LMFDB - Embedded newform 225.4.e.c.151.2

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			151.2
Root			$0.500000 - 1.98116i$ of defining polynomial
Character	$\chi$	$=$	225.151
Dual form			225.4.e.c.76.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0874923 + 0.151541i) q^{2} +(-5.19394 - 0.151541i) q^{3} +(3.98469 + 6.90169i) q^{4} +(0.477395 - 0.773837i) q^{6} +(4.23186 - 7.32979i) q^{7} -2.79440 q^{8} +(26.9541 + 1.57419i) q^{9} +O(q^{10})$	\(q+(-0.0874923 + 0.151541i) q^{2} +(-5.19394 - 0.151541i) q^{3} +(3.98469 + 6.90169i) q^{4} +(0.477395 - 0.773837i) q^{6} +(4.23186 - 7.32979i) q^{7} -2.79440 q^{8} +(26.9541 + 1.57419i) q^{9} +(15.7541 - 27.2870i) q^{11} +(-19.6504 - 36.4508i) q^{12} +(13.4348 + 23.2697i) q^{13} +(0.740510 + 1.28260i) q^{14} +(-31.6330 + 54.7900i) q^{16} +44.3307 q^{17} +(-2.59683 + 3.94692i) q^{18} -90.2082 q^{19} +(-23.0908 + 37.4292i) q^{21} +(2.75673 + 4.77480i) q^{22} +(97.1287 + 168.232i) q^{23} +(14.5139 + 0.423466i) q^{24} -4.70176 q^{26} +(-139.759 - 12.2609i) q^{27} +67.4506 q^{28} +(-1.87186 + 3.24215i) q^{29} +(125.832 + 217.947i) q^{31} +(-16.7129 - 28.9476i) q^{32} +(-85.9611 + 139.339i) q^{33} +(-3.87859 + 6.71792i) q^{34} +(96.5390 + 192.301i) q^{36} +62.2293 q^{37} +(7.89252 - 13.6703i) q^{38} +(-66.2532 - 122.898i) q^{39} +(102.173 + 176.969i) q^{41} +(-3.65180 - 6.77397i) q^{42} +(-263.831 + 456.968i) q^{43} +251.101 q^{44} -33.9920 q^{46} +(77.8637 - 134.864i) q^{47} +(172.603 - 279.782i) q^{48} +(135.683 + 235.009i) q^{49} +(-230.251 - 6.71792i) q^{51} +(-107.067 + 185.445i) q^{52} +141.694 q^{53} +(14.0859 - 20.1065i) q^{54} +(-11.8255 + 20.4823i) q^{56} +(468.536 + 13.6703i) q^{57} +(-0.327546 - 0.567326i) q^{58} +(246.923 + 427.683i) q^{59} +(379.742 - 657.732i) q^{61} -44.0373 q^{62} +(125.604 - 190.906i) q^{63} -500.280 q^{64} +(-13.5947 - 25.2178i) q^{66} +(-271.795 - 470.763i) q^{67} +(176.644 + 305.956i) q^{68} +(-478.987 - 888.505i) q^{69} -928.207 q^{71} +(-75.3203 - 4.39891i) q^{72} -608.739 q^{73} +(-5.44459 + 9.43030i) q^{74} +(-359.452 - 622.589i) q^{76} +(-133.338 - 230.949i) q^{77} +(24.4207 + 0.712510i) q^{78} +(-307.420 + 532.467i) q^{79} +(724.044 + 84.8617i) q^{81} -35.7573 q^{82} +(537.655 - 931.246i) q^{83} +(-350.334 - 10.2215i) q^{84} +(-46.1663 - 79.9623i) q^{86} +(10.2136 - 16.5559i) q^{87} +(-44.0233 + 76.2506i) q^{88} +1505.15 q^{89} +227.416 q^{91} +(-774.055 + 1340.70i) q^{92} +(-620.536 - 1151.07i) q^{93} +(13.6249 + 23.5991i) q^{94} +(82.4190 + 152.885i) q^{96} +(-166.369 + 288.160i) q^{97} -47.4848 q^{98} +(467.593 - 710.695i) 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 $

$2$	−0.0874923	+	0.151541i	−0.0309332	+	0.0535779i	−0.881078	−	0.472972i	$-0.843181\pi$
$2$	−0.0874923	+	0.151541i	−0.0309332	+	0.0535779i	0.850144	+	0.526550i	$0.176515\pi$
$3$	−5.19394	−	0.151541i	−0.999575	−	0.0291641i
$3$	−5.19394	−	0.151541i	−0.999575	−	0.0291641i
$4$	3.98469	+	6.90169i	0.498086	+	0.862711i
$5$		0			0
$5$		0			0
$6$	0.477395	−	0.773837i	0.0324826	−	0.0526529i
$7$	4.23186	−	7.32979i	0.228499	−	0.395772i	−0.728865	−	0.684658i	$-0.759952\pi$
$7$	4.23186	−	7.32979i	0.228499	−	0.395772i	0.957363	+	0.288886i	$0.0932850\pi$
$8$	−2.79440			−0.123496
$9$	26.9541	+	1.57419i	0.998299	+	0.0583034i
$10$		0			0
$11$	15.7541	−	27.2870i	0.431823	−	0.747939i	−0.565208	−	0.824949i	$-0.691204\pi$
$11$	15.7541	−	27.2870i	0.431823	−	0.747939i	0.997030	+	0.0770098i	$0.0245373\pi$
$12$	−19.6504	−	36.4508i	−0.472714	−	0.876870i
$13$	13.4348	+	23.2697i	0.286626	+	0.496451i	0.973002	−	0.230796i	$-0.0741330\pi$
$13$	13.4348	+	23.2697i	0.286626	+	0.496451i	−0.686376	+	0.727247i	$0.740800\pi$
$14$	0.740510	+	1.28260i	0.0141364	+	0.0244850i
$15$		0			0
$16$	−31.6330	+	54.7900i	−0.494266	+	0.856094i
$17$	44.3307			0.632457			0.316229	−	0.948683i	$-0.397583\pi$
$17$	44.3307			0.632457			0.316229	+	0.948683i	$0.397583\pi$
$18$	−2.59683	+	3.94692i	−0.0340044	+	0.0516832i
$19$	−90.2082			−1.08922			−0.544610	−	0.838689i	$-0.683322\pi$
$19$	−90.2082			−1.08922			−0.544610	+	0.838689i	$0.683322\pi$
$20$		0			0
$21$	−23.0908	+	37.4292i	−0.239944	+	0.388939i
$22$	2.75673	+	4.77480i	0.0267153	+	0.0462723i
$23$	97.1287	+	168.232i	0.880553	+	1.52516i	0.850727	+	0.525608i	$0.176162\pi$
$23$	97.1287	+	168.232i	0.880553	+	1.52516i	0.0298265	+	0.999555i	$0.490505\pi$
$24$	14.5139	+	0.423466i	0.123443	+	0.00360165i
$25$		0			0
$26$	−4.70176			−0.0354650
$27$	−139.759	−	12.2609i	−0.996174	−	0.0873931i
$28$	67.4506			0.455248
$29$	−1.87186	+	3.24215i	−0.0119860	+	0.0207604i	−0.871956	−	0.489584i	$-0.837149\pi$
$29$	−1.87186	+	3.24215i	−0.0119860	+	0.0207604i	0.859970	+	0.510344i	$0.170482\pi$
$30$		0			0
$31$	125.832	+	217.947i	0.729035	+	1.26273i	0.957292	+	0.289124i	$0.0933641\pi$
$31$	125.832	+	217.947i	0.729035	+	1.26273i	−0.228257	+	0.973601i	$0.573303\pi$
$32$	−16.7129	−	28.9476i	−0.0923265	−	0.159914i
$33$	−85.9611	+	139.339i	−0.453452	+	0.735027i
$34$	−3.87859	+	6.71792i	−0.0195639	+	0.0338857i
$35$		0			0
$36$	96.5390	+	192.301i	0.446940	+	0.890283i
$37$	62.2293			0.276498			0.138249	−	0.990397i	$-0.455853\pi$
$37$	62.2293			0.276498			0.138249	+	0.990397i	$0.455853\pi$
$38$	7.89252	−	13.6703i	0.0336931	−	0.0583581i
$39$	−66.2532	−	122.898i	−0.272026	−	0.504599i
$40$		0			0
$41$	102.173	+	176.969i	0.389188	+	0.674094i	0.992341	−	0.123532i	$-0.0394223\pi$
$41$	102.173	+	176.969i	0.389188	+	0.674094i	−0.603152	+	0.797626i	$0.706089\pi$
$42$	−3.65180	−	6.77397i	−0.0134163	−	0.0248868i
$43$	−263.831	+	456.968i	−0.935669	+	1.62063i	−0.162233	+	0.986752i	$0.551870\pi$
$43$	−263.831	+	456.968i	−0.935669	+	1.62063i	−0.773436	+	0.633874i	$0.781464\pi$
$44$	251.101			0.860340
$45$		0			0
$46$	−33.9920			−0.108953
$47$	77.8637	−	134.864i	0.241651	−	0.418551i	−0.719534	−	0.694457i	$-0.755645\pi$
$47$	77.8637	−	134.864i	0.241651	−	0.418551i	0.961185	+	0.275906i	$0.0889778\pi$
$48$	172.603	−	279.782i	0.519023	−	0.841315i
$49$	135.683	+	235.009i	0.395577	+	0.685159i
$50$		0			0
$51$	−230.251	−	6.71792i	−0.632188	−	0.0184450i
$52$	−107.067	+	185.445i	−0.285529	+	0.494551i
$53$	141.694			0.367230			0.183615	−	0.982998i	$-0.441220\pi$
$53$	141.694			0.367230			0.183615	+	0.982998i	$0.441220\pi$
$54$	14.0859	−	20.1065i	0.0354972	−	0.0506695i
$55$		0			0
$56$	−11.8255	+	20.4823i	−0.0282187	+	0.0488762i
$57$	468.536	+	13.6703i	1.08876	+	0.0317661i
$58$	−0.327546	−	0.567326i	−0.000741533	−	0.00128437i
$59$	246.923	+	427.683i	0.544857	+	0.943721i	0.998616	+	0.0525961i	$0.0167496\pi$
$59$	246.923	+	427.683i	0.544857	+	0.943721i	−0.453758	+	0.891125i	$0.649917\pi$
$60$		0			0
$61$	379.742	−	657.732i	0.797065	−	1.38056i	−0.124455	−	0.992225i	$-0.539718\pi$
$61$	379.742	−	657.732i	0.797065	−	1.38056i	0.921520	−	0.388331i	$-0.126948\pi$
$62$	−44.0373			−0.0902055
$63$	125.604	−	190.906i	0.251185	−	0.381776i
$64$	−500.280			−0.977108
$65$		0			0
$66$	−13.5947	−	25.2178i	−0.0253545	−	0.0470317i
$67$	−271.795	−	470.763i	−0.495598	−	0.858401i	0.504389	−	0.863476i	$-0.331718\pi$
$67$	−271.795	−	470.763i	−0.495598	−	0.858401i	−0.999987	+	0.00507574i	$0.998384\pi$
$68$	176.644	+	305.956i	0.315018	+	0.545627i
$69$	−478.987	−	888.505i	−0.835699	−	1.55019i
$70$		0			0
$71$	−928.207			−1.55152			−0.775760	−	0.631028i	$-0.782633\pi$
$71$	−928.207			−1.55152			−0.775760	+	0.631028i	$0.782633\pi$
$72$	−75.3203	−	4.39891i	−0.123286	−	0.00720024i
$73$	−608.739			−0.975993			−0.487997	−	0.872845i	$-0.662272\pi$
$73$	−608.739			−0.975993			−0.487997	+	0.872845i	$0.662272\pi$
$74$	−5.44459	+	9.43030i	−0.00855298	+	0.0148142i
$75$		0			0
$76$	−359.452	−	622.589i	−0.542526	−	0.939682i
$77$	−133.338	−	230.949i	−0.197342	−	0.341806i
$78$	24.4207	+	0.712510i	0.0354500	+	0.00103431i
$79$	−307.420	+	532.467i	−0.437816	+	0.758319i	−0.997521	−	0.0703726i	$-0.977581\pi$
