LMFDB - Embedded newform 225.4.f.c.107.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,4,Mod(107,225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(225, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1]))

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

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

chi := DirichletCharacter("225.107");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	225.f (of order $4$, degree $2$, 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:	$13.2754297513$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 16x^{10} - 14x^{8} - 512x^{6} + 3889x^{4} + 126224x^{2} + 506944 $ x^12 - 16x^10 - 14x^8 - 512x^6 + 3889x^4 + 126224*x^2 + 506944
Coefficient ring:	$\Z[a_1, \ldots, a_{29}]$
Coefficient ring index:	$ 2^{11}\cdot 3^{4} $
Twist minimal:	no (minimal twist has level 45)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			107.2
Root			$-0.347140 - 2.27426i$ of defining polynomial
Character	$\chi$	$=$	225.107
Dual form			225.4.f.c.143.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.62140 + 2.62140i) q^{2} -5.74350i q^{4} +(10.8652 + 10.8652i) q^{7} +(-5.91519 - 5.91519i) q^{8} +O(q^{10})$	\(q+(-2.62140 + 2.62140i) q^{2} -5.74350i q^{4} +(10.8652 + 10.8652i) q^{7} +(-5.91519 - 5.91519i) q^{8} +37.8905i q^{11} +(48.1085 - 48.1085i) q^{13} -56.9640 q^{14} +76.9602 q^{16} +(-60.3458 + 60.3458i) q^{17} +109.678i q^{19} +(-99.3262 - 99.3262i) q^{22} +(39.7660 + 39.7660i) q^{23} +252.224i q^{26} +(62.4042 - 62.4042i) q^{28} -90.3553 q^{29} -233.678 q^{31} +(-154.422 + 154.422i) q^{32} -316.381i q^{34} +(19.0042 + 19.0042i) q^{37} +(-287.509 - 287.509i) q^{38} -260.783i q^{41} +(-176.216 + 176.216i) q^{43} +217.624 q^{44} -208.485 q^{46} +(-145.788 + 145.788i) q^{47} -106.896i q^{49} +(-276.311 - 276.311i) q^{52} +(-183.285 - 183.285i) q^{53} -128.539i q^{56} +(236.858 - 236.858i) q^{58} -279.564 q^{59} -390.267 q^{61} +(612.563 - 612.563i) q^{62} -193.924i q^{64} +(-150.444 - 150.444i) q^{67} +(346.596 + 346.596i) q^{68} +470.042i q^{71} +(-480.765 + 480.765i) q^{73} -99.6355 q^{74} +629.934 q^{76} +(-411.687 + 411.687i) q^{77} +1322.44i q^{79} +(683.618 + 683.618i) q^{82} +(456.192 + 456.192i) q^{83} -923.868i q^{86} +(224.129 - 224.129i) q^{88} +1364.85 q^{89} +1045.41 q^{91} +(228.396 - 228.396i) q^{92} -764.340i q^{94} +(785.308 + 785.308i) q^{97} +(280.218 + 280.218i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 24 q^{7}+O(q^{10}) $ 12 * q - 24 * q^7	$ 12 q - 24 q^{7} + 108 q^{13} - 648 q^{16} - 1056 q^{22} + 576 q^{28} - 1248 q^{31} - 828 q^{37} + 96 q^{43} + 672 q^{46} + 312 q^{52} + 3864 q^{58} + 96 q^{61} - 1632 q^{67} - 3972 q^{73} - 480 q^{76} + 7848 q^{82} - 7968 q^{88} + 4752 q^{91} - 2772 q^{97}+O(q^{100}) $ 12 * q - 24 * q^7 + 108 * q^13 - 648 * q^16 - 1056 * q^22 + 576 * q^28 - 1248 * q^31 - 828 * q^37 + 96 * q^43 + 672 * q^46 + 312 * q^52 + 3864 * q^58 + 96 * q^61 - 1632 * q^67 - 3972 * q^73 - 480 * q^76 + 7848 * q^82 - 7968 * q^88 + 4752 * q^91 - 2772 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−2.62140	+	2.62140i	−0.926806	+	0.926806i	−0.997498	−	0.0706924i	$-0.977479\pi$
$2$	−2.62140	+	2.62140i	−0.926806	+	0.926806i	0.0706924	+	0.997498i	$0.477479\pi$
$3$		0			0
$3$		0			0
$4$		−	5.74350i		−	0.717938i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	10.8652	+	10.8652i	0.586664	+	0.586664i	0.936726	−	0.350062i	$-0.113840\pi$
$7$	10.8652	+	10.8652i	0.586664	+	0.586664i	−0.350062	+	0.936726i	$0.613840\pi$
$8$	−5.91519	−	5.91519i	−0.261417	−	0.261417i
$9$		0			0
$10$		0			0
$11$			37.8905i			1.03858i	0.854597	+	0.519291i	$0.173804\pi$
$11$			37.8905i			1.03858i	−0.854597	+	0.519291i	$0.826196\pi$
$12$		0			0
$13$	48.1085	−	48.1085i	1.02638	−	1.02638i	0.0267344	−	0.999643i	$-0.491489\pi$
$13$	48.1085	−	48.1085i	1.02638	−	1.02638i	0.999643	−	0.0267344i	$-0.00851083\pi$
$14$	−56.9640			−1.08745
$15$		0			0
$16$	76.9602			1.20250
$17$	−60.3458	+	60.3458i	−0.860942	+	0.860942i	−0.991448	−	0.130506i	$-0.958340\pi$
$17$	−60.3458	+	60.3458i	−0.860942	+	0.860942i	0.130506	+	0.991448i	$0.458340\pi$
$18$		0			0
$19$			109.678i			1.32430i	0.749369	+	0.662152i	$0.230357\pi$
$19$			109.678i			1.32430i	−0.749369	+	0.662152i	$0.769643\pi$
$20$		0			0
$21$		0			0
$22$	−99.3262	−	99.3262i	−0.962564	−	0.962564i
$23$	39.7660	+	39.7660i	0.360512	+	0.360512i	0.864002	−	0.503489i	$-0.167951\pi$
$23$	39.7660	+	39.7660i	0.360512	+	0.360512i	−0.503489	+	0.864002i	$0.667951\pi$
$24$		0			0
$25$		0			0
$26$			252.224i			1.90250i
$27$		0			0
$28$	62.4042	−	62.4042i	0.421188	−	0.421188i
$29$	−90.3553			−0.578571			−0.289285	−	0.957243i	$-0.593418\pi$
$29$	−90.3553			−0.578571			−0.289285	+	0.957243i	$0.593418\pi$
$30$		0			0
$31$	−233.678			−1.35386			−0.676932	−	0.736046i	$-0.736691\pi$
$31$	−233.678			−1.35386			−0.676932	+	0.736046i	$0.736691\pi$
$32$	−154.422	+	154.422i	−0.853070	+	0.853070i
$33$		0			0
$34$		−	316.381i		−	1.59585i
$35$		0			0
$36$		0			0
$37$	19.0042	+	19.0042i	0.0844399	+	0.0844399i	0.748065	−	0.663625i	$-0.230983\pi$
$37$	19.0042	+	19.0042i	0.0844399	+	0.0844399i	−0.663625	+	0.748065i	$0.730983\pi$
$38$	−287.509	−	287.509i	−1.22737	−	1.22737i
$39$		0			0
$40$		0			0
$41$		−	260.783i		−	0.993354i	−0.867935	−	0.496677i	$-0.834553\pi$
$41$		−	260.783i		−	0.993354i	0.867935	−	0.496677i	$-0.165447\pi$
$42$		0			0
$43$	−176.216	+	176.216i	−0.624948	+	0.624948i	−0.946792	−	0.321845i	$-0.895697\pi$
$43$	−176.216	+	176.216i	−0.624948	+	0.624948i	0.321845	+	0.946792i	$0.395697\pi$
$44$	217.624			0.745638
$45$		0			0
$46$	−208.485			−0.668250
$47$	−145.788	+	145.788i	−0.452456	+	0.452456i	−0.896169	−	0.443713i	$-0.853661\pi$
$47$	−145.788	+	145.788i	−0.452456	+	0.452456i	0.443713	+	0.896169i	$0.353661\pi$
$48$		0			0
$49$		−	106.896i		−	0.311650i
$50$		0			0
$51$		0			0
$52$	−276.311	−	276.311i	−0.736875	−	0.736875i
$53$	−183.285	−	183.285i	−0.475022	−	0.475022i	0.428513	−	0.903535i	$-0.359038\pi$
$53$	−183.285	−	183.285i	−0.475022	−	0.475022i	−0.903535	+	0.428513i	$0.859038\pi$
$54$		0			0
$55$		0			0
$56$		−	128.539i		−	0.306728i
$57$		0			0
$58$	236.858	−	236.858i	0.536223	−	0.536223i
$59$	−279.564			−0.616883			−0.308441	−	0.951243i	$-0.599807\pi$
$59$	−279.564			−0.616883			−0.308441	+	0.951243i	$0.599807\pi$
$60$		0			0
$61$	−390.267			−0.819157			−0.409578	−	0.912275i	$-0.634324\pi$
