LMFDB - Embedded newform 225.4.k.c.124.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,4,Mod(49,225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(225, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 3]))

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

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

chi := DirichletCharacter("225.49");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	225.k (of order $6$, 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:	$13.2754297513$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 23x^{10} + 198x^{8} - 719x^{6} + 886x^{4} + 585x^{2} + 81 $ x^12 - 23x^10 + 198x^8 - 719x^6 + 886x^4 + 585*x^2 + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6}\cdot 3^{2} $
Twist minimal:	no (minimal twist has level 45)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			124.1
Root			$-2.88506 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	225.124
Dual form			225.4.k.c.49.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.96084 - 2.28679i) q^{2} +(-3.96084 + 3.36330i) q^{3} +(6.45882 + 11.1870i) q^{4} +(23.3794 - 4.26387i) q^{6} +(-17.4197 - 10.0573i) q^{7} -22.4912i q^{8} +(4.37646 - 26.6429i) q^{9} +O(q^{10})$	\(q+(-3.96084 - 2.28679i) q^{2} +(-3.96084 + 3.36330i) q^{3} +(6.45882 + 11.1870i) q^{4} +(23.3794 - 4.26387i) q^{6} +(-17.4197 - 10.0573i) q^{7} -22.4912i q^{8} +(4.37646 - 26.6429i) q^{9} +(-33.1708 + 57.4535i) q^{11} +(-63.2076 - 22.5870i) q^{12} +(-40.5305 + 23.4003i) q^{13} +(45.9977 + 79.6704i) q^{14} +(0.237854 - 0.411975i) q^{16} +47.6233i q^{17} +(-78.2613 + 95.5203i) q^{18} +9.95276 q^{19} +(102.822 - 18.7524i) q^{21} +(262.768 - 151.709i) q^{22} +(8.30695 - 4.79602i) q^{23} +(75.6447 + 89.0841i) q^{24} +214.046 q^{26} +(72.2737 + 120.248i) q^{27} -259.832i q^{28} +(-89.3675 + 154.789i) q^{29} +(-77.0186 - 133.400i) q^{31} +(-157.708 + 91.0527i) q^{32} +(-61.8491 - 339.127i) q^{33} +(108.905 - 188.628i) q^{34} +(326.322 - 123.123i) q^{36} -248.864i q^{37} +(-39.4213 - 22.7599i) q^{38} +(81.8326 - 229.001i) q^{39} +(-124.832 - 216.216i) q^{41} +(-450.145 - 160.857i) q^{42} +(183.809 + 106.122i) q^{43} -856.976 q^{44} -43.8700 q^{46} +(411.963 + 237.847i) q^{47} +(0.443494 + 2.43174i) q^{48} +(30.7973 + 53.3425i) q^{49} +(-160.171 - 188.628i) q^{51} +(-523.559 - 302.277i) q^{52} -546.314i q^{53} +(-11.2831 - 641.556i) q^{54} +(-226.200 + 391.790i) q^{56} +(-39.4213 + 33.4741i) q^{57} +(707.940 - 408.729i) q^{58} +(-209.648 - 363.121i) q^{59} +(272.605 - 472.165i) q^{61} +704.502i q^{62} +(-344.192 + 420.097i) q^{63} +829.068 q^{64} +(-530.538 + 1484.66i) q^{66} +(387.872 - 223.938i) q^{67} +(-532.762 + 307.590i) q^{68} +(-16.7720 + 46.9350i) q^{69} +409.542 q^{71} +(-599.232 - 98.4319i) q^{72} -358.548i q^{73} +(-569.100 + 985.710i) q^{74} +(64.2831 + 111.342i) q^{76} +(1155.65 - 667.215i) q^{77} +(-847.803 + 719.902i) q^{78} +(-325.776 + 564.260i) q^{79} +(-690.693 - 233.204i) q^{81} +1141.86i q^{82} +(704.202 + 406.571i) q^{83} +(873.893 + 1029.15i) q^{84} +(-485.359 - 840.667i) q^{86} +(-166.631 - 913.663i) q^{87} +(1292.20 + 746.051i) q^{88} +201.000 q^{89} +941.373 q^{91} +(107.306 + 61.9532i) q^{92} +(753.723 + 269.340i) q^{93} +(-1087.81 - 1884.14i) q^{94} +(318.418 - 891.064i) q^{96} +(218.367 + 126.074i) q^{97} -281.708i q^{98} +(1385.56 + 1135.21i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 22 q^{4} + 168 q^{6} - 114 q^{9}+O(q^{10}) $ 12 * q + 22 * q^4 + 168 * q^6 - 114 * q^9	$ 12 q + 22 q^{4} + 168 q^{6} - 114 q^{9} - 28 q^{11} - 54 q^{14} + 26 q^{16} + 656 q^{19} - 288 q^{21} + 126 q^{24} + 1736 q^{26} - 670 q^{29} + 704 q^{31} - 104 q^{34} + 2172 q^{36} + 780 q^{39} - 374 q^{41} - 3928 q^{44} - 804 q^{46} + 860 q^{49} - 360 q^{51} - 1278 q^{54} - 1410 q^{56} - 596 q^{59} + 2878 q^{61} + 6276 q^{64} - 1932 q^{66} + 1746 q^{69} + 280 q^{71} - 640 q^{74} - 408 q^{76} - 764 q^{79} - 2502 q^{81} + 1818 q^{84} - 3160 q^{86} - 6876 q^{89} - 2840 q^{91} - 4154 q^{94} + 2310 q^{96} + 1524 q^{99}+O(q^{100}) $ 12 * q + 22 * q^4 + 168 * q^6 - 114 * q^9 - 28 * q^11 - 54 * q^14 + 26 * q^16 + 656 * q^19 - 288 * q^21 + 126 * q^24 + 1736 * q^26 - 670 * q^29 + 704 * q^31 - 104 * q^34 + 2172 * q^36 + 780 * q^39 - 374 * q^41 - 3928 * q^44 - 804 * q^46 + 860 * q^49 - 360 * q^51 - 1278 * q^54 - 1410 * q^56 - 596 * q^59 + 2878 * q^61 + 6276 * q^64 - 1932 * q^66 + 1746 * q^69 + 280 * q^71 - 640 * q^74 - 408 * q^76 - 764 * q^79 - 2502 * q^81 + 1818 * q^84 - 3160 * q^86 - 6876 * q^89 - 2840 * q^91 - 4154 * q^94 + 2310 * q^96 + 1524 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$

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 $

$2$	−3.96084	−	2.28679i	−1.40037	−	0.808502i	−0.405937	−	0.913901i	$-0.633055\pi$
$2$	−3.96084	−	2.28679i	−1.40037	−	0.808502i	−0.994430	+	0.105398i	$0.966388\pi$
$3$	−3.96084	+	3.36330i	−0.762263	+	0.647267i
$3$	−3.96084	+	3.36330i	−0.762263	+	0.647267i
$4$	6.45882	+	11.1870i	0.807352	+	1.39838i
$5$		0			0
$5$		0			0
$6$	23.3794	−	4.26387i	1.59077	−	0.290120i
$7$	−17.4197	−	10.0573i	−0.940575	−	0.543041i	−0.0504348	−	0.998727i	$-0.516061\pi$
$7$	−17.4197	−	10.0573i	−0.940575	−	0.543041i	−0.890141	+	0.455686i	$0.849394\pi$
$8$		−	22.4912i		−	0.993981i
$9$	4.37646	−	26.6429i	0.162091	−	0.986776i
$10$		0			0
$11$	−33.1708	+	57.4535i	−0.909215	+	1.57481i	−0.0940582	+	0.995567i	$0.529984\pi$
$11$	−33.1708	+	57.4535i	−0.909215	+	1.57481i	−0.815157	+	0.579240i	$0.803349\pi$
$12$	−63.2076	−	22.5870i	−1.52054	−	0.543358i
$13$	−40.5305	+	23.4003i	−0.864703	+	0.499237i	−0.865584	−	0.500763i	$-0.833053\pi$
$13$	−40.5305	+	23.4003i	−0.864703	+	0.499237i	0.000881222		1.00000i	$0.499719\pi$
$14$	45.9977	+	79.6704i	0.878101	+	1.52092i
$15$		0			0
$16$	0.237854	−	0.411975i	0.00371647	−	0.00643711i
$17$			47.6233i			0.679432i	0.940528	+	0.339716i	$0.110331\pi$
$17$			47.6233i			0.679432i	−0.940528	+	0.339716i	$0.889669\pi$
$18$	−78.2613	+	95.5203i	−1.02480	+	1.25080i
$19$	9.95276			0.120175			0.0600874	−	0.998193i	$-0.480862\pi$
$19$	9.95276			0.120175			0.0600874	+	0.998193i	$0.480862\pi$
$20$		0			0
$21$	102.822	−	18.7524i	1.06846	−	0.194863i
$22$	262.768	−	151.709i	2.54647	−	1.47021i
$23$	8.30695	−	4.79602i	0.0753095	−	0.0434800i	−0.461872	−	0.886946i	$-0.652822\pi$
$23$	8.30695	−	4.79602i	0.0753095	−	0.0434800i	0.537182	+	0.843466i	$0.319489\pi$
$24$	75.6447	+	89.0841i	0.643371	+	0.757675i
$25$		0			0
$26$	214.046			1.61454
$27$	72.2737	+	120.248i	0.515151	+	0.857099i
$28$		−	259.832i		−	1.75370i
$29$	−89.3675	+	154.789i	−0.572246	+	0.991158i	0.424089	+	0.905620i	$0.360594\pi$
$29$	−89.3675	+	154.789i	−0.572246	+	0.991158i	−0.996335	+	0.0855380i	$0.972739\pi$
$30$		0			0
$31$	−77.0186	−	133.400i	−0.446224	−	0.772883i	0.551912	−	0.833902i	$-0.313898\pi$
$31$	−77.0186	−	133.400i	−0.446224	−	0.772883i	−0.998137	+	0.0610190i	$0.980565\pi$
$32$	−157.708	+	91.0527i	−0.871222	+	0.503000i
$33$	−61.8491	−	339.127i	−0.326259	−	1.78892i
$34$	108.905	−	188.628i	0.549323	−	0.951455i
$35$		0			0
$36$	326.322	−	123.123i	1.51075	−	0.570012i
$37$		−	248.864i		−	1.10576i	−0.833262	−	0.552878i	$-0.813529\pi$
$37$		−	248.864i		−	1.10576i	0.833262	−	0.552878i	$-0.186471\pi$
$38$	−39.4213	−	22.7599i	−0.168289	−	0.0971616i
$39$	81.8326	−	229.001i	0.335992	−	0.940244i
$40$		0			0
$41$	−124.832	−	216.216i	−0.475500	−	0.823590i	0.524106	−	0.851653i	$-0.324400\pi$
$41$	−124.832	−	216.216i	−0.475500	−	0.823590i	−0.999606	+	0.0280628i	$0.991066\pi$
$42$	−450.145	−	160.857i	−1.65378	−	0.590972i
$43$	183.809	+	106.122i	0.651876	+	0.376361i	0.789175	−	0.614169i	$-0.210509\pi$
$43$	183.809	+	106.122i	0.651876	+	0.376361i	−0.137299	+	0.990530i	$0.543842\pi$
$44$	−856.976			−2.93623
$45$		0			0
$46$	−43.8700			−0.140615
$47$	411.963	+	237.847i	1.27853	+	0.738160i	0.976578	−	0.215163i	$-0.0690282\pi$
$47$	411.963	+	237.847i	1.27853	+	0.738160i	0.301953	+	0.953323i	$0.402362\pi$
$48$	0.443494	+	2.43174i	0.00133360	+	0.00731232i
$49$	30.7973	+	53.3425i	0.0897880	+	0.155517i
$50$		0			0
$51$	−160.171	−	188.628i	−0.439774	−	0.517906i
$52$	−523.559	−	302.277i	−1.39624	−	0.806120i
$53$		−	546.314i		−	1.41589i	−0.706269	−	0.707944i	$-0.749623\pi$
