LMFDB - Embedded newform 245.4.b.d.99.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [245,4,Mod(99,245)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(245, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("245.99");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 245 = 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	245.b (of order $2$, degree $1$, 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:	$10$
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} + 55x^{8} + 983x^{6} + 6409x^{4} + 13560x^{2} + 3600 $ x^10 + 55x^8 + 983x^6 + 6409x^4 + 13560x^2 + 3600
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{3}\cdot 7^{4} $
Twist minimal:	no (minimal twist has level 35)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			99.1
Root			$-4.31366i$ of defining polynomial
Character	$\chi$	$=$	245.99
Dual form			245.4.b.d.99.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-5.31366i q^{2} -1.93939i q^{3} -20.2350 q^{4} +(2.32771 + 10.9353i) q^{5} -10.3052 q^{6} +65.0123i q^{8} +23.2388 q^{9} +(58.1067 - 12.3686i) q^{10} +25.5420 q^{11} +39.2434i q^{12} +64.1014i q^{13} +(21.2079 - 4.51433i) q^{15} +183.574 q^{16} -27.6952i q^{17} -123.483i q^{18} +0.792436 q^{19} +(-47.1011 - 221.276i) q^{20} -135.721i q^{22} +108.606i q^{23} +126.084 q^{24} +(-114.164 + 50.9086i) q^{25} +340.613 q^{26} -97.4324i q^{27} +234.000 q^{29} +(-23.9876 - 112.691i) q^{30} -129.204 q^{31} -455.349i q^{32} -49.5357i q^{33} -147.163 q^{34} -470.236 q^{36} -38.3108i q^{37} -4.21073i q^{38} +124.317 q^{39} +(-710.932 + 151.330i) q^{40} +403.216 q^{41} +172.895i q^{43} -516.840 q^{44} +(54.0931 + 254.124i) q^{45} +577.097 q^{46} +206.943i q^{47} -356.020i q^{48} +(270.511 + 606.626i) q^{50} -53.7117 q^{51} -1297.09i q^{52} +144.031i q^{53} -517.722 q^{54} +(59.4542 + 279.310i) q^{55} -1.53684i q^{57} -1243.40i q^{58} -679.086 q^{59} +(-429.140 + 91.3471i) q^{60} +574.717 q^{61} +686.544i q^{62} -950.977 q^{64} +(-700.971 + 149.209i) q^{65} -263.216 q^{66} -515.640i q^{67} +560.411i q^{68} +210.630 q^{69} +556.612 q^{71} +1510.81i q^{72} +173.243i q^{73} -203.571 q^{74} +(98.7314 + 221.407i) q^{75} -16.0349 q^{76} -660.580i q^{78} -79.3290 q^{79} +(427.306 + 2007.44i) q^{80} +438.488 q^{81} -2142.55i q^{82} -1043.56i q^{83} +(302.856 - 64.4663i) q^{85} +918.703 q^{86} -453.817i q^{87} +1660.54i q^{88} +652.060 q^{89} +(1350.33 - 287.432i) q^{90} -2197.65i q^{92} +250.576i q^{93} +1099.62 q^{94} +(1.84456 + 8.66556i) q^{95} -883.097 q^{96} +515.714i q^{97} +593.564 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 36 q^{4} - 6 q^{5} - 12 q^{6} - 46 q^{9} + 16 q^{10} + 84 q^{11} + 8 q^{15} + 148 q^{16} - 72 q^{19} + 68 q^{20} - 72 q^{24} - 362 q^{25} + 620 q^{26} + 88 q^{29} + 52 q^{30} - 120 q^{31} - 964 q^{34}+ \cdots - 5304 q^{99}+O(q^{100}) $ 10 * q - 36 * q^4 - 6 * q^5 - 12 * q^6 - 46 * q^9 + 16 * q^10 + 84 * q^11 + 8 * q^15 + 148 * q^16 - 72 * q^19 + 68 * q^20 - 72 * q^24 - 362 * q^25 + 620 * q^26 + 88 * q^29 + 52 * q^30 - 120 * q^31 - 964 * q^34 - 420 * q^36 + 212 * q^39 - 1396 * q^40 + 852 * q^41 - 1424 * q^44 + 510 * q^45 + 176 * q^46 + 1644 * q^50 + 1276 * q^51 + 996 * q^54 + 1136 * q^55 - 864 * q^59 - 1692 * q^60 + 884 * q^61 - 2724 * q^64 + 520 * q^65 - 1148 * q^66 - 4808 * q^69 + 880 * q^71 + 3024 * q^74 - 720 * q^75 + 2672 * q^76 - 3580 * q^79 + 2316 * q^80 - 302 * q^81 + 1572 * q^85 + 2432 * q^86 + 1492 * q^89 + 7748 * q^90 - 1652 * q^94 - 1628 * q^95 - 4080 * q^96 - 5304 * q^99

Character values

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

$n$	$101$	$197$
$\chi(n)$	$1$	$-1$

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 $

$2$		−	5.31366i		−	1.87866i	−0.343013	−	0.939331i	$-0.611447\pi$
$2$		−	5.31366i		−	1.87866i	0.343013	−	0.939331i	$-0.388553\pi$
$3$		−	1.93939i		−	0.373235i	−0.982433	−	0.186617i	$-0.940247\pi$
$3$		−	1.93939i		−	0.373235i	0.982433	−	0.186617i	$-0.0597525\pi$
$4$	−20.2350			−2.52937
$5$	2.32771	+	10.9353i	0.208197	+	0.978087i
$5$	2.32771	+	10.9353i	0.208197	+	0.978087i
$6$	−10.3052			−0.701182
$7$		0			0
$7$		0			0
$8$			65.0123i			2.87317i
$9$	23.2388			0.860696
$10$	58.1067	−	12.3686i	1.83749	−	0.391131i
$11$	25.5420			0.700108			0.350054	−	0.936730i	$-0.386163\pi$
$11$	25.5420			0.700108			0.350054	+	0.936730i	$0.386163\pi$
$12$			39.2434i			0.944049i
$13$			64.1014i			1.36758i	0.729679	+	0.683790i	$0.239670\pi$
$13$			64.1014i			1.36758i	−0.729679	+	0.683790i	$0.760330\pi$
$14$		0			0
$15$	21.2079	−	4.51433i	0.365056	−	0.0777063i
$16$	183.574			2.86834
$17$		−	27.6952i		−	0.395122i	−0.980291	−	0.197561i	$-0.936698\pi$
$17$		−	27.6952i		−	0.395122i	0.980291	−	0.197561i	$-0.0633020\pi$
$18$		−	123.483i		−	1.61696i
$19$	0.792436			0.00956828			0.00478414	−	0.999989i	$-0.498477\pi$
$19$	0.792436			0.00956828			0.00478414	+	0.999989i	$0.498477\pi$
$20$	−47.1011	−	221.276i	−0.526606	−	2.47394i
$21$		0			0
$22$		−	135.721i		−	1.31527i
$23$			108.606i			0.984609i	0.870423	+	0.492305i	$0.163845\pi$
$23$			108.606i			0.984609i	−0.870423	+	0.492305i	$0.836155\pi$
$24$	126.084			1.07237
$25$	−114.164	+	50.9086i	−0.913308	+	0.407269i
$26$	340.613			2.56922
$27$		−	97.4324i		−	0.694477i
$28$		0			0
$29$	234.000			1.49837			0.749186	−	0.662360i	$-0.230445\pi$
$29$	234.000			1.49837			0.749186	+	0.662360i	$0.230445\pi$
$30$	−23.9876	−	112.691i	−0.145984	−	0.685817i
$31$	−129.204			−0.748570			−0.374285	−	0.927314i	$-0.622112\pi$
$31$	−129.204			−0.748570			−0.374285	+	0.927314i	$0.622112\pi$
$32$		−	455.349i		−	2.51547i
$33$		−	49.5357i		−	0.261305i
$34$	−147.163			−0.742300
$35$		0			0
$36$	−470.236			−2.17702
$37$		−	38.3108i		−	0.170223i	−0.996371	−	0.0851116i	$-0.972875\pi$
$37$		−	38.3108i		−	0.170223i	0.996371	−	0.0851116i	$-0.0271247\pi$
$38$		−	4.21073i		−	0.0179756i
$39$	124.317			0.510429
$40$	−710.932	+	151.330i	−2.81021	+	0.598183i
$41$	403.216			1.53590			0.767949	−	0.640511i	$-0.221278\pi$
$41$	403.216			1.53590			0.767949	+	0.640511i	$0.221278\pi$
$42$		0			0
$43$			172.895i			0.613167i	0.951844	+	0.306584i	$0.0991859\pi$
$43$			172.895i			0.613167i	−0.951844	+	0.306584i	$0.900814\pi$
$44$	−516.840			−1.77083
$45$	54.0931	+	254.124i	0.179194	+	0.841835i
$46$	577.097			1.84975
$47$			206.943i			0.642250i	0.947037	+	0.321125i	$0.104061\pi$
$47$			206.943i			0.642250i	−0.947037	+	0.321125i	$0.895939\pi$
$48$		−	356.020i		−	1.07056i
$49$		0			0
$50$	270.511	+	606.626i	0.765120	+	1.71580i
$51$	−53.7117			−0.147473
$52$		−	1297.09i		−	3.45911i
$53$			144.031i			0.373287i	0.982428	+	0.186643i	$0.0597609\pi$
$53$			144.031i			0.373287i	−0.982428	+	0.186643i	$0.940239\pi$
$54$	−517.722			−1.30469
$55$	59.4542	+	279.310i	0.145760	+	0.684767i
$56$		0			0
$57$		−	1.53684i		−	0.00357122i
$58$		−	1243.40i		−	2.81493i