$61$	−390.267			−0.819157			−0.409578	+	0.912275i	$0.634324\pi$
$62$	612.563	−	612.563i	1.25477	−	1.25477i
$63$		0			0
$64$		−	193.924i		−	0.378757i
$65$		0			0
$66$		0			0
$67$	−150.444	−	150.444i	−0.274324	−	0.274324i	0.556514	−	0.830838i	$-0.312139\pi$
$67$	−150.444	−	150.444i	−0.274324	−	0.274324i	−0.830838	+	0.556514i	$0.812139\pi$
$68$	346.596	+	346.596i	0.618103	+	0.618103i
$69$		0			0
$70$		0			0
$71$			470.042i			0.785686i	0.919605	+	0.392843i	$0.128508\pi$
$71$			470.042i			0.785686i	−0.919605	+	0.392843i	$0.871492\pi$
$72$		0			0
$73$	−480.765	+	480.765i	−0.770812	+	0.770812i	−0.978249	−	0.207436i	$-0.933488\pi$
$73$	−480.765	+	480.765i	−0.770812	+	0.770812i	0.207436	+	0.978249i	$0.433488\pi$
$74$	−99.6355			−0.156519
$75$		0			0
$76$	629.934			0.950769
$77$	−411.687	+	411.687i	−0.609299	+	0.609299i
$78$		0			0
$79$			1322.44i			1.88337i	0.336497	+	0.941685i	$0.390758\pi$
$79$			1322.44i			1.88337i	−0.336497	+	0.941685i	$0.609242\pi$
$80$		0			0
$81$		0			0
$82$	683.618	+	683.618i	0.920646	+	0.920646i
$83$	456.192	+	456.192i	0.603296	+	0.603296i	0.941186	−	0.337890i	$-0.109713\pi$
$83$	456.192	+	456.192i	0.603296	+	0.603296i	−0.337890	+	0.941186i	$0.609713\pi$
$84$		0			0
$85$		0			0
$86$		−	923.868i		−	1.15841i
$87$		0			0
$88$	224.129	−	224.129i	0.271503	−	0.271503i
$89$	1364.85			1.62555			0.812774	−	0.582580i	$-0.197957\pi$
$89$	1364.85			1.62555			0.812774	+	0.582580i	$0.197957\pi$
$90$		0			0
$91$	1045.41			1.20428
$92$	228.396	−	228.396i	0.258825	−	0.258825i
$93$		0			0
$94$		−	764.340i		−	0.838677i
$95$		0			0
$96$		0			0
$97$	785.308	+	785.308i	0.822020	+	0.822020i	0.986398	−	0.164377i	$-0.0525614\pi$
$97$	785.308	+	785.308i	0.822020	+	0.822020i	−0.164377	+	0.986398i	$0.552561\pi$
$98$	280.218	+	280.218i	0.288839	+	0.288839i
$99$		0			0
$100$		0			0
$101$			111.555i			0.109902i	0.998489	+	0.0549510i	$0.0175003\pi$
$101$			111.555i			0.109902i	−0.998489	+	0.0549510i	$0.982500\pi$
$102$		0			0
$103$	−13.8820	+	13.8820i	−0.0132800	+	0.0132800i	−0.713716	−	0.700436i	$-0.752989\pi$
$103$	−13.8820	+	13.8820i	−0.0132800	+	0.0132800i	0.700436	+	0.713716i	$0.252989\pi$
$104$	−569.142			−0.536624
$105$		0			0
$106$	960.929			0.880507
$107$	776.165	−	776.165i	0.701259	−	0.701259i	−0.263422	−	0.964681i	$-0.584851\pi$
$107$	776.165	−	776.165i	0.701259	−	0.701259i	0.964681	+	0.263422i	$0.0848510\pi$
$108$		0			0
$109$			410.579i			0.360792i	0.983594	+	0.180396i	$0.0577379\pi$
$109$			410.579i			0.360792i	−0.983594	+	0.180396i	$0.942262\pi$
$110$		0			0
$111$		0			0
$112$	836.186	+	836.186i	0.705465	+	0.705465i
$113$	521.328	+	521.328i	0.434004	+	0.434004i	0.889988	−	0.455984i	$-0.150713\pi$
$113$	521.328	+	521.328i	0.434004	+	0.434004i	−0.455984	+	0.889988i	$0.650713\pi$
$114$		0			0
$115$		0			0
$116$			518.956i			0.415378i
$117$		0			0
$118$	732.849	−	732.849i	0.571730	−	0.571730i
$119$	−1311.34			−1.01017
$120$		0			0
$121$	−104.688			−0.0786538
$122$	1023.05	−	1023.05i	0.759199	−	0.759199i
$123$		0			0
$124$			1342.13i			0.971990i
$125$		0			0
$126$		0			0
$127$	−786.555	−	786.555i	−0.549571	−	0.549571i	0.376746	−	0.926317i	$-0.377043\pi$
$127$	−786.555	−	786.555i	−0.549571	−	0.549571i	−0.926317	+	0.376746i	$0.877043\pi$
$128$	−727.025	−	727.025i	−0.502036	−	0.502036i
$129$		0			0
$130$		0			0
$131$		−	448.364i		−	0.299036i	−0.988759	−	0.149518i	$-0.952228\pi$
$131$		−	448.364i		−	0.299036i	0.988759	−	0.149518i	$-0.0477722\pi$
$132$		0			0
$133$	−1191.67	+	1191.67i	−0.776922	+	0.776922i
$134$	788.751			0.508490
$135$		0			0
$136$	713.914			0.450129
$137$	−950.120	+	950.120i	−0.592512	+	0.592512i	−0.938309	−	0.345797i	$-0.887609\pi$
$137$	−950.120	+	950.120i	−0.592512	+	0.592512i	0.345797	+	0.938309i	$0.387609\pi$
$138$		0			0
$139$			112.735i			0.0687918i	0.999408	+	0.0343959i	$0.0109507\pi$
$139$			112.735i			0.0687918i	−0.999408	+	0.0343959i	$0.989049\pi$
$140$		0			0
$141$		0			0
$142$	−1232.17	−	1232.17i	−0.728179	−	0.728179i
$143$	1822.85	+	1822.85i	1.06598	+	1.06598i
$144$		0			0
$145$		0			0
$146$		−	2520.56i		−	1.42879i
$147$		0			0
$148$	109.151	−	109.151i	0.0606226	−	0.0606226i
$149$	1492.95			0.820852			0.410426	−	0.911894i	$-0.365380\pi$
$149$	1492.95			0.820852			0.410426	+	0.911894i	$0.365380\pi$
$150$		0			0
$151$	−2939.54			−1.58422			−0.792108	−	0.610381i	$-0.791016\pi$
$151$	−2939.54			−1.58422			−0.792108	+	0.610381i	$0.791016\pi$
$152$	648.764	−	648.764i	0.346196	−	0.346196i
$153$		0			0
$154$		−	2158.39i		−	1.12940i
$155$		0			0
$156$		0			0
$157$	−156.386	−	156.386i	−0.0794967	−	0.0794967i	0.666240	−	0.745737i	$-0.267902\pi$
$157$	−156.386	−	156.386i	−0.0794967	−	0.0794967i	−0.745737	+	0.666240i	$0.767902\pi$
$158$	−3466.65	−	3466.65i	−1.74552	−	1.74552i
$159$		0			0
$160$		0			0
$161$			864.129i			0.422999i
$162$		0			0
$163$	239.292	−	239.292i	0.114986	−	0.114986i	−0.647272	−	0.762259i	$-0.724090\pi$
$163$	239.292	−	239.292i	0.114986	−	0.114986i	0.762259	+	0.647272i	$0.224090\pi$
$164$	−1497.81			−0.713167
$165$		0			0
$166$	−2391.72			−1.11828
$167$	−677.159	+	677.159i	−0.313773	+	0.313773i	−0.846369	−	0.532596i	$-0.821216\pi$
$167$	−677.159	+	677.159i	−0.313773	+	0.313773i	0.532596	+	0.846369i	$0.321216\pi$
$168$		0			0
$169$		−	2431.86i		−	1.10690i
$170$		0			0
$171$		0			0
$172$	1012.10	+	1012.10i	0.448674	+	0.448674i
$173$	−441.523	−	441.523i	−0.194037	−	0.194037i	0.603401	−	0.797438i	$-0.293812\pi$
$173$	−441.523	−	441.523i	−0.194037	−	0.194037i	−0.797438	+	0.603401i	$0.793812\pi$
$174$		0			0
$175$		0			0
$176$			2916.06i			1.24890i
$177$		0			0
$178$	−3577.82	+	3577.82i	−1.50657	+	1.50657i
$179$	4724.27			1.97267			0.986337	−	0.164737i	$-0.0526776\pi$
$179$	4724.27			1.97267			0.986337	+	0.164737i	$0.0526776\pi$
$180$		0			0
$181$	−1548.35			−0.635847			−0.317923	−	0.948116i	$-0.602985\pi$
$181$	−1548.35			−0.635847			−0.317923	+	0.948116i	$0.602985\pi$
$182$	−2740.45	+	2740.45i	−1.11613	+	1.11613i
$183$		0			0
$184$		−	470.447i		−	0.188488i
$185$		0			0
$186$		0			0
$187$	−2286.53	−	2286.53i	−0.894159	−	0.894159i
$188$	837.336	+	837.336i	0.324835	+	0.324835i
$189$		0			0
$190$		0			0
$191$		−	1090.71i		−	0.413200i	−0.978426	−	0.206600i	$-0.933760\pi$
$191$		−	1090.71i		−	0.413200i	0.978426	−	0.206600i	$-0.0662398\pi$
$192$		0			0
$193$	2825.69	−	2825.69i	1.05387	−	1.05387i	0.0554112	−	0.998464i	$-0.482353\pi$
