LMFDB - Embedded newform 225.4.e.c.151.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,4,Mod(76,225)]

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, 0]))

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

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

chi := DirichletCharacter("225.76");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	225.e (of order $3$, 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:	$13.2754297513$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.15759792.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 16x^{4} - 27x^{3} + 52x^{2} - 39x + 9 $ x^6 - 3x^5 + 16x^4 - 27x^3 + 52x^2 - 39*x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 45)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			151.1
Root			$0.500000 + 2.88506i$ of defining polynomial
Character	$\chi$	$=$	225.151
Dual form			225.4.e.c.76.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.28679 + 3.96084i) q^{2} +(-3.36330 - 3.96084i) q^{3} +(-6.45882 - 11.1870i) q^{4} +(23.3794 - 4.26387i) q^{6} +(-10.0573 + 17.4197i) q^{7} +22.4912 q^{8} +(-4.37646 + 26.6429i) q^{9} +O(q^{10})$	\(q+(-2.28679 + 3.96084i) q^{2} +(-3.36330 - 3.96084i) q^{3} +(-6.45882 - 11.1870i) q^{4} +(23.3794 - 4.26387i) q^{6} +(-10.0573 + 17.4197i) q^{7} +22.4912 q^{8} +(-4.37646 + 26.6429i) q^{9} +(-33.1708 + 57.4535i) q^{11} +(-22.5870 + 63.2076i) q^{12} +(-23.4003 - 40.5305i) q^{13} +(-45.9977 - 79.6704i) q^{14} +(0.237854 - 0.411975i) q^{16} +47.6233 q^{17} +(-95.5203 - 78.2613i) q^{18} -9.95276 q^{19} +(102.822 - 18.7524i) q^{21} +(-151.709 - 262.768i) q^{22} +(4.79602 + 8.30695i) q^{23} +(-75.6447 - 89.0841i) q^{24} +214.046 q^{26} +(120.248 - 72.2737i) q^{27} +259.832 q^{28} +(89.3675 - 154.789i) q^{29} +(-77.0186 - 133.400i) q^{31} +(91.0527 + 157.708i) q^{32} +(339.127 - 61.8491i) q^{33} +(-108.905 + 188.628i) q^{34} +(326.322 - 123.123i) q^{36} -248.864 q^{37} +(22.7599 - 39.4213i) q^{38} +(-81.8326 + 229.001i) q^{39} +(-124.832 - 216.216i) q^{41} +(-160.857 + 450.145i) q^{42} +(-106.122 + 183.809i) q^{43} +856.976 q^{44} -43.8700 q^{46} +(237.847 - 411.963i) q^{47} +(-2.43174 + 0.443494i) q^{48} +(-30.7973 - 53.3425i) q^{49} +(-160.171 - 188.628i) q^{51} +(-302.277 + 523.559i) q^{52} +546.314 q^{53} +(11.2831 + 641.556i) q^{54} +(-226.200 + 391.790i) q^{56} +(33.4741 + 39.4213i) q^{57} +(408.729 + 707.940i) q^{58} +(209.648 + 363.121i) q^{59} +(272.605 - 472.165i) q^{61} +704.502 q^{62} +(-420.097 - 344.192i) q^{63} -829.068 q^{64} +(-530.538 + 1484.66i) q^{66} +(-223.938 - 387.872i) q^{67} +(-307.590 - 532.762i) q^{68} +(16.7720 - 46.9350i) q^{69} +409.542 q^{71} +(-98.4319 + 599.232i) q^{72} +358.548 q^{73} +(569.100 - 985.710i) q^{74} +(64.2831 + 111.342i) q^{76} +(-667.215 - 1155.65i) q^{77} +(-719.902 - 847.803i) q^{78} +(325.776 - 564.260i) q^{79} +(-690.693 - 233.204i) q^{81} +1141.86 q^{82} +(-406.571 + 704.202i) q^{83} +(-873.893 - 1029.15i) q^{84} +(-485.359 - 840.667i) q^{86} +(-913.663 + 166.631i) q^{87} +(-746.051 + 1292.20i) q^{88} -201.000 q^{89} +941.373 q^{91} +(61.9532 - 107.306i) q^{92} +(-269.340 + 753.723i) q^{93} +(1087.81 + 1884.14i) q^{94} +(318.418 - 891.064i) q^{96} +(126.074 - 218.367i) q^{97} +281.708 q^{98} +(-1385.56 - 1135.21i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - q^{2} - 9 q^{3} - 11 q^{4} + 84 q^{6} - 43 q^{7} + 54 q^{8} + 57 q^{9}+O(q^{10}) $ 6 * q - q^2 - 9 * q^3 - 11 * q^4 + 84 * q^6 - 43 * q^7 + 54 * q^8 + 57 * q^9	\( 6 q - q^{2} - 9 q^{3} - 11 q^{4} + 84 q^{6} - 43 q^{7} + 54 q^{8} + 57 q^{9} - 14 q^{11} - 75 q^{12} + 40 q^{13} + 27 q^{14} + 13 q^{16} + 332 q^{17} - 3 q^{18} - 328 q^{19} - 144 q^{21} - 376 q^{22} + 171 q^{23} - 63 q^{24} + 868 q^{26} - 162 q^{27} + 1034 q^{28} + 335 q^{29} + 352 q^{31} - 77 q^{32} + 708 q^{33} + 52 q^{34} + 1086 q^{36} - 804 q^{37} - 178 q^{38} - 390 q^{39} - 187 q^{41} - 513 q^{42} - 602 q^{43} + 1964 q^{44} - 402 q^{46} + 665 q^{47} + 1074 q^{48} - 430 q^{49} - 180 q^{51} - 456 q^{52} + 1460 q^{53} + 639 q^{54} - 705 q^{56} + 486 q^{57} + 217 q^{58} + 298 q^{59} + 1439 q^{61} + 3228 q^{62} - 2205 q^{63} - 3138 q^{64} - 966 q^{66} - 1849 q^{67} - 710 q^{68} - 873 q^{69} + 140 q^{71} - 261 q^{72} + 736 q^{73} + 320 q^{74} - 204 q^{76} - 948 q^{77} + 432 q^{78} + 382 q^{79} - 1251 q^{81} + 1150 q^{82} - 831 q^{83} - 909 q^{84} - 1580 q^{86} - 258 q^{87} - 1428 q^{88} + 3438 q^{89} - 1420 q^{91} - 1623 q^{92} - 2178 q^{93} + 2077 q^{94} + 1155 q^{96} - 282 q^{97} - 4328 q^{98} - 762 q^{99}+O(q^{100}) \) 6 * q - q^2 - 9 * q^3 - 11 * q^4 + 84 * q^6 - 43 * q^7 + 54 * q^8 + 57 * q^9 - 14 * q^11 - 75 * q^12 + 40 * q^13 + 27 * q^14 + 13 * q^16 + 332 * q^17 - 3 * q^18 - 328 * q^19 - 144 * q^21 - 376 * q^22 + 171 * q^23 - 63 * q^24 + 868 * q^26 - 162 * q^27 + 1034 * q^28 + 335 * q^29 + 352 * q^31 - 77 * q^32 + 708 * q^33 + 52 * q^34 + 1086 * q^36 - 804 * q^37 - 178 * q^38 - 390 * q^39 - 187 * q^41 - 513 * q^42 - 602 * q^43 + 1964 * q^44 - 402 * q^46 + 665 * q^47 + 1074 * q^48 - 430 * q^49 - 180 * q^51 - 456 * q^52 + 1460 * q^53 + 639 * q^54 - 705 * q^56 + 486 * q^57 + 217 * q^58 + 298 * q^59 + 1439 * q^61 + 3228 * q^62 - 2205 * q^63 - 3138 * q^64 - 966 * q^66 - 1849 * q^67 - 710 * q^68 - 873 * q^69 + 140 * q^71 - 261 * q^72 + 736 * q^73 + 320 * q^74 - 204 * q^76 - 948 * q^77 + 432 * q^78 + 382 * q^79 - 1251 * q^81 + 1150 * q^82 - 831 * q^83 - 909 * q^84 - 1580 * q^86 - 258 * q^87 - 1428 * q^88 + 3438 * q^89 - 1420 * q^91 - 1623 * q^92 - 2178 * q^93 + 2077 * q^94 + 1155 * q^96 - 282 * q^97 - 4328 * q^98 - 762 * 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 $

$2$	−2.28679	+	3.96084i	−0.808502	+	1.40037i	0.105398	+	0.994430i	$0.466388\pi$
$2$	−2.28679	+	3.96084i	−0.808502	+	1.40037i	−0.913901	+	0.405937i	$0.866945\pi$
$3$	−3.36330	−	3.96084i	−0.647267	−	0.762263i
$3$	−3.36330	−	3.96084i	−0.647267	−	0.762263i
$4$	−6.45882	−	11.1870i	−0.807352	−	1.39838i
$5$		0			0
$5$		0			0
$6$	23.3794	−	4.26387i	1.59077	−	0.290120i
$7$	−10.0573	+	17.4197i	−0.543041	+	0.940575i	0.455686	+	0.890141i	$0.349394\pi$
$7$	−10.0573	+	17.4197i	−0.543041	+	0.940575i	−0.998727	+	0.0504348i	$0.983939\pi$
$8$	22.4912			0.993981
$9$	−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	$0.803349\pi$
$12$	−22.5870	+	63.2076i	−0.543358	+	1.52054i
$13$	−23.4003	−	40.5305i	−0.499237	−	0.864703i	0.500763	−	0.865584i	$-0.333053\pi$
$13$	−23.4003	−	40.5305i	−0.499237	−	0.864703i	−1.00000		0.000881222i	$0.999719\pi$
$14$	−45.9977	−	79.6704i	−0.878101	−	1.52092i
$15$		0			0
$16$	0.237854	−	0.411975i	0.00371647	−	0.00643711i
$17$	47.6233			0.679432			0.339716	−	0.940528i	$-0.389669\pi$
$17$	47.6233			0.679432			0.339716	+	0.940528i	$0.389669\pi$
$18$	−95.5203	−	78.2613i	−1.25080	−	1.02480i
$19$	−9.95276			−0.120175			−0.0600874	−	0.998193i	$-0.519138\pi$
$19$	−9.95276			−0.120175			−0.0600874	+	0.998193i	$0.519138\pi$
$20$		0			0
$21$	102.822	−	18.7524i	1.06846	−	0.194863i
$22$	−151.709	−	262.768i	−1.47021	−	2.54647i
$23$	4.79602	+	8.30695i	0.0434800	+	0.0753095i	0.886946	−	0.461872i	$-0.152822\pi$
$23$	4.79602	+	8.30695i	0.0434800	+	0.0753095i	−0.843466	+	0.537182i	$0.819489\pi$
$24$	−75.6447	−	89.0841i	−0.643371	−	0.757675i
$25$		0			0
$26$	214.046			1.61454
$27$	120.248	−	72.2737i	0.857099	−	0.515151i
$28$	259.832			1.75370
$29$	89.3675	−	154.789i	0.572246	−	0.991158i	−0.424089	−	0.905620i	$-0.639406\pi$
$29$	89.3675	−	154.789i	0.572246	−	0.991158i	0.996335	−	0.0855380i	$-0.0272609\pi$
$30$		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	$0.980565\pi$
$32$	91.0527	+	157.708i	0.503000	+	0.871222i
$33$	339.127	−	61.8491i	1.78892	−	0.326259i
$34$	−108.905	+	188.628i	−0.549323	+	0.951455i
$35$		0			0
$36$	326.322	−	123.123i	1.51075	−	0.570012i
$37$	−248.864			−1.10576			−0.552878	−	0.833262i	$-0.686471\pi$
