LMFDB - Embedded newform 666.4.s.d.307.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [666,4,Mod(307,666)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(666, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5]))

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

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

chi := DirichletCharacter("666.307");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 666 = 2 \cdot 3^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	666.s (of order $6$, 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:	$39.2952720638$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 346 x^{18} + 50697 x^{16} + 4104768 x^{14} + 200532432 x^{12} + 6039270720 x^{10} + \cdots + 1118416232704 $ x^20 + 346x^18 + 50697x^16 + 4104768x^14 + 200532432x^12 + 6039270720x^10 + 109290291168x^8 + 1091662316544x^6 + 4894436404224x^4 + 5352885383680*x^2 + 1118416232704
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{18}\cdot 3^{2} $
Twist minimal:	no (minimal twist has level 74)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			307.3
Root			$1.08183i$ of defining polynomial
Character	$\chi$	$=$	666.307
Dual form			666.4.s.d.397.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.73205 + 1.00000i) q^{2} +(2.00000 - 3.46410i) q^{4} +(-2.09330 - 1.20857i) q^{5} +(17.5687 - 30.4298i) q^{7} +8.00000i q^{8} +O(q^{10})$	\(q+(-1.73205 + 1.00000i) q^{2} +(2.00000 - 3.46410i) q^{4} +(-2.09330 - 1.20857i) q^{5} +(17.5687 - 30.4298i) q^{7} +8.00000i q^{8} +4.83427 q^{10} -30.7561 q^{11} +(-21.4108 - 12.3615i) q^{13} +70.2747i q^{14} +(-8.00000 - 13.8564i) q^{16} +(52.4721 - 30.2948i) q^{17} +(-31.8446 - 18.3855i) q^{19} +(-8.37319 + 4.83427i) q^{20} +(53.2712 - 30.7561i) q^{22} -195.332i q^{23} +(-59.5787 - 103.193i) q^{25} +49.4460 q^{26} +(-70.2747 - 121.719i) q^{28} +21.4124i q^{29} +179.129i q^{31} +(27.7128 + 16.0000i) q^{32} +(-60.5895 + 104.944i) q^{34} +(-73.5529 + 42.4658i) q^{35} +(3.36467 + 225.037i) q^{37} +73.5419 q^{38} +(9.66853 - 16.7464i) q^{40} +(-153.955 + 266.659i) q^{41} +395.356i q^{43} +(-61.5123 + 106.542i) q^{44} +(195.332 + 338.324i) q^{46} +475.963 q^{47} +(-445.816 - 772.176i) q^{49} +(206.387 + 119.157i) q^{50} +(-85.6430 + 49.4460i) q^{52} +(-74.3189 - 128.724i) q^{53} +(64.3818 + 37.1708i) q^{55} +(243.439 + 140.549i) q^{56} +(-21.4124 - 37.0873i) q^{58} +(-622.521 + 359.413i) q^{59} +(139.304 + 80.4270i) q^{61} +(-179.129 - 310.260i) q^{62} -64.0000 q^{64} +(29.8794 + 51.7527i) q^{65} +(262.311 - 454.336i) q^{67} -242.358i q^{68} +(84.9316 - 147.106i) q^{70} +(-175.491 + 303.959i) q^{71} -537.269 q^{73} +(-230.865 - 386.411i) q^{74} +(-127.378 + 73.5419i) q^{76} +(-540.344 + 935.904i) q^{77} +(-169.357 - 97.7786i) q^{79} +38.6741i q^{80} -615.822i q^{82} +(-254.149 - 440.199i) q^{83} -146.453 q^{85} +(-395.356 - 684.776i) q^{86} -246.049i q^{88} +(158.871 - 91.7241i) q^{89} +(-752.317 + 434.350i) q^{91} +(-676.648 - 390.663i) q^{92} +(-824.392 + 475.963i) q^{94} +(44.4401 + 76.9725i) q^{95} -686.636i q^{97} +(1544.35 + 891.632i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 40 q^{4} + 18 q^{5} - 2 q^{7}+O(q^{10}) $ 20 * q + 40 * q^4 + 18 * q^5 - 2 * q^7	$ 20 q + 40 q^{4} + 18 q^{5} - 2 q^{7} - 16 q^{10} + 16 q^{11} - 150 q^{13} - 160 q^{16} - 90 q^{17} + 162 q^{19} + 72 q^{20} + 532 q^{25} - 528 q^{26} + 8 q^{28} - 488 q^{34} + 342 q^{35} - 112 q^{37} - 144 q^{38} - 32 q^{40} + 498 q^{41} + 32 q^{44} - 424 q^{47} + 84 q^{49} - 1008 q^{50} - 600 q^{52} + 142 q^{53} - 540 q^{55} + 224 q^{58} - 1590 q^{59} - 1542 q^{61} - 8 q^{62} - 1280 q^{64} + 694 q^{65} + 62 q^{67} - 368 q^{70} + 178 q^{71} - 528 q^{73} + 560 q^{74} + 648 q^{76} - 3468 q^{77} - 3474 q^{79} - 938 q^{83} - 1100 q^{85} + 2120 q^{86} - 510 q^{89} + 666 q^{91} - 1344 q^{92} + 264 q^{94} - 4126 q^{95} + 816 q^{98}+O(q^{100}) $ 20 * q + 40 * q^4 + 18 * q^5 - 2 * q^7 - 16 * q^10 + 16 * q^11 - 150 * q^13 - 160 * q^16 - 90 * q^17 + 162 * q^19 + 72 * q^20 + 532 * q^25 - 528 * q^26 + 8 * q^28 - 488 * q^34 + 342 * q^35 - 112 * q^37 - 144 * q^38 - 32 * q^40 + 498 * q^41 + 32 * q^44 - 424 * q^47 + 84 * q^49 - 1008 * q^50 - 600 * q^52 + 142 * q^53 - 540 * q^55 + 224 * q^58 - 1590 * q^59 - 1542 * q^61 - 8 * q^62 - 1280 * q^64 + 694 * q^65 + 62 * q^67 - 368 * q^70 + 178 * q^71 - 528 * q^73 + 560 * q^74 + 648 * q^76 - 3468 * q^77 - 3474 * q^79 - 938 * q^83 - 1100 * q^85 + 2120 * q^86 - 510 * q^89 + 666 * q^91 - 1344 * q^92 + 264 * q^94 - 4126 * q^95 + 816 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/666\mathbb{Z}\right)^\times$.

$n$	$371$	$631$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−1.73205	+	1.00000i	−0.612372	+	0.353553i
$2$	−1.73205	+	1.00000i	−0.612372	+	0.353553i
$3$		0			0
$3$		0			0
$4$	2.00000	−	3.46410i	0.250000	−	0.433013i
$5$	−2.09330	−	1.20857i	−0.187230	−	0.108097i	0.403455	−	0.914999i	$-0.367809\pi$
$5$	−2.09330	−	1.20857i	−0.187230	−	0.108097i	−0.590685	+	0.806902i	$0.701143\pi$
$6$		0			0
$7$	17.5687	−	30.4298i	0.948619	−	1.64306i	0.200281	−	0.979739i	$-0.435815\pi$
$7$	17.5687	−	30.4298i	0.948619	−	1.64306i	0.748338	−	0.663318i	$-0.230852\pi$
$8$			8.00000i			0.353553i
$9$		0			0
$10$	4.83427			0.152873
$11$	−30.7561			−0.843029			−0.421515	−	0.906822i	$-0.638501\pi$
$11$	−30.7561			−0.843029			−0.421515	+	0.906822i	$0.638501\pi$
$12$		0			0
$13$	−21.4108	−	12.3615i	−0.456790	−	0.263728i	0.253903	−	0.967230i	$-0.418286\pi$
$13$	−21.4108	−	12.3615i	−0.456790	−	0.263728i	−0.710694	+	0.703501i	$0.751619\pi$
$14$			70.2747i			1.34155i
$15$		0			0
$16$	−8.00000	−	13.8564i	−0.125000	−	0.216506i
$17$	52.4721	−	30.2948i	0.748609	−	0.432209i	−0.0765824	−	0.997063i	$-0.524401\pi$
$17$	52.4721	−	30.2948i	0.748609	−	0.432209i	0.825191	+	0.564854i	$0.191067\pi$
$18$		0			0
$19$	−31.8446	−	18.3855i	−0.384507	−	0.221996i	0.295270	−	0.955414i	$-0.404590\pi$
$19$	−31.8446	−	18.3855i	−0.384507	−	0.221996i	−0.679778	+	0.733418i	$0.737924\pi$
$20$	−8.37319	+	4.83427i	−0.0936152	+	0.0540487i
$21$		0			0
$22$	53.2712	−	30.7561i	0.516248	−	0.298056i
$23$		−	195.332i		−	1.77084i	−0.464787	−	0.885422i	$-0.653869\pi$
$23$		−	195.332i		−	1.77084i	0.464787	−	0.885422i	$-0.346131\pi$
$24$		0			0
$25$	−59.5787	−	103.193i	−0.476630	−	0.825547i
$26$	49.4460			0.372968
$27$		0			0
$28$	−70.2747	−	121.719i	−0.474309	−	0.821528i
$29$			21.4124i			0.137110i	0.997647	+	0.0685548i	$0.0218388\pi$
$29$			21.4124i			0.137110i	−0.997647	+	0.0685548i	$0.978161\pi$
$30$		0			0
$31$			179.129i			1.03782i	0.854828	+	0.518911i	$0.173663\pi$
$31$			179.129i			1.03782i	−0.854828	+	0.518911i	$0.826337\pi$
$32$	27.7128	+	16.0000i	0.153093	+	0.0883883i
$33$		0			0
$34$	−60.5895	+	104.944i	−0.305618	+	0.529346i
$35$	−73.5529	+	42.4658i	−0.355220	+	0.205087i
$36$		0			0
$37$	3.36467	+	225.037i	0.0149499	+	0.999888i
$37$	3.36467	+	225.037i	0.0149499	+	0.999888i
$38$	73.5419			0.313949
$39$		0			0
$40$	9.66853	−	16.7464i	0.0382182	−	0.0661959i
$41$	−153.955	+	266.659i	−0.586434	+	1.01573i	0.408261	+	0.912865i	$0.366135\pi$
$41$	−153.955	+	266.659i	−0.586434	+	1.01573i	−0.994695	+	0.102869i	$0.967198\pi$
$42$		0			0
$43$			395.356i			1.40212i	0.713102	+	0.701060i	$0.247289\pi$
$43$			395.356i			1.40212i	−0.713102	+	0.701060i	$0.752711\pi$
$44$	−61.5123	+	106.542i	−0.210757	+	0.365042i
$45$		0			0
$46$	195.332	+	338.324i	0.626088	+	1.08442i
$47$	475.963			1.47716			0.738578	−	0.674168i	$-0.235498\pi$
