LMFDB - Embedded newform 225.4.e.f.151.4

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			151.4
Character	$\chi$	$=$	225.151
Dual form			225.4.e.f.76.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.832171 + 1.44136i) q^{2} +(-4.88113 - 1.78172i) q^{3} +(2.61498 + 4.52928i) q^{4} +(6.63004 - 5.55278i) q^{6} +(5.28358 - 9.15142i) q^{7} -22.0192 q^{8} +(20.6509 + 17.3936i) q^{9} +O(q^{10})$	\(q+(-0.832171 + 1.44136i) q^{2} +(-4.88113 - 1.78172i) q^{3} +(2.61498 + 4.52928i) q^{4} +(6.63004 - 5.55278i) q^{6} +(5.28358 - 9.15142i) q^{7} -22.0192 q^{8} +(20.6509 + 17.3936i) q^{9} +(-14.5398 + 25.1837i) q^{11} +(-4.69416 - 26.7672i) q^{12} +(11.7510 + 20.3533i) q^{13} +(8.79368 + 15.2311i) q^{14} +(-2.59614 + 4.49664i) q^{16} -35.6583 q^{17} +(-42.2557 + 15.2910i) q^{18} +23.7670 q^{19} +(-42.0951 + 35.2555i) q^{21} +(-24.1993 - 41.9143i) q^{22} +(-39.4733 - 68.3697i) q^{23} +(107.479 + 39.2321i) q^{24} -39.1153 q^{26} +(-69.8093 - 121.695i) q^{27} +55.2658 q^{28} +(-74.0997 + 128.344i) q^{29} +(-170.912 - 296.028i) q^{31} +(-92.3976 - 160.037i) q^{32} +(115.841 - 97.0192i) q^{33} +(29.6738 - 51.3966i) q^{34} +(-24.7789 + 139.018i) q^{36} -337.627 q^{37} +(-19.7782 + 34.2569i) q^{38} +(-21.0942 - 120.284i) q^{39} +(-177.023 - 306.613i) q^{41} +(-15.7855 - 90.0129i) q^{42} +(-9.76327 + 16.9105i) q^{43} -152.086 q^{44} +131.394 q^{46} +(-56.0915 + 97.1533i) q^{47} +(20.6839 - 17.3231i) q^{48} +(115.668 + 200.342i) q^{49} +(174.053 + 63.5333i) q^{51} +(-61.4572 + 106.447i) q^{52} -699.829 q^{53} +(233.500 + 0.650493i) q^{54} +(-116.340 + 201.507i) q^{56} +(-116.010 - 42.3462i) q^{57} +(-123.327 - 213.609i) q^{58} +(-13.7297 - 23.7805i) q^{59} +(412.663 - 714.754i) q^{61} +568.912 q^{62} +(268.287 - 97.0847i) q^{63} +266.024 q^{64} +(43.4401 + 247.706i) q^{66} +(412.657 + 714.743i) q^{67} +(-93.2460 - 161.507i) q^{68} +(70.8584 + 404.052i) q^{69} -337.616 q^{71} +(-454.717 - 382.994i) q^{72} +717.566 q^{73} +(280.963 - 486.642i) q^{74} +(62.1504 + 107.648i) q^{76} +(153.645 + 266.120i) q^{77} +(190.927 + 69.6926i) q^{78} +(155.091 - 268.625i) q^{79} +(123.922 + 718.390i) q^{81} +589.253 q^{82} +(-276.069 + 478.166i) q^{83} +(-269.760 - 98.4684i) q^{84} +(-16.2494 - 28.1448i) q^{86} +(590.364 - 494.441i) q^{87} +(320.155 - 554.525i) q^{88} -1085.33 q^{89} +248.349 q^{91} +(206.444 - 357.571i) q^{92} +(306.804 + 1749.47i) q^{93} +(-93.3554 - 161.696i) q^{94} +(165.863 + 945.791i) q^{96} +(-583.915 + 1011.37i) q^{97} -385.021 q^{98} +(-738.298 + 267.167i) 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 $

$2$	−0.832171	+	1.44136i	−0.294217	+	0.509599i	−0.974802	−	0.223070i	$-0.928392\pi$
$2$	−0.832171	+	1.44136i	−0.294217	+	0.509599i	0.680586	+	0.732669i	$0.261725\pi$
$3$	−4.88113	−	1.78172i	−0.939375	−	0.342893i
$3$	−4.88113	−	1.78172i	−0.939375	−	0.342893i
$4$	2.61498	+	4.52928i	0.326873	+	0.566160i
$5$		0			0
$5$		0			0
$6$	6.63004	−	5.55278i	0.451117	−	0.377819i
$7$	5.28358	−	9.15142i	0.285286	−	0.494130i	−0.687392	−	0.726286i	$-0.741245\pi$
$7$	5.28358	−	9.15142i	0.285286	−	0.494130i	0.972679	+	0.232156i	$0.0745780\pi$
$8$	−22.0192			−0.973120
$9$	20.6509	+	17.3936i	0.764849	+	0.644209i
$10$		0			0
$11$	−14.5398	+	25.1837i	−0.398539	+	0.690289i	−0.993546	−	0.113431i	$-0.963816\pi$
$11$	−14.5398	+	25.1837i	−0.398539	+	0.690289i	0.595007	+	0.803720i	$0.297149\pi$
$12$	−4.69416	−	26.7672i	−0.112924	−	0.643919i
$13$	11.7510	+	20.3533i	0.250703	+	0.434230i	0.963719	−	0.266917i	$-0.0860050\pi$
$13$	11.7510	+	20.3533i	0.250703	+	0.434230i	−0.713017	+	0.701147i	$0.752672\pi$
$14$	8.79368	+	15.2311i	0.167872	+	0.290763i
$15$		0			0
$16$	−2.59614	+	4.49664i	−0.0405646	+	0.0702600i
$17$	−35.6583			−0.508731			−0.254365	−	0.967108i	$-0.581867\pi$
$17$	−35.6583			−0.508731			−0.254365	+	0.967108i	$0.581867\pi$
$18$	−42.2557	+	15.2910i	−0.553320	+	0.200229i
$19$	23.7670			0.286975			0.143488	−	0.989652i	$-0.454168\pi$
$19$	23.7670			0.286975			0.143488	+	0.989652i	$0.454168\pi$
$20$		0			0
$21$	−42.0951	+	35.2555i	−0.437424	+	0.366351i
$22$	−24.1993	−	41.9143i	−0.234514	−	0.406190i
$23$	−39.4733	−	68.3697i	−0.357858	−	0.619829i	0.629744	−	0.776802i	$-0.283160\pi$
$23$	−39.4733	−	68.3697i	−0.357858	−	0.619829i	−0.987603	+	0.156974i	$0.949826\pi$
$24$	107.479	+	39.2321i	0.914124	+	0.333676i
$25$		0			0
$26$	−39.1153			−0.295044
$27$	−69.8093	−	121.695i	−0.497585	−	0.867415i
$28$	55.2658			0.373009
$29$	−74.0997	+	128.344i	−0.474481	+	0.821826i	−0.999573	−	0.0292198i	$-0.990698\pi$
$29$	−74.0997	+	128.344i	−0.474481	+	0.821826i	0.525092	+	0.851046i	$0.324031\pi$
$30$		0			0
$31$	−170.912	−	296.028i	−0.990217	−	1.71511i	−0.615951	−	0.787784i	$-0.711228\pi$
$31$	−170.912	−	296.028i	−0.990217	−	1.71511i	−0.374265	−	0.927322i	$-0.622105\pi$
$32$	−92.3976	−	160.037i	−0.510429	−	0.884090i
$33$	115.841	−	97.0192i	0.611072	−	0.511784i
$34$	29.6738	−	51.3966i	0.149677	−	0.259248i
$35$		0			0
$36$	−24.7789	+	139.018i	−0.114717	+	0.643602i
$37$	−337.627			−1.50015			−0.750074	−	0.661354i	$-0.769982\pi$
$37$	−337.627			−1.50015			−0.750074	+	0.661354i	$0.769982\pi$
$38$	−19.7782	+	34.2569i	−0.0844329	+	0.146242i
$39$	−21.0942	−	120.284i	−0.0866095	−	0.493868i
$40$		0			0
$41$	−177.023	−	306.613i	−0.674301	−	1.16792i	−0.976673	−	0.214733i	$-0.931112\pi$
$41$	−177.023	−	306.613i	−0.674301	−	1.16792i	0.302372	−	0.953190i	$-0.402222\pi$
$42$	−15.7855	−	90.0129i	−0.0579943	−	0.330697i
$43$	−9.76327	+	16.9105i	−0.0346252	+	0.0599727i	−0.882819	−	0.469714i	$-0.844357\pi$
$43$	−9.76327	+	16.9105i	−0.0346252	+	0.0599727i	0.848193	+	0.529687i	$0.177690\pi$
$44$	−152.086			−0.521086
$45$		0			0
$46$	131.394			0.421152
$47$	−56.0915	+	97.1533i	−0.174080	+	0.301516i	−0.939843	−	0.341608i	$-0.889029\pi$
$47$	−56.0915	+	97.1533i	−0.174080	+	0.301516i	0.765762	+	0.643124i	$0.222362\pi$
$48$	20.6839	−	17.3231i	0.0621970	−	0.0520912i
$49$	115.668	+	200.342i	0.337223	+	0.584088i
$50$		0			0
$51$	174.053	+	63.5333i	0.477889	+	0.174440i
$52$	−61.4572	+	106.447i	−0.163896	+	0.283876i
$53$	−699.829			−1.81375			−0.906876	−	0.421398i	$-0.861540\pi$
$53$	−699.829			−1.81375			−0.906876	+	0.421398i	$0.861540\pi$
$54$	233.500	+	0.650493i	0.588431	+	0.00163927i
$55$		0			0
$56$	−116.340	+	201.507i	−0.277618	+	0.480848i
$57$	−116.010	−	42.3462i	−0.269577	−	0.0984017i
$58$	−123.327	−	213.609i	−0.279201	−	0.483590i
$59$	−13.7297	−	23.7805i	−0.0302958	−	0.0524739i	0.850480	−	0.526007i	$-0.176312\pi$
$59$	−13.7297	−	23.7805i	−0.0302958	−	0.0524739i	−0.880776	+	0.473534i	$0.842978\pi$
$60$		0			0
$61$	412.663	−	714.754i	0.866166	−	1.50024i	0.000280785	−	1.00000i	$-0.499911\pi$
$61$	412.663	−	714.754i	0.866166	−	1.50024i	0.865885	−	0.500243i	$-0.166756\pi$
$62$	568.912			1.16535
$63$	268.287	−	97.0847i	0.536524	−	0.194151i
$64$	266.024			0.519579
$65$		0			0
$66$	43.4401	+	247.706i	0.0810168	+	0.461977i
$67$	412.657	+	714.743i	0.752449	+	1.30328i	0.946633	+	0.322315i	$0.104461\pi$
$67$	412.657	+	714.743i	0.752449	+	1.30328i	−0.194183	+	0.980965i	$0.562206\pi$
$68$	−93.2460	−	161.507i	−0.166290	−	0.288023i
$69$	70.8584	+	404.052i	0.123628	+	0.704958i
$70$		0			0
$71$	−337.616			−0.564332			−0.282166	−	0.959366i	$-0.591053\pi$
$71$	−337.616			−0.564332			−0.282166	+	0.959366i	$0.591053\pi$
$72$	−454.717	−	382.994i	−0.744290	−	0.626893i
$73$	717.566			1.15048			0.575238	−	0.817986i	$-0.304909\pi$
$73$	717.566			1.15048			0.575238	+	0.817986i	$0.304909\pi$
$74$	280.963	−	486.642i	0.441369	−	0.764473i
$75$		0			0
$76$	62.1504	+	107.648i	0.0938044	+	0.162474i
$77$	153.645	+	266.120i	0.227395	+	0.393860i
$78$	190.927	+	69.6926i	0.277157	+	0.101168i
$79$	155.091	−	268.625i	0.220875	−	0.382566i	−0.734199	−	0.678934i	$-0.762442\pi$