$37$	−248.864			−1.10576			−0.552878	+	0.833262i	$0.686471\pi$
$38$	22.7599	−	39.4213i	0.0971616	−	0.168289i
$39$	−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	$0.991066\pi$
$42$	−160.857	+	450.145i	−0.590972	+	1.65378i
$43$	−106.122	+	183.809i	−0.376361	+	0.651876i	−0.990530	−	0.137299i	$-0.956158\pi$
$43$	−106.122	+	183.809i	−0.376361	+	0.651876i	0.614169	+	0.789175i	$0.289491\pi$
$44$	856.976			2.93623
$45$		0			0
$46$	−43.8700			−0.140615
$47$	237.847	−	411.963i	0.738160	−	1.27853i	−0.215163	−	0.976578i	$-0.569028\pi$
$47$	237.847	−	411.963i	0.738160	−	1.27853i	0.953323	−	0.301953i	$-0.0976384\pi$
$48$	−2.43174	+	0.443494i	−0.00731232	+	0.00133360i
$49$	−30.7973	−	53.3425i	−0.0897880	−	0.155517i
$50$		0			0
$51$	−160.171	−	188.628i	−0.439774	−	0.517906i
$52$	−302.277	+	523.559i	−0.806120	+	1.39624i
$53$	546.314			1.41589			0.707944	−	0.706269i	$-0.249623\pi$
$53$	546.314			1.41589			0.707944	+	0.706269i	$0.249623\pi$
$54$	11.2831	+	641.556i	0.0284341	+	1.61675i
$55$		0			0
$56$	−226.200	+	391.790i	−0.539773	+	0.934914i
$57$	33.4741	+	39.4213i	0.0777851	+	0.0916048i
$58$	408.729	+	707.940i	0.925324	+	1.60271i
$59$	209.648	+	363.121i	0.462608	+	0.801261i	0.999090	−	0.0426512i	$-0.0135804\pi$
$59$	209.648	+	363.121i	0.462608	+	0.801261i	−0.536482	+	0.843912i	$0.680247\pi$
$60$		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	$-0.0272386\pi$
$62$	704.502			1.44309
$63$	−420.097	−	344.192i	−0.840115	−	0.688319i
$64$	−829.068			−1.61927
$65$		0			0
$66$	−530.538	+	1484.66i	−0.989466	+	2.76893i
$67$	−223.938	−	387.872i	−0.408335	−	0.707256i	0.586369	−	0.810044i	$-0.300557\pi$
$67$	−223.938	−	387.872i	−0.408335	−	0.707256i	−0.994703	+	0.102788i	$0.967224\pi$
$68$	−307.590	−	532.762i	−0.548541	−	0.950102i
$69$	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	$0.388801\pi$
$72$	−98.4319	+	599.232i	−0.161115	+	0.980836i
$73$	358.548			0.574861			0.287431	−	0.957801i	$-0.407199\pi$
$73$	358.548			0.574861			0.287431	+	0.957801i	$0.407199\pi$
$74$	569.100	−	985.710i	0.894007	−	1.54847i
$75$		0			0
$76$	64.2831	+	111.342i	0.0970234	+	0.168049i
$77$	−667.215	−	1155.65i	−0.987483	−	1.71037i
$78$	−719.902	−	847.803i	−1.04504	−	1.23070i
$79$	325.776	−	564.260i	0.463958	−	0.803598i	−0.535196	−	0.844728i	$-0.679762\pi$
$79$	325.776	−	564.260i	0.463958	−	0.803598i	0.999154	+	0.0411297i	$0.0130957\pi$
$80$		0			0
$81$	−690.693	−	233.204i	−0.947453	−	0.319895i
$82$	1141.86			1.53777
$83$	−406.571	+	704.202i	−0.537675	+	0.931280i	0.461354	+	0.887216i	$0.347364\pi$
$83$	−406.571	+	704.202i	−0.537675	+	0.931280i	−0.999029	+	0.0440636i	$0.985970\pi$
$84$	−873.893	−	1029.15i	−1.13511	−	1.33678i
$85$		0			0
$86$	−485.359	−	840.667i	−0.608577	−	1.05409i
$87$	−913.663	+	166.631i	−1.12592	+	0.205342i
$88$	−746.051	+	1292.20i	−0.903743	+	1.56533i
$89$	−201.000			−0.239393			−0.119696	−	0.992811i	$-0.538192\pi$
$89$	−201.000			−0.239393			−0.119696	+	0.992811i	$0.538192\pi$
$90$		0			0
$91$	941.373			1.08442
$92$	61.9532	−	107.306i	0.0702073	−	0.121603i
$93$	−269.340	+	753.723i	−0.300314	+	0.840402i
$94$	1087.81	+	1884.14i	1.19361	+	2.06739i
$95$		0			0
$96$	318.418	−	891.064i	0.338525	−	0.947331i
$97$	126.074	−	218.367i	0.131968	−	0.228576i	−0.792467	−	0.609915i	$-0.791204\pi$
$97$	126.074	−	218.367i	0.131968	−	0.228576i	0.924435	+	0.381339i	$0.124537\pi$
$98$	281.708			0.290375
$99$	−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	$0.173504\pi$
$102$	1113.40	−	203.060i	1.08082	−	0.197117i
$103$	−720.176	−	1247.38i	−0.688942	−	1.19328i	−0.972180	−	0.234233i	$-0.924742\pi$
$103$	−720.176	−	1247.38i	−0.688942	−	1.19328i	0.283238	−	0.959050i	$-0.408591\pi$
$104$	−526.301	−	911.581i	−0.496232	−	0.859498i
$105$		0			0
$106$	−1249.31	+	2163.86i	−1.14475	+	1.98276i
$107$	−355.755			−0.321422			−0.160711	−	0.987002i	$-0.551379\pi$
$107$	−355.755			−0.321422			−0.160711	+	0.987002i	$0.551379\pi$
$108$	−1585.18	−	878.409i	−1.41236	−	0.782638i
$109$	−1522.51			−1.33789			−0.668946	−	0.743311i	$-0.733254\pi$
$109$	−1522.51			−1.33789			−0.668946	+	0.743311i	$0.733254\pi$
$110$		0			0
$111$	837.004	+	985.710i	0.715720	+	0.842878i
$112$	4.78432	+	8.28669i	0.00403639	+	0.00699124i
$113$	−406.499	−	704.077i	−0.338409	−	0.586142i	0.645725	−	0.763570i	$-0.276555\pi$
$113$	−406.499	−	704.077i	−0.338409	−	0.586142i	−0.984134	+	0.177429i	$0.943222\pi$
$114$	−232.689	+	42.4373i	−0.191170	+	0.0348650i
$115$		0			0
$116$	−2308.83			−1.84802
$117$	1182.26	−	446.073i	0.934190	−	0.352474i
$118$	−1917.69			−1.49608
$119$	−478.960	+	829.584i	−0.368960	+	0.639057i
$120$		0			0
$121$	−1535.10	−	2658.87i	−1.15334	−	1.99765i
$122$	1246.78	+	2159.49i	0.925231	+	1.60255i
$123$	−436.547	+	1221.64i	−0.320017	+	0.895539i
$124$	−994.899	+	1723.22i	−0.720521	+	1.24798i
$125$		0			0
$126$	2323.96	−	876.841i	1.64313	−	0.619962i
$127$	864.662			0.604144			0.302072	−	0.953285i	$-0.402322\pi$
$127$	864.662			0.604144			0.302072	+	0.953285i	$0.402322\pi$
$128$	1167.48	−	2022.14i	0.806187	−	1.39636i
$129$	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	$0.574487\pi$
$132$	−2882.27	−	3394.34i	−1.90052	−	2.23818i
$133$	100.098	−	173.374i	0.0652599	−	0.113033i
$134$	2048.40			1.32056
$135$		0			0
$136$	1071.11			0.675343
$137$	−1149.58	+	1991.13i	−0.716900	+	1.24171i	0.245322	+	0.969442i	$0.421106\pi$
$137$	−1149.58	+	1991.13i	−0.716900	+	1.24171i	−0.962222	+	0.272266i	$0.912227\pi$
$138$	147.548	+	173.762i	0.0910152	+	0.107185i
$139$	1066.98	+	1848.06i	0.651077	+	1.12770i	0.982862	+	0.184343i	$0.0590157\pi$
$139$	1066.98	+	1848.06i	0.651077	+	1.12770i	−0.331785	+	0.943355i	$0.607651\pi$
$140$		0			0
$141$	−2431.67	+	443.481i	−1.45236	+	0.264878i
$142$	−936.536	+	1622.13i	−0.553467	+	0.958634i
$143$	3104.83			1.81565
$144$	9.93528	+	8.14012i	0.00574958	+	0.00471072i
$145$		0			0
$146$	−819.924	+	1420.15i	−0.464777	+	0.805017i
$147$	−107.700	+	301.390i	−0.0604284	+	0.169103i
$148$	1607.37	+	2784.04i	0.892735	+	1.54626i
$149$	−875.309	−	1516.08i	−0.481263	−	0.833572i	0.518506	−	0.855074i	$-0.326488\pi$
$149$	−875.309	−	1516.08i	−0.481263	−	0.833572i	−0.999769	+	0.0215024i	$0.993155\pi$
$150$		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	$0.242516\pi$
$152$	−223.850			−0.119451
$153$	−208.421	+	1268.83i	−0.110130	+	0.670447i
$154$	6103.12			3.19353
$155$		0			0
$156$	3090.38	−	563.615i	1.58608	−	0.289265i
$157$	−129.697	−	224.642i	−0.0659298	−	0.114194i	0.831176	−	0.556009i	$-0.187668\pi$
$157$	−129.697	−	224.642i	−0.0659298	−	0.114194i	−0.897106	+	0.441815i	$0.854335\pi$
$158$	1489.96	+	2580.69i	0.750222	+	1.29942i
$159$	−1837.42	−	2163.86i	−0.916457	−	1.07928i
$160$		0			0
$161$	−192.939			−0.0944457
$162$	2503.15	−	2202.44i	1.21399	−	1.06815i
$163$	1201.80			0.577498			0.288749	−	0.957405i	$-0.406761\pi$
$163$	1201.80			0.577498			0.288749	+	0.957405i	$0.406761\pi$
$164$	−1612.54	+	2792.99i	−0.767792	+	1.32986i
$165$		0			0
$166$	−1859.49	−	3220.72i	−0.869422	−	1.50588i
$167$	−839.452	−	1453.97i	−0.388975	−	0.673724i	0.603337	−	0.797486i	$-0.293837\pi$
$167$	−839.452	−	1453.97i	−0.388975	−	0.673724i	−0.992312	+	0.123762i	$0.960504\pi$
$168$	2312.60	−	421.765i	1.06203	−	0.193690i
$169$	3.35162	−	5.80518i	0.00152554	−	0.00264232i
$170$		0			0
$171$	43.5578	−	265.171i	0.0194792	−	0.118586i
$172$	2741.70			1.21542
$173$	465.899	−	806.961i	0.204749	−	0.354636i	−0.745303	−	0.666725i	$-0.767695\pi$
$173$	465.899	−	806.961i	0.204749	−	0.354636i	0.950053	+	0.312089i	$0.101029\pi$
$174$	1429.36	−	3999.92i	0.622754	−	1.74272i
$175$		0			0
$176$	15.7796	+	27.3311i	0.00675814	+	0.0117054i
$177$	733.155	−	2051.67i	0.311341	−	0.871259i
$178$	459.644	−	796.127i	0.193549	−	0.335237i
$179$	1023.40			0.427333			0.213667	−	0.976907i	$-0.431459\pi$
$179$	1023.40			0.427333			0.213667	+	0.976907i	$0.431459\pi$