$47$	475.963			1.47716			0.738578	+	0.674168i	$0.235498\pi$
$48$		0			0
$49$	−445.816	−	772.176i	−1.29976	−	2.25124i
$50$	206.387	+	119.157i	0.583750	+	0.337028i
$51$		0			0
$52$	−85.6430	+	49.4460i	−0.228395	+	0.131864i
$53$	−74.3189	−	128.724i	−0.192613	−	0.333615i	0.753503	−	0.657445i	$-0.228363\pi$
$53$	−74.3189	−	128.724i	−0.192613	−	0.333615i	−0.946115	+	0.323830i	$0.895029\pi$
$54$		0			0
$55$	64.3818	+	37.1708i	0.157841	+	0.0911293i
$56$	243.439	+	140.549i	0.580908	+	0.335387i
$57$		0			0
$58$	−21.4124	−	37.0873i	−0.0484756	−	0.0839622i
$59$	−622.521	+	359.413i	−1.37365	+	0.793077i	−0.991386	−	0.130976i	$-0.958189\pi$
$59$	−622.521	+	359.413i	−1.37365	+	0.793077i	−0.382264	+	0.924053i	$0.624856\pi$
$60$		0			0
$61$	139.304	+	80.4270i	0.292394	+	0.168813i	0.639021	−	0.769189i	$-0.279340\pi$
$61$	139.304	+	80.4270i	0.292394	+	0.168813i	−0.346627	+	0.938003i	$0.612673\pi$
$62$	−179.129	−	310.260i	−0.366926	−	0.635534i
$63$		0			0
$64$	−64.0000			−0.125000
$65$	29.8794	+	51.7527i	0.0570167	+	0.0987558i
$66$		0			0
$67$	262.311	−	454.336i	0.478304	−	0.828447i	−0.521387	−	0.853321i	$-0.674585\pi$
$67$	262.311	−	454.336i	0.478304	−	0.828447i	0.999691	+	0.0248737i	$0.00791837\pi$
$68$		−	242.358i		−	0.432209i
$69$		0			0
$70$	84.9316	−	147.106i	0.145018	−	0.251179i
$71$	−175.491	+	303.959i	−0.293337	+	0.508075i	−0.974597	−	0.223967i	$-0.928099\pi$
$71$	−175.491	+	303.959i	−0.293337	+	0.508075i	0.681260	+	0.732042i	$0.261432\pi$
$72$		0			0
$73$	−537.269			−0.861405			−0.430702	−	0.902494i	$-0.641734\pi$
$73$	−537.269			−0.861405			−0.430702	+	0.902494i	$0.641734\pi$
$74$	−230.865	−	386.411i	−0.362669	−	0.607018i
$75$		0			0
$76$	−127.378	+	73.5419i	−0.192254	+	0.110998i
$77$	−540.344	+	935.904i	−0.799713	+	1.38514i
$78$		0			0
$79$	−169.357	−	97.7786i	−0.241192	−	0.139252i	0.374532	−	0.927214i	$-0.377803\pi$
$79$	−169.357	−	97.7786i	−0.241192	−	0.139252i	−0.615725	+	0.787961i	$0.711137\pi$
$80$			38.6741i			0.0540487i
$81$		0			0
$82$		−	615.822i		−	0.829343i
$83$	−254.149	−	440.199i	−0.336102	−	0.582146i	0.647594	−	0.761986i	$-0.275775\pi$
$83$	−254.149	−	440.199i	−0.336102	−	0.582146i	−0.983696	+	0.179840i	$0.942442\pi$
$84$		0			0
$85$	−146.453			−0.186883
$86$	−395.356	−	684.776i	−0.495724	−	0.858620i
$87$		0			0
$88$		−	246.049i		−	0.298056i
$89$	158.871	−	91.7241i	0.189216	−	0.109244i	−0.402399	−	0.915464i	$-0.631824\pi$
$89$	158.871	−	91.7241i	0.189216	−	0.109244i	0.591616	+	0.806220i	$0.298490\pi$
$90$		0			0
$91$	−752.317	+	434.350i	−0.866640	+	0.500355i
$92$	−676.648	−	390.663i	−0.766798	−	0.442711i
$93$		0			0
$94$	−824.392	+	475.963i	−0.904570	+	0.522254i
$95$	44.4401	+	76.9725i	0.0479943	+	0.0831286i
$96$		0			0
$97$		−	686.636i		−	0.718735i	−0.933196	−	0.359368i	$-0.882992\pi$
$97$		−	686.636i		−	0.718735i	0.933196	−	0.359368i	$-0.117008\pi$
$98$	1544.35	+	891.632i	1.59187	+	0.919066i
$99$		0			0
$100$	−476.630			−0.476630
$101$	−432.142			−0.425740			−0.212870	−	0.977081i	$-0.568281\pi$
$101$	−432.142			−0.425740			−0.212870	+	0.977081i	$0.568281\pi$
$102$		0			0
$103$		−	131.764i		−	0.126050i	−0.998012	−	0.0630248i	$-0.979925\pi$
$103$		−	131.764i		−	0.126050i	0.998012	−	0.0630248i	$-0.0200747\pi$
$104$	98.8921	−	171.286i	0.0932420	−	0.161500i
$105$		0			0
$106$	257.448	+	148.638i	0.235902	+	0.136198i
$107$	833.526	−	1443.71i	0.753084	−	1.30438i	−0.193237	−	0.981152i	$-0.561899\pi$
$107$	833.526	−	1443.71i	0.753084	−	1.30438i	0.946321	−	0.323228i	$-0.104768\pi$
$108$		0			0
$109$	−1392.08	+	803.717i	−1.22327	+	0.706258i	−0.965615	−	0.259978i	$-0.916285\pi$
$109$	−1392.08	+	803.717i	−1.22327	+	0.706258i	−0.257660	+	0.966236i	$0.582951\pi$
$110$	−148.683			−0.128876
$111$		0			0
$112$	−562.197			−0.474309
$113$	317.415	−	183.260i	0.264247	−	0.152563i	−0.362023	−	0.932169i	$-0.617914\pi$
$113$	317.415	−	183.260i	0.264247	−	0.152563i	0.626270	+	0.779606i	$0.284581\pi$
$114$		0			0
$115$	−236.071	+	408.887i	−0.191424	+	0.331556i
$116$	74.1747	+	42.8248i	0.0593702	+	0.0342774i
$117$		0			0
$118$	718.825	−	1245.04i	0.560790	−	0.971317i
$119$		−	2128.95i		−	1.64001i
$120$		0			0
$121$	−385.061			−0.289302
$122$	−321.708			−0.238738
$123$		0			0
$124$	620.521	+	358.258i	0.449390	+	0.259456i
$125$			590.161i			0.422285i
$126$		0			0
$127$	98.6351	+	170.841i	0.0689170	+	0.119368i	0.898425	−	0.439127i	$-0.144712\pi$
$127$	98.6351	+	170.841i	0.0689170	+	0.119368i	−0.829508	+	0.558495i	$0.811379\pi$
$128$	110.851	−	64.0000i	0.0765466	−	0.0441942i
$129$		0			0
$130$	−103.505	−	59.7588i	−0.0698309	−	0.0403169i
$131$	−2075.76	+	1198.44i	−1.38443	+	0.799300i	−0.992680	−	0.120773i	$-0.961463\pi$
$131$	−2075.76	+	1198.44i	−1.38443	+	0.799300i	−0.391748	+	0.920073i	$0.628129\pi$
$132$		0			0
$133$	−1118.93	+	646.016i	−0.729502	+	0.421178i
$134$			1049.24i			0.676424i
$135$		0			0
$136$	242.358	+	419.777i	0.152809	+	0.264673i
$137$	−783.748			−0.488760			−0.244380	−	0.969680i	$-0.578584\pi$
$137$	−783.748			−0.488760			−0.244380	+	0.969680i	$0.578584\pi$
$138$		0			0
$139$	64.1646	+	111.136i	0.0391538	+	0.0678163i	0.884938	−	0.465708i	$-0.154200\pi$
$139$	64.1646	+	111.136i	0.0391538	+	0.0678163i	−0.845784	+	0.533525i	$0.820867\pi$
$140$			339.726i			0.205087i
$141$		0			0
$142$		−	701.963i		−	0.414841i
$143$	658.512	+	380.192i	0.385088	+	0.222331i
$144$		0			0
$145$	25.8783	−	44.8225i	0.0148212	−	0.0256711i
$146$	930.577	−	537.269i	0.527501	−	0.304553i
$147$		0			0
$148$	786.281	+	438.419i	0.436702	+	0.243499i
$149$	−1616.00			−0.888510			−0.444255	−	0.895900i	$-0.646532\pi$
$149$	−1616.00			−0.888510			−0.444255	+	0.895900i	$0.646532\pi$
$150$		0			0
$151$	−73.8288	+	127.875i	−0.0397888	+	0.0689162i	−0.885234	−	0.465146i	$-0.846002\pi$
$151$	−73.8288	+	127.875i	−0.0397888	+	0.0689162i	0.845445	+	0.534062i	$0.179335\pi$
$152$	147.084	−	254.756i	0.0784873	−	0.135944i
$153$		0			0
$154$		−	2161.38i		−	1.13097i
$155$	216.489	−	374.970i	0.112186	−	0.194312i
$156$		0			0
$157$	−1334.28	−	2311.03i	−0.678260	−	1.17478i	−0.975505	−	0.219979i	$-0.929401\pi$
$157$	−1334.28	−	2311.03i	−0.678260	−	1.17478i	0.297245	−	0.954801i	$-0.403932\pi$
$158$	391.114			0.196933
$159$		0			0
$160$	−38.6741	−	66.9856i	−0.0191091	−	0.0330980i
$161$	−5943.90	−	3431.71i	−2.90960	−	1.67986i
$162$		0			0
$163$	2249.86	−	1298.96i	1.08112	−	0.624184i	0.149921	−	0.988698i	$-0.452098\pi$
$163$	2249.86	−	1298.96i	1.08112	−	0.624184i	0.931198	+	0.364514i	$0.118765\pi$
$164$	615.822	+	1066.63i	0.293217	+	0.507867i
$165$		0			0
$166$	880.398	+	508.298i	0.411640	+	0.237660i
$167$	−1948.39	−	1124.90i	−0.902820	−	0.521243i	−0.0247059	−	0.999695i	$-0.507865\pi$
$167$	−1948.39	−	1124.90i	−0.902820	−	0.521243i	−0.878114	+	0.478451i	$0.841198\pi$
$168$		0			0
$169$	−792.886	−	1373.32i	−0.360895	−	0.625088i
$170$	253.664	−	146.453i	0.114442	−	0.0660731i
$171$		0			0
$172$	1369.55	+	790.711i	0.607136	+	0.350530i
$173$	1342.96	+	2326.08i	0.590193	+	1.02224i	0.994206	+	0.107491i	$0.0342818\pi$
$173$	1342.96	+	2326.08i	0.590193	+	1.02224i	−0.404013	+	0.914753i	$0.632385\pi$
$174$		0			0
$175$	−4186.88			−1.80856
$176$	246.049	+	426.169i	0.105379	+	0.182521i
$177$		0			0
$178$	−183.448	+	317.742i	−0.0772473	+	0.133796i
$179$			2780.19i			1.16090i	0.814295	+	0.580451i	$0.197124\pi$
$179$			2780.19i			1.16090i	−0.814295	+	0.580451i	$0.802876\pi$
$180$		0			0
$181$	−1448.48	+	2508.84i	−0.594832	+	1.03028i	0.398738	+	0.917065i	$0.369448\pi$