$53$		−	546.314i		−	1.41589i	0.706269	−	0.707944i	$-0.250377\pi$
$54$	−11.2831	−	641.556i	−0.0284341	−	1.61675i
$55$		0			0
$56$	−226.200	+	391.790i	−0.539773	+	0.934914i
$57$	−39.4213	+	33.4741i	−0.0916048	+	0.0777851i
$58$	707.940	−	408.729i	1.60271	−	0.925324i
$59$	−209.648	−	363.121i	−0.462608	−	0.801261i	0.536482	−	0.843912i	$-0.319753\pi$
$59$	−209.648	−	363.121i	−0.462608	−	0.801261i	−0.999090	+	0.0426512i	$0.986420\pi$
$60$		0			0
$61$	272.605	−	472.165i	0.572188	−	0.991059i	−0.424153	−	0.905591i	$-0.639428\pi$
$61$	272.605	−	472.165i	0.572188	−	0.991059i	0.996341	−	0.0854682i	$-0.0272386\pi$
$62$			704.502i			1.44309i
$63$	−344.192	+	420.097i	−0.688319	+	0.840115i
$64$	829.068			1.61927
$65$		0			0
$66$	−530.538	+	1484.66i	−0.989466	+	2.76893i
$67$	387.872	−	223.938i	0.707256	−	0.408335i	−0.102788	−	0.994703i	$-0.532776\pi$
$67$	387.872	−	223.938i	0.707256	−	0.408335i	0.810044	+	0.586369i	$0.199443\pi$
$68$	−532.762	+	307.590i	−0.950102	+	0.548541i
$69$	−16.7720	+	46.9350i	−0.0292625	+	0.0818885i
$70$		0			0
$71$	409.542			0.684559			0.342279	−	0.939598i	$-0.388801\pi$
$71$	409.542			0.684559			0.342279	+	0.939598i	$0.388801\pi$
$72$	−599.232	−	98.4319i	−0.980836	−	0.161115i
$73$		−	358.548i		−	0.574861i	−0.957801	−	0.287431i	$-0.907199\pi$
$73$		−	358.548i		−	0.574861i	0.957801	−	0.287431i	$-0.0928011\pi$
$74$	−569.100	+	985.710i	−0.894007	+	1.54847i
$75$		0			0
$76$	64.2831	+	111.342i	0.0970234	+	0.168049i
$77$	1155.65	−	667.215i	1.71037	−	0.987483i
$78$	−847.803	+	719.902i	−1.23070	+	1.04504i
$79$	−325.776	+	564.260i	−0.463958	+	0.803598i	−0.999154	−	0.0411297i	$-0.986904\pi$
$79$	−325.776	+	564.260i	−0.463958	+	0.803598i	0.535196	+	0.844728i	$0.320238\pi$
$80$		0			0
$81$	−690.693	−	233.204i	−0.947453	−	0.319895i
$82$			1141.86i			1.53777i
$83$	704.202	+	406.571i	0.931280	+	0.537675i	0.887216	−	0.461354i	$-0.152636\pi$
$83$	704.202	+	406.571i	0.931280	+	0.537675i	0.0440636	+	0.999029i	$0.485970\pi$
$84$	873.893	+	1029.15i	1.13511	+	1.33678i
$85$		0			0
$86$	−485.359	−	840.667i	−0.608577	−	1.05409i
$87$	−166.631	−	913.663i	−0.205342	−	1.12592i
$88$	1292.20	+	746.051i	1.56533	+	0.903743i
$89$	201.000			0.239393			0.119696	−	0.992811i	$-0.461808\pi$
$89$	201.000			0.239393			0.119696	+	0.992811i	$0.461808\pi$
$90$		0			0
$91$	941.373			1.08442
$92$	107.306	+	61.9532i	0.121603	+	0.0702073i
$93$	753.723	+	269.340i	0.840402	+	0.300314i
$94$	−1087.81	−	1884.14i	−1.19361	−	2.06739i
$95$		0			0
$96$	318.418	−	891.064i	0.338525	−	0.947331i
$97$	218.367	+	126.074i	0.228576	+	0.131968i	0.609915	−	0.792467i	$-0.291204\pi$
$97$	218.367	+	126.074i	0.228576	+	0.131968i	−0.381339	+	0.924435i	$0.624537\pi$
$98$		−	281.708i		−	0.290375i
$99$	1385.56	+	1135.21i	1.40661	+	1.15245i
$100$		0			0
$101$	−21.8013	+	37.7610i	−0.0214783	+	0.0372016i	−0.876565	−	0.481284i	$-0.840171\pi$
$101$	−21.8013	+	37.7610i	−0.0214783	+	0.0372016i	0.855086	+	0.518485i	$0.173504\pi$
$102$	203.060	+	1113.40i	0.197117	+	1.08082i
$103$	−1247.38	+	720.176i	−1.19328	+	0.688942i	−0.959050	−	0.283238i	$-0.908591\pi$
$103$	−1247.38	+	720.176i	−1.19328	+	0.688942i	−0.234233	+	0.972180i	$0.575258\pi$
$104$	526.301	+	911.581i	0.496232	+	0.859498i
$105$		0			0
$106$	−1249.31	+	2163.86i	−1.14475	+	1.98276i
$107$		−	355.755i		−	0.321422i	−0.987002	−	0.160711i	$-0.948621\pi$
$107$		−	355.755i		−	0.321422i	0.987002	−	0.160711i	$-0.0513786\pi$
$108$	−878.409	+	1585.18i	−0.782638	+	1.41236i
$109$	1522.51			1.33789			0.668946	−	0.743311i	$-0.266746\pi$
$109$	1522.51			1.33789			0.668946	+	0.743311i	$0.266746\pi$
$110$		0			0
$111$	837.004	+	985.710i	0.715720	+	0.842878i
$112$	−8.28669	+	4.78432i	−0.00699124	+	0.00403639i
$113$	−704.077	+	406.499i	−0.586142	+	0.338409i	−0.763570	−	0.645725i	$-0.776555\pi$
$113$	−704.077	+	406.499i	−0.586142	+	0.338409i	0.177429	+	0.984134i	$0.443222\pi$
$114$	232.689	−	42.4373i	0.191170	−	0.0348650i
$115$		0			0
$116$	−2308.83			−1.84802
$117$	446.073	+	1182.26i	0.352474	+	0.934190i
$118$			1917.69i			1.49608i
$119$	478.960	−	829.584i	0.368960	−	0.639057i
$120$		0			0
$121$	−1535.10	−	2658.87i	−1.15334	−	1.99765i
$122$	−2159.49	+	1246.78i	−1.60255	+	0.925231i
$123$	1221.64	+	436.547i	0.895539	+	0.320017i
$124$	994.899	−	1723.22i	0.720521	−	1.24798i
$125$		0			0
$126$	2323.96	−	876.841i	1.64313	−	0.619962i
$127$			864.662i			0.604144i	0.953285	+	0.302072i	$0.0976784\pi$
$127$			864.662i			0.604144i	−0.953285	+	0.302072i	$0.902322\pi$
$128$	−2022.14	−	1167.48i	−1.39636	−	0.806187i
$129$	−1084.96	+	197.872i	−0.740507	+	0.135052i
$130$		0			0
$131$	1089.26	+	1886.65i	0.726482	+	1.25830i	0.958361	+	0.285559i	$0.0921792\pi$
$131$	1089.26	+	1886.65i	0.726482	+	1.25830i	−0.231879	+	0.972745i	$0.574487\pi$
$132$	3394.34	−	2882.27i	2.23818	−	1.90052i
$133$	−173.374	−	100.098i	−0.113033	−	0.0652599i
$134$	−2048.40			−1.32056
$135$		0			0
$136$	1071.11			0.675343
$137$	−1991.13	−	1149.58i	−1.24171	−	0.716900i	−0.272266	−	0.962222i	$-0.587773\pi$
$137$	−1991.13	−	1149.58i	−1.24171	−	0.716900i	−0.969442	+	0.245322i	$0.921106\pi$
$138$	173.762	−	147.548i	0.107185	−	0.0910152i
$139$	−1066.98	−	1848.06i	−0.651077	−	1.12770i	−0.982862	−	0.184343i	$-0.940984\pi$
$139$	−1066.98	−	1848.06i	−0.651077	−	1.12770i	0.331785	−	0.943355i	$-0.392349\pi$
$140$		0			0
$141$	−2431.67	+	443.481i	−1.45236	+	0.264878i
$142$	−1622.13	−	936.536i	−0.958634	−	0.553467i
$143$		−	3104.83i		−	1.81565i
$144$	−9.93528	−	8.14012i	−0.00574958	−	0.00471072i
$145$		0			0
$146$	−819.924	+	1420.15i	−0.464777	+	0.805017i
$147$	−301.390	−	107.700i	−0.169103	−	0.0604284i
$148$	2784.04	−	1607.37i	1.54626	−	0.892735i
$149$	875.309	+	1516.08i	0.481263	+	0.833572i	0.999769	−	0.0215024i	$-0.00684497\pi$
$149$	875.309	+	1516.08i	0.481263	+	0.833572i	−0.518506	+	0.855074i	$0.673512\pi$
$150$		0			0
$151$	−437.977	+	758.598i	−0.236040	+	0.408833i	−0.959574	−	0.281455i	$-0.909183\pi$
$151$	−437.977	+	758.598i	−0.236040	+	0.408833i	0.723534	+	0.690288i	$0.242516\pi$
$152$		−	223.850i		−	0.119451i
$153$	1268.83	+	208.421i	0.670447	+	0.110130i
$154$	−6103.12			−3.19353
$155$		0			0
$156$	3090.38	−	563.615i	1.58608	−	0.289265i
$157$	224.642	−	129.697i	0.114194	−	0.0659298i	−0.441815	−	0.897106i	$-0.645665\pi$
$157$	224.642	−	129.697i	0.114194	−	0.0659298i	0.556009	+	0.831176i	$0.312332\pi$
$158$	2580.69	−	1489.96i	1.29942	−	0.750222i
$159$	1837.42	+	2163.86i	0.916457	+	1.07928i
$160$		0			0
$161$	−192.939			−0.0944457
$162$	2202.44	+	2503.15i	1.06815	+	1.21399i
$163$		−	1201.80i		−	0.577498i	−0.957405	−	0.288749i	$-0.906761\pi$
$163$		−	1201.80i		−	0.577498i	0.957405	−	0.288749i	$-0.0932393\pi$
$164$	1612.54	−	2792.99i	0.767792	−	1.32986i
$165$		0			0
$166$	−1859.49	−	3220.72i	−0.869422	−	1.50588i
$167$	1453.97	−	839.452i	0.673724	−	0.388975i	−0.123762	−	0.992312i	$-0.539496\pi$
$167$	1453.97	−	839.452i	0.673724	−	0.388975i	0.797486	+	0.603337i	$0.206163\pi$
$168$	−421.765	−	2312.60i	−0.193690	−	1.06203i
$169$	−3.35162	+	5.80518i	−0.00152554	+	0.00264232i
$170$		0			0
$171$	43.5578	−	265.171i	0.0194792	−	0.118586i
$172$			2741.70i			1.21542i
$173$	−806.961	−	465.899i	−0.354636	−	0.204749i	0.312089	−	0.950053i	$-0.398971\pi$
$173$	−806.961	−	465.899i	−0.354636	−	0.204749i	−0.666725	+	0.745303i	$0.732305\pi$
$174$	−1429.36	+	3999.92i	−0.622754	+	1.74272i
$175$		0			0
$176$	15.7796	+	27.3311i	0.00675814	+	0.0117054i
$177$	2051.67	+	733.155i	0.871259	+	0.311341i
$178$	−796.127	−	459.644i	−0.335237	−	0.193549i
$179$	−1023.40			−0.427333			−0.213667	−	0.976907i	$-0.568541\pi$
$179$	−1023.40			−0.427333			−0.213667	+	0.976907i	$0.568541\pi$
$180$		0			0
$181$	2639.93			1.08411			0.542056	−	0.840342i	$-0.317646\pi$
$181$	2639.93			1.08411			0.542056	+	0.840342i	$0.317646\pi$
$182$	−3728.62	−	2152.72i	−1.51859	−	0.876760i
$183$	508.289	+	2787.02i	0.205322	+	1.12581i
$184$	−107.868	−	186.833i	−0.0432182	−	0.0748562i
$185$		0			0
$186$	−2369.45	−	2790.42i	−0.934067	−	1.10002i
$187$	−2736.13	−	1579.70i	−1.06997	−	0.617750i
$188$			6144.84i			2.38382i
$189$	−49.6230	−	2821.56i	−0.0190981	−	1.08591i
$190$		0			0
$191$	406.640	−	704.322i	0.154050	−	0.266822i	−0.778663	−	0.627442i	$-0.784102\pi$
$191$	406.640	−	704.322i	0.154050	−	0.266822i	0.932713	+	0.360621i	$0.117435\pi$
