LMFDB - Embedded newform 115.3.c.c.114.16

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			114.16
Root			$-4.79117 + 1.42993i$ of defining polynomial
Character	$\chi$	$=$	115.114
Dual form			115.3.c.c.114.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.13699i q^{2} +3.84414i q^{3} -0.566730 q^{4} +(4.79117 + 1.42993i) q^{5} -8.21490 q^{6} +2.33853 q^{7} +7.33687i q^{8} -5.77745 q^{9} +O(q^{10})$	\(q+2.13699i q^{2} +3.84414i q^{3} -0.566730 q^{4} +(4.79117 + 1.42993i) q^{5} -8.21490 q^{6} +2.33853 q^{7} +7.33687i q^{8} -5.77745 q^{9} +(-3.05575 + 10.2387i) q^{10} -12.3663i q^{11} -2.17859i q^{12} -19.6832i q^{13} +4.99742i q^{14} +(-5.49686 + 18.4179i) q^{15} -17.9457 q^{16} -24.3623 q^{17} -12.3464i q^{18} -19.9606i q^{19} +(-2.71530 - 0.810386i) q^{20} +8.98965i q^{21} +26.4267 q^{22} +(21.3708 + 8.50221i) q^{23} -28.2040 q^{24} +(20.9106 + 13.7021i) q^{25} +42.0629 q^{26} +12.3880i q^{27} -1.32532 q^{28} +8.59423 q^{29} +(-39.3590 - 11.7467i) q^{30} -2.00733 q^{31} -9.00242i q^{32} +47.5378 q^{33} -52.0620i q^{34} +(11.2043 + 3.34394i) q^{35} +3.27426 q^{36} -61.1018 q^{37} +42.6556 q^{38} +75.6651 q^{39} +(-10.4912 + 35.1522i) q^{40} +27.4276 q^{41} -19.2108 q^{42} +37.3111 q^{43} +7.00835i q^{44} +(-27.6807 - 8.26135i) q^{45} +(-18.1691 + 45.6693i) q^{46} +16.3480i q^{47} -68.9860i q^{48} -43.5313 q^{49} +(-29.2812 + 44.6857i) q^{50} -93.6523i q^{51} +11.1551i q^{52} -44.5454 q^{53} -26.4730 q^{54} +(17.6829 - 59.2490i) q^{55} +17.1575i q^{56} +76.7314 q^{57} +18.3658i q^{58} +58.7542 q^{59} +(3.11524 - 10.4380i) q^{60} +39.7731i q^{61} -4.28965i q^{62} -13.5107 q^{63} -52.5449 q^{64} +(28.1457 - 94.3056i) q^{65} +101.588i q^{66} -44.9441 q^{67} +13.8069 q^{68} +(-32.6837 + 82.1526i) q^{69} +(-7.14596 + 23.9435i) q^{70} +15.8619 q^{71} -42.3884i q^{72} -101.380i q^{73} -130.574i q^{74} +(-52.6728 + 80.3833i) q^{75} +11.3123i q^{76} -28.9189i q^{77} +161.696i q^{78} +138.784i q^{79} +(-85.9811 - 25.6612i) q^{80} -99.6181 q^{81} +58.6125i q^{82} +30.6120 q^{83} -5.09471i q^{84} +(-116.724 - 34.8364i) q^{85} +79.7334i q^{86} +33.0374i q^{87} +90.7298 q^{88} +53.2636i q^{89} +(17.6544 - 59.1535i) q^{90} -46.0298i q^{91} +(-12.1115 - 4.81846i) q^{92} -7.71648i q^{93} -34.9355 q^{94} +(28.5423 - 95.6345i) q^{95} +34.6066 q^{96} -168.145 q^{97} -93.0259i q^{98} +71.4456i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$			2.13699i			1.06850i	0.845328	+	0.534248i	$0.179405\pi$
$2$			2.13699i			1.06850i	−0.845328	+	0.534248i	$0.820595\pi$
$3$			3.84414i			1.28138i	0.767799	+	0.640691i	$0.221352\pi$
$3$			3.84414i			1.28138i	−0.767799	+	0.640691i	$0.778648\pi$
$4$	−0.566730			−0.141683
$5$	4.79117	+	1.42993i	0.958234	+	0.285986i
$5$	4.79117	+	1.42993i	0.958234	+	0.285986i
$6$	−8.21490			−1.36915
$7$	2.33853			0.334076			0.167038	−	0.985950i	$-0.446580\pi$
$7$	2.33853			0.334076			0.167038	+	0.985950i	$0.446580\pi$
$8$			7.33687i			0.917108i
$9$	−5.77745			−0.641939
$10$	−3.05575	+	10.2387i	−0.305575	+	1.02387i
$11$		−	12.3663i		−	1.12421i	−0.827066	−	0.562104i	$-0.809992\pi$
$11$		−	12.3663i		−	1.12421i	0.827066	−	0.562104i	$-0.190008\pi$
$12$		−	2.17859i		−	0.181549i
$13$		−	19.6832i		−	1.51409i	−0.653361	−	0.757047i	$-0.726641\pi$
$13$		−	19.6832i		−	1.51409i	0.653361	−	0.757047i	$-0.273359\pi$
$14$			4.99742i			0.356958i
$15$	−5.49686	+	18.4179i	−0.366458	+	1.22786i
$16$	−17.9457			−1.12161
$17$	−24.3623			−1.43308			−0.716539	−	0.697547i	$-0.754275\pi$
$17$	−24.3623			−1.43308			−0.716539	+	0.697547i	$0.754275\pi$
$18$		−	12.3464i		−	0.685909i
$19$		−	19.9606i		−	1.05056i	−0.850930	−	0.525279i	$-0.823961\pi$
$19$		−	19.9606i		−	1.05056i	0.850930	−	0.525279i	$-0.176039\pi$
$20$	−2.71530	−	0.810386i	−0.135765	−	0.0405193i
$21$			8.98965i			0.428078i
$22$	26.4267			1.20121
$23$	21.3708	+	8.50221i	0.929167	+	0.369661i
$23$	21.3708	+	8.50221i	0.929167	+	0.369661i
$24$	−28.2040			−1.17517
$25$	20.9106	+	13.7021i	0.836424	+	0.548083i
$26$	42.0629			1.61780
$27$			12.3880i			0.458813i
$28$	−1.32532			−0.0473327
$29$	8.59423			0.296353			0.148176	−	0.988961i	$-0.452660\pi$
$29$	8.59423			0.296353			0.148176	+	0.988961i	$0.452660\pi$
$30$	−39.3590	−	11.7467i	−1.31197	−	0.391558i
$31$	−2.00733			−0.0647527			−0.0323764	−	0.999476i	$-0.510308\pi$
$31$	−2.00733			−0.0647527			−0.0323764	+	0.999476i	$0.510308\pi$
$32$		−	9.00242i		−	0.281326i
$33$	47.5378			1.44054
$34$		−	52.0620i		−	1.53124i
$35$	11.2043	+	3.34394i	0.320123	+	0.0955411i
$36$	3.27426			0.0909515
$37$	−61.1018			−1.65140			−0.825700	−	0.564110i	$-0.809220\pi$
$37$	−61.1018			−1.65140			−0.825700	+	0.564110i	$0.809220\pi$
$38$	42.6556			1.12252
$39$	75.6651			1.94013
$40$	−10.4912	+	35.1522i	−0.262280	+	0.878804i
$41$	27.4276			0.668965			0.334482	−	0.942402i	$-0.391438\pi$
$41$	27.4276			0.668965			0.334482	+	0.942402i	$0.391438\pi$
$42$	−19.2108			−0.457400
$43$	37.3111			0.867699			0.433850	−	0.900985i	$-0.357155\pi$
$43$	37.3111			0.867699			0.433850	+	0.900985i	$0.357155\pi$
$44$			7.00835i			0.159281i
$45$	−27.6807	−	8.26135i	−0.615127	−	0.183586i
$46$	−18.1691	+	45.6693i	−0.394981	+	0.992810i
$47$			16.3480i			0.347829i	0.984761	+	0.173915i	$0.0556417\pi$
$47$			16.3480i			0.347829i	−0.984761	+	0.173915i	$0.944358\pi$
$48$		−	68.9860i		−	1.43721i
$49$	−43.5313			−0.888393
$50$	−29.2812	+	44.6857i	−0.585625	+	0.893715i
$51$		−	93.6523i		−	1.83632i
$52$			11.1551i			0.214521i
$53$	−44.5454			−0.840480			−0.420240	−	0.907413i	$-0.638054\pi$
$53$	−44.5454			−0.840480			−0.420240	+	0.907413i	$0.638054\pi$
$54$	−26.4730			−0.490240
$55$	17.6829	−	59.2490i	0.321508	−	1.07725i
$56$			17.1575i			0.306384i
$57$	76.7314			1.34616
$58$			18.3658i			0.316651i
$59$	58.7542			0.995834			0.497917	−	0.867225i	$-0.334098\pi$
$59$	58.7542			0.995834			0.497917	+	0.867225i	$0.334098\pi$
$60$	3.11524	−	10.4380i	0.0519207	−	0.173967i
$61$			39.7731i			0.652018i	0.945367	+	0.326009i	$0.105704\pi$
$61$			39.7731i			0.652018i	−0.945367	+	0.326009i	$0.894296\pi$
$62$		−	4.28965i		−	0.0691880i
$63$	−13.5107			−0.214456
$64$	−52.5449			−0.821014
$65$	28.1457	−	94.3056i	0.433010	−	1.45086i
$66$			101.588i			1.53921i
$67$	−44.9441			−0.670807			−0.335403	−	0.942075i	$-0.608873\pi$
$67$	−44.9441			−0.670807			−0.335403	+	0.942075i	$0.608873\pi$
$68$	13.8069			0.203042
$69$	−32.6837	+	82.1526i	−0.473677	+	1.19062i
$70$	−7.14596	+	23.9435i	−0.102085	+	0.342050i
$71$	15.8619			0.223406			0.111703	−	0.993742i	$-0.464369\pi$
$71$	15.8619			0.223406			0.111703	+	0.993742i	$0.464369\pi$
$72$		−	42.3884i		−	0.588727i
$73$		−	101.380i		−	1.38877i	−0.719604	−	0.694385i	$-0.755677\pi$
$73$		−	101.380i		−	1.38877i	0.719604	−	0.694385i	$-0.244323\pi$
$74$		−	130.574i		−	1.76451i
$75$	−52.6728	+	80.3833i	−0.702304	+	1.07178i
$76$			11.3123i			0.148846i
$77$		−	28.9189i		−	0.375571i
$78$			161.696i			2.07302i
$79$			138.784i			1.75676i	0.477965	+	0.878379i	$0.341375\pi$
