LMFDB - Embedded newform 51.4.e.a.13.2

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			13.2
Root			$-4.35402i$ of defining polynomial
Character	$\chi$	$=$	51.13
Dual form			51.4.e.a.4.7

$q$-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 $\left(\mathbb{Z}/51\mathbb{Z}\right)^\times$.

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

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	$-0.797978\pi$
$2$		−	3.35402i		−	1.18582i	0.805267	−	0.592912i	$-0.202022\pi$
$3$	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	−0.997728	−	0.0673767i	$-0.978537\pi$
$5$	−11.9082	−	11.9082i	−1.06510	−	1.06510i	−0.0673767	−	0.997728i	$-0.521463\pi$
$6$	7.11495	−	7.11495i	0.484111	−	0.484111i
$7$	17.4318	−	17.4318i	0.941230	−	0.941230i	−0.0571362	−	0.998366i	$-0.518197\pi$
$7$	17.4318	−	17.4318i	0.941230	−	0.941230i	0.998366	+	0.0571362i	$0.0181969\pi$
$8$		−	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	−0.986641	−	0.162913i	$-0.947911\pi$
$11$	−30.0520	+	30.0520i	−0.823728	+	0.823728i	0.162913	+	0.986641i	$0.447911\pi$
$12$	−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	$0.164087\pi$
$19$			81.6537i			0.985929i	−0.870049	+	0.492965i	$0.835913\pi$
$20$	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	−0.151754	−	0.988418i	$-0.548492\pi$
$23$	92.2875	−	92.2875i	0.836664	−	0.836664i	0.988418	+	0.151754i	$0.0484923\pi$
$24$	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	0.999999	−	0.00157095i	$-0.000500049\pi$
$29$	155.924	+	155.924i	0.998428	+	0.998428i	−0.00157095	+	0.999999i	$0.500500\pi$
$30$	−169.453			−1.03126
$31$	−89.6703	−	89.6703i	−0.519525	−	0.519525i	0.397903	−	0.917428i	$-0.369738\pi$
$31$	−89.6703	−	89.6703i	−0.519525	−	0.519525i	−0.917428	+	0.397903i	$0.869738\pi$
$32$			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	0.298308	−	0.954470i	$-0.403578\pi$
$37$	−147.677	−	147.677i	−0.656162	−	0.656162i	−0.954470	+	0.298308i	$0.903578\pi$
$38$	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	−0.592271	−	0.805739i	$-0.701768\pi$
$41$	56.0414	−	56.0414i	0.213468	−	0.213468i	0.805739	+	0.592271i	$0.201768\pi$
$42$		−	248.053i		−	0.911320i
$43$			256.206i			0.908630i	0.890841	+	0.454315i	$0.150116\pi$
$43$			256.206i			0.908630i	−0.890841	+	0.454315i	$0.849884\pi$
$44$	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	$-0.968189\pi$
$53$		−	76.9927i		−	0.199543i	0.995010	−	0.0997714i	$-0.0318111\pi$
$54$	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	$0.246120\pi$
$59$			633.045i			1.39687i	−0.715673	+	0.698436i	$0.753880\pi$
$60$			164.170i			0.353237i
$61$	133.723	−	133.723i	0.280680	−	0.280680i	−0.552700	−	0.833380i	$-0.686402\pi$
$61$	133.723	−	133.723i	0.280680	−	0.280680i	0.833380	+	0.552700i	$0.186402\pi$
$62$	−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	0.305557	−	0.952174i	$-0.401157\pi$
$71$	−386.843	−	386.843i	−0.646617	−	0.646617i	−0.952174	+	0.305557i	$0.901157\pi$
$72$	143.401			0.234722
$73$	−510.031	−	510.031i	−0.817734	−	0.817734i	0.168045	−	0.985779i	$-0.446255\pi$
$73$	−510.031	−	510.031i	−0.817734	−	0.817734i	−0.985779	+	0.168045i	$0.946255\pi$
$74$	−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	−0.866085	−	0.499897i	$-0.833371\pi$
$79$	−257.125	+	257.125i	−0.366188	+	0.366188i	0.499897	+	0.866085i	$0.333371\pi$
