LMFDB - Embedded newform 225.4.e.e.76.11

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			76.11
Character	$\chi$	$=$	225.76
Dual form			225.4.e.e.151.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.16773 + 3.75461i) q^{2} +(0.193913 - 5.19253i) q^{3} +(-5.39807 + 9.34974i) q^{4} +(19.9163 - 10.5279i) q^{6} +(6.50075 + 11.2596i) q^{7} -12.1226 q^{8} +(-26.9248 - 2.01380i) q^{9} +O(q^{10})$	\(q+(2.16773 + 3.75461i) q^{2} +(0.193913 - 5.19253i) q^{3} +(-5.39807 + 9.34974i) q^{4} +(19.9163 - 10.5279i) q^{6} +(6.50075 + 11.2596i) q^{7} -12.1226 q^{8} +(-26.9248 - 2.01380i) q^{9} +(17.2761 + 29.9230i) q^{11} +(47.5021 + 29.8427i) q^{12} +(-3.77884 + 6.54514i) q^{13} +(-28.1837 + 48.8156i) q^{14} +(16.9062 + 29.2824i) q^{16} +82.0901 q^{17} +(-50.8046 - 105.458i) q^{18} +146.406 q^{19} +(59.7265 - 31.5720i) q^{21} +(-74.8995 + 129.730i) q^{22} +(-93.9451 + 162.718i) q^{23} +(-2.35072 + 62.9468i) q^{24} -32.7659 q^{26} +(-15.6778 + 139.417i) q^{27} -140.366 q^{28} +(-21.8589 - 37.8607i) q^{29} +(29.3391 - 50.8168i) q^{31} +(-121.786 + 210.940i) q^{32} +(158.726 - 83.9041i) q^{33} +(177.949 + 308.216i) q^{34} +(164.171 - 240.869i) q^{36} -329.358 q^{37} +(317.368 + 549.697i) q^{38} +(33.2531 + 20.8909i) q^{39} +(86.4845 - 149.796i) q^{41} +(248.011 + 155.811i) q^{42} +(-78.3437 - 135.695i) q^{43} -373.030 q^{44} -814.589 q^{46} +(-84.6230 - 146.571i) q^{47} +(155.328 - 82.1077i) q^{48} +(86.9806 - 150.655i) q^{49} +(15.9183 - 426.255i) q^{51} +(-40.7969 - 70.6623i) q^{52} +609.837 q^{53} +(-557.443 + 243.355i) q^{54} +(-78.8058 - 136.496i) q^{56} +(28.3899 - 760.217i) q^{57} +(94.7682 - 164.143i) q^{58} +(297.215 - 514.792i) q^{59} +(-162.538 - 281.525i) q^{61} +254.396 q^{62} +(-152.357 - 316.254i) q^{63} -785.498 q^{64} +(659.102 + 414.075i) q^{66} +(-344.191 + 596.156i) q^{67} +(-443.128 + 767.521i) q^{68} +(826.700 + 519.366i) q^{69} -515.170 q^{71} +(326.398 + 24.4124i) q^{72} -1088.37 q^{73} +(-713.959 - 1236.61i) q^{74} +(-790.310 + 1368.86i) q^{76} +(-224.615 + 389.044i) q^{77} +(-6.35373 + 170.138i) q^{78} +(262.896 + 455.349i) q^{79} +(720.889 + 108.442i) q^{81} +749.899 q^{82} +(-179.006 - 310.048i) q^{83} +(-27.2188 + 728.855i) q^{84} +(339.655 - 588.300i) q^{86} +(-200.832 + 106.161i) q^{87} +(-209.430 - 362.744i) q^{88} +1517.67 q^{89} -98.2610 q^{91} +(-1014.25 - 1756.72i) q^{92} +(-258.179 - 162.198i) q^{93} +(366.879 - 635.453i) q^{94} +(1071.70 + 673.283i) q^{96} +(-197.680 - 342.393i) q^{97} +754.200 q^{98} +(-404.896 - 840.462i) 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 $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

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

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 $

$2$	2.16773	+	3.75461i	0.766407	+	1.32746i	0.939500	+	0.342550i	$0.111291\pi$
$2$	2.16773	+	3.75461i	0.766407	+	1.32746i	−0.173093	+	0.984906i	$0.555376\pi$
$3$	0.193913	−	5.19253i	0.0373185	−	0.999303i
$3$	0.193913	−	5.19253i	0.0373185	−	0.999303i
$4$	−5.39807	+	9.34974i	−0.674759	+	1.16872i
$5$		0			0
$5$		0			0
$6$	19.9163	−	10.5279i	1.35513	−	0.716334i
$7$	6.50075	+	11.2596i	0.351007	+	0.607963i	0.986426	−	0.164205i	$-0.0525059\pi$
$7$	6.50075	+	11.2596i	0.351007	+	0.607963i	−0.635419	+	0.772168i	$0.719173\pi$
$8$	−12.1226			−0.535747
$9$	−26.9248	−	2.01380i	−0.997215	−	0.0745850i
$10$		0			0
$11$	17.2761	+	29.9230i	0.473539	+	0.820194i	0.999541	−	0.0302897i	$-0.00964297\pi$
$11$	17.2761	+	29.9230i	0.473539	+	0.820194i	−0.526002	+	0.850483i	$0.676310\pi$
$12$	47.5021	+	29.8427i	1.14272	+	0.717904i
$13$	−3.77884	+	6.54514i	−0.0806200	+	0.139638i	−0.903516	−	0.428553i	$-0.859023\pi$
$13$	−3.77884	+	6.54514i	−0.0806200	+	0.139638i	0.822896	+	0.568191i	$0.192357\pi$
$14$	−28.1837	+	48.8156i	−0.538029	+	0.931894i
$15$		0			0
$16$	16.9062	+	29.2824i	0.264159	+	0.457537i
$17$	82.0901			1.17116			0.585581	−	0.810614i	$-0.300866\pi$
$17$	82.0901			1.17116			0.585581	+	0.810614i	$0.300866\pi$
$18$	−50.8046	−	105.458i	−0.665264	−	1.38092i
$19$	146.406			1.76778			0.883890	−	0.467696i	$-0.154916\pi$
$19$	146.406			1.76778			0.883890	+	0.467696i	$0.154916\pi$
$20$		0			0
$21$	59.7265	−	31.5720i	0.620638	−	0.328075i
$22$	−74.8995	+	129.730i	−0.725847	+	1.25720i
$23$	−93.9451	+	162.718i	−0.851691	+	1.47517i	0.0279894	+	0.999608i	$0.491090\pi$
$23$	−93.9451	+	162.718i	−0.851691	+	1.47517i	−0.879681	+	0.475565i	$0.842244\pi$
$24$	−2.35072	+	62.9468i	−0.0199933	+	0.535374i
$25$		0			0
$26$	−32.7659			−0.247151
$27$	−15.6778	+	139.417i	−0.111748	+	0.993737i
$28$	−140.366			−0.947382
$29$	−21.8589	−	37.8607i	−0.139969	−	0.242433i	0.787516	−	0.616295i	$-0.211367\pi$
$29$	−21.8589	−	37.8607i	−0.139969	−	0.242433i	−0.927485	+	0.373861i	$0.878034\pi$
$30$		0			0
$31$	29.3391	−	50.8168i	0.169982	−	0.294418i	−0.768431	−	0.639933i	$-0.778962\pi$
$31$	29.3391	−	50.8168i	0.169982	−	0.294418i	0.938413	+	0.345514i	$0.112296\pi$
$32$	−121.786	+	210.940i	−0.672780	+	1.16529i
$33$	158.726	−	83.9041i	0.837294	−	0.442601i
$34$	177.949	+	308.216i	0.897587	+	1.55467i
$35$		0			0
$36$	164.171	−	240.869i	0.760049	−	1.11514i
$37$	−329.358			−1.46341			−0.731705	−	0.681621i	$-0.761275\pi$
$37$	−329.358			−1.46341			−0.731705	+	0.681621i	$0.761275\pi$
$38$	317.368	+	549.697i	1.35484	+	2.34665i
$39$	33.2531	+	20.8909i	0.136532	+	0.0857750i
$40$		0			0
$41$	86.4845	−	149.796i	0.329429	−	0.570588i	−0.652969	−	0.757384i	$-0.726477\pi$
$41$	86.4845	−	149.796i	0.329429	−	0.570588i	0.982399	+	0.186796i	$0.0598103\pi$
$42$	248.011	+	155.811i	0.911166	+	0.572431i
$43$	−78.3437	−	135.695i	−0.277844	−	0.481240i	0.693004	−	0.720933i	$-0.256287\pi$
$43$	−78.3437	−	135.695i	−0.277844	−	0.481240i	−0.970849	+	0.239693i	$0.922953\pi$
$44$	−373.030			−1.27810
$45$		0			0
$46$	−814.589			−2.61097
$47$	−84.6230	−	146.571i	−0.262628	−	0.454886i	0.704311	−	0.709891i	$-0.251256\pi$
$47$	−84.6230	−	146.571i	−0.262628	−	0.454886i	−0.966940	+	0.255006i	$0.917923\pi$
$48$	155.328	−	82.1077i	0.467076	−	0.246900i
$49$	86.9806	−	150.655i	0.253588	−	0.439227i
$50$		0			0
$51$	15.9183	−	426.255i	0.0437061	−	1.17035i
$52$	−40.7969	−	70.6623i	−0.108798	−	0.188444i
$53$	609.837			1.58052			0.790259	−	0.612772i	$-0.209946\pi$
$53$	609.837			1.58052			0.790259	+	0.612772i	$0.209946\pi$
$54$	−557.443	+	243.355i	−1.40479	+	0.613267i
$55$		0			0
$56$	−78.8058	−	136.496i	−0.188051	−	0.325714i
$57$	28.3899	−	760.217i	0.0659709	−	1.76655i
$58$	94.7682	−	164.143i	0.214546	−	0.371605i
$59$	297.215	−	514.792i	0.655833	−	1.13594i	−0.325852	−	0.945421i	$-0.605651\pi$
$59$	297.215	−	514.792i	0.655833	−	1.13594i	0.981684	−	0.190514i	$-0.0610156\pi$
$60$		0			0
$61$	−162.538	−	281.525i	−0.341163	−	0.590911i	0.643486	−	0.765458i	$-0.277487\pi$
$61$	−162.538	−	281.525i	−0.341163	−	0.590911i	−0.984649	+	0.174547i	$0.944154\pi$
$62$	254.396			0.521103
$63$	−152.357	−	316.254i	−0.304685	−	0.632449i
$64$	−785.498			−1.53418
$65$		0			0
$66$	659.102	+	414.075i	1.22924	+	0.772258i
$67$	−344.191	+	596.156i	−0.627606	+	1.08705i	0.360425	+	0.932788i	$0.382632\pi$
$67$	−344.191	+	596.156i	−0.627606	+	1.08705i	−0.988031	+	0.154257i	$0.950702\pi$
$68$	−443.128	+	767.521i	−0.790253	+	1.36876i
$69$	826.700	+	519.366i	1.44236	+	0.906149i
$70$		0			0
$71$	−515.170			−0.861119			−0.430560	−	0.902562i	$-0.641684\pi$
$71$	−515.170			−0.861119			−0.430560	+	0.902562i	$0.641684\pi$
$72$	326.398	+	24.4124i	0.534255	+	0.0399587i
$73$	−1088.37			−1.74499			−0.872497	−	0.488619i	$-0.837501\pi$
$73$	−1088.37			−1.74499			−0.872497	+	0.488619i	$0.837501\pi$
$74$	−713.959	−	1236.61i	−1.12157	−	1.94261i
$75$		0			0
$76$	−790.310	+	1368.86i	−1.19283	+	2.06603i
$77$	−224.615	+	389.044i	−0.332431	+	0.575788i
$78$	−6.35373	+	170.138i	−0.00922331	+	0.246979i
