LMFDB - Embedded newform 136.4.h.a.101.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [136,4,Mod(101,136)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(136, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 1]))

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

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

chi := DirichletCharacter("136.101");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 136 = 2^{3} \cdot 17 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	136.h (of order $2$, degree $1$, 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:	$8.02425976078$
Analytic rank:	$0$
Dimension:	$52$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			101.16
Character	$\chi$	$=$	136.101
Dual form			136.4.h.a.101.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.98225 + 2.01760i) q^{2} +0.0741700 q^{3} +(-0.141403 - 7.99875i) q^{4} -17.3656 q^{5} +(-0.147023 + 0.149645i) q^{6} +22.3324i q^{7} +(16.4186 + 15.5702i) q^{8} -26.9945 q^{9} +O(q^{10})$	\(q+(-1.98225 + 2.01760i) q^{2} +0.0741700 q^{3} +(-0.141403 - 7.99875i) q^{4} -17.3656 q^{5} +(-0.147023 + 0.149645i) q^{6} +22.3324i q^{7} +(16.4186 + 15.5702i) q^{8} -26.9945 q^{9} +(34.4229 - 35.0368i) q^{10} +62.5853 q^{11} +(-0.0104879 - 0.593268i) q^{12} -75.3060i q^{13} +(-45.0578 - 44.2683i) q^{14} -1.28801 q^{15} +(-63.9600 + 2.26210i) q^{16} +(67.1809 - 19.9933i) q^{17} +(53.5097 - 54.4640i) q^{18} -99.5556i q^{19} +(2.45556 + 138.903i) q^{20} +1.65639i q^{21} +(-124.059 + 126.272i) q^{22} -83.3842i q^{23} +(1.21777 + 1.15484i) q^{24} +176.565 q^{25} +(151.937 + 149.275i) q^{26} -4.00477 q^{27} +(178.631 - 3.15787i) q^{28} +93.0996 q^{29} +(2.55315 - 2.59868i) q^{30} +127.204i q^{31} +(122.220 - 133.530i) q^{32} +4.64196 q^{33} +(-92.8305 + 175.176i) q^{34} -387.816i q^{35} +(3.81711 + 215.922i) q^{36} -221.411 q^{37} +(200.863 + 197.344i) q^{38} -5.58545i q^{39} +(-285.118 - 270.386i) q^{40} +73.5978i q^{41} +(-3.34194 - 3.28338i) q^{42} -210.100i q^{43} +(-8.84977 - 500.604i) q^{44} +468.776 q^{45} +(168.236 + 165.288i) q^{46} +163.391 q^{47} +(-4.74392 + 0.167780i) q^{48} -155.735 q^{49} +(-349.995 + 356.237i) q^{50} +(4.98281 - 1.48291i) q^{51} +(-602.354 + 10.6485i) q^{52} +2.84772i q^{53} +(7.93845 - 8.08003i) q^{54} -1086.83 q^{55} +(-347.719 + 366.665i) q^{56} -7.38404i q^{57} +(-184.546 + 187.838i) q^{58} +326.354i q^{59} +(0.182129 + 10.3025i) q^{60} -225.228 q^{61} +(-256.646 - 252.149i) q^{62} -602.851i q^{63} +(27.1381 + 511.280i) q^{64} +1307.74i q^{65} +(-9.20150 + 9.36560i) q^{66} -330.624i q^{67} +(-169.421 - 534.536i) q^{68} -6.18461i q^{69} +(782.456 + 768.746i) q^{70} -636.622i q^{71} +(-443.211 - 420.310i) q^{72} -1094.13i q^{73} +(438.891 - 446.718i) q^{74} +13.0958 q^{75} +(-796.320 + 14.0775i) q^{76} +1397.68i q^{77} +(11.2692 + 11.0717i) q^{78} -18.7611i q^{79} +(1110.71 - 39.2828i) q^{80} +728.554 q^{81} +(-148.491 - 145.889i) q^{82} -953.977i q^{83} +(13.2491 - 0.234220i) q^{84} +(-1166.64 + 347.196i) q^{85} +(423.897 + 416.469i) q^{86} +6.90520 q^{87} +(1027.56 + 974.465i) q^{88} +797.377 q^{89} +(-929.230 + 945.802i) q^{90} +1681.76 q^{91} +(-666.969 + 11.7908i) q^{92} +9.43472i q^{93} +(-323.881 + 329.657i) q^{94} +1728.84i q^{95} +(9.06510 - 9.90390i) q^{96} -1396.19i q^{97} +(308.705 - 314.211i) q^{98} -1689.46 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q - 2 q^{2} + 10 q^{4} - 2 q^{8} + 428 q^{9}+O(q^{10}) $ 52 * q - 2 * q^2 + 10 * q^4 - 2 * q^8 + 428 * q^9	$ 52 q - 2 q^{2} + 10 q^{4} - 2 q^{8} + 428 q^{9} - 232 q^{15} - 78 q^{16} - 28 q^{17} - 2 q^{18} + 1052 q^{25} + 448 q^{26} - 368 q^{30} + 958 q^{32} - 344 q^{33} - 198 q^{34} + 138 q^{36} - 524 q^{38} + 936 q^{47} - 1964 q^{49} - 1038 q^{50} - 1424 q^{52} - 1384 q^{55} + 2320 q^{60} - 2078 q^{64} - 1888 q^{66} - 874 q^{68} + 2472 q^{70} - 4010 q^{72} + 436 q^{76} + 1884 q^{81} - 2264 q^{84} - 1420 q^{86} + 1976 q^{87} - 224 q^{89} + 80 q^{94} + 5746 q^{98}+O(q^{100}) $ 52 * q - 2 * q^2 + 10 * q^4 - 2 * q^8 + 428 * q^9 - 232 * q^15 - 78 * q^16 - 28 * q^17 - 2 * q^18 + 1052 * q^25 + 448 * q^26 - 368 * q^30 + 958 * q^32 - 344 * q^33 - 198 * q^34 + 138 * q^36 - 524 * q^38 + 936 * q^47 - 1964 * q^49 - 1038 * q^50 - 1424 * q^52 - 1384 * q^55 + 2320 * q^60 - 2078 * q^64 - 1888 * q^66 - 874 * q^68 + 2472 * q^70 - 4010 * q^72 + 436 * q^76 + 1884 * q^81 - 2264 * q^84 - 1420 * q^86 + 1976 * q^87 - 224 * q^89 + 80 * q^94 + 5746 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/136\mathbb{Z}\right)^\times$.

$n$	$69$	$103$	$105$
$\chi(n)$	$-1$	$1$	$-1$

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 $

$2$	−1.98225	+	2.01760i	−0.700830	+	0.713329i
$2$	−1.98225	+	2.01760i	−0.700830	+	0.713329i
$3$	0.0741700			0.0142740			0.00713702	−	0.999975i	$-0.497728\pi$
$3$	0.0741700			0.0142740			0.00713702	+	0.999975i	$0.497728\pi$
$4$	−0.141403	−	7.99875i	−0.0176754	−	0.999844i
$5$	−17.3656			−1.55323			−0.776614	−	0.629977i	$-0.783064\pi$
$5$	−17.3656			−1.55323			−0.776614	+	0.629977i	$0.783064\pi$
$6$	−0.147023	+	0.149645i	−0.0100037	+	0.0101821i
$7$			22.3324i			1.20583i	0.797804	+	0.602917i	$0.205995\pi$
$7$			22.3324i			1.20583i	−0.797804	+	0.602917i	$0.794005\pi$
$8$	16.4186	+	15.5702i	0.725605	+	0.688112i
$9$	−26.9945			−0.999796
$10$	34.4229	−	35.0368i	1.08855	−	1.10796i
$11$	62.5853			1.71547			0.857735	−	0.514091i	$-0.171871\pi$
$11$	62.5853			1.71547			0.857735	+	0.514091i	$0.171871\pi$
$12$	−0.0104879	−	0.593268i	−0.000252300	−	0.0142718i
$13$		−	75.3060i		−	1.60663i	−0.595557	−	0.803313i	$-0.703069\pi$
$13$		−	75.3060i		−	1.60663i	0.595557	−	0.803313i	$-0.296931\pi$
$14$	−45.0578	−	44.2683i	−0.860157	−	0.845085i
$15$	−1.28801			−0.0221708
$16$	−63.9600	+	2.26210i	−0.999375	+	0.0353453i
$17$	67.1809	−	19.9933i	0.958456	−	0.285241i
$17$	67.1809	−	19.9933i	0.958456	−	0.285241i
$18$	53.5097	−	54.4640i	0.700687	−	0.713183i
$19$		−	99.5556i		−	1.20209i	−0.799217	−	0.601043i	$-0.794752\pi$
$19$		−	99.5556i		−	1.20209i	0.799217	−	0.601043i	$-0.205248\pi$
$20$	2.45556	+	138.903i	0.0274540	+	1.55299i
$21$			1.65639i			0.0172121i
$22$	−124.059	+	126.272i	−1.20225	+	1.22369i
$23$		−	83.3842i		−	0.755948i	−0.925816	−	0.377974i	$-0.876621\pi$
$23$		−	83.3842i		−	0.755948i	0.925816	−	0.377974i	$-0.123379\pi$
$24$	1.21777	+	1.15484i	0.0103573	+	0.00982213i
$25$	176.565			1.41252
$26$	151.937	+	149.275i	1.14605	+	1.12597i
$27$	−4.00477			−0.0285452
$28$	178.631	−	3.15787i	1.20565	−	0.0213136i
$29$	93.0996			0.596143			0.298072	−	0.954543i	$-0.403657\pi$
$29$	93.0996			0.596143			0.298072	+	0.954543i	$0.403657\pi$
$30$	2.55315	−	2.59868i	0.0155380	−	0.0158151i
$31$			127.204i			0.736984i	0.929631	+	0.368492i	$0.120126\pi$
$31$			127.204i			0.736984i	−0.929631	+	0.368492i	$0.879874\pi$
$32$	122.220	−	133.530i	0.675179	−	0.737654i
$33$	4.64196			0.0244867
$34$	−92.8305	+	175.176i	−0.468244	+	0.883599i
$35$		−	387.816i		−	1.87294i
$36$	3.81711	+	215.922i	0.0176718	+	0.999640i
$37$	−221.411			−0.983776			−0.491888	−	0.870658i	$-0.663693\pi$
$37$	−221.411			−0.983776			−0.491888	+	0.870658i	$0.663693\pi$
$38$	200.863	+	197.344i	0.857482	+	0.842457i
$39$		−	5.58545i		−	0.0229330i
$40$	−285.118	−	270.386i	−1.12703	−	1.06879i
$41$			73.5978i			0.280343i	0.990127	+	0.140171i	$0.0447653\pi$
$41$			73.5978i			0.280343i	−0.990127	+	0.140171i	$0.955235\pi$
$42$	−3.34194	−	3.28338i	−0.0122779	−	0.0120628i
$43$		−	210.100i		−	0.745114i	−0.928009	−	0.372557i	$-0.878481\pi$
$43$		−	210.100i		−	0.745114i	0.928009	−	0.372557i	$-0.121519\pi$
$44$	−8.84977	−	500.604i	−0.0303217	−	1.71520i
$45$	468.776			1.55291
$46$	168.236	+	165.288i	0.539239	+	0.529791i
$47$	163.391			0.507085			0.253542	−	0.967324i	$-0.418404\pi$
$47$	163.391			0.507085			0.253542	+	0.967324i	$0.418404\pi$
$48$	−4.74392	+	0.167780i	−0.0142651	+	0.000504520i
$49$	−155.735			−0.454038
$50$	−349.995	+	356.237i	−0.989934	+	1.00759i
$51$	4.98281	−	1.48291i	0.0136810	−	0.00407153i
$52$	−602.354	+	10.6485i	−1.60637	+	0.0283978i
$53$			2.84772i			0.00738046i	0.999993	+	0.00369023i	$0.00117464\pi$
$53$			2.84772i			0.00738046i	−0.999993	+	0.00369023i	$0.998825\pi$
