LMFDB - Embedded newform 51.4.e.a.4.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(51, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3]))

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

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

chi := DirichletCharacter("51.4");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 51 = 3 \cdot 17 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	51.e (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:	$3.00909741029$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 88 x^{14} + 3086 x^{12} + 54880 x^{10} + 516641 x^{8} + 2403800 x^{6} + 4378064 x^{4} + \cdots + 295936 $ x^16 + 88x^14 + 3086x^12 + 54880x^10 + 516641x^8 + 2403800x^6 + 4378064x^4 + 2140928*x^2 + 295936
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{6}\cdot 3^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			4.7
Root			$4.35402i$ of defining polynomial
Character	$\chi$	$=$	51.4
Dual form			51.4.e.a.13.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+3.35402i q^{2} +(2.12132 - 2.12132i) q^{3} -3.24945 q^{4} +(-11.9082 + 11.9082i) q^{5} +(7.11495 + 7.11495i) q^{6} +(17.4318 + 17.4318i) q^{7} +15.9334i q^{8} -9.00000i q^{9} +(-39.9404 - 39.9404i) q^{10} +(-30.0520 - 30.0520i) q^{11} +(-6.89312 + 6.89312i) q^{12} +55.8783 q^{13} +(-58.4667 + 58.4667i) q^{14} +50.5223i q^{15} -79.4367 q^{16} +(57.3482 - 40.3011i) q^{17} +30.1862 q^{18} -81.6537i q^{19} +(38.6952 - 38.6952i) q^{20} +73.9570 q^{21} +(100.795 - 100.795i) q^{22} +(92.2875 + 92.2875i) q^{23} +(33.7999 + 33.7999i) q^{24} -158.612i q^{25} +187.417i q^{26} +(-19.0919 - 19.0919i) q^{27} +(-56.6438 - 56.6438i) q^{28} +(155.924 - 155.924i) q^{29} -169.453 q^{30} +(-89.6703 + 89.6703i) q^{31} -138.965i q^{32} -127.500 q^{33} +(135.171 + 192.347i) q^{34} -415.164 q^{35} +29.2450i q^{36} +(-147.677 + 147.677i) q^{37} +273.868 q^{38} +(118.536 - 118.536i) q^{39} +(-189.739 - 189.739i) q^{40} +(56.0414 + 56.0414i) q^{41} +248.053i q^{42} -256.206i q^{43} +(97.6522 + 97.6522i) q^{44} +(107.174 + 107.174i) q^{45} +(-309.534 + 309.534i) q^{46} -231.122 q^{47} +(-168.511 + 168.511i) q^{48} +264.737i q^{49} +531.987 q^{50} +(36.1625 - 207.146i) q^{51} -181.574 q^{52} +76.9927i q^{53} +(64.0345 - 64.0345i) q^{54} +715.731 q^{55} +(-277.749 + 277.749i) q^{56} +(-173.214 - 173.214i) q^{57} +(522.973 + 522.973i) q^{58} -633.045i q^{59} -164.170i q^{60} +(133.723 + 133.723i) q^{61} +(-300.756 - 300.756i) q^{62} +(156.886 - 156.886i) q^{63} -169.404 q^{64} +(-665.412 + 665.412i) q^{65} -427.636i q^{66} +681.108 q^{67} +(-186.350 + 130.956i) q^{68} +391.543 q^{69} -1392.47i q^{70} +(-386.843 + 386.843i) q^{71} +143.401 q^{72} +(-510.031 + 510.031i) q^{73} +(-495.312 - 495.312i) q^{74} +(-336.466 - 336.466i) q^{75} +265.330i q^{76} -1047.72i q^{77} +(397.572 + 397.572i) q^{78} +(-257.125 - 257.125i) q^{79} +(945.950 - 945.950i) q^{80} -81.0000 q^{81} +(-187.964 + 187.964i) q^{82} +280.677i q^{83} -240.319 q^{84} +(-203.001 + 1162.83i) q^{85} +859.321 q^{86} -661.531i q^{87} +(478.831 - 478.831i) q^{88} +440.149 q^{89} +(-359.464 + 359.464i) q^{90} +(974.061 + 974.061i) q^{91} +(-299.883 - 299.883i) q^{92} +380.439i q^{93} -775.188i q^{94} +(972.351 + 972.351i) q^{95} +(-294.788 - 294.788i) q^{96} +(-627.434 + 627.434i) q^{97} -887.934 q^{98} +(-270.468 + 270.468i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 48 q^{4} - 32 q^{5} + 12 q^{6} - 8 q^{7} - 20 q^{10} + 96 q^{11} + 120 q^{13} - 288 q^{14} - 200 q^{16} + 16 q^{17} - 72 q^{18} + 384 q^{20} + 168 q^{21} + 4 q^{22} + 208 q^{23} + 312 q^{24} + 904 q^{28}+ \cdots + 864 q^{99}+O(q^{100}) $ 16 * q - 48 * q^4 - 32 * q^5 + 12 * q^6 - 8 * q^7 - 20 * q^10 + 96 * q^11 + 120 * q^13 - 288 * q^14 - 200 * q^16 + 16 * q^17 - 72 * q^18 + 384 * q^20 + 168 * q^21 + 4 * q^22 + 208 * q^23 + 312 * q^24 + 904 * q^28 + 320 * q^29 - 432 * q^30 - 624 * q^31 - 72 * q^33 - 788 * q^34 - 1184 * q^35 + 256 * q^37 - 168 * q^38 - 24 * q^39 - 664 * q^40 + 800 * q^41 + 128 * q^44 + 288 * q^45 + 572 * q^46 + 368 * q^47 + 96 * q^48 - 720 * q^50 - 120 * q^51 - 3160 * q^52 + 108 * q^54 + 4296 * q^55 + 576 * q^56 - 1080 * q^57 + 1368 * q^58 - 1296 * q^61 + 536 * q^62 - 72 * q^63 + 1752 * q^64 - 4288 * q^65 - 1248 * q^67 - 240 * q^68 + 576 * q^69 + 1488 * q^71 + 864 * q^72 - 1208 * q^73 + 2272 * q^74 + 1200 * q^75 + 564 * q^78 - 1256 * q^79 + 384 * q^80 - 1296 * q^81 + 3564 * q^82 - 2088 * q^84 + 3216 * q^85 + 3224 * q^86 - 1296 * q^88 - 2608 * q^89 - 180 * q^90 - 56 * q^91 - 5072 * q^92 + 160 * q^95 - 408 * q^96 - 4456 * q^97 - 1208 * q^98 + 864 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/51\mathbb{Z}\right)^\times$.

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

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 $

$2$			3.35402i			1.18582i	0.805267	+	0.592912i	$0.202022\pi$
$2$			3.35402i			1.18582i	−0.805267	+	0.592912i	$0.797978\pi$
$3$	2.12132	−	2.12132i	0.408248	−	0.408248i
$3$	2.12132	−	2.12132i	0.408248	−	0.408248i
$4$	−3.24945			−0.406181
$5$	−11.9082	+	11.9082i	−1.06510	+	1.06510i	−0.0673767	+	0.997728i	$0.521463\pi$
$5$	−11.9082	+	11.9082i	−1.06510	+	1.06510i	−0.997728	+	0.0673767i	$0.978537\pi$
$6$	7.11495	+	7.11495i	0.484111	+	0.484111i
$7$	17.4318	+	17.4318i	0.941230	+	0.941230i	0.998366	−	0.0571362i	$-0.0181969\pi$
$7$	17.4318	+	17.4318i	0.941230	+	0.941230i	−0.0571362	+	0.998366i	$0.518197\pi$
$8$			15.9334i			0.704166i
$9$		−	9.00000i		−	0.333333i
$10$	−39.9404	−	39.9404i	−1.26303	−	1.26303i
$11$	−30.0520	−	30.0520i	−0.823728	−	0.823728i	0.162913	−	0.986641i	$-0.447911\pi$
$11$	−30.0520	−	30.0520i	−0.823728	−	0.823728i	−0.986641	+	0.162913i	$0.947911\pi$
$12$	−6.89312	+	6.89312i	−0.165823	+	0.165823i
$13$	55.8783			1.19214			0.596072	−	0.802931i	$-0.296727\pi$
$13$	55.8783			1.19214			0.596072	+	0.802931i	$0.296727\pi$
$14$	−58.4667	+	58.4667i	−1.11613	+	1.11613i
$15$			50.5223i			0.869654i
$16$	−79.4367			−1.24120
$17$	57.3482	−	40.3011i	0.818176	−	0.574968i
$17$	57.3482	−	40.3011i	0.818176	−	0.574968i
$18$	30.1862			0.395275
$19$		−	81.6537i		−	0.985929i	−0.870049	−	0.492965i	$-0.835913\pi$
$19$		−	81.6537i		−	0.985929i	0.870049	−	0.492965i	$-0.164087\pi$
$20$	38.6952	−	38.6952i	0.432625	−	0.432625i
$21$	73.9570			0.768511
$22$	100.795	−	100.795i	0.976797	−	0.976797i
$23$	92.2875	+	92.2875i	0.836664	+	0.836664i	0.988418	−	0.151754i	$-0.0484923\pi$
$23$	92.2875	+	92.2875i	0.836664	+	0.836664i	−0.151754	+	0.988418i	$0.548492\pi$
$24$	33.7999	+	33.7999i	0.287474	+	0.287474i
$25$		−	158.612i		−	1.26889i
$26$			187.417i			1.41367i
$27$	−19.0919	−	19.0919i	−0.136083	−	0.136083i
$28$	−56.6438	−	56.6438i	−0.382310	−	0.382310i
$29$	155.924	−	155.924i	0.998428	−	0.998428i	−0.00157095	−	0.999999i	$-0.500500\pi$
$29$	155.924	−	155.924i	0.998428	−	0.998428i	0.999999	+	0.00157095i	$0.000500049\pi$
$30$	−169.453			−1.03126
$31$	−89.6703	+	89.6703i	−0.519525	+	0.519525i	−0.917428	−	0.397903i	$-0.869738\pi$
$31$	−89.6703	+	89.6703i	−0.519525	+	0.519525i	0.397903	+	0.917428i	$0.369738\pi$
$32$		−	138.965i		−	0.767678i
$33$	−127.500			−0.672571
$34$	135.171	+	192.347i	0.681811	+	0.970214i
$35$	−415.164			−2.00502
$36$			29.2450i			0.135394i
$37$	−147.677	+	147.677i	−0.656162	+	0.656162i	−0.954470	−	0.298308i	$-0.903578\pi$
$37$	−147.677	+	147.677i	−0.656162	+	0.656162i	0.298308	+	0.954470i	$0.403578\pi$
$38$	273.868			1.16914
$39$	118.536	−	118.536i	0.486690	−	0.486690i
$40$	−189.739	−	189.739i	−0.750010	−	0.750010i
$41$	56.0414	+	56.0414i	0.213468	+	0.213468i	0.805739	−	0.592271i	$-0.201768\pi$
$41$	56.0414	+	56.0414i	0.213468	+	0.213468i	−0.592271	+	0.805739i	$0.701768\pi$
$42$			248.053i			0.911320i
$43$		−	256.206i		−	0.908630i	−0.890841	−	0.454315i	$-0.849884\pi$
$43$		−	256.206i		−	0.908630i	0.890841	−	0.454315i	$-0.150116\pi$
$44$	97.6522	+	97.6522i	0.334582	+	0.334582i
$45$	107.174	+	107.174i	0.355035	+	0.355035i
$46$	−309.534	+	309.534i	−0.992137	+	0.992137i
$47$	−231.122			−0.717290			−0.358645	−	0.933474i	$-0.616761\pi$
$47$	−231.122			−0.717290			−0.358645	+	0.933474i	$0.616761\pi$
$48$	−168.511	+	168.511i	−0.506717	+	0.506717i
$49$			264.737i			0.771829i
$50$	531.987			1.50469
$51$	36.1625	−	207.146i	0.0992894	−	0.568749i
$52$	−181.574			−0.484226
