LMFDB - Embedded newform 450.3.i.b.401.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [450,3,Mod(101,450)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(450, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 0]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("450.101");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 450 = 2 \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	450.i (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$12.2616118962$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{-2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{2} + 4 $ x^4 - 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 18)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			401.1
Root			$-1.22474 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	450.401
Dual form			450.3.i.b.101.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.22474 + 0.707107i) q^{2} +(2.44949 - 1.73205i) q^{3} +(1.00000 - 1.73205i) q^{4} +(-1.77526 + 3.85337i) q^{6} +(-4.17423 - 7.22999i) q^{7} +2.82843i q^{8} +(3.00000 - 8.48528i) q^{9} +O(q^{10})$	\(q+(-1.22474 + 0.707107i) q^{2} +(2.44949 - 1.73205i) q^{3} +(1.00000 - 1.73205i) q^{4} +(-1.77526 + 3.85337i) q^{6} +(-4.17423 - 7.22999i) q^{7} +2.82843i q^{8} +(3.00000 - 8.48528i) q^{9} +(0.825765 - 0.476756i) q^{11} +(-0.550510 - 5.97469i) q^{12} +(-4.84847 + 8.39780i) q^{13} +(10.2247 + 5.90326i) q^{14} +(-2.00000 - 3.46410i) q^{16} -18.8776i q^{17} +(2.32577 + 12.5136i) q^{18} -24.6969 q^{19} +(-22.7474 - 10.4798i) q^{21} +(-0.674235 + 1.16781i) q^{22} +(-0.825765 - 0.476756i) q^{23} +(4.89898 + 6.92820i) q^{24} -13.7135i q^{26} +(-7.34847 - 25.9808i) q^{27} -16.6969 q^{28} +(11.8485 - 6.84072i) q^{29} +(-1.52270 + 2.63740i) q^{31} +(4.89898 + 2.82843i) q^{32} +(1.19694 - 2.59808i) q^{33} +(13.3485 + 23.1202i) q^{34} +(-11.6969 - 13.6814i) q^{36} -46.6969 q^{37} +(30.2474 - 17.4634i) q^{38} +(2.66913 + 28.9681i) q^{39} +(-9.45459 - 5.45861i) q^{41} +(35.2702 - 3.24980i) q^{42} +(22.5227 + 39.0105i) q^{43} -1.90702i q^{44} +1.34847 q^{46} +(-39.2196 + 22.6435i) q^{47} +(-10.8990 - 5.02118i) q^{48} +(-10.3485 + 17.9241i) q^{49} +(-32.6969 - 46.2405i) q^{51} +(9.69694 + 16.7956i) q^{52} -94.3879i q^{53} +(27.3712 + 26.6237i) q^{54} +(20.4495 - 11.8065i) q^{56} +(-60.4949 + 42.7764i) q^{57} +(-9.67423 + 16.7563i) q^{58} +(-16.2650 - 9.39063i) q^{59} +(-6.54541 - 11.3370i) q^{61} -4.30686i q^{62} +(-73.8712 + 13.7296i) q^{63} -8.00000 q^{64} +(0.371173 + 4.02834i) q^{66} +(37.5227 - 64.9912i) q^{67} +(-32.6969 - 18.8776i) q^{68} +(-2.84847 + 0.262459i) q^{69} -18.0204i q^{71} +(24.0000 + 8.48528i) q^{72} +7.90918 q^{73} +(57.1918 - 33.0197i) q^{74} +(-24.6969 + 42.7764i) q^{76} +(-6.89388 - 3.98018i) q^{77} +(-23.7526 - 33.5912i) q^{78} +(21.8712 + 37.8820i) q^{79} +(-63.0000 - 50.9117i) q^{81} +15.4393 q^{82} +(112.871 - 65.1662i) q^{83} +(-40.8990 + 28.9199i) q^{84} +(-55.1691 - 31.8519i) q^{86} +(17.1742 - 37.2784i) q^{87} +(1.34847 + 2.33562i) q^{88} -145.300i q^{89} +80.9546 q^{91} +(-1.65153 + 0.953512i) q^{92} +(0.838264 + 9.09769i) q^{93} +(32.0227 - 55.4650i) q^{94} +(16.8990 - 1.55708i) q^{96} +(-54.9393 - 95.1576i) q^{97} -29.2699i q^{98} +(-1.56811 - 8.43712i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{4} - 12 q^{6} - 2 q^{7} + 12 q^{9}+O(q^{10}) $ 4 * q + 4 * q^4 - 12 * q^6 - 2 * q^7 + 12 * q^9	$ 4 q + 4 q^{4} - 12 q^{6} - 2 q^{7} + 12 q^{9} + 18 q^{11} - 12 q^{12} + 10 q^{13} + 36 q^{14} - 8 q^{16} + 24 q^{18} - 40 q^{19} - 42 q^{21} + 12 q^{22} - 18 q^{23} - 8 q^{28} + 18 q^{29} + 38 q^{31} - 54 q^{33} + 24 q^{34} + 12 q^{36} - 128 q^{37} + 72 q^{38} - 102 q^{39} - 126 q^{41} + 48 q^{42} + 46 q^{43} - 24 q^{46} - 54 q^{47} - 24 q^{48} - 12 q^{49} - 72 q^{51} - 20 q^{52} + 36 q^{54} + 72 q^{56} - 144 q^{57} - 24 q^{58} + 126 q^{59} + 62 q^{61} - 222 q^{63} - 32 q^{64} - 72 q^{66} + 106 q^{67} - 72 q^{68} + 18 q^{69} + 96 q^{72} + 208 q^{73} + 72 q^{74} - 40 q^{76} + 90 q^{77} - 144 q^{78} + 14 q^{79} - 252 q^{81} - 144 q^{82} + 378 q^{83} - 144 q^{84} - 108 q^{86} + 54 q^{87} - 24 q^{88} + 412 q^{91} - 36 q^{92} - 222 q^{93} + 84 q^{94} + 48 q^{96} - 14 q^{97} + 126 q^{99}+O(q^{100}) $ 4 * q + 4 * q^4 - 12 * q^6 - 2 * q^7 + 12 * q^9 + 18 * q^11 - 12 * q^12 + 10 * q^13 + 36 * q^14 - 8 * q^16 + 24 * q^18 - 40 * q^19 - 42 * q^21 + 12 * q^22 - 18 * q^23 - 8 * q^28 + 18 * q^29 + 38 * q^31 - 54 * q^33 + 24 * q^34 + 12 * q^36 - 128 * q^37 + 72 * q^38 - 102 * q^39 - 126 * q^41 + 48 * q^42 + 46 * q^43 - 24 * q^46 - 54 * q^47 - 24 * q^48 - 12 * q^49 - 72 * q^51 - 20 * q^52 + 36 * q^54 + 72 * q^56 - 144 * q^57 - 24 * q^58 + 126 * q^59 + 62 * q^61 - 222 * q^63 - 32 * q^64 - 72 * q^66 + 106 * q^67 - 72 * q^68 + 18 * q^69 + 96 * q^72 + 208 * q^73 + 72 * q^74 - 40 * q^76 + 90 * q^77 - 144 * q^78 + 14 * q^79 - 252 * q^81 - 144 * q^82 + 378 * q^83 - 144 * q^84 - 108 * q^86 + 54 * q^87 - 24 * q^88 + 412 * q^91 - 36 * q^92 - 222 * q^93 + 84 * q^94 + 48 * q^96 - 14 * q^97 + 126 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/450\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$

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 $

$2$	−1.22474	+	0.707107i	−0.612372	+	0.353553i
$2$	−1.22474	+	0.707107i	−0.612372	+	0.353553i
$3$	2.44949	−	1.73205i	0.816497	−	0.577350i
$3$	2.44949	−	1.73205i	0.816497	−	0.577350i
$4$	1.00000	−	1.73205i	0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$	−1.77526	+	3.85337i	−0.295876	+	0.642229i
$7$	−4.17423	−	7.22999i	−0.596319	−	1.03286i	−0.993359	−	0.115054i	$-0.963296\pi$
$7$	−4.17423	−	7.22999i	−0.596319	−	1.03286i	0.397040	−	0.917801i	$-0.370037\pi$
$8$			2.82843i			0.353553i
$9$	3.00000	−	8.48528i	0.333333	−	0.942809i
$10$		0			0
$11$	0.825765	−	0.476756i	0.0750696	−	0.0433414i	−0.461995	−	0.886882i	$-0.652866\pi$
$11$	0.825765	−	0.476756i	0.0750696	−	0.0433414i	0.537065	+	0.843541i	$0.319533\pi$
$12$	−0.550510	−	5.97469i	−0.0458759	−	0.497891i
$13$	−4.84847	+	8.39780i	−0.372959	+	0.645984i	−0.990019	−	0.140932i	$-0.954990\pi$
$13$	−4.84847	+	8.39780i	−0.372959	+	0.645984i	0.617060	+	0.786916i	$0.288324\pi$
$14$	10.2247	+	5.90326i	0.730339	+	0.421661i
$15$		0			0
$16$	−2.00000	−	3.46410i	−0.125000	−	0.216506i
$17$		−	18.8776i		−	1.11045i	−0.831701	−	0.555223i	$-0.812633\pi$
$17$		−	18.8776i		−	1.11045i	0.831701	−	0.555223i	$-0.187367\pi$
$18$	2.32577	+	12.5136i	0.129209	+	0.695201i
$19$	−24.6969			−1.29984			−0.649919	−	0.760003i	$-0.725197\pi$
$19$	−24.6969			−1.29984			−0.649919	+	0.760003i	$0.725197\pi$
$20$		0			0
$21$	−22.7474	−	10.4798i	−1.08321	−	0.499038i
$22$	−0.674235	+	1.16781i	−0.0306470	+	0.0530822i
$23$	−0.825765	−	0.476756i	−0.0359028	−	0.0207285i	0.481941	−	0.876204i	$-0.339932\pi$
$23$	−0.825765	−	0.476756i	−0.0359028	−	0.0207285i	−0.517844	+	0.855475i	$0.673265\pi$
$24$	4.89898	+	6.92820i	0.204124	+	0.288675i
$25$		0			0
$26$		−	13.7135i		−	0.527444i
$27$	−7.34847	−	25.9808i	−0.272166	−	0.962250i
$28$	−16.6969			−0.596319
$29$	11.8485	−	6.84072i	0.408568	−	0.235887i	−0.281606	−	0.959530i	$-0.590867\pi$
$29$	11.8485	−	6.84072i	0.408568	−	0.235887i	0.690174	+	0.723643i	$0.257534\pi$
$30$		0			0
$31$	−1.52270	+	2.63740i	−0.0491195	+	0.0850774i	−0.889540	−	0.456858i	$-0.848975\pi$
$31$	−1.52270	+	2.63740i	−0.0491195	+	0.0850774i	0.840420	+	0.541935i	$0.182308\pi$
$32$	4.89898	+	2.82843i	0.153093	+	0.0883883i
$33$	1.19694	−	2.59808i	0.0362709	−	0.0787296i
$34$	13.3485	+	23.1202i	0.392602	+	0.680007i
$35$		0			0
$36$	−11.6969	−	13.6814i	−0.324915	−	0.380040i
$37$	−46.6969			−1.26208			−0.631040	−	0.775751i	$-0.717372\pi$
$37$	−46.6969			−1.26208			−0.631040	+	0.775751i	$0.717372\pi$
$38$	30.2474	−	17.4634i	0.795985	−	0.459562i
$39$	2.66913	+	28.9681i	0.0684393	+	0.742772i
$40$		0			0
$41$	−9.45459	−	5.45861i	−0.230600	−	0.133137i	0.380249	−	0.924884i	$-0.375838\pi$
$41$	−9.45459	−	5.45861i	−0.230600	−	0.133137i	−0.610849	+	0.791747i	$0.709172\pi$
$42$	35.2702	−	3.24980i	0.839766	−	0.0773763i
$43$	22.5227	+	39.0105i	0.523784	+	0.907220i	0.999617	+	0.0276845i	$0.00881337\pi$
$43$	22.5227	+	39.0105i	0.523784	+	0.907220i	−0.475833	+	0.879536i	$0.657853\pi$
$44$		−	1.90702i		−	0.0433414i
$45$		0			0
$46$	1.34847			0.0293145
$47$	−39.2196	+	22.6435i	−0.834460	+	0.481776i	−0.855377	−	0.518005i	$-0.826675\pi$
$47$	−39.2196	+	22.6435i	−0.834460	+	0.481776i	0.0209170	+	0.999781i	$0.493341\pi$
$48$	−10.8990	−	5.02118i	−0.227062	−	0.104608i
$49$	−10.3485	+	17.9241i	−0.211193	+	0.365797i
$50$		0			0
$51$	−32.6969	−	46.2405i	−0.641116	−	0.906676i
