LMFDB - Embedded newform 825.2.f.f.626.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [825,2,Mod(626,825)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(825, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 1]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("825.626");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 825 = 3 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	825.f (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.58765816676$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 32x^{14} + 384x^{12} + 2192x^{10} + 6394x^{8} + 9216x^{6} + 5376x^{4} + 432x^{2} + 9 $ x^16 + 32x^14 + 384x^12 + 2192x^10 + 6394x^8 + 9216x^6 + 5376x^4 + 432*x^2 + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{11} $
Twist minimal:	no (minimal twist has level 165)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			626.12
Root			$-1.18041i$ of defining polynomial
Character	$\chi$	$=$	825.626
Dual form			825.2.f.f.626.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.50597 q^{2} +(0.796225 + 1.53819i) q^{3} +0.267949 q^{4} +(1.19909 + 2.31647i) q^{6} +2.12976i q^{7} -2.60842 q^{8} +(-1.73205 + 2.44949i) q^{9} +O(q^{10})$	\(q+1.50597 q^{2} +(0.796225 + 1.53819i) q^{3} +0.267949 q^{4} +(1.19909 + 2.31647i) q^{6} +2.12976i q^{7} -2.60842 q^{8} +(-1.73205 + 2.44949i) q^{9} +(3.27598 + 0.517638i) q^{11} +(0.213348 + 0.412157i) q^{12} +2.12976i q^{13} +3.20736i q^{14} -4.46410 q^{16} -4.11439 q^{17} +(-2.60842 + 3.68886i) q^{18} +4.63294i q^{19} +(-3.27598 + 1.69577i) q^{21} +(4.93353 + 0.779548i) q^{22} -5.32844i q^{23} +(-2.07689 - 4.01224i) q^{24} +3.20736i q^{26} +(-5.14688 - 0.713876i) q^{27} +0.570669i q^{28} +8.95015 q^{29} +3.46410 q^{31} -1.50597 q^{32} +(1.81219 + 5.45123i) q^{33} -6.19615 q^{34} +(-0.464102 + 0.656339i) q^{36} +1.16575 q^{37} +6.97707i q^{38} +(-3.27598 + 1.69577i) q^{39} -2.39818 q^{41} +(-4.93353 + 2.55378i) q^{42} +9.50749i q^{43} +(0.877796 + 0.138701i) q^{44} -8.02448i q^{46} -3.07638i q^{47} +(-3.55443 - 6.86663i) q^{48} +2.46410 q^{49} +(-3.27598 - 6.32871i) q^{51} +0.570669i q^{52} +4.50413i q^{53} +(-7.75105 - 1.07508i) q^{54} -5.55532i q^{56} +(-7.12633 + 3.68886i) q^{57} +13.4787 q^{58} -4.89898i q^{59} +3.39154i q^{61} +5.21684 q^{62} +(-5.21684 - 3.68886i) q^{63} +6.66025 q^{64} +(2.72911 + 8.20940i) q^{66} +12.3129 q^{67} -1.10245 q^{68} +(8.19615 - 4.24264i) q^{69} -13.3843i q^{71} +(4.51791 - 6.38929i) q^{72} -2.12976i q^{73} +1.75559 q^{74} +1.24139i q^{76} +(-1.10245 + 6.97707i) q^{77} +(-4.93353 + 2.55378i) q^{78} -13.8988i q^{79} +(-3.00000 - 8.48528i) q^{81} -3.61160 q^{82} -9.33123 q^{83} +(-0.877796 + 0.454381i) q^{84} +14.3180i q^{86} +(7.12633 + 13.7670i) q^{87} +(-8.54513 - 1.35022i) q^{88} -4.62158i q^{89} -4.53590 q^{91} -1.42775i q^{92} +(2.75821 + 5.32844i) q^{93} -4.63294i q^{94} +(-1.19909 - 2.31647i) q^{96} -1.16575 q^{97} +3.71087 q^{98} +(-6.94211 + 7.12791i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 32 q^{4}+O(q^{10}) $ 16 * q + 32 * q^4	$ 16 q + 32 q^{4} - 16 q^{16} - 16 q^{34} + 48 q^{36} - 16 q^{49} - 32 q^{64} - 48 q^{66} + 48 q^{69} - 48 q^{81} - 128 q^{91} - 48 q^{99}+O(q^{100}) $ 16 * q + 32 * q^4 - 16 * q^16 - 16 * q^34 + 48 * q^36 - 16 * q^49 - 32 * q^64 - 48 * q^66 + 48 * q^69 - 48 * q^81 - 128 * q^91 - 48 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/825\mathbb{Z}\right)^\times$.

$n$	$376$	$551$	$727$
$\chi(n)$	$-1$	$-1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.50597			1.06488			0.532441	−	0.846467i	$-0.321275\pi$
$2$	1.50597			1.06488			0.532441	+	0.846467i	$0.321275\pi$
$3$	0.796225	+	1.53819i	0.459701	+	0.888074i
$3$	0.796225	+	1.53819i	0.459701	+	0.888074i
$4$	0.267949			0.133975
$5$		0			0
$5$		0			0
$6$	1.19909	+	2.31647i	0.489527	+	0.945694i
$7$			2.12976i			0.804975i	0.915425	+	0.402488i	$0.131854\pi$
$7$			2.12976i			0.804975i	−0.915425	+	0.402488i	$0.868146\pi$
$8$	−2.60842			−0.922215
$9$	−1.73205	+	2.44949i	−0.577350	+	0.816497i
$10$		0			0
$11$	3.27598	+	0.517638i	0.987745	+	0.156074i
$11$	3.27598	+	0.517638i	0.987745	+	0.156074i
$12$	0.213348	+	0.412157i	0.0615882	+	0.118979i
$13$			2.12976i			0.590690i	0.955391	+	0.295345i	$0.0954347\pi$
$13$			2.12976i			0.590690i	−0.955391	+	0.295345i	$0.904565\pi$
$14$			3.20736i			0.857204i
$15$		0			0
$16$	−4.46410			−1.11603
$17$	−4.11439			−0.997886			−0.498943	−	0.866635i	$-0.666278\pi$
$17$	−4.11439			−0.997886			−0.498943	+	0.866635i	$0.666278\pi$
$18$	−2.60842	+	3.68886i	−0.614810	+	0.869473i
$19$			4.63294i			1.06287i	0.847100	+	0.531434i	$0.178347\pi$
$19$			4.63294i			1.06287i	−0.847100	+	0.531434i	$0.821653\pi$
$20$		0			0
$21$	−3.27598	+	1.69577i	−0.714878	+	0.370048i
$22$	4.93353	+	0.779548i	1.05183	+	0.166200i
$23$		−	5.32844i		−	1.11106i	−0.831497	−	0.555529i	$-0.812516\pi$
$23$		−	5.32844i		−	1.11106i	0.831497	−	0.555529i	$-0.187484\pi$
$24$	−2.07689	−	4.01224i	−0.423943	−	0.818995i
$25$		0			0
$26$			3.20736i			0.629016i
$27$	−5.14688	−	0.713876i	−0.990518	−	0.137386i
$28$			0.570669i			0.107846i
$29$	8.95015			1.66200			0.831000	−	0.556272i	$-0.187769\pi$
$29$	8.95015			1.66200			0.831000	+	0.556272i	$0.187769\pi$
$30$		0			0
$31$	3.46410			0.622171			0.311086	−	0.950382i	$-0.399307\pi$
$31$	3.46410			0.622171			0.311086	+	0.950382i	$0.399307\pi$
$32$	−1.50597			−0.266221
$33$	1.81219	+	5.45123i	0.315462	+	0.948938i
$34$	−6.19615			−1.06263
$35$		0			0
$36$	−0.464102	+	0.656339i	−0.0773503	+	0.109390i
$37$	1.16575			0.191649			0.0958244	−	0.995398i	$-0.469451\pi$
$37$	1.16575			0.191649			0.0958244	+	0.995398i	$0.469451\pi$
$38$			6.97707i			1.13183i
$39$	−3.27598	+	1.69577i	−0.524577	+	0.271541i
$40$		0			0
$41$	−2.39818			−0.374533			−0.187267	−	0.982309i	$-0.559963\pi$
$41$	−2.39818			−0.374533			−0.187267	+	0.982309i	$0.559963\pi$
$42$	−4.93353	+	2.55378i	−0.761261	+	0.394058i
$43$			9.50749i			1.44988i	0.688813	+	0.724939i	$0.258132\pi$
$43$			9.50749i			1.44988i	−0.688813	+	0.724939i	$0.741868\pi$
$44$	0.877796	+	0.138701i	0.132333	+	0.0209099i
$45$		0			0
$46$		−	8.02448i		−	1.18315i
$47$		−	3.07638i		−	0.448736i	−0.974505	−	0.224368i	$-0.927968\pi$
$47$		−	3.07638i		−	0.448736i	0.974505	−	0.224368i	$-0.0720317\pi$
$48$	−3.55443	−	6.86663i	−0.513038	−	0.991113i
$49$	2.46410			0.352015
$50$		0			0
$51$	−3.27598	−	6.32871i	−0.458729	−	0.886197i
$52$			0.570669i			0.0791375i
$53$			4.50413i			0.618690i	0.950950	+	0.309345i	$0.100110\pi$
$53$			4.50413i			0.618690i	−0.950950	+	0.309345i	$0.899890\pi$
$54$	−7.75105	−	1.07508i	−1.05478	−	0.146299i
$55$		0			0
$56$		−	5.55532i		−	0.742361i
$57$	−7.12633	+	3.68886i	−0.943906	+	0.488602i
$58$	13.4787			1.76984
$59$		−	4.89898i		−	0.637793i	−0.947790	−	0.318896i	$-0.896688\pi$
$59$		−	4.89898i		−	0.637793i	0.947790	−	0.318896i	$-0.103312\pi$
$60$		0			0
$61$			3.39154i			0.434243i	0.976145	+	0.217121i	$0.0696668\pi$
$61$			3.39154i			0.434243i	−0.976145	+	0.217121i	$0.930333\pi$