$80$	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	$-0.940580\pi$
$83$		−	280.677i		−	0.371185i	0.982627	−	0.185592i	$-0.0594204\pi$
$84$	−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	0.297848	−	0.954613i	$-0.403731\pi$
$97$	−627.434	−	627.434i	−0.656766	−	0.656766i	−0.954613	+	0.297848i	$0.903731\pi$
$98$	−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	0.995115	+	0.0987257i	$0.0314766\pi$
$107$	1210.68	+	1210.68i	1.09384	+	1.09384i	0.0987257	+	0.995115i	$0.468523\pi$
$108$	62.0381	−	62.0381i	0.0552742	−	0.0552742i
$109$	6.84383	−	6.84383i	0.00601394	−	0.00601394i	−0.704093	−	0.710107i	$-0.748646\pi$
$109$	6.84383	−	6.84383i	0.00601394	−	0.00601394i	0.710107	+	0.704093i	$0.248646\pi$
$110$		−	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	−0.970911	−	0.239439i	$-0.923036\pi$
$113$	−878.649	+	878.649i	−0.731472	+	0.731472i	0.239439	+	0.970911i	$0.423036\pi$
$114$	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	$0.211056\pi$
$127$			1761.90i			1.23105i	−0.788117	+	0.615525i	$0.788944\pi$
$128$			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	0.688243	−	0.725481i	$-0.258382\pi$
$131$	−55.8332	−	55.8332i	−0.0372380	−	0.0372380i	−0.725481	+	0.688243i	$0.758382\pi$
$132$	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	0.469590	−	0.882884i	$-0.344402\pi$
$139$	−677.301	−	677.301i	−0.413294	−	0.413294i	−0.882884	+	0.469590i	$0.844402\pi$
$140$	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	$0.366565\pi$
$151$			3389.72i			1.82683i	−0.407027	+	0.913416i	$0.633435\pi$
$152$	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	−0.942617	−	0.333877i	$-0.891643\pi$
$163$	−1266.81	+	1266.81i	−0.608739	+	0.608739i	0.333877	+	0.942617i	$0.391643\pi$
$164$	−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	0.498447	−	0.866920i	$-0.333904\pi$
$167$	−795.209	−	795.209i	−0.368474	−	0.368474i	−0.866920	+	0.498447i	$0.833904\pi$
$168$		−	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	0.0933416	−	0.995634i	$-0.470245\pi$
$173$	−2053.13	−	2053.13i	−0.902292	−	0.902292i	−0.995634	+	0.0933416i	$0.970245\pi$
$174$	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	$-0.990924\pi$
$179$		−	136.544i		−	0.0570154i	0.999594	−	0.0285077i	$-0.00907551\pi$
$180$	−348.256	+	348.256i	−0.144208	+	0.144208i
$181$	−1641.88	+	1641.88i	−0.674252	+	0.674252i	−0.958694	−	0.284441i	$-0.908192\pi$
$181$	−1641.88	+	1641.88i	−0.674252	+	0.674252i	0.284441	+	0.958694i	$0.408192\pi$
$182$	−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	0.434578	−	0.900634i	$-0.356898\pi$
$193$	3580.03	−	3580.03i	1.33521	−	1.33521i	0.900634	−	0.434578i	$-0.143102\pi$
$194$	−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	−0.879494	−	0.475910i	$-0.842119\pi$
$197$	−1115.92	+	1115.92i	−0.403584	+	0.403584i	0.475910	+	0.879494i	$0.342119\pi$
$198$	−907.154	+	907.154i	−0.325599	+	0.325599i
$199$	470.721	+	470.721i	0.167681	+	0.167681i	0.785959	−	0.618278i	$-0.212169\pi$
$199$	470.721	+	470.721i	0.167681	+	0.167681i	−0.618278	+	0.785959i	$0.712169\pi$
$200$	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	0.00977143	−	0.999952i	$-0.496890\pi$
$211$	3094.75	−	3094.75i	1.00972	−	1.00972i	0.999952	−	0.00977143i	$-0.00311039\pi$
$212$			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	$-0.742788\pi$
