LMFDB - Embedded newform 175.4.e.c.151.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [175,4,Mod(51,175)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(175, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("175.51");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 175 = 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	175.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:	$10.3253342510$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 35)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			151.2
Root			$-0.707107 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	175.151
Dual form			175.4.e.c.51.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.792893 - 1.37333i) q^{2} +(-2.62132 + 4.54026i) q^{3} +(2.74264 - 4.75039i) q^{4} +8.31371 q^{6} +(5.10660 - 17.8023i) q^{7} -21.3848 q^{8} +(-0.242641 - 0.420266i) q^{9} +O(q^{10})$	\(q+(-0.792893 - 1.37333i) q^{2} +(-2.62132 + 4.54026i) q^{3} +(2.74264 - 4.75039i) q^{4} +8.31371 q^{6} +(5.10660 - 17.8023i) q^{7} -21.3848 q^{8} +(-0.242641 - 0.420266i) q^{9} +(-14.0711 + 24.3718i) q^{11} +(14.3787 + 24.9046i) q^{12} +3.85786 q^{13} +(-28.4975 + 7.10228i) q^{14} +(-4.98528 - 8.63476i) q^{16} +(19.1838 - 33.2273i) q^{17} +(-0.384776 + 0.666452i) q^{18} +(-58.3848 - 101.125i) q^{19} +(67.4411 + 69.8509i) q^{21} +44.6274 q^{22} +(-88.2315 - 152.821i) q^{23} +(56.0563 - 97.0924i) q^{24} +(-3.05887 - 5.29813i) q^{26} -139.007 q^{27} +(-70.5624 - 73.0837i) q^{28} -209.853 q^{29} +(103.711 - 179.632i) q^{31} +(-93.4447 + 161.851i) q^{32} +(-73.7696 - 127.773i) q^{33} -60.8427 q^{34} -2.66190 q^{36} +(-7.83348 - 13.5680i) q^{37} +(-92.5858 + 160.363i) q^{38} +(-10.1127 + 17.5157i) q^{39} -10.5736 q^{41} +(42.4548 - 148.003i) q^{42} +325.929 q^{43} +(77.1838 + 133.686i) q^{44} +(-139.916 + 242.342i) q^{46} +(-94.2548 - 163.254i) q^{47} +52.2721 q^{48} +(-290.845 - 181.819i) q^{49} +(100.574 + 174.199i) q^{51} +(10.5807 - 18.3264i) q^{52} +(-137.591 + 238.314i) q^{53} +(110.218 + 190.903i) q^{54} +(-109.204 + 380.699i) q^{56} +612.181 q^{57} +(166.391 + 288.197i) q^{58} +(-21.9096 + 37.9485i) q^{59} +(-427.551 - 740.540i) q^{61} -328.926 q^{62} +(-8.72078 + 2.17344i) q^{63} +216.602 q^{64} +(-116.983 + 202.620i) q^{66} +(-272.710 + 472.347i) q^{67} +(-105.228 - 182.261i) q^{68} +925.132 q^{69} +1026.97 q^{71} +(5.18882 + 8.98729i) q^{72} +(-126.439 + 218.998i) q^{73} +(-12.4222 + 21.5159i) q^{74} -640.514 q^{76} +(362.019 + 374.955i) q^{77} +32.0732 q^{78} +(461.321 + 799.031i) q^{79} +(370.934 - 642.476i) q^{81} +(8.38373 + 14.5210i) q^{82} +960.071 q^{83} +(516.786 - 128.796i) q^{84} +(-258.427 - 447.608i) q^{86} +(550.091 - 952.786i) q^{87} +(300.907 - 521.186i) q^{88} +(66.6026 + 115.359i) q^{89} +(19.7006 - 68.6789i) q^{91} -967.949 q^{92} +(543.718 + 941.747i) q^{93} +(-149.468 + 258.886i) q^{94} +(-489.897 - 848.526i) q^{96} +1021.11 q^{97} +(-19.0881 + 543.590i) q^{98} +13.6569 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 6 q^{2} - 2 q^{3} - 6 q^{4} - 12 q^{6} - 22 q^{7} - 12 q^{8} + 16 q^{9}+O(q^{10}) $ 4 * q - 6 * q^2 - 2 * q^3 - 6 * q^4 - 12 * q^6 - 22 * q^7 - 12 * q^8 + 16 * q^9	\( 4 q - 6 q^{2} - 2 q^{3} - 6 q^{4} - 12 q^{6} - 22 q^{7} - 12 q^{8} + 16 q^{9} - 28 q^{11} + 66 q^{12} + 72 q^{13} + 84 q^{14} + 14 q^{16} - 76 q^{17} + 72 q^{18} - 160 q^{19} + 134 q^{21} + 88 q^{22} - 22 q^{23} + 162 q^{24} - 148 q^{26} + 4 q^{27} - 138 q^{28} - 500 q^{29} + 132 q^{31} + 42 q^{32} - 148 q^{33} + 888 q^{34} - 384 q^{36} - 416 q^{37} - 376 q^{38} + 84 q^{39} - 212 q^{41} + 546 q^{42} + 1332 q^{43} + 156 q^{44} + 402 q^{46} - 196 q^{47} + 260 q^{48} - 230 q^{49} + 572 q^{51} - 348 q^{52} - 952 q^{53} - 402 q^{54} - 714 q^{56} + 944 q^{57} + 510 q^{58} - 840 q^{59} - 98 q^{61} + 8 q^{62} - 544 q^{63} - 1204 q^{64} - 236 q^{66} - 1286 q^{67} - 1524 q^{68} + 2852 q^{69} + 2128 q^{71} + 264 q^{72} - 172 q^{73} - 1792 q^{74} - 288 q^{76} + 724 q^{77} - 856 q^{78} + 1240 q^{79} + 754 q^{81} + 438 q^{82} + 3812 q^{83} - 156 q^{84} - 2018 q^{86} + 970 q^{87} + 604 q^{88} - 650 q^{89} - 996 q^{91} - 5484 q^{92} + 1332 q^{93} - 332 q^{94} - 1722 q^{96} + 1256 q^{97} - 3066 q^{98} + 32 q^{99}+O(q^{100}) \) 4 * q - 6 * q^2 - 2 * q^3 - 6 * q^4 - 12 * q^6 - 22 * q^7 - 12 * q^8 + 16 * q^9 - 28 * q^11 + 66 * q^12 + 72 * q^13 + 84 * q^14 + 14 * q^16 - 76 * q^17 + 72 * q^18 - 160 * q^19 + 134 * q^21 + 88 * q^22 - 22 * q^23 + 162 * q^24 - 148 * q^26 + 4 * q^27 - 138 * q^28 - 500 * q^29 + 132 * q^31 + 42 * q^32 - 148 * q^33 + 888 * q^34 - 384 * q^36 - 416 * q^37 - 376 * q^38 + 84 * q^39 - 212 * q^41 + 546 * q^42 + 1332 * q^43 + 156 * q^44 + 402 * q^46 - 196 * q^47 + 260 * q^48 - 230 * q^49 + 572 * q^51 - 348 * q^52 - 952 * q^53 - 402 * q^54 - 714 * q^56 + 944 * q^57 + 510 * q^58 - 840 * q^59 - 98 * q^61 + 8 * q^62 - 544 * q^63 - 1204 * q^64 - 236 * q^66 - 1286 * q^67 - 1524 * q^68 + 2852 * q^69 + 2128 * q^71 + 264 * q^72 - 172 * q^73 - 1792 * q^74 - 288 * q^76 + 724 * q^77 - 856 * q^78 + 1240 * q^79 + 754 * q^81 + 438 * q^82 + 3812 * q^83 - 156 * q^84 - 2018 * q^86 + 970 * q^87 + 604 * q^88 - 650 * q^89 - 996 * q^91 - 5484 * q^92 + 1332 * q^93 - 332 * q^94 - 1722 * q^96 + 1256 * q^97 - 3066 * q^98 + 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/175\mathbb{Z}\right)^\times$.

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

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 $

$2$	−0.792893	−	1.37333i	−0.280330	−	0.485546i	0.691136	−	0.722725i	$-0.257111\pi$
$2$	−0.792893	−	1.37333i	−0.280330	−	0.485546i	−0.971466	+	0.237179i	$0.923777\pi$
$3$	−2.62132	+	4.54026i	−0.504473	+	0.873773i	0.495513	+	0.868600i	$0.334980\pi$
$3$	−2.62132	+	4.54026i	−0.504473	+	0.873773i	−0.999987	+	0.00517309i	$0.998353\pi$
$4$	2.74264	−	4.75039i	0.342830	−	0.593799i
$5$		0			0
$5$		0			0
$6$	8.31371			0.565676
$7$	5.10660	−	17.8023i	0.275731	−	0.961235i
$7$	5.10660	−	17.8023i	0.275731	−	0.961235i
$8$	−21.3848			−0.945083
$9$	−0.242641	−	0.420266i	−0.00898669	−	0.0155654i
$10$		0			0
$11$	−14.0711	+	24.3718i	−0.385690	+	0.668034i	−0.991865	−	0.127297i	$-0.959370\pi$
$11$	−14.0711	+	24.3718i	−0.385690	+	0.668034i	0.606175	+	0.795331i	$0.292703\pi$
$12$	14.3787	+	24.9046i	0.345897	+	0.599112i
$13$	3.85786			0.0823061			0.0411530	−	0.999153i	$-0.486897\pi$
$13$	3.85786			0.0823061			0.0411530	+	0.999153i	$0.486897\pi$
$14$	−28.4975	+	7.10228i	−0.544019	+	0.135583i
$15$		0			0
$16$	−4.98528	−	8.63476i	−0.0778950	−	0.134918i
$17$	19.1838	−	33.2273i	0.273691	−	0.474047i	−0.696113	−	0.717932i	$-0.745089\pi$
$17$	19.1838	−	33.2273i	0.273691	−	0.474047i	0.969804	+	0.243885i	$0.0784221\pi$
$18$	−0.384776	+	0.666452i	−0.00503848	+	0.00872690i
$19$	−58.3848	−	101.125i	−0.704968	−	1.22104i	−0.966703	−	0.255900i	$-0.917628\pi$
$19$	−58.3848	−	101.125i	−0.704968	−	1.22104i	0.261735	−	0.965140i	$-0.415705\pi$
$20$		0			0
$21$	67.4411	+	69.8509i	0.700803	+	0.725843i
$22$	44.6274			0.432482
$23$	−88.2315	−	152.821i	−0.799893	−	1.38546i	−0.919685	−	0.392656i	$-0.871556\pi$
$23$	−88.2315	−	152.821i	−0.799893	−	1.38546i	0.119792	−	0.992799i	$-0.461777\pi$
$24$	56.0563	−	97.0924i	0.476769	−	0.825788i
$25$		0			0
$26$	−3.05887	−	5.29813i	−0.0230729	−	0.0399634i
$27$	−139.007			−0.990812
$28$	−70.5624	−	73.0837i	−0.476252	−	0.493269i
$29$	−209.853			−1.34375			−0.671874	−	0.740666i	$-0.734510\pi$
$29$	−209.853			−1.34375			−0.671874	+	0.740666i	$0.734510\pi$
$30$		0			0
$31$	103.711	−	179.632i	0.600871	−	1.04074i	−0.391819	−	0.920042i	$-0.628154\pi$
$31$	103.711	−	179.632i	0.600871	−	1.04074i	0.992690	−	0.120696i	$-0.0385126\pi$
$32$	−93.4447	+	161.851i	−0.516214	+	0.894109i
$33$	−73.7696	−	127.773i	−0.389140	−	0.674011i
$34$	−60.8427			−0.306895
$35$		0			0
$36$	−2.66190			−0.0123236
$37$	−7.83348	−	13.5680i	−0.0348058	−	0.0602855i	0.848098	−	0.529840i	$-0.177748\pi$
$37$	−7.83348	−	13.5680i	−0.0348058	−	0.0602855i	−0.882904	+	0.469554i	$0.844415\pi$
$38$	−92.5858	+	160.363i	−0.395247	+	0.684588i
$39$	−10.1127	+	17.5157i	−0.0415212	+	0.0719169i
$40$		0			0
$41$	−10.5736			−0.0402760			−0.0201380	−	0.999797i	$-0.506411\pi$
$41$	−10.5736			−0.0402760			−0.0201380	+	0.999797i	$0.506411\pi$
$42$	42.4548	−	148.003i	0.155974	−	0.543748i
$43$	325.929			1.15590			0.577950	−	0.816072i	$-0.303853\pi$
$43$	325.929			1.15590			0.577950	+	0.816072i	$0.303853\pi$