$62$	5.21684			0.662539
$63$	−5.21684	−	3.68886i	−0.657260	−	0.464753i
$64$	6.66025			0.832532
$65$		0			0
$66$	2.72911	+	8.20940i	0.335930	+	1.01051i
$67$	12.3129			1.50426			0.752131	−	0.659014i	$-0.229026\pi$
$67$	12.3129			1.50426			0.752131	+	0.659014i	$0.229026\pi$
$68$	−1.10245			−0.133691
$69$	8.19615	−	4.24264i	0.986701	−	0.510754i
$70$		0			0
$71$		−	13.3843i		−	1.58842i	−0.607644	−	0.794210i	$-0.707885\pi$
$71$		−	13.3843i		−	1.58842i	0.607644	−	0.794210i	$-0.292115\pi$
$72$	4.51791	−	6.38929i	0.532441	−	0.752986i
$73$		−	2.12976i		−	0.249270i	−0.992203	−	0.124635i	$-0.960224\pi$
$73$		−	2.12976i		−	0.249270i	0.992203	−	0.124635i	$-0.0397760\pi$
$74$	1.75559			0.204084
$75$		0			0
$76$			1.24139i			0.142397i
$77$	−1.10245	+	6.97707i	−0.125636	+	0.795111i
$78$	−4.93353	+	2.55378i	−0.558613	+	0.289159i
$79$		−	13.8988i		−	1.56374i	−0.623443	−	0.781869i	$-0.714266\pi$
$79$		−	13.8988i		−	1.56374i	0.623443	−	0.781869i	$-0.285734\pi$
$80$		0			0
$81$	−3.00000	−	8.48528i	−0.333333	−	0.942809i
$82$	−3.61160			−0.398834
$83$	−9.33123			−1.02424			−0.512118	−	0.858915i	$-0.671139\pi$
$83$	−9.33123			−1.02424			−0.512118	+	0.858915i	$0.671139\pi$
$84$	−0.877796	+	0.454381i	−0.0957754	+	0.0495770i
$85$		0			0
$86$			14.3180i			1.54395i
$87$	7.12633	+	13.7670i	0.764023	+	1.47598i
$88$	−8.54513	−	1.35022i	−0.910914	−	0.143934i
$89$		−	4.62158i		−	0.489886i	−0.969537	−	0.244943i	$-0.921231\pi$
$89$		−	4.62158i		−	0.489886i	0.969537	−	0.244943i	$-0.0787693\pi$
$90$		0			0
$91$	−4.53590			−0.475491
$92$		−	1.42775i		−	0.148853i
$93$	2.75821	+	5.32844i	0.286013	+	0.552534i
$94$		−	4.63294i		−	0.477851i
$95$		0			0
$96$	−1.19909	−	2.31647i	−0.122382	−	0.236424i
$97$	−1.16575			−0.118364			−0.0591822	−	0.998247i	$-0.518849\pi$
$97$	−1.16575			−0.118364			−0.0591822	+	0.998247i	$0.518849\pi$
$98$	3.71087			0.374854
$99$	−6.94211	+	7.12791i	−0.697709	+	0.716382i
$100$		0			0
$101$	8.95015			0.890573			0.445286	−	0.895388i	$-0.353102\pi$
$101$	8.95015			0.890573			0.445286	+	0.895388i	$0.353102\pi$
$102$	−4.93353	−	9.53085i	−0.488493	−	0.943695i
$103$	5.94311			0.585592			0.292796	−	0.956175i	$-0.405414\pi$
$103$	5.94311			0.585592			0.292796	+	0.956175i	$0.405414\pi$
$104$		−	5.55532i		−	0.544744i
$105$		0			0
$106$			6.78309i			0.658832i
$107$	−1.10245			−0.106578			−0.0532888	−	0.998579i	$-0.516970\pi$
$107$	−1.10245			−0.106578			−0.0532888	+	0.998579i	$0.516970\pi$
$108$	−1.37910	−	0.191282i	−0.132704	−	0.0184062i
$109$			12.6574i			1.21236i	0.795327	+	0.606180i	$0.207299\pi$
$109$			12.6574i			1.21236i	−0.795327	+	0.606180i	$0.792701\pi$
$110$		0			0
$111$	0.928203	+	1.79315i	0.0881012	+	0.170198i
$112$		−	9.50749i		−	0.898373i
$113$		−	10.6569i		−	1.00252i	−0.865298	−	0.501258i	$-0.832871\pi$
$113$		−	10.6569i		−	1.00252i	0.865298	−	0.501258i	$-0.167129\pi$
$114$	−10.7321	+	5.55532i	−1.00515	+	0.520303i
$115$		0			0
$116$	2.39818			0.222666
$117$	−5.21684	−	3.68886i	−0.482297	−	0.341035i
$118$		−	7.37772i		−	0.679174i
$119$		−	8.76268i		−	0.803274i
$120$		0			0
$121$	10.4641	+	3.39154i	0.951282	+	0.308322i
$122$			5.10757i			0.462418i
$123$	−1.90949	−	3.68886i	−0.172173	−	0.332613i
$124$	0.928203			0.0833551
$125$		0			0
$126$	−7.85641	−	5.55532i	−0.699904	−	0.494907i
$127$			10.6488i			0.944930i	0.881349	+	0.472465i	$0.156636\pi$
$127$			10.6488i			0.944930i	−0.881349	+	0.472465i	$0.843364\pi$
$128$	13.0421			1.15277
$129$	−14.6243	+	7.57010i	−1.28760	+	0.666510i
$130$		0			0
$131$		0			0			−	1.00000i	$-0.5\pi$
$131$		0			0				1.00000i	$0.5\pi$
$132$	0.485576	+	1.46065i	0.0422639	+	0.127134i
$133$	−9.86707			−0.855583
$134$	18.5429			1.60186
$135$		0			0
$136$	10.7321			0.920266
$137$			2.25207i			0.192407i	0.995362	+	0.0962034i	$0.0306699\pi$
$137$			2.25207i			0.192407i	−0.995362	+	0.0962034i	$0.969330\pi$
$138$	12.3432	−	6.38929i	1.05072	−	0.543893i
$139$		−	17.2904i		−	1.46655i	−0.679933	−	0.733274i	$-0.737991\pi$
$139$		−	17.2904i		−	1.46655i	0.679933	−	0.733274i	$-0.262009\pi$
$140$		0			0
$141$	4.73205	−	2.44949i	0.398511	−	0.206284i
$142$		−	20.1563i		−	1.69148i
$143$	−1.10245	+	6.97707i	−0.0921913	+	0.583452i
$144$	7.73205	−	10.9348i	0.644338	−	0.911231i
$145$		0			0
$146$		−	3.20736i		−	0.265443i
$147$	1.96198	+	3.79025i	0.161821	+	0.312615i
$148$	0.312363			0.0256761
$149$	15.5021			1.26998			0.634991	−	0.772519i	$-0.281004\pi$
$149$	15.5021			1.26998			0.634991	+	0.772519i	$0.281004\pi$
$150$		0			0
$151$			10.5073i			0.855069i	0.903999	+	0.427535i	$0.140618\pi$
$151$			10.5073i			0.855069i	−0.903999	+	0.427535i	$0.859382\pi$
$152$		−	12.0846i		−	0.980194i
$153$	7.12633	−	10.0782i	0.576130	−	0.814771i
$154$	−1.66025	+	10.5073i	−0.133787	+	0.846700i
$155$		0			0
$156$	−0.877796	+	0.454381i	−0.0702800	+	0.0363796i
$157$	−8.70131			−0.694440			−0.347220	−	0.937784i	$-0.612874\pi$
$157$	−8.70131			−0.694440			−0.347220	+	0.937784i	$0.612874\pi$
$158$		−	20.9312i		−	1.66520i
$159$	−6.92820	+	3.58630i	−0.549442	+	0.284412i
$160$		0			0
$161$	11.3483			0.894374
$162$	−4.51791	−	12.7786i	−0.354961	−	1.00398i
$163$	−5.94311			−0.465500			−0.232750	−	0.972537i	$-0.574772\pi$
$163$	−5.94311			−0.465500			−0.232750	+	0.972537i	$0.574772\pi$
$164$	−0.642592			−0.0501780
$165$		0			0
$166$	−14.0526			−1.09069
$167$	13.1502			1.01759			0.508797	−	0.860886i	$-0.330090\pi$
$167$	13.1502			1.01759			0.508797	+	0.860886i	$0.330090\pi$
$168$	8.54513	−	4.42328i	0.659271	−	0.341264i
$169$	8.46410			0.651085
$170$		0			0
$171$	−11.3483	−	8.02448i	−0.867829	−	0.613647i
$172$			2.54752i			0.194247i
$173$	14.5481			1.10607			0.553034	−	0.833158i	$-0.313470\pi$
$173$	14.5481			1.10607			0.553034	+	0.833158i	$0.313470\pi$
$174$	10.7321	+	20.7327i	0.813595	+	1.57174i
$175$		0			0
$176$	−14.6243	−	2.31079i	−1.10235	−	0.174182i
$177$	7.53556	−	3.90069i	0.566407	−	0.293194i
$178$		−	6.95996i		−	0.521671i
$179$			19.3185i			1.44393i	0.691928	+	0.721967i	$0.256762\pi$
$179$			19.3185i			1.44393i	−0.691928	+	0.721967i	$0.743238\pi$
$180$		0			0
$181$	−9.46410			−0.703461			−0.351731	−	0.936101i	$-0.614407\pi$
$181$	−9.46410			−0.703461			−0.351731	+	0.936101i	$0.614407\pi$
$182$	−6.83093			−0.506342
$183$	−5.21684	+	2.70043i	−0.385640	+	0.199622i
$184$			13.8988i			1.02463i
$185$		0			0
$186$	4.15378	+	8.02448i	0.304570	+	0.588384i
$187$	−13.4787	−	2.12976i	−0.985657	−	0.155744i
$188$		−	0.824313i		−	0.0601192i
$189$	1.52039	−	10.9616i	0.110592	−	0.797342i
$190$		0			0
$191$			9.52056i			0.688883i	0.938808	+	0.344442i	$0.111932\pi$
$191$			9.52056i			0.688883i	−0.938808	+	0.344442i	$0.888068\pi$
$192$	5.30306	+	10.2447i	0.382716	+	0.739350i
$193$		−	10.6488i		−	0.766519i	−0.923641	−	0.383260i	$-0.874801\pi$
$193$		−	10.6488i		−	0.766519i	0.923641	−	0.383260i	$-0.125199\pi$
$194$	−1.75559			−0.126044
$195$		0			0
$196$	0.660254			0.0471610
$197$	−7.93338			−0.565230			−0.282615	−	0.959233i	$-0.591202\pi$
$197$	−7.93338			−0.565230			−0.282615	+	0.959233i	$0.591202\pi$
