LMFDB - Embedded newform 175.4.k.d.149.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [175,4,Mod(74,175)]

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([3, 4]))

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

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

chi := DirichletCharacter("175.74");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 175 = 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	175.k (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$10.3253342510$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 75 x^{18} + 3638 x^{16} - 105775 x^{14} + 2246038 x^{12} - 30934571 x^{10} + 307864753 x^{8} + \cdots + 16777216 $ x^20 - 75x^18 + 3638x^16 - 105775x^14 + 2246038x^12 - 30934571x^10 + 307864753x^8 - 1719258496x^6 + 6352449536x^4 - 328728576*x^2 + 16777216
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{20} $
Twist minimal:	no (minimal twist has level 35)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			149.3
Root			$-3.33093 + 1.92311i$ of defining polynomial
Character	$\chi$	$=$	175.149
Dual form			175.4.k.d.74.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-3.33093 - 1.92311i) q^{2} +(7.76647 - 4.48397i) q^{3} +(3.39672 + 5.88330i) q^{4} -34.4927 q^{6} +(13.8005 + 12.3509i) q^{7} +4.64067i q^{8} +(26.7120 - 46.2666i) q^{9} +(-11.5560 - 20.0155i) q^{11} +(52.7611 + 30.4617i) q^{12} -61.0473i q^{13} +(-22.2164 - 67.6800i) q^{14} +(36.0983 - 62.5241i) q^{16} +(0.596093 - 0.344154i) q^{17} +(-177.952 + 102.741i) q^{18} +(31.6124 - 54.7542i) q^{19} +(162.563 + 34.0419i) q^{21} +88.8938i q^{22} +(107.822 + 62.2508i) q^{23} +(20.8086 + 36.0416i) q^{24} +(-117.401 + 203.344i) q^{26} -236.970i q^{27} +(-25.7876 + 123.145i) q^{28} -104.167 q^{29} +(-140.011 - 242.506i) q^{31} +(-208.330 + 120.280i) q^{32} +(-179.498 - 103.633i) q^{33} -2.64739 q^{34} +362.934 q^{36} +(228.519 + 131.936i) q^{37} +(-210.597 + 121.588i) q^{38} +(-273.735 - 474.122i) q^{39} -243.366 q^{41} +(-476.018 - 426.017i) q^{42} -172.541i q^{43} +(78.5049 - 135.975i) q^{44} +(-239.431 - 414.706i) q^{46} +(92.9951 + 53.6907i) q^{47} -647.456i q^{48} +(37.9094 + 340.899i) q^{49} +(3.08636 - 5.34573i) q^{51} +(359.160 - 207.361i) q^{52} +(-38.8054 + 22.4043i) q^{53} +(-455.720 + 789.330i) q^{54} +(-57.3165 + 64.0437i) q^{56} -566.996i q^{57} +(346.973 + 200.325i) q^{58} +(228.623 + 395.986i) q^{59} +(-236.901 + 410.324i) q^{61} +1077.03i q^{62} +(940.076 - 308.586i) q^{63} +347.672 q^{64} +(398.597 + 690.391i) q^{66} +(-198.713 + 114.727i) q^{67} +(4.04953 + 2.33800i) q^{68} +1116.52 q^{69} +407.688 q^{71} +(214.708 + 123.962i) q^{72} +(301.789 - 174.238i) q^{73} +(-507.454 - 878.937i) q^{74} +429.514 q^{76} +(87.7317 - 418.952i) q^{77} +2105.69i q^{78} +(420.068 - 727.579i) q^{79} +(-341.342 - 591.221i) q^{81} +(810.635 + 468.020i) q^{82} +885.652i q^{83} +(351.902 + 1072.04i) q^{84} +(-331.816 + 574.722i) q^{86} +(-809.010 + 467.082i) q^{87} +(92.8854 - 53.6274i) q^{88} +(-428.048 + 741.401i) q^{89} +(753.991 - 842.486i) q^{91} +845.795i q^{92} +(-2174.78 - 1255.61i) q^{93} +(-206.507 - 357.680i) q^{94} +(-1078.66 + 1868.30i) q^{96} +189.436i q^{97} +(529.313 - 1208.41i) q^{98} -1234.74 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 70 q^{4} + 64 q^{6} + 162 q^{9} - 94 q^{11} - 14 q^{14} - 342 q^{16} - 42 q^{19} + 356 q^{21} + 1696 q^{24} + 94 q^{26} - 760 q^{29} - 776 q^{31} - 520 q^{34} + 4916 q^{36} + 28 q^{39} - 1124 q^{41}+ \cdots - 140 q^{99}+O(q^{100}) $ 20 * q + 70 * q^4 + 64 * q^6 + 162 * q^9 - 94 * q^11 - 14 * q^14 - 342 * q^16 - 42 * q^19 + 356 * q^21 + 1696 * q^24 + 94 * q^26 - 760 * q^29 - 776 * q^31 - 520 * q^34 + 4916 * q^36 + 28 * q^39 - 1124 * q^41 + 2182 * q^44 - 674 * q^46 - 1996 * q^49 - 1464 * q^51 - 1548 * q^54 - 2676 * q^56 + 1416 * q^59 - 3888 * q^61 + 500 * q^64 - 2964 * q^66 - 1496 * q^69 + 3456 * q^71 - 6570 * q^74 + 2764 * q^76 + 436 * q^79 + 910 * q^81 + 1468 * q^84 + 8528 * q^86 + 4644 * q^89 + 1048 * q^91 - 5354 * q^94 - 9184 * q^96 - 140 * q^99

Character values

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

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

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 $

$2$	−3.33093	−	1.92311i	−1.17766	−	0.679923i	−0.222189	−	0.975004i	$-0.571320\pi$
$2$	−3.33093	−	1.92311i	−1.17766	−	0.679923i	−0.955472	+	0.295081i	$0.904653\pi$
$3$	7.76647	−	4.48397i	1.49466	−	0.862941i	0.494677	−	0.869077i	$-0.335286\pi$
$3$	7.76647	−	4.48397i	1.49466	−	0.862941i	0.999981	+	0.00613580i	$0.00195310\pi$
$4$	3.39672	+	5.88330i	0.424591	+	0.735412i
$5$		0			0
$5$		0			0
$6$	−34.4927			−2.34693
$7$	13.8005	+	12.3509i	0.745159	+	0.666887i
$7$	13.8005	+	12.3509i	0.745159	+	0.666887i
$8$			4.64067i			0.205090i
$9$	26.7120	−	46.2666i	0.989335	−	1.71358i
$10$		0			0
$11$	−11.5560	−	20.0155i	−0.316751	−	0.548628i	0.663057	−	0.748569i	$-0.269259\pi$
$11$	−11.5560	−	20.0155i	−0.316751	−	0.548628i	−0.979808	+	0.199940i	$0.935925\pi$
$12$	52.7611	+	30.4617i	1.26924	+	0.732793i
$13$		−	61.0473i		−	1.30242i	−0.758897	−	0.651211i	$-0.774261\pi$
$13$		−	61.0473i		−	1.30242i	0.758897	−	0.651211i	$-0.225739\pi$
$14$	−22.2164	−	67.6800i	−0.424113	−	1.29202i
$15$		0			0
$16$	36.0983	−	62.5241i	0.564036	−	0.976939i
$17$	0.596093	−	0.344154i	0.00850434	−	0.00490998i	−0.495742	−	0.868470i	$-0.665104\pi$
$17$	0.596093	−	0.344154i	0.00850434	−	0.00490998i	0.504246	+	0.863560i	$0.331770\pi$
$18$	−177.952	+	102.741i	−2.33020	+	1.34534i
$19$	31.6124	−	54.7542i	0.381704	−	0.661130i	−0.609602	−	0.792707i	$-0.708671\pi$
$19$	31.6124	−	54.7542i	0.381704	−	0.661130i	0.991306	+	0.131577i	$0.0420041\pi$
$20$		0			0
$21$	162.563	+	34.0419i	1.68924	+	0.353740i
$22$			88.8938i			0.861464i
$23$	107.822	+	62.2508i	0.977493	+	0.564356i	0.901512	−	0.432753i	$-0.142458\pi$
$23$	107.822	+	62.2508i	0.977493	+	0.564356i	0.0759809	+	0.997109i	$0.475791\pi$
$24$	20.8086	+	36.0416i	0.176981	+	0.306540i
$25$		0			0
$26$	−117.401	+	203.344i	−0.885547	+	1.53381i
$27$		−	236.970i		−	1.68907i
$28$	−25.7876	+	123.145i	−0.174050	+	0.831153i
$29$	−104.167			−0.667011			−0.333506	−	0.942748i	$-0.608232\pi$
$29$	−104.167			−0.667011			−0.333506	+	0.942748i	$0.608232\pi$
$30$		0			0
$31$	−140.011	−	242.506i	−0.811185	−	1.40501i	−0.912035	−	0.410112i	$-0.865490\pi$
$31$	−140.011	−	242.506i	−0.811185	−	1.40501i	0.100850	−	0.994902i	$-0.467844\pi$
$32$	−208.330	+	120.280i	−1.15087	+	0.664457i
$33$	−179.498	−	103.633i	−0.946868	−	0.546674i
$34$	−2.64739			−0.0133536
$35$		0			0
$36$	362.934			1.68025
$37$	228.519	+	131.936i	1.01536	+	0.586219i	0.912757	−	0.408504i	$-0.133949\pi$
$37$	228.519	+	131.936i	1.01536	+	0.586219i	0.102604	+	0.994722i	$0.467283\pi$
$38$	−210.597	+	121.588i	−0.899035	+	0.519058i
$39$	−273.735	−	474.122i	−1.12391	−	1.94668i
$40$		0			0
$41$	−243.366			−0.927009			−0.463505	−	0.886095i	$-0.653408\pi$
$41$	−243.366			−0.927009			−0.463505	+	0.886095i	$0.653408\pi$
$42$	−476.018	−	426.017i	−1.74884	−	1.56514i
$43$		−	172.541i		−	0.611913i	−0.952046	−	0.305956i	$-0.901024\pi$
$43$		−	172.541i		−	0.611913i	0.952046	−	0.305956i	$-0.0989762\pi$
$44$	78.5049	−	135.975i	0.268979	−	0.465885i
$45$		0			0
$46$	−239.431	−	414.706i	−0.767437	−	1.32924i
$47$	92.9951	+	53.6907i	0.288611	+	0.166630i	0.637315	−	0.770603i	$-0.280045\pi$
$47$	92.9951	+	53.6907i	0.288611	+	0.166630i	−0.348704	+	0.937233i	$0.613378\pi$
$48$		−	647.456i		−	1.94692i
$49$	37.9094	+	340.899i	0.110523	+	0.993874i
$50$		0			0
$51$	3.08636	−	5.34573i	0.00847405	−	0.0146775i
$52$	359.160	−	207.361i	0.957817	−	0.552996i
$53$	−38.8054	+	22.4043i	−0.100572	+	0.0580654i	−0.549443	−	0.835532i	$-0.685160\pi$
$53$	−38.8054	+	22.4043i	−0.100572	+	0.0580654i	0.448870	+	0.893597i	$0.351827\pi$
$54$	−455.720	+	789.330i	−1.14844	+	1.98915i
$55$		0			0
$56$	−57.3165	+	64.0437i	−0.136772	+	0.152825i
$57$		−	566.996i		−	1.31755i
$58$	346.973	+	200.325i	0.785513	+	0.453516i
$59$	228.623	+	395.986i	0.504477	+	0.873780i	0.999987	+	0.00517746i	$0.00164804\pi$
