LMFDB - Embedded newform 115.3.d.a.91.1

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			91.1
Root			$-4.73103 + 2.23607i$ of defining polynomial
Character	$\chi$	$=$	115.91
Dual form			115.3.d.a.91.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -4.73103 q^{3} -3.00000 q^{4} -2.23607i q^{5} +4.73103 q^{6} +7.39757i q^{7} +7.00000 q^{8} +13.3827 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -4.73103 q^{3} -3.00000 q^{4} -2.23607i q^{5} +4.73103 q^{6} +7.39757i q^{7} +7.00000 q^{8} +13.3827 q^{9} +2.23607i q^{10} -16.9416i q^{11} +14.1931 q^{12} +13.8447 q^{13} -7.39757i q^{14} +10.5789i q^{15} +5.00000 q^{16} +30.3580i q^{17} -13.3827 q^{18} +6.01884i q^{19} +6.70820i q^{20} -34.9981i q^{21} +16.9416i q^{22} +(-1.34836 - 22.9604i) q^{23} -33.1172 q^{24} -5.00000 q^{25} -13.8447 q^{26} -20.7346 q^{27} -22.1927i q^{28} +42.3862 q^{29} -10.5789i q^{30} -17.1480 q^{31} -33.0000 q^{32} +80.1513i q^{33} -30.3580i q^{34} +16.5415 q^{35} -40.1480 q^{36} -28.2115i q^{37} -6.01884i q^{38} -65.4999 q^{39} -15.6525i q^{40} +69.8826 q^{41} +34.9981i q^{42} +17.7093i q^{43} +50.8248i q^{44} -29.9246i q^{45} +(1.34836 + 22.9604i) q^{46} +49.6895 q^{47} -23.6552 q^{48} -5.72398 q^{49} +5.00000 q^{50} -143.625i q^{51} -41.5342 q^{52} +40.2492i q^{53} +20.7346 q^{54} -37.8826 q^{55} +51.7830i q^{56} -28.4753i q^{57} -42.3862 q^{58} +40.6066 q^{59} -31.7367i q^{60} +2.84083i q^{61} +17.1480 q^{62} +98.9992i q^{63} +13.0000 q^{64} -30.9578i q^{65} -80.1513i q^{66} +35.2619i q^{67} -91.0740i q^{68} +(6.37914 + 108.627i) q^{69} -16.5415 q^{70} +9.88257 q^{71} +93.6787 q^{72} +30.3862 q^{73} +28.2115i q^{74} +23.6552 q^{75} -18.0565i q^{76} +125.327 q^{77} +65.4999 q^{78} +98.0510i q^{79} -11.1803i q^{80} -22.3482 q^{81} -69.8826 q^{82} -100.271i q^{83} +104.994i q^{84} +67.8826 q^{85} -17.7093i q^{86} -200.530 q^{87} -118.591i q^{88} -28.3683i q^{89} +29.9246i q^{90} +102.417i q^{91} +(4.04509 + 68.8813i) q^{92} +81.1278 q^{93} -49.6895 q^{94} +13.4585 q^{95} +156.124 q^{96} -174.330i q^{97} +5.72398 q^{98} -226.724i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	$0.580431\pi$
$3$	−4.73103			−1.57701			−0.788505	−	0.615028i	$-0.789145\pi$
$3$	−4.73103			−1.57701			−0.788505	+	0.615028i	$0.789145\pi$
$4$	−3.00000			−0.750000
$5$		−	2.23607i		−	0.447214i
$5$		−	2.23607i		−	0.447214i
$6$	4.73103			0.788505
$7$			7.39757i			1.05680i	0.848997	+	0.528398i	$0.177207\pi$
$7$			7.39757i			1.05680i	−0.848997	+	0.528398i	$0.822793\pi$
$8$	7.00000			0.875000
$9$	13.3827			1.48696
$10$			2.23607i			0.223607i
$11$		−	16.9416i		−	1.54015i	−0.637956	−	0.770073i	$-0.720220\pi$
$11$		−	16.9416i		−	1.54015i	0.637956	−	0.770073i	$-0.279780\pi$
$12$	14.1931			1.18276
$13$	13.8447			1.06498			0.532490	−	0.846436i	$-0.321256\pi$
$13$	13.8447			1.06498			0.532490	+	0.846436i	$0.321256\pi$
$14$		−	7.39757i		−	0.528398i
$15$			10.5789i			0.705261i
$16$	5.00000			0.312500
$17$			30.3580i			1.78577i	0.450290	+	0.892883i	$0.351321\pi$
$17$			30.3580i			1.78577i	−0.450290	+	0.892883i	$0.648679\pi$
$18$	−13.3827			−0.743482
$19$			6.01884i			0.316781i	0.987377	+	0.158391i	$0.0506305\pi$
$19$			6.01884i			0.316781i	−0.987377	+	0.158391i	$0.949369\pi$
$20$			6.70820i			0.335410i
$21$		−	34.9981i		−	1.66658i
$22$			16.9416i			0.770073i
$23$	−1.34836	−	22.9604i	−0.0586244	−	0.998280i
$23$	−1.34836	−	22.9604i	−0.0586244	−	0.998280i
$24$	−33.1172			−1.37988
$25$	−5.00000			−0.200000
$26$	−13.8447			−0.532490
$27$	−20.7346			−0.767947
$28$		−	22.1927i		−	0.792596i
$29$	42.3862			1.46159			0.730796	−	0.682595i	$-0.239149\pi$
$29$	42.3862			1.46159			0.730796	+	0.682595i	$0.239149\pi$
$30$		−	10.5789i		−	0.352630i
$31$	−17.1480			−0.553162			−0.276581	−	0.960991i	$-0.589201\pi$
$31$	−17.1480			−0.553162			−0.276581	+	0.960991i	$0.589201\pi$
$32$	−33.0000			−1.03125
$33$			80.1513i			2.42883i
$34$		−	30.3580i		−	0.892883i
$35$	16.5415			0.472613
$36$	−40.1480			−1.11522
$37$		−	28.2115i		−	0.762474i	−0.924477	−	0.381237i	$-0.875498\pi$
$37$		−	28.2115i		−	0.762474i	0.924477	−	0.381237i	$-0.124502\pi$
$38$		−	6.01884i		−	0.158391i
$39$	−65.4999			−1.67948
$40$		−	15.6525i		−	0.391312i
$41$	69.8826			1.70445			0.852226	−	0.523173i	$-0.175252\pi$
$41$	69.8826			1.70445			0.852226	+	0.523173i	$0.175252\pi$
$42$			34.9981i			0.833289i
$43$			17.7093i			0.411845i	0.978568	+	0.205923i	$0.0660195\pi$
$43$			17.7093i			0.411845i	−0.978568	+	0.205923i	$0.933980\pi$
$44$			50.8248i			1.15511i
$45$		−	29.9246i		−	0.664990i
$46$	1.34836	+	22.9604i	0.0293122	+	0.499140i
$47$	49.6895			1.05722			0.528611	−	0.848864i	$-0.322713\pi$
$47$	49.6895			1.05722			0.528611	+	0.848864i	$0.322713\pi$
$48$	−23.6552			−0.492816
$49$	−5.72398			−0.116816
$50$	5.00000			0.100000
$51$		−	143.625i		−	2.81617i
$52$	−41.5342			−0.798735
$53$			40.2492i			0.759419i	0.925106	+	0.379710i	$0.123976\pi$
$53$			40.2492i			0.759419i	−0.925106	+	0.379710i	$0.876024\pi$
$54$	20.7346			0.383973
$55$	−37.8826			−0.688774
$56$			51.7830i			0.924696i
$57$		−	28.4753i		−	0.499567i
$58$	−42.3862			−0.730796
$59$	40.6066			0.688247			0.344123	−	0.938924i	$-0.388176\pi$
$59$	40.6066			0.688247			0.344123	+	0.938924i	$0.388176\pi$
$60$		−	31.7367i		−	0.528946i
$61$			2.84083i			0.0465710i	0.999729	+	0.0232855i	$0.00741267\pi$
$61$			2.84083i			0.0465710i	−0.999729	+	0.0232855i	$0.992587\pi$
$62$	17.1480			0.276581
$63$			98.9992i			1.57142i
$64$	13.0000			0.203125
$65$		−	30.9578i		−	0.476273i
$66$		−	80.1513i		−	1.21441i
$67$			35.2619i			0.526297i	0.964755	+	0.263149i	$0.0847610\pi$
$67$			35.2619i			0.526297i	−0.964755	+	0.263149i	$0.915239\pi$
$68$		−	91.0740i		−	1.33932i
$69$	6.37914	+	108.627i	0.0924514	+	1.57430i
$70$	−16.5415			−0.236307
$71$	9.88257			0.139191			0.0695956	−	0.997575i	$-0.477829\pi$
$71$	9.88257			0.139191			0.0695956	+	0.997575i	$0.477829\pi$
$72$	93.6787			1.30109
$73$	30.3862			0.416249			0.208125	−	0.978102i	$-0.433264\pi$
$73$	30.3862			0.416249			0.208125	+	0.978102i	$0.433264\pi$
$74$			28.2115i			0.381237i
$75$	23.6552			0.315402
$76$		−	18.0565i		−	0.237586i
$77$	125.327			1.62762
$78$	65.4999			0.839742
$79$			98.0510i			1.24115i	0.784146	+	0.620576i	$0.213101\pi$
$79$			98.0510i			1.24115i	−0.784146	+	0.620576i	$0.786899\pi$
$80$		−	11.1803i		−	0.139754i
$81$	−22.3482			−0.275903
$82$	−69.8826			−0.852226