$53$			76.9927i			0.199543i	0.995010	+	0.0997714i	$0.0318111\pi$
$53$			76.9927i			0.199543i	−0.995010	+	0.0997714i	$0.968189\pi$
$54$	64.0345	−	64.0345i	0.161370	−	0.161370i
$55$	715.731			1.75471
$56$	−277.749	+	277.749i	−0.662782	+	0.662782i
$57$	−173.214	−	173.214i	−0.402504	−	0.402504i
$58$	522.973	+	522.973i	1.18396	+	1.18396i
$59$		−	633.045i		−	1.39687i	−0.715673	−	0.698436i	$-0.753880\pi$
$59$		−	633.045i		−	1.39687i	0.715673	−	0.698436i	$-0.246120\pi$
$60$		−	164.170i		−	0.353237i
$61$	133.723	+	133.723i	0.280680	+	0.280680i	0.833380	−	0.552700i	$-0.186402\pi$
$61$	133.723	+	133.723i	0.280680	+	0.280680i	−0.552700	+	0.833380i	$0.686402\pi$
$62$	−300.756	−	300.756i	−0.616065	−	0.616065i
$63$	156.886	−	156.886i	0.313743	−	0.313743i
$64$	−169.404			−0.330866
$65$	−665.412	+	665.412i	−1.26976	+	1.26976i
$66$		−	427.636i		−	0.797551i
$67$	681.108			1.24195			0.620975	−	0.783831i	$-0.286737\pi$
$67$	681.108			1.24195			0.620975	+	0.783831i	$0.286737\pi$
$68$	−186.350	+	130.956i	−0.332327	+	0.233541i
$69$	391.543			0.683133
$70$		−	1392.47i		−	2.37760i
$71$	−386.843	+	386.843i	−0.646617	+	0.646617i	−0.952174	−	0.305557i	$-0.901157\pi$
$71$	−386.843	+	386.843i	−0.646617	+	0.646617i	0.305557	+	0.952174i	$0.401157\pi$
$72$	143.401			0.234722
$73$	−510.031	+	510.031i	−0.817734	+	0.817734i	−0.985779	−	0.168045i	$-0.946255\pi$
$73$	−510.031	+	510.031i	−0.817734	+	0.817734i	0.168045	+	0.985779i	$0.446255\pi$
$74$	−495.312	−	495.312i	−0.778093	−	0.778093i
$75$	−336.466	−	336.466i	−0.518024	−	0.518024i
$76$			265.330i			0.400466i
$77$		−	1047.72i		−	1.55064i
$78$	397.572	+	397.572i	0.577130	+	0.577130i
$79$	−257.125	−	257.125i	−0.366188	−	0.366188i	0.499897	−	0.866085i	$-0.333371\pi$
$79$	−257.125	−	257.125i	−0.366188	−	0.366188i	−0.866085	+	0.499897i	$0.833371\pi$
$80$	945.950	−	945.950i	1.32201	−	1.32201i
$81$	−81.0000			−0.111111
$82$	−187.964	+	187.964i	−0.253136	+	0.253136i
$83$			280.677i			0.371185i	0.982627	+	0.185592i	$0.0594204\pi$
$83$			280.677i			0.371185i	−0.982627	+	0.185592i	$0.940580\pi$
$84$	−240.319			−0.312155
$85$	−203.001	+	1162.83i	−0.259042	+	1.48384i
$86$	859.321			1.07748
$87$		−	661.531i		−	0.815213i
$88$	478.831	−	478.831i	0.580041	−	0.580041i
$89$	440.149			0.524221			0.262111	−	0.965038i	$-0.415581\pi$
$89$	440.149			0.524221			0.262111	+	0.965038i	$0.415581\pi$
$90$	−359.464	+	359.464i	−0.421009	+	0.421009i
$91$	974.061	+	974.061i	1.12208	+	1.12208i
$92$	−299.883	−	299.883i	−0.339837	−	0.339837i
$93$			380.439i			0.424190i
$94$		−	775.188i		−	0.850580i
$95$	972.351	+	972.351i	1.05012	+	1.05012i
$96$	−294.788	−	294.788i	−0.313403	−	0.313403i
$97$	−627.434	+	627.434i	−0.656766	+	0.656766i	−0.954613	−	0.297848i	$-0.903731\pi$
$97$	−627.434	+	627.434i	−0.656766	+	0.656766i	0.297848	+	0.954613i	$0.403731\pi$
$98$	−887.934			−0.915254
$99$	−270.468	+	270.468i	−0.274576	+	0.274576i
$100$			515.401i			0.515401i
$101$	−579.381			−0.570798			−0.285399	−	0.958409i	$-0.592126\pi$
$101$	−579.381			−0.570798			−0.285399	+	0.958409i	$0.592126\pi$
$102$	694.770	+	121.290i	0.674436	+	0.117740i
$103$	−104.665			−0.100126			−0.0500628	−	0.998746i	$-0.515942\pi$
$103$	−104.665			−0.100126			−0.0500628	+	0.998746i	$0.515942\pi$
$104$			890.334i			0.839466i
$105$	−880.697	+	880.697i	−0.818545	+	0.818545i
$106$	−258.235			−0.236623
$107$	1210.68	−	1210.68i	1.09384	−	1.09384i	0.0987257	−	0.995115i	$-0.468523\pi$
$107$	1210.68	−	1210.68i	1.09384	−	1.09384i	0.995115	−	0.0987257i	$-0.0314766\pi$
$108$	62.0381	+	62.0381i	0.0552742	+	0.0552742i
$109$	6.84383	+	6.84383i	0.00601394	+	0.00601394i	0.710107	−	0.704093i	$-0.248646\pi$
$109$	6.84383	+	6.84383i	0.00601394	+	0.00601394i	−0.704093	+	0.710107i	$0.748646\pi$
$110$			2400.58i			2.08078i
$111$			626.541i			0.535754i
$112$	−1384.73	−	1384.73i	−1.16825	−	1.16825i
$113$	−878.649	−	878.649i	−0.731472	−	0.731472i	0.239439	−	0.970911i	$-0.423036\pi$
$113$	−878.649	−	878.649i	−0.731472	−	0.731472i	−0.970911	+	0.239439i	$0.923036\pi$
$114$	580.962	−	580.962i	0.477299	−	0.477299i
$115$	−2197.96			−1.78227
$116$	−506.668	+	506.668i	−0.405542	+	0.405542i
$117$		−	502.905i		−	0.397381i
$118$	2123.24			1.65644
$119$	1702.21	+	297.163i	1.31127	+	0.228915i
$120$	−804.995			−0.612380
$121$			475.241i			0.357055i
$122$	−448.510	+	448.510i	−0.332838	+	0.332838i
$123$	237.764			0.174296
$124$	291.379	−	291.379i	0.211021	−	0.211021i
$125$	400.257	+	400.257i	0.286401	+	0.286401i
$126$	526.200	+	526.200i	0.372045	+	0.372045i
$127$		−	1761.90i		−	1.23105i	−0.788117	−	0.615525i	$-0.788944\pi$
$127$		−	1761.90i		−	1.23105i	0.788117	−	0.615525i	$-0.211056\pi$
$128$		−	1679.90i		−	1.16003i
$129$	−543.496	−	543.496i	−0.370947	−	0.370947i
$130$	−2231.80	−	2231.80i	−1.50571	−	1.50571i
$131$	−55.8332	+	55.8332i	−0.0372380	+	0.0372380i	−0.725481	−	0.688243i	$-0.758382\pi$
$131$	−55.8332	+	55.8332i	−0.0372380	+	0.0372380i	0.688243	+	0.725481i	$0.258382\pi$
$132$	414.303			0.273185
$133$	1423.37	−	1423.37i	0.927986	−	0.927986i
$134$			2284.45i			1.47273i
$135$	454.701			0.289885
$136$	642.135	+	913.755i	0.404872	+	0.576131i
$137$	−929.313			−0.579537			−0.289768	−	0.957097i	$-0.593578\pi$
$137$	−929.313			−0.579537			−0.289768	+	0.957097i	$0.593578\pi$
$138$			1313.24i			0.810076i
$139$	−677.301	+	677.301i	−0.413294	+	0.413294i	−0.882884	−	0.469590i	$-0.844402\pi$
$139$	−677.301	+	677.301i	−0.413294	+	0.413294i	0.469590	+	0.882884i	$0.344402\pi$
$140$	1349.05			0.814399
$141$	−490.284	+	490.284i	−0.292832	+	0.292832i
$142$	−1297.48	−	1297.48i	−0.766774	−	0.766774i
$143$	−1679.25	−	1679.25i	−0.982001	−	0.982001i
$144$			714.930i			0.413733i
$145$			3713.56i			2.12686i
$146$	−1710.65	−	1710.65i	−0.969690	−	0.969690i
$147$	561.592	+	561.592i	0.315098	+	0.315098i
$148$	479.869	−	479.869i	0.266520	−	0.266520i
$149$	2851.93			1.56805			0.784024	−	0.620731i	$-0.213164\pi$
$149$	2851.93			1.56805			0.784024	+	0.620731i	$0.213164\pi$
$150$	1128.51	−	1128.51i	0.614286	−	0.614286i
$151$		−	3389.72i		−	1.82683i	−0.407027	−	0.913416i	$-0.633435\pi$
$151$		−	3389.72i		−	1.82683i	0.407027	−	0.913416i	$-0.366565\pi$
$152$	1301.03			0.694257
$153$	−362.710	−	516.134i	−0.191656	−	0.272725i
$154$	3514.08			1.83878
$155$		−	2135.63i		−	1.10670i
$156$	−385.176	+	385.176i	−0.197684	+	0.197684i
$157$	490.585			0.249382			0.124691	−	0.992196i	$-0.460206\pi$
$157$	490.585			0.249382			0.124691	+	0.992196i	$0.460206\pi$
$158$	862.404	−	862.404i	0.434235	−	0.434235i
$159$	163.326	+	163.326i	0.0814630	+	0.0814630i
$160$	1654.82	+	1654.82i	0.817657	+	0.817657i
$161$			3217.48i			1.57499i
$162$		−	271.676i		−	0.131758i
$163$	−1266.81	−	1266.81i	−0.608739	−	0.608739i	0.333877	−	0.942617i	$-0.391643\pi$
$163$	−1266.81	−	1266.81i	−0.608739	−	0.608739i	−0.942617	+	0.333877i	$0.891643\pi$
$164$	−182.104	−	182.104i	−0.0867068	−	0.0867068i
$165$	1518.30	−	1518.30i	0.716358	−	0.716358i
$166$	−941.397			−0.440160
$167$	−795.209	+	795.209i	−0.368474	+	0.368474i	−0.866920	−	0.498447i	$-0.833904\pi$
$167$	−795.209	+	795.209i	−0.368474	+	0.368474i	0.498447	+	0.866920i	$0.333904\pi$
$168$			1178.39i			0.541159i
$169$	925.388			0.421205
$170$	−3900.16	−	680.871i	−1.75958	−	0.307179i
$171$	−734.884			−0.328643
$172$			832.529i			0.369068i
$173$	−2053.13	+	2053.13i	−0.902292	+	0.902292i	−0.995634	−	0.0933416i	$-0.970245\pi$
$173$	−2053.13	+	2053.13i	−0.902292	+	0.902292i	0.0933416	+	0.995634i	$0.470245\pi$
$174$	2218.79			0.966700
$175$	2764.89	−	2764.89i	1.19432	−	1.19432i
$176$	2387.23	+	2387.23i	1.02241	+	1.02241i
$177$	−1342.89	−	1342.89i	−0.570270	−	0.570270i
$178$			1476.27i			0.621635i
$179$			136.544i			0.0570154i	0.999594	+	0.0285077i	$0.00907551\pi$
$179$			136.544i			0.0570154i	−0.999594	+	0.0285077i	$0.990924\pi$
$180$	−348.256	−	348.256i	−0.144208	−	0.144208i
$181$	−1641.88	−	1641.88i	−0.674252	−	0.674252i	0.284441	−	0.958694i	$-0.408192\pi$
$181$	−1641.88	−	1641.88i	−0.674252	−	0.674252i	−0.958694	+	0.284441i	$0.908192\pi$
$182$	−3267.02	+	3267.02i	−1.33059	+	1.33059i
$183$	567.340			0.229175
$184$	−1470.46	+	1470.46i	−0.589150	+	0.589150i
$185$		−	3517.15i		−	1.39776i
$186$	−1276.00			−0.503015
$187$	−2934.55	−	512.300i	−1.14757	−	0.200337i
$188$	751.019			0.291349
$189$		−	665.613i		−	0.256170i
