LMFDB - Embedded newform 40.3.e.c.19.7

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			19.7
Root			$-1.34500 - 1.48020i$ of defining polynomial
Character	$\chi$	$=$	40.19
Dual form			40.3.e.c.19.8

$q$-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} +(2.21158 - 9.75238i) 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} +(-11.4609 - 16.3905i) 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} +(46.7141 + 10.5935i) 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} +(-39.6760 - 5.08080i) 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} +(-14.3732 - 47.8896i) 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} +(78.5107 - 54.8978i) 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} +(-16.9794 + 74.8741i) 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} +(-60.8847 + 51.8946i) 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} +(-30.8388 + 135.990i) 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	$0.294286\pi$
$3$			4.79002i			1.59667i	−0.602212	+	0.798336i	$0.705714\pi$
$4$	−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	$-0.684761\pi$
$7$	−7.67752			−1.09679			−0.548394	+	0.836220i	$0.684761\pi$
$8$	−6.40747	−	4.79002i	−0.800934	−	0.598752i
$9$	−13.9443			−1.54936
$10$	2.21158	−	9.75238i	0.221158	−	0.975238i
$11$	−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	$-0.550529\pi$
$13$	−4.10995			−0.316150			−0.158075	+	0.987427i	$0.550529\pi$
$14$	−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	$0.0211883\pi$
$17$			2.26154i			0.133032i	−0.997785	+	0.0665159i	$0.978812\pi$
$18$	−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	$0.255978\pi$
$20$	−11.4609	−	16.3905i	−0.573044	−	0.819525i
$21$		−	36.7754i		−	1.75121i
$22$	−0.635021	+	0.698854i	−0.0288646	+	0.0317661i
$23$	−9.73249			−0.423152			−0.211576	−	0.977362i	$-0.567860\pi$
$23$	−9.73249			−0.423152			−0.211576	+	0.977362i	$0.567860\pi$
$24$	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	$0.744639\pi$
$30$	46.7141	+	10.5935i	1.55714	+	0.353116i
$31$		−	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	$-0.253515\pi$
$37$	51.7449			1.39851			0.699256	+	0.714872i	$0.253515\pi$
$38$	35.4550	−	39.0190i	0.933027	−	1.02682i
$39$		−	19.6867i		−	0.504787i
$40$	−39.6760	−	5.08080i	−0.991900	−	0.127020i
$41$	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	$0.0345381\pi$
$43$			9.31310i			0.216584i	−0.994119	+	0.108292i	$0.965462\pi$
$44$	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	$-0.529715\pi$
$47$	−8.76226			−0.186431			−0.0932156	+	0.995646i	$0.529715\pi$
$48$	−14.5701	−	75.2426i	−0.303544	−	1.56755i
$49$	9.94427			0.202944
$50$	−14.3732	−	47.8896i	−0.287463	−	0.957792i
$51$	−10.8328			−0.212408
$52$	1.56986	+	16.3647i	0.0301896	+	0.314705i
$53$	−39.9002			−0.752834			−0.376417	−	0.926450i	$-0.622844\pi$
$53$	−39.9002			−0.752834			−0.376417	+	0.926450i	$0.622844\pi$
$54$	−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	$0.726987\pi$
$60$	78.5107	−	54.8978i	1.30851	−	0.914964i
$61$			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	$-0.808503\pi$
$67$		−	75.8395i		−	1.13193i	0.824428	−	0.565966i	$-0.191497\pi$
$68$	9.00482	−	0.863831i	0.132424	−	0.0127034i
$69$		−	46.6188i		−	0.675635i
$70$	−16.9794	+	74.8741i	−0.242563	+	1.06963i
$71$		−	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	$-0.806399\pi$
$73$		−	83.4249i		−	1.14281i	0.820669	−	0.571403i	$-0.193601\pi$
$74$	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	$0.779884\pi$
$80$	−60.8847	+	51.8946i	−0.761059	+	0.648683i
$81$	−12.0557			−0.148836
$82$	20.2499	−	22.2854i	0.246950	−	0.271774i
$83$		−	0.266939i		−	0.00321613i	−0.999999	−	0.00160806i	$-0.999488\pi$
$83$		−	0.266939i		−	0.00321613i	0.999999	−	0.00160806i	$-0.000511863\pi$