$79$			138.784i			1.75676i	−0.477965	+	0.878379i	$0.658625\pi$
$80$	−85.9811	−	25.6612i	−1.07476	−	0.320765i
$81$	−99.6181			−1.22985
$82$			58.6125i			0.714786i
$83$	30.6120			0.368819			0.184410	−	0.982849i	$-0.440963\pi$
$83$	30.6120			0.368819			0.184410	+	0.982849i	$0.440963\pi$
$84$		−	5.09471i		−	0.0606513i
$85$	−116.724	−	34.8364i	−1.37322	−	0.409840i
$86$			79.7334i			0.927133i
$87$			33.0374i			0.379741i
$88$	90.7298			1.03102
$89$			53.2636i			0.598467i	0.954180	+	0.299234i	$0.0967310\pi$
$89$			53.2636i			0.598467i	−0.954180	+	0.299234i	$0.903269\pi$
$90$	17.6544	−	59.1535i	0.196160	−	0.657261i
$91$		−	46.0298i		−	0.505822i
$92$	−12.1115	−	4.81846i	−0.131647	−	0.0523746i
$93$		−	7.71648i		−	0.0829729i
$94$	−34.9355			−0.371654
$95$	28.5423	−	95.6345i	0.300445	−	1.00668i
$96$	34.6066			0.360485
$97$	−168.145			−1.73345			−0.866725	−	0.498786i	$-0.833779\pi$
$97$	−168.145			−1.73345			−0.866725	+	0.498786i	$0.833779\pi$
$98$		−	93.0259i		−	0.949244i
$99$			71.4456i			0.721673i
$100$	−11.8507	−	7.76539i	−0.118507	−	0.0776539i
$101$	−14.4712			−0.143279			−0.0716394	−	0.997431i	$-0.522823\pi$
$101$	−14.4712			−0.143279			−0.0716394	+	0.997431i	$0.522823\pi$
$102$	200.134			1.96210
$103$	1.16024			0.0112645			0.00563223	−	0.999984i	$-0.498207\pi$
$103$	1.16024			0.0112645			0.00563223	+	0.999984i	$0.498207\pi$
$104$	144.413			1.38859
$105$	−12.8546	+	43.0709i	−0.122425	+	0.410199i
$106$		−	95.1932i		−	0.898049i
$107$	16.7596			0.156632			0.0783160	−	0.996929i	$-0.475046\pi$
$107$	16.7596			0.156632			0.0783160	+	0.996929i	$0.475046\pi$
$108$		−	7.02063i		−	0.0650059i
$109$		−	82.3078i		−	0.755118i	−0.925986	−	0.377559i	$-0.876764\pi$
$109$		−	82.3078i		−	0.755118i	0.925986	−	0.377559i	$-0.123236\pi$
$110$	126.615	+	37.7883i	1.15104	+	0.343530i
$111$		−	234.884i		−	2.11607i
$112$	−41.9666			−0.374702
$113$	75.8482			0.671223			0.335611	−	0.942001i	$-0.391057\pi$
$113$	75.8482			0.671223			0.335611	+	0.942001i	$0.391057\pi$
$114$			163.974i			1.43837i
$115$	90.2337	+	71.2943i	0.784641	+	0.619951i
$116$	−4.87061			−0.0419880
$117$			113.719i			0.971955i
$118$			125.557i			1.06404i
$119$	−56.9720			−0.478756
$120$	−135.130	−	40.3297i	−1.12608	−	0.336081i
$121$	−31.9252			−0.263844
$122$	−84.9948			−0.696678
$123$			105.436i			0.857199i
$124$	1.13762			0.00917433
$125$	80.5931	+	95.5497i	0.644745	+	0.764398i
$126$		−	28.8723i		−	0.229145i
$127$		−	79.3431i		−	0.624749i	−0.949959	−	0.312374i	$-0.898876\pi$
$127$		−	79.3431i		−	0.624749i	0.949959	−	0.312374i	$-0.101124\pi$
$128$		−	148.298i		−	1.15857i
$129$			143.429i			1.11185i
$130$	201.530	+	60.1470i	1.55023	+	0.462669i
$131$	58.7025			0.448110			0.224055	−	0.974576i	$-0.428070\pi$
$131$	58.7025			0.448110			0.224055	+	0.974576i	$0.428070\pi$
$132$	−26.9411			−0.204099
$133$		−	46.6784i		−	0.350966i
$134$		−	96.0450i		−	0.716754i
$135$	−17.7139	+	59.3528i	−0.131214	+	0.439650i
$136$		−	178.743i		−	1.31429i
$137$	−10.1807			−0.0743120			−0.0371560	−	0.999309i	$-0.511830\pi$
$137$	−10.1807			−0.0743120			−0.0371560	+	0.999309i	$0.511830\pi$
$138$	−175.559	−	69.8448i	−1.27217	−	0.506122i
$139$	238.702			1.71728			0.858642	−	0.512576i	$-0.171309\pi$
$139$	238.702			1.71728			0.858642	+	0.512576i	$0.171309\pi$
$140$	−6.34981	−	1.89511i	−0.0453558	−	0.0135365i
$141$	−62.8439			−0.445702
$142$			33.8966i			0.238709i
$143$	−243.408			−1.70216
$144$	103.681			0.720004
$145$	41.1764	+	12.2892i	0.283975	+	0.0847528i
$146$	216.648			1.48389
$147$		−	167.341i		−	1.13837i
$148$	34.6282			0.233975
$149$		−	150.837i		−	1.01233i	−0.862437	−	0.506165i	$-0.831063\pi$
$149$		−	150.837i		−	1.01233i	0.862437	−	0.506165i	$-0.168937\pi$
$150$	−171.778	−	112.561i	−1.14519	−	0.750409i
$151$	−162.017			−1.07296			−0.536480	−	0.843913i	$-0.680246\pi$
$151$	−162.017			−1.07296			−0.536480	+	0.843913i	$0.680246\pi$
$152$	146.448			0.963475
$153$	140.752			0.919948
$154$	61.7995			0.401296
$155$	−9.61747	−	2.87035i	−0.0620482	−	0.0185184i
$156$	−42.8817			−0.274883
$157$	200.263			1.27556			0.637782	−	0.770217i	$-0.279852\pi$
$157$	200.263			1.27556			0.637782	+	0.770217i	$0.279852\pi$
$158$	−296.580			−1.87709
$159$		−	171.239i		−	1.07698i
$160$	12.8728	−	43.1321i	0.0804552	−	0.269576i
$161$	49.9763	+	19.8827i	0.310412	+	0.123495i
$162$		−	212.883i		−	1.31409i
$163$			9.02746i			0.0553832i	0.999617	+	0.0276916i	$0.00881563\pi$
$163$			9.02746i			0.0553832i	−0.999617	+	0.0276916i	$0.991184\pi$
$164$	−15.5440			−0.0947807
$165$	227.762	+	67.9758i	1.38037	+	0.411975i
$166$			65.4176i			0.394082i
$167$		−	155.707i		−	0.932376i	−0.884686	−	0.466188i	$-0.845627\pi$
$167$		−	155.707i		−	0.932376i	0.884686	−	0.466188i	$-0.154373\pi$
$168$	−65.9558			−0.392594
$169$	−218.429			−1.29248
$170$	74.4451	−	249.438i	0.437913	−	1.46728i
$171$			115.321i			0.674393i
$172$	−21.1453			−0.122938
$173$			259.361i			1.49919i	0.661894	+	0.749597i	$0.269753\pi$
$173$			259.361i			1.49919i	−0.661894	+	0.749597i	$0.730247\pi$
$174$	−70.6007			−0.405751
$175$	48.9000	+	32.0427i	0.279429	+	0.183101i
$176$			221.922i			1.26092i
$177$			225.860i			1.27604i
$178$	−113.824			−0.639459
$179$	−258.737			−1.44546			−0.722729	−	0.691132i	$-0.757112\pi$
$179$	−258.737			−1.44546			−0.722729	+	0.691132i	$0.757112\pi$
$180$	15.6875	+	4.68196i	0.0871528	+	0.0260109i
$181$			65.0695i			0.359500i	0.983712	+	0.179750i	$0.0575289\pi$
$181$			65.0695i			0.359500i	−0.983712	+	0.179750i	$0.942471\pi$
$182$	98.3653			0.540468
$183$	−152.894			−0.835484
$184$	−62.3796	+	156.795i	−0.339019	+	0.852146i
$185$	−292.749	−	87.3714i	−1.58243	−	0.472278i
$186$	16.4901			0.0886562
$187$			301.271i			1.61108i
$188$		−	9.26489i		−	0.0492813i
$189$			28.9696i			0.153278i
$190$	204.370	+	60.9946i	1.07563	+	0.321024i
$191$			38.2257i			0.200135i	0.994981	+	0.100067i	$0.0319058\pi$
$191$			38.2257i			0.200135i	−0.994981	+	0.100067i	$0.968094\pi$
$192$		−	201.990i		−	1.05203i
$193$			291.214i			1.50888i	0.656368	+	0.754441i	$0.272092\pi$
$193$			291.214i			1.50888i	−0.656368	+	0.754441i	$0.727908\pi$
$194$		−	359.324i		−	1.85218i
$195$	362.524	+	108.196i	1.85910	+	0.554851i
$196$	24.6705			0.125870
$197$			220.114i			1.11733i	0.829393	+	0.558666i	$0.188687\pi$
$197$			220.114i			1.11733i	−0.829393	+	0.558666i	$0.811313\pi$
$198$	−152.679			−0.771104
$199$		−	96.6571i		−	0.485714i	−0.970062	−	0.242857i	$-0.921915\pi$
$199$		−	96.6571i		−	0.485714i	0.970062	−	0.242857i	$-0.0780846\pi$
$200$	−100.530	+	153.418i	−0.502652	+	0.767091i
$201$		−	172.771i		−	0.859559i
$202$		−	30.9247i		−	0.153093i
$203$	20.0979			0.0990042
$204$			53.0756i			0.260174i
$205$	131.410	+	39.2195i	0.641025	+	0.191315i
$206$			2.47942i			0.0120360i
$207$	−123.469	−	49.1211i	−0.596468	−	0.237300i
$208$			353.230i			1.69822i
$209$	−246.838			−1.18105
$210$	−92.0421	−	27.4701i	−0.438296	−	0.130810i
$211$	26.8501			0.127252			0.0636259	−	0.997974i	$-0.479734\pi$