$190$	−3261.29	+	3261.29i	−1.24526	+	1.24526i
$191$	−1346.87			−0.510242			−0.255121	−	0.966909i	$-0.582115\pi$
$191$	−1346.87			−0.510242			−0.255121	+	0.966909i	$0.582115\pi$
$192$	−359.359	+	359.359i	−0.135076	+	0.135076i
$193$	3580.03	+	3580.03i	1.33521	+	1.33521i	0.900634	+	0.434578i	$0.143102\pi$
$193$	3580.03	+	3580.03i	1.33521	+	1.33521i	0.434578	+	0.900634i	$0.356898\pi$
$194$	−2104.43	−	2104.43i	−0.778809	−	0.778809i
$195$			2823.10i			1.03675i
$196$		−	860.249i		−	0.313502i
$197$	−1115.92	−	1115.92i	−0.403584	−	0.403584i	0.475910	−	0.879494i	$-0.342119\pi$
$197$	−1115.92	−	1115.92i	−0.403584	−	0.403584i	−0.879494	+	0.475910i	$0.842119\pi$
$198$	−907.154	−	907.154i	−0.325599	−	0.325599i
$199$	470.721	−	470.721i	0.167681	−	0.167681i	−0.618278	−	0.785959i	$-0.712169\pi$
$199$	470.721	−	470.721i	0.167681	−	0.167681i	0.785959	+	0.618278i	$0.212169\pi$
$200$	2527.23			0.893512
$201$	1444.85	−	1444.85i	0.507024	−	0.507024i
$202$		−	1943.25i		−	0.676866i
$203$	5436.09			1.87950
$204$	−117.508	+	673.108i	−0.0403294	+	0.231015i
$205$	−1334.71			−0.454732
$206$		−	351.048i		−	0.118732i
$207$	830.587	−	830.587i	0.278888	−	0.278888i
$208$	−4438.79			−1.47969
$209$	−2453.86	+	2453.86i	−0.812137	+	0.812137i
$210$	−2953.87	−	2953.87i	−0.970651	−	0.970651i
$211$	3094.75	+	3094.75i	1.00972	+	1.00972i	0.999952	+	0.00977143i	$0.00311039\pi$
$211$	3094.75	+	3094.75i	1.00972	+	1.00972i	0.00977143	+	0.999952i	$0.496890\pi$
$212$		−	250.184i		−	0.0810505i
$213$			1641.23i			0.527960i
$214$	4060.65	+	4060.65i	1.29710	+	1.29710i
$215$	3050.96	+	3050.96i	0.967786	+	0.967786i
$216$	304.200	−	304.200i	0.0958248	−	0.0958248i
$217$	−3126.23			−0.977984
$218$	−22.9543	+	22.9543i	−0.00713148	+	0.00713148i
$219$			2163.88i			0.667677i
$220$	−2325.73			−0.712731
$221$	3204.52	−	2251.96i	0.975383	−	0.685444i
$222$	−2101.43			−0.635310
$223$			4814.96i			1.44589i	0.690906	+	0.722945i	$0.257212\pi$
$223$			4814.96i			1.44589i	−0.690906	+	0.722945i	$0.742788\pi$
$224$	2422.41	−	2422.41i	0.722562	−	0.722562i
$225$	−1427.51			−0.422965
$226$	2947.00	−	2947.00i	0.867398	−	0.867398i
$227$	−938.074	−	938.074i	−0.274283	−	0.274283i	0.556539	−	0.830822i	$-0.312129\pi$
$227$	−938.074	−	938.074i	−0.274283	−	0.274283i	−0.830822	+	0.556539i	$0.812129\pi$
$228$	562.849	+	562.849i	0.163489	+	0.163489i
$229$			4821.14i			1.39122i	0.718418	+	0.695611i	$0.244866\pi$
$229$			4821.14i			1.39122i	−0.718418	+	0.695611i	$0.755134\pi$
$230$		−	7372.00i		−	2.11346i
$231$	−2222.55	−	2222.55i	−0.633044	−	0.633044i
$232$	2484.41	+	2484.41i	0.703058	+	0.703058i
$233$	2613.59	−	2613.59i	0.734857	−	0.734857i	−0.236721	−	0.971578i	$-0.576073\pi$
$233$	2613.59	−	2613.59i	0.734857	−	0.734857i	0.971578	+	0.236721i	$0.0760726\pi$
$234$	1686.75			0.471224
$235$	2752.25	−	2752.25i	0.763989	−	0.763989i
$236$			2057.05i			0.567382i
$237$	−1090.89			−0.298991
$238$	−996.691	+	5709.23i	−0.271453	+	1.55494i
$239$	302.431			0.0818521			0.0409261	−	0.999162i	$-0.486969\pi$
$239$	302.431			0.0818521			0.0409261	+	0.999162i	$0.486969\pi$
$240$		−	4013.33i		−	1.07941i
$241$	4552.78	−	4552.78i	1.21689	−	1.21689i	0.248172	−	0.968716i	$-0.420170\pi$
$241$	4552.78	−	4552.78i	1.21689	−	1.21689i	0.968716	−	0.248172i	$-0.0798299\pi$
$242$	−1593.97			−0.423405
$243$	−171.827	+	171.827i	−0.0453609	+	0.0453609i
$244$	−434.526	−	434.526i	−0.114007	−	0.114007i
$245$	−3152.55	−	3152.55i	−0.822078	−	0.822078i
$246$			797.464i			0.206685i
$247$		−	4562.68i		−	1.17537i
$248$	−1428.76	−	1428.76i	−0.365831	−	0.365831i
$249$	595.406	+	595.406i	0.151536	+	0.151536i
$250$	−1342.47	+	1342.47i	−0.339621	+	0.339621i
$251$	−2896.91			−0.728492			−0.364246	−	0.931303i	$-0.618673\pi$
$251$	−2896.91			−0.728492			−0.364246	+	0.931303i	$0.618673\pi$
$252$	−509.794	+	509.794i	−0.127437	+	0.127437i
$253$		−	5546.84i		−	1.37837i
$254$	5909.45			1.45981
$255$	2036.11	+	2897.37i	0.500023	+	0.711530i
$256$	4279.19			1.04472
$257$			5439.49i			1.32026i	0.751152	+	0.660129i	$0.229498\pi$
$257$			5439.49i			1.32026i	−0.751152	+	0.660129i	$0.770502\pi$
$258$	1822.90	−	1822.90i	0.439878	−	0.439878i
$259$	−5148.57			−1.23520
$260$	2162.22	−	2162.22i	0.515751	−	0.515751i
$261$	−1403.32	−	1403.32i	−0.332809	−	0.332809i
$262$	−187.266	−	187.266i	−0.0441577	−	0.0441577i
$263$		−	6793.03i		−	1.59268i	−0.604846	−	0.796342i	$-0.706766\pi$
$263$		−	6793.03i		−	1.59268i	0.604846	−	0.796342i	$-0.293234\pi$
$264$		−	2031.51i		−	0.473601i
$265$	−916.847	−	916.847i	−0.212534	−	0.212534i
$266$	4774.02	+	4774.02i	1.10043	+	1.10043i
$267$	933.697	−	933.697i	0.214012	−	0.214012i
$268$	−2213.22			−0.504456
$269$	−4255.36	+	4255.36i	−0.964512	+	0.964512i	−0.999392	−	0.0348793i	$-0.988895\pi$
$269$	−4255.36	+	4255.36i	−0.964512	+	0.964512i	0.0348793	+	0.999392i	$0.488895\pi$
$270$			1525.08i			0.343752i
$271$	−6622.55			−1.48447			−0.742235	−	0.670140i	$-0.766234\pi$
$271$	−6622.55			−1.48447			−0.742235	+	0.670140i	$0.766234\pi$
$272$	−4555.55	+	3201.38i	−1.01552	+	0.713649i
$273$	4132.59			0.916175
$274$		−	3116.93i		−	0.687229i
$275$	−4766.60	+	4766.60i	−1.04522	+	1.04522i
$276$	−1272.30			−0.277476
$277$	−4765.53	+	4765.53i	−1.03369	+	1.03369i	−0.0342806	+	0.999412i	$0.510914\pi$
$277$	−4765.53	+	4765.53i	−1.03369	+	1.03369i	−0.999412	+	0.0342806i	$0.989086\pi$
$278$	−2271.68	−	2271.68i	−0.490095	−	0.490095i
$279$	807.033	+	807.033i	0.173175	+	0.173175i
$280$		−	6615.00i		−	1.41186i
$281$			3246.90i			0.689303i	0.938731	+	0.344651i	$0.112003\pi$
$281$			3246.90i			0.689303i	−0.938731	+	0.344651i	$0.887997\pi$
$282$	−1644.42	−	1644.42i	−0.347248	−	0.347248i
$283$	−1779.17	−	1779.17i	−0.373713	−	0.373713i	0.495114	−	0.868828i	$-0.335126\pi$
$283$	−1779.17	−	1779.17i	−0.373713	−	0.373713i	−0.868828	+	0.495114i	$0.835126\pi$
$284$	1257.02	−	1257.02i	0.262643	−	0.262643i
$285$	4125.34			0.857417
$286$	5632.25	−	5632.25i	1.16448	−	1.16448i
$287$			1953.81i			0.401846i
$288$	−1250.68			−0.255893
$289$	1664.64	−	4622.39i	0.338824	−	0.940850i
$290$	−12455.4			−2.52208
$291$			2661.98i			0.536247i
$292$	1657.32	−	1657.32i	0.332148	−	0.332148i
$293$	2983.23			0.594820			0.297410	−	0.954750i	$-0.403877\pi$
$293$	2983.23			0.594820			0.297410	+	0.954750i	$0.403877\pi$
$294$	−1883.59	+	1883.59i	−0.373651	+	0.373651i
$295$	7538.44	+	7538.44i	1.48781	+	1.48781i
$296$	−2353.01	−	2353.01i	−0.462046	−	0.462046i
$297$			1147.50i			0.224190i
$298$			9565.43i			1.85943i
$299$	5156.87	+	5156.87i	0.997423	+	0.997423i
$300$	1093.33	+	1093.33i	0.210411	+	0.210411i
$301$	4466.14	−	4466.14i	0.855230	−	0.855230i
$302$	11369.2			2.16630
$303$	−1229.05	+	1229.05i	−0.233027	+	0.233027i
$304$			6486.30i			1.22373i
$305$	−3184.81			−0.597908
$306$	1731.12	−	1216.54i	0.323405	−	0.227270i
$307$	999.847			0.185877			0.0929386	−	0.995672i	$-0.470374\pi$
$307$	999.847			0.185877			0.0929386	+	0.995672i	$0.470374\pi$
$308$			3404.51i			0.629838i
$309$	−222.028	+	222.028i	−0.0408761	+	0.0408761i
$310$	7162.94			1.31235
$311$	−3377.02	+	3377.02i	−0.615733	+	0.615733i	−0.944434	−	0.328701i	$-0.893389\pi$
$311$	−3377.02	+	3377.02i	−0.615733	+	0.615733i	0.328701	+	0.944434i	$0.393389\pi$
$312$	1888.68	+	1888.68i	0.342711	+	0.342711i
$313$	4323.97	+	4323.97i	0.780848	+	0.780848i	0.979974	−	0.199126i	$-0.0638102\pi$
$313$	4323.97	+	4323.97i	0.780848	+	0.780848i	−0.199126	+	0.979974i	$0.563810\pi$
$314$			1645.43i			0.295723i
$315$			3736.48i			0.668339i
$316$	835.515	+	835.515i	0.148739	+	0.148739i
$317$	−1346.73	−	1346.73i	−0.238612	−	0.238612i	0.577663	−	0.816275i	$-0.303965\pi$
$317$	−1346.73	−	1346.73i	−0.238612	−	0.238612i	−0.816275	+	0.577663i	$0.803965\pi$
$318$	−547.800	+	547.800i	−0.0966009	+	0.0966009i
$319$	−9371.66			−1.64487
$320$	2017.30	−	2017.30i	0.352407	−	0.352407i
$321$		−	5136.48i		−	0.893117i
$322$	−10791.5			−1.86766
$323$	−3290.74	−	4682.70i	−0.566877	−	0.806664i
$324$	263.205			0.0451312
$325$		−	8862.96i		−	1.51270i
$326$	4248.92	−	4248.92i	0.721858	−	0.721858i
$327$	29.0359			0.00491036
$328$	−892.933	+	892.933i	−0.150317	+	0.150317i
$329$	−4028.88	−	4028.88i	−0.675135	−	0.675135i
$330$	5092.39	+	5092.39i	0.849476	+	0.849476i
$331$		−	8019.25i		−	1.33166i	−0.746105	−	0.665828i	$-0.768079\pi$
$331$		−	8019.25i		−	1.33166i	0.746105	−	0.665828i	$-0.231921\pi$