$79$	−307.420	+	532.467i	−0.437816	+	0.758319i	0.559705	+	0.828692i	$0.310915\pi$
$80$		0			0
$81$	724.044	+	84.8617i	0.993201	+	0.116408i
$82$	−35.7573			−0.0481553
$83$	537.655	−	931.246i	0.711028	−	1.23154i	−0.253444	−	0.967350i	$-0.581563\pi$
$83$	537.655	−	931.246i	0.711028	−	1.23154i	0.964472	−	0.264186i	$-0.0851033\pi$
$84$	−350.334	−	10.2215i	−0.455055	−	0.0132769i
$85$		0			0
$86$	−46.1663	−	79.9623i	−0.0578865	−	0.100262i
$87$	10.2136	−	16.5559i	0.0125864	−	0.0204020i
$88$	−44.0233	+	76.2506i	−0.0533284	+	0.0923675i
$89$	1505.15			1.79265			0.896324	−	0.443400i	$-0.146228\pi$
$89$	1505.15			1.79265			0.896324	+	0.443400i	$0.146228\pi$
$90$		0			0
$91$	227.416			0.261975
$92$	−774.055	+	1340.70i	−0.877183	+	1.51933i
$93$	−620.536	−	1151.07i	−0.691898	−	1.28345i
$94$	13.6249	+	23.5991i	0.0149501	+	0.0258943i
$95$		0			0
$96$	82.4190	+	152.885i	0.0876234	+	0.162539i
$97$	−166.369	+	288.160i	−0.174147	+	0.301631i	−0.939866	−	0.341544i	$-0.889050\pi$
$97$	−166.369	+	288.160i	−0.174147	+	0.301631i	0.765719	+	0.643175i	$0.222383\pi$
$98$	−47.4848			−0.0489458
$99$	467.593	−	710.695i	0.474695	−	0.721490i
$100$		0			0
$101$	247.493	−	428.670i	0.243826	−	0.422319i	−0.717975	−	0.696069i	$-0.754931\pi$
$101$	247.493	−	428.670i	0.243826	−	0.422319i	0.961801	+	0.273750i	$0.0882640\pi$
$102$	21.1632	−	34.3047i	0.0205438	−	0.0333007i
$103$	−315.015	−	545.622i	−0.301353	−	0.521959i	0.675090	−	0.737736i	$-0.264105\pi$
$103$	−315.015	−	545.622i	−0.301353	−	0.521959i	−0.976443	+	0.215777i	$0.930772\pi$
$104$	−37.5421	−	65.0248i	−0.0353972	−	0.0613097i
$105$		0			0
$106$	−12.3971	+	21.4725i	−0.0113596	+	0.0196754i
$107$	1561.00			1.41035			0.705175	−	0.709034i	$-0.250869\pi$
$107$	1561.00			1.41035			0.705175	+	0.709034i	$0.250869\pi$
$108$	−472.277	−	1013.43i	−0.420786	−	0.902939i
$109$	−936.140			−0.822623			−0.411311	−	0.911495i	$-0.634929\pi$
$109$	−936.140			−0.822623			−0.411311	+	0.911495i	$0.634929\pi$
$110$		0			0
$111$	−323.215	−	9.43030i	−0.276381	−	0.00806382i
$112$	267.733	+	463.727i	0.225878	+	0.391233i
$113$	677.490	+	1173.45i	0.564008	+	0.976890i	0.997141	+	0.0755602i	$0.0240745\pi$
$113$	677.490	+	1173.45i	0.564008	+	0.976890i	−0.433134	+	0.901330i	$0.642592\pi$
$114$	−43.0649	+	69.8065i	−0.0353807	+	0.0573506i
$115$		0			0
$116$	−29.8351			−0.0238803
$117$	325.491	+	648.363i	0.257194	+	0.512318i
$118$	−86.4153			−0.0674167
$119$	187.601	−	324.935i	0.144516	−	0.250309i
$120$		0			0
$121$	169.115	+	292.915i	0.127058	+	0.220071i
$122$	66.4490	+	115.093i	0.0493115	+	0.0854101i
$123$	−503.862	−	934.648i	−0.369363	−	0.685157i
$124$	−1002.80	+	1736.90i	−0.726244	+	1.25789i
$125$		0			0
$126$	17.9407	+	35.7370i	0.0126848	+	0.0252675i
$127$	1182.37			0.826126			0.413063	−	0.910702i	$-0.364459\pi$
$127$	1182.37			0.826126			0.413063	+	0.910702i	$0.364459\pi$
$128$	177.474	−	307.393i	0.122552	−	0.212266i
$129$	1439.57	−	2333.48i	0.982535	−	1.59265i
$130$		0			0
$131$	−1126.87	−	1951.80i	−0.751569	−	1.30176i	−0.947062	−	0.321050i	$-0.895964\pi$
$131$	−1126.87	−	1951.80i	−0.751569	−	1.30176i	0.195494	−	0.980705i	$-0.437369\pi$
$132$	−1304.21	−	38.0522i	−0.859974	−	0.0250910i
$133$	−381.748	+	661.207i	−0.248885	+	0.431082i
$134$	95.1199			0.0613217
$135$		0			0
$136$	−123.877			−0.0781059
$137$	236.856	−	410.246i	0.147708	−	0.255837i	−0.782672	−	0.622434i	$-0.786144\pi$
$137$	236.856	−	410.246i	0.147708	−	0.255837i	0.930380	+	0.366597i	$0.119477\pi$
$138$	176.553	+	5.15119i	0.108907	+	0.00317753i
$139$	68.5193	+	118.679i	0.0418110	+	0.0724188i	0.886174	−	0.463353i	$-0.153354\pi$
$139$	68.5193	+	118.679i	0.0418110	+	0.0724188i	−0.844363	+	0.535772i	$0.820021\pi$
$140$		0			0
$141$	−424.857	+	688.675i	−0.253755	+	0.411326i
$142$	81.2110	−	140.662i	0.0479935	−	0.0831272i
$143$	846.613			0.495086
$144$	−938.889	+	1427.02i	−0.543339	+	0.825820i
$145$		0			0
$146$	53.2600	−	92.2490i	0.0301906	−	0.0522917i
$147$	−669.115	−	1241.19i	−0.375426	−	0.696404i
$148$	247.965	+	429.487i	0.137720	+	0.238538i
$149$	71.5553	+	123.937i	0.0393426	+	0.0681433i	0.885026	−	0.465541i	$-0.154140\pi$
$149$	71.5553	+	123.937i	0.0393426	+	0.0681433i	−0.845684	+	0.533685i	$0.820807\pi$
$150$		0			0
$151$	−108.421	+	187.790i	−0.0584314	+	0.101206i	−0.893761	−	0.448543i	$-0.851943\pi$
$151$	−108.421	+	187.790i	−0.0584314	+	0.101206i	0.835330	+	0.549749i	$0.185277\pi$
$152$	252.077			0.134514
$153$	1194.89	+	69.7850i	0.631381	+	0.0368744i
$154$	46.6644			0.0244177
$155$		0			0
$156$	584.202	−	946.967i	0.299831	−	0.486013i
$157$	674.215	+	1167.78i	0.342728	+	0.593622i	0.984938	−	0.172906i	$-0.0553158\pi$
$157$	674.215	+	1167.78i	0.342728	+	0.593622i	−0.642211	+	0.766528i	$0.721983\pi$
$158$	−53.7938	−	93.1736i	−0.0270861	−	0.0469145i
$159$	−735.951	−	21.4725i	−0.367074	−	0.0107099i
$160$		0			0
$161$	1644.14			0.804822
$162$	−76.2083	+	102.298i	−0.0369598	+	0.0496127i
$163$	−1039.85			−0.499676			−0.249838	−	0.968288i	$-0.580377\pi$
$163$	−1039.85			−0.499676			−0.249838	+	0.968288i	$0.580377\pi$
$164$	−814.254	+	1410.33i	−0.387699	+	0.671514i
$165$		0			0
$166$	94.0813	+	162.954i	0.0439887	+	0.0761907i
$167$	−1663.52	−	2881.31i	−0.770822	−	1.33510i	−0.937113	−	0.349026i	$-0.886513\pi$
$167$	−1663.52	−	2881.31i	−0.770822	−	1.33510i	0.166291	−	0.986077i	$-0.446821\pi$
$168$	64.5248	−	104.592i	0.0296321	−	0.0480324i
$169$	737.513	−	1277.41i	0.335691	−	0.581434i
$170$		0			0
$171$	−2431.48	−	142.005i	−1.08737	−	0.0635052i
$172$	−4205.13			−1.86418
$173$	−597.127	+	1034.25i	−0.262420	+	0.454525i	−0.966885	−	0.255214i	$-0.917854\pi$
$173$	−597.127	+	1034.25i	−0.262420	+	0.454525i	0.704464	+	0.709740i	$0.251187\pi$
$174$	1.61528	+	2.99630i	0.000703760	+	0.00130545i
$175$		0			0
$176$	996.702	+	1726.34i	0.426871	+	0.739362i
$177$	−1217.69	−	2258.78i	−0.517103	−	0.959210i
$178$	−131.689	+	228.092i	−0.0554523	+	0.0960463i
$179$	2323.70			0.970288			0.485144	−	0.874434i	$-0.338767\pi$
$179$	2323.70			0.970288			0.485144	+	0.874434i	$0.338767\pi$
$180$		0			0
$181$	2527.12			1.03779			0.518893	−	0.854839i	$-0.326344\pi$
$181$	2527.12			1.03779			0.518893	+	0.854839i	$0.326344\pi$
$182$	−19.8972	+	34.4629i	−0.00810372	+	0.0140361i
$183$	−2072.03	+	3358.68i	−0.836988	+	1.35672i
$184$	−271.416	−	470.106i	−0.108745	−	0.188352i
$185$		0			0
$186$	228.727	+	6.67346i	0.0901671	+	0.00263076i
$187$	698.391	−	1209.65i	0.273109	−	0.473039i
$188$	1241.05			0.481452
$189$	−681.311	+	972.520i	−0.262212	+	0.374288i
$190$		0			0
$191$	−1194.43	+	2068.82i	−0.452493	+	0.783741i	−0.998540	−	0.0540134i	$-0.982799\pi$
$191$	−1194.43	+	2068.82i	−0.452493	+	0.783741i	0.546047	+	0.837754i	$0.316132\pi$
$192$	2598.42	+	75.8129i	0.976693	+	0.0284965i
$193$	1773.99	+	3072.64i	0.661629	+	1.14597i	0.980188	+	0.198072i	$0.0634679\pi$
$193$	1773.99	+	3072.64i	0.661629	+	1.14597i	−0.318559	+	0.947903i	$0.603199\pi$
$194$	−29.1120	−	50.4235i	−0.0107738	−	0.0186608i
$195$		0			0
$196$	−1081.31	+	1872.88i	−0.394063	+	0.682536i
$197$	1239.26			0.448192			0.224096	−	0.974567i	$-0.428057\pi$
$197$	1239.26			0.448192			0.224096	+	0.974567i	$0.428057\pi$
$198$	66.7887	+	133.040i	0.0239720	+	0.0477512i
$199$	516.657			0.184044			0.0920222	−	0.995757i	$-0.470667\pi$
$199$	516.657			0.184044			0.0920222	+	0.995757i	$0.470667\pi$
$200$		0			0
$201$	1340.35	+	2486.30i	0.470353	+	0.872489i
$202$	43.3074	+	75.0107i	0.0150847	+	0.0261274i
$203$	15.8429	+	27.4406i	0.00547759	+	0.00948746i
$204$	−871.114	−	1615.89i	−0.298971	−	0.554583i
$205$		0			0
$206$	110.246			0.0372873
$207$	2353.18	+	4687.43i	0.790133	+	1.57391i
$208$	−1699.93			−0.566678
$209$	−1421.15	+	2461.51i	−0.470350	+	0.814670i
$210$		0			0
$211$	8.92159	+	15.4527i	0.00291084	+	0.00504173i	0.867477	−	0.497477i	$-0.165740\pi$
$211$	8.92159	+	15.4527i	0.00291084	+	0.00504173i	−0.864566	+	0.502519i	$0.832407\pi$