$52$	9.69694	+	16.7956i	0.186480	+	0.322992i
$53$		−	94.3879i		−	1.78090i	−0.455077	−	0.890452i	$-0.650388\pi$
$53$		−	94.3879i		−	1.78090i	0.455077	−	0.890452i	$-0.349612\pi$
$54$	27.3712	+	26.6237i	0.506874	+	0.493031i
$55$		0			0
$56$	20.4495	−	11.8065i	0.365169	−	0.210831i
$57$	−60.4949	+	42.7764i	−1.06131	+	0.750462i
$58$	−9.67423	+	16.7563i	−0.166797	+	0.288901i
$59$	−16.2650	−	9.39063i	−0.275679	−	0.159163i	0.355787	−	0.934567i	$-0.384213\pi$
$59$	−16.2650	−	9.39063i	−0.275679	−	0.159163i	−0.631466	+	0.775404i	$0.717546\pi$
$60$		0			0
$61$	−6.54541	−	11.3370i	−0.107302	−	0.185852i	0.807375	−	0.590039i	$-0.200888\pi$
$61$	−6.54541	−	11.3370i	−0.107302	−	0.185852i	−0.914676	+	0.404187i	$0.867554\pi$
$62$		−	4.30686i		−	0.0694654i
$63$	−73.8712	+	13.7296i	−1.17256	+	0.217930i
$64$	−8.00000			−0.125000
$65$		0			0
$66$	0.371173	+	4.02834i	0.00562383	+	0.0610355i
$67$	37.5227	−	64.9912i	0.560040	−	0.970018i	−0.437452	−	0.899242i	$-0.644119\pi$
$67$	37.5227	−	64.9912i	0.560040	−	0.970018i	0.997492	−	0.0707765i	$-0.0225477\pi$
$68$	−32.6969	−	18.8776i	−0.480837	−	0.277612i
$69$	−2.84847	+	0.262459i	−0.0412822	+	0.00380375i
$70$		0			0
$71$		−	18.0204i		−	0.253808i	−0.991915	−	0.126904i	$-0.959496\pi$
$71$		−	18.0204i		−	0.253808i	0.991915	−	0.126904i	$-0.0405041\pi$
$72$	24.0000	+	8.48528i	0.333333	+	0.117851i
$73$	7.90918			0.108345			0.0541725	−	0.998532i	$-0.482748\pi$
$73$	7.90918			0.108345			0.0541725	+	0.998532i	$0.482748\pi$
$74$	57.1918	−	33.0197i	0.772863	−	0.446212i
$75$		0			0
$76$	−24.6969	+	42.7764i	−0.324960	+	0.562847i
$77$	−6.89388	−	3.98018i	−0.0895309	−	0.0516907i
$78$	−23.7526	−	33.5912i	−0.304520	−	0.430656i
$79$	21.8712	+	37.8820i	0.276850	+	0.479519i	0.970600	−	0.240697i	$-0.0773761\pi$
$79$	21.8712	+	37.8820i	0.276850	+	0.479519i	−0.693750	+	0.720216i	$0.744043\pi$
$80$		0			0
$81$	−63.0000	−	50.9117i	−0.777778	−	0.628539i
$82$	15.4393			0.188284
$83$	112.871	−	65.1662i	1.35989	−	0.785135i	0.370284	−	0.928918i	$-0.379260\pi$
$83$	112.871	−	65.1662i	1.35989	−	0.785135i	0.989609	+	0.143783i	$0.0459269\pi$
$84$	−40.8990	+	28.9199i	−0.486893	+	0.344285i
$85$		0			0
$86$	−55.1691	−	31.8519i	−0.641502	−	0.370371i
$87$	17.1742	−	37.2784i	0.197405	−	0.428488i
$88$	1.34847	+	2.33562i	0.0153235	+	0.0265411i
$89$		−	145.300i		−	1.63258i	−0.577642	−	0.816290i	$-0.696027\pi$
$89$		−	145.300i		−	1.63258i	0.577642	−	0.816290i	$-0.303973\pi$
$90$		0			0
$91$	80.9546			0.889611
$92$	−1.65153	+	0.953512i	−0.0179514	+	0.0103643i
$93$	0.838264	+	9.09769i	0.00901359	+	0.0978246i
$94$	32.0227	−	55.4650i	0.340667	−	0.590053i
$95$		0			0
$96$	16.8990	−	1.55708i	0.176031	−	0.0162196i
$97$	−54.9393	−	95.1576i	−0.566384	−	0.981007i	−0.996919	−	0.0784327i	$-0.975008\pi$
$97$	−54.9393	−	95.1576i	−0.566384	−	0.981007i	0.430535	−	0.902574i	$-0.358325\pi$
$98$		−	29.2699i		−	0.298672i
$99$	−1.56811	−	8.43712i	−0.0158395	−	0.0852234i
$100$		0			0
$101$	127.772	−	73.7695i	1.26507	−	0.730391i	0.291022	−	0.956716i	$-0.406005\pi$
$101$	127.772	−	73.7695i	1.26507	−	0.730391i	0.974052	+	0.226326i	$0.0726714\pi$
$102$	72.7423	+	33.5125i	0.713160	+	0.328554i
$103$	−51.5681	+	89.3186i	−0.500661	+	0.867171i	0.499338	+	0.866407i	$0.333576\pi$
$103$	−51.5681	+	89.3186i	−0.500661	+	0.867171i	−1.00000		0.000763745i	$0.999757\pi$
$104$	−23.7526	−	13.7135i	−0.228390	−	0.131861i
$105$		0			0
$106$	66.7423	+	115.601i	0.629645	+	1.09058i
$107$			36.0408i			0.336830i	0.985716	+	0.168415i	$0.0538649\pi$
$107$			36.0408i			0.336830i	−0.985716	+	0.168415i	$0.946135\pi$
$108$	−52.3485	−	13.2528i	−0.484708	−	0.122711i
$109$	−148.272			−1.36030			−0.680149	−	0.733074i	$-0.738085\pi$
$109$	−148.272			−1.36030			−0.680149	+	0.733074i	$0.738085\pi$
$110$		0			0
$111$	−114.384	+	80.8815i	−1.03048	+	0.728662i
$112$	−16.6969	+	28.9199i	−0.149080	+	0.258214i
$113$	148.166	+	85.5439i	1.31121	+	0.757025i	0.982296	−	0.187336i	$-0.0599852\pi$
$113$	148.166	+	85.5439i	1.31121	+	0.757025i	0.328910	+	0.944361i	$0.393319\pi$
$114$	43.8434	−	95.1665i	0.384591	−	0.834794i
$115$		0			0
$116$		−	27.3629i		−	0.235887i
$117$	56.7122	+	66.3340i	0.484720	+	0.566957i
$118$	26.5607			0.225091
$119$	−136.485	+	78.7995i	−1.14693	+	0.662180i
$120$		0			0
$121$	−60.0454	+	104.002i	−0.496243	+	0.859518i
$122$	16.0329	+	9.25660i	0.131417	+	0.0758738i
$123$	−32.6135	+	3.00502i	−0.265151	+	0.0244311i
$124$	3.04541	+	5.27480i	0.0245597	+	0.0425387i
$125$		0			0
$126$	80.7650	−	69.0501i	0.640992	−	0.548016i
$127$	78.0908			0.614888			0.307444	−	0.951566i	$-0.400526\pi$
$127$	78.0908			0.614888			0.307444	+	0.951566i	$0.400526\pi$
$128$	9.79796	−	5.65685i	0.0765466	−	0.0441942i
$129$	122.737	+	56.5453i	0.951452	+	0.438335i
$130$		0			0
$131$	202.704	+	117.031i	1.54736	+	0.893369i	0.998342	+	0.0575598i	$0.0183320\pi$
$131$	202.704	+	117.031i	1.54736	+	0.893369i	0.549019	+	0.835810i	$0.315001\pi$
$132$	−3.30306	−	4.67123i	−0.0250232	−	0.0353881i
$133$	103.091	+	178.559i	0.775119	+	1.34255i
$134$			106.130i			0.792017i
$135$		0			0
$136$	53.3939			0.392602
$137$	−129.758	+	74.9156i	−0.947136	+	0.546829i	−0.892190	−	0.451660i	$-0.850832\pi$
$137$	−129.758	+	74.9156i	−0.947136	+	0.546829i	−0.0549460	+	0.998489i	$0.517499\pi$
$138$	3.30306	−	2.33562i	0.0239352	−	0.0169248i
$139$	42.2650	−	73.2052i	0.304065	−	0.526656i	−0.672988	−	0.739654i	$-0.734989\pi$
$139$	42.2650	−	73.2052i	0.304065	−	0.526656i	0.977053	+	0.212998i	$0.0683226\pi$
$140$		0			0
$141$	−56.8485	+	123.395i	−0.403181	+	0.875144i
$142$	12.7423	+	22.0704i	0.0897348	+	0.155425i
$143$			9.24614i			0.0646584i
$144$	−35.3939	+	6.57826i	−0.245791	+	0.0456823i
$145$		0			0
$146$	−9.68673	+	5.59264i	−0.0663475	+	0.0383057i
$147$	5.69694	+	61.8289i	0.0387547	+	0.420605i
$148$	−46.6969	+	80.8815i	−0.315520	+	0.546496i
$149$	100.030	+	57.7524i	0.671343	+	0.387600i	0.796585	−	0.604526i	$-0.206638\pi$
$149$	100.030	+	57.7524i	0.671343	+	0.387600i	−0.125242	+	0.992126i	$0.539971\pi$
$150$		0			0
$151$	32.3865	+	56.0950i	0.214480	+	0.371490i	0.953112	−	0.302619i	$-0.0978610\pi$
$151$	32.3865	+	56.0950i	0.214480	+	0.371490i	−0.738632	+	0.674109i	$0.764528\pi$
$152$		−	69.8535i		−	0.459562i
$153$	−160.182	−	56.6328i	−1.04694	−	0.370149i
$154$	11.2577			0.0731016
$155$		0			0
$156$	52.8434	+	24.3450i	0.338740	+	0.156058i
$157$	−10.4092	+	18.0292i	−0.0663005	+	0.114836i	−0.897270	−	0.441482i	$-0.854453\pi$
$157$	−10.4092	+	18.0292i	−0.0663005	+	0.114836i	0.830970	+	0.556318i	$0.187786\pi$
$158$	−53.5732	−	30.9305i	−0.339071	−	0.195763i
$159$	−163.485	−	231.202i	−1.02821	−	1.45410i
$160$		0			0
$161$			7.96036i			0.0494433i
$162$	113.159	+	17.8061i	0.698512	+	0.109914i
$163$	−133.060			−0.816320			−0.408160	−	0.912910i	$-0.633829\pi$
$163$	−133.060			−0.816320			−0.408160	+	0.912910i	$0.633829\pi$
$164$	−18.9092	+	10.9172i	−0.115300	+	0.0665684i
$165$		0			0
$166$	−92.1589	+	159.624i	−0.555174	+	0.961590i
$167$	255.053	+	147.255i	1.52726	+	0.881765i	0.999475	+	0.0323885i	$0.0103114\pi$
$167$	255.053	+	147.255i	1.52726	+	0.881765i	0.527787	+	0.849377i	$0.323022\pi$
$168$	29.6413	−	64.3395i	0.176436	−	0.382973i
$169$	37.4847	+	64.9254i	0.221803	+	0.384174i
$170$		0			0
$171$	−74.0908	+	209.560i	−0.433280	+	1.22550i
$172$	90.0908			0.523784
$173$	59.9847	−	34.6322i	0.346732	−	0.200186i	−0.316513	−	0.948588i	$-0.602512\pi$
$173$	59.9847	−	34.6322i	0.346732	−	0.200186i	0.663245	+	0.748402i	$0.269179\pi$
$174$	5.32577	+	57.8006i	0.0306078	+	0.332187i
$175$		0			0
$176$	−3.30306	−	1.90702i	−0.0187674	−	0.0108354i
$177$	−56.1061	+	5.16964i	−0.316984	+	0.0292070i
$178$	102.742	+	177.955i	0.577204	+	0.999747i
$179$		−	47.4829i		−	0.265268i	−0.991165	−	0.132634i	$-0.957657\pi$
$179$		−	47.4829i		−	0.265268i	0.991165	−	0.132634i	$-0.0423435\pi$
$180$		0			0
$181$	242.879			1.34187			0.670935	−	0.741516i	$-0.265893\pi$
$181$	242.879			1.34187			0.670935	+	0.741516i	$0.265893\pi$
$182$	−99.1487	+	57.2435i	−0.544773	+	0.314525i
$183$	−35.6691	−	16.4328i	−0.194913	−	0.0897969i
$184$	1.34847	−	2.33562i	0.00732864	−	0.0126936i
$185$		0			0
$186$	−7.45969	−	10.5496i	−0.0401059	−	0.0567183i
$187$	−9.00000	−	15.5885i	−0.0481283	−	0.0833607i
$188$			90.5739i			0.481776i
$189$	−157.166	+	161.579i	−0.831568	+	0.854916i
$190$		0			0
$191$	6.52270	−	3.76588i	0.0341503	−	0.0197167i	−0.482828	−	0.875715i	$-0.660390\pi$
$191$	6.52270	−	3.76588i	0.0341503	−	0.0197167i	0.516978	+	0.855999i	$0.327057\pi$
$192$	−19.5959	+	13.8564i	−0.102062	+	0.0721688i
$193$	172.727	−	299.172i	0.894959	−	1.55011i	0.0611031	−	0.998131i	$-0.480538\pi$
