LMFDB - Embedded newform 115.3.d.a.91.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [115,3,Mod(91,115)]

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([0, 1]))

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

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

chi := DirichletCharacter("115.91");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 115 = 5 \cdot 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	115.d (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:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} - 34x^{4} + 50x^{3} + 690x^{2} - 600x + 4725 $ x^6 - 2x^5 - 34x^4 + 50x^3 + 690x^2 - 600*x + 4725
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			91.6
Root			$5.33482 - 2.23607i$ of defining polynomial
Character	$\chi$	$=$	115.91
Dual form			115.3.d.a.91.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +5.33482 q^{3} -3.00000 q^{4} +2.23607i q^{5} -5.33482 q^{6} +13.3268i q^{7} +7.00000 q^{8} +19.4603 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +5.33482 q^{3} -3.00000 q^{4} +2.23607i q^{5} -5.33482 q^{6} +13.3268i q^{7} +7.00000 q^{8} +19.4603 q^{9} -2.23607i q^{10} -9.13348i q^{11} -16.0045 q^{12} -0.209300 q^{13} -13.3268i q^{14} +11.9290i q^{15} +5.00000 q^{16} -4.28293i q^{17} -19.4603 q^{18} -26.7432i q^{19} -6.70820i q^{20} +71.0962i q^{21} +9.13348i q^{22} +(14.7952 + 17.6097i) q^{23} +37.3438 q^{24} -5.00000 q^{25} +0.209300 q^{26} +55.8041 q^{27} -39.9804i q^{28} -18.0089 q^{29} -11.9290i q^{30} -35.3810 q^{31} -33.0000 q^{32} -48.7255i q^{33} +4.28293i q^{34} -29.7996 q^{35} -58.3810 q^{36} -13.2372i q^{37} +26.7432i q^{38} -1.11658 q^{39} +15.6525i q^{40} +11.5769 q^{41} -71.0962i q^{42} -48.4567i q^{43} +27.4004i q^{44} +43.5147i q^{45} +(-14.7952 - 17.6097i) q^{46} +21.5814 q^{47} +26.6741 q^{48} -128.604 q^{49} +5.00000 q^{50} -22.8487i q^{51} +0.627900 q^{52} -40.2492i q^{53} -55.8041 q^{54} +20.4231 q^{55} +93.2876i q^{56} -142.670i q^{57} +18.0089 q^{58} +105.181 q^{59} -35.7871i q^{60} -81.0661i q^{61} +35.3810 q^{62} +259.344i q^{63} +13.0000 q^{64} -0.468009i q^{65} +48.7255i q^{66} +58.3370i q^{67} +12.8488i q^{68} +(78.9296 + 93.9449i) q^{69} +29.7996 q^{70} -48.4231 q^{71} +136.222 q^{72} -30.0089 q^{73} +13.2372i q^{74} -26.6741 q^{75} +80.2296i q^{76} +121.720 q^{77} +1.11658 q^{78} +26.2952i q^{79} +11.1803i q^{80} +122.562 q^{81} -11.5769 q^{82} -14.7308i q^{83} -213.288i q^{84} +9.57693 q^{85} +48.4567i q^{86} -96.0746 q^{87} -63.9343i q^{88} +142.013i q^{89} -43.5147i q^{90} -2.78930i q^{91} +(-44.3855 - 52.8292i) q^{92} -188.752 q^{93} -21.5814 q^{94} +59.7996 q^{95} -176.049 q^{96} +13.2072i q^{97} +128.604 q^{98} -177.741i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{2} + 2 q^{3} - 18 q^{4} - 2 q^{6} + 42 q^{8} + 48 q^{9}+O(q^{10}) $ 6 * q - 6 * q^2 + 2 * q^3 - 18 * q^4 - 2 * q^6 + 42 * q^8 + 48 * q^9	$ 6 q - 6 q^{2} + 2 q^{3} - 18 q^{4} - 2 q^{6} + 42 q^{8} + 48 q^{9} - 6 q^{12} - 10 q^{13} + 30 q^{16} - 48 q^{18} - 10 q^{23} + 14 q^{24} - 30 q^{25} + 10 q^{26} + 56 q^{27} + 72 q^{29} - 6 q^{31} - 198 q^{32} + 10 q^{35} - 144 q^{36} - 148 q^{39} + 142 q^{41} + 10 q^{46} + 112 q^{47} + 10 q^{48} - 304 q^{49} + 30 q^{50} + 30 q^{52} - 56 q^{54} + 50 q^{55} - 72 q^{58} + 236 q^{59} + 6 q^{62} + 78 q^{64} + 156 q^{69} - 10 q^{70} - 218 q^{71} + 336 q^{72} - 10 q^{75} + 184 q^{77} + 148 q^{78} + 354 q^{81} - 142 q^{82} + 130 q^{85} - 584 q^{87} + 30 q^{92} - 176 q^{93} - 112 q^{94} + 170 q^{95} - 66 q^{96} + 304 q^{98}+O(q^{100}) $ 6 * q - 6 * q^2 + 2 * q^3 - 18 * q^4 - 2 * q^6 + 42 * q^8 + 48 * q^9 - 6 * q^12 - 10 * q^13 + 30 * q^16 - 48 * q^18 - 10 * q^23 + 14 * q^24 - 30 * q^25 + 10 * q^26 + 56 * q^27 + 72 * q^29 - 6 * q^31 - 198 * q^32 + 10 * q^35 - 144 * q^36 - 148 * q^39 + 142 * q^41 + 10 * q^46 + 112 * q^47 + 10 * q^48 - 304 * q^49 + 30 * q^50 + 30 * q^52 - 56 * q^54 + 50 * q^55 - 72 * q^58 + 236 * q^59 + 6 * q^62 + 78 * q^64 + 156 * q^69 - 10 * q^70 - 218 * q^71 + 336 * q^72 - 10 * q^75 + 184 * q^77 + 148 * q^78 + 354 * q^81 - 142 * q^82 + 130 * q^85 - 584 * q^87 + 30 * q^92 - 176 * q^93 - 112 * q^94 + 170 * q^95 - 66 * q^96 + 304 * q^98

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 $

$2$	−1.00000			−0.500000			−0.250000	−	0.968246i	$-0.580431\pi$
$2$	−1.00000			−0.500000			−0.250000	+	0.968246i	$0.580431\pi$
$3$	5.33482			1.77827			0.889137	−	0.457640i	$-0.151305\pi$
$3$	5.33482			1.77827			0.889137	+	0.457640i	$0.151305\pi$
$4$	−3.00000			−0.750000
$5$			2.23607i			0.447214i
$5$			2.23607i			0.447214i
$6$	−5.33482			−0.889137
$7$			13.3268i			1.90383i	0.306363	+	0.951915i	$0.400888\pi$
$7$			13.3268i			1.90383i	−0.306363	+	0.951915i	$0.599112\pi$
$8$	7.00000			0.875000
$9$	19.4603			2.16226
$10$		−	2.23607i		−	0.223607i
$11$		−	9.13348i		−	0.830316i	−0.909749	−	0.415158i	$-0.863726\pi$
$11$		−	9.13348i		−	0.830316i	0.909749	−	0.415158i	$-0.136274\pi$
$12$	−16.0045			−1.33371
$13$	−0.209300			−0.0161000			−0.00805001	−	0.999968i	$-0.502562\pi$
$13$	−0.209300			−0.0161000			−0.00805001	+	0.999968i	$0.502562\pi$
$14$		−	13.3268i		−	0.951915i
$15$			11.9290i			0.795269i
$16$	5.00000			0.312500
$17$		−	4.28293i		−	0.251937i	−0.992034	−	0.125969i	$-0.959796\pi$
$17$		−	4.28293i		−	0.251937i	0.992034	−	0.125969i	$-0.0402039\pi$
$18$	−19.4603			−1.08113
$19$		−	26.7432i		−	1.40754i	−0.710429	−	0.703769i	$-0.751499\pi$
$19$		−	26.7432i		−	1.40754i	0.710429	−	0.703769i	$-0.248501\pi$
$20$		−	6.70820i		−	0.335410i
$21$			71.0962i			3.38553i
$22$			9.13348i			0.415158i
$23$	14.7952	+	17.6097i	0.643268	+	0.765641i
$23$	14.7952	+	17.6097i	0.643268	+	0.765641i
$24$	37.3438			1.55599
$25$	−5.00000			−0.200000
$26$	0.209300			0.00805001
$27$	55.8041			2.06682
$28$		−	39.9804i		−	1.42787i
$29$	−18.0089			−0.620998			−0.310499	−	0.950574i	$-0.600496\pi$
$29$	−18.0089			−0.620998			−0.310499	+	0.950574i	$0.600496\pi$
$30$		−	11.9290i		−	0.397634i
$31$	−35.3810			−1.14132			−0.570662	−	0.821185i	$-0.693313\pi$
$31$	−35.3810			−1.14132			−0.570662	+	0.821185i	$0.693313\pi$
$32$	−33.0000			−1.03125
$33$		−	48.7255i		−	1.47653i
$34$			4.28293i			0.125969i
$35$	−29.7996			−0.851418
$36$	−58.3810			−1.62170
$37$		−	13.2372i		−	0.357762i	−0.983871	−	0.178881i	$-0.942752\pi$
$37$		−	13.2372i		−	0.357762i	0.983871	−	0.178881i	$-0.0572478\pi$
$38$			26.7432i			0.703769i
$39$	−1.11658			−0.0286302
$40$			15.6525i			0.391312i
$41$	11.5769			0.282364			0.141182	−	0.989984i	$-0.454910\pi$
$41$	11.5769			0.282364			0.141182	+	0.989984i	$0.454910\pi$
$42$		−	71.0962i		−	1.69277i
$43$		−	48.4567i		−	1.12690i	−0.826150	−	0.563450i	$-0.809474\pi$
$43$		−	48.4567i		−	1.12690i	0.826150	−	0.563450i	$-0.190526\pi$
$44$			27.4004i			0.622737i
$45$			43.5147i			0.966992i
$46$	−14.7952	−	17.6097i	−0.321634	−	0.382820i