$59$	228.623	+	395.986i	0.504477	+	0.873780i	−0.495509	+	0.868603i	$0.665019\pi$
$60$		0			0
$61$	−236.901	+	410.324i	−0.497247	+	0.861256i	−0.999995	−	0.00317642i	$-0.998989\pi$
$61$	−236.901	+	410.324i	−0.497247	+	0.861256i	0.502748	+	0.864433i	$0.332322\pi$
$62$			1077.03i			2.20617i
$63$	940.076	−	308.586i	1.87998	−	0.617113i
$64$	347.672			0.679047
$65$		0			0
$66$	398.597	+	690.391i	0.743393	+	1.28759i
$67$	−198.713	+	114.727i	−0.362338	+	0.209196i	−0.670106	−	0.742266i	$-0.733751\pi$
$67$	−198.713	+	114.727i	−0.362338	+	0.209196i	0.307768	+	0.951461i	$0.400418\pi$
$68$	4.04953	+	2.33800i	0.00722172	+	0.00416946i
$69$	1116.52			1.94802
$70$		0			0
$71$	407.688			0.681460			0.340730	−	0.940161i	$-0.389326\pi$
$71$	407.688			0.681460			0.340730	+	0.940161i	$0.389326\pi$
$72$	214.708	+	123.962i	0.351438	+	0.202903i
$73$	301.789	−	174.238i	0.483859	−	0.279356i	−0.238165	−	0.971225i	$-0.576546\pi$
$73$	301.789	−	174.238i	0.483859	−	0.279356i	0.722023	+	0.691869i	$0.243212\pi$
$74$	−507.454	−	878.937i	−0.797167	−	1.38073i
$75$		0			0
$76$	429.514			0.648271
$77$	87.7317	−	418.952i	0.129844	−	0.620052i
$78$			2105.69i			3.05670i
$79$	420.068	−	727.579i	0.598244	−	1.03619i	−0.394836	−	0.918752i	$-0.629199\pi$
$79$	420.068	−	727.579i	0.598244	−	1.03619i	0.993080	−	0.117438i	$-0.0374682\pi$
$80$		0			0
$81$	−341.342	−	591.221i	−0.468233	−	0.811003i
$82$	810.635	+	468.020i	1.09170	+	0.630295i
$83$			885.652i			1.17124i	0.810586	+	0.585620i	$0.199149\pi$
$83$			885.652i			1.17124i	−0.810586	+	0.585620i	$0.800851\pi$
$84$	351.902	+	1072.04i	0.457091	+	1.39248i
$85$		0			0
$86$	−331.816	+	574.722i	−0.416054	+	0.720626i
$87$	−809.010	+	467.082i	−0.996954	+	0.575592i
$88$	92.8854	−	53.6274i	0.112518	−	0.0649625i
$89$	−428.048	+	741.401i	−0.509809	+	0.883015i	0.490127	+	0.871651i	$0.336951\pi$
$89$	−428.048	+	741.401i	−0.509809	+	0.883015i	−0.999935	+	0.0113636i	$0.996383\pi$
$90$		0			0
$91$	753.991	−	842.486i	0.868569	−	0.970511i
$92$			845.795i			0.958481i
$93$	−2174.78	−	1255.61i	−2.42489	−	1.40001i
$94$	−206.507	−	357.680i	−0.226591	−	0.392467i
$95$		0			0
$96$	−1078.66	+	1868.30i	−1.14678	+	1.98627i
$97$			189.436i			0.198292i	0.995073	+	0.0991459i	$0.0316111\pi$
$97$			189.436i			0.198292i	−0.995073	+	0.0991459i	$0.968389\pi$
$98$	529.313	−	1208.41i	0.545599	−	1.24559i
$99$	−1234.74			−1.25349
$100$		0			0
$101$	−397.902	−	689.186i	−0.392007	−	0.678976i	0.600707	−	0.799469i	$-0.294886\pi$
$101$	−397.902	−	689.186i	−0.392007	−	0.678976i	−0.992714	+	0.120493i	$0.961552\pi$
$102$	−20.5609	+	11.8708i	−0.0199591	+	0.0115234i
$103$	1680.70	+	970.353i	1.60781	+	0.928269i	0.989859	+	0.142052i	$0.0453699\pi$
$103$	1680.70	+	970.353i	1.60781	+	0.928269i	0.617950	+	0.786218i	$0.287963\pi$
$104$	283.300			0.267114
$105$		0			0
$106$	172.344			0.157920
$107$	−423.217	−	244.344i	−0.382373	−	0.220763i	0.296477	−	0.955040i	$-0.404188\pi$
$107$	−423.217	−	244.344i	−0.382373	−	0.220763i	−0.678850	+	0.734277i	$0.737521\pi$
$108$	1394.16	−	804.921i	1.24216	−	0.717163i
$109$	815.027	+	1411.67i	0.716197	+	1.24049i	0.962496	+	0.271295i	$0.0874519\pi$
$109$	815.027	+	1411.67i	0.716197	+	1.24049i	−0.246300	+	0.969194i	$0.579215\pi$
$110$		0			0
$111$	2366.38			2.02349
$112$	1270.41	−	417.019i	1.07180	−	0.351826i
$113$		−	345.925i		−	0.287981i	−0.989579	−	0.143991i	$-0.954007\pi$
$113$		−	345.925i		−	0.287981i	0.989579	−	0.143991i	$-0.0459935\pi$
$114$	−1090.40	+	1888.62i	−0.895834	+	1.55163i
$115$		0			0
$116$	−353.827	−	612.846i	−0.283207	−	0.490528i
$117$	−2824.45	−	1630.70i	−2.23180	−	1.28853i
$118$		−	1758.67i		−	1.37202i
$119$	12.4770	+	2.61278i	0.00961149	+	0.00201272i
$120$		0			0
$121$	398.419	−	690.082i	0.299338	−	0.518469i
$122$	1578.20	−	911.174i	1.17118	−	0.676179i
$123$	−1890.09	+	1091.25i	−1.38556	+	0.799954i
$124$	951.158	−	1647.45i	0.688843	−	1.19311i
$125$		0			0
$126$	−3724.77	−	779.995i	−2.63356	−	0.551488i
$127$		−	1665.24i		−	1.16351i	−0.813362	−	0.581757i	$-0.802365\pi$
$127$		−	1665.24i		−	1.16351i	0.813362	−	0.581757i	$-0.197635\pi$
$128$	508.573	+	293.625i	0.351187	+	0.202758i
$129$	−773.669	−	1340.03i	−0.528045	−	0.914601i
$130$		0			0
$131$	−338.374	+	586.080i	−0.225678	+	0.390886i	−0.956523	−	0.291658i	$-0.905793\pi$
$131$	−338.374	+	586.080i	−0.225678	+	0.390886i	0.730844	+	0.682544i	$0.239126\pi$
$132$		−	1408.06i		−	0.928451i
$133$	1112.53	−	365.195i	0.725329	−	0.238094i
$134$	882.531			0.568948
$135$		0			0
$136$	1.59711	+	2.76627i	0.00100699	+	0.00174416i
$137$	−895.673	+	517.117i	−0.558558	+	0.322484i	−0.752567	−	0.658516i	$-0.771184\pi$
$137$	−895.673	+	517.117i	−0.558558	+	0.322484i	0.194008	+	0.981000i	$0.437851\pi$
$138$	−3719.06	−	2147.20i	−2.29411	−	1.32451i
$139$	−435.826			−0.265944			−0.132972	−	0.991120i	$-0.542452\pi$
$139$	−435.826			−0.265944			−0.132972	+	0.991120i	$0.542452\pi$
$140$		0			0
$141$	962.992			0.575167
$142$	−1357.98	−	784.030i	−0.802529	−	0.463341i
$143$	−1221.90	+	705.462i	−0.714546	+	0.412543i
$144$	−1928.52	−	3340.29i	−1.11604	−	1.93304i
$145$		0			0
$146$	−1340.31			−0.759762
$147$	1823.00	+	2477.59i	1.02285	+	1.39013i
$148$			1792.60i			0.995612i
$149$	1059.97	−	1835.93i	0.582795	−	1.00943i	−0.412351	−	0.911025i	$-0.635292\pi$
$149$	1059.97	−	1835.93i	0.582795	−	1.00943i	0.995146	−	0.0984057i	$-0.0313743\pi$
$150$		0			0
$151$	1200.20	+	2078.81i	0.646827	+	1.12034i	0.983876	+	0.178850i	$0.0572376\pi$
$151$	1200.20	+	2078.81i	0.646827	+	1.12034i	−0.337050	+	0.941487i	$0.609429\pi$
$152$	254.096	+	146.702i	0.135591	+	0.0782838i
$153$		−	36.7723i		−	0.0194305i
$154$	−1097.92	+	1226.78i	−0.574500	+	0.641928i
$155$		0			0
$156$	1859.60	−	3220.93i	0.954406	−	1.65308i
$157$	−438.372	+	253.094i	−0.222840	+	0.128657i	−0.607265	−	0.794500i	$-0.707733\pi$
$157$	−438.372	+	253.094i	−0.222840	+	0.128657i	0.384425	+	0.923156i	$0.374400\pi$
$158$	−2798.43	+	1615.68i	−1.40906	+	0.813520i
$159$	−200.921	+	348.005i	−0.100214	+	0.173576i
$160$		0			0
$161$	719.140	+	2190.79i	0.352026	+	1.07241i
$162$			2625.75i			1.27345i
$163$	2252.49	+	1300.47i	1.08238	+	0.624913i	0.931538	−	0.363644i	$-0.118468\pi$
$163$	2252.49	+	1300.47i	1.08238	+	0.624913i	0.150844	+	0.988558i	$0.451801\pi$
$164$	−826.647	−	1431.79i	−0.393599	−	0.681734i
$165$		0			0
$166$	1703.21	−	2950.04i	0.796353	−	1.37932i
$167$			546.077i			0.253034i	0.991964	+	0.126517i	$0.0403798\pi$
$167$			546.077i			0.253034i	−0.991964	+	0.126517i	$0.959620\pi$
$168$	−157.977	+	754.399i	−0.0725487	+	0.346447i
$169$	−1529.78			−0.696303
$170$		0			0
$171$	−1688.86	−	2925.19i	−0.755266	−	1.30816i
$172$	1015.11	−	586.074i	0.450008	−	0.259812i
$173$	−2615.67	−	1510.16i	−1.14951	−	0.663673i	−0.200746	−	0.979643i	$-0.564336\pi$
$173$	−2615.67	−	1510.16i	−1.14951	−	0.663673i	−0.948769	+	0.315971i	$0.897670\pi$
$174$	3593.01			1.56543
$175$		0			0
$176$	−1668.61			−0.714636
$177$	3551.18	+	2050.28i	1.50804	+	0.870668i
$178$	2851.59	−	1646.37i	1.20076	−	0.693262i
$179$	999.583	+	1731.33i	0.417387	+	0.722936i	0.995676	−	0.0928961i	$-0.0296125\pi$
$179$	999.583	+	1731.33i	0.417387	+	0.722936i	−0.578288	+	0.815832i	$0.696279\pi$
$180$		0			0
$181$	−681.145			−0.279719			−0.139859	−	0.990171i	$-0.544665\pi$
$181$	−681.145			−0.279719			−0.139859	+	0.990171i	$0.544665\pi$
$182$	−4131.69	+	1356.25i	−1.68275	+	0.552374i
$183$			4249.03i			1.71638i
$184$	−288.885	+	500.364i	−0.115744	+	0.200474i
$185$		0			0
$186$	4829.37	+	8364.71i	1.90380	+	3.29747i
$187$	−13.7769	−	7.95408i	−0.00538751	−	0.00311048i
$188$			729.491i			0.282998i
$189$	2926.80	−	3270.31i	1.12642	−	1.25862i
$190$		0			0
$191$	806.381	−	1396.69i	0.305485	−	0.529116i	−0.671884	−	0.740656i	$-0.734515\pi$
$191$	806.381	−	1396.69i	0.305485	−	0.529116i	0.977369	+	0.211541i	$0.0678480\pi$
$192$	2700.18	−	1558.95i	1.01494	−	0.585977i
$193$	−700.547	+	404.461i	−0.261277	+	0.150848i	−0.624917	−	0.780691i	$-0.714867\pi$
$193$	−700.547	+	404.461i	−0.261277	+	0.150848i	0.363640	+	0.931540i	$0.381534\pi$
