LMFDB - Embedded newform 245.4.e.o.116.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [245,4,Mod(116,245)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(245, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([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("245.116");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 245 = 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	245.e (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$14.4554679514$
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:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 2^{4}\cdot 3 $
Twist minimal:	no (minimal twist has level 35)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			116.1
Root			$2.60181 - 4.50647i$ of defining polynomial
Character	$\chi$	$=$	245.116
Dual form			245.4.e.o.226.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.60181 - 4.50647i) q^{2} +(2.45326 - 4.24917i) q^{3} +(-9.53885 + 16.5218i) q^{4} +(-2.50000 - 4.33013i) q^{5} -25.5317 q^{6} +57.6442 q^{8} +(1.46305 + 2.53407i) q^{9} +O(q^{10})$	\(q+(-2.60181 - 4.50647i) q^{2} +(2.45326 - 4.24917i) q^{3} +(-9.53885 + 16.5218i) q^{4} +(-2.50000 - 4.33013i) q^{5} -25.5317 q^{6} +57.6442 q^{8} +(1.46305 + 2.53407i) q^{9} +(-13.0091 + 22.5324i) q^{10} +(-28.3386 + 49.0839i) q^{11} +(46.8025 + 81.0644i) q^{12} +43.4297 q^{13} -24.5326 q^{15} +(-73.6685 - 127.598i) q^{16} +(-19.9193 + 34.5013i) q^{17} +(7.61315 - 13.1864i) q^{18} +(26.1940 + 45.3693i) q^{19} +95.3885 q^{20} +294.927 q^{22} +(26.7579 + 46.3460i) q^{23} +(141.416 - 244.940i) q^{24} +(-12.5000 + 21.6506i) q^{25} +(-112.996 - 195.715i) q^{26} +146.833 q^{27} +49.6376 q^{29} +(63.8292 + 110.555i) q^{30} +(-36.8930 + 63.9006i) q^{31} +(-152.767 + 264.599i) q^{32} +(139.044 + 240.831i) q^{33} +207.305 q^{34} -55.8231 q^{36} +(153.540 + 265.938i) q^{37} +(136.304 - 236.085i) q^{38} +(106.544 - 184.540i) q^{39} +(-144.110 - 249.607i) q^{40} -292.064 q^{41} -365.956 q^{43} +(-540.635 - 936.407i) q^{44} +(7.31524 - 12.6704i) q^{45} +(139.238 - 241.167i) q^{46} +(-221.226 - 383.175i) q^{47} -722.912 q^{48} +130.091 q^{50} +(97.7346 + 169.281i) q^{51} +(-414.269 + 717.536i) q^{52} +(-12.8856 + 22.3185i) q^{53} +(-382.032 - 661.698i) q^{54} +283.386 q^{55} +257.043 q^{57} +(-129.148 - 223.690i) q^{58} +(188.300 - 326.146i) q^{59} +(234.013 - 405.322i) q^{60} +(316.287 + 547.826i) q^{61} +383.955 q^{62} +411.183 q^{64} +(-108.574 - 188.056i) q^{65} +(723.531 - 1253.19i) q^{66} +(-255.549 + 442.624i) q^{67} +(-380.015 - 658.206i) q^{68} +262.576 q^{69} +134.881 q^{71} +(84.3362 + 146.075i) q^{72} +(204.708 - 354.564i) q^{73} +(798.962 - 1383.84i) q^{74} +(61.3315 + 106.229i) q^{75} -999.443 q^{76} -1108.83 q^{78} +(463.424 + 802.674i) q^{79} +(-368.343 + 637.988i) q^{80} +(320.717 - 555.498i) q^{81} +(759.897 + 1316.18i) q^{82} -296.372 q^{83} +199.193 q^{85} +(952.150 + 1649.17i) q^{86} +(121.774 - 210.918i) q^{87} +(-1633.55 + 2829.40i) q^{88} +(244.391 + 423.297i) q^{89} -76.1315 q^{90} -1020.96 q^{92} +(181.016 + 313.529i) q^{93} +(-1151.18 + 1993.90i) q^{94} +(130.970 - 226.847i) q^{95} +(749.552 + 1298.26i) q^{96} +475.907 q^{97} -165.843 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - q^{2} - 8 q^{3} - 35 q^{4} - 25 q^{5} - 32 q^{6} + 66 q^{8} - 81 q^{9}+O(q^{10}) $ 10 * q - q^2 - 8 * q^3 - 35 * q^4 - 25 * q^5 - 32 * q^6 + 66 * q^8 - 81 * q^9	\( 10 q - q^{2} - 8 q^{3} - 35 q^{4} - 25 q^{5} - 32 q^{6} + 66 q^{8} - 81 q^{9} - 5 q^{10} - 47 q^{11} - 98 q^{12} - 2 q^{13} + 80 q^{15} - 171 q^{16} - 2 q^{17} + 51 q^{18} - 21 q^{19} + 350 q^{20} + 1046 q^{22} - 201 q^{23} + 848 q^{24} - 125 q^{25} - 47 q^{26} + 1036 q^{27} + 380 q^{29} + 80 q^{30} + 388 q^{31} + 95 q^{32} - 262 q^{33} - 260 q^{34} + 2458 q^{36} + 145 q^{37} + 835 q^{38} - 14 q^{39} - 165 q^{40} + 562 q^{41} + 1136 q^{43} - 1091 q^{44} - 405 q^{45} - 337 q^{46} - 473 q^{47} - 140 q^{48} + 50 q^{50} - 732 q^{51} - 379 q^{52} - 351 q^{53} - 774 q^{54} + 470 q^{55} + 1908 q^{57} - 1818 q^{58} + 708 q^{59} - 490 q^{60} + 1944 q^{61} - 896 q^{62} - 250 q^{64} + 5 q^{65} + 1482 q^{66} - 1118 q^{67} - 3118 q^{68} - 748 q^{69} + 1728 q^{71} + 2219 q^{72} - 1652 q^{73} + 3285 q^{74} - 200 q^{75} - 1382 q^{76} - 11148 q^{78} - 218 q^{79} - 855 q^{80} + 455 q^{81} + 1027 q^{82} + 3004 q^{83} + 20 q^{85} + 4264 q^{86} + 390 q^{87} - 2131 q^{88} + 2322 q^{89} - 510 q^{90} - 5914 q^{92} + 2288 q^{93} - 2677 q^{94} - 105 q^{95} + 4592 q^{96} - 1196 q^{97} + 70 q^{99}+O(q^{100}) \) 10 * q - q^2 - 8 * q^3 - 35 * q^4 - 25 * q^5 - 32 * q^6 + 66 * q^8 - 81 * q^9 - 5 * q^10 - 47 * q^11 - 98 * q^12 - 2 * q^13 + 80 * q^15 - 171 * q^16 - 2 * q^17 + 51 * q^18 - 21 * q^19 + 350 * q^20 + 1046 * q^22 - 201 * q^23 + 848 * q^24 - 125 * q^25 - 47 * q^26 + 1036 * q^27 + 380 * q^29 + 80 * q^30 + 388 * q^31 + 95 * q^32 - 262 * q^33 - 260 * q^34 + 2458 * q^36 + 145 * q^37 + 835 * q^38 - 14 * q^39 - 165 * q^40 + 562 * q^41 + 1136 * q^43 - 1091 * q^44 - 405 * q^45 - 337 * q^46 - 473 * q^47 - 140 * q^48 + 50 * q^50 - 732 * q^51 - 379 * q^52 - 351 * q^53 - 774 * q^54 + 470 * q^55 + 1908 * q^57 - 1818 * q^58 + 708 * q^59 - 490 * q^60 + 1944 * q^61 - 896 * q^62 - 250 * q^64 + 5 * q^65 + 1482 * q^66 - 1118 * q^67 - 3118 * q^68 - 748 * q^69 + 1728 * q^71 + 2219 * q^72 - 1652 * q^73 + 3285 * q^74 - 200 * q^75 - 1382 * q^76 - 11148 * q^78 - 218 * q^79 - 855 * q^80 + 455 * q^81 + 1027 * q^82 + 3004 * q^83 + 20 * q^85 + 4264 * q^86 + 390 * q^87 - 2131 * q^88 + 2322 * q^89 - 510 * q^90 - 5914 * q^92 + 2288 * q^93 - 2677 * q^94 - 105 * q^95 + 4592 * q^96 - 1196 * q^97 + 70 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/245\mathbb{Z}\right)^\times$.