$198$	−10.4546	+	10.7344i	−0.742978	+	0.762862i
$199$	−10.9282			−0.774680			−0.387340	−	0.921937i	$-0.626606\pi$
$199$	−10.9282			−0.774680			−0.387340	+	0.921937i	$0.626606\pi$
$200$		0			0
$201$	9.80385	+	18.9396i	0.691510	+	1.33589i
$202$	13.4787			0.948355
$203$			19.0617i			1.33787i
$204$	−0.877796	−	1.69577i	−0.0614580	−	0.118728i
$205$		0			0
$206$	8.95015			0.623586
$207$	13.0520	+	9.22913i	0.907174	+	0.641469i
$208$		−	9.50749i		−	0.659226i
$209$	−2.39818	+	15.1774i	−0.165886	+	1.04984i
$210$		0			0
$211$		−	1.24139i		−	0.0854609i	−0.999087	−	0.0427305i	$-0.986394\pi$
$211$		−	1.24139i		−	0.0854609i	0.999087	−	0.0427305i	$-0.0136057\pi$
$212$			1.20688i			0.0828887i
$213$	20.5875	−	10.6569i	1.41063	−	0.730198i
$214$	−1.66025			−0.113493
$215$		0			0
$216$	13.4252	+	1.86209i	0.913470	+	0.126699i
$217$			7.37772i			0.500832i
$218$			19.0617i			1.29102i
$219$	3.27598	−	1.69577i	0.221370	−	0.114590i
$220$		0			0
$221$		−	8.76268i		−	0.589442i
$222$	1.39785	+	2.70043i	0.0938174	+	0.181241i
$223$	−12.6253			−0.845451			−0.422725	−	0.906258i	$-0.638926\pi$
$223$	−12.6253			−0.845451			−0.422725	+	0.906258i	$0.638926\pi$
$224$		−	3.20736i		−	0.214301i
$225$		0			0
$226$		−	16.0490i		−	1.06756i
$227$	−9.33123			−0.619335			−0.309668	−	0.950845i	$-0.600218\pi$
$227$	−9.33123			−0.619335			−0.309668	+	0.950845i	$0.600218\pi$
$228$	−1.90949	+	0.988427i	−0.126459	+	0.0654602i
$229$	−21.3205			−1.40890			−0.704449	−	0.709754i	$-0.748806\pi$
$229$	−21.3205			−1.40890			−0.704449	+	0.709754i	$0.748806\pi$
$230$		0			0
$231$	−11.6098	+	3.85955i	−0.763872	+	0.253939i
$232$	−23.3457			−1.53272
$233$	10.1383			0.664180			0.332090	−	0.943248i	$-0.392246\pi$
$233$	10.1383			0.664180			0.332090	+	0.943248i	$0.392246\pi$
$234$	−7.85641	−	5.55532i	−0.513589	−	0.363163i
$235$		0			0
$236$		−	1.31268i		−	0.0854480i
$237$	21.3790	−	11.0666i	1.38872	−	0.718852i
$238$		−	13.1963i		−	0.855392i
$239$	−16.1447			−1.04431			−0.522157	−	0.852849i	$-0.674872\pi$
$239$	−16.1447			−1.04431			−0.522157	+	0.852849i	$0.674872\pi$
$240$		0			0
$241$		−	12.6574i		−	0.815336i	−0.913130	−	0.407668i	$-0.866342\pi$
$241$		−	12.6574i		−	0.815336i	0.913130	−	0.407668i	$-0.133658\pi$
$242$	15.7586	+	5.10757i	1.01300	+	0.328327i
$243$	10.6633	−	11.3708i	0.684050	−	0.729435i
$244$			0.908762i			0.0581775i
$245$		0			0
$246$	−2.87564	−	5.55532i	−0.183344	−	0.354194i
$247$	−9.86707			−0.627826
$248$	−9.03583			−0.573776
$249$	−7.42976	−	14.3532i	−0.470842	−	0.909597i
$250$		0			0
$251$			16.9706i			1.07117i	0.844481	+	0.535586i	$0.179909\pi$
$251$			16.9706i			1.07117i	−0.844481	+	0.535586i	$0.820091\pi$
$252$	−1.39785	−	0.988427i	−0.0880561	−	0.0622651i
$253$	2.75821	−	17.4559i	0.173407	−	1.09744i
$254$			16.0368i			1.00624i
$255$		0			0
$256$	6.32051			0.395032
$257$		−	29.7186i		−	1.85379i	−0.375315	−	0.926897i	$-0.622465\pi$
$257$		−	29.7186i		−	1.85379i	0.375315	−	0.926897i	$-0.377535\pi$
$258$	−22.0238	+	11.4004i	−1.37114	+	0.709755i
$259$			2.48278i			0.154273i
$260$		0			0
$261$	−15.5021	+	21.9233i	−0.959556	+	1.35702i
$262$		0			0
$263$	−15.3551			−0.946837			−0.473418	−	0.880838i	$-0.656980\pi$
$263$	−15.3551			−0.946837			−0.473418	+	0.880838i	$0.656980\pi$
$264$	−4.72696	−	14.2191i	−0.290924	−	0.875125i
$265$		0			0
$266$	−14.8595			−0.911095
$267$	7.10886	−	3.67982i	0.435055	−	0.225201i
$268$	3.29923			0.201533
$269$		−	8.48528i		−	0.517357i	−0.965964	−	0.258678i	$-0.916713\pi$
$269$		−	8.48528i		−	0.517357i	0.965964	−	0.258678i	$-0.0832870\pi$
$270$		0			0
$271$		−	24.0734i		−	1.46236i	−0.682186	−	0.731179i	$-0.738971\pi$
$271$		−	24.0734i		−	1.46236i	0.682186	−	0.731179i	$-0.261029\pi$
$272$	18.3671			1.11367
$273$	−3.61160	−	6.97707i	−0.218584	−	0.422271i
$274$			3.39154i			0.204891i
$275$		0			0
$276$	2.19615	−	1.13681i	0.132193	−	0.0684280i
$277$			16.8852i			1.01453i	0.861789	+	0.507267i	$0.169344\pi$
$277$			16.8852i			1.01453i	−0.861789	+	0.507267i	$0.830656\pi$
$278$		−	26.0388i		−	1.56170i
$279$	−6.00000	+	8.48528i	−0.359211	+	0.508001i
$280$		0			0
$281$	5.90937			0.352523			0.176262	−	0.984343i	$-0.443599\pi$
$281$	5.90937			0.352523			0.176262	+	0.984343i	$0.443599\pi$
$282$	7.12633	−	3.68886i	0.424367	−	0.219668i
$283$			25.4043i			1.51013i	0.655652	+	0.755063i	$0.272394\pi$
$283$			25.4043i			1.51013i	−0.655652	+	0.755063i	$0.727606\pi$
$284$		−	3.58630i		−	0.212808i
$285$		0			0
$286$	−1.66025	+	10.5073i	−0.0981729	+	0.621308i
$287$		−	5.10757i		−	0.301490i
$288$	2.60842	−	3.68886i	0.153703	−	0.217368i
$289$	−0.0717968			−0.00422334
$290$		0			0
$291$	−0.928203	−	1.79315i	−0.0544122	−	0.105116i
$292$		−	0.570669i		−	0.0333959i
$293$	−4.11439			−0.240365			−0.120183	−	0.992752i	$-0.538348\pi$
$293$	−4.11439			−0.240365			−0.120183	+	0.992752i	$0.538348\pi$
$294$	2.95469	+	5.70801i	0.172321	+	0.332898i
$295$		0			0
$296$	−3.04078			−0.176742
$297$	−16.4916	−	5.00287i	−0.956937	−	0.290296i
$298$	23.3457			1.35238
$299$	11.3483			0.656291
$300$		0			0
$301$	−20.2487			−1.16712
$302$			15.8236i			0.910548i
$303$	7.12633	+	13.7670i	0.409397	+	0.790894i
$304$		−	20.6819i		−	1.18619i
$305$		0			0
$306$	10.7321	−	15.1774i	0.613511	−	0.867635i
$307$			9.50749i			0.542621i	0.962492	+	0.271310i	$0.0874570\pi$
$307$			9.50749i			0.542621i	−0.962492	+	0.271310i	$0.912543\pi$
$308$	−0.295400	+	1.86950i	−0.0168320	+	0.106525i
$309$	4.73205	+	9.14162i	0.269197	+	0.520049i
$310$		0			0
$311$		−	14.6969i		−	0.833387i	−0.909047	−	0.416693i	$-0.863189\pi$
$311$		−	14.6969i		−	0.833387i	0.909047	−	0.416693i	$-0.136811\pi$
$312$	8.54513	−	4.42328i	0.483773	−	0.250419i
$313$	−30.4546			−1.72140			−0.860698	−	0.509117i	$-0.829972\pi$
$313$	−30.4546			−1.72140			−0.860698	+	0.509117i	$0.829972\pi$
$314$	−13.1039			−0.739497
$315$		0			0
$316$		−	3.72417i		−	0.209501i
$317$			22.9624i			1.28970i	0.764311	+	0.644848i	$0.223079\pi$
$317$			22.9624i			1.28970i	−0.764311	+	0.644848i	$0.776921\pi$
$318$	−10.4337	+	5.40087i	−0.585091	+	0.302866i
$319$	29.3205	+	4.63294i	1.64163	+	0.259395i
$320$		0			0
$321$	−0.877796	−	1.69577i	−0.0489938	−	0.0946488i
$322$	17.0903			0.952403
$323$		−	19.0617i		−	1.06062i
$324$	−0.803848	−	2.27362i	−0.0446582	−	0.126312i
$325$		0			0
$326$	−8.95015			−0.495703
$327$	−19.4695	+	10.0782i	−1.07667	+	0.557323i
$328$	6.25547			0.345400
$329$	6.55196			0.361221
$330$		0			0
$331$	8.53590			0.469175			0.234588	−	0.972095i	$-0.424626\pi$
$331$	8.53590			0.469175			0.234588	+	0.972095i	$0.424626\pi$
$332$	−2.50029			−0.137222
$333$	−2.01915	+	2.85550i	−0.110649	+	0.156481i
$334$	19.8038			1.08362
$335$		0			0
$336$	14.6243	−	7.57010i	0.797822	−	0.412983i
$337$		−	16.8852i		−	0.919796i	−0.887972	−	0.459898i	$-0.847886\pi$
$337$		−	16.8852i		−	0.919796i	0.887972	−	0.459898i	$-0.152114\pi$
$338$	12.7467			0.693329
$339$	16.3923	−	8.48528i	0.890308	−	0.460857i
$340$		0			0
$341$	11.3483	+	1.79315i	0.614547	+	0.0971046i