$180$		0			0
$181$	2639.93			1.08411			0.542056	−	0.840342i	$-0.317646\pi$
$181$	2639.93			1.08411			0.542056	+	0.840342i	$0.317646\pi$
$182$	−2152.72	+	3728.62i	−0.876760	+	1.51859i
$183$	−2787.02	+	508.289i	−1.12581	+	0.205322i
$184$	107.868	+	186.833i	0.0432182	+	0.0748562i
$185$		0			0
$186$	−2369.45	−	2790.42i	−0.934067	−	1.10002i
$187$	−1579.70	+	2736.13i	−0.617750	+	1.06997i
$188$	−6144.84			−2.38382
$189$	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	$0.117435\pi$
$192$	2788.40	+	3283.80i	1.04810	+	1.23431i
$193$	−407.121	−	705.154i	−0.151840	−	0.262995i	0.780064	−	0.625700i	$-0.215187\pi$
$193$	−407.121	−	705.154i	−0.151840	−	0.262995i	−0.931904	+	0.362705i	$0.881853\pi$
$194$	576.612	+	998.720i	0.213393	+	0.369608i
$195$		0			0
$196$	−397.828	+	689.059i	−0.144981	+	0.251115i
$197$	−4078.41			−1.47500			−0.737499	−	0.675348i	$-0.763994\pi$
$197$	−4078.41			−1.47500			−0.737499	+	0.675348i	$0.763994\pi$
$198$	7664.87	−	2891.99i	2.75110	−	1.03800i
$199$	−1342.49			−0.478224			−0.239112	−	0.970992i	$-0.576856\pi$
$199$	−1342.49			−0.478224			−0.239112	+	0.970992i	$0.576856\pi$
$200$		0			0
$201$	−783.129	+	2191.51i	−0.274814	+	0.769042i
$202$	−99.7101	−	172.703i	−0.0347306	−	0.0601551i
$203$	1797.58	+	3113.51i	0.621506	+	1.07648i
$204$	−1075.67	+	3010.15i	−0.369175	+	1.03310i
$205$		0			0
$206$	6587.56			2.22805
$207$	−242.311	+	91.4250i	−0.0813613	+	0.0306980i
$208$	−22.2634			−0.00742159
$209$	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	$0.673222\pi$
$212$	−3528.55	−	6111.62i	−1.14312	−	1.97994i
$213$	−1377.41	−	1622.13i	−0.443092	−	0.521814i
$214$	813.536	−	1409.09i	0.259870	−	0.450108i
$215$		0			0
$216$	2704.52	−	1625.52i	0.851940	−	0.512050i
$217$	3098.39			0.969273
$218$	3481.66	−	6030.42i	1.08169	−	1.87354i
$219$	−1205.90	−	1420.15i	−0.372089	−	0.438196i
$220$		0			0
$221$	−1114.40	−	1930.20i	−0.339198	−	0.587507i
$222$	−5818.29	+	1061.12i	−1.75900	+	0.320802i
$223$	1753.43	−	3037.03i	0.526539	−	0.911993i	−0.472982	−	0.881072i	$-0.656823\pi$
$223$	1753.43	−	3037.03i	0.526539	−	0.911993i	0.999522	−	0.0309212i	$-0.00984409\pi$
$224$	−3662.97			−1.09260
$225$		0			0
$226$	3718.31			1.09442
$227$	326.413	−	565.364i	0.0954396	−	0.165306i	−0.814352	−	0.580371i	$-0.802908\pi$
$227$	326.413	−	565.364i	0.0954396	−	0.165306i	0.909792	+	0.415064i	$0.136241\pi$
$228$	224.803	−	629.090i	0.0652979	−	0.182730i
$229$	−2291.78	−	3969.47i	−0.661331	−	1.14546i	−0.980266	−	0.197682i	$-0.936659\pi$
$229$	−2291.78	−	3969.47i	−0.661331	−	1.14546i	0.318935	−	0.947776i	$-0.396675\pi$
$230$		0			0
$231$	−2333.30	+	6529.52i	−0.664588	+	1.85979i
$232$	2009.98	−	3481.39i	0.568801	−	0.985192i
$233$	−317.527			−0.0892785			−0.0446392	−	0.999003i	$-0.514214\pi$
$233$	−317.527			−0.0892785			−0.0446392	+	0.999003i	$0.514214\pi$
$234$	−936.765	+	5702.83i	−0.261702	+	1.59319i
$235$		0			0
$236$	2708.16	−	4690.67i	0.746975	−	1.29380i
$237$	−3330.62	+	607.430i	−0.912858	+	0.166485i
$238$	−2190.56	−	3794.17i	−0.596610	−	1.03336i
$239$	−928.835	−	1608.79i	−0.251386	−	0.435414i	0.712521	−	0.701650i	$-0.247553\pi$
$239$	−928.835	−	1608.79i	−0.251386	−	0.435414i	−0.963908	+	0.266236i	$0.914220\pi$
$240$		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	$0.0228485\pi$
$242$	14041.8			3.72993
$243$	1399.33	+	3520.06i	0.369411	+	0.929266i
$244$	−7042.82			−1.84783
$245$		0			0
$246$	−3840.41	−	4522.72i	−0.995349	−	1.17219i
$247$	232.898	+	403.390i	0.0599956	+	0.103915i
$248$	−1732.24	−	3000.33i	−0.443538	−	0.768231i
$249$	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	$0.750999\pi$
$252$	−1137.15	+	6922.70i	−0.284260	+	1.73051i
$253$	−636.351			−0.158131
$254$	−1977.30	+	3424.78i	−0.488452	+	0.846024i
$255$		0			0
$256$	2023.31	+	3504.47i	0.493971	+	0.855584i
$257$	−586.731	−	1016.25i	−0.142410	−	0.246661i	0.785994	−	0.618234i	$-0.212152\pi$
$257$	−586.731	−	1016.25i	−0.142410	−	0.246661i	−0.928404	+	0.371574i	$0.878818\pi$
$258$	−1697.34	+	4749.84i	−0.409580	+	1.14617i
$259$	2502.89	−	4335.14i	0.600472	−	1.04005i
$260$		0			0
$261$	3732.92	+	3058.44i	0.885295	+	0.725336i
$262$	−9963.64			−2.34945
$263$	−1448.98	+	2509.71i	−0.339726	+	0.588423i	−0.984381	−	0.176051i	$-0.943668\pi$
$263$	−1448.98	+	2509.71i	−0.339726	+	0.588423i	0.644655	+	0.764474i	$0.277001\pi$
$264$	7627.38	−	1391.06i	1.77815	−	0.324295i
$265$		0			0
$266$	457.804	+	792.940i	0.105526	+	0.182776i
$267$	676.022	+	796.127i	0.154951	+	0.182480i
$268$	−2892.75	+	5010.40i	−0.659340	+	1.14201i
$269$	2930.13			0.664138			0.332069	−	0.943255i	$-0.392253\pi$
$269$	2930.13			0.664138			0.332069	+	0.943255i	$0.392253\pi$
$270$		0			0
$271$	−668.881			−0.149932			−0.0749661	−	0.997186i	$-0.523885\pi$
$271$	−668.881			−0.149932			−0.0749661	+	0.997186i	$0.523885\pi$
$272$	11.3274	−	19.6196i	0.00252509	−	0.00437358i
$273$	−3166.12	−	3728.62i	−0.701912	−	0.826617i
$274$	−5257.70	−	9106.60i	−1.15923	−	2.00785i
$275$		0			0
$276$	−633.389	+	115.516i	−0.138136	+	0.0251929i
$277$	−316.315	+	547.874i	−0.0686121	+	0.118840i	−0.898291	−	0.439402i	$-0.855190\pi$
$277$	−316.315	+	547.874i	−0.0686121	+	0.118840i	0.829679	+	0.558241i	$0.188524\pi$
$278$	−9759.80			−2.10559
$279$	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	$0.0420286\pi$
$282$	3804.16	−	10645.6i	0.803313	−	2.24800i
$283$	252.184	+	436.796i	0.0529710	+	0.0917485i	0.891295	−	0.453424i	$-0.149798\pi$
$283$	252.184	+	436.796i	0.0529710	+	0.0917485i	−0.838324	+	0.545172i	$0.816464\pi$
$284$	−2645.16	−	4581.55i	−0.552680	−	0.957270i
$285$		0			0
$286$	−7100.08	+	12297.7i	−1.46796	+	2.54258i
$287$	5021.88			1.03286
$288$	−4600.29	+	1735.71i	−0.941232	+	0.355131i
$289$	−2645.02			−0.538372
$290$		0			0
$291$	−1288.94	+	235.074i	−0.259654	+	0.0473549i
$292$	−2315.80	−	4011.08i	−0.464116	−	0.803872i
$293$	3099.25	+	5368.06i	0.617953	+	1.07033i	0.989859	+	0.142055i	$0.0453710\pi$
$293$	3099.25	+	5368.06i	0.617953	+	1.07033i	−0.371906	+	0.928270i	$0.621296\pi$
$294$	−947.467	−	1115.80i	−0.187950	−	0.221343i
$295$		0			0
$296$	−5597.26			−1.09910
$297$	163.666	+	9306.02i	0.0319760	+	1.81815i
$298$	8006.60			1.55641
$299$	224.457	−	388.770i	0.0434136	−	0.0751945i
$300$		0			0
$301$	−2134.60	−	3697.24i	−0.408759	−	0.707991i
$302$	−2003.12	−	3469.51i	−0.381678	−	0.661086i
$303$	222.889	−	40.6500i	0.0422596	−	0.00770719i
$304$	−2.36730	+	4.10029i	−0.000446626	+	0.000773578i
$305$		0			0
$306$	−4548.99	−	3727.06i	−0.849832	−	0.696281i
$307$	1966.79			0.365636			0.182818	−	0.983147i	$-0.441478\pi$
$307$	1966.79			0.365636			0.182818	+	0.983147i	$0.441478\pi$
$308$	−8618.84	+	14928.3i	−1.59449	+	2.76174i
$309$	−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	$0.765910\pi$
$312$	−1840.51	+	5150.51i	−0.333970	+	0.934584i
$313$	5151.20	−	8922.14i	0.930234	−	1.61121i	0.147314	−	0.989090i	$-0.452937\pi$
$313$	5151.20	−	8922.14i	0.930234	−	1.61121i	0.782920	−	0.622122i	$-0.213729\pi$
$314$	1186.36			0.213218
$315$		0			0
$316$	−8416.51			−1.49831
$317$	−850.916	+	1473.83i	−0.150764	+	0.261131i	−0.931509	−	0.363719i	$-0.881507\pi$
$317$	−850.916	+	1473.83i	−0.150764	+	0.261131i	0.780745	+	0.624850i	$0.214840\pi$
$318$	12772.5	−	2329.41i	2.25235	−	0.410777i
$319$	5928.78	+	10268.9i	1.04059	+	1.80235i
$320$		0			0
$321$	1196.51	+	1409.09i	0.208046	+	0.245008i
$322$	441.212	−	764.201i	0.0763596	−	0.132259i
$323$	−473.983			−0.0816506
$324$	1852.21	+	9233.01i	0.317595	+	1.58316i
$325$		0			0
$326$	−2748.26	+	4760.13i	−0.466908	+	0.808709i
$327$	5120.66	+	6030.42i	0.865973	+	1.01983i
$328$	−2807.63	−	4862.95i	−0.472638	−	0.818633i
$329$	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	$-0.0772271\pi$
$332$	10503.9			1.73637
$333$	1089.14	−	6630.47i	0.179233	−	1.09113i
$334$	7678.61			1.25795
$335$		0			0