$193$	172.727	−	299.172i	0.894959	−	1.55011i	0.833856	−	0.551983i	$-0.186129\pi$
$194$	134.573	+	77.6959i	0.693676	+	0.400494i
$195$		0			0
$196$	20.6969	+	35.8481i	0.105597	+	0.182899i
$197$			77.2247i			0.392004i	0.980604	+	0.196002i	$0.0627959\pi$
$197$			77.2247i			0.392004i	−0.980604	+	0.196002i	$0.937204\pi$
$198$	7.88648	+	9.22450i	0.0398307	+	0.0465884i
$199$	153.485			0.771280			0.385640	−	0.922649i	$-0.373981\pi$
$199$	153.485			0.771280			0.385640	+	0.922649i	$0.373981\pi$
$200$		0			0
$201$	−20.6566	−	224.187i	−0.102769	−	1.11536i
$202$	−104.326	+	180.698i	−0.516464	+	0.894542i
$203$	−98.9166	−	57.1095i	−0.487274	−	0.281328i
$204$	−112.788	+	10.3923i	−0.552881	+	0.0509427i
$205$		0			0
$206$		−	145.857i		−	0.708042i
$207$	−6.52270	+	5.57658i	−0.0315106	+	0.0269400i
$208$	38.7878			0.186480
$209$	−20.3939	+	11.7744i	−0.0975784	+	0.0563369i
$210$		0			0
$211$	25.7804	−	44.6529i	0.122182	−	0.211625i	−0.798446	−	0.602066i	$-0.794344\pi$
$211$	25.7804	−	44.6529i	0.122182	−	0.211625i	0.920628	+	0.390441i	$0.127678\pi$
$212$	−163.485	−	94.3879i	−0.771154	−	0.445226i
$213$	−31.2122	−	44.1408i	−0.146536	−	0.207234i
$214$	−25.4847	−	44.1408i	−0.119087	−	0.206265i
$215$		0			0
$216$	73.4847	−	20.7846i	0.340207	−	0.0962250i
$217$	25.4245			0.117164
$218$	181.596	−	104.844i	0.833009	−	0.480938i
$219$	19.3735	−	13.6991i	0.0884633	−	0.0625530i
$220$		0			0
$221$	158.530	+	91.5274i	0.717331	+	0.414151i
$222$	82.8990	−	179.941i	0.373419	−	0.810543i
$223$	156.614	+	271.263i	0.702303	+	1.21642i	0.967656	+	0.252273i	$0.0811781\pi$
$223$	156.614	+	271.263i	0.702303	+	1.21642i	−0.265353	+	0.964151i	$0.585489\pi$
$224$		−	47.2261i		−	0.210831i
$225$		0			0
$226$	−241.955			−1.07060
$227$	66.0528	−	38.1356i	0.290982	−	0.167998i	−0.347403	−	0.937716i	$-0.612936\pi$
$227$	66.0528	−	38.1356i	0.290982	−	0.167998i	0.638384	+	0.769718i	$0.279603\pi$
$228$	13.5959	+	147.557i	0.0596312	+	0.647178i
$229$	60.7724	−	105.261i	0.265382	−	0.459655i	−0.702282	−	0.711899i	$-0.747835\pi$
$229$	60.7724	−	105.261i	0.265382	−	0.459655i	0.967664	+	0.252244i	$0.0811686\pi$
$230$		0			0
$231$	−23.7804	+	2.19113i	−0.102945	+	0.00948541i
$232$	19.3485	+	33.5125i	0.0833986	+	0.144451i
$233$		−	151.021i		−	0.648157i	−0.946030	−	0.324079i	$-0.894946\pi$
$233$		−	151.021i		−	0.648157i	0.946030	−	0.324079i	$-0.105054\pi$
$234$	−116.363	−	41.1406i	−0.497279	−	0.175815i
$235$		0			0
$236$	−32.5301	+	18.7813i	−0.137839	+	0.0795816i
$237$	119.187	+	54.9095i	0.502898	+	0.231686i
$238$	111.439	−	193.019i	0.468232	−	0.811002i
$239$	−75.9620	−	43.8567i	−0.317833	−	0.183501i	0.332593	−	0.943070i	$-0.392076\pi$
$239$	−75.9620	−	43.8567i	−0.317833	−	0.183501i	−0.650426	+	0.759570i	$0.725410\pi$
$240$		0			0
$241$	−100.894	−	174.753i	−0.418647	−	0.725118i	0.577157	−	0.816633i	$-0.304162\pi$
$241$	−100.894	−	174.753i	−0.418647	−	0.725118i	−0.995804	+	0.0915158i	$0.970829\pi$
$242$		−	169.834i		−	0.701794i
$243$	−242.499	−	15.5885i	−0.997940	−	0.0641500i
$244$	−26.1816			−0.107302
$245$		0			0
$246$	37.8184	−	26.7416i	0.153733	−	0.108706i
$247$	119.742	−	207.400i	0.484787	−	0.839675i
$248$	−7.45969	−	4.30686i	−0.0300794	−	0.0173664i
$249$	163.606	−	355.123i	0.657051	−	1.42619i
$250$		0			0
$251$		−	52.6261i		−	0.209666i	−0.994490	−	0.104833i	$-0.966569\pi$
$251$		−	52.6261i		−	0.209666i	0.994490	−	0.104833i	$-0.0334307\pi$
$252$	−50.0908	+	141.678i	−0.198773	+	0.562215i
$253$	−0.909185			−0.00359362
$254$	−95.6413	+	55.2185i	−0.376541	+	0.217396i
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$	69.8939	+	40.3532i	0.271961	+	0.157017i	0.629778	−	0.776775i	$-0.283146\pi$
$257$	69.8939	+	40.3532i	0.271961	+	0.157017i	−0.357818	+	0.933791i	$0.616479\pi$
$258$	−190.305	+	17.5348i	−0.737618	+	0.0679644i
$259$	194.924	+	337.618i	0.752602	+	1.30355i
$260$		0			0
$261$	−22.5000	−	121.060i	−0.0862069	−	0.463830i
$262$	−331.015			−1.26342
$263$	−401.614	+	231.872i	−1.52705	+	0.881641i	−0.527564	+	0.849515i	$0.676894\pi$
$263$	−401.614	+	231.872i	−1.52705	+	0.881641i	−0.999484	+	0.0321259i	$0.989772\pi$
$264$	7.34847	+	3.38545i	0.0278351	+	0.0128237i
$265$		0			0
$266$	−252.520	−	145.792i	−0.949323	−	0.548092i
$267$	−251.666	−	355.910i	−0.942570	−	1.33300i
$268$	−75.0454	−	129.982i	−0.280020	−	0.485009i
$269$			43.4762i			0.161622i	0.996729	+	0.0808109i	$0.0257510\pi$
$269$			43.4762i			0.161622i	−0.996729	+	0.0808109i	$0.974249\pi$
$270$		0			0
$271$	−342.636			−1.26434			−0.632169	−	0.774830i	$-0.717835\pi$
$271$	−342.636			−1.26434			−0.632169	+	0.774830i	$0.717835\pi$
$272$	−65.3939	+	37.7552i	−0.240419	+	0.138806i
$273$	198.297	−	140.217i	0.726364	−	0.513617i
$274$	105.947	−	183.505i	0.386667	−	0.669726i
$275$		0			0
$276$	−2.39388	+	5.19615i	−0.00867347	+	0.0188266i
$277$	−24.5000	−	42.4352i	−0.0884477	−	0.153196i	0.818407	−	0.574638i	$-0.194857\pi$
$277$	−24.5000	−	42.4352i	−0.0884477	−	0.153196i	−0.906855	+	0.421442i	$0.861524\pi$
$278$			119.544i			0.430013i
$279$	17.8110	+	20.8328i	0.0638386	+	0.0746694i
$280$		0			0
$281$	−17.8791	+	10.3225i	−0.0636266	+	0.0367349i	−0.531476	−	0.847073i	$-0.678362\pi$
$281$	−17.8791	+	10.3225i	−0.0636266	+	0.0367349i	0.467849	+	0.883808i	$0.345029\pi$
$282$	−17.6288	−	191.326i	−0.0625136	−	0.678460i
$283$	26.7043	−	46.2533i	0.0943616	−	0.163439i	−0.814980	−	0.579489i	$-0.803252\pi$
$283$	26.7043	−	46.2533i	0.0943616	−	0.163439i	0.909342	+	0.416049i	$0.136586\pi$
$284$	−31.2122	−	18.0204i	−0.109902	−	0.0634521i
$285$		0			0
$286$	−6.53801	−	11.3242i	−0.0228602	−	0.0395950i
$287$			91.1421i			0.317568i
$288$	38.6969	−	33.0839i	0.134364	−	0.114875i
$289$	−67.3633			−0.233091
$290$		0			0
$291$	−299.391	−	137.930i	−1.02884	−	0.473986i
$292$	7.90918	−	13.6991i	0.0270862	−	0.0469148i
$293$	12.9245	+	7.46196i	0.0441109	+	0.0254674i	0.521893	−	0.853011i	$-0.325226\pi$
$293$	12.9245	+	7.46196i	0.0441109	+	0.0254674i	−0.477782	+	0.878478i	$0.658559\pi$
$294$	−50.6969	−	71.6963i	−0.172439	−	0.243865i
$295$		0			0
$296$		−	132.079i		−	0.446212i
$297$	−18.4546	−	17.9506i	−0.0621367	−	0.0604397i
$298$	−163.348			−0.548149
$299$	8.00740	−	4.62307i	0.0267806	−	0.0154618i
$300$		0			0
$301$	188.030	−	325.678i	0.624685	−	1.08199i
$302$	−79.3304	−	45.8014i	−0.262683	−	0.151660i
$303$	185.205	−	402.006i	0.611237	−	1.32675i
$304$	49.3939	+	85.5527i	0.162480	+	0.281423i
$305$		0			0
$306$	236.227	−	43.9048i	0.771984	−	0.143480i
$307$	−65.9092			−0.214688			−0.107344	−	0.994222i	$-0.534235\pi$
$307$	−65.9092			−0.214688			−0.107344	+	0.994222i	$0.534235\pi$
$308$	−13.7878	+	7.96036i	−0.0447654	+	0.0258453i
$309$	28.3888	+	308.104i	0.0918731	+	0.997099i
$310$		0			0
$311$	−216.659	−	125.088i	−0.696652	−	0.402213i	0.109447	−	0.993993i	$-0.465092\pi$
$311$	−216.659	−	125.088i	−0.696652	−	0.402213i	−0.806099	+	0.591780i	$0.798425\pi$
$312$	−81.9342	+	7.54945i	−0.262610	+	0.0241969i
$313$	−213.197	−	369.268i	−0.681140	−	1.17977i	−0.974633	−	0.223808i	$-0.928151\pi$
$313$	−213.197	−	369.268i	−0.681140	−	1.17977i	0.293493	−	0.955961i	$-0.405182\pi$
$314$		−	29.4416i		−	0.0937631i
$315$		0			0
$316$	87.4847			0.276850
$317$	401.818	−	231.990i	1.26756	−	0.731829i	0.293038	−	0.956101i	$-0.405334\pi$
$317$	401.818	−	231.990i	1.26756	−	0.731829i	0.974527	+	0.224272i	$0.0720005\pi$
$318$	363.712	+	167.563i	1.14375	+	0.526927i
$319$	6.52270	−	11.2977i	0.0204473	−	0.0354158i
$320$		0			0
$321$	62.4245	+	88.2816i	0.194469	+	0.275020i
$322$	−5.62883	−	9.74941i	−0.0174808	−	0.0302777i
$323$			466.219i			1.44340i
$324$	−151.182	+	58.2075i	−0.466610	+	0.179653i
$325$		0			0
$326$	162.965	−	94.0878i	0.499892	−	0.288613i
$327$	−363.192	+	256.815i	−1.11068	+	0.785368i
$328$	15.4393	−	26.7416i	0.0470710	−	0.0815293i
$329$	327.424	+	189.038i	0.995210	+	0.574585i
$330$		0			0
$331$	−236.401	−	409.459i	−0.714203	−	1.23704i	−0.963266	−	0.268549i	$-0.913456\pi$
$331$	−236.401	−	409.459i	−0.714203	−	1.23704i	0.249063	−	0.968487i	$-0.419877\pi$
$332$		−	260.665i		−	0.785135i
$333$	−140.091	+	396.237i	−0.420693	+	1.18990i
$334$	−416.499			−1.24700
$335$		0			0
$336$	9.19184	+	99.7591i	0.0273567	+	0.296902i
$337$	152.803	−	264.663i	0.453422	−	0.785349i	−0.545174	−	0.838323i	$-0.683537\pi$
$337$	152.803	−	264.663i	0.453422	−	0.785349i	0.998596	+	0.0529735i	$0.0168699\pi$
$338$	−91.8184	−	53.0114i	−0.271652	−	0.156838i
$339$	511.098	−	47.0928i	1.50766	−	0.138917i
$340$		0			0
$341$			2.90383i			0.00851564i
$342$	−57.4393	−	309.048i	−0.167951	−	0.903650i
$343$	−236.287			−0.688884
$344$	−110.338	+	63.7038i	−0.320751	+	0.185186i
$345$		0			0