$n$	$101$	$197$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	−2.60181	−	4.50647i	−0.919879	−	1.59328i	−0.799596	−	0.600538i	$-0.794953\pi$
$2$	−2.60181	−	4.50647i	−0.919879	−	1.59328i	−0.120283	−	0.992740i	$-0.538380\pi$
$3$	2.45326	−	4.24917i	0.472130	−	0.817753i	−0.527362	−	0.849641i	$-0.676819\pi$
$3$	2.45326	−	4.24917i	0.472130	−	0.817753i	0.999491	+	0.0318881i	$0.0101520\pi$
$4$	−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
$6$	−25.5317			−1.73721
$7$		0			0
$7$		0			0
$8$	57.6442			2.54754
$9$	1.46305	+	2.53407i	0.0541869	+	0.0938545i
$10$	−13.0091	+	22.5324i	−0.411383	+	0.712536i
$11$	−28.3386	+	49.0839i	−0.776764	+	1.34539i	0.157034	+	0.987593i	$0.449807\pi$
$11$	−28.3386	+	49.0839i	−0.776764	+	1.34539i	−0.933798	+	0.357802i	$0.883526\pi$
$12$	46.8025	+	81.0644i	1.12589	+	1.95011i
$13$	43.4297			0.926556			0.463278	−	0.886213i	$-0.346673\pi$
$13$	43.4297			0.926556			0.463278	+	0.886213i	$0.346673\pi$
$14$		0			0
$15$	−24.5326			−0.422286
$16$	−73.6685	−	127.598i	−1.15107	−	1.99371i
$17$	−19.9193	+	34.5013i	−0.284185	+	0.492223i	−0.972411	−	0.233273i	$-0.925056\pi$
$17$	−19.9193	+	34.5013i	−0.284185	+	0.492223i	0.688226	+	0.725496i	$0.258390\pi$
$18$	7.61315	−	13.1864i	0.0996909	−	0.172670i
$19$	26.1940	+	45.3693i	0.316280	+	0.547813i	0.979709	−	0.200427i	$-0.0642328\pi$
$19$	26.1940	+	45.3693i	0.316280	+	0.547813i	−0.663429	+	0.748239i	$0.730899\pi$
$20$	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	$-0.0886720\pi$
$23$	26.7579	+	46.3460i	0.242583	+	0.420166i	−0.718866	+	0.695148i	$0.755339\pi$
$24$	141.416	−	244.940i	1.20277	−	2.08326i
$25$	−12.5000	+	21.6506i	−0.100000	+	0.173205i
$26$	−112.996	−	195.715i	−0.852320	−	1.47626i
$27$	146.833			1.04659
$28$		0			0
$29$	49.6376			0.317844			0.158922	−	0.987291i	$-0.449198\pi$
$29$	49.6376			0.317844			0.158922	+	0.987291i	$0.449198\pi$
$30$	63.8292	+	110.555i	0.388452	+	0.672818i
$31$	−36.8930	+	63.9006i	−0.213748	+	0.370222i	−0.952884	−	0.303333i	$-0.901900\pi$
$31$	−36.8930	+	63.9006i	−0.213748	+	0.370222i	0.739137	+	0.673555i	$0.235234\pi$
$32$	−152.767	+	264.599i	−0.843924	+	1.46172i
$33$	139.044	+	240.831i	0.733467	+	1.27040i
$34$	207.305			1.04566
$35$		0			0
$36$	−55.8231			−0.258440
$37$	153.540	+	265.938i	0.682210	+	1.18162i	0.974305	+	0.225232i	$0.0723141\pi$
$37$	153.540	+	265.938i	0.682210	+	1.18162i	−0.292096	+	0.956389i	$0.594353\pi$
$38$	136.304	−	236.085i	0.581879	−	1.00784i
$39$	106.544	−	184.540i	0.437455	−	0.757694i
$40$	−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
$45$	7.31524	−	12.6704i	0.0242331	−	0.0419730i
$46$	139.238	−	241.167i	0.446294	−	0.773004i
$47$	−221.226	−	383.175i	−0.686577	−	1.18919i	−0.972938	−	0.231065i	$-0.925779\pi$
$47$	−221.226	−	383.175i	−0.686577	−	1.18919i	0.286361	−	0.958122i	$-0.407554\pi$
$48$	−722.912			−2.17382
$49$		0			0
$50$	130.091			0.367952
$51$	97.7346	+	169.281i	0.268345	+	0.464787i
$52$	−414.269	+	717.536i	−1.10479	+	1.91354i
$53$	−12.8856	+	22.3185i	−0.0333957	+	0.0578430i	−0.882240	−	0.470800i	$-0.843965\pi$
$53$	−12.8856	+	22.3185i	−0.0333957	+	0.0578430i	0.848845	+	0.528643i	$0.177299\pi$
$54$	−382.032	−	661.698i	−0.962739	−	1.66751i
$55$	283.386			0.694759
$56$		0			0
$57$	257.043			0.597300
$58$	−129.148	−	223.690i	−0.292378	−	0.506413i
$59$	188.300	−	326.146i	0.415502	−	0.719670i	−0.579979	−	0.814631i	$-0.696939\pi$
$59$	188.300	−	326.146i	0.415502	−	0.719670i	0.995481	+	0.0949609i	$0.0302726\pi$
$60$	234.013	−	405.322i	0.503515	−	0.872114i
$61$	316.287	+	547.826i	0.663876	+	1.14987i	0.979589	+	0.201012i	$0.0644231\pi$
$61$	316.287	+	547.826i	0.663876	+	1.14987i	−0.315713	+	0.948855i	$0.602244\pi$
$62$	383.955			0.786489
$63$		0			0
$64$	411.183			0.803092
$65$	−108.574	−	188.056i	−0.207184	−	0.358854i
$66$	723.531	−	1253.19i	1.34940	−	2.33723i
$67$	−255.549	+	442.624i	−0.465974	+	0.807091i	−0.999245	−	0.0388534i	$-0.987629\pi$
$67$	−255.549	+	442.624i	−0.465974	+	0.807091i	0.533271	+	0.845945i	$0.320963\pi$
$68$	−380.015	−	658.206i	−0.677700	−	1.17381i
$69$	262.576			0.458123
$70$		0			0
$71$	134.881			0.225457			0.112728	−	0.993626i	$-0.464041\pi$
$71$	134.881			0.225457			0.112728	+	0.993626i	$0.464041\pi$
$72$	84.3362	+	146.075i	0.138043	+	0.239098i
$73$	204.708	−	354.564i	0.328208	−	0.568474i	−0.653948	−	0.756540i	$-0.726888\pi$
$73$	204.708	−	354.564i	0.328208	−	0.568474i	0.982156	+	0.188066i	$0.0602218\pi$
$74$	798.962	−	1383.84i	1.25510	−	2.17390i
$75$	61.3315	+	106.229i	0.0944260	+	0.163551i
$76$	−999.443			−1.50847
$77$		0			0
$78$	−1108.83			−1.60962
$79$	463.424	+	802.674i	0.659991	+	1.14314i	0.980618	+	0.195932i	$0.0627731\pi$
$79$	463.424	+	802.674i	0.659991	+	1.14314i	−0.320627	+	0.947206i	$0.603894\pi$
$80$	−368.343	+	637.988i	−0.514774	+	0.891616i
$81$	320.717	−	555.498i	0.439941	−	0.762000i
$82$	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
$87$	121.774	−	210.918i	0.150063	−	0.259918i
$88$	−1633.55	+	2829.40i	−1.97884	+	3.42744i
$89$	244.391	+	423.297i	0.291071	+	0.504150i	0.974063	−	0.226275i	$-0.0726550\pi$
$89$	244.391	+	423.297i	0.291071	+	0.504150i	−0.682992	+	0.730426i	$0.739322\pi$
$90$	−76.1315			−0.0891662
$91$		0			0
$92$	−1020.96			−1.15698
$93$	181.016	+	313.529i	0.201833	+	0.349586i
$94$	−1151.18	+	1993.90i	−1.26314	+	2.18782i
$95$	130.970	−	226.847i	0.141445	−	0.244989i
$96$	749.552	+	1298.26i	0.796883	+	1.38024i
$97$	475.907			0.498155			0.249077	−	0.968484i	$-0.419873\pi$
$97$	475.907			0.498155			0.249077	+	0.968484i	$0.419873\pi$
$98$		0			0
$99$	−165.843			−0.168362
$100$	−238.471	−	413.044i	−0.238471	−	0.413044i
$101$	38.7904	−	67.1870i	0.0382158	−	0.0661917i	−0.846285	−	0.532731i	$-0.821166\pi$
$101$	38.7904	−	67.1870i	0.0382158	−	0.0661917i	0.884501	+	0.466539i	$0.154499\pi$
$102$	508.574	−	880.876i	0.493689	−	0.855095i
$103$	568.886	+	985.340i	0.544214	+	0.942606i	0.998656	+	0.0518297i	$0.0165053\pi$
$103$	568.886	+	985.340i	0.544214	+	0.942606i	−0.454442	+	0.890776i	$0.650161\pi$
$104$	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	$-0.177474\pi$
$107$	−37.5702	−	65.0735i	−0.0339444	−	0.0587934i	−0.882499	+	0.470315i	$0.844140\pi$
$108$	−1400.62	+	2425.94i	−1.24791	+	2.16145i
$109$	−41.4673	+	71.8235i	−0.0364390	+	0.0631142i	−0.883670	−	0.468111i	$-0.844935\pi$
$109$	−41.4673	+	71.8235i	−0.0364390	+	0.0631142i	0.847231	+	0.531225i	$0.178268\pi$
$110$	−737.317	−	1277.07i	−0.639094	−	1.10694i
$111$	1506.69			1.28837
$112$		0			0
$113$	714.602			0.594903			0.297452	−	0.954737i	$-0.403863\pi$
$113$	714.602			0.594903			0.297452	+	0.954737i	$0.403863\pi$
$114$	−668.777	−	1158.35i	−0.549444	−	0.951666i
$115$	133.789	−	231.730i	0.108486	−	0.187904i
$116$	−473.485	+	820.101i	−0.378983	+	0.656418i
$117$	63.5397	+	110.054i	0.0502072	+	0.0869615i
$118$	−1959.69			−1.52885
$119$		0			0
$120$	−1414.16			−1.07579
$121$	−940.651	−	1629.26i	−0.706725	−	1.22408i
$122$	1645.84	−	2850.68i	1.22137	−	2.11548i
$123$	−716.510	+	1241.03i	−0.525248	+	0.909756i
$124$	−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
$129$	−897.786	+	1555.01i	−0.612757	+	1.06133i
$130$	−564.980	+	978.573i	−0.381169	+	0.660204i
$131$	91.9544	+	159.270i	0.0613289	+	0.106225i	0.895060	−	0.445946i	$-0.147133\pi$
$131$	91.9544	+	159.270i	0.0613289	+	0.106225i	−0.833731	+	0.552171i	$0.813799\pi$
$132$	−5305.27			−3.49822
$133$		0			0
$134$	2659.56			1.71456
$135$	−367.082	−	635.805i	−0.234025	−	0.405344i
$136$	−1148.23	+	1988.80i	−0.723972	+	1.25396i
$137$	−443.874	+	768.812i	−0.276808	+	0.479445i	−0.970590	−	0.240740i	$-0.922610\pi$
$137$	−443.874	+	768.812i	−0.276808	+	0.479445i	0.693782	+	0.720185i	$0.255943\pi$
$138$	−683.174	−	1183.29i	−0.421417	−	0.729917i
$139$	2335.25			1.42499			0.712495	−	0.701678i	$-0.247565\pi$
$139$	2335.25			1.42499			0.712495	+	0.701678i	$0.247565\pi$
$140$		0			0
$141$	−2170.90			−1.29661
$142$	−350.935	−	607.837i	−0.207393	−	0.359215i
$143$	−1230.74	+	2131.70i	−0.719716	+	1.24658i