$192$	−3283.80	+	2788.40i	−1.23431	+	1.04810i
$193$	−705.154	+	407.121i	−0.262995	+	0.151840i	−0.625700	−	0.780064i	$-0.715187\pi$
$193$	−705.154	+	407.121i	−0.262995	+	0.151840i	0.362705	+	0.931904i	$0.381853\pi$
$194$	−576.612	−	998.720i	−0.213393	−	0.369608i
$195$		0			0
$196$	−397.828	+	689.059i	−0.144981	+	0.251115i
$197$		−	4078.41i		−	1.47500i	−0.675348	−	0.737499i	$-0.736006\pi$
$197$		−	4078.41i		−	1.47500i	0.675348	−	0.737499i	$-0.263994\pi$
$198$	−2891.99	−	7664.87i	−1.03800	−	2.75110i
$199$	1342.49			0.478224			0.239112	−	0.970992i	$-0.423144\pi$
$199$	1342.49			0.478224			0.239112	+	0.970992i	$0.423144\pi$
$200$		0			0
$201$	−783.129	+	2191.51i	−0.274814	+	0.769042i
$202$	172.703	−	99.7101i	0.0601551	−	0.0347306i
$203$	3113.51	−	1797.58i	1.07648	−	0.621506i
$204$	1075.67	−	3010.15i	0.369175	−	1.03310i
$205$		0			0
$206$	6587.56			2.22805
$207$	−91.4250	−	242.311i	−0.0306980	−	0.0813613i
$208$			22.2634i			0.00742159i
$209$	−330.141	+	571.821i	−0.109265	+	0.189252i
$210$		0			0
$211$	1477.49	+	2559.08i	0.482059	+	0.834950i	0.999788	−	0.0205943i	$-0.00655583\pi$
$211$	1477.49	+	2559.08i	0.482059	+	0.834950i	−0.517729	+	0.855545i	$0.673222\pi$
$212$	6111.62	−	3528.55i	1.97994	−	1.14312i
$213$	−1622.13	+	1377.41i	−0.521814	+	0.443092i
$214$	−813.536	+	1409.09i	−0.259870	+	0.450108i
$215$		0			0
$216$	2704.52	−	1625.52i	0.851940	−	0.512050i
$217$			3098.39i			0.969273i
$218$	−6030.42	−	3481.66i	−1.87354	−	1.08169i
$219$	1205.90	+	1420.15i	0.372089	+	0.438196i
$220$		0			0
$221$	−1114.40	−	1930.20i	−0.339198	−	0.587507i
$222$	−1061.12	−	5818.29i	−0.320802	−	1.75900i
$223$	−3037.03	−	1753.43i	−0.911993	−	0.526539i	−0.0309212	−	0.999522i	$-0.509844\pi$
$223$	−3037.03	−	1753.43i	−0.911993	−	0.526539i	−0.881072	+	0.472982i	$0.843177\pi$
$224$	3662.97			1.09260
$225$		0			0
$226$	3718.31			1.09442
$227$	565.364	+	326.413i	0.165306	+	0.0954396i	0.580371	−	0.814352i	$-0.302908\pi$
$227$	565.364	+	326.413i	0.165306	+	0.0954396i	−0.415064	+	0.909792i	$0.636241\pi$
$228$	−629.090	−	224.803i	−0.182730	−	0.0652979i
$229$	2291.78	+	3969.47i	0.661331	+	1.14546i	0.980266	+	0.197682i	$0.0633414\pi$
$229$	2291.78	+	3969.47i	0.661331	+	1.14546i	−0.318935	+	0.947776i	$0.603325\pi$
$230$		0			0
$231$	−2333.30	+	6529.52i	−0.664588	+	1.85979i
$232$	3481.39	+	2009.98i	0.985192	+	0.568801i
$233$			317.527i			0.0892785i	0.999003	+	0.0446392i	$0.0142138\pi$
$233$			317.527i			0.0892785i	−0.999003	+	0.0446392i	$0.985786\pi$
$234$	936.765	−	5702.83i	0.261702	−	1.59319i
$235$		0			0
$236$	2708.16	−	4690.67i	0.746975	−	1.29380i
$237$	−607.430	−	3330.62i	−0.166485	−	0.912858i
$238$	−3794.17	+	2190.56i	−1.03336	+	0.596610i
$239$	928.835	+	1608.79i	0.251386	+	0.435414i	0.963908	−	0.266236i	$-0.0857802\pi$
$239$	928.835	+	1608.79i	0.251386	+	0.435414i	−0.712521	+	0.701650i	$0.752447\pi$
$240$		0			0
$241$	1633.47	−	2829.25i	0.436602	−	0.756217i	−0.560823	−	0.827936i	$-0.689515\pi$
$241$	1633.47	−	2829.25i	0.436602	−	0.756217i	0.997425	+	0.0717190i	$0.0228485\pi$
$242$			14041.8i			3.72993i
$243$	3520.06	−	1399.33i	0.929266	−	0.369411i
$244$	7042.82			1.84783
$245$		0			0
$246$	−3840.41	−	4522.72i	−0.995349	−	1.17219i
$247$	−403.390	+	232.898i	−0.103915	+	0.0599956i
$248$	−3000.33	+	1732.24i	−0.768231	+	0.443538i
$249$	−4156.65	+	758.079i	−1.05790	+	0.192937i
$250$		0			0
$251$	−5641.37			−1.41865			−0.709323	−	0.704884i	$-0.750999\pi$
$251$	−5641.37			−1.41865			−0.709323	+	0.704884i	$0.750999\pi$
$252$	−6922.70	−	1137.15i	−1.73051	−	0.284260i
$253$			636.351i			0.158131i
$254$	1977.30	−	3424.78i	0.488452	−	0.846024i
$255$		0			0
$256$	2023.31	+	3504.47i	0.493971	+	0.855584i
$257$	1016.25	−	586.731i	0.246661	−	0.142410i	−0.371574	−	0.928404i	$-0.621182\pi$
$257$	1016.25	−	586.731i	0.246661	−	0.142410i	0.618234	+	0.785994i	$0.287848\pi$
$258$	4749.84	+	1697.34i	1.14617	+	0.409580i
$259$	−2502.89	+	4335.14i	−0.600472	+	1.04005i
$260$		0			0
$261$	3732.92	+	3058.44i	0.885295	+	0.725336i
$262$		−	9963.64i		−	2.34945i
$263$	2509.71	+	1448.98i	0.588423	+	0.339726i	0.764474	−	0.644655i	$-0.222999\pi$
$263$	2509.71	+	1448.98i	0.588423	+	0.339726i	−0.176051	+	0.984381i	$0.556332\pi$
$264$	−7627.38	+	1391.06i	−1.77815	+	0.324295i
$265$		0			0
$266$	457.804	+	792.940i	0.105526	+	0.182776i
$267$	−796.127	+	676.022i	−0.182480	+	0.154951i
$268$	5010.40	+	2892.75i	1.14201	+	0.659340i
$269$	−2930.13			−0.664138			−0.332069	−	0.943255i	$-0.607747\pi$
$269$	−2930.13			−0.664138			−0.332069	+	0.943255i	$0.607747\pi$
$270$		0			0
$271$	−668.881			−0.149932			−0.0749661	−	0.997186i	$-0.523885\pi$
$271$	−668.881			−0.149932			−0.0749661	+	0.997186i	$0.523885\pi$
$272$	19.6196	+	11.3274i	0.00437358	+	0.00252509i
$273$	−3728.62	+	3166.12i	−0.826617	+	0.701912i
$274$	5257.70	+	9106.60i	1.15923	+	2.00785i
$275$		0			0
$276$	−633.389	+	115.516i	−0.138136	+	0.0251929i
$277$	−547.874	−	316.315i	−0.118840	−	0.0686121i	0.439402	−	0.898291i	$-0.355190\pi$
$277$	−547.874	−	316.315i	−0.118840	−	0.0686121i	−0.558241	+	0.829679i	$0.688524\pi$
$278$			9759.80i			2.10559i
$279$	−3891.24	+	1468.18i	−0.834991	+	0.315046i
$280$		0			0
$281$	1797.65	−	3113.62i	0.381633	−	0.661007i	−0.609663	−	0.792661i	$-0.708695\pi$
$281$	1797.65	−	3113.62i	0.381633	−	0.661007i	0.991296	+	0.131653i	$0.0420286\pi$
$282$	10645.6	+	3804.16i	2.24800	+	0.803313i
$283$	436.796	−	252.184i	0.0917485	−	0.0529710i	−0.453424	−	0.891295i	$-0.649798\pi$
$283$	436.796	−	252.184i	0.0917485	−	0.0529710i	0.545172	+	0.838324i	$0.316464\pi$
$284$	2645.16	+	4581.55i	0.552680	+	0.957270i
$285$		0			0
$286$	−7100.08	+	12297.7i	−1.46796	+	2.54258i
$287$			5021.88i			1.03286i
$288$	1735.71	+	4600.29i	0.355131	+	0.941232i
$289$	2645.02			0.538372
$290$		0			0
$291$	−1288.94	+	235.074i	−0.259654	+	0.0473549i
$292$	4011.08	−	2315.80i	0.803872	−	0.464116i
$293$	5368.06	−	3099.25i	1.07033	−	0.617953i	0.142055	−	0.989859i	$-0.454629\pi$
$293$	5368.06	−	3099.25i	1.07033	−	0.617953i	0.928270	+	0.371906i	$0.121296\pi$
$294$	947.467	+	1115.80i	0.187950	+	0.221343i
$295$		0			0
$296$	−5597.26			−1.09910
$297$	−9306.02	+	163.666i	−1.81815	+	0.0319760i
$298$		−	8006.60i		−	1.55641i
$299$	−224.457	+	388.770i	−0.0434136	+	0.0751945i
$300$		0			0
$301$	−2134.60	−	3697.24i	−0.408759	−	0.707991i
$302$	3469.51	−	2003.12i	0.661086	−	0.381678i
$303$	−40.6500	−	222.889i	−0.00770719	−	0.0422596i
$304$	2.36730	−	4.10029i	0.000446626	−	0.000773578i
$305$		0			0
$306$	−4548.99	−	3727.06i	−0.849832	−	0.696281i
$307$			1966.79i			0.365636i	0.983147	+	0.182818i	$0.0585220\pi$
$307$			1966.79i			0.365636i	−0.983147	+	0.182818i	$0.941478\pi$
$308$	14928.3	+	8618.84i	2.76174	+	1.59449i
$309$	2518.51	−	7047.81i	0.463666	−	1.29753i
$310$		0			0
$311$	1153.05	+	1997.15i	0.210237	+	0.364141i	0.951789	−	0.306755i	$-0.0992431\pi$
$311$	1153.05	+	1997.15i	0.210237	+	0.364141i	−0.741552	+	0.670896i	$0.765910\pi$
$312$	−5150.51	−	1840.51i	−0.934584	−	0.333970i
$313$	−8922.14	−	5151.20i	−1.61121	−	0.930234i	−0.989090	−	0.147314i	$-0.952937\pi$
$313$	−8922.14	−	5151.20i	−1.61121	−	0.930234i	−0.622122	−	0.782920i	$-0.713729\pi$
$314$	−1186.36			−0.213218
$315$		0			0
$316$	−8416.51			−1.49831
$317$	−1473.83	−	850.916i	−0.261131	−	0.150764i	0.363719	−	0.931509i	$-0.381507\pi$
$317$	−1473.83	−	850.916i	−0.261131	−	0.150764i	−0.624850	+	0.780745i	$0.714840\pi$
$318$	−2329.41	−	12772.5i	−0.410777	−	2.25235i
$319$	−5928.78	−	10268.9i	−1.04059	−	1.80235i
$320$		0			0
$321$	1196.51	+	1409.09i	0.208046	+	0.245008i
$322$	764.201	+	441.212i	0.132259	+	0.0763596i
$323$			473.983i			0.0816506i
$324$	−1852.21	−	9233.01i	−0.317595	−	1.58316i
$325$		0			0
$326$	−2748.26	+	4760.13i	−0.466908	+	0.808709i
$327$	−6030.42	+	5120.66i	−1.01983	+	0.865973i
$328$	−4862.95	+	2807.63i	−0.818633	+	0.472638i
$329$	−4784.18	−	8286.44i	−0.801703	−	1.38859i
$330$		0			0
$331$	4175.74	−	7232.60i	0.693413	−	1.20103i	−0.277300	−	0.960783i	$-0.589440\pi$
$331$	4175.74	−	7232.60i	0.693413	−	1.20103i	0.970713	−	0.240243i	$-0.0772271\pi$
$332$			10503.9i			1.73637i
$333$	−6630.47	−	1089.14i	−1.09113	−	0.179233i
$334$	−7678.61			−1.25795
$335$		0			0
$336$	16.7311	−	46.8205i	0.00271654	−	0.00760199i
$337$	6804.73	−	3928.71i	1.09993	−	0.635046i	0.163729	−	0.986505i	$-0.447648\pi$