$79$	155.091	−	268.625i	0.220875	−	0.382566i	0.955074	+	0.296368i	$0.0957755\pi$
$80$		0			0
$81$	123.922	+	718.390i	0.169989	+	0.985446i
$82$	589.253			0.793563
$83$	−276.069	+	478.166i	−0.365091	+	0.632356i	−0.988791	−	0.149308i	$-0.952295\pi$
$83$	−276.069	+	478.166i	−0.365091	+	0.632356i	0.623700	+	0.781664i	$0.285629\pi$
$84$	−269.760	−	98.4684i	−0.350396	−	0.127902i
$85$		0			0
$86$	−16.2494	−	28.1448i	−0.0203747	−	0.0352899i
$87$	590.364	−	494.441i	0.727514	−	0.609306i
$88$	320.155	−	554.525i	0.387826	−	0.671734i
$89$	−1085.33			−1.29264			−0.646319	−	0.763067i	$-0.723692\pi$
$89$	−1085.33			−1.29264			−0.646319	+	0.763067i	$0.723692\pi$
$90$		0			0
$91$	248.349			0.286088
$92$	206.444	−	357.571i	0.233948	−	0.405210i
$93$	306.804	+	1749.47i	0.342087	+	1.95066i
$94$	−93.3554	−	161.696i	−0.102435	−	0.177422i
$95$		0			0
$96$	165.863	+	945.791i	0.176337	+	1.00551i
$97$	−583.915	+	1011.37i	−0.611212	+	1.05865i	0.379825	+	0.925058i	$0.375984\pi$
$97$	−583.915	+	1011.37i	−0.611212	+	1.05865i	−0.991037	+	0.133591i	$0.957349\pi$
$98$	−385.021			−0.396867
$99$	−738.298	+	267.167i	−0.749513	+	0.271225i
$100$		0			0
$101$	−640.039	+	1108.58i	−0.630557	+	1.09216i	0.356881	+	0.934150i	$0.383840\pi$
$101$	−640.039	+	1108.58i	−0.630557	+	1.09216i	−0.987438	+	0.158006i	$0.949493\pi$
$102$	−236.416	+	198.003i	−0.229497	+	0.192208i
$103$	−62.4748	−	108.210i	−0.0597653	−	0.103517i	0.834595	−	0.550865i	$-0.185702\pi$
$103$	−62.4748	−	108.210i	−0.0597653	−	0.103517i	−0.894360	+	0.447348i	$0.852369\pi$
$104$	−258.747	−	448.163i	−0.243964	−	0.422558i
$105$		0			0
$106$	582.377	−	1008.71i	0.533636	−	0.924285i
$107$	1350.01			1.21973			0.609863	−	0.792507i	$-0.291225\pi$
$107$	1350.01			1.21973			0.609863	+	0.792507i	$0.291225\pi$
$108$	368.641	−	634.416i	0.328449	−	0.565248i
$109$	−1143.61			−1.00494			−0.502468	−	0.864596i	$-0.667574\pi$
$109$	−1143.61			−1.00494			−0.502468	+	0.864596i	$0.667574\pi$
$110$		0			0
$111$	1648.00	+	601.557i	1.40920	+	0.514390i
$112$	27.4338	+	47.5167i	0.0231451	+	0.0400884i
$113$	329.517	+	570.740i	0.274322	+	0.475139i	0.969964	−	0.243249i	$-0.0782133\pi$
$113$	329.517	+	570.740i	0.274322	+	0.475139i	−0.695642	+	0.718389i	$0.744880\pi$
$114$	157.576	−	131.973i	0.129460	−	0.108425i
$115$		0			0
$116$	−775.077			−0.620380
$117$	−111.349	+	624.707i	−0.0879850	+	0.493625i
$118$	45.7018			0.0356542
$119$	−188.404	+	326.325i	−0.145134	+	0.251379i
$120$		0			0
$121$	242.686	+	420.345i	0.182334	+	0.315811i
$122$	686.813	+	1189.59i	0.509681	+	0.882794i
$123$	317.774	+	1812.02i	0.232949	+	1.32833i
$124$	893.865	−	1548.22i	0.647350	−	1.12124i
$125$		0			0
$126$	−83.3267	+	467.490i	−0.0589153	+	0.330535i
$127$	−1564.04			−1.09281			−0.546403	−	0.837522i	$-0.684003\pi$
$127$	−1564.04			−1.09281			−0.546403	+	0.837522i	$0.684003\pi$
$128$	517.803	−	896.861i	0.357561	−	0.619313i
$129$	77.7856	−	65.1469i	0.0530903	−	0.0444641i
$130$		0			0
$131$	−1089.75	−	1887.50i	−0.726807	−	1.25887i	−0.958226	−	0.286012i	$-0.907670\pi$
$131$	−1089.75	−	1887.50i	−0.726807	−	1.25887i	0.231419	−	0.972854i	$-0.425663\pi$
$132$	742.351	+	270.974i	0.489495	+	0.178677i
$133$	125.575	−	217.502i	0.0818701	−	0.141803i
$134$	−1373.60			−0.885533
$135$		0			0
$136$	785.168			0.495056
$137$	526.947	−	912.698i	0.328614	−	0.569176i	−0.653623	−	0.756820i	$-0.726752\pi$
$137$	526.947	−	912.698i	0.328614	−	0.569176i	0.982237	+	0.187644i	$0.0600852\pi$
$138$	−641.352	−	234.108i	−0.395619	−	0.144410i
$139$	−243.303	−	421.413i	−0.148465	−	0.257150i	0.782195	−	0.623034i	$-0.214100\pi$
$139$	−243.303	−	421.413i	−0.148465	−	0.257150i	−0.930660	+	0.365884i	$0.880767\pi$
$140$		0			0
$141$	446.890	−	374.279i	0.266914	−	0.223546i
$142$	280.954	−	486.626i	0.166036	−	0.287583i
$143$	−683.429			−0.399659
$144$	−131.826	+	47.7035i	−0.0762880	+	0.0276062i
$145$		0			0
$146$	−597.138	+	1034.27i	−0.338489	+	0.586281i
$147$	−207.635	−	1183.98i	−0.116500	−	0.664309i
$148$	−882.888	−	1529.21i	−0.490358	−	0.849324i
$149$	1623.33	+	2811.69i	0.892540	+	1.54592i	0.836821	+	0.547477i	$0.184412\pi$
$149$	1623.33	+	2811.69i	0.892540	+	1.54592i	0.0557190	+	0.998446i	$0.482255\pi$
$150$		0			0
$151$	764.874	−	1324.80i	0.412216	−	0.713978i	−0.582916	−	0.812532i	$-0.698088\pi$
$151$	764.874	−	1324.80i	0.412216	−	0.713978i	0.995132	+	0.0985540i	$0.0314217\pi$
$152$	−523.331			−0.279261
$153$	−736.378	−	620.229i	−0.389102	−	0.327729i
$154$	−511.435			−0.267614
$155$		0			0
$156$	489.640	−	410.082i	0.251298	−	0.210467i
$157$	365.776	+	633.543i	0.185937	+	0.322052i	0.943892	−	0.330255i	$-0.107135\pi$
$157$	365.776	+	633.543i	0.185937	+	0.322052i	−0.757955	+	0.652307i	$0.773801\pi$
$158$	258.124	+	447.084i	0.129970	+	0.225115i
$159$	3415.96	+	1246.90i	1.70379	+	0.621922i
$160$		0			0
$161$	−834.240			−0.408368
$162$	−1138.58	−	419.207i	−0.552195	−	0.203309i
$163$	−132.833			−0.0638298			−0.0319149	−	0.999491i	$-0.510161\pi$
$163$	−132.833			−0.0638298			−0.0319149	+	0.999491i	$0.510161\pi$
$164$	925.824	−	1603.57i	0.440821	−	0.763525i
$165$		0			0
$166$	−459.474	−	795.832i	−0.214832	−	0.372099i
$167$	684.073	+	1184.85i	0.316977	+	0.549021i	0.979856	−	0.199706i	$-0.0639988\pi$
$167$	684.073	+	1184.85i	0.316977	+	0.549021i	−0.662879	+	0.748727i	$0.730665\pi$
$168$	926.901	−	776.296i	0.425666	−	0.356503i
$169$	822.329	−	1424.32i	0.374296	−	0.648300i
$170$		0			0
$171$	490.811	+	413.395i	0.219493	+	0.184872i
$172$	−102.123			−0.0452722
$173$	1058.70	−	1833.72i	0.465268	−	0.805867i	−0.533946	−	0.845519i	$-0.679291\pi$
$173$	1058.70	−	1833.72i	0.465268	−	0.805867i	0.999214	+	0.0396515i	$0.0126248\pi$
$174$	221.385	+	1262.39i	0.0964547	+	0.550008i
$175$		0			0
$176$	−75.4948	−	130.761i	−0.0323332	−	0.0560027i
$177$	24.6462	+	140.538i	0.0104662	+	0.0596809i
$178$	903.180	−	1564.35i	0.380316	−	0.658726i
$179$	2224.74			0.928966			0.464483	−	0.885582i	$-0.346240\pi$
$179$	2224.74			0.928966			0.464483	+	0.885582i	$0.346240\pi$
$180$		0			0
$181$	−723.066			−0.296934			−0.148467	−	0.988917i	$-0.547434\pi$
$181$	−723.066			−0.296934			−0.148467	+	0.988917i	$0.547434\pi$
$182$	−206.669	+	357.961i	−0.0841720	+	0.145790i
$183$	−3287.76	+	2753.56i	−1.32808	+	1.11229i
$184$	869.169	+	1505.44i	0.348239	+	0.603168i
$185$		0			0
$186$	−2776.94	−	1013.64i	−1.09470	−	0.399591i
$187$	518.467	−	898.010i	0.202749	−	0.351171i
$188$	−586.713			−0.227609
$189$	−1482.52	−	4.13007i	−0.570570	−	0.00158952i
$190$		0			0
$191$	125.680	−	217.685i	0.0476121	−	0.0824666i	−0.841237	−	0.540666i	$-0.818172\pi$
$191$	125.680	−	217.685i	0.0476121	−	0.0824666i	0.888849	+	0.458200i	$0.151506\pi$
$192$	−1298.50	−	473.981i	−0.488079	−	0.178160i
$193$	−190.385	−	329.756i	−0.0710061	−	0.122986i	0.828336	−	0.560231i	$-0.189288\pi$
$193$	−190.385	−	329.756i	−0.0710061	−	0.122986i	−0.899343	+	0.437245i	$0.855954\pi$
$194$	−971.833	−	1683.26i	−0.359658	−	0.622945i
$195$		0			0
$196$	−604.938	+	1047.78i	−0.220458	+	0.381845i
$197$	−4369.98			−1.58045			−0.790225	−	0.612817i	$-0.790036\pi$
$197$	−4369.98			−1.58045			−0.790225	+	0.612817i	$0.790036\pi$
$198$	229.306	−	1286.48i	0.0823034	−	0.461750i
$199$	−985.541			−0.351071			−0.175536	−	0.984473i	$-0.556166\pi$
$199$	−985.541			−0.351071			−0.175536	+	0.984473i	$0.556166\pi$
$200$		0			0
$201$	−740.761	−	4224.00i	−0.259946	−	1.48228i
$202$	−1065.24	−	1845.06i	−0.371041	−	0.642661i
$203$	783.022	+	1356.23i	0.270726	+	0.468911i
$204$	167.386	+	954.474i	0.0574478	+	0.327581i
$205$		0			0
$206$	207.959			0.0703358
$207$	374.039	−	2098.48i	0.125592	−	0.704611i
$208$	−122.029			−0.0406787
$209$	−345.569	+	598.542i	−0.114371	+	0.198096i
$210$		0			0
$211$	−480.664	−	832.535i	−0.156826	−	0.271631i	0.776896	−	0.629628i	$-0.216793\pi$
$211$	−480.664	−	832.535i	−0.156826	−	0.271631i	−0.933722	+	0.357998i	$0.883460\pi$