$47$	21.5814			0.459179			0.229589	−	0.973288i	$-0.426262\pi$
$47$	21.5814			0.459179			0.229589	+	0.973288i	$0.426262\pi$
$48$	26.6741			0.555711
$49$	−128.604			−2.62457
$50$	5.00000			0.100000
$51$		−	22.8487i		−	0.448014i
$52$	0.627900			0.0120750
$53$		−	40.2492i		−	0.759419i	−0.925106	−	0.379710i	$-0.876024\pi$
$53$		−	40.2492i		−	0.759419i	0.925106	−	0.379710i	$-0.123976\pi$
$54$	−55.8041			−1.03341
$55$	20.4231			0.371329
$56$			93.2876i			1.66585i
$57$		−	142.670i		−	2.50299i
$58$	18.0089			0.310499
$59$	105.181			1.78272			0.891362	−	0.453293i	$-0.149751\pi$
$59$	105.181			1.78272			0.891362	+	0.453293i	$0.149751\pi$
$60$		−	35.7871i		−	0.596451i
$61$		−	81.0661i		−	1.32895i	−0.747310	−	0.664476i	$-0.768655\pi$
$61$		−	81.0661i		−	1.32895i	0.747310	−	0.664476i	$-0.231345\pi$
$62$	35.3810			0.570662
$63$			259.344i			4.11658i
$64$	13.0000			0.203125
$65$		−	0.468009i		−	0.00720014i
$66$			48.7255i			0.738265i
$67$			58.3370i			0.870701i	0.900261	+	0.435351i	$0.143376\pi$
$67$			58.3370i			0.870701i	−0.900261	+	0.435351i	$0.856624\pi$
$68$			12.8488i			0.188953i
$69$	78.9296	+	93.9449i	1.14391	+	1.36152i
$70$	29.7996			0.425709
$71$	−48.4231			−0.682015			−0.341008	−	0.940061i	$-0.610768\pi$
$71$	−48.4231			−0.682015			−0.341008	+	0.940061i	$0.610768\pi$
$72$	136.222			1.89198
$73$	−30.0089			−0.411081			−0.205541	−	0.978649i	$-0.565895\pi$
$73$	−30.0089			−0.411081			−0.205541	+	0.978649i	$0.565895\pi$
$74$			13.2372i			0.178881i
$75$	−26.6741			−0.355655
$76$			80.2296i			1.05565i
$77$	121.720			1.58078
$78$	1.11658			0.0143151
$79$			26.2952i			0.332851i	0.986054	+	0.166425i	$0.0532225\pi$
$79$			26.2952i			0.332851i	−0.986054	+	0.166425i	$0.946778\pi$
$80$			11.1803i			0.139754i
$81$	122.562			1.51311
$82$	−11.5769			−0.141182
$83$		−	14.7308i		−	0.177480i	−0.996055	−	0.0887400i	$-0.971716\pi$
$83$		−	14.7308i		−	0.177480i	0.996055	−	0.0887400i	$-0.0282840\pi$
$84$		−	213.288i		−	2.53915i
$85$	9.57693			0.112670
$86$			48.4567i			0.563450i
$87$	−96.0746			−1.10431
$88$		−	63.9343i		−	0.726526i
$89$			142.013i			1.59565i	0.602887	+	0.797827i	$0.294017\pi$
$89$			142.013i			1.59565i	−0.602887	+	0.797827i	$0.705983\pi$
$90$		−	43.5147i		−	0.483496i
$91$		−	2.78930i		−	0.0306517i
$92$	−44.3855	−	52.8292i	−0.482451	−	0.574231i
$93$	−188.752			−2.02959
$94$	−21.5814			−0.229589
$95$	59.7996			0.629470
$96$	−176.049			−1.83385
$97$			13.2072i			0.136157i	0.997680	+	0.0680784i	$0.0216868\pi$
$97$			13.2072i			0.136157i	−0.997680	+	0.0680784i	$0.978313\pi$
$98$	128.604			1.31228
$99$		−	177.741i		−	1.79536i
$100$	15.0000			0.150000
$101$	102.846			1.01828			0.509139	−	0.860684i	$-0.329964\pi$
$101$	102.846			1.01828			0.509139	+	0.860684i	$0.329964\pi$
$102$			22.8487i			0.224007i
$103$		−	101.196i		−	0.982488i	−0.871022	−	0.491244i	$-0.836542\pi$
$103$		−	101.196i		−	0.982488i	0.871022	−	0.491244i	$-0.163458\pi$
$104$	−1.46510			−0.0140875
$105$	−158.976			−1.51406
$106$			40.2492i			0.379710i
$107$		−	85.7074i		−	0.801004i	−0.916296	−	0.400502i	$-0.868836\pi$
$107$		−	85.7074i		−	0.801004i	0.916296	−	0.400502i	$-0.131164\pi$
$108$	−167.412			−1.55011
$109$			27.2808i			0.250283i	0.992139	+	0.125141i	$0.0399385\pi$
$109$			27.2808i			0.250283i	−0.992139	+	0.125141i	$0.960062\pi$
$110$	−20.4231			−0.185664
$111$		−	70.6182i		−	0.636200i
$112$			66.6340i			0.594947i
$113$			61.6939i			0.545964i	0.962019	+	0.272982i	$0.0880099\pi$
$113$			61.6939i			0.545964i	−0.962019	+	0.272982i	$0.911990\pi$
$114$			142.670i			1.25149i
$115$	−39.3766	+	33.0830i	−0.342405	+	0.287678i
$116$	54.0268			0.465749
$117$	−4.07305			−0.0348124
$118$	−105.181			−0.891362
$119$	57.0778			0.479645
$120$			83.5032i			0.695860i
$121$	37.5796			0.310575
$122$			81.0661i			0.664476i
$123$	61.7609			0.502121
$124$	106.143			0.855993
$125$		−	11.1803i		−	0.0894427i
$126$		−	259.344i		−	2.05829i
$127$	−76.3256			−0.600989			−0.300494	−	0.953784i	$-0.597152\pi$
$127$	−76.3256			−0.600989			−0.300494	+	0.953784i	$0.597152\pi$
$128$	119.000			0.929688
$129$		−	258.508i		−	2.00394i
$130$			0.468009i			0.00360007i
$131$	−53.6082			−0.409223			−0.204612	−	0.978843i	$-0.565593\pi$
$131$	−53.6082			−0.409223			−0.204612	+	0.978843i	$0.565593\pi$
$132$			146.176i			1.10740i
$133$	356.402			2.67971
$134$		−	58.3370i		−	0.435351i
$135$			124.782i			0.924310i
$136$		−	29.9805i		−	0.220445i
$137$			210.141i			1.53387i	0.641722	+	0.766937i	$0.278220\pi$
$137$			210.141i			1.53387i	−0.641722	+	0.766937i	$0.721780\pi$
$138$	−78.9296	−	93.9449i	−0.571954	−	0.680760i
$139$	−95.9607			−0.690365			−0.345182	−	0.938536i	$-0.612183\pi$
$139$	−95.9607			−0.690365			−0.345182	+	0.938536i	$0.612183\pi$
$140$	89.3989			0.638564
$141$	115.133			0.816546
$142$	48.4231			0.341008
$143$			1.91164i			0.0133681i
$144$	97.3017			0.675707
$145$		−	40.2692i		−	0.277719i
$146$	30.0089			0.205541
$147$	−686.078			−4.66720
$148$			39.7116i			0.268322i
$149$			96.4654i			0.647418i	0.946157	+	0.323709i	$0.104930\pi$
$149$			96.4654i			0.647418i	−0.946157	+	0.323709i	$0.895070\pi$
$150$	26.6741			0.177827
$151$	33.9204			0.224639			0.112319	−	0.993672i	$-0.464172\pi$
$151$	33.9204			0.224639			0.112319	+	0.993672i	$0.464172\pi$
$152$		−	187.202i		−	1.23160i
$153$		−	83.3474i		−	0.544754i
$154$	−121.720			−0.790390
$155$		−	79.1144i		−	0.510416i
$156$	3.34974			0.0214727
$157$			128.418i			0.817946i	0.912546	+	0.408973i	$0.134113\pi$
$157$			128.418i			0.817946i	−0.912546	+	0.408973i	$0.865887\pi$
$158$		−	26.2952i		−	0.166425i
$159$		−	214.723i		−	1.35046i
$160$		−	73.7902i		−	0.461189i
$161$	−234.682	+	197.172i	−1.45765	+	1.22467i
$162$	−122.562			−0.756556
$163$	−15.3721			−0.0943074			−0.0471537	−	0.998888i	$-0.515015\pi$
$163$	−15.3721			−0.0943074			−0.0471537	+	0.998888i	$0.515015\pi$
$164$	−34.7308			−0.211773
$165$	108.953			0.660324
$166$			14.7308i			0.0887400i
$167$	−53.1807			−0.318447			−0.159224	−	0.987243i	$-0.550899\pi$
$167$	−53.1807			−0.318447			−0.159224	+	0.987243i	$0.550899\pi$
$168$			497.673i			2.96234i
$169$	−168.956			−0.999741
$170$	−9.57693			−0.0563349
$171$		−	520.432i		−	3.04346i
$172$			145.370i			0.845175i
$173$	−210.552			−1.21706			−0.608531	−	0.793530i	$-0.708241\pi$
$173$	−210.552			−1.21706			−0.608531	+	0.793530i	$0.708241\pi$
$174$	96.0746			0.552153
$175$		−	66.6340i		−	0.380766i
$176$		−	45.6674i		−	0.259474i
$177$	561.120			3.17017
$178$		−	142.013i		−	0.797827i
$179$	−77.6082			−0.433566			−0.216783	−	0.976220i	$-0.569556\pi$
$179$	−77.6082			−0.433566			−0.216783	+	0.976220i	$0.569556\pi$
$180$		−	130.544i		−	0.725244i
$181$		−	284.295i		−	1.57069i	−0.619058	−	0.785345i	$-0.712485\pi$
$181$		−	284.295i		−	1.57069i	0.619058	−	0.785345i	$-0.287515\pi$
$182$			2.78930i			0.0153258i
$183$		−	432.473i		−	2.36324i
$184$	103.566	+	123.268i	0.562860	+	0.669936i