$44$	77.1838	+	133.686i	0.264452	+	0.458044i
$45$		0			0
$46$	−139.916	+	242.342i	−0.448468	+	0.776770i
$47$	−94.2548	−	163.254i	−0.292521	−	0.506661i	0.681884	−	0.731460i	$-0.261161\pi$
$47$	−94.2548	−	163.254i	−0.292521	−	0.506661i	−0.974405	+	0.224799i	$0.927827\pi$
$48$	52.2721			0.157184
$49$	−290.845	−	181.819i	−0.847945	−	0.530084i
$50$		0			0
$51$	100.574	+	174.199i	0.276140	+	0.478288i
$52$	10.5807	−	18.3264i	0.0282170	−	0.0488733i
$53$	−137.591	+	238.314i	−0.356595	+	0.617641i	−0.987390	−	0.158309i	$-0.949396\pi$
$53$	−137.591	+	238.314i	−0.356595	+	0.617641i	0.630794	+	0.775950i	$0.282729\pi$
$54$	110.218	+	190.903i	0.277755	+	0.481085i
$55$		0			0
$56$	−109.204	+	380.699i	−0.260588	+	0.908446i
$57$	612.181			1.42255
$58$	166.391	+	288.197i	0.376693	+	0.652451i
$59$	−21.9096	+	37.9485i	−0.0483455	+	0.0837369i	−0.889186	−	0.457547i	$-0.848728\pi$
$59$	−21.9096	+	37.9485i	−0.0483455	+	0.0837369i	0.840840	+	0.541284i	$0.182062\pi$
$60$		0			0
$61$	−427.551	−	740.540i	−0.897414	−	1.55437i	−0.830788	−	0.556589i	$-0.812110\pi$
$61$	−427.551	−	740.540i	−0.897414	−	1.55437i	−0.0666267	−	0.997778i	$-0.521224\pi$
$62$	−328.926			−0.673768
$63$	−8.72078	+	2.17344i	−0.0174399	+	0.00434646i
$64$	216.602			0.423051
$65$		0			0
$66$	−116.983	+	202.620i	−0.218175	+	0.377891i
$67$	−272.710	+	472.347i	−0.497265	+	0.861289i	−0.999995	−	0.00315473i	$-0.998996\pi$
$67$	−272.710	+	472.347i	−0.497265	+	0.861289i	0.502730	+	0.864444i	$0.332329\pi$
$68$	−105.228	−	182.261i	−0.187659	−	0.325035i
$69$	925.132			1.61410
$70$		0			0
$71$	1026.97			1.71661			0.858306	−	0.513138i	$-0.171517\pi$
$71$	1026.97			1.71661			0.858306	+	0.513138i	$0.171517\pi$
$72$	5.18882	+	8.98729i	0.00849317	+	0.0147106i
$73$	−126.439	+	218.998i	−0.202719	+	0.351120i	−0.949404	−	0.314058i	$-0.898311\pi$
$73$	−126.439	+	218.998i	−0.202719	+	0.351120i	0.746684	+	0.665179i	$0.231645\pi$
$74$	−12.4222	+	21.5159i	−0.0195142	+	0.0337997i
$75$		0			0
$76$	−640.514			−0.966737
$77$	362.019	+	374.955i	0.535791	+	0.554936i
$78$	32.0732			0.0465586
$79$	461.321	+	799.031i	0.656996	+	1.13795i	0.981390	+	0.192028i	$0.0615063\pi$
$79$	461.321	+	799.031i	0.656996	+	1.13795i	−0.324394	+	0.945922i	$0.605160\pi$
$80$		0			0
$81$	370.934	−	642.476i	0.508825	−	0.881311i
$82$	8.38373	+	14.5210i	0.0112906	+	0.0195559i
$83$	960.071			1.26966			0.634828	−	0.772653i	$-0.281071\pi$
$83$	960.071			1.26966			0.634828	+	0.772653i	$0.281071\pi$
$84$	516.786	−	128.796i	0.671262	−	0.167295i
$85$		0			0
$86$	−258.427	−	447.608i	−0.324034	−	0.561243i
$87$	550.091	−	952.786i	0.677885	−	1.17413i
$88$	300.907	−	521.186i	0.364509	−	0.631347i
$89$	66.6026	+	115.359i	0.0793243	+	0.137394i	0.902959	−	0.429728i	$-0.141390\pi$
$89$	66.6026	+	115.359i	0.0793243	+	0.137394i	−0.823634	+	0.567121i	$0.808057\pi$
$90$		0			0
$91$	19.7006	−	68.6789i	0.0226943	−	0.0791155i
$92$	−967.949			−1.09691
$93$	543.718	+	941.747i	0.606246	+	1.05005i
$94$	−149.468	+	258.886i	−0.164005	+	0.284065i
$95$		0			0
$96$	−489.897	−	848.526i	−0.520832	−	0.902108i
$97$	1021.11			1.06884			0.534421	−	0.845218i	$-0.320530\pi$
$97$	1021.11			1.06884			0.534421	+	0.845218i	$0.320530\pi$
$98$	−19.0881	+	543.590i	−0.0196754	+	0.560315i
$99$	13.6569			0.0138643
$100$		0			0
$101$	−481.779	+	834.466i	−0.474642	+	0.822104i	−0.999578	−	0.0290376i	$-0.990756\pi$
$101$	−481.779	+	834.466i	−0.474642	+	0.822104i	0.524936	+	0.851141i	$0.324089\pi$
$102$	159.488	−	276.242i	0.154820	−	0.268157i
$103$	−899.150	−	1557.37i	−0.860155	−	1.48983i	−0.871779	−	0.489899i	$-0.837034\pi$
$103$	−899.150	−	1557.37i	−0.860155	−	1.48983i	0.0116248	−	0.999932i	$-0.496300\pi$
$104$	−82.4996			−0.0777860
$105$		0			0
$106$	436.379			0.399858
$107$	139.501	+	241.624i	0.126038	+	0.218305i	0.922138	−	0.386860i	$-0.126440\pi$
$107$	139.501	+	241.624i	0.126038	+	0.218305i	−0.796100	+	0.605165i	$0.793107\pi$
$108$	−381.247	+	660.339i	−0.339680	+	0.588344i
$109$	−390.537	+	676.429i	−0.343180	+	0.594405i	−0.985021	−	0.172432i	$-0.944837\pi$
$109$	−390.537	+	676.429i	−0.343180	+	0.594405i	0.641841	+	0.766837i	$0.278171\pi$
$110$		0			0
$111$	82.1362			0.0702345
$112$	−179.177	+	44.6553i	−0.151166	+	0.0376744i
$113$	587.239			0.488874			0.244437	−	0.969665i	$-0.421397\pi$
$113$	587.239			0.488874			0.244437	+	0.969665i	$0.421397\pi$
$114$	−485.394	−	840.727i	−0.398783	−	0.690713i
$115$		0			0
$116$	−575.551	+	996.883i	−0.460677	+	0.797916i
$117$	−0.936075	−	1.62133i	−0.000739659	−	0.00128113i
$118$	69.4879			0.0542108
$119$	−493.558	−	511.194i	−0.380205	−	0.393791i
$120$		0			0
$121$	269.510	+	466.805i	0.202487	+	0.350718i
$122$	−678.004	+	1174.34i	−0.503145	+	0.871472i
$123$	27.7168	−	48.0069i	0.0203182	−	0.0351921i
$124$	−568.882	−	985.333i	−0.411993	−	0.713593i
$125$		0			0
$126$	9.89949	+	10.2532i	0.00699934	+	0.00724944i
$127$	−1559.62			−1.08972			−0.544860	−	0.838527i	$-0.683417\pi$
$127$	−1559.62			−1.08972			−0.544860	+	0.838527i	$0.683417\pi$
$128$	575.815	+	997.341i	0.397620	+	0.688698i
$129$	−854.364	+	1479.80i	−0.583121	+	1.00999i
$130$		0			0
$131$	826.823	+	1432.10i	0.551449	+	0.955138i	0.998170	+	0.0604645i	$0.0192582\pi$
$131$	826.823	+	1432.10i	0.551449	+	0.955138i	−0.446721	+	0.894673i	$0.647408\pi$
$132$	−809.294			−0.533636
$133$	−2098.41	+	522.977i	−1.36809	+	0.340962i
$134$	864.918			0.557594
$135$		0			0
$136$	−410.241	+	710.557i	−0.258661	+	0.448013i
$137$	−148.329	+	256.913i	−0.0925007	+	0.160216i	−0.908563	−	0.417748i	$-0.862819\pi$
$137$	−148.329	+	256.913i	−0.0925007	+	0.160216i	0.816062	+	0.577964i	$0.196153\pi$
$138$	−733.531	−	1270.51i	−0.452480	−	0.783719i
$139$	237.868			0.145149			0.0725745	−	0.997363i	$-0.476879\pi$
$139$	237.868			0.145149			0.0725745	+	0.997363i	$0.476879\pi$
$140$		0			0
$141$	988.288			0.590276
$142$	−814.281	−	1410.38i	−0.481218	−	0.833494i
$143$	−54.2843	+	94.0231i	−0.0317446	+	0.0549833i
$144$	−2.41926	+	4.19029i	−0.00140004	+	0.00242494i
$145$		0			0
$146$	401.009			0.227313
$147$	1587.90	−	843.908i	0.890939	−	0.473499i
$148$	−85.9377			−0.0477299
$149$	−1368.56	−	2370.41i	−0.752459	−	1.30330i	−0.946628	−	0.322329i	$-0.895534\pi$
$149$	−1368.56	−	2370.41i	−0.752459	−	1.30330i	0.194169	−	0.980968i	$-0.437799\pi$
$150$		0			0
$151$	1781.82	−	3086.21i	0.960283	−	1.66326i	0.238495	−	0.971144i	$-0.423346\pi$
$151$	1781.82	−	3086.21i	0.960283	−	1.66326i	0.721788	−	0.692114i	$-0.243321\pi$
$152$	1248.55	+	2162.54i	0.666253	+	1.15398i
$153$	−18.6190			−0.00983831
$154$	227.894	−	794.472i	0.119248	−	0.415717i
$155$		0			0
$156$	55.4710	+	96.0786i	0.0284694	+	0.0493105i
$157$	624.539	−	1081.73i	0.317475	−	0.549884i	−0.662485	−	0.749075i	$-0.730498\pi$
$157$	624.539	−	1081.73i	0.317475	−	0.549884i	0.979961	+	0.199191i	$0.0638316\pi$
$158$	731.556	−	1267.09i	0.368351	−	0.638003i
$159$	−721.339	−	1249.40i	−0.359786	−	0.623167i
$160$		0			0
$161$	−3171.14	+	790.327i	−1.55230	+	0.386873i
$162$	−1176.44			−0.570556
$163$	−982.318	−	1701.42i	−0.472031	−	0.817582i	0.527457	−	0.849582i	$-0.323146\pi$
$163$	−982.318	−	1701.42i	−0.472031	−	0.817582i	−0.999488	+	0.0320000i	$0.989812\pi$
$164$	−28.9996	+	50.2287i	−0.0138078	+	0.0239159i
$165$		0			0
$166$	−761.234	−	1318.50i	−0.355923	−	0.616477i
$167$	939.402			0.435288			0.217644	−	0.976028i	$-0.430163\pi$
$167$	939.402			0.435288			0.217644	+	0.976028i	$0.430163\pi$
$168$	−1442.21	−	1493.75i	−0.662317	−	0.685982i
$169$	−2182.12			−0.993226
$170$		0			0
$171$	−28.3330	+	49.0743i	−0.0126707	+	0.0219462i
$172$	893.906	−	1548.29i	0.396277	−	0.686372i
$173$	−1351.22	−	2340.38i	−0.593821	−	1.02853i	−0.993712	−	0.111966i	$-0.964285\pi$
$173$	−1351.22	−	2340.38i	−0.593821	−	1.02853i	0.399891	−	0.916563i	$-0.369048\pi$
$174$	−1744.66			−0.760126
$175$		0			0
$176$	280.593			0.120173
$177$	−114.864	−	198.951i	−0.0487781	−	0.0844861i
$178$	105.617	−	182.935i	0.0444740	−	0.0770312i
$179$	717.024	−	1241.92i	0.299402	−	0.518579i	−0.676597	−	0.736353i	$-0.736546\pi$
$179$	717.024	−	1241.92i	0.299402	−	0.518579i	0.975999	+	0.217774i	$0.0698796\pi$
$180$		0			0
$181$	2711.21			1.11339			0.556693	−	0.830718i	$-0.312070\pi$
$181$	2711.21			1.11339			0.556693	+	0.830718i	$0.312070\pi$
$182$	−109.939	+	27.3996i	−0.0447761	+	0.0111593i
$183$	4482.99			1.81089
$184$	1886.81	+	3268.05i	0.755965	+	1.30937i
$185$		0			0
$186$	862.220	−	1493.41i	0.339898	−	0.588721i
