LMFDB - Embedded newform 225.4.e.f.151.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,4,Mod(76,225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(225, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0]))

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

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

chi := DirichletCharacter("225.76");

S:= CuspForms(chi, 4);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$13.2754297513$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			151.6
Character	$\chi$	$=$	225.151
Dual form			225.4.e.f.76.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.238017 + 0.412258i) q^{2} +(3.09012 + 4.17746i) q^{3} +(3.88670 + 6.73195i) q^{4} +(-2.45769 + 0.279619i) q^{6} +(-6.34045 + 10.9820i) q^{7} -7.50869 q^{8} +(-7.90234 + 25.8177i) q^{9} +O(q^{10})$	\(q+(-0.238017 + 0.412258i) q^{2} +(3.09012 + 4.17746i) q^{3} +(3.88670 + 6.73195i) q^{4} +(-2.45769 + 0.279619i) q^{6} +(-6.34045 + 10.9820i) q^{7} -7.50869 q^{8} +(-7.90234 + 25.8177i) q^{9} +(0.794994 - 1.37697i) q^{11} +(-16.1121 + 37.0390i) q^{12} +(-5.36718 - 9.29622i) q^{13} +(-3.01828 - 5.22781i) q^{14} +(-29.3064 + 50.7601i) q^{16} -69.7787 q^{17} +(-8.76266 - 9.40287i) q^{18} +98.5661 q^{19} +(-65.4695 + 7.44864i) q^{21} +(0.378445 + 0.655486i) q^{22} +(15.7777 + 27.3278i) q^{23} +(-23.2027 - 31.3672i) q^{24} +5.10993 q^{26} +(-132.272 + 46.7680i) q^{27} -98.5736 q^{28} +(150.627 - 260.893i) q^{29} +(58.6364 + 101.561i) q^{31} +(-43.9856 - 76.1853i) q^{32} +(8.20886 - 0.933944i) q^{33} +(16.6086 - 28.7669i) q^{34} +(-204.517 + 47.1473i) q^{36} -169.562 q^{37} +(-23.4605 + 40.6347i) q^{38} +(22.2494 - 51.1476i) q^{39} +(-70.9376 - 122.868i) q^{41} +(12.5121 - 28.7633i) q^{42} +(-150.121 + 260.018i) q^{43} +12.3596 q^{44} -15.0215 q^{46} +(-243.712 + 422.122i) q^{47} +(-302.608 + 34.4286i) q^{48} +(91.0974 + 157.785i) q^{49} +(-215.625 - 291.498i) q^{51} +(41.7212 - 72.2632i) q^{52} +459.166 q^{53} +(12.2024 - 65.6616i) q^{54} +(47.6084 - 82.4602i) q^{56} +(304.581 + 411.756i) q^{57} +(71.7037 + 124.194i) q^{58} +(250.099 + 433.185i) q^{59} +(-290.915 + 503.880i) q^{61} -55.8259 q^{62} +(-233.425 - 250.479i) q^{63} -427.024 q^{64} +(-1.56883 + 3.60647i) q^{66} +(-250.468 - 433.823i) q^{67} +(-271.209 - 469.747i) q^{68} +(-65.4059 + 150.357i) q^{69} +1066.69 q^{71} +(59.3362 - 193.857i) q^{72} +435.288 q^{73} +(40.3588 - 69.9034i) q^{74} +(383.096 + 663.542i) q^{76} +(10.0812 + 17.4612i) q^{77} +(15.7903 + 21.3465i) q^{78} +(-187.644 + 325.009i) q^{79} +(-604.106 - 408.040i) q^{81} +67.5375 q^{82} +(646.617 - 1119.97i) q^{83} +(-304.604 - 411.787i) q^{84} +(-71.4630 - 123.778i) q^{86} +(1555.33 - 176.954i) q^{87} +(-5.96936 + 10.3392i) q^{88} -403.296 q^{89} +136.121 q^{91} +(-122.646 + 212.430i) q^{92} +(-243.074 + 558.787i) q^{93} +(-116.016 - 200.945i) q^{94} +(182.340 - 419.170i) q^{96} +(790.735 - 1369.59i) q^{97} -86.7311 q^{98} +(29.2679 + 31.4062i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 4 q^{2} + q^{3} - 48 q^{4} - 13 q^{6} - 6 q^{7} - 90 q^{8} - 61 q^{9}+O(q^{10}) $ 24 * q + 4 * q^2 + q^3 - 48 * q^4 - 13 * q^6 - 6 * q^7 - 90 * q^8 - 61 * q^9	\( 24 q + 4 q^{2} + q^{3} - 48 q^{4} - 13 q^{6} - 6 q^{7} - 90 q^{8} - 61 q^{9} - 29 q^{11} + 77 q^{12} - 24 q^{13} + 69 q^{14} - 192 q^{16} - 158 q^{17} - 125 q^{18} - 150 q^{19} - 60 q^{21} + 18 q^{22} + 318 q^{23} + 342 q^{24} - 308 q^{26} + 394 q^{27} + 192 q^{28} - 106 q^{29} - 60 q^{31} + 914 q^{32} + 80 q^{33} + 108 q^{34} + 1303 q^{36} - 168 q^{37} + 640 q^{38} - 410 q^{39} + 353 q^{41} - 1521 q^{42} + 426 q^{43} + 1142 q^{44} + 540 q^{46} + 1210 q^{47} - 2680 q^{48} - 666 q^{49} - 1369 q^{51} + 75 q^{52} - 896 q^{53} - 2128 q^{54} + 570 q^{56} - 1544 q^{57} - 594 q^{58} - 482 q^{59} - 402 q^{61} - 5088 q^{62} + 1038 q^{63} + 1950 q^{64} + 2041 q^{66} + 201 q^{67} + 3437 q^{68} + 2856 q^{69} - 1888 q^{71} + 5493 q^{72} - 906 q^{73} - 10 q^{74} + 462 q^{76} + 2652 q^{77} + 4589 q^{78} - 258 q^{79} + 3071 q^{81} + 1746 q^{82} + 3012 q^{83} - 2703 q^{84} - 1952 q^{86} - 2708 q^{87} + 216 q^{88} - 1476 q^{89} - 1236 q^{91} + 5232 q^{92} - 3024 q^{93} - 63 q^{94} - 10424 q^{96} + 318 q^{97} - 15022 q^{98} - 1697 q^{99}+O(q^{100}) \) 24 * q + 4 * q^2 + q^3 - 48 * q^4 - 13 * q^6 - 6 * q^7 - 90 * q^8 - 61 * q^9 - 29 * q^11 + 77 * q^12 - 24 * q^13 + 69 * q^14 - 192 * q^16 - 158 * q^17 - 125 * q^18 - 150 * q^19 - 60 * q^21 + 18 * q^22 + 318 * q^23 + 342 * q^24 - 308 * q^26 + 394 * q^27 + 192 * q^28 - 106 * q^29 - 60 * q^31 + 914 * q^32 + 80 * q^33 + 108 * q^34 + 1303 * q^36 - 168 * q^37 + 640 * q^38 - 410 * q^39 + 353 * q^41 - 1521 * q^42 + 426 * q^43 + 1142 * q^44 + 540 * q^46 + 1210 * q^47 - 2680 * q^48 - 666 * q^49 - 1369 * q^51 + 75 * q^52 - 896 * q^53 - 2128 * q^54 + 570 * q^56 - 1544 * q^57 - 594 * q^58 - 482 * q^59 - 402 * q^61 - 5088 * q^62 + 1038 * q^63 + 1950 * q^64 + 2041 * q^66 + 201 * q^67 + 3437 * q^68 + 2856 * q^69 - 1888 * q^71 + 5493 * q^72 - 906 * q^73 - 10 * q^74 + 462 * q^76 + 2652 * q^77 + 4589 * q^78 - 258 * q^79 + 3071 * q^81 + 1746 * q^82 + 3012 * q^83 - 2703 * q^84 - 1952 * q^86 - 2708 * q^87 + 216 * q^88 - 1476 * q^89 - 1236 * q^91 + 5232 * q^92 - 3024 * q^93 - 63 * q^94 - 10424 * q^96 + 318 * q^97 - 15022 * q^98 - 1697 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	−0.238017	+	0.412258i	−0.0841519	+	0.145755i	−0.905030	−	0.425349i	$-0.860151\pi$
$2$	−0.238017	+	0.412258i	−0.0841519	+	0.145755i	0.820878	+	0.571104i	$0.193485\pi$
$3$	3.09012	+	4.17746i	0.594694	+	0.803953i
$3$	3.09012	+	4.17746i	0.594694	+	0.803953i
$4$	3.88670	+	6.73195i	0.485837	+	0.841494i
$5$		0			0
$5$		0			0
$6$	−2.45769	+	0.279619i	−0.167225	+	0.0190256i
$7$	−6.34045	+	10.9820i	−0.342352	+	0.592971i	−0.984869	−	0.173300i	$-0.944557\pi$
$7$	−6.34045	+	10.9820i	−0.342352	+	0.592971i	0.642517	+	0.766271i	$0.277890\pi$
$8$	−7.50869			−0.331840
$9$	−7.90234	+	25.8177i	−0.292679	+	0.956211i
$10$		0			0
$11$	0.794994	−	1.37697i	0.0217909	−	0.0377429i	−0.854924	−	0.518753i	$-0.826397\pi$
$11$	0.794994	−	1.37697i	0.0217909	−	0.0377429i	0.876715	+	0.481010i	$0.159730\pi$
$12$	−16.1121	+	37.0390i	−0.387597	+	0.891021i
$13$	−5.36718	−	9.29622i	−0.114507	−	0.198331i	0.803076	−	0.595877i	$-0.203195\pi$
$13$	−5.36718	−	9.29622i	−0.114507	−	0.198331i	−0.917582	+	0.397546i	$0.869862\pi$
$14$	−3.01828	−	5.22781i	−0.0576191	−	0.0997993i
$15$		0			0
$16$	−29.3064	+	50.7601i	−0.457912	+	0.793127i
$17$	−69.7787			−0.995519			−0.497760	−	0.867315i	$-0.665844\pi$
$17$	−69.7787			−0.995519			−0.497760	+	0.867315i	$0.665844\pi$
$18$	−8.76266	−	9.40287i	−0.114743	−	0.123127i
$19$	98.5661			1.19014			0.595069	−	0.803675i	$-0.297125\pi$
$19$	98.5661			1.19014			0.595069	+	0.803675i	$0.297125\pi$
$20$		0			0
$21$	−65.4695	+	7.44864i	−0.680315	+	0.0774013i
$22$	0.378445	+	0.655486i	0.00366749	+	0.00635227i
$23$	15.7777	+	27.3278i	0.143038	+	0.247750i	0.928639	−	0.370984i	$-0.120979\pi$
$23$	15.7777	+	27.3278i	0.143038	+	0.247750i	−0.785601	+	0.618734i	$0.787646\pi$
$24$	−23.2027	−	31.3672i	−0.197343	−	0.266784i
$25$		0			0
$26$	5.10993			0.0385438
$27$	−132.272	+	46.7680i	−0.942802	+	0.333352i
$28$	−98.5736			−0.665309
$29$	150.627	−	260.893i	0.964507	−	1.67058i	0.253574	−	0.967316i	$-0.418394\pi$
$29$	150.627	−	260.893i	0.964507	−	1.67058i	0.710933	−	0.703260i	$-0.248273\pi$
$30$		0			0
$31$	58.6364	+	101.561i	0.339723	+	0.588417i	0.984380	−	0.176054i	$-0.0563334\pi$
$31$	58.6364	+	101.561i	0.339723	+	0.588417i	−0.644658	+	0.764471i	$0.723000\pi$
$32$	−43.9856	−	76.1853i	−0.242988	−	0.420868i
$33$	8.20886	−	0.933944i	0.0433024	−	0.00492663i
$34$	16.6086	−	28.7669i	0.0837748	−	0.145102i
$35$		0			0
$36$	−204.517	+	47.1473i	−0.946840	+	0.218275i
$37$	−169.562			−0.753402			−0.376701	−	0.926335i	$-0.622941\pi$
$37$	−169.562			−0.753402			−0.376701	+	0.926335i	$0.622941\pi$
$38$	−23.4605	+	40.6347i	−0.100152	+	0.173469i
$39$	22.2494	−	51.1476i	0.0913526	−	0.210004i
$40$		0			0
$41$	−70.9376	−	122.868i	−0.270210	−	0.468017i	0.698706	−	0.715409i	$-0.253760\pi$
$41$	−70.9376	−	122.868i	−0.270210	−	0.468017i	−0.968915	+	0.247392i	$0.920426\pi$
$42$	12.5121	−	28.7633i	0.0459682	−	0.105673i
$43$	−150.121	+	260.018i	−0.532402	+	0.922147i	0.466882	+	0.884319i	$0.345377\pi$
$43$	−150.121	+	260.018i	−0.532402	+	0.922147i	−0.999284	+	0.0378277i	$0.987956\pi$
$44$	12.3596			0.0423472
$45$		0			0
$46$	−15.0215			−0.0481478