$181$	−1448.48	+	2508.84i	−0.594832	+	1.03028i	−0.993571	+	0.113215i	$0.963885\pi$
$182$	868.701	−	1504.63i	0.353804	−	0.612807i
$183$		0			0
$184$	1562.65			0.626088
$185$	264.929	−	475.136i	0.105286	−	0.188825i
$186$		0			0
$187$	−1613.84	+	931.750i	−0.631099	+	0.364365i
$188$	951.926	−	1648.78i	0.369289	−	0.639627i
$189$		0			0
$190$	−153.945	−	88.8802i	−0.0587808	−	0.0339371i
$191$			941.250i			0.356578i	0.983978	+	0.178289i	$0.0570563\pi$
$191$			941.250i			0.356578i	−0.983978	+	0.178289i	$0.942944\pi$
$192$		0			0
$193$		−	174.577i		−	0.0651106i	−0.999470	−	0.0325553i	$-0.989635\pi$
$193$		−	174.577i		−	0.0651106i	0.999470	−	0.0325553i	$-0.0103645\pi$
$194$	686.636	+	1189.29i	0.254111	+	0.440134i
$195$		0			0
$196$	−3566.53			−1.29976
$197$	−1016.31	−	1760.30i	−0.367558	−	0.636629i	0.621625	−	0.783315i	$-0.286473\pi$
$197$	−1016.31	−	1760.30i	−0.367558	−	0.636629i	−0.989183	+	0.146686i	$0.953139\pi$
$198$		0			0
$199$		−	5212.24i		−	1.85671i	−0.371693	−	0.928356i	$-0.621223\pi$
$199$		−	5212.24i		−	1.85671i	0.371693	−	0.928356i	$-0.378777\pi$
$200$	825.547	−	476.630i	0.291875	−	0.168514i
$201$		0			0
$202$	748.491	−	432.142i	0.260711	−	0.150522i
$203$	651.575	+	376.187i	0.225279	+	0.130065i
$204$		0			0
$205$	644.550	−	372.131i	0.219597	−	0.126784i
$206$	131.764	+	228.222i	0.0445653	+	0.0771893i
$207$		0			0
$208$			395.568i			0.131864i
$209$	979.415	+	565.466i	0.324151	+	0.187149i
$210$		0			0
$211$	4949.27			1.61479			0.807397	−	0.590008i	$-0.200876\pi$
$211$	4949.27			1.61479			0.807397	+	0.590008i	$0.200876\pi$
$212$	−594.551			−0.192613
$213$		0			0
$214$			3334.11i			1.06502i
$215$	477.813	−	827.597i	0.151566	−	0.262519i
$216$		0			0
$217$	5450.86	+	3147.06i	1.70520	+	0.984498i
$218$	1607.43	−	2784.16i	0.499400	−	0.864986i
$219$		0			0
$220$	257.527	−	148.683i	0.0789203	−	0.0455647i
$221$	−1497.96			−0.455943
$222$		0			0
$223$	−4887.83			−1.46777			−0.733886	−	0.679273i	$-0.762295\pi$
$223$	−4887.83			−1.46777			−0.733886	+	0.679273i	$0.762295\pi$
$224$	973.754	−	562.197i	0.290454	−	0.167694i
$225$		0			0
$226$	−366.520	+	634.831i	−0.107878	+	0.186851i
$227$	−1375.49	−	794.138i	−0.402177	−	0.232197i	0.285246	−	0.958454i	$-0.407925\pi$
$227$	−1375.49	−	794.138i	−0.402177	−	0.232197i	−0.687423	+	0.726257i	$0.741258\pi$
$228$		0			0
$229$	2147.56	−	3719.68i	0.619715	−	1.07338i	−0.369823	−	0.929102i	$-0.620582\pi$
$229$	2147.56	−	3719.68i	0.619715	−	1.07338i	0.989538	−	0.144275i	$-0.0460850\pi$
$230$		−	944.285i		−	0.270714i
$231$		0			0
$232$	−171.299			−0.0484756
$233$	4284.13			1.20456			0.602280	−	0.798285i	$-0.294259\pi$
$233$	4284.13			1.20456			0.602280	+	0.798285i	$0.294259\pi$
$234$		0			0
$235$	−996.333	−	575.233i	−0.276568	−	0.159677i
$236$			2875.30i			0.793077i
$237$		0			0
$238$	2128.95	+	3687.46i	0.579830	+	1.00430i
$239$	2586.72	−	1493.44i	0.700087	−	0.404196i	−0.107293	−	0.994227i	$-0.534218\pi$
$239$	2586.72	−	1493.44i	0.700087	−	0.404196i	0.807380	+	0.590032i	$0.200885\pi$
$240$		0			0
$241$	−2153.67	−	1243.42i	−0.575643	−	0.332348i	0.183757	−	0.982972i	$-0.441174\pi$
$241$	−2153.67	−	1243.42i	−0.575643	−	0.332348i	−0.759400	+	0.650624i	$0.774507\pi$
$242$	666.945	−	385.061i	0.177160	−	0.102284i
$243$		0			0
$244$	557.215	−	321.708i	0.146197	−	0.0844067i
$245$			2155.19i			0.562001i
$246$		0			0
$247$	454.544	+	787.294i	0.117093	+	0.202811i
$248$	−1433.03			−0.366926
$249$		0			0
$250$	−590.161	−	1022.19i	−0.149300	−	0.258596i
$251$			3778.67i			0.950230i	0.879924	+	0.475115i	$0.157594\pi$
$251$			3778.67i			0.950230i	−0.879924	+	0.475115i	$0.842406\pi$
$252$		0			0
$253$			6007.64i			1.49287i
$254$	−341.682	−	197.270i	−0.0844057	−	0.0487316i
$255$		0			0
$256$	−128.000	+	221.703i	−0.0312500	+	0.0541266i
$257$	2467.69	−	1424.72i	0.598951	−	0.345804i	−0.169678	−	0.985500i	$-0.554273\pi$
$257$	2467.69	−	1424.72i	0.598951	−	0.345804i	0.768629	+	0.639695i	$0.220939\pi$
$258$		0			0
$259$	6906.95	+	3851.22i	1.65705	+	0.923949i
$260$	239.035			0.0570167
$261$		0			0
$262$	2396.88	−	4151.52i	0.565190	−	0.978938i
$263$	−1519.21	+	2631.35i	−0.356192	+	0.616943i	−0.987321	−	0.158735i	$-0.949259\pi$
$263$	−1519.21	+	2631.35i	−0.356192	+	0.616943i	0.631129	+	0.775678i	$0.282592\pi$
$264$		0			0
$265$			359.277i			0.0832838i
$266$	1292.03	−	2237.87i	0.297818	−	0.515836i
$267$		0			0
$268$	−1049.24	−	1817.34i	−0.239152	−	0.414223i
$269$	3077.86			0.697623			0.348812	−	0.937193i	$-0.386585\pi$
$269$	3077.86			0.697623			0.348812	+	0.937193i	$0.386585\pi$
$270$		0			0
$271$	3497.01	+	6057.00i	0.783868	+	1.35770i	0.929673	+	0.368385i	$0.120089\pi$
$271$	3497.01	+	6057.00i	0.783868	+	1.35770i	−0.145805	+	0.989313i	$0.546577\pi$
$272$	−839.553	−	484.716i	−0.187152	−	0.108052i
$273$		0			0
$274$	1357.49	−	783.748i	0.299303	−	0.172803i
$275$	1832.41	+	3173.83i	0.401813	+	0.695960i
$276$		0			0
$277$	4400.31	+	2540.52i	0.954473	+	0.551065i	0.894468	−	0.447133i	$-0.147555\pi$
$277$	4400.31	+	2540.52i	0.954473	+	0.551065i	0.0600057	+	0.998198i	$0.480888\pi$
$278$	−222.273	−	128.329i	−0.0479534	−	0.0276859i
$279$		0			0
$280$	−339.726	−	588.424i	−0.0725091	−	0.125589i
$281$	−5617.85	+	3243.47i	−1.19264	+	0.688573i	−0.958905	−	0.283727i	$-0.908429\pi$
$281$	−5617.85	+	3243.47i	−1.19264	+	0.688573i	−0.233738	+	0.972300i	$0.575096\pi$
$282$		0			0
$283$	−4432.45	−	2559.07i	−0.931030	−	0.537531i	−0.0438930	−	0.999036i	$-0.513976\pi$
$283$	−4432.45	−	2559.07i	−0.931030	−	0.537531i	−0.887137	+	0.461506i	$0.847309\pi$
$284$	701.963	+	1215.84i	0.146669	+	0.254037i
$285$		0			0
$286$	−1520.77			−0.314423
$287$	5409.59	+	9369.68i	1.11261	+	1.92709i
$288$		0			0
$289$	−620.955	+	1075.53i	−0.126390	+	0.218914i
$290$			103.513i			0.0209604i
$291$		0			0
$292$	−1074.54	+	1861.15i	−0.215351	+	0.372999i
$293$	−1013.89	+	1756.10i	−0.202156	+	0.350145i	−0.949223	−	0.314604i	$-0.898128\pi$
$293$	−1013.89	+	1756.10i	−0.202156	+	0.350145i	0.747067	+	0.664749i	$0.231462\pi$
$294$		0			0
$295$	1737.50			0.342919
$296$	−1800.30	+	26.9173i	−0.353514	+	0.00528560i
$297$		0			0
$298$	2799.00	−	1616.00i	0.544099	−	0.314136i
$299$	−2414.59	+	4182.20i	−0.467022	+	0.808905i
$300$		0			0
$301$	12030.6	+	6945.87i	2.30376	+	1.33008i
$302$		−	295.315i		−	0.0562698i
$303$		0			0
$304$			588.335i			0.110998i
$305$	−194.403	−	336.715i	−0.0364966	−	0.0632140i
$306$		0			0
$307$	−1962.05			−0.364756			−0.182378	−	0.983228i	$-0.558379\pi$
$307$	−1962.05			−0.364756			−0.182378	+	0.983228i	$0.558379\pi$
$308$	2161.38	+	3743.61i	0.399857	+	0.692572i
$309$		0			0
$310$			865.957i			0.158655i
$311$	1570.81	−	906.908i	0.286407	−	0.165357i	−0.349913	−	0.936782i	$-0.613789\pi$
$311$	1570.81	−	906.908i	0.286407	−	0.165357i	0.636320	+	0.771425i	$0.280456\pi$
$312$		0			0
$313$	−388.171	+	224.110i	−0.0700981	+	0.0404711i	−0.534639	−	0.845080i	$-0.679553\pi$
$313$	−388.171	+	224.110i	−0.0700981	+	0.0404711i	0.464541	+	0.885551i	$0.346219\pi$
$314$	4622.07	+	2668.55i	0.830695	+	0.479602i
$315$		0			0
$316$	−677.430	+	391.114i	−0.120596	+	0.0696262i
$317$	−2602.41	−	4507.51i	−0.461092	−	0.798634i	0.537924	−	0.842993i	$-0.319209\pi$
$317$	−2602.41	−	4507.51i	−0.461092	−	0.798634i	−0.999016	+	0.0443591i	$0.985875\pi$
$318$		0			0
$319$		−	658.562i		−	0.115587i
$320$	133.971	+	77.3483i	0.0234038	+	0.0135122i
$321$		0			0
$322$	13726.9			2.37568
$323$	−2227.93			−0.383794
$324$		0			0
$325$			2945.93i			0.502803i
$326$	−2597.91	+	4499.71i	−0.441365	+	0.764466i
$327$		0			0
$328$	−2133.27	−	1231.64i	−0.359116	−	0.207336i