$337$	6804.73	−	3928.71i	1.09993	−	0.635046i	0.936203	+	0.351459i	$0.114314\pi$
$338$	26.5504	−	15.3289i	0.00427264	−	0.00246681i
$339$	1421.56	−	3978.10i	0.227753	−	0.637347i
$340$		0			0
$341$	10219.1			1.62286
$342$	−778.916	+	950.691i	−0.123155	+	0.150314i
$343$			5660.34i			0.891048i
$344$	2386.82	−	4134.10i	0.374095	−	0.647952i
$345$		0			0
$346$	2130.83	+	3690.70i	0.331081	+	0.573449i
$347$	−1049.78	+	606.088i	−0.162406	+	0.0937652i	−0.579000	−	0.815327i	$-0.696557\pi$
$347$	−1049.78	+	606.088i	−0.162406	+	0.0937652i	0.416594	+	0.909093i	$0.363224\pi$
$348$	9144.91	−	7765.29i	1.40867	−	1.19616i
$349$	699.332	−	1211.28i	0.107262	−	0.185783i	−0.807398	−	0.590007i	$-0.799125\pi$
$349$	699.332	−	1211.28i	0.107262	−	0.185783i	0.914660	+	0.404224i	$0.132458\pi$
$350$		0			0
$351$	−5743.12	−	3182.47i	−0.873348	−	0.483954i
$352$		−	12081.2i		−	1.82934i
$353$	−2276.28	−	1314.21i	−0.343214	−	0.198154i	0.318479	−	0.947930i	$-0.396828\pi$
$353$	−2276.28	−	1314.21i	−0.343214	−	0.198154i	−0.661692	+	0.749776i	$0.730161\pi$
$354$	−6449.75	−	7595.64i	−0.968362	−	1.14041i
$355$		0			0
$356$	1298.22	+	2248.59i	0.193274	+	0.334761i
$357$	893.053	+	4896.73i	0.132396	+	0.725946i
$358$	4053.53	+	2340.31i	0.598424	+	0.345500i
$359$	−3677.48			−0.540640			−0.270320	−	0.962770i	$-0.587130\pi$
$359$	−3677.48			−0.540640			−0.270320	+	0.962770i	$0.587130\pi$
$360$		0			0
$361$	−6759.94			−0.985558
$362$	−10456.3	−	6036.96i	−1.51815	−	0.876507i
$363$	15022.9	+	5368.36i	2.17217	+	0.776215i
$364$	6080.16	+	10531.1i	0.875513	+	1.51643i
$365$		0			0
$366$	4360.08	−	12201.3i	0.622692	−	1.74255i
$367$	9898.47	+	5714.88i	1.40789	+	0.812846i	0.995185	−	0.0980185i	$-0.0312504\pi$
$367$	9898.47	+	5714.88i	1.40789	+	0.812846i	0.412706	+	0.910864i	$0.364584\pi$
$368$		−	4.56301i		−	0.000646368i
$369$	−6306.94	+	2379.64i	−0.889773	+	0.335715i
$370$		0			0
$371$	−5494.43	+	9516.63i	−0.768886	+	1.33175i
$372$	1855.05	+	10171.5i	0.258549	+	1.41766i
$373$	1957.13	−	1129.95i	0.271679	−	0.156854i	−0.357971	−	0.933733i	$-0.616531\pi$
$373$	1957.13	−	1129.95i	0.271679	−	0.156854i	0.629650	+	0.776879i	$0.283198\pi$
$374$	7224.90	+	12513.9i	0.998905	+	1.73015i
$375$		0			0
$376$	5349.47	−	9265.55i	0.733717	−	1.27084i
$377$		−	8364.90i		−	1.14274i
$378$	−6255.76	+	11289.2i	−0.851221	+	1.53612i
$379$	11815.8			1.60142			0.800709	−	0.599053i	$-0.204456\pi$
$379$	11815.8			1.60142			0.800709	+	0.599053i	$0.204456\pi$
$380$		0			0
$381$	−2908.12	−	3424.78i	−0.391043	−	0.460517i
$382$	−3221.27	+	1859.80i	−0.431452	+	0.249099i
$383$	−6997.68	+	4040.11i	−0.933589	+	0.539008i	−0.887945	−	0.459950i	$-0.847867\pi$
$383$	−6997.68	+	4040.11i	−0.933589	+	0.539008i	−0.0456440	+	0.998958i	$0.514534\pi$
$384$	11936.0	−	2176.85i	1.58621	−	0.289289i
$385$		0			0
$386$	3724.00			0.491054
$387$	3631.85	−	4432.78i	0.477047	−	0.582251i
$388$			3257.17i			0.426180i
$389$	1550.22	−	2685.05i	0.202054	−	0.349968i	−0.747136	−	0.664671i	$-0.768572\pi$
$389$	1550.22	−	2685.05i	0.202054	−	0.349968i	0.949190	+	0.314703i	$0.101905\pi$
$390$		0			0
$391$	228.402	+	395.604i	0.0295417	+	0.0511677i
$392$	1199.74	−	692.669i	0.154581	−	0.0892476i
$393$	−10659.8	−	3809.22i	−1.36823	−	0.488931i
$394$	−9326.47	+	16153.9i	−1.19254	+	2.06554i
$395$		0			0
$396$	−3750.52	+	22832.4i	−0.475936	+	2.89740i
$397$			11990.1i			1.51578i	0.652382	+	0.757890i	$0.273770\pi$
$397$			11990.1i			1.51578i	−0.652382	+	0.757890i	$0.726230\pi$
$398$	−5317.38	−	3069.99i	−0.669689	−	0.386645i
$399$	1023.36	−	186.638i	0.128402	−	0.0234176i
$400$		0			0
$401$	−6426.63	−	11131.3i	−0.800326	−	1.38620i	−0.919402	−	0.393320i	$-0.871327\pi$
$401$	−6426.63	−	11131.3i	−0.800326	−	1.38620i	0.119076	−	0.992885i	$-0.462007\pi$
$402$	8113.38	−	6889.38i	1.00661	−	0.854753i
$403$	6243.21	+	3604.52i	0.771703	+	0.445543i
$404$	−563.243			−0.0693623
$405$		0			0
$406$	−16442.8			−2.00996
$407$	14298.1	+	8255.02i	1.74135	+	1.00537i
$408$	−4242.48	+	3602.45i	−0.514789	+	0.437127i
$409$	1112.54	+	1926.98i	0.134503	+	0.232966i	0.925408	−	0.378974i	$-0.123723\pi$
$409$	1112.54	+	1926.98i	0.134503	+	0.232966i	−0.790904	+	0.611940i	$0.790390\pi$
$410$		0			0
$411$	11752.9	−	2143.47i	1.41053	−	0.257249i
$412$	−16113.2	−	9302.97i	−1.92680	−	1.11244i
$413$			8433.95i			1.00486i
$414$	−191.995	+	1168.82i	−0.0227924	+	0.138755i
$415$		0			0
$416$	4261.32	−	7380.83i	0.502232	−	0.869891i
$417$	10441.7	+	3731.29i	1.22621	+	0.438183i
$418$	2615.27	−	1509.93i	0.306021	−	0.176682i
$419$	4838.33	+	8380.23i	0.564123	+	0.977090i	0.997131	+	0.0756998i	$0.0241191\pi$
$419$	4838.33	+	8380.23i	0.564123	+	0.977090i	−0.433007	+	0.901390i	$0.642548\pi$
$420$		0			0
$421$	4981.30	−	8627.87i	0.576660	−	0.998804i	−0.419199	−	0.907894i	$-0.637689\pi$
$421$	4981.30	−	8627.87i	0.576660	−	0.998804i	0.995859	−	0.0909098i	$-0.0289775\pi$
$422$		−	13514.8i		−	1.55898i
$423$	8139.88	−	9934.98i	0.935637	−	1.14197i
$424$	−12287.3			−1.40737
$425$		0			0
$426$	9574.84	−	1746.23i	1.08897	−	0.198604i
$427$	−9497.39	+	5483.32i	−1.07637	+	0.621444i
$428$	3979.83	−	2297.76i	0.449468	−	0.259500i
$429$	10442.5	+	12297.7i	1.17521	+	1.38401i
$430$		0			0
$431$	−2461.47			−0.275092			−0.137546	−	0.990495i	$-0.543922\pi$
$431$	−2461.47			−0.275092			−0.137546	+	0.990495i	$0.543922\pi$
$432$	66.7297	−	1.17358i	0.00743179	−	0.000130704i
$433$			7818.49i			0.867743i	0.900975	+	0.433871i	$0.142853\pi$
$433$			7818.49i			0.867743i	−0.900975	+	0.433871i	$0.857147\pi$
$434$	7085.36	−	12272.2i	0.783660	−	1.35734i
$435$		0			0
$436$	9833.63	+	17032.3i	1.08015	+	1.87087i
$437$	82.6770	−	47.7336i	0.00905030	−	0.00522519i
$438$	−1528.80	−	8382.64i	−0.166779	−	0.914470i
$439$	3105.91	−	5379.60i	0.337670	−	0.584862i	−0.646324	−	0.763063i	$-0.723694\pi$
$439$	3105.91	−	5379.60i	0.337670	−	0.584862i	0.983994	+	0.178201i	$0.0570278\pi$
$440$		0			0
$441$	1555.98	−	587.080i	0.168015	−	0.0633927i
$442$			10193.6i			1.09697i
$443$	−2584.52	−	1492.17i	−0.277188	−	0.160034i	0.354962	−	0.934881i	$-0.384494\pi$
$443$	−2584.52	−	1492.17i	−0.277188	−	0.160034i	−0.632150	+	0.774846i	$0.717827\pi$
$444$	−5621.08	+	15730.1i	−0.600822	+	1.68134i
$445$		0			0
$446$	8019.45	+	13890.1i	0.851417	+	1.47470i
$447$	−8565.99	−	3061.02i	−0.906392	−	0.323896i
$448$	−14442.1	−	8338.16i	−1.52305	−	0.879333i
$449$	810.476			0.0851865			0.0425932	−	0.999092i	$-0.486438\pi$
$449$	810.476			0.0851865			0.0425932	+	0.999092i	$0.486438\pi$
$450$		0			0
$451$	16563.1			1.72933
$452$	−9095.01	−	5251.01i	−0.946446	−	0.546431i
$453$	−816.637	−	4477.73i	−0.0846996	−	0.464420i
$454$	−1492.88	−	2585.74i	−0.154326	−	0.267301i
$455$		0			0
$456$	752.873	+	886.632i	0.0773169	+	0.0910534i
$457$	1361.20	+	785.887i	0.139331	+	0.0804425i	0.568045	−	0.822998i	$-0.307700\pi$
$457$	1361.20	+	785.887i	0.139331	+	0.0804425i	−0.428714	+	0.903440i	$0.641033\pi$
$458$		−	20963.2i		−	2.13875i
$459$	−5726.59	+	3441.91i	−0.582341	+	0.350010i
$460$		0			0
$461$	−1031.35	+	1786.34i	−0.104196	+	0.180474i	−0.913410	−	0.407042i	$-0.866560\pi$
$461$	−1031.35	+	1786.34i	−0.104196	+	0.180474i	0.809213	+	0.587515i	$0.199894\pi$
$462$	24173.5	−	20526.6i	2.43431	−	2.06707i
$463$	2410.35	−	1391.62i	0.241940	−	0.139684i	−0.374128	−	0.927377i	$-0.622058\pi$
$463$	2410.35	−	1391.62i	0.241940	−	0.139684i	0.616068	+	0.787693i	$0.288725\pi$
$464$	42.5128	+	73.6344i	0.00425347	+	0.00736722i
$465$		0			0
$466$	726.118	−	1257.67i	0.0721819	−	0.125023i
$467$		−	10939.7i		−	1.08400i	−0.840379	−	0.541999i	$-0.817668\pi$
$467$		−	10939.7i		−	1.08400i	0.840379	−	0.541999i	$-0.182332\pi$
$468$	−10344.9	+	12626.2i	−1.02178	+	1.24711i
$469$	−9008.83			−0.886970
$470$		0			0
$471$	−453.561	+	1269.25i	−0.0443716	+	0.124170i
$472$	−8167.04	+	4715.24i	−0.796438	+	0.459823i
$473$	−12194.2	+	7040.33i	−1.18539	+	0.684386i
$474$	−5210.51	+	14581.1i	−0.504908	+	1.41294i
$475$		0			0
$476$	12374.1			1.19152
$477$	−14555.4	−	2390.92i	−1.39716	−	0.229503i
$478$		−	8496.21i		−	0.812986i
$479$	7311.85	−	12664.5i	0.697467	−	1.20805i	−0.271875	−	0.962333i	$-0.587644\pi$
$479$	7311.85	−	12664.5i	0.697467	−	1.20805i	0.969342	−	0.245716i	$-0.0790230\pi$
$480$		0			0
$481$	5823.49	+	10086.6i	0.552034	+	0.956151i
