LMFDB - Embedded newform 405.4.e.p.136.1

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			136.1
Root			$0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	405.136
Dual form			405.4.e.p.271.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.366025 + 0.633975i) q^{2} +(3.73205 + 6.46410i) q^{4} +(2.50000 + 4.33013i) q^{5} +(3.46410 - 6.00000i) q^{7} -11.3205 q^{8} +O(q^{10})$	\(q+(-0.366025 + 0.633975i) q^{2} +(3.73205 + 6.46410i) q^{4} +(2.50000 + 4.33013i) q^{5} +(3.46410 - 6.00000i) q^{7} -11.3205 q^{8} -3.66025 q^{10} +(18.7487 - 32.4737i) q^{11} +(19.4641 + 33.7128i) q^{13} +(2.53590 + 4.39230i) q^{14} +(-25.7128 + 44.5359i) q^{16} +80.9948 q^{17} +112.779 q^{19} +(-18.6603 + 32.3205i) q^{20} +(13.7250 + 23.7724i) q^{22} +(6.71281 + 11.6269i) q^{23} +(-12.5000 + 21.6506i) q^{25} -28.4974 q^{26} +51.7128 q^{28} +(-21.7154 + 37.6122i) q^{29} +(74.8923 + 129.717i) q^{31} +(-64.1051 - 111.033i) q^{32} +(-29.6462 + 51.3487i) q^{34} +34.6410 q^{35} -218.344 q^{37} +(-41.2801 + 71.4993i) q^{38} +(-28.3013 - 49.0192i) q^{40} +(-186.069 - 322.281i) q^{41} +(-230.100 + 398.545i) q^{43} +279.885 q^{44} -9.82824 q^{46} +(-107.144 + 185.578i) q^{47} +(147.500 + 255.477i) q^{49} +(-9.15064 - 15.8494i) q^{50} +(-145.282 + 251.636i) q^{52} +445.205 q^{53} +187.487 q^{55} +(-39.2154 + 67.9230i) q^{56} +(-15.8968 - 27.5340i) q^{58} +(-200.749 - 347.707i) q^{59} +(-0.723122 + 1.25248i) q^{61} -109.650 q^{62} -317.549 q^{64} +(-97.3205 + 168.564i) q^{65} +(408.033 + 706.734i) q^{67} +(302.277 + 523.559i) q^{68} +(-12.6795 + 21.9615i) q^{70} +147.518 q^{71} +432.651 q^{73} +(79.9193 - 138.424i) q^{74} +(420.899 + 729.018i) q^{76} +(-129.895 - 224.985i) q^{77} +(-192.067 + 332.669i) q^{79} -257.128 q^{80} +272.424 q^{82} +(-630.615 + 1092.26i) q^{83} +(202.487 + 350.718i) q^{85} +(-168.445 - 291.755i) q^{86} +(-212.245 + 367.619i) q^{88} +513.000 q^{89} +269.703 q^{91} +(-50.1051 + 86.7846i) q^{92} +(-78.4346 - 135.853i) q^{94} +(281.949 + 488.349i) q^{95} +(548.051 - 949.252i) q^{97} -215.955 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/405\mathbb{Z}\right)^\times$.

