LMFDB - Embedded newform 522.3.f.h.505.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [522,3,Mod(307,522)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(522, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("522.307");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 522 = 2 \cdot 3^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	522.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:	$14.2234697996$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 4 x^{9} + 8 x^{8} + 96 x^{7} + 1204 x^{6} - 1792 x^{5} + 2144 x^{4} + 13632 x^{3} + 39204 x^{2} + \cdots + 288 $ x^10 - 4x^9 + 8x^8 + 96x^7 + 1204x^6 - 1792x^5 + 2144x^4 + 13632x^3 + 39204x^2 + 4752*x + 288
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			505.4
Root			$2.05251 + 2.05251i$ of defining polynomial
Character	$\chi$	$=$	522.505
Dual form			522.3.f.h.307.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 + 1.00000i) q^{2} +2.00000i q^{4} +2.10502i q^{5} -5.61134 q^{7} +(-2.00000 + 2.00000i) q^{8} +O(q^{10})$	\(q+(1.00000 + 1.00000i) q^{2} +2.00000i q^{4} +2.10502i q^{5} -5.61134 q^{7} +(-2.00000 + 2.00000i) q^{8} +(-2.10502 + 2.10502i) q^{10} +(-13.5036 - 13.5036i) q^{11} -14.7565i q^{13} +(-5.61134 - 5.61134i) q^{14} -4.00000 q^{16} +(-3.75925 - 3.75925i) q^{17} +(-5.29169 - 5.29169i) q^{19} -4.21003 q^{20} -27.0071i q^{22} -2.47836 q^{23} +20.5689 q^{25} +(14.7565 - 14.7565i) q^{26} -11.2227i q^{28} +(13.4387 + 25.6983i) q^{29} +(-21.1537 - 21.1537i) q^{31} +(-4.00000 - 4.00000i) q^{32} -7.51851i q^{34} -11.8120i q^{35} +(31.1010 - 31.1010i) q^{37} -10.5834i q^{38} +(-4.21003 - 4.21003i) q^{40} +(-23.5134 + 23.5134i) q^{41} +(-15.4174 - 15.4174i) q^{43} +(27.0071 - 27.0071i) q^{44} +(-2.47836 - 2.47836i) q^{46} +(-12.0149 + 12.0149i) q^{47} -17.5129 q^{49} +(20.5689 + 20.5689i) q^{50} +29.5130 q^{52} -65.9840 q^{53} +(28.4252 - 28.4252i) q^{55} +(11.2227 - 11.2227i) q^{56} +(-12.2596 + 39.1370i) q^{58} -32.0757 q^{59} +(-58.4876 - 58.4876i) q^{61} -42.3073i q^{62} -8.00000i q^{64} +31.0627 q^{65} +20.4446i q^{67} +(7.51851 - 7.51851i) q^{68} +(11.8120 - 11.8120i) q^{70} +60.6159i q^{71} +(89.6840 - 89.6840i) q^{73} +62.2019 q^{74} +(10.5834 - 10.5834i) q^{76} +(75.7731 + 75.7731i) q^{77} +(-80.1492 - 80.1492i) q^{79} -8.42006i q^{80} -47.0269 q^{82} -65.4392 q^{83} +(7.91329 - 7.91329i) q^{85} -30.8348i q^{86} +54.0143 q^{88} +(118.436 + 118.436i) q^{89} +82.8037i q^{91} -4.95673i q^{92} -24.0299 q^{94} +(11.1391 - 11.1391i) q^{95} +(-108.724 + 108.724i) q^{97} +(-17.5129 - 17.5129i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 10 q^{2} - 20 q^{8}+O(q^{10}) $ 10 * q + 10 * q^2 - 20 * q^8	$ 10 q + 10 q^{2} - 20 q^{8} + 12 q^{10} - 40 q^{16} - 6 q^{17} - 32 q^{19} + 24 q^{20} - 16 q^{23} - 110 q^{25} + 4 q^{26} - 22 q^{29} - 8 q^{31} - 40 q^{32} + 46 q^{37} + 24 q^{40} + 58 q^{41} + 56 q^{43} - 16 q^{46} - 192 q^{47} - 50 q^{49} - 110 q^{50} + 8 q^{52} + 180 q^{53} + 48 q^{55} - 46 q^{58} + 24 q^{59} + 22 q^{61} + 248 q^{65} + 12 q^{68} - 48 q^{70} - 62 q^{73} + 92 q^{74} + 64 q^{76} + 192 q^{77} - 200 q^{79} + 116 q^{82} - 296 q^{83} - 196 q^{85} - 26 q^{89} - 384 q^{94} - 32 q^{95} + 10 q^{97} - 50 q^{98}+O(q^{100}) $ 10 * q + 10 * q^2 - 20 * q^8 + 12 * q^10 - 40 * q^16 - 6 * q^17 - 32 * q^19 + 24 * q^20 - 16 * q^23 - 110 * q^25 + 4 * q^26 - 22 * q^29 - 8 * q^31 - 40 * q^32 + 46 * q^37 + 24 * q^40 + 58 * q^41 + 56 * q^43 - 16 * q^46 - 192 * q^47 - 50 * q^49 - 110 * q^50 + 8 * q^52 + 180 * q^53 + 48 * q^55 - 46 * q^58 + 24 * q^59 + 22 * q^61 + 248 * q^65 + 12 * q^68 - 48 * q^70 - 62 * q^73 + 92 * q^74 + 64 * q^76 + 192 * q^77 - 200 * q^79 + 116 * q^82 - 296 * q^83 - 196 * q^85 - 26 * q^89 - 384 * q^94 - 32 * q^95 + 10 * q^97 - 50 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/522\mathbb{Z}\right)^\times$.

$n$	$379$	$407$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$

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 $

$2$	1.00000	+	1.00000i	0.500000	+	0.500000i
$2$	1.00000	+	1.00000i	0.500000	+	0.500000i
$3$		0			0
$3$		0			0
$4$			2.00000i			0.500000i
$5$			2.10502i			0.421003i	0.977594	+	0.210502i	$0.0675097\pi$
$5$			2.10502i			0.421003i	−0.977594	+	0.210502i	$0.932490\pi$
$6$		0			0
$7$	−5.61134			−0.801620			−0.400810	−	0.916161i	$-0.631271\pi$
$7$	−5.61134			−0.801620			−0.400810	+	0.916161i	$0.631271\pi$
$8$	−2.00000	+	2.00000i	−0.250000	+	0.250000i
$9$		0			0
$10$	−2.10502	+	2.10502i	−0.210502	+	0.210502i
$11$	−13.5036	−	13.5036i	−1.22760	−	1.22760i	−0.964870	−	0.262726i	$-0.915378\pi$
$11$	−13.5036	−	13.5036i	−1.22760	−	1.22760i	−0.262726	−	0.964870i	$-0.584622\pi$
$12$		0			0
$13$		−	14.7565i		−	1.13512i	−0.823334	−	0.567558i	$-0.807888\pi$
$13$		−	14.7565i		−	1.13512i	0.823334	−	0.567558i	$-0.192112\pi$
$14$	−5.61134	−	5.61134i	−0.400810	−	0.400810i
$15$		0			0
$16$	−4.00000			−0.250000
$17$	−3.75925	−	3.75925i	−0.221133	−	0.221133i	0.587843	−	0.808975i	$-0.299977\pi$
$17$	−3.75925	−	3.75925i	−0.221133	−	0.221133i	−0.808975	+	0.587843i	$0.799977\pi$
$18$		0			0
$19$	−5.29169	−	5.29169i	−0.278510	−	0.278510i	0.554004	−	0.832514i	$-0.313099\pi$
$19$	−5.29169	−	5.29169i	−0.278510	−	0.278510i	−0.832514	+	0.554004i	$0.813099\pi$
$20$	−4.21003			−0.210502
$21$		0			0
$22$		−	27.0071i		−	1.22760i
$23$	−2.47836			−0.107755			−0.0538775	−	0.998548i	$-0.517158\pi$
$23$	−2.47836			−0.107755			−0.0538775	+	0.998548i	$0.517158\pi$
$24$		0			0
$25$	20.5689			0.822756
$26$	14.7565	−	14.7565i	0.567558	−	0.567558i
$27$		0			0
$28$		−	11.2227i		−	0.400810i
$29$	13.4387	+	25.6983i	0.463403	+	0.886148i
$29$	13.4387	+	25.6983i	0.463403	+	0.886148i
$30$		0			0
$31$	−21.1537	−	21.1537i	−0.682376	−	0.682376i	0.278159	−	0.960535i	$-0.410276\pi$
$31$	−21.1537	−	21.1537i	−0.682376	−	0.682376i	−0.960535	+	0.278159i	$0.910276\pi$
$32$	−4.00000	−	4.00000i	−0.125000	−	0.125000i
$33$		0			0
$34$		−	7.51851i		−	0.221133i
$35$		−	11.8120i		−	0.337484i
$36$		0			0
$37$	31.1010	−	31.1010i	0.840567	−	0.840567i	−0.148366	−	0.988933i	$-0.547401\pi$
$37$	31.1010	−	31.1010i	0.840567	−	0.840567i	0.988933	+	0.148366i	$0.0474013\pi$
$38$		−	10.5834i		−	0.278510i
$39$		0			0
$40$	−4.21003	−	4.21003i	−0.105251	−	0.105251i
$41$	−23.5134	+	23.5134i	−0.573499	+	0.573499i	−0.933104	−	0.359606i	$-0.882911\pi$
$41$	−23.5134	+	23.5134i	−0.573499	+	0.573499i	0.359606	+	0.933104i	$0.382911\pi$
$42$		0			0
$43$	−15.4174	−	15.4174i	−0.358544	−	0.358544i	0.504732	−	0.863276i	$-0.331591\pi$
$43$	−15.4174	−	15.4174i	−0.358544	−	0.358544i	−0.863276	+	0.504732i	$0.831591\pi$
$44$	27.0071	−	27.0071i	0.613798	−	0.613798i
$45$		0			0
$46$	−2.47836	−	2.47836i	−0.0538775	−	0.0538775i
$47$	−12.0149	+	12.0149i	−0.255637	+	0.255637i	−0.823277	−	0.567640i	$-0.807857\pi$
$47$	−12.0149	+	12.0149i	−0.255637	+	0.255637i	0.567640	+	0.823277i	$0.307857\pi$
$48$		0			0
$49$	−17.5129			−0.357406
$50$	20.5689	+	20.5689i	0.411378	+	0.411378i
$51$		0			0
$52$	29.5130			0.567558
$53$	−65.9840			−1.24498			−0.622491	−	0.782627i	$-0.713879\pi$
