LMFDB - Embedded newform 115.3.c.c.114.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [115,3,Mod(114,115)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(115, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("115.114");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 115 = 5 \cdot 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	115.c (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:	$3.13352304014$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 6 x^{18} - 827 x^{16} - 12720 x^{14} + 346250 x^{12} + 9668500 x^{10} + 216406250 x^{8} + \cdots + 95367431640625 $ x^20 + 6x^18 - 827x^16 - 12720x^14 + 346250x^12 + 9668500x^10 + 216406250x^8 - 4968750000x^6 - 201904296875x^4 + 915527343750*x^2 + 95367431640625
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4}\cdot 5 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			114.12
Root			$-1.45055 + 4.78497i$ of defining polynomial
Character	$\chi$	$=$	115.114
Dual form			115.3.c.c.114.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.436812i q^{2} -4.79508i q^{3} +3.80920 q^{4} +(1.45055 + 4.78497i) q^{5} +2.09455 q^{6} +5.38385 q^{7} +3.41115i q^{8} -13.9928 q^{9} +O(q^{10})$	\(q+0.436812i q^{2} -4.79508i q^{3} +3.80920 q^{4} +(1.45055 + 4.78497i) q^{5} +2.09455 q^{6} +5.38385 q^{7} +3.41115i q^{8} -13.9928 q^{9} +(-2.09013 + 0.633615i) q^{10} -12.9895i q^{11} -18.2654i q^{12} -9.52336i q^{13} +2.35173i q^{14} +(22.9443 - 6.95548i) q^{15} +13.7468 q^{16} -19.7991 q^{17} -6.11221i q^{18} +27.9683i q^{19} +(5.52541 + 18.2269i) q^{20} -25.8160i q^{21} +5.67397 q^{22} +(-20.2492 + 10.9073i) q^{23} +16.3567 q^{24} +(-20.7918 + 13.8816i) q^{25} +4.15991 q^{26} +23.9408i q^{27} +20.5081 q^{28} +12.1341 q^{29} +(3.03823 + 10.0223i) q^{30} +37.0645 q^{31} +19.6493i q^{32} -62.2857 q^{33} -8.64849i q^{34} +(7.80951 + 25.7615i) q^{35} -53.3013 q^{36} +35.6466 q^{37} -12.2169 q^{38} -45.6652 q^{39} +(-16.3222 + 4.94802i) q^{40} -32.0781 q^{41} +11.2767 q^{42} -29.4476 q^{43} -49.4796i q^{44} +(-20.2972 - 66.9550i) q^{45} +(-4.76443 - 8.84509i) q^{46} +82.6329i q^{47} -65.9168i q^{48} -20.0142 q^{49} +(-6.06365 - 9.08211i) q^{50} +94.9384i q^{51} -36.2763i q^{52} -11.4311 q^{53} -10.4576 q^{54} +(62.1544 - 18.8419i) q^{55} +18.3651i q^{56} +134.110 q^{57} +5.30033i q^{58} +19.5213 q^{59} +(87.3993 - 26.4948i) q^{60} +21.8377i q^{61} +16.1902i q^{62} -75.3350 q^{63} +46.4040 q^{64} +(45.5690 - 13.8141i) q^{65} -27.2071i q^{66} -106.068 q^{67} -75.4188 q^{68} +(52.3013 + 97.0966i) q^{69} +(-11.2529 + 3.41129i) q^{70} +13.5108 q^{71} -47.7314i q^{72} -7.93498i q^{73} +15.5708i q^{74} +(66.5635 + 99.6985i) q^{75} +106.537i q^{76} -69.9336i q^{77} -19.9471i q^{78} -123.502i q^{79} +(19.9403 + 65.7778i) q^{80} -11.1371 q^{81} -14.0121i q^{82} +129.448 q^{83} -98.3381i q^{84} +(-28.7195 - 94.7383i) q^{85} -12.8631i q^{86} -58.1841i q^{87} +44.3091 q^{88} -49.8029i q^{89} +(29.2467 - 8.86603i) q^{90} -51.2723i q^{91} +(-77.1333 + 