$83$		−	100.271i		−	1.20808i	−0.796953	−	0.604041i	$-0.793556\pi$
$83$		−	100.271i		−	1.20808i	0.796953	−	0.604041i	$-0.206444\pi$
$84$			104.994i			1.24993i
$85$	67.8826			0.798618
$86$		−	17.7093i		−	0.205923i
$87$	−200.530			−2.30495
$88$		−	118.591i		−	1.34763i
$89$		−	28.3683i		−	0.318745i	−0.987219	−	0.159373i	$-0.949053\pi$
$89$		−	28.3683i		−	0.318745i	0.987219	−	0.159373i	$-0.0509471\pi$
$90$			29.9246i			0.332495i
$91$			102.417i			1.12547i
$92$	4.04509	+	68.8813i	0.0439683	+	0.748710i
$93$	81.1278			0.872342
$94$	−49.6895			−0.528611
$95$	13.4585			0.141669
$96$	156.124			1.62629
$97$		−	174.330i		−	1.79722i	−0.438753	−	0.898608i	$-0.644580\pi$
$97$		−	174.330i		−	1.79722i	0.438753	−	0.898608i	$-0.355420\pi$
$98$	5.72398			0.0584080
$99$		−	226.724i		−	2.29014i
$100$	15.0000			0.150000
$101$	−13.7651			−0.136289			−0.0681443	−	0.997675i	$-0.521708\pi$
$101$	−13.7651			−0.136289			−0.0681443	+	0.997675i	$0.521708\pi$
$102$			143.625i			1.40809i
$103$			65.7767i			0.638609i	0.947652	+	0.319304i	$0.103449\pi$
$103$			65.7767i			0.638609i	−0.947652	+	0.319304i	$0.896551\pi$
$104$	96.9132			0.931857
$105$	−78.2582			−0.745316
$106$		−	40.2492i		−	0.379710i
$107$			116.455i			1.08836i	0.838968	+	0.544181i	$0.183160\pi$
$107$			116.455i			1.08836i	−0.838968	+	0.544181i	$0.816840\pi$
$108$	62.2037			0.575960
$109$		−	130.903i		−	1.20094i	−0.799647	−	0.600471i	$-0.794980\pi$
$109$		−	130.903i		−	1.20094i	0.799647	−	0.600471i	$-0.205020\pi$
$110$	37.8826			0.344387
$111$			133.470i			1.20243i
$112$			36.9878i			0.330248i
$113$			10.5022i			0.0929398i	0.998920	+	0.0464699i	$0.0147972\pi$
$113$			10.5022i			0.0929398i	−0.998920	+	0.0464699i	$0.985203\pi$
$114$			28.4753i			0.249784i
$115$	−51.3411	+	3.01503i	−0.446444	+	0.0262176i
$116$	−127.159			−1.09619
$117$	185.280			1.58359
$118$	−40.6066			−0.344123
$119$	−224.575			−1.88719
$120$			74.0524i			0.617103i
$121$	−166.018			−1.37205
$122$		−	2.84083i		−	0.0232855i
$123$	−330.617			−2.68794
$124$	51.4440			0.414871
$125$			11.1803i			0.0894427i
$126$		−	98.9992i		−	0.785708i
$127$	−188.758			−1.48628			−0.743141	−	0.669135i	$-0.766665\pi$
$127$	−188.758			−1.48628			−0.743141	+	0.669135i	$0.766665\pi$
$128$	119.000			0.929688
$129$		−	83.7835i		−	0.649484i
$130$			30.9578i			0.238137i
$131$	99.4691			0.759306			0.379653	−	0.925129i	$-0.376043\pi$
$131$	99.4691			0.759306			0.379653	+	0.925129i	$0.376043\pi$
$132$		−	240.454i		−	1.82162i
$133$	−44.5248			−0.334773
$134$		−	35.2619i		−	0.263149i
$135$			46.3639i			0.343436i
$136$			212.506i			1.56254i
$137$			80.6789i			0.588897i	0.955667	+	0.294448i	$0.0951359\pi$
$137$			80.6789i			0.588897i	−0.955667	+	0.294448i	$0.904864\pi$
$138$	−6.37914	−	108.627i	−0.0462257	−	0.787149i
$139$	125.870			0.905538			0.452769	−	0.891628i	$-0.350436\pi$
$139$	125.870			0.905538			0.452769	+	0.891628i	$0.350436\pi$
$140$	−49.6244			−0.354460
$141$	−235.083			−1.66725
$142$	−9.88257			−0.0695956
$143$		−	234.552i		−	1.64022i
$144$	66.9134			0.464676
$145$		−	94.7784i		−	0.653644i
$146$	−30.3862			−0.208125
$147$	27.0803			0.184220
$148$			84.6346i			0.571856i
$149$			68.6512i			0.460746i	0.973102	+	0.230373i	$0.0739947\pi$
$149$			68.6512i			0.460746i	−0.973102	+	0.230373i	$0.926005\pi$
$150$	−23.6552			−0.157701
$151$	83.8681			0.555418			0.277709	−	0.960665i	$-0.410425\pi$
$151$	83.8681			0.555418			0.277709	+	0.960665i	$0.410425\pi$
$152$			42.1319i			0.277184i
$153$			406.271i			2.65537i
$154$	−125.327			−0.813809
$155$			38.3441i			0.247381i
$156$	196.500			1.25961
$157$			26.6761i			0.169911i	0.996385	+	0.0849556i	$0.0270748\pi$
$157$			26.6761i			0.169911i	−0.996385	+	0.0849556i	$0.972925\pi$
$158$		−	98.0510i		−	0.620576i
$159$		−	190.420i		−	1.19761i
$160$			73.7902i			0.461189i
$161$	169.851	−	9.97460i	1.05498	−	0.0619540i
$162$	22.3482			0.137952
$163$	−57.5342			−0.352971			−0.176485	−	0.984303i	$-0.556473\pi$
$163$	−57.5342			−0.352971			−0.176485	+	0.984303i	$0.556473\pi$
$164$	−209.648			−1.27834
$165$	179.224			1.08620
$166$			100.271i			0.604041i
$167$	11.3934			0.0682242			0.0341121	−	0.999418i	$-0.489140\pi$
$167$	11.3934			0.0682242			0.0341121	+	0.999418i	$0.489140\pi$
$168$		−	244.987i		−	1.45826i
$169$	22.6767			0.134182
$170$	−67.8826			−0.399309
$171$			80.5482i			0.471042i
$172$		−	53.1280i		−	0.308884i
$173$	229.875			1.32876			0.664378	−	0.747397i	$-0.268697\pi$
$173$	229.875			1.32876			0.664378	+	0.747397i	$0.268697\pi$
$174$	200.530			1.15247
$175$		−	36.9878i		−	0.211359i
$176$		−	84.7080i		−	0.481295i
$177$	−192.111			−1.08537
$178$			28.3683i			0.159373i
$179$	75.4691			0.421615			0.210808	−	0.977528i	$-0.432391\pi$
$179$	75.4691			0.421615			0.210808	+	0.977528i	$0.432391\pi$
$180$			89.7737i			0.498743i
$181$			119.179i			0.658445i	0.944252	+	0.329222i	$0.106787\pi$
$181$			119.179i			0.658445i	−0.944252	+	0.329222i	$0.893213\pi$
$182$		−	102.417i		−	0.562733i
$183$		−	13.4401i		−	0.0734429i
$184$	−9.43853	−	160.723i	−0.0512964	−	0.873495i
$185$	−63.0829			−0.340989
$186$	−81.1278			−0.436171
$187$	514.313			2.75034
$188$	−149.068			−0.792917
$189$		−	153.385i		−	0.811562i
$190$	−13.4585			−0.0708344
$191$			111.457i			0.583547i	0.956487	+	0.291773i	$0.0942453\pi$
$191$			111.457i			0.583547i	−0.956487	+	0.291773i	$0.905755\pi$
$192$	−61.5034			−0.320330
$193$	125.123			0.648305			0.324153	−	0.946005i	$-0.394921\pi$
$193$	125.123			0.648305			0.324153	+	0.946005i	$0.394921\pi$
$194$			174.330i			0.898608i
$195$			146.462i			0.751088i
$196$	17.1719			0.0876120
$197$	−296.716			−1.50617			−0.753087	−	0.657921i	$-0.771436\pi$
$197$	−296.716			−1.50617			−0.753087	+	0.657921i	$0.771436\pi$
$198$			226.724i			1.14507i
$199$		−	195.027i		−	0.980034i	−0.871713	−	0.490017i	$-0.836990\pi$
$199$		−	195.027i		−	0.980034i	0.871713	−	0.490017i	$-0.163010\pi$
$200$	−35.0000			−0.175000
$201$		−	166.825i		−	0.829977i
$202$	13.7651			0.0681443
$203$			313.555i			1.54460i
$204$			430.874i			2.11213i
$205$		−	156.262i		−	0.762255i
$206$		−	65.7767i		−	0.319304i
$207$	−18.0447	−	307.272i	−0.0871724	−	1.48441i
$208$	69.2237			0.332806
$209$	101.969			0.487889
$210$	78.2582			0.372658
$211$	195.386			0.925998			0.462999	−	0.886359i	$-0.346773\pi$
$211$	195.386			0.925998			0.462999	+	0.886359i	$0.346773\pi$
$212$		−	120.748i		−	0.569564i
$213$	−46.7548			−0.219506
$214$		−	116.455i		−	0.544181i
$215$	39.5993			0.184183