$342$	−17.0903	−	12.0846i	−0.924135	−	0.653462i
$343$			20.1563i			1.08834i
$344$		−	24.7995i		−	1.33710i
$345$		0			0
$346$	21.9090			1.17783
$347$	−27.4029			−1.47106			−0.735532	−	0.677490i	$-0.763068\pi$
$347$	−27.4029			−1.47106			−0.735532	+	0.677490i	$0.763068\pi$
$348$	1.90949	+	3.68886i	0.102360	+	0.197744i
$349$			25.3148i			1.35507i	0.735490	+	0.677536i	$0.236952\pi$
$349$			25.3148i			1.35507i	−0.735490	+	0.677536i	$0.763048\pi$
$350$		0			0
$351$	1.52039	−	10.9616i	0.0811523	−	0.585089i
$352$	−4.93353	−	0.779548i	−0.262958	−	0.0415501i
$353$		−	1.64863i		−	0.0877475i	−0.999037	−	0.0438738i	$-0.986030\pi$
$353$		−	1.64863i		−	0.0877475i	0.999037	−	0.0438738i	$-0.0139699\pi$
$354$	11.3483	−	5.87433i	0.603157	−	0.312217i
$355$		0			0
$356$		−	1.23835i		−	0.0656323i
$357$	13.4787	−	6.97707i	0.713366	−	0.369266i
$358$			29.0931i			1.53762i
$359$	−1.75559			−0.0926566			−0.0463283	−	0.998926i	$-0.514752\pi$
$359$	−1.75559			−0.0926566			−0.0463283	+	0.998926i	$0.514752\pi$
$360$		0			0
$361$	−2.46410			−0.129690
$362$	−14.2527			−0.749103
$363$	3.11494	+	18.7962i	0.163492	+	0.986545i
$364$	−1.21539			−0.0637038
$365$		0			0
$366$	−7.85641	+	4.06678i	−0.410661	+	0.212574i
$367$	−14.9568			−0.780738			−0.390369	−	0.920659i	$-0.627652\pi$
$367$	−14.9568			−0.780738			−0.390369	+	0.920659i	$0.627652\pi$
$368$			23.7867i			1.23997i
$369$	4.15378	−	5.87433i	0.216237	−	0.305805i
$370$		0			0
$371$	−9.59274			−0.498030
$372$	0.739059	+	1.42775i	0.0383184	+	0.0740255i
$373$		−	9.50749i		−	0.492279i	−0.969234	−	0.246140i	$-0.920838\pi$
$373$		−	9.50749i		−	0.492279i	0.969234	−	0.246140i	$-0.0791621\pi$
$374$	−20.2985	−	3.20736i	−1.04961	−	0.165849i
$375$		0			0
$376$			8.02448i			0.413831i
$377$			19.0617i			0.981728i
$378$	2.28966	−	16.5079i	0.117767	−	0.849076i
$379$	2.92820			0.150412			0.0752058	−	0.997168i	$-0.476039\pi$
$379$	2.92820			0.150412			0.0752058	+	0.997168i	$0.476039\pi$
$380$		0			0
$381$	−16.3799	+	8.47886i	−0.839168	+	0.434385i
$382$			14.3377i			0.733580i
$383$			20.9312i			1.06953i	0.844999	+	0.534767i	$0.179601\pi$
$383$			20.9312i			1.06953i	−0.844999	+	0.534767i	$0.820399\pi$
$384$	10.3844	+	20.0612i	0.529929	+	1.02374i
$385$		0			0
$386$		−	16.0368i		−	0.816253i
$387$	−23.2885	−	16.4675i	−1.18382	−	0.837088i
$388$	−0.312363			−0.0158578
$389$		−	20.9086i		−	1.06011i	−0.847964	−	0.530054i	$-0.822172\pi$
$389$		−	20.9086i		−	1.06011i	0.847964	−	0.530054i	$-0.177828\pi$
$390$		0			0
$391$			21.9233i			1.10871i
$392$	−6.42741			−0.324633
$393$		0			0
$394$	−11.9474			−0.601903
$395$		0			0
$396$	−1.86013	+	1.90992i	−0.0934752	+	0.0959769i
$397$	−5.20405			−0.261184			−0.130592	−	0.991436i	$-0.541688\pi$
$397$	−5.20405			−0.261184			−0.130592	+	0.991436i	$0.541688\pi$
$398$	−16.4576			−0.824943
$399$	−7.85641	−	15.1774i	−0.393312	−	0.759821i
$400$		0			0
$401$			25.7332i			1.28506i	0.766262	+	0.642528i	$0.222115\pi$
$401$			25.7332i			1.28506i	−0.766262	+	0.642528i	$0.777885\pi$
$402$	14.7643	+	28.5225i	0.736377	+	1.42257i
$403$			7.37772i			0.367511i
$404$	2.39818			0.119314
$405$		0			0
$406$			28.7064i			1.42467i
$407$	3.81899	+	0.603439i	0.189300	+	0.0299114i
$408$	8.54513	+	16.5079i	0.423047	+	0.817264i
$409$		−	19.4405i		−	0.961271i	−0.876920	−	0.480636i	$-0.840406\pi$
$409$		−	19.4405i		−	0.961271i	0.876920	−	0.480636i	$-0.159594\pi$
$410$		0			0
$411$	−3.46410	+	1.79315i	−0.170872	+	0.0884496i
$412$	1.59245			0.0784544
$413$	10.4337			0.513408
$414$	19.6559	+	13.8988i	0.966034	+	0.683089i
$415$		0			0
$416$		−	3.20736i		−	0.157254i
$417$	26.5958	−	13.7670i	1.30240	−	0.674174i
$418$	−3.61160	+	22.8567i	−0.176649	+	1.11796i
$419$		−	1.23835i		−	0.0604973i	−0.999542	−	0.0302486i	$-0.990370\pi$
$419$		−	1.23835i		−	0.0604973i	0.999542	−	0.0302486i	$-0.00962991\pi$
$420$		0			0
$421$	8.78461			0.428136			0.214068	−	0.976819i	$-0.431329\pi$
$421$	8.78461			0.428136			0.214068	+	0.976819i	$0.431329\pi$
$422$		−	1.86950i		−	0.0910058i
$423$	7.53556	+	5.32844i	0.366391	+	0.259078i
$424$		−	11.7487i		−	0.570565i
$425$		0			0
$426$	31.0042	−	16.0490i	1.50216	−	0.777575i
$427$	−7.22319			−0.349555
$428$	−0.295400			−0.0142787
$429$	−11.6098	+	3.85955i	−0.560529	+	0.186341i
$430$		0			0
$431$	19.6559			0.946791			0.473395	−	0.880850i	$-0.343028\pi$
$431$	19.6559			0.946791			0.473395	+	0.880850i	$0.343028\pi$
$432$	22.9762	+	3.18682i	1.10544	+	0.153326i
$433$	37.6778			1.81068			0.905339	−	0.424689i	$-0.139617\pi$
$433$	37.6778			1.81068			0.905339	+	0.424689i	$0.139617\pi$
$434$			11.1106i			0.533328i
$435$		0			0
$436$			3.39154i			0.162426i
$437$	24.6863			1.18091
$438$	4.93353	−	2.55378i	0.235733	−	0.122025i
$439$		−	8.02448i		−	0.382988i	−0.981494	−	0.191494i	$-0.938667\pi$
$439$		−	8.02448i		−	0.382988i	0.981494	−	0.191494i	$-0.0613332\pi$
$440$		0			0
$441$	−4.26795	+	6.03579i	−0.203236	+	0.287419i
$442$		−	13.1963i		−	0.627686i
$443$		−	34.4436i		−	1.63646i	−0.574888	−	0.818232i	$-0.694954\pi$
$443$		−	34.4436i		−	1.63646i	0.574888	−	0.818232i	$-0.305046\pi$
$444$	0.248711	+	0.480473i	0.0118033	+	0.0228023i
$445$		0			0
$446$	−19.0133			−0.900306
$447$	12.3432	+	23.8452i	0.583812	+	1.12784i
$448$			14.1848i			0.670168i
$449$		−	15.7322i		−	0.742449i	−0.928543	−	0.371225i	$-0.878938\pi$
$449$		−	15.7322i		−	0.742449i	0.928543	−	0.371225i	$-0.121062\pi$
$450$		0			0
$451$	−7.85641	−	1.24139i	−0.369944	−	0.0584548i
$452$		−	2.85550i		−	0.134312i
$453$	−16.1622	+	8.36615i	−0.759364	+	0.393076i
$454$	−14.0526			−0.659519
$455$		0			0
$456$	18.5885	−	9.62209i	0.870484	−	0.450596i
$457$		−	3.27110i		−	0.153016i	−0.997069	−	0.0765079i	$-0.975623\pi$
$457$		−	3.27110i		−	0.153016i	0.997069	−	0.0765079i	$-0.0243770\pi$
$458$	−32.1081			−1.50031
$459$	21.1763	+	2.93716i	0.988424	+	0.137095i
$460$		0			0
$461$	18.5429			0.863628			0.431814	−	0.901963i	$-0.357874\pi$
$461$	18.5429			0.863628			0.431814	+	0.901963i	$0.357874\pi$
$462$	−17.4841	+	5.81236i	−0.813434	+	0.270416i
$463$	7.10886			0.330377			0.165188	−	0.986262i	$-0.447177\pi$
$463$	7.10886			0.330377			0.165188	+	0.986262i	$0.447177\pi$
$464$	−39.9544			−1.85483
$465$		0			0
$466$	15.2679			0.707274
$467$		−	4.12157i		−	0.190723i	−0.995443	−	0.0953616i	$-0.969599\pi$
$467$		−	4.12157i		−	0.190723i	0.995443	−	0.0953616i	$-0.0304007\pi$
$468$	−1.39785	−	0.988427i	−0.0646155	−	0.0456901i
$469$			26.2236i			1.21089i
$470$		0			0
$471$	−6.92820	−	13.3843i	−0.319235	−	0.616714i
$472$			12.7786i			0.588182i
$473$	−4.92144	+	31.1463i	−0.226288	+	1.43211i
$474$	32.1962	−	16.6660i	1.47882	−	0.765493i
$475$		0			0
$476$		−	2.34795i		−	0.107618i
$477$	−11.0328	−	7.80138i	−0.505158	−	0.357201i
$478$	−24.3135			−1.11207
$479$	−24.4523			−1.11725			−0.558626	−	0.829420i	$-0.688671\pi$
$479$	−24.4523			−1.11725			−0.558626	+	0.829420i	$0.688671\pi$
$480$		0			0
$481$			2.48278i			0.113205i
$482$		−	19.0617i		−	0.868237i
$483$	9.03583	+	17.4559i	0.411144	+	0.794270i