$223$		−	4814.96i		−	1.44589i	0.690906	−	0.722945i	$-0.257212\pi$
$224$	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	−0.830822	−	0.556539i	$-0.812129\pi$
$227$	−938.074	+	938.074i	−0.274283	+	0.274283i	0.556539	+	0.830822i	$0.312129\pi$
$228$	562.849	−	562.849i	0.163489	−	0.163489i
$229$		−	4821.14i		−	1.39122i	−0.718418	−	0.695611i	$-0.755134\pi$
$229$		−	4821.14i		−	1.39122i	0.718418	−	0.695611i	$-0.244866\pi$
$230$			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	0.971578	−	0.236721i	$-0.0760726\pi$
$233$	2613.59	+	2613.59i	0.734857	+	0.734857i	−0.236721	+	0.971578i	$0.576073\pi$
$234$	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	0.968716	+	0.248172i	$0.0798299\pi$
$241$	4552.78	+	4552.78i	1.21689	+	1.21689i	0.248172	+	0.968716i	$0.420170\pi$
$242$	−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	$-0.770502\pi$
$257$		−	5439.49i		−	1.32026i	0.751152	−	0.660129i	$-0.229498\pi$
$258$	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	$0.293234\pi$
$263$			6793.03i			1.59268i	−0.604846	+	0.796342i	$0.706766\pi$
$264$			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	0.0348793	−	0.999392i	$-0.488895\pi$
$269$	−4255.36	−	4255.36i	−0.964512	−	0.964512i	−0.999392	+	0.0348793i	$0.988895\pi$
$270$		−	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	−0.999412	−	0.0342806i	$-0.989086\pi$
$277$	−4765.53	−	4765.53i	−1.03369	−	1.03369i	−0.0342806	−	0.999412i	$-0.510914\pi$
$278$	−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	$-0.887997\pi$
$281$		−	3246.90i		−	0.689303i	0.938731	−	0.344651i	$-0.112003\pi$
$282$	−1644.42	+	1644.42i	−0.347248	+	0.347248i
$283$	−1779.17	+	1779.17i	−0.373713	+	0.373713i	−0.868828	−	0.495114i	$-0.835126\pi$
$283$	−1779.17	+	1779.17i	−0.373713	+	0.373713i	0.495114	+	0.868828i	$0.335126\pi$
$284$	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	0.328701	−	0.944434i	$-0.393389\pi$
$311$	−3377.02	−	3377.02i	−0.615733	−	0.615733i	−0.944434	+	0.328701i	$0.893389\pi$
$312$	1888.68	−	1888.68i	0.342711	−	0.342711i
$313$	4323.97	−	4323.97i	0.780848	−	0.780848i	−0.199126	−	0.979974i	$-0.563810\pi$
$313$	4323.97	−	4323.97i	0.780848	−	0.780848i	0.979974	+	0.199126i	$0.0638102\pi$
$314$		−	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	−0.816275	−	0.577663i	$-0.803965\pi$
$317$	−1346.73	+	1346.73i	−0.238612	+	0.238612i	0.577663	+	0.816275i	$0.303965\pi$
$318$	−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	$0.231921\pi$
$331$			8019.25i			1.33166i	−0.746105	+	0.665828i	$0.768079\pi$
$332$			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	−0.811449	−	0.584423i	$-0.801321\pi$
$337$	−8635.56	−	8635.56i	−1.39587	−	1.39587i	−0.584423	−	0.811449i	$-0.698679\pi$
$338$		−	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	−0.481701	−	0.876336i	$-0.659981\pi$
$347$	2550.88	−	2550.88i	0.394635	−	0.394635i	0.876336	+	0.481701i	$0.159981\pi$
$348$		−	2149.61i		−	0.331124i
$349$		−	2728.68i		−	0.418519i	−0.977860	−	0.209259i	$-0.932895\pi$
$349$		−	2728.68i		−	0.418519i	0.977860	−	0.209259i	$-0.0671053\pi$
$350$	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	$-0.835870\pi$
$359$		−	6707.98i		−	0.986166i	0.869982	−	0.493083i	$-0.164130\pi$
$360$	−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	−0.810206	−	0.586145i	$-0.800645\pi$
