LMFDB - Embedded newform 102.4.f.c.55.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [102,4,Mod(13,102)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(102, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("102.13");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 102 = 2 \cdot 3 \cdot 17 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	102.f (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.01819482059$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 886x^{10} + 292945x^{8} + 42943904x^{6} + 2387634208x^{4} + 5944075264x^{2} + 2089586944 $ x^12 + 886x^10 + 292945x^8 + 42943904x^6 + 2387634208x^4 + 5944075264*x^2 + 2089586944
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6}\cdot 3^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			55.5
Root			$-1.47294i$ of defining polynomial
Character	$\chi$	$=$	102.55
Dual form			102.4.f.c.13.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.00000i q^{2} +(2.12132 - 2.12132i) q^{3} -4.00000 q^{4} +(0.627312 - 0.627312i) q^{5} +(4.24264 + 4.24264i) q^{6} +(13.3596 + 13.3596i) q^{7} -8.00000i q^{8} -9.00000i q^{9} +(1.25462 + 1.25462i) q^{10} +(42.2481 + 42.2481i) q^{11} +(-8.48528 + 8.48528i) q^{12} +36.6745 q^{13} +(-26.7192 + 26.7192i) q^{14} -2.66146i q^{15} +16.0000 q^{16} +(32.8910 - 61.8965i) q^{17} +18.0000 q^{18} +117.094i q^{19} +(-2.50925 + 2.50925i) q^{20} +56.6800 q^{21} +(-84.4962 + 84.4962i) q^{22} +(-131.972 - 131.972i) q^{23} +(-16.9706 - 16.9706i) q^{24} +124.213i q^{25} +73.3490i q^{26} +(-19.0919 - 19.0919i) q^{27} +(-53.4384 - 53.4384i) q^{28} +(-92.5725 + 92.5725i) q^{29} +5.32292 q^{30} +(168.965 - 168.965i) q^{31} +32.0000i q^{32} +179.243 q^{33} +(123.793 + 65.7820i) q^{34} +16.7613 q^{35} +36.0000i q^{36} +(9.98581 - 9.98581i) q^{37} -234.189 q^{38} +(77.7984 - 77.7984i) q^{39} +(-5.01850 - 5.01850i) q^{40} +(-339.782 - 339.782i) q^{41} +113.360i q^{42} -194.715i q^{43} +(-168.992 - 168.992i) q^{44} +(-5.64581 - 5.64581i) q^{45} +(263.944 - 263.944i) q^{46} +40.2448 q^{47} +(33.9411 - 33.9411i) q^{48} +13.9584i q^{49} -248.426 q^{50} +(-61.5300 - 201.075i) q^{51} -146.698 q^{52} -40.8393i q^{53} +(38.1838 - 38.1838i) q^{54} +53.0055 q^{55} +(106.877 - 106.877i) q^{56} +(248.395 + 248.395i) q^{57} +(-185.145 - 185.145i) q^{58} -447.653i q^{59} +10.6458i q^{60} +(109.224 + 109.224i) q^{61} +(337.931 + 337.931i) q^{62} +(120.236 - 120.236i) q^{63} -64.0000 q^{64} +(23.0064 - 23.0064i) q^{65} +358.487i q^{66} -438.990 q^{67} +(-131.564 + 247.586i) q^{68} -559.910 q^{69} +33.5226i q^{70} +(-429.965 + 429.965i) q^{71} -72.0000 q^{72} +(-258.367 + 258.367i) q^{73} +(19.9716 + 19.9716i) q^{74} +(263.495 + 263.495i) q^{75} -468.378i q^{76} +1128.84i q^{77} +(155.597 + 155.597i) q^{78} +(943.212 + 943.212i) q^{79} +(10.0370 - 10.0370i) q^{80} -81.0000 q^{81} +(679.563 - 679.563i) q^{82} -516.632i q^{83} -226.720 q^{84} +(-18.1955 - 59.4614i) q^{85} +389.430 q^{86} +392.752i q^{87} +(337.985 - 337.985i) q^{88} -821.409 q^{89} +(11.2916 - 11.2916i) q^{90} +(489.957 + 489.957i) q^{91} +(527.888 + 527.888i) q^{92} -716.860i q^{93} +80.4897i q^{94} +(73.4548 + 73.4548i) q^{95} +(67.8823 + 67.8823i) q^{96} +(-939.582 + 939.582i) q^{97} -27.9168 q^{98} +(380.233 - 380.233i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 48 q^{4} + 16 q^{5} - 12 q^{7} + 32 q^{10} - 32 q^{11} - 68 q^{13} + 24 q^{14} + 192 q^{16} + 64 q^{17} + 216 q^{18} - 64 q^{20} - 168 q^{21} + 64 q^{22} - 112 q^{23} + 48 q^{28} - 296 q^{29} - 168 q^{30}+ \cdots - 288 q^{99}+O(q^{100}) $ 12 * q - 48 * q^4 + 16 * q^5 - 12 * q^7 + 32 * q^10 - 32 * q^11 - 68 * q^13 + 24 * q^14 + 192 * q^16 + 64 * q^17 + 216 * q^18 - 64 * q^20 - 168 * q^21 + 64 * q^22 - 112 * q^23 + 48 * q^28 - 296 * q^29 - 168 * q^30 + 520 * q^31 + 204 * q^33 + 144 * q^34 + 392 * q^35 - 828 * q^37 - 280 * q^38 + 312 * q^39 - 128 * q^40 + 8 * q^41 + 128 * q^44 - 144 * q^45 + 224 * q^46 - 2920 * q^47 + 752 * q^50 + 420 * q^51 + 272 * q^52 + 1156 * q^55 - 96 * q^56 + 312 * q^57 - 592 * q^58 - 1124 * q^61 + 1040 * q^62 - 108 * q^63 - 768 * q^64 + 3288 * q^65 - 2008 * q^67 - 256 * q^68 + 468 * q^69 - 2184 * q^71 - 864 * q^72 + 2456 * q^73 - 1656 * q^74 - 192 * q^75 + 624 * q^78 + 2652 * q^79 + 256 * q^80 - 972 * q^81 - 16 * q^82 + 672 * q^84 + 3444 * q^85 - 184 * q^86 - 256 * q^88 + 5304 * q^89 + 288 * q^90 - 1420 * q^91 + 448 * q^92 - 2920 * q^95 + 2688 * q^97 - 4168 * q^98 - 288 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/102\mathbb{Z}\right)^\times$.

$n$	$35$	$37$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$			2.00000i			0.707107i
$2$			2.00000i			0.707107i
$3$	2.12132	−	2.12132i	0.408248	−	0.408248i
$3$	2.12132	−	2.12132i	0.408248	−	0.408248i
$4$	−4.00000			−0.500000
$5$	0.627312	−	0.627312i	0.0561085	−	0.0561085i	−0.678496	−	0.734604i	$-0.737368\pi$
$5$	0.627312	−	0.627312i	0.0561085	−	0.0561085i	0.734604	+	0.678496i	$0.237368\pi$
$6$	4.24264	+	4.24264i	0.288675	+	0.288675i
$7$	13.3596	+	13.3596i	0.721351	+	0.721351i	0.968880	−	0.247529i	$-0.0796186\pi$
$7$	13.3596	+	13.3596i	0.721351	+	0.721351i	−0.247529	+	0.968880i	$0.579619\pi$
$8$		−	8.00000i		−	0.353553i
$9$		−	9.00000i		−	0.333333i
$10$	1.25462	+	1.25462i	0.0396747	+	0.0396747i
$11$	42.2481	+	42.2481i	1.15803	+	1.15803i	0.984900	+	0.173126i	$0.0553867\pi$
$11$	42.2481	+	42.2481i	1.15803	+	1.15803i	0.173126	+	0.984900i	$0.444613\pi$
$12$	−8.48528	+	8.48528i	−0.204124	+	0.204124i
$13$	36.6745			0.782437			0.391219	−	0.920298i	$-0.372054\pi$
$13$	36.6745			0.782437			0.391219	+	0.920298i	$0.372054\pi$
$14$	−26.7192	+	26.7192i	−0.510072	+	0.510072i
$15$		−	2.66146i		−	0.0458124i
$16$	16.0000			0.250000
$17$	32.8910	−	61.8965i	0.469250	−	0.883066i
$17$	32.8910	−	61.8965i	0.469250	−	0.883066i
$18$	18.0000			0.235702
$19$			117.094i			1.41386i	0.707284	+	0.706929i	$0.249920\pi$
$19$			117.094i			1.41386i	−0.707284	+	0.706929i	$0.750080\pi$
$20$	−2.50925	+	2.50925i	−0.0280543	+	0.0280543i
$21$	56.6800			0.588981
$22$	−84.4962	+	84.4962i	−0.818848	+	0.818848i
$23$	−131.972	−	131.972i	−1.19644	−	1.19644i	−0.975225	−	0.221213i	$-0.928998\pi$
$23$	−131.972	−	131.972i	−1.19644	−	1.19644i	−0.221213	−	0.975225i	$-0.571002\pi$
$24$	−16.9706	−	16.9706i	−0.144338	−	0.144338i
$25$			124.213i			0.993704i
$26$			73.3490i			0.553267i
$27$	−19.0919	−	19.0919i	−0.136083	−	0.136083i
$28$	−53.4384	−	53.4384i	−0.360676	−	0.360676i
$29$	−92.5725	+	92.5725i	−0.592768	+	0.592768i	−0.938378	−	0.345610i	$-0.887672\pi$
$29$	−92.5725	+	92.5725i	−0.592768	+	0.592768i	0.345610	+	0.938378i	$0.387672\pi$
$30$	5.32292			0.0323943
$31$	168.965	−	168.965i	0.978938	−	0.978938i	−0.0208446	−	0.999783i	$-0.506636\pi$
$31$	168.965	−	168.965i	0.978938	−	0.978938i	0.999783	+	0.0208446i	$0.00663551\pi$
$32$			32.0000i			0.176777i
$33$	179.243			0.945524
$34$	123.793	+	65.7820i	0.624422	+	0.331810i
$35$	16.7613			0.0809479
$36$			36.0000i			0.166667i
$37$	9.98581	−	9.98581i	0.0443691	−	0.0443691i	−0.684574	−	0.728943i	$-0.740012\pi$
$37$	9.98581	−	9.98581i	0.0443691	−	0.0443691i	0.728943	+	0.684574i	$0.240012\pi$
$38$	−234.189			−0.999749
$39$	77.7984	−	77.7984i	0.319429	−	0.319429i
$40$	−5.01850	−	5.01850i	−0.0198374	−	0.0198374i
$41$	−339.782	−	339.782i	−1.29427	−	1.29427i	−0.932121	−	0.362147i	$-0.882044\pi$
$41$	−339.782	−	339.782i	−1.29427	−	1.29427i	−0.362147	−	0.932121i	$-0.617956\pi$
$42$			113.360i			0.416472i
$43$		−	194.715i		−	0.690553i	−0.938501	−	0.345277i	$-0.887785\pi$
$43$		−	194.715i		−	0.690553i	0.938501	−	0.345277i	$-0.112215\pi$
$44$	−168.992	−	168.992i	−0.579013	−	0.579013i
$45$	−5.64581	−	5.64581i	−0.0187028	−	0.0187028i
$46$	263.944	−	263.944i	0.846010	−	0.846010i
$47$	40.2448			0.124900			0.0624501	−	0.998048i	$-0.480109\pi$
$47$	40.2448			0.124900			0.0624501	+	0.998048i	$0.480109\pi$
$48$	33.9411	−	33.9411i	0.102062	−	0.102062i
$49$			13.9584i			0.0406950i
$50$	−248.426			−0.702655
$51$	−61.5300	−	201.075i	−0.168940	−	0.552080i
$52$	−146.698			−0.391219
$53$		−	40.8393i		−	0.105844i	−0.998599	−	0.0529218i	$-0.983147\pi$
$53$		−	40.8393i		−	0.105844i	0.998599	−	0.0529218i	$-0.0168534\pi$
$54$	38.1838	−	38.1838i	0.0962250	−	0.0962250i
$55$	53.0055			0.129950
$56$	106.877	−	106.877i	0.255036	−	0.255036i
$57$	248.395	+	248.395i	0.577205	+	0.577205i