$194$	364.307	−	630.998i	0.134823	−	0.233521i
$195$		0			0
$196$	−1876.84	+	1380.97i	−0.683980	+	0.503269i
$197$			3704.23i			1.33967i	0.742509	+	0.669836i	$0.233636\pi$
$197$			3704.23i			1.33967i	−0.742509	+	0.669836i	$0.766364\pi$
$198$	4112.81	+	2374.53i	1.47619	+	0.852277i
$199$	−183.964	−	318.635i	−0.0655319	−	0.113505i	0.831398	−	0.555678i	$-0.187541\pi$
$199$	−183.964	−	318.635i	−0.0655319	−	0.113505i	−0.896930	+	0.442173i	$0.854208\pi$
$200$		0			0
$201$	−1028.87	+	1782.05i	−0.361047	+	0.625353i
$202$			3060.84i			1.06614i
$203$	−1437.56	−	1286.56i	−0.497029	−	0.444821i
$204$	41.9340			0.0143920
$205$		0			0
$206$	−3732.20	−	6464.35i	−1.26230	−	2.18637i
$207$	5760.27	−	3325.69i	1.93414	−	1.11667i
$208$	−3816.93	−	2203.71i	−1.27239	−	0.734613i
$209$	−1461.25			−0.483620
$210$		0			0
$211$	−1073.36			−0.350205			−0.175102	−	0.984550i	$-0.556026\pi$
$211$	−1073.36			−0.350205			−0.175102	+	0.984550i	$0.556026\pi$
$212$	−263.622	−	152.202i	−0.0854040	−	0.0493080i
$213$	3166.30	−	1828.06i	1.01855	−	0.588060i
$214$	939.803	+	1627.79i	0.300204	+	0.519968i
$215$		0			0
$216$	1099.70			0.346412
$217$	1062.95	−	5075.98i	0.332524	−	1.58793i
$218$		−	6269.55i		−	1.94783i
$219$	1562.55	−	2706.42i	0.482135	−	0.835083i
$220$		0			0
$221$	−21.0097	−	36.3899i	−0.00639487	−	0.0110762i
$222$	−7882.26	−	4550.82i	−2.38298	−	1.37582i
$223$			1725.16i			0.518050i	0.965871	+	0.259025i	$0.0834012\pi$
$223$			1725.16i			0.518050i	−0.965871	+	0.259025i	$0.916599\pi$
$224$	−4360.63	−	913.150i	−1.30070	−	0.272377i
$225$		0			0
$226$	−665.252	+	1152.25i	−0.195805	+	0.339144i
$227$	−3132.40	+	1808.49i	−0.915880	+	0.528784i	−0.882318	−	0.470653i	$-0.844018\pi$
$227$	−3132.40	+	1808.49i	−0.915880	+	0.528784i	−0.0335619	+	0.999437i	$0.510685\pi$
$228$	3335.81	−	1925.93i	0.968944	−	0.559420i
$229$	730.893	−	1265.94i	0.210912	−	0.365309i	−0.741089	−	0.671407i	$-0.765690\pi$
$229$	730.893	−	1265.94i	0.210912	−	0.365309i	0.952000	+	0.306098i	$0.0990235\pi$
$230$		0			0
$231$	−1197.20	−	3647.17i	−0.340997	−	1.03881i
$232$		−	483.404i		−	0.136798i
$233$	1849.24	+	1067.66i	0.519947	+	0.300192i	0.736913	−	0.675988i	$-0.236283\pi$
$233$	1849.24	+	1067.66i	0.519947	+	0.300192i	−0.216966	+	0.976179i	$0.569616\pi$
$234$	6272.04	+	10863.5i	1.75220	+	3.03491i
$235$		0			0
$236$	−1553.14	+	2690.11i	−0.428392	+	0.741998i
$237$		−	7534.29i		−	2.06500i
$238$	−36.5354	−	32.6977i	−0.00995058	−	0.00890537i
$239$	−5952.35			−1.61099			−0.805493	−	0.592605i	$-0.798100\pi$
$239$	−5952.35			−1.61099			−0.805493	+	0.592605i	$0.798100\pi$
$240$		0			0
$241$	1923.78	+	3332.08i	0.514197	+	0.890615i	0.999864	+	0.0164713i	$0.00524321\pi$
$241$	1923.78	+	3332.08i	0.514197	+	0.890615i	−0.485668	+	0.874144i	$0.661423\pi$
$242$	−2654.21	+	1532.41i	−0.705037	+	0.407054i
$243$	238.954	+	137.960i	0.0630819	+	0.0364203i
$244$	−3218.75			−0.844505
$245$		0			0
$246$	8394.36			2.17563
$247$	−3342.60	−	1929.85i	−0.861071	−	0.497139i
$248$	1125.39	−	649.745i	0.288155	−	0.166366i
$249$	3971.24	+	6878.39i	1.01071	+	1.75060i
$250$		0			0
$251$	−1731.69			−0.435470			−0.217735	−	0.976008i	$-0.569867\pi$
$251$	−1731.69			−0.435470			−0.217735	+	0.976008i	$0.569867\pi$
$252$	5008.68	+	4482.57i	1.25205	+	1.12054i
$253$		−	2877.47i		−	0.715041i
$254$	−3202.45	+	5546.80i	−0.791100	+	1.37023i
$255$		0			0
$256$	−2520.03	−	4364.83i	−0.615243	−	1.06563i
$257$	3511.24	+	2027.21i	0.852237	+	0.492039i	0.861405	−	0.507919i	$-0.169585\pi$
$257$	3511.24	+	2027.21i	0.852237	+	0.492039i	−0.00916808	+	0.999958i	$0.502918\pi$
$258$			5951.41i			1.43612i
$259$	1524.16	+	4643.21i	0.365663	+	1.11396i
$260$		0			0
$261$	−2782.51	+	4819.46i	−0.659898	+	1.14298i
$262$	2254.20	−	1301.46i	0.531545	−	0.306888i
$263$	5486.98	−	3167.91i	1.28647	−	0.742744i	0.308447	−	0.951242i	$-0.400191\pi$
$263$	5486.98	−	3167.91i	1.28647	−	0.742744i	0.978023	+	0.208498i	$0.0668574\pi$
$264$	480.928	−	832.992i	0.112118	−	0.194194i
$265$		0			0
$266$	−4408.08	−	923.085i	−1.01608	−	0.212774i
$267$			7677.42i			1.75974i
$268$	−1349.95	−	779.392i	−0.307691	−	0.177645i
$269$	−660.817	−	1144.57i	−0.149780	−	0.259426i	0.781366	−	0.624073i	$-0.214523\pi$
$269$	−660.817	−	1144.57i	−0.149780	−	0.259426i	−0.931146	+	0.364647i	$0.881190\pi$
$270$		0			0
$271$	1168.00	−	2023.04i	0.261812	−	0.453471i	−0.704912	−	0.709295i	$-0.749013\pi$
$271$	1168.00	−	2023.04i	0.261812	−	0.453471i	0.966723	+	0.255824i	$0.0823467\pi$
$272$		−	49.6936i		−	0.0110776i
$273$	2078.16	−	9924.02i	0.460719	−	2.20011i
$274$	3977.90			0.877056
$275$		0			0
$276$	3792.52	+	6568.84i	0.827113	+	1.43260i
$277$	−6135.99	+	3542.61i	−1.33096	+	0.768430i	−0.985447	−	0.169984i	$-0.945628\pi$
$277$	−6135.99	+	3542.61i	−1.33096	+	0.768430i	−0.345513	+	0.938414i	$0.612295\pi$
$278$	1451.71	+	838.142i	0.313192	+	0.180822i
$279$	−14959.9			−3.21013
$280$		0			0
$281$	2123.17			0.450738			0.225369	−	0.974273i	$-0.427641\pi$
$281$	2123.17			0.450738			0.225369	+	0.974273i	$0.427641\pi$
$282$	−3207.66	−	1851.94i	−0.677352	−	0.391069i
$283$	−5102.30	+	2945.82i	−1.07173	+	0.618765i	−0.928654	−	0.370946i	$-0.879033\pi$
$283$	−5102.30	+	2945.82i	−1.07173	+	0.618765i	−0.143078	+	0.989711i	$0.545700\pi$
$284$	1384.80	+	2398.55i	0.289342	+	0.501154i
$285$		0			0
$286$	5426.73			1.12199
$287$	−3358.58	−	3005.79i	−0.690769	−	0.618210i
$288$			12851.7i			2.62948i
$289$	−2456.26	+	4254.37i	−0.499952	+	0.865942i
$290$		0			0
$291$	849.426	+	1471.25i	0.171114	+	0.296378i
$292$	2050.19	+	1183.67i	0.410884	+	0.237224i
$293$			8137.75i			1.62257i	0.584652	+	0.811284i	$0.301231\pi$
$293$			8137.75i			1.62257i	−0.584652	+	0.811284i	$0.698769\pi$
$294$	−1307.60	−	11758.5i	−0.259390	−	2.33256i
$295$		0			0
$296$	−612.269	+	1060.48i	−0.120228	+	0.208241i
$297$	−4743.08	+	2738.42i	−0.926671	+	0.535014i
$298$	−7061.40	+	4076.90i	−1.37267	+	0.792512i
$299$	3800.25	−	6582.22i	0.735030	−	1.27311i
$300$		0			0
$301$	2131.04	−	2381.16i	0.408077	−	0.455972i
$302$		−	9232.47i		−	1.75917i
$303$	−6180.58	−	3568.36i	−1.17183	−	0.676558i
$304$	−2282.31	−	3953.07i	−0.430589	−	0.745803i
$305$		0			0
$306$	−70.7172	+	122.486i	−0.0132112	+	0.0228825i
$307$		−	4797.24i		−	0.891833i	−0.895075	−	0.445917i	$-0.852878\pi$
$307$		−	4797.24i		−	0.891833i	0.895075	−	0.445917i	$-0.147122\pi$
$308$	2762.82	−	906.913i	0.511124	−	0.167780i
$309$	17404.1			3.20417
$310$		0			0
$311$	−2594.76	−	4494.26i	−0.473105	−	0.819442i	0.526421	−	0.850224i	$-0.323533\pi$
$311$	−2594.76	−	4494.26i	−0.473105	−	0.819442i	−0.999526	+	0.0307823i	$0.990200\pi$
$312$	2200.24	−	1270.31i	0.399244	−	0.230504i
$313$	−1944.44	−	1122.62i	−0.351138	−	0.202729i	0.314049	−	0.949407i	$-0.398314\pi$
$313$	−1944.44	−	1122.62i	−0.351138	−	0.202729i	−0.665186	+	0.746678i	$0.731648\pi$
$314$	1946.91			0.349907
$315$		0			0
$316$	5707.42			1.01604
$317$	8437.05	+	4871.13i	1.49486	+	0.863060i	0.999983	−	0.00590040i	$-0.00187817\pi$
$317$	8437.05	+	4871.13i	1.49486	+	0.863060i	0.494881	+	0.868961i	$0.335212\pi$
$318$	1338.50	−	772.786i	0.236036	−	0.136276i
$319$	1203.75	+	2084.96i	0.211276	+	0.365941i
$320$		0			0
$321$	−4382.53			−0.762022
$322$	1817.73	−	8680.35i	0.314591	−	1.50229i
$323$		−	43.5181i		−	0.00749663i
$324$	2318.89	−	4016.43i	0.397614	−	0.688688i
$325$		0			0
$326$	−5001.91	−	8663.57i	−0.849786	−	1.47187i
$327$	12659.8	+	7309.12i	2.14094	+	1.23607i
$328$		−	1129.38i		−	0.190121i
$329$	620.252	+	1889.54i	0.103938	+	0.316637i
$330$		0			0
$331$	−5665.38	+	9812.73i	−0.940778	+	1.62948i	−0.176786	+	0.984249i	$0.556570\pi$
$331$	−5665.38	+	9812.73i	−0.940778	+	1.62948i	−0.763992	+	0.645226i	$0.776763\pi$
$332$	−5210.56	+	3008.32i	−0.861345	+	0.497298i
$333$	12208.4	−	7048.54i	2.00906	−	1.15993i
$334$	1050.17	−	1818.94i	0.172044	−	0.297988i
$335$		0			0
$336$	7996.68	−	8935.23i	1.29838	−	1.45076i
$337$			3637.35i			0.587950i	0.955813	+	0.293975i	$0.0949782\pi$
$337$			3637.35i			0.587950i	−0.955813	+	0.293975i	$0.905022\pi$
$338$	5095.58	+	2941.94i	0.820009	+	0.473433i