$187$	539.872	+	935.086i	0.211120	+	0.365670i
$188$	−1034.03			−0.401140
$189$	−709.854	+	2474.65i	−0.273197	+	0.952404i
$190$		0			0
$191$	1747.30	+	3026.41i	0.661938	+	1.14651i	0.980106	+	0.198476i	$0.0635992\pi$
$191$	1747.30	+	3026.41i	0.661938	+	1.14651i	−0.318168	+	0.948034i	$0.603067\pi$
$192$	−567.784	+	983.430i	−0.213418	+	0.369651i
$193$	−814.881	+	1411.41i	−0.303919	+	0.526403i	−0.977020	−	0.213147i	$-0.931629\pi$
$193$	−814.881	+	1411.41i	−0.303919	+	0.526403i	0.673101	+	0.739551i	$0.264962\pi$
$194$	−809.629	−	1402.32i	−0.299629	−	0.518972i
$195$		0			0
$196$	−1661.39	+	882.966i	−0.605464	+	0.321781i
$197$	−693.696			−0.250882			−0.125441	−	0.992101i	$-0.540035\pi$
$197$	−693.696			−0.250882			−0.125441	+	0.992101i	$0.540035\pi$
$198$	−10.8284	−	18.7554i	−0.00388658	−	0.00673175i
$199$	1902.81	−	3295.76i	0.677821	−	1.17402i	−0.297815	−	0.954624i	$-0.596258\pi$
$199$	1902.81	−	3295.76i	0.677821	−	1.17402i	0.975636	−	0.219397i	$-0.0704089\pi$
$200$		0			0
$201$	−1429.72	−	2476.35i	−0.501714	−	0.868995i
$202$	1528.00			0.532226
$203$	−1071.63	+	3735.87i	−0.370512	+	1.29166i
$204$	1103.35			0.378676
$205$		0			0
$206$	−1425.86	+	2469.66i	−0.482254	+	0.835289i
$207$	−42.8171	+	74.1614i	−0.0143768	+	0.0249013i
$208$	−19.2325	−	33.3117i	−0.00641123	−	0.0111046i
$209$	3286.14			1.08760
$210$		0			0
$211$	−627.239			−0.204649			−0.102324	−	0.994751i	$-0.532628\pi$
$211$	−627.239			−0.204649			−0.102324	+	0.994751i	$0.532628\pi$
$212$	754.724	+	1307.22i	0.244503	+	0.423492i
$213$	−2692.03	+	4662.73i	−0.865985	+	1.49993i
$214$	221.220	−	383.164i	0.0706648	−	0.122395i
$215$		0			0
$216$	2972.64			0.936400
$217$	−2668.26	−	2763.60i	−0.834716	−	0.864541i
$218$	1238.62			0.384815
$219$	−662.872	−	1148.13i	−0.204533	−	0.354262i
$220$		0			0
$221$	74.0084	−	128.186i	0.0225264	−	0.0390169i
$222$	−65.1253	−	112.800i	−0.0196888	−	0.0341021i
$223$	2000.99			0.600878			0.300439	−	0.953801i	$-0.402867\pi$
$223$	2000.99			0.600878			0.300439	+	0.953801i	$0.402867\pi$
$224$	2404.14	+	2490.04i	0.717113	+	0.742736i
$225$		0			0
$226$	−465.618	−	806.473i	−0.137046	−	0.237371i
$227$	−796.121	+	1378.92i	−0.232777	+	0.403182i	−0.958624	−	0.284674i	$-0.908115\pi$
$227$	−796.121	+	1378.92i	−0.232777	+	0.403182i	0.725847	+	0.687856i	$0.241448\pi$
$228$	1678.99	−	2908.10i	0.487693	−	0.844709i
$229$	1962.58	+	3399.29i	0.566336	+	0.980923i	0.996924	+	0.0783742i	$0.0249729\pi$
$229$	1962.58	+	3399.29i	0.566336	+	0.980923i	−0.430588	+	0.902549i	$0.641694\pi$
$230$		0			0
$231$	−2651.36	+	660.785i	−0.755181	+	0.188210i
$232$	4487.66			1.26995
$233$	1084.88	+	1879.06i	0.305032	+	0.528331i	0.977269	−	0.212005i	$-0.0679994\pi$
$233$	1084.88	+	1879.06i	0.305032	+	0.528331i	−0.672236	+	0.740337i	$0.734666\pi$
$234$	−1.48441	+	2.57108i	−0.000414698	+	0.000718277i
$235$		0			0
$236$	120.180	+	208.158i	0.0331486	+	0.0574151i
$237$	−4837.08			−1.32575
$238$	−310.700	+	1083.14i	−0.0846204	+	0.294998i
$239$	1057.70			0.286262			0.143131	−	0.989704i	$-0.454283\pi$
$239$	1057.70			0.286262			0.143131	+	0.989704i	$0.454283\pi$
$240$		0			0
$241$	−1199.62	+	2077.80i	−0.320640	+	0.555365i	−0.980620	−	0.195918i	$-0.937231\pi$
$241$	−1199.62	+	2077.80i	−0.320640	+	0.555365i	0.659980	+	0.751283i	$0.270565\pi$
$242$	427.385	−	740.253i	0.113526	−	0.196633i
$243$	68.0749	+	117.909i	0.0179712	+	0.0311271i
$244$	−4690.47			−1.23064
$245$		0			0
$246$	−87.9058			−0.0227832
$247$	−225.241	−	390.128i	−0.0580231	−	0.100499i
$248$	−2217.83	+	3841.39i	−0.567872	+	0.983584i
$249$	−2516.65	+	4358.97i	−0.640508	+	1.10939i
$250$		0			0
$251$	−3812.95			−0.958848			−0.479424	−	0.877583i	$-0.659154\pi$
$251$	−3812.95			−0.958848			−0.479424	+	0.877583i	$0.659154\pi$
$252$	−13.5933	+	47.3881i	−0.00339800	+	0.0118459i
$253$	4966.05			1.23404
$254$	1236.62	+	2141.88i	0.305481	+	0.529109i
$255$		0			0
$256$	1779.53	−	3082.23i	0.434455	−	0.752499i
$257$	1745.08	+	3022.57i	0.423561	+	0.733629i	0.996285	−	0.0861194i	$-0.0274466\pi$
$257$	1745.08	+	3022.57i	0.423561	+	0.733629i	−0.572724	+	0.819748i	$0.694113\pi$
$258$	2709.68			0.653865
$259$	−281.544	+	70.1678i	−0.0675455	+	0.0168340i
$260$		0			0
$261$	50.9188	+	88.1940i	0.0120758	+	0.0209160i
$262$	1311.16	−	2271.00i	0.309175	−	0.535508i
$263$	3562.28	−	6170.05i	0.835207	−	1.44662i	−0.0586547	−	0.998278i	$-0.518681\pi$
$263$	3562.28	−	6170.05i	0.835207	−	1.44662i	0.893862	−	0.448343i	$-0.147986\pi$
$264$	1577.55	+	2732.39i	0.367770	+	0.636996i
$265$		0			0
$266$	2382.04	+	2467.15i	0.549069	+	0.568687i
$267$	−698.347			−0.160068
$268$	1495.89	+	2590.96i	0.340955	+	0.590552i
$269$	213.971	−	370.609i	0.0484984	−	0.0840017i	−0.840757	−	0.541412i	$-0.817890\pi$
$269$	213.971	−	370.609i	0.0484984	−	0.0840017i	0.889256	+	0.457411i	$0.151223\pi$
$270$		0			0
$271$	−4094.29	−	7091.52i	−0.917751	−	1.58959i	−0.802824	−	0.596217i	$-0.796670\pi$
$271$	−4094.29	−	7091.52i	−0.917751	−	1.58959i	−0.114927	−	0.993374i	$-0.536663\pi$
$272$	−382.546			−0.0852767
$273$	260.179	+	269.475i	0.0576803	+	0.0597413i
$274$	470.436			0.103723
$275$		0			0
$276$	2537.30	−	4394.74i	0.553362	−	0.958450i
$277$	−2084.98	+	3611.29i	−0.452254	+	0.783326i	−0.998526	−	0.0542815i	$-0.982713\pi$
$277$	−2084.98	+	3611.29i	−0.452254	+	0.783326i	0.546272	+	0.837608i	$0.316046\pi$
$278$	−188.604	−	326.672i	−0.0406896	−	0.0704765i
$279$	−100.658			−0.0215994
$280$		0			0
$281$	1284.60			0.272714			0.136357	−	0.990660i	$-0.456461\pi$
$281$	1284.60			0.272714			0.136357	+	0.990660i	$0.456461\pi$
$282$	−783.607	−	1357.25i	−0.165472	−	0.286606i
$283$	2394.67	−	4147.70i	0.502998	−	0.871219i	−0.496996	−	0.867753i	$-0.665563\pi$
$283$	2394.67	−	4147.70i	0.502998	−	0.871219i	0.999994	−	0.00346581i	$-0.00110320\pi$
$284$	2816.62	−	4878.53i	0.588506	−	1.01932i
$285$		0			0
$286$	172.167			0.0355959
$287$	−53.9951	+	188.234i	−0.0111053	+	0.0387147i
$288$	90.6939			0.0185562
$289$	1720.47	+	2979.93i	0.350186	+	0.606541i
$290$		0			0
$291$	−2676.65	+	4636.09i	−0.539202	+	0.933926i
$292$	693.551	+	1201.27i	0.138997	+	0.240749i
$293$	−6983.27			−1.39238			−0.696189	−	0.717858i	$-0.745123\pi$
$293$	−6983.27			−1.39238			−0.696189	+	0.717858i	$0.745123\pi$
$294$	−2418.00	−	1511.59i	−0.479662	−	0.299856i
$295$		0			0
$296$	167.517	+	290.148i	0.0328944	+	0.0569747i
$297$	1955.98	−	3387.85i	0.382146	−	0.661897i
$298$	−2170.24	+	3758.96i	−0.421874	+	0.730707i
$299$	−340.385	−	589.564i	−0.0658361	−	0.114031i
$300$		0			0
$301$	1664.39	−	5802.29i	0.318717	−	1.11109i
$302$	−5651.18			−1.07678
$303$	−2525.80	−	4374.81i	−0.478888	−	0.829459i
$304$	−582.129	+	1008.28i	−0.109827	+	0.190226i
$305$		0			0
$306$	14.7629	+	25.5701i	0.00275797	+	0.00477695i
$307$	2069.43			0.384719			0.192359	−	0.981325i	$-0.438386\pi$
$307$	2069.43			0.384719			0.192359	+	0.981325i	$0.438386\pi$
$308$	2774.07	−	691.368i	0.513206	−	0.127904i
$309$	9427.84			1.73570
$310$		0			0
$311$	−1060.98	+	1837.67i	−0.193449	+	0.335064i	−0.946391	−	0.323023i	$-0.895301\pi$
$311$	−1060.98	+	1837.67i	−0.193449	+	0.335064i	0.752942	+	0.658087i	$0.228634\pi$
$312$	216.258	−	374.569i	0.0392410	−	0.0679674i
$313$	764.398	+	1323.98i	0.138039	+	0.239091i	0.926754	−	0.375668i	$-0.122587\pi$
$313$	764.398	+	1323.98i	0.138039	+	0.239091i	−0.788715	+	0.614759i	$0.789253\pi$
$314$	−1980.77			−0.355992
$315$		0			0
$316$	5060.95			0.900951
$317$	2571.22	+	4453.49i	0.455565	+	0.789062i	0.998721	−	0.0505699i	$-0.0161038\pi$
$317$	2571.22	+	4453.49i	0.455565	+	0.789062i	−0.543155	+	0.839632i	$0.682770\pi$
$318$	−1143.89	+	1981.28i	−0.201718	+	0.349385i
$319$	2952.85	−	5114.49i	0.518270	−	0.897669i
$320$		0			0
$321$	−1462.71			−0.254332
$322$	3599.76	+	3728.38i	0.623002	+	0.645262i
$323$	−4480.16			−0.771773
$324$	−2034.67	−	3524.16i	−0.348881	−	0.604280i
$325$		0			0
$326$	−1557.75	+	2698.10i	−0.264649	+	0.458386i
$327$	−2047.44	−	3546.28i	−0.346250	−	0.599723i
$328$	226.114			0.0380642
$329$	−3387.62	+	844.281i	−0.567677	+	0.141479i
$330$		0			0
$331$	2887.02	+	5000.47i	0.479411	+	0.830364i	0.999721	−	0.0236134i	$-0.00751706\pi$
$331$	2887.02	+	5000.47i	0.479411	+	0.830364i	−0.520310	+	0.853977i	$0.674184\pi$
$332$	2633.13	−	4560.71i	0.435276	−	0.753921i
$333$	−3.80144	+	6.58429i	−0.000625579	+	0.00108353i
$334$	−744.845	−	1290.11i	−0.122024	−	0.211352i
$335$		0			0
$336$	266.933	−	930.564i	0.0433404	−	0.151091i