$212$	−1830.04	−	3169.72i	−0.592866	−	1.02687i
$213$	1647.95	+	601.537i	0.530120	+	0.193505i
$214$	−1123.44	+	1945.86i	−0.358864	+	0.621570i
$215$		0			0
$216$	1537.14	+	2679.62i	0.484210	+	0.844099i
$217$	−3612.11			−1.12998
$218$	951.679	−	1648.36i	0.295669	−	0.512114i
$219$	−3502.54	−	1278.50i	−1.08073	−	0.394490i
$220$		0			0
$221$	−419.020	−	725.765i	−0.127540	−	0.220906i
$222$	−2238.48	+	1874.77i	−0.676743	+	0.566784i
$223$	−2396.87	+	4151.50i	−0.719758	+	1.24666i	0.241337	+	0.970441i	$0.422414\pi$
$223$	−2396.87	+	4151.50i	−0.719758	+	1.24666i	−0.961095	+	0.276217i	$0.910919\pi$
$224$	−1952.76			−0.582474
$225$		0			0
$226$	−1096.86			−0.322840
$227$	2115.92	−	3664.89i	0.618673	−	1.07157i	−0.371055	−	0.928611i	$-0.621004\pi$
$227$	2115.92	−	3664.89i	0.618673	−	1.07157i	0.989728	−	0.142962i	$-0.0456628\pi$
$228$	−111.566	−	636.177i	−0.0324063	−	0.184789i
$229$	801.351	+	1387.98i	0.231243	+	0.400525i	0.958174	−	0.286185i	$-0.0923873\pi$
$229$	801.351	+	1387.98i	0.231243	+	0.400525i	−0.726931	+	0.686711i	$0.759054\pi$
$230$		0			0
$231$	−275.808	−	1572.72i	−0.0785576	−	0.447954i
$232$	1631.61	−	2826.04i	0.461727	−	0.799735i
$233$	−6094.84			−1.71368			−0.856838	−	0.515586i	$-0.827574\pi$
$233$	−6094.84			−1.71368			−0.856838	+	0.515586i	$0.827574\pi$
$234$	−807.767	−	680.358i	−0.225664	−	0.190070i
$235$		0			0
$236$	71.8058	−	124.371i	0.0198058	−	0.0343046i
$237$	−1235.64	+	1034.87i	−0.338663	+	0.283637i
$238$	−313.568	−	543.116i	−0.0854017	−	0.147920i
$239$	1939.22	+	3358.83i	0.524844	+	0.909057i	0.999581	+	0.0289294i	$0.00920978\pi$
$239$	1939.22	+	3358.83i	0.524844	+	0.909057i	−0.474737	+	0.880128i	$0.657457\pi$
$240$		0			0
$241$	−3253.39	+	5635.04i	−0.869583	+	1.50616i	−0.00715909	+	0.999974i	$0.502279\pi$
$241$	−3253.39	+	5635.04i	−0.869583	+	1.50616i	−0.862424	+	0.506187i	$0.831055\pi$
$242$	−807.826			−0.214583
$243$	675.092	−	3727.35i	0.178219	−	0.983991i
$244$	4316.43			1.13250
$245$		0			0
$246$	−2876.22	−	1049.89i	−0.745453	−	0.272107i
$247$	279.286	+	483.737i	0.0719455	+	0.124613i
$248$	3763.35	+	6518.31i	0.963600	+	1.66900i
$249$	2199.49	−	1842.11i	0.559787	−	0.468832i
$250$		0			0
$251$	7716.46			1.94047			0.970236	−	0.242161i	$-0.0778562\pi$
$251$	7716.46			1.94047			0.970236	+	0.242161i	$0.0778562\pi$
$252$	1141.29	+	961.275i	0.285296	+	0.240296i
$253$	2295.74			0.570482
$254$	1301.55	−	2254.35i	0.321522	−	0.556892i
$255$		0			0
$256$	1925.90	+	3335.75i	0.470190	+	0.814393i
$257$	1268.87	+	2197.75i	0.307977	+	0.533432i	0.977920	−	0.208981i	$-0.0670146\pi$
$257$	1268.87	+	2197.75i	0.307977	+	0.533432i	−0.669942	+	0.742413i	$0.733681\pi$
$258$	29.1693	+	166.331i	0.00703878	+	0.0401368i
$259$	−1783.88	+	3089.76i	−0.427972	+	0.741268i
$260$		0			0
$261$	−3762.60	+	1361.57i	−0.892335	+	0.322908i
$262$	3627.43			0.855356
$263$	3100.17	−	5369.65i	0.726861	−	1.25896i	−0.231342	−	0.972872i	$-0.574312\pi$
$263$	3100.17	−	5369.65i	0.726861	−	1.25896i	0.958203	−	0.286088i	$-0.0923550\pi$
$264$	−2550.73	+	2136.28i	−0.594646	+	0.498027i
$265$		0			0
$266$	209.000	+	361.998i	0.0481751	+	0.0834418i
$267$	5297.64	+	1933.76i	1.21427	+	0.443236i
$268$	−2158.18	+	3738.08i	−0.491910	+	0.852014i
$269$	1737.04			0.393715			0.196858	−	0.980432i	$-0.436926\pi$
$269$	1737.04			0.393715			0.196858	+	0.980432i	$0.436926\pi$
$270$		0			0
$271$	−2510.25			−0.562683			−0.281341	−	0.959608i	$-0.590779\pi$
$271$	−2510.25			−0.562683			−0.281341	+	0.959608i	$0.590779\pi$
$272$	92.5739	−	160.343i	0.0206365	−	0.0357434i
$273$	−1212.22	−	442.488i	−0.268744	−	0.0980975i
$274$	877.019	+	1519.04i	0.193367	+	0.334922i
$275$		0			0
$276$	−1644.77	+	1377.53i	−0.358709	+	0.300425i
$277$	−489.727	+	848.232i	−0.106227	+	0.183990i	−0.914239	−	0.405176i	$-0.867210\pi$
$277$	−489.727	+	848.232i	−0.106227	+	0.183990i	0.808012	+	0.589166i	$0.200544\pi$
$278$	809.879			0.174724
$279$	1619.52	−	9086.05i	0.347520	−	1.94970i
$280$		0			0
$281$	841.453	−	1457.44i	0.178636	−	0.309407i	−0.762777	−	0.646661i	$-0.776165\pi$
$281$	841.453	−	1457.44i	0.178636	−	0.309407i	0.941414	+	0.337254i	$0.109498\pi$
$282$	167.582	+	955.594i	0.0353879	+	0.201790i
$283$	1209.16	+	2094.33i	0.253984	+	0.439913i	0.964619	−	0.263648i	$-0.0849257\pi$
$283$	1209.16	+	2094.33i	0.253984	+	0.439913i	−0.710635	+	0.703561i	$0.751592\pi$
$284$	−882.859	−	1529.16i	−0.184465	−	0.319503i
$285$		0			0
$286$	568.730	−	985.069i	0.117586	−	0.203666i
$287$	−3741.26			−0.769475
$288$	875.537	−	4912.05i	0.179137	−	1.00502i
$289$	−3641.48			−0.741193
$290$		0			0
$291$	4652.14	−	3896.26i	0.937160	−	0.784889i
$292$	1876.42	+	3250.06i	0.376059	+	0.651354i
$293$	899.642	+	1558.23i	0.179378	+	0.310691i	0.941668	−	0.336545i	$-0.109258\pi$
$293$	899.642	+	1558.23i	0.179378	+	0.310691i	−0.762290	+	0.647236i	$0.775925\pi$
$294$	1879.34	+	686.001i	0.372807	+	0.136083i
$295$		0			0
$296$	7434.26			1.45982
$297$	4079.75	+	11.3655i	0.797074	+	0.00222052i
$298$	−5403.55			−1.05040
$299$	927.699	−	1606.82i	0.179432	−	0.310785i
$300$		0			0
$301$	103.170	+	178.696i	0.0197562	+	0.0342188i
$302$	1273.01	+	2204.92i	0.242562	+	0.420129i
$303$	5099.29	−	4270.75i	0.966821	−	0.809731i
$304$	−61.7024	+	106.872i	−0.0116410	+	0.0201629i
$305$		0			0
$306$	1506.77	−	545.251i	0.281491	−	0.101863i
$307$	7372.67			1.37062			0.685311	−	0.728251i	$-0.259666\pi$
$307$	7372.67			1.37062			0.685311	+	0.728251i	$0.259666\pi$
$308$	−803.556	+	1391.80i	−0.148659	+	0.257484i
$309$	112.149	+	639.498i	0.0206470	+	0.117734i
$310$		0			0
$311$	2854.02	+	4943.30i	0.520374	+	0.901315i	0.999719	+	0.0236884i	$0.00754096\pi$
$311$	2854.02	+	4943.30i	0.520374	+	0.901315i	−0.479345	+	0.877627i	$0.659126\pi$
$312$	464.477	+	2648.56i	0.0842815	+	0.480593i
$313$	355.174	−	615.180i	0.0641394	−	0.111093i	−0.832173	−	0.554517i	$-0.812903\pi$
$313$	355.174	−	615.180i	0.0641394	−	0.111093i	0.896312	+	0.443424i	$0.146236\pi$
$314$	−1217.55			−0.218823
$315$		0			0
$316$	1622.24			0.288792
$317$	−4149.33	+	7186.85i	−0.735172	+	1.27336i	0.219476	+	0.975618i	$0.429565\pi$
$317$	−4149.33	+	7186.85i	−0.735172	+	1.27336i	−0.954648	+	0.297737i	$0.903768\pi$
$318$	−4639.90	+	3886.00i	−0.818215	+	0.685270i
$319$	−2154.79	−	3732.21i	−0.378198	−	0.655059i
$320$		0			0
$321$	−6589.59	−	2405.35i	−1.14578	−	0.418235i
$322$	694.230	−	1202.44i	0.120149	−	0.208104i
$323$	−847.493			−0.145993
$324$	−2929.74	+	2439.86i	−0.502356	+	0.418357i
$325$		0			0
$326$	110.540	−	191.460i	0.0187798	−	0.0325276i
$327$	5582.11	+	2037.60i	0.944011	+	0.344585i
$328$	3897.90	+	6751.36i	0.656176	+	1.13653i
$329$	592.727	+	1026.63i	0.0993255	+	0.172037i
$330$		0			0
$331$	−2168.95	+	3756.74i	−0.360171	+	0.623834i	−0.987989	−	0.154526i	$-0.950615\pi$
$331$	−2168.95	+	3756.74i	−0.360171	+	0.623834i	0.627818	+	0.778360i	$0.283948\pi$
$332$	−2887.67			−0.477353
$333$	−6972.30	−	5872.56i	−1.14739	−	0.966409i
$334$	−2277.06			−0.373040
$335$		0			0
$336$	−49.2464	−	280.815i	−0.00799586	−	0.0455943i
$337$	−2537.40	−	4394.90i	−0.410151	−	0.710402i	0.584755	−	0.811210i	$-0.301191\pi$
$337$	−2537.40	−	4394.90i	−0.410151	−	0.710402i	−0.994906	+	0.100808i	$0.967857\pi$
$338$	1368.64	+	2370.55i	0.220249	+	0.381482i
$339$	−591.516	−	3372.97i	−0.0947692	−	0.540397i
$340$		0			0
$341$	9940.14			1.57856
$342$	−1004.29	+	363.421i	−0.158789	+	0.0574607i
$343$	6069.09			0.955394
$344$	214.979	−	372.355i	0.0336945	−	0.0583606i
$345$		0			0
$346$	1762.03	+	3051.93i	0.273779	+	0.474199i
$347$	2267.51	+	3927.45i	0.350797	+	0.607598i	0.986389	−	0.164427i	$-0.0525774\pi$
$347$	2267.51	+	3927.45i	0.350797	+	0.607598i	−0.635592	+	0.772025i	$0.719244\pi$
$348$	3783.26	+	1380.97i	0.582770	+	0.212724i
$349$	−1041.87	+	1804.56i	−0.159799	+	0.276780i	−0.934796	−	0.355185i	$-0.884418\pi$