$216$	−145.142			−0.671953
$217$		−	126.854i		−	0.584579i
$218$			130.903i			0.600471i
$219$	−143.758			−0.656430
$220$	113.648			0.516581
$221$			420.299i			1.90180i
$222$		−	133.470i		−	0.601215i
$223$	−65.3033			−0.292840			−0.146420	−	0.989223i	$-0.546775\pi$
$223$	−65.3033			−0.292840			−0.146420	+	0.989223i	$0.546775\pi$
$224$		−	244.120i		−	1.08982i
$225$	−66.9134			−0.297393
$226$		−	10.5022i		−	0.0464699i
$227$		−	248.917i		−	1.09655i	−0.836299	−	0.548274i	$-0.815285\pi$
$227$		−	248.917i		−	1.09655i	0.836299	−	0.548274i	$-0.184715\pi$
$228$			85.4260i			0.374676i
$229$			203.690i			0.889476i	0.895661	+	0.444738i	$0.146703\pi$
$229$			203.690i			0.889476i	−0.895661	+	0.444738i	$0.853297\pi$
$230$	51.3411	−	3.01503i	0.223222	−	0.0131088i
$231$	−592.924			−2.56677
$232$	296.703			1.27889
$233$	170.311			0.730946			0.365473	−	0.930822i	$-0.380907\pi$
$233$	170.311			0.730946			0.365473	+	0.930822i	$0.380907\pi$
$234$	−185.280			−0.791793
$235$		−	111.109i		−	0.472804i
$236$	−121.820			−0.516185
$237$		−	463.883i		−	1.95731i
$238$	224.575			0.943594
$239$	232.938			0.974637			0.487318	−	0.873224i	$-0.337975\pi$
$239$	232.938			0.974637			0.487318	+	0.873224i	$0.337975\pi$
$240$			52.8946i			0.220394i
$241$			373.790i			1.55100i	0.631349	+	0.775499i	$0.282502\pi$
$241$			373.790i			1.55100i	−0.631349	+	0.775499i	$0.717498\pi$
$242$	166.018			0.686024
$243$	292.341			1.20305
$244$		−	8.52249i		−	0.0349282i
$245$			12.7992i			0.0522417i
$246$	330.617			1.34397
$247$			83.3293i			0.337366i
$248$	−120.036			−0.484016
$249$			474.385i			1.90516i
$250$		−	11.1803i		−	0.0447214i
$251$		−	84.1207i		−	0.335142i	−0.985860	−	0.167571i	$-0.946408\pi$
$251$		−	84.1207i		−	0.335142i	0.985860	−	0.167571i	$-0.0535924\pi$
$252$		−	296.998i		−	1.17856i
$253$	−388.987	+	22.8434i	−1.53750	+	0.0902902i
$254$	188.758			0.743141
$255$	−321.155			−1.25943
$256$	−171.000			−0.667969
$257$	−327.255			−1.27337			−0.636684	−	0.771125i	$-0.719694\pi$
$257$	−327.255			−1.27337			−0.636684	+	0.771125i	$0.719694\pi$
$258$			83.7835i			0.324742i
$259$	208.697			0.805779
$260$			92.8733i			0.357205i
$261$	567.241			2.17334
$262$	−99.4691			−0.379653
$263$		−	434.052i		−	1.65039i	−0.564849	−	0.825194i	$-0.691066\pi$
$263$		−	434.052i		−	1.65039i	0.564849	−	0.825194i	$-0.308934\pi$
$264$			561.059i			2.12522i
$265$	90.0000			0.339623
$266$	44.5248			0.167386
$267$			134.211i			0.502664i
$268$		−	105.786i		−	0.394723i
$269$	−2.80140			−0.0104141			−0.00520706	−	0.999986i	$-0.501657\pi$
$269$	−2.80140			−0.0104141			−0.00520706	+	0.999986i	$0.501657\pi$
$270$		−	46.3639i		−	0.171718i
$271$	192.728			0.711175			0.355588	−	0.934643i	$-0.384281\pi$
$271$	192.728			0.711175			0.355588	+	0.934643i	$0.384281\pi$
$272$			151.790i			0.558052i
$273$		−	484.540i		−	1.77487i
$274$		−	80.6789i		−	0.294448i
$275$			84.7080i			0.308029i
$276$	−19.1374	−	325.880i	−0.0693385	−	1.18072i
$277$	320.620			1.15747			0.578736	−	0.815515i	$-0.303546\pi$
$277$	320.620			1.15747			0.578736	+	0.815515i	$0.303546\pi$
$278$	−125.870			−0.452769
$279$	−229.486			−0.822531
$280$	115.790			0.413537
$281$		−	481.983i		−	1.71524i	−0.514283	−	0.857621i	$-0.671942\pi$
$281$		−	481.983i		−	1.71524i	0.514283	−	0.857621i	$-0.328058\pi$
$282$	235.083			0.833626
$283$			88.7608i			0.313642i	0.987627	+	0.156821i	$0.0501246\pi$
$283$			88.7608i			0.313642i	−0.987627	+	0.156821i	$0.949875\pi$
$284$	−29.6477			−0.104393
$285$	−63.6728			−0.223413
$286$			234.552i			0.820112i
$287$			516.961i			1.80126i
$288$	−441.628			−1.53343
$289$	−632.609			−2.18896
$290$			94.7784i			0.326822i
$291$			824.761i			2.83423i
$292$	−91.1586			−0.312187
$293$		−	212.736i		−	0.726062i	−0.931777	−	0.363031i	$-0.881742\pi$
$293$		−	212.736i		−	0.726062i	0.931777	−	0.363031i	$-0.118258\pi$
$294$	−27.0803			−0.0921100
$295$		−	90.7990i		−	0.307793i
$296$		−	197.481i		−	0.667165i
$297$			351.277i			1.18275i
$298$		−	68.6512i		−	0.230373i
$299$	−18.6677	−	317.881i	−0.0624338	−	1.06315i
$300$	−70.9655			−0.236552
$301$	−131.006			−0.435236
$302$	−83.8681			−0.277709
$303$	65.1233			0.214928
$304$			30.0942i			0.0989941i
$305$	6.35229			0.0208272
$306$		−	406.271i		−	1.32768i
$307$	−411.377			−1.33999			−0.669995	−	0.742365i	$-0.733704\pi$
$307$	−411.377			−1.33999			−0.669995	+	0.742365i	$0.733704\pi$
$308$	−375.980			−1.22071
$309$		−	311.192i		−	1.00709i
$310$		−	38.3441i		−	0.123691i
$311$	−146.924			−0.472424			−0.236212	−	0.971702i	$-0.575906\pi$
$311$	−146.924			−0.472424			−0.236212	+	0.971702i	$0.575906\pi$
$312$	−458.499			−1.46955
$313$			336.949i			1.07652i	0.842780	+	0.538258i	$0.180917\pi$
$313$			336.949i			1.07652i	−0.842780	+	0.538258i	$0.819083\pi$
$314$		−	26.6761i		−	0.0849556i
$315$	221.369			0.702758
$316$		−	294.153i		−	0.930864i
$317$	−400.963			−1.26487			−0.632434	−	0.774614i	$-0.717944\pi$
$317$	−400.963			−1.26487			−0.632434	+	0.774614i	$0.717944\pi$
$318$			190.420i			0.598806i
$319$		−	718.090i		−	2.25107i
$320$		−	29.0689i		−	0.0908403i
$321$		−	550.951i		−	1.71636i
$322$	−169.851	+	9.97460i	−0.527489	+	0.0309770i
$323$	−182.720			−0.565697
$324$	67.0445			0.206927
$325$	−69.2237			−0.212996
$326$	57.5342			0.176485
$327$			619.305i			1.89390i
$328$	489.178			1.49140
$329$			367.581i			1.11727i
$330$	−179.224			−0.543102
$331$	−605.346			−1.82884			−0.914419	−	0.404768i	$-0.867352\pi$
$331$	−605.346			−1.82884			−0.914419	+	0.404768i	$0.867352\pi$
$332$			300.813i			0.906062i
$333$		−	377.546i		−	1.13377i
$334$	−11.3934			−0.0341121
$335$	78.8481			0.235367
$336$		−	174.991i		−	0.520805i
$337$			381.287i			1.13142i	0.824605	+	0.565708i	$0.191397\pi$
$337$			381.287i			1.13142i	−0.824605	+	0.565708i	$0.808603\pi$
$338$	−22.6767			−0.0670909
$339$		−	49.6862i		−	0.146567i
$340$	−203.648			−0.598964
$341$			290.515i			0.851949i
$342$		−	80.5482i		−	0.235521i
$343$			320.137i			0.933345i
$344$			123.965i			0.360365i
$345$	242.896	−	14.2642i	0.704048	−	0.0413455i
$346$	−229.875			−0.664378
$347$	549.405			1.58330			0.791650	−	0.610975i	$-0.209222\pi$
$347$	549.405			1.58330			0.791650	+	0.610975i	$0.209222\pi$
$348$	601.591			1.72871
$349$	355.772			1.01940			0.509702	−	0.860351i	$-0.329756\pi$
$349$	355.772			1.01940			0.509702	+	0.860351i	$0.329756\pi$
$350$			36.9878i			0.105680i
$351$	−287.064			−0.817848
$352$			559.073i			1.58828i
