LMFDB - Embedded newform 405.4.e.o.271.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [405,4,Mod(136,405)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(405, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("405.136");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 405 = 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	405.e (of order $3$, degree $2$, not 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:	$23.8957735523$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			271.2
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	405.271
Dual form			405.4.e.o.136.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.366025 + 0.633975i) q^{2} +(3.73205 - 6.46410i) q^{4} +(-2.50000 + 4.33013i) q^{5} +(3.46410 + 6.00000i) q^{7} +11.3205 q^{8} +O(q^{10})$	\(q+(0.366025 + 0.633975i) q^{2} +(3.73205 - 6.46410i) q^{4} +(-2.50000 + 4.33013i) q^{5} +(3.46410 + 6.00000i) q^{7} +11.3205 q^{8} -3.66025 q^{10} +(-18.7487 - 32.4737i) q^{11} +(19.4641 - 33.7128i) q^{13} +(-2.53590 + 4.39230i) q^{14} +(-25.7128 - 44.5359i) q^{16} -80.9948 q^{17} +112.779 q^{19} +(18.6603 + 32.3205i) q^{20} +(13.7250 - 23.7724i) q^{22} +(-6.71281 + 11.6269i) q^{23} +(-12.5000 - 21.6506i) q^{25} +28.4974 q^{26} +51.7128 q^{28} +(21.7154 + 37.6122i) q^{29} +(74.8923 - 129.717i) q^{31} +(64.1051 - 111.033i) q^{32} +(-29.6462 - 51.3487i) q^{34} -34.6410 q^{35} -218.344 q^{37} +(41.2801 + 71.4993i) q^{38} +(-28.3013 + 49.0192i) q^{40} +(186.069 - 322.281i) q^{41} +(-230.100 - 398.545i) q^{43} -279.885 q^{44} -9.82824 q^{46} +(107.144 + 185.578i) q^{47} +(147.500 - 255.477i) q^{49} +(9.15064 - 15.8494i) q^{50} +(-145.282 - 251.636i) q^{52} -445.205 q^{53} +187.487 q^{55} +(39.2154 + 67.9230i) q^{56} +(-15.8968 + 27.5340i) q^{58} +(200.749 - 347.707i) q^{59} +(-0.723122 - 1.25248i) q^{61} +109.650 q^{62} -317.549 q^{64} +(97.3205 + 168.564i) q^{65} +(408.033 - 706.734i) q^{67} +(-302.277 + 523.559i) q^{68} +(-12.6795 - 21.9615i) q^{70} -147.518 q^{71} +432.651 q^{73} +(-79.9193 - 138.424i) q^{74} +(420.899 - 729.018i) q^{76} +(129.895 - 224.985i) q^{77} +(-192.067 - 332.669i) q^{79} +257.128 q^{80} +272.424 q^{82} +(630.615 + 1092.26i) q^{83} +(202.487 - 350.718i) q^{85} +(168.445 - 291.755i) q^{86} +(-212.245 - 367.619i) q^{88} -513.000 q^{89} +269.703 q^{91} +(50.1051 + 86.7846i) q^{92} +(-78.4346 + 135.853i) q^{94} +(-281.949 + 488.349i) q^{95} +(548.051 + 949.252i) q^{97} +215.955 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} + 8 q^{4} - 10 q^{5} - 24 q^{8}+O(q^{10}) $ 4 * q - 2 * q^2 + 8 * q^4 - 10 * q^5 - 24 * q^8	$ 4 q - 2 q^{2} + 8 q^{4} - 10 q^{5} - 24 q^{8} + 20 q^{10} + 22 q^{11} + 64 q^{13} - 24 q^{14} + 8 q^{16} + 64 q^{17} - 20 q^{19} + 40 q^{20} + 190 q^{22} + 84 q^{23} - 50 q^{25} - 80 q^{26} + 96 q^{28} + 170 q^{29} + 258 q^{31} + 104 q^{32} - 368 q^{34} + 152 q^{37} + 418 q^{38} + 60 q^{40} + 578 q^{41} - 380 q^{43} - 496 q^{44} - 552 q^{46} + 484 q^{47} + 590 q^{49} - 50 q^{50} - 304 q^{52} - 1088 q^{53} - 220 q^{55} + 240 q^{56} + 314 q^{58} + 706 q^{59} - 668 q^{61} - 372 q^{62} + 448 q^{64} + 320 q^{65} + 1452 q^{67} - 544 q^{68} - 120 q^{70} - 1948 q^{71} + 2368 q^{73} - 964 q^{74} + 776 q^{76} + 672 q^{77} - 408 q^{79} - 80 q^{80} - 580 q^{82} + 444 q^{83} - 160 q^{85} + 556 q^{86} - 1812 q^{88} - 2052 q^{89} + 192 q^{91} + 48 q^{92} + 580 q^{94} + 50 q^{95} + 668 q^{97} - 1180 q^{98}+O(q^{100}) $ 4 * q - 2 * q^2 + 8 * q^4 - 10 * q^5 - 24 * q^8 + 20 * q^10 + 22 * q^11 + 64 * q^13 - 24 * q^14 + 8 * q^16 + 64 * q^17 - 20 * q^19 + 40 * q^20 + 190 * q^22 + 84 * q^23 - 50 * q^25 - 80 * q^26 + 96 * q^28 + 170 * q^29 + 258 * q^31 + 104 * q^32 - 368 * q^34 + 152 * q^37 + 418 * q^38 + 60 * q^40 + 578 * q^41 - 380 * q^43 - 496 * q^44 - 552 * q^46 + 484 * q^47 + 590 * q^49 - 50 * q^50 - 304 * q^52 - 1088 * q^53 - 220 * q^55 + 240 * q^56 + 314 * q^58 + 706 * q^59 - 668 * q^61 - 372 * q^62 + 448 * q^64 + 320 * q^65 + 1452 * q^67 - 544 * q^68 - 120 * q^70 - 1948 * q^71 + 2368 * q^73 - 964 * q^74 + 776 * q^76 + 672 * q^77 - 408 * q^79 - 80 * q^80 - 580 * q^82 + 444 * q^83 - 160 * q^85 + 556 * q^86 - 1812 * q^88 - 2052 * q^89 + 192 * q^91 + 48 * q^92 + 580 * q^94 + 50 * q^95 + 668 * q^97 - 1180 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/405\mathbb{Z}\right)^\times$.

$n$	$82$	$326$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	0.366025	+	0.633975i	0.129410	+	0.224144i	0.923448	−	0.383724i	$-0.125358\pi$
$2$	0.366025	+	0.633975i	0.129410	+	0.224144i	−0.794038	+	0.607868i	$0.792025\pi$
$3$		0			0
$3$		0			0
$4$	3.73205	−	6.46410i	0.466506	−	0.808013i
$5$	−2.50000	+	4.33013i	−0.223607	+	0.387298i
$5$	−2.50000	+	4.33013i	−0.223607	+	0.387298i
$6$		0			0
$7$	3.46410	+	6.00000i	0.187044	+	0.323970i	0.944263	−	0.329191i	$-0.106776\pi$
$7$	3.46410	+	6.00000i	0.187044	+	0.323970i	−0.757219	+	0.653161i	$0.773443\pi$
$8$	11.3205			0.500301
$9$		0			0
$10$	−3.66025			−0.115747
$11$	−18.7487	−	32.4737i	−0.513904	−	0.890109i	−0.999870	−	0.0161306i	$-0.994865\pi$
$11$	−18.7487	−	32.4737i	−0.513904	−	0.890109i	0.485965	−	0.873978i	$-0.338468\pi$
$12$		0			0
$13$	19.4641	−	33.7128i	0.415259	−	0.719250i	−0.580196	−	0.814477i	$-0.697024\pi$
$13$	19.4641	−	33.7128i	0.415259	−	0.719250i	0.995456	+	0.0952265i	$0.0303575\pi$
$14$	−2.53590	+	4.39230i	−0.0484105	+	0.0838495i
$15$		0			0
$16$	−25.7128	−	44.5359i	−0.401763	−	0.695873i
$17$	−80.9948			−1.15554			−0.577769	−	0.816201i	$-0.696076\pi$
$17$	−80.9948			−1.15554			−0.577769	+	0.816201i	$0.696076\pi$
$18$		0			0
$19$	112.779			1.36176			0.680878	−	0.732396i	$-0.261598\pi$
$19$	112.779			1.36176			0.680878	+	0.732396i	$0.261598\pi$
$20$	18.6603	+	32.3205i	0.208628	+	0.361354i
$21$		0			0
$22$	13.7250	−	23.7724i	0.133008	−	0.230377i
$23$	−6.71281	+	11.6269i	−0.0608573	+	0.105408i	−0.894849	−	0.446369i	$-0.852717\pi$
$23$	−6.71281	+	11.6269i	−0.0608573	+	0.105408i	0.833992	+	0.551777i	$0.186050\pi$
$24$		0			0
$25$	−12.5000	−	21.6506i	−0.100000	−	0.173205i
$26$	28.4974			0.214954
$27$		0			0
$28$	51.7128			0.349029
$29$	21.7154	+	37.6122i	0.139050	+	0.240841i	0.927137	−	0.374722i	$-0.122262\pi$
$29$	21.7154	+	37.6122i	0.139050	+	0.240841i	−0.788087	+	0.615563i	$0.788928\pi$
$30$		0			0
$31$	74.8923	−	129.717i	0.433905	−	0.751546i	−0.563301	−	0.826252i	$-0.690469\pi$
$31$	74.8923	−	129.717i	0.433905	−	0.751546i	0.997206	+	0.0747066i	$0.0238020\pi$
$32$	64.1051	−	111.033i	0.354134	−	0.613378i
$33$		0			0
$34$	−29.6462	−	51.3487i	−0.149538	−	0.259007i
$35$	−34.6410			−0.167297
$36$		0			0
$37$	−218.344			−0.970147			−0.485074	−	0.874473i	$-0.661207\pi$
$37$	−218.344			−0.970147			−0.485074	+	0.874473i	$0.661207\pi$
$38$	41.2801	+	71.4993i	0.176224	+	0.305229i
$39$		0			0
$40$	−28.3013	+	49.0192i	−0.111871	+	0.193766i
$41$	186.069	−	322.281i	0.708759	−	1.22761i	−0.256558	−	0.966529i	$-0.582589\pi$
$41$	186.069	−	322.281i	0.708759	−	1.22761i	0.965318	−	0.261078i	$-0.0840781\pi$
$42$		0			0
$43$	−230.100	−	398.545i	−0.816045	−	1.41343i	−0.908575	−	0.417721i	$-0.862829\pi$
$43$	−230.100	−	398.545i	−0.816045	−	1.41343i	0.0925309	−	0.995710i	$-0.470504\pi$
$44$	−279.885			−0.958959
$45$		0			0
$46$	−9.82824			−0.0315021
$47$	107.144	+	185.578i	0.332521	+	0.575944i	0.983006	−	0.183576i	$-0.0587673\pi$
$47$	107.144	+	185.578i	0.332521	+	0.575944i	−0.650484	+	0.759520i	$0.725434\pi$
$48$		0			0
$49$	147.500	−	255.477i	0.430029	−	0.744832i