$53$	−65.9840			−1.24498			−0.622491	+	0.782627i	$0.713879\pi$
$54$		0			0
$55$	28.4252	−	28.4252i	0.516822	−	0.516822i
$56$	11.2227	−	11.2227i	0.200405	−	0.200405i
$57$		0			0
$58$	−12.2596	+	39.1370i	−0.211372	+	0.674775i
$59$	−32.0757			−0.543656			−0.271828	−	0.962346i	$-0.587628\pi$
$59$	−32.0757			−0.543656			−0.271828	+	0.962346i	$0.587628\pi$
$60$		0			0
$61$	−58.4876	−	58.4876i	−0.958812	−	0.958812i	0.0403722	−	0.999185i	$-0.487146\pi$
$61$	−58.4876	−	58.4876i	−0.958812	−	0.958812i	−0.999185	+	0.0403722i	$0.987146\pi$
$62$		−	42.3073i		−	0.682376i
$63$		0			0
$64$		−	8.00000i		−	0.125000i
$65$	31.0627			0.477887
$66$		0			0
$67$			20.4446i			0.305143i	0.988292	+	0.152571i	$0.0487554\pi$
$67$			20.4446i			0.305143i	−0.988292	+	0.152571i	$0.951245\pi$
$68$	7.51851	−	7.51851i	0.110566	−	0.110566i
$69$		0			0
$70$	11.8120	−	11.8120i	0.168742	−	0.168742i
$71$			60.6159i			0.853746i	0.904312	+	0.426873i	$0.140385\pi$
$71$			60.6159i			0.853746i	−0.904312	+	0.426873i	$0.859615\pi$
$72$		0			0
$73$	89.6840	−	89.6840i	1.22855	−	1.22855i	0.264036	−	0.964513i	$-0.414946\pi$
$73$	89.6840	−	89.6840i	1.22855	−	1.22855i	0.964513	−	0.264036i	$-0.0850536\pi$
$74$	62.2019			0.840567
$75$		0			0
$76$	10.5834	−	10.5834i	0.139255	−	0.139255i
$77$	75.7731	+	75.7731i	0.984066	+	0.984066i
$78$		0			0
$79$	−80.1492	−	80.1492i	−1.01455	−	1.01455i	−0.999893	−	0.0146537i	$-0.995335\pi$
$79$	−80.1492	−	80.1492i	−1.01455	−	1.01455i	−0.0146537	−	0.999893i	$-0.504665\pi$
$80$		−	8.42006i		−	0.105251i
$81$		0			0
$82$	−47.0269			−0.573499
$83$	−65.4392			−0.788424			−0.394212	−	0.919020i	$-0.628982\pi$
$83$	−65.4392			−0.788424			−0.394212	+	0.919020i	$0.628982\pi$
$84$		0			0
$85$	7.91329	−	7.91329i	0.0930975	−	0.0930975i
$86$		−	30.8348i		−	0.358544i
$87$		0			0
$88$	54.0143			0.613798
$89$	118.436	+	118.436i	1.33074	+	1.33074i	0.904709	+	0.426030i	$0.140088\pi$
$89$	118.436	+	118.436i	1.33074	+	1.33074i	0.426030	+	0.904709i	$0.359912\pi$
$90$		0			0
$91$			82.8037i			0.909930i
$92$		−	4.95673i		−	0.0538775i
$93$		0			0
$94$	−24.0299			−0.255637
$95$	11.1391	−	11.1391i	0.117254	−	0.117254i
$96$		0			0
$97$	−108.724	+	108.724i	−1.12087	+	1.12087i	−0.129259	+	0.991611i	$0.541260\pi$
$97$	−108.724	+	108.724i	−1.12087	+	1.12087i	−0.991611	+	0.129259i	$0.958740\pi$
$98$	−17.5129	−	17.5129i	−0.178703	−	0.178703i
$99$		0			0
$100$			41.1378i			0.411378i
$101$	−27.3276	−	27.3276i	−0.270570	−	0.270570i	0.558759	−	0.829330i	$-0.311278\pi$
$101$	−27.3276	−	27.3276i	−0.270570	−	0.270570i	−0.829330	+	0.558759i	$0.811278\pi$
$102$		0			0
$103$	−15.2942			−0.148488			−0.0742439	−	0.997240i	$-0.523654\pi$
$103$	−15.2942			−0.148488			−0.0742439	+	0.997240i	$0.523654\pi$
$104$	29.5130	+	29.5130i	0.283779	+	0.283779i
$105$		0			0
$106$	−65.9840	−	65.9840i	−0.622491	−	0.622491i
$107$	−107.617			−1.00576			−0.502882	−	0.864355i	$-0.667727\pi$
$107$	−107.617			−1.00576			−0.502882	+	0.864355i	$0.667727\pi$
$108$		0			0
$109$		−	93.0050i		−	0.853257i	−0.904427	−	0.426628i	$-0.859701\pi$
$109$		−	93.0050i		−	0.853257i	0.904427	−	0.426628i	$-0.140299\pi$
$110$	56.8504			0.516822
$111$		0			0
$112$	22.4453			0.200405
$113$	56.1127	−	56.1127i	0.496573	−	0.496573i	−0.413797	−	0.910369i	$-0.635798\pi$
$113$	56.1127	−	56.1127i	0.496573	−	0.496573i	0.910369	+	0.413797i	$0.135798\pi$
$114$		0			0
$115$		−	5.21699i		−	0.0453652i
$116$	−51.3966	+	26.8774i	−0.443074	+	0.231702i
$117$		0			0
$118$	−32.0757	−	32.0757i	−0.271828	−	0.271828i
$119$	21.0944	+	21.0944i	0.177264	+	0.177264i
$120$		0			0
$121$			243.692i			2.01399i
$122$		−	116.975i		−	0.958812i
$123$		0			0
$124$	42.3073	−	42.3073i	0.341188	−	0.341188i
$125$			95.9233i			0.767386i
$126$		0			0
$127$	169.448	+	169.448i	1.33424	+	1.33424i	0.901539	+	0.432698i	$0.142438\pi$
$127$	169.448	+	169.448i	1.33424	+	1.33424i	0.432698	+	0.901539i	$0.357562\pi$
$128$	8.00000	−	8.00000i	0.0625000	−	0.0625000i
$129$		0			0
$130$	31.0627	+	31.0627i	0.238944	+	0.238944i
$131$	46.9561	−	46.9561i	0.358444	−	0.358444i	−0.504795	−	0.863239i	$-0.668432\pi$
$131$	46.9561	−	46.9561i	0.358444	−	0.358444i	0.863239	+	0.504795i	$0.168432\pi$
$132$		0			0
$133$	29.6935	+	29.6935i	0.223259	+	0.223259i
$134$	−20.4446	+	20.4446i	−0.152571	+	0.152571i
$135$		0			0
$136$	15.0370			0.110566
$137$	−137.929	−	137.929i	−1.00678	−	1.00678i	−0.999977	−	0.00680762i	$-0.997833\pi$
$137$	−137.929	−	137.929i	−1.00678	−	1.00678i	−0.00680762	−	0.999977i	$-0.502167\pi$
$138$		0			0
$139$	197.811			1.42310			0.711551	−	0.702634i	$-0.247993\pi$
$139$	197.811			1.42310			0.711551	+	0.702634i	$0.247993\pi$
$140$	23.6239			0.168742
$141$		0			0
$142$	−60.6159	+	60.6159i	−0.426873	+	0.426873i
$143$	−199.265	+	199.265i	−1.39346	+	1.39346i
$144$		0			0
$145$	−54.0953	+	28.2887i	−0.373071	+	0.195094i
$146$	179.368			1.22855
$147$		0			0
$148$	62.2019	+	62.2019i	0.420283	+	0.420283i
$149$			40.1174i			0.269244i	0.990897	+	0.134622i	$0.0429820\pi$
$149$			40.1174i			0.269244i	−0.990897	+	0.134622i	$0.957018\pi$
$150$		0			0
$151$			39.8281i			0.263762i	0.991266	+	0.131881i	$0.0421017\pi$
$151$			39.8281i			0.263762i	−0.991266	+	0.131881i	$0.957898\pi$
$152$	21.1668			0.139255
$153$		0			0
$154$			151.546i			0.984066i
$155$	44.5288	−	44.5288i	0.287283	−	0.287283i
$156$		0			0
$157$	−23.9244	+	23.9244i	−0.152385	+	0.152385i	−0.779182	−	0.626797i	$-0.784365\pi$
$157$	−23.9244	+	23.9244i	−0.152385	+	0.152385i	0.626797	+	0.779182i	$0.284365\pi$
$158$		−	160.298i		−	1.01455i
$159$		0			0
$160$	8.42006	−	8.42006i	0.0526254	−	0.0526254i
$161$	13.9069			0.0863784
$162$		0			0
$163$	−1.28721	+	1.28721i	−0.00789701	+	0.00789701i	−0.711044	−	0.703147i	$-0.751777\pi$
$163$	−1.28721	+	1.28721i	−0.00789701	+	0.00789701i	0.703147	+	0.711044i	$0.251777\pi$
$164$	−47.0269	−	47.0269i	−0.286749	−	0.286749i
$165$		0			0
$166$	−65.4392	−	65.4392i	−0.394212	−	0.394212i
$167$		−	61.6031i		−	0.368881i	−0.982844	−	0.184440i	$-0.940953\pi$
$167$		−	61.6031i		−	0.368881i	0.982844	−	0.184440i	$-0.0590473\pi$
$168$		0			0
$169$	−48.7542			−0.288486
$170$	15.8266			0.0930975
$171$		0			0
$172$	30.8348	−	30.8348i	0.179272	−	0.179272i
$173$			55.0580i			0.318254i	0.987258	+	0.159127i	$0.0508680\pi$
$173$			55.0580i			0.318254i	−0.987258	+	0.159127i	$0.949132\pi$
$174$		0			0
$175$	−115.419			−0.659538
$176$	54.0143	+	54.0143i	0.306899	+	0.306899i
$177$		0			0
$178$			236.872i			1.33074i
$179$		−	42.2602i		−	0.236091i	−0.993008	−	0.118045i	$-0.962337\pi$
$179$		−	42.2602i		−	0.236091i	0.993008	−	0.118045i	$-0.0376628\pi$
$180$		0			0
$181$	−58.4039			−0.322673			−0.161337	−	0.986899i	$-0.551580\pi$
$181$	−58.4039			−0.322673			−0.161337	+	0.986899i	$0.551580\pi$
$182$	−82.8037	+	82.8037i	−0.454965	+	0.454965i
$183$		0			0
$184$	4.95673	−	4.95673i	0.0269387	−	0.0269387i
$185$	65.4680	+	65.4680i	0.353881	+	0.353881i
$186$		0			0
$187$			101.527i			0.542923i
$188$	−24.0299	−	24.0299i	−0.127819	−	0.127819i
$189$		0			0