$337$	484.761			0.0783579			0.0391790	−	0.999232i	$-0.487526\pi$
$337$	484.761			0.0783579			0.0391790	+	0.999232i	$0.487526\pi$
$338$	1730.19	+	2996.77i	0.278431	+	0.482257i
$339$	−1539.34	+	2666.22i	−0.246624	+	0.427165i
$340$		0			0
$341$	2918.64	+	5055.23i	0.463499	+	0.802804i
$342$	89.8603			0.0142079
$343$	−4722.03	+	4249.24i	−0.743339	+	0.668914i
$344$	−6969.92			−1.09242
$345$		0			0
$346$	−2142.74	+	3711.34i	−0.332932	+	0.576655i
$347$	−3899.11	+	6753.45i	−0.603213	+	1.04480i	0.389118	+	0.921188i	$0.372780\pi$
$347$	−3899.11	+	6753.45i	−0.603213	+	1.04480i	−0.992331	+	0.123608i	$0.960553\pi$
$348$	−3017.41	−	5226.30i	−0.464799	−	0.805055i
$349$	−662.157			−0.101560			−0.0507800	−	0.998710i	$-0.516171\pi$
$349$	−662.157			−0.101560			−0.0507800	+	0.998710i	$0.516171\pi$
$350$		0			0
$351$	−536.271			−0.0815499
$352$	−2629.73	−	4554.83i	−0.398197	−	0.689697i
$353$	3313.07	−	5738.40i	0.499538	−	0.865225i	−0.500462	−	0.865759i	$-0.666836\pi$
$353$	3313.07	−	5738.40i	0.499538	−	0.865225i	1.00000		0.000533475i	$0.000169810\pi$
$354$	−182.150	+	315.493i	−0.0273479	+	0.0473680i
$355$		0			0
$356$	730.668			0.108779
$357$	3614.73	−	900.881i	0.535887	−	0.133556i
$358$	−2274.10			−0.335725
$359$	−5199.03	−	9004.98i	−0.764329	−	1.32386i	−0.940601	−	0.339515i	$-0.889737\pi$
$359$	−5199.03	−	9004.98i	−0.764329	−	1.32386i	0.176272	−	0.984342i	$-0.443596\pi$
$360$		0			0
$361$	−3388.06	+	5868.30i	−0.493959	+	0.855562i
$362$	−2149.70	−	3723.39i	−0.312116	−	0.540600i
$363$	−2825.89			−0.408597
$364$	−272.220	−	281.947i	−0.0391984	−	0.0405990i
$365$		0			0
$366$	−3554.53	−	6156.63i	−0.507646	−	0.879269i
$367$	1123.15	−	1945.36i	0.159750	−	0.276694i	−0.775029	−	0.631926i	$-0.782265\pi$
$367$	1123.15	−	1945.36i	0.159750	−	0.276694i	0.934778	+	0.355232i	$0.115598\pi$
$368$	−879.718	+	1523.72i	−0.124615	+	0.215840i
$369$	2.56558	+	4.44372i	0.000361948	+	0.000626913i
$370$		0			0
$371$	3539.93	+	3666.41i	0.495374	+	0.513075i
$372$	5964.89			0.831358
$373$	96.0126	+	166.299i	0.0133280	+	0.0230848i	0.872612	−	0.488413i	$-0.162424\pi$
$373$	96.0126	+	166.299i	0.0133280	+	0.0230848i	−0.859284	+	0.511498i	$0.829091\pi$
$374$	856.122	−	1482.85i	0.118366	−	0.205017i
$375$		0			0
$376$	2015.62	+	3491.15i	0.276456	+	0.478836i
$377$	−809.584			−0.110599
$378$	3961.35	−	987.268i	0.539021	−	0.134338i
$379$	−4565.76			−0.618805			−0.309403	−	0.950931i	$-0.600129\pi$
$379$	−4565.76			−0.618805			−0.309403	+	0.950931i	$0.600129\pi$
$380$		0			0
$381$	4088.28	−	7081.10i	0.549734	−	0.952168i
$382$	2770.84	−	4799.24i	0.371122	−	0.642803i
$383$	693.535	+	1201.24i	0.0925273	+	0.160262i	0.908574	−	0.417724i	$-0.137172\pi$
$383$	693.535	+	1201.24i	0.0925273	+	0.160262i	−0.816047	+	0.577986i	$0.803839\pi$
$384$	−6037.58			−0.802355
$385$		0			0
$386$	2584.45			0.340791
$387$	−79.0836	−	136.977i	−0.0103877	−	0.0179921i
$388$	2800.53	−	4850.66i	0.366431	−	0.634678i
$389$	−2291.50	+	3969.00i	−0.298673	+	0.517317i	−0.975833	−	0.218519i	$-0.929877\pi$
$389$	−2291.50	+	3969.00i	−0.298673	+	0.517317i	0.677160	+	0.735836i	$0.263211\pi$
$390$		0			0
$391$	−6770.45			−0.875694
$392$	6219.66	+	3888.15i	0.801378	+	0.500973i
$393$	−8669.47			−1.11277
$394$	550.026	+	952.674i	0.0703298	+	0.121815i
$395$		0			0
$396$	37.4558	−	64.8754i	0.00475310	−	0.00823261i
$397$	−4480.53	−	7760.50i	−0.566426	−	0.981079i	−0.996915	−	0.0784836i	$-0.974992\pi$
$397$	−4480.53	−	7760.50i	−0.566426	−	0.981079i	0.430489	−	0.902596i	$-0.358341\pi$
$398$	−6034.89			−0.760054
$399$	3126.16	−	10898.2i	0.392240	−	1.36740i
$400$		0			0
$401$	−5814.64	−	10071.2i	−0.724113	−	1.25420i	−0.959338	−	0.282259i	$-0.908916\pi$
$401$	−5814.64	−	10071.2i	−0.724113	−	1.25420i	0.235225	−	0.971941i	$-0.424417\pi$
$402$	−2267.23	+	3926.95i	−0.281291	+	0.487211i
$403$	400.102	−	692.997i	0.0494553	−	0.0856591i
$404$	2642.69	+	4577.28i	0.325443	+	0.563684i
$405$		0			0
$406$	5980.28	−	1490.43i	0.731025	−	0.182190i
$407$	440.902			0.0536970
$408$	−2150.74	−	3725.20i	−0.260975	−	0.452021i
$409$	−2160.07	+	3741.34i	−0.261145	+	0.452317i	−0.966546	−	0.256491i	$-0.917433\pi$
$409$	−2160.07	+	3741.34i	−0.261145	+	0.452317i	0.705401	+	0.708808i	$0.250767\pi$
$410$		0			0
$411$	−777.635	−	1346.90i	−0.0933282	−	0.161649i
$412$	−9864.19			−1.17955
$413$	563.688	+	583.830i	0.0671605	+	0.0695602i
$414$	135.798			0.0161210
$415$		0			0
$416$	−360.497	+	624.399i	−0.0424875	+	0.0735906i
$417$	−623.528	+	1079.98i	−0.0732238	+	0.126827i
$418$	−2605.56	−	4512.97i	−0.304886	−	0.528077i
$419$	7824.02			0.912240			0.456120	−	0.889918i	$-0.349239\pi$
$419$	7824.02			0.912240			0.456120	+	0.889918i	$0.349239\pi$
$420$		0			0
$421$	6944.28			0.803904			0.401952	−	0.915661i	$-0.368332\pi$
$421$	6944.28			0.803904			0.401952	+	0.915661i	$0.368332\pi$
$422$	497.333	+	861.407i	0.0573692	+	0.0993664i
$423$	−45.7401	+	79.2242i	−0.00525759	+	0.00910641i
$424$	2942.35	−	5096.30i	0.337012	−	0.583722i
$425$		0			0
$426$	8537.97			0.971047
$427$	−15366.7	+	3829.76i	−1.74156	+	0.434039i
$428$	1530.41			0.172839
$429$	−284.593	−	492.929i	−0.0320286	−	0.0554752i
$430$		0			0
$431$	−1628.68	+	2820.96i	−0.182020	+	0.315268i	−0.942568	−	0.334013i	$-0.891597\pi$
$431$	−1628.68	+	2820.96i	−0.182020	+	0.315268i	0.760548	+	0.649282i	$0.224930\pi$
$432$	692.990	+	1200.29i	0.0771794	+	0.133679i
$433$	16857.1			1.87090			0.935449	−	0.353461i	$-0.114995\pi$
$433$	16857.1			1.87090			0.935449	+	0.353461i	$0.114995\pi$
$434$	−1679.69	+	5855.65i	−0.185779	+	0.647650i
$435$		0			0
$436$	2142.20	+	3710.40i	0.235305	+	0.407560i
$437$	−10302.8	+	17844.9i	−1.12780	+	1.95340i
$438$	−1051.17	+	1820.69i	−0.114674	+	0.198620i
$439$	−3976.51	−	6887.52i	−0.432320	−	0.748800i	0.564753	−	0.825260i	$-0.308972\pi$
$439$	−3976.51	−	6887.52i	−0.432320	−	0.748800i	−0.997073	+	0.0764599i	$0.975638\pi$
$440$		0			0
$441$	−5.84134	+	166.349i	−0.000630746	+	0.0179623i
$442$	−234.723			−0.0252593
$443$	−4854.88	−	8408.90i	−0.520683	−	0.901849i	−0.999711	−	0.0240492i	$-0.992344\pi$
$443$	−4854.88	−	8408.90i	−0.520683	−	0.901849i	0.479028	−	0.877800i	$-0.340989\pi$
$444$	225.270	−	390.179i	0.0240785	−	0.0417052i
$445$		0			0
$446$	−1586.57	−	2748.02i	−0.168444	−	0.291754i
$447$	14349.7			1.51838
$448$	1106.10	−	3856.02i	0.116648	−	0.406652i
$449$	−11758.3			−1.23588			−0.617938	−	0.786227i	$-0.712032\pi$
$449$	−11758.3			−1.23588			−0.617938	+	0.786227i	$0.712032\pi$
$450$		0			0
$451$	148.782	−	257.698i	0.0155341	−	0.0269058i
$452$	1610.59	−	2789.62i	0.167601	−	0.290293i
$453$	9341.46	+	16179.9i	0.968874	+	1.67814i
$454$	2524.96			0.261018
$455$		0			0
$456$	−13091.3			−1.34443
$457$	1375.09	+	2381.72i	0.140753	+	0.243791i	0.927780	−	0.373127i	$-0.121714\pi$
$457$	1375.09	+	2381.72i	0.140753	+	0.243791i	−0.787028	+	0.616918i	$0.788381\pi$
$458$	3112.23	−	5390.55i	0.317522	−	0.549964i
$459$	−2666.68	+	4618.83i	−0.271176	+	0.469691i
$460$		0			0
$461$	−3041.43			−0.307275			−0.153637	−	0.988127i	$-0.549099\pi$
$461$	−3041.43			−0.307275			−0.153637	+	0.988127i	$0.549099\pi$
$462$	3009.72	+	3117.26i	0.303084	+	0.313914i
$463$	−5422.89			−0.544327			−0.272163	−	0.962251i	$-0.587739\pi$
$463$	−5422.89			−0.544327			−0.272163	+	0.962251i	$0.587739\pi$
$464$	1046.18	+	1812.03i	0.104671	+	0.181296i
$465$		0			0
$466$	1720.38	−	2979.79i	0.171019	−	0.296214i
$467$	−2773.80	−	4804.36i	−0.274853	−	0.476059i	0.695245	−	0.718772i	$-0.255296\pi$
$467$	−2773.80	−	4804.36i	−0.274853	−	0.476059i	−0.970098	+	0.242714i	$0.921962\pi$
$468$	−10.2693			−0.00101431
$469$	7016.25	+	7266.95i	0.690790	+	0.715473i
$470$		0			0
$471$	3274.23	+	5671.14i	0.320316	+	0.554803i
$472$	468.532	−	811.521i	0.0456905	−	0.0791383i
$473$	−4586.17	+	7943.48i	−0.445819	+	0.772181i
$474$	3835.29	+	6642.91i	0.371647	+	0.643711i
$475$		0			0
$476$	−3782.03	+	942.575i	−0.364178	+	0.0907623i
$477$	133.541			0.0128185
$478$	−838.640	−	1452.57i	−0.0802479	−	0.138993i
$479$	−564.275	+	977.353i	−0.0538254	+	0.0932284i	−0.891683	−	0.452661i	$-0.850475\pi$
$479$	−564.275	+	977.353i	−0.0538254	+	0.0932284i	0.837857	+	0.545889i	$0.183808\pi$
$480$		0			0
$481$	−30.2205	−	52.3434i	−0.00286473	−	0.00496186i
$482$	3804.68			0.359540
$483$	4724.28	−	16469.5i	0.445056	−	1.55153i
$484$	2956.68			0.277674
$485$		0			0
$486$	107.952	−	186.979i	0.0100757	−	0.0174517i
$487$	2403.09	−	4162.27i	0.223602	−	0.387291i	−0.732297	−	0.680986i	$-0.761552\pi$