$339$	−1551.12	−	2686.61i	−0.248511	−	0.430433i
$340$		0			0
$341$	−3235.93	+	5604.79i	−0.513887	+	0.890078i
$342$			12991.5i			2.05409i
$343$	−3687.24	+	5172.80i	−0.580444	+	0.814300i
$344$	800.705			0.125497
$345$		0			0
$346$	5808.42	+	10060.5i	0.902492	+	1.56316i
$347$	−3490.19	+	2015.06i	−0.539951	+	0.311741i	−0.745059	−	0.666998i	$-0.767579\pi$
$347$	−3490.19	+	2015.06i	−0.539951	+	0.311741i	0.205108	+	0.978739i	$0.434245\pi$
$348$	−5495.97	−	3173.10i	−0.846594	−	0.488782i
$349$	−2887.69			−0.442906			−0.221453	−	0.975171i	$-0.571080\pi$
$349$	−2887.69			−0.442906			−0.221453	+	0.975171i	$0.571080\pi$
$350$		0			0
$351$	−14466.4			−2.19988
$352$	4814.92	+	2779.90i	0.729080	+	0.420935i
$353$	454.592	−	262.459i	0.0685425	−	0.0395731i	−0.465337	−	0.885134i	$-0.654067\pi$
$353$	454.592	−	262.459i	0.0685425	−	0.0395731i	0.533880	+	0.845561i	$0.320734\pi$
$354$	−7885.83	−	13658.7i	−1.18397	−	2.05070i
$355$		0			0
$356$	−5815.84			−0.865840
$357$	108.618	−	35.6545i	0.0161027	−	0.00528582i
$358$		−	7689.25i		−	1.13517i
$359$	−1642.66	+	2845.17i	−0.241493	+	0.418279i	−0.961140	−	0.276062i	$-0.910971\pi$
$359$	−1642.66	+	2845.17i	−0.241493	+	0.418279i	0.719646	+	0.694341i	$0.244304\pi$
$360$		0			0
$361$	1430.82	+	2478.25i	0.208605	+	0.361314i
$362$	2268.84	+	1309.92i	0.329414	+	0.190187i
$363$		−	7146.00i		−	1.03324i
$364$	7517.70	+	1574.26i	1.08251	+	0.226686i
$365$		0			0
$366$	8171.36	−	14153.2i	1.16701	−	2.02131i
$367$	7840.95	−	4526.98i	1.11524	−	0.643886i	0.175061	−	0.984558i	$-0.443988\pi$
$367$	7840.95	−	4526.98i	1.11524	−	0.643886i	0.940182	+	0.340671i	$0.110654\pi$
$368$	7784.35	−	4494.30i	1.10268	−	0.636635i
$369$	−6500.80	+	11259.7i	−0.917122	+	1.58850i
$370$		0			0
$371$	−812.249	−	170.091i	−0.113665	−	0.0238024i
$372$		−	17059.9i		−	2.37772i
$373$	−4511.22	−	2604.55i	−0.626225	−	0.361551i	0.153064	−	0.988216i	$-0.451086\pi$
$373$	−4511.22	−	2604.55i	−0.626225	−	0.361551i	−0.779289	+	0.626665i	$0.784419\pi$
$374$	30.5932	+	52.9889i	0.00422977	+	0.00732618i
$375$		0			0
$376$	−249.161	+	431.559i	−0.0341742	+	0.0591914i
$377$			6359.12i			0.868730i
$378$	−16038.1	+	5264.61i	−2.18231	+	0.716356i
$379$	−3200.68			−0.433794			−0.216897	−	0.976194i	$-0.569594\pi$
$379$	−3200.68			−0.433794			−0.216897	+	0.976194i	$0.569594\pi$
$380$		0			0
$381$	−7466.90	−	12933.1i	−1.00404	−	1.73906i
$382$	−5371.99	+	3101.52i	−0.719516	+	0.415413i
$383$	−1907.69	−	1101.40i	−0.254513	−	0.146943i	0.367316	−	0.930096i	$-0.380277\pi$
$383$	−1907.69	−	1101.40i	−0.254513	−	0.146943i	−0.621829	+	0.783153i	$0.713610\pi$
$384$	5266.42			0.699872
$385$		0			0
$386$	3111.29			0.410261
$387$	−7982.89	−	4608.92i	−1.04856	−	0.605387i
$388$	−1114.51	+	643.462i	−0.145826	+	0.0841929i
$389$	−3120.79	−	5405.38i	−0.406762	−	0.704533i	0.587762	−	0.809034i	$-0.300009\pi$
$389$	−3120.79	−	5405.38i	−0.406762	−	0.704533i	−0.994525	+	0.104500i	$0.966676\pi$
$390$		0			0
$391$	85.6955			0.0110839
$392$	−1582.00	+	175.925i	−0.203834	+	0.0226672i
$393$			6069.04i			0.778988i
$394$	7123.65	−	12338.5i	0.910874	−	1.57768i
$395$		0			0
$396$	−4194.05	−	7264.32i	−0.532220	−	0.921832i
$397$	−9012.87	−	5203.58i	−1.13940	−	0.657834i	−0.193120	−	0.981175i	$-0.561861\pi$
$397$	−9012.87	−	5203.58i	−1.13940	−	0.657834i	−0.946283	+	0.323341i	$0.895194\pi$
$398$			1415.13i			0.178227i
$399$	7002.92	−	7824.84i	0.878658	−	0.981785i
$400$		0			0
$401$	7486.63	−	12967.2i	0.932330	−	1.61484i	0.153003	−	0.988226i	$-0.451105\pi$
$401$	7486.63	−	12967.2i	0.932330	−	1.61484i	0.779327	−	0.626618i	$-0.215561\pi$
$402$	6854.15	−	3957.25i	0.850383	−	0.490969i
$403$	−14804.4	+	8547.30i	−1.82992	+	1.05651i
$404$	2703.12	−	4681.95i	0.332885	−	0.576573i
$405$		0			0
$406$	2314.21	+	7050.03i	0.282888	+	0.861791i
$407$		−	6098.58i		−	0.742741i
$408$	24.8077	+	14.3228i	0.00301021	+	0.00173795i
$409$	−3529.55	−	6113.36i	−0.426711	−	0.739086i	0.569867	−	0.821737i	$-0.306995\pi$
$409$	−3529.55	−	6113.36i	−0.426711	−	0.739086i	−0.996579	+	0.0826512i	$0.973661\pi$
$410$		0			0
$411$	−4637.48	+	8032.35i	−0.556569	+	0.964006i
$412$			13184.1i			1.57654i
$413$	−1735.68	+	8288.52i	−0.206797	+	0.987534i
$414$	−25582.7			−3.03701
$415$		0			0
$416$	7342.75	+	12718.0i	0.865404	+	1.49892i
$417$	−3384.83	+	1954.23i	−0.397496	+	0.229494i
$418$	4867.31	+	2810.14i	0.569540	+	0.328824i
$419$	−928.543			−0.108263			−0.0541316	−	0.998534i	$-0.517239\pi$
$419$	−928.543			−0.108263			−0.0541316	+	0.998534i	$0.517239\pi$
$420$		0			0
$421$	7105.06			0.822517			0.411258	−	0.911519i	$-0.365089\pi$
$421$	7105.06			0.822517			0.411258	+	0.911519i	$0.365089\pi$
$422$	3575.29	+	2064.19i	0.412423	+	0.238112i
$423$	4968.18	−	2868.38i	0.571066	−	0.329705i
$424$	−103.971	−	180.083i	−0.0119087	−	0.0206264i
$425$		0			0
$426$	−14062.3			−1.59934
$427$	−8337.24	+	2736.75i	−0.944888	+	0.310165i
$428$		−	3319.88i		−	0.374936i
$429$	−6326.54	+	10957.9i	−0.712001	+	1.23322i
$430$		0			0
$431$	2159.64	+	3740.60i	0.241360	+	0.418047i	0.961102	−	0.276194i	$-0.0890734\pi$
$431$	2159.64	+	3740.60i	0.241360	+	0.418047i	−0.719742	+	0.694241i	$0.755740\pi$
$432$	−14816.3	−	8554.21i	−1.65012	−	0.952696i
$433$		−	4600.60i		−	0.510602i	−0.966862	−	0.255301i	$-0.917825\pi$
$433$		−	4600.60i		−	0.510602i	0.966862	−	0.255301i	$-0.0821745\pi$
$434$	−13302.3	+	14863.6i	−1.47127	+	1.64395i
$435$		0			0
$436$	−5536.84	+	9590.10i	−0.608181	+	1.05340i
$437$	6816.99	−	3935.79i	0.746226	−	0.430834i
$438$	−10409.5	+	6009.94i	−1.13558	+	0.655630i
$439$	961.868	−	1666.00i	0.104573	−	0.181125i	−0.808991	−	0.587821i	$-0.799986\pi$
$439$	961.868	−	1666.00i	0.104573	−	0.181125i	0.913564	+	0.406696i	$0.133319\pi$
$440$		0			0
$441$	16784.9	+	7352.16i	1.81242	+	0.793884i
$442$			161.616i			0.0173921i
$443$	−3927.32	−	2267.44i	−0.421202	−	0.243181i	0.274390	−	0.961619i	$-0.411524\pi$
$443$	−3927.32	−	2267.44i	−0.421202	−	0.243181i	−0.695591	+	0.718438i	$0.744858\pi$
$444$	8037.96	+	13922.1i	0.859154	+	1.48810i
$445$		0			0
$446$	3317.67	−	5746.38i	0.352234	−	0.610088i
$447$		−	19011.6i		−	2.01167i
$448$	4798.06	+	4294.07i	0.505997	+	0.452847i
$449$	17431.9			1.83221			0.916105	−	0.400937i	$-0.131316\pi$
$449$	17431.9			1.83221			0.916105	+	0.400937i	$0.131316\pi$
$450$		0			0
$451$	2812.33	+	4871.10i	0.293631	+	0.508583i
$452$	2035.18	−	1175.01i	0.211785	−	0.122274i
$453$	18642.6	+	10763.3i	1.93357	+	1.11635i
$454$	13911.7			1.43813
$455$		0			0
$456$	2631.24			0.270217
$457$	1699.42	+	981.162i	0.173951	+	0.100431i	0.584448	−	0.811431i	$-0.301311\pi$
$457$	1699.42	+	981.162i	0.173951	+	0.100431i	−0.410496	+	0.911862i	$0.634645\pi$
$458$	−4869.10	+	2811.18i	−0.496765	+	0.286807i
$459$	−81.5542	−	141.256i	−0.00829330	−	0.0143644i
$460$		0			0
$461$	14344.4			1.44920			0.724602	−	0.689167i	$-0.242024\pi$
$461$	14344.4			1.44920			0.724602	+	0.689167i	$0.242024\pi$
$462$	−3026.11	+	14450.8i	−0.304734	+	1.45522i
$463$		−	11657.8i		−	1.17016i	−0.810975	−	0.585081i	$-0.801063\pi$
$463$		−	11657.8i		−	1.17016i	0.810975	−	0.585081i	$-0.198937\pi$
$464$	−3760.25	+	6512.95i	−0.376219	+	0.651630i
$465$		0			0
$466$	−4106.46	−	7112.59i	−0.408214	−	0.707048i
$467$	14301.3	+	8256.88i	1.41710	+	0.818164i	0.996043	−	0.0888691i	$-0.0283253\pi$
$467$	14301.3	+	8256.88i	1.41710	+	0.818164i	0.421059	+	0.907033i	$0.361659\pi$
$468$		−	22156.1i		−	2.18839i
$469$	−4159.33	−	870.995i	−0.409509	−	0.0857544i
$470$		0			0
$471$	−2269.73	+	3931.30i	−0.222046	+	0.384596i
$472$	−1837.64	+	1060.96i	−0.179204	+	0.103463i
$473$	−3453.50	+	1993.88i	−0.335713	+	0.193824i
$474$	−14489.3	+	25096.2i	−1.40404	+	2.43187i
$475$		0			0
$476$	27.0092	+	82.2810i	0.00260077	+	0.00792299i
$477$			2393.86i			0.229785i
$478$	19826.9	+	11447.0i	1.89720	+	1.09535i
$479$	−7810.03	−	13527.4i	−0.744988	−	1.29036i	−0.950200	−	0.311640i	$-0.899122\pi$
$479$	−7810.03	−	13527.4i	−0.744988	−	1.29036i	0.205212	−	0.978718i	$-0.434212\pi$
$480$		0			0
$481$	8054.32	−	13950.5i	0.763504	−	1.32243i
$482$		−	14798.6i		−	1.39846i