$212$	564.607	+	977.928i	0.182912	+	0.316813i
$213$	4821.05	+	140.662i	1.55086	+	0.0452487i
$214$	−136.575	+	236.555i	−0.0436266	+	0.0755635i
$215$		0			0
$216$	390.543	+	34.2618i	0.123024	+	0.0107927i
$217$	2130.01			0.666334
$218$	81.9050	−	141.864i	0.0254464	−	0.0440744i
$219$	3161.76	+	92.2490i	0.975578	+	0.0284640i
$220$		0			0
$221$	595.573	+	1031.56i	0.181279	+	0.313984i
$222$	29.7079	−	48.1554i	0.00898138	−	0.0145584i
$223$	494.777	−	856.978i	0.148577	−	0.257343i	−0.782125	−	0.623122i	$-0.785864\pi$
$223$	494.777	−	856.978i	0.148577	−	0.257343i	0.930702	+	0.365779i	$0.119197\pi$
$224$	−282.906			−0.0843860
$225$		0			0
$226$	−237.101			−0.0697863
$227$	−1713.57	+	2967.98i	−0.501028	+	0.867806i	0.498971	+	0.866619i	$0.333711\pi$
$227$	−1713.57	+	2967.98i	−0.501028	+	0.867806i	−0.999999	+	0.00118754i	$0.999622\pi$
$228$	1772.62	+	3288.16i	0.514890	+	0.955104i
$229$	−549.805	−	952.290i	−0.158656	−	0.274800i	0.775728	−	0.631067i	$-0.217383\pi$
$229$	−549.805	−	952.290i	−0.158656	−	0.274800i	−0.934384	+	0.356267i	$0.884049\pi$
$230$		0			0
$231$	657.554	+	1219.74i	0.187290	+	0.347416i
$232$	5.23071	−	9.05985i	0.00148023	−	0.00256383i
$233$	−4459.91			−1.25399			−0.626993	−	0.779025i	$-0.715715\pi$
$233$	−4459.91			−1.25399			−0.626993	+	0.779025i	$0.715715\pi$
$234$	−126.732	−	7.40147i	−0.0354047	−	0.00206773i
$235$		0			0
$236$	−1967.82	+	3408.37i	−0.542772	+	0.940109i
$237$	1677.41	−	2719.02i	0.459745	−	0.745228i
$238$	32.8273	+	56.8586i	0.00894067	+	0.0154857i
$239$	−3272.23	−	5667.66i	−0.885618	−	1.53394i	−0.845003	−	0.534761i	$-0.820402\pi$
$239$	−3272.23	−	5667.66i	−0.885618	−	1.53394i	−0.0406148	−	0.999175i	$-0.512932\pi$
$240$		0			0
$241$	105.162	−	182.147i	0.0281083	−	0.0486851i	−0.851629	−	0.524145i	$-0.824385\pi$
$241$	105.162	−	182.147i	0.0281083	−	0.0486851i	0.879737	+	0.475460i	$0.157718\pi$
$242$	−59.1849			−0.0157213
$243$	−3747.78	−	550.489i	−0.989384	−	0.145325i
$244$	6052.61			1.58803
$245$		0			0
$246$	185.722	+	5.41871i	0.0481349	+	0.00140441i
$247$	−1211.93	−	2099.12i	−0.312199	−	0.540744i
$248$	−351.624	−	609.031i	−0.0900329	−	0.155942i
$249$	−2933.67	+	4755.36i	−0.746642	+	1.21028i
$250$		0			0
$251$	816.143			0.205237			0.102618	−	0.994721i	$-0.467278\pi$
$251$	816.143			0.205237			0.102618	+	0.994721i	$0.467278\pi$
$252$	1818.07	+	106.180i	0.454474	+	0.0265425i
$253$	6120.71			1.52097
$254$	−103.448	+	179.177i	−0.0255547	+	0.0442621i
$255$		0			0
$256$	−1970.06	−	3412.25i	−0.480972	−	0.833069i
$257$	−2086.17	−	3613.36i	−0.506350	−	0.877023i	−0.999973	−	0.00734758i	$-0.997661\pi$
$257$	−2086.17	−	3613.36i	−0.506350	−	0.877023i	0.493623	−	0.869676i	$-0.335672\pi$
$258$	227.667	+	422.316i	0.0549378	+	0.101908i
$259$	263.346	−	456.128i	0.0631795	−	0.109430i
$260$		0			0
$261$	−55.5579	+	84.4425i	−0.0131760	+	0.0200263i
$262$	394.371			0.0929937
$263$	−1408.52	+	2439.64i	−0.330241	+	0.571994i	−0.982559	−	0.185951i	$-0.940463\pi$
$263$	−1408.52	+	2439.64i	−0.330241	+	0.571994i	0.652318	+	0.757945i	$0.273797\pi$
$264$	240.209	−	389.370i	0.0559995	−	0.0907729i
$265$		0			0
$266$	−66.8001	−	115.701i	−0.0153976	−	0.0266695i
$267$	−7817.66	−	228.092i	−1.79189	−	0.0522810i
$268$	2166.04	−	3751.69i	0.493701	−	0.855115i
$269$	−102.610			−0.0232573			−0.0116287	−	0.999932i	$-0.503702\pi$
$269$	−102.610			−0.0232573			−0.0116287	+	0.999932i	$0.503702\pi$
$270$		0			0
$271$	−3337.27			−0.748061			−0.374031	−	0.927416i	$-0.622025\pi$
$271$	−3337.27			−0.748061			−0.374031	+	0.927416i	$0.622025\pi$
$272$	−1402.31	+	2428.88i	−0.312602	+	0.541443i
$273$	−1181.19	−	34.4629i	−0.261863	−	0.00764026i
$274$	41.4461	+	71.7867i	0.00913814	+	0.0158277i
$275$		0			0
$276$	4223.57	−	6846.23i	0.921120	−	1.49310i
$277$	316.941	−	548.959i	0.0687479	−	0.119075i	−0.829603	−	0.558354i	$-0.811433\pi$
$277$	316.941	−	548.959i	0.0687479	−	0.119075i	0.898350	+	0.439280i	$0.144766\pi$
$278$	−23.9796			−0.00517339
$279$	3048.59	+	6072.65i	0.654173	+	1.30308i
$280$		0			0
$281$	3101.20	−	5371.44i	0.658370	−	1.14033i	−0.322667	−	0.946513i	$-0.604579\pi$
$281$	3101.20	−	5371.44i	0.658370	−	1.14033i	0.981037	−	0.193818i	$-0.0620872\pi$
$282$	−67.1909	−	124.637i	−0.0141885	−	0.0263193i
$283$	−3740.06	−	6477.98i	−0.785596	−	1.36069i	−0.928642	−	0.370976i	$-0.879023\pi$
$283$	−3740.06	−	6477.98i	−0.785596	−	1.36069i	0.143047	−	0.989716i	$-0.454310\pi$
$284$	−3698.62	−	6406.19i	−0.772791	−	1.33851i
$285$		0			0
$286$	−74.0722	+	128.297i	−0.0153146	+	0.0265257i
$287$	1729.52			0.355716
$288$	−404.911	−	806.564i	−0.0828459	−	0.165025i
$289$	−2947.79			−0.599998
$290$		0			0
$291$	907.780	−	1471.47i	0.182869	−	0.296424i
$292$	−2425.64	−	4201.33i	−0.486129	−	0.842000i
$293$	−2418.26	−	4188.54i	−0.482171	−	0.835144i	0.517620	−	0.855611i	$-0.326818\pi$
$293$	−2418.26	−	4188.54i	−0.482171	−	0.835144i	−0.999791	+	0.0204666i	$0.993485\pi$
$294$	246.633	+	7.19590i	0.0489250	+	0.00142746i
$295$		0			0
$296$	−173.893			−0.0341464
$297$	−2536.35	+	3620.45i	−0.495535	+	0.707339i
$298$	−25.0422			−0.00486796
$299$	−2609.81	+	4520.31i	−0.504779	+	0.874303i
$300$		0			0
$301$	2232.99	+	3867.65i	0.427599	+	0.740623i
$302$	−18.9719	−	32.8604i	−0.00361494	−	0.00626126i
$303$	−1350.42	+	2188.98i	−0.256039	+	0.415029i
$304$	2853.56	−	4942.51i	0.538365	−	0.932475i
$305$		0			0
$306$	−115.119	+	174.970i	−0.0215063	+	0.0326874i
$307$	5611.86			1.04328			0.521638	−	0.853167i	$-0.325321\pi$
$307$	5611.86			1.04328			0.521638	+	0.853167i	$0.325321\pi$
$308$	1062.63	−	1840.52i	0.196587	−	0.340498i
$309$	1553.49	+	2881.67i	0.286002	+	0.530525i
$310$		0			0
$311$	−5460.70	−	9458.21i	−0.995653	−	1.72452i	−0.578489	−	0.815690i	$-0.696358\pi$
$311$	−5460.70	−	9458.21i	−0.995653	−	1.72452i	−0.417163	−	0.908831i	$-0.636976\pi$
$312$	185.138	+	343.424i	0.0335941	+	0.0623159i
$313$	2490.36	−	4313.44i	0.449724	−	0.778946i	−0.548643	−	0.836056i	$-0.684856\pi$
$313$	2490.36	−	4313.44i	0.449724	−	0.778946i	0.998368	+	0.0571109i	$0.0181889\pi$
$314$	−235.955			−0.0424067
$315$		0			0
$316$	−4899.89			−0.872280
$317$	−1878.06	+	3252.90i	−0.332752	+	0.576344i	−0.983050	−	0.183335i	$-0.941311\pi$
$317$	−1878.06	+	3252.90i	−0.332752	+	0.576344i	0.650298	+	0.759679i	$0.274644\pi$
$318$	67.6440	−	109.648i	0.0119286	−	0.0193357i
$319$	58.9789	+	102.154i	0.0103517	+	0.0179296i
$320$		0			0
$321$	−8107.73	−	236.555i	−1.40975	−	0.0411316i
$322$	−143.849	+	249.155i	−0.0248957	+	0.0431206i
$323$	−3998.99			−0.688885
$324$	2299.40	+	5335.27i	0.394273	+	0.914827i
$325$		0			0
$326$	90.9788	−	157.580i	0.0154566	−	0.0267716i
$327$	4862.25	+	141.864i	0.822273	+	0.0239911i
$328$	−285.511	−	494.520i	−0.0480632	−	0.0832479i
$329$	−659.016	−	1141.45i	−0.110434	−	0.191277i
$330$		0			0
$331$	453.477	−	785.445i	0.0753031	−	0.130429i	−0.825915	−	0.563795i	$-0.809341\pi$
$331$	453.477	−	785.445i	0.0753031	−	0.130429i	0.901218	+	0.433366i	$0.142674\pi$
$332$	8569.55			1.41661
$333$	1677.33	+	97.9609i	0.276028	+	0.0161208i
$334$	582.182			0.0953759
$335$		0			0
$336$	−1320.32	−	2449.14i	−0.214372	−	0.397654i
$337$	4939.35	+	8555.20i	0.798408	+	1.38288i	0.920653	+	0.390383i	$0.127657\pi$
$337$	4939.35	+	8555.20i	0.798408	+	1.38288i	−0.122245	+	0.992500i	$0.539009\pi$
$338$	129.053	+	223.527i	0.0207680	+	0.0359712i
$339$	−3341.02	−	6197.48i	−0.535278	−	0.992923i
$340$		0			0
$341$	7929.49			1.25925
$342$	234.255	−	356.045i	0.0370382	−	0.0562944i
$343$	5199.81			0.818553
$344$	737.247	−	1276.95i	0.115551	−	0.200141i
$345$		0			0
$346$	−104.488	−	180.979i	−0.0162350	−	0.0281199i
$347$	−1754.86	−	3039.50i	−0.271486	−	0.470228i	0.697757	−	0.716335i	$-0.254182\pi$
$347$	−1754.86	−	3039.50i	−0.271486	−	0.470228i	−0.969243	+	0.246107i	$0.920848\pi$
$348$	154.962	+	4.52124i	0.0238702	+	0.000696448i
$349$	5196.48	−	9000.57i	0.797024	−	1.38049i	−0.124522	−	0.992217i	$-0.539740\pi$