$346$	−48.9773	+	84.8312i	−0.141553	+	0.245177i
$347$	−115.766	−	66.8373i	−0.333618	−	0.192615i	0.323828	−	0.946116i	$-0.395030\pi$
$347$	−115.766	−	66.8373i	−0.333618	−	0.192615i	−0.657446	+	0.753501i	$0.728363\pi$
$348$	−47.3939	−	67.0251i	−0.136189	−	0.192601i
$349$	49.3786	+	85.5262i	0.141486	+	0.245061i	0.928056	−	0.372440i	$-0.121479\pi$
$349$	49.3786	+	85.5262i	0.141486	+	0.245061i	−0.786570	+	0.617500i	$0.788145\pi$
$350$		0			0
$351$	253.810	+	64.2560i	0.723105	+	0.183065i
$352$	5.39388			0.0153235
$353$	282.424	−	163.058i	0.800068	−	0.461919i	−0.0434270	−	0.999057i	$-0.513828\pi$
$353$	282.424	−	163.058i	0.800068	−	0.461919i	0.843495	+	0.537137i	$0.180494\pi$
$354$	65.0602	−	46.0045i	0.183786	−	0.129956i
$355$		0			0
$356$	−251.666	−	145.300i	−0.706928	−	0.408145i
$357$	−197.833	+	429.417i	−0.554155	+	1.20285i
$358$	33.5755	+	58.1545i	0.0937863	+	0.162443i
$359$			418.736i			1.16639i	0.812331	+	0.583197i	$0.198199\pi$
$359$			418.736i			1.16639i	−0.812331	+	0.583197i	$0.801801\pi$
$360$		0			0
$361$	248.939			0.689581
$362$	−297.464	+	171.741i	−0.821725	+	0.474423i
$363$	33.0556	+	358.753i	0.0910623	+	0.988300i
$364$	80.9546	−	140.217i	0.222403	−	0.385213i
$365$		0			0
$366$	55.3054	−	5.09586i	0.151108	−	0.0139231i
$367$	93.6135	+	162.143i	0.255078	+	0.441808i	0.964917	−	0.262557i	$-0.0845656\pi$
$367$	93.6135	+	162.143i	0.255078	+	0.441808i	−0.709839	+	0.704364i	$0.751232\pi$
$368$			3.81405i			0.0103643i
$369$	−74.6816	+	63.8490i	−0.202389	+	0.173033i
$370$		0			0
$371$	−682.423	+	393.997i	−1.83942	+	1.06199i
$372$	16.5959	+	7.64577i	0.0446127	+	0.0205531i
$373$	225.515	−	390.603i	0.604597	−	1.04719i	−0.387518	−	0.921862i	$-0.626667\pi$
$373$	225.515	−	390.603i	0.604597	−	1.04719i	0.992115	−	0.125331i	$-0.0399993\pi$
$374$	22.0454	+	12.7279i	0.0589449	+	0.0340319i
$375$		0			0
$376$	−64.0454	−	110.930i	−0.170334	−	0.295026i
$377$			132.668i			0.351905i
$378$	78.2350	−	309.027i	0.206971	−	0.817531i
$379$	−489.666			−1.29200			−0.645998	−	0.763339i	$-0.723558\pi$
$379$	−489.666			−1.29200			−0.645998	+	0.763339i	$0.723558\pi$
$380$		0			0
$381$	191.283	−	135.257i	0.502054	−	0.355006i
$382$	−5.32577	+	9.22450i	−0.0139418	+	0.0241479i
$383$	−89.2492	−	51.5281i	−0.233027	−	0.134538i	0.378941	−	0.925421i	$-0.376288\pi$
$383$	−89.2492	−	51.5281i	−0.233027	−	0.134538i	−0.611968	+	0.790883i	$0.709622\pi$
$384$	14.2020	−	30.8270i	0.0369845	−	0.0802786i
$385$		0			0
$386$			488.546i			1.26566i
$387$	398.583	−	74.0801i	1.02993	−	0.191421i
$388$	−219.757			−0.566384
$389$	29.6816	−	17.1367i	0.0763024	−	0.0440532i	−0.461363	−	0.887211i	$-0.652640\pi$
$389$	29.6816	−	17.1367i	0.0763024	−	0.0440532i	0.537666	+	0.843158i	$0.319306\pi$
$390$		0			0
$391$	−9.00000	+	15.5885i	−0.0230179	+	0.0398682i
$392$	−50.6969	−	29.2699i	−0.129329	−	0.0746681i
$393$	699.227	−	64.4270i	1.77920	−	0.163936i
$394$	−54.6061	−	94.5806i	−0.138594	−	0.240052i
$395$		0			0
$396$	−16.1816	−	5.72107i	−0.0408627	−	0.0144471i
$397$	−8.27245			−0.0208374			−0.0104187	−	0.999946i	$-0.503316\pi$
$397$	−8.27245			−0.0208374			−0.0104187	+	0.999946i	$0.503316\pi$
$398$	−187.980	+	108.530i	−0.472311	+	0.272689i
$399$	561.792	+	258.819i	1.40800	+	0.648669i
$400$		0			0
$401$	358.636	+	207.059i	0.894355	+	0.516356i	0.875364	−	0.483464i	$-0.160622\pi$
$401$	358.636	+	207.059i	0.894355	+	0.516356i	0.0189903	+	0.999820i	$0.493955\pi$
$402$	183.823	+	259.965i	0.457271	+	0.646679i
$403$	−14.7656	−	25.5747i	−0.0366391	−	0.0634608i
$404$		−	295.078i		−	0.730391i
$405$		0			0
$406$	161.530			0.397857
$407$	−38.5607	+	22.2630i	−0.0947438	+	0.0547003i
$408$	130.788	−	92.4809i	0.320558	−	0.226669i
$409$	163.106	−	282.508i	0.398792	−	0.690729i	−0.594785	−	0.803885i	$-0.702763\pi$
$409$	163.106	−	282.508i	0.398792	−	0.690729i	0.993577	+	0.113156i	$0.0360960\pi$
$410$		0			0
$411$	−188.082	+	408.252i	−0.457621	+	0.993314i
$412$	103.136	+	178.637i	0.250331	+	0.433585i
$413$			156.795i			0.379648i
$414$	4.04541	−	11.4421i	0.00977152	−	0.0276380i
$415$		0			0
$416$	−47.5051	+	27.4271i	−0.114195	+	0.0659305i
$417$	−23.2673	−	252.521i	−0.0557970	−	0.605565i
$418$	16.6515	−	28.8413i	0.0398362	−	0.0689983i
$419$	−468.325	−	270.388i	−1.11772	−	0.645317i	−0.176903	−	0.984228i	$-0.556608\pi$
$419$	−468.325	−	270.388i	−1.11772	−	0.645317i	−0.940818	+	0.338912i	$0.889941\pi$
$420$		0			0
$421$	−141.848	−	245.689i	−0.336932	−	0.583584i	0.646922	−	0.762556i	$-0.276056\pi$
$421$	−141.848	−	245.689i	−0.336932	−	0.583584i	−0.983854	+	0.178973i	$0.942723\pi$
$422$			72.9179i			0.172791i
$423$	74.4773	+	400.720i	0.176069	+	0.947329i
$424$	266.969			0.629645
$425$		0			0
$426$	69.4393	+	31.9908i	0.163003	+	0.0750958i
$427$	−54.6441	+	94.6464i	−0.127972	+	0.221654i
$428$	62.4245	+	36.0408i	0.145852	+	0.0842075i
$429$	16.0148	+	22.6483i	0.0373305	+	0.0527933i
$430$		0			0
$431$			257.429i			0.597282i	0.954365	+	0.298641i	$0.0965334\pi$
$431$			257.429i			0.597282i	−0.954365	+	0.298641i	$0.903467\pi$
$432$	−75.3031	+	77.4174i	−0.174313	+	0.179207i
$433$	−476.272			−1.09994			−0.549968	−	0.835186i	$-0.685360\pi$
$433$	−476.272			−1.09994			−0.549968	+	0.835186i	$0.685360\pi$
$434$	−31.1385	+	17.9778i	−0.0717477	+	0.0414236i
$435$		0			0
$436$	−148.272	+	256.815i	−0.340074	+	0.589026i
$437$	20.3939	+	11.7744i	0.0466679	+	0.0269437i
$438$	−14.0408	+	30.4770i	−0.0320567	+	0.0695822i
$439$	278.931	+	483.123i	0.635379	+	1.10051i	0.986435	+	0.164154i	$0.0524894\pi$
$439$	278.931	+	483.123i	0.635379	+	1.10051i	−0.351056	+	0.936355i	$0.614177\pi$
$440$		0			0
$441$	121.045	+	141.582i	0.274479	+	0.321047i
$442$	−258.879			−0.585698
$443$	−720.400	+	415.923i	−1.62619	+	0.938879i	−0.640969	+	0.767567i	$0.721467\pi$
$443$	−720.400	+	415.923i	−1.62619	+	0.938879i	−0.985217	+	0.171312i	$0.945199\pi$
$444$	25.7071	+	279.000i	0.0578990	+	0.628378i
$445$		0			0
$446$	−383.623	−	221.485i	−0.860142	−	0.496603i
$447$	345.053	−	31.7933i	0.771930	−	0.0711259i
$448$	33.3939	+	57.8399i	0.0745399	+	0.129107i
$449$		−	729.927i		−	1.62567i	−0.582492	−	0.812836i	$-0.697922\pi$
$449$		−	729.927i		−	1.62567i	0.582492	−	0.812836i	$-0.302078\pi$
$450$		0			0
$451$	−10.4097			−0.0230814
$452$	296.333	−	171.088i	0.655603	−	0.378513i
$453$	176.490	+	81.3092i	0.389602	+	0.179490i
$454$	−53.9319	+	93.4128i	−0.118793	+	0.205755i
$455$		0			0
$456$	−120.990	−	171.105i	−0.265328	−	0.375231i
$457$	354.818	+	614.563i	0.776407	+	1.34478i	0.934000	+	0.357272i	$0.116293\pi$
$457$	354.818	+	614.563i	0.776407	+	1.34478i	−0.157594	+	0.987504i	$0.550374\pi$
$458$			171.890i			0.375307i
$459$	−490.454	+	138.721i	−1.06853	+	0.302225i
$460$		0			0
$461$	−7.96990	+	4.60142i	−0.0172883	+	0.00998140i	−0.508619	−	0.860992i	$-0.669844\pi$
$461$	−7.96990	+	4.60142i	−0.0172883	+	0.00998140i	0.491331	+	0.870973i	$0.336511\pi$
$462$	27.5755	−	19.4988i	0.0596872	−	0.0422053i
$463$	−27.5987	+	47.8024i	−0.0596085	+	0.103245i	−0.894290	−	0.447488i	$-0.852319\pi$
$463$	−27.5987	+	47.8024i	−0.0596085	+	0.103245i	0.834681	+	0.550733i	$0.185652\pi$
$464$	−47.3939	−	27.3629i	−0.102142	−	0.0589717i
$465$		0			0
$466$	106.788	+	184.962i	0.229158	+	0.396914i
$467$		−	625.811i		−	1.34007i	−0.742331	−	0.670033i	$-0.766280\pi$
$467$		−	625.811i		−	1.34007i	0.742331	−	0.670033i	$-0.233720\pi$
$468$	171.606	−	31.8945i	0.366680	−	0.0681506i
$469$	−626.514			−1.33585
$470$		0			0
$471$	5.73036	+	62.1917i	0.0121664	+	0.132042i
$472$	26.5607	−	46.0045i	0.0562727	−	0.0974672i
$473$	37.1969	+	21.4757i	0.0786405	+	0.0454031i
$474$	−184.800	+	17.0276i	−0.389874	+	0.0359231i
$475$		0			0
$476$			315.198i			0.662180i
$477$	−800.908	−	283.164i	−1.67905	−	0.593635i
$478$	124.045			0.259509
$479$	267.856	−	154.647i	0.559199	−	0.322854i	−0.193625	−	0.981076i	$-0.562024\pi$
$479$	267.856	−	154.647i	0.559199	−	0.322854i	0.752824	+	0.658222i	$0.228691\pi$
$480$		0			0
$481$	226.409	−	392.151i	0.470704	−	0.815283i
$482$	247.139	+	142.685i	0.512736	+	0.296028i
$483$	13.7878	+	19.4988i	0.0285461	+	0.0403702i
$484$	120.091	+	208.003i	0.248122	+	0.429759i
$485$		0			0
$486$	308.023	−	152.381i	0.633792	−	0.313541i
$487$	28.3337			0.0581800			0.0290900	−	0.999577i	$-0.490739\pi$
$487$	28.3337			0.0581800			0.0290900	+	0.999577i	$0.490739\pi$
$488$	32.0658	−	18.5132i	0.0657086	−	0.0379369i
$489$	−325.930	+	230.467i	−0.666523	+	0.471303i
$490$		0			0
$491$	822.461	+	474.848i	1.67507	+	0.967105i	0.964727	+	0.263254i	$0.0847956\pi$
$491$	822.461	+	474.848i	1.67507	+	0.967105i	0.710348	+	0.703851i	$0.248538\pi$
$492$	−27.4087	+	59.4933i	−0.0557087	+	0.120921i