$483$	15408.6	+	13790.1i	1.45159	+	1.29911i
$484$	5413.28			0.508384
$485$		0			0
$486$	−530.625	−	919.070i	−0.0495260	−	0.0857816i
$487$	1646.65	−	950.691i	0.153217	−	0.0884598i	−0.421431	−	0.906860i	$-0.638472\pi$
$487$	1646.65	−	950.691i	0.153217	−	0.0884598i	0.574648	+	0.818400i	$0.305139\pi$
$488$	−1904.18	−	1099.38i	−0.176635	−	0.101980i
$489$	23325.1			2.15705
$490$		0			0
$491$	−15964.1			−1.46731			−0.733654	−	0.679524i	$-0.762186\pi$
$491$	−15964.1			−1.46731			−0.733654	+	0.679524i	$0.762186\pi$
$492$	−12840.3	−	7413.33i	−1.17659	−	0.679306i
$493$	−62.0932	+	35.8495i	−0.00567249	+	0.00327501i
$494$	7422.64	+	12856.4i	0.676033	+	1.17092i
$495$		0			0
$496$	−20216.7			−1.83015
$497$	5626.31	+	5035.33i	0.507796	+	0.454457i
$498$		−	30548.6i		−	2.74882i
$499$	−3424.59	+	5931.56i	−0.307226	+	0.532130i	−0.977754	−	0.209753i	$-0.932734\pi$
$499$	−3424.59	+	5931.56i	−0.307226	+	0.532130i	0.670529	+	0.741884i	$0.266067\pi$
$500$		0			0
$501$	2448.59	+	4241.09i	0.218354	+	0.378199i
$502$	5768.12	+	3330.23i	0.512836	+	0.296086i
$503$			766.190i			0.0679179i	0.999423	+	0.0339590i	$0.0108116\pi$
$503$			766.190i			0.0679179i	−0.999423	+	0.0339590i	$0.989188\pi$
$504$	1432.04	+	4362.58i	0.126564	+	0.385565i
$505$		0			0
$506$	−5533.71	+	9584.66i	−0.486173	+	0.842076i
$507$	−11881.0	+	6859.49i	−1.04074	+	0.600869i
$508$	9797.12	−	5656.37i	0.855663	−	0.494017i
$509$	6802.36	−	11782.0i	0.592356	−	1.02599i	−0.401558	−	0.915834i	$-0.631531\pi$
$509$	6802.36	−	11782.0i	0.592356	−	1.02599i	0.993914	−	0.110157i	$-0.0351355\pi$
$510$		0			0
$511$	6316.84	+	1322.79i	0.546850	+	0.114515i
$512$			14687.2i			1.26776i
$513$	−12975.1	−	7491.18i	−1.11669	−	0.644724i
$514$	−7797.12	−	13505.0i	−0.669098	−	1.15891i
$515$		0			0
$516$	5255.88	−	9103.46i	0.448406	−	0.776662i
$517$		−	2481.80i		−	0.211120i
$518$	3852.54	−	18397.3i	0.326778	−	1.56049i
$519$	−27086.1			−2.29084
$520$		0			0
$521$	−9214.16	−	15959.4i	−0.774817	−	1.34202i	−0.934897	−	0.354919i	$-0.884509\pi$
$521$	−9214.16	−	15959.4i	−0.774817	−	1.34202i	0.160080	−	0.987104i	$-0.448825\pi$
$522$	18536.7	−	10702.2i	1.55427	−	0.897359i
$523$	3758.66	+	2170.06i	0.314254	+	0.181435i	0.648828	−	0.760935i	$-0.275259\pi$
$523$	3758.66	+	2170.06i	0.314254	+	0.181435i	−0.334575	+	0.942369i	$0.608593\pi$
$524$	−4597.45			−0.383283
$525$		0			0
$526$	−24369.0			−2.02003
$527$	−166.919	−	96.3708i	−0.0137972	−	0.00796581i
$528$	−12959.2	+	7481.98i	−1.06814	+	0.616688i
$529$	1666.82	+	2887.03i	0.136996	+	0.237283i
$530$		0			0
$531$	24427.9			1.99639
$532$	5927.52	+	5304.89i	0.483065	+	0.432324i
$533$			14856.8i			1.20736i
$534$	14764.5	−	25572.9i	1.19649	−	2.07238i
$535$		0			0
$536$	−532.409	−	922.160i	−0.0429041	−	0.0743120i
$537$	15526.5	+	8964.21i	1.24770	+	0.720362i
$538$			5083.30i			0.407354i
$539$	6385.19	−	4698.19i	0.510259	−	0.375446i
$540$		0			0
$541$	−6308.12	+	10926.0i	−0.501308	+	0.868290i	0.498691	+	0.866780i	$0.333814\pi$
$541$	−6308.12	+	10926.0i	−0.501308	+	0.868290i	−0.999999	+	0.00151060i	$0.999519\pi$
$542$	−7781.05	+	4492.39i	−0.616651	+	0.356024i
$543$	−5290.09	+	3054.24i	−0.418084	+	0.241381i
$544$	−82.7895	+	143.396i	−0.00652495	+	0.0113015i
$545$		0			0
$546$	−26007.2	+	29059.7i	−2.03847	+	2.27773i
$547$			20677.8i			1.61630i	0.588975	+	0.808151i	$0.299532\pi$
$547$			20677.8i			1.61630i	−0.588975	+	0.808151i	$0.700468\pi$
$548$	−6084.71	−	3513.01i	−0.474317	−	0.273847i
$549$	12656.2	+	21921.2i	0.983887	+	1.70414i
$550$		0			0
$551$	−3292.96	+	5703.58i	−0.254601	+	0.440981i
$552$			5181.41i			0.399521i
$553$	14783.4	−	4852.75i	1.13681	−	0.373164i
$554$	27251.4			2.08989
$555$		0			0
$556$	−1480.38	−	2564.09i	−0.112917	−	0.195579i
$557$	−879.164	+	507.586i	−0.0668786	+	0.0386124i	−0.533066	−	0.846073i	$-0.678960\pi$
$557$	−879.164	+	507.586i	−0.0668786	+	0.0386124i	0.466188	+	0.884686i	$0.345627\pi$
$558$	49830.5	+	28769.6i	3.78045	+	2.18264i
$559$	−10533.2			−0.796969
$560$		0			0
$561$	−142.664			−0.0107366
$562$	−7072.11	−	4083.09i	−0.530817	−	0.306467i
$563$	−4587.03	+	2648.32i	−0.343375	+	0.198248i	−0.661763	−	0.749713i	$-0.730192\pi$
$563$	−4587.03	+	2648.32i	−0.343375	+	0.198248i	0.318388	+	0.947960i	$0.396858\pi$
$564$	3271.02	+	5665.57i	0.244210	+	0.422985i
$565$		0			0
$566$	22660.5			1.68285
$567$	2591.43	−	12375.0i	0.191940	−	0.916584i
$568$			1891.94i			0.139761i
$569$	7370.61	−	12766.3i	0.543044	−	0.940580i	−0.455683	−	0.890142i	$-0.650605\pi$
$569$	7370.61	−	12766.3i	0.543044	−	0.940580i	0.998727	−	0.0504381i	$-0.0160618\pi$
$570$		0			0
$571$	−6830.70	−	11831.1i	−0.500624	−	0.867105i	−1.00000		0.000720144i	$-0.999771\pi$
$571$	−6830.70	−	11831.1i	−0.500624	−	0.867105i	0.499376	−	0.866385i	$-0.333563\pi$
$572$	−8300.88	−	4792.52i	−0.606779	−	0.350324i
$573$		−	14463.2i		−	1.05446i
$574$	5406.71	+	16471.0i	0.393156	+	1.19771i
$575$		0			0
$576$	9287.03	−	16085.6i	0.671805	−	1.16360i
$577$	934.107	−	539.307i	0.0673958	−	0.0389110i	−0.465923	−	0.884825i	$-0.654278\pi$
$577$	934.107	−	539.307i	0.0673958	−	0.0389110i	0.533319	+	0.845914i	$0.320944\pi$
$578$	16363.3	−	9447.34i	1.17755	−	0.679857i
$579$	−3627.18	+	6282.46i	−0.260346	+	0.450933i
$580$		0			0
$581$	−10938.6	+	12222.5i	−0.781085	+	0.872760i
$582$		−	6534.17i		−	0.465378i
$583$	896.868	+	517.807i	0.0637126	+	0.0367845i
$584$	808.579	+	1400.50i	0.0572932	+	0.0992347i
$585$		0			0
$586$	15649.8	−	27106.3i	1.10322	−	1.91084i
$587$			3863.36i			0.271649i	0.990733	+	0.135824i	$0.0433683\pi$
$587$			3863.36i			0.271649i	−0.990733	+	0.135824i	$0.956632\pi$
$588$	−8384.19	+	19141.0i	−0.588024	+	1.34245i
$589$	−17704.3			−1.23853
$590$		0			0
$591$	16609.7	+	28768.8i	1.15606	+	2.00235i
$592$	16498.3	−	9525.31i	1.14540	−	0.661297i
$593$	−8175.98	−	4720.41i	−0.566185	−	0.326887i	0.189439	−	0.981892i	$-0.439333\pi$
$593$	−8175.98	−	4720.41i	−0.566185	−	0.326887i	−0.755624	+	0.655006i	$0.772666\pi$
$594$	21065.1			1.45507
$595$		0			0
$596$	14401.8			0.989797
$597$	−2857.50	−	1649.78i	−0.195896	−	0.113100i
$598$	−25316.7	+	14616.6i	−1.73123	+	0.999527i
$599$	−10684.5	−	18506.0i	−0.728807	−	1.26233i	−0.957388	−	0.288806i	$-0.906742\pi$
$599$	−10684.5	−	18506.0i	−0.728807	−	1.26233i	0.228581	−	0.973525i	$-0.426592\pi$
$600$		0			0
$601$	5801.37			0.393748			0.196874	−	0.980429i	$-0.436921\pi$
$601$	5801.37			0.393748			0.196874	+	0.980429i	$0.436921\pi$
$602$	−11677.6	+	3833.24i	−0.790602	+	0.259520i
$603$			12258.4i			0.827859i
$604$	−8153.49	+	14122.3i	−0.549273	+	0.951369i
$605$		0			0
$606$	13724.7	+	23771.9i	0.920014	+	1.59351i
$607$	−23157.5	−	13370.0i	−1.54849	−	0.894023i	−0.998257	−	0.0590141i	$-0.981204\pi$
$607$	−23157.5	−	13370.0i	−1.54849	−	0.894023i	−0.550236	−	0.835009i	$-0.685462\pi$
$608$			15209.3i			1.01450i
$609$	−16933.7	−	3546.04i	−1.12674	−	0.235949i
$610$		0			0
$611$	3277.68	−	5677.10i	0.217022	−	0.375894i
$612$	216.342	−	124.905i	0.0142894	−	0.00824999i
$613$	7222.43	−	4169.87i	0.475875	−	0.274746i	−0.242821	−	0.970071i	$-0.578073\pi$
$613$	7222.43	−	4169.87i	0.475875	−	0.274746i	0.718696	+	0.695325i	$0.244739\pi$
$614$	−9225.63	+	15979.3i	−0.606378	+	1.05028i
$615$		0			0
$616$	1944.22	+	407.134i	0.127167	+	0.0266297i
$617$		−	26639.2i		−	1.73818i	−0.494658	−	0.869088i	$-0.664707\pi$
$617$		−	26639.2i		−	1.73818i	0.494658	−	0.869088i	$-0.335293\pi$
$618$	−57972.0	−	33470.1i	−3.77342	−	2.17859i
$619$	13930.2	+	24127.7i	0.904523	+	1.56668i	0.821556	+	0.570128i	$0.193107\pi$
$619$	13930.2	+	24127.7i	0.904523	+	1.56668i	0.0829678	+	0.996552i	$0.473560\pi$
$620$		0			0
$621$	14751.6	−	25550.5i	0.953237	−	1.65105i
$622$			19960.1i			1.28670i
$623$	−15064.3	+	4944.94i	−0.968760	+	0.318001i
$624$	−39525.5			−2.53571
$625$		0			0
$626$	4317.85	+	7478.74i	0.275681	+	0.477493i
$627$	−11348.7	+	6552.19i	−0.722846	+	0.417335i
$628$	−2978.06	−	1719.38i	−0.189232	−	0.109253i
$629$	181.625			0.0115133
$630$		0			0
$631$	−10886.7			−0.686833			−0.343417	−	0.939183i	$-0.611584\pi$