$58$	−185.145	−	185.145i	−0.419150	−	0.419150i
$59$		−	447.653i		−	0.987788i	−0.869522	−	0.493894i	$-0.835573\pi$
$59$		−	447.653i		−	0.987788i	0.869522	−	0.493894i	$-0.164427\pi$
$60$			10.6458i			0.0229062i
$61$	109.224	+	109.224i	0.229257	+	0.229257i	0.812382	−	0.583125i	$-0.198170\pi$
$61$	109.224	+	109.224i	0.229257	+	0.229257i	−0.583125	+	0.812382i	$0.698170\pi$
$62$	337.931	+	337.931i	0.692214	+	0.692214i
$63$	120.236	−	120.236i	0.240450	−	0.240450i
$64$	−64.0000			−0.125000
$65$	23.0064	−	23.0064i	0.0439014	−	0.0439014i
$66$			358.487i			0.668586i
$67$	−438.990			−0.800464			−0.400232	−	0.916414i	$-0.631071\pi$
$67$	−438.990			−0.800464			−0.400232	+	0.916414i	$0.631071\pi$
$68$	−131.564	+	247.586i	−0.234625	+	0.441533i
$69$	−559.910			−0.976888
$70$			33.5226i			0.0572388i
$71$	−429.965	+	429.965i	−0.718697	+	0.718697i	−0.968338	−	0.249641i	$-0.919687\pi$
$71$	−429.965	+	429.965i	−0.718697	+	0.718697i	0.249641	+	0.968338i	$0.419687\pi$
$72$	−72.0000			−0.117851
$73$	−258.367	+	258.367i	−0.414240	+	0.414240i	−0.883213	−	0.468973i	$-0.844624\pi$
$73$	−258.367	+	258.367i	−0.414240	+	0.414240i	0.468973	+	0.883213i	$0.344624\pi$
$74$	19.9716	+	19.9716i	0.0313737	+	0.0313737i
$75$	263.495	+	263.495i	0.405678	+	0.405678i
$76$		−	468.378i		−	0.706929i
$77$			1128.84i			1.67069i
$78$	155.597	+	155.597i	0.225870	+	0.225870i
$79$	943.212	+	943.212i	1.34329	+	1.34329i	0.892766	+	0.450520i	$0.148761\pi$
$79$	943.212	+	943.212i	1.34329	+	1.34329i	0.450520	+	0.892766i	$0.351239\pi$
$80$	10.0370	−	10.0370i	0.0140271	−	0.0140271i
$81$	−81.0000			−0.111111
$82$	679.563	−	679.563i	0.915186	−	0.915186i
$83$		−	516.632i		−	0.683226i	−0.939841	−	0.341613i	$-0.889027\pi$
$83$		−	516.632i		−	0.683226i	0.939841	−	0.341613i	$-0.110973\pi$
$84$	−226.720			−0.294490
$85$	−18.1955	−	59.4614i	−0.0232186	−	0.0758764i
$86$	389.430			0.488295
$87$			392.752i			0.483993i
$88$	337.985	−	337.985i	0.409424	−	0.409424i
$89$	−821.409			−0.978305			−0.489153	−	0.872198i	$-0.662694\pi$
$89$	−821.409			−0.978305			−0.489153	+	0.872198i	$0.662694\pi$
$90$	11.2916	−	11.2916i	0.0132249	−	0.0132249i
$91$	489.957	+	489.957i	0.564412	+	0.564412i
$92$	527.888	+	527.888i	0.598219	+	0.598219i
$93$		−	716.860i		−	0.799300i
$94$			80.4897i			0.0883178i
$95$	73.4548	+	73.4548i	0.0793295	+	0.0793295i
$96$	67.8823	+	67.8823i	0.0721688	+	0.0721688i
$97$	−939.582	+	939.582i	−0.983506	+	0.983506i	−0.999866	−	0.0163600i	$-0.994792\pi$
$97$	−939.582	+	939.582i	−0.983506	+	0.983506i	0.0163600	+	0.999866i	$0.494792\pi$
$98$	−27.9168			−0.0287757
$99$	380.233	−	380.233i	0.386008	−	0.386008i
$100$		−	496.852i		−	0.496852i
$101$	798.976			0.787140			0.393570	−	0.919295i	$-0.371240\pi$
$101$	798.976			0.787140			0.393570	+	0.919295i	$0.371240\pi$
$102$	402.150	−	123.060i	0.390380	−	0.119458i
$103$	−59.1043			−0.0565410			−0.0282705	−	0.999600i	$-0.509000\pi$
$103$	−59.1043			−0.0565410			−0.0282705	+	0.999600i	$0.509000\pi$
$104$		−	293.396i		−	0.276633i
$105$	35.5561	−	35.5561i	0.0330468	−	0.0330468i
$106$	81.6787			0.0748428
$107$	572.335	−	572.335i	0.517100	−	0.517100i	−0.399593	−	0.916693i	$-0.630848\pi$
$107$	572.335	−	572.335i	0.517100	−	0.517100i	0.916693	+	0.399593i	$0.130848\pi$
$108$	76.3675	+	76.3675i	0.0680414	+	0.0680414i
$109$	−1169.67	−	1169.67i	−1.02783	−	1.02783i	−0.999601	−	0.0282336i	$-0.991012\pi$
$109$	−1169.67	−	1169.67i	−1.02783	−	1.02783i	−0.0282336	−	0.999601i	$-0.508988\pi$
$110$			106.011i			0.0918886i
$111$		−	42.3662i		−	0.0362272i
$112$	213.754	+	213.754i	0.180338	+	0.180338i
$113$	339.967	+	339.967i	0.283021	+	0.283021i	0.834313	−	0.551292i	$-0.185865\pi$
$113$	339.967	+	339.967i	0.283021	+	0.283021i	−0.551292	+	0.834313i	$0.685865\pi$
$114$	−496.790	+	496.790i	−0.408146	+	0.408146i
$115$	−165.575			−0.134261
$116$	370.290	−	370.290i	0.296384	−	0.296384i
$117$		−	330.071i		−	0.260812i
$118$	895.307			0.698472
$119$	1266.32	−	387.502i	0.975494	−	0.298507i
$120$	−21.2917			−0.0161971
$121$			2238.80i			1.68205i
$122$	−218.448	+	218.448i	−0.162109	+	0.162109i
$123$	−1441.57			−1.05677
$124$	−675.862	+	675.862i	−0.489469	+	0.489469i
$125$	156.334	+	156.334i	0.111864	+	0.111864i
$126$	240.473	+	240.473i	0.170024	+	0.170024i
$127$		−	1505.29i		−	1.05176i	−0.850560	−	0.525878i	$-0.823737\pi$
$127$		−	1505.29i		−	1.05176i	0.850560	−	0.525878i	$-0.176263\pi$
$128$		−	128.000i		−	0.0883883i
$129$	−413.053	−	413.053i	−0.281917	−	0.281917i
$130$	46.0127	+	46.0127i	0.0310430	+	0.0310430i
$131$	799.501	−	799.501i	0.533227	−	0.533227i	−0.388305	−	0.921531i	$-0.626939\pi$
$131$	799.501	−	799.501i	0.533227	−	0.533227i	0.921531	+	0.388305i	$0.126939\pi$
$132$	−716.974			−0.472762
$133$	−1564.34	+	1564.34i	−1.01989	+	1.01989i
$134$		−	877.979i		−	0.566014i
$135$	−23.9531			−0.0152708
$136$	−495.172	−	263.128i	−0.312211	−	0.165905i
$137$	−1079.13			−0.672966			−0.336483	−	0.941690i	$-0.609237\pi$
$137$	−1079.13			−0.672966			−0.336483	+	0.941690i	$0.609237\pi$
$138$		−	1119.82i		−	0.690764i
$139$	494.859	−	494.859i	0.301967	−	0.301967i	−0.539816	−	0.841783i	$-0.681506\pi$
$139$	494.859	−	494.859i	0.301967	−	0.301967i	0.841783	+	0.539816i	$0.181506\pi$
$140$	−67.0452			−0.0404739
$141$	85.3722	−	85.3722i	0.0509903	−	0.0509903i
$142$	−859.931	−	859.931i	−0.508196	−	0.508196i
$143$	1549.43	+	1549.43i	0.906082	+	0.906082i
$144$		−	144.000i		−	0.0833333i
$145$			116.144i			0.0665187i
$146$	−516.733	−	516.733i	−0.292912	−	0.292912i
$147$	29.6102	+	29.6102i	0.0166137	+	0.0166137i
$148$	−39.9432	+	39.9432i	−0.0221845	+	0.0221845i
$149$	−1357.34			−0.746293			−0.373147	−	0.927772i	$-0.621721\pi$
$149$	−1357.34			−0.746293			−0.373147	+	0.927772i	$0.621721\pi$
$150$	−526.991	+	526.991i	−0.286858	+	0.286858i
$151$		−	1762.54i		−	0.949889i	−0.880016	−	0.474945i	$-0.842468\pi$
$151$		−	1762.54i		−	0.949889i	0.880016	−	0.474945i	$-0.157532\pi$
$152$	936.756			0.499874
$153$	−557.069	−	296.019i	−0.294355	−	0.156417i
$154$	−2257.67			−1.18135
$155$		−	211.988i		−	0.109854i
$156$	−311.194	+	311.194i	−0.159714	+	0.159714i
$157$	64.0852			0.0325768			0.0162884	−	0.999867i	$-0.494815\pi$
$157$	64.0852			0.0325768			0.0162884	+	0.999867i	$0.494815\pi$
$158$	−1886.42	+	1886.42i	−0.949847	+	0.949847i
$159$	−86.6333	−	86.6333i	−0.0432105	−	0.0432105i
$160$	20.0740	+	20.0740i	0.00991868	+	0.00991868i
$161$		−	3526.19i		−	1.72610i
$162$		−	162.000i		−	0.0785674i
$163$	−1670.87	−	1670.87i	−0.802902	−	0.802902i	0.180646	−	0.983548i	$-0.442181\pi$
$163$	−1670.87	−	1670.87i	−0.802902	−	0.802902i	−0.983548	+	0.180646i	$0.942181\pi$
$164$	1359.13	+	1359.13i	0.647134	+	0.647134i
$165$	112.442	−	112.442i	0.0530519	−	0.0530519i
$166$	1033.26			0.483114
$167$	1534.17	−	1534.17i	0.710885	−	0.710885i	−0.255836	−	0.966720i	$-0.582351\pi$
$167$	1534.17	−	1534.17i	0.710885	−	0.710885i	0.966720	+	0.255836i	$0.0823506\pi$
$168$		−	453.440i		−	0.208236i
$169$	−851.979			−0.387792
$170$	118.923	−	36.3910i	0.0536527	−	0.0164180i
$171$	1053.85			0.471286
$172$			778.861i			0.345277i
$173$	2355.07	−	2355.07i	1.03499	−	1.03499i	0.0356213	−	0.999365i	$-0.488659\pi$
$173$	2355.07	−	2355.07i	1.03499	−	1.03499i	0.999365	−	0.0356213i	$-0.0113410\pi$
$174$	−785.503			−0.342235
$175$	−1659.44	+	1659.44i	−0.716809	+	0.716809i
$176$	675.970	+	675.970i	0.289506	+	0.289506i
$177$	−949.616	−	949.616i	−0.403263	−	0.403263i
$178$		−	1642.82i		−	0.691766i
$179$			3541.26i			1.47870i	0.673324	+	0.739348i	$0.264866\pi$
$179$			3541.26i			1.47870i	−0.673324	+	0.739348i	$0.735134\pi$
$180$	22.5832	+	22.5832i	0.00935142	+	0.00935142i
$181$	1214.57	+	1214.57i	0.498775	+	0.498775i	0.911057	−	0.412281i	$-0.135268\pi$
$181$	1214.57	+	1214.57i	0.498775	+	0.498775i	−0.412281	+	0.911057i	$0.635268\pi$
$182$	−979.915	+	979.915i	−0.399099	+	0.399099i
$183$	463.398			0.187188
$184$	−1055.78	+	1055.78i	−0.423005	+	0.423005i
$185$		−	12.5284i		−	0.00497897i
$186$	1433.72			0.565190
$187$	4004.59	−	1225.43i	1.56602	−	0.479209i
$188$	−160.979			−0.0624501
$189$		−	510.120i		−	0.196327i
$190$	−146.910	+	146.910i	−0.0560944	+	0.0560944i
$191$	1714.57			0.649538			0.324769	−	0.945793i	$-0.394713\pi$
$191$	1714.57			0.649538			0.324769	+	0.945793i	$0.394713\pi$
$192$	−135.765	+	135.765i	−0.0510310	+	0.0510310i
$193$	2471.05	+	2471.05i	0.921605	+	0.921605i	0.997143	−	0.0755380i	$-0.0240674\pi$