$211$	26.8501			0.127252			0.0636259	+	0.997974i	$0.479734\pi$
$212$	25.2452			0.119081
$213$			60.9753i			0.286269i
$214$			35.8152i			0.167361i
$215$	178.764	+	53.3523i	0.831459	+	0.248150i
$216$	−90.8888			−0.420781
$217$	−4.69421			−0.0216323
$218$	175.891			0.806840
$219$	389.720			1.77954
$220$	−10.0215	+	33.5782i	−0.0455521	+	0.152628i
$221$			479.529i			2.16981i
$222$	501.945			2.26101
$223$		−	345.589i		−	1.54973i	−0.632128	−	0.774864i	$-0.717819\pi$
$223$		−	345.589i		−	1.54973i	0.632128	−	0.774864i	$-0.282181\pi$
$224$		−	21.0524i		−	0.0939840i
$225$	−120.810	−	79.1631i	−0.536933	−	0.351836i
$226$			162.087i			0.717198i
$227$	138.589			0.610523			0.305262	−	0.952268i	$-0.401256\pi$
$227$	138.589			0.610523			0.305262	+	0.952268i	$0.401256\pi$
$228$	−43.4860			−0.190728
$229$		−	432.525i		−	1.88876i	−0.328860	−	0.944379i	$-0.606665\pi$
$229$		−	432.525i		−	1.88876i	0.328860	−	0.944379i	$-0.393335\pi$
$230$	−152.355	+	192.829i	−0.662415	+	0.838385i
$231$	111.169			0.481249
$232$			63.0547i			0.271787i
$233$		−	91.2442i		−	0.391606i	−0.980643	−	0.195803i	$-0.937269\pi$
$233$		−	91.2442i		−	0.391606i	0.980643	−	0.195803i	$-0.0627313\pi$
$234$	−243.016			−1.03853
$235$	−23.3765	+	78.3259i	−0.0994743	+	0.333302i
$236$	−33.2978			−0.141092
$237$	−533.505			−2.25108
$238$		−	121.749i		−	0.511549i
$239$	−253.670			−1.06138			−0.530691	−	0.847565i	$-0.678068\pi$
$239$	−253.670			−1.06138			−0.530691	+	0.847565i	$0.678068\pi$
$240$	98.6453	−	330.524i	0.411022	−	1.37718i
$241$		−	14.3316i		−	0.0594674i	−0.999558	−	0.0297337i	$-0.990534\pi$
$241$		−	14.3316i		−	0.0594674i	0.999558	−	0.0297337i	$-0.00946593\pi$
$242$		−	68.2238i		−	0.281917i
$243$		−	271.455i		−	1.11710i
$244$		−	22.5406i		−	0.0923796i
$245$	−208.566	−	62.2467i	−0.851289	−	0.254068i
$246$	−225.315			−0.915914
$247$	−392.889			−1.59064
$248$		−	14.7275i		−	0.0593852i
$249$			117.677i			0.472598i
$250$	−204.189	+	172.227i	−0.816755	+	0.688907i
$251$			105.762i			0.421361i	0.977555	+	0.210680i	$0.0675679\pi$
$251$			105.762i			0.421361i	−0.977555	+	0.210680i	$0.932432\pi$
$252$	7.65694			0.0303847
$253$	105.141	−	264.278i	0.415576	−	1.04458i
$254$	169.555			0.667541
$255$	133.916	−	448.704i	0.525162	−	1.75962i
$256$	106.731			0.416918
$257$		−	188.201i		−	0.732298i	−0.930556	−	0.366149i	$-0.880676\pi$
$257$		−	188.201i		−	0.732298i	0.930556	−	0.366149i	$-0.119324\pi$
$258$	−306.507			−1.18801
$259$	−142.888			−0.551693
$260$	−15.9510	+	53.4459i	−0.0613500	+	0.205561i
$261$	−49.6527			−0.190240
$262$			125.447i			0.478804i
$263$	397.936			1.51307			0.756533	−	0.653956i	$-0.226892\pi$
$263$	397.936			1.51307			0.756533	+	0.653956i	$0.226892\pi$
$264$			348.779i			1.32113i
$265$	−213.425	−	63.6969i	−0.805376	−	0.240366i
$266$	99.7514			0.375005
$267$	−204.753			−0.766865
$268$	25.4712			0.0950416
$269$	206.028			0.765904			0.382952	−	0.923768i	$-0.374907\pi$
$269$	206.028			0.765904			0.382952	+	0.923768i	$0.374907\pi$
$270$	−126.836	−	37.8545i	−0.469764	−	0.140202i
$271$	391.537			1.44479			0.722394	−	0.691482i	$-0.243042\pi$
$271$	391.537			1.44479			0.722394	+	0.691482i	$0.243042\pi$
$272$	437.200			1.60735
$273$	176.945			0.648151
$274$		−	21.7561i		−	0.0794020i
$275$	169.444	−	258.586i	0.616160	−	0.940315i
$276$	18.5229	−	46.5584i	0.0671118	−	0.168690i
$277$		−	343.730i		−	1.24090i	−0.784245	−	0.620452i	$-0.786949\pi$
$277$		−	343.730i		−	1.24090i	0.784245	−	0.620452i	$-0.213051\pi$
$278$			510.105i			1.83491i
$279$	11.5973			0.0415673
$280$	−24.5340	+	82.2044i	−0.0876215	+	0.293587i
$281$			411.806i			1.46550i	0.680497	+	0.732751i	$0.261764\pi$
$281$			411.806i			1.46550i	−0.680497	+	0.732751i	$0.738236\pi$
$282$		−	134.297i		−	0.476230i
$283$	−435.711			−1.53962			−0.769808	−	0.638276i	$-0.779648\pi$
$283$	−435.711			−1.53962			−0.769808	+	0.638276i	$0.779648\pi$
$284$	−8.98939			−0.0316528
$285$	367.633	+	109.721i	1.28994	+	0.384985i
$286$		−	520.162i		−	1.81875i
$287$	64.1402			0.223485
$288$			52.0110i			0.180594i
$289$	304.522			1.05371
$290$	−26.2618	+	87.9936i	−0.0905580	+	0.303426i
$291$		−	646.372i		−	2.22121i
$292$			57.4552i			0.196764i
$293$	−500.103			−1.70683			−0.853417	−	0.521228i	$-0.825474\pi$
$293$	−500.103			−1.70683			−0.853417	+	0.521228i	$0.825474\pi$
$294$	357.605			1.21634
$295$	281.501	+	84.0144i	0.954241	+	0.284795i
$296$		−	448.296i		−	1.51451i
$297$	153.193			0.515802
$298$	322.338			1.08167
$299$	167.351	−	420.647i	0.559702	−	1.40685i
$300$	29.8513	−	45.5557i	0.0995043	−	0.151852i
$301$	87.2530			0.289877
$302$		−	346.229i		−	1.14645i
$303$		−	55.6292i		−	0.183595i
$304$			358.207i			1.17831i
$305$	−56.8728	+	190.560i	−0.186468	+	0.624786i
$306$			300.786i			0.982960i
$307$			90.7144i			0.295487i	0.989026	+	0.147743i	$0.0472010\pi$
$307$			90.7144i			0.295487i	−0.989026	+	0.147743i	$0.952799\pi$
$308$			16.3892i			0.0532118i
$309$			4.46013i			0.0144341i
$310$	6.13391	−	20.5525i	0.0197868	−	0.0662982i
$311$	−441.291			−1.41894			−0.709470	−	0.704735i	$-0.751066\pi$
$311$	−441.291			−1.41894			−0.709470	+	0.704735i	$0.751066\pi$
$312$			555.145i			1.77931i
$313$	147.103			0.469977			0.234989	−	0.971998i	$-0.424495\pi$
$313$	147.103			0.469977			0.234989	+	0.971998i	$0.424495\pi$
$314$			427.961i			1.36293i
$315$	−64.7322	−	19.3194i	−0.205499	−	0.0613315i
$316$		−	78.6530i		−	0.248902i
$317$			424.155i			1.33803i	0.743250	+	0.669014i	$0.233283\pi$
$317$			424.155i			1.33803i	−0.743250	+	0.669014i	$0.766717\pi$
$318$	365.936			1.15074
$319$		−	106.279i		−	0.333162i
$320$	−251.751	−	75.1356i	−0.786723	−	0.234799i
$321$			64.4264i			0.200705i
$322$	−42.4891	+	106.799i	−0.131954	+	0.331674i
$323$			486.286i			1.50553i
$324$	56.4566			0.174249
$325$	269.701	−	411.588i	0.829850	−	1.26642i
$326$	−19.2916			−0.0591767
$327$	316.403			0.967594
$328$			201.232i			0.613513i
$329$			38.2302i			0.116201i
$330$	−145.264	+	486.725i	−0.440193	+	1.47492i
$331$	382.184			1.15464			0.577318	−	0.816520i	$-0.304099\pi$
$331$	382.184			1.15464			0.577318	+	0.816520i	$0.304099\pi$
$332$	−17.3488			−0.0522553
$333$	353.012			1.06010
$334$	332.744			0.996240
$335$	−215.335	−	64.2669i	−0.642790	−	0.191842i
$336$		−	161.326i		−	0.480136i
$337$	−285.987			−0.848625			−0.424312	−	0.905516i	$-0.639484\pi$
$337$	−285.987			−0.848625			−0.424312	+	0.905516i	$0.639484\pi$
$338$		−	466.781i		−	1.38101i
$339$			291.571i			0.860092i
$340$	66.1510	+	19.7429i	0.194562	+	0.0580673i
$341$			24.8233i			0.0727955i
$342$	−246.440			−0.720586
$343$	−216.387			−0.630866
$344$			273.746i			0.795774i
$345$	−274.066	+	346.871i	−0.794393	+	1.00542i
$346$	−554.251			−1.60188
$347$		−	72.4616i		−	0.208823i	−0.994534	−	0.104411i	$-0.966704\pi$
$347$		−	72.4616i		−	0.208823i	0.994534	−	0.104411i	$-0.0332959\pi$
$348$		−	18.7233i		−	0.0538027i
$349$	−16.9935			−0.0486919			−0.0243459	−	0.999704i	$-0.507750\pi$