$47$	−243.712	+	422.122i	−0.756364	+	1.31006i	0.188330	+	0.982106i	$0.439693\pi$
$47$	−243.712	+	422.122i	−0.756364	+	1.31006i	−0.944694	+	0.327954i	$0.893641\pi$
$48$	−302.608	+	34.4286i	−0.909953	+	0.103528i
$49$	91.0974	+	157.785i	0.265590	+	0.460016i
$50$		0			0
$51$	−215.625	−	291.498i	−0.592029	−	0.800350i
$52$	41.7212	−	72.2632i	0.111263	−	0.192713i
$53$	459.166			1.19002			0.595012	−	0.803717i	$-0.297147\pi$
$53$	459.166			1.19002			0.595012	+	0.803717i	$0.297147\pi$
$54$	12.2024	−	65.6616i	0.0307508	−	0.165471i
$55$		0			0
$56$	47.6084	−	82.4602i	0.113606	−	0.196772i
$57$	304.581	+	411.756i	0.707767	+	0.956814i
$58$	71.7037	+	124.194i	0.162330	+	0.281164i
$59$	250.099	+	433.185i	0.551867	+	0.955862i	0.998140	+	0.0609650i	$0.0194178\pi$
$59$	250.099	+	433.185i	0.551867	+	0.955862i	−0.446273	+	0.894897i	$0.647249\pi$
$60$		0			0
$61$	−290.915	+	503.880i	−0.610621	+	1.05763i	0.380515	+	0.924775i	$0.375747\pi$
$61$	−290.915	+	503.880i	−0.610621	+	1.05763i	−0.991136	+	0.132852i	$0.957587\pi$
$62$	−55.8259			−0.114353
$63$	−233.425	−	250.479i	−0.466806	−	0.500911i
$64$	−427.024			−0.834032
$65$		0			0
$66$	−1.56883	+	3.60647i	−0.00292589	+	0.00672614i
$67$	−250.468	−	433.823i	−0.456709	−	0.791044i	0.542075	−	0.840330i	$-0.317639\pi$
$67$	−250.468	−	433.823i	−0.456709	−	0.791044i	−0.998785	+	0.0492862i	$0.984305\pi$
$68$	−271.209	−	469.747i	−0.483660	−	0.837724i
$69$	−65.4059	+	150.357i	−0.114115	+	0.262331i
$70$		0			0
$71$	1066.69			1.78299			0.891495	−	0.453031i	$-0.149657\pi$
$71$	1066.69			1.78299			0.891495	+	0.453031i	$0.149657\pi$
$72$	59.3362	−	193.857i	0.0971227	−	0.317309i
$73$	435.288			0.697899			0.348950	−	0.937141i	$-0.386538\pi$
$73$	435.288			0.697899			0.348950	+	0.937141i	$0.386538\pi$
$74$	40.3588	−	69.9034i	0.0634002	−	0.109812i
$75$		0			0
$76$	383.096	+	663.542i	0.578213	+	1.00149i
$77$	10.0812	+	17.4612i	0.0149203	+	0.0258427i
$78$	15.7903	+	21.3465i	0.0229218	+	0.0309874i
$79$	−187.644	+	325.009i	−0.267236	+	0.462866i	−0.968147	−	0.250383i	$-0.919444\pi$
$79$	−187.644	+	325.009i	−0.267236	+	0.462866i	0.700911	+	0.713248i	$0.252777\pi$
$80$		0			0
$81$	−604.106	−	408.040i	−0.828678	−	0.559726i
$82$	67.5375			0.0909546
$83$	646.617	−	1119.97i	0.855126	−	1.48112i	−0.0214014	−	0.999771i	$-0.506813\pi$
$83$	646.617	−	1119.97i	0.855126	−	1.48112i	0.876528	−	0.481351i	$-0.159854\pi$
$84$	−304.604	−	411.787i	−0.395655	−	0.534877i
$85$		0			0
$86$	−71.4630	−	123.778i	−0.0896053	−	0.155201i
$87$	1555.33	−	176.954i	1.91665	−	0.218062i
$88$	−5.96936	+	10.3392i	−0.00723109	+	0.0125246i
$89$	−403.296			−0.480330			−0.240165	−	0.970732i	$-0.577201\pi$
$89$	−403.296			−0.480330			−0.240165	+	0.970732i	$0.577201\pi$
$90$		0			0
$91$	136.121			0.156806
$92$	−122.646	+	212.430i	−0.138987	+	0.240732i
$93$	−243.074	+	558.787i	−0.271028	+	0.623049i
$94$	−116.016	−	200.945i	−0.127299	−	0.220488i
$95$		0			0
$96$	182.340	−	419.170i	0.193854	−	0.445639i
$97$	790.735	−	1369.59i	0.827700	−	1.43362i	−0.0721373	−	0.997395i	$-0.522982\pi$
$97$	790.735	−	1369.59i	0.827700	−	1.43362i	0.899838	−	0.436225i	$-0.143685\pi$
$98$	−86.7311			−0.0893996
$99$	29.2679	+	31.4062i	0.0297124	+	0.0318832i
$100$		0			0
$101$	577.422	−	1000.12i	0.568867	−	0.985307i	−0.427811	−	0.903868i	$-0.640715\pi$
$101$	577.422	−	1000.12i	0.568867	−	0.985307i	0.996678	−	0.0814388i	$-0.0259515\pi$
$102$	171.495	−	19.5114i	0.166476	−	0.0189404i
$103$	725.615	+	1256.80i	0.694145	+	1.20229i	0.970468	+	0.241230i	$0.0775507\pi$
$103$	725.615	+	1256.80i	0.694145	+	1.20229i	−0.276323	+	0.961065i	$0.589116\pi$
$104$	40.3004	+	69.8024i	0.0379979	+	0.0658143i
$105$		0			0
$106$	−109.290	+	189.295i	−0.100143	+	0.173452i
$107$	136.728			0.123533			0.0617664	−	0.998091i	$-0.480327\pi$
$107$	136.728			0.123533			0.0617664	+	0.998091i	$0.480327\pi$
$108$	−828.939	−	708.673i	−0.738562	−	0.631408i
$109$	40.1176			0.0352529			0.0176265	−	0.999845i	$-0.494389\pi$
$109$	40.1176			0.0352529			0.0176265	+	0.999845i	$0.494389\pi$
$110$		0			0
$111$	−523.967	−	708.339i	−0.448043	−	0.605699i
$112$	−371.631	−	643.684i	−0.313534	−	0.543057i
$113$	989.231	+	1713.40i	0.823531	+	1.42640i	0.903037	+	0.429564i	$0.141333\pi$
$113$	989.231	+	1713.40i	0.823531	+	1.42640i	−0.0795054	+	0.996834i	$0.525334\pi$
$114$	−242.245	+	27.5609i	−0.199021	+	0.0226431i
$115$		0			0
$116$	2341.76			1.87437
$117$	282.420	−	65.1062i	0.223160	−	0.0514450i
$118$	−238.112			−0.185763
$119$	442.428	−	766.309i	0.340818	−	0.590314i
$120$		0			0
$121$	664.236	+	1150.49i	0.499050	+	0.864381i
$122$	−138.486	−	239.865i	−0.102770	−	0.178003i
$123$	294.069	−	676.014i	0.215571	−	0.495562i
$124$	−455.804	+	789.475i	−0.330100	+	0.571750i
$125$		0			0
$126$	158.821	−	36.6130i	0.112293	−	0.0258869i
$127$	1318.35			0.921142			0.460571	−	0.887623i	$-0.347645\pi$
$127$	1318.35			0.921142			0.460571	+	0.887623i	$0.347645\pi$
$128$	453.524	−	785.527i	0.313174	−	0.542433i
$129$	−1550.11	+	176.360i	−1.05798	+	0.120369i
$130$		0			0
$131$	−792.463	−	1372.59i	−0.528533	−	0.915446i	−0.999447	−	0.0332667i	$-0.989409\pi$
$131$	−792.463	−	1372.59i	−0.528533	−	0.915446i	0.470913	−	0.882179i	$-0.343924\pi$
$132$	38.1926	+	51.6317i	0.0251836	+	0.0340452i
$133$	−624.953	+	1082.45i	−0.407446	+	0.705717i
$134$	238.463			0.153732
$135$		0			0
$136$	523.947			0.330353
$137$	−190.760	+	330.406i	−0.118961	+	0.206047i	−0.919356	−	0.393426i	$-0.871290\pi$
$137$	−190.760	+	330.406i	−0.118961	+	0.206047i	0.800395	+	0.599473i	$0.204623\pi$
$138$	−46.4182	−	62.7517i	−0.0286332	−	0.0387086i
$139$	1231.19	+	2132.49i	0.751283	+	1.30126i	0.947201	+	0.320641i	$0.103898\pi$
$139$	1231.19	+	2132.49i	0.751283	+	1.30126i	−0.195918	+	0.980620i	$0.562769\pi$
$140$		0			0
$141$	−2516.50	+	286.309i	−1.50303	+	0.171004i
$142$	−253.890	+	439.750i	−0.150042	+	0.259880i
$143$	−17.0675			−0.00998080
$144$	−1078.92	−	1157.75i	−0.624375	−	0.669992i
$145$		0			0
$146$	−103.606	+	179.451i	−0.0587295	+	0.101723i
$147$	−377.640	+	868.131i	−0.211886	+	0.487090i
$148$	−659.037	−	1141.48i	−0.366030	−	0.633983i
$149$	−192.172	−	332.852i	−0.105660	−	0.183008i	0.808348	−	0.588705i	$-0.200362\pi$
$149$	−192.172	−	332.852i	−0.105660	−	0.183008i	−0.914008	+	0.405697i	$0.867029\pi$
$150$		0			0
$151$	−398.550	+	690.308i	−0.214792	+	0.372030i	−0.953208	−	0.302315i	$-0.902241\pi$
$151$	−398.550	+	690.308i	−0.214792	+	0.372030i	0.738417	+	0.674345i	$0.235574\pi$
$152$	−740.102			−0.394935
$153$	551.415	−	1801.53i	0.291368	−	0.951926i
$154$	−9.59804			−0.00502229
$155$		0			0
$156$	430.800	−	49.0133i	0.221100	−	0.0251551i
$157$	435.496	+	754.300i	0.221378	+	0.383438i	0.955227	−	0.295875i	$-0.0956112\pi$
$157$	435.496	+	754.300i	0.221378	+	0.383438i	−0.733849	+	0.679313i	$0.762278\pi$
$158$	−89.3252	−	154.716i	−0.0449768	−	0.0779021i
$159$	1418.88	+	1918.15i	0.707700	+	0.956723i
$160$		0			0
$161$	−400.152			−0.195878
$162$	312.006	−	151.927i	0.151318	−	0.0736822i
$163$	−31.2604			−0.0150215			−0.00751074	−	0.999972i	$-0.502391\pi$
$163$	−31.2604			−0.0150215			−0.00751074	+	0.999972i	$0.502391\pi$
$164$	551.426	−	955.097i	0.262556	−	0.454759i
$165$		0			0
$166$	307.813	+	533.147i	0.143921	+	0.249278i
$167$	18.6415	+	32.2881i	0.00863787	+	0.0149612i	0.870312	−	0.492501i	$-0.163917\pi$
$167$	18.6415	+	32.2881i	0.00863787	+	0.0149612i	−0.861674	+	0.507462i	$0.830584\pi$
$168$	491.590	−	55.9295i	0.225756	−	0.0256849i
$169$	1040.89	−	1802.87i	0.473776	−	0.820605i
$170$		0			0
$171$	−778.903	+	2544.75i	−0.348329	+	1.13802i
$172$	−2333.90			−1.03464
$173$	590.590	−	1022.93i	0.259548	−	0.449550i	−0.706573	−	0.707640i	$-0.749760\pi$
$173$	590.590	−	1022.93i	0.259548	−	0.449550i	0.966121	+	0.258090i	$0.0830932\pi$
$174$	−297.244	+	683.315i	−0.129506	+	0.297712i
$175$		0			0
$176$	46.5967	+	80.7079i	0.0199566	+	0.0345658i
$177$	−1036.78	+	2383.37i	−0.440276	+	1.01212i
$178$	95.9916	−	166.262i	0.0404206	−	0.0700106i
$179$	−429.484			−0.179336			−0.0896680	−	0.995972i	$-0.528581\pi$
$179$	−429.484			−0.179336			−0.0896680	+	0.995972i	$0.528581\pi$
$180$		0			0
$181$	−1787.97			−0.734246			−0.367123	−	0.930172i	$-0.619657\pi$
$181$	−1787.97			−0.734246			−0.367123	+	0.930172i	$0.619657\pi$
$182$	−32.3992	+	56.1171i	−0.0131956	+	0.0228554i
$183$	−3003.90	+	341.762i	−1.21341	+	0.138053i
$184$	−118.470	−	205.196i	−0.0474659	−	0.0822134i
$185$		0			0
$186$	−172.509	−	233.211i	−0.0680051	−	0.0919346i