$n$	$82$	$326$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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	$-0.874642\pi$
$2$	−0.366025	+	0.633975i	−0.129410	+	0.224144i	0.794038	+	0.607868i	$0.207975\pi$
$3$		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	−0.757219	−	0.653161i	$-0.773443\pi$
$7$	3.46410	−	6.00000i	0.187044	−	0.323970i	0.944263	+	0.329191i	$0.106776\pi$
$8$	−11.3205			−0.500301
$9$		0			0
$10$	−3.66025			−0.115747
$11$	18.7487	−	32.4737i	0.513904	−	0.890109i	−0.485965	−	0.873978i	$-0.661532\pi$
$11$	18.7487	−	32.4737i	0.513904	−	0.890109i	0.999870	−	0.0161306i	$-0.00513476\pi$
$12$		0			0
$13$	19.4641	+	33.7128i	0.415259	+	0.719250i	0.995456	−	0.0952265i	$-0.0303575\pi$
$13$	19.4641	+	33.7128i	0.415259	+	0.719250i	−0.580196	+	0.814477i	$0.697024\pi$
$14$	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	$-0.303924\pi$
$17$	80.9948			1.15554			0.577769	+	0.816201i	$0.303924\pi$
$18$		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	$-0.147283\pi$
$23$	6.71281	+	11.6269i	0.0608573	+	0.105408i	−0.833992	+	0.551777i	$0.813950\pi$
$24$		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	$-0.877738\pi$
$29$	−21.7154	+	37.6122i	−0.139050	+	0.240841i	0.788087	+	0.615563i	$0.211072\pi$
$30$		0			0
$31$	74.8923	+	129.717i	0.433905	+	0.751546i	0.997206	−	0.0747066i	$-0.0238020\pi$
$31$	74.8923	+	129.717i	0.433905	+	0.751546i	−0.563301	+	0.826252i	$0.690469\pi$
$32$	−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	−0.965318	−	0.261078i	$-0.915922\pi$
$41$	−186.069	−	322.281i	−0.708759	−	1.22761i	0.256558	−	0.966529i	$-0.417411\pi$
$42$		0			0
$43$	−230.100	+	398.545i	−0.816045	+	1.41343i	0.0925309	+	0.995710i	$0.470504\pi$
$43$	−230.100	+	398.545i	−0.816045	+	1.41343i	−0.908575	+	0.417721i	$0.862829\pi$
$44$	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	$-0.941233\pi$
$47$	−107.144	+	185.578i	−0.332521	+	0.575944i	0.650484	+	0.759520i	$0.274566\pi$
$48$		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	$-0.304254\pi$
$53$	445.205			1.15384			0.576921	+	0.816800i	$0.304254\pi$
$54$		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	$-0.312742\pi$
$59$	−200.749	−	347.707i	−0.442970	−	0.767247i	−0.997908	+	0.0646445i	$0.979409\pi$
$60$		0			0
$61$	−0.723122	+	1.25248i	−0.00151781	+	0.00262892i	−0.866783	−	0.498685i	$-0.833816\pi$
$61$	−0.723122	+	1.25248i	−0.00151781	+	0.00262892i	0.865266	+	0.501314i	$0.167150\pi$
$62$	−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	0.950652	+	0.310259i	$0.100416\pi$
$67$	408.033	+	706.734i	0.744018	+	1.28868i	−0.206634	+	0.978418i	$0.566251\pi$
$68$	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	$-0.460655\pi$
$71$	147.518			0.246580			0.123290	+	0.992371i	$0.460655\pi$
$72$		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	−0.969764	−	0.244044i	$-0.921526\pi$
$79$	−192.067	+	332.669i	−0.273534	+	0.473775i	0.696230	+	0.717819i	$0.254859\pi$
$80$	−257.128			−0.359347
$81$		0			0
$82$	272.424			0.366881
$83$	−630.615	+	1092.26i	−0.833964	+	1.44447i	0.0609071	+	0.998143i	$0.480601\pi$
$83$	−630.615	+	1092.26i	−0.833964	+	1.44447i	−0.894871	+	0.446325i	$0.852733\pi$
$84$		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	$-0.401178\pi$
$89$	513.000			0.610988			0.305494	+	0.952194i	$0.401178\pi$
$90$		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	−0.422513	−	0.906357i	$-0.638852\pi$
$97$	548.051	−	949.252i	0.573672	−	0.993629i	0.996185	−	0.0872717i	$-0.0278148\pi$
$98$	−215.955			−0.222599