$59$	−679.086			−1.49846			−0.749232	−	0.662307i	$-0.769577\pi$
$59$	−679.086			−1.49846			−0.749232	+	0.662307i	$0.769577\pi$
$60$	−429.140	+	91.3471i	−0.923362	+	0.196548i
$61$	574.717			1.20631			0.603155	−	0.797624i	$-0.293910\pi$
$61$	574.717			1.20631			0.603155	+	0.797624i	$0.293910\pi$
$62$			686.544i			1.40631i
$63$		0			0
$64$	−950.977			−1.85738
$65$	−700.971	+	149.209i	−1.33761	+	0.284725i
$66$	−263.216			−0.490903
$67$		−	515.640i		−	0.940230i	−0.882605	−	0.470115i	$-0.844212\pi$
$67$		−	515.640i		−	0.940230i	0.882605	−	0.470115i	$-0.155788\pi$
$68$			560.411i			0.999409i
$69$	210.630			0.367491
$70$		0			0
$71$	556.612			0.930391			0.465195	−	0.885208i	$-0.345984\pi$
$71$	556.612			0.930391			0.465195	+	0.885208i	$0.345984\pi$
$72$			1510.81i			2.47292i
$73$			173.243i			0.277762i	0.990309	+	0.138881i	$0.0443505\pi$
$73$			173.243i			0.277762i	−0.990309	+	0.138881i	$0.955650\pi$
$74$	−203.571			−0.319792
$75$	98.7314	+	221.407i	0.152007	+	0.340879i
$76$	−16.0349			−0.0242017
$77$		0			0
$78$		−	660.580i		−	0.958923i
$79$	−79.3290			−0.112977			−0.0564887	−	0.998403i	$-0.517990\pi$
$79$	−79.3290			−0.112977			−0.0564887	+	0.998403i	$0.517990\pi$
$80$	427.306	+	2007.44i	0.597178	+	2.80548i
$81$	438.488			0.601493
$82$		−	2142.55i		−	2.88543i
$83$		−	1043.56i		−	1.38007i	−0.723777	−	0.690034i	$-0.757596\pi$
$83$		−	1043.56i		−	1.38007i	0.723777	−	0.690034i	$-0.242404\pi$
$84$		0			0
$85$	302.856	−	64.4663i	0.386463	−	0.0822630i
$86$	918.703			1.15193
$87$		−	453.817i		−	0.559245i
$88$			1660.54i			2.01153i
$89$	652.060			0.776609			0.388304	−	0.921531i	$-0.373061\pi$
$89$	652.060			0.776609			0.388304	+	0.921531i	$0.373061\pi$
$90$	1350.33	−	287.432i	1.58152	−	0.336645i
$91$		0			0
$92$		−	2197.65i		−	2.49044i
$93$			250.576i			0.279393i
$94$	1099.62			1.20657
$95$	1.84456	+	8.66556i	0.00199208	+	0.00935861i
$96$	−883.097			−0.938861
$97$			515.714i			0.539823i	0.962885	+	0.269912i	$0.0869945\pi$
$97$			515.714i			0.539823i	−0.962885	+	0.269912i	$0.913005\pi$
$98$		0			0
$99$	593.564			0.602580
$100$	2310.09	−	1030.13i	2.31009	−	1.03013i
$101$	536.339			0.528394			0.264197	−	0.964469i	$-0.414893\pi$
$101$	536.339			0.528394			0.264197	+	0.964469i	$0.414893\pi$
$102$			285.405i			0.277052i
$103$		−	381.693i		−	0.365139i	−0.983193	−	0.182570i	$-0.941559\pi$
$103$		−	381.693i		−	0.365139i	0.983193	−	0.182570i	$-0.0584415\pi$
$104$	−4167.38			−3.92928
$105$		0			0
$106$	765.332			0.701279
$107$			1381.12i			1.24783i	0.781492	+	0.623915i	$0.214459\pi$
$107$			1381.12i			1.24783i	−0.781492	+	0.623915i	$0.785541\pi$
$108$			1971.54i			1.75659i
$109$	390.582			0.343220			0.171610	−	0.985165i	$-0.445103\pi$
$109$	390.582			0.343220			0.171610	+	0.985165i	$0.445103\pi$
$110$	1484.16	−	315.919i	1.28644	−	0.273834i
$111$	−74.2995			−0.0635333
$112$		0			0
$113$			1643.15i			1.36792i	0.729521	+	0.683958i	$0.239743\pi$
$113$			1643.15i			1.36792i	−0.729521	+	0.683958i	$0.760257\pi$
$114$	−8.16624			−0.00670911
$115$	−1187.65	+	252.804i	−0.963033	+	0.204992i
$116$	−4734.99			−3.78994
$117$			1489.64i			1.17707i
$118$			3608.43i			2.81511i
$119$		0			0
$120$	293.487	+	1378.77i	0.223263	+	1.04887i
$121$	−678.609			−0.509849
$122$		−	3053.85i		−	2.26625i
$123$		−	781.992i		−	0.573251i
$124$	2614.43			1.89341
$125$	−822.443	−	1129.92i	−0.588492	−	0.808503i
$126$		0			0
$127$			192.032i			0.134174i	0.997747	+	0.0670869i	$0.0213705\pi$
$127$			192.032i			0.134174i	−0.997747	+	0.0670869i	$0.978630\pi$
$128$			1410.38i			0.973914i
$129$	335.310			0.228856
$130$	792.848	+	3724.72i	0.534903	+	2.51292i
$131$	−2082.90			−1.38919			−0.694594	−	0.719402i	$-0.744416\pi$
$131$	−2082.90			−1.38919			−0.694594	+	0.719402i	$0.744416\pi$
$132$			1002.35i			0.660936i
$133$		0			0
$134$	−2739.93			−1.76637
$135$	1065.46	−	226.794i	0.679259	−	0.144588i
$136$	1800.53			1.13525
$137$			78.1709i			0.0487488i	0.999703	+	0.0243744i	$0.00775939\pi$
$137$			78.1709i			0.0487488i	−0.999703	+	0.0243744i	$0.992241\pi$
$138$		−	1119.21i		−	0.690390i
$139$	1393.67			0.850426			0.425213	−	0.905093i	$-0.360199\pi$
$139$	1393.67			0.850426			0.425213	+	0.905093i	$0.360199\pi$
$140$		0			0
$141$	401.342			0.239710
$142$		−	2957.65i		−	1.74789i
$143$			1637.28i			0.957454i
$144$	4266.03			2.46877
$145$	544.685	+	2558.88i	0.311956	+	1.46554i
$146$	920.556			0.521820
$147$		0			0
$148$			775.217i			0.430557i
$149$	−32.5002			−0.0178693			−0.00893463	−	0.999960i	$-0.502844\pi$
$149$	−32.5002			−0.0178693			−0.00893463	+	0.999960i	$0.502844\pi$
$150$	1176.48	−	524.625i	0.640396	−	0.285570i
$151$	466.762			0.251553			0.125777	−	0.992059i	$-0.459858\pi$
$151$	466.762			0.251553			0.125777	+	0.992059i	$0.459858\pi$
$152$			51.5181i			0.0274913i
$153$		−	643.602i		−	0.340080i
$154$		0			0
$155$	−300.749	−	1412.89i	−0.155850	−	0.732167i
$156$	−2515.56			−1.29106
$157$			1673.50i			0.850701i	0.905029	+	0.425351i	$0.139849\pi$
$157$			1673.50i			0.850701i	−0.905029	+	0.425351i	$0.860151\pi$
$158$			421.527i			0.212246i
$159$	279.332			0.139324
$160$	4979.39	−	1059.92i	2.46035	−	0.523712i
$161$		0			0
$162$		−	2329.98i		−	1.13000i
$163$			1869.36i			0.898279i	0.893462	+	0.449139i	$0.148269\pi$
$163$			1869.36i			0.898279i	−0.893462	+	0.449139i	$0.851731\pi$
$164$	−8159.06			−3.88485
$165$	541.690	−	115.305i	0.255579	−	0.0544028i
$166$	−5545.12			−2.59268
$167$			46.5250i			0.0215581i	0.999942	+	0.0107791i	$0.00343115\pi$
$167$			46.5250i			0.0215581i	−0.999942	+	0.0107791i	$0.996569\pi$
$168$		0			0
$169$	−1911.99			−0.870275
$170$	−342.552	−	1609.28i	−0.154544	−	0.726034i
$171$	18.4152			0.00823538
$172$		−	3498.52i		−	1.55093i
$173$		−	2496.28i		−	1.09704i	−0.836137	−	0.548521i	$-0.815191\pi$
$173$		−	2496.28i		−	1.09704i	0.836137	−	0.548521i	$-0.184809\pi$
$174$	−2411.43			−1.05063
$175$		0			0
$176$	4688.83			2.00815
$177$			1317.01i			0.559279i
$178$		−	3464.82i		−	1.45898i
$179$	−2975.70			−1.24254			−0.621269	−	0.783598i	$-0.713382\pi$
$179$	−2975.70			−1.24254			−0.621269	+	0.783598i	$0.713382\pi$
$180$	−1094.57	−	5142.19i	−0.453247	−	2.12931i
$181$	−966.273			−0.396809			−0.198405	−	0.980120i	$-0.563576\pi$
$181$	−966.273			−0.396809			−0.198405	+	0.980120i	$0.563576\pi$
$182$		0			0
$183$		−	1114.60i		−	0.450237i
$184$	−7060.76			−2.82895
$185$	418.942	−	89.1764i	0.166493	−	0.0354399i
$186$	1331.47			0.524884
$187$		−	707.389i		−	0.276628i
$188$		−	4187.48i		−	1.62449i
$189$		0			0
$190$	46.0458	−	9.80136i	0.0175817	−	0.00374245i
$191$	−1545.50			−0.585488			−0.292744	−	0.956191i	$-0.594568\pi$
$191$	−1545.50			−0.585488			−0.292744	+	0.956191i	$0.594568\pi$
$192$			1844.31i			0.693238i
$193$		−	2304.05i		−	0.859322i	−0.902990	−	0.429661i	$-0.858633\pi$
$193$		−	2304.05i		−	0.859322i	0.902990	−	0.429661i	$-0.141367\pi$
$194$	2740.33			1.01415