$353$	−123.524			−0.349925			−0.174963	−	0.984575i	$-0.555980\pi$
$353$	−123.524			−0.349925			−0.174963	+	0.984575i	$0.555980\pi$
$354$	192.111			0.542686
$355$		−	22.0981i		−	0.0622482i
$356$			85.1049i			0.239059i
$357$	1062.47			2.97612
$358$	−75.4691			−0.210808
$359$		−	231.668i		−	0.645313i	−0.946516	−	0.322657i	$-0.895424\pi$
$359$		−	231.668i		−	0.645313i	0.946516	−	0.322657i	$-0.104576\pi$
$360$		−	209.472i		−	0.581866i
$361$	324.774			0.899650
$362$		−	119.179i		−	0.329222i
$363$	785.436			2.16373
$364$		−	307.252i		−	0.844099i
$365$		−	67.9456i		−	0.186152i
$366$			13.4401i			0.0367215i
$367$			200.756i			0.547019i	0.961869	+	0.273509i	$0.0881844\pi$
$367$			200.756i			0.547019i	−0.961869	+	0.273509i	$0.911816\pi$
$368$	−6.74181	−	114.802i	−0.0183201	−	0.311963i
$369$	935.215			2.53446
$370$	63.0829			0.170494
$371$	−297.746			−0.802551
$372$	−243.383			−0.654257
$373$		−	147.414i		−	0.395211i	−0.980282	−	0.197606i	$-0.936683\pi$
$373$		−	147.414i		−	0.395211i	0.980282	−	0.197606i	$-0.0633165\pi$
$374$	−514.313			−1.37517
$375$		−	52.8946i		−	0.141052i
$376$	347.826			0.925070
$377$	586.826			1.55657
$378$			153.385i			0.405781i
$379$		−	234.528i		−	0.618808i	−0.950931	−	0.309404i	$-0.899870\pi$
$379$		−	234.528i		−	0.618808i	0.950931	−	0.309404i	$-0.100130\pi$
$380$	−40.3756			−0.106252
$381$	893.020			2.34388
$382$		−	111.457i		−	0.291773i
$383$		−	234.044i		−	0.611081i	−0.952179	−	0.305541i	$-0.901163\pi$
$383$		−	234.044i		−	0.611081i	0.952179	−	0.305541i	$-0.0988372\pi$
$384$	−562.993			−1.46613
$385$		−	280.239i		−	0.727893i
$386$	−125.123			−0.324153
$387$			236.998i			0.612399i
$388$			522.990i			1.34791i
$389$			131.490i			0.338021i	0.985614	+	0.169010i	$0.0540571\pi$
$389$			131.490i			0.338021i	−0.985614	+	0.169010i	$0.945943\pi$
$390$		−	146.462i		−	0.375544i
$391$	697.033	−	40.9336i	1.78269	−	0.104689i
$392$	−40.0679			−0.102214
$393$	−470.592			−1.19743
$394$	296.716			0.753087
$395$	219.249			0.555060
$396$			680.172i			1.71761i
$397$	−126.113			−0.317665			−0.158833	−	0.987306i	$-0.550773\pi$
$397$	−126.113			−0.317665			−0.158833	+	0.987306i	$0.550773\pi$
$398$			195.027i			0.490017i
$399$	210.648			0.527940
$400$	−25.0000			−0.0625000
$401$		−	761.107i		−	1.89802i	−0.315244	−	0.949011i	$-0.602086\pi$
$401$		−	761.107i		−	1.89802i	0.315244	−	0.949011i	$-0.397914\pi$
$402$			166.825i			0.414988i
$403$	−237.410			−0.589106
$404$	41.2954			0.102216
$405$			49.9720i			0.123388i
$406$		−	313.555i		−	0.772302i
$407$	−477.949			−1.17432
$408$		−	1005.37i		−	2.46415i
$409$	−115.134			−0.281500			−0.140750	−	0.990045i	$-0.544951\pi$
$409$	−115.134			−0.281500			−0.140750	+	0.990045i	$0.544951\pi$
$410$			156.262i			0.381127i
$411$		−	381.694i		−	0.928697i
$412$		−	197.330i		−	0.478957i
$413$			300.390i			0.727336i
$414$	18.0447	+	307.272i	0.0435862	+	0.742203i
$415$	−224.213			−0.540271
$416$	−456.876			−1.09826
$417$	−595.494			−1.42804
$418$	−101.969			−0.243945
$419$			253.837i			0.605815i	0.953020	+	0.302908i	$0.0979574\pi$
$419$			253.837i			0.605815i	−0.953020	+	0.302908i	$0.902043\pi$
$420$	234.775			0.558987
$421$		−	378.206i		−	0.898353i	−0.893443	−	0.449176i	$-0.851718\pi$
$421$		−	378.206i		−	0.898353i	0.893443	−	0.449176i	$-0.148282\pi$
$422$	−195.386			−0.462999
$423$	664.978			1.57205
$424$			281.745i			0.664492i
$425$		−	151.790i		−	0.357153i
$426$	46.7548			0.109753
$427$	−21.0152			−0.0492160
$428$		−	349.364i		−	0.816271i
$429$			1109.67i			2.58665i
$430$	−39.5993			−0.0920914
$431$			801.659i			1.86000i	0.367561	+	0.929999i	$0.380193\pi$
$431$			801.659i			1.86000i	−0.367561	+	0.929999i	$0.619807\pi$
$432$	−103.673			−0.239983
$433$			651.032i			1.50354i	0.659427	+	0.751769i	$0.270799\pi$
$433$			651.032i			1.50354i	−0.659427	+	0.751769i	$0.729201\pi$
$434$			126.854i			0.292289i
$435$			448.400i			1.03080i
$436$			392.708i			0.900707i
$437$	138.195	−	8.11558i	0.316236	−	0.0185711i
$438$	143.758			0.328215
$439$	−247.011			−0.562668			−0.281334	−	0.959610i	$-0.590777\pi$
$439$	−247.011			−0.562668			−0.281334	+	0.959610i	$0.590777\pi$
$440$	−265.178			−0.602677
$441$	−76.6022			−0.173701
$442$		−	420.299i		−	0.950902i
$443$	−221.043			−0.498969			−0.249485	−	0.968379i	$-0.580261\pi$
$443$	−221.043			−0.498969			−0.249485	+	0.968379i	$0.580261\pi$
$444$		−	400.409i		−	0.901822i
$445$	−63.4335			−0.142547
$446$	65.3033			0.146420
$447$		−	324.791i		−	0.726602i
$448$			96.1684i			0.214662i
$449$	−768.822			−1.71230			−0.856149	−	0.516729i	$-0.827149\pi$
$449$	−768.822			−1.71230			−0.856149	+	0.516729i	$0.827149\pi$
$450$	66.9134			0.148696
$451$		−	1183.92i		−	2.62511i
$452$		−	31.5066i		−	0.0697048i
$453$	−396.783			−0.875900
$454$			248.917i			0.548274i
$455$	229.012			0.503323
$456$		−	199.327i		−	0.437121i
$457$			112.926i			0.247102i	0.992338	+	0.123551i	$0.0394283\pi$
$457$			112.926i			0.247102i	−0.992338	+	0.123551i	$0.960572\pi$
$458$		−	203.690i		−	0.444738i
$459$		−	629.460i		−	1.37137i
$460$	154.023	−	9.04509i	0.334833	−	0.0196632i
$461$	−388.330			−0.842365			−0.421183	−	0.906976i	$-0.638385\pi$
$461$	−388.330			−0.842365			−0.421183	+	0.906976i	$0.638385\pi$
$462$	592.924			1.28339
$463$	51.6362			0.111525			0.0557626	−	0.998444i	$-0.482241\pi$
$463$	51.6362			0.111525			0.0557626	+	0.998444i	$0.482241\pi$
$464$	211.931			0.456748
$465$		−	181.407i		−	0.390123i
$466$	−170.311			−0.365473
$467$		−	388.028i		−	0.830895i	−0.909617	−	0.415447i	$-0.863625\pi$
$467$		−	388.028i		−	0.830895i	0.909617	−	0.415447i	$-0.136375\pi$
$468$	−555.839			−1.18769
$469$	−260.852			−0.556189
$470$			111.109i			0.236402i
$471$		−	126.205i		−	0.267952i
$472$	284.246			0.602216
$473$	300.025			0.634302
$474$			463.883i			0.978655i
$475$		−	30.0942i		−	0.0633562i
$476$	673.726			1.41539
$477$			538.642i			1.12923i
$478$	−232.938			−0.487318
$479$			393.672i			0.821863i	0.911666	+	0.410931i	$0.134796\pi$
$479$			393.672i			0.821863i	−0.911666	+	0.410931i	$0.865204\pi$
$480$		−	349.104i		−	0.727300i
$481$		−	390.581i		−	0.812019i
$482$		−	373.790i		−	0.775499i
$483$	−803.572	+	47.1901i	−1.66371	+	0.0977022i
$484$	498.053			1.02904
$485$	−389.814			−0.803739
$486$	−292.341			−0.601525
$487$	−551.219			−1.13187			−0.565933	−	0.824451i	$-0.691484\pi$
$487$	−551.219			−1.13187			−0.565933	+	0.824451i	$0.691484\pi$
$488$			19.8858i			0.0407496i
$489$	272.196			0.556638