$631$	−10886.7			−0.686833			−0.343417	+	0.939183i	$0.611584\pi$
$632$	3376.45	+	1949.39i	0.212513	+	0.122694i
$633$	−8336.23	+	4812.92i	−0.523437	+	0.302206i
$634$	−18735.5	−	32450.8i	−1.17363	−	2.03278i
$635$		0			0
$636$	−2729.89			−0.170200
$637$	20811.0	−	2314.27i	1.29444	−	0.143948i
$638$		−	9259.80i		−	0.574607i
$639$	10890.2	−	18862.4i	0.674193	−	1.16774i
$640$		0			0
$641$	8425.73	+	14593.8i	0.519183	+	0.899251i	0.999751	+	0.0222942i	$0.00709704\pi$
$641$	8425.73	+	14593.8i	0.519183	+	0.899251i	−0.480568	+	0.876957i	$0.659570\pi$
$642$	14597.9	+	8428.10i	0.897404	+	0.518116i
$643$		−	4793.72i		−	0.294006i	−0.989136	−	0.147003i	$-0.953037\pi$
$643$		−	4793.72i		−	0.294006i	0.989136	−	0.147003i	$-0.0469627\pi$
$644$	−10446.4	+	11672.4i	−0.639199	+	0.714221i
$645$		0			0
$646$	−83.6902	+	144.956i	−0.00509713	+	0.00882850i
$647$	−23109.5	+	13342.3i	−1.40422	+	0.810725i	−0.994822	−	0.101633i	$-0.967593\pi$
$647$	−23109.5	+	13342.3i	−1.40422	+	0.810725i	−0.409394	+	0.912358i	$0.634260\pi$
$648$	2743.66	−	1584.05i	0.166329	−	0.0960300i
$649$	5283.92	−	9152.01i	0.319587	−	0.553541i
$650$		0			0
$651$	−14505.2	−	44188.7i	−0.873278	−	2.66036i
$652$			17669.4i			1.06133i
$653$	15191.7	+	8770.94i	0.910409	+	0.525625i	0.880563	−	0.473929i	$-0.157165\pi$
$653$	15191.7	+	8770.94i	0.910409	+	0.525625i	0.0298466	+	0.999554i	$0.490498\pi$
$654$	−28112.5	−	48692.3i	−1.68087	−	2.91135i
$655$		0			0
$656$	−8785.10	+	15216.2i	−0.522867	+	0.905632i
$657$		−	18617.0i		−	1.10551i
$658$	1567.78	−	7486.72i	0.0928850	−	0.443561i
$659$	26285.3			1.55377			0.776883	−	0.629645i	$-0.216800\pi$
$659$	26285.3			1.55377			0.776883	+	0.629645i	$0.216800\pi$
$660$		0			0
$661$	−12522.1	−	21689.0i	−0.736845	−	1.27625i	−0.953909	−	0.300096i	$-0.902981\pi$
$661$	−12522.1	−	21689.0i	−0.736845	−	1.27625i	0.217064	−	0.976157i	$-0.430352\pi$
$662$	37742.0	−	21790.3i	2.21584	−	1.27931i
$663$	−326.343	−	188.414i	−0.0191163	−	0.0110368i
$664$	−4110.02			−0.240210
$665$		0			0
$666$	−54220.6			−3.15466
$667$	−11231.4	−	6484.48i	−0.651999	−	0.376432i
$668$	−3212.73	+	1854.87i	−0.186084	+	0.107436i
$669$	7735.57	+	13398.4i	0.447047	+	0.774308i
$670$		0			0
$671$	10950.5			0.630013
$672$	−37961.3	+	12461.0i	−2.17915	+	0.715319i
$673$		−	20799.4i		−	1.19132i	−0.803238	−	0.595658i	$-0.796891\pi$
$673$		−	20799.4i		−	1.19132i	0.803238	−	0.595658i	$-0.203109\pi$
$674$	6995.04	−	12115.8i	0.399761	−	0.692406i
$675$		0			0
$676$	−5196.24	−	9000.14i	−0.295644	−	0.512070i
$677$	−25783.8	−	14886.3i	−1.46374	−	0.845089i	−0.464556	−	0.885543i	$-0.653786\pi$
$677$	−25783.8	−	14886.3i	−1.46374	−	0.845089i	−0.999181	+	0.0404540i	$0.987120\pi$
$678$			11931.9i			0.675873i
$679$	−2339.71	+	2614.32i	−0.132238	+	0.147759i
$680$		0			0
$681$	−16218.5	+	28091.2i	−0.912619	+	1.58070i
$682$	21557.3	−	12446.1i	1.21037	−	0.698807i
$683$	−20689.6	+	11945.2i	−1.15910	+	0.669208i	−0.951089	−	0.308918i	$-0.900033\pi$
$683$	−20689.6	+	11945.2i	−1.15910	+	0.669208i	−0.208014	+	0.978126i	$0.566700\pi$
$684$	11473.2	−	19872.2i	0.641357	−	1.11086i
$685$		0			0
$686$	22229.8	−	10139.2i	1.23723	−	0.564312i
$687$		−	13109.2i		−	0.728017i
$688$	−10788.0	−	6228.44i	−0.597802	−	0.345141i
$689$	1367.72	+	2368.97i	0.0756257	+	0.130987i
$690$		0			0
$691$	12648.8	−	21908.3i	0.696356	−	1.20612i	−0.273365	−	0.961910i	$-0.588137\pi$
$691$	12648.8	−	21908.3i	0.696356	−	1.20612i	0.969721	−	0.244214i	$-0.0785300\pi$
$692$		−	20518.4i		−	1.12716i
$693$	−17040.0	−	15250.1i	−0.934049	−	0.835937i
$694$	15500.8			0.847839
$695$		0			0
$696$	−2167.57	−	3754.35i	−0.118048	−	0.204466i
$697$	−145.069	+	83.7554i	−0.00788360	+	0.00455160i
$698$	9618.68	+	5553.34i	0.521593	+	0.301142i
$699$	19149.4			1.03619
$700$		0			0
$701$	18659.1			1.00534			0.502670	−	0.864478i	$-0.332351\pi$
$701$	18659.1			1.00534			0.502670	+	0.864478i	$0.332351\pi$
$702$	48186.5	+	27820.5i	2.59071	+	1.49575i
$703$	14448.1	−	8341.59i	0.775134	−	0.447524i
$704$	−4017.69	−	6958.84i	−0.215088	−	0.372544i
$705$		0			0
$706$	−2018.95			−0.107627
$707$	3020.83	−	14425.6i	0.160693	−	0.767369i
$708$			27856.9i			1.47871i
$709$	−12847.4	+	22252.3i	−0.680528	+	1.17871i	0.294292	+	0.955715i	$0.404916\pi$
$709$	−12847.4	+	22252.3i	−0.680528	+	1.17871i	−0.974820	+	0.222993i	$0.928417\pi$
$710$		0			0
$711$	−22441.7	−	38870.2i	−1.18373	−	2.05028i
$712$	−3440.59	−	1986.43i	−0.181098	−	0.104557i
$713$		−	34863.2i		−	1.83119i
$714$	−430.367	−	90.1221i	−0.0225575	−	0.00472372i
$715$		0			0
$716$	−6790.62	+	11761.7i	−0.354438	+	0.613904i
$717$	−46228.8	+	26690.2i	−2.40787	+	1.39019i
$718$	10943.1	−	6318.03i	0.568795	−	0.328394i
$719$	−13627.3	+	23603.2i	−0.706834	+	1.22427i	0.259191	+	0.965826i	$0.416544\pi$
$719$	−13627.3	+	23603.2i	−0.706834	+	1.22427i	−0.966025	+	0.258447i	$0.916789\pi$
$720$		0			0
$721$	11209.8	+	34149.6i	0.579022	+	1.76394i
$722$		−	11006.5i		−	0.567340i
$723$	29881.9	+	17252.3i	1.53710	+	0.887443i
$724$	−2313.66	−	4007.38i	−0.118766	−	0.205709i
$725$		0			0
$726$	−13742.6	+	23802.8i	−0.702527	+	1.21681i
$727$		−	13194.3i		−	0.673110i	−0.941664	−	0.336555i	$-0.890738\pi$
$727$		−	13194.3i		−	0.673110i	0.941664	−	0.336555i	$-0.109262\pi$
$728$	3909.69	+	3499.02i	0.199042	+	0.178135i
$729$	20906.9			1.06218
$730$		0			0
$731$	−59.3807	−	102.850i	−0.00300448	−	0.00520391i
$732$	−24998.3	+	14432.8i	−1.26225	+	0.728758i
$733$	5030.70	+	2904.47i	0.253497	+	0.146356i	0.621364	−	0.783522i	$-0.286579\pi$
$733$	5030.70	+	2904.47i	0.253497	+	0.146356i	−0.367868	+	0.929878i	$0.619912\pi$
$734$	−34823.5			−1.75117
$735$		0			0
$736$	−29950.0			−1.49996
$737$	4592.64	+	2651.56i	0.229542	+	0.132526i
$738$	43307.4	−	25003.5i	2.16012	−	1.24715i
$739$	6968.34	+	12069.5i	0.346867	+	0.600791i	0.985691	−	0.168562i	$-0.0539122\pi$
$739$	6968.34	+	12069.5i	0.346867	+	0.600791i	−0.638824	+	0.769353i	$0.720579\pi$
$740$		0			0
$741$	−34613.6			−1.71601
$742$	2378.44	+	2128.61i	0.117675	+	0.105315i
$743$		−	32424.2i		−	1.60098i	−0.599347	−	0.800489i	$-0.704573\pi$
$743$		−	32424.2i		−	1.60098i	0.599347	−	0.800489i	$-0.295427\pi$
$744$	5826.87	−	10092.4i	0.287128	−	0.497321i
$745$		0			0
$746$	10017.7	+	17351.2i	0.491654	+	0.851570i
$747$	40976.1	+	23657.6i	2.00701	+	1.15875i
$748$		−	108.071i		−	0.00528272i
$749$	−2822.74	−	8599.19i	−0.137704	−	0.419503i
$750$		0			0
$751$	17644.2	−	30560.6i	0.857316	−	1.48491i	−0.0171639	−	0.999853i	$-0.505464\pi$
$751$	17644.2	−	30560.6i	0.857316	−	1.48491i	0.874480	−	0.485062i	$-0.161203\pi$
$752$	6713.93	−	3876.29i	0.325574	−	0.187970i
$753$	−13449.1	+	7764.83i	−0.650879	+	0.375785i
$754$	12229.3	−	21181.8i	0.590670	−	1.02307i
$755$		0			0
$756$	29181.7	+	6110.88i	1.40388	+	0.293982i
$757$			2079.86i			0.0998595i	0.998753	+	0.0499298i	$0.0158998\pi$
$757$			2079.86i			0.0998595i	−0.998753	+	0.0499298i	$0.984100\pi$
$758$	10661.2	+	6155.27i	0.510862	+	0.294947i
$759$	−12902.5	−	22347.8i	−0.617038	−	1.06874i
$760$		0			0
$761$	−6125.72	+	10610.1i	−0.291797	+	0.505407i	−0.974235	−	0.225537i	$-0.927586\pi$
$761$	−6125.72	+	10610.1i	−0.291797	+	0.505407i	0.682438	+	0.730944i	$0.260920\pi$
$762$			57438.8i			2.73069i
$763$	−6187.60	+	29548.1i	−0.293586	+	1.40198i
$764$	10956.2			0.518824
$765$		0			0
$766$	4236.25	+	7337.40i	0.199820	+	0.346098i
$767$	24173.9	−	13956.8i	1.13803	−	0.657042i
$768$	−39143.5	−	22599.5i	−1.83916	−	1.06184i
$769$	−4335.87			−0.203323			−0.101661	−	0.994819i	$-0.532416\pi$
$769$	−4335.87			−0.203323			−0.101661	+	0.994819i	$0.532416\pi$
$770$		0			0
$771$	36359.9			1.69840
$772$	−4759.13	−	2747.68i	−0.221871	−	0.128098i
$773$	−26326.7	+	15199.7i	−1.22498	+	0.707240i	−0.965975	−	0.258637i	$-0.916727\pi$
$773$	−26326.7	+	15199.7i	−1.22498	+	0.707240i	−0.259001	+	0.965877i	$0.583393\pi$
$774$	17727.0	+	30704.0i	0.823233	+	1.42588i
$775$		0			0
$776$	−879.109			−0.0406677
$777$	32657.4	+	29227.0i	1.50782	+	1.34944i
$778$			24006.6i			1.10627i
$779$	−7693.37	+	13325.3i	−0.353843	+	0.612874i
$780$		0			0
$781$	−4711.23	−	8160.10i	−0.215853	−	0.373868i