$482$	−12939.8	+	7470.81i	−1.22281	+	0.705987i
$483$	764.201	−	648.913i	0.0719925	−	0.0611316i
$484$	19829.9	−	34346.4i	1.86231	−	3.22562i
$485$		0			0
$486$	−17142.3	−	2507.13i	−1.59998	−	0.234003i
$487$		−	16473.6i		−	1.53284i	−0.642341	−	0.766419i	$-0.722037\pi$
$487$		−	16473.6i		−	1.53284i	0.642341	−	0.766419i	$-0.277963\pi$
$488$	−10619.6	−	6131.22i	−0.985093	−	0.568744i
$489$	4042.01	+	4760.13i	0.373795	+	0.440206i
$490$		0			0
$491$	−10264.6	−	17778.8i	−0.943450	−	1.63410i	−0.758825	−	0.651295i	$-0.774226\pi$
$491$	−10264.6	−	17778.8i	−0.943450	−	1.63410i	−0.184626	−	0.982809i	$-0.559107\pi$
$492$	3006.68	+	16486.0i	0.275511	+	1.51067i
$493$	−7371.56	−	4255.97i	−0.673425	−	0.388802i
$494$	2130.35			0.194026
$495$		0			0
$496$	−73.2768			−0.00663352
$497$	−7134.10	−	4118.87i	−0.643879	−	0.371744i
$498$	18197.4	+	6502.76i	1.63744	+	0.585132i
$499$	−7202.31	−	12474.8i	−0.646131	−	1.11913i	−0.984039	−	0.177953i	$-0.943053\pi$
$499$	−7202.31	−	12474.8i	−0.646131	−	1.11913i	0.337908	−	0.941179i	$-0.390281\pi$
$500$		0			0
$501$	−2935.63	+	8215.08i	−0.261785	+	0.732580i
$502$	22344.5	+	12900.6i	1.98663	+	1.14698i
$503$		−	2953.63i		−	0.261821i	−0.991394	−	0.130910i	$-0.958210\pi$
$503$		−	2953.63i		−	0.261821i	0.991394	−	0.130910i	$-0.0417901\pi$
$504$	9448.49	+	7741.30i	0.835058	+	0.684176i
$505$		0			0
$506$	1455.20	−	2520.48i	0.127849	−	0.221441i
$507$	−6.24932	−	34.2659i	−0.000547420	−	0.00300158i
$508$	−9672.98	+	5584.69i	−0.844821	+	0.487757i
$509$	−8684.44	−	15041.9i	−0.756250	−	1.30986i	−0.944750	−	0.327790i	$-0.893696\pi$
$509$	−8684.44	−	15041.9i	−0.756250	−	1.30986i	0.188500	−	0.982073i	$-0.439637\pi$
$510$		0			0
$511$	−3606.02	+	6245.80i	−0.312174	+	0.540701i
$512$			172.223i			0.0148657i
$513$	719.323	+	1196.80i	0.0619082	+	0.103002i
$514$	−5366.92			−0.460554
$515$		0			0
$516$	−9221.16	−	10859.4i	−0.786703	−	0.926473i
$517$	−27330.3	+	15779.1i	−2.32492	+	1.34229i
$518$	19827.1	−	11447.2i	1.68176	−	0.970966i
$519$	4763.20	−	868.699i	0.402854	−	0.0734714i
$520$		0			0
$521$	−6146.30			−0.516841			−0.258421	−	0.966033i	$-0.583202\pi$
$521$	−6146.30			−0.516841			−0.258421	+	0.966033i	$0.583202\pi$
$522$	−7791.48	−	20650.4i	−0.653303	−	1.73150i
$523$		−	4554.68i		−	0.380807i	−0.981706	−	0.190404i	$-0.939020\pi$
$523$		−	4554.68i		−	0.380807i	0.981706	−	0.190404i	$-0.0609797\pi$
$524$	−14070.7	+	24371.1i	−1.17305	+	2.03179i
$525$		0			0
$526$	−6627.03	−	11478.4i	−0.549339	−	0.951483i
$527$	6352.96	−	3667.88i	0.525122	−	0.303179i
$528$	−154.423	−	55.1824i	−0.0127280	−	0.00454831i
$529$	−6037.50	+	10457.3i	−0.496219	+	0.859476i
$530$		0			0
$531$	−10592.1	+	3996.46i	−0.865649	+	0.326613i
$532$		−	2586.05i		−	0.210751i
$533$	10119.0	+	5842.22i	0.822333	+	0.474774i
$534$	4699.25	−	857.037i	0.380817	−	0.0694525i
$535$		0			0
$536$	−5036.64	−	8723.72i	−0.405877	−	0.702999i
$537$	4053.53	−	3442.01i	0.325741	−	0.276599i
$538$	11605.8	+	6700.59i	0.930037	+	0.536957i
$539$	−4086.28			−0.326547
$540$		0			0
$541$	18091.8			1.43776			0.718879	−	0.695135i	$-0.244655\pi$
$541$	18091.8			1.43776			0.718879	+	0.695135i	$0.244655\pi$
$542$	2649.33	+	1529.59i	0.209960	+	0.121221i
$543$	−10456.3	+	8878.86i	−0.826379	+	0.701710i
$544$	−4336.23	−	7510.58i	−0.341754	−	0.591936i
$545$		0			0
$546$	22008.7	−	4013.89i	1.72507	−	0.314613i
$547$	13667.1	+	7890.69i	1.06830	+	0.616786i	0.927718	−	0.373283i	$-0.121768\pi$
$547$	13667.1	+	7890.69i	1.06830	+	0.616786i	0.140586	+	0.990068i	$0.455101\pi$
$548$		−	29699.7i		−	2.31516i
$549$	−11386.8	−	9329.41i	−0.885206	−	0.725263i
$550$		0			0
$551$	−889.453	+	1540.58i	−0.0687694	+	0.119112i
$552$	1055.62	+	377.223i	0.0813956	+	0.0290864i
$553$	11349.8	−	6552.83i	0.872774	−	0.503896i
$554$	1446.69	+	2505.75i	0.110946	+	0.192164i
$555$		0			0
$556$	13782.8	−	23872.5i	1.05130	−	1.82090i
$557$			13954.5i			1.06153i	0.847519	+	0.530766i	$0.178096\pi$
$557$			13954.5i			1.06153i	−0.847519	+	0.530766i	$0.821904\pi$
$558$	18770.0	+	3083.22i	1.42401	+	0.233913i
$559$	−9933.18			−0.751572
$560$		0			0
$561$	16150.4	−	2945.46i	1.21545	−	0.221671i
$562$	−14240.4	+	8221.69i	−1.06885	+	0.617102i
$563$	−11781.4	+	6801.97i	−0.881927	+	0.509181i	−0.871293	−	0.490762i	$-0.836718\pi$
$563$	−11781.4	+	6801.97i	−0.881927	+	0.509181i	−0.0106339	+	0.999943i	$0.503385\pi$
$564$	−20666.9	−	24338.7i	−1.54297	−	1.81710i
$565$		0			0
$566$	−2306.77			−0.171309
$567$	9686.28	+	11008.8i	0.717435	+	0.815392i
$568$		−	9211.10i		−	0.680438i
$569$	−6229.30	+	10789.5i	−0.458956	+	0.794935i	−0.998906	−	0.0467619i	$-0.985110\pi$
$569$	−6229.30	+	10789.5i	−0.458956	+	0.794935i	0.539950	+	0.841697i	$0.318443\pi$
$570$		0			0
$571$	6728.56	+	11654.2i	0.493137	+	0.854139i	0.999969	−	0.00790629i	$-0.00251668\pi$
$571$	6728.56	+	11654.2i	0.493137	+	0.854139i	−0.506831	+	0.862045i	$0.669183\pi$
$572$	34733.7	−	20053.5i	2.53897	−	1.46587i
$573$	758.207	+	4157.36i	0.0552785	+	0.303100i
$574$	11484.0	−	19890.8i	0.835074	−	1.44639i
$575$		0			0
$576$	3628.38	−	22088.8i	0.262470	−	1.59786i
$577$		−	3722.70i		−	0.268592i	−0.990941	−	0.134296i	$-0.957123\pi$
$577$		−	3722.70i		−	0.268592i	0.990941	−	0.134296i	$-0.0428774\pi$
$578$	−10476.5	−	6048.61i	−0.753918	−	0.435275i
$579$	1423.73	−	3984.18i	0.102190	−	0.285971i
$580$		0			0
$581$	−8177.99	−	14164.7i	−0.583959	−	1.01145i
$582$	5642.86	+	2016.45i	0.401897	+	0.143616i
$583$	31387.7	+	18121.7i	2.22975	+	1.28735i
$584$	−8064.19			−0.571401
$585$		0			0
$586$	−28349.3			−1.99847
$587$	−15190.4	−	8770.16i	−1.06810	−	0.616667i	−0.140437	−	0.990090i	$-0.544851\pi$
$587$	−15190.4	−	8770.16i	−1.06810	−	0.616667i	−0.927661	+	0.373423i	$0.878184\pi$
$588$	−741.777	−	4067.27i	−0.0520244	−	0.285257i
$589$	−766.548	−	1327.70i	−0.0536249	−	0.0928810i
$590$		0			0
$591$	13716.9	+	16153.9i	0.954718	+	1.12434i
$592$	−102.526	−	59.1933i	−0.00711788	−	0.00410951i
$593$		−	22350.6i		−	1.54777i	−0.633325	−	0.773886i	$-0.718310\pi$
$593$		−	22350.6i		−	1.54777i	0.633325	−	0.773886i	$-0.281690\pi$
$594$	37233.9	+	20632.7i	2.57193	+	1.42520i
$595$		0			0
$596$	−11306.9	+	19584.2i	−0.777097	+	1.34597i
$597$	−5317.38	+	4515.19i	−0.364533	+	0.309539i
$598$	1778.07	−	1026.57i	0.121590	−	0.0702000i
$599$	−1280.81	−	2218.43i	−0.0873665	−	0.151323i	0.819031	−	0.573750i	$-0.194512\pi$
$599$	−1280.81	−	2218.43i	−0.0873665	−	0.151323i	−0.906397	+	0.422427i	$0.861178\pi$
$600$		0			0
$601$	−6692.51	+	11591.8i	−0.454232	+	0.786752i	−0.998644	−	0.0520656i	$-0.983420\pi$
$601$	−6692.51	+	11591.8i	−0.454232	+	0.786752i	0.544412	+	0.838818i	$0.316753\pi$
$602$			19525.6i			1.32193i
$603$	−4268.87	−	11314.1i	−0.288295	−	0.764091i
$604$	−11315.3			−0.762270
$605$		0			0
$606$	−348.693	+	975.786i	−0.0233741	+	0.0654103i
$607$	24793.1	−	14314.3i	1.65786	−	0.957166i	0.684161	−	0.729331i	$-0.260169\pi$
$607$	24793.1	−	14314.3i	1.65786	−	0.957166i	0.973700	−	0.227835i	$-0.0731646\pi$
$608$	−1569.63	+	906.226i	−0.104699	+	0.0604479i
$609$	−6286.29	+	17591.6i	−0.418281	+	1.17052i
$610$		0			0
$611$	−22262.8			−1.47407
$612$	5863.50	+	15540.5i	0.387284	+	1.02645i
$613$			7188.12i			0.473614i	0.971557	+	0.236807i	$0.0761010\pi$
$613$			7188.12i			0.473614i	−0.971557	+	0.236807i	$0.923899\pi$
$614$	4497.63	−	7790.12i	0.295618	−	0.512025i
$615$		0			0
$616$	−15006.5	−	25992.0i	−0.981539	−	1.70008i
$617$	−13452.6	+	7766.88i	−0.877767	+	0.506779i	−0.869922	−	0.493190i	$-0.835831\pi$
$617$	−13452.6	+	7766.88i	−0.877767	+	0.506779i	−0.00784559	+	0.999969i	$0.502497\pi$
$618$	−26092.3	+	22155.9i	−1.69836	+	1.44214i
$619$	−11079.9	+	19191.0i	−0.719450	+	1.24612i	0.241769	+	0.970334i	$0.422272\pi$
$619$	−11079.9	+	19191.0i	−0.719450	+	1.24612i	−0.961218	+	0.275789i	$0.911061\pi$
$620$		0			0
$621$	1177.08	+	652.265i	0.0760624	+	0.0421490i
$622$		−	10547.2i		−	0.679908i
$623$	−3501.36	−	2021.51i	−0.225167	−	0.130000i
$624$	−74.8785	−	88.1818i	−0.00480375	−	0.00565721i
$625$		0			0
$626$	23559.4	+	40806.1i	1.50419	+	2.60534i
$627$	−615.569	−	3375.25i	−0.0392081	−	0.214983i
$628$	2901.85	+	1675.38i	0.184389	+	0.106457i
$629$	11851.7			0.751287
$630$		0			0
$631$	−25582.8			−1.61400			−0.807002	−	0.590549i	$-0.798911\pi$
$631$	−25582.8			−1.61400			−0.807002	+	0.590549i	$0.798911\pi$