$487$	2403.09	−	4162.27i	0.223602	−	0.387291i	0.955899	+	0.293695i	$0.0948850\pi$
$488$	9143.08	+	15836.3i	0.848131	+	1.46901i
$489$	10299.9			0.952508
$490$		0			0
$491$	−12452.1			−1.14451			−0.572255	−	0.820076i	$-0.693931\pi$
$491$	−12452.1			−1.14451			−0.572255	+	0.820076i	$0.693931\pi$
$492$	−152.034	−	263.331i	−0.0139314	−	0.0241298i
$493$	−4025.77	+	6972.83i	−0.367772	+	0.636999i
$494$	−357.183	+	618.660i	−0.0325313	+	0.0563458i
$495$		0			0
$496$	−2068.11			−0.187219
$497$	5244.35	−	18282.5i	0.473323	−	1.65007i
$498$	7981.75			0.718214
$499$	5898.68	+	10216.8i	0.529180	+	0.916567i	0.999421	+	0.0340289i	$0.0108338\pi$
$499$	5898.68	+	10216.8i	0.529180	+	0.916567i	−0.470240	+	0.882538i	$0.655833\pi$
$500$		0			0
$501$	−2462.47	+	4265.13i	−0.219591	+	0.380343i
$502$	3023.26	+	5236.44i	0.268794	+	0.465565i
$503$	−2900.55			−0.257116			−0.128558	−	0.991702i	$-0.541035\pi$
$503$	−2900.55			−0.257116			−0.128558	+	0.991702i	$0.541035\pi$
$504$	186.492	−	46.4784i	0.0164822	−	0.00410777i
$505$		0			0
$506$	−3937.54	−	6820.03i	−0.345939	−	0.599184i
$507$	5720.03	−	9907.38i	0.501056	−	0.867854i
$508$	−4277.49	+	7408.83i	−0.373588	+	0.647074i
$509$	−4743.42	−	8215.85i	−0.413062	−	0.715444i	0.582161	−	0.813074i	$-0.302207\pi$
$509$	−4743.42	−	8215.85i	−0.413062	−	0.715444i	−0.995223	+	0.0976294i	$0.968874\pi$
$510$		0			0
$511$	3253.00	+	3369.24i	0.281613	+	0.291676i
$512$	3569.14			0.308076
$513$	8115.90	+	14057.2i	0.698491	+	1.20982i
$514$	2767.33	−	4793.15i	0.237474	−	0.411317i
$515$		0			0
$516$	4686.43	+	8117.13i	0.399823	+	0.692513i
$517$	5305.06			0.451289
$518$	319.598	+	331.018i	0.0271087	+	0.0280774i
$519$	14167.9			1.19827
$520$		0			0
$521$	10176.5	−	17626.2i	0.855740	−	1.48219i	−0.0202163	−	0.999796i	$-0.506435\pi$
$521$	10176.5	−	17626.2i	0.855740	−	1.48219i	0.875957	−	0.482390i	$-0.160231\pi$
$522$	80.7464	−	139.857i	0.00677045	−	0.0117268i
$523$	4614.44	+	7992.45i	0.385804	+	0.668232i	0.991880	−	0.127174i	$-0.0405907\pi$
$523$	4614.44	+	7992.45i	0.385804	+	0.668232i	−0.606076	+	0.795407i	$0.707257\pi$
$524$	9070.71			0.756213
$525$		0			0
$526$	−11298.0			−0.936535
$527$	−3979.12	−	6892.04i	−0.328906	−	0.569681i
$528$	−735.524	+	1273.96i	−0.0606242	+	0.105004i
$529$	−9486.09	+	16430.4i	−0.779658	+	1.35041i
$530$		0			0
$531$	21.2646			0.00173787
$532$	−3270.85	+	11402.6i	−0.266559	+	0.929261i
$533$	−40.7915			−0.00331496
$534$	553.715	+	959.062i	0.0448719	+	0.0777203i
$535$		0			0
$536$	5831.83	−	10101.0i	0.469957	−	0.813989i
$537$	3759.10	+	6510.95i	0.302080	+	0.523219i
$538$	−678.626			−0.0543822
$539$	8523.75	−	4530.04i	0.681158	−	0.362009i
$540$		0			0
$541$	348.637	+	603.857i	0.0277062	+	0.0479886i	0.879546	−	0.475814i	$-0.157846\pi$
$541$	348.637	+	603.857i	0.0277062	+	0.0479886i	−0.851840	+	0.523802i	$0.824513\pi$
$542$	−6492.67	+	11245.6i	−0.514546	+	0.891220i
$543$	−7106.96	+	12309.6i	−0.561674	+	0.972847i
$544$	3585.24	+	6209.82i	0.282566	+	0.489419i
$545$		0			0
$546$	163.785	−	570.977i	0.0128376	−	0.0447537i
$547$	8032.62			0.627879			0.313940	−	0.949443i	$-0.398351\pi$
$547$	8032.62			0.627879			0.313940	+	0.949443i	$0.398351\pi$
$548$	813.626	+	1409.24i	0.0634240	+	0.109854i
$549$	−207.482	+	359.370i	−0.0161296	+	0.0279372i
$550$		0			0
$551$	12252.2	+	21221.4i	0.947299	+	1.64077i
$552$	−19783.7			−1.52546
$553$	16580.4	−	4132.25i	1.27499	−	0.317760i
$554$	6612.66			0.507121
$555$		0			0
$556$	652.386	−	1129.97i	0.0497614	−	0.0861893i
$557$	6793.37	−	11766.5i	0.516776	−	0.895083i	−0.483034	−	0.875602i	$-0.660465\pi$
$557$	6793.37	−	11766.5i	0.516776	−	0.895083i	0.999810	−	0.0194814i	$-0.00620150\pi$
$558$	79.8108	+	138.236i	0.00605495	+	0.0104875i
$559$	1257.39			0.0951376
$560$		0			0
$561$	−5660.71			−0.426017
$562$	−1018.55	−	1764.18i	−0.0764500	−	0.132415i
$563$	8607.90	−	14909.3i	0.644369	−	1.11608i	−0.340078	−	0.940397i	$-0.610453\pi$
$563$	8607.90	−	14909.3i	0.644369	−	1.11608i	0.984447	−	0.175683i	$-0.0562133\pi$
$564$	2710.52	−	4694.76i	0.202364	−	0.350505i
$565$		0			0
$566$	−7594.88			−0.564022
$567$	−9543.35	−	9884.35i	−0.706848	−	0.732105i
$568$	−21961.6			−1.62234
$569$	9220.75	+	15970.8i	0.679357	+	1.17668i	0.975175	+	0.221437i	$0.0710746\pi$
$569$	9220.75	+	15970.8i	0.679357	+	1.17668i	−0.295818	+	0.955244i	$0.595592\pi$
$570$		0			0
$571$	5390.17	−	9336.04i	0.395046	−	0.684240i	−0.598061	−	0.801451i	$-0.704062\pi$
$571$	5390.17	−	9336.04i	0.395046	−	0.684240i	0.993107	+	0.117210i	$0.0373952\pi$
$572$	297.765	+	515.743i	0.0217660	+	0.0376998i
$573$	−18320.9			−1.33572
$574$	301.321	−	75.0967i	0.0219109	−	0.00546076i
$575$		0			0
$576$	−52.5565	−	91.0305i	−0.00380183	−	0.00658496i
$577$	−6481.49	+	11226.3i	−0.467640	+	0.809975i	−0.999316	−	0.0369719i	$-0.988229\pi$
$577$	−6481.49	+	11226.3i	−0.467640	+	0.809975i	0.531677	+	0.846947i	$0.321562\pi$
$578$	2728.29	−	4725.54i	0.196336	−	0.340063i
$579$	−4272.13	−	7399.54i	−0.306638	−	0.531113i
$580$		0			0
$581$	4902.70	−	17091.5i	0.350083	−	1.22044i
$582$	8489.18			0.604619
$583$	−3872.10	−	6706.67i	−0.275070	−	0.476436i
$584$	2703.86	−	4683.22i	0.191587	−	0.331838i
$585$		0			0
$586$	5536.99	+	9590.34i	0.390326	+	0.676064i
$587$	16181.8			1.13781			0.568905	−	0.822403i	$-0.307367\pi$
$587$	16181.8			1.13781			0.568905	+	0.822403i	$0.307367\pi$
$588$	346.153	−	9857.70i	0.0242774	−	0.691368i
$589$	−24220.5			−1.69438
$590$		0			0
$591$	1818.40	−	3149.56i	0.126563	−	0.219214i
$592$	−78.1042	+	135.280i	−0.00542240	+	0.00939188i
$593$	373.815	+	647.467i	0.0258866	+	0.0448369i	0.878678	−	0.477414i	$-0.158426\pi$
$593$	373.815	+	647.467i	0.0258866	+	0.0448369i	−0.852792	+	0.522251i	$0.825092\pi$
$594$	−6203.53			−0.428508
$595$		0			0
$596$	−15013.8			−1.03186
$597$	9975.73	+	17278.5i	0.683885	+	1.18452i
$598$	−539.778	+	934.923i	−0.0369117	+	0.0639329i
$599$	−1924.93	+	3334.08i	−0.131303	+	0.227424i	−0.924179	−	0.381959i	$-0.875249\pi$
$599$	−1924.93	+	3334.08i	−0.131303	+	0.227424i	0.792876	+	0.609383i	$0.208583\pi$
$600$		0			0
$601$	1808.82			0.122768			0.0613838	−	0.998114i	$-0.480449\pi$
$601$	1808.82			0.122768			0.0613838	+	0.998114i	$0.480449\pi$
$602$	−9288.15	+	2314.84i	−0.628832	+	0.156721i
$603$	264.682			0.0178751
$604$	−9773.80	−	16928.7i	−0.658427	−	1.14043i
$605$		0			0
$606$	−4005.37	+	6937.51i	−0.268494	+	0.465045i
$607$	268.046	+	464.270i	0.0179237	+	0.0310447i	0.874848	−	0.484397i	$-0.160961\pi$
$607$	268.046	+	464.270i	0.0179237	+	0.0310447i	−0.856924	+	0.515442i	$0.827628\pi$
$608$	21823.0			1.45566
$609$	−14152.7	−	14658.4i	−0.941702	−	0.975351i
$610$		0			0
$611$	−363.622	−	629.812i	−0.0240762	−	0.0417013i
$612$	−51.0654	+	88.4478i	−0.00337287	+	0.00584198i
$613$	7367.99	−	12761.7i	0.485465	−	0.840851i	−0.514395	−	0.857553i	$-0.671984\pi$
$613$	7367.99	−	12761.7i	0.485465	−	0.840851i	0.999861	+	0.0167026i	$0.00531685\pi$
$614$	−1640.84	−	2842.01i	−0.107848	−	0.186799i
$615$		0			0
$616$	−7741.70	−	8018.32i	−0.506367	−	0.524460i
$617$	−9604.91			−0.626709			−0.313354	−	0.949636i	$-0.601453\pi$
$617$	−9604.91			−0.626709			−0.313354	+	0.949636i	$0.601453\pi$
$618$	−7475.27	−	12947.6i	−0.486569	−	0.842762i
$619$	4297.11	−	7442.81i	0.279023	−	0.483283i	−0.692119	−	0.721783i	$-0.743323\pi$
$619$	4297.11	−	7442.81i	0.279023	−	0.483283i	0.971142	+	0.238501i	$0.0766560\pi$
$620$		0			0
$621$	12264.8	+	21243.3i	0.792544	+	1.37273i
$622$	3364.98			0.216918
$623$	2393.77	−	596.588i	0.153940	−	0.0383656i
$624$	201.659			0.0129372
$625$		0			0
$626$	1212.17	−	2099.54i	0.0773932	−	0.134049i
$627$	−8614.04	+	14920.0i	−0.548663	+	0.950312i
$628$	−3425.77	−	5933.61i	−0.217680	−	0.377033i
$629$	−601.102			−0.0381042
$630$		0			0
$631$	−14803.3			−0.933933			−0.466966	−	0.884275i	$-0.654653\pi$
$631$	−14803.3			−0.933933			−0.466966	+	0.884275i	$0.654653\pi$
$632$	−9865.24	−	17087.1i	−0.620915	−	1.07546i
$633$	1644.19	−	2847.83i	0.103240	−	0.178817i
$634$	4077.41	−	7062.28i	0.255417	−	0.442396i
$635$		0			0
$636$	−7913.50			−0.493381
$637$	−1122.04	−	701.432i	−0.0697911	−	0.0436291i
$638$	−9365.19			−0.581146
$639$	−249.186	−	431.603i	−0.0154267	−	0.0267198i
$640$		0			0
$641$	4645.16	−	8045.65i	0.286229	−	0.495763i	−0.686678	−	0.726962i	$-0.740932\pi$
$641$	4645.16	−	8045.65i	0.286229	−	0.495763i	0.972906	+	0.231199i	$0.0742649\pi$
$642$	1159.77	+	2008.79i	0.0712970	+	0.123490i