$187$	−55.4736	+	96.0832i	−0.0216932	+	0.0375738i
$188$	−3788.94			−1.46988
$189$	325.056	−	1749.13i	0.125102	−	0.673178i
$190$		0			0
$191$	−392.583	+	679.974i	−0.148724	+	0.257598i	−0.930756	−	0.365640i	$-0.880850\pi$
$191$	−392.583	+	679.974i	−0.148724	+	0.257598i	0.782032	+	0.623238i	$0.214183\pi$
$192$	−1319.56	−	1783.88i	−0.495994	−	0.670522i
$193$	238.539	+	413.162i	0.0889659	+	0.154093i	0.907074	−	0.420971i	$-0.138310\pi$
$193$	238.539	+	413.162i	0.0889659	+	0.154093i	−0.818108	+	0.575064i	$0.804977\pi$
$194$	376.417	+	651.974i	0.139305	+	0.241284i
$195$		0			0
$196$	−708.136	+	1226.53i	−0.258067	+	0.446985i
$197$	−4628.37			−1.67390			−0.836949	−	0.547281i	$-0.815663\pi$
$197$	−4628.37			−1.67390			−0.836949	+	0.547281i	$0.815663\pi$
$198$	−19.9137	+	4.59070i	−0.00714751	+	0.00164771i
$199$	2533.85			0.902611			0.451305	−	0.892370i	$-0.350958\pi$
$199$	2533.85			0.902611			0.451305	+	0.892370i	$0.350958\pi$
$200$		0			0
$201$	1038.30	−	2386.88i	0.364359	−	0.837601i
$202$	274.873	+	476.094i	0.0957425	+	0.165831i
$203$	1910.08	+	3308.36i	0.660402	+	1.14385i
$204$	1124.28	−	2584.54i	0.385861	−	0.887029i
$205$		0			0
$206$	−690.836			−0.233654
$207$	−830.222	+	191.391i	−0.278765	+	0.0642636i
$208$	629.170			0.209736
$209$	78.3594	−	135.722i	0.0259341	−	0.0449192i
$210$		0			0
$211$	−1382.70	−	2394.90i	−0.451131	−	0.781382i	0.547325	−	0.836920i	$-0.315646\pi$
$211$	−1382.70	−	2394.90i	−0.451131	−	0.781382i	−0.998457	+	0.0555378i	$0.982313\pi$
$212$	1784.64	+	3091.08i	0.578158	+	1.00140i
$213$	3296.18	+	4456.03i	1.06033	+	1.43344i
$214$	−32.5437	+	56.3673i	−0.0103955	+	0.0180056i
$215$		0			0
$216$	993.185	−	351.166i	0.312860	−	0.110620i
$217$	−1487.12			−0.465219
$218$	−9.54869	+	16.5388i	−0.00296660	+	0.00513830i
$219$	1345.09	+	1818.40i	0.415036	+	0.561078i
$220$		0			0
$221$	374.515	+	648.679i	0.113994	+	0.197443i
$222$	416.732	−	47.4128i	0.125988	−	0.0143339i
$223$	−234.694	+	406.502i	−0.0704767	+	0.122069i	−0.899110	−	0.437722i	$-0.855785\pi$
$223$	−234.694	+	406.502i	−0.0704767	+	0.122069i	0.828634	+	0.559791i	$0.189119\pi$
$224$	1115.55			0.332750
$225$		0			0
$226$	−941.817			−0.277207
$227$	2143.99	−	3713.50i	0.626879	−	1.08579i	−0.361295	−	0.932452i	$-0.617665\pi$
$227$	2143.99	−	3713.50i	0.626879	−	1.08579i	0.988174	−	0.153335i	$-0.0490015\pi$
$228$	−1588.11	+	3650.79i	−0.461294	+	1.06044i
$229$	−2052.30	−	3554.69i	−0.592227	−	1.02577i	−0.993932	−	0.109998i	$-0.964916\pi$
$229$	−2052.30	−	3554.69i	−0.592227	−	1.02577i	0.401705	−	0.915769i	$-0.368418\pi$
$230$		0			0
$231$	−41.7913	+	96.0711i	−0.0119033	+	0.0273637i
$232$	−1131.01	+	1958.97i	−0.320062	+	0.554364i
$233$	−4272.57			−1.20131			−0.600656	−	0.799508i	$-0.705094\pi$
$233$	−4272.57			−1.20131			−0.600656	+	0.799508i	$0.705094\pi$
$234$	−40.3804	+	131.927i	−0.0112810	+	0.0368560i
$235$		0			0
$236$	−1944.12	+	3367.31i	−0.536235	+	0.928786i
$237$	−1937.56	+	220.441i	−0.531045	+	0.0604185i
$238$	210.611	+	364.790i	0.0573610	+	0.0993521i
$239$	780.619	+	1352.07i	0.211272	+	0.365934i	0.952113	−	0.305747i	$-0.0989061\pi$
$239$	780.619	+	1352.07i	0.211272	+	0.365934i	−0.740841	+	0.671681i	$0.765573\pi$
$240$		0			0
$241$	2410.77	−	4175.58i	0.644362	−	1.11607i	−0.340086	−	0.940394i	$-0.610456\pi$
$241$	2410.77	−	4175.58i	0.644362	−	1.11607i	0.984448	−	0.175674i	$-0.0562105\pi$
$242$	−632.399			−0.167984
$243$	−162.187	−	3784.52i	−0.0428161	−	0.999083i
$244$	−4522.80			−1.18665
$245$		0			0
$246$	208.699	+	282.135i	0.0540901	+	0.0731232i
$247$	−529.021	−	916.292i	−0.136279	−	0.236042i
$248$	−440.282	−	762.591i	−0.112734	−	0.195260i
$249$	6676.77	−	759.634i	1.69929	−	0.193333i
$250$		0			0
$251$	−3487.72			−0.877063			−0.438532	−	0.898716i	$-0.644501\pi$
$251$	−3487.72			−0.877063			−0.438532	+	0.898716i	$0.644501\pi$
$252$	778.962	−	2544.94i	0.194722	−	0.636176i
$253$	50.1728			0.0124677
$254$	−313.791	+	543.503i	−0.0775158	+	0.134261i
$255$		0			0
$256$	−1492.20	−	2584.57i	−0.364308	−	0.631000i
$257$	2460.87	+	4262.35i	0.597295	+	1.03454i	0.993219	+	0.116261i	$0.0370910\pi$
$257$	2460.87	+	4262.35i	0.597295	+	1.03454i	−0.395924	+	0.918283i	$0.629576\pi$
$258$	296.247	−	681.021i	0.0714865	−	0.164335i
$259$	1075.10	−	1862.13i	0.257929	−	0.446745i
$260$		0			0
$261$	5545.36	+	5950.51i	1.31513	+	1.41121i
$262$	754.480			0.177908
$263$	2758.58	−	4777.99i	0.646772	−	1.12024i	−0.337117	−	0.941463i	$-0.609452\pi$
$263$	2758.58	−	4777.99i	0.646772	−	1.12024i	0.983889	−	0.178780i	$-0.0572149\pi$
$264$	−61.6377	+	7.01269i	−0.0143695	+	0.00163485i
$265$		0			0
$266$	−297.500	−	515.284i	−0.0685747	−	0.118775i
$267$	−1246.23	−	1684.75i	−0.285649	−	0.386162i
$268$	1946.98	−	3372.28i	0.443772	−	0.768636i
$269$	−7844.13			−1.77794			−0.888969	−	0.457968i	$-0.848577\pi$
$269$	−7844.13			−1.77794			−0.888969	+	0.457968i	$0.848577\pi$
$270$		0			0
$271$	4301.35			0.964164			0.482082	−	0.876126i	$-0.339881\pi$
$271$	4301.35			0.964164			0.482082	+	0.876126i	$0.339881\pi$
$272$	2044.96	−	3541.98i	0.455860	−	0.789573i
$273$	420.631	+	568.641i	0.0932517	+	0.126065i
$274$	−90.8083	−	157.285i	−0.0200216	−	0.0346785i
$275$		0			0
$276$	−1266.41	+	144.083i	−0.276192	+	0.0314231i
$277$	−925.922	+	1603.74i	−0.200842	+	0.347869i	−0.948800	−	0.315877i	$-0.897701\pi$
$277$	−925.922	+	1603.74i	−0.200842	+	0.347869i	0.747958	+	0.663746i	$0.231034\pi$
$278$	−1172.18			−0.252888
$279$	−3085.44	+	711.285i	−0.662081	+	0.152629i
$280$		0			0
$281$	−3470.93	+	6011.82i	−0.736862	+	1.27628i	0.217040	+	0.976163i	$0.430360\pi$
$281$	−3470.93	+	6011.82i	−0.736862	+	1.27628i	−0.953902	+	0.300119i	$0.902974\pi$
$282$	480.937	−	1105.59i	0.101558	−	0.233465i
$283$	−3216.21	−	5570.64i	−0.675562	−	1.17011i	−0.976304	−	0.216402i	$-0.930568\pi$
$283$	−3216.21	−	5570.64i	−0.675562	−	1.17011i	0.300743	−	0.953705i	$-0.402765\pi$
$284$	4145.88	+	7180.87i	0.866242	+	1.50038i
$285$		0			0
$286$	4.06236	−	7.03621i	0.000839903	−	0.00145476i
$287$	1799.10			0.370027
$288$	2314.52	−	533.564i	0.473556	−	0.109169i
$289$	−43.9287			−0.00894133
$290$		0			0
$291$	8164.88	−	928.941i	1.64479	−	0.187132i
$292$	1691.83	+	2930.34i	0.339065	+	0.587278i
$293$	3820.89	+	6617.98i	0.761840	+	1.31955i	0.941901	+	0.335890i	$0.109037\pi$
$293$	3820.89	+	6617.98i	0.761840	+	1.31955i	−0.180062	+	0.983655i	$0.557630\pi$
$294$	−268.009	−	362.316i	−0.0531654	−	0.0718731i
$295$		0			0
$296$	1273.19			0.250009
$297$	−40.7569	+	219.314i	−0.00796281	+	0.0428481i
$298$	182.961			0.0355660
$299$	169.364	−	293.347i	0.0327577	−	0.0567380i
$300$		0			0
$301$	−1903.67	−	3297.26i	−0.364538	−	0.631398i
$302$	−189.724	−	328.611i	−0.0361502	−	0.0626140i
$303$	5962.28	−	678.344i	1.13044	−	0.128613i
$304$	−2888.61	+	5003.23i	−0.544978	+	0.943930i
$305$		0			0
$306$	611.448	+	656.120i	0.114229	+	0.122575i
$307$	4517.66			0.839857			0.419929	−	0.907557i	$-0.362055\pi$
$307$	4517.66			0.839857			0.419929	+	0.907557i	$0.362055\pi$
$308$	−78.3654	+	135.733i	−0.0144977	+	0.0251107i
$309$	−3008.00	+	6914.89i	−0.553784	+	1.27306i
$310$		0			0
$311$	−1966.54	−	3406.15i	−0.358560	−	0.621044i	0.629160	−	0.777275i	$-0.283399\pi$
$311$	−1966.54	−	3406.15i	−0.358560	−	0.621044i	−0.987721	+	0.156231i	$0.950066\pi$
$312$	−167.064	+	384.051i	−0.0303145	+	0.0696879i
$313$	1583.09	−	2742.00i	0.285884	−	0.495165i	−0.686939	−	0.726715i	$-0.741046\pi$
$313$	1583.09	−	2742.00i	0.285884	−	0.495165i	0.972823	+	0.231549i	$0.0743795\pi$
$314$	−414.622			−0.0745175
$315$		0			0
$316$	−2917.26			−0.519332
$317$	3920.86	−	6791.13i	0.694692	−	1.20324i	−0.275592	−	0.961275i	$-0.588874\pi$
$317$	3920.86	−	6791.13i	0.694692	−	1.20324i	0.970284	−	0.241967i	$-0.0777927\pi$
$318$	−1128.49	+	128.391i	−0.199002	+	0.0226410i
$319$	−239.495	−	414.817i	−0.0420349	−	0.0728066i
$320$		0			0
$321$	422.506	+	571.176i	0.0734641	+	0.0993145i
$322$	95.2431	−	164.966i	0.0164835	−	0.0285503i
$323$	−6877.82			−1.18480
$324$	398.932	−	5652.74i	0.0684040	−	0.969263i
$325$		0			0
$326$	7.44051	−	12.8873i	0.00126409	−	0.00218946i
$327$	123.968	+	167.590i	0.0209647	+	0.0283417i
$328$	532.648	+	922.574i	0.0896664	+	0.155307i
$329$	−3090.49	−	5352.89i	−0.517885	−	0.897004i
$330$		0			0
$331$	5426.53	−	9399.03i	0.901115	−	1.56078i	0.0750663	−	0.997179i	$-0.476083\pi$
$331$	5426.53	−	9399.03i	0.901115	−	1.56078i	0.826049	−	0.563599i	$-0.190584\pi$
$332$	10052.8			1.66181
$333$	1339.94	−	4377.70i	0.220505	−	0.720411i
$334$	−17.7480			−0.00290757
$335$		0			0