$193$	2471.05	+	2471.05i	0.921605	+	0.921605i	−0.0755380	+	0.997143i	$0.524067\pi$
$194$	−1879.16	−	1879.16i	−0.695444	−	0.695444i
$195$		−	97.6078i		−	0.0358453i
$196$		−	55.8336i		−	0.0203475i
$197$	1958.83	+	1958.83i	0.708430	+	0.708430i	0.966205	−	0.257775i	$-0.0829893\pi$
$197$	1958.83	+	1958.83i	0.708430	+	0.708430i	−0.257775	+	0.966205i	$0.582989\pi$
$198$	760.466	+	760.466i	0.272949	+	0.272949i
$199$	2353.94	−	2353.94i	0.838525	−	0.838525i	−0.150140	−	0.988665i	$-0.547972\pi$
$199$	2353.94	−	2353.94i	0.838525	−	0.838525i	0.988665	+	0.150140i	$0.0479723\pi$
$200$	993.704			0.351327
$201$	−931.238	+	931.238i	−0.326788	+	0.326788i
$202$			1597.95i			0.556592i
$203$	−2473.46			−0.855188
$204$	246.120	+	804.299i	0.0844698	+	0.276040i
$205$	−426.298			−0.145239
$206$		−	118.209i		−	0.0399805i
$207$	−1187.75	+	1187.75i	−0.398813	+	0.398813i
$208$	586.792			0.195609
$209$	−4947.02	+	4947.02i	−1.63728	+	1.63728i
$210$	71.1121	+	71.1121i	0.0233676	+	0.0233676i
$211$	−2737.29	−	2737.29i	−0.893092	−	0.893092i	0.101721	−	0.994813i	$-0.467565\pi$
$211$	−2737.29	−	2737.29i	−0.893092	−	0.893092i	−0.994813	+	0.101721i	$0.967565\pi$
$212$			163.357i			0.0529218i
$213$			1824.19i			0.586814i
$214$	1144.67	+	1144.67i	0.365645	+	0.365645i
$215$	−122.147	−	122.147i	−0.0387459	−	0.0387459i
$216$	−152.735	+	152.735i	−0.0481125	+	0.0481125i
$217$	4514.62			1.41232
$218$	2339.34	−	2339.34i	0.726789	−	0.726789i
$219$			1096.16i			0.338226i
$220$	−212.022			−0.0649751
$221$	1206.26	−	2270.03i	0.367158	−	0.690943i
$222$	84.7324			0.0256165
$223$		−	5294.36i		−	1.58985i	−0.606708	−	0.794925i	$-0.707510\pi$
$223$		−	5294.36i		−	1.58985i	0.606708	−	0.794925i	$-0.292490\pi$
$224$	−427.508	+	427.508i	−0.127518	+	0.127518i
$225$	1117.92			0.331235
$226$	−679.934	+	679.934i	−0.200126	+	0.200126i
$227$	3694.32	+	3694.32i	1.08018	+	1.08018i	0.996492	+	0.0836858i	$0.0266692\pi$
$227$	3694.32	+	3694.32i	1.08018	+	1.08018i	0.0836858	+	0.996492i	$0.473331\pi$
$228$	−993.579	−	993.579i	−0.288603	−	0.288603i
$229$			1878.50i			0.542074i	0.962569	+	0.271037i	$0.0873666\pi$
$229$			1878.50i			0.542074i	−0.962569	+	0.271037i	$0.912633\pi$
$230$		−	331.151i		−	0.0949367i
$231$	2394.62	+	2394.62i	0.682055	+	0.682055i
$232$	740.580	+	740.580i	0.209575	+	0.209575i
$233$	1174.15	−	1174.15i	0.330133	−	0.330133i	−0.522504	−	0.852637i	$-0.675002\pi$
$233$	1174.15	−	1174.15i	0.330133	−	0.330133i	0.852637	+	0.522504i	$0.175002\pi$
$234$	660.141			0.184422
$235$	25.2461	−	25.2461i	0.00700797	−	0.00700797i
$236$			1790.61i			0.493894i
$237$	4001.71			1.09679
$238$	775.005	+	2532.65i	0.211076	+	0.689779i
$239$	−5017.17			−1.35788			−0.678941	−	0.734192i	$-0.737561\pi$
$239$	−5017.17			−1.35788			−0.678941	+	0.734192i	$0.737561\pi$
$240$		−	42.5834i		−	0.0114531i
$241$	−4152.16	+	4152.16i	−1.10981	+	1.10981i	−0.116635	+	0.993175i	$0.537211\pi$
$241$	−4152.16	+	4152.16i	−1.10981	+	1.10981i	−0.993175	+	0.116635i	$0.962789\pi$
$242$	−4477.61			−1.18939
$243$	−171.827	+	171.827i	−0.0453609	+	0.0453609i
$244$	−436.896	−	436.896i	−0.114629	−	0.114629i
$245$	8.75628	+	8.75628i	0.00228334	+	0.00228334i
$246$		−	2883.14i		−	0.747246i
$247$			4294.38i			1.10626i
$248$	−1351.72	−	1351.72i	−0.346107	−	0.346107i
$249$	−1095.94	−	1095.94i	−0.278926	−	0.278926i
$250$	−312.669	+	312.669i	−0.0790996	+	0.0790996i
$251$	−6899.16			−1.73495			−0.867473	−	0.497485i	$-0.834257\pi$
$251$	−6899.16			−1.73495			−0.867473	+	0.497485i	$0.834257\pi$
$252$	−480.946	+	480.946i	−0.120225	+	0.120225i
$253$		−	11151.1i		−	2.77101i
$254$	3010.58			0.743704
$255$	−164.735	−	87.5382i	−0.0404554	−	0.0214975i
$256$	256.000			0.0625000
$257$		−	1910.33i		−	0.463669i	−0.972755	−	0.231835i	$-0.925527\pi$
$257$		−	1910.33i		−	0.463669i	0.972755	−	0.231835i	$-0.0744728\pi$
$258$	826.107	−	826.107i	0.199346	−	0.199346i
$259$	266.813			0.0640114
$260$	−92.0255	+	92.0255i	−0.0219507	+	0.0219507i
$261$	833.152	+	833.152i	0.197589	+	0.197589i
$262$	1599.00	+	1599.00i	0.377048	+	0.377048i
$263$			2690.00i			0.630693i	0.948977	+	0.315346i	$0.102121\pi$
$263$			2690.00i			0.630693i	−0.948977	+	0.315346i	$0.897879\pi$
$264$		−	1433.95i		−	0.334293i
$265$	−25.6190	−	25.6190i	−0.00593873	−	0.00593873i
$266$	−3128.67	−	3128.67i	−0.721170	−	0.721170i
$267$	−1742.47	+	1742.47i	−0.399391	+	0.399391i
$268$	1755.96			0.400232
$269$	−1335.48	+	1335.48i	−0.302698	+	0.302698i	−0.842069	−	0.539370i	$-0.818662\pi$
$269$	−1335.48	+	1335.48i	−0.302698	+	0.302698i	0.539370	+	0.842069i	$0.318662\pi$
$270$		−	47.9063i		−	0.0107981i
$271$	4172.66			0.935317			0.467659	−	0.883909i	$-0.345098\pi$
$271$	4172.66			0.935317			0.467659	+	0.883909i	$0.345098\pi$
$272$	526.256	−	990.344i	0.117312	−	0.220766i
$273$	2078.71			0.460840
$274$		−	2158.26i		−	0.475859i
$275$	−5247.76	+	5247.76i	−1.15073	+	1.15073i
$276$	2239.64			0.488444
$277$	−523.661	+	523.661i	−0.113588	+	0.113588i	−0.761616	−	0.648028i	$-0.775594\pi$
$277$	−523.661	+	523.661i	−0.113588	+	0.113588i	0.648028	+	0.761616i	$0.275594\pi$
$278$	989.719	+	989.719i	0.213523	+	0.213523i
$279$	−1520.69	−	1520.69i	−0.326313	−	0.326313i
$280$		−	134.090i		−	0.0286194i
$281$		−	325.056i		−	0.0690078i	−0.999405	−	0.0345039i	$-0.989015\pi$
$281$		−	325.056i		−	0.0690078i	0.999405	−	0.0345039i	$-0.0109851\pi$
$282$	170.744	+	170.744i	0.0360556	+	0.0360556i
$283$	3413.26	+	3413.26i	0.716952	+	0.716952i	0.967980	−	0.251028i	$-0.0807686\pi$
$283$	3413.26	+	3413.26i	0.716952	+	0.716952i	−0.251028	+	0.967980i	$0.580769\pi$
$284$	1719.86	−	1719.86i	0.359349	−	0.359349i
$285$	311.642			0.0647723
$286$	−3098.86	+	3098.86i	−0.640697	+	0.640697i
$287$		−	9078.70i		−	1.86724i
$288$	288.000			0.0589256
$289$	−2749.36	−	4071.68i	−0.559609	−	0.828756i
$290$	−232.287			−0.0470358
$291$			3986.31i			0.803029i
$292$	1033.47	−	1033.47i	0.207120	−	0.207120i
$293$	−1038.13			−0.206991			−0.103496	−	0.994630i	$-0.533003\pi$
$293$	−1038.13			−0.206991			−0.103496	+	0.994630i	$0.533003\pi$
$294$	−59.2205	+	59.2205i	−0.0117476	+	0.0117476i
$295$	−280.818	−	280.818i	−0.0554233	−	0.0554233i
$296$	−79.8865	−	79.8865i	−0.0156868	−	0.0156868i
$297$		−	1613.19i		−	0.315175i
$298$		−	2714.68i		−	0.527709i
$299$	−4840.01	−	4840.01i	−0.936138	−	0.936138i
$300$	−1053.98	−	1053.98i	−0.202839	−	0.202839i
$301$	2601.32	−	2601.32i	0.498131	−	0.498131i
$302$	3525.07			0.671673
$303$	1694.88	−	1694.88i	0.321348	−	0.321348i
$304$			1873.51i			0.353465i
$305$	137.035			0.0257266
$306$	592.038	−	1114.14i	0.110603	−	0.208141i
$307$	−6737.14			−1.25247			−0.626236	−	0.779634i	$-0.715405\pi$
$307$	−6737.14			−1.25247			−0.626236	+	0.779634i	$0.715405\pi$
$308$		−	4515.34i		−	0.835343i
$309$	−125.379	+	125.379i	−0.0230828	+	0.0230828i
$310$	423.976			0.0776782
$311$	−3357.08	+	3357.08i	−0.612098	+	0.612098i	−0.943492	−	0.331395i	$-0.892481\pi$
$311$	−3357.08	+	3357.08i	−0.612098	+	0.612098i	0.331395	+	0.943492i	$0.392481\pi$
$312$	−622.387	−	622.387i	−0.112935	−	0.112935i
$313$	4263.10	+	4263.10i	0.769854	+	0.769854i	0.978081	−	0.208226i	$-0.0667691\pi$
$313$	4263.10	+	4263.10i	0.769854	+	0.769854i	−0.208226	+	0.978081i	$0.566769\pi$
$314$			128.170i			0.0230353i
$315$		−	150.852i		−	0.0269826i
$316$	−3772.85	−	3772.85i	−0.671643	−	0.671643i
$317$	−4955.80	−	4955.80i	−0.878062	−	0.878062i	0.115272	−	0.993334i	$-0.463226\pi$
$317$	−4955.80	−	4955.80i	−0.878062	−	0.878062i	−0.993334	+	0.115272i	$0.963226\pi$
$318$	173.267	−	173.267i	0.0305544	−	0.0305544i
$319$	−7822.02			−1.37288
$320$	−40.1480	+	40.1480i	−0.00701356	+	0.00701356i
$321$		−	2428.21i		−	0.422211i
$322$	7052.38			1.22054
$323$	7247.74	+	3851.36i	1.24853	+	0.663453i
$324$	324.000			0.0555556
$325$			4555.45i			0.777511i
$326$	3341.75	−	3341.75i	0.567737	−	0.567737i
$327$	−4962.49			−0.839224
$328$	−2718.25	+	2718.25i	−0.457593	+	0.457593i
$329$	537.655	+	537.655i	0.0900970	+	0.0900970i
$330$	224.883	+	224.883i	0.0375134	+	0.0375134i
$331$		−	5517.53i		−	0.916227i	−0.888894	−	0.458113i	$-0.848525\pi$
$331$		−	5517.53i		−	0.916227i	0.888894	−	0.458113i	$-0.151475\pi$
$332$			2066.53i			0.341613i
$333$	−89.8723	−	89.8723i	−0.0147897	−	0.0147897i
$334$	3068.34	+	3068.34i	0.502671	+	0.502671i
$335$	−275.384	+	275.384i	−0.0449129	+	0.0449129i