$144$	215.561	−	373.363i	0.124746	−	0.216066i
$145$	−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	0.980451	+	0.196766i	$0.0630439\pi$
$149$	1201.54	+	2081.12i	0.660629	+	1.14424i	−0.319821	+	0.947478i	$0.603623\pi$
$150$	319.146	−	552.777i	0.173721	−	0.300894i
$151$	−617.188	+	1069.00i	−0.332623	+	0.576120i	−0.983025	−	0.183470i	$-0.941267\pi$
$151$	−617.188	+	1069.00i	−0.332623	+	0.576120i	0.650402	+	0.759590i	$0.274600\pi$
$152$	1509.93	+	2615.28i	0.805735	+	1.39557i
$153$	−116.572			−0.0615965
$154$		0			0
$155$	368.930			0.191182
$156$	2032.62	+	3520.60i	1.04320	+	1.80688i
$157$	716.244	−	1240.57i	0.364092	−	0.630627i	−0.624538	−	0.780995i	$-0.714713\pi$
$157$	716.244	−	1240.57i	0.364092	−	0.630627i	0.988630	+	0.150368i	$0.0480459\pi$
$158$	2411.48	−	4176.81i	1.21422	−	2.10310i
$159$	63.2233	+	109.506i	0.0315342	+	0.0546188i
$160$	1527.67			0.754829
$161$		0			0
$162$	−3337.78			−1.61877
$163$	430.415	+	745.500i	0.206826	+	0.358234i	0.950713	−	0.310072i	$-0.100353\pi$
$163$	430.415	+	745.500i	0.206826	+	0.358234i	−0.743887	+	0.668306i	$0.767020\pi$
$164$	2785.96	−	4825.42i	1.32651	−	2.29757i
$165$	695.219	−	1204.15i	0.328016	−	0.568141i
$166$	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
$171$	−76.6461	+	132.755i	−0.0342765	+	0.0593686i
$172$	3490.80	−	6046.25i	1.54751	−	2.68036i
$173$	−1305.25	−	2260.75i	−0.573618	−	0.993536i	−0.996190	−	0.0872067i	$-0.972206\pi$
$173$	−1305.25	−	2260.75i	−0.573618	−	0.993536i	0.422572	−	0.906329i	$-0.361127\pi$
$174$	−1267.33			−0.552161
$175$		0			0
$176$	8350.65			3.57644
$177$	−923.899	−	1600.24i	−0.392342	−	0.679556i
$178$	1271.72	−	2202.68i	0.535501	−	0.927515i
$179$	−675.224	+	1169.52i	−0.281947	+	0.488347i	−0.971864	−	0.235541i	$-0.924314\pi$
$179$	−675.224	+	1169.52i	−0.281947	+	0.488347i	0.689917	+	0.723889i	$0.257647\pi$
$180$	139.558	+	241.721i	0.0577890	+	0.100094i
$181$	−2846.61			−1.16899			−0.584493	−	0.811399i	$-0.698707\pi$
$181$	−2846.61			−1.16899			−0.584493	+	0.811399i	$0.698707\pi$
$182$		0			0
$183$	3103.74			1.25374
$184$	1542.44	+	2671.58i	0.617989	+	1.07039i
$185$	767.698	−	1329.69i	0.305093	−	0.528437i
$186$	941.940	−	1631.49i	0.371325	−	0.643154i
$187$	−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	−0.922065	−	0.387036i	$-0.873499\pi$
$191$	−2101.75	−	3640.33i	−0.796215	−	1.37909i	0.125849	−	0.992049i	$-0.459834\pi$
$192$	1008.74	−	1747.19i	0.379163	−	0.656730i
$193$	−69.2923	+	120.018i	−0.0258434	+	0.0447620i	−0.878658	−	0.477452i	$-0.841560\pi$
$193$	−69.2923	+	120.018i	−0.0258434	+	0.0447620i	0.852814	+	0.522214i	$0.174894\pi$
$194$	−1238.22	−	2144.66i	−0.458242	−	0.793699i
$195$	−1065.44			−0.391272
$196$		0			0
$197$	1473.76			0.532998			0.266499	−	0.963835i	$-0.414133\pi$
$197$	1473.76			0.532998			0.266499	+	0.963835i	$0.414133\pi$
$198$	431.492	+	747.365i	0.154873	+	0.268247i
$199$	−1804.80	+	3126.00i	−0.642909	+	1.11355i	0.341872	+	0.939747i	$0.388939\pi$
$199$	−1804.80	+	3126.00i	−0.642909	+	1.11355i	−0.984780	+	0.173804i	$0.944394\pi$
$200$	−720.552	+	1248.03i	−0.254754	+	0.441246i
$201$	1253.86	+	2171.74i	0.440001	+	0.762104i
$202$	−403.702			−0.140616
$203$		0			0
$204$	−3729.10			−1.27985
$205$	730.161	+	1264.68i	0.248764	+	0.430872i
$206$	2960.27	−	5127.34i	1.00122	−	1.73417i
$207$	−78.2961	+	135.613i	−0.0262896	+	0.0455350i
$208$	−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
$213$	330.898	−	573.132i	0.106445	−	0.184368i
$214$	−195.501	+	338.618i	−0.0624495	+	0.108166i
$215$	914.891	+	1584.64i	0.290210	+	0.502658i
$216$	8464.06			2.66623
$217$		0			0
$218$	431.561			0.134078
$219$	−1004.40	−	1739.67i	−0.309914	−	0.536787i
$220$	−2703.18	+	4682.04i	−0.828400	+	1.43483i
$221$	−865.091	+	1498.38i	−0.263314	+	0.456073i
$222$	−3920.12	−	6789.85i	−1.18514	−	2.05272i
$223$	−5258.44			−1.57906			−0.789532	−	0.613709i	$-0.789677\pi$
$223$	−5258.44			−1.57906			−0.789532	+	0.613709i	$0.789677\pi$
$224$		0			0
$225$	−73.1524			−0.0216748
$226$	−1859.26	−	3220.33i	−0.547239	−	0.947846i
$227$	−3353.93	+	5809.18i	−0.980652	+	1.69854i	−0.320795	+	0.947149i	$0.603950\pi$
$227$	−3353.93	+	5809.18i	−0.980652	+	1.69854i	−0.659857	+	0.751391i	$0.729383\pi$
$228$	−2451.89	+	4246.80i	−0.712195	+	1.23356i
$229$	600.126	+	1039.45i	0.173177	+	0.299951i	0.939529	−	0.342470i	$-0.111264\pi$
$229$	600.126	+	1039.45i	0.173177	+	0.299951i	−0.766352	+	0.642421i	$0.777930\pi$
$230$	−1392.38			−0.399178
$231$		0			0
$232$	2861.32			0.809719
$233$	−3175.71	−	5500.49i	−0.892909	−	1.54656i	−0.836372	−	0.548163i	$-0.815327\pi$
$233$	−3175.71	−	5500.49i	−0.892909	−	1.54656i	−0.0565373	−	0.998400i	$-0.518006\pi$
$234$	330.637	−	572.680i	0.0923692	−	0.159988i
$235$	−1106.13	+	1915.87i	−0.307047	+	0.531820i
$236$	3592.34	+	6222.11i	0.990853	+	1.71621i
$237$	4547.59			1.24640
$238$		0			0
$239$	−3003.73			−0.812951			−0.406475	−	0.913662i	$-0.633242\pi$
$239$	−3003.73			−0.812951			−0.406475	+	0.913662i	$0.633242\pi$
$240$	1807.28	+	3130.30i	0.486081	+	0.841917i
$241$	2846.16	−	4929.70i	0.760736	−	1.31763i	−0.181736	−	0.983347i	$-0.558172\pi$
$241$	2846.16	−	4929.70i	0.760736	−	1.31763i	0.942472	−	0.334286i	$-0.108495\pi$
$242$	−4894.79	+	8478.03i	−1.30020	+	2.25202i
$243$	408.642	+	707.789i	0.107878	+	0.186850i
$244$	−12068.1			−3.16631
$245$		0			0
$246$	7456.89			1.93266
$247$	1137.60	+	1970.38i	0.293051	+	0.507579i
$248$	−2126.67	+	3683.50i	−0.544531	+	0.943155i
$249$	−727.077	+	1259.33i	−0.185047	+	0.320510i
$250$	−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
$255$	488.673	−	846.406i	0.120007	−	0.207859i
$256$	2437.31	−	4221.54i	0.595045	−	1.03065i
$257$	1545.90	+	2677.59i	0.375217	+	0.649896i	0.990360	−	0.138521i	$-0.0442347\pi$
$257$	1545.90	+	2677.59i	0.375217	+	0.649896i	−0.615142	+	0.788416i	$0.710901\pi$
$258$	9343.48			2.25465
$259$		0			0
$260$	4142.69			0.988150
$261$	72.6221	+	125.785i	0.0172230	+	0.0298311i
$262$	478.496	−	828.779i	0.112830	−	0.195428i
$263$	−992.413	+	1718.91i	−0.232680	+	0.403013i	−0.958596	−	0.284770i	$-0.908083\pi$
$263$	−992.413	+	1718.91i	−0.232680	+	0.403013i	0.725916	+	0.687783i	$0.241416\pi$
$264$	8015.06	+	13882.5i	1.86853	+	3.23640i
$265$	128.856			0.0298700
$266$		0			0
$267$	2398.21			0.549694
$268$	−4875.29	−	8444.25i	−1.11121	−	1.92468i
$269$	3090.37	−	5352.68i	0.700458	−	1.21323i	−0.267848	−	0.963461i	$-0.586313\pi$
$269$	3090.37	−	5352.68i	0.700458	−	1.21323i	0.968306	−	0.249767i	$-0.0803540\pi$
$270$	−1910.16	+	3308.49i	−0.430550	+	0.745734i
$271$	−3059.49	−	5299.20i	−0.685797	−	1.18784i	−0.973186	−	0.230022i	$-0.926120\pi$
$271$	−3059.49	−	5299.20i	−0.685797	−	1.18784i	0.287388	−	0.957814i	$-0.407213\pi$
$272$	5869.71			1.30847
$273$		0			0
$274$	4619.50			1.01852
$275$	−708.465	−	1227.10i	−0.155353	−	0.269079i
$276$	−2504.67	+	4338.22i	−0.546245	+	0.946125i
$277$	−1647.42	+	2853.41i	−0.357342	+	0.618935i	−0.987516	−	0.157519i	$-0.949650\pi$
$277$	−1647.42	+	2853.41i	−0.357342	+	0.618935i	0.630174	+	0.776454i	$0.282984\pi$
$278$	−6075.89	−	10523.7i	−1.31082	−	2.27040i
$279$	−215.905			−0.0463294
$280$		0			0
$281$	−4604.53			−0.977521			−0.488760	−	0.872418i	$-0.662551\pi$
$281$	−4604.53			−0.977521			−0.488760	+	0.872418i	$0.662551\pi$
$282$	5648.27	+	9783.09i	1.19273	+	2.06587i
$283$	−609.776	+	1056.16i	−0.128083	+	0.221846i	−0.922934	−	0.384959i	$-0.874216\pi$
$283$	−609.776	+	1056.16i	−0.128083	+	0.221846i	0.794851	+	0.606805i	$0.207549\pi$
$284$	−1286.61	+	2228.47i	−0.268825	+	0.465618i
$285$	−642.607	−	1113.03i	−0.133560	−	0.231333i
$286$	12808.6			2.64821
$287$		0			0
$288$	−894.019			−0.182919
$289$	1662.94	+	2880.30i	0.338478	+	0.586260i
$290$	−645.738	+	1118.45i	−0.130755	+	0.226475i
$291$	1167.52	−	2022.21i	0.235194	−	0.407368i
$292$	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
$297$	−4161.04	+	7207.13i	−0.812956	+	1.40808i
$298$	6252.35	−	10829.4i	1.21540	−	2.10513i
$299$	1162.09	+	2012.79i	0.224767	+	0.389307i
