LMFDB - Embedded newform 315.4.j.g.226.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,4,Mod(46,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

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

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

chi := DirichletCharacter("315.46");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	315.j (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:	$18.5856016518$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + 38 x^{8} - 5 x^{7} + 1102 x^{6} - 137 x^{5} + 11161 x^{4} + 10784 x^{3} + 81600 x^{2} + \cdots + 4096 $ x^10 - x^9 + 38x^8 - 5x^7 + 1102x^6 - 137x^5 + 11161x^4 + 10784x^3 + 81600x^2 + 18432x + 4096
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 35)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			226.5
Root			$2.60181 - 4.50647i$ of defining polynomial
Character	$\chi$	$=$	315.226
Dual form			315.4.j.g.46.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.60181 - 4.50647i) q^{2} +(-9.53885 - 16.5218i) q^{4} +(-2.50000 + 4.33013i) q^{5} +(-18.0302 + 4.23212i) q^{7} -57.6442 q^{8} +O(q^{10})$	\(q+(2.60181 - 4.50647i) q^{2} +(-9.53885 - 16.5218i) q^{4} +(-2.50000 + 4.33013i) q^{5} +(-18.0302 + 4.23212i) q^{7} -57.6442 q^{8} +(13.0091 + 22.5324i) q^{10} +(28.3386 + 49.0839i) q^{11} -43.4297 q^{13} +(-27.8393 + 92.2639i) q^{14} +(-73.6685 + 127.598i) q^{16} +(-19.9193 - 34.5013i) q^{17} +(-26.1940 + 45.3693i) q^{19} +95.3885 q^{20} +294.927 q^{22} +(-26.7579 + 46.3460i) q^{23} +(-12.5000 - 21.6506i) q^{25} +(-112.996 + 195.715i) q^{26} +(241.910 + 257.522i) q^{28} -49.6376 q^{29} +(36.8930 + 63.9006i) q^{31} +(152.767 + 264.599i) q^{32} -207.305 q^{34} +(26.7499 - 88.6535i) q^{35} +(153.540 - 265.938i) q^{37} +(136.304 + 236.085i) q^{38} +(144.110 - 249.607i) q^{40} -292.064 q^{41} -365.956 q^{43} +(540.635 - 936.407i) q^{44} +(139.238 + 241.167i) q^{46} +(-221.226 + 383.175i) q^{47} +(307.178 - 152.612i) q^{49} -130.091 q^{50} +(414.269 + 717.536i) q^{52} +(12.8856 + 22.3185i) q^{53} -283.386 q^{55} +(1039.34 - 243.957i) q^{56} +(-129.148 + 223.690i) q^{58} +(188.300 + 326.146i) q^{59} +(-316.287 + 547.826i) q^{61} +383.955 q^{62} +411.183 q^{64} +(108.574 - 188.056i) q^{65} +(-255.549 - 442.624i) q^{67} +(-380.015 + 658.206i) q^{68} +(-329.916 - 351.207i) q^{70} -134.881 q^{71} +(-204.708 - 354.564i) q^{73} +(-798.962 - 1383.84i) q^{74} +999.443 q^{76} +(-718.680 - 765.061i) q^{77} +(463.424 - 802.674i) q^{79} +(-368.343 - 637.988i) q^{80} +(-759.897 + 1316.18i) q^{82} -296.372 q^{83} +199.193 q^{85} +(-952.150 + 1649.17i) q^{86} +(-1633.55 - 2829.40i) q^{88} +(244.391 - 423.297i) q^{89} +(783.047 - 183.800i) q^{91} +1020.96 q^{92} +(1151.18 + 1993.90i) q^{94} +(-130.970 - 226.847i) q^{95} -475.907 q^{97} +(111.477 - 1781.36i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + q^{2} - 35 q^{4} - 25 q^{5} - 62 q^{7} - 66 q^{8}+O(q^{10}) $ 10 * q + q^2 - 35 * q^4 - 25 * q^5 - 62 * q^7 - 66 * q^8	$ 10 q + q^{2} - 35 q^{4} - 25 q^{5} - 62 q^{7} - 66 q^{8} + 5 q^{10} + 47 q^{11} + 2 q^{13} - 7 q^{14} - 171 q^{16} - 2 q^{17} + 21 q^{19} + 350 q^{20} + 1046 q^{22} + 201 q^{23} - 125 q^{25} - 47 q^{26} + 597 q^{28} - 380 q^{29} - 388 q^{31} - 95 q^{32} + 260 q^{34} + 95 q^{35} + 145 q^{37} + 835 q^{38} + 165 q^{40} + 562 q^{41} + 1136 q^{43} + 1091 q^{44} - 337 q^{46} - 473 q^{47} + 998 q^{49} - 50 q^{50} + 379 q^{52} + 351 q^{53} - 470 q^{55} + 1338 q^{56} - 1818 q^{58} + 708 q^{59} - 1944 q^{61} - 896 q^{62} - 250 q^{64} - 5 q^{65} - 1118 q^{67} - 3118 q^{68} + 865 q^{70} - 1728 q^{71} + 1652 q^{73} - 3285 q^{74} + 1382 q^{76} - 787 q^{77} - 218 q^{79} - 855 q^{80} - 1027 q^{82} + 3004 q^{83} + 20 q^{85} - 4264 q^{86} - 2131 q^{88} + 2322 q^{89} + 524 q^{91} + 5914 q^{92} + 2677 q^{94} + 105 q^{95} + 1196 q^{97} - 2971 q^{98}+O(q^{100}) $ 10 * q + q^2 - 35 * q^4 - 25 * q^5 - 62 * q^7 - 66 * q^8 + 5 * q^10 + 47 * q^11 + 2 * q^13 - 7 * q^14 - 171 * q^16 - 2 * q^17 + 21 * q^19 + 350 * q^20 + 1046 * q^22 + 201 * q^23 - 125 * q^25 - 47 * q^26 + 597 * q^28 - 380 * q^29 - 388 * q^31 - 95 * q^32 + 260 * q^34 + 95 * q^35 + 145 * q^37 + 835 * q^38 + 165 * q^40 + 562 * q^41 + 1136 * q^43 + 1091 * q^44 - 337 * q^46 - 473 * q^47 + 998 * q^49 - 50 * q^50 + 379 * q^52 + 351 * q^53 - 470 * q^55 + 1338 * q^56 - 1818 * q^58 + 708 * q^59 - 1944 * q^61 - 896 * q^62 - 250 * q^64 - 5 * q^65 - 1118 * q^67 - 3118 * q^68 + 865 * q^70 - 1728 * q^71 + 1652 * q^73 - 3285 * q^74 + 1382 * q^76 - 787 * q^77 - 218 * q^79 - 855 * q^80 - 1027 * q^82 + 3004 * q^83 + 20 * q^85 - 4264 * q^86 - 2131 * q^88 + 2322 * q^89 + 524 * q^91 + 5914 * q^92 + 2677 * q^94 + 105 * q^95 + 1196 * q^97 - 2971 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	2.60181	−	4.50647i	0.919879	−	1.59328i	0.120283	−	0.992740i	$-0.461620\pi$
$2$	2.60181	−	4.50647i	0.919879	−	1.59328i	0.799596	−	0.600538i	$-0.205047\pi$
$3$		0			0
$3$		0			0
$4$	−9.53885	−	16.5218i	−1.19236	−	2.06522i
$5$	−2.50000	+	4.33013i	−0.223607	+	0.387298i
$5$	−2.50000	+	4.33013i	−0.223607	+	0.387298i
$6$		0			0
$7$	−18.0302	+	4.23212i	−0.973541	+	0.228513i
$7$	−18.0302	+	4.23212i	−0.973541	+	0.228513i
$8$	−57.6442			−2.54754
$9$		0			0
$10$	13.0091	+	22.5324i	0.411383	+	0.712536i
$11$	28.3386	+	49.0839i	0.776764	+	1.34539i	0.933798	+	0.357802i	$0.116474\pi$
$11$	28.3386	+	49.0839i	0.776764	+	1.34539i	−0.157034	+	0.987593i	$0.550193\pi$
$12$		0			0
$13$	−43.4297			−0.926556			−0.463278	−	0.886213i	$-0.653327\pi$
$13$	−43.4297			−0.926556			−0.463278	+	0.886213i	$0.653327\pi$
$14$	−27.8393	+	92.2639i	−0.531455	+	1.76133i
$15$		0			0
$16$	−73.6685	+	127.598i	−1.15107	+	1.99371i
$17$	−19.9193	−	34.5013i	−0.284185	−	0.492223i	0.688226	−	0.725496i	$-0.258390\pi$
$17$	−19.9193	−	34.5013i	−0.284185	−	0.492223i	−0.972411	+	0.233273i	$0.925056\pi$
$18$		0			0
$19$	−26.1940	+	45.3693i	−0.316280	+	0.547813i	−0.979709	−	0.200427i	$-0.935767\pi$
$19$	−26.1940	+	45.3693i	−0.316280	+	0.547813i	0.663429	+	0.748239i	$0.269101\pi$
$20$	95.3885			1.06648
$21$		0			0
$22$	294.927			2.85812
$23$	−26.7579	+	46.3460i	−0.242583	+	0.420166i	−0.961449	−	0.274982i	$-0.911328\pi$
$23$	−26.7579	+	46.3460i	−0.242583	+	0.420166i	0.718866	+	0.695148i	$0.244661\pi$
$24$		0			0
$25$	−12.5000	−	21.6506i	−0.100000	−	0.173205i
$26$	−112.996	+	195.715i	−0.852320	+	1.47626i
$27$		0			0
$28$	241.910	+	257.522i	1.63274	+	1.73811i
$29$	−49.6376			−0.317844			−0.158922	−	0.987291i	$-0.550802\pi$
$29$	−49.6376			−0.317844			−0.158922	+	0.987291i	$0.550802\pi$
$30$		0			0
$31$	36.8930	+	63.9006i	0.213748	+	0.370222i	0.952884	−	0.303333i	$-0.0980996\pi$
$31$	36.8930	+	63.9006i	0.213748	+	0.370222i	−0.739137	+	0.673555i	$0.764766\pi$
$32$	152.767	+	264.599i	0.843924	+	1.46172i
$33$		0			0
$34$	−207.305			−1.04566
$35$	26.7499	−	88.6535i	0.129188	−	0.428148i
$36$		0			0
$37$	153.540	−	265.938i	0.682210	−	1.18162i	−0.292096	−	0.956389i	$-0.594353\pi$
$37$	153.540	−	265.938i	0.682210	−	1.18162i	0.974305	−	0.225232i	$-0.0723141\pi$
$38$	136.304	+	236.085i	0.581879	+	1.00784i
$39$		0			0
$40$	144.110	−	249.607i	0.569647	−	0.986657i
$41$	−292.064			−1.11251			−0.556254	−	0.831012i	$-0.687762\pi$
$41$	−292.064			−1.11251			−0.556254	+	0.831012i	$0.687762\pi$
$42$		0			0
$43$	−365.956			−1.29786			−0.648928	−	0.760850i	$-0.724783\pi$
$43$	−365.956			−1.29786			−0.648928	+	0.760850i	$0.724783\pi$
$44$	540.635	−	936.407i	1.85236	−	3.20838i
$45$		0			0
$46$	139.238	+	241.167i	0.446294	+	0.773004i
$47$	−221.226	+	383.175i	−0.686577	+	1.18919i	0.286361	+	0.958122i	$0.407554\pi$
$47$	−221.226	+	383.175i	−0.686577	+	1.18919i	−0.972938	+	0.231065i	$0.925779\pi$