$490$		−	12.7992i		−	0.0261208i
$491$	−429.833			−0.875424			−0.437712	−	0.899115i	$-0.644211\pi$
$491$	−429.833			−0.875424			−0.437712	+	0.899115i	$0.644211\pi$
$492$	991.850			2.01596
$493$			1286.76i			2.61006i
$494$		−	83.3293i		−	0.168683i
$495$	−506.970			−1.02418
$496$	−85.7401			−0.172863
$497$			73.1070i			0.147097i
$498$		−	474.385i		−	0.952580i
$499$	695.248			1.39328			0.696641	−	0.717420i	$-0.254677\pi$
$499$	695.248			1.39328			0.696641	+	0.717420i	$0.254677\pi$
$500$		−	33.5410i		−	0.0670820i
$501$	−53.9028			−0.107590
$502$			84.1207i			0.167571i
$503$			79.9845i			0.159015i	0.996834	+	0.0795075i	$0.0253347\pi$
$503$			79.9845i			0.159015i	−0.996834	+	0.0795075i	$0.974665\pi$
$504$			692.994i			1.37499i
$505$			30.7798i			0.0609501i
$506$	388.987	−	22.8434i	0.768748	−	0.0451451i
$507$	−107.284			−0.211606
$508$	566.274			1.11471
$509$	5.84516			0.0114836			0.00574181	−	0.999984i	$-0.498172\pi$
$509$	5.84516			0.0114836			0.00574181	+	0.999984i	$0.498172\pi$
$510$	321.155			0.629715
$511$			224.784i			0.439890i
$512$	−305.000			−0.595703
$513$		−	124.798i		−	0.243271i
$514$	327.255			0.636684
$515$	147.081			0.285595
$516$			251.350i			0.487113i
$517$		−	841.819i		−	1.62828i
$518$	−208.697			−0.402889
$519$	−1087.54			−2.09546
$520$		−	216.704i		−	0.416739i
$521$		−	925.289i		−	1.77599i	−0.459856	−	0.887993i	$-0.652099\pi$
$521$		−	925.289i		−	1.77599i	0.459856	−	0.887993i	$-0.347901\pi$
$522$	−567.241			−1.08667
$523$			578.949i			1.10698i	0.832857	+	0.553488i	$0.186704\pi$
$523$			578.949i			1.10698i	−0.832857	+	0.553488i	$0.813296\pi$
$524$	−298.407			−0.569480
$525$			174.991i			0.333315i
$526$			434.052i			0.825194i
$527$		−	520.579i		−	0.987817i
$528$			400.756i			0.759008i
$529$	−525.364	+	61.9180i	−0.993126	+	0.117047i
$530$	−90.0000			−0.169811
$531$	543.424			1.02340
$532$	133.574			0.251080
$533$	967.506			1.81521
$534$		−	134.211i		−	0.251332i
$535$	260.401			0.486730
$536$			246.833i			0.460510i
$537$	−357.047			−0.664892
$538$	2.80140			0.00520706
$539$			96.9734i			0.179914i
$540$		−	139.092i		−	0.257577i
$541$	−161.610			−0.298725			−0.149363	−	0.988782i	$-0.547722\pi$
$541$	−161.610			−0.298725			−0.149363	+	0.988782i	$0.547722\pi$
$542$	−192.728			−0.355588
$543$		−	563.838i		−	1.03837i
$544$		−	1001.81i		−	1.84157i
$545$	−292.707			−0.537078
$546$			484.540i			0.887436i
$547$	−39.5119			−0.0722337			−0.0361169	−	0.999348i	$-0.511499\pi$
$547$	−39.5119			−0.0722337			−0.0361169	+	0.999348i	$0.511499\pi$
$548$		−	242.037i		−	0.441673i
$549$			38.0179i			0.0692493i
$550$		−	84.7080i		−	0.154015i
$551$			255.116i			0.463005i
$552$	44.6540	+	760.386i	0.0808950	+	1.37751i
$553$	−725.339			−1.31164
$554$	−320.620			−0.578736
$555$	298.447			0.537743
$556$	−377.609			−0.679154
$557$		−	587.320i		−	1.05444i	−0.849730	−	0.527218i	$-0.823235\pi$
$557$		−	587.320i		−	1.05444i	0.849730	−	0.527218i	$-0.176765\pi$
$558$	229.486			0.411266
$559$			245.181i			0.438607i
$560$	82.7073			0.147692
$561$	−2433.23			−4.33731
$562$			481.983i			0.857621i
$563$			180.142i			0.319968i	0.987120	+	0.159984i	$0.0511443\pi$
$563$			180.142i			0.319968i	−0.987120	+	0.159984i	$0.948856\pi$
$564$	705.248			1.25044
$565$	23.4836			0.0415639
$566$		−	88.7608i		−	0.156821i
$567$		−	165.322i		−	0.291573i
$568$	69.1780			0.121792
$569$			759.111i			1.33411i	0.745007	+	0.667057i	$0.232446\pi$
$569$			759.111i			1.33411i	−0.745007	+	0.667057i	$0.767554\pi$
$570$	63.6728			0.111707
$571$		−	243.396i		−	0.426262i	−0.977024	−	0.213131i	$-0.931634\pi$
$571$		−	243.396i		−	0.426262i	0.977024	−	0.213131i	$-0.0683661\pi$
$572$			703.656i			1.23017i
$573$		−	527.309i		−	0.920260i
$574$		−	516.961i		−	0.900629i
$575$	6.74181	+	114.802i	0.0117249	+	0.199656i
$576$	173.975			0.302039
$577$	−224.674			−0.389384			−0.194692	−	0.980864i	$-0.562371\pi$
$577$	−224.674			−0.389384			−0.194692	+	0.980864i	$0.562371\pi$
$578$	632.609			1.09448
$579$	−591.961			−1.02238
$580$			284.335i			0.490233i
$581$	741.760			1.27670
$582$		−	824.761i		−	1.41711i
$583$	681.886			1.16962
$584$	212.703			0.364218
$585$		−	414.298i		−	0.708201i
$586$			212.736i			0.363031i
$587$	355.464			0.605561			0.302780	−	0.953060i	$-0.402085\pi$
$587$	355.464			0.605561			0.302780	+	0.953060i	$0.402085\pi$
$588$	−81.2410			−0.138165
$589$		−	103.211i		−	0.175231i
$590$			90.7990i			0.153897i
$591$	1403.77			2.37525
$592$		−	141.058i		−	0.238273i
$593$	−614.157			−1.03568			−0.517839	−	0.855478i	$-0.673263\pi$
$593$	−614.157			−1.03568			−0.517839	+	0.855478i	$0.673263\pi$
$594$		−	351.277i		−	0.591375i
$595$			502.166i			0.843976i
$596$		−	205.954i		−	0.345560i
$597$			922.678i			1.54553i
$598$	18.6677	+	317.881i	0.0312169	+	0.531574i
$599$	557.741			0.931120			0.465560	−	0.885016i	$-0.345853\pi$
$599$	557.741			0.931120			0.465560	+	0.885016i	$0.345853\pi$
$600$	165.586			0.275977
$601$	−588.078			−0.978500			−0.489250	−	0.872144i	$-0.662729\pi$
$601$	−588.078			−0.978500			−0.489250	+	0.872144i	$0.662729\pi$
$602$	131.006			0.217618
$603$			471.899i			0.782585i
$604$	−251.604			−0.416563
$605$			371.227i			0.613599i
$606$	−65.1233			−0.107464
$607$	154.978			0.255318			0.127659	−	0.991818i	$-0.459254\pi$
$607$	154.978			0.255318			0.127659	+	0.991818i	$0.459254\pi$
$608$		−	198.622i		−	0.326681i
$609$		−	1483.44i		−	2.43586i
$610$	−6.35229			−0.0104136
$611$	687.938			1.12592
$612$		−	1218.81i		−	1.99153i
$613$		−	952.132i		−	1.55323i	−0.629974	−	0.776617i	$-0.716934\pi$
$613$		−	952.132i		−	1.55323i	0.629974	−	0.776617i	$-0.283066\pi$
$614$	411.377			0.669995
$615$			739.281i			1.20208i
$616$	877.286			1.42417
$617$		−	844.964i		−	1.36947i	−0.728792	−	0.684735i	$-0.759918\pi$
$617$		−	844.964i		−	1.36947i	0.728792	−	0.684735i	$-0.240082\pi$
$618$			311.192i			0.503546i
$619$			303.263i			0.489924i	0.969533	+	0.244962i	$0.0787755\pi$
$619$			303.263i			0.489924i	−0.969533	+	0.244962i	$0.921225\pi$
$620$		−	115.032i		−	0.185536i
$621$	27.9577	+	476.075i	0.0450204	+	0.766626i
$622$	146.924			0.236212
$623$	209.856			0.336848
$624$	−327.499			−0.524839
$625$	25.0000			0.0400000
$626$		−	336.949i		−	0.538258i
$627$	−482.418			−0.769406
$628$		−	80.0282i		−	0.127433i
$629$	856.446			1.36160
$630$	−221.369			−0.351379
$631$			1211.50i			1.91996i	0.280066	+	0.959981i	$0.409644\pi$
$631$			1211.50i			1.91996i	−0.280066	+	0.959981i	$0.590356\pi$