$336$	16.7311	−	46.8205i	0.00271654	−	0.00760199i
$337$	−3928.71	−	6804.73i	−0.635046	−	1.09993i	−0.986505	−	0.163729i	$-0.947648\pi$
$337$	−3928.71	−	6804.73i	−0.635046	−	1.09993i	0.351459	−	0.936203i	$-0.385686\pi$
$338$	15.3289	+	26.5504i	0.00246681	+	0.00427264i
$339$	−1421.56	+	3978.10i	−0.227753	+	0.637347i
$340$		0			0
$341$	10219.1			1.62286
$342$	950.691	+	778.916i	0.150314	+	0.123155i
$343$	−5660.34			−0.891048
$344$	−2386.82	+	4134.10i	−0.374095	+	0.647952i
$345$		0			0
$346$	2130.83	+	3690.70i	0.331081	+	0.573449i
$347$	606.088	+	1049.78i	0.0937652	+	0.162406i	0.909093	−	0.416594i	$-0.136776\pi$
$347$	606.088	+	1049.78i	0.0937652	+	0.162406i	−0.815327	+	0.579000i	$0.803443\pi$
$348$	7765.29	+	9144.91i	1.19616	+	1.40867i
$349$	−699.332	+	1211.28i	−0.107262	+	0.185783i	−0.914660	−	0.404224i	$-0.867542\pi$
$349$	−699.332	+	1211.28i	−0.107262	+	0.185783i	0.807398	+	0.590007i	$0.200875\pi$
$350$		0			0
$351$	−5743.12	−	3182.47i	−0.873348	−	0.483954i
$352$	−12081.2			−1.82934
$353$	1314.21	−	2276.28i	0.198154	−	0.343214i	−0.749776	−	0.661692i	$-0.769839\pi$
$353$	1314.21	−	2276.28i	0.198154	−	0.343214i	0.947930	+	0.318479i	$0.103172\pi$
$354$	6449.75	+	7595.64i	0.968362	+	1.14041i
$355$		0			0
$356$	1298.22	+	2248.59i	0.193274	+	0.334761i
$357$	4896.73	−	893.053i	0.725946	−	0.132396i
$358$	−2340.31	+	4053.53i	−0.345500	+	0.598424i
$359$	3677.48			0.540640			0.270320	−	0.962770i	$-0.412870\pi$
$359$	3677.48			0.540640			0.270320	+	0.962770i	$0.412870\pi$
$360$		0			0
$361$	−6759.94			−0.985558
$362$	−6036.96	+	10456.3i	−0.876507	+	1.51815i
$363$	−5368.36	+	15022.9i	−0.776215	+	2.17217i
$364$	−6080.16	−	10531.1i	−0.875513	−	1.51643i
$365$		0			0
$366$	4360.08	−	12201.3i	0.622692	−	1.74255i
$367$	5714.88	−	9898.47i	0.812846	−	1.40789i	−0.0980185	−	0.995185i	$-0.531250\pi$
$367$	5714.88	−	9898.47i	0.812846	−	1.40789i	0.910864	−	0.412706i	$-0.135416\pi$
$368$	4.56301			0.000646368
$369$	6306.94	−	2379.64i	0.889773	−	0.335715i
$370$		0			0
$371$	−5494.43	+	9516.63i	−0.768886	+	1.33175i
$372$	10171.5	−	1855.05i	1.41766	−	0.258549i
$373$	1129.95	+	1957.13i	0.156854	+	0.271679i	0.933733	−	0.357971i	$-0.116531\pi$
$373$	1129.95	+	1957.13i	0.156854	+	0.271679i	−0.776879	+	0.629650i	$0.783198\pi$
$374$	−7224.90	−	12513.9i	−0.998905	−	1.73015i
$375$		0			0
$376$	5349.47	−	9265.55i	0.733717	−	1.27084i
$377$	−8364.90			−1.14274
$378$	−11289.2	−	6255.76i	−1.53612	−	0.851221i
$379$	−11815.8			−1.60142			−0.800709	−	0.599053i	$-0.795544\pi$
$379$	−11815.8			−1.60142			−0.800709	+	0.599053i	$0.795544\pi$
$380$		0			0
$381$	−2908.12	−	3424.78i	−0.391043	−	0.460517i
$382$	1859.80	+	3221.27i	0.249099	+	0.431452i
$383$	−4040.11	−	6997.68i	−0.539008	−	0.933589i	−0.998958	−	0.0456440i	$-0.985466\pi$
$383$	−4040.11	−	6997.68i	−0.539008	−	0.933589i	0.459950	−	0.887945i	$-0.347867\pi$
$384$	−11936.0	+	2176.85i	−1.58621	+	0.289289i
$385$		0			0
$386$	3724.00			0.491054
$387$	−4432.78	−	3631.85i	−0.582251	−	0.477047i
$388$	−3257.17			−0.426180
$389$	−1550.22	+	2685.05i	−0.202054	+	0.349968i	−0.949190	−	0.314703i	$-0.898095\pi$
$389$	−1550.22	+	2685.05i	−0.202054	+	0.349968i	0.747136	+	0.664671i	$0.231428\pi$
$390$		0			0
$391$	228.402	+	395.604i	0.0295417	+	0.0511677i
$392$	−692.669	−	1199.74i	−0.0892476	−	0.154581i
$393$	3809.22	−	10659.8i	0.488931	−	1.36823i
$394$	9326.47	−	16153.9i	1.19254	−	2.06554i
$395$		0			0
$396$	−3750.52	+	22832.4i	−0.475936	+	2.89740i
$397$	11990.1			1.51578			0.757890	−	0.652382i	$-0.226230\pi$
$397$	11990.1			1.51578			0.757890	+	0.652382i	$0.226230\pi$
$398$	3069.99	−	5317.38i	0.386645	−	0.669689i
$399$	−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	$-0.462007\pi$
$402$	−6889.38	−	8113.38i	−0.854753	−	1.00661i
$403$	−3604.52	+	6243.21i	−0.445543	+	0.771703i
$404$	563.243			0.0693623
$405$		0			0
$406$	−16442.8			−2.00996
$407$	8255.02	−	14298.1i	1.00537	−	1.74135i
$408$	−3602.45	−	4242.48i	−0.437127	−	0.514789i
$409$	−1112.54	−	1926.98i	−0.134503	−	0.232966i	0.790904	−	0.611940i	$-0.209610\pi$
$409$	−1112.54	−	1926.98i	−0.134503	−	0.232966i	−0.925408	+	0.378974i	$0.876277\pi$
$410$		0			0
$411$	11752.9	−	2143.47i	1.41053	−	0.257249i
$412$	−9302.97	+	16113.2i	−1.11244	+	1.92680i
$413$	−8433.95			−1.00486
$414$	191.995	−	1168.82i	0.0227924	−	0.138755i
$415$		0			0
$416$	4261.32	−	7380.83i	0.502232	−	0.869891i
$417$	3731.29	−	10441.7i	0.438183	−	1.22621i
$418$	1509.93	+	2615.27i	0.176682	+	0.306021i
$419$	−4838.33	−	8380.23i	−0.564123	−	0.977090i	−0.997131	−	0.0756998i	$-0.975881\pi$
$419$	−4838.33	−	8380.23i	−0.564123	−	0.977090i	0.433007	−	0.901390i	$-0.357452\pi$
$420$		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	$-0.0289775\pi$
$422$	−13514.8			−1.55898
$423$	9934.98	+	8139.88i	1.14197	+	0.935637i
$424$	12287.3			1.40737
$425$		0			0
$426$	9574.84	−	1746.23i	1.08897	−	0.198604i
$427$	5483.32	+	9497.39i	0.621444	+	1.07637i
$428$	2297.76	+	3979.83i	0.259500	+	0.449468i
$429$	−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	$0.543922\pi$
$432$	−1.17358	−	66.7297i	−0.000130704	−	0.00743179i
$433$	−7818.49			−0.867743			−0.433871	−	0.900975i	$-0.642853\pi$
$433$	−7818.49			−0.867743			−0.433871	+	0.900975i	$0.642853\pi$
$434$	−7085.36	+	12272.2i	−0.783660	+	1.35734i
$435$		0			0
$436$	9833.63	+	17032.3i	1.08015	+	1.87087i
$437$	−47.7336	−	82.6770i	−0.00522519	−	0.00905030i
$438$	8382.64	−	1528.80i	0.914470	−	0.166779i
$439$	−3105.91	+	5379.60i	−0.337670	+	0.584862i	−0.983994	−	0.178201i	$-0.942972\pi$
$439$	−3105.91	+	5379.60i	−0.337670	+	0.584862i	0.646324	+	0.763063i	$0.276306\pi$
$440$		0			0
$441$	1555.98	−	587.080i	0.168015	−	0.0633927i
$442$	10193.6			1.09697
$443$	1492.17	−	2584.52i	0.160034	−	0.277188i	−0.774846	−	0.632150i	$-0.782173\pi$
$443$	1492.17	−	2584.52i	0.160034	−	0.277188i	0.934881	+	0.354962i	$0.115506\pi$
$444$	5621.08	−	15730.1i	0.600822	−	1.68134i
$445$		0			0
$446$	8019.45	+	13890.1i	0.851417	+	1.47470i
$447$	−3061.02	+	8565.99i	−0.323896	+	0.906392i
$448$	8338.16	−	14442.1i	0.879333	−	1.52305i
$449$	−810.476			−0.0851865			−0.0425932	−	0.999092i	$-0.513562\pi$
$449$	−810.476			−0.0851865			−0.0425932	+	0.999092i	$0.513562\pi$
$450$		0			0
$451$	16563.1			1.72933
$452$	−5251.01	+	9095.01i	−0.546431	+	0.946446i
$453$	4477.73	−	816.637i	0.464420	−	0.0846996i
$454$	1492.88	+	2585.74i	0.154326	+	0.267301i
$455$		0			0
$456$	752.873	+	886.632i	0.0773169	+	0.0910534i
$457$	785.887	−	1361.20i	0.0804425	−	0.139331i	−0.822998	−	0.568045i	$-0.807700\pi$
$457$	785.887	−	1361.20i	0.0804425	−	0.139331i	0.903440	+	0.428714i	$0.141033\pi$
$458$	20963.2			2.13875
$459$	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	$0.199894\pi$
$462$	−20526.6	−	24173.5i	−2.06707	−	2.43431i
$463$	1391.62	+	2410.35i	0.139684	+	0.241940i	0.927377	−	0.374128i	$-0.122058\pi$
$463$	1391.62	+	2410.35i	0.139684	+	0.241940i	−0.787693	+	0.616068i	$0.788725\pi$
$464$	−42.5128	−	73.6344i	−0.00425347	−	0.00736722i
$465$		0			0
$466$	726.118	−	1257.67i	0.0721819	−	0.125023i
$467$	−10939.7			−1.08400			−0.541999	−	0.840379i	$-0.682332\pi$
$467$	−10939.7			−1.08400			−0.541999	+	0.840379i	$0.682332\pi$
$468$	−12626.2	−	10344.9i	−1.24711	−	1.02178i
$469$	9008.83			0.886970
$470$		0			0
$471$	−453.561	+	1269.25i	−0.0443716	+	0.124170i
$472$	4715.24	+	8167.04i	0.459823	+	0.796438i
$473$	−7040.33	−	12194.2i	−0.684386	−	1.18539i
$474$	5210.51	−	14581.1i	0.504908	−	1.41294i
$475$		0			0
$476$	12374.1			1.19152
$477$	−2390.92	+	14555.4i	−0.229503	+	1.39716i
$478$	8496.21			0.812986
$479$	−7311.85	+	12664.5i	−0.697467	+	1.20805i	0.271875	+	0.962333i	$0.412356\pi$
$479$	−7311.85	+	12664.5i	−0.697467	+	1.20805i	−0.969342	+	0.245716i	$0.920977\pi$
$480$		0			0
$481$	5823.49	+	10086.6i	0.552034	+	0.956151i
$482$	7470.81	+	12939.8i	0.705987	+	1.22281i