$349$	−1041.87	+	1804.56i	−0.159799	+	0.276780i	0.774997	+	0.631965i	$0.217751\pi$
$350$		0			0
$351$	1656.56	−	2850.88i	0.251911	−	0.433530i
$352$	5373.78			0.813704
$353$	4211.89	−	7295.21i	0.635060	−	1.09996i	−0.351442	−	0.936210i	$-0.614309\pi$
$353$	4211.89	−	7295.21i	0.635060	−	1.09996i	0.986502	−	0.163747i	$-0.0523581\pi$
$354$	−223.077	−	81.4279i	−0.0334926	−	0.0122256i
$355$		0			0
$356$	−2838.12	−	4915.77i	−0.422528	−	0.731841i
$357$	1501.04	−	1257.15i	0.222531	−	0.186374i
$358$	−1851.36	+	3206.66i	−0.273317	+	0.473400i
$359$	−9286.16			−1.36519			−0.682597	−	0.730795i	$-0.739150\pi$
$359$	−9286.16			−1.36519			−0.682597	+	0.730795i	$0.739150\pi$
$360$		0			0
$361$	−6294.13			−0.917645
$362$	601.714	−	1042.20i	0.0873630	−	0.151317i
$363$	−435.646	−	2484.16i	−0.0629903	−	0.359186i
$364$	649.428	+	1124.84i	0.0935145	+	0.161972i
$365$		0			0
$366$	−1232.90	−	7030.28i	−0.176078	−	1.00404i
$367$	76.2330	−	132.039i	0.0108429	−	0.0187804i	−0.860553	−	0.509361i	$-0.829882\pi$
$367$	76.2330	−	132.039i	0.0108429	−	0.0187804i	0.871396	+	0.490580i	$0.163215\pi$
$368$	409.912			0.0580656
$369$	1677.43	−	9410.91i	0.236648	−	1.32768i
$370$		0			0
$371$	−3697.60	+	6404.43i	−0.517439	+	0.896230i
$372$	−7121.57	+	5964.44i	−0.992570	+	0.831296i
$373$	3414.46	+	5914.03i	0.473979	+	0.820956i	0.999556	−	0.0297898i	$-0.00948381\pi$
$373$	3414.46	+	5914.03i	0.473979	+	0.820956i	−0.525577	+	0.850746i	$0.676150\pi$
$374$	862.906	+	1494.60i	0.119304	+	0.206641i
$375$		0			0
$376$	1235.09	−	2139.24i	0.169401	−	0.293411i
$377$	−3482.97			−0.475815
$378$	1239.67	−	2133.42i	0.168681	−	0.290294i
$379$	−6963.21			−0.943736			−0.471868	−	0.881669i	$-0.656420\pi$
$379$	−6963.21			−0.943736			−0.471868	+	0.881669i	$0.656420\pi$
$380$		0			0
$381$	7634.30	+	2786.69i	1.02655	+	0.374715i
$382$	209.175	+	362.302i	0.0280166	+	0.0485261i
$383$	183.927	+	318.571i	0.0245385	+	0.0425018i	0.878034	−	0.478599i	$-0.158855\pi$
$383$	183.927	+	318.571i	0.0245385	+	0.0425018i	−0.853495	+	0.521100i	$0.825522\pi$
$384$	−4125.42	+	3455.12i	−0.548241	+	0.459162i
$385$		0			0
$386$	633.730			0.0835648
$387$	−495.756	+	179.398i	−0.0651180	+	0.0235642i
$388$	−6107.71			−0.799154
$389$	2765.15	−	4789.39i	0.360408	−	0.624246i	−0.627620	−	0.778520i	$-0.715971\pi$
$389$	2765.15	−	4789.39i	0.360408	−	0.624246i	0.988028	+	0.154274i	$0.0493040\pi$
$390$		0			0
$391$	1407.55	+	2437.95i	0.182053	+	0.315326i
$392$	−2546.91	−	4411.37i	−0.328159	−	0.568388i
$393$	1956.21	+	11154.8i	0.251088	+	1.43176i
$394$	3636.57	−	6298.73i	0.464995	−	0.805395i
$395$		0			0
$396$	−3140.71	−	2645.33i	−0.398552	−	0.335688i
$397$	−9871.38			−1.24794			−0.623968	−	0.781450i	$-0.714480\pi$
$397$	−9871.38			−1.24794			−0.623968	+	0.781450i	$0.714480\pi$
$398$	820.139	−	1420.52i	0.103291	−	0.178905i
$399$	−1000.48	+	837.917i	−0.125530	+	0.105134i
$400$		0			0
$401$	950.974	+	1647.14i	0.118427	+	0.205122i	0.919145	−	0.393920i	$-0.128881\pi$
$401$	950.974	+	1647.14i	0.118427	+	0.205122i	−0.800717	+	0.599042i	$0.795548\pi$
$402$	6704.75	+	2447.38i	0.831847	+	0.303643i
$403$	4016.77	−	6957.25i	0.496500	−	0.859963i
$404$	−6694.76			−0.824447
$405$		0			0
$406$	−2606.43			−0.318609
$407$	4909.03	−	8502.70i	0.597867	−	1.03554i
$408$	−3832.51	−	1398.95i	−0.465043	−	0.169751i
$409$	−2105.94	−	3647.59i	−0.254601	−	0.440982i	0.710186	−	0.704014i	$-0.248611\pi$
$409$	−2105.94	−	3647.59i	−0.254601	−	0.440982i	−0.964787	+	0.263032i	$0.915278\pi$
$410$		0			0
$411$	−4198.27	+	3516.13i	−0.503858	+	0.421990i
$412$	326.741	−	565.932i	0.0390713	−	0.0676735i
$413$	−290.168			−0.0345719
$414$	2713.41	+	2285.42i	0.322118	+	0.271310i
$415$		0			0
$416$	2171.52	−	3761.19i	0.255932	−	0.443287i
$417$	436.753	+	2490.47i	0.0512899	+	0.292468i
$418$	−575.144	−	996.179i	−0.0672996	−	0.116566i
$419$	8364.24	+	14487.3i	0.975226	+	1.68914i	0.679188	+	0.733965i	$0.262332\pi$
$419$	8364.24	+	14487.3i	0.975226	+	1.68914i	0.296038	+	0.955176i	$0.404334\pi$
$420$		0			0
$421$	−6570.41	+	11380.3i	−0.760623	+	1.31744i	0.181907	+	0.983316i	$0.441773\pi$
$421$	−6570.41	+	11380.3i	−0.760623	+	1.31744i	−0.942530	+	0.334122i	$0.891560\pi$
$422$	1599.98			0.184563
$423$	−2848.19	+	1030.67i	−0.327385	+	0.118470i
$424$	15409.7			1.76500
$425$		0			0
$426$	−2238.41	+	1874.71i	−0.254580	+	0.213216i
$427$	−4360.68	−	7552.91i	−0.494210	−	0.855998i
$428$	3530.26	+	6114.59i	0.398695	+	0.690560i
$429$	3335.91	+	1217.68i	0.375429	+	0.137040i
$430$		0			0
$431$	−5801.99			−0.648426			−0.324213	−	0.945984i	$-0.605100\pi$
$431$	−5801.99			−0.648426			−0.324213	+	0.945984i	$0.605100\pi$
$432$	728.453	+	2.02935i	0.0811290	+	0.000226012i
$433$	−9599.49			−1.06541			−0.532705	−	0.846301i	$-0.678824\pi$
$433$	−9599.49			−1.06541			−0.532705	+	0.846301i	$0.678824\pi$
$434$	3005.89	−	5206.36i	0.332460	−	0.575837i
$435$		0			0
$436$	−2990.52	−	5179.74i	−0.328486	−	0.568955i
$437$	−938.162	−	1624.94i	−0.102696	−	0.177876i
$438$	4757.49	−	3984.49i	0.519000	−	0.434672i
$439$	−7018.70	+	12156.7i	−0.763062	+	1.32166i	0.178202	+	0.983994i	$0.442972\pi$
$439$	−7018.70	+	12156.7i	−0.763062	+	1.32166i	−0.941265	+	0.337669i	$0.890362\pi$
$440$		0			0
$441$	−1096.04	+	6149.14i	−0.118350	+	0.663982i
$442$	1394.79			0.150098
$443$	3565.25	−	6175.19i	0.382370	−	0.662285i	−0.609030	−	0.793147i	$-0.708441\pi$
$443$	3565.25	−	6175.19i	0.382370	−	0.662285i	0.991401	+	0.130862i	$0.0417745\pi$
$444$	1584.87	+	9037.32i	0.169402	+	0.965974i
$445$		0			0
$446$	−3989.21	−	6909.51i	−0.423530	−	0.733575i
$447$	−2914.04	−	16616.6i	−0.308343	−	1.75825i
$448$	1405.56	−	2434.50i	0.148229	−	0.256740i
$449$	15299.1			1.60804			0.804019	−	0.594604i	$-0.202691\pi$
$449$	15299.1			1.60804			0.804019	+	0.594604i	$0.202691\pi$
$450$		0			0
$451$	10295.5			1.07494
$452$	−1723.36	+	2984.95i	−0.179337	+	0.310620i
$453$	−6093.88	+	5103.74i	−0.632043	+	0.529347i
$454$	3521.62	+	6099.63i	0.364048	+	0.630550i
$455$		0			0
$456$	2554.45	+	932.430i	0.262331	+	0.0957566i
$457$	960.083	−	1662.91i	0.0982731	−	0.170214i	−0.812697	−	0.582687i	$-0.802001\pi$
$457$	960.083	−	1662.91i	0.0982731	−	0.170214i	0.910970	+	0.412473i	$0.135335\pi$
$458$	−2667.44			−0.272143
$459$	2489.28	+	4339.44i	0.253137	+	0.441280i
$460$		0			0
$461$	−3344.76	+	5793.30i	−0.337920	+	0.585295i	−0.984041	−	0.177940i	$-0.943057\pi$
$461$	−3344.76	+	5793.30i	−0.337920	+	0.585295i	0.646121	+	0.763235i	$0.276390\pi$
$462$	2496.38	+	911.234i	0.251390	+	0.0917629i
$463$	−7723.08	−	13376.8i	−0.775209	−	1.34270i	−0.934677	−	0.355498i	$-0.884311\pi$
$463$	−7723.08	−	13376.8i	−0.775209	−	1.34270i	0.159468	−	0.987203i	$-0.449022\pi$
$464$	−384.746	−	666.399i	−0.0384943	−	0.0666741i
$465$		0			0
$466$	5071.95	−	8784.88i	0.504192	−	0.873287i
$467$	6054.68			0.599951			0.299976	−	0.953947i	$-0.403021\pi$
$467$	6054.68			0.599951			0.299976	+	0.953947i	$0.403021\pi$
$468$	−3120.65	+	1129.26i	−0.308231	+	0.111539i
$469$	8721.22			0.858654
$470$		0			0
$471$	−656.605	−	3744.12i	−0.0642351	−	0.366284i
$472$	302.317	+	523.628i	0.0294815	+	0.0510634i
$473$	−283.913	−	491.751i	−0.0275990	−	0.0478029i
$474$	−463.359	−	2642.18i	−0.0449004	−	0.256033i
$475$		0			0
$476$	−1970.69			−0.189761
$477$	−14452.1	−	12172.6i	−1.38725	−	1.16844i
$478$	−6455.05			−0.617672
$479$	−1528.14	+	2646.81i	−0.145767	+	0.252476i	−0.929659	−	0.368421i	$-0.879898\pi$
$479$	−1528.14	+	2646.81i	−0.145767	+	0.252476i	0.783892	+	0.620897i	$0.213232\pi$
$480$		0			0
$481$	−3967.44	−	6871.81i	−0.376091	−	0.651409i
$482$	−5414.76	−	9378.64i	−0.511692	−	0.886276i
$483$	4072.04	+	1486.38i	0.383611	+	0.140026i
$484$	−1269.24	+	2198.39i	−0.119200	+	0.206460i
$485$		0			0
$486$	4810.67	+	4074.85i	0.449005	+	0.380327i
$487$	−2335.83			−0.217344			−0.108672	−	0.994078i	$-0.534660\pi$