$185$	29.5993			0.159996
$186$	188.752			1.01479
$187$	−39.1181			−0.209187
$188$	−64.7442			−0.344384
$189$			743.691i			3.93487i
$190$	−59.7996			−0.314735
$191$			180.041i			0.942621i	0.881967	+	0.471311i	$0.156219\pi$
$191$			180.041i			0.942621i	−0.881967	+	0.471311i	$0.843781\pi$
$192$	69.3527			0.361212
$193$	351.132			1.81934			0.909669	−	0.415333i	$-0.136335\pi$
$193$	351.132			1.81934			0.909669	+	0.415333i	$0.136335\pi$
$194$		−	13.2072i		−	0.0680784i
$195$		−	2.49675i		−	0.0128038i
$196$	385.811			1.96842
$197$	−37.4750			−0.190228			−0.0951142	−	0.995466i	$-0.530322\pi$
$197$	−37.4750			−0.190228			−0.0951142	+	0.995466i	$0.530322\pi$
$198$			177.741i			0.897680i
$199$			130.818i			0.657379i	0.944438	+	0.328689i	$0.106607\pi$
$199$			130.818i			0.657379i	−0.944438	+	0.328689i	$0.893393\pi$
$200$	−35.0000			−0.175000
$201$			311.217i			1.54835i
$202$	−102.846			−0.509139
$203$		−	240.002i		−	1.18227i
$204$			68.5461i			0.336010i
$205$			25.8868i			0.126277i
$206$			101.196i			0.491244i
$207$	287.919	+	342.692i	1.39091	+	1.65552i
$208$	−1.04650			−0.00503125
$209$	−244.258			−1.16870
$210$	158.976			0.757028
$211$	−251.309			−1.19104			−0.595520	−	0.803340i	$-0.703054\pi$
$211$	−251.309			−1.19104			−0.595520	+	0.803340i	$0.703054\pi$
$212$			120.748i			0.569564i
$213$	−258.329			−1.21281
$214$			85.7074i			0.400502i
$215$	108.352			0.503965
$216$	390.629			1.80847
$217$		−	471.516i		−	2.17289i
$218$		−	27.2808i		−	0.125141i
$219$	−160.092			−0.731016
$220$	−61.2692			−0.278496
$221$			0.896418i			0.00405619i
$222$			70.6182i			0.318100i
$223$	−97.5903			−0.437625			−0.218812	−	0.975767i	$-0.570218\pi$
$223$	−97.5903			−0.437625			−0.218812	+	0.975767i	$0.570218\pi$
$224$		−	439.785i		−	1.96332i
$225$	−97.3017			−0.432452
$226$		−	61.6939i		−	0.272982i
$227$		−	217.721i		−	0.959123i	−0.877508	−	0.479562i	$-0.840796\pi$
$227$		−	217.721i		−	0.959123i	0.877508	−	0.479562i	$-0.159204\pi$
$228$			428.011i			1.87724i
$229$			189.395i			0.827051i	0.910493	+	0.413525i	$0.135703\pi$
$229$			189.395i			0.827051i	−0.910493	+	0.413525i	$0.864297\pi$
$230$	39.3766	−	33.0830i	0.171202	−	0.143839i
$231$	649.355			2.81106
$232$	−126.063			−0.543373
$233$	198.419			0.851582			0.425791	−	0.904822i	$-0.359996\pi$
$233$	198.419			0.851582			0.425791	+	0.904822i	$0.359996\pi$
$234$	4.07305			0.0174062
$235$			48.2575i			0.205351i
$236$	−315.542			−1.33704
$237$			140.280i			0.591900i
$238$	−57.0778			−0.239823
$239$	−73.2165			−0.306345			−0.153173	−	0.988199i	$-0.548949\pi$
$239$	−73.2165			−0.306345			−0.153173	+	0.988199i	$0.548949\pi$
$240$			59.6451i			0.248521i
$241$			384.345i			1.59479i	0.603455	+	0.797397i	$0.293790\pi$
$241$			384.345i			1.59479i	−0.603455	+	0.797397i	$0.706210\pi$
$242$	−37.5796			−0.155288
$243$	151.610			0.623908
$244$			243.198i			0.996714i
$245$		−	287.567i		−	1.17374i
$246$	−61.7609			−0.251060
$247$			5.59736i			0.0226614i
$248$	−247.667			−0.998659
$249$		−	78.5864i		−	0.315608i
$250$			11.1803i			0.0447214i
$251$		−	393.897i		−	1.56931i	−0.619933	−	0.784655i	$-0.712840\pi$
$251$		−	393.897i		−	1.56931i	0.619933	−	0.784655i	$-0.287160\pi$
$252$		−	778.033i		−	3.08743i
$253$	160.838	−	135.131i	0.635724	−	0.534116i
$254$	76.3256			0.300494
$255$	51.0912			0.200358
$256$	−171.000			−0.667969
$257$	341.270			1.32790			0.663950	−	0.747777i	$-0.268879\pi$
$257$	341.270			1.32790			0.663950	+	0.747777i	$0.268879\pi$
$258$			258.508i			1.00197i
$259$	176.410			0.681118
$260$			1.40403i			0.00540011i
$261$	−350.460			−1.34276
$262$	53.6082			0.204612
$263$		−	122.869i		−	0.467182i	−0.972335	−	0.233591i	$-0.924952\pi$
$263$		−	122.869i		−	0.467182i	0.972335	−	0.233591i	$-0.0750477\pi$
$264$		−	341.078i		−	1.29196i
$265$	90.0000			0.339623
$266$	−356.402			−1.33986
$267$			757.615i			2.83751i
$268$		−	175.011i		−	0.653026i
$269$	134.705			0.500762			0.250381	−	0.968147i	$-0.419444\pi$
$269$	134.705			0.500762			0.250381	+	0.968147i	$0.419444\pi$
$270$		−	124.782i		−	0.462155i
$271$	−437.814			−1.61555			−0.807775	−	0.589491i	$-0.799328\pi$
$271$	−437.814			−1.61555			−0.807775	+	0.589491i	$0.799328\pi$
$272$		−	21.4147i		−	0.0787304i
$273$		−	14.8804i		−	0.0545071i
$274$		−	210.141i		−	0.766937i
$275$			45.6674i			0.166063i
$276$	−236.789	−	281.835i	−0.857931	−	1.02114i
$277$	−395.764			−1.42875			−0.714375	−	0.699763i	$-0.753289\pi$
$277$	−395.764			−1.42875			−0.714375	+	0.699763i	$0.753289\pi$
$278$	95.9607			0.345182
$279$	−688.527			−2.46784
$280$	−208.598			−0.744991
$281$			108.944i			0.387701i	0.981031	+	0.193851i	$0.0620977\pi$
$281$			108.944i			0.387701i	−0.981031	+	0.193851i	$0.937902\pi$
$282$	−115.133			−0.408273
$283$			327.084i			1.15577i	0.816117	+	0.577886i	$0.196122\pi$
$283$			327.084i			1.15577i	−0.816117	+	0.577886i	$0.803878\pi$
$284$	145.269			0.511511
$285$	319.021			1.11937
$286$		−	1.91164i		−	0.00668405i
$287$			154.283i			0.537573i
$288$	−642.191			−2.22983
$289$	270.656			0.936528
$290$			40.2692i			0.138859i
$291$			70.4581i			0.242124i
$292$	90.0268			0.308311
$293$			179.275i			0.611860i	0.952054	+	0.305930i	$0.0989674\pi$
$293$			179.275i			0.611860i	−0.952054	+	0.305930i	$0.901033\pi$
$294$	686.078			2.33360
$295$			235.191i			0.797258i
$296$		−	92.6604i		−	0.313042i
$297$		−	509.686i		−	1.71611i
$298$		−	96.4654i		−	0.323709i
$299$	−3.09663	−	3.68572i	−0.0103566	−	0.0123268i
$300$	80.0224			0.266741
$301$	645.773			2.14542
$302$	−33.9204			−0.112319
$303$	548.666			1.81078
$304$		−	133.716i		−	0.439855i
$305$	181.269			0.594325
$306$			83.3474i			0.272377i
$307$	−527.044			−1.71676			−0.858378	−	0.513018i	$-0.828527\pi$
$307$	−527.044			−1.71676			−0.858378	+	0.513018i	$0.828527\pi$
$308$	−365.160			−1.18558
$309$		−	539.864i		−	1.74713i
$310$			79.1144i			0.255208i
$311$	150.873			0.485122			0.242561	−	0.970136i	$-0.422013\pi$
$311$	150.873			0.485122			0.242561	+	0.970136i	$0.422013\pi$
$312$	−7.81606			−0.0250515
$313$			329.623i			1.05311i	0.850142	+	0.526554i	$0.176516\pi$
$313$			329.623i			1.05311i	−0.850142	+	0.526554i	$0.823484\pi$
$314$		−	128.418i		−	0.408973i
$315$	−579.911			−1.84099
$316$		−	78.8856i		−	0.249638i
$317$	112.968			0.356365			0.178183	−	0.983997i	$-0.442978\pi$
$317$	112.968			0.356365			0.178183	+	0.983997i	$0.442978\pi$
$318$			214.723i			0.675228i
$319$			164.484i			0.515625i
$320$			29.0689i			0.0908403i
$321$		−	457.234i		−	1.42440i
$322$	234.682	−	197.172i	0.728825	−	0.612337i
$323$	−114.539			−0.354611
$324$	−367.686			−1.13483
$325$	1.04650			0.00322000
$326$	15.3721			0.0471537
$327$			145.538i			0.445072i
$328$	81.0385			0.247069
$329$			287.611i			0.874198i
$330$	−108.953			−0.330162
$331$	160.041			0.483508			0.241754	−	0.970338i	$-0.422277\pi$
$331$	160.041			0.483508			0.241754	+	0.970338i	$0.422277\pi$
$332$			44.1925i			0.133110i
