LMFDB - Embedded newform 40.3.e.c.19.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [40,3,Mod(19,40)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(40, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 1]))

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

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

chi := DirichletCharacter("40.19");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 40 = 2^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	40.e (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:	$1.08992105744$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.53824000000.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 6x^{6} + 36x^{4} + 96x^{2} + 256 $ x^8 + 6x^6 + 36x^4 + 96*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{5} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			19.2
Root			$1.34500 + 1.48020i$ of defining polynomial
Character	$\chi$	$=$	40.19
Dual form			40.3.e.c.19.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.34500 + 1.48020i) q^{2} -4.79002i q^{3} +(-0.381966 - 3.98172i) q^{4} +(-4.35250 - 2.46084i) q^{5} +(7.09017 + 6.44256i) q^{6} +7.67752 q^{7} +(6.40747 + 4.79002i) q^{8} -13.9443 q^{9} +O(q^{10})$	\(q+(-1.34500 + 1.48020i) q^{2} -4.79002i q^{3} +(-0.381966 - 3.98172i) q^{4} +(-4.35250 - 2.46084i) q^{5} +(7.09017 + 6.44256i) q^{6} +7.67752 q^{7} +(6.40747 + 4.79002i) q^{8} -13.9443 q^{9} +(9.49663 - 3.13274i) q^{10} -0.472136 q^{11} +(-19.0725 + 1.82962i) q^{12} +4.10995 q^{13} +(-10.3262 + 11.3642i) q^{14} +(-11.7875 + 20.8486i) q^{15} +(-15.7082 + 3.04176i) q^{16} -2.26154i q^{17} +(18.7550 - 20.6403i) q^{18} +26.3607 q^{19} +(-8.13587 + 18.2704i) q^{20} -36.7754i q^{21} +(0.635021 - 0.698854i) q^{22} +9.73249 q^{23} +(22.9443 - 30.6919i) q^{24} +(12.8885 + 21.4216i) q^{25} +(-5.52786 + 6.08353i) q^{26} +23.6832i q^{27} +(-2.93255 - 30.5697i) q^{28} +41.6971i q^{29} +(-15.0059 - 45.4890i) q^{30} -22.0104i q^{31} +(16.6251 - 27.3424i) q^{32} +2.26154i q^{33} +(3.34752 + 3.04176i) q^{34} +(-33.4164 - 18.8931i) q^{35} +(5.32624 + 55.5222i) q^{36} -51.7449 q^{37} +(-35.4550 + 39.0190i) q^{38} -19.6867i q^{39} +(-16.1011 - 36.6163i) q^{40} +15.0557 q^{41} +(54.4349 + 49.4629i) q^{42} -9.31310i q^{43} +(0.180340 + 1.87991i) q^{44} +(60.6925 + 34.3146i) q^{45} +(-13.0902 + 14.4060i) q^{46} +8.76226 q^{47} +(14.5701 + 75.2426i) q^{48} +9.94427 q^{49} +(-49.0433 - 9.73442i) q^{50} -10.8328 q^{51} +(-1.56986 - 16.3647i) q^{52} +39.9002 q^{53} +(-35.0557 - 31.8538i) q^{54} +(2.05497 + 1.16185i) q^{55} +(49.1935 + 36.7754i) q^{56} -126.268i q^{57} +(-61.7200 - 56.0825i) q^{58} -77.1935 q^{59} +(87.5156 + 38.9709i) q^{60} +14.7650i q^{61} +(32.5797 + 29.6039i) q^{62} -107.057 q^{63} +(18.1115 + 61.3838i) q^{64} +(-17.8885 - 10.1139i) q^{65} +(-3.34752 - 3.04176i) q^{66} +75.8395i q^{67} +(-9.00482 + 0.863831i) q^{68} -46.6188i q^{69} +(72.9105 - 24.0517i) q^{70} -81.0705i q^{71} +(-89.3476 - 66.7933i) q^{72} +83.4249i q^{73} +(69.5967 - 76.5927i) q^{74} +(102.610 - 61.7364i) q^{75} +(-10.0689 - 104.961i) q^{76} -3.62483 q^{77} +(29.1402 + 26.4786i) q^{78} +100.757i q^{79} +(75.8553 + 25.4161i) q^{80} -12.0557 q^{81} +(-20.2499 + 22.2854i) q^{82} +0.266939i q^{83} +(-146.430 + 14.0470i) q^{84} +(-5.56528 + 9.84336i) q^{85} +(13.7852 + 12.5261i) q^{86} +199.730 q^{87} +(-3.02520 - 2.26154i) q^{88} +85.5542 q^{89} +(-132.424 + 43.6838i) q^{90} +31.5542 q^{91} +(-3.71748 - 38.7521i) q^{92} -105.430 q^{93} +(-11.7852 + 12.9699i) q^{94} +(-114.735 - 64.8694i) q^{95} +(-130.971 - 79.6344i) q^{96} +99.1297i q^{97} +(-13.3750 + 14.7195i) q^{98} +6.58359 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 12 q^{4} + 12 q^{6} - 40 q^{9}+O(q^{10}) $ 8 * q - 12 * q^4 + 12 * q^6 - 40 * q^9	$ 8 q - 12 q^{4} + 12 q^{6} - 40 q^{9} + 20 q^{10} + 32 q^{11} - 20 q^{14} - 72 q^{16} + 32 q^{19} + 20 q^{20} + 112 q^{24} - 40 q^{25} - 80 q^{26} + 100 q^{30} + 152 q^{34} - 160 q^{35} - 20 q^{36} - 80 q^{40} + 192 q^{41} - 88 q^{44} - 60 q^{46} + 8 q^{49} - 200 q^{50} + 128 q^{51} - 352 q^{54} - 224 q^{59} + 360 q^{60} + 288 q^{64} - 152 q^{66} + 340 q^{70} + 360 q^{74} + 320 q^{75} + 152 q^{76} - 280 q^{80} - 168 q^{81} - 760 q^{84} + 316 q^{86} + 112 q^{89} - 340 q^{90} - 320 q^{91} - 300 q^{94} - 368 q^{96} + 160 q^{99}+O(q^{100}) $ 8 * q - 12 * q^4 + 12 * q^6 - 40 * q^9 + 20 * q^10 + 32 * q^11 - 20 * q^14 - 72 * q^16 + 32 * q^19 + 20 * q^20 + 112 * q^24 - 40 * q^25 - 80 * q^26 + 100 * q^30 + 152 * q^34 - 160 * q^35 - 20 * q^36 - 80 * q^40 + 192 * q^41 - 88 * q^44 - 60 * q^46 + 8 * q^49 - 200 * q^50 + 128 * q^51 - 352 * q^54 - 224 * q^59 + 360 * q^60 + 288 * q^64 - 152 * q^66 + 340 * q^70 + 360 * q^74 + 320 * q^75 + 152 * q^76 - 280 * q^80 - 168 * q^81 - 760 * q^84 + 316 * q^86 + 112 * q^89 - 340 * q^90 - 320 * q^91 - 300 * q^94 - 368 * q^96 + 160 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/40\mathbb{Z}\right)^\times$.

$n$	$17$	$21$	$31$
$\chi(n)$	$-1$	$-1$	$-1$

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 $

$2$	−1.34500	+	1.48020i	−0.672499	+	0.740098i
$2$	−1.34500	+	1.48020i	−0.672499	+	0.740098i
$3$		−	4.79002i		−	1.59667i	−0.602212	−	0.798336i	$-0.705714\pi$
$3$		−	4.79002i		−	1.59667i	0.602212	−	0.798336i	$-0.294286\pi$
$4$	−0.381966	−	3.98172i	−0.0954915	−	0.995430i
$5$	−4.35250	−	2.46084i	−0.870500	−	0.492168i
$5$	−4.35250	−	2.46084i	−0.870500	−	0.492168i
$6$	7.09017	+	6.44256i	1.18169	+	1.07376i
$7$	7.67752			1.09679			0.548394	−	0.836220i	$-0.315239\pi$
$7$	7.67752			1.09679			0.548394	+	0.836220i	$0.315239\pi$
$8$	6.40747	+	4.79002i	0.800934	+	0.598752i
$9$	−13.9443			−1.54936
$10$	9.49663	−	3.13274i	0.949663	−	0.313274i
$11$	−0.472136			−0.0429215			−0.0214607	−	0.999770i	$-0.506832\pi$
$11$	−0.472136			−0.0429215			−0.0214607	+	0.999770i	$0.506832\pi$
$12$	−19.0725	+	1.82962i	−1.58938	+	0.152469i
$13$	4.10995			0.316150			0.158075	−	0.987427i	$-0.449471\pi$
$13$	4.10995			0.316150			0.158075	+	0.987427i	$0.449471\pi$
$14$	−10.3262	+	11.3642i	−0.737588	+	0.811731i
$15$	−11.7875	+	20.8486i	−0.785831	+	1.38990i
$16$	−15.7082	+	3.04176i	−0.981763	+	0.190110i
$17$		−	2.26154i		−	0.133032i	−0.997785	−	0.0665159i	$-0.978812\pi$
$17$		−	2.26154i		−	0.133032i	0.997785	−	0.0665159i	$-0.0211883\pi$
$18$	18.7550	−	20.6403i	1.04194	−	1.14668i
$19$	26.3607			1.38740			0.693702	−	0.720262i	$-0.255978\pi$
$19$	26.3607			1.38740			0.693702	+	0.720262i	$0.255978\pi$
$20$	−8.13587	+	18.2704i	−0.406793	+	0.913520i
$21$		−	36.7754i		−	1.75121i
$22$	0.635021	−	0.698854i	0.0288646	−	0.0317661i
$23$	9.73249			0.423152			0.211576	−	0.977362i	$-0.432140\pi$
$23$	9.73249			0.423152			0.211576	+	0.977362i	$0.432140\pi$
$24$	22.9443	−	30.6919i	0.956011	−	1.27883i
$25$	12.8885	+	21.4216i	0.515542	+	0.856864i
$26$	−5.52786	+	6.08353i	−0.212610	+	0.233982i
$27$			23.6832i			0.877154i
$28$	−2.93255	−	30.5697i	−0.104734	−	1.09178i
$29$			41.6971i			1.43783i	0.695097	+	0.718916i	$0.255361\pi$
$29$			41.6971i			1.43783i	−0.695097	+	0.718916i	$0.744639\pi$
$30$	−15.0059	−	45.4890i	−0.500196	−	1.51630i
$31$		−	22.0104i		−	0.710013i	−0.934864	−	0.355007i	$-0.884479\pi$
$31$		−	22.0104i		−	0.710013i	0.934864	−	0.355007i	$-0.115521\pi$
$32$	16.6251	−	27.3424i	0.519534	−	0.854450i
$33$			2.26154i			0.0685315i
$34$	3.34752	+	3.04176i	0.0984566	+	0.0894637i
$35$	−33.4164	−	18.8931i	−0.954755	−	0.539804i
$36$	5.32624	+	55.5222i	0.147951	+	1.54228i
$37$	−51.7449			−1.39851			−0.699256	−	0.714872i	$-0.746485\pi$
$37$	−51.7449			−1.39851			−0.699256	+	0.714872i	$0.746485\pi$
$38$	−35.4550	+	39.0190i	−0.933027	+	1.02682i
$39$		−	19.6867i		−	0.504787i
$40$	−16.1011	−	36.6163i	−0.402527	−	0.915408i
$41$	15.0557			0.367213			0.183606	−	0.983000i	$-0.441223\pi$
$41$	15.0557			0.367213			0.183606	+	0.983000i	$0.441223\pi$
$42$	54.4349	+	49.4629i	1.29607	+	1.17769i
$43$		−	9.31310i		−	0.216584i	−0.994119	−	0.108292i	$-0.965462\pi$
$43$		−	9.31310i		−	0.216584i	0.994119	−	0.108292i	$-0.0345381\pi$
$44$	0.180340	+	1.87991i	0.00409863	+	0.0427253i
$45$	60.6925	+	34.3146i	1.34872	+	0.762547i
$46$	−13.0902	+	14.4060i	−0.284569	+	0.313174i
$47$	8.76226			0.186431			0.0932156	−	0.995646i	$-0.470285\pi$
$47$	8.76226			0.186431			0.0932156	+	0.995646i	$0.470285\pi$
$48$	14.5701	+	75.2426i	0.303544	+	1.56755i
$49$	9.94427			0.202944
$50$	−49.0433	−	9.73442i	−0.980865	−	0.194688i
$51$	−10.8328			−0.212408
$52$	−1.56986	−	16.3647i	−0.0301896	−	0.314705i
$53$	39.9002			0.752834			0.376417	−	0.926450i	$-0.377156\pi$
$53$	39.9002			0.752834			0.376417	+	0.926450i	$0.377156\pi$