$300$	−2340.13			−0.450358
$301$		0			0
$302$	6423.23			1.22389
$303$	−190.326	−	329.654i	−0.0360856	−	0.0625021i
$304$	3859.35	−	6684.58i	0.728121	−	1.26114i
$305$	1581.44	−	2739.13i	0.296894	−	0.514236i
$306$	303.298	+	525.327i	0.0566613	+	0.0981403i
$307$	−846.546			−0.157378			−0.0786888	−	0.996899i	$-0.525073\pi$
$307$	−846.546			−0.157378			−0.0786888	+	0.996899i	$0.525073\pi$
$308$		0			0
$309$	5582.50			1.02776
$310$	−959.887	−	1662.57i	−0.175864	−	0.304606i
$311$	980.793	−	1698.78i	0.178829	−	0.309740i	−0.762651	−	0.646810i	$-0.776103\pi$
$311$	980.793	−	1698.78i	0.178829	−	0.309740i	0.941480	+	0.337070i	$0.109436\pi$
$312$	6141.66	−	10637.7i	1.11443	−	1.93025i
$313$	3264.98	+	5655.11i	0.589609	+	1.02123i	0.994284	+	0.106772i	$0.0340515\pi$
$313$	3264.98	+	5655.11i	0.589609	+	1.02123i	−0.404674	+	0.914461i	$0.632615\pi$
$314$	−7454.13			−1.33968
$315$		0			0
$316$	−17682.1			−3.14778
$317$	3845.26	+	6660.19i	0.681298	+	1.18004i	0.974585	+	0.224019i	$0.0719176\pi$
$317$	3845.26	+	6660.19i	0.681298	+	1.18004i	−0.293287	+	0.956025i	$0.594749\pi$
$318$	328.990	−	569.828i	0.0580153	−	0.100485i
$319$	−1406.66	+	2436.40i	−0.246890	+	0.427625i
$320$	−1027.96	−	1780.47i	−0.179577	−	0.311036i
$321$	−368.678			−0.0641047
$322$		0			0
$323$	−2087.07			−0.359528
$324$	6118.54	+	10597.6i	1.04913	+	1.81715i
$325$	−542.871	+	940.281i	−0.0926556	+	0.160484i
$326$	2239.72	−	3879.30i	0.380511	−	0.659064i
$327$	203.460	+	352.403i	0.0344079	+	0.0595962i
$328$	−16835.8			−2.83415
$329$		0			0
$330$	−7235.31			−1.20694
$331$	−3263.13	−	5651.92i	−0.541867	−	0.938542i	−0.998797	−	0.0490389i	$-0.984384\pi$
$331$	−3263.13	−	5651.92i	−0.541867	−	0.938542i	0.456929	−	0.889503i	$-0.348949\pi$
$332$	2827.05	−	4896.59i	0.467332	−	0.809444i
$333$	−449.271	+	778.161i	−0.0739337	+	0.128057i
$334$	−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
$339$	1753.10	−	3036.46i	0.280872	−	0.486484i
$340$	−1900.08	+	3291.03i	−0.303077	+	0.524944i
$341$	−2090.99	−	3621.70i	−0.332063	−	0.575150i
$342$	797.675			0.126121
$343$		0			0
$344$	−21095.3			−3.30634
$345$	−656.440	−	1136.99i	−0.102439	−	0.177430i
$346$	−6792.01	+	11764.1i	−1.05532	+	1.82787i
$347$	4214.64	−	7299.98i	0.652029	−	1.12935i	−0.330601	−	0.943771i	$-0.607251\pi$
$347$	4214.64	−	7299.98i	0.652029	−	1.12935i	0.982630	−	0.185576i	$-0.0594152\pi$
$348$	2323.16	+	4023.84i	0.357858	+	0.619829i
$349$	135.644			0.0208047			0.0104023	−	0.999946i	$-0.496689\pi$
$349$	135.644			0.0208047			0.0104023	+	0.999946i	$0.496689\pi$
$350$		0			0
$351$	6376.91			0.969727
$352$	−8658.38	−	14996.7i	−1.31106	−	2.27082i
$353$	1162.07	−	2012.77i	0.175215	−	0.303481i	−0.765021	−	0.644005i	$-0.777271\pi$
$353$	1162.07	−	2012.77i	0.175215	−	0.303481i	0.940236	+	0.340525i	$0.110605\pi$
$354$	−4807.62	+	8327.04i	−0.721814	+	1.25022i
$355$	−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	$-0.0385905\pi$
$359$	2663.65	+	4613.58i	0.391594	+	0.678260i	−0.601066	+	0.799199i	$0.705257\pi$
$360$	421.681	−	730.373i	0.0617348	−	0.106928i
$361$	2057.25	−	3563.26i	0.299934	−	0.519501i
$362$	7406.33	+	12828.1i	1.07533	+	1.86252i
$363$	−9230.64			−1.33466
$364$		0			0
$365$	−2047.08			−0.293559
$366$	−8075.34	−	13986.9i	−1.15329	−	1.99756i
$367$	−3645.81	+	6314.73i	−0.518555	+	0.898164i	0.481212	+	0.876604i	$0.340197\pi$
$367$	−3645.81	+	6314.73i	−0.518555	+	0.898164i	−0.999768	+	0.0215599i	$0.993137\pi$
$368$	3942.43	−	6828.49i	0.558460	−	0.967282i
$369$	−427.304	−	740.112i	−0.0602834	−	0.104414i
$370$	−7989.62			−1.12260
$371$		0			0
$372$	−6906.75			−0.962629
$373$	830.751	+	1438.90i	0.115321	+	0.199742i	0.917908	−	0.396793i	$-0.129877\pi$
$373$	830.751	+	1438.90i	0.115321	+	0.199742i	−0.802587	+	0.596535i	$0.796544\pi$
$374$	−5874.74	+	10175.4i	−0.812235	+	1.40683i
$375$	306.657	−	531.146i	0.0422286	−	0.0731420i
$376$	−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
$381$	4616.19	−	7995.48i	0.620721	−	1.07512i
$382$	−10936.7	+	18942.9i	−1.46484	+	2.53718i
$383$	−5470.58	−	9475.33i	−0.729853	−	1.26414i	−0.956945	−	0.290269i	$-0.906255\pi$
$383$	−5470.58	−	9475.33i	−0.729853	−	1.26414i	0.227092	−	0.973873i	$-0.427078\pi$
$384$	1494.64			0.198628
$385$		0			0
$386$	721.142			0.0950911
$387$	−535.411	−	927.360i	−0.0703269	−	0.121810i
$388$	−4539.60	+	7862.83i	−0.593978	+	1.02880i
$389$	3118.40	−	5401.23i	0.406450	−	0.703992i	−0.588039	−	0.808833i	$-0.700100\pi$
$389$	3118.40	−	5401.23i	0.406450	−	0.703992i	0.994489	+	0.104840i	$0.0334331\pi$
$390$	2772.08	+	4801.39i	0.359923	+	0.623404i
$391$	−2132.00			−0.275754
$392$		0			0
$393$	902.351			0.115821
$394$	−3834.43	−	6641.43i	−0.490294	−	0.849215i
$395$	2317.12	−	4013.37i	0.295157	−	0.511227i
$396$	1581.95	−	2740.02i	0.200747	−	0.347705i
$397$	−5723.91	−	9914.10i	−0.723614	−	1.25334i	−0.959542	−	0.281565i	$-0.909146\pi$
$397$	−5723.91	−	9914.10i	−0.723614	−	1.25334i	0.235928	−	0.971771i	$-0.424187\pi$
$398$	18783.0			2.36559
$399$		0			0
$400$	3683.43			0.460428
$401$	4616.74	+	7996.42i	0.574935	+	0.995816i	0.996049	+	0.0888085i	$0.0283059\pi$
$401$	4616.74	+	7996.42i	0.574935	+	0.995816i	−0.421114	+	0.907008i	$0.638361\pi$
$402$	6524.59	−	11300.9i	0.809495	−	1.40209i
$403$	−1602.25	+	2775.18i	−0.198049	+	0.343032i
$404$	740.032	+	1281.77i	0.0911336	+	0.157848i
$405$	−3207.17			−0.393495
$406$		0			0
$407$	−17404.4			−2.11966
$408$	5633.83	+	9758.08i	0.683618	+	1.18406i
$409$	−2217.57	+	3840.95i	−0.268097	+	0.464358i	−0.968370	−	0.249517i	$-0.919728\pi$
$409$	−2217.57	+	3840.95i	−0.268097	+	0.464358i	0.700273	+	0.713875i	$0.253062\pi$
$410$	3799.48	−	6580.90i	0.457666	−	0.792701i
$411$	2177.87	+	3772.19i	0.261379	+	0.452721i
$412$	−21706.1			−2.59559
$413$		0			0
$414$	814.847			0.0967332
$415$	740.930	+	1283.33i	0.0876405	+	0.151798i
$416$	−6634.61	+	11491.5i	−0.781943	+	1.35437i
$417$	5728.98	−	9922.88i	0.672780	−	1.16529i
$418$	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
$423$	647.328	−	1121.21i	0.0744070	−	0.128877i
$424$	−742.778	+	1286.53i	−0.0850767	+	0.147357i
$425$	−497.983	−	862.533i	−0.0568370	−	0.0984447i
$426$	−3443.74			−0.391666
$427$		0			0
$428$	1433.51			0.161895
$429$	6038.63	+	10459.2i	0.679598	+	1.17710i
$430$	4760.75	−	8245.86i	0.533916	−	0.924769i
$431$	1120.60	−	1940.94i	0.125238	−	0.216918i	−0.796588	−	0.604522i	$-0.793364\pi$
$431$	1120.60	−	1940.94i	0.125238	−	0.216918i	0.921826	+	0.387604i	$0.126697\pi$
$432$	−10817.0	−	18735.5i	−1.20470	−	2.08661i
$433$	14181.1			1.57391			0.786954	−	0.617012i	$-0.211657\pi$
$433$	14181.1			1.57391			0.786954	+	0.617012i	$0.211657\pi$
$434$		0			0
$435$	−1217.74			−0.134221
$436$	−791.101	−	1370.23i	−0.0868965	−	0.150509i
$437$	−1401.79	+	2427.98i	−0.153448	+	0.265780i
$438$	−5226.53	+	9052.61i	−0.570167	+	0.987558i
$439$	4346.32	+	7528.05i	0.472525	+	0.818438i	0.999506	−	0.0314396i	$-0.0100092\pi$
$439$	4346.32	+	7528.05i	0.472525	+	0.818438i	−0.526980	+	0.849878i	$0.676676\pi$
$440$	16335.5			1.76992
$441$		0			0
$442$	9003.22			0.968867
$443$	4696.85	+	8135.18i	0.503734	+	0.872492i	0.999991	+	0.00431671i	$0.00137406\pi$
$443$	4696.85	+	8135.18i	0.503734	+	0.872492i	−0.496257	+	0.868176i	$0.665293\pi$
$444$	−14372.1	+	24893.2i	−1.53619	+	2.66076i
$445$	1221.95	−	2116.48i	0.130171	−	0.225463i
$446$	13681.5	+	23697.0i	1.45255	+	2.51589i
$447$	11790.7			1.24761
$448$		0			0
$449$	9511.86			0.999761			0.499880	−	0.866094i	$-0.333377\pi$
$449$	9511.86			0.999761			0.499880	+	0.866094i	$0.333377\pi$
$450$	190.329	+	329.659i	0.0199382	+	0.0345339i
$451$	8276.69	−	14335.7i	0.864156	−	1.49676i
$452$	−6816.48	+	11806.5i	−0.709337	+	1.22861i
$453$	3028.25	+	5245.08i	0.314083	+	0.544007i
$454$	34905.2			3.60833
$455$		0			0
$456$	14817.0			1.52165
$457$	683.607	+	1184.04i	0.0699732	+	0.121197i	0.898889	−	0.438176i	$-0.144375\pi$
$457$	683.607	+	1184.04i	0.0699732	+	0.121197i	−0.828916	+	0.559373i	$0.811042\pi$
$458$	3122.83	−	5408.90i	0.318603	−	0.551837i