$79$	262.896	+	455.349i	0.374406	+	0.648491i	0.990238	−	0.139387i	$-0.0445131\pi$
$79$	262.896	+	455.349i	0.374406	+	0.648491i	−0.615832	+	0.787878i	$0.711180\pi$
$80$		0			0
$81$	720.889	+	108.442i	0.988874	+	0.148755i
$82$	749.899			1.00991
$83$	−179.006	−	310.048i	−0.236729	−	0.410027i	0.723045	−	0.690801i	$-0.242742\pi$
$83$	−179.006	−	310.048i	−0.236729	−	0.410027i	−0.959774	+	0.280775i	$0.909409\pi$
$84$	−27.2188	+	728.855i	−0.0353549	+	0.946722i
$85$		0			0
$86$	339.655	−	588.300i	0.425884	−	0.737652i
$87$	−200.832	+	106.161i	−0.247488	+	0.130824i
$88$	−209.430	−	362.744i	−0.253697	−	0.439416i
$89$	1517.67			1.80756			0.903779	−	0.427999i	$-0.140781\pi$
$89$	1517.67			1.80756			0.903779	+	0.427999i	$0.140781\pi$
$90$		0			0
$91$	−98.2610			−0.113193
$92$	−1014.25	−	1756.72i	−1.14937	−	1.99077i
$93$	−258.179	−	162.198i	−0.287870	−	0.180851i
$94$	366.879	−	635.453i	0.402560	−	0.697255i
$95$		0			0
$96$	1071.70	+	673.283i	1.13937	+	0.715798i
$97$	−197.680	−	342.393i	−0.206922	−	0.358399i	0.743822	−	0.668378i	$-0.233011\pi$
$97$	−197.680	−	342.393i	−0.206922	−	0.358399i	−0.950743	+	0.309979i	$0.899678\pi$
$98$	754.200			0.777405
$99$	−404.896	−	840.462i	−0.411046	−	0.853228i
$100$		0			0
$101$	−166.629	−	288.610i	−0.164160	−	0.284334i	0.772197	−	0.635384i	$-0.219158\pi$
$101$	−166.629	−	288.610i	−0.164160	−	0.284334i	−0.936357	+	0.351050i	$0.885825\pi$
$102$	1634.93	−	864.238i	1.58708	−	0.838944i
$103$	815.444	−	1412.39i	0.780078	−	1.35114i	−0.151817	−	0.988409i	$-0.548513\pi$
$103$	815.444	−	1412.39i	0.780078	−	1.35114i	0.931896	−	0.362727i	$-0.118154\pi$
$104$	45.8092	−	79.3439i	0.0431919	−	0.0748106i
$105$		0			0
$106$	1321.96	+	2289.70i	1.21132	+	2.09807i
$107$	688.472			0.622029			0.311015	−	0.950405i	$-0.399331\pi$
$107$	688.472			0.622029			0.311015	+	0.950405i	$0.399331\pi$
$108$	−1218.89	−	899.168i	−1.08599	−	0.801134i
$109$	−1188.95			−1.04478			−0.522390	−	0.852707i	$-0.674959\pi$
$109$	−1188.95			−1.04478			−0.522390	+	0.852707i	$0.674959\pi$
$110$		0			0
$111$	−63.8668	+	1710.20i	−0.0546123	+	1.46239i
$112$	−219.806	+	380.715i	−0.185444	+	0.321198i
$113$	134.208	−	232.455i	0.111727	−	0.193518i	−0.804739	−	0.593628i	$-0.797695\pi$
$113$	134.208	−	232.455i	0.111727	−	0.193518i	0.916467	+	0.400111i	$0.131028\pi$
$114$	2915.86	−	1541.35i	2.39557	−	1.26632i
$115$		0			0
$116$	471.984			0.377781
$117$	114.925	−	168.617i	0.0908104	−	0.133236i
$118$	2577.12			2.01054
$119$	533.647	+	924.303i	0.411087	+	0.712023i
$120$		0			0
$121$	68.5754	−	118.776i	0.0515217	−	0.0892382i
$122$	704.678	−	1220.54i	0.522939	−	0.905756i
$123$	−761.048	−	478.121i	−0.557897	−	0.350493i
$124$	316.749	+	548.625i	0.229394	+	0.397323i
$125$		0			0
$126$	857.144	−	1257.59i	0.606036	−	0.889169i
$127$	145.302			0.101523			0.0507616	−	0.998711i	$-0.483835\pi$
$127$	145.302			0.101523			0.0507616	+	0.998711i	$0.483835\pi$
$128$	−728.455	−	1261.72i	−0.503023	−	0.871261i
$129$	−719.794	+	380.489i	−0.491274	+	0.259692i
$130$		0			0
$131$	134.659	−	233.237i	0.0898110	−	0.155557i	−0.817620	−	0.575758i	$-0.804707\pi$
$131$	134.659	−	233.237i	0.0898110	−	0.155557i	0.907431	+	0.420201i	$0.138040\pi$
$132$	−72.3352	+	1936.97i	−0.0476968	+	1.27721i
$133$	951.747	+	1648.47i	0.620504	+	1.07474i
$134$	−2984.45			−1.92401
$135$		0			0
$136$	−995.143			−0.627447
$137$	−413.688	−	716.528i	−0.257984	−	0.446841i	0.707718	−	0.706495i	$-0.249725\pi$
$137$	−413.688	−	716.528i	−0.257984	−	0.446841i	−0.965702	+	0.259654i	$0.916391\pi$
$138$	−157.959	+	4229.78i	−0.0974375	+	2.60915i
$139$	84.9350	−	147.112i	0.0518280	−	0.0897687i	−0.838947	−	0.544212i	$-0.816829\pi$
$139$	84.9350	−	147.112i	0.0518280	−	0.0897687i	0.890775	+	0.454444i	$0.150162\pi$
$140$		0			0
$141$	−777.486	+	410.986i	−0.464370	+	0.245470i
$142$	−1116.75	−	1934.26i	−0.659968	−	1.14310i
$143$	−261.134			−0.152707
$144$	−396.227	−	822.467i	−0.229298	−	0.475965i
$145$		0			0
$146$	−2359.30	−	4086.42i	−1.33738	−	2.31640i
$147$	−765.413	−	480.863i	−0.429457	−	0.269802i
$148$	1777.90	−	3079.41i	0.987450	−	1.71031i
$149$	−873.174	+	1512.38i	−0.480089	+	0.831538i	−0.999739	−	0.0228410i	$-0.992729\pi$
$149$	−873.174	+	1512.38i	−0.480089	+	0.831538i	0.519650	+	0.854379i	$0.326062\pi$
$150$		0			0
$151$	−171.419	−	296.906i	−0.0923832	−	0.160012i	0.816130	−	0.577868i	$-0.196115\pi$
$151$	−171.419	−	296.906i	−0.0923832	−	0.160012i	−0.908513	+	0.417856i	$0.862782\pi$
$152$	−1774.82			−0.947082
$153$	−2210.26	−	165.313i	−1.16790	−	0.0873512i
$154$	−1947.61			−1.01911
$155$		0			0
$156$	−374.827	+	198.137i	−0.192373	+	0.101690i
$157$	−1747.85	+	3027.36i	−0.888494	+	1.53892i	−0.0468373	+	0.998903i	$0.514914\pi$
$157$	−1747.85	+	3027.36i	−0.888494	+	1.53892i	−0.841656	+	0.540014i	$0.818419\pi$
$158$	−1139.77	+	1974.15i	−0.573895	+	0.994016i
$159$	118.255	−	3166.60i	0.0589826	−	1.57942i
$160$		0			0
$161$	−2442.85			−1.19580
$162$	1155.53	+	2941.73i	0.560415	+	1.42669i
$163$	−663.542			−0.318851			−0.159425	−	0.987210i	$-0.550964\pi$
$163$	−663.542			−0.318851			−0.159425	+	0.987210i	$0.550964\pi$
$164$	933.699	+	1617.21i	0.444571	+	0.770020i
$165$		0			0
$166$	776.074	−	1344.20i	0.362862	−	0.628495i
$167$	1229.82	−	2130.11i	0.569858	−	0.987023i	−0.426721	−	0.904383i	$-0.640331\pi$
$167$	1229.82	−	2130.11i	0.569858	−	0.987023i	0.996579	−	0.0826401i	$-0.0263352\pi$
$168$	−724.039	+	382.733i	−0.332505	+	0.175765i
$169$	1069.94	+	1853.19i	0.487001	+	0.843510i
$170$		0			0
$171$	−3941.95	−	294.831i	−1.76286	−	0.131850i
$172$	1691.62			0.749912
$173$	−763.873	−	1323.07i	−0.335701	−	0.581451i	0.647918	−	0.761710i	$-0.275640\pi$
$173$	−763.873	−	1323.07i	−0.335701	−	0.581451i	−0.983619	+	0.180259i	$0.942306\pi$
$174$	−833.943	−	523.917i	−0.363339	−	0.228264i
$175$		0			0
$176$	−584.144	+	1011.77i	−0.250179	+	0.433323i
$177$	−2615.44	−	1643.12i	−1.11067	−	0.697767i
$178$	3289.89	+	5698.26i	1.38533	+	2.39945i
$179$	1006.17			0.420137			0.210069	−	0.977687i	$-0.432631\pi$
$179$	1006.17			0.420137			0.210069	+	0.977687i	$0.432631\pi$
$180$		0			0
$181$	591.861			0.243053			0.121527	−	0.992588i	$-0.461221\pi$
$181$	591.861			0.243053			0.121527	+	0.992588i	$0.461221\pi$
$182$	−213.003	−	368.932i	−0.0867518	−	0.150259i
$183$	−1493.35	+	789.395i	−0.603231	+	0.318873i
$184$	1138.86	−	1972.56i	0.456291	−	0.790319i
$185$		0			0
$186$	49.3307	−	1320.96i	0.0194468	−	0.520740i
$187$	1418.19	+	2456.38i	0.554591	+	0.960580i
$188$	1827.20			0.708843
$189$	−1671.70	+	729.792i	−0.643379	+	0.280870i
$190$		0			0
$191$	−1822.29	−	3156.29i	−0.690345	−	1.19571i	−0.971725	−	0.236117i	$-0.924125\pi$
$191$	−1822.29	−	3156.29i	−0.690345	−	1.19571i	0.281379	−	0.959597i	$-0.409208\pi$
$192$	−152.318	+	4078.72i	−0.0572531	+	1.53311i
$193$	6.70078	−	11.6061i	0.00249913	−	0.00432862i	−0.864773	−	0.502163i	$-0.832538\pi$
$193$	6.70078	−	11.6061i	0.00249913	−	0.00432862i	0.867272	+	0.497834i	$0.165871\pi$
$194$	857.034	−	1484.43i	0.317173	−	0.549359i
$195$		0			0
$196$	939.055	+	1626.49i	0.342221	+	0.592745i
$197$	63.1983			0.0228563			0.0114281	−	0.999935i	$-0.496362\pi$
$197$	63.1983			0.0228563			0.0114281	+	0.999935i	$0.496362\pi$
$198$	2277.90	−	3342.12i	0.817594	−	1.19957i
$199$	−4902.79			−1.74648			−0.873240	−	0.487291i	$-0.837985\pi$
$199$	−4902.79			−1.74648			−0.873240	+	0.487291i	$0.837985\pi$
$200$		0			0
$201$	3028.82	+	1902.82i	1.06287	+	0.667736i
$202$	722.411	−	1251.25i	0.251627	−	0.435831i
$203$	284.198	−	492.246i	0.0982602	−	0.170192i
$204$	3899.45	+	2449.79i	1.33831	+	0.840783i
$205$		0			0
$206$	7070.64			2.39143
$207$	2857.13	−	4191.95i	0.959345	−	1.40754i
$208$	−255.543			−0.0851861
$209$	2529.32	+	4380.90i	0.837112	+	1.44992i
$210$		0			0
$211$	1556.11	−	2695.26i	0.507711	−	0.879381i	−0.492249	−	0.870454i	$-0.663825\pi$