$329$	8362.04	−	14483.5i	1.40126	−	2.42705i
$330$		0			0
$331$	2601.67	−	1502.08i	0.432027	−	0.249431i	−0.268183	−	0.963368i	$-0.586423\pi$
$331$	2601.67	−	1502.08i	0.432027	−	0.249431i	0.700210	+	0.713937i	$0.253090\pi$
$332$	−2033.19			−0.336102
$333$		0			0
$334$	4499.61			0.737149
$335$	−1098.19	+	634.040i	−0.179106	+	0.103407i
$336$		0			0
$337$	5990.82	−	10376.4i	0.968370	−	1.67727i	0.268095	−	0.963393i	$-0.413606\pi$
$337$	5990.82	−	10376.4i	0.968370	−	1.67727i	0.700275	−	0.713873i	$-0.253061\pi$
$338$	2746.64	+	1585.77i	0.442004	+	0.255191i
$339$		0			0
$340$	−292.906	+	507.328i	−0.0467207	+	0.0809227i
$341$		−	5509.31i		−	0.874915i
$342$		0			0
$343$	−19277.5			−3.03465
$344$	−3162.84			−0.495724
$345$		0			0
$346$	−4652.15	−	2685.92i	−0.722836	−	0.417330i
$347$		−	1120.38i		−	0.173328i	−0.996238	−	0.0866641i	$-0.972379\pi$
$347$		−	1120.38i		−	0.173328i	0.996238	−	0.0866641i	$-0.0276207\pi$
$348$		0			0
$349$	1024.21	+	1773.98i	0.157091	+	0.272089i	0.933818	−	0.357747i	$-0.116455\pi$
$349$	1024.21	+	1773.98i	0.157091	+	0.272089i	−0.776728	+	0.629837i	$0.783122\pi$
$350$	7251.88	−	4186.88i	1.10751	−	0.639423i
$351$		0			0
$352$	−852.339	−	492.098i	−0.129062	−	0.0745140i
$353$	8958.91	−	5172.43i	1.35081	−	0.779889i	0.362444	−	0.932006i	$-0.381942\pi$
$353$	8958.91	−	5172.43i	1.35081	−	0.779889i	0.988362	+	0.152117i	$0.0486091\pi$
$354$		0			0
$355$	734.710	−	424.185i	0.109843	−	0.0634180i
$356$		−	733.793i		−	0.109244i
$357$		0			0
$358$	−2780.19	−	4815.44i	−0.410441	−	0.710904i
$359$	−3790.62			−0.557274			−0.278637	−	0.960397i	$-0.589883\pi$
$359$	−3790.62			−0.557274			−0.278637	+	0.960397i	$0.589883\pi$
$360$		0			0
$361$	−2753.45	−	4769.11i	−0.401436	−	0.695308i
$362$		−	5793.92i		−	0.841220i
$363$		0			0
$364$			3474.80i			0.500355i
$365$	1124.66	+	649.325i	0.161281	+	0.0931157i
$366$		0			0
$367$	−3690.64	+	6392.38i	−0.524931	+	0.909208i	0.474647	+	0.880176i	$0.342576\pi$
$367$	−3690.64	+	6392.38i	−0.524931	+	0.909208i	−0.999578	+	0.0290317i	$0.990758\pi$
$368$	−2706.59	+	1562.65i	−0.383399	+	0.221356i
$369$		0			0
$370$	16.2657	+	1087.89i	0.00228544	+	0.152856i
$371$	−5222.73			−0.730865
$372$		0			0
$373$	3768.93	−	6527.97i	0.523184	−	0.906181i	−0.476452	−	0.879201i	$-0.658077\pi$
$373$	3768.93	−	6527.97i	0.523184	−	0.906181i	0.999636	−	0.0269809i	$-0.00858933\pi$
$374$	1863.50	−	3227.68i	0.257645	−	0.446254i
$375$		0			0
$376$			3807.70i			0.522254i
$377$	264.689	−	458.456i	0.0361597	−	0.0626304i
$378$		0			0
$379$	6662.09	+	11539.1i	0.902925	+	1.56391i	0.823678	+	0.567058i	$0.191918\pi$
$379$	6662.09	+	11539.1i	0.902925	+	1.56391i	0.0792474	+	0.996855i	$0.474748\pi$
$380$	355.521			0.0479943
$381$		0			0
$382$	−941.250	−	1630.29i	−0.126069	−	0.218359i
$383$	−2070.31	−	1195.30i	−0.276209	−	0.159469i	0.355497	−	0.934677i	$-0.384312\pi$
$383$	−2070.31	−	1195.30i	−0.276209	−	0.159469i	−0.631706	+	0.775208i	$0.717645\pi$
$384$		0			0
$385$	2262.20	−	1306.08i	0.299461	−	0.172894i
$386$	174.577	+	302.377i	0.0230201	+	0.0398719i
$387$		0			0
$388$	−2378.58	−	1373.27i	−0.311222	−	0.179684i
$389$	9036.26	+	5217.09i	1.17778	+	0.679992i	0.955500	−	0.294991i	$-0.0953166\pi$
$389$	9036.26	+	5217.09i	1.17778	+	0.679992i	0.222280	+	0.974983i	$0.428650\pi$
$390$		0			0
$391$	−5917.52	−	10249.4i	−0.765376	−	1.32567i
$392$	6177.41	−	3566.53i	0.795934	−	0.459533i
$393$		0			0
$394$	3520.59	+	2032.62i	0.450165	+	0.259903i
$395$	236.344	+	409.359i	0.0301057	+	0.0521446i
$396$		0			0
$397$	−5948.23			−0.751972			−0.375986	−	0.926625i	$-0.622696\pi$
$397$	−5948.23			−0.751972			−0.375986	+	0.926625i	$0.622696\pi$
$398$	5212.24	+	9027.86i	0.656447	+	1.13700i
$399$		0			0
$400$	−953.260	+	1651.09i	−0.119157	+	0.206387i
$401$		−	2498.02i		−	0.311085i	−0.987829	−	0.155543i	$-0.950287\pi$
$401$		−	2498.02i		−	0.311085i	0.987829	−	0.155543i	$-0.0497126\pi$
$402$		0			0
$403$	2214.30	−	3835.29i	0.273703	−	0.474068i
$404$	−864.283	+	1496.98i	−0.106435	+	0.184351i
$405$		0			0
$406$	−1504.75			−0.183939
$407$	−103.484	−	6921.27i	−0.0126032	−	0.842935i
$408$		0			0
$409$	2314.13	−	1336.06i	0.279771	−	0.161526i	−0.353549	−	0.935416i	$-0.615025\pi$
$409$	2314.13	−	1336.06i	0.279771	−	0.161526i	0.633320	+	0.773890i	$0.281692\pi$
$410$	−744.262	+	1289.10i	−0.0896499	+	0.155278i
$411$		0			0
$412$	−456.444	−	263.528i	−0.0545811	−	0.0315124i
$413$			25257.6i			3.00931i
$414$		0			0
$415$			1228.62i			0.145327i
$416$	−395.568	−	685.144i	−0.0466210	−	0.0807499i
$417$		0			0
$418$	−2261.86			−0.264668
$419$	−5436.14	−	9415.66i	−0.633825	−	1.09782i	−0.986763	−	0.162170i	$-0.948151\pi$
$419$	−5436.14	−	9415.66i	−0.633825	−	1.09782i	0.352938	−	0.935647i	$-0.385183\pi$
$420$		0			0
$421$			845.331i			0.0978596i	0.998802	+	0.0489298i	$0.0155811\pi$
$421$			845.331i			0.0978596i	−0.998802	+	0.0489298i	$0.984419\pi$
$422$	−8572.38	+	4949.27i	−0.988855	+	0.570916i
$423$		0			0
$424$	1029.79	−	594.551i	0.117951	−	0.0680989i
$425$	−6252.44	−	3609.85i	−0.713618	−	0.412008i
$426$		0			0
$427$	4894.76	−	2825.99i	0.554740	−	0.320279i
$428$	−3334.11	−	5774.84i	−0.376542	−	0.652190i
$429$		0			0
$430$			1911.25i			0.214346i
$431$	985.219	+	568.816i	0.110107	+	0.0635706i	0.554042	−	0.832488i	$-0.313085\pi$
$431$	985.219	+	568.816i	0.110107	+	0.0635706i	−0.443935	+	0.896059i	$0.646418\pi$
$432$		0			0
$433$	−3557.78			−0.394863			−0.197432	−	0.980317i	$-0.563260\pi$
$433$	−3557.78			−0.394863			−0.197432	+	0.980317i	$0.563260\pi$
$434$	−12588.2			−1.39229
$435$		0			0
$436$			6429.73i			0.706258i
$437$	−3591.26	+	6220.25i	−0.393120	+	0.680903i
$438$		0			0
$439$	8448.51	+	4877.75i	0.918508	+	0.530301i	0.883159	−	0.469074i	$-0.155412\pi$
$439$	8448.51	+	4877.75i	0.918508	+	0.530301i	0.0353495	+	0.999375i	$0.488746\pi$
$440$	−297.367	+	515.054i	−0.0322191	+	0.0558051i
$441$		0			0
$442$	2594.54	−	1497.96i	0.279207	−	0.161200i
$443$	−17334.6			−1.85913			−0.929563	−	0.368662i	$-0.879816\pi$
$443$	−17334.6			−1.85913			−0.929563	+	0.368662i	$0.879816\pi$
$444$		0			0
$445$	−443.419			−0.0472361
$446$	8465.96	−	4887.83i	0.898823	−	0.518936i
$447$		0			0
$448$	−1124.39	+	1947.51i	−0.118577	+	0.205382i
$449$	−4700.27	−	2713.70i	−0.494030	−	0.285228i	0.232215	−	0.972664i	$-0.425403\pi$
$449$	−4700.27	−	2713.70i	−0.494030	−	0.285228i	−0.726245	+	0.687436i	$0.758736\pi$
$450$		0			0
$451$	4735.07	−	8201.39i	0.494381	−	0.856294i
$452$		−	1466.08i		−	0.152563i
$453$		0			0
$454$	3176.55			0.328376
$455$	2099.77			0.216348
$456$		0			0
$457$	4749.19	+	2741.95i	0.486122	+	0.280663i	0.722964	−	0.690885i	$-0.242779\pi$
$457$	4749.19	+	2741.95i	0.486122	+	0.280663i	−0.236842	+	0.971548i	$0.576112\pi$
$458$			8590.23i			0.876409i
$459$		0			0
$460$	944.285	+	1635.55i	0.0957119	+	0.165778i
$461$	7747.47	−	4473.00i	0.782724	−	0.451906i	−0.0546709	−	0.998504i	$-0.517411\pi$
$461$	7747.47	−	4473.00i	0.782724	−	0.451906i	0.837395	+	0.546599i	$0.184078\pi$
$462$		0			0
$463$	8533.19	+	4926.64i	0.856524	+	0.494515i	0.862847	−	0.505465i	$-0.168679\pi$
$463$	8533.19	+	4926.64i	0.856524	+	0.494515i	−0.00632253	+	0.999980i	$0.502013\pi$
$464$	296.699	−	171.299i	0.0296851	−	0.0171387i
$465$		0			0
$466$	−7420.33	+	4284.13i	−0.737640	+	0.425877i
$467$			13076.2i			1.29571i	0.761764	+	0.647855i	$0.224334\pi$
$467$			13076.2i			1.29571i	−0.761764	+	0.647855i	$0.775666\pi$
$468$		0			0
$469$	−9216.90	−	15964.1i	−0.907456	−	1.57176i
$470$	2300.93			0.225817
$471$		0			0