$333$		−	257.601i		−	0.773575i
$334$	53.1807			0.159224
$335$	−130.445			−0.389389
$336$			355.481i			1.05798i
$337$		−	482.196i		−	1.43085i	−0.698691	−	0.715424i	$-0.746234\pi$
$337$		−	482.196i		−	1.43085i	0.698691	−	0.715424i	$-0.253766\pi$
$338$	168.956			0.499870
$339$			329.126i			0.970873i
$340$	−28.7308			−0.0845023
$341$			323.152i			0.947660i
$342$			520.432i			1.52173i
$343$		−	1060.86i		−	3.09290i
$344$		−	339.197i		−	0.986037i
$345$	−210.067	+	176.492i	−0.608890	+	0.511571i
$346$	210.552			0.608531
$347$	−124.244			−0.358052			−0.179026	−	0.983844i	$-0.557295\pi$
$347$	−124.244			−0.358052			−0.179026	+	0.983844i	$0.557295\pi$
$348$	288.224			0.828229
$349$	−151.318			−0.433577			−0.216789	−	0.976219i	$-0.569558\pi$
$349$	−151.318			−0.433577			−0.216789	+	0.976219i	$0.569558\pi$
$350$			66.6340i			0.190383i
$351$	−11.6798			−0.0332758
$352$			301.405i			0.856263i
$353$	−280.780			−0.795411			−0.397705	−	0.917513i	$-0.630193\pi$
$353$	−280.780			−0.795411			−0.397705	+	0.917513i	$0.630193\pi$
$354$	−561.120			−1.58509
$355$		−	108.277i		−	0.305006i
$356$		−	426.039i		−	1.19674i
$357$	304.500			0.852941
$358$	77.6082			0.216783
$359$			32.4114i			0.0902825i	0.998981	+	0.0451413i	$0.0143738\pi$
$359$			32.4114i			0.0902825i	−0.998981	+	0.0451413i	$0.985626\pi$
$360$			304.603i			0.846118i
$361$	−354.199			−0.981162
$362$			284.295i			0.785345i
$363$	200.481			0.552288
$364$			8.36791i			0.0229888i
$365$		−	67.1020i		−	0.183841i
$366$			432.473i			1.18162i
$367$			598.829i			1.63169i	0.578274	+	0.815843i	$0.303727\pi$
$367$			598.829i			1.63169i	−0.578274	+	0.815843i	$0.696273\pi$
$368$	73.9759	+	88.0487i	0.201021	+	0.239263i
$369$	225.291			0.610545
$370$	−29.5993			−0.0799981
$371$	536.394			1.44580
$372$	566.255			1.52219
$373$		−	174.832i		−	0.468718i	−0.972150	−	0.234359i	$-0.924701\pi$
$373$		−	174.832i		−	0.468718i	0.972150	−	0.234359i	$-0.0752991\pi$
$374$	39.1181			0.104594
$375$		−	59.6451i		−	0.159054i
$376$	151.070			0.401781
$377$	3.76927			0.00999808
$378$		−	743.691i		−	1.96744i
$379$			447.801i			1.18153i	0.806842	+	0.590767i	$0.201175\pi$
$379$			447.801i			1.18153i	−0.806842	+	0.590767i	$0.798825\pi$
$380$	−179.399			−0.472102
$381$	−407.184			−1.06872
$382$		−	180.041i		−	0.471311i
$383$			199.226i			0.520173i	0.965585	+	0.260086i	$0.0837510\pi$
$383$			199.226i			0.520173i	−0.965585	+	0.260086i	$0.916249\pi$
$384$	634.844			1.65324
$385$			272.174i			0.706946i
$386$	−351.132			−0.909669
$387$		−	942.984i		−	2.43665i
$388$		−	39.6216i		−	0.102118i
$389$		−	375.510i		−	0.965322i	−0.875807	−	0.482661i	$-0.839670\pi$
$389$		−	375.510i		−	0.965322i	0.875807	−	0.482661i	$-0.160330\pi$
$390$			2.49675i			0.00640192i
$391$	75.4213	−	63.3667i	0.192893	−	0.162063i
$392$	−900.226			−2.29650
$393$	−285.990			−0.727711
$394$	37.4750			0.0951142
$395$	−58.7979			−0.148855
$396$			533.222i			1.34652i
$397$	541.468			1.36390			0.681949	−	0.731399i	$-0.261132\pi$
$397$	541.468			1.36390			0.681949	+	0.731399i	$0.261132\pi$
$398$		−	130.818i		−	0.328689i
$399$	1901.34			4.76526
$400$	−25.0000			−0.0625000
$401$			291.755i			0.727569i	0.931483	+	0.363785i	$0.118516\pi$
$401$			291.755i			0.727569i	−0.931483	+	0.363785i	$0.881484\pi$
$402$		−	311.217i		−	0.774173i
$403$	7.40526			0.0183753
$404$	−308.538			−0.763709
$405$			274.057i			0.676684i
$406$			240.002i			0.591137i
$407$	−120.902			−0.297056
$408$		−	159.941i		−	0.392012i
$409$	−141.725			−0.346515			−0.173257	−	0.984877i	$-0.555429\pi$
$409$	−141.725			−0.346515			−0.173257	+	0.984877i	$0.555429\pi$
$410$		−	25.8868i		−	0.0631385i
$411$			1121.06i			2.72765i
$412$			303.589i			0.736866i
$413$			1401.72i			3.39400i
$414$	−287.919	−	342.692i	−0.695457	−	0.827758i
$415$	32.9391			0.0793714
$416$	6.90690			0.0166031
$417$	−511.933			−1.22766
$418$	244.258			0.584350
$419$		−	438.321i		−	1.04611i	−0.852299	−	0.523056i	$-0.824792\pi$
$419$		−	438.321i		−	1.04611i	0.852299	−	0.523056i	$-0.175208\pi$
$420$	476.928			1.13554
$421$			84.6730i			0.201124i	0.994931	+	0.100562i	$0.0320640\pi$
$421$			84.6730i			0.201124i	−0.994931	+	0.100562i	$0.967936\pi$
$422$	251.309			0.595520
$423$	419.982			0.992864
$424$		−	281.745i		−	0.664492i
$425$			21.4147i			0.0503874i
$426$	258.329			0.606405
$427$	1080.35			2.53010
$428$			257.122i			0.600753i
$429$			10.1983i			0.0237721i
$430$	−108.352			−0.251982
$431$		−	475.343i		−	1.10288i	−0.834213	−	0.551442i	$-0.814078\pi$
$431$		−	475.343i		−	1.10288i	0.834213	−	0.551442i	$-0.185922\pi$
$432$	279.021			0.645881
$433$			348.487i			0.804821i	0.915459	+	0.402410i	$0.131827\pi$
$433$			348.487i			0.804821i	−0.915459	+	0.402410i	$0.868173\pi$
$434$			471.516i			1.08644i
$435$		−	214.829i		−	0.493860i
$436$		−	81.8425i		−	0.187712i
$437$	470.941	−	395.670i	1.07767	−	0.905424i
$438$	160.092			0.365508
$439$	−433.893			−0.988366			−0.494183	−	0.869358i	$-0.664533\pi$
$439$	−433.893			−0.988366			−0.494183	+	0.869358i	$0.664533\pi$
$440$	142.962			0.324913
$441$	−2502.67			−5.67500
$442$		−	0.896418i		−	0.00202810i
$443$	−344.496			−0.777642			−0.388821	−	0.921313i	$-0.627118\pi$
$443$	−344.496			−0.777642			−0.388821	+	0.921313i	$0.627118\pi$
$444$			211.854i			0.477150i
$445$	−317.551			−0.713598
$446$	97.5903			0.218812
$447$			514.626i			1.15129i
$448$			173.248i			0.386715i
$449$	5.29512			0.0117931			0.00589656	−	0.999983i	$-0.498123\pi$
$449$	5.29512			0.0117931			0.00589656	+	0.999983i	$0.498123\pi$
$450$	97.3017			0.216226
$451$		−	105.738i		−	0.234451i
$452$		−	185.082i		−	0.409473i
$453$	180.959			0.399469
$454$			217.721i			0.479562i
$455$	6.23707			0.0137078
$456$		−	998.692i		−	2.19011i
$457$		−	492.595i		−	1.07789i	−0.842341	−	0.538944i	$-0.818823\pi$
$457$		−	492.595i		−	1.07789i	0.842341	−	0.538944i	$-0.181177\pi$
$458$		−	189.395i		−	0.413525i
$459$		−	239.005i		−	0.520709i
$460$	118.130	−	99.2490i	0.256804	−	0.215759i
$461$	754.998			1.63774			0.818870	−	0.573979i	$-0.194601\pi$
$461$	754.998			1.63774			0.818870	+	0.573979i	$0.194601\pi$
$462$	−649.355			−1.40553
$463$	485.794			1.04923			0.524616	−	0.851339i	$-0.324209\pi$
$463$	485.794			1.04923			0.524616	+	0.851339i	$0.324209\pi$
$464$	−90.0447			−0.194062
$465$		−	422.062i		−	0.907659i
$466$	−198.419			−0.425791
$467$		−	653.618i		−	1.39961i	−0.714334	−	0.699805i	$-0.753270\pi$
$467$		−	653.618i		−	1.39961i	0.714334	−	0.699805i	$-0.246730\pi$
$468$	12.2192			0.0261093
$469$	−777.446			−1.65767
$470$		−	48.2575i		−	0.102675i
$471$			685.085i			1.45453i
$472$	736.265			1.55988
$473$	−442.578			−0.935683
$474$		−	140.280i		−	0.295950i
$475$			133.716i			0.281508i
$476$	−171.233			−0.359734
$477$		−	783.264i		−	1.64206i
$478$	73.2165			0.153173
$479$		−	567.455i		−	1.18467i	−0.805693	−	0.592333i	$-0.798207\pi$
$479$		−	567.455i		−	1.18467i	0.805693	−	0.592333i	$-0.201793\pi$