$84$	−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	$0.340404\pi$
$90$	−30.8388	+	135.990i	−0.342653	+	1.51100i
$91$	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	$-0.829284\pi$
$97$		−	99.1297i		−	1.02196i	0.859594	−	0.510978i	$-0.170716\pi$
$98$	13.3750	−	14.7195i	0.136480	−	0.150199i
$99$	6.58359			0.0665009
$100$	−90.2179	−	43.1363i	−0.902179	−	0.431363i
$101$			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	$-0.664641\pi$
$103$	−101.863			−0.988958			−0.494479	+	0.869190i	$0.664641\pi$
$104$	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	$-0.950724\pi$
$107$		−	32.9962i		−	0.308376i	0.988042	−	0.154188i	$-0.0492762\pi$
$108$	−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	$-0.313272\pi$
$110$	−1.04416	+	4.60445i	−0.00949240	+	0.0418586i
$111$			247.859i			2.23296i
$112$	120.600	−	23.3532i	1.07679	−	0.208511i
$113$			76.6403i			0.678233i	0.940744	+	0.339116i	$0.110128\pi$
$113$			76.6403i			0.678233i	−0.940744	+	0.339116i	$0.889872\pi$
$114$	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
$120$	24.3371	−	190.049i	0.202809	−	1.58374i
$121$	−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	$-0.309708\pi$
$127$	142.962			1.12569			0.562843	+	0.826564i	$0.309708\pi$
$128$	115.220	+	55.7526i	0.900156	+	0.435567i
$129$	−44.6099			−0.345813
$130$	−9.08946	+	40.0818i	−0.0699189	+	0.308321i
$131$	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	$0.307488\pi$
$137$			225.398i			1.64524i	−0.568592	+	0.822620i	$0.692512\pi$
$138$	−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	$0.386039\pi$
$140$	87.9911	+	125.838i	0.628508	+	0.898845i
$141$		−	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	$0.777992\pi$
$150$	229.392	−	68.8477i	1.52928	−	0.458984i
$151$			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	$-0.335396\pi$
$157$	155.235			0.988756			0.494378	+	0.869247i	$0.335396\pi$
$158$	149.141	+	135.518i	0.943928	+	0.857710i
$159$		−	191.123i		−	1.20203i
$160$	−5.07544	+	159.919i	−0.0317215	+	0.999497i
$161$	74.7214			0.464108
$162$	−16.2149	+	17.8449i	−0.100092	+	0.110153i
$163$			90.4765i			0.555070i	0.960715	+	0.277535i	$0.0895175\pi$
$163$			90.4765i			0.555070i	−0.960715	+	0.277535i	$0.910482\pi$
$164$	−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	$-0.402436\pi$
$167$	100.778			0.603461			0.301730	+	0.953393i	$0.402436\pi$
$168$	−176.155	+	235.638i	−1.04854	+	1.40261i
$169$	−152.108			−0.900049
$170$	22.0554	+	5.00157i	0.129738	+	0.0294210i
$171$	−367.580			−2.14959
$172$	37.0822	−	3.55729i	0.215594	−	0.0206819i
$173$	−54.6556			−0.315928			−0.157964	−	0.987445i	$-0.550493\pi$
$173$	−54.6556			−0.315928			−0.157964	+	0.987445i	$0.550493\pi$
$174$	−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	$0.596434\pi$
$180$	159.814	+	228.553i	0.887854	+	1.26974i
$181$			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
$190$	58.2986	−	257.079i	0.306835	−	1.35305i
$191$		−	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	$0.0904168\pi$
$193$			108.176i			0.560496i	−0.959928	+	0.280248i	$0.909583\pi$
$194$	−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	$-0.786049\pi$
$197$	−308.300			−1.56497			−0.782487	+	0.622667i	$0.786049\pi$
$198$	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	$-0.213989\pi$
$200$	−185.193	+	75.5221i	−0.925965	+	0.377610i
$201$	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
$210$	−358.648	−	81.3317i	−1.70785	−	0.387294i
$211$	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
$220$	5.41109	+	7.73854i	0.0245959	+	0.0351752i
$221$		−	9.29480i		−	0.0420579i
$222$	366.880	+	333.370i	1.65261	+	1.50167i
$223$	177.782			0.797229			0.398615	−	0.917118i	$-0.369491\pi$
$223$	177.782			0.797229			0.398615	+	0.917118i	$0.369491\pi$
