LMFDB - Embedded newform 448.4.i.g.65.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [448,4,Mod(65,448)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(448, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

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

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

chi := DirichletCharacter("448.65");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 448 = 2^{6} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	448.i (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$26.4328556826$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{37})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 10x^{2} + 9x + 81 $ x^4 - x^3 + 10x^2 + 9x + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 28)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			65.1
Root			$1.77069 + 3.06693i$ of defining polynomial
Character	$\chi$	$=$	448.65
Dual form			448.4.i.g.193.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-3.04138 - 5.26783i) q^{3} +(-9.58276 + 16.5978i) q^{5} +(6.16553 - 17.4639i) q^{7} +(-5.00000 + 8.66025i) q^{9} +(13.2897 + 23.0184i) q^{11} -10.3311 q^{13} +116.579 q^{15} +(50.6655 + 87.7553i) q^{17} +(46.8759 - 81.1914i) q^{19} +(-110.748 + 20.6353i) q^{21} +(-4.28967 + 7.42992i) q^{23} +(-121.159 - 209.853i) q^{25} -103.407 q^{27} -52.3174 q^{29} +(-27.7103 - 47.9957i) q^{31} +(80.8379 - 140.015i) q^{33} +(230.779 + 269.686i) q^{35} +(214.238 - 371.071i) q^{37} +(31.4207 + 54.4222i) q^{39} -137.007 q^{41} -172.000 q^{43} +(-95.8276 - 165.978i) q^{45} +(-24.6207 + 42.6443i) q^{47} +(-266.973 - 215.348i) q^{49} +(308.186 - 533.794i) q^{51} +(-237.238 - 410.908i) q^{53} -509.407 q^{55} -570.269 q^{57} +(-98.5311 - 170.661i) q^{59} +(-200.562 + 347.384i) q^{61} +(120.414 + 140.714i) q^{63} +(99.0000 - 171.473i) q^{65} +(-62.7103 - 108.617i) q^{67} +52.1861 q^{69} -788.635 q^{71} +(-302.328 - 523.647i) q^{73} +(-736.979 + 1276.49i) q^{75} +(483.928 - 90.1685i) q^{77} +(391.504 - 678.104i) q^{79} +(449.500 + 778.557i) q^{81} -339.283 q^{83} -1942.06 q^{85} +(159.117 + 275.599i) q^{87} +(-255.983 + 443.375i) q^{89} +(-63.6963 + 180.420i) q^{91} +(-168.555 + 291.946i) q^{93} +(898.400 + 1556.08i) q^{95} -672.290 q^{97} -265.793 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 14 q^{5} - 24 q^{7} - 20 q^{9} - 32 q^{11} + 56 q^{13} + 296 q^{15} + 154 q^{17} + 224 q^{19} - 370 q^{21} + 68 q^{23} - 144 q^{25} + 472 q^{29} - 196 q^{31} + 518 q^{33} + 400 q^{35} + 346 q^{37}+ \cdots + 640 q^{99}+O(q^{100}) $ 4 * q - 14 * q^5 - 24 * q^7 - 20 * q^9 - 32 * q^11 + 56 * q^13 + 296 * q^15 + 154 * q^17 + 224 * q^19 - 370 * q^21 + 68 * q^23 - 144 * q^25 + 472 * q^29 - 196 * q^31 + 518 * q^33 + 400 * q^35 + 346 * q^37 + 296 * q^39 - 840 * q^41 - 688 * q^43 - 140 * q^45 + 84 * q^47 + 100 * q^49 + 296 * q^51 - 438 * q^53 - 1624 * q^55 + 444 * q^57 + 56 * q^59 + 98 * q^61 + 360 * q^63 + 396 * q^65 - 336 * q^67 + 1036 * q^69 - 1792 * q^71 - 966 * q^73 - 2072 * q^75 + 2398 * q^77 - 52 * q^79 + 1798 * q^81 + 784 * q^83 - 3340 * q^85 + 2072 * q^87 - 294 * q^89 - 1520 * q^91 + 518 * q^93 + 1124 * q^95 - 840 * q^97 + 640 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/448\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$197$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−3.04138	−	5.26783i	−0.585314	−	1.01379i	−0.994836	−	0.101494i	$-0.967638\pi$
$3$	−3.04138	−	5.26783i	−0.585314	−	1.01379i	0.409522	−	0.912300i	$-0.365695\pi$
$4$		0			0
$5$	−9.58276	+	16.5978i	−0.857108	+	1.48456i	0.0175669	+	0.999846i	$0.494408\pi$
$5$	−9.58276	+	16.5978i	−0.857108	+	1.48456i	−0.874675	+	0.484709i	$0.838925\pi$
$6$		0			0
$7$	6.16553	−	17.4639i	0.332907	−	0.942960i
$7$	6.16553	−	17.4639i	0.332907	−	0.942960i
$8$		0			0
$9$	−5.00000	+	8.66025i	−0.185185	+	0.320750i
$10$		0			0
$11$	13.2897	+	23.0184i	0.364271	+	0.630937i	0.988659	−	0.150178i	$-0.0479847\pi$
$11$	13.2897	+	23.0184i	0.364271	+	0.630937i	−0.624388	+	0.781115i	$0.714651\pi$
$12$		0			0
$13$	−10.3311			−0.220409			−0.110205	−	0.993909i	$-0.535151\pi$
$13$	−10.3311			−0.220409			−0.110205	+	0.993909i	$0.535151\pi$
$14$		0			0
$15$	116.579			2.00671
$16$		0			0
$17$	50.6655	+	87.7553i	0.722835	+	1.25199i	0.959859	+	0.280483i	$0.0904947\pi$
$17$	50.6655	+	87.7553i	0.722835	+	1.25199i	−0.237024	+	0.971504i	$0.576172\pi$
$18$		0			0
$19$	46.8759	−	81.1914i	0.566003	−	0.980346i	−0.430952	−	0.902375i	$-0.641822\pi$
$19$	46.8759	−	81.1914i	0.566003	−	0.980346i	0.996956	−	0.0779715i	$-0.0248443\pi$
$20$		0			0
$21$	−110.748	+	20.6353i	−1.15082	+	0.214428i
$22$		0			0
$23$	−4.28967	+	7.42992i	−0.0388895	+	0.0673585i	−0.884815	−	0.465942i	$-0.845715\pi$
$23$	−4.28967	+	7.42992i	−0.0388895	+	0.0673585i	0.845926	+	0.533301i	$0.179049\pi$
$24$		0			0
$25$	−121.159	−	209.853i	−0.969269	−	1.67882i
$26$		0			0
$27$	−103.407			−0.737062
$28$		0			0
$29$	−52.3174			−0.335003			−0.167502	−	0.985872i	$-0.553570\pi$
$29$	−52.3174			−0.335003			−0.167502	+	0.985872i	$0.553570\pi$
$30$		0			0
$31$	−27.7103	−	47.9957i	−0.160546	−	0.278074i	0.774519	−	0.632551i	$-0.217992\pi$
$31$	−27.7103	−	47.9957i	−0.160546	−	0.278074i	−0.935065	+	0.354477i	$0.884659\pi$
$32$		0			0
$33$	80.8379	−	140.015i	0.426426	−	0.738592i
$34$		0			0
$35$	230.779	+	269.686i	1.11454	+	1.30244i
$36$		0			0
$37$	214.238	−	371.071i	0.951906	−	1.64875i	0.210610	−	0.977570i	$-0.432455\pi$
$37$	214.238	−	371.071i	0.951906	−	1.64875i	0.741295	−	0.671179i	$-0.234212\pi$
$38$		0			0
$39$	31.4207	+	54.4222i	0.129009	+	0.223449i
$40$		0			0
$41$	−137.007			−0.521875			−0.260938	−	0.965356i	$-0.584032\pi$
$41$	−137.007			−0.521875			−0.260938	+	0.965356i	$0.584032\pi$
$42$		0			0
$43$	−172.000			−0.609994			−0.304997	−	0.952353i	$-0.598656\pi$
$43$	−172.000			−0.609994			−0.304997	+	0.952353i	$0.598656\pi$
$44$		0			0
$45$	−95.8276	−	165.978i	−0.317448	−	0.549835i
$46$		0			0
$47$	−24.6207	+	42.6443i	−0.0764107	+	0.132347i	−0.901699	−	0.432365i	$-0.857679\pi$
$47$	−24.6207	+	42.6443i	−0.0764107	+	0.132347i	0.825288	+	0.564712i	$0.191013\pi$
$48$		0			0
$49$	−266.973	−	215.348i	−0.778346	−	0.627836i
$50$		0			0
$51$	308.186	−	533.794i	0.846171	−	1.46561i
$52$		0			0
$53$	−237.238	−	410.908i	−0.614852	−	1.06495i	−0.990410	−	0.138156i	$-0.955882\pi$
$53$	−237.238	−	410.908i	−0.614852	−	1.06495i	0.375559	−	0.926799i	$-0.377451\pi$
$54$		0			0
$55$	−509.407			−1.24888
$56$		0			0
$57$	−570.269			−1.32516
$58$		0			0
$59$	−98.5311	−	170.661i	−0.217418	−	0.376579i	0.736600	−	0.676329i	$-0.236430\pi$
$59$	−98.5311	−	170.661i	−0.217418	−	0.376579i	−0.954018	+	0.299750i	$0.903097\pi$
$60$		0			0
$61$	−200.562	+	347.384i	−0.420973	+	0.729147i	−0.996035	−	0.0889631i	$-0.971645\pi$
