LMFDB - Embedded newform 115.3.c.c.114.15

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			114.15
Root			$4.79117 - 1.42993i$ of defining polynomial
Character	$\chi$	$=$	115.114
Dual form			115.3.c.c.114.5

$q$-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	$-0.553420\pi$
$7$	−2.33853			−0.334076			−0.167038	+	0.985950i	$0.553420\pi$
$8$			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	$0.190008\pi$
$11$			12.3663i			1.12421i	−0.827066	+	0.562104i	$0.809992\pi$
$12$		−	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	$-0.245725\pi$
$17$	24.3623			1.43308			0.716539	+	0.697547i	$0.245725\pi$
$18$		−	12.3464i		−	0.685909i
$19$			19.9606i			1.05056i	0.850930	+	0.525279i	$0.176039\pi$
$19$			19.9606i			1.05056i	−0.850930	+	0.525279i	$0.823961\pi$
$20$	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	$-0.190780\pi$
$37$	61.1018			1.65140			0.825700	+	0.564110i	$0.190780\pi$
$38$	−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	$-0.642845\pi$
$43$	−37.3111			−0.867699			−0.433850	+	0.900985i	$0.642845\pi$
$44$		−	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	$-0.361946\pi$
$53$	44.5454			0.840480			0.420240	+	0.907413i	$0.361946\pi$
$54$	−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	$-0.894296\pi$
$61$		−	39.7731i		−	0.652018i	0.945367	−	0.326009i	$-0.105704\pi$
$62$		−	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	$-0.391127\pi$
$67$	44.9441			0.670807			0.335403	+	0.942075i	$0.391127\pi$
$68$	−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	$-0.658625\pi$
$79$		−	138.784i		−	1.75676i	0.477965	−	0.878379i	$-0.341375\pi$
$80$	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	$-0.559037\pi$
$83$	−30.6120			−0.368819			−0.184410	+	0.982849i	$0.559037\pi$
$84$			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	$-0.903269\pi$
$89$		−	53.2636i		−	0.598467i	0.954180	−	0.299234i	$-0.0967310\pi$
$90$	−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	$-0.166221\pi$
$97$	168.145			1.73345			0.866725	+	0.498786i	$0.166221\pi$
$98$		−	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	$-0.501793\pi$
$103$	−1.16024			−0.0112645			−0.00563223	+	0.999984i	$0.501793\pi$
$104$	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	$-0.524954\pi$
$107$	−16.7596			−0.156632			−0.0783160	+	0.996929i	$0.524954\pi$
$108$		−	7.02063i		−	0.0650059i
$109$			82.3078i			0.755118i	0.925986	+	0.377559i	$0.123236\pi$
$109$			82.3078i			0.755118i	−0.925986	+	0.377559i	$0.876764\pi$
$110$	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	$-0.608943\pi$
$113$	−75.8482			−0.671223			−0.335611	+	0.942001i	$0.608943\pi$
$114$		−	163.974i		−	1.43837i
$115$	114.549	−	10.1767i	0.996077	−	0.0884930i
$116$	−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	$-0.488170\pi$
$137$	10.1807			0.0743120			0.0371560	+	0.999309i	$0.488170\pi$
$138$	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	$0.168937\pi$
$149$			150.837i			1.01233i	−0.862437	+	0.506165i	$0.831063\pi$
$150$	−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	$-0.720148\pi$
$157$	−200.263			−1.27556			−0.637782	+	0.770217i	$0.720148\pi$
$158$	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	$-0.942471\pi$
$181$		−	65.0695i		−	0.359500i	0.983712	−	0.179750i	$-0.0575289\pi$
$182$	−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	$-0.968094\pi$
$191$		−	38.2257i		−	0.200135i	0.994981	−	0.100067i	$-0.0319058\pi$
$192$		−	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	$0.0780846\pi$
$199$			96.6571i			0.485714i	−0.970062	+	0.242857i	$0.921915\pi$
$200$	−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	$-0.598744\pi$
$227$	−138.589			−0.610523			−0.305262	+	0.952268i	$0.598744\pi$
$228$	43.4860			0.190728
$229$			432.525i			1.88876i	0.328860	+	0.944379i	$0.393335\pi$
$229$			432.525i			1.88876i	−0.328860	+	0.944379i	$0.606665\pi$
$230$	21.7475	+	244.790i	0.0945544	+	1.06430i
$231$	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	$0.00946593\pi$
$241$			14.3316i			0.0594674i	−0.999558	+	0.0297337i	$0.990534\pi$
$242$		−	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	$-0.932432\pi$
$251$		−	105.762i		−	0.421361i	0.977555	−	0.210680i	$-0.0675679\pi$
$252$	−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	$-0.773108\pi$
$263$	−397.936			−1.51307			−0.756533	+	0.653956i	$0.773108\pi$
$264$		−	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	$-0.738236\pi$
$281$		−	411.806i		−	1.46550i	0.680497	−	0.732751i	$-0.261764\pi$
$282$		−	134.297i		−	0.476230i
$283$	435.711			1.53962			0.769808	−	0.638276i	$-0.220352\pi$
$283$	435.711			1.53962			0.769808	+	0.638276i	$0.220352\pi$