$50$	9.15064	−	15.8494i	0.0258819	−	0.0448288i
$51$		0			0
$52$	−145.282	−	251.636i	−0.387442	−	0.671070i
$53$	−445.205			−1.15384			−0.576921	−	0.816800i	$-0.695746\pi$
$53$	−445.205			−1.15384			−0.576921	+	0.816800i	$0.695746\pi$
$54$		0			0
$55$	187.487			0.459650
$56$	39.2154	+	67.9230i	0.0935782	+	0.162082i
$57$		0			0
$58$	−15.8968	+	27.5340i	−0.0359888	+	0.0623344i
$59$	200.749	−	347.707i	0.442970	−	0.767247i	−0.554938	−	0.831892i	$-0.687258\pi$
$59$	200.749	−	347.707i	0.442970	−	0.767247i	0.997908	+	0.0646445i	$0.0205913\pi$
$60$		0			0
$61$	−0.723122	−	1.25248i	−0.00151781	−	0.00262892i	0.865266	−	0.501314i	$-0.167150\pi$
$61$	−0.723122	−	1.25248i	−0.00151781	−	0.00262892i	−0.866783	+	0.498685i	$0.833816\pi$
$62$	109.650			0.224606
$63$		0			0
$64$	−317.549			−0.620212
$65$	97.3205	+	168.564i	0.185710	+	0.321658i
$66$		0			0
$67$	408.033	−	706.734i	0.744018	−	1.28868i	−0.206634	−	0.978418i	$-0.566251\pi$
$67$	408.033	−	706.734i	0.744018	−	1.28868i	0.950652	−	0.310259i	$-0.100416\pi$
$68$	−302.277	+	523.559i	−0.539066	+	0.933689i
$69$		0			0
$70$	−12.6795	−	21.9615i	−0.0216498	−	0.0374986i
$71$	−147.518			−0.246580			−0.123290	−	0.992371i	$-0.539345\pi$
$71$	−147.518			−0.246580			−0.123290	+	0.992371i	$0.539345\pi$
$72$		0			0
$73$	432.651			0.693671			0.346836	−	0.937926i	$-0.387256\pi$
$73$	432.651			0.693671			0.346836	+	0.937926i	$0.387256\pi$
$74$	−79.9193	−	138.424i	−0.125546	−	0.217453i
$75$		0			0
$76$	420.899	−	729.018i	0.635268	−	1.10032i
$77$	129.895	−	224.985i	0.192245	−	0.332979i
$78$		0			0
$79$	−192.067	−	332.669i	−0.273534	−	0.473775i	0.696230	−	0.717819i	$-0.254859\pi$
$79$	−192.067	−	332.669i	−0.273534	−	0.473775i	−0.969764	+	0.244044i	$0.921526\pi$
$80$	257.128			0.359347
$81$		0			0
$82$	272.424			0.366881
$83$	630.615	+	1092.26i	0.833964	+	1.44447i	0.894871	+	0.446325i	$0.147267\pi$
$83$	630.615	+	1092.26i	0.833964	+	1.44447i	−0.0609071	+	0.998143i	$0.519399\pi$
$84$		0			0
$85$	202.487	−	350.718i	0.258386	−	0.447538i
$86$	168.445	−	291.755i	0.211208	−	0.365823i
$87$		0			0
$88$	−212.245	−	367.619i	−0.257107	−	0.445322i
$89$	−513.000			−0.610988			−0.305494	−	0.952194i	$-0.598822\pi$
$89$	−513.000			−0.610988			−0.305494	+	0.952194i	$0.598822\pi$
$90$		0			0
$91$	269.703			0.310687
$92$	50.1051	+	86.7846i	0.0567806	+	0.0983470i
$93$		0			0
$94$	−78.4346	+	135.853i	−0.0860628	+	0.149065i
$95$	−281.949	+	488.349i	−0.304498	+	0.527406i
$96$		0			0
$97$	548.051	+	949.252i	0.573672	+	0.993629i	0.996185	+	0.0872717i	$0.0278148\pi$
$97$	548.051	+	949.252i	0.573672	+	0.993629i	−0.422513	+	0.906357i	$0.638852\pi$
$98$	215.955			0.222599
$99$		0			0
$100$	−186.603			−0.186603
$101$	−597.043	−	1034.11i	−0.588198	−	1.01879i	−0.994468	−	0.105036i	$-0.966504\pi$
$101$	−597.043	−	1034.11i	−0.588198	−	1.01879i	0.406270	−	0.913753i	$-0.366829\pi$
$102$		0			0
$103$	−90.7513	+	157.186i	−0.0868154	+	0.150369i	−0.906163	−	0.422928i	$-0.861002\pi$
$103$	−90.7513	+	157.186i	−0.0868154	+	0.150369i	0.819348	+	0.573297i	$0.194336\pi$
$104$	220.344	−	381.646i	0.207754	−	0.359841i
$105$		0			0
$106$	−162.956	−	282.249i	−0.149318	−	0.258627i
$107$	611.667			0.552636			0.276318	−	0.961066i	$-0.410886\pi$
$107$	611.667			0.552636			0.276318	+	0.961066i	$0.410886\pi$
$108$		0			0
$109$	550.467			0.483717			0.241859	−	0.970312i	$-0.422243\pi$
$109$	550.467			0.483717			0.241859	+	0.970312i	$0.422243\pi$
$110$	68.6250	+	118.862i	0.0594831	+	0.103028i
$111$		0			0
$112$	178.144	−	308.554i	0.150295	−	0.260318i
$113$	237.951	−	412.144i	0.198094	−	0.343108i	−0.749817	−	0.661646i	$-0.769858\pi$
$113$	237.951	−	412.144i	0.198094	−	0.343108i	0.947910	+	0.318538i	$0.103192\pi$
$114$		0			0
$115$	−33.5641	−	58.1347i	−0.0272162	−	0.0471399i
$116$	324.172			0.259471
$117$		0			0
$118$	293.917			0.229298
$119$	−280.574	−	485.969i	−0.216136	−	0.374359i
$120$		0			0
$121$	−37.5284	+	65.0010i	−0.0281956	+	0.0488362i
$122$	0.529362	−	0.916883i	0.000392838	−	0.000680415i
$123$		0			0
$124$	−559.004	−	968.223i	−0.404839	−	0.701202i
$125$	125.000			0.0894427
$126$		0			0
$127$	−1645.91			−1.15001			−0.575003	−	0.818152i	$-0.694999\pi$
$127$	−1645.91			−1.15001			−0.575003	+	0.818152i	$0.694999\pi$
$128$	−629.072	−	1089.58i	−0.434395	−	0.752395i
$129$		0			0
$130$	−71.2436	+	123.397i	−0.0480652	+	0.0832513i
$131$	−193.354	+	334.898i	−0.128957	+	0.223360i	−0.923273	−	0.384145i	$-0.874496\pi$
$131$	−193.354	+	334.898i	−0.128957	+	0.223360i	0.794316	+	0.607505i	$0.207830\pi$
$132$		0			0
$133$	390.679	+	676.677i	0.254708	+	0.441168i
$134$	597.402			0.385132
$135$		0			0
$136$	−916.903			−0.578116
$137$	1486.61	+	2574.88i	0.927078	+	1.60575i	0.788185	+	0.615439i	$0.211021\pi$
$137$	1486.61	+	2574.88i	0.927078	+	1.60575i	0.138893	+	0.990307i	$0.455646\pi$
$138$		0			0
$139$	−1173.68	+	2032.87i	−0.716187	+	1.24047i	0.246313	+	0.969190i	$0.420781\pi$
$139$	−1173.68	+	2032.87i	−0.716187	+	1.24047i	−0.962500	+	0.271282i	$0.912552\pi$
$140$	−129.282	+	223.923i	−0.0780452	+	0.135178i
$141$		0			0
$142$	−53.9954	−	93.5227i	−0.0319098	−	0.0552694i
$143$	−1459.71			−0.853614
$144$		0			0
$145$	−217.154			−0.124370
$146$	158.361	+	274.290i	0.0897677	+	0.155482i
$147$		0			0
$148$	−814.869	+	1411.39i	−0.452580	+	0.783891i
$149$	−701.046	+	1214.25i	−0.385449	+	0.667618i	−0.991831	−	0.127556i	$-0.959287\pi$
$149$	−701.046	+	1214.25i	−0.385449	+	0.667618i	0.606382	+	0.795173i	$0.292620\pi$
$150$		0			0
$151$	1470.63	+	2547.21i	0.792571	+	1.37277i	0.924370	+	0.381497i	$0.124591\pi$
$151$	1470.63	+	2547.21i	0.792571	+	1.37277i	−0.131799	+	0.991276i	$0.542075\pi$
$152$	1276.72			0.681288
$153$		0			0
$154$	190.179			0.0995135
$155$	374.462	+	648.586i	0.194048	+	0.336101i
$156$		0			0
$157$	−1275.99	+	2210.08i	−0.648631	+	1.12346i	0.334819	+	0.942282i	$0.391325\pi$
$157$	−1275.99	+	2210.08i	−0.648631	+	1.12346i	−0.983450	+	0.181179i	$0.942009\pi$
$158$	140.603	−	243.531i	0.0707958	−	0.122622i
$159$		0			0
$160$	320.526	+	555.167i	0.158374	+	0.274311i
$161$	−93.0155			−0.0455320
$162$		0			0
$163$	351.559			0.168934			0.0844669	−	0.996426i	$-0.473081\pi$
$163$	351.559			0.168934			0.0844669	+	0.996426i	$0.473081\pi$
$164$	−1388.84	−	2405.54i	−0.661281	−	1.14537i
$165$		0			0
$166$	−461.642	+	799.588i	−0.215846	+	0.373856i
$167$	10.4947	−	18.1773i	0.00486288	−	0.00842276i	−0.863584	−	0.504205i	$-0.831785\pi$
$167$	10.4947	−	18.1773i	0.00486288	−	0.00842276i	0.868447	+	0.495783i	$0.165119\pi$
$168$		0			0
$169$	340.797	+	590.279i	0.155119	+	0.268675i
$170$	296.462			0.133750
$171$		0			0
$172$	−3434.98			−1.52276
$173$	−2262.30	−	3918.43i	−0.994219	−	1.72204i	−0.590098	−	0.807332i	$-0.700911\pi$
$173$	−2262.30	−	3918.43i	−0.994219	−	1.72204i	−0.404121	−	0.914706i	$-0.632423\pi$
$174$		0			0
$175$	86.6025	−	150.000i	0.0374088	−	0.0647939i
$176$	−964.164	+	1669.98i	−0.412935	+	0.715225i
$177$		0			0
$178$	−187.771	−	325.229i	−0.0790676	−	0.136949i
$179$	−3626.79			−1.51441			−0.757204	−	0.653179i	$-0.773435\pi$
$179$	−3626.79			−1.51441			−0.757204	+	0.653179i	$0.773435\pi$
$180$		0			0
$181$	3551.41			1.45842			0.729210	−	0.684289i	$-0.239888\pi$
$181$	3551.41			1.45842			0.729210	+	0.684289i	$0.239888\pi$
$182$	98.7180	+	170.985i	0.0402058	+	0.0696386i
$183$		0			0
$184$	−75.9925	+	131.623i	−0.0304469	+	0.0527357i
$185$	545.859	−	945.455i	0.216932	−	0.375736i
$186$		0			0
$187$	1518.55	+	2630.20i	0.593836	+	1.02855i
$188$	1599.46			0.620493
