LMFDB - Embedded newform 243.4.e.c.55.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [243,4,Mod(28,243)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(243, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([8]))

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

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

chi := DirichletCharacter("243.28");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 243 = 3^{5} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	243.e (of order $9$, degree $6$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$14.3374641314$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$8$ over $\Q(\zeta_{9})$
Twist minimal:	no (minimal twist has level 27)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			55.7
Character	$\chi$	$=$	243.55
Dual form			243.4.e.c.190.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.91280 - 1.42414i) q^{2} +(7.15349 - 6.00249i) q^{4} +(2.58756 + 14.6748i) q^{5} +(3.34538 + 2.80711i) q^{7} +(2.78612 - 4.82571i) q^{8} +O(q^{10})$	\(q+(3.91280 - 1.42414i) q^{2} +(7.15349 - 6.00249i) q^{4} +(2.58756 + 14.6748i) q^{5} +(3.34538 + 2.80711i) q^{7} +(2.78612 - 4.82571i) q^{8} +(31.0237 + 53.7346i) q^{10} +(-11.2362 + 63.7239i) q^{11} +(3.38506 + 1.23206i) q^{13} +(17.0876 + 6.21936i) q^{14} +(-8.94347 + 50.7209i) q^{16} +(-18.0500 - 31.2635i) q^{17} +(37.4017 - 64.7817i) q^{19} +(106.596 + 89.4443i) q^{20} +(46.7868 + 265.341i) q^{22} +(160.602 - 134.761i) q^{23} +(-91.1929 + 33.1915i) q^{25} +14.9997 q^{26} +40.7808 q^{28} +(-84.3064 + 30.6850i) q^{29} +(-18.9578 + 15.9075i) q^{31} +(44.9808 + 255.099i) q^{32} +(-115.150 - 96.6221i) q^{34} +(-32.5374 + 56.3564i) q^{35} +(38.9926 + 67.5371i) q^{37} +(54.0872 - 306.744i) q^{38} +(78.0256 + 28.3990i) q^{40} +(112.663 + 41.0058i) q^{41} +(54.5017 - 309.094i) q^{43} +(302.124 + 523.294i) q^{44} +(436.484 - 756.013i) q^{46} +(223.765 + 187.762i) q^{47} +(-56.2496 - 319.007i) q^{49} +(-309.551 + 259.744i) q^{50} +(31.6104 - 11.5053i) q^{52} +512.684 q^{53} -964.210 q^{55} +(22.8669 - 8.32289i) q^{56} +(-286.174 + 240.129i) q^{58} +(-0.614011 - 3.48223i) q^{59} +(-276.655 - 232.141i) q^{61} +(-51.5236 + 89.2414i) q^{62} +(333.285 + 577.266i) q^{64} +(-9.32119 + 52.8631i) q^{65} +(-177.368 - 64.5567i) q^{67} +(-316.779 - 115.298i) q^{68} +(-47.0528 + 266.850i) q^{70} +(-243.711 - 422.120i) q^{71} +(-24.5604 + 42.5399i) q^{73} +(248.753 + 208.728i) q^{74} +(-121.299 - 687.919i) q^{76} +(-216.469 + 181.639i) q^{77} +(-543.271 + 197.734i) q^{79} -767.462 q^{80} +499.225 q^{82} +(-500.182 + 182.051i) q^{83} +(412.080 - 345.776i) q^{85} +(-226.940 - 1287.04i) q^{86} +(276.207 + 231.765i) q^{88} +(358.549 - 621.025i) q^{89} +(7.86579 + 13.6239i) q^{91} +(339.962 - 1928.02i) q^{92} +(1142.95 + 416.000i) q^{94} +(1047.44 + 381.236i) q^{95} +(-57.7162 + 327.325i) q^{97} +(-674.406 - 1168.11i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 3 q^{2} + 3 q^{4} - 21 q^{5} + 3 q^{7} - 75 q^{8}+O(q^{10}) $ 48 * q + 3 * q^2 + 3 * q^4 - 21 * q^5 + 3 * q^7 - 75 * q^8	$ 48 q + 3 q^{2} + 3 q^{4} - 21 q^{5} + 3 q^{7} - 75 q^{8} - 3 q^{10} - 159 q^{11} + 3 q^{13} - 336 q^{14} - 45 q^{16} - 207 q^{17} - 3 q^{19} + 681 q^{20} + 111 q^{22} + 33 q^{23} + 435 q^{25} + 1914 q^{26} - 12 q^{28} - 51 q^{29} + 111 q^{31} + 1647 q^{32} - 513 q^{34} - 1257 q^{35} - 3 q^{37} - 525 q^{38} - 6 q^{40} + 447 q^{41} + 516 q^{43} - 2211 q^{44} - 3 q^{46} + 2109 q^{47} - 591 q^{49} - 4938 q^{50} - 1350 q^{52} + 2736 q^{53} - 12 q^{55} - 7773 q^{56} - 888 q^{58} + 3048 q^{59} + 57 q^{61} - 2118 q^{62} - 195 q^{64} + 3297 q^{65} + 2082 q^{67} + 3573 q^{68} + 1524 q^{70} - 3105 q^{71} - 219 q^{73} + 9006 q^{74} - 1425 q^{76} - 8985 q^{77} - 1401 q^{79} + 9870 q^{80} - 12 q^{82} - 8511 q^{83} - 1827 q^{85} + 12507 q^{86} - 3693 q^{88} - 5202 q^{89} + 267 q^{91} + 5118 q^{92} - 2211 q^{94} + 5178 q^{95} + 1569 q^{97} - 4392 q^{98}+O(q^{100}) $ 48 * q + 3 * q^2 + 3 * q^4 - 21 * q^5 + 3 * q^7 - 75 * q^8 - 3 * q^10 - 159 * q^11 + 3 * q^13 - 336 * q^14 - 45 * q^16 - 207 * q^17 - 3 * q^19 + 681 * q^20 + 111 * q^22 + 33 * q^23 + 435 * q^25 + 1914 * q^26 - 12 * q^28 - 51 * q^29 + 111 * q^31 + 1647 * q^32 - 513 * q^34 - 1257 * q^35 - 3 * q^37 - 525 * q^38 - 6 * q^40 + 447 * q^41 + 516 * q^43 - 2211 * q^44 - 3 * q^46 + 2109 * q^47 - 591 * q^49 - 4938 * q^50 - 1350 * q^52 + 2736 * q^53 - 12 * q^55 - 7773 * q^56 - 888 * q^58 + 3048 * q^59 + 57 * q^61 - 2118 * q^62 - 195 * q^64 + 3297 * q^65 + 2082 * q^67 + 3573 * q^68 + 1524 * q^70 - 3105 * q^71 - 219 * q^73 + 9006 * q^74 - 1425 * q^76 - 8985 * q^77 - 1401 * q^79 + 9870 * q^80 - 12 * q^82 - 8511 * q^83 - 1827 * q^85 + 12507 * q^86 - 3693 * q^88 - 5202 * q^89 + 267 * q^91 + 5118 * q^92 - 2211 * q^94 + 5178 * q^95 + 1569 * q^97 - 4392 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/243\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{8}{9}\right)$

Coefficient data

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

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

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

$2$	3.91280	−	1.42414i	1.38339	−	0.503511i	0.460182	−	0.887824i	$-0.347784\pi$
$2$	3.91280	−	1.42414i	1.38339	−	0.503511i	0.923203	+	0.384313i	$0.125562\pi$
$3$		0			0
$3$		0			0
$4$	7.15349	−	6.00249i	0.894187	−	0.750312i
$5$	2.58756	+	14.6748i	0.231439	+	1.31255i	0.849985	+	0.526806i	$0.176611\pi$
$5$	2.58756	+	14.6748i	0.231439	+	1.31255i	−0.618546	+	0.785748i	$0.712278\pi$
$6$		0			0
$7$	3.34538	+	2.80711i	0.180634	+	0.151570i	0.728621	−	0.684917i	$-0.240161\pi$
$7$	3.34538	+	2.80711i	0.180634	+	0.151570i	−0.547988	+	0.836486i	$0.684606\pi$
$8$	2.78612	−	4.82571i	0.123130	−	0.213268i
$9$		0			0
$10$	31.0237	+	53.7346i	0.981055	+	1.69924i
$11$	−11.2362	+	63.7239i	−0.307987	+	1.74668i	0.301116	+	0.953587i	$0.402641\pi$
$11$	−11.2362	+	63.7239i	−0.307987	+	1.74668i	−0.609103	+	0.793091i	$0.708470\pi$
$12$		0			0
$13$	3.38506	+	1.23206i	0.0722189	+	0.0262855i	0.377877	−	0.925856i	$-0.376654\pi$
$13$	3.38506	+	1.23206i	0.0722189	+	0.0262855i	−0.305658	+	0.952141i	$0.598876\pi$
$14$	17.0876	+	6.21936i	0.326203	+	0.118728i
$15$		0			0
$16$	−8.94347	+	50.7209i	−0.139742	+	0.792515i
$17$	−18.0500	−	31.2635i	−0.257516	−	0.446030i	0.708060	−	0.706152i	$-0.249571\pi$
$17$	−18.0500	−	31.2635i	−0.257516	−	0.446030i	−0.965576	+	0.260122i	$0.916237\pi$
$18$		0			0
$19$	37.4017	−	64.7817i	0.451608	−	0.782207i	−0.546878	−	0.837212i	$-0.684184\pi$
$19$	37.4017	−	64.7817i	0.451608	−	0.782207i	0.998486	+	0.0550047i	$0.0175174\pi$
$20$	106.596	+	89.4443i	1.19177	+	1.00002i
$21$		0			0
$22$	46.7868	+	265.341i	0.453408	+	2.57140i
$23$	160.602	−	134.761i	1.45599	−	1.22172i	0.527931	−	0.849287i	$-0.322968\pi$
$23$	160.602	−	134.761i	1.45599	−	1.22172i	0.928059	−	0.372433i	$-0.121476\pi$
$24$		0			0
$25$	−91.1929	+	33.1915i	−0.729543	+	0.265532i
$26$	14.9997			0.113142
$27$		0			0
$28$	40.7808			0.275245
$29$	−84.3064	+	30.6850i	−0.539838	+	0.196485i	−0.597526	−	0.801850i	$-0.703849\pi$
$29$	−84.3064	+	30.6850i	−0.539838	+	0.196485i	0.0576877	+	0.998335i	$0.481627\pi$
$30$		0			0
$31$	−18.9578	+	15.9075i	−0.109836	+	0.0921634i	−0.696052	−	0.717992i	$-0.745062\pi$
$31$	−18.9578	+	15.9075i	−0.109836	+	0.0921634i	0.586216	+	0.810155i	$0.300617\pi$
$32$	44.9808	+	255.099i	0.248486	+	1.40923i
$33$		0			0
$34$	−115.150	−	96.6221i	−0.580824	−	0.487369i
$35$	−32.5374	+	56.3564i	−0.157138	+	0.272171i
$36$		0			0
$37$	38.9926	+	67.5371i	0.173252	+	0.300082i	0.939555	−	0.342398i	$-0.111239\pi$
$37$	38.9926	+	67.5371i	0.173252	+	0.300082i	−0.766303	+	0.642480i	$0.777906\pi$
$38$	54.0872	−	306.744i	0.230897	−	1.30948i
$39$		0			0
$40$	78.0256	+	28.3990i	0.308423	+	0.112257i
$41$	112.663	+	41.0058i	0.429145	+	0.156196i	0.547557	−	0.836769i	$-0.315558\pi$
$41$	112.663	+	41.0058i	0.429145	+	0.156196i	−0.118412	+	0.992965i	$0.537780\pi$
$42$		0			0
$43$	54.5017	−	309.094i	0.193289	−	1.09620i	−0.721546	−	0.692367i	$-0.756568\pi$
$43$	54.5017	−	309.094i	0.193289	−	1.09620i	0.914834	−	0.403829i	$-0.132321\pi$