$195$	289.375	+	1359.45i	0.106270	+	0.499244i
$196$		0			0
$197$			222.021i			0.0802960i	0.999194	+	0.0401480i	$0.0127829\pi$
$197$			222.021i			0.0802960i	−0.999194	+	0.0401480i	$0.987217\pi$
$198$		−	3153.99i		−	1.13204i
$199$	3580.56			1.27547			0.637736	−	0.770255i	$-0.279871\pi$
$199$	3580.56			1.27547			0.637736	+	0.770255i	$0.279871\pi$
$200$	−3309.69	−	7422.04i	−1.17015	−	2.62409i
$201$	−1000.02			−0.350927
$202$		−	2849.92i		−	0.992673i
$203$		0			0
$204$	1086.85			0.373014
$205$	938.570	+	4409.31i	0.319769	+	1.50224i
$206$	−2028.19			−0.685973
$207$			2523.88i			0.847449i
$208$			11767.3i			3.92268i
$209$	20.2404			0.00669883
$210$		0			0
$211$	−4181.04			−1.36415			−0.682073	−	0.731284i	$-0.738921\pi$
$211$	−4181.04			−1.36415			−0.682073	+	0.731284i	$0.738921\pi$
$212$		−	2914.46i		−	0.944180i
$213$		−	1079.49i		−	0.347254i
$214$	7338.79			2.34425
$215$	−1890.66	+	402.449i	−0.599731	+	0.127659i
$216$	6334.31			1.99535
$217$		0			0
$218$		−	2075.42i		−	0.644794i
$219$	335.986			0.103670
$220$	−1203.05	−	5651.83i	−0.368681	−	1.73203i
$221$	1775.30			0.540361
$222$			394.802i			0.119357i
$223$		−	2361.52i		−	0.709145i	−0.935028	−	0.354573i	$-0.884626\pi$
$223$		−	2361.52i		−	0.709145i	0.935028	−	0.354573i	$-0.115374\pi$
$224$		0			0
$225$	−2653.02	+	1183.05i	−0.786081	+	0.350534i
$226$	8731.14			2.56985
$227$			586.877i			0.171596i	0.996313	+	0.0857982i	$0.0273440\pi$
$227$			586.877i			0.171596i	−0.996313	+	0.0857982i	$0.972656\pi$
$228$			31.0979i			0.00903292i
$229$	−4619.55			−1.33305			−0.666526	−	0.745482i	$-0.732219\pi$
$229$	−4619.55			−1.33305			−0.666526	+	0.745482i	$0.732219\pi$
$230$	1343.31	+	6310.76i	0.385111	+	1.80921i
$231$		0			0
$232$			15212.9i			4.30507i
$233$		−	5120.44i		−	1.43971i	−0.694127	−	0.719853i	$-0.744209\pi$
$233$		−	5120.44i		−	1.43971i	0.694127	−	0.719853i	$-0.255791\pi$
$234$	7915.43			2.21132
$235$	−2262.99	+	481.703i	−0.628176	+	0.133714i
$236$	13741.3			3.79017
$237$			153.850i			0.0421671i
$238$		0			0
$239$	−1127.51			−0.305158			−0.152579	−	0.988291i	$-0.548758\pi$
$239$	−1127.51			−0.305158			−0.152579	+	0.988291i	$0.548758\pi$
$240$	3893.20	−	828.711i	1.04710	−	0.222888i
$241$	3549.53			0.948736			0.474368	−	0.880327i	$-0.342677\pi$
$241$	3549.53			0.948736			0.474368	+	0.880327i	$0.342677\pi$
$242$			3605.89i			0.957833i
$243$		−	3481.07i		−	0.918975i
$244$	−11629.4			−3.05120
$245$		0			0
$246$	−4155.24			−1.07694
$247$			50.7963i			0.0130854i
$248$		−	8399.84i		−	2.15077i
$249$	−2023.87			−0.515090
$250$	−6003.99	+	4370.18i	−1.51890	+	1.10558i
$251$	−4717.19			−1.18624			−0.593120	−	0.805114i	$-0.702104\pi$
$251$	−4717.19			−1.18624			−0.593120	+	0.805114i	$0.702104\pi$
$252$		0			0
$253$			2774.02i			0.689333i
$254$	1020.39			0.252067
$255$	−125.025	−	587.355i	−0.0307034	−	0.144242i
$256$	−113.552			−0.0277227
$257$			6260.31i			1.51948i	0.650224	+	0.759742i	$0.274675\pi$
$257$			6260.31i			1.51948i	−0.650224	+	0.759742i	$0.725325\pi$
$258$		−	1781.72i		−	0.429942i
$259$		0			0
$260$	14184.1	−	3019.25i	3.38331	−	0.720176i
$261$	5437.88			1.28964
$262$			11067.8i			2.60981i
$263$		−	5753.04i		−	1.34885i	−0.738344	−	0.674425i	$-0.764392\pi$
$263$		−	5753.04i		−	1.34885i	0.738344	−	0.674425i	$-0.235608\pi$
$264$	3220.43			0.750772
$265$	−1575.03	+	335.262i	−0.365107	+	0.0777170i
$266$		0			0
$267$		−	1264.60i		−	0.289858i
$268$			10433.9i			2.37819i
$269$	−7059.21			−1.60003			−0.800014	−	0.599982i	$-0.795174\pi$
$269$	−7059.21			−1.60003			−0.800014	+	0.599982i	$0.795174\pi$
$270$	−1205.11	−	5661.47i	−0.271631	−	1.27610i
$271$	8534.52			1.91305			0.956523	−	0.291658i	$-0.0942069\pi$
$271$	8534.52			1.91305			0.956523	+	0.291658i	$0.0942069\pi$
$272$		−	5084.11i		−	1.13334i
$273$		0			0
$274$	415.373			0.0915826
$275$	−2915.96	+	1300.30i	−0.639415	+	0.285132i
$276$	−4262.08			−0.929519
$277$			1313.94i			0.285008i	0.989794	+	0.142504i	$0.0455154\pi$
$277$			1313.94i			0.285008i	−0.989794	+	0.142504i	$0.954485\pi$
$278$		−	7405.47i		−	1.59766i
$279$	−3002.54			−0.644291
$280$		0			0
$281$	−247.229			−0.0524856			−0.0262428	−	0.999656i	$-0.508354\pi$
$281$	−247.229			−0.0524856			−0.0262428	+	0.999656i	$0.508354\pi$
$282$		−	2132.60i		−	0.450334i
$283$			9074.90i			1.90617i	0.302697	+	0.953087i	$0.402113\pi$
$283$			9074.90i			1.90617i	−0.302697	+	0.953087i	$0.597887\pi$
$284$	−11263.0			−2.35330
$285$	16.8059	−	3.57731i	0.00349296	−	0.000743515i
$286$	8699.92			1.79873
$287$		0			0
$288$		−	10581.7i		−	2.16505i
$289$	4145.98			0.843879
$290$	13597.0	−	2894.27i	2.75325	−	0.586060i
$291$	1000.17			0.201481
$292$		−	3505.57i		−	0.702562i
$293$			2740.72i			0.546466i	0.961948	+	0.273233i	$0.0880930\pi$
$293$			2740.72i			0.546466i	−0.961948	+	0.273233i	$0.911907\pi$
$294$		0			0
$295$	−1580.71	−	7426.04i	−0.311975	−	1.46563i
$296$	2490.68			0.489080
$297$		−	2488.61i		−	0.486209i
$298$			172.695i			0.0335703i
$299$	−6961.83			−1.34653
$300$	−1997.83	−	4480.16i	−0.384482	−	0.862208i
$301$		0			0
$302$		−	2480.21i		−	0.472584i
$303$		−	1040.17i		−	0.197215i
$304$	145.470			0.0274451
$305$	1337.77	+	6284.73i	0.251150	+	1.17988i
$306$	−3419.88			−0.638894
$307$		−	6985.46i		−	1.29864i	−0.760517	−	0.649318i	$-0.775054\pi$
$307$		−	6985.46i		−	1.29864i	0.760517	−	0.649318i	$-0.224946\pi$
$308$		0			0
$309$	−740.250			−0.136283
$310$	−7507.60	+	1598.08i	−1.37549	+	0.292789i
$311$	356.841			0.0650630			0.0325315	−	0.999471i	$-0.489643\pi$
$311$	356.841			0.0650630			0.0325315	+	0.999471i	$0.489643\pi$
$312$			8082.16i			1.46655i
$313$		−	6630.12i		−	1.19731i	−0.801009	−	0.598653i	$-0.795703\pi$
$313$		−	6630.12i		−	1.19731i	0.801009	−	0.598653i	$-0.204297\pi$
$314$	8892.42			1.59818
$315$		0			0
$316$	1605.22			0.285762
$317$		−	2494.05i		−	0.441891i	−0.975286	−	0.220946i	$-0.929086\pi$
$317$		−	2494.05i		−	0.441891i	0.975286	−	0.220946i	$-0.0709144\pi$
$318$		−	1484.27i		−	0.261742i
$319$	5976.83			1.04902
$320$	−2213.60	−	10399.3i	−0.386700	−	1.81668i
$321$	2678.52			0.465734
$322$		0			0
$323$		−	21.9467i		−	0.00378063i
$324$	−8872.79			−1.52140
$325$	−3263.31	−	7318.05i	−0.556973	−	1.24902i
$326$	9933.13			1.68756
$327$		−	757.489i		−	0.128102i
$328$			26214.0i			4.41289i
$329$		0			0
$330$	−612.690	−	2878.35i	−0.102204	−	0.480146i
$331$	−4682.47			−0.777558			−0.388779	−	0.921331i	$-0.627103\pi$
$331$	−4682.47			−0.777558			−0.388779	+	0.921331i	$0.627103\pi$
$332$			21116.4i			3.49070i
$333$		−	890.297i		−	0.146510i
$334$	247.218			0.0405005
$335$	5638.70	−	1200.26i	0.919627	−	0.195753i
$336$		0			0
$337$			3596.60i			0.581363i	0.956820	+	0.290681i	$0.0938820\pi$
$337$			3596.60i			0.581363i	−0.956820	+	0.290681i	$0.906118\pi$
$338$			10159.7i			1.63495i
$339$	3186.70			0.510554
$340$	−6128.28	+	1304.47i	−0.977509	+	0.208073i