41.5480i) q^{92} -177.727i q^{93} -36.0950 q^{94} +(-133.828 + 40.5693i) q^{95} +94.2201 q^{96} +76.4896 q^{97} -8.74243i q^{98} +181.759i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 56 q^{4} - 8 q^{6} - 72 q^{9}+O(q^{10}) $ 20 * q - 56 * q^4 - 8 * q^6 - 72 * q^9	$ 20 q - 56 q^{4} - 8 q^{6} - 72 q^{9} + 88 q^{16} + 44 q^{24} - 12 q^{25} - 56 q^{26} + 236 q^{31} + 92 q^{35} - 32 q^{36} - 168 q^{39} + 124 q^{41} - 248 q^{46} + 88 q^{49} + 200 q^{50} - 196 q^{54} + 268 q^{55} + 56 q^{59} - 28 q^{64} + 376 q^{69} - 636 q^{70} - 196 q^{71} + 428 q^{75} - 988 q^{81} - 284 q^{85} + 276 q^{94} + 184 q^{95} - 264 q^{96}+O(q^{100}) $ 20 * q - 56 * q^4 - 8 * q^6 - 72 * q^9 + 88 * q^16 + 44 * q^24 - 12 * q^25 - 56 * q^26 + 236 * q^31 + 92 * q^35 - 32 * q^36 - 168 * q^39 + 124 * q^41 - 248 * q^46 + 88 * q^49 + 200 * q^50 - 196 * q^54 + 268 * q^55 + 56 * q^59 - 28 * q^64 + 376 * q^69 - 636 * q^70 - 196 * q^71 + 428 * q^75 - 988 * q^81 - 284 * q^85 + 276 * q^94 + 184 * q^95 - 264 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/115\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$-1$	$-1$

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 $

$2$			0.436812i			0.218406i	0.994019	+	0.109203i	$0.0348298\pi$
$2$			0.436812i			0.218406i	−0.994019	+	0.109203i	$0.965170\pi$
$3$		−	4.79508i		−	1.59836i	−0.601092	−	0.799180i	$-0.705267\pi$
$3$		−	4.79508i		−	1.59836i	0.601092	−	0.799180i	$-0.294733\pi$
$4$	3.80920			0.952299
$5$	1.45055	+	4.78497i	0.290109	+	0.956994i
$5$	1.45055	+	4.78497i	0.290109	+	0.956994i
$6$	2.09455			0.349091
$7$	5.38385			0.769121			0.384561	−	0.923100i	$-0.374353\pi$
$7$	5.38385			0.769121			0.384561	+	0.923100i	$0.374353\pi$
$8$			3.41115i			0.426393i
$9$	−13.9928			−1.55475
$10$	−2.09013	+	0.633615i	−0.209013	+	0.0633615i
$11$		−	12.9895i		−	1.18086i	−0.807087	−	0.590432i	$-0.798957\pi$
$11$		−	12.9895i		−	1.18086i	0.807087	−	0.590432i	$-0.201043\pi$
$12$		−	18.2654i		−	1.52212i
$13$		−	9.52336i		−	0.732566i	−0.930504	−	0.366283i	$-0.880630\pi$
$13$		−	9.52336i		−	0.732566i	0.930504	−	0.366283i	$-0.119370\pi$
$14$			2.35173i			0.167980i
$15$	22.9443	−	6.95548i	1.52962	−	0.463699i
$16$	13.7468			0.859172
$17$	−19.7991			−1.16466			−0.582328	−	0.812954i	$-0.697858\pi$
$17$	−19.7991			−1.16466			−0.582328	+	0.812954i	$0.697858\pi$
$18$		−	6.11221i		−	0.339567i
$19$			27.9683i			1.47202i	0.676972	+	0.736008i	$0.263292\pi$
$19$			27.9683i			1.47202i	−0.676972	+	0.736008i	$0.736708\pi$
$20$	5.52541	+	18.2269i	0.276270	+	0.911344i
$21$		−	25.8160i		−	1.22933i
$22$	5.67397			0.257908
$23$	−20.2492	+	10.9073i	−0.880401	+	0.474230i
$23$	−20.2492	+	10.9073i	−0.880401	+	0.474230i
$24$	16.3567			0.681530
$25$	−20.7918	+	13.8816i	−0.831674	+	0.555265i
$26$	4.15991			0.159997
$27$			23.9408i			0.886696i
$28$	20.5081			0.732433
$29$	12.1341			0.418418			0.209209	−	0.977871i	$-0.432911\pi$
$29$	12.1341			0.418418			0.209209	+	0.977871i	$0.432911\pi$
$30$	3.03823	+	10.0223i	0.101274	+	0.334078i