$44$	302.124	+	523.294i	1.03516	+	1.79294i
$45$		0			0
$46$	436.484	−	756.013i	1.39904	−	2.42322i
$47$	223.765	+	187.762i	0.694458	+	0.582720i	0.920191	−	0.391469i	$-0.128033\pi$
$47$	223.765	+	187.762i	0.694458	+	0.582720i	−0.225733	+	0.974189i	$0.572478\pi$
$48$		0			0
$49$	−56.2496	−	319.007i	−0.163993	−	0.930051i
$50$	−309.551	+	259.744i	−0.875541	+	0.734666i
$51$		0			0
$52$	31.6104	−	11.5053i	0.0842995	−	0.0306825i
$53$	512.684			1.32873			0.664364	−	0.747409i	$-0.268702\pi$
$53$	512.684			1.32873			0.664364	+	0.747409i	$0.268702\pi$
$54$		0			0
$55$	−964.210			−2.36389
$56$	22.8669	−	8.32289i	0.0545665	−	0.0198606i
$57$		0			0
$58$	−286.174	+	240.129i	−0.647872	+	0.543629i
$59$	−0.614011	−	3.48223i	−0.00135487	−	0.00768385i	0.984123	−	0.177489i	$-0.0567973\pi$
$59$	−0.614011	−	3.48223i	−0.00135487	−	0.00768385i	−0.985478	+	0.169805i	$0.945686\pi$
$60$		0			0
$61$	−276.655	−	232.141i	−0.580690	−	0.487257i	0.304484	−	0.952518i	$-0.401516\pi$
$61$	−276.655	−	232.141i	−0.580690	−	0.487257i	−0.885174	+	0.465261i	$0.845961\pi$
$62$	−51.5236	+	89.2414i	−0.105540	+	0.182801i
$63$		0			0
$64$	333.285	+	577.266i	0.650946	+	1.12747i
$65$	−9.32119	+	52.8631i	−0.0177869	+	0.100875i
$66$		0			0
$67$	−177.368	−	64.5567i	−0.323417	−	0.117714i	0.175209	−	0.984531i	$-0.443940\pi$
$67$	−177.368	−	64.5567i	−0.323417	−	0.117714i	−0.498627	+	0.866817i	$0.666162\pi$
$68$	−316.779	−	115.298i	−0.564928	−	0.205617i
$69$		0			0
$70$	−47.0528	+	266.850i	−0.0803412	+	0.455638i
$71$	−243.711	−	422.120i	−0.407369	−	0.705583i	0.587225	−	0.809423i	$-0.300220\pi$
$71$	−243.711	−	422.120i	−0.407369	−	0.705583i	−0.994594	+	0.103840i	$0.966887\pi$
$72$		0			0
$73$	−24.5604	+	42.5399i	−0.0393778	+	0.0682044i	−0.885043	−	0.465510i	$-0.845871\pi$
$73$	−24.5604	+	42.5399i	−0.0393778	+	0.0682044i	0.845665	+	0.533714i	$0.179204\pi$
$74$	248.753	+	208.728i	0.390769	+	0.327894i
$75$		0			0
$76$	−121.299	−	687.919i	−0.183078	−	1.03829i
$77$	−216.469	+	181.639i	−0.320376	+	0.268828i
$78$		0			0
$79$	−543.271	+	197.734i	−0.773706	+	0.281606i	−0.698546	−	0.715566i	$-0.746169\pi$
$79$	−543.271	+	197.734i	−0.773706	+	0.281606i	−0.0751603	+	0.997171i	$0.523947\pi$
$80$	−767.462			−1.07256
$81$		0			0
$82$	499.225			0.672319
$83$	−500.182	+	182.051i	−0.661471	+	0.240756i	−0.650871	−	0.759188i	$-0.725596\pi$
$83$	−500.182	+	182.051i	−0.661471	+	0.240756i	−0.0105998	+	0.999944i	$0.503374\pi$
$84$		0			0
$85$	412.080	−	345.776i	0.525840	−	0.441232i
$86$	−226.940	−	1287.04i	−0.284554	−	1.61378i
$87$		0			0
$88$	276.207	+	231.765i	0.334588	+	0.280753i
$89$	358.549	−	621.025i	0.427035	−	0.739646i	−0.569573	−	0.821941i	$-0.692892\pi$
$89$	358.549	−	621.025i	0.427035	−	0.739646i	0.996608	+	0.0822947i	$0.0262249\pi$
$90$		0			0
$91$	7.86579	+	13.6239i	0.00906108	+	0.0156943i
$92$	339.962	−	1928.02i	0.385255	−	2.18489i
$93$		0			0
$94$	1142.95	+	416.000i	1.25411	+	0.456458i
$95$	1047.44	+	381.236i	1.13121	+	0.411727i
$96$		0			0
$97$	−57.7162	+	327.325i	−0.0604144	+	0.342627i	0.939586	+	0.342314i	$0.111211\pi$
$97$	−57.7162	+	327.325i	−0.0604144	+	0.342627i	−1.00000		0.000312781i	$0.999900\pi$
$98$	−674.406	−	1168.11i	−0.695156	−	1.20405i
$99$		0			0
$100$	−453.116	+	784.820i	−0.453116	+	0.784820i
$101$	482.811	+	405.126i	0.475658	+	0.399124i	0.848853	−	0.528628i	$-0.177293\pi$
$101$	482.811	+	405.126i	0.475658	+	0.399124i	−0.373195	+	0.927753i	$0.621738\pi$
$102$		0			0
$103$	187.227	+	1061.82i	0.179107	+	1.01577i	0.933295	+	0.359110i	$0.116920\pi$
$103$	187.227	+	1061.82i	0.179107	+	1.01577i	−0.754188	+	0.656659i	$0.771969\pi$
$104$	15.3767	−	12.9026i	0.0144982	−	0.0121654i
$105$		0			0
$106$	2006.03	−	730.137i	1.83814	−	0.669030i
$107$	−541.712			−0.489432			−0.244716	−	0.969595i	$-0.578695\pi$
$107$	−541.712			−0.489432			−0.244716	+	0.969595i	$0.578695\pi$
$108$		0			0
$109$	−401.921			−0.353184			−0.176592	−	0.984284i	$-0.556507\pi$
$109$	−401.921			−0.353184			−0.176592	+	0.984284i	$0.556507\pi$
$110$	−3772.76	+	1373.17i	−3.27017	+	1.19025i
$111$		0			0
$112$	−172.299	+	144.576i	−0.145363	+	0.121974i
$113$	−4.47523	−	25.3803i	−0.00372561	−	0.0211290i	0.982888	−	0.184203i	$-0.0589703\pi$
$113$	−4.47523	−	25.3803i	−0.00372561	−	0.0211290i	−0.986614	+	0.163074i	$0.947859\pi$
$114$		0			0
$115$	2393.16	+	2008.10i	1.94055	+	1.62831i
$116$	−418.899	+	725.554i	−0.335291	+	0.580741i
$117$		0			0
$118$	−7.36170	−	12.7508i	−0.00574321	−	0.00994754i
$119$	27.3759	−	155.257i	0.0210886	−	0.119600i
$120$		0			0
$121$	−2683.75	−	976.804i	−2.01634	−	0.733887i
$122$	−1413.10	−	514.327i	−1.04866	−	0.381680i
$123$		0			0
$124$	−40.1299	+	227.588i	−0.0290627	+	0.164823i
$125$	208.278	+	360.748i	0.149031	+	0.258130i
$126$		0			0
$127$	−956.295	+	1656.35i	−0.668169	+	1.15730i	0.310246	+	0.950656i	$0.399588\pi$
$127$	−956.295	+	1656.35i	−0.668169	+	1.15730i	−0.978416	+	0.206647i	$0.933745\pi$
$128$	538.735	+	452.052i	0.372015	+	0.312157i
$129$		0			0
$130$	38.8127	+	220.118i	0.0261854	+	0.148505i
$131$	1782.25	−	1495.48i	1.18867	−	0.997411i	0.188787	−	0.982018i	$-0.439545\pi$
$131$	1782.25	−	1495.48i	1.18867	−	0.997411i	0.999882	−	0.0153928i	$-0.00489987\pi$
$132$		0			0
$133$	306.972	−	111.729i	0.200135	−	0.0728430i
$134$	−785.945			−0.506681
$135$		0			0
$136$	−201.158			−0.126832
$137$	1726.70	−	628.466i	1.07680	−	0.391923i	0.258085	−	0.966122i	$-0.416909\pi$
$137$	1726.70	−	628.466i	1.07680	−	0.391923i	0.818716	+	0.574199i	$0.194686\pi$
$138$		0			0
$139$	1775.63	−	1489.93i	1.08350	−	0.909166i	0.0872951	−	0.996182i	$-0.472178\pi$
$139$	1775.63	−	1489.93i	1.08350	−	0.909166i	0.996207	+	0.0870164i	$0.0277332\pi$
$140$	105.523	+	598.451i	0.0637023	+	0.361274i
$141$		0			0
$142$	−1554.75	−	1304.59i	−0.918816	−	0.770979i
$143$	−116.547	+	201.865i	−0.0681548	+	0.118048i
$144$		0			0
$145$	−668.445	−	1157.78i	−0.382837	−	0.663093i
$146$	−35.5172	+	201.428i	−0.0201330	+	0.114180i
$147$		0			0
$148$	684.324	+	249.074i	0.380075	+	0.138336i
$149$	−61.6822	−	22.4505i	−0.0339141	−	0.0123437i	0.325007	−	0.945711i	$-0.394633\pi$
$149$	−61.6822	−	22.4505i	−0.0339141	−	0.0123437i	−0.358922	+	0.933368i	$0.616855\pi$
$150$		0			0
$151$	−22.3654	+	126.840i	−0.0120534	+	0.0683584i	−0.990241	−	0.139364i	$-0.955494\pi$
$151$	−22.3654	+	126.840i	−0.0120534	+	0.0683584i	0.978188	+	0.207723i	$0.0666052\pi$
$152$	−208.412	−	360.979i	−0.111213	−	0.192627i
$153$		0			0
$154$	−588.322	+	1019.00i	−0.307846	+	0.533205i
$155$	−282.494	−	237.040i	−0.146390	−	0.122836i
$156$		0			0
$157$	−258.567	−	1466.41i	−0.131439	−	0.745426i	−0.977274	−	0.211982i	$-0.932008\pi$
$157$	−258.567	−	1466.41i	−0.131439	−	0.745426i	0.845835	−	0.533445i	$-0.179103\pi$
$158$	−1844.11	+	1547.39i	−0.928542	+	0.779139i
$159$		0			0
$160$	−3627.13	+	1320.17i	−1.79219	+	0.652303i
$161$	915.563			0.448177
$162$		0			0
$163$	2721.50			1.30776			0.653879	−	0.756599i	$-0.273141\pi$
$163$	2721.50			1.30776			0.653879	+	0.756599i	$0.273141\pi$
$164$	1052.07	−	382.921i	0.500931	−	0.182324i
$165$		0			0
$166$	−1697.85	+	1424.66i	−0.793846	+	0.666116i
$167$	267.569	+	1517.46i	0.123983	+	0.703140i	0.981907	+	0.189364i	$0.0606426\pi$
$167$	267.569	+	1517.46i	0.123983	+	0.703140i	−0.857924	+	0.513776i	$0.828246\pi$
$168$		0			0
$169$	−1673.06	−	1403.86i	−0.761520	−	0.638991i
$170$	1119.95	−	1939.82i	0.505274	−	0.875160i
$171$		0			0
$172$	−1465.46	−	2538.25i	−0.649652	−	1.12523i
$173$	582.642	−	3304.33i	0.256055	−	1.45216i	−0.537296	−	0.843394i	$-0.680554\pi$
$173$	582.642	−	3304.33i	0.256055	−	1.45216i	0.793351	−	0.608765i	$-0.208335\pi$
$174$		0			0
$175$	−398.248	−	144.950i	−0.172027	−	0.0626126i
$176$	−3131.64	−	1139.82i	−1.34123	−	0.488168i
$177$		0			0
$178$	518.502	−	2940.57i	0.218334	−	1.23823i
$179$	990.380	+	1715.39i	0.413545	+	0.716280i	0.995274	−	0.0971019i	$-0.0309573\pi$
$179$	990.380	+	1715.39i	0.413545	+	0.716280i	−0.581730	+	0.813382i	$0.697624\pi$
$180$		0			0
$181$	946.317	−	1639.07i	0.388614	−	0.673100i	−0.603649	−	0.797250i	$-0.706287\pi$
$181$	946.317	−	1639.07i	0.388614	−	0.673100i	0.992263	+	0.124150i	$0.0396205\pi$
$182$	50.1797	+	42.1058i	0.0204372	+	0.0171488i