$349$	−16.9935			−0.0486919			−0.0243459	+	0.999704i	$0.507750\pi$
$350$	−68.4750	+	104.499i	−0.195643	+	0.298568i
$351$	243.835			0.694686
$352$	−111.327			−0.316269
$353$		−	276.942i		−	0.784537i	−0.919851	−	0.392269i	$-0.871690\pi$
$353$		−	276.942i		−	0.784537i	0.919851	−	0.392269i	$-0.128310\pi$
$354$	−482.660			−1.36345
$355$	75.9968	+	22.6814i	0.214076	+	0.0638912i
$356$		−	30.1861i		−	0.0847924i
$357$		−	219.009i		−	0.613469i
$358$		−	552.918i		−	1.54446i
$359$			112.871i			0.314403i	0.987567	+	0.157202i	$0.0502473\pi$
$359$			112.871i			0.314403i	−0.987567	+	0.157202i	$0.949753\pi$
$360$	60.6124	−	203.090i	0.168368	−	0.564138i
$361$	−37.4250			−0.103670
$362$	−139.053			−0.384124
$363$		−	122.725i		−	0.338085i
$364$			26.0865i			0.0716662i
$365$	144.967	−	485.729i	0.397169	−	1.33077i
$366$		−	326.732i		−	0.892711i
$367$	−67.7715			−0.184664			−0.0923318	−	0.995728i	$-0.529432\pi$
$367$	−67.7715			−0.184664			−0.0923318	+	0.995728i	$0.529432\pi$
$368$	−383.515	−	152.578i	−1.04216	−	0.414615i
$369$	−158.461			−0.429434
$370$	186.712	−	625.602i	0.504627	−	1.69082i
$371$	−104.171			−0.280784
$372$			4.37316i			0.0117558i
$373$	609.585			1.63428			0.817138	−	0.576442i	$-0.195560\pi$
$373$	609.585			1.63428			0.817138	+	0.576442i	$0.195560\pi$
$374$	−643.814			−1.72143
$375$	−367.307	+	309.812i	−0.979485	+	0.826164i
$376$	−119.943			−0.318997
$377$		−	169.162i		−	0.448706i
$378$	−61.9078			−0.163777
$379$			394.880i			1.04190i	0.853587	+	0.520950i	$0.174422\pi$
$379$			394.880i			1.04190i	−0.853587	+	0.520950i	$0.825578\pi$
$380$	−16.1758	+	54.1990i	−0.0425678	+	0.142629i
$381$	305.006			0.800541
$382$	−81.6881			−0.213843
$383$	288.405			0.753016			0.376508	−	0.926413i	$-0.377125\pi$
$383$	288.405			0.753016			0.376508	+	0.926413i	$0.377125\pi$
$384$	570.077			1.48458
$385$	41.3521	−	138.556i	0.107408	−	0.359884i
$386$	−622.322			−1.61223
$387$	−215.563			−0.557010
$388$	95.2927			0.245600
$389$			332.932i			0.855865i	0.903811	+	0.427933i	$0.140758\pi$
$389$			332.932i			0.855865i	−0.903811	+	0.427933i	$0.859242\pi$
$390$	−231.214	+	774.711i	−0.592856	+	1.98644i
$391$	−520.643	−	207.133i	−1.33157	−	0.529753i
$392$		−	319.383i		−	0.814753i
$393$			225.661i			0.574200i
$394$	−470.382			−1.19386
$395$	−198.451	+	664.937i	−0.502409	+	1.68338i
$396$		−	40.4904i		−	0.102248i
$397$		−	573.612i		−	1.44487i	−0.691441	−	0.722433i	$-0.743024\pi$
$397$		−	573.612i		−	1.44487i	0.691441	−	0.722433i	$-0.256976\pi$
$398$	206.555			0.518983
$399$	179.439			0.449721
$400$	−375.256	−	245.894i	−0.938140	−	0.614735i
$401$			102.519i			0.255658i	0.991796	+	0.127829i	$0.0408008\pi$
$401$			102.519i			0.255658i	−0.991796	+	0.127829i	$0.959199\pi$
$402$	369.211			0.918435
$403$			39.5108i			0.0980417i
$404$	8.20124			0.0203001
$405$	−477.287	−	142.447i	−1.17849	−	0.351721i
$406$			42.9489i			0.105786i
$407$			755.603i			1.85652i
$408$	687.114			1.68410
$409$	−291.413			−0.712501			−0.356250	−	0.934391i	$-0.615945\pi$
$409$	−291.413			−0.712501			−0.356250	+	0.934391i	$0.615945\pi$
$410$	−83.8118	+	280.822i	−0.204419	+	0.684932i
$411$		−	39.1362i		−	0.0952220i
$412$	−0.657543			−0.00159598
$413$	137.398			0.332684
$414$	104.971	−	263.852i	0.253554	−	0.637323i
$415$	146.667	+	43.7731i	0.353415	+	0.105477i
$416$	−177.197			−0.425953
$417$			917.606i			2.20050i
$418$		−	527.491i		−	1.26194i
$419$			713.172i			1.70208i	0.525099	+	0.851041i	$0.324028\pi$
$419$			713.172i			1.70208i	−0.525099	+	0.851041i	$0.675972\pi$
$420$	7.28508	−	24.4096i	0.0173454	−	0.0581181i
$421$		−	281.934i		−	0.669677i	−0.942276	−	0.334839i	$-0.891318\pi$
$421$		−	281.934i		−	0.669677i	0.942276	−	0.334839i	$-0.108682\pi$
$422$			57.3785i			0.135968i
$423$		−	94.4495i		−	0.223285i
$424$		−	326.824i		−	0.770811i
$425$	−509.430	−	333.814i	−1.19866	−	0.785446i
$426$	−130.304			−0.305877
$427$			93.0106i			0.217823i
$428$	−9.49819			−0.0221920
$429$		−	935.697i		−	2.18111i
$430$	−114.013	+	382.016i	−0.265147	+	0.888410i
$431$			428.026i			0.993099i	0.868008	+	0.496550i	$0.165400\pi$
$431$			428.026i			0.993099i	−0.868008	+	0.496550i	$0.834600\pi$
$432$		−	222.311i		−	0.514609i
$433$	423.200			0.977366			0.488683	−	0.872461i	$-0.337477\pi$
$433$	423.200			0.977366			0.488683	+	0.872461i	$0.337477\pi$
$434$		−	10.0315i		−	0.0231140i
$435$	−47.2413	+	158.288i	−0.108601	+	0.363880i
$436$			46.6464i			0.106987i
$437$	169.709	−	426.574i	0.388350	−	0.976143i
$438$			832.828i			1.90143i
$439$	717.383			1.63413			0.817065	−	0.576546i	$-0.195600\pi$
$439$	717.383			1.63413			0.817065	+	0.576546i	$0.195600\pi$
$440$	434.702	+	129.737i	0.987959	+	0.294858i
$441$	251.500			0.570294
$442$	−1024.75			−2.31844
$443$			840.142i			1.89648i	0.317549	+	0.948242i	$0.397140\pi$
$443$			840.142i			1.89648i	−0.317549	+	0.948242i	$0.602860\pi$
$444$			133.116i			0.299811i
$445$	−76.1632	+	255.195i	−0.171153	+	0.573471i
$446$	738.521			1.65588
$447$	579.840			1.29718
$448$	−122.878			−0.274281
$449$	−27.4190			−0.0610669			−0.0305334	−	0.999534i	$-0.509721\pi$
$449$	−27.4190			−0.0610669			−0.0305334	+	0.999534i	$0.509721\pi$
$450$	169.171	−	258.170i	0.375935	−	0.573710i
$451$		−	339.177i		−	0.752056i
$452$	−42.9855			−0.0951006
$453$		−	622.816i		−	1.37487i
$454$			296.163i			0.652342i
$455$	65.8194	−	220.537i	0.144658	−	0.484696i
$456$			562.968i			1.23458i
$457$	−688.774			−1.50717			−0.753583	−	0.657353i	$-0.771676\pi$
$457$	−688.774			−1.50717			−0.753583	+	0.657353i	$0.771676\pi$
$458$	924.303			2.01813
$459$		−	301.799i		−	0.657515i
$460$	−51.1382	−	40.4047i	−0.111170	−	0.0878362i
$461$	354.516			0.769014			0.384507	−	0.923122i	$-0.374371\pi$
$461$	354.516			0.769014			0.384507	+	0.923122i	$0.374371\pi$
$462$			237.566i			0.514213i
$463$			37.2091i			0.0803652i	0.999192	+	0.0401826i	$0.0127940\pi$
$463$			37.2091i			0.0803652i	−0.999192	+	0.0401826i	$0.987206\pi$
$464$	−154.230			−0.332392
$465$	11.0340	−	36.9710i	0.0237291	−	0.0795074i
$466$	194.988			0.418429
$467$	406.456			0.870354			0.435177	−	0.900345i	$-0.356686\pi$
$467$	406.456			0.870354			0.435177	+	0.900345i	$0.356686\pi$
$468$		−	64.4479i		−	0.137709i
$469$	−105.103			−0.224100
$470$	−167.382	−	49.9553i	−0.356131	−	0.106288i
$471$			769.842i			1.63448i
$472$			431.072i			0.913287i
$473$		−	461.399i		−	0.975475i
$474$		−	1140.10i		−	2.40527i
$475$	273.502	−	417.388i	0.575793	−	0.878711i
$476$	32.2878			0.0678314
$477$	257.359			0.539536
$478$		−	542.091i		−	1.13408i
$479$		−	410.394i		−	0.856773i	−0.903596	−	0.428386i	$-0.859082\pi$
$479$		−	410.394i		−	0.856773i	0.903596	−	0.428386i	$-0.140918\pi$
$480$	165.806	+	49.4851i	0.345429	+	0.103094i
$481$			1202.68i			2.50037i
$482$	30.6266			0.0635407
$483$	−76.4319	+	192.116i	−0.158244	+	0.397756i
$484$	18.0930			0.0373822
$485$	−805.610	−	240.435i	−1.66105	−	0.495743i
$486$	580.097			1.19361
$487$			140.203i			0.287891i	0.989586	+	0.143945i	$0.0459789\pi$