$211$	1556.11	−	2695.26i	0.507711	−	0.879381i	0.999960	−	0.00892670i	$-0.00284149\pi$
$212$	−3291.94	+	5701.81i	−1.06647	+	1.84718i
$213$	−99.8980	+	2675.04i	−0.0321357	+	0.860519i
$214$	1492.42	+	2584.95i	0.476728	+	0.825717i
$215$		0			0
$216$	190.055	−	1690.10i	0.0598685	−	0.532391i
$217$	762.904			0.238660
$218$	−2577.32	−	4464.06i	−0.800727	−	1.38690i
$219$	−211.050	+	5651.42i	−0.0651206	+	1.74378i
$220$		0			0
$221$	−310.205	+	537.291i	−0.0944192	+	0.163539i
$222$	−6559.60	+	3467.46i	−1.98311	+	1.04829i
$223$	−2434.71	−	4217.05i	−0.731123	−	1.26634i	−0.956404	−	0.292048i	$-0.905663\pi$
$223$	−2434.71	−	4217.05i	−0.731123	−	1.26634i	0.225281	−	0.974294i	$-0.427670\pi$
$224$	−3166.81			−0.944603
$225$		0			0
$226$	1163.70			0.342515
$227$	3293.59	+	5704.67i	0.963011	+	1.66798i	0.714867	+	0.699260i	$0.246487\pi$
$227$	3293.59	+	5704.67i	0.963011	+	1.66798i	0.248144	+	0.968723i	$0.420180\pi$
$228$	6954.58	+	4369.15i	2.02008	+	1.26910i
$229$	−8.21503	+	14.2288i	−0.00237059	+	0.00410598i	−0.867208	−	0.497946i	$-0.834088\pi$
$229$	−8.21503	+	14.2288i	−0.00237059	+	0.00410598i	0.864838	+	0.502052i	$0.167421\pi$
$230$		0			0
$231$	1976.57	+	1241.76i	0.562981	+	0.353687i
$232$	264.986	+	458.969i	0.0749879	+	0.129883i
$233$	707.542			0.198938			0.0994692	−	0.995041i	$-0.468286\pi$
$233$	707.542			0.198938			0.0994692	+	0.995041i	$0.468286\pi$
$234$	882.216	+	65.9839i	0.246463	+	0.0184338i
$235$		0			0
$236$	3208.78	+	5557.77i	0.885058	+	1.53297i
$237$	2415.39	−	1276.80i	0.662012	−	0.349945i
$238$	−2313.60	+	4007.27i	−0.630120	+	1.09140i
$239$	3056.02	−	5293.18i	0.827102	−	1.43258i	−0.0731999	−	0.997317i	$-0.523321\pi$
$239$	3056.02	−	5293.18i	0.827102	−	1.43258i	0.900302	−	0.435266i	$-0.143346\pi$
$240$		0			0
$241$	−1544.12	−	2674.49i	−0.412719	−	0.714850i	0.582467	−	0.812854i	$-0.302087\pi$
$241$	−1544.12	−	2674.49i	−0.412719	−	0.714850i	−0.995186	+	0.0980044i	$0.968754\pi$
$242$	594.611			0.157946
$243$	702.879	−	3722.21i	0.185554	−	0.982634i
$244$	3509.58			0.920810
$245$		0			0
$246$	145.415	−	3893.87i	0.0376883	−	1.00920i
$247$	−553.244	+	958.246i	−0.142518	+	0.246849i
$248$	−355.665	+	616.030i	−0.0910676	+	0.157734i
$249$	−1644.65	+	869.375i	−0.418575	+	0.221263i
$250$		0			0
$251$	2743.28			0.689859			0.344929	−	0.938629i	$-0.387903\pi$
$251$	2743.28			0.689859			0.344929	+	0.938629i	$0.387903\pi$
$252$	3779.33	+	282.669i	0.944743	+	0.0706605i
$253$	−6492.00			−1.61324
$254$	314.974	+	545.552i	0.0778081	+	0.134768i
$255$		0			0
$256$	16.1888	−	28.0399i	0.00395235	−	0.00684568i
$257$	−360.023	+	623.578i	−0.0873838	+	0.151353i	−0.906404	−	0.422411i	$-0.861184\pi$
$257$	−360.023	+	623.578i	−0.0873838	+	0.151353i	0.819021	+	0.573764i	$0.194517\pi$
$258$	−2988.91	−	1877.75i	−0.721245	−	0.453115i
$259$	−2141.08	−	3708.45i	−0.513668	−	0.889699i
$260$		0			0
$261$	512.303	+	1063.41i	0.121497	+	0.252197i
$262$	1167.62			0.275327
$263$	2614.08	+	4527.72i	0.612894	+	1.06156i	0.990750	+	0.135699i	$0.0433279\pi$
$263$	2614.08	+	4527.72i	0.612894	+	1.06156i	−0.377857	+	0.925864i	$0.623339\pi$
$264$	−1924.17	+	1017.13i	−0.448578	+	0.237122i
$265$		0			0
$266$	−4126.26	+	7146.88i	−0.951116	+	1.64738i
$267$	294.295	−	7880.55i	0.0674554	−	1.80630i
$268$	−3715.94	−	6436.19i	−0.846966	−	1.46699i
$269$	320.400			0.0726213			0.0363107	−	0.999341i	$-0.488439\pi$
$269$	320.400			0.0726213			0.0363107	+	0.999341i	$0.488439\pi$
$270$		0			0
$271$	−1044.06			−0.234029			−0.117014	−	0.993130i	$-0.537332\pi$
$271$	−1044.06			−0.234029			−0.117014	+	0.993130i	$0.537332\pi$
$272$	1387.83	+	2403.79i	0.309373	+	0.535850i
$273$	−19.0541	+	510.224i	−0.00422419	+	0.113114i
$274$	1793.52	−	3106.48i	0.395441	−	0.684923i
$275$		0			0
$276$	−9318.52	+	4925.85i	−2.03228	+	1.07428i
$277$	−1665.66	−	2885.01i	−0.361299	−	0.625789i	0.626876	−	0.779119i	$-0.284333\pi$
$277$	−1665.66	−	2885.01i	−0.361299	−	0.625789i	−0.988175	+	0.153330i	$0.951000\pi$
$278$	736.463			0.158885
$279$	−892.283	+	1309.15i	−0.191468	+	0.280920i
$280$		0			0
$281$	2800.64	+	4850.86i	0.594563	+	1.02981i	0.993608	+	0.112883i	$0.0360084\pi$
$281$	2800.64	+	4850.86i	0.594563	+	1.02981i	−0.399045	+	0.916931i	$0.630658\pi$
$282$	−3228.47	−	2028.25i	−0.681746	−	0.428300i
$283$	−3133.92	+	5428.11i	−0.658277	+	1.14017i	0.322785	+	0.946472i	$0.395381\pi$
$283$	−3133.92	+	5428.11i	−0.658277	+	1.14017i	−0.981062	+	0.193696i	$0.937952\pi$
$284$	2780.93	−	4816.71i	0.581048	−	1.00640i
$285$		0			0
$286$	−566.066	−	980.455i	−0.117036	−	0.202712i
$287$	2248.85			0.462529
$288$	3703.86	−	5434.26i	0.757819	−	1.11186i
$289$	1825.78			0.371622
$290$		0			0
$291$	−1816.22	+	960.068i	−0.365871	+	0.193403i
$292$	5875.12	−	10176.0i	1.17745	−	2.03940i
$293$	−1051.43	+	1821.13i	−0.209642	+	0.363111i	−0.951602	−	0.307334i	$-0.900563\pi$
$293$	−1051.43	+	1821.13i	−0.209642	+	0.363111i	0.741960	+	0.670445i	$0.233897\pi$
$294$	146.249	−	3916.21i	0.0290116	−	0.776864i
$295$		0			0
$296$	3992.67			0.784018
$297$	−4442.64	+	1939.46i	−0.867973	+	0.378918i
$298$	−7571.21			−1.47177
$299$	−710.006	−	1229.77i	−0.137327	−	0.237857i
$300$		0			0
$301$	1018.59	−	1764.24i	0.195051	−	0.337838i
$302$	743.178	−	1287.22i	0.141606	−	0.245269i
$303$	−1530.93	+	809.260i	−0.290262	+	0.153435i
$304$	2475.16	+	4287.11i	0.466975	+	0.808824i
$305$		0			0
$306$	−4170.55	−	8657.02i	−0.779132	−	1.61728i
$307$	2020.07			0.375543			0.187771	−	0.982213i	$-0.439874\pi$
$307$	2020.07			0.375543			0.187771	+	0.982213i	$0.439874\pi$
$308$	−2424.97	−	4200.18i	−0.448622	−	0.777037i
$309$	−7175.76	−	4508.10i	−1.32108	−	0.829957i
$310$		0			0
$311$	−2696.66	+	4670.75i	−0.491684	+	0.851621i	−0.999954	−	0.00957637i	$-0.996952\pi$
$311$	−2696.66	+	4670.75i	−0.491684	+	0.851621i	0.508270	+	0.861198i	$0.330285\pi$
$312$	−403.113	−	253.252i	−0.0731467	−	0.0459537i
$313$	1555.89	+	2694.87i	0.280971	+	0.486656i	0.971624	−	0.236530i	$-0.0760103\pi$
$313$	1555.89	+	2694.87i	0.280971	+	0.486656i	−0.690653	+	0.723186i	$0.742677\pi$
$314$	−15155.4			−2.72379
$315$		0			0
$316$	−5676.53			−1.01054
$317$	−2466.79	−	4272.60i	−0.437062	−	0.757013i	0.560399	−	0.828222i	$-0.310648\pi$
$317$	−2466.79	−	4272.60i	−0.437062	−	0.757013i	−0.997461	+	0.0712090i	$0.977314\pi$
$318$	12145.7	−	6420.31i	2.14181	−	1.13218i
$319$	755.271	−	1308.17i	0.132561	−	0.229603i
$320$		0			0
$321$	133.504	−	3574.92i	0.0232132	−	0.621596i
$322$	−5295.44	−	9171.96i	−0.916469	−	1.58737i
$323$	12018.5			2.07036
$324$	−4905.32	+	6154.75i	−0.841104	+	1.05534i
$325$		0			0
$326$	−1438.38	−	2491.34i	−0.244369	−	0.423260i
$327$	−230.553	+	6173.68i	−0.0389896	+	1.04405i
$328$	−1048.41	+	1815.91i	−0.176491	+	0.305691i
$329$	1100.23	−	1905.65i	0.184369	−	0.319336i
$330$		0			0
$331$	−4386.39	−	7597.45i	−0.728392	−	1.26161i	−0.957563	−	0.288226i	$-0.906935\pi$
$331$	−4386.39	−	7597.45i	−0.728392	−	1.26161i	0.229171	−	0.973386i	$-0.426399\pi$
$332$	3865.16			0.638940
$333$	8867.91	+	663.260i	1.45933	+	0.109148i
$334$	10663.7			1.74697
$335$		0			0
$336$	1934.25	+	1215.17i	0.314053	+	0.197301i
$337$	−5171.06	+	8956.54i	−0.835863	+	1.44776i	0.0574635	+	0.998348i	$0.481699\pi$
$337$	−5171.06	+	8956.54i	−0.835863	+	1.44776i	−0.893326	+	0.449409i	$0.851635\pi$
$338$	−4638.68	+	8034.43i	−0.746482	+	1.29294i
$339$	−1181.00	−	741.954i	−0.189213	−	0.118871i
$340$		0			0
$341$	2027.46			0.321973
$342$	−7438.09	−	15439.6i	−1.17604	−	2.44116i
$343$	6721.27			1.05806
$344$	949.727	+	1644.98i	0.148854	+	0.257823i
$345$		0			0
$346$	3311.74	−	5736.10i	0.514567	−	0.891256i
$347$	669.161	−	1159.02i	0.103523	−	0.179307i	−0.809611	−	0.586967i	$-0.800322\pi$
$347$	669.161	−	1159.02i	0.103523	−	0.179307i	0.913134	+	0.407660i	$0.133655\pi$
$348$	91.5236	−	2450.79i	0.0140982	−	0.377518i