$632$	12690.9	+	7327.10i	0.798761	+	0.461165i
$633$	−14459.0	−	5166.88i	−0.907891	−	0.324431i
$634$	3891.73	+	6740.68i	0.243786	+	0.422250i
$635$		0			0
$636$	−12339.6	+	34531.2i	−0.769334	+	2.15291i
$637$	−2496.46	−	1441.33i	−0.155280	−	0.0896510i
$638$			54231.5i			3.36527i
$639$	1792.34	−	10911.4i	0.110961	−	0.675506i
$640$		0			0
$641$	−1905.34	+	3300.14i	−0.117405	+	0.203351i	−0.918738	−	0.394867i	$-0.870791\pi$
$641$	−1905.34	+	3300.14i	−0.117405	+	0.203351i	0.801334	+	0.598217i	$0.204124\pi$
$642$	−1516.89	−	8317.33i	−0.0932507	−	0.511306i
$643$	23140.3	−	13360.0i	1.41923	−	0.819391i	0.422996	−	0.906131i	$-0.360978\pi$
$643$	23140.3	−	13360.0i	1.41923	−	0.819391i	0.996231	+	0.0867402i	$0.0276450\pi$
$644$	−1246.16	−	2158.41i	−0.0762509	−	0.132071i
$645$		0			0
$646$	1083.90	−	1877.37i	0.0660147	−	0.114341i
$647$		−	5114.23i		−	0.310759i	−0.987855	−	0.155380i	$-0.950340\pi$
$647$		−	5114.23i		−	0.310759i	0.987855	−	0.155380i	$-0.0496601\pi$
$648$	−5245.03	+	15534.5i	−0.317970	+	0.941750i
$649$	27816.8			1.68244
$650$		0			0
$651$	−10420.8	−	12272.2i	−0.627378	−	0.738842i
$652$	13444.5	−	7762.20i	0.807559	−	0.466244i
$653$	−7682.56	+	4435.53i	−0.460401	+	0.265813i	−0.712213	−	0.701964i	$-0.752307\pi$
$653$	−7682.56	+	4435.53i	−0.460401	+	0.265813i	0.251812	+	0.967776i	$0.418974\pi$
$654$	35595.4	−	6491.79i	2.12827	−	0.388148i
$655$		0			0
$656$	−118.767			−0.00706872
$657$	−9552.78	−	1569.17i	−0.567259	−	0.0931799i
$658$			43761.7i			2.59272i
$659$	−12102.2	+	20961.7i	−0.715382	+	1.23908i	0.247430	+	0.968906i	$0.420414\pi$
$659$	−12102.2	+	20961.7i	−0.715382	+	1.23908i	−0.962812	+	0.270172i	$0.912920\pi$
$660$		0			0
$661$	−10689.8	−	18515.2i	−0.629023	−	1.08950i	−0.987748	−	0.156056i	$-0.950122\pi$
$661$	−10689.8	−	18515.2i	−0.629023	−	1.08950i	0.358726	−	0.933443i	$-0.383211\pi$
$662$	−33078.9	+	19098.1i	−1.94207	+	1.12125i
$663$	10905.8	+	3897.14i	0.638832	+	0.228284i
$664$	9144.28	−	15838.4i	0.534438	−	0.925674i
$665$		0			0
$666$	23771.6	+	19476.4i	1.38308	+	1.13318i
$667$			1714.43i			0.0995248i
$668$	18781.9	+	10843.7i	1.08787	+	0.628079i
$669$	17926.5	−	3269.38i	1.03599	−	0.188941i
$670$		0			0
$671$	18085.0	+	31324.2i	1.04048	+	1.80217i
$672$	−14508.4	+	12319.6i	−0.832849	+	0.707203i
$673$	−25722.1	−	14850.7i	−1.47328	−	0.850597i	−0.473730	−	0.880670i	$-0.657093\pi$
$673$	−25722.1	−	14850.7i	−1.47328	−	0.850597i	−0.999548	+	0.0300732i	$0.990426\pi$
$674$	−35936.6			−2.05375
$675$		0			0
$676$	−86.5900			−0.00492661
$677$	2304.91	+	1330.74i	0.130849	+	0.0755459i	0.563996	−	0.825778i	$-0.309263\pi$
$677$	2304.91	+	1330.74i	0.130849	+	0.0755459i	−0.433147	+	0.901324i	$0.642597\pi$
$678$	−14727.6	+	12505.8i	−0.834235	+	0.708381i
$679$	−2535.93	−	4392.36i	−0.143328	−	0.248252i
$680$		0			0
$681$	−3337.14	+	608.618i	−0.187782	+	0.0342471i
$682$	−40476.1	−	23368.9i	−2.27259	−	1.31208i
$683$			28698.1i			1.60776i	0.594789	+	0.803882i	$0.297235\pi$
$683$			28698.1i			1.60776i	−0.594789	+	0.803882i	$0.702765\pi$
$684$	3247.80	−	1225.41i	0.181554	−	0.0685010i
$685$		0			0
$686$	12944.0	−	22419.7i	0.720415	−	1.24780i
$687$	−22427.9	−	8014.51i	−1.24553	−	0.445084i
$688$	87.4396	−	50.4833i	0.00484535	−	0.00279747i
$689$	12783.9	+	22142.4i	0.706863	+	1.22432i
$690$		0			0
$691$	−8412.62	+	14571.1i	−0.463142	+	0.802186i	−0.999116	−	0.0420492i	$-0.986611\pi$
$691$	−8412.62	+	14571.1i	−0.463142	+	0.802186i	0.535973	+	0.844235i	$0.319945\pi$
$692$		−	12036.6i		−	0.661220i
$693$	−12718.9	−	33710.0i	−0.697189	−	1.84781i
$694$	5543.99			0.303238
$695$		0			0
$696$	−20549.4	+	3747.74i	−1.11914	+	0.204106i
$697$	10296.9	−	5944.92i	0.559574	−	0.323070i
$698$	−5539.88	+	3198.45i	−0.300412	+	0.173443i
$699$	−1067.94	−	1257.67i	−0.0577870	−	0.0680537i
$700$		0			0
$701$	−998.795			−0.0538145			−0.0269073	−	0.999638i	$-0.508566\pi$
$701$	−998.795			−0.0538145			−0.0269073	+	0.999638i	$0.508566\pi$
$702$	15469.9	+	25738.6i	0.831730	+	1.38382i
$703$		−	2476.88i		−	0.132884i
$704$	−27500.8	+	47632.9i	−1.47227	+	2.55004i
$705$		0			0
$706$	6010.66	+	10410.8i	0.320417	+	0.554978i
$707$	759.545	−	438.523i	0.0404040	−	0.0233272i
$708$	5049.54	+	27687.3i	0.268041	+	1.46971i
$709$	16626.9	−	28798.6i	0.880727	−	1.52546i	0.0301937	−	0.999544i	$-0.490388\pi$
$709$	16626.9	−	28798.6i	0.880727	−	1.52546i	0.850534	−	0.525921i	$-0.176279\pi$
$710$		0			0
$711$	13607.8	+	11149.1i	0.717768	+	0.588078i
$712$		−	4520.73i		−	0.237952i
$713$	−1279.58	−	738.765i	−0.0672099	−	0.0388036i
$714$	7660.56	−	21437.4i	0.401526	−	1.12363i
$715$		0			0
$716$	−6609.97	−	11448.8i	−0.345009	−	0.597573i
$717$	−9089.81	−	3248.21i	−0.473452	−	0.169186i
$718$	14565.9	+	8409.62i	0.757095	+	0.437109i
$719$	−1178.94			−0.0611503			−0.0305752	−	0.999532i	$-0.509734\pi$
$719$	−1178.94			−0.0611503			−0.0305752	+	0.999532i	$0.509734\pi$
$720$		0			0
$721$	28972.0			1.49650
$722$	26775.0	+	15458.6i	1.38014	+	0.796826i
$723$	3045.71	+	16700.1i	0.156668	+	0.859034i
$724$	17050.8	+	29532.9i	0.875260	+	1.51600i
$725$		0			0
$726$	−47226.8	−	55617.4i	−2.41426	−	2.84319i
$727$	10978.3	+	6338.35i	0.560061	+	0.323351i	0.753170	−	0.657826i	$-0.228524\pi$
$727$	10978.3	+	6338.35i	0.560061	+	0.323351i	−0.193109	+	0.981177i	$0.561857\pi$
$728$		−	21172.6i		−	1.07790i
$729$	−9236.02	+	17381.5i	−0.469238	+	0.883072i
$730$		0			0
$731$	−5053.90	+	8753.61i	−0.255712	+	0.442906i
$732$	−27895.5	+	23687.1i	−1.40853	+	1.19604i
$733$	8492.98	−	4903.42i	0.427961	−	0.247083i	−0.270517	−	0.962715i	$-0.587195\pi$
$733$	8492.98	−	4903.42i	0.427961	−	0.247083i	0.698478	+	0.715632i	$0.253861\pi$
$734$	−26137.5	−	45271.4i	−1.31438	−	2.27657i
$735$		0			0
$736$	−873.381	+	1512.74i	−0.0437408	+	0.0757613i
$737$			29712.8i			1.48506i
$738$	30422.5	+	4997.30i	1.51744	+	0.249259i
$739$	29970.4			1.49185			0.745927	−	0.666028i	$-0.232007\pi$
$739$	29970.4			1.49185			0.745927	+	0.666028i	$0.232007\pi$
$740$		0			0
$741$	814.460	−	2279.19i	0.0403778	−	0.112994i
$742$	43525.1	−	25129.2i	2.15345	−	1.24329i
$743$	18790.6	−	10848.8i	0.927808	−	0.535670i	0.0416904	−	0.999131i	$-0.486726\pi$
$743$	18790.6	−	10848.8i	0.927808	−	0.535670i	0.886118	+	0.463460i	$0.153392\pi$
$744$	6057.78	−	16952.1i	0.298507	−	0.835344i
$745$		0			0
$746$	−10335.8			−0.507267
$747$	13914.2	−	16982.7i	0.681516	−	0.831812i
$748$		−	40812.1i		−	1.99497i
$749$	−3577.92	+	6197.14i	−0.174545	+	0.302321i
$750$		0			0
$751$	−8512.10	−	14743.4i	−0.413596	−	0.716370i	0.581684	−	0.813415i	$-0.302394\pi$
$751$	−8512.10	−	14743.4i	−0.413596	−	0.716370i	−0.995280	+	0.0970452i	$0.969061\pi$
$752$	195.974	−	113.146i	0.00950324	−	0.00548670i
$753$	22344.5	−	18973.6i	1.08138	−	0.918243i
$754$	−19128.8	+	33132.0i	−0.923911	+	1.60026i
$755$		0			0
$756$	31244.2	−	18779.0i	1.50310	−	0.903422i
$757$		−	30745.2i		−	1.47616i	−0.674714	−	0.738080i	$-0.735733\pi$
$757$		−	30745.2i		−	1.47616i	0.674714	−	0.738080i	$-0.264267\pi$
$758$	−46800.5	−	27020.3i	−2.24257	−	1.29475i
$759$	−2140.24	−	2520.48i	−0.102353	−	0.120537i
$760$		0			0
$761$	−10748.3	−	18616.6i	−0.511992	−	0.886797i	−0.999903	−	0.0139035i	$-0.995574\pi$
$761$	−10748.3	−	18616.6i	−0.511992	−	0.886797i	0.487911	−	0.872893i	$-0.337759\pi$
$762$	3686.81	+	20215.3i	0.175274	+	0.961052i
$763$	−26521.7	−	15312.3i	−1.25839	−	0.726530i
$764$	10505.7			0.497489
$765$		0			0
$766$	36955.5			1.74316
$767$	16994.3	+	9811.66i	0.800037	+	0.461902i
$768$	−19800.6	−	7075.65i	−0.930327	−	0.332449i
$769$	11028.7	+	19102.4i	0.517174	+	0.895772i	0.999801	+	0.0199457i	$0.00634935\pi$
$769$	11028.7	+	19102.4i	0.517174	+	0.895772i	−0.482627	+	0.875826i	$0.660317\pi$
$770$		0			0
$771$	−2051.84	+	5741.89i	−0.0958434	+	0.268209i
$772$	−9108.93	−	5259.04i	−0.424660	−	0.245178i
$773$			30155.8i			1.40314i	0.712601	+	0.701570i	$0.247517\pi$
$773$			30155.8i			1.40314i	−0.712601	+	0.701570i	$0.752483\pi$
$774$	−24522.0	+	9252.26i	−1.13879	+	0.429671i
$775$		0			0
$776$	2835.57	−	4911.35i	0.131174	−	0.227200i
$777$	−4666.81	−	25588.7i	−0.215471	−	1.18146i
$778$	−12280.3	+	7090.04i	−0.565900	+	0.326723i
$779$	−1242.42	−	2151.94i	−0.0571431	−	0.0989747i
$780$		0			0
$781$	−13584.8	+	23529.6i	−0.622411	+	1.07805i
$782$		−	2089.23i		−	0.0955381i
