728			−0.638642	+	0.769504i	$0.720503\pi$
$294$	−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	$-0.463117\pi$
$313$	72.3728			0.231223			0.115612	+	0.993295i	$0.463117\pi$
$314$			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	$-0.116532\pi$
$337$	629.335			1.86746			0.933732	+	0.357973i	$0.116532\pi$
$338$			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
$345$	78.6908	+	103.047i	0.228089	+	0.298687i
$346$	−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	$-0.793965\pi$
$359$		−	432.967i		−	1.20604i	0.797728	−	0.603018i	$-0.206035\pi$
$360$	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	$-0.491767\pi$
$367$	18.9820			0.0517222			0.0258611	+	0.999666i	$0.491767\pi$
$368$	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	$-0.580834\pi$
$373$	−187.416			−0.502455			−0.251228	+	0.967928i	$0.580834\pi$
$374$	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	$0.331569\pi$
$379$			654.337i			1.72648i	−0.504792	+	0.863241i	$0.668431\pi$
$380$	−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	$-0.221457\pi$
$383$	587.972			1.53517			0.767587	+	0.640944i	$0.221457\pi$
$384$	−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	$-0.927066\pi$
$389$		−	176.707i		−	0.454259i	0.973865	−	0.227130i	$-0.0729341\pi$
$390$	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	$0.133005\pi$
$401$			325.446i			0.811586i	−0.913965	+	0.405793i	$0.866995\pi$
$402$	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	$0.185654\pi$
$419$			461.518i			1.10148i	−0.834678	+	0.550738i	$0.814346\pi$
$420$	11.2518	+	2.28070i	0.0267899	+	0.00543024i
$421$		−	376.842i		−	0.895112i	−0.894256	−	0.447556i	$-0.852295\pi$
$421$		−	376.842i		−	0.895112i	0.894256	−	0.447556i	$-0.147705\pi$
$422$		−	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	$-0.908521\pi$
$431$		−	244.334i		−	0.566901i	0.958987	−	0.283450i	$-0.0914791\pi$
$432$			330.804i			0.765749i
$433$	−440.925			−1.01830			−0.509152	−	0.860677i	$-0.670041\pi$
$433$	−440.925			−1.01830			−0.509152	+	0.860677i	$0.670041\pi$
$434$			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	$-0.426036\pi$
$457$	210.475			0.460559			0.230279	+	0.973125i	$0.426036\pi$
$458$	−175.273			−0.382693
$459$		−	28.6466i		−	0.0624110i
$460$	39.4168	−	30.1002i	0.0856886	−	0.0654353i
$461$	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	$-0.389910\pi$
$467$	316.631			0.678010			0.339005	+	0.940785i	$0.389910\pi$
$468$		−	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	$0.0749669\pi$
$479$			223.544i			0.466689i	−0.972394	+	0.233344i	$0.925033\pi$
$480$	−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	$-0.215438\pi$
$503$	784.248			1.55914			0.779570	+	0.626315i	$0.215438\pi$
$504$			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	$-0.889333\pi$
$521$		−	355.019i		−	0.681418i	0.940169	−	0.340709i	$-0.110667\pi$
$522$			453.841i			0.869427i
$523$	−349.799			−0.668832			−0.334416	−	0.942426i	$-0.608539\pi$
$523$	−349.799			−0.668832			−0.334416	+	0.942426i	$0.608539\pi$
$524$	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	$-0.822888\pi$
$557$	−945.958			−1.69831			−0.849155	+	0.528144i	$0.822888\pi$
$558$			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	$-0.346246\pi$
$563$	522.991			0.928936			0.464468	+	0.885590i	$0.346246\pi$
$564$	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	$-0.960643\pi$
$569$		−	140.348i		−	0.246658i	0.992366	−	0.123329i	$-0.0393570\pi$
$570$	230.118	+	46.6443i	0.403716	+	0.0818321i
$571$		−	171.380i		−	0.300141i	−0.988675	−	0.150070i	$-0.952050\pi$
$571$		−	171.380i		−	0.300141i	0.988675	−	0.150070i	$-0.0479500\pi$
$572$	−33.3983			−0.0583886
$573$	−416.009			−0.726018
$574$			157.965i			0.275201i
$575$	251.236	+	517.209i	0.436933	+	0.899494i
$576$	−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	$-0.480456\pi$
$613$	75.2299			0.122724			0.0613621	+	0.998116i	$0.480456\pi$
$614$	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	$-0.420445\pi$
$617$	305.214			0.494674			0.247337	+	0.968930i	$0.420445\pi$
$618$	−184.553			−0.298629
$619$		−	456.404i		−	0.737325i	−0.929563	−	0.368662i	$-0.879816\pi$
$619$		−	456.404i		−	0.737325i	0.929563	−	0.368662i	$-0.120184\pi$
$620$	−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	$-0.644759\pi$
$631$		−	1133.73i		−	1.79672i	0.439260	−	0.898360i	$-0.355241\pi$
$632$	−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	$0.249127\pi$
$641$			904.020i			1.41033i	−0.709044	+	0.705164i	$0.750873\pi$
$642$	−255.490			−0.397960