$99$		0			0
$100$	−186.603			−0.186603
$101$	597.043	−	1034.11i	0.588198	−	1.01879i	−0.406270	−	0.913753i	$-0.633171\pi$
$101$	597.043	−	1034.11i	0.588198	−	1.01879i	0.994468	−	0.105036i	$-0.0334959\pi$
$102$		0			0
$103$	−90.7513	−	157.186i	−0.0868154	−	0.150369i	0.819348	−	0.573297i	$-0.194336\pi$
$103$	−90.7513	−	157.186i	−0.0868154	−	0.150369i	−0.906163	+	0.422928i	$0.861002\pi$
$104$	−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	$-0.589114\pi$
$107$	−611.667			−0.552636			−0.276318	+	0.961066i	$0.589114\pi$
$108$		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	$-0.230142\pi$
$113$	−237.951	−	412.144i	−0.198094	−	0.343108i	−0.947910	+	0.318538i	$0.896808\pi$
$114$		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	$-0.125504\pi$
$131$	193.354	+	334.898i	0.128957	+	0.223360i	−0.794316	+	0.607505i	$0.792170\pi$
$132$		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	−0.138893	+	0.990307i	$0.544354\pi$
$137$	−1486.61	+	2574.88i	−0.927078	+	1.60575i	−0.788185	+	0.615439i	$0.788979\pi$
$138$		0			0
$139$	−1173.68	−	2032.87i	−0.716187	−	1.24047i	−0.962500	−	0.271282i	$-0.912552\pi$
$139$	−1173.68	−	2032.87i	−0.716187	−	1.24047i	0.246313	−	0.969190i	$-0.420781\pi$
$140$	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	$-0.0407132\pi$
$149$	701.046	+	1214.25i	0.385449	+	0.667618i	−0.606382	+	0.795173i	$0.707380\pi$
$150$		0			0
$151$	1470.63	−	2547.21i	0.792571	−	1.37277i	−0.131799	−	0.991276i	$-0.542075\pi$
$151$	1470.63	−	2547.21i	0.792571	−	1.37277i	0.924370	−	0.381497i	$-0.124591\pi$
$152$	−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	−0.983450	−	0.181179i	$-0.942009\pi$
$157$	−1275.99	−	2210.08i	−0.648631	−	1.12346i	0.334819	−	0.942282i	$-0.391325\pi$
$158$	−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	$-0.168215\pi$
$167$	−10.4947	−	18.1773i	−0.00486288	−	0.00842276i	−0.868447	+	0.495783i	$0.834881\pi$
$168$		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	0.404121	−	0.914706i	$-0.367577\pi$
$173$	2262.30	−	3918.43i	0.994219	−	1.72204i	0.590098	−	0.807332i	$-0.299089\pi$
$174$		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	$-0.226565\pi$
$179$	3626.79			1.51441			0.757204	+	0.653179i	$0.226565\pi$
$180$		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	$-0.816464\pi$
$191$	139.825	−	242.185i	0.0529707	−	0.0917479i	0.891295	+	0.453424i	$0.149798\pi$
$192$		0			0
$193$	−133.080	−	230.501i	−0.0496336	−	0.0859679i	0.840141	−	0.542368i	$-0.182472\pi$
$193$	−133.080	−	230.501i	−0.0496336	−	0.0859679i	−0.889775	+	0.456400i	$0.849139\pi$
$194$	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	$-0.826768\pi$
$197$	−4731.12			−1.71106			−0.855528	+	0.517756i	$0.826768\pi$
$198$		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	0.552992	−	0.833187i	$-0.313486\pi$
$211$	−1364.10	−	2362.69i	−0.445065	−	0.770875i	−0.998057	+	0.0623117i	$0.980153\pi$
$212$	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	−0.446386	−	0.894841i	$-0.647289\pi$
$223$	1837.42	−	3182.51i	0.551762	−	0.955680i	0.998148	−	0.0608392i	$-0.0193777\pi$
$224$	−888.267			−0.264954
$225$		0			0
$226$	348.385			0.102541
$227$	−2886.96	+	5000.36i	−0.844115	+	1.46205i	0.0422732	+	0.999106i	$0.486540\pi$
$227$	−2886.96	+	5000.36i	−0.844115	+	1.46205i	−0.886388	+	0.462943i	$0.846793\pi$
$228$		0			0
$229$	−2409.14	−	4172.75i	−0.695198	−	1.20412i	−0.970114	−	0.242650i	$-0.921983\pi$
$229$	−2409.14	−	4172.75i	−0.695198	−	1.20412i	0.274916	−	0.961468i	$-0.411350\pi$