$783$	−25071.9	+	440.943i	−1.14431	+	0.0201252i
$784$	29.3010			0.00133478
$785$		0			0
$786$	33510.7	+	39464.4i	1.52072	+	1.79090i
$787$	2813.47	−	1624.36i	0.127433	−	0.0735733i	−0.434929	−	0.900465i	$-0.643226\pi$
$787$	2813.47	−	1624.36i	0.127433	−	0.0735733i	0.562361	+	0.826892i	$0.309893\pi$
$788$	45625.2	−	26341.7i	2.06260	−	1.19084i
$789$	−14813.9	+	2701.72i	−0.668427	+	0.121906i
$790$		0			0
$791$	16353.1			0.735081
$792$	25532.3	−	31162.9i	1.14552	−	1.39814i
$793$			25516.1i			1.14263i
$794$	27418.8	−	47490.8i	1.22551	−	2.12265i
$795$		0			0
$796$	8670.90	+	15018.4i	0.386095	+	0.668737i
$797$	23997.7	−	13855.1i	1.06655	−	0.615775i	0.139316	−	0.990248i	$-0.455510\pi$
$797$	23997.7	−	13855.1i	1.06655	−	0.615775i	0.927238	+	0.374473i	$0.122176\pi$
$798$	−4480.18	−	1600.98i	−0.198743	−	0.0710199i
$799$	−11327.1	+	19619.0i	−0.501530	+	0.868675i
$800$		0			0
$801$	879.667	−	5355.23i	0.0388034	−	0.236227i
$802$			58785.4i			2.58826i
$803$	20599.8	+	11893.3i	0.905296	+	0.522673i
$804$	−29574.6	+	5393.73i	−1.29728	+	0.236595i
$805$		0			0
$806$	−16485.6	−	28553.8i	−0.720445	−	1.24785i
$807$	11605.8	−	9854.90i	0.506248	−	0.429875i
$808$	849.290	+	490.338i	0.0369776	+	0.0213491i
$809$	2244.10			0.0975259			0.0487630	−	0.998810i	$-0.484472\pi$
$809$	2244.10			0.0975259			0.0487630	+	0.998810i	$0.484472\pi$
$810$		0			0
$811$	−2739.73			−0.118625			−0.0593126	−	0.998239i	$-0.518891\pi$
$811$	−2739.73			−0.118625			−0.0593126	+	0.998239i	$0.518891\pi$
$812$	40219.2	+	23220.6i	1.73820	+	1.00355i
$813$	2649.33	−	2249.65i	0.114288	−	0.0970462i
$814$	−37755.0	−	65393.5i	−1.62569	−	2.81578i
$815$		0			0
$816$	−115.808	+	21.1207i	−0.00496823	+	0.000906092i
$817$	1829.41	+	1056.21i	0.0783390	+	0.0452290i
$818$		−	10176.6i		−	0.434984i
$819$	4119.88	−	25080.9i	0.175776	−	1.07008i
$820$		0			0
$821$	8616.06	−	14923.5i	0.366264	−	0.634388i	−0.622714	−	0.782449i	$-0.713970\pi$
$821$	8616.06	−	14923.5i	0.366264	−	0.634388i	0.988978	+	0.148062i	$0.0473034\pi$
$822$	−51453.1	−	18386.6i	−2.18325	−	0.780177i
$823$	16702.1	−	9642.94i	0.707409	−	0.408422i	−0.102692	−	0.994713i	$-0.532746\pi$
$823$	16702.1	−	9642.94i	0.707409	−	0.408422i	0.810101	+	0.586291i	$0.199412\pi$
$824$	16197.6	+	28055.1i	0.684795	+	1.18610i
$825$		0			0
$826$	19286.7	−	33405.5i	0.812433	−	1.40717i
$827$		−	26379.4i		−	1.10919i	−0.832120	−	0.554595i	$-0.812873\pi$
$827$		−	26379.4i		−	1.10919i	0.832120	−	0.554595i	$-0.187127\pi$
$828$	2120.24	−	2587.82i	0.0889896	−	0.108615i
$829$	8718.15			0.365252			0.182626	−	0.983182i	$-0.441540\pi$
$829$	8718.15			0.365252			0.182626	+	0.983182i	$0.441540\pi$
$830$		0			0
$831$	3233.90	−	589.790i	0.134997	−	0.0246205i
$832$	−33602.6	+	19400.4i	−1.40019	+	0.808401i
$833$	−2540.35	+	1466.67i	−0.105664	+	0.0610049i
$834$	−32825.1	−	38657.0i	−1.36288	−	1.60501i
$835$		0			0
$836$	−8529.28			−0.352860
$837$	10474.6	−	18902.6i	0.432565	−	0.780610i
$838$		−	44256.9i		−	1.82438i
$839$	−6738.10	+	11670.7i	−0.277265	+	0.480236i	−0.970704	−	0.240279i	$-0.922761\pi$
$839$	−6738.10	+	11670.7i	−0.277265	+	0.480236i	0.693439	+	0.720515i	$0.256095\pi$
$840$		0			0
$841$	−3778.58	−	6544.70i	−0.154930	−	0.268346i
$842$	−39460.2	+	22782.4i	−1.61507	+	0.932462i
$843$	3351.83	+	18378.6i	0.136943	+	0.750880i
$844$	−19085.6	+	33057.3i	−0.778383	+	1.34820i
$845$		0			0
$846$	−54959.9	+	20736.6i	−2.23352	+	0.842718i
$847$			61755.7i			2.50526i
$848$	−225.068	−	129.943i	−0.00911423	−	0.00526210i
$849$	−881.907	+	2467.93i	−0.0356501	+	0.0997636i
$850$		0			0
$851$	−1193.56	−	2067.30i	−0.0480783	−	0.0832740i
$852$	−25886.1	−	9250.31i	−1.04090	−	0.371960i
$853$	24453.6	+	14118.3i	0.981567	+	0.566708i	0.902743	−	0.430181i	$-0.141550\pi$
$853$	24453.6	+	14118.3i	0.981567	+	0.566708i	0.0788242	+	0.996889i	$0.474883\pi$
$854$	50156.8			2.00975
$855$		0			0
$856$	−8001.36			−0.319487
$857$	7324.98	+	4229.08i	0.291968	+	0.168568i	0.638829	−	0.769349i	$-0.279419\pi$
$857$	7324.98	+	4229.08i	0.291968	+	0.168568i	−0.346861	+	0.937917i	$0.612752\pi$
$858$	−13238.6	−	72588.9i	−0.526757	−	2.88828i
$859$	−11527.2	−	19965.6i	−0.457860	−	0.793036i	0.540988	−	0.841030i	$-0.318050\pi$
$859$	−11527.2	−	19965.6i	−0.457860	−	0.793036i	−0.998848	+	0.0479940i	$0.984717\pi$
$860$		0			0
$861$	−16890.1	−	19890.8i	−0.668539	−	0.787315i
$862$	9749.48	+	5628.86i	0.385230	+	0.222413i
$863$		−	42314.4i		−	1.66906i	−0.550963	−	0.834529i	$-0.685740\pi$
$863$		−	42314.4i		−	1.66906i	0.550963	−	0.834529i	$-0.314260\pi$
$864$	−22347.0	−	12383.3i	−0.879932	−	0.487602i
$865$		0			0
$866$	17879.2	−	30967.8i	0.701572	−	1.21516i
$867$	−10476.5	+	8895.99i	−0.410381	+	0.348470i
$868$	−34661.7	+	20011.9i	−1.35541	+	0.782545i
$869$	−21612.5	−	37433.9i	−0.843674	−	1.46129i
$870$		0			0
$871$	−10480.4	+	18152.7i	−0.407711	+	0.706176i
$872$		−	34243.1i		−	1.32984i
$873$	4314.67	−	5266.19i	0.167273	−	0.204162i
$874$	−436.627			−0.0168983
$875$		0			0
$876$	−8098.51	+	22663.0i	−0.312356	+	0.874098i
$877$	8816.15	−	5090.00i	0.339453	−	0.195983i	−0.320577	−	0.947222i	$-0.603877\pi$
$877$	8816.15	−	5090.00i	0.339453	−	0.195983i	0.660030	+	0.751239i	$0.270544\pi$
$878$	−24604.0	+	14205.2i	−0.945725	+	0.546014i
$879$	−10838.3	+	30330.0i	−0.415890	+	1.16383i
$880$		0			0
$881$	6030.64			0.230621			0.115311	−	0.993329i	$-0.463214\pi$
$881$	6030.64			0.230621			0.115311	+	0.993329i	$0.463214\pi$
$882$	−7505.53	−	1232.88i	−0.286535	−	0.0470673i
$883$		−	30238.0i		−	1.15242i	−0.817301	−	0.576211i	$-0.804531\pi$
$883$		−	30238.0i		−	1.15242i	0.817301	−	0.576211i	$-0.195469\pi$
$884$	14395.4	−	24933.6i	0.547704	−	0.948651i
$885$		0			0
$886$	6824.57	+	11820.5i	0.258776	+	0.448214i
$887$	−16260.7	+	9388.09i	−0.615535	+	0.355379i	−0.775129	−	0.631804i	$-0.782315\pi$
$887$	−16260.7	+	9388.09i	−0.615535	+	0.355379i	0.159594	+	0.987183i	$0.448982\pi$
$888$	22169.8	−	18825.2i	0.837805	−	0.711412i
$889$	8696.14	−	15062.1i	0.328075	−	0.568243i
$890$		0			0
$891$	36309.2	−	31947.2i	1.36521	−	1.20120i
$892$		−	45300.3i		−	1.70041i
$893$	4100.17	+	2367.23i	0.153647	+	0.0887082i
$894$	26928.6	+	31712.8i	1.00741	+	1.18639i
$895$		0			0
$896$	23483.4	+	40674.4i	0.875586	+	1.51656i
$897$	−418.514	−	2294.77i	−0.0155783	−	0.0854182i
$898$	−3210.16	−	1853.39i	−0.119292	−	0.0688735i
$899$	27531.8			1.02140
$900$		0			0
$901$	26017.3			0.962000
$902$	−65603.8	−	37876.4i	−2.42169	−	1.39817i
$903$	20889.7	+	7464.86i	0.769841	+	0.275100i
$904$	9142.66	+	15835.6i	0.336372	+	0.582614i
$905$		0			0
$906$	−7005.07	+	19603.0i	−0.256874	+	0.718838i
$907$	−32608.1	−	18826.3i	−1.19375	−	0.689213i	−0.234597	−	0.972093i	$-0.575377\pi$
$907$	−32608.1	−	18826.3i	−1.19375	−	0.689213i	−0.959155	+	0.282880i	$0.908710\pi$
$908$			8432.97i			0.308214i
$909$	910.651	+	746.111i	0.0332282	+	0.0272243i
$910$		0			0
$911$	23793.1	−	41210.8i	0.865312	−	1.49877i	−0.00142411	−	0.999999i	$-0.500453\pi$
$911$	23793.1	−	41210.8i	0.865312	−	1.49877i	0.866737	−	0.498766i	$-0.166213\pi$
$912$	4.41399	+	24.2025i	0.000160265	+	0.000878756i
$913$	−46717.9	+	26972.6i	−1.69347	+	0.977724i
$914$	−3594.32	−	6225.54i	−0.130076	−	0.225298i
$915$		0			0
$916$	−29604.3	+	51276.2i	−1.06785	+	1.84958i
$917$		−	43819.9i		−	1.57804i
$918$	30553.0	−	537.340i	1.09848	−	0.0193190i
$919$	−32177.3			−1.15499			−0.577493	−	0.816396i	$-0.695969\pi$
$919$	−32177.3			−1.15499			−0.577493	+	0.816396i	$0.695969\pi$
$920$		0			0
$921$	−6614.88	−	7790.12i	−0.236664	−	0.278711i
$922$	8169.99	−	4716.94i	0.291827	−	0.168486i
$923$	−16598.9	+	9583.40i	−0.591940	+	0.341757i
$924$	−88116.2	+	16070.4i	−3.13724	+	0.572161i
$925$		0			0
$926$	−12729.3			−0.451741
$927$	13728.5	+	36385.7i	0.486411	+	1.28917i
$928$		−	32548.6i		−	1.15136i
$929$	20321.8	−	35198.4i	0.717694	−	1.24308i	−0.244218	−	0.969720i	$-0.578531\pi$
$929$	20321.8	−	35198.4i	0.717694	−	1.24308i	0.961911	−	0.273362i	$-0.0881355\pi$
$930$		0			0
$931$	306.518	+	530.905i	0.0107903	+	0.0186893i
$932$	−3552.18	+	2050.85i	−0.124845	+	0.0720792i
$933$	−11284.1	−	4032.31i	−0.395952	−	0.141492i
$934$	−25016.7	+	43330.2i	−0.876415	+	1.51799i
$935$		0			0
$936$	26590.5	−	10032.7i	0.928567	−	0.350352i
$937$		−	6077.87i		−	0.211905i	−0.994371	−	0.105953i	$-0.966211\pi$
$937$		−	6077.87i		−	0.211905i	0.994371	−	0.105953i	$-0.0337892\pi$