$643$	1049.41			1.63206			0.816028	−	0.578013i	$-0.196172\pi$
$643$	1049.41			1.63206			0.816028	+	0.578013i	$0.196172\pi$
$644$	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	$-0.794819\pi$
$659$		−	791.953i		−	1.20175i	0.799343	−	0.600875i	$-0.205181\pi$
$660$	4.27097	−	21.0707i	0.00647116	−	0.0319253i
$661$			197.840i			0.299304i	0.988739	+	0.149652i	$0.0478153\pi$
$661$			197.840i			0.299304i	−0.988739	+	0.149652i	$0.952185\pi$
$662$		−	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	$-0.845238\pi$
$677$	−1197.09			−1.76823			−0.884115	+	0.467269i	$0.845238\pi$
$678$	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
$690$	−216.920	+	165.649i	−0.314376	+	0.240070i
$691$	−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	$0.138900\pi$
$701$			592.555i			0.845300i	−0.906293	+	0.422650i	$0.861100\pi$
$702$			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	$-0.844435\pi$
$709$		−	665.746i		−	0.938993i	0.882934	−	0.469496i	$-0.155565\pi$
$710$	−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	$-0.599570\pi$
$727$	−447.443			−0.615465			−0.307732	+	0.951473i	$0.599570\pi$
$728$	−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	$-0.629939\pi$
$733$	−581.960			−0.793942			−0.396971	+	0.917831i	$0.629939\pi$
$734$			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	$-0.478178\pi$
$743$	101.796			0.137006			0.0685032	+	0.997651i	$0.478178\pi$
$744$	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	$0.0808022\pi$
$751$			377.197i			0.502260i	−0.967953	+	0.251130i	$0.919198\pi$
$752$			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	$-0.426274\pi$
$757$	347.543			0.459106			0.229553	+	0.973296i	$0.426274\pi$
$758$	−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	$-0.761055\pi$
$769$		−	1049.11i		−	1.36426i	0.731233	−	0.682128i	$-0.238945\pi$
$770$	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	$-0.739410\pi$
$773$	−1056.22			−1.36639			−0.683195	+	0.730236i	$0.739410\pi$
$774$		−	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	$-0.258715\pi$
$787$	1082.10			1.37497			0.687485	+	0.726199i	$0.258715\pi$
$788$		−	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	$-0.765987\pi$
$797$	−1182.29			−1.48343			−0.741715	+	0.670715i	$0.765987\pi$
$798$			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
$805$	−431.608	+	329.594i	−0.536160	+	0.409433i
$806$	−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	$-0.740211\pi$
$827$	−1133.04			−1.37006			−0.685031	+	0.728514i	$0.740211\pi$
$828$	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	$-0.698855\pi$
$839$		−	1361.07i		−	1.62225i	0.584871	−	0.811126i	$-0.301145\pi$
$840$	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	$0.0402534\pi$
$881$			222.229i			0.252246i	−0.992015	+	0.126123i	$0.959747\pi$
$882$		−	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	$-0.552373\pi$
$907$	−297.121			−0.327586			−0.163793	+	0.986495i	$0.552373\pi$
$908$	−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	$0.108381\pi$
$911$			608.455i			0.667898i	−0.942591	+	0.333949i	$0.891619\pi$
$912$	−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	$0.282538\pi$
$919$			1425.50i			1.55114i	−0.631261	+	0.775570i	$0.717462\pi$
$920$	−524.330	−	686.619i	−0.569923	−	0.746324i
$921$	−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	$-0.478974\pi$
$937$	123.699			0.132016			0.0660082	+	0.997819i	$0.478974\pi$
$938$			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	$-0.949921\pi$
$941$		−	294.870i		−	0.313359i	0.987650	−	0.156679i	$-0.0500789\pi$
$942$	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	$-0.637540\pi$
$953$	−798.182			−0.837547			−0.418774	+	0.908091i	$0.637540\pi$
$954$		−	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	$0.385920\pi$
$971$			1818.61i			1.87292i	−0.350768	+	0.936462i	$0.614080\pi$
$972$			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	$-0.248126\pi$
$977$	1389.80			1.42252			0.711258	+	0.702931i	$0.248126\pi$
$978$		−	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	$-0.290137\pi$
$983$	1204.31			1.22514			0.612568	+	0.790418i	$0.290137\pi$
$984$	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.114.14	yes	20
5.2	odd	4		575.3.d.i.551.8		20
5.3	odd	4		575.3.d.i.551.13		20
5.4	even	2	inner	115.3.c.c.114.7	✓	20
23.22	odd	2	inner	115.3.c.c.114.13	yes	20
115.22	even	4		575.3.d.i.551.7		20
115.68	even	4		575.3.d.i.551.14		20
115.114	odd	2	inner	115.3.c.c.114.8	yes	20

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

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