$487$	−2335.83			−0.217344			−0.108672	+	0.994078i	$0.534660\pi$
$488$	−9086.51	+	15738.3i	−0.842883	+	1.45992i
$489$	648.374	+	236.671i	0.0599601	+	0.0218868i
$490$		0			0
$491$	−2748.50	−	4760.54i	−0.252624	−	0.437557i	0.711624	−	0.702561i	$-0.247960\pi$
$491$	−2748.50	−	4760.54i	−0.252624	−	0.437557i	−0.964247	+	0.265004i	$0.914627\pi$
$492$	−7376.19	+	6177.70i	−0.675903	+	0.566082i
$493$	2642.27	−	4576.55i	0.241383	−	0.418088i
$494$	−929.654			−0.0846703
$495$		0			0
$496$	1774.84			0.160671
$497$	−1783.82	+	3089.66i	−0.160996	+	0.278854i
$498$	824.801	+	4703.22i	0.0742173	+	0.423205i
$499$	−8741.68	−	15141.0i	−0.784231	−	1.35833i	−0.929457	−	0.368930i	$-0.879724\pi$
$499$	−8741.68	−	15141.0i	−0.784231	−	1.35833i	0.145226	−	0.989399i	$-0.453609\pi$
$500$		0			0
$501$	−1227.98	−	7002.24i	−0.109505	−	0.624425i
$502$	−6421.41	+	11122.2i	−0.570920	+	0.988862i
$503$	−6699.56			−0.593874			−0.296937	−	0.954897i	$-0.595965\pi$
$503$	−6699.56			−0.593874			−0.296937	+	0.954897i	$0.595965\pi$
$504$	−5907.47	+	2137.73i	−0.522102	+	0.188932i
$505$		0			0
$506$	−1910.45	+	3308.99i	−0.167845	+	0.290717i
$507$	−6551.63	+	5487.11i	−0.573902	+	0.480653i
$508$	−4089.95	−	7083.99i	−0.357209	−	0.618703i
$509$	−1316.44	−	2280.13i	−0.114637	−	0.198556i	0.802998	−	0.595982i	$-0.203237\pi$
$509$	−1316.44	−	2280.13i	−0.114637	−	0.198556i	−0.917634	+	0.397426i	$0.869904\pi$
$510$		0			0
$511$	3791.31	−	6566.75i	0.328215	−	0.568485i
$512$	1874.14			0.161770
$513$	−1659.16	−	2892.33i	−0.142795	−	0.248927i
$514$	−4223.68			−0.362448
$515$		0			0
$516$	498.477	+	181.955i	0.0425276	+	0.0155235i
$517$	−1631.12	−	2825.18i	−0.138756	−	0.240332i
$518$	−2968.98	−	5142.42i	−0.251833	−	0.436187i
$519$	−8434.82	+	7064.32i	−0.713386	+	0.597474i
$520$		0			0
$521$	−18292.5			−1.53821			−0.769105	−	0.639122i	$-0.779298\pi$
$521$	−18292.5			−1.53821			−0.769105	+	0.639122i	$0.779298\pi$
$522$	1168.62	−	6556.33i	0.0979866	−	0.549737i
$523$	16446.5			1.37506			0.687530	−	0.726156i	$-0.258695\pi$
$523$	16446.5			1.37506			0.687530	+	0.726156i	$0.258695\pi$
$524$	5699.34	−	9871.55i	0.475147	−	0.822979i
$525$		0			0
$526$	5159.74	+	8936.93i	0.427710	+	0.740815i
$527$	6094.44	+	10555.9i	0.503754	+	0.872527i
$528$	135.521	+	772.772i	0.0111700	+	0.0636943i
$529$	2967.22	−	5139.38i	0.243875	−	0.422404i
$530$		0			0
$531$	130.099	−	729.899i	0.0106324	−	0.0596515i
$532$	1313.50			0.107044
$533$	4160.38	−	7206.00i	0.338098	−	0.585603i
$534$	−7195.79	+	6026.61i	−0.583132	+	0.488383i
$535$		0			0
$536$	−9086.37	−	15738.1i	−0.732223	−	1.26825i
$537$	−10859.3	−	3963.87i	−0.872647	−	0.318535i
$538$	−1445.52	+	2503.71i	−0.115838	+	0.200637i
$539$	−6727.15			−0.537586
$540$		0			0
$541$	13884.4			1.10340			0.551698	−	0.834044i	$-0.313980\pi$
$541$	13884.4			1.10340			0.551698	+	0.834044i	$0.313980\pi$
$542$	2088.96	−	3618.19i	0.165551	−	0.286742i
$543$	3529.38	+	1288.30i	0.278932	+	0.101816i
$544$	3294.75	+	5706.67i	0.259671	+	0.449763i
$545$		0			0
$546$	1646.56	−	1379.03i	0.129059	−	0.108090i
$547$	−3391.55	+	5874.33i	−0.265104	+	0.459174i	−0.967591	−	0.252523i	$-0.918740\pi$
$547$	−3391.55	+	5874.33i	−0.265104	+	0.459174i	0.702487	+	0.711697i	$0.252073\pi$
$548$	5511.83			0.429660
$549$	20954.1	−	7582.61i	1.62896	−	0.589468i
$550$		0			0
$551$	−1761.13	+	3050.36i	−0.136164	+	0.235844i
$552$	−1560.25	−	8896.89i	−0.120305	−	0.686009i
$553$	−1638.87	−	2838.61i	−0.126025	−	0.218282i
$554$	−815.074	−	1411.75i	−0.0625075	−	0.108266i
$555$		0			0
$556$	1272.47	−	2203.98i	0.0970586	−	0.168110i
$557$	8088.38			0.615288			0.307644	−	0.951501i	$-0.400459\pi$
$557$	8088.38			0.615288			0.307644	+	0.951501i	$0.400459\pi$
$558$	11748.6	+	9895.46i	0.891320	+	0.750732i
$559$	−458.912			−0.0347226
$560$		0			0
$561$	−4130.71	+	3459.55i	−0.310871	+	0.260360i
$562$	1400.46	+	2425.68i	0.105116	+	0.182066i
$563$	−83.7997	−	145.145i	−0.00627307	−	0.0108653i	0.862872	−	0.505423i	$-0.168663\pi$
$563$	−83.7997	−	145.145i	−0.00627307	−	0.0108653i	−0.869145	+	0.494558i	$0.835330\pi$
$564$	2863.82	+	1045.36i	0.213810	+	0.0780453i
$565$		0			0
$566$	−4024.93			−0.298905
$567$	7229.04	+	2661.61i	0.535434	+	0.197138i
$568$	7434.02			0.549163
$569$	−3653.15	+	6327.45i	−0.269153	+	0.466187i	−0.968643	−	0.248455i	$-0.920077\pi$
$569$	−3653.15	+	6327.45i	−0.269153	+	0.466187i	0.699490	+	0.714642i	$0.253410\pi$
$570$		0			0
$571$	−11611.2	−	20111.1i	−0.850985	−	1.47395i	−0.880320	−	0.474380i	$-0.842672\pi$
$571$	−11611.2	−	20111.1i	−0.850985	−	1.47395i	0.0293354	−	0.999570i	$-0.490661\pi$
$572$	−1787.16	−	3095.44i	−0.130638	−	0.226271i
$573$	−1001.32	+	838.621i	−0.0730028	+	0.0611412i
$574$	3113.36	−	5392.51i	0.226393	−	0.392123i
$575$		0			0
$576$	5493.65	+	4627.13i	0.397399	+	0.334717i
$577$	−5447.52			−0.393038			−0.196519	−	0.980500i	$-0.562964\pi$
$577$	−5447.52			−0.393038			−0.196519	+	0.980500i	$0.562964\pi$
$578$	3030.34	−	5248.70i	0.218072	−	0.377711i
$579$	341.759	+	1948.79i	0.0245303	+	0.139878i
$580$		0			0
$581$	2917.27	+	5052.85i	0.208311	+	0.360805i
$582$	1744.54	+	9947.78i	0.124250	+	0.708503i
$583$	10175.4	−	17624.3i	0.722850	−	1.25201i
$584$	−15800.2			−1.11955
$585$		0			0
$586$	−2994.62			−0.211104
$587$	6436.20	−	11147.8i	0.452556	−	0.783850i	−0.545988	−	0.837793i	$-0.683846\pi$
$587$	6436.20	−	11147.8i	0.452556	−	0.783850i	0.998544	+	0.0539429i	$0.0171789\pi$
$588$	4819.64	−	4036.54i	0.338025	−	0.283102i
$589$	−4062.07	−	7035.72i	−0.284168	−	0.492193i
$590$		0			0
$591$	21330.5	+	7786.10i	1.48463	+	0.541924i
$592$	876.525	−	1518.19i	0.0608529	−	0.105400i
$593$	−16563.3			−1.14700			−0.573501	−	0.819205i	$-0.694415\pi$
$593$	−16563.3			−1.14700			−0.573501	+	0.819205i	$0.694415\pi$
$594$	−3411.43	+	5870.94i	−0.235644	+	0.405535i
$595$		0			0
$596$	−8489.96	+	14705.0i	−0.583494	+	1.01064i
$597$	4810.56	+	1755.96i	0.329787	+	0.120380i
$598$	1544.01	+	2674.30i	0.105584	+	0.182877i
$599$	−7881.18	−	13650.6i	−0.537590	−	0.931133i	−0.999033	−	0.0439629i	$-0.986002\pi$
$599$	−7881.18	−	13650.6i	−0.537590	−	0.931133i	0.461444	−	0.887170i	$-0.347332\pi$
$600$		0			0
$601$	6317.51	−	10942.3i	0.428780	−	0.742668i	−0.567985	−	0.823039i	$-0.692277\pi$
$601$	6317.51	−	10942.3i	0.428780	−	0.742668i	0.996765	+	0.0803703i	$0.0256103\pi$
$602$	−343.420			−0.0232504
$603$	−3910.24	+	21937.7i	−0.264075	+	1.48155i
$604$	8000.53			0.538968
$605$		0			0
$606$	1912.22	+	10903.9i	0.128182	+	0.730927i
$607$	9672.84	+	16753.8i	0.646801	+	1.12029i	0.983882	+	0.178817i	$0.0572271\pi$
$607$	9672.84	+	16753.8i	0.646801	+	1.12029i	−0.337081	+	0.941476i	$0.609440\pi$
$608$	−2196.02	−	3803.61i	−0.146481	−	0.253712i
$609$	−1405.60	−	8015.09i	−0.0935270	−	0.533313i
$610$		0			0
$611$	−2636.52			−0.174570
$612$	883.576	−	4957.15i	0.0583602	−	0.327420i
$613$	4801.16			0.316341			0.158170	−	0.987412i	$-0.449440\pi$
$613$	4801.16			0.316341			0.158170	+	0.987412i	$0.449440\pi$
$614$	−6135.33	+	10626.7i	−0.403260	+	0.698467i
$615$		0			0
$616$	−3383.13	−	5859.75i	−0.221283	−	0.383273i
$617$	11018.4	+	19084.5i	0.718939	+	1.24524i	0.961420	+	0.275083i	$0.0887055\pi$
$617$	11018.4	+	19084.5i	0.718939	+	1.24524i	−0.242481	+	0.970156i	$0.577961\pi$
$618$	−1015.08	−	370.525i	−0.0660717	−	0.0241176i
$619$	727.050	−	1259.29i	0.0472094	−	0.0817690i	−0.841455	−	0.540327i	$-0.818301\pi$
$619$	727.050	−	1259.29i	0.0472094	−	0.0817690i	0.888664	+	0.458558i	$0.151634\pi$
$620$		0			0
$621$	−5564.64	+	9576.54i	−0.359584	+	0.618829i
$622$	−9500.12			−0.612412
$623$	−5734.43	+	9932.32i	−0.368772	+	0.638732i
$624$	595.638	+	217.421i	0.0382125	+	0.0139484i
$625$		0			0
$626$	591.131	+	1023.87i	0.0377418	+	0.0653707i
$627$	2753.20	−	2305.86i	0.175363	−	0.146869i
$628$	−1913.00	+	3313.41i	−0.121555	+	0.210540i
$629$	12039.2			0.763171
$630$		0			0