$332$		−	912.046i		−	0.150768i
$333$	1329.09	+	1329.09i	0.218721	+	0.218721i
$334$	−2667.15	−	2667.15i	−0.436946	−	0.436946i
$335$	−8110.79	+	8110.79i	−1.32281	+	1.32281i
$336$	−5874.90			−0.953875
$337$	−8635.56	+	8635.56i	−1.39587	+	1.39587i	−0.584423	+	0.811449i	$0.698679\pi$
$337$	−8635.56	+	8635.56i	−1.39587	+	1.39587i	−0.811449	+	0.584423i	$0.801321\pi$
$338$			3103.77i			0.499476i
$339$	−3727.79			−0.597244
$340$	659.642	−	3778.56i	0.105218	−	0.602709i
$341$	5389.54			0.855894
$342$		−	2464.81i		−	0.389713i
$343$	1364.26	−	1364.26i	0.214762	−	0.214762i
$344$	4082.25			0.639826
$345$	−4662.58	+	4662.58i	−0.727608	+	0.727608i
$346$	−6886.24	−	6886.24i	−1.06996	−	1.06996i
$347$	2550.88	+	2550.88i	0.394635	+	0.394635i	0.876336	−	0.481701i	$-0.159981\pi$
$347$	2550.88	+	2550.88i	0.394635	+	0.394635i	−0.481701	+	0.876336i	$0.659981\pi$
$348$			2149.61i			0.331124i
$349$			2728.68i			0.418519i	0.977860	+	0.209259i	$0.0671053\pi$
$349$			2728.68i			0.418519i	−0.977860	+	0.209259i	$0.932895\pi$
$350$	9273.51	+	9273.51i	1.41626	+	1.41626i
$351$	−1066.82	−	1066.82i	−0.162230	−	0.162230i
$352$	−4176.16	+	4176.16i	−0.632358	+	0.632358i
$353$	2513.16			0.378929			0.189465	−	0.981888i	$-0.439325\pi$
$353$	2513.16			0.378929			0.189465	+	0.981888i	$0.439325\pi$
$354$	4504.08	−	4504.08i	0.676241	−	0.676241i
$355$		−	9213.22i		−	1.37743i
$356$	−1430.24			−0.212929
$357$	4241.30	−	2980.55i	0.628778	−	0.441869i
$358$	−457.970			−0.0676102
$359$			6707.98i			0.986166i	0.869982	+	0.493083i	$0.164130\pi$
$359$			6707.98i			0.986166i	−0.869982	+	0.493083i	$0.835870\pi$
$360$	−1707.65	+	1707.65i	−0.250003	+	0.250003i
$361$	191.665			0.0279436
$362$	5506.88	−	5506.88i	0.799545	−	0.799545i
$363$	1008.14	+	1008.14i	0.145767	+	0.145767i
$364$	−3165.16	−	3165.16i	−0.455768	−	0.455768i
$365$		−	12147.1i		−	1.74194i
$366$			1902.87i			0.271761i
$367$	−1575.31	−	1575.31i	−0.224062	−	0.224062i	0.586145	−	0.810206i	$-0.300645\pi$
$367$	−1575.31	−	1575.31i	−0.224062	−	0.224062i	−0.810206	+	0.586145i	$0.800645\pi$
$368$	−7331.01	−	7331.01i	−1.03847	−	1.03847i
$369$	504.373	−	504.373i	0.0711561	−	0.0711561i
$370$	11796.6			1.65750
$371$	−1342.12	+	1342.12i	−0.187816	+	0.187816i
$372$		−	1236.22i		−	0.172298i
$373$	6113.83			0.848691			0.424346	−	0.905500i	$-0.360504\pi$
$373$	6113.83			0.848691			0.424346	+	0.905500i	$0.360504\pi$
$374$	1718.27	−	9842.55i	0.237565	−	1.36082i
$375$	1698.15			0.233845
$376$		−	3682.57i		−	0.505091i
$377$	8712.79	−	8712.79i	1.19027	−	1.19027i
$378$	2232.48			0.303773
$379$	1321.68	−	1321.68i	0.179129	−	0.179129i	−0.611847	−	0.790976i	$-0.709573\pi$
$379$	1321.68	−	1321.68i	0.179129	−	0.179129i	0.790976	+	0.611847i	$0.209573\pi$
$380$	−3159.60	−	3159.60i	−0.426538	−	0.426538i
$381$	−3737.56	−	3737.56i	−0.502574	−	0.502574i
$382$		−	4517.43i		−	0.605058i
$383$			3159.66i			0.421544i	0.977535	+	0.210772i	$0.0675977\pi$
$383$			3159.66i			0.421544i	−0.977535	+	0.210772i	$0.932402\pi$
$384$	−3563.60	−	3563.60i	−0.473579	−	0.473579i
$385$	12476.5	+	12476.5i	1.65159	+	1.65159i
$386$	−12007.5	+	12007.5i	−1.58333	+	1.58333i
$387$	−2305.86			−0.302877
$388$	2038.81	−	2038.81i	0.266766	−	0.266766i
$389$			4591.25i			0.598420i	0.954187	+	0.299210i	$0.0967231\pi$
$389$			4591.25i			0.598420i	−0.954187	+	0.299210i	$0.903277\pi$
$390$	−9468.74			−1.22941
$391$	9011.81	+	1573.24i	1.16559	+	0.203484i
$392$	−4218.18			−0.543495
$393$			236.880i			0.0304047i
$394$	3742.82	−	3742.82i	0.478580	−	0.478580i
$395$	6123.82			0.780057
$396$	878.870	−	878.870i	0.111527	−	0.111527i
$397$	−7829.84	−	7829.84i	−0.989845	−	0.989845i	0.0101040	−	0.999949i	$-0.496784\pi$
$397$	−7829.84	−	7829.84i	−0.989845	−	0.989845i	−0.999949	+	0.0101040i	$0.996784\pi$
$398$	1578.81	+	1578.81i	0.198840	+	0.198840i
$399$		−	6038.86i		−	0.757698i
$400$			12599.6i			1.57495i
$401$	5641.36	+	5641.36i	0.702533	+	0.702533i	0.964954	−	0.262420i	$-0.0845207\pi$
$401$	5641.36	+	5641.36i	0.702533	+	0.702533i	−0.262420	+	0.964954i	$0.584521\pi$
$402$	4846.05	+	4846.05i	0.601241	+	0.601241i
$403$	−5010.63	+	5010.63i	−0.619348	+	0.619348i
$404$	1882.67			0.231847
$405$	964.566	−	964.566i	0.118345	−	0.118345i
$406$			18232.7i			2.22876i
$407$	8875.98			1.08100
$408$	3300.54	+	576.193i	0.400493	+	0.0699162i
$409$	−7832.34			−0.946906			−0.473453	−	0.880819i	$-0.656993\pi$
$409$	−7832.34			−0.946906			−0.473453	+	0.880819i	$0.656993\pi$
$410$		−	4476.64i		−	0.539233i
$411$	−1971.37	+	1971.37i	−0.236595	+	0.236595i
$412$	340.103			0.0406691
$413$	11035.1	−	11035.1i	1.31478	−	1.31478i
$414$	2785.81	+	2785.81i	0.330712	+	0.330712i
$415$	−3342.37	−	3342.37i	−0.395350	−	0.395350i
$416$		−	7765.11i		−	0.915182i
$417$			2873.54i			0.337453i
$418$	−8230.28	−	8230.28i	−0.963053	−	0.963053i
$419$	3717.06	+	3717.06i	0.433390	+	0.433390i	0.889780	−	0.456390i	$-0.150858\pi$
$419$	3717.06	+	3717.06i	0.433390	+	0.433390i	−0.456390	+	0.889780i	$0.650858\pi$
$420$	2861.78	−	2861.78i	0.332477	−	0.332477i
$421$	3469.89			0.401691			0.200846	−	0.979623i	$-0.435631\pi$
$421$	3469.89			0.401691			0.200846	+	0.979623i	$0.435631\pi$
$422$	−10379.9	+	10379.9i	−1.19736	+	1.19736i
$423$			2080.10i			0.239097i
$424$	−1226.76			−0.140511
$425$	−6392.23	−	9096.11i	−0.729573	−	1.03818i
$426$	−5504.73			−0.626068
$427$			4662.08i			0.528370i
$428$	−3934.04	+	3934.04i	−0.444297	+	0.444297i
$429$	−7124.47			−0.801801
$430$	−10233.0	+	10233.0i	−1.14762	+	1.14762i
$431$	6483.95	+	6483.95i	0.724643	+	0.724643i	0.969547	−	0.244905i	$-0.0787566\pi$
$431$	6483.95	+	6483.95i	0.724643	+	0.724643i	−0.244905	+	0.969547i	$0.578757\pi$
$432$	1516.60	+	1516.60i	0.168906	+	0.168906i
$433$			2879.08i			0.319538i	0.987154	+	0.159769i	$0.0510749\pi$
$433$			2879.08i			0.319538i	−0.987154	+	0.159769i	$0.948925\pi$
$434$		−	10485.5i		−	1.15972i
$435$	7877.66	+	7877.66i	0.868287	+	0.868287i
$436$	−22.2386	−	22.2386i	−0.00244275	−	0.00244275i
$437$	7535.62	−	7535.62i	0.824891	−	0.824891i
$438$	−7257.69			−0.791748
$439$	7737.14	−	7737.14i	0.841170	−	0.841170i	−0.147841	−	0.989011i	$-0.547232\pi$
$439$	7737.14	−	7737.14i	0.841170	−	0.841170i	0.989011	+	0.147841i	$0.0472325\pi$
$440$			11404.1i			1.23561i
$441$	2382.63			0.257276
$442$	7553.11	+	10748.0i	0.812816	+	1.15663i
$443$	3073.02			0.329580			0.164790	−	0.986329i	$-0.447305\pi$
$443$	3073.02			0.329580			0.164790	+	0.986329i	$0.447305\pi$
$444$		−	2035.91i		−	0.217613i
$445$	−5241.39	+	5241.39i	−0.558350	+	0.558350i
$446$	−16149.5			−1.71457
$447$	6049.86	−	6049.86i	0.640153	−	0.640153i
$448$	−2953.01	−	2953.01i	−0.311421	−	0.311421i
$449$	−10538.0	−	10538.0i	−1.10762	−	1.10762i	−0.993463	−	0.114152i	$-0.963585\pi$
$449$	−10538.0	−	10538.0i	−1.10762	−	1.10762i	−0.114152	−	0.993463i	$-0.536415\pi$
$450$		−	4787.88i		−	0.501562i
$451$		−	3368.31i		−	0.351680i
$452$	2855.12	+	2855.12i	0.297110	+	0.297110i
$453$	−7190.69	−	7190.69i	−0.745801	−	0.745801i
$454$	3146.32	−	3146.32i	0.325251	−	0.325251i
$455$	−23198.7			−2.39027
$456$	2759.89	−	2759.89i	0.283429	−	0.283429i
$457$			10638.2i			1.08891i	0.838789	+	0.544456i	$0.183264\pi$
$457$			10638.2i			1.08891i	−0.838789	+	0.544456i	$0.816736\pi$
$458$	−16170.2			−1.64975
$459$	−1864.31	−	325.462i	−0.189583	−	0.0330965i
$460$	7142.16			0.723923
$461$		−	1579.43i		−	0.159570i	−0.996812	−	0.0797848i	$-0.974577\pi$
$461$		−	1579.43i		−	0.159570i	0.996812	−	0.0797848i	$-0.0254233\pi$
$462$	7454.48	−	7454.48i	0.750680	−	0.750680i
$463$	−2791.55			−0.280204			−0.140102	−	0.990137i	$-0.544743\pi$
$463$	−2791.55			−0.280204			−0.140102	+	0.990137i	$0.544743\pi$
$464$	−12386.1	+	12386.1i	−1.23925	+	1.23925i
$465$	−4530.35	−	4530.35i	−0.451807	−	0.451807i
$466$	8766.02	+	8766.02i	0.871412	+	0.871412i
$467$		−	6637.75i		−	0.657727i	−0.944377	−	0.328864i	$-0.893334\pi$
$467$		−	6637.75i		−	0.657727i	0.944377	−	0.328864i	$-0.106666\pi$
$468$			1634.16i			0.161409i
$469$	11873.0	+	11873.0i	1.16896	+	1.16896i
$470$	9231.12	+	9231.12i	0.905957	+	0.905957i
$471$	1040.69	−	1040.69i	0.101810	−	0.101810i
$472$	10086.6			0.983629
$473$	−7699.50	+	7699.50i	−0.748464	+	0.748464i
$474$		−	3658.87i		−	0.354552i
$475$	−12951.2			−1.25104
$476$	−5531.23	−	965.615i	−0.532612	−	0.0929809i
$477$	692.935			0.0665143
$478$			1014.36i			0.0970623i