$183$		0			0
$184$	−202.860	−	1150.48i	−0.0812774	−	0.460947i
$185$	−890.198	+	746.965i	−0.353777	+	0.296854i
$186$		0			0
$187$	2195.04	−	798.931i	0.858382	−	0.312426i
$188$	2727.74			1.05820
$189$		0			0
$190$	4641.36			1.77221
$191$	−639.223	+	232.658i	−0.242160	+	0.0881390i	−0.460249	−	0.887790i	$-0.652240\pi$
$191$	−639.223	+	232.658i	−0.242160	+	0.0881390i	0.218089	+	0.975929i	$0.430018\pi$
$192$		0			0
$193$	1806.37	−	1515.72i	0.673705	−	0.565306i	−0.240455	−	0.970660i	$-0.577296\pi$
$193$	1806.37	−	1515.72i	0.673705	−	0.565306i	0.914159	+	0.405355i	$0.132852\pi$
$194$	240.326	+	1362.95i	0.0889401	+	0.504404i
$195$		0			0
$196$	−2317.22	−	1944.38i	−0.844468	−	0.708593i
$197$	−738.044	+	1278.33i	−0.266921	+	0.462321i	−0.968065	−	0.250699i	$-0.919340\pi$
$197$	−738.044	+	1278.33i	−0.266921	+	0.462321i	0.701144	+	0.713020i	$0.252673\pi$
$198$		0			0
$199$	−2103.44	−	3643.26i	−0.749289	−	1.29781i	−0.948164	−	0.317782i	$-0.897062\pi$
$199$	−2103.44	−	3643.26i	−0.749289	−	1.29781i	0.198875	−	0.980025i	$-0.436271\pi$
$200$	−93.9022	+	532.546i	−0.0331994	+	0.188283i
$201$		0			0
$202$	2466.10	+	897.587i	0.858982	+	0.312644i
$203$	−368.173	−	134.004i	−0.127294	−	0.0463313i
$204$		0			0
$205$	−310.231	+	1759.41i	−0.105695	+	0.599426i
$206$	2244.77	+	3888.05i	0.759225	+	1.31502i
$207$		0			0
$208$	−92.7654	+	160.674i	−0.0309237	+	0.0535614i
$209$	3707.88	+	3111.28i	1.22718	+	1.02972i
$210$		0			0
$211$	450.211	+	2553.27i	0.146890	+	0.833055i	0.965830	+	0.259176i	$0.0834509\pi$
$211$	450.211	+	2553.27i	0.146890	+	0.833055i	−0.818940	+	0.573879i	$0.805438\pi$
$212$	3667.48	−	3077.39i	1.18813	−	0.996961i
$213$		0			0
$214$	−2119.61	+	771.475i	−0.677073	+	0.246434i
$215$	4676.93			1.48355
$216$		0			0
$217$	−108.075			−0.0338093
$218$	−1572.64	+	572.394i	−0.488590	+	0.177832i
$219$		0			0
$220$	−6897.47	+	5787.66i	−2.11376	+	1.77366i
$221$	−22.5817	−	128.067i	−0.00687336	−	0.0389807i
$222$		0			0
$223$	2090.11	+	1753.81i	0.627643	+	0.526655i	0.900196	−	0.435486i	$-0.143423\pi$
$223$	2090.11	+	1753.81i	0.627643	+	0.526655i	−0.272552	+	0.962141i	$0.587868\pi$
$224$	−565.612	+	979.669i	−0.168712	+	0.292218i
$225$		0			0
$226$	−53.6559	−	92.9347i	−0.0157926	−	0.0273536i
$227$	−530.116	+	3006.44i	−0.155000	+	0.879049i	0.803786	+	0.594919i	$0.202816\pi$
$227$	−530.116	+	3006.44i	−0.155000	+	0.879049i	−0.958786	+	0.284130i	$0.908295\pi$
$228$		0			0
$229$	3371.17	+	1227.01i	0.972810	+	0.354074i	0.779041	−	0.626973i	$-0.215707\pi$
$229$	3371.17	+	1227.01i	0.972810	+	0.354074i	0.193769	+	0.981047i	$0.437929\pi$
$230$	12223.8	+	4449.09i	3.50440	+	1.27550i
$231$		0			0
$232$	−86.8111	+	492.330i	−0.0245665	+	0.139323i
$233$	−2364.17	−	4094.87i	−0.664730	−	1.15135i	−0.979358	−	0.202131i	$-0.935213\pi$
$233$	−2364.17	−	4094.87i	−0.664730	−	1.15135i	0.314629	−	0.949215i	$-0.398120\pi$
$234$		0			0
$235$	−2176.36	+	3769.56i	−0.604127	+	1.04638i
$236$	−25.2944	−	21.2245i	−0.00697679	−	0.00585422i
$237$		0			0
$238$	−113.991	−	646.476i	−0.0310460	−	0.176071i
$239$	−3078.11	+	2582.84i	−0.833082	+	0.699039i	−0.955996	−	0.293378i	$-0.905220\pi$
$239$	−3078.11	+	2582.84i	−0.833082	+	0.699039i	0.122914	+	0.992417i	$0.460776\pi$
$240$		0			0
$241$	1519.72	−	553.133i	0.406199	−	0.147844i	−0.130837	−	0.991404i	$-0.541766\pi$
$241$	1519.72	−	553.133i	0.406199	−	0.147844i	0.537035	+	0.843560i	$0.319544\pi$
$242$	−11892.1			−3.15889
$243$		0			0
$244$	−3372.48			−0.884840
$245$	4535.82	−	1650.90i	1.18279	−	0.430500i
$246$		0			0
$247$	206.422	−	173.209i	0.0531754	−	0.0446194i
$248$	23.9461	+	135.805i	0.00613136	+	0.0347726i
$249$		0			0
$250$	1328.71	+	1114.92i	0.336139	+	0.282054i
$251$	−3119.82	+	5403.69i	−0.784548	+	1.35888i	0.144721	+	0.989473i	$0.453772\pi$
$251$	−3119.82	+	5403.69i	−0.784548	+	1.35888i	−0.929269	+	0.369404i	$0.879562\pi$
$252$		0			0
$253$	6782.92	+	11748.4i	1.68553	+	2.91942i
$254$	−1382.91	+	7842.88i	−0.341621	+	1.93743i
$255$		0			0
$256$	−2259.21	−	822.285i	−0.551565	−	0.200753i
$257$	677.780	+	246.692i	0.164509	+	0.0598763i	0.422962	−	0.906148i	$-0.360990\pi$
$257$	677.780	+	246.692i	0.164509	+	0.0598763i	−0.258453	+	0.966024i	$0.583213\pi$
$258$		0			0
$259$	−59.1390	+	335.394i	−0.0141881	+	0.0804647i
$260$	250.631	+	434.106i	0.0597827	+	0.103547i
$261$		0			0
$262$	4843.80	−	8389.70i	1.14218	−	1.97831i
$263$	−3792.12	−	3181.97i	−0.889095	−	0.746040i	0.0789332	−	0.996880i	$-0.474849\pi$
$263$	−3792.12	−	3181.97i	−0.889095	−	0.746040i	−0.968028	+	0.250840i	$0.919293\pi$
$264$		0			0
$265$	1326.60	+	7523.55i	0.307519	+	1.74403i
$266$	1042.01	−	874.346i	0.240186	−	0.201540i
$267$		0			0
$268$	−1656.30	+	602.845i	−0.377518	+	0.137405i
$269$	6217.27			1.40920			0.704598	−	0.709607i	$-0.251127\pi$
$269$	6217.27			1.40920			0.704598	+	0.709607i	$0.251127\pi$
$270$		0			0
$271$	−2888.86			−0.647549			−0.323774	−	0.946134i	$-0.604952\pi$
$271$	−2888.86			−0.647549			−0.323774	+	0.946134i	$0.604952\pi$
$272$	1747.14	−	635.908i	0.389471	−	0.141756i
$273$		0			0
$274$	5861.20	−	4918.13i	1.29229	−	1.08436i
$275$	−1090.43	−	6184.11i	−0.239110	−	1.35606i
$276$		0			0
$277$	85.8530	+	72.0392i	0.0186224	+	0.0156261i	0.652051	−	0.758175i	$-0.273909\pi$
$277$	85.8530	+	72.0392i	0.0186224	+	0.0156261i	−0.633429	+	0.773801i	$0.718353\pi$
$278$	4825.81	−	8358.55i	1.04113	−	1.80328i
$279$		0			0
$280$	181.306	+	314.032i	0.0386969	+	0.0670250i
$281$	−200.198	+	1135.38i	−0.0425010	+	0.241035i	−0.998656	−	0.0518254i	$-0.983496\pi$
$281$	−200.198	+	1135.38i	−0.0425010	+	0.241035i	0.956155	+	0.292861i	$0.0946072\pi$
$282$		0			0
$283$	565.756	+	205.918i	0.118836	+	0.0432529i	0.400754	−	0.916186i	$-0.368748\pi$
$283$	565.756	+	205.918i	0.118836	+	0.0432529i	−0.281918	+	0.959439i	$0.590970\pi$
$284$	−4277.16	−	1556.76i	−0.893671	−	0.325270i
$285$		0			0
$286$	−168.540	+	955.839i	−0.0348461	+	0.197622i
$287$	261.792	+	453.436i	0.0538434	+	0.0932596i
$288$		0			0
$289$	1804.90	−	3126.17i	0.367371	−	0.636306i
$290$	−4264.34	−	3578.21i	−0.863485	−	0.724550i
$291$		0			0
$292$	79.6527	+	451.733i	0.0159634	+	0.0905331i
$293$	2510.50	−	2106.56i	0.500563	−	0.420023i	−0.357231	−	0.934016i	$-0.616279\pi$
$293$	2510.50	−	2106.56i	0.500563	−	0.420023i	0.857794	+	0.513994i	$0.171835\pi$
$294$		0			0
$295$	49.5122	−	18.0210i	0.00977191	−	0.00355668i
$296$	434.552			0.0853305
$297$		0			0
$298$	−273.323			−0.0531315
$299$	709.679	−	258.302i	0.137264	−	0.0499599i
$300$		0			0
$301$	1049.99	−	881.047i	0.201065	−	0.168713i
$302$	93.1276	+	528.153i	0.0177447	+	0.100635i
$303$		0			0
$304$	2951.29	+	2476.42i	0.556802	+	0.467213i
$305$	2690.77	−	4660.55i	0.505157	−	0.874958i
$306$		0			0
$307$	−2478.68	−	4293.19i	−0.460800	−	0.798129i	0.538201	−	0.842816i	$-0.319104\pi$
$307$	−2478.68	−	4293.19i	−0.460800	−	0.798129i	−0.999001	+	0.0446877i	$0.985771\pi$
$308$	−458.223	+	2598.71i	−0.0847717	+	0.480764i
$309$		0			0
$310$	−1442.92	−	525.180i	−0.264363	−	0.0962201i
$311$	−3119.47	−	1135.39i	−0.568775	−	0.207017i	0.0415939	−	0.999135i	$-0.486756\pi$
$311$	−3119.47	−	1135.39i	−0.568775	−	0.207017i	−0.610369	+	0.792118i	$0.708979\pi$
$312$		0			0
$313$	−319.649	+	1812.82i	−0.0577240	+	0.327369i	−0.999972	−	0.00754825i	$-0.997597\pi$
$313$	−319.649	+	1812.82i	−0.0577240	+	0.327369i	0.942248	+	0.334917i	$0.108708\pi$
$314$	−3100.10	−	5369.52i	−0.557161	−	0.965031i
$315$		0			0
$316$	−2699.39	+	4675.47i	−0.480545	+	0.832329i
$317$	−5726.00	−	4804.69i	−1.01452	−	0.851287i	−0.0255949	−	0.999672i	$-0.508148\pi$
$317$	−5726.00	−	4804.69i	−1.01452	−	0.851287i	−0.988930	+	0.148385i	$0.952592\pi$
$318$		0			0
$319$	−1008.08	−	5717.11i	−0.176933	−	1.00344i
$320$	−7608.87	+	6384.60i	−1.32921	+	1.11534i
$321$		0			0
$322$	3582.42	−	1303.89i	0.620001	−	0.225662i
$323$	−2700.40			−0.465184
$324$		0			0
$325$	−349.587			−0.0596665
$326$	10648.7	−	3875.81i	1.80913	−	0.658470i
$327$		0			0
$328$	511.774	−	429.429i	0.0861523	−	0.0722904i
$329$	221.514	+	1256.27i	0.0371200	+	0.210518i
$330$		0			0
$331$	−7099.01	−	5956.78i	−1.17884	−	0.989166i	−0.999986	−	0.00529099i	$-0.998316\pi$