$190$	22.2782			0.117254
$191$	−221.577	−	221.577i	−1.16009	−	1.16009i	−0.984456	−	0.175634i	$-0.943803\pi$
$191$	−221.577	−	221.577i	−1.16009	−	1.16009i	−0.175634	−	0.984456i	$-0.556197\pi$
$192$		0			0
$193$	139.816	+	139.816i	0.724437	+	0.724437i	0.969506	−	0.245069i	$-0.0788106\pi$
$193$	139.816	+	139.816i	0.724437	+	0.724437i	−0.245069	+	0.969506i	$0.578811\pi$
$194$	−217.449			−1.12087
$195$		0			0
$196$		−	35.0258i		−	0.178703i
$197$	−134.573			−0.683111			−0.341556	−	0.939862i	$-0.610954\pi$
$197$	−134.573			−0.683111			−0.341556	+	0.939862i	$0.610954\pi$
$198$		0			0
$199$	137.004			0.688464			0.344232	−	0.938885i	$-0.388139\pi$
$199$	137.004			0.688464			0.344232	+	0.938885i	$0.388139\pi$
$200$	−41.1378	+	41.1378i	−0.205689	+	0.205689i
$201$		0			0
$202$		−	54.6552i		−	0.270570i
$203$	−75.4090	−	144.202i	−0.371473	−	0.710353i
$204$		0			0
$205$	−49.4962	−	49.4962i	−0.241445	−	0.241445i
$206$	−15.2942	−	15.2942i	−0.0742439	−	0.0742439i
$207$		0			0
$208$			59.0260i			0.283779i
$209$			142.913i			0.683796i
$210$		0			0
$211$	−2.20762	+	2.20762i	−0.0104627	+	0.0104627i	−0.712319	−	0.701856i	$-0.752355\pi$
$211$	−2.20762	+	2.20762i	−0.0104627	+	0.0104627i	0.701856	+	0.712319i	$0.252355\pi$
$212$		−	131.968i		−	0.622491i
$213$		0			0
$214$	−107.617	−	107.617i	−0.502882	−	0.502882i
$215$	32.4539	−	32.4539i	0.150948	−	0.150948i
$216$		0			0
$217$	118.700	+	118.700i	0.547006	+	0.547006i
$218$	93.0050	−	93.0050i	0.426628	−	0.426628i
$219$		0			0
$220$	56.8504	+	56.8504i	0.258411	+	0.258411i
$221$	−55.4734	+	55.4734i	−0.251011	+	0.251011i
$222$		0			0
$223$	−246.088			−1.10353			−0.551766	−	0.833999i	$-0.686046\pi$
$223$	−246.088			−1.10353			−0.551766	+	0.833999i	$0.686046\pi$
$224$	22.4453	+	22.4453i	0.100202	+	0.100202i
$225$		0			0
$226$	112.225			0.496573
$227$	30.1681			0.132899			0.0664495	−	0.997790i	$-0.478833\pi$
$227$	30.1681			0.132899			0.0664495	+	0.997790i	$0.478833\pi$
$228$		0			0
$229$	4.83045	−	4.83045i	0.0210937	−	0.0210937i	−0.696481	−	0.717575i	$-0.745252\pi$
$229$	4.83045	−	4.83045i	0.0210937	−	0.0210937i	0.717575	+	0.696481i	$0.245252\pi$
$230$	5.21699	−	5.21699i	0.0226826	−	0.0226826i
$231$		0			0
$232$	−78.2739	−	24.5192i	−0.337388	−	0.105686i
$233$	7.43976			0.0319303			0.0159651	−	0.999873i	$-0.494918\pi$
$233$	7.43976			0.0319303			0.0159651	+	0.999873i	$0.494918\pi$
$234$		0			0
$235$	−25.2916	−	25.2916i	−0.107624	−	0.107624i
$236$		−	64.1514i		−	0.271828i
$237$		0			0
$238$			42.1889i			0.177264i
$239$	365.434			1.52901			0.764505	−	0.644617i	$-0.222983\pi$
$239$	365.434			1.52901			0.764505	+	0.644617i	$0.222983\pi$
$240$		0			0
$241$			124.875i			0.518155i	0.965857	+	0.259078i	$0.0834185\pi$
$241$			124.875i			0.518155i	−0.965857	+	0.259078i	$0.916581\pi$
$242$	−243.692	+	243.692i	−1.00699	+	1.00699i
$243$		0			0
$244$	116.975	−	116.975i	0.479406	−	0.479406i
$245$		−	36.8649i		−	0.150469i
$246$		0			0
$247$	−78.0868	+	78.0868i	−0.316141	+	0.316141i
$248$	84.6146			0.341188
$249$		0			0
$250$	−95.9233	+	95.9233i	−0.383693	+	0.383693i
$251$	−24.3153	−	24.3153i	−0.0968736	−	0.0968736i	0.657009	−	0.753883i	$-0.271821\pi$
$251$	−24.3153	−	24.3153i	−0.0968736	−	0.0968736i	−0.753883	+	0.657009i	$0.771821\pi$
$252$		0			0
$253$	33.4667	+	33.4667i	0.132280	+	0.132280i
$254$			338.896i			1.33424i
$255$		0			0
$256$	16.0000			0.0625000
$257$	224.398			0.873142			0.436571	−	0.899670i	$-0.356193\pi$
$257$	224.398			0.873142			0.436571	+	0.899670i	$0.356193\pi$
$258$		0			0
$259$	−174.518	+	174.518i	−0.673815	+	0.673815i
$260$			62.1253i			0.238944i
$261$		0			0
$262$	93.9123			0.358444
$263$	94.9149	+	94.9149i	0.360893	+	0.360893i	0.864142	−	0.503249i	$-0.167862\pi$
$263$	94.9149	+	94.9149i	0.360893	+	0.360893i	−0.503249	+	0.864142i	$0.667862\pi$
$264$		0			0
$265$		−	138.897i		−	0.524141i
$266$			59.3869i			0.223259i
$267$		0			0
$268$	−40.8892			−0.152571
$269$	238.834	−	238.834i	0.887859	−	0.887859i	−0.106458	−	0.994317i	$-0.533951\pi$
$269$	238.834	−	238.834i	0.887859	−	0.887859i	0.994317	+	0.106458i	$0.0339509\pi$
$270$		0			0
$271$	−141.722	+	141.722i	−0.522959	+	0.522959i	−0.918464	−	0.395505i	$-0.870570\pi$
$271$	−141.722	+	141.722i	−0.522959	+	0.522959i	0.395505	+	0.918464i	$0.370570\pi$
$272$	15.0370	+	15.0370i	0.0552831	+	0.0552831i
$273$		0			0
$274$		−	275.859i		−	1.00678i
$275$	−277.754	−	277.754i	−1.01001	−	1.01001i
$276$		0			0
$277$	261.412			0.943724			0.471862	−	0.881672i	$-0.343582\pi$
$277$	261.412			0.943724			0.471862	+	0.881672i	$0.343582\pi$
$278$	197.811	+	197.811i	0.711551	+	0.711551i
$279$		0			0
$280$	23.6239	+	23.6239i	0.0843711	+	0.0843711i
$281$	287.459			1.02299			0.511493	−	0.859287i	$-0.329092\pi$
$281$	287.459			1.02299			0.511493	+	0.859287i	$0.329092\pi$
$282$		0			0
$283$		−	330.346i		−	1.16730i	−0.812005	−	0.583650i	$-0.801624\pi$
$283$		−	330.346i		−	1.16730i	0.812005	−	0.583650i	$-0.198376\pi$
$284$	−121.232			−0.426873
$285$		0			0
$286$	−398.531			−1.39346
$287$	131.942	−	131.942i	0.459728	−	0.459728i
$288$		0			0
$289$		−	260.736i		−	0.902201i
$290$	−82.3839	−	25.8066i	−0.284083	−	0.0889884i
$291$		0			0
$292$	179.368	+	179.368i	0.614274	+	0.614274i
$293$	371.916	+	371.916i	1.26934	+	1.26934i	0.946431	+	0.322907i	$0.104660\pi$
$293$	371.916	+	371.916i	1.26934	+	1.26934i	0.322907	+	0.946431i	$0.395340\pi$
$294$		0			0
$295$		−	67.5198i		−	0.228881i
$296$			124.404i			0.420283i
$297$		0			0
$298$	−40.1174	+	40.1174i	−0.134622	+	0.134622i
$299$			36.5719i			0.122314i
$300$		0			0
$301$	86.5122	+	86.5122i	0.287416	+	0.287416i
$302$	−39.8281	+	39.8281i	−0.131881	+	0.131881i
$303$		0			0
$304$	21.1668	+	21.1668i	0.0696275	+	0.0696275i
$305$	123.117	−	123.117i	0.403663	−	0.403663i
$306$		0			0
$307$	−192.949	−	192.949i	−0.628498	−	0.628498i	0.319192	−	0.947690i	$-0.396589\pi$
$307$	−192.949	−	192.949i	−0.628498	−	0.628498i	−0.947690	+	0.319192i	$0.896589\pi$
$308$	−151.546	+	151.546i	−0.492033	+	0.492033i
$309$		0			0
$310$	89.0576			0.287283
$311$	−400.986	−	400.986i	−1.28934	−	1.28934i	−0.935185	−	0.354158i	$-0.884767\pi$
$311$	−400.986	−	400.986i	−1.28934	−	1.28934i	−0.354158	−	0.935185i	$-0.615233\pi$
$312$		0			0
$313$	−243.545			−0.778099			−0.389050	−	0.921217i	$-0.627197\pi$
$313$	−243.545			−0.778099			−0.389050	+	0.921217i	$0.627197\pi$
$314$	−47.8489			−0.152385
$315$		0			0
$316$	160.298	−	160.298i	0.507273	−	0.507273i
$317$	20.7584	−	20.7584i	0.0654839	−	0.0654839i	−0.673606	−	0.739090i	$-0.735256\pi$
$317$	20.7584	−	20.7584i	0.0654839	−	0.0654839i	0.739090	+	0.673606i	$0.235256\pi$
$318$		0			0
$319$	165.548	−	528.489i	0.518960	−	1.65670i
$320$	16.8401			0.0526254
$321$		0			0
$322$	13.9069	+	13.9069i	0.0431892	+	0.0431892i
$323$			39.7856i			0.123175i
$324$		0			0
$325$		−	303.525i		−	0.933923i
$326$	−2.57443			−0.00789701
$327$		0			0
$328$		−	94.0538i		−	0.286749i
$329$	67.4199	−	67.4199i	0.204924	−	0.204924i
$330$		0			0
$331$	277.933	−	277.933i	0.839676	−	0.839676i	−0.149140	−	0.988816i	$-0.547651\pi$