$459$	−2924.81	+	5065.93i	−0.297426	+	0.515157i
$460$	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
$465$	905.081	−	1567.65i	0.0902627	−	0.156340i
$466$	−16525.2	+	28622.5i	−1.64274	+	2.84530i
$467$	−4249.87	−	7360.99i	−0.421115	−	0.729392i	0.574934	−	0.818200i	$-0.305028\pi$
$467$	−4249.87	−	7360.99i	−0.421115	−	0.729392i	−0.996049	+	0.0888078i	$0.971694\pi$
$468$	−2424.38			−0.239460
$469$		0			0
$470$	11511.8			1.12978
$471$	−3514.26	−	6086.88i	−0.343798	−	0.595475i
$472$	10854.4	−	18800.4i	1.05851	−	1.83339i
$473$	10370.7	−	17962.6i	1.00813	−	1.74613i
$474$	−11832.0	−	20493.6i	−1.14654	−	1.98587i
$475$	−1309.70			−0.126512
$476$		0			0
$477$	−75.4088			−0.00723843
$478$	7815.15	+	13536.2i	0.747817	+	1.29526i
$479$	−361.486	+	626.113i	−0.0344817	+	0.0597240i	−0.882751	−	0.469841i	$-0.844311\pi$
$479$	−361.486	+	626.113i	−0.0344817	+	0.0597240i	0.848270	+	0.529565i	$0.177645\pi$
$480$	3747.76	−	6491.31i	0.356377	−	0.617263i
$481$	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
$486$	2126.42	−	3683.07i	0.198470	−	0.343760i
$487$	−1153.66	+	1998.19i	−0.107345	+	0.185927i	−0.914694	−	0.404147i	$-0.867568\pi$
$487$	−1153.66	+	1998.19i	−0.107345	+	0.185927i	0.807349	+	0.590075i	$0.200902\pi$
$488$	18232.1	+	31579.0i	1.69125	+	2.92933i
$489$	4223.67			0.390595
$490$		0			0
$491$	−8668.77			−0.796774			−0.398387	−	0.917217i	$-0.630430\pi$
$491$	−8668.77			−0.796774			−0.398387	+	0.917217i	$0.630430\pi$
$492$	−13669.4	−	23676.0i	−1.25257	−	2.16951i
$493$	−988.748	+	1712.56i	−0.0903265	+	0.156450i
$494$	5919.63	−	10253.1i	0.539143	−	0.933823i
$495$	414.607	+	718.120i	0.0376469	+	0.0652063i
$496$	10871.4			0.984155
$497$		0			0
$498$	7566.87			0.680883
$499$	−9960.86	−	17252.7i	−0.893606	−	1.54777i	−0.835520	−	0.549460i	$-0.814834\pi$
$499$	−9960.86	−	17252.7i	−0.893606	−	1.54777i	−0.0580860	−	0.998312i	$-0.518500\pi$
$500$	−1192.36	+	2065.22i	−0.106648	+	0.184719i
$501$	3303.97	−	5722.65i	0.294632	−	0.510318i
$502$	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
$507$	−762.622	+	1320.90i	−0.0668032	+	0.115707i
$508$	−17948.9	+	31088.3i	−1.56762	+	2.71520i
$509$	−9232.52	−	15991.2i	−0.803977	−	1.39253i	−0.916980	−	0.398934i	$-0.869380\pi$
$509$	−9232.52	−	15991.2i	−0.803977	−	1.39253i	0.113003	−	0.993595i	$-0.463953\pi$
$510$	−5085.74			−0.441569
$511$		0			0
$512$	−22928.6			−1.97913
$513$	3846.14	+	6661.71i	0.331016	+	0.573337i
$514$	8044.31	−	13933.1i	0.690310	−	1.19565i
$515$	2844.43	−	4926.70i	0.243380	−	0.421546i
$516$	−17127.7	−	29666.0i	−1.46125	−	2.53096i
$517$	25076.9			2.13323
$518$		0			0
$519$	−12808.4			−1.08329
$520$	−6258.67	−	10840.3i	−0.527810	−	0.914193i
$521$	−2167.92	+	3754.95i	−0.182300	+	0.315753i	−0.942663	−	0.333745i	$-0.891688\pi$
$521$	−2167.92	+	3754.95i	−0.182300	+	0.315753i	0.760363	+	0.649498i	$0.225021\pi$
$522$	377.898	−	654.539i	0.0316861	−	0.0548820i
$523$	−4186.60	−	7251.40i	−0.350033	−	0.606275i	0.636222	−	0.771506i	$-0.280496\pi$
$523$	−4186.60	−	7251.40i	−0.350033	−	0.606275i	−0.986255	+	0.165231i	$0.947163\pi$
$524$	−3508.56			−0.292504
$525$		0			0
$526$	10328.3			0.856150
$527$	−1469.77	−	2545.71i	−0.121488	−	0.210423i
$528$	20486.3	−	35483.3i	1.68854	−	2.92465i
$529$	4651.53	−	8056.69i	0.382307	−	0.662175i
$530$	−335.258	−	580.685i	−0.0274768	−	0.0475912i
$531$	1101.97			0.0900591
$532$		0			0
$533$	−12684.3			−1.03080
$534$	−6239.70	−	10807.5i	−0.505652	−	0.875815i
$535$	−187.851	+	325.368i	−0.0151804	+	0.0262932i
$536$	−14730.9	+	25514.7i	−1.18709	+	2.05610i
$537$	3313.00	+	5738.28i	0.266231	+	0.461126i
$538$	−32162.2			−2.57735
$539$		0			0
$540$	14006.2			1.11617
$541$	−5937.49	−	10284.0i	−0.471853	−	0.817274i	0.527628	−	0.849475i	$-0.323081\pi$
$541$	−5937.49	−	10284.0i	−0.471853	−	0.817274i	−0.999481	+	0.0322016i	$0.989748\pi$
$542$	−15920.5	+	27575.0i	−1.26170	+	2.18533i
$543$	−6983.46	+	12095.7i	−0.551913	+	0.955942i
$544$	−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
$549$	−925.486	+	1602.99i	−0.0719468	+	0.124616i
$550$	−3686.58	+	6385.35i	−0.285812	+	0.495040i
$551$	1300.21	+	2252.02i	0.100528	+	0.174119i
$552$	15136.0			1.16708
$553$		0			0
$554$	17145.1			1.31485
$555$	−3766.72	−	6524.15i	−0.288087	−	0.498982i
$556$	−22275.6	+	38582.5i	−1.69909	+	2.94292i
$557$	1976.09	−	3422.69i	0.150323	−	0.260366i	−0.781023	−	0.624502i	$-0.785302\pi$
$557$	1976.09	−	3422.69i	0.150323	−	0.260366i	0.931346	+	0.364135i	$0.118635\pi$
$558$	561.744	+	972.969i	0.0426174	+	0.0738155i
$559$	−15893.4			−1.20254
$560$		0			0
$561$	−11078.6			−0.833762
$562$	11980.1	+	20750.2i	0.899201	+	1.55746i
$563$	159.733	−	276.666i	0.0119573	−	0.0207106i	−0.859985	−	0.510320i	$-0.829527\pi$
$563$	159.733	−	276.666i	0.0119573	−	0.0207106i	0.871942	+	0.489609i	$0.162860\pi$
$564$	20707.9	−	35867.1i	1.54603	−	2.67780i
$565$	−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	0.835813	+	0.549014i	$0.184996\pi$
$569$	12125.5	+	21001.9i	0.893366	+	1.54736i	0.0575529	+	0.998342i	$0.481670\pi$
$570$	−3343.88	+	5791.77i	−0.245719	+	0.425598i
$571$	1413.73	−	2448.66i	0.103613	−	0.179463i	−0.809558	−	0.587040i	$-0.800293\pi$
$571$	1413.73	−	2448.66i	0.103613	−	0.179463i	0.913171	+	0.407578i	$0.133626\pi$
$572$	−23479.6	−	40667.9i	−1.71632	−	2.97274i
$573$	−20624.5			−1.50367
$574$		0			0
$575$	−1337.89			−0.0970332
$576$	601.580	+	1041.97i	0.0435171	+	0.0753738i
$577$	9130.11	−	15813.8i	0.658738	−	1.14097i	−0.322205	−	0.946670i	$-0.604424\pi$
$577$	9130.11	−	15813.8i	0.658738	−	1.14097i	0.980943	−	0.194297i	$-0.0622426\pi$
$578$	8653.31	−	14988.0i	0.622717	−	1.07858i
$579$	339.984	+	588.869i	0.0244028	+	0.0422669i
$580$	4734.85			0.338973
$581$		0			0
$582$	−12150.7			−0.865400
$583$	−730.318	−	1264.95i	−0.0518811	−	0.0898607i
$584$	11800.2	−	20438.6i	0.836123	−	1.44821i
$585$	317.698	−	550.270i	0.0224534	−	0.0388904i
$586$	−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
$591$	3615.50	−	6262.23i	0.251644	−	0.435861i
$592$	22622.1	−	39182.6i	1.57054	−	2.72026i
$593$	−317.332	−	549.634i	−0.0219751	−	0.0380620i	0.854829	−	0.518910i	$-0.173662\pi$
$593$	−317.332	−	549.634i	−0.0219751	−	0.0380620i	−0.876804	+	0.480848i	$0.840329\pi$
$594$	43304.9			2.99128
$595$		0			0
$596$	−45845.1			−3.15082
$597$	8855.28	+	15337.8i	0.607073	+	1.05148i
$598$	6047.07	−	10473.8i	0.413517	−	0.716232i
$599$	−4318.74	+	7480.27i	−0.294589	+	0.510243i	−0.974889	−	0.222690i	$-0.928516\pi$
$599$	−4318.74	+	7480.27i	−0.294589	+	0.510243i	0.680300	+	0.732934i	$0.261849\pi$
$600$	3535.40	+	6123.50i	0.240554	+	0.416651i
$601$	19947.7			1.35388			0.676941	−	0.736037i	$-0.263305\pi$
$601$	19947.7			1.35388			0.676941	+	0.736037i	$0.263305\pi$
$602$		0			0
$603$	−1495.52			−0.100999
$604$	−11774.5	−	20394.1i	−0.793210	−	1.37388i
$605$	−4703.25	+	8146.28i	−0.316057	+	0.547427i
$606$	−990.385	+	1715.40i	−0.0663888	+	0.114989i
$607$	618.585	+	1071.42i	0.0413634	+	0.0716435i	0.885966	−	0.463750i	$-0.153497\pi$
$607$	618.585	+	1071.42i	0.0413634	+	0.0716435i	−0.844603	+	0.535394i	$0.820163\pi$
$608$	−16006.3			−1.06766
$609$		0			0
$610$	−16458.4			−1.09243
$611$	−9607.78	−	16641.2i	−0.636152	−	1.10185i
$612$	1111.96	−	1925.97i	0.0734450	−	0.127210i
$613$	−8763.81	+	15179.4i	−0.577434	+	1.00014i	0.418339	+	0.908291i	$0.362612\pi$
$613$	−8763.81	+	15179.4i	−0.577434	+	1.00014i	−0.995773	+	0.0918535i	$0.970721\pi$
$614$	2202.55	+	3814.94i	0.144768	+	0.250746i
$615$	7165.10			0.469796
$616$		0			0
$617$	18508.3			1.20764			0.603821	−	0.797120i	$-0.293644\pi$
$617$	18508.3			1.20764			0.603821	+	0.797120i	$0.293644\pi$
$618$	−14524.6	−	25157.4i	−0.945414	−	1.63750i
$619$	−3014.92	+	5221.99i	−0.195767	+	0.339079i	−0.947152	−	0.320786i	$-0.896053\pi$
$619$	−3014.92	+	5221.99i	−0.195767	+	0.339079i	0.751385	+	0.659865i	$0.229386\pi$
$620$	−3519.17	+	6095.38i	−0.227957	+	0.394833i
$621$	3928.94	+	6805.12i	0.253886	+	0.439743i
$622$	−10207.4			−0.658003
$623$		0			0
$624$	−31395.8			−2.01417