$367$	−1575.31	+	1575.31i	−0.224062	+	0.224062i	0.586145	+	0.810206i	$0.300645\pi$
$368$	−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	0.790976	−	0.611847i	$-0.209573\pi$
$379$	1321.68	+	1321.68i	0.179129	+	0.179129i	−0.611847	+	0.790976i	$0.709573\pi$
$380$	−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	$-0.932402\pi$
$383$		−	3159.66i		−	0.421544i	0.977535	−	0.210772i	$-0.0675977\pi$
$384$	−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	$-0.903277\pi$
$389$		−	4591.25i		−	0.598420i	0.954187	−	0.299210i	$-0.0967231\pi$
$390$	−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	−0.999949	−	0.0101040i	$-0.996784\pi$
$397$	−7829.84	+	7829.84i	−0.989845	+	0.989845i	0.0101040	+	0.999949i	$0.496784\pi$
$398$	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	−0.262420	−	0.964954i	$-0.584521\pi$
$401$	5641.36	−	5641.36i	0.702533	−	0.702533i	0.964954	+	0.262420i	$0.0845207\pi$
$402$	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	−0.456390	−	0.889780i	$-0.650858\pi$
$419$	3717.06	−	3717.06i	0.433390	−	0.433390i	0.889780	+	0.456390i	$0.150858\pi$
$420$	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	−0.244905	−	0.969547i	$-0.578757\pi$
$431$	6483.95	−	6483.95i	0.724643	−	0.724643i	0.969547	+	0.244905i	$0.0787566\pi$
$432$	1516.60	−	1516.60i	0.168906	−	0.168906i
$433$		−	2879.08i		−	0.319538i	−0.987154	−	0.159769i	$-0.948925\pi$
$433$		−	2879.08i		−	0.319538i	0.987154	−	0.159769i	$-0.0510749\pi$
$434$			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	0.989011	−	0.147841i	$-0.0472325\pi$
$439$	7737.14	+	7737.14i	0.841170	+	0.841170i	−0.147841	+	0.989011i	$0.547232\pi$
$440$		−	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	−0.114152	+	0.993463i	$0.536415\pi$
$449$	−10538.0	+	10538.0i	−1.10762	+	1.10762i	−0.993463	+	0.114152i	$0.963585\pi$
$450$			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	$-0.816736\pi$
$457$		−	10638.2i		−	1.08891i	0.838789	−	0.544456i	$-0.183264\pi$
$458$	−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	$0.0254233\pi$
$461$			1579.43i			0.159570i	−0.996812	+	0.0797848i	$0.974577\pi$
$462$	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	$0.106666\pi$
$467$			6637.75i			0.657727i	−0.944377	+	0.328864i	$0.893334\pi$
$468$		−	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	0.609389	−	0.792871i	$-0.291415\pi$
$479$	−1923.52	−	1923.52i	−0.183482	−	0.183482i	−0.792871	+	0.609389i	$0.791415\pi$
$480$	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	−0.535081	−	0.844801i	$-0.679719\pi$
$487$	3328.61	−	3328.61i	0.309720	−	0.309720i	0.844801	+	0.535081i	$0.179719\pi$
$488$	−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	$0.153063\pi$
$491$			10064.8i			0.925088i	−0.886596	+	0.462544i	$0.846937\pi$
$492$	−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	−0.860696	−	0.509119i	$-0.829971\pi$
$499$	−3918.97	+	3918.97i	−0.351578	+	0.351578i	0.509119	+	0.860696i	$0.329971\pi$
$500$	−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	−0.259645	−	0.965704i	$-0.583605\pi$
$503$	7965.14	−	7965.14i	0.706060	−	0.706060i	0.965704	+	0.259645i	$0.0836054\pi$
$504$	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	−0.474070	−	0.880487i	$-0.657216\pi$
$521$	4833.13	−	4833.13i	0.406417	−	0.406417i	0.880487	+	0.474070i	$0.157216\pi$