$48$		0			0
$49$	307.178	−	152.612i	0.895563	−	0.444934i
$50$	−130.091			−0.367952
$51$		0			0
$52$	414.269	+	717.536i	1.10479	+	1.91354i
$53$	12.8856	+	22.3185i	0.0333957	+	0.0578430i	0.882240	−	0.470800i	$-0.156035\pi$
$53$	12.8856	+	22.3185i	0.0333957	+	0.0578430i	−0.848845	+	0.528643i	$0.822701\pi$
$54$		0			0
$55$	−283.386			−0.694759
$56$	1039.34	−	243.957i	2.48013	−	0.582146i
$57$		0			0
$58$	−129.148	+	223.690i	−0.292378	+	0.506413i
$59$	188.300	+	326.146i	0.415502	+	0.719670i	0.995481	−	0.0949609i	$-0.0302726\pi$
$59$	188.300	+	326.146i	0.415502	+	0.719670i	−0.579979	+	0.814631i	$0.696939\pi$
$60$		0			0
$61$	−316.287	+	547.826i	−0.663876	+	1.14987i	0.315713	+	0.948855i	$0.397756\pi$
$61$	−316.287	+	547.826i	−0.663876	+	1.14987i	−0.979589	+	0.201012i	$0.935577\pi$
$62$	383.955			0.786489
$63$		0			0
$64$	411.183			0.803092
$65$	108.574	−	188.056i	0.207184	−	0.358854i
$66$		0			0
$67$	−255.549	−	442.624i	−0.465974	−	0.807091i	0.533271	−	0.845945i	$-0.320963\pi$
$67$	−255.549	−	442.624i	−0.465974	−	0.807091i	−0.999245	+	0.0388534i	$0.987629\pi$
$68$	−380.015	+	658.206i	−0.677700	+	1.17381i
$69$		0			0
$70$	−329.916	−	351.207i	−0.563322	−	0.599676i
$71$	−134.881			−0.225457			−0.112728	−	0.993626i	$-0.535959\pi$
$71$	−134.881			−0.225457			−0.112728	+	0.993626i	$0.535959\pi$
$72$		0			0
$73$	−204.708	−	354.564i	−0.328208	−	0.568474i	0.653948	−	0.756540i	$-0.273112\pi$
$73$	−204.708	−	354.564i	−0.328208	−	0.568474i	−0.982156	+	0.188066i	$0.939778\pi$
$74$	−798.962	−	1383.84i	−1.25510	−	2.17390i
$75$		0			0
$76$	999.443			1.50847
$77$	−718.680	−	765.061i	−1.06365	−	1.13230i
$78$		0			0
$79$	463.424	−	802.674i	0.659991	−	1.14314i	−0.320627	−	0.947206i	$-0.603894\pi$
$79$	463.424	−	802.674i	0.659991	−	1.14314i	0.980618	−	0.195932i	$-0.0627731\pi$
$80$	−368.343	−	637.988i	−0.514774	−	0.891616i
$81$		0			0
$82$	−759.897	+	1316.18i	−1.02337	+	1.77253i
$83$	−296.372			−0.391940			−0.195970	−	0.980610i	$-0.562786\pi$
$83$	−296.372			−0.391940			−0.195970	+	0.980610i	$0.562786\pi$
$84$		0			0
$85$	199.193			0.254183
$86$	−952.150	+	1649.17i	−1.19387	+	2.06785i
$87$		0			0
$88$	−1633.55	−	2829.40i	−1.97884	−	3.42744i
$89$	244.391	−	423.297i	0.291071	−	0.504150i	−0.682992	−	0.730426i	$-0.739322\pi$
$89$	244.391	−	423.297i	0.291071	−	0.504150i	0.974063	+	0.226275i	$0.0726550\pi$
$90$		0			0
$91$	783.047	−	183.800i	0.902040	−	0.211730i
$92$	1020.96			1.15698
$93$		0			0
$94$	1151.18	+	1993.90i	1.26314	+	2.18782i
$95$	−130.970	−	226.847i	−0.141445	−	0.244989i
$96$		0			0
$97$	−475.907			−0.498155			−0.249077	−	0.968484i	$-0.580127\pi$
$97$	−475.907			−0.498155			−0.249077	+	0.968484i	$0.580127\pi$
$98$	111.477	−	1781.36i	0.114907	−	1.83617i
$99$		0			0
$100$	−238.471	+	413.044i	−0.238471	+	0.413044i
$101$	38.7904	+	67.1870i	0.0382158	+	0.0661917i	0.884501	−	0.466539i	$-0.154499\pi$
$101$	38.7904	+	67.1870i	0.0382158	+	0.0661917i	−0.846285	+	0.532731i	$0.821166\pi$
$102$		0			0
$103$	−568.886	+	985.340i	−0.544214	+	0.942606i	0.454442	+	0.890776i	$0.349839\pi$
$103$	−568.886	+	985.340i	−0.544214	+	0.942606i	−0.998656	+	0.0518297i	$0.983495\pi$
$104$	2503.47			2.36044
$105$		0			0
$106$	134.103			0.122880
$107$	37.5702	−	65.0735i	0.0339444	−	0.0587934i	−0.848554	−	0.529109i	$-0.822526\pi$
$107$	37.5702	−	65.0735i	0.0339444	−	0.0587934i	0.882499	+	0.470315i	$0.155860\pi$
$108$		0			0
$109$	−41.4673	−	71.8235i	−0.0364390	−	0.0631142i	0.847231	−	0.531225i	$-0.178268\pi$
$109$	−41.4673	−	71.8235i	−0.0364390	−	0.0631142i	−0.883670	+	0.468111i	$0.844935\pi$
$110$	−737.317	+	1277.07i	−0.639094	+	1.10694i
$111$		0			0
$112$	788.251	−	2612.39i	0.665024	−	2.20400i
$113$	−714.602			−0.594903			−0.297452	−	0.954737i	$-0.596137\pi$
$113$	−714.602			−0.594903			−0.297452	+	0.954737i	$0.596137\pi$
$114$		0			0
$115$	−133.789	−	231.730i	−0.108486	−	0.187904i
$116$	473.485	+	820.101i	0.378983	+	0.656418i
$117$		0			0
$118$	1959.69			1.52885
$119$	505.164	+	537.765i	0.389145	+	0.414259i
$120$		0			0
$121$	−940.651	+	1629.26i	−0.706725	+	1.22408i
$122$	1645.84	+	2850.68i	1.22137	+	2.11548i
$123$		0			0
$124$	703.834	−	1219.08i	0.509727	−	0.882873i
$125$	125.000			0.0894427
$126$		0			0
$127$	1881.66			1.31473			0.657363	−	0.753574i	$-0.271672\pi$
$127$	1881.66			1.31473			0.657363	+	0.753574i	$0.271672\pi$
$128$	−152.312	+	263.812i	−0.105177	+	0.182171i
$129$		0			0
$130$	−564.980	−	978.573i	−0.381169	−	0.660204i
$131$	91.9544	−	159.270i	0.0613289	−	0.106225i	−0.833731	−	0.552171i	$-0.813799\pi$
$131$	91.9544	−	159.270i	0.0613289	−	0.106225i	0.895060	+	0.445946i	$0.147133\pi$
$132$		0			0
$133$	280.275	−	928.876i	0.182729	−	0.605592i
$134$	−2659.56			−1.71456
$135$		0			0
$136$	1148.23	+	1988.80i	0.723972	+	1.25396i
$137$	443.874	+	768.812i	0.276808	+	0.479445i	0.970590	−	0.240740i	$-0.0773901\pi$
$137$	443.874	+	768.812i	0.276808	+	0.479445i	−0.693782	+	0.720185i	$0.744057\pi$
$138$		0			0
$139$	−2335.25			−1.42499			−0.712495	−	0.701678i	$-0.752435\pi$
$139$	−2335.25			−1.42499			−0.712495	+	0.701678i	$0.752435\pi$
$140$	−1719.88	+	403.696i	−1.03826	+	0.243704i
$141$		0			0
$142$	−350.935	+	607.837i	−0.207393	+	0.359215i
$143$	−1230.74	−	2131.70i	−0.719716	−	1.24658i
$144$		0			0
$145$	124.094	−	214.937i	0.0710720	−	0.123100i
$146$	−2130.44			−1.20765
$147$		0			0
$148$	−5858.36			−3.25375
$149$	−1201.54	+	2081.12i	−0.660629	+	1.14424i	0.319821	+	0.947478i	$0.396377\pi$
$149$	−1201.54	+	2081.12i	−0.660629	+	1.14424i	−0.980451	+	0.196766i	$0.936956\pi$
$150$		0			0
$151$	−617.188	−	1069.00i	−0.332623	−	0.576120i	0.650402	−	0.759590i	$-0.274600\pi$
$151$	−617.188	−	1069.00i	−0.332623	−	0.576120i	−0.983025	+	0.183470i	$0.941267\pi$
$152$	1509.93	−	2615.28i	0.805735	−	1.39557i
$153$		0			0
$154$	−5317.60	+	1248.17i	−2.78249	+	0.653118i
$155$	−368.930			−0.191182
$156$		0			0
$157$	−716.244	−	1240.57i	−0.364092	−	0.630627i	0.624538	−	0.780995i	$-0.285287\pi$
$157$	−716.244	−	1240.57i	−0.364092	−	0.630627i	−0.988630	+	0.150368i	$0.951954\pi$
$158$	−2411.48	−	4176.81i	−1.21422	−	2.10310i
$159$		0			0
$160$	−1527.67			−0.754829
$161$	286.309	−	948.872i	0.140151	−	0.464482i
$162$		0			0
$163$	430.415	−	745.500i	0.206826	−	0.358234i	−0.743887	−	0.668306i	$-0.767020\pi$
$163$	430.415	−	745.500i	0.206826	−	0.358234i	0.950713	+	0.310072i	$0.100353\pi$
$164$	2785.96	+	4825.42i	1.32651	+	2.29757i
$165$		0			0
$166$	−771.104	+	1335.59i	−0.360538	+	0.624470i
$167$	1346.77			0.624049			0.312024	−	0.950074i	$-0.398993\pi$
$167$	1346.77			0.624049			0.312024	+	0.950074i	$0.398993\pi$
$168$		0			0
$169$	−310.861			−0.141493
$170$	518.264	−	897.659i	0.233818	−	0.404984i
$171$		0			0
$172$	3490.80	+	6046.25i	1.54751	+	2.68036i
$173$	−1305.25	+	2260.75i	−0.573618	+	0.993536i	0.422572	+	0.906329i	$0.361127\pi$
$173$	−1305.25	+	2260.75i	−0.573618	+	0.993536i	−0.996190	+	0.0872067i	$0.972206\pi$
$174$		0			0
$175$	317.006	+	337.464i	0.136934	+	0.145771i
$176$	−8350.65			−3.57644
$177$		0			0
$178$	−1271.72	−	2202.68i	−0.535501	−	0.927515i
$179$	675.224	+	1169.52i	0.281947	+	0.488347i	0.971864	−	0.235541i	$-0.0756863\pi$
$179$	675.224	+	1169.52i	0.281947	+	0.488347i	−0.689917	+	0.723889i	$0.742353\pi$
$180$		0			0
$181$	2846.61			1.16899			0.584493	−	0.811399i	$-0.301293\pi$
$181$	2846.61			1.16899			0.584493	+	0.811399i	$0.301293\pi$
$182$	1209.05	−	4006.99i	0.492423	−	1.63197i
$183$		0			0
$184$	1542.44	−	2671.58i	0.617989	−	1.07039i
$185$	767.698	+	1329.69i	0.305093	+	0.528437i
$186$		0			0
$187$	1128.97	−	1955.44i	0.441490	−	0.764683i
$188$	8440.97			3.27458
$189$		0			0