$349$	5196.48	−	9000.57i	0.797024	−	1.38049i	0.921546	−	0.388269i	$-0.126927\pi$
$350$		0			0
$351$	−1592.33	−	3416.88i	−0.242143	−	0.519600i
$352$	−1053.19			−0.159475
$353$	4042.70	−	7002.16i	0.609550	−	1.05577i	−0.381765	−	0.924259i	$-0.624684\pi$
$353$	4042.70	−	7002.16i	0.609550	−	1.05577i	0.991315	−	0.131512i	$-0.0419830\pi$
$354$	448.836	+	13.0955i	0.0673881	+	0.00196615i
$355$		0			0
$356$	5997.56	+	10388.1i	0.892893	+	1.54654i
$357$	−1023.63	+	1659.26i	−0.151754	+	0.245987i
$358$	−203.306	+	352.136i	−0.0300141	+	0.0519860i
$359$	−8189.49			−1.20397			−0.601984	−	0.798508i	$-0.705623\pi$
$359$	−8189.49			−1.20397			−0.601984	+	0.798508i	$0.705623\pi$
$360$		0			0
$361$	1278.52			0.186400
$362$	−221.103	+	382.962i	−0.0321020	+	0.0556024i
$363$	−833.983	−	1547.01i	−0.120586	−	0.223683i
$364$	906.184	+	1569.56i	0.130486	+	0.226008i
$365$		0			0
$366$	−327.691	−	607.856i	−0.0467996	−	0.0868119i
$367$	−4497.33	+	7789.60i	−0.639669	+	1.10794i	0.345836	+	0.938295i	$0.387595\pi$
$367$	−4497.33	+	7789.60i	−0.639669	+	1.10794i	−0.985505	+	0.169645i	$0.945738\pi$
$368$	−12289.9			−1.74091
$369$	2475.39	+	4930.86i	0.349224	+	0.695638i
$370$		0			0
$371$	599.629	−	1038.59i	0.0839116	−	0.145339i
$372$	5471.71	−	8869.42i	0.762621	−	1.23618i
$373$	−464.934	−	805.288i	−0.0645398	−	0.111786i	0.831950	−	0.554851i	$-0.187225\pi$
$373$	−464.934	−	805.288i	−0.0645398	−	0.111786i	−0.896490	+	0.443064i	$0.853891\pi$
$374$	122.208	+	211.670i	0.0168963	+	0.0292652i
$375$		0			0
$376$	−217.582	+	376.863i	−0.0298429	+	0.0516894i
$377$	−100.592			−0.0137420
$378$	−87.7673	−	188.335i	−0.0119425	−	0.0256267i
$379$	3449.71			0.467546			0.233773	−	0.972291i	$-0.424893\pi$
$379$	3449.71			0.467546			0.233773	+	0.972291i	$0.424893\pi$
$380$		0			0
$381$	−6141.14	−	179.177i	−0.825775	−	0.0240932i
$382$	−209.007	−	362.012i	−0.0279941	−	0.0484872i
$383$	−2673.07	−	4629.89i	−0.356625	−	0.617692i	0.630770	−	0.775970i	$-0.282739\pi$
$383$	−2673.07	−	4629.89i	−0.356625	−	0.617692i	−0.987395	+	0.158278i	$0.949406\pi$
$384$	−968.370	+	1569.69i	−0.128690	+	0.208601i
$385$		0			0
$386$	−620.841			−0.0818652
$387$	−7830.66	+	11901.8i	−1.02857	+	1.56332i
$388$	−2651.72			−0.346960
$389$	−3861.72	+	6688.70i	−0.503334	+	0.871801i	0.496658	+	0.867946i	$0.334560\pi$
$389$	−3861.72	+	6688.70i	−0.503334	+	0.871801i	−0.999993	+	0.00385448i	$0.998773\pi$
$390$		0			0
$391$	4305.78	+	7457.83i	0.556912	+	0.964600i
$392$	−379.151	−	656.709i	−0.0488521	−	0.0846144i
$393$	5557.14	+	10308.3i	0.713284	+	1.32312i
$394$	−108.426	+	187.799i	−0.0138640	+	0.0240132i
$395$		0			0
$396$	6768.20	+	395.282i	0.858876	+	0.0501607i
$397$	−7125.03			−0.900744			−0.450372	−	0.892841i	$-0.648709\pi$
$397$	−7125.03			−0.900744			−0.450372	+	0.892841i	$0.648709\pi$
$398$	−45.2035	+	78.2948i	−0.00569308	+	0.00986071i
$399$	2082.98	−	3376.42i	0.261352	−	0.423640i
$400$		0			0
$401$	896.547	+	1552.86i	0.111649	+	0.193382i	0.916435	−	0.400183i	$-0.131053\pi$
$401$	896.547	+	1552.86i	0.111649	+	0.193382i	−0.804786	+	0.593565i	$0.797720\pi$
$402$	−494.047	−	14.4146i	−0.0612956	−	0.00178839i
$403$	−3381.05	+	5856.15i	−0.417921	+	0.723860i
$404$	3944.73			0.485786
$405$		0			0
$406$	−5.54451			−0.000677757
$407$	980.369	−	1698.05i	0.119398	−	0.206804i
$408$	643.412	+	18.7725i	0.0780727	+	0.00227789i
$409$	−1569.87	−	2719.09i	−0.189792	−	0.328729i	0.755389	−	0.655277i	$-0.227448\pi$
$409$	−1569.87	−	2719.09i	−0.189792	−	0.328729i	−0.945181	+	0.326548i	$0.894115\pi$
$410$		0			0
$411$	−1292.38	+	2094.90i	−0.155106	+	0.251420i
$412$	2510.48	−	4348.27i	0.300200	−	0.519961i
$413$	4179.77			0.497997
$414$	−916.224	−	53.5100i	−0.108768	−	0.00635235i
$415$		0			0
$416$	449.068	−	777.808i	0.0529263	−	0.0916711i
$417$	−337.900	−	626.795i	−0.0396812	−	0.0736074i
$418$	−248.680	−	430.726i	−0.0290989	−	0.0504007i
$419$	−1228.70	−	2128.17i	−0.143260	−	0.248133i	0.785463	−	0.618909i	$-0.212425\pi$
$419$	−1228.70	−	2128.17i	−0.143260	−	0.248133i	−0.928722	+	0.370776i	$0.879092\pi$
$420$		0			0
$421$	1339.33	−	2319.80i	0.155048	−	0.268551i	−0.778029	−	0.628229i	$-0.783780\pi$
$421$	1339.33	−	2319.80i	0.155048	−	0.268551i	0.933076	+	0.359678i	$0.117113\pi$
$422$	−3.12228			−0.000360167
$423$	2311.04	−	3512.56i	0.265643	−	0.403750i
$424$	−395.949			−0.0453514
$425$		0			0
$426$	−443.121	+	718.281i	−0.0503974	+	0.0816921i
$427$	−3214.03	−	5566.86i	−0.364257	−	0.630911i
$428$	6220.09	+	10773.5i	0.702476	+	1.21672i
$429$	−4397.26	−	128.297i	−0.494876	−	0.0144388i
$430$		0			0
$431$	−9472.42			−1.05863			−0.529316	−	0.848425i	$-0.677551\pi$
$431$	−9472.42			−1.05863			−0.529316	+	0.848425i	$0.677551\pi$
$432$	5092.79	−	7269.57i	0.567192	−	0.809623i
$433$	4238.21			0.470382			0.235191	−	0.971949i	$-0.424428\pi$
$433$	4238.21			0.470382			0.235191	+	0.971949i	$0.424428\pi$
$434$	−186.360	+	322.784i	−0.0206119	+	0.0357008i
$435$		0			0
$436$	−3730.23	−	6460.94i	−0.409737	−	0.709686i
$437$	−8761.80	−	15175.9i	−0.959116	−	1.66124i
$438$	−290.609	+	471.065i	−0.0317028	+	0.0513889i
$439$	−2429.47	+	4207.96i	−0.264128	+	0.457483i	−0.967335	−	0.253503i	$-0.918417\pi$
$439$	−2429.47	+	4207.96i	−0.264128	+	0.457483i	0.703207	+	0.710985i	$0.251751\pi$
$440$		0			0
$441$	3287.25	+	6548.05i	0.354957	+	0.707057i
$442$	−208.432			−0.0224301
$443$	1167.88	−	2022.82i	0.125254	−	0.216946i	−0.796578	−	0.604535i	$-0.793359\pi$
$443$	1167.88	−	2022.82i	0.125254	−	0.216946i	0.921832	+	0.387589i	$0.126692\pi$
$444$	−1222.83	−	2268.31i	−0.130705	−	0.242453i
$445$		0			0
$446$	86.5783	+	149.958i	0.00919193	+	0.0159209i
$447$	−352.873	−	654.568i	−0.0373385	−	0.0692617i
$448$	−2117.11	+	3666.94i	−0.223268	+	0.386712i
$449$	13290.5			1.39692			0.698460	−	0.715649i	$-0.253869\pi$
$449$	13290.5			1.39692			0.698460	+	0.715649i	$0.253869\pi$
$450$		0			0
$451$	6438.58			0.672241
$452$	−5399.17	+	9351.64i	−0.561849	+	0.973151i
$453$	591.588	−	958.941i	0.0613582	−	0.0994591i
$454$	−299.848	−	519.351i	−0.0309968	−	0.0536880i
$455$		0			0
$456$	−1309.28	−	38.2001i	−0.134457	−	0.00392299i
$457$	2587.31	−	4481.35i	0.264834	−	0.458706i	−0.702686	−	0.711500i	$-0.748016\pi$
$457$	2587.31	−	4481.35i	0.264834	−	0.458706i	0.967520	+	0.252794i	$0.0813495\pi$
$458$	192.415			0.0196309
$459$	−6195.63	−	543.534i	−0.630037	−	0.0552724i
$460$		0			0
$461$	−3170.44	+	5491.37i	−0.320309	+	0.554791i	−0.980552	−	0.196261i	$-0.937120\pi$
$461$	−3170.44	+	5491.37i	−0.320309	+	0.554791i	0.660243	+	0.751052i	$0.270453\pi$
$462$	−242.372	−	7.07157i	−0.0244073	−	0.000712119i
$463$	1591.40	+	2756.38i	0.159737	+	0.276673i	0.934774	−	0.355243i	$-0.115602\pi$
$463$	1591.40	+	2756.38i	0.159737	+	0.276673i	−0.775036	+	0.631916i	$0.782269\pi$
$464$	−118.425	−	205.118i	−0.0118486	−	0.0205223i
$465$		0			0
$466$	390.208	−	675.860i	0.0387898	−	0.0671859i
$467$	8576.23			0.849808			0.424904	−	0.905238i	$-0.360308\pi$
$467$	8576.23			0.849808			0.424904	+	0.905238i	$0.360308\pi$
$468$	−3177.82	+	4829.96i	−0.313877	+	0.477062i
$469$	−4600.79			−0.452974
$470$		0			0
$471$	−3324.87	−	6167.53i	−0.325269	−	0.603365i
$472$	−690.000	−	1195.11i	−0.0672877	−	0.116546i
$473$	8312.84	+	14398.3i	0.808086	+	1.39965i
$474$	265.282	+	492.090i	0.0257064	+	0.0476845i
$475$		0			0
$476$	2990.13			0.287925
$477$	3819.23	+	223.054i	0.366605	+	0.0214107i
$478$	1145.18			0.109580
$479$	−1458.82	+	2526.76i	−0.139155	+	0.241024i	−0.927177	−	0.374623i	$-0.877772\pi$
$479$	−1458.82	+	2526.76i	−0.139155	+	0.241024i	0.788022	+	0.615647i	$0.211105\pi$
$480$		0			0
$481$	836.037	+	1448.06i	0.0792516	+	0.137268i
$482$	18.4018	+	31.8729i	0.00173896	+	0.00301197i
$483$	−8539.56	−	249.155i	−0.804479	−	0.0234719i
$484$	−1347.74	+	2334.35i	−0.126572	+	0.219229i
$485$		0			0
$486$	411.324	−	519.779i	0.0383910	−	0.0485137i
$487$	14061.0			1.30834			0.654172	−	0.756346i	$-0.273017\pi$