$189$		0			0
$190$	−412.801			−0.157620
$191$	−139.825	−	242.185i	−0.0529707	−	0.0917479i	0.838324	−	0.545172i	$-0.183536\pi$
$191$	−139.825	−	242.185i	−0.0529707	−	0.0917479i	−0.891295	+	0.453424i	$0.850202\pi$
$192$		0			0
$193$	−133.080	+	230.501i	−0.0496336	+	0.0859679i	−0.889775	−	0.456400i	$-0.849139\pi$
$193$	−133.080	+	230.501i	−0.0496336	+	0.0859679i	0.840141	+	0.542368i	$0.182472\pi$
$194$	−401.201	+	694.901i	−0.148477	+	0.257170i
$195$		0			0
$196$	−1100.95	−	1906.91i	−0.401223	−	0.694938i
$197$	4731.12			1.71106			0.855528	−	0.517756i	$-0.173232\pi$
$197$	4731.12			1.71106			0.855528	+	0.517756i	$0.173232\pi$
$198$		0			0
$199$	2879.69			1.02581			0.512904	−	0.858446i	$-0.328570\pi$
$199$	2879.69			1.02581			0.512904	+	0.858446i	$0.328570\pi$
$200$	−141.506	−	245.096i	−0.0500301	−	0.0866546i
$201$		0			0
$202$	437.066	−	757.021i	0.152237	−	0.263682i
$203$	−150.449	+	260.585i	−0.0520169	+	0.0900959i
$204$		0			0
$205$	930.346	+	1611.41i	0.316967	+	0.549003i
$206$	−132.869			−0.0449390
$207$		0			0
$208$	−2001.91			−0.667343
$209$	−2114.47	−	3662.37i	−0.699813	−	1.21211i
$210$		0			0
$211$	−1364.10	+	2362.69i	−0.445065	+	0.770875i	−0.998057	−	0.0623117i	$-0.980153\pi$
$211$	−1364.10	+	2362.69i	−0.445065	+	0.770875i	0.552992	+	0.833187i	$0.313486\pi$
$212$	−1661.53	+	2877.85i	−0.538275	+	0.932319i
$213$		0			0
$214$	223.886	+	387.781i	0.0715164	+	0.123870i
$215$	2301.00			0.729892
$216$		0			0
$217$	1037.74			0.324637
$218$	201.485	+	348.982i	0.0625976	+	0.108422i
$219$		0			0
$220$	699.711	−	1211.94i	0.214430	−	0.371403i
$221$	−1576.49	+	2730.56i	−0.479848	+	0.831120i
$222$		0			0
$223$	1837.42	+	3182.51i	0.551762	+	0.955680i	0.998148	+	0.0608392i	$0.0193777\pi$
$223$	1837.42	+	3182.51i	0.551762	+	0.955680i	−0.446386	+	0.894841i	$0.647289\pi$
$224$	888.267			0.264954
$225$		0			0
$226$	348.385			0.102541
$227$	2886.96	+	5000.36i	0.844115	+	1.46205i	0.886388	+	0.462943i	$0.153207\pi$
$227$	2886.96	+	5000.36i	0.844115	+	1.46205i	−0.0422732	+	0.999106i	$0.513460\pi$
$228$		0			0
$229$	−2409.14	+	4172.75i	−0.695198	+	1.20412i	0.274916	+	0.961468i	$0.411350\pi$
$229$	−2409.14	+	4172.75i	−0.695198	+	1.20412i	−0.970114	+	0.242650i	$0.921983\pi$
$230$	24.5706	−	42.5575i	0.00704408	−	0.0122007i
$231$		0			0
$232$	245.829	+	425.789i	0.0695667	+	0.120493i
$233$	−91.0828			−0.0256096			−0.0128048	−	0.999918i	$-0.504076\pi$
$233$	−91.0828			−0.0256096			−0.0128048	+	0.999918i	$0.504076\pi$
$234$		0			0
$235$	−1071.44			−0.297416
$236$	−1498.41	−	2595.32i	−0.413297	−	0.715851i
$237$		0			0
$238$	205.395	−	355.754i	0.0559402	−	0.0968912i
$239$	2743.42	−	4751.74i	0.742498	−	1.28604i	−0.208856	−	0.977946i	$-0.566974\pi$
$239$	2743.42	−	4751.74i	0.742498	−	1.28604i	0.951354	−	0.308098i	$-0.0996926\pi$
$240$		0			0
$241$	−1508.60	−	2612.97i	−0.403225	−	0.698406i	0.590888	−	0.806754i	$-0.298778\pi$
$241$	−1508.60	−	2612.97i	−0.403225	−	0.698406i	−0.994113	+	0.108347i	$0.965444\pi$
$242$	−54.9453			−0.0145951
$243$		0			0
$244$	−10.7949			−0.00283227
$245$	737.500	+	1277.39i	0.192315	+	0.333099i
$246$		0			0
$247$	2195.15	−	3802.11i	0.565482	−	0.979444i
$248$	847.819	−	1468.47i	0.217083	−	0.375999i
$249$		0			0
$250$	45.7532	+	79.2468i	0.0115747	+	0.0200480i
$251$	2740.98			0.689280			0.344640	−	0.938735i	$-0.388001\pi$
$251$	2740.98			0.689280			0.344640	+	0.938735i	$0.388001\pi$
$252$		0			0
$253$	503.426			0.125099
$254$	−602.444	−	1043.46i	−0.148822	−	0.257767i
$255$		0			0
$256$	−809.682	+	1402.41i	−0.197676	+	0.342385i
$257$	−1260.70	+	2183.60i	−0.305993	+	0.529996i	−0.977482	−	0.211019i	$-0.932322\pi$
$257$	−1260.70	+	2183.60i	−0.305993	+	0.529996i	0.671489	+	0.741015i	$0.265655\pi$
$258$		0			0
$259$	−756.364	−	1310.06i	−0.181460	−	0.314298i
$260$	1452.82			0.346539
$261$		0			0
$262$	−283.089			−0.0667531
$263$	−2243.86	−	3886.48i	−0.526092	−	0.911219i	−0.999538	−	0.0303955i	$-0.990323\pi$
$263$	−2243.86	−	3886.48i	−0.526092	−	0.911219i	0.473446	−	0.880823i	$-0.343010\pi$
$264$		0			0
$265$	1113.01	−	1927.79i	0.258007	−	0.446881i
$266$	−285.997	+	495.362i	−0.0659234	+	0.114183i
$267$		0			0
$268$	−3045.60	−	5275.14i	−0.694178	−	1.20235i
$269$	−8531.47			−1.93373			−0.966864	−	0.255291i	$-0.917829\pi$
$269$	−8531.47			−1.93373			−0.966864	+	0.255291i	$0.917829\pi$
$270$		0			0
$271$	−123.097			−0.0275927			−0.0137964	−	0.999905i	$-0.504392\pi$
$271$	−123.097			−0.0275927			−0.0137964	+	0.999905i	$0.504392\pi$
$272$	2082.61	+	3607.18i	0.464252	+	0.804108i
$273$		0			0
$274$	−1088.27	+	1884.95i	−0.239945	+	0.415598i
$275$	−468.718	+	811.843i	−0.102781	+	0.178022i
$276$		0			0
$277$	3278.79	+	5679.03i	0.711204	+	1.23184i	0.964405	+	0.264428i	$0.0851831\pi$
$277$	3278.79	+	5679.03i	0.711204	+	1.23184i	−0.253201	+	0.967414i	$0.581484\pi$
$278$	−1718.38			−0.370726
$279$		0			0
$280$	−392.154			−0.0836989
$281$	3542.02	+	6134.96i	0.751954	+	1.30242i	0.946874	+	0.321604i	$0.104222\pi$
$281$	3542.02	+	6134.96i	0.751954	+	1.30242i	−0.194920	+	0.980819i	$0.562445\pi$
$282$		0			0
$283$	−1036.47	+	1795.21i	−0.217709	+	0.377082i	−0.954107	−	0.299466i	$-0.903192\pi$
$283$	−1036.47	+	1795.21i	−0.217709	+	0.377082i	0.736399	+	0.676548i	$0.236525\pi$
$284$	−550.545	+	953.572i	−0.115031	+	0.199240i
$285$		0			0
$286$	−534.290	−	925.417i	−0.110466	−	0.191332i
$287$	2578.25			0.530276
$288$		0			0
$289$	1647.16			0.335267
$290$	−79.4838	−	137.670i	−0.0160947	−	0.0278768i
$291$		0			0
$292$	1614.68	−	2796.70i	0.323602	−	0.560495i
$293$	3564.20	−	6173.38i	0.710658	−	1.23090i	−0.253952	−	0.967217i	$-0.581730\pi$
$293$	3564.20	−	6173.38i	0.710658	−	1.23090i	0.964610	−	0.263680i	$-0.0849362\pi$
$294$		0			0
$295$	1003.74	+	1738.53i	0.198102	+	0.343123i
$296$	−2471.76			−0.485365
$297$		0			0
$298$	−1026.40			−0.199523
$299$	261.318	+	452.616i	0.0505431	+	0.0875433i
$300$		0			0
$301$	1594.18	−	2761.20i	0.305272	−	0.528747i
$302$	−1076.58	+	1864.68i	−0.205132	+	0.355300i
$303$		0			0
$304$	−2899.88	−	5022.73i	−0.547103	−	0.947610i
$305$	7.23122			0.00135757
$306$		0			0
$307$	−6334.70			−1.17766			−0.588828	−	0.808259i	$-0.700410\pi$
$307$	−6334.70			−1.17766			−0.588828	+	0.808259i	$0.700410\pi$
$308$	−969.549	−	1679.31i	−0.179367	−	0.310673i
$309$		0			0
$310$	−274.125	+	474.798i	−0.0502234	+	0.0869894i
$311$	3696.95	−	6403.30i	0.674067	−	1.16752i	−0.302674	−	0.953094i	$-0.597879\pi$
$311$	3696.95	−	6403.30i	0.674067	−	1.16752i	0.976741	−	0.214423i	$-0.0687872\pi$
$312$		0			0
$313$	466.528	+	808.050i	0.0842482	+	0.145922i	0.905071	−	0.425261i	$-0.139818\pi$
$313$	466.528	+	808.050i	0.0842482	+	0.145922i	−0.820822	+	0.571184i	$0.806484\pi$
$314$	−1868.18			−0.335756
$315$		0			0
$316$	−2867.21			−0.510421
$317$	4367.34	+	7564.45i	0.773799	+	1.34026i	0.935467	+	0.353413i	$0.114979\pi$
$317$	4367.34	+	7564.45i	0.773799	+	1.34026i	−0.161669	+	0.986845i	$0.551688\pi$
$318$		0			0
$319$	814.271	−	1410.36i	0.142917	−	0.247539i
$320$	793.872	−	1375.03i	0.138684	−	0.240207i
$321$		0			0
$322$	−34.0460	−	58.9694i	−0.00589227	−	0.0102057i
$323$	−9134.55			−1.57356
$324$		0			0
$325$	−973.205			−0.166104
$326$	128.679	+	222.879i	0.0218617	+	0.0378655i
$327$		0			0
$328$	2106.40	−	3648.39i	0.354593	−	0.614172i
$329$	−742.313	+	1285.72i	−0.124392	+	0.215454i
$330$		0			0
$331$	645.266	+	1117.63i	0.107151	+	0.185591i	0.914615	−	0.404326i	$-0.132494\pi$
$331$	645.266	+	1117.63i	0.107151	+	0.185591i	−0.807464	+	0.589917i	$0.799160\pi$