$341$	−3300.12			−0.524080
$342$		−	97.8523i		−	0.0154715i
$343$		0			0
$344$	−11240.3			−1.76173
$345$	490.285	+	2303.31i	0.0765103	+	0.359438i
$346$	−13264.4			−2.06097
$347$			1899.51i			0.293865i	0.989147	+	0.146932i	$0.0469400\pi$
$347$			1899.51i			0.293865i	−0.989147	+	0.146932i	$0.953060\pi$
$348$			9182.97i			1.41454i
$349$	−1037.55			−0.159137			−0.0795683	−	0.996829i	$-0.525354\pi$
$349$	−1037.55			−0.159137			−0.0795683	+	0.996829i	$0.525354\pi$
$350$		0			0
$351$	6245.56			0.949752
$352$		−	11630.5i		−	1.76110i
$353$		−	4087.08i		−	0.616242i	−0.951347	−	0.308121i	$-0.900300\pi$
$353$		−	4087.08i		−	0.616242i	0.951347	−	0.308121i	$-0.0997001\pi$
$354$	6998.13			1.05070
$355$	1295.63	+	6086.75i	0.193704	+	0.910003i
$356$	−13194.4			−1.96433
$357$		0			0
$358$			15811.8i			2.33431i
$359$	−3472.67			−0.510530			−0.255265	−	0.966871i	$-0.582163\pi$
$359$	−3472.67			−0.510530			−0.255265	+	0.966871i	$0.582163\pi$
$360$	−16521.2	+	3516.72i	−2.41873	+	0.514854i
$361$	−6858.37			−0.999908
$362$			5134.44i			0.745470i
$363$			1316.08i			0.190293i
$364$		0			0
$365$	−1894.48	+	403.260i	−0.271675	+	0.0578290i
$366$	−5922.59			−0.845844
$367$		−	8769.14i		−	1.24726i	−0.781719	−	0.623631i	$-0.785657\pi$
$367$		−	8769.14i		−	1.24726i	0.781719	−	0.623631i	$-0.214343\pi$
$368$			19937.3i			2.82419i
$369$	9370.25			1.32194
$370$	−473.853	−	2226.11i	−0.0665796	−	0.312784i
$371$		0			0
$372$		−	5070.39i		−	0.706687i
$373$		−	11368.9i		−	1.57817i	−0.614284	−	0.789085i	$-0.710555\pi$
$373$		−	11368.9i		−	1.57817i	0.614284	−	0.789085i	$-0.289445\pi$
$374$	−3758.82			−0.519690
$375$	−2191.35	+	1595.03i	−0.301762	+	0.219646i
$376$	−13453.8			−1.84529
$377$			14999.8i			2.04914i
$378$		0			0
$379$	12137.4			1.64500			0.822501	−	0.568764i	$-0.192578\pi$
$379$	12137.4			1.64500			0.822501	+	0.568764i	$0.192578\pi$
$380$	−37.3246	−	175.347i	−0.00503871	−	0.0236714i
$381$	372.424			0.0500784
$382$			8212.24i			1.09993i
$383$		−	9869.61i		−	1.31675i	−0.752692	−	0.658373i	$-0.771245\pi$
$383$		−	9869.61i		−	1.31675i	0.752692	−	0.658373i	$-0.228755\pi$
$384$	2735.27			0.363499
$385$		0			0
$386$	−12242.9			−1.61438
$387$			4017.86i			0.527751i
$388$		−	10435.5i		−	1.36541i
$389$	−57.1166			−0.00744454			−0.00372227	−	0.999993i	$-0.501185\pi$
$389$	−57.1166			−0.00744454			−0.00372227	+	0.999993i	$0.501185\pi$
$390$	7223.67	−	1537.64i	0.937910	−	0.199644i
$391$	3007.88			0.389041
$392$		0			0
$393$			4039.54i			0.518494i
$394$	1179.74			0.150849
$395$	−184.655	−	867.490i	−0.0235215	−	0.110502i
$396$	−12010.7			−1.52415
$397$			7436.17i			0.940078i	0.882646	+	0.470039i	$0.155760\pi$
$397$			7436.17i			0.940078i	−0.882646	+	0.470039i	$0.844240\pi$
$398$		−	19025.8i		−	2.39618i
$399$		0			0
$400$	−20957.4	+	9345.47i	−2.61968	+	1.16818i
$401$	−12465.0			−1.55230			−0.776149	−	0.630550i	$-0.782829\pi$
$401$	−12465.0			−1.55230			−0.776149	+	0.630550i	$0.782829\pi$
$402$			5313.79i			0.659273i
$403$		−	8282.15i		−	1.02373i
$404$	−10852.8			−1.33650
$405$	1020.67	+	4795.02i	0.125229	+	0.588312i
$406$		0			0
$407$		−	978.533i		−	0.119175i
$408$		−	3491.92i		−	0.423715i
$409$	−1708.72			−0.206578			−0.103289	−	0.994651i	$-0.532937\pi$
$409$	−1708.72			−0.206578			−0.103289	+	0.994651i	$0.532937\pi$
$410$	23429.6	−	4987.24i	2.82220	−	0.600737i
$411$	151.604			0.0181948
$412$			7723.54i			0.923571i
$413$		0			0
$414$	13411.0			1.59207
$415$	11411.7	−	2429.10i	1.34983	−	0.287325i
$416$	29188.5			3.44011
$417$		−	2702.86i		−	0.317409i
$418$		−	107.550i		−	0.0125848i
$419$	10618.8			1.23810			0.619050	−	0.785352i	$-0.287518\pi$
$419$	10618.8			1.23810			0.619050	+	0.785352i	$0.287518\pi$
$420$		0			0
$421$	13273.5			1.53661			0.768304	−	0.640085i	$-0.221101\pi$
$421$	13273.5			1.53661			0.768304	+	0.640085i	$0.221101\pi$
$422$			22216.6i			2.56277i
$423$			4809.10i			0.552781i
$424$	−9363.80			−1.07251
$425$	1409.92	+	3161.78i	0.160921	+	0.360868i
$426$	−5736.02			−0.652373
$427$		0			0
$428$		−	27946.9i		−	3.15622i
$429$	3175.31			0.357355
$430$	2138.47	+	10046.3i	0.239829	+	1.12669i
$431$	7918.20			0.884934			0.442467	−	0.896785i	$-0.354103\pi$
$431$	7918.20			0.884934			0.442467	+	0.896785i	$0.354103\pi$
$432$		−	17886.0i		−	1.99199i
$433$		−	4433.34i		−	0.492038i	−0.969265	−	0.246019i	$-0.920877\pi$
$433$		−	4433.34i		−	0.492038i	0.969265	−	0.246019i	$-0.0791226\pi$
$434$		0			0
$435$	4962.65	−	1056.35i	0.546990	−	0.116433i
$436$	−7903.40			−0.868129
$437$			86.0637i			0.00942102i
$438$		−	1785.31i		−	0.194761i
$439$	12958.4			1.40882			0.704408	−	0.709796i	$-0.251213\pi$
$439$	12958.4			1.40882			0.704408	+	0.709796i	$0.251213\pi$
$440$	−18158.6	+	3865.26i	−1.96745	+	0.418793i
$441$		0			0
$442$		−	9433.34i		−	1.01515i
$443$		−	12040.4i		−	1.29133i	−0.763621	−	0.645664i	$-0.776580\pi$
$443$		−	12040.4i		−	1.29133i	0.763621	−	0.645664i	$-0.223420\pi$
$444$	1503.45			0.160699
$445$	1517.80	+	7130.50i	0.161687	+	0.759591i
$446$	−12548.3			−1.33224
$447$			63.0304i			0.00666943i
$448$		0			0
$449$	−11586.3			−1.21780			−0.608899	−	0.793247i	$-0.708389\pi$
$449$	−11586.3			−1.21780			−0.608899	+	0.793247i	$0.708389\pi$
$450$	6286.34	+	14097.2i	0.658536	+	1.47678i
$451$	10298.9			1.07529
$452$		−	33249.1i		−	3.45997i
$453$		−	905.232i		−	0.0938886i
$454$	3118.46			0.322371
$455$		0			0
$456$	99.9135			0.0102607
$457$		−	9734.34i		−	0.996396i	−0.867063	−	0.498198i	$-0.833995\pi$
$457$		−	9734.34i		−	0.996396i	0.867063	−	0.498198i	$-0.166005\pi$
$458$			24546.7i			2.50435i
$459$	−2698.41			−0.274403
$460$	24032.0	−	5115.48i	2.43587	−	0.518501i
$461$	1343.41			0.135724			0.0678621	−	0.997695i	$-0.478382\pi$
$461$	1343.41			0.135724			0.0678621	+	0.997695i	$0.478382\pi$
$462$		0			0
$463$		−	6613.72i		−	0.663857i	−0.943305	−	0.331929i	$-0.892301\pi$
$463$		−	6613.72i		−	0.663857i	0.943305	−	0.331929i	$-0.107699\pi$
$464$	42956.3			4.29784
$465$	−2740.13	+	583.268i	−0.273270	+	0.0581686i
$466$	−27208.3			−2.70472
$467$		−	14688.9i		−	1.45551i	−0.685838	−	0.727755i	$-0.740564\pi$
$467$		−	14688.9i		−	1.45551i	0.685838	−	0.727755i	$-0.259436\pi$
$468$		−	30142.8i		−	2.97724i
$469$		0			0
$470$	2559.60	+	12024.8i	0.251204	+	1.18013i
$471$	3245.57			0.317511
$472$		−	44148.9i		−	4.30534i
$473$			4416.07i			0.429283i
$474$	817.504			0.0792177
$475$	−90.4673	+	40.3418i	−0.00873879	+	0.00389686i
$476$		0			0
$477$			3347.11i			0.321286i
$478$			5991.22i			0.573288i
$479$	−15298.6			−1.45931			−0.729657	−	0.683813i	$-0.760320\pi$
$479$	−15298.6			−1.45931			−0.729657	+	0.683813i	$0.760320\pi$
$480$	−2055.59	−	9656.97i	−0.195468	−	0.918288i
$481$	2455.78			0.232794
$482$		−	18861.0i		−	1.78235i
$483$		0			0
$484$	13731.6			1.28960
$485$	−5639.52	+	1200.43i	−0.527994	+	0.112389i
$486$	−18497.2			−1.72644
$487$			9653.80i			0.898266i	0.893465	+	0.449133i	$0.148267\pi$