$522$	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	0.354775	−	0.934952i	$-0.384557\pi$
$541$	−7300.56	−	7300.56i	−0.580176	−	0.580176i	−0.934952	+	0.354775i	$0.884557\pi$
$542$			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	0.997513	−	0.0704770i	$-0.0224521\pi$
$547$	11859.8	+	11859.8i	0.927036	+	0.927036i	−0.0704770	+	0.997513i	$0.522452\pi$
$548$	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	$-0.972297\pi$
$563$		−	2322.28i		−	0.173841i	0.996215	−	0.0869204i	$-0.0277026\pi$
$564$	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	$-0.703950\pi$
$569$		−	21761.5i		−	1.60332i	0.597778	−	0.801662i	$-0.296050\pi$
$570$		−	13836.5i		−	1.01675i
$571$	1228.39	−	1228.39i	0.0900292	−	0.0900292i	−0.660658	−	0.750687i	$-0.729723\pi$
$571$	1228.39	−	1228.39i	0.0900292	−	0.0900292i	0.750687	+	0.660658i	$0.229723\pi$
$572$	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	$-0.884421\pi$
$587$		−	10102.5i		−	0.710352i	0.934799	−	0.355176i	$-0.115579\pi$
$588$	−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	$-0.813211\pi$
$593$		−	15991.8i		−	1.10742i	0.832708	−	0.553712i	$-0.186789\pi$
$594$	−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	−0.496977	−	0.867764i	$-0.665557\pi$
$601$	5463.07	−	5463.07i	0.370787	−	0.370787i	0.867764	+	0.496977i	$0.165557\pi$
$602$	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	0.942789	−	0.333391i	$-0.108193\pi$
$607$	9113.48	+	9113.48i	0.609398	+	0.609398i	−0.333391	+	0.942789i	$0.608193\pi$
$608$	−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	0.998531	−	0.0541757i	$-0.0172531\pi$
$617$	14473.2	+	14473.2i	0.944356	+	0.944356i	−0.0541757	+	0.998531i	$0.517253\pi$
$618$	−744.686	+	744.686i	−0.0484720	+	0.0484720i
$619$	−11487.6	+	11487.6i	−0.745925	+	0.745925i	−0.973711	−	0.227786i	$-0.926851\pi$
$619$	−11487.6	+	11487.6i	−0.745925	+	0.745925i	0.227786	+	0.973711i	$0.426851\pi$
$620$		−	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	$-0.975072\pi$
$631$		−	2480.05i		−	0.156464i	0.996935	−	0.0782322i	$-0.0249276\pi$
$632$	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	0.240105	−	0.970747i	$-0.422818\pi$
$641$	−11857.5	−	11857.5i	−0.730642	−	0.730642i	−0.970747	+	0.240105i	$0.922818\pi$
$642$	17227.9			1.05908
$643$	240.253	+	240.253i	0.0147351	+	0.0147351i	0.714436	−	0.699701i	$-0.246683\pi$
$643$	240.253	+	240.253i	0.0147351	+	0.0147351i	−0.699701	+	0.714436i	$0.746683\pi$
$644$			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	−0.986765	−	0.162154i	$-0.948156\pi$
$653$	−13760.0	+	13760.0i	−0.824611	+	0.824611i	0.162154	+	0.986765i	$0.448156\pi$
$654$		−	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	$0.139193\pi$
$661$			14393.6i			0.846970i	−0.905903	+	0.423485i	$0.860807\pi$
$662$	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	−0.968483	−	0.249081i	$-0.919871\pi$
$673$	−12560.1	+	12560.1i	−0.719402	+	0.719402i	0.249081	+	0.968483i	$0.419871\pi$
$674$	−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	0.960704	−	0.277576i	$-0.0895311\pi$
$677$	12033.3	+	12033.3i	0.683128	+	0.683128i	−0.277576	+	0.960704i	$0.589531\pi$
$678$			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	0.445027	−	0.895517i	$-0.353194\pi$
$683$	−8041.12	−	8041.12i	−0.450490	−	0.450490i	−0.895517	+	0.445027i	$0.853194\pi$