$61$	−200.562	+	347.384i	−0.420973	+	0.729147i	0.575062	+	0.818110i	$0.304978\pi$
$62$		0			0
$63$	120.414	+	140.714i	0.240805	+	0.281402i
$64$		0			0
$65$	99.0000	−	171.473i	0.188914	−	0.327209i
$66$		0			0
$67$	−62.7103	−	108.617i	−0.114348	−	0.198056i	0.803171	−	0.595748i	$-0.203144\pi$
$67$	−62.7103	−	108.617i	−0.114348	−	0.198056i	−0.917519	+	0.397693i	$0.869811\pi$
$68$		0			0
$69$	52.1861			0.0910502
$70$		0			0
$71$	−788.635			−1.31822			−0.659111	−	0.752046i	$-0.729067\pi$
$71$	−788.635			−1.31822			−0.659111	+	0.752046i	$0.729067\pi$
$72$		0			0
$73$	−302.328	−	523.647i	−0.484723	−	0.839565i	0.515123	−	0.857116i	$-0.327746\pi$
$73$	−302.328	−	523.647i	−0.484723	−	0.839565i	−0.999846	+	0.0175515i	$0.994413\pi$
$74$		0			0
$75$	−736.979	+	1276.49i	−1.13465	+	1.96528i
$76$		0			0
$77$	483.928	−	90.1685i	0.716216	−	0.133450i
$78$		0			0
$79$	391.504	−	678.104i	0.557565	−	0.965730i	−0.440134	−	0.897932i	$-0.645069\pi$
$79$	391.504	−	678.104i	0.557565	−	0.965730i	0.997699	−	0.0677984i	$-0.0215975\pi$
$80$		0			0
$81$	449.500	+	778.557i	0.616598	+	1.06798i
$82$		0			0
$83$	−339.283			−0.448689			−0.224344	−	0.974510i	$-0.572024\pi$
$83$	−339.283			−0.448689			−0.224344	+	0.974510i	$0.572024\pi$
$84$		0			0
$85$	−1942.06			−2.47819
$86$		0			0
$87$	159.117	+	275.599i	0.196082	+	0.339624i
$88$		0			0
$89$	−255.983	+	443.375i	−0.304878	+	0.528064i	−0.977234	−	0.212164i	$-0.931949\pi$
$89$	−255.983	+	443.375i	−0.304878	+	0.528064i	0.672356	+	0.740228i	$0.265282\pi$
$90$		0			0
$91$	−63.6963	+	180.420i	−0.0733757	+	0.207837i
$92$		0			0
$93$	−168.555	+	291.946i	−0.187940	+	0.325521i
$94$		0			0
$95$	898.400	+	1556.08i	0.970252	+	1.68053i
$96$		0			0
$97$	−672.290			−0.703719			−0.351859	−	0.936053i	$-0.614450\pi$
$97$	−672.290			−0.703719			−0.351859	+	0.936053i	$0.614450\pi$
$98$		0			0
$99$	−265.793			−0.269831
$100$		0			0
$101$	66.8864	+	115.851i	0.0658955	+	0.114134i	0.897091	−	0.441846i	$-0.145676\pi$
$101$	66.8864	+	115.851i	0.0658955	+	0.114134i	−0.831195	+	0.555980i	$0.812343\pi$
$102$		0			0
$103$	580.372	−	1005.23i	0.555202	−	0.961638i	−0.442686	−	0.896677i	$-0.645974\pi$
$103$	580.372	−	1005.23i	0.555202	−	0.961638i	0.997888	−	0.0649611i	$-0.0206923\pi$
$104$		0			0
$105$	718.773	−	2035.92i	0.668048	−	1.89225i
$106$		0			0
$107$	654.393	−	1133.44i	0.591239	−	1.02406i	−0.402827	−	0.915276i	$-0.631972\pi$
$107$	654.393	−	1133.44i	0.591239	−	1.02406i	0.994066	−	0.108780i	$-0.0346943\pi$
$108$		0			0
$109$	−522.921	−	905.725i	−0.459511	−	0.795897i	0.539424	−	0.842034i	$-0.318642\pi$
$109$	−522.921	−	905.725i	−0.459511	−	0.795897i	−0.998935	+	0.0461377i	$0.985309\pi$
$110$		0			0
$111$	−2606.32			−2.22866
$112$		0			0
$113$	−117.587			−0.0978905			−0.0489453	−	0.998801i	$-0.515586\pi$
$113$	−117.587			−0.0978905			−0.0489453	+	0.998801i	$0.515586\pi$
$114$		0			0
$115$	−82.2138	−	142.398i	−0.0666650	−	0.115467i
$116$		0			0
$117$	51.6553	−	89.4695i	0.0408165	−	0.0706962i
$118$		0			0
$119$	1844.92	−	343.758i	1.42121	−	0.264809i
$120$		0			0
$121$	312.269	−	540.866i	0.234613	−	0.406361i
$122$		0			0
$123$	416.690	+	721.728i	0.305461	+	0.529074i
$124$		0			0
$125$	2248.45			1.60886
$126$		0			0
$127$	1788.63			1.24973			0.624865	−	0.780733i	$-0.285154\pi$
$127$	1788.63			1.24973			0.624865	+	0.780733i	$0.285154\pi$
$128$		0			0
$129$	523.118	+	906.066i	0.357038	+	0.618408i
$130$		0			0
$131$	974.642	−	1688.13i	0.650037	−	1.12590i	−0.333076	−	0.942900i	$-0.608087\pi$
$131$	974.642	−	1688.13i	0.650037	−	1.12590i	0.983113	−	0.182997i	$-0.0585800\pi$
$132$		0			0
$133$	−1128.90	−	1319.22i	−0.736000	−	0.860082i
$134$		0			0
$135$	990.924	−	1716.33i	0.631742	−	1.09421i
$136$		0			0
$137$	285.769	+	494.967i	0.178211	+	0.308671i	0.941268	−	0.337661i	$-0.109636\pi$
$137$	285.769	+	494.967i	0.178211	+	0.308671i	−0.763057	+	0.646332i	$0.776302\pi$
$138$		0			0
$139$	1176.58			0.717958			0.358979	−	0.933346i	$-0.383125\pi$
$139$	1176.58			0.717958			0.358979	+	0.933346i	$0.383125\pi$
$140$		0			0
$141$	299.524			0.178897
$142$		0			0
$143$	−137.296	−	237.804i	−0.0802887	−	0.139064i
$144$		0			0
$145$	501.345	−	868.355i	0.287134	−	0.497331i
$146$		0			0
$147$	−322.449	+	2061.32i	−0.180919	+	1.15656i
$148$		0			0
$149$	886.666	−	1535.75i	0.487507	−	0.844387i	−0.512390	−	0.858753i	$-0.671240\pi$
$149$	886.666	−	1535.75i	0.487507	−	0.844387i	0.999897	+	0.0143663i	$0.00457309\pi$
$150$		0			0
$151$	−251.504	−	435.617i	−0.135544	−	0.234768i	0.790261	−	0.612770i	$-0.209945\pi$
$151$	−251.504	−	435.617i	−0.135544	−	0.234768i	−0.925805	+	0.378002i	$0.876611\pi$
$152$		0			0
$153$	−1013.31			−0.535433
$154$		0			0
$155$	1062.17			0.550421
$156$		0			0
$157$	1168.16	+	2023.31i	0.593815	+	1.02852i	0.993713	+	0.111958i	$0.0357123\pi$
$157$	1168.16	+	2023.31i	0.593815	+	1.02852i	−0.399898	+	0.916560i	$0.630954\pi$
$158$		0			0
$159$	−1443.06	+	2499.46i	−0.719763	+	1.24667i
$160$		0			0
$161$	103.307	+	120.724i	0.0505698	+	0.0590953i
$162$		0			0
$163$	868.297	−	1503.93i	0.417241	−	0.722683i	−0.578420	−	0.815739i	$-0.696330\pi$
$163$	868.297	−	1503.93i	0.417241	−	0.722683i	0.995661	+	0.0930567i	$0.0296638\pi$
$164$		0			0
$165$	1549.30	+	2683.47i	0.730987	+	1.26611i
$166$		0			0
$167$	−668.331			−0.309683			−0.154841	−	0.987939i	$-0.549487\pi$
$167$	−668.331			−0.309683			−0.154841	+	0.987939i	$0.549487\pi$
$168$		0			0
$169$	−2090.27			−0.951420
$170$		0			0
$171$	468.759	+	811.914i	0.209631	+	0.363091i
$172$		0			0
$173$	−1072.62	+	1857.83i	−0.471385	+	0.816462i	−0.999464	−	0.0327327i	$-0.989579\pi$
$173$	−1072.62	+	1857.83i	−0.471385	+	0.816462i	0.528079	+	0.849195i	$0.322912\pi$
$174$		0			0
$175$	−4411.85	+	822.044i	−1.90574	+	0.355090i
$176$		0			0
$177$	−599.341	+	1038.09i	−0.254516	+	0.440834i
$178$		0			0
$179$	−1883.77	−	3262.79i	−0.786591	−	1.36242i	−0.928044	−	0.372471i	$-0.878511\pi$
$179$	−1883.77	−	3262.79i	−0.786591	−	1.36242i	0.141453	−	0.989945i	$-0.454823\pi$
$180$		0			0
$181$	1752.51			0.719686			0.359843	−	0.933013i	$-0.382830\pi$
$181$	1752.51			0.719686			0.359843	+	0.933013i	$0.382830\pi$
$182$		0			0
$183$	2439.94			0.985606
$184$		0			0
$185$	4105.98	+	7111.77i	1.63177	+	2.82631i
$186$		0			0
$187$	−1346.66	+	2332.48i	−0.526616	+	0.912126i
$188$		0			0
$189$	−637.558	+	1805.88i	−0.245373	+	0.695020i
$190$		0			0
$191$	−1005.56	+	1741.68i	−0.380941	+	0.659809i	−0.991197	−	0.132395i	$-0.957733\pi$
$191$	−1005.56	+	1741.68i	−0.380941	+	0.659809i	0.610256	+	0.792204i	$0.291067\pi$
$192$		0			0
$193$	789.976	+	1368.28i	0.294631	+	0.510315i	0.974899	−	0.222648i	$-0.0714700\pi$
$193$	789.976	+	1368.28i	0.294631	+	0.510315i	−0.680268	+	0.732963i	$0.738137\pi$
$194$		0			0
$195$	−1204.39			−0.442297
$196$		0			0