$483$	648.913	+	764.201i	0.0611316	+	0.0719925i
$484$	−19829.9	+	34346.4i	−1.86231	+	3.22562i
$485$		0			0
$486$	−17142.3	−	2507.13i	−1.59998	−	0.234003i
$487$	−16473.6			−1.53284			−0.766419	−	0.642341i	$-0.777963\pi$
$487$	−16473.6			−1.53284			−0.766419	+	0.642341i	$0.777963\pi$
$488$	6131.22	−	10619.6i	0.568744	−	0.985093i
$489$	−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	$-0.559107\pi$
$492$	16486.0	−	3006.68i	1.51067	−	0.275511i
$493$	4255.97	−	7371.56i	0.388802	−	0.673425i
$494$	−2130.35			−0.194026
$495$		0			0
$496$	−73.2768			−0.00663352
$497$	−4118.87	+	7134.10i	−0.371744	+	0.643879i
$498$	−6502.76	+	18197.4i	−0.585132	+	1.63744i
$499$	7202.31	+	12474.8i	0.646131	+	1.11913i	0.984039	+	0.177953i	$0.0569475\pi$
$499$	7202.31	+	12474.8i	0.646131	+	1.11913i	−0.337908	+	0.941179i	$0.609719\pi$
$500$		0			0
$501$	−2935.63	+	8215.08i	−0.261785	+	0.732580i
$502$	12900.6	−	22344.5i	1.14698	−	1.98663i
$503$	2953.63			0.261821			0.130910	−	0.991394i	$-0.458210\pi$
$503$	2953.63			0.261821			0.130910	+	0.991394i	$0.458210\pi$
$504$	−9448.49	−	7741.30i	−0.835058	−	0.684176i
$505$		0			0
$506$	1455.20	−	2520.48i	0.127849	−	0.221441i
$507$	−34.2659	+	6.24932i	−0.00300158	+	0.000547420i
$508$	−5584.69	−	9672.98i	−0.487757	−	0.844821i
$509$	8684.44	+	15041.9i	0.756250	+	1.30986i	0.944750	+	0.327790i	$0.106304\pi$
$509$	8684.44	+	15041.9i	0.756250	+	1.30986i	−0.188500	+	0.982073i	$0.560363\pi$
$510$		0			0
$511$	−3606.02	+	6245.80i	−0.312174	+	0.540701i
$512$	172.223			0.0148657
$513$	−1196.80	+	719.323i	−0.103002	+	0.0619082i
$514$	5366.92			0.460554
$515$		0			0
$516$	−9221.16	−	10859.4i	−0.786703	−	0.926473i
$517$	15779.1	+	27330.3i	1.34229	+	2.32492i
$518$	11447.2	+	19827.1i	0.970966	+	1.68176i
$519$	−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	$0.583202\pi$
$522$	−20650.4	+	7791.48i	−1.73150	+	0.653303i
$523$	4554.68			0.380807			0.190404	−	0.981706i	$-0.439020\pi$
$523$	4554.68			0.380807			0.190404	+	0.981706i	$0.439020\pi$
$524$	14070.7	−	24371.1i	1.17305	−	2.03179i
$525$		0			0
$526$	−6627.03	−	11478.4i	−0.549339	−	0.951483i
$527$	−3667.88	−	6352.96i	−0.303179	−	0.525122i
$528$	55.1824	−	154.423i	0.00454831	−	0.0127280i
$529$	6037.50	−	10457.3i	0.496219	−	0.859476i
$530$		0			0
$531$	−10592.1	+	3996.46i	−0.865649	+	0.326613i
$532$	−2586.05			−0.210751
$533$	−5842.22	+	10119.0i	−0.474774	+	0.822333i
$534$	−4699.25	+	857.037i	−0.380817	+	0.0694525i
$535$		0			0
$536$	−5036.64	−	8723.72i	−0.405877	−	0.702999i
$537$	−3442.01	−	4053.53i	−0.276599	−	0.325741i
$538$	−6700.59	+	11605.8i	−0.536957	+	0.930037i
$539$	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	$0.244655\pi$
$542$	1529.59	−	2649.33i	0.121221	−	0.209960i
$543$	−8878.86	−	10456.3i	−0.701710	−	0.826379i
$544$	4336.23	+	7510.58i	0.341754	+	0.591936i
$545$		0			0
$546$	22008.7	−	4013.89i	1.72507	−	0.314613i
$547$	7890.69	−	13667.1i	0.616786	−	1.06830i	−0.373283	−	0.927718i	$-0.621768\pi$
$547$	7890.69	−	13667.1i	0.616786	−	1.06830i	0.990068	−	0.140586i	$-0.0448987\pi$
$548$	29699.7			2.31516
$549$	11386.8	+	9329.41i	0.885206	+	0.725263i
$550$		0			0
$551$	−889.453	+	1540.58i	−0.0687694	+	0.119112i
$552$	377.223	−	1055.62i	0.0290864	−	0.0813956i
$553$	6552.83	+	11349.8i	0.503896	+	0.872774i
$554$	−1446.69	−	2505.75i	−0.110946	−	0.192164i
$555$		0			0
$556$	13782.8	−	23872.5i	1.05130	−	1.82090i
$557$	13954.5			1.06153			0.530766	−	0.847519i	$-0.321904\pi$
$557$	13954.5			1.06153			0.530766	+	0.847519i	$0.321904\pi$
$558$	−3083.22	+	18770.0i	−0.233913	+	1.42401i
$559$	9933.18			0.751572
$560$		0			0
$561$	16150.4	−	2945.46i	1.21545	−	0.221671i
$562$	8221.69	+	14240.4i	0.617102	+	1.06885i
$563$	−6801.97	−	11781.4i	−0.509181	−	0.881927i	−0.999943	−	0.0106339i	$-0.996615\pi$
$563$	−6801.97	−	11781.4i	−0.509181	−	0.881927i	0.490762	−	0.871293i	$-0.336718\pi$
$564$	20666.9	+	24338.7i	1.54297	+	1.81710i
$565$		0			0
$566$	−2306.77			−0.171309
$567$	11008.8	−	9686.28i	0.815392	−	0.717435i
$568$	9211.10			0.680438
$569$	6229.30	−	10789.5i	0.458956	−	0.794935i	−0.539950	−	0.841697i	$-0.681557\pi$
$569$	6229.30	−	10789.5i	0.458956	−	0.794935i	0.998906	+	0.0467619i	$0.0148902\pi$
$570$		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	$0.669183\pi$
$572$	−20053.5	−	34733.7i	−1.46587	−	2.53897i
$573$	−4157.36	+	758.207i	−0.303100	+	0.0552785i
$574$	−11484.0	+	19890.8i	−0.835074	+	1.44639i
$575$		0			0
$576$	3628.38	−	22088.8i	0.262470	−	1.59786i
$577$	−3722.70			−0.268592			−0.134296	−	0.990941i	$-0.542877\pi$
$577$	−3722.70			−0.268592			−0.134296	+	0.990941i	$0.542877\pi$
$578$	6048.61	−	10476.5i	0.435275	−	0.753918i
$579$	−1423.73	+	3984.18i	−0.102190	+	0.285971i
$580$		0			0
$581$	−8177.99	−	14164.7i	−0.583959	−	1.01145i
$582$	2016.45	−	5642.86i	0.143616	−	0.401897i
$583$	−18121.7	+	31387.7i	−1.28735	+	2.22975i
$584$	8064.19			0.571401
$585$		0			0
$586$	−28349.3			−1.99847
$587$	−8770.16	+	15190.4i	−0.616667	+	1.06810i	0.373423	+	0.927661i	$0.378184\pi$
$587$	−8770.16	+	15190.4i	−0.616667	+	1.06810i	−0.990090	+	0.140437i	$0.955149\pi$
$588$	4067.27	−	741.777i	0.285257	−	0.0520244i
$589$	766.548	+	1327.70i	0.0536249	+	0.0928810i
$590$		0			0
$591$	13716.9	+	16153.9i	0.954718	+	1.12434i
$592$	−59.1933	+	102.526i	−0.00410951	+	0.00711788i
$593$	22350.6			1.54777			0.773886	−	0.633325i	$-0.218310\pi$
$593$	22350.6			1.54777			0.773886	+	0.633325i	$0.218310\pi$
$594$	−37233.9	−	20632.7i	−2.57193	−	1.42520i
$595$		0			0
$596$	−11306.9	+	19584.2i	−0.777097	+	1.34597i
$597$	4515.19	+	5317.38i	0.309539	+	0.364533i
$598$	1026.57	+	1778.07i	0.0702000	+	0.121590i
$599$	1280.81	+	2218.43i	0.0873665	+	0.151323i	0.906397	−	0.422427i	$-0.138822\pi$
$599$	1280.81	+	2218.43i	0.0873665	+	0.151323i	−0.819031	+	0.573750i	$0.805488\pi$
$600$		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	$0.316753\pi$
$602$	19525.6			1.32193
$603$	11314.1	−	4268.87i	0.764091	−	0.288295i
$604$	11315.3			0.762270
$605$		0			0
$606$	−348.693	+	975.786i	−0.0233741	+	0.0654103i
$607$	−14314.3	−	24793.1i	−0.957166	−	1.65786i	−0.729331	−	0.684161i	$-0.760169\pi$
$607$	−14314.3	−	24793.1i	−0.957166	−	1.65786i	−0.227835	−	0.973700i	$-0.573165\pi$
$608$	−906.226	−	1569.63i	−0.0604479	−	0.104699i
$609$	6286.29	−	17591.6i	0.418281	−	1.17052i
$610$		0			0
$611$	−22262.8			−1.47407
$612$	15540.5	−	5863.50i	1.02645	−	0.387284i
$613$	−7188.12			−0.473614			−0.236807	−	0.971557i	$-0.576101\pi$
$613$	−7188.12			−0.473614			−0.236807	+	0.971557i	$0.576101\pi$
$614$	−4497.63	+	7790.12i	−0.295618	+	0.512025i
$615$		0			0
$616$	−15006.5	−	25992.0i	−0.981539	−	1.70008i
$617$	7766.88	+	13452.6i	0.506779	+	0.877767i	0.999969	+	0.00784559i	$0.00249736\pi$
$617$	7766.88	+	13452.6i	0.506779	+	0.877767i	−0.493190	+	0.869922i	$0.664169\pi$
$618$	−22155.9	−	26092.3i	−1.44214	−	1.69836i
$619$	11079.9	−	19191.0i	0.719450	−	1.24612i	−0.241769	−	0.970334i	$-0.577728\pi$
$619$	11079.9	−	19191.0i	0.719450	−	1.24612i	0.961218	−	0.275789i	$-0.0889392\pi$
$620$		0			0
$621$	1177.08	+	652.265i	0.0760624	+	0.0421490i
$622$	−10547.2			−0.679908
$623$	2021.51	−	3501.36i	0.130000	−	0.225167i
$624$	74.8785	+	88.1818i	0.00480375	+	0.00565721i
$625$		0			0
$626$	23559.4	+	40806.1i	1.50419	+	2.60534i
$627$	−3375.25	+	615.569i	−0.214983	+	0.0392081i
$628$	−1675.38	+	2901.85i	−0.106457	+	0.184389i
$629$	−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	$0.798911\pi$
$632$	7327.10	−	12690.9i	0.461165	−	0.798761i
$633$	5166.88	−	14459.0i	0.324431	−	0.907891i
$634$	−3891.73	−	6740.68i	−0.243786	−	0.422250i
$635$		0			0
$636$	−12339.6	+	34531.2i	−0.769334	+	2.15291i
$637$	−1441.33	+	2496.46i	−0.0896510	+	0.155280i
$638$	−54231.5			−3.36527
$639$	−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	$0.204124\pi$
$642$	−8317.33	+	1516.89i	−0.511306	+	0.0932507i