$487$			140.203i			0.287891i	−0.989586	+	0.143945i	$0.954021\pi$
$488$	−291.810			−0.597971
$489$	−34.7029			−0.0709670
$490$	133.021	−	445.703i	0.271471	−	0.909598i
$491$	−665.690			−1.35578			−0.677892	−	0.735161i	$-0.737106\pi$
$491$	−665.690			−1.35578			−0.677892	+	0.735161i	$0.737106\pi$
$492$		−	59.7535i		−	0.121450i
$493$	−209.375			−0.424696
$494$		−	839.599i		−	1.69959i
$495$	−102.162	+	342.308i	−0.206389	+	0.691531i
$496$	36.0231			0.0726272
$497$	37.0934			0.0746346
$498$	−251.475			−0.504969
$499$	−112.118			−0.224686			−0.112343	−	0.993669i	$-0.535836\pi$
$499$	−112.118			−0.224686			−0.112343	+	0.993669i	$0.535836\pi$
$500$	−45.6746	−	54.1509i	−0.0913492	−	0.108302i
$501$	598.560			1.19473
$502$	−226.011			−0.450222
$503$	−515.824			−1.02549			−0.512747	−	0.858540i	$-0.671372\pi$
$503$	−515.824			−1.02549			−0.512747	+	0.858540i	$0.671372\pi$
$504$		−	99.1264i		−	0.196679i
$505$	−69.3337	−	20.6928i	−0.137295	−	0.0409758i
$506$	564.760	+	224.685i	1.11613	+	0.444041i
$507$		−	839.673i		−	1.65616i
$508$			44.9661i			0.0885160i
$509$	−139.263			−0.273602			−0.136801	−	0.990599i	$-0.543682\pi$
$509$	−139.263			−0.273602			−0.136801	+	0.990599i	$0.543682\pi$
$510$	958.876	+	286.178i	1.88015	+	0.561133i
$511$		−	237.081i		−	0.463954i
$512$		−	365.107i		−	0.713099i
$513$	247.271			0.482009
$514$	402.183			0.782458
$515$	5.55890	+	1.65906i	0.0107940	+	0.00322148i
$516$		−	81.2856i		−	0.157530i
$517$	202.164			0.391032
$518$		−	305.351i		−	0.589481i
$519$	−997.020			−1.92104
$520$	691.908	+	206.501i	1.33059	+	0.397117i
$521$		−	372.767i		−	0.715484i	−0.933821	−	0.357742i	$-0.883547\pi$
$521$		−	372.767i		−	0.715484i	0.933821	−	0.357742i	$-0.116453\pi$
$522$		−	106.107i		−	0.203271i
$523$	−67.0135			−0.128133			−0.0640665	−	0.997946i	$-0.520407\pi$
$523$	−67.0135			−0.128133			−0.0640665	+	0.997946i	$0.520407\pi$
$524$	−33.2685			−0.0634894
$525$	−123.177	+	187.979i	−0.234623	+	0.358055i
$526$			850.386i			1.61670i
$527$	48.9033			0.0927956
$528$	−853.101			−1.61572
$529$	384.425	+	363.399i	0.726701	+	0.686954i
$530$	136.120	−	456.087i	0.256830	−	0.860541i
$531$	−339.449			−0.639264
$532$			26.4541i			0.0497257i
$533$		−	539.863i		−	1.01288i
$534$		−	437.555i		−	0.819391i
$535$	80.2982	+	23.9651i	0.150090	+	0.0447946i
$536$		−	329.748i		−	0.615202i
$537$		−	994.622i		−	1.85218i
$538$			440.280i			0.818365i
$539$			538.321i			0.998739i
$540$	10.0390	−	33.6370i	0.0185908	−	0.0622908i
$541$	855.637			1.58158			0.790792	−	0.612084i	$-0.209669\pi$
$541$	855.637			1.58158			0.790792	+	0.612084i	$0.209669\pi$
$542$			836.712i			1.54375i
$543$	−250.137			−0.460657
$544$			219.320i			0.403161i
$545$	117.695	−	394.351i	0.215953	−	0.723579i
$546$			378.130i			0.692546i
$547$			526.976i			0.963394i	0.876338	+	0.481697i	$0.159979\pi$
$547$			526.976i			0.963394i	−0.876338	+	0.481697i	$0.840021\pi$
$548$	5.76973			0.0105287
$549$		−	229.787i		−	0.418556i
$550$	552.597	+	362.100i	1.00472	+	0.658364i
$551$		−	171.546i		−	0.311335i
$552$	−602.742	−	239.796i	−1.09192	−	0.434413i
$553$			324.550i			0.586890i
$554$	734.549			1.32590
$555$	335.868	−	1125.37i	0.605168	−	2.02769i
$556$	−135.280			−0.243309
$557$	380.054			0.682322			0.341161	−	0.940005i	$-0.389180\pi$
$557$	380.054			0.682322			0.341161	+	0.940005i	$0.389180\pi$
$558$			24.7833i			0.0444144i
$559$		−	734.402i		−	1.31378i
$560$	−201.069	−	60.0094i	−0.359052	−	0.107160i
$561$	−1158.13			−2.06440
$562$	−880.026			−1.56588
$563$	−658.179			−1.16906			−0.584529	−	0.811373i	$-0.698721\pi$
$563$	−658.179			−1.16906			−0.584529	+	0.811373i	$0.698721\pi$
$564$	35.6156			0.0631482
$565$	363.401	+	108.458i	0.643188	+	0.191960i
$566$		−	931.111i		−	1.64507i
$567$	−232.960			−0.410864
$568$			116.376i			0.204888i
$569$			149.979i			0.263583i	0.991277	+	0.131792i	$0.0420730\pi$
$569$			149.979i			0.263583i	−0.991277	+	0.131792i	$0.957927\pi$
$570$	−234.472	+	785.628i	−0.411354	+	1.37830i
$571$		−	158.157i		−	0.276982i	−0.990364	−	0.138491i	$-0.955775\pi$
$571$		−	158.157i		−	0.276982i	0.990364	−	0.138491i	$-0.0442253\pi$
$572$	137.947			0.241166
$573$	−146.945			−0.256449
$574$			137.067i			0.238793i
$575$	330.379	+	470.611i	0.574572	+	0.818454i
$576$	303.575			0.527040
$577$			1023.66i			1.77411i	0.461663	+	0.887055i	$0.347253\pi$
$577$			1023.66i			1.77411i	−0.461663	+	0.887055i	$0.652747\pi$
$578$			650.761i			1.12588i
$579$	−1119.47			−1.93345
$580$	−23.3359	−	6.96464i	−0.0402343	−	0.0120080i
$581$	71.5871			0.123214
$582$	1381.29			2.37335
$583$			550.862i			0.944874i
$584$	743.813			1.27365
$585$	−162.610	+	544.846i	−0.277966	+	0.931360i
$586$		−	1068.71i		−	1.82375i
$587$		−	704.152i		−	1.19958i	−0.800159	−	0.599788i	$-0.795251\pi$
$587$		−	704.152i		−	1.19958i	0.800159	−	0.599788i	$-0.204749\pi$
$588$			94.8370i			0.161287i
$589$			40.0676i			0.0680264i
$590$	−179.538	+	601.566i	−0.304302	+	1.01960i
$591$	−846.151			−1.43173
$592$	1096.52			1.85222
$593$		−	470.048i		−	0.792662i	−0.918108	−	0.396331i	$-0.870283\pi$
$593$		−	470.048i		−	0.792662i	0.918108	−	0.396331i	$-0.129717\pi$
$594$			327.372i			0.551132i
$595$	−272.962	−	81.4660i	−0.458760	−	0.136918i
$596$			85.4840i			0.143430i
$597$	371.564			0.622385
$598$	898.918	+	357.627i	1.50321	+	0.598039i
$599$	−393.455			−0.656853			−0.328426	−	0.944530i	$-0.606518\pi$
$599$	−393.455			−0.656853			−0.328426	+	0.944530i	$0.606518\pi$
$600$	−589.762	−	386.453i	−0.982936	−	0.644089i
$601$	−752.280			−1.25171			−0.625857	−	0.779938i	$-0.715251\pi$
$601$	−752.280			−1.25171			−0.625857	+	0.779938i	$0.715251\pi$
$602$			186.459i			0.309732i
$603$	259.662			0.430617
$604$	91.8199			0.152020
$605$	−152.959	−	45.6508i	−0.252825	−	0.0754559i
$606$	118.879			0.196170
$607$			58.2233i			0.0959198i	0.998849	+	0.0479599i	$0.0152720\pi$
$607$			58.2233i			0.0959198i	−0.998849	+	0.0479599i	$0.984728\pi$
$608$	−179.694			−0.295549
$609$			77.2591i			0.126862i
$610$	−407.224	−	121.537i	−0.667581	−	0.199240i
$611$	321.781			0.526646
$612$	−79.7684			−0.130341
$613$	−510.208			−0.832313			−0.416157	−	0.909293i	$-0.636623\pi$
$613$	−510.208			−0.832313			−0.416157	+	0.909293i	$0.636623\pi$
$614$	−193.856			−0.315726
$615$	−150.766	+	505.159i	−0.245147	+	0.821397i
$616$	212.174			0.344439
$617$	−216.428			−0.350775			−0.175387	−	0.984499i	$-0.556118\pi$
$617$	−216.428			−0.350775			−0.175387	+	0.984499i	$0.556118\pi$
$618$	−9.53125			−0.0154227
$619$			935.658i			1.51156i	0.654823	+	0.755782i	$0.272743\pi$
$619$			935.658i			1.51156i	−0.654823	+	0.755782i	$0.727257\pi$
$620$	5.45052	+	1.62671i	0.00879115	+	0.00262373i
$621$	−105.325	+	264.741i	−0.169605	+	0.426314i
$622$		−	943.034i		−	1.51613i
$623$			124.558i			0.199933i
$624$	−1357.87			−2.17607
$625$	249.506	+	573.037i	0.399209	+	0.916860i
$626$			314.357i			0.502168i
$627$		−	948.883i		−	1.51337i
$628$	−113.495			−0.180725
$629$	1488.58			2.36658