$336$	1540.58	−	3541.53i	0.250135	−	0.575019i
$337$	3258.64	+	5644.13i	0.526735	+	0.912331i	0.999515	+	0.0311507i	$0.00991719\pi$
$337$	3258.64	+	5644.13i	0.526735	+	0.912331i	−0.472780	+	0.881180i	$0.656749\pi$
$338$	495.499	+	858.229i	0.0797384	+	0.138111i
$339$	−4100.81	+	9427.08i	−0.657008	+	1.51035i
$340$		0			0
$341$	186.462			0.0296114
$342$	−863.701	−	926.804i	−0.136560	−	0.146537i
$343$	−6659.94			−1.04841
$344$	1127.21	−	1952.39i	0.176672	−	0.306005i
$345$		0			0
$346$	281.142	+	486.952i	0.0436829	+	0.0756609i
$347$	−2969.27	−	5142.93i	−0.459363	−	0.795640i	0.539564	−	0.841944i	$-0.318589\pi$
$347$	−2969.27	−	5142.93i	−0.459363	−	0.795640i	−0.998927	+	0.0463041i	$0.985256\pi$
$348$	7236.33	+	9782.62i	1.11468	+	1.50691i
$349$	3648.27	−	6318.99i	0.559563	−	0.969192i	−0.437970	−	0.898990i	$-0.644302\pi$
$349$	3648.27	−	6318.99i	0.559563	−	0.969192i	0.997533	−	0.0702022i	$-0.0223644\pi$
$350$		0			0
$351$	1144.69	+	978.613i	0.174071	+	0.148816i
$352$	−139.873			−0.0211797
$353$	−625.356	+	1083.15i	−0.0942900	+	0.163315i	−0.909312	−	0.416115i	$-0.863391\pi$
$353$	−625.356	+	1083.15i	−0.0942900	+	0.163315i	0.815022	+	0.579430i	$0.196725\pi$
$354$	−735.795	−	994.704i	−0.110472	−	0.149344i
$355$		0			0
$356$	−1567.49	−	2714.97i	−0.233362	−	0.404195i
$357$	4568.38	−	519.757i	0.677267	−	0.0770545i
$358$	102.225	−	177.058i	0.0150915	−	0.0261392i
$359$	−10928.3			−1.60661			−0.803303	−	0.595570i	$-0.796926\pi$
$359$	−10928.3			−1.60661			−0.803303	+	0.595570i	$0.796926\pi$
$360$		0			0
$361$	2856.27			0.416427
$362$	425.567	−	737.104i	0.0617882	−	0.107020i
$363$	−2753.56	+	6329.97i	−0.398139	+	0.915254i
$364$	529.062	+	916.362i	0.0761823	+	0.131952i
$365$		0			0
$366$	574.087	−	1319.73i	0.0819891	−	0.188479i
$367$	3215.66	−	5569.68i	0.457373	−	0.792194i	−0.541448	−	0.840734i	$-0.682124\pi$
$367$	3215.66	−	5569.68i	0.457373	−	0.792194i	0.998821	+	0.0485405i	$0.0154570\pi$
$368$	−1849.55			−0.261996
$369$	3732.73	−	860.504i	0.526607	−	0.121398i
$370$		0			0
$371$	−2911.32	+	5042.55i	−0.407407	+	0.705650i
$372$	−4706.49	+	535.470i	−0.655968	+	0.0746312i
$373$	−2455.85	−	4253.66i	−0.340909	−	0.590472i	0.643693	−	0.765284i	$-0.277402\pi$
$373$	−2455.85	−	4253.66i	−0.340909	−	0.590472i	−0.984602	+	0.174812i	$0.944068\pi$
$374$	−26.4074	−	45.7389i	−0.00365105	−	0.00632381i
$375$		0			0
$376$	1829.96	−	3169.58i	0.250992	−	0.434731i
$377$	−3233.76			−0.441770
$378$	643.726	+	550.331i	0.0875918	+	0.0748836i
$379$	4805.81			0.651340			0.325670	−	0.945483i	$-0.394410\pi$
$379$	4805.81			0.651340			0.325670	+	0.945483i	$0.394410\pi$
$380$		0			0
$381$	4073.87	+	5507.37i	0.547797	+	0.740554i
$382$	−186.883	−	323.691i	−0.0250308	−	0.0433547i
$383$	2116.08	+	3665.15i	0.282314	+	0.488983i	0.971954	−	0.235170i	$-0.0755645\pi$
$383$	2116.08	+	3665.15i	0.282314	+	0.488983i	−0.689640	+	0.724152i	$0.742231\pi$
$384$	4682.95	−	532.792i	0.622333	−	0.0708045i
$385$		0			0
$386$	−227.106			−0.0299466
$387$	−5526.75	−	5930.53i	−0.725944	−	0.778982i
$388$	12293.4			1.60851
$389$	1758.54	−	3045.89i	0.229208	−	0.396999i	−0.728366	−	0.685188i	$-0.759720\pi$
$389$	1758.54	−	3045.89i	0.229208	−	0.396999i	0.957573	+	0.288189i	$0.0930532\pi$
$390$		0			0
$391$	−1100.95	−	1906.90i	−0.142398	−	0.246640i
$392$	−684.022	−	1184.76i	−0.0881335	−	0.152652i
$393$	3285.12	−	7551.94i	0.421660	−	0.969325i
$394$	1101.63	−	1908.09i	0.140862	−	0.243980i
$395$		0			0
$396$	−97.6697	+	319.096i	−0.0123942	+	0.0404929i
$397$	3925.05			0.496203			0.248101	−	0.968734i	$-0.420193\pi$
$397$	3925.05			0.496203			0.248101	+	0.968734i	$0.420193\pi$
$398$	−603.100	+	1044.60i	−0.0759564	+	0.131560i
$399$	−6453.07	+	734.184i	−0.809669	+	0.0921182i
$400$		0			0
$401$	−403.676	−	699.188i	−0.0502709	−	0.0870718i	0.839795	−	0.542904i	$-0.182675\pi$
$401$	−403.676	−	699.188i	−0.0502709	−	0.0870718i	−0.890066	+	0.455832i	$0.849342\pi$
$402$	736.879	+	996.169i	0.0914233	+	0.123593i
$403$	629.424	−	1090.19i	0.0778011	−	0.134755i
$404$	8977.05			1.10551
$405$		0			0
$406$	−1818.53			−0.222296
$407$	−134.801	+	233.482i	−0.0164173	+	0.0284356i
$408$	1619.06	+	2188.77i	0.196459	+	0.265588i
$409$	−404.224	−	700.137i	−0.0488694	−	0.0846444i	0.840556	−	0.541725i	$-0.182228\pi$
$409$	−404.224	−	700.137i	−0.0488694	−	0.0846444i	−0.889425	+	0.457080i	$0.848895\pi$
$410$		0			0
$411$	−1969.73	+	224.101i	−0.236398	+	0.0268956i
$412$	−5640.49	+	9769.61i	−0.674482	+	1.16824i
$413$	−6342.97			−0.755732
$414$	118.705	−	387.821i	0.0140919	−	0.0460395i
$415$		0			0
$416$	−472.157	+	817.800i	−0.0556476	+	0.0963844i
$417$	−5103.85	+	11732.9i	−0.599369	+	1.37785i
$418$	37.3018	+	64.6086i	0.00436481	+	0.00756008i
$419$	−880.089	−	1524.36i	−0.102614	−	0.177732i	0.810147	−	0.586227i	$-0.199387\pi$
$419$	−880.089	−	1524.36i	−0.102614	−	0.177732i	−0.912761	+	0.408495i	$0.866054\pi$
$420$		0			0
$421$	−7287.86	+	12622.9i	−0.843678	+	1.46129i	0.0430868	+	0.999071i	$0.486281\pi$
$421$	−7287.86	+	12622.9i	−0.843678	+	1.46129i	−0.886765	+	0.462221i	$0.847053\pi$
$422$	1316.42			0.151854
$423$	−8972.32	−	9627.84i	−1.03132	−	1.10667i
$424$	−3447.73			−0.394898
$425$		0			0
$426$	−2621.59	+	298.265i	−0.298160	+	0.0339225i
$427$	−3689.07	−	6389.65i	−0.418095	−	0.724161i
$428$	531.421	+	920.447i	0.0600168	+	0.103952i
$429$	−52.7405	−	71.2987i	−0.00593552	−	0.00802409i
$430$		0			0
$431$	5715.34			0.638743			0.319371	−	0.947630i	$-0.396528\pi$
$431$	5715.34			0.638743			0.319371	+	0.947630i	$0.396528\pi$
$432$	1502.45	−	8084.72i	0.167330	−	0.900408i
$433$	−12751.4			−1.41523			−0.707614	−	0.706599i	$-0.750228\pi$
$433$	−12751.4			−1.41523			−0.707614	+	0.706599i	$0.750228\pi$
$434$	353.962	−	613.079i	0.0391491	−	0.0678082i
$435$		0			0
$436$	155.925	+	270.070i	0.0171272	+	0.0296651i
$437$	1555.15	+	2693.60i	0.170235	+	0.294856i
$438$	−1069.81	+	121.715i	−0.116706	+	0.0132780i
$439$	−2420.51	+	4192.44i	−0.263154	+	0.455796i	−0.967078	−	0.254479i	$-0.918096\pi$
$439$	−2420.51	+	4192.44i	−0.263154	+	0.455796i	0.703924	+	0.710275i	$0.251429\pi$
$440$		0			0
$441$	−4793.54	+	1105.05i	−0.517605	+	0.119323i
$442$	−356.564			−0.0383711
$443$	4472.98	−	7747.43i	0.479724	−	0.830907i	−0.520005	−	0.854163i	$-0.674070\pi$
$443$	4472.98	−	7747.43i	0.479724	−	0.830907i	0.999730	+	0.0232564i	$0.00740339\pi$
$444$	2732.01	−	6280.42i	0.292016	−	0.671297i
$445$		0			0
$446$	−111.723	−	193.509i	−0.0118615	−	0.0205447i
$447$	796.640	−	1831.34i	0.0842948	−	0.193780i
$448$	2707.53	−	4689.57i	0.285533	−	0.494557i
$449$	−2743.57			−0.288367			−0.144184	−	0.989551i	$-0.546056\pi$
$449$	−2743.57			−0.288367			−0.144184	+	0.989551i	$0.546056\pi$
$450$		0			0
$451$	−225.580			−0.0235524
$452$	−7689.68	+	13318.9i	−0.800204	+	1.38599i
$453$	−4115.30	+	468.209i	−0.426829	+	0.0485615i
$454$	1020.61	+	1767.76i	0.105506	+	0.182742i
$455$		0			0
$456$	−2287.00	−	3091.75i	−0.234865	−	0.317509i
$457$	−2806.35	+	4860.74i	−0.287255	+	0.497540i	−0.973153	−	0.230157i	$-0.926076\pi$
$457$	−2806.35	+	4860.74i	−0.287255	+	0.497540i	0.685899	+	0.727697i	$0.259409\pi$
$458$	1953.93			0.199348
$459$	9229.74	−	3263.41i	0.938578	−	0.331858i
$460$		0			0
$461$	−6273.50	+	10866.0i	−0.633809	+	1.09779i	0.352957	+	0.935640i	$0.385176\pi$
$461$	−6273.50	+	10866.0i	−0.633809	+	1.09779i	−0.986766	+	0.162150i	$0.948157\pi$
$462$	−29.6591	−	40.0954i	−0.00298672	−	0.00403768i
$463$	5361.12	+	9285.74i	0.538126	+	0.932062i	0.999005	+	0.0445990i	$0.0142010\pi$
$463$	5361.12	+	9285.74i	0.538126	+	0.932062i	−0.460879	+	0.887463i	$0.652466\pi$
$464$	8828.65	+	15291.7i	0.883319	+	1.52995i
$465$		0			0
$466$	1016.95	−	1761.40i	0.101093	−	0.175098i
$467$	−12798.4			−1.26818			−0.634089	−	0.773260i	$-0.718625\pi$
$467$	−12798.4			−1.26818			−0.634089	+	0.773260i	$0.718625\pi$
$468$	1535.97	+	1648.19i	0.151710	+	0.162794i
$469$	6352.31			0.625421
$470$		0			0
$471$	−1805.33	+	4150.14i	−0.176614	+	0.406005i
$472$	−1877.92	−	3252.65i	−0.183132	−	0.317193i
$473$	238.691	+	413.425i	0.0232030	+	0.0401888i
$474$	370.293	−	851.242i	0.0358822	−	0.0824870i
$475$		0			0
$476$	6878.34			0.662328
$477$	−3628.49	+	11854.6i	−0.348296	+	1.13791i
$478$	−743.203			−0.0711158
$479$	−1207.38	+	2091.25i	−0.115171	+	0.199481i	−0.917848	−	0.396932i	$-0.870075\pi$
$479$	−1207.38	+	2091.25i	−0.115171	+	0.199481i	0.802677	+	0.596413i	$0.203408\pi$
$480$		0			0
$481$	910.070	+	1576.29i	0.0862695	+	0.149423i
$482$	1147.61	+	1987.72i	0.108449	+	0.187839i