$643$	13360.0	+	23140.3i	0.819391	+	1.41923i	0.906131	+	0.422996i	$0.139022\pi$
$643$	13360.0	+	23140.3i	0.819391	+	1.41923i	−0.0867402	+	0.996231i	$0.527645\pi$
$644$	1246.16	+	2158.41i	0.0762509	+	0.132071i
$645$		0			0
$646$	1083.90	−	1877.37i	0.0660147	−	0.114341i
$647$	−5114.23			−0.310759			−0.155380	−	0.987855i	$-0.549660\pi$
$647$	−5114.23			−0.310759			−0.155380	+	0.987855i	$0.549660\pi$
$648$	−15534.5	−	5245.03i	−0.941750	−	0.317970i
$649$	−27816.8			−1.68244
$650$		0			0
$651$	−10420.8	−	12272.2i	−0.627378	−	0.738842i
$652$	−7762.20	−	13444.5i	−0.466244	−	0.807559i
$653$	−4435.53	−	7682.56i	−0.265813	−	0.460401i	0.701964	−	0.712213i	$-0.252307\pi$
$653$	−4435.53	−	7682.56i	−0.265813	−	0.460401i	−0.967776	+	0.251812i	$0.918974\pi$
$654$	−35595.4	+	6491.79i	−2.12827	+	0.388148i
$655$		0			0
$656$	−118.767			−0.00706872
$657$	−1569.17	+	9552.78i	−0.0931799	+	0.567259i
$658$	−43761.7			−2.59272
$659$	12102.2	−	20961.7i	0.715382	−	1.23908i	−0.247430	−	0.968906i	$-0.579586\pi$
$659$	12102.2	−	20961.7i	0.715382	−	1.23908i	0.962812	−	0.270172i	$-0.0870805\pi$
$660$		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	$-0.383211\pi$
$662$	19098.1	+	33078.9i	1.12125	+	1.94207i
$663$	−3897.14	+	10905.8i	−0.228284	+	0.638832i
$664$	−9144.28	+	15838.4i	−0.534438	+	0.925674i
$665$		0			0
$666$	23771.6	+	19476.4i	1.38308	+	1.13318i
$667$	1714.43			0.0995248
$668$	−10843.7	+	18781.9i	−0.628079	+	1.08787i
$669$	−17926.5	+	3269.38i	−1.03599	+	0.188941i
$670$		0			0
$671$	18085.0	+	31324.2i	1.04048	+	1.80217i
$672$	12319.6	+	14508.4i	0.707203	+	0.832849i
$673$	14850.7	−	25722.1i	0.850597	−	1.47328i	−0.0300732	−	0.999548i	$-0.509574\pi$
$673$	14850.7	−	25722.1i	0.850597	−	1.47328i	0.880670	−	0.473730i	$-0.157093\pi$
$674$	35936.6			2.05375
$675$		0			0
$676$	−86.5900			−0.00492661
$677$	1330.74	−	2304.91i	0.0755459	−	0.130849i	−0.825778	−	0.563996i	$-0.809263\pi$
$677$	1330.74	−	2304.91i	0.0755459	−	0.130849i	0.901324	+	0.433147i	$0.142597\pi$
$678$	−12505.8	−	14727.6i	−0.708381	−	0.834235i
$679$	2535.93	+	4392.36i	0.143328	+	0.248252i
$680$		0			0
$681$	−3337.14	+	608.618i	−0.187782	+	0.0342471i
$682$	−23368.9	+	40476.1i	−1.31208	+	2.27259i
$683$	−28698.1			−1.60776			−0.803882	−	0.594789i	$-0.797235\pi$
$683$	−28698.1			−1.60776			−0.803882	+	0.594789i	$0.797235\pi$
$684$	−3247.80	+	1225.41i	−0.181554	+	0.0685010i
$685$		0			0
$686$	12944.0	−	22419.7i	0.720415	−	1.24780i
$687$	−8014.51	+	22427.9i	−0.445084	+	1.24553i
$688$	50.4833	+	87.4396i	0.00279747	+	0.00484535i
$689$	−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	$0.319945\pi$
$692$	−12036.6			−0.661220
$693$	33710.0	−	12718.9i	1.84781	−	0.697189i
$694$	−5543.99			−0.303238
$695$		0			0
$696$	−20549.4	+	3747.74i	−1.11914	+	0.204106i
$697$	−5944.92	−	10296.9i	−0.323070	−	0.559574i
$698$	−3198.45	−	5539.88i	−0.173443	−	0.300412i
$699$	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	$0.508566\pi$
$702$	25738.6	−	15469.9i	1.38382	−	0.831730i
$703$	2476.88			0.132884
$704$	27500.8	−	47632.9i	1.47227	−	2.55004i
$705$		0			0
$706$	6010.66	+	10410.8i	0.320417	+	0.554978i
$707$	−438.523	−	759.545i	−0.0233272	−	0.0404040i
$708$	−27687.3	+	5049.54i	−1.46971	+	0.268041i
$709$	−16626.9	+	28798.6i	−0.880727	+	1.52546i	−0.0301937	+	0.999544i	$0.509612\pi$
$709$	−16626.9	+	28798.6i	−0.880727	+	1.52546i	−0.850534	+	0.525921i	$0.823721\pi$
$710$		0			0
$711$	13607.8	+	11149.1i	0.717768	+	0.588078i
$712$	−4520.73			−0.237952
$713$	738.765	−	1279.58i	0.0388036	−	0.0672099i
$714$	−7660.56	+	21437.4i	−0.401526	+	1.12363i
$715$		0			0
$716$	−6609.97	−	11448.8i	−0.345009	−	0.597573i
$717$	−3248.21	+	9089.81i	−0.169186	+	0.473452i
$718$	−8409.62	+	14565.9i	−0.437109	+	0.757095i
$719$	1178.94			0.0611503			0.0305752	−	0.999532i	$-0.490266\pi$
$719$	1178.94			0.0611503			0.0305752	+	0.999532i	$0.490266\pi$
$720$		0			0
$721$	28972.0			1.49650
$722$	15458.6	−	26775.0i	0.796826	−	1.38014i
$723$	−16700.1	+	3045.71i	−0.859034	+	0.156668i
$724$	−17050.8	−	29532.9i	−0.875260	−	1.51600i
$725$		0			0
$726$	−47226.8	−	55617.4i	−2.41426	−	2.84319i
$727$	6338.35	−	10978.3i	0.323351	−	0.560061i	−0.657826	−	0.753170i	$-0.728524\pi$
$727$	6338.35	−	10978.3i	0.323351	−	0.560061i	0.981177	+	0.193109i	$0.0618571\pi$
$728$	21172.6			1.07790
$729$	9236.02	−	17381.5i	0.469238	−	0.883072i
$730$		0			0
$731$	−5053.90	+	8753.61i	−0.255712	+	0.442906i
$732$	23687.1	+	27895.5i	1.19604	+	1.40853i
$733$	4903.42	+	8492.98i	0.247083	+	0.427961i	0.962715	−	0.270517i	$-0.0871945\pi$
$733$	4903.42	+	8492.98i	0.247083	+	0.427961i	−0.715632	+	0.698478i	$0.753861\pi$
$734$	26137.5	+	45271.4i	1.31438	+	2.27657i
$735$		0			0
$736$	−873.381	+	1512.74i	−0.0437408	+	0.0757613i
$737$	29712.8			1.48506
$738$	−4997.30	+	30422.5i	−0.249259	+	1.51744i
$739$	−29970.4			−1.49185			−0.745927	−	0.666028i	$-0.767993\pi$
$739$	−29970.4			−1.49185			−0.745927	+	0.666028i	$0.767993\pi$
$740$		0			0
$741$	814.460	−	2279.19i	0.0403778	−	0.112994i
$742$	−25129.2	−	43525.1i	−1.24329	−	2.15345i
$743$	10848.8	+	18790.6i	0.535670	+	0.927808i	0.999131	+	0.0416904i	$0.0132743\pi$
$743$	10848.8	+	18790.6i	0.535670	+	0.927808i	−0.463460	+	0.886118i	$0.653392\pi$
$744$	−6057.78	+	16952.1i	−0.298507	+	0.835344i
$745$		0			0
$746$	−10335.8			−0.507267
$747$	−16982.7	−	13914.2i	−0.831812	−	0.681516i
$748$	40812.1			1.99497
$749$	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	$0.969061\pi$
$752$	−113.146	−	195.974i	−0.00548670	−	0.00950324i
$753$	18973.6	+	22344.5i	0.918243	+	1.08138i
$754$	19128.8	−	33132.0i	0.923911	−	1.60026i
$755$		0			0
$756$	31244.2	−	18779.0i	1.50310	−	0.903422i
$757$	−30745.2			−1.47616			−0.738080	−	0.674714i	$-0.764267\pi$
$757$	−30745.2			−1.47616			−0.738080	+	0.674714i	$0.764267\pi$
$758$	27020.3	−	46800.5i	1.29475	−	2.24257i
$759$	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	$-0.337759\pi$
$762$	20215.3	−	3686.81i	0.961052	−	0.175274i
$763$	15312.3	−	26521.7i	0.726530	−	1.25839i
$764$	−10505.7			−0.497489
$765$		0			0
$766$	36955.5			1.74316
$767$	9811.66	−	16994.3i	0.461902	−	0.800037i
$768$	7075.65	−	19800.6i	0.332449	−	0.930327i
$769$	−11028.7	−	19102.4i	−0.517174	−	0.895772i	−0.999801	−	0.0199457i	$-0.993651\pi$
$769$	−11028.7	−	19102.4i	−0.517174	−	0.895772i	0.482627	−	0.875826i	$-0.339683\pi$
$770$		0			0
$771$	−2051.84	+	5741.89i	−0.0958434	+	0.268209i
$772$	−5259.04	+	9108.93i	−0.245178	+	0.424660i
$773$	−30155.8			−1.40314			−0.701570	−	0.712601i	$-0.747517\pi$
$773$	−30155.8			−1.40314			−0.701570	+	0.712601i	$0.747517\pi$
$774$	24522.0	−	9252.26i	1.13879	−	0.429671i
$775$		0			0
$776$	2835.57	−	4911.35i	0.131174	−	0.227200i
$777$	−25588.7	+	4666.81i	−1.18146	+	0.215471i
$778$	−7090.04	−	12280.3i	−0.326723	−	0.565900i
$779$	1242.42	+	2151.94i	0.0571431	+	0.0989747i
$780$		0			0
$781$	−13584.8	+	23529.6i	−0.622411	+	1.07805i
$782$	−2089.23			−0.0955381
$783$	−440.943	−	25071.9i	−0.0201252	−	1.14431i
$784$	−29.3010			−0.00133478
$785$		0			0
$786$	33510.7	+	39464.4i	1.52072	+	1.79090i
$787$	−1624.36	−	2813.47i	−0.0735733	−	0.127433i	0.826892	−	0.562361i	$-0.190107\pi$
$787$	−1624.36	−	2813.47i	−0.0735733	−	0.127433i	−0.900465	+	0.434929i	$0.856774\pi$
$788$	26341.7	+	45625.2i	1.19084	+	2.06260i
$789$	14813.9	−	2701.72i	0.668427	−	0.121906i
$790$		0			0
$791$	16353.1			0.735081
$792$	−31162.9	−	25532.3i	−1.39814	−	1.14552i
$793$	−25516.1			−1.14263
$794$	−27418.8	+	47490.8i	−1.22551	+	2.12265i
$795$		0			0
$796$	8670.90	+	15018.4i	0.386095	+	0.668737i
$797$	−13855.1	−	23997.7i	−0.615775	−	1.06655i	−0.990248	−	0.139316i	$-0.955510\pi$
$797$	−13855.1	−	23997.7i	−0.615775	−	1.06655i	0.374473	−	0.927238i	$-0.377824\pi$
$798$	1600.98	−	4480.18i	0.0710199	−	0.198743i
$799$	11327.1	−	19619.0i	0.501530	−	0.868675i
$800$		0			0