$54$	−35.0557	−	31.8538i	−0.649180	−	0.589885i
$55$	2.05497	+	1.16185i	0.0373631	+	0.0211246i
$56$	49.1935	+	36.7754i	0.878455	+	0.656704i
$57$		−	126.268i		−	2.21523i
$58$	−61.7200	−	56.0825i	−1.06414	−	0.966940i
$59$	−77.1935			−1.30836			−0.654182	−	0.756337i	$-0.726987\pi$
$59$	−77.1935			−1.30836			−0.654182	+	0.756337i	$0.726987\pi$
$60$	87.5156	+	38.9709i	1.45859	+	0.649516i
$61$			14.7650i			0.242050i	0.992649	+	0.121025i	$0.0386181\pi$
$61$			14.7650i			0.242050i	−0.992649	+	0.121025i	$0.961382\pi$
$62$	32.5797	+	29.6039i	0.525480	+	0.477483i
$63$	−107.057			−1.69932
$64$	18.1115	+	61.3838i	0.282992	+	0.959122i
$65$	−17.8885	−	10.1139i	−0.275208	−	0.155599i
$66$	−3.34752	−	3.04176i	−0.0507201	−	0.0460873i
$67$			75.8395i			1.13193i	0.824428	+	0.565966i	$0.191497\pi$
$67$			75.8395i			1.13193i	−0.824428	+	0.565966i	$0.808503\pi$
$68$	−9.00482	+	0.863831i	−0.132424	+	0.0127034i
$69$		−	46.6188i		−	0.675635i
$70$	72.9105	−	24.0517i	1.04158	−	0.343595i
$71$		−	81.0705i		−	1.14184i	−0.821006	−	0.570919i	$-0.806587\pi$
$71$		−	81.0705i		−	1.14184i	0.821006	−	0.570919i	$-0.193413\pi$
$72$	−89.3476	−	66.7933i	−1.24094	−	0.927685i
$73$			83.4249i			1.14281i	0.820669	+	0.571403i	$0.193601\pi$
$73$			83.4249i			1.14281i	−0.820669	+	0.571403i	$0.806399\pi$
$74$	69.5967	−	76.5927i	0.940497	−	1.03504i
$75$	102.610	−	61.7364i	1.36813	−	0.823151i
$76$	−10.0689	−	104.961i	−0.132485	−	1.38106i
$77$	−3.62483			−0.0470757
$78$	29.1402	+	26.4786i	0.373592	+	0.339469i
$79$			100.757i			1.27541i	0.770281	+	0.637704i	$0.220116\pi$
$79$			100.757i			1.27541i	−0.770281	+	0.637704i	$0.779884\pi$
$80$	75.8553	+	25.4161i	0.948191	+	0.317701i
$81$	−12.0557			−0.148836
$82$	−20.2499	+	22.2854i	−0.246950	+	0.271774i
$83$			0.266939i			0.00321613i	0.999999	+	0.00160806i	$0.000511863\pi$
$83$			0.266939i			0.00321613i	−0.999999	+	0.00160806i	$0.999488\pi$
$84$	−146.430	+	14.0470i	−1.74321	+	0.167226i
$85$	−5.56528	+	9.84336i	−0.0654739	+	0.115804i
$86$	13.7852	+	12.5261i	0.160293	+	0.145652i
$87$	199.730			2.29575
$88$	−3.02520	−	2.26154i	−0.0343773	−	0.0256993i
$89$	85.5542			0.961283			0.480641	−	0.876917i	$-0.340404\pi$
$89$	85.5542			0.961283			0.480641	+	0.876917i	$0.340404\pi$
$90$	−132.424	+	43.6838i	−1.47137	+	0.485375i
$91$	31.5542			0.346749
$92$	−3.71748	−	38.7521i	−0.0404074	−	0.421218i
$93$	−105.430			−1.13366
$94$	−11.7852	+	12.9699i	−0.125375	+	0.137977i
$95$	−114.735	−	64.8694i	−1.20774	−	0.682836i
$96$	−130.971	−	79.6344i	−1.36428	−	0.829525i
$97$			99.1297i			1.02196i	0.859594	+	0.510978i	$0.170716\pi$
$97$			99.1297i			1.02196i	−0.859594	+	0.510978i	$0.829284\pi$
$98$	−13.3750	+	14.7195i	−0.136480	+	0.150199i
$99$	6.58359			0.0665009
$100$	80.3719	−	59.5009i	0.803719	−	0.595009i
$101$			105.405i			1.04361i	0.853065	+	0.521805i	$0.174741\pi$
$101$			105.405i			1.04361i	−0.853065	+	0.521805i	$0.825259\pi$
$102$	14.5701	−	16.0347i	0.142844	−	0.157203i
$103$	101.863			0.988958			0.494479	−	0.869190i	$-0.335359\pi$
$103$	101.863			0.988958			0.494479	+	0.869190i	$0.335359\pi$
$104$	26.3344	+	19.6867i	0.253215	+	0.189295i
$105$	−90.4984	+	160.065i	−0.861890	+	1.52443i
$106$	−53.6656	+	59.0601i	−0.506280	+	0.557171i
$107$			32.9962i			0.308376i	0.988042	+	0.154188i	$0.0492762\pi$
$107$			32.9962i			0.308376i	−0.988042	+	0.154188i	$0.950724\pi$
$108$	94.2997	−	9.04616i	0.873145	−	0.0837607i
$109$		−	181.554i		−	1.66563i	−0.553552	−	0.832814i	$-0.686728\pi$
$109$		−	181.554i		−	1.66563i	0.553552	−	0.832814i	$-0.313272\pi$
$110$	−4.48370	+	1.47908i	−0.0407609	+	0.0134462i
$111$			247.859i			2.23296i
$112$	−120.600	+	23.3532i	−1.07679	+	0.208511i
$113$		−	76.6403i		−	0.678233i	−0.940744	−	0.339116i	$-0.889872\pi$
$113$		−	76.6403i		−	0.678233i	0.940744	−	0.339116i	$-0.110128\pi$
$114$	186.902	+	169.830i	1.63949	+	1.48974i
$115$	−42.3607	−	23.9501i	−0.368354	−	0.208262i
$116$	166.026	−	15.9269i	1.43126	−	0.137301i
$117$	−57.3102			−0.489831
$118$	103.825	−	114.262i	0.879873	−	0.968318i
$119$		−	17.3630i		−	0.145908i
$120$	−175.393	+	77.1245i	−1.46161	+	0.642704i
$121$	−120.777			−0.998158
$122$	−21.8552	−	19.8589i	−0.179141	−	0.162778i
$123$		−	72.1172i		−	0.586319i
$124$	−87.6393	+	8.40723i	−0.706769	+	0.0678002i
$125$	−3.38228	−	124.954i	−0.0270582	−	0.999634i
$126$	143.992	−	158.466i	1.14279	−	1.25767i
$127$	−142.962			−1.12569			−0.562843	−	0.826564i	$-0.690292\pi$
$127$	−142.962			−1.12569			−0.562843	+	0.826564i	$0.690292\pi$
$128$	−115.220	−	55.7526i	−0.900156	−	0.435567i
$129$	−44.6099			−0.345813
$130$	39.0306	−	12.8754i	0.300236	−	0.0990414i
$131$	110.138			0.840746			0.420373	−	0.907351i	$-0.361899\pi$
$131$	110.138			0.840746			0.420373	+	0.907351i	$0.361899\pi$
$132$	9.00482	−	0.863831i	0.0682183	−	0.00654418i
$133$	202.385			1.52169
$134$	−112.257	−	102.004i	−0.837741	−	0.761223i
$135$	58.2804	−	103.081i	0.431707	−	0.763563i
$136$	10.8328	−	14.4908i	0.0796531	−	0.106550i
$137$		−	225.398i		−	1.64524i	−0.568592	−	0.822620i	$-0.692512\pi$
$137$		−	225.398i		−	1.64524i	0.568592	−	0.822620i	$-0.307488\pi$
$138$	69.0050	+	62.7021i	0.500036	+	0.454363i
$139$	97.4164			0.700837			0.350419	−	0.936593i	$-0.386039\pi$
$139$	97.4164			0.700837			0.350419	+	0.936593i	$0.386039\pi$
$140$	−62.4633	+	140.271i	−0.446166	+	1.00194i
$141$		−	41.9714i		−	0.297669i
$142$	120.000	+	109.040i	0.845073	+	0.767885i
$143$	−1.94045			−0.0135696
$144$	219.039	−	42.4152i	1.52111	−	0.294550i
$145$	102.610	−	181.487i	0.707655	−	1.25163i
$146$	−123.485	−	112.206i	−0.845790	−	0.768536i
$147$		−	47.6332i		−	0.324036i
$148$	19.7648	+	206.034i	0.133546	+	1.39212i
$149$			191.397i			1.28454i	0.766477	+	0.642271i	$0.222008\pi$
$149$			191.397i			1.28454i	−0.766477	+	0.642271i	$0.777992\pi$
$150$	−46.6280	+	234.918i	−0.310854	+	1.56612i
$151$			68.3549i			0.452682i	0.974048	+	0.226341i	$0.0726763\pi$
$151$			68.3549i			0.452682i	−0.974048	+	0.226341i	$0.927324\pi$
$152$	168.905	+	126.268i	1.11122	+	0.830711i
$153$			31.5355i			0.206115i
$154$	4.87539	−	5.36547i	0.0316584	−	0.0348407i
$155$	−54.1641	+	95.8004i	−0.349446	+	0.618067i
$156$	−78.3870	+	7.51965i	−0.502481	+	0.0482029i
$157$	−155.235			−0.988756			−0.494378	−	0.869247i	$-0.664604\pi$
$157$	−155.235			−0.988756			−0.494378	+	0.869247i	$0.664604\pi$
$158$	−149.141	−	135.518i	−0.943928	−	0.857710i
$159$		−	191.123i		−	1.20203i
$160$	−139.646	+	78.0962i	−0.872787	+	0.488101i
$161$	74.7214			0.464108
$162$	16.2149	−	17.8449i	0.100092	−	0.110153i
$163$		−	90.4765i		−	0.555070i	−0.960715	−	0.277535i	$-0.910482\pi$
$163$		−	90.4765i		−	0.555070i	0.960715	−	0.277535i	$-0.0895175\pi$
$164$	−5.75078	−	59.9477i	−0.0350657	−	0.365535i
$165$	5.56528	−	9.84336i	0.0337290	−	0.0596567i
$166$	−0.395122	−	0.359032i	−0.00238025	−	0.00216284i
$167$	−100.778			−0.603461			−0.301730	−	0.953393i	$-0.597564\pi$
$167$	−100.778			−0.603461			−0.301730	+	0.953393i	$0.597564\pi$
$168$	176.155	−	235.638i	1.04854	−	1.40261i
$169$	−152.108			−0.900049
$170$	−7.08481	−	21.4770i	−0.0416754	−	0.126335i
$171$	−367.580			−2.14959
$172$	−37.0822	+	3.55729i	−0.215594	+	0.0206819i
$173$	54.6556			0.315928			0.157964	−	0.987445i	$-0.449507\pi$
$173$	54.6556			0.315928			0.157964	+	0.987445i	$0.449507\pi$
$174$	−268.636	+	295.640i	−1.54389	+	1.69908i
$175$	98.9520	+	164.465i	0.565440	+	0.939799i
$176$	7.41641	−	1.43613i	0.0421387	−	0.00815981i
$177$			369.758i			2.08903i
$178$	−115.070	+	126.637i	−0.646461	+	0.711444i
$179$	−106.807			−0.596684			−0.298342	−	0.954459i	$-0.596434\pi$
$179$	−106.807			−0.596684			−0.298342	+	0.954459i	$0.596434\pi$
$180$	113.449	−	254.767i	0.630271	−	1.41537i
$181$			144.778i			0.799879i	0.916542	+	0.399939i	$0.130969\pi$
$181$			144.778i			0.799879i	−0.916542	+	0.399939i	$0.869031\pi$
$182$	−42.4403	+	46.7064i	−0.233188	+	0.256629i
$183$	70.7248			0.386474
$184$	62.3607	+	46.6188i	0.338917	+	0.253363i
$185$	225.220	+	127.336i	1.21740	+	0.688302i
$186$	141.803	−	156.058i	0.762384	−	0.839019i
$187$			1.06775i			0.00570992i
$188$	−3.34689	−	34.8889i	−0.0178026	−	0.185579i
$189$			181.828i			0.962052i
$190$	250.338	−	82.5811i	1.31757	−	0.434638i
$191$		−	210.809i		−	1.10371i	−0.833939	−	0.551857i	$-0.813919\pi$
$191$		−	210.809i		−	1.10371i	0.833939	−	0.551857i	$-0.186081\pi$
$192$	294.030	−	86.7542i	1.53140	−	0.451845i
$193$		−	108.176i		−	0.560496i	−0.959928	−	0.280248i	$-0.909583\pi$
$193$		−	108.176i		−	0.560496i	0.959928	−	0.280248i	$-0.0904168\pi$
$194$	−146.731	−	133.329i	−0.756347	−	0.687263i
$195$	−48.4458	+	85.6864i	−0.248440	+	0.439418i