$193$	2825.69	−	2825.69i	1.05387	−	1.05387i	0.998464	−	0.0554112i	$-0.0176470\pi$
$194$	−4117.22			−1.52371
$195$		0			0
$196$	−613.958			−0.223746
$197$	−1163.99	+	1163.99i	−0.420969	+	0.420969i	−0.885537	−	0.464569i	$-0.846209\pi$
$197$	−1163.99	+	1163.99i	−0.420969	+	0.420969i	0.464569	+	0.885537i	$0.346209\pi$
$198$		0			0
$199$		−	520.257i		−	0.185327i	−0.995697	−	0.0926633i	$-0.970462\pi$
$199$		−	520.257i		−	0.185327i	0.995697	−	0.0926633i	$-0.0295380\pi$
$200$		0			0
$201$		0			0
$202$	−292.430	−	292.430i	−0.101858	−	0.101858i
$203$	−981.726	−	981.726i	−0.339427	−	0.339427i
$204$		0			0
$205$		0			0
$206$		−	72.7808i		−	0.0246159i
$207$		0			0
$208$	3702.44	−	3702.44i	1.23422	−	1.23422i
$209$	−4155.74			−1.37540
$210$		0			0
$211$	5524.38			1.80244			0.901219	−	0.433365i	$-0.142674\pi$
$211$	5524.38			1.80244			0.901219	+	0.433365i	$0.142674\pi$
$212$	−1052.70	+	1052.70i	−0.341036	+	0.341036i
$213$		0			0
$214$			4069.28i			1.29986i
$215$		0			0
$216$		0			0
$217$	−2538.95	−	2538.95i	−0.794263	−	0.794263i
$218$	−1076.29	−	1076.29i	−0.334384	−	0.334384i
$219$		0			0
$220$		0			0
$221$			5806.30i			1.76730i
$222$		0			0
$223$	−323.198	+	323.198i	−0.0970537	+	0.0970537i	−0.753967	−	0.656913i	$-0.771862\pi$
$223$	−323.198	+	323.198i	−0.0970537	+	0.0970537i	0.656913	+	0.753967i	$0.271862\pi$
$224$	−3355.65			−1.00093
$225$		0			0
$226$	−2733.22			−0.804474
$227$	2739.76	−	2739.76i	0.801077	−	0.801077i	−0.182187	−	0.983264i	$-0.558318\pi$
$227$	2739.76	−	2739.76i	0.801077	−	0.801077i	0.983264	+	0.182187i	$0.0583177\pi$
$228$		0			0
$229$			230.334i			0.0664667i	0.999448	+	0.0332333i	$0.0105804\pi$
$229$			230.334i			0.0664667i	−0.999448	+	0.0332333i	$0.989420\pi$
$230$		0			0
$231$		0			0
$232$	534.468	+	534.468i	0.151248	+	0.151248i
$233$	350.156	+	350.156i	0.0984526	+	0.0984526i	0.754618	−	0.656165i	$-0.227822\pi$
$233$	350.156	+	350.156i	0.0984526	+	0.0984526i	−0.656165	+	0.754618i	$0.727822\pi$
$234$		0			0
$235$		0			0
$236$			1605.67i			0.442883i
$237$		0			0
$238$	3437.54	−	3437.54i	0.936229	−	0.936229i
$239$	1013.20			0.274218			0.137109	−	0.990556i	$-0.456219\pi$
$239$	1013.20			0.274218			0.137109	+	0.990556i	$0.456219\pi$
$240$		0			0
$241$	2584.30			0.690744			0.345372	−	0.938466i	$-0.387753\pi$
$241$	2584.30			0.690744			0.345372	+	0.938466i	$0.387753\pi$
$242$	274.430	−	274.430i	0.0728968	−	0.0728968i
$243$		0			0
$244$			2241.50i			0.588104i
$245$		0			0
$246$		0			0
$247$	5276.43	+	5276.43i	1.35924	+	1.35924i
$248$	1382.25	+	1382.25i	0.353923	+	0.353923i
$249$		0			0
$250$		0			0
$251$			1708.34i			0.429599i	0.976658	+	0.214800i	$0.0689099\pi$
$251$			1708.34i			0.429599i	−0.976658	+	0.214800i	$0.931090\pi$
$252$		0			0
$253$	−1506.75	+	1506.75i	−0.374422	+	0.374422i
$254$	4123.76			1.01869
$255$		0			0
$256$	5363.04			1.30934
$257$	−2659.48	+	2659.48i	−0.645500	+	0.645500i	−0.951902	−	0.306402i	$-0.900875\pi$
$257$	−2659.48	+	2659.48i	−0.645500	+	0.645500i	0.306402	+	0.951902i	$0.400875\pi$
$258$		0			0
$259$			412.969i			0.0990757i
$260$		0			0
$261$		0			0
$262$	1175.34	+	1175.34i	0.277148	+	0.277148i
$263$	2307.03	+	2307.03i	0.540903	+	0.540903i	0.923794	−	0.382891i	$-0.125071\pi$
$263$	2307.03	+	2307.03i	0.540903	+	0.540903i	−0.382891	+	0.923794i	$0.625071\pi$
$264$		0			0
$265$		0			0
$266$		−	6247.68i		−	1.44011i
$267$		0			0
$268$	−864.078	+	864.078i	−0.196948	+	0.196948i
$269$	−447.584			−0.101449			−0.0507243	−	0.998713i	$-0.516153\pi$
$269$	−447.584			−0.101449			−0.0507243	+	0.998713i	$0.516153\pi$
$270$		0			0
$271$	1573.15			0.352627			0.176314	−	0.984334i	$-0.443583\pi$
$271$	1573.15			0.352627			0.176314	+	0.984334i	$0.443583\pi$
$272$	−4644.23	+	4644.23i	−1.03529	+	1.03529i
$273$		0			0
$274$		−	4981.29i		−	1.09829i
$275$		0			0
$276$		0			0
$277$	−5816.91	−	5816.91i	−1.26175	−	1.26175i	−0.950245	−	0.311504i	$-0.899167\pi$
$277$	−5816.91	−	5816.91i	−1.26175	−	1.26175i	−0.311504	−	0.950245i	$-0.600833\pi$
$278$	−295.524	−	295.524i	−0.0637566	−	0.0637566i
$279$		0			0
$280$		0			0
$281$		−	140.032i		−	0.0297281i	−0.999890	−	0.0148640i	$-0.995268\pi$
$281$		−	140.032i		−	0.0297281i	0.999890	−	0.0148640i	$-0.00473155\pi$
$282$		0			0
$283$	−4431.85	+	4431.85i	−0.930905	+	0.930905i	−0.997763	−	0.0668572i	$-0.978703\pi$
$283$	−4431.85	+	4431.85i	−0.930905	+	0.930905i	0.0668572	+	0.997763i	$0.478703\pi$
$284$	2699.69			0.564074
$285$		0			0
$286$	−9556.87			−1.97591
$287$	2833.46	−	2833.46i	0.582765	−	0.582765i
$288$		0			0
$289$		−	2370.24i		−	0.482442i
$290$		0			0
$291$		0			0
$292$	2761.28	+	2761.28i	0.553395	+	0.553395i
$293$	1244.45	+	1244.45i	0.248127	+	0.248127i	0.820202	−	0.572074i	$-0.193861\pi$
$293$	1244.45	+	1244.45i	0.248127	+	0.248127i	−0.572074	+	0.820202i	$0.693861\pi$
$294$		0			0
$295$		0			0
$296$		−	224.827i		−	0.0441480i
$297$		0			0
$298$	−3913.61	+	3913.61i	−0.760771	+	0.760771i
$299$	3826.17			0.740043
$300$		0			0
$301$	−3829.24			−0.733269
$302$	7705.73	−	7705.73i	1.46826	−	1.46826i
$303$		0			0
$304$			8440.82i			1.59248i
$305$		0			0
$306$		0			0
$307$	7327.60	+	7327.60i	1.36224	+	1.36224i	0.871053	+	0.491189i	$0.163437\pi$
$307$	7327.60	+	7327.60i	1.36224	+	1.36224i	0.491189	+	0.871053i	$0.336563\pi$
$308$	2364.52	+	2364.52i	0.437439	+	0.437439i
$309$		0			0
$310$		0			0
$311$		−	7489.38i		−	1.36554i	−0.730632	−	0.682771i	$-0.760775\pi$
$311$		−	7489.38i		−	1.36554i	0.730632	−	0.682771i	$-0.239225\pi$
$312$		0			0
$313$	2456.04	−	2456.04i	0.443525	−	0.443525i	−0.449670	−	0.893195i	$-0.648458\pi$
$313$	2456.04	−	2456.04i	0.443525	−	0.443525i	0.893195	+	0.449670i	$0.148458\pi$
$314$	819.903			0.147356
$315$		0			0
$316$	7595.44			1.35214
$317$	6724.30	−	6724.30i	1.19140	−	1.19140i	0.214728	−	0.976674i	$-0.431113\pi$
$317$	6724.30	−	6724.30i	1.19140	−	1.19140i	0.976674	−	0.214728i	$-0.0688866\pi$
$318$		0			0
$319$		−	3423.60i		−	0.600894i
$320$		0			0
$321$		0			0
$322$	−2265.23	−	2265.23i	−0.392038	−	0.392038i
$323$	−6618.59	−	6618.59i	−1.14015	−	1.14015i
$324$		0			0
$325$		0			0
$326$			1254.56i			0.213140i
$327$		0			0
$328$	−1542.58	+	1542.58i	−0.259679	+	0.259679i
$329$	−3168.03			−0.530879
$330$		0			0
$331$	−199.080			−0.0330586			−0.0165293	−	0.999863i	$-0.505262\pi$
$331$	−199.080			−0.0330586			−0.0165293	+	0.999863i	$0.505262\pi$
$332$	2620.14	−	2620.14i	0.433129	−	0.433129i
$333$		0			0
$334$		−	3550.21i		−	0.581614i
$335$		0			0
$336$		0			0