$487$	14061.0			1.30834			0.654172	+	0.756346i	$0.273017\pi$
$488$	−1061.15	+	1837.96i	−0.0984343	+	0.170493i
$489$	5400.92	+	157.580i	0.499464	+	0.0145726i
$490$		0			0
$491$	466.331	+	807.709i	0.0428620	+	0.0742391i	0.886661	−	0.462421i	$-0.153019\pi$
$491$	466.331	+	807.709i	0.0428620	+	0.0742391i	−0.843799	+	0.536660i	$0.819686\pi$
$492$	4442.91	−	7201.78i	0.407118	−	0.659921i
$493$	−82.9806	+	143.727i	−0.00758065	+	0.0131301i
$494$	424.137			0.0386292
$495$		0			0
$496$	−15921.8			−1.44135
$497$	−3928.04	+	6803.57i	−0.354521	+	0.614048i
$498$	−463.959	−	860.629i	−0.0417480	−	0.0774412i
$499$	7215.39	+	12497.4i	0.647305	+	1.12117i	0.983764	+	0.179467i	$0.0574374\pi$
$499$	7215.39	+	12497.4i	0.647305	+	1.12117i	−0.336459	+	0.941698i	$0.609229\pi$
$500$		0			0
$501$	8203.60	+	15217.4i	0.731557	+	1.35701i
$502$	−71.4062	+	123.679i	−0.00634864	+	0.0109962i
$503$	3230.55			0.286368			0.143184	−	0.989696i	$-0.454266\pi$
$503$	3230.55			0.286368			0.143184	+	0.989696i	$0.454266\pi$
$504$	−350.988	+	533.467i	−0.0310203	+	0.0471478i
$505$		0			0
$506$	−535.515	+	927.539i	−0.0470485	+	0.0814904i
$507$	−4024.18	+	6523.03i	−0.352505	+	0.571397i
$508$	4711.36	+	8160.32i	0.411482	+	0.712708i
$509$	180.378	+	312.424i	0.0157075	+	0.0272062i	0.873772	−	0.486335i	$-0.161667\pi$
$509$	180.378	+	312.424i	0.0157075	+	0.0272062i	−0.858065	+	0.513541i	$0.828333\pi$
$510$		0			0
$511$	−2576.10	+	4461.93i	−0.223013	+	0.386270i
$512$	3529.04			0.304615
$513$	12607.4	+	1106.03i	1.08505	+	0.0951903i
$514$	730.096			0.0626521
$515$		0			0
$516$	21841.2	+	637.250i	1.86338	+	0.0543670i
$517$	−2453.35	−	4249.33i	−0.208701	−	0.361480i
$518$	46.0814	+	79.8154i	0.00390869	+	0.00677005i
$519$	3258.18	−	5281.37i	0.275565	−	0.446679i
$520$		0			0
$521$	−11698.8			−0.983747			−0.491873	−	0.870667i	$-0.663688\pi$
$521$	−11698.8			−0.983747			−0.491873	+	0.870667i	$0.663688\pi$
$522$	−7.93562	−	15.8074i	−0.000665388	−	0.00132542i
$523$	−18557.3			−1.55154			−0.775770	−	0.631015i	$-0.782638\pi$
$523$	−18557.3			−1.55154			−0.775770	+	0.631015i	$0.782638\pi$
$524$	8980.49	−	15554.7i	0.748692	−	1.29677i
$525$		0			0
$526$	−246.470	−	426.899i	−0.0204308	−	0.0353872i
$527$	5578.21	+	9661.75i	0.461083	+	0.798619i
$528$	−4915.20	−	9117.54i	−0.405126	−	0.751496i
$529$	−12784.5	+	22143.3i	−1.05075	+	1.81995i
$530$		0			0
$531$	5982.32	+	11916.5i	0.488909	+	0.973883i
$532$	−6084.59			−0.495866
$533$	−2745.34	+	4755.07i	−0.223103	+	0.386426i
$534$	718.551	−	1164.74i	0.0582298	−	0.0943882i
$535$		0			0
$536$	759.503	+	1315.50i	0.0612044	+	0.106009i
$537$	−12069.2	−	352.136i	−0.969875	−	0.0282976i
$538$	8.97756	−	15.5496i	0.000719424	−	0.00124608i
$539$	8550.26			0.683276
$540$		0			0
$541$	22755.3			1.80837			0.904185	−	0.427140i	$-0.140479\pi$
$541$	22755.3			1.80837			0.904185	+	0.427140i	$0.140479\pi$
$542$	291.985	−	505.733i	0.0231399	−	0.0400795i
$543$	−13125.7	−	382.962i	−1.03734	−	0.0302661i
$544$	−740.893	−	1283.26i	−0.0583925	−	0.101139i
$545$		0			0
$546$	108.567	−	175.983i	0.00850962	−	0.0137937i
$547$	2899.05	−	5021.30i	0.226608	−	0.392496i	−0.730193	−	0.683241i	$-0.760570\pi$
$547$	2899.05	−	5021.30i	0.226608	−	0.392496i	0.956801	+	0.290745i	$0.0939032\pi$
$548$	3775.18			0.294284
$549$	11271.0	−	17130.8i	0.876200	−	1.33174i
$550$		0			0
$551$	168.857	−	292.468i	0.0130554	−	0.0226127i
$552$	1338.48	+	2482.84i	0.103205	+	0.191443i
$553$	2601.92	+	4506.65i	0.200081	+	0.346550i
$554$	55.4599	+	96.0593i	0.00425318	+	0.00736673i
$555$		0			0
$556$	−546.056	+	945.797i	−0.0416510	+	0.0721416i
$557$	−15740.3			−1.19738			−0.598688	−	0.800982i	$-0.704311\pi$
$557$	−15740.3			−1.19738			−0.598688	+	0.800982i	$0.704311\pi$
$558$	−1186.98	−	69.3231i	−0.0900521	−	0.00525929i
$559$	−14178.0			−1.07275
$560$		0			0
$561$	−3810.72	+	6177.01i	−0.286789	+	0.464873i
$562$	542.662	+	939.919i	0.0407310	+	0.0705482i
$563$	1909.56	+	3307.45i	0.142946	+	0.247589i	0.928605	−	0.371071i	$-0.121009\pi$
$563$	1909.56	+	3307.45i	0.142946	+	0.247589i	−0.785659	+	0.618660i	$0.787676\pi$
$564$	−6445.94	−	188.070i	−0.481247	−	0.0140411i
$565$		0			0
$566$	1308.91			0.0972040
$567$	3686.07	−	4947.97i	0.273016	−	0.366482i
$568$	2593.78			0.191607
$569$	−4445.56	+	7699.93i	−0.327535	+	0.567308i	−0.982022	−	0.188766i	$-0.939551\pi$
$569$	−4445.56	+	7699.93i	−0.327535	+	0.567308i	0.654487	+	0.756073i	$0.272885\pi$
$570$		0			0
$571$	−4193.31	−	7263.03i	−0.307329	−	0.532309i	0.670448	−	0.741956i	$-0.266102\pi$
$571$	−4193.31	−	7263.03i	−0.307329	−	0.532309i	−0.977777	+	0.209647i	$0.932768\pi$
$572$	3373.49	+	5843.06i	0.246596	+	0.427116i
$573$	6517.33	−	10564.3i	0.475158	−	0.770211i
$574$	−151.320	+	262.094i	−0.0110034	+	0.0190585i
$575$		0			0
$576$	−13484.6	−	787.536i	−0.975446	−	0.0569687i
$577$	−16922.3			−1.22095			−0.610473	−	0.792037i	$-0.709021\pi$
$577$	−16922.3			−1.22095			−0.610473	+	0.792037i	$0.709021\pi$
$578$	257.909	−	446.711i	0.0185599	−	0.0321466i
$579$	−8748.35	−	16227.9i	−0.627926	−	1.16478i
$580$		0			0
$581$	−4550.56	−	7881.80i	−0.324938	−	0.562809i
$582$	143.565	+	266.309i	0.0102250	+	0.0189671i
$583$	2232.27	−	3866.40i	0.158578	−	0.274666i
$584$	1701.06			0.120531
$585$		0			0
$586$	846.315			0.0596603
$587$	7619.29	−	13197.0i	0.535744	−	0.927936i	−0.463383	−	0.886158i	$-0.653365\pi$
$587$	7619.29	−	13197.0i	0.535744	−	0.927936i	0.999127	−	0.0417777i	$-0.0133021\pi$
$588$	5900.07	−	9563.77i	0.413800	−	0.670754i
$589$	−11351.1	−	19660.6i	−0.794079	−	1.37539i
$590$		0			0
$591$	−6436.66	−	187.799i	−0.448002	−	0.0130711i
$592$	−1968.50	+	3409.55i	−0.136664	+	0.236709i
$593$	16960.2			1.17449			0.587245	−	0.809409i	$-0.300213\pi$
$593$	16960.2			1.17449			0.587245	+	0.809409i	$0.300213\pi$
$594$	−326.735	−	701.123i	−0.0225692	−	0.0484300i
$595$		0			0
$596$	−570.252	+	987.705i	−0.0391920	+	0.0678825i
$597$	−2683.49	−	78.2948i	−0.183966	−	0.00536749i
$598$	−456.676	−	790.986i	−0.0312289	−	0.0540900i
$599$	12456.1	+	21574.5i	0.849651	+	1.47164i	0.881520	+	0.472147i	$0.156521\pi$
$599$	12456.1	+	21574.5i	0.849651	+	1.47164i	−0.0318690	+	0.999492i	$0.510146\pi$
$600$		0			0
$601$	2175.63	−	3768.31i	0.147664	−	0.255761i	−0.782700	−	0.622399i	$-0.786158\pi$
$601$	2175.63	−	3768.31i	0.147664	−	0.255761i	0.930364	+	0.366638i	$0.119491\pi$
$602$	−781.476			−0.0529080
$603$	−6584.91	−	13116.8i	−0.444707	−	0.885835i
$604$	−1728.09			−0.116416
$605$		0			0
$606$	−213.569	−	396.164i	−0.0143163	−	0.0265562i
$607$	13911.8	+	24096.0i	0.930254	+	1.61125i	0.782885	+	0.622166i	$0.213747\pi$
$607$	13911.8	+	24096.0i	0.930254	+	1.61125i	0.147369	+	0.989082i	$0.452919\pi$
$608$	1507.64	+	2611.31i	0.100564	+	0.174182i
$609$	−78.1285	−	144.926i	−0.00519856	−	0.00964317i
$610$		0			0
$611$	4184.33			0.277054
$612$	4279.64	+	8524.84i	0.282670	+	0.563066i
$613$	−20034.6			−1.32005			−0.660024	−	0.751244i	$-0.729454\pi$
$613$	−20034.6			−1.32005			−0.660024	+	0.751244i	$0.729454\pi$
$614$	−490.994	+	850.427i	−0.0322719	+	0.0558965i
$615$		0			0
$616$	372.600	+	645.363i	0.0243709	+	0.0422117i
$617$	3776.95	+	6541.86i	0.246441	+	0.426848i	0.962536	−	0.271155i	$-0.0874055\pi$
$617$	3776.95	+	6541.86i	0.246441	+	0.426848i	−0.716095	+	0.698003i	$0.754072\pi$
$618$	−572.609	−	16.7067i	−0.0372714	−	0.00108745i
$619$	−6192.54	+	10725.8i	−0.402099	+	0.696456i	−0.993979	−	0.109570i	$-0.965053\pi$
$619$	−6192.54	+	10725.8i	−0.402099	+	0.696456i	0.591880	+	0.806026i	$0.298386\pi$
$620$		0			0
$621$	−11512.0	−	24702.8i	−0.743896	−	1.59628i
$622$	1911.08			0.123195
$623$	6369.58	−	11032.4i	0.409618	−	0.709479i
$624$	8829.35	+	257.610i	0.566437	+	0.0165267i
$625$		0			0
$626$	435.775	+	754.785i	0.0278228	+	0.0481906i
$627$	7754.40	−	12569.6i	0.493909	−	0.800606i
$628$	−5373.08	+	9306.45i	−0.341416	+	0.591350i
$629$	2758.67			0.174873
$630$		0			0
$631$	−1325.17			−0.0836043			−0.0418022	−	0.999126i	$-0.513310\pi$