$349$	−5056.17	−	8757.55i	−0.775503	−	1.34321i	−0.934511	−	0.355934i	$-0.884163\pi$
$349$	−5056.17	−	8757.55i	−0.775503	−	1.34321i	0.159008	−	0.987277i	$-0.449170\pi$
$350$		0			0
$351$	−853.262	−	629.448i	−0.129754	−	0.0957193i
$352$	−8415.95			−1.27435
$353$	822.140	+	1423.99i	0.123961	+	0.214706i	0.921326	−	0.388791i	$-0.127107\pi$
$353$	822.140	+	1423.99i	0.123961	+	0.214706i	−0.797366	+	0.603497i	$0.793774\pi$
$354$	499.737	−	13381.8i	0.0750303	−	2.00914i
$355$		0			0
$356$	−8192.50	+	14189.8i	−1.21967	+	2.11253i
$357$	4902.96	−	2591.74i	0.726868	−	0.384229i
$358$	2181.10	+	3777.77i	0.321996	+	0.557714i
$359$	11283.0			1.65876			0.829379	−	0.558686i	$-0.188694\pi$
$359$	11283.0			1.65876			0.829379	+	0.558686i	$0.188694\pi$
$360$		0			0
$361$	14575.7			2.12504
$362$	1282.99	+	2222.21i	0.186278	+	0.322643i
$363$	−603.451	−	379.112i	−0.0872533	−	0.0548160i
$364$	530.420	−	918.715i	0.0763780	−	0.132291i
$365$		0			0
$366$	−6201.04	−	3895.74i	−0.885610	−	0.556376i
$367$	−139.011	−	240.774i	−0.0197720	−	0.0342461i	0.855970	−	0.517025i	$-0.172961\pi$
$367$	−139.011	−	240.774i	−0.0197720	−	0.0342461i	−0.875742	+	0.482779i	$0.839627\pi$
$368$	−6353.01			−0.899928
$369$	−2630.23	+	3859.05i	−0.371069	+	0.544429i
$370$		0			0
$371$	3964.39	+	6866.53i	0.554774	+	0.960896i
$372$	2910.18	−	1538.34i	0.405607	−	0.214407i
$373$	4916.70	−	8515.98i	0.682513	−	1.18215i	−0.291699	−	0.956510i	$-0.594220\pi$
$373$	4916.70	−	8515.98i	0.682513	−	1.18215i	0.974212	−	0.225637i	$-0.0724462\pi$
$374$	−6148.51	+	10649.5i	−0.850085	+	1.47239i
$375$		0			0
$376$	1025.85	+	1776.82i	0.140702	+	0.243704i
$377$	330.405			0.0451372
$378$	−6363.88	−	4694.61i	−0.865933	−	0.638796i
$379$	13511.9			1.83129			0.915644	−	0.401990i	$-0.131681\pi$
$379$	13511.9			1.83129			0.915644	+	0.401990i	$0.131681\pi$
$380$		0			0
$381$	28.1758	−	754.484i	0.00378869	−	0.101452i
$382$	7900.43	−	13683.9i	1.05817	−	1.83281i
$383$	−694.822	+	1203.47i	−0.0926991	+	0.160559i	−0.908646	−	0.417567i	$-0.862883\pi$
$383$	−694.822	+	1203.47i	−0.0926991	+	0.160559i	0.815947	+	0.578127i	$0.196216\pi$
$384$	−6692.78	+	3537.86i	−0.889426	+	0.470158i
$385$		0			0
$386$	58.1018			0.00766141
$387$	1836.13	+	3811.34i	0.241177	+	0.500623i
$388$	4268.38			0.558490
$389$	453.369	+	785.258i	0.0590918	+	0.102350i	0.894058	−	0.447951i	$-0.147846\pi$
$389$	453.369	+	785.258i	0.0590918	+	0.102350i	−0.834966	+	0.550301i	$0.814513\pi$
$390$		0			0
$391$	−7711.96	+	13357.5i	−0.997469	+	1.72767i
$392$	−1054.43	+	1826.32i	−0.135859	+	0.235314i
$393$	−1184.98	−	744.450i	−0.152097	−	0.0955536i
$394$	136.997	+	237.285i	0.0175172	+	0.0303407i
$395$		0			0
$396$	10043.8	+	751.206i	1.27454	+	0.0953271i
$397$	−1904.52			−0.240769			−0.120384	−	0.992727i	$-0.538413\pi$
$397$	−1904.52			−0.240769			−0.120384	+	0.992727i	$0.538413\pi$
$398$	−10627.9	−	18408.1i	−1.33851	−	2.31837i
$399$	8744.32	−	4622.32i	1.09715	−	0.579963i
$400$		0			0
$401$	5206.91	−	9018.64i	0.648431	−	1.12312i	−0.335067	−	0.942194i	$-0.608759\pi$
$401$	5206.91	−	9018.64i	0.648431	−	1.12312i	0.983498	−	0.180921i	$-0.0579078\pi$
$402$	−578.722	+	15496.8i	−0.0718011	+	1.92267i
$403$	221.735	+	384.057i	0.0274080	+	0.0474720i
$404$	3597.90			0.443075
$405$		0			0
$406$	2464.26			0.301229
$407$	−5690.02	−	9855.40i	−0.692982	−	1.20028i
$408$	−192.971	+	5167.31i	−0.0234154	+	0.627010i
$409$	−3124.74	+	5412.21i	−0.377771	+	0.654319i	−0.990738	−	0.135790i	$-0.956643\pi$
$409$	−3124.74	+	5412.21i	−0.377771	+	0.654319i	0.612966	+	0.790109i	$0.289976\pi$
$410$		0			0
$411$	−3800.82	+	2009.14i	−0.456157	+	0.241128i
$412$	8803.65	+	15248.4i	1.05273	+	1.82338i
$413$	7728.48			0.920808
$414$	21932.6	+	1640.42i	2.60370	+	0.194739i
$415$		0			0
$416$	−920.420	−	1594.21i	−0.108479	−	0.187891i
$417$	−747.413	−	469.555i	−0.0877721	−	0.0551419i
$418$	−10965.7	+	18993.2i	−1.28314	+	2.22246i
$419$	−1495.14	+	2589.65i	−0.174325	+	0.301940i	−0.939927	−	0.341374i	$-0.889108\pi$
$419$	−1495.14	+	2589.65i	−0.174325	+	0.301940i	0.765602	+	0.643314i	$0.222441\pi$
$420$		0			0
$421$	2346.32	+	4063.95i	0.271622	+	0.470463i	0.969277	−	0.245971i	$-0.0791067\pi$
$421$	2346.32	+	4063.95i	0.271622	+	0.470463i	−0.697656	+	0.716433i	$0.745773\pi$
$422$	13492.9			1.55645
$423$	1983.29	+	4116.82i	0.227969	+	0.473207i
$424$	−7392.79			−0.846758
$425$		0			0
$426$	−10260.3	+	5423.67i	−1.16693	+	0.616849i
$427$	2113.24	−	3660.24i	0.239501	−	0.414828i
$428$	−3716.43	+	6437.04i	−0.419720	+	0.726977i
$429$	−50.6371	+	1355.94i	−0.00569879	+	0.152601i
$430$		0			0
$431$	817.709			0.0913866			0.0456933	−	0.998956i	$-0.485450\pi$
$431$	817.709			0.0913866			0.0456933	+	0.998956i	$0.485450\pi$
$432$	−4347.52	+	1897.93i	−0.484190	+	0.211376i
$433$	−5547.29			−0.615671			−0.307836	−	0.951440i	$-0.599605\pi$
$433$	−5547.29			−0.615671			−0.307836	+	0.951440i	$0.599605\pi$
$434$	1653.77	+	2864.41i	0.182911	+	0.316811i
$435$		0			0
$436$	6418.06	−	11116.4i	0.704975	−	1.22105i
$437$	−13754.1	+	23822.8i	−1.50560	+	2.60778i
$438$	−21676.4	+	11458.3i	−2.36470	+	1.25000i
$439$	−6690.82	−	11588.8i	−0.727416	−	1.25992i	−0.957972	−	0.286862i	$-0.907388\pi$
$439$	−6690.82	−	11588.8i	−0.727416	−	1.25992i	0.230556	−	0.973059i	$-0.425946\pi$
$440$		0			0
$441$	−2645.32	+	3881.19i	−0.285641	+	0.419089i
$442$	−2689.76			−0.289454
$443$	−5418.44	−	9385.00i	−0.581123	−	1.00654i	−0.995347	−	0.0963598i	$-0.969280\pi$
$443$	−5418.44	−	9385.00i	−0.581123	−	1.00654i	0.414223	−	0.910175i	$-0.364053\pi$
$444$	−15645.2	−	9828.95i	−1.67227	−	1.05059i
$445$		0			0
$446$	10555.6	−	18282.8i	1.12068	−	1.94107i
$447$	7683.77	+	4827.26i	0.813043	+	0.510786i
$448$	−5106.32	−	8844.41i	−0.538507	−	0.932721i
$449$	2970.62			0.312232			0.156116	−	0.987739i	$-0.450103\pi$
$449$	2970.62			0.312232			0.156116	+	0.987739i	$0.450103\pi$
$450$		0			0
$451$	5976.44			0.623991
$452$	1448.93	+	2509.61i	0.150778	+	0.261155i
$453$	−1574.94	+	832.524i	−0.163349	+	0.0863475i
$454$	−14279.2	+	24732.3i	−1.47612	+	2.55671i
$455$		0			0
$456$	−344.159	+	9215.79i	−0.0353437	+	0.946423i
$457$	8088.16	+	14009.1i	0.827896	+	1.43396i	0.899686	+	0.436538i	$0.143796\pi$
$457$	8088.16	+	14009.1i	0.827896	+	1.43396i	−0.0717901	+	0.997420i	$0.522871\pi$
$458$	−71.2317			−0.00726733
$459$	−1286.99	+	11444.8i	−0.130875	+	1.16383i
$460$		0			0
$461$	−2865.91	−	4963.90i	−0.289541	−	0.501500i	0.684159	−	0.729333i	$-0.260169\pi$
$461$	−2865.91	−	4963.90i	−0.289541	−	0.501500i	−0.973700	+	0.227833i	$0.926836\pi$
$462$	−377.667	+	10113.0i	−0.0380317	+	1.01840i
$463$	7020.03	−	12159.1i	0.704641	−	1.22047i	−0.262181	−	0.965019i	$-0.584442\pi$
$463$	7020.03	−	12159.1i	0.704641	−	1.22047i	0.966821	−	0.255454i	$-0.0822251\pi$
$464$	739.101	−	1280.16i	0.0739481	−	0.128082i
$465$		0			0
$466$	1533.76	+	2656.55i	0.152468	+	0.264082i
$467$	−3.48921			−0.000345742			−0.000172871	−	1.00000i	$-0.500055\pi$
$467$	−3.48921			−0.000345742			−0.000172871		1.00000i	$0.500055\pi$
$468$	956.148	+	1984.72i	0.0944401	+	0.196034i
$469$	−8949.99			−0.881177
$470$		0			0
$471$	15380.7	+	9662.80i	1.50469	+	0.945305i
$472$	−3603.01	+	6240.60i	−0.351360	+	0.608574i
$473$	2706.94	−	4688.56i	0.263140	−	0.455772i
$474$	10029.8	+	6301.12i	0.971907	+	0.610591i
$475$		0			0
$476$	−11522.7			−1.10954
$477$	−16419.7	−	1228.09i	−1.57612	−	0.117883i
$478$	26498.4			2.53559
$479$	1825.54	+	3161.93i	0.174136	+	0.301612i	0.939862	−	0.341555i	$-0.110954\pi$
$479$	1825.54	+	3161.93i	0.174136	+	0.301612i	−0.765726	+	0.643167i	$0.777620\pi$
$480$		0			0
$481$	1244.59	−	2155.69i	0.117980	−	0.204348i
$482$	6694.44	−	11595.1i	0.632621	−	1.09573i
$483$	−473.700	+	12684.6i	−0.0446255	+	1.19497i
$484$	740.350	+	1282.32i	0.0695295	+	0.120429i
$485$		0			0
$486$	15499.1	−	5429.70i	1.44661	−	0.506782i