$224$	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	$0.147792\pi$
$227$			203.301i			0.895601i	−0.894134	+	0.447800i	$0.852208\pi$
$228$	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	$-0.0566425\pi$
$230$	−21.5241	+	94.9149i	−0.0935832	+	0.412674i
$231$			17.3630i			0.0751645i
$232$	199.730	−	267.173i	0.860905	−	1.15161i
$233$		−	56.2864i		−	0.241573i	−0.992679	−	0.120786i	$-0.961458\pi$
$233$		−	56.2864i		−	0.241573i	0.992679	−	0.120786i	$-0.0385416\pi$
$234$	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	$0.728301\pi$
$240$	−248.576	−	291.639i	−1.03573	−	1.21516i
$241$	−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
$250$	−180.408	−	173.070i	−0.721631	−	0.692278i
$251$	−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	$-0.656413\pi$
$257$		−	453.183i		−	1.76336i	0.471849	−	0.881679i	$-0.343587\pi$
$258$	−60.0002	+	66.0314i	−0.232559	+	0.255936i
$259$	−397.272			−1.53387
$260$	47.1036	+	67.3640i	0.181168	+	0.259092i
$261$		−	581.436i		−	2.22772i
$262$	148.135	−	163.026i	0.565401	−	0.622235i
$263$	21.0921			0.0801981			0.0400990	−	0.999196i	$-0.487233\pi$
$263$	21.0921			0.0801981			0.0400990	+	0.999196i	$0.487233\pi$
$264$	−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	$0.945050\pi$
$270$	−230.967	−	52.3771i	−0.855434	−	0.193989i
$271$		−	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	$-0.459600\pi$
$277$	70.1251			0.253159			0.126580	+	0.991956i	$0.459600\pi$
$278$	131.025	−	144.195i	0.471312	−	0.518689i
$279$			306.919i			1.10007i
$280$	304.613	+	39.0079i	1.08790	+	0.139314i
$281$	−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	$0.346374\pi$
$283$			501.350i			1.77156i	−0.464110	+	0.885778i	$0.653626\pi$
$284$	−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
$290$	406.646	+	92.2163i	1.40223	+	0.317987i
$291$	474.833			1.63173
$292$	−332.175	+	31.8655i	−1.13758	+	0.109128i
$293$	324.026			1.10589			0.552945	−	0.833218i	$-0.313504\pi$
$293$	324.026			1.10589			0.552945	+	0.833218i	$0.313504\pi$
$294$	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
$300$	206.623	−	432.145i	0.688745	−	1.44048i
$301$		−	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	$0.00510509\pi$
$307$			9.84697i			0.0320748i	−0.999871	+	0.0160374i	$0.994895\pi$
$308$	−1.38456	−	14.4331i	−0.00449533	−	0.0468606i
$309$		−	487.924i		−	1.57904i
$310$	−214.654	−	48.6777i	−0.692432	−	0.157025i
$311$		−	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	$-0.862779\pi$
$313$		−	261.582i		−	0.835727i	0.908510	−	0.417863i	$-0.137221\pi$
$314$	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	$-0.330228\pi$
$317$	322.341			1.01685			0.508425	+	0.861107i	$0.330228\pi$
$318$	−282.899	−	257.059i	−0.889620	−	0.808363i
$319$		−	19.6867i		−	0.0617138i
$320$	229.886	+	222.604i	0.718393	+	0.695637i
$321$	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
$330$	−22.0554	−	5.00157i	−0.0668345	−	0.0151563i
$331$	−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	$-0.945441\pi$
$337$		−	114.960i		−	0.341129i	0.985347	−	0.170564i	$-0.0545591\pi$
$338$	−204.585	+	225.150i	−0.605282	+	0.666125i
$339$	−367.108			−1.08292
$340$	37.0677	−	25.9192i	0.109023	−	0.0762331i
$341$			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	$-0.933485\pi$
$347$		−	143.967i		−	0.414892i	0.978246	−	0.207446i	$-0.0665151\pi$
$348$	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	$-0.0164028\pi$
$350$	110.350	+	367.673i	0.315286	+	1.05049i
$351$			97.3365i			0.277312i
$352$	7.84930	−	12.9093i	0.0222991	−	0.0366742i
$353$			252.536i			0.715400i	0.933837	+	0.357700i	$0.116439\pi$
$353$			252.536i			0.715400i	−0.933837	+	0.357700i	$0.883561\pi$
$354$	−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	$0.689757\pi$