$801$	879.667	−	5355.23i	0.0388034	−	0.236227i
$802$	58785.4			2.58826
$803$	−11893.3	+	20599.8i	−0.522673	+	0.905296i
$804$	29574.6	−	5393.73i	1.29728	−	0.236595i
$805$		0			0
$806$	−16485.6	−	28553.8i	−0.720445	−	1.24785i
$807$	−9854.90	−	11605.8i	−0.429875	−	0.506248i
$808$	−490.338	+	849.290i	−0.0213491	+	0.0369776i
$809$	−2244.10			−0.0975259			−0.0487630	−	0.998810i	$-0.515528\pi$
$809$	−2244.10			−0.0975259			−0.0487630	+	0.998810i	$0.515528\pi$
$810$		0			0
$811$	−2739.73			−0.118625			−0.0593126	−	0.998239i	$-0.518891\pi$
$811$	−2739.73			−0.118625			−0.0593126	+	0.998239i	$0.518891\pi$
$812$	23220.6	−	40219.2i	1.00355	−	1.73820i
$813$	2249.65	+	2649.33i	0.0970462	+	0.114288i
$814$	37755.0	+	65393.5i	1.62569	+	2.81578i
$815$		0			0
$816$	−115.808	+	21.1207i	−0.00496823	+	0.000906092i
$817$	1056.21	−	1829.41i	0.0452290	−	0.0783390i
$818$	10176.6			0.434984
$819$	−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	$0.0473034\pi$
$822$	−18386.6	+	51453.1i	−0.780177	+	2.18325i
$823$	9642.94	+	16702.1i	0.408422	+	0.707409i	0.994713	−	0.102692i	$-0.0327457\pi$
$823$	9642.94	+	16702.1i	0.408422	+	0.707409i	−0.586291	+	0.810101i	$0.699412\pi$
$824$	−16197.6	−	28055.1i	−0.684795	−	1.18610i
$825$		0			0
$826$	19286.7	−	33405.5i	0.812433	−	1.40717i
$827$	−26379.4			−1.10919			−0.554595	−	0.832120i	$-0.687127\pi$
$827$	−26379.4			−1.10919			−0.554595	+	0.832120i	$0.687127\pi$
$828$	2587.82	+	2120.24i	0.108615	+	0.0889896i
$829$	−8718.15			−0.365252			−0.182626	−	0.983182i	$-0.558460\pi$
$829$	−8718.15			−0.365252			−0.182626	+	0.983182i	$0.558460\pi$
$830$		0			0
$831$	3233.90	−	589.790i	0.134997	−	0.0246205i
$832$	19400.4	+	33602.6i	0.808401	+	1.40019i
$833$	−1466.67	−	2540.35i	−0.0610049	−	0.105664i
$834$	32825.1	+	38657.0i	1.36288	+	1.60501i
$835$		0			0
$836$	−8529.28			−0.352860
$837$	−18902.6	−	10474.6i	−0.780610	−	0.432565i
$838$	44256.9			1.82438
$839$	6738.10	−	11670.7i	0.277265	−	0.480236i	−0.693439	−	0.720515i	$-0.743905\pi$
$839$	6738.10	−	11670.7i	0.277265	−	0.480236i	0.970704	+	0.240279i	$0.0772388\pi$
$840$		0			0
$841$	−3778.58	−	6544.70i	−0.154930	−	0.268346i
$842$	22782.4	+	39460.2i	0.932462	+	1.61507i
$843$	−18378.6	+	3351.83i	−0.750880	+	0.136943i
$844$	19085.6	−	33057.3i	0.778383	−	1.34820i
$845$		0			0
$846$	−54959.9	+	20736.6i	−2.23352	+	0.842718i
$847$	61755.7			2.50526
$848$	129.943	−	225.068i	0.00526210	−	0.00911423i
$849$	881.907	−	2467.93i	0.0356501	−	0.0997636i
$850$		0			0
$851$	−1193.56	−	2067.30i	−0.0480783	−	0.0832740i
$852$	−9250.31	+	25886.1i	−0.371960	+	1.04090i
$853$	−14118.3	+	24453.6i	−0.566708	+	0.981567i	0.430181	+	0.902743i	$0.358450\pi$
$853$	−14118.3	+	24453.6i	−0.566708	+	0.981567i	−0.996889	+	0.0788242i	$0.974883\pi$
$854$	−50156.8			−2.00975
$855$		0			0
$856$	−8001.36			−0.319487
$857$	4229.08	−	7324.98i	0.168568	−	0.291968i	−0.769349	−	0.638829i	$-0.779419\pi$
$857$	4229.08	−	7324.98i	0.168568	−	0.291968i	0.937917	+	0.346861i	$0.112752\pi$
$858$	72588.9	−	13238.6i	2.88828	−	0.526757i
$859$	11527.2	+	19965.6i	0.457860	+	0.793036i	0.998848	−	0.0479940i	$-0.0152828\pi$
$859$	11527.2	+	19965.6i	0.457860	+	0.793036i	−0.540988	+	0.841030i	$0.681950\pi$
$860$		0			0
$861$	−16890.1	−	19890.8i	−0.668539	−	0.787315i
$862$	5628.86	−	9749.48i	0.222413	−	0.385230i
$863$	42314.4			1.66906			0.834529	−	0.550963i	$-0.185740\pi$
$863$	42314.4			1.66906			0.834529	+	0.550963i	$0.185740\pi$
$864$	22347.0	+	12383.3i	0.879932	+	0.487602i
$865$		0			0
$866$	17879.2	−	30967.8i	0.701572	−	1.21516i
$867$	8895.99	+	10476.5i	0.348470	+	0.410381i
$868$	−20011.9	−	34661.7i	−0.782545	−	1.35541i
$869$	21612.5	+	37433.9i	0.843674	+	1.46129i
$870$		0			0
$871$	−10480.4	+	18152.7i	−0.407711	+	0.706176i
$872$	−34243.1			−1.32984
$873$	5266.19	+	4314.67i	0.204162	+	0.167273i
$874$	436.627			0.0168983
$875$		0			0
$876$	−8098.51	+	22663.0i	−0.312356	+	0.874098i
$877$	−5090.00	−	8816.15i	−0.195983	−	0.339453i	0.751239	−	0.660030i	$-0.229456\pi$
$877$	−5090.00	−	8816.15i	−0.195983	−	0.339453i	−0.947222	+	0.320577i	$0.896123\pi$
$878$	−14205.2	−	24604.0i	−0.546014	−	0.945725i
$879$	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	$0.463214\pi$
$882$	−1232.88	+	7505.53i	−0.0470673	+	0.286535i
$883$	30238.0			1.15242			0.576211	−	0.817301i	$-0.304531\pi$
$883$	30238.0			1.15242			0.576211	+	0.817301i	$0.304531\pi$
$884$	−14395.4	+	24933.6i	−0.547704	+	0.948651i
$885$		0			0
$886$	6824.57	+	11820.5i	0.258776	+	0.448214i
$887$	9388.09	+	16260.7i	0.355379	+	0.615535i	0.987183	−	0.159594i	$-0.0510184\pi$
$887$	9388.09	+	16260.7i	0.355379	+	0.615535i	−0.631804	+	0.775129i	$0.717685\pi$
$888$	18825.2	+	22169.8i	0.711412	+	0.837805i
$889$	−8696.14	+	15062.1i	−0.328075	+	0.568243i
$890$		0			0
$891$	36309.2	−	31947.2i	1.36521	−	1.20120i
$892$	−45300.3			−1.70041
$893$	−2367.23	+	4100.17i	−0.0887082	+	0.153647i
$894$	−26928.6	−	31712.8i	−1.00741	−	1.18639i
$895$		0			0
$896$	23483.4	+	40674.4i	0.875586	+	1.51656i
$897$	−2294.77	+	418.514i	−0.0854182	+	0.0155783i
$898$	1853.39	−	3210.16i	0.0688735	−	0.119292i
$899$	−27531.8			−1.02140
$900$		0			0
$901$	26017.3			0.962000
$902$	−37876.4	+	65603.8i	−1.39817	+	2.42169i
$903$	−7464.86	+	20889.7i	−0.275100	+	0.769841i
$904$	−9142.66	−	15835.6i	−0.336372	−	0.582614i
$905$		0			0
$906$	−7005.07	+	19603.0i	−0.256874	+	0.718838i
$907$	−18826.3	+	32608.1i	−0.689213	+	1.19375i	0.282880	+	0.959155i	$0.408710\pi$
$907$	−18826.3	+	32608.1i	−0.689213	+	1.19375i	−0.972093	+	0.234597i	$0.924623\pi$
$908$	−8432.97			−0.308214
$909$	−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	$-0.166213\pi$
$912$	24.2025	−	4.41399i	0.000878756	−	0.000160265i
$913$	−26972.6	−	46717.9i	−0.977724	−	1.69347i
$914$	3594.32	+	6225.54i	0.130076	+	0.225298i
$915$		0			0
$916$	−29604.3	+	51276.2i	−1.06785	+	1.84958i
$917$	−43819.9			−1.57804
$918$	537.340	+	30553.0i	0.0193190	+	1.09848i
$919$	32177.3			1.15499			0.577493	−	0.816396i	$-0.304031\pi$
$919$	32177.3			1.15499			0.577493	+	0.816396i	$0.304031\pi$
$920$		0			0
$921$	−6614.88	−	7790.12i	−0.236664	−	0.278711i
$922$	−4716.94	−	8169.99i	−0.168486	−	0.291827i
$923$	−9583.40	−	16598.9i	−0.341757	−	0.591940i
$924$	88116.2	−	16070.4i	3.13724	−	0.572161i
$925$		0			0
$926$	−12729.3			−0.451741
$927$	36385.7	−	13728.5i	1.28917	−	0.486411i
$928$	32548.6			1.15136
$929$	−20321.8	+	35198.4i	−0.717694	+	1.24308i	0.244218	+	0.969720i	$0.421469\pi$
$929$	−20321.8	+	35198.4i	−0.717694	+	1.24308i	−0.961911	+	0.273362i	$0.911864\pi$
$930$		0			0
$931$	306.518	+	530.905i	0.0107903	+	0.0186893i
$932$	2050.85	+	3552.18i	0.0720792	+	0.124845i
$933$	4032.31	−	11284.1i	0.141492	−	0.395952i
$934$	25016.7	−	43330.2i	0.876415	−	1.51799i
$935$		0			0
$936$	26590.5	−	10032.7i	0.928567	−	0.350352i
$937$	−6077.87			−0.211905			−0.105953	−	0.994371i	$-0.533789\pi$
$937$	−6077.87			−0.211905			−0.105953	+	0.994371i	$0.533789\pi$
$938$	−20601.3	+	35682.5i	−0.717118	+	1.24208i
$939$	−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	$0.841409\pi$
$942$	−3990.09	−	4698.99i	−0.138009	−	0.162528i
$943$	1197.39	−	2073.95i	0.0413494	−	0.0716193i
$944$	199.463			0.00687707
$945$		0			0
$946$	64399.0			2.21331
$947$	−5304.36	+	9187.43i	−0.182015	+	0.315260i	−0.942567	−	0.334018i	$-0.891595\pi$
$947$	−5304.36	+	9187.43i	−0.182015	+	0.315260i	0.760551	+	0.649278i	$0.224929\pi$
$948$	28307.2	+	33336.4i	0.969806	+	1.14211i
$949$	−8390.14	−	14532.1i	−0.286992	−	0.497085i
$950$		0			0
$951$	8699.48	−	1586.59i	0.296635	−	0.0540995i
$952$	−10772.4	+	18658.4i	−0.366739	+	0.635211i
$953$	43623.4			1.48279			0.741396	−	0.671068i	$-0.234164\pi$
$953$	43623.4			1.48279			0.741396	+	0.671068i	$0.234164\pi$
$954$	−52184.1	−	42755.3i	−1.77099	−	1.45100i
$955$		0			0
$956$	−11998.4	+	20781.8i	−0.405915	+	0.703065i