$782$	−285.446	−	164.802i	−0.0130531	−	0.00753621i
$783$			24684.4i			1.12663i
$784$	22682.9	+	9935.62i	1.03329	+	0.452606i
$785$		0			0
$786$	11671.4	−	20215.5i	0.529652	−	0.917384i
$787$	30548.4	−	17637.1i	1.38365	−	0.798850i	0.391059	−	0.920365i	$-0.372109\pi$
$787$	30548.4	−	17637.1i	1.38365	−	0.798850i	0.992590	+	0.121515i	$0.0387754\pi$
$788$	−21793.1	+	12582.2i	−0.985211	+	0.568812i
$789$	28409.6	−	49206.9i	1.28189	−	2.22030i
$790$		0			0
$791$	4272.49	−	4773.94i	0.192051	−	0.214592i
$792$		−	5729.99i		−	0.257079i
$793$	25049.2	+	14462.2i	1.12172	+	0.647625i
$794$	20014.1	+	34665.5i	0.894554	+	1.54941i
$795$		0			0
$796$	1249.75	−	2164.63i	0.0556484	−	0.0963859i
$797$		−	27524.0i		−	1.22328i	−0.791138	−	0.611638i	$-0.790511\pi$
$797$		−	27524.0i		−	1.22328i	0.791138	−	0.611638i	$-0.209489\pi$
$798$	−38374.3	+	12596.6i	−1.70230	+	0.558790i
$799$	73.9116			0.00327260
$800$		0			0
$801$	22868.1	+	39608.7i	1.00874	+	1.74720i
$802$	−49874.9	+	28795.3i	−2.19594	+	1.26783i
$803$	−6974.92	−	4026.97i	−0.306525	−	0.176972i
$804$	−13979.1			−0.613189
$805$		0			0
$806$	65749.7			2.87337
$807$	−10264.4	−	5926.17i	−0.447739	−	0.258502i
$808$	3198.28	−	1846.53i	0.139251	−	0.0803968i
$809$	−3533.68	−	6120.51i	−0.153569	−	0.265990i	0.778968	−	0.627064i	$-0.215743\pi$
$809$	−3533.68	−	6120.51i	−0.153569	−	0.265990i	−0.932537	+	0.361074i	$0.882410\pi$
$810$		0			0
$811$	−37757.5			−1.63483			−0.817413	−	0.576052i	$-0.804593\pi$
$811$	−37757.5			−1.63483			−0.817413	+	0.576052i	$0.804593\pi$
$812$	2686.21	−	12827.7i	0.116093	−	0.554389i
$813$		−	20949.1i		−	0.903713i
$814$	−11728.3	+	20313.9i	−0.505007	+	0.874697i
$815$		0			0
$816$	−222.825	−	385.944i	−0.00955935	−	0.0165573i
$817$	−9447.34	−	5454.43i	−0.404554	−	0.233569i
$818$			27150.9i			1.16052i
$819$	−18838.3	−	57389.1i	−0.803742	−	2.44852i
$820$		0			0
$821$	12653.7	−	21916.9i	0.537902	−	0.931673i	−0.461115	−	0.887340i	$-0.652551\pi$
$821$	12653.7	−	21916.9i	0.537902	−	0.931673i	0.999017	−	0.0443325i	$-0.0141161\pi$
$822$	30894.2	−	17836.8i	1.31090	−	0.756848i
$823$	22070.5	−	12742.4i	0.934786	−	0.539699i	0.0464643	−	0.998920i	$-0.485205\pi$
$823$	22070.5	−	12742.4i	0.934786	−	0.539699i	0.888322	+	0.459221i	$0.151871\pi$
$824$	−4503.08	+	7799.57i	−0.190379	+	0.329746i
$825$		0			0
$826$	21721.2	−	24270.6i	0.914984	−	1.02237i
$827$			34985.7i			1.47107i	0.677488	+	0.735534i	$0.263069\pi$
$827$			34985.7i			1.47107i	−0.677488	+	0.735534i	$0.736931\pi$
$828$	39132.1	+	22592.9i	1.64243	+	0.948259i
$829$	1949.04	+	3375.84i	0.0816564	+	0.141433i	0.903962	−	0.427614i	$-0.140646\pi$
$829$	1949.04	+	3375.84i	0.0816564	+	0.141433i	−0.822305	+	0.569047i	$0.807312\pi$
$830$		0			0
$831$	−31770.0	+	55027.2i	−1.32622	+	2.29708i
$832$		−	21224.4i		−	0.884405i
$833$	139.919	+	190.161i	0.00581983	+	0.00790957i
$834$	15032.8			0.624154
$835$		0			0
$836$	−4963.45	−	8596.95i	−0.205340	−	0.355660i
$837$	−57466.7	+	33178.4i	−2.37317	+	1.37015i
$838$	3092.91	+	1785.69i	0.127497	+	0.0736106i
$839$	−22118.8			−0.910161			−0.455081	−	0.890450i	$-0.650390\pi$
$839$	−22118.8			−0.910161			−0.455081	+	0.890450i	$0.650390\pi$
$840$		0			0
$841$	−13538.2			−0.555096
$842$	−23666.5	−	13663.8i	−0.968646	−	0.559248i
$843$	16489.5	−	9520.22i	0.673699	−	0.388961i
$844$	−3645.91	−	6314.91i	−0.148694	−	0.257545i
$845$		0			0
$846$	−22064.9			−0.896697
$847$	14021.5	−	4602.65i	0.568814	−	0.186717i
$848$			3235.03i			0.131004i
$849$	−26417.9	+	45757.2i	−1.06792	+	1.84968i
$850$		0			0
$851$	16426.2	+	28451.0i	0.661672	+	1.14605i
$852$	21510.1	+	12418.9i	0.864934	+	0.499370i
$853$		−	33152.4i		−	1.33074i	−0.746516	−	0.665368i	$-0.768275\pi$
$853$		−	33152.4i		−	1.33074i	0.746516	−	0.665368i	$-0.231725\pi$
$854$	33033.8	+	6917.54i	1.32365	+	0.277182i
$855$		0			0
$856$	1133.92	−	1964.01i	0.0452764	−	0.0784210i
$857$	−8960.11	+	5173.12i	−0.357143	+	0.206197i	−0.667827	−	0.744317i	$-0.732775\pi$
$857$	−8960.11	+	5173.12i	−0.357143	+	0.206197i	0.310684	+	0.950513i	$0.399442\pi$
$858$	42146.5	−	24333.3i	1.67699	−	0.968212i
$859$	−5952.82	+	10310.6i	−0.236447	+	0.409538i	−0.959692	−	0.281053i	$-0.909316\pi$
$859$	−5952.82	+	10310.6i	−0.236447	+	0.409538i	0.723245	+	0.690591i	$0.242650\pi$
$860$		0			0
$861$	−39562.2	−	8284.63i	−1.56594	−	0.327920i
$862$		−	16612.9i		−	0.656424i
$863$	26675.6	+	15401.2i	1.05220	+	0.607487i	0.923264	−	0.384166i	$-0.125511\pi$
$863$	26675.6	+	15401.2i	1.05220	+	0.607487i	0.128935	+	0.991653i	$0.458844\pi$
$864$	28502.6	+	49368.0i	1.12231	+	1.94391i
$865$		0			0
$866$	−8847.47	+	15324.3i	−0.347170	+	0.601316i
$867$			44055.3i			1.72572i
$868$	33474.1	−	10988.1i	1.30897	−	0.429676i
$869$	−19417.2			−0.757977
$870$		0			0
$871$	7003.77	+	12130.9i	0.272461	+	0.471917i
$872$	−6551.08	+	3782.27i	−0.254412	+	0.146885i
$873$	8764.56	+	5060.22i	0.339789	+	0.196177i
$874$	−30275.9			−1.17173
$875$		0			0
$876$	21230.3			0.818841
$877$	18786.9	+	10846.6i	0.723363	+	0.417634i	0.815989	−	0.578067i	$-0.196193\pi$
$877$	18786.9	+	10846.6i	0.723363	+	0.417634i	−0.0926262	+	0.995701i	$0.529526\pi$
$878$	−6407.83	+	3699.56i	−0.246303	+	0.142203i
$879$	36489.5	+	63201.6i	1.40018	+	2.42518i
$880$		0			0
$881$	−29963.1			−1.14584			−0.572918	−	0.819612i	$-0.694189\pi$
$881$	−29963.1			−1.14584			−0.572918	+	0.819612i	$0.694189\pi$
$882$	−41770.2	−	56768.7i	−1.59464	−	2.16724i
$883$			4090.61i			0.155900i	0.996957	+	0.0779501i	$0.0248375\pi$
$883$			4090.61i			0.155900i	−0.996957	+	0.0779501i	$0.975163\pi$
$884$	142.728	−	247.213i	0.00543040	−	0.00940573i
$885$		0			0
$886$	8721.07	+	15105.3i	0.330689	+	0.572770i
$887$	24958.3	+	14409.7i	0.944778	+	0.545468i	0.891455	−	0.453110i	$-0.149685\pi$
$887$	24958.3	+	14409.7i	0.944778	+	0.545468i	0.0533229	+	0.998577i	$0.483019\pi$
$888$			10981.6i			0.414998i
$889$	20567.3	−	22981.2i	0.775933	−	0.867003i
$890$		0			0
$891$	−7889.07	+	13664.3i	−0.296626	+	0.513771i
$892$	−10149.6	+	5859.89i	−0.380981	+	0.219959i
$893$	5879.59	−	3394.58i	0.220328	−	0.127206i
$894$	−36561.4	+	63326.2i	−1.36778	+	2.36907i
$895$		0			0
$896$	3392.04	+	10333.5i	0.126473	+	0.385289i
$897$		−	68160.8i		−	2.53715i
$898$	−58064.5	−	33523.5i	−2.15772	−	1.24576i
$899$	14584.5	+	25261.2i	0.541070	+	0.937160i
$900$		0			0
$901$	−15.4211	+	26.7101i	−0.000570200	+	0.000987616i
$902$		−	21633.7i		−	0.798585i
$903$	5873.62	−	28048.7i	0.216458	−	1.03367i
$904$	1605.32			0.0590621
$905$		0			0
$906$	−41398.2	−	71703.7i	−1.51806	−	2.62936i
$907$	−17873.7	+	10319.4i	−0.654340	+	0.377784i	−0.790117	−	0.612956i	$-0.789980\pi$
$907$	−17873.7	+	10319.4i	−0.654340	+	0.377784i	0.135777	+	0.990739i	$0.456647\pi$
$908$	−21279.8	−	12285.9i	−0.777748	−	0.449033i
$909$	−42515.1			−1.55130
$910$		0			0
$911$	−15080.1			−0.548435			−0.274218	−	0.961668i	$-0.588419\pi$
$911$	−15080.1			−0.548435			−0.274218	+	0.961668i	$0.588419\pi$
$912$	−35450.9	−	20467.6i	−1.28717	−	0.743147i
$913$	17726.8	−	10234.6i	0.642576	−	0.370991i
$914$	−3773.77	−	6536.36i	−0.136570	−	0.236547i
$915$		0			0
$916$	9930.56			0.358204
$917$	−11908.4	+	3908.99i	−0.428843	+	0.140770i
$918$			627.352i			0.0225552i
$919$	−1082.14	+	1874.33i	−0.0388429	+	0.0672778i	−0.884793	−	0.465984i	$-0.845701\pi$
$919$	−1082.14	+	1874.33i	−0.0388429	+	0.0672778i	0.845950	+	0.533262i	$0.179034\pi$
$920$		0			0
$921$	−21510.7	−	37257.6i	−0.769600	−	1.33299i
$922$	−47780.0	−	27585.8i	−1.70667	−	0.985347i
$923$		−	24888.3i		−	0.887549i
$924$	17390.8	−	19431.9i	0.619172	−	0.691844i
$925$		0			0
$926$	−22419.3	+	38831.4i	−0.795620	+	1.37805i
$927$	89789.9	−	51840.2i	3.18132	−	1.83674i
$928$	21701.2	−	12529.2i	0.767646	−	0.443201i
$929$	6819.56	−	11811.8i	0.240842	−	0.417151i	−0.720112	−	0.693858i	$-0.755910\pi$
$929$	6819.56	−	11811.8i	0.240842	−	0.417151i	0.960954	+	0.276707i	$0.0892430\pi$
$930$		0			0
$931$	19864.0	+	8700.91i	0.699267	+	0.306295i
$932$			14506.2i			0.509834i
$933$	−40304.3	−	23269.7i	−1.41426	−	0.816523i
$934$	−31757.8	−	55006.1i	−1.11258	−	1.92704i
$935$		0			0