$190$	−1363.04			−0.520448
$191$	2101.75	−	3640.33i	0.796215	−	1.37909i	−0.125849	−	0.992049i	$-0.540166\pi$
$191$	2101.75	−	3640.33i	0.796215	−	1.37909i	0.922065	−	0.387036i	$-0.126501\pi$
$192$		0			0
$193$	−69.2923	−	120.018i	−0.0258434	−	0.0447620i	0.852814	−	0.522214i	$-0.174894\pi$
$193$	−69.2923	−	120.018i	−0.0258434	−	0.0447620i	−0.878658	+	0.477452i	$0.841560\pi$
$194$	−1238.22	+	2144.66i	−0.458242	+	0.793699i
$195$		0			0
$196$	−5451.55	−	3619.38i	−1.98672	−	1.31902i
$197$	−1473.76			−0.532998			−0.266499	−	0.963835i	$-0.585867\pi$
$197$	−1473.76			−0.532998			−0.266499	+	0.963835i	$0.585867\pi$
$198$		0			0
$199$	1804.80	+	3126.00i	0.642909	+	1.11355i	0.984780	+	0.173804i	$0.0556059\pi$
$199$	1804.80	+	3126.00i	0.642909	+	1.11355i	−0.341872	+	0.939747i	$0.611061\pi$
$200$	720.552	+	1248.03i	0.254754	+	0.441246i
$201$		0			0
$202$	403.702			0.140616
$203$	894.977	−	210.072i	0.309434	−	0.0726315i
$204$		0			0
$205$	730.161	−	1264.68i	0.248764	−	0.430872i
$206$	2960.27	+	5127.34i	1.00122	+	1.73417i
$207$		0			0
$208$	3199.40	−	5541.53i	1.06653	−	1.84729i
$209$	−2969.20			−0.982699
$210$		0			0
$211$	1782.00			0.581412			0.290706	−	0.956812i	$-0.406110\pi$
$211$	1782.00			0.581412			0.290706	+	0.956812i	$0.406110\pi$
$212$	245.827	−	425.785i	0.0796390	−	0.137939i
$213$		0			0
$214$	−195.501	−	338.618i	−0.0624495	−	0.108166i
$215$	914.891	−	1584.64i	0.290210	−	0.502658i
$216$		0			0
$217$	−935.625	−	996.006i	−0.292693	−	0.311582i
$218$	−431.561			−0.134078
$219$		0			0
$220$	2703.18	+	4682.04i	0.828400	+	1.43483i
$221$	865.091	+	1498.38i	0.263314	+	0.456073i
$222$		0			0
$223$	5258.44			1.57906			0.789532	−	0.613709i	$-0.210323\pi$
$223$	5258.44			1.57906			0.789532	+	0.613709i	$0.210323\pi$
$224$	−3874.23	−	4124.26i	−1.15562	−	1.23020i
$225$		0			0
$226$	−1859.26	+	3220.33i	−0.547239	+	0.947846i
$227$	−3353.93	−	5809.18i	−0.980652	−	1.69854i	−0.659857	−	0.751391i	$-0.729383\pi$
$227$	−3353.93	−	5809.18i	−0.980652	−	1.69854i	−0.320795	−	0.947149i	$-0.603950\pi$
$228$		0			0
$229$	−600.126	+	1039.45i	−0.173177	+	0.299951i	−0.939529	−	0.342470i	$-0.888736\pi$
$229$	−600.126	+	1039.45i	−0.173177	+	0.299951i	0.766352	+	0.642421i	$0.222070\pi$
$230$	−1392.38			−0.399178
$231$		0			0
$232$	2861.32			0.809719
$233$	3175.71	−	5500.49i	0.892909	−	1.54656i	0.0565373	−	0.998400i	$-0.481994\pi$
$233$	3175.71	−	5500.49i	0.892909	−	1.54656i	0.836372	−	0.548163i	$-0.184673\pi$
$234$		0			0
$235$	−1106.13	−	1915.87i	−0.307047	−	0.531820i
$236$	3592.34	−	6222.11i	0.990853	−	1.71621i
$237$		0			0
$238$	3737.76	−	877.343i	1.01800	−	0.238948i
$239$	3003.73			0.812951			0.406475	−	0.913662i	$-0.366758\pi$
$239$	3003.73			0.812951			0.406475	+	0.913662i	$0.366758\pi$
$240$		0			0
$241$	−2846.16	−	4929.70i	−0.760736	−	1.31763i	−0.942472	−	0.334286i	$-0.891505\pi$
$241$	−2846.16	−	4929.70i	−0.760736	−	1.31763i	0.181736	−	0.983347i	$-0.441828\pi$
$242$	4894.79	+	8478.03i	1.30020	+	2.25202i
$243$		0			0
$244$	12068.1			3.16631
$245$	−107.115	+	1711.65i	−0.0279319	+	0.446340i
$246$		0			0
$247$	1137.60	−	1970.38i	0.293051	−	0.507579i
$248$	−2126.67	−	3683.50i	−0.544531	−	0.943155i
$249$		0			0
$250$	325.226	−	563.309i	0.0822765	−	0.142507i
$251$	−6973.37			−1.75361			−0.876803	−	0.480850i	$-0.840328\pi$
$251$	−6973.37			−1.75361			−0.876803	+	0.480850i	$0.840328\pi$
$252$		0			0
$253$	−3033.12			−0.753719
$254$	4895.72	−	8479.64i	1.20939	−	2.09472i
$255$		0			0
$256$	2437.31	+	4221.54i	0.595045	+	1.03065i
$257$	1545.90	−	2677.59i	0.375217	−	0.649896i	−0.615142	−	0.788416i	$-0.710901\pi$
$257$	1545.90	−	2677.59i	0.375217	−	0.649896i	0.990360	+	0.138521i	$0.0442347\pi$
$258$		0			0
$259$	−1642.87	+	5444.73i	−0.394143	+	1.30625i
$260$	−4142.69			−0.988150
$261$		0			0
$262$	−478.496	−	828.779i	−0.112830	−	0.195428i
$263$	992.413	+	1718.91i	0.232680	+	0.403013i	0.958596	−	0.284770i	$-0.0919172\pi$
$263$	992.413	+	1718.91i	0.232680	+	0.403013i	−0.725916	+	0.687783i	$0.758584\pi$
$264$		0			0
$265$	−128.856			−0.0298700
$266$	−3456.73	−	3679.81i	−0.796788	−	0.848210i
$267$		0			0
$268$	−4875.29	+	8444.25i	−1.11121	+	1.92468i
$269$	3090.37	+	5352.68i	0.700458	+	1.21323i	0.968306	+	0.249767i	$0.0803540\pi$
$269$	3090.37	+	5352.68i	0.700458	+	1.21323i	−0.267848	+	0.963461i	$0.586313\pi$
$270$		0			0
$271$	3059.49	−	5299.20i	0.685797	−	1.18784i	−0.287388	−	0.957814i	$-0.592787\pi$
$271$	3059.49	−	5299.20i	0.685797	−	1.18784i	0.973186	−	0.230022i	$-0.0738797\pi$
$272$	5869.71			1.30847
$273$		0			0
$274$	4619.50			1.01852
$275$	708.465	−	1227.10i	0.155353	−	0.269079i
$276$		0			0
$277$	−1647.42	−	2853.41i	−0.357342	−	0.618935i	0.630174	−	0.776454i	$-0.282984\pi$
$277$	−1647.42	−	2853.41i	−0.357342	−	0.618935i	−0.987516	+	0.157519i	$0.949650\pi$
$278$	−6075.89	+	10523.7i	−1.31082	+	2.27040i
$279$		0			0
$280$	−1541.98	+	5110.36i	−0.329110	+	1.09072i
$281$	4604.53			0.977521			0.488760	−	0.872418i	$-0.337449\pi$
$281$	4604.53			0.977521			0.488760	+	0.872418i	$0.337449\pi$
$282$		0			0
$283$	609.776	+	1056.16i	0.128083	+	0.221846i	0.922934	−	0.384959i	$-0.125784\pi$
$283$	609.776	+	1056.16i	0.128083	+	0.221846i	−0.794851	+	0.606805i	$0.792451\pi$
$284$	1286.61	+	2228.47i	0.268825	+	0.465618i
$285$		0			0
$286$	−12808.6			−2.64821
$287$	5265.99	−	1236.05i	1.08307	−	0.254223i
$288$		0			0
$289$	1662.94	−	2880.30i	0.338478	−	0.586260i
$290$	−645.738	−	1118.45i	−0.130755	−	0.226475i
$291$		0			0
$292$	−3905.35	+	6764.27i	−0.782683	+	1.35565i
$293$	8434.81			1.68180			0.840899	−	0.541192i	$-0.182027\pi$
$293$	8434.81			1.68180			0.840899	+	0.541192i	$0.182027\pi$
$294$		0			0
$295$	−1883.00			−0.371636
$296$	−8850.66	+	15329.8i	−1.73795	+	3.01022i
$297$		0			0
$298$	6252.35	+	10829.4i	1.21540	+	2.10513i
$299$	1162.09	−	2012.79i	0.224767	−	0.389307i
$300$		0			0
$301$	6598.28	−	1548.77i	1.26352	−	0.296577i
$302$	−6423.23			−1.22389
$303$		0			0
$304$	−3859.35	−	6684.58i	−0.728121	−	1.26114i
$305$	−1581.44	−	2739.13i	−0.296894	−	0.514236i
$306$		0			0
$307$	846.546			0.157378			0.0786888	−	0.996899i	$-0.474927\pi$
$307$	846.546			0.157378			0.0786888	+	0.996899i	$0.474927\pi$
$308$	−5784.78	+	19171.7i	−1.07019	+	3.54678i
$309$		0			0
$310$	−959.887	+	1662.57i	−0.175864	+	0.304606i
$311$	980.793	+	1698.78i	0.178829	+	0.309740i	0.941480	−	0.337070i	$-0.109436\pi$
$311$	980.793	+	1698.78i	0.178829	+	0.309740i	−0.762651	+	0.646810i	$0.776103\pi$
$312$		0			0
$313$	−3264.98	+	5655.11i	−0.589609	+	1.02123i	0.404674	+	0.914461i	$0.367385\pi$
$313$	−3264.98	+	5655.11i	−0.589609	+	1.02123i	−0.994284	+	0.106772i	$0.965948\pi$
$314$	−7454.13			−1.33968
$315$		0			0
$316$	−17682.1			−3.14778
$317$	−3845.26	+	6660.19i	−0.681298	+	1.18004i	0.293287	+	0.956025i	$0.405251\pi$
$317$	−3845.26	+	6660.19i	−0.681298	+	1.18004i	−0.974585	+	0.224019i	$0.928082\pi$
$318$		0			0
$319$	−1406.66	−	2436.40i	−0.246890	−	0.427625i
$320$	−1027.96	+	1780.47i	−0.179577	+	0.311036i
$321$		0			0
$322$	−3531.14	−	3759.03i	−0.611127	−	0.650567i
$323$	2087.07			0.359528
$324$		0			0
$325$	542.871	+	940.281i	0.0926556	+	0.160484i
$326$	−2239.72	−	3879.30i	−0.380511	−	0.659064i
$327$		0			0
$328$	16835.8			2.83415
$329$	2367.11	−	7844.98i	0.396666	−	1.31461i
$330$		0			0
$331$	−3263.13	+	5651.92i	−0.541867	+	0.938542i	0.456929	+	0.889503i	$0.348949\pi$
$331$	−3263.13	+	5651.92i	−0.541867	+	0.938542i	−0.998797	+	0.0490389i	$0.984384\pi$
$332$	2827.05	+	4896.59i	0.467332	+	0.809444i
$333$		0			0
$334$	3504.04	−	6069.18i	0.574050	−	0.994283i
$335$	2555.49			0.416780
$336$		0			0
$337$	1217.56			0.196809			0.0984047	−	0.995146i	$-0.468626\pi$