$957$	20733.4	−	58020.4i	0.700329	−	1.95981i
$958$	−33441.3	−	57922.1i	−1.12781	−	1.95342i
$959$	−23123.3	−	40050.7i	−0.778613	−	1.34860i
$960$		0			0
$961$	3031.76	−	5251.17i	0.101768	−	0.176267i
$962$	−53268.4			−1.78528
$963$	1556.95	−	9478.35i	0.0520996	−	0.317171i
$964$	−42201.2			−1.40997
$965$		0			0
$966$	−4510.80	+	822.668i	−0.150241	+	0.0274005i
$967$	2540.19	+	4399.73i	0.0844745	+	0.146314i	0.905167	−	0.425056i	$-0.139746\pi$
$967$	2540.19	+	4399.73i	0.0844745	+	0.146314i	−0.820693	+	0.571370i	$0.806412\pi$
$968$	−34526.3	−	59801.3i	−1.14640	−	1.98563i
$969$	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	$0.447820\pi$
$972$	30340.9	−	38389.7i	1.00122	−	1.26682i
$973$	−42923.4			−1.41425
$974$	37671.8	−	65249.4i	1.23930	−	2.14654i
$975$		0			0
$976$	−129.680	−	224.613i	−0.00425304	−	0.00736648i
$977$	12290.4	+	21287.6i	0.402461	+	0.697084i	0.994022	−	0.109177i	$-0.0348214\pi$
$977$	12290.4	+	21287.6i	0.402461	+	0.697084i	−0.591561	+	0.806260i	$0.701488\pi$
$978$	28097.3	−	5124.31i	0.918664	−	0.167543i
$979$	6667.32	−	11548.1i	0.217659	−	0.376997i
$980$		0			0
$981$	6663.21	−	40564.2i	0.216860	−	1.32020i
$982$	93891.8			3.05113
$983$	−15930.3	+	27592.1i	−0.516885	+	0.895270i	0.482923	+	0.875663i	$0.339575\pi$
$983$	−15930.3	+	27592.1i	−0.516885	+	0.895270i	−0.999808	+	0.0196076i	$0.993758\pi$
$984$	−9818.48	+	27476.1i	−0.318091	+	0.890149i
$985$		0			0
$986$	19465.0	+	33714.4i	0.628695	+	1.08893i
$987$	16730.6	−	46819.1i	0.539556	−	1.50990i
$988$	3008.49	−	5210.85i	0.0968752	−	0.167793i
$989$	−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	$0.701562\pi$
$992$	14025.5	−	24292.9i	0.448902	−	0.777520i
$993$	−42691.4	+	7785.95i	−1.36432	+	0.248821i
$994$	−18838.0	−	32628.4i	−0.601112	−	1.04116i
$995$		0			0
$996$	−35327.7	−	41604.2i	−1.12390	−	1.32357i
$997$	−1867.06	+	3233.84i	−0.0593083	+	0.102725i	−0.894155	−	0.447757i	$-0.852223\pi$
$997$	−1867.06	+	3233.84i	−0.0593083	+	0.102725i	0.834847	+	0.550482i	$0.185556\pi$
$998$	−65880.7			−2.08959
$999$	−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.e.c.151.1		6
5.2	odd	4		225.4.k.c.124.1		12
5.3	odd	4		225.4.k.c.124.6		12
5.4	even	2		45.4.e.b.16.3	✓	6
9.2	odd	6		2025.4.a.q.1.1		3
9.4	even	3	inner	225.4.e.c.76.1		6
9.7	even	3		2025.4.a.s.1.3		3
15.14	odd	2		135.4.e.b.46.1		6
45.4	even	6		45.4.e.b.31.3	yes	6
45.13	odd	12		225.4.k.c.49.1		12
45.14	odd	6		135.4.e.b.91.1		6
45.22	odd	12		225.4.k.c.49.6		12
45.29	odd	6		405.4.a.j.1.3		3
45.34	even	6		405.4.a.h.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.4.e.b.16.3	✓	6	5.4	even	2
45.4.e.b.31.3	yes	6	45.4	even	6
135.4.e.b.46.1		6	15.14	odd	2
135.4.e.b.91.1		6	45.14	odd	6
225.4.e.c.76.1		6	9.4	even	3	inner
225.4.e.c.151.1		6	1.1	even	1	trivial
225.4.k.c.49.1		12	45.13	odd	12
225.4.k.c.49.6		12	45.22	odd	12
225.4.k.c.124.1		12	5.2	odd	4
225.4.k.c.124.6		12	5.3	odd	4
405.4.a.h.1.1		3	45.34	even	6
405.4.a.j.1.3		3	45.29	odd	6
2025.4.a.q.1.1		3	9.2	odd	6
2025.4.a.s.1.3		3	9.7	even	3

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.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.28679 + 3.96084i) q^{2} +(-3.36330 - 3.96084i) q^{3} +(-6.45882 - 11.1870i) q^{4} +(23.3794 - 4.26387i) q^{6} +(-10.0573 + 17.4197i) q^{7} +22.4912 q^{8} +(-4.37646 + 26.6429i) q^{9} +O(q^{10})\)	\(q+(-2.28679 + 3.96084i) q^{2} +(-3.36330 - 3.96084i) q^{3} +(-6.45882 - 11.1870i) q^{4} +(23.3794 - 4.26387i) q^{6} +(-10.0573 + 17.4197i) q^{7} +22.4912 q^{8} +(-4.37646 + 26.6429i) q^{9} +(-33.1708 + 57.4535i) q^{11} +(-22.5870 + 63.2076i) q^{12} +(-23.4003 - 40.5305i) q^{13} +(-45.9977 - 79.6704i) q^{14} +(0.237854 - 0.411975i) q^{16} +47.6233 q^{17} +(-95.5203 - 78.2613i) q^{18} -9.95276 q^{19} +(102.822 - 18.7524i) q^{21} +(-151.709 - 262.768i) q^{22} +(4.79602 + 8.30695i) q^{23} +(-75.6447 - 89.0841i) q^{24} +214.046 q^{26} +(120.248 - 72.2737i) q^{27} +259.832 q^{28} +(89.3675 - 154.789i) q^{29} +(-77.0186 - 133.400i) q^{31} +(91.0527 + 157.708i) q^{32} +(339.127 - 61.8491i) q^{33} +(-108.905 + 188.628i) q^{34} +(326.322 - 123.123i) q^{36} -248.864 q^{37} +(22.7599 - 39.4213i) q^{38} +(-81.8326 + 229.001i) q^{39} +(-124.832 - 216.216i) q^{41} +(-160.857 + 450.145i) q^{42} +(-106.122 + 183.809i) q^{43} +856.976 q^{44} -43.8700 q^{46} +(237.847 - 411.963i) q^{47} +(-2.43174 + 0.443494i) q^{48} +(-30.7973 - 53.3425i) q^{49} +(-160.171 - 188.628i) q^{51} +(-302.277 + 523.559i) q^{52} +546.314 q^{53} +(11.2831 + 641.556i) q^{54} +(-226.200 + 391.790i) q^{56} +(33.4741 + 39.4213i) q^{57} +(408.729 + 707.940i) q^{58} +(209.648 + 363.121i) q^{59} +(272.605 - 472.165i) q^{61} +704.502 q^{62} +(-420.097 - 344.192i) q^{63} -829.068 q^{64} +(-530.538 + 1484.66i) q^{66} +(-223.938 - 387.872i) q^{67} +(-307.590 - 532.762i) q^{68} +(16.7720 - 46.9350i) q^{69} +409.542 q^{71} +(-98.4319 + 599.232i) q^{72} +358.548 q^{73} +(569.100 - 985.710i) q^{74} +(64.2831 + 111.342i) q^{76} +(-667.215 - 1155.65i) q^{77} +(-719.902 - 847.803i) q^{78} +(325.776 - 564.260i) q^{79} +(-690.693 - 233.204i) q^{81} +1141.86 q^{82} +(-406.571 + 704.202i) q^{83} +(-873.893 - 1029.15i) q^{84} +(-485.359 - 840.667i) q^{86} +(-913.663 + 166.631i) q^{87} +(-746.051 + 1292.20i) q^{88} -201.000 q^{89} +941.373 q^{91} +(61.9532 - 107.306i) q^{92} +(-269.340 + 753.723i) q^{93} +(1087.81 + 1884.14i) q^{94} +(318.418 - 891.064i) q^{96} +(126.074 - 218.367i) q^{97} +281.708 q^{98} +(-1385.56 - 1135.21i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - q^{2} - 9 q^{3} - 11 q^{4} + 84 q^{6} - 43 q^{7} + 54 q^{8} + 57 q^{9}+O(q^{10}) \) 6 * q - q^2 - 9 * q^3 - 11 * q^4 + 84 * q^6 - 43 * q^7 + 54 * q^8 + 57 * q^9	\( 6 q - q^{2} - 9 q^{3} - 11 q^{4} + 84 q^{6} - 43 q^{7} + 54 q^{8} + 57 q^{9} - 14 q^{11} - 75 q^{12} + 40 q^{13} + 27 q^{14} + 13 q^{16} + 332 q^{17} - 3 q^{18} - 328 q^{19} - 144 q^{21} - 376 q^{22} + 171 q^{23} - 63 q^{24} + 868 q^{26} - 162 q^{27} + 1034 q^{28} + 335 q^{29} + 352 q^{31} - 77 q^{32} + 708 q^{33} + 52 q^{34} + 1086 q^{36} - 804 q^{37} - 178 q^{38} - 390 q^{39} - 187 q^{41} - 513 q^{42} - 602 q^{43} + 1964 q^{44} - 402 q^{46} + 665 q^{47} + 1074 q^{48} - 430 q^{49} - 180 q^{51} - 456 q^{52} + 1460 q^{53} + 639 q^{54} - 705 q^{56} + 486 q^{57} + 217 q^{58} + 298 q^{59} + 1439 q^{61} + 3228 q^{62} - 2205 q^{63} - 3138 q^{64} - 966 q^{66} - 1849 q^{67} - 710 q^{68} - 873 q^{69} + 140 q^{71} - 261 q^{72} + 736 q^{73} + 320 q^{74} - 204 q^{76} - 948 q^{77} + 432 q^{78} + 382 q^{79} - 1251 q^{81} + 1150 q^{82} - 831 q^{83} - 909 q^{84} - 1580 q^{86} - 258 q^{87} - 1428 q^{88} + 3438 q^{89} - 1420 q^{91} - 1623 q^{92} - 2178 q^{93} + 2077 q^{94} + 1155 q^{96} - 282 q^{97} - 4328 q^{98} - 762 q^{99}+O(q^{100}) \) 6 * q - q^2 - 9 * q^3 - 11 * q^4 + 84 * q^6 - 43 * q^7 + 54 * q^8 + 57 * q^9 - 14 * q^11 - 75 * q^12 + 40 * q^13 + 27 * q^14 + 13 * q^16 + 332 * q^17 - 3 * q^18 - 328 * q^19 - 144 * q^21 - 376 * q^22 + 171 * q^23 - 63 * q^24 + 868 * q^26 - 162 * q^27 + 1034 * q^28 + 335 * q^29 + 352 * q^31 - 77 * q^32 + 708 * q^33 + 52 * q^34 + 1086 * q^36 - 804 * q^37 - 178 * q^38 - 390 * q^39 - 187 * q^41 - 513 * q^42 - 602 * q^43 + 1964 * q^44 - 402 * q^46 + 665 * q^47 + 1074 * q^48 - 430 * q^49 - 180 * q^51 - 456 * q^52 + 1460 * q^53 + 639 * q^54 - 705 * q^56 + 486 * q^57 + 217 * q^58 + 298 * q^59 + 1439 * q^61 + 3228 * q^62 - 2205 * q^63 - 3138 * q^64 - 966 * q^66 - 1849 * q^67 - 710 * q^68 - 873 * q^69 + 140 * q^71 - 261 * q^72 + 736 * q^73 + 320 * q^74 - 204 * q^76 - 948 * q^77 + 432 * q^78 + 382 * q^79 - 1251 * q^81 + 1150 * q^82 - 831 * q^83 - 909 * q^84 - 1580 * q^86 - 258 * q^87 - 1428 * q^88 + 3438 * q^89 - 1420 * q^91 - 1623 * q^92 - 2178 * q^93 + 2077 * q^94 + 1155 * q^96 - 282 * q^97 - 4328 * q^98 - 762 * q^99

Introduction

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