$480$		−	393.658i		−	0.820121i
$481$			2.77055i			0.00575998i
$482$		−	384.345i		−	0.797397i
$483$	−1251.98	+	1051.88i	−2.59210	+	2.17781i
$484$	−112.739			−0.232932
$485$	−29.5322			−0.0608911
$486$	−151.610			−0.311954
$487$	482.712			0.991195			0.495597	−	0.868552i	$-0.334949\pi$
$487$	482.712			0.991195			0.495597	+	0.868552i	$0.334949\pi$
$488$		−	567.462i		−	1.16283i
$489$	−82.0074			−0.167704
$490$			287.567i			0.586871i
$491$	157.402			0.320575			0.160288	−	0.987070i	$-0.448758\pi$
$491$	157.402			0.320575			0.160288	+	0.987070i	$0.448758\pi$
$492$	−185.283			−0.376591
$493$			77.1311i			0.156453i
$494$		−	5.59736i		−	0.0113307i
$495$	397.440			0.802909
$496$	−176.905			−0.356664
$497$		−	645.325i		−	1.29844i
$498$			78.5864i			0.157804i
$499$	−355.399			−0.712222			−0.356111	−	0.934444i	$-0.615898\pi$
$499$	−355.399			−0.712222			−0.356111	+	0.934444i	$0.615898\pi$
$500$			33.5410i			0.0670820i
$501$	−283.710			−0.566287
$502$			393.897i			0.784655i
$503$			273.687i			0.544109i	0.962282	+	0.272054i	$0.0877031\pi$
$503$			273.687i			0.544109i	−0.962282	+	0.272054i	$0.912297\pi$
$504$			1815.41i			3.60200i
$505$			229.971i			0.455388i
$506$	−160.838	+	135.131i	−0.317862	+	0.267058i
$507$	−901.352			−1.77781
$508$	228.977			0.450742
$509$	526.617			1.03461			0.517306	−	0.855801i	$-0.326935\pi$
$509$	526.617			1.03461			0.517306	+	0.855801i	$0.326935\pi$
$510$	−51.0912			−0.100179
$511$		−	399.923i		−	0.782629i
$512$	−305.000			−0.595703
$513$		−	1492.38i		−	2.90913i
$514$	−341.270			−0.663950
$515$	226.282			0.439382
$516$			775.524i			1.50295i
$517$		−	197.113i		−	0.381263i
$518$	−176.410			−0.340559
$519$	−1123.26			−2.16427
$520$		−	3.27607i		−	0.00630013i
$521$		−	766.122i		−	1.47048i	−0.677805	−	0.735242i	$-0.737069\pi$
$521$		−	766.122i		−	1.47048i	0.677805	−	0.735242i	$-0.262931\pi$
$522$	350.460			0.671380
$523$		−	98.8958i		−	0.189093i	−0.995520	−	0.0945467i	$-0.969860\pi$
$523$		−	98.8958i		−	0.189093i	0.995520	−	0.0945467i	$-0.0301402\pi$
$524$	160.825			0.306917
$525$		−	355.481i		−	0.677106i
$526$			122.869i			0.233591i
$527$			151.535i			0.287542i
$528$		−	243.627i		−	0.461416i
$529$	−91.2058	+	521.078i	−0.172412	+	0.985025i
$530$	−90.0000			−0.169811
$531$	2046.85			3.85471
$532$	−1069.20			−2.00978
$533$	−2.42305			−0.00454606
$534$		−	757.615i		−	1.41875i
$535$	191.648			0.358220
$536$			408.359i			0.761863i
$537$	−414.026			−0.770999
$538$	−134.705			−0.250381
$539$			1174.60i			2.17922i
$540$		−	374.345i		−	0.693232i
$541$	−565.771			−1.04579			−0.522894	−	0.852398i	$-0.675148\pi$
$541$	−565.771			−1.04579			−0.522894	+	0.852398i	$0.675148\pi$
$542$	437.814			0.807775
$543$		−	1516.66i		−	2.79312i
$544$			141.337i			0.259810i
$545$	−61.0018			−0.111930
$546$			14.8804i			0.0272535i
$547$	376.413			0.688141			0.344071	−	0.938944i	$-0.388194\pi$
$547$	376.413			0.688141			0.344071	+	0.938944i	$0.388194\pi$
$548$		−	630.422i		−	1.15041i
$549$		−	1577.57i		−	2.87354i
$550$		−	45.6674i		−	0.0830316i
$551$			481.617i			0.874078i
$552$	552.507	+	657.614i	1.00092	+	1.19133i
$553$	−350.431			−0.633691
$554$	395.764			0.714375
$555$	157.907			0.284517
$556$	287.882			0.517773
$557$			738.343i			1.32557i	0.748809	+	0.662786i	$0.230626\pi$
$557$			738.343i			1.32557i	−0.748809	+	0.662786i	$0.769374\pi$
$558$	688.527			1.23392
$559$			10.1420i			0.0181431i
$560$	−148.998			−0.266068
$561$	−208.688			−0.371993
$562$		−	108.944i		−	0.193851i
$563$			555.234i			0.986206i	0.869971	+	0.493103i	$0.164137\pi$
$563$			555.234i			0.986206i	−0.869971	+	0.493103i	$0.835863\pi$
$564$	−345.399			−0.612409
$565$	−137.952			−0.244162
$566$		−	327.084i		−	0.577886i
$567$			1633.36i			2.88071i
$568$	−338.962			−0.596763
$569$			122.014i			0.214436i	0.994236	+	0.107218i	$0.0341943\pi$
$569$			122.014i			0.214436i	−0.994236	+	0.107218i	$0.965806\pi$
$570$	−319.021			−0.559685
$571$		−	608.941i		−	1.06645i	−0.845975	−	0.533223i	$-0.820981\pi$
$571$		−	608.941i		−	1.06645i	0.845975	−	0.533223i	$-0.179019\pi$
$572$		−	5.73491i		−	0.0100261i
$573$			960.485i			1.67624i
$574$		−	154.283i		−	0.268787i
$575$	−73.9759	−	88.0487i	−0.128654	−	0.153128i
$576$	252.985			0.439209
$577$	181.376			0.314343			0.157171	−	0.987571i	$-0.449763\pi$
$577$	181.376			0.314343			0.157171	+	0.987571i	$0.449763\pi$
$578$	−270.656			−0.468264
$579$	1873.23			3.23528
$580$			120.808i			0.208289i
$581$	196.315			0.337892
$582$		−	70.4581i		−	0.121062i
$583$	−367.615			−0.630558
$584$	−210.063			−0.359696
$585$		−	9.10762i		−	0.0155686i
$586$		−	179.275i		−	0.305930i
$587$	420.983			0.717177			0.358589	−	0.933496i	$-0.383258\pi$
$587$	420.983			0.717177			0.358589	+	0.933496i	$0.383258\pi$
$588$	2058.24			3.50040
$589$			946.203i			1.60646i
$590$		−	235.191i		−	0.398629i
$591$	−199.922			−0.338278
$592$		−	66.1860i		−	0.111801i
$593$	725.928			1.22416			0.612081	−	0.790795i	$-0.290333\pi$
$593$	725.928			1.22416			0.612081	+	0.790795i	$0.290333\pi$
$594$			509.686i			0.858056i
$595$			127.630i			0.214504i
$596$		−	289.396i		−	0.485564i
$597$			697.893i			1.16900i
$598$	3.09663	+	3.68572i	0.00517831	+	0.00616341i
$599$	239.250			0.399415			0.199708	−	0.979856i	$-0.436001\pi$
$599$	239.250			0.399415			0.199708	+	0.979856i	$0.436001\pi$
$600$	−186.719			−0.311198
$601$	81.9642			0.136380			0.0681899	−	0.997672i	$-0.478278\pi$
$601$	81.9642			0.136380			0.0681899	+	0.997672i	$0.478278\pi$
$602$	−645.773			−1.07271
$603$			1135.26i			1.88268i
$604$	−101.761			−0.168479
$605$			84.0306i			0.138894i
$606$	−548.666			−0.905390
$607$	167.515			0.275972			0.137986	−	0.990434i	$-0.455937\pi$
$607$	167.515			0.275972			0.137986	+	0.990434i	$0.455937\pi$
$608$			882.526i			1.45152i
$609$		−	1280.37i		−	2.10241i
$610$	−181.269			−0.297163
$611$	−4.51699			−0.00739278
$612$			250.042i			0.408565i
$613$		−	572.127i		−	0.933323i	−0.884436	−	0.466662i	$-0.845457\pi$
$613$		−	572.127i		−	0.933323i	0.884436	−	0.466662i	$-0.154543\pi$
$614$	527.044			0.858378
$615$			138.102i			0.224555i
$616$	852.040			1.38318
$617$			27.2917i			0.0442329i	0.999755	+	0.0221164i	$0.00704045\pi$
$617$			27.2917i			0.0442329i	−0.999755	+	0.0221164i	$0.992960\pi$
$618$			539.864i			0.873567i
$619$		−	512.542i		−	0.828016i	−0.910273	−	0.414008i	$-0.864129\pi$
$619$		−	512.542i		−	0.828016i	0.910273	−	0.414008i	$-0.135871\pi$
$620$			237.343i			0.382812i
$621$	825.632	+	982.696i	1.32952	+	1.58244i
$622$	−150.873			−0.242561
$623$	−1892.58			−3.03785
$624$	−5.58290			−0.00894695
$625$	25.0000			0.0400000
$626$		−	329.623i		−	0.526554i
$627$	−1303.08			−2.07827
$628$		−	385.253i		−	0.613459i
$629$	−56.6940			−0.0901336
$630$	579.911			0.920494
$631$		−	808.913i		−	1.28195i	−0.767560	−	0.640977i	$-0.778529\pi$
$631$		−	808.913i		−	1.28195i	0.767560	−	0.640977i	$-0.221471\pi$