$331$	−7099.01	−	5956.78i	−1.17884	−	0.989166i	−0.178856	−	0.983875i	$-0.557240\pi$
$332$	−2485.29	+	4304.64i	−0.410837	+	0.711590i
$333$		0			0
$334$	3208.02	+	5556.46i	0.525554	+	0.910287i
$335$	488.406	−	2769.89i	0.0796551	−	0.451747i
$336$		0			0
$337$	−9981.01	−	3632.79i	−1.61335	−	0.587213i	−0.631255	−	0.775576i	$-0.717460\pi$
$337$	−9981.01	−	3632.79i	−1.61335	−	0.587213i	−0.982100	+	0.188363i	$0.939682\pi$
$338$	−8545.66	−	3110.36i	−1.37521	−	0.500537i
$339$		0			0
$340$	872.293	−	4947.02i	0.139137	−	0.789087i
$341$	−800.671	−	1386.80i	−0.127152	−	0.220233i
$342$		0			0
$343$	1456.27	−	2522.33i	0.229245	−	0.397064i
$344$	−1339.75	−	1124.18i	−0.209984	−	0.176197i
$345$		0			0
$346$	−2426.07	−	13759.0i	−0.376955	−	2.13782i
$347$	−2943.14	+	2469.59i	−0.455321	+	0.382059i	−0.841406	−	0.540404i	$-0.818271\pi$
$347$	−2943.14	+	2469.59i	−0.455321	+	0.382059i	0.386085	+	0.922463i	$0.373827\pi$
$348$		0			0
$349$	−415.033	+	151.060i	−0.0636568	+	0.0231692i	−0.373652	−	0.927569i	$-0.621895\pi$
$349$	−415.033	+	151.060i	−0.0636568	+	0.0231692i	0.309995	+	0.950738i	$0.399672\pi$
$350$	−1764.69			−0.269505
$351$		0			0
$352$	−16761.3			−2.53801
$353$	−10096.1	+	3674.67i	−1.52227	+	0.554060i	−0.961713	−	0.274059i	$-0.911634\pi$
$353$	−10096.1	+	3674.67i	−1.52227	+	0.554060i	−0.560553	+	0.828118i	$0.689411\pi$
$354$		0			0
$355$	5563.91	−	4668.67i	0.831836	−	0.697993i
$356$	−1162.82	−	6594.68i	−0.173116	−	0.981791i
$357$		0			0
$358$	6318.12	+	5301.53i	0.932746	+	0.782667i
$359$	−5923.26	+	10259.4i	−0.870801	+	1.50827i	−0.00963217	+	0.999954i	$0.503066\pi$
$359$	−5923.26	+	10259.4i	−0.870801	+	1.50827i	−0.861169	+	0.508319i	$0.830267\pi$
$360$		0			0
$361$	631.722	+	1094.17i	0.0921011	+	0.159524i
$362$	1368.48	−	7761.05i	0.198690	−	1.12683i
$363$		0			0
$364$	138.045	+	50.2444i	0.0198779	+	0.00723496i
$365$	−687.817	−	250.345i	−0.0986355	−	0.0359004i
$366$		0			0
$367$	222.886	−	1264.05i	0.0317018	−	0.179790i	−0.964845	−	0.262818i	$-0.915348\pi$
$367$	222.886	−	1264.05i	0.0317018	−	0.179790i	0.996547	+	0.0830283i	$0.0264592\pi$
$368$	5398.86	+	9351.10i	0.764769	+	1.32462i
$369$		0			0
$370$	−2419.39	+	4190.50i	−0.339940	+	0.588794i
$371$	1715.13	+	1439.16i	0.240013	+	0.201395i
$372$		0			0
$373$	1026.83	+	5823.47i	0.142540	+	0.808386i	0.969309	+	0.245844i	$0.0790652\pi$
$373$	1026.83	+	5823.47i	0.142540	+	0.808386i	−0.826769	+	0.562541i	$0.809824\pi$
$374$	7450.98	−	6252.12i	1.03016	−	0.864410i
$375$		0			0
$376$	1529.52	−	556.700i	0.209784	−	0.0763553i
$377$	−323.188			−0.0441512
$378$		0			0
$379$	−6388.36			−0.865825			−0.432913	−	0.901436i	$-0.642514\pi$
$379$	−6388.36			−0.865825			−0.432913	+	0.901436i	$0.642514\pi$
$380$	9781.21	−	3560.07i	1.32044	−	0.480599i
$381$		0			0
$382$	−2169.82	+	1820.69i	−0.290621	+	0.243860i
$383$	2225.39	+	12620.8i	0.296899	+	1.68380i	0.659384	+	0.751806i	$0.270817\pi$
$383$	2225.39	+	12620.8i	0.296899	+	1.68380i	−0.362486	+	0.931989i	$0.618072\pi$
$384$		0			0
$385$	−3225.65	−	2706.64i	−0.426999	−	0.358294i
$386$	4909.35	−	8503.24i	0.647356	−	1.12125i
$387$		0			0
$388$	1551.89	+	2687.96i	0.203055	+	0.351702i
$389$	−1230.93	+	6980.93i	−0.160438	+	0.909890i	0.793206	+	0.608953i	$0.208410\pi$
$389$	−1230.93	+	6980.93i	−0.160438	+	0.909890i	−0.953644	+	0.300937i	$0.902701\pi$
$390$		0			0
$391$	−7111.95	−	2588.54i	−0.919864	−	0.334803i
$392$	−1696.15	−	617.350i	−0.218543	−	0.0795430i
$393$		0			0
$394$	−1067.30	+	6052.93i	−0.136471	+	0.773965i
$395$	−4307.46	−	7460.75i	−0.548689	−	0.950357i
$396$		0			0
$397$	5314.08	−	9204.25i	0.671803	−	1.16360i	−0.305589	−	0.952163i	$-0.598853\pi$
$397$	5314.08	−	9204.25i	0.671803	−	1.16360i	0.977392	−	0.211434i	$-0.0678133\pi$
$398$	−13418.9	−	11259.8i	−1.69002	−	1.41809i
$399$		0			0
$400$	−867.923	−	4922.24i	−0.108490	−	0.615280i
$401$	7345.40	−	6163.52i	0.914743	−	0.767560i	−0.0582725	−	0.998301i	$-0.518559\pi$
$401$	7345.40	−	6163.52i	0.914743	−	0.767560i	0.973015	+	0.230740i	$0.0741148\pi$
$402$		0			0
$403$	−83.7722	+	30.4906i	−0.0103548	+	0.00376884i
$404$	5885.55			0.724795
$405$		0			0
$406$	−1631.43			−0.199425
$407$	−4741.85	+	1725.89i	−0.577506	+	0.210195i
$408$		0			0
$409$	−8853.19	+	7428.71i	−1.07032	+	0.898107i	−0.995082	−	0.0990581i	$-0.968417\pi$
$409$	−8853.19	+	7428.71i	−1.07032	+	0.898107i	−0.0752409	+	0.997165i	$0.523973\pi$
$410$	1291.78	+	7326.03i	0.155601	+	0.882455i
$411$		0			0
$412$	7712.89	+	6471.88i	0.922298	+	0.773900i
$413$	7.72090	−	13.3730i	0.000919904	−	0.00159332i
$414$		0			0
$415$	−3965.82	−	6869.01i	−0.469095	−	0.812497i
$416$	−162.034	+	918.942i	−0.0190971	+	0.108305i
$417$		0			0
$418$	18939.1	+	6893.28i	2.21613	+	0.806607i
$419$	−9341.66	−	3400.08i	−1.08919	−	0.396432i	−0.265868	−	0.964009i	$-0.585659\pi$
$419$	−9341.66	−	3400.08i	−1.08919	−	0.396432i	−0.823320	+	0.567577i	$0.807881\pi$
$420$		0			0
$421$	1674.83	−	9498.40i	0.193886	−	1.09958i	−0.720110	−	0.693859i	$-0.755909\pi$
$421$	1674.83	−	9498.40i	0.193886	−	1.09958i	0.913996	−	0.405722i	$-0.132980\pi$
$422$	5397.82	+	9349.29i	0.622658	+	1.07847i
$423$		0			0
$424$	1428.40	−	2474.06i	0.163607	−	0.283375i
$425$	2683.71	+	2251.90i	0.306304	+	0.257020i
$426$		0			0
$427$	−273.872	−	1553.20i	−0.0310389	−	0.176030i
$428$	−3875.13	+	3251.62i	−0.437644	+	0.367227i
$429$		0			0
$430$	18299.9	−	6660.62i	2.05232	−	0.746985i
$431$	−12396.5			−1.38542			−0.692711	−	0.721215i	$-0.743584\pi$
$431$	−12396.5			−1.38542			−0.692711	+	0.721215i	$0.743584\pi$
$432$		0			0
$433$	8212.00			0.911417			0.455709	−	0.890129i	$-0.349386\pi$
$433$	8212.00			0.911417			0.455709	+	0.890129i	$0.349386\pi$
$434$	−422.877	+	153.915i	−0.0467713	+	0.0170233i
$435$		0			0
$436$	−2875.14	+	2412.53i	−0.315812	+	0.264998i
$437$	−2723.25	−	15444.3i	−0.298103	−	1.69062i
$438$		0			0
$439$	4083.04	+	3426.07i	0.443901	+	0.372477i	0.837167	−	0.546947i	$-0.184210\pi$
$439$	4083.04	+	3426.07i	0.443901	+	0.372477i	−0.393266	+	0.919425i	$0.628655\pi$
$440$	−2686.41	+	4652.99i	−0.291067	+	0.504143i
$441$		0			0
$442$	−270.744	−	468.943i	−0.0291357	−	0.0504646i
$443$	−1114.85	+	6322.60i	−0.119566	+	0.678095i	0.864821	+	0.502080i	$0.167432\pi$
$443$	−1114.85	+	6322.60i	−0.119566	+	0.678095i	−0.984388	+	0.176015i	$0.943679\pi$
$444$		0			0
$445$	10041.2	+	3654.69i	1.06966	+	0.389324i
$446$	10675.9	+	3885.71i	1.13345	+	0.412542i
$447$		0			0
$448$	−505.484	+	2866.74i	−0.0533078	+	0.302323i
$449$	−7773.82	−	13464.7i	−0.817081	−	1.41523i	−0.907824	−	0.419351i	$-0.862258\pi$
$449$	−7773.82	−	13464.7i	−0.817081	−	1.41523i	0.0907432	−	0.995874i	$-0.471076\pi$
$450$		0			0
$451$	−3878.95	+	6718.54i	−0.404995	+	0.701472i
$452$	−184.358	−	154.695i	−0.0191847	−	0.0160979i
$453$		0			0
$454$	2207.36	+	12518.6i	0.228186	+	1.29411i
$455$	−179.576	+	150.682i	−0.0185025	+	0.0155254i
$456$		0			0
$457$	−17086.7	+	6219.05i	−1.74898	+	0.636576i	−0.999671	−	0.0256477i	$-0.991835\pi$
$457$	−17086.7	+	6219.05i	−1.74898	+	0.636576i	−0.749306	+	0.662223i	$0.769613\pi$
$458$	14938.2			1.52405
$459$		0			0
$460$	29173.0			2.95695
$461$	14082.5	−	5125.62i	1.42275	−	0.517839i	0.487906	−	0.872896i	$-0.337761\pi$
$461$	14082.5	−	5125.62i	1.42275	−	0.517839i	0.934845	+	0.355057i	$0.115539\pi$
$462$		0			0
$463$	−4463.96	+	3745.71i	−0.448073	+	0.375978i	−0.838720	−	0.544562i	$-0.816696\pi$
$463$	−4463.96	+	3745.71i	−0.448073	+	0.375978i	0.390647	+	0.920541i	$0.372251\pi$
$464$	−802.381	−	4550.53i	−0.0802793	−	0.455287i
$465$		0			0
$466$	−15082.2	−	12655.5i	−1.49929	−	1.25806i
$467$	5542.30	−	9599.55i	0.549180	−	0.951208i	−0.449150	−	0.893456i	$-0.648273\pi$
$467$	5542.30	−	9599.55i	0.549180	−	0.951208i	0.998331	−	0.0577523i	$-0.0183934\pi$
$468$		0			0
$469$	−412.147	−	713.859i	−0.0405782	−	0.0702835i
$470$	−3147.26	+	17849.0i	−0.308877	+	1.75173i
$471$		0			0
$472$	−18.5149	−	6.73888i	−0.00180555	−	0.000657165i
$473$	19084.3	+	6946.11i	1.85517	+	0.675227i
$474$		0			0
$475$	−1260.57	+	7149.05i	−0.121766	+	0.690570i
$476$	−736.094	−	1274.95i	−0.0708798	−	0.122767i
$477$		0			0
$478$	−8365.72	+	14489.8i	−0.800500	+	1.38651i