$630$	41.2854	−	138.332i	0.0655324	−	0.219575i
$631$			63.6033i			0.100798i	0.998729	+	0.0503988i	$0.0160492\pi$
$631$			63.6033i			0.100798i	−0.998729	+	0.0503988i	$0.983951\pi$
$632$	−1018.24			−1.61114
$633$			103.216i			0.163058i
$634$	−906.415			−1.42968
$635$	113.455	−	380.146i	0.178670	−	0.598655i
$636$			97.0464i			0.152589i
$637$			856.836i			1.34511i
$638$	227.117			0.355982
$639$	−91.6410			−0.143413
$640$	212.055	−	710.519i	0.331336	−	1.11019i
$641$		−	852.374i		−	1.32976i	−0.746952	−	0.664878i	$-0.768484\pi$
$641$		−	852.374i		−	1.32976i	0.746952	−	0.664878i	$-0.231516\pi$
$642$	−137.679			−0.214453
$643$	876.571			1.36325			0.681626	−	0.731701i	$-0.261273\pi$
$643$	876.571			1.36325			0.681626	+	0.731701i	$0.261273\pi$
$644$	−28.3231	−	11.2681i	−0.0439800	−	0.0174971i
$645$	−205.094	+	687.193i	−0.317975	+	1.06542i
$646$	−1039.19			−1.60865
$647$		−	169.890i		−	0.262581i	−0.991344	−	0.131291i	$-0.958088\pi$
$647$		−	169.890i		−	0.262581i	0.991344	−	0.131291i	$-0.0419121\pi$
$648$		−	730.885i		−	1.12791i
$649$		−	726.571i		−	1.11952i
$650$	879.559	+	576.349i	1.35317	+	0.886691i
$651$		−	18.0452i		−	0.0277192i
$652$		−	5.11614i		−	0.00784683i
$653$			518.968i			0.794745i	0.917657	+	0.397372i	$0.130078\pi$
$653$			518.968i			0.794745i	−0.917657	+	0.397372i	$0.869922\pi$
$654$			676.151i			1.03387i
$655$	281.253	+	83.9405i	0.429394	+	0.128153i
$656$	−492.208			−0.750317
$657$			585.719i			0.891505i
$658$	−81.6976			−0.124160
$659$			798.984i			1.21242i	0.795305	+	0.606210i	$0.207311\pi$
$659$			798.984i			1.21242i	−0.795305	+	0.606210i	$0.792689\pi$
$660$	−129.079	−	38.5240i	−0.195575	−	0.0583696i
$661$		−	172.343i		−	0.260730i	−0.991466	−	0.130365i	$-0.958385\pi$
$661$		−	172.343i		−	0.260730i	0.991466	−	0.130365i	$-0.0416149\pi$
$662$			816.724i			1.23372i
$663$	−1843.38			−2.78036
$664$			224.596i			0.338247i
$665$	66.7469	−	223.644i	0.100371	−	0.336307i
$666$			754.384i			1.13271i
$667$	183.666	+	73.0699i	0.275361	+	0.109550i
$668$			88.2438i			0.132102i
$669$	1328.49			1.98579
$670$	137.338	−	460.168i	0.204982	−	0.686818i
$671$	491.846			0.733004
$672$	80.9285			0.120429
$673$		−	159.935i		−	0.237645i	−0.992916	−	0.118822i	$-0.962088\pi$
$673$		−	159.935i		−	0.237645i	0.992916	−	0.118822i	$-0.0379119\pi$
$674$		−	611.151i		−	0.906752i
$675$	−169.741	+	259.040i	−0.251468	+	0.383762i
$676$	123.790			0.183122
$677$	383.674			0.566727			0.283363	−	0.959013i	$-0.408550\pi$
$677$	383.674			0.566727			0.283363	+	0.959013i	$0.408550\pi$
$678$	−623.085			−0.919005
$679$	−393.211			−0.579104
$680$	255.590	−	856.388i	0.375868	−	1.25939i
$681$			532.755i			0.782314i
$682$	−53.0471			−0.0777817
$683$		−	438.070i		−	0.641391i	−0.947182	−	0.320696i	$-0.896083\pi$
$683$		−	438.070i		−	0.641391i	0.947182	−	0.320696i	$-0.103917\pi$
$684$		−	65.3561i		−	0.0955498i
$685$	−48.7776	−	14.5578i	−0.0712082	−	0.0212522i
$686$		−	462.417i		−	0.674078i
$687$	1662.69			2.42022
$688$	−669.575			−0.973219
$689$			876.797i			1.27257i
$690$	−741.261	−	585.676i	−1.07429	−	0.848806i
$691$	−20.2356			−0.0292846			−0.0146423	−	0.999893i	$-0.504661\pi$
$691$	−20.2356			−0.0292846			−0.0146423	+	0.999893i	$0.504661\pi$
$692$		−	146.988i		−	0.212410i
$693$			167.078i			0.241093i
$694$	154.850			0.223126
$695$	1143.66	+	341.328i	1.64556	+	0.491119i
$696$	−242.391			−0.348263
$697$	−668.199			−0.958678
$698$		−	36.3149i		−	0.0520270i
$699$	350.756			0.501797
$700$	−27.7131	−	18.1596i	−0.0395902	−	0.0259423i
$701$		−	1191.83i		−	1.70019i	−0.526630	−	0.850095i	$-0.676545\pi$
$701$		−	1191.83i		−	1.70019i	0.526630	−	0.850095i	$-0.323455\pi$
$702$			521.073i			0.742269i
$703$			1219.63i			1.73489i
$704$			649.785i			0.922990i
$705$	−301.096	−	89.8625i	−0.427086	−	0.127465i
$706$	591.822			0.838275
$707$	−33.8412			−0.0478659
$708$		−	128.001i		−	0.180793i
$709$			224.172i			0.316181i	0.987425	+	0.158090i	$0.0505338\pi$
$709$			224.172i			0.316181i	−0.987425	+	0.158090i	$0.949466\pi$
$710$	−48.4699	+	162.404i	−0.0682674	+	0.228739i
$711$		−	801.817i		−	1.12773i
$712$	−390.788			−0.548859
$713$	−42.8984	−	17.0668i	−0.0601660	−	0.0239366i
$714$	468.019			0.655489
$715$	−1166.21	−	348.057i	−1.63106	−	0.486794i
$716$	146.634			0.204796
$717$		−	975.146i		−	1.36004i
$718$	−241.204			−0.335939
$719$	−307.494			−0.427669			−0.213834	−	0.976870i	$-0.568595\pi$
$719$	−307.494			−0.427669			−0.213834	+	0.976870i	$0.568595\pi$
$720$	496.751	+	148.256i	0.689932	+	0.205911i
$721$	2.71325			0.00376318
$722$		−	79.9768i		−	0.110771i
$723$	55.0929			0.0762005
$724$		−	36.8769i		−	0.0509349i
$725$	179.710	+	117.759i	0.247876	+	0.162426i
$726$	262.262			0.361243
$727$	230.522			0.317086			0.158543	−	0.987352i	$-0.449320\pi$
$727$	230.522			0.317086			0.158543	+	0.987352i	$0.449320\pi$
$728$	337.714			0.463893
$729$	146.949			0.201576
$730$	1038.00	+	309.792i	1.42192	+	0.424373i
$731$	−908.984			−1.24348
$732$	86.6494			0.118374
$733$	954.400			1.30205			0.651023	−	0.759058i	$-0.274340\pi$
$733$	954.400			1.30205			0.651023	+	0.759058i	$0.274340\pi$
$734$		−	144.827i		−	0.197312i
$735$	239.285	−	801.757i	0.325558	−	1.09083i
$736$	76.5404	−	192.389i	0.103995	−	0.261398i
$737$			555.791i			0.754127i
$738$		−	338.630i		−	0.458849i
$739$	−267.111			−0.361450			−0.180725	−	0.983534i	$-0.557844\pi$
$739$	−267.111			−0.361450			−0.180725	+	0.983534i	$0.557844\pi$
$740$	165.910	+	49.5160i	0.224202	+	0.0669135i
$741$		−	1510.32i		−	2.03822i
$742$		−	222.612i		−	0.300016i
$743$	−568.660			−0.765356			−0.382678	−	0.923882i	$-0.624998\pi$
$743$	−568.660			−0.765356			−0.382678	+	0.923882i	$0.624998\pi$
$744$	56.6148			0.0760951
$745$	215.687	−	722.686i	0.289512	−	0.970048i
$746$			1302.68i			1.74622i
$747$	−176.859			−0.236759
$748$		−	170.740i		−	0.228262i
$749$	39.1929			0.0523269
$750$	−662.065	−	784.932i	−0.882753	−	1.04658i
$751$			1022.64i			1.36170i	0.732421	+	0.680852i	$0.238391\pi$
$751$			1022.64i			1.36170i	−0.732421	+	0.680852i	$0.761609\pi$
$752$		−	293.376i		−	0.390128i
$753$	−406.563			−0.539924
$754$	361.498			0.479440
$755$	−776.250	−	231.673i	−1.02815	−	0.306852i
$756$		−	16.4180i		−	0.0217169i
$757$	−828.595			−1.09458			−0.547288	−	0.836944i	$-0.684340\pi$
$757$	−828.595			−1.09458			−0.547288	+	0.836944i	$0.684340\pi$
$758$	−843.855			−1.11327
$759$	1015.92	+	404.176i	1.33850	+	0.532512i
$760$	701.658	+	209.411i	0.923234	+	0.275541i
$761$	339.901			0.446650			0.223325	−	0.974744i	$-0.428309\pi$
$761$	339.901			0.446650			0.223325	+	0.974744i	$0.428309\pi$
$762$			651.796i			0.855375i
$763$		−	192.479i		−	0.252266i
$764$		−	21.6637i		−	0.0283556i
$765$	674.367	+	201.266i	0.881525	+	0.263092i
$766$			616.319i			0.804594i
$767$		−	1156.47i		−	1.50779i
$768$			410.290i			0.534232i
$769$		−	52.1119i		−	0.0677658i	−0.999426	−	0.0338829i	$-0.989213\pi$
$769$		−	52.1119i		−	0.0677658i	0.999426	−	0.0338829i	$-0.0107873\pi$
$770$	296.092	+	88.3691i	0.384535	+	0.114765i