$479$	−1923.52	+	1923.52i	−0.183482	+	0.183482i	−0.792871	−	0.609389i	$-0.791415\pi$
$479$	−1923.52	+	1923.52i	−0.183482	+	0.183482i	0.609389	+	0.792871i	$0.291415\pi$
$480$	7020.81			0.667614
$481$	−8251.95	+	8251.95i	−0.782238	+	0.782238i
$482$	15270.1	+	15270.1i	1.44302	+	1.44302i
$483$	6825.30	+	6825.30i	0.642986	+	0.642986i
$484$		−	1544.27i		−	0.145029i
$485$		−	14943.3i		−	1.39905i
$486$	−576.311	−	576.311i	−0.0537901	−	0.0537901i
$487$	3328.61	+	3328.61i	0.309720	+	0.309720i	0.844801	−	0.535081i	$-0.179719\pi$
$487$	3328.61	+	3328.61i	0.309720	+	0.309720i	−0.535081	+	0.844801i	$0.679719\pi$
$488$	−2130.67	+	2130.67i	−0.197645	+	0.197645i
$489$	−5374.63			−0.497033
$490$	10573.7	−	10573.7i	0.974841	−	0.974841i
$491$		−	10064.8i		−	0.925088i	−0.886596	−	0.462544i	$-0.846937\pi$
$491$		−	10064.8i		−	0.925088i	0.886596	−	0.462544i	$-0.153063\pi$
$492$	−772.600			−0.0707958
$493$	2658.06	−	15225.9i	0.242826	−	1.39095i
$494$	15303.3			1.39378
$495$		−	6441.58i		−	0.584904i
$496$	7123.11	−	7123.11i	0.644833	−	0.644833i
$497$	−13486.7			−1.21723
$498$	−1997.00	+	1997.00i	−0.179695	+	0.179695i
$499$	−3918.97	−	3918.97i	−0.351578	−	0.351578i	0.509119	−	0.860696i	$-0.329971\pi$
$499$	−3918.97	−	3918.97i	−0.351578	−	0.351578i	−0.860696	+	0.509119i	$0.829971\pi$
$500$	−1300.61	−	1300.61i	−0.116330	−	0.116330i
$501$			3373.79i			0.300858i
$502$		−	9716.29i		−	0.863863i
$503$	7965.14	+	7965.14i	0.706060	+	0.706060i	0.965704	−	0.259645i	$-0.0836054\pi$
$503$	7965.14	+	7965.14i	0.706060	+	0.706060i	−0.259645	+	0.965704i	$0.583605\pi$
$504$	2499.74	+	2499.74i	0.220927	+	0.220927i
$505$	6899.40	−	6899.40i	0.607959	−	0.607959i
$506$	18604.2			1.63450
$507$	1963.04	−	1963.04i	0.171956	−	0.171956i
$508$			5725.20i			0.500029i
$509$	5617.41			0.489169			0.244585	−	0.969628i	$-0.421348\pi$
$509$	5617.41			0.489169			0.244585	+	0.969628i	$0.421348\pi$
$510$	−9717.83	+	6829.14i	−0.843750	+	0.592940i
$511$	−17781.5			−1.53935
$512$			913.281i			0.0788315i
$513$	−1558.92	+	1558.92i	−0.134168	+	0.134168i
$514$	−18244.2			−1.56559
$515$	1246.37	−	1246.37i	0.106644	−	0.106644i
$516$	1766.06	+	1766.06i	0.150671	+	0.150671i
$517$	6945.67	+	6945.67i	0.590852	+	0.590852i
$518$		−	17268.4i		−	1.46473i
$519$			8710.69i			0.736719i
$520$	−10602.3	−	10602.3i	−0.894119	−	0.894119i
$521$	4833.13	+	4833.13i	0.406417	+	0.406417i	0.880487	−	0.474070i	$-0.157216\pi$
$521$	4833.13	+	4833.13i	0.406417	+	0.406417i	−0.474070	+	0.880487i	$0.657216\pi$
$522$	4706.76	−	4706.76i	0.394654	−	0.394654i
$523$	15447.5			1.29153			0.645767	−	0.763534i	$-0.276538\pi$
$523$	15447.5			1.29153			0.645767	+	0.763534i	$0.276538\pi$
$524$	181.427	−	181.427i	0.0151253	−	0.0151253i
$525$		−	11730.4i		−	0.975160i
$526$	22783.9			1.88864
$527$	−1528.62	+	8756.25i	−0.126353	+	0.723772i
$528$	10128.1			0.834794
$529$			4866.96i			0.400013i
$530$	3075.12	−	3075.12i	0.252028	−	0.252028i
$531$	−5697.40			−0.465624
$532$	−4625.18	+	4625.18i	−0.376930	+	0.376930i
$533$	3131.50	+	3131.50i	0.254485	+	0.254485i
$534$	3131.64	+	3131.64i	0.253781	+	0.253781i
$535$			28834.1i			2.33011i
$536$			10852.4i			0.874538i
$537$	289.653	+	289.653i	0.0232764	+	0.0232764i
$538$	−14272.6	−	14272.6i	−1.14374	−	1.14374i
$539$	7955.87	−	7955.87i	0.635777	−	0.635777i
$540$	−1477.53			−0.117746
$541$	−7300.56	+	7300.56i	−0.580176	+	0.580176i	−0.934952	−	0.354775i	$-0.884557\pi$
$541$	−7300.56	+	7300.56i	−0.580176	+	0.580176i	0.354775	+	0.934952i	$0.384557\pi$
$542$		−	22212.2i		−	1.76032i
$543$	−6965.89			−0.550525
$544$	−5600.42	−	7969.37i	−0.441390	−	0.628096i
$545$	−162.996			−0.0128109
$546$			13860.8i			1.08642i
$547$	11859.8	−	11859.8i	0.927036	−	0.927036i	−0.0704770	−	0.997513i	$-0.522452\pi$
$547$	11859.8	−	11859.8i	0.927036	−	0.927036i	0.997513	+	0.0704770i	$0.0224521\pi$
$548$	3019.75			0.235397
$549$	1203.51	−	1203.51i	0.0935601	−	0.0935601i
$550$	−15987.3	−	15987.3i	−1.23945	−	1.23945i
$551$	−12731.8	−	12731.8i	−0.984379	−	0.984379i
$552$			6238.62i			0.481039i
$553$		−	8964.33i		−	0.689335i
$554$	−15983.7	−	15983.7i	−1.22578	−	1.22578i
$555$	−7461.00	−	7461.00i	−0.570634	−	0.570634i
$556$	2200.85	−	2200.85i	0.167872	−	0.167872i
$557$	2794.92			0.212611			0.106306	−	0.994334i	$-0.466098\pi$
$557$	2794.92			0.212611			0.106306	+	0.994334i	$0.466098\pi$
$558$	−2706.80	+	2706.80i	−0.205355	+	0.205355i
$559$		−	14316.4i		−	1.08322i
$560$	32979.3			2.48862
$561$	−7311.88	+	5138.38i	−0.550282	+	0.386707i
$562$	−10890.2			−0.817392
$563$			2322.28i			0.173841i	0.996215	+	0.0869204i	$0.0277026\pi$
$563$			2322.28i			0.173841i	−0.996215	+	0.0869204i	$0.972297\pi$
$564$	1593.15	−	1593.15i	0.118943	−	0.118943i
$565$	20926.3			1.55819
$566$	5967.38	−	5967.38i	0.443159	−	0.443159i
$567$	−1411.98	−	1411.98i	−0.104581	−	0.104581i
$568$	−6163.74	−	6163.74i	−0.455325	−	0.455325i
$569$			21761.5i			1.60332i	0.597778	+	0.801662i	$0.296050\pi$
$569$			21761.5i			1.60332i	−0.597778	+	0.801662i	$0.703950\pi$
$570$			13836.5i			1.01675i
$571$	1228.39	+	1228.39i	0.0900292	+	0.0900292i	0.750687	−	0.660658i	$-0.229723\pi$
$571$	1228.39	+	1228.39i	0.0900292	+	0.0900292i	−0.660658	+	0.750687i	$0.729723\pi$
$572$	5456.64	+	5456.64i	0.398870	+	0.398870i
$573$	−2857.15	+	2857.15i	−0.208305	+	0.208305i
$574$	−6553.11			−0.476519
$575$	14637.9	−	14637.9i	1.06164	−	1.06164i
$576$			1524.63i			0.110289i
$577$	−26921.6			−1.94239			−0.971195	−	0.238284i	$-0.923415\pi$
$577$	−26921.6			−1.94239			−0.971195	+	0.238284i	$0.923415\pi$
$578$	15503.6	+	5583.25i	1.11568	+	0.401786i
$579$	15188.8			1.09020
$580$		−	12067.0i		−	0.863890i
$581$	−4892.72	+	4892.72i	−0.349370	+	0.349370i
$582$	−8928.33			−0.635895
$583$	2313.78	−	2313.78i	0.164369	−	0.164369i
$584$	−8126.55	−	8126.55i	−0.575820	−	0.575820i
$585$	5988.71	+	5988.71i	0.423252	+	0.423252i
$586$			10005.8i			0.705353i
$587$			10102.5i			0.710352i	0.934799	+	0.355176i	$0.115579\pi$
$587$			10102.5i			0.710352i	−0.934799	+	0.355176i	$0.884421\pi$
$588$	−1824.86	−	1824.86i	−0.127987	−	0.127987i
$589$	7321.92	+	7321.92i	0.512214	+	0.512214i
$590$	−25284.1	+	25284.1i	−1.76429	+	1.76429i
$591$	−4734.45			−0.329525
$592$	11731.0	−	11731.0i	0.814426	−	0.814426i
$593$			15991.8i			1.10742i	0.832708	+	0.553712i	$0.186789\pi$
$593$			15991.8i			1.10742i	−0.832708	+	0.553712i	$0.813211\pi$
$594$	−3848.73			−0.265850
$595$	−23808.9	+	16731.6i	−1.64046	+	1.15282i
$596$	−9267.19			−0.636911
$597$		−	1997.10i		−	0.136911i
$598$	−17296.2	+	17296.2i	−1.18277	+	1.18277i
$599$	−17280.7			−1.17875			−0.589373	−	0.807861i	$-0.700625\pi$
$599$	−17280.7			−1.17875			−0.589373	+	0.807861i	$0.700625\pi$
$600$	5361.07	−	5361.07i	0.364775	−	0.364775i
$601$	5463.07	+	5463.07i	0.370787	+	0.370787i	0.867764	−	0.496977i	$-0.165557\pi$
$601$	5463.07	+	5463.07i	0.370787	+	0.370787i	−0.496977	+	0.867764i	$0.665557\pi$
$602$	14979.5	+	14979.5i	1.01415	+	1.01415i
$603$		−	6129.97i		−	0.413983i
$604$			11014.7i			0.742024i
$605$	−5659.27	−	5659.27i	−0.380301	−	0.380301i
$606$	−4122.27	−	4122.27i	−0.276329	−	0.276329i
$607$	9113.48	−	9113.48i	0.609398	−	0.609398i	−0.333391	−	0.942789i	$-0.608193\pi$
$607$	9113.48	−	9113.48i	0.609398	−	0.609398i	0.942789	+	0.333391i	$0.108193\pi$
$608$	−11347.0			−0.756876
$609$	11531.7	−	11531.7i	0.767303	−	0.767303i
$610$		−	10681.9i		−	0.709014i
$611$	−12914.7			−0.855112
$612$	1178.61	+	1677.15i	0.0778470	+	0.110776i
$613$	9361.69			0.616827			0.308414	−	0.951252i	$-0.400202\pi$
$613$	9361.69			0.616827			0.308414	+	0.951252i	$0.400202\pi$
$614$			3353.51i			0.220418i
$615$	−2831.34	+	2831.34i	−0.185644	+	0.185644i
$616$	16693.8			1.09190
$617$	14473.2	−	14473.2i	0.944356	−	0.944356i	−0.0541757	−	0.998531i	$-0.517253\pi$
$617$	14473.2	−	14473.2i	0.944356	−	0.944356i	0.998531	+	0.0541757i	$0.0172531\pi$
$618$	−744.686	−	744.686i	−0.0484720	−	0.0484720i
$619$	−11487.6	−	11487.6i	−0.745925	−	0.745925i	0.227786	−	0.973711i	$-0.426851\pi$
$619$	−11487.6	−	11487.6i	−0.745925	−	0.745925i	−0.973711	+	0.227786i	$0.926851\pi$
$620$			6939.61i			0.449519i
$621$		−	3523.88i		−	0.227711i
$622$	−11326.6	−	11326.6i	−0.730152	−	0.730152i
$623$	7672.60	+	7672.60i	0.493413	+	0.493413i
$624$	−9416.09	+	9416.09i	−0.604079	+	0.604079i
$625$	10293.8			0.658801
$626$	−14502.7	+	14502.7i	−0.925949	+	0.925949i