$625$	−312.500	−	541.266i	−0.0200000	−	0.0346410i
$626$	16989.7	−	29427.1i	1.08474	−	1.87882i
$627$	−7284.22	+	12616.6i	−0.463962	+	0.803605i
$628$	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
$633$	4371.71	−	7572.02i	0.274502	−	0.475451i
$634$	20009.3	−	34657.1i	1.25342	−	2.17099i
$635$	−4704.14	−	8147.82i	−0.293982	−	0.509191i
$636$	−2412.31			−0.150400
$637$		0			0
$638$	14639.4			0.908434
$639$	197.337	+	341.798i	0.0122168	+	0.0211601i
$640$	761.559	−	1319.06i	0.0470364	−	0.0814694i
$641$	937.912	−	1624.51i	0.0577930	−	0.100100i	−0.835681	−	0.549214i	$-0.814927\pi$
$641$	937.912	−	1624.51i	0.0577930	−	0.100100i	0.893474	+	0.449114i	$0.148260\pi$
$642$	959.231	+	1661.44i	0.0589686	+	0.102137i
$643$	20619.9			1.26465			0.632325	−	0.774703i	$-0.282101\pi$
$643$	20619.9			1.26465			0.632325	+	0.774703i	$0.282101\pi$
$644$		0			0
$645$	8977.86			0.548066
$646$	5430.16	+	9405.31i	0.330723	+	0.572828i
$647$	−5763.57	+	9982.80i	−0.350216	+	0.606591i	−0.986287	−	0.165039i	$-0.947225\pi$
$647$	−5763.57	+	9982.80i	−0.350216	+	0.606591i	0.636072	+	0.771630i	$0.280558\pi$
$648$	18487.5	−	32021.2i	1.12077	−	1.94122i
$649$	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	$-0.123459\pi$
$653$	2258.11	+	3911.15i	0.135324	+	0.234388i	−0.790397	+	0.612595i	$0.790126\pi$
$654$	1058.73	−	1833.77i	0.0633022	−	0.109643i
$655$	459.772	−	796.348i	0.0274271	−	0.0475052i
$656$	21516.0	+	37266.7i	1.28057	+	2.21802i
$657$	1197.99			0.0711384
$658$		0			0
$659$	−27663.5			−1.63523			−0.817615	−	0.575766i	$-0.804704\pi$
$659$	−27663.5			−1.63523			−0.817615	+	0.575766i	$0.804704\pi$
$660$	13263.2	+	22972.5i	0.782225	+	1.35485i
$661$	−15755.4	+	27289.2i	−0.927103	+	1.60579i	−0.138959	+	0.990298i	$0.544376\pi$
$661$	−15755.4	+	27289.2i	−0.927103	+	1.60579i	−0.788144	+	0.615491i	$0.788958\pi$
$662$	−16980.1	+	29410.4i	−0.996905	+	1.72669i
$663$	4244.58	+	7351.83i	0.248636	+	0.430651i
$664$	−17084.1			−0.998482
$665$		0			0
$666$	4675.68			0.272040
$667$	1328.20	+	2300.51i	0.0771035	+	0.133547i
$668$	−12846.6	+	22251.0i	−0.744089	+	1.28880i
$669$	−12900.3	+	22344.0i	−0.745523	+	1.29128i
$670$	−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
$675$	−1835.41	+	3179.03i	−0.104659	+	0.181275i
$676$	2965.26	−	5135.97i	0.168710	−	0.292215i
$677$	−12498.9	−	21648.6i	−0.709557	−	1.22899i	−0.965022	−	0.262170i	$-0.915562\pi$
$677$	−12498.9	−	21648.6i	−0.709557	−	1.22899i	0.255465	−	0.966818i	$-0.417771\pi$
$678$	−18245.0			−1.03347
$679$		0			0
$680$	11482.3			0.647541
$681$	16456.1	+	28502.8i	0.925990	+	1.60386i
$682$	−10880.7	+	18846.0i	−0.610916	+	1.05814i
$683$	6630.90	−	11485.0i	0.371485	−	0.643431i	−0.618309	−	0.785935i	$-0.712182\pi$
$683$	6630.90	−	11485.0i	0.371485	−	0.643431i	0.989794	+	0.142504i	$0.0455154\pi$
$684$	−1462.23	−	2532.66i	−0.0817395	−	0.141577i
$685$	4438.74			0.247585
$686$		0			0
$687$	5889.06			0.327047
$688$	26959.5	+	46695.2i	1.49392	+	2.58755i
$689$	−559.617	+	969.284i	−0.0309430	+	0.0535948i
$690$	−3415.87	+	5916.46i	−0.188464	+	0.326429i
$691$	−12321.8	−	21341.9i	−0.678353	−	1.17494i	−0.975477	−	0.220103i	$-0.929361\pi$
$691$	−12321.8	−	21341.9i	−0.678353	−	1.17494i	0.297123	−	0.954839i	$-0.403973\pi$
$692$	49802.2			2.73583
$693$		0			0
$694$	−43862.8			−2.39915
$695$	−5838.13	−	10111.9i	−0.318637	−	0.551896i
$696$	7019.55	−	12158.2i	0.382292	−	0.662150i
$697$	5817.73	−	10076.6i	0.316158	−	0.547602i
$698$	−352.919	−	611.274i	−0.0191378	−	0.0331476i
$699$	−31163.4			−1.68628
$700$		0			0
$701$	20723.2			1.11656			0.558278	−	0.829654i	$-0.311462\pi$
$701$	20723.2			1.11656			0.558278	+	0.829654i	$0.311462\pi$
$702$	−16591.5	−	28737.3i	−0.892032	−	1.54504i
$703$	−8043.63	+	13932.0i	−0.431538	+	0.747446i
$704$	−11652.3	+	20182.4i	−0.623813	+	1.08048i
$705$	5427.25	+	9400.27i	0.289932	+	0.502177i
$706$	−12094.0			−0.644705
$707$		0			0
$708$	35251.7			1.87124
$709$	−12967.9	−	22461.0i	−0.686910	−	1.18976i	−0.972833	−	0.231510i	$-0.925633\pi$
$709$	−12967.9	−	22461.0i	−0.686910	−	1.18976i	0.285923	−	0.958253i	$-0.407700\pi$
$710$	−1754.67	+	3039.18i	−0.0927489	+	0.160646i
$711$	−1356.02	+	2348.70i	−0.0715257	+	0.123886i
$712$	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
$717$	−7368.93	+	12763.4i	−0.383818	+	0.664793i
$718$	13860.6	−	24007.3i	0.720438	−	1.24784i
$719$	−6826.85	−	11824.4i	−0.354101	−	0.613320i	0.632863	−	0.774264i	$-0.281880\pi$
$719$	−6826.85	−	11824.4i	−0.354101	−	0.613320i	−0.986964	+	0.160943i	$0.948546\pi$
$720$	−2155.61			−0.111576
$721$		0			0
$722$	−21410.3			−1.10361
$723$	−13964.7	−	24187.6i	−0.718332	−	1.24419i
$724$	27153.3	−	47031.0i	1.39385	−	2.41422i
$725$	−620.470	+	1074.69i	−0.0317844	+	0.0550521i
$726$	24016.4	+	41597.6i	1.22773	+	2.12649i
$727$	−17709.4			−0.903448			−0.451724	−	0.892158i	$-0.649191\pi$
$727$	−17709.4			−0.903448			−0.451724	+	0.892158i	$0.649191\pi$
$728$		0			0
$729$	21328.7			1.08361
$730$	5326.11	+	9225.09i	0.270038	+	0.467720i
$731$	7289.61	−	12626.0i	0.368832	−	0.638835i
$732$	−29606.1	+	51279.3i	−1.49491	+	2.58926i
$733$	5936.73	+	10282.7i	0.299152	+	0.518146i	0.975942	−	0.218030i	$-0.0699630\pi$
$733$	5936.73	+	10282.7i	0.299152	+	0.518146i	−0.676790	+	0.736176i	$0.736630\pi$
$734$	37942.9			1.90803
$735$		0			0
$736$	−16350.8			−0.818886
$737$	−14483.8	−	25086.7i	−0.723904	−	1.25384i
$738$	−2223.53	+	3851.27i	−0.110907	+	0.192096i
$739$	−15651.4	+	27109.0i	−0.779087	+	1.34942i	0.153382	+	0.988167i	$0.450983\pi$
$739$	−15651.4	+	27109.0i	−0.779087	+	1.34942i	−0.932469	+	0.361250i	$0.882350\pi$
$740$	14645.9	+	25367.5i	0.727560	+	1.26017i
$741$	11163.3			0.553433
$742$		0			0
$743$	−10385.8			−0.512808			−0.256404	−	0.966570i	$-0.582538\pi$
$743$	−10385.8			−0.512808			−0.256404	+	0.966570i	$0.582538\pi$
$744$	10434.5	+	18073.1i	0.514178	+	0.890583i
$745$	6007.69	−	10405.6i	0.295442	−	0.511721i
$746$	4322.92	−	7487.51i	0.212163	−	0.367476i
$747$	−433.606	−	751.028i	−0.0212380	−	0.0367854i
$748$	43076.4			2.10565
$749$		0			0
$750$	−3191.46			−0.155381
$751$	−8285.63	−	14351.1i	−0.402593	−	0.697311i	0.591445	−	0.806345i	$-0.298558\pi$
$751$	−8285.63	−	14351.1i	−0.402593	−	0.697311i	−0.994038	+	0.109034i	$0.965224\pi$
$752$	−32594.8	+	56455.8i	−1.58060	+	2.73768i
$753$	−17107.5	+	29631.0i	−0.827929	+	1.43402i
$754$	−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
$759$	−7441.04	+	12888.3i	−0.355853	+	0.616356i
$760$	7549.66	−	13076.4i	0.360335	−	0.624119i
$761$	8210.95	+	14221.8i	0.391126	+	0.677449i	0.992598	−	0.121444i	$-0.0387525\pi$
$761$	8210.95	+	14221.8i	0.391126	+	0.677449i	−0.601473	+	0.798893i	$0.705419\pi$
$762$	−48041.9			−2.28395
$763$		0			0
$764$	80193.0			3.79749
$765$	291.429	+	504.770i	0.0137734	+	0.0238562i
$766$	−28466.9	+	49306.0i	−1.34275	+	2.32572i
$767$	8177.83	−	14164.4i	0.384986	−	0.666815i
$768$	−11958.7	−	20713.0i	−0.561877	−	0.973200i
$769$	−17603.4			−0.825479			−0.412739	−	0.910849i	$-0.635428\pi$
$769$	−17603.4			−0.825479			−0.412739	+	0.910849i	$0.635428\pi$
$770$		0			0
$771$	15170.0			0.708605
$772$	−1321.94	−	2289.66i	−0.0616290	−	0.106744i
$773$	7954.16	−	13777.0i	0.370105	−	0.641041i	−0.619476	−	0.785015i	$-0.712655\pi$
$773$	7954.16	−	13777.0i	0.370105	−	0.641041i	0.989581	+	0.143975i	$0.0459883\pi$
$774$	−2786.08	+	4825.63i	−0.129384	+	0.224100i
$775$	−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
$780$	10163.1	−	17603.0i	0.466535	−	0.808062i
$781$	−3822.34	+	6620.48i	−0.175127	+	0.303328i
$782$	5547.06	+	9607.79i	0.253660	+	0.439353i
$783$	7288.43			0.332653
$784$		0			0
$785$	−7162.44			−0.325654
$786$	−2347.75	−	4066.42i	−0.106541	−	0.184535i
$787$	9494.43	−	16444.8i	0.430038	−	0.744847i	−0.566838	−	0.823829i	$-0.691834\pi$
$787$	9494.43	−	16444.8i	0.430038	−	0.744847i	0.996876	+	0.0789818i	$0.0251669\pi$
$788$	−14057.9	+	24349.0i	−0.635524	+	1.10076i
$789$	4869.29	+	8433.86i	0.219710	+	0.380549i
$790$	−24114.8			−1.08603
$791$		0			0
$792$	−9559.87			−0.428908