$493$	−129.136	−	223.670i	−0.261940	−	0.453693i
$494$			338.682i			0.685592i
$495$		0			0
$496$	12.1816			0.0245597
$497$	−130.287	+	75.2214i	−0.262147	+	0.151351i
$498$	50.7344	+	550.621i	0.101876	+	1.10566i
$499$	280.113	−	485.170i	0.561349	−	0.972284i	−0.436030	−	0.899932i	$-0.643616\pi$
$499$	280.113	−	485.170i	0.561349	−	0.972284i	0.997379	−	0.0723525i	$-0.0230507\pi$
$500$		0			0
$501$	879.802	−	81.0653i	1.75609	−	0.161807i
$502$	37.2122	+	64.4535i	0.0741280	+	0.128393i
$503$		−	897.832i		−	1.78495i	−0.451094	−	0.892477i	$-0.648966\pi$
$503$		−	897.832i		−	1.78495i	0.451094	−	0.892477i	$-0.351034\pi$
$504$	−38.8332	−	208.939i	−0.0770499	−	0.414562i
$505$		0			0
$506$	1.11352	−	0.642891i	0.00220063	−	0.00127053i
$507$	204.272	+	94.1087i	0.402904	+	0.185619i
$508$	78.0908	−	135.257i	0.153722	−	0.266254i
$509$	−170.454	−	98.4114i	−0.334879	−	0.193343i	0.323126	−	0.946356i	$-0.395266\pi$
$509$	−170.454	−	98.4114i	−0.334879	−	0.193343i	−0.658005	+	0.753013i	$0.728600\pi$
$510$		0			0
$511$	−33.0148	−	57.1833i	−0.0646082	−	0.111905i
$512$		−	22.6274i		−	0.0441942i
$513$	181.485	+	641.645i	0.353771	+	1.25077i
$514$	−114.136			−0.222055
$515$		0			0
$516$	220.677	−	156.042i	0.427668	−	0.302407i
$517$	−21.5908	+	37.3964i	−0.0417617	+	0.0723334i
$518$	−477.464	−	275.664i	−0.921746	−	0.532170i
$519$	86.9472	−	188.728i	0.167528	−	0.363637i
$520$		0			0
$521$			375.837i			0.721377i	0.932686	+	0.360688i	$0.117458\pi$
$521$			375.837i			0.721377i	−0.932686	+	0.360688i	$0.882542\pi$
$522$	113.159	+	132.357i	0.216780	+	0.253558i
$523$	−91.1827			−0.174345			−0.0871727	−	0.996193i	$-0.527783\pi$
$523$	−91.1827			−0.174345			−0.0871727	+	0.996193i	$0.527783\pi$
$524$	405.409	−	234.063i	0.773681	−	0.446685i
$525$		0			0
$526$	327.916	−	567.967i	0.623415	−	1.07979i
$527$	49.7878	+	28.7450i	0.0944739	+	0.0545445i
$528$	−11.3939	+	1.04984i	−0.0215793	+	0.00198833i
$529$	−264.045	−	457.340i	−0.499141	−	0.864537i
$530$		0			0
$531$	−128.477	+	109.842i	−0.241953	+	0.206858i
$532$	412.363			0.775119
$533$	91.6806	−	52.9318i	0.172009	−	0.0993092i
$534$	559.893	+	257.944i	1.04849	+	0.483041i
$535$		0			0
$536$	183.823	+	106.130i	0.342953	+	0.198004i
$537$	−82.2429	−	116.309i	−0.153152	−	0.216590i
$538$	−30.7423	−	53.2473i	−0.0571419	−	0.0989727i
$539$			19.7348i			0.0366137i
$540$		0			0
$541$	−38.8490			−0.0718096			−0.0359048	−	0.999355i	$-0.511431\pi$
$541$	−38.8490			−0.0718096			−0.0359048	+	0.999355i	$0.511431\pi$
$542$	419.641	−	242.280i	0.774246	−	0.447011i
$543$	594.929	−	420.678i	1.09563	−	0.774729i
$544$	53.3939	−	92.4809i	0.0981505	−	0.170002i
$545$		0			0
$546$	−143.715	+	311.948i	−0.263214	+	0.571333i
$547$	−233.022	−	403.606i	−0.426000	−	0.737854i	0.570513	−	0.821289i	$-0.306744\pi$
$547$	−233.022	−	403.606i	−0.426000	−	0.737854i	−0.996513	+	0.0834344i	$0.973411\pi$
$548$			299.662i			0.546829i
$549$	−115.834	+	21.5287i	−0.210990	+	0.0392144i
$550$		0			0
$551$	−292.621	+	168.945i	−0.531072	+	0.306615i
$552$	−0.742346	−	8.05669i	−0.00134483	−	0.0145954i
$553$	182.591	−	316.257i	0.330182	−	0.571893i
$554$	60.0125	+	34.6482i	0.108326	+	0.0625419i
$555$		0			0
$556$	−84.5301	−	146.410i	−0.152033	−	0.263328i
$557$			695.042i			1.24783i	0.781492	+	0.623916i	$0.214459\pi$
$557$			695.042i			1.24783i	−0.781492	+	0.623916i	$0.785541\pi$
$558$	−36.5449	−	12.9206i	−0.0654926	−	0.0231551i
$559$	−436.803			−0.781400
$560$		0			0
$561$	−49.0454	−	22.5953i	−0.0874250	−	0.0402768i
$562$	14.5982	−	25.2848i	0.0259755	−	0.0449908i
$563$	473.780	+	273.537i	0.841528	+	0.485857i	0.857783	−	0.514011i	$-0.171841\pi$
$563$	473.780	+	273.537i	0.841528	+	0.485857i	−0.0162552	+	0.999868i	$0.505174\pi$
$564$	156.879	+	221.860i	0.278153	+	0.393368i
$565$		0			0
$566$			75.5313i			0.133447i
$567$	−105.114	+	668.006i	−0.185386	+	1.17814i
$568$	50.9694			0.0897348
$569$	215.954	−	124.681i	0.379533	−	0.219123i	−0.298082	−	0.954540i	$-0.596347\pi$
$569$	215.954	−	124.681i	0.379533	−	0.219123i	0.677615	+	0.735417i	$0.263014\pi$
$570$		0			0
$571$	−36.9166	+	63.9414i	−0.0646525	+	0.111981i	−0.896540	−	0.442963i	$-0.853927\pi$
$571$	−36.9166	+	63.9414i	−0.0646525	+	0.111981i	0.831887	+	0.554945i	$0.187261\pi$
$572$	16.0148	+	9.24614i	0.0279979	+	0.0161646i
$573$	9.45459	−	20.5222i	0.0165002	−	0.0358153i
$574$	−64.4472	−	111.626i	−0.112277	−	0.194470i
$575$		0			0
$576$	−24.0000	+	67.8823i	−0.0416667	+	0.117851i
$577$	43.9092			0.0760991			0.0380496	−	0.999276i	$-0.487886\pi$
$577$	43.9092			0.0760991			0.0380496	+	0.999276i	$0.487886\pi$
$578$	82.5028	−	47.6330i	0.142738	−	0.0824101i
$579$	−95.0880	−	1031.99i	−0.164228	−	1.78237i
$580$		0			0
$581$	−942.302	−	544.038i	−1.62186	−	0.936382i
$582$	464.209	−	42.7724i	0.797610	−	0.0734921i
$583$	−45.0000	−	77.9423i	−0.0771870	−	0.133692i
$584$			22.3706i			0.0383057i
$585$		0			0
$586$	−21.1056			−0.0360164
$587$	381.386	−	220.194i	0.649721	−	0.375117i	−0.138628	−	0.990345i	$-0.544269\pi$
$587$	381.386	−	220.194i	0.649721	−	0.375117i	0.788349	+	0.615228i	$0.210936\pi$
$588$	112.788	+	51.9615i	0.191816	+	0.0883699i
$589$	37.6061	−	65.1357i	0.0638474	−	0.110587i
$590$		0			0
$591$	133.757	+	189.161i	0.226323	+	0.320070i
$592$	93.3939	+	161.763i	0.157760	+	0.273248i
$593$		−	347.232i		−	0.585551i	−0.956181	−	0.292776i	$-0.905421\pi$
$593$		−	347.232i		−	0.585551i	0.956181	−	0.292776i	$-0.0945789\pi$
$594$	35.2951	+	8.93552i	0.0594194	+	0.0150430i
$595$		0			0
$596$	200.060	−	115.505i	0.335671	−	0.193800i
$597$	375.959	−	265.843i	0.629747	−	0.445299i
$598$	−6.53801	+	11.3242i	−0.0109331	+	0.0189367i
$599$	−684.083	−	394.956i	−1.14204	−	0.659359i	−0.195107	−	0.980782i	$-0.562505\pi$
$599$	−684.083	−	394.956i	−1.14204	−	0.659359i	−0.946936	+	0.321423i	$0.895839\pi$
$600$		0			0
$601$	353.455	+	612.201i	0.588111	+	1.01864i	0.994480	+	0.104929i	$0.0334614\pi$
$601$	353.455	+	612.201i	0.588111	+	1.01864i	−0.406369	+	0.913709i	$0.633205\pi$
$602$			531.829i			0.883438i
$603$	−438.901	−	513.364i	−0.727862	−	0.851351i
$604$	129.546			0.214480
$605$		0			0
$606$	57.4324	+	623.314i	0.0947729	+	1.02857i
$607$	−596.628	+	1033.39i	−0.982913	+	1.70246i	−0.332048	+	0.943263i	$0.607739\pi$
$607$	−596.628	+	1033.39i	−0.982913	+	1.70246i	−0.650866	+	0.759193i	$0.725594\pi$
$608$	−120.990	−	69.8535i	−0.198996	−	0.114891i
$609$	−341.212	+	31.4394i	−0.560282	+	0.0516246i
$610$		0			0
$611$		−	439.145i		−	0.718731i
$612$	−258.272	+	220.810i	−0.422014	+	0.360801i
$613$	−629.181			−1.02640			−0.513198	−	0.858270i	$-0.671539\pi$
$613$	−629.181			−1.02640			−0.513198	+	0.858270i	$0.671539\pi$
$614$	80.7219	−	46.6048i	0.131469	−	0.0759036i
$615$		0			0
$616$	11.2577	−	19.4988i	0.0182754	−	0.0316539i
$617$	−166.909	−	96.3648i	−0.270516	−	0.156183i	0.358606	−	0.933489i	$-0.383252\pi$
$617$	−166.909	−	96.3648i	−0.270516	−	0.156183i	−0.629122	+	0.777306i	$0.716586\pi$
$618$	−252.631	−	357.274i	−0.408788	−	0.578114i
$619$	76.4773	+	132.463i	0.123550	+	0.213994i	0.921165	−	0.389172i	$-0.127239\pi$
$619$	76.4773	+	132.463i	0.123550	+	0.213994i	−0.797615	+	0.603166i	$0.793905\pi$
$620$		0			0
$621$	−6.31837	+	24.9574i	−0.0101745	+	0.0401891i
$622$	353.803			0.568814
$623$	−1050.51	+	606.515i	−1.68622	+	0.973539i
$624$	95.0102	−	67.1824i	0.152260	−	0.107664i
$625$		0			0
$626$	522.224	+	301.506i	0.834223	+	0.481639i
$627$	−29.5607	+	64.1645i	−0.0471463	+	0.102336i
$628$	20.8184	+	36.0585i	0.0331503	+	0.0574180i
$629$			881.525i			1.40147i
$630$		0			0
$631$	44.8786			0.0711229			0.0355615	−	0.999367i	$-0.488678\pi$
$631$	44.8786			0.0711229			0.0355615	+	0.999367i	$0.488678\pi$
$632$	−107.146	+	61.8610i	−0.169535	+	0.0978814i
$633$	−14.1924	−	154.030i	−0.0224208	−	0.243333i
$634$	−328.083	+	568.256i	−0.517481	+	0.896303i
$635$		0			0
$636$	−563.939	+	51.9615i	−0.886696	+	0.0817005i
$637$	−100.348	−	173.809i	−0.157533	−	0.272855i
$638$			18.4490i			0.0289169i
$639$	−152.908	−	54.0612i	−0.239293	−	0.0846028i
$640$		0			0
$641$	−209.106	+	120.727i	−0.326219	+	0.188342i	−0.654161	−	0.756355i	$-0.726978\pi$
$641$	−209.106	+	120.727i	−0.326219	+	0.188342i	0.327942	+	0.944698i	$0.393645\pi$
$642$	−138.879	−	63.9816i	−0.216322	−	0.0996598i
$643$	395.704	−	685.380i	0.615403	−	1.06591i	−0.374910	−	0.927061i	$-0.622326\pi$
$643$	395.704	−	685.380i	0.615403	−	1.06591i	0.990314	−	0.138849i	$-0.0443402\pi$
$644$	13.7878	+	7.96036i	0.0214096	+	0.0123608i
$645$		0			0
$646$	−329.666	−	570.999i	−0.510319	−	0.883899i
$647$			294.028i			0.454448i	0.973842	+	0.227224i	$0.0729650\pi$
$647$			294.028i			0.454448i	−0.973842	+	0.227224i	$0.927035\pi$