$196$	−3.79837	−	39.5953i	−0.0193795	−	0.202017i
$197$	308.300			1.56497			0.782487	−	0.622667i	$-0.213951\pi$
$197$	308.300			1.56497			0.782487	+	0.622667i	$0.213951\pi$
$198$	−8.85491	+	9.74501i	−0.0447218	+	0.0492172i
$199$		−	247.859i		−	1.24552i	−0.782412	−	0.622761i	$-0.786011\pi$
$199$		−	247.859i		−	1.24552i	0.782412	−	0.622761i	$-0.213989\pi$
$200$	−20.0269	+	198.995i	−0.100134	+	0.994974i
$201$	363.272			1.80733
$202$	−156.020	−	141.769i	−0.772375	−	0.701826i
$203$			320.130i			1.57700i
$204$	4.13777	+	43.1332i	0.0202832	+	0.211437i
$205$	−65.5301	−	37.0497i	−0.319659	−	0.180730i
$206$	−137.005	+	150.777i	−0.665073	+	0.731926i
$207$	−135.712			−0.655616
$208$	−64.5599	+	12.5015i	−0.310384	+	0.0601033i
$209$	−12.4458			−0.0595494
$210$	−115.208	−	349.243i	−0.548609	−	1.66306i
$211$	230.584			1.09281			0.546407	−	0.837520i	$-0.315995\pi$
$211$	230.584			1.09281			0.546407	+	0.837520i	$0.315995\pi$
$212$	−15.2405	−	158.871i	−0.0718892	−	0.749393i
$213$	−388.329			−1.82314
$214$	−48.8409	−	44.3799i	−0.228229	−	0.207383i
$215$	−22.9180	+	40.5353i	−0.106595	+	0.188536i
$216$	−113.443	+	151.749i	−0.525198	+	0.702543i
$217$		−	168.985i		−	0.778734i
$218$	268.735	+	244.189i	1.23273	+	1.12013i
$219$	399.607			1.82469
$220$	3.84123	−	8.62611i	0.0174602	−	0.0392096i
$221$		−	9.29480i		−	0.0420579i
$222$	−366.880	−	333.370i	−1.65261	−	1.50167i
$223$	−177.782			−0.797229			−0.398615	−	0.917118i	$-0.630509\pi$
$223$	−177.782			−0.797229			−0.398615	+	0.917118i	$0.630509\pi$
$224$	127.639	−	209.922i	0.569818	−	0.937151i
$225$	−179.721	−	298.709i	−0.798762	−	1.32759i
$226$	113.443	+	103.081i	0.501959	+	0.456110i
$227$		−	203.301i		−	0.895601i	−0.894134	−	0.447800i	$-0.852208\pi$
$227$		−	203.301i		−	0.895601i	0.894134	−	0.447800i	$-0.147792\pi$
$228$	−502.764	+	48.2301i	−2.20511	+	0.211536i
$229$		−	81.0705i		−	0.354020i	−0.984209	−	0.177010i	$-0.943358\pi$
$229$		−	81.0705i		−	0.354020i	0.984209	−	0.177010i	$-0.0566425\pi$
$230$	92.4258	−	30.4893i	0.401851	−	0.132562i
$231$			17.3630i			0.0751645i
$232$	−199.730	+	267.173i	−0.860905	+	1.15161i
$233$			56.2864i			0.241573i	0.992679	+	0.120786i	$0.0385416\pi$
$233$			56.2864i			0.241573i	−0.992679	+	0.120786i	$0.961458\pi$
$234$	77.0820	−	84.8304i	0.329410	−	0.362523i
$235$	−38.1378	−	21.5625i	−0.162288	−	0.0917554i
$236$	29.4853	+	307.363i	0.124938	+	1.30239i
$237$	482.629			2.03641
$238$	25.7007	+	23.3532i	0.107986	+	0.0981227i
$239$			360.235i			1.50726i	0.657300	+	0.753629i	$0.271699\pi$
$239$			360.235i			1.50726i	−0.657300	+	0.753629i	$0.728301\pi$
$240$	121.743	−	363.348i	0.507264	−	1.51395i
$241$	−197.495			−0.819483			−0.409741	−	0.912202i	$-0.634381\pi$
$241$	−197.495			−0.819483			−0.409741	+	0.912202i	$0.634381\pi$
$242$	162.445	−	178.774i	0.671260	−	0.738735i
$243$			270.896i			1.11480i
$244$	58.7902	−	5.63974i	0.240944	−	0.0231137i
$245$	−43.2825	−	24.4713i	−0.176663	−	0.0998827i
$246$	106.748	+	96.9974i	0.433934	+	0.394298i
$247$	108.341			0.438627
$248$	105.430	−	141.031i	0.425122	−	0.568674i
$249$	1.27864			0.00513510
$250$	189.506	+	163.057i	0.758024	+	0.652227i
$251$	−178.361			−0.710600			−0.355300	−	0.934752i	$-0.615621\pi$
$251$	−178.361			−0.710600			−0.355300	+	0.934752i	$0.615621\pi$
$252$	40.8923	+	426.273i	0.162271	+	1.69156i
$253$	−4.59506			−0.0181623
$254$	192.284	−	211.612i	0.757022	−	0.833119i
$255$	47.1498	+	26.6578i	0.184901	+	0.104540i
$256$	237.495	−	95.5613i	0.927716	−	0.373286i
$257$			453.183i			1.76336i	0.471849	+	0.881679i	$0.343587\pi$
$257$			453.183i			1.76336i	−0.471849	+	0.881679i	$0.656413\pi$
$258$	60.0002	−	66.0314i	0.232559	−	0.255936i
$259$	−397.272			−1.53387
$260$	−33.4380	+	75.0904i	−0.128608	+	0.288809i
$261$		−	581.436i		−	2.22772i
$262$	−148.135	+	163.026i	−0.565401	+	0.622235i
$263$	−21.0921			−0.0801981			−0.0400990	−	0.999196i	$-0.512767\pi$
$263$	−21.0921			−0.0801981			−0.0400990	+	0.999196i	$0.512767\pi$
$264$	−10.8328	+	14.4908i	−0.0410334	+	0.0548892i
$265$	−173.666	−	98.1879i	−0.655342	−	0.370520i
$266$	−272.207	+	299.569i	−1.02333	+	1.12620i
$267$		−	409.806i		−	1.53485i
$268$	301.972	−	28.9681i	1.12676	−	0.108090i
$269$			92.4148i			0.343549i	0.985136	+	0.171775i	$0.0549501\pi$
$269$			92.4148i			0.343549i	−0.985136	+	0.171775i	$0.945050\pi$
$270$	74.1931	+	224.910i	0.274789	+	0.833000i
$271$		−	188.799i		−	0.696675i	−0.937369	−	0.348337i	$-0.886746\pi$
$271$		−	188.799i		−	0.696675i	0.937369	−	0.348337i	$-0.113254\pi$
$272$	6.87907	+	35.5247i	0.0252907	+	0.130606i
$273$		−	151.145i		−	0.553645i
$274$	333.633	+	303.159i	1.21764	+	1.10642i
$275$	−6.08514	−	10.1139i	−0.0221278	−	0.0367779i
$276$	−185.623	+	17.8068i	−0.672547	+	0.0645174i
$277$	−70.1251			−0.253159			−0.126580	−	0.991956i	$-0.540400\pi$
$277$	−70.1251			−0.253159			−0.126580	+	0.991956i	$0.540400\pi$
$278$	−131.025	+	144.195i	−0.471312	+	0.518689i
$279$			306.919i			1.10007i
$280$	−123.616	−	281.122i	−0.441487	−	1.00401i
$281$	−506.269			−1.80167			−0.900835	−	0.434161i	$-0.857045\pi$
$281$	−506.269			−1.80167			−0.900835	+	0.434161i	$0.857045\pi$
$282$	62.1259	+	56.4514i	0.220305	+	0.200182i
$283$		−	501.350i		−	1.77156i	−0.464110	−	0.885778i	$-0.653626\pi$
$283$		−	501.350i		−	1.77156i	0.464110	−	0.885778i	$-0.346374\pi$
$284$	−322.800	+	30.9662i	−1.13662	+	0.109036i
$285$	−310.726	+	549.582i	−1.09026	+	1.92836i
$286$	2.60990	−	2.87225i	0.00912554	−	0.0100428i
$287$	115.591			0.402755
$288$	−231.825	+	381.270i	−0.804947	+	1.32385i
$289$	283.885			0.982303
$290$	130.626	+	395.982i	0.450435	+	1.36546i
$291$	474.833			1.63173
$292$	332.175	−	31.8655i	1.13758	−	0.109128i
$293$	−324.026			−1.10589			−0.552945	−	0.833218i	$-0.686496\pi$
$293$	−324.026			−1.10589			−0.552945	+	0.833218i	$0.686496\pi$
$294$	70.5066	+	64.0666i	0.239818	+	0.217913i
$295$	335.985	+	189.961i	1.13893	+	0.643935i
$296$	−331.554	−	247.859i	−1.12012	−	0.837362i
$297$		−	11.1817i		−	0.0376487i
$298$	−283.305	−	257.428i	−0.950688	−	0.863853i
$299$	40.0000			0.133779
$300$	−285.010	−	384.983i	−0.950035	−	1.28328i
$301$		−	71.5015i		−	0.237546i
$302$	−101.179	−	91.9372i	−0.335029	−	0.304428i
$303$	504.890			1.66630
$304$	−414.079	+	80.1830i	−1.36210	+	0.263760i
$305$	36.3344	−	64.2648i	0.119129	−	0.210704i
$306$	−46.6788	−	42.4152i	−0.152545	−	0.138612i
$307$		−	9.84697i		−	0.0320748i	−0.999871	−	0.0160374i	$-0.994895\pi$
$307$		−	9.84697i		−	0.0320748i	0.999871	−	0.0160374i	$-0.00510509\pi$
$308$	1.38456	+	14.4331i	0.00449533	+	0.0468606i
$309$		−	487.924i		−	1.57904i
$310$	−68.9529	−	209.025i	−0.222429	−	0.674273i
$311$		−	200.417i		−	0.644429i	−0.946667	−	0.322214i	$-0.895573\pi$
$311$		−	200.417i		−	0.644429i	0.946667	−	0.322214i	$-0.104427\pi$
$312$	94.2997	−	126.142i	0.302243	−	0.404302i
$313$			261.582i			0.835727i	0.908510	+	0.417863i	$0.137221\pi$
$313$			261.582i			0.835727i	−0.908510	+	0.417863i	$0.862779\pi$
$314$	208.790	−	229.778i	0.664937	−	0.731777i
$315$	465.967	+	263.451i	1.47926	+	0.836352i
$316$	401.187	−	38.4858i	1.26958	−	0.121791i
$317$	−322.341			−1.01685			−0.508425	−	0.861107i	$-0.669772\pi$
$317$	−322.341			−1.01685			−0.508425	+	0.861107i	$0.669772\pi$
$318$	282.899	+	257.059i	0.889620	+	0.808363i
$319$		−	19.6867i		−	0.0617138i
$320$	72.2256	−	311.743i	0.225705	−	0.974196i
$321$	158.053			0.492376
$322$	−100.500	+	110.602i	−0.312112	+	0.343485i
$323$		−	59.6157i		−	0.184569i
$324$	4.60488	+	48.0025i	0.0142126	+	0.148156i
$325$	52.9712	+	88.0416i	0.162988	+	0.270897i
$326$	133.923	+	121.691i	0.410807	+	0.373284i
$327$	−869.645			−2.65946
$328$	96.4692	+	72.1172i	0.294113	+	0.219870i
$329$	67.2724			0.204475
$330$	7.08481	+	21.4770i	0.0214691	+	0.0650818i
$331$	−61.0883			−0.184557			−0.0922783	−	0.995733i	$-0.529415\pi$
$331$	−61.0883			−0.184557			−0.0922783	+	0.995733i	$0.529415\pi$
$332$	1.06287	−	0.101961i	0.00320143	−	0.000307113i
$333$	721.545			2.16680
$334$	135.546	−	149.171i	0.405826	−	0.446620i
$335$	186.629	−	330.091i	0.557101	−	0.985348i
$336$	111.862	+	577.676i	0.332923	+	1.71927i
$337$			114.960i			0.341129i	0.985347	+	0.170564i	$0.0545591\pi$
$337$			114.960i			0.341129i	−0.985347	+	0.170564i	$0.945441\pi$
$338$	204.585	−	225.150i	0.605282	−	0.666125i
$339$	−367.108			−1.08292
$340$	41.3192	+	18.3996i	0.121527	+	0.0541164i
$341$			10.3919i			0.0304748i
$342$	494.395	−	544.092i	1.44560	−	1.59091i
$343$	−299.851			−0.874201
$344$	44.6099	−	59.6734i	0.129680	−	0.173469i
$345$	−114.721	+	202.908i	−0.332526	+	0.588140i
$346$	−73.5116	+	80.9010i	−0.212461	+	0.233818i