$643$	1861.78			0.114186			0.0570928	−	0.998369i	$-0.481817\pi$
$643$	1861.78			0.114186			0.0570928	+	0.998369i	$0.481817\pi$
$644$	−4942.93	+	17231.7i	−0.302451	+	1.05439i
$645$		0			0
$646$	3552.29	+	6152.74i	0.216351	+	0.374731i
$647$	14763.7	−	25571.5i	0.897095	−	1.55381i	0.0659057	−	0.997826i	$-0.479006\pi$
$647$	14763.7	−	25571.5i	0.897095	−	1.55381i	0.831190	−	0.555989i	$-0.187660\pi$
$648$	−7932.33	+	13739.2i	−0.480882	+	0.832912i
$649$	−616.583	−	1067.95i	−0.0372927	−	0.0645929i
$650$		0			0
$651$	19541.8	−	4870.31i	1.17650	−	0.293214i
$652$	−10776.6			−0.647306
$653$	2596.28	+	4496.88i	0.155590	+	0.269489i	0.933274	−	0.359166i	$-0.116939\pi$
$653$	2596.28	+	4496.88i	0.155590	+	0.269489i	−0.777684	+	0.628656i	$0.783606\pi$
$654$	−3246.81	+	5623.64i	−0.194129	+	0.336241i
$655$		0			0
$656$	52.7123	+	91.3004i	0.00313730	+	0.00543397i
$657$	122.717			0.00728711
$658$	3845.50	+	3982.91i	0.227832	+	0.235972i
$659$	−11740.1			−0.693976			−0.346988	−	0.937870i	$-0.612795\pi$
$659$	−11740.1			−0.693976			−0.346988	+	0.937870i	$0.612795\pi$
$660$		0			0
$661$	−4396.25	+	7614.53i	−0.258690	+	0.448065i	−0.965891	−	0.258948i	$-0.916624\pi$
$661$	−4396.25	+	7614.53i	−0.258690	+	0.448065i	0.707201	+	0.707013i	$0.249958\pi$
$662$	4578.20	−	7929.67i	0.268787	−	0.465552i
$663$	387.999	+	672.034i	0.0227280	+	0.0393660i
$664$	−20530.9			−1.19993
$665$		0			0
$666$	12.0565			0.000701474
$667$	18515.6	+	32070.0i	1.07485	+	1.86170i
$668$	2576.44	−	4462.53i	0.149230	−	0.258474i
$669$	−5245.22	+	9084.99i	−0.303127	+	0.525032i
$670$		0			0
$671$	24064.4			1.38449
$672$	−17607.4	+	4388.22i	−1.01075	+	0.251903i
$673$	−30366.5			−1.73929			−0.869646	−	0.493676i	$-0.835653\pi$
$673$	−30366.5			−1.73929			−0.869646	+	0.493676i	$0.835653\pi$
$674$	−384.364	−	665.738i	−0.0219661	−	0.0380464i
$675$		0			0
$676$	−5984.76	+	10365.9i	−0.340508	+	0.589777i
$677$	−8708.45	−	15083.5i	−0.494377	−	0.856286i	0.505602	−	0.862767i	$-0.331270\pi$
$677$	−8708.45	−	15083.5i	−0.494377	−	0.856286i	−0.999979	+	0.00648104i	$0.997937\pi$
$678$	4882.13			0.276544
$679$	5214.39	−	18178.1i	0.294712	−	1.02741i
$680$		0			0
$681$	−4173.78	−	7229.19i	−0.234860	−	0.406789i
$682$	4628.34	−	8016.52i	0.259866	−	0.450100i
$683$	4414.16	−	7645.55i	0.247296	−	0.428329i	−0.715479	−	0.698635i	$-0.753791\pi$
$683$	4414.16	−	7645.55i	0.247296	−	0.428329i	0.962775	+	0.270305i	$0.0871246\pi$
$684$	155.415	+	269.186i	0.00868776	+	0.0150476i
$685$		0			0
$686$	9579.68	+	3115.71i	0.533169	+	0.173409i
$687$	−20578.2			−1.14281
$688$	−1624.85	−	2814.32i	−0.0900388	−	0.155952i
$689$	−530.807	+	919.384i	−0.0293500	+	0.0508356i
$690$		0			0
$691$	−5315.51	−	9206.74i	−0.292636	−	0.506861i	0.681796	−	0.731542i	$-0.261199\pi$
$691$	−5315.51	−	9206.74i	−0.292636	−	0.506861i	−0.974432	+	0.224681i	$0.927866\pi$
$692$	−14823.6			−0.814319
$693$	69.7401	−	243.124i	0.00382281	−	0.0133268i
$694$	12366.3			0.676395
$695$		0			0
$696$	−11763.6	+	20375.1i	−0.640657	+	1.10965i
$697$	−202.841	+	351.332i	−0.0110232	+	0.0190927i
$698$	525.020	+	909.361i	0.0284703	+	0.0493121i
$699$	−11375.2			−0.615523
$700$		0			0
$701$	30120.7			1.62289			0.811443	−	0.584431i	$-0.198682\pi$
$701$	30120.7			1.62289			0.811443	+	0.584431i	$0.198682\pi$
$702$	425.205	+	736.477i	0.0228609	+	0.0395962i
$703$	−914.712	+	1584.33i	−0.0490740	+	0.0849986i
$704$	−3047.82	+	5278.99i	−0.163166	+	0.282613i
$705$		0			0
$706$	−10507.6			−0.560142
$707$	12395.2	+	12838.1i	0.659362	+	0.682921i
$708$	−1260.12			−0.0668904
$709$	−2207.47	−	3823.45i	−0.116930	−	0.202529i	0.801620	−	0.597834i	$-0.203972\pi$
$709$	−2207.47	−	3823.45i	−0.116930	−	0.202529i	−0.918550	+	0.395306i	$0.870639\pi$
$710$		0			0
$711$	223.870	−	387.755i	0.0118084	−	0.0204528i
$712$	−1424.28	−	2466.93i	−0.0749680	−	0.129848i
$713$	−36602.2			−1.92253
$714$	−4103.30	−	4249.92i	−0.215073	−	0.222758i
$715$		0			0
$716$	−3933.08	−	6812.30i	−0.205288	−	0.355569i
$717$	−2772.56	+	4802.21i	−0.144412	+	0.250128i
$718$	−8244.54	+	14280.0i	−0.428529	+	0.742234i
$719$	−8567.98	−	14840.2i	−0.444411	−	0.769743i	0.553600	−	0.832783i	$-0.313254\pi$
$719$	−8567.98	−	14840.2i	−0.444411	−	0.769743i	−0.998011	+	0.0630401i	$0.979920\pi$
$720$		0			0
$721$	−32316.5	+	8054.07i	−1.66925	+	0.416019i
$722$	10745.5			0.553886
$723$	−6289.18	−	10893.2i	−0.323509	−	0.560334i
$724$	7435.88	−	12879.3i	0.381702	−	0.661128i
$725$		0			0
$726$	2240.63	+	3880.88i	0.114542	+	0.198393i
$727$	3271.77			0.166909			0.0834546	−	0.996512i	$-0.473405\pi$
$727$	3271.77			0.166909			0.0834546	+	0.996512i	$0.473405\pi$
$728$	−421.292	+	1468.68i	−0.0214480	+	0.0747707i
$729$	19316.6			0.981386
$730$		0			0
$731$	6252.54	−	10829.7i	0.316359	−	0.547951i
$732$	12295.2	−	21296.0i	0.620826	−	1.07530i
$733$	2234.92	+	3870.99i	0.112618	+	0.195059i	0.916825	−	0.399290i	$-0.130743\pi$
$733$	2234.92	+	3870.99i	0.112618	+	0.195059i	−0.804207	+	0.594349i	$0.797410\pi$
$734$	−3562.16			−0.179130
$735$		0			0
$736$	32979.1			1.65166
$737$	−7674.63	−	13292.9i	−0.383580	−	0.664381i
$738$	4.06847	−	7.04679i	0.000202930	−	0.000351485i
$739$	1237.60	−	2143.58i	0.0616046	−	0.106702i	−0.833578	−	0.552401i	$-0.813712\pi$
$739$	1237.60	−	2143.58i	0.0616046	−	0.106702i	0.895183	+	0.445699i	$0.147045\pi$
$740$		0			0
$741$	2361.71			0.117084
$742$	2228.42	−	7768.57i	0.110253	−	0.384357i
$743$	−9240.48			−0.456259			−0.228129	−	0.973631i	$-0.573261\pi$
$743$	−9240.48			−0.456259			−0.228129	+	0.973631i	$0.573261\pi$
$744$	−11627.3	−	20139.0i	−0.572953	−	0.992383i
$745$		0			0
$746$	152.255	−	263.714i	0.00747248	−	0.0129427i
$747$	−232.952	−	403.485i	−0.0114100	−	0.0197627i
$748$	5922.70			0.289513
$749$	5013.84	−	1249.57i	0.244595	−	0.0609592i
$750$		0			0
$751$	−2526.23	−	4375.57i	−0.122748	−	0.212605i	0.798103	−	0.602522i	$-0.205837\pi$
$751$	−2526.23	−	4375.57i	−0.122748	−	0.212605i	−0.920850	+	0.389916i	$0.872504\pi$
$752$	−939.774	+	1627.74i	−0.0455718	+	0.0789327i
$753$	9994.95	−	17311.8i	0.483713	−	0.837816i
$754$	641.913	+	1111.83i	0.0310041	+	0.0537007i
$755$		0			0
$756$	9808.68	+	10159.2i	0.471876	+	0.488737i
$757$	37779.2			1.81388			0.906942	−	0.421256i	$-0.138411\pi$
$757$	37779.2			1.81388			0.906942	+	0.421256i	$0.138411\pi$
$758$	3620.16	+	6270.30i	0.173470	+	0.300458i
$759$	−13017.6	+	22547.1i	−0.622541	+	1.07827i
$760$		0			0
$761$	−3751.35	−	6497.52i	−0.178694	−	0.309507i	0.762739	−	0.646706i	$-0.223854\pi$
$761$	−3751.35	−	6497.52i	−0.178694	−	0.309507i	−0.941434	+	0.337199i	$0.890521\pi$
$762$	−12966.3			−0.616428
$763$	10047.7	+	10406.7i	0.476738	+	0.493772i
$764$	19168.9			0.907729
$765$		0			0
$766$	1099.80	−	1904.91i	0.0518764	−	0.0898525i
$767$	−84.5243	+	146.400i	−0.00397913	+	0.00689206i
$768$	9329.43	+	16159.0i	0.438342	+	0.759231i
$769$	24209.4			1.13526			0.567628	−	0.823285i	$-0.307861\pi$
$769$	24209.4			1.13526			0.567628	+	0.823285i	$0.307861\pi$
$770$		0			0
$771$	−18297.7			−0.854701
$772$	4469.85	+	7742.01i	0.208385	+	0.360934i
$773$	3760.50	−	6513.37i	0.174975	−	0.303065i	−0.765178	−	0.643819i	$-0.777349\pi$
$773$	3760.50	−	6513.37i	0.174975	−	0.303065i	0.940153	+	0.340754i	$0.110682\pi$
$774$	−125.410	+	217.216i	−0.00582398	+	0.0100874i
$775$		0			0
$776$	−21836.1			−1.01014
$777$	419.437	−	1462.22i	0.0193658	−	0.0675118i
$778$	7267.67			0.334908
$779$	617.337	+	1069.26i	0.0283933	+	0.0491787i
$780$		0			0
$781$	−14450.6	+	25029.2i	−0.662080	+	1.14676i
$782$	5368.24	+	9298.07i	0.245483	+	0.425190i
$783$	29171.0			1.33140
$784$	−120.016	+	3417.80i	−0.00546719	+	0.155694i
$785$		0			0
$786$	6873.96	+	11906.1i	0.311942	+	0.540299i
$787$	−8060.68	+	13961.5i	−0.365098	+	0.632368i	−0.988792	−	0.149300i	$-0.952298\pi$
$787$	−8060.68	+	13961.5i	−0.365098	+	0.632368i	0.623694	+	0.781669i	$0.285631\pi$
$788$	−1902.56	+	3295.33i	−0.0860099	+	0.148974i
$789$	18675.7	+	32347.3i	0.842679	+	1.45956i
$790$		0			0
$791$	2998.79	−	10454.2i	0.134798	−	0.469923i
$792$	−292.049			−0.0131029
$793$	−1649.43	−	2856.90i	−0.0738627	−	0.127934i
$794$	−7105.16	+	12306.5i	−0.317573	+	0.550052i
$795$		0			0
$796$	−10437.4	−	18078.2i	−0.464755	−	0.804979i
$797$	32223.0			1.43212			0.716058	−	0.698041i	$-0.245944\pi$
$797$	32223.0			1.43212			0.716058	+	0.698041i	$0.245944\pi$
$798$	−17445.6	+	4347.88i	−0.773894	+	0.192874i
$799$	−7232.65			−0.320241
$800$		0			0
$801$	32.3210	−	55.9816i	0.00142573	−	0.00246943i