$337$	−3308.77	−	3308.77i	−0.534838	−	0.534838i	0.387170	−	0.922008i	$-0.373453\pi$
$337$	−3308.77	−	3308.77i	−0.534838	−	0.534838i	−0.922008	+	0.387170i	$0.873453\pi$
$338$	6374.88	+	6374.88i	1.02588	+	1.02588i
$339$		0			0
$340$		0			0
$341$		−	8854.16i		−	1.40610i
$342$		0			0
$343$	4888.20	−	4888.20i	0.769498	−	0.769498i
$344$	2084.71			0.326744
$345$		0			0
$346$	2314.82			0.359669
$347$	−2371.68	+	2371.68i	−0.366912	+	0.366912i	−0.866350	−	0.499438i	$-0.833540\pi$
$347$	−2371.68	+	2371.68i	−0.366912	+	0.366912i	0.499438	+	0.866350i	$0.333540\pi$
$348$		0			0
$349$			8208.92i			1.25906i	0.776975	+	0.629532i	$0.216753\pi$
$349$			8208.92i			1.25906i	−0.776975	+	0.629532i	$0.783247\pi$
$350$		0			0
$351$		0			0
$352$	−5851.13	−	5851.13i	−0.885984	−	0.885984i
$353$	−6800.98	−	6800.98i	−1.02544	−	1.02544i	−0.999668	−	0.0257707i	$-0.991796\pi$
$353$	−6800.98	−	6800.98i	−1.02544	−	1.02544i	−0.0257707	−	0.999668i	$-0.508204\pi$
$354$		0			0
$355$		0			0
$356$		−	7839.01i		−	1.16704i
$357$		0			0
$358$	−12384.2	+	12384.2i	−1.82829	+	1.82829i
$359$	−1778.14			−0.261411			−0.130705	−	0.991421i	$-0.541724\pi$
$359$	−1778.14			−0.261411			−0.130705	+	0.991421i	$0.541724\pi$
$360$		0			0
$361$	−5170.20			−0.753783
$362$	4058.86	−	4058.86i	0.589306	−	0.589306i
$363$		0			0
$364$		−	6004.34i		−	0.864596i
$365$		0			0
$366$		0			0
$367$	4673.56	+	4673.56i	0.664735	+	0.664735i	0.956492	−	0.291757i	$-0.0942400\pi$
$367$	4673.56	+	4673.56i	0.664735	+	0.664735i	−0.291757	+	0.956492i	$0.594240\pi$
$368$	3060.40	+	3060.40i	0.433517	+	0.433517i
$369$		0			0
$370$		0			0
$371$		−	3982.85i		−	0.557357i
$372$		0			0
$373$	5729.37	−	5729.37i	0.795323	−	0.795323i	−0.187031	−	0.982354i	$-0.559886\pi$
$373$	5729.37	−	5729.37i	0.795323	−	0.795323i	0.982354	+	0.187031i	$0.0598865\pi$
$374$	11987.8			1.65742
$375$		0			0
$376$	1724.73			0.236559
$377$	−4346.86	+	4346.86i	−0.593832	+	0.593832i
$378$		0			0
$379$			153.883i			0.0208561i	0.999946	+	0.0104280i	$0.00331941\pi$
$379$			153.883i			0.0208561i	−0.999946	+	0.0104280i	$0.996681\pi$
$380$		0			0
$381$		0			0
$382$	2859.19	+	2859.19i	0.382956	+	0.382956i
$383$	4297.76	+	4297.76i	0.573382	+	0.573382i	0.933072	−	0.359690i	$-0.117118\pi$
$383$	4297.76	+	4297.76i	0.573382	+	0.573382i	−0.359690	+	0.933072i	$0.617118\pi$
$384$		0			0
$385$		0			0
$386$			14814.6i			1.95347i
$387$		0			0
$388$	4510.42	−	4510.42i	0.590160	−	0.590160i
$389$	−7833.00			−1.02095			−0.510474	−	0.859893i	$-0.670530\pi$
$389$	−7833.00			−1.02095			−0.510474	+	0.859893i	$0.670530\pi$
$390$		0			0
$391$	−4799.42			−0.620760
$392$	−632.310	+	632.310i	−0.0814706	+	0.0814706i
$393$		0			0
$394$		−	6102.57i		−	0.780312i
$395$		0			0
$396$		0			0
$397$	10195.4	+	10195.4i	1.28889	+	1.28889i	0.935459	+	0.353435i	$0.114987\pi$
$397$	10195.4	+	10195.4i	1.28889	+	1.28889i	0.353435	+	0.935459i	$0.385013\pi$
$398$	1363.80	+	1363.80i	0.171762	+	0.171762i
$399$		0			0
$400$		0			0
$401$			10778.3i			1.34226i	0.741341	+	0.671128i	$0.234190\pi$
$401$			10778.3i			1.34226i	−0.741341	+	0.671128i	$0.765810\pi$
$402$		0			0
$403$	−11241.9	+	11241.9i	−1.38957	+	1.38957i
$404$	640.714			0.0789028
$405$		0			0
$406$	5147.00			0.629165
$407$	−720.079	+	720.079i	−0.0876978	+	0.0876978i
$408$		0			0
$409$			4629.92i			0.559743i	0.960037	+	0.279872i	$0.0902919\pi$
$409$			4629.92i			0.559743i	−0.960037	+	0.279872i	$0.909708\pi$
$410$		0			0
$411$		0			0
$412$	79.7315	+	79.7315i	0.00953420	+	0.00953420i
$413$	−3037.51	−	3037.51i	−0.361903	−	0.361903i
$414$		0			0
$415$		0			0
$416$			14858.0i			1.75114i
$417$		0			0
$418$	10893.9	−	10893.9i	1.27473	−	1.27473i
$419$	−11276.5			−1.31478			−0.657389	−	0.753551i	$-0.728339\pi$
$419$	−11276.5			−1.31478			−0.657389	+	0.753551i	$0.728339\pi$
$420$		0			0
$421$	3387.58			0.392163			0.196082	−	0.980588i	$-0.437178\pi$
$421$	3387.58			0.392163			0.196082	+	0.980588i	$0.437178\pi$
$422$	−14481.6	+	14481.6i	−1.67051	+	1.67051i
$423$		0			0
$424$			2168.33i			0.248358i
$425$		0			0
$426$		0			0
$427$	−4240.32	−	4240.32i	−0.480570	−	0.480570i
$428$	−4457.91	−	4457.91i	−0.503461	−	0.503461i
$429$		0			0
$430$		0			0
$431$		−	16161.7i		−	1.80623i	−0.429402	−	0.903113i	$-0.641276\pi$
$431$		−	16161.7i		−	1.80623i	0.429402	−	0.903113i	$-0.358724\pi$
$432$		0			0
$433$	3808.79	−	3808.79i	0.422722	−	0.422722i	−0.463418	−	0.886140i	$-0.653377\pi$
$433$	3808.79	−	3808.79i	0.422722	−	0.422722i	0.886140	+	0.463418i	$0.153377\pi$
$434$	13311.2			1.47226
$435$		0			0
$436$	2358.16			0.259026
$437$	−4361.44	+	4361.44i	−0.477428	+	0.477428i
$438$		0			0
$439$			1607.30i			0.174744i	0.996176	+	0.0873718i	$0.0278468\pi$
$439$			1607.30i			0.174744i	−0.996176	+	0.0873718i	$0.972153\pi$
$440$		0			0
$441$		0			0
$442$	−15220.6	−	15220.6i	−1.63795	−	1.63795i
$443$	8296.60	+	8296.60i	0.889805	+	0.889805i	0.994504	−	0.104699i	$-0.0333880\pi$
$443$	8296.60	+	8296.60i	0.889805	+	0.889805i	−0.104699	+	0.994504i	$0.533388\pi$
$444$		0			0
$445$		0			0
$446$		−	1694.47i		−	0.179900i
$447$		0			0
$448$	2107.02	−	2107.02i	0.222203	−	0.222203i
$449$	−15061.8			−1.58309			−0.791547	−	0.611108i	$-0.790724\pi$
$449$	−15061.8			−1.58309			−0.791547	+	0.611108i	$0.790724\pi$
$450$		0			0
$451$	9881.20			1.03168
$452$	2994.25	−	2994.25i	0.311588	−	0.311588i
$453$		0			0
$454$			14364.0i			1.48489i
$455$		0			0
$456$		0			0
$457$	−2671.27	−	2671.27i	−0.273428	−	0.273428i	0.557050	−	0.830479i	$-0.311933\pi$
$457$	−2671.27	−	2671.27i	−0.273428	−	0.273428i	−0.830479	+	0.557050i	$0.811933\pi$
$458$	−603.797	−	603.797i	−0.0616017	−	0.0616017i
$459$		0			0
$460$		0			0
$461$			12809.1i			1.29410i	0.762449	+	0.647049i	$0.223997\pi$
$461$			12809.1i			1.29410i	−0.762449	+	0.647049i	$0.776003\pi$
$462$		0			0
$463$	11154.1	−	11154.1i	1.11960	−	1.11960i	0.127804	−	0.991799i	$-0.459207\pi$
$463$	11154.1	−	11154.1i	1.11960	−	1.11960i	0.991799	−	0.127804i	$-0.0407927\pi$
$464$	−6953.76			−0.695733
$465$		0			0
$466$	−1835.80			−0.182493
$467$	7905.44	−	7905.44i	0.783341	−	0.783341i	−0.197052	−	0.980393i	$-0.563137\pi$
$467$	7905.44	−	7905.44i	0.783341	−	0.783341i	0.980393	+	0.197052i	$0.0631368\pi$
$468$		0			0
$469$		−	3269.21i		−	0.321872i
$470$		0			0
$471$		0			0
$472$	1653.67	+	1653.67i	0.161263	+	0.161263i
$473$	−6676.92	−	6676.92i	−0.649060	−	0.649060i
$474$		0			0
$475$		0			0
$476$			7531.66i			0.725238i
$477$		0			0