$347$			143.967i			0.414892i	0.978246	+	0.207446i	$0.0665151\pi$
$347$			143.967i			0.414892i	−0.978246	+	0.207446i	$0.933485\pi$
$348$	−76.2901	−	795.269i	−0.219224	−	2.28526i
$349$		−	35.9526i		−	0.103016i	−0.998673	−	0.0515080i	$-0.983597\pi$
$349$		−	35.9526i		−	0.103016i	0.998673	−	0.0515080i	$-0.0164028\pi$
$350$	−376.530	−	74.7362i	−1.07580	−	0.213532i
$351$			97.3365i			0.277312i
$352$	−7.84930	+	12.9093i	−0.0222991	+	0.0366742i
$353$		−	252.536i		−	0.715400i	−0.933837	−	0.357700i	$-0.883561\pi$
$353$		−	252.536i		−	0.715400i	0.933837	−	0.357700i	$-0.116439\pi$
$354$	−547.315	−	497.324i	−1.54609	−	1.40487i
$355$	−199.502	+	352.860i	−0.561976	+	0.993971i
$356$	−32.6788	−	340.653i	−0.0917943	−	0.956890i
$357$	−83.1691			−0.232967
$358$	143.654	−	158.095i	0.401269	−	0.441605i
$359$			594.152i			1.65502i	0.561452	+	0.827509i	$0.310243\pi$
$359$			594.152i			1.65502i	−0.561452	+	0.827509i	$0.689757\pi$
$360$	224.518	+	510.588i	0.623661	+	1.41830i
$361$	333.885			0.924890
$362$	−214.300	−	194.726i	−0.591989	−	0.537917i
$363$			578.524i			1.59373i
$364$	−12.0526	−	125.640i	−0.0331116	−	0.345165i
$365$	205.295	−	363.107i	0.562453	−	0.994814i
$366$	−95.1246	+	104.687i	−0.259903	+	0.286029i
$367$	88.9062			0.242251			0.121126	−	0.992637i	$-0.461350\pi$
$367$	88.9062			0.242251			0.121126	+	0.992637i	$0.461350\pi$
$368$	−152.880	+	29.6039i	−0.415435	+	0.0804455i
$369$	−209.941			−0.568946
$370$	−491.402	+	162.103i	−1.32811	+	0.438117i
$371$	306.334			0.825699
$372$	40.2708	+	419.794i	0.108255	+	1.12848i
$373$	83.6542			0.224274			0.112137	−	0.993693i	$-0.464230\pi$
$373$	83.6542			0.224274			0.112137	+	0.993693i	$0.464230\pi$
$374$	−1.58049	−	1.43613i	−0.00422590	−	0.00383991i
$375$	−598.533	+	16.2012i	−1.59609	+	0.0432031i
$376$	56.1440	+	41.9714i	0.149319	+	0.111626i
$377$			171.373i			0.454570i
$378$	−269.141	−	244.558i	−0.712013	−	0.646978i
$379$	−135.135			−0.356556			−0.178278	−	0.983980i	$-0.557053\pi$
$379$	−135.135			−0.356556			−0.178278	+	0.983980i	$0.557053\pi$
$380$	−214.467	+	481.620i	−0.564387	+	1.26742i
$381$			684.791i			1.79735i
$382$	312.039	+	283.538i	0.816857	+	0.742246i
$383$	498.526			1.30164			0.650818	−	0.759234i	$-0.274426\pi$
$383$	498.526			1.30164			0.650818	+	0.759234i	$0.274426\pi$
$384$	−267.056	+	551.906i	−0.695458	+	1.43726i
$385$	15.7771	+	8.92013i	0.0409794	+	0.0231692i
$386$	160.122	+	145.496i	0.414823	+	0.376933i
$387$			129.864i			0.335567i
$388$	394.707	−	37.8642i	1.01729	−	0.0975880i
$389$			308.420i			0.792854i	0.918066	+	0.396427i	$0.129750\pi$
$389$			308.420i			0.792854i	−0.918066	+	0.396427i	$0.870250\pi$
$390$	−61.6733	−	186.957i	−0.158137	−	0.479378i
$391$		−	22.0104i		−	0.0562926i
$392$	63.7177	+	47.6332i	0.162545	+	0.121513i
$393$		−	527.562i		−	1.34240i
$394$	−414.663	+	456.345i	−1.05244	+	1.15824i
$395$	247.947	−	438.546i	0.627715	−	1.11024i
$396$	−2.51471	−	26.2140i	−0.00635027	−	0.0661970i
$397$	297.682			0.749828			0.374914	−	0.927060i	$-0.377672\pi$
$397$	297.682			0.749828			0.374914	+	0.927060i	$0.377672\pi$
$398$	366.880	+	333.370i	0.921810	+	0.837612i
$399$		−	969.426i		−	2.42964i
$400$	−267.615	−	297.291i	−0.669038	−	0.743228i
$401$	148.663			0.370729			0.185365	−	0.982670i	$-0.440653\pi$
$401$	148.663			0.370729			0.185365	+	0.982670i	$0.440653\pi$
$402$	−488.600	+	537.715i	−1.21542	+	1.33760i
$403$		−	90.4616i		−	0.224470i
$404$	419.692	−	40.2610i	1.03884	−	0.0996559i
$405$	52.4726	+	29.6672i	0.129562	+	0.0732524i
$406$	−473.856	−	430.574i	−1.16713	−	1.06053i
$407$	24.4306			0.0600261
$408$	−69.4110	−	51.8894i	−0.170125	−	0.127180i
$409$	442.387			1.08163			0.540815	−	0.841141i	$-0.318116\pi$
$409$	442.387			1.08163			0.540815	+	0.841141i	$0.318116\pi$
$410$	142.979	−	47.1657i	0.348728	−	0.115038i
$411$	−1079.66			−2.62691
$412$	−38.9081	−	405.589i	−0.0944371	−	0.984439i
$413$	−592.654			−1.43500
$414$	182.533	−	200.881i	0.440901	−	0.485220i
$415$	0.656893	−	1.16185i	0.00158287	−	0.00279964i
$416$	68.3282	−	112.376i	0.164250	−	0.270134i
$417$		−	466.626i		−	1.11901i
$418$	16.7396	−	18.4223i	0.0400469	−	0.0440724i
$419$	536.184			1.27968			0.639838	−	0.768510i	$-0.279001\pi$
$419$	536.184			1.27968			0.639838	+	0.768510i	$0.279001\pi$
$420$	671.902	+	299.200i	1.59977	+	0.712381i
$421$			514.582i			1.22228i	0.791521	+	0.611142i	$0.209290\pi$
$421$			514.582i			1.22228i	−0.791521	+	0.611142i	$0.790710\pi$
$422$	−310.134	+	341.309i	−0.734915	+	0.808789i
$423$	−122.183			−0.288850
$424$	255.659	+	191.123i	0.602970	+	0.450761i
$425$	48.4458	−	29.1480i	0.113990	−	0.0685834i
$426$	522.302	−	574.804i	1.22606	−	1.34931i
$427$			113.359i			0.265477i
$428$	131.382	−	12.6034i	0.306967	−	0.0294473i
$429$			9.29480i			0.0216662i
$430$	−29.1755	−	88.4430i	−0.0678500	−	0.205681i
$431$		−	86.8151i		−	0.201427i	−0.994915	−	0.100714i	$-0.967887\pi$
$431$		−	86.8151i		−	0.201427i	0.994915	−	0.100714i	$-0.0321126\pi$
$432$	−72.0386	−	372.020i	−0.166756	−	0.861157i
$433$			494.017i			1.14092i	0.821327	+	0.570458i	$0.193234\pi$
$433$			494.017i			1.14092i	−0.821327	+	0.570458i	$0.806766\pi$
$434$	250.132	+	227.285i	0.576340	+	0.523698i
$435$	−869.325	−	491.503i	−1.99845	−	1.12989i
$436$	−722.895	+	69.3473i	−1.65802	+	0.159053i
$437$	256.555			0.587082
$438$	−537.470	+	591.497i	−1.22710	+	1.35045i
$439$		−	524.700i		−	1.19522i	−0.801789	−	0.597608i	$-0.796118\pi$
$439$		−	524.700i		−	1.19522i	0.801789	−	0.597608i	$-0.203882\pi$
$440$	7.60190	+	17.2879i	0.0172770	+	0.0392906i
$441$	−138.666			−0.314435
$442$	13.7581	+	12.5015i	0.0311270	+	0.0282839i
$443$		−	496.575i		−	1.12094i	−0.828176	−	0.560469i	$-0.810621\pi$
$443$		−	496.575i		−	1.12094i	0.828176	−	0.560469i	$-0.189379\pi$
$444$	986.906	−	94.6737i	2.22276	−	0.213229i
$445$	−372.375	−	210.535i	−0.836797	−	0.473112i
$446$	239.116	−	263.153i	0.536136	−	0.590028i
$447$	916.795			2.05099
$448$	139.051	+	471.275i	0.310382	+	1.05195i
$449$	−332.158			−0.739773			−0.369886	−	0.929077i	$-0.620603\pi$
$449$	−332.158			−0.739773			−0.369886	+	0.929077i	$0.620603\pi$
$450$	683.873	+	135.739i	1.51972	+	0.301643i
$451$	−7.10835			−0.0157613
$452$	−305.160	+	29.2740i	−0.675133	+	0.0647655i
$453$	327.421			0.722785
$454$	300.926	+	273.440i	0.662833	+	0.602290i
$455$	−137.340	−	77.6497i	−0.301845	−	0.170659i
$456$	604.827	−	809.060i	1.32637	−	1.77425i
$457$		−	252.788i		−	0.553147i	−0.960993	−	0.276574i	$-0.910801\pi$
$457$		−	252.788i		−	0.553147i	0.960993	−	0.276574i	$-0.0891990\pi$
$458$	120.000	+	109.040i	0.262010	+	0.238078i
$459$	53.5604			0.116689
$460$	−79.1822	+	177.817i	−0.172135	+	0.386558i
$461$		−	832.716i		−	1.80633i	−0.429299	−	0.903163i	$-0.641239\pi$
$461$		−	832.716i		−	1.80633i	0.429299	−	0.903163i	$-0.358761\pi$
$462$	−25.7007	−	23.3532i	−0.0556292	−	0.0505480i
$463$	−854.205			−1.84494			−0.922468	−	0.386074i	$-0.873831\pi$
$463$	−854.205			−1.84494			−0.922468	+	0.386074i	$0.873831\pi$
$464$	−126.833	−	654.987i	−0.273347	−	1.41161i
$465$	458.885	+	259.447i	0.986850	+	0.557950i
$466$	−83.3150	−	75.7051i	−0.178788	−	0.162457i
$467$		−	102.726i		−	0.219970i	−0.993933	−	0.109985i	$-0.964920\pi$
$467$		−	102.726i		−	0.219970i	0.993933	−	0.109985i	$-0.0350802\pi$
$468$	21.8905	+	228.193i	0.0467747	+	0.487592i
$469$			582.259i			1.24149i
$470$	83.2120	−	27.4499i	0.177047	−	0.0584040i
$471$			743.577i			1.57872i
$472$	−494.615	−	369.758i	−1.04791	−	0.783386i
$473$			4.39705i			0.00929608i
$474$	−649.135	+	714.386i	−1.36948	+	1.50714i
$475$	339.751	+	564.688i	0.715265	+	1.18882i
$476$	−69.1347	+	6.63208i	−0.145241	+	0.0139329i
$477$	−556.379			−1.16641
$478$	−533.218	−	484.515i	−1.11552	−	1.01363i
$479$			268.772i			0.561111i	0.959838	+	0.280556i	$0.0905187\pi$
$479$			268.772i			0.561111i	−0.959838	+	0.280556i	$0.909481\pi$
$480$	374.082	+	668.906i	0.779338	+	1.39356i
$481$	−212.669			−0.442139
$482$	265.631	−	292.332i	0.551101	−	0.606498i
$483$		−	357.917i		−	0.741028i
$484$	46.1327	+	480.901i	0.0953156	+	0.993596i
$485$	243.942	−	431.462i	0.502973	−	0.889612i
$486$	−400.979	−	364.354i	−0.825059	−	0.749699i
$487$	504.065			1.03504			0.517520	−	0.855671i	$-0.326855\pi$
$487$	504.065			1.03504			0.517520	+	0.855671i	$0.326855\pi$
$488$	−70.7248	+	94.6066i	−0.144928	+	0.193866i
$489$	−433.384			−0.886266
$490$	94.4371	−	31.1528i	0.192729	−	0.0635772i
$491$	130.020			0.264807			0.132403	−	0.991196i	$-0.457731\pi$
$491$	130.020			0.264807			0.132403	+	0.991196i	$0.457731\pi$
$492$	−287.151	+	27.5463i	−0.583639	+	0.0559885i
$493$	94.2997			0.191277
$494$	−145.718	+	160.366i	−0.294976	+	0.324627i