$230$	−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	$-0.495924\pi$
$233$	91.0828			0.0256096			0.0128048	+	0.999918i	$0.495924\pi$
$234$		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	−0.951354	−	0.308098i	$-0.900307\pi$
$239$	−2743.42	−	4751.74i	−0.742498	−	1.28604i	0.208856	−	0.977946i	$-0.433026\pi$
$240$		0			0
$241$	−1508.60	+	2612.97i	−0.403225	+	0.698406i	−0.994113	−	0.108347i	$-0.965444\pi$
$241$	−1508.60	+	2612.97i	−0.403225	+	0.698406i	0.590888	+	0.806754i	$0.298778\pi$
$242$	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	$-0.611999\pi$
$251$	−2740.98			−0.689280			−0.344640	+	0.938735i	$0.611999\pi$
$252$		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	$-0.0676781\pi$
$257$	1260.70	+	2183.60i	0.305993	+	0.529996i	−0.671489	+	0.741015i	$0.734345\pi$
$258$		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	−0.473446	−	0.880823i	$-0.656990\pi$
$263$	2243.86	−	3886.48i	0.526092	−	0.911219i	0.999538	−	0.0303955i	$-0.00967668\pi$
$264$		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	$-0.0821712\pi$
$269$	8531.47			1.93373			0.966864	+	0.255291i	$0.0821712\pi$
$270$		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	−0.253201	−	0.967414i	$-0.581484\pi$
$277$	3278.79	−	5679.03i	0.711204	−	1.23184i	0.964405	−	0.264428i	$-0.0851831\pi$
$278$	1718.38			0.370726
$279$		0			0
$280$	−392.154			−0.0836989
$281$	−3542.02	+	6134.96i	−0.751954	+	1.30242i	0.194920	+	0.980819i	$0.437555\pi$
$281$	−3542.02	+	6134.96i	−0.751954	+	1.30242i	−0.946874	+	0.321604i	$0.895778\pi$
$282$		0			0
$283$	−1036.47	−	1795.21i	−0.217709	−	0.377082i	0.736399	−	0.676548i	$-0.236525\pi$
$283$	−1036.47	−	1795.21i	−0.217709	−	0.377082i	−0.954107	+	0.299466i	$0.903192\pi$
$284$	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	−0.964610	−	0.263680i	$-0.915064\pi$
$293$	−3564.20	−	6173.38i	−0.710658	−	1.23090i	0.253952	−	0.967217i	$-0.418270\pi$
$294$		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	−0.976741	−	0.214423i	$-0.931213\pi$
$311$	−3696.95	−	6403.30i	−0.674067	−	1.16752i	0.302674	−	0.953094i	$-0.402121\pi$
$312$		0			0
$313$	466.528	−	808.050i	0.0842482	−	0.145922i	−0.820822	−	0.571184i	$-0.806484\pi$
$313$	466.528	−	808.050i	0.0842482	−	0.145922i	0.905071	+	0.425261i	$0.139818\pi$
$314$	1868.18			0.335756
$315$		0			0
$316$	−2867.21			−0.510421
$317$	−4367.34	+	7564.45i	−0.773799	+	1.34026i	0.161669	+	0.986845i	$0.448312\pi$
$317$	−4367.34	+	7564.45i	−0.773799	+	1.34026i	−0.935467	+	0.353413i	$0.885021\pi$
$318$		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	−0.807464	−	0.589917i	$-0.799160\pi$
$331$	645.266	−	1117.63i	0.107151	−	0.185591i	0.914615	+	0.404326i	$0.132494\pi$
$332$	−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	0.914028	+	0.405651i	$0.132955\pi$
$337$	5000.66	+	8661.40i	0.808318	+	1.40005i	−0.105710	+	0.994397i	$0.533711\pi$
$338$	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	−1.00000		0.000399827i	$-0.999873\pi$
$347$	−3234.18	−	5601.77i	−0.500346	−	0.866625i	0.499654	−	0.866225i	$-0.333461\pi$
$348$		0			0
$349$	−5584.89	+	9673.32i	−0.856597	+	1.48367i	0.0185577	+	0.999828i	$0.494093\pi$
$349$	−5584.89	+	9673.32i	−0.856597	+	1.48367i	−0.875155	+	0.483842i	$0.839241\pi$
$350$	−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	$-0.877068\pi$
$353$	−908.387	+	1573.37i	−0.136965	+	0.237230i	0.789382	+	0.613903i	$0.210401\pi$
$354$		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	$-0.478503\pi$
$359$	918.073			0.134969			0.0674847	+	0.997720i	$0.478503\pi$