$54$	7.93845	−	8.08003i	0.0200053	−	0.0203621i
$55$	−1086.83			−2.66452
$56$	−347.719	+	366.665i	−0.829749	+	0.874959i
$57$		−	7.38404i		−	0.0171586i
$58$	−184.546	+	187.838i	−0.417795	+	0.425246i
$59$			326.354i			0.720131i	0.932927	+	0.360065i	$0.117246\pi$
$59$			326.354i			0.720131i	−0.932927	+	0.360065i	$0.882754\pi$
$60$	0.182129	+	10.3025i	0.000391879	+	0.0221674i
$61$	−225.228			−0.472745			−0.236373	−	0.971662i	$-0.575959\pi$
$61$	−225.228			−0.472745			−0.236373	+	0.971662i	$0.575959\pi$
$62$	−256.646	−	252.149i	−0.525712	−	0.516500i
$63$		−	602.851i		−	1.20559i
$64$	27.1381	+	511.280i	0.0530042	+	0.998594i
$65$			1307.74i			2.49546i
$66$	−9.20150	+	9.36560i	−0.0171610	+	0.0174671i
$67$		−	330.624i		−	0.602868i	−0.953487	−	0.301434i	$-0.902535\pi$
$67$		−	330.624i		−	0.602868i	0.953487	−	0.301434i	$-0.0974653\pi$
$68$	−169.421	−	534.536i	−0.302137	−	0.953264i
$69$		−	6.18461i		−	0.0107904i
$70$	782.456	+	768.746i	1.33602	+	1.31261i
$71$		−	636.622i		−	1.06413i	−0.846704	−	0.532065i	$-0.821416\pi$
$71$		−	636.622i		−	1.06413i	0.846704	−	0.532065i	$-0.178584\pi$
$72$	−443.211	−	420.310i	−0.725457	−	0.687972i
$73$		−	1094.13i		−	1.75422i	−0.480288	−	0.877111i	$-0.659468\pi$
$73$		−	1094.13i		−	1.75422i	0.480288	−	0.877111i	$-0.340532\pi$
$74$	438.891	−	446.718i	0.689460	−	0.701756i
$75$	13.0958			0.0201623
$76$	−796.320	+	14.0775i	−1.20190	+	0.0212474i
$77$			1397.68i			2.06857i
$78$	11.2692	+	11.0717i	0.0163588	+	0.0160721i
$79$		−	18.7611i		−	0.0267189i	−0.999911	−	0.0133595i	$-0.995747\pi$
$79$		−	18.7611i		−	0.0267189i	0.999911	−	0.0133595i	$-0.00425257\pi$
$80$	1110.71	−	39.2828i	1.55226	−	0.0548993i
$81$	728.554			0.999389
$82$	−148.491	−	145.889i	−0.199976	−	0.196472i
$83$		−	953.977i		−	1.26160i	−0.775946	−	0.630799i	$-0.782727\pi$
$83$		−	953.977i		−	1.26160i	0.775946	−	0.630799i	$-0.217273\pi$
$84$	13.2491	−	0.234220i	0.0172094	−	0.000304232i
$85$	−1166.64	+	347.196i	−1.48870	+	0.443044i
$86$	423.897	+	416.469i	0.531511	+	0.522198i
$87$	6.90520			0.00850937
$88$	1027.56	+	974.465i	1.24475	+	1.18044i
$89$	797.377			0.949684			0.474842	−	0.880071i	$-0.342505\pi$
$89$	797.377			0.949684			0.474842	+	0.880071i	$0.342505\pi$
$90$	−929.230	+	945.802i	−1.08833	+	1.10774i
$91$	1681.76			1.93733
$92$	−666.969	+	11.7908i	−0.755830	+	0.0133617i
$93$			9.43472i			0.0105197i
$94$	−323.881	+	329.657i	−0.355380	+	0.361718i
$95$			1728.84i			1.86711i
$96$	9.06510	−	9.90390i	0.00963753	−	0.0105293i
$97$		−	1396.19i		−	1.46146i	−0.682665	−	0.730732i	$-0.739179\pi$
$97$		−	1396.19i		−	1.46146i	0.682665	−	0.730732i	$-0.260821\pi$
$98$	308.705	−	314.211i	0.318203	−	0.323878i
$99$	−1689.46			−1.71512
$100$	−24.9668	−	1412.30i	−0.0249668	−	1.41230i
$101$		−	783.768i		−	0.772156i	−0.922466	−	0.386078i	$-0.873830\pi$
$101$		−	783.768i		−	0.772156i	0.922466	−	0.386078i	$-0.126170\pi$
$102$	−6.88524	+	12.9928i	−0.00668373	+	0.0126125i
$103$	−1102.23			−1.05443			−0.527215	−	0.849732i	$-0.676764\pi$
$103$	−1102.23			−1.05443			−0.527215	+	0.849732i	$0.676764\pi$
$104$	1172.53	−	1236.42i	1.10554	−	1.16578i
$105$		−	28.7643i		−	0.0267344i
$106$	−5.74555	−	5.64488i	−0.00526469	−	0.00517244i
$107$	1224.33			1.10617			0.553085	−	0.833125i	$-0.313450\pi$
$107$	1224.33			1.10617			0.553085	+	0.833125i	$0.313450\pi$
$108$	0.566289	+	32.0332i	0.000504548	+	0.0285407i
$109$	17.3959			0.0152864			0.00764321	−	0.999971i	$-0.497567\pi$
$109$	17.3959			0.0152864			0.00764321	+	0.999971i	$0.497567\pi$
$110$	2154.37	−	2192.79i	1.86737	−	1.90068i
$111$	−16.4221			−0.0140425
$112$	−50.5181	−	1428.38i	−0.0426206	−	1.20508i
$113$			1900.05i			1.58179i	0.611953	+	0.790894i	$0.290384\pi$
$113$			1900.05i			1.58179i	−0.611953	+	0.790894i	$0.709616\pi$
$114$	14.8980	+	14.6370i	0.0122397	+	0.0120253i
$115$			1448.02i			1.17416i
$116$	−13.1646	−	744.680i	−0.0105371	−	0.596050i
$117$			2032.85i			1.60630i
$118$	−658.452	−	646.914i	−0.513690	−	0.504689i
$119$	446.498	+	1500.31i	0.343953	+	1.15574i
$120$	−21.1472	−	20.0545i	−0.0160873	−	0.0152560i
$121$	2585.92			1.94284
$122$	446.457	−	454.419i	0.331314	−	0.337223i
$123$			5.45875i			0.00400162i
$124$	1017.47	−	17.9871i	0.736869	−	0.0130265i
$125$	−895.453			−0.640734
$126$	1216.31	+	1195.00i	0.859981	+	0.844913i
$127$	−205.605			−0.143658			−0.0718288	−	0.997417i	$-0.522884\pi$
$127$	−205.605			−0.143658			−0.0718288	+	0.997417i	$0.522884\pi$
$128$	−1085.35	−	958.729i	−0.749473	−	0.662035i
$129$		−	15.5831i		−	0.0106358i
$130$	−2638.49	−	2592.25i	−1.78008	−	1.74889i
$131$	−1380.10			−0.920454			−0.460227	−	0.887801i	$-0.652232\pi$
$131$	−1380.10			−0.920454			−0.460227	+	0.887801i	$0.652232\pi$
$132$	−0.656388	−	37.1298i	−0.000432812	−	0.0244829i
$133$	2223.31			1.44952
$134$	667.066	+	655.378i	0.430043	+	0.422508i
$135$	69.5454			0.0443371
$136$	1414.31	+	717.758i	0.891738	+	0.452553i
$137$	−1194.79			−0.745092			−0.372546	−	0.928014i	$-0.621515\pi$
$137$	−1194.79			−0.745092			−0.372546	+	0.928014i	$0.621515\pi$
$138$	12.4781	+	12.2594i	0.00769712	+	0.00756225i
$139$	−619.145			−0.377807			−0.188904	−	0.981996i	$-0.560493\pi$
$139$	−619.145			−0.377807			−0.188904	+	0.981996i	$0.560493\pi$
$140$	−3102.04	+	54.8384i	−1.87264	+	0.0331049i
$141$	12.1187			0.00723815
$142$	1284.45	+	1261.94i	0.759074	+	0.745773i
$143$		−	4713.05i		−	2.75612i
$144$	1726.57	−	61.0643i	0.999172	−	0.0353381i
$145$	−1616.73			−0.925947
$146$	2207.51	+	2168.83i	1.25134	+	1.22941i
$147$	−11.5509			−0.00648095
$148$	31.3082	+	1771.01i	0.0173887	+	0.983622i
$149$			167.437i			0.0920602i	0.998940	+	0.0460301i	$0.0146570\pi$
$149$			167.437i			0.0920602i	−0.998940	+	0.0460301i	$0.985343\pi$
$150$	−25.9591	+	26.4221i	−0.0141304	+	0.0143824i
$151$	1475.25			0.795061			0.397531	−	0.917589i	$-0.369867\pi$
$151$	1475.25			0.795061			0.397531	+	0.917589i	$0.369867\pi$
$152$	1550.10	−	1634.56i	0.827169	−	0.872239i
$153$	−1813.51	+	539.710i	−0.958261	+	0.285183i
$154$	−2819.95	−	2770.54i	−1.47557	−	1.44972i
$155$		−	2208.98i		−	1.14470i
$156$	−44.6766	+	0.789802i	−0.0229294	+	0.000405351i
$157$			341.194i			0.173441i	0.996233	+	0.0867205i	$0.0276387\pi$
$157$			341.194i			0.173441i	−0.996233	+	0.0867205i	$0.972361\pi$
$158$	37.8525	+	37.1892i	0.0190594	+	0.0187254i
$159$			0.211215i			0.000105349i
$160$	−2122.43	+	2318.82i	−1.04871	+	1.14574i
$161$	1862.17			0.911548
$162$	−1444.17	+	1469.93i	−0.700401	+	0.712893i
$163$	−1716.60			−0.824875			−0.412437	−	0.910986i	$-0.635322\pi$
$163$	−1716.60			−0.824875			−0.412437	+	0.910986i	$0.635322\pi$
$164$	588.690	−	10.4070i	0.280299	−	0.00495517i
$165$	−80.6104			−0.0380334
$166$	1924.74	+	1891.02i	0.899934	+	0.884165i
$167$		−	3343.32i		−	1.54918i	−0.632461	−	0.774592i	$-0.717955\pi$
$167$		−	3343.32i		−	1.54918i	0.632461	−	0.774592i	$-0.282045\pi$
$168$	−25.7904	+	27.1956i	−0.0118439	+	0.0124892i
$169$	−3474.00			−1.58125
$170$	1612.06	−	3042.03i	0.727290	−	1.37243i
$171$			2687.45i			1.20184i
$172$	−1680.53	+	29.7088i	−0.744997	+	0.0131702i
$173$	−1958.82			−0.860846			−0.430423	−	0.902627i	$-0.641636\pi$
$173$	−1958.82			−0.860846			−0.430423	+	0.902627i	$0.641636\pi$
$174$	−13.6878	+	13.9319i	−0.00596362	+	0.00606998i
$175$			3943.11i			1.70326i
$176$	−4002.96	+	141.574i	−1.71440	+	0.0606339i
$177$			24.2057i			0.0102792i
$178$	−1580.60	+	1608.79i	−0.665567	+	0.677437i
$179$			1997.03i			0.833883i	0.908933	+	0.416941i	$0.136898\pi$
$179$			1997.03i			0.833883i	−0.908933	+	0.416941i	$0.863102\pi$
$180$	−66.2865	−	3749.62i	−0.0274484	−	1.55267i
$181$	−537.433			−0.220702			−0.110351	−	0.993893i	$-0.535197\pi$
$181$	−537.433			−0.220702			−0.110351	+	0.993893i	$0.535197\pi$
$182$	−3333.67	+	3393.12i	−1.35774	+	1.38195i
$183$	−16.7052			−0.00674798
$184$	1298.31	−	1369.05i	0.520177	−	0.548519i
$185$	3844.94			1.52803
$186$	−19.0355	−	18.7019i	−0.00750403	−	0.00737254i
$187$	4204.53	−	1251.29i	1.64420	−	0.489322i
$188$	−23.1040	−	1306.92i	−0.00896294	−	0.507006i
$189$		−	89.4361i		−	0.0344207i
$190$	−3488.11	−	3426.99i	−1.33186	−	1.30853i
$191$	−1810.54			−0.685894			−0.342947	−	0.939355i	$-0.611425\pi$
$191$	−1810.54			−0.685894			−0.342947	+	0.939355i	$0.611425\pi$
$192$	2.01284	+	37.9217i	0.000756583	+	0.0142540i