$479$	−3485.28	−	2924.50i	−0.332457	−	0.278964i	0.461243	−	0.887274i	$-0.347404\pi$
$479$	−3485.28	−	2924.50i	−0.332457	−	0.278964i	−0.793700	+	0.608309i	$0.791848\pi$
$480$		0			0
$481$	48.7823	+	276.658i	0.00462429	+	0.0262256i
$482$	5158.63	−	4328.61i	0.487488	−	0.409051i
$483$		0			0
$484$	−25061.4	+	9121.61i	−2.35363	+	0.856650i
$485$	−4952.77			−0.463699
$486$		0			0
$487$	11089.7			1.03187			0.515936	−	0.856627i	$-0.327444\pi$
$487$	11089.7			1.03187			0.515936	+	0.856627i	$0.327444\pi$
$488$	−1891.04	+	688.283i	−0.175417	+	0.0638466i
$489$		0			0
$490$	15396.7	−	12919.3i	1.41949	−	1.19109i
$491$	2562.51	+	14532.7i	0.235528	+	1.33575i	0.841499	+	0.540259i	$0.181674\pi$
$491$	2562.51	+	14532.7i	0.235528	+	1.33575i	−0.605971	+	0.795487i	$0.707215\pi$
$492$		0			0
$493$	2481.05	+	2081.85i	0.226655	+	0.190186i
$494$	561.015	−	971.706i	0.0510956	−	0.0885002i
$495$		0			0
$496$	−637.293	−	1103.82i	−0.0576922	−	0.0999258i
$497$	369.630	−	2096.28i	0.0333605	−	0.189197i
$498$		0			0
$499$	4120.89	+	1499.88i	0.369692	+	0.134557i	0.520184	−	0.854054i	$-0.325863\pi$
$499$	4120.89	+	1499.88i	0.369692	+	0.134557i	−0.150492	+	0.988611i	$0.548086\pi$
$500$	3655.30	+	1330.42i	0.326940	+	0.118996i
$501$		0			0
$502$	−4511.62	+	25586.7i	−0.401122	+	2.27488i
$503$	−4598.51	−	7964.85i	−0.407629	−	0.706034i	0.586995	−	0.809591i	$-0.300311\pi$
$503$	−4598.51	−	7964.85i	−0.407629	−	0.706034i	−0.994624	+	0.103557i	$0.966978\pi$
$504$		0			0
$505$	−4695.85	+	8133.44i	−0.413787	+	0.716700i
$506$	43271.6	+	36309.2i	3.80169	+	3.19000i
$507$		0			0
$508$	3101.39	+	17588.9i	0.270870	+	1.53618i
$509$	−5104.80	+	4283.44i	−0.444531	+	0.373006i	−0.837402	−	0.546588i	$-0.815927\pi$
$509$	−5104.80	+	4283.44i	−0.444531	+	0.373006i	0.392870	+	0.919594i	$0.371482\pi$
$510$		0			0
$511$	−201.578	+	73.3685i	−0.0174507	+	0.00635153i
$512$	−15637.0			−1.34974
$513$		0			0
$514$	3003.34			0.257727
$515$	−15097.5	+	5495.05i	−1.29180	+	0.470176i
$516$		0			0
$517$	−14479.2	+	12149.5i	−1.23171	+	1.03353i
$518$	246.250	+	1396.55i	0.0208873	+	0.118458i
$519$		0			0
$520$	229.132	+	192.264i	0.0193233	+	0.0162141i
$521$	−7880.24	+	13649.0i	−0.662648	+	1.14774i	0.317269	+	0.948335i	$0.397234\pi$
$521$	−7880.24	+	13649.0i	−0.662648	+	1.14774i	−0.979917	+	0.199404i	$0.936099\pi$
$522$		0			0
$523$	641.174	+	1110.55i	0.0536072	+	0.0928504i	0.891584	−	0.452856i	$-0.149595\pi$
$523$	641.174	+	1110.55i	0.0536072	+	0.0928504i	−0.837977	+	0.545706i	$0.816261\pi$
$524$	3772.66	−	21395.8i	0.314522	−	1.78374i
$525$		0			0
$526$	−19369.4	−	7049.88i	−1.60560	−	0.584391i
$527$	839.511	+	305.557i	0.0693922	+	0.0252567i
$528$		0			0
$529$	5519.65	−	31303.5i	0.453657	−	2.57282i
$530$	15905.4	+	27548.9i	1.30356	+	2.25782i
$531$		0			0
$532$	1525.27	−	2641.85i	0.124303	−	0.215298i
$533$	330.848	+	277.614i	0.0268867	+	0.0225606i
$534$		0			0
$535$	−1401.71	−	7949.51i	−0.113274	−	0.642406i
$536$	−805.701	+	676.064i	−0.0649272	+	0.0544804i
$537$		0			0
$538$	24327.0	−	8854.29i	1.94946	−	0.709546i
$539$	20960.4			1.67501
$540$		0			0
$541$	3014.37			0.239553			0.119776	−	0.992801i	$-0.461782\pi$
$541$	3014.37			0.239553			0.119776	+	0.992801i	$0.461782\pi$
$542$	−11303.5	+	4114.15i	−0.895809	+	0.326048i
$543$		0			0
$544$	7163.37	−	6010.78i	0.564572	−	0.473732i
$545$	−1040.00	−	5898.12i	−0.0817405	−	0.463573i
$546$		0			0
$547$	−4627.67	−	3883.07i	−0.361727	−	0.303525i	0.443752	−	0.896150i	$-0.353647\pi$
$547$	−4627.67	−	3883.07i	−0.361727	−	0.303525i	−0.805479	+	0.592625i	$0.798092\pi$
$548$	8579.55	−	14860.2i	0.668796	−	1.15839i
$549$		0			0
$550$	−13073.7	−	22644.3i	−1.01357	−	1.75556i
$551$	−1165.38	+	6609.18i	−0.0901030	+	0.510999i
$552$		0			0
$553$	−2372.51	−	863.524i	−0.182440	−	0.0664029i
$554$	438.520	+	159.608i	0.0336299	+	0.0122403i
$555$		0			0
$556$	3758.65	−	21316.4i	0.286695	−	1.62593i
$557$	6681.15	+	11572.1i	0.508240	+	0.880297i	0.999954	+	0.00954076i	$0.00303697\pi$
$557$	6681.15	+	11572.1i	0.508240	+	0.880297i	−0.491715	+	0.870756i	$0.663630\pi$
$558$		0			0
$559$	565.314	−	979.152i	0.0427732	−	0.0740854i
$560$	−2567.45	−	2154.35i	−0.193741	−	0.162568i
$561$		0			0
$562$	833.607	+	4727.62i	0.0625686	+	0.354844i
$563$	−17321.3	+	14534.3i	−1.29663	+	1.08800i	−0.305916	+	0.952058i	$0.598963\pi$
$563$	−17321.3	+	14534.3i	−1.29663	+	1.08800i	−0.990716	+	0.135945i	$0.956593\pi$
$564$		0			0
$565$	360.871	−	131.346i	0.0268707	−	0.00978014i
$566$	2506.95			0.186175
$567$		0			0
$568$	−2716.03			−0.200638
$569$	−819.206	+	298.167i	−0.0603566	+	0.0219680i	−0.372022	−	0.928224i	$-0.621335\pi$
$569$	−819.206	+	298.167i	−0.0603566	+	0.0219680i	0.311665	+	0.950192i	$0.399113\pi$
$570$		0			0
$571$	7029.65	−	5898.58i	0.515205	−	0.432308i	−0.347752	−	0.937587i	$-0.613055\pi$
$571$	7029.65	−	5898.58i	0.515205	−	0.432308i	0.862956	+	0.505279i	$0.168610\pi$
$572$	377.977	+	2143.61i	0.0276294	+	0.156694i
$573$		0			0
$574$	1670.10	+	1401.38i	0.121443	+	0.101903i
$575$	−10172.8	+	17619.8i	−0.737802	+	1.27791i
$576$		0			0
$577$	−8210.92	−	14221.7i	−0.592418	−	1.02610i	−0.993906	−	0.110234i	$-0.964840\pi$
$577$	−8210.92	−	14221.7i	−0.592418	−	1.02610i	0.401488	−	0.915864i	$-0.368493\pi$
$578$	2610.09	−	14802.5i	0.187829	−	1.06523i
$579$		0			0
$580$	−11731.3	−	4269.84i	−0.839854	−	0.305682i
$581$	−2184.34	−	795.035i	−0.155975	−	0.0567704i
$582$		0			0
$583$	−5760.64	+	32670.2i	−0.409231	+	2.32086i
$584$	136.857	+	237.043i	0.00969721	+	0.0167961i
$585$		0			0
$586$	6823.05	−	11817.9i	0.480986	−	0.833092i
$587$	−1679.01	−	1408.86i	−0.118058	−	0.0990627i	0.581847	−	0.813298i	$-0.302330\pi$
$587$	−1679.01	−	1408.86i	−0.118058	−	0.0990627i	−0.699906	+	0.714235i	$0.746775\pi$
$588$		0			0
$589$	321.459	+	1823.08i	0.0224881	+	0.127536i
$590$	168.067	−	141.025i	0.0117275	−	0.00984053i
$591$		0			0
$592$	−3774.27	+	1373.72i	−0.262030	+	0.0953711i
$593$	23259.5			1.61071			0.805357	−	0.592790i	$-0.201974\pi$
$593$	23259.5			1.61071			0.805357	+	0.592790i	$0.201974\pi$
$594$		0			0
$595$	2349.20			0.161862
$596$	−576.002	+	209.648i	−0.0395872	+	0.0144086i
$597$		0			0
$598$	2408.98	−	2021.37i	0.164733	−	0.138227i
$599$	−1914.89	−	10859.9i	−0.130618	−	0.740771i	−0.977811	−	0.209487i	$-0.932821\pi$
$599$	−1914.89	−	10859.9i	−0.130618	−	0.740771i	0.847194	−	0.531284i	$-0.178290\pi$
$600$		0			0
$601$	−11425.9	−	9587.46i	−0.775494	−	0.650717i	0.166616	−	0.986022i	$-0.446716\pi$
$601$	−11425.9	−	9587.46i	−0.775494	−	0.650717i	−0.942110	+	0.335305i	$0.891161\pi$
$602$	2853.67	−	4942.70i	0.193201	−	0.334634i
$603$		0			0
$604$	601.368	+	1041.60i	0.0405121	+	0.0701690i
$605$	7390.04	−	41911.0i	0.496608	−	2.81640i
$606$		0			0
$607$	23681.8	+	8619.46i	1.58355	+	0.576364i	0.975972	−	0.217897i	$-0.0699197\pi$
$607$	23681.8	+	8619.46i	1.58355	+	0.576364i	0.607576	+	0.794261i	$0.292142\pi$
$608$	18208.1	+	6627.20i	1.21453	+	0.442053i
$609$		0			0
$610$	3891.16	−	22067.8i	0.258276	−	1.46476i
$611$	526.126	+	911.276i	0.0348359	+	0.0603376i
$612$		0			0
$613$	8169.19	−	14149.4i	0.538255	−	0.932285i	−0.460743	−	0.887534i	$-0.652417\pi$
$613$	8169.19	−	14149.4i	0.538255	−	0.932285i	0.998998	−	0.0447517i	$-0.0142497\pi$
$614$	−15812.7	−	13268.4i	−1.03933	−	0.872102i
$615$		0			0
$616$	273.428	+	1550.69i	0.0178843	+	0.101427i
$617$	1147.65	−	962.996i	0.0748830	−	0.0628343i	−0.604578	−	0.796546i	$-0.706658\pi$
$617$	1147.65	−	962.996i	0.0748830	−	0.0628343i	0.679461	+	0.733712i	$0.262214\pi$
$618$		0			0
$619$	−3618.81	+	1317.14i	−0.234980	+	0.0855256i	−0.456826	−	0.889556i	$-0.651014\pi$
$619$	−3618.81	+	1317.14i	−0.234980	+	0.0855256i	0.221846	+	0.975082i	$0.428792\pi$
$620$	−3443.65			−0.223065
$621$		0			0
$622$	−13822.8			−0.891070
$623$	2942.77	−	1071.08i	0.189245	−	0.0688795i
$624$		0			0
$625$	−14047.6	+	11787.3i	−0.899047	+	0.754390i
$626$	1330.99	+	7548.43i	0.0849794	+	0.481942i
$627$		0			0
$628$	−10651.7	−	8937.88i	−0.676833	−	0.567930i
$629$	1407.63	−	2438.09i	0.0892304	−	0.154552i
$630$		0			0
$631$	2206.90	+	3822.46i	0.139232	+	0.241157i	0.927206	−	0.374552i	$-0.122203\pi$
$631$	2206.90	+	3822.46i	0.139232	+	0.241157i	−0.787974	+	0.615708i	$0.788870\pi$