$360$	553.253	+	70.8480i	1.53681	+	0.196800i
$361$	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	$-0.538650\pi$
$367$	−88.9062			−0.242251			−0.121126	+	0.992637i	$0.538650\pi$
$368$	152.880	−	29.6039i	0.415435	−	0.0804455i
$369$	−209.941			−0.568946
$370$	114.438	−	504.636i	0.309291	−	1.36388i
$371$	306.334			0.825699
$372$	−40.2708	−	419.794i	−0.108255	−	1.12848i
$373$	−83.6542			−0.224274			−0.112137	−	0.993693i	$-0.535770\pi$
$373$	−83.6542			−0.224274			−0.112137	+	0.993693i	$0.535770\pi$
$374$	−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	$0.557053\pi$
$380$	−302.117	−	432.064i	−0.795044	−	1.13701i
$381$			684.791i			1.79735i
$382$	−312.039	−	283.538i	−0.816857	−	0.742246i
$383$	−498.526			−1.30164			−0.650818	−	0.759234i	$-0.725574\pi$
$383$	−498.526			−1.30164			−0.650818	+	0.759234i	$0.725574\pi$
$384$	−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	$0.870250\pi$
$390$	−191.992	−	43.5387i	−0.492288	−	0.111638i
$391$		−	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	$-0.622328\pi$
$397$	−297.682			−0.749828			−0.374914	+	0.927060i	$0.622328\pi$
$398$	−366.880	−	333.370i	−0.921810	−	0.837612i
$399$		−	969.426i		−	2.42964i
$400$	−137.296	+	375.699i	−0.343241	+	0.939247i
$401$	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	$0.318116\pi$
$410$	33.2969	−	146.829i	0.0812119	−	0.358120i
$411$	−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	$0.279001\pi$
$420$	−602.768	+	421.479i	−1.43516	+	1.00352i
$421$			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
$430$	90.8249	+	20.5966i	0.211221	+	0.0478991i
$431$		−	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	$-0.806766\pi$
$433$		−	494.017i		−	1.14092i	0.821327	−	0.570458i	$-0.193234\pi$
$434$	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	$-0.203882\pi$
$440$	18.7325	+	2.39883i	0.0425738	+	0.00545188i
$441$	−138.666			−0.314435
$442$	−13.7581	−	12.5015i	−0.0311270	−	0.0282839i
$443$			496.575i			1.12094i	0.828176	+	0.560469i	$0.189379\pi$
$443$			496.575i			1.12094i	−0.828176	+	0.560469i	$0.810621\pi$
$444$	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	$0.620603\pi$
$450$	200.423	+	667.785i	0.445385	+	1.48397i
$451$	−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	$0.0891990\pi$
$457$			252.788i			0.553147i	−0.960993	+	0.276574i	$0.910801\pi$
$458$	−120.000	−	109.040i	−0.262010	−	0.238078i
$459$	53.5604			0.116689
$460$	111.543	+	159.520i	0.242485	+	0.346783i
$461$		−	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	$-0.126169\pi$
$463$	854.205			1.84494			0.922468	+	0.386074i	$0.126169\pi$
$464$	−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	$0.0350802\pi$
$467$			102.726i			0.219970i	−0.993933	+	0.109985i	$0.964920\pi$
$468$	−21.8905	−	228.193i	−0.0467747	−	0.487592i
$469$			582.259i			1.24149i
$470$	−19.3784	+	85.4529i	−0.0412307	+	0.181815i
$471$			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	$0.909481\pi$
$480$	−766.017	−	24.3114i	−1.59587	−	0.0506489i
$481$	−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	$-0.673145\pi$
$487$	−504.065			−1.03504			−0.517520	+	0.855671i	$0.673145\pi$
$488$	70.7248	−	94.6066i	0.144928	−	0.193866i
$489$	−433.384			−0.886266
$490$	21.9925	−	96.9803i	0.0448827	−	0.197919i
$491$	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	$0.268212\pi$
$500$	−498.825	+	34.2610i	−0.997650	+	0.0685220i
$501$			482.728i			0.963529i
$502$	−239.895	+	264.009i	−0.477878	+	0.525914i
$503$	550.015			1.09347			0.546735	−	0.837306i	$-0.315871\pi$
$503$	550.015			1.09347			0.546735	+	0.837306i	$0.315871\pi$
$504$	−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	$-0.111666\pi$
$510$	−23.9576	+	105.646i	−0.0469757	+	0.207149i
$511$			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