$472$	−2875.30	−	4980.17i	−0.280395	−	0.485659i
$473$		−	12159.6i		−	1.18203i
$474$		0			0
$475$			4381.53i			0.423239i
$476$	−7374.91	−	4257.91i	−0.710144	−	0.410002i
$477$		0			0
$478$	−2986.88	+	5173.44i	−0.285809	+	0.495036i
$479$	−4654.65	+	2687.37i	−0.444001	+	0.256344i	−0.705293	−	0.708916i	$-0.749185\pi$
$479$	−4654.65	+	2687.37i	−0.444001	+	0.256344i	0.261292	+	0.965260i	$0.415851\pi$
$480$		0			0
$481$	2709.76	−	4859.81i	0.256870	−	0.460682i
$482$	4973.68			0.470011
$483$		0			0
$484$	−770.121	+	1333.89i	−0.0723254	+	0.125271i
$485$	−829.845	+	1437.33i	−0.0776935	+	0.134569i
$486$		0			0
$487$			3620.65i			0.336894i	0.985711	+	0.168447i	$0.0538752\pi$
$487$			3620.65i			0.336894i	−0.985711	+	0.168447i	$0.946125\pi$
$488$	−643.416	+	1114.43i	−0.0596846	+	0.103377i
$489$		0			0
$490$	−2155.19	−	3732.91i	−0.198697	−	0.344154i
$491$	−188.535			−0.0173288			−0.00866441	−	0.999962i	$-0.502758\pi$
$491$	−188.535			−0.0173288			−0.00866441	+	0.999962i	$0.502758\pi$
$492$		0			0
$493$	648.683	+	1123.55i	0.0592601	+	0.102641i
$494$	−1574.59	−	909.088i	−0.143409	−	0.0827972i
$495$		0			0
$496$	2482.08	−	1433.03i	0.224695	−	0.129728i
$497$	6166.28	+	10680.3i	0.556530	+	0.963939i
$498$		0			0
$499$	−15097.0	−	8716.25i	−1.35438	−	0.781950i	−0.365518	−	0.930804i	$-0.619108\pi$
$499$	−15097.0	−	8716.25i	−1.35438	−	0.781950i	−0.988859	+	0.148854i	$0.952441\pi$
$500$	2044.38	+	1180.32i	0.182855	+	0.105571i
$501$		0			0
$502$	−3778.67	−	6544.85i	−0.335957	−	0.581895i
$503$	14686.4	−	8479.20i	1.30186	−	0.751628i	0.321135	−	0.947034i	$-0.395936\pi$
$503$	14686.4	−	8479.20i	1.30186	−	0.751628i	0.980722	+	0.195406i	$0.0626024\pi$
$504$		0			0
$505$	904.602	+	522.272i	0.0797114	+	0.0460214i
$506$	−6007.64	−	10405.5i	−0.527811	−	0.914195i
$507$		0			0
$508$	789.081			0.0689170
$509$	−8525.33	−	14766.3i	−0.742394	−	1.28586i	−0.951402	−	0.307951i	$-0.900357\pi$
$509$	−8525.33	−	14766.3i	−0.742394	−	1.28586i	0.209008	−	0.977914i	$-0.432977\pi$
$510$		0			0
$511$	−9439.10	+	16349.0i	−0.817145	+	1.41534i
$512$		−	512.000i		−	0.0441942i
$513$		0			0
$514$	−2849.44	+	4935.38i	−0.244521	+	0.423522i
$515$	−159.246	+	275.822i	−0.0136256	+	0.0236003i
$516$		0			0
$517$	−14638.8			−1.24529
$518$	−15814.4	+	236.451i	−1.34140	+	0.0200561i
$519$		0			0
$520$	−414.021	+	239.035i	−0.0349154	+	0.0201584i
$521$	5758.45	−	9973.93i	0.484227	−	0.838706i	−0.515609	−	0.856824i	$-0.672434\pi$
$521$	5758.45	−	9973.93i	0.484227	−	0.838706i	0.999836	+	0.0181182i	$0.00576753\pi$
$522$		0			0
$523$	19413.7	+	11208.5i	1.62314	+	0.937120i	0.986073	+	0.166311i	$0.0531855\pi$
$523$	19413.7	+	11208.5i	1.62314	+	0.937120i	0.637066	+	0.770809i	$0.280148\pi$
$524$			9587.53i			0.799300i
$525$		0			0
$526$		−	6076.84i		−	0.503732i
$527$	5426.67	+	9399.26i	0.448557	+	0.776923i
$528$		0			0
$529$	−25987.4			−2.13589
$530$	−359.277	−	622.286i	−0.0294453	−	0.0510007i
$531$		0			0
$532$			5168.13i			0.421178i
$533$	6592.61	−	3806.24i	0.535755	−	0.309318i
$534$		0			0
$535$	−3489.64	+	2014.74i	−0.282000	+	0.162813i
$536$	3634.69	+	2098.49i	0.292900	+	0.169106i
$537$		0			0
$538$	−5331.02	+	3077.86i	−0.427205	+	0.246647i
$539$	13711.6	+	23749.2i	1.09573	+	1.89786i
$540$		0			0
$541$		−	6623.81i		−	0.526395i	−0.964742	−	0.263198i	$-0.915223\pi$
$541$		−	6623.81i		−	0.526395i	0.964742	−	0.263198i	$-0.0847771\pi$
$542$	−12114.0	−	6994.02i	−0.960038	−	0.554278i
$543$		0			0
$544$	1938.86			0.152809
$545$	3885.38			0.305379
$546$		0			0
$547$			8352.48i			0.652882i	0.945218	+	0.326441i	$0.105849\pi$
$547$			8352.48i			0.652882i	−0.945218	+	0.326441i	$0.894151\pi$
$548$	−1567.50	+	2714.98i	−0.122190	+	0.211639i
$549$		0			0
$550$	−6347.66	−	3664.82i	−0.492118	−	0.284125i
$551$	393.677	−	681.868i	0.0304377	−	0.0527197i
$552$		0			0
$553$	−5950.77	+	3435.68i	−0.457599	+	0.264195i
$554$	−10162.1			−0.779324
$555$		0			0
$556$	513.317			0.0391538
$557$	14404.0	−	8316.15i	1.09572	−	0.632615i	0.160628	−	0.987015i	$-0.448648\pi$
$557$	14404.0	−	8316.15i	1.09572	−	0.632615i	0.935094	+	0.354400i	$0.115315\pi$
$558$		0			0
$559$	4887.19	−	8464.86i	0.369778	−	0.640475i
$560$	1176.85	+	679.453i	0.0888051	+	0.0512717i
$561$		0			0
$562$	6486.93	−	11235.7i	0.486894	−	0.843326i
$563$		−	24833.4i		−	1.85898i	−0.368850	−	0.929489i	$-0.620248\pi$
$563$		−	24833.4i		−	1.85898i	0.368850	−	0.929489i	$-0.379752\pi$
$564$		0			0
$565$	−885.927			−0.0659668
$566$	10236.3			0.760183
$567$		0			0
$568$	−2431.67	−	1403.93i	−0.179632	−	0.103710i
$569$		−	22465.8i		−	1.65521i	−0.561311	−	0.827605i	$-0.689703\pi$
$569$		−	22465.8i		−	1.65521i	0.561311	−	0.827605i	$-0.310297\pi$
$570$		0			0
$571$	2611.95	+	4524.02i	0.191430	+	0.331566i	0.945724	−	0.324970i	$-0.105354\pi$
$571$	2611.95	+	4524.02i	0.191430	+	0.331566i	−0.754294	+	0.656536i	$0.772021\pi$
$572$	2634.05	−	1520.77i	0.192544	−	0.111165i
$573$		0			0
$574$	−18739.4	−	10819.2i	−1.36266	−	0.786731i
$575$	−20156.9	+	11637.6i	−1.46192	+	0.844038i
$576$		0			0
$577$	13260.4	−	7655.87i	0.956734	−	0.552371i	0.0615680	−	0.998103i	$-0.480390\pi$
$577$	13260.4	−	7655.87i	0.956734	−	0.552371i	0.895166	+	0.445732i	$0.147057\pi$
$578$		−	2483.82i		−	0.178743i
$579$		0			0
$580$	−103.513	−	179.290i	−0.00741061	−	0.0128355i
$581$	−17860.2			−1.27533
$582$		0			0
$583$	2285.76	+	3959.05i	0.162378	+	0.281247i
$584$		−	4298.15i		−	0.304553i
$585$		0			0
$586$		−	4055.54i		−	0.285892i
$587$	15276.2	+	8819.71i	1.07413	+	0.620150i	0.929307	−	0.369307i	$-0.120405\pi$
$587$	15276.2	+	8819.71i	1.07413	+	0.620150i	0.144824	+	0.989457i	$0.453738\pi$
$588$		0			0
$589$	3293.37	−	5704.28i	0.230392	−	0.399051i
$590$	−3009.43	+	1737.50i	−0.209994	+	0.121240i
$591$		0			0
$592$	3091.29	−	1846.92i	0.214613	−	0.128223i
$593$	−13084.9			−0.906125			−0.453062	−	0.891479i	$-0.649669\pi$
$593$	−13084.9			−0.906125			−0.453062	+	0.891479i	$0.649669\pi$
$594$		0			0
$595$	−2572.98	+	4456.54i	−0.177281	+	0.307059i
$596$	−3232.00	+	5598.00i	−0.222128	+	0.384736i
$597$		0			0
$598$		−	9658.37i		−	0.660468i
$599$	6838.77	−	11845.1i	0.466485	−	0.807976i	−0.532782	−	0.846252i	$-0.678853\pi$
$599$	6838.77	−	11845.1i	0.466485	−	0.807976i	0.999267	+	0.0382767i	$0.0121868\pi$
$600$		0			0
$601$	−12314.8	−	21329.8i	−0.835824	−	1.44769i	−0.893358	−	0.449346i	$-0.851657\pi$
$601$	−12314.8	−	21329.8i	−0.835824	−	1.44769i	0.0575343	−	0.998344i	$-0.481676\pi$
$602$	−27783.5			−1.88101
$603$		0			0
$604$	295.315	+	511.501i	0.0198944	+	0.0344581i
$605$	806.047	+	465.371i	0.0541661	+	0.0312728i
$606$		0			0
$607$	−5741.86	+	3315.06i	−0.383945	+	0.221671i	−0.679533	−	0.733645i	$-0.737818\pi$
$607$	−5741.86	+	3315.06i	−0.383945	+	0.221671i	0.295588	+	0.955315i	$0.404484\pi$
$608$	−588.335	−	1019.03i	−0.0392436	−	0.0679720i
$609$		0			0
$610$	673.431	+	388.806i	0.0446991	+	0.0258070i
$611$	−10190.7	−	5883.62i	−0.674751	−	0.389568i
$612$		0			0
$613$	−14786.9	−	25611.6i	−0.974284	−	1.68751i	−0.682279	−	0.731092i	$-0.739011\pi$
$613$	−14786.9	−	25611.6i	−0.974284	−	1.68751i	−0.292004	−	0.956417i	$-0.594322\pi$
$614$	3398.37	−	1962.05i	0.223367	−	0.128961i
$615$		0			0
$616$	−7487.23	−	4322.75i	−0.489722	−	0.282741i
$617$	3136.77	+	5433.05i	0.204671	+	0.354500i	0.950028	−	0.312165i	$-0.101054\pi$
$617$	3136.77	+	5433.05i	0.204671	+	0.354500i	−0.745357	+	0.666665i	$0.767721\pi$
$618$		0			0
$619$	−1919.99			−0.124670			−0.0623350	−	0.998055i	$-0.519855\pi$
$619$	−1919.99			−0.124670			−0.0623350	+	0.998055i	$0.519855\pi$