$483$	−1236.52	−	1671.62i	−0.116487	−	0.157477i
$484$	−5163.37	+	8943.21i	−0.484914	+	0.839896i
$485$		0			0
$486$	1598.80	+	833.919i	0.149225	+	0.0778340i
$487$	−16386.9			−1.52477			−0.762384	−	0.647125i	$-0.775971\pi$
$487$	−16386.9			−1.52477			−0.762384	+	0.647125i	$0.775971\pi$
$488$	2184.39	−	3783.48i	0.202629	−	0.350963i
$489$	−96.5982	−	130.589i	−0.00893317	−	0.0120766i
$490$		0			0
$491$	−7935.54	−	13744.8i	−0.729381	−	1.26332i	−0.957145	−	0.289609i	$-0.906475\pi$
$491$	−7935.54	−	13744.8i	−0.729381	−	1.26332i	0.227764	−	0.973716i	$-0.426858\pi$
$492$	5693.85	−	647.805i	0.521745	−	0.0593604i
$493$	−10510.6	+	18204.8i	−0.960186	+	1.66309i
$494$	503.665			0.0458724
$495$		0			0
$496$	−6873.68			−0.622252
$497$	−6763.26	+	11714.3i	−0.610410	+	1.05726i
$498$	−1276.02	+	2933.36i	−0.114819	+	0.263950i
$499$	−5730.39	−	9925.33i	−0.514083	−	0.890419i	−0.999867	−	0.0163392i	$-0.994799\pi$
$499$	−5730.39	−	9925.33i	−0.514083	−	0.890419i	0.485783	−	0.874079i	$-0.338534\pi$
$500$		0			0
$501$	−77.2776	+	177.648i	−0.00689123	+	0.0158418i
$502$	830.138	−	1437.84i	0.0738065	−	0.127837i
$503$	1038.52			0.0920585			0.0460293	−	0.998940i	$-0.485343\pi$
$503$	1038.52			0.0920585			0.0460293	+	0.998940i	$0.485343\pi$
$504$	1752.71	+	1880.77i	0.154905	+	0.166222i
$505$		0			0
$506$	−11.9420	+	20.6841i	−0.00104918	+	0.00181724i
$507$	10747.9	−	1222.81i	0.941479	−	0.107115i
$508$	5124.04	+	8875.10i	0.447525	+	0.775135i
$509$	2514.44	+	4355.14i	0.218960	+	0.379249i	0.954490	−	0.298242i	$-0.0964003\pi$
$509$	2514.44	+	4355.14i	0.218960	+	0.379249i	−0.735530	+	0.677492i	$0.763067\pi$
$510$		0			0
$511$	−2759.92	+	4780.33i	−0.238927	+	0.413834i
$512$	8677.07			0.748976
$513$	−13037.5	+	4609.74i	−1.12206	+	0.396735i
$514$	−2342.92			−0.201054
$515$		0			0
$516$	−7212.04	−	9749.79i	−0.615295	−	0.831803i
$517$	387.499	+	671.169i	0.0329636	+	0.0570947i
$518$	511.785	+	886.438i	0.0434104	+	0.0751889i
$519$	6098.25	−	693.815i	0.515768	−	0.0586803i
$520$		0			0
$521$	7057.78			0.593487			0.296744	−	0.954957i	$-0.404099\pi$
$521$	7057.78			0.593487			0.296744	+	0.954957i	$0.404099\pi$
$522$	−3773.04	+	869.797i	−0.316363	+	0.0729310i
$523$	14453.5			1.20843			0.604215	−	0.796821i	$-0.293487\pi$
$523$	14453.5			1.20843			0.604215	+	0.796821i	$0.293487\pi$
$524$	6160.13	−	10669.7i	0.513562	−	0.889515i
$525$		0			0
$526$	1313.18	+	2274.49i	0.108854	+	0.188541i
$527$	−4091.57	−	7086.81i	−0.338201	−	0.585781i
$528$	−193.165	+	444.053i	−0.0159212	+	0.0366002i
$529$	5585.63	−	9674.59i	0.459080	−	0.795150i
$530$		0			0
$531$	−13160.2	+	3033.81i	−1.07553	+	0.247940i
$532$	−9716.01			−0.791809
$533$	−761.469	+	1318.90i	−0.0618816	+	0.107182i
$534$	991.180	−	112.769i	0.0803231	−	0.00913858i
$535$		0			0
$536$	1880.68	+	3257.44i	0.151554	+	0.262500i
$537$	−1327.16	−	1794.15i	−0.106650	−	0.144178i
$538$	1867.04	−	3233.81i	0.149617	−	0.259144i
$539$	289.687			0.0231498
$540$		0			0
$541$	4101.59			0.325954			0.162977	−	0.986630i	$-0.447890\pi$
$541$	4101.59			0.325954			0.162977	+	0.986630i	$0.447890\pi$
$542$	−1023.80	+	1773.27i	−0.0811362	+	0.140532i
$543$	−5525.03	−	7469.16i	−0.436651	−	0.590299i
$544$	3069.26	+	5316.11i	0.241900	+	0.418982i
$545$		0			0
$546$	−334.544	+	38.0620i	−0.0262219	+	0.00298334i
$547$	8410.52	−	14567.4i	0.657418	−	1.13868i	−0.323863	−	0.946104i	$-0.604982\pi$
$547$	8410.52	−	14567.4i	0.657418	−	1.13868i	0.981282	−	0.192578i	$-0.0616848\pi$
$548$	−2965.70			−0.231183
$549$	−10710.1	−	11492.6i	−0.832598	−	0.893428i
$550$		0			0
$551$	14846.7	−	25715.2i	1.14790	−	1.98821i
$552$	491.112	−	1128.98i	0.0378680	−	0.0870521i
$553$	−2379.50	−	4121.41i	−0.182977	−	0.316926i
$554$	−440.771	−	763.438i	−0.0338025	−	0.0585476i
$555$		0			0
$556$	−9570.54	+	16576.7i	−0.730002	+	1.26440i
$557$	−12248.8			−0.931771			−0.465885	−	0.884845i	$-0.654264\pi$
$557$	−12248.8			−0.931771			−0.465885	+	0.884845i	$0.654264\pi$
$558$	441.156	−	1441.30i	0.0334688	−	0.109346i
$559$	3222.91			0.243854
$560$		0			0
$561$	−572.804	+	65.1694i	−0.0431084	+	0.00490455i
$562$	−1652.28	−	2861.84i	−0.124017	−	0.214803i
$563$	−4422.86	−	7660.62i	−0.331086	−	0.573457i	0.651639	−	0.758529i	$-0.274082\pi$
$563$	−4422.86	−	7660.62i	−0.331086	−	0.573457i	−0.982725	+	0.185072i	$0.940748\pi$
$564$	−11708.3	−	15828.1i	−0.874127	−	1.18171i
$565$		0			0
$566$	3062.06			0.227399
$567$	8311.39	−	4047.12i	0.615601	−	0.299759i
$568$	−8009.40			−0.591667
$569$	4049.35	−	7013.68i	0.298344	−	0.516747i	−0.677413	−	0.735603i	$-0.736899\pi$
$569$	4049.35	−	7013.68i	0.298344	−	0.516747i	0.975757	+	0.218856i	$0.0702325\pi$
$570$		0			0
$571$	8189.02	+	14183.8i	0.600175	+	1.03953i	0.992794	+	0.119832i	$0.0382356\pi$
$571$	8189.02	+	14183.8i	0.600175	+	1.03953i	−0.392619	+	0.919701i	$0.628431\pi$
$572$	−66.3361	−	114.897i	−0.00484904	−	0.00839879i
$573$	−4053.69	+	461.200i	−0.295542	+	0.0336246i
$574$	−428.218	+	741.696i	−0.0311385	+	0.0539334i
$575$		0			0
$576$	3374.49	−	11024.8i	0.244104	−	0.797510i
$577$	24920.9			1.79804			0.899020	−	0.437907i	$-0.144280\pi$
$577$	24920.9			1.79804			0.899020	+	0.437907i	$0.144280\pi$
$578$	10.4558	−	18.1100i	0.000752430	−	0.00130325i
$579$	−988.853	+	2273.21i	−0.0709764	+	0.163163i
$580$		0			0
$581$	8199.69	+	14202.3i	0.585509	+	1.01413i
$582$	−1560.42	+	3587.15i	−0.111137	+	0.255484i
$583$	365.034	−	632.257i	0.0259317	−	0.0449150i
$584$	−3268.44			−0.231591
$585$		0			0
$586$	−3637.76			−0.256441
$587$	4182.25	−	7243.86i	0.294071	−	0.509346i	−0.680697	−	0.732565i	$-0.738323\pi$
$587$	4182.25	−	7243.86i	0.294071	−	0.509346i	0.974768	+	0.223219i	$0.0716564\pi$
$588$	−7311.99	+	831.905i	−0.512826	+	0.0583456i
$589$	5779.56	+	10010.5i	0.404317	+	0.700297i
$590$		0			0
$591$	−14302.2	−	19334.8i	−0.995456	−	1.34573i
$592$	4969.25	−	8607.00i	0.344992	−	0.597543i
$593$	27169.7			1.88150			0.940749	−	0.339105i	$-0.110124\pi$
$593$	27169.7			1.88150			0.940749	+	0.339105i	$0.110124\pi$
$594$	−80.7132	−	69.0030i	−0.00557526	−	0.00476637i
$595$		0			0
$596$	1493.83	−	2587.39i	0.102667	−	0.177825i
$597$	7829.88	+	10585.0i	0.536777	+	0.725656i
$598$	80.6231	+	139.643i	0.00551325	+	0.00954923i
$599$	−10666.2	−	18474.4i	−0.727560	−	1.26017i	−0.957911	−	0.287064i	$-0.907321\pi$
$599$	−10666.2	−	18474.4i	−0.727560	−	1.26017i	0.230351	−	0.973108i	$-0.426013\pi$
$600$		0			0
$601$	−292.016	+	505.786i	−0.0198196	+	0.0343285i	−0.875765	−	0.482738i	$-0.839643\pi$
$601$	−292.016	+	505.786i	−0.0198196	+	0.0343285i	0.855946	+	0.517066i	$0.172976\pi$
$602$	1812.43			0.122706
$603$	13179.6	−	3038.28i	0.890074	−	0.205188i
$604$	−6196.17			−0.417415
$605$		0			0
$606$	−1139.47	+	2619.46i	−0.0763827	+	0.175591i
$607$	−5635.12	−	9760.32i	−0.376808	−	0.652651i	0.613788	−	0.789471i	$-0.289645\pi$
$607$	−5635.12	−	9760.32i	−0.376808	−	0.652651i	−0.990596	+	0.136820i	$0.956312\pi$
$608$	−4335.49	−	7509.29i	−0.289190	−	0.500891i
$609$	−7918.17	+	18202.5i	−0.526864	+	1.21117i
$610$		0			0
$611$	5232.19			0.346435
$612$	14271.0	−	3289.88i	0.942598	−	0.217297i
$613$	4271.02			0.281411			0.140706	−	0.990051i	$-0.455063\pi$
$613$	4271.02			0.281411			0.140706	+	0.990051i	$0.455063\pi$
$614$	−1075.28	+	1862.44i	−0.0706756	+	0.122414i
$615$		0			0
$616$	−75.6968	−	131.111i	−0.00495115	−	0.00857565i
$617$	3598.08	+	6232.06i	0.234770	+	0.406634i	0.959206	−	0.282708i	$-0.0912329\pi$
$617$	3598.08	+	6232.06i	0.234770	+	0.406634i	−0.724436	+	0.689342i	$0.757900\pi$
$618$	−2134.76	−	2885.94i	−0.138953	−	0.187847i
$619$	−5128.24	+	8882.36i	−0.332991	+	0.576757i	−0.983097	−	0.183087i	$-0.941391\pi$
$619$	−5128.24	+	8882.36i	−0.332991	+	0.576757i	0.650106	+	0.759843i	$0.274724\pi$
$620$		0			0
$621$	−3365.01	−	2876.80i	−0.217445	−	0.185897i
$622$	1872.28			0.120694
$623$	2557.08	−	4428.99i	0.164442	−	0.284822i
$624$	1944.21	+	2628.33i	0.124729	+	0.168618i
$625$		0			0
$626$	753.607	+	1305.29i	0.0481153	+	0.0833382i
$627$	809.115	−	92.0552i	0.0515358	−	0.00586337i
$628$	−3385.28	+	5863.47i	−0.215107	+	0.372576i
$629$	11831.8			0.750026
$630$		0			0
$631$	15187.7			0.958183			0.479091	−	0.877765i	$-0.340966\pi$
$631$	15187.7			0.958183			0.479091	+	0.877765i	$0.340966\pi$
$632$	1408.96	−	2440.39i	0.0886795	−	0.153597i
$633$	5731.90	−	13176.7i	0.359909	−	0.827371i
$634$	1866.47	+	3232.81i	0.116919	+	0.202510i
$635$		0			0
$636$	−7398.14	+	17007.1i	−0.461250	+	1.06034i
$637$	977.872	−	1693.72i	0.0608237	−	0.105350i
$638$	228.016			0.0141493