$487$			9653.80i			0.898266i	−0.893465	+	0.449133i	$0.851733\pi$
$488$			37363.7i			3.46593i
$489$	3625.41			0.335269
$490$		0			0
$491$	20142.6			1.85137			0.925684	−	0.378297i	$-0.123490\pi$
$491$	20142.6			1.85137			0.925684	+	0.378297i	$0.123490\pi$
$492$			15823.6i			1.44996i
$493$		−	6480.69i		−	0.592039i
$494$	269.914			0.0245830
$495$	1381.64	+	6490.83i	0.125455	+	0.589376i
$496$	−23718.4			−2.14715
$497$		0			0
$498$			10754.1i			0.967679i
$499$	1309.29			0.117459			0.0587293	−	0.998274i	$-0.481295\pi$
$499$	1309.29			0.117459			0.0587293	+	0.998274i	$0.481295\pi$
$500$	16642.1	+	22863.8i	1.48851	+	2.04500i
$501$	90.2299			0.00804625
$502$			25065.5i			2.22855i
$503$		−	2186.17i		−	0.193791i	−0.995295	−	0.0968953i	$-0.969109\pi$
$503$		−	2186.17i		−	0.193791i	0.995295	−	0.0968953i	$-0.0308912\pi$
$504$		0			0
$505$	1248.44	+	5865.06i	0.110010	+	0.516815i
$506$	14740.2			1.29502
$507$			3708.09i			0.324817i
$508$		−	3885.76i		−	0.339375i
$509$	3591.11			0.312718			0.156359	−	0.987700i	$-0.450024\pi$
$509$	3591.11			0.312718			0.156359	+	0.987700i	$0.450024\pi$
$510$	−3121.01	+	664.340i	−0.270981	+	0.0576813i
$511$		0			0
$512$			11886.4i			1.02600i
$513$		−	77.2089i		−	0.00664495i
$514$	33265.2			2.85460
$515$	4173.94	−	888.470i	0.357138	−	0.0760207i
$516$	−6784.97			−0.578860
$517$			5285.73i			0.449644i
$518$		0			0
$519$	−4841.24			−0.409455
$520$	−9700.46	−	45571.8i	−0.818064	−	3.84318i
$521$	8605.34			0.723621			0.361811	−	0.932252i	$-0.382159\pi$
$521$	8605.34			0.723621			0.361811	+	0.932252i	$0.382159\pi$
$522$		−	28895.1i		−	2.42280i
$523$		−	22536.4i		−	1.88423i	−0.335297	−	0.942113i	$-0.608837\pi$
$523$		−	22536.4i		−	1.88423i	0.335297	−	0.942113i	$-0.391163\pi$
$524$	42147.3			3.51377
$525$		0			0
$526$	−30569.7			−2.53403
$527$			3578.32i			0.295776i
$528$		−	9093.45i		−	0.749510i
$529$	371.637			0.0305447
$530$	1781.47	+	8369.17i	0.146004	+	0.685912i
$531$	−15781.1			−1.28972
$532$		0			0
$533$			25846.7i			2.10046i
$534$	−6719.63			−0.544544
$535$	−15103.0	+	3214.84i	−1.22049	+	0.259794i
$536$	33522.9			2.70144
$537$			5771.03i			0.463758i
$538$			37510.2i			3.00591i
$539$		0			0
$540$	−21559.5	+	4589.17i	−1.71810	+	0.365716i
$541$	8782.44			0.697942			0.348971	−	0.937134i	$-0.386531\pi$
$541$	8782.44			0.697942			0.348971	+	0.937134i	$0.386531\pi$
$542$		−	45349.5i		−	3.59396i
$543$			1873.98i			0.148103i
$544$	−12611.0			−0.993917
$545$	909.161	+	4271.15i	0.0714572	+	0.335699i
$546$		0			0
$547$		−	22593.0i		−	1.76601i	−0.469366	−	0.883004i	$-0.655518\pi$
$547$		−	22593.0i		−	1.76601i	0.469366	−	0.883004i	$-0.344482\pi$
$548$		−	1581.78i		−	0.123304i
$549$	13355.7			1.03827
$550$	6909.37	+	15494.4i	0.535667	+	1.20124i
$551$	185.430			0.0143368
$552$			13693.5i			1.05586i
$553$		0			0
$554$	6981.84			0.535433
$555$	−172.947	−	812.490i	−0.0132274	−	0.0621411i
$556$	−28200.8			−2.15104
$557$			7264.13i			0.552587i	0.961073	+	0.276294i	$0.0891062\pi$
$557$			7264.13i			0.552587i	−0.961073	+	0.276294i	$0.910894\pi$
$558$			15954.5i			1.21040i
$559$	−11082.8			−0.838555
$560$		0			0
$561$	−1371.90			−0.103247
$562$			1313.69i			0.0986027i
$563$		−	3851.42i		−	0.288309i	−0.989555	−	0.144154i	$-0.953954\pi$
$563$		−	3851.42i		−	0.288309i	0.989555	−	0.144154i	$-0.0460462\pi$
$564$	−8121.14			−0.606315
$565$	−17968.4	+	3824.78i	−1.33794	+	0.284796i
$566$	48220.9			3.58105
$567$		0			0
$568$			36186.7i			2.67317i
$569$	−16580.3			−1.22158			−0.610792	−	0.791791i	$-0.709149\pi$
$569$	−16580.3			−1.22158			−0.610792	+	0.791791i	$0.709149\pi$
$570$	−19.0086	−	89.3006i	−0.00139681	−	0.00656209i
$571$	6385.86			0.468021			0.234010	−	0.972234i	$-0.424815\pi$
$571$	6385.86			0.468021			0.234010	+	0.972234i	$0.424815\pi$
$572$		−	33130.2i		−	2.42175i
$573$			2997.32i			0.218525i
$574$		0			0
$575$	−5529.00	−	12398.9i	−0.401001	−	0.899252i
$576$	−22099.6			−1.59864
$577$		−	11059.1i		−	0.797912i	−0.916970	−	0.398956i	$-0.869373\pi$
$577$		−	11059.1i		−	0.797912i	0.916970	−	0.398956i	$-0.130627\pi$
$578$		−	22030.3i		−	1.58536i
$579$	−4468.44			−0.320729
$580$	−11021.7	−	51778.7i	−0.789052	−	3.70689i
$581$		0			0
$582$		−	5314.56i		−	0.378515i
$583$			3678.84i			0.261341i
$584$	−11263.0			−0.798055
$585$	−16289.7	+	3467.45i	−1.15128	+	0.245062i
$586$	14563.2			1.02662
$587$		−	7871.25i		−	0.553461i	−0.960948	−	0.276730i	$-0.910749\pi$
$587$		−	7871.25i		−	0.553461i	0.960948	−	0.276730i	$-0.0892509\pi$
$588$		0			0
$589$	−102.386			−0.00716253
$590$	−39459.4	+	8399.37i	−2.75342	+	0.586096i
$591$	430.584			0.0299693
$592$		−	7032.85i		−	0.488258i
$593$			2018.06i			0.139750i	0.997556	+	0.0698750i	$0.0222600\pi$
$593$			2018.06i			0.139750i	−0.997556	+	0.0698750i	$0.977740\pi$
$594$	−13223.6			−0.913422
$595$		0			0
$596$	657.640			0.0451980
$597$		−	6944.08i		−	0.476051i
$598$			36992.8i			2.52968i
$599$	1356.67			0.0925409			0.0462705	−	0.998929i	$-0.485266\pi$
$599$	1356.67			0.0925409			0.0462705	+	0.998929i	$0.485266\pi$
$600$	−14394.2	+	6418.76i	−0.979401	+	0.436741i
$601$	−11178.7			−0.758715			−0.379358	−	0.925250i	$-0.623855\pi$
$601$	−11178.7			−0.758715			−0.379358	+	0.925250i	$0.623855\pi$
$602$		0			0
$603$		−	11982.8i		−	0.809252i
$604$	−9444.91			−0.636272
$605$	−1579.60	−	7420.82i	−0.106149	−	0.498676i
$606$	−5527.10			−0.370500
$607$			9404.67i			0.628870i	0.949279	+	0.314435i	$0.101815\pi$
$607$			9404.67i			0.628870i	−0.949279	+	0.314435i	$0.898185\pi$
$608$		−	360.835i		−	0.0240687i
$609$		0			0
$610$	33394.9	−	7108.47i	2.21659	−	0.471825i
$611$	−13265.3			−0.878328
$612$			13023.3i			0.860187i
$613$		−	18938.0i		−	1.24779i	−0.781507	−	0.623897i	$-0.785548\pi$
$613$		−	18938.0i		−	1.24779i	0.781507	−	0.623897i	$-0.214452\pi$
$614$	−37118.4			−2.43970
$615$	8551.35	−	1820.25i	0.560689	−	0.119349i
$616$		0			0
$617$		−	17716.9i		−	1.15600i	−0.816036	−	0.578001i	$-0.803833\pi$
$617$		−	17716.9i		−	1.15600i	0.816036	−	0.578001i	$-0.196167\pi$
$618$			3933.43i			0.256029i
$619$	−6240.33			−0.405202			−0.202601	−	0.979261i	$-0.564939\pi$
$619$	−6240.33			−0.405202			−0.202601	+	0.979261i	$0.564939\pi$
$620$	6085.63	+	28589.7i	0.394202	+	1.85192i
$621$	10581.8			0.683788
$622$		−	1896.13i		−	0.122231i
$623$		0			0
$624$	22821.4			1.46408
$625$	10441.6	−	11623.8i	0.668264	−	0.743924i
$626$	−35230.2			−2.24933
$627$		−	39.2539i		−	0.00250024i
$628$		−	33863.2i		−	2.15174i
$629$	−1061.03			−0.0672589
$630$		0			0
$631$	−25887.7			−1.63323			−0.816617	−	0.577179i	$-0.804153\pi$
$631$	−25887.7			−1.63323			−0.816617	+	0.577179i	$0.804153\pi$
$632$		−	5157.37i		−	0.324603i
$633$			8108.65i			0.509147i
$634$	−13252.5			−0.830165
$635$	−2099.94	+	446.994i	−0.131234	+	0.0279345i
$636$	−5652.27			−0.352401
$637$		0			0
$638$		−	31758.8i		−	1.97076i