$620$	−865.957	−	1499.88i	−0.0560930	−	0.0971559i
$621$		0			0
$622$	−1813.82	+	3141.62i	−0.116925	+	0.202520i
$623$		−	6445.88i		−	0.414524i
$624$		0			0
$625$	−6734.09	+	11663.8i	−0.430982	+	0.746483i
$626$	448.221	−	776.341i	0.0286174	−	0.0495668i
$627$		0			0
$628$	−10674.2			−0.678260
$629$	6994.00	+	11706.2i	0.443353	+	0.742063i
$630$		0			0
$631$	−10495.6	+	6059.62i	−0.662158	+	0.382297i	−0.793099	−	0.609093i	$-0.791534\pi$
$631$	−10495.6	+	6059.62i	−0.662158	+	0.382297i	0.130941	+	0.991390i	$0.458200\pi$
$632$	782.228	−	1354.86i	0.0492332	−	0.0852744i
$633$		0			0
$634$	9015.02	+	5204.83i	0.564720	+	0.326041i
$635$		−	476.829i		−	0.0297990i
$636$		0			0
$637$			22043.8i			1.37113i
$638$	658.562	+	1140.66i	0.0408663	+	0.0707826i
$639$		0			0
$640$	−309.393			−0.0191091
$641$	5662.72	+	9808.12i	0.348930	+	0.604364i	0.986060	−	0.166392i	$-0.0532118\pi$
$641$	5662.72	+	9808.12i	0.348930	+	0.604364i	−0.637130	+	0.770757i	$0.719878\pi$
$642$		0			0
$643$		−	30231.6i		−	1.85415i	−0.374877	−	0.927075i	$-0.622315\pi$
$643$		−	30231.6i		−	1.85415i	0.374877	−	0.927075i	$-0.377685\pi$
$644$	−23775.6	+	13726.9i	−1.45480	+	0.839928i
$645$		0			0
$646$	3858.89	−	2227.93i	0.235025	−	0.135692i
$647$	12084.2	+	6976.82i	0.734280	+	0.423937i	0.819986	−	0.572384i	$-0.193981\pi$
$647$	12084.2	+	6976.82i	0.734280	+	0.423937i	−0.0857058	+	0.996320i	$0.527315\pi$
$648$		0			0
$649$	19146.3	−	11054.1i	1.15803	−	0.668587i
$650$	−2945.93	−	5102.50i	−0.177768	−	0.307903i
$651$		0			0
$652$		−	10391.6i		−	0.624184i
$653$	−8531.98	−	4925.94i	−0.511305	−	0.295202i	0.222065	−	0.975032i	$-0.428720\pi$
$653$	−8531.98	−	4925.94i	−0.511305	−	0.295202i	−0.733370	+	0.679830i	$0.762054\pi$
$654$		0			0
$655$	5793.58			0.345609
$656$	4926.58			0.293217
$657$		0			0
$658$			33448.1i			1.98168i
$659$	3105.35	−	5378.63i	0.183562	−	0.317939i	−0.759529	−	0.650474i	$-0.774570\pi$
$659$	3105.35	−	5378.63i	0.183562	−	0.317939i	0.943091	+	0.332535i	$0.107904\pi$
$660$		0			0
$661$	26768.0	+	15454.5i	1.57512	+	0.909395i	0.995526	+	0.0944883i	$0.0301215\pi$
$661$	26768.0	+	15454.5i	1.57512	+	0.909395i	0.579592	+	0.814907i	$0.303212\pi$
$662$	−3004.15	+	5203.35i	−0.176374	+	0.305489i
$663$		0			0
$664$	3521.59	−	2033.19i	0.205820	−	0.118830i
$665$	3123.01			0.182113
$666$		0			0
$667$	4182.51			0.242800
$668$	−7793.56	+	4499.61i	−0.451410	+	0.260622i
$669$		0			0
$670$	1268.08	−	2196.38i	0.0731197	−	0.126647i
$671$	−4284.44	−	2473.62i	−0.246496	−	0.142315i
$672$		0			0
$673$	8279.83	−	14341.1i	0.474241	−	0.821409i	−0.525324	−	0.850902i	$-0.676056\pi$
$673$	8279.83	−	14341.1i	0.474241	−	0.821409i	0.999565	+	0.0294932i	$0.00938935\pi$
$674$			23963.3i			1.36948i
$675$		0			0
$676$	−6343.09			−0.360895
$677$	−13557.8			−0.769670			−0.384835	−	0.922985i	$-0.625742\pi$
$677$	−13557.8			−0.769670			−0.384835	+	0.922985i	$0.625742\pi$
$678$		0			0
$679$	−20894.2	−	12063.3i	−1.18092	−	0.681806i
$680$		−	1171.62i		−	0.0660731i
$681$		0			0
$682$	5509.31	+	9542.41i	0.309329	+	0.535774i
$683$	−12394.3	+	7155.85i	−0.694370	+	0.400894i	−0.805247	−	0.592940i	$-0.797967\pi$
$683$	−12394.3	+	7155.85i	−0.694370	+	0.400894i	0.110877	+	0.993834i	$0.464634\pi$
$684$		0			0
$685$	1640.62	+	947.211i	0.0915107	+	0.0528337i
$686$	33389.6	−	19277.5i	1.85834	−	1.07291i
$687$		0			0
$688$	5478.21	−	3162.84i	0.303568	−	0.175265i
$689$			3674.77i			0.203190i
$690$		0			0
$691$	−1170.55	−	2027.45i	−0.0644425	−	0.111618i	0.832004	−	0.554770i	$-0.187194\pi$
$691$	−1170.55	−	2027.45i	−0.0644425	−	0.111618i	−0.896447	+	0.443152i	$0.853860\pi$
$692$	10743.7			0.590193
$693$		0			0
$694$	1120.38	+	1940.55i	0.0612808	+	0.106141i
$695$		−	310.189i		−	0.0169297i
$696$		0			0
$697$			18656.2i			1.01385i
$698$	−3547.97	−	2048.42i	−0.192396	−	0.111080i
$699$		0			0
$700$	−8373.75	+	14503.8i	−0.452140	+	0.783130i
$701$	8348.99	−	4820.29i	0.449839	−	0.259715i	−0.257923	−	0.966165i	$-0.583038\pi$
$701$	8348.99	−	4820.29i	0.449839	−	0.259715i	0.707762	+	0.706451i	$0.249705\pi$
$702$		0			0
$703$	4030.26	−	7228.07i	0.216222	−	0.387783i
$704$	1968.39			0.105379
$705$		0			0
$706$	−10344.9	+	17917.8i	−0.551464	+	0.955164i
$707$	−7592.15	+	13150.0i	−0.403865	+	0.699514i
$708$		0			0
$709$			4234.12i			0.224282i	0.993692	+	0.112141i	$0.0357708\pi$
$709$			4234.12i			0.224282i	−0.993692	+	0.112141i	$0.964229\pi$
$710$	−848.370	+	1469.42i	−0.0448433	+	0.0776709i
$711$		0			0
$712$	733.793	+	1270.97i	0.0386237	+	0.0668981i
$713$	34989.5			1.83782
$714$		0			0
$715$	−918.975	−	1591.71i	−0.0480667	−	0.0832540i
$716$	9630.88	+	5560.39i	0.502685	+	0.290226i
$717$		0			0
$718$	6565.55	−	3790.62i	0.341259	−	0.197026i
$719$	9867.50	+	17091.0i	0.511816	+	0.886491i	0.999906	+	0.0136979i	$0.00436031\pi$
$719$	9867.50	+	17091.0i	0.511816	+	0.886491i	−0.488090	+	0.872793i	$0.662306\pi$
$720$		0			0
$721$	−4009.56	−	2314.92i	−0.207107	−	0.119573i
$722$	9538.23	+	5506.90i	0.491657	+	0.283858i
$723$		0			0
$724$	5793.92	+	10035.4i	0.297416	+	0.515140i
$725$	2209.62	−	1275.72i	0.113191	−	0.0653506i
$726$		0			0
$727$	−4747.65	−	2741.06i	−0.242202	−	0.139835i	0.373986	−	0.927434i	$-0.377991\pi$
$727$	−4747.65	−	2741.06i	−0.242202	−	0.139835i	−0.616188	+	0.787599i	$0.711324\pi$
$728$	−3474.80	−	6018.54i	−0.176902	−	0.306404i
$729$		0			0
$730$	−2597.30			−0.131685
$731$	11977.2	+	20745.1i	0.606009	+	1.04964i
$732$		0			0
$733$	−5485.74	+	9501.58i	−0.276426	+	0.478784i	−0.970494	−	0.241125i	$-0.922483\pi$
$733$	−5485.74	+	9501.58i	−0.276426	+	0.478784i	0.694068	+	0.719910i	$0.255817\pi$
$734$		−	14762.6i		−	0.742365i
$735$		0			0
$736$	3125.30	−	5413.19i	0.156522	−	0.271104i
$737$	−8067.67	+	13973.6i	−0.403224	+	0.698405i
$738$		0			0
$739$	−13737.2			−0.683803			−0.341901	−	0.939736i	$-0.611071\pi$
$739$	−13737.2			−0.683803			−0.341901	+	0.939736i	$0.611071\pi$
$740$	−1116.06	−	1868.01i	−0.0554422	−	0.0927967i
$741$		0			0
$742$	9046.04	−	5222.73i	0.447561	−	0.258400i
$743$	−11581.6	+	20059.9i	−0.571853	+	0.990479i	0.424522	+	0.905418i	$0.360442\pi$
$743$	−11581.6	+	20059.9i	−0.571853	+	0.990479i	−0.996376	+	0.0850617i	$0.972891\pi$
$744$		0			0
$745$	3382.78	+	1953.05i	0.166356	+	0.0960457i
$746$			15075.7i			0.739894i
$747$		0			0
$748$			7454.00i			0.364365i
$749$	−29287.9	−	50728.1i	−1.42878	−	2.47472i
$750$		0			0
$751$	23859.2			1.15930			0.579651	−	0.814865i	$-0.303189\pi$
$751$	23859.2			1.15930			0.579651	+	0.814865i	$0.303189\pi$
$752$	−3807.70	−	6595.14i	−0.184645	−	0.319814i
$753$		0			0
$754$			1058.76i			0.0511375i
$755$	309.092	−	178.454i	0.0148993	−	0.00860213i
$756$		0			0
$757$	−20035.6	+	11567.5i	−0.961961	+	0.555388i	−0.896776	−	0.442485i	$-0.854097\pi$
$757$	−20035.6	+	11567.5i	−0.961961	+	0.555388i	−0.0651850	+	0.997873i	$0.520764\pi$
$758$	−23078.2	−	13324.2i	−1.10585	−	0.638465i
$759$		0			0
$760$	−615.780	+	355.521i	−0.0293904	+	0.0169686i
$761$	870.578	+	1507.89i	0.0414697	+	0.0718276i	0.886015	−	0.463656i	$-0.153463\pi$
$761$	870.578	+	1507.89i	0.0414697	+	0.0718276i	−0.844546	+	0.535484i	$0.820129\pi$
$762$		0			0
$763$			56480.9i			2.67988i
$764$	3260.59	+	1882.50i	0.154403	+	0.0891446i
$765$		0			0
$766$	4781.18			0.225524
$767$	17771.5			0.836627
$768$		0			0
$769$			2182.13i			0.102327i	0.998690	+	0.0511637i	$0.0162930\pi$
$769$			2182.13i			0.102327i	−0.998690	+	0.0511637i	$0.983707\pi$
$770$	−2612.17	+	4524.41i	−0.122255	+	0.211751i
$771$		0			0
$772$	−604.753	−	349.154i	−0.0281937	−	0.0162776i