$684$	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	−0.995597	−	0.0937419i	$-0.970117\pi$
$691$	−16381.5	+	16381.5i	−0.901855	+	0.901855i	0.0937419	+	0.995597i	$0.470117\pi$
$692$	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	0.998832	+	0.0483115i	$0.0153840\pi$
$709$	19768.6	+	19768.6i	1.04714	+	1.04714i	0.0483115	+	0.998832i	$0.484616\pi$
$710$	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	0.957296	+	0.289111i	$0.0933597\pi$
$719$	24030.0	+	24030.0i	1.24641	+	1.24641i	0.289111	+	0.957296i	$0.406640\pi$
$720$	−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	$-0.952677\pi$
$733$		−	5879.10i		−	0.296247i	0.988969	−	0.148124i	$-0.0473234\pi$
$734$	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	$-0.991955\pi$
$739$		−	1015.40i		−	0.0505440i	0.999681	−	0.0252720i	$-0.00804519\pi$
$740$		−	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	0.968771	−	0.247959i	$-0.0797598\pi$
$743$	14598.4	+	14598.4i	0.720811	+	0.720811i	−0.247959	+	0.968771i	$0.579760\pi$
$744$	−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	0.882302	−	0.470684i	$-0.155993\pi$
$751$	8471.38	+	8471.38i	0.411618	+	0.411618i	−0.470684	+	0.882302i	$0.655993\pi$
$752$	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	$-0.934980\pi$
$757$		−	8449.86i		−	0.405701i	0.979210	−	0.202850i	$-0.0650205\pi$
$758$	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	$-0.802247\pi$
$773$		−	25018.8i		−	1.16412i	0.813146	−	0.582060i	$-0.197753\pi$
$774$			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	0.201352	−	0.979519i	$-0.435466\pi$
$787$	−17180.5	−	17180.5i	−0.778167	−	0.778167i	−0.979519	+	0.201352i	$0.935466\pi$
$788$	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	$-0.755824\pi$
$797$		−	31232.7i		−	1.38810i	0.719926	−	0.694051i	$-0.244176\pi$
$798$	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	−0.423155	−	0.906057i	$-0.639078\pi$
$809$	11111.7	−	11111.7i	0.482902	−	0.482902i	0.906057	+	0.423155i	$0.139078\pi$
$810$	3235.17	−	3235.17i	0.140336	−	0.140336i
$811$	24543.9	+	24543.9i	1.06270	+	1.06270i	0.997898	+	0.0648062i	$0.0206429\pi$
$811$	24543.9	+	24543.9i	1.06270	+	1.06270i	0.0648062	+	0.997898i	$0.479357\pi$
$812$	−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	0.750444	−	0.660934i	$-0.229840\pi$
$821$	2105.65	+	2105.65i	0.0895099	+	0.0895099i	−0.660934	+	0.750444i	$0.729840\pi$
$822$	−6612.01	+	6612.01i	−0.280560	+	0.280560i
$823$	11713.0	−	11713.0i	0.496097	−	0.496097i	−0.414123	−	0.910221i	$-0.635912\pi$
$823$	11713.0	−	11713.0i	0.496097	−	0.496097i	0.910221	+	0.414123i	$0.135912\pi$
$824$			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	−0.327823	+	0.944739i	$0.606315\pi$
$827$	−30264.8	+	30264.8i	−1.27256	+	1.27256i	−0.944739	+	0.327823i	$0.893685\pi$
$828$	−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	−0.978578	−	0.205875i	$-0.933996\pi$
$839$	−18778.3	+	18778.3i	−0.772703	+	0.772703i	0.205875	+	0.978578i	$0.433996\pi$
$840$	−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	0.613091	−	0.790012i	$-0.289926\pi$
$853$	−4407.60	−	4407.60i	−0.176921	−	0.176921i	−0.790012	+	0.613091i	$0.789926\pi$
$854$	−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	−0.374951	−	0.927045i	$-0.622340\pi$
$857$	13851.1	−	13851.1i	0.552094	−	0.552094i	0.927045	+	0.374951i	$0.122340\pi$