$337$	1217.56			0.196809			0.0984047	+	0.995146i	$0.468626\pi$
$338$	−808.802	+	1400.89i	−0.130157	+	0.225438i
$339$		0			0
$340$	−1900.08	−	3291.03i	−0.303077	−	0.524944i
$341$	−2090.99	+	3621.70i	−0.332063	+	0.575150i
$342$		0			0
$343$	−4892.62	+	4051.65i	−0.770194	+	0.637809i
$344$	21095.3			3.30634
$345$		0			0
$346$	6792.01	+	11764.1i	1.05532	+	1.82787i
$347$	−4214.64	−	7299.98i	−0.652029	−	1.12935i	−0.982630	−	0.185576i	$-0.940585\pi$
$347$	−4214.64	−	7299.98i	−0.652029	−	1.12935i	0.330601	−	0.943771i	$-0.392749\pi$
$348$		0			0
$349$	−135.644			−0.0208047			−0.0104023	−	0.999946i	$-0.503311\pi$
$349$	−135.644			−0.0208047			−0.0104023	+	0.999946i	$0.503311\pi$
$350$	2345.56	−	550.560i	0.358216	−	0.0840819i
$351$		0			0
$352$	−8658.38	+	14996.7i	−1.31106	+	2.27082i
$353$	1162.07	+	2012.77i	0.175215	+	0.303481i	0.940236	−	0.340525i	$-0.110605\pi$
$353$	1162.07	+	2012.77i	0.175215	+	0.303481i	−0.765021	+	0.644005i	$0.777271\pi$
$354$		0			0
$355$	337.202	−	584.052i	0.0504136	−	0.0873190i
$356$	−9324.82			−1.38824
$357$		0			0
$358$	7027.22			1.03743
$359$	−2663.65	+	4613.58i	−0.391594	+	0.678260i	−0.992660	−	0.120939i	$-0.961409\pi$
$359$	−2663.65	+	4613.58i	−0.391594	+	0.678260i	0.601066	+	0.799199i	$0.294743\pi$
$360$		0			0
$361$	2057.25	+	3563.26i	0.299934	+	0.519501i
$362$	7406.33	−	12828.1i	1.07533	−	1.86252i
$363$		0			0
$364$	−10506.1	−	11184.1i	−1.51282	−	1.61046i
$365$	2047.08			0.293559
$366$		0			0
$367$	3645.81	+	6314.73i	0.518555	+	0.898164i	0.999768	+	0.0215599i	$0.00686325\pi$
$367$	3645.81	+	6314.73i	0.518555	+	0.898164i	−0.481212	+	0.876604i	$0.659803\pi$
$368$	−3942.43	−	6828.49i	−0.558460	−	0.967282i
$369$		0			0
$370$	7989.62			1.12260
$371$	−326.784	−	347.874i	−0.0457299	−	0.0486811i
$372$		0			0
$373$	830.751	−	1438.90i	0.115321	−	0.199742i	−0.802587	−	0.596535i	$-0.796544\pi$
$373$	830.751	−	1438.90i	0.115321	−	0.199742i	0.917908	+	0.396793i	$0.129877\pi$
$374$	−5874.74	−	10175.4i	−0.812235	−	1.40683i
$375$		0			0
$376$	12752.4	−	22087.8i	1.74908	−	3.02950i
$377$	2155.75			0.294500
$378$		0			0
$379$	409.820			0.0555436			0.0277718	−	0.999614i	$-0.491159\pi$
$379$	409.820			0.0555436			0.0277718	+	0.999614i	$0.491159\pi$
$380$	−2498.61	+	4327.71i	−0.337305	+	0.584229i
$381$		0			0
$382$	−10936.7	−	18942.9i	−1.46484	−	2.53718i
$383$	−5470.58	+	9475.33i	−0.729853	+	1.26414i	0.227092	+	0.973873i	$0.427078\pi$
$383$	−5470.58	+	9475.33i	−0.729853	+	1.26414i	−0.956945	+	0.290269i	$0.906255\pi$
$384$		0			0
$385$	5109.51	−	1199.32i	0.676376	−	0.158762i
$386$	−721.142			−0.0950911
$387$		0			0
$388$	4539.60	+	7862.83i	0.593978	+	1.02880i
$389$	−3118.40	−	5401.23i	−0.406450	−	0.703992i	0.588039	−	0.808833i	$-0.299900\pi$
$389$	−3118.40	−	5401.23i	−0.406450	−	0.703992i	−0.994489	+	0.104840i	$0.966567\pi$
$390$		0			0
$391$	2132.00			0.275754
$392$	−17707.0	+	8797.21i	−2.28148	+	1.13349i
$393$		0			0
$394$	−3834.43	+	6641.43i	−0.490294	+	0.849215i
$395$	2317.12	+	4013.37i	0.295157	+	0.511227i
$396$		0			0
$397$	5723.91	−	9914.10i	0.723614	−	1.25334i	−0.235928	−	0.971771i	$-0.575813\pi$
$397$	5723.91	−	9914.10i	0.723614	−	1.25334i	0.959542	−	0.281565i	$-0.0908537\pi$
$398$	18783.0			2.36559
$399$		0			0
$400$	3683.43			0.460428
$401$	−4616.74	+	7996.42i	−0.574935	+	0.995816i	0.421114	+	0.907008i	$0.361639\pi$
$401$	−4616.74	+	7996.42i	−0.574935	+	0.995816i	−0.996049	+	0.0888085i	$0.971694\pi$
$402$		0			0
$403$	−1602.25	−	2775.18i	−0.198049	−	0.343032i
$404$	740.032	−	1281.77i	0.0911336	−	0.157848i
$405$		0			0
$406$	1381.88	−	4579.76i	0.168920	−	0.559826i
$407$	17404.4			2.11966
$408$		0			0
$409$	2217.57	+	3840.95i	0.268097	+	0.464358i	0.968370	−	0.249517i	$-0.0802718\pi$
$409$	2217.57	+	3840.95i	0.268097	+	0.464358i	−0.700273	+	0.713875i	$0.746938\pi$
$410$	−3799.48	−	6580.90i	−0.457666	−	0.792701i
$411$		0			0
$412$	21706.1			2.59559
$413$	−4775.39	−	5083.57i	−0.568962	−	0.605681i
$414$		0			0
$415$	740.930	−	1283.33i	0.0876405	−	0.151798i
$416$	−6634.61	−	11491.5i	−0.781943	−	1.35437i
$417$		0			0
$418$	−7725.31	+	13380.6i	−0.903965	+	1.56571i
$419$	6434.23			0.750197			0.375099	−	0.926985i	$-0.377609\pi$
$419$	6434.23			0.750197			0.375099	+	0.926985i	$0.377609\pi$
$420$		0			0
$421$	−9442.51			−1.09311			−0.546556	−	0.837423i	$-0.684061\pi$
$421$	−9442.51			−1.09311			−0.546556	+	0.837423i	$0.684061\pi$
$422$	4636.43	−	8030.53i	0.534829	−	0.926351i
$423$		0			0
$424$	−742.778	−	1286.53i	−0.0850767	−	0.147357i
$425$	−497.983	+	862.533i	−0.0568370	+	0.0984447i
$426$		0			0
$427$	3384.27	−	11216.0i	0.383551	−	1.27115i
$428$	−1433.51			−0.161895
$429$		0			0
$430$	−4760.75	−	8245.86i	−0.533916	−	0.924769i
$431$	−1120.60	−	1940.94i	−0.125238	−	0.216918i	0.796588	−	0.604522i	$-0.206636\pi$
$431$	−1120.60	−	1940.94i	−0.125238	−	0.216918i	−0.921826	+	0.387604i	$0.873303\pi$
$432$		0			0
$433$	−14181.1			−1.57391			−0.786954	−	0.617012i	$-0.788343\pi$
$433$	−14181.1			−1.57391			−0.786954	+	0.617012i	$0.788343\pi$
$434$	−6922.79	+	1624.94i	−0.765679	+	0.179723i
$435$		0			0
$436$	−791.101	+	1370.23i	−0.0868965	+	0.150509i
$437$	−1401.79	−	2427.98i	−0.153448	−	0.265780i
$438$		0			0
$439$	−4346.32	+	7528.05i	−0.472525	+	0.818438i	−0.999506	−	0.0314396i	$-0.989991\pi$
$439$	−4346.32	+	7528.05i	−0.472525	+	0.818438i	0.526980	+	0.849878i	$0.323324\pi$
$440$	16335.5			1.76992
$441$		0			0
$442$	9003.22			0.968867
$443$	−4696.85	+	8135.18i	−0.503734	+	0.872492i	0.496257	+	0.868176i	$0.334707\pi$
$443$	−4696.85	+	8135.18i	−0.503734	+	0.872492i	−0.999991	+	0.00431671i	$0.998626\pi$
$444$		0			0
$445$	1221.95	+	2116.48i	0.130171	+	0.225463i
$446$	13681.5	−	23697.0i	1.45255	−	2.51589i
$447$		0			0
$448$	−7413.72	+	1740.18i	−0.781842	+	0.183517i
$449$	−9511.86			−0.999761			−0.499880	−	0.866094i	$-0.666623\pi$
$449$	−9511.86			−0.999761			−0.499880	+	0.866094i	$0.666623\pi$
$450$		0			0
$451$	−8276.69	−	14335.7i	−0.864156	−	1.49676i
$452$	6816.48	+	11806.5i	0.709337	+	1.22861i
$453$		0			0
$454$	−34905.2			−3.60833
$455$	−1161.74	+	3850.19i	−0.119700	+	0.396703i
$456$		0			0
$457$	683.607	−	1184.04i	0.0699732	−	0.121197i	−0.828916	−	0.559373i	$-0.811042\pi$
$457$	683.607	−	1184.04i	0.0699732	−	0.121197i	0.898889	+	0.438176i	$0.144375\pi$
$458$	3122.83	+	5408.90i	0.318603	+	0.551837i
$459$		0			0
$460$	−2552.40	+	4420.88i	−0.258709	+	0.448097i
$461$	−8760.60			−0.885080			−0.442540	−	0.896749i	$-0.645922\pi$
$461$	−8760.60			−0.885080			−0.442540	+	0.896749i	$0.645922\pi$
$462$		0			0
$463$	10357.4			1.03963			0.519817	−	0.854278i	$-0.326000\pi$
$463$	10357.4			1.03963			0.519817	+	0.854278i	$0.326000\pi$
$464$	3656.73	−	6333.64i	0.365861	−	0.633689i
$465$		0			0
$466$	−16525.2	−	28622.5i	−1.64274	−	2.84530i
$467$	−4249.87	+	7360.99i	−0.421115	+	0.729392i	−0.996049	−	0.0888078i	$-0.971694\pi$
$467$	−4249.87	+	7360.99i	−0.421115	+	0.729392i	0.574934	+	0.818200i	$0.305028\pi$
$468$		0			0
$469$	6480.85	+	6899.09i	0.638076	+	0.679255i
$470$	−11511.8			−1.12978
$471$		0			0
$472$	−10854.4	−	18800.4i	−1.05851	−	1.83339i
$473$	−10370.7	−	17962.6i	−1.00813	−	1.74613i
$474$		0			0
$475$	1309.70			0.126512
$476$	4066.15	−	13475.9i	0.391537	−	1.29762i
$477$		0			0
$478$	7815.15	−	13536.2i	0.747817	−	1.29526i
$479$	−361.486	−	626.113i	−0.0344817	−	0.0597240i	0.848270	−	0.529565i	$-0.177645\pi$
$479$	−361.486	−	626.113i	−0.0344817	−	0.0597240i	−0.882751	+	0.469841i	$0.844311\pi$
$480$		0			0
$481$	−6668.18	+	11549.6i	−0.632106	+	1.09484i
$482$	−29620.7			−2.79914
$483$		0			0
$484$	35890.9			3.37067
$485$	1189.77	−	2060.74i	0.111391	−	0.192935i
$486$		0			0