$495$	−28.6551	−	16.2012i	−0.0578891	−	0.0327296i
$496$	66.9505	+	345.744i	0.134981	+	0.697065i
$497$		−	622.421i		−	1.25236i
$498$	−1.71977	+	1.89264i	−0.00345335	+	0.00380048i
$499$	664.184			1.33103			0.665515	−	0.746384i	$-0.268212\pi$
$499$	664.184			1.33103			0.665515	+	0.746384i	$0.268212\pi$
$500$	−496.241	+	61.1955i	−0.992482	+	0.122391i
$501$			482.728i			0.963529i
$502$	239.895	−	264.009i	0.477878	−	0.525914i
$503$	−550.015			−1.09347			−0.546735	−	0.837306i	$-0.684129\pi$
$503$	−550.015			−1.09347			−0.546735	+	0.837306i	$0.684129\pi$
$504$	−685.967	−	512.807i	−1.36105	−	1.01747i
$505$	259.384	−	458.774i	0.513631	−	0.908463i
$506$	6.18034	−	6.80159i	0.0122141	−	0.0134419i
$507$			728.602i			1.43708i
$508$	54.6067	+	569.235i	0.107493	+	1.12054i
$509$		−	349.843i		−	0.687314i	−0.939095	−	0.343657i	$-0.888334\pi$
$509$		−	349.843i		−	0.687314i	0.939095	−	0.343657i	$-0.111666\pi$
$510$	−102.875	+	33.9364i	−0.201716	+	0.0665419i
$511$			640.496i			1.25342i
$512$	−177.981	+	480.070i	−0.347619	+	0.937636i
$513$			624.304i			1.21697i
$514$	−670.800	−	609.530i	−1.30506	−	1.18586i
$515$	−443.358	−	250.668i	−0.860888	−	0.486733i
$516$	17.0395	+	177.624i	0.0330222	+	0.344233i
$517$	−4.13698			−0.00800189
$518$	534.330	−	588.041i	1.03153	−	1.13522i
$519$		−	261.801i		−	0.504434i
$520$	−66.1746	−	150.491i	−0.127259	−	0.289406i
$521$	29.7771			0.0571537			0.0285769	−	0.999592i	$-0.490902\pi$
$521$	29.7771			0.0571537			0.0285769	+	0.999592i	$0.490902\pi$
$522$	860.640	+	782.030i	1.64874	+	1.49814i
$523$			603.023i			1.15301i	0.817094	+	0.576504i	$0.195584\pi$
$523$			603.023i			1.15301i	−0.817094	+	0.576504i	$0.804416\pi$
$524$	−42.0689	−	438.538i	−0.0802841	−	0.836904i
$525$	787.789	−	473.982i	1.50055	−	0.902823i
$526$	28.3688	−	31.2205i	0.0539331	−	0.0593545i
$527$	−49.7774			−0.0944543
$528$	−6.87907	−	35.5247i	−0.0130285	−	0.0672817i
$529$	−434.279			−0.820943
$530$	378.917	−	124.997i	0.714938	−	0.235843i
$531$	1076.41			2.02713
$532$	−77.3040	−	805.839i	−0.145308	−	1.51473i
$533$	61.8782			0.116094
$534$	606.594	+	551.188i	1.13594	+	1.03219i
$535$	81.1985	−	143.616i	0.151773	−	0.268442i
$536$	−363.272	+	485.939i	−0.677747	+	0.906603i
$537$			511.605i			0.952710i
$538$	−136.792	−	124.298i	−0.254260	−	0.231036i
$539$	−4.69505			−0.00871066
$540$	−432.701	−	192.683i	−0.801298	−	0.356820i
$541$		−	163.368i		−	0.301974i	−0.988536	−	0.150987i	$-0.951755\pi$
$541$		−	163.368i		−	0.301974i	0.988536	−	0.150987i	$-0.0482451\pi$
$542$	279.460	+	253.934i	0.515608	+	0.468513i
$543$	693.490			1.27714
$544$	−61.8359	−	37.5983i	−0.113669	−	0.0691145i
$545$	−446.774	+	790.212i	−0.819769	+	1.44993i
$546$	223.724	+	203.290i	0.409752	+	0.372325i
$547$			524.218i			0.958350i	0.877719	+	0.479175i	$0.159064\pi$
$547$			524.218i			0.958350i	−0.877719	+	0.479175i	$0.840936\pi$
$548$	−897.471	+	86.0943i	−1.63772	+	0.157106i
$549$		−	205.888i		−	0.375023i
$550$	23.1551	+	4.59597i	0.0421002	+	0.00835631i
$551$			1099.16i			1.99485i
$552$	223.305	−	298.709i	0.404538	−	0.541139i
$553$			773.566i			1.39885i
$554$	94.3181	−	103.799i	0.170249	−	0.187363i
$555$	609.941	−	1078.81i	1.09899	−	1.94380i
$556$	−37.2098	−	387.885i	−0.0669240	−	0.697635i
$557$	−589.515			−1.05837			−0.529187	−	0.848505i	$-0.677503\pi$
$557$	−589.515			−1.05837			−0.529187	+	0.848505i	$0.677503\pi$
$558$	−454.301	−	412.805i	−0.814159	−	0.739795i
$559$		−	38.2763i		−	0.0684728i
$560$	582.380	+	195.132i	1.03996	+	0.348451i
$561$	5.11456			0.00911687
$562$	680.931	−	749.378i	1.21162	−	1.33341i
$563$			557.763i			0.990698i	0.868694	+	0.495349i	$0.164960\pi$
$563$			557.763i			0.990698i	−0.868694	+	0.495349i	$0.835040\pi$
$564$	−167.118	+	16.0316i	−0.296309	+	0.0284249i
$565$	−188.599	+	333.577i	−0.333804	+	0.590402i
$566$	742.097	+	674.315i	1.31113	+	1.19137i
$567$	−92.5581			−0.163242
$568$	388.329	−	519.457i	0.683678	−	0.914538i
$569$	−542.715			−0.953805			−0.476903	−	0.878956i	$-0.658241\pi$
$569$	−542.715			−0.953805			−0.476903	+	0.878956i	$0.658241\pi$
$570$	−395.565	−	1199.12i	−0.693974	−	2.10372i
$571$	−476.695			−0.834842			−0.417421	−	0.908713i	$-0.637066\pi$
$571$	−476.695			−0.834842			−0.417421	+	0.908713i	$0.637066\pi$
$572$	0.741187	+	7.72634i	0.00129578	+	0.0135076i
$573$	−1009.78			−1.76227
$574$	−155.469	+	171.097i	−0.270852	+	0.298078i
$575$	125.438	+	208.486i	0.218152	+	0.362584i
$576$	−252.551	−	855.953i	−0.438457	−	1.48603i
$577$		−	865.659i		−	1.50027i	−0.661282	−	0.750137i	$-0.729987\pi$
$577$		−	865.659i		−	1.50027i	0.661282	−	0.750137i	$-0.270013\pi$
$578$	−381.825	+	420.206i	−0.660597	+	0.727001i
$579$	−518.164			−0.894929
$580$	−761.823	−	339.242i	−1.31349	−	0.584900i
$581$			2.04943i			0.00352741i
$582$	−638.649	+	702.846i	−1.09733	+	1.20764i
$583$	−18.8383			−0.0323127
$584$	−399.607	+	534.543i	−0.684258	+	0.915313i
$585$	249.443	+	141.031i	0.426398	+	0.241079i
$586$	435.813	−	479.622i	0.743709	−	0.818467i
$587$		−	567.091i		−	0.966083i	−0.875597	−	0.483041i	$-0.839532\pi$
$587$		−	567.091i		−	0.966083i	0.875597	−	0.483041i	$-0.160468\pi$
$588$	−189.662	+	18.1943i	−0.322555	+	0.0309427i
$589$		−	580.209i		−	0.985075i
$590$	−733.078	+	241.827i	−1.24250	+	0.409876i
$591$		−	1476.76i		−	2.49875i
$592$	812.820	−	157.396i	1.37301	−	0.265871i
$593$		−	421.774i		−	0.711254i	−0.934628	−	0.355627i	$-0.884267\pi$
$593$		−	421.774i		−	0.711254i	0.934628	−	0.355627i	$-0.115733\pi$
$594$	16.5511	+	15.0393i	0.0278638	+	0.0253187i
$595$	−42.7276	+	75.5725i	−0.0718110	+	0.127013i
$596$	762.089	−	73.1071i	1.27867	−	0.122663i
$597$	−1187.25			−1.98869
$598$	−53.7999	+	59.2079i	−0.0899664	+	0.0990098i
$599$			120.444i			0.201075i	0.994933	+	0.100538i	$0.0320563\pi$
$599$			120.444i			0.201075i	−0.994933	+	0.100538i	$0.967944\pi$
$600$	953.189	+	95.9292i	1.58865	+	0.159882i
$601$	340.158			0.565986			0.282993	−	0.959122i	$-0.408673\pi$
$601$	340.158			0.565986			0.282993	+	0.959122i	$0.408673\pi$
$602$	105.836	+	96.1693i	0.175808	+	0.159750i
$603$		−	1057.53i		−	1.75377i
$604$	272.170	−	26.1093i	0.450613	−	0.0432273i
$605$	525.682	+	297.213i	0.868897	+	0.491261i
$606$	−679.076	+	747.337i	−1.12059	+	1.23323i
$607$	115.621			0.190479			0.0952396	−	0.995454i	$-0.469638\pi$
$607$	115.621			0.190479			0.0952396	+	0.995454i	$0.469638\pi$
$608$	438.248	−	720.764i	0.720803	−	1.18547i
$609$	1533.43			2.51795
$610$	46.2550	+	140.218i	0.0758279	+	0.229866i
$611$	36.0124			0.0589401
$612$	125.566	−	12.0455i	0.205173	−	0.0196822i
$613$	1095.63			1.78733			0.893663	−	0.448738i	$-0.148126\pi$
$613$	1095.63			1.78733			0.893663	+	0.448738i	$0.148126\pi$
$614$	14.5755	+	13.2442i	0.0237385	+	0.0215703i
$615$	−177.469	+	313.890i	−0.288567	+	0.510391i
$616$	−23.2260	−	17.3630i	−0.0377046	−	0.0281867i
$617$			716.775i			1.16171i	0.814007	+	0.580855i	$0.197282\pi$
$617$			716.775i			1.16171i	−0.814007	+	0.580855i	$0.802718\pi$
$618$	722.224	+	656.257i	1.16865	+	1.06190i
$619$	118.584			0.191573			0.0957864	−	0.995402i	$-0.469463\pi$
$619$	118.584			0.191573			0.0957864	+	0.995402i	$0.469463\pi$
$620$	402.139	+	179.074i	0.648612	+	0.288829i
$621$			230.496i			0.371169i
$622$	296.657	+	269.561i	0.476941	+	0.433378i
$623$	656.844			1.05432
$624$	59.8823	+	309.243i	0.0959653	+	0.495582i
$625$	−292.771	+	552.187i	−0.468433	+	0.883499i
$626$	−387.193	−	351.828i	−0.618520	−	0.562025i
$627$			59.6157i			0.0950809i
$628$	59.2944	+	618.101i	0.0944178	+	0.984238i
$629$			117.023i			0.186046i
$630$	−1016.68	+	335.383i	−1.61378	+	0.532354i
$631$		−	1168.62i		−	1.85201i	−0.377515	−	0.926004i	$-0.623221\pi$
$631$		−	1168.62i		−	1.85201i	0.377515	−	0.926004i	$-0.376779\pi$
$632$	−482.629	+	645.600i	−0.763654	+	1.02152i
$633$		−	1104.50i		−	1.74486i
$634$	433.548	−	477.128i	0.683830	−	0.752569i
$635$	622.243	+	351.807i	0.979910	+	0.554026i
$636$	−760.997	+	73.0023i	−1.19654	+	0.114784i
$637$	40.8704			0.0641608
$638$	29.1402	+	26.4786i	0.0456743	+	0.0415025i
$639$			1130.47i			1.76912i
$640$	364.297	+	526.201i	0.569215	+	0.822189i
$641$	−244.158			−0.380902			−0.190451	−	0.981697i	$-0.560995\pi$
$641$	−244.158			−0.380902			−0.190451	+	0.981697i	$0.560995\pi$
$642$	−212.580	+	233.949i	−0.331122	+	0.364407i
$643$		−	868.847i		−	1.35124i	−0.737250	−	0.675620i	$-0.763876\pi$
$643$		−	868.847i		−	1.35124i	0.737250	−	0.675620i	$-0.236124\pi$
$644$	−28.5410	−	297.520i	−0.0443184	−	0.461987i
$645$	194.165	+	109.778i	0.301031	+	0.170198i
$646$	88.2430	+	80.1830i	0.136599	+	0.124122i
$647$	−35.1333			−0.0543019			−0.0271510	−	0.999631i	$-0.508643\pi$