$487$	13646.8			1.26981			0.634903	−	0.772592i	$-0.281040\pi$
$487$	13646.8			1.26981			0.634903	+	0.772592i	$0.281040\pi$
$488$	1970.38	+	3412.80i	0.182777	+	0.316579i
$489$	−128.669	+	3445.46i	−0.0118990	+	0.318628i
$490$		0			0
$491$	−20.8492	+	36.1118i	−0.00191631	+	0.00331915i	−0.866982	−	0.498340i	$-0.833943\pi$
$491$	−20.8492	+	36.1118i	−0.00191631	+	0.00331915i	0.865066	+	0.501659i	$0.167277\pi$
$492$	8578.50	−	4534.67i	0.786074	−	0.415525i
$493$	−1794.40	−	3107.99i	−0.163926	−	0.283929i
$494$	−4797.12			−0.436908
$495$		0			0
$496$	1984.05			0.179610
$497$	−3348.99	−	5800.62i	−0.302259	−	0.523528i
$498$	−6829.31	−	4290.45i	−0.614515	−	0.386063i
$499$	1196.47	−	2072.34i	0.107337	−	0.185913i	−0.807354	−	0.590068i	$-0.799101\pi$
$499$	1196.47	−	2072.34i	0.107337	−	0.185913i	0.914691	+	0.404155i	$0.132434\pi$
$500$		0			0
$501$	−10822.2	−	6798.94i	−0.965070	−	0.606295i
$502$	5946.69	+	10300.0i	0.528713	+	0.915757i
$503$	1254.89			0.111238			0.0556190	−	0.998452i	$-0.482287\pi$
$503$	1254.89			0.111238			0.0556190	+	0.998452i	$0.482287\pi$
$504$	1846.95	+	3833.81i	0.163234	+	0.338833i
$505$		0			0
$506$	−14072.9	−	24375.0i	−1.23640	−	2.14150i
$507$	9830.23	−	5196.35i	0.861097	−	0.455183i
$508$	−784.349	+	1358.53i	−0.0685037	+	0.118652i
$509$	−273.965	+	474.521i	−0.0238571	+	0.0413217i	−0.877707	−	0.479197i	$-0.840928\pi$
$509$	−273.965	+	474.521i	−0.0238571	+	0.0413217i	0.853850	+	0.520519i	$0.174261\pi$
$510$		0			0
$511$	−7075.25	−	12254.7i	−0.612506	−	1.06089i
$512$	−11514.9			−0.993929
$513$	−2295.32	+	20411.5i	−0.197545	+	1.75671i
$514$	−3121.73			−0.267886
$515$		0			0
$516$	328.027	−	8783.80i	0.0279856	−	0.749390i
$517$	2923.90	−	5064.35i	0.248729	−	0.430812i
$518$	9282.53	−	16077.8i	0.787357	−	1.36374i
$519$	−7018.20	+	3709.88i	−0.593573	+	0.313768i
$520$		0			0
$521$	12151.4			1.02181			0.510903	−	0.859638i	$-0.329311\pi$
$521$	12151.4			1.02181			0.510903	+	0.859638i	$0.329311\pi$
$522$	−2882.17	+	4228.68i	−0.241665	+	0.354568i
$523$	18913.8			1.58134			0.790672	−	0.612241i	$-0.209732\pi$
$523$	18913.8			1.58134			0.790672	+	0.612241i	$0.209732\pi$
$524$	1453.80	+	2518.06i	0.121202	+	0.209927i
$525$		0			0
$526$	−11333.2	+	19629.7i	−0.939452	+	1.62718i
$527$	2408.45	−	4171.55i	0.199077	−	0.344812i
$528$	5140.37	+	3229.38i	0.423685	+	0.266176i
$529$	−11567.9	−	20036.1i	−0.950757	−	1.64676i
$530$		0			0
$531$	−9039.14	+	13262.1i	−0.738730	+	1.08386i
$532$	−20550.4			−1.67476
$533$	653.621	+	1132.11i	0.0531172	+	0.0920017i
$534$	30226.4	−	15977.9i	2.44948	−	1.29482i
$535$		0			0
$536$	4172.48	−	7226.94i	0.336238	−	0.582381i
$537$	195.109	−	5224.56i	0.0156789	−	0.419845i
$538$	694.540	+	1202.98i	0.0556575	+	0.0964016i
$539$	6010.73			0.480335
$540$		0			0
$541$	−9936.16			−0.789628			−0.394814	−	0.918761i	$-0.629191\pi$
$541$	−9936.16			−0.789628			−0.394814	+	0.918761i	$0.629191\pi$
$542$	−2263.23	−	3920.02i	−0.179361	−	0.310663i
$543$	114.769	−	3073.26i	0.00907039	−	0.242884i
$544$	−9997.44	+	17316.1i	−0.787935	+	1.36474i
$545$		0			0
$546$	−1957.00	+	1034.48i	−0.153391	+	0.0810840i
$547$	−6359.84	−	11015.6i	−0.497125	−	0.861045i	0.502870	−	0.864362i	$-0.332278\pi$
$547$	−6359.84	−	11015.6i	−0.497125	−	0.861045i	−0.999994	+	0.00331677i	$0.998944\pi$
$548$	8932.47			0.696307
$549$	3809.38	+	7907.32i	0.296139	+	0.614711i
$550$		0			0
$551$	−3200.27	−	5543.03i	−0.247434	−	0.428568i
$552$	−10021.7	−	6296.05i	−0.772741	−	0.485467i
$553$	−3418.04	+	5920.22i	−0.262839	+	0.455250i
$554$	7221.40	−	12507.8i	0.553805	−	0.959218i
$555$		0			0
$556$	916.971	+	1588.24i	0.0699429	+	0.121145i
$557$	−16006.5			−1.21763			−0.608813	−	0.793314i	$-0.708354\pi$
$557$	−16006.5			−1.21763			−0.608813	+	0.793314i	$0.708354\pi$
$558$	−6849.57	−	512.302i	−0.519651	−	0.0388665i
$559$	1184.19			0.0895993
$560$		0			0
$561$	13029.9	−	6887.69i	0.980608	−	0.518358i
$562$	−12142.1	+	21030.7i	−0.911355	+	1.57851i
$563$	−2313.29	+	4006.74i	−0.173168	+	0.299936i	−0.939526	−	0.342478i	$-0.888734\pi$
$563$	−2313.29	+	4006.74i	−0.173168	+	0.299936i	0.766358	+	0.642414i	$0.222067\pi$
$564$	354.318	−	9487.82i	0.0264530	−	0.708350i
$565$		0			0
$566$	−27173.9			−2.01803
$567$	3465.30	+	8821.90i	0.256665	+	0.653412i
$568$	6245.19			0.461342
$569$	−8429.52	−	14600.4i	−0.621061	−	1.07571i	−0.989288	−	0.145974i	$-0.953369\pi$
$569$	−8429.52	−	14600.4i	−0.621061	−	1.07571i	0.368227	−	0.929736i	$-0.379965\pi$
$570$		0			0
$571$	−8074.57	+	13985.6i	−0.591787	+	1.02501i	0.402205	+	0.915550i	$0.368244\pi$
$571$	−8074.57	+	13985.6i	−0.591787	+	1.02501i	−0.993992	+	0.109455i	$0.965089\pi$
$572$	1409.62	−	2441.53i	0.103040	−	0.178471i
$573$	−16742.5	+	8850.23i	−1.22064	+	0.645242i
$574$	4874.90	+	8443.58i	0.354485	+	0.613986i
$575$		0			0
$576$	21149.4	+	1581.83i	1.52990	+	0.114427i
$577$	7430.10			0.536082			0.268041	−	0.963408i	$-0.413624\pi$
$577$	7430.10			0.536082			0.268041	+	0.963408i	$0.413624\pi$
$578$	3957.79	+	6855.10i	0.284814	+	0.493312i
$579$	−58.9656	−	37.0446i	−0.00423234	−	0.00265893i
$580$		0			0
$581$	2327.35	−	4031.09i	0.166187	−	0.287845i
$582$	−7541.75	−	4738.03i	−0.537140	−	0.337453i
$583$	10535.6	+	18248.2i	0.748437	+	1.29633i
$584$	13193.9			0.934875
$585$		0			0
$586$	−9116.84			−0.642685
$587$	−8576.06	−	14854.2i	−0.603019	−	1.04446i	−0.992361	−	0.123366i	$-0.960631\pi$
$587$	−8576.06	−	14854.2i	−0.603019	−	1.04446i	0.389343	−	0.921093i	$-0.372702\pi$
$588$	8627.70	−	4560.68i	0.605103	−	0.319863i
$589$	4295.41	−	7439.87i	0.300491	−	0.520466i
$590$		0			0
$591$	12.2549	−	328.159i	0.000852963	−	0.0228404i
$592$	−5568.19	−	9644.39i	−0.386573	−	0.669564i
$593$	−15477.7			−1.07183			−0.535913	−	0.844273i	$-0.680033\pi$
$593$	−15477.7			−1.07183			−0.535913	+	0.844273i	$0.680033\pi$
$594$	−16912.3	−	12476.2i	−1.16822	−	0.861790i
$595$		0			0
$596$	−9426.92	−	16327.9i	−0.647889	−	1.12218i
$597$	−950.713	+	25457.9i	−0.0651760	+	1.74526i
$598$	3078.20	−	5331.59i	0.210496	−	0.364590i
$599$	−9479.61	+	16419.2i	−0.646622	+	1.11998i	0.337302	+	0.941396i	$0.390486\pi$
$599$	−9479.61	+	16419.2i	−0.646622	+	1.11998i	−0.983924	+	0.178586i	$0.942848\pi$
$600$		0			0
$601$	1046.80	+	1813.12i	0.0710482	+	0.123059i	0.899361	−	0.437207i	$-0.144032\pi$
$601$	1046.80	+	1813.12i	0.0710482	+	0.123059i	−0.828313	+	0.560266i	$0.810699\pi$
$602$	8832.06			0.597953
$603$	10467.8	−	15358.3i	0.706935	−	1.03721i
$604$	3701.33			0.249346
$605$		0			0
$606$	−6357.09	−	3993.78i	−0.426137	−	0.267716i
$607$	3067.63	−	5313.28i	0.205125	−	0.355288i	−0.745047	−	0.667012i	$-0.767573\pi$
$607$	3067.63	−	5313.28i	0.205125	−	0.355288i	0.950173	+	0.311724i	$0.100906\pi$
$608$	−17830.2	+	30882.8i	−1.18933	+	2.05997i
$609$	−2500.89	−	1571.16i	−0.166406	−	0.104543i
$610$		0			0
$611$	1279.11			0.0846924
$612$	13476.8	−	19773.0i	0.890141	−	1.30600i
$613$	−12762.8			−0.840922			−0.420461	−	0.907311i	$-0.638132\pi$
$613$	−12762.8			−0.840922			−0.420461	+	0.907311i	$0.638132\pi$
$614$	4378.96	+	7584.59i	0.287819	+	0.498516i
$615$		0			0
$616$	2722.91	−	4716.21i	0.178099	−	0.308477i
$617$	−367.040	+	635.732i	−0.0239489	+	0.0414807i	−0.877751	−	0.479116i	$-0.840957\pi$
$617$	−367.040	+	635.732i	−0.0239489	+	0.0414807i	0.853803	+	0.520597i	$0.174291\pi$
$618$	1371.09	−	36714.5i	0.0892446	−	2.38976i
$619$	5324.85	+	9222.91i	0.345757	+	0.598869i	0.985491	−	0.169727i	$-0.0542887\pi$
$619$	5324.85	+	9222.91i	0.345757	+	0.598869i	−0.639734	+	0.768597i	$0.720955\pi$
$620$		0			0
$621$	−21212.8	−	15648.6i	−1.37076	−	1.01120i
$622$	−23382.5			−1.50732
$623$	9865.99	+	17088.4i	0.634466	+	1.09893i
$624$	−49.5530	+	1326.91i	−0.00317902	+	0.0851267i
$625$		0			0
$626$	−6745.47	+	11683.5i	−0.430676	+	0.745952i
$627$	23238.5	−	12284.0i	1.48015	−	0.782420i
$628$	−18870.0	−	32683.9i	−1.19904	−	2.07680i