$284$	−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	$-0.174526\pi$
$293$	500.103			1.70683			0.853417	+	0.521228i	$0.174526\pi$
$294$	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	$-0.575505\pi$
$313$	−147.103			−0.469977			−0.234989	+	0.971998i	$0.575505\pi$
$314$		−	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	$-0.360516\pi$
$337$	285.987			0.848625			0.424312	+	0.905516i	$0.360516\pi$
$338$		−	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
$345$	39.1207	+	440.342i	0.113393	+	1.27635i
$346$	−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	$-0.949753\pi$
$359$		−	112.871i		−	0.314403i	0.987567	−	0.157202i	$-0.0502473\pi$
$360$	−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	$-0.470568\pi$
$367$	67.7715			0.184664			0.0923318	+	0.995728i	$0.470568\pi$
$368$	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	$-0.804440\pi$
$373$	−609.585			−1.63428			−0.817138	+	0.576442i	$0.804440\pi$
$374$	−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	$-0.825578\pi$
$379$		−	394.880i		−	1.04190i	0.853587	−	0.520950i	$-0.174422\pi$
$380$	−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	$-0.622875\pi$
$383$	−288.405			−0.753016			−0.376508	+	0.926413i	$0.622875\pi$
$384$	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	$-0.859242\pi$
$389$		−	332.932i		−	0.855865i	0.903811	−	0.427933i	$-0.140758\pi$
$390$	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	$-0.959199\pi$
$401$		−	102.519i		−	0.255658i	0.991796	−	0.127829i	$-0.0408008\pi$
$402$	−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	$-0.675972\pi$
$419$		−	713.172i		−	1.70208i	0.525099	−	0.851041i	$-0.324028\pi$
$420$	7.28508	−	24.4096i	0.0173454	−	0.0581181i
$421$			281.934i			0.669677i	0.942276	+	0.334839i	$0.108682\pi$
$421$			281.934i			0.669677i	−0.942276	+	0.334839i	$0.891318\pi$
$422$			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	$-0.834600\pi$
$431$		−	428.026i		−	0.993099i	0.868008	−	0.496550i	$-0.165400\pi$
$432$		−	222.311i		−	0.514609i
$433$	−423.200			−0.977366			−0.488683	−	0.872461i	$-0.662523\pi$
$433$	−423.200			−0.977366			−0.488683	+	0.872461i	$0.662523\pi$
$434$			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	$-0.228324\pi$
$457$	688.774			1.50717			0.753583	+	0.657353i	$0.228324\pi$
$458$	−924.303			−2.01813
$459$			301.799i			0.657515i
$460$	−64.9183	+	5.76744i	−0.141127	+	0.0125379i
$461$	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	$-0.643314\pi$
$467$	−406.456			−0.870354			−0.435177	+	0.900345i	$0.643314\pi$
$468$		−	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	$0.140918\pi$
$479$			410.394i			0.856773i	−0.903596	+	0.428386i	$0.859082\pi$
$480$	−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	$-0.328628\pi$
$503$	515.824			1.02549			0.512747	+	0.858540i	$0.328628\pi$
$504$			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	$0.116453\pi$
$521$			372.767i			0.715484i	−0.933821	+	0.357742i	$0.883547\pi$
$522$		−	106.107i		−	0.203271i
$523$	67.0135			0.128133			0.0640665	−	0.997946i	$-0.479593\pi$
$523$	67.0135			0.128133			0.0640665	+	0.997946i	$0.479593\pi$
$524$	−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	$-0.610820\pi$
$557$	−380.054			−0.682322			−0.341161	+	0.940005i	$0.610820\pi$
$558$			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	$-0.301279\pi$
$563$	658.179			1.16906			0.584529	+	0.811373i	$0.301279\pi$
$564$	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	$-0.957927\pi$
$569$		−	149.979i		−	0.263583i	0.991277	−	0.131792i	$-0.0420730\pi$
$570$	−234.472	+	785.628i	−0.411354	+	1.37830i
$571$			158.157i			0.276982i	0.990364	+	0.138491i	$0.0442253\pi$
$571$			158.157i			0.276982i	−0.990364	+	0.138491i	$0.955775\pi$
$572$	−137.947			−0.241166
$573$	146.945			0.256449
$574$		−	137.067i		−	0.238793i
$575$	−563.375	−	115.039i	−0.979782	−	0.200067i
$576$	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	$-0.363377\pi$
$613$	510.208			0.832313			0.416157	+	0.909293i	$0.363377\pi$
$614$	−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	$-0.443882\pi$
$617$	216.428			0.350775			0.175387	+	0.984499i	$0.443882\pi$
$618$	9.53125			0.0154227
$619$		−	935.658i		−	1.51156i	−0.654823	−	0.755782i	$-0.727257\pi$
$619$		−	935.658i		−	1.51156i	0.654823	−	0.755782i	$-0.272743\pi$
$620$	−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	$-0.983951\pi$
$631$		−	63.6033i		−	0.100798i	0.998729	−	0.0503988i	$-0.0160492\pi$
$632$	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	$0.231516\pi$
$641$			852.374i			1.32976i	−0.746952	+	0.664878i	$0.768484\pi$
$642$	137.679			0.214453