$858$			23895.6i			0.950795i
$859$			23713.4i			0.941898i	0.882160	+	0.470949i	$0.156088\pi$
$859$			23713.4i			0.941898i	−0.882160	+	0.470949i	$0.843912\pi$
$860$	−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	−0.597806	−	0.801641i	$-0.703961\pi$
$877$	5293.93	−	5293.93i	0.203835	−	0.203835i	0.801641	+	0.597806i	$0.203961\pi$
$878$	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	0.982090	−	0.188412i	$-0.0603339\pi$
$881$	20754.3	+	20754.3i	0.793678	+	0.793678i	−0.188412	+	0.982090i	$0.560334\pi$
$882$		−	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	0.210555	−	0.977582i	$-0.432473\pi$
$887$	−20262.6	−	20262.6i	−0.767027	−	0.767027i	−0.977582	+	0.210555i	$0.932473\pi$
$888$	−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	−0.925438	−	0.378899i	$-0.876303\pi$
$907$	−14929.0	+	14929.0i	−0.546539	+	0.546539i	0.378899	+	0.925438i	$0.376303\pi$
$908$	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	−0.264179	−	0.964474i	$-0.585101\pi$
$911$	19255.7	−	19255.7i	0.700294	−	0.700294i	0.964474	+	0.264179i	$0.0851010\pi$
$912$	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	−0.0606733	−	0.998158i	$-0.519325\pi$
$929$	26545.3	−	26545.3i	0.937484	−	0.937484i	0.998158	+	0.0606733i	$0.0193248\pi$
$930$	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	$0.0875326\pi$
$937$			15576.6i			0.543078i	−0.962427	+	0.271539i	$0.912467\pi$
$938$	−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	−0.991892	−	0.127082i	$-0.959439\pi$
$941$	−24963.5	+	24963.5i	−0.864810	+	0.864810i	0.127082	+	0.991892i	$0.459439\pi$
$942$	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	−0.990644	−	0.136469i	$-0.956425\pi$
$947$	−32846.8	−	32846.8i	−1.12711	−	1.12711i	−0.136469	−	0.990644i	$-0.543575\pi$
$948$	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	$-0.738347\pi$
$967$		−	44054.0i		−	1.46503i	0.680752	−	0.732514i	$-0.261653\pi$
$968$	−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	$-0.963985\pi$
$971$		−	6832.21i		−	0.225804i	0.993606	−	0.112902i	$-0.0360147\pi$
$972$	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	$0.0259713\pi$
$977$			4977.75i			0.163002i	−0.996673	+	0.0815008i	$0.974029\pi$
$978$			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	0.486444	−	0.873712i	$-0.338294\pi$
$983$	−11935.6	−	11935.6i	−0.387269	−	0.387269i	−0.873712	+	0.486444i	$0.838294\pi$
$984$		−	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	0.646792	−	0.762666i	$-0.276110\pi$
$991$	−3614.91	−	3614.91i	−0.115874	−	0.115874i	−0.762666	+	0.646792i	$0.776110\pi$
$992$	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	−0.999400	−	0.0346301i	$-0.988975\pi$
$997$	−30371.5	+	30371.5i	−0.964770	+	0.964770i	0.0346301	+	0.999400i	$0.488975\pi$
$998$	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.13.2	yes	16
3.2	odd	2		153.4.f.b.64.7		16
17.2	even	8		867.4.a.q.1.7		8
17.4	even	4	inner	51.4.e.a.4.7	✓	16
17.15	even	8		867.4.a.p.1.7		8
51.38	odd	4		153.4.f.b.55.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
51.4.e.a.4.7	✓	16	17.4	even	4	inner
51.4.e.a.13.2	yes	16	1.1	even	1	trivial
153.4.f.b.55.2		16	51.38	odd	4
153.4.f.b.64.7		16	3.2	odd	2
867.4.a.p.1.7		8	17.15	even	8
867.4.a.q.1.7		8	17.2	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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more