$197$	26.4132			0.00955262			0.00477631	−	0.999989i	$-0.498480\pi$
$197$	26.4132			0.00955262			0.00477631	+	0.999989i	$0.498480\pi$
$198$		0			0
$199$	−28.7731	−	49.8365i	−0.0102496	−	0.0177528i	0.860855	−	0.508850i	$-0.169929\pi$
$199$	−28.7731	−	49.8365i	−0.0102496	−	0.0177528i	−0.871105	+	0.491097i	$0.836596\pi$
$200$		0			0
$201$	−381.452	+	660.694i	−0.133858	+	0.231850i
$202$		0			0
$203$	−322.564	+	913.663i	−0.111525	+	0.315894i
$204$		0			0
$205$	1312.90	−	2274.02i	0.447303	−	0.774752i
$206$		0			0
$207$	−42.8967	−	74.2992i	−0.0144035	−	0.0249476i
$208$		0			0
$209$	2491.86			0.824715
$210$		0			0
$211$	−1193.90			−0.389534			−0.194767	−	0.980850i	$-0.562395\pi$
$211$	−1193.90			−0.389534			−0.194767	+	0.980850i	$0.562395\pi$
$212$		0			0
$213$	2398.54	+	4154.39i	0.771574	+	1.33640i
$214$		0			0
$215$	1648.24	−	2854.83i	0.522831	−	0.905570i
$216$		0			0
$217$	−1009.04	+	188.011i	−0.315659	+	0.0588156i
$218$		0			0
$219$	−1838.99	+	3185.22i	−0.567430	+	0.982818i
$220$		0			0
$221$	−523.428	−	906.604i	−0.159319	−	0.275949i
$222$		0			0
$223$	2921.66			0.877348			0.438674	−	0.898646i	$-0.355448\pi$
$223$	2921.66			0.877348			0.438674	+	0.898646i	$0.355448\pi$
$224$		0			0
$225$	2423.17			0.717977
$226$		0			0
$227$	1556.17	+	2695.37i	0.455008	+	0.788097i	0.998689	−	0.0511954i	$-0.0163031\pi$
$227$	1556.17	+	2695.37i	0.455008	+	0.788097i	−0.543681	+	0.839292i	$0.682970\pi$
$228$		0			0
$229$	−2667.65	+	4620.51i	−0.769797	+	1.33333i	0.167876	+	0.985808i	$0.446309\pi$
$229$	−2667.65	+	4620.51i	−0.769797	+	1.33333i	−0.937673	+	0.347519i	$0.887024\pi$
$230$		0			0
$231$	−1946.80	−	2275.01i	−0.554502	−	0.647985i
$232$		0			0
$233$	2619.04	−	4536.31i	0.736390	−	1.27547i	−0.217720	−	0.976011i	$-0.569862\pi$
$233$	2619.04	−	4536.31i	0.736390	−	1.27547i	0.954111	−	0.299454i	$-0.0968046\pi$
$234$		0			0
$235$	−471.869	−	817.301i	−0.130984	−	0.226872i
$236$		0			0
$237$	−4762.85			−1.30540
$238$		0			0
$239$	−4181.05			−1.13159			−0.565794	−	0.824547i	$-0.691430\pi$
$239$	−4181.05			−1.13159			−0.565794	+	0.824547i	$0.691430\pi$
$240$		0			0
$241$	−2732.44	−	4732.72i	−0.730340	−	1.26499i	−0.956738	−	0.290950i	$-0.906029\pi$
$241$	−2732.44	−	4732.72i	−0.730340	−	1.26499i	0.226399	−	0.974035i	$-0.427305\pi$
$242$		0			0
$243$	1338.21	−	2317.84i	0.353276	−	0.611892i
$244$		0			0
$245$	6132.64	−	2367.54i	1.59918	−	0.617374i
$246$		0			0
$247$	−484.277	+	838.792i	−0.124752	+	0.216077i
$248$		0			0
$249$	1031.89	+	1787.28i	0.262624	+	0.454878i
$250$		0			0
$251$	−5718.95			−1.43816			−0.719078	−	0.694930i	$-0.755436\pi$
$251$	−5718.95			−1.43816			−0.719078	+	0.694930i	$0.755436\pi$
$252$		0			0
$253$	−228.033			−0.0566653
$254$		0			0
$255$	5906.55	+	10230.5i	1.45052	+	2.51238i
$256$		0			0
$257$	−509.140	+	881.857i	−0.123577	+	0.214042i	−0.921176	−	0.389147i	$-0.872770\pi$
$257$	−509.140	+	881.857i	−0.123577	+	0.214042i	0.797599	+	0.603188i	$0.206103\pi$
$258$		0			0
$259$	−5159.44	−	6029.27i	−1.23781	−	1.44649i
$260$		0			0
$261$	261.587	−	453.082i	0.0620376	−	0.107452i
$262$		0			0
$263$	−4112.15	−	7122.46i	−0.964130	−	1.66992i	−0.711934	−	0.702246i	$-0.752181\pi$
$263$	−4112.15	−	7122.46i	−0.964130	−	1.66992i	−0.252196	−	0.967676i	$-0.581153\pi$
$264$		0			0
$265$	9093.58			2.10798
$266$		0			0
$267$	3114.17			0.713797
$268$		0			0
$269$	−2933.94	−	5081.74i	−0.665002	−	1.15182i	−0.979285	−	0.202488i	$-0.935097\pi$
$269$	−2933.94	−	5081.74i	−0.665002	−	1.15182i	0.314282	−	0.949330i	$-0.398236\pi$
$270$		0			0
$271$	3108.39	−	5383.88i	0.696757	−	1.20682i	−0.272828	−	0.962063i	$-0.587959\pi$
$271$	3108.39	−	5383.88i	0.696757	−	1.20682i	0.969585	−	0.244755i	$-0.0787076\pi$
$272$		0			0
$273$	1144.15	−	213.185i	0.253652	−	0.0472620i
$274$		0			0
$275$	3220.32	−	5577.75i	0.706154	−	1.22310i
$276$		0			0
$277$	738.762	+	1279.57i	0.160245	+	0.277553i	0.934957	−	0.354762i	$-0.115438\pi$
$277$	738.762	+	1279.57i	0.160245	+	0.277553i	−0.774711	+	0.632315i	$0.782105\pi$
$278$		0			0
$279$	554.207			0.118923
$280$		0			0
$281$	−3611.93			−0.766797			−0.383398	−	0.923583i	$-0.625246\pi$
$281$	−3611.93			−0.766797			−0.383398	+	0.923583i	$0.625246\pi$
$282$		0			0
$283$	3814.04	+	6606.10i	0.801134	+	1.38760i	0.918870	+	0.394560i	$0.129103\pi$
$283$	3814.04	+	6606.10i	0.801134	+	1.38760i	−0.117736	+	0.993045i	$0.537564\pi$
$284$		0			0
$285$	5464.76	−	9465.24i	1.13580	−	1.96727i
$286$		0			0
$287$	−844.719	+	2392.67i	−0.173736	+	0.492107i
$288$		0			0
$289$	−2677.49	+	4637.55i	−0.544981	+	0.943935i
$290$		0			0
$291$	2044.69	+	3541.51i	0.411896	+	0.713426i
$292$		0			0
$293$	5393.67			1.07543			0.537716	−	0.843126i	$-0.319287\pi$
$293$	5393.67			1.07543			0.537716	+	0.843126i	$0.319287\pi$
$294$		0			0
$295$	3776.80			0.745403
$296$		0			0
$297$	−1374.24	−	2380.26i	−0.268491	−	0.465040i
$298$		0			0
$299$	44.3168	−	76.7589i	0.00857159	−	0.0148464i
$300$		0			0
$301$	−1060.47	+	3003.78i	−0.203071	+	0.575200i
$302$		0			0
$303$	406.854	−	704.692i	0.0771391	−	0.133609i
$304$		0			0
$305$	−3843.88	−	6657.80i	−0.721639	−	1.24992i
$306$		0			0
$307$	8054.16			1.49731			0.748656	−	0.662958i	$-0.230699\pi$
$307$	8054.16			1.49731			0.748656	+	0.662958i	$0.230699\pi$
$308$		0			0
$309$	−7060.54			−1.29987
$310$		0			0
$311$	1142.30	+	1978.53i	0.208277	+	0.360746i	0.951172	−	0.308662i	$-0.0998812\pi$
$311$	1142.30	+	1978.53i	0.208277	+	0.360746i	−0.742895	+	0.669408i	$0.766548\pi$
$312$		0			0
$313$	−4168.07	+	7219.30i	−0.752694	+	1.30370i	0.193819	+	0.981037i	$0.437912\pi$
$313$	−4168.07	+	7219.30i	−0.752694	+	1.30370i	−0.946513	+	0.322666i	$0.895421\pi$
$314$		0			0
$315$	−3489.45	+	650.176i	−0.624153	+	0.116296i
$316$		0			0
$317$	−5208.09	+	9020.68i	−0.922762	+	1.59827i	−0.127642	+	0.991820i	$0.540741\pi$
$317$	−5208.09	+	9020.68i	−0.922762	+	1.59827i	−0.795121	+	0.606451i	$0.792593\pi$
$318$		0			0
$319$	−695.280	−	1204.26i	−0.122032	−	0.211366i
$320$		0			0
$321$	−7961.03			−1.38424
$322$		0			0
$323$	9499.96			1.63651
$324$		0			0
$325$	1251.70	+	2168.00i	0.213636	+	0.370028i
$326$		0			0
$327$	−3180.80	+	5509.31i	−0.537917	+	0.931699i
$328$		0			0
$329$	592.935	+	692.897i	0.0993604	+	0.116111i
$330$		0			0
$331$	−3471.94	+	6013.58i	−0.576541	+	0.998598i	0.419331	+	0.907833i	$0.362265\pi$
$331$	−3471.94	+	6013.58i	−0.576541	+	0.998598i	−0.995872	+	0.0907649i	$0.971069\pi$
$332$		0			0
$333$	2142.38	+	3710.71i	0.352558	+	0.610648i
$334$		0			0
$335$	2403.75			0.392033
$336$		0			0
$337$	4951.93			0.800442			0.400221	−	0.916419i	$-0.368933\pi$
$337$	4951.93			0.800442			0.400221	+	0.916419i	$0.368933\pi$
$338$		0			0
$339$	357.626	+	619.427i	0.0572967	+	0.0992408i
$340$		0			0
$341$	736.522	−	1275.69i	0.116965	−	0.202589i
$342$		0			0
$343$	−5406.83	+	3334.64i	−0.851141	+	0.524938i