$31$	37.0645			1.19563			0.597814	−	0.801635i	$-0.296036\pi$
$31$	37.0645			1.19563			0.597814	+	0.801635i	$0.296036\pi$
$32$			19.6493i			0.614041i
$33$	−62.2857			−1.88745
$34$		−	8.64849i		−	0.254367i
$35$	7.80951	+	25.7615i	0.223129	+	0.736044i
$36$	−53.3013			−1.48059
$37$	35.6466			0.963421			0.481710	−	0.876330i	$-0.340016\pi$
$37$	35.6466			0.963421			0.481710	+	0.876330i	$0.340016\pi$
$38$	−12.2169			−0.321497
$39$	−45.6652			−1.17090
$40$	−16.3222	+	4.94802i	−0.408056	+	0.123701i
$41$	−32.0781			−0.782392			−0.391196	−	0.920307i	$-0.627939\pi$
$41$	−32.0781			−0.782392			−0.391196	+	0.920307i	$0.627939\pi$
$42$	11.2767			0.268493
$43$	−29.4476			−0.684829			−0.342414	−	0.939549i	$-0.611245\pi$
$43$	−29.4476			−0.684829			−0.342414	+	0.939549i	$0.611245\pi$
$44$		−	49.4796i		−	1.12454i
$45$	−20.2972	−	66.9550i	−0.451048	−	1.48789i
$46$	−4.76443	−	8.84509i	−0.103575	−	0.192285i
$47$			82.6329i			1.75815i	0.476686	+	0.879074i	$0.341838\pi$
$47$			82.6329i			1.75815i	−0.476686	+	0.879074i	$0.658162\pi$
$48$		−	65.9168i		−	1.37327i
$49$	−20.0142			−0.408453
$50$	−6.06365	−	9.08211i	−0.121273	−	0.181642i
$51$			94.9384i			1.86154i
$52$		−	36.2763i		−	0.697622i
$53$	−11.4311			−0.215681			−0.107841	−	0.994168i	$-0.534394\pi$
$53$	−11.4311			−0.215681			−0.107841	+	0.994168i	$0.534394\pi$
$54$	−10.4576			−0.193660
$55$	62.1544	−	18.8419i	1.13008	−	0.342580i
$56$			18.3651i			0.327948i
$57$	134.110			2.35281
$58$			5.30033i			0.0913849i
$59$	19.5213			0.330869			0.165434	−	0.986221i	$-0.447097\pi$
$59$	19.5213			0.330869			0.165434	+	0.986221i	$0.447097\pi$
$60$	87.3993	−	26.4948i	1.45666	−	0.441580i
$61$			21.8377i			0.357994i	0.983850	+	0.178997i	$0.0572853\pi$
$61$			21.8377i			0.357994i	−0.983850	+	0.178997i	$0.942715\pi$
$62$			16.1902i			0.261132i
$63$	−75.3350			−1.19579
$64$	46.4040			0.725062
$65$	45.5690	−	13.8141i	0.701061	−	0.212524i
$66$		−	27.2071i		−	0.412229i
$67$	−106.068			−1.58310			−0.791549	−	0.611106i	$-0.790725\pi$
$67$	−106.068			−1.58310			−0.791549	+	0.611106i	$0.790725\pi$
$68$	−75.4188			−1.10910
$69$	52.3013	+	97.0966i	0.757990	+	1.40720i
$70$	−11.2529	+	3.41129i	−0.160756	+	0.0487326i
$71$	13.5108			0.190293			0.0951465	−	0.995463i	$-0.469668\pi$
$71$	13.5108			0.190293			0.0951465	+	0.995463i	$0.469668\pi$
$72$		−	47.7314i		−	0.662937i
$73$		−	7.93498i		−	0.108698i	−0.998522	−	0.0543492i	$-0.982692\pi$
$73$		−	7.93498i		−	0.108698i	0.998522	−	0.0543492i	$-0.0173084\pi$
$74$			15.5708i			0.210417i
$75$	66.5635	+	99.6985i	0.887513	+	1.32931i
$76$			106.537i			1.40180i
$77$		−	69.9336i		−	0.908228i
$78$		−	19.9471i		−	0.255732i
$79$		−	123.502i		−	1.56331i	−0.623708	−	0.781657i	$-0.714375\pi$
$79$		−	123.502i		−	1.56331i	0.623708	−	0.781657i	$-0.285625\pi$
$80$	19.9403	+	65.7778i	0.249254	+	0.822222i
$81$	−11.1371			−0.137495
$82$		−	14.0121i		−	0.170879i
$83$	129.448			1.55962			0.779809	−	0.626017i	$-0.215316\pi$
$83$	129.448			1.55962			0.779809	+	0.626017i	$0.215316\pi$