$802$	−9220.77	+	15970.9i	−0.405981	+	0.703180i
$803$	−3558.25	−	6163.07i	−0.156374	−	0.270847i
$804$	−15684.8			−0.688011
$805$		0			0
$806$	−1268.95			−0.0554552
$807$	1121.77	+	1942.97i	0.0489323	+	0.0847532i
$808$	10302.7	−	17844.9i	0.448576	−	0.776956i
$809$	12272.2	−	21256.0i	0.533334	−	0.923761i	−0.465908	−	0.884833i	$-0.654272\pi$
$809$	12272.2	−	21256.0i	0.533334	−	0.923761i	0.999242	−	0.0389282i	$-0.0123944\pi$
$810$		0			0
$811$	18783.9			0.813308			0.406654	−	0.913582i	$-0.366695\pi$
$811$	18783.9			0.813308			0.406654	+	0.913582i	$0.366695\pi$
$812$	14807.7	+	15336.8i	0.639962	+	0.662829i
$813$	42929.8			1.85192
$814$	−349.588	−	605.504i	−0.0150529	−	0.0260724i
$815$		0			0
$816$	1002.78	−	1736.86i	0.0430198	−	0.0745125i
$817$	−19029.3	−	32959.7i	−0.814872	−	1.41140i
$818$	6850.80			0.292827
$819$	−33.6436	+	8.38482i	−0.00143541	+	0.000357740i
$820$		0			0
$821$	−9042.53	−	15662.1i	−0.384393	−	0.665788i	0.607292	−	0.794479i	$-0.292256\pi$
$821$	−9042.53	−	15662.1i	−0.384393	−	0.665788i	−0.991685	+	0.128691i	$0.958923\pi$
$822$	−1233.16	+	2135.90i	−0.0523254	+	0.0906303i
$823$	3717.59	−	6439.06i	0.157457	−	0.272723i	−0.776494	−	0.630125i	$-0.783004\pi$
$823$	3717.59	−	6439.06i	0.157457	−	0.272723i	0.933951	+	0.357401i	$0.116337\pi$
$824$	19228.1	+	33304.1i	0.812917	+	1.40801i
$825$		0			0
$826$	354.847	−	1237.05i	0.0149476	−	0.0521093i
$827$	−26487.2			−1.11373			−0.556863	−	0.830604i	$-0.687995\pi$
$827$	−26487.2			−1.11373			−0.556863	+	0.830604i	$0.687995\pi$
$828$	234.864	+	406.796i	0.00985759	+	0.0170738i
$829$	9688.53	−	16781.0i	0.405906	−	0.703051i	−0.588520	−	0.808483i	$-0.700289\pi$
$829$	9688.53	−	16781.0i	0.405906	−	0.703051i	0.994427	+	0.105432i	$0.0336226\pi$
$830$		0			0
$831$	−10930.8	−	18932.7i	−0.456300	−	0.790334i
$832$	835.622			0.0348197
$833$	−11620.8	+	6176.02i	−0.483359	+	0.256887i
$834$	1977.56			0.0821073
$835$		0			0
$836$	9012.71	−	15610.5i	0.372860	−	0.645813i
$837$	−14416.5	+	24970.2i	−0.595350	+	1.03118i
$838$	−6203.61	−	10745.0i	−0.255728	−	0.442934i
$839$	−4645.97			−0.191176			−0.0955880	−	0.995421i	$-0.530473\pi$
$839$	−4645.97			−0.191176			−0.0955880	+	0.995421i	$0.530473\pi$
$840$		0			0
$841$	19649.2			0.805658
$842$	−5506.07	−	9536.80i	−0.225358	−	0.390332i
$843$	−3367.35	+	5832.41i	−0.137577	+	0.238291i
$844$	−1720.29	+	2979.63i	−0.0701598	+	0.121520i
$845$		0			0
$846$	145.068			0.00589544
$847$	9686.50	−	2414.12i	0.392954	−	0.0979339i
$848$	2743.72			0.111108
$849$	12554.4	+	21744.9i	0.507499	+	0.879013i
$850$		0			0
$851$	−1382.32	+	2394.25i	−0.0556819	+	0.0964438i
$852$	14766.5	+	25576.4i	0.593772	+	1.02844i
$853$	−32566.5			−1.30722			−0.653609	−	0.756833i	$-0.726746\pi$
$853$	−32566.5			−1.30722			−0.653609	+	0.756833i	$0.726746\pi$
$854$	17443.6	+	18066.9i	0.698957	+	0.723932i
$855$		0			0
$856$	−2983.21	−	5167.07i	−0.119117	−	0.206316i
$857$	67.4706	−	116.862i	0.00268932	−	0.00465805i	−0.864678	−	0.502327i	$-0.832477\pi$
$857$	67.4706	−	116.862i	0.00268932	−	0.00465805i	0.867367	+	0.497669i	$0.165811\pi$
$858$	−451.304	+	781.681i	−0.0179572	+	0.0311027i
$859$	5190.45	+	8990.13i	0.206165	+	0.357089i	0.950503	−	0.310714i	$-0.100568\pi$
$859$	5190.45	+	8990.13i	0.206165	+	0.357089i	−0.744338	+	0.667803i	$0.767235\pi$
$860$		0			0
$861$	−713.095	−	738.575i	−0.0282256	−	0.0292341i
$862$	5165.48			0.204103
$863$	12674.6	+	21953.1i	0.499941	+	0.865924i	1.00000		6.76895e-5i	$-2.15462e-5\pi$
$863$	12674.6	+	21953.1i	0.499941	+	0.865924i	−0.500059	+	0.865992i	$0.666688\pi$
$864$	12989.5	−	22498.4i	0.511471	−	0.885894i
$865$		0			0
$866$	−13365.9	−	23150.3i	−0.524469	−	0.908407i
$867$	−18039.6			−0.706639
$868$	−20446.3	+	5095.72i	−0.799529	+	0.199263i
$869$	−25965.1			−1.01359
$870$		0			0
$871$	−1052.08	+	1822.25i	−0.0409280	+	0.0708893i
$872$	8351.54	−	14465.3i	0.324333	−	0.561762i
$873$	−247.762	−	429.136i	−0.00960536	−	0.0166370i
$874$	32675.9			1.26462
$875$		0			0
$876$	−7272.08			−0.280480
$877$	−11259.7	−	19502.3i	−0.433537	−	0.750909i	0.563638	−	0.826022i	$-0.309401\pi$
$877$	−11259.7	−	19502.3i	−0.433537	−	0.750909i	−0.997175	+	0.0751134i	$0.976068\pi$
$878$	−6305.90	+	10922.1i	−0.242385	+	0.419823i
$879$	18305.4	−	31705.9i	0.702418	−	1.21662i
$880$		0			0
$881$	−12419.9			−0.474958			−0.237479	−	0.971393i	$-0.576321\pi$
$881$	−12419.9			−0.474958			−0.237479	+	0.971393i	$0.576321\pi$
$882$	233.084	−	123.875i	0.00889835	−	0.00472912i
$883$	46011.8			1.75359			0.876794	−	0.480866i	$-0.159678\pi$
$883$	46011.8			1.75359			0.876794	+	0.480866i	$0.159678\pi$
$884$	−405.957	−	703.138i	−0.0154455	−	0.0267524i
$885$		0			0
$886$	−7698.81	+	13334.7i	−0.291926	+	0.505631i
$887$	−14043.3	−	24323.8i	−0.531600	−	0.920759i	−0.999320	−	0.0368816i	$-0.988258\pi$
$887$	−14043.3	−	24323.8i	−0.531600	−	0.920759i	0.467719	−	0.883877i	$-0.345076\pi$
$888$	−1756.46			−0.0663774
$889$	−7964.38	+	27764.9i	−0.300469	+	1.04748i
$890$		0			0
$891$	10438.9	+	18080.6i	0.392497	+	0.679825i
$892$	5487.98	−	9505.47i	0.205999	−	0.356801i
$893$	−11006.1	+	19063.1i	−0.412436	+	0.714359i
$894$	−11377.8	−	19706.9i	−0.425648	−	0.737244i
$895$		0			0
$896$	20695.4	−	5157.82i	0.771637	−	0.192311i
$897$	3569.03			0.132850
$898$	9323.08	+	16148.0i	0.346453	+	0.600075i
$899$	−21764.0	+	37696.3i	−0.807419	+	1.39849i
$900$		0			0
$901$	5279.02	+	9143.53i	0.195194	+	0.338086i
$902$	−471.872			−0.0174187
$903$	21981.0	+	22766.4i	0.810058	+	0.839002i
$904$	−12558.0			−0.462026
$905$		0			0
$906$	14813.6	−	25657.8i	0.543209	−	0.940866i
$907$	−15229.4	+	26378.1i	−0.557534	+	0.965677i	0.440168	+	0.897916i	$0.354919\pi$
$907$	−15229.4	+	26378.1i	−0.557534	+	0.965677i	−0.997702	+	0.0677613i	$0.978414\pi$
$908$	4366.95	+	7563.78i	0.159606	+	0.276446i
$909$	467.597			0.0170618
$910$		0			0
$911$	−26850.4			−0.976502			−0.488251	−	0.872703i	$-0.662365\pi$
$911$	−26850.4			−0.976502			−0.488251	+	0.872703i	$0.662365\pi$
$912$	−3051.89	−	5286.03i	−0.110810	−	0.191928i
$913$	−13509.2	+	23398.7i	−0.489693	+	0.848174i
$914$	2180.60	−	3776.91i	0.0789144	−	0.136684i
$915$		0			0
$916$	21530.6			0.776628
$917$	29716.9	−	7406.20i	1.07016	−	0.266711i
$918$	8457.57			0.304076
$919$	19047.9	+	32992.0i	0.683714	+	1.18423i	0.973839	+	0.227238i	$0.0729697\pi$
$919$	19047.9	+	32992.0i	0.683714	+	1.18423i	−0.290125	+	0.956989i	$0.593697\pi$
$920$		0			0
$921$	−5424.64	+	9395.76i	−0.194080	+	0.336157i
$922$	2411.53	+	4176.89i	0.0861383	+	0.149196i
$923$	3961.93			0.141288
$924$	−4132.74	+	14407.3i	−0.147140	+	0.512950i
$925$		0			0
$926$	4299.78	+	7447.43i	0.152591	+	0.264296i
$927$	−436.341	+	755.765i	−0.0154599	+	0.0267773i
$928$	19609.6	−	33964.9i	0.693661	−	1.20146i
$929$	−18177.5	−	31484.4i	−0.641964	−	1.11191i	−0.984994	−	0.172590i	$-0.944786\pi$
$929$	−18177.5	−	31484.4i	−0.641964	−	1.11191i	0.343030	−	0.939325i	$-0.388547\pi$
$930$		0			0
$931$	−1405.56	+	40027.3i	−0.0494793	+	1.40907i
$932$	11901.7			0.418297
$933$	−5562.34	−	9634.25i	−0.195180	−	0.338061i
$934$	−4398.65	+	7618.69i	−0.154099	+	0.266907i
$935$		0			0
$936$	20.0178	+	34.6718i	0.000699039	+	0.00121077i
$937$	−37878.5			−1.32064			−0.660318	−	0.750986i	$-0.729579\pi$
$937$	−37878.5			−1.32064			−0.660318	+	0.750986i	$0.729579\pi$
$938$	4416.79	−	15397.6i	0.153746	−	0.535979i
$939$	−8014.93			−0.278549
$940$		0			0
$941$	−27062.8	+	46874.1i	−0.937536	+	1.62386i	−0.167489	+	0.985874i	$0.553566\pi$
$941$	−27062.8	+	46874.1i	−0.937536	+	1.62386i	−0.770047	+	0.637987i	$0.779767\pi$
$942$	5192.24	−	8993.22i	0.179588	−	0.311056i
$943$	932.924	+	1615.87i	0.0322165	+	0.0558007i
$944$	436.902			0.0150635
$945$		0			0
$946$	14545.4			0.499906
$947$	−19172.9	−	33208.5i	−0.657906	−	1.13953i	−0.981157	−	0.193213i	$-0.938109\pi$
$947$	−19172.9	−	33208.5i	−0.657906	−	1.13953i	0.323251	−	0.946313i	$-0.395224\pi$
$948$	−13266.4	+	22978.0i	−0.454506	+	0.787227i
$949$	−487.783	+	844.865i	−0.0166850	+	0.0288993i
$950$		0			0
$951$	−26960.0			−0.919282
$952$	10554.6	+	10931.8i	0.359325	+	0.372165i
$953$	15096.4			0.513137			0.256569	−	0.966526i	$-0.417408\pi$
$953$	15096.4			0.513137			0.256569	+	0.966526i	$0.417408\pi$
$954$	−105.883	−	183.395i	−0.00359340	−	0.00622395i
$955$		0			0
$956$	2900.88	−	5024.47i	0.0981393	−	0.169982i
$957$	15480.7	+	26813.4i	0.522906	+	0.905701i
$958$	1789.64			0.0603556
$959$	3816.19	+	3952.55i	0.128500	+	0.133091i