$331$	277.933	−	277.933i	0.839676	−	0.839676i	0.988816	+	0.149140i	$0.0476506\pi$
$332$		−	130.878i		−	0.394212i
$333$		0			0
$334$	61.6031	−	61.6031i	0.184440	−	0.184440i
$335$	−43.0362			−0.128466
$336$		0			0
$337$	270.767	−	270.767i	0.803463	−	0.803463i	−0.180172	−	0.983635i	$-0.557665\pi$
$337$	270.767	−	270.767i	0.803463	−	0.803463i	0.983635	+	0.180172i	$0.0576655\pi$
$338$	−48.7542	−	48.7542i	−0.144243	−	0.144243i
$339$		0			0
$340$	15.8266	+	15.8266i	0.0465487	+	0.0465487i
$341$			571.300i			1.67537i
$342$		0			0
$343$	373.226			1.08812
$344$	61.6696			0.179272
$345$		0			0
$346$	−55.0580	+	55.0580i	−0.159127	+	0.159127i
$347$			122.863i			0.354071i	0.984204	+	0.177035i	$0.0566507\pi$
$347$			122.863i			0.354071i	−0.984204	+	0.177035i	$0.943349\pi$
$348$		0			0
$349$	−132.409			−0.379396			−0.189698	−	0.981842i	$-0.560751\pi$
$349$	−132.409			−0.379396			−0.189698	+	0.981842i	$0.560751\pi$
$350$	−115.419	−	115.419i	−0.329769	−	0.329769i
$351$		0			0
$352$			108.029i			0.306899i
$353$		−	92.9741i		−	0.263383i	−0.991291	−	0.131691i	$-0.957959\pi$
$353$		−	92.9741i		−	0.263383i	0.991291	−	0.131691i	$-0.0420408\pi$
$354$		0			0
$355$	−127.598			−0.359430
$356$	−236.872	+	236.872i	−0.665370	+	0.665370i
$357$		0			0
$358$	42.2602	−	42.2602i	0.118045	−	0.118045i
$359$	−331.444	−	331.444i	−0.923242	−	0.923242i	0.0740149	−	0.997257i	$-0.476419\pi$
$359$	−331.444	−	331.444i	−0.923242	−	0.923242i	−0.997257	+	0.0740149i	$0.976419\pi$
$360$		0			0
$361$		−	304.996i		−	0.844864i
$362$	−58.4039	−	58.4039i	−0.161337	−	0.161337i
$363$		0			0
$364$	−165.607			−0.454965
$365$	188.786	+	188.786i	0.517223	+	0.517223i
$366$		0			0
$367$	−293.812	−	293.812i	−0.800577	−	0.800577i	0.182609	−	0.983186i	$-0.441546\pi$
$367$	−293.812	−	293.812i	−0.800577	−	0.800577i	−0.983186	+	0.182609i	$0.941546\pi$
$368$	9.91345			0.0269387
$369$		0			0
$370$			130.936i			0.353881i
$371$	370.259			0.998001
$372$		0			0
$373$	−407.090			−1.09139			−0.545697	−	0.837983i	$-0.683735\pi$
$373$	−407.090			−1.09139			−0.545697	+	0.837983i	$0.683735\pi$
$374$	−101.527	+	101.527i	−0.271462	+	0.271462i
$375$		0			0
$376$		−	48.0598i		−	0.127819i
$377$	379.217	−	198.308i	1.00588	−	0.526016i
$378$		0			0
$379$	343.209	+	343.209i	0.905565	+	0.905565i	0.995911	−	0.0903451i	$-0.0287970\pi$
$379$	343.209	+	343.209i	0.905565	+	0.905565i	−0.0903451	+	0.995911i	$0.528797\pi$
$380$	22.2782	+	22.2782i	0.0586268	+	0.0586268i
$381$		0			0
$382$		−	443.154i		−	1.16009i
$383$			312.930i			0.817049i	0.912747	+	0.408524i	$0.133956\pi$
$383$			312.930i			0.817049i	−0.912747	+	0.408524i	$0.866044\pi$
$384$		0			0
$385$	−159.503	+	159.503i	−0.414295	+	0.414295i
$386$			279.633i			0.724437i
$387$		0			0
$388$	−217.449	−	217.449i	−0.560435	−	0.560435i
$389$	−23.6481	+	23.6481i	−0.0607919	+	0.0607919i	−0.736849	−	0.676057i	$-0.763687\pi$
$389$	−23.6481	+	23.6481i	−0.0607919	+	0.0607919i	0.676057	+	0.736849i	$0.263687\pi$
$390$		0			0
$391$	9.31679	+	9.31679i	0.0238281	+	0.0238281i
$392$	35.0258	−	35.0258i	0.0893515	−	0.0893515i
$393$		0			0
$394$	−134.573	−	134.573i	−0.341556	−	0.341556i
$395$	168.715	−	168.715i	0.427127	−	0.427127i
$396$		0			0
$397$	453.764			1.14298			0.571491	−	0.820609i	$-0.306365\pi$
$397$	453.764			1.14298			0.571491	+	0.820609i	$0.306365\pi$
$398$	137.004	+	137.004i	0.344232	+	0.344232i
$399$		0			0
$400$	−82.2756			−0.205689
$401$	368.308			0.918474			0.459237	−	0.888314i	$-0.348123\pi$
$401$	368.308			0.918474			0.459237	+	0.888314i	$0.348123\pi$
$402$		0			0
$403$	−312.154	+	312.154i	−0.774575	+	0.774575i
$404$	54.6552	−	54.6552i	0.135285	−	0.135285i
$405$		0			0
$406$	68.7927	−	219.611i	0.169440	−	0.540913i
$407$	−839.948			−2.06375
$408$		0			0
$409$	−125.408	−	125.408i	−0.306621	−	0.306621i	0.536977	−	0.843597i	$-0.319566\pi$
$409$	−125.408	−	125.408i	−0.306621	−	0.306621i	−0.843597	+	0.536977i	$0.819566\pi$
$410$		−	98.9924i		−	0.241445i
$411$		0			0
$412$		−	30.5885i		−	0.0742439i
$413$	179.987			0.435805
$414$		0			0
$415$		−	137.750i		−	0.331929i
$416$	−59.0260	+	59.0260i	−0.141889	+	0.141889i
$417$		0			0
$418$	−142.913	+	142.913i	−0.341898	+	0.341898i
$419$		−	571.234i		−	1.36333i	−0.731666	−	0.681664i	$-0.761257\pi$
$419$		−	571.234i		−	1.36333i	0.731666	−	0.681664i	$-0.238743\pi$
$420$		0			0
$421$	−543.843	+	543.843i	−1.29179	+	1.29179i	−0.358107	+	0.933680i	$0.616578\pi$
$421$	−543.843	+	543.843i	−1.29179	+	1.29179i	−0.933680	+	0.358107i	$0.883422\pi$
$422$	−4.41524			−0.0104627
$423$		0			0
$424$	131.968	−	131.968i	0.311245	−	0.311245i
$425$	−77.3237	−	77.3237i	−0.181938	−	0.181938i
$426$		0			0
$427$	328.193	+	328.193i	0.768603	+	0.768603i
$428$		−	215.234i		−	0.502882i
$429$		0			0
$430$	64.9077			0.150948
$431$	−671.611			−1.55826			−0.779131	−	0.626861i	$-0.784339\pi$
$431$	−671.611			−1.55826			−0.779131	+	0.626861i	$0.784339\pi$
$432$		0			0
$433$	76.9067	−	76.9067i	0.177614	−	0.177614i	−0.612701	−	0.790315i	$-0.709917\pi$
$433$	76.9067	−	76.9067i	0.177614	−	0.177614i	0.790315	+	0.612701i	$0.209917\pi$
$434$			237.401i			0.547006i
$435$		0			0
$436$	186.010			0.426628
$437$	13.1147	+	13.1147i	0.0300108	+	0.0300108i
$438$		0			0
$439$		−	760.226i		−	1.73172i	−0.500285	−	0.865861i	$-0.666771\pi$
$439$		−	760.226i		−	1.73172i	0.500285	−	0.865861i	$-0.333229\pi$
$440$			113.701i			0.258411i
$441$		0			0
$442$	−110.947			−0.251011
$443$	172.849	−	172.849i	0.390179	−	0.390179i	−0.484572	−	0.874751i	$-0.661025\pi$
$443$	172.849	−	172.849i	0.390179	−	0.390179i	0.874751	+	0.484572i	$0.161025\pi$
$444$		0			0
$445$	−249.309	+	249.309i	−0.560245	+	0.560245i
$446$	−246.088	−	246.088i	−0.551766	−	0.551766i
$447$		0			0
$448$			44.8907i			0.100202i
$449$	−75.8300	−	75.8300i	−0.168887	−	0.168887i	0.617603	−	0.786490i	$-0.288104\pi$
$449$	−75.8300	−	75.8300i	−0.168887	−	0.168887i	−0.786490	+	0.617603i	$0.788104\pi$
$450$		0			0
$451$	635.031			1.40805
$452$	112.225	+	112.225i	0.248286	+	0.248286i
$453$		0			0
$454$	30.1681	+	30.1681i	0.0664495	+	0.0664495i
$455$	−174.303			−0.383084
$456$		0			0
$457$		−	243.195i		−	0.532155i	−0.963952	−	0.266077i	$-0.914272\pi$
$457$		−	243.195i		−	0.532155i	0.963952	−	0.266077i	$-0.0857276\pi$
$458$	9.66090			0.0210937
$459$		0			0
$460$	10.4340			0.0226826
$461$	473.324	−	473.324i	1.02673	−	1.02673i	0.0271010	−	0.999633i	$-0.491372\pi$
$461$	473.324	−	473.324i	1.02673	−	1.02673i	0.999633	−	0.0271010i	$-0.00862757\pi$
$462$		0			0
$463$			491.254i			1.06102i	0.847678	+	0.530511i	$0.178000\pi$
$463$			491.254i			1.06102i	−0.847678	+	0.530511i	$0.822000\pi$
$464$	−53.7548	−	102.793i	−0.115851	−	0.221537i
$465$		0			0
$466$	7.43976	+	7.43976i	0.0159651	+	0.0159651i
$467$	−462.274	−	462.274i	−0.989880	−	0.989880i	0.0100691	−	0.999949i	$-0.496795\pi$
$467$	−462.274	−	462.274i	−0.989880	−	0.989880i	−0.999949	+	0.0100691i	$0.996795\pi$
$468$		0			0
$469$		−	114.721i		−	0.244609i
$470$		−	50.5833i		−	0.107624i
$471$		0			0
$472$	64.1514	−	64.1514i	0.135914	−	0.135914i