$639$	−8429.31	+	27539.3i	−0.521844	+	1.70491i
$640$		0			0
$641$	14196.7	−	24589.4i	0.874783	−	1.51517i	0.0177891	−	0.999842i	$-0.494337\pi$
$641$	14196.7	−	24589.4i	0.874783	−	1.51517i	0.856994	−	0.515327i	$-0.172329\pi$
$642$	−336.036	+	38.2317i	−0.0206578	+	0.00235029i
$643$	5844.00	+	10122.1i	0.358421	+	0.620804i	0.987697	−	0.156378i	$-0.0499818\pi$
$643$	5844.00	+	10122.1i	0.358421	+	0.620804i	−0.629276	+	0.777182i	$0.716649\pi$
$644$	−1555.27	−	2693.80i	−0.0951648	−	0.164830i
$645$		0			0
$646$	1637.04	−	2835.44i	0.0997036	−	0.172692i
$647$	−12800.8			−0.777822			−0.388911	−	0.921275i	$-0.627149\pi$
$647$	−12800.8			−0.777822			−0.388911	+	0.921275i	$0.627149\pi$
$648$	4536.04	+	3063.85i	0.274989	+	0.185740i
$649$	795.310			0.0481027
$650$		0			0
$651$	−4595.39	−	6212.40i	−0.276663	−	0.374014i
$652$	−121.500	−	210.443i	−0.00729799	−	0.0126405i
$653$	3079.46	+	5333.78i	0.184546	+	0.319643i	0.943423	−	0.331590i	$-0.107585\pi$
$653$	3079.46	+	5333.78i	0.184546	+	0.319643i	−0.758877	+	0.651233i	$0.774252\pi$
$654$	−98.5968	+	11.2176i	−0.00589517	+	0.000670709i
$655$		0			0
$656$	8315.69			0.494929
$657$	−3439.80	+	11238.1i	−0.204261	+	0.667339i
$658$	2942.36			0.174324
$659$	−8289.10	+	14357.1i	−0.489981	+	0.848672i	−0.999934	−	0.0115307i	$-0.996330\pi$
$659$	−8289.10	+	14357.1i	−0.489981	+	0.848672i	0.509953	+	0.860202i	$0.329663\pi$
$660$		0			0
$661$	11469.8	+	19866.4i	0.674925	+	1.16900i	0.976491	+	0.215559i	$0.0691573\pi$
$661$	11469.8	+	19866.4i	0.674925	+	1.16900i	−0.301566	+	0.953445i	$0.597509\pi$
$662$	2583.22	+	4474.27i	0.151661	+	0.262685i
$663$	−1552.53	+	3569.01i	−0.0909433	+	0.209063i
$664$	−4855.25	+	8409.53i	−0.283765	+	0.491496i
$665$		0			0
$666$	1485.82	+	1594.37i	0.0864478	+	0.0927637i
$667$	9506.20			0.551847
$668$	−144.908	+	250.988i	−0.00839319	+	0.0145374i
$669$	−2423.38	+	275.715i	−0.140050	+	0.0159338i
$670$		0			0
$671$	462.552	+	801.163i	0.0266119	+	0.0460932i
$672$	3447.19	+	4660.18i	0.197884	+	0.267515i
$673$	−1181.62	+	2046.62i	−0.0676790	+	0.117223i	−0.897879	−	0.440242i	$-0.854893\pi$
$673$	−1181.62	+	2046.62i	−0.0676790	+	0.117223i	0.830200	+	0.557465i	$0.188226\pi$
$674$	−3102.46			−0.177303
$675$		0			0
$676$	16182.4			0.920712
$677$	7824.09	−	13551.7i	0.444172	−	0.769328i	−0.553822	−	0.832635i	$-0.686831\pi$
$677$	7824.09	−	13551.7i	0.444172	−	0.769328i	0.997994	+	0.0633068i	$0.0201647\pi$
$678$	−2910.33	−	3934.40i	−0.164853	−	0.222861i
$679$	10027.2	+	17367.7i	0.566730	+	0.981605i
$680$		0			0
$681$	22138.2	−	2518.72i	1.24572	−	0.141729i
$682$	−44.3813	+	76.8706i	−0.00249186	+	0.00431602i
$683$	19626.7			1.09955			0.549777	−	0.835311i	$-0.314713\pi$
$683$	19626.7			1.09955			0.549777	+	0.835311i	$0.314713\pi$
$684$	−20158.5	+	4647.12i	−1.12687	+	0.259777i
$685$		0			0
$686$	1585.18	−	2745.62i	0.0882253	−	0.152811i
$687$	8507.72	−	19557.8i	0.472474	−	1.08614i
$688$	−8799.02	−	15240.3i	−0.487586	−	0.844524i
$689$	−2464.42	−	4268.51i	−0.136266	−	0.236019i
$690$		0			0
$691$	51.5955	−	89.3660i	0.00284050	−	0.00491989i	−0.864602	−	0.502458i	$-0.832429\pi$
$691$	51.5955	−	89.3660i	0.00284050	−	0.00491989i	0.867442	+	0.497538i	$0.165763\pi$
$692$	9181.78			0.504391
$693$	−530.473	+	122.290i	−0.0290779	+	0.00670332i
$694$	2826.96			0.154625
$695$		0			0
$696$	−11678.5	+	1328.69i	−0.636021	+	0.0723619i
$697$	4949.93	+	8573.54i	0.268999	+	0.465920i
$698$	1736.71	+	3008.06i	0.0941766	+	0.163119i
$699$	−13202.8	−	17848.5i	−0.714412	−	0.965797i
$700$		0			0
$701$	−17977.8			−0.968631			−0.484316	−	0.874893i	$-0.660931\pi$
$701$	−17977.8			−0.968631			−0.484316	+	0.874893i	$0.660931\pi$
$702$	−675.898	+	238.981i	−0.0363392	+	0.0128487i
$703$	−16713.1			−0.896651
$704$	−339.482	+	588.000i	−0.0181743	+	0.0314788i
$705$		0			0
$706$	−297.692	−	515.617i	−0.0158694	−	0.0274865i
$707$	7322.22	+	12682.5i	0.389506	+	0.674644i
$708$	−20074.4	+	2283.92i	−1.06560	+	0.121236i
$709$	−5385.10	+	9327.26i	−0.285249	+	0.494066i	−0.972670	−	0.232194i	$-0.925410\pi$
$709$	−5385.10	+	9327.26i	−0.285249	+	0.494066i	0.687421	+	0.726260i	$0.258743\pi$
$710$		0			0
$711$	−6908.16	−	7412.87i	−0.364383	−	0.391005i
$712$	3028.23			0.159393
$713$	−1850.30	+	3204.81i	−0.0971868	+	0.168333i
$714$	−873.080	+	2007.06i	−0.0457622	+	0.105200i
$715$		0			0
$716$	−1669.27	−	2891.27i	−0.0871280	−	0.150910i
$717$	−3236.02	+	7439.06i	−0.168551	+	0.387471i
$718$	2601.12	−	4505.27i	0.135199	−	0.234171i
$719$	24138.7			1.25205			0.626023	−	0.779804i	$-0.284681\pi$
$719$	24138.7			1.25205			0.626023	+	0.779804i	$0.284681\pi$
$720$		0			0
$721$	−18402.9			−0.950568
$722$	−679.843	+	1177.52i	−0.0350431	+	0.0606964i
$723$	24892.9	−	2832.13i	1.28046	−	0.145682i
$724$	−6949.28	−	12036.5i	−0.356724	−	0.617864i
$725$		0			0
$726$	−1954.19	−	2641.82i	−0.0998991	−	0.135051i
$727$	5395.46	−	9345.20i	0.275250	−	0.476746i	−0.694949	−	0.719059i	$-0.744573\pi$
$727$	5395.46	−	9345.20i	0.275250	−	0.476746i	0.970198	+	0.242313i	$0.0779062\pi$
$728$	−1022.09			−0.0520347
$729$	15308.5	−	12372.1i	0.777753	−	0.628570i
$730$		0			0
$731$	10475.3	−	18143.7i	0.530016	−	0.918015i
$732$	−13976.0	−	18893.8i	−0.705692	−	0.954009i
$733$	10492.9	+	18174.3i	0.528738	+	0.915801i	0.999438	+	0.0335082i	$0.0106680\pi$
$733$	10492.9	+	18174.3i	0.528738	+	0.915801i	−0.470700	+	0.882293i	$0.655999\pi$
$734$	1530.77	+	2651.36i	0.0769776	+	0.133329i
$735$		0			0
$736$	1387.99	−	2404.06i	0.0695134	−	0.120401i
$737$	−796.481			−0.0398084
$738$	−533.705	+	1743.66i	−0.0266205	+	0.0869717i
$739$	1773.47			0.0882790			0.0441395	−	0.999025i	$-0.485945\pi$
$739$	1773.47			0.0882790			0.0441395	+	0.999025i	$0.485945\pi$
$740$		0			0
$741$	2193.03	−	5041.42i	0.108722	−	0.249934i
$742$	−1385.89	−	2400.43i	−0.0685682	−	0.118764i
$743$	2640.39	+	4573.28i	0.130372	+	0.225811i	0.923820	−	0.382827i	$-0.125050\pi$
$743$	2640.39	+	4573.28i	0.130372	+	0.225811i	−0.793448	+	0.608638i	$0.791716\pi$
$744$	1825.17	−	4195.76i	0.0899381	−	0.206753i
$745$		0			0
$746$	2338.14			0.114753
$747$	23805.4	+	25544.6i	1.16599	+	1.25117i
$748$	−862.437			−0.0421575
$749$	−866.918	+	1501.55i	−0.0422917	+	0.0732514i
$750$		0			0
$751$	−5514.51	−	9551.40i	−0.267946	−	0.464095i	0.700386	−	0.713765i	$-0.253011\pi$
$751$	−5514.51	−	9551.40i	−0.267946	−	0.464095i	−0.968331	+	0.249669i	$0.919678\pi$
$752$	−14284.6	−	24741.7i	−0.692696	−	1.19978i
$753$	−10777.5	−	14569.8i	−0.521584	−	0.705117i
$754$	769.692	−	1333.15i	0.0371758	−	0.0643904i
$755$		0			0
$756$	13038.5	−	4610.09i	0.627255	−	0.221782i
$757$	−19897.2			−0.955318			−0.477659	−	0.878545i	$-0.658514\pi$
$757$	−19897.2			−0.955318			−0.477659	+	0.878545i	$0.658514\pi$
$758$	−1143.87	+	1981.24i	−0.0548115	+	0.0949363i
$759$	155.040	+	209.595i	0.00741448	+	0.0100235i
$760$		0			0
$761$	12636.2	+	21886.5i	0.601920	+	1.04256i	0.992530	+	0.122000i	$0.0389307\pi$
$761$	12636.2	+	21886.5i	0.601920	+	1.04256i	−0.390610	+	0.920556i	$0.627736\pi$
$762$	−3240.11	+	368.636i	−0.154038	+	0.0175253i
$763$	−254.364	+	440.571i	−0.0120689	+	0.0209040i
$764$	−6103.40			−0.289023
$765$		0			0
$766$	−2014.65			−0.0950292
$767$	2684.65	−	4649.96i	0.126385	−	0.218905i
$768$	6185.87	−	14220.3i	0.290642	−	0.668137i
$769$	−15167.1	−	26270.1i	−0.711233	−	1.23189i	−0.964395	−	0.264467i	$-0.914804\pi$
$769$	−15167.1	−	26270.1i	−0.711233	−	1.23189i	0.253162	−	0.967424i	$-0.418529\pi$
$770$		0			0
$771$	−10201.4	+	23451.3i	−0.476517	+	1.09543i
$772$	−1854.26	+	3211.67i	−0.0864458	+	0.149729i
$773$	6671.36			0.310417			0.155208	−	0.987882i	$-0.450395\pi$
$773$	6671.36			0.310417			0.155208	+	0.987882i	$0.450395\pi$
$774$	3760.37	−	866.877i	0.174630	−	0.0402574i
$775$		0			0
$776$	−5937.38	+	10283.8i	−0.274664	+	0.475732i
$777$	11101.2	−	1263.01i	0.512551	−	0.0583143i
$778$	837.129	+	1449.95i	0.0385765	+	0.0668165i
$779$	−6992.04	−	12110.6i	−0.321586	−	0.557004i
$780$		0			0
$781$	848.008	−	1468.79i	0.0388529	−	0.0672952i
$782$	1048.18			0.0479321
$783$	−7722.18	+	41553.3i	−0.352450	+	1.89654i
$784$	−10678.9			−0.486468
$785$		0			0
$786$	2331.43	+	3151.81i	0.105801	+	0.143030i
$787$	−10503.1	−	18192.0i	−0.475726	−	0.823981i	0.523888	−	0.851787i	$-0.324481\pi$
$787$	−10503.1	−	18192.0i	−0.475726	−	0.823981i	−0.999613	+	0.0278064i	$0.991148\pi$
$788$	−17989.1	−	31158.0i	−0.813241	−	1.40858i
$789$	28484.2	−	3240.73i	1.28525	−	0.146227i
$790$		0			0
$791$	−25088.7			−1.12775
$792$	−219.763	−	235.819i	−0.00985978	−	0.0105801i