$632$			184.066i			0.291244i
$633$	−1340.69			−2.11800
$634$	−112.968			−0.178183
$635$		−	170.669i		−	0.268770i
$636$			644.168i			1.01284i
$637$	26.9168			0.0422555
$638$		−	164.484i		−	0.257812i
$639$	−942.330			−1.47469
$640$			266.092i			0.415769i
$641$		−	47.2502i		−	0.0737133i	−0.999321	−	0.0368566i	$-0.988266\pi$
$641$		−	47.2502i		−	0.0737133i	0.999321	−	0.0368566i	$-0.0117345\pi$
$642$			457.234i			0.712202i
$643$		−	346.007i		−	0.538114i	−0.963124	−	0.269057i	$-0.913288\pi$
$643$		−	346.007i		−	0.538114i	0.963124	−	0.269057i	$-0.0867120\pi$
$644$	704.045	−	591.517i	1.09324	−	0.918505i
$645$	578.041			0.896188
$646$	114.539			0.177306
$647$	−983.274			−1.51974			−0.759871	−	0.650073i	$-0.774738\pi$
$647$	−983.274			−1.51974			−0.759871	+	0.650073i	$0.774738\pi$
$648$	857.934			1.32397
$649$		−	960.665i		−	1.48022i
$650$	−1.04650			−0.00161000
$651$		−	2515.46i		−	3.86399i
$652$	46.1163			0.0707305
$653$	786.821			1.20493			0.602466	−	0.798144i	$-0.294185\pi$
$653$	786.821			1.20493			0.602466	+	0.798144i	$0.294185\pi$
$654$		−	145.538i		−	0.222536i
$655$		−	119.872i		−	0.183010i
$656$	57.8846			0.0882388
$657$	−583.985			−0.888865
$658$		−	287.611i		−	0.437099i
$659$			273.239i			0.414626i	0.978275	+	0.207313i	$0.0664719\pi$
$659$			273.239i			0.414626i	−0.978275	+	0.207313i	$0.933528\pi$
$660$	−326.860			−0.495243
$661$			393.023i			0.594588i	0.954786	+	0.297294i	$0.0960842\pi$
$661$			393.023i			0.594588i	−0.954786	+	0.297294i	$0.903916\pi$
$662$	−160.041			−0.241754
$663$			4.78223i			0.00721302i
$664$		−	103.116i		−	0.155295i
$665$			796.938i			1.19840i
$666$			257.601i			0.386788i
$667$	−266.445	−	317.133i	−0.399468	−	0.475461i
$668$	159.542			0.238835
$669$	−520.627			−0.778217
$670$	130.445			0.194695
$671$	−740.415			−1.10345
$672$		−	2346.17i		−	3.49133i
$673$	161.597			0.240115			0.120058	−	0.992767i	$-0.461692\pi$
$673$	161.597			0.240115			0.120058	+	0.992767i	$0.461692\pi$
$674$			482.196i			0.715424i
$675$	−279.021			−0.413364
$676$	506.869			0.749806
$677$			1205.97i			1.78135i	0.454642	+	0.890674i	$0.349767\pi$
$677$			1205.97i			1.78135i	−0.454642	+	0.890674i	$0.650233\pi$
$678$		−	329.126i		−	0.485437i
$679$	−176.010			−0.259219
$680$	67.0385			0.0985860
$681$		−	1161.50i		−	1.70559i
$682$		−	323.152i		−	0.473830i
$683$	1237.31			1.81159			0.905794	−	0.423718i	$-0.139275\pi$
$683$	1237.31			1.81159			0.905794	+	0.423718i	$0.139275\pi$
$684$			1561.30i			2.28260i
$685$	−469.889			−0.685969
$686$			1060.86i			1.54645i
$687$			1010.39i			1.47072i
$688$		−	242.283i		−	0.352156i
$689$			8.42417i			0.0122267i
$690$	210.067	−	176.492i	0.304445	−	0.255786i
$691$	217.753			0.315128			0.157564	−	0.987509i	$-0.449636\pi$
$691$	217.753			0.315128			0.157564	+	0.987509i	$0.449636\pi$
$692$	631.656			0.912797
$693$	2368.71			3.41806
$694$	124.244			0.179026
$695$		−	214.575i		−	0.308740i
$696$	−672.522			−0.966267
$697$		−	49.5832i		−	0.0711380i
$698$	151.318			0.216789
$699$	1058.53			1.51435
$700$			199.902i			0.285574i
$701$		−	1110.53i		−	1.58421i	−0.610382	−	0.792107i	$-0.708984\pi$
$701$		−	1110.53i		−	1.58421i	0.610382	−	0.792107i	$-0.291016\pi$
$702$	11.6798			0.0166379
$703$	−354.005			−0.503564
$704$		−	118.735i		−	0.168658i
$705$			257.445i			0.365170i
$706$	280.780			0.397705
$707$			1370.61i			1.93863i
$708$	−1683.36			−2.37763
$709$			824.177i			1.16245i	0.813743	+	0.581225i	$0.197426\pi$
$709$			824.177i			1.16245i	−0.813743	+	0.581225i	$0.802574\pi$
$710$			108.277i			0.152503i
$711$			511.714i			0.719710i
$712$			994.092i			1.39620i
$713$	−523.469	−	623.051i	−0.734178	−	0.873844i
$714$	−304.500			−0.426471
$715$	−4.27455			−0.00597839
$716$	232.825			0.325174
$717$	−390.597			−0.544766
$718$		−	32.4114i		−	0.0451413i
$719$	−503.996			−0.700969			−0.350484	−	0.936569i	$-0.613983\pi$
$719$	−503.996			−0.700969			−0.350484	+	0.936569i	$0.613983\pi$
$720$			217.573i			0.302185i
$721$	1348.62			1.87049
$722$	354.199			0.490581
$723$			2050.41i			2.83598i
$724$			852.885i			1.17802i
$725$	90.0447			0.124200
$726$	−200.481			−0.276144
$727$		−	885.024i		−	1.21736i	−0.793414	−	0.608682i	$-0.791698\pi$
$727$		−	885.024i		−	1.21736i	0.793414	−	0.608682i	$-0.208302\pi$
$728$		−	19.5251i		−	0.0268202i
$729$	−294.247			−0.403631
$730$			67.1020i			0.0919206i
$731$	−207.537			−0.283908
$732$			1297.42i			1.77243i
$733$			694.999i			0.948157i	0.880483	+	0.474078i	$0.157219\pi$
$733$			694.999i			0.948157i	−0.880483	+	0.474078i	$0.842781\pi$
$734$		−	598.829i		−	0.815843i
$735$		−	1534.12i		−	2.08724i
$736$	−488.241	−	581.121i	−0.663370	−	0.789567i
$737$	532.819			0.722957
$738$	−225.291			−0.305272
$739$	−896.852			−1.21360			−0.606801	−	0.794854i	$-0.707547\pi$
$739$	−896.852			−1.21360			−0.606801	+	0.794854i	$0.707547\pi$
$740$	−88.7979			−0.119997
$741$			29.8609i			0.0402981i
$742$	−536.394			−0.722902
$743$			624.806i			0.840924i	0.907310	+	0.420462i	$0.138132\pi$
$743$			624.806i			0.840924i	−0.907310	+	0.420462i	$0.861868\pi$
$744$	−1321.26			−1.77589
$745$	−215.703			−0.289534
$746$			174.832i			0.234359i
$747$		−	286.667i		−	0.383758i
$748$	117.354			0.156891
$749$	1142.21			1.52497
$750$			59.6451i			0.0795269i
$751$			222.153i			0.295810i	0.989002	+	0.147905i	$0.0472530\pi$
$751$			222.153i			0.295810i	−0.989002	+	0.147905i	$0.952747\pi$
$752$	107.907			0.143493
$753$		−	2101.37i		−	2.79066i
$754$	−3.76927			−0.00499904
$755$			75.8484i			0.100461i
$756$		−	2231.07i		−	2.95115i
$757$		−	857.347i		−	1.13256i	−0.824213	−	0.566279i	$-0.808382\pi$
$757$		−	857.347i		−	1.13256i	0.824213	−	0.566279i	$-0.191618\pi$
$758$		−	447.801i		−	0.590767i
$759$	858.043	−	720.902i	1.13049	−	0.949805i
$760$	418.598			0.550786
$761$	1238.43			1.62737			0.813686	−	0.581305i	$-0.197458\pi$
$761$	1238.43			1.62737			0.813686	+	0.581305i	$0.197458\pi$
$762$	407.184			0.534362
$763$	−363.566			−0.476496
$764$		−	540.122i		−	0.706966i
$765$	186.370			0.243621
$766$		−	199.226i		−	0.260086i
$767$	−22.0143			−0.0287019
$768$	−912.255			−1.18783
$769$			738.967i			0.960946i	0.877010	+	0.480473i	$0.159535\pi$
$769$			738.967i			0.960946i	−0.877010	+	0.480473i	$0.840465\pi$
$770$		−	272.174i		−	0.353473i
$771$	1820.62			2.36137
$772$	−1053.40			−1.36450
$773$			454.937i			0.588535i	0.955723	+	0.294267i	$0.0950756\pi$
$773$			454.937i			0.588535i	−0.955723	+	0.294267i	$0.904924\pi$
$774$			942.984i			1.21833i
$775$	176.905			0.228265
$776$			92.4504i			0.119137i
$777$	941.114			1.21122
$778$			375.510i			0.482661i
$779$		−	309.604i		−	0.397438i
$780$			7.49024i			0.00960288i
$781$			442.271i			0.566288i
$782$	−75.4213	+	63.3667i	−0.0964467	+	0.0810316i
$783$	−1004.97			−1.28349
$784$	−643.019			−0.820177
$785$	−287.150			−0.365797
$786$	285.990			0.363856
$787$			384.797i			0.488941i	0.969657	+	0.244471i	$0.0786141\pi$