$487$	−1153.66	−	1998.19i	−0.107345	−	0.185927i	0.807349	−	0.590075i	$-0.200902\pi$
$487$	−1153.66	−	1998.19i	−0.107345	−	0.185927i	−0.914694	+	0.404147i	$0.867568\pi$
$488$	18232.1	−	31579.0i	1.69125	−	2.92933i
$489$		0			0
$490$	7434.82	+	4936.11i	0.685450	+	0.455083i
$491$	8668.77			0.796774			0.398387	−	0.917217i	$-0.369570\pi$
$491$	8668.77			0.796774			0.398387	+	0.917217i	$0.369570\pi$
$492$		0			0
$493$	988.748	+	1712.56i	0.0903265	+	0.156450i
$494$	−5919.63	−	10253.1i	−0.539143	−	0.933823i
$495$		0			0
$496$	−10871.4			−0.984155
$497$	2431.93	−	570.833i	0.219491	−	0.0515198i
$498$		0			0
$499$	−9960.86	+	17252.7i	−0.893606	+	1.54777i	−0.0580860	+	0.998312i	$0.518500\pi$
$499$	−9960.86	+	17252.7i	−0.893606	+	1.54777i	−0.835520	+	0.549460i	$0.814834\pi$
$500$	−1192.36	−	2065.22i	−0.106648	−	0.184719i
$501$		0			0
$502$	−18143.4	+	31425.3i	−1.61311	+	2.79398i
$503$	−17007.8			−1.50763			−0.753817	−	0.657084i	$-0.771790\pi$
$503$	−17007.8			−1.50763			−0.753817	+	0.657084i	$0.771790\pi$
$504$		0			0
$505$	−387.904			−0.0341812
$506$	−7891.62	+	13668.7i	−0.693330	+	1.20088i
$507$		0			0
$508$	−17948.9	−	31088.3i	−1.56762	−	2.71520i
$509$	−9232.52	+	15991.2i	−0.803977	+	1.39253i	0.113003	+	0.993595i	$0.463953\pi$
$509$	−9232.52	+	15991.2i	−0.803977	+	1.39253i	−0.916980	+	0.398934i	$0.869380\pi$
$510$		0			0
$511$	5191.48	+	5526.52i	0.449428	+	0.478432i
$512$	22928.6			1.97913
$513$		0			0
$514$	−8044.31	−	13933.1i	−0.690310	−	1.19565i
$515$	−2844.43	−	4926.70i	−0.243380	−	0.421546i
$516$		0			0
$517$	−25076.9			−2.13323
$518$	20262.1	+	21569.7i	1.71866	+	1.82957i
$519$		0			0
$520$	−6258.67	+	10840.3i	−0.527810	+	0.914193i
$521$	−2167.92	−	3754.95i	−0.182300	−	0.315753i	0.760363	−	0.649498i	$-0.225021\pi$
$521$	−2167.92	−	3754.95i	−0.182300	−	0.315753i	−0.942663	+	0.333745i	$0.891688\pi$
$522$		0			0
$523$	4186.60	−	7251.40i	0.350033	−	0.606275i	−0.636222	−	0.771506i	$-0.719504\pi$
$523$	4186.60	−	7251.40i	0.350033	−	0.606275i	0.986255	+	0.165231i	$0.0528371\pi$
$524$	−3508.56			−0.292504
$525$		0			0
$526$	10328.3			0.856150
$527$	1469.77	−	2545.71i	0.121488	−	0.210423i
$528$		0			0
$529$	4651.53	+	8056.69i	0.382307	+	0.662175i
$530$	−335.258	+	580.685i	−0.0274768	+	0.0475912i
$531$		0			0
$532$	−18020.2	+	4229.77i	−1.46856	+	0.344706i
$533$	12684.3			1.03080
$534$		0			0
$535$	187.851	+	325.368i	0.0151804	+	0.0262932i
$536$	14730.9	+	25514.7i	1.18709	+	2.05610i
$537$		0			0
$538$	32162.2			2.57735
$539$	16195.8	+	10752.7i	1.29425	+	0.859278i
$540$		0			0
$541$	−5937.49	+	10284.0i	−0.471853	+	0.817274i	−0.999481	−	0.0322016i	$-0.989748\pi$
$541$	−5937.49	+	10284.0i	−0.471853	+	0.817274i	0.527628	+	0.849475i	$0.323081\pi$
$542$	−15920.5	−	27575.0i	−1.26170	−	2.18533i
$543$		0			0
$544$	6086.02	−	10541.3i	0.479661	−	0.830798i
$545$	414.673			0.0325920
$546$		0			0
$547$	25018.5			1.95560			0.977802	−	0.209532i	$-0.0671939\pi$
$547$	25018.5			1.95560			0.977802	+	0.209532i	$0.0671939\pi$
$548$	8468.09	−	14667.2i	0.660107	−	1.14334i
$549$		0			0
$550$	−3686.58	−	6385.35i	−0.285812	−	0.495040i
$551$	1300.21	−	2252.02i	0.100528	−	0.174119i
$552$		0			0
$553$	−4958.62	+	16433.7i	−0.381306	+	1.26371i
$554$	−17145.1			−1.31485
$555$		0			0
$556$	22275.6	+	38582.5i	1.69909	+	2.94292i
$557$	−1976.09	−	3422.69i	−0.150323	−	0.260366i	0.781023	−	0.624502i	$-0.214698\pi$
$557$	−1976.09	−	3422.69i	−0.150323	−	0.260366i	−0.931346	+	0.364135i	$0.881365\pi$
$558$		0			0
$559$	15893.4			1.20254
$560$	9341.35	+	9944.20i	0.704900	+	0.750391i
$561$		0			0
$562$	11980.1	−	20750.2i	0.899201	−	1.55746i
$563$	159.733	+	276.666i	0.0119573	+	0.0207106i	0.871942	−	0.489609i	$-0.162860\pi$
$563$	159.733	+	276.666i	0.0119573	+	0.0207106i	−0.859985	+	0.510320i	$0.829527\pi$
$564$		0			0
$565$	1786.50	−	3094.32i	0.133024	−	0.230405i
$566$	6346.09			0.471283
$567$		0			0
$568$	7775.10			0.574359
$569$	−12125.5	+	21001.9i	−0.893366	+	1.54736i	−0.0575529	+	0.998342i	$0.518330\pi$
$569$	−12125.5	+	21001.9i	−0.893366	+	1.54736i	−0.835813	+	0.549014i	$0.815004\pi$
$570$		0			0
$571$	1413.73	+	2448.66i	0.103613	+	0.179463i	0.913171	−	0.407578i	$-0.133626\pi$
$571$	1413.73	+	2448.66i	0.103613	+	0.179463i	−0.809558	+	0.587040i	$0.800293\pi$
$572$	−23479.6	+	40667.9i	−1.71632	+	2.97274i
$573$		0			0
$574$	8130.88	−	26947.0i	0.591248	−	1.95949i
$575$	1337.89			0.0970332
$576$		0			0
$577$	−9130.11	−	15813.8i	−0.658738	−	1.14097i	−0.980943	−	0.194297i	$-0.937757\pi$
$577$	−9130.11	−	15813.8i	−0.658738	−	1.14097i	0.322205	−	0.946670i	$-0.395576\pi$
$578$	−8653.31	−	14988.0i	−0.622717	−	1.07858i
$579$		0			0
$580$	−4734.85			−0.338973
$581$	5343.65	−	1254.28i	0.381570	−	0.0895636i
$582$		0			0
$583$	−730.318	+	1264.95i	−0.0518811	+	0.0898607i
$584$	11800.2	+	20438.6i	0.836123	+	1.44821i
$585$		0			0
$586$	21945.8	−	38011.2i	1.54705	−	2.67957i
$587$	−7749.13			−0.544873			−0.272437	−	0.962174i	$-0.587830\pi$
$587$	−7749.13			−0.544873			−0.272437	+	0.962174i	$0.587830\pi$
$588$		0			0
$589$	−3865.50			−0.270416
$590$	−4899.22	+	8485.70i	−0.341861	+	0.592120i
$591$		0			0
$592$	22622.1	+	39182.6i	1.57054	+	2.72026i
$593$	−317.332	+	549.634i	−0.0219751	+	0.0380620i	−0.876804	−	0.480848i	$-0.840329\pi$
$593$	−317.332	+	549.634i	−0.0219751	+	0.0380620i	0.854829	+	0.518910i	$0.173662\pi$
$594$		0			0
$595$	−3591.50	+	843.011i	−0.247458	+	0.0580842i
$596$	45845.1			3.15082
$597$		0			0
$598$	−6047.07	−	10473.8i	−0.413517	−	0.716232i
$599$	4318.74	+	7480.27i	0.294589	+	0.510243i	0.974889	−	0.222690i	$-0.0714839\pi$
$599$	4318.74	+	7480.27i	0.294589	+	0.510243i	−0.680300	+	0.732934i	$0.738151\pi$
$600$		0			0
$601$	−19947.7			−1.35388			−0.676941	−	0.736037i	$-0.736695\pi$
$601$	−19947.7			−1.35388			−0.676941	+	0.736037i	$0.736695\pi$
$602$	10188.0	−	33764.6i	0.689752	−	2.28595i
$603$		0			0
$604$	−11774.5	+	20394.1i	−0.793210	+	1.37388i
$605$	−4703.25	−	8146.28i	−0.316057	−	0.547427i
$606$		0			0
$607$	−618.585	+	1071.42i	−0.0413634	+	0.0716435i	−0.885966	−	0.463750i	$-0.846503\pi$
$607$	−618.585	+	1071.42i	−0.0413634	+	0.0716435i	0.844603	+	0.535394i	$0.179837\pi$
$608$	−16006.3			−1.06766
$609$		0			0
$610$	−16458.4			−1.09243
$611$	9607.78	−	16641.2i	0.636152	−	1.10185i
$612$		0			0
$613$	−8763.81	−	15179.4i	−0.577434	−	1.00014i	−0.995773	−	0.0918535i	$-0.970721\pi$
$613$	−8763.81	−	15179.4i	−0.577434	−	1.00014i	0.418339	−	0.908291i	$-0.362612\pi$
$614$	2202.55	−	3814.94i	0.144768	−	0.250746i
$615$		0			0
$616$	41427.7	+	44101.3i	2.70969	+	2.88457i
$617$	−18508.3			−1.20764			−0.603821	−	0.797120i	$-0.706356\pi$
$617$	−18508.3			−1.20764			−0.603821	+	0.797120i	$0.706356\pi$
$618$		0			0
$619$	3014.92	+	5221.99i	0.195767	+	0.339079i	0.947152	−	0.320786i	$-0.103947\pi$
$619$	3014.92	+	5221.99i	0.195767	+	0.339079i	−0.751385	+	0.659865i	$0.770614\pi$
$620$	3519.17	+	6095.38i	0.227957	+	0.394833i
$621$		0			0
$622$	10207.4			0.658003
$623$	−2614.97	+	8666.43i	−0.168165	+	0.557325i
$624$		0			0
$625$	−312.500	+	541.266i	−0.0200000	+	0.0346410i
$626$	16989.7	+	29427.1i	1.08474	+	1.87882i
$627$		0			0
$628$	−13664.3	+	23667.2i	−0.868256	+	1.50386i
$629$	−12233.6			−0.775495
$630$		0			0
$631$	5728.80			0.361426			0.180713	−	0.983536i	$-0.442160\pi$
$631$	5728.80			0.361426			0.180713	+	0.983536i	$0.442160\pi$
$632$	−26713.7	+	46269.5i	−1.68135	+	2.91218i
$633$		0			0
$634$	20009.3	+	34657.1i	1.25342	+	2.17099i
$635$	−4704.14	+	8147.82i	−0.293982	+	0.509191i
$636$		0			0
$637$	−13340.7	+	6627.91i	−0.829790	+	0.412256i
$638$	−14639.4			−0.908434
$639$		0			0
$640$	−761.559	−	1319.06i	−0.0470364	−	0.0814694i