$647$	−35.1333			−0.0543019			−0.0271510	+	0.999631i	$0.508643\pi$
$648$	−77.2468	−	57.7472i	−0.119208	−	0.0891160i
$649$	36.4458			0.0561569
$650$	−201.565	−	40.0079i	−0.310100	−	0.0615507i
$651$	−809.443			−1.24338
$652$	−360.252	+	34.5589i	−0.552534	+	0.0530045i
$653$	580.068			0.888313			0.444157	−	0.895949i	$-0.353503\pi$
$653$	580.068			0.888313			0.444157	+	0.895949i	$0.353503\pi$
$654$	1169.67	−	1287.25i	1.78849	−	1.96827i
$655$	−479.375	−	271.031i	−0.731870	−	0.413788i
$656$	−236.498	+	45.7960i	−0.360516	+	0.0698109i
$657$		−	1163.30i		−	1.77062i
$658$	−90.4812	+	99.5764i	−0.137509	+	0.151332i
$659$	−992.788			−1.50651			−0.753253	−	0.657731i	$-0.771517\pi$
$659$	−992.788			−1.50651			−0.753253	+	0.657731i	$0.771517\pi$
$660$	−41.3192	−	18.3996i	−0.0626049	−	0.0278782i
$661$		−	719.647i		−	1.08872i	−0.838850	−	0.544362i	$-0.816772\pi$
$661$		−	719.647i		−	1.08872i	0.838850	−	0.544362i	$-0.183228\pi$
$662$	82.1635	−	90.4226i	0.124114	−	0.136590i
$663$	−44.5223			−0.0671528
$664$	−1.27864	+	1.71040i	−0.00192566	+	0.00257591i
$665$	−880.879	−	498.036i	−1.32463	−	0.748926i
$666$	−970.476	+	1068.03i	−1.45717	+	1.60365i
$667$			405.817i			0.608421i
$668$	38.4938	+	401.270i	0.0576254	+	0.600703i
$669$			851.580i			1.27291i
$670$	237.585	+	720.219i	0.354605	+	1.07495i
$671$		−	6.97110i		−	0.0103891i
$672$	−1005.53	−	611.395i	−1.49632	−	0.909813i
$673$			189.591i			0.281711i	0.990030	+	0.140855i	$0.0449852\pi$
$673$			189.591i			0.281711i	−0.990030	+	0.140855i	$0.955015\pi$
$674$	−170.164	−	154.621i	−0.252469	−	0.229409i
$675$	−507.331	+	305.241i	−0.751602	+	0.452209i
$676$	58.1002	+	605.653i	0.0859471	+	0.895936i
$677$	327.192			0.483297			0.241649	−	0.970364i	$-0.422312\pi$
$677$	327.192			0.483297			0.241649	+	0.970364i	$0.422312\pi$
$678$	493.760	−	543.393i	0.728259	−	0.801464i
$679$			761.070i			1.12087i
$680$	−82.8093	+	36.4132i	−0.121778	+	0.0535489i
$681$	−973.817			−1.42998
$682$	−15.3821	−	13.9771i	−0.0225544	−	0.0204943i
$683$			673.539i			0.986148i	0.869987	+	0.493074i	$0.164127\pi$
$683$			673.539i			0.986148i	−0.869987	+	0.493074i	$0.835873\pi$
$684$	140.403	+	1463.60i	0.205268	+	2.13977i
$685$	−554.668	+	981.044i	−0.809734	+	1.43218i
$686$	403.299	−	443.839i	0.587899	−	0.646995i
$687$	−388.329			−0.565254
$688$	28.3282	+	146.292i	0.0411748	+	0.212634i
$689$	163.988			0.238008
$690$	−146.045	−	442.721i	−0.211659	−	0.641625i
$691$	237.036			0.343033			0.171516	−	0.985181i	$-0.445133\pi$
$691$	237.036			0.343033			0.171516	+	0.985181i	$0.445133\pi$
$692$	−20.8766	−	217.623i	−0.0301685	−	0.314485i
$693$	50.5456			0.0729374
$694$	−213.100	−	193.636i	−0.307061	−	0.279014i
$695$	−424.005	−	239.726i	−0.610079	−	0.344930i
$696$	1279.76	+	956.710i	1.83874	+	1.37458i
$697$		−	34.0491i		−	0.0488510i
$698$	53.2170	+	48.3562i	0.0762421	+	0.0692782i
$699$	269.613			0.385712
$700$	617.057	−	456.819i	0.881509	−	0.652599i
$701$			476.306i			0.679466i	0.940522	+	0.339733i	$0.110337\pi$
$701$			476.306i			0.679466i	−0.940522	+	0.339733i	$0.889663\pi$
$702$	−144.077	−	130.917i	−0.205238	−	0.186492i
$703$	−1364.03			−1.94030
$704$	−8.55107	−	28.9815i	−0.0121464	−	0.0411669i
$705$	−103.285	+	182.681i	−0.146503	+	0.259121i
$706$	373.803	+	339.661i	0.529467	+	0.481106i
$707$			809.246i			1.14462i
$708$	1472.27	−	141.235i	2.07948	−	0.199485i
$709$		−	964.778i		−	1.36076i	−0.732860	−	0.680380i	$-0.761815\pi$
$709$		−	964.778i		−	1.36076i	0.732860	−	0.680380i	$-0.238185\pi$
$710$	−253.973	−	769.897i	−0.357708	−	1.08436i
$711$		−	1404.99i		−	1.97607i
$712$	548.186	+	409.806i	0.769924	+	0.575570i
$713$		−	214.216i		−	0.300443i
$714$	111.862	−	123.107i	0.156670	−	0.172418i
$715$	8.44582	+	4.77514i	0.0118123	+	0.00667852i
$716$	40.7965	+	425.274i	0.0569783	+	0.593958i
$717$	1725.53			2.40660
$718$	−879.461	−	799.132i	−1.22488	−	1.11300i
$719$		−	899.974i		−	1.25170i	−0.779943	−	0.625851i	$-0.784752\pi$
$719$		−	899.974i		−	1.25170i	0.779943	−	0.625851i	$-0.215248\pi$
$720$	−1057.75	−	354.409i	−1.46909	−	0.492234i
$721$	782.053			1.08468
$722$	−449.075	+	494.216i	−0.621987	+	0.684510i
$723$			946.006i			1.30845i
$724$	576.466	−	55.3003i	0.796224	−	0.0763816i
$725$	−893.220	+	537.415i	−1.23203	+	0.741262i
$726$	−856.330	−	778.114i	−1.17952	−	1.07178i
$727$	908.888			1.25019			0.625095	−	0.780549i	$-0.285060\pi$
$727$	908.888			1.25019			0.625095	+	0.780549i	$0.285060\pi$
$728$	202.183	+	151.145i	0.277723	+	0.207617i
$729$	1189.09			1.63113
$730$	261.348	+	792.255i	0.358012	+	1.08528i
$731$	−21.0619			−0.0288125
$732$	−27.0145	−	281.606i	−0.0369050	−	0.384708i
$733$	433.283			0.591109			0.295554	−	0.955326i	$-0.404496\pi$
$733$	433.283			0.591109			0.295554	+	0.955326i	$0.404496\pi$
$734$	−119.579	+	131.599i	−0.162914	+	0.179290i
$735$	−117.218	+	207.324i	−0.159480	+	0.282073i
$736$	161.803	−	266.110i	0.219842	−	0.361562i
$737$		−	35.8065i		−	0.0485842i
$738$	282.370	−	310.754i	0.382616	−	0.421076i
$739$	−886.138			−1.19910			−0.599552	−	0.800336i	$-0.704655\pi$
$739$	−886.138			−1.19910			−0.599552	+	0.800336i	$0.704655\pi$
$740$	420.990	−	945.400i	0.568905	−	1.27757i
$741$		−	518.955i		−	0.700344i
$742$	−412.019	+	453.435i	−0.555281	+	0.611099i
$743$	895.305			1.20499			0.602493	−	0.798124i	$-0.294174\pi$
$743$	895.305			1.20499			0.602493	+	0.798124i	$0.294174\pi$
$744$	−675.542	−	505.013i	−0.907986	−	0.678781i
$745$	470.997	−	833.055i	0.632211	−	1.11820i
$746$	−112.515	+	123.825i	−0.150824	+	0.165985i
$747$		−	3.72226i		−	0.00498295i
$748$	4.25150	−	0.407846i	0.00568382	−	0.000545248i
$749$			253.329i			0.338223i
$750$	781.044	−	907.737i	1.04139	−	1.21032i
$751$			1297.13i			1.72720i	0.504176	+	0.863601i	$0.331796\pi$
$751$			1297.13i			1.72720i	−0.504176	+	0.863601i	$0.668204\pi$
$752$	−137.639	+	26.6527i	−0.183031	+	0.0354425i
$753$			854.351i			1.13460i
$754$	−253.666	−	230.496i	−0.336427	−	0.305698i
$755$	168.210	−	297.515i	0.222795	−	0.394060i
$756$	723.988	−	69.4520i	0.957656	−	0.0918678i
$757$	−421.694			−0.557060			−0.278530	−	0.960428i	$-0.589847\pi$
$757$	−421.694			−0.557060			−0.278530	+	0.960428i	$0.589847\pi$
$758$	181.756	−	200.026i	0.239783	−	0.263886i
$759$			22.0104i			0.0289992i
$760$	−424.435	−	965.231i	−0.558468	−	1.27004i
$761$	1415.76			1.86039			0.930196	−	0.367063i	$-0.119637\pi$
$761$	1415.76			1.86039			0.930196	+	0.367063i	$0.119637\pi$
$762$	−1013.63	−	921.042i	−1.33022	−	1.20872i
$763$		−	1393.88i		−	1.82684i
$764$	−839.384	+	80.5220i	−1.09867	+	0.105395i
$765$	77.6038	−	137.258i	0.101443	−	0.179423i
$766$	−670.517	+	737.917i	−0.875348	+	0.963339i
$767$	−317.261			−0.413639
$768$	−457.740	−	1137.61i	−0.596016	−	1.48126i
$769$	−414.210			−0.538635			−0.269318	−	0.963051i	$-0.586798\pi$
$769$	−414.210			−0.538635			−0.269318	+	0.963051i	$0.586798\pi$
$770$	−34.4237	+	11.3557i	−0.0447061	+	0.0147476i
$771$	2170.76			2.81551
$772$	−430.726	+	41.3195i	−0.557935	+	0.0535226i
$773$	−727.056			−0.940564			−0.470282	−	0.882516i	$-0.655848\pi$
$773$	−727.056			−0.940564			−0.470282	+	0.882516i	$0.655848\pi$
$774$	−192.225	−	174.667i	−0.248352	−	0.225668i
$775$	471.498	−	283.682i	0.608385	−	0.366042i
$776$	−474.833	+	635.171i	−0.611898	+	0.818519i
$777$			1902.94i			2.44909i
$778$	−456.522	−	414.824i	−0.586790	−	0.533193i
$779$	396.879			0.509473
$780$	359.684	+	160.168i	0.461134	+	0.205344i
$781$			38.2763i			0.0490094i
$782$	32.5797	+	29.6039i	0.0416621	+	0.0378567i
$783$	−987.519			−1.26120
$784$	−156.207	+	30.2481i	−0.199243	+	0.0385818i
$785$	675.659	+	382.008i	0.860713	+	0.486634i
$786$	780.895	+	709.569i	0.993506	+	0.902760i
$787$		−	1030.11i		−	1.30890i	−0.756104	−	0.654451i	$-0.772900\pi$
$787$		−	1030.11i		−	1.30890i	0.756104	−	0.654451i	$-0.227100\pi$
$788$	−117.760	−	1227.56i	−0.149442	−	1.55782i
$789$			101.032i			0.128050i
$790$	315.646	+	956.854i	0.399552	+	1.21121i
$791$		−	588.407i		−	0.743878i
$792$	42.1842	+	31.5355i	0.0532629	+	0.0398176i
$793$			60.6835i			0.0765239i
$794$	−400.381	+	440.627i	−0.504258	+	0.554946i
$795$	−470.322	+	831.861i	−0.591600	+	1.04637i
$796$	−986.906	+	94.6737i	−1.23983	+	0.118937i
$797$	−371.202			−0.465750			−0.232875	−	0.972507i	$-0.574813\pi$
$797$	−371.202			−0.465750			−0.232875	+	0.972507i	$0.574813\pi$
$798$	1434.94	+	1303.87i	1.79817	+	1.63393i
$799$		−	19.8162i		−	0.0248013i
$800$	799.991	+	3.73224i	0.999989	+	0.00466530i
$801$	−1192.99			−1.48938
$802$	−199.951	+	220.050i	−0.249315	+	0.274376i
$803$		−	39.3879i		−	0.0490509i
$804$	−138.758	−	1446.45i	−0.172584	−	1.79907i
$805$	−325.225	−	183.877i	−0.404006	−	0.228419i