$960$		0			0
$961$	−6616.31	−	11459.8i	−0.222091	−	0.384673i
$962$	−47.9233	+	83.0055i	−0.00160614	+	0.00278192i
$963$	67.6975	−	117.255i	0.00226534	−	0.00392368i
$964$	6580.25	+	11397.3i	0.219850	+	0.380792i
$965$		0			0
$966$	−26363.9	+	6570.55i	−0.878101	+	0.218845i
$967$	−6917.06			−0.230029			−0.115014	−	0.993364i	$-0.536691\pi$
$967$	−6917.06			−0.230029			−0.115014	+	0.993364i	$0.536691\pi$
$968$	−5763.41	−	9982.52i	−0.191367	−	0.331457i
$969$	11743.9	−	20341.1i	0.389339	−	0.674355i
$970$		0			0
$971$	−19758.8	−	34223.3i	−0.653029	−	1.13108i	−0.982384	−	0.186874i	$-0.940164\pi$
$971$	−19758.8	−	34223.3i	−0.653029	−	1.13108i	0.329355	−	0.944206i	$-0.393169\pi$
$972$	746.820			0.0246443
$973$	1214.70	−	4234.60i	0.0400220	−	0.139522i
$974$	−7621.57			−0.250730
$975$		0			0
$976$	−4262.92	+	7383.60i	−0.139808	+	0.242155i
$977$	−19429.2	+	33652.4i	−0.636229	+	1.10198i	0.350024	+	0.936741i	$0.386173\pi$
$977$	−19429.2	+	33652.4i	−0.636229	+	1.10198i	−0.986253	+	0.165240i	$0.947160\pi$
$978$	−8166.70	−	14145.1i	−0.267017	−	0.462487i
$979$	−3748.68			−0.122378
$980$		0			0
$981$	379.040			0.0123362
$982$	9873.16	+	17100.8i	0.320840	+	0.555712i
$983$	−255.115	+	441.872i	−0.00827762	+	0.0143373i	−0.870135	−	0.492814i	$-0.835968\pi$
$983$	−255.115	+	441.872i	−0.00827762	+	0.0143373i	0.861857	+	0.507151i	$0.169302\pi$
$984$	−592.717	+	1026.62i	−0.0192024	+	0.0332595i
$985$		0			0
$986$	12768.0			0.412390
$987$	5046.80	−	17593.8i	0.162757	−	0.567394i
$988$	−2471.02			−0.0795683
$989$	−28757.2	−	49808.9i	−0.924596	−	1.60145i
$990$		0			0
$991$	18111.4	−	31369.9i	0.580553	−	1.00555i	−0.414861	−	0.909885i	$-0.636170\pi$
$991$	18111.4	−	31369.9i	0.580553	−	1.00555i	0.995414	−	0.0956623i	$-0.0304969\pi$
$992$	19382.4	+	33571.3i	0.620355	+	1.07449i
$993$	−30271.2			−0.967400
$994$	−29266.2	+	7293.87i	−0.933870	+	0.232744i
$995$		0			0
$996$	13804.6	+	23910.2i	0.439171	+	0.760666i
$997$	−10428.0	+	18061.9i	−0.331253	+	0.573747i	−0.982758	−	0.184898i	$-0.940805\pi$
$997$	−10428.0	+	18061.9i	−0.331253	+	0.573747i	0.651505	+	0.758644i	$0.274138\pi$
$998$	9354.04	−	16201.7i	0.296690	−	0.513883i
$999$	1088.91	+	1886.05i	0.0344861	+	0.0597316i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	175.4.e.c.151.2		4
5.2	odd	4		175.4.k.c.74.3		8
5.3	odd	4		175.4.k.c.74.2		8
5.4	even	2		35.4.e.b.11.1	✓	4
7.2	even	3	inner	175.4.e.c.51.2		4
7.3	odd	6		1225.4.a.v.1.1		2
7.4	even	3		1225.4.a.x.1.1		2
15.14	odd	2		315.4.j.c.46.2		4
20.19	odd	2		560.4.q.i.81.1		4
35.2	odd	12		175.4.k.c.149.2		8
35.4	even	6		245.4.a.g.1.2		2
35.9	even	6		35.4.e.b.16.1	yes	4
35.19	odd	6		245.4.e.l.226.1		4
35.23	odd	12		175.4.k.c.149.3		8
35.24	odd	6		245.4.a.h.1.2		2
35.34	odd	2		245.4.e.l.116.1		4
105.44	odd	6		315.4.j.c.226.2		4
105.59	even	6		2205.4.a.bg.1.1		2
105.74	odd	6		2205.4.a.bf.1.1		2
140.79	odd	6		560.4.q.i.401.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.4.e.b.11.1	✓	4	5.4	even	2
35.4.e.b.16.1	yes	4	35.9	even	6
175.4.e.c.51.2		4	7.2	even	3	inner
175.4.e.c.151.2		4	1.1	even	1	trivial
175.4.k.c.74.2		8	5.3	odd	4
175.4.k.c.74.3		8	5.2	odd	4
175.4.k.c.149.2		8	35.2	odd	12
175.4.k.c.149.3		8	35.23	odd	12
245.4.a.g.1.2		2	35.4	even	6
245.4.a.h.1.2		2	35.24	odd	6
245.4.e.l.116.1		4	35.34	odd	2
245.4.e.l.226.1		4	35.19	odd	6
315.4.j.c.46.2		4	15.14	odd	2
315.4.j.c.226.2		4	105.44	odd	6
560.4.q.i.81.1		4	20.19	odd	2
560.4.q.i.401.1		4	140.79	odd	6
1225.4.a.v.1.1		2	7.3	odd	6
1225.4.a.x.1.1		2	7.4	even	3
2205.4.a.bf.1.1		2	105.74	odd	6
2205.4.a.bg.1.1		2	105.59	even	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:	\( N \)	\(=\)	\( 175 = 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	175.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.792893 - 1.37333i) q^{2} +(-2.62132 + 4.54026i) q^{3} +(2.74264 - 4.75039i) q^{4} +8.31371 q^{6} +(5.10660 - 17.8023i) q^{7} -21.3848 q^{8} +(-0.242641 - 0.420266i) q^{9} +O(q^{10})\)	\(q+(-0.792893 - 1.37333i) q^{2} +(-2.62132 + 4.54026i) q^{3} +(2.74264 - 4.75039i) q^{4} +8.31371 q^{6} +(5.10660 - 17.8023i) q^{7} -21.3848 q^{8} +(-0.242641 - 0.420266i) q^{9} +(-14.0711 + 24.3718i) q^{11} +(14.3787 + 24.9046i) q^{12} +3.85786 q^{13} +(-28.4975 + 7.10228i) q^{14} +(-4.98528 - 8.63476i) q^{16} +(19.1838 - 33.2273i) q^{17} +(-0.384776 + 0.666452i) q^{18} +(-58.3848 - 101.125i) q^{19} +(67.4411 + 69.8509i) q^{21} +44.6274 q^{22} +(-88.2315 - 152.821i) q^{23} +(56.0563 - 97.0924i) q^{24} +(-3.05887 - 5.29813i) q^{26} -139.007 q^{27} +(-70.5624 - 73.0837i) q^{28} -209.853 q^{29} +(103.711 - 179.632i) q^{31} +(-93.4447 + 161.851i) q^{32} +(-73.7696 - 127.773i) q^{33} -60.8427 q^{34} -2.66190 q^{36} +(-7.83348 - 13.5680i) q^{37} +(-92.5858 + 160.363i) q^{38} +(-10.1127 + 17.5157i) q^{39} -10.5736 q^{41} +(42.4548 - 148.003i) q^{42} +325.929 q^{43} +(77.1838 + 133.686i) q^{44} +(-139.916 + 242.342i) q^{46} +(-94.2548 - 163.254i) q^{47} +52.2721 q^{48} +(-290.845 - 181.819i) q^{49} +(100.574 + 174.199i) q^{51} +(10.5807 - 18.3264i) q^{52} +(-137.591 + 238.314i) q^{53} +(110.218 + 190.903i) q^{54} +(-109.204 + 380.699i) q^{56} +612.181 q^{57} +(166.391 + 288.197i) q^{58} +(-21.9096 + 37.9485i) q^{59} +(-427.551 - 740.540i) q^{61} -328.926 q^{62} +(-8.72078 + 2.17344i) q^{63} +216.602 q^{64} +(-116.983 + 202.620i) q^{66} +(-272.710 + 472.347i) q^{67} +(-105.228 - 182.261i) q^{68} +925.132 q^{69} +1026.97 q^{71} +(5.18882 + 8.98729i) q^{72} +(-126.439 + 218.998i) q^{73} +(-12.4222 + 21.5159i) q^{74} -640.514 q^{76} +(362.019 + 374.955i) q^{77} +32.0732 q^{78} +(461.321 + 799.031i) q^{79} +(370.934 - 642.476i) q^{81} +(8.38373 + 14.5210i) q^{82} +960.071 q^{83} +(516.786 - 128.796i) q^{84} +(-258.427 - 447.608i) q^{86} +(550.091 - 952.786i) q^{87} +(300.907 - 521.186i) q^{88} +(66.6026 + 115.359i) q^{89} +(19.7006 - 68.6789i) q^{91} -967.949 q^{92} +(543.718 + 941.747i) q^{93} +(-149.468 + 258.886i) q^{94} +(-489.897 - 848.526i) q^{96} +1021.11 q^{97} +(-19.0881 + 543.590i) q^{98} +13.6569 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 6 q^{2} - 2 q^{3} - 6 q^{4} - 12 q^{6} - 22 q^{7} - 12 q^{8} + 16 q^{9}+O(q^{10}) \) 4 * q - 6 * q^2 - 2 * q^3 - 6 * q^4 - 12 * q^6 - 22 * q^7 - 12 * q^8 + 16 * q^9	\( 4 q - 6 q^{2} - 2 q^{3} - 6 q^{4} - 12 q^{6} - 22 q^{7} - 12 q^{8} + 16 q^{9} - 28 q^{11} + 66 q^{12} + 72 q^{13} + 84 q^{14} + 14 q^{16} - 76 q^{17} + 72 q^{18} - 160 q^{19} + 134 q^{21} + 88 q^{22} - 22 q^{23} + 162 q^{24} - 148 q^{26} + 4 q^{27} - 138 q^{28} - 500 q^{29} + 132 q^{31} + 42 q^{32} - 148 q^{33} + 888 q^{34} - 384 q^{36} - 416 q^{37} - 376 q^{38} + 84 q^{39} - 212 q^{41} + 546 q^{42} + 1332 q^{43} + 156 q^{44} + 402 q^{46} - 196 q^{47} + 260 q^{48} - 230 q^{49} + 572 q^{51} - 348 q^{52} - 952 q^{53} - 402 q^{54} - 714 q^{56} + 944 q^{57} + 510 q^{58} - 840 q^{59} - 98 q^{61} + 8 q^{62} - 544 q^{63} - 1204 q^{64} - 236 q^{66} - 1286 q^{67} - 1524 q^{68} + 2852 q^{69} + 2128 q^{71} + 264 q^{72} - 172 q^{73} - 1792 q^{74} - 288 q^{76} + 724 q^{77} - 856 q^{78} + 1240 q^{79} + 754 q^{81} + 438 q^{82} + 3812 q^{83} - 156 q^{84} - 2018 q^{86} + 970 q^{87} + 604 q^{88} - 650 q^{89} - 996 q^{91} - 5484 q^{92} + 1332 q^{93} - 332 q^{94} - 1722 q^{96} + 1256 q^{97} - 3066 q^{98} + 32 q^{99}+O(q^{100}) \) 4 * q - 6 * q^2 - 2 * q^3 - 6 * q^4 - 12 * q^6 - 22 * q^7 - 12 * q^8 + 16 * q^9 - 28 * q^11 + 66 * q^12 + 72 * q^13 + 84 * q^14 + 14 * q^16 - 76 * q^17 + 72 * q^18 - 160 * q^19 + 134 * q^21 + 88 * q^22 - 22 * q^23 + 162 * q^24 - 148 * q^26 + 4 * q^27 - 138 * q^28 - 500 * q^29 + 132 * q^31 + 42 * q^32 - 148 * q^33 + 888 * q^34 - 384 * q^36 - 416 * q^37 - 376 * q^38 + 84 * q^39 - 212 * q^41 + 546 * q^42 + 1332 * q^43 + 156 * q^44 + 402 * q^46 - 196 * q^47 + 260 * q^48 - 230 * q^49 + 572 * q^51 - 348 * q^52 - 952 * q^53 - 402 * q^54 - 714 * q^56 + 944 * q^57 + 510 * q^58 - 840 * q^59 - 98 * q^61 + 8 * q^62 - 544 * q^63 - 1204 * q^64 - 236 * q^66 - 1286 * q^67 - 1524 * q^68 + 2852 * q^69 + 2128 * q^71 + 264 * q^72 - 172 * q^73 - 1792 * q^74 - 288 * q^76 + 724 * q^77 - 856 * q^78 + 1240 * q^79 + 754 * q^81 + 438 * q^82 + 3812 * q^83 - 156 * q^84 - 2018 * q^86 + 970 * q^87 + 604 * q^88 - 650 * q^89 - 996 * q^91 - 5484 * q^92 + 1332 * q^93 - 332 * q^94 - 1722 * q^96 + 1256 * q^97 - 3066 * q^98 + 32 * q^99

Introduction

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