$336$	906.880			0.147245
$337$	−4890.83	+	4890.83i	−0.790566	+	0.790566i	−0.981586	−	0.191020i	$-0.938820\pi$
$337$	−4890.83	+	4890.83i	−0.790566	+	0.790566i	0.191020	+	0.981586i	$0.438820\pi$
$338$		−	1703.96i		−	0.274211i
$339$	1442.36			0.231086
$340$	72.7820	+	237.846i	0.0116093	+	0.0379382i
$341$	14276.9			2.26727
$342$			2107.70i			0.333250i
$343$	4395.87	−	4395.87i	0.691996	−	0.691996i
$344$	−1557.72			−0.244147
$345$	−351.239	+	351.239i	−0.0548117	+	0.0548117i
$346$	4710.14	+	4710.14i	0.731846	+	0.731846i
$347$	−2668.86	−	2668.86i	−0.412887	−	0.412887i	0.469856	−	0.882743i	$-0.344306\pi$
$347$	−2668.86	−	2668.86i	−0.412887	−	0.412887i	−0.882743	+	0.469856i	$0.844306\pi$
$348$		−	1571.01i		−	0.241997i
$349$		−	529.191i		−	0.0811660i	−0.999176	−	0.0405830i	$-0.987078\pi$
$349$		−	529.191i		−	0.0811660i	0.999176	−	0.0405830i	$-0.0129215\pi$
$350$	−3318.87	−	3318.87i	−0.506861	−	0.506861i
$351$	−700.186	−	700.186i	−0.106476	−	0.106476i
$352$	−1351.94	+	1351.94i	−0.204712	+	0.204712i
$353$	−3779.39			−0.569849			−0.284924	−	0.958550i	$-0.591968\pi$
$353$	−3779.39			−0.569849			−0.284924	+	0.958550i	$0.591968\pi$
$354$	1899.23	−	1899.23i	0.285150	−	0.285150i
$355$			539.445i			0.0806501i
$356$	3285.64			0.489153
$357$	1864.26	−	3508.30i	0.276379	−	0.520109i
$358$	−7082.53			−1.04560
$359$			3764.01i			0.553362i	0.960962	+	0.276681i	$0.0892346\pi$
$359$			3764.01i			0.553362i	−0.960962	+	0.276681i	$0.910765\pi$
$360$	−45.1665	+	45.1665i	−0.00661245	+	0.00661245i
$361$	−6852.11			−0.998996
$362$	−2429.14	+	2429.14i	−0.352687	+	0.352687i
$363$	4749.22	+	4749.22i	0.686692	+	0.686692i
$364$	−1959.83	−	1959.83i	−0.282206	−	0.282206i
$365$			324.153i			0.0464848i
$366$			926.795i			0.132362i
$367$	5235.63	+	5235.63i	0.744680	+	0.744680i	0.973475	−	0.228794i	$-0.0734784\pi$
$367$	5235.63	+	5235.63i	0.744680	+	0.744680i	−0.228794	+	0.973475i	$0.573478\pi$
$368$	−2111.55	−	2111.55i	−0.299110	−	0.299110i
$369$	−3058.04	+	3058.04i	−0.431423	+	0.431423i
$370$	25.0569			0.00352066
$371$	545.598	−	545.598i	0.0763505	−	0.0763505i
$372$			2867.44i			0.399650i
$373$	11940.8			1.65756			0.828779	−	0.559576i	$-0.189036\pi$
$373$	11940.8			1.65756			0.828779	+	0.559576i	$0.189036\pi$
$374$	2450.85	+	8009.19i	0.338852	+	1.10734i
$375$	663.270			0.0913364
$376$		−	321.959i		−	0.0441589i
$377$	−3395.05	+	3395.05i	−0.463804	+	0.463804i
$378$	1020.24			0.138824
$379$	6453.66	−	6453.66i	0.874676	−	0.874676i	−0.118302	−	0.992978i	$-0.537745\pi$
$379$	6453.66	−	6453.66i	0.874676	−	0.874676i	0.992978	+	0.118302i	$0.0377450\pi$
$380$	−293.819	−	293.819i	−0.0396647	−	0.0396647i
$381$	−3193.21	−	3193.21i	−0.429378	−	0.429378i
$382$			3429.14i			0.459293i
$383$			9261.13i			1.23557i	0.786349	+	0.617783i	$0.211969\pi$
$383$			9261.13i			1.23557i	−0.786349	+	0.617783i	$0.788031\pi$
$384$	−271.529	−	271.529i	−0.0360844	−	0.0360844i
$385$	708.133	+	708.133i	0.0937397	+	0.0937397i
$386$	−4942.09	+	4942.09i	−0.651673	+	0.651673i
$387$	−1752.44			−0.230184
$388$	3758.33	−	3758.33i	0.491753	−	0.491753i
$389$		−	1854.73i		−	0.241745i	−0.992668	−	0.120872i	$-0.961431\pi$
$389$		−	1854.73i		−	0.241745i	0.992668	−	0.120872i	$-0.0385692\pi$
$390$	195.216			0.0253465
$391$	−12509.3	+	3827.92i	−1.61796	+	0.495105i
$392$	111.667			0.0143879
$393$		−	3391.99i		−	0.435378i
$394$	−3917.66	+	3917.66i	−0.500936	+	0.500936i
$395$	1183.38			0.150740
$396$	−1520.93	+	1520.93i	−0.193004	+	0.193004i
$397$	6661.82	+	6661.82i	0.842185	+	0.842185i	0.989143	−	0.146958i	$-0.0469483\pi$
$397$	6661.82	+	6661.82i	0.842185	+	0.842185i	−0.146958	+	0.989143i	$0.546948\pi$
$398$	4707.88	+	4707.88i	0.592927	+	0.592927i
$399$			6636.92i			0.832736i
$400$			1987.41i			0.248426i
$401$	2394.37	+	2394.37i	0.298178	+	0.298178i	0.840300	−	0.542122i	$-0.182379\pi$
$401$	2394.37	+	2394.37i	0.298178	+	0.298178i	−0.542122	+	0.840300i	$0.682379\pi$
$402$	−1862.48	−	1862.48i	−0.231074	−	0.231074i
$403$	6196.73	−	6196.73i	0.765958	−	0.765958i
$404$	−3195.91			−0.393570
$405$	−50.8123	+	50.8123i	−0.00623428	+	0.00623428i
$406$		−	4946.93i		−	0.604709i
$407$	843.763			0.102761
$408$	−1608.60	+	492.240i	−0.195190	+	0.0597292i
$409$	−9820.58			−1.18728			−0.593638	−	0.804732i	$-0.702309\pi$
$409$	−9820.58			−1.18728			−0.593638	+	0.804732i	$0.702309\pi$
$410$		−	852.597i		−	0.102699i
$411$	−2289.18	+	2289.18i	−0.274737	+	0.274737i
$412$	236.417			0.0282705
$413$	5980.48	−	5980.48i	0.712542	−	0.712542i
$414$	−2375.50	−	2375.50i	−0.282003	−	0.282003i
$415$	−324.090	−	324.090i	−0.0383348	−	0.0383348i
$416$			1173.58i			0.138317i
$417$		−	2099.51i		−	0.246555i
$418$	−9894.04	−	9894.04i	−1.15773	−	1.15773i
$419$	7003.20	+	7003.20i	0.816537	+	0.816537i	0.985604	−	0.169068i	$-0.0540757\pi$
$419$	7003.20	+	7003.20i	0.816537	+	0.816537i	−0.169068	+	0.985604i	$0.554076\pi$
$420$	−142.224	+	142.224i	−0.0165234	+	0.0165234i
$421$	4639.35			0.537074			0.268537	−	0.963269i	$-0.413460\pi$
$421$	4639.35			0.537074			0.268537	+	0.963269i	$0.413460\pi$
$422$	5474.57	−	5474.57i	0.631512	−	0.631512i
$423$		−	362.204i		−	0.0416334i
$424$	−326.715			−0.0374214
$425$	7688.35	+	4085.49i	0.877505	+	0.466295i
$426$	−3648.38			−0.414940
$427$			2918.38i			0.330750i
$428$	−2289.34	+	2289.34i	−0.258550	+	0.258550i
$429$	6573.67			0.739813
$430$	244.294	−	244.294i	0.0273975	−	0.0273975i
$431$	1789.91	+	1789.91i	0.200039	+	0.200039i	0.800017	−	0.599978i	$-0.204824\pi$
$431$	1789.91	+	1789.91i	0.200039	+	0.200039i	−0.599978	+	0.800017i	$0.704824\pi$
$432$	−305.470	−	305.470i	−0.0340207	−	0.0340207i
$433$			7126.68i			0.790962i	0.918474	+	0.395481i	$0.129422\pi$
$433$			7126.68i			0.790962i	−0.918474	+	0.395481i	$0.870578\pi$
$434$			9029.25i			0.998658i
$435$	246.378	+	246.378i	0.0271561	+	0.0271561i
$436$	4678.68	+	4678.68i	0.513917	+	0.513917i
$437$	15453.2	−	15453.2i	1.69160	−	1.69160i
$438$	−2192.31			−0.239162
$439$	−11492.7	+	11492.7i	−1.24947	+	1.24947i	−0.293509	+	0.955956i	$0.594823\pi$
$439$	−11492.7	+	11492.7i	−1.24947	+	1.24947i	−0.955956	+	0.293509i	$0.905177\pi$
$440$		−	424.044i		−	0.0459443i
$441$	125.626			0.0135650
$442$	4540.05	+	2412.53i	0.488571	+	0.259620i
$443$	9083.04			0.974149			0.487075	−	0.873360i	$-0.338064\pi$
$443$	9083.04			0.974149			0.487075	+	0.873360i	$0.338064\pi$
$444$			169.465i			0.0181136i
$445$	−515.280	+	515.280i	−0.0548912	+	0.0548912i
$446$	10588.7			1.12419
$447$	−2879.35	+	2879.35i	−0.304673	+	0.304673i
$448$	−855.015	−	855.015i	−0.0901689	−	0.0901689i
$449$	−1287.46	−	1287.46i	−0.135321	−	0.135321i	0.636202	−	0.771523i	$-0.280505\pi$
$449$	−1287.46	−	1287.46i	−0.135321	−	0.135321i	−0.771523	+	0.636202i	$0.780505\pi$
$450$			2235.83i			0.234218i
$451$		−	28710.3i		−	2.99759i
$452$	−1359.87	−	1359.87i	−0.141511	−	0.141511i
$453$	−3738.91	−	3738.91i	−0.387791	−	0.387791i
$454$	−7388.63	+	7388.63i	−0.763801	+	0.763801i
$455$	614.712			0.0633366
$456$	1987.16	−	1987.16i	0.204073	−	0.204073i
$457$		−	16585.9i		−	1.69772i	−0.528621	−	0.848858i	$-0.677291\pi$
$457$		−	16585.9i		−	1.69772i	0.528621	−	0.848858i	$-0.322709\pi$
$458$	−3757.01			−0.383304
$459$	−1809.67	+	553.770i	−0.184027	+	0.0563132i
$460$	662.302			0.0671304
$461$		−	7357.94i		−	0.743370i	−0.928359	−	0.371685i	$-0.878780\pi$
$461$		−	7357.94i		−	0.743370i	0.928359	−	0.371685i	$-0.121220\pi$
$462$	−4789.25	+	4789.25i	−0.482286	+	0.482286i
$463$	14132.1			1.41852			0.709258	−	0.704949i	$-0.249030\pi$
$463$	14132.1			1.41852			0.709258	+	0.704949i	$0.249030\pi$
$464$	−1481.16	+	1481.16i	−0.148192	+	0.148192i
$465$	−449.695	−	449.695i	−0.0448475	−	0.0448475i
$466$	2348.30	+	2348.30i	0.233439	+	0.233439i
$467$		−	3807.01i		−	0.377232i	−0.982051	−	0.188616i	$-0.939600\pi$
$467$		−	3807.01i		−	0.377232i	0.982051	−	0.188616i	$-0.0604002\pi$
$468$			1320.28i			0.130406i
$469$	−5864.73	−	5864.73i	−0.577416	−	0.577416i
$470$	50.4922	+	50.4922i	0.00495538	+	0.00495538i
$471$	135.945	−	135.945i	0.0132994	−	0.0132994i
$472$	−3581.23			−0.349236
$473$	8226.35	−	8226.35i	0.799678	−	0.799678i
$474$			8003.42i			0.775547i
$475$	−14544.7			−1.40496
$476$	−5065.30	+	1550.01i	−0.487747	+	0.149253i
$477$	−367.554			−0.0352812
$478$		−	10034.3i		−	0.960168i
$479$	−9933.89	+	9933.89i	−0.947581	+	0.947581i	−0.998693	−	0.0511122i	$-0.983723\pi$