$936$	7567.53	−	13107.3i	0.264265	−	0.457721i
$937$			6568.49i			0.229011i	0.993423	+	0.114505i	$0.0365283\pi$
$937$			6568.49i			0.229011i	−0.993423	+	0.114505i	$0.963472\pi$
$938$	12179.4	+	10900.1i	0.423957	+	0.379424i
$939$	−20135.2			−0.699774
$940$		0			0
$941$	−4727.25	−	8187.84i	−0.163766	−	0.283652i	0.772450	−	0.635075i	$-0.219031\pi$
$941$	−4727.25	−	8187.84i	−0.163766	−	0.283652i	−0.936216	+	0.351424i	$0.885698\pi$
$942$	15120.6	−	8729.91i	0.522991	−	0.301949i
$943$	−26240.1	−	15149.7i	−0.906145	−	0.523163i
$944$	33011.6			1.13817
$945$		0			0
$946$	15337.8			0.527141
$947$	−29511.3	−	17038.4i	−1.01266	−	0.584660i	−0.100691	−	0.994918i	$-0.532105\pi$
$947$	−29511.3	−	17038.4i	−1.01266	−	0.584660i	−0.911969	+	0.410258i	$0.865439\pi$
$948$	44326.5	−	25591.9i	1.51863	−	0.876779i
$949$	−10636.7	−	18423.4i	−0.363839	−	0.630188i
$950$		0			0
$951$	87368.1			2.97908
$952$	−12.1251	+	57.9017i	−0.000412789	+	0.00197122i
$953$			32862.3i			1.11702i	0.829499	+	0.558508i	$0.188626\pi$
$953$			32862.3i			1.11702i	−0.829499	+	0.558508i	$0.811374\pi$
$954$	4603.66	−	7973.77i	0.156236	−	0.270608i
$955$		0			0
$956$	−20218.5	−	35019.5i	−0.684010	−	1.18474i
$957$	18697.8	+	10795.2i	0.631572	+	0.364638i
$958$			60078.3i			2.02614i
$959$	−18747.6	−	3925.90i	−0.631275	−	0.132194i
$960$		0			0
$961$	−24310.7	+	42107.4i	−0.816042	+	1.41343i
$962$	−53656.8	+	30978.7i	−1.79830	+	1.03825i
$963$	−22610.0	+	13053.9i	−0.756590	+	0.436817i
$964$	−13069.1	+	22636.3i	−0.436646	+	0.756293i
$965$		0			0
$966$	−24805.1	−	75566.4i	−0.826182	−	2.51688i
$967$			57597.8i			1.91543i	0.287720	+	0.957715i	$0.407103\pi$
$967$			57597.8i			1.91543i	−0.287720	+	0.957715i	$0.592897\pi$
$968$	3202.44	+	1848.93i	0.106333	+	0.0613913i
$969$	−195.134	−	337.982i	−0.00646915	−	0.0112049i
$970$		0			0
$971$	14092.8	−	24409.5i	0.465768	−	0.806734i	−0.533468	−	0.845820i	$-0.679111\pi$
$971$	14092.8	−	24409.5i	0.465768	−	0.806734i	0.999236	+	0.0390865i	$0.0124448\pi$
$972$			1874.45i			0.0618549i
$973$	−6014.63	−	5382.85i	−0.198171	−	0.177355i
$974$	−7313.15			−0.240583
$975$		0			0
$976$	17103.4	+	29624.0i	0.560930	+	0.971560i
$977$	38333.4	−	22131.8i	1.25526	−	0.724727i	0.283114	−	0.959086i	$-0.408633\pi$
$977$	38333.4	−	22131.8i	1.25526	−	0.724727i	0.972150	+	0.234359i	$0.0752992\pi$
$978$	−77694.4	−	44856.9i	−2.54028	−	1.46663i
$979$	19786.0			0.645929
$980$		0			0
$981$	87084.1			2.83423
$982$	53175.1	+	30700.7i	1.72799	+	0.997656i
$983$	−127.652	+	73.6999i	−0.00414187	+	0.00239131i	−0.502070	−	0.864827i	$-0.667428\pi$
$983$	−127.652	+	73.6999i	−0.00414187	+	0.00239131i	0.497928	+	0.867219i	$0.334095\pi$
$984$	−5064.11	−	8771.29i	−0.164063	−	0.284165i
$985$		0			0
$986$	275.771			0.00890703
$987$	13289.8	+	11893.8i	0.428591	+	0.383571i
$988$		−	26220.7i		−	0.844323i
$989$	10740.8	−	18603.6i	0.345337	−	0.598141i
$990$		0			0
$991$	−6243.42	−	10813.9i	−0.200130	−	0.346635i	0.748440	−	0.663202i	$-0.230803\pi$
$991$	−6243.42	−	10813.9i	−0.200130	−	0.346635i	−0.948570	+	0.316567i	$0.897470\pi$
$992$	58337.1	+	33681.0i	1.86714	+	1.07800i
$993$			101614.i			3.24734i
$994$	−9057.35	−	27592.3i	−0.289016	−	0.880459i
$995$		0			0
$996$	−26978.4	+	46728.0i	−0.858277	+	1.48658i
$997$	−5734.08	+	3310.57i	−0.182147	+	0.105162i	−0.588301	−	0.808642i	$-0.700203\pi$
$997$	−5734.08	+	3310.57i	−0.182147	+	0.105162i	0.406154	+	0.913805i	$0.366870\pi$
$998$	22814.1	−	13171.7i	0.723615	−	0.417780i
$999$	31264.8	−	54152.2i	0.990164	−	1.71501i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	175.4.k.d.149.3		20
5.2	odd	4		175.4.e.d.51.4		10
5.3	odd	4		35.4.e.c.16.2	yes	10
5.4	even	2	inner	175.4.k.d.149.8		20
7.4	even	3	inner	175.4.k.d.74.8		20
15.8	even	4		315.4.j.g.226.4		10
20.3	even	4		560.4.q.n.401.1		10
35.2	odd	12		1225.4.a.bg.1.2		5
35.3	even	12		245.4.e.o.116.2		10
35.4	even	6	inner	175.4.k.d.74.3		20
35.12	even	12		1225.4.a.bf.1.2		5
35.13	even	4		245.4.e.o.226.2		10
35.18	odd	12		35.4.e.c.11.2	✓	10
35.23	odd	12		245.4.a.m.1.4		5
35.32	odd	12		175.4.e.d.151.4		10
35.33	even	12		245.4.a.n.1.4		5
105.23	even	12		2205.4.a.bu.1.2		5
105.53	even	12		315.4.j.g.46.4		10
105.68	odd	12		2205.4.a.bt.1.2		5
140.123	even	12		560.4.q.n.81.1		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.4.e.c.11.2	✓	10	35.18	odd	12
35.4.e.c.16.2	yes	10	5.3	odd	4
175.4.e.d.51.4		10	5.2	odd	4
175.4.e.d.151.4		10	35.32	odd	12
175.4.k.d.74.3		20	35.4	even	6	inner
175.4.k.d.74.8		20	7.4	even	3	inner
175.4.k.d.149.3		20	1.1	even	1	trivial
175.4.k.d.149.8		20	5.4	even	2	inner
245.4.a.m.1.4		5	35.23	odd	12
245.4.a.n.1.4		5	35.33	even	12
245.4.e.o.116.2		10	35.3	even	12
245.4.e.o.226.2		10	35.13	even	4
315.4.j.g.46.4		10	105.53	even	12
315.4.j.g.226.4		10	15.8	even	4
560.4.q.n.81.1		10	140.123	even	12
560.4.q.n.401.1		10	20.3	even	4
1225.4.a.bf.1.2		5	35.12	even	12
1225.4.a.bg.1.2		5	35.2	odd	12
2205.4.a.bt.1.2		5	105.68	odd	12
2205.4.a.bu.1.2		5	105.23	even	12

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.k (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-3.33093 - 1.92311i) q^{2} +(7.76647 - 4.48397i) q^{3} +(3.39672 + 5.88330i) q^{4} -34.4927 q^{6} +(13.8005 + 12.3509i) q^{7} +4.64067i q^{8} +(26.7120 - 46.2666i) q^{9} +(-11.5560 - 20.0155i) q^{11} +(52.7611 + 30.4617i) q^{12} -61.0473i q^{13} +(-22.2164 - 67.6800i) q^{14} +(36.0983 - 62.5241i) q^{16} +(0.596093 - 0.344154i) q^{17} +(-177.952 + 102.741i) q^{18} +(31.6124 - 54.7542i) q^{19} +(162.563 + 34.0419i) q^{21} +88.8938i q^{22} +(107.822 + 62.2508i) q^{23} +(20.8086 + 36.0416i) q^{24} +(-117.401 + 203.344i) q^{26} -236.970i q^{27} +(-25.7876 + 123.145i) q^{28} -104.167 q^{29} +(-140.011 - 242.506i) q^{31} +(-208.330 + 120.280i) q^{32} +(-179.498 - 103.633i) q^{33} -2.64739 q^{34} +362.934 q^{36} +(228.519 + 131.936i) q^{37} +(-210.597 + 121.588i) q^{38} +(-273.735 - 474.122i) q^{39} -243.366 q^{41} +(-476.018 - 426.017i) q^{42} -172.541i q^{43} +(78.5049 - 135.975i) q^{44} +(-239.431 - 414.706i) q^{46} +(92.9951 + 53.6907i) q^{47} -647.456i q^{48} +(37.9094 + 340.899i) q^{49} +(3.08636 - 5.34573i) q^{51} +(359.160 - 207.361i) q^{52} +(-38.8054 + 22.4043i) q^{53} +(-455.720 + 789.330i) q^{54} +(-57.3165 + 64.0437i) q^{56} -566.996i q^{57} +(346.973 + 200.325i) q^{58} +(228.623 + 395.986i) q^{59} +(-236.901 + 410.324i) q^{61} +1077.03i q^{62} +(940.076 - 308.586i) q^{63} +347.672 q^{64} +(398.597 + 690.391i) q^{66} +(-198.713 + 114.727i) q^{67} +(4.04953 + 2.33800i) q^{68} +1116.52 q^{69} +407.688 q^{71} +(214.708 + 123.962i) q^{72} +(301.789 - 174.238i) q^{73} +(-507.454 - 878.937i) q^{74} +429.514 q^{76} +(87.7317 - 418.952i) q^{77} +2105.69i q^{78} +(420.068 - 727.579i) q^{79} +(-341.342 - 591.221i) q^{81} +(810.635 + 468.020i) q^{82} +885.652i q^{83} +(351.902 + 1072.04i) q^{84} +(-331.816 + 574.722i) q^{86} +(-809.010 + 467.082i) q^{87} +(92.8854 - 53.6274i) q^{88} +(-428.048 + 741.401i) q^{89} +(753.991 - 842.486i) q^{91} +845.795i q^{92} +(-2174.78 - 1255.61i) q^{93} +(-206.507 - 357.680i) q^{94} +(-1078.66 + 1868.30i) q^{96} +189.436i q^{97} +(529.313 - 1208.41i) q^{98} -1234.74 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 70 q^{4} + 64 q^{6} + 162 q^{9} - 94 q^{11} - 14 q^{14} - 342 q^{16} - 42 q^{19} + 356 q^{21} + 1696 q^{24} + 94 q^{26} - 760 q^{29} - 776 q^{31} - 520 q^{34} + 4916 q^{36} + 28 q^{39} - 1124 q^{41}+ \cdots - 140 q^{99}+O(q^{100}) \) 20 * q + 70 * q^4 + 64 * q^6 + 162 * q^9 - 94 * q^11 - 14 * q^14 - 342 * q^16 - 42 * q^19 + 356 * q^21 + 1696 * q^24 + 94 * q^26 - 760 * q^29 - 776 * q^31 - 520 * q^34 + 4916 * q^36 + 28 * q^39 - 1124 * q^41 + 2182 * q^44 - 674 * q^46 - 1996 * q^49 - 1464 * q^51 - 1548 * q^54 - 2676 * q^56 + 1416 * q^59 - 3888 * q^61 + 500 * q^64 - 2964 * q^66 - 1496 * q^69 + 3456 * q^71 - 6570 * q^74 + 2764 * q^76 + 436 * q^79 + 910 * q^81 + 1468 * q^84 + 8528 * q^86 + 4644 * q^89 + 1048 * q^91 - 5354 * q^94 - 9184 * q^96 - 140 * q^99

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