$806$	133.901	+	121.671i	0.166130	+	0.150956i
$807$	442.668			0.548536
$808$	−504.890	+	675.378i	−0.624864	+	0.835863i
$809$	77.7771			0.0961398			0.0480699	−	0.998844i	$-0.484693\pi$
$809$	77.7771			0.0961398			0.0480699	+	0.998844i	$0.484693\pi$
$810$	−114.489	+	37.7674i	−0.141344	+	0.0466265i
$811$	−1407.90			−1.73600			−0.868000	−	0.496564i	$-0.834595\pi$
$811$	−1407.90			−1.73600			−0.868000	+	0.496564i	$0.834595\pi$
$812$	1274.67	−	122.279i	1.56979	−	0.150590i
$813$	−904.350			−1.11236
$814$	−32.8591	+	36.1621i	−0.0403675	+	0.0444252i
$815$	−222.648	+	393.799i	−0.273188	+	0.483189i
$816$	170.164	−	32.9509i	0.208534	−	0.0403810i
$817$		−	245.500i		−	0.300489i
$818$	−595.009	+	654.820i	−0.727395	+	0.800513i
$819$	−440.000			−0.537241
$820$	−122.491	+	275.074i	−0.149380	+	0.335456i
$821$		−	820.275i		−	0.999116i	−0.866280	−	0.499558i	$-0.833496\pi$
$821$		−	820.275i		−	0.999116i	0.866280	−	0.499558i	$-0.166504\pi$
$822$	1452.14	−	1598.11i	1.76659	−	1.94417i
$823$	1385.41			1.68336			0.841681	−	0.539976i	$-0.181567\pi$
$823$	1385.41			1.68336			0.841681	+	0.539976i	$0.181567\pi$
$824$	652.683	+	487.924i	0.792091	+	0.592141i
$825$	−48.4458	+	29.1480i	−0.0587222	+	0.0353309i
$826$	797.118	−	877.245i	0.965034	−	1.06204i
$827$		−	258.898i		−	0.313057i	−0.987673	−	0.156529i	$-0.949970\pi$
$827$		−	258.898i		−	0.313057i	0.987673	−	0.156529i	$-0.0500303\pi$
$828$	51.8376	+	540.369i	0.0626057	+	0.652620i
$829$			1299.31i			1.56732i	0.621190	+	0.783660i	$0.286649\pi$
$829$			1299.31i			1.56732i	−0.621190	+	0.783660i	$0.713351\pi$
$830$	0.836249	+	2.53502i	0.00100753	+	0.00305424i
$831$			335.901i			0.404213i
$832$	74.4371	+	252.284i	0.0894677	+	0.303226i
$833$		−	22.4894i		−	0.0269980i
$834$	690.699	+	627.611i	0.828176	+	0.752531i
$835$	438.636	+	247.998i	0.525313	+	0.297004i
$836$	4.75388	+	49.5558i	0.00568646	+	0.0592773i
$837$	521.276			0.622791
$838$	−721.166	+	793.658i	−0.860580	+	0.947086i
$839$		−	804.961i		−	0.959429i	−0.877425	−	0.479715i	$-0.840740\pi$
$839$		−	804.961i		−	0.959429i	0.877425	−	0.479715i	$-0.159260\pi$
$840$	−1346.58	+	592.124i	−1.60307	+	0.704910i
$841$	−897.650			−1.06736
$842$	−761.683	−	692.111i	−0.904611	−	0.821985i
$843$			2425.04i			2.87668i
$844$	−88.0751	−	918.120i	−0.104354	−	1.08782i
$845$	662.052	+	374.314i	0.783493	+	0.442975i
$846$	164.336	−	180.855i	0.194251	−	0.213777i
$847$	−927.268			−1.09477
$848$	−626.760	+	121.367i	−0.739104	+	0.143121i
$849$	−2401.48			−2.82859
$850$	−22.0148	+	110.913i	−0.0258997	+	0.130486i
$851$	−503.607			−0.591782
$852$	148.329	+	1546.22i	0.174095	+	1.81481i
$853$	−470.811			−0.551948			−0.275974	−	0.961165i	$-0.589000\pi$
$853$	−470.811			−0.551948			−0.275974	+	0.961165i	$0.589000\pi$
$854$	−167.793	−	152.467i	−0.196479	−	0.178533i
$855$	1599.89	+	904.556i	1.87122	+	1.05796i
$856$	−158.053	+	211.423i	−0.184641	+	0.246989i
$857$			266.105i			0.310508i	0.987875	+	0.155254i	$0.0496196\pi$
$857$			266.105i			0.310508i	−0.987875	+	0.155254i	$0.950380\pi$
$858$	−13.7581	−	12.5015i	−0.0160351	−	0.0145705i
$859$	1442.02			1.67872			0.839360	−	0.543576i	$-0.182930\pi$
$859$	1442.02			1.67872			0.839360	+	0.543576i	$0.182930\pi$
$860$	170.154	+	75.7701i	0.197854	+	0.0881048i
$861$		−	553.681i		−	0.643067i
$862$	128.503	+	116.766i	0.149076	+	0.135459i
$863$	364.495			0.422358			0.211179	−	0.977447i	$-0.432270\pi$
$863$	364.495			0.422358			0.211179	+	0.977447i	$0.432270\pi$
$864$	647.554	+	393.734i	0.749484	+	0.455711i
$865$	−237.889	−	134.499i	−0.275016	−	0.155490i
$866$	−731.242	−	664.451i	−0.844391	−	0.767265i
$867$		−	1359.82i		−	1.56842i
$868$	−672.852	+	64.5466i	−0.775176	+	0.0743625i
$869$		−	47.5711i		−	0.0547424i
$870$	1896.76	−	625.702i	2.18019	−	0.719198i
$871$			311.696i			0.357860i
$872$	869.645	−	1163.30i	0.997299	−	1.33406i
$873$		−	1382.29i		−	1.58338i
$874$	−345.066	+	379.752i	−0.394812	+	0.434499i
$875$	−25.9675	−	959.338i	−0.0296771	−	1.09639i
$876$	−152.636	−	1591.12i	−0.174242	−	1.81635i
$877$	−77.4289			−0.0882883			−0.0441442	−	0.999025i	$-0.514056\pi$
$877$	−77.4289			−0.0882883			−0.0441442	+	0.999025i	$0.514056\pi$
$878$	776.659	+	705.719i	0.884577	+	0.803781i
$879$			1552.09i			1.76574i
$880$	−35.8140	−	11.9998i	−0.0406977	−	0.0136362i
$881$	724.932			0.822851			0.411426	−	0.911443i	$-0.365031\pi$
$881$	724.932			0.822851			0.411426	+	0.911443i	$0.365031\pi$
$882$	186.505	−	205.252i	0.211457	−	0.232713i
$883$		−	493.342i		−	0.558711i	−0.960188	−	0.279356i	$-0.909879\pi$
$883$		−	493.342i		−	0.558711i	0.960188	−	0.279356i	$-0.0901208\pi$
$884$	−37.0093	+	3.55030i	−0.0418657	+	0.00401618i
$885$	909.915	−	1609.37i	1.02815	−	1.81850i
$886$	735.029	+	667.892i	0.829604	+	0.753828i
$887$	−1514.47			−1.70741			−0.853705	−	0.520758i	$-0.825649\pi$
$887$	−1514.47			−1.70741			−0.853705	+	0.520758i	$0.825649\pi$
$888$	−1187.25	+	1588.15i	−1.33699	+	1.78846i
$889$	−1097.59			−1.23464
$890$	812.476	−	268.019i	0.912895	−	0.301145i
$891$	5.69194			0.00638826
$892$	67.9067	+	707.879i	0.0761286	+	0.793586i
$893$	230.979			0.258655
$894$	−1233.09	+	1357.04i	−1.37929	+	1.51794i
$895$	464.876	+	262.834i	0.519414	+	0.293669i
$896$	−884.604	−	428.041i	−0.987281	−	0.477725i
$897$		−	191.601i		−	0.213602i
$898$	446.751	−	491.659i	0.497496	−	0.547505i
$899$	917.771			1.02088
$900$	−1120.73	+	829.697i	−1.24525	+	0.921885i
$901$		−	90.2359i		−	0.100151i
$902$	9.56071	−	10.5218i	0.0105995	−	0.0116649i
$903$	−342.493			−0.379284
$904$	367.108	−	491.071i	0.406093	−	0.543220i
$905$	356.276	−	630.147i	0.393675	−	0.696295i
$906$	−440.381	+	484.648i	−0.486072	+	0.534932i
$907$		−	851.570i		−	0.938887i	−0.882963	−	0.469443i	$-0.844455\pi$
$907$		−	851.570i		−	0.938887i	0.882963	−	0.469443i	$-0.155545\pi$
$908$	−809.489	+	77.6542i	−0.891508	+	0.0855223i
$909$		−	1469.79i		−	1.61693i
$910$	299.658	−	98.8510i	0.329295	−	0.108627i
$911$			517.728i			0.568308i	0.958779	+	0.284154i	$0.0917127\pi$
$911$			517.728i			0.568308i	−0.958779	+	0.284154i	$0.908287\pi$
$912$	384.078	+	1983.45i	0.421138	+	2.17483i
$913$		−	0.126031i		−	0.000138041i
$914$	374.177	+	340.000i	0.409383	+	0.371991i
$915$	−307.830	−	174.042i	−0.336426	−	0.190210i
$916$	−322.800	+	30.9662i	−0.352402	+	0.0338059i
$917$	845.585			0.922121
$918$	−72.0386	+	79.2799i	−0.0784734	+	0.0863616i
$919$		−	657.730i		−	0.715701i	−0.933779	−	0.357851i	$-0.883510\pi$
$919$		−	657.730i		−	0.715701i	0.933779	−	0.357851i	$-0.116490\pi$
$920$	−156.704	−	356.368i	−0.170330	−	0.387357i
$921$	−47.1672			−0.0512130
$922$	1232.58	+	1120.00i	1.33686	+	1.21475i
$923$		−	333.195i		−	0.360992i
$924$	69.1347	−	6.63208i	0.0748211	−	0.00717758i
$925$	−666.917	−	1108.46i	−0.720991	−	1.19833i
$926$	1148.90	−	1264.39i	1.24072	−	1.36543i
$927$	−1420.40			−1.53226
$928$	1140.10	+	693.218i	1.22856	+	0.747002i
$929$	1206.28			1.29847			0.649237	−	0.760586i	$-0.275088\pi$
$929$	1206.28			1.29847			0.649237	+	0.760586i	$0.275088\pi$
$930$	−1001.23	+	330.286i	−1.07659	+	0.355146i
$931$	262.138			0.281566
$932$	224.117	−	21.4995i	0.240469	−	0.0230681i
$933$	−960.003			−1.02894
$934$	152.055	+	138.166i	0.162799	+	0.147929i
$935$	2.62757	−	4.64740i	0.00281024	−	0.00497048i
$936$	−367.214	−	274.517i	−0.392322	−	0.293287i
$937$			216.730i			0.231302i	0.993290	+	0.115651i	$0.0368954\pi$
$937$			216.730i			0.231302i	−0.993290	+	0.115651i	$0.963105\pi$
$938$	−861.858	−	783.136i	−0.918825	−	0.834900i
$939$	1252.98			1.33438
$940$	−71.2886	+	160.090i	−0.0758389	+	0.170309i
$941$			749.322i			0.796304i	0.917320	+	0.398152i	$0.130348\pi$
$941$			749.322i			0.796304i	−0.917320	+	0.398152i	$0.869652\pi$
$942$	−1100.64	−	1000.11i	−1.16841	−	1.06169i
$943$	146.530			0.155387
$944$	1212.57	−	234.804i	1.28450	−	0.248733i
$945$	447.449	−	791.406i	0.473491	−	0.837466i
$946$	−6.50850	−	5.91402i	−0.00688002	−	0.00625160i
$947$			114.160i			0.120549i	0.998182	+	0.0602743i	$0.0191976\pi$
$947$			114.160i			0.120549i	−0.998182	+	0.0602743i	$0.980802\pi$
$948$	−184.348	−	1921.69i	−0.194460	−	2.02710i
$949$			342.872i			0.361298i
$950$	−1292.81	−	256.606i	−1.36086	−	0.270112i
$951$			1544.02i			1.62358i
$952$	83.1691	−	111.253i	0.0873625	−	0.116862i
$953$			820.680i			0.861154i	0.902554	+	0.430577i	$0.141690\pi$
$953$			820.680i			0.861154i	−0.902554	+	0.430577i	$0.858310\pi$
$954$	748.328	−	823.551i	0.784411	−	0.863261i
$955$	−518.768	+	917.548i	−0.543212	+	0.960783i
$956$	1434.35	−	137.597i	1.50037	−	0.143930i
$957$	−94.2997			−0.0985368
$958$	−397.836	−	361.498i	−0.415278	−	0.377347i
$959$		−	1730.50i		−	1.80448i
$960$	−1493.25	−	345.962i	−1.55547	−	0.360377i