$632$			686.357i			1.08601i
$633$	−924.376			−1.46031
$634$	400.963			0.632434
$635$			422.075i			0.664686i
$636$			571.261i			0.898209i
$637$	−79.2470			−0.124407
$638$			718.090i			1.12553i
$639$	132.255			0.206972
$640$		−	266.092i		−	0.415769i
$641$			492.485i			0.768307i	0.923269	+	0.384154i	$0.125507\pi$
$641$			492.485i			0.768307i	−0.923269	+	0.384154i	$0.874493\pi$
$642$			550.951i			0.858179i
$643$			448.951i			0.698213i	0.937083	+	0.349106i	$0.113515\pi$
$643$			448.951i			0.698213i	−0.937083	+	0.349106i	$0.886485\pi$
$644$	−509.554	+	29.9238i	−0.791233	+	0.0464655i
$645$	−187.346			−0.290458
$646$	182.720			0.282848
$647$	1045.09			1.61528			0.807641	−	0.589675i	$-0.200744\pi$
$647$	1045.09			1.61528			0.807641	+	0.589675i	$0.200744\pi$
$648$	−156.437			−0.241415
$649$		−	687.940i		−	1.06000i
$650$	69.2237			0.106498
$651$			600.148i			0.921887i
$652$	172.603			0.264728
$653$	775.801			1.18806			0.594029	−	0.804444i	$-0.297537\pi$
$653$	775.801			1.18806			0.594029	+	0.804444i	$0.297537\pi$
$654$		−	619.305i		−	0.946949i
$655$		−	222.420i		−	0.339572i
$656$	349.413			0.532642
$657$	406.648			0.618947
$658$		−	367.581i		−	0.558634i
$659$			184.054i			0.279293i	0.990201	+	0.139647i	$0.0445967\pi$
$659$			184.054i			0.279293i	−0.990201	+	0.139647i	$0.955403\pi$
$660$	−537.671			−0.814653
$661$		−	507.423i		−	0.767660i	−0.923404	−	0.383830i	$-0.874605\pi$
$661$		−	507.423i		−	0.767660i	0.923404	−	0.383830i	$-0.125395\pi$
$662$	605.346			0.914419
$663$		−	1988.45i		−	2.99917i
$664$		−	701.896i		−	1.05707i
$665$			99.5604i			0.149715i
$666$			377.546i			0.566886i
$667$	−57.1519	−	973.206i	−0.0856851	−	1.45908i
$668$	−34.1803			−0.0511682
$669$	308.952			0.461812
$670$	−78.8481			−0.117684
$671$	48.1282			0.0717261
$672$			1154.94i			1.71866i
$673$	−767.114			−1.13984			−0.569921	−	0.821699i	$-0.693026\pi$
$673$	−767.114			−1.13984			−0.569921	+	0.821699i	$0.693026\pi$
$674$		−	381.287i		−	0.565708i
$675$	103.673			0.153589
$676$	−68.0302			−0.100636
$677$			62.9632i			0.0930032i	0.998918	+	0.0465016i	$0.0148073\pi$
$677$			62.9632i			0.0930032i	−0.998918	+	0.0465016i	$0.985193\pi$
$678$			49.6862i			0.0732835i
$679$	1289.62			1.89929
$680$	475.178			0.698791
$681$			1177.63i			1.72927i
$682$		−	290.515i		−	0.425975i
$683$	−644.810			−0.944084			−0.472042	−	0.881576i	$-0.656483\pi$
$683$	−644.810			−0.944084			−0.472042	+	0.881576i	$0.656483\pi$
$684$		−	241.645i		−	0.353281i
$685$	180.403			0.263363
$686$		−	320.137i		−	0.466672i
$687$		−	963.664i		−	1.40271i
$688$			88.5467i			0.128702i
$689$			557.240i			0.808766i
$690$	−242.896	+	14.2642i	−0.352024	+	0.0206728i
$691$	−65.6173			−0.0949599			−0.0474800	−	0.998872i	$-0.515119\pi$
$691$	−65.6173			−0.0949599			−0.0474800	+	0.998872i	$0.515119\pi$
$692$	−689.624			−0.996567
$693$	1677.20			2.42021
$694$	−549.405			−0.791650
$695$		−	281.453i		−	0.404969i
$696$	−1403.71			−2.01683
$697$			2121.50i			3.04375i
$698$	−355.772			−0.509702
$699$	−805.745			−1.15271
$700$			110.963i			0.158519i
$701$		−	510.716i		−	0.728553i	−0.931291	−	0.364276i	$-0.881316\pi$
$701$		−	510.716i		−	0.728553i	0.931291	−	0.364276i	$-0.118684\pi$
$702$	287.064			0.408924
$703$	169.801			0.241537
$704$		−	220.241i		−	0.312842i
$705$			525.660i			0.745618i
$706$	123.524			0.174963
$707$		−	101.829i		−	0.144029i
$708$	576.333			0.814029
$709$		−	776.700i		−	1.09549i	−0.836647	−	0.547743i	$-0.815487\pi$
$709$		−	776.700i		−	1.09549i	0.836647	−	0.547743i	$-0.184513\pi$
$710$			22.0981i			0.0311241i
$711$			1312.18i			1.84555i
$712$		−	198.578i		−	0.278902i
$713$	23.1217	+	393.726i	0.0324288	+	0.552210i
$714$	−1062.47			−1.48806
$715$	−524.474			−0.733530
$716$	−226.407			−0.316211
$717$	−1102.04			−1.53701
$718$			231.668i			0.322657i
$719$	871.038			1.21146			0.605729	−	0.795671i	$-0.292882\pi$
$719$	871.038			1.21146			0.605729	+	0.795671i	$0.292882\pi$
$720$		−	149.623i		−	0.207809i
$721$	−486.587			−0.674879
$722$	−324.774			−0.449825
$723$		−	1768.41i		−	2.44594i
$724$		−	357.536i		−	0.493834i
$725$	−211.931			−0.292319
$726$	−785.436			−1.08187
$727$			67.3522i			0.0926440i	0.998927	+	0.0463220i	$0.0147500\pi$
$727$			67.3522i			0.0926440i	−0.998927	+	0.0463220i	$0.985250\pi$
$728$			716.921i			0.984782i
$729$	−1181.94			−1.62132
$730$			67.9456i			0.0930762i
$731$	−537.620			−0.735459
$732$			40.3202i			0.0550822i
$733$		−	330.102i		−	0.450343i	−0.974319	−	0.225172i	$-0.927706\pi$
$733$		−	330.102i		−	0.450343i	0.974319	−	0.225172i	$-0.0722943\pi$
$734$		−	200.756i		−	0.273509i
$735$		−	60.5535i		−	0.0823857i
$736$	44.4959	+	757.695i	0.0604565	+	1.02948i
$737$	597.393			0.810575
$738$	−935.215			−1.26723
$739$	−256.434			−0.347001			−0.173501	−	0.984834i	$-0.555508\pi$
$739$	−256.434			−0.347001			−0.173501	+	0.984834i	$0.555508\pi$
$740$	189.249			0.255742
$741$		−	394.234i		−	0.532029i
$742$	297.746			0.401275
$743$		−	129.457i		−	0.174235i	−0.996198	−	0.0871175i	$-0.972234\pi$
$743$		−	129.457i		−	0.174235i	0.996198	−	0.0871175i	$-0.0277656\pi$
$744$	567.895			0.763299
$745$	153.509			0.206052
$746$			147.414i			0.197606i
$747$		−	1341.89i		−	1.79638i
$748$	−1542.94			−2.06275
$749$	−861.482			−1.15018
$750$			52.8946i			0.0705261i
$751$		−	25.6109i		−	0.0341023i	−0.999855	−	0.0170512i	$-0.994572\pi$
$751$		−	25.6109i		−	0.0341023i	0.999855	−	0.0170512i	$-0.00542782\pi$
$752$	248.447			0.330382
$753$			397.978i			0.528523i
$754$	−586.826			−0.778283
$755$		−	187.535i		−	0.248390i
$756$			460.156i			0.608672i
$757$			1057.96i			1.39757i	0.715332	+	0.698785i	$0.246275\pi$
$757$			1057.96i			1.39757i	−0.715332	+	0.698785i	$0.753725\pi$
$758$			234.528i			0.309404i
$759$	1840.31	−	108.073i	2.42465	−	0.142389i
$760$	94.2098			0.123960
$761$	1074.33			1.41174			0.705869	−	0.708343i	$-0.250557\pi$
$761$	1074.33			1.41174			0.705869	+	0.708343i	$0.250557\pi$
$762$	−893.020			−1.17194
$763$	968.361			1.26915
$764$		−	334.372i		−	0.437660i
$765$	908.450			1.18752
$766$			234.044i			0.305541i
$767$	562.187			0.732969
$768$	809.007			1.05339
$769$			354.829i			0.461416i	0.973023	+	0.230708i	$0.0741043\pi$
$769$			354.829i			0.461416i	−0.973023	+	0.230708i	$0.925896\pi$
$770$			280.239i			0.363947i
$771$	1548.26			2.00811
$772$	−375.369			−0.486229
$773$		−	421.630i		−	0.545446i	−0.962093	−	0.272723i	$-0.912076\pi$
$773$		−	421.630i		−	0.545446i	0.962093	−	0.272723i	$-0.0879243\pi$