$479$	−9933.89	+	9933.89i	−0.947581	+	0.947581i	0.0511122	+	0.998693i	$0.483723\pi$
$480$	85.1667			0.00809857
$481$	366.225	−	366.225i	0.0347160	−	0.0347160i
$482$	−8304.32	−	8304.32i	−0.784754	−	0.784754i
$483$	−7480.18	−	7480.18i	−0.704679	−	0.704679i
$484$		−	8955.21i		−	0.841023i
$485$			1178.82i			0.110366i
$486$	−343.654	−	343.654i	−0.0320750	−	0.0320750i
$487$	−3604.14	−	3604.14i	−0.335358	−	0.335358i	0.519259	−	0.854617i	$-0.326208\pi$
$487$	−3604.14	−	3604.14i	−0.335358	−	0.335358i	−0.854617	+	0.519259i	$0.826208\pi$
$488$	873.791	−	873.791i	0.0810546	−	0.0810546i
$489$	−7088.92			−0.655567
$490$	−17.5126	+	17.5126i	−0.00161456	+	0.00161456i
$491$			6390.91i			0.587409i	0.955896	+	0.293704i	$0.0948882\pi$
$491$			6390.91i			0.587409i	−0.955896	+	0.293704i	$0.905112\pi$
$492$	5766.29			0.528383
$493$	2685.11	+	8774.72i	0.245297	+	0.801609i
$494$	−8588.77			−0.782241
$495$		−	477.049i		−	0.0433167i
$496$	2703.45	−	2703.45i	0.244735	−	0.244735i
$497$	−11488.3			−1.03687
$498$	2191.89	−	2191.89i	0.197230	−	0.197230i
$499$	3683.71	+	3683.71i	0.330472	+	0.330472i	0.852766	−	0.522293i	$-0.174923\pi$
$499$	3683.71	+	3683.71i	0.330472	+	0.330472i	−0.522293	+	0.852766i	$0.674923\pi$
$500$	−625.337	−	625.337i	−0.0559319	−	0.0559319i
$501$		−	6508.94i		−	0.580435i
$502$		−	13798.3i		−	1.22679i
$503$	7846.34	+	7846.34i	0.695529	+	0.695529i	0.963443	−	0.267914i	$-0.0863344\pi$
$503$	7846.34	+	7846.34i	0.695529	+	0.695529i	−0.267914	+	0.963443i	$0.586334\pi$
$504$	−961.892	−	961.892i	−0.0850121	−	0.0850121i
$505$	501.208	−	501.208i	0.0441652	−	0.0441652i
$506$	22302.3			1.95940
$507$	−1807.32	+	1807.32i	−0.158316	+	0.158316i
$508$			6021.17i			0.525878i
$509$	−2967.70			−0.258430			−0.129215	−	0.991617i	$-0.541246\pi$
$509$	−2967.70			−0.258430			−0.129215	+	0.991617i	$0.541246\pi$
$510$	175.076	−	329.470i	0.0152010	−	0.0286063i
$511$	−6903.36			−0.597625
$512$			512.000i			0.0441942i
$513$	2235.55	−	2235.55i	0.192402	−	0.192402i
$514$	3820.66			0.327864
$515$	−37.0769	+	37.0769i	−0.00317243	+	0.00317243i
$516$	1652.21	+	1652.21i	0.140959	+	0.140959i
$517$	1700.27	+	1700.27i	0.144638	+	0.144638i
$518$			533.626i			0.0452629i
$519$		−	9991.72i		−	0.845063i
$520$	−184.051	−	184.051i	−0.0155215	−	0.0155215i
$521$	212.645	+	212.645i	0.0178813	+	0.0178813i	0.715991	−	0.698110i	$-0.245975\pi$
$521$	212.645	+	212.645i	0.0178813	+	0.0178813i	−0.698110	+	0.715991i	$0.745975\pi$
$522$	−1666.30	+	1666.30i	−0.139717	+	0.139717i
$523$	−6172.53			−0.516073			−0.258036	−	0.966135i	$-0.583075\pi$
$523$	−6172.53			−0.516073			−0.258036	+	0.966135i	$0.583075\pi$
$524$	−3198.00	+	3198.00i	−0.266613	+	0.266613i
$525$			7040.39i			0.585272i
$526$	−5379.99			−0.445967
$527$	−4900.93	−	16015.8i	−0.405100	−	1.32383i
$528$	2867.90			0.236381
$529$			22666.3i			1.86293i
$530$	51.2380	−	51.2380i	0.00419932	−	0.00419932i
$531$	−4028.88			−0.329263
$532$	6257.35	−	6257.35i	0.509944	−	0.509944i
$533$	−12461.3	−	12461.3i	−1.01268	−	1.01268i
$534$	−3484.94	−	3484.94i	−0.282412	−	0.282412i
$535$		−	718.066i		−	0.0580274i
$536$			3511.92i			0.283007i
$537$	7512.15	+	7512.15i	0.603675	+	0.603675i
$538$	−2670.97	−	2670.97i	−0.214040	−	0.214040i
$539$	−589.716	+	589.716i	−0.0471259	+	0.0471259i
$540$	95.8126			0.00763540
$541$	−5979.83	+	5979.83i	−0.475218	+	0.475218i	−0.903599	−	0.428380i	$-0.859084\pi$
$541$	−5979.83	+	5979.83i	−0.475218	+	0.475218i	0.428380	+	0.903599i	$0.359084\pi$
$542$			8345.32i			0.661369i
$543$	5152.99			0.407248
$544$	1980.69	+	1052.51i	0.156105	+	0.0829524i
$545$	−1467.50			−0.115341
$546$			4157.43i			0.325863i
$547$	−2674.04	+	2674.04i	−0.209019	+	0.209019i	−0.803851	−	0.594831i	$-0.797219\pi$
$547$	−2674.04	+	2674.04i	−0.209019	+	0.209019i	0.594831	+	0.803851i	$0.297219\pi$
$548$	4316.52			0.336483
$549$	983.015	−	983.015i	0.0764190	−	0.0764190i
$550$	−10495.5	−	10495.5i	−0.813692	−	0.813692i
$551$	−10839.7	−	10839.7i	−0.838090	−	0.838090i
$552$			4479.28i			0.345382i
$553$			25201.9i			1.93796i
$554$	−1047.32	−	1047.32i	−0.0803186	−	0.0803186i
$555$	−26.5768	−	26.5768i	−0.00203266	−	0.00203266i
$556$	−1979.44	+	1979.44i	−0.150984	+	0.150984i
$557$	−24045.8			−1.82918			−0.914589	−	0.404385i	$-0.867485\pi$
$557$	−24045.8			−1.82918			−0.914589	+	0.404385i	$0.867485\pi$
$558$	3041.38	−	3041.38i	0.230738	−	0.230738i
$559$		−	7141.09i		−	0.540315i
$560$	268.181			0.0202370
$561$	5895.50	−	11094.5i	0.443687	−	0.834959i
$562$	650.111			0.0487959
$563$			13789.7i			1.03227i	0.856507	+	0.516135i	$0.172630\pi$
$563$			13789.7i			1.03227i	−0.856507	+	0.516135i	$0.827370\pi$
$564$	−341.489	+	341.489i	−0.0254952	+	0.0254952i
$565$	426.531			0.0317598
$566$	−6826.53	+	6826.53i	−0.506962	+	0.506962i
$567$	−1082.13	−	1082.13i	−0.0801501	−	0.0801501i
$568$	3439.72	+	3439.72i	0.254098	+	0.254098i
$569$			19638.1i			1.44687i	0.690390	+	0.723437i	$0.257439\pi$
$569$			19638.1i			1.44687i	−0.690390	+	0.723437i	$0.742561\pi$
$570$			623.285i			0.0458009i
$571$	10800.7	+	10800.7i	0.791585	+	0.791585i	0.981752	−	0.190167i	$-0.0609029\pi$
$571$	10800.7	+	10800.7i	0.791585	+	0.791585i	−0.190167	+	0.981752i	$0.560903\pi$
$572$	−6197.71	−	6197.71i	−0.453041	−	0.453041i
$573$	3637.15	−	3637.15i	0.265173	−	0.265173i
$574$	18157.4			1.32034
$575$	16392.6	−	16392.6i	1.18891	−	1.18891i
$576$			576.000i			0.0416667i
$577$	−11093.2			−0.800371			−0.400186	−	0.916434i	$-0.631054\pi$
$577$	−11093.2			−0.800371			−0.400186	+	0.916434i	$0.631054\pi$
$578$	8143.36	−	5498.72i	0.586019	−	0.395704i
$579$	10483.8			0.752487
$580$		−	464.575i		−	0.0332593i
$581$	6902.01	−	6902.01i	0.492846	−	0.492846i
$582$	−7972.62			−0.567828
$583$	1725.38	−	1725.38i	0.122570	−	0.122570i
$584$	2066.93	+	2066.93i	0.146456	+	0.146456i
$585$	−207.057	−	207.057i	−0.0146338	−	0.0146338i
$586$		−	2076.27i		−	0.146365i
$587$		−	9450.73i		−	0.664520i	−0.943188	−	0.332260i	$-0.892189\pi$
$587$		−	9450.73i		−	0.664520i	0.943188	−	0.332260i	$-0.107811\pi$
$588$	−118.441	−	118.441i	−0.00830684	−	0.00830684i
$589$	19784.9	+	19784.9i	1.38408	+	1.38408i
$590$	561.637	−	561.637i	0.0391902	−	0.0391902i
$591$	8310.60			0.578431
$592$	159.773	−	159.773i	0.0110923	−	0.0110923i
$593$			15181.4i			1.05131i	0.850698	+	0.525655i	$0.176180\pi$
$593$			15181.4i			1.05131i	−0.850698	+	0.525655i	$0.823820\pi$
$594$	3226.38			0.222862
$595$	551.296	−	1037.47i	0.0379848	−	0.0714823i
$596$	5429.36			0.373147
$597$		−	9986.93i		−	0.684653i
$598$	9680.03	−	9680.03i	0.661949	−	0.661949i
$599$	−3015.99			−0.205726			−0.102863	−	0.994696i	$-0.532800\pi$
$599$	−3015.99			−0.205726			−0.102863	+	0.994696i	$0.532800\pi$
$600$	2107.96	−	2107.96i	0.143429	−	0.143429i
$601$	−8784.18	−	8784.18i	−0.596197	−	0.596197i	0.343102	−	0.939298i	$-0.388522\pi$
$601$	−8784.18	−	8784.18i	−0.596197	−	0.596197i	−0.939298	+	0.343102i	$0.888522\pi$
$602$	5202.64	+	5202.64i	0.352232	+	0.352232i
$603$			3950.91i			0.266821i
$604$			7050.15i			0.474945i
$605$	1404.43	+	1404.43i	0.0943771	+	0.0943771i
$606$	3389.77	+	3389.77i	0.227228	+	0.227228i
$607$	1724.59	−	1724.59i	0.115319	−	0.115319i	−0.647092	−	0.762412i	$-0.724015\pi$
$607$	1724.59	−	1724.59i	0.115319	−	0.115319i	0.762412	+	0.647092i	$0.224015\pi$
$608$	−3747.02			−0.249937
$609$	−5247.01	+	5247.01i	−0.349129	+	0.349129i
$610$			274.070i			0.0181914i
$611$	1475.96			0.0977266
$612$	2228.28	+	1184.08i	0.147178	+	0.0782083i
$613$	14288.9			0.941477			0.470738	−	0.882273i	$-0.343988\pi$
$613$	14288.9			0.941477			0.470738	+	0.882273i	$0.343988\pi$
$614$		−	13474.3i		−	0.885631i
$615$	−904.316	+	904.316i	−0.0592935	+	0.0592935i
$616$	9030.69			0.590677
$617$	7112.45	−	7112.45i	0.464078	−	0.464078i	−0.435911	−	0.899990i	$-0.643574\pi$
$617$	7112.45	−	7112.45i	0.464078	−	0.464078i	0.899990	+	0.435911i	$0.143574\pi$
$618$	−250.758	−	250.758i	−0.0163220	−	0.0163220i
$619$	18525.5	+	18525.5i	1.20291	+	1.20291i	0.973277	+	0.229634i	$0.0737529\pi$
$619$	18525.5	+	18525.5i	1.20291	+	1.20291i	0.229634	+	0.973277i	$0.426247\pi$
$620$			847.952i			0.0549268i
$621$			5039.19i			0.325629i
$622$	−6714.15	−	6714.15i	−0.432818	−	0.432818i
$623$	−10973.7	−	10973.7i	−0.705702	−	0.705702i
$624$	1244.77	−	1244.77i	0.0798572	−	0.0798572i
$625$	−15330.5			−0.981151
$626$	−8526.19	+	8526.19i	−0.544369	+	0.544369i
$627$			20988.4i			1.33684i