$631$	2680.50			0.169111			0.0845554	−	0.996419i	$-0.473053\pi$
$631$	2680.50			0.169111			0.0845554	+	0.996419i	$0.473053\pi$
$632$	−3414.98	+	5914.91i	−0.214937	+	0.372283i
$633$	862.840	+	4920.12i	0.0541782	+	0.308937i
$634$	−6905.90	−	11961.4i	−0.432600	−	0.749285i
$635$		0			0
$636$	3285.11	+	18732.5i	0.204816	+	1.16791i
$637$	−2718.42	+	4708.43i	−0.169086	+	0.292865i
$638$	7172.63			0.445089
$639$	−6972.08	−	5872.37i	−0.431629	−	0.363548i
$640$		0			0
$641$	11176.6	−	19358.5i	0.688690	−	1.19285i	−0.283572	−	0.958951i	$-0.591519\pi$
$641$	11176.6	−	19358.5i	0.688690	−	1.19285i	0.972262	−	0.233895i	$-0.0751472\pi$
$642$	8950.64	−	7496.33i	0.550240	−	0.460836i
$643$	6558.35	+	11359.4i	0.402233	+	0.696688i	0.993995	−	0.109424i	$-0.0349008\pi$
$643$	6558.35	+	11359.4i	0.402233	+	0.696688i	−0.591762	+	0.806113i	$0.701567\pi$
$644$	−2181.52	−	3778.51i	−0.133485	−	0.231202i
$645$		0			0
$646$	705.259	−	1221.54i	0.0429536	−	0.0743979i
$647$	21272.7			1.29261			0.646303	−	0.763081i	$-0.276314\pi$
$647$	21272.7			1.29261			0.646303	+	0.763081i	$0.276314\pi$
$648$	−2728.66	−	15818.4i	−0.165420	−	0.958957i
$649$	798.510			0.0482962
$650$		0			0
$651$	17631.2	+	6435.77i	1.06148	+	0.387462i
$652$	−347.355	−	601.637i	−0.0208642	−	0.0361379i
$653$	−6489.93	−	11240.9i	−0.388929	−	0.673644i	0.603377	−	0.797456i	$-0.293821\pi$
$653$	−6489.93	−	11240.9i	−0.388929	−	0.673644i	−0.992306	+	0.123812i	$0.960488\pi$
$654$	−7582.19	+	6350.22i	−0.453344	+	0.379684i
$655$		0			0
$656$	1838.30			0.109411
$657$	14818.4	+	12481.1i	0.879941	+	0.741147i
$658$	−1973.00			−0.116893
$659$	−14864.1	+	25745.4i	−0.878640	+	1.52185i	−0.0258068	+	0.999667i	$0.508215\pi$
$659$	−14864.1	+	25745.4i	−0.878640	+	1.52185i	−0.852834	+	0.522183i	$0.825118\pi$
$660$		0			0
$661$	3469.44	+	6009.24i	0.204153	+	0.353604i	0.949863	−	0.312667i	$-0.101223\pi$
$661$	3469.44	+	6009.24i	0.204153	+	0.353604i	−0.745709	+	0.666272i	$0.767889\pi$
$662$	−3609.88	−	6252.50i	−0.211937	−	0.367085i
$663$	752.184	+	4289.13i	0.0440609	+	0.251246i
$664$	6078.82	−	10528.8i	0.355277	−	0.615358i
$665$		0			0
$666$	14266.6	−	5162.64i	0.830061	−	0.300373i
$667$	11699.8			0.679188
$668$	−3577.68	+	6196.73i	−0.207223	+	0.358920i
$669$	19096.2	−	15993.5i	1.10359	−	0.924279i
$670$		0			0
$671$	12000.1	+	20784.8i	0.690401	+	1.19581i
$672$	9531.68	+	3479.27i	0.547161	+	0.199726i
$673$	−6886.81	+	11928.3i	−0.394453	+	0.683213i	−0.993031	−	0.117851i	$-0.962399\pi$
$673$	−6886.81	+	11928.3i	−0.394453	+	0.683213i	0.598578	+	0.801065i	$0.295733\pi$
$674$	8446.19			0.482693
$675$		0			0
$676$	8601.51			0.489389
$677$	−6080.24	+	10531.3i	−0.345174	+	0.597859i	−0.985385	−	0.170340i	$-0.945513\pi$
$677$	−6080.24	+	10531.3i	−0.345174	+	0.597859i	0.640211	+	0.768199i	$0.278847\pi$
$678$	5353.91	+	1954.30i	0.303268	+	0.110700i
$679$	6170.31	+	10687.3i	0.348741	+	0.604037i
$680$		0			0
$681$	−16857.9	+	14118.8i	−0.948600	+	0.794470i
$682$	−8271.89	+	14327.3i	−0.464439	+	0.804431i
$683$	−7397.68			−0.414443			−0.207221	−	0.978294i	$-0.566442\pi$
$683$	−7397.68			−0.414443			−0.207221	+	0.978294i	$0.566442\pi$
$684$	−588.921	+	3304.04i	−0.0329210	+	0.184698i
$685$		0			0
$686$	−5050.52	+	8747.76i	−0.281093	+	0.486867i
$687$	−1438.51	−	8202.70i	−0.0798870	−	0.455535i
$688$	−50.6936	−	87.8039i	−0.00280912	−	0.00486554i
$689$	−8223.67	−	14243.8i	−0.454712	−	0.787585i
$690$		0			0
$691$	11338.7	−	19639.3i	0.624235	−	1.08121i	−0.364453	−	0.931222i	$-0.618744\pi$
$691$	11338.7	−	19639.3i	0.624235	−	1.08121i	0.988688	−	0.149985i	$-0.0479225\pi$
$692$	11073.9			0.608333
$693$	−1455.90	+	8168.08i	−0.0798052	+	0.447734i
$694$	−7547.84			−0.412842
$695$		0			0
$696$	−12999.3	+	10887.2i	−0.707958	+	0.592928i
$697$	6312.34	+	10933.3i	0.343037	+	0.594158i
$698$	−1734.02	−	3003.41i	−0.0940310	−	0.162866i
$699$	29749.7	+	10859.3i	1.60978	+	0.587607i
$700$		0			0
$701$	−18577.8			−1.00096			−0.500479	−	0.865748i	$-0.666843\pi$
$701$	−18577.8			−1.00096			−0.500479	+	0.865748i	$0.666843\pi$
$702$	2730.61	+	4760.13i	0.146810	+	0.255925i
$703$	−8024.38			−0.430505
$704$	−3867.95	+	6699.48i	−0.207072	+	0.358660i
$705$		0			0
$706$	7010.03	+	12141.7i	0.373691	+	0.647252i
$707$	6763.39	+	11714.5i	0.359778	+	0.623154i
$708$	−572.089	+	479.135i	−0.0303678	+	0.0254336i
$709$	−4891.93	+	8473.07i	−0.259126	+	0.448819i	−0.966008	−	0.258512i	$-0.916768\pi$
$709$	−4891.93	+	8473.07i	−0.259126	+	0.448819i	0.706882	+	0.707331i	$0.250101\pi$
$710$		0			0
$711$	7875.15	−	2849.77i	0.415388	−	0.150316i
$712$	23898.1			1.25789
$713$	−13492.9	+	23370.4i	−0.708715	+	1.22753i
$714$	562.886	+	3209.71i	0.0295035	+	0.168236i
$715$		0			0
$716$	5817.66	+	10076.5i	0.303654	+	0.525944i
$717$	−3481.10	−	19850.0i	−0.181316	−	1.03391i
$718$	7727.68	−	13384.7i	0.401663	−	0.695701i
$719$	−15405.6			−0.799073			−0.399537	−	0.916717i	$-0.630829\pi$
$719$	−15405.6			−0.799073			−0.399537	+	0.916717i	$0.630829\pi$
$720$		0			0
$721$	−1320.36			−0.0682009
$722$	5237.79	−	9072.12i	0.269987	−	0.467631i
$723$	25920.3	−	21708.7i	1.33332	−	1.11668i
$724$	−1890.80	−	3274.97i	−0.0970597	−	0.168112i
$725$		0			0
$726$	3943.11	+	1439.32i	0.201574	+	0.0735788i
$727$	7374.44	−	12772.9i	0.376207	−	0.651610i	−0.614300	−	0.789073i	$-0.710561\pi$
$727$	7374.44	−	12772.9i	0.376207	−	0.651610i	0.990507	+	0.137463i	$0.0438947\pi$
$728$	−5468.44			−0.278398
$729$	−9936.32	+	16990.9i	−0.504817	+	0.863226i
$730$		0			0
$731$	348.142	−	603.000i	0.0176149	−	0.0305099i
$732$	−21069.1	−	7690.68i	−1.06385	−	0.388327i
$733$	11399.6	+	19744.7i	0.574425	+	0.994933i	0.996104	+	0.0881879i	$0.0281076\pi$
$733$	11399.6	+	19744.7i	0.574425	+	0.994933i	−0.421679	+	0.906745i	$0.638559\pi$
$734$	126.878	+	219.759i	0.00638030	+	0.0110510i
$735$		0			0
$736$	−7294.47	+	12634.4i	−0.365323	+	0.632758i
$737$	−23999.9			−1.19952
$738$	12168.6	+	10249.3i	0.606956	+	0.511220i
$739$	−23076.7			−1.14870			−0.574350	−	0.818610i	$-0.694745\pi$
$739$	−23076.7			−1.14870			−0.574350	+	0.818610i	$0.694745\pi$
$740$		0			0
$741$	−501.346	−	2858.80i	−0.0248548	−	0.141728i
$742$	−6154.07	−	10659.2i	−0.304478	−	0.527372i
$743$	3949.16	+	6840.14i	0.194994	+	0.337740i	0.946899	−	0.321532i	$-0.104198\pi$
$743$	3949.16	+	6840.14i	0.194994	+	0.337740i	−0.751905	+	0.659272i	$0.770865\pi$
$744$	−6755.58	−	38522.0i	−0.332892	−	1.89823i
$745$		0			0
$746$	−11365.7			−0.557811
$747$	−14018.1	+	5072.72i	−0.686609	+	0.248462i
$748$	5423.12			0.265092
$749$	7132.89	−	12354.5i	0.347971	−	0.602704i
$750$		0			0
$751$	−1487.18	−	2575.86i	−0.0722607	−	0.125159i	0.827631	−	0.561273i	$-0.189688\pi$
$751$	−1487.18	−	2575.86i	−0.0722607	−	0.125159i	−0.899892	+	0.436113i	$0.856355\pi$
$752$	−291.242	−	504.446i	−0.0141230	−	0.0244618i
$753$	−37665.1	−	13748.6i	−1.82283	−	0.665374i
$754$	2898.43	−	5020.23i	0.139993	−	0.242475i
$755$		0			0
$756$	−3858.07	−	6725.57i	−0.185604	−	0.323554i
$757$	−24466.0			−1.17468			−0.587340	−	0.809340i	$-0.699825\pi$
$757$	−24466.0			−1.17468			−0.587340	+	0.809340i	$0.699825\pi$
$758$	5794.58	−	10036.5i	0.277663	−	0.480927i
$759$	−11205.8	−	4090.37i	−0.535896	−	0.195614i
$760$		0			0
$761$	−8145.43	−	14108.3i	−0.388005	−	0.672044i	0.604176	−	0.796851i	$-0.293502\pi$
$761$	−8145.43	−	14108.3i	−0.388005	−	0.672044i	−0.992181	+	0.124807i	$0.960169\pi$
$762$	−10369.7	+	8684.79i	−0.492984	+	0.412883i
$763$	−6042.35	+	10465.7i	−0.286694	+	0.496569i
$764$	1314.61			0.0622524
$765$		0			0
$766$	−612.235			−0.0288785
$767$	322.675	−	558.889i	0.0151905	−	0.0263107i
$768$	−3457.18	−	19713.7i	−0.162435	−	0.926245i
$769$	12453.0	+	21569.2i	0.583962	+	1.01145i	0.995004	+	0.0998355i	$0.0318317\pi$
$769$	12453.0	+	21569.2i	0.583962	+	1.01145i	−0.411042	+	0.911616i	$0.634835\pi$
$770$		0			0
$771$	−2277.76	−	12988.3i	−0.106396	−	0.606696i