$641$	−937.912	−	1624.51i	−0.0577930	−	0.100100i	0.835681	−	0.549214i	$-0.185073\pi$
$641$	−937.912	−	1624.51i	−0.0577930	−	0.100100i	−0.893474	+	0.449114i	$0.851740\pi$
$642$		0			0
$643$	−20619.9			−1.26465			−0.632325	−	0.774703i	$-0.717899\pi$
$643$	−20619.9			−1.26465			−0.632325	+	0.774703i	$0.717899\pi$
$644$	−18408.1	+	4320.82i	−1.12637	+	0.264386i
$645$		0			0
$646$	5430.16	−	9405.31i	0.330723	−	0.572828i
$647$	−5763.57	−	9982.80i	−0.350216	−	0.606591i	0.636072	−	0.771630i	$-0.280558\pi$
$647$	−5763.57	−	9982.80i	−0.350216	−	0.606591i	−0.986287	+	0.165039i	$0.947225\pi$
$648$		0			0
$649$	−10672.3	+	18485.0i	−0.645494	+	1.11803i
$650$	5649.80			0.340928
$651$		0			0
$652$	−16422.6			−0.986443
$653$	−2258.11	+	3911.15i	−0.135324	+	0.234388i	−0.925721	−	0.378207i	$-0.876541\pi$
$653$	−2258.11	+	3911.15i	−0.135324	+	0.234388i	0.790397	+	0.612595i	$0.209874\pi$
$654$		0			0
$655$	459.772	+	796.348i	0.0274271	+	0.0475052i
$656$	21516.0	−	37266.7i	1.28057	−	2.21802i
$657$		0			0
$658$	−29194.4	−	31078.5i	−1.72966	−	1.84129i
$659$	27663.5			1.63523			0.817615	−	0.575766i	$-0.195296\pi$
$659$	27663.5			1.63523			0.817615	+	0.575766i	$0.195296\pi$
$660$		0			0
$661$	15755.4	+	27289.2i	0.927103	+	1.60579i	0.788144	+	0.615491i	$0.211042\pi$
$661$	15755.4	+	27289.2i	0.927103	+	1.60579i	0.138959	+	0.990298i	$0.455624\pi$
$662$	16980.1	+	29410.4i	0.996905	+	1.72669i
$663$		0			0
$664$	17084.1			0.998482
$665$	3321.46	+	3535.82i	0.193685	+	0.206185i
$666$		0			0
$667$	1328.20	−	2300.51i	0.0771035	−	0.133547i
$668$	−12846.6	−	22251.0i	−0.744089	−	1.28880i
$669$		0			0
$670$	6648.91	−	11516.2i	0.383387	−	0.664047i
$671$	−35852.5			−2.06270
$672$		0			0
$673$	−9072.58			−0.519647			−0.259823	−	0.965656i	$-0.583664\pi$
$673$	−9072.58			−0.519647			−0.259823	+	0.965656i	$0.583664\pi$
$674$	3167.86	−	5486.90i	0.181041	−	0.313572i
$675$		0			0
$676$	2965.26	+	5135.97i	0.168710	+	0.292215i
$677$	−12498.9	+	21648.6i	−0.709557	+	1.22899i	0.255465	+	0.966818i	$0.417771\pi$
$677$	−12498.9	+	21648.6i	−0.709557	+	1.22899i	−0.965022	+	0.262170i	$0.915562\pi$
$678$		0			0
$679$	8580.71	−	2014.10i	0.484974	−	0.113835i
$680$	−11482.3			−0.647541
$681$		0			0
$682$	10880.7	+	18846.0i	0.610916	+	1.05814i
$683$	−6630.90	−	11485.0i	−0.371485	−	0.643431i	0.618309	−	0.785935i	$-0.287818\pi$
$683$	−6630.90	−	11485.0i	−0.371485	−	0.643431i	−0.989794	+	0.142504i	$0.954485\pi$
$684$		0			0
$685$	−4438.74			−0.247585
$686$	5528.98	+	32590.1i	0.307722	+	1.81384i
$687$		0			0
$688$	26959.5	−	46695.2i	1.49392	−	2.58755i
$689$	−559.617	−	969.284i	−0.0309430	−	0.0535948i
$690$		0			0
$691$	12321.8	−	21341.9i	0.678353	−	1.17494i	−0.297123	−	0.954839i	$-0.596027\pi$
$691$	12321.8	−	21341.9i	0.678353	−	1.17494i	0.975477	−	0.220103i	$-0.0706395\pi$
$692$	49802.2			2.73583
$693$		0			0
$694$	−43862.8			−2.39915
$695$	5838.13	−	10111.9i	0.318637	−	0.551896i
$696$		0			0
$697$	5817.73	+	10076.6i	0.316158	+	0.547602i
$698$	−352.919	+	611.274i	−0.0191378	+	0.0331476i
$699$		0			0
$700$	2551.64	−	8456.52i	0.137775	−	0.456609i
$701$	−20723.2			−1.11656			−0.558278	−	0.829654i	$-0.688538\pi$
$701$	−20723.2			−1.11656			−0.558278	+	0.829654i	$0.688538\pi$
$702$		0			0
$703$	8043.63	+	13932.0i	0.431538	+	0.747446i
$704$	11652.3	+	20182.4i	0.623813	+	1.08048i
$705$		0			0
$706$	12094.0			0.644705
$707$	−983.744	−	1047.23i	−0.0523303	−	0.0557075i
$708$		0			0
$709$	−12967.9	+	22461.0i	−0.686910	+	1.18976i	0.285923	+	0.958253i	$0.407700\pi$
$709$	−12967.9	+	22461.0i	−0.686910	+	1.18976i	−0.972833	+	0.231510i	$0.925633\pi$
$710$	−1754.67	−	3039.18i	−0.0927489	−	0.160646i
$711$		0			0
$712$	−14087.7	+	24400.6i	−0.741515	+	1.28434i
$713$	−3948.72			−0.207406
$714$		0			0
$715$	12307.4			0.643733
$716$	12881.7	−	22311.8i	0.672363	−	1.16457i
$717$		0			0
$718$	13860.6	+	24007.3i	0.720438	+	1.24784i
$719$	−6826.85	+	11824.4i	−0.354101	+	0.613320i	−0.986964	−	0.160943i	$-0.948546\pi$
$719$	−6826.85	+	11824.4i	−0.354101	+	0.613320i	0.632863	+	0.774264i	$0.281880\pi$
$720$		0			0
$721$	6087.07	−	20173.5i	0.314416	−	1.04203i
$722$	21410.3			1.10361
$723$		0			0
$724$	−27153.3	−	47031.0i	−1.39385	−	2.41422i
$725$	620.470	+	1074.69i	0.0317844	+	0.0550521i
$726$		0			0
$727$	17709.4			0.903448			0.451724	−	0.892158i	$-0.350809\pi$
$727$	17709.4			0.903448			0.451724	+	0.892158i	$0.350809\pi$
$728$	−45138.1	+	10595.0i	−2.29798	+	0.539391i
$729$		0			0
$730$	5326.11	−	9225.09i	0.270038	−	0.467720i
$731$	7289.61	+	12626.0i	0.368832	+	0.638835i
$732$		0			0
$733$	−5936.73	+	10282.7i	−0.299152	+	0.518146i	−0.975942	−	0.218030i	$-0.930037\pi$
$733$	−5936.73	+	10282.7i	−0.299152	+	0.518146i	0.676790	+	0.736176i	$0.263370\pi$
$734$	37942.9			1.90803
$735$		0			0
$736$	−16350.8			−0.818886
$737$	14483.8	−	25086.7i	0.723904	−	1.25384i
$738$		0			0
$739$	−15651.4	−	27109.0i	−0.779087	−	1.34942i	−0.932469	−	0.361250i	$-0.882350\pi$
$739$	−15651.4	−	27109.0i	−0.779087	−	1.34942i	0.153382	−	0.988167i	$-0.450983\pi$
$740$	14645.9	−	25367.5i	0.727560	−	1.26017i
$741$		0			0
$742$	−2417.91	+	567.542i	−0.119629	+	0.0280797i
$743$	10385.8			0.512808			0.256404	−	0.966570i	$-0.417462\pi$
$743$	10385.8			0.512808			0.256404	+	0.966570i	$0.417462\pi$
$744$		0			0
$745$	−6007.69	−	10405.6i	−0.295442	−	0.511721i
$746$	−4322.92	−	7487.51i	−0.212163	−	0.367476i
$747$		0			0
$748$	−43076.4			−2.10565
$749$	−402.000	+	1332.29i	−0.0196112	+	0.0649946i
$750$		0			0
$751$	−8285.63	+	14351.1i	−0.402593	+	0.697311i	−0.994038	−	0.109034i	$-0.965224\pi$
$751$	−8285.63	+	14351.1i	−0.402593	+	0.697311i	0.591445	+	0.806345i	$0.298558\pi$
$752$	−32594.8	−	56455.8i	−1.58060	−	2.73768i
$753$		0			0
$754$	5608.84	−	9714.80i	0.270905	−	0.469220i
$755$	6171.88			0.297507
$756$		0			0
$757$	16463.8			0.790473			0.395236	−	0.918579i	$-0.370663\pi$
$757$	16463.8			0.790473			0.395236	+	0.918579i	$0.370663\pi$
$758$	1066.27	−	1846.84i	0.0510934	−	0.0884964i
$759$		0			0
$760$	7549.66	+	13076.4i	0.360335	+	0.624119i
$761$	8210.95	−	14221.8i	0.391126	−	0.677449i	−0.601473	−	0.798893i	$-0.705419\pi$
$761$	8210.95	−	14221.8i	0.391126	−	0.677449i	0.992598	+	0.121444i	$0.0387525\pi$
$762$		0			0
$763$	1051.63	+	1119.50i	0.0498973	+	0.0531174i
$764$	−80193.0			−3.79749
$765$		0			0
$766$	28466.9	+	49306.0i	1.34275	+	2.32572i
$767$	−8177.83	−	14164.4i	−0.384986	−	0.666815i
$768$		0			0
$769$	17603.4			0.825479			0.412739	−	0.910849i	$-0.364572\pi$
$769$	17603.4			0.825479			0.412739	+	0.910849i	$0.364572\pi$
$770$	7889.27	−	26146.3i	0.369233	−	1.22370i
$771$		0			0
$772$	−1321.94	+	2289.66i	−0.0616290	+	0.106744i
$773$	7954.16	+	13777.0i	0.370105	+	0.641041i	0.989581	−	0.143975i	$-0.0459883\pi$
$773$	7954.16	+	13777.0i	0.370105	+	0.641041i	−0.619476	+	0.785015i	$0.712655\pi$
$774$		0			0
$775$	922.326	−	1597.51i	0.0427496	−	0.0740444i
$776$	27433.3			1.26907
$777$		0			0
$778$	−32454.0			−1.49554
$779$	7650.34	−	13250.8i	0.351864	−	0.609446i
$780$		0			0
$781$	−3822.34	−	6620.48i	−0.175127	−	0.303328i
$782$	5547.06	−	9607.79i	0.253660	−	0.439353i
$783$		0			0
$784$	−3156.39	+	50437.9i	−0.143786	+	2.29765i
$785$	7162.44			0.325654
$786$		0			0
$787$	−9494.43	−	16444.8i	−0.430038	−	0.744847i	0.566838	−	0.823829i	$-0.308166\pi$
$787$	−9494.43	−	16444.8i	−0.430038	−	0.744847i	−0.996876	+	0.0789818i	$0.974833\pi$
$788$	14057.9	+	24349.0i	0.635524	+	1.10076i
$789$		0			0
$790$	24114.8			1.08603
$791$	12884.4	−	3024.28i	0.579163	−	0.135943i
$792$		0			0
$793$	13736.3	−	23791.9i	0.615119	−	1.06542i
$794$	−29785.1	−	51589.2i	−1.33128	−	2.30584i
$795$		0			0
$796$	34431.4	−	59637.0i	1.53315	−	2.65550i