$787$			384.797i			0.488941i	−0.969657	+	0.244471i	$0.921386\pi$
$788$	112.425			0.142671
$789$		−	655.484i		−	0.830778i
$790$	58.7979			0.0744277
$791$	−822.182			−1.03942
$792$		−	1244.18i		−	1.57094i
$793$			16.9671i			0.0213961i
$794$	−541.468			−0.681949
$795$	480.134			0.603942
$796$		−	392.455i		−	0.493034i
$797$		−	97.3580i		−	0.122156i	−0.998133	−	0.0610778i	$-0.980546\pi$
$797$		−	97.3580i		−	0.122156i	0.998133	−	0.0610778i	$-0.0194538\pi$
$798$	−1901.34			−2.38263
$799$		−	92.4317i		−	0.115684i
$800$	165.000			0.206250
$801$			2763.62i			3.45022i
$802$		−	291.755i		−	0.363785i
$803$			274.086i			0.341327i
$804$		−	933.652i		−	1.16126i
$805$	−440.891	−	524.764i	−0.547691	−	0.651881i
$806$	−7.40526			−0.00918766
$807$	718.627			0.890492
$808$	719.923			0.890994
$809$	−108.042			−0.133550			−0.0667751	−	0.997768i	$-0.521271\pi$
$809$	−108.042			−0.133550			−0.0667751	+	0.997768i	$0.521271\pi$
$810$		−	274.057i		−	0.338342i
$811$	−922.081			−1.13697			−0.568484	−	0.822695i	$-0.692470\pi$
$811$	−922.081			−1.13697			−0.568484	+	0.822695i	$0.692470\pi$
$812$			720.005i			0.886706i
$813$	−2335.66			−2.87289
$814$	120.902			0.148528
$815$		−	34.3731i		−	0.0421755i
$816$		−	114.243i		−	0.140004i
$817$	−1295.89			−1.58615
$818$	141.725			0.173257
$819$		−	54.2808i		−	0.0662769i
$820$		−	77.6604i		−	0.0947078i
$821$	78.1484			0.0951868			0.0475934	−	0.998867i	$-0.484845\pi$
$821$	78.1484			0.0951868			0.0475934	+	0.998867i	$0.484845\pi$
$822$		−	1121.06i		−	1.36382i
$823$	412.735			0.501501			0.250750	−	0.968052i	$-0.419323\pi$
$823$	412.735			0.501501			0.250750	+	0.968052i	$0.419323\pi$
$824$		−	708.374i		−	0.859677i
$825$			243.627i			0.295306i
$826$		−	1401.72i		−	1.69700i
$827$		−	1270.38i		−	1.53613i	−0.640373	−	0.768064i	$-0.721220\pi$
$827$		−	1270.38i		−	1.53613i	0.640373	−	0.768064i	$-0.278780\pi$
$828$	−863.758	−	1028.07i	−1.04319	−	1.24164i
$829$	1034.62			1.24804			0.624018	−	0.781410i	$-0.285499\pi$
$829$	1034.62			1.24804			0.624018	+	0.781410i	$0.285499\pi$
$830$	−32.9391			−0.0396857
$831$	−2111.33			−2.54071
$832$	−2.72090			−0.00327031
$833$			550.801i			0.661226i
$834$	511.933			0.613829
$835$		−	118.916i		−	0.142414i
$836$	732.775			0.876526
$837$	−1974.41			−2.35891
$838$			438.321i			0.523056i
$839$		−	673.016i		−	0.802164i	−0.916042	−	0.401082i	$-0.868634\pi$
$839$		−	673.016i		−	0.802164i	0.916042	−	0.401082i	$-0.131366\pi$
$840$	−1112.83			−1.32480
$841$	−516.678			−0.614361
$842$		−	84.6730i		−	0.100562i
$843$			581.198i			0.689440i
$844$	753.928			0.893280
$845$		−	377.798i		−	0.447098i
$846$	−419.982			−0.496432
$847$			500.816i			0.591283i
$848$		−	201.246i		−	0.237319i
$849$			1744.93i			2.05528i
$850$		−	21.4147i		−	0.0251937i
$851$	233.104	−	195.847i	0.273917	−	0.230137i
$852$	774.986			0.909608
$853$	−64.8855			−0.0760674			−0.0380337	−	0.999276i	$-0.512109\pi$
$853$	−64.8855			−0.0760674			−0.0380337	+	0.999276i	$0.512109\pi$
$854$	−1080.35			−1.26505
$855$	1163.72			1.36108
$856$		−	599.952i		−	0.700878i
$857$	1140.41			1.33070			0.665349	−	0.746533i	$-0.268283\pi$
$857$	1140.41			1.33070			0.665349	+	0.746533i	$0.268283\pi$
$858$		−	10.1983i		−	0.0118861i
$859$	290.141			0.337766			0.168883	−	0.985636i	$-0.445984\pi$
$859$	290.141			0.337766			0.168883	+	0.985636i	$0.445984\pi$
$860$	−325.057			−0.377974
$861$			823.075i			0.955953i
$862$			475.343i			0.551442i
$863$	1264.66			1.46542			0.732712	−	0.680539i	$-0.238254\pi$
$863$	1264.66			1.46542			0.732712	+	0.680539i	$0.238254\pi$
$864$	−1841.54			−2.13141
$865$		−	470.808i		−	0.544287i
$866$		−	348.487i		−	0.402410i
$867$	1443.90			1.66540
$868$			1414.55i			1.62966i
$869$	240.167			0.276371
$870$			214.829i			0.246930i
$871$		−	12.2099i		−	0.0140183i
$872$			190.966i			0.218997i
$873$			257.017i			0.294406i
$874$	−470.941	+	395.670i	−0.538834	+	0.452712i
$875$	148.998			0.170284
$876$	480.277			0.548262
$877$	521.497			0.594637			0.297318	−	0.954778i	$-0.403908\pi$
$877$	521.497			0.594637			0.297318	+	0.954778i	$0.403908\pi$
$878$	433.893			0.494183
$879$			956.401i			1.08806i
$880$	102.115			0.116040
$881$			1525.59i			1.73166i	0.500342	+	0.865828i	$0.333208\pi$
$881$			1525.59i			1.73166i	−0.500342	+	0.865828i	$0.666792\pi$
$882$	2502.67			2.83750
$883$	167.182			0.189335			0.0946673	−	0.995509i	$-0.469821\pi$
$883$	167.182			0.189335			0.0946673	+	0.995509i	$0.469821\pi$
$884$		−	2.68925i		−	0.00304214i
$885$			1254.70i			1.41774i
$886$	344.496			0.388821
$887$	30.9159			0.0348544			0.0174272	−	0.999848i	$-0.494452\pi$
$887$	30.9159			0.0348544			0.0174272	+	0.999848i	$0.494452\pi$
$888$		−	494.327i		−	0.556675i
$889$		−	1017.18i		−	1.14418i
$890$	317.551			0.356799
$891$		−	1119.42i		−	1.25636i
$892$	292.771			0.328219
$893$		−	577.156i		−	0.646311i
$894$		−	514.626i		−	0.575644i
$895$		−	173.537i		−	0.193896i
$896$			1585.89i			1.76997i
$897$	−16.5200	−	19.6627i	−0.0184169	−	0.0219205i
$898$	−5.29512			−0.00589656
$899$	637.175			0.708760
$900$	291.905			0.324339
$901$	−172.385			−0.191326
$902$			105.738i			0.117226i
$903$	3445.08			3.81515
$904$			431.857i			0.477718i
$905$	635.703			0.702434
$906$	−180.959			−0.199734
$907$		−	760.531i		−	0.838513i	−0.907868	−	0.419256i	$-0.862291\pi$
$907$		−	760.531i		−	0.838513i	0.907868	−	0.419256i	$-0.137709\pi$
$908$			653.163i			0.719343i
$909$	2001.42			2.20178
$910$	−6.23707			−0.00685392
$911$			1296.62i			1.42330i	0.702535	+	0.711649i	$0.252051\pi$
$911$			1296.62i			1.42330i	−0.702535	+	0.711649i	$0.747949\pi$
$912$		−	713.352i		−	0.782184i
$913$	−134.544			−0.147364
$914$			492.595i			0.538944i
$915$	967.039			1.05687
$916$		−	568.184i		−	0.620288i
$917$		−	714.427i		−	0.779091i
$918$			239.005i			0.260354i
$919$			993.374i			1.08093i	0.841367	+	0.540465i	$0.181752\pi$
$919$			993.374i			1.08093i	−0.841367	+	0.540465i	$0.818248\pi$
$920$	−275.636	+	231.581i	−0.299604	+	0.251719i
$921$	−2811.69			−3.05286
$922$	−754.998			−0.818870
$923$	10.1350			0.0109805
$924$	−1948.07			−2.10830
$925$			66.1860i			0.0715525i
$926$	−485.794			−0.524616
$927$		−	1969.32i		−	2.12440i
$928$	594.295			0.640404
$929$	638.201			0.686976			0.343488	−	0.939157i	$-0.388392\pi$
$929$	638.201			0.686976			0.343488	+	0.939157i	$0.388392\pi$
$930$			422.062i			0.453830i
$931$			3439.28i			3.69418i
$932$	−595.256			−0.638686
$933$	804.881			0.862680
$934$			653.618i			0.699805i
$935$		−	87.4706i		−	0.0935515i
$936$	−28.5114			−0.0304609
$937$		−	670.422i		−	0.715498i	−0.933818	−	0.357749i	$-0.883544\pi$
$937$		−	670.422i		−	0.715498i	0.933818	−	0.357749i	$-0.116456\pi$
$938$	777.446			0.828833
$939$			1758.48i			1.87272i
$940$		−	144.772i		−	0.154013i
$941$			272.324i			0.289398i	0.989476	+	0.144699i	$0.0462215\pi$
$941$			272.324i			0.289398i	−0.989476	+	0.144699i	$0.953779\pi$
$942$		−	685.085i		−	0.727266i