$193$			2270.61i			0.846851i	0.905931	+	0.423425i	$0.139172\pi$
$193$			2270.61i			0.846851i	−0.905931	+	0.423425i	$0.860828\pi$
$194$	2816.96	+	2767.60i	1.04250	+	1.02424i
$195$			96.9948i			0.0356202i
$196$	22.0214	+	1245.69i	0.00802531	+	0.453967i
$197$	3414.23			1.23479			0.617396	−	0.786652i	$-0.288188\pi$
$197$	3414.23			1.23479			0.617396	+	0.786652i	$0.288188\pi$
$198$	3348.92	−	3408.65i	1.20201	−	1.22345i
$199$			628.204i			0.223780i	0.993721	+	0.111890i	$0.0356904\pi$
$199$			628.204i			0.223780i	−0.993721	+	0.111890i	$0.964310\pi$
$200$	2898.94	+	2749.15i	1.02493	+	0.971970i
$201$		−	24.5224i		−	0.00860535i
$202$	1581.33	+	1553.62i	0.550801	+	0.541150i
$203$			2079.13i			0.718850i
$204$	−12.5660	−	39.6465i	−0.00431272	−	0.0136069i
$205$		−	1278.07i		−	0.435436i
$206$	2184.90	−	2223.86i	0.738976	−	0.752155i
$207$			2250.91i			0.755794i
$208$	170.350	+	4816.57i	0.0567867	+	1.60562i
$209$		−	6230.72i		−	2.06214i
$210$	58.0348	+	57.0179i	0.0190704	+	0.0187362i
$211$	168.439			0.0549564			0.0274782	−	0.999622i	$-0.491252\pi$
$211$	168.439			0.0549564			0.0274782	+	0.999622i	$0.491252\pi$
$212$	22.7782	−	0.402677i	0.00737930	−	0.000130453i
$213$		−	47.2183i		−	0.0151894i
$214$	−2426.92	+	2470.20i	−0.775237	+	0.789063i
$215$			3648.51i			1.15733i
$216$	−65.7526	−	62.3551i	−0.0207125	−	0.0196423i
$217$	−2840.77			−0.888681
$218$	−34.4829	+	35.0978i	−0.0107132	+	0.0109042i
$219$		−	81.1516i		−	0.0250398i
$220$	153.682	+	8693.30i	0.0470965	+	2.66410i
$221$	−1505.62	−	5059.12i	−0.458275	−	1.53988i
$222$	32.5525	−	33.1331i	0.00984137	−	0.0100169i
$223$	5890.95			1.76900			0.884500	−	0.466540i	$-0.154500\pi$
$223$	5890.95			1.76900			0.884500	+	0.466540i	$0.154500\pi$
$224$	2982.03	+	2729.47i	0.889489	+	0.814154i
$225$	−4766.28			−1.41223
$226$	−3833.55	−	3766.37i	−1.12833	−	1.10856i
$227$	−2963.13			−0.866388			−0.433194	−	0.901301i	$-0.642614\pi$
$227$	−2963.13			−0.866388			−0.433194	+	0.901301i	$0.642614\pi$
$228$	−59.0631	+	1.04413i	−0.0171559	+	0.000303286i
$229$		−	4665.91i		−	1.34643i	−0.739448	−	0.673213i	$-0.764914\pi$
$229$		−	4665.91i		−	1.34643i	0.739448	−	0.673213i	$-0.235086\pi$
$230$	−2921.52	−	2870.33i	−0.837561	−	0.822886i
$231$			103.666i			0.0295269i
$232$	1528.56	+	1449.58i	0.432564	+	0.410213i
$233$			92.7784i			0.0260863i	0.999915	+	0.0130432i	$0.00415189\pi$
$233$			92.7784i			0.0260863i	−0.999915	+	0.0130432i	$0.995848\pi$
$234$	−4101.47	−	4029.61i	−1.14582	−	1.12574i
$235$	−2837.38			−0.787619
$236$	2610.43	−	46.1476i	0.720018	−	0.0127286i
$237$		−	1.39152i		−	0.000381387i
$238$	−3912.09	−	2073.13i	−1.06547	−	0.564625i
$239$	3237.67			0.876266			0.438133	−	0.898910i	$-0.355640\pi$
$239$	3237.67			0.876266			0.438133	+	0.898910i	$0.355640\pi$
$240$	82.3811	−	2.91360i	0.0221570	−	0.000783635i
$241$		−	1681.04i		−	0.449316i	−0.974438	−	0.224658i	$-0.927873\pi$
$241$		−	1681.04i		−	0.449316i	0.974438	−	0.224658i	$-0.0721265\pi$
$242$	−5125.93	+	5217.35i	−1.36160	+	1.38588i
$243$	162.166			0.0428105
$244$	31.8480	+	1801.54i	0.00835597	+	0.472671i
$245$	2704.43			0.705224
$246$	−11.0136	−	10.8206i	−0.00285447	−	0.00280445i
$247$	−7497.14			−1.93130
$248$	−1980.59	+	2088.51i	−0.507127	+	0.534759i
$249$		−	70.7565i		−	0.0180081i
$250$	1775.01	−	1806.66i	0.449046	−	0.457054i
$251$			653.059i			0.164226i	0.996623	+	0.0821130i	$0.0261668\pi$
$251$			653.059i			0.164226i	−0.996623	+	0.0821130i	$0.973833\pi$
$252$	−4822.06	+	85.2452i	−1.20540	+	0.0213093i
$253$		−	5218.62i		−	1.29681i
$254$	407.560	−	414.829i	0.100680	−	0.102475i
$255$	−86.5295	+	25.7516i	−0.0212498	+	0.00632402i
$256$	4085.77	−	289.368i	0.997501	−	0.0706465i
$257$	−1636.18			−0.397130			−0.198565	−	0.980088i	$-0.563628\pi$
$257$	−1636.18			−0.397130			−0.198565	+	0.980088i	$0.563628\pi$
$258$	31.4404	+	30.8895i	0.00758681	+	0.00745387i
$259$		−	4944.63i		−	1.18627i
$260$	10460.3	−	184.918i	2.49507	−	0.0441082i
$261$	−2513.18			−0.596022
$262$	2735.69	−	2784.48i	0.645081	−	0.656586i
$263$	5502.33			1.29007			0.645034	−	0.764154i	$-0.276843\pi$
$263$	5502.33			1.29007			0.645034	+	0.764154i	$0.276843\pi$
$264$	76.2142	+	72.2761i	0.0177677	+	0.0168496i
$265$		−	49.4524i		−	0.0114635i
$266$	−4407.15	+	4485.75i	−1.01586	+	1.03398i
$267$	59.1415			0.0135558
$268$	−2644.58	+	46.7513i	−0.602774	+	0.0106559i
$269$	6822.32			1.54634			0.773168	−	0.634201i	$-0.218671\pi$
$269$	6822.32			1.54634			0.773168	+	0.634201i	$0.218671\pi$
$270$	−137.856	+	140.315i	−0.0310728	+	0.0316270i
$271$	4780.17			1.07149			0.535747	−	0.844379i	$-0.320030\pi$
$271$	4780.17			1.07149			0.535747	+	0.844379i	$0.320030\pi$
$272$	−4251.66	+	1430.74i	−0.947775	+	0.318939i
$273$	124.736			0.0276534
$274$	2368.36	−	2410.60i	0.522183	−	0.531495i
$275$	11050.4			2.42313
$276$	−49.4691	+	0.874524i	−0.0107887	+	0.000190725i
$277$	−3596.56			−0.780132			−0.390066	−	0.920787i	$-0.627548\pi$
$277$	−3596.56			−0.780132			−0.390066	+	0.920787i	$0.627548\pi$
$278$	1227.30	−	1249.19i	0.264779	−	0.269501i
$279$		−	3433.81i		−	0.736834i
$280$	6038.36	−	6367.37i	1.28879	−	1.35901i
$281$	−3084.37			−0.654797			−0.327398	−	0.944886i	$-0.606172\pi$
$281$	−3084.37			−0.654797			−0.327398	+	0.944886i	$0.606172\pi$
$282$	−24.0222	+	24.4507i	−0.00507271	+	0.00516318i
$283$	251.886			0.0529083			0.0264541	−	0.999650i	$-0.491578\pi$
$283$	251.886			0.0529083			0.0264541	+	0.999650i	$0.491578\pi$
$284$	−5092.18	+	90.0205i	−1.06396	+	0.0188089i
$285$			128.228i			0.0266512i
$286$	9509.04	+	9342.42i	1.96602	+	1.93157i
$287$	−1643.61			−0.338047
$288$	−3299.28	+	3604.57i	−0.675041	+	0.737504i
$289$	4113.53	−	2686.34i	0.837276	−	0.546781i
$290$	3204.76	−	3261.91i	0.648931	−	0.660504i
$291$		−	103.556i		−	0.0208610i
$292$	−8751.67	+	154.714i	−1.75395	+	0.0310066i
$293$			109.394i			0.0218118i	0.999941	+	0.0109059i	$0.00347152\pi$
$293$			109.394i			0.0218118i	−0.999941	+	0.0109059i	$0.996528\pi$
$294$	22.8967	−	23.3050i	0.00454204	−	0.00462305i
$295$		−	5667.34i		−	1.11853i
$296$	−3635.25	−	3447.41i	−0.713833	−	0.676948i
$297$	−250.640			−0.0489684
$298$	−337.820	−	331.901i	−0.0656692	−	0.0645185i
$299$	−6279.33			−1.21453
$300$	−1.85179	−	104.750i	−0.000356378	−	0.0201592i
$301$	4692.02			0.898484
$302$	−2924.31	+	2976.46i	−0.557202	+	0.567140i
$303$		−	58.1321i		−	0.0110218i
$304$	225.205	+	6367.58i	0.0424881	+	1.20133i
$305$	3911.22			0.734281
$306$	2505.91	−	4728.78i	0.468149	−	0.883419i
$307$			2337.41i			0.434537i	0.976112	+	0.217268i	$0.0697147\pi$
$307$			2337.41i			0.434537i	−0.976112	+	0.217268i	$0.930285\pi$
$308$	11179.7	−	197.636i	2.06825	−	0.0365629i
$309$	−81.7527			−0.0150510
$310$	4456.82	+	4378.73i	0.816550	+	0.802243i
$311$			3255.84i			0.593640i	0.954933	+	0.296820i	$0.0959261\pi$
$311$			3255.84i			0.593640i	−0.954933	+	0.296820i	$0.904074\pi$
$312$	86.9666	−	91.7051i	0.0157805	−	0.0166403i
$313$			8760.71i			1.58206i	0.611778	+	0.791029i	$0.290455\pi$
$313$			8760.71i			1.58206i	−0.611778	+	0.791029i	$0.709545\pi$
$314$	−688.392	−	676.330i	−0.123720	−	0.121553i
$315$			10468.9i			1.87256i
$316$	−150.066	+	2.65289i	−0.0267147	+	0.000472268i
$317$	−8086.71			−1.43279			−0.716396	−	0.697694i	$-0.754210\pi$
$317$	−8086.71			−1.43279			−0.716396	+	0.697694i	$0.754210\pi$
$318$	−0.426148	−	0.418681i	−7.51484e−5	−	7.38316e-5i
$319$	5826.67			1.02267
$320$	−471.270	−	8878.70i	−0.0823276	−	1.55104i
$321$	90.8085			0.0157895
$322$	−3691.27	+	3757.10i	−0.638840	+	0.650233i
$323$	−1990.45	−	6688.23i	−0.342884	−	1.15215i
$324$	−103.020	−	5827.52i	−0.0176646	−	0.999233i
$325$		−	13296.4i		−	2.26939i
$326$	3402.73	−	3463.41i	0.578097	−	0.588407i
$327$	1.29025			0.000218199
$328$	−1145.93	+	1208.37i	−0.192907	+	0.203418i
$329$			3648.90i			0.611461i
$330$	159.790	−	162.639i	0.0266549	−	0.0271303i
$331$		−	6473.73i		−	1.07501i	−0.843260	−	0.537505i	$-0.819367\pi$
$331$		−	6473.73i		−	1.07501i	0.843260	−	0.537505i	$-0.180633\pi$
$332$	−7630.62	+	134.896i	−1.26140	+	0.0222993i
$333$	5976.87			0.983576
$334$	6745.48	+	6627.28i	1.10508	+	1.08571i
$335$			5741.49i			0.936391i
$336$	−3.74693	−	105.943i	−0.000608368	−	0.0172014i
$337$			8226.09i			1.32968i	0.746984	+	0.664842i	$0.231501\pi$