$520$	163.066	+	20.8818i	0.313589	+	0.0401573i
$521$	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	$-0.804416\pi$
$523$		−	603.023i		−	1.15301i	0.817094	−	0.576504i	$-0.195584\pi$
$524$	−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
$530$	−88.2423	+	389.122i	−0.166495	+	0.734192i
$531$	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
$540$	−388.178	+	271.430i	−0.718849	+	0.502648i
$541$		−	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	$-0.840936\pi$
$547$		−	524.218i		−	0.958350i	0.877719	−	0.479175i	$-0.159064\pi$
$548$	897.471	−	86.0943i	1.63772	−	0.157106i
$549$		−	205.888i		−	0.375023i
$550$	6.78608	+	22.6104i	0.0123383	+	0.0411098i
$551$			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	$-0.322497\pi$
$557$	589.515			1.05837			0.529187	+	0.848505i	$0.322497\pi$
$558$	454.301	+	412.805i	0.814159	+	0.739795i
$559$		−	38.2763i		−	0.0684728i
$560$	467.443	−	398.422i	0.834720	−	0.711468i
$561$	5.11456			0.00911687
$562$	−680.931	+	749.378i	−1.21162	+	1.33341i
$563$		−	557.763i		−	0.990698i	−0.868694	−	0.495349i	$-0.835040\pi$
$563$		−	557.763i		−	0.990698i	0.868694	−	0.495349i	$-0.164960\pi$
$564$	−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	$0.658241\pi$
$570$	1231.41	+	279.252i	2.16038	+	0.489915i
$571$	−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	$0.270013\pi$
$577$			865.659i			1.50027i	−0.661282	+	0.750137i	$0.729987\pi$
$578$	381.825	−	420.206i	0.660597	−	0.727001i
$579$	−518.164			−0.894929
$580$	683.436	−	477.886i	1.17834	−	0.823941i
$581$			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	$0.160468\pi$
$587$			567.091i			0.966083i	−0.875597	+	0.483041i	$0.839532\pi$
$588$	189.662	−	18.1943i	0.322555	−	0.0309427i
$589$		−	580.209i		−	0.985075i
$590$	−170.719	+	752.820i	−0.289355	+	1.27597i
$591$		−	1476.76i		−	2.49875i
$592$	−812.820	+	157.396i	−1.37301	+	0.265871i
$593$			421.774i			0.711254i	0.934628	+	0.355627i	$0.115733\pi$
$593$			421.774i			0.711254i	−0.934628	+	0.355627i	$0.884267\pi$
$594$	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	$0.967944\pi$
$600$	−361.752	−	887.077i	−0.602920	−	1.47846i
$601$	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	$-0.530362\pi$
$607$	−115.621			−0.190479			−0.0952396	+	0.995454i	$0.530362\pi$
$608$	−438.248	+	720.764i	−0.720803	+	1.18547i
$609$	1533.43			2.51795
$610$	143.994	+	32.6540i	0.236056	+	0.0535311i
$611$	36.0124			0.0589401
$612$	−125.566	+	12.0455i	−0.205173	+	0.0196822i
$613$	−1095.63			−1.78733			−0.893663	−	0.448738i	$-0.851874\pi$
$613$	−1095.63			−1.78733			−0.893663	+	0.448738i	$0.851874\pi$
$614$	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	$-0.802718\pi$
$617$		−	716.775i		−	1.16171i	0.814007	−	0.580855i	$-0.197282\pi$
$618$	−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	$0.469463\pi$
$620$	−360.761	+	252.259i	−0.581873	+	0.406869i
$621$			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
$630$	236.766	−	1044.06i	0.375818	−	1.65725i
$631$		−	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
$640$	638.693	−	40.8748i	0.997958	−	0.0638669i
$641$	−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	$0.236124\pi$
$643$			868.847i			1.35124i	−0.737250	+	0.675620i	$0.763876\pi$
$644$	−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	$-0.491357\pi$
$647$	35.1333			0.0543019			0.0271510	+	0.999631i	$0.491357\pi$
$648$	77.2468	+	57.7472i	0.119208	+	0.0891160i
$649$	36.4458			0.0561569
$650$	59.0729	+	196.824i	0.0908813	+	0.302806i
$651$	−809.443			−1.24338
$652$	360.252	−	34.5589i	0.552534	−	0.0530045i
$653$	−580.068			−0.888313			−0.444157	−	0.895949i	$-0.646497\pi$
$653$	−580.068			−0.888313			−0.444157	+	0.895949i	$0.646497\pi$
$654$	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	$0.771517\pi$