$772$	995.705	−	1724.61i	0.0464200	−	0.0804017i
$773$	21955.7			1.02160			0.510798	−	0.859701i	$-0.329350\pi$
$773$	21955.7			1.02160			0.510798	+	0.859701i	$0.329350\pi$
$774$	153.976	−	863.854i	0.00715056	−	0.0401170i
$775$		0			0
$776$	12857.3	−	22269.5i	0.594782	−	1.03019i
$777$	14212.4	−	11903.2i	0.656201	−	0.549581i
$778$	4602.16	+	7971.18i	0.212076	+	0.367327i
$779$	−4207.31	−	7287.27i	−0.193508	−	0.335165i
$780$		0			0
$781$	4908.88	−	8502.42i	0.224908	−	0.389553i
$782$	−4685.29			−0.214253
$783$	20791.7	+	57.9223i	0.948959	+	0.00264365i
$784$	−1201.16			−0.0547174
$785$		0			0
$786$	−17706.0	−	6463.07i	−0.803499	−	0.293295i
$787$	1691.08	+	2929.04i	0.0765955	+	0.132667i	0.901779	−	0.432197i	$-0.142262\pi$
$787$	1691.08	+	2929.04i	0.0765955	+	0.132667i	−0.825183	+	0.564865i	$0.808928\pi$
$788$	−11427.4	−	19792.9i	−0.516606	−	0.894788i
$789$	−24699.5	+	20686.3i	−1.11448	+	0.933400i
$790$		0			0
$791$	6964.12			0.313041
$792$	16256.7	−	5882.80i	0.729366	−	0.263934i
$793$	19396.8			0.868600
$794$	8214.68	−	14228.2i	0.367164	−	0.635946i
$795$		0			0
$796$	−2577.17	−	4463.79i	−0.114756	−	0.198763i
$797$	−9008.39	−	15603.0i	−0.400368	−	0.693458i	0.593402	−	0.804906i	$-0.297784\pi$
$797$	−9008.39	−	15603.0i	−0.400368	−	0.693458i	−0.993770	+	0.111448i	$0.964451\pi$
$798$	−375.175	−	2139.34i	−0.0166429	−	0.0949020i
$799$	2000.13	−	3464.32i	0.0885600	−	0.153390i
$800$		0			0
$801$	−22413.1	−	18877.9i	−0.988673	−	0.832729i
$802$	−3165.49			−0.139373
$803$	−10433.3	+	18071.0i	−0.458509	+	0.794161i
$804$	17194.6	−	14400.8i	0.754237	−	0.631688i
$805$		0			0
$806$	6685.28	+	11579.2i	0.292157	+	0.506031i
$807$	−8478.74	−	3094.93i	−0.369846	−	0.135002i
$808$	14093.1	−	24410.0i	0.613607	−	1.06280i
$809$	18030.0			0.783559			0.391780	−	0.920059i	$-0.371860\pi$
$809$	18030.0			0.783559			0.391780	+	0.920059i	$0.371860\pi$
$810$		0			0
$811$	−35444.8			−1.53469			−0.767347	−	0.641233i	$-0.778423\pi$
$811$	−35444.8			−1.53469			−0.767347	+	0.641233i	$0.778423\pi$
$812$	−4095.18	+	7093.06i	−0.176986	+	0.306549i
$813$	12252.9	+	4472.58i	0.528570	+	0.192940i
$814$	8170.31	+	14151.4i	0.351805	+	0.609344i
$815$		0			0
$816$	−737.552	+	617.713i	−0.0316415	+	0.0265004i
$817$	−232.044	+	401.912i	−0.00993659	+	0.0172107i
$818$	7010.00			0.299632
$819$	5128.63	+	4319.69i	0.218814	+	0.184301i
$820$		0			0
$821$	11304.9	−	19580.6i	0.480563	−	0.832360i	−0.519188	−	0.854660i	$-0.673766\pi$
$821$	11304.9	−	19580.6i	0.480563	−	0.832360i	0.999751	+	0.0222999i	$0.00709887\pi$
$822$	−1574.34	−	8977.25i	−0.0668021	−	0.380922i
$823$	−16926.0	−	29316.8i	−0.716895	−	1.24170i	−0.962224	−	0.272259i	$-0.912229\pi$
$823$	−16926.0	−	29316.8i	−0.716895	−	1.24170i	0.245329	−	0.969440i	$-0.421104\pi$
$824$	1375.64	+	2382.69i	0.0581588	+	0.100734i
$825$		0			0
$826$	241.469	−	418.237i	0.0101716	−	0.0176178i
$827$	−29173.2			−1.22667			−0.613333	−	0.789824i	$-0.710172\pi$
$827$	−29173.2			−1.22667			−0.613333	+	0.789824i	$0.710172\pi$
$828$	10482.7	−	3793.37i	0.439976	−	0.159213i
$829$	20552.8			0.861073			0.430537	−	0.902573i	$-0.358324\pi$
$829$	20552.8			0.861073			0.430537	+	0.902573i	$0.358324\pi$
$830$		0			0
$831$	3901.74	−	3267.78i	0.162876	−	0.136412i
$832$	3126.04	+	5414.47i	0.130260	+	0.225616i
$833$	−4124.52	−	7143.87i	−0.171556	−	0.297143i
$834$	−3953.13	−	1442.98i	−0.164131	−	0.0599116i
$835$		0			0
$836$	−3614.62			−0.149539
$837$	−24093.9	+	41464.7i	−0.994991	+	1.71234i
$838$	−27841.9			−1.14771
$839$	−6923.52	+	11991.9i	−0.284895	+	0.493452i	−0.972584	−	0.232553i	$-0.925292\pi$
$839$	−6923.52	+	11991.9i	−0.284895	+	0.493452i	0.687689	+	0.726005i	$0.258625\pi$
$840$		0			0
$841$	1212.98	+	2100.95i	0.0497348	+	0.0861432i
$842$	−10935.4	−	18940.7i	−0.447576	−	0.775225i
$843$	−6703.99	+	5614.72i	−0.273900	+	0.229396i
$844$	2513.86	−	4354.13i	0.102524	−	0.177577i
$845$		0			0
$846$	884.612	−	4962.97i	0.0359499	−	0.201691i
$847$	5129.01			0.208069
$848$	1816.85	−	3146.88i	0.0735742	−	0.127434i
$849$	−2170.57	−	12377.1i	−0.0877430	−	0.500332i
$850$		0			0
$851$	13327.2	+	23083.4i	0.536840	+	0.929835i
$852$	1584.82	+	9037.03i	0.0637266	+	0.363384i
$853$	−18976.1	+	32867.6i	−0.761701	+	1.31930i	0.180272	+	0.983617i	$0.442302\pi$
$853$	−18976.1	+	32867.6i	−0.761701	+	1.31930i	−0.941973	+	0.335688i	$0.891031\pi$
$854$	14515.3			0.581620
$855$		0			0
$856$	−29726.2			−1.18694
$857$	2960.12	−	5127.08i	0.117988	−	0.204361i	−0.800982	−	0.598688i	$-0.795689\pi$
$857$	2960.12	−	5127.08i	0.117988	−	0.204361i	0.918970	+	0.394327i	$0.129022\pi$
$858$	−4531.17	+	3794.94i	−0.180293	+	0.150999i
$859$	10240.2	+	17736.5i	0.406740	+	0.704494i	0.994522	−	0.104525i	$-0.0333322\pi$
$859$	10240.2	+	17736.5i	0.406740	+	0.704494i	−0.587782	+	0.809019i	$0.699999\pi$
$860$		0			0
$861$	18261.6	+	6665.88i	0.722825	+	0.263847i
$862$	4828.24	−	8362.76i	0.190778	−	0.330437i
$863$	21117.9			0.832980			0.416490	−	0.909140i	$-0.363260\pi$
$863$	21117.9			0.832980			0.416490	+	0.909140i	$0.363260\pi$
$864$	−13025.5	+	22416.4i	−0.512890	+	0.882664i
$865$		0			0
$866$	7988.42	−	13836.3i	0.313461	−	0.542931i
$867$	17774.6	+	6488.11i	0.696258	+	0.254150i
$868$	−9445.60	−	16360.3i	−0.369360	−	0.639751i
$869$	4509.99	+	7811.54i	0.176054	+	0.304935i
$870$		0			0
$871$	−9698.25	+	16797.9i	−0.377282	+	0.653472i
$872$	25181.4			0.977923
$873$	−29649.8	+	10729.3i	−1.14948	+	0.415959i
$874$	3122.84			0.120860
$875$		0			0
$876$	−3368.37	−	19207.2i	−0.129916	−	0.740813i
$877$	−14201.6	−	24597.9i	−0.546812	−	0.947107i	−0.998490	−	0.0549258i	$-0.982508\pi$
$877$	−14201.6	−	24597.9i	−0.546812	−	0.947107i	0.451678	−	0.892181i	$-0.350826\pi$
$878$	−11681.5	−	20233.0i	−0.449012	−	0.777711i
$879$	−1614.95	−	9208.82i	−0.0619691	−	0.353363i
$880$		0			0
$881$	14925.4			0.570772			0.285386	−	0.958413i	$-0.407878\pi$
$881$	14925.4			0.570772			0.285386	+	0.958413i	$0.407878\pi$
$882$	−7951.04	−	6696.92i	−0.303544	−	0.255666i
$883$	−10817.4			−0.412271			−0.206136	−	0.978523i	$-0.566089\pi$
$883$	−10817.4			−0.412271			−0.206136	+	0.978523i	$0.566089\pi$
$884$	2191.46	−	3795.72i	0.0833788	−	0.144416i
$885$		0			0
$886$	5933.79	+	10277.6i	0.225000	+	0.389711i
$887$	−7105.65	−	12307.3i	−0.268979	−	0.465885i	0.699619	−	0.714516i	$-0.253353\pi$
$887$	−7105.65	−	12307.3i	−0.268979	−	0.465885i	−0.968598	+	0.248630i	$0.920020\pi$
$888$	−36287.6	−	13245.8i	−1.37132	−	0.500563i
$889$	−8263.74	+	14313.2i	−0.311763	+	0.539989i
$890$		0			0
$891$	−19893.6	−	7324.46i	−0.747990	−	0.275397i
$892$	−25071.1			−0.941078
$893$	−1333.13	+	2309.04i	−0.0499568	+	0.0865277i
$894$	26375.5	+	9627.63i	0.986720	+	0.360175i
$895$		0			0
$896$	−5471.71	−	9477.27i	−0.204014	−	0.353363i
$897$	−7391.13	+	6190.21i	−0.275120	+	0.230418i
$898$	−12731.5	+	22051.5i	−0.473112	+	0.819454i
$899$	50658.1			1.87936
$900$		0			0
$901$	24954.7			0.922711
$902$	−8567.65	+	14839.6i	−0.316265	+	0.547788i
$903$	−185.200	−	1056.06i	−0.00682512	−	0.0389185i
$904$	−7255.70	−	12567.2i	−0.266948	−	0.462367i
$905$		0			0
$906$	−2285.18	−	13030.7i	−0.0837971	−	0.477831i
$907$	14121.3	−	24458.7i	0.516967	−	0.895412i	−0.482839	−	0.875709i	$-0.660394\pi$
$907$	14121.3	−	24458.7i	0.516967	−	0.895412i	0.999806	−	0.0197034i	$-0.00627220\pi$
$908$	22132.4			0.808910
$909$	−32499.6	+	11760.6i	−1.18586	+	0.429124i
$910$		0			0
$911$	15380.3	−	26639.5i	0.559355	−	0.968832i	−0.438195	−	0.898880i	$-0.644382\pi$
$911$	15380.3	−	26639.5i	0.559355	−	0.968832i	0.997550	−	0.0699518i	$-0.0222846\pi$
$912$	491.594	−	411.719i	0.0178490	−	0.0149489i
$913$	−8028.00	−	13904.9i	−0.291006	−	0.504037i
$914$	1597.91	+	2767.66i	0.0578272	+	0.100160i
$915$		0			0
$916$	−4191.04	+	7259.09i	−0.151174	+	0.261842i
$917$	−23031.1			−0.829392
$918$	−8326.22	−	23.1955i	−0.299353	−	0.000833949i