$627$			10410.8i			0.663107i
$628$	−1594.13			−0.101294
$629$	−2517.48	+	14420.6i	−0.159584	+	0.914127i
$630$	−12532.2			−0.792533
$631$			2480.05i			0.156464i	0.996935	+	0.0782322i	$0.0249276\pi$
$631$			2480.05i			0.156464i	−0.996935	+	0.0782322i	$0.975072\pi$
$632$	4096.89	−	4096.89i	0.257857	−	0.257857i
$633$	13129.9			0.824436
$634$	4516.96	−	4516.96i	0.282952	−	0.282952i
$635$	20981.1	+	20981.1i	1.31120	+	1.31120i
$636$	−530.720	−	530.720i	−0.0330887	−	0.0330887i
$637$			14793.1i			0.920130i
$638$		−	31432.7i		−	1.95052i
$639$	3481.58	+	3481.58i	0.215539	+	0.215539i
$640$	20004.6	+	20004.6i	1.23555	+	1.23555i
$641$	−11857.5	+	11857.5i	−0.730642	+	0.730642i	−0.970747	−	0.240105i	$-0.922818\pi$
$641$	−11857.5	+	11857.5i	−0.730642	+	0.730642i	0.240105	+	0.970747i	$0.422818\pi$
$642$	17227.9			1.05908
$643$	240.253	−	240.253i	0.0147351	−	0.0147351i	−0.699701	−	0.714436i	$-0.746683\pi$
$643$	240.253	−	240.253i	0.0147351	−	0.0147351i	0.714436	+	0.699701i	$0.246683\pi$
$644$		−	10455.0i		−	0.639729i
$645$	12944.1			0.790194
$646$	15705.9	−	11037.2i	0.956562	−	0.672217i
$647$	−4602.65			−0.279673			−0.139837	−	0.990175i	$-0.544658\pi$
$647$	−4602.65			−0.279673			−0.139837	+	0.990175i	$0.544658\pi$
$648$		−	1290.61i		−	0.0782406i
$649$	−19024.2	+	19024.2i	−1.15064	+	1.15064i
$650$	29726.5			1.79380
$651$	−6631.74	+	6631.74i	−0.399260	+	0.399260i
$652$	4116.44	+	4116.44i	0.247258	+	0.247258i
$653$	−13760.0	−	13760.0i	−0.824611	−	0.824611i	0.162154	−	0.986765i	$-0.448156\pi$
$653$	−13760.0	−	13760.0i	−0.824611	−	0.824611i	−0.986765	+	0.162154i	$0.948156\pi$
$654$			97.3869i			0.00582283i
$655$		−	1329.75i		−	0.0793246i
$656$	−4451.75	−	4451.75i	−0.264956	−	0.264956i
$657$	4590.28	+	4590.28i	0.272578	+	0.272578i
$658$	13512.9	−	13512.9i	0.800592	−	0.800592i
$659$	−18144.0			−1.07252			−0.536261	−	0.844052i	$-0.680164\pi$
$659$	−18144.0			−1.07252			−0.536261	+	0.844052i	$0.680164\pi$
$660$	−4933.62	+	4933.62i	−0.290971	+	0.290971i
$661$		−	14393.6i		−	0.846970i	−0.905903	−	0.423485i	$-0.860807\pi$
$661$		−	14393.6i		−	0.846970i	0.905903	−	0.423485i	$-0.139193\pi$
$662$	26896.7			1.57911
$663$	2020.70	−	11574.9i	0.118367	−	0.678030i
$664$	−4472.16			−0.261375
$665$			33899.7i			1.97680i
$666$	−4457.81	+	4457.81i	−0.259364	+	0.259364i
$667$	28779.7			1.67070
$668$	2583.99	−	2583.99i	0.149667	−	0.149667i
$669$	10214.1	+	10214.1i	0.590282	+	0.590282i
$670$	−27203.7	−	27203.7i	−1.56862	−	1.56862i
$671$		−	8037.29i		−	0.462409i
$672$		−	10277.4i		−	0.589969i
$673$	−12560.1	−	12560.1i	−0.719402	−	0.719402i	0.249081	−	0.968483i	$-0.419871\pi$
$673$	−12560.1	−	12560.1i	−0.719402	−	0.719402i	−0.968483	+	0.249081i	$0.919871\pi$
$674$	−28963.8	−	28963.8i	−1.65526	−	1.65526i
$675$	−3028.20	+	3028.20i	−0.172675	+	0.172675i
$676$	−3007.00			−0.171085
$677$	12033.3	−	12033.3i	0.683128	−	0.683128i	−0.277576	−	0.960704i	$-0.589531\pi$
$677$	12033.3	−	12033.3i	0.683128	−	0.683128i	0.960704	+	0.277576i	$0.0895311\pi$
$678$		−	12503.1i		−	0.708227i
$679$	−21874.7			−1.23634
$680$	−18527.9	−	3234.51i	−1.04487	−	0.182409i
$681$	−3979.91			−0.223951
$682$			18076.6i			1.01494i
$683$	−8041.12	+	8041.12i	−0.450490	+	0.450490i	−0.895517	−	0.445027i	$-0.853194\pi$
$683$	−8041.12	+	8041.12i	−0.450490	+	0.450490i	0.445027	+	0.895517i	$0.353194\pi$
$684$	2387.97			0.133489
$685$	11066.5	−	11066.5i	0.617267	−	0.617267i
$686$	4575.77	+	4575.77i	0.254670	+	0.254670i
$687$	10227.2	+	10227.2i	0.567964	+	0.567964i
$688$			20352.2i			1.12779i
$689$			4302.23i			0.237884i
$690$	−15638.4	−	15638.4i	−0.862816	−	0.862816i
$691$	−16381.5	−	16381.5i	−0.901855	−	0.901855i	0.0937419	−	0.995597i	$-0.470117\pi$
$691$	−16381.5	−	16381.5i	−0.901855	−	0.901855i	−0.995597	+	0.0937419i	$0.970117\pi$
$692$	6671.54	−	6671.54i	0.366494	−	0.366494i
$693$	−9429.49			−0.516878
$694$	−8555.69	+	8555.69i	−0.467968	+	0.467968i
$695$		−	16130.9i		−	0.880403i
$696$	10540.5			0.574045
$697$	5472.41	+	955.347i	0.297392	+	0.0519173i
$698$	−9152.05			−0.496290
$699$		−	11088.5i		−	0.600008i
$700$	−8984.37	+	8984.37i	−0.485111	+	0.485111i
$701$	−25706.5			−1.38505			−0.692525	−	0.721394i	$-0.743502\pi$
$701$	−25706.5			−1.38505			−0.692525	+	0.721394i	$0.743502\pi$
$702$	3578.14	−	3578.14i	0.192377	−	0.192377i
$703$	12058.4	+	12058.4i	0.646929	+	0.646929i
$704$	5090.91	+	5090.91i	0.272544	+	0.272544i
$705$		−	11676.8i		−	0.623794i
$706$			8429.19i			0.449344i
$707$	−10099.7	−	10099.7i	−0.537252	−	0.537252i
$708$	4363.65	+	4363.65i	0.231633	+	0.231633i
$709$	19768.6	−	19768.6i	1.04714	−	1.04714i	0.0483115	−	0.998832i	$-0.484616\pi$
$709$	19768.6	−	19768.6i	1.04714	−	1.04714i	0.998832	−	0.0483115i	$-0.0153840\pi$
$710$	30901.3			1.63339
$711$	−2314.13	+	2314.13i	−0.122063	+	0.122063i
$712$			7013.09i			0.369139i
$713$	−16550.9			−0.869335
$714$	9996.81	+	14225.4i	0.523979	+	0.745620i
$715$	39993.9			2.09187
$716$		−	443.691i		−	0.0231586i
$717$	641.554	−	641.554i	0.0334160	−	0.0334160i
$718$	−22498.7			−1.16942
$719$	24030.0	−	24030.0i	1.24641	−	1.24641i	0.289111	−	0.957296i	$-0.406640\pi$
$719$	24030.0	−	24030.0i	1.24641	−	1.24641i	0.957296	−	0.289111i	$-0.0933597\pi$
$720$	−8513.55	−	8513.55i	−0.440668	−	0.440668i
$721$	−1824.50	−	1824.50i	−0.0942413	−	0.0942413i
$722$			642.849i			0.0331362i
$723$		−	19315.8i		−	0.993585i
$724$	5335.19	+	5335.19i	0.273868	+	0.273868i
$725$	−24731.4	−	24731.4i	−1.26690	−	1.26690i
$726$	−3381.31	+	3381.31i	−0.172854	+	0.172854i
$727$	2058.35			0.105007			0.0525034	−	0.998621i	$-0.483280\pi$
$727$	2058.35			0.105007			0.0525034	+	0.998621i	$0.483280\pi$
$728$	−15520.2	+	15520.2i	−0.790131	+	0.790131i
$729$			729.000i			0.0370370i
$730$	40741.7			2.06564
$731$	−10325.4	−	14693.0i	−0.522433	−	0.743420i
$732$	−1843.54			−0.0930863
$733$			5879.10i			0.296247i	0.988969	+	0.148124i	$0.0473234\pi$
$733$			5879.10i			0.296247i	−0.988969	+	0.148124i	$0.952677\pi$
$734$	5283.63	−	5283.63i	0.265698	−	0.265698i
$735$	−13375.1			−0.671224
$736$	12824.7	−	12824.7i	0.642288	−	0.642288i
$737$	−20468.6	−	20468.6i	−1.02303	−	1.02303i
$738$	1691.68	+	1691.68i	0.0843787	+	0.0843787i
$739$			1015.40i			0.0505440i	0.999681	+	0.0252720i	$0.00804519\pi$
$739$			1015.40i			0.0505440i	−0.999681	+	0.0252720i	$0.991955\pi$
$740$			11428.8i			0.567744i
$741$	−9678.90	−	9678.90i	−0.479842	−	0.479842i
$742$	−4501.51	−	4501.51i	−0.222717	−	0.222717i
$743$	14598.4	−	14598.4i	0.720811	−	0.720811i	−0.247959	−	0.968771i	$-0.579760\pi$
$743$	14598.4	−	14598.4i	0.720811	−	0.720811i	0.968771	+	0.247959i	$0.0797598\pi$
$744$	−6061.70			−0.298700
$745$	−33961.4	+	33961.4i	−1.67013	+	1.67013i
$746$			20505.9i			1.00640i
$747$	2526.10			0.123728
$748$	9535.68	+	1664.69i	0.466122	+	0.0813733i
$749$	42208.8			2.05911
$750$			5695.62i			0.277299i
$751$	8471.38	−	8471.38i	0.411618	−	0.411618i	−0.470684	−	0.882302i	$-0.655993\pi$
$751$	8471.38	−	8471.38i	0.411618	−	0.411618i	0.882302	+	0.470684i	$0.155993\pi$
$752$	18359.6			0.890299
$753$	−6145.28	+	6145.28i	−0.297405	+	0.297405i
$754$	29222.9	+	29222.9i	1.41145	+	1.41145i
$755$	40365.6	+	40365.6i	1.94577	+	1.94577i
$756$			2162.87i			0.104052i
$757$			8449.86i			0.405701i	0.979210	+	0.202850i	$0.0650205\pi$
$757$			8449.86i			0.405701i	−0.979210	+	0.202850i	$0.934980\pi$
$758$	4432.93	+	4432.93i	0.212416	+	0.212416i
$759$	−11766.6	−	11766.6i	−0.562716	−	0.562716i
$760$	−15492.9	+	15492.9i	−0.739457	+	0.739457i
$761$	8080.05			0.384890			0.192445	−	0.981308i	$-0.438358\pi$
$761$	8080.05			0.384890			0.192445	+	0.981308i	$0.438358\pi$
$762$	12535.8	−	12535.8i	0.595965	−	0.595965i
$763$			238.601i			0.0113210i
$764$	4376.59			0.207251
$765$	10465.5	+	1827.01i	0.494614	+	0.0863474i
$766$	−10597.6			−0.499877
$767$		−	35373.5i		−	1.66527i
$768$	9077.53	−	9077.53i	0.426506	−	0.426506i
$769$	−24375.9			−1.14307			−0.571533	−	0.820579i	$-0.693651\pi$
$769$	−24375.9			−1.14307			−0.571533	+	0.820579i	$0.693651\pi$
$770$	−41846.4	+	41846.4i	−1.95849	+	1.95849i
$771$	11538.9	+	11538.9i	0.538993	+	0.538993i
$772$	−11633.1	−	11633.1i	−0.542338	−	0.542338i
$773$			25018.8i			1.16412i	0.813146	+	0.582060i	$0.197753\pi$
$773$			25018.8i			1.16412i	−0.813146	+	0.582060i	$0.802247\pi$
$774$		−	7733.89i		−	0.359159i