$660$	−37.0677	+	25.9192i	−0.0561633	+	0.0392716i
$661$		−	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
$670$	−739.615	−	167.725i	−1.10390	−	0.250335i
$671$		−	6.97110i		−	0.0103891i
$672$	1005.53	+	611.395i	1.49632	+	0.909813i
$673$		−	189.591i		−	0.281711i	−0.990030	−	0.140855i	$-0.955015\pi$
$673$		−	189.591i		−	0.281711i	0.990030	−	0.140855i	$-0.0449852\pi$
$674$	−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	$-0.577688\pi$
$677$	−327.192			−0.483297			−0.241649	+	0.970364i	$0.577688\pi$
$678$	−493.760	+	543.393i	−0.728259	+	0.801464i
$679$			761.070i			1.12087i
$680$	11.4904	−	89.7289i	0.0168977	−	0.131954i
$681$	−973.817			−1.42998
$682$	15.3821	+	13.9771i	0.0225544	+	0.0204943i
$683$		−	673.539i		−	0.986148i	−0.869987	−	0.493074i	$-0.835873\pi$
$683$		−	673.539i		−	0.986148i	0.869987	−	0.493074i	$-0.164127\pi$
$684$	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
$690$	−454.644	−	103.101i	−0.658905	−	0.149422i
$691$	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
$700$	692.649	+	331.179i	0.989499	+	0.473113i
$701$			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	$-0.238185\pi$
$710$	−790.631	−	179.294i	−1.11356	−	0.252526i
$711$		−	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	$-0.215248\pi$
$720$	848.993	−	723.633i	1.17916	−	1.00505i
$721$	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	$-0.714940\pi$
$727$	−908.888			−1.25019			−0.625095	+	0.780549i	$0.714940\pi$
$728$	−202.183	−	151.145i	−0.277723	−	0.207617i
$729$	1189.09			1.63113
$730$	−813.591	−	184.500i	−1.11451	−	0.252740i
$731$	−21.0619			−0.0288125
$732$	27.0145	+	281.606i	0.0369050	+	0.384708i
$733$	−433.283			−0.591109			−0.295554	−	0.955326i	$-0.595504\pi$
$733$	−433.283			−0.591109			−0.295554	+	0.955326i	$0.595504\pi$
$734$	−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	$0.704655\pi$
$740$	−593.042	−	848.124i	−0.801408	−	1.14611i
$741$		−	518.955i		−	0.700344i
$742$	412.019	−	453.435i	0.555281	−	0.611099i
$743$	−895.305			−1.20499			−0.602493	−	0.798124i	$-0.705826\pi$
$743$	−895.305			−1.20499			−0.602493	+	0.798124i	$0.705826\pi$
$744$	−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
$750$	829.006	−	864.156i	1.10534	−	1.15221i
$751$			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	$-0.410153\pi$
$757$	421.694			0.557060			0.278530	+	0.960428i	$0.410153\pi$
$758$	−181.756	+	200.026i	−0.239783	+	0.263886i
$759$			22.0104i			0.0289992i
$760$	−1045.89	−	133.933i	−1.37617	−	0.176228i
$761$	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	$0.586798\pi$
$770$	8.01659	−	35.3507i	0.0104112	−	0.0459101i
$771$	2170.76			2.81551
$772$	430.726	−	41.3195i	0.557935	−	0.0535226i
$773$	727.056			0.940564			0.470282	−	0.882516i	$-0.344152\pi$
$773$	727.056			0.940564			0.470282	+	0.882516i	$0.344152\pi$
$774$	−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
$780$	−322.675	+	225.627i	−0.413686	+	0.289265i
$781$			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	$0.227100\pi$
$787$			1030.11i			1.30890i	−0.756104	+	0.654451i	$0.772900\pi$
$788$	117.760	+	1227.56i	0.149442	+	1.55782i
$789$			101.032i			0.128050i
$790$	982.623	+	222.832i	1.24383	+	0.282066i
$791$		−	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	$-0.425187\pi$
$797$	371.202			0.465750			0.232875	+	0.972507i	$0.425187\pi$
$798$	−1434.94	−	1303.87i	−1.79817	−	1.63393i
$799$		−	19.8162i		−	0.0248013i
$800$	371.445	+	708.540i	0.464307	+	0.885675i
$801$	−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	$0.484693\pi$
$810$	−26.6622	+	117.572i	−0.0329162	+	0.145151i
$811$	−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
$820$	−172.552	−	246.771i	−0.210429	−	0.300940i
$821$		−	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	$-0.818433\pi$