$628$	−256.341			−0.0162884
$629$	−289.643	−	946.530i	−0.0183606	−	0.0600010i
$630$	301.703			0.0190796
$631$			2855.15i			0.180129i	0.995936	+	0.0900647i	$0.0287074\pi$
$631$			2855.15i			0.180129i	−0.995936	+	0.0900647i	$0.971293\pi$
$632$	7545.69	−	7545.69i	0.474923	−	0.474923i
$633$	−11613.3			−0.729207
$634$	9911.61	−	9911.61i	0.620884	−	0.620884i
$635$	−944.288	−	944.288i	−0.0590125	−	0.0590125i
$636$	346.533	+	346.533i	0.0216052	+	0.0216052i
$637$			511.918i			0.0318413i
$638$		−	15644.0i		−	0.970773i
$639$	3869.69	+	3869.69i	0.239566	+	0.239566i
$640$	−80.2960	−	80.2960i	−0.00495934	−	0.00495934i
$641$	−8924.27	+	8924.27i	−0.549902	+	0.549902i	−0.926412	−	0.376510i	$-0.877124\pi$
$641$	−8924.27	+	8924.27i	−0.549902	+	0.549902i	0.376510	+	0.926412i	$0.377124\pi$
$642$	4856.42			0.298548
$643$	−12572.4	+	12572.4i	−0.771084	+	0.771084i	−0.978296	−	0.207212i	$-0.933561\pi$
$643$	−12572.4	+	12572.4i	−0.771084	+	0.771084i	0.207212	+	0.978296i	$0.433561\pi$
$644$			14104.8i			0.863052i
$645$	−518.227			−0.0316359
$646$	−7702.71	+	14495.5i	−0.469132	+	0.882844i
$647$	−2887.24			−0.175439			−0.0877197	−	0.996145i	$-0.527958\pi$
$647$	−2887.24			−0.175439			−0.0877197	+	0.996145i	$0.527958\pi$
$648$			648.000i			0.0392837i
$649$	18912.5	−	18912.5i	1.14388	−	1.14388i
$650$	−9110.90			−0.549783
$651$	9576.96	−	9576.96i	0.576576	−	0.576576i
$652$	6683.50	+	6683.50i	0.401451	+	0.401451i
$653$	18139.5	+	18139.5i	1.08706	+	1.08706i	0.995829	+	0.0912348i	$0.0290814\pi$
$653$	18139.5	+	18139.5i	1.08706	+	1.08706i	0.0912348	+	0.995829i	$0.470919\pi$
$654$		−	9924.97i		−	0.593421i
$655$		−	1003.07i		−	0.0598371i
$656$	−5436.51	−	5436.51i	−0.323567	−	0.323567i
$657$	2325.30	+	2325.30i	0.138080	+	0.138080i
$658$	−1075.31	+	1075.31i	−0.0637082	+	0.0637082i
$659$	−22255.0			−1.31552			−0.657762	−	0.753226i	$-0.728497\pi$
$659$	−22255.0			−1.31552			−0.657762	+	0.753226i	$0.728497\pi$
$660$	−449.766	+	449.766i	−0.0265260	+	0.0265260i
$661$		−	5678.09i		−	0.334118i	−0.985947	−	0.167059i	$-0.946573\pi$
$661$		−	5678.09i		−	0.334118i	0.985947	−	0.167059i	$-0.0534271\pi$
$662$	11035.1			0.647870
$663$	−2256.58	−	7374.32i	−0.132185	−	0.431968i
$664$	−4133.06			−0.241557
$665$			1962.65i			0.114449i
$666$	179.745	−	179.745i	0.0104579	−	0.0104579i
$667$	24434.0			1.41842
$668$	−6136.69	+	6136.69i	−0.355442	+	0.355442i
$669$	−11231.0	−	11231.0i	−0.649054	−	0.649054i
$670$	−550.767	−	550.767i	−0.0317582	−	0.0317582i
$671$			9229.00i			0.530971i
$672$			1813.76i			0.104118i
$673$	−4858.59	−	4858.59i	−0.278284	−	0.278284i	0.554140	−	0.832423i	$-0.313047\pi$
$673$	−4858.59	−	4858.59i	−0.278284	−	0.278284i	−0.832423	+	0.554140i	$0.813047\pi$
$674$	−9781.66	−	9781.66i	−0.559014	−	0.559014i
$675$	2371.46	−	2371.46i	0.135226	−	0.135226i
$676$	3407.92			0.193896
$677$	−7021.42	+	7021.42i	−0.398604	+	0.398604i	−0.877741	−	0.479136i	$-0.840950\pi$
$677$	−7021.42	+	7021.42i	−0.398604	+	0.398604i	0.479136	+	0.877741i	$0.340950\pi$
$678$			2884.71i			0.163402i
$679$	−25104.9			−1.41891
$680$	−475.691	+	145.564i	−0.0268264	+	0.00820901i
$681$	15673.7			0.881962
$682$			28553.9i			1.60320i
$683$	−3467.32	+	3467.32i	−0.194251	+	0.194251i	−0.797530	−	0.603279i	$-0.793860\pi$
$683$	−3467.32	+	3467.32i	−0.194251	+	0.194251i	0.603279	+	0.797530i	$0.293860\pi$
$684$	−4215.40			−0.235643
$685$	−676.952	+	676.952i	−0.0377591	+	0.0377591i
$686$	8791.74	+	8791.74i	0.489315	+	0.489315i
$687$	3984.91	+	3984.91i	0.221301	+	0.221301i
$688$		−	3115.44i		−	0.172638i
$689$		−	1497.76i		−	0.0828160i
$690$	−702.477	−	702.477i	−0.0387577	−	0.0387577i
$691$	−1652.39	−	1652.39i	−0.0909692	−	0.0909692i	0.660158	−	0.751127i	$-0.270489\pi$
$691$	−1652.39	−	1652.39i	−0.0909692	−	0.0909692i	−0.751127	+	0.660158i	$0.770489\pi$
$692$	−9420.28	+	9420.28i	−0.517493	+	0.517493i
$693$	10159.5			0.556895
$694$	5337.71	−	5337.71i	0.291955	−	0.291955i
$695$		−	620.863i		−	0.0338858i
$696$	3142.01			0.171117
$697$	−32207.1	+	9855.54i	−1.75026	+	0.535589i
$698$	1058.38			0.0573930
$699$		−	4981.49i		−	0.269552i
$700$	6637.75	−	6637.75i	0.358405	−	0.358405i
$701$	11924.7			0.642498			0.321249	−	0.946995i	$-0.395897\pi$
$701$	11924.7			0.642498			0.321249	+	0.946995i	$0.395897\pi$
$702$	1400.37	−	1400.37i	0.0752900	−	0.0752900i
$703$	1169.28	+	1169.28i	0.0627316	+	0.0627316i
$704$	−2703.88	−	2703.88i	−0.144753	−	0.144753i
$705$		−	107.110i		−	0.00572198i
$706$		−	7558.78i		−	0.402944i
$707$	10674.0	+	10674.0i	0.567804	+	0.567804i
$708$	3798.47	+	3798.47i	0.201631	+	0.201631i
$709$	−5684.64	+	5684.64i	−0.301116	+	0.301116i	−0.841450	−	0.540334i	$-0.818298\pi$
$709$	−5684.64	+	5684.64i	−0.301116	+	0.301116i	0.540334	+	0.841450i	$0.318298\pi$
$710$	−1078.89			−0.0570282
$711$	8488.91	−	8488.91i	0.447762	−	0.447762i
$712$			6571.27i			0.345883i
$713$	−44597.4			−2.34248
$714$	7016.59	+	3728.53i	0.367772	+	0.195430i
$715$	1943.95			0.101678
$716$		−	14165.1i		−	0.739348i
$717$	−10643.0	+	10643.0i	−0.554353	+	0.554353i
$718$	−7528.03			−0.391286
$719$	11496.3	−	11496.3i	0.596299	−	0.596299i	−0.343027	−	0.939326i	$-0.611452\pi$
$719$	11496.3	−	11496.3i	0.596299	−	0.596299i	0.939326	+	0.343027i	$0.111452\pi$
$720$	−90.3330	−	90.3330i	−0.00467571	−	0.00467571i
$721$	−789.611	−	789.611i	−0.0407859	−	0.0407859i
$722$		−	13704.2i		−	0.706397i
$723$			17616.1i			0.906156i
$724$	−4858.28	−	4858.28i	−0.249388	−	0.249388i
$725$	−11498.7	−	11498.7i	−0.589036	−	0.589036i
$726$	−9498.44	+	9498.44i	−0.485565	+	0.485565i
$727$	32634.5			1.66485			0.832426	−	0.554136i	$-0.186951\pi$
$727$	32634.5			1.66485			0.832426	+	0.554136i	$0.186951\pi$
$728$	3919.66	−	3919.66i	0.199550	−	0.199550i
$729$			729.000i			0.0370370i
$730$	−648.306			−0.0328697
$731$	−12052.2	−	6404.38i	−0.609804	−	0.324042i
$732$	−1853.59			−0.0935938
$733$		−	30175.2i		−	1.52053i	−0.649614	−	0.760264i	$-0.725070\pi$
$733$		−	30175.2i		−	1.52053i	0.649614	−	0.760264i	$-0.274930\pi$
$734$	−10471.3	+	10471.3i	−0.526568	+	0.526568i
$735$	37.1497			0.00186434
$736$	4223.11	−	4223.11i	0.211502	−	0.211502i
$737$	−18546.5	−	18546.5i	−0.926958	−	0.926958i
$738$	−6116.07	−	6116.07i	−0.305062	−	0.305062i
$739$		−	25108.8i		−	1.24985i	−0.780684	−	0.624926i	$-0.785129\pi$
$739$		−	25108.8i		−	1.24985i	0.780684	−	0.624926i	$-0.214871\pi$
$740$			50.1138i			0.00248948i
$741$	9109.76	+	9109.76i	0.451627	+	0.451627i
$742$	1091.20	+	1091.20i	0.0539879	+	0.0539879i
$743$	−2678.14	+	2678.14i	−0.132236	+	0.132236i	−0.770127	−	0.637891i	$-0.779807\pi$
$743$	−2678.14	+	2678.14i	−0.132236	+	0.132236i	0.637891	+	0.770127i	$0.279807\pi$
$744$	−5734.88			−0.282595
$745$	−851.476	+	851.476i	−0.0418734	+	0.0418734i
$746$			23881.5i			1.17207i
$747$	−4649.69			−0.227742
$748$	−16018.4	+	4901.71i	−0.783008	+	0.239605i
$749$	15292.3			0.746022
$750$			1326.54i			0.0645846i
$751$	25642.8	−	25642.8i	1.24596	−	1.24596i	0.288478	−	0.957487i	$-0.406851\pi$
$751$	25642.8	−	25642.8i	1.24596	−	1.24596i	0.957487	−	0.288478i	$-0.0931491\pi$
$752$	643.918			0.0312251
$753$	−14635.3	+	14635.3i	−0.708289	+	0.708289i
$754$	−6790.10	−	6790.10i	−0.327959	−	0.327959i
$755$	−1105.66	−	1105.66i	−0.0532969	−	0.0532969i
$756$			2040.48i			0.0981635i
$757$		−	19664.2i		−	0.944132i	−0.881563	−	0.472066i	$-0.843508\pi$
$757$		−	19664.2i		−	0.944132i	0.881563	−	0.472066i	$-0.156492\pi$
$758$	12907.3	+	12907.3i	0.618489	+	0.618489i
$759$	−23655.1	−	23655.1i	−1.13126	−	1.13126i
$760$	587.638	−	587.638i	0.0280472	−	0.0280472i
$761$	9962.11			0.474542			0.237271	−	0.971444i	$-0.423747\pi$
$761$	9962.11			0.474542			0.237271	+	0.971444i	$0.423747\pi$
$762$	6386.41	−	6386.41i	0.303616	−	0.303616i
$763$		−	31252.7i		−	1.48286i
$764$	−6858.27			−0.324769
$765$	−535.153	+	163.760i	−0.0252921	+	0.00773953i
$766$	−18522.3			−0.873677
$767$		−	16417.5i		−	0.772882i
$768$	543.058	−	543.058i	0.0255155	−	0.0255155i
$769$	−5619.91			−0.263536			−0.131768	−	0.991281i	$-0.542065\pi$
$769$	−5619.91			−0.263536			−0.131768	+	0.991281i	$0.542065\pi$
$770$	−1416.27	+	1416.27i	−0.0662840	+	0.0662840i
$771$	−4052.42	−	4052.42i	−0.189292	−	0.189292i
$772$	−9884.18	−	9884.18i	−0.460802	−	0.460802i
$773$			10503.4i			0.488722i	0.969684	+	0.244361i	$0.0785783\pi$
$773$			10503.4i			0.488722i	−0.969684	+	0.244361i	$0.921422\pi$
$774$		−	3504.87i		−	0.162765i