$773$	−11423.2	+	19785.6i	−0.531519	+	0.920618i	0.467804	+	0.883832i	$0.345045\pi$
$773$	−11423.2	+	19785.6i	−0.531519	+	0.920618i	−0.999323	+	0.0367861i	$0.988288\pi$
$774$		0			0
$775$	18484.9	−	10672.3i	0.856772	−	0.494657i
$776$	5493.09			0.254111
$777$		0			0
$778$	−20868.4			−0.961654
$779$	9805.29	−	5661.09i	0.450977	−	0.260372i
$780$		0			0
$781$	5397.42	−	9348.60i	0.247292	−	0.428322i
$782$	20498.9	+	11835.0i	0.937390	+	0.541202i
$783$		0			0
$784$	−7133.06	+	12354.8i	−0.324939	+	0.562811i
$785$			6450.24i			0.293273i
$786$		0			0
$787$	−26769.3			−1.21248			−0.606241	−	0.795281i	$-0.707323\pi$
$787$	−26769.3			−1.21248			−0.606241	+	0.795281i	$0.707323\pi$
$788$	−8130.46			−0.367558
$789$		0			0
$790$	−818.719	−	472.688i	−0.0368718	−	0.0212879i
$791$		−	12878.5i		−	0.578897i
$792$		0			0
$793$	−1988.40	−	3444.01i	−0.0890417	−	0.154225i
$794$	10302.6	−	5948.23i	0.460487	−	0.265862i
$795$		0			0
$796$	−18055.7	−	10424.5i	−0.803980	−	0.464178i
$797$	20462.2	−	11813.9i	0.909422	−	0.525055i	0.0291768	−	0.999574i	$-0.490711\pi$
$797$	20462.2	−	11813.9i	0.909422	−	0.525055i	0.880245	+	0.474519i	$0.157378\pi$
$798$		0			0
$799$	24974.8	−	14419.2i	1.10581	−	0.638441i
$800$		−	3813.04i		−	0.168514i
$801$		0			0
$802$	2498.02	+	4326.70i	0.109985	+	0.190500i
$803$	16524.3			0.726189
$804$		0			0
$805$	8294.91	+	14367.2i	0.363177	+	0.629040i
$806$			8857.21i			0.387075i
$807$		0			0
$808$		−	3457.13i		−	0.150522i
$809$	13271.5	+	7662.31i	0.576763	+	0.332994i	0.759846	−	0.650103i	$-0.225274\pi$
$809$	13271.5	+	7662.31i	0.576763	+	0.332994i	−0.183083	+	0.983098i	$0.558608\pi$
$810$		0			0
$811$	15970.3	−	27661.4i	0.691483	−	1.19768i	−0.279869	−	0.960038i	$-0.590291\pi$
$811$	15970.3	−	27661.4i	0.691483	−	1.19768i	0.971352	−	0.237646i	$-0.0763757\pi$
$812$	2606.30	−	1504.75i	0.112639	−	0.0650324i
$813$		0			0
$814$	7100.51	+	11884.5i	0.305740	+	0.511734i
$815$	−6279.50			−0.269891
$816$		0			0
$817$	7268.79	−	12589.9i	0.311264	−	0.539126i
$818$	−2672.12	+	4628.25i	−0.114216	+	0.197828i
$819$		0			0
$820$		−	2977.05i		−	0.126784i
$821$	11992.4	−	20771.5i	0.509790	−	0.882983i	−0.490145	−	0.871641i	$-0.663056\pi$
$821$	11992.4	−	20771.5i	0.509790	−	0.882983i	0.999936	−	0.0113420i	$-0.00361034\pi$
$822$		0			0
$823$	−2796.32	−	4843.37i	−0.118437	−	0.205139i	0.800712	−	0.599050i	$-0.204455\pi$
$823$	−2796.32	−	4843.37i	−0.118437	−	0.205139i	−0.919148	+	0.393911i	$0.871122\pi$
$824$	1054.11			0.0445653
$825$		0			0
$826$	−25257.6	−	43747.5i	−1.06395	−	1.84282i
$827$	−6096.43	−	3519.77i	−0.256340	−	0.147998i	0.366324	−	0.930488i	$-0.380616\pi$
$827$	−6096.43	−	3519.77i	−0.256340	−	0.147998i	−0.622664	+	0.782489i	$0.713950\pi$
$828$		0			0
$829$	−28005.1	+	16168.8i	−1.17329	+	0.677400i	−0.954453	−	0.298361i	$-0.903560\pi$
$829$	−28005.1	+	16168.8i	−1.17329	+	0.677400i	−0.218839	+	0.975761i	$0.570227\pi$
$830$	−1228.62	−	2128.04i	−0.0513809	−	0.0889944i
$831$		0			0
$832$	1370.29	+	791.137i	0.0570988	+	0.0329660i
$833$	−46785.8	−	27011.8i	−1.94602	−	1.12353i
$834$		0			0
$835$	2719.04	+	4709.52i	0.112690	+	0.195185i
$836$	3917.66	−	2261.86i	0.162076	−	0.0935743i
$837$		0			0
$838$	18831.3	+	10872.3i	0.776274	+	0.448182i
$839$	3829.53	+	6632.94i	0.157581	+	0.272937i	0.933996	−	0.357284i	$-0.116297\pi$
$839$	3829.53	+	6632.94i	0.157581	+	0.272937i	−0.776415	+	0.630222i	$0.782964\pi$
$840$		0			0
$841$	23930.5			0.981201
$842$	−845.331	−	1464.16i	−0.0345986	−	0.0599265i
$843$		0			0
$844$	9898.53	−	17144.8i	0.403699	−	0.699226i
$845$			3833.02i			0.156047i
$846$		0			0
$847$	−6765.00	+	11717.3i	−0.274437	+	0.475339i
$848$	−1189.10	+	2059.58i	−0.0481532	+	0.0834038i
$849$		0			0
$850$	14439.4			0.582667
$851$	43956.8	−	657.226i	1.77065	−	0.0264740i
$852$		0			0
$853$	37682.8	−	21756.2i	1.51258	−	0.873290i	0.512691	−	0.858573i	$-0.328649\pi$
$853$	37682.8	−	21756.2i	1.51258	−	0.873290i	0.999892	−	0.0147172i	$-0.00468480\pi$
$854$	−5651.98	+	9789.52i	−0.226472	+	0.392260i
$855$		0			0
$856$	11549.7	+	6668.21i	0.461168	+	0.266256i
$857$		−	44145.9i		−	1.75962i	−0.475323	−	0.879811i	$-0.657669\pi$
$857$		−	44145.9i		−	1.75962i	0.475323	−	0.879811i	$-0.342331\pi$
$858$		0			0
$859$		−	9543.68i		−	0.379076i	−0.981873	−	0.189538i	$-0.939301\pi$
$859$		−	9543.68i		−	0.379076i	0.981873	−	0.189538i	$-0.0606990\pi$
$860$	−1911.25	−	3310.39i	−0.0757828	−	0.131260i
$861$		0			0
$862$	−2275.27			−0.0899024
$863$	5198.62	+	9004.27i	0.205056	+	0.355167i	0.950150	−	0.311792i	$-0.100929\pi$
$863$	5198.62	+	9004.27i	0.205056	+	0.355167i	−0.745095	+	0.666959i	$0.767596\pi$
$864$		0			0
$865$		−	6492.23i		−	0.255194i
$866$	6162.25	−	3557.78i	0.241803	−	0.139605i
$867$		0			0
$868$	21803.4	−	12588.2i	0.852600	−	0.492249i
$869$	5208.78	+	3007.29i	0.203332	+	0.117394i
$870$		0			0
$871$	−11232.5	+	6485.12i	−0.436969	+	0.252284i
$872$	−6429.73	−	11136.6i	−0.249700	−	0.432493i
$873$		0			0
$874$		−	14365.0i		−	0.555955i
$875$	17958.5	+	10368.3i	0.693838	+	0.400587i
$876$		0			0
$877$	−11549.7			−0.444704			−0.222352	−	0.974967i	$-0.571373\pi$
$877$	−11549.7			−0.444704			−0.222352	+	0.974967i	$0.571373\pi$
$878$	−19511.0			−0.749959
$879$		0			0
$880$		−	1189.47i		−	0.0455647i
$881$	−842.208	+	1458.75i	−0.0322074	+	0.0557848i	−0.881680	−	0.471848i	$-0.843587\pi$
$881$	−842.208	+	1458.75i	−0.0322074	+	0.0557848i	0.849472	+	0.527633i	$0.176920\pi$
$882$		0			0
$883$	−15215.3	−	8784.58i	−0.579884	−	0.334796i	0.181204	−	0.983446i	$-0.442001\pi$
$883$	−15215.3	−	8784.58i	−0.579884	−	0.334796i	−0.761087	+	0.648650i	$0.775334\pi$
$884$	−2995.91	+	5189.07i	−0.113986	+	0.197429i
$885$		0			0
$886$	30024.5	−	17334.6i	1.13848	−	0.657301i
$887$	−42315.6			−1.60182			−0.800912	−	0.598782i	$-0.795651\pi$
$887$	−42315.6			−1.60182			−0.800912	+	0.598782i	$0.795651\pi$
$888$		0			0
$889$	6931.55			0.261504
$890$	768.024	−	443.419i	0.0289261	−	0.0167005i
$891$		0			0
$892$	−9775.65	+	16931.9i	−0.366943	+	0.635564i
$893$	−15156.8	−	8750.80i	−0.567978	−	0.327922i
$894$		0			0
$895$	3360.05	−	5819.78i	0.125491	−	0.217356i
$896$		−	4497.58i		−	0.167694i
$897$		0			0
$898$	10854.8			0.403374
$899$	−3835.58			−0.142296
$900$		0			0
$901$	−7799.33	−	4502.94i	−0.288383	−	0.166498i
$902$			18940.3i			0.699161i
$903$		0			0
$904$	1466.08	+	2539.32i	0.0539392	+	0.0934254i
$905$	6064.20	−	3501.17i	0.222741	−	0.128600i
$906$		0			0
$907$	1845.10	+	1065.27i	0.0675476	+	0.0389986i	0.533393	−	0.845867i	$-0.320917\pi$
$907$	1845.10	+	1065.27i	0.0675476	+	0.0389986i	−0.465846	+	0.884866i	$0.654250\pi$
$908$	−5501.95	+	3176.55i	−0.201089	+	0.116099i
$909$		0			0
$910$	−3636.90	+	2099.77i	−0.132486	+	0.0764907i
$911$			11911.4i			0.433196i	0.976261	+	0.216598i	$0.0694961\pi$
$911$			11911.4i			0.433196i	−0.976261	+	0.216598i	$0.930504\pi$
$912$		0			0
$913$	7816.64	+	13538.8i	0.283344	+	0.490766i
$914$	−10967.8			−0.396917
$915$		0			0
$916$	−8590.23	−	14878.7i	−0.309857	−	0.536689i
$917$			84220.1i			3.03292i
$918$		0			0
$919$			8874.32i			0.318539i	0.987235	+	0.159269i	$0.0509138\pi$
$919$			8874.32i			0.318539i	−0.987235	+	0.159269i	$0.949086\pi$
$920$	−3271.10	−	1888.57i	−0.117223	−	0.0676786i
$921$		0			0
$922$	−8946.01	+	15494.9i	−0.319546	+	0.553469i
$923$	7514.78	−	4338.66i	0.267987	−	0.154722i
$924$		0			0
$925$	23021.9	−	13754.6i	0.818329	−	0.488918i
$926$	−19706.5			−0.699349
$927$		0			0
$928$	−342.598	+	593.398i	−0.0121189	+	0.0209905i
$929$	−5914.60	+	10244.4i	−0.208882	+	0.361795i	−0.951363	−	0.308073i	$-0.900316\pi$