$793$	6245.57			0.279681
$794$	−934.230	+	1618.13i	−0.0417564	+	0.0723242i
$795$		0			0
$796$	9848.29	+	17057.7i	0.438522	+	0.759542i
$797$	4566.27	+	7909.00i	0.202943	+	0.351507i	0.949475	−	0.313842i	$-0.101616\pi$
$797$	4566.27	+	7909.00i	0.202943	+	0.351507i	−0.746533	+	0.665349i	$0.768283\pi$
$798$	1233.27	−	2835.08i	0.0547084	−	0.125765i
$799$	17005.9	−	29455.1i	0.752975	−	1.30419i
$800$		0			0
$801$	3186.99	−	10412.2i	0.140583	−	0.459296i
$802$	384.328			0.0169216
$803$	346.051	−	599.379i	0.0152078	−	0.0263407i
$804$	20104.0	−	2287.28i	0.881856	−	0.100331i
$805$		0			0
$806$	299.628	+	518.970i	0.0130942	+	0.0226798i
$807$	−24239.3	−	32768.5i	−1.05733	−	1.42938i
$808$	−4335.68	+	7509.61i	−0.188773	+	0.326964i
$809$	17687.6			0.768681			0.384341	−	0.923191i	$-0.374429\pi$
$809$	17687.6			0.768681			0.384341	+	0.923191i	$0.374429\pi$
$810$		0			0
$811$	−7211.00			−0.312223			−0.156111	−	0.987739i	$-0.549896\pi$
$811$	−7211.00			−0.312223			−0.156111	+	0.987739i	$0.549896\pi$
$812$	−14847.8	+	25717.2i	−0.641695	+	1.11145i
$813$	13291.7	+	17968.7i	0.573382	+	0.775142i
$814$	−64.1699	−	111.146i	−0.00276309	−	0.00478581i
$815$		0			0
$816$	21115.6	−	2402.38i	0.905876	−	0.103064i
$817$	−14796.9	+	25628.9i	−0.633631	+	1.09748i
$818$	384.850			0.0164498
$819$	−1075.68	+	3514.34i	−0.0458940	+	0.149940i
$820$		0			0
$821$	−21037.2	+	36437.6i	−0.894281	+	1.54894i	−0.0595894	+	0.998223i	$0.518979\pi$
$821$	−21037.2	+	36437.6i	−0.894281	+	1.54894i	−0.834692	+	0.550717i	$0.814354\pi$
$822$	376.442	−	865.376i	0.0159731	−	0.0367195i
$823$	−10437.6	−	18078.5i	−0.442081	−	0.765707i	0.555763	−	0.831341i	$-0.312426\pi$
$823$	−10437.6	−	18078.5i	−0.442081	−	0.765707i	−0.997844	+	0.0656341i	$0.979093\pi$
$824$	−5448.41	−	9436.93i	−0.230345	−	0.398970i
$825$		0			0
$826$	1509.74	−	2614.94i	0.0635962	−	0.110152i
$827$	3128.34			0.131540			0.0657698	−	0.997835i	$-0.479050\pi$
$827$	3128.34			0.131540			0.0657698	+	0.997835i	$0.479050\pi$
$828$	−4515.26	−	4845.14i	−0.189512	−	0.203358i
$829$	−6854.35			−0.287167			−0.143583	−	0.989638i	$-0.545863\pi$
$829$	−6854.35			−0.287167			−0.143583	+	0.989638i	$0.545863\pi$
$830$		0			0
$831$	−9560.78	+	1087.76i	−0.399109	+	0.0454078i
$832$	2291.92	+	3969.71i	0.0955022	+	0.165415i
$833$	−6356.66	−	11010.1i	−0.264400	−	0.457954i
$834$	−3622.18	−	4896.74i	−0.150391	−	0.203310i
$835$		0			0
$836$	1218.24			0.0503990
$837$	−12505.7	−	10691.3i	−0.516442	−	0.441514i
$838$	837.906			0.0345405
$839$	−20793.2	+	36014.9i	−0.855615	+	1.48197i	0.0204588	+	0.999791i	$0.493487\pi$
$839$	−20793.2	+	36014.9i	−0.855615	+	1.48197i	−0.876074	+	0.482178i	$0.839846\pi$
$840$		0			0
$841$	−33182.4	−	57473.6i	−1.36055	−	2.35654i
$842$	−3469.27	−	6008.96i	−0.141994	−	0.245941i
$843$	−35839.7	+	4077.58i	−1.46428	+	0.166595i
$844$	10748.2	−	18616.5i	0.438352	−	0.759249i
$845$		0			0
$846$	6104.73	−	1407.32i	0.248091	−	0.0571922i
$847$	−16846.2			−0.683404
$848$	−13456.5	+	23307.3i	−0.544926	+	0.943840i
$849$	13332.7	−	30649.5i	0.538958	−	1.23897i
$850$		0			0
$851$	−2675.31	−	4633.77i	−0.107765	−	0.186655i
$852$	−17186.6	+	39509.0i	−0.691082	+	1.58868i
$853$	9160.28	−	15866.1i	0.367693	−	0.636863i	−0.621512	−	0.783405i	$-0.713481\pi$
$853$	9160.28	−	15866.1i	0.367693	−	0.636863i	0.989204	+	0.146542i	$0.0468145\pi$
$854$	3512.25			0.140734
$855$		0			0
$856$	−1026.65			−0.0409931
$857$	−6189.48	+	10720.5i	−0.246708	+	0.427310i	−0.962610	−	0.270890i	$-0.912682\pi$
$857$	−6189.48	+	10720.5i	−0.246708	+	0.427310i	0.715903	+	0.698200i	$0.246015\pi$
$858$	41.9467	−	4.77239i	0.00166904	−	0.000189891i
$859$	14758.5	+	25562.5i	0.586210	+	1.01534i	0.994723	+	0.102593i	$0.0327139\pi$
$859$	14758.5	+	25562.5i	0.586210	+	1.01534i	−0.408514	+	0.912752i	$0.633953\pi$
$860$		0			0
$861$	5559.45	+	7515.69i	0.220053	+	0.297484i
$862$	−1360.35	+	2356.19i	−0.0537514	+	0.0931001i
$863$	−41307.0			−1.62932			−0.814661	−	0.579937i	$-0.803077\pi$
$863$	−41307.0			−1.62932			−0.814661	+	0.579937i	$0.803077\pi$
$864$	9381.08	+	8020.03i	0.369387	+	0.315795i
$865$		0			0
$866$	3035.06	−	5256.88i	0.119094	−	0.206277i
$867$	−135.745	−	183.511i	−0.00531735	−	0.00718840i
$868$	−5780.00	−	10011.3i	−0.226021	−	0.391479i
$869$	298.352	+	516.760i	0.0116466	+	0.0201725i
$870$		0			0
$871$	−2688.61	+	4656.81i	−0.104593	+	0.181160i
$872$	−301.230			−0.0116983
$873$	29111.1	+	31237.9i	1.12859	+	1.21105i
$874$	−1480.61			−0.0573025
$875$		0			0
$876$	−7013.42	+	16122.7i	−0.270504	+	0.621843i
$877$	19153.4	+	33174.7i	0.737475	+	1.27734i	0.953629	+	0.300984i	$0.0973152\pi$
$877$	19153.4	+	33174.7i	0.737475	+	1.27734i	−0.216155	+	0.976359i	$0.569352\pi$
$878$	−1152.25	−	1995.75i	−0.0442898	−	0.0767122i
$879$	−15839.3	+	36412.0i	−0.607790	+	1.39721i
$880$		0			0
$881$	−47903.1			−1.83189			−0.915946	−	0.401301i	$-0.868558\pi$
$881$	−47903.1			−1.83189			−0.915946	+	0.401301i	$0.868558\pi$
$882$	685.379	−	2239.20i	0.0261654	−	0.0854849i
$883$	39098.9			1.49013			0.745064	−	0.666993i	$-0.232419\pi$
$883$	39098.9			1.49013			0.745064	+	0.666993i	$0.232419\pi$
$884$	−2911.25	+	5042.43i	−0.110765	+	0.191850i
$885$		0			0
$886$	2129.30	+	3688.05i	0.0807394	+	0.139845i
$887$	14117.0	+	24451.4i	0.534389	+	0.925590i	0.999193	+	0.0401756i	$0.0127917\pi$
$887$	14117.0	+	24451.4i	0.534389	+	0.925590i	−0.464803	+	0.885414i	$0.653875\pi$
$888$	3934.31	+	5318.70i	0.148679	+	0.200995i
$889$	−8358.96	+	14478.1i	−0.315355	+	0.546211i
$890$		0			0
$891$	−1042.12	+	507.446i	−0.0391833	+	0.0190798i
$892$	−3648.74			−0.136961
$893$	−24021.8	+	41606.9i	−0.900177	+	1.55915i
$894$	565.371	+	764.313i	0.0211508	+	0.0285933i
$895$		0			0
$896$	5751.09	+	9961.18i	0.214431	+	0.371406i
$897$	1748.80	−	198.965i	0.0650955	−	0.00740609i
$898$	653.016	−	1131.06i	0.0242666	−	0.0420311i
$899$	35328.9			1.31066
$900$		0			0
$901$	−32040.0			−1.18469
$902$	53.6919	−	92.9971i	0.00198198	−	0.00343289i
$903$	7891.59	−	18141.4i	0.290826	−	0.668559i
$904$	−7427.83	−	12865.4i	−0.273281	−	0.473336i
$905$		0			0
$906$	786.491	−	1808.01i	0.0288404	−	0.0662992i
$907$	−9530.28	+	16506.9i	−0.348895	+	0.604304i	−0.986053	−	0.166429i	$-0.946776\pi$
$907$	−9530.28	+	16506.9i	−0.348895	+	0.604304i	0.637159	+	0.770733i	$0.280110\pi$
$908$	33332.1			1.21824
$909$	21257.9	+	22811.0i	0.775665	+	0.832336i
$910$		0			0
$911$	727.041	−	1259.27i	0.0264412	−	0.0457975i	−0.852502	−	0.522724i	$-0.824916\pi$
$911$	727.041	−	1259.27i	0.0264412	−	0.0457975i	0.878943	+	0.476926i	$0.158249\pi$
$912$	−29826.9	+	3393.49i	−1.08297	+	0.123212i
$913$	−1028.11	−	1780.74i	−0.0372679	−	0.0645499i
$914$	−1335.92	−	2313.88i	−0.0483461	−	0.0837379i
$915$		0			0
$916$	15953.3	−	27632.0i	0.575451	−	0.996711i
$917$	20098.3			0.723778
$918$	−851.470	+	4581.79i	−0.0306130	+	0.164729i
$919$	−6383.04			−0.229115			−0.114558	−	0.993417i	$-0.536545\pi$
$919$	−6383.04			−0.229115			−0.114558	+	0.993417i	$0.536545\pi$
$920$		0			0
$921$	13960.1	+	18872.3i	0.499458	+	0.675205i
$922$	−2986.41	−	5172.61i	−0.106673	−	0.184762i
$923$	−5725.09	−	9916.14i	−0.204164	−	0.353623i
$924$	−809.176	+	92.0622i	−0.0288095	+	0.00327773i
$925$		0			0
$926$	−5104.16			−0.181137
$927$	−38181.8	+	8802.02i	−1.35281	+	0.311862i
$928$	−26501.7			−0.937456
$929$	−14466.9	+	25057.5i	−0.510920	+	0.884939i	0.489000	+	0.872284i	$0.337362\pi$
$929$	−14466.9	+	25057.5i	−0.510920	+	0.884939i	−0.999920	+	0.0126553i	$0.995972\pi$
$930$		0			0
$931$	8979.11	+	15552.3i	0.316089	+	0.547482i
$932$	−16606.2	−	28762.8i	−0.583641	−	1.01090i
$933$	8152.20	−	18740.5i	0.286057	−	0.657596i
$934$	3046.24	−	5276.25i	0.106720	−	0.184844i
$935$		0			0
$936$	−2120.60	+	488.862i	−0.0740536	+	0.0170715i
$937$	−8282.43			−0.288768			−0.144384	−	0.989522i	$-0.546120\pi$
$937$	−8282.43			−0.288768			−0.144384	+	0.989522i	$0.546120\pi$
$938$	−1511.96	+	2618.80i	−0.0526304	+	0.0911585i
$939$	16346.5	−	1859.79i	0.568103	−	0.0646346i
$940$		0			0
$941$	18408.2	+	31883.9i	0.637715	+	1.10455i	0.985933	+	0.167141i	$0.0534534\pi$
$941$	18408.2	+	31883.9i	0.637715	+	1.10455i	−0.348219	+	0.937413i	$0.613213\pi$
$942$	−1281.23	−	1732.07i	−0.0443151	−	0.0599085i
$943$	2238.47	−	3877.14i	0.0773007	−	0.133889i
$944$	−29318.0			−1.01083
$945$		0			0
$946$	−227.250			−0.00781031
$947$	−465.404	+	806.104i	−0.0159700	+	0.0276609i	−0.873900	−	0.486106i	$-0.838417\pi$
$947$	−465.404	+	806.104i	−0.0159700	+	0.0276609i	0.857930	+	0.513767i	$0.171750\pi$