$771$	723.471			0.938354
$772$		−	165.040i		−	0.213782i
$773$	−279.360			−0.361397			−0.180699	−	0.983539i	$-0.557836\pi$
$773$	−279.360			−0.361397			−0.180699	+	0.983539i	$0.557836\pi$
$774$		−	460.656i		−	0.595162i
$775$	−41.9745	−	27.5047i	−0.0541607	−	0.0354899i
$776$		−	1233.66i		−	1.58976i
$777$		−	549.284i		−	0.706929i
$778$	−711.472			−0.914488
$779$		−	547.470i		−	0.702786i
$780$	−205.454	−	61.3179i	−0.263402	−	0.0786128i
$781$		−	196.152i		−	0.251155i
$782$	442.642	−	1112.61i	0.566039	−	1.42277i
$783$			106.465i			0.135971i
$784$	781.201			0.996430
$785$	959.496	+	286.363i	1.22229	+	0.364794i
$786$	−482.235			−0.613530
$787$	1169.59			1.48613			0.743066	−	0.669218i	$-0.233371\pi$
$787$	1169.59			1.48613			0.743066	+	0.669218i	$0.233371\pi$
$788$		−	124.745i		−	0.158306i
$789$			1529.72i			1.93881i
$790$	−1420.96	−	424.089i	−1.79869	−	0.536821i
$791$	177.373			0.224239
$792$	−524.187			−0.661852
$793$	782.863			0.987217
$794$	1225.80			1.54383
$795$	244.860	−	820.435i	0.308000	−	1.03199i
$796$			54.7785i			0.0688173i
$797$	−556.581			−0.698345			−0.349173	−	0.937058i	$-0.613537\pi$
$797$	−556.581			−0.698345			−0.349173	+	0.937058i	$0.613537\pi$
$798$			383.459i			0.480525i
$799$		−	398.274i		−	0.498466i
$800$	123.352	−	188.246i	0.154190	−	0.235307i
$801$		−	307.727i		−	0.384179i
$802$	−219.082			−0.273169
$803$	−1253.70			−1.56127
$804$			97.9148i			0.121785i
$805$	211.014	+	166.724i	0.262129	+	0.207110i
$806$	−84.4342			−0.104757
$807$			792.002i			0.981415i
$808$		−	106.173i		−	0.131402i
$809$	−734.308			−0.907674			−0.453837	−	0.891085i	$-0.649945\pi$
$809$	−734.308			−0.907674			−0.453837	+	0.891085i	$0.649945\pi$
$810$	304.408	−	1019.96i	0.375813	−	1.25921i
$811$	1190.06			1.46739			0.733696	−	0.679477i	$-0.237793\pi$
$811$	1190.06			1.46739			0.733696	+	0.679477i	$0.237793\pi$
$812$	−11.3901			−0.0140272
$813$			1505.13i			1.85132i
$814$	−1614.72			−1.98368
$815$	−12.9086	+	43.2521i	−0.0158388	+	0.0530700i
$816$			1680.66i			2.05963i
$817$		−	744.751i		−	0.911567i
$818$		−	622.746i		−	0.761304i
$819$			265.935i			0.324707i
$820$	−74.4741	−	22.2269i	−0.0908221	−	0.0271060i
$821$	821.953			1.00116			0.500580	−	0.865690i	$-0.333120\pi$
$821$	821.953			1.00116			0.500580	+	0.865690i	$0.333120\pi$
$822$	83.6338			0.101744
$823$		−	696.134i		−	0.845850i	−0.906165	−	0.422925i	$-0.861003\pi$
$823$		−	696.134i		−	0.845850i	0.906165	−	0.422925i	$-0.138997\pi$
$824$			8.51252i			0.0103307i
$825$	994.044	+	651.367i	1.20490	+	0.789536i
$826$			293.619i			0.355471i
$827$	553.782			0.669627			0.334814	−	0.942284i	$-0.391327\pi$
$827$	553.782			0.669627			0.334814	+	0.942284i	$0.391327\pi$
$828$	69.9736	+	27.8384i	0.0845091	+	0.0336213i
$829$	−681.344			−0.821887			−0.410943	−	0.911661i	$-0.634801\pi$
$829$	−681.344			−0.821887			−0.410943	+	0.911661i	$0.634801\pi$
$830$	−93.5427	+	313.427i	−0.112702	+	0.377623i
$831$	1321.35			1.59007
$832$			1034.25i			1.24309i
$833$	1060.52			1.27314
$834$	−1960.92			−2.35122
$835$	222.650	−	746.018i	0.266647	−	0.893434i
$836$	139.891			0.167334
$837$		−	24.8668i		−	0.0297094i
$838$	−1524.04			−1.81867
$839$		−	84.8332i		−	0.101112i	−0.998721	−	0.0505561i	$-0.983901\pi$
$839$		−	84.8332i		−	0.101112i	0.998721	−	0.0505561i	$-0.0160994\pi$
$840$	−316.006	−	94.3123i	−0.376197	−	0.112277i
$841$	−767.139			−0.912175
$842$	602.491			0.715547
$843$	−1583.04			−1.87787
$844$	−15.2168			−0.0180294
$845$	−1046.53	−	312.339i	−1.23850	−	0.369632i
$846$	201.838			0.238579
$847$	−74.6580			−0.0881440
$848$	799.401			0.942689
$849$		−	1674.94i		−	1.97284i
$850$	713.359	−	1088.65i	0.839245	−	1.28076i
$851$	−1305.80	−	519.500i	−1.53443	−	0.610459i
$852$		−	34.5565i		−	0.0405593i
$853$		−	1252.43i		−	1.46827i	−0.679006	−	0.734133i	$-0.737589\pi$
$853$		−	1252.43i		−	1.46827i	0.679006	−	0.734133i	$-0.262411\pi$
$854$	−198.763			−0.232743
$855$	−164.901	+	552.523i	−0.192867	+	0.646226i
$856$			122.963i			0.143648i
$857$		−	124.596i		−	0.145386i	−0.997354	−	0.0726932i	$-0.976841\pi$
$857$		−	124.596i		−	0.145386i	0.997354	−	0.0726932i	$-0.0231594\pi$
$858$	1999.58			2.33051
$859$	828.896			0.964954			0.482477	−	0.875909i	$-0.339737\pi$
$859$	828.896			0.964954			0.482477	+	0.875909i	$0.339737\pi$
$860$	−101.311	−	30.2363i	−0.117803	−	0.0351585i
$861$			246.564i			0.286369i
$862$	−914.687			−1.06112
$863$			714.172i			0.827545i	0.910380	+	0.413773i	$0.135789\pi$
$863$			714.172i			0.827545i	−0.910380	+	0.413773i	$0.864211\pi$
$864$	111.522			0.129076
$865$	−370.868	+	1242.64i	−0.428749	+	1.43658i
$866$			904.374i			1.04431i
$867$			1170.63i			1.35021i
$868$	2.66035			0.00306492
$869$	1716.24			1.97496
$870$	−338.260	−	100.954i	−0.388805	−	0.116039i
$871$			884.644i			1.01566i
$872$	603.882			0.692525
$873$	971.447			1.11277
$874$	911.585	+	362.667i	1.04300	+	0.414951i
$875$	188.469	+	223.446i	0.215394	+	0.255367i
$876$	−220.866			−0.252130
$877$			400.666i			0.456860i	0.973560	+	0.228430i	$0.0733591\pi$
$877$			400.666i			0.456860i	−0.973560	+	0.228430i	$0.926641\pi$
$878$			1533.04i			1.74606i
$879$		−	1922.47i		−	2.18711i
$880$	−317.334	+	1063.27i	−0.360606	+	1.20826i
$881$		−	623.139i		−	0.707308i	−0.935376	−	0.353654i	$-0.884939\pi$
$881$		−	623.139i		−	0.707308i	0.935376	−	0.353654i	$-0.115061\pi$
$882$			537.453i			0.609357i
$883$		−	1007.56i		−	1.14107i	−0.821275	−	0.570533i	$-0.806737\pi$
$883$		−	1007.56i		−	1.14107i	0.821275	−	0.570533i	$-0.193263\pi$
$884$		−	271.764i		−	0.307425i
$885$	−322.964	+	1082.13i	−0.364931	+	1.22275i
$886$	−1795.38			−2.02638
$887$			83.9997i			0.0947010i	0.998878	+	0.0473505i	$0.0150778\pi$
$887$			83.9997i			0.0947010i	−0.998878	+	0.0473505i	$0.984922\pi$
$888$	1723.31			1.94067
$889$		−	185.546i		−	0.208713i
$890$	−545.349	−	162.760i	−0.612751	−	0.182877i
$891$			1231.91i			1.38261i
$892$			195.856i			0.219569i
$893$	326.315			0.365414
$894$			1239.11i			1.38603i
$895$	−1239.65	−	369.976i	−1.38509	−	0.413381i
$896$		−	346.798i		−	0.387052i
$897$	1617.03	+	643.321i	1.80271	+	0.717192i
$898$		−	58.5942i		−	0.0652497i
$899$	−17.2515			−0.0191896
$900$	68.4666	+	44.8641i	0.0760740	+	0.0498490i
$901$	1085.23			1.20447
$902$	724.819			0.803568
$903$			335.413i			0.371443i
$904$			556.488i			0.615584i
$905$	−93.0449	+	311.759i	−0.102812	+	0.344485i
$906$	1330.95			1.46904
$907$	−1450.67			−1.59942			−0.799709	−	0.600387i	$-0.795013\pi$
$907$	−1450.67			−1.59942			−0.799709	+	0.600387i	$0.795013\pi$
$908$	−78.5425			−0.0865006
$909$	83.6063			0.0919762
$910$	471.285	+	140.656i	0.517895	+	0.154567i
$911$			1100.55i			1.20807i	0.796958	+	0.604035i	$0.206441\pi$
$911$			1100.55i			1.20807i	−0.796958	+	0.604035i	$0.793559\pi$
$912$	−1377.00			−1.50987
$913$		−	378.557i		−	0.414630i
$914$		−	1471.90i		−	1.61040i
$915$	−732.539	−	218.627i	−0.800589	−	0.238937i
$916$			245.125i			0.267604i
$917$	137.277			0.149703