$473$			416.379i			0.880295i
$474$		0			0
$475$	−108.844	−	108.844i	−0.229146	−	0.229146i
$476$	−42.1889	+	42.1889i	−0.0886321	+	0.0886321i
$477$		0			0
$478$	365.434	+	365.434i	0.764505	+	0.764505i
$479$	150.712	−	150.712i	0.314640	−	0.314640i	−0.532064	−	0.846704i	$-0.678584\pi$
$479$	150.712	−	150.712i	0.314640	−	0.314640i	0.846704	+	0.532064i	$0.178584\pi$
$480$		0			0
$481$	−458.941	−	458.941i	−0.954140	−	0.954140i
$482$	−124.875	+	124.875i	−0.259078	+	0.259078i
$483$		0			0
$484$	−487.385			−1.00699
$485$	−228.867	−	228.867i	−0.471890	−	0.471890i
$486$		0			0
$487$	−57.3072			−0.117674			−0.0588370	−	0.998268i	$-0.518739\pi$
$487$	−57.3072			−0.117674			−0.0588370	+	0.998268i	$0.518739\pi$
$488$	233.950			0.479406
$489$		0			0
$490$	36.8649	−	36.8649i	0.0752345	−	0.0752345i
$491$	422.253	−	422.253i	0.859986	−	0.859986i	−0.131350	−	0.991336i	$-0.541931\pi$
$491$	422.253	−	422.253i	0.859986	−	0.859986i	0.991336	+	0.131350i	$0.0419313\pi$
$492$		0			0
$493$	46.0869	−	147.126i	0.0934825	−	0.298430i
$494$	−156.174			−0.316141
$495$		0			0
$496$	84.6146	+	84.6146i	0.170594	+	0.170594i
$497$		−	340.136i		−	0.684379i
$498$		0			0
$499$		−	422.238i		−	0.846168i	−0.906091	−	0.423084i	$-0.860948\pi$
$499$		−	422.238i		−	0.846168i	0.906091	−	0.423084i	$-0.139052\pi$
$500$	−191.847			−0.383693
$501$		0			0
$502$		−	48.6305i		−	0.0968736i
$503$	−480.153	+	480.153i	−0.954579	+	0.954579i	−0.999012	−	0.0444332i	$-0.985852\pi$
$503$	−480.153	+	480.153i	−0.954579	+	0.954579i	0.0444332	+	0.999012i	$0.485852\pi$
$504$		0			0
$505$	57.5250	−	57.5250i	0.113911	−	0.113911i
$506$			66.9335i			0.132280i
$507$		0			0
$508$	−338.896	+	338.896i	−0.667118	+	0.667118i
$509$	−131.660			−0.258664			−0.129332	−	0.991601i	$-0.541283\pi$
$509$	−131.660			−0.258664			−0.129332	+	0.991601i	$0.541283\pi$
$510$		0			0
$511$	−503.247	+	503.247i	−0.984829	+	0.984829i
$512$	16.0000	+	16.0000i	0.0312500	+	0.0312500i
$513$		0			0
$514$	224.398	+	224.398i	0.436571	+	0.436571i
$515$		−	32.1946i		−	0.0625138i
$516$		0			0
$517$	324.489			0.627638
$518$	−349.036			−0.673815
$519$		0			0
$520$	−62.1253	+	62.1253i	−0.119472	+	0.119472i
$521$			998.315i			1.91615i	0.286514	+	0.958076i	$0.407504\pi$
$521$			998.315i			1.91615i	−0.286514	+	0.958076i	$0.592496\pi$
$522$		0			0
$523$	311.302			0.595224			0.297612	−	0.954687i	$-0.403810\pi$
$523$	311.302			0.595224			0.297612	+	0.954687i	$0.403810\pi$
$524$	93.9123	+	93.9123i	0.179222	+	0.179222i
$525$		0			0
$526$			189.830i			0.360893i
$527$			159.044i			0.301791i
$528$		0			0
$529$	−522.858			−0.988389
$530$	138.897	−	138.897i	0.262071	−	0.262071i
$531$		0			0
$532$	−59.3869	+	59.3869i	−0.111630	+	0.111630i
$533$	346.976	+	346.976i	0.650987	+	0.650987i
$534$		0			0
$535$		−	226.535i		−	0.423430i
$536$	−40.8892	−	40.8892i	−0.0762857	−	0.0762857i
$537$		0			0
$538$	477.668			0.887859
$539$	236.487	+	236.487i	0.438750	+	0.438750i
$540$		0			0
$541$	629.971	+	629.971i	1.16446	+	1.16446i	0.983489	+	0.180967i	$0.0579226\pi$
$541$	629.971	+	629.971i	1.16446	+	1.16446i	0.180967	+	0.983489i	$0.442077\pi$
$542$	−283.444			−0.522959
$543$		0			0
$544$			30.0740i			0.0552831i
$545$	195.777			0.359224
$546$		0			0
$547$	−804.243			−1.47028			−0.735140	−	0.677916i	$-0.762883\pi$
$547$	−804.243			−1.47028			−0.735140	+	0.677916i	$0.762883\pi$
$548$	275.859	−	275.859i	0.503392	−	0.503392i
$549$		0			0
$550$		−	555.507i		−	1.01001i
$551$	64.8739	−	207.101i	0.117739	−	0.375863i
$552$		0			0
$553$	449.744	+	449.744i	0.813280	+	0.813280i
$554$	261.412	+	261.412i	0.471862	+	0.471862i
$555$		0			0
$556$			395.623i			0.711551i
$557$			108.392i			0.194600i	0.995255	+	0.0973001i	$0.0310207\pi$
$557$			108.392i			0.194600i	−0.995255	+	0.0973001i	$0.968979\pi$
$558$		0			0
$559$	−227.507	+	227.507i	−0.406989	+	0.406989i
$560$			47.2478i			0.0843711i
$561$		0			0
$562$	287.459	+	287.459i	0.511493	+	0.511493i
$563$	567.053	−	567.053i	1.00720	−	1.00720i	0.00722546	−	0.999974i	$-0.497700\pi$
$563$	567.053	−	567.053i	1.00720	−	1.00720i	0.999974	−	0.00722546i	$-0.00229996\pi$
$564$		0			0
$565$	118.118	+	118.118i	0.209059	+	0.209059i
$566$	330.346	−	330.346i	0.583650	−	0.583650i
$567$		0			0
$568$	−121.232	−	121.232i	−0.213436	−	0.213436i
$569$	−733.597	+	733.597i	−1.28927	+	1.28927i	−0.354045	+	0.935228i	$0.615194\pi$
$569$	−733.597	+	733.597i	−1.28927	+	1.28927i	−0.935228	+	0.354045i	$0.884806\pi$
$570$		0			0
$571$	517.048			0.905513			0.452756	−	0.891634i	$-0.350441\pi$
$571$	517.048			0.905513			0.452756	+	0.891634i	$0.350441\pi$
$572$	−398.531	−	398.531i	−0.696732	−	0.696732i
$573$		0			0
$574$	263.884			0.459728
$575$	−50.9772			−0.0886560
$576$		0			0
$577$	359.283	−	359.283i	0.622675	−	0.622675i	−0.323540	−	0.946215i	$-0.604873\pi$
$577$	359.283	−	359.283i	0.622675	−	0.622675i	0.946215	+	0.323540i	$0.104873\pi$
$578$	260.736	−	260.736i	0.451100	−	0.451100i
$579$		0			0
$580$	−56.5773	−	108.191i	−0.0975471	−	0.186535i
$581$	367.201			0.632016
$582$		0			0
$583$	891.019	+	891.019i	1.52834	+	1.52834i
$584$			358.736i			0.614274i
$585$		0			0
$586$			743.832i			1.26934i
$587$	−870.274			−1.48258			−0.741290	−	0.671185i	$-0.765786\pi$
$587$	−870.274			−1.48258			−0.741290	+	0.671185i	$0.765786\pi$
$588$		0			0
$589$			223.877i			0.380097i
$590$	67.5198	−	67.5198i	0.114440	−	0.114440i
$591$		0			0
$592$	−124.404	+	124.404i	−0.210142	+	0.210142i
$593$		−	300.316i		−	0.506435i	−0.967409	−	0.253217i	$-0.918511\pi$
$593$		−	300.316i		−	0.506435i	0.967409	−	0.253217i	$-0.0814888\pi$
$594$		0			0
$595$	−44.4041	+	44.4041i	−0.0746288	+	0.0746288i
$596$	−80.2347			−0.134622
$597$		0			0
$598$	−36.5719	+	36.5719i	−0.0611571	+	0.0611571i
$599$	455.885	+	455.885i	0.761077	+	0.761077i	0.976517	−	0.215440i	$-0.0691187\pi$
$599$	455.885	+	455.885i	0.761077	+	0.761077i	−0.215440	+	0.976517i	$0.569119\pi$
$600$		0			0
$601$	−236.020	−	236.020i	−0.392712	−	0.392712i	0.482941	−	0.875653i	$-0.339569\pi$
$601$	−236.020	−	236.020i	−0.392712	−	0.392712i	−0.875653	+	0.482941i	$0.839569\pi$
$602$			173.024i			0.287416i
$603$		0			0
$604$	−79.6562			−0.131881
$605$	−512.977			−0.847895
$606$		0			0
$607$	−551.803	+	551.803i	−0.909065	+	0.909065i	−0.996197	−	0.0871316i	$-0.972230\pi$
$607$	−551.803	+	551.803i	−0.909065	+	0.909065i	0.0871316	+	0.996197i	$0.472230\pi$
$608$			42.3335i			0.0696275i
$609$		0			0
$610$	246.234			0.403663
$611$	177.298	+	177.298i	0.290177	+	0.290177i
$612$		0			0
$613$			698.725i			1.13984i	0.821699	+	0.569922i	$0.193027\pi$
$613$			698.725i			1.13984i	−0.821699	+	0.569922i	$0.806973\pi$
$614$		−	385.898i		−	0.628498i
$615$		0			0
$616$	−303.092			−0.492033
$617$	−336.935	+	336.935i	−0.546085	+	0.546085i	−0.925306	−	0.379221i	$-0.876192\pi$
$617$	−336.935	+	336.935i	−0.546085	+	0.546085i	0.379221	+	0.925306i	$0.376192\pi$
$618$		0			0
$619$	−344.270	+	344.270i	−0.556172	+	0.556172i	−0.928215	−	0.372043i	$-0.878657\pi$
$619$	−344.270	+	344.270i	−0.556172	+	0.556172i	0.372043	+	0.928215i	$0.378657\pi$