$823$	−1385.41			−1.68336			−0.841681	+	0.539976i	$0.818433\pi$
$824$	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	$0.0500303\pi$
$827$			258.898i			0.313057i	−0.987673	+	0.156529i	$0.949970\pi$
$828$	−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	$0.713351\pi$
$830$	−2.60329	−	0.590355i	−0.00313649	−	0.000711271i
$831$			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	$-0.159260\pi$
$840$	−186.849	+	1459.10i	−0.222439	+	1.73703i
$841$	−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
$850$	108.304	−	32.5055i	0.127417	−	0.0382417i
$851$	−503.607			−0.591782
$852$	−148.329	−	1546.22i	−0.174095	−	1.81481i
$853$	470.811			0.551948			0.275974	−	0.961165i	$-0.411000\pi$
$853$	470.811			0.551948			0.275974	+	0.961165i	$0.411000\pi$
$854$	−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	$-0.950380\pi$
$857$		−	266.105i		−	0.310508i	0.987875	−	0.155254i	$-0.0496196\pi$
$858$	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	$0.182930\pi$
$860$	152.646	−	106.736i	0.177496	−	0.124112i
$861$		−	553.681i		−	0.643067i
$862$	−128.503	−	116.766i	−0.149076	−	0.135459i
$863$	−364.495			−0.422358			−0.211179	−	0.977447i	$-0.567730\pi$
$863$	−364.495			−0.422358			−0.211179	+	0.977447i	$0.567730\pi$
$864$	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
$870$	−441.718	+	1947.84i	−0.507722	+	2.23890i
$871$			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	$-0.485944\pi$
$877$	77.4289			0.0882883			0.0441442	+	0.999025i	$0.485944\pi$
$878$	−776.659	−	705.719i	−0.884577	−	0.803781i
$879$			1552.09i			1.76574i
$880$	28.7459	−	24.5013i	0.0326657	−	0.0278424i
$881$	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	$0.0901208\pi$
$883$			493.342i			0.558711i	−0.960188	+	0.279356i	$0.909879\pi$
$884$	−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	$-0.174351\pi$
$887$	1514.47			1.70741			0.853705	+	0.520758i	$0.174351\pi$
$888$	1187.25	−	1588.15i	1.33699	−	1.78846i
$889$	−1097.59			−1.23464
$890$	189.210	−	834.357i	0.212595	−	0.937480i
$891$	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
$900$	1258.02	+	601.504i	1.39780	+	0.668337i
$901$		−	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	$0.155545\pi$
$907$			851.570i			0.938887i	−0.882963	+	0.469443i	$0.844455\pi$
$908$	809.489	−	77.6542i	0.891508	−	0.0855223i
$909$		−	1469.79i		−	1.61693i
$910$	69.7844	−	307.728i	0.0766862	−	0.338163i
$911$			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	$-0.116490\pi$
$920$	386.146	+	49.4488i	0.419724	+	0.0537487i
$921$	−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	$0.275088\pi$
$930$	233.167	−	1028.20i	0.250717	−	1.10559i
$931$	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	$-0.963105\pi$
$937$		−	216.730i		−	0.231302i	0.993290	−	0.115651i	$-0.0368954\pi$
$938$	861.858	+	783.136i	0.918825	+	0.834900i
$939$	1252.98			1.33438
$940$	100.423	+	143.618i	0.106833	+	0.152785i
$941$			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	$-0.980802\pi$
$947$		−	114.160i		−	0.120549i	0.998182	−	0.0602743i	$-0.0191976\pi$
$948$	184.348	+	1921.69i	0.194460	+	2.02710i
$949$			342.872i			0.361298i
$950$	−378.886	−	1262.40i	−0.398827	−	1.32884i
$951$			1544.02i			1.62358i
$952$	−83.1691	+	111.253i	−0.0873625	+	0.116862i
$953$		−	820.680i		−	0.861154i	−0.902554	−	0.430577i	$-0.858310\pi$
$953$		−	820.680i		−	0.861154i	0.902554	−	0.430577i	$-0.141690\pi$
$954$	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
$960$	−1066.28	+	1101.16i	−1.11070	+	1.14704i
$961$	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	$-0.694296\pi$
$967$	−1108.56			−1.14639			−0.573194	+	0.819420i	$0.694296\pi$
$968$	773.876	+	578.524i	0.799459	+	0.597649i
$969$	−285.560			−0.294696