$774$		−	236.998i		−	0.306199i
$775$	85.7401			0.110632
$776$		−	1220.31i		−	1.57256i
$777$	−987.351			−1.27072
$778$		−	131.490i		−	0.169010i
$779$			420.612i			0.539939i
$780$		−	439.387i		−	0.563316i
$781$		−	167.427i		−	0.214375i
$782$	−697.033	+	40.9336i	−0.891347	+	0.0523447i
$783$	−878.859			−1.12243
$784$	−28.6199			−0.0365050
$785$	59.6495			0.0759866
$786$	470.592			0.598717
$787$		−	818.127i		−	1.03955i	−0.854303	−	0.519776i	$-0.826016\pi$
$787$		−	818.127i		−	1.03955i	0.854303	−	0.519776i	$-0.173984\pi$
$788$	890.148			1.12963
$789$			2053.52i			2.60268i
$790$	−219.249			−0.277530
$791$	−77.6907			−0.0982183
$792$		−	1587.07i		−	2.00387i
$793$			39.3305i			0.0495971i
$794$	126.113			0.158833
$795$	−425.793			−0.535589
$796$			585.081i			0.735026i
$797$		−	948.359i		−	1.18991i	−0.803759	−	0.594955i	$-0.797170\pi$
$797$		−	948.359i		−	1.18991i	0.803759	−	0.594955i	$-0.202830\pi$
$798$	−210.648			−0.263970
$799$			1508.47i			1.88795i
$800$	165.000			0.206250
$801$		−	379.644i		−	0.473962i
$802$			761.107i			0.949011i
$803$		−	514.791i		−	0.641084i
$804$			500.476i			0.622483i
$805$	−22.3039	−	379.799i	−0.0277067	−	0.471800i
$806$	237.410			0.294553
$807$	13.2535			0.0164232
$808$	−96.3560			−0.119252
$809$	−672.293			−0.831017			−0.415509	−	0.909589i	$-0.636396\pi$
$809$	−672.293			−0.831017			−0.415509	+	0.909589i	$0.636396\pi$
$810$		−	49.9720i		−	0.0616938i
$811$	−378.524			−0.466738			−0.233369	−	0.972388i	$-0.574975\pi$
$811$	−378.524			−0.466738			−0.233369	+	0.972388i	$0.574975\pi$
$812$		−	940.664i		−	1.15845i
$813$	−911.805			−1.12153
$814$	477.949			0.587160
$815$			128.650i			0.157853i
$816$		−	718.124i		−	0.880054i
$817$	−106.590			−0.130465
$818$	115.134			0.140750
$819$			1370.62i			1.67353i
$820$			468.787i			0.571691i
$821$	−797.381			−0.971231			−0.485616	−	0.874172i	$-0.661405\pi$
$821$	−797.381			−0.971231			−0.485616	+	0.874172i	$0.661405\pi$
$822$			381.694i			0.464348i
$823$	557.455			0.677345			0.338672	−	0.940904i	$-0.390022\pi$
$823$	557.455			0.677345			0.338672	+	0.940904i	$0.390022\pi$
$824$			460.437i			0.558783i
$825$		−	400.756i		−	0.485765i
$826$		−	300.390i		−	0.363668i
$827$		−	534.678i		−	0.646527i	−0.946309	−	0.323264i	$-0.895220\pi$
$827$		−	534.678i		−	0.646527i	0.946309	−	0.323264i	$-0.104780\pi$
$828$	54.1341	+	921.816i	0.0653793	+	1.11330i
$829$	−1218.60			−1.46997			−0.734984	−	0.678085i	$-0.762810\pi$
$829$	−1218.60			−1.46997			−0.734984	+	0.678085i	$0.762810\pi$
$830$	224.213			0.270136
$831$	−1516.86			−1.82535
$832$	179.982			0.216324
$833$		−	173.769i		−	0.208606i
$834$	595.494			0.714022
$835$		−	25.4765i		−	0.0305108i
$836$	−305.906			−0.365917
$837$	355.556			0.424799
$838$		−	253.837i		−	0.302908i
$839$			1512.85i			1.80315i	0.432619	+	0.901577i	$0.357589\pi$
$839$			1512.85i			1.80315i	−0.432619	+	0.901577i	$0.642411\pi$
$840$	−547.807			−0.652152
$841$	955.590			1.13625
$842$			378.206i			0.449176i
$843$			2280.28i			2.70495i
$844$	−586.157			−0.694499
$845$		−	50.7067i		−	0.0600079i
$846$	−664.978			−0.786026
$847$		−	1228.13i		−	1.44997i
$848$			201.246i			0.237319i
$849$		−	419.930i		−	0.494617i
$850$			151.790i			0.178577i
$851$	−647.749	+	38.0394i	−0.761163	+	0.0446996i
$852$	140.264			0.164629
$853$	741.519			0.869307			0.434653	−	0.900598i	$-0.356871\pi$
$853$	741.519			0.869307			0.434653	+	0.900598i	$0.356871\pi$
$854$	21.0152			0.0246080
$855$	180.111			0.210656
$856$			815.183i			0.952317i
$857$	−277.933			−0.324310			−0.162155	−	0.986765i	$-0.551844\pi$
$857$	−277.933			−0.324310			−0.162155	+	0.986765i	$0.551844\pi$
$858$		−	1109.67i		−	1.29333i
$859$	−1512.21			−1.76043			−0.880215	−	0.474574i	$-0.842602\pi$
$859$	−1512.21			−1.76043			−0.880215	+	0.474574i	$0.842602\pi$
$860$	−118.798			−0.138137
$861$		−	2445.76i		−	2.84060i
$862$		−	801.659i		−	0.929999i
$863$	−1008.72			−1.16885			−0.584424	−	0.811448i	$-0.698679\pi$
$863$	−1008.72			−1.16885			−0.584424	+	0.811448i	$0.698679\pi$
$864$	684.240			0.791945
$865$		−	514.015i		−	0.594238i
$866$		−	651.032i		−	0.751769i
$867$	2992.89			3.45201
$868$			380.561i			0.438434i
$869$	1661.14			1.91156
$870$		−	448.400i		−	0.515402i
$871$			488.192i			0.560496i
$872$		−	916.319i		−	1.05082i
$873$		−	2333.00i		−	2.67239i
$874$	−138.195	+	8.11558i	−0.158118	+	0.00928556i
$875$	−82.7073			−0.0945226
$876$	431.274			0.492322
$877$	−1314.49			−1.49885			−0.749423	−	0.662092i	$-0.769669\pi$
$877$	−1314.49			−1.49885			−0.749423	+	0.662092i	$0.769669\pi$
$878$	247.011			0.281334
$879$			1006.46i			1.14501i
$880$	−189.413			−0.215242
$881$			1048.30i			1.18990i	0.803762	+	0.594951i	$0.202829\pi$
$881$			1048.30i			1.18990i	−0.803762	+	0.594951i	$0.797171\pi$
$882$	76.6022			0.0868505
$883$	641.613			0.726629			0.363314	−	0.931667i	$-0.381645\pi$
$883$	641.613			0.726629			0.363314	+	0.931667i	$0.381645\pi$
$884$		−	1260.90i		−	1.42635i
$885$			429.573i			0.485393i
$886$	221.043			0.249485
$887$	418.361			0.471658			0.235829	−	0.971795i	$-0.424219\pi$
$887$	418.361			0.471658			0.235829	+	0.971795i	$0.424219\pi$
$888$			934.288i			1.05213i
$889$		−	1396.35i		−	1.57070i
$890$	63.4335			0.0712735
$891$			378.614i			0.424931i
$892$	195.910			0.219630
$893$			299.073i			0.334908i
$894$			324.791i			0.363301i
$895$		−	168.754i		−	0.188552i
$896$			880.310i			0.982489i
$897$	88.3176	+	1503.91i	0.0984588	+	1.67660i
$898$	768.822			0.856149
$899$	−726.839			−0.808497
$900$	200.740			0.223045
$901$	−1221.89			−1.35614
$902$			1183.92i			1.31255i
$903$	619.794			0.686372
$904$			73.5154i			0.0813223i
$905$	266.491			0.294466
$906$	396.783			0.437950
$907$			41.1303i			0.0453477i	0.999743	+	0.0226738i	$0.00721793\pi$
$907$			41.1303i			0.0453477i	−0.999743	+	0.0226738i	$0.992782\pi$
$908$			746.750i			0.822412i
$909$	−184.214			−0.202656
$910$	−229.012			−0.251662
$911$			142.023i			0.155898i	0.996957	+	0.0779492i	$0.0248372\pi$
$911$			142.023i			0.155898i	−0.996957	+	0.0779492i	$0.975163\pi$
$912$		−	142.377i		−	0.156115i
$913$	−1698.75			−1.86062
$914$		−	112.926i		−	0.123551i
$915$	−30.0529			−0.0328447
$916$		−	611.070i		−	0.667107i
$917$			735.829i			0.802431i
$918$			629.460i			0.685686i
$919$		−	1288.94i		−	1.40255i	−0.712891	−	0.701275i	$-0.752615\pi$
$919$		−	1288.94i		−	1.40255i	0.712891	−	0.701275i	$-0.247385\pi$
$920$	−359.388	+	21.1052i	−0.390639	+	0.0229404i