$918$	644.942			0.702552
$919$		−	1317.01i		−	1.43309i	−0.697540	−	0.716546i	$-0.745722\pi$
$919$		−	1317.01i		−	1.43309i	0.697540	−	0.716546i	$-0.254278\pi$
$920$	−523.077	+	662.032i	−0.568562	+	0.719600i
$921$	−348.719			−0.378631
$922$			757.597i			0.821688i
$923$		−	312.212i		−	0.338258i
$924$	−63.0026			−0.0681847
$925$	−1277.67	−	837.222i	−1.38127	−	0.905105i
$926$	−79.5155			−0.0858699
$927$	−6.70322			−0.00723109
$928$		−	77.3688i		−	0.0833716i
$929$	−1281.15			−1.37906			−0.689532	−	0.724255i	$-0.742184\pi$
$929$	−1281.15			−1.37906			−0.689532	+	0.724255i	$0.742184\pi$
$930$	79.0066	+	23.5796i	0.0849533	+	0.0253545i
$931$			868.910i			0.933308i
$932$			51.7109i			0.0554838i
$933$		−	1696.38i		−	1.81820i
$934$			868.592i			0.929970i
$935$	−430.798	+	1443.44i	−0.460746	+	1.54379i
$936$	−834.339			−0.891388
$937$	17.7790			0.0189744			0.00948722	−	0.999955i	$-0.496980\pi$
$937$	17.7790			0.0189744			0.00948722	+	0.999955i	$0.496980\pi$
$938$		−	224.604i		−	0.239450i
$939$			565.485i			0.602220i
$940$	13.2482	−	44.3897i	0.0140938	−	0.0472230i
$941$		−	1773.82i		−	1.88504i	−0.334153	−	0.942519i	$-0.608450\pi$
$941$		−	1773.82i		−	1.88504i	0.334153	−	0.942519i	$-0.391550\pi$
$942$	−1645.14			−1.74644
$943$	586.150	+	233.195i	0.621580	+	0.247290i
$944$	−1054.39			−1.11694
$945$	−41.4245	+	138.798i	−0.0438355	+	0.146876i
$946$	986.007			1.04229
$947$		−	1187.61i		−	1.25408i	−0.778987	−	0.627040i	$-0.784266\pi$
$947$		−	1187.61i		−	1.25408i	0.778987	−	0.627040i	$-0.215734\pi$
$948$	302.354			0.318938
$949$	−1995.49			−2.10273
$950$	891.954	+	584.470i	0.938899	+	0.615232i
$951$	−1630.51			−1.71452
$952$		−	417.996i		−	0.439071i
$953$	181.658			0.190617			0.0953086	−	0.995448i	$-0.469616\pi$
$953$	181.658			0.190617			0.0953086	+	0.995448i	$0.469616\pi$
$954$			549.974i			0.576492i
$955$	−54.6602	+	183.146i	−0.0572358	+	0.191776i
$956$	143.763			0.150379
$957$	408.551			0.426908
$958$	877.008			0.915458
$959$	−23.8080			−0.0248258
$960$	288.832	−	967.769i	0.300867	−	1.00809i
$961$	−956.971			−0.995807
$962$	−2570.12			−2.67164
$963$	−96.8278			−0.100548
$964$			8.12218i			0.00842550i
$965$	−416.416	+	1395.26i	−0.431520	+	1.44586i
$966$	−410.551	−	163.334i	−0.425001	−	0.169083i
$967$		−	1264.97i		−	1.30814i	−0.756436	−	0.654068i	$-0.773061\pi$
$967$		−	1264.97i		−	1.30814i	0.756436	−	0.654068i	$-0.226939\pi$
$968$		−	234.231i		−	0.241974i
$969$	−1869.35			−1.92916
$970$	513.808	−	1721.58i	0.529699	−	1.77483i
$971$			1449.14i			1.49242i	0.665708	+	0.746212i	$0.268130\pi$
$971$			1449.14i			1.49242i	−0.665708	+	0.746212i	$0.731870\pi$
$972$			153.842i			0.158273i
$973$	558.213			0.573703
$974$	−299.612			−0.307610
$975$	1582.20	+	1036.77i	1.62277	+	1.06335i
$976$		−	713.758i		−	0.731309i
$977$	569.734			0.583146			0.291573	−	0.956549i	$-0.405821\pi$
$977$	569.734			0.583146			0.291573	+	0.956549i	$0.405821\pi$
$978$		−	74.1597i		−	0.0758279i
$979$	658.673			0.672802
$980$	118.201	+	35.2771i	0.120613	+	0.0359971i
$981$			475.529i			0.484739i
$982$		−	1422.57i		−	1.44865i
$983$	1205.40			1.22625			0.613123	−	0.789988i	$-0.289913\pi$
$983$	1205.40			1.22625			0.613123	+	0.789988i	$0.289913\pi$
$984$	−773.566			−0.786145
$985$	−314.748	+	1054.60i	−0.319541	+	1.07066i
$986$		−	447.433i		−	0.453786i
$987$	−146.962			−0.148898
$988$	222.662			0.225366
$989$	797.368	+	317.226i	0.806237	+	0.320755i
$990$	−731.509	−	218.320i	−0.738898	−	0.220525i
$991$	742.126			0.748865			0.374433	−	0.927254i	$-0.377837\pi$
$991$	742.126			0.748865			0.374433	+	0.927254i	$0.377837\pi$
$992$			18.0709i			0.0182166i
$993$			1469.17i			1.47953i
$994$			79.2683i			0.0797468i
$995$	138.213	−	463.101i	0.138908	−	0.465428i
$996$		−	66.6911i		−	0.0669590i
$997$		−	828.202i		−	0.830694i	−0.909663	−	0.415347i	$-0.863660\pi$
$997$		−	828.202i		−	0.830694i	0.909663	−	0.415347i	$-0.136340\pi$
$998$		−	239.596i		−	0.240076i
$999$		−	756.926i		−	0.757684i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	115.3.c.c.114.16	yes	20
5.2	odd	4		575.3.d.i.551.6		20
5.3	odd	4		575.3.d.i.551.15		20
5.4	even	2	inner	115.3.c.c.114.5	✓	20
23.22	odd	2	inner	115.3.c.c.114.15	yes	20
115.22	even	4		575.3.d.i.551.5		20
115.68	even	4		575.3.d.i.551.16		20
115.114	odd	2	inner	115.3.c.c.114.6	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.3.c.c.114.5	✓	20	5.4	even	2	inner
115.3.c.c.114.6	yes	20	115.114	odd	2	inner
115.3.c.c.114.15	yes	20	23.22	odd	2	inner
115.3.c.c.114.16	yes	20	1.1	even	1	trivial
575.3.d.i.551.5		20	115.22	even	4
575.3.d.i.551.6		20	5.2	odd	4
575.3.d.i.551.15		20	5.3	odd	4
575.3.d.i.551.16		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)

\(f(q)\)	\(=\)	\(q+2.13699i q^{2} +3.84414i q^{3} -0.566730 q^{4} +(4.79117 + 1.42993i) q^{5} -8.21490 q^{6} +2.33853 q^{7} +7.33687i q^{8} -5.77745 q^{9} +O(q^{10})\)	\(q+2.13699i q^{2} +3.84414i q^{3} -0.566730 q^{4} +(4.79117 + 1.42993i) q^{5} -8.21490 q^{6} +2.33853 q^{7} +7.33687i q^{8} -5.77745 q^{9} +(-3.05575 + 10.2387i) q^{10} -12.3663i q^{11} -2.17859i q^{12} -19.6832i q^{13} +4.99742i q^{14} +(-5.49686 + 18.4179i) q^{15} -17.9457 q^{16} -24.3623 q^{17} -12.3464i q^{18} -19.9606i q^{19} +(-2.71530 - 0.810386i) q^{20} +8.98965i q^{21} +26.4267 q^{22} +(21.3708 + 8.50221i) q^{23} -28.2040 q^{24} +(20.9106 + 13.7021i) q^{25} +42.0629 q^{26} +12.3880i q^{27} -1.32532 q^{28} +8.59423 q^{29} +(-39.3590 - 11.7467i) q^{30} -2.00733 q^{31} -9.00242i q^{32} +47.5378 q^{33} -52.0620i q^{34} +(11.2043 + 3.34394i) q^{35} +3.27426 q^{36} -61.1018 q^{37} +42.6556 q^{38} +75.6651 q^{39} +(-10.4912 + 35.1522i) q^{40} +27.4276 q^{41} -19.2108 q^{42} +37.3111 q^{43} +7.00835i q^{44} +(-27.6807 - 8.26135i) q^{45} +(-18.1691 + 45.6693i) q^{46} +16.3480i q^{47} -68.9860i q^{48} -43.5313 q^{49} +(-29.2812 + 44.6857i) q^{50} -93.6523i q^{51} +11.1551i q^{52} -44.5454 q^{53} -26.4730 q^{54} +(17.6829 - 59.2490i) q^{55} +17.1575i q^{56} +76.7314 q^{57} +18.3658i q^{58} +58.7542 q^{59} +(3.11524 - 10.4380i) q^{60} +39.7731i q^{61} -4.28965i q^{62} -13.5107 q^{63} -52.5449 q^{64} +(28.1457 - 94.3056i) q^{65} +101.588i q^{66} -44.9441 q^{67} +13.8069 q^{68} +(-32.6837 + 82.1526i) q^{69} +(-7.14596 + 23.9435i) q^{70} +15.8619 q^{71} -42.3884i q^{72} -101.380i q^{73} -130.574i q^{74} +(-52.6728 + 80.3833i) q^{75} +11.3123i q^{76} -28.9189i q^{77} +161.696i q^{78} +138.784i q^{79} +(-85.9811 - 25.6612i) q^{80} -99.6181 q^{81} +58.6125i q^{82} +30.6120 q^{83} -5.09471i q^{84} +(-116.724 - 34.8364i) q^{85} +79.7334i q^{86} +33.0374i q^{87} +90.7298 q^{88} +53.2636i q^{89} +(17.6544 - 59.1535i) q^{90} -46.0298i q^{91} +(-12.1115 - 4.81846i) q^{92} -7.71648i q^{93} -34.9355 q^{94} +(28.5423 - 95.6345i) q^{95} +34.6066 q^{96} -168.145 q^{97} -93.0259i q^{98} +71.4456i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 56 q^{4} - 8 q^{6} - 72 q^{9}+O(q^{10}) \) 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