$793$	13736.3	+	23791.9i	0.615119	+	1.06542i
$794$	−29785.1	+	51589.2i	−1.33128	+	2.30584i
$795$	316.116	−	547.530i	0.0141025	−	0.0244263i
$796$	−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
$801$	−715.110	+	1238.61i	−0.0315445	+	0.0546367i
$802$	24023.8	−	41610.4i	1.05774	−	1.83206i
$803$	11602.2	+	20095.7i	0.509881	+	0.883140i
$804$	−47841.4			−2.09855
$805$		0			0
$806$	16675.0			0.728726
$807$	−15162.9	−	26263.0i	−0.661414	−	1.14560i
$808$	2236.04	−	3872.94i	0.0973561	−	0.168626i
$809$	−13321.8	+	23074.1i	−0.578950	+	1.00277i	0.416650	+	0.909067i	$0.363204\pi$
$809$	−13321.8	+	23074.1i	−0.578950	+	1.00277i	−0.995600	+	0.0937039i	$0.970129\pi$
$810$	8344.45	+	14453.0i	0.361968	+	0.626947i
$811$	−15678.2			−0.678835			−0.339418	−	0.940636i	$-0.610230\pi$
$811$	−15678.2			−0.678835			−0.339418	+	0.940636i	$0.610230\pi$
$812$		0			0
$813$	−30022.9			−1.29514
$814$	45282.9	+	78432.3i	1.94983	+	3.37721i
$815$	2152.07	−	3727.50i	0.0924955	−	0.160207i
$816$	14399.9	−	24941.4i	0.617767	−	1.07000i
$817$	−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	$-0.0975637\pi$
$821$	5066.92	+	8776.17i	0.215392	+	0.373070i	−0.738002	+	0.674799i	$0.764230\pi$
$822$	11332.8	−	19629.0i	0.480873	−	0.832897i
$823$	7031.33	−	12178.6i	0.297809	−	0.515820i	−0.677826	−	0.735223i	$-0.737078\pi$
$823$	7031.33	−	12178.6i	0.297809	−	0.515820i	0.975634	+	0.219403i	$0.0704109\pi$
$824$	32793.0	+	56799.1i	1.38640	+	2.40132i
$825$	−6952.19			−0.293387
$826$		0			0
$827$	−13697.4			−0.575942			−0.287971	−	0.957639i	$-0.592981\pi$
$827$	−13697.4			−0.575942			−0.287971	+	0.957639i	$0.592981\pi$
$828$	−1493.71	−	2587.18i	−0.0626933	−	0.108588i
$829$	8777.47	−	15203.0i	0.367737	−	0.636940i	−0.621474	−	0.783435i	$-0.713466\pi$
$829$	8777.47	−	15203.0i	0.367737	−	0.636940i	0.989211	+	0.146495i	$0.0467992\pi$
$830$	3855.52	−	6677.96i	0.161237	−	0.279271i
$831$	8083.09	+	14000.3i	0.337424	+	0.584436i
$832$	17857.6			0.744110
$833$		0			0
$834$	−59622.9			−2.47551
$835$	−3366.92	−	5831.68i	−0.139542	−	0.241693i
$836$	28322.8	−	49056.5i	1.17173	−	2.02949i
$837$	−5417.11	+	9382.71i	−0.223707	+	0.387472i
$838$	−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
$843$	−11296.1	+	19565.4i	−0.461517	+	0.799370i
$844$	−16998.2	+	29441.8i	−0.693250	+	1.20074i
$845$	777.152	+	1346.07i	0.0316389	+	0.0548001i
$846$	−6736.90			−0.273782
$847$		0			0
$848$	3797.05			0.153763
$849$	2991.88	+	5182.08i	0.120943	+	0.209480i
$850$	−2591.32	+	4488.30i	−0.104566	+	0.181114i
$851$	−8216.79	+	14231.9i	−0.330985	+	0.573282i
$852$	6312.77	+	10934.0i	0.253840	+	0.439664i
$853$	16014.1			0.642804			0.321402	−	0.946943i	$-0.395846\pi$
$853$	16014.1			0.642804			0.321402	+	0.946943i	$0.395846\pi$
$854$		0			0
$855$	766.461			0.0306578
$856$	−2165.71	−	3751.11i	−0.0864746	−	0.149778i
$857$	21748.7	−	37669.9i	0.866886	−	1.50149i	0.00172420	−	0.999999i	$-0.499451\pi$
$857$	21748.7	−	37669.9i	0.866886	−	1.50149i	0.865162	−	0.501492i	$-0.167215\pi$
$858$	31422.8	−	54425.8i	1.25030	−	2.16558i
$859$	12639.3	+	21891.9i	0.502034	+	0.869548i	0.999997	+	0.00235021i	$0.000748096\pi$
$859$	12639.3	+	21891.9i	0.502034	+	0.869548i	−0.497963	+	0.867198i	$0.665919\pi$
$860$	−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	$-0.0683866\pi$
$863$	7703.88	+	13343.5i	0.303874	+	0.526325i	−0.673136	+	0.739519i	$0.735053\pi$
$864$	−22431.2	+	38851.9i	−0.883245	+	1.52982i
$865$	−6526.23	+	11303.8i	−0.256530	+	0.444323i
$866$	−36896.7	−	63906.9i	−1.44781	−	2.50767i
$867$	16318.5			0.639221
$868$		0			0
$869$	−52531.1			−2.05063
$870$	3168.33	+	5487.70i	0.123467	+	0.213851i
$871$	−11098.4	+	19223.0i	−0.431752	+	0.747816i
$872$	−2390.35	+	4140.21i	−0.0928297	+	0.160786i
$873$	696.274	+	1205.98i	0.0269935	+	0.0467541i
$874$	14588.8			0.564615
$875$		0			0
$876$	38323.3			1.47811
$877$	−16394.3	−	28395.7i	−0.631238	−	1.09334i	−0.987299	−	0.158874i	$-0.949214\pi$
$877$	−16394.3	−	28395.7i	−0.631238	−	1.09334i	0.356061	−	0.934463i	$-0.384120\pi$
$878$	22616.6	−	39173.1i	0.869333	−	1.50573i
$879$	20692.8	−	35840.9i	0.794027	−	1.37530i
$880$	−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
$885$	−4619.49	+	8001.20i	−0.175461	+	0.303907i
$886$	24440.6	−	42332.4i	0.926749	−	1.60518i
$887$	2.79803	+	4.84633i	0.000105917	+	0.000183454i	0.866078	−	0.499908i	$-0.166633\pi$
$887$	2.79803	+	4.84633i	0.000105917	+	0.000183454i	−0.865972	+	0.500092i	$0.833300\pi$
$888$	86851.9			3.28216
$889$		0			0
$890$	−12717.2			−0.478967
$891$	18177.3	+	31484.0i	0.683460	+	1.18379i
$892$	50159.5	−	86878.8i	1.88281	−	3.26112i
$893$	11589.6	−	20073.8i	0.434301	−	0.752231i
$894$	−30677.3	−	53134.6i	−1.14765	−	1.98779i
$895$	6752.24			0.252181
$896$		0			0
$897$	11403.6			0.424476
$898$	−24748.1	−	42864.9i	−0.919659	−	1.59290i
$899$	−1831.28	+	3171.87i	−0.0679384	+	0.117673i
$900$	697.789	−	1208.61i	0.0258440	−	0.0447632i
$901$	−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
$906$	15757.9	−	27293.4i	0.577836	−	1.00084i
$907$	3861.66	−	6688.58i	0.141372	−	0.244863i	−0.786642	−	0.617410i	$-0.788182\pi$
$907$	3861.66	−	6688.58i	0.141372	−	0.244863i	0.928013	+	0.372547i	$0.121515\pi$
$908$	−63985.2	−	110826.i	−2.33857	−	4.05053i
$909$	227.009			0.00828318
$910$		0			0
$911$	6805.43			0.247502			0.123751	−	0.992313i	$-0.460508\pi$
$911$	6805.43			0.247502			0.123751	+	0.992313i	$0.460508\pi$
$912$	−18936.0	−	32798.0i	−0.687535	−	1.19085i
$913$	8398.76	−	14547.1i	0.304445	−	0.527314i
$914$	3557.23	−	6161.30i	0.128734	−	0.222974i
$915$	−7759.35	−	13439.6i	−0.280345	−	0.485572i
$916$	−22898.0			−0.825953
$917$		0			0
$918$	30439.3			1.09438
$919$	22590.1	+	39127.2i	0.810858	+	1.40445i	0.912264	+	0.409602i	$0.134333\pi$
$919$	22590.1	+	39127.2i	0.810858	+	1.40445i	−0.101406	+	0.994845i	$0.532334\pi$
$920$	7712.19	−	13357.9i	0.276373	−	0.478692i
$921$	−2076.80	+	3597.12i	−0.0743027	+	0.128696i
$922$	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
$927$	−1664.61	+	2883.20i	−0.0589785	+	0.102154i
$928$	−7582.96	+	13134.1i	−0.268236	+	0.464598i
$929$	2596.11	+	4496.59i	0.0916852	+	0.158803i	0.908220	−	0.418492i	$-0.137441\pi$
$929$	2596.11	+	4496.59i	0.0916852	+	0.158803i	−0.816535	+	0.577296i	$0.804108\pi$
$930$	−9419.40			−0.332123
$931$		0			0
$932$	121171.			4.25866
$933$	−4812.28	−	8335.11i	−0.168861	−	0.292475i
$934$	−22114.7	+	38303.8i	−0.774749	+	1.34191i
$935$	−5644.86	+	9777.18i	−0.197440	+	0.341976i
$936$	3662.69	+	6343.97i	0.127905	+	0.221538i
$937$	7107.58			0.247806			0.123903	−	0.992294i	$-0.460459\pi$
$937$	7107.58			0.247806			0.123903	+	0.992294i	$0.460459\pi$
$938$		0			0
$939$	32039.4			1.11349
$940$	−21102.4	−	36550.5i	−0.732218	−	1.26824i
$941$	−21831.5	+	37813.3i	−0.756309	+	1.30997i	0.188411	+	0.982090i	$0.439666\pi$
$941$	−21831.5	+	37813.3i	−0.756309	+	1.30997i	−0.944721	+	0.327876i	$0.893667\pi$
$942$	−18286.9	+	31673.9i	−0.632505	+	1.09553i
$943$	−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	$-0.252020\pi$
$947$	−7721.04	−	13373.2i	−0.264942	−	0.458893i	−0.967548	+	0.252686i	$0.918686\pi$
$948$	−43378.8	+	75134.3i	−1.48616	+	2.57410i
$949$	8890.39	−	15398.6i	0.304104	−	0.526723i
$950$	3407.59	+	5902.12i	0.116376	+	0.201569i
$951$	37733.7			1.28664
$952$		0			0
$953$	44561.5			1.51468			0.757339	−	0.653022i	$-0.226499\pi$
$953$	44561.5			1.51468			0.757339	+	0.653022i	$0.226499\pi$
$954$	196.200	+	339.828i	0.00665848	+	0.0115328i
$955$	−10508.7	+	18201.7i	−0.356078	+	0.616746i
$956$	28652.1	−	49627.0i	0.969327	−	1.67892i
$957$	6901.79	+	11954.3i	0.233128	+	0.403789i
$958$	3762.08			0.126876
$959$		0			0
$960$	−10087.4			−0.339134
$961$	12173.3	+	21084.8i	0.408624	+	0.707757i
$962$	34698.7	−	60099.9i	1.16292	−	2.01424i
$963$	109.934	−	190.411i	0.00367869	−	0.00637167i
$964$	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
$969$	−5120.12	+	8868.31i	−0.169744	+	0.294005i
$970$	−6191.10	+	10723.3i	−0.204932	+	0.354953i