$337$			8226.09i			1.32968i	−0.746984	+	0.664842i	$0.768499\pi$
$338$	6886.32	−	7009.13i	1.10818	−	1.12795i
$339$			140.927i			0.0225785i
$340$	2942.10	+	9282.54i	0.469288	+	1.48064i
$341$			7961.10i			1.26427i
$342$	−5422.20	−	5327.19i	−0.857307	−	0.842285i
$343$			4182.07i			0.658340i
$344$	3271.29	−	3449.53i	0.512722	−	0.540658i
$345$			107.400i			0.0167600i
$346$	3882.86	−	3952.11i	0.603306	−	0.614066i
$347$	−9552.28			−1.47779			−0.738895	−	0.673820i	$-0.764652\pi$
$347$	−9552.28			−1.47779			−0.738895	+	0.673820i	$0.764652\pi$
$348$	−0.976418	−	55.2330i	−0.000150407	−	0.00850804i
$349$			7353.28i			1.12783i	0.825834	+	0.563914i	$0.190705\pi$
$349$			7353.28i			1.12783i	−0.825834	+	0.563914i	$0.809295\pi$
$350$	−7955.61	−	7816.21i	−1.21499	−	1.19370i
$351$			301.584i			0.0458614i
$352$	7649.20	−	8356.99i	1.15825	−	1.26542i
$353$	−5697.06			−0.858991			−0.429495	−	0.903069i	$-0.641309\pi$
$353$	−5697.06			−0.858991			−0.429495	+	0.903069i	$0.641309\pi$
$354$	−48.8374	−	47.9817i	−0.00733243	−	0.00720395i
$355$			11055.3i			1.65284i
$356$	−112.752	−	6378.02i	−0.0167861	−	0.949535i
$357$	33.1168	+	111.278i	0.00490960	+	0.0164971i
$358$	−4029.20	−	3958.60i	−0.594832	−	0.584410i
$359$	−4654.57			−0.684286			−0.342143	−	0.939648i	$-0.611153\pi$
$359$	−4654.57			−0.684286			−0.342143	+	0.939648i	$0.611153\pi$
$360$	7696.63	+	7298.94i	1.12680	+	1.06858i
$361$	−3052.32			−0.445009
$362$	1065.32	−	1084.32i	0.154674	−	0.157433i
$363$	191.798			0.0277322
$364$	−237.807	−	13452.0i	−0.0342430	−	1.93702i
$365$			19000.2i			2.72471i
$366$	33.1137	−	33.7043i	0.00472919	−	0.00481353i
$367$		−	11694.9i		−	1.66341i	−0.555220	−	0.831704i	$-0.687366\pi$
$367$		−	11694.9i		−	1.66341i	0.555220	−	0.831704i	$-0.312634\pi$
$368$	188.623	+	5333.25i	0.0267192	+	0.755475i
$369$		−	1986.74i		−	0.280285i
$370$	−7621.61	+	7757.54i	−1.07089	+	1.08999i
$371$	−63.5963			−0.00889961
$372$	75.4660	−	1.33410i	0.0105181	−	0.000185941i
$373$		−	8084.20i		−	1.12221i	−0.827745	−	0.561104i	$-0.810377\pi$
$373$		−	8084.20i		−	1.12221i	0.827745	−	0.561104i	$-0.189623\pi$
$374$	−5809.82	+	10963.4i	−0.803259	+	1.51579i
$375$	−66.4158			−0.00914586
$376$	2682.64	+	2544.03i	0.367943	+	0.348931i
$377$		−	7010.96i		−	0.957779i
$378$	180.446	+	177.284i	0.0245533	+	0.0241231i
$379$	−3912.91			−0.530323			−0.265162	−	0.964204i	$-0.585425\pi$
$379$	−3912.91			−0.530323			−0.265162	+	0.964204i	$0.585425\pi$
$380$	13828.6	−	244.464i	1.86682	−	0.0330020i
$381$	−15.2498			−0.00205057
$382$	3588.93	−	3652.93i	0.480695	−	0.489268i
$383$	907.329			0.121050			0.0605252	−	0.998167i	$-0.480722\pi$
$383$	907.329			0.121050			0.0605252	+	0.998167i	$0.480722\pi$
$384$	−80.5006	−	71.1090i	−0.0106980	−	0.00944991i
$385$		−	24271.6i		−	3.21297i
$386$	−4581.18	−	4500.91i	−0.604083	−	0.593498i
$387$			5671.54i			0.744962i
$388$	−11167.8	+	197.426i	−1.46124	+	0.0258320i
$389$			10732.1i			1.39881i	0.714724	+	0.699407i	$0.246552\pi$
$389$			10732.1i			1.39881i	−0.714724	+	0.699407i	$0.753448\pi$
$390$	−195.697	−	192.268i	−0.0254089	−	0.0249637i
$391$	−1667.13	−	5601.82i	−0.215627	−	0.724543i
$392$	−2556.94	−	2424.82i	−0.329452	−	0.312429i
$393$	−102.362			−0.0131386
$394$	−6767.85	+	6888.55i	−0.865379	+	0.880813i
$395$			325.799i			0.0415006i
$396$	238.895	+	13513.6i	0.0303155	+	1.71485i
$397$	9853.87			1.24572			0.622861	−	0.782333i	$-0.285970\pi$
$397$	9853.87			1.24572			0.622861	+	0.782333i	$0.285970\pi$
$398$	−1267.46	−	1245.25i	−0.159629	−	0.156832i
$399$	164.903			0.0206904
$400$	−11293.1	+	399.407i	−1.41164	+	0.0499259i
$401$			7418.95i			0.923902i	0.886906	+	0.461951i	$0.152850\pi$
$401$			7418.95i			0.923902i	−0.886906	+	0.461951i	$0.847150\pi$
$402$	49.4763	+	48.6094i	0.00613845	+	0.00603089i
$403$	9579.22			1.18406
$404$	−6269.16	+	110.827i	−0.772036	+	0.0136482i
$405$	−12651.8			−1.55228
$406$	−4194.86	−	4121.36i	−0.512777	−	0.503792i
$407$	−13857.1			−1.68764
$408$	104.900	+	53.2361i	0.0127287	+	0.00645976i
$409$	1814.00			0.219307			0.109653	−	0.993970i	$-0.465026\pi$
$409$	1814.00			0.219307			0.109653	+	0.993970i	$0.465026\pi$
$410$	2578.63	+	2533.45i	0.310609	+	0.305166i
$411$	−88.6175			−0.0106355
$412$	155.860	+	8816.49i	0.0186375	+	1.05427i
$413$	−7288.27			−0.868359
$414$	−4541.44	−	4461.86i	−0.539129	−	0.529683i
$415$			16566.4i			1.95955i
$416$	−10055.6	−	9203.94i	−1.18513	−	1.08476i
$417$	−45.9220			−0.00539283
$418$	12571.1	+	12350.8i	1.47099	+	1.44521i
$419$	10912.4			1.27233			0.636167	−	0.771552i	$-0.280519\pi$
$419$	10912.4			1.27233			0.636167	+	0.771552i	$0.280519\pi$
$420$	−230.078	+	4.06737i	−0.0267302	+	0.000472541i
$421$			11131.8i			1.28868i	0.764740	+	0.644338i	$0.222867\pi$
$421$			11131.8i			1.28868i	−0.764740	+	0.644338i	$0.777133\pi$
$422$	−333.887	+	339.841i	−0.0385150	+	0.0392019i
$423$	−4410.65			−0.506982
$424$	−44.3395	+	46.7554i	−0.00507858	+	0.00535529i
$425$	11861.8	−	3530.11i	1.35384	−	0.402907i
$426$	95.2676	+	93.5983i	0.0108350	+	0.0106452i
$427$		−	5029.87i		−	0.570053i
$428$	−173.124	−	9793.10i	−0.0195520	−	1.10600i
$429$		−	349.567i		−	0.0393409i
$430$	−7361.23	−	7232.24i	−0.825558	−	0.811093i
$431$		−	4554.70i		−	0.509031i	−0.967069	−	0.254516i	$-0.918084\pi$
$431$		−	4554.70i		−	0.509031i	0.967069	−	0.254516i	$-0.0819160\pi$
$432$	256.145	−	9.05920i	0.0285273	−	0.00100894i
$433$	4519.31			0.501580			0.250790	−	0.968042i	$-0.419310\pi$
$433$	4519.31			0.501580			0.250790	+	0.968042i	$0.419310\pi$
$434$	5631.10	−	5731.52i	0.622814	−	0.633922i
$435$	−119.913			−0.0132170
$436$	−2.45983	−	139.145i	−0.000270194	−	0.0152840i
$437$	−8301.36			−0.908714
$438$	163.731	+	160.862i	0.0178616	+	0.0175486i
$439$			2602.30i			0.282918i	0.989944	+	0.141459i	$0.0451793\pi$
$439$			2602.30i			0.282918i	−0.989944	+	0.141459i	$0.954821\pi$
$440$	−17844.2	−	16922.2i	−1.93339	−	1.83349i
$441$	4203.99			0.453945
$442$	13191.8	+	6990.70i	1.41961	+	0.752293i
$443$			7533.16i			0.807926i	0.914775	+	0.403963i	$0.132367\pi$
$443$			7533.16i			0.807926i	−0.914775	+	0.403963i	$0.867633\pi$
$444$	2.32213	+	131.356i	0.000248206	+	0.0140403i
$445$	−13847.0			−1.47508
$446$	−11677.3	+	11885.6i	−1.23977	+	1.26188i
$447$			12.4188i			0.00131407i
$448$	−11418.1	+	606.059i	−1.20414	+	0.0639143i
$449$			16145.6i			1.69701i	0.529186	+	0.848506i	$0.322497\pi$
$449$			16145.6i			1.69701i	−0.529186	+	0.848506i	$0.677503\pi$
$450$	9447.93	−	9616.43i	0.989733	−	1.00738i
$451$			4606.14i			0.480920i
$452$	15198.1	−	268.674i	1.58154	−	0.0279588i
$453$	109.419			0.0113487
$454$	5873.66	−	5978.41i	0.607191	−	0.618019i
$455$	−29204.8			−3.00911
$456$	114.971	−	121.235i	0.0118070	−	0.0124504i
$457$	−4234.31			−0.433419			−0.216710	−	0.976236i	$-0.569532\pi$
$457$	−4234.31			−0.433419			−0.216710	+	0.976236i	$0.569532\pi$
$458$	9413.92	+	9248.97i	0.960445	+	0.943616i
$459$	−269.044	+	80.0687i	−0.0273593	+	0.00814224i
$460$	11582.3	−	204.755i	1.17398	−	0.0207538i
$461$		−	12098.5i		−	1.22230i	−0.791514	−	0.611151i	$-0.790707\pi$
$461$		−	12098.5i		−	1.22230i	0.791514	−	0.611151i	$-0.209293\pi$
$462$	−209.156	−	205.491i	−0.0210624	−	0.0206933i
$463$	1921.13			0.192835			0.0964174	−	0.995341i	$-0.469262\pi$
$463$	1921.13			0.192835			0.0964174	+	0.995341i	$0.469262\pi$
$464$	−5954.65	+	210.601i	−0.595771	+	0.0210709i
$465$		−	163.840i		−	0.0163395i
$466$	−187.190	−	183.910i	−0.0186081	−	0.0182821i
$467$		−	1205.99i		−	0.119500i	−0.998213	−	0.0597501i	$-0.980970\pi$
$467$		−	1205.99i		−	0.119500i	0.998213	−	0.0597501i	$-0.0190304\pi$
$468$	16260.2	−	287.452i	1.60605	−	0.0283920i
$469$	7383.62			0.726959
$470$	5624.39	−	5724.70i	0.551986	−	0.561831i
$471$			25.3064i			0.00247570i
$472$	−5081.40	+	5358.27i	−0.495530	+	0.522530i
$473$		−	13149.2i		−	1.27822i
$474$	2.80752	+	2.75833i	0.000272054	+	0.000267287i
$475$		−	17578.0i		−	1.69797i
$476$	11937.5	−	3783.58i	1.14948	−	0.364328i
$477$		−	76.8727i		−	0.00737895i
$478$	−6417.86	+	6532.32i	−0.614113	+	0.625066i
$479$			4682.24i			0.446633i	0.974746	+	0.223316i	$0.0716883\pi$
$479$			4682.24i			0.446633i	−0.974746	+	0.223316i	$0.928312\pi$
$480$	−157.421	+	171.987i	−0.0149693	+	0.0163544i
$481$			16673.6i			1.58056i