$632$	−559.411	+	3172.58i	−0.0352092	+	0.199681i
$633$		0			0
$634$	−29247.3	−	10645.1i	−1.83211	−	0.666834i
$635$	−26781.1	−	9747.53i	−1.67366	−	0.609164i
$636$		0			0
$637$	202.628	−	1149.16i	0.0126035	−	0.0714779i
$638$	−12086.4	−	20934.3i	−0.750009	−	1.29905i
$639$		0			0
$640$	−5239.77	+	9075.54i	−0.323625	+	0.560535i
$641$	−6396.07	−	5366.94i	−0.394118	−	0.330704i	0.424097	−	0.905617i	$-0.360592\pi$
$641$	−6396.07	−	5366.94i	−0.394118	−	0.330704i	−0.818215	+	0.574913i	$0.805036\pi$
$642$		0			0
$643$	−2729.87	−	15481.8i	−0.167427	−	0.949524i	−0.946527	−	0.322625i	$-0.895435\pi$
$643$	−2729.87	−	15481.8i	−0.167427	−	0.949524i	0.779100	−	0.626899i	$-0.215676\pi$
$644$	6549.47	−	5495.66i	0.400754	−	0.336272i
$645$		0			0
$646$	−10566.1	+	3845.76i	−0.643529	+	0.234225i
$647$	−19577.5			−1.18960			−0.594800	−	0.803874i	$-0.702769\pi$
$647$	−19577.5			−1.18960			−0.594800	+	0.803874i	$0.702769\pi$
$648$		0			0
$649$	228.800			0.0138385
$650$	−1367.87	+	497.863i	−0.0825417	+	0.0300427i
$651$		0			0
$652$	19468.2	−	16335.8i	1.16938	−	0.981226i
$653$	589.813	+	3345.00i	0.0353464	+	0.200459i	0.997367	−	0.0725169i	$-0.0231031\pi$
$653$	589.813	+	3345.00i	0.0353464	+	0.200459i	−0.962021	+	0.272976i	$0.911992\pi$
$654$		0			0
$655$	26557.6	+	22284.5i	1.58426	+	1.32935i
$656$	−3087.45	+	5347.62i	−0.183757	+	0.318276i
$657$		0			0
$658$	2655.85	+	4600.07i	0.157349	+	0.272537i
$659$	−2182.29	+	12376.4i	−0.128998	+	0.731586i	0.849854	+	0.527018i	$0.176690\pi$
$659$	−2182.29	+	12376.4i	−0.128998	+	0.731586i	−0.978852	+	0.204568i	$0.934421\pi$
$660$		0			0
$661$	10323.4	+	3757.39i	0.607461	+	0.221098i	0.627392	−	0.778704i	$-0.284122\pi$
$661$	10323.4	+	3757.39i	0.607461	+	0.221098i	−0.0199308	+	0.999801i	$0.506345\pi$
$662$	−36260.3	−	13197.7i	−2.12885	−	0.774838i
$663$		0			0
$664$	−515.042	+	2920.95i	−0.0301017	+	0.170715i
$665$	2433.91	+	4215.66i	0.141929	+	0.245829i
$666$		0			0
$667$	−9404.61	+	16289.3i	−0.545949	+	0.945611i
$668$	11022.6	+	9249.04i	0.638438	+	0.535713i
$669$		0			0
$670$	−2033.68	−	11533.6i	−0.117266	−	0.665047i
$671$	17901.5	−	15021.2i	1.02993	−	0.864211i
$672$		0			0
$673$	16390.3	−	5965.57i	0.938780	−	0.341688i	0.173096	−	0.984905i	$-0.444623\pi$
$673$	16390.3	−	5965.57i	0.938780	−	0.341688i	0.765684	+	0.643217i	$0.222401\pi$
$674$	−44227.4			−2.52756
$675$		0			0
$676$	−20394.9			−1.16038
$677$	−1713.11	+	623.520i	−0.0972527	+	0.0353971i	−0.390188	−	0.920735i	$-0.627590\pi$
$677$	−1713.11	+	623.520i	−0.0972527	+	0.0353971i	0.292936	+	0.956132i	$0.405368\pi$
$678$		0			0
$679$	−1111.92	+	933.012i	−0.0628447	+	0.0527330i
$680$	−520.509	−	2951.95i	−0.0293538	−	0.166474i
$681$		0			0
$682$	−5107.88	−	4286.02i	−0.286790	−	0.240645i
$683$	−3996.62	+	6922.34i	−0.223904	+	0.387813i	−0.955990	−	0.293399i	$-0.905213\pi$
$683$	−3996.62	+	6922.34i	−0.223904	+	0.387813i	0.732086	+	0.681212i	$0.238547\pi$
$684$		0			0
$685$	13690.6	+	23712.7i	0.763634	+	1.32265i
$686$	2105.93	−	11943.3i	0.117208	−	0.664720i
$687$		0			0
$688$	15190.1	+	5528.75i	0.841741	+	0.306369i
$689$	1735.47	+	631.658i	0.0959594	+	0.0349264i
$690$		0			0
$691$	854.171	−	4844.25i	0.0470249	−	0.266691i	−0.952226	−	0.305395i	$-0.901212\pi$
$691$	854.171	−	4844.25i	0.0470249	−	0.266691i	0.999251	+	0.0387033i	$0.0123227\pi$
$692$	−15666.3	−	27134.8i	−0.860611	−	1.49062i
$693$		0			0
$694$	−7998.89	+	13854.5i	−0.437513	+	0.757794i
$695$	26459.0	+	22201.7i	1.44409	+	1.21174i
$696$		0			0
$697$	−751.572	−	4262.38i	−0.0408434	−	0.231634i
$698$	−1408.81	+	1182.13i	−0.0763960	+	0.0641038i
$699$		0			0
$700$	−3718.92	+	1353.58i	−0.200803	+	0.0730863i
$701$	31745.0			1.71040			0.855202	−	0.518295i	$-0.173433\pi$
$701$	31745.0			1.71040			0.855202	+	0.518295i	$0.173433\pi$
$702$		0			0
$703$	5833.56			0.312968
$704$	−40530.5	+	14751.9i	−2.16981	+	0.789748i
$705$		0			0
$706$	−34270.7	+	28756.5i	−1.82691	+	1.53296i
$707$	477.953	+	2710.61i	0.0254247	+	0.144191i
$708$		0			0
$709$	8555.77	+	7179.14i	0.453200	+	0.380280i	0.840622	−	0.541623i	$-0.182190\pi$
$709$	8555.77	+	7179.14i	0.453200	+	0.380280i	−0.387422	+	0.921903i	$0.626634\pi$
$710$	15121.6	−	26191.4i	0.799302	−	1.38443i
$711$		0			0
$712$	−1997.92	−	3460.50i	−0.105162	−	0.182146i
$713$	−900.948	+	5109.53i	−0.0473223	+	0.268378i
$714$		0			0
$715$	−3263.91	−	1187.96i	−0.170718	−	0.0621362i
$716$	17381.3	+	6326.27i	0.907219	+	0.330201i
$717$		0			0
$718$	−8565.71	+	48578.5i	−0.445222	+	2.52498i
$719$	−6886.08	−	11927.0i	−0.357173	−	0.618642i	0.630314	−	0.776340i	$-0.282926\pi$
$719$	−6886.08	−	11927.0i	−0.357173	−	0.618642i	−0.987487	+	0.157698i	$0.949593\pi$
$720$		0			0
$721$	−2354.30	+	4077.76i	−0.121607	+	0.210629i
$722$	4030.07	+	3381.63i	0.207733	+	0.174309i
$723$		0			0
$724$	−3069.03	−	17405.3i	−0.157541	−	0.893459i
$725$	6669.66	−	5596.51i	0.341662	−	0.286689i
$726$		0			0
$727$	11307.9	−	4115.72i	0.576871	−	0.209964i	−0.0370742	−	0.999313i	$-0.511804\pi$
$727$	11307.9	−	4115.72i	0.576871	−	0.209964i	0.613945	+	0.789349i	$0.289582\pi$
$728$	87.6602			0.00446278
$729$		0			0
$730$	−3047.82			−0.154527
$731$	−10647.1	+	3875.23i	−0.538711	+	0.196075i
$732$		0			0
$733$	15838.2	−	13289.8i	0.798087	−	0.669675i	−0.149646	−	0.988740i	$-0.547813\pi$
$733$	15838.2	−	13289.8i	0.798087	−	0.669675i	0.947733	+	0.319065i	$0.103369\pi$
$734$	−928.080	−	5263.40i	−0.0466704	−	0.264681i
$735$		0			0
$736$	41601.3	+	34907.6i	2.08348	+	1.74825i
$737$	6106.75	−	10577.2i	0.305217	−	0.528652i
$738$		0			0
$739$	10970.6	+	19001.6i	0.546087	+	0.945851i	0.998538	+	0.0540615i	$0.0172167\pi$
$739$	10970.6	+	19001.6i	0.546087	+	0.945851i	−0.452450	+	0.891790i	$0.649450\pi$
$740$	−1884.37	+	10686.8i	−0.0936094	+	0.530885i
$741$		0			0
$742$	8760.53	+	3188.57i	0.433435	+	0.157758i
$743$	−4143.47	−	1508.10i	−0.204589	−	0.0744642i	0.237693	−	0.971340i	$-0.423609\pi$
$743$	−4143.47	−	1508.10i	−0.204589	−	0.0744642i	−0.442282	+	0.896876i	$0.645831\pi$
$744$		0			0
$745$	169.850	−	963.266i	0.00835278	−	0.0473709i
$746$	12311.3	+	21323.7i	0.604219	+	1.04654i
$747$		0			0
$748$	10906.7	−	18890.9i	0.533137	−	0.923421i
$749$	−1812.23	−	1520.64i	−0.0884080	−	0.0741831i
$750$		0			0
$751$	−3758.74	−	21316.9i	−0.182634	−	1.03577i	−0.928957	−	0.370187i	$-0.879294\pi$
$751$	−3758.74	−	21316.9i	−0.182634	−	1.03577i	0.746323	−	0.665584i	$-0.231818\pi$
$752$	−11524.7	+	9670.36i	−0.558859	+	0.468938i
$753$		0			0
$754$	−1264.57	+	460.266i	−0.0610782	+	0.0222306i
$755$	−1919.23			−0.0925138
$756$		0			0
$757$	−31885.6			−1.53091			−0.765456	−	0.643488i	$-0.777487\pi$
$757$	−31885.6			−1.53091			−0.765456	+	0.643488i	$0.777487\pi$
$758$	−24996.4	+	9097.94i	−1.19777	+	0.435953i
$759$		0			0
$760$	4758.03	−	3992.46i	0.227094	−	0.190555i
$761$	−2586.51	−	14668.8i	−0.123207	−	0.698743i	−0.982356	−	0.187018i	$-0.940118\pi$
$761$	−2586.51	−	14668.8i	−0.123207	−	0.698743i	0.859149	−	0.511725i	$-0.170993\pi$
$762$		0			0
$763$	−1344.58	−	1128.24i	−0.0637970	−	0.0535320i
$764$	−3176.15	+	5501.25i	−0.150404	+	0.260508i
$765$		0			0
$766$	26681.4	+	46213.5i	1.25853	+	2.17985i
$767$	2.21185	−	12.5440i	0.000104127	−	0.000590533i
$768$		0			0
$769$	24207.6	+	8810.84i	1.13517	+	0.413169i	0.840168	−	0.542327i	$-0.182457\pi$
$769$	24207.6	+	8810.84i	1.13517	+	0.413169i	0.295005	+	0.955496i	$0.404679\pi$
$770$	−16476.0	−	5996.77i	−0.771109	−	0.280661i
$771$		0			0
$772$	3823.72	−	21685.4i	0.178263	−	1.01098i
$773$	−2229.04	−	3860.81i	−0.103717	−	0.179643i	0.809496	−	0.587125i	$-0.199740\pi$
$773$	−2229.04	−	3860.81i	−0.103717	−	0.179643i	−0.913213	+	0.407482i	$0.866407\pi$
$774$		0			0
$775$	1200.82	−	2079.89i	0.0556578	−	0.0964022i
$776$	1418.77	+	1190.49i	0.0656325	+	0.0550722i
$777$		0			0
$778$	5125.48	+	29068.0i	0.236192	+	1.33951i
$779$	6870.20	−	5764.78i	0.315983	−	0.265141i
$780$		0			0
$781$	29637.5	−	10787.2i	1.35789	−	0.494232i
$782$	−31514.1			−1.44110
$783$		0			0
$784$	16683.4			0.759995
$785$	20850.2	−	7588.84i	0.947993	−	0.345041i
$786$		0			0
$787$	25239.8	−	21178.7i	1.14320	−	0.959262i	0.143665	−	0.989626i	$-0.454111\pi$