$929$	−5914.60	+	10244.4i	−0.208882	+	0.361795i	0.742480	+	0.669868i	$0.233649\pi$
$930$		0			0
$931$			32786.1i			1.15416i
$932$	8568.26	−	14840.7i	0.301140	−	0.521590i
$933$		0			0
$934$	−13076.2	−	22648.7i	−0.458102	−	0.793457i
$935$	4504.33			0.157548
$936$		0			0
$937$	16338.6	+	28299.3i	0.569646	+	0.986656i	0.996601	+	0.0823831i	$0.0262531\pi$
$937$	16338.6	+	28299.3i	0.569646	+	0.986656i	−0.426955	+	0.904273i	$0.640414\pi$
$938$	31928.3	+	18433.8i	1.11140	+	0.641669i
$939$		0			0
$940$	−3985.33	+	2300.93i	−0.138284	+	0.0798384i
$941$	−7753.63	−	13429.7i	−0.268609	−	0.465245i	0.699894	−	0.714247i	$-0.253231\pi$
$941$	−7753.63	−	13429.7i	−0.268609	−	0.465245i	−0.968503	+	0.249002i	$0.919897\pi$
$942$		0			0
$943$	52086.9	+	30072.4i	1.79871	+	1.03848i
$944$	9960.34	+	5750.60i	0.343412	+	0.198269i
$945$		0			0
$946$	12159.6	+	21061.1i	0.417910	+	0.723841i
$947$	−24902.0	+	14377.2i	−0.854494	+	0.493342i	−0.862165	−	0.506628i	$-0.830892\pi$
$947$	−24902.0	+	14377.2i	−0.854494	+	0.493342i	0.00767053	+	0.999971i	$0.497558\pi$
$948$		0			0
$949$	11503.3	+	6641.45i	0.393482	+	0.227177i
$950$	−4381.53	−	7589.03i	−0.149637	−	0.259180i
$951$		0			0
$952$	17031.6			0.579830
$953$	−24371.6	−	42212.9i	−0.828409	−	1.43485i	−0.899286	−	0.437362i	$-0.855913\pi$
$953$	−24371.6	−	42212.9i	−0.828409	−	1.43485i	0.0708763	−	0.997485i	$-0.477420\pi$
$954$		0			0
$955$	1137.56	−	1970.32i	0.0385452	−	0.0667623i
$956$		−	11947.5i		−	0.404196i
$957$		0			0
$958$	5374.73	−	9309.31i	0.181263	−	0.313956i
$959$	−13769.4	+	23849.3i	−0.463647	+	0.803060i
$960$		0			0
$961$	−2296.17			−0.0770759
$962$	166.369	+	11127.2i	0.00557585	+	0.372926i
$963$		0			0
$964$	−8614.67	+	4973.68i	−0.287822	+	0.166174i
$965$	−210.988	+	365.442i	−0.00703829	+	0.0121907i
$966$		0			0
$967$	−21891.4	−	12639.0i	−0.728006	−	0.420314i	0.0896864	−	0.995970i	$-0.471414\pi$
$967$	−21891.4	−	12639.0i	−0.728006	−	0.420314i	−0.817692	+	0.575656i	$0.804747\pi$
$968$		−	3080.48i		−	0.102284i
$969$		0			0
$970$		−	3319.38i		−	0.109875i
$971$	8031.29	+	13910.6i	0.265434	+	0.459745i	0.967677	−	0.252192i	$-0.0811515\pi$
$971$	8031.29	+	13910.6i	0.265434	+	0.459745i	−0.702243	+	0.711937i	$0.747818\pi$
$972$		0			0
$973$	4509.15			0.148568
$974$	−3620.65	−	6271.15i	−0.119110	−	0.206304i
$975$		0			0
$976$		−	2573.66i		−	0.0844067i
$977$	20554.4	−	11867.1i	0.673075	−	0.388600i	−0.124165	−	0.992262i	$-0.539625\pi$
$977$	20554.4	−	11867.1i	0.673075	−	0.388600i	0.797241	+	0.603661i	$0.206292\pi$
$978$		0			0
$979$	−4886.25	+	2821.08i	−0.159515	+	0.0920960i
$980$	7465.81	+	4310.39i	0.243354	+	0.140500i
$981$		0			0
$982$	326.551	−	188.535i	0.0106117	−	0.00612666i
$983$	−12773.5	−	22124.4i	−0.414458	−	0.717862i	0.580914	−	0.813965i	$-0.302695\pi$
$983$	−12773.5	−	22124.4i	−0.414458	−	0.717862i	−0.995371	+	0.0961033i	$0.969362\pi$
$984$		0			0
$985$			4913.10i			0.158928i
$986$	−2247.10	−	1297.37i	−0.0725785	−	0.0419032i
$987$		0			0
$988$	3636.35			0.117093
$989$	77225.4			2.48294
$990$		0			0
$991$		−	50314.7i		−	1.61281i	−0.591360	−	0.806407i	$-0.701409\pi$
$991$		−	50314.7i		−	1.61281i	0.591360	−	0.806407i	$-0.298591\pi$
$992$	−2866.06	+	4964.17i	−0.0917314	+	0.158884i
$993$		0			0
$994$	−21360.6	−	12332.6i	−0.681607	−	0.393526i
$995$	−6299.33	+	10910.8i	−0.200706	+	0.347633i
$996$		0			0
$997$	−37385.2	+	21584.4i	−1.18756	+	0.685641i	−0.957752	−	0.287594i	$-0.907144\pi$
$997$	−37385.2	+	21584.4i	−1.18756	+	0.685641i	−0.229812	+	0.973235i	$0.573811\pi$
$998$	34865.0			1.10584
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	666.4.s.d.307.3		20
3.2	odd	2		74.4.e.a.11.8	✓	20
37.27	even	6	inner	666.4.s.d.397.3		20
111.101	odd	6		74.4.e.a.27.8	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.4.e.a.11.8	✓	20	3.2	odd	2
74.4.e.a.27.8	yes	20	111.101	odd	6
666.4.s.d.307.3		20	1.1	even	1	trivial
666.4.s.d.397.3		20	37.27	even	6	inner

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:	\( N \)	\(=\)	\( 666 = 2 \cdot 3^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	666.s (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.73205 + 1.00000i) q^{2} +(2.00000 - 3.46410i) q^{4} +(-2.09330 - 1.20857i) q^{5} +(17.5687 - 30.4298i) q^{7} +8.00000i q^{8} +O(q^{10})\)	\(q+(-1.73205 + 1.00000i) q^{2} +(2.00000 - 3.46410i) q^{4} +(-2.09330 - 1.20857i) q^{5} +(17.5687 - 30.4298i) q^{7} +8.00000i q^{8} +4.83427 q^{10} -30.7561 q^{11} +(-21.4108 - 12.3615i) q^{13} +70.2747i q^{14} +(-8.00000 - 13.8564i) q^{16} +(52.4721 - 30.2948i) q^{17} +(-31.8446 - 18.3855i) q^{19} +(-8.37319 + 4.83427i) q^{20} +(53.2712 - 30.7561i) q^{22} -195.332i q^{23} +(-59.5787 - 103.193i) q^{25} +49.4460 q^{26} +(-70.2747 - 121.719i) q^{28} +21.4124i q^{29} +179.129i q^{31} +(27.7128 + 16.0000i) q^{32} +(-60.5895 + 104.944i) q^{34} +(-73.5529 + 42.4658i) q^{35} +(3.36467 + 225.037i) q^{37} +73.5419 q^{38} +(9.66853 - 16.7464i) q^{40} +(-153.955 + 266.659i) q^{41} +395.356i q^{43} +(-61.5123 + 106.542i) q^{44} +(195.332 + 338.324i) q^{46} +475.963 q^{47} +(-445.816 - 772.176i) q^{49} +(206.387 + 119.157i) q^{50} +(-85.6430 + 49.4460i) q^{52} +(-74.3189 - 128.724i) q^{53} +(64.3818 + 37.1708i) q^{55} +(243.439 + 140.549i) q^{56} +(-21.4124 - 37.0873i) q^{58} +(-622.521 + 359.413i) q^{59} +(139.304 + 80.4270i) q^{61} +(-179.129 - 310.260i) q^{62} -64.0000 q^{64} +(29.8794 + 51.7527i) q^{65} +(262.311 - 454.336i) q^{67} -242.358i q^{68} +(84.9316 - 147.106i) q^{70} +(-175.491 + 303.959i) q^{71} -537.269 q^{73} +(-230.865 - 386.411i) q^{74} +(-127.378 + 73.5419i) q^{76} +(-540.344 + 935.904i) q^{77} +(-169.357 - 97.7786i) q^{79} +38.6741i q^{80} -615.822i q^{82} +(-254.149 - 440.199i) q^{83} -146.453 q^{85} +(-395.356 - 684.776i) q^{86} -246.049i q^{88} +(158.871 - 91.7241i) q^{89} +(-752.317 + 434.350i) q^{91} +(-676.648 - 390.663i) q^{92} +(-824.392 + 475.963i) q^{94} +(44.4401 + 76.9725i) q^{95} -686.636i q^{97} +(1544.35 + 891.632i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 40 q^{4} + 18 q^{5} - 2 q^{7}+O(q^{10}) \) 20 * q + 40 * q^4 + 18 * q^5 - 2 * q^7	\( 20 q + 40 q^{4} + 18 q^{5} - 2 q^{7} - 16 q^{10} + 16 q^{11} - 150 q^{13} - 160 q^{16} - 90 q^{17} + 162 q^{19} + 72 q^{20} + 532 q^{25} - 528 q^{26} + 8 q^{28} - 488 q^{34} + 342 q^{35} - 112 q^{37} - 144 q^{38} - 32 q^{40} + 498 q^{41} + 32 q^{44} - 424 q^{47} + 84 q^{49} - 1008 q^{50} - 600 q^{52} + 142 q^{53} - 540 q^{55} + 224 q^{58} - 1590 q^{59} - 1542 q^{61} - 8 q^{62} - 1280 q^{64} + 694 q^{65} + 62 q^{67} - 368 q^{70} + 178 q^{71} - 528 q^{73} + 560 q^{74} + 648 q^{76} - 3468 q^{77} - 3474 q^{79} - 938 q^{83} - 1100 q^{85} + 2120 q^{86} - 510 q^{89} + 666 q^{91} - 1344 q^{92} + 264 q^{94} - 4126 q^{95} + 816 q^{98}+O(q^{100}) \) 20 * q + 40 * q^4 + 18 * q^5 - 2 * q^7 - 16 * q^10 + 16 * q^11 - 150 * q^13 - 160 * q^16 - 90 * q^17 + 162 * q^19 + 72 * q^20 + 532 * q^25 - 528 * q^26 + 8 * q^28 - 488 * q^34 + 342 * q^35 - 112 * q^37 - 144 * q^38 - 32 * q^40 + 498 * q^41 + 32 * q^44 - 424 * q^47 + 84 * q^49 - 1008 * q^50 - 600 * q^52 + 142 * q^53 - 540 * q^55 + 224 * q^58 - 1590 * q^59 - 1542 * q^61 - 8 * q^62 - 1280 * q^64 + 694 * q^65 + 62 * q^67 - 368 * q^70 + 178 * q^71 - 528 * q^73 + 560 * q^74 + 648 * q^76 - 3468 * q^77 - 3474 * q^79 - 938 * q^83 - 1100 * q^85 + 2120 * q^86 - 510 * q^89 + 666 * q^91 - 1344 * q^92 + 264 * q^94 - 4126 * q^95 + 816 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more