$938$	35682.5	+	20601.3i	1.24208	+	0.717118i
$939$	52664.2	−	9604.75i	1.83028	−	0.333801i
$940$		0			0
$941$	−732.293	−	1268.37i	−0.0253688	−	0.0439401i	0.853062	−	0.521809i	$-0.174743\pi$
$941$	−732.293	−	1268.37i	−0.0253688	−	0.0439401i	−0.878431	+	0.477869i	$0.841409\pi$
$942$	4698.99	−	3990.09i	0.162528	−	0.138009i
$943$	−2073.95	−	1197.39i	−0.0716193	−	0.0413494i
$944$	−199.463			−0.00687707
$945$		0			0
$946$	64399.0			2.21331
$947$	−9187.43	−	5304.36i	−0.315260	−	0.182015i	0.334018	−	0.942567i	$-0.391595\pi$
$947$	−9187.43	−	5304.36i	−0.315260	−	0.182015i	−0.649278	+	0.760551i	$0.724929\pi$
$948$	33336.4	−	28307.2i	1.14211	−	0.969806i
$949$	8390.14	+	14532.1i	0.286992	+	0.497085i
$950$		0			0
$951$	8699.48	−	1586.59i	0.296635	−	0.0540995i
$952$	−18658.4	−	10772.4i	−0.635211	−	0.366739i
$953$		−	43623.4i		−	1.48279i	−0.671068	−	0.741396i	$-0.734164\pi$
$953$		−	43623.4i		−	1.48279i	0.671068	−	0.741396i	$-0.265836\pi$
$954$	52184.1	+	42755.3i	1.77099	+	1.45100i
$955$		0			0
$956$	−11998.4	+	20781.8i	−0.405915	+	0.703065i
$957$	58020.4	+	20733.4i	1.95981	+	0.700329i
$958$	−57922.1	+	33441.3i	−1.95342	+	1.12781i
$959$	23123.3	+	40050.7i	0.778613	+	1.34860i
$960$		0			0
$961$	3031.76	−	5251.17i	0.101768	−	0.176267i
$962$		−	53268.4i		−	1.78528i
$963$	−9478.35	−	1556.95i	−0.317171	−	0.0520996i
$964$	42201.2			1.40997
$965$		0			0
$966$	−4510.80	+	822.668i	−0.150241	+	0.0274005i
$967$	−4399.73	+	2540.19i	−0.146314	+	0.0844745i	−0.571370	−	0.820693i	$-0.693588\pi$
$967$	−4399.73	+	2540.19i	−0.146314	+	0.0844745i	0.425056	+	0.905167i	$0.360254\pi$
$968$	−59801.3	+	34526.3i	−1.98563	+	1.14640i
$969$	−1594.15	−	1877.37i	−0.0528497	−	0.0622393i
$970$		0			0
$971$	9875.60			0.326388			0.163194	−	0.986594i	$-0.447820\pi$
$971$	9875.60			0.326388			0.163194	+	0.986594i	$0.447820\pi$
$972$	38389.7	+	30340.9i	1.26682	+	1.00122i
$973$			42923.4i			1.41425i
$974$	−37671.8	+	65249.4i	−1.23930	+	2.14654i
$975$		0			0
$976$	−129.680	−	224.613i	−0.00425304	−	0.00736648i
$977$	−21287.6	+	12290.4i	−0.697084	+	0.402461i	−0.806260	−	0.591561i	$-0.798512\pi$
$977$	−21287.6	+	12290.4i	−0.697084	+	0.402461i	0.109177	+	0.994022i	$0.465179\pi$
$978$	−5124.31	−	28097.3i	−0.167543	−	0.918664i
$979$	−6667.32	+	11548.1i	−0.217659	+	0.376997i
$980$		0			0
$981$	6663.21	−	40564.2i	0.216860	−	1.32020i
$982$			93891.8i			3.05113i
$983$	27592.1	+	15930.3i	0.895270	+	0.516885i	0.875663	−	0.482923i	$-0.160425\pi$
$983$	27592.1	+	15930.3i	0.895270	+	0.516885i	0.0196076	+	0.999808i	$0.493758\pi$
$984$	9818.48	−	27476.1i	0.318091	−	0.890149i
$985$		0			0
$986$	19465.0	+	33714.4i	0.628695	+	1.08893i
$987$	46819.1	+	16730.6i	1.50990	+	0.539556i
$988$	−5210.85	−	3008.49i	−0.167793	−	0.0968752i
$989$	2035.86			0.0654566
$990$		0			0
$991$	−36921.3			−1.18350			−0.591748	−	0.806123i	$-0.701562\pi$
$991$	−36921.3			−1.18350			−0.591748	+	0.806123i	$0.701562\pi$
$992$	24292.9	+	14025.5i	0.777520	+	0.448902i
$993$	7785.95	+	42691.4i	0.248821	+	1.36432i
$994$	18838.0	+	32628.4i	0.601112	+	1.04116i
$995$		0			0
$996$	−35327.7	−	41604.2i	−1.12390	−	1.32357i
$997$	−3233.84	−	1867.06i	−0.102725	−	0.0593083i	0.447757	−	0.894155i	$-0.352223\pi$
$997$	−3233.84	−	1867.06i	−0.102725	−	0.0593083i	−0.550482	+	0.834847i	$0.685556\pi$
$998$			65880.7i			2.08959i
$999$	29925.3	−	17986.3i	0.947743	−	0.569632i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.4.k.c.124.1		12
5.2	odd	4		45.4.e.b.16.3	✓	6
5.3	odd	4		225.4.e.c.151.1		6
5.4	even	2	inner	225.4.k.c.124.6		12
9.4	even	3	inner	225.4.k.c.49.6		12
15.2	even	4		135.4.e.b.46.1		6
45.2	even	12		405.4.a.j.1.3		3
45.4	even	6	inner	225.4.k.c.49.1		12
45.7	odd	12		405.4.a.h.1.1		3
45.13	odd	12		225.4.e.c.76.1		6
45.22	odd	12		45.4.e.b.31.3	yes	6
45.32	even	12		135.4.e.b.91.1		6
45.38	even	12		2025.4.a.q.1.1		3
45.43	odd	12		2025.4.a.s.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.4.e.b.16.3	✓	6	5.2	odd	4
45.4.e.b.31.3	yes	6	45.22	odd	12
135.4.e.b.46.1		6	15.2	even	4
135.4.e.b.91.1		6	45.32	even	12
225.4.e.c.76.1		6	45.13	odd	12
225.4.e.c.151.1		6	5.3	odd	4
225.4.k.c.49.1		12	45.4	even	6	inner
225.4.k.c.49.6		12	9.4	even	3	inner
225.4.k.c.124.1		12	1.1	even	1	trivial
225.4.k.c.124.6		12	5.4	even	2	inner
405.4.a.h.1.1		3	45.7	odd	12
405.4.a.j.1.3		3	45.2	even	12
2025.4.a.q.1.1		3	45.38	even	12
2025.4.a.s.1.3		3	45.43	odd	12

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:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	225.k (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-3.96084 - 2.28679i) q^{2} +(-3.96084 + 3.36330i) q^{3} +(6.45882 + 11.1870i) q^{4} +(23.3794 - 4.26387i) q^{6} +(-17.4197 - 10.0573i) q^{7} -22.4912i q^{8} +(4.37646 - 26.6429i) q^{9} +O(q^{10})\)	\(q+(-3.96084 - 2.28679i) q^{2} +(-3.96084 + 3.36330i) q^{3} +(6.45882 + 11.1870i) q^{4} +(23.3794 - 4.26387i) q^{6} +(-17.4197 - 10.0573i) q^{7} -22.4912i q^{8} +(4.37646 - 26.6429i) q^{9} +(-33.1708 + 57.4535i) q^{11} +(-63.2076 - 22.5870i) q^{12} +(-40.5305 + 23.4003i) q^{13} +(45.9977 + 79.6704i) q^{14} +(0.237854 - 0.411975i) q^{16} +47.6233i q^{17} +(-78.2613 + 95.5203i) q^{18} +9.95276 q^{19} +(102.822 - 18.7524i) q^{21} +(262.768 - 151.709i) q^{22} +(8.30695 - 4.79602i) q^{23} +(75.6447 + 89.0841i) q^{24} +214.046 q^{26} +(72.2737 + 120.248i) q^{27} -259.832i q^{28} +(-89.3675 + 154.789i) q^{29} +(-77.0186 - 133.400i) q^{31} +(-157.708 + 91.0527i) q^{32} +(-61.8491 - 339.127i) q^{33} +(108.905 - 188.628i) q^{34} +(326.322 - 123.123i) q^{36} -248.864i q^{37} +(-39.4213 - 22.7599i) q^{38} +(81.8326 - 229.001i) q^{39} +(-124.832 - 216.216i) q^{41} +(-450.145 - 160.857i) q^{42} +(183.809 + 106.122i) q^{43} -856.976 q^{44} -43.8700 q^{46} +(411.963 + 237.847i) q^{47} +(0.443494 + 2.43174i) q^{48} +(30.7973 + 53.3425i) q^{49} +(-160.171 - 188.628i) q^{51} +(-523.559 - 302.277i) q^{52} -546.314i q^{53} +(-11.2831 - 641.556i) q^{54} +(-226.200 + 391.790i) q^{56} +(-39.4213 + 33.4741i) q^{57} +(707.940 - 408.729i) q^{58} +(-209.648 - 363.121i) q^{59} +(272.605 - 472.165i) q^{61} +704.502i q^{62} +(-344.192 + 420.097i) q^{63} +829.068 q^{64} +(-530.538 + 1484.66i) q^{66} +(387.872 - 223.938i) q^{67} +(-532.762 + 307.590i) q^{68} +(-16.7720 + 46.9350i) q^{69} +409.542 q^{71} +(-599.232 - 98.4319i) q^{72} -358.548i q^{73} +(-569.100 + 985.710i) q^{74} +(64.2831 + 111.342i) q^{76} +(1155.65 - 667.215i) q^{77} +(-847.803 + 719.902i) q^{78} +(-325.776 + 564.260i) q^{79} +(-690.693 - 233.204i) q^{81} +1141.86i q^{82} +(704.202 + 406.571i) q^{83} +(873.893 + 1029.15i) q^{84} +(-485.359 - 840.667i) q^{86} +(-166.631 - 913.663i) q^{87} +(1292.20 + 746.051i) q^{88} +201.000 q^{89} +941.373 q^{91} +(107.306 + 61.9532i) q^{92} +(753.723 + 269.340i) q^{93} +(-1087.81 - 1884.14i) q^{94} +(318.418 - 891.064i) q^{96} +(218.367 + 126.074i) q^{97} -281.708i q^{98} +(1385.56 + 1135.21i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 22 q^{4} + 168 q^{6} - 114 q^{9}+O(q^{10}) \) 12 * q + 22 * q^4 + 168 * q^6 - 114 * q^9	\( 12 q + 22 q^{4} + 168 q^{6} - 114 q^{9} - 28 q^{11} - 54 q^{14} + 26 q^{16} + 656 q^{19} - 288 q^{21} + 126 q^{24} + 1736 q^{26} - 670 q^{29} + 704 q^{31} - 104 q^{34} + 2172 q^{36} + 780 q^{39} - 374 q^{41} - 3928 q^{44} - 804 q^{46} + 860 q^{49} - 360 q^{51} - 1278 q^{54} - 1410 q^{56} - 596 q^{59} + 2878 q^{61} + 6276 q^{64} - 1932 q^{66} + 1746 q^{69} + 280 q^{71} - 640 q^{74} - 408 q^{76} - 764 q^{79} - 2502 q^{81} + 1818 q^{84} - 3160 q^{86} - 6876 q^{89} - 2840 q^{91} - 4154 q^{94} + 2310 q^{96} + 1524 q^{99}+O(q^{100}) \) 12 * q + 22 * q^4 + 168 * q^6 - 114 * q^9 - 28 * q^11 - 54 * q^14 + 26 * q^16 + 656 * q^19 - 288 * q^21 + 126 * q^24 + 1736 * q^26 - 670 * q^29 + 704 * q^31 - 104 * q^34 + 2172 * q^36 + 780 * q^39 - 374 * q^41 - 3928 * q^44 - 804 * q^46 + 860 * q^49 - 360 * q^51 - 1278 * q^54 - 1410 * q^56 - 596 * q^59 + 2878 * q^61 + 6276 * q^64 - 1932 * q^66 + 1746 * q^69 + 280 * q^71 - 640 * q^74 - 408 * q^76 - 764 * q^79 - 2502 * q^81 + 1818 * q^84 - 3160 * q^86 - 6876 * q^89 - 2840 * q^91 - 4154 * q^94 + 2310 * q^96 + 1524 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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