$919$	9067.61			0.325476			0.162738	−	0.986669i	$-0.447967\pi$
$919$	9067.61			0.325476			0.162738	+	0.986669i	$0.447967\pi$
$920$		0			0
$921$	−35987.0	−	13136.1i	−1.28753	−	0.469976i
$922$	−5566.83	−	9642.03i	−0.198844	−	0.344407i
$923$	−3967.31	−	6871.59i	−0.141480	−	0.245050i
$924$	6402.07	−	5361.85i	0.227936	−	0.190900i
$925$		0			0
$926$	25707.7			0.912318
$927$	591.996	−	3321.29i	0.0209749	−	0.117676i
$928$	27386.5			0.968757
$929$	−13529.2	+	23433.2i	−0.477802	+	0.827578i	−0.999676	−	0.0254448i	$-0.991900\pi$
$929$	−13529.2	+	23433.2i	−0.477802	+	0.827578i	0.521874	+	0.853023i	$0.325233\pi$
$930$		0			0
$931$	2749.08	+	4761.54i	0.0967748	+	0.167619i
$932$	−15937.9	−	27605.3i	−0.560154	−	0.970215i
$933$	−5123.25	−	29214.0i	−0.179772	−	1.02510i
$934$	−5038.53	+	8726.99i	−0.176516	+	0.305734i
$935$		0			0
$936$	2451.82	−	13755.5i	0.0856200	−	0.480357i
$937$	3320.73			0.115778			0.0578888	−	0.998323i	$-0.481563\pi$
$937$	3320.73			0.115778			0.0578888	+	0.998323i	$0.481563\pi$
$938$	−7257.55	+	12570.4i	−0.252630	+	0.437569i
$939$	−2829.73	+	2369.95i	−0.0983438	+	0.0823647i
$940$		0			0
$941$	6934.00	+	12010.0i	0.240215	+	0.416064i	0.960775	−	0.277328i	$-0.0894488\pi$
$941$	6934.00	+	12010.0i	0.240215	+	0.416064i	−0.720561	+	0.693392i	$0.756115\pi$
$942$	5943.04	+	2169.34i	0.205557	+	0.0750328i
$943$	−13975.3	+	24206.0i	−0.482608	+	0.835902i
$944$	142.577			0.00491576
$945$		0			0
$946$	945.056			0.0324804
$947$	15184.1	−	26299.6i	0.521032	−	0.902454i	−0.478669	−	0.877995i	$-0.658881\pi$
$947$	15184.1	−	26299.6i	0.521032	−	0.902454i	0.999701	−	0.0244583i	$-0.00778609\pi$
$948$	−7918.37	−	2890.38i	−0.271284	−	0.0990245i
$949$	8432.10	+	14604.8i	0.288427	+	0.499571i
$950$		0			0
$951$	33058.4	−	27687.0i	1.12723	−	0.944073i
$952$	4148.49	−	7185.40i	0.141233	−	0.244622i
$953$	55107.7			1.87315			0.936576	−	0.350464i	$-0.113976\pi$
$953$	55107.7			1.87315			0.936576	+	0.350464i	$0.113976\pi$
$954$	29571.7	−	10701.1i	1.00358	−	0.363166i
$955$		0			0
$956$	−10142.1	+	17566.6i	−0.343115	+	0.594292i
$957$	3868.07	+	22056.7i	0.130655	+	0.745027i
$958$	−2543.34	−	4405.20i	−0.0857743	−	0.148565i
$959$	−5568.33	−	9644.62i	−0.187498	−	0.324756i
$960$		0			0
$961$	−43526.4	+	75389.9i	−1.46106	+	2.53063i
$962$	13206.4			0.442609
$963$	27879.0	+	23481.6i	0.932906	+	0.785759i
$964$	−34030.3			−1.13697
$965$		0			0
$966$	−5531.05	+	4632.35i	−0.184222	+	0.154289i
$967$	1366.23	+	2366.37i	0.0454342	+	0.0786943i	0.887848	−	0.460137i	$-0.152200\pi$
$967$	1366.23	+	2366.37i	0.0454342	+	0.0786943i	−0.842414	+	0.538831i	$0.818866\pi$
$968$	−5343.75	−	9255.65i	−0.177433	−	0.307322i
$969$	4136.73	+	1510.00i	0.137142	+	0.0500599i
$970$		0			0
$971$	−52740.8			−1.74308			−0.871542	−	0.490321i	$-0.836880\pi$
$971$	−52740.8			−1.74308			−0.871542	+	0.490321i	$0.836880\pi$
$972$	18647.6	−	6689.28i	0.615352	−	0.220739i
$973$	−5142.04			−0.169421
$974$	1943.81	−	3366.78i	0.0639464	−	0.110758i
$975$		0			0
$976$	2142.66	+	3711.20i	0.0702714	+	0.121714i
$977$	12493.6	+	21639.6i	0.409116	+	0.708611i	0.994791	−	0.101936i	$-0.0325036\pi$
$977$	12493.6	+	21639.6i	0.409116	+	0.708611i	−0.585674	+	0.810546i	$0.699170\pi$
$978$	−880.687	+	737.592i	−0.0287948	+	0.0241161i
$979$	15780.5	−	27332.7i	0.515166	−	0.892294i
$980$		0			0
$981$	−23616.6	−	19891.6i	−0.768624	−	0.647389i
$982$	9148.89			0.297304
$983$	−5551.41	+	9615.32i	−0.180125	+	0.311985i	−0.941923	−	0.335829i	$-0.890983\pi$
$983$	−5551.41	+	9615.32i	−0.180125	+	0.311985i	0.761798	+	0.647814i	$0.224317\pi$
$984$	−6997.12	−	39899.3i	−0.226687	−	1.29262i
$985$		0			0
$986$	4397.64	+	7616.94i	0.142038	+	0.246017i
$987$	−1064.00	−	6067.21i	−0.0343137	−	0.195665i
$988$	−1460.65	+	2529.93i	−0.0470340	+	0.0814653i
$989$	1541.55			0.0495637
$990$		0			0
$991$	4790.04			0.153543			0.0767713	−	0.997049i	$-0.475539\pi$
$991$	4790.04			0.153543			0.0767713	+	0.997049i	$0.475539\pi$
$992$	−31583.7	+	54704.6i	−1.01087	+	1.75088i
$993$	17280.4	−	14472.7i	0.552243	−	0.462514i
$994$	−2968.88	−	5142.26i	−0.0947357	−	0.164087i
$995$		0			0
$996$	14095.1	+	5145.02i	0.448413	+	0.163681i
$997$	18138.0	−	31415.9i	0.576164	−	0.997945i	−0.419750	−	0.907640i	$-0.637882\pi$
$997$	18138.0	−	31415.9i	0.576164	−	0.997945i	0.995914	−	0.0903053i	$-0.0287843\pi$
$998$	29098.3			0.922936
$999$	23569.5	+	41087.4i	0.746452	+	1.30125i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.4.e.f.151.4	yes	24
5.2	odd	4		225.4.k.e.124.9		48
5.3	odd	4		225.4.k.e.124.16		48
5.4	even	2		225.4.e.e.151.9	yes	24
9.2	odd	6		2025.4.a.bj.1.4		12
9.4	even	3	inner	225.4.e.f.76.4	yes	24
9.7	even	3		2025.4.a.bf.1.9		12
45.4	even	6		225.4.e.e.76.9	✓	24
45.13	odd	12		225.4.k.e.49.9		48
45.22	odd	12		225.4.k.e.49.16		48
45.29	odd	6		2025.4.a.be.1.9		12
45.34	even	6		2025.4.a.bi.1.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.4.e.e.76.9	✓	24	45.4	even	6
225.4.e.e.151.9	yes	24	5.4	even	2
225.4.e.f.76.4	yes	24	9.4	even	3	inner
225.4.e.f.151.4	yes	24	1.1	even	1	trivial
225.4.k.e.49.9		48	45.13	odd	12
225.4.k.e.49.16		48	45.22	odd	12
225.4.k.e.124.9		48	5.2	odd	4
225.4.k.e.124.16		48	5.3	odd	4
2025.4.a.be.1.9		12	45.29	odd	6
2025.4.a.bf.1.9		12	9.7	even	3
2025.4.a.bi.1.4		12	45.34	even	6
2025.4.a.bj.1.4		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)

\(f(q)\)	\(=\)	\(q+(-0.832171 + 1.44136i) q^{2} +(-4.88113 - 1.78172i) q^{3} +(2.61498 + 4.52928i) q^{4} +(6.63004 - 5.55278i) q^{6} +(5.28358 - 9.15142i) q^{7} -22.0192 q^{8} +(20.6509 + 17.3936i) q^{9} +O(q^{10})\)	\(q+(-0.832171 + 1.44136i) q^{2} +(-4.88113 - 1.78172i) q^{3} +(2.61498 + 4.52928i) q^{4} +(6.63004 - 5.55278i) q^{6} +(5.28358 - 9.15142i) q^{7} -22.0192 q^{8} +(20.6509 + 17.3936i) q^{9} +(-14.5398 + 25.1837i) q^{11} +(-4.69416 - 26.7672i) q^{12} +(11.7510 + 20.3533i) q^{13} +(8.79368 + 15.2311i) q^{14} +(-2.59614 + 4.49664i) q^{16} -35.6583 q^{17} +(-42.2557 + 15.2910i) q^{18} +23.7670 q^{19} +(-42.0951 + 35.2555i) q^{21} +(-24.1993 - 41.9143i) q^{22} +(-39.4733 - 68.3697i) q^{23} +(107.479 + 39.2321i) q^{24} -39.1153 q^{26} +(-69.8093 - 121.695i) q^{27} +55.2658 q^{28} +(-74.0997 + 128.344i) q^{29} +(-170.912 - 296.028i) q^{31} +(-92.3976 - 160.037i) q^{32} +(115.841 - 97.0192i) q^{33} +(29.6738 - 51.3966i) q^{34} +(-24.7789 + 139.018i) q^{36} -337.627 q^{37} +(-19.7782 + 34.2569i) q^{38} +(-21.0942 - 120.284i) q^{39} +(-177.023 - 306.613i) q^{41} +(-15.7855 - 90.0129i) q^{42} +(-9.76327 + 16.9105i) q^{43} -152.086 q^{44} +131.394 q^{46} +(-56.0915 + 97.1533i) q^{47} +(20.6839 - 17.3231i) q^{48} +(115.668 + 200.342i) q^{49} +(174.053 + 63.5333i) q^{51} +(-61.4572 + 106.447i) q^{52} -699.829 q^{53} +(233.500 + 0.650493i) q^{54} +(-116.340 + 201.507i) q^{56} +(-116.010 - 42.3462i) q^{57} +(-123.327 - 213.609i) q^{58} +(-13.7297 - 23.7805i) q^{59} +(412.663 - 714.754i) q^{61} +568.912 q^{62} +(268.287 - 97.0847i) q^{63} +266.024 q^{64} +(43.4401 + 247.706i) q^{66} +(412.657 + 714.743i) q^{67} +(-93.2460 - 161.507i) q^{68} +(70.8584 + 404.052i) q^{69} -337.616 q^{71} +(-454.717 - 382.994i) q^{72} +717.566 q^{73} +(280.963 - 486.642i) q^{74} +(62.1504 + 107.648i) q^{76} +(153.645 + 266.120i) q^{77} +(190.927 + 69.6926i) q^{78} +(155.091 - 268.625i) q^{79} +(123.922 + 718.390i) q^{81} +589.253 q^{82} +(-276.069 + 478.166i) q^{83} +(-269.760 - 98.4684i) q^{84} +(-16.2494 - 28.1448i) q^{86} +(590.364 - 494.441i) q^{87} +(320.155 - 554.525i) q^{88} -1085.33 q^{89} +248.349 q^{91} +(206.444 - 357.571i) q^{92} +(306.804 + 1749.47i) q^{93} +(-93.3554 - 161.696i) q^{94} +(165.863 + 945.791i) q^{96} +(-583.915 + 1011.37i) q^{97} -385.021 q^{98} +(-738.298 + 267.167i) 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

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