$332$	9413.95			1.55620
$333$		0			0
$334$	15.3652			0.00251721
$335$	2040.17	+	3533.67i	0.332735	+	0.576314i
$336$		0			0
$337$	5000.66	−	8661.40i	0.808318	−	1.40005i	−0.105710	−	0.994397i	$-0.533711\pi$
$337$	5000.66	−	8661.40i	0.808318	−	1.40005i	0.914028	−	0.405651i	$-0.132955\pi$
$338$	−249.481	+	432.114i	−0.0401479	+	0.0695382i
$339$		0			0
$340$	−1511.38	−	2617.79i	−0.241077	−	0.417558i
$341$	−5616.54			−0.891943
$342$		0			0
$343$	4420.19			0.695825
$344$	−2604.85	−	4511.73i	−0.408267	−	0.707140i
$345$		0			0
$346$	1656.12	−	2868.49i	0.257323	−	0.445696i
$347$	3234.18	−	5601.77i	0.500346	−	0.866625i	−0.499654	−	0.866225i	$-0.666539\pi$
$347$	3234.18	−	5601.77i	0.500346	−	0.866625i	1.00000		0.000399827i	$-0.000127269\pi$
$348$		0			0
$349$	−5584.89	−	9673.32i	−0.856597	−	1.48367i	−0.875155	−	0.483842i	$-0.839241\pi$
$349$	−5584.89	−	9673.32i	−0.856597	−	1.48367i	0.0185577	−	0.999828i	$-0.494093\pi$
$350$	126.795			0.0193642
$351$		0			0
$352$	−4807.55			−0.727964
$353$	908.387	+	1573.37i	0.136965	+	0.237230i	0.926346	−	0.376673i	$-0.122932\pi$
$353$	908.387	+	1573.37i	0.136965	+	0.237230i	−0.789382	+	0.613903i	$0.789599\pi$
$354$		0			0
$355$	368.795	−	638.772i	0.0551369	−	0.0955000i
$356$	−1914.54	+	3316.08i	−0.285030	+	0.493686i
$357$		0			0
$358$	−1327.50	−	2299.29i	−0.195979	−	0.339445i
$359$	−918.073			−0.134969			−0.0674847	−	0.997720i	$-0.521497\pi$
$359$	−918.073			−0.134969			−0.0674847	+	0.997720i	$0.521497\pi$
$360$		0			0
$361$	5860.21			0.854382
$362$	1299.91	+	2251.50i	0.188734	+	0.326896i
$363$		0			0
$364$	1006.54	−	1743.38i	0.144937	−	0.251039i
$365$	−1081.63	+	1873.44i	−0.155110	+	0.268658i
$366$		0			0
$367$	−3677.14	−	6368.99i	−0.523011	−	0.905881i	−0.999641	−	0.0267777i	$-0.991475\pi$
$367$	−3677.14	−	6368.99i	−0.523011	−	0.905881i	0.476630	−	0.879104i	$-0.341858\pi$
$368$	690.421			0.0978008
$369$		0			0
$370$	799.193			0.112292
$371$	−1542.24	−	2671.23i	−0.215819	−	0.373810i
$372$		0			0
$373$	301.303	−	521.873i	0.0418255	−	0.0724438i	−0.844355	−	0.535784i	$-0.820016\pi$
$373$	301.303	−	521.873i	0.0418255	−	0.0724438i	0.886180	+	0.463341i	$0.153349\pi$
$374$	−1111.66	+	1925.44i	−0.153696	+	0.266209i
$375$		0			0
$376$	1212.92	+	2100.84i	0.166361	+	0.288145i
$377$	1690.68			0.230967
$378$		0			0
$379$	13319.0			1.80515			0.902575	−	0.430533i	$-0.141674\pi$
$379$	13319.0			1.80515			0.902575	+	0.430533i	$0.141674\pi$
$380$	2104.49	+	3645.09i	0.284101	+	0.492077i
$381$		0			0
$382$	102.359	−	177.291i	0.0137098	−	0.0237461i
$383$	−4268.87	+	7393.91i	−0.569528	+	0.986452i	0.427084	+	0.904212i	$0.359541\pi$
$383$	−4268.87	+	7393.91i	−0.569528	+	0.986452i	−0.996613	+	0.0822399i	$0.973793\pi$
$384$		0			0
$385$	649.474	+	1124.92i	0.0859748	+	0.148913i
$386$	−194.842			−0.0256922
$387$		0			0
$388$	8181.42			1.07049
$389$	−6319.99	−	10946.5i	−0.823744	−	1.42677i	−0.902875	−	0.429902i	$-0.858548\pi$
$389$	−6319.99	−	10946.5i	−0.823744	−	1.42677i	0.0791316	−	0.996864i	$-0.474785\pi$
$390$		0			0
$391$	543.703	−	941.722i	0.0703229	−	0.121803i
$392$	1669.77	−	2892.14i	0.215144	−	0.372640i
$393$		0			0
$394$	1731.71	+	2999.41i	0.221427	+	0.383523i
$395$	1920.67			0.244656
$396$		0			0
$397$	5473.94			0.692013			0.346006	−	0.938232i	$-0.387538\pi$
$397$	5473.94			0.692013			0.346006	+	0.938232i	$0.387538\pi$
$398$	1054.04	+	1825.65i	0.132749	+	0.229929i
$399$		0			0
$400$	−642.820	+	1113.40i	−0.0803525	+	0.139175i
$401$	6522.82	−	11297.9i	0.812305	−	1.40695i	−0.0989419	−	0.995093i	$-0.531546\pi$
$401$	6522.82	−	11297.9i	0.812305	−	1.40695i	0.911247	−	0.411860i	$-0.135121\pi$
$402$		0			0
$403$	−2915.42	−	5049.66i	−0.360366	−	0.624172i
$404$	−8912.79			−1.09759
$405$		0			0
$406$	−220.272			−0.0269259
$407$	4093.66	+	7090.43i	0.498563	+	0.863537i
$408$		0			0
$409$	3591.36	−	6220.41i	0.434184	−	0.752029i	−0.563045	−	0.826426i	$-0.690370\pi$
$409$	3591.36	−	6220.41i	0.434184	−	0.752029i	0.997229	+	0.0743978i	$0.0237035\pi$
$410$	−681.061	+	1179.63i	−0.0820370	+	0.142092i
$411$		0			0
$412$	677.377	+	1173.25i	0.0809999	+	0.140296i
$413$	2781.66			0.331420
$414$		0			0
$415$	−6306.15			−0.745920
$416$	−2495.50	−	4322.33i	−0.294115	−	0.509422i
$417$		0			0
$418$	1547.90	−	2681.04i	0.181125	−	0.313718i
$419$	4360.20	−	7552.09i	0.508376	−	0.880534i	−0.491577	−	0.870834i	$-0.663579\pi$
$419$	4360.20	−	7552.09i	0.508376	−	0.880534i	0.999953	−	0.00969927i	$-0.00308742\pi$
$420$		0			0
$421$	−3276.51	−	5675.09i	−0.379305	−	0.656976i	0.611656	−	0.791124i	$-0.290504\pi$
$421$	−3276.51	−	5675.09i	−0.379305	−	0.656976i	−0.990961	+	0.134148i	$0.957170\pi$
$422$	−1997.18			−0.230383
$423$		0			0
$424$	−5039.95			−0.577268
$425$	1012.44	+	1753.59i	0.115554	+	0.200145i
$426$		0			0
$427$	5.00994	−	8.67747i	0.000567794	−	0.000983448i
$428$	2282.77	−	3953.88i	0.257808	−	0.446537i
$429$		0			0
$430$	842.224	+	1458.78i	0.0944550	+	0.163601i
$431$	−5217.70			−0.583127			−0.291564	−	0.956551i	$-0.594176\pi$
$431$	−5217.70			−0.583127			−0.291564	+	0.956551i	$0.594176\pi$
$432$		0			0
$433$	3377.56			0.374862			0.187431	−	0.982278i	$-0.439984\pi$
$433$	3377.56			0.374862			0.187431	+	0.982278i	$0.439984\pi$
$434$	379.839	+	657.900i	0.0420111	+	0.0727654i
$435$		0			0
$436$	2054.37	−	3558.27i	0.225657	−	0.390850i
$437$	−757.067	+	1311.28i	−0.0828729	+	0.143540i
$438$		0			0
$439$	−1069.46	−	1852.36i	−0.116270	−	0.201386i	0.802017	−	0.597302i	$-0.203761\pi$
$439$	−1069.46	−	1852.36i	−0.116270	−	0.201386i	−0.918287	+	0.395916i	$0.870427\pi$
$440$	2122.45			0.229963
$441$		0			0
$442$	−2308.14			−0.248387
$443$	4256.31	+	7372.15i	0.456486	+	0.790658i	0.998772	−	0.0495363i	$-0.0157744\pi$
$443$	4256.31	+	7372.15i	0.456486	+	0.790658i	−0.542286	+	0.840194i	$0.682441\pi$
$444$		0			0
$445$	1282.50	−	2221.36i	0.136621	−	0.236634i
$446$	−1345.09	+	2329.76i	−0.142807	+	0.247348i
$447$		0			0
$448$	−1100.02	−	1905.29i	−0.116007	−	0.200930i
$449$	4542.67			0.477465			0.238733	−	0.971085i	$-0.423268\pi$
$449$	4542.67			0.477465			0.238733	+	0.971085i	$0.423268\pi$
$450$		0			0
$451$	−13954.2			−1.45694
$452$	−1776.09	−	3076.28i	−0.184824	−	0.320124i
$453$		0			0
$454$	−2113.40	+	3660.51i	−0.218473	+	0.378406i
$455$	−674.256	+	1167.85i	−0.0694717	+	0.120329i
$456$		0			0
$457$	8971.10	+	15538.4i	0.918272	+	1.59049i	0.802039	+	0.597271i	$0.203748\pi$
$457$	8971.10	+	15538.4i	0.918272	+	1.59049i	0.116232	+	0.993222i	$0.462918\pi$
$458$	−3527.22			−0.359861
$459$		0			0
$460$	−501.051			−0.0507862
$461$	−2590.44	−	4486.78i	−0.261711	−	0.453297i	0.704985	−	0.709222i	$-0.250954\pi$
$461$	−2590.44	−	4486.78i	−0.261711	−	0.453297i	−0.966697	+	0.255924i	$0.917620\pi$
$462$		0			0
$463$	−7096.44	+	12291.4i	−0.712310	+	1.23376i	0.251677	+	0.967811i	$0.419018\pi$
$463$	−7096.44	+	12291.4i	−0.712310	+	1.23376i	−0.963988	+	0.265947i	$0.914315\pi$
$464$	1116.73	−	1934.23i	0.111730	−	0.193522i
$465$		0			0
$466$	−33.3386	−	57.7442i	−0.00331413	−	0.00574023i
$467$	11886.3			1.17780			0.588901	−	0.808205i	$-0.299561\pi$
$467$	11886.3			1.17780			0.588901	+	0.808205i	$0.299561\pi$
$468$		0			0
$469$	5653.88			0.556656
$470$	−392.173	−	679.263i	−0.0384885	−	0.0666640i
$471$		0			0
$472$	2272.58	−	3936.22i	0.221618	−	0.383854i
$473$	−8628.16	+	14944.4i	−0.838738	+	1.45274i
$474$		0			0
$475$	−1409.74	−	2441.75i	−0.136176	−	0.235863i
$476$	−4188.47			−0.403316
$477$		0			0
$478$	4016.65			0.384345