$631$	−1325.17			−0.0836043			−0.0418022	+	0.999126i	$0.513310\pi$
$632$	859.053	−	1487.92i	0.0540685	−	0.0936494i
$633$	−43.9965	−	81.6122i	−0.00276257	−	0.00512447i
$634$	−328.632	−	569.207i	−0.0205862	−	0.0356563i
$635$		0			0
$636$	−2784.34	−	5164.86i	−0.173595	−	0.322013i
$637$	−3645.74	+	6314.60i	−0.226765	+	0.392769i
$638$	−20.6408			−0.00128084
$639$	−25019.0	−	1461.18i	−1.54888	−	0.0904589i
$640$		0			0
$641$	11255.8	−	19495.6i	0.693568	−	1.20129i	−0.277094	−	0.960843i	$-0.589371\pi$
$641$	11255.8	−	19495.6i	0.693568	−	1.20129i	0.970661	−	0.240451i	$-0.0772955\pi$
$642$	745.212	−	1207.96i	0.0458118	−	0.0742590i
$643$	2807.31	+	4862.40i	0.172176	+	0.298218i	0.939180	−	0.343424i	$-0.111587\pi$
$643$	2807.31	+	4862.40i	0.172176	+	0.298218i	−0.767004	+	0.641642i	$0.778253\pi$
$644$	6551.38	+	11347.3i	0.400871	+	0.694328i
$645$		0			0
$646$	349.881	−	606.012i	0.0213094	−	0.0369090i
$647$	11753.6			0.714188			0.357094	−	0.934068i	$-0.383768\pi$
$647$	11753.6			0.714188			0.357094	+	0.934068i	$0.383768\pi$
$648$	−2023.27	−	237.137i	−0.122656	−	0.0143760i
$649$	15560.2			0.941127
$650$		0			0
$651$	−11063.2	−	322.784i	−0.666051	−	0.0194330i
$652$	−4143.48	−	7176.71i	−0.248882	−	0.431076i
$653$	−12929.1	−	22393.9i	−0.774816	−	1.34202i	−0.934898	−	0.354916i	$-0.884509\pi$
$653$	−12929.1	−	22393.9i	−0.774816	−	1.34202i	0.160082	−	0.987104i	$-0.448824\pi$
$654$	−446.908	+	724.420i	−0.0267209	+	0.0433135i
$655$		0			0
$656$	−12928.1			−0.769450
$657$	−16408.0	−	958.272i	−0.974333	−	0.0569037i
$658$	230.635			0.0136643
$659$	8847.75	−	15324.8i	0.523004	−	0.905869i	−0.476638	−	0.879100i	$-0.658145\pi$
$659$	8847.75	−	15324.8i	0.523004	−	0.905869i	0.999642	−	0.0267695i	$-0.00852201\pi$
$660$		0			0
$661$	−3115.05	−	5395.42i	−0.183300	−	0.317485i	0.759702	−	0.650271i	$-0.225345\pi$
$661$	−3115.05	−	5395.42i	−0.183300	−	0.317485i	−0.943002	+	0.332786i	$0.892011\pi$
$662$	79.3515	+	137.441i	0.00465873	+	0.00806916i
$663$	−2937.05	−	5448.13i	−0.172044	−	0.319137i
$664$	−1502.42	+	2602.27i	−0.0878091	+	0.152090i
$665$		0			0
$666$	−161.599	+	245.614i	−0.00940214	+	0.0142903i
$667$	−727.243			−0.0422174
$668$	13257.2	−	22962.2i	0.767872	−	1.32999i
$669$	−2699.71	+	4376.12i	−0.156019	+	0.252901i
$670$		0			0
$671$	−11965.0	−	20724.0i	−0.688381	−	1.19231i
$672$	1469.40	+	42.8719i	0.0843501	+	0.00246104i
$673$	−3025.84	+	5240.91i	−0.173310	+	0.300182i	−0.939575	−	0.342343i	$-0.888780\pi$
$673$	−3025.84	+	5240.91i	−0.173310	+	0.300182i	0.766265	+	0.642524i	$0.222113\pi$
$674$	−1728.62			−0.0987892
$675$		0			0
$676$	11755.0			0.668812
$677$	14049.3	−	24334.1i	0.797576	−	1.38144i	−0.123614	−	0.992330i	$-0.539449\pi$
$677$	14049.3	−	24334.1i	0.797576	−	1.38144i	0.921190	−	0.389112i	$-0.127218\pi$
$678$	1231.49	+	35.9305i	0.0697566	+	0.00203525i
$679$	1408.10	+	2438.90i	0.0795846	+	0.137845i
$680$		0			0
$681$	9349.93	−	15155.9i	0.526124	−	0.852825i
$682$	−693.769	+	1201.64i	−0.0389528	+	0.0674682i
$683$	8335.71			0.466994			0.233497	−	0.972358i	$-0.424983\pi$
$683$	8335.71			0.466994			0.233497	+	0.972358i	$0.424983\pi$
$684$	−8708.61	−	17347.1i	−0.486816	−	0.969714i
$685$		0			0
$686$	−454.944	+	787.986i	−0.0253205	+	0.0438563i
$687$	2711.34	+	5029.46i	0.150574	+	0.279310i
$688$	−16691.5	−	28910.6i	−0.924939	−	1.60204i
$689$	1903.63	+	3297.18i	0.105258	+	0.182312i
$690$		0			0
$691$	8442.55	−	14622.9i	0.464790	−	0.805039i	−0.534402	−	0.845230i	$-0.679463\pi$
$691$	8442.55	−	14622.9i	0.464790	−	0.805039i	0.999192	+	0.0401909i	$0.0127966\pi$
$692$	−9517.46			−0.522832
$693$	−3230.46	−	6434.92i	−0.177078	−	0.352731i
$694$	614.146			0.0335917
$695$		0			0
$696$	−28.5409	+	46.2637i	−0.00155437	+	0.00251957i
$697$	4529.39	+	7845.14i	0.246145	+	0.426335i
$698$	909.305	+	1574.96i	0.0493090	+	0.0854057i
$699$	23164.5	+	675.860i	1.25345	+	0.0365714i
$700$		0			0
$701$	16875.2			0.909226			0.454613	−	0.890689i	$-0.349778\pi$
$701$	16875.2			0.909226			0.454613	+	0.890689i	$0.349778\pi$
$702$	657.115	+	57.6479i	0.0353293	+	0.00309940i
$703$	−5613.59			−0.301167
$704$	−7881.47	+	13651.1i	−0.421938	+	0.730817i
$705$		0			0
$706$	707.410	+	1225.27i	0.0377106	+	0.0653168i
$707$	−2094.71	−	3628.14i	−0.111428	−	0.192999i
$708$	10737.3	−	17404.6i	0.569959	−	0.923879i
$709$	9503.71	−	16460.9i	0.503412	−	0.871936i	−0.496580	−	0.867991i	$-0.665411\pi$
$709$	9503.71	−	16460.9i	0.503412	−	0.871936i	0.999992	−	0.00394482i	$-0.00125568\pi$
$710$		0			0
$711$	−9124.43	+	13868.2i	−0.481284	+	0.731503i
$712$	−4205.99			−0.221385
$713$	−24443.8	+	42337.9i	−1.28391	+	2.22379i
$714$	−161.887	−	300.295i	−0.00848524	−	0.0157398i
$715$		0			0
$716$	9259.23	+	16037.4i	0.483287	+	0.837078i
$717$	16136.9	+	29933.4i	0.840506	+	1.55911i
$718$	716.517	−	1241.04i	0.0372426	−	0.0645061i
$719$	17588.1			0.912275			0.456138	−	0.889909i	$-0.349233\pi$
$719$	17588.1			0.912275			0.456138	+	0.889909i	$0.349233\pi$
$720$		0			0
$721$	−5332.40			−0.275435
$722$	−111.861	+	193.748i	−0.00576596	+	0.00998693i
$723$	−573.810	+	930.123i	−0.0295162	+	0.0478446i
$724$	10069.8	+	17441.4i	0.516907	+	0.895309i
$725$		0			0
$726$	307.403	+	8.96895i	0.0157146	+	0.000458497i
$727$	2802.69	−	4854.40i	0.142979	−	0.247648i	−0.785638	−	0.618687i	$-0.787665\pi$
$727$	2802.69	−	4854.40i	0.142979	−	0.247648i	0.928617	+	0.371039i	$0.120998\pi$
$728$	−635.491			−0.0323528
$729$	19382.3	+	3427.15i	0.984725	+	0.174117i
$730$		0			0
$731$	−11695.8	+	20257.7i	−0.591771	+	1.02498i
$732$	−31436.9	−	917.220i	−1.58735	−	0.0463134i
$733$	7460.04	+	12921.2i	0.375911	+	0.651097i	0.990463	−	0.137779i	$-0.0439964\pi$
$733$	7460.04	+	12921.2i	0.375911	+	0.651097i	−0.614552	+	0.788877i	$0.710663\pi$
$734$	−786.963	−	1363.06i	−0.0395740	−	0.0685443i
$735$		0			0
$736$	3246.60	−	5623.27i	0.162597	−	0.281626i
$737$	−17127.6			−0.856042
$738$	−963.806	−	56.2889i	−0.0480734	−	0.00280762i
$739$	−27418.8			−1.36484			−0.682421	−	0.730959i	$-0.739073\pi$
$739$	−27418.8			−1.36484			−0.682421	+	0.730959i	$0.739073\pi$
$740$		0			0
$741$	5976.58	+	11086.4i	0.296296	+	0.549619i
$742$	104.926	+	181.737i	0.00519131	+	0.00899161i
$743$	−12272.1	−	21255.9i	−0.605948	−	1.04953i	−0.991901	−	0.127014i	$-0.959461\pi$
$743$	−12272.1	−	21255.9i	−0.605948	−	1.04953i	0.385953	−	0.922518i	$-0.373873\pi$
$744$	1734.02	+	3216.56i	0.0854467	+	0.158501i
$745$		0			0
$746$	162.712			0.00798569
$747$	15957.9	−	24254.5i	0.781621	−	1.18799i
$748$	11131.5			0.544128
$749$	6605.92	−	11441.8i	0.322263	−	0.558176i
$750$		0			0
$751$	−767.283	−	1328.97i	−0.0372817	−	0.0645738i	0.846782	−	0.531939i	$-0.178537\pi$
$751$	−767.283	−	1328.97i	−0.0372817	−	0.0645738i	−0.884064	+	0.467365i	$0.845203\pi$
$752$	4926.13	+	8532.30i	0.238880	+	0.413752i
$753$	−4239.00	−	123.679i	−0.205150	−	0.00598555i
$754$	8.80102	−	15.2438i	0.000425085	−	0.000736269i
$755$		0			0
$756$	−9426.85	−	827.005i	−0.453507	−	0.0397856i
$757$	18051.1			0.866681			0.433341	−	0.901230i	$-0.357335\pi$
$757$	18051.1			0.866681			0.433341	+	0.901230i	$0.357335\pi$
$758$	−301.823	+	522.773i	−0.0144627	+	0.0250501i
$759$	−31790.6	−	927.539i	−1.52032	−	0.0443578i
$760$		0			0
$761$	−6462.29	−	11193.0i	−0.307829	−	0.533176i	0.670058	−	0.742309i	$-0.266269\pi$
$761$	−6462.29	−	11193.0i	−0.307829	−	0.533176i	−0.977887	+	0.209133i	$0.932936\pi$
$762$	564.455	−	914.958i	0.0268347	−	0.0434980i
$763$	−3961.61	+	6861.71i	−0.187968	+	0.325571i
$764$	−19037.8			−0.901522
$765$		0			0
$766$	935.491			0.0441262
$767$	−6634.70	+	11491.6i	−0.312341	+	0.540990i
$768$	9715.30	+	18021.6i	0.456472	+	0.846741i
$769$	1686.16	+	2920.51i	0.0790695	+	0.136952i	0.902849	−	0.429958i	$-0.141472\pi$
$769$	1686.16	+	2920.51i	0.0790695	+	0.136952i	−0.823779	+	0.566911i	$0.808138\pi$
$770$		0			0
$771$	10287.9	+	19083.7i	0.480557	+	0.891418i
$772$	−14137.6	+	24487.0i	−0.659097	+	1.14159i