$360$		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	0.476630	+	0.879104i	$0.341858\pi$
$367$	−3677.14	+	6368.99i	−0.523011	+	0.905881i	−0.999641	+	0.0267777i	$0.991475\pi$
$368$	−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	0.886180	−	0.463341i	$-0.153349\pi$
$373$	301.303	+	521.873i	0.0418255	+	0.0724438i	−0.844355	+	0.535784i	$0.820016\pi$
$374$	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	0.996613	+	0.0822399i	$0.0262074\pi$
$383$	4268.87	+	7393.91i	0.569528	+	0.986452i	−0.427084	+	0.904212i	$0.640459\pi$
$384$		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	−0.0791316	−	0.996864i	$-0.525215\pi$
$389$	6319.99	−	10946.5i	0.823744	−	1.42677i	0.902875	−	0.429902i	$-0.141452\pi$
$390$		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	−0.911247	−	0.411860i	$-0.864879\pi$
$401$	−6522.82	−	11297.9i	−0.812305	−	1.40695i	0.0989419	−	0.995093i	$-0.468454\pi$
$402$		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	0.997229	−	0.0743978i	$-0.0237035\pi$
$409$	3591.36	+	6220.41i	0.434184	+	0.752029i	−0.563045	+	0.826426i	$0.690370\pi$
$410$	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	−0.999953	−	0.00969927i	$-0.996913\pi$
$419$	−4360.20	−	7552.09i	−0.508376	−	0.880534i	0.491577	−	0.870834i	$-0.336421\pi$
$420$		0			0
$421$	−3276.51	+	5675.09i	−0.379305	+	0.656976i	−0.990961	−	0.134148i	$-0.957170\pi$
$421$	−3276.51	+	5675.09i	−0.379305	+	0.656976i	0.611656	+	0.791124i	$0.290504\pi$
$422$	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	$-0.405824\pi$
$431$	5217.70			0.583127			0.291564	+	0.956551i	$0.405824\pi$
$432$		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	−0.918287	−	0.395916i	$-0.870427\pi$
$439$	−1069.46	+	1852.36i	−0.116270	+	0.201386i	0.802017	+	0.597302i	$0.203761\pi$
$440$	−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	$-0.984226\pi$
$443$	−4256.31	+	7372.15i	−0.456486	+	0.790658i	0.542286	+	0.840194i	$0.317559\pi$
$444$		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	$-0.576732\pi$
$449$	−4542.67			−0.477465			−0.238733	+	0.971085i	$0.576732\pi$
$450$		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	0.116232	−	0.993222i	$-0.462918\pi$
$457$	8971.10	−	15538.4i	0.918272	−	1.59049i	0.802039	−	0.597271i	$-0.203748\pi$
$458$	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	$-0.749046\pi$
$461$	2590.44	−	4486.78i	0.261711	−	0.453297i	0.966697	+	0.255924i	$0.0823798\pi$
$462$		0			0
$463$	−7096.44	−	12291.4i	−0.712310	−	1.23376i	−0.963988	−	0.265947i	$-0.914315\pi$
$463$	−7096.44	−	12291.4i	−0.712310	−	1.23376i	0.251677	−	0.967811i	$-0.419018\pi$
$464$	−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	$-0.700439\pi$
$467$	−11886.3			−1.17780			−0.588901	+	0.808205i	$0.700439\pi$
$468$		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	$-0.767284\pi$
$479$	2159.73	−	3740.76i	0.206014	−	0.356826i	0.950455	+	0.310861i	$0.100618\pi$
$480$		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	$-0.124151\pi$
$491$	1448.87	+	2509.51i	0.133170	+	0.230657i	−0.791727	+	0.610875i	$0.790818\pi$
$492$		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	−0.976385	−	0.216037i	$-0.930687\pi$
$499$	−7527.29	−	13037.6i	−0.675286	−	1.16963i	0.301099	−	0.953593i	$-0.402646\pi$
$500$	−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	$-0.257326\pi$
$503$	15582.5			1.38129			0.690646	+	0.723193i	$0.257326\pi$
$504$		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	$-0.223388\pi$