$478$	−2655.99	+	2655.99i	−0.254147	+	0.254147i
$479$	10715.8			1.02217			0.511085	−	0.859530i	$-0.329244\pi$
$479$	10715.8			1.02217			0.511085	+	0.859530i	$0.329244\pi$
$480$		0			0
$481$	1828.53			0.173334
$482$	−6774.48	+	6774.48i	−0.640185	+	0.640185i
$483$		0			0
$484$			601.277i			0.0564685i
$485$		0			0
$486$		0			0
$487$	4489.84	+	4489.84i	0.417770	+	0.417770i	0.884435	−	0.466664i	$-0.154544\pi$
$487$	4489.84	+	4489.84i	0.417770	+	0.417770i	−0.466664	+	0.884435i	$0.654544\pi$
$488$	2308.50	+	2308.50i	0.214141	+	0.214141i
$489$		0			0
$490$		0			0
$491$			15174.1i			1.39470i	0.716729	+	0.697352i	$0.245638\pi$
$491$			15174.1i			1.39470i	−0.716729	+	0.697352i	$0.754362\pi$
$492$		0			0
$493$	5452.56	−	5452.56i	0.498116	−	0.498116i
$494$	−27663.3			−2.51950
$495$		0			0
$496$	−17983.9			−1.62802
$497$	−5107.09	+	5107.09i	−0.460934	+	0.460934i
$498$		0			0
$499$		−	8887.20i		−	0.797286i	−0.917106	−	0.398643i	$-0.869481\pi$
$499$		−	8887.20i		−	0.797286i	0.917106	−	0.398643i	$-0.130519\pi$
$500$		0			0
$501$		0			0
$502$	−4478.25	−	4478.25i	−0.398155	−	0.398155i
$503$	−12740.5	−	12740.5i	−1.12936	−	1.12936i	−0.990281	−	0.139084i	$-0.955584\pi$
$503$	−12740.5	−	12740.5i	−1.12936	−	1.12936i	−0.139084	−	0.990281i	$-0.544416\pi$
$504$		0			0
$505$		0			0
$506$		−	7899.61i		−	0.694033i
$507$		0			0
$508$	−4517.58	+	4517.58i	−0.394558	+	0.394558i
$509$	9257.00			0.806108			0.403054	−	0.915176i	$-0.367949\pi$
$509$	9257.00			0.806108			0.403054	+	0.915176i	$0.367949\pi$
$510$		0			0
$511$	−10447.2			−0.904416
$512$	−8242.49	+	8242.49i	−0.711465	+	0.711465i
$513$		0			0
$514$		−	13943.1i		−	1.19651i
$515$		0			0
$516$		0			0
$517$	−5523.99	−	5523.99i	−0.469913	−	0.469913i
$518$	−1082.56	−	1082.56i	−0.0918240	−	0.0918240i
$519$		0			0
$520$		0			0
$521$		−	13563.3i		−	1.14054i	−0.821458	−	0.570268i	$-0.806839\pi$
$521$		−	13563.3i		−	1.14054i	0.821458	−	0.570268i	$-0.193161\pi$
$522$		0			0
$523$	−11193.8	+	11193.8i	−0.935894	+	0.935894i	−0.998065	−	0.0621714i	$-0.980197\pi$
$523$	−11193.8	+	11193.8i	−0.935894	+	0.935894i	0.0621714	+	0.998065i	$0.480197\pi$
$524$	−2575.18			−0.214689
$525$		0			0
$526$	−12095.3			−1.00262
$527$	14101.5	−	14101.5i	1.16560	−	1.16560i
$528$		0			0
$529$		−	9004.33i		−	0.740062i
$530$		0			0
$531$		0			0
$532$	6844.34	+	6844.34i	0.557782	+	0.557782i
$533$	−12545.9	−	12545.9i	−1.01956	−	1.01956i
$534$		0			0
$535$		0			0
$536$			1779.81i			0.143426i
$537$		0			0
$538$	1173.30	−	1173.30i	0.0940231	−	0.0940231i
$539$	4050.34			0.323675
$540$		0			0
$541$	1383.33			0.109934			0.0549668	−	0.998488i	$-0.482495\pi$
$541$	1383.33			0.109934			0.0549668	+	0.998488i	$0.482495\pi$
$542$	−4123.86	+	4123.86i	−0.326817	+	0.326817i
$543$		0			0
$544$		−	18637.5i		−	1.46889i
$545$		0			0
$546$		0			0
$547$	−2181.76	−	2181.76i	−0.170540	−	0.170540i	0.616677	−	0.787217i	$-0.288479\pi$
$547$	−2181.76	−	2181.76i	−0.170540	−	0.170540i	−0.787217	+	0.616677i	$0.788479\pi$
$548$	5457.01	+	5457.01i	0.425387	+	0.425387i
$549$		0			0
$550$		0			0
$551$		−	9909.96i		−	0.766204i
$552$		0			0
$553$	−14368.5	+	14368.5i	−1.10491	+	1.10491i
$554$	30496.9			2.33879
$555$		0			0
$556$	647.494			0.0493882
$557$	−15674.9	+	15674.9i	−1.19240	+	1.19240i	−0.216007	+	0.976392i	$0.569303\pi$
$557$	−15674.9	+	15674.9i	−1.19240	+	1.19240i	−0.976392	+	0.216007i	$0.930697\pi$
$558$		0			0
$559$			16955.0i			1.28286i
$560$		0			0
$561$		0			0
$562$	367.080	+	367.080i	0.0275522	+	0.0275522i
$563$	8213.60	+	8213.60i	0.614852	+	0.614852i	0.944206	−	0.329354i	$-0.106831\pi$
$563$	8213.60	+	8213.60i	0.614852	+	0.614852i	−0.329354	+	0.944206i	$0.606831\pi$
$564$		0			0
$565$		0			0
$566$		−	23235.3i		−	1.72554i
$567$		0			0
$568$	2780.39	−	2780.39i	0.205392	−	0.205392i
$569$	16902.1			1.24530			0.622648	−	0.782502i	$-0.286057\pi$
$569$	16902.1			1.24530			0.622648	+	0.782502i	$0.286057\pi$
$570$		0			0
$571$	6507.12			0.476908			0.238454	−	0.971154i	$-0.423359\pi$
$571$	6507.12			0.476908			0.238454	+	0.971154i	$0.423359\pi$
$572$	10469.6	−	10469.6i	0.765305	−	0.765305i
$573$		0			0
$574$			14855.3i			1.08022i
$575$		0			0
$576$		0			0
$577$	−7884.54	−	7884.54i	−0.568870	−	0.568870i	0.362942	−	0.931812i	$-0.381772\pi$
$577$	−7884.54	−	7884.54i	−0.568870	−	0.568870i	−0.931812	+	0.362942i	$0.881772\pi$
$578$	6213.35	+	6213.35i	0.447130	+	0.447130i
$579$		0			0
$580$		0			0
$581$			9913.20i			0.707864i
$582$		0			0
$583$	6944.77	−	6944.77i	0.493350	−	0.493350i
$584$	5687.63			0.403007
$585$		0			0
$586$	−6524.39			−0.459932
$587$	9548.44	−	9548.44i	0.671390	−	0.671390i	−0.286646	−	0.958037i	$-0.592540\pi$
$587$	9548.44	−	9548.44i	0.671390	−	0.671390i	0.958037	+	0.286646i	$0.0925404\pi$
$588$		0			0
$589$		−	25629.2i		−	1.79293i
$590$		0			0
$591$		0			0
$592$	1462.57	+	1462.57i	0.101539	+	0.101539i
$593$	3491.97	+	3491.97i	0.241818	+	0.241818i	0.817602	−	0.575784i	$-0.195303\pi$
$593$	3491.97	+	3491.97i	0.241818	+	0.241818i	−0.575784	+	0.817602i	$0.695303\pi$
$594$		0			0
$595$		0			0
$596$		−	8574.75i		−	0.589321i
$597$		0			0
$598$	−10029.9	+	10029.9i	−0.685876	+	0.685876i
$599$	−11203.0			−0.764175			−0.382087	−	0.924126i	$-0.624795\pi$
$599$	−11203.0			−0.764175			−0.382087	+	0.924126i	$0.624795\pi$
$600$		0			0
$601$	−13953.5			−0.947048			−0.473524	−	0.880781i	$-0.657018\pi$
$601$	−13953.5			−0.947048			−0.473524	+	0.880781i	$0.657018\pi$
$602$	10038.0	−	10038.0i	0.679598	−	0.679598i
$603$		0			0
$604$			16883.3i			1.13737i
$605$		0			0
$606$		0			0
$607$	1292.54	+	1292.54i	0.0864293	+	0.0864293i	0.749000	−	0.662570i	$-0.230534\pi$
$607$	1292.54	+	1292.54i	0.0864293	+	0.0864293i	−0.662570	+	0.749000i	$0.730534\pi$
$608$	−16936.7	−	16936.7i	−1.12972	−	1.12972i
$609$		0			0
$610$		0			0
$611$			14027.3i			0.928780i
$612$		0			0
$613$	−225.964	+	225.964i	−0.0148884	+	0.0148884i	−0.714512	−	0.699623i	$-0.753351\pi$
$613$	−225.964	+	225.964i	−0.0148884	+	0.0148884i	0.699623	+	0.714512i	$0.253351\pi$
$614$	−38417.2			−2.52507
$615$		0			0
$616$	4870.41			0.318562
$617$	2717.41	−	2717.41i	0.177308	−	0.177308i	−0.612873	−	0.790181i	$-0.709986\pi$
$617$	2717.41	−	2717.41i	0.177308	−	0.177308i	0.790181	+	0.612873i	$0.209986\pi$
$618$		0			0
$619$			8870.55i			0.575989i	0.957632	+	0.287995i	$0.0929886\pi$
$619$			8870.55i			0.575989i	−0.957632	+	0.287995i	$0.907011\pi$
$620$		0			0
$621$		0			0
$622$	19632.7	+	19632.7i	1.26559	+	1.26559i