$921$	1946.24			2.11318
$922$	388.330			0.421183
$923$	136.822			0.148236
$924$	1778.77			1.92508
$925$			141.058i			0.152495i
$926$	−51.6362			−0.0557626
$927$			880.268i			0.949588i
$928$	−1398.74			−1.50727
$929$	981.566			1.05658			0.528291	−	0.849063i	$-0.322833\pi$
$929$	981.566			1.05658			0.528291	+	0.849063i	$0.322833\pi$
$930$			181.407i			0.195062i
$931$		−	34.4517i		−	0.0370051i
$932$	−510.932			−0.548210
$933$	695.101			0.745017
$934$			388.028i			0.415447i
$935$		−	1150.04i		−	1.22999i
$936$	1296.96			1.38564
$937$		−	1180.83i		−	1.26023i	−0.776504	−	0.630113i	$-0.783009\pi$
$937$		−	1180.83i		−	1.26023i	0.776504	−	0.630113i	$-0.216991\pi$
$938$	260.852			0.278094
$939$		−	1594.12i		−	1.69768i
$940$			333.327i			0.354603i
$941$			104.030i			0.110553i	0.998471	+	0.0552764i	$0.0176040\pi$
$941$			104.030i			0.110553i	−0.998471	+	0.0552764i	$0.982396\pi$
$942$			126.205i			0.133976i
$943$	−94.2270	−	1604.53i	−0.0999226	−	1.70152i
$944$	203.033			0.215077
$945$	−342.980			−0.362942
$946$	−300.025			−0.317151
$947$	−806.025			−0.851135			−0.425568	−	0.904927i	$-0.639926\pi$
$947$	−806.025			−0.851135			−0.425568	+	0.904927i	$0.639926\pi$
$948$			1391.65i			1.46798i
$949$	420.689			0.443297
$950$			30.0942i			0.0316781i
$951$	1896.97			1.99471
$952$	−1572.03			−1.65129
$953$			133.702i			0.140296i	0.997537	+	0.0701480i	$0.0223471\pi$
$953$			133.702i			0.140296i	−0.997537	+	0.0701480i	$0.977653\pi$
$954$		−	538.642i		−	0.564614i
$955$	249.226			0.260970
$956$	−698.815			−0.730978
$957$			3397.31i			3.54996i
$958$		−	393.672i		−	0.410931i
$959$	−596.827			−0.622343
$960$			137.526i			0.143256i
$961$	−666.946			−0.694012
$962$			390.581i			0.406010i
$963$			1558.48i			1.61835i
$964$		−	1121.37i		−	1.16325i
$965$		−	279.783i		−	0.289931i
$966$	803.572	−	47.1901i	0.831856	−	0.0488511i
$967$	1392.07			1.43958			0.719790	−	0.694192i	$-0.244238\pi$
$967$	1392.07			1.43958			0.719790	+	0.694192i	$0.244238\pi$
$968$	−1162.12			−1.20054
$969$	864.455			0.892110
$970$	389.814			0.401870
$971$			44.5482i			0.0458787i	0.999737	+	0.0229394i	$0.00730247\pi$
$971$			44.5482i			0.0458787i	−0.999737	+	0.0229394i	$0.992698\pi$
$972$	−877.023			−0.902287
$973$			931.130i			0.956968i
$974$	551.219			0.565933
$975$	327.499			0.335897
$976$			14.2041i			0.0145534i
$977$			796.273i			0.815018i	0.913201	+	0.407509i	$0.133603\pi$
$977$			796.273i			0.815018i	−0.913201	+	0.407509i	$0.866397\pi$
$978$	−272.196			−0.278319
$979$	−480.604			−0.490914
$980$		−	38.3976i		−	0.0391813i
$981$		−	1751.83i		−	1.78576i
$982$	429.833			0.437712
$983$		−	207.733i		−	0.211325i	−0.994402	−	0.105663i	$-0.966304\pi$
$983$		−	207.733i		−	0.211325i	0.994402	−	0.105663i	$-0.0336964\pi$
$984$	−2314.32			−2.35195
$985$			663.477i			0.673581i
$986$		−	1286.76i		−	1.30503i
$987$		−	1739.04i		−	1.76194i
$988$		−	249.988i		−	0.253024i
$989$	406.614	−	23.8786i	0.411137	−	0.0241442i
$990$	506.970			0.512091
$991$	28.3036			0.0285606			0.0142803	−	0.999898i	$-0.495454\pi$
$991$	28.3036			0.0285606			0.0142803	+	0.999898i	$0.495454\pi$
$992$	565.884			0.570448
$993$	2863.91			2.88410
$994$		−	73.1070i		−	0.0735483i
$995$	−436.093			−0.438285
$996$		−	1423.15i		−	1.42887i
$997$	1747.49			1.75275			0.876376	−	0.481628i	$-0.159954\pi$
$997$	1747.49			1.75275			0.876376	+	0.481628i	$0.159954\pi$
$998$	−695.248			−0.696641
$999$			584.954i			0.585539i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	115.3.d.a.91.1	✓	6
3.2	odd	2		1035.3.g.a.91.5		6
4.3	odd	2		1840.3.k.a.321.5		6
5.2	odd	4		575.3.c.c.574.5		12
5.3	odd	4		575.3.c.c.574.8		12
5.4	even	2		575.3.d.e.551.5		6
23.22	odd	2	inner	115.3.d.a.91.2	yes	6
69.68	even	2		1035.3.g.a.91.2		6
92.91	even	2		1840.3.k.a.321.6		6
115.22	even	4		575.3.c.c.574.6		12
115.68	even	4		575.3.c.c.574.7		12
115.114	odd	2		575.3.d.e.551.6		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.3.d.a.91.1	✓	6	1.1	even	1	trivial
115.3.d.a.91.2	yes	6	23.22	odd	2	inner
575.3.c.c.574.5		12	5.2	odd	4
575.3.c.c.574.6		12	115.22	even	4
575.3.c.c.574.7		12	115.68	even	4
575.3.c.c.574.8		12	5.3	odd	4
575.3.d.e.551.5		6	5.4	even	2
575.3.d.e.551.6		6	115.114	odd	2
1035.3.g.a.91.2		6	69.68	even	2
1035.3.g.a.91.5		6	3.2	odd	2
1840.3.k.a.321.5		6	4.3	odd	2
1840.3.k.a.321.6		6	92.91	even	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -4.73103 q^{3} -3.00000 q^{4} -2.23607i q^{5} +4.73103 q^{6} +7.39757i q^{7} +7.00000 q^{8} +13.3827 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -4.73103 q^{3} -3.00000 q^{4} -2.23607i q^{5} +4.73103 q^{6} +7.39757i q^{7} +7.00000 q^{8} +13.3827 q^{9} +2.23607i q^{10} -16.9416i q^{11} +14.1931 q^{12} +13.8447 q^{13} -7.39757i q^{14} +10.5789i q^{15} +5.00000 q^{16} +30.3580i q^{17} -13.3827 q^{18} +6.01884i q^{19} +6.70820i q^{20} -34.9981i q^{21} +16.9416i q^{22} +(-1.34836 - 22.9604i) q^{23} -33.1172 q^{24} -5.00000 q^{25} -13.8447 q^{26} -20.7346 q^{27} -22.1927i q^{28} +42.3862 q^{29} -10.5789i q^{30} -17.1480 q^{31} -33.0000 q^{32} +80.1513i q^{33} -30.3580i q^{34} +16.5415 q^{35} -40.1480 q^{36} -28.2115i q^{37} -6.01884i q^{38} -65.4999 q^{39} -15.6525i q^{40} +69.8826 q^{41} +34.9981i q^{42} +17.7093i q^{43} +50.8248i q^{44} -29.9246i q^{45} +(1.34836 + 22.9604i) q^{46} +49.6895 q^{47} -23.6552 q^{48} -5.72398 q^{49} +5.00000 q^{50} -143.625i q^{51} -41.5342 q^{52} +40.2492i q^{53} +20.7346 q^{54} -37.8826 q^{55} +51.7830i q^{56} -28.4753i q^{57} -42.3862 q^{58} +40.6066 q^{59} -31.7367i q^{60} +2.84083i q^{61} +17.1480 q^{62} +98.9992i q^{63} +13.0000 q^{64} -30.9578i q^{65} -80.1513i q^{66} +35.2619i q^{67} -91.0740i q^{68} +(6.37914 + 108.627i) q^{69} -16.5415 q^{70} +9.88257 q^{71} +93.6787 q^{72} +30.3862 q^{73} +28.2115i q^{74} +23.6552 q^{75} -18.0565i q^{76} +125.327 q^{77} +65.4999 q^{78} +98.0510i q^{79} -11.1803i q^{80} -22.3482 q^{81} -69.8826 q^{82} -100.271i q^{83} +104.994i q^{84} +67.8826 q^{85} -17.7093i q^{86} -200.530 q^{87} -118.591i q^{88} -28.3683i q^{89} +29.9246i q^{90} +102.417i q^{91} +(4.04509 + 68.8813i) q^{92} +81.1278 q^{93} -49.6895 q^{94} +13.4585 q^{95} +156.124 q^{96} -174.330i q^{97} +5.72398 q^{98} -226.724i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{2} + 2 q^{3} - 18 q^{4} - 2 q^{6} + 42 q^{8} + 48 q^{9}+O(q^{10}) \) 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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