$648$	144.000	−	178.191i	0.222222	−	0.274986i
$649$	−17.9082			−0.0275935
$650$		0			0
$651$	62.2770	−	44.0365i	0.0956636	−	0.0676444i
$652$	−133.060	+	230.467i	−0.204080	+	0.353477i
$653$	665.379	+	384.156i	1.01896	+	0.588295i	0.913802	−	0.406161i	$-0.133133\pi$
$653$	665.379	+	384.156i	1.01896	+	0.588295i	0.105155	+	0.994456i	$0.466466\pi$
$654$	263.221	−	571.349i	0.402479	−	0.873622i
$655$		0			0
$656$			43.6689i			0.0665684i
$657$	23.7276	−	67.1117i	0.0361150	−	0.102149i
$658$	−534.681			−0.812585
$659$	−373.204	+	215.469i	−0.566318	+	0.326964i	−0.755678	−	0.654944i	$-0.772692\pi$
$659$	−373.204	+	215.469i	−0.566318	+	0.326964i	0.189359	+	0.981908i	$0.439359\pi$
$660$		0			0
$661$	−506.136	+	876.653i	−0.765712	+	1.32625i	0.174157	+	0.984718i	$0.444280\pi$
$661$	−506.136	+	876.653i	−0.765712	+	1.32625i	−0.939869	+	0.341534i	$0.889053\pi$
$662$	579.062	+	334.322i	0.874717	+	0.505018i
$663$	546.848	−	50.3868i	0.824808	−	0.0759981i
$664$	184.318	+	319.248i	0.277587	+	0.480795i
$665$		0			0
$666$	−108.606	−	584.348i	−0.163072	−	0.877399i
$667$	−13.0454			−0.0195583
$668$	510.106	−	294.510i	0.763631	−	0.440883i
$669$	853.464	+	393.192i	1.27573	+	0.587731i
$670$		0			0
$671$	−10.8099	−	6.24112i	−0.0161102	−	0.00930123i
$672$	−81.7980	−	115.680i	−0.121723	−	0.172143i
$673$	281.606	+	487.755i	0.418433	+	0.724748i	0.995782	−	0.0917499i	$-0.0292460\pi$
$673$	281.606	+	487.755i	0.418433	+	0.724748i	−0.577349	+	0.816498i	$0.695913\pi$
$674$			432.192i			0.641235i
$675$		0			0
$676$	149.939			0.221803
$677$	303.227	−	175.068i	0.447897	−	0.258594i	−0.259044	−	0.965865i	$-0.583408\pi$
$677$	303.227	−	175.068i	0.447897	−	0.258594i	0.706942	+	0.707272i	$0.250074\pi$
$678$	−592.665	+	419.078i	−0.874138	+	0.618109i
$679$	−458.659	+	794.421i	−0.675492	+	1.16999i
$680$		0			0
$681$	95.7429	−	207.820i	0.140592	−	0.305168i
$682$	−2.05332	−	3.55645i	−0.00301073	−	0.00521474i
$683$			502.818i			0.736190i	0.929788	+	0.368095i	$0.119990\pi$
$683$			502.818i			0.736190i	−0.929788	+	0.368095i	$0.880010\pi$
$684$	288.879	+	337.890i	0.422337	+	0.493991i
$685$		0			0
$686$	289.392	−	167.080i	0.421854	−	0.243557i
$687$	−33.4559	−	363.097i	−0.0486985	−	0.528525i
$688$	90.0908	−	156.042i	0.130946	−	0.226805i
$689$	792.650	+	457.637i	1.15044	+	0.664205i
$690$		0			0
$691$	−188.159	−	325.902i	−0.272300	−	0.471638i	0.697150	−	0.716925i	$-0.254451\pi$
$691$	−188.159	−	325.902i	−0.272300	−	0.471638i	−0.969450	+	0.245287i	$0.921118\pi$
$692$		−	138.529i		−	0.200186i
$693$	−54.4546	+	46.5559i	−0.0785781	+	0.0671803i
$694$	189.044			0.272398
$695$		0			0
$696$	105.439	+	48.5761i	0.151493	+	0.0697932i
$697$	−103.045	+	178.480i	−0.147841	+	0.256069i
$698$	−120.952	−	69.8318i	−0.173284	−	0.100046i
$699$	−261.576	−	369.924i	−0.374214	−	0.529218i
$700$		0			0
$701$		−	489.681i		−	0.698546i	−0.937021	−	0.349273i	$-0.886429\pi$
$701$		−	489.681i		−	0.698546i	0.937021	−	0.349273i	$-0.113571\pi$
$702$	−356.288	+	100.774i	−0.507533	+	0.143552i
$703$	1153.27			1.64050
$704$	−6.60612	+	3.81405i	−0.00938370	+	0.00541768i
$705$		0			0
$706$	−230.598	+	399.408i	−0.326626	+	0.565733i
$707$	−1066.70	−	615.862i	−1.50878	−	0.871092i
$708$	−47.1520	+	102.348i	−0.0665989	+	0.144560i
$709$	−237.014	−	410.521i	−0.334294	−	0.579014i	0.649055	−	0.760741i	$-0.275164\pi$
$709$	−237.014	−	410.521i	−0.334294	−	0.579014i	−0.983349	+	0.181728i	$0.941831\pi$
$710$		0			0
$711$	387.053	−	71.9371i	0.544378	−	0.101177i
$712$	410.969			0.577204
$713$	2.51479	−	1.45192i	0.00352706	−	0.00203635i
$714$	−61.3485	−	665.815i	−0.0859222	−	0.932514i
$715$		0			0
$716$	−82.2429	−	47.4829i	−0.114864	−	0.0663170i
$717$	−262.030	+	24.1435i	−0.365453	+	0.0336730i
$718$	−296.091	−	512.844i	−0.412383	−	0.714268i
$719$			108.122i			0.150379i	0.997169	+	0.0751894i	$0.0239561\pi$
$719$			108.122i			0.150379i	−0.997169	+	0.0751894i	$0.976044\pi$
$720$		0			0
$721$	861.030			1.19422
$722$	−304.886	+	176.026i	−0.422280	+	0.243804i
$723$	−549.820	−	253.303i	−0.760470	−	0.350350i
$724$	242.879	−	420.678i	0.335468	−	0.581047i
$725$		0			0
$726$	−294.161	−	416.007i	−0.405181	−	0.573012i
$727$	−222.296	−	385.027i	−0.305771	−	0.529611i	0.671662	−	0.740858i	$-0.265581\pi$
$727$	−222.296	−	385.027i	−0.305771	−	0.529611i	−0.977433	+	0.211247i	$0.932248\pi$
$728$			228.974i			0.314525i
$729$	−621.000	+	381.838i	−0.851852	+	0.523783i
$730$		0			0
$731$	736.423	−	425.174i	1.00742	−	0.581634i
$732$	−64.1316	+	45.3479i	−0.0876115	+	0.0619507i
$733$	−358.181	+	620.388i	−0.488651	+	0.846368i	−0.999915	−	0.0130556i	$-0.995844\pi$
$733$	−358.181	+	620.388i	−0.488651	+	0.846368i	0.511264	+	0.859424i	$0.329177\pi$
$734$	−229.305	−	132.390i	−0.312405	−	0.180367i
$735$		0			0
$736$	−2.69694	−	4.67123i	−0.00366432	−	0.00634679i
$737$		−	71.5567i		−	0.0970918i
$738$	46.3179	−	131.007i	0.0627613	−	0.177516i
$739$	933.362			1.26301			0.631504	−	0.775373i	$-0.282438\pi$
$739$	933.362			1.26301			0.631504	+	0.775373i	$0.282438\pi$
$740$		0			0
$741$	−65.9194	−	715.424i	−0.0889600	−	0.965484i
$742$	557.196	−	965.093i	0.750939	−	1.30066i
$743$	13.7793	+	7.95550i	0.0185455	+	0.0107073i	0.509244	−	0.860622i	$-0.329925\pi$
$743$	13.7793	+	7.95550i	0.0185455	+	0.0107073i	−0.490699	+	0.871329i	$0.663258\pi$
$744$	−25.7321	+	2.37097i	−0.0345862	+	0.00318679i
$745$		0			0
$746$			637.852i			0.855030i
$747$	−214.340	−	1153.24i	−0.286934	−	1.54383i
$748$	−36.0000			−0.0481283
$749$	260.574	−	150.443i	0.347896	−	0.200858i
$750$		0			0
$751$	−404.916	+	701.334i	−0.539169	+	0.933867i	0.459781	+	0.888033i	$0.347928\pi$
$751$	−404.916	+	701.334i	−0.539169	+	0.933867i	−0.998949	+	0.0458347i	$0.985405\pi$
$752$	156.879	+	90.5739i	0.208615	+	0.120444i
$753$	−91.1510	−	128.907i	−0.121050	−	0.171191i
$754$	−93.8105	−	162.484i	−0.124417	−	0.215497i
$755$		0			0
$756$	122.697	+	433.799i	0.162298	+	0.573808i
$757$	−689.637			−0.911013			−0.455506	−	0.890232i	$-0.650542\pi$
$757$	−689.637			−0.911013			−0.455506	+	0.890232i	$0.650542\pi$
$758$	599.716	−	346.246i	0.791182	−	0.456789i
$759$	−2.22704	+	1.57475i	−0.00293417	+	0.00207477i
$760$		0			0
$761$	−825.393	−	476.541i	−1.08462	−	0.626204i	−0.152479	−	0.988307i	$-0.548726\pi$
$761$	−825.393	−	476.541i	−1.08462	−	0.626204i	−0.932138	+	0.362103i	$0.882059\pi$
$762$	−138.631	+	300.913i	−0.181931	+	0.394899i
$763$	618.924	+	1072.01i	0.811172	+	1.40499i
$764$		−	15.0635i		−	0.0197167i
$765$		0			0
$766$	145.743			0.190266
$767$	157.721	−	91.0604i	0.205634	−	0.118723i
$768$	4.40408	+	47.7975i	0.00573448	+	0.0622364i
$769$	328.348	−	568.715i	0.426980	−	0.739552i	−0.569623	−	0.821906i	$-0.692911\pi$
$769$	328.348	−	568.715i	0.426980	−	0.739552i	0.996603	+	0.0823545i	$0.0262440\pi$
$770$		0			0
$771$	241.098	−	22.2149i	0.312708	−	0.0288131i
$772$	−345.454	−	598.344i	−0.447479	−	0.775057i
$773$		−	278.021i		−	0.359665i	−0.983697	−	0.179832i	$-0.942445\pi$
$773$		−	278.021i		−	0.359665i	0.983697	−	0.179832i	$-0.0575555\pi$
$774$	−435.780	+	372.570i	−0.563023	+	0.481356i
$775$		0			0
$776$	269.146	−	155.392i	0.346838	−	0.200247i
$777$	1062.24	+	489.374i	1.36710	+	0.629825i
$778$	−24.2350	+	41.9762i	−0.0311503	+	0.0539539i
$779$	233.499	+	134.811i	0.299743	+	0.173056i
$780$		0			0
$781$	−8.59133	−	14.8806i	−0.0110004	−	0.0190533i
$782$		−	25.4558i		−	0.0325522i
$783$	−264.795	−	257.563i	−0.338180	−	0.328944i
$784$	82.7878			0.105597
$785$		0			0
$786$	−810.817	+	573.334i	−1.03157	+	0.729433i
$787$	410.977	−	711.833i	0.522207	−	0.904489i	−0.477459	−	0.878654i	$-0.658442\pi$
$787$	410.977	−	711.833i	0.522207	−	0.904489i	0.999666	−	0.0258350i	$-0.00822444\pi$
$788$	133.757	+	77.2247i	0.169743	+	0.0980009i
$789$	−582.135	+	1263.58i	−0.737813	+	1.60150i
$790$		0			0
$791$		−	1428.32i		−	1.80572i
$792$	23.8638	−	4.43529i	0.0301310	−	0.00560011i
$793$	126.941			0.160077
$794$	10.1316	−	5.84950i	0.0127602	−	0.00736713i
$795$		0			0
$796$	153.485	−	265.843i	0.192820	−	0.333974i
$797$	−1145.33	−	661.257i	−1.43705	−	0.829683i	−0.439409	−	0.898287i	$-0.644812\pi$
$797$	−1145.33	−	661.257i	−1.43705	−	0.829683i	−0.997644	+	0.0686043i	$0.978145\pi$
$798$	−871.065	+	80.2602i	−1.09156	+	0.100577i
$799$	427.454	+	740.372i	0.534986	+	0.926624i
$800$		0			0
$801$	−1232.91	−	435.899i	−1.53921	−	0.544193i
$802$	−585.650			−0.730238
$803$	6.53113	−	3.77075i	0.00813341	−	0.00469583i
$804$	−408.959	−	188.408i	−0.508656	−	0.234339i
$805$		0			0
$806$	36.1681	+	20.8817i	0.0448736	+	0.0259078i
$807$	75.3031	+	106.495i	0.0933123	+	0.131964i
$808$	208.652	+	361.395i	0.258232	+	0.447271i