$479$	−2159.73	−	3740.76i	−0.206014	−	0.356826i	0.744442	−	0.667688i	$-0.232716\pi$
$479$	−2159.73	−	3740.76i	−0.206014	−	0.356826i	−0.950455	+	0.310861i	$0.899382\pi$
$480$		0			0
$481$	−4249.86	+	7360.97i	−0.402863	+	0.697779i
$482$	1104.37	−	1912.82i	0.104362	−	0.180761i
$483$		0			0
$484$	280.115	+	485.174i	0.0263069	+	0.0455648i
$485$	−5480.51			−0.513108
$486$		0			0
$487$	−6436.94			−0.598944			−0.299472	−	0.954105i	$-0.596810\pi$
$487$	−6436.94			−0.598944			−0.299472	+	0.954105i	$0.596810\pi$
$488$	−8.18611	−	14.1788i	−0.000759361	−	0.00131525i
$489$		0			0
$490$	−539.887	+	935.113i	−0.0497748	+	0.0862124i
$491$	−1448.87	+	2509.51i	−0.133170	+	0.230657i	−0.924897	−	0.380218i	$-0.875849\pi$
$491$	−1448.87	+	2509.51i	−0.133170	+	0.230657i	0.791727	+	0.610875i	$0.209182\pi$
$492$		0			0
$493$	−1758.83	−	3046.39i	−0.160677	−	0.278301i
$494$	3213.92			0.292715
$495$		0			0
$496$	−7702.77			−0.697307
$497$	−511.017	−	885.108i	−0.0461213	−	0.0798844i
$498$		0			0
$499$	−7527.29	+	13037.6i	−0.675286	+	1.16963i	0.301099	+	0.953593i	$0.402646\pi$
$499$	−7527.29	+	13037.6i	−0.675286	+	1.16963i	−0.976385	+	0.216037i	$0.930687\pi$
$500$	466.506	−	808.013i	0.0417256	−	0.0722709i
$501$		0			0
$502$	1003.27	+	1737.71i	0.0891994	+	0.154498i
$503$	−15582.5			−1.38129			−0.690646	−	0.723193i	$-0.742674\pi$
$503$	−15582.5			−1.38129			−0.690646	+	0.723193i	$0.742674\pi$
$504$		0			0
$505$	5970.43			0.526101
$506$	184.267	+	319.160i	0.0161891	+	0.0280403i
$507$		0			0
$508$	−6142.61	+	10639.3i	−0.536485	+	0.929219i
$509$	2035.51	−	3525.60i	0.177254	−	0.307013i	−0.763685	−	0.645589i	$-0.776612\pi$
$509$	2035.51	−	3525.60i	0.177254	−	0.307013i	0.940939	+	0.338576i	$0.109945\pi$
$510$		0			0
$511$	1498.75	+	2595.91i	0.129747	+	0.224728i
$512$	−11250.6			−0.971116
$513$		0			0
$514$	−1845.79			−0.158394
$515$	−453.756	−	785.929i	−0.0388250	−	0.0672469i
$516$		0			0
$517$	4017.61	−	6958.70i	0.341768	−	0.591960i
$518$	553.697	−	959.031i	0.0469653	−	0.0813464i
$519$		0			0
$520$	1101.72	+	1908.23i	0.0929106	+	0.160926i
$521$	18597.9			1.56389			0.781947	−	0.623345i	$-0.214227\pi$
$521$	18597.9			1.56389			0.781947	+	0.623345i	$0.214227\pi$
$522$		0			0
$523$	−12073.5			−1.00944			−0.504722	−	0.863282i	$-0.668405\pi$
$523$	−12073.5			−1.00944			−0.504722	+	0.863282i	$0.668405\pi$
$524$	1443.21	+	2499.72i	0.120319	+	0.208398i
$525$		0			0
$526$	1642.62	−	2845.10i	0.136163	−	0.235841i
$527$	−6065.89	+	10506.4i	−0.501393	+	0.868439i
$528$		0			0
$529$	5993.38	+	10380.8i	0.492593	+	0.853196i
$530$	1629.56			0.133554
$531$		0			0
$532$	5832.14			0.475292
$533$	−7243.34	−	12545.8i	−0.588638	−	1.01955i
$534$		0			0
$535$	−1529.17	+	2648.59i	−0.123573	+	0.214035i
$536$	4619.14	−	8000.59i	0.372233	−	0.644726i
$537$		0			0
$538$	−3122.74	−	5408.74i	−0.250243	−	0.433433i
$539$	−11061.7			−0.883976
$540$		0			0
$541$	1802.04			0.143208			0.0716041	−	0.997433i	$-0.477188\pi$
$541$	1802.04			0.143208			0.0716041	+	0.997433i	$0.477188\pi$
$542$	−45.0567	−	78.0405i	−0.00357076	−	0.00618474i
$543$		0			0
$544$	−5192.18	+	8993.13i	−0.409215	+	0.708781i
$545$	−1376.17	+	2383.59i	−0.108162	+	0.187343i
$546$		0			0
$547$	−3294.86	−	5706.87i	−0.257547	−	0.446084i	0.708037	−	0.706175i	$-0.249581\pi$
$547$	−3294.86	−	5706.87i	−0.257547	−	0.446084i	−0.965584	+	0.260091i	$0.916248\pi$
$548$	22192.4			1.72995
$549$		0			0
$550$	−686.250			−0.0532033
$551$	2449.05	+	4241.88i	0.189352	+	0.327968i
$552$		0			0
$553$	1330.68	−	2304.80i	0.102326	−	0.177233i
$554$	−2400.24	+	4157.34i	−0.184073	+	0.318824i
$555$		0			0
$556$	8760.44	+	15173.5i	0.668211	+	1.15738i
$557$	21128.6			1.60727			0.803633	−	0.595125i	$-0.202897\pi$
$557$	21128.6			1.60727			0.803633	+	0.595125i	$0.202897\pi$
$558$		0			0
$559$	−17914.8			−1.35548
$560$	890.718	+	1542.77i	0.0672138	+	0.116418i
$561$		0			0
$562$	−2592.94	+	4491.10i	−0.194620	+	0.337092i
$563$	55.2137	−	95.6330i	0.00413318	−	0.00715888i	−0.863951	−	0.503575i	$-0.832018\pi$
$563$	55.2137	−	95.6330i	0.00413318	−	0.00715888i	0.868085	+	0.496416i	$0.165351\pi$
$564$		0			0
$565$	1189.76	+	2060.72i	0.0885901	+	0.153443i
$566$	−1517.49			−0.112694
$567$		0			0
$568$	−1669.98			−0.123364
$569$	3465.04	+	6001.63i	0.255294	+	0.442182i	0.964975	−	0.262341i	$-0.0844945\pi$
$569$	3465.04	+	6001.63i	0.255294	+	0.442182i	−0.709682	+	0.704523i	$0.751161\pi$
$570$		0			0
$571$	−10632.3	+	18415.7i	−0.779244	+	1.34969i	0.153134	+	0.988205i	$0.451063\pi$
$571$	−10632.3	+	18415.7i	−0.779244	+	1.34969i	−0.932378	+	0.361484i	$0.882270\pi$
$572$	−5447.70	+	9435.70i	−0.398217	+	0.689731i
$573$		0			0
$574$	943.705	+	1634.55i	0.0686228	+	0.118858i
$575$	335.641			0.0243429
$576$		0			0
$577$	2927.39			0.211211			0.105606	−	0.994408i	$-0.466322\pi$
$577$	2927.39			0.211211			0.105606	+	0.994408i	$0.466322\pi$
$578$	602.904	+	1044.26i	0.0433867	+	0.0751480i
$579$		0			0
$580$	−810.429	+	1403.70i	−0.0580194	+	0.100493i
$581$	−4369.03	+	7567.38i	−0.311976	+	0.540358i
$582$		0			0
$583$	8347.02	+	14457.5i	0.592965	+	1.02704i
$584$	4897.83			0.347044
$585$		0			0
$586$	5218.35			0.367864
$587$	−10875.2	−	18836.4i	−0.764683	−	1.32447i	−0.940414	−	0.340031i	$-0.889562\pi$
$587$	−10875.2	−	18836.4i	−0.764683	−	1.32447i	0.175732	−	0.984438i	$-0.443771\pi$
$588$		0			0
$589$	8446.31	−	14629.4i	0.590873	−	1.02342i
$590$	−734.791	+	1272.70i	−0.0512727	+	0.0888069i
$591$		0			0
$592$	5614.23	+	9724.12i	0.389769	+	0.675100i
$593$	5635.88			0.390283			0.195142	−	0.980775i	$-0.437483\pi$
$593$	5635.88			0.390283			0.195142	+	0.980775i	$0.437483\pi$
$594$		0			0
$595$	2805.74			0.193318
$596$	5232.68	+	9063.27i	0.359629	+	0.622896i
$597$		0			0
$598$	−191.298	+	331.338i	−0.0130815	+	0.0226579i
$599$	−9162.20	+	15869.4i	−0.624970	+	1.08248i	0.363576	+	0.931564i	$0.381556\pi$
$599$	−9162.20	+	15869.4i	−0.624970	+	1.08248i	−0.988547	+	0.150916i	$0.951778\pi$
$600$		0			0
$601$	1251.95	+	2168.44i	0.0849719	+	0.147176i	0.905379	−	0.424604i	$-0.139587\pi$
$601$	1251.95	+	2168.44i	0.0849719	+	0.147176i	−0.820407	+	0.571779i	$0.806253\pi$
$602$	2334.04			0.158021
$603$		0			0
$604$	21953.9			1.47896
$605$	−187.642	−	325.005i	−0.0126095	−	0.0218402i
$606$		0			0
$607$	−8733.32	+	15126.6i	−0.583978	+	1.01148i	0.411024	+	0.911624i	$0.365171\pi$
$607$	−8733.32	+	15126.6i	−0.583978	+	1.01148i	−0.995002	+	0.0998550i	$0.968162\pi$
$608$	7229.74	−	12522.3i	0.482245	−	0.835272i
$609$		0			0
$610$	2.64681	+	4.58441i	0.000175682	+	0.000304291i
$611$	8341.82			0.552330
$612$		0			0
$613$	−2244.45			−0.147883			−0.0739417	−	0.997263i	$-0.523558\pi$
$613$	−2244.45			−0.147883			−0.0739417	+	0.997263i	$0.523558\pi$
$614$	−2318.66	−	4016.04i	−0.152400	−	0.263964i
$615$		0			0
$616$	1470.48	−	2546.94i	0.0961805	−	0.166589i
$617$	2904.92	−	5031.47i	0.189542	−	0.328297i	−0.755555	−	0.655085i	$-0.772633\pi$
$617$	2904.92	−	5031.47i	0.189542	−	0.328297i	0.945098	+	0.326788i	$0.105966\pi$
$618$		0			0
$619$	771.742	+	1336.70i	0.0501114	+	0.0867954i	0.889993	−	0.455974i	$-0.150709\pi$
$619$	771.742	+	1336.70i	0.0501114	+	0.0867954i	−0.839882	+	0.542770i	$0.817376\pi$
$620$	5590.04			0.362099
$621$		0			0
$622$	5412.71			0.348922
$623$	−1777.08	−	3078.00i	−0.114281	−	0.197941i
$624$		0			0
$625$	−312.500	+	541.266i	−0.0200000	+	0.0346410i
$626$	−341.522	+	591.533i	−0.0218050	+	0.0377675i
$627$		0			0
$628$	9524.11	+	16496.2i	0.605181	+	1.04820i
$629$	17684.7			1.12104
$630$		0			0