$970$	−966.750	−	219.233i	−0.996650	−	0.226013i
$971$	−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	$-0.842619\pi$
$977$		−	927.224i		−	0.949052i	0.880241	−	0.474526i	$-0.157381\pi$
$978$	−582.900	+	641.494i	−0.596012	+	0.655924i
$979$	−40.3932			−0.0412597
$980$	−113.970	−	162.991i	−0.116296	−	0.166318i
$981$			2531.63i			2.58066i
$982$	174.877	−	192.455i	0.178082	−	0.195983i
$983$	354.106			0.360230			0.180115	−	0.983646i	$-0.442353\pi$
$983$	354.106			0.360230			0.180115	+	0.983646i	$0.442353\pi$
$984$	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
$990$	14.5601	−	64.2057i	0.0147072	−	0.0648542i
$991$		−	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	$-0.428890\pi$
$997$	441.759			0.443088			0.221544	+	0.975150i	$0.428890\pi$
$998$	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.19.7	yes	8
3.2	odd	2		360.3.p.g.19.2		8
4.3	odd	2		160.3.e.c.79.2		8
5.2	odd	4		200.3.g.h.51.6		8
5.3	odd	4		200.3.g.h.51.3		8
5.4	even	2	inner	40.3.e.c.19.2	yes	8
8.3	odd	2	inner	40.3.e.c.19.1	✓	8
8.5	even	2		160.3.e.c.79.1		8
12.11	even	2		1440.3.p.g.559.2		8
15.14	odd	2		360.3.p.g.19.7		8
16.3	odd	4		1280.3.h.m.1279.13		16
16.5	even	4		1280.3.h.m.1279.16		16
16.11	odd	4		1280.3.h.m.1279.4		16
16.13	even	4		1280.3.h.m.1279.1		16
20.3	even	4		800.3.g.h.751.7		8
20.7	even	4		800.3.g.h.751.2		8
20.19	odd	2		160.3.e.c.79.7		8
24.5	odd	2		1440.3.p.g.559.7		8
24.11	even	2		360.3.p.g.19.8		8
40.3	even	4		200.3.g.h.51.4		8
40.13	odd	4		800.3.g.h.751.8		8
40.19	odd	2	inner	40.3.e.c.19.8	yes	8
40.27	even	4		200.3.g.h.51.5		8
40.29	even	2		160.3.e.c.79.8		8
40.37	odd	4		800.3.g.h.751.1		8
60.59	even	2		1440.3.p.g.559.8		8
80.19	odd	4		1280.3.h.m.1279.2		16
80.29	even	4		1280.3.h.m.1279.14		16
80.59	odd	4		1280.3.h.m.1279.15		16
80.69	even	4		1280.3.h.m.1279.3		16
120.29	odd	2		1440.3.p.g.559.1		8
120.59	even	2		360.3.p.g.19.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
40.3.e.c.19.1	✓	8	8.3	odd	2	inner
40.3.e.c.19.2	yes	8	5.4	even	2	inner
40.3.e.c.19.7	yes	8	1.1	even	1	trivial
40.3.e.c.19.8	yes	8	40.19	odd	2	inner
160.3.e.c.79.1		8	8.5	even	2
160.3.e.c.79.2		8	4.3	odd	2
160.3.e.c.79.7		8	20.19	odd	2
160.3.e.c.79.8		8	40.29	even	2
200.3.g.h.51.3		8	5.3	odd	4
200.3.g.h.51.4		8	40.3	even	4
200.3.g.h.51.5		8	40.27	even	4
200.3.g.h.51.6		8	5.2	odd	4
360.3.p.g.19.1		8	120.59	even	2
360.3.p.g.19.2		8	3.2	odd	2
360.3.p.g.19.7		8	15.14	odd	2
360.3.p.g.19.8		8	24.11	even	2
800.3.g.h.751.1		8	40.37	odd	4
800.3.g.h.751.2		8	20.7	even	4
800.3.g.h.751.7		8	20.3	even	4
800.3.g.h.751.8		8	40.13	odd	4
1280.3.h.m.1279.1		16	16.13	even	4
1280.3.h.m.1279.2		16	80.19	odd	4
1280.3.h.m.1279.3		16	80.69	even	4
1280.3.h.m.1279.4		16	16.11	odd	4
1280.3.h.m.1279.13		16	16.3	odd	4
1280.3.h.m.1279.14		16	80.29	even	4
1280.3.h.m.1279.15		16	80.59	odd	4
1280.3.h.m.1279.16		16	16.5	even	4
1440.3.p.g.559.1		8	120.29	odd	2
1440.3.p.g.559.2		8	12.11	even	2
1440.3.p.g.559.7		8	24.5	odd	2
1440.3.p.g.559.8		8	60.59	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} +(2.21158 - 9.75238i) 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} +(-11.4609 - 16.3905i) 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} +(46.7141 + 10.5935i) 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} +(-39.6760 - 5.08080i) 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} +(-14.3732 - 47.8896i) 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} +(78.5107 - 54.8978i) 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} +(-16.9794 + 74.8741i) 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} +(-60.8847 + 51.8946i) 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} +(-30.8388 + 135.990i) 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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