$787$	25239.8	−	21178.7i	1.14320	−	0.959262i	0.999539	+	0.0303647i	$0.00966686\pi$
$788$	2393.57	+	13574.6i	0.108207	+	0.613675i
$789$		0			0
$790$	−27479.4	−	23058.0i	−1.23756	−	1.03844i
$791$	56.2739	−	97.4692i	0.00252954	−	0.00438130i
$792$		0			0
$793$	−650.482	−	1126.67i	−0.0291290	−	0.0504529i
$794$	7684.76	−	43582.4i	0.343478	−	1.94796i
$795$		0			0
$796$	−36915.5	−	13436.2i	−1.64376	−	0.598281i
$797$	10856.5	+	3951.44i	0.482505	+	0.175617i	0.571809	−	0.820387i	$-0.306242\pi$
$797$	10856.5	+	3951.44i	0.482505	+	0.175617i	−0.0893039	+	0.996004i	$0.528464\pi$
$798$		0			0
$799$	1831.12	−	10384.8i	0.0810767	−	0.459809i
$800$	−12569.0	−	21770.2i	−0.555478	−	0.962116i
$801$		0			0
$802$	19963.4	−	34577.6i	0.878967	−	1.52241i
$803$	−2434.84	−	2043.07i	−0.107003	−	0.0897864i
$804$		0			0
$805$	2369.08	+	13435.7i	0.103725	+	0.588256i
$806$	−284.361	+	238.607i	−0.0124270	+	0.0104275i
$807$		0			0
$808$	3300.19	−	1201.17i	0.143688	−	0.0522983i
$809$	−15334.9			−0.666435			−0.333217	−	0.942850i	$-0.608134\pi$
$809$	−15334.9			−0.666435			−0.333217	+	0.942850i	$0.608134\pi$
$810$		0			0
$811$	−45665.6			−1.97723			−0.988616	−	0.150463i	$-0.951924\pi$
$811$	−45665.6			−1.97723			−0.988616	+	0.150463i	$0.951924\pi$
$812$	−3438.09	+	1251.36i	−0.148588	+	0.0540815i
$813$		0			0
$814$	−16096.0	+	13506.2i	−0.693078	+	0.581561i
$815$	7042.06	+	39937.5i	0.302666	+	1.71650i
$816$		0			0
$817$	−17985.2	−	15091.4i	−0.770162	−	0.646242i
$818$	−24061.2	+	41675.3i	−1.02846	+	1.78135i
$819$		0			0
$820$	8341.59	+	14448.1i	0.355245	+	0.615303i
$821$	354.682	−	2011.50i	0.0150773	−	0.0855077i	−0.976341	−	0.216238i	$-0.930621\pi$
$821$	354.682	−	2011.50i	0.0150773	−	0.0855077i	0.991418	+	0.130731i	$0.0417323\pi$
$822$		0			0
$823$	5949.74	+	2165.53i	0.251999	+	0.0917201i	0.464931	−	0.885347i	$-0.346079\pi$
$823$	5949.74	+	2165.53i	0.251999	+	0.0917201i	−0.212932	+	0.977067i	$0.568301\pi$
$824$	5645.67	+	2054.85i	0.238685	+	0.0868741i
$825$		0			0
$826$	11.1653	−	63.3215i	0.000470327	−	0.00266736i
$827$	6730.29	+	11657.2i	0.282993	+	0.490158i	0.972120	−	0.234482i	$-0.0753393\pi$
$827$	6730.29	+	11657.2i	0.282993	+	0.490158i	−0.689127	+	0.724640i	$0.742006\pi$
$828$		0			0
$829$	16283.6	−	28204.1i	0.682212	−	1.18163i	−0.292093	−	0.956390i	$-0.594352\pi$
$829$	16283.6	−	28204.1i	0.682212	−	1.18163i	0.974304	−	0.225235i	$-0.0723151\pi$
$830$	−25299.9	−	21229.2i	−1.05804	−	0.887802i
$831$		0			0
$832$	416.961	+	2364.70i	0.0173744	+	0.0985353i
$833$	−8957.98	+	7516.64i	−0.372600	+	0.312648i
$834$		0			0
$835$	−21576.0	+	7853.04i	−0.894215	+	0.325468i
$836$	45199.8			1.86994
$837$		0			0
$838$	−41394.3			−1.70637
$839$	21778.1	−	7926.57i	0.896141	−	0.326169i	0.147436	−	0.989072i	$-0.452898\pi$
$839$	21778.1	−	7926.57i	0.896141	−	0.326169i	0.748705	+	0.662903i	$0.230676\pi$
$840$		0			0
$841$	−12517.1	+	10503.1i	−0.513226	+	0.430647i
$842$	−6973.84	−	39550.6i	−0.285433	−	1.61877i
$843$		0			0
$844$	18546.6	+	15562.4i	0.756398	+	0.634693i
$845$	16272.3	−	28184.4i	0.662465	−	1.14742i
$846$		0			0
$847$	−6236.16	−	10801.4i	−0.252984	−	0.438180i
$848$	−4585.18	+	26003.8i	−0.185679	+	1.05304i
$849$		0			0
$850$	13707.9	+	4989.26i	0.553149	+	0.201330i
$851$	15363.6	+	5591.90i	0.618870	+	0.225250i
$852$		0			0
$853$	−6240.84	+	35393.5i	−0.250507	+	1.42069i	0.556842	+	0.830619i	$0.312013\pi$
$853$	−6240.84	+	35393.5i	−0.250507	+	1.42069i	−0.807348	+	0.590075i	$0.799098\pi$
$854$	−3283.59	−	5687.35i	−0.131572	−	0.227889i
$855$		0			0
$856$	−1509.27	+	2614.14i	−0.0602640	+	0.104380i
$857$	−863.147	−	724.267i	−0.0344044	−	0.0288687i	0.625423	−	0.780286i	$-0.284926\pi$
$857$	−863.147	−	724.267i	−0.0344044	−	0.0288687i	−0.659828	+	0.751417i	$0.729371\pi$
$858$		0			0
$859$	3360.35	+	19057.5i	0.133473	+	0.756965i	0.975911	+	0.218171i	$0.0700090\pi$
$859$	3360.35	+	19057.5i	0.133473	+	0.756965i	−0.842437	+	0.538795i	$0.818880\pi$
$860$	33456.3	−	28073.2i	1.32657	−	1.11313i
$861$		0			0
$862$	−48505.0	+	17654.4i	−1.91657	+	0.697576i
$863$	−11181.1			−0.441030			−0.220515	−	0.975384i	$-0.570774\pi$
$863$	−11181.1			−0.441030			−0.220515	+	0.975384i	$0.570774\pi$
$864$		0			0
$865$	49998.0			1.96530
$866$	32132.0	−	11695.1i	1.26084	−	0.458909i
$867$		0			0
$868$	−773.114	+	648.720i	−0.0302318	+	0.0253675i
$869$	−6496.08	−	36841.1i	−0.253584	−	1.43815i
$870$		0			0
$871$	−520.864	−	437.056i	−0.0202627	−	0.0170024i
$872$	−1119.80	+	1939.55i	−0.0434877	+	0.0753229i
$873$		0			0
$874$	−32650.5	−	56552.3i	−1.26364	−	2.18869i
$875$	−315.890	+	1791.50i	−0.0122046	+	0.0692157i
$876$		0			0
$877$	−31117.5	−	11325.9i	−1.19814	−	0.436086i	−0.335562	−	0.942018i	$-0.608926\pi$
$877$	−31117.5	−	11325.9i	−1.19814	−	0.436086i	−0.862573	+	0.505932i	$0.831149\pi$
$878$	20855.3	+	7590.72i	0.801633	+	0.291771i
$879$		0			0
$880$	8623.38	−	48905.6i	0.330334	−	1.87342i
$881$	24719.6	+	42815.5i	0.945316	+	1.63734i	0.755118	+	0.655589i	$0.227580\pi$
$881$	24719.6	+	42815.5i	0.945316	+	1.63734i	0.190198	+	0.981746i	$0.439087\pi$
$882$		0			0
$883$	1865.43	−	3231.03i	0.0710950	−	0.123140i	−0.828286	−	0.560305i	$-0.810684\pi$
$883$	1865.43	−	3231.03i	0.0710950	−	0.123140i	0.899381	+	0.437165i	$0.144017\pi$
$884$	−930.262	−	780.582i	−0.0353938	−	0.0296989i
$885$		0			0
$886$	4642.13	+	26326.8i	0.176022	+	0.998269i
$887$	−23954.0	+	20099.8i	−0.906761	+	0.760863i	−0.971500	−	0.237039i	$-0.923823\pi$
$887$	−23954.0	+	20099.8i	−0.906761	+	0.760863i	0.0647387	+	0.997902i	$0.479379\pi$
$888$		0			0
$889$	−7848.74	+	2856.71i	−0.296106	+	0.107774i
$890$	44494.0			1.67578
$891$		0			0
$892$	25478.9			0.956386
$893$	20532.7	−	7473.30i	0.769430	−	0.280050i
$894$		0			0
$895$	−22610.3	+	18972.3i	−0.844447	+	0.708575i
$896$	533.314	+	3024.58i	0.0198848	+	0.112772i
$897$		0			0
$898$	−49593.0	−	41613.5i	−1.84292	−	1.54639i
$899$	1110.14	−	1922.82i	0.0411850	−	0.0713345i
$900$		0			0
$901$	−9253.95	−	16028.3i	−0.342168	−	0.592653i
$902$	−5609.40	+	31812.5i	−0.207065	+	1.17432i
$903$		0			0
$904$	−134.946	−	49.1164i	−0.00496488	−	0.00180707i
$905$	26501.7	+	9645.82i	0.973421	+	0.354296i
$906$		0			0
$907$	−1235.49	+	7006.83i	−0.0452303	+	0.256514i	−0.999035	−	0.0439124i	$-0.986018\pi$
$907$	−1235.49	+	7006.83i	−0.0452303	+	0.256514i	0.953805	+	0.300426i	$0.0971289\pi$
$908$	14253.9	+	24688.5i	0.520962	+	0.902333i
$909$		0			0
$910$	−488.051	+	845.330i	−0.0177788	+	0.0307939i
$911$	−13030.5	−	10933.9i	−0.473895	−	0.397645i	0.374318	−	0.927300i	$-0.377877\pi$
$911$	−13030.5	−	10933.9i	−0.473895	−	0.397645i	−0.848213	+	0.529655i	$0.822321\pi$
$912$		0			0
$913$	−5980.85	−	33919.1i	−0.216799	−	1.22953i
$914$	−58000.1	+	48667.9i	−2.09899	+	1.76126i
$915$		0			0
$916$	31480.8	−	11458.1i	1.13554	−	0.413302i
$917$	10160.3			0.365891
$918$		0			0
$919$	−29056.8			−1.04298			−0.521488	−	0.853258i	$-0.674623\pi$
$919$	−29056.8			−1.04298			−0.521488	+	0.853258i	$0.674623\pi$
$920$	16358.1	−	5953.86i	0.586207	−	0.213362i
$921$		0			0
$922$	47802.5	−	40111.1i	1.70747	−	1.43274i
$923$	−304.899	−	1729.17i	−0.0108731	−	0.0616644i
$924$		0			0
$925$	−5797.50	−	4864.68i	−0.206076	−	0.172919i
$926$	−12132.2	+	21013.6i	−0.430549	+	0.745732i
$927$		0			0
$928$	−11619.9	−	20126.2i	−0.411036	−	0.711934i
$929$	−2531.09	+	14354.5i	−0.0893891	+	0.506951i	0.906934	+	0.421273i	$0.138417\pi$
$929$	−2531.09	+	14354.5i	−0.0893891	+	0.506951i	−0.996323	+	0.0856777i	$0.972694\pi$
$930$		0			0
$931$	−22769.7	−	8287.48i	−0.801553	−	0.291741i
$932$	−41491.5	−	15101.7i	−1.45826	−	0.530763i
$933$		0			0
$934$	8014.80	−	45454.2i	0.280784	−	1.59241i
$935$	17404.0	+	30144.6i	0.608739	+	1.05437i
$936$		0			0
$937$	−25157.6	+	43574.2i	−0.877121	+	1.51922i	−0.0226353	+	0.999744i	$0.507206\pi$
$937$	−25157.6	+	43574.2i	−0.877121	+	1.51922i	−0.854486	+	0.519475i	$0.826128\pi$
$938$	−2629.29	−	2206.23i	−0.0915237	−	0.0767975i
$939$		0			0
$940$	7058.21	+	40029.1i	0.244908	+	1.38894i
$941$	−8486.51	+	7121.02i	−0.293998	+	0.246694i	−0.777841	−	0.628461i	$-0.783685\pi$
$941$	−8486.51	+	7121.02i	−0.293998	+	0.246694i	0.483843	+	0.875155i	$0.339241\pi$
$942$		0			0