$643$	−876.571			−1.36325			−0.681626	−	0.731701i	$-0.738727\pi$
$643$	−876.571			−1.36325			−0.681626	+	0.731701i	$0.738727\pi$
$644$	−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	$-0.792689\pi$
$659$		−	798.984i		−	1.21242i	0.795305	−	0.606210i	$-0.207311\pi$
$660$	−129.079	−	38.5240i	−0.195575	−	0.0583696i
$661$			172.343i			0.260730i	0.991466	+	0.130365i	$0.0416149\pi$
$661$			172.343i			0.260730i	−0.991466	+	0.130365i	$0.958385\pi$
$662$			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	$-0.591450\pi$
$677$	−383.674			−0.566727			−0.283363	+	0.959013i	$0.591450\pi$
$678$	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
$690$	−941.007	+	83.6006i	−1.36378	+	0.121160i
$691$	−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	$0.323455\pi$
$701$			1191.83i			1.70019i	−0.526630	+	0.850095i	$0.676545\pi$
$702$			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	$-0.949466\pi$
$709$		−	224.172i		−	0.316181i	0.987425	−	0.158090i	$-0.0505338\pi$
$710$	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	$-0.550680\pi$
$727$	−230.522			−0.317086			−0.158543	+	0.987352i	$0.550680\pi$
$728$	−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	$-0.725660\pi$
$733$	−954.400			−1.30205			−0.651023	+	0.759058i	$0.725660\pi$
$734$			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	$-0.375002\pi$
$743$	568.660			0.765356			0.382678	+	0.923882i	$0.375002\pi$
$744$	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	$-0.761609\pi$
$751$		−	1022.64i		−	1.36170i	0.732421	−	0.680852i	$-0.238391\pi$
$752$		−	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	$-0.315660\pi$
$757$	828.595			1.09458			0.547288	+	0.836944i	$0.315660\pi$
$758$	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	$0.0107873\pi$
$769$			52.1119i			0.0677658i	−0.999426	+	0.0338829i	$0.989213\pi$
$770$	−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	$-0.442164\pi$
$773$	279.360			0.361397			0.180699	+	0.983539i	$0.442164\pi$
$774$			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	$-0.766629\pi$
$787$	−1169.59			−1.48613			−0.743066	+	0.669218i	$0.766629\pi$
$788$		−	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	$-0.386463\pi$
$797$	556.581			0.698345			0.349173	+	0.937058i	$0.386463\pi$
$798$			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
$805$	−267.876	+	23.7985i	−0.332765	+	0.0295634i
$806$	−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	$-0.608673\pi$
$827$	−553.782			−0.669627			−0.334814	+	0.942284i	$0.608673\pi$
$828$	−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	$0.0160994\pi$
$839$			84.8332i			0.101112i	−0.998721	+	0.0505561i	$0.983901\pi$
$840$	−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	$0.115061\pi$
$881$			623.139i			0.707308i	−0.935376	+	0.353654i	$0.884939\pi$
$882$			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	$-0.204987\pi$
$907$	1450.67			1.59942			0.799709	+	0.600387i	$0.204987\pi$
$908$	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	$-0.793559\pi$
$911$		−	1100.55i		−	1.20807i	0.796958	−	0.604035i	$-0.206441\pi$
$912$	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	$0.254278\pi$
$919$			1317.01i			1.43309i	−0.697540	+	0.716546i	$0.745722\pi$
$920$	74.6651	+	840.429i	0.0811577	+	0.913510i
$921$	−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	$-0.503020\pi$
$937$	−17.7790			−0.0189744			−0.00948722	+	0.999955i	$0.503020\pi$
$938$		−	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	$0.391550\pi$
$941$			1773.82i			1.88504i	−0.334153	+	0.942519i	$0.608450\pi$
$942$	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	$-0.530384\pi$
$953$	−181.658			−0.190617			−0.0953086	+	0.995448i	$0.530384\pi$
$954$		−	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	$-0.731870\pi$
$971$		−	1449.14i		−	1.49242i	0.665708	−	0.746212i	$-0.268130\pi$
$972$			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	$-0.594179\pi$
$977$	−569.734			−0.583146			−0.291573	+	0.956549i	$0.594179\pi$
$978$		−	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	$-0.710087\pi$
$983$	−1205.40			−1.22625			−0.613123	+	0.789988i	$0.710087\pi$
$984$	−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.114.15	yes	20
5.2	odd	4		575.3.d.i.551.5		20
5.3	odd	4		575.3.d.i.551.16		20
5.4	even	2	inner	115.3.c.c.114.6	yes	20
23.22	odd	2	inner	115.3.c.c.114.16	yes	20
115.22	even	4		575.3.d.i.551.6		20
115.68	even	4		575.3.d.i.551.15		20
115.114	odd	2	inner	115.3.c.c.114.5	✓	20

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

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

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