$961$	476.542			0.495881
$962$	286.039	−	314.792i	0.297338	−	0.327226i
$963$		−	460.109i		−	0.477787i
$964$	75.4365	+	786.371i	0.0782536	+	0.815738i
$965$	−266.203	+	470.835i	−0.275858	+	0.487912i
$966$	529.787	+	481.397i	0.548434	+	0.498340i
$967$	1108.56			1.14639			0.573194	−	0.819420i	$-0.305704\pi$
$967$	1108.56			1.14639			0.573194	+	0.819420i	$0.305704\pi$
$968$	−773.876	−	578.524i	−0.799459	−	0.597649i
$969$	−285.560			−0.294696
$970$	310.547	+	941.397i	0.320152	+	0.970513i
$971$	−1372.41			−1.41340			−0.706698	−	0.707516i	$-0.749816\pi$
$971$	−1372.41			−1.41340			−0.706698	+	0.707516i	$0.749816\pi$
$972$	1078.63	−	103.473i	1.10970	−	0.106454i
$973$	747.916			0.768670
$974$	−677.966	+	746.115i	−0.696063	+	0.766032i
$975$	421.721	−	253.733i	0.432534	−	0.260239i
$976$	−44.9117	−	231.932i	−0.0460161	−	0.237635i
$977$			927.224i			0.949052i	0.880241	+	0.474526i	$0.157381\pi$
$977$			927.224i			0.949052i	−0.880241	+	0.474526i	$0.842619\pi$
$978$	582.900	−	641.494i	0.596012	−	0.655924i
$979$	−40.3932			−0.0412597
$980$	−80.9053	+	181.686i	−0.0825564	+	0.185394i
$981$			2531.63i			2.58066i
$982$	−174.877	+	192.455i	−0.178082	+	0.195983i
$983$	−354.106			−0.360230			−0.180115	−	0.983646i	$-0.557647\pi$
$983$	−354.106			−0.360230			−0.180115	+	0.983646i	$0.557647\pi$
$984$	345.443	−	462.089i	0.351060	−	0.469603i
$985$	−1341.88	−	758.677i	−1.36231	−	0.770230i
$986$	−126.833	+	139.582i	−0.128634	+	0.141564i
$987$		−	322.236i		−	0.326480i
$988$	−41.3826	−	431.383i	−0.0418852	−	0.436623i
$989$		−	90.6396i		−	0.0916478i
$990$	62.5219	−	20.6247i	0.0631535	−	0.0208330i
$991$		−	537.545i		−	0.542427i	−0.962519	−	0.271213i	$-0.912575\pi$
$991$		−	537.545i		−	0.542427i	0.962519	−	0.271213i	$-0.0874249\pi$
$992$	−601.817	−	365.925i	−0.606671	−	0.368876i
$993$			292.614i			0.294677i
$994$	921.305	+	837.154i	0.926866	+	0.842207i
$995$	−609.941	+	1078.81i	−0.613006	+	1.08423i
$996$	−0.488397	−	5.09119i	−0.000490359	−	0.00511164i
$997$	−441.759			−0.443088			−0.221544	−	0.975150i	$-0.571110\pi$
$997$	−441.759			−0.443088			−0.221544	+	0.975150i	$0.571110\pi$
$998$	−893.326	+	983.123i	−0.895116	+	0.985094i
$999$		−	1225.48i		−	1.22671i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	40.3.e.c.19.2	yes	8
3.2	odd	2		360.3.p.g.19.7		8
4.3	odd	2		160.3.e.c.79.7		8
5.2	odd	4		200.3.g.h.51.3		8
5.3	odd	4		200.3.g.h.51.6		8
5.4	even	2	inner	40.3.e.c.19.7	yes	8
8.3	odd	2	inner	40.3.e.c.19.8	yes	8
8.5	even	2		160.3.e.c.79.8		8
12.11	even	2		1440.3.p.g.559.8		8
15.14	odd	2		360.3.p.g.19.2		8
16.3	odd	4		1280.3.h.m.1279.2		16
16.5	even	4		1280.3.h.m.1279.3		16
16.11	odd	4		1280.3.h.m.1279.15		16
16.13	even	4		1280.3.h.m.1279.14		16
20.3	even	4		800.3.g.h.751.2		8
20.7	even	4		800.3.g.h.751.7		8
20.19	odd	2		160.3.e.c.79.2		8
24.5	odd	2		1440.3.p.g.559.1		8
24.11	even	2		360.3.p.g.19.1		8
40.3	even	4		200.3.g.h.51.5		8
40.13	odd	4		800.3.g.h.751.1		8
40.19	odd	2	inner	40.3.e.c.19.1	✓	8
40.27	even	4		200.3.g.h.51.4		8
40.29	even	2		160.3.e.c.79.1		8
40.37	odd	4		800.3.g.h.751.8		8
60.59	even	2		1440.3.p.g.559.2		8
80.19	odd	4		1280.3.h.m.1279.13		16
80.29	even	4		1280.3.h.m.1279.1		16
80.59	odd	4		1280.3.h.m.1279.4		16
80.69	even	4		1280.3.h.m.1279.16		16
120.29	odd	2		1440.3.p.g.559.7		8
120.59	even	2		360.3.p.g.19.8		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
40.3.e.c.19.1	✓	8	40.19	odd	2	inner
40.3.e.c.19.2	yes	8	1.1	even	1	trivial
40.3.e.c.19.7	yes	8	5.4	even	2	inner
40.3.e.c.19.8	yes	8	8.3	odd	2	inner
160.3.e.c.79.1		8	40.29	even	2
160.3.e.c.79.2		8	20.19	odd	2
160.3.e.c.79.7		8	4.3	odd	2
160.3.e.c.79.8		8	8.5	even	2
200.3.g.h.51.3		8	5.2	odd	4
200.3.g.h.51.4		8	40.27	even	4
200.3.g.h.51.5		8	40.3	even	4
200.3.g.h.51.6		8	5.3	odd	4
360.3.p.g.19.1		8	24.11	even	2
360.3.p.g.19.2		8	15.14	odd	2
360.3.p.g.19.7		8	3.2	odd	2
360.3.p.g.19.8		8	120.59	even	2
800.3.g.h.751.1		8	40.13	odd	4
800.3.g.h.751.2		8	20.3	even	4
800.3.g.h.751.7		8	20.7	even	4
800.3.g.h.751.8		8	40.37	odd	4
1280.3.h.m.1279.1		16	80.29	even	4
1280.3.h.m.1279.2		16	16.3	odd	4
1280.3.h.m.1279.3		16	16.5	even	4
1280.3.h.m.1279.4		16	80.59	odd	4
1280.3.h.m.1279.13		16	80.19	odd	4
1280.3.h.m.1279.14		16	16.13	even	4
1280.3.h.m.1279.15		16	16.11	odd	4
1280.3.h.m.1279.16		16	80.69	even	4
1440.3.p.g.559.1		8	24.5	odd	2
1440.3.p.g.559.2		8	60.59	even	2
1440.3.p.g.559.7		8	120.29	odd	2
1440.3.p.g.559.8		8	12.11	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:	\( N \)	\(=\)	\( 40 = 2^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	40.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.34500 + 1.48020i) q^{2} -4.79002i q^{3} +(-0.381966 - 3.98172i) q^{4} +(-4.35250 - 2.46084i) q^{5} +(7.09017 + 6.44256i) q^{6} +7.67752 q^{7} +(6.40747 + 4.79002i) q^{8} -13.9443 q^{9} +O(q^{10})\)	\(q+(-1.34500 + 1.48020i) q^{2} -4.79002i q^{3} +(-0.381966 - 3.98172i) q^{4} +(-4.35250 - 2.46084i) q^{5} +(7.09017 + 6.44256i) q^{6} +7.67752 q^{7} +(6.40747 + 4.79002i) q^{8} -13.9443 q^{9} +(9.49663 - 3.13274i) q^{10} -0.472136 q^{11} +(-19.0725 + 1.82962i) q^{12} +4.10995 q^{13} +(-10.3262 + 11.3642i) q^{14} +(-11.7875 + 20.8486i) q^{15} +(-15.7082 + 3.04176i) q^{16} -2.26154i q^{17} +(18.7550 - 20.6403i) q^{18} +26.3607 q^{19} +(-8.13587 + 18.2704i) q^{20} -36.7754i q^{21} +(0.635021 - 0.698854i) q^{22} +9.73249 q^{23} +(22.9443 - 30.6919i) q^{24} +(12.8885 + 21.4216i) q^{25} +(-5.52786 + 6.08353i) q^{26} +23.6832i q^{27} +(-2.93255 - 30.5697i) q^{28} +41.6971i q^{29} +(-15.0059 - 45.4890i) q^{30} -22.0104i q^{31} +(16.6251 - 27.3424i) q^{32} +2.26154i q^{33} +(3.34752 + 3.04176i) q^{34} +(-33.4164 - 18.8931i) q^{35} +(5.32624 + 55.5222i) q^{36} -51.7449 q^{37} +(-35.4550 + 39.0190i) q^{38} -19.6867i q^{39} +(-16.1011 - 36.6163i) q^{40} +15.0557 q^{41} +(54.4349 + 49.4629i) q^{42} -9.31310i q^{43} +(0.180340 + 1.87991i) q^{44} +(60.6925 + 34.3146i) q^{45} +(-13.0902 + 14.4060i) q^{46} +8.76226 q^{47} +(14.5701 + 75.2426i) q^{48} +9.94427 q^{49} +(-49.0433 - 9.73442i) q^{50} -10.8328 q^{51} +(-1.56986 - 16.3647i) q^{52} +39.9002 q^{53} +(-35.0557 - 31.8538i) q^{54} +(2.05497 + 1.16185i) q^{55} +(49.1935 + 36.7754i) q^{56} -126.268i q^{57} +(-61.7200 - 56.0825i) q^{58} -77.1935 q^{59} +(87.5156 + 38.9709i) q^{60} +14.7650i q^{61} +(32.5797 + 29.6039i) q^{62} -107.057 q^{63} +(18.1115 + 61.3838i) q^{64} +(-17.8885 - 10.1139i) q^{65} +(-3.34752 - 3.04176i) q^{66} +75.8395i q^{67} +(-9.00482 + 0.863831i) q^{68} -46.6188i q^{69} +(72.9105 - 24.0517i) q^{70} -81.0705i q^{71} +(-89.3476 - 66.7933i) q^{72} +83.4249i q^{73} +(69.5967 - 76.5927i) q^{74} +(102.610 - 61.7364i) q^{75} +(-10.0689 - 104.961i) q^{76} -3.62483 q^{77} +(29.1402 + 26.4786i) q^{78} +100.757i q^{79} +(75.8553 + 25.4161i) q^{80} -12.0557 q^{81} +(-20.2499 + 22.2854i) q^{82} +0.266939i q^{83} +(-146.430 + 14.0470i) q^{84} +(-5.56528 + 9.84336i) q^{85} +(13.7852 + 12.5261i) q^{86} +199.730 q^{87} +(-3.02520 - 2.26154i) q^{88} +85.5542 q^{89} +(-132.424 + 43.6838i) q^{90} +31.5542 q^{91} +(-3.71748 - 38.7521i) q^{92} -105.430 q^{93} +(-11.7852 + 12.9699i) q^{94} +(-114.735 - 64.8694i) q^{95} +(-130.971 - 79.6344i) q^{96} +99.1297i q^{97} +(-13.3750 + 14.7195i) q^{98} +6.58359 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 12 q^{4} + 12 q^{6} - 40 q^{9}+O(q^{10}) \) 8 * q - 12 * q^4 + 12 * q^6 - 40 * q^9	\( 8 q - 12 q^{4} + 12 q^{6} - 40 q^{9} + 20 q^{10} + 32 q^{11} - 20 q^{14} - 72 q^{16} + 32 q^{19} + 20 q^{20} + 112 q^{24} - 40 q^{25} - 80 q^{26} + 100 q^{30} + 152 q^{34} - 160 q^{35} - 20 q^{36} - 80 q^{40} + 192 q^{41} - 88 q^{44} - 60 q^{46} + 8 q^{49} - 200 q^{50} + 128 q^{51} - 352 q^{54} - 224 q^{59} + 360 q^{60} + 288 q^{64} - 152 q^{66} + 340 q^{70} + 360 q^{74} + 320 q^{75} + 152 q^{76} - 280 q^{80} - 168 q^{81} - 760 q^{84} + 316 q^{86} + 112 q^{89} - 340 q^{90} - 320 q^{91} - 300 q^{94} - 368 q^{96} + 160 q^{99}+O(q^{100}) \) 8 * q - 12 * q^4 + 12 * q^6 - 40 * q^9 + 20 * q^10 + 32 * q^11 - 20 * q^14 - 72 * q^16 + 32 * q^19 + 20 * q^20 + 112 * q^24 - 40 * q^25 - 80 * q^26 + 100 * q^30 + 152 * q^34 - 160 * q^35 - 20 * q^36 - 80 * q^40 + 192 * q^41 - 88 * q^44 - 60 * q^46 + 8 * q^49 - 200 * q^50 + 128 * q^51 - 352 * q^54 - 224 * q^59 + 360 * q^60 + 288 * q^64 - 152 * q^66 + 340 * q^70 + 360 * q^74 + 320 * q^75 + 152 * q^76 - 280 * q^80 - 168 * q^81 - 760 * q^84 + 316 * q^86 + 112 * q^89 - 340 * q^90 - 320 * q^91 - 300 * q^94 - 368 * q^96 + 160 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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