$809$		−	235.681i		−	0.291324i	−0.989334	−	0.145662i	$-0.953469\pi$
$809$		−	235.681i		−	0.291324i	0.989334	−	0.145662i	$-0.0465311\pi$
$810$		0			0
$811$	−587.362			−0.724244			−0.362122	−	0.932131i	$-0.617948\pi$
$811$	−587.362			−0.724244			−0.362122	+	0.932131i	$0.617948\pi$
$812$	−197.833	+	114.219i	−0.243637	+	0.140664i
$813$	−839.283	+	593.462i	−1.03233	+	0.729966i
$814$	31.4847	−	54.5331i	0.0386790	−	0.0669940i
$815$		0			0
$816$	−94.7878	+	205.746i	−0.116161	+	0.252140i
$817$	−556.242	−	963.439i	−0.680835	−	1.17924i
$818$			461.334i			0.563978i
$819$	242.864	−	686.922i	0.296537	−	0.838733i
$820$		0			0
$821$	−817.453	+	471.956i	−0.995679	+	0.574856i	−0.906967	−	0.421202i	$-0.861608\pi$
$821$	−817.453	+	471.956i	−0.995679	+	0.574856i	−0.0887121	+	0.996057i	$0.528275\pi$
$822$	−58.3247	−	632.999i	−0.0709547	−	0.770071i
$823$	−807.871	+	1399.27i	−0.981617	+	1.70021i	−0.325520	+	0.945535i	$0.605539\pi$
$823$	−807.871	+	1399.27i	−0.981617	+	1.70021i	−0.656097	+	0.754676i	$0.727794\pi$
$824$	−252.631	−	145.857i	−0.306591	−	0.177010i
$825$		0			0
$826$	−110.871	−	192.034i	−0.134226	−	0.232486i
$827$			582.354i			0.704177i	0.935967	+	0.352088i	$0.114528\pi$
$827$			582.354i			0.704177i	−0.935967	+	0.352088i	$0.885472\pi$
$828$	3.13622	+	16.8742i	0.00378771	+	0.0203795i
$829$	877.121			1.05805			0.529024	−	0.848607i	$-0.322558\pi$
$829$	877.121			1.05805			0.529024	+	0.848607i	$0.322558\pi$
$830$		0			0
$831$	−133.512	−	61.5095i	−0.160665	−	0.0740186i
$832$	38.7878	−	67.1824i	0.0466199	−	0.0807480i
$833$	338.363	+	195.354i	0.406198	+	0.234519i
$834$	207.056	+	292.821i	0.248268	+	0.351104i
$835$		0			0
$836$			47.0976i			0.0563369i
$837$	79.7112	+	20.1802i	0.0952344	+	0.0241101i
$838$	764.772			0.912616
$839$	−984.778	+	568.562i	−1.17375	+	0.677666i	−0.954561	−	0.298016i	$-0.903675\pi$
$839$	−984.778	+	568.562i	−1.17375	+	0.677666i	−0.219191	+	0.975682i	$0.570342\pi$
$840$		0			0
$841$	−326.909	+	566.223i	−0.388715	+	0.673274i
$842$	347.456	+	200.604i	0.412656	+	0.238247i
$843$	−25.9155	+	56.2523i	−0.0307421	+	0.0667287i
$844$	−51.5607	−	89.3058i	−0.0610909	−	0.105813i
$845$		0			0
$846$	−374.568	−	438.117i	−0.442751	−	0.517868i
$847$	1002.57			1.18368
$848$	−326.969	+	188.776i	−0.385577	+	0.222613i
$849$	−14.7010	−	159.550i	−0.0173157	−	0.187927i
$850$		0			0
$851$	38.5607	+	22.2630i	0.0453122	+	0.0261610i
$852$	−107.666	+	9.92041i	−0.126369	+	0.0116437i
$853$	−159.909	−	276.970i	−0.187466	−	0.324701i	0.756939	−	0.653486i	$-0.226694\pi$
$853$	−159.909	−	276.970i	−0.187466	−	0.324701i	−0.944405	+	0.328785i	$0.893361\pi$
$854$		−	154.557i		−	0.180980i
$855$		0			0
$856$	−101.939			−0.119087
$857$	−691.061	+	398.984i	−0.806372	+	0.465559i	−0.845694	−	0.533668i	$-0.820813\pi$
$857$	−691.061	+	398.984i	−0.806372	+	0.465559i	0.0393225	+	0.999227i	$0.487480\pi$
$858$	−35.6288	−	16.4143i	−0.0415254	−	0.0191308i
$859$	233.901	−	405.128i	0.272294	−	0.471627i	−0.697155	−	0.716921i	$-0.745551\pi$
$859$	233.901	−	405.128i	0.272294	−	0.471627i	0.969449	+	0.245293i	$0.0788843\pi$
$860$		0			0
$861$	157.863	+	223.252i	0.183348	+	0.259293i
$862$	−182.030	−	315.284i	−0.211171	−	0.365759i
$863$		−	1304.85i		−	1.51199i	−0.654578	−	0.755994i	$-0.727154\pi$
$863$		−	1304.85i		−	1.51199i	0.654578	−	0.755994i	$-0.272846\pi$
$864$	37.4847	−	148.064i	0.0433851	−	0.171370i
$865$		0			0
$866$	583.312	−	336.775i	0.673571	−	0.388886i
$867$	−165.006	+	116.677i	−0.190318	+	0.134575i
$868$	25.4245	−	44.0365i	0.0292909	−	0.0507333i
$869$	36.1209	+	20.8544i	0.0415661	+	0.0239982i
$870$		0			0
$871$	363.855	+	630.216i	0.417744	+	0.723554i
$872$		−	419.378i		−	0.480938i
$873$	−972.257	+	180.702i	−1.11370	+	0.206990i
$874$	−33.3031			−0.0381042
$875$		0			0
$876$	−4.35409	−	47.2549i	−0.00497042	−	0.0539440i
$877$	−186.878	+	323.682i	−0.213088	+	0.369079i	−0.952679	−	0.303977i	$-0.901685\pi$
$877$	−186.878	+	323.682i	−0.213088	+	0.369079i	0.739592	+	0.673056i	$0.235019\pi$
$878$	−683.240	−	394.469i	−0.778177	−	0.449281i
$879$	44.5829	−	4.10789i	0.0507200	−	0.00467336i
$880$		0			0
$881$		−	229.979i		−	0.261043i	−0.991445	−	0.130522i	$-0.958335\pi$
$881$		−	229.979i		−	0.261043i	0.991445	−	0.130522i	$-0.0416652\pi$
$882$	−248.363	−	87.8097i	−0.281591	−	0.0995575i
$883$	1381.79			1.56488			0.782439	−	0.622728i	$-0.213976\pi$
$883$	1381.79			1.56488			0.782439	+	0.622728i	$0.213976\pi$
$884$	317.060	−	183.055i	0.358665	−	0.207076i
$885$		0			0
$886$	588.204	−	1018.80i	0.663888	−	1.14989i
$887$	−758.794	−	438.090i	−0.855461	−	0.493901i	0.00702852	−	0.999975i	$-0.497763\pi$
$887$	−758.794	−	438.090i	−0.855461	−	0.493901i	−0.862490	+	0.506075i	$0.831096\pi$
$888$	−228.767	−	323.526i	−0.257621	−	0.364331i
$889$	−325.969	−	564.596i	−0.366670	−	0.635091i
$890$		0			0
$891$	−76.2957	−	12.0055i	−0.0856293	−	0.0134742i
$892$	626.454			0.702303
$893$	968.605	−	559.224i	1.08466	−	0.626231i
$894$	−400.120	+	282.928i	−0.447562	+	0.316474i
$895$		0			0
$896$	−81.7980	−	47.2261i	−0.0912924	−	0.0527077i
$897$	11.6066	−	25.1934i	0.0129394	−	0.0280863i
$898$	516.136	+	893.974i	0.574762	+	0.995517i
$899$			41.6655i			0.0463465i
$900$		0			0
$901$	−1781.82			−1.97760
$902$	12.7492	−	7.36077i	0.0141344	−	0.00816050i
$903$	−103.512	−	1123.42i	−0.114632	−	1.24410i
$904$	−241.955	+	419.078i	−0.267649	+	0.463581i
$905$		0			0
$906$	−273.649	+	25.2141i	−0.302041	+	0.0278302i
$907$	590.037	+	1021.97i	0.650537	+	1.12676i	0.982993	+	0.183644i	$0.0587894\pi$
$907$	590.037	+	1021.97i	0.650537	+	1.12676i	−0.332456	+	0.943119i	$0.607877\pi$
$908$		−	152.542i		−	0.167998i
$909$	−242.637	−	1305.49i	−0.266928	−	1.43619i
$910$		0			0
$911$	1100.13	−	635.158i	1.20760	−	0.697210i	0.245368	−	0.969430i	$-0.421091\pi$
$911$	1100.13	−	635.158i	1.20760	−	0.697210i	0.962235	+	0.272220i	$0.0877578\pi$
$912$	269.171	+	124.008i	0.295144	+	0.135973i
$913$	62.1367	−	107.624i	0.0680578	−	0.117880i
$914$	−869.123	−	501.788i	−0.950900	−	0.549002i
$915$		0			0
$916$	−121.545	−	210.522i	−0.132691	−	0.229827i
$917$		−	1954.07i		−	2.13093i
$918$	502.590	−	516.702i	0.547484	−	0.562856i
$919$	1316.63			1.43268			0.716340	−	0.697751i	$-0.245816\pi$
$919$	1316.63			1.43268			0.716340	+	0.697751i	$0.245816\pi$
$920$		0			0
$921$	−161.444	+	114.158i	−0.175292	+	0.123950i
$922$	6.50740	−	11.2711i	0.00705791	−	0.0122247i
$923$	151.332	+	87.3713i	0.163956	+	0.0946602i
$924$	−19.9852	+	43.3799i	−0.0216290	+	0.0469480i
$925$		0			0
$926$		−	78.0610i		−	0.0842991i
$927$	603.189	+	705.526i	0.650689	+	0.761085i
$928$	77.3939			0.0833986
$929$	543.424	−	313.746i	0.584956	−	0.337724i	−0.178145	−	0.984004i	$-0.557009\pi$
$929$	543.424	−	313.746i	0.584956	−	0.337724i	0.763100	+	0.646280i	$0.223676\pi$
$930$		0			0
$931$	255.576	−	442.670i	0.274517	−	0.475478i
$932$	−261.576	−	151.021i	−0.280660	−	0.162039i
$933$	−747.363	+	68.8623i	−0.801032	+	0.0738074i
$934$	442.515	+	766.459i	0.473785	+	0.820620i
$935$		0			0
$936$	−187.621	+	160.406i	−0.200450	+	0.171374i
$937$	−469.789			−0.501375			−0.250688	−	0.968068i	$-0.580657\pi$
$937$	−469.789			−0.501375			−0.250688	+	0.968068i	$0.580657\pi$
$938$	767.320	−	443.012i	0.818039	−	0.472295i
$939$	−1161.81	−	535.250i	−1.23729	−	0.570021i
$940$		0			0
$941$	805.984	+	465.335i	0.856518	+	0.494511i	0.862845	−	0.505469i	$-0.168680\pi$
$941$	805.984	+	465.335i	0.856518	+	0.494511i	−0.00632656	+	0.999980i	$0.502014\pi$
$942$	−50.9944	−	72.1169i	−0.0541342	−	0.0765573i
$943$	5.20485	+	9.01506i	0.00551946	+	0.00955998i
$944$			75.1250i			0.0795816i
$945$		0			0
$946$	−60.7423			−0.0642097
$947$	3.14465	−	1.81556i	0.00332064	−	0.00191717i	−0.498339	−	0.866982i	$-0.666056\pi$
$947$	3.14465	−	1.81556i	0.00332064	−	0.00191717i	0.501659	+	0.865065i	$0.332723\pi$
$948$	214.293	−	151.528i	0.226047	−	0.159840i
$949$	−38.3474	+	66.4197i	−0.0404083	+	0.0699892i
$950$		0			0
$951$	582.431	−	1264.23i	0.612440	−	1.32936i
$952$	−222.879	−	386.037i	−0.234116	−	0.405501i
$953$		−	719.641i		−	0.755132i	−0.925983	−	0.377566i	$-0.876761\pi$
$953$		−	719.641i		−	0.755132i	0.925983	−	0.377566i	$-0.123239\pi$
$954$	1181.14	−	219.524i	1.23809	−	0.230109i
$955$		0			0
$956$	−151.924	+	87.7133i	−0.158916	+	0.0917504i
$957$	−3.59082	−	38.9711i	−0.00375216	−	0.0407222i
$958$	−218.704	+	378.806i	−0.228292	+	0.395413i
$959$	1083.28	+	625.431i	1.12959	+	0.652170i
$960$		0			0
$961$	475.863	+	824.218i	0.495175	+	0.857667i
$962$			640.380i			0.665676i
$963$	305.816	+	108.122i	0.317566	+	0.112277i
$964$	−403.576			−0.418647
$965$		0			0
$966$	−30.6742	−	14.1317i	−0.0317539	−	0.0146291i