$797$	33731.8			1.49917			0.749586	−	0.661906i	$-0.230252\pi$
$797$	33731.8			1.49917			0.749586	+	0.661906i	$0.230252\pi$
$798$		0			0
$799$	17626.7			0.780460
$800$	3819.16	−	6614.99i	0.168785	−	0.292344i
$801$		0			0
$802$	24023.8	+	41610.4i	1.05774	+	1.83206i
$803$	11602.2	−	20095.7i	0.509881	−	0.883140i
$804$		0			0
$805$	3392.97	+	3611.93i	0.148554	+	0.158142i
$806$	−16675.0			−0.728726
$807$		0			0
$808$	−2236.04	−	3872.94i	−0.0973561	−	0.168626i
$809$	13321.8	+	23074.1i	0.578950	+	1.00277i	0.995600	+	0.0937039i	$0.0298707\pi$
$809$	13321.8	+	23074.1i	0.578950	+	1.00277i	−0.416650	+	0.909067i	$0.636796\pi$
$810$		0			0
$811$	15678.2			0.678835			0.339418	−	0.940636i	$-0.389770\pi$
$811$	15678.2			0.678835			0.339418	+	0.940636i	$0.389770\pi$
$812$	−12007.8	−	12782.8i	−0.518955	−	0.552447i
$813$		0			0
$814$	45282.9	−	78432.3i	1.94983	−	3.37721i
$815$	2152.07	+	3727.50i	0.0924955	+	0.160207i
$816$		0			0
$817$	9585.86	−	16603.2i	0.410486	−	0.710982i
$818$	23078.8			0.986469
$819$		0			0
$820$	−27859.6			−1.18646
$821$	−5066.92	+	8776.17i	−0.215392	+	0.373070i	−0.953394	−	0.301729i	$-0.902436\pi$
$821$	−5066.92	+	8776.17i	−0.215392	+	0.373070i	0.738002	+	0.674799i	$0.235770\pi$
$822$		0			0
$823$	7031.33	+	12178.6i	0.297809	+	0.515820i	0.975634	−	0.219403i	$-0.0704109\pi$
$823$	7031.33	+	12178.6i	0.297809	+	0.515820i	−0.677826	+	0.735223i	$0.737078\pi$
$824$	32793.0	−	56799.1i	1.38640	−	2.40132i
$825$		0			0
$826$	−35333.6	+	8293.64i	−1.48839	+	0.349362i
$827$	13697.4			0.575942			0.287971	−	0.957639i	$-0.407019\pi$
$827$	13697.4			0.575942			0.287971	+	0.957639i	$0.407019\pi$
$828$		0			0
$829$	−8777.47	−	15203.0i	−0.367737	−	0.636940i	0.621474	−	0.783435i	$-0.286534\pi$
$829$	−8777.47	−	15203.0i	−0.367737	−	0.636940i	−0.989211	+	0.146495i	$0.953201\pi$
$830$	−3855.52	−	6677.96i	−0.161237	−	0.279271i
$831$		0			0
$832$	−17857.6			−0.744110
$833$	−11384.1	−	7558.11i	−0.473513	−	0.314373i
$834$		0			0
$835$	−3366.92	+	5831.68i	−0.139542	+	0.241693i
$836$	28322.8	+	49056.5i	1.17173	+	2.02949i
$837$		0			0
$838$	16740.7	−	28995.7i	0.690091	−	1.19527i
$839$	−1415.03			−0.0582268			−0.0291134	−	0.999576i	$-0.509268\pi$
$839$	−1415.03			−0.0582268			−0.0291134	+	0.999576i	$0.509268\pi$
$840$		0			0
$841$	−21925.1			−0.898975
$842$	−24567.6	+	42552.4i	−1.00553	+	1.74163i
$843$		0			0
$844$	−16998.2	−	29441.8i	−0.693250	−	1.20074i
$845$	777.152	−	1346.07i	0.0316389	−	0.0548001i
$846$		0			0
$847$	10064.9	−	33356.8i	0.408306	−	1.35319i
$848$	−3797.05			−0.153763
$849$		0			0
$850$	2591.32	+	4488.30i	0.104566	+	0.181114i
$851$	8216.79	+	14231.9i	0.330985	+	0.573282i
$852$		0			0
$853$	−16014.1			−0.642804			−0.321402	−	0.946943i	$-0.604154\pi$
$853$	−16014.1			−0.642804			−0.321402	+	0.946943i	$0.604154\pi$
$854$	−41739.3	−	44433.0i	−1.67247	−	1.78040i
$855$		0			0
$856$	−2165.71	+	3751.11i	−0.0864746	+	0.149778i
$857$	21748.7	+	37669.9i	0.866886	+	1.50149i	0.865162	+	0.501492i	$0.167215\pi$
$857$	21748.7	+	37669.9i	0.866886	+	1.50149i	0.00172420	+	0.999999i	$0.499451\pi$
$858$		0			0
$859$	−12639.3	+	21891.9i	−0.502034	+	0.869548i	0.497963	+	0.867198i	$0.334081\pi$
$859$	−12639.3	+	21891.9i	−0.502034	+	0.869548i	−0.999997	+	0.00235021i	$0.999252\pi$
$860$	−34908.0			−1.38413
$861$		0			0
$862$	−11662.4			−0.460814
$863$	−7703.88	+	13343.5i	−0.303874	+	0.526325i	−0.977010	−	0.213194i	$-0.931613\pi$
$863$	−7703.88	+	13343.5i	−0.303874	+	0.526325i	0.673136	+	0.739519i	$0.264947\pi$
$864$		0			0
$865$	−6526.23	−	11303.8i	−0.256530	−	0.444323i
$866$	−36896.7	+	63906.9i	−1.44781	+	2.50767i
$867$		0			0
$868$	−7531.01	+	24958.9i	−0.294492	+	0.975993i
$869$	52531.1			2.05063
$870$		0			0
$871$	11098.4	+	19223.0i	0.431752	+	0.747816i
$872$	2390.35	+	4140.21i	0.0928297	+	0.160786i
$873$		0			0
$874$	−14588.8			−0.564615
$875$	−2253.78	+	529.016i	−0.0870761	+	0.0204388i
$876$		0			0
$877$	−16394.3	+	28395.7i	−0.631238	+	1.09334i	0.356061	+	0.934463i	$0.384120\pi$
$877$	−16394.3	+	28395.7i	−0.631238	+	1.09334i	−0.987299	+	0.158874i	$0.949214\pi$
$878$	22616.6	+	39173.1i	0.869333	+	1.50573i
$879$		0			0
$880$	20876.6	−	36159.4i	0.799717	−	1.38515i
$881$	30457.9			1.16476			0.582379	−	0.812918i	$-0.302122\pi$
$881$	30457.9			1.16476			0.582379	+	0.812918i	$0.302122\pi$
$882$		0			0
$883$	37997.3			1.44814			0.724071	−	0.689725i	$-0.242269\pi$
$883$	37997.3			1.44814			0.724071	+	0.689725i	$0.242269\pi$
$884$	16503.9	−	28585.7i	0.627927	−	1.08760i
$885$		0			0
$886$	24440.6	+	42332.4i	0.926749	+	1.60518i
$887$	2.79803	−	4.84633i	0.000105917	−	0.000183454i	−0.865972	−	0.500092i	$-0.833300\pi$
$887$	2.79803	−	4.84633i	0.000105917	−	0.000183454i	0.866078	+	0.499908i	$0.166633\pi$
$888$		0			0
$889$	−33926.7	+	7963.41i	−1.27994	+	0.300432i
$890$	12717.2			0.478967
$891$		0			0
$892$	−50159.5	−	86878.8i	−1.88281	−	3.26112i
$893$	−11589.6	−	20073.8i	−0.434301	−	0.752231i
$894$		0			0
$895$	−6752.24			−0.252181
$896$	1629.73	−	5401.19i	0.0607651	−	0.201385i
$897$		0			0
$898$	−24748.1	+	42864.9i	−0.919659	+	1.59290i
$899$	−1831.28	−	3171.87i	−0.0679384	−	0.117673i
$900$		0			0
$901$	513.344	−	889.138i	0.0189811	−	0.0328762i
$902$	−86137.6			−3.17968
$903$		0			0
$904$	41192.6			1.51554
$905$	−7116.51	+	12326.2i	−0.261393	+	0.452746i
$906$		0			0
$907$	3861.66	+	6688.58i	0.141372	+	0.244863i	0.928013	−	0.372547i	$-0.121515\pi$
$907$	3861.66	+	6688.58i	0.141372	+	0.244863i	−0.786642	+	0.617410i	$0.788182\pi$
$908$	−63985.2	+	110826.i	−2.33857	+	4.05053i
$909$		0			0
$910$	14328.2	+	15252.8i	0.521949	+	0.555634i
$911$	−6805.43			−0.247502			−0.123751	−	0.992313i	$-0.539492\pi$
$911$	−6805.43			−0.247502			−0.123751	+	0.992313i	$0.539492\pi$
$912$		0			0
$913$	−8398.76	−	14547.1i	−0.304445	−	0.527314i
$914$	−3557.23	−	6161.30i	−0.128734	−	0.222974i
$915$		0			0
$916$	22898.0			0.825953
$917$	−983.909	+	3260.83i	−0.0354324	+	0.117429i
$918$		0			0
$919$	22590.1	−	39127.2i	0.810858	−	1.40445i	−0.101406	−	0.994845i	$-0.532334\pi$
$919$	22590.1	−	39127.2i	0.810858	−	1.40445i	0.912264	−	0.409602i	$-0.134333\pi$
$920$	7712.19	+	13357.9i	0.276373	+	0.478692i
$921$		0			0
$922$	−22793.4	+	39479.4i	−0.814167	+	1.41018i
$923$	5857.84			0.208898
$924$		0			0
$925$	−7676.98			−0.272884
$926$	26948.1	−	46675.4i	0.956337	−	1.65643i
$927$		0			0
$928$	−7582.96	−	13134.1i	−0.268236	−	0.464598i
$929$	2596.11	−	4496.59i	0.0916852	−	0.158803i	−0.816535	−	0.577296i	$-0.804108\pi$
$929$	2596.11	−	4496.59i	0.0916852	−	0.158803i	0.908220	+	0.418492i	$0.137441\pi$
$930$		0			0
$931$	−1122.31	+	17934.0i	−0.0395081	+	0.631325i
$932$	−121171.			−4.25866
$933$		0			0
$934$	22114.7	+	38303.8i	0.774749	+	1.34191i
$935$	5644.86	+	9777.18i	0.197440	+	0.341976i
$936$		0			0
$937$	−7107.58			−0.247806			−0.123903	−	0.992294i	$-0.539541\pi$
$937$	−7107.58			−0.247806			−0.123903	+	0.992294i	$0.539541\pi$
$938$	47952.5	−	11255.6i	1.66920	−	0.391800i
$939$		0			0
$940$	−21102.4	+	36550.5i	−0.732218	+	1.26824i
$941$	−21831.5	−	37813.3i	−0.756309	−	1.30997i	−0.944721	−	0.327876i	$-0.893667\pi$
$941$	−21831.5	−	37813.3i	−0.756309	−	1.30997i	0.188411	−	0.982090i	$-0.439666\pi$
$942$		0			0
$943$	7815.03	−	13536.0i	0.269875	−	0.467438i
$944$	−55487.2			−1.91309
$945$		0			0
$946$	−107930.			−3.70943
$947$	7721.04	−	13373.2i	0.264942	−	0.458893i	−0.702606	−	0.711579i	$-0.747980\pi$
$947$	7721.04	−	13373.2i	0.264942	−	0.458893i	0.967548	+	0.252686i	$0.0813138\pi$
$948$		0			0
$949$	8890.39	+	15398.6i	0.304104	+	0.526723i
$950$	3407.59	−	5902.12i	0.116376	−	0.201569i
$951$		0			0
$952$	−29119.8	−	30999.0i	−0.991363	−	1.05534i