$773$	27152.6			1.26341			0.631703	−	0.775211i	$-0.282356\pi$
$773$	27152.6			1.26341			0.631703	+	0.775211i	$0.282356\pi$
$774$	−1118.49	−	2227.99i	−0.0519424	−	0.103467i
$775$		0			0
$776$	464.901	−	805.232i	0.0215064	−	0.0372502i
$777$	−1436.92	+	2329.19i	−0.0663441	+	0.107541i
$778$	−675.742	−	1170.42i	−0.0311395	−	0.0539352i
$779$	−9216.83	−	15964.0i	−0.423912	−	0.734236i
$780$		0			0
$781$	−14623.1	+	25327.9i	−0.669982	+	1.16044i
$782$	−1506.89			−0.0689083
$783$	301.361	−	430.170i	0.0137545	−	0.0196335i
$784$	−17168.2			−0.782080
$785$		0			0
$786$	−2048.34	−	59.7635i	−0.0929541	−	0.00271208i
$787$	−12606.0	−	21834.3i	−0.570974	−	0.988957i	−0.996466	−	0.0839943i	$-0.973232\pi$
$787$	−12606.0	−	21834.3i	−0.570974	−	0.988957i	0.425492	−	0.904962i	$-0.360101\pi$
$788$	4938.08	+	8553.01i	0.223238	+	0.386660i
$789$	7685.50	−	12457.9i	0.346782	−	0.562120i
$790$		0			0
$791$	11468.2			0.515500
$792$	−1306.64	+	1985.96i	−0.0586230	+	0.0891011i
$793$	20407.0			0.913838
$794$	623.386	−	1079.74i	0.0278629	−	0.0482599i
$795$		0			0
$796$	2058.72	+	3565.80i	0.0916700	+	0.158777i
$797$	19588.5	+	33928.2i	0.870588	+	1.50790i	0.861390	+	0.507945i	$0.169595\pi$
$797$	19588.5	+	33928.2i	0.870588	+	1.50790i	0.00919851	+	0.999958i	$0.497072\pi$
$798$	329.422	+	611.068i	0.0146133	+	0.0271072i
$799$	3451.75	−	5978.61i	0.152834	−	0.264716i
$800$		0			0
$801$	40569.9	+	2369.40i	1.78960	+	0.104517i
$802$	−313.764			−0.0138147
$803$	−9590.16	+	16610.6i	−0.421456	+	0.729983i
$804$	−11818.8	+	19157.8i	−0.518430	+	0.840353i
$805$		0			0
$806$	−591.631	−	1024.74i	−0.0258552	−	0.0447826i
$807$	532.949	+	15.5496i	0.0232474	+	0.000678279i
$808$	−691.593	+	1197.87i	−0.0301116	+	0.0521548i
$809$	−36739.0			−1.59663			−0.798316	−	0.602239i	$-0.794275\pi$
$809$	−36739.0			−1.59663			−0.798316	+	0.602239i	$0.794275\pi$
$810$		0			0
$811$	−29660.0			−1.28422			−0.642111	−	0.766611i	$-0.721941\pi$
$811$	−29660.0			−1.28422			−0.642111	+	0.766611i	$0.721941\pi$
$812$	−126.258	+	218.685i	−0.00545662	+	0.00945115i
$813$	17333.6	+	505.733i	0.747743	+	0.0218165i
$814$	171.549	+	297.132i	0.00738674	+	0.0127942i
$815$		0			0
$816$	7651.61	−	12402.9i	0.328260	−	0.532096i
$817$	23799.7	−	41222.2i	1.01915	−	1.76522i
$818$	549.405			0.0234835
$819$	6129.80	+	357.997i	0.261529	+	0.0152740i
$820$		0			0
$821$	−10056.6	+	17418.6i	−0.427501	+	0.740453i	−0.996650	−	0.0817808i	$-0.973939\pi$
$821$	−10056.6	+	17418.6i	−0.427501	+	0.740453i	0.569149	+	0.822234i	$0.307273\pi$
$822$	−204.390	−	379.137i	−0.00867265	−	0.0160875i
$823$	2687.02	+	4654.06i	0.113808	+	0.197121i	0.917303	−	0.398191i	$-0.130362\pi$
$823$	2687.02	+	4654.06i	0.113808	+	0.197121i	−0.803495	+	0.595312i	$0.797029\pi$
$824$	880.277	+	1524.68i	0.0372159	+	0.0644598i
$825$		0			0
$826$	−365.697	+	633.406i	−0.0154046	+	0.0266816i
$827$	−27865.2			−1.17167			−0.585833	−	0.810432i	$-0.699233\pi$
$827$	−27865.2			−1.17167			−0.585833	+	0.810432i	$0.699233\pi$
$828$	−22974.5	+	34918.9i	−0.964273	+	1.46560i
$829$	24363.1			1.02070			0.510352	−	0.859965i	$-0.329515\pi$
$829$	24363.1			1.02070			0.510352	+	0.859965i	$0.329515\pi$
$830$		0			0
$831$	−1729.36	+	2803.23i	−0.0721913	+	0.117019i
$832$	−6721.15	−	11641.4i	−0.280065	−	0.485086i
$833$	6014.91	+	10418.1i	0.250185	+	0.433333i
$834$	124.549	+	3.63390i	0.00517119	+	0.000150877i
$835$		0			0
$836$	−22651.4			−0.937099
$837$	−14914.0	−	32003.0i	−0.615892	−	1.32161i
$838$	430.007			0.0177259
$839$	17765.3	−	30770.4i	0.731020	−	1.26616i	−0.225428	−	0.974260i	$-0.572378\pi$
$839$	17765.3	−	30770.4i	0.731020	−	1.26616i	0.956448	−	0.291903i	$-0.0942886\pi$
$840$		0			0
$841$	12187.5	+	21109.4i	0.499713	+	0.865528i
$842$	234.363	+	405.928i	0.00959226	+	0.0166143i
$843$	−16921.4	+	27429.0i	−0.691347	+	1.12065i
$844$	−71.0996	+	123.148i	−0.00289970	+	0.00502243i
$845$		0			0
$846$	330.098	+	657.540i	0.0134149	+	0.0267219i
$847$	2862.68			0.116131
$848$	−4482.22	+	7763.42i	−0.181509	+	0.314383i
$849$	18444.0	+	34213.0i	0.745578	+	1.38302i
$850$		0			0
$851$	6044.25	+	10468.9i	0.243471	+	0.421705i
$852$	18239.6	+	33833.9i	0.733426	+	1.36048i
$853$	17223.8	−	29832.4i	0.691360	−	1.19747i	−0.280032	−	0.959991i	$-0.590345\pi$
$853$	17223.8	−	29832.4i	0.691360	−	1.19747i	0.971392	−	0.237480i	$-0.0763214\pi$
$854$	1124.81			0.0450705
$855$		0			0
$856$	−4362.05			−0.174173
$857$	10003.4	−	17326.4i	0.398729	−	0.690618i	−0.594841	−	0.803844i	$-0.702785\pi$
$857$	10003.4	−	17326.4i	0.398729	−	0.690618i	0.993569	+	0.113225i	$0.0361182\pi$
$858$	404.169	−	655.141i	0.0160817	−	0.0260678i
$859$	−893.190	−	1547.05i	−0.0354776	−	0.0614490i	0.847741	−	0.530410i	$-0.177962\pi$
$859$	−893.190	−	1547.05i	−0.0354776	−	0.0614490i	−0.883219	+	0.468961i	$0.844629\pi$
$860$		0			0
$861$	−8983.04	−	262.094i	−0.355565	−	0.0103741i
$862$	828.764	−	1435.46i	0.0327469	−	0.0567192i
$863$	−12151.9			−0.479322			−0.239661	−	0.970857i	$-0.577036\pi$
$863$	−12151.9			−0.479322			−0.239661	+	0.970857i	$0.577036\pi$
$864$	1980.86	+	4250.61i	0.0779978	+	0.167371i
$865$		0			0
$866$	−370.811	+	642.263i	−0.0145504	+	0.0252021i
$867$	15310.7	+	446.711i	0.599743	+	0.0174984i
$868$	8487.43	+	14700.7i	0.331892	+	0.574854i
$869$	9686.27	+	16777.1i	0.378118	+	0.654919i
$870$		0			0
$871$	7303.02	−	12649.2i	0.284102	−	0.492080i
$872$	2615.94			0.101591
$873$	−4937.94	+	7505.18i	−0.191436	+	0.290964i
$874$	3066.36			0.118674
$875$		0			0
$876$	11961.9	+	22189.0i	0.461366	+	0.855819i
$877$	−9436.64	−	16344.7i	−0.363344	−	0.629330i	0.625165	−	0.780493i	$-0.285032\pi$
$877$	−9436.64	−	16344.7i	−0.363344	−	0.629330i	−0.988509	+	0.151163i	$0.951698\pi$
$878$	−425.119	−	736.328i	−0.0163406	−	0.0283028i
$879$	11925.5	+	22121.5i	0.457609	+	0.848851i
$880$		0			0
$881$	23587.2			0.902014			0.451007	−	0.892520i	$-0.351065\pi$
$881$	23587.2			0.902014			0.451007	+	0.892520i	$0.351065\pi$
$882$	−1279.91	−	74.7502i	−0.0488625	−	0.00285371i
$883$	29504.5			1.12447			0.562234	−	0.826978i	$-0.309942\pi$
$883$	29504.5			1.12447			0.562234	+	0.826978i	$0.309942\pi$
$884$	−4746.35	+	8220.92i	−0.180585	+	0.312782i
$885$		0			0
$886$	204.360	+	353.963i	0.00774901	+	0.0134217i
$887$	1238.02	+	2144.31i	0.0468643	+	0.0811714i	0.888506	−	0.458865i	$-0.151744\pi$
$887$	1238.02	+	2144.31i	0.0468643	+	0.0811714i	−0.841642	+	0.540036i	$0.818410\pi$
$888$	903.192	+	26.3520i	0.0341319	+	0.000995850i
$889$	5003.60	−	8666.49i	0.188769	−	0.326957i
$890$		0			0
$891$	13722.3	−	18420.0i	0.515953	−	0.692586i
$892$	7886.13			0.296017
$893$	−7023.94	+	12165.8i	−0.263211	+	0.455894i
$894$	130.068	+	3.79492i	0.00486589	+	0.000141970i
$895$		0			0
$896$	−1502.09	−	2601.69i	−0.0560058	−	0.0970048i
$897$	14240.2	−	23082.8i	0.530063	−	0.859210i
$898$	−1162.82	+	2014.06i	−0.0432112	+	0.0748440i
$899$	−942.157			−0.0349529
$900$		0			0
$901$	6281.40			0.232257
$902$	−563.326	+	975.709i	−0.0207946	+	0.0360173i
$903$	−11011.9	−	20426.7i	−0.405817	−	0.752778i
$904$	−1893.17	−	3279.07i	−0.0696527	−	0.120642i
$905$		0			0
$906$	93.5595	+	173.550i	0.00343080	+	0.00636403i
$907$	−13375.5	+	23167.1i	−0.489666	+	0.848126i	−0.999929	−	0.0118922i	$-0.996215\pi$
$907$	−13375.5	+	23167.1i	−0.489666	+	0.848126i	0.510264	+	0.860018i	$0.329548\pi$
$908$	−27312.1			−0.998221
$909$	7345.75	−	11164.8i	0.268034	−	0.407385i
$910$		0			0
$911$	−6334.11	+	10971.0i	−0.230360	+	0.398996i	−0.957914	−	0.287055i	$-0.907324\pi$
$911$	−6334.11	+	10971.0i	−0.230360	+	0.398996i	0.727554	+	0.686051i	$0.240657\pi$
$912$	−15570.2	+	25238.7i	−0.565330	+	0.916377i
$913$	−16940.6	−	29341.9i	−0.614076	−	1.06361i
$914$	452.739	+	784.167i	0.0163843	+	0.0283785i
$915$		0			0
$916$	4381.61	−	7589.16i	0.158048	−	0.273748i
$917$	−19075.1			−0.686930
$918$	624.437	−	891.337i	0.0224504	−	0.0320463i
$919$	46565.5			1.67144			0.835721	−	0.549155i	$-0.185050\pi$