$620$	89.0576	+	89.0576i	0.143641	+	0.143641i
$621$		0			0
$622$		−	801.972i		−	1.28934i
$623$	−664.583	−	664.583i	−1.06675	−	1.06675i
$624$		0			0
$625$	312.303			0.499684
$626$	−243.545	−	243.545i	−0.389050	−	0.389050i
$627$		0			0
$628$	−47.8489	−	47.8489i	−0.0761925	−	0.0761925i
$629$	−233.833			−0.371753
$630$		0			0
$631$			536.982i			0.851001i	0.904958	+	0.425501i	$0.139902\pi$
$631$			536.982i			0.851001i	−0.904958	+	0.425501i	$0.860098\pi$
$632$	320.597			0.507273
$633$		0			0
$634$	41.5168			0.0654839
$635$	−356.691	+	356.691i	−0.561718	+	0.561718i
$636$		0			0
$637$			258.429i			0.405697i
$638$	694.037	−	362.940i	1.08783	−	0.568872i
$639$		0			0
$640$	16.8401	+	16.8401i	0.0263127	+	0.0263127i
$641$	309.470	+	309.470i	0.482793	+	0.482793i	0.906022	−	0.423230i	$-0.139104\pi$
$641$	309.470	+	309.470i	0.482793	+	0.482793i	−0.423230	+	0.906022i	$0.639104\pi$
$642$		0			0
$643$			640.687i			0.996403i	0.867061	+	0.498202i	$0.166006\pi$
$643$			640.687i			0.996403i	−0.867061	+	0.498202i	$0.833994\pi$
$644$			27.8139i			0.0431892i
$645$		0			0
$646$	−39.7856	+	39.7856i	−0.0615876	+	0.0615876i
$647$		−	725.965i		−	1.12205i	−0.827800	−	0.561024i	$-0.810408\pi$
$647$		−	725.965i		−	1.12205i	0.827800	−	0.561024i	$-0.189592\pi$
$648$		0			0
$649$	433.136	+	433.136i	0.667390	+	0.667390i
$650$	303.525	−	303.525i	0.466962	−	0.466962i
$651$		0			0
$652$	−2.57443	−	2.57443i	−0.00394851	−	0.00394851i
$653$	−8.81499	+	8.81499i	−0.0134992	+	0.0134992i	−0.713824	−	0.700325i	$-0.753038\pi$
$653$	−8.81499	+	8.81499i	−0.0134992	+	0.0134992i	0.700325	+	0.713824i	$0.253038\pi$
$654$		0			0
$655$	98.8434	+	98.8434i	0.150906	+	0.150906i
$656$	94.0538	−	94.0538i	0.143375	−	0.143375i
$657$		0			0
$658$	134.840			0.204924
$659$	155.294	+	155.294i	0.235650	+	0.235650i	0.815046	−	0.579396i	$-0.196711\pi$
$659$	155.294	+	155.294i	0.235650	+	0.235650i	−0.579396	+	0.815046i	$0.696711\pi$
$660$		0			0
$661$	−342.761			−0.518550			−0.259275	−	0.965804i	$-0.583484\pi$
$661$	−342.761			−0.518550			−0.259275	+	0.965804i	$0.583484\pi$
$662$	555.865			0.839676
$663$		0			0
$664$	130.878	−	130.878i	0.197106	−	0.197106i
$665$	−62.5052	+	62.5052i	−0.0939928	+	0.0939928i
$666$		0			0
$667$	−33.3060	−	63.6897i	−0.0499340	−	0.0954867i
$668$	123.206			0.184440
$669$		0			0
$670$	−43.0362	−	43.0362i	−0.0642331	−	0.0642331i
$671$			1579.58i			2.35407i
$672$		0			0
$673$			210.555i			0.312860i	0.987689	+	0.156430i	$0.0499986\pi$
$673$			210.555i			0.312860i	−0.987689	+	0.156430i	$0.950001\pi$
$674$	541.534			0.803463
$675$		0			0
$676$		−	97.5083i		−	0.144243i
$677$	90.7657	−	90.7657i	0.134070	−	0.134070i	−0.636887	−	0.770957i	$-0.719778\pi$
$677$	90.7657	−	90.7657i	0.134070	−	0.134070i	0.770957	+	0.636887i	$0.219778\pi$
$678$		0			0
$679$	610.089	−	610.089i	0.898511	−	0.898511i
$680$			31.6531i			0.0465487i
$681$		0			0
$682$	−571.300	+	571.300i	−0.837683	+	0.837683i
$683$	922.155			1.35015			0.675077	−	0.737747i	$-0.264110\pi$
$683$	922.155			1.35015			0.675077	+	0.737747i	$0.264110\pi$
$684$		0			0
$685$	290.344	−	290.344i	0.423859	−	0.423859i
$686$	373.226	+	373.226i	0.544062	+	0.544062i
$687$		0			0
$688$	61.6696	+	61.6696i	0.0896360	+	0.0896360i
$689$			973.693i			1.41320i
$690$		0			0
$691$	−981.161			−1.41991			−0.709957	−	0.704245i	$-0.751286\pi$
$691$	−981.161			−1.41991			−0.709957	+	0.704245i	$0.751286\pi$
$692$	−110.116			−0.159127
$693$		0			0
$694$	−122.863	+	122.863i	−0.177035	+	0.177035i
$695$			416.396i			0.599131i
$696$		0			0
$697$	176.786			0.253638
$698$	−132.409	−	132.409i	−0.189698	−	0.189698i
$699$		0			0
$700$		−	230.838i		−	0.329769i
$701$		−	625.727i		−	0.892620i	−0.894878	−	0.446310i	$-0.852738\pi$
$701$		−	625.727i		−	0.892620i	0.894878	−	0.446310i	$-0.147262\pi$
$702$		0			0
$703$	−329.153			−0.468212
$704$	−108.029	+	108.029i	−0.153450	+	0.153450i
$705$		0			0
$706$	92.9741	−	92.9741i	0.131691	−	0.131691i
$707$	153.344	+	153.344i	0.216895	+	0.216895i
$708$		0			0
$709$			251.052i			0.354092i	0.984203	+	0.177046i	$0.0566542\pi$
$709$			251.052i			0.354092i	−0.984203	+	0.177046i	$0.943346\pi$
$710$	−127.598	−	127.598i	−0.179715	−	0.179715i
$711$		0			0
$712$	−473.743			−0.665370
$713$	52.4264	+	52.4264i	0.0735294	+	0.0735294i
$714$		0			0
$715$	−419.457	−	419.457i	−0.586653	−	0.586653i
$716$	84.5205			0.118045
$717$		0			0
$718$		−	662.888i		−	0.923242i
$719$	809.581			1.12598			0.562991	−	0.826463i	$-0.309651\pi$
$719$	809.581			1.12598			0.562991	+	0.826463i	$0.309651\pi$
$720$		0			0
$721$	85.8212			0.119031
$722$	304.996	−	304.996i	0.422432	−	0.422432i
$723$		0			0
$724$		−	116.808i		−	0.161337i
$725$	276.419	+	528.586i	0.381268	+	0.729084i
$726$		0			0
$727$	−453.684	−	453.684i	−0.624050	−	0.624050i	0.322515	−	0.946564i	$-0.395472\pi$
$727$	−453.684	−	453.684i	−0.624050	−	0.624050i	−0.946564	+	0.322515i	$0.895472\pi$
$728$	−165.607	−	165.607i	−0.227483	−	0.227483i
$729$		0			0
$730$			377.573i			0.517223i
$731$			115.916i			0.158571i
$732$		0			0
$733$	2.06963	−	2.06963i	0.00282350	−	0.00282350i	−0.705694	−	0.708517i	$-0.749364\pi$
$733$	2.06963	−	2.06963i	0.00282350	−	0.00282350i	0.708517	+	0.705694i	$0.249364\pi$
$734$		−	587.623i		−	0.800577i
$735$		0			0
$736$	9.91345	+	9.91345i	0.0134694	+	0.0134694i
$737$	276.075	−	276.075i	0.374593	−	0.374593i
$738$		0			0
$739$	48.6910	+	48.6910i	0.0658877	+	0.0658877i	0.739283	−	0.673395i	$-0.235165\pi$
$739$	48.6910	+	48.6910i	0.0658877	+	0.0658877i	−0.673395	+	0.739283i	$0.735165\pi$
$740$	−130.936	+	130.936i	−0.176941	+	0.176941i
$741$		0			0
$742$	370.259	+	370.259i	0.499001	+	0.499001i
$743$	−916.050	+	916.050i	−1.23291	+	1.23291i	−0.270066	+	0.962842i	$0.587045\pi$
$743$	−916.050	+	916.050i	−1.23291	+	1.23291i	−0.962842	+	0.270066i	$0.912955\pi$
$744$		0			0
$745$	−84.4477			−0.113353
$746$	−407.090	−	407.090i	−0.545697	−	0.545697i
$747$		0			0
$748$	−203.053			−0.271462
$749$	603.874			0.806241
$750$		0			0
$751$	214.024	−	214.024i	0.284985	−	0.284985i	−0.550108	−	0.835093i	$-0.685414\pi$
$751$	214.024	−	214.024i	0.284985	−	0.284985i	0.835093	+	0.550108i	$0.185414\pi$
$752$	48.0598	−	48.0598i	0.0639093	−	0.0639093i
$753$		0			0
$754$	577.525	+	180.909i	0.765948	+	0.239932i
$755$	−83.8388			−0.111045
$756$		0			0
$757$	−15.4202	−	15.4202i	−0.0203702	−	0.0203702i	0.696848	−	0.717219i	$-0.254585\pi$
$757$	−15.4202	−	15.4202i	−0.0203702	−	0.0203702i	−0.717219	+	0.696848i	$0.754585\pi$
$758$			686.419i			0.905565i
$759$		0			0
$760$			44.5564i			0.0586268i
$761$	−1117.40			−1.46834			−0.734168	−	0.678968i	$-0.762427\pi$
$761$	−1117.40			−1.46834			−0.734168	+	0.678968i	$0.762427\pi$
$762$		0			0
$763$			521.882i			0.683987i
$764$	443.154	−	443.154i	0.580045	−	0.580045i
$765$		0			0
$766$	−312.930	+	312.930i	−0.408524	+	0.408524i
$767$			473.325i			0.617112i
$768$		0			0
$769$	972.034	−	972.034i	1.26402	−	1.26402i	0.314898	−	0.949125i	$-0.398030\pi$
$769$	972.034	−	972.034i	1.26402	−	1.26402i	0.949125	−	0.314898i	$-0.101970\pi$