$967$	16.8870	−	29.2491i	0.0174633	−	0.0302473i	−0.857162	−	0.515047i	$-0.827774\pi$
$967$	16.8870	−	29.2491i	0.0174633	−	0.0302473i	0.874625	+	0.484800i	$0.161108\pi$
$968$	−294.161	−	169.834i	−0.303886	−	0.175448i
$969$	807.514	+	1142.00i	0.833348	+	1.17853i
$970$		0			0
$971$		−	970.472i		−	0.999456i	−0.866182	−	0.499728i	$-0.833433\pi$
$971$		−	970.472i		−	0.999456i	0.866182	−	0.499728i	$-0.166567\pi$
$972$	−269.499	+	404.433i	−0.277263	+	0.416083i
$973$	−705.697			−0.725279
$974$	−34.7015	+	20.0349i	−0.0356278	+	0.0205697i
$975$		0			0
$976$	−26.1816	+	45.3479i	−0.0268254	+	0.0464630i
$977$	1359.92	+	785.151i	1.39194	+	0.803635i	0.993529	−	0.113574i	$-0.0362300\pi$
$977$	1359.92	+	785.151i	1.39194	+	0.803635i	0.398406	+	0.917209i	$0.369563\pi$
$978$	236.216	−	512.730i	0.241529	−	0.524264i
$979$	−69.2724	−	119.983i	−0.0707584	−	0.122557i
$980$		0			0
$981$	−444.817	+	1258.13i	−0.453433	+	1.28250i
$982$	−1343.07			−1.36769
$983$	671.930	−	387.939i	0.683551	−	0.394648i	−0.117641	−	0.993056i	$-0.537533\pi$
$983$	671.930	−	387.939i	0.683551	−	0.394648i	0.801192	+	0.598408i	$0.204200\pi$
$984$	−8.49948	−	92.2450i	−0.00863769	−	0.0937449i
$985$		0			0
$986$	316.318	+	182.626i	0.320809	+	0.185219i
$987$	1129.45	−	104.068i	1.14432	−	0.105438i
$988$	−239.485	−	414.800i	−0.242393	−	0.419838i
$989$		−	42.9513i		−	0.0434290i
$990$		0			0
$991$	870.454			0.878359			0.439180	−	0.898399i	$-0.355269\pi$
$991$	870.454			0.878359			0.439180	+	0.898399i	$0.355269\pi$
$992$	−14.9194	+	8.61371i	−0.0150397	+	0.00868318i
$993$	−1288.27	−	593.507i	−1.29735	−	0.597690i
$994$	106.379	−	184.254i	0.107021	−	0.185366i
$995$		0			0
$996$	−451.485	−	638.496i	−0.453298	−	0.641060i
$997$	622.499	+	1078.20i	0.624372	+	1.08144i	0.988662	+	0.150159i	$0.0479784\pi$
$997$	622.499	+	1078.20i	0.624372	+	1.08144i	−0.364290	+	0.931286i	$0.618688\pi$
$998$			792.279i			0.793867i
$999$	343.151	+	1213.22i	0.343495	+	1.21444i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	450.3.i.b.401.1		4
3.2	odd	2		1350.3.i.b.1151.2		4
5.2	odd	4		450.3.k.a.149.1		8
5.3	odd	4		450.3.k.a.149.4		8
5.4	even	2		18.3.d.a.5.2	✓	4
9.2	odd	6	inner	450.3.i.b.101.1		4
9.7	even	3		1350.3.i.b.251.2		4
15.2	even	4		1350.3.k.a.449.4		8
15.8	even	4		1350.3.k.a.449.1		8
15.14	odd	2		54.3.d.a.17.1		4
20.19	odd	2		144.3.q.c.113.2		4
40.19	odd	2		576.3.q.e.257.1		4
40.29	even	2		576.3.q.f.257.2		4
45.2	even	12		450.3.k.a.299.4		8
45.4	even	6		162.3.b.a.161.4		4
45.7	odd	12		1350.3.k.a.899.1		8
45.14	odd	6		162.3.b.a.161.1		4
45.29	odd	6		18.3.d.a.11.2	yes	4
45.34	even	6		54.3.d.a.35.1		4
45.38	even	12		450.3.k.a.299.1		8
45.43	odd	12		1350.3.k.a.899.4		8
60.59	even	2		432.3.q.d.17.1		4
120.29	odd	2		1728.3.q.d.449.2		4
120.59	even	2		1728.3.q.c.449.1		4
180.59	even	6		1296.3.e.g.161.2		4
180.79	odd	6		432.3.q.d.305.1		4
180.119	even	6		144.3.q.c.65.2		4
180.139	odd	6		1296.3.e.g.161.4		4
360.29	odd	6		576.3.q.f.65.2		4
360.259	odd	6		1728.3.q.c.1601.1		4
360.299	even	6		576.3.q.e.65.1		4
360.349	even	6		1728.3.q.d.1601.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
18.3.d.a.5.2	✓	4	5.4	even	2
18.3.d.a.11.2	yes	4	45.29	odd	6
54.3.d.a.17.1		4	15.14	odd	2
54.3.d.a.35.1		4	45.34	even	6
144.3.q.c.65.2		4	180.119	even	6
144.3.q.c.113.2		4	20.19	odd	2
162.3.b.a.161.1		4	45.14	odd	6
162.3.b.a.161.4		4	45.4	even	6
432.3.q.d.17.1		4	60.59	even	2
432.3.q.d.305.1		4	180.79	odd	6
450.3.i.b.101.1		4	9.2	odd	6	inner
450.3.i.b.401.1		4	1.1	even	1	trivial
450.3.k.a.149.1		8	5.2	odd	4
450.3.k.a.149.4		8	5.3	odd	4
450.3.k.a.299.1		8	45.38	even	12
450.3.k.a.299.4		8	45.2	even	12
576.3.q.e.65.1		4	360.299	even	6
576.3.q.e.257.1		4	40.19	odd	2
576.3.q.f.65.2		4	360.29	odd	6
576.3.q.f.257.2		4	40.29	even	2
1296.3.e.g.161.2		4	180.59	even	6
1296.3.e.g.161.4		4	180.139	odd	6
1350.3.i.b.251.2		4	9.7	even	3
1350.3.i.b.1151.2		4	3.2	odd	2
1350.3.k.a.449.1		8	15.8	even	4
1350.3.k.a.449.4		8	15.2	even	4
1350.3.k.a.899.1		8	45.7	odd	12
1350.3.k.a.899.4		8	45.43	odd	12
1728.3.q.c.449.1		4	120.59	even	2
1728.3.q.c.1601.1		4	360.259	odd	6
1728.3.q.d.449.2		4	120.29	odd	2
1728.3.q.d.1601.2		4	360.349	even	6

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:	\( N \)	\(=\)	\( 450 = 2 \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	450.i (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.22474 + 0.707107i) q^{2} +(2.44949 - 1.73205i) q^{3} +(1.00000 - 1.73205i) q^{4} +(-1.77526 + 3.85337i) q^{6} +(-4.17423 - 7.22999i) q^{7} +2.82843i q^{8} +(3.00000 - 8.48528i) q^{9} +O(q^{10})\)	\(q+(-1.22474 + 0.707107i) q^{2} +(2.44949 - 1.73205i) q^{3} +(1.00000 - 1.73205i) q^{4} +(-1.77526 + 3.85337i) q^{6} +(-4.17423 - 7.22999i) q^{7} +2.82843i q^{8} +(3.00000 - 8.48528i) q^{9} +(0.825765 - 0.476756i) q^{11} +(-0.550510 - 5.97469i) q^{12} +(-4.84847 + 8.39780i) q^{13} +(10.2247 + 5.90326i) q^{14} +(-2.00000 - 3.46410i) q^{16} -18.8776i q^{17} +(2.32577 + 12.5136i) q^{18} -24.6969 q^{19} +(-22.7474 - 10.4798i) q^{21} +(-0.674235 + 1.16781i) q^{22} +(-0.825765 - 0.476756i) q^{23} +(4.89898 + 6.92820i) q^{24} -13.7135i q^{26} +(-7.34847 - 25.9808i) q^{27} -16.6969 q^{28} +(11.8485 - 6.84072i) q^{29} +(-1.52270 + 2.63740i) q^{31} +(4.89898 + 2.82843i) q^{32} +(1.19694 - 2.59808i) q^{33} +(13.3485 + 23.1202i) q^{34} +(-11.6969 - 13.6814i) q^{36} -46.6969 q^{37} +(30.2474 - 17.4634i) q^{38} +(2.66913 + 28.9681i) q^{39} +(-9.45459 - 5.45861i) q^{41} +(35.2702 - 3.24980i) q^{42} +(22.5227 + 39.0105i) q^{43} -1.90702i q^{44} +1.34847 q^{46} +(-39.2196 + 22.6435i) q^{47} +(-10.8990 - 5.02118i) q^{48} +(-10.3485 + 17.9241i) q^{49} +(-32.6969 - 46.2405i) q^{51} +(9.69694 + 16.7956i) q^{52} -94.3879i q^{53} +(27.3712 + 26.6237i) q^{54} +(20.4495 - 11.8065i) q^{56} +(-60.4949 + 42.7764i) q^{57} +(-9.67423 + 16.7563i) q^{58} +(-16.2650 - 9.39063i) q^{59} +(-6.54541 - 11.3370i) q^{61} -4.30686i q^{62} +(-73.8712 + 13.7296i) q^{63} -8.00000 q^{64} +(0.371173 + 4.02834i) q^{66} +(37.5227 - 64.9912i) q^{67} +(-32.6969 - 18.8776i) q^{68} +(-2.84847 + 0.262459i) q^{69} -18.0204i q^{71} +(24.0000 + 8.48528i) q^{72} +7.90918 q^{73} +(57.1918 - 33.0197i) q^{74} +(-24.6969 + 42.7764i) q^{76} +(-6.89388 - 3.98018i) q^{77} +(-23.7526 - 33.5912i) q^{78} +(21.8712 + 37.8820i) q^{79} +(-63.0000 - 50.9117i) q^{81} +15.4393 q^{82} +(112.871 - 65.1662i) q^{83} +(-40.8990 + 28.9199i) q^{84} +(-55.1691 - 31.8519i) q^{86} +(17.1742 - 37.2784i) q^{87} +(1.34847 + 2.33562i) q^{88} -145.300i q^{89} +80.9546 q^{91} +(-1.65153 + 0.953512i) q^{92} +(0.838264 + 9.09769i) q^{93} +(32.0227 - 55.4650i) q^{94} +(16.8990 - 1.55708i) q^{96} +(-54.9393 - 95.1576i) q^{97} -29.2699i q^{98} +(-1.56811 - 8.43712i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{4} - 12 q^{6} - 2 q^{7} + 12 q^{9}+O(q^{10}) \) 4 * q + 4 * q^4 - 12 * q^6 - 2 * q^7 + 12 * q^9	\( 4 q + 4 q^{4} - 12 q^{6} - 2 q^{7} + 12 q^{9} + 18 q^{11} - 12 q^{12} + 10 q^{13} + 36 q^{14} - 8 q^{16} + 24 q^{18} - 40 q^{19} - 42 q^{21} + 12 q^{22} - 18 q^{23} - 8 q^{28} + 18 q^{29} + 38 q^{31} - 54 q^{33} + 24 q^{34} + 12 q^{36} - 128 q^{37} + 72 q^{38} - 102 q^{39} - 126 q^{41} + 48 q^{42} + 46 q^{43} - 24 q^{46} - 54 q^{47} - 24 q^{48} - 12 q^{49} - 72 q^{51} - 20 q^{52} + 36 q^{54} + 72 q^{56} - 144 q^{57} - 24 q^{58} + 126 q^{59} + 62 q^{61} - 222 q^{63} - 32 q^{64} - 72 q^{66} + 106 q^{67} - 72 q^{68} + 18 q^{69} + 96 q^{72} + 208 q^{73} + 72 q^{74} - 40 q^{76} + 90 q^{77} - 144 q^{78} + 14 q^{79} - 252 q^{81} - 144 q^{82} + 378 q^{83} - 144 q^{84} - 108 q^{86} + 54 q^{87} - 24 q^{88} + 412 q^{91} - 36 q^{92} - 222 q^{93} + 84 q^{94} + 48 q^{96} - 14 q^{97} + 126 q^{99}+O(q^{100}) \) 4 * q + 4 * q^4 - 12 * q^6 - 2 * q^7 + 12 * q^9 + 18 * q^11 - 12 * q^12 + 10 * q^13 + 36 * q^14 - 8 * q^16 + 24 * q^18 - 40 * q^19 - 42 * q^21 + 12 * q^22 - 18 * q^23 - 8 * q^28 + 18 * q^29 + 38 * q^31 - 54 * q^33 + 24 * q^34 + 12 * q^36 - 128 * q^37 + 72 * q^38 - 102 * q^39 - 126 * q^41 + 48 * q^42 + 46 * q^43 - 24 * q^46 - 54 * q^47 - 24 * q^48 - 12 * q^49 - 72 * q^51 - 20 * q^52 + 36 * q^54 + 72 * q^56 - 144 * q^57 - 24 * q^58 + 126 * q^59 + 62 * q^61 - 222 * q^63 - 32 * q^64 - 72 * q^66 + 106 * q^67 - 72 * q^68 + 18 * q^69 + 96 * q^72 + 208 * q^73 + 72 * q^74 - 40 * q^76 + 90 * q^77 - 144 * q^78 + 14 * q^79 - 252 * q^81 - 144 * q^82 + 378 * q^83 - 144 * q^84 - 108 * q^86 + 54 * q^87 - 24 * q^88 + 412 * q^91 - 36 * q^92 - 222 * q^93 + 84 * q^94 + 48 * q^96 - 14 * q^97 + 126 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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