$629$	−27037.1			−1.71389
$630$		0			0
$631$	−3465.43			−0.218632			−0.109316	−	0.994007i	$-0.534866\pi$
$631$	−3465.43			−0.218632			−0.109316	+	0.994007i	$0.534866\pi$
$632$	−3186.98	−	5520.00i	−0.200587	−	0.347427i
$633$	−13693.5	−	8602.79i	−0.859821	−	0.540174i
$634$	10694.6	−	18523.7i	0.669935	−	1.16036i
$635$		0			0
$636$	28968.5	+	18199.2i	1.80609	+	1.13466i
$637$	657.371	+	1138.60i	0.0408885	+	0.0708209i
$638$	6548.89			0.406384
$639$	13870.9	+	1037.45i	0.858721	+	0.0642266i
$640$		0			0
$641$	14605.0	+	25296.7i	0.899945	+	1.55875i	0.827563	+	0.561373i	$0.189727\pi$
$641$	14605.0	+	25296.7i	0.899945	+	1.55875i	0.0723819	+	0.997377i	$0.476940\pi$
$642$	13711.8	−	7248.19i	0.842932	−	0.445581i
$643$	8512.87	−	14744.7i	0.522107	−	0.904316i	−0.477562	−	0.878598i	$-0.658479\pi$
$643$	8512.87	−	14744.7i	0.522107	−	0.904316i	0.999669	−	0.0257183i	$-0.00818729\pi$
$644$	13186.7	−	22840.0i	0.806877	−	1.39755i
$645$		0			0
$646$	26052.7	+	45124.7i	1.58674	+	2.74831i
$647$	8673.26			0.527019			0.263509	−	0.964657i	$-0.415120\pi$
$647$	8673.26			0.527019			0.263509	+	0.964657i	$0.415120\pi$
$648$	−8739.03	−	1314.60i	−0.529786	−	0.0796948i
$649$	20538.8			1.24225
$650$		0			0
$651$	147.937	−	3961.40i	0.00890645	−	0.238494i
$652$	3581.85	−	6203.95i	0.215147	−	0.372646i
$653$	540.335	−	935.888i	0.0323812	−	0.0560859i	−0.849381	−	0.527781i	$-0.823024\pi$
$653$	540.335	−	935.888i	0.0323812	−	0.0560859i	0.881762	+	0.471695i	$0.156358\pi$
$654$	−23679.5	+	12517.2i	−1.41582	+	0.748412i
$655$		0			0
$656$	5848.49			0.348087
$657$	29304.3	+	2191.76i	1.74013	+	0.130150i
$658$	9539.95			0.565206
$659$	−3484.81	−	6035.86i	−0.205992	−	0.356789i	0.744456	−	0.667671i	$-0.232709\pi$
$659$	−3484.81	−	6035.86i	−0.205992	−	0.356789i	−0.950448	+	0.310882i	$0.899375\pi$
$660$		0			0
$661$	−5448.66	+	9437.36i	−0.320618	+	0.555326i	−0.980616	−	0.195941i	$-0.937224\pi$
$661$	−5448.66	+	9437.36i	−0.320618	+	0.555326i	0.659998	+	0.751267i	$0.270557\pi$
$662$	19017.0	−	32938.4i	1.11649	−	1.93382i
$663$	2729.75	+	1714.94i	0.159901	+	0.100456i
$664$	2170.02	+	3758.58i	0.126827	+	0.219671i
$665$		0			0
$666$	16732.9	+	34733.3i	0.973554	+	2.02085i
$667$	8214.14			0.476841
$668$	13277.3	+	22997.0i	0.769034	+	1.33201i
$669$	−22369.3	+	11824.6i	−1.29274	+	0.683356i
$670$		0			0
$671$	5616.05	−	9727.28i	0.323108	−	0.559639i
$672$	−614.084	+	16443.7i	−0.0352512	+	0.943945i
$673$	−14803.9	−	25641.2i	−0.847919	−	1.46864i	−0.883062	−	0.469257i	$-0.844522\pi$
$673$	−14803.9	−	25641.2i	−0.847919	−	1.46864i	0.0351426	−	0.999382i	$-0.488811\pi$
$674$	−44837.8			−2.56244
$675$		0			0
$676$	−23102.5			−1.31443
$677$	−3193.71	−	5531.66i	−0.181306	−	0.314031i	0.761020	−	0.648729i	$-0.224699\pi$
$677$	−3193.71	−	5531.66i	−0.181306	−	0.314031i	−0.942326	+	0.334698i	$0.891366\pi$
$678$	225.657	−	6042.56i	0.0127821	−	0.342276i
$679$	2570.14	−	4451.62i	0.145262	−	0.251601i
$680$		0			0
$681$	30260.4	−	15995.9i	1.70276	−	0.900093i
$682$	4394.97	+	7612.31i	0.246762	+	0.427405i
$683$	−19929.2			−1.11650			−0.558251	−	0.829672i	$-0.688527\pi$
$683$	−19929.2			−1.11650			−0.558251	+	0.829672i	$0.688527\pi$
$684$	24035.5	−	35264.7i	1.34360	−	1.97131i
$685$		0			0
$686$	14569.9	+	25235.8i	0.810904	+	1.40453i
$687$	72.2907	+	45.4159i	0.00401465	+	0.00252216i
$688$	2648.99	−	4588.18i	0.146790	−	0.254248i
$689$	−2304.47	+	3991.46i	−0.127421	+	0.220700i
$690$		0			0
$691$	−6473.59	−	11212.6i	−0.356392	−	0.617289i	0.630963	−	0.775813i	$-0.282660\pi$
$691$	−6473.59	−	11212.6i	−0.356392	−	0.617289i	−0.987355	+	0.158524i	$0.949327\pi$
$692$	16493.8			0.906069
$693$	6831.16	−	10022.6i	0.374451	−	0.549390i
$694$	5802.23			0.317362
$695$		0			0
$696$	2434.60	−	1286.95i	0.132591	−	0.0700886i
$697$	7099.52	−	12296.7i	0.385815	−	0.668252i
$698$	21920.8	−	37967.9i	1.18870	−	2.05889i
$699$	137.201	−	3673.94i	0.00742408	−	0.198800i
$700$		0			0
$701$	−10692.9			−0.576125			−0.288063	−	0.957612i	$-0.593011\pi$
$701$	−10692.9			−0.576125			−0.288063	+	0.957612i	$0.593011\pi$
$702$	513.696	−	4568.14i	0.0276185	−	0.245603i
$703$	−48220.0			−2.58699
$704$	−13570.3	−	23504.5i	−0.726492	−	1.25832i
$705$		0			0
$706$	−3564.35	+	6173.63i	−0.190009	+	0.329104i
$707$	2166.42	−	3752.35i	0.115243	−	0.199607i
$708$	29481.1	−	15584.0i	1.56493	−	0.827234i
$709$	11786.7	+	20415.2i	0.624343	+	1.08139i	0.988668	+	0.150122i	$0.0479665\pi$
$709$	11786.7	+	20415.2i	0.624343	+	1.08139i	−0.364325	+	0.931272i	$0.618700\pi$
$710$		0			0
$711$	−6161.44	−	12789.6i	−0.324996	−	0.674610i
$712$	−18398.1			−0.968394
$713$	5512.52	+	9547.97i	0.289545	+	0.501507i
$714$	20359.3	+	12790.5i	1.06712	+	0.670410i
$715$		0			0
$716$	−5431.37	+	9407.41i	−0.283492	+	0.491022i
$717$	−26892.4	−	16894.9i	−1.40072	−	0.879988i
$718$	24458.5	+	42363.3i	1.27128	+	2.20193i
$719$	27013.2			1.40114			0.700572	−	0.713581i	$-0.252928\pi$
$719$	27013.2			1.40114			0.700572	+	0.713581i	$0.252928\pi$
$720$		0			0
$721$	21204.0			1.09525
$722$	31596.1	+	54726.0i	1.62865	+	2.82090i
$723$	−14186.8	+	7499.25i	−0.729754	+	0.385754i
$724$	−3194.91	+	5533.74i	−0.164003	+	0.284061i
$725$		0			0
$726$	115.303	−	3087.54i	0.00589432	−	0.157836i
$727$	−8927.02	−	15462.1i	−0.455412	−	0.788797i	0.543299	−	0.839539i	$-0.317175\pi$
$727$	−8927.02	−	15462.1i	−0.455412	−	0.788797i	−0.998712	+	0.0507416i	$0.983842\pi$
$728$	1191.18			0.0606428
$729$	−19191.4	−	4371.50i	−0.975025	−	0.222095i
$730$		0			0
$731$	−6431.24	−	11139.2i	−0.325401	−	0.563611i
$732$	680.552	−	18223.6i	0.0343633	−	0.920169i
$733$	4795.40	−	8305.88i	0.241640	−	0.418533i	−0.719541	−	0.694449i	$-0.755648\pi$
$733$	4795.40	−	8305.88i	0.241640	−	0.418533i	0.961182	+	0.275916i	$0.0889813\pi$
$734$	602.676	−	1043.87i	0.0303068	−	0.0524929i
$735$		0			0
$736$	−22882.4	−	39633.5i	−1.14600	−	1.98493i
$737$	−23785.1			−1.18878
$738$	−20190.9	−	1510.14i	−1.00710	−	0.0753240i
$739$	−6237.43			−0.310484			−0.155242	−	0.987876i	$-0.549616\pi$
$739$	−6237.43			−0.310484			−0.155242	+	0.987876i	$0.549616\pi$
$740$		0			0
$741$	4868.44	+	3058.55i	0.241359	+	0.151631i
$742$	−17187.4	+	29769.5i	−0.850365	+	1.47288i
$743$	−8567.24	+	14838.9i	−0.423017	+	0.732687i	−0.996233	−	0.0867173i	$-0.972362\pi$
$743$	−8567.24	+	14838.9i	−0.423017	+	0.732687i	0.573216	+	0.819404i	$0.305696\pi$
$744$	3129.79	+	1966.26i	0.154225	+	0.0968905i
$745$		0			0
$746$	42632.3			2.09233
$747$	4195.34	+	8708.47i	0.205488	+	0.426541i
$748$	−30622.1			−1.49686
$749$	4475.59	+	7751.94i	0.218337	+	0.378171i
$750$		0			0
$751$	−19570.8	+	33897.7i	−0.950932	+	1.64706i	−0.207518	+	0.978231i	$0.566538\pi$
$751$	−19570.8	+	33897.7i	−0.950932	+	1.64706i	−0.743414	+	0.668831i	$0.766795\pi$
$752$	2861.30	−	4955.92i	0.138751	−	0.240324i
$753$	531.958	−	14244.6i	0.0257445	−	0.689378i
$754$	716.227	+	1240.54i	0.0345934	+	0.0599176i
$755$		0			0
$756$	2200.63	−	19569.5i	0.105868	−	0.941448i
$757$	−3774.26			−0.181212			−0.0906062	−	0.995887i	$-0.528880\pi$
$757$	−3774.26			−0.181212			−0.0906062	+	0.995887i	$0.528880\pi$
$758$	29290.0	+	50731.8i	1.40351	+	2.43095i
$759$	−1258.88	+	33709.9i	−0.0602036	+	1.61211i
$760$		0			0
$761$	−12998.9	+	22514.8i	−0.619200	+	1.07249i	0.370432	+	0.928860i	$0.379210\pi$
$761$	−12998.9	+	22514.8i	−0.619200	+	1.07249i	−0.989632	+	0.143627i	$0.954124\pi$
$762$	2893.87	−	1529.73i	0.137577	−	0.0727245i
$763$	−7729.08	−	13387.2i	−0.366725	−	0.635187i
$764$	39347.3			1.86327
$765$		0			0
$766$	−6024.73			−0.284181
$767$	2246.25	+	3890.63i	0.105746	+	0.183158i
$768$	−142.459	−	89.4984i	−0.00669341	−	0.00420507i
$769$	−7817.68	+	13540.6i	−0.366597	+	0.634964i	−0.989031	−	0.147708i	$-0.952810\pi$
$769$	−7817.68	+	13540.6i	−0.366597	+	0.634964i	0.622434	+	0.782672i	$0.286144\pi$
$770$		0			0