$482$	3391.66	+	3332.23i	0.320510	+	0.314894i
$483$	138.117			0.0130115
$484$	−365.658	−	20684.1i	−0.0343405	−	1.94254i
$485$			24245.8i			2.26999i
$486$	−321.453	+	327.185i	−0.0300028	+	0.0305379i
$487$		−	14671.6i		−	1.36516i	−0.730809	−	0.682582i	$-0.760857\pi$
$487$		−	14671.6i		−	1.36516i	0.730809	−	0.682582i	$-0.239143\pi$
$488$	−3697.92	−	3506.84i	−0.343026	−	0.325302i
$489$	−127.320			−0.0117743
$490$	−5360.85	+	5456.46i	−0.494242	+	0.503057i
$491$		−	20506.8i		−	1.88484i	−0.334427	−	0.942422i	$-0.608543\pi$
$491$		−	20506.8i		−	1.88484i	0.334427	−	0.942422i	$-0.391457\pi$
$492$	43.6632	−	0.771886i	0.00400099	−	7.07303e-5i
$493$	6254.51	−	1861.37i	0.571377	−	0.170044i
$494$	14861.2	−	15126.2i	1.35351	−	1.37765i
$495$	29338.5			2.66397
$496$	−287.748	−	8135.97i	−0.0260489	−	0.736523i
$497$	14217.3			1.28316
$498$	142.758	+	140.257i	0.0128457	+	0.0126206i
$499$	−6913.78			−0.620247			−0.310124	−	0.950696i	$-0.600370\pi$
$499$	−6913.78			−0.620247			−0.310124	+	0.950696i	$0.600370\pi$
$500$	126.620	+	7162.51i	0.0113252	+	0.640634i
$501$		−	247.974i		−	0.0221131i
$502$	−1317.61	−	1294.52i	−0.117147	−	0.115094i
$503$		−	12839.4i		−	1.13813i	−0.822293	−	0.569065i	$-0.807305\pi$
$503$		−	12839.4i		−	1.13813i	0.822293	−	0.569065i	$-0.192695\pi$
$504$	9386.51	−	9897.95i	0.829580	−	0.874781i
$505$			13610.6i			1.19933i
$506$	10529.1	+	10344.6i	0.925049	+	0.908840i
$507$	−257.667			−0.0225708
$508$	29.0733	+	1644.59i	0.00253921	+	0.143635i
$509$		−	7857.20i		−	0.684213i	−0.939661	−	0.342106i	$-0.888860\pi$
$509$		−	7857.20i		−	0.684213i	0.939661	−	0.342106i	$-0.111140\pi$
$510$	119.566	−	225.628i	0.0103814	−	0.0195901i
$511$	24434.5			2.11530
$512$	−7515.16	+	8817.03i	−0.648684	+	0.761057i
$513$			398.698i			0.0343137i
$514$	3243.32	−	3301.16i	0.278320	−	0.283284i
$515$	19141.0			1.63777
$516$	−124.645	+	2.20350i	−0.0106341	+	0.000187992i
$517$	10225.9			0.869889
$518$	9976.28	+	9801.47i	0.846202	+	0.831374i
$519$	−145.286			−0.0122877
$520$	−20361.7	+	21471.1i	−1.71715	+	1.81071i
$521$			11238.7i			0.945057i	0.881315	+	0.472529i	$0.156659\pi$
$521$			11238.7i			0.945057i	−0.881315	+	0.472529i	$0.843341\pi$
$522$	4981.73	−	5070.58i	0.417710	−	0.425159i
$523$		−	16546.3i		−	1.38340i	−0.722186	−	0.691699i	$-0.756862\pi$
$523$		−	16546.3i		−	1.38340i	0.722186	−	0.691699i	$-0.243138\pi$
$524$	195.150	+	11039.0i	0.0162694	+	0.920310i
$525$			292.461i			0.0243124i
$526$	−10907.0	+	11101.5i	−0.904119	+	0.920243i
$527$	2543.23	+	8545.67i	0.210218	+	0.706367i
$528$	−296.900	+	10.5006i	−0.0244714	+	0.000865490i
$529$	5214.08			0.428543
$530$	99.7750	+	98.0268i	0.00817726	+	0.00803398i
$531$		−	8809.77i		−	0.719984i
$532$	−314.384	−	17783.7i	−0.0256208	−	1.44929i
$533$	5542.36			0.450406
$534$	−117.233	+	119.324i	−0.00950032	+	0.00966975i
$535$	−21261.2			−1.71814
$536$	5147.88	−	5428.37i	0.414840	−	0.437444i
$537$			148.120i			0.0119029i
$538$	−13523.5	+	13764.7i	−1.08372	+	1.10305i
$539$	−9746.72			−0.778889
$540$	−9.83395	−	556.276i	−0.000783678	−	0.0443302i
$541$	2403.44			0.191002			0.0955010	−	0.995429i	$-0.469555\pi$
$541$	2403.44			0.191002			0.0955010	+	0.995429i	$0.469555\pi$
$542$	−9475.48	+	9644.47i	−0.750935	+	0.764327i
$543$	−39.8614			−0.00315031
$544$	5541.17	−	11414.2i	0.436720	−	0.899597i
$545$	−302.090			−0.0237433
$546$	−247.258	+	251.668i	−0.0193804	+	0.0197260i
$547$	−20450.9			−1.59857			−0.799286	−	0.600951i	$-0.794789\pi$
$547$	−20450.9			−1.59857			−0.799286	+	0.600951i	$0.794789\pi$
$548$	168.947	+	9556.81i	0.0131698	+	0.744976i
$549$	6079.91			0.472649
$550$	−21904.5	+	22295.2i	−1.69820	+	1.72849i
$551$		−	9268.58i		−	0.716615i
$552$	96.2955	−	101.542i	0.00742502	−	0.00782958i
$553$	418.981			0.0322186
$554$	7129.27	−	7256.42i	0.546740	−	0.556491i
$555$	285.179			0.0218111
$556$	87.5492	+	4952.39i	0.00667790	+	0.377748i
$557$			849.470i			0.0646198i	0.999478	+	0.0323099i	$0.0102863\pi$
$557$			849.470i			0.0646198i	−0.999478	+	0.0323099i	$0.989714\pi$
$558$	6928.04	+	6806.65i	0.525605	+	0.516395i
$559$	−15821.8			−1.19712
$560$	877.278	+	24804.7i	0.0661995	+	1.87177i
$561$	311.851	−	92.8081i	0.0234694	−	0.00698460i
$562$	6113.97	−	6223.01i	0.458901	−	0.467085i
$563$			1065.17i			0.0797361i	0.999205	+	0.0398680i	$0.0126938\pi$
$563$			1065.17i			0.0797361i	−0.999205	+	0.0398680i	$0.987306\pi$
$564$	−1.71362	−	96.9345i	−0.000127937	−	0.00723702i
$565$		−	32995.6i		−	2.45688i
$566$	−499.299	+	508.204i	−0.0370797	+	0.0377410i
$567$			16270.4i			1.20510i
$568$	9912.33	−	10452.4i	0.732240	−	0.772137i
$569$	24782.8			1.82592			0.912961	−	0.408048i	$-0.133790\pi$
$569$	24782.8			1.82592			0.912961	+	0.408048i	$0.133790\pi$
$570$	−258.714	−	254.180i	−0.0190111	−	0.0186780i
$571$	12597.6			0.923280			0.461640	−	0.887067i	$-0.347261\pi$
$571$	12597.6			0.923280			0.461640	+	0.887067i	$0.347261\pi$
$572$	−37698.5	+	666.441i	−2.75569	+	0.0487156i
$573$	−134.288			−0.00979048
$574$	3258.05	−	3316.15i	0.236913	−	0.241139i
$575$		−	14722.7i		−	1.06779i
$576$	−732.580	−	13801.8i	−0.0529934	−	0.998391i
$577$	−25747.2			−1.85766			−0.928830	−	0.370505i	$-0.879185\pi$
$577$	−25747.2			−1.85766			−0.928830	+	0.370505i	$0.879185\pi$
$578$	−2734.09	+	13624.4i	−0.196753	+	0.980453i
$579$			168.411i			0.0120880i
$580$	228.611	+	12931.8i	0.0163665	+	0.925802i
$581$	21304.6			1.52128
$582$	208.934	+	205.273i	0.0148807	+	0.0146200i
$583$			178.225i			0.0126610i
$584$	17035.8	−	17964.0i	1.20710	−	1.27287i
$585$		−	35301.7i		−	2.49495i
$586$	−220.712	−	216.845i	−0.0155589	−	0.0152863i
$587$			17172.8i			1.20749i	0.797176	+	0.603747i	$0.206326\pi$
$587$			17172.8i			1.20749i	−0.797176	+	0.603747i	$0.793674\pi$
$588$	1.63333	+	92.3925i	0.000114554	+	0.00647994i
$589$	12663.9			0.885918
$590$	11434.4	+	11234.1i	0.797877	+	0.783897i
$591$	253.234			0.0176255
$592$	14161.4	−	500.854i	0.983161	−	0.0347719i
$593$	5621.80			0.389308			0.194654	−	0.980872i	$-0.437642\pi$
$593$	5621.80			0.389308			0.194654	+	0.980872i	$0.437642\pi$
$594$	496.830	−	505.691i	0.0343185	−	0.0349306i
$595$	−7753.72	−	26053.8i	−0.534238	−	1.79513i
$596$	1339.29	−	23.6761i	0.0920458	−	0.00162720i
$597$			46.5939i			0.00319424i
$598$	12447.2	−	12669.2i	0.851175	−	0.866355i
$599$	−4214.51			−0.287479			−0.143740	−	0.989616i	$-0.545913\pi$
$599$	−4214.51			−0.287479			−0.143740	+	0.989616i	$0.545913\pi$
$600$	215.014	+	203.904i	0.0146299	+	0.0138739i
$601$		−	16937.9i		−	1.14960i	−0.818293	−	0.574801i	$-0.805079\pi$
$601$		−	16937.9i		−	1.14960i	0.818293	−	0.574801i	$-0.194921\pi$
$602$	−9300.75	+	9466.62i	−0.629685	+	0.640915i
$603$			8925.03i			0.602745i
$604$	−208.605	−	11800.2i	−0.0140530	−	0.794937i
$605$	−44906.1			−3.01767
$606$	117.287	+	115.232i	0.00786215	+	0.00772439i
$607$		−	8620.85i		−	0.576457i	−0.957562	−	0.288228i	$-0.906934\pi$
$607$		−	8620.85i		−	0.576457i	0.957562	−	0.288228i	$-0.0930663\pi$
$608$	−13293.6	−	12167.7i	−0.886723	−	0.811623i
$609$			154.210i			0.0102609i
$610$	−7753.00	+	7891.27i	−0.514606	+	0.523784i
$611$		−	12304.3i		−	0.814696i
$612$	4573.44	+	14429.5i	0.302076	+	0.953070i
$613$		−	5413.39i		−	0.356680i	−0.983969	−	0.178340i	$-0.942927\pi$
$613$		−	5413.39i		−	0.356680i	0.983969	−	0.178340i	$-0.0570727\pi$
$614$	−4715.94	−	4633.31i	−0.309967	−	0.304536i
$615$		−	94.7946i		−	0.00621543i
$616$	−21762.1	+	22947.9i	−1.42341	+	1.50097i
$617$		−	1030.74i		−	0.0672547i	−0.999434	−	0.0336274i	$-0.989294\pi$
$617$		−	1030.74i		−	0.0672547i	0.999434	−	0.0336274i	$-0.0107059\pi$
$618$	162.054	−	164.944i	0.0105482	−	0.0107363i
$619$	19679.7			1.27786			0.638929	−	0.769266i	$-0.279378\pi$
$619$	19679.7			1.27786			0.638929	+	0.769266i	$0.279378\pi$
$620$	−17669.0	+	312.356i	−1.14453	+	0.0202331i
$621$			333.935i			0.0215786i
$622$	−6568.98	−	6453.88i	−0.423460	−	0.416040i
$623$			17807.3i			1.14516i
$624$	12.6349	+	357.246i	0.000810575	+	0.0229187i
$625$	−6520.49			−0.417311
$626$	−17675.6	−	17365.9i	−1.12853	−	1.10875i
$627$		−	462.133i		−	0.0294351i
$628$	2729.12	−	48.2460i	0.173414	−	0.00306564i
$629$	−14874.6	+	4426.74i	−0.942906	+	0.280613i
$630$	−21122.0	−	20751.9i	−1.33575	−	1.31234i