$639$	12935.0			0.800783
$640$	−15423.0	+	3282.95i	−0.952573	+	0.202766i
$641$	18798.4			1.15834			0.579168	−	0.815208i	$-0.303378\pi$
$641$	18798.4			1.15834			0.579168	+	0.815208i	$0.303378\pi$
$642$		−	14232.8i		−	0.874956i
$643$			2287.70i			0.140308i	0.997536	+	0.0701541i	$0.0223491\pi$
$643$			2287.70i			0.140308i	−0.997536	+	0.0701541i	$0.977651\pi$
$644$		0			0
$645$	780.503	+	3666.73i	0.0476469	+	0.223841i
$646$	−116.617			−0.00710253
$647$			1769.31i			0.107510i	0.998554	+	0.0537548i	$0.0171189\pi$
$647$			1769.31i			0.107510i	−0.998554	+	0.0537548i	$0.982881\pi$
$648$			28507.1i			1.72819i
$649$	−17345.2			−1.04909
$650$	−38885.6	+	17340.1i	−2.34649	+	1.04636i
$651$		0			0
$652$		−	37826.4i		−	2.27208i
$653$			3891.48i			0.233209i	0.993178	+	0.116604i	$0.0372010\pi$
$653$			3891.48i			0.233209i	−0.993178	+	0.116604i	$0.962799\pi$
$654$	−4025.04			−0.240660
$655$	−4848.38	−	22777.2i	−0.289224	−	1.35875i
$656$	74019.8			4.40547
$657$			4025.96i			0.239068i
$658$		0			0
$659$	−20097.6			−1.18800			−0.594001	−	0.804465i	$-0.702452\pi$
$659$	−20097.6			−1.18800			−0.594001	+	0.804465i	$0.702452\pi$
$660$	−10961.1	+	2333.18i	−0.646453	+	0.137605i
$661$	27167.9			1.59865			0.799326	−	0.600898i	$-0.205190\pi$
$661$	27167.9			1.59865			0.799326	+	0.600898i	$0.205190\pi$
$662$			24881.0i			1.46077i
$663$		−	3442.99i		−	0.201681i
$664$	67844.3			3.96516
$665$		0			0
$666$	−4730.73			−0.275243
$667$			25414.0i			1.47531i
$668$		−	941.430i		−	0.0545285i
$669$	−4579.91			−0.264678
$670$	−6377.77	−	29962.1i	−0.367753	−	1.72767i
$671$	14679.4			0.844548
$672$		0			0
$673$			25909.7i			1.48402i	0.670389	+	0.742010i	$0.266127\pi$
$673$			25909.7i			1.48402i	−0.670389	+	0.742010i	$0.733873\pi$
$674$	19111.1			1.09218
$675$	4960.15	+	11123.2i	0.282839	+	0.634271i
$676$	38689.1			2.20125
$677$			4359.22i			0.247472i	0.992315	+	0.123736i	$0.0394875\pi$
$677$			4359.22i			0.247472i	−0.992315	+	0.123736i	$0.960512\pi$
$678$		−	16933.0i		−	0.959159i
$679$		0			0
$680$	4191.11	+	19689.4i	0.236355	+	1.11037i
$681$	1138.18			0.0640458
$682$			17535.7i			0.984569i
$683$			29721.9i			1.66512i	0.553937	+	0.832559i	$0.313125\pi$
$683$			29721.9i			1.66512i	−0.553937	+	0.832559i	$0.686875\pi$
$684$	−372.632			−0.0208303
$685$	−854.826	+	181.959i	−0.0476806	+	0.0101493i
$686$		0			0
$687$			8959.10i			0.497541i
$688$			31738.9i			1.75877i
$689$	−9232.60			−0.510499
$690$	12239.0	−	2605.21i	0.675262	−	0.143737i
$691$	4929.13			0.271365			0.135682	−	0.990752i	$-0.456677\pi$
$691$	4929.13			0.271365			0.135682	+	0.990752i	$0.456677\pi$
$692$			50512.0i			2.77482i
$693$		0			0
$694$	10093.4			0.552073
$695$	3244.05	+	15240.2i	0.177056	+	0.831791i
$696$	29503.7			1.60680
$697$		−	11167.1i		−	0.606866i
$698$			5513.18i			0.298964i
$699$	−9930.51			−0.537348
$700$		0			0
$701$	−19358.8			−1.04304			−0.521520	−	0.853239i	$-0.674635\pi$
$701$	−19358.8			−1.04304			−0.521520	+	0.853239i	$0.674635\pi$
$702$		−	33186.7i		−	1.78426i
$703$		−	30.3589i		−	0.00162874i
$704$	−24289.8			−1.30036
$705$	934.208	+	4388.82i	0.0499068	+	0.234457i
$706$	−21717.3			−1.15771
$707$		0			0
$708$		−	26649.6i		−	1.41462i
$709$	17186.3			0.910359			0.455180	−	0.890400i	$-0.349575\pi$
$709$	17186.3			0.910359			0.455180	+	0.890400i	$0.349575\pi$
$710$	32342.9	−	6884.54i	1.70959	−	0.363905i
$711$	−1843.51			−0.0972392
$712$			42391.9i			2.23133i
$713$		−	14032.4i		−	0.737049i
$714$		0			0
$715$	−17904.2	+	3811.10i	−0.936473	+	0.199339i
$716$	60213.1			3.14284
$717$			2186.68i			0.113896i
$718$			18452.6i			0.959113i
$719$	−15107.3			−0.783598			−0.391799	−	0.920051i	$-0.628147\pi$
$719$	−15107.3			−0.783598			−0.391799	+	0.920051i	$0.628147\pi$
$720$	9930.07	+	46650.5i	0.513989	+	2.41467i
$721$		0			0
$722$			36443.0i			1.87849i
$723$		−	6883.91i		−	0.354102i
$724$	19552.5			1.00368
$725$	−26714.3	+	11912.6i	−1.36848	+	0.610240i
$726$	6993.22			0.357497
$727$		−	15840.9i		−	0.808124i	−0.914732	−	0.404062i	$-0.867598\pi$
$727$		−	15840.9i		−	0.808124i	0.914732	−	0.404062i	$-0.132402\pi$
$728$		0			0
$729$	5088.04			0.258499
$730$	2142.79	+	10066.6i	0.108641	+	0.510385i
$731$	4788.35			0.242276
$732$			22553.8i			1.13882i
$733$			27639.7i			1.39276i	0.717671	+	0.696382i	$0.245208\pi$
$733$			27639.7i			1.39276i	−0.717671	+	0.696382i	$0.754792\pi$
$734$	−46596.2			−2.34318
$735$		0			0
$736$	49453.8			2.47675
$737$		−	13170.4i		−	0.658263i
$738$		−	49790.3i		−	2.48348i
$739$	−34874.4			−1.73596			−0.867982	−	0.496597i	$-0.834583\pi$
$739$	−34874.4			−1.73596			−0.867982	+	0.496597i	$0.834583\pi$
$740$	−8477.27	+	1804.48i	−0.421123	+	0.0896406i
$741$	98.5136			0.00488392
$742$		0			0
$743$		−	27686.7i		−	1.36706i	−0.729922	−	0.683530i	$-0.760444\pi$
$743$		−	27686.7i		−	1.36706i	0.729922	−	0.683530i	$-0.239556\pi$
$744$	−16290.5			−0.802741
$745$	−75.6510	−	355.401i	−0.00372032	−	0.0174777i
$746$	−60410.2			−2.96485
$747$		−	24251.1i		−	1.18782i
$748$			14314.0i			0.699694i
$749$		0			0
$750$	8475.46	+	11644.1i	0.412640	+	0.566908i
$751$	4806.85			0.233561			0.116781	−	0.993158i	$-0.462743\pi$
$751$	4806.85			0.233561			0.116781	+	0.993158i	$0.462743\pi$
$752$			37989.3i			1.84219i
$753$			9148.45i			0.442747i
$754$	79703.6			3.84965
$755$	1086.49	+	5104.21i	0.0523726	+	0.246041i
$756$		0			0
$757$			40166.6i			1.92851i	0.264983	+	0.964253i	$0.414634\pi$
$757$			40166.6i			1.92851i	−0.264983	+	0.964253i	$0.585366\pi$
$758$		−	64493.9i		−	3.09040i
$759$	5379.90			0.257283
$760$	−563.368	+	119.919i	−0.0268888	+	0.00572359i
$761$	−25912.3			−1.23432			−0.617162	−	0.786836i	$-0.711718\pi$
$761$	−25912.3			−1.23432			−0.617162	+	0.786836i	$0.711718\pi$
$762$		−	1978.93i		−	0.0940803i
$763$		0			0
$764$	31273.1			1.48092
$765$	7038.01	−	1498.12i	0.332627	−	0.0708034i
$766$	−52443.7			−2.47372
$767$		−	43530.4i		−	2.04927i
$768$			220.221i			0.0103471i
$769$	−23231.3			−1.08939			−0.544697	−	0.838633i	$-0.683355\pi$
$769$	−23231.3			−1.08939			−0.544697	+	0.838633i	$0.683355\pi$
$770$		0			0
$771$	12141.2			0.567125
$772$			46622.4i			2.17354i
$773$		−	836.306i		−	0.0389131i	−0.999811	−	0.0194566i	$-0.993806\pi$
$773$		−	836.306i		−	0.0389131i	0.999811	−	0.0194566i	$-0.00619360\pi$
$774$	21349.5			0.991465
$775$	14750.4	−	6577.58i	0.683675	−	0.304869i
$776$	−33527.8			−1.55100
$777$		0			0
$778$			303.498i			0.0139858i
$779$	319.523			0.0146959
$780$	−5855.48	−	27508.5i	−0.268795	−	1.26277i
$781$	14217.0			0.651374
$782$		−	15982.8i		−	0.730875i
$783$		−	22799.2i		−	1.04058i
$784$		0			0
$785$	−18300.3	+	3895.43i	−0.832060	+	0.177113i
$786$	21464.7			0.974074
$787$			31945.6i			1.44693i	0.690359	+	0.723467i	$0.257453\pi$
$787$			31945.6i			1.44693i	−0.690359	+	0.723467i	$0.742547\pi$
$788$		−	4492.58i		−	0.203098i
$789$	−11157.4			−0.503438