$631$	7992.93			0.504269			0.252134	−	0.967692i	$-0.418868\pi$
$631$	7992.93			0.504269			0.252134	+	0.967692i	$0.418868\pi$
$632$	−2174.29	−	3765.98i	−0.136849	−	0.237030i
$633$		0			0
$634$	−3197.11	+	5537.56i	−0.200274	+	0.346884i
$635$	4114.77	−	7126.99i	0.257149	−	0.445395i
$636$		0			0
$637$	−5741.91	−	9945.28i	−0.357147	−	0.618597i
$638$	1192.18			0.0739791
$639$		0			0
$640$	6290.72			0.388535
$641$	−13064.9	−	22629.1i	−0.805044	−	1.39438i	−0.916261	−	0.400581i	$-0.868808\pi$
$641$	−13064.9	−	22629.1i	−0.805044	−	1.39438i	0.111217	−	0.993796i	$-0.464525\pi$
$642$		0			0
$643$	14386.1	−	24917.4i	0.882319	−	1.52822i	0.0335621	−	0.999437i	$-0.489315\pi$
$643$	14386.1	−	24917.4i	0.882319	−	1.52822i	0.848756	−	0.528784i	$-0.177352\pi$
$644$	−347.138	+	601.261i	−0.0212409	+	0.0367904i
$645$		0			0
$646$	−3343.48	−	5791.08i	−0.203634	−	0.352704i
$647$	−7156.38			−0.434847			−0.217424	−	0.976077i	$-0.569765\pi$
$647$	−7156.38			−0.434847			−0.217424	+	0.976077i	$0.569765\pi$
$648$		0			0
$649$	−15055.1			−0.910578
$650$	−356.218	−	616.987i	−0.0214954	−	0.0372311i
$651$		0			0
$652$	1312.04	−	2272.51i	0.0788087	−	0.136501i
$653$	−7717.43	+	13367.0i	−0.462491	+	0.801057i	−0.999084	−	0.0427836i	$-0.986377\pi$
$653$	−7717.43	+	13367.0i	−0.462491	+	0.801057i	0.536594	+	0.843841i	$0.319711\pi$
$654$		0			0
$655$	−966.768	−	1674.49i	−0.0576714	−	0.0998898i
$656$	−19137.5			−1.13901
$657$		0			0
$658$	−1086.82			−0.0643901
$659$	3231.32	+	5596.81i	0.191008	+	0.330836i	0.945585	−	0.325376i	$-0.105491\pi$
$659$	3231.32	+	5596.81i	0.191008	+	0.330836i	−0.754577	+	0.656212i	$0.772158\pi$
$660$		0			0
$661$	−873.801	+	1513.47i	−0.0514174	+	0.0890576i	−0.890589	−	0.454810i	$-0.849707\pi$
$661$	−873.801	+	1513.47i	−0.0514174	+	0.0890576i	0.839171	+	0.543867i	$0.183041\pi$
$662$	−472.368	+	818.165i	−0.0277328	+	0.0480345i
$663$		0			0
$664$	7138.88	+	12364.9i	0.417233	+	0.722668i
$665$	−3906.79			−0.227818
$666$		0			0
$667$	−583.085			−0.0338488
$668$	−78.3332	−	135.677i	−0.00453713	−	0.00785854i
$669$		0			0
$670$	−1493.51	+	2586.83i	−0.0861181	+	0.149161i
$671$	−27.1152	+	46.9650i	−0.00156002	+	0.00270203i
$672$		0			0
$673$	2739.19	+	4744.42i	0.156892	+	0.271744i	0.933746	−	0.357936i	$-0.116519\pi$
$673$	2739.19	+	4744.42i	0.156892	+	0.271744i	−0.776855	+	0.629680i	$0.783186\pi$
$674$	7321.47			0.418416
$675$		0			0
$676$	5087.49			0.289457
$677$	2009.27	+	3480.15i	0.114066	+	0.197567i	0.917406	−	0.397953i	$-0.130279\pi$
$677$	2009.27	+	3480.15i	0.114066	+	0.197567i	−0.803340	+	0.595520i	$0.796946\pi$
$678$		0			0
$679$	−3797.01	+	6576.61i	−0.214604	+	0.371704i
$680$	2292.26	−	3970.31i	0.129271	−	0.223903i
$681$		0			0
$682$	−2055.80	−	3560.74i	−0.115426	−	0.199924i
$683$	9894.95			0.554348			0.277174	−	0.960820i	$-0.410602\pi$
$683$	9894.95			0.554348			0.277174	+	0.960820i	$0.410602\pi$
$684$		0			0
$685$	−14866.1			−0.829204
$686$	1617.90	+	2802.29i	0.0900464	+	0.155965i
$687$		0			0
$688$	−11833.0	+	20495.4i	−0.655713	+	1.13573i
$689$	−8665.52	+	15009.1i	−0.479144	+	0.829901i
$690$		0			0
$691$	−10924.0	−	18920.9i	−0.601400	−	1.04166i	−0.992609	−	0.121354i	$-0.961276\pi$
$691$	−10924.0	−	18920.9i	−0.601400	−	1.04166i	0.391209	−	0.920302i	$-0.372057\pi$
$692$	−33772.1			−1.85524
$693$		0			0
$694$	4735.18			0.258998
$695$	−5868.38	−	10164.3i	−0.320289	−	0.554756i
$696$		0			0
$697$	−15070.6	+	26103.1i	−0.818998	+	1.41855i
$698$	4088.43	−	7081.36i	0.221704	−	0.384002i
$699$		0			0
$700$	−646.410	−	1119.62i	−0.0349029	−	0.0604535i
$701$	15506.5			0.835480			0.417740	−	0.908567i	$-0.362822\pi$
$701$	15506.5			0.835480			0.417740	+	0.908567i	$0.362822\pi$
$702$		0			0
$703$	−24624.7			−1.32110
$704$	5953.63	+	10312.0i	0.318730	+	0.552056i
$705$		0			0
$706$	−664.986	+	1151.79i	−0.0354491	+	0.0613996i
$707$	4136.44	−	7164.52i	0.220038	−	0.381117i
$708$		0			0
$709$	−3199.85	−	5542.30i	−0.169496	−	0.293576i	0.768747	−	0.639553i	$-0.220881\pi$
$709$	−3199.85	−	5542.30i	−0.169496	−	0.293576i	−0.938243	+	0.345977i	$0.887547\pi$
$710$	539.954			0.0285410
$711$		0			0
$712$	−5807.42			−0.305677
$713$	1005.48	+	1741.54i	0.0528126	+	0.0914741i
$714$		0			0
$715$	3649.27	−	6320.72i	0.190874	−	0.330603i
$716$	−13535.4	+	23443.9i	−0.706481	+	1.22366i
$717$		0			0
$718$	−336.038	−	582.035i	−0.0174663	−	0.0302526i
$719$	1771.66			0.0918941			0.0459470	−	0.998944i	$-0.485369\pi$
$719$	1771.66			0.0918941			0.0459470	+	0.998944i	$0.485369\pi$
$720$		0			0
$721$	−1257.49			−0.0649532
$722$	2144.98	+	3715.22i	0.110565	+	0.191504i
$723$		0			0
$724$	13254.0	−	22956.7i	0.680363	−	1.17842i
$725$	542.885	−	940.304i	0.0278100	−	0.0481683i
$726$		0			0
$727$	−4787.53	−	8292.25i	−0.244236	−	0.423030i	0.717680	−	0.696373i	$-0.245204\pi$
$727$	−4787.53	−	8292.25i	−0.244236	−	0.423030i	−0.961917	+	0.273343i	$0.911871\pi$
$728$	3053.17			0.155437
$729$		0			0
$730$	−1583.61			−0.0802907
$731$	18636.9	+	32280.1i	0.942970	+	1.63327i
$732$		0			0
$733$	9895.25	−	17139.1i	0.498622	−	0.863638i	−0.501377	−	0.865229i	$-0.667173\pi$
$733$	9895.25	−	17139.1i	0.498622	−	0.863638i	0.999999	+	0.00159099i	$0.000506428\pi$
$734$	2691.85	−	4662.42i	0.135365	−	0.234459i
$735$		0			0
$736$	860.651	+	1490.69i	0.0431033	+	0.0746571i
$737$	−30600.4			−1.52942
$738$		0			0
$739$	−13106.5			−0.652407			−0.326203	−	0.945300i	$-0.605769\pi$
$739$	−13106.5			−0.652407			−0.326203	+	0.945300i	$0.605769\pi$
$740$	−4074.35	−	7056.97i	−0.202400	−	0.350567i
$741$		0			0
$742$	1128.99	−	1955.48i	0.0558581	−	0.0967491i
$743$	8534.44	−	14782.1i	0.421398	−	0.729882i	−0.574679	−	0.818379i	$-0.694873\pi$
$743$	8534.44	−	14782.1i	0.421398	−	0.729882i	0.996076	+	0.0884970i	$0.0282064\pi$
$744$		0			0
$745$	−3505.23	−	6071.24i	−0.172378	−	0.298568i
$746$	441.139			0.0216505
$747$		0			0
$748$	22669.2			1.10811
$749$	2118.88	+	3670.00i	0.103367	+	0.179037i
$750$		0			0
$751$	−2056.46	+	3561.90i	−0.0999220	+	0.173070i	−0.911652	−	0.410963i	$-0.865193\pi$
$751$	−2056.46	+	3561.90i	−0.0999220	+	0.173070i	0.811730	+	0.584033i	$0.198526\pi$
$752$	5509.93	−	9543.47i	0.267189	−	0.462785i
$753$		0			0
$754$	618.833	+	1071.85i	0.0298893	+	0.0517698i
$755$	−14706.3			−0.708897
$756$		0			0
$757$	17493.6			0.839915			0.419958	−	0.907544i	$-0.362045\pi$
$757$	17493.6			0.839915			0.419958	+	0.907544i	$0.362045\pi$
$758$	4875.10	+	8443.92i	0.233604	+	0.404613i
$759$		0			0
$760$	−3191.80	+	5528.36i	−0.152341	+	0.263862i
$761$	−2606.02	+	4513.76i	−0.124137	+	0.215011i	−0.921395	−	0.388627i	$-0.872949\pi$
$761$	−2606.02	+	4513.76i	−0.124137	+	0.215011i	0.797258	+	0.603638i	$0.206283\pi$
$762$		0			0
$763$	1906.87	+	3302.80i	0.0904763	+	0.156710i
$764$	−2087.34			−0.0988447
$765$		0			0
$766$	−6250.07			−0.294809
$767$	−7814.79	−	13535.6i	−0.367895	−	0.637213i
$768$		0			0
$769$	11662.3	−	20199.7i	0.546885	−	0.947232i	−0.451601	−	0.892220i	$-0.649147\pi$
$769$	11662.3	−	20199.7i	0.546885	−	0.947232i	0.998486	−	0.0550119i	$-0.0175197\pi$
$770$	−475.448	+	823.501i	−0.0222519	+	0.0385414i
$771$		0			0
$772$	993.321	+	1720.48i	0.0463088	+	0.0802092i
$773$	−20455.0			−0.951765			−0.475883	−	0.879509i	$-0.657871\pi$
$773$	−20455.0			−0.951765			−0.475883	+	0.879509i	$0.657871\pi$
$774$		0			0
$775$	−3744.62			−0.173562
$776$	6204.22	+	10746.0i	0.287008	+	0.497113i
$777$		0			0
$778$	4626.56	−	8013.43i	0.213201	−	0.369274i
$779$	20984.8	−	36346.7i	0.965158	−	1.67170i
$780$		0			0
$781$	2765.77	+	4790.46i	0.126718	+	0.219483i