$775$	14222.8	+	14222.8i	0.659222	+	0.659222i
$776$	−9997.19	−	9997.19i	−0.462472	−	0.462472i
$777$	−10921.8	+	10921.8i	−0.504268	+	0.504268i
$778$	−15399.1			−0.709622
$779$	4575.99	−	4575.99i	0.210465	−	0.210465i
$780$		−	9173.53i		−	0.421109i
$781$	23250.8			1.06527
$782$	−5276.67	+	30225.8i	−0.241296	+	1.38219i
$783$	−5953.78			−0.271738
$784$		−	21029.8i		−	0.957992i
$785$	−5842.00	+	5842.00i	−0.265618	+	0.265618i
$786$	−794.501			−0.0360546
$787$	−17180.5	+	17180.5i	−0.778167	+	0.778167i	−0.979519	−	0.201352i	$-0.935466\pi$
$787$	−17180.5	+	17180.5i	−0.778167	+	0.778167i	0.201352	+	0.979519i	$0.435466\pi$
$788$	3626.12	+	3626.12i	0.163928	+	0.163928i
$789$	−14410.2	−	14410.2i	−0.650211	−	0.650211i
$790$			20539.4i			0.925012i
$791$		−	30632.9i		−	1.37697i
$792$	−4309.48	−	4309.48i	−0.193347	−	0.193347i
$793$	7472.23	+	7472.23i	0.334611	+	0.334611i
$794$	26261.4	−	26261.4i	1.17378	−	1.17378i
$795$	−3889.85			−0.173533
$796$	−1529.58	+	1529.58i	−0.0681089	+	0.0681089i
$797$			31232.7i			1.38810i	0.719926	+	0.694051i	$0.244176\pi$
$797$			31232.7i			1.38810i	−0.719926	+	0.694051i	$0.755824\pi$
$798$	20254.5			0.898497
$799$	−13254.4	+	9314.47i	−0.586869	+	0.412419i
$800$	−22041.4			−0.974102
$801$		−	3961.34i		−	0.174740i
$802$	−18921.2	+	18921.2i	−0.833082	+	0.833082i
$803$	30654.9			1.34718
$804$	−4694.96	+	4694.96i	−0.205943	+	0.205943i
$805$	−38314.5	−	38314.5i	−1.67753	−	1.67753i
$806$	−16805.7	−	16805.7i	−0.734438	−	0.734438i
$807$			18054.0i			0.787521i
$808$		−	9231.54i		−	0.401936i
$809$	11111.7	+	11111.7i	0.482902	+	0.482902i	0.906057	−	0.423155i	$-0.139078\pi$
$809$	11111.7	+	11111.7i	0.482902	+	0.482902i	−0.423155	+	0.906057i	$0.639078\pi$
$810$	3235.17	+	3235.17i	0.140336	+	0.140336i
$811$	24543.9	−	24543.9i	1.06270	−	1.06270i	0.0648062	−	0.997898i	$-0.479357\pi$
$811$	24543.9	−	24543.9i	1.06270	−	1.06270i	0.997898	−	0.0648062i	$-0.0206429\pi$
$812$	−17664.3			−0.763417
$813$	−14048.5	+	14048.5i	−0.606032	+	0.606032i
$814$			29770.2i			1.28187i
$815$	30171.0			1.29674
$816$	−2872.63	+	16455.0i	−0.123238	+	0.705930i
$817$	−20920.2			−0.895845
$818$		−	26269.8i		−	1.12286i
$819$	8766.55	−	8766.55i	0.374027	−	0.374027i
$820$	4337.06			0.184703
$821$	2105.65	−	2105.65i	0.0895099	−	0.0895099i	−0.660934	−	0.750444i	$-0.729840\pi$
$821$	2105.65	−	2105.65i	0.0895099	−	0.0895099i	0.750444	+	0.660934i	$0.229840\pi$
$822$	−6612.01	−	6612.01i	−0.280560	−	0.280560i
$823$	11713.0	+	11713.0i	0.496097	+	0.496097i	0.910221	−	0.414123i	$-0.135912\pi$
$823$	11713.0	+	11713.0i	0.496097	+	0.496097i	−0.414123	+	0.910221i	$0.635912\pi$
$824$		−	1667.67i		−	0.0705051i
$825$			20223.0i			0.853422i
$826$	37012.0	+	37012.0i	1.55910	+	1.55910i
$827$	−30264.8	−	30264.8i	−1.27256	−	1.27256i	−0.944739	−	0.327823i	$-0.893685\pi$
$827$	−30264.8	−	30264.8i	−1.27256	−	1.27256i	−0.327823	−	0.944739i	$-0.606315\pi$
$828$	−2698.95	+	2698.95i	−0.113279	+	0.113279i
$829$	−33758.6			−1.41433			−0.707167	−	0.707046i	$-0.750027\pi$
$829$	−33758.6			−1.41433			−0.707167	+	0.707046i	$0.750027\pi$
$830$	11210.4	−	11210.4i	0.468816	−	0.468816i
$831$			20218.4i			0.844007i
$832$	−9465.99			−0.394440
$833$	10669.2	+	15182.2i	0.443777	+	0.631492i
$834$	−9637.92			−0.400161
$835$		−	18939.1i		−	0.784926i
$836$	7973.67	−	7973.67i	0.329875	−	0.329875i
$837$	3423.95			0.141397
$838$	−12467.1	+	12467.1i	−0.513924	+	0.513924i
$839$	−18778.3	−	18778.3i	−0.772703	−	0.772703i	0.205875	−	0.978578i	$-0.433996\pi$
$839$	−18778.3	−	18778.3i	−0.772703	−	0.772703i	−0.978578	+	0.205875i	$0.933996\pi$
$840$	−14032.5	−	14032.5i	−0.576391	−	0.576391i
$841$		−	24235.7i		−	0.993716i
$842$			11638.1i			0.476336i
$843$	6887.72	+	6887.72i	0.281407	+	0.281407i
$844$	−10056.2	−	10056.2i	−0.410130	−	0.410130i
$845$	−11019.7	+	11019.7i	−0.448627	+	0.448627i
$846$	−6976.69			−0.283527
$847$	−8284.31	+	8284.31i	−0.336071	+	0.336071i
$848$		−	6116.05i		−	0.247672i
$849$	−7548.39			−0.305136
$850$	30508.5	−	21439.7i	1.23110	−	0.865146i
$851$	−27257.5			−1.09797
$852$		−	5333.10i		−	0.214447i
$853$	−4407.60	+	4407.60i	−0.176921	+	0.176921i	−0.790012	−	0.613091i	$-0.789926\pi$
$853$	−4407.60	+	4407.60i	−0.176921	+	0.176921i	0.613091	+	0.790012i	$0.289926\pi$
$854$	−15636.7			−0.626554
$855$	8751.16	−	8751.16i	0.350039	−	0.350039i
$856$	19290.3	+	19290.3i	0.770245	+	0.770245i
$857$	13851.1	+	13851.1i	0.552094	+	0.552094i	0.927045	−	0.374951i	$-0.122340\pi$
$857$	13851.1	+	13851.1i	0.552094	+	0.552094i	−0.374951	+	0.927045i	$0.622340\pi$
$858$		−	23895.6i		−	0.950795i
$859$		−	23713.4i		−	0.941898i	−0.882160	−	0.470949i	$-0.843912\pi$
$859$		−	23713.4i		−	0.941898i	0.882160	−	0.470949i	$-0.156088\pi$
$860$	−9913.94	−	9913.94i	−0.393096	−	0.393096i
$861$	4144.66	+	4144.66i	0.164053	+	0.164053i
$862$	−21747.3	+	21747.3i	−0.859299	+	0.859299i
$863$	10642.1			0.419771			0.209886	−	0.977726i	$-0.432691\pi$
$863$	10642.1			0.419771			0.209886	+	0.977726i	$0.432691\pi$
$864$	−2653.10	+	2653.10i	−0.104468	+	0.104468i
$865$		−	48898.3i		−	1.92207i
$866$	−9656.49			−0.378916
$867$	−6274.34	−	13336.8i	−0.245776	−	0.522425i
$868$	10158.5			0.397239
$869$			15454.2i			0.603279i
$870$	−26421.8	+	26421.8i	−1.02964	+	1.02964i
$871$	38059.2			1.48058
$872$	−109.046	+	109.046i	−0.00423481	+	0.00423481i
$873$	5646.91	+	5646.91i	0.218922	+	0.218922i
$874$	25274.6	+	25274.6i	0.978177	+	0.978177i
$875$			13954.4i			0.539138i
$876$		−	7031.41i		−	0.271198i
$877$	5293.93	+	5293.93i	0.203835	+	0.203835i	0.801641	−	0.597806i	$-0.203961\pi$
$877$	5293.93	+	5293.93i	0.203835	+	0.203835i	−0.597806	+	0.801641i	$0.703961\pi$
$878$	25950.5	+	25950.5i	0.997480	+	0.997480i
$879$	6328.39	−	6328.39i	0.242834	−	0.242834i
$880$	−56855.3			−2.17795
$881$	20754.3	−	20754.3i	0.793678	−	0.793678i	−0.188412	−	0.982090i	$-0.560334\pi$
$881$	20754.3	−	20754.3i	0.793678	−	0.793678i	0.982090	+	0.188412i	$0.0603339\pi$
$882$			7991.40i			0.305085i
$883$	−26493.4			−1.00971			−0.504855	−	0.863204i	$-0.668454\pi$
$883$	−26493.4			−1.00971			−0.504855	+	0.863204i	$0.668454\pi$
$884$	−10412.9	+	7317.62i	−0.396182	+	0.278414i
$885$	31982.9			1.21479
$886$			10307.0i			0.390824i
$887$	−20262.6	+	20262.6i	−0.767027	+	0.767027i	−0.977582	−	0.210555i	$-0.932473\pi$
$887$	−20262.6	+	20262.6i	−0.767027	+	0.767027i	0.210555	+	0.977582i	$0.432473\pi$
$888$	−9982.96			−0.377259
$889$	30713.1	−	30713.1i	1.15870	−	1.15870i
$890$	−17579.7	−	17579.7i	−0.662106	−	0.662106i
$891$	2434.21	+	2434.21i	0.0915253	+	0.0915253i
$892$		−	15645.9i		−	0.587293i
$893$			18872.0i			0.707197i
$894$	20291.3	+	20291.3i	0.759109	+	0.759109i
$895$	−1625.99	−	1625.99i	−0.0607273	−	0.0607273i
$896$	29283.7	−	29283.7i	1.09185	−	1.09185i
$897$	21878.7			0.814393
$898$	35344.7	−	35344.7i	1.31344	−	1.31344i
$899$			27963.5i			1.03742i
$900$	4638.61			0.171800
$901$	3102.89	+	4415.40i	0.114731	+	0.163261i
$902$	11297.4			0.417031
$903$		−	18948.2i		−	0.698293i
$904$	13999.9	−	13999.9i	0.515077	−	0.515077i
$905$	39103.7			1.43630
$906$	24117.7	−	24117.7i	0.884390	−	0.884390i
$907$	−14929.0	−	14929.0i	−0.546539	−	0.546539i	0.378899	−	0.925438i	$-0.376303\pi$
$907$	−14929.0	−	14929.0i	−0.546539	−	0.546539i	−0.925438	+	0.378899i	$0.876303\pi$
$908$	3048.22	+	3048.22i	0.111408	+	0.111408i
$909$			5214.43i			0.190266i
$910$		−	77808.9i		−	2.83444i
$911$	19255.7	+	19255.7i	0.700294	+	0.700294i	0.964474	−	0.264179i	$-0.0851010\pi$
$911$	19255.7	+	19255.7i	0.700294	+	0.700294i	−0.264179	+	0.964474i	$0.585101\pi$
$912$	13759.5	+	13759.5i	0.499587	+	0.499587i
$913$	8434.90	−	8434.90i	0.305755	−	0.305755i
$914$	−35680.7			−1.29126
$915$	−6756.01	+	6756.01i	−0.244095	+	0.244095i
$916$		−	15666.0i		−	0.565088i
$917$	−1946.55			−0.0700990
$918$	1091.61	−	6252.93i	0.0392466	−	0.224812i
$919$	−14081.0			−0.505428			−0.252714	−	0.967541i	$-0.581323\pi$
$919$	−14081.0			−0.505428			−0.252714	+	0.967541i	$0.581323\pi$
$920$		−	35021.1i		−	1.25501i
$921$	2121.00	−	2121.00i	0.0758840	−	0.0758840i
$922$	5297.46			0.189222
$923$	−21616.1	+	21616.1i	−0.770860	+	0.770860i
$924$	7222.07	+	7222.07i	0.257130	+	0.257130i
$925$	23423.3	+	23423.3i	0.832600	+	0.832600i
$926$		−	9362.91i		−	0.332273i
$927$			941.985i			0.0333752i
$928$	−21667.9	−	21667.9i	−0.766471	−	0.766471i