$344$		0			0
$345$	−500.087	+	866.176i	−0.0780399	+	0.135169i
$346$		0			0
$347$	−3637.68	−	6300.64i	−0.562769	−	0.974744i	−0.997253	−	0.0740648i	$-0.976403\pi$
$347$	−3637.68	−	6300.64i	−0.562769	−	0.974744i	0.434485	−	0.900679i	$-0.356931\pi$
$348$		0			0
$349$	−3433.29			−0.526589			−0.263294	−	0.964716i	$-0.584809\pi$
$349$	−3433.29			−0.526589			−0.263294	+	0.964716i	$0.584809\pi$
$350$		0			0
$351$	1068.30			0.162455
$352$		0			0
$353$	−3079.54	−	5333.93i	−0.464328	−	0.804239i	0.534843	−	0.844951i	$-0.320371\pi$
$353$	−3079.54	−	5333.93i	−0.464328	−	0.804239i	−0.999171	+	0.0407124i	$0.987037\pi$
$354$		0			0
$355$	7557.30	−	13089.6i	1.12986	−	1.95697i
$356$		0			0
$357$	−7421.98	−	8673.25i	−1.10032	−	1.28582i
$358$		0			0
$359$	4003.31	−	6933.94i	0.588542	−	1.01939i	−0.405881	−	0.913926i	$-0.633035\pi$
$359$	4003.31	−	6933.94i	0.588542	−	1.01939i	0.994424	−	0.105459i	$-0.0336313\pi$
$360$		0			0
$361$	−965.192	−	1671.76i	−0.140719	−	0.243733i
$362$		0			0
$363$	−3798.92			−0.549288
$364$		0			0
$365$	11588.5			1.66184
$366$		0			0
$367$	592.247	+	1025.80i	0.0842372	+	0.145903i	0.905066	−	0.425271i	$-0.139821\pi$
$367$	592.247	+	1025.80i	0.0842372	+	0.145903i	−0.820829	+	0.571174i	$0.806488\pi$
$368$		0			0
$369$	685.034	−	1186.51i	0.0966435	−	0.167391i
$370$		0			0
$371$	−8638.74	+	1609.63i	−1.20890	+	0.225250i
$372$		0			0
$373$	−472.109	+	817.717i	−0.0655359	+	0.113511i	−0.896932	−	0.442169i	$-0.854209\pi$
$373$	−472.109	+	817.717i	−0.0655359	+	0.113511i	0.831396	+	0.555681i	$0.187542\pi$
$374$		0			0
$375$	−6838.39	−	11844.4i	−0.941688	−	1.63105i
$376$		0			0
$377$	540.493			0.0738377
$378$		0			0
$379$	−2906.32			−0.393898			−0.196949	−	0.980414i	$-0.563103\pi$
$379$	−2906.32			−0.393898			−0.196949	+	0.980414i	$0.563103\pi$
$380$		0			0
$381$	−5439.92	−	9422.22i	−0.731484	−	1.26697i
$382$		0			0
$383$	−573.420	+	993.192i	−0.0765023	+	0.132506i	−0.901739	−	0.432282i	$-0.857709\pi$
$383$	−573.420	+	993.192i	−0.0765023	+	0.132506i	0.825236	+	0.564788i	$0.191042\pi$
$384$		0			0
$385$	−3140.76	+	8896.21i	−0.415761	+	1.17764i
$386$		0			0
$387$	860.000	−	1489.56i	0.112962	−	0.195656i
$388$		0			0
$389$	−2794.74	−	4840.64i	−0.364265	−	0.630926i	0.624393	−	0.781110i	$-0.285346\pi$
$389$	−2794.74	−	4840.64i	−0.364265	−	0.630926i	−0.988658	+	0.150185i	$0.952013\pi$
$390$		0			0
$391$	−869.353			−0.112443
$392$		0			0
$393$	−11857.0			−1.52190
$394$		0			0
$395$	7503.37	+	12996.2i	0.955787	+	1.65547i
$396$		0			0
$397$	1577.05	−	2731.53i	0.199370	−	0.345319i	−0.748954	−	0.662622i	$-0.769444\pi$
$397$	1577.05	−	2731.53i	0.199370	−	0.345319i	0.948324	+	0.317303i	$0.102777\pi$
$398$		0			0
$399$	−3516.01	+	9959.10i	−0.441155	+	1.24957i
$400$		0			0
$401$	3195.88	−	5535.43i	0.397992	−	0.689342i	−0.595486	−	0.803365i	$-0.703041\pi$
$401$	3195.88	−	5535.43i	0.397992	−	0.689342i	0.993478	+	0.114024i	$0.0363740\pi$
$402$		0			0
$403$	286.277	+	495.846i	0.0353858	+	0.0612899i
$404$		0			0
$405$	−17229.8			−2.11397
$406$		0			0
$407$	11388.6			1.38701
$408$		0			0
$409$	−98.3151	−	170.287i	−0.0118860	−	0.0205871i	0.860021	−	0.510258i	$-0.170450\pi$
$409$	−98.3151	−	170.287i	−0.0118860	−	0.0205871i	−0.871907	+	0.489671i	$0.837117\pi$
$410$		0			0
$411$	1738.27	−	3010.77i	0.208619	−	0.361339i
$412$		0			0
$413$	−3587.89	+	668.519i	−0.427479	+	0.0796506i
$414$		0			0
$415$	3251.27	−	5631.36i	0.384575	−	0.666103i
$416$		0			0
$417$	−3578.43	−	6198.02i	−0.420231	−	0.727862i
$418$		0			0
$419$	−15699.9			−1.83052			−0.915262	−	0.402858i	$-0.868017\pi$
$419$	−15699.9			−1.83052			−0.915262	+	0.402858i	$0.868017\pi$
$420$		0			0
$421$	8097.20			0.937372			0.468686	−	0.883365i	$-0.344728\pi$
$421$	8097.20			0.937372			0.468686	+	0.883365i	$0.344728\pi$
$422$		0			0
$423$	−246.207	−	426.443i	−0.0283002	−	0.0490175i
$424$		0			0
$425$	12277.1	−	21264.6i	1.40124	−	2.42703i
$426$		0			0
$427$	4830.09	+	5644.39i	0.547411	+	0.639699i
$428$		0			0
$429$	−835.140	+	1446.51i	−0.0939882	+	0.162792i
$430$		0			0
$431$	5789.18	+	10027.1i	0.646995	+	1.12063i	0.983837	+	0.179067i	$0.0573078\pi$
$431$	5789.18	+	10027.1i	0.646995	+	1.12063i	−0.336842	+	0.941561i	$0.609359\pi$
$432$		0			0
$433$	−7270.25			−0.806896			−0.403448	−	0.915003i	$-0.632188\pi$
$433$	−7270.25			−0.806896			−0.403448	+	0.915003i	$0.632188\pi$
$434$		0			0
$435$	−6099.12			−0.672254
$436$		0			0
$437$	402.164	+	696.568i	0.0440231	+	0.0762503i
$438$		0			0
$439$	−2063.69	+	3574.42i	−0.224362	+	0.388606i	−0.956128	−	0.292950i	$-0.905363\pi$
$439$	−2063.69	+	3574.42i	−0.224362	+	0.388606i	0.731766	+	0.681556i	$0.238696\pi$
$440$		0			0
$441$	3199.83	−	1235.31i	0.345517	−	0.133389i
$442$		0			0
$443$	95.2195	−	164.925i	0.0102122	−	0.0176881i	−0.860874	−	0.508818i	$-0.830083\pi$
$443$	95.2195	−	164.925i	0.0102122	−	0.0176881i	0.871086	+	0.491130i	$0.163416\pi$
$444$		0			0
$445$	−4906.05	−	8497.52i	−0.522627	−	0.905216i
$446$		0			0
$447$	−10786.8			−1.14138
$448$		0			0
$449$	17175.2			1.80523			0.902613	−	0.430454i	$-0.141646\pi$
$449$	17175.2			1.80523			0.902613	+	0.430454i	$0.141646\pi$
$450$		0			0
$451$	−1820.78	−	3153.68i	−0.190104	−	0.329270i
$452$		0			0
$453$	−1529.84	+	2649.76i	−0.158671	+	0.274826i
$454$		0			0
$455$	−2384.19	−	2786.14i	−0.245654	−	0.287069i
$456$		0			0
$457$	1752.90	−	3036.11i	0.179425	−	0.310773i	−0.762259	−	0.647272i	$-0.775910\pi$
$457$	1752.90	−	3036.11i	0.179425	−	0.310773i	0.941684	+	0.336499i	$0.109243\pi$
$458$		0			0
$459$	−5239.17	−	9074.51i	−0.532774	−	0.922792i
$460$		0			0
$461$	−5983.80			−0.604541			−0.302270	−	0.953222i	$-0.597745\pi$
$461$	−5983.80			−0.604541			−0.302270	+	0.953222i	$0.597745\pi$
$462$		0			0
$463$	−14057.4			−1.41102			−0.705510	−	0.708700i	$-0.749282\pi$
$463$	−14057.4			−1.41102			−0.705510	+	0.708700i	$0.749282\pi$
$464$		0			0
$465$	−3230.45	−	5595.31i	−0.322169	−	0.558013i
$466$		0			0
$467$	−9386.91	+	16258.6i	−0.930137	+	1.61105i	−0.147054	+	0.989128i	$0.546979\pi$
$467$	−9386.91	+	16258.6i	−0.930137	+	1.61105i	−0.783083	+	0.621917i	$0.786354\pi$
$468$		0			0
$469$	−2283.52	+	425.480i	−0.224826	+	0.0418910i
$470$		0			0
$471$	7105.61	−	12307.3i	0.695137	−	1.20401i
$472$		0			0
$473$	−2285.82	−	3959.16i	−0.222204	−	0.384868i
$474$		0			0
$475$	−22717.7			−2.19444
$476$		0			0
$477$	4744.76			0.455446
$478$		0			0
$479$	131.887	+	228.435i	0.0125805	+	0.0217901i	0.872247	−	0.489065i	$-0.162662\pi$
$479$	131.887	+	228.435i	0.0125805	+	0.0217901i	−0.859667	+	0.510855i	$0.829329\pi$
$480$		0			0
$481$	−2213.30	+	3833.55i	−0.209809	+	0.363399i
$482$		0			0
$483$	321.755	−	911.370i	0.0303113	−	0.0858567i
$484$		0			0
$485$	6442.39	−	11158.6i	0.603163	−	1.04471i
$486$		0			0