$631$	−22362.5			−1.41083			−0.705417	−	0.708793i	$-0.749240\pi$
$631$	−22362.5			−1.41083			−0.705417	+	0.708793i	$0.749240\pi$
$632$	292.115	−	308.031i	0.0183856	−	0.0193874i
$633$	12.4931			0.000784449
$634$	16029.9	−	16315.7i	1.00414	−	1.02205i
$635$	3570.46			0.223133
$636$	1.68946	−	0.0298666i	0.000105332	−	1.86209e-6i
$637$			11727.8i			0.729469i
$638$	−11549.9	+	11755.9i	−0.716715	+	0.729497i
$639$			17185.3i			1.06391i
$640$	18847.8	+	16648.9i	1.16410	+	1.02829i
$641$			3639.34i			0.224252i	0.993694	+	0.112126i	$0.0357660\pi$
$641$			3639.34i			0.224252i	−0.993694	+	0.112126i	$0.964234\pi$
$642$	−180.005	+	183.215i	−0.0110658	+	0.0112631i
$643$	12532.0			0.768607			0.384303	−	0.923207i	$-0.374442\pi$
$643$	12532.0			0.768607			0.384303	+	0.923207i	$0.374442\pi$
$644$	−263.317	−	14895.0i	−0.0161120	−	0.911406i
$645$			270.610i			0.0165198i
$646$	17439.7	+	9241.80i	1.06216	+	0.562869i
$647$	−10837.5			−0.658528			−0.329264	−	0.944238i	$-0.606801\pi$
$647$	−10837.5			−0.658528			−0.329264	+	0.944238i	$0.606801\pi$
$648$	11961.8	+	11343.7i	0.725161	+	0.687691i
$649$			20425.0i			1.23536i
$650$	26826.8	+	26356.7i	1.61882	+	1.59045i
$651$	−210.700			−0.0126851
$652$	242.733	+	13730.7i	0.0145800	+	0.824746i
$653$	−11538.7			−0.691491			−0.345745	−	0.938328i	$-0.612374\pi$
$653$	−11538.7			−0.691491			−0.345745	+	0.938328i	$0.612374\pi$
$654$	−2.55760	+	2.60321i	−0.000152920	+	0.000155648i
$655$	23966.2			1.42967
$656$	−166.486	−	4707.32i	−0.00990880	−	0.280167i
$657$			29535.5i			1.75386i
$658$	−7362.02	−	7233.02i	−0.436172	−	0.428530i
$659$			25213.1i			1.49039i	0.666849	+	0.745193i	$0.267643\pi$
$659$			25213.1i			1.49039i	−0.666849	+	0.745193i	$0.732357\pi$
$660$	11.3986	+	644.783i	0.000672257	+	0.0380275i
$661$			16257.2i			0.956632i	0.878188	+	0.478316i	$0.158753\pi$
$661$			16257.2i			0.956632i	−0.878188	+	0.478316i	$0.841247\pi$
$662$	13061.4	+	12832.5i	0.766836	+	0.753399i
$663$	−111.672	−	375.235i	−0.00654143	−	0.0219803i
$664$	14853.6	−	15662.9i	0.868120	−	0.915421i
$665$	−38609.2			−2.25143
$666$	−11847.6	+	12058.9i	−0.689319	+	0.701613i
$667$		−	7763.03i		−	0.450653i
$668$	−26742.4	+	472.757i	−1.54894	+	0.0273825i
$669$	436.932			0.0252508
$670$	−11584.0	−	11381.0i	−0.667955	−	0.656251i
$671$	−14095.9			−0.810981
$672$	221.178	+	202.445i	0.0126966	+	0.0116213i
$673$		−	15342.7i		−	0.878777i	−0.898297	−	0.439389i	$-0.855195\pi$
$673$		−	15342.7i		−	0.878777i	0.898297	−	0.439389i	$-0.144805\pi$
$674$	−16596.9	−	16306.1i	−0.948502	−	0.931882i
$675$	−707.102			−0.0403205
$676$	491.235	+	27787.6i	0.0279492	+	1.58100i
$677$	8344.74			0.473729			0.236864	−	0.971543i	$-0.423880\pi$
$677$	8344.74			0.473729			0.236864	+	0.971543i	$0.423880\pi$
$678$	−284.334	−	279.352i	−0.0161059	−	0.0158237i
$679$	31180.3			1.76228
$680$	−24560.4	−	12464.3i	−1.38507	−	0.702918i
$681$	−219.776			−0.0123669
$682$	−16062.3	−	15780.9i	−0.901843	−	0.886041i
$683$	6383.55			0.357628			0.178814	−	0.983883i	$-0.442774\pi$
$683$	6383.55			0.357628			0.178814	+	0.983883i	$0.442774\pi$
$684$	21496.3	−	380.015i	1.20165	−	0.0212430i
$685$	20748.2			1.15730
$686$	−8437.74	−	8289.90i	−0.469613	−	0.461384i
$687$		−	346.070i		−	0.0192189i
$688$	475.266	+	13438.0i	0.0263363	+	0.744648i
$689$	214.450			0.0118576
$690$	−216.689	−	212.892i	−0.0119554	−	0.0117459i
$691$	−33017.1			−1.81770			−0.908850	−	0.417123i	$-0.863038\pi$
$691$	−33017.1			−1.81770			−0.908850	+	0.417123i	$0.863038\pi$
$692$	276.984	+	15668.1i	0.0152158	+	0.860711i
$693$		−	37729.6i		−	2.06815i
$694$	18935.0	−	19272.7i	1.03568	−	1.05415i
$695$	10751.8			0.586821
$696$	113.373	+	107.515i	0.00617444	+	0.00585540i
$697$	1471.46	+	4944.36i	0.0799651	+	0.268696i
$698$	−14836.0	−	14576.0i	−0.804512	−	0.790415i
$699$			6.88138i			0.000372357i
$700$	31539.9	−	557.569i	1.70300	−	0.0301059i
$701$			7053.95i			0.380063i	0.981778	+	0.190031i	$0.0608590\pi$
$701$			7053.95i			0.380063i	−0.981778	+	0.190031i	$0.939141\pi$
$702$	−608.475	−	597.813i	−0.0327142	−	0.0321410i
$703$			22042.7i			1.18258i
$704$	1698.45	+	31998.6i	0.0909271	+	1.71306i
$705$	−210.449			−0.0112425
$706$	11293.0	−	11494.4i	0.602006	−	0.612743i
$707$	17503.4			0.931093
$708$	193.615	−	3.42277i	0.0102776	−	0.000181689i
$709$	−29626.7			−1.56933			−0.784664	−	0.619922i	$-0.787164\pi$
$709$	−29626.7			−1.56933			−0.784664	+	0.619922i	$0.787164\pi$
$710$	−22305.2	−	21914.4i	−1.17901	−	1.15836i
$711$			506.448i			0.0267135i
$712$	13091.8	+	12415.3i	0.689095	+	0.653489i
$713$	10606.8			0.557121
$714$	−290.160	−	153.764i	−0.0152086	−	0.00805948i
$715$			81845.0i			4.28088i
$716$	15973.7	−	282.387i	0.833752	−	0.0147392i
$717$	240.138			0.0125079
$718$	9226.49	−	9391.04i	0.479568	−	0.488121i
$719$		−	26492.5i		−	1.37414i	−0.726593	−	0.687068i	$-0.758897\pi$
$719$		−	26492.5i		−	1.37414i	0.726593	−	0.687068i	$-0.241103\pi$
$720$	−29982.9	+	1060.42i	−1.55194	+	0.0548882i
$721$		−	24615.5i		−	1.27147i
$722$	6050.44	−	6158.35i	0.311876	−	0.317438i
$723$		−	124.683i		−	0.00641355i
$724$	75.9948	+	4298.79i	0.00390100	+	0.220667i
$725$	16438.1			0.842063
$726$	−380.190	+	386.971i	−0.0194355	+	0.0197821i
$727$	23186.1			1.18284			0.591421	−	0.806363i	$-0.298567\pi$
$727$	23186.1			1.18284			0.591421	+	0.806363i	$0.298567\pi$
$728$	27612.1	+	26185.4i	1.40573	+	1.33310i
$729$	−19658.9			−0.998778
$730$	−38334.8	−	37663.1i	−1.94361	−	1.90955i
$731$	−4200.59	−	14114.7i	−0.212537	−	0.714159i
$732$	2.36217	+	133.620i	0.000119273	+	0.00674693i
$733$		−	31571.3i		−	1.59088i	−0.606036	−	0.795438i	$-0.707241\pi$
$733$		−	31571.3i		−	1.59088i	0.606036	−	0.795438i	$-0.292759\pi$
$734$	23595.7	+	23182.2i	1.18656	+	1.16577i
$735$	200.588			0.0100664
$736$	−11134.3	−	10191.2i	−0.557628	−	0.510400i
$737$		−	20692.2i		−	1.03420i
$738$	4008.43	+	3938.20i	0.199936	+	0.196432i
$739$			14205.3i			0.707104i	0.935415	+	0.353552i	$0.115026\pi$
$739$			14205.3i			0.707104i	−0.935415	+	0.353552i	$0.884974\pi$
$740$	−543.687	−	30754.7i	−0.0270085	−	1.52779i
$741$	−556.063			−0.0275675
$742$	126.064	−	128.312i	0.00623711	−	0.00634835i
$743$		−	13061.1i		−	0.644906i	−0.946586	−	0.322453i	$-0.895493\pi$
$743$		−	13061.1i		−	0.644906i	0.946586	−	0.322453i	$-0.104507\pi$
$744$	−146.900	+	154.905i	−0.00723875	+	0.00763317i
$745$		−	2907.65i		−	0.142990i
$746$	16310.7	+	16024.9i	0.800504	+	0.786477i
$747$			25752.1i			1.26134i
$748$	−10603.3	−	33454.1i	−0.518308	−	1.63530i
$749$			27342.2i			1.33386i
$750$	131.652	−	134.000i	0.00640969	−	0.00652400i
$751$		−	20340.6i		−	0.988335i	−0.869367	−	0.494167i	$-0.835473\pi$
$751$		−	20340.6i		−	0.988335i	0.869367	−	0.494167i	$-0.164527\pi$
$752$	−10450.5	+	369.606i	−0.506768	+	0.0179231i
$753$			48.4374i			0.00234417i
$754$	14145.3	+	13897.4i	0.683211	+	0.671240i
$755$	−25618.6			−1.23491
$756$	−715.377	+	12.6466i	−0.0344154	+	0.000608401i
$757$			15960.2i			0.766294i	0.923687	+	0.383147i	$0.125160\pi$
$757$			15960.2i			0.766294i	−0.923687	+	0.383147i	$0.874840\pi$
$758$	7756.34	−	7894.67i	0.371666	−	0.378295i
$759$		−	387.066i		−	0.0185107i
$760$	−26918.4	+	28385.1i	−1.28478	+	1.35479i
$761$	4117.41			0.196131			0.0980657	−	0.995180i	$-0.468734\pi$
$761$	4117.41			0.196131			0.0980657	+	0.995180i	$0.468734\pi$
$762$	30.2288	−	30.7679i	0.00143710	−	0.00146273i
$763$			388.491i			0.0184329i
$764$	256.016	+	14482.0i	0.0121235	+	0.685787i
$765$	31492.8	−	9372.39i	1.48840	−	0.442954i
$766$	−1798.55	+	1830.62i	−0.0848358	+	0.0863488i
$767$	24576.4			1.15698
$768$	303.041	−	21.4624i	0.0142384	−	0.00100841i
$769$	10952.3			0.513588			0.256794	−	0.966466i	$-0.417334\pi$
$769$	10952.3			0.513588			0.256794	+	0.966466i	$0.417334\pi$
$770$	48970.2	+	48112.2i	2.29190	+	2.25174i
$771$	−121.356			−0.00566865
$772$	18162.0	−	321.072i	0.846718	−	0.0149684i
$773$			13654.4i			0.635334i	0.948202	+	0.317667i	$0.102899\pi$
$773$			13654.4i			0.635334i	−0.948202	+	0.317667i	$0.897101\pi$
$774$	−11442.9	−	11242.4i	−0.531403	−	0.522092i
$775$			22459.7i			1.04100i
$776$	21739.0	−	22923.5i	1.00565	−	1.06044i
$777$		−	366.743i		−	0.0169329i
$778$	−21653.0	−	21273.6i	−0.997814	−	0.980330i
$779$	7327.07			0.336996
$780$	775.837	−	13.7154i	0.0356147	−	0.000629602i