$484$	2.80385	+	0.908762i	0.127448	+	0.0413074i
$485$		0			0
$486$	16.0586	−	17.1240i	0.728433	−	0.776762i
$487$	32.0470			1.45219			0.726095	−	0.687594i	$-0.241333\pi$
$487$	32.0470			1.45219			0.726095	+	0.687594i	$0.241333\pi$
$488$		−	8.84657i		−	0.400465i
$489$	−4.73205	−	9.14162i	−0.213991	−	0.413398i
$490$		0			0
$491$	−19.6559			−0.887058			−0.443529	−	0.896260i	$-0.646274\pi$
$491$	−19.6559			−0.887058			−0.443529	+	0.896260i	$0.646274\pi$
$492$	−0.511648	−	0.988427i	−0.0230669	−	0.0445617i
$493$	−36.8244			−1.65849
$494$	−14.8595			−0.668561
$495$		0			0
$496$	−15.4641			−0.694359
$497$	28.5053			1.27864
$498$	−11.1890	−	21.6155i	−0.501391	−	0.968613i
$499$	−2.92820			−0.131084			−0.0655422	−	0.997850i	$-0.520878\pi$
$499$	−2.92820			−0.131084			−0.0655422	+	0.997850i	$0.520878\pi$
$500$		0			0
$501$	10.4705	+	20.2275i	0.467789	+	0.903699i
$502$			25.5572i			1.14067i
$503$	−25.7888			−1.14987			−0.574933	−	0.818201i	$-0.694972\pi$
$503$	−25.7888			−1.14987			−0.574933	+	0.818201i	$0.694972\pi$
$504$	13.6077	+	9.62209i	0.606135	+	0.428602i
$505$		0			0
$506$	4.15378	−	26.2880i	0.184658	−	1.16865i
$507$	6.73933	+	13.0194i	0.299304	+	0.578211i
$508$			2.85334i			0.126597i
$509$			36.5665i			1.62078i	0.585890	+	0.810390i	$0.300745\pi$
$509$			36.5665i			1.62078i	−0.585890	+	0.810390i	$0.699255\pi$
$510$		0			0
$511$	4.53590			0.200656
$512$	−16.5657			−0.732107
$513$	3.30734	−	23.8452i	0.146023	−	1.05279i
$514$		−	44.7553i		−	1.97407i
$515$		0			0
$516$	−3.91857	+	2.02840i	−0.172506	+	0.0892954i
$517$	1.59245	−	10.0782i	0.0700359	−	0.443237i
$518$			3.73900i			0.164282i
$519$	11.5835	+	22.3777i	0.508461	+	0.982271i
$520$		0			0
$521$		−	21.5921i		−	0.945969i	−0.881071	−	0.472984i	$-0.843177\pi$
$521$		−	21.5921i		−	0.945969i	0.881071	−	0.472984i	$-0.156823\pi$
$522$	−23.3457	+	33.0158i	−1.02181	+	1.44506i
$523$			3.27110i			0.143035i	0.997439	+	0.0715177i	$0.0227842\pi$
$523$			3.27110i			0.143035i	−0.997439	+	0.0715177i	$0.977216\pi$
$524$		0			0
$525$		0			0
$526$	−23.1244			−1.00827
$527$	−14.2527			−0.620856
$528$	−8.08982	−	24.3349i	−0.352064	−	1.05904i
$529$	−5.39230			−0.234448
$530$		0			0
$531$	12.0000	+	8.48528i	0.520756	+	0.368230i
$532$	−2.64387			−0.114626
$533$		−	5.10757i		−	0.221233i
$534$	10.7057	−	5.54170i	0.463283	−	0.239813i
$535$		0			0
$536$	−32.1172			−1.38725
$537$	−29.7155	+	15.3819i	−1.28232	+	0.663778i
$538$		−	12.7786i		−	0.550924i
$539$	8.07235	+	1.27551i	0.347701	+	0.0549402i
$540$		0			0
$541$		−	6.78309i		−	0.291628i	−0.989312	−	0.145814i	$-0.953420\pi$
$541$		−	6.78309i		−	0.291628i	0.989312	−	0.145814i	$-0.0465801\pi$
$542$		−	36.2539i		−	1.55724i
$543$	−7.53556	−	14.5576i	−0.323382	−	0.624725i
$544$	6.19615			0.265658
$545$		0			0
$546$	−5.43896	−	10.5073i	−0.232766	−	0.449669i
$547$		−	25.4043i		−	1.08621i	−0.839665	−	0.543104i	$-0.817249\pi$
$547$		−	25.4043i		−	1.08621i	0.839665	−	0.543104i	$-0.182751\pi$
$548$			0.603439i			0.0257776i
$549$	−8.30755	−	5.87433i	−0.354558	−	0.250710i
$550$		0			0
$551$			41.4655i			1.76649i
$552$	−21.3790	+	11.0666i	−0.909951	+	0.471025i
$553$	29.6012			1.25877
$554$			25.4286i			1.08036i
$555$		0			0
$556$		−	4.63294i		−	0.196480i
$557$	4.11439			0.174332			0.0871661	−	0.996194i	$-0.472219\pi$
$557$	4.11439			0.174332			0.0871661	+	0.996194i	$0.472219\pi$
$558$	−9.03583	+	12.7786i	−0.382517	+	0.540961i
$559$	−20.2487			−0.856429
$560$		0			0
$561$	−7.45607	−	22.4285i	−0.314796	−	0.946932i
$562$	8.89934			0.375396
$563$	33.4268			1.40877			0.704385	−	0.709818i	$-0.251223\pi$
$563$	33.4268			1.40877			0.704385	+	0.709818i	$0.251223\pi$
$564$	1.26795	−	0.656339i	0.0533903	−	0.0276368i
$565$		0			0
$566$			38.2581i			1.60811i
$567$	18.0717	−	6.38929i	0.758938	−	0.268325i
$568$			34.9118i			1.46486i
$569$	2.39818			0.100537			0.0502686	−	0.998736i	$-0.483992\pi$
$569$	2.39818			0.100537			0.0502686	+	0.998736i	$0.483992\pi$
$570$		0			0
$571$		−	7.11572i		−	0.297784i	−0.988853	−	0.148892i	$-0.952429\pi$
$571$		−	7.11572i		−	0.297784i	0.988853	−	0.148892i	$-0.0475706\pi$
$572$	−0.295400	+	1.86950i	−0.0123513	+	0.0781677i
$573$	−14.6444	+	7.58051i	−0.611779	+	0.316680i
$574$		−	7.69185i		−	0.321052i
$575$		0			0
$576$	−11.5359	+	16.3142i	−0.480662	+	0.679759i
$577$	35.6586			1.48449			0.742244	−	0.670129i	$-0.233761\pi$
$577$	35.6586			1.48449			0.742244	+	0.670129i	$0.233761\pi$
$578$	−0.108124			−0.00449736
$579$	16.3799	−	8.47886i	0.680726	−	0.352369i
$580$		0			0
$581$		−	19.8733i		−	0.824484i
$582$	−1.39785	−	2.70043i	−0.0579426	−	0.111937i
$583$	−2.33151	+	14.7554i	−0.0965612	+	0.611108i
$584$			5.55532i			0.229881i
$585$		0			0
$586$	−6.19615			−0.255961
$587$		−	8.62570i		−	0.356021i	−0.984029	−	0.178010i	$-0.943034\pi$
$587$		−	8.62570i		−	0.356021i	0.984029	−	0.178010i	$-0.0569660\pi$
$588$	0.525711	+	1.01560i	0.0216800	+	0.0418825i
$589$			16.0490i			0.661286i
$590$		0			0
$591$	−6.31676	−	12.2030i	−0.259837	−	0.501966i
$592$	−5.20405			−0.213885
$593$	−11.7524			−0.482612			−0.241306	−	0.970449i	$-0.577576\pi$
$593$	−11.7524			−0.482612			−0.241306	+	0.970449i	$0.577576\pi$
$594$	−24.8358	−	7.53417i	−1.01903	−	0.309131i
$595$		0			0
$596$	4.15378			0.170145
$597$	−8.70131	−	16.8096i	−0.356121	−	0.687973i
$598$	17.0903			0.698873
$599$			18.0058i			0.735699i	0.929885	+	0.367849i	$0.119906\pi$
$599$			18.0058i			0.735699i	−0.929885	+	0.367849i	$0.880094\pi$
$600$		0			0
$601$		−	3.39154i		−	0.138344i	−0.997605	−	0.0691720i	$-0.977964\pi$
$601$		−	3.39154i		−	0.138344i	0.997605	−	0.0691720i	$-0.0220357\pi$
$602$	−30.4940			−1.24284
$603$	−21.3266	+	30.1603i	−0.868486	+	1.22822i
$604$			2.81541i			0.114558i
$605$		0			0
$606$	10.7321	+	20.7327i	0.435960	+	0.842210i
$607$			30.8051i			1.25034i	0.780488	+	0.625171i	$0.214971\pi$
$607$			30.8051i			1.25034i	−0.780488	+	0.625171i	$0.785029\pi$
$608$		−	6.97707i		−	0.282958i
$609$	−29.3205	+	15.1774i	−1.18813	+	0.615020i
$610$		0			0
$611$	6.55196			0.265064
$612$	1.90949	−	2.70043i	0.0771868	−	0.109159i
$613$		−	45.5606i		−	1.84017i	−0.391714	−	0.920087i	$-0.628118\pi$
$613$		−	45.5606i		−	1.84017i	0.391714	−	0.920087i	$-0.371882\pi$
$614$			14.3180i			0.577827i
$615$		0			0
$616$	2.87564	−	18.1991i	0.115863	−	0.733263i
$617$		−	11.0986i		−	0.446814i	−0.974725	−	0.223407i	$-0.928282\pi$
$617$		−	11.0986i		−	0.446814i	0.974725	−	0.223407i	$-0.0717179\pi$
$618$	7.12633	+	13.7670i	0.286663	+	0.553791i
$619$	−1.60770			−0.0646187			−0.0323094	−	0.999478i	$-0.510286\pi$
$619$	−1.60770			−0.0646187			−0.0323094	+	0.999478i	$0.510286\pi$
$620$		0			0
$621$	−3.80385	+	27.4249i	−0.152643	+	1.10052i
$622$		−	22.1332i		−	0.887459i
$623$	9.84287			0.394346
$624$	14.6243	−	7.57010i	0.585441	−	0.303047i
$625$		0			0
$626$	−45.8637			−1.83308
$627$	−25.2552	+	8.39578i	−1.00860	+	0.335295i
$628$	−2.33151			−0.0930373
$629$	−4.79637			−0.191244
$630$		0			0
$631$	38.6410			1.53827			0.769137	−	0.639084i	$-0.220686\pi$