$487$	6327.46	+	10959.5i	0.588757	+	1.01976i	0.994396	+	0.105724i	$0.0337159\pi$
$487$	6327.46	+	10959.5i	0.588757	+	1.01976i	−0.405638	+	0.914034i	$0.632951\pi$
$488$		0			0
$489$	−10563.3			−0.976868
$490$		0			0
$491$	19041.6			1.75017			0.875087	−	0.483965i	$-0.160804\pi$
$491$	19041.6			1.75017			0.875087	+	0.483965i	$0.160804\pi$
$492$		0			0
$493$	−2650.69	−	4591.12i	−0.242152	−	0.419419i
$494$		0			0
$495$	2547.03	−	4411.59i	0.231274	−	0.400579i
$496$		0			0
$497$	−4862.35	+	13772.6i	−0.438845	+	1.24303i
$498$		0			0
$499$	8999.69	−	15587.9i	0.807378	−	1.39842i	−0.107296	−	0.994227i	$-0.534219\pi$
$499$	8999.69	−	15587.9i	0.807378	−	1.39842i	0.914674	−	0.404192i	$-0.132447\pi$
$500$		0			0
$501$	2032.65	+	3520.65i	0.181262	+	0.313954i
$502$		0			0
$503$	−15245.1			−1.35139			−0.675693	−	0.737183i	$-0.736155\pi$
$503$	−15245.1			−1.35139			−0.675693	+	0.737183i	$0.736155\pi$
$504$		0			0
$505$	−2563.83			−0.225918
$506$		0			0
$507$	6357.31	+	11011.2i	0.556879	+	0.964543i
$508$		0			0
$509$	2403.92	−	4163.72i	0.209336	−	0.362581i	−0.742170	−	0.670212i	$-0.766203\pi$
$509$	2403.92	−	4163.72i	0.209336	−	0.362581i	0.951506	+	0.307632i	$0.0995364\pi$
$510$		0			0
$511$	−11008.9	+	2051.25i	−0.953043	+	0.177577i
$512$		0			0
$513$	−4847.29	+	8395.75i	−0.417179	+	0.722576i
$514$		0			0
$515$	11123.1	+	19265.8i	0.951736	+	1.64846i
$516$		0			0
$517$	−1308.80			−0.111337
$518$		0			0
$519$	13048.9			1.10363
$520$		0			0
$521$	150.113	+	260.003i	0.0126230	+	0.0218636i	0.872268	−	0.489028i	$-0.162649\pi$
$521$	150.113	+	260.003i	0.0126230	+	0.0218636i	−0.859645	+	0.510892i	$0.829315\pi$
$522$		0			0
$523$	−397.744	+	688.913i	−0.0332546	+	0.0575986i	−0.882174	−	0.470924i	$-0.843921\pi$
$523$	−397.744	+	688.913i	−0.0332546	+	0.0575986i	0.848919	+	0.528523i	$0.177254\pi$
$524$		0			0
$525$	17748.5	+	20740.7i	1.47544	+	1.72419i
$526$		0			0
$527$	2807.92	−	4863.45i	0.232096	−	0.402003i
$528$		0			0
$529$	6046.70	+	10473.2i	0.496975	+	0.860786i
$530$		0			0
$531$	1970.62			0.161050
$532$		0			0
$533$	1415.42			0.115026
$534$		0			0
$535$	12541.8	+	21723.0i	1.01351	+	1.75545i
$536$		0			0
$537$	−11458.5	+	19846.8i	−0.920806	+	1.59488i
$538$		0			0
$539$	1408.98	−	9007.18i	0.112596	−	0.719790i
$540$		0			0
$541$	−9334.84	+	16168.4i	−0.741841	+	1.28491i	0.209815	+	0.977741i	$0.432714\pi$
$541$	−9334.84	+	16168.4i	−0.741841	+	1.28491i	−0.951656	+	0.307166i	$0.900619\pi$
$542$		0			0
$543$	−5330.06	−	9231.93i	−0.421242	−	0.729613i
$544$		0			0
$545$	20044.1			1.57540
$546$		0			0
$547$	−3264.72			−0.255191			−0.127596	−	0.991826i	$-0.540726\pi$
$547$	−3264.72			−0.255191			−0.127596	+	0.991826i	$0.540726\pi$
$548$		0			0
$549$	−2005.62	−	3473.84i	−0.155916	−	0.270054i
$550$		0			0
$551$	−2452.42	+	4247.72i	−0.189613	+	0.328419i
$552$		0			0
$553$	−9428.49	−	11018.0i	−0.725028	−	0.847259i
$554$		0			0
$555$	24975.7	−	43259.2i	1.91020	−	3.30856i
$556$		0			0
$557$	6702.35	+	11608.8i	0.509852	+	0.883090i	0.999935	+	0.0114139i	$0.00363322\pi$
$557$	6702.35	+	11608.8i	0.509852	+	0.883090i	−0.490083	+	0.871676i	$0.663033\pi$
$558$		0			0
$559$	1776.94			0.134448
$560$		0			0
$561$	16382.8			1.23294
$562$		0			0
$563$	−4649.50	−	8053.17i	−0.348051	−	0.602843i	0.637852	−	0.770159i	$-0.279823\pi$
$563$	−4649.50	−	8053.17i	−0.348051	−	0.602843i	−0.985903	+	0.167316i	$0.946490\pi$
$564$		0			0
$565$	1126.81	−	1951.69i	0.0839028	−	0.145324i
$566$		0			0
$567$	16368.0	−	3049.79i	1.21233	−	0.225889i
$568$		0			0
$569$	−10098.9	+	17491.8i	−0.744055	+	1.28874i	0.206581	+	0.978430i	$0.433766\pi$
$569$	−10098.9	+	17491.8i	−0.744055	+	1.28874i	−0.950635	+	0.310311i	$0.899567\pi$
$570$		0			0
$571$	4706.78	+	8152.38i	0.344961	+	0.597490i	0.985347	−	0.170564i	$-0.0545589\pi$
$571$	4706.78	+	8152.38i	0.344961	+	0.597490i	−0.640386	+	0.768053i	$0.721226\pi$
$572$		0			0
$573$	12233.2			0.891880
$574$		0			0
$575$	2078.92			0.150777
$576$		0			0
$577$	−3868.85	−	6701.05i	−0.279138	−	0.483481i	0.692033	−	0.721866i	$-0.256715\pi$
$577$	−3868.85	−	6701.05i	−0.279138	−	0.483481i	−0.971171	+	0.238385i	$0.923382\pi$
$578$		0			0
$579$	4805.24	−	8322.91i	0.344903	−	0.597389i
$580$		0			0
$581$	−2091.86	+	5925.19i	−0.149372	+	0.423095i
$582$		0			0
$583$	6305.63	−	10921.7i	0.447946	−	0.775865i
$584$		0			0
$585$	990.000	+	1714.73i	0.0699683	+	0.121189i
$586$		0			0
$587$	16755.0			1.17811			0.589057	−	0.808091i	$-0.299499\pi$
$587$	16755.0			1.17811			0.589057	+	0.808091i	$0.299499\pi$
$588$		0			0
$589$	−5195.78			−0.363478
$590$		0			0
$591$	−80.3328	−	139.140i	−0.00559128	−	0.00968438i
$592$		0			0
$593$	5886.45	−	10195.6i	0.407635	−	0.706044i	−0.586989	−	0.809595i	$-0.699687\pi$
$593$	5886.45	−	10195.6i	0.407635	−	0.706044i	0.994624	+	0.103550i	$0.0330203\pi$
$594$		0			0
$595$	−11973.8	+	33915.9i	−0.825007	+	2.33683i
$596$		0			0
$597$	−175.020	+	303.144i	−0.0119985	+	0.0207820i
$598$		0			0
$599$	−12629.7	−	21875.2i	−0.861493	−	1.49215i	−0.870487	−	0.492191i	$-0.836196\pi$
$599$	−12629.7	−	21875.2i	−0.861493	−	1.49215i	0.00899417	−	0.999960i	$-0.497137\pi$
$600$		0			0
$601$	187.801			0.0127464			0.00637319	−	0.999980i	$-0.497971\pi$
$601$	187.801			0.0127464			0.00637319	+	0.999980i	$0.497971\pi$
$602$		0			0
$603$	1254.21			0.0847019
$604$		0			0
$605$	5984.81	+	10366.0i	0.402177	+	0.696591i
$606$		0			0
$607$	8827.63	−	15289.9i	0.590284	−	1.02240i	−0.403910	−	0.914799i	$-0.632349\pi$
$607$	8827.63	−	15289.9i	0.590284	−	1.02240i	0.994194	−	0.107603i	$-0.0343176\pi$
$608$		0			0
$609$	5794.06	−	1079.59i	0.385529	−	0.0718342i
$610$		0			0
$611$	254.358	−	440.561i	0.0168416	−	0.0291705i
$612$		0			0
$613$	−502.463	−	870.291i	−0.0331065	−	0.0573421i	0.848997	−	0.528397i	$-0.177207\pi$
$613$	−502.463	−	870.291i	−0.0331065	−	0.0573421i	−0.882104	+	0.471055i	$0.843873\pi$
$614$		0			0
$615$	−15972.2			−1.04725
$616$		0			0
$617$	8416.05			0.549137			0.274568	−	0.961568i	$-0.411465\pi$
$617$	8416.05			0.549137			0.274568	+	0.961568i	$0.411465\pi$
$618$		0			0
$619$	−3142.62	−	5443.17i	−0.204059	−	0.353440i	0.745774	−	0.666200i	$-0.232080\pi$
$619$	−3142.62	−	5443.17i	−0.204059	−	0.353440i	−0.949832	+	0.312759i	$0.898747\pi$
$620$		0			0
$621$	443.582	−	768.306i	0.0286640	−	0.0496474i
$622$		0			0
$623$	6164.77	+	7204.09i	0.396447	+	0.463284i
$624$		0			0
$625$	−6401.51	+	11087.7i	−0.409697	+	0.709616i
$626$		0			0
$627$	−7578.69	−	13126.7i	−0.482717	−	0.836091i
$628$		0			0
$629$	43417.9			2.75228
$630$		0			0
$631$	−15928.9			−1.00495			−0.502473	−	0.864593i	$-0.667576\pi$
$631$	−15928.9			−1.00495			−0.502473	+	0.864593i	$0.667576\pi$
$632$		0			0
$633$	3631.12	+	6289.28i	0.228000	+	0.394907i
$634$		0			0
$635$	−17140.1	+	29687.5i	−1.07115	+	1.85529i
$636$		0			0
$637$	2758.11	+	2224.77i	0.171554	+	0.138381i