$929$	26545.3	+	26545.3i	0.937484	+	0.937484i	0.998158	−	0.0606733i	$-0.0193248\pi$
$929$	26545.3	+	26545.3i	0.937484	+	0.937484i	−0.0606733	+	0.998158i	$0.519325\pi$
$930$	15194.9	−	15194.9i	0.535764	−	0.535764i
$931$	21616.8			0.760968
$932$	−8492.71	+	8492.71i	−0.298485	+	0.298485i
$933$			14327.5i			0.502744i
$934$	22263.2			0.779949
$935$	41045.9	−	28844.8i	1.43566	−	1.00890i
$936$	8013.01			0.279822
$937$		−	15576.6i		−	0.543078i	−0.962427	−	0.271539i	$-0.912467\pi$
$937$		−	15576.6i		−	0.543078i	0.962427	−	0.271539i	$-0.0875326\pi$
$938$	−39822.1	+	39822.1i	−1.38618	+	1.38618i
$939$	18345.1			0.637560
$940$	−8943.31	+	8943.31i	−0.310318	+	0.310318i
$941$	−24963.5	−	24963.5i	−0.864810	−	0.864810i	0.127082	−	0.991892i	$-0.459439\pi$
$941$	−24963.5	−	24963.5i	−0.864810	−	0.864810i	−0.991892	+	0.127082i	$0.959439\pi$
$942$	3490.49	+	3490.49i	0.120729	+	0.120729i
$943$			10343.8i			0.357203i
$944$			50287.0i			1.73379i
$945$	7926.27	+	7926.27i	0.272848	+	0.272848i
$946$	−25824.3	−	25824.3i	−0.887547	−	0.887547i
$947$	−32846.8	+	32846.8i	−1.12711	+	1.12711i	−0.136469	+	0.990644i	$0.543575\pi$
$947$	−32846.8	+	32846.8i	−1.12711	+	1.12711i	−0.990644	+	0.136469i	$0.956425\pi$
$948$	3544.79			0.121445
$949$	−28499.7	+	28499.7i	−0.974856	+	0.974856i
$950$		−	43438.7i		−	1.48351i
$951$	−5713.69			−0.194826
$952$	−4734.83	+	27122.0i	−0.161194	+	0.923350i
$953$	24064.4			0.817968			0.408984	−	0.912542i	$-0.365883\pi$
$953$	24064.4			0.817968			0.408984	+	0.912542i	$0.365883\pi$
$954$			2324.12i			0.0788743i
$955$	16038.9	−	16038.9i	0.543461	−	0.543461i
$956$	−982.734			−0.0332468
$957$	−19880.3	+	19880.3i	−0.671514	+	0.671514i
$958$	−6451.53	−	6451.53i	−0.217578	−	0.217578i
$959$	−16199.6	−	16199.6i	−0.545478	−	0.545478i
$960$		−	8558.66i		−	0.287739i
$961$			13709.5i			0.460189i
$962$	−27677.2	−	27677.2i	−0.927598	−	0.927598i
$963$	−10896.1	−	10896.1i	−0.364613	−	0.364613i
$964$	−14794.0	+	14794.0i	−0.494277	+	0.494277i
$965$	−85263.5			−2.84428
$966$	−22892.2	+	22892.2i	−0.762468	+	0.762468i
$967$			44054.0i			1.46503i	0.680752	+	0.732514i	$0.261653\pi$
$967$			44054.0i			1.46503i	−0.680752	+	0.732514i	$0.738347\pi$
$968$	−7572.22			−0.251426
$969$	−16914.2	−	2952.80i	−0.560746	−	0.0978923i
$970$	50120.0			1.65903
$971$			6832.21i			0.225804i	0.993606	+	0.112902i	$0.0360147\pi$
$971$			6832.21i			0.225804i	−0.993606	+	0.112902i	$0.963985\pi$
$972$	558.343	−	558.343i	0.0184247	−	0.0184247i
$973$	−23613.2			−0.778010
$974$	−11164.2	+	11164.2i	−0.367273	+	0.367273i
$975$	−18801.2	−	18801.2i	−0.617559	−	0.617559i
$976$	−10622.5	−	10622.5i	−0.348380	−	0.348380i
$977$		−	4977.75i		−	0.163002i	−0.996673	−	0.0815008i	$-0.974029\pi$
$977$		−	4977.75i		−	0.163002i	0.996673	−	0.0815008i	$-0.0259713\pi$
$978$		−	18026.6i		−	0.589395i
$979$	−13227.3	−	13227.3i	−0.431816	−	0.431816i
$980$	10244.0	+	10244.0i	0.333912	+	0.333912i
$981$	61.5944	−	61.5944i	0.00200465	−	0.00200465i
$982$	33757.6			1.09699
$983$	−11935.6	+	11935.6i	−0.387269	+	0.387269i	−0.873712	−	0.486444i	$-0.838294\pi$
$983$	−11935.6	+	11935.6i	−0.387269	+	0.387269i	0.486444	+	0.873712i	$0.338294\pi$
$984$			3788.40i			0.122733i
$985$	26577.3			0.859718
$986$	51068.0	+	8915.20i	1.64943	+	0.287949i
$987$	−17093.1			−0.551245
$988$			14826.2i			0.477412i
$989$	23644.6	−	23644.6i	0.760218	−	0.760218i
$990$	21605.2			0.693594
$991$	−3614.91	+	3614.91i	−0.115874	+	0.115874i	−0.762666	−	0.646792i	$-0.776110\pi$
$991$	−3614.91	+	3614.91i	−0.115874	+	0.115874i	0.646792	+	0.762666i	$0.276110\pi$
$992$	12461.0	+	12461.0i	0.398828	+	0.398828i
$993$	−17011.4	−	17011.4i	−0.543646	−	0.543646i
$994$		−	45234.8i		−	1.44342i
$995$			11210.9i			0.357196i
$996$	−1934.74	−	1934.74i	−0.0615508	−	0.0615508i
$997$	−30371.5	−	30371.5i	−0.964770	−	0.964770i	0.0346301	−	0.999400i	$-0.488975\pi$
$997$	−30371.5	−	30371.5i	−0.964770	−	0.964770i	−0.999400	+	0.0346301i	$0.988975\pi$
$998$	13144.3	−	13144.3i	0.416910	−	0.416910i
$999$	5638.87			0.178585

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	51.4.e.a.4.7	✓	16
3.2	odd	2		153.4.f.b.55.2		16
17.8	even	8		867.4.a.p.1.7		8
17.9	even	8		867.4.a.q.1.7		8
17.13	even	4	inner	51.4.e.a.13.2	yes	16
51.47	odd	4		153.4.f.b.64.7		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
51.4.e.a.4.7	✓	16	1.1	even	1	trivial
51.4.e.a.13.2	yes	16	17.13	even	4	inner
153.4.f.b.55.2		16	3.2	odd	2
153.4.f.b.64.7		16	51.47	odd	4
867.4.a.p.1.7		8	17.8	even	8
867.4.a.q.1.7		8	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:	\( N \)	\(=\)	\( 51 = 3 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	51.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+3.35402i q^{2} +(2.12132 - 2.12132i) q^{3} -3.24945 q^{4} +(-11.9082 + 11.9082i) q^{5} +(7.11495 + 7.11495i) q^{6} +(17.4318 + 17.4318i) q^{7} +15.9334i q^{8} -9.00000i q^{9} +(-39.9404 - 39.9404i) q^{10} +(-30.0520 - 30.0520i) q^{11} +(-6.89312 + 6.89312i) q^{12} +55.8783 q^{13} +(-58.4667 + 58.4667i) q^{14} +50.5223i q^{15} -79.4367 q^{16} +(57.3482 - 40.3011i) q^{17} +30.1862 q^{18} -81.6537i q^{19} +(38.6952 - 38.6952i) q^{20} +73.9570 q^{21} +(100.795 - 100.795i) q^{22} +(92.2875 + 92.2875i) q^{23} +(33.7999 + 33.7999i) q^{24} -158.612i q^{25} +187.417i q^{26} +(-19.0919 - 19.0919i) q^{27} +(-56.6438 - 56.6438i) q^{28} +(155.924 - 155.924i) q^{29} -169.453 q^{30} +(-89.6703 + 89.6703i) q^{31} -138.965i q^{32} -127.500 q^{33} +(135.171 + 192.347i) q^{34} -415.164 q^{35} +29.2450i q^{36} +(-147.677 + 147.677i) q^{37} +273.868 q^{38} +(118.536 - 118.536i) q^{39} +(-189.739 - 189.739i) q^{40} +(56.0414 + 56.0414i) q^{41} +248.053i q^{42} -256.206i q^{43} +(97.6522 + 97.6522i) q^{44} +(107.174 + 107.174i) q^{45} +(-309.534 + 309.534i) q^{46} -231.122 q^{47} +(-168.511 + 168.511i) q^{48} +264.737i q^{49} +531.987 q^{50} +(36.1625 - 207.146i) q^{51} -181.574 q^{52} +76.9927i q^{53} +(64.0345 - 64.0345i) q^{54} +715.731 q^{55} +(-277.749 + 277.749i) q^{56} +(-173.214 - 173.214i) q^{57} +(522.973 + 522.973i) q^{58} -633.045i q^{59} -164.170i q^{60} +(133.723 + 133.723i) q^{61} +(-300.756 - 300.756i) q^{62} +(156.886 - 156.886i) q^{63} -169.404 q^{64} +(-665.412 + 665.412i) q^{65} -427.636i q^{66} +681.108 q^{67} +(-186.350 + 130.956i) q^{68} +391.543 q^{69} -1392.47i q^{70} +(-386.843 + 386.843i) q^{71} +143.401 q^{72} +(-510.031 + 510.031i) q^{73} +(-495.312 - 495.312i) q^{74} +(-336.466 - 336.466i) q^{75} +265.330i q^{76} -1047.72i q^{77} +(397.572 + 397.572i) q^{78} +(-257.125 - 257.125i) q^{79} +(945.950 - 945.950i) q^{80} -81.0000 q^{81} +(-187.964 + 187.964i) q^{82} +280.677i q^{83} -240.319 q^{84} +(-203.001 + 1162.83i) q^{85} +859.321 q^{86} -661.531i q^{87} +(478.831 - 478.831i) q^{88} +440.149 q^{89} +(-359.464 + 359.464i) q^{90} +(974.061 + 974.061i) q^{91} +(-299.883 - 299.883i) q^{92} +380.439i q^{93} -775.188i q^{94} +(972.351 + 972.351i) q^{95} +(-294.788 - 294.788i) q^{96} +(-627.434 + 627.434i) q^{97} -887.934 q^{98} +(-270.468 + 270.468i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 48 q^{4} - 32 q^{5} + 12 q^{6} - 8 q^{7} - 20 q^{10} + 96 q^{11} + 120 q^{13} - 288 q^{14} - 200 q^{16} + 16 q^{17} - 72 q^{18} + 384 q^{20} + 168 q^{21} + 4 q^{22} + 208 q^{23} + 312 q^{24} + 904 q^{28}+ \cdots + 864 q^{99}+O(q^{100}) \) 16 * q - 48 * q^4 - 32 * q^5 + 12 * q^6 - 8 * q^7 - 20 * q^10 + 96 * q^11 + 120 * q^13 - 288 * q^14 - 200 * q^16 + 16 * q^17 - 72 * q^18 + 384 * q^20 + 168 * q^21 + 4 * q^22 + 208 * q^23 + 312 * q^24 + 904 * q^28 + 320 * q^29 - 432 * q^30 - 624 * q^31 - 72 * q^33 - 788 * q^34 - 1184 * q^35 + 256 * q^37 - 168 * q^38 - 24 * q^39 - 664 * q^40 + 800 * q^41 + 128 * q^44 + 288 * q^45 + 572 * q^46 + 368 * q^47 + 96 * q^48 - 720 * q^50 - 120 * q^51 - 3160 * q^52 + 108 * q^54 + 4296 * q^55 + 576 * q^56 - 1080 * q^57 + 1368 * q^58 - 1296 * q^61 + 536 * q^62 - 72 * q^63 + 1752 * q^64 - 4288 * q^65 - 1248 * q^67 - 240 * q^68 + 576 * q^69 + 1488 * q^71 + 864 * q^72 - 1208 * q^73 + 2272 * q^74 + 1200 * q^75 + 564 * q^78 - 1256 * q^79 + 384 * q^80 - 1296 * q^81 + 3564 * q^82 - 2088 * q^84 + 3216 * q^85 + 3224 * q^86 - 1296 * q^88 - 2608 * q^89 - 180 * q^90 - 56 * q^91 - 5072 * q^92 + 160 * q^95 - 408 * q^96 - 4456 * q^97 - 1208 * q^98 + 864 * q^99

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