$771$	3168.14	+	1990.35i	0.147987	+	0.0929712i
$772$	72.3426	+	125.301i	0.00337262	+	0.00584156i
$773$	5936.28			0.276213			0.138107	−	0.990417i	$-0.455898\pi$
$773$	5936.28			0.276213			0.138107	+	0.990417i	$0.455898\pi$
$774$	−10329.9	+	15155.9i	−0.479715	+	0.703833i
$775$		0			0
$776$	2396.40	+	4150.68i	0.110858	+	0.192011i
$777$	−19671.4	+	10398.5i	−0.908248	+	0.480108i
$778$	−1965.56	+	3404.45i	−0.0905767	+	0.156883i
$779$	12661.8	−	21930.9i	0.582358	−	1.00867i
$780$		0			0
$781$	−8900.11	−	15415.4i	−0.407773	−	0.706284i
$782$	−66869.7			−3.05787
$783$	5621.14	−	2453.94i	0.256556	−	0.112001i
$784$	5882.04			0.267950
$785$		0			0
$786$	226.416	−	6062.89i	0.0102748	−	0.275135i
$787$	−5193.86	+	8996.04i	−0.235249	+	0.407464i	−0.959345	−	0.282236i	$-0.908924\pi$
$787$	−5193.86	+	8996.04i	−0.235249	+	0.407464i	0.724096	+	0.689699i	$0.242257\pi$
$788$	−341.149	+	590.887i	−0.0154225	+	0.0267126i
$789$	24017.2	−	12695.7i	1.08370	−	0.572851i
$790$		0			0
$791$	3489.80			0.156869
$792$	4908.38	+	10188.6i	0.220217	+	0.457114i
$793$	2456.82			0.110018
$794$	−4128.48	−	7150.73i	−0.184527	−	0.319610i
$795$		0			0
$796$	26465.6	−	45839.8i	1.17845	−	2.04114i
$797$	−697.430	+	1207.98i	−0.0309966	+	0.0536876i	−0.881108	−	0.472916i	$-0.843201\pi$
$797$	−697.430	+	1207.98i	−0.0309966	+	0.0536876i	0.850111	+	0.526604i	$0.176535\pi$
$798$	36310.3	+	22811.6i	1.61074	+	1.01193i
$799$	−6946.71	−	12032.0i	−0.307580	−	0.532745i
$800$		0			0
$801$	−40863.0	−	3056.28i	−1.80252	−	0.134817i
$802$	45148.6			1.98785
$803$	−18802.8	−	32567.4i	−0.826323	−	1.43123i
$804$	−34140.7	+	18047.1i	−1.49757	+	0.791630i
$805$		0			0
$806$	−961.322	+	1665.06i	−0.0420113	+	0.0727658i
$807$	62.1296	−	1663.69i	0.00271012	−	0.0725708i
$808$	2019.97	+	3498.69i	0.0879483	+	0.152331i
$809$	−7633.11			−0.331726			−0.165863	−	0.986149i	$-0.553041\pi$
$809$	−7633.11			−0.331726			−0.165863	+	0.986149i	$0.553041\pi$
$810$		0			0
$811$	−38117.1			−1.65040			−0.825199	−	0.564842i	$-0.808937\pi$
$811$	−38117.1			−1.65040			−0.825199	+	0.564842i	$0.808937\pi$
$812$	3068.25	+	5314.36i	0.132604	+	0.229677i
$813$	−202.456	+	5421.29i	−0.00873361	+	0.233866i
$814$	24668.8	−	42727.6i	1.06221	−	1.83981i
$815$		0			0
$816$	12750.9	−	6740.23i	0.547022	−	0.289161i
$817$	−11470.0	−	19866.6i	−0.491167	−	0.850727i
$818$	−27094.3			−1.15811
$819$	2645.66	+	197.878i	0.112878	+	0.00844250i
$820$		0			0
$821$	−1965.53	−	3404.41i	−0.0835537	−	0.144719i	0.821220	−	0.570611i	$-0.193294\pi$
$821$	−1965.53	−	3404.41i	−0.0835537	−	0.144719i	−0.904774	+	0.425892i	$0.859960\pi$
$822$	−15782.7	−	9915.32i	−0.669689	−	0.420726i
$823$	−10749.1	+	18618.0i	−0.455274	+	0.788558i	−0.998704	−	0.0508966i	$-0.983792\pi$
$823$	−10749.1	+	18618.0i	−0.455274	+	0.788558i	0.543430	+	0.839455i	$0.317125\pi$
$824$	−9885.27	+	17121.8i	−0.417925	+	0.723867i
$825$		0			0
$826$	16753.2	+	29017.5i	0.705714	+	1.22233i
$827$	5272.26			0.221686			0.110843	−	0.993838i	$-0.464645\pi$
$827$	5272.26			0.221686			0.110843	+	0.993838i	$0.464645\pi$
$828$	23770.7	+	49341.9i	0.997690	+	2.07095i
$829$	−13595.1			−0.569573			−0.284786	−	0.958591i	$-0.591923\pi$
$829$	−13595.1			−0.569573			−0.284786	+	0.958591i	$0.591923\pi$
$830$		0			0
$831$	−15303.5	+	8089.57i	−0.638836	+	0.337694i
$832$	2968.27	−	5141.19i	0.123685	−	0.214229i
$833$	7140.24	−	12367.3i	0.296992	−	0.514406i
$834$	142.810	−	3824.11i	0.00592937	−	0.158775i
$835$		0			0
$836$	−54613.8			−2.25940
$837$	6624.77	+	4887.07i	0.273579	+	0.201818i
$838$	−12964.2			−0.534416
$839$	−7738.30	−	13403.1i	−0.318422	−	0.551522i	0.661737	−	0.749736i	$-0.269819\pi$
$839$	−7738.30	−	13403.1i	−0.318422	−	0.551522i	−0.980159	+	0.198213i	$0.936486\pi$
$840$		0			0
$841$	11238.9	−	19466.3i	0.460817	−	0.798159i
$842$	−10172.4	+	17619.1i	−0.416346	+	0.721132i
$843$	25731.3	−	13601.8i	1.05128	−	0.555718i
$844$	16800.0	+	29098.4i	0.685165	+	1.18674i
$845$		0			0
$846$	−11157.8	+	16370.6i	−0.453444	+	0.665288i
$847$	1783.16			0.0723380
$848$	10310.0	+	17857.5i	0.417508	+	0.723146i
$849$	27577.9	+	17325.6i	1.11481	+	0.700367i
$850$		0			0
$851$	30941.6	−	53592.4i	1.24637	−	2.15878i
$852$	−24471.7	−	15374.1i	−0.984020	−	0.618201i
$853$	15155.0	+	26249.2i	0.608320	+	1.05364i	0.991517	+	0.129974i	$0.0414894\pi$
$853$	15155.0	+	26249.2i	0.608320	+	1.05364i	−0.383198	+	0.923666i	$0.625177\pi$
$854$	18323.7			0.734221
$855$		0			0
$856$	−8346.06			−0.333250
$857$	15576.6	+	26979.5i	0.620872	+	1.07538i	0.989324	+	0.145734i	$0.0465545\pi$
$857$	15576.6	+	26979.5i	0.620872	+	1.07538i	−0.368452	+	0.929647i	$0.620112\pi$
$858$	−5200.81	+	2749.19i	−0.206938	+	0.109389i
$859$	8955.94	−	15512.1i	0.355731	−	0.616144i	−0.631512	−	0.775366i	$-0.717565\pi$
$859$	8955.94	−	15512.1i	0.355731	−	0.616144i	0.987243	+	0.159222i	$0.0508987\pi$
$860$		0			0
$861$	436.081	−	11677.3i	0.0172609	−	0.462206i
$862$	1772.57	+	3070.18i	0.0700394	+	0.121312i
$863$	34410.6			1.35730			0.678649	−	0.734462i	$-0.262566\pi$
$863$	34410.6			1.35730			0.678649	+	0.734462i	$0.262566\pi$
$864$	−27499.4	−	20286.2i	−1.08281	−	0.798785i
$865$		0			0
$866$	−12025.0	−	20827.9i	−0.471855	−	0.817276i
$867$	354.042	−	9480.43i	0.0138684	−	0.371364i
$868$	−4118.21	+	7132.95i	−0.161038	+	0.278926i
$869$	−9083.62	+	15733.3i	−0.354592	+	0.614172i
$870$		0			0
$871$	−2601.28	−	4505.55i	−0.101195	−	0.175275i
$872$	14413.2			0.559738
$873$	4633.00	+	9616.94i	0.179614	+	0.372834i
$874$	−119261.			−4.61562
$875$		0			0
$876$	−51700.0	−	32480.0i	−1.99404	−	1.25274i
$877$	−14114.7	+	24447.3i	−0.543464	+	0.941308i	0.455237	+	0.890370i	$0.349554\pi$
$877$	−14114.7	+	24447.3i	−0.543464	+	0.941308i	−0.998702	+	0.0509378i	$0.983779\pi$
$878$	29007.7	−	50242.9i	1.11499	−	1.93122i
$879$	9252.39	+	5812.72i	0.355034	+	0.223047i
$880$		0			0
$881$	−20204.7			−0.772661			−0.386331	−	0.922360i	$-0.626258\pi$
$881$	−20204.7			−0.772661			−0.386331	+	0.922360i	$0.626258\pi$
$882$	−20306.7	−	1518.81i	−0.775240	−	0.0579828i
$883$	19916.7			0.759061			0.379530	−	0.925179i	$-0.376086\pi$
$883$	19916.7			0.759061			0.379530	+	0.925179i	$0.376086\pi$
$884$	−3349.02	−	5800.67i	−0.127420	−	0.220699i
$885$		0			0
$886$	23491.4	−	40688.2i	0.890754	−	1.54283i
$887$	−3513.60	+	6085.74i	−0.133005	+	0.230371i	−0.924834	−	0.380372i	$-0.875796\pi$
$887$	−3513.60	+	6085.74i	−0.133005	+	0.230371i	0.791829	+	0.610743i	$0.209129\pi$
$888$	774.229	−	20732.1i	0.0292584	−	0.783471i
$889$	944.570	+	1636.04i	0.0356354	+	0.0617223i
$890$		0			0
$891$	9209.21	+	23444.6i	0.346263	+	0.881509i
$892$	52571.0			1.97333
$893$	−12389.3	−	21458.9i	−0.464269	−	0.804137i
$894$	−1468.15	+	39313.8i	−0.0549244	+	1.47075i
$895$		0			0
$896$	9471.00	−	16404.3i	0.353129	−	0.611638i
$897$	−6523.28	+	3448.26i	−0.242816	+	0.128355i
$898$	6439.49	+	11153.5i	0.239297	+	0.414474i
$899$	−2565.28			−0.0951689
$900$		0			0
$901$	50061.5			1.85104
$902$	12955.3	+	22439.2i	0.478231	+	0.828320i
$903$	−8963.37	−	5631.15i	−0.330324	−	0.207523i
$904$	−1626.94	+	2817.95i	−0.0598576	+	0.103676i
$905$		0			0
$906$	−6539.83	−	4108.59i	−0.239814	−	0.150661i
$907$	3186.11	+	5518.50i	0.116641	+	0.202027i	0.918434	−	0.395573i	$-0.129454\pi$
$907$	3186.11	+	5518.50i	0.116641	+	0.202027i	−0.801794	+	0.597601i	$0.796121\pi$
$908$	−71116.2			−2.59920
$909$	3905.25	+	8106.31i	0.142496	+	0.295786i
$910$		0			0
$911$	17448.0	+	30220.8i	0.634553	+	1.09908i	0.986610	+	0.163099i	$0.0521491\pi$
$911$	17448.0	+	30220.8i	0.634553	+	1.09908i	−0.352057	+	0.935979i	$0.614518\pi$
$912$	22740.9	−	12021.0i	0.825688	−	0.436466i
$913$	6185.05	−	10712.8i	0.224201	−	0.388327i
$914$	−35065.9	+	60735.8i	−1.26901	+	2.19799i
$915$		0			0
$916$	−88.6906	−	153.617i	−0.00319915	−	0.00554109i
$917$	3501.54			0.126097
$918$	−45760.6	+	19977.0i	−1.64523	+	0.718235i