$638$		0			0
$639$	3943.17	−	6829.78i	0.244115	−	0.422820i
$640$		0			0
$641$	6341.52	+	10983.8i	0.390756	+	0.676810i	0.992550	−	0.121842i	$-0.0388801\pi$
$641$	6341.52	+	10983.8i	0.390756	+	0.676810i	−0.601793	+	0.798652i	$0.705547\pi$
$642$		0			0
$643$	−1461.21			−0.0896179			−0.0448090	−	0.998996i	$-0.514268\pi$
$643$	−1461.21			−0.0896179			−0.0448090	+	0.998996i	$0.514268\pi$
$644$		0			0
$645$	−20051.6			−1.22408
$646$		0			0
$647$	12000.7	+	20785.8i	0.729206	+	1.26302i	0.957219	+	0.289364i	$0.0934438\pi$
$647$	12000.7	+	20785.8i	0.729206	+	1.26302i	−0.228013	+	0.973658i	$0.573223\pi$
$648$		0			0
$649$	2618.89	−	4536.05i	0.158398	−	0.274354i
$650$		0			0
$651$	4059.28	+	4743.63i	0.244387	+	0.285588i
$652$		0			0
$653$	4548.57	−	7878.35i	0.272587	−	0.472135i	−0.696937	−	0.717133i	$-0.745454\pi$
$653$	4548.57	−	7878.35i	0.272587	−	0.472135i	0.969524	+	0.244998i	$0.0787874\pi$
$654$		0			0
$655$	18679.5	+	32353.9i	1.11430	+	1.93003i
$656$		0			0
$657$	6046.55			0.359054
$658$		0			0
$659$	−15018.0			−0.887738			−0.443869	−	0.896092i	$-0.646394\pi$
$659$	−15018.0			−0.887738			−0.443869	+	0.896092i	$0.646394\pi$
$660$		0			0
$661$	−12248.6	−	21215.2i	−0.720748	−	1.24837i	−0.960700	−	0.277588i	$-0.910465\pi$
$661$	−12248.6	−	21215.2i	−0.720748	−	1.24837i	0.239952	−	0.970785i	$-0.422868\pi$
$662$		0			0
$663$	−3183.89	+	5514.66i	−0.186504	+	0.323034i
$664$		0			0
$665$	32714.2	−	6095.52i	1.90767	−	0.355450i
$666$		0			0
$667$	224.424	−	388.714i	0.0130281	−	0.0225653i
$668$		0			0
$669$	−8885.87	−	15390.8i	−0.513524	−	0.889450i
$670$		0			0
$671$	−10661.6			−0.613394
$672$		0			0
$673$	1378.86			0.0789762			0.0394881	−	0.999220i	$-0.487427\pi$
$673$	1378.86			0.0789762			0.0394881	+	0.999220i	$0.487427\pi$
$674$		0			0
$675$	12528.7	+	21700.3i	0.714412	+	1.23740i
$676$		0			0
$677$	−6267.48	+	10855.6i	−0.355804	+	0.616270i	−0.987255	−	0.159145i	$-0.949126\pi$
$677$	−6267.48	+	10855.6i	−0.355804	+	0.616270i	0.631452	+	0.775415i	$0.282459\pi$
$678$		0			0
$679$	−4145.02	+	11740.8i	−0.234273	+	0.663578i
$680$		0			0
$681$	9465.83	−	16395.3i	0.532645	−	0.922568i
$682$		0			0
$683$	−13527.1	−	23429.5i	−0.757830	−	1.31260i	−0.943955	−	0.330075i	$-0.892926\pi$
$683$	−13527.1	−	23429.5i	−0.757830	−	1.31260i	0.186124	−	0.982526i	$-0.440407\pi$
$684$		0			0
$685$	−10953.8			−0.610985
$686$		0			0
$687$	32453.4			1.80229
$688$		0			0
$689$	2450.92	+	4245.11i	0.135519	+	0.234726i
$690$		0			0
$691$	12921.8	−	22381.1i	0.711385	−	1.23215i	−0.252952	−	0.967479i	$-0.581402\pi$
$691$	12921.8	−	22381.1i	0.711385	−	1.23215i	0.964337	−	0.264676i	$-0.0852651\pi$
$692$		0			0
$693$	−1638.76	+	4641.78i	−0.0898285	+	0.254439i
$694$		0			0
$695$	−11274.9	+	19528.7i	−0.615368	+	1.06585i
$696$		0			0
$697$	−6941.52	−	12023.1i	−0.377230	−	0.653381i
$698$		0			0
$699$	−31862.0			−1.72408
$700$		0			0
$701$	29351.6			1.58145			0.790723	−	0.612174i	$-0.209705\pi$
$701$	29351.6			1.58145			0.790723	+	0.612174i	$0.209705\pi$
$702$		0			0
$703$	−20085.2	−	34788.6i	−1.07756	−	1.86639i
$704$		0			0
$705$	−2870.27	+	4971.45i	−0.153334	+	0.265582i
$706$		0			0
$707$	2435.59	−	453.815i	0.129561	−	0.0241407i
$708$		0			0
$709$	−8506.71	+	14734.0i	−0.450601	+	0.780464i	−0.998423	−	0.0561308i	$-0.982124\pi$
$709$	−8506.71	+	14734.0i	−0.450601	+	0.780464i	0.547822	+	0.836595i	$0.315457\pi$
$710$		0			0
$711$	3915.04	+	6781.04i	0.206505	+	0.357678i
$712$		0			0
$713$	475.473			0.0249742
$714$		0			0
$715$	5262.71			0.275265
$716$		0			0
$717$	12716.2	+	22025.0i	0.662334	+	1.14720i
$718$		0			0
$719$	7273.25	−	12597.6i	0.377255	−	0.653425i	−0.613407	−	0.789767i	$-0.710201\pi$
$719$	7273.25	−	12597.6i	0.377255	−	0.653425i	0.990662	+	0.136342i	$0.0435347\pi$
$720$		0			0
$721$	−13977.0	−	16333.3i	−0.721955	−	0.843669i
$722$		0			0
$723$	−16620.8	+	28788.0i	−0.854956	+	1.48083i
$724$		0			0
$725$	6338.70	+	10979.0i	0.324708	+	0.562411i
$726$		0			0
$727$	−25023.9			−1.27660			−0.638298	−	0.769790i	$-0.720361\pi$
$727$	−25023.9			−1.27660			−0.638298	+	0.769790i	$0.720361\pi$
$728$		0			0
$729$	7993.00			0.406086
$730$		0			0
$731$	−8714.47	−	15093.9i	−0.440925	−	0.763705i
$732$		0			0
$733$	−6449.58	+	11171.0i	−0.324994	+	0.562907i	−0.981511	−	0.191405i	$-0.938696\pi$
$733$	−6449.58	+	11171.0i	−0.324994	+	0.562907i	0.656517	+	0.754311i	$0.272029\pi$
$734$		0			0
$735$	−31123.5	−	25105.1i	−1.56191	−	1.25988i
$736$		0			0
$737$	1666.80	−	2886.98i	0.0833071	−	0.144292i
$738$		0			0
$739$	7626.63	+	13209.7i	0.379635	+	0.657547i	0.991009	−	0.133795i	$-0.0427163\pi$
$739$	7626.63	+	13209.7i	0.379635	+	0.657547i	−0.611374	+	0.791342i	$0.709383\pi$
$740$		0			0
$741$	5891.48			0.292077
$742$		0			0
$743$	7984.56			0.394247			0.197123	−	0.980379i	$-0.436840\pi$
$743$	7984.56			0.394247			0.197123	+	0.980379i	$0.436840\pi$
$744$		0			0
$745$	16993.4	+	29433.5i	0.835692	+	1.44746i
$746$		0			0
$747$	1696.42	−	2938.28i	0.0830905	−	0.143917i
$748$		0			0
$749$	−15759.6	−	18416.5i	−0.768816	−	0.898430i
$750$		0			0
$751$	16390.8	−	28389.7i	0.796416	−	1.37943i	−0.125521	−	0.992091i	$-0.540060\pi$
$751$	16390.8	−	28389.7i	0.796416	−	1.37943i	0.921936	−	0.387341i	$-0.126606\pi$
$752$		0			0
$753$	17393.5	+	30126.4i	0.841773	+	1.45799i
$754$		0			0
$755$	9640.40			0.464702
$756$		0			0
$757$	16431.5			0.788920			0.394460	−	0.918913i	$-0.370932\pi$
$757$	16431.5			0.788920			0.394460	+	0.918913i	$0.370932\pi$
$758$		0			0
$759$	693.536	+	1201.24i	0.0331670	+	0.0574469i
$760$		0			0
$761$	16929.2	−	29322.2i	0.806415	−	1.39675i	−0.108917	−	0.994051i	$-0.534738\pi$
$761$	16929.2	−	29322.2i	0.806415	−	1.39675i	0.915332	−	0.402701i	$-0.131928\pi$
$762$		0			0
$763$	−19041.5	+	3547.94i	−0.903473	+	0.168341i
$764$		0			0
$765$	9710.31	−	16818.8i	0.458924	−	0.794880i
$766$		0			0
$767$	1017.93	+	1763.11i	0.0479209	+	0.0830014i
$768$		0			0
$769$	−36173.6			−1.69630			−0.848149	−	0.529758i	$-0.822283\pi$
$769$	−36173.6			−1.69630			−0.848149	+	0.529758i	$0.822283\pi$
$770$		0			0
$771$	6193.96			0.289326
$772$		0			0
$773$	10406.4	+	18024.4i	0.484208	+	0.838673i	0.999835	−	0.0181398i	$-0.00577440\pi$
$773$	10406.4	+	18024.4i	0.484208	+	0.838673i	−0.515627	+	0.856813i	$0.672441\pi$
$774$		0			0
$775$	−6714.69	+	11630.2i	−0.311224	+	0.539057i
$776$		0			0
$777$	−16069.3	+	45516.4i	−0.741935	+	2.10153i
$778$		0			0
$779$	−6422.31	+	11123.8i	−0.295383	+	0.511618i
$780$		0			0
$781$	−10480.7	−	18153.1i	−0.480190	−	0.831714i
$782$		0			0
$783$	5409.98			0.246918
$784$		0			0
$785$	−44776.6			−2.03586
$786$		0			0
$787$	14861.1	+	25740.2i	0.673114	+	1.16587i	0.977016	+	0.213165i	$0.0683772\pi$
$787$	14861.1	+	25740.2i	0.673114	+	1.16587i	−0.303902	+	0.952703i	$0.598289\pi$
$788$		0			0