$509$	−2035.51	−	3525.60i	−0.177254	−	0.307013i	−0.940939	+	0.338576i	$0.890055\pi$
$510$		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	$-0.785773\pi$
$521$	−18597.9			−1.56389			−0.781947	+	0.623345i	$0.785773\pi$
$522$		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	−0.965584	−	0.260091i	$-0.916248\pi$
$547$	−3294.86	+	5706.87i	−0.257547	+	0.446084i	0.708037	+	0.706175i	$0.249581\pi$
$548$	−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	$-0.797103\pi$
$557$	−21128.6			−1.60727			−0.803633	+	0.595125i	$0.797103\pi$
$558$		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	$-0.167982\pi$
$563$	−55.2137	−	95.6330i	−0.00413318	−	0.00715888i	−0.868085	+	0.496416i	$0.834649\pi$
$564$		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	$-0.915506\pi$
$569$	−3465.04	+	6001.63i	−0.255294	+	0.442182i	0.709682	+	0.704523i	$0.248839\pi$
$570$		0			0
$571$	−10632.3	−	18415.7i	−0.779244	−	1.34969i	−0.932378	−	0.361484i	$-0.882270\pi$
$571$	−10632.3	−	18415.7i	−0.779244	−	1.34969i	0.153134	−	0.988205i	$-0.451063\pi$
$572$	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	−0.175732	−	0.984438i	$-0.556229\pi$
$587$	10875.2	−	18836.4i	0.764683	−	1.32447i	0.940414	−	0.340031i	$-0.110438\pi$
$588$		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	$-0.562517\pi$
$593$	−5635.88			−0.390283			−0.195142	+	0.980775i	$0.562517\pi$
$594$		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	0.988547	+	0.150916i	$0.0482223\pi$
$599$	9162.20	+	15869.4i	0.624970	+	1.08248i	−0.363576	+	0.931564i	$0.618444\pi$
$600$		0			0
$601$	1251.95	−	2168.44i	0.0849719	−	0.147176i	−0.820407	−	0.571779i	$-0.806253\pi$
$601$	1251.95	−	2168.44i	0.0849719	−	0.147176i	0.905379	+	0.424604i	$0.139587\pi$
$602$	−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	−0.995002	−	0.0998550i	$-0.968162\pi$
$607$	−8733.32	−	15126.6i	−0.583978	−	1.01148i	0.411024	−	0.911624i	$-0.365171\pi$
$608$	−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	$-0.227367\pi$
$617$	−2904.92	−	5031.47i	−0.189542	−	0.328297i	−0.945098	+	0.326788i	$0.894034\pi$
$618$		0			0
$619$	771.742	−	1336.70i	0.0501114	−	0.0867954i	−0.839882	−	0.542770i	$-0.817376\pi$
$619$	771.742	−	1336.70i	0.0501114	−	0.0867954i	0.889993	+	0.455974i	$0.150709\pi$
$620$	−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	−0.111217	−	0.993796i	$-0.535475\pi$
$641$	13064.9	−	22629.1i	0.805044	−	1.39438i	0.916261	−	0.400581i	$-0.131192\pi$
$642$		0			0
$643$	14386.1	+	24917.4i	0.882319	+	1.52822i	0.848756	+	0.528784i	$0.177352\pi$
$643$	14386.1	+	24917.4i	0.882319	+	1.52822i	0.0335621	+	0.999437i	$0.489315\pi$
$644$	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	$-0.430235\pi$
$647$	7156.38			0.434847			0.217424	+	0.976077i	$0.430235\pi$
$648$		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	$-0.0136226\pi$
$653$	7717.43	+	13367.0i	0.462491	+	0.801057i	−0.536594	+	0.843841i	$0.680289\pi$
$654$		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	$-0.894509\pi$
$659$	−3231.32	+	5596.81i	−0.191008	+	0.330836i	0.754577	+	0.656212i	$0.227842\pi$
$660$		0			0
$661$	−873.801	−	1513.47i	−0.0514174	−	0.0890576i	0.839171	−	0.543867i	$-0.183041\pi$
$661$	−873.801	−	1513.47i	−0.0514174	−	0.0890576i	−0.890589	+	0.454810i	$0.849707\pi$
$662$	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	−0.776855	−	0.629680i	$-0.783186\pi$
$673$	2739.19	−	4744.42i	0.156892	−	0.271744i	0.933746	+	0.357936i	$0.116519\pi$
$674$	−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	$-0.869721\pi$