$943$	171.283	+	203.867i	0.181636	+	0.216189i
$944$	525.903			0.557101
$945$	−1662.94			−1.75973
$946$	442.578			0.467841
$947$	−598.249			−0.631730			−0.315865	−	0.948804i	$-0.602295\pi$
$947$	−598.249			−0.631730			−0.315865	+	0.948804i	$0.602295\pi$
$948$		−	420.841i		−	0.443925i
$949$	6.28088			0.00661842
$950$		−	133.716i		−	0.140754i
$951$	602.664			0.633716
$952$	399.545			0.419690
$953$		−	1155.75i		−	1.21275i	−0.795179	−	0.606375i	$-0.792623\pi$
$953$		−	1155.75i		−	1.21275i	0.795179	−	0.606375i	$-0.207377\pi$
$954$			783.264i			0.821031i
$955$	−402.583			−0.421553
$956$	219.649			0.229759
$957$			877.495i			0.916922i
$958$			567.455i			0.592333i
$959$	−2800.51			−2.92024
$960$			155.077i			0.161539i
$961$	290.818			0.302620
$962$		−	2.77055i		−	0.00287999i
$963$		−	1667.90i		−	1.73198i
$964$		−	1153.04i		−	1.19610i
$965$			785.156i			0.813633i
$966$	1251.98	−	1051.88i	1.29605	−	1.08890i
$967$	530.971			0.549091			0.274546	−	0.961574i	$-0.411473\pi$
$967$	530.971			0.549091			0.274546	+	0.961574i	$0.411473\pi$
$968$	263.057			0.271753
$969$	−611.047			−0.630596
$970$	29.5322			0.0304456
$971$		−	626.789i		−	0.645509i	−0.946483	−	0.322754i	$-0.895391\pi$
$971$		−	626.789i		−	0.645509i	0.946483	−	0.322754i	$-0.104609\pi$
$972$	−454.829			−0.467931
$973$		−	1278.85i		−	1.31434i
$974$	−482.712			−0.495597
$975$	5.58290			0.00572605
$976$		−	405.330i		−	0.415297i
$977$			1426.66i			1.46025i	0.683315	+	0.730124i	$0.260538\pi$
$977$			1426.66i			1.46025i	−0.683315	+	0.730124i	$0.739462\pi$
$978$	82.0074			0.0838522
$979$	1297.07			1.32490
$980$			862.700i			0.880306i
$981$			530.894i			0.541177i
$982$	−157.402			−0.160288
$983$		−	637.973i		−	0.649006i	−0.945885	−	0.324503i	$-0.894803\pi$
$983$		−	637.973i		−	0.649006i	0.945885	−	0.324503i	$-0.105197\pi$
$984$	432.326			0.439356
$985$		−	83.7966i		−	0.0850727i
$986$		−	77.1311i		−	0.0782263i
$987$			1534.35i			1.55456i
$988$		−	16.7921i		−	0.0169960i
$989$	853.309	−	716.925i	0.862800	−	0.724899i
$990$	−397.440			−0.401455
$991$	−1567.24			−1.58148			−0.790739	−	0.612154i	$-0.790303\pi$
$991$	−1567.24			−1.58148			−0.790739	+	0.612154i	$0.790303\pi$
$992$	1167.57			1.17699
$993$	853.791			0.859810
$994$			645.325i			0.649220i
$995$	−292.519			−0.293989
$996$			235.759i			0.236706i
$997$	1445.92			1.45027			0.725134	−	0.688607i	$-0.241778\pi$
$997$	1445.92			1.45027			0.725134	+	0.688607i	$0.241778\pi$
$998$	355.399			0.356111
$999$		−	738.690i		−	0.739430i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	115.3.d.a.91.6	yes	6
3.2	odd	2		1035.3.g.a.91.3		6
4.3	odd	2		1840.3.k.a.321.2		6
5.2	odd	4		575.3.c.c.574.1		12
5.3	odd	4		575.3.c.c.574.12		12
5.4	even	2		575.3.d.e.551.1		6
23.22	odd	2	inner	115.3.d.a.91.5	✓	6
69.68	even	2		1035.3.g.a.91.4		6
92.91	even	2		1840.3.k.a.321.1		6
115.22	even	4		575.3.c.c.574.2		12
115.68	even	4		575.3.c.c.574.11		12
115.114	odd	2		575.3.d.e.551.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.3.d.a.91.5	✓	6	23.22	odd	2	inner
115.3.d.a.91.6	yes	6	1.1	even	1	trivial
575.3.c.c.574.1		12	5.2	odd	4
575.3.c.c.574.2		12	115.22	even	4
575.3.c.c.574.11		12	115.68	even	4
575.3.c.c.574.12		12	5.3	odd	4
575.3.d.e.551.1		6	5.4	even	2
575.3.d.e.551.2		6	115.114	odd	2
1035.3.g.a.91.3		6	3.2	odd	2
1035.3.g.a.91.4		6	69.68	even	2
1840.3.k.a.321.1		6	92.91	even	2
1840.3.k.a.321.2		6	4.3	odd	2

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.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +5.33482 q^{3} -3.00000 q^{4} +2.23607i q^{5} -5.33482 q^{6} +13.3268i q^{7} +7.00000 q^{8} +19.4603 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +5.33482 q^{3} -3.00000 q^{4} +2.23607i q^{5} -5.33482 q^{6} +13.3268i q^{7} +7.00000 q^{8} +19.4603 q^{9} -2.23607i q^{10} -9.13348i q^{11} -16.0045 q^{12} -0.209300 q^{13} -13.3268i q^{14} +11.9290i q^{15} +5.00000 q^{16} -4.28293i q^{17} -19.4603 q^{18} -26.7432i q^{19} -6.70820i q^{20} +71.0962i q^{21} +9.13348i q^{22} +(14.7952 + 17.6097i) q^{23} +37.3438 q^{24} -5.00000 q^{25} +0.209300 q^{26} +55.8041 q^{27} -39.9804i q^{28} -18.0089 q^{29} -11.9290i q^{30} -35.3810 q^{31} -33.0000 q^{32} -48.7255i q^{33} +4.28293i q^{34} -29.7996 q^{35} -58.3810 q^{36} -13.2372i q^{37} +26.7432i q^{38} -1.11658 q^{39} +15.6525i q^{40} +11.5769 q^{41} -71.0962i q^{42} -48.4567i q^{43} +27.4004i q^{44} +43.5147i q^{45} +(-14.7952 - 17.6097i) q^{46} +21.5814 q^{47} +26.6741 q^{48} -128.604 q^{49} +5.00000 q^{50} -22.8487i q^{51} +0.627900 q^{52} -40.2492i q^{53} -55.8041 q^{54} +20.4231 q^{55} +93.2876i q^{56} -142.670i q^{57} +18.0089 q^{58} +105.181 q^{59} -35.7871i q^{60} -81.0661i q^{61} +35.3810 q^{62} +259.344i q^{63} +13.0000 q^{64} -0.468009i q^{65} +48.7255i q^{66} +58.3370i q^{67} +12.8488i q^{68} +(78.9296 + 93.9449i) q^{69} +29.7996 q^{70} -48.4231 q^{71} +136.222 q^{72} -30.0089 q^{73} +13.2372i q^{74} -26.6741 q^{75} +80.2296i q^{76} +121.720 q^{77} +1.11658 q^{78} +26.2952i q^{79} +11.1803i q^{80} +122.562 q^{81} -11.5769 q^{82} -14.7308i q^{83} -213.288i q^{84} +9.57693 q^{85} +48.4567i q^{86} -96.0746 q^{87} -63.9343i q^{88} +142.013i q^{89} -43.5147i q^{90} -2.78930i q^{91} +(-44.3855 - 52.8292i) q^{92} -188.752 q^{93} -21.5814 q^{94} +59.7996 q^{95} -176.049 q^{96} +13.2072i q^{97} +128.604 q^{98} -177.741i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{2} + 2 q^{3} - 18 q^{4} - 2 q^{6} + 42 q^{8} + 48 q^{9}+O(q^{10}) \) 6 * q - 6 * q^2 + 2 * q^3 - 18 * q^4 - 2 * q^6 + 42 * q^8 + 48 * q^9	\( 6 q - 6 q^{2} + 2 q^{3} - 18 q^{4} - 2 q^{6} + 42 q^{8} + 48 q^{9} - 6 q^{12} - 10 q^{13} + 30 q^{16} - 48 q^{18} - 10 q^{23} + 14 q^{24} - 30 q^{25} + 10 q^{26} + 56 q^{27} + 72 q^{29} - 6 q^{31} - 198 q^{32} + 10 q^{35} - 144 q^{36} - 148 q^{39} + 142 q^{41} + 10 q^{46} + 112 q^{47} + 10 q^{48} - 304 q^{49} + 30 q^{50} + 30 q^{52} - 56 q^{54} + 50 q^{55} - 72 q^{58} + 236 q^{59} + 6 q^{62} + 78 q^{64} + 156 q^{69} - 10 q^{70} - 218 q^{71} + 336 q^{72} - 10 q^{75} + 184 q^{77} + 148 q^{78} + 354 q^{81} - 142 q^{82} + 130 q^{85} - 584 q^{87} + 30 q^{92} - 176 q^{93} - 112 q^{94} + 170 q^{95} - 66 q^{96} + 304 q^{98}+O(q^{100}) \) 6 * q - 6 * q^2 + 2 * q^3 - 18 * q^4 - 2 * q^6 + 42 * q^8 + 48 * q^9 - 6 * q^12 - 10 * q^13 + 30 * q^16 - 48 * q^18 - 10 * q^23 + 14 * q^24 - 30 * q^25 + 10 * q^26 + 56 * q^27 + 72 * q^29 - 6 * q^31 - 198 * q^32 + 10 * q^35 - 144 * q^36 - 148 * q^39 + 142 * q^41 + 10 * q^46 + 112 * q^47 + 10 * q^48 - 304 * q^49 + 30 * q^50 + 30 * q^52 - 56 * q^54 + 50 * q^55 - 72 * q^58 + 236 * q^59 + 6 * q^62 + 78 * q^64 + 156 * q^69 - 10 * q^70 - 218 * q^71 + 336 * q^72 - 10 * q^75 + 184 * q^77 + 148 * q^78 + 354 * q^81 - 142 * q^82 + 130 * q^85 - 584 * q^87 + 30 * q^92 - 176 * q^93 - 112 * q^94 + 170 * q^95 - 66 * q^96 + 304 * q^98

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