$948$	−9014.69	−	12186.7i	−0.308843	−	0.417518i
$949$	−2336.27	−	4046.54i	−0.0799141	−	0.138415i
$950$		0			0
$951$	40485.6	−	4606.15i	1.38048	−	0.157061i
$952$	−3322.06	+	5753.97i	−0.113097	+	0.195890i
$953$	11327.1			0.385016			0.192508	−	0.981295i	$-0.438338\pi$
$953$	11327.1			0.385016			0.192508	+	0.981295i	$0.438338\pi$
$954$	−4023.52	−	4317.48i	−0.136547	−	0.146524i
$955$		0			0
$956$	−6068.05	+	10510.2i	−0.205287	+	0.355568i
$957$	992.815	−	2282.31i	0.0335352	−	0.0770917i
$958$	−574.756	−	995.507i	−0.0193836	−	0.0335734i
$959$	−2419.00	−	4189.84i	−0.0814533	−	0.141081i
$960$		0			0
$961$	8019.05	−	13889.4i	0.269177	−	0.466228i
$962$	−866.451			−0.0290390
$963$	−1080.47	+	3530.00i	−0.0361555	+	0.118123i
$964$	37479.7			1.25222
$965$		0			0
$966$	983.451	−	111.890i	0.0327557	−	0.00372670i
$967$	20908.9	+	36215.3i	0.695330	+	1.20435i	0.970069	+	0.242829i	$0.0780752\pi$
$967$	20908.9	+	36215.3i	0.695330	+	1.20435i	−0.274739	+	0.961519i	$0.588591\pi$
$968$	−4987.54	−	8638.67i	−0.165605	−	0.286836i
$969$	−21253.3	−	28731.8i	−0.704596	−	0.952527i
$970$		0			0
$971$	−40444.6			−1.33669			−0.668346	−	0.743850i	$-0.732997\pi$
$971$	−40444.6			−1.33669			−0.668346	+	0.743850i	$0.732997\pi$
$972$	24846.9	−	15801.1i	0.819921	−	0.521421i
$973$	−31225.3			−1.02881
$974$	3900.37	−	6755.64i	0.128312	−	0.222243i
$975$		0			0
$976$	−17051.3	−	29533.8i	−0.559221	−	0.968600i
$977$	−21271.4	−	36843.1i	−0.696553	−	1.20646i	−0.969655	−	0.244479i	$-0.921383\pi$
$977$	−21271.4	−	36843.1i	−0.696553	−	1.20646i	0.273102	−	0.961985i	$-0.411950\pi$
$978$	76.8284	−	8.74098i	0.00251197	−	0.000285793i
$979$	−320.618	+	555.327i	−0.0104668	+	0.0181290i
$980$		0			0
$981$	−317.023	+	1035.74i	−0.0103178	+	0.0337092i
$982$	7555.19			0.245515
$983$	−8943.52	+	15490.6i	−0.290187	+	0.502619i	−0.973854	−	0.227175i	$-0.927051\pi$
$983$	−8943.52	+	15490.6i	−0.290187	+	0.502619i	0.683667	+	0.729794i	$0.260384\pi$
$984$	−2208.07	+	5075.98i	−0.0715352	+	0.164447i
$985$		0			0
$986$	−5003.39	−	8666.13i	−0.161603	−	0.279904i
$987$	12811.5	−	29451.5i	0.413165	−	0.949797i
$988$	4112.29	−	7122.70i	0.132418	−	0.229355i
$989$	−9474.29			−0.304616
$990$		0			0
$991$	41046.0			1.31571			0.657856	−	0.753144i	$-0.271464\pi$
$991$	41046.0			1.31571			0.657856	+	0.753144i	$0.271464\pi$
$992$	5158.31	−	8934.46i	0.165097	−	0.285957i
$993$	56032.7	−	6374.99i	1.79068	−	0.203730i
$994$	−3219.55	−	5576.42i	−0.102734	−	0.177941i
$995$		0			0
$996$	31064.4	+	41995.3i	0.988266	+	1.33601i
$997$	12415.4	−	21504.2i	0.394384	−	0.683093i	−0.598638	−	0.801019i	$-0.704291\pi$
$997$	12415.4	−	21504.2i	0.394384	−	0.683093i	0.993022	+	0.117926i	$0.0376247\pi$
$998$	5455.74			0.173044
$999$	22428.3	−	7930.09i	0.710309	−	0.251148i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.4.e.f.151.6	yes	24
5.2	odd	4		225.4.k.e.124.12		48
5.3	odd	4		225.4.k.e.124.13		48
5.4	even	2		225.4.e.e.151.7	yes	24
9.2	odd	6		2025.4.a.bj.1.6		12
9.4	even	3	inner	225.4.e.f.76.6	yes	24
9.7	even	3		2025.4.a.bf.1.7		12
45.4	even	6		225.4.e.e.76.7	✓	24
45.13	odd	12		225.4.k.e.49.12		48
45.22	odd	12		225.4.k.e.49.13		48
45.29	odd	6		2025.4.a.be.1.7		12
45.34	even	6		2025.4.a.bi.1.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.4.e.e.76.7	✓	24	45.4	even	6
225.4.e.e.151.7	yes	24	5.4	even	2
225.4.e.f.76.6	yes	24	9.4	even	3	inner
225.4.e.f.151.6	yes	24	1.1	even	1	trivial
225.4.k.e.49.12		48	45.13	odd	12
225.4.k.e.49.13		48	45.22	odd	12
225.4.k.e.124.12		48	5.2	odd	4
225.4.k.e.124.13		48	5.3	odd	4
2025.4.a.be.1.7		12	45.29	odd	6
2025.4.a.bf.1.7		12	9.7	even	3
2025.4.a.bi.1.6		12	45.34	even	6
2025.4.a.bj.1.6		12	9.2	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-0.238017 + 0.412258i) q^{2} +(3.09012 + 4.17746i) q^{3} +(3.88670 + 6.73195i) q^{4} +(-2.45769 + 0.279619i) q^{6} +(-6.34045 + 10.9820i) q^{7} -7.50869 q^{8} +(-7.90234 + 25.8177i) q^{9} +O(q^{10})\)	\(q+(-0.238017 + 0.412258i) q^{2} +(3.09012 + 4.17746i) q^{3} +(3.88670 + 6.73195i) q^{4} +(-2.45769 + 0.279619i) q^{6} +(-6.34045 + 10.9820i) q^{7} -7.50869 q^{8} +(-7.90234 + 25.8177i) q^{9} +(0.794994 - 1.37697i) q^{11} +(-16.1121 + 37.0390i) q^{12} +(-5.36718 - 9.29622i) q^{13} +(-3.01828 - 5.22781i) q^{14} +(-29.3064 + 50.7601i) q^{16} -69.7787 q^{17} +(-8.76266 - 9.40287i) q^{18} +98.5661 q^{19} +(-65.4695 + 7.44864i) q^{21} +(0.378445 + 0.655486i) q^{22} +(15.7777 + 27.3278i) q^{23} +(-23.2027 - 31.3672i) q^{24} +5.10993 q^{26} +(-132.272 + 46.7680i) q^{27} -98.5736 q^{28} +(150.627 - 260.893i) q^{29} +(58.6364 + 101.561i) q^{31} +(-43.9856 - 76.1853i) q^{32} +(8.20886 - 0.933944i) q^{33} +(16.6086 - 28.7669i) q^{34} +(-204.517 + 47.1473i) q^{36} -169.562 q^{37} +(-23.4605 + 40.6347i) q^{38} +(22.2494 - 51.1476i) q^{39} +(-70.9376 - 122.868i) q^{41} +(12.5121 - 28.7633i) q^{42} +(-150.121 + 260.018i) q^{43} +12.3596 q^{44} -15.0215 q^{46} +(-243.712 + 422.122i) q^{47} +(-302.608 + 34.4286i) q^{48} +(91.0974 + 157.785i) q^{49} +(-215.625 - 291.498i) q^{51} +(41.7212 - 72.2632i) q^{52} +459.166 q^{53} +(12.2024 - 65.6616i) q^{54} +(47.6084 - 82.4602i) q^{56} +(304.581 + 411.756i) q^{57} +(71.7037 + 124.194i) q^{58} +(250.099 + 433.185i) q^{59} +(-290.915 + 503.880i) q^{61} -55.8259 q^{62} +(-233.425 - 250.479i) q^{63} -427.024 q^{64} +(-1.56883 + 3.60647i) q^{66} +(-250.468 - 433.823i) q^{67} +(-271.209 - 469.747i) q^{68} +(-65.4059 + 150.357i) q^{69} +1066.69 q^{71} +(59.3362 - 193.857i) q^{72} +435.288 q^{73} +(40.3588 - 69.9034i) q^{74} +(383.096 + 663.542i) q^{76} +(10.0812 + 17.4612i) q^{77} +(15.7903 + 21.3465i) q^{78} +(-187.644 + 325.009i) q^{79} +(-604.106 - 408.040i) q^{81} +67.5375 q^{82} +(646.617 - 1119.97i) q^{83} +(-304.604 - 411.787i) q^{84} +(-71.4630 - 123.778i) q^{86} +(1555.33 - 176.954i) q^{87} +(-5.96936 + 10.3392i) q^{88} -403.296 q^{89} +136.121 q^{91} +(-122.646 + 212.430i) q^{92} +(-243.074 + 558.787i) q^{93} +(-116.016 - 200.945i) q^{94} +(182.340 - 419.170i) q^{96} +(790.735 - 1369.59i) q^{97} -86.7311 q^{98} +(29.2679 + 31.4062i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 4 q^{2} + q^{3} - 48 q^{4} - 13 q^{6} - 6 q^{7} - 90 q^{8} - 61 q^{9}+O(q^{10}) \) 24 * q + 4 * q^2 + q^3 - 48 * q^4 - 13 * q^6 - 6 * q^7 - 90 * q^8 - 61 * q^9	\( 24 q + 4 q^{2} + q^{3} - 48 q^{4} - 13 q^{6} - 6 q^{7} - 90 q^{8} - 61 q^{9} - 29 q^{11} + 77 q^{12} - 24 q^{13} + 69 q^{14} - 192 q^{16} - 158 q^{17} - 125 q^{18} - 150 q^{19} - 60 q^{21} + 18 q^{22} + 318 q^{23} + 342 q^{24} - 308 q^{26} + 394 q^{27} + 192 q^{28} - 106 q^{29} - 60 q^{31} + 914 q^{32} + 80 q^{33} + 108 q^{34} + 1303 q^{36} - 168 q^{37} + 640 q^{38} - 410 q^{39} + 353 q^{41} - 1521 q^{42} + 426 q^{43} + 1142 q^{44} + 540 q^{46} + 1210 q^{47} - 2680 q^{48} - 666 q^{49} - 1369 q^{51} + 75 q^{52} - 896 q^{53} - 2128 q^{54} + 570 q^{56} - 1544 q^{57} - 594 q^{58} - 482 q^{59} - 402 q^{61} - 5088 q^{62} + 1038 q^{63} + 1950 q^{64} + 2041 q^{66} + 201 q^{67} + 3437 q^{68} + 2856 q^{69} - 1888 q^{71} + 5493 q^{72} - 906 q^{73} - 10 q^{74} + 462 q^{76} + 2652 q^{77} + 4589 q^{78} - 258 q^{79} + 3071 q^{81} + 1746 q^{82} + 3012 q^{83} - 2703 q^{84} - 1952 q^{86} - 2708 q^{87} + 216 q^{88} - 1476 q^{89} - 1236 q^{91} + 5232 q^{92} - 3024 q^{93} - 63 q^{94} - 10424 q^{96} + 318 q^{97} - 15022 q^{98} - 1697 q^{99}+O(q^{100}) \) 24 * q + 4 * q^2 + q^3 - 48 * q^4 - 13 * q^6 - 6 * q^7 - 90 * q^8 - 61 * q^9 - 29 * q^11 + 77 * q^12 - 24 * q^13 + 69 * q^14 - 192 * q^16 - 158 * q^17 - 125 * q^18 - 150 * q^19 - 60 * q^21 + 18 * q^22 + 318 * q^23 + 342 * q^24 - 308 * q^26 + 394 * q^27 + 192 * q^28 - 106 * q^29 - 60 * q^31 + 914 * q^32 + 80 * q^33 + 108 * q^34 + 1303 * q^36 - 168 * q^37 + 640 * q^38 - 410 * q^39 + 353 * q^41 - 1521 * q^42 + 426 * q^43 + 1142 * q^44 + 540 * q^46 + 1210 * q^47 - 2680 * q^48 - 666 * q^49 - 1369 * q^51 + 75 * q^52 - 896 * q^53 - 2128 * q^54 + 570 * q^56 - 1544 * q^57 - 594 * q^58 - 482 * q^59 - 402 * q^61 - 5088 * q^62 + 1038 * q^63 + 1950 * q^64 + 2041 * q^66 + 201 * q^67 + 3437 * q^68 + 2856 * q^69 - 1888 * q^71 + 5493 * q^72 - 906 * q^73 - 10 * q^74 + 462 * q^76 + 2652 * q^77 + 4589 * q^78 - 258 * q^79 + 3071 * q^81 + 1746 * q^82 + 3012 * q^83 - 2703 * q^84 - 1952 * q^86 - 2708 * q^87 + 216 * q^88 - 1476 * q^89 - 1236 * q^91 + 5232 * q^92 - 3024 * q^93 - 63 * q^94 - 10424 * q^96 + 318 * q^97 - 15022 * q^98 - 1697 * q^99

Introduction

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