$631$	38.6410			1.53827			0.769137	+	0.639084i	$0.220686\pi$
$632$			36.2539i			1.44210i
$633$	1.90949	−	0.988427i	0.0758956	−	0.0392865i
$634$			34.5807i			1.37338i
$635$		0			0
$636$	−1.85641	+	0.960947i	−0.0736113	+	0.0381040i
$637$			5.24796i			0.207932i
$638$	44.1558	+	6.97707i	1.74815	+	0.276225i
$639$	32.7846	+	23.1822i	1.29694	+	0.917074i
$640$		0			0
$641$		−	3.30890i		−	0.130694i	−0.997863	−	0.0653469i	$-0.979185\pi$
$641$		−	3.30890i		−	0.130694i	0.997863	−	0.0653469i	$-0.0208154\pi$
$642$	−1.32194	−	2.55378i	−0.0521727	−	0.100790i
$643$	29.7155			1.17187			0.585933	−	0.810359i	$-0.300728\pi$
$643$	29.7155			1.17187			0.585933	+	0.810359i	$0.300728\pi$
$644$	3.04078			0.119823
$645$		0			0
$646$		−	28.7064i		−	1.12944i
$647$			11.9229i			0.468739i	0.972148	+	0.234370i	$0.0753026\pi$
$647$			11.9229i			0.468739i	−0.972148	+	0.234370i	$0.924697\pi$
$648$	7.82526	+	22.1332i	0.307405	+	0.869473i
$649$	2.53590	−	16.0490i	0.0995427	−	0.629977i
$650$		0			0
$651$	−11.3483	+	5.87433i	−0.444776	+	0.230233i
$652$	−1.59245			−0.0623652
$653$		−	17.8548i		−	0.698713i	−0.936990	−	0.349357i	$-0.886400\pi$
$653$		−	17.8548i		−	0.698713i	0.936990	−	0.349357i	$-0.113600\pi$
$654$	−29.3205	+	15.1774i	−1.14652	+	0.593484i
$655$		0			0
$656$	10.7057			0.417989
$657$	5.21684	+	3.68886i	0.203528	+	0.143916i
$658$	9.86707			0.384658
$659$	−21.4115			−0.834073			−0.417036	−	0.908890i	$-0.636931\pi$
$659$	−21.4115			−0.834073			−0.417036	+	0.908890i	$0.636931\pi$
$660$		0			0
$661$	−4.53590			−0.176426			−0.0882130	−	0.996102i	$-0.528116\pi$
$661$	−4.53590			−0.176426			−0.0882130	+	0.996102i	$0.528116\pi$
$662$	12.8548			0.499617
$663$	13.4787	−	6.97707i	0.523468	−	0.270967i
$664$	24.3397			0.944565
$665$		0			0
$666$	−3.04078	+	4.30031i	−0.117828	+	0.166634i
$667$		−	47.6903i		−	1.84658i
$668$	3.52359			0.136332
$669$	−10.0526	−	19.4201i	−0.388654	−	0.750823i
$670$		0			0
$671$	−1.75559	+	11.1106i	−0.0677739	+	0.428921i
$672$	4.93353	−	2.55378i	0.190315	−	0.0985144i
$673$		−	49.8201i		−	1.92042i	−0.279272	−	0.960212i	$-0.590093\pi$
$673$		−	49.8201i		−	1.92042i	0.279272	−	0.960212i	$-0.409907\pi$
$674$		−	25.4286i		−	0.979475i
$675$		0			0
$676$	2.26795			0.0872288
$677$	−13.9573			−0.536421			−0.268211	−	0.963360i	$-0.586432\pi$
$677$	−13.9573			−0.536421			−0.268211	+	0.963360i	$0.586432\pi$
$678$	24.6863	−	12.7786i	0.948073	−	0.490759i
$679$		−	2.48278i		−	0.0952805i
$680$		0			0
$681$	−7.42976	−	14.3532i	−0.284709	−	0.550015i
$682$	17.0903	+	2.70043i	0.654420	+	0.103405i
$683$		−	8.02226i		−	0.306963i	−0.988152	−	0.153482i	$-0.950951\pi$
$683$		−	8.02226i		−	0.306963i	0.988152	−	0.153482i	$-0.0490486\pi$
$684$	−3.04078	−	2.15015i	−0.116267	−	0.0822132i
$685$		0			0
$686$			30.3548i			1.15895i
$687$	−16.9759	−	32.7950i	−0.647672	−	1.25121i
$688$		−	42.4424i		−	1.61810i
$689$	−9.59274			−0.365454
$690$		0			0
$691$	−29.8564			−1.13579			−0.567896	−	0.823101i	$-0.692242\pi$
$691$	−29.8564			−1.13579			−0.567896	+	0.823101i	$0.692242\pi$
$692$	3.89814			0.148185
$693$	−15.1808	−	14.7851i	−0.576670	−	0.561638i
$694$	−41.2679			−1.56651
$695$		0			0
$696$	−18.5885	−	35.9101i	−0.704594	−	1.36117i
$697$	9.86707			0.373742
$698$			38.1234i			1.44299i
$699$	8.07235	+	15.5946i	0.305324	+	0.589841i
$700$		0			0
$701$	19.0133			0.718122			0.359061	−	0.933314i	$-0.383097\pi$
$701$	19.0133			0.718122			0.359061	+	0.933314i	$0.383097\pi$
$702$	2.28966	−	16.5079i	0.0864177	−	0.623051i
$703$			5.40087i			0.203698i
$704$	21.8189	+	3.44760i	0.822329	+	0.129936i
$705$		0			0
$706$		−	2.48278i		−	0.0934408i
$707$			19.0617i			0.716889i
$708$	2.01915	−	1.04519i	0.0758842	−	0.0392805i
$709$	29.0718			1.09181			0.545907	−	0.837846i	$-0.316185\pi$
$709$	29.0718			1.09181			0.545907	+	0.837846i	$0.316185\pi$
$710$		0			0
$711$	34.0450	+	24.0734i	1.27679	+	0.902825i
$712$			12.0550i			0.451781i
$713$		−	18.4583i		−	0.691268i
$714$	20.2985	−	10.5073i	0.759651	−	0.393225i
$715$		0			0
$716$			5.17638i			0.193450i
$717$	−12.8548	−	24.8336i	−0.480072	−	0.927428i
$718$	−2.64387			−0.0986684
$719$			6.48906i			0.242001i	0.992652	+	0.121001i	$0.0386103\pi$
$719$			6.48906i			0.242001i	−0.992652	+	0.121001i	$0.961390\pi$
$720$		0			0
$721$			12.6574i			0.471387i
$722$	−3.71087			−0.138104
$723$	19.4695	−	10.0782i	0.724079	−	0.374811i
$724$	−2.53590			−0.0942459
$725$		0			0
$726$	4.69102	+	28.3065i	0.174100	+	1.05055i
$727$	31.7347			1.17697			0.588487	−	0.808507i	$-0.299724\pi$
$727$	31.7347			1.17697			0.588487	+	0.808507i	$0.299724\pi$
$728$	11.8315			0.438505
$729$	25.9808	+	7.34847i	0.962250	+	0.272166i
$730$		0			0
$731$		−	39.1175i		−	1.44681i
$732$	−1.39785	+	0.723579i	−0.0516659	+	0.0267442i
$733$		−	2.12976i		−	0.0786647i	−0.999226	−	0.0393323i	$-0.987477\pi$
$733$		−	2.12976i		−	0.0786647i	0.999226	−	0.0393323i	$-0.0125231\pi$
$734$	−22.5245			−0.831394
$735$		0			0
$736$			8.02448i			0.295786i
$737$	40.3369	+	6.37363i	1.48583	+	0.234776i
$738$	6.25547	−	8.84657i	0.230267	−	0.325647i
$739$			42.6052i			1.56726i	0.621230	+	0.783629i	$0.286633\pi$
$739$			42.6052i			1.56726i	−0.621230	+	0.783629i	$0.713367\pi$
$740$		0			0
$741$	−7.85641	−	15.1774i	−0.288612	−	0.557556i
$742$	−14.4464			−0.530344
$743$	−19.1741			−0.703430			−0.351715	−	0.936107i	$-0.614401\pi$
$743$	−19.1741			−0.703430			−0.351715	+	0.936107i	$0.614401\pi$
$744$	−7.19455	−	13.8988i	−0.263765	−	0.509555i
$745$		0			0
$746$		−	14.3180i		−	0.524219i
$747$	16.1622	−	22.8567i	0.591342	−	0.836285i
$748$	−3.61160	−	0.570669i	−0.132053	−	0.0208657i
$749$		−	2.34795i		−	0.0857924i
$750$		0			0
$751$	−31.7128			−1.15722			−0.578608	−	0.815605i	$-0.696404\pi$
$751$	−31.7128			−1.15722			−0.578608	+	0.815605i	$0.696404\pi$
$752$			13.7333i			0.500801i
$753$	−26.1039	+	13.5124i	−0.951280	+	0.492419i
$754$			28.7064i			1.04542i
$755$		0			0
$756$	0.407387	−	2.93716i	0.0148165	−	0.106824i
$757$	7.84792			0.285237			0.142619	−	0.989778i	$-0.454448\pi$
$757$	7.84792			0.285237			0.142619	+	0.989778i	$0.454448\pi$
$758$	4.40979			0.160171
$759$	29.0466	−	9.65617i	1.05432	−	0.350497i
$760$		0			0
$761$	−49.5471			−1.79608			−0.898040	−	0.439913i	$-0.855009\pi$
$761$	−49.5471			−1.79608			−0.898040	+	0.439913i	$0.855009\pi$
$762$	−24.6677	+	12.7689i	−0.893615	+	0.462569i
$763$	−26.9573			−0.975921
$764$			2.55103i			0.0922929i
$765$		0			0
$766$			31.5218i			1.13893i
$767$	10.4337			0.376738
$768$	5.03255	+	9.72214i	0.181596	+	0.350817i
$769$		−	43.8466i		−	1.58115i	−0.612366	−	0.790574i	$-0.709782\pi$
$769$		−	43.8466i		−	1.58115i	0.612366	−	0.790574i	$-0.290218\pi$
$770$		0			0
$771$	45.7128	−	23.6627i	1.64631	−	0.852191i
$772$		−	2.85334i		−	0.102694i
$773$			26.8631i			0.966198i	0.875566	+	0.483099i	$0.160489\pi$
$773$			26.8631i			0.966198i	−0.875566	+	0.483099i	$0.839511\pi$
$774$	−35.0718	−	24.7995i	−1.26063	−	0.891400i
$775$		0			0
$776$	3.04078			0.109157
$777$	−3.81899	+	1.97685i	−0.137005	+	0.0709193i