$623$	14829.3	+	14829.3i	0.953650	+	0.953650i
$624$		0			0
$625$		0			0
$626$			12876.5i			0.822123i
$627$		0			0
$628$	−898.205	+	898.205i	−0.0570737	+	0.0570737i
$629$	−2293.65			−0.145396
$630$		0			0
$631$	29762.7			1.87771			0.938853	−	0.344318i	$-0.111890\pi$
$631$	29762.7			1.87771			0.938853	+	0.344318i	$0.111890\pi$
$632$	7822.48	−	7822.48i	0.492344	−	0.492344i
$633$		0			0
$634$			35254.2i			2.20840i
$635$		0			0
$636$		0			0
$637$	−5142.61	−	5142.61i	−0.319871	−	0.319871i
$638$	8974.65	+	8974.65i	0.556912	+	0.556912i
$639$		0			0
$640$		0			0
$641$		−	5168.75i		−	0.318492i	−0.987239	−	0.159246i	$-0.949094\pi$
$641$		−	5168.75i		−	0.318492i	0.987239	−	0.159246i	$-0.0509063\pi$
$642$		0			0
$643$	2078.46	−	2078.46i	0.127475	−	0.127475i	−0.640491	−	0.767966i	$-0.721269\pi$
$643$	2078.46	−	2078.46i	0.127475	−	0.127475i	0.767966	+	0.640491i	$0.221269\pi$
$644$	4963.13			0.303687
$645$		0			0
$646$	34700.0			2.11339
$647$	10765.7	−	10765.7i	0.654164	−	0.654164i	−0.299829	−	0.953993i	$-0.596930\pi$
$647$	10765.7	−	10765.7i	0.654164	−	0.654164i	0.953993	+	0.299829i	$0.0969297\pi$
$648$		0			0
$649$		−	10592.8i		−	0.640684i
$650$		0			0
$651$		0			0
$652$	−1374.37	−	1374.37i	−0.0825530	−	0.0825530i
$653$	12815.1	+	12815.1i	0.767984	+	0.767984i	0.977751	−	0.209767i	$-0.0672707\pi$
$653$	12815.1	+	12815.1i	0.767984	+	0.767984i	−0.209767	+	0.977751i	$0.567271\pi$
$654$		0			0
$655$		0			0
$656$		−	20069.9i		−	1.19451i
$657$		0			0
$658$	8304.68	−	8304.68i	0.492022	−	0.492022i
$659$	16634.8			0.983307			0.491654	−	0.870791i	$-0.336393\pi$
$659$	16634.8			0.983307			0.491654	+	0.870791i	$0.336393\pi$
$660$		0			0
$661$	−10835.6			−0.637601			−0.318800	−	0.947822i	$-0.603280\pi$
$661$	−10835.6			−0.637601			−0.318800	+	0.947822i	$0.603280\pi$
$662$	521.868	−	521.868i	0.0306389	−	0.0306389i
$663$		0			0
$664$		−	5396.92i		−	0.315423i
$665$		0			0
$666$		0			0
$667$	−3593.07	−	3593.07i	−0.208582	−	0.208582i
$668$	3889.27	+	3889.27i	0.225270	+	0.225270i
$669$		0			0
$670$		0			0
$671$		−	14787.4i		−	0.850762i
$672$		0			0
$673$	16220.3	−	16220.3i	0.929045	−	0.929045i	−0.0685992	−	0.997644i	$-0.521853\pi$
$673$	16220.3	−	16220.3i	0.929045	−	0.929045i	0.997644	+	0.0685992i	$0.0218530\pi$
$674$	17347.3			0.991382
$675$		0			0
$676$	−13967.4			−0.794685
$677$	−11196.6	+	11196.6i	−0.635626	+	0.635626i	−0.949473	−	0.313847i	$-0.898382\pi$
$677$	−11196.6	+	11196.6i	−0.635626	+	0.635626i	0.313847	+	0.949473i	$0.398382\pi$
$678$		0			0
$679$			17065.0i			0.964500i
$680$		0			0
$681$		0			0
$682$	23210.3	+	23210.3i	1.30318	+	1.30318i
$683$	15428.1	+	15428.1i	0.864331	+	0.864331i	0.991838	−	0.127507i	$-0.0406975\pi$
$683$	15428.1	+	15428.1i	0.864331	+	0.864331i	−0.127507	+	0.991838i	$0.540697\pi$
$684$		0			0
$685$		0			0
$686$			25627.9i			1.42635i
$687$		0			0
$688$	−13561.6	+	13561.6i	−0.751501	+	0.751501i
$689$	−17635.2			−0.975104
$690$		0			0
$691$	21858.6			1.20339			0.601693	−	0.798728i	$-0.294493\pi$
$691$	21858.6			1.20339			0.601693	+	0.798728i	$0.294493\pi$
$692$	−2535.89	+	2535.89i	−0.139307	+	0.139307i
$693$		0			0
$694$		−	12434.2i		−	0.680112i
$695$		0			0
$696$		0			0
$697$	15737.2	+	15737.2i	0.855220	+	0.855220i
$698$	−21518.9	−	21518.9i	−1.16691	−	1.16691i
$699$		0			0
$700$		0			0
$701$			8846.82i			0.476662i	0.971184	+	0.238331i	$0.0766002\pi$
$701$			8846.82i			0.476662i	−0.971184	+	0.238331i	$0.923400\pi$
$702$		0			0
$703$	−2084.34	+	2084.34i	−0.111824	+	0.111824i
$704$	7347.86			0.393371
$705$		0			0
$706$	35656.2			1.90076
$707$	−1212.06	+	1212.06i	−0.0644755	+	0.0644755i
$708$		0			0
$709$		−	23189.8i		−	1.22837i	−0.789163	−	0.614184i	$-0.789485\pi$
$709$		−	23189.8i		−	1.22837i	0.789163	−	0.614184i	$-0.210515\pi$
$710$		0			0
$711$		0			0
$712$	−8073.34	−	8073.34i	−0.424945	−	0.424945i
$713$	−9292.43	−	9292.43i	−0.488084	−	0.488084i
$714$		0			0
$715$		0			0
$716$		−	27133.9i		−	1.41626i
$717$		0			0
$718$	4661.21	−	4661.21i	0.242277	−	0.242277i
$719$	7005.29			0.363356			0.181678	−	0.983358i	$-0.441847\pi$
$719$	7005.29			0.363356			0.181678	+	0.983358i	$0.441847\pi$
$720$		0			0
$721$	−301.661			−0.0155818
$722$	13553.2	−	13553.2i	0.698611	−	0.698611i
$723$		0			0
$724$			8892.98i			0.456498i
$725$		0			0
$726$		0			0
$727$	16025.7	+	16025.7i	0.817553	+	0.817553i	0.985753	−	0.168200i	$-0.0537954\pi$
$727$	16025.7	+	16025.7i	0.817553	+	0.817553i	−0.168200	+	0.985753i	$0.553795\pi$
$728$	−6183.82	−	6183.82i	−0.314818	−	0.314818i
$729$		0			0
$730$		0			0
$731$		−	21267.8i		−	1.07609i
$732$		0			0
$733$	3319.43	−	3319.43i	0.167266	−	0.167266i	−0.618511	−	0.785777i	$-0.712264\pi$
$733$	3319.43	−	3319.43i	0.167266	−	0.167266i	0.785777	+	0.618511i	$0.212264\pi$
$734$	−24502.5			−1.23216
$735$		0			0
$736$	−12281.5			−0.615084
$737$	5700.41	−	5700.41i	0.284908	−	0.284908i
$738$		0			0
$739$			19979.4i			0.994526i	0.867600	+	0.497263i	$0.165662\pi$
$739$			19979.4i			0.994526i	−0.867600	+	0.497263i	$0.834338\pi$
$740$		0			0
$741$		0			0
$742$	10440.7	+	10440.7i	0.516562	+	0.516562i
$743$	14574.6	+	14574.6i	0.719637	+	0.719637i	0.968531	−	0.248894i	$-0.0800670\pi$
$743$	14574.6	+	14574.6i	0.719637	+	0.719637i	−0.248894	+	0.968531i	$0.580067\pi$
$744$		0			0
$745$		0			0
$746$			30038.0i			1.47422i
$747$		0			0
$748$	−13132.7	+	13132.7i	−0.641951	+	0.641951i
$749$	16866.3			0.822807
$750$		0			0
$751$	−11620.1			−0.564612			−0.282306	−	0.959324i	$-0.591099\pi$
$751$	−11620.1			−0.564612			−0.282306	+	0.959324i	$0.591099\pi$
$752$	−11219.9	+	11219.9i	−0.544079	+	0.544079i
$753$		0			0
$754$		−	22789.7i		−	1.10073i
$755$		0			0
$756$		0			0
$757$	−10502.0	−	10502.0i	−0.504229	−	0.504229i	0.408520	−	0.912749i	$-0.366045\pi$
$757$	−10502.0	−	10502.0i	−0.504229	−	0.504229i	−0.912749	+	0.408520i	$0.866045\pi$
$758$	−403.390	−	403.390i	−0.0193296	−	0.0193296i
$759$		0			0
$760$		0			0
$761$			36489.6i			1.73817i	0.494664	+	0.869085i	$0.335291\pi$
$761$			36489.6i			1.73817i	−0.494664	+	0.869085i	$0.664709\pi$
$762$		0			0
$763$	−4461.01	+	4461.01i	−0.211664	+	0.211664i
$764$	−6264.50			−0.296652
$765$		0			0
$766$	−22532.3			−1.06283
$767$	−13449.4	+	13449.4i	−0.633154	+	0.633154i
$768$		0			0
$769$			30323.9i			1.42199i	0.703198	+	0.710994i	$0.251755\pi$
$769$			30323.9i			1.42199i	−0.703198	+	0.710994i	$0.748245\pi$
$770$		0			0
$771$		0			0