$781$		−	39843.2i		−	1.82548i
$782$	14606.9	+	7740.59i	0.667955	+	0.353968i
$783$	−372.843			−0.0170170
$784$	9960.81	−	352.288i	0.453754	−	0.0160481i
$785$		−	5925.04i		−	0.269393i
$786$	202.906	−	206.525i	0.00920791	−	0.00937213i
$787$	−12703.7			−0.575399			−0.287699	−	0.957721i	$-0.592890\pi$
$787$	−12703.7			−0.575399			−0.287699	+	0.957721i	$0.592890\pi$
$788$	−482.784	−	27309.6i	−0.0218255	−	1.23460i
$789$	408.108			0.0184145
$790$	−657.331	−	645.814i	−0.0296035	−	0.0290848i
$791$	−42432.7			−1.90738
$792$	−27738.5	−	26305.2i	−1.24450	−	1.18020i
$793$			16961.0i			0.759525i
$794$	−19532.8	+	19881.1i	−0.873039	+	0.888609i
$795$		−	3.66789i		−	0.000163631i
$796$	5024.85	−	88.8301i	0.223745	−	0.00395540i
$797$			23759.3i			1.05596i	0.849257	+	0.527979i	$0.177050\pi$
$797$			23759.3i			1.05596i	−0.849257	+	0.527979i	$0.822950\pi$
$798$	−326.879	+	332.708i	−0.0145005	+	0.0147591i
$799$	10976.7	−	3266.72i	0.486019	−	0.144641i
$800$	21579.8	−	23576.6i	0.953702	−	1.04195i
$801$	−21524.8			−0.949490
$802$	−14968.5	−	14706.2i	−0.659045	−	0.647498i
$803$		−	68476.4i		−	3.00932i
$804$	−196.149	+	3.46755i	−0.00860401	+	0.000152103i
$805$	−32337.7			−1.41584
$806$	−18988.4	+	19327.0i	−0.829823	+	0.844622i
$807$	506.012			0.0220725
$808$	12203.4	−	12868.3i	0.531330	−	0.560280i
$809$			8146.86i			0.354052i	0.984206	+	0.177026i	$0.0566477\pi$
$809$			8146.86i			0.354052i	−0.984206	+	0.177026i	$0.943352\pi$
$810$	25079.0	−	25526.2i	1.08788	−	1.10728i
$811$	−8350.91			−0.361578			−0.180789	−	0.983522i	$-0.557865\pi$
$811$	−8350.91			−0.361578			−0.180789	+	0.983522i	$0.557865\pi$
$812$	16630.5	−	293.997i	0.718738	−	0.0127060i
$813$	354.546			0.0152945
$814$	27468.1	−	27958.0i	1.18275	−	1.20384i
$815$	29809.8			1.28122
$816$	−315.346	+	106.118i	−0.0135286	+	0.00455255i
$817$	−20916.6			−0.895691
$818$	−3595.79	+	3659.92i	−0.153697	+	0.156438i
$819$	−45398.3			−1.93693
$820$	−10223.0	+	180.724i	−0.435368	+	0.00769651i
$821$	−21197.4			−0.901088			−0.450544	−	0.892754i	$-0.648770\pi$
$821$	−21197.4			−0.901088			−0.450544	+	0.892754i	$0.648770\pi$
$822$	175.662	−	178.794i	0.00745365	−	0.00758658i
$823$			36354.9i			1.53979i	0.638168	+	0.769897i	$0.279693\pi$
$823$			36354.9i			1.53979i	−0.638168	+	0.769897i	$0.720307\pi$
$824$	−18097.1	−	17162.0i	−0.765099	−	0.725566i
$825$	819.606			0.0345879
$826$	14447.1	−	14704.8i	0.608572	−	0.619425i
$827$	9957.18			0.418676			0.209338	−	0.977843i	$-0.432869\pi$
$827$	9957.18			0.418676			0.209338	+	0.977843i	$0.432869\pi$
$828$	18004.5	−	318.287i	0.755676	−	0.0133590i
$829$			10099.2i			0.423110i	0.977366	+	0.211555i	$0.0678528\pi$
$829$			10099.2i			0.423110i	−0.977366	+	0.211555i	$0.932147\pi$
$830$	−33424.3	−	32838.7i	−1.39780	−	1.37331i
$831$	−266.757			−0.0111356
$832$	38502.5	−	2043.67i	1.60437	−	0.0851579i
$833$	−10462.4	+	3113.66i	−0.435175	+	0.129510i
$834$	91.0287	−	92.6522i	0.00377946	−	0.00384686i
$835$			58058.8i			2.40624i
$836$	−49838.0	+	881.044i	−2.06182	+	0.0364492i
$837$		−	509.423i		−	0.0210373i
$838$	−21631.1	+	22016.9i	−0.891689	+	0.907592i
$839$		−	5391.05i		−	0.221835i	−0.993830	−	0.110918i	$-0.964621\pi$
$839$		−	5391.05i		−	0.221835i	0.993830	−	0.110918i	$-0.0353790\pi$
$840$	447.866	−	472.268i	0.0183962	−	0.0193986i
$841$	−15721.5			−0.644613
$842$	−22459.6	−	22066.1i	−0.919250	−	0.903143i
$843$	−228.768			−0.00934659
$844$	−23.8178	−	1347.30i	−0.000971377	−	0.0549478i
$845$	60328.1			2.45604
$846$	8743.00	−	8898.92i	0.355308	−	0.361644i
$847$			57749.7i			2.34274i
$848$	−6.44182	−	182.140i	−0.000260865	−	0.00737584i
$849$	18.6824			0.000755215
$850$	−16390.6	+	30929.8i	−0.661403	+	1.24810i
$851$			18462.2i			0.743683i
$852$	−377.687	+	6.67683i	−0.0151870	+	0.000268479i
$853$	40811.4			1.63817			0.819084	−	0.573674i	$-0.194482\pi$
$853$	40811.4			1.63817			0.819084	+	0.573674i	$0.194482\pi$
$854$	10148.3	+	9970.44i	0.406635	+	0.399510i
$855$		−	46669.3i		−	1.86673i
$856$	20101.7	+	19063.0i	0.802643	+	0.761169i
$857$		−	5699.01i		−	0.227158i	−0.993529	−	0.113579i	$-0.963768\pi$
$857$		−	5699.01i		−	0.227158i	0.993529	−	0.113579i	$-0.0362315\pi$
$858$	705.286	+	692.928i	0.0280630	+	0.0275713i
$859$			2828.67i			0.112355i	0.998421	+	0.0561774i	$0.0178913\pi$
$859$			2828.67i			0.112355i	−0.998421	+	0.0561774i	$0.982109\pi$
$860$	29183.5	−	515.912i	1.15715	−	0.0204563i
$861$	−121.907			−0.00482529
$862$	9189.56	+	9028.54i	0.363106	+	0.356744i
$863$	44058.3			1.73785			0.868924	−	0.494946i	$-0.164812\pi$
$863$	44058.3			1.73785			0.868924	+	0.494946i	$0.164812\pi$
$864$	−489.465	+	534.756i	−0.0192731	+	0.0210564i
$865$	34016.1			1.33709
$866$	−8958.38	+	9118.15i	−0.351522	+	0.357791i
$867$	305.101	−	199.246i	0.0119513	−	0.00780477i
$868$	401.694	+	22722.6i	0.0157078	+	0.888542i
$869$		−	1174.17i		−	0.0458355i
$870$	237.697	−	241.936i	0.00926286	−	0.00942806i
$871$	−24898.0			−0.968583
$872$	285.615	+	270.857i	0.0110919	+	0.0105188i
$873$			37689.6i			1.46117i
$874$	16455.3	−	16748.8i	0.636854	−	0.648212i
$875$		−	19997.6i		−	0.772620i
$876$	−649.112	+	11.4751i	−0.0250359	+	0.000442589i
$877$	−9130.12			−0.351542			−0.175771	−	0.984431i	$-0.556242\pi$
$877$	−9130.12			−0.351542			−0.175771	+	0.984431i	$0.556242\pi$
$878$	−5250.39	−	5158.39i	−0.201813	−	0.198277i
$879$			8.11373i			0.000311342i
$880$	69513.8	−	2458.52i	2.66285	−	0.0941782i
$881$			29609.9i			1.13233i	0.824292	+	0.566165i	$0.191573\pi$
$881$			29609.9i			1.13233i	−0.824292	+	0.566165i	$0.808427\pi$
$882$	−8333.34	+	8481.96i	−0.318138	+	0.323812i
$883$		−	456.368i		−	0.0173930i	−0.999962	−	0.00869649i	$-0.997232\pi$
$883$		−	456.368i		−	0.0173930i	0.999962	−	0.00869649i	$-0.00276821\pi$
$884$	−40253.8	+	12758.4i	−1.53154	+	0.485421i
$885$		−	420.347i		−	0.0159659i
$886$	−15198.9	−	14932.6i	−0.576316	−	0.566218i
$887$		−	40199.2i		−	1.52171i	−0.648921	−	0.760856i	$-0.724779\pi$
$887$		−	40199.2i		−	1.52171i	0.648921	−	0.760856i	$-0.275221\pi$
$888$	−269.626	−	255.695i	−0.0101893	−	0.00966278i
$889$		−	4591.66i		−	0.173227i
$890$	27448.1	−	27937.6i	1.03378	−	1.05221i
$891$	45596.8			1.71442
$892$	−833.000	−	47120.2i	−0.0312678	−	1.76872i
$893$		−	16266.5i		−	0.609559i
$894$	−25.0562	−	24.6171i	−0.000937364	−	0.000920940i
$895$		−	34679.6i		−	1.29521i
$896$	21410.7	−	24238.5i	0.798305	−	0.903740i
$897$	−465.738			−0.0173362
$898$	−32575.3	−	32004.6i	−1.21053	−	1.18932i
$899$			11842.6i			0.439348i
$900$	673.967	+	38124.3i	0.0249618	+	1.41201i
$901$	56.9353	+	191.312i	0.00210521	+	0.00707384i
$902$	−9293.34	−	9130.50i	−0.343054	−	0.337043i
$903$	348.008			0.0128250
$904$	−29584.2	+	31196.2i	−1.08845	+	1.14775i
$905$	9332.85			0.342801
$906$	−216.896	+	220.764i	−0.00795353	+	0.00809537i
$907$	20901.0			0.765168			0.382584	−	0.923921i	$-0.375034\pi$
$907$	20901.0			0.765168			0.382584	+	0.923921i	$0.375034\pi$
$908$	418.997	+	23701.4i	0.0153138	+	0.866253i
$909$			21157.4i			0.771999i
$910$	57891.2	−	58923.6i	2.10887	−	2.14648i
$911$			44659.2i			1.62418i	0.583535	+	0.812088i	$0.301669\pi$
$911$			44659.2i			1.62418i	−0.583535	+	0.812088i	$0.698331\pi$
$912$	16.7034	+	472.284i	0.000606476	+	0.0171479i
$913$		−	59704.9i		−	2.16423i
$914$	8393.44	−	8543.13i	0.303753	−	0.309170i
$915$	290.095			0.0104812
$916$	−37321.4	+	659.775i	−1.34622	+	0.0237987i
$917$		−	30820.8i		−	1.10992i
$918$	371.765	−	701.539i	0.0133661	−	0.0252225i
$919$	36085.5			1.29527			0.647633	−	0.761952i	$-0.275759\pi$
$919$	36085.5			1.29527			0.647633	+	0.761952i	$0.275759\pi$
$920$	−22545.9	+	23774.4i	−0.807953	+	0.851975i
$921$			173.365i			0.00620259i
$922$	24409.8	+	23982.1i	0.871903	+	0.856625i
$923$	−47941.5			−1.70966
$924$	829.198	−	14.6587i	0.0295223	−	0.000521900i
$925$	−39093.3			−1.38960
$926$	−3808.15	+	3876.07i	−0.135144	+	0.137555i
$927$	29754.2			1.05422
$928$	11378.7	−	12431.6i	0.402503	−	0.439747i
$929$		−	4044.77i		−	0.142847i	−0.997446	−	0.0714233i	$-0.977246\pi$
$929$		−	4044.77i		−	0.142847i	0.997446	−	0.0714233i	$-0.0227541\pi$
$930$	330.563	+	324.771i	0.0116555	+	0.0114512i
$931$			15504.3i			0.545792i
$932$	742.111	−	13.1192i	0.0260823	−	0.000461087i
$933$			241.486i			0.00847363i
$934$	2433.21	+	2390.57i	0.0852430	+	0.0837493i