$782$	796.037			0.0364018
$783$		0			0
$784$	−15170.6			−0.691079
$785$	−6379.95	−	11050.4i	−0.290077	−	0.502427i
$786$		0			0
$787$	−4555.49	+	7890.33i	−0.206335	+	0.357382i	−0.950557	−	0.310549i	$-0.899487\pi$
$787$	−4555.49	+	7890.33i	−0.206335	+	0.357382i	0.744222	+	0.667932i	$0.232820\pi$
$788$	17656.8	−	30582.4i	0.798219	−	1.38256i
$789$		0			0
$790$	703.013	+	1217.65i	0.0316608	+	0.0548382i
$791$	3297.15			0.148209
$792$		0			0
$793$	−56.2997			−0.00252114
$794$	2003.60	+	3470.34i	0.0895530	+	0.155110i
$795$		0			0
$796$	10747.2	−	18614.6i	0.478546	−	0.828867i
$797$	−3962.54	+	6863.33i	−0.176111	+	0.305033i	−0.940545	−	0.339668i	$-0.889685\pi$
$797$	−3962.54	+	6863.33i	−0.176111	+	0.305033i	0.764434	+	0.644702i	$0.223018\pi$
$798$		0			0
$799$	−8678.08	−	15030.9i	−0.384241	−	0.665524i
$800$	−3205.26			−0.141654
$801$		0			0
$802$	9550.08			0.420480
$803$	−8111.65	−	14049.8i	−0.356481	−	0.617443i
$804$		0			0
$805$	232.539	−	402.769i	0.0101813	−	0.0176345i
$806$	2134.24	−	3696.61i	0.0932696	−	0.161548i
$807$		0			0
$808$	−6758.84	−	11706.6i	−0.294276	−	0.509701i
$809$	33705.8			1.46481			0.732406	−	0.680868i	$-0.238397\pi$
$809$	33705.8			1.46481			0.732406	+	0.680868i	$0.238397\pi$
$810$		0			0
$811$	10424.5			0.451360			0.225680	−	0.974201i	$-0.427540\pi$
$811$	10424.5			0.451360			0.225680	+	0.974201i	$0.427540\pi$
$812$	1122.96	+	1945.03i	0.0485324	+	0.0840606i
$813$		0			0
$814$	−2996.77	+	5190.55i	−0.129038	+	0.223500i
$815$	−878.897	+	1522.29i	−0.0377748	+	0.0654278i
$816$		0			0
$817$	−25950.5	−	44947.7i	−1.11125	−	1.92475i
$818$	5258.11			0.224750
$819$		0			0
$820$	13888.4			0.591468
$821$	−4733.83	−	8199.23i	−0.201232	−	0.348545i	0.747693	−	0.664044i	$-0.231161\pi$
$821$	−4733.83	−	8199.23i	−0.201232	−	0.348545i	−0.948926	+	0.315499i	$0.897828\pi$
$822$		0			0
$823$	−580.274	+	1005.06i	−0.0245772	+	0.0425690i	−0.878052	−	0.478564i	$-0.841157\pi$
$823$	−580.274	+	1005.06i	−0.0245772	+	0.0425690i	0.853475	+	0.521133i	$0.174491\pi$
$824$	−1027.35	+	1779.42i	−0.0434338	+	0.0752296i
$825$		0			0
$826$	1018.16	+	1763.50i	0.0428889	+	0.0742857i
$827$	−26499.9			−1.11426			−0.557128	−	0.830426i	$-0.688097\pi$
$827$	−26499.9			−1.11426			−0.557128	+	0.830426i	$0.688097\pi$
$828$		0			0
$829$	653.861			0.0273939			0.0136969	−	0.999906i	$-0.495640\pi$
$829$	653.861			0.0273939			0.0136969	+	0.999906i	$0.495640\pi$
$830$	−2308.21	−	3997.94i	−0.0965292	−	0.167193i
$831$		0			0
$832$	−6180.80	+	10705.5i	−0.257549	+	0.446088i
$833$	−11946.7	+	20692.4i	−0.496915	+	0.860682i
$834$		0			0
$835$	52.4733	+	90.8864i	0.00217475	+	0.00376677i
$836$	−31565.2			−1.30587
$837$		0			0
$838$	6383.77			0.263155
$839$	20634.8	+	35740.6i	0.849099	+	1.47068i	0.882013	+	0.471224i	$0.156188\pi$
$839$	20634.8	+	35740.6i	0.849099	+	1.47068i	−0.0329145	+	0.999458i	$0.510479\pi$
$840$		0			0
$841$	11251.4	−	19488.0i	0.461330	−	0.799047i
$842$	2398.57	−	4154.45i	0.0981714	−	0.170038i
$843$		0			0
$844$	10181.8	+	17635.4i	0.415251	+	0.719236i
$845$	−3407.97			−0.138743
$846$		0			0
$847$	−520.008			−0.0210953
$848$	11447.5	+	19827.6i	0.463571	+	0.802928i
$849$		0			0
$850$	−741.154	+	1283.72i	−0.0299075	+	0.0518013i
$851$	1465.70	−	2538.67i	0.0590406	−	0.102261i
$852$		0			0
$853$	−2534.70	−	4390.22i	−0.101743	−	0.176223i	0.810660	−	0.585517i	$-0.199108\pi$
$853$	−2534.70	−	4390.22i	−0.101743	−	0.176223i	−0.912403	+	0.409294i	$0.865775\pi$
$854$	7.33506			0.000293912
$855$		0			0
$856$	6924.38			0.276484
$857$	−21819.5	−	37792.4i	−0.869707	−	1.50638i	−0.862296	−	0.506405i	$-0.830974\pi$
$857$	−21819.5	−	37792.4i	−0.869707	−	1.50638i	−0.00741160	−	0.999973i	$-0.502359\pi$
$858$		0			0
$859$	6449.06	−	11170.1i	0.256157	−	0.443678i	−0.709052	−	0.705156i	$-0.750877\pi$
$859$	6449.06	−	11170.1i	0.256157	−	0.443678i	0.965209	+	0.261479i	$0.0842101\pi$
$860$	8587.45	−	14873.9i	0.340499	−	0.589762i
$861$		0			0
$862$	−1909.81	−	3307.89i	−0.0754622	−	0.130704i
$863$	−8962.98			−0.353538			−0.176769	−	0.984252i	$-0.556565\pi$
$863$	−8962.98			−0.353538			−0.176769	+	0.984252i	$0.556565\pi$
$864$		0			0
$865$	22623.0			0.889256
$866$	1236.27	+	2141.29i	0.0485107	+	0.0840230i
$867$		0			0
$868$	3872.89	−	6708.05i	0.151445	−	0.262311i
$869$	−7202.00	+	12474.2i	−0.281141	+	0.486950i
$870$		0			0
$871$	−15884.0	−	27511.9i	−0.617921	−	1.07027i
$872$	6231.56			0.242004
$873$		0			0
$874$	−1108.42			−0.0428982
$875$	433.013	+	750.000i	0.0167297	+	0.0289767i
$876$		0			0
$877$	18860.1	−	32666.6i	0.726179	−	1.25778i	−0.232308	−	0.972642i	$-0.574628\pi$
$877$	18860.1	−	32666.6i	0.726179	−	1.25778i	0.958487	−	0.285136i	$-0.0920388\pi$
$878$	782.900	−	1356.02i	0.0300929	−	0.0521225i
$879$		0			0
$880$	−4820.82	−	8349.91i	−0.184670	−	0.319858i
$881$	7961.44			0.304458			0.152229	−	0.988345i	$-0.451355\pi$
$881$	7961.44			0.304458			0.152229	+	0.988345i	$0.451355\pi$
$882$		0			0
$883$	−37426.4			−1.42639			−0.713193	−	0.700968i	$-0.752752\pi$
$883$	−37426.4			−1.42639			−0.713193	+	0.700968i	$0.752752\pi$
$884$	11767.1	+	20381.2i	0.447704	+	0.775446i
$885$		0			0
$886$	−3115.84	+	5396.79i	−0.118147	+	0.204637i
$887$	13426.7	−	23255.6i	0.508256	−	0.880325i	−0.491699	−	0.870766i	$-0.663624\pi$
$887$	13426.7	−	23255.6i	0.508256	−	0.880325i	0.999954	−	0.00955935i	$-0.00304288\pi$
$888$		0			0
$889$	−5701.59	−	9875.44i	−0.215101	−	0.372567i
$890$	1877.71			0.0707202
$891$		0			0
$892$	27429.4			1.02960
$893$	12083.6	+	20929.4i	0.452813	+	0.784295i
$894$		0			0
$895$	9066.97	−	15704.5i	0.338632	−	0.586527i
$896$	4358.34	−	7548.86i	0.162502	−	0.281462i
$897$		0			0
$898$	1662.73	+	2879.94i	0.0617885	+	0.107021i
$899$	6505.26			0.241338
$900$		0			0
$901$	36059.3			1.33331
$902$	−5107.60	−	8846.63i	−0.188542	−	0.326564i
$903$		0			0
$904$	2693.73	−	4665.67i	0.0991063	−	0.171657i
$905$	−8878.52	+	15378.1i	−0.326113	+	0.564844i
$906$		0			0
$907$	−13575.4	−	23513.4i	−0.496985	−	0.860803i	0.503009	−	0.864281i	$-0.332226\pi$
$907$	−13575.4	−	23513.4i	−0.496985	−	0.860803i	−0.999994	+	0.00347836i	$0.998893\pi$
$908$	43097.1			1.57514
$909$		0			0
$910$	−987.180			−0.0359612
$911$	7650.25	+	13250.6i	0.278226	+	0.481902i	0.970944	−	0.239307i	$-0.0769202\pi$
$911$	7650.25	+	13250.6i	0.278226	+	0.481902i	−0.692718	+	0.721209i	$0.743587\pi$
$912$		0			0
$913$	23646.4	−	40956.8i	0.857156	−	1.48464i
$914$	−6567.30	+	11374.9i	−0.237666	+	0.411650i
$915$		0			0
$916$	17982.1	+	31145.8i	0.648628	+	1.12346i
$917$	−2679.19			−0.0964826
$918$		0			0
$919$	−26325.6			−0.944943			−0.472471	−	0.881346i	$-0.656638\pi$
$919$	−26325.6			−0.944943			−0.472471	+	0.881346i	$0.656638\pi$
$920$	−379.962	−	658.114i	−0.0136163	−	0.0235841i
$921$		0			0
$922$	1896.34	−	3284.55i	0.0677359	−	0.117322i
$923$	−2871.31	+	4973.25i	−0.102395	+	0.177353i
$924$		0			0
$925$	2729.29	+	4727.28i	0.0970147	+	0.168034i
$926$	−10389.9			−0.368719
$927$		0			0
$928$	5568.27			0.196969
$929$	17753.5	+	30750.0i	0.626991	+	1.08598i	0.988152	+	0.153477i	$0.0490469\pi$
$929$	17753.5	+	30750.0i	0.626991	+	1.08598i	−0.361162	+	0.932503i	$0.617620\pi$
$930$		0			0
$931$	16635.0	−	28812.6i	0.585595	−	1.01428i
$932$	−339.926	+	588.769i	−0.0119470	+	0.0206929i
$933$		0			0
$934$	4350.70	+	7535.63i	0.152419	+	0.263997i
$935$	−15185.5			−0.531143
$936$		0			0
$937$	35105.4			1.22395			0.611975	−	0.790877i	$-0.290375\pi$
$937$	35105.4			1.22395			0.611975	+	0.790877i	$0.290375\pi$