$772$	−16229.4	−	16229.4i	−0.756617	−	0.756617i
$773$	10327.2	+	10327.2i	0.480522	+	0.480522i	0.905298	−	0.424777i	$-0.139647\pi$
$773$	10327.2	+	10327.2i	0.480522	+	0.480522i	−0.424777	+	0.905298i	$0.639647\pi$
$774$		0			0
$775$		0			0
$776$		−	9290.49i		−	0.429780i
$777$		0			0
$778$	20533.4	−	20533.4i	0.946220	−	0.946220i
$779$	28602.1			1.31550
$780$		0			0
$781$	−17810.1			−0.816000
$782$	12581.2	−	12581.2i	0.575324	−	0.575324i
$783$		0			0
$784$		−	8226.74i		−	0.374760i
$785$		0			0
$786$		0			0
$787$	−21521.8	−	21521.8i	−0.974802	−	0.974802i	0.0248882	−	0.999690i	$-0.492077\pi$
$787$	−21521.8	−	21521.8i	−0.974802	−	0.974802i	−0.999690	+	0.0248882i	$0.992077\pi$
$788$	6685.38	+	6685.38i	0.302229	+	0.302229i
$789$		0			0
$790$		0			0
$791$			11328.6i			0.509229i
$792$		0			0
$793$	−18775.2	+	18775.2i	−0.840764	+	0.840764i
$794$	−53452.3			−2.38911
$795$		0			0
$796$	−2988.10			−0.133053
$797$	−17277.8	+	17277.8i	−0.767895	+	0.767895i	−0.977736	−	0.209841i	$-0.932706\pi$
$797$	−17277.8	+	17277.8i	−0.767895	+	0.767895i	0.209841	+	0.977736i	$0.432706\pi$
$798$		0			0
$799$		−	17595.4i		−	0.779076i
$800$		0			0
$801$		0			0
$802$	−28254.4	−	28254.4i	−1.24401	−	1.24401i
$803$	−18216.4	−	18216.4i	−0.800552	−	0.800552i
$804$		0			0
$805$		0			0
$806$		−	58939.0i		−	2.57573i
$807$		0			0
$808$	659.866	−	659.866i	0.0287302	−	0.0287302i
$809$	41260.2			1.79312			0.896558	−	0.442926i	$-0.146059\pi$
$809$	41260.2			1.79312			0.896558	+	0.442926i	$0.146059\pi$
$810$		0			0
$811$	−23357.1			−1.01132			−0.505659	−	0.862733i	$-0.668751\pi$
$811$	−23357.1			−1.01132			−0.505659	+	0.862733i	$0.668751\pi$
$812$	−5638.54	+	5638.54i	−0.243687	+	0.243687i
$813$		0			0
$814$		−	3775.24i		−	0.162558i
$815$		0			0
$816$		0			0
$817$	−19327.0	−	19327.0i	−0.827621	−	0.827621i
$818$	−12136.9	−	12136.9i	−0.518773	−	0.518773i
$819$		0			0
$820$		0			0
$821$			8296.46i			0.352678i	0.984330	+	0.176339i	$0.0564254\pi$
$821$			8296.46i			0.352678i	−0.984330	+	0.176339i	$0.943575\pi$
$822$		0			0
$823$	−17980.5	+	17980.5i	−0.761555	+	0.761555i	−0.976603	−	0.215048i	$-0.931009\pi$
$823$	−17980.5	+	17980.5i	−0.761555	+	0.761555i	0.215048	+	0.976603i	$0.431009\pi$
$824$	164.230			0.00694322
$825$		0			0
$826$	15925.1			0.670827
$827$	9128.21	−	9128.21i	0.383820	−	0.383820i	−0.488656	−	0.872476i	$-0.662513\pi$
$827$	9128.21	−	9128.21i	0.383820	−	0.383820i	0.872476	+	0.488656i	$0.162513\pi$
$828$		0			0
$829$			24401.3i			1.02231i	0.859489	+	0.511154i	$0.170782\pi$
$829$			24401.3i			1.02231i	−0.859489	+	0.511154i	$0.829218\pi$
$830$		0			0
$831$		0			0
$832$	−9329.38	−	9329.38i	−0.388748	−	0.388748i
$833$	6450.73	+	6450.73i	0.268313	+	0.268313i
$834$		0			0
$835$		0			0
$836$			23868.5i			0.987452i
$837$		0			0
$838$	29560.2	−	29560.2i	1.21854	−	1.21854i
$839$	−38174.8			−1.57084			−0.785422	−	0.618960i	$-0.787554\pi$
$839$	−38174.8			−1.57084			−0.785422	+	0.618960i	$0.787554\pi$
$840$		0			0
$841$	−16224.9			−0.665256
$842$	−8880.22	+	8880.22i	−0.363459	+	0.363459i
$843$		0			0
$844$		−	31729.3i		−	1.29404i
$845$		0			0
$846$		0			0
$847$	−1137.45	−	1137.45i	−0.0461433	−	0.0461433i
$848$	−14105.7	−	14105.7i	−0.571216	−	0.571216i
$849$		0			0
$850$		0			0
$851$			1511.44i			0.0608833i
$852$		0			0
$853$	−1757.73	+	1757.73i	−0.0705550	+	0.0705550i	−0.741504	−	0.670949i	$-0.765887\pi$
$853$	−1757.73	+	1757.73i	−0.0705550	+	0.0705550i	0.670949	+	0.741504i	$0.265887\pi$
$854$	22231.2			0.890790
$855$		0			0
$856$	−9182.33			−0.366642
$857$	−7091.77	+	7091.77i	−0.282672	+	0.282672i	−0.834174	−	0.551501i	$-0.814055\pi$
$857$	−7091.77	+	7091.77i	−0.282672	+	0.282672i	0.551501	+	0.834174i	$0.314055\pi$
$858$		0			0
$859$		−	16842.4i		−	0.668982i	−0.942399	−	0.334491i	$-0.891436\pi$
$859$		−	16842.4i		−	0.668982i	0.942399	−	0.334491i	$-0.108564\pi$
$860$		0			0
$861$		0			0
$862$	42366.4	+	42366.4i	1.67402	+	1.67402i
$863$	−33056.1	−	33056.1i	−1.30387	−	1.30387i	−0.925759	−	0.378114i	$-0.876573\pi$
$863$	−33056.1	−	33056.1i	−1.30387	−	1.30387i	−0.378114	−	0.925759i	$-0.623427\pi$
$864$		0			0
$865$		0			0
$866$			19968.7i			0.783562i
$867$		0			0
$868$	−14582.5	+	14582.5i	−0.570231	+	0.570231i
$869$	−50107.9			−1.95603
$870$		0			0
$871$	−14475.3			−0.563120
$872$	2428.65	−	2428.65i	0.0943171	−	0.0943171i
$873$		0			0
$874$		−	22866.2i		−	0.884966i
$875$		0			0
$876$		0			0
$877$	−1780.97	−	1780.97i	−0.0685738	−	0.0685738i	0.671988	−	0.740562i	$-0.265441\pi$
$877$	−1780.97	−	1780.97i	−0.0685738	−	0.0685738i	−0.740562	+	0.671988i	$0.765441\pi$
$878$	−4213.39	−	4213.39i	−0.161953	−	0.161953i
$879$		0			0
$880$		0			0
$881$		−	2698.82i		−	0.103207i	−0.998668	−	0.0516036i	$-0.983567\pi$
$881$		−	2698.82i		−	0.103207i	0.998668	−	0.0516036i	$-0.0164332\pi$
$882$		0			0
$883$	−6744.66	+	6744.66i	−0.257051	+	0.257051i	−0.823854	−	0.566803i	$-0.808180\pi$
$883$	−6744.66	+	6744.66i	−0.257051	+	0.257051i	0.566803	+	0.823854i	$0.308180\pi$
$884$	33348.5			1.26881
$885$		0			0
$886$	−43497.5			−1.64935
$887$	1302.99	−	1302.99i	0.0493238	−	0.0493238i	−0.682015	−	0.731338i	$-0.738896\pi$
$887$	1302.99	−	1302.99i	0.0493238	−	0.0493238i	0.731338	+	0.682015i	$0.238896\pi$
$888$		0			0
$889$		−	17092.1i		−	0.644827i
$890$		0			0
$891$		0			0
$892$	1856.29	+	1856.29i	0.0696785	+	0.0696785i
$893$	−15989.7	−	15989.7i	−0.599189	−	0.599189i
$894$		0			0
$895$		0			0
$896$		−	15798.5i		−	0.589052i
$897$		0			0
$898$	39483.0	−	39483.0i	1.46722	−	1.46722i
$899$	21114.0			0.783306
$900$		0			0
$901$	22121.0			0.817933
$902$	−25902.6	+	25902.6i	−0.956167	+	0.956167i
$903$		0			0
$904$		−	6167.50i		−	0.226912i
$905$		0			0
$906$		0			0
$907$	3070.33	+	3070.33i	0.112402	+	0.112402i	0.761071	−	0.648669i	$-0.224674\pi$
$907$	3070.33	+	3070.33i	0.112402	+	0.112402i	−0.648669	+	0.761071i	$0.724674\pi$
$908$	−15735.8	−	15735.8i	−0.575123	−	0.575123i
$909$		0			0
$910$		0			0
$911$		−	19102.6i		−	0.694727i	−0.937731	−	0.347364i	$-0.887077\pi$
$911$		−	19102.6i		−	0.694727i	0.937731	−	0.347364i	$-0.112923\pi$
$912$		0			0
$913$	−17285.3	+	17285.3i	−0.626572	+	0.626572i
$914$	14004.9			0.506830
$915$		0			0
$916$	1322.92			0.0477189
$917$	4871.55	−	4871.55i	0.175434	−	0.175434i
$918$		0			0
$919$		−	29786.7i		−	1.06917i	−0.845113	−	0.534587i	$-0.820467\pi$
$919$		−	29786.7i		−	1.06917i	0.845113	−	0.534587i	$-0.179533\pi$
$920$		0			0
$921$		0			0
$922$	−33577.8	−	33577.8i	−1.19938	−	1.19938i