$778$		−	31.4877i		−	1.12889i
$779$		−	11.1106i		−	0.398080i
$780$		0			0
$781$	6.92820	−	43.8466i	0.247911	−	1.56895i
$782$			33.0158i			1.18064i
$783$	−46.0653	−	6.38929i	−1.64624	−	0.228335i
$784$	−11.0000			−0.392857
$785$		0			0
$786$		0			0
$787$		−	22.2861i		−	0.794413i	−0.917729	−	0.397206i	$-0.869980\pi$
$787$		−	22.2861i		−	0.794413i	0.917729	−	0.397206i	$-0.130020\pi$
$788$	−2.12574			−0.0757264
$789$	−12.2261	−	23.6191i	−0.435262	−	0.840861i
$790$		0			0
$791$	22.6967			0.807000
$792$	18.1079	−	18.5926i	0.643438	−	0.660658i
$793$	−7.22319			−0.256503
$794$	−7.83714			−0.278130
$795$		0			0
$796$	−2.92820			−0.103787
$797$		−	35.2679i		−	1.24925i	−0.780923	−	0.624627i	$-0.785251\pi$
$797$		−	35.2679i		−	1.24925i	0.780923	−	0.624627i	$-0.214749\pi$
$798$	−11.8315	−	22.8567i	−0.418831	−	0.809120i
$799$			12.6574i			0.447787i
$800$		0			0
$801$	11.3205	+	8.00481i	0.399990	+	0.282836i
$802$			38.7535i			1.36843i
$803$	1.10245	−	6.97707i	0.0389045	−	0.246215i
$804$	2.62693	+	5.07484i	0.0926448	+	0.178976i
$805$		0			0
$806$			11.1106i			0.391355i
$807$	13.0520	−	6.75620i	0.459451	−	0.237829i
$808$	−23.3457			−0.821300
$809$	7.66496			0.269486			0.134743	−	0.990881i	$-0.456979\pi$
$809$	7.66496			0.269486			0.134743	+	0.990881i	$0.456979\pi$
$810$		0			0
$811$			36.7309i			1.28980i	0.764269	+	0.644898i	$0.223100\pi$
$811$			36.7309i			1.28980i	−0.764269	+	0.644898i	$0.776900\pi$
$812$			5.10757i			0.179241i
$813$	37.0295	−	19.1679i	1.29868	−	0.672247i
$814$	5.75129	+	0.908762i	0.201583	+	0.0318521i
$815$		0			0
$816$	14.6243	+	28.2520i	0.511953	+	0.989018i
$817$	−44.0476			−1.54103
$818$		−	29.2768i		−	1.02364i
$819$	7.85641	−	11.1106i	0.274525	−	0.388237i
$820$		0			0
$821$	41.7100			1.45569			0.727844	−	0.685743i	$-0.240523\pi$
$821$	41.7100			1.45569			0.727844	+	0.685743i	$0.240523\pi$
$822$	−5.21684	+	2.70043i	−0.181958	+	0.0941884i
$823$	22.4923			0.784034			0.392017	−	0.919958i	$-0.371778\pi$
$823$	22.4923			0.784034			0.392017	+	0.919958i	$0.371778\pi$
$824$	−15.5021			−0.540042
$825$		0			0
$826$	15.7128			0.546719
$827$	40.0415			1.39238			0.696189	−	0.717859i	$-0.254878\pi$
$827$	40.0415			1.39238			0.696189	+	0.717859i	$0.254878\pi$
$828$	3.49726	+	2.47294i	0.121538	+	0.0859406i
$829$	44.1051			1.53183			0.765917	−	0.642939i	$-0.222285\pi$
$829$	44.1051			1.53183			0.765917	+	0.642939i	$0.222285\pi$
$830$		0			0
$831$	−25.9726	+	13.4444i	−0.900981	+	0.466382i
$832$			14.1848i			0.491769i
$833$	−10.1383			−0.351270
$834$	40.0526	−	20.7327i	1.38691	−	0.717916i
$835$		0			0
$836$	−0.642592	+	4.06678i	−0.0222245	+	0.140652i
$837$	−17.8293	−	2.47294i	−0.616271	−	0.0854773i
$838$		−	1.86492i		−	0.0644225i
$839$		−	29.0421i		−	1.00265i	−0.865260	−	0.501323i	$-0.832847\pi$
$839$		−	29.0421i		−	1.00265i	0.865260	−	0.501323i	$-0.167153\pi$
$840$		0			0
$841$	51.1051			1.76225
$842$	13.2294			0.455914
$843$	4.70519	+	9.08973i	0.162055	+	0.313067i
$844$		−	0.332630i		−	0.0114496i
$845$		0			0
$846$	11.3483	+	8.02448i	0.390164	+	0.275887i
$847$	−7.22319	+	22.2861i	−0.248192	+	0.765759i
$848$		−	20.1069i		−	0.690474i
$849$	−39.0766	+	20.2275i	−1.34110	+	0.694207i
$850$		0			0
$851$		−	6.21166i		−	0.212933i
$852$	5.51641	−	2.85550i	0.188989	−	0.0978280i
$853$		−	29.6638i		−	1.01567i	−0.861455	−	0.507835i	$-0.830446\pi$
$853$		−	29.6638i		−	1.01567i	0.861455	−	0.507835i	$-0.169554\pi$
$854$	−10.8779			−0.372235
$855$		0			0
$856$	2.87564			0.0982875
$857$	−34.8246			−1.18959			−0.594793	−	0.803879i	$-0.702766\pi$
$857$	−34.8246			−1.18959			−0.594793	+	0.803879i	$0.702766\pi$
$858$	−17.4841	+	5.81236i	−0.596897	+	0.198431i
$859$	−39.4641			−1.34650			−0.673249	−	0.739416i	$-0.735102\pi$
$859$	−39.4641			−1.34650			−0.673249	+	0.739416i	$0.735102\pi$
$860$		0			0
$861$	7.85641	−	4.06678i	0.267746	−	0.138595i
$862$	29.6012			1.00822
$863$			4.12157i			0.140300i	0.997536	+	0.0701499i	$0.0223477\pi$
$863$			4.12157i			0.140300i	−0.997536	+	0.0701499i	$0.977652\pi$
$864$	7.75105	+	1.07508i	0.263696	+	0.0365749i
$865$		0			0
$866$	56.7417			1.92816
$867$	−0.0571664	−	0.110437i	−0.00194147	−	0.00375064i
$868$			1.97685i			0.0670988i
$869$	7.19455	−	45.5322i	0.244059	−	1.54458i
$870$		0			0
$871$			26.2236i			0.888553i
$872$		−	33.0158i		−	1.11806i
$873$	2.01915	−	2.85550i	0.0683377	−	0.0966442i
$874$	37.1769			1.25753
$875$		0			0
$876$	0.877796	−	0.454381i	0.0296580	−	0.0153521i
$877$		−	44.4192i		−	1.49993i	−0.661477	−	0.749966i	$-0.730070\pi$
$877$		−	44.4192i		−	1.49993i	0.661477	−	0.749966i	$-0.269930\pi$
$878$		−	12.0846i		−	0.407837i
$879$	−3.27598	−	6.32871i	−0.110496	−	0.213462i
$880$		0			0
$881$			5.85993i			0.197426i	0.995116	+	0.0987130i	$0.0314726\pi$
$881$			5.85993i			0.197426i	−0.995116	+	0.0987130i	$0.968527\pi$
$882$	−6.42741	+	9.08973i	−0.216422	+	0.306067i
$883$	15.8102			0.532055			0.266027	−	0.963965i	$-0.414289\pi$
$883$	15.8102			0.532055			0.266027	+	0.963965i	$0.414289\pi$
$884$		−	2.34795i		−	0.0789702i
$885$		0			0
$886$		−	51.8711i		−	1.74264i
$887$	−9.33123			−0.313312			−0.156656	−	0.987653i	$-0.550071\pi$
$887$	−9.33123			−0.313312			−0.156656	+	0.987653i	$0.550071\pi$
$888$	−2.42114	−	4.67729i	−0.0812482	−	0.156960i
$889$	−22.6795			−0.760646
$890$		0			0
$891$	−5.43564	−	29.3505i	−0.182101	−	0.983280i
$892$	−3.38293			−0.113269
$893$	14.2527			0.476947
$894$	18.5885	+	35.9101i	0.621691	+	1.20101i
$895$		0			0
$896$			27.7766i			0.927951i
$897$	9.03583	+	17.4559i	0.301697	+	0.582835i
$898$		−	23.6923i		−	0.790621i
$899$	31.0042			1.03405
$900$		0			0
$901$		−	18.5317i		−	0.617382i
$902$	−11.8315	−	1.86950i	−0.393947	−	0.0622475i
$903$	−16.1225	−	31.1463i	−0.536524	−	1.03649i
$904$			27.7976i			0.924535i
$905$		0			0
$906$	−24.3397	+	12.5992i	−0.808634	+	0.418580i
$907$	−38.7292			−1.28598			−0.642991	−	0.765874i	$-0.722307\pi$
$907$	−38.7292			−1.28598			−0.642991	+	0.765874i	$0.722307\pi$
$908$	−2.50029			−0.0829752
$909$	−15.5021	+	21.9233i	−0.514172	+	0.727150i
$910$		0			0
$911$		−	53.2596i		−	1.76457i	−0.470715	−	0.882285i	$-0.656004\pi$
$911$		−	53.2596i		−	1.76457i	0.470715	−	0.882285i	$-0.343996\pi$
$912$	31.8127	−	16.4675i	1.05342	−	0.545292i
$913$	−30.5689	−	4.83020i	−1.01168	−	0.159856i
$914$		−	4.92619i		−	0.162944i
$915$		0			0
$916$	−5.71281			−0.188757
$917$		0			0
$918$	31.8909	+	4.42328i	1.05256	+	0.145990i
$919$		−	24.0734i		−	0.794110i	−0.917795	−	0.397055i	$-0.870032\pi$
$919$		−	24.0734i		−	0.794110i	0.917795	−	0.397055i	$-0.129968\pi$
$920$		0			0
$921$	−14.6243	+	7.57010i	−0.481887	+	0.249443i
$922$	27.9250			0.919663
$923$	28.5053			0.938264
$924$	−3.11085	+	1.03416i	−0.102339	+	0.0340214i
$925$		0			0
$926$	10.7057			0.351812
$927$	−10.2938	+	14.5576i	−0.338091	+	0.478134i
$928$	−13.4787			−0.442459
$929$			7.52433i			0.246865i	0.992353	+	0.123433i	$0.0393903\pi$
$929$			7.52433i			0.246865i	−0.992353	+	0.123433i	$0.960610\pi$
$930$		0			0
$931$			11.4160i			0.374145i