$943$	23619.8	−	8596.89i	0.815658	−	0.296875i
$944$	182.113			0.00627890
$945$		0			0
$946$	84565.3			2.90640
$947$	−12593.7	+	4583.74i	−0.432144	+	0.157288i	−0.548928	−	0.835870i	$-0.684964\pi$
$947$	−12593.7	+	4583.74i	−0.432144	+	0.157288i	0.116783	+	0.993157i	$0.462742\pi$
$948$		0			0
$949$	−135.550	+	113.740i	−0.00463661	+	0.00389058i
$950$	5248.91	+	29768.1i	0.179260	+	1.01664i
$951$		0			0
$952$	−672.950	−	564.672i	−0.0229101	−	0.0192239i
$953$	−10756.1	+	18630.2i	−0.365609	+	0.633254i	−0.988874	−	0.148757i	$-0.952473\pi$
$953$	−10756.1	+	18630.2i	−0.365609	+	0.633254i	0.623265	+	0.782011i	$0.285806\pi$
$954$		0			0
$955$	−5068.24	−	8778.46i	−0.171732	−	0.297449i
$956$	−6515.76	+	36952.7i	−0.220434	+	1.25014i
$957$		0			0
$958$	−17802.1	−	6479.45i	−0.600377	−	0.218519i
$959$	7540.64	+	2744.57i	0.253910	+	0.0924158i
$960$		0			0
$961$	−5066.80	+	28735.3i	−0.170078	+	0.964562i
$962$	584.877	+	1013.04i	0.0196021	+	0.0339518i
$963$		0			0
$964$	7551.14	−	13079.0i	0.252288	−	0.436976i
$965$	26917.0	+	22586.0i	0.897916	+	0.753441i
$966$		0			0
$967$	−4111.11	−	23315.3i	−0.136716	−	0.775355i	−0.973649	−	0.228050i	$-0.926765\pi$
$967$	−4111.11	−	23315.3i	−0.136716	−	0.775355i	0.836933	−	0.547305i	$-0.184346\pi$
$968$	−12191.0	+	10229.5i	−0.404787	+	0.339657i
$969$		0			0
$970$	−19379.2	+	7053.46i	−0.641474	+	0.233477i
$971$	4744.36			0.156801			0.0784005	−	0.996922i	$-0.475019\pi$
$971$	4744.36			0.156801			0.0784005	+	0.996922i	$0.475019\pi$
$972$		0			0
$973$	10122.6			0.333519
$974$	43391.8	−	15793.3i	1.42748	−	0.519559i
$975$		0			0
$976$	14248.7	−	11956.1i	0.467305	−	0.392115i
$977$	6003.74	+	34048.9i	0.196599	+	1.11497i	0.910124	+	0.414336i	$0.135986\pi$
$977$	6003.74	+	34048.9i	0.196599	+	1.11497i	−0.713525	+	0.700629i	$0.752903\pi$
$978$		0			0
$979$	35545.3	+	29826.1i	1.16040	+	0.973693i
$980$	22537.4	−	39036.0i	0.734624	−	1.27241i
$981$		0			0
$982$	30723.2	+	53214.2i	0.998389	+	1.72926i
$983$	7692.18	−	43624.5i	0.249586	−	1.41547i	−0.560012	−	0.828485i	$-0.689203\pi$
$983$	7692.18	−	43624.5i	0.249586	−	1.41547i	0.809597	−	0.586985i	$-0.199685\pi$
$984$		0			0
$985$	−20669.0	−	7522.89i	−0.668597	−	0.243349i
$986$	12672.7	+	4612.49i	0.409312	+	0.148977i
$987$		0			0
$988$	436.955	−	2478.09i	0.0140702	−	0.0797962i
$989$	−32900.7	−	56985.7i	−1.05782	−	1.83220i
$990$		0			0
$991$	19091.3	−	33067.2i	0.611964	−	1.05995i	−0.378945	−	0.925419i	$-0.623713\pi$
$991$	19091.3	−	33067.2i	0.611964	−	1.05995i	0.990909	−	0.134533i	$-0.0429535\pi$
$992$	−4910.71	−	4120.57i	−0.157173	−	0.131883i
$993$		0			0
$994$	−1539.11	−	8728.72i	−0.0491123	−	0.278530i
$995$	48021.3	−	40294.7i	1.53003	−	1.28385i
$996$		0			0
$997$	−25728.4	+	9364.36i	−0.817277	+	0.297465i	−0.716626	−	0.697457i	$-0.754315\pi$
$997$	−25728.4	+	9364.36i	−0.817277	+	0.297465i	−0.100651	+	0.994922i	$0.532092\pi$
$998$	18260.3			0.579178
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	243.4.e.c.55.7		48
3.2	odd	2		243.4.e.b.55.2		48
9.2	odd	6		81.4.e.a.46.7		48
9.4	even	3		243.4.e.d.217.2		48
9.5	odd	6		243.4.e.a.217.7		48
9.7	even	3		27.4.e.a.16.2	✓	48
27.2	odd	18		729.4.a.c.1.21		24
27.4	even	9	inner	243.4.e.c.190.7		48
27.5	odd	18		243.4.e.a.28.7		48
27.13	even	9		27.4.e.a.22.2	yes	48
27.14	odd	18		81.4.e.a.37.7		48
27.22	even	9		243.4.e.d.28.2		48
27.23	odd	18		243.4.e.b.190.2		48
27.25	even	9		729.4.a.d.1.4		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.4.e.a.16.2	✓	48	9.7	even	3
27.4.e.a.22.2	yes	48	27.13	even	9
81.4.e.a.37.7		48	27.14	odd	18
81.4.e.a.46.7		48	9.2	odd	6
243.4.e.a.28.7		48	27.5	odd	18
243.4.e.a.217.7		48	9.5	odd	6
243.4.e.b.55.2		48	3.2	odd	2
243.4.e.b.190.2		48	27.23	odd	18
243.4.e.c.55.7		48	1.1	even	1	trivial
243.4.e.c.190.7		48	27.4	even	9	inner
243.4.e.d.28.2		48	27.22	even	9
243.4.e.d.217.2		48	9.4	even	3
729.4.a.c.1.21		24	27.2	odd	18
729.4.a.d.1.4		24	27.25	even	9

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:	\( N \)	\(=\)	\( 243 = 3^{5} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	243.e (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(3.91280 - 1.42414i) q^{2} +(7.15349 - 6.00249i) q^{4} +(2.58756 + 14.6748i) q^{5} +(3.34538 + 2.80711i) q^{7} +(2.78612 - 4.82571i) q^{8} +O(q^{10})\)	\(q+(3.91280 - 1.42414i) q^{2} +(7.15349 - 6.00249i) q^{4} +(2.58756 + 14.6748i) q^{5} +(3.34538 + 2.80711i) q^{7} +(2.78612 - 4.82571i) q^{8} +(31.0237 + 53.7346i) q^{10} +(-11.2362 + 63.7239i) q^{11} +(3.38506 + 1.23206i) q^{13} +(17.0876 + 6.21936i) q^{14} +(-8.94347 + 50.7209i) q^{16} +(-18.0500 - 31.2635i) q^{17} +(37.4017 - 64.7817i) q^{19} +(106.596 + 89.4443i) q^{20} +(46.7868 + 265.341i) q^{22} +(160.602 - 134.761i) q^{23} +(-91.1929 + 33.1915i) q^{25} +14.9997 q^{26} +40.7808 q^{28} +(-84.3064 + 30.6850i) q^{29} +(-18.9578 + 15.9075i) q^{31} +(44.9808 + 255.099i) q^{32} +(-115.150 - 96.6221i) q^{34} +(-32.5374 + 56.3564i) q^{35} +(38.9926 + 67.5371i) q^{37} +(54.0872 - 306.744i) q^{38} +(78.0256 + 28.3990i) q^{40} +(112.663 + 41.0058i) q^{41} +(54.5017 - 309.094i) q^{43} +(302.124 + 523.294i) q^{44} +(436.484 - 756.013i) q^{46} +(223.765 + 187.762i) q^{47} +(-56.2496 - 319.007i) q^{49} +(-309.551 + 259.744i) q^{50} +(31.6104 - 11.5053i) q^{52} +512.684 q^{53} -964.210 q^{55} +(22.8669 - 8.32289i) q^{56} +(-286.174 + 240.129i) q^{58} +(-0.614011 - 3.48223i) q^{59} +(-276.655 - 232.141i) q^{61} +(-51.5236 + 89.2414i) q^{62} +(333.285 + 577.266i) q^{64} +(-9.32119 + 52.8631i) q^{65} +(-177.368 - 64.5567i) q^{67} +(-316.779 - 115.298i) q^{68} +(-47.0528 + 266.850i) q^{70} +(-243.711 - 422.120i) q^{71} +(-24.5604 + 42.5399i) q^{73} +(248.753 + 208.728i) q^{74} +(-121.299 - 687.919i) q^{76} +(-216.469 + 181.639i) q^{77} +(-543.271 + 197.734i) q^{79} -767.462 q^{80} +499.225 q^{82} +(-500.182 + 182.051i) q^{83} +(412.080 - 345.776i) q^{85} +(-226.940 - 1287.04i) q^{86} +(276.207 + 231.765i) q^{88} +(358.549 - 621.025i) q^{89} +(7.86579 + 13.6239i) q^{91} +(339.962 - 1928.02i) q^{92} +(1142.95 + 416.000i) q^{94} +(1047.44 + 381.236i) q^{95} +(-57.7162 + 327.325i) q^{97} +(-674.406 - 1168.11i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 3 q^{2} + 3 q^{4} - 21 q^{5} + 3 q^{7} - 75 q^{8}+O(q^{10}) \) 48 * q + 3 * q^2 + 3 * q^4 - 21 * q^5 + 3 * q^7 - 75 * q^8	\( 48 q + 3 q^{2} + 3 q^{4} - 21 q^{5} + 3 q^{7} - 75 q^{8} - 3 q^{10} - 159 q^{11} + 3 q^{13} - 336 q^{14} - 45 q^{16} - 207 q^{17} - 3 q^{19} + 681 q^{20} + 111 q^{22} + 33 q^{23} + 435 q^{25} + 1914 q^{26} - 12 q^{28} - 51 q^{29} + 111 q^{31} + 1647 q^{32} - 513 q^{34} - 1257 q^{35} - 3 q^{37} - 525 q^{38} - 6 q^{40} + 447 q^{41} + 516 q^{43} - 2211 q^{44} - 3 q^{46} + 2109 q^{47} - 591 q^{49} - 4938 q^{50} - 1350 q^{52} + 2736 q^{53} - 12 q^{55} - 7773 q^{56} - 888 q^{58} + 3048 q^{59} + 57 q^{61} - 2118 q^{62} - 195 q^{64} + 3297 q^{65} + 2082 q^{67} + 3573 q^{68} + 1524 q^{70} - 3105 q^{71} - 219 q^{73} + 9006 q^{74} - 1425 q^{76} - 8985 q^{77} - 1401 q^{79} + 9870 q^{80} - 12 q^{82} - 8511 q^{83} - 1827 q^{85} + 12507 q^{86} - 3693 q^{88} - 5202 q^{89} + 267 q^{91} + 5118 q^{92} - 2211 q^{94} + 5178 q^{95} + 1569 q^{97} - 4392 q^{98}+O(q^{100}) \) 48 * q + 3 * q^2 + 3 * q^4 - 21 * q^5 + 3 * q^7 - 75 * q^8 - 3 * q^10 - 159 * q^11 + 3 * q^13 - 336 * q^14 - 45 * q^16 - 207 * q^17 - 3 * q^19 + 681 * q^20 + 111 * q^22 + 33 * q^23 + 435 * q^25 + 1914 * q^26 - 12 * q^28 - 51 * q^29 + 111 * q^31 + 1647 * q^32 - 513 * q^34 - 1257 * q^35 - 3 * q^37 - 525 * q^38 - 6 * q^40 + 447 * q^41 + 516 * q^43 - 2211 * q^44 - 3 * q^46 + 2109 * q^47 - 591 * q^49 - 4938 * q^50 - 1350 * q^52 + 2736 * q^53 - 12 * q^55 - 7773 * q^56 - 888 * q^58 + 3048 * q^59 + 57 * q^61 - 2118 * q^62 - 195 * q^64 + 3297 * q^65 + 2082 * q^67 + 3573 * q^68 + 1524 * q^70 - 3105 * q^71 - 219 * q^73 + 9006 * q^74 - 1425 * q^76 - 8985 * q^77 - 1401 * q^79 + 9870 * q^80 - 12 * q^82 - 8511 * q^83 - 1827 * q^85 + 12507 * q^86 - 3693 * q^88 - 5202 * q^89 + 267 * q^91 + 5118 * q^92 - 2211 * q^94 + 5178 * q^95 + 1569 * q^97 - 4392 * q^98

Introduction

L-functions

Modular forms

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