$677$	−2009.27	+	3480.15i	−0.114066	+	0.197567i	0.803340	+	0.595520i	$0.203054\pi$
$678$		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	$-0.589398\pi$
$683$	−9894.95			−0.554348			−0.277174	+	0.960820i	$0.589398\pi$
$684$		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	0.391209	+	0.920302i	$0.372057\pi$
$691$	−10924.0	+	18920.9i	−0.601400	+	1.04166i	−0.992609	+	0.121354i	$0.961276\pi$
$692$	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	$-0.637178\pi$
$701$	−15506.5			−0.835480			−0.417740	+	0.908567i	$0.637178\pi$
$702$		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	−0.938243	−	0.345977i	$-0.887547\pi$
$709$	−3199.85	+	5542.30i	−0.169496	+	0.293576i	0.768747	+	0.639553i	$0.220881\pi$
$710$	−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	$-0.514631\pi$
$719$	−1771.66			−0.0918941			−0.0459470	+	0.998944i	$0.514631\pi$
$720$		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	−0.961917	−	0.273343i	$-0.911871\pi$
$727$	−4787.53	+	8292.25i	−0.244236	+	0.423030i	0.717680	+	0.696373i	$0.245204\pi$
$728$	−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	0.999999	−	0.00159099i	$-0.000506428\pi$
$733$	9895.25	+	17139.1i	0.498622	+	0.863638i	−0.501377	+	0.865229i	$0.667173\pi$
$734$	−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	$-0.305127\pi$
$743$	−8534.44	−	14782.1i	−0.421398	−	0.729882i	−0.996076	+	0.0884970i	$0.971794\pi$
$744$		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	0.811730	−	0.584033i	$-0.198526\pi$
$751$	−2056.46	−	3561.90i	−0.0999220	−	0.173070i	−0.911652	+	0.410963i	$0.865193\pi$
$752$	−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	$-0.127051\pi$
$761$	2606.02	+	4513.76i	0.124137	+	0.215011i	−0.797258	+	0.603638i	$0.793717\pi$
$762$		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	0.998486	+	0.0550119i	$0.0175197\pi$
$769$	11662.3	+	20199.7i	0.546885	+	0.947232i	−0.451601	+	0.892220i	$0.649147\pi$
$770$	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	$-0.342129\pi$
$773$	20455.0			0.951765			0.475883	+	0.879509i	$0.342129\pi$
$774$		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	0.744222	−	0.667932i	$-0.232820\pi$
$787$	−4555.49	−	7890.33i	−0.206335	−	0.357382i	−0.950557	+	0.310549i	$0.899487\pi$
$788$	−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	$-0.110315\pi$
$797$	3962.54	+	6863.33i	0.176111	+	0.305033i	−0.764434	+	0.644702i	$0.776982\pi$
$798$		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	$-0.761603\pi$
$809$	−33705.8			−1.46481			−0.732406	+	0.680868i	$0.761603\pi$
$810$		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	$-0.768839\pi$
$821$	4733.83	−	8199.23i	0.201232	−	0.348545i	0.948926	+	0.315499i	$0.102172\pi$
$822$		0			0
$823$	−580.274	−	1005.06i	−0.0245772	−	0.0425690i	0.853475	−	0.521133i	$-0.174491\pi$
$823$	−580.274	−	1005.06i	−0.0245772	−	0.0425690i	−0.878052	+	0.478564i	$0.841157\pi$
$824$	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	$-0.311903\pi$
$827$	26499.9			1.11426			0.557128	+	0.830426i	$0.311903\pi$
$828$		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	0.0329145	+	0.999458i	$0.489521\pi$
$839$	−20634.8	+	35740.6i	−0.849099	+	1.47068i	−0.882013	+	0.471224i	$0.843812\pi$
$840$		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	−0.912403	−	0.409294i	$-0.865775\pi$
$853$	−2534.70	+	4390.22i	−0.101743	+	0.176223i	0.810660	+	0.585517i	$0.199108\pi$
$854$	−7.33506			−0.000293912
$855$		0			0
$856$	6924.38			0.276484