$938$	2069.46	+	3584.41i	0.0720366	+	0.124771i
$939$		0			0
$940$	−3998.65	+	6925.87i	−0.138746	+	0.240316i
$941$	1787.23	−	3095.58i	0.0619151	−	0.107240i	−0.833406	−	0.552661i	$-0.813613\pi$
$941$	1787.23	−	3095.58i	0.0619151	−	0.107240i	0.895321	+	0.445421i	$0.146946\pi$
$942$		0			0
$943$	2498.10	+	4326.83i	0.0862664	+	0.149418i
$944$	−20647.3			−0.711876
$945$		0			0
$946$	−12632.5			−0.434163
$947$	−16529.2	−	28629.5i	−0.567189	−	0.982400i	−0.996842	−	0.0794061i	$-0.974698\pi$
$947$	−16529.2	−	28629.5i	−0.567189	−	0.982400i	0.429653	−	0.902994i	$-0.358636\pi$
$948$		0			0
$949$	8421.17	−	14585.9i	0.288053	−	0.498923i
$950$	1032.00	−	1787.48i	0.0352449	−	0.0610459i
$951$		0			0
$952$	−3176.24	−	5501.42i	−0.108133	−	0.187292i
$953$	1355.24			0.0460656			0.0230328	−	0.999735i	$-0.492668\pi$
$953$	1355.24			0.0460656			0.0230328	+	0.999735i	$0.492668\pi$
$954$		0			0
$955$	1398.25			0.0473784
$956$	−20477.2	−	35467.5i	−0.692760	−	1.19990i
$957$		0			0
$958$	1581.03	−	2738.43i	0.0533203	−	0.0923534i
$959$	−10299.5	+	17839.3i	−0.346809	+	0.600690i
$960$		0			0
$961$	3677.79	+	6370.11i	0.123453	+	0.213827i
$962$	−6222.23			−0.208537
$963$		0			0
$964$	−22520.6			−0.752428
$965$	−665.399	−	1152.50i	−0.0221968	−	0.0384460i
$966$		0			0
$967$	−28059.0	+	48599.6i	−0.933110	+	1.61619i	−0.155139	+	0.987893i	$0.549583\pi$
$967$	−28059.0	+	48599.6i	−0.933110	+	1.61619i	−0.777971	+	0.628301i	$0.783751\pi$
$968$	−424.840	+	735.844i	−0.0141063	+	0.0244328i
$969$		0			0
$970$	−2006.01	−	3474.51i	−0.0664010	−	0.115010i
$971$	32718.5			1.08135			0.540673	−	0.841233i	$-0.318170\pi$
$971$	32718.5			1.08135			0.540673	+	0.841233i	$0.318170\pi$
$972$		0			0
$973$	−16262.9			−0.535834
$974$	−2356.08	−	4080.86i	−0.0775090	−	0.134250i
$975$		0			0
$976$	−37.1870	+	64.4098i	−0.00121960	+	0.00211241i
$977$	4425.44	−	7665.09i	0.144915	−	0.251001i	−0.784426	−	0.620222i	$-0.787042\pi$
$977$	4425.44	−	7665.09i	0.144915	−	0.251001i	0.929341	+	0.369222i	$0.120376\pi$
$978$		0			0
$979$	9618.09	+	16659.0i	0.313989	+	0.543845i
$980$	11009.5			0.358864
$981$		0			0
$982$	−2121.29			−0.0689338
$983$	17054.0	+	29538.3i	0.553343	+	0.958419i	0.998030	+	0.0627329i	$0.0199816\pi$
$983$	17054.0	+	29538.3i	0.553343	+	0.958419i	−0.444687	+	0.895686i	$0.646685\pi$
$984$		0			0
$985$	−11827.8	+	20486.3i	−0.382604	+	0.662689i
$986$	1287.56	−	2230.11i	0.0415864	−	0.0720297i
$987$		0			0
$988$	−16384.8	−	28379.4i	−0.527602	−	0.913834i
$989$	6178.47			0.198649
$990$		0			0
$991$	−52154.2			−1.67178			−0.835890	−	0.548897i	$-0.815048\pi$
$991$	−52154.2			−1.67178			−0.835890	+	0.548897i	$0.815048\pi$
$992$	−9601.96	−	16631.1i	−0.307321	−	0.532296i
$993$		0			0
$994$	374.091	−	647.944i	0.0119371	−	0.0206756i
$995$	−7199.23	+	12469.4i	−0.229378	+	0.397294i
$996$		0			0
$997$	−1055.55	−	1828.27i	−0.0335302	−	0.0580760i	0.848773	−	0.528757i	$-0.177342\pi$
$997$	−1055.55	−	1828.27i	−0.0335302	−	0.0580760i	−0.882304	+	0.470681i	$0.844008\pi$
$998$	−11020.7			−0.349554
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	405.4.e.o.271.2		4
3.2	odd	2		405.4.e.p.271.1		4
9.2	odd	6		405.4.e.p.136.1		4
9.4	even	3		405.4.a.f.1.1	yes	2
9.5	odd	6		405.4.a.c.1.2	✓	2
9.7	even	3	inner	405.4.e.o.136.2		4
45.4	even	6		2025.4.a.i.1.2		2
45.14	odd	6		2025.4.a.m.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
405.4.a.c.1.2	✓	2	9.5	odd	6
405.4.a.f.1.1	yes	2	9.4	even	3
405.4.e.o.136.2		4	9.7	even	3	inner
405.4.e.o.271.2		4	1.1	even	1	trivial
405.4.e.p.136.1		4	9.2	odd	6
405.4.e.p.271.1		4	3.2	odd	2
2025.4.a.i.1.2		2	45.4	even	6
2025.4.a.m.1.1		2	45.14	odd	6

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:	\( N \)	\(=\)	\( 405 = 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	405.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.366025 + 0.633975i) q^{2} +(3.73205 - 6.46410i) q^{4} +(-2.50000 + 4.33013i) q^{5} +(3.46410 + 6.00000i) q^{7} +11.3205 q^{8} +O(q^{10})\)	\(q+(0.366025 + 0.633975i) q^{2} +(3.73205 - 6.46410i) q^{4} +(-2.50000 + 4.33013i) q^{5} +(3.46410 + 6.00000i) q^{7} +11.3205 q^{8} -3.66025 q^{10} +(-18.7487 - 32.4737i) q^{11} +(19.4641 - 33.7128i) q^{13} +(-2.53590 + 4.39230i) q^{14} +(-25.7128 - 44.5359i) q^{16} -80.9948 q^{17} +112.779 q^{19} +(18.6603 + 32.3205i) q^{20} +(13.7250 - 23.7724i) q^{22} +(-6.71281 + 11.6269i) q^{23} +(-12.5000 - 21.6506i) q^{25} +28.4974 q^{26} +51.7128 q^{28} +(21.7154 + 37.6122i) q^{29} +(74.8923 - 129.717i) q^{31} +(64.1051 - 111.033i) q^{32} +(-29.6462 - 51.3487i) q^{34} -34.6410 q^{35} -218.344 q^{37} +(41.2801 + 71.4993i) q^{38} +(-28.3013 + 49.0192i) q^{40} +(186.069 - 322.281i) q^{41} +(-230.100 - 398.545i) q^{43} -279.885 q^{44} -9.82824 q^{46} +(107.144 + 185.578i) q^{47} +(147.500 - 255.477i) q^{49} +(9.15064 - 15.8494i) q^{50} +(-145.282 - 251.636i) q^{52} -445.205 q^{53} +187.487 q^{55} +(39.2154 + 67.9230i) q^{56} +(-15.8968 + 27.5340i) q^{58} +(200.749 - 347.707i) q^{59} +(-0.723122 - 1.25248i) q^{61} +109.650 q^{62} -317.549 q^{64} +(97.3205 + 168.564i) q^{65} +(408.033 - 706.734i) q^{67} +(-302.277 + 523.559i) q^{68} +(-12.6795 - 21.9615i) q^{70} -147.518 q^{71} +432.651 q^{73} +(-79.9193 - 138.424i) q^{74} +(420.899 - 729.018i) q^{76} +(129.895 - 224.985i) q^{77} +(-192.067 - 332.669i) q^{79} +257.128 q^{80} +272.424 q^{82} +(630.615 + 1092.26i) q^{83} +(202.487 - 350.718i) q^{85} +(168.445 - 291.755i) q^{86} +(-212.245 - 367.619i) q^{88} -513.000 q^{89} +269.703 q^{91} +(50.1051 + 86.7846i) q^{92} +(-78.4346 + 135.853i) q^{94} +(-281.949 + 488.349i) q^{95} +(548.051 + 949.252i) q^{97} +215.955 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} + 8 q^{4} - 10 q^{5} - 24 q^{8}+O(q^{10}) \) 4 * q - 2 * q^2 + 8 * q^4 - 10 * q^5 - 24 * q^8	\( 4 q - 2 q^{2} + 8 q^{4} - 10 q^{5} - 24 q^{8} + 20 q^{10} + 22 q^{11} + 64 q^{13} - 24 q^{14} + 8 q^{16} + 64 q^{17} - 20 q^{19} + 40 q^{20} + 190 q^{22} + 84 q^{23} - 50 q^{25} - 80 q^{26} + 96 q^{28} + 170 q^{29} + 258 q^{31} + 104 q^{32} - 368 q^{34} + 152 q^{37} + 418 q^{38} + 60 q^{40} + 578 q^{41} - 380 q^{43} - 496 q^{44} - 552 q^{46} + 484 q^{47} + 590 q^{49} - 50 q^{50} - 304 q^{52} - 1088 q^{53} - 220 q^{55} + 240 q^{56} + 314 q^{58} + 706 q^{59} - 668 q^{61} - 372 q^{62} + 448 q^{64} + 320 q^{65} + 1452 q^{67} - 544 q^{68} - 120 q^{70} - 1948 q^{71} + 2368 q^{73} - 964 q^{74} + 776 q^{76} + 672 q^{77} - 408 q^{79} - 80 q^{80} - 580 q^{82} + 444 q^{83} - 160 q^{85} + 556 q^{86} - 1812 q^{88} - 2052 q^{89} + 192 q^{91} + 48 q^{92} + 580 q^{94} + 50 q^{95} + 668 q^{97} - 1180 q^{98}+O(q^{100}) \) 4 * q - 2 * q^2 + 8 * q^4 - 10 * q^5 - 24 * q^8 + 20 * q^10 + 22 * q^11 + 64 * q^13 - 24 * q^14 + 8 * q^16 + 64 * q^17 - 20 * q^19 + 40 * q^20 + 190 * q^22 + 84 * q^23 - 50 * q^25 - 80 * q^26 + 96 * q^28 + 170 * q^29 + 258 * q^31 + 104 * q^32 - 368 * q^34 + 152 * q^37 + 418 * q^38 + 60 * q^40 + 578 * q^41 - 380 * q^43 - 496 * q^44 - 552 * q^46 + 484 * q^47 + 590 * q^49 - 50 * q^50 - 304 * q^52 - 1088 * q^53 - 220 * q^55 + 240 * q^56 + 314 * q^58 + 706 * q^59 - 668 * q^61 - 372 * q^62 + 448 * q^64 + 320 * q^65 + 1452 * q^67 - 544 * q^68 - 120 * q^70 - 1948 * q^71 + 2368 * q^73 - 964 * q^74 + 776 * q^76 + 672 * q^77 - 408 * q^79 - 80 * q^80 - 580 * q^82 + 444 * q^83 - 160 * q^85 + 556 * q^86 - 1812 * q^88 - 2052 * q^89 + 192 * q^91 + 48 * q^92 + 580 * q^94 + 50 * q^95 + 668 * q^97 - 1180 * q^98

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