$919$	46565.5			1.67144			0.835721	+	0.549155i	$0.185050\pi$
$920$		0			0
$921$	−29147.7	−	850.427i	−1.04283	−	0.0304262i
$922$	−554.779	−	960.905i	−0.0198163	−	0.0343229i
$923$	−12470.3	−	21599.1i	−0.444706	−	0.770253i
$924$	−5798.13	+	9398.53i	−0.206433	+	0.334620i
$925$		0			0
$926$	−556.940			−0.0197648
$927$	−7632.03	−	15202.6i	−0.270408	−	0.538641i
$928$	125.136			0.00442651
$929$	−2305.46	+	3993.17i	−0.0814205	+	0.141024i	−0.903860	−	0.427828i	$-0.859279\pi$
$929$	−2305.46	+	3993.17i	−0.0814205	+	0.141024i	0.822440	+	0.568852i	$0.192612\pi$
$930$		0			0
$931$	−12239.7	−	21199.8i	−0.430870	−	0.746289i
$932$	−17771.4	−	30780.9i	−0.624593	−	1.08183i
$933$	26929.3	+	49952.9i	0.944935	+	1.75283i
$934$	−750.354	+	1299.65i	−0.0262873	+	0.0455309i
$935$		0			0
$936$	−909.551	−	1811.78i	−0.0317624	−	0.0632692i
$937$	6625.43			0.230996			0.115498	−	0.993308i	$-0.463154\pi$
$937$	6625.43			0.230996			0.115498	+	0.993308i	$0.463154\pi$
$938$	402.534	−	697.209i	0.0140119	−	0.0242694i
$939$	−13588.5	+	22026.4i	−0.472250	+	0.765498i
$940$		0			0
$941$	21721.3	+	37622.4i	0.752491	+	1.30335i	0.946612	+	0.322375i	$0.104481\pi$
$941$	21721.3	+	37622.4i	0.752491	+	1.30335i	−0.194121	+	0.980978i	$0.562185\pi$
$942$	1225.53	+	35.7568i	0.0423886	+	0.00123675i
$943$	−19847.8	+	34377.4i	−0.685402	+	1.18715i
$944$	−31243.7			−1.07722
$945$		0			0
$946$	−2909.24			−0.0999868
$947$	16461.2	−	28511.7i	0.564855	−	0.978357i	−0.432208	−	0.901774i	$-0.642265\pi$
$947$	16461.2	−	28511.7i	0.564855	−	0.978357i	0.997063	−	0.0765835i	$-0.0244012\pi$
$948$	25449.8	+	742.536i	0.871909	+	0.0254393i
$949$	−8178.28	−	14165.2i	−0.279745	−	0.484533i
$950$		0			0
$951$	10247.5	−	16610.8i	0.349419	−	0.566394i
$952$	−524.232	+	907.996i	−0.0178471	+	0.0309121i
$953$	−20253.5			−0.688430			−0.344215	−	0.938891i	$-0.611855\pi$
$953$	−20253.5			−0.688430			−0.344215	+	0.938891i	$0.611855\pi$
$954$	−367.955	+	559.255i	−0.0124874	+	0.0189796i
$955$		0			0
$956$	26077.6	−	45167.8i	0.882229	−	1.52806i
$957$	−290.853	−	539.522i	−0.00982437	−	0.0182239i
$958$	−255.272	−	442.144i	−0.00860904	−	0.0149113i
$959$	−2004.68	−	3472.20i	−0.0675020	−	0.116917i
$960$		0			0
$961$	−16771.8	+	29049.7i	−0.562983	+	0.975116i
$962$	−292.587			−0.00980602
$963$	42075.3	+	2457.31i	1.40795	+	0.0822282i
$964$	1676.16			0.0560015
$965$		0			0
$966$	784.903	−	1272.30i	0.0261427	−	0.0423762i
$967$	1618.56	+	2803.43i	0.0538257	+	0.0932289i	0.891683	−	0.452661i	$-0.149525\pi$
$967$	1618.56	+	2803.43i	0.0538257	+	0.0932289i	−0.837857	+	0.545890i	$0.816192\pi$
$968$	−472.573	−	818.521i	−0.0156912	−	0.0271780i
$969$	20770.5	+	606.012i	0.688592	+	0.0200907i
$970$		0			0
$971$	−1731.06			−0.0572114			−0.0286057	−	0.999591i	$-0.509107\pi$
$971$	−1731.06			−0.0572114			−0.0286057	+	0.999591i	$0.509107\pi$
$972$	−11134.4	−	28059.5i	−0.367425	−	0.925936i
$973$	1159.86			0.0382151
$974$	−1230.23	+	2130.81i	−0.0404712	+	0.0700982i
$975$		0			0
$976$	24024.8	+	41612.1i	0.787924	+	1.36472i
$977$	17273.4	+	29918.5i	0.565636	+	0.979710i	0.996990	+	0.0775275i	$0.0247026\pi$
$977$	17273.4	+	29918.5i	0.565636	+	0.979710i	−0.431354	+	0.902183i	$0.641964\pi$
$978$	−496.418	+	804.674i	−0.0162308	+	0.0263094i
$979$	23712.3	−	41071.0i	0.774106	−	1.34079i
$980$		0			0
$981$	−25232.8	−	1473.66i	−0.821224	−	0.0479617i
$982$	−163.201			−0.00530343
$983$	10226.6	−	17713.0i	0.331818	−	0.574726i	−0.651050	−	0.759035i	$-0.725671\pi$
$983$	10226.6	−	17713.0i	0.331818	−	0.574726i	0.982868	+	0.184309i	$0.0590046\pi$
$984$	1407.99	+	2611.78i	0.0456149	+	0.0846142i
$985$		0			0
$986$	−14.5203	−	25.1500i	−0.000468987	−	0.000812310i
$987$	3249.91	+	6028.49i	0.104808	+	0.194416i
$988$	9658.31	−	16728.7i	0.311004	−	0.538675i
$989$	−102502.			−3.29563
$990$		0			0
$991$	−5387.77			−0.172703			−0.0863513	−	0.996265i	$-0.527521\pi$
$991$	−5387.77			−0.172703			−0.0863513	+	0.996265i	$0.527521\pi$
$992$	4206.03	−	7285.05i	0.134618	−	0.233166i
$993$	−2474.36	+	4010.84i	−0.0790750	+	0.128177i
$994$	−687.347	−	1190.52i	−0.0219329	−	0.0379889i
$995$		0			0
$996$	−44509.8	−	1298.64i	−1.41601	−	0.0413142i
$997$	−10922.4	+	18918.2i	−0.346958	+	0.600949i	−0.985707	−	0.168466i	$-0.946119\pi$
$997$	−10922.4	+	18918.2i	−0.346958	+	0.600949i	0.638750	+	0.769415i	$0.279452\pi$
$998$	−2525.16			−0.0800929
$999$	−8697.13	−	762.988i	−0.275440	−	0.0241640i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.4.e.c.151.2		6
5.2	odd	4		225.4.k.c.124.3		12
5.3	odd	4		225.4.k.c.124.4		12
5.4	even	2		45.4.e.b.16.2	✓	6
9.2	odd	6		2025.4.a.q.1.2		3
9.4	even	3	inner	225.4.e.c.76.2		6
9.7	even	3		2025.4.a.s.1.2		3
15.14	odd	2		135.4.e.b.46.2		6
45.4	even	6		45.4.e.b.31.2	yes	6
45.13	odd	12		225.4.k.c.49.3		12
45.14	odd	6		135.4.e.b.91.2		6
45.22	odd	12		225.4.k.c.49.4		12
45.29	odd	6		405.4.a.j.1.2		3
45.34	even	6		405.4.a.h.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.4.e.b.16.2	✓	6	5.4	even	2
45.4.e.b.31.2	yes	6	45.4	even	6
135.4.e.b.46.2		6	15.14	odd	2
135.4.e.b.91.2		6	45.14	odd	6
225.4.e.c.76.2		6	9.4	even	3	inner
225.4.e.c.151.2		6	1.1	even	1	trivial
225.4.k.c.49.3		12	45.13	odd	12
225.4.k.c.49.4		12	45.22	odd	12
225.4.k.c.124.3		12	5.2	odd	4
225.4.k.c.124.4		12	5.3	odd	4
405.4.a.h.1.2		3	45.34	even	6
405.4.a.j.1.2		3	45.29	odd	6
2025.4.a.q.1.2		3	9.2	odd	6
2025.4.a.s.1.2		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)

\(f(q)\)	\(=\)	\(q+(-0.0874923 + 0.151541i) q^{2} +(-5.19394 - 0.151541i) q^{3} +(3.98469 + 6.90169i) q^{4} +(0.477395 - 0.773837i) q^{6} +(4.23186 - 7.32979i) q^{7} -2.79440 q^{8} +(26.9541 + 1.57419i) q^{9} +O(q^{10})\)	\(q+(-0.0874923 + 0.151541i) q^{2} +(-5.19394 - 0.151541i) q^{3} +(3.98469 + 6.90169i) q^{4} +(0.477395 - 0.773837i) q^{6} +(4.23186 - 7.32979i) q^{7} -2.79440 q^{8} +(26.9541 + 1.57419i) q^{9} +(15.7541 - 27.2870i) q^{11} +(-19.6504 - 36.4508i) q^{12} +(13.4348 + 23.2697i) q^{13} +(0.740510 + 1.28260i) q^{14} +(-31.6330 + 54.7900i) q^{16} +44.3307 q^{17} +(-2.59683 + 3.94692i) q^{18} -90.2082 q^{19} +(-23.0908 + 37.4292i) q^{21} +(2.75673 + 4.77480i) q^{22} +(97.1287 + 168.232i) q^{23} +(14.5139 + 0.423466i) q^{24} -4.70176 q^{26} +(-139.759 - 12.2609i) q^{27} +67.4506 q^{28} +(-1.87186 + 3.24215i) q^{29} +(125.832 + 217.947i) q^{31} +(-16.7129 - 28.9476i) q^{32} +(-85.9611 + 139.339i) q^{33} +(-3.87859 + 6.71792i) q^{34} +(96.5390 + 192.301i) q^{36} +62.2293 q^{37} +(7.89252 - 13.6703i) q^{38} +(-66.2532 - 122.898i) q^{39} +(102.173 + 176.969i) q^{41} +(-3.65180 - 6.77397i) q^{42} +(-263.831 + 456.968i) q^{43} +251.101 q^{44} -33.9920 q^{46} +(77.8637 - 134.864i) q^{47} +(172.603 - 279.782i) q^{48} +(135.683 + 235.009i) q^{49} +(-230.251 - 6.71792i) q^{51} +(-107.067 + 185.445i) q^{52} +141.694 q^{53} +(14.0859 - 20.1065i) q^{54} +(-11.8255 + 20.4823i) q^{56} +(468.536 + 13.6703i) q^{57} +(-0.327546 - 0.567326i) q^{58} +(246.923 + 427.683i) q^{59} +(379.742 - 657.732i) q^{61} -44.0373 q^{62} +(125.604 - 190.906i) q^{63} -500.280 q^{64} +(-13.5947 - 25.2178i) q^{66} +(-271.795 - 470.763i) q^{67} +(176.644 + 305.956i) q^{68} +(-478.987 - 888.505i) q^{69} -928.207 q^{71} +(-75.3203 - 4.39891i) q^{72} -608.739 q^{73} +(-5.44459 + 9.43030i) q^{74} +(-359.452 - 622.589i) q^{76} +(-133.338 - 230.949i) q^{77} +(24.4207 + 0.712510i) q^{78} +(-307.420 + 532.467i) q^{79} +(724.044 + 84.8617i) q^{81} -35.7573 q^{82} +(537.655 - 931.246i) q^{83} +(-350.334 - 10.2215i) q^{84} +(-46.1663 - 79.9623i) q^{86} +(10.2136 - 16.5559i) q^{87} +(-44.0233 + 76.2506i) q^{88} +1505.15 q^{89} +227.416 q^{91} +(-774.055 + 1340.70i) q^{92} +(-620.536 - 1151.07i) q^{93} +(13.6249 + 23.5991i) q^{94} +(82.4190 + 152.885i) q^{96} +(-166.369 + 288.160i) q^{97} -47.4848 q^{98} +(467.593 - 710.695i) 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

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