$857$	21819.5	−	37792.4i	0.869707	−	1.50638i	0.00741160	−	0.999973i	$-0.497641\pi$
$857$	21819.5	−	37792.4i	0.869707	−	1.50638i	0.862296	−	0.506405i	$-0.169026\pi$
$858$		0			0
$859$	6449.06	+	11170.1i	0.256157	+	0.443678i	0.965209	−	0.261479i	$-0.0842101\pi$
$859$	6449.06	+	11170.1i	0.256157	+	0.443678i	−0.709052	+	0.705156i	$0.750877\pi$
$860$	−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	$-0.443435\pi$
$863$	8962.98			0.353538			0.176769	+	0.984252i	$0.443435\pi$
$864$		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	0.958487	+	0.285136i	$0.0920388\pi$
$877$	18860.1	+	32666.6i	0.726179	+	1.25778i	−0.232308	+	0.972642i	$0.574628\pi$
$878$	−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	$-0.548645\pi$
$881$	−7961.44			−0.304458			−0.152229	+	0.988345i	$0.548645\pi$
$882$		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	−0.999954	−	0.00955935i	$-0.996957\pi$
$887$	−13426.7	−	23255.6i	−0.508256	−	0.880325i	0.491699	−	0.870766i	$-0.336376\pi$
$888$		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	−0.999994	−	0.00347836i	$-0.998893\pi$
$907$	−13575.4	+	23513.4i	−0.496985	+	0.860803i	0.503009	+	0.864281i	$0.332226\pi$
$908$	−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	$-0.923080\pi$
$911$	−7650.25	+	13250.6i	−0.278226	+	0.481902i	0.692718	+	0.721209i	$0.256413\pi$
$912$		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	0.361162	+	0.932503i	$0.382380\pi$
$929$	−17753.5	+	30750.0i	−0.626991	+	1.08598i	−0.988152	+	0.153477i	$0.950953\pi$
$930$		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	$-0.186387\pi$
$941$	−1787.23	−	3095.58i	−0.0619151	−	0.107240i	−0.895321	+	0.445421i	$0.853054\pi$
$942$		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	−0.429653	−	0.902994i	$-0.641364\pi$
$947$	16529.2	−	28629.5i	0.567189	−	0.982400i	0.996842	−	0.0794061i	$-0.0253024\pi$
$948$		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	$-0.507332\pi$
$953$	−1355.24			−0.0460656			−0.0230328	+	0.999735i	$0.507332\pi$
$954$		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	−0.777971	−	0.628301i	$-0.783751\pi$
$967$	−28059.0	−	48599.6i	−0.933110	−	1.61619i	−0.155139	−	0.987893i	$-0.549583\pi$
$968$	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	$-0.681830\pi$
$971$	−32718.5			−1.08135			−0.540673	+	0.841233i	$0.681830\pi$
$972$		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	$-0.212958\pi$
$977$	−4425.44	−	7665.09i	−0.144915	−	0.251001i	−0.929341	+	0.369222i	$0.879624\pi$
$978$		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	0.444687	+	0.895686i	$0.353315\pi$
$983$	−17054.0	+	29538.3i	−0.553343	+	0.958419i	−0.998030	+	0.0627329i	$0.980018\pi$
$984$		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	−0.882304	−	0.470681i	$-0.844008\pi$
$997$	−1055.55	+	1828.27i	−0.0335302	+	0.0580760i	0.848773	+	0.528757i	$0.177342\pi$
$998$	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.p.136.1		4
3.2	odd	2		405.4.e.o.136.2		4
9.2	odd	6		405.4.a.f.1.1	yes	2
9.4	even	3	inner	405.4.e.p.271.1		4
9.5	odd	6		405.4.e.o.271.2		4
9.7	even	3		405.4.a.c.1.2	✓	2
45.29	odd	6		2025.4.a.i.1.2		2
45.34	even	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	9.7	even	3
405.4.a.f.1.1	yes	2	9.2	odd	6
405.4.e.o.136.2		4	3.2	odd	2
405.4.e.o.271.2		4	9.5	odd	6
405.4.e.p.136.1		4	1.1	even	1	trivial
405.4.e.p.271.1		4	9.4	even	3	inner
2025.4.a.i.1.2		2	45.29	odd	6
2025.4.a.m.1.1		2	45.34	even	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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