$789$	−25013.3	+	43324.2i	−1.12864	+	1.95486i
$790$		0			0
$791$	−724.984	+	2053.52i	−0.0325885	+	0.0923068i
$792$		0			0
$793$	2072.02	−	3588.84i	0.0927863	−	0.160711i
$794$		0			0
$795$	−27657.1	−	47903.4i	−1.23383	−	2.13706i
$796$		0			0
$797$	−6475.82			−0.287811			−0.143905	−	0.989591i	$-0.545966\pi$
$797$	−6475.82			−0.287811			−0.143905	+	0.989591i	$0.545966\pi$
$798$		0			0
$799$	−4989.69			−0.220929
$800$		0			0
$801$	−2559.83	−	4433.75i	−0.112918	−	0.195579i
$802$		0			0
$803$	8035.67	−	13918.2i	0.353141	−	0.611659i
$804$		0			0
$805$	−2993.72	+	557.808i	−0.131074	+	0.0244226i
$806$		0			0
$807$	−17846.5	+	30911.0i	−0.778470	+	1.34835i
$808$		0			0
$809$	19709.4	+	34137.7i	0.856547	+	1.48358i	0.875202	+	0.483757i	$0.160728\pi$
$809$	19709.4	+	34137.7i	0.856547	+	1.48358i	−0.0186550	+	0.999826i	$0.505938\pi$
$810$		0			0
$811$	38728.6			1.67688			0.838438	−	0.544997i	$-0.183469\pi$
$811$	38728.6			1.67688			0.838438	+	0.544997i	$0.183469\pi$
$812$		0			0
$813$	−37815.2			−1.63129
$814$		0			0
$815$	16641.4	+	28823.7i	0.715241	+	1.23883i
$816$		0			0
$817$	−8062.65	+	13964.9i	−0.345259	+	0.598006i
$818$		0			0
$819$	−1244.00	−	1453.73i	−0.0530756	−	0.0620236i
$820$		0			0
$821$	16005.0	−	27721.4i	0.680363	−	1.17842i	−0.294508	−	0.955649i	$-0.595156\pi$
$821$	16005.0	−	27721.4i	0.680363	−	1.17842i	0.974870	−	0.222774i	$-0.0715111\pi$
$822$		0			0
$823$	5068.92	+	8779.63i	0.214692	+	0.371858i	0.953177	−	0.302412i	$-0.0977919\pi$
$823$	5068.92	+	8779.63i	0.214692	+	0.371858i	−0.738485	+	0.674270i	$0.764459\pi$
$824$		0			0
$825$	−39176.9			−1.65329
$826$		0			0
$827$	9064.96			0.381160			0.190580	−	0.981672i	$-0.438963\pi$
$827$	9064.96			0.381160			0.190580	+	0.981672i	$0.438963\pi$
$828$		0			0
$829$	9655.15	+	16723.2i	0.404508	+	0.700629i	0.994264	−	0.106953i	$-0.0341093\pi$
$829$	9655.15	+	16723.2i	0.404508	+	0.700629i	−0.589756	+	0.807582i	$0.700776\pi$
$830$		0			0
$831$	4493.71	−	7783.34i	0.187587	−	0.324911i
$832$		0			0
$833$	5371.59	−	34339.0i	0.223427	−	1.42830i
$834$		0			0
$835$	6404.46	−	11092.8i	0.265432	−	0.459741i
$836$		0			0
$837$	2865.44	+	4963.09i	0.118332	+	0.204958i
$838$		0			0
$839$	−11458.4			−0.471498			−0.235749	−	0.971814i	$-0.575754\pi$
$839$	−11458.4			−0.471498			−0.235749	+	0.971814i	$0.575754\pi$
$840$		0			0
$841$	−21651.9			−0.887773
$842$		0			0
$843$	10985.3	+	19027.0i	0.448817	+	0.777374i
$844$		0			0
$845$	20030.6	−	34693.9i	0.815470	−	1.41244i
$846$		0			0
$847$	−7520.31	−	8788.15i	−0.305078	−	0.356511i
$848$		0			0
$849$	23199.9	−	40183.4i	0.937830	−	1.62437i
$850$		0			0
$851$	1838.02	+	3183.54i	0.0740382	+	0.128238i
$852$		0			0
$853$	−6203.94			−0.249026			−0.124513	−	0.992218i	$-0.539737\pi$
$853$	−6203.94			−0.249026			−0.124513	+	0.992218i	$0.539737\pi$
$854$		0			0
$855$	−17968.0			−0.718705
$856$		0			0
$857$	7788.91	+	13490.8i	0.310460	+	0.537732i	0.978462	−	0.206427i	$-0.0661837\pi$
$857$	7788.91	+	13490.8i	0.310460	+	0.537732i	−0.668002	+	0.744159i	$0.732850\pi$
$858$		0			0
$859$	5946.86	−	10300.3i	0.236210	−	0.409127i	−0.723414	−	0.690415i	$-0.757428\pi$
$859$	5946.86	−	10300.3i	0.236210	−	0.409127i	0.959624	+	0.281287i	$0.0907614\pi$
$860$		0			0
$861$	15173.3	−	2827.18i	0.600585	−	0.111905i
$862$		0			0
$863$	−5836.78	+	10109.6i	−0.230227	+	0.398765i	−0.957875	−	0.287186i	$-0.907280\pi$
$863$	−5836.78	+	10109.6i	−0.230227	+	0.398765i	0.727648	+	0.685951i	$0.240614\pi$
$864$		0			0
$865$	−20557.3	−	35606.2i	−0.808056	−	1.39959i
$866$		0			0
$867$	32573.1			1.27594
$868$		0			0
$869$	20811.8			0.812420
$870$		0			0
$871$	647.864	+	1122.13i	0.0252032	+	0.0436533i
$872$		0			0
$873$	3361.45	−	5822.20i	0.130318	−	0.225718i
$874$		0			0
$875$	13862.9	−	39266.6i	0.535600	−	1.51709i
$876$		0			0
$877$	−1531.83	+	2653.20i	−0.0589808	+	0.102158i	−0.894008	−	0.448051i	$-0.852118\pi$
$877$	−1531.83	+	2653.20i	−0.0589808	+	0.102158i	0.835027	+	0.550208i	$0.185452\pi$
$878$		0			0
$879$	−16404.2	−	28412.9i	−0.629466	−	1.09027i
$880$		0			0
$881$	19236.9			0.735649			0.367825	−	0.929895i	$-0.380103\pi$
$881$	19236.9			0.735649			0.367825	+	0.929895i	$0.380103\pi$
$882$		0			0
$883$	−35556.9			−1.35514			−0.677569	−	0.735459i	$-0.736966\pi$
$883$	−35556.9			−1.35514			−0.677569	+	0.735459i	$0.736966\pi$
$884$		0			0
$885$	−11486.7	−	19895.5i	−0.436295	−	0.755685i
$886$		0			0
$887$	11609.4	−	20108.0i	0.439464	−	0.761174i	−0.558184	−	0.829717i	$-0.688502\pi$
$887$	11609.4	−	20108.0i	0.439464	−	0.761174i	0.997648	+	0.0685430i	$0.0218350\pi$
$888$		0			0
$889$	11027.9	−	31236.5i	0.416044	−	1.17844i
$890$		0			0
$891$	−11947.4	+	20693.5i	−0.449218	+	0.778069i
$892$		0			0
$893$	2308.23	+	3997.98i	0.0864973	+	0.149818i
$894$		0			0
$895$	72207.0			2.69678
$896$		0			0
$897$	−539.137			−0.0200683
$898$		0			0
$899$	1449.73	+	2511.01i	0.0537834	+	0.0931555i
$900$		0			0
$901$	24039.6	−	41637.8i	0.888873	−	1.53957i
$902$		0			0
$903$	19048.7	−	3549.28i	0.701995	−	0.130800i
$904$		0			0
$905$	−16793.9	+	29087.9i	−0.616849	+	1.06841i
$906$		0			0
$907$	10258.4	+	17768.0i	0.375549	+	0.650470i	0.990409	−	0.138166i	$-0.0441208\pi$
$907$	10258.4	+	17768.0i	0.375549	+	0.650470i	−0.614860	+	0.788636i	$0.710787\pi$
$908$		0			0
$909$	−1337.73			−0.0488115
$910$		0			0
$911$	−18247.6			−0.663634			−0.331817	−	0.943344i	$-0.607662\pi$
$911$	−18247.6			−0.663634			−0.331817	+	0.943344i	$0.607662\pi$
$912$		0			0
$913$	−4508.96	−	7809.75i	−0.163444	−	0.283094i
$914$		0			0
$915$	−23381.4	+	40497.8i	−0.844771	+	1.46319i
$916$		0			0
$917$	−23472.1	−	27429.2i	−0.845274	−	0.987778i
$918$		0			0
$919$	−13681.1	+	23696.3i	−0.491074	+	0.850566i	−0.999947	−	0.0102758i	$-0.996729\pi$
$919$	−13681.1	+	23696.3i	−0.491074	+	0.850566i	0.508873	+	0.860842i	$0.330062\pi$
$920$		0			0
$921$	−24495.8	−	42427.9i	−0.876398	−	1.51797i
$922$		0			0
$923$	8147.42			0.290548
$924$		0			0
$925$	−103827.			−3.69061
$926$		0			0
$927$	5803.72	+	10052.3i	0.205630	+	0.356162i
$928$		0			0
$929$	−21771.3	+	37709.0i	−0.768884	+	1.33175i	0.169285	+	0.985567i	$0.445854\pi$
$929$	−21771.3	+	37709.0i	−0.768884	+	1.33175i	−0.938169	+	0.346178i	$0.887479\pi$
$930$		0			0
$931$	−29998.9	+	11581.3i	−1.05604	+	0.407691i
$932$		0			0
$933$	6948.36	−	12034.9i	0.243815	−	0.422299i
$934$		0			0
$935$	−25809.4	−	44703.1i	−0.902734	−	1.56358i
$936$		0			0
$937$	32990.1			1.15020			0.575101	−	0.818083i	$-0.304963\pi$
$937$	32990.1			1.15020			0.575101	+	0.818083i	$0.304963\pi$
$938$		0			0
$939$	50706.7			1.76225
$940$		0			0
$941$	−8655.80	−	14992.3i	−0.299863	−	0.519378i	0.676241	−	0.736680i	$-0.263608\pi$
$941$	−8655.80	−	14992.3i	−0.299863	−	0.519378i	−0.976104	+	0.217302i	$0.930274\pi$
$942$		0			0
$943$	587.714	−	1017.95i	0.0202954	−	0.0351527i
$944$		0			0