$84$		−	98.3381i		−	1.17069i
$85$	−28.7195	−	94.7383i	−0.337877	−	1.11457i
$86$		−	12.8631i		−	0.149570i
$87$		−	58.1841i		−	0.668783i
$88$	44.3091			0.503513
$89$		−	49.8029i		−	0.559583i	−0.960061	−	0.279792i	$-0.909735\pi$
$89$		−	49.8029i		−	0.559583i	0.960061	−	0.279792i	$-0.0902654\pi$
$90$	29.2467	−	8.86603i	0.324964	−	0.0985115i
$91$		−	51.2723i		−	0.563432i
$92$	−77.1333	+	41.5480i	−0.838405	+	0.451609i
$93$		−	177.727i		−	1.91104i
$94$	−36.0950			−0.383990
$95$	−133.828	+	40.5693i	−1.40871	+	0.427045i
$96$	94.2201			0.981459
$97$	76.4896			0.788553			0.394276	−	0.918992i	$-0.370995\pi$
$97$	76.4896			0.788553			0.394276	+	0.918992i	$0.370995\pi$
$98$		−	8.74243i		−	0.0892085i
$99$			181.759i			1.83595i
$100$	−79.2002	+	52.8778i	−0.792002	+	0.528778i
$101$	−166.677			−1.65026			−0.825132	−	0.564940i	$-0.808899\pi$
$101$	−166.677			−1.65026			−0.825132	+	0.564940i	$0.808899\pi$
$102$	−41.4702			−0.406571
$103$	75.3869			0.731912			0.365956	−	0.930632i	$-0.380742\pi$
$103$	75.3869			0.731912			0.365956	+	0.930632i	$0.380742\pi$
$104$	32.4856			0.312361
$105$	123.529	−	37.4472i	1.17646	−	0.356640i
$106$		−	4.99324i		−	0.0471060i
$107$	−14.8761			−0.139029			−0.0695144	−	0.997581i	$-0.522145\pi$
$107$	−14.8761			−0.139029			−0.0695144	+	0.997581i	$0.522145\pi$
$108$			91.1952i			0.844400i
$109$		−	36.5838i		−	0.335631i	−0.985818	−	0.167816i	$-0.946329\pi$
$109$		−	36.5838i		−	0.335631i	0.985818	−	0.167816i	$-0.0536714\pi$
$110$	8.23035	+	27.1498i	0.0748213	+	0.246816i
$111$		−	170.928i		−	1.53989i
$112$	74.0104			0.660807
$113$	−128.571			−1.13780			−0.568898	−	0.822408i	$-0.692630\pi$
$113$	−128.571			−1.13780			−0.568898	+	0.822408i	$0.692630\pi$
$114$			58.5809i			0.513868i
$115$	−81.5634	−	81.0704i	−0.709247	−	0.704960i
$116$	46.2213			0.398459
$117$			133.258i			1.13896i
$118$			8.52711i			0.0722637i
$119$	−106.596			−0.895761
$120$	23.7262	+	78.2664i	0.197718	+	0.652220i
$121$	−47.7275			−0.394442
$122$	−9.53894			−0.0781881
$123$			153.817i			1.25054i
$124$	141.186			1.13860
$125$	−96.5826	−	79.3524i	−0.772661	−	0.634819i
$126$		−	32.9072i		−	0.261168i
$127$		−	36.8155i		−	0.289886i	−0.989440	−	0.144943i	$-0.953700\pi$
$127$		−	36.8155i		−	0.289886i	0.989440	−	0.144943i	$-0.0462999\pi$
$128$			98.8671i			0.772399i
$129$			141.204i			1.09460i
$130$	6.03414	+	19.9050i	0.0464165	+	0.153116i
$131$	147.987			1.12968			0.564838	−	0.825202i	$-0.308939\pi$
$131$	147.987			1.12968			0.564838	+	0.825202i	$0.308939\pi$
$132$	−237.259			−1.79741
$133$			150.577i			1.13216i
$134$		−	46.3315i		−	0.345758i
$135$	−114.556	+	34.7272i	−0.848562	+	0.257238i
$136$		−	67.5378i		−	0.496601i
$137$	101.516			0.740992			0.370496	−	0.928834i	$-0.379188\pi$
$137$	101.516			0.740992			0.370496	+	0.928834i	$0.379188\pi$
$138$	−42.4129	+	22.8458i	−0.307340	+	0.165549i
$139$	−70.4227			−0.506638			−0.253319	−	0.967383i	$-0.581522\pi$
$139$	−70.4227			−0.506638			−0.253319	+	0.967383i	$0.581522\pi$
$140$	29.7480	+	98.1307i	0.212485	+	0.700934i