$770$	−319.007			−0.414295
$771$		0			0
$772$	−279.633	+	279.633i	−0.362218	+	0.362218i
$773$	−488.572	−	488.572i	−0.632046	−	0.632046i	0.316535	−	0.948581i	$-0.397481\pi$
$773$	−488.572	−	488.572i	−0.632046	−	0.632046i	−0.948581	+	0.316535i	$0.897481\pi$
$774$		0			0
$775$	−435.108	−	435.108i	−0.561429	−	0.561429i
$776$		−	434.898i		−	0.560435i
$777$		0			0
$778$	−47.2961			−0.0607919
$779$	248.852			0.319450
$780$		0			0
$781$	818.531	−	818.531i	1.04806	−	1.04806i
$782$			18.6336i			0.0238281i
$783$		0			0
$784$	70.0516			0.0893515
$785$	−50.3613	−	50.3613i	−0.0641545	−	0.0641545i
$786$		0			0
$787$			373.182i			0.474183i	0.971487	+	0.237092i	$0.0761942\pi$
$787$			373.182i			0.474183i	−0.971487	+	0.237092i	$0.923806\pi$
$788$		−	269.146i		−	0.341556i
$789$		0			0
$790$	337.431			0.427127
$791$	−314.867	+	314.867i	−0.398063	+	0.398063i
$792$		0			0
$793$	−863.071	+	863.071i	−1.08836	+	1.08836i
$794$	453.764	+	453.764i	0.571491	+	0.571491i
$795$		0			0
$796$			274.009i			0.344232i
$797$	−617.010	−	617.010i	−0.774166	−	0.774166i	0.204666	−	0.978832i	$-0.434389\pi$
$797$	−617.010	−	617.010i	−0.774166	−	0.774166i	−0.978832	+	0.204666i	$0.934389\pi$
$798$		0			0
$799$	90.3344			0.113059
$800$	−82.2756	−	82.2756i	−0.102845	−	0.102845i
$801$		0			0
$802$	368.308	+	368.308i	0.459237	+	0.459237i
$803$	−2422.11			−3.01632
$804$		0			0
$805$			29.2743i			0.0363656i
$806$	−624.308			−0.774575
$807$		0			0
$808$	109.310			0.135285
$809$	914.906	−	914.906i	1.13091	−	1.13091i	0.140884	−	0.990026i	$-0.455006\pi$
$809$	914.906	−	914.906i	1.13091	−	1.13091i	0.990026	−	0.140884i	$-0.0449943\pi$
$810$		0			0
$811$		−	489.553i		−	0.603641i	−0.953365	−	0.301821i	$-0.902406\pi$
$811$		−	489.553i		−	0.603641i	0.953365	−	0.301821i	$-0.0975943\pi$
$812$	288.403	−	150.818i	0.355177	−	0.185737i
$813$		0			0
$814$	−839.948	−	839.948i	−1.03188	−	1.03188i
$815$	−2.70960	−	2.70960i	−0.00332467	−	0.00332467i
$816$		0			0
$817$			163.168i			0.199716i
$818$		−	250.816i		−	0.306621i
$819$		0			0
$820$	98.9924	−	98.9924i	0.120722	−	0.120722i
$821$		−	1321.42i		−	1.60952i	−0.593601	−	0.804760i	$-0.702294\pi$
$821$		−	1321.42i		−	1.60952i	0.593601	−	0.804760i	$-0.297706\pi$
$822$		0			0
$823$	870.924	+	870.924i	1.05823	+	1.05823i	0.998196	+	0.0600342i	$0.0191210\pi$
$823$	870.924	+	870.924i	1.05823	+	1.05823i	0.0600342	+	0.998196i	$0.480879\pi$
$824$	30.5885	−	30.5885i	0.0371220	−	0.0371220i
$825$		0			0
$826$	179.987	+	179.987i	0.217903	+	0.217903i
$827$	1000.07	−	1000.07i	1.20927	−	1.20927i	0.238005	−	0.971264i	$-0.423506\pi$
$827$	1000.07	−	1000.07i	1.20927	−	1.20927i	0.971264	−	0.238005i	$-0.0764936\pi$
$828$		0			0
$829$	−1005.97	−	1005.97i	−1.21348	−	1.21348i	−0.969876	−	0.243600i	$-0.921672\pi$
$829$	−1005.97	−	1005.97i	−1.21348	−	1.21348i	−0.243600	−	0.969876i	$-0.578328\pi$
$830$	137.750	−	137.750i	0.165964	−	0.165964i
$831$		0			0
$832$	−118.052			−0.141889
$833$	65.8354	+	65.8354i	0.0790341	+	0.0790341i
$834$		0			0
$835$	129.676			0.155300
$836$	−285.827			−0.341898
$837$		0			0
$838$	571.234	−	571.234i	0.681664	−	0.681664i
$839$	126.097	−	126.097i	0.150294	−	0.150294i	−0.627955	−	0.778249i	$-0.716108\pi$
$839$	126.097	−	126.097i	0.150294	−	0.150294i	0.778249	+	0.627955i	$0.216108\pi$
$840$		0			0
$841$	−479.803	+	690.702i	−0.570515	+	0.821287i
$842$	−1087.69			−1.29179
$843$		0			0
$844$	−4.41524	−	4.41524i	−0.00523133	−	0.00523133i
$845$		−	102.628i		−	0.121454i
$846$		0			0
$847$		−	1367.44i		−	1.61445i
$848$	263.936			0.311245
$849$		0			0
$850$		−	154.647i		−	0.181938i
$851$	−77.0795	+	77.0795i	−0.0905752	+	0.0905752i
$852$		0			0
$853$	585.790	−	585.790i	0.686741	−	0.686741i	−0.274769	−	0.961510i	$-0.588602\pi$
$853$	585.790	−	585.790i	0.686741	−	0.686741i	0.961510	+	0.274769i	$0.0886015\pi$
$854$			656.387i			0.768603i
$855$		0			0
$856$	215.234	−	215.234i	0.251441	−	0.251441i
$857$	−1295.24			−1.51136			−0.755680	−	0.654941i	$-0.772694\pi$
$857$	−1295.24			−1.51136			−0.755680	+	0.654941i	$0.772694\pi$
$858$		0			0
$859$	167.580	−	167.580i	0.195087	−	0.195087i	−0.602803	−	0.797890i	$-0.705950\pi$
$859$	167.580	−	167.580i	0.195087	−	0.195087i	0.797890	+	0.602803i	$0.205950\pi$
$860$	64.9077	+	64.9077i	0.0754741	+	0.0754741i
$861$		0			0
$862$	−671.611	−	671.611i	−0.779131	−	0.779131i
$863$			1473.90i			1.70787i	0.520376	+	0.853937i	$0.325792\pi$
$863$			1473.90i			1.70787i	−0.520376	+	0.853937i	$0.674208\pi$
$864$		0			0
$865$	−115.898			−0.133986
$866$	153.813			0.177614
$867$		0			0
$868$	−237.401	+	237.401i	−0.273503	+	0.273503i
$869$			2164.60i			2.49091i
$870$		0			0
$871$	301.690			0.346372
$872$	186.010	+	186.010i	0.213314	+	0.213314i
$873$		0			0
$874$			26.2295i			0.0300108i
$875$		−	538.258i		−	0.615152i
$876$		0			0
$877$	−1338.15			−1.52582			−0.762912	−	0.646503i	$-0.776231\pi$
$877$	−1338.15			−1.52582			−0.762912	+	0.646503i	$0.776231\pi$
$878$	760.226	−	760.226i	0.865861	−	0.865861i
$879$		0			0
$880$	−113.701	+	113.701i	−0.129206	+	0.129206i
$881$	223.361	+	223.361i	0.253532	+	0.253532i	0.822417	−	0.568885i	$-0.192625\pi$
$881$	223.361	+	223.361i	0.253532	+	0.253532i	−0.568885	+	0.822417i	$0.692625\pi$
$882$		0			0
$883$		−	81.2390i		−	0.0920034i	−0.998941	−	0.0460017i	$-0.985352\pi$
$883$		−	81.2390i		−	0.0920034i	0.998941	−	0.0460017i	$-0.0146480\pi$
$884$	−110.947	−	110.947i	−0.125505	−	0.125505i
$885$		0			0
$886$	345.699			0.390179
$887$	−231.006	−	231.006i	−0.260436	−	0.260436i	0.564795	−	0.825231i	$-0.308955\pi$
$887$	−231.006	−	231.006i	−0.260436	−	0.260436i	−0.825231	+	0.564795i	$0.808955\pi$
$888$		0			0
$889$	−950.830	−	950.830i	−1.06955	−	1.06955i
$890$	−498.618			−0.560245
$891$		0			0
$892$		−	492.175i		−	0.551766i
$893$	127.159			0.142395
$894$		0			0
$895$	88.9585			0.0993950
$896$	−44.8907	+	44.8907i	−0.0501012	+	0.0501012i
$897$		0			0
$898$		−	151.660i		−	0.168887i
$899$	259.335	−	827.890i	0.288471	−	0.920901i
$900$		0			0
$901$	248.051	+	248.051i	0.275306	+	0.275306i
$902$	635.031	+	635.031i	0.704025	+	0.704025i
$903$		0			0
$904$			224.451i			0.248286i
$905$		−	122.941i		−	0.135846i
$906$		0			0
$907$	669.321	−	669.321i	0.737950	−	0.737950i	−0.234231	−	0.972181i	$-0.575257\pi$
$907$	669.321	−	669.321i	0.737950	−	0.737950i	0.972181	+	0.234231i	$0.0752572\pi$
$908$			60.3362i			0.0664495i
$909$		0			0
$910$	−174.303	−	174.303i	−0.191542	−	0.191542i
$911$	438.449	−	438.449i	0.481283	−	0.481283i	−0.424258	−	0.905541i	$-0.639465\pi$
$911$	438.449	−	438.449i	0.481283	−	0.481283i	0.905541	+	0.424258i	$0.139465\pi$
$912$		0			0
$913$	883.662	+	883.662i	0.967866	+	0.967866i
$914$	243.195	−	243.195i	0.266077	−	0.266077i
$915$		0			0
$916$	9.66090	+	9.66090i	0.0105468	+	0.0105468i
$917$	−263.487	+	263.487i	−0.287336	+	0.287336i
$918$		0			0
$919$	762.770			0.830000			0.415000	−	0.909821i	$-0.363782\pi$
$919$	762.770			0.830000			0.415000	+	0.909821i	$0.363782\pi$
$920$	10.4340	+	10.4340i	0.0113413	+	0.0113413i
$921$		0			0
$922$	946.648			1.02673
$923$	894.479			0.969099