$945$	−23864.2	−	27887.4i	−0.821484	−	0.959977i
$946$		0			0
$947$	667.854	−	1156.76i	0.0229169	−	0.0396933i	−0.854339	−	0.519715i	$-0.826038\pi$
$947$	667.854	−	1156.76i	0.0229169	−	0.0396933i	0.877256	+	0.480022i	$0.159371\pi$
$948$		0			0
$949$	3123.36	+	5409.82i	0.106837	+	0.185048i
$950$		0			0
$951$	63359.2			2.16042
$952$		0			0
$953$	18877.6			0.641663			0.320831	−	0.947136i	$-0.396038\pi$
$953$	18877.6			0.641663			0.320831	+	0.947136i	$0.396038\pi$
$954$		0			0
$955$	−19272.1	−	33380.2i	−0.653015	−	1.13106i
$956$		0			0
$957$	−4229.22	+	7325.23i	−0.142854	+	0.247431i
$958$		0			0
$959$	10406.0	−	1938.90i	0.350392	−	0.0652872i
$960$		0			0
$961$	13359.8	−	23139.8i	0.448450	−	0.776738i
$962$		0			0
$963$	6543.93	+	11334.4i	0.218977	+	0.379280i
$964$		0			0
$965$	−30280.6			−1.01012
$966$		0			0
$967$	39814.6			1.32405			0.662023	−	0.749483i	$-0.269698\pi$
$967$	39814.6			1.32405			0.662023	+	0.749483i	$0.269698\pi$
$968$		0			0
$969$	−28893.0	−	50044.1i	−0.957871	−	1.65908i
$970$		0			0
$971$	11422.4	−	19784.2i	0.377511	−	0.653868i	−0.613189	−	0.789936i	$-0.710114\pi$
$971$	11422.4	−	19784.2i	0.377511	−	0.653868i	0.990699	+	0.136069i	$0.0434468\pi$
$972$		0			0
$973$	7254.23	−	20547.6i	0.239013	−	0.677006i
$974$		0			0
$975$	7613.77	−	13187.4i	0.250088	−	0.433165i
$976$		0			0
$977$	−12198.3	−	21128.1i	−0.399446	−	0.691860i	0.594212	−	0.804308i	$-0.297464\pi$
$977$	−12198.3	−	21128.1i	−0.399446	−	0.691860i	−0.993658	+	0.112448i	$0.964131\pi$
$978$		0			0
$979$	−13607.7			−0.444233
$980$		0			0
$981$	10458.4			0.340379
$982$		0			0
$983$	16487.8	+	28557.6i	0.534972	+	0.926599i	0.999165	+	0.0408650i	$0.0130113\pi$
$983$	16487.8	+	28557.6i	0.534972	+	0.926599i	−0.464192	+	0.885734i	$0.653655\pi$
$984$		0			0
$985$	−253.112	+	438.403i	−0.00818763	+	0.0141814i
$986$		0			0
$987$	1846.72	−	5230.84i	0.0595561	−	0.168693i
$988$		0			0
$989$	737.823	−	1277.95i	0.0237224	−	0.0410883i
$990$		0			0
$991$	−5938.57	−	10285.9i	−0.190358	−	0.329710i	0.755011	−	0.655712i	$-0.227632\pi$
$991$	−5938.57	−	10285.9i	−0.190358	−	0.329710i	−0.945369	+	0.326002i	$0.894298\pi$
$992$		0			0
$993$	42238.0			1.34983
$994$		0			0
$995$	1102.90			0.0351401
$996$		0			0
$997$	8193.17	+	14191.0i	0.260261	+	0.450786i	0.966311	−	0.257376i	$-0.0828580\pi$
$997$	8193.17	+	14191.0i	0.260261	+	0.450786i	−0.706050	+	0.708162i	$0.749525\pi$
$998$		0			0
$999$	−22153.7	+	38371.3i	−0.701614	+	1.21523i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	448.4.i.g.65.1		4
4.3	odd	2		448.4.i.h.65.2		4
7.4	even	3	inner	448.4.i.g.193.1		4
8.3	odd	2		28.4.e.a.9.1	✓	4
8.5	even	2		112.4.i.d.65.2		4
24.11	even	2		252.4.k.c.37.1		4
28.11	odd	6		448.4.i.h.193.2		4
40.3	even	4		700.4.r.d.149.4		8
40.19	odd	2		700.4.i.g.401.2		4
40.27	even	4		700.4.r.d.149.1		8
56.3	even	6		196.4.e.g.165.2		4
56.5	odd	6		784.4.a.ba.1.2		2
56.11	odd	6		28.4.e.a.25.1	yes	4
56.19	even	6		196.4.a.g.1.1		2
56.27	even	2		196.4.e.g.177.2		4
56.37	even	6		784.4.a.u.1.1		2
56.51	odd	6		196.4.a.e.1.2		2
56.53	even	6		112.4.i.d.81.2		4
168.11	even	6		252.4.k.c.109.1		4
168.59	odd	6		1764.4.k.ba.361.2		4
168.83	odd	2		1764.4.k.ba.1549.2		4
168.107	even	6		1764.4.a.z.1.2		2
168.131	odd	6		1764.4.a.n.1.1		2
280.67	even	12		700.4.r.d.249.4		8
280.123	even	12		700.4.r.d.249.1		8
280.179	odd	6		700.4.i.g.501.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
28.4.e.a.9.1	✓	4	8.3	odd	2
28.4.e.a.25.1	yes	4	56.11	odd	6
112.4.i.d.65.2		4	8.5	even	2
112.4.i.d.81.2		4	56.53	even	6
196.4.a.e.1.2		2	56.51	odd	6
196.4.a.g.1.1		2	56.19	even	6
196.4.e.g.165.2		4	56.3	even	6
196.4.e.g.177.2		4	56.27	even	2
252.4.k.c.37.1		4	24.11	even	2
252.4.k.c.109.1		4	168.11	even	6
448.4.i.g.65.1		4	1.1	even	1	trivial
448.4.i.g.193.1		4	7.4	even	3	inner
448.4.i.h.65.2		4	4.3	odd	2
448.4.i.h.193.2		4	28.11	odd	6
700.4.i.g.401.2		4	40.19	odd	2
700.4.i.g.501.2		4	280.179	odd	6
700.4.r.d.149.1		8	40.27	even	4
700.4.r.d.149.4		8	40.3	even	4
700.4.r.d.249.1		8	280.123	even	12
700.4.r.d.249.4		8	280.67	even	12
784.4.a.u.1.1		2	56.37	even	6
784.4.a.ba.1.2		2	56.5	odd	6
1764.4.a.n.1.1		2	168.131	odd	6
1764.4.a.z.1.2		2	168.107	even	6
1764.4.k.ba.361.2		4	168.59	odd	6
1764.4.k.ba.1549.2		4	168.83	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 448 = 2^{6} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	448.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-3.04138 - 5.26783i) q^{3} +(-9.58276 + 16.5978i) q^{5} +(6.16553 - 17.4639i) q^{7} +(-5.00000 + 8.66025i) q^{9} +(13.2897 + 23.0184i) q^{11} -10.3311 q^{13} +116.579 q^{15} +(50.6655 + 87.7553i) q^{17} +(46.8759 - 81.1914i) q^{19} +(-110.748 + 20.6353i) q^{21} +(-4.28967 + 7.42992i) q^{23} +(-121.159 - 209.853i) q^{25} -103.407 q^{27} -52.3174 q^{29} +(-27.7103 - 47.9957i) q^{31} +(80.8379 - 140.015i) q^{33} +(230.779 + 269.686i) q^{35} +(214.238 - 371.071i) q^{37} +(31.4207 + 54.4222i) q^{39} -137.007 q^{41} -172.000 q^{43} +(-95.8276 - 165.978i) q^{45} +(-24.6207 + 42.6443i) q^{47} +(-266.973 - 215.348i) q^{49} +(308.186 - 533.794i) q^{51} +(-237.238 - 410.908i) q^{53} -509.407 q^{55} -570.269 q^{57} +(-98.5311 - 170.661i) q^{59} +(-200.562 + 347.384i) q^{61} +(120.414 + 140.714i) q^{63} +(99.0000 - 171.473i) q^{65} +(-62.7103 - 108.617i) q^{67} +52.1861 q^{69} -788.635 q^{71} +(-302.328 - 523.647i) q^{73} +(-736.979 + 1276.49i) q^{75} +(483.928 - 90.1685i) q^{77} +(391.504 - 678.104i) q^{79} +(449.500 + 778.557i) q^{81} -339.283 q^{83} -1942.06 q^{85} +(159.117 + 275.599i) q^{87} +(-255.983 + 443.375i) q^{89} +(-63.6963 + 180.420i) q^{91} +(-168.555 + 291.946i) q^{93} +(898.400 + 1556.08i) q^{95} -672.290 q^{97} -265.793 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 14 q^{5} - 24 q^{7} - 20 q^{9} - 32 q^{11} + 56 q^{13} + 296 q^{15} + 154 q^{17} + 224 q^{19} - 370 q^{21} + 68 q^{23} - 144 q^{25} + 472 q^{29} - 196 q^{31} + 518 q^{33} + 400 q^{35} + 346 q^{37}+ \cdots + 640 q^{99}+O(q^{100}) \) 4 * q - 14 * q^5 - 24 * q^7 - 20 * q^9 - 32 * q^11 + 56 * q^13 + 296 * q^15 + 154 * q^17 + 224 * q^19 - 370 * q^21 + 68 * q^23 - 144 * q^25 + 472 * q^29 - 196 * q^31 + 518 * q^33 + 400 * q^35 + 346 * q^37 + 296 * q^39 - 840 * q^41 - 688 * q^43 - 140 * q^45 + 84 * q^47 + 100 * q^49 + 296 * q^51 - 438 * q^53 - 1624 * q^55 + 444 * q^57 + 56 * q^59 + 98 * q^61 + 360 * q^63 + 396 * q^65 - 336 * q^67 + 1036 * q^69 - 1792 * q^71 - 966 * q^73 - 2072 * q^75 + 2398 * q^77 - 52 * q^79 + 1798 * q^81 + 784 * q^83 - 3340 * q^85 + 2072 * q^87 - 294 * q^89 - 1520 * q^91 + 518 * q^93 + 1124 * q^95 - 840 * q^97 + 640 * q^99

Introduction

L-functions

Modular forms

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Database

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