$775$	20987.7	+	20987.7i	0.972774	+	0.972774i
$776$	7516.66	+	7516.66i	0.347722	+	0.347722i
$777$	565.996	−	565.996i	0.0261325	−	0.0261325i
$778$	3709.47			0.170939
$779$	39786.6	−	39786.6i	1.82991	−	1.82991i
$780$			390.431i			0.0179227i
$781$	−36330.4			−1.66454
$782$	−7655.84	−	25018.6i	−0.350092	−	1.14407i
$783$	3534.77			0.161331
$784$			223.334i			0.0101738i
$785$	40.2014	−	40.2014i	0.00182784	−	0.00182784i
$786$	6783.99			0.307859
$787$	10847.6	−	10847.6i	0.491327	−	0.491327i	−0.417397	−	0.908724i	$-0.637058\pi$
$787$	10847.6	−	10847.6i	0.491327	−	0.491327i	0.908724	+	0.417397i	$0.137058\pi$
$788$	−7835.31	−	7835.31i	−0.354215	−	0.354215i
$789$	5706.34	+	5706.34i	0.257479	+	0.257479i
$790$			2366.75i			0.106589i
$791$			9083.65i			0.408315i
$792$	−3041.86	−	3041.86i	−0.136475	−	0.136475i
$793$	4005.73	+	4005.73i	0.179379	+	0.179379i
$794$	−13323.6	+	13323.6i	−0.595514	+	0.595514i
$795$	−108.692			−0.00484895
$796$	−9415.77	+	9415.77i	−0.419263	+	0.419263i
$797$			14361.1i			0.638266i	0.947710	+	0.319133i	$0.103392\pi$
$797$			14361.1i			0.638266i	−0.947710	+	0.319133i	$0.896608\pi$
$798$	−13273.8			−0.588833
$799$	1323.69	−	2491.02i	0.0586094	−	0.110295i
$800$	−3974.81			−0.175664
$801$			7392.68i			0.326102i
$802$	−4788.74	+	4788.74i	−0.210843	+	0.210843i
$803$	−21831.0			−0.959401
$804$	3724.95	−	3724.95i	0.163394	−	0.163394i
$805$	−2212.02	−	2212.02i	−0.0968492	−	0.0968492i
$806$	12393.5	+	12393.5i	0.541614	+	0.541614i
$807$			5665.98i			0.247152i
$808$		−	6391.81i		−	0.278296i
$809$	1637.58	+	1637.58i	0.0711671	+	0.0711671i	0.741794	−	0.670627i	$-0.233975\pi$
$809$	1637.58	+	1637.58i	0.0711671	+	0.0711671i	−0.670627	+	0.741794i	$0.733975\pi$
$810$	−101.625	−	101.625i	−0.00440830	−	0.00440830i
$811$	−9288.28	+	9288.28i	−0.402165	+	0.402165i	−0.878995	−	0.476831i	$-0.841786\pi$
$811$	−9288.28	+	9288.28i	−0.402165	+	0.402165i	0.476831	+	0.878995i	$0.341786\pi$
$812$	9893.86			0.427594
$813$	8851.55	−	8851.55i	0.381842	−	0.381842i
$814$			1687.53i			0.0726631i
$815$	−2096.32			−0.0900993
$816$	−984.480	−	3217.20i	−0.0422349	−	0.138020i
$817$	22800.1			0.976345
$818$		−	19641.2i		−	0.839531i
$819$	4409.62	−	4409.62i	0.188137	−	0.188137i
$820$	1705.19			0.0726195
$821$	27821.9	−	27821.9i	1.18269	−	1.18269i	0.203651	−	0.979043i	$-0.434719\pi$
$821$	27821.9	−	27821.9i	1.18269	−	1.18269i	0.979043	−	0.203651i	$-0.0652809\pi$
$822$	−4578.36	−	4578.36i	−0.194269	−	0.194269i
$823$	18037.7	+	18037.7i	0.763981	+	0.763981i	0.977039	−	0.213059i	$-0.0683426\pi$
$823$	18037.7	+	18037.7i	0.763981	+	0.763981i	−0.213059	+	0.977039i	$0.568343\pi$
$824$			472.834i			0.0199903i
$825$			22264.4i			0.939570i
$826$	11961.0	+	11961.0i	0.503844	+	0.503844i
$827$	26547.7	+	26547.7i	1.11627	+	1.11627i	0.992284	+	0.123984i	$0.0395672\pi$
$827$	26547.7	+	26547.7i	1.11627	+	1.11627i	0.123984	+	0.992284i	$0.460433\pi$
$828$	4751.00	−	4751.00i	0.199406	−	0.199406i
$829$	14101.2			0.590778			0.295389	−	0.955377i	$-0.404551\pi$
$829$	14101.2			0.590778			0.295389	+	0.955377i	$0.404551\pi$
$830$	648.180	−	648.180i	0.0271068	−	0.0271068i
$831$			2221.71i			0.0927439i
$832$	−2347.17			−0.0978046
$833$	863.977	+	459.106i	0.0359364	+	0.0190961i
$834$	4199.02			0.174341
$835$		−	1924.81i		−	0.0797734i
$836$	19788.1	−	19788.1i	0.818642	−	0.818642i
$837$	−6451.74			−0.266433
$838$	−14006.4	+	14006.4i	−0.577379	+	0.577379i
$839$	25296.6	+	25296.6i	1.04093	+	1.04093i	0.999126	+	0.0418004i	$0.0133094\pi$
$839$	25296.6	+	25296.6i	1.04093	+	1.04093i	0.0418004	+	0.999126i	$0.486691\pi$
$840$	−284.449	−	284.449i	−0.0116838	−	0.0116838i
$841$			7249.68i			0.297252i
$842$			9278.70i			0.379769i
$843$	−689.547	−	689.547i	−0.0281723	−	0.0281723i
$844$	10949.1	+	10949.1i	0.446546	+	0.446546i
$845$	−534.457	+	534.457i	−0.0217584	+	0.0217584i
$846$	724.407			0.0294393
$847$	−29909.5	+	29909.5i	−1.21335	+	1.21335i
$848$		−	653.429i		−	0.0264609i
$849$	14481.2			0.585389
$850$	−8170.98	+	15376.7i	−0.329720	+	0.620490i
$851$	−2635.70			−0.106170
$852$		−	7296.75i		−	0.293407i
$853$	2228.52	−	2228.52i	0.0894527	−	0.0894527i	−0.660964	−	0.750417i	$-0.729853\pi$
$853$	2228.52	−	2228.52i	0.0894527	−	0.0894527i	0.750417	+	0.660964i	$0.229853\pi$
$854$	−5836.75			−0.233875
$855$	661.093	−	661.093i	0.0264432	−	0.0264432i
$856$	−4578.68	−	4578.68i	−0.182823	−	0.182823i
$857$	−16676.2	−	16676.2i	−0.664701	−	0.664701i	0.291784	−	0.956484i	$-0.405751\pi$
$857$	−16676.2	−	16676.2i	−0.664701	−	0.664701i	−0.956484	+	0.291784i	$0.905751\pi$
$858$			13147.3i			0.523127i
$859$		−	36967.7i		−	1.46836i	−0.678954	−	0.734181i	$-0.737567\pi$
$859$		−	36967.7i		−	1.46836i	0.678954	−	0.734181i	$-0.262433\pi$
$860$	488.589	+	488.589i	0.0193730	+	0.0193730i
$861$	−19258.8	−	19258.8i	−0.762299	−	0.762299i
$862$	−3579.81	+	3579.81i	−0.141449	+	0.141449i
$863$	46451.4			1.83224			0.916120	−	0.400905i	$-0.131304\pi$
$863$	46451.4			1.83224			0.916120	+	0.400905i	$0.131304\pi$
$864$	610.940	−	610.940i	0.0240563	−	0.0240563i
$865$		−	2954.73i		−	0.116143i
$866$	−14253.4			−0.559295
$867$	−14469.6	−	2805.06i	−0.566798	−	0.109879i
$868$	−18058.5			−0.706158
$869$			79697.8i			3.11112i
$870$	−492.756	+	492.756i	−0.0192023	+	0.0192023i
$871$	−16099.7			−0.626313
$872$	−9357.36	+	9357.36i	−0.363395	+	0.363395i
$873$	8456.24	+	8456.24i	0.327835	+	0.327835i
$874$	30906.4	+	30906.4i	1.19614	+	1.19614i
$875$			4177.13i			0.161386i
$876$		−	4384.63i		−	0.169113i
$877$	−20316.0	−	20316.0i	−0.782237	−	0.782237i	0.197971	−	0.980208i	$-0.436565\pi$
$877$	−20316.0	−	20316.0i	−0.782237	−	0.782237i	−0.980208	+	0.197971i	$0.936565\pi$
$878$	−22985.3	−	22985.3i	−0.883506	−	0.883506i
$879$	−2202.21	+	2202.21i	−0.0845038	+	0.0845038i
$880$	848.088			0.0324875
$881$	−18664.0	+	18664.0i	−0.713743	+	0.713743i	−0.967316	−	0.253574i	$-0.918394\pi$
$881$	−18664.0	+	18664.0i	−0.713743	+	0.713743i	0.253574	+	0.967316i	$0.418394\pi$
$882$			251.251i			0.00959191i
$883$	−29247.0			−1.11466			−0.557328	−	0.830293i	$-0.688173\pi$
$883$	−29247.0			−1.11466			−0.557328	+	0.830293i	$0.688173\pi$
$884$	−4825.05	+	9080.10i	−0.183579	+	0.345472i
$885$	−1191.41			−0.0452530
$886$			18166.1i			0.688828i
$887$	25818.9	−	25818.9i	0.977353	−	0.977353i	−0.0223957	−	0.999749i	$-0.507129\pi$
$887$	25818.9	−	25818.9i	0.977353	−	0.977353i	0.999749	+	0.0223957i	$0.00712937\pi$
$888$	−338.930			−0.0128083
$889$	20110.1	−	20110.1i	0.758686	−	0.758686i
$890$	−1030.56	−	1030.56i	−0.0388140	−	0.0388140i
$891$	−3422.10	−	3422.10i	−0.128669	−	0.128669i
$892$			21177.4i			0.794925i
$893$			4712.45i			0.176591i
$894$	−5758.71	−	5758.71i	−0.215436	−	0.215436i
$895$	2221.48	+	2221.48i	0.0829674	+	0.0829674i
$896$	1710.03	−	1710.03i	0.0637590	−	0.0637590i
$897$	−20534.4			−0.764353
$898$	2574.92	−	2574.92i	0.0956864	−	0.0956864i
$899$			31283.1i			1.16057i
$900$	−4471.67			−0.165617
$901$	−2527.81	−	1343.25i	−0.0934669	−	0.0496671i
$902$	57420.5			2.11962
$903$		−	11036.5i		−	0.406723i
$904$	2719.73	−	2719.73i	0.100063	−	0.100063i
$905$	1523.83			0.0559711
$906$	7477.81	−	7477.81i	0.274209	−	0.274209i
$907$	3588.37	+	3588.37i	0.131367	+	0.131367i	0.769733	−	0.638366i	$-0.220389\pi$
$907$	3588.37	+	3588.37i	0.131367	+	0.131367i	−0.638366	+	0.769733i	$0.720389\pi$
$908$	−14777.3	−	14777.3i	−0.540089	−	0.540089i
$909$		−	7190.79i		−	0.262380i
$910$			1229.42i			0.0447858i
$911$	−924.244	−	924.244i	−0.0336131	−	0.0336131i	0.690100	−	0.723714i	$-0.257566\pi$
$911$	−924.244	−	924.244i	−0.0336131	−	0.0336131i	−0.723714	+	0.690100i	$0.757566\pi$
$912$	3974.32	+	3974.32i	0.144301	+	0.144301i
$913$	21826.7	−	21826.7i	0.791193	−	0.791193i
$914$	33171.8			1.20047
$915$	290.695	−	290.695i	0.0105028	−	0.0105028i
$916$		−	7514.02i		−	0.271037i
$917$	21362.0			0.769287
$918$	−1107.54	−	3619.35i	−0.0398194	−	0.130127i
$919$	−34616.0			−1.24252			−0.621260	−	0.783605i	$-0.713379\pi$
$919$	−34616.0			−1.24252			−0.621260	+	0.783605i	$0.713379\pi$
$920$			1324.60i			0.0474684i
$921$	−14291.6	+	14291.6i	−0.511319	+	0.511319i
$922$	14715.9			0.525642
$923$	−15768.8	+	15768.8i	−0.562335	+	0.562335i
$924$	−9578.49	−	9578.49i	−0.341027	−	0.341027i
$925$	1240.37	+	1240.37i	0.0440897	+	0.0440897i
$926$			28264.1i			1.00304i
$927$			531.939i			0.0188470i
$928$	−2962.32	−	2962.32i	−0.104788	−	0.104788i