$923$	22613.0	+	22613.0i	0.806410	+	0.806410i
$924$		0			0
$925$		0			0
$926$			58478.9i			2.07531i
$927$		0			0
$928$	13952.9	−	13952.9i	0.493561	−	0.493561i
$929$	−7724.87			−0.272815			−0.136407	−	0.990653i	$-0.543556\pi$
$929$	−7724.87			−0.272815			−0.136407	+	0.990653i	$0.543556\pi$
$930$		0			0
$931$	11724.1			0.412720
$932$	2011.12	−	2011.12i	0.0706829	−	0.0706829i
$933$		0			0
$934$			41446.7i			1.45201i
$935$		0			0
$936$		0			0
$937$	20722.5	+	20722.5i	0.722492	+	0.722492i	0.969112	−	0.246620i	$-0.0793199\pi$
$937$	20722.5	+	20722.5i	0.722492	+	0.722492i	−0.246620	+	0.969112i	$0.579320\pi$
$938$	8569.92	+	8569.92i	0.298313	+	0.298313i
$939$		0			0
$940$		0			0
$941$		−	21780.7i		−	0.754548i	−0.926102	−	0.377274i	$-0.876862\pi$
$941$		−	21780.7i		−	0.754548i	0.926102	−	0.377274i	$-0.123138\pi$
$942$		0			0
$943$	10370.3	−	10370.3i	0.358116	−	0.358116i
$944$	−21515.3			−0.741803
$945$		0			0
$946$	35005.8			1.20310
$947$	−29938.4	+	29938.4i	−1.02731	+	1.02731i	−0.0276975	+	0.999616i	$0.508818\pi$
$947$	−29938.4	+	29938.4i	−1.02731	+	1.02731i	−0.999616	+	0.0276975i	$0.991182\pi$
$948$		0			0
$949$			46257.8i			1.58229i
$950$		0			0
$951$		0			0
$952$	7756.79	+	7756.79i	0.264075	+	0.264075i
$953$	29572.1	+	29572.1i	1.00518	+	1.00518i	0.999987	+	0.00519163i	$0.00165255\pi$
$953$	29572.1	+	29572.1i	1.00518	+	1.00518i	0.00519163	+	0.999987i	$0.498347\pi$
$954$		0			0
$955$		0			0
$956$		−	5819.29i		−	0.196872i
$957$		0			0
$958$	−28090.5	+	28090.5i	−0.947353	+	0.947353i
$959$	−20646.4			−0.695212
$960$		0			0
$961$	24814.3			0.832945
$962$	−4793.32	+	4793.32i	−0.160647	+	0.160647i
$963$		0			0
$964$		−	14842.9i		−	0.495911i
$965$		0			0
$966$		0			0
$967$	9478.37	+	9478.37i	0.315206	+	0.315206i	0.846922	−	0.531717i	$-0.178453\pi$
$967$	9478.37	+	9478.37i	0.315206	+	0.315206i	−0.531717	+	0.846922i	$0.678453\pi$
$968$	619.250	+	619.250i	0.0205614	+	0.0205614i
$969$		0			0
$970$		0			0
$971$			8382.79i			0.277051i	0.990359	+	0.138525i	$0.0442363\pi$
$971$			8382.79i			0.277051i	−0.990359	+	0.138525i	$0.955764\pi$
$972$		0			0
$973$	−1224.89	+	1224.89i	−0.0403577	+	0.0403577i
$974$	−23539.4			−0.774384
$975$		0			0
$976$	−30035.0			−0.985039
$977$	−24277.3	+	24277.3i	−0.794986	+	0.794986i	−0.982300	−	0.187314i	$-0.940022\pi$
$977$	−24277.3	+	24277.3i	−0.794986	+	0.794986i	0.187314	+	0.982300i	$0.440022\pi$
$978$		0			0
$979$			51714.8i			1.68826i
$980$		0			0
$981$		0			0
$982$	−39777.5	−	39777.5i	−1.29262	−	1.29262i
$983$	14666.4	+	14666.4i	0.475876	+	0.475876i	0.903810	−	0.427934i	$-0.140758\pi$
$983$	14666.4	+	14666.4i	0.475876	+	0.475876i	−0.427934	+	0.903810i	$0.640758\pi$
$984$		0			0
$985$		0			0
$986$			28586.7i			0.923313i
$987$		0			0
$988$	30305.2	−	30305.2i	0.975847	−	0.975847i
$989$	−14014.8			−0.450603
$990$		0			0
$991$	17192.0			0.551080			0.275540	−	0.961290i	$-0.411143\pi$
$991$	17192.0			0.551080			0.275540	+	0.961290i	$0.411143\pi$
$992$	36085.0	−	36085.0i	1.15494	−	1.15494i
$993$		0			0
$994$		−	26775.5i		−	0.854393i
$995$		0			0
$996$		0			0
$997$	−13617.4	−	13617.4i	−0.432566	−	0.432566i	0.456935	−	0.889500i	$-0.348947\pi$
$997$	−13617.4	−	13617.4i	−0.432566	−	0.432566i	−0.889500	+	0.456935i	$0.848947\pi$
$998$	23296.9	+	23296.9i	0.738929	+	0.738929i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.4.f.c.107.2		12
3.2	odd	2	inner	225.4.f.c.107.5		12
5.2	odd	4		45.4.f.a.8.2	✓	12
5.3	odd	4	inner	225.4.f.c.143.5		12
5.4	even	2		45.4.f.a.17.5	yes	12
15.2	even	4		45.4.f.a.8.5	yes	12
15.8	even	4	inner	225.4.f.c.143.2		12
15.14	odd	2		45.4.f.a.17.2	yes	12
20.7	even	4		720.4.w.d.593.2		12
20.19	odd	2		720.4.w.d.17.5		12
60.47	odd	4		720.4.w.d.593.5		12
60.59	even	2		720.4.w.d.17.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.4.f.a.8.2	✓	12	5.2	odd	4
45.4.f.a.8.5	yes	12	15.2	even	4
45.4.f.a.17.2	yes	12	15.14	odd	2
45.4.f.a.17.5	yes	12	5.4	even	2
225.4.f.c.107.2		12	1.1	even	1	trivial
225.4.f.c.107.5		12	3.2	odd	2	inner
225.4.f.c.143.2		12	15.8	even	4	inner
225.4.f.c.143.5		12	5.3	odd	4	inner
720.4.w.d.17.2		12	60.59	even	2
720.4.w.d.17.5		12	20.19	odd	2
720.4.w.d.593.2		12	20.7	even	4
720.4.w.d.593.5		12	60.47	odd	4

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:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	225.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.62140 + 2.62140i) q^{2} -5.74350i q^{4} +(10.8652 + 10.8652i) q^{7} +(-5.91519 - 5.91519i) q^{8} +O(q^{10})\)	\(q+(-2.62140 + 2.62140i) q^{2} -5.74350i q^{4} +(10.8652 + 10.8652i) q^{7} +(-5.91519 - 5.91519i) q^{8} +37.8905i q^{11} +(48.1085 - 48.1085i) q^{13} -56.9640 q^{14} +76.9602 q^{16} +(-60.3458 + 60.3458i) q^{17} +109.678i q^{19} +(-99.3262 - 99.3262i) q^{22} +(39.7660 + 39.7660i) q^{23} +252.224i q^{26} +(62.4042 - 62.4042i) q^{28} -90.3553 q^{29} -233.678 q^{31} +(-154.422 + 154.422i) q^{32} -316.381i q^{34} +(19.0042 + 19.0042i) q^{37} +(-287.509 - 287.509i) q^{38} -260.783i q^{41} +(-176.216 + 176.216i) q^{43} +217.624 q^{44} -208.485 q^{46} +(-145.788 + 145.788i) q^{47} -106.896i q^{49} +(-276.311 - 276.311i) q^{52} +(-183.285 - 183.285i) q^{53} -128.539i q^{56} +(236.858 - 236.858i) q^{58} -279.564 q^{59} -390.267 q^{61} +(612.563 - 612.563i) q^{62} -193.924i q^{64} +(-150.444 - 150.444i) q^{67} +(346.596 + 346.596i) q^{68} +470.042i q^{71} +(-480.765 + 480.765i) q^{73} -99.6355 q^{74} +629.934 q^{76} +(-411.687 + 411.687i) q^{77} +1322.44i q^{79} +(683.618 + 683.618i) q^{82} +(456.192 + 456.192i) q^{83} -923.868i q^{86} +(224.129 - 224.129i) q^{88} +1364.85 q^{89} +1045.41 q^{91} +(228.396 - 228.396i) q^{92} -764.340i q^{94} +(785.308 + 785.308i) q^{97} +(280.218 + 280.218i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 24 q^{7}+O(q^{10}) \) 12 * q - 24 * q^7	\( 12 q - 24 q^{7} + 108 q^{13} - 648 q^{16} - 1056 q^{22} + 576 q^{28} - 1248 q^{31} - 828 q^{37} + 96 q^{43} + 672 q^{46} + 312 q^{52} + 3864 q^{58} + 96 q^{61} - 1632 q^{67} - 3972 q^{73} - 480 q^{76} + 7848 q^{82} - 7968 q^{88} + 4752 q^{91} - 2772 q^{97}+O(q^{100}) \) 12 * q - 24 * q^7 + 108 * q^13 - 648 * q^16 - 1056 * q^22 + 576 * q^28 - 1248 * q^31 - 828 * q^37 + 96 * q^43 + 672 * q^46 + 312 * q^52 + 3864 * q^58 + 96 * q^61 - 1632 * q^67 - 3972 * q^73 - 480 * q^76 + 7848 * q^82 - 7968 * q^88 + 4752 * q^91 - 2772 * q^97

Introduction

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