$790$	−4609.55	+	981.193i	−0.207595	+	0.0441890i
$791$		0			0
$792$			38589.0i			1.73131i
$793$			36840.2i			1.64973i
$794$	39513.3			1.76609
$795$	650.203	+	3054.59i	0.0290067	+	0.136271i
$796$	−72452.4			−3.22614
$797$			5628.83i			0.250168i	0.992146	+	0.125084i	$0.0399200\pi$
$797$			5628.83i			0.250168i	−0.992146	+	0.125084i	$0.960080\pi$
$798$		0			0
$799$	5731.32			0.253767
$800$	23181.2	+	51984.2i	1.02447	+	2.29740i
$801$	15153.1			0.668424
$802$			66234.6i			2.91624i
$803$			4424.97i			0.194463i
$804$	20235.4			0.887623
$805$		0			0
$806$	−44008.5			−1.92324
$807$			13690.5i			0.597186i
$808$			34868.7i			1.51816i
$809$	27890.7			1.21210			0.606048	−	0.795428i	$-0.292754\pi$
$809$	27890.7			1.21210			0.606048	+	0.795428i	$0.292754\pi$
$810$	25479.1	−	5423.50i	1.10524	−	0.235262i
$811$	12170.3			0.526949			0.263474	−	0.964666i	$-0.415132\pi$
$811$	12170.3			0.526949			0.263474	+	0.964666i	$0.415132\pi$
$812$		0			0
$813$		−	16551.7i		−	0.714015i
$814$	−5199.59			−0.223889
$815$	−20442.1	+	4351.32i	−0.878595	+	0.187019i
$816$	−9860.04			−0.423003
$817$			137.008i			0.00586696i
$818$			9079.53i			0.388091i
$819$		0			0
$820$	−18991.9	−	89222.1i	−0.808813	−	3.79972i
$821$	−30932.3			−1.31491			−0.657457	−	0.753492i	$-0.728368\pi$
$821$	−30932.3			−1.31491			−0.657457	+	0.753492i	$0.728368\pi$
$822$		−	805.569i		−	0.0341818i
$823$		−	25949.0i		−	1.09906i	−0.835475	−	0.549528i	$-0.814807\pi$
$823$		−	25949.0i		−	1.09906i	0.835475	−	0.549528i	$-0.185193\pi$
$824$	24814.7			1.04911
$825$	2521.79	+	5655.17i	0.106421	+	0.238652i
$826$		0			0
$827$		−	27728.5i		−	1.16592i	−0.812502	−	0.582959i	$-0.801895\pi$
$827$		−	27728.5i		−	1.16592i	0.812502	−	0.582959i	$-0.198105\pi$
$828$		−	51070.6i		−	2.14351i
$829$	−10650.1			−0.446194			−0.223097	−	0.974796i	$-0.571617\pi$
$829$	−10650.1			−0.446194			−0.223097	+	0.974796i	$0.571617\pi$
$830$	−12907.4	−	60637.8i	−0.539787	−	2.53587i
$831$	2548.24			0.106375
$832$		−	60959.0i		−	2.54011i
$833$		0			0
$834$	−14362.1			−0.596304
$835$	−508.767	+	108.297i	−0.0210857	+	0.00448833i
$836$	−409.563			−0.0169438
$837$			12588.6i			0.519865i
$838$		−	56424.8i		−	2.32597i
$839$	29761.9			1.22466			0.612332	−	0.790601i	$-0.290232\pi$
$839$	29761.9			1.22466			0.612332	+	0.790601i	$0.290232\pi$
$840$		0			0
$841$	30367.2			1.24512
$842$		−	70531.0i		−	2.88677i
$843$			479.473i			0.0195895i
$844$	84603.2			3.45043
$845$	−4450.57	−	20908.3i	−0.181188	−	0.851205i
$846$	25553.9			1.03849
$847$		0			0
$848$			26440.3i			1.07071i
$849$	17599.7			0.711451
$850$	16800.6	−	7491.85i	0.677949	−	0.302316i
$851$	4160.80			0.167603
$852$			21843.4i			0.878334i
$853$			24410.2i			0.979824i	0.871772	+	0.489912i	$0.162971\pi$
$853$			24410.2i			0.979824i	−0.871772	+	0.489912i	$0.837029\pi$
$854$		0			0
$855$	42.8653	+	201.377i	0.00171458	+	0.00805491i
$856$	−89789.8			−3.58522
$857$			15189.3i			0.605433i	0.953081	+	0.302717i	$0.0978936\pi$
$857$			15189.3i			0.605433i	−0.953081	+	0.302717i	$0.902106\pi$
$858$		−	16872.5i		−	0.671349i
$859$	−10339.1			−0.410668			−0.205334	−	0.978692i	$-0.565828\pi$
$859$	−10339.1			−0.410668			−0.205334	+	0.978692i	$0.565828\pi$
$860$	38257.5	−	8143.53i	1.51694	−	0.322898i
$861$		0			0
$862$		−	42074.6i		−	1.66249i
$863$			27566.6i			1.08734i	0.839298	+	0.543671i	$0.182966\pi$
$863$			27566.6i			1.08734i	−0.839298	+	0.543671i	$0.817034\pi$
$864$	−44365.7			−1.74693
$865$	27297.6	−	5810.60i	1.07300	−	0.228400i
$866$	−23557.2			−0.924373
$867$		−	8040.65i		−	0.314965i
$868$		0			0
$869$	−2026.22			−0.0790964
$870$	−5613.10	−	26369.8i	−0.218738	−	1.02761i
$871$	33053.2			1.28584
$872$			25392.6i			0.986127i
$873$			11984.6i			0.464624i
$874$	457.313			0.0176989
$875$		0			0
$876$	−6798.65			−0.262221
$877$			6032.49i			0.232272i	0.993233	+	0.116136i	$0.0370508\pi$
$877$			6032.49i			0.232272i	−0.993233	+	0.116136i	$0.962949\pi$
$878$		−	68856.4i		−	2.64669i
$879$	5315.31			0.203960
$880$	10914.2	+	51274.0i	0.418089	+	1.96414i
$881$	−44253.2			−1.69231			−0.846156	−	0.532935i	$-0.821089\pi$
$881$	−44253.2			−1.69231			−0.846156	+	0.532935i	$0.821089\pi$
$882$		0			0
$883$		−	7744.13i		−	0.295142i	−0.989051	−	0.147571i	$-0.952854\pi$
$883$		−	7744.13i		−	0.295142i	0.989051	−	0.147571i	$-0.0471456\pi$
$884$	−35923.1			−1.36677
$885$	−14401.9	+	3065.61i	−0.547024	+	0.116440i
$886$	−63978.8			−2.42597
$887$			18632.5i			0.705318i	0.935752	+	0.352659i	$0.114722\pi$
$887$			18632.5i			0.705318i	−0.935752	+	0.352659i	$0.885278\pi$
$888$		−	4830.38i		−	0.182542i
$889$		0			0
$890$	37889.0	−	8065.09i	1.42701	−	0.303756i
$891$	11199.8			0.421110
$892$			47785.3i			1.79369i
$893$			163.989i			0.00614522i
$894$	334.922			0.0125296
$895$	−6926.56	−	32540.3i	−0.258692	−	1.21531i
$896$		0			0
$897$			13501.7i			0.502573i
$898$			61565.7i			2.28783i
$899$	−30233.7			−1.12164
$900$	53683.8	−	23939.0i	1.98829	−	0.886631i
$901$	3988.97			0.147494
$902$		−	54725.0i		−	2.02011i
$903$		0			0
$904$	−106825.			−3.93025
$905$	−2249.20	−	10566.5i	−0.0826143	−	0.388114i
$906$	−4810.09			−0.176385
$907$		−	1258.19i		−	0.0460612i	−0.999735	−	0.0230306i	$-0.992668\pi$
$907$		−	1258.19i		−	0.0460612i	0.999735	−	0.0230306i	$-0.00733151\pi$
$908$		−	11875.4i		−	0.434030i
$909$	12463.9			0.454786
$910$		0			0
$911$	27133.6			0.986800			0.493400	−	0.869802i	$-0.335754\pi$
$911$	27133.6			0.986800			0.493400	+	0.869802i	$0.335754\pi$
$912$		−	282.123i		−	0.0102435i
$913$		−	26654.6i		−	0.966197i
$914$	−51724.9			−1.87189
$915$	12188.5	−	2594.46i	0.440371	−	0.0937379i
$916$	93476.5			3.37178
$917$		0			0
$918$			14338.4i			0.515510i
$919$	−42534.1			−1.52673			−0.763367	−	0.645965i	$-0.776455\pi$
$919$	−42534.1			−1.52673			−0.763367	+	0.645965i	$0.776455\pi$
$920$	−16435.4	−	77211.8i	−0.588977	−	2.76696i
$921$	−13547.5			−0.484697
$922$		−	7138.42i		−	0.254980i
$923$			35679.7i			1.27238i
$924$		0			0
$925$	1950.35	+	4373.70i	0.0693266	+	0.155466i
$926$	−35143.1			−1.24716
$927$		−	8870.08i		−	0.314274i
$928$		−	106552.i		−	3.76911i
$929$	41849.0			1.47795			0.738977	−	0.673730i	$-0.235309\pi$
$929$	41849.0			1.47795			0.738977	+	0.673730i	$0.235309\pi$
$930$	3099.28	+	14560.1i	0.109279	+	0.513382i
$931$		0			0
$932$			103612.i			3.64155i
$933$		−	692.053i		−	0.0242838i
$934$	−78051.9			−2.73441
$935$	7735.54	−	1646.60i	0.270566	−	0.0575930i
$936$	−96844.9			−3.38192
$937$		−	33281.9i		−	1.16038i	−0.814482	−	0.580188i	$-0.802979\pi$
$937$		−	33281.9i		−	1.16038i	0.814482	−	0.580188i	$-0.197021\pi$
$938$		0			0
$939$	−12858.4			−0.446876
$940$	45791.5	−	9747.24i	1.58889	−	0.338213i
$941$	−12740.6			−0.441373			−0.220687	−	0.975345i	$-0.570830\pi$
$941$	−12740.6			−0.441373			−0.220687	+	0.975345i	$0.570830\pi$
$942$		−	17245.8i		−	0.596496i
$943$			43791.9i			1.51226i
$944$	−124662.			−4.29810