$971$	−8855.15	−	15337.6i	−0.292662	−	0.506906i	0.681776	−	0.731561i	$-0.261208\pi$
$971$	−8855.15	−	15337.6i	−0.292662	−	0.506906i	−0.974438	+	0.224655i	$0.927875\pi$
$972$	−15591.9			−0.514517
$973$		0			0
$974$	12006.4			0.394979
$975$	2663.61	+	4613.50i	0.0874910	+	0.151539i
$976$	46600.8	−	80715.0i	1.52834	−	2.64716i
$977$	28778.7	−	49846.2i	0.942387	−	1.63226i	0.181488	−	0.983393i	$-0.441909\pi$
$977$	28778.7	−	49846.2i	0.942387	−	1.63226i	0.760900	−	0.648870i	$-0.224758\pi$
$978$	−10989.2	−	19033.9i	−0.359301	−	0.622327i
$979$	−27702.7			−0.904375
$980$		0			0
$981$	−242.675			−0.00789806
$982$	22554.5	+	39065.5i	0.732936	+	1.26948i
$983$	−12494.4	+	21640.9i	−0.405401	+	0.702175i	−0.994368	−	0.105982i	$-0.966202\pi$
$983$	−12494.4	+	21640.9i	−0.405401	+	0.702175i	0.588967	+	0.808157i	$0.299535\pi$
$984$	−41302.6	+	71538.2i	−1.33809	+	2.31764i
$985$	−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
$990$	2157.46	−	3736.83i	0.0692611	−	0.119964i
$991$	−30786.6	+	53324.0i	−0.986850	+	1.70927i	−0.353443	+	0.935456i	$0.614989\pi$
$991$	−30786.6	+	53324.0i	−0.986850	+	1.70927i	−0.633407	+	0.773819i	$0.718344\pi$
$992$	−11272.0	−	19523.7i	−0.360774	−	0.624879i
$993$	−32021.2			−1.02333
$994$		0			0
$995$	18048.0			0.575035
$996$	−13871.0	−	24025.2i	−0.441283	−	0.764325i
$997$	−4696.60	+	8134.74i	−0.149190	+	0.258405i	−0.930928	−	0.365202i	$-0.881000\pi$
$997$	−4696.60	+	8134.74i	−0.149190	+	0.258405i	0.781738	+	0.623607i	$0.214333\pi$
$998$	−51832.6	+	89776.7i	−1.64402	+	2.84753i
$999$	22544.7	+	39048.5i	0.713995	+	1.23668i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	245.4.e.o.116.1		10
7.2	even	3	inner	245.4.e.o.226.1		10
7.3	odd	6		245.4.a.m.1.5		5
7.4	even	3		245.4.a.n.1.5		5
7.5	odd	6		35.4.e.c.16.1	yes	10
7.6	odd	2		35.4.e.c.11.1	✓	10
21.5	even	6		315.4.j.g.226.5		10
21.11	odd	6		2205.4.a.bt.1.1		5
21.17	even	6		2205.4.a.bu.1.1		5
21.20	even	2		315.4.j.g.46.5		10
28.19	even	6		560.4.q.n.401.4		10
28.27	even	2		560.4.q.n.81.4		10
35.4	even	6		1225.4.a.bf.1.1		5
35.12	even	12		175.4.k.d.149.1		20
35.13	even	4		175.4.k.d.74.1		20
35.19	odd	6		175.4.e.d.51.5		10
35.24	odd	6		1225.4.a.bg.1.1		5
35.27	even	4		175.4.k.d.74.10		20
35.33	even	12		175.4.k.d.149.10		20
35.34	odd	2		175.4.e.d.151.5		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.4.e.c.11.1	✓	10	7.6	odd	2
35.4.e.c.16.1	yes	10	7.5	odd	6
175.4.e.d.51.5		10	35.19	odd	6
175.4.e.d.151.5		10	35.34	odd	2
175.4.k.d.74.1		20	35.13	even	4
175.4.k.d.74.10		20	35.27	even	4
175.4.k.d.149.1		20	35.12	even	12
175.4.k.d.149.10		20	35.33	even	12
245.4.a.m.1.5		5	7.3	odd	6
245.4.a.n.1.5		5	7.4	even	3
245.4.e.o.116.1		10	1.1	even	1	trivial
245.4.e.o.226.1		10	7.2	even	3	inner
315.4.j.g.46.5		10	21.20	even	2
315.4.j.g.226.5		10	21.5	even	6
560.4.q.n.81.4		10	28.27	even	2
560.4.q.n.401.4		10	28.19	even	6
1225.4.a.bf.1.1		5	35.4	even	6
1225.4.a.bg.1.1		5	35.24	odd	6
2205.4.a.bt.1.1		5	21.11	odd	6
2205.4.a.bu.1.1		5	21.17	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 245 = 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	245.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.60181 - 4.50647i) q^{2} +(2.45326 - 4.24917i) q^{3} +(-9.53885 + 16.5218i) q^{4} +(-2.50000 - 4.33013i) q^{5} -25.5317 q^{6} +57.6442 q^{8} +(1.46305 + 2.53407i) q^{9} +O(q^{10})\)	\(q+(-2.60181 - 4.50647i) q^{2} +(2.45326 - 4.24917i) q^{3} +(-9.53885 + 16.5218i) q^{4} +(-2.50000 - 4.33013i) q^{5} -25.5317 q^{6} +57.6442 q^{8} +(1.46305 + 2.53407i) q^{9} +(-13.0091 + 22.5324i) q^{10} +(-28.3386 + 49.0839i) q^{11} +(46.8025 + 81.0644i) q^{12} +43.4297 q^{13} -24.5326 q^{15} +(-73.6685 - 127.598i) q^{16} +(-19.9193 + 34.5013i) q^{17} +(7.61315 - 13.1864i) q^{18} +(26.1940 + 45.3693i) q^{19} +95.3885 q^{20} +294.927 q^{22} +(26.7579 + 46.3460i) q^{23} +(141.416 - 244.940i) q^{24} +(-12.5000 + 21.6506i) q^{25} +(-112.996 - 195.715i) q^{26} +146.833 q^{27} +49.6376 q^{29} +(63.8292 + 110.555i) q^{30} +(-36.8930 + 63.9006i) q^{31} +(-152.767 + 264.599i) q^{32} +(139.044 + 240.831i) q^{33} +207.305 q^{34} -55.8231 q^{36} +(153.540 + 265.938i) q^{37} +(136.304 - 236.085i) q^{38} +(106.544 - 184.540i) q^{39} +(-144.110 - 249.607i) q^{40} -292.064 q^{41} -365.956 q^{43} +(-540.635 - 936.407i) q^{44} +(7.31524 - 12.6704i) q^{45} +(139.238 - 241.167i) q^{46} +(-221.226 - 383.175i) q^{47} -722.912 q^{48} +130.091 q^{50} +(97.7346 + 169.281i) q^{51} +(-414.269 + 717.536i) q^{52} +(-12.8856 + 22.3185i) q^{53} +(-382.032 - 661.698i) q^{54} +283.386 q^{55} +257.043 q^{57} +(-129.148 - 223.690i) q^{58} +(188.300 - 326.146i) q^{59} +(234.013 - 405.322i) q^{60} +(316.287 + 547.826i) q^{61} +383.955 q^{62} +411.183 q^{64} +(-108.574 - 188.056i) q^{65} +(723.531 - 1253.19i) q^{66} +(-255.549 + 442.624i) q^{67} +(-380.015 - 658.206i) q^{68} +262.576 q^{69} +134.881 q^{71} +(84.3362 + 146.075i) q^{72} +(204.708 - 354.564i) q^{73} +(798.962 - 1383.84i) q^{74} +(61.3315 + 106.229i) q^{75} -999.443 q^{76} -1108.83 q^{78} +(463.424 + 802.674i) q^{79} +(-368.343 + 637.988i) q^{80} +(320.717 - 555.498i) q^{81} +(759.897 + 1316.18i) q^{82} -296.372 q^{83} +199.193 q^{85} +(952.150 + 1649.17i) q^{86} +(121.774 - 210.918i) q^{87} +(-1633.55 + 2829.40i) q^{88} +(244.391 + 423.297i) q^{89} -76.1315 q^{90} -1020.96 q^{92} +(181.016 + 313.529i) q^{93} +(-1151.18 + 1993.90i) q^{94} +(130.970 - 226.847i) q^{95} +(749.552 + 1298.26i) q^{96} +475.907 q^{97} -165.843 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - q^{2} - 8 q^{3} - 35 q^{4} - 25 q^{5} - 32 q^{6} + 66 q^{8} - 81 q^{9}+O(q^{10}) \) 10 * q - q^2 - 8 * q^3 - 35 * q^4 - 25 * q^5 - 32 * q^6 + 66 * q^8 - 81 * q^9	\( 10 q - q^{2} - 8 q^{3} - 35 q^{4} - 25 q^{5} - 32 q^{6} + 66 q^{8} - 81 q^{9} - 5 q^{10} - 47 q^{11} - 98 q^{12} - 2 q^{13} + 80 q^{15} - 171 q^{16} - 2 q^{17} + 51 q^{18} - 21 q^{19} + 350 q^{20} + 1046 q^{22} - 201 q^{23} + 848 q^{24} - 125 q^{25} - 47 q^{26} + 1036 q^{27} + 380 q^{29} + 80 q^{30} + 388 q^{31} + 95 q^{32} - 262 q^{33} - 260 q^{34} + 2458 q^{36} + 145 q^{37} + 835 q^{38} - 14 q^{39} - 165 q^{40} + 562 q^{41} + 1136 q^{43} - 1091 q^{44} - 405 q^{45} - 337 q^{46} - 473 q^{47} - 140 q^{48} + 50 q^{50} - 732 q^{51} - 379 q^{52} - 351 q^{53} - 774 q^{54} + 470 q^{55} + 1908 q^{57} - 1818 q^{58} + 708 q^{59} - 490 q^{60} + 1944 q^{61} - 896 q^{62} - 250 q^{64} + 5 q^{65} + 1482 q^{66} - 1118 q^{67} - 3118 q^{68} - 748 q^{69} + 1728 q^{71} + 2219 q^{72} - 1652 q^{73} + 3285 q^{74} - 200 q^{75} - 1382 q^{76} - 11148 q^{78} - 218 q^{79} - 855 q^{80} + 455 q^{81} + 1027 q^{82} + 3004 q^{83} + 20 q^{85} + 4264 q^{86} + 390 q^{87} - 2131 q^{88} + 2322 q^{89} - 510 q^{90} - 5914 q^{92} + 2288 q^{93} - 2677 q^{94} - 105 q^{95} + 4592 q^{96} - 1196 q^{97} + 70 q^{99}+O(q^{100}) \) 10 * q - q^2 - 8 * q^3 - 35 * q^4 - 25 * q^5 - 32 * q^6 + 66 * q^8 - 81 * q^9 - 5 * q^10 - 47 * q^11 - 98 * q^12 - 2 * q^13 + 80 * q^15 - 171 * q^16 - 2 * q^17 + 51 * q^18 - 21 * q^19 + 350 * q^20 + 1046 * q^22 - 201 * q^23 + 848 * q^24 - 125 * q^25 - 47 * q^26 + 1036 * q^27 + 380 * q^29 + 80 * q^30 + 388 * q^31 + 95 * q^32 - 262 * q^33 - 260 * q^34 + 2458 * q^36 + 145 * q^37 + 835 * q^38 - 14 * q^39 - 165 * q^40 + 562 * q^41 + 1136 * q^43 - 1091 * q^44 - 405 * q^45 - 337 * q^46 - 473 * q^47 - 140 * q^48 + 50 * q^50 - 732 * q^51 - 379 * q^52 - 351 * q^53 - 774 * q^54 + 470 * q^55 + 1908 * q^57 - 1818 * q^58 + 708 * q^59 - 490 * q^60 + 1944 * q^61 - 896 * q^62 - 250 * q^64 + 5 * q^65 + 1482 * q^66 - 1118 * q^67 - 3118 * q^68 - 748 * q^69 + 1728 * q^71 + 2219 * q^72 - 1652 * q^73 + 3285 * q^74 - 200 * q^75 - 1382 * q^76 - 11148 * q^78 - 218 * q^79 - 855 * q^80 + 455 * q^81 + 1027 * q^82 + 3004 * q^83 + 20 * q^85 + 4264 * q^86 + 390 * q^87 - 2131 * q^88 + 2322 * q^89 - 510 * q^90 - 5914 * q^92 + 2288 * q^93 - 2677 * q^94 - 105 * q^95 + 4592 * q^96 - 1196 * q^97 + 70 * q^99

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