$953$	−44561.5			−1.51468			−0.757339	−	0.653022i	$-0.773501\pi$
$953$	−44561.5			−1.51468			−0.757339	+	0.653022i	$0.773501\pi$
$954$		0			0
$955$	10508.7	+	18201.7i	0.356078	+	0.616746i
$956$	−28652.1	−	49627.0i	−0.969327	−	1.67892i
$957$		0			0
$958$	−3762.08			−0.126876
$959$	−11256.8	−	11983.3i	−0.379043	−	0.403505i
$960$		0			0
$961$	12173.3	−	21084.8i	0.408624	−	0.707757i
$962$	34698.7	+	60099.9i	1.16292	+	2.01424i
$963$		0			0
$964$	−54298.2	+	94047.2i	−1.81414	+	3.14218i
$965$	692.923			0.0231150
$966$		0			0
$967$	−34733.3			−1.15506			−0.577532	−	0.816368i	$-0.695984\pi$
$967$	−34733.3			−1.15506			−0.577532	+	0.816368i	$0.695984\pi$
$968$	54223.1	−	93917.1i	1.80041	−	3.11840i
$969$		0			0
$970$	−6191.10	−	10723.3i	−0.204932	−	0.354953i
$971$	−8855.15	+	15337.6i	−0.292662	+	0.506906i	−0.974438	−	0.224655i	$-0.927875\pi$
$971$	−8855.15	+	15337.6i	−0.292662	+	0.506906i	0.681776	+	0.731561i	$0.261208\pi$
$972$		0			0
$973$	42105.1	−	9883.08i	1.38729	−	0.325629i
$974$	−12006.4			−0.394979
$975$		0			0
$976$	−46600.8	−	80715.0i	−1.52834	−	2.64716i
$977$	−28778.7	−	49846.2i	−0.942387	−	1.63226i	−0.760900	−	0.648870i	$-0.775242\pi$
$977$	−28778.7	−	49846.2i	−0.942387	−	1.63226i	−0.181488	−	0.983393i	$-0.558091\pi$
$978$		0			0
$979$	27702.7			0.904375
$980$	29301.3	−	14557.5i	0.955097	−	0.474511i
$981$		0			0
$982$	22554.5	−	39065.5i	0.732936	−	1.26948i
$983$	−12494.4	−	21640.9i	−0.405401	−	0.702175i	0.588967	−	0.808157i	$-0.299535\pi$
$983$	−12494.4	−	21640.9i	−0.405401	−	0.702175i	−0.994368	+	0.105982i	$0.966202\pi$
$984$		0			0
$985$	3684.39	−	6381.55i	0.119182	−	0.206429i
$986$	10290.1			0.332358
$987$		0			0
$988$	−43405.5			−1.39769
$989$	9792.23	−	16960.6i	0.314838	−	0.545315i
$990$		0			0
$991$	−30786.6	−	53324.0i	−0.986850	−	1.70927i	−0.633407	−	0.773819i	$-0.718344\pi$
$991$	−30786.6	−	53324.0i	−0.986850	−	1.70927i	−0.353443	−	0.935456i	$-0.614989\pi$
$992$	−11272.0	+	19523.7i	−0.360774	+	0.624879i
$993$		0			0
$994$	3754.99	−	12444.6i	0.119820	−	0.397103i
$995$	−18048.0			−0.575035
$996$		0			0
$997$	4696.60	+	8134.74i	0.149190	+	0.258405i	0.930928	−	0.365202i	$-0.119000\pi$
$997$	4696.60	+	8134.74i	0.149190	+	0.258405i	−0.781738	+	0.623607i	$0.785667\pi$
$998$	51832.6	+	89776.7i	1.64402	+	2.84753i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.4.j.g.226.5		10
3.2	odd	2		35.4.e.c.16.1	yes	10
7.2	even	3		2205.4.a.bu.1.1		5
7.4	even	3	inner	315.4.j.g.46.5		10
7.5	odd	6		2205.4.a.bt.1.1		5
12.11	even	2		560.4.q.n.401.4		10
15.2	even	4		175.4.k.d.149.1		20
15.8	even	4		175.4.k.d.149.10		20
15.14	odd	2		175.4.e.d.51.5		10
21.2	odd	6		245.4.a.m.1.5		5
21.5	even	6		245.4.a.n.1.5		5
21.11	odd	6		35.4.e.c.11.1	✓	10
21.17	even	6		245.4.e.o.116.1		10
21.20	even	2		245.4.e.o.226.1		10
84.11	even	6		560.4.q.n.81.4		10
105.32	even	12		175.4.k.d.74.10		20
105.44	odd	6		1225.4.a.bg.1.1		5
105.53	even	12		175.4.k.d.74.1		20
105.74	odd	6		175.4.e.d.151.5		10
105.89	even	6		1225.4.a.bf.1.1		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.4.e.c.11.1	✓	10	21.11	odd	6
35.4.e.c.16.1	yes	10	3.2	odd	2
175.4.e.d.51.5		10	15.14	odd	2
175.4.e.d.151.5		10	105.74	odd	6
175.4.k.d.74.1		20	105.53	even	12
175.4.k.d.74.10		20	105.32	even	12
175.4.k.d.149.1		20	15.2	even	4
175.4.k.d.149.10		20	15.8	even	4
245.4.a.m.1.5		5	21.2	odd	6
245.4.a.n.1.5		5	21.5	even	6
245.4.e.o.116.1		10	21.17	even	6
245.4.e.o.226.1		10	21.20	even	2
315.4.j.g.46.5		10	7.4	even	3	inner
315.4.j.g.226.5		10	1.1	even	1	trivial
560.4.q.n.81.4		10	84.11	even	6
560.4.q.n.401.4		10	12.11	even	2
1225.4.a.bf.1.1		5	105.89	even	6
1225.4.a.bg.1.1		5	105.44	odd	6
2205.4.a.bt.1.1		5	7.5	odd	6
2205.4.a.bu.1.1		5	7.2	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:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	315.j (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.60181 - 4.50647i) q^{2} +(-9.53885 - 16.5218i) q^{4} +(-2.50000 + 4.33013i) q^{5} +(-18.0302 + 4.23212i) q^{7} -57.6442 q^{8} +O(q^{10})\)	\(q+(2.60181 - 4.50647i) q^{2} +(-9.53885 - 16.5218i) q^{4} +(-2.50000 + 4.33013i) q^{5} +(-18.0302 + 4.23212i) q^{7} -57.6442 q^{8} +(13.0091 + 22.5324i) q^{10} +(28.3386 + 49.0839i) q^{11} -43.4297 q^{13} +(-27.8393 + 92.2639i) q^{14} +(-73.6685 + 127.598i) q^{16} +(-19.9193 - 34.5013i) q^{17} +(-26.1940 + 45.3693i) q^{19} +95.3885 q^{20} +294.927 q^{22} +(-26.7579 + 46.3460i) q^{23} +(-12.5000 - 21.6506i) q^{25} +(-112.996 + 195.715i) q^{26} +(241.910 + 257.522i) q^{28} -49.6376 q^{29} +(36.8930 + 63.9006i) q^{31} +(152.767 + 264.599i) q^{32} -207.305 q^{34} +(26.7499 - 88.6535i) q^{35} +(153.540 - 265.938i) q^{37} +(136.304 + 236.085i) q^{38} +(144.110 - 249.607i) q^{40} -292.064 q^{41} -365.956 q^{43} +(540.635 - 936.407i) q^{44} +(139.238 + 241.167i) q^{46} +(-221.226 + 383.175i) q^{47} +(307.178 - 152.612i) q^{49} -130.091 q^{50} +(414.269 + 717.536i) q^{52} +(12.8856 + 22.3185i) q^{53} -283.386 q^{55} +(1039.34 - 243.957i) q^{56} +(-129.148 + 223.690i) q^{58} +(188.300 + 326.146i) q^{59} +(-316.287 + 547.826i) q^{61} +383.955 q^{62} +411.183 q^{64} +(108.574 - 188.056i) q^{65} +(-255.549 - 442.624i) q^{67} +(-380.015 + 658.206i) q^{68} +(-329.916 - 351.207i) q^{70} -134.881 q^{71} +(-204.708 - 354.564i) q^{73} +(-798.962 - 1383.84i) q^{74} +999.443 q^{76} +(-718.680 - 765.061i) q^{77} +(463.424 - 802.674i) q^{79} +(-368.343 - 637.988i) q^{80} +(-759.897 + 1316.18i) q^{82} -296.372 q^{83} +199.193 q^{85} +(-952.150 + 1649.17i) q^{86} +(-1633.55 - 2829.40i) q^{88} +(244.391 - 423.297i) q^{89} +(783.047 - 183.800i) q^{91} +1020.96 q^{92} +(1151.18 + 1993.90i) q^{94} +(-130.970 - 226.847i) q^{95} -475.907 q^{97} +(111.477 - 1781.36i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + q^{2} - 35 q^{4} - 25 q^{5} - 62 q^{7} - 66 q^{8}+O(q^{10}) \) 10 * q + q^2 - 35 * q^4 - 25 * q^5 - 62 * q^7 - 66 * q^8	\( 10 q + q^{2} - 35 q^{4} - 25 q^{5} - 62 q^{7} - 66 q^{8} + 5 q^{10} + 47 q^{11} + 2 q^{13} - 7 q^{14} - 171 q^{16} - 2 q^{17} + 21 q^{19} + 350 q^{20} + 1046 q^{22} + 201 q^{23} - 125 q^{25} - 47 q^{26} + 597 q^{28} - 380 q^{29} - 388 q^{31} - 95 q^{32} + 260 q^{34} + 95 q^{35} + 145 q^{37} + 835 q^{38} + 165 q^{40} + 562 q^{41} + 1136 q^{43} + 1091 q^{44} - 337 q^{46} - 473 q^{47} + 998 q^{49} - 50 q^{50} + 379 q^{52} + 351 q^{53} - 470 q^{55} + 1338 q^{56} - 1818 q^{58} + 708 q^{59} - 1944 q^{61} - 896 q^{62} - 250 q^{64} - 5 q^{65} - 1118 q^{67} - 3118 q^{68} + 865 q^{70} - 1728 q^{71} + 1652 q^{73} - 3285 q^{74} + 1382 q^{76} - 787 q^{77} - 218 q^{79} - 855 q^{80} - 1027 q^{82} + 3004 q^{83} + 20 q^{85} - 4264 q^{86} - 2131 q^{88} + 2322 q^{89} + 524 q^{91} + 5914 q^{92} + 2677 q^{94} + 105 q^{95} + 1196 q^{97} - 2971 q^{98}+O(q^{100}) \) 10 * q + q^2 - 35 * q^4 - 25 * q^5 - 62 * q^7 - 66 * q^8 + 5 * q^10 + 47 * q^11 + 2 * q^13 - 7 * q^14 - 171 * q^16 - 2 * q^17 + 21 * q^19 + 350 * q^20 + 1046 * q^22 + 201 * q^23 - 125 * q^25 - 47 * q^26 + 597 * q^28 - 380 * q^29 - 388 * q^31 - 95 * q^32 + 260 * q^34 + 95 * q^35 + 145 * q^37 + 835 * q^38 + 165 * q^40 + 562 * q^41 + 1136 * q^43 + 1091 * q^44 - 337 * q^46 - 473 * q^47 + 998 * q^49 - 50 * q^50 + 379 * q^52 + 351 * q^53 - 470 * q^55 + 1338 * q^56 - 1818 * q^58 + 708 * q^59 - 1944 * q^61 - 896 * q^62 - 250 * q^64 - 5 * q^65 - 1118 * q^67 - 3118 * q^68 + 865 * q^70 - 1728 * q^71 + 1652 * q^73 - 3285 * q^74 + 1382 * q^76 - 787 * q^77 - 218 * q^79 - 855 * q^80 - 1027 * q^82 + 3004 * q^83 + 20 * q^85 - 4264 * q^86 - 2131 * q^88 + 2322 * q^89 + 524 * q^91 + 5914 * q^92 + 2677 * q^94 + 105 * q^95 + 1196 * q^97 - 2971 * q^98

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