$945$		0			0
$946$	23465.5			0.806478
$947$		−	20681.5i		−	0.709670i	−0.934929	−	0.354835i	$-0.884537\pi$
$947$		−	20681.5i		−	0.709670i	0.934929	−	0.354835i	$-0.115463\pi$
$948$		−	3113.14i		−	0.106656i
$949$	−11105.1			−0.379861
$950$	214.363	+	480.712i	0.00732088	+	0.0164172i
$951$	−4836.92			−0.164929
$952$		0			0
$953$			6702.50i			0.227823i	0.993491	+	0.113912i	$0.0363380\pi$
$953$			6702.50i			0.227823i	−0.993491	+	0.113912i	$0.963662\pi$
$954$	17785.4			0.603588
$955$	−3597.47	−	16900.6i	−0.121897	−	0.572659i
$956$	22815.2			0.771857
$957$		−	11591.4i		−	0.391532i
$958$			81291.6i			2.74156i
$959$		0			0
$960$	−20168.2	+	4293.02i	−0.678047	+	0.144330i
$961$	−13097.4			−0.439643
$962$		−	13049.2i		−	0.437341i
$963$			32095.5i			1.07400i
$964$	−71824.6			−2.39970
$965$	25195.6	−	5363.16i	0.840492	−	0.178908i
$966$		0			0
$967$			36459.9i			1.21248i	0.795280	+	0.606242i	$0.207324\pi$
$967$			36459.9i			1.21248i	−0.795280	+	0.606242i	$0.792676\pi$
$968$		−	44117.9i		−	1.46488i
$969$	−42.5631			−0.00141107
$970$	6378.69	+	29966.5i	0.211142	+	0.991922i
$971$	15789.7			0.521850			0.260925	−	0.965359i	$-0.415973\pi$
$971$	15789.7			0.521850			0.260925	+	0.965359i	$0.415973\pi$
$972$			70439.3i			2.32443i
$973$		0			0
$974$	51297.0			1.68754
$975$	−14192.5	+	6328.83i	−0.466179	+	0.207882i
$976$	105503.			3.46011
$977$			34429.2i			1.12742i	0.825974	+	0.563709i	$0.190626\pi$
$977$			34429.2i			1.12742i	−0.825974	+	0.563709i	$0.809374\pi$
$978$		−	19264.2i		−	0.629857i
$979$	16654.9			0.543710
$980$		0			0
$981$	9076.65			0.295408
$982$		−	107031.i		−	3.47809i
$983$			21047.5i			0.682922i	0.939896	+	0.341461i	$0.110922\pi$
$983$			21047.5i			0.682922i	−0.939896	+	0.341461i	$0.889078\pi$
$984$	50839.1			1.64704
$985$	−2427.87	+	516.799i	−0.0785365	+	0.0167174i
$986$	−34436.1			−1.11224
$987$		0			0
$988$		−	1027.86i		−	0.0330978i
$989$	−18777.5			−0.603730
$990$	34490.0	−	7341.58i	1.10724	−	0.235688i
$991$	23839.1			0.764150			0.382075	−	0.924131i	$-0.375210\pi$
$991$	23839.1			0.764150			0.382075	+	0.924131i	$0.375210\pi$
$992$			58832.7i			1.88301i
$993$			9081.12i			0.290212i
$994$		0			0
$995$	8334.49	+	39154.6i	0.265549	+	1.24752i
$996$	40952.8			1.30285
$997$			7853.62i			0.249475i	0.992190	+	0.124738i	$0.0398089\pi$
$997$			7853.62i			0.249475i	−0.992190	+	0.124738i	$0.960191\pi$
$998$		−	6957.12i		−	0.220665i
$999$	−3732.71			−0.118216

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	245.4.b.d.99.1		10
5.2	odd	4		1225.4.a.bh.1.5		5
5.3	odd	4		1225.4.a.be.1.1		5
5.4	even	2	inner	245.4.b.d.99.10		10
7.2	even	3		245.4.j.f.214.1		20
7.3	odd	6		245.4.j.e.79.10		20
7.4	even	3		245.4.j.f.79.10		20
7.5	odd	6		245.4.j.e.214.1		20
7.6	odd	2		35.4.b.a.29.1	✓	10
21.20	even	2		315.4.d.c.64.10		10
28.27	even	2		560.4.g.f.449.5		10
35.4	even	6		245.4.j.f.79.1		20
35.9	even	6		245.4.j.f.214.10		20
35.13	even	4		175.4.a.i.1.1		5
35.19	odd	6		245.4.j.e.214.10		20
35.24	odd	6		245.4.j.e.79.1		20
35.27	even	4		175.4.a.j.1.5		5
35.34	odd	2		35.4.b.a.29.10	yes	10
105.62	odd	4		1575.4.a.bn.1.1		5
105.83	odd	4		1575.4.a.bq.1.5		5
105.104	even	2		315.4.d.c.64.1		10
140.139	even	2		560.4.g.f.449.6		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.4.b.a.29.1	✓	10	7.6	odd	2
35.4.b.a.29.10	yes	10	35.34	odd	2
175.4.a.i.1.1		5	35.13	even	4
175.4.a.j.1.5		5	35.27	even	4
245.4.b.d.99.1		10	1.1	even	1	trivial
245.4.b.d.99.10		10	5.4	even	2	inner
245.4.j.e.79.1		20	35.24	odd	6
245.4.j.e.79.10		20	7.3	odd	6
245.4.j.e.214.1		20	7.5	odd	6
245.4.j.e.214.10		20	35.19	odd	6
245.4.j.f.79.1		20	35.4	even	6
245.4.j.f.79.10		20	7.4	even	3
245.4.j.f.214.1		20	7.2	even	3
245.4.j.f.214.10		20	35.9	even	6
315.4.d.c.64.1		10	105.104	even	2
315.4.d.c.64.10		10	21.20	even	2
560.4.g.f.449.5		10	28.27	even	2
560.4.g.f.449.6		10	140.139	even	2
1225.4.a.be.1.1		5	5.3	odd	4
1225.4.a.bh.1.5		5	5.2	odd	4
1575.4.a.bn.1.1		5	105.62	odd	4
1575.4.a.bq.1.5		5	105.83	odd	4

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.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-5.31366i q^{2} -1.93939i q^{3} -20.2350 q^{4} +(2.32771 + 10.9353i) q^{5} -10.3052 q^{6} +65.0123i q^{8} +23.2388 q^{9} +(58.1067 - 12.3686i) q^{10} +25.5420 q^{11} +39.2434i q^{12} +64.1014i q^{13} +(21.2079 - 4.51433i) q^{15} +183.574 q^{16} -27.6952i q^{17} -123.483i q^{18} +0.792436 q^{19} +(-47.1011 - 221.276i) q^{20} -135.721i q^{22} +108.606i q^{23} +126.084 q^{24} +(-114.164 + 50.9086i) q^{25} +340.613 q^{26} -97.4324i q^{27} +234.000 q^{29} +(-23.9876 - 112.691i) q^{30} -129.204 q^{31} -455.349i q^{32} -49.5357i q^{33} -147.163 q^{34} -470.236 q^{36} -38.3108i q^{37} -4.21073i q^{38} +124.317 q^{39} +(-710.932 + 151.330i) q^{40} +403.216 q^{41} +172.895i q^{43} -516.840 q^{44} +(54.0931 + 254.124i) q^{45} +577.097 q^{46} +206.943i q^{47} -356.020i q^{48} +(270.511 + 606.626i) q^{50} -53.7117 q^{51} -1297.09i q^{52} +144.031i q^{53} -517.722 q^{54} +(59.4542 + 279.310i) q^{55} -1.53684i q^{57} -1243.40i q^{58} -679.086 q^{59} +(-429.140 + 91.3471i) q^{60} +574.717 q^{61} +686.544i q^{62} -950.977 q^{64} +(-700.971 + 149.209i) q^{65} -263.216 q^{66} -515.640i q^{67} +560.411i q^{68} +210.630 q^{69} +556.612 q^{71} +1510.81i q^{72} +173.243i q^{73} -203.571 q^{74} +(98.7314 + 221.407i) q^{75} -16.0349 q^{76} -660.580i q^{78} -79.3290 q^{79} +(427.306 + 2007.44i) q^{80} +438.488 q^{81} -2142.55i q^{82} -1043.56i q^{83} +(302.856 - 64.4663i) q^{85} +918.703 q^{86} -453.817i q^{87} +1660.54i q^{88} +652.060 q^{89} +(1350.33 - 287.432i) q^{90} -2197.65i q^{92} +250.576i q^{93} +1099.62 q^{94} +(1.84456 + 8.66556i) q^{95} -883.097 q^{96} +515.714i q^{97} +593.564 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 36 q^{4} - 6 q^{5} - 12 q^{6} - 46 q^{9} + 16 q^{10} + 84 q^{11} + 8 q^{15} + 148 q^{16} - 72 q^{19} + 68 q^{20} - 72 q^{24} - 362 q^{25} + 620 q^{26} + 88 q^{29} + 52 q^{30} - 120 q^{31} - 964 q^{34}+ \cdots - 5304 q^{99}+O(q^{100}) \) 10 * q - 36 * q^4 - 6 * q^5 - 12 * q^6 - 46 * q^9 + 16 * q^10 + 84 * q^11 + 8 * q^15 + 148 * q^16 - 72 * q^19 + 68 * q^20 - 72 * q^24 - 362 * q^25 + 620 * q^26 + 88 * q^29 + 52 * q^30 - 120 * q^31 - 964 * q^34 - 420 * q^36 + 212 * q^39 - 1396 * q^40 + 852 * q^41 - 1424 * q^44 + 510 * q^45 + 176 * q^46 + 1644 * q^50 + 1276 * q^51 + 996 * q^54 + 1136 * q^55 - 864 * q^59 - 1692 * q^60 + 884 * q^61 - 2724 * q^64 + 520 * q^65 - 1148 * q^66 - 4808 * q^69 + 880 * q^71 + 3024 * q^74 - 720 * q^75 + 2672 * q^76 - 3580 * q^79 + 2316 * q^80 - 302 * q^81 + 1572 * q^85 + 2432 * q^86 + 1492 * q^89 + 7748 * q^90 - 1652 * q^94 - 1628 * q^95 - 4080 * q^96 - 5304 * q^99

Introduction

L-functions

Modular forms

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Database

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