$924$		0			0
$925$	639.713	−	639.713i	0.691582	−	0.691582i
$926$	−491.254	+	491.254i	−0.530511	+	0.530511i
$927$		0			0
$928$	49.0384	−	156.548i	0.0528431	−	0.168694i
$929$	140.665			0.151416			0.0757078	−	0.997130i	$-0.475878\pi$
$929$	140.665			0.151416			0.0757078	+	0.997130i	$0.475878\pi$
$930$		0			0
$931$	92.6728	+	92.6728i	0.0995411	+	0.0995411i
$932$			14.8795i			0.0159651i
$933$		0			0
$934$		−	924.548i		−	0.989880i
$935$	−213.715			−0.228572
$936$		0			0
$937$			272.439i			0.290756i	0.989376	+	0.145378i	$0.0464399\pi$
$937$			272.439i			0.290756i	−0.989376	+	0.145378i	$0.953560\pi$
$938$	114.721	−	114.721i	0.122304	−	0.122304i
$939$		0			0
$940$	50.5833	−	50.5833i	0.0538120	−	0.0538120i
$941$		−	1010.00i		−	1.07332i	−0.843797	−	0.536662i	$-0.819685\pi$
$941$		−	1010.00i		−	1.07332i	0.843797	−	0.536662i	$-0.180315\pi$
$942$		0			0
$943$	58.2749	−	58.2749i	0.0617973	−	0.0617973i
$944$	128.303			0.135914
$945$		0			0
$946$	−416.379	+	416.379i	−0.440147	+	0.440147i
$947$	−416.390	−	416.390i	−0.439694	−	0.439694i	0.452215	−	0.891909i	$-0.350634\pi$
$947$	−416.390	−	416.390i	−0.439694	−	0.439694i	−0.891909	+	0.452215i	$0.850634\pi$
$948$		0			0
$949$	−1323.42	−	1323.42i	−1.39454	−	1.39454i
$950$		−	217.689i		−	0.229146i
$951$		0			0
$952$	−84.3777			−0.0886321
$953$	−1043.49			−1.09496			−0.547479	−	0.836820i	$-0.684412\pi$
$953$	−1043.49			−1.09496			−0.547479	+	0.836820i	$0.684412\pi$
$954$		0			0
$955$	466.423	−	466.423i	0.488401	−	0.488401i
$956$			730.867i			0.764505i
$957$		0			0
$958$	301.425			0.314640
$959$	773.969	+	773.969i	0.807058	+	0.807058i
$960$		0			0
$961$		−	66.0454i		−	0.0687257i
$962$		−	917.883i		−	0.954140i
$963$		0			0
$964$	−249.751			−0.259078
$965$	−294.315	+	294.315i	−0.304990	+	0.304990i
$966$		0			0
$967$	−267.895	+	267.895i	−0.277038	+	0.277038i	−0.831925	−	0.554888i	$-0.812761\pi$
$967$	−267.895	+	267.895i	−0.277038	+	0.277038i	0.554888	+	0.831925i	$0.312761\pi$
$968$	−487.385	−	487.385i	−0.503497	−	0.503497i
$969$		0			0
$970$		−	457.733i		−	0.471890i
$971$	−920.289	−	920.289i	−0.947775	−	0.947775i	0.0509277	−	0.998702i	$-0.483782\pi$
$971$	−920.289	−	920.289i	−0.947775	−	0.947775i	−0.998702	+	0.0509277i	$0.983782\pi$
$972$		0			0
$973$	−1109.99			−1.14079
$974$	−57.3072	−	57.3072i	−0.0588370	−	0.0588370i
$975$		0			0
$976$	233.950	+	233.950i	0.239703	+	0.239703i
$977$	−1565.15			−1.60200			−0.801000	−	0.598665i	$-0.795698\pi$
$977$	−1565.15			−1.60200			−0.801000	+	0.598665i	$0.795698\pi$
$978$		0			0
$979$		−	3198.61i		−	3.26722i
$980$	73.7298			0.0752345
$981$		0			0
$982$	844.506			0.859986
$983$	−718.622	+	718.622i	−0.731050	+	0.731050i	−0.970828	−	0.239778i	$-0.922925\pi$
$983$	−718.622	+	718.622i	−0.731050	+	0.731050i	0.239778	+	0.970828i	$0.422925\pi$
$984$		0			0
$985$		−	283.278i		−	0.287592i
$986$	193.213	−	101.039i	0.195956	−	0.102473i
$987$		0			0
$988$	−156.174	−	156.174i	−0.158070	−	0.158070i
$989$	38.2099	+	38.2099i	0.0386349	+	0.0386349i
$990$		0			0
$991$		−	449.212i		−	0.453292i	−0.973977	−	0.226646i	$-0.927224\pi$
$991$		−	449.212i		−	0.453292i	0.973977	−	0.226646i	$-0.0727760\pi$
$992$			169.229i			0.170594i
$993$		0			0
$994$	340.136	−	340.136i	0.342190	−	0.342190i
$995$			288.396i			0.289846i
$996$		0			0
$997$	752.971	+	752.971i	0.755237	+	0.755237i	0.975451	−	0.220214i	$-0.0706757\pi$
$997$	752.971	+	752.971i	0.755237	+	0.755237i	−0.220214	+	0.975451i	$0.570676\pi$
$998$	422.238	−	422.238i	0.423084	−	0.423084i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	522.3.f.h.505.4	yes	10
3.2	odd	2		522.3.f.g.505.2	yes	10
29.17	odd	4	inner	522.3.f.h.307.2	yes	10
87.17	even	4		522.3.f.g.307.4	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
522.3.f.g.307.4	✓	10	87.17	even	4
522.3.f.g.505.2	yes	10	3.2	odd	2
522.3.f.h.307.2	yes	10	29.17	odd	4	inner
522.3.f.h.505.4	yes	10	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:	\( N \)	\(=\)	\( 522 = 2 \cdot 3^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	522.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 + 1.00000i) q^{2} +2.00000i q^{4} +2.10502i q^{5} -5.61134 q^{7} +(-2.00000 + 2.00000i) q^{8} +O(q^{10})\)	\(q+(1.00000 + 1.00000i) q^{2} +2.00000i q^{4} +2.10502i q^{5} -5.61134 q^{7} +(-2.00000 + 2.00000i) q^{8} +(-2.10502 + 2.10502i) q^{10} +(-13.5036 - 13.5036i) q^{11} -14.7565i q^{13} +(-5.61134 - 5.61134i) q^{14} -4.00000 q^{16} +(-3.75925 - 3.75925i) q^{17} +(-5.29169 - 5.29169i) q^{19} -4.21003 q^{20} -27.0071i q^{22} -2.47836 q^{23} +20.5689 q^{25} +(14.7565 - 14.7565i) q^{26} -11.2227i q^{28} +(13.4387 + 25.6983i) q^{29} +(-21.1537 - 21.1537i) q^{31} +(-4.00000 - 4.00000i) q^{32} -7.51851i q^{34} -11.8120i q^{35} +(31.1010 - 31.1010i) q^{37} -10.5834i q^{38} +(-4.21003 - 4.21003i) q^{40} +(-23.5134 + 23.5134i) q^{41} +(-15.4174 - 15.4174i) q^{43} +(27.0071 - 27.0071i) q^{44} +(-2.47836 - 2.47836i) q^{46} +(-12.0149 + 12.0149i) q^{47} -17.5129 q^{49} +(20.5689 + 20.5689i) q^{50} +29.5130 q^{52} -65.9840 q^{53} +(28.4252 - 28.4252i) q^{55} +(11.2227 - 11.2227i) q^{56} +(-12.2596 + 39.1370i) q^{58} -32.0757 q^{59} +(-58.4876 - 58.4876i) q^{61} -42.3073i q^{62} -8.00000i q^{64} +31.0627 q^{65} +20.4446i q^{67} +(7.51851 - 7.51851i) q^{68} +(11.8120 - 11.8120i) q^{70} +60.6159i q^{71} +(89.6840 - 89.6840i) q^{73} +62.2019 q^{74} +(10.5834 - 10.5834i) q^{76} +(75.7731 + 75.7731i) q^{77} +(-80.1492 - 80.1492i) q^{79} -8.42006i q^{80} -47.0269 q^{82} -65.4392 q^{83} +(7.91329 - 7.91329i) q^{85} -30.8348i q^{86} +54.0143 q^{88} +(118.436 + 118.436i) q^{89} +82.8037i q^{91} -4.95673i q^{92} -24.0299 q^{94} +(11.1391 - 11.1391i) q^{95} +(-108.724 + 108.724i) q^{97} +(-17.5129 - 17.5129i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 10 q^{2} - 20 q^{8}+O(q^{10}) \) 10 * q + 10 * q^2 - 20 * q^8	\( 10 q + 10 q^{2} - 20 q^{8} + 12 q^{10} - 40 q^{16} - 6 q^{17} - 32 q^{19} + 24 q^{20} - 16 q^{23} - 110 q^{25} + 4 q^{26} - 22 q^{29} - 8 q^{31} - 40 q^{32} + 46 q^{37} + 24 q^{40} + 58 q^{41} + 56 q^{43} - 16 q^{46} - 192 q^{47} - 50 q^{49} - 110 q^{50} + 8 q^{52} + 180 q^{53} + 48 q^{55} - 46 q^{58} + 24 q^{59} + 22 q^{61} + 248 q^{65} + 12 q^{68} - 48 q^{70} - 62 q^{73} + 92 q^{74} + 64 q^{76} + 192 q^{77} - 200 q^{79} + 116 q^{82} - 296 q^{83} - 196 q^{85} - 26 q^{89} - 384 q^{94} - 32 q^{95} + 10 q^{97} - 50 q^{98}+O(q^{100}) \) 10 * q + 10 * q^2 - 20 * q^8 + 12 * q^10 - 40 * q^16 - 6 * q^17 - 32 * q^19 + 24 * q^20 - 16 * q^23 - 110 * q^25 + 4 * q^26 - 22 * q^29 - 8 * q^31 - 40 * q^32 + 46 * q^37 + 24 * q^40 + 58 * q^41 + 56 * q^43 - 16 * q^46 - 192 * q^47 - 50 * q^49 - 110 * q^50 + 8 * q^52 + 180 * q^53 + 48 * q^55 - 46 * q^58 + 24 * q^59 + 22 * q^61 + 248 * q^65 + 12 * q^68 - 48 * q^70 - 62 * q^73 + 92 * q^74 + 64 * q^76 + 192 * q^77 - 200 * q^79 + 116 * q^82 - 296 * q^83 - 196 * q^85 - 26 * q^89 - 384 * q^94 - 32 * q^95 + 10 * q^97 - 50 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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