$932$	2.71654			0.0889833
$933$	22.6067	−	11.7021i	0.740109	−	0.383109i
$934$		−	6.20696i		−	0.203098i
$935$		0			0
$936$	13.6077	+	9.62209i	0.444781	+	0.314508i
$937$		−	59.1747i		−	1.93315i	−0.256379	−	0.966576i	$-0.582529\pi$
$937$		−	59.1747i		−	1.93315i	0.256379	−	0.966576i	$-0.417471\pi$
$938$			39.4920i			1.28946i
$939$	−24.2487	−	46.8449i	−0.791327	−	1.52873i
$940$		0			0
$941$	−23.3393			−0.760838			−0.380419	−	0.924814i	$-0.624220\pi$
$941$	−23.3393			−0.760838			−0.380419	+	0.924814i	$0.624220\pi$
$942$	−10.4337	−	20.1563i	−0.339947	−	0.656728i
$943$			12.7786i			0.416128i
$944$			21.8695i			0.711793i
$945$		0			0
$946$	−7.41154	+	46.9055i	−0.240970	+	1.52503i
$947$		−	39.5512i		−	1.28524i	−0.766185	−	0.642620i	$-0.777847\pi$
$947$		−	39.5512i		−	1.28524i	0.766185	−	0.642620i	$-0.222153\pi$
$948$	5.72848	−	2.96528i	0.186053	−	0.0963079i
$949$	4.53590			0.147241
$950$		0			0
$951$	−35.3205	+	18.2832i	−1.14535	+	0.592875i
$952$			22.8567i			0.740791i
$953$	32.6197			1.05666			0.528328	−	0.849040i	$-0.322819\pi$
$953$	32.6197			1.05666			0.528328	+	0.849040i	$0.322819\pi$
$954$	−16.6151	−	11.7487i	−0.537934	−	0.380377i
$955$		0			0
$956$	−4.32596			−0.139912
$957$	16.2194	+	48.7893i	0.524299	+	1.57714i
$958$	−36.8244			−1.18974
$959$	−4.79637			−0.154883
$960$		0			0
$961$	−19.0000			−0.612903
$962$			3.73900i			0.120550i
$963$	1.90949	−	2.70043i	0.0615326	−	0.0870203i
$964$		−	3.39154i		−	0.109234i
$965$		0			0
$966$	13.6077	+	26.2880i	0.437820	+	0.845804i
$967$		−	9.50749i		−	0.305740i	−0.988246	−	0.152870i	$-0.951148\pi$
$967$		−	9.50749i		−	0.305740i	0.988246	−	0.152870i	$-0.0488516\pi$
$968$	−27.2948	−	8.84657i	−0.877287	−	0.284339i
$969$	29.3205	−	15.1774i	0.941910	−	0.487569i
$970$		0			0
$971$		−	13.4586i		−	0.431907i	−0.976404	−	0.215953i	$-0.930714\pi$
$971$		−	13.4586i		−	0.431907i	0.976404	−	0.215953i	$-0.0692859\pi$
$972$	2.85722	−	3.04679i	0.0916454	−	0.0977257i
$973$	36.8244			1.18054
$974$	48.2619			1.54641
$975$		0			0
$976$		−	15.1402i		−	0.484626i
$977$			20.2686i			0.648449i	0.945980	+	0.324225i	$0.105103\pi$
$977$			20.2686i			0.648449i	−0.945980	+	0.324225i	$0.894897\pi$
$978$	−7.12633	−	13.7670i	−0.227875	−	0.440221i
$979$	2.39230	−	15.1402i	0.0764584	−	0.483883i
$980$		0			0
$981$	−31.0042	−	21.9233i	−0.989888	−	0.699957i
$982$	−29.6012			−0.944612
$983$			15.9853i			0.509853i	0.966960	+	0.254926i	$0.0820512\pi$
$983$			15.9853i			0.509853i	−0.966960	+	0.254926i	$0.917949\pi$
$984$	4.98076	+	9.62209i	0.158781	+	0.306741i
$985$		0			0
$986$	−55.4565			−1.76609
$987$	5.21684	+	10.0782i	0.166054	+	0.320791i
$988$	−2.64387			−0.0841128
$989$	50.6601			1.61090
$990$		0			0
$991$	0.248711			0.00790058			0.00395029	−	0.999992i	$-0.498743\pi$
$991$	0.248711			0.00790058			0.00395029	+	0.999992i	$0.498743\pi$
$992$	−5.21684			−0.165635
$993$	6.79650	+	13.1298i	0.215680	+	0.416662i
$994$	42.9282			1.36160
$995$		0			0
$996$	−1.99080	−	3.84593i	−0.0630808	−	0.121863i
$997$			40.1597i			1.27187i	0.771742	+	0.635935i	$0.219386\pi$
$997$			40.1597i			1.27187i	−0.771742	+	0.635935i	$0.780614\pi$
$998$	−4.40979			−0.139589
$999$	−6.00000	−	0.832204i	−0.189832	−	0.0263298i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	825.2.f.f.626.12		16
3.2	odd	2	inner	825.2.f.f.626.7		16
5.2	odd	4		165.2.d.c.164.11	yes	16
5.3	odd	4		165.2.d.c.164.6	yes	16
5.4	even	2	inner	825.2.f.f.626.5		16
11.10	odd	2	inner	825.2.f.f.626.8		16
15.2	even	4		165.2.d.c.164.5	✓	16
15.8	even	4		165.2.d.c.164.12	yes	16
15.14	odd	2	inner	825.2.f.f.626.10		16
33.32	even	2	inner	825.2.f.f.626.11		16
55.32	even	4		165.2.d.c.164.7	yes	16
55.43	even	4		165.2.d.c.164.10	yes	16
55.54	odd	2	inner	825.2.f.f.626.9		16
165.32	odd	4		165.2.d.c.164.9	yes	16
165.98	odd	4		165.2.d.c.164.8	yes	16
165.164	even	2	inner	825.2.f.f.626.6		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.2.d.c.164.5	✓	16	15.2	even	4
165.2.d.c.164.6	yes	16	5.3	odd	4
165.2.d.c.164.7	yes	16	55.32	even	4
165.2.d.c.164.8	yes	16	165.98	odd	4
165.2.d.c.164.9	yes	16	165.32	odd	4
165.2.d.c.164.10	yes	16	55.43	even	4
165.2.d.c.164.11	yes	16	5.2	odd	4
165.2.d.c.164.12	yes	16	15.8	even	4
825.2.f.f.626.5		16	5.4	even	2	inner
825.2.f.f.626.6		16	165.164	even	2	inner
825.2.f.f.626.7		16	3.2	odd	2	inner
825.2.f.f.626.8		16	11.10	odd	2	inner
825.2.f.f.626.9		16	55.54	odd	2	inner
825.2.f.f.626.10		16	15.14	odd	2	inner
825.2.f.f.626.11		16	33.32	even	2	inner
825.2.f.f.626.12		16	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	825.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.50597 q^{2} +(0.796225 + 1.53819i) q^{3} +0.267949 q^{4} +(1.19909 + 2.31647i) q^{6} +2.12976i q^{7} -2.60842 q^{8} +(-1.73205 + 2.44949i) q^{9} +O(q^{10})\)	\(q+1.50597 q^{2} +(0.796225 + 1.53819i) q^{3} +0.267949 q^{4} +(1.19909 + 2.31647i) q^{6} +2.12976i q^{7} -2.60842 q^{8} +(-1.73205 + 2.44949i) q^{9} +(3.27598 + 0.517638i) q^{11} +(0.213348 + 0.412157i) q^{12} +2.12976i q^{13} +3.20736i q^{14} -4.46410 q^{16} -4.11439 q^{17} +(-2.60842 + 3.68886i) q^{18} +4.63294i q^{19} +(-3.27598 + 1.69577i) q^{21} +(4.93353 + 0.779548i) q^{22} -5.32844i q^{23} +(-2.07689 - 4.01224i) q^{24} +3.20736i q^{26} +(-5.14688 - 0.713876i) q^{27} +0.570669i q^{28} +8.95015 q^{29} +3.46410 q^{31} -1.50597 q^{32} +(1.81219 + 5.45123i) q^{33} -6.19615 q^{34} +(-0.464102 + 0.656339i) q^{36} +1.16575 q^{37} +6.97707i q^{38} +(-3.27598 + 1.69577i) q^{39} -2.39818 q^{41} +(-4.93353 + 2.55378i) q^{42} +9.50749i q^{43} +(0.877796 + 0.138701i) q^{44} -8.02448i q^{46} -3.07638i q^{47} +(-3.55443 - 6.86663i) q^{48} +2.46410 q^{49} +(-3.27598 - 6.32871i) q^{51} +0.570669i q^{52} +4.50413i q^{53} +(-7.75105 - 1.07508i) q^{54} -5.55532i q^{56} +(-7.12633 + 3.68886i) q^{57} +13.4787 q^{58} -4.89898i q^{59} +3.39154i q^{61} +5.21684 q^{62} +(-5.21684 - 3.68886i) q^{63} +6.66025 q^{64} +(2.72911 + 8.20940i) q^{66} +12.3129 q^{67} -1.10245 q^{68} +(8.19615 - 4.24264i) q^{69} -13.3843i q^{71} +(4.51791 - 6.38929i) q^{72} -2.12976i q^{73} +1.75559 q^{74} +1.24139i q^{76} +(-1.10245 + 6.97707i) q^{77} +(-4.93353 + 2.55378i) q^{78} -13.8988i q^{79} +(-3.00000 - 8.48528i) q^{81} -3.61160 q^{82} -9.33123 q^{83} +(-0.877796 + 0.454381i) q^{84} +14.3180i q^{86} +(7.12633 + 13.7670i) q^{87} +(-8.54513 - 1.35022i) q^{88} -4.62158i q^{89} -4.53590 q^{91} -1.42775i q^{92} +(2.75821 + 5.32844i) q^{93} -4.63294i q^{94} +(-1.19909 - 2.31647i) q^{96} -1.16575 q^{97} +3.71087 q^{98} +(-6.94211 + 7.12791i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 32 q^{4}+O(q^{10}) \) 16 * q + 32 * q^4	\( 16 q + 32 q^{4} - 16 q^{16} - 16 q^{34} + 48 q^{36} - 16 q^{49} - 32 q^{64} - 48 q^{66} + 48 q^{69} - 48 q^{81} - 128 q^{91} - 48 q^{99}+O(q^{100}) \) 16 * q + 32 * q^4 - 16 * q^16 - 16 * q^34 + 48 * q^36 - 16 * q^49 - 32 * q^64 - 48 * q^66 + 48 * q^69 - 48 * q^81 - 128 * q^91 - 48 * q^99

Introduction

L-functions

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