$935$	−73014.3	+	21729.4i	−2.55382	+	0.760029i
$936$	−31651.8	+	33376.4i	−1.10531	+	1.16554i
$937$	13027.9			0.454220			0.227110	−	0.973869i	$-0.427072\pi$
$937$	13027.9			0.454220			0.227110	+	0.973869i	$0.427072\pi$
$938$	−14636.1	+	14897.2i	−0.509475	+	0.518561i
$939$			649.782i			0.0225824i
$940$	401.215	+	22695.5i	0.0139215	+	0.787496i
$941$	1461.82			0.0506420			0.0253210	−	0.999679i	$-0.491939\pi$
$941$	1461.82			0.0506420			0.0253210	+	0.999679i	$0.491939\pi$
$942$	−51.0581	−	50.1634i	−0.00176599	−	0.00173505i
$943$	6136.89			0.211924
$944$	−738.246	−	20873.6i	−0.0254532	−	0.719681i
$945$			1553.11i			0.0534633i
$946$	26529.7	+	26064.9i	0.911792	+	0.895815i
$947$	25266.4			0.866997			0.433499	−	0.901154i	$-0.357279\pi$
$947$	25266.4			0.866997			0.433499	+	0.901154i	$0.357279\pi$
$948$	−11.1304	+	0.196765i	−0.000381327	+	6.74117e-6i
$949$	−82394.5			−2.81838
$950$	35465.4	+	34843.9i	1.21121	+	1.18999i
$951$	−599.792			−0.0204517
$952$	−16029.2	+	31585.0i	−0.545704	+	1.07529i
$953$	−47488.6			−1.61417			−0.807086	−	0.590433i	$-0.798957\pi$
$953$	−47488.6			−1.61417			−0.807086	+	0.590433i	$0.798957\pi$
$954$	155.098	+	152.381i	0.00526362	+	0.00517139i
$955$	31441.1			1.06535
$956$	−457.818	−	25897.3i	−0.0154884	−	0.876129i
$957$	432.164			0.0145976
$958$	−9446.88	−	9281.35i	−0.318596	−	0.313013i
$959$		−	26682.4i		−	0.898458i
$960$	−34.9542	−	658.533i	−0.00117515	−	0.0221397i
$961$	13610.2			0.456855
$962$	−33640.6	−	33051.1i	−1.12746	−	1.10770i
$963$	−33050.1			−1.10595
$964$	−13446.2	+	237.704i	−0.449246	+	0.00794185i
$965$		−	39430.6i		−	1.31535i
$966$	−273.782	+	278.665i	−0.00911882	+	0.00928145i
$967$	−37164.8			−1.23592			−0.617962	−	0.786208i	$-0.712042\pi$
$967$	−37164.8			−1.23592			−0.617962	+	0.786208i	$0.712042\pi$
$968$	42457.1	+	40263.3i	1.40973	+	1.33689i
$969$	−147.632	−	496.066i	−0.00489433	−	0.0164458i
$970$	−48918.2	−	48061.1i	−1.61925	−	1.59087i
$971$		−	38718.8i		−	1.27965i	−0.768519	−	0.639827i	$-0.779006\pi$
$971$		−	38718.8i		−	1.27965i	0.768519	−	0.639827i	$-0.220994\pi$
$972$	−22.9308	−	1297.12i	−0.000756693	−	0.0428038i
$973$		−	13827.0i		−	0.455573i
$974$	29601.4	+	29082.8i	0.973810	+	0.956747i
$975$		−	986.194i		−	0.0323933i
$976$	14405.6	−	509.488i	0.472450	−	0.0167093i
$977$	20345.1			0.666219			0.333109	−	0.942888i	$-0.391902\pi$
$977$	20345.1			0.666219			0.333109	+	0.942888i	$0.391902\pi$
$978$	252.380	−	256.881i	0.00825177	−	0.00839894i
$979$	49904.1			1.62915
$980$	−382.416	−	21632.1i	−0.0124651	−	0.705114i
$981$	−469.592			−0.0152833
$982$	41374.4	+	40649.5i	1.34451	+	1.32095i
$983$			9685.74i			0.314270i	0.987577	+	0.157135i	$0.0502258\pi$
$983$			9685.74i			0.314270i	−0.987577	+	0.157135i	$0.949774\pi$
$984$	−84.9938	+	89.6249i	−0.00275356	+	0.00290359i
$985$	−59290.3			−1.91791
$986$	−8642.48	+	16308.8i	−0.279141	+	0.526752i
$987$			270.639i			0.00872801i
$988$	1060.12	+	59967.7i	0.0341366	+	1.93100i
$989$	−17519.0			−0.563267
$990$	−58156.1	+	59193.3i	−1.86699	+	1.90029i
$991$			41871.0i			1.34216i	0.741386	+	0.671078i	$0.234169\pi$
$991$			41871.0i			1.34216i	−0.741386	+	0.671078i	$0.765831\pi$
$992$	16985.5	+	15546.9i	0.543639	+	0.497596i
$993$		−	480.157i		−	0.0153447i
$994$	−28182.2	+	28684.8i	−0.899279	+	0.915318i
$995$		−	10909.1i		−	0.347581i
$996$	−565.964	+	10.0052i	−0.0180053	+	0.000318300i
$997$	10315.0			0.327662			0.163831	−	0.986488i	$-0.447615\pi$
$997$	10315.0			0.327662			0.163831	+	0.986488i	$0.447615\pi$
$998$	13704.8	−	13949.2i	0.434688	−	0.442440i
$999$	886.701			0.0280820

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	136.4.h.a.101.16	yes	52
4.3	odd	2		544.4.h.a.305.26		52
8.3	odd	2		544.4.h.a.305.28		52
8.5	even	2	inner	136.4.h.a.101.13	✓	52
17.16	even	2	inner	136.4.h.a.101.15	yes	52
68.67	odd	2		544.4.h.a.305.27		52
136.67	odd	2		544.4.h.a.305.25		52
136.101	even	2	inner	136.4.h.a.101.14	yes	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
136.4.h.a.101.13	✓	52	8.5	even	2	inner
136.4.h.a.101.14	yes	52	136.101	even	2	inner
136.4.h.a.101.15	yes	52	17.16	even	2	inner
136.4.h.a.101.16	yes	52	1.1	even	1	trivial
544.4.h.a.305.25		52	136.67	odd	2
544.4.h.a.305.26		52	4.3	odd	2
544.4.h.a.305.27		52	68.67	odd	2
544.4.h.a.305.28		52	8.3	odd	2

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:	\( N \)	\(=\)	\( 136 = 2^{3} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	136.h (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.98225 + 2.01760i) q^{2} +0.0741700 q^{3} +(-0.141403 - 7.99875i) q^{4} -17.3656 q^{5} +(-0.147023 + 0.149645i) q^{6} +22.3324i q^{7} +(16.4186 + 15.5702i) q^{8} -26.9945 q^{9} +O(q^{10})\)	\(q+(-1.98225 + 2.01760i) q^{2} +0.0741700 q^{3} +(-0.141403 - 7.99875i) q^{4} -17.3656 q^{5} +(-0.147023 + 0.149645i) q^{6} +22.3324i q^{7} +(16.4186 + 15.5702i) q^{8} -26.9945 q^{9} +(34.4229 - 35.0368i) q^{10} +62.5853 q^{11} +(-0.0104879 - 0.593268i) q^{12} -75.3060i q^{13} +(-45.0578 - 44.2683i) q^{14} -1.28801 q^{15} +(-63.9600 + 2.26210i) q^{16} +(67.1809 - 19.9933i) q^{17} +(53.5097 - 54.4640i) q^{18} -99.5556i q^{19} +(2.45556 + 138.903i) q^{20} +1.65639i q^{21} +(-124.059 + 126.272i) q^{22} -83.3842i q^{23} +(1.21777 + 1.15484i) q^{24} +176.565 q^{25} +(151.937 + 149.275i) q^{26} -4.00477 q^{27} +(178.631 - 3.15787i) q^{28} +93.0996 q^{29} +(2.55315 - 2.59868i) q^{30} +127.204i q^{31} +(122.220 - 133.530i) q^{32} +4.64196 q^{33} +(-92.8305 + 175.176i) q^{34} -387.816i q^{35} +(3.81711 + 215.922i) q^{36} -221.411 q^{37} +(200.863 + 197.344i) q^{38} -5.58545i q^{39} +(-285.118 - 270.386i) q^{40} +73.5978i q^{41} +(-3.34194 - 3.28338i) q^{42} -210.100i q^{43} +(-8.84977 - 500.604i) q^{44} +468.776 q^{45} +(168.236 + 165.288i) q^{46} +163.391 q^{47} +(-4.74392 + 0.167780i) q^{48} -155.735 q^{49} +(-349.995 + 356.237i) q^{50} +(4.98281 - 1.48291i) q^{51} +(-602.354 + 10.6485i) q^{52} +2.84772i q^{53} +(7.93845 - 8.08003i) q^{54} -1086.83 q^{55} +(-347.719 + 366.665i) q^{56} -7.38404i q^{57} +(-184.546 + 187.838i) q^{58} +326.354i q^{59} +(0.182129 + 10.3025i) q^{60} -225.228 q^{61} +(-256.646 - 252.149i) q^{62} -602.851i q^{63} +(27.1381 + 511.280i) q^{64} +1307.74i q^{65} +(-9.20150 + 9.36560i) q^{66} -330.624i q^{67} +(-169.421 - 534.536i) q^{68} -6.18461i q^{69} +(782.456 + 768.746i) q^{70} -636.622i q^{71} +(-443.211 - 420.310i) q^{72} -1094.13i q^{73} +(438.891 - 446.718i) q^{74} +13.0958 q^{75} +(-796.320 + 14.0775i) q^{76} +1397.68i q^{77} +(11.2692 + 11.0717i) q^{78} -18.7611i q^{79} +(1110.71 - 39.2828i) q^{80} +728.554 q^{81} +(-148.491 - 145.889i) q^{82} -953.977i q^{83} +(13.2491 - 0.234220i) q^{84} +(-1166.64 + 347.196i) q^{85} +(423.897 + 416.469i) q^{86} +6.90520 q^{87} +(1027.56 + 974.465i) q^{88} +797.377 q^{89} +(-929.230 + 945.802i) q^{90} +1681.76 q^{91} +(-666.969 + 11.7908i) q^{92} +9.43472i q^{93} +(-323.881 + 329.657i) q^{94} +1728.84i q^{95} +(9.06510 - 9.90390i) q^{96} -1396.19i q^{97} +(308.705 - 314.211i) q^{98} -1689.46 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q - 2 q^{2} + 10 q^{4} - 2 q^{8} + 428 q^{9}+O(q^{10}) \) 52 * q - 2 * q^2 + 10 * q^4 - 2 * q^8 + 428 * q^9	\( 52 q - 2 q^{2} + 10 q^{4} - 2 q^{8} + 428 q^{9} - 232 q^{15} - 78 q^{16} - 28 q^{17} - 2 q^{18} + 1052 q^{25} + 448 q^{26} - 368 q^{30} + 958 q^{32} - 344 q^{33} - 198 q^{34} + 138 q^{36} - 524 q^{38} + 936 q^{47} - 1964 q^{49} - 1038 q^{50} - 1424 q^{52} - 1384 q^{55} + 2320 q^{60} - 2078 q^{64} - 1888 q^{66} - 874 q^{68} + 2472 q^{70} - 4010 q^{72} + 436 q^{76} + 1884 q^{81} - 2264 q^{84} - 1420 q^{86} + 1976 q^{87} - 224 q^{89} + 80 q^{94} + 5746 q^{98}+O(q^{100}) \) 52 * q - 2 * q^2 + 10 * q^4 - 2 * q^8 + 428 * q^9 - 232 * q^15 - 78 * q^16 - 28 * q^17 - 2 * q^18 + 1052 * q^25 + 448 * q^26 - 368 * q^30 + 958 * q^32 - 344 * q^33 - 198 * q^34 + 138 * q^36 - 524 * q^38 + 936 * q^47 - 1964 * q^49 - 1038 * q^50 - 1424 * q^52 - 1384 * q^55 + 2320 * q^60 - 2078 * q^64 - 1888 * q^66 - 874 * q^68 + 2472 * q^70 - 4010 * q^72 + 436 * q^76 + 1884 * q^81 - 2264 * q^84 - 1420 * q^86 + 1976 * q^87 - 224 * q^89 + 80 * q^94 + 5746 * q^98

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