$929$	8614.76	+	8614.76i	0.304242	+	0.304242i	0.842671	−	0.538429i	$-0.180982\pi$
$929$	8614.76	+	8614.76i	0.304242	+	0.304242i	−0.538429	+	0.842671i	$0.680982\pi$
$930$	899.389	−	899.389i	0.0317120	−	0.0317120i
$931$	−1634.45			−0.0575370
$932$	−4696.59	+	4696.59i	−0.165066	+	0.165066i
$933$			14242.9i			0.499776i
$934$	7614.02			0.266743
$935$	1743.40	−	3280.86i	0.0609791	−	0.114755i
$936$	−2640.57			−0.0922111
$937$			37258.1i			1.29901i	0.760359	+	0.649503i	$0.225023\pi$
$937$			37258.1i			1.29901i	−0.760359	+	0.649503i	$0.774977\pi$
$938$	11729.5	−	11729.5i	0.408295	−	0.408295i
$939$	18086.8			0.628583
$940$	−100.984	+	100.984i	−0.00350398	+	0.00350398i
$941$	−22818.6	−	22818.6i	−0.790505	−	0.790505i	0.191071	−	0.981576i	$-0.438804\pi$
$941$	−22818.6	−	22818.6i	−0.790505	−	0.790505i	−0.981576	+	0.191071i	$0.938804\pi$
$942$	271.891	+	271.891i	0.00940411	+	0.00940411i
$943$			89683.4i			3.09702i
$944$		−	7162.46i		−	0.246947i
$945$	−320.005	−	320.005i	−0.0110156	−	0.0110156i
$946$	16452.7	+	16452.7i	0.565458	+	0.565458i
$947$	19534.7	−	19534.7i	0.670318	−	0.670318i	−0.287471	−	0.957789i	$-0.592814\pi$
$947$	19534.7	−	19534.7i	0.670318	−	0.670318i	0.957789	+	0.287471i	$0.0928145\pi$
$948$	−16006.8			−0.548394
$949$	−9475.47	+	9475.47i	−0.324117	+	0.324117i
$950$		−	29089.3i		−	0.993454i
$951$	−21025.7			−0.716935
$952$	−3100.02	−	10130.6i	−0.105538	−	0.344889i
$953$	34202.3			1.16256			0.581281	−	0.813703i	$-0.302552\pi$
$953$	34202.3			1.16256			0.581281	+	0.813703i	$0.302552\pi$
$954$		−	735.108i		−	0.0249476i
$955$	1075.57	−	1075.57i	0.0364446	−	0.0364446i
$956$	20068.7			0.678941
$957$	−16593.0	+	16593.0i	−0.560476	+	0.560476i
$958$	−19867.8	−	19867.8i	−0.670041	−	0.670041i
$959$	−14416.8	−	14416.8i	−0.485445	−	0.485445i
$960$			170.333i			0.00572655i
$961$		−	27307.6i		−	0.916640i
$962$	732.449	+	732.449i	0.0245479	+	0.0245479i
$963$	−5151.02	−	5151.02i	−0.172367	−	0.172367i
$964$	16608.6	−	16608.6i	0.554905	−	0.554905i
$965$	3100.23			0.103420
$966$	14960.4	−	14960.4i	0.498284	−	0.498284i
$967$			12249.7i			0.407367i	0.979037	+	0.203684i	$0.0652914\pi$
$967$			12249.7i			0.407367i	−0.979037	+	0.203684i	$0.934709\pi$
$968$	17910.4			0.594693
$969$	23544.7	−	7204.82i	0.780564	−	0.238857i
$970$	−2357.64			−0.0780406
$971$		−	10482.5i		−	0.346445i	−0.984883	−	0.173222i	$-0.944582\pi$
$971$		−	10482.5i		−	0.346445i	0.984883	−	0.173222i	$-0.0554180\pi$
$972$	687.308	−	687.308i	0.0226805	−	0.0226805i
$973$	13222.3			0.435649
$974$	7208.28	−	7208.28i	0.237134	−	0.237134i
$975$	9663.57	+	9663.57i	0.317417	+	0.317417i
$976$	1747.58	+	1747.58i	0.0573143	+	0.0573143i
$977$		−	47676.1i		−	1.56120i	−0.625031	−	0.780600i	$-0.714914\pi$
$977$		−	47676.1i		−	1.56120i	0.625031	−	0.780600i	$-0.285086\pi$
$978$		−	14177.8i		−	0.463556i
$979$	−34703.0	−	34703.0i	−1.13290	−	1.13290i
$980$	−35.0251	−	35.0251i	−0.00114167	−	0.00114167i
$981$	−10527.0	+	10527.0i	−0.342612	+	0.342612i
$982$	−12781.8			−0.415361
$983$	−26910.2	+	26910.2i	−0.873145	+	0.873145i	−0.992814	−	0.119669i	$-0.961817\pi$
$983$	−26910.2	+	26910.2i	−0.873145	+	0.873145i	0.119669	+	0.992814i	$0.461817\pi$
$984$			11532.6i			0.373623i
$985$	2457.59			0.0794979
$986$	−17549.4	+	5370.22i	−0.566823	+	0.173451i
$987$	2281.08			0.0735639
$988$		−	17177.5i		−	0.553128i
$989$	−25697.0	+	25697.0i	−0.826205	+	0.826205i
$990$	954.099			0.0306295
$991$	−17817.0	+	17817.0i	−0.571116	+	0.571116i	−0.932440	−	0.361325i	$-0.882325\pi$
$991$	−17817.0	+	17817.0i	−0.571116	+	0.571116i	0.361325	+	0.932440i	$0.382325\pi$
$992$	5406.89	+	5406.89i	0.173053	+	0.173053i
$993$	−11704.5	−	11704.5i	−0.374048	−	0.374048i
$994$		−	22976.7i		−	0.733175i
$995$		−	2953.31i		−	0.0940968i
$996$	4383.77	+	4383.77i	0.139463	+	0.139463i
$997$	9887.89	+	9887.89i	0.314095	+	0.314095i	0.846494	−	0.532399i	$-0.178709\pi$
$997$	9887.89	+	9887.89i	0.314095	+	0.314095i	−0.532399	+	0.846494i	$0.678709\pi$
$998$	−7367.43	+	7367.43i	−0.233679	+	0.233679i
$999$	−381.296			−0.0120757

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	102.4.f.c.55.5	yes	12
3.2	odd	2		306.4.g.g.55.4		12
17.8	even	8		1734.4.a.bd.1.4		6
17.9	even	8		1734.4.a.be.1.3		6
17.13	even	4	inner	102.4.f.c.13.5	✓	12
51.47	odd	4		306.4.g.g.217.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
102.4.f.c.13.5	✓	12	17.13	even	4	inner
102.4.f.c.55.5	yes	12	1.1	even	1	trivial
306.4.g.g.55.4		12	3.2	odd	2
306.4.g.g.217.4		12	51.47	odd	4
1734.4.a.bd.1.4		6	17.8	even	8
1734.4.a.be.1.3		6	17.9	even	8

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:	\( N \)	\(=\)	\( 102 = 2 \cdot 3 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	102.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+2.00000i q^{2} +(2.12132 - 2.12132i) q^{3} -4.00000 q^{4} +(0.627312 - 0.627312i) q^{5} +(4.24264 + 4.24264i) q^{6} +(13.3596 + 13.3596i) q^{7} -8.00000i q^{8} -9.00000i q^{9} +(1.25462 + 1.25462i) q^{10} +(42.2481 + 42.2481i) q^{11} +(-8.48528 + 8.48528i) q^{12} +36.6745 q^{13} +(-26.7192 + 26.7192i) q^{14} -2.66146i q^{15} +16.0000 q^{16} +(32.8910 - 61.8965i) q^{17} +18.0000 q^{18} +117.094i q^{19} +(-2.50925 + 2.50925i) q^{20} +56.6800 q^{21} +(-84.4962 + 84.4962i) q^{22} +(-131.972 - 131.972i) q^{23} +(-16.9706 - 16.9706i) q^{24} +124.213i q^{25} +73.3490i q^{26} +(-19.0919 - 19.0919i) q^{27} +(-53.4384 - 53.4384i) q^{28} +(-92.5725 + 92.5725i) q^{29} +5.32292 q^{30} +(168.965 - 168.965i) q^{31} +32.0000i q^{32} +179.243 q^{33} +(123.793 + 65.7820i) q^{34} +16.7613 q^{35} +36.0000i q^{36} +(9.98581 - 9.98581i) q^{37} -234.189 q^{38} +(77.7984 - 77.7984i) q^{39} +(-5.01850 - 5.01850i) q^{40} +(-339.782 - 339.782i) q^{41} +113.360i q^{42} -194.715i q^{43} +(-168.992 - 168.992i) q^{44} +(-5.64581 - 5.64581i) q^{45} +(263.944 - 263.944i) q^{46} +40.2448 q^{47} +(33.9411 - 33.9411i) q^{48} +13.9584i q^{49} -248.426 q^{50} +(-61.5300 - 201.075i) q^{51} -146.698 q^{52} -40.8393i q^{53} +(38.1838 - 38.1838i) q^{54} +53.0055 q^{55} +(106.877 - 106.877i) q^{56} +(248.395 + 248.395i) q^{57} +(-185.145 - 185.145i) q^{58} -447.653i q^{59} +10.6458i q^{60} +(109.224 + 109.224i) q^{61} +(337.931 + 337.931i) q^{62} +(120.236 - 120.236i) q^{63} -64.0000 q^{64} +(23.0064 - 23.0064i) q^{65} +358.487i q^{66} -438.990 q^{67} +(-131.564 + 247.586i) q^{68} -559.910 q^{69} +33.5226i q^{70} +(-429.965 + 429.965i) q^{71} -72.0000 q^{72} +(-258.367 + 258.367i) q^{73} +(19.9716 + 19.9716i) q^{74} +(263.495 + 263.495i) q^{75} -468.378i q^{76} +1128.84i q^{77} +(155.597 + 155.597i) q^{78} +(943.212 + 943.212i) q^{79} +(10.0370 - 10.0370i) q^{80} -81.0000 q^{81} +(679.563 - 679.563i) q^{82} -516.632i q^{83} -226.720 q^{84} +(-18.1955 - 59.4614i) q^{85} +389.430 q^{86} +392.752i q^{87} +(337.985 - 337.985i) q^{88} -821.409 q^{89} +(11.2916 - 11.2916i) q^{90} +(489.957 + 489.957i) q^{91} +(527.888 + 527.888i) q^{92} -716.860i q^{93} +80.4897i q^{94} +(73.4548 + 73.4548i) q^{95} +(67.8823 + 67.8823i) q^{96} +(-939.582 + 939.582i) q^{97} -27.9168 q^{98} +(380.233 - 380.233i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 48 q^{4} + 16 q^{5} - 12 q^{7} + 32 q^{10} - 32 q^{11} - 68 q^{13} + 24 q^{14} + 192 q^{16} + 64 q^{17} + 216 q^{18} - 64 q^{20} - 168 q^{21} + 64 q^{22} - 112 q^{23} + 48 q^{28} - 296 q^{29} - 168 q^{30}+ \cdots - 288 q^{99}+O(q^{100}) \) 12 * q - 48 * q^4 + 16 * q^5 - 12 * q^7 + 32 * q^10 - 32 * q^11 - 68 * q^13 + 24 * q^14 + 192 * q^16 + 64 * q^17 + 216 * q^18 - 64 * q^20 - 168 * q^21 + 64 * q^22 - 112 * q^23 + 48 * q^28 - 296 * q^29 - 168 * q^30 + 520 * q^31 + 204 * q^33 + 144 * q^34 + 392 * q^35 - 828 * q^37 - 280 * q^38 + 312 * q^39 - 128 * q^40 + 8 * q^41 + 128 * q^44 - 144 * q^45 + 224 * q^46 - 2920 * q^47 + 752 * q^50 + 420 * q^51 + 272 * q^52 + 1156 * q^55 - 96 * q^56 + 312 * q^57 - 592 * q^58 - 1124 * q^61 + 1040 * q^62 - 108 * q^63 - 768 * q^64 + 3288 * q^65 - 2008 * q^67 - 256 * q^68 + 468 * q^69 - 2184 * q^71 - 864 * q^72 + 2456 * q^73 - 1656 * q^74 - 192 * q^75 + 624 * q^78 + 2652 * q^79 + 256 * q^80 - 972 * q^81 - 16 * q^82 + 672 * q^84 + 3444 * q^85 - 184 * q^86 - 256 * q^88 + 5304 * q^89 + 288 * q^90 - 1420 * q^91 + 448 * q^92 - 2920 * q^95 + 2688 * q^97 - 4168 * q^98 - 288 * q^99

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