$919$	−702.234			−0.0252063			−0.0126031	−	0.999921i	$-0.504012\pi$
$919$	−702.234			−0.0252063			−0.0126031	+	0.999921i	$0.504012\pi$
$920$		0			0
$921$	391.718	−	10489.3i	0.0140147	−	0.375281i
$922$	12425.0	−	21520.7i	0.443813	−	0.768707i
$923$	1946.74	−	3371.86i	0.0694235	−	0.120245i
$924$	−22279.8	+	11777.3i	−0.793237	+	0.419312i
$925$		0			0
$926$	60870.0			2.16017
$927$	−24799.9	+	36386.2i	−0.878680	+	1.28919i
$928$	10648.5			0.376673
$929$	15286.7	+	26477.3i	0.539871	+	0.935084i	0.998910	+	0.0466681i	$0.0148603\pi$
$929$	15286.7	+	26477.3i	0.539871	+	0.935084i	−0.459039	+	0.888416i	$0.651806\pi$
$930$		0			0
$931$	12734.5	−	22056.7i	0.448287	−	0.776456i
$932$	−3819.37	+	6615.33i	−0.134235	+	0.232503i
$933$	23730.1	+	14908.2i	0.832679	+	0.523122i
$934$	−7.56366	−	13.1006i	−0.000264979	−	0.000458957i
$935$		0			0
$936$	−1393.19	+	2044.07i	−0.0486514	+	0.0713808i
$937$	13601.7			0.474224			0.237112	−	0.971482i	$-0.423799\pi$
$937$	13601.7			0.474224			0.237112	+	0.971482i	$0.423799\pi$
$938$	−19401.1	−	33603.7i	−0.675341	−	1.16972i
$939$	14294.9	−	7556.42i	0.496802	−	0.262614i
$940$		0			0
$941$	−23803.1	+	41228.2i	−0.824611	+	1.42827i	0.0776049	+	0.996984i	$0.475273\pi$
$941$	−23803.1	+	41228.2i	−0.824611	+	1.42827i	−0.902216	+	0.431284i	$0.858061\pi$
$942$	−2938.83	+	78695.1i	−0.101648	+	2.72189i
$943$	16249.6	+	28145.1i	0.561144	+	0.971931i
$944$	20099.1			0.692976
$945$		0			0
$946$	23471.6			0.806690
$947$	−24267.1	−	42031.9i	−0.832710	−	1.44230i	−0.895882	−	0.444293i	$-0.853455\pi$
$947$	−24267.1	−	42031.9i	−0.832710	−	1.44230i	0.0631720	−	0.998003i	$-0.479878\pi$
$948$	−1100.75	+	29475.6i	−0.0377117	+	1.00983i
$949$	4112.79	−	7123.56i	0.140681	−	0.243667i
$950$		0			0
$951$	−22664.0	+	11980.4i	−0.772797	+	0.408507i
$952$	−6469.17	−	11204.9i	−0.220238	−	0.381464i
$953$	−30379.5			−1.03262			−0.516312	−	0.856401i	$-0.672695\pi$
$953$	−30379.5			−1.03262			−0.516312	+	0.856401i	$0.672695\pi$
$954$	−30982.5	−	64311.9i	−1.05146	−	2.18257i
$955$		0			0
$956$	32993.2	+	57146.0i	1.11619	+	1.93330i
$957$	−6646.25	−	4175.44i	−0.224496	−	0.141037i
$958$	−7914.54	+	13708.4i	−0.266918	+	0.462315i
$959$	5378.56	−	9315.94i	0.181108	−	0.313689i
$960$		0			0
$961$	13173.9	+	22817.9i	0.442212	+	0.765934i
$962$	10791.7			0.361683
$963$	−18537.0	−	1386.44i	−0.620297	−	0.0463941i
$964$	33341.0			1.11394
$965$		0			0
$966$	−48652.6	+	25718.2i	−1.62047	+	0.856593i
$967$	−16161.9	+	27993.3i	−0.537470	+	0.930925i	0.461570	+	0.887104i	$0.347286\pi$
$967$	−16161.9	+	27993.3i	−0.537470	+	0.930925i	−0.999039	+	0.0438207i	$0.986047\pi$
$968$	−831.310	+	1439.87i	−0.0276026	+	0.0478091i
$969$	2330.53	−	62406.3i	0.0772627	−	2.06892i
$970$		0			0
$971$	−27461.7			−0.907609			−0.453805	−	0.891101i	$-0.649934\pi$
$971$	−27461.7			−0.907609			−0.453805	+	0.891101i	$0.649934\pi$
$972$	31007.5	+	26664.5i	1.02322	+	0.879902i
$973$	2208.56			0.0727681
$974$	29582.5	+	51238.4i	0.973188	+	1.68561i
$975$		0			0
$976$	5495.81	−	9519.02i	0.180242	−	0.312189i
$977$	−21771.9	+	37710.1i	−0.712943	+	1.23485i	0.250804	+	0.968038i	$0.419305\pi$
$977$	−21771.9	+	37710.1i	−0.712943	+	1.23485i	−0.963747	+	0.266816i	$0.914028\pi$
$978$	−13215.3	+	6985.72i	−0.432085	+	0.228404i
$979$	26219.4	+	45413.3i	0.855949	+	1.48255i
$980$		0			0
$981$	32012.3	+	2394.31i	1.04187	+	0.0779249i
$982$	−180.781			−0.00587470
$983$	−17184.5	−	29764.4i	−0.557579	−	0.965756i	−0.997698	−	0.0678161i	$-0.978397\pi$
$983$	−17184.5	−	29764.4i	−0.557579	−	0.965756i	0.440118	−	0.897940i	$-0.354936\pi$
$984$	9225.85	+	5796.05i	0.298892	+	0.187776i
$985$		0			0
$986$	7779.53	−	13474.5i	0.251268	−	0.435210i
$987$	−9681.78	−	6082.48i	−0.312234	−	0.196158i
$988$	−5972.90	−	10345.4i	−0.192331	−	0.333128i
$989$	29440.0			0.946550
$990$		0			0
$991$	4360.89			0.139786			0.0698931	−	0.997554i	$-0.477734\pi$
$991$	4360.89			0.139786			0.0698931	+	0.997554i	$0.477734\pi$
$992$	7146.19	+	12377.6i	0.228722	+	0.396157i
$993$	−40300.6	+	21303.2i	−1.28792	+	0.680803i
$994$	14519.4	−	25148.3i	0.463307	−	0.802471i
$995$		0			0
$996$	749.504	−	20070.0i	0.0238443	−	0.638495i
$997$	−14677.3	−	25421.9i	−0.466235	−	0.807543i	0.533021	−	0.846102i	$-0.321057\pi$
$997$	−14677.3	−	25421.9i	−0.466235	−	0.807543i	−0.999256	+	0.0385591i	$0.987723\pi$
$998$	10374.4			0.329056
$999$	5163.60	−	45918.3i	0.163533	−	1.45424i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.4.e.e.76.11	✓	24
5.2	odd	4		225.4.k.e.49.4		48
5.3	odd	4		225.4.k.e.49.21		48
5.4	even	2		225.4.e.f.76.2	yes	24
9.4	even	3		2025.4.a.bi.1.2		12
9.5	odd	6		2025.4.a.be.1.11		12
9.7	even	3	inner	225.4.e.e.151.11	yes	24
45.4	even	6		2025.4.a.bf.1.11		12
45.7	odd	12		225.4.k.e.124.21		48
45.14	odd	6		2025.4.a.bj.1.2		12
45.34	even	6		225.4.e.f.151.2	yes	24
45.43	odd	12		225.4.k.e.124.4		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.4.e.e.76.11	✓	24	1.1	even	1	trivial
225.4.e.e.151.11	yes	24	9.7	even	3	inner
225.4.e.f.76.2	yes	24	5.4	even	2
225.4.e.f.151.2	yes	24	45.34	even	6
225.4.k.e.49.4		48	5.2	odd	4
225.4.k.e.49.21		48	5.3	odd	4
225.4.k.e.124.4		48	45.43	odd	12
225.4.k.e.124.21		48	45.7	odd	12
2025.4.a.be.1.11		12	9.5	odd	6
2025.4.a.bf.1.11		12	45.4	even	6
2025.4.a.bi.1.2		12	9.4	even	3
2025.4.a.bj.1.2		12	45.14	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)

\(f(q)\)	\(=\)	\(q+(2.16773 + 3.75461i) q^{2} +(0.193913 - 5.19253i) q^{3} +(-5.39807 + 9.34974i) q^{4} +(19.9163 - 10.5279i) q^{6} +(6.50075 + 11.2596i) q^{7} -12.1226 q^{8} +(-26.9248 - 2.01380i) q^{9} +O(q^{10})\)	\(q+(2.16773 + 3.75461i) q^{2} +(0.193913 - 5.19253i) q^{3} +(-5.39807 + 9.34974i) q^{4} +(19.9163 - 10.5279i) q^{6} +(6.50075 + 11.2596i) q^{7} -12.1226 q^{8} +(-26.9248 - 2.01380i) q^{9} +(17.2761 + 29.9230i) q^{11} +(47.5021 + 29.8427i) q^{12} +(-3.77884 + 6.54514i) q^{13} +(-28.1837 + 48.8156i) q^{14} +(16.9062 + 29.2824i) q^{16} +82.0901 q^{17} +(-50.8046 - 105.458i) q^{18} +146.406 q^{19} +(59.7265 - 31.5720i) q^{21} +(-74.8995 + 129.730i) q^{22} +(-93.9451 + 162.718i) q^{23} +(-2.35072 + 62.9468i) q^{24} -32.7659 q^{26} +(-15.6778 + 139.417i) q^{27} -140.366 q^{28} +(-21.8589 - 37.8607i) q^{29} +(29.3391 - 50.8168i) q^{31} +(-121.786 + 210.940i) q^{32} +(158.726 - 83.9041i) q^{33} +(177.949 + 308.216i) q^{34} +(164.171 - 240.869i) q^{36} -329.358 q^{37} +(317.368 + 549.697i) q^{38} +(33.2531 + 20.8909i) q^{39} +(86.4845 - 149.796i) q^{41} +(248.011 + 155.811i) q^{42} +(-78.3437 - 135.695i) q^{43} -373.030 q^{44} -814.589 q^{46} +(-84.6230 - 146.571i) q^{47} +(155.328 - 82.1077i) q^{48} +(86.9806 - 150.655i) q^{49} +(15.9183 - 426.255i) q^{51} +(-40.7969 - 70.6623i) q^{52} +609.837 q^{53} +(-557.443 + 243.355i) q^{54} +(-78.8058 - 136.496i) q^{56} +(28.3899 - 760.217i) q^{57} +(94.7682 - 164.143i) q^{58} +(297.215 - 514.792i) q^{59} +(-162.538 - 281.525i) q^{61} +254.396 q^{62} +(-152.357 - 316.254i) q^{63} -785.498 q^{64} +(659.102 + 414.075i) q^{66} +(-344.191 + 596.156i) q^{67} +(-443.128 + 767.521i) q^{68} +(826.700 + 519.366i) q^{69} -515.170 q^{71} +(326.398 + 24.4124i) q^{72} -1088.37 q^{73} +(-713.959 - 1236.61i) q^{74} +(-790.310 + 1368.86i) q^{76} +(-224.615 + 389.044i) q^{77} +(-6.35373 + 170.138i) q^{78} +(262.896 + 455.349i) q^{79} +(720.889 + 108.442i) q^{81} +749.899 q^{82} +(-179.006 - 310.048i) q^{83} +(-27.2188 + 728.855i) q^{84} +(339.655 - 588.300i) q^{86} +(-200.832 + 106.161i) q^{87} +(-209.430 - 362.744i) q^{88} +1517.67 q^{89} -98.2610 q^{91} +(-1014.25 - 1756.72i) q^{92} +(-258.179 - 162.198i) q^{93} +(366.879 - 635.453i) q^{94} +(1071.70 + 673.283i) q^{96} +(-197.680 - 342.393i) q^{97} +754.200 q^{98} +(-404.896 - 840.462i) 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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