$141$	396.231			2.81015
$142$			5.90168i			0.0415611i
$143$	−123.704			−0.865061
$144$	−192.355			−1.33580
$145$	17.6011	+	58.0614i	0.121387	+	0.400423i
$146$	3.46609			0.0237403
$147$			95.9696i			0.652855i
$148$	135.785			0.917465
$149$		−	173.077i		−	1.16159i	−0.814049	−	0.580797i	$-0.802741\pi$
$149$		−	173.077i		−	1.16159i	0.814049	−	0.580797i	$-0.197259\pi$
$150$	−43.5495	+	29.0757i	−0.290330	+	0.193838i
$151$	−165.606			−1.09673			−0.548364	−	0.836240i	$-0.684749\pi$
$151$	−165.606			−1.09673			−0.548364	+	0.836240i	$0.684749\pi$
$152$	−95.4040			−0.627658
$153$	277.045			1.81075
$154$	30.5478			0.198362
$155$	53.7637	+	177.352i	0.346862	+	1.14421i
$156$	−173.948			−1.11505
$157$	106.514			0.678432			0.339216	−	0.940709i	$-0.389838\pi$
$157$	106.514			0.678432			0.339216	+	0.940709i	$0.389838\pi$
$158$	53.9470			0.341437
$159$			54.8130i			0.344736i
$160$	−94.0214	+	28.5022i	−0.587634	+	0.178139i
$161$	−109.019	+	58.7232i	−0.677135	+	0.364740i
$162$		−	4.86480i		−	0.0300296i
$163$		−	226.465i		−	1.38936i	−0.719321	−	0.694678i	$-0.755547\pi$
$163$		−	226.465i		−	1.38936i	0.719321	−	0.694678i	$-0.244453\pi$
$164$	−122.192			−0.745071
$165$	−90.3483	−	298.035i	−0.547565	−	1.80627i
$166$			56.5445i			0.340630i
$167$		−	89.6291i		−	0.536701i	−0.963321	−	0.268351i	$-0.913521\pi$
$167$		−	89.6291i		−	0.536701i	0.963321	−	0.268351i	$-0.0864786\pi$
$168$	88.0621			0.524179
$169$	78.3057			0.463347
$170$	41.3828	−	12.5450i	0.243428	−	0.0737943i
$171$		−	391.355i		−	2.28862i
$172$	−112.172			−0.652161
$173$			42.9060i			0.248012i	0.992281	+	0.124006i	$0.0395742\pi$
$173$			42.9060i			0.248012i	−0.992281	+	0.124006i	$0.960426\pi$
$174$	25.4155			0.146066
$175$	−111.940	+	74.7365i	−0.639658	+	0.427066i
$176$		−	178.564i		−	1.01457i
$177$		−	93.6060i		−	0.528848i
$178$	21.7545			0.122216
$179$	110.640			0.618098			0.309049	−	0.951046i	$-0.399989\pi$
$179$	110.640			0.618098			0.309049	+	0.951046i	$0.399989\pi$
$180$	−77.3159	−	255.045i	−0.429533	−	1.41692i
$181$			278.258i			1.53734i	0.639647	+	0.768669i	$0.279081\pi$
$181$			278.258i			1.53734i	−0.639647	+	0.768669i	$0.720919\pi$
$182$	22.3963			0.123057
$183$	104.713			0.572204
$184$	−37.2064	−	69.0731i	−0.202208	−	0.375397i
$185$	51.7070	+	170.568i	0.279497	+	0.921988i
$186$	77.6332			0.417383
$187$			257.181i			1.37530i
$188$			314.765i			1.67428i
$189$			128.894i			0.681977i
$190$	−17.7211	−	58.4574i	−0.0932692	−	0.307671i
$191$			23.0239i			0.120544i	0.998182	+	0.0602721i	$0.0191968\pi$
$191$			23.0239i			0.120544i	−0.998182	+	0.0602721i	$0.980803\pi$
$192$		−	222.511i		−	1.15891i
$193$		−	235.370i		−	1.21953i	−0.792581	−	0.609766i	$-0.791263\pi$
$193$		−	235.370i		−	1.21953i	0.792581	−	0.609766i	$-0.208737\pi$
$194$			33.4116i			0.172224i
$195$	−66.2395	−	218.507i	−0.339690	−	1.12055i
$196$	−76.2380			−0.388969
$197$			8.37012i			0.0424879i	0.999774	+	0.0212440i	$0.00676267\pi$
$197$			8.37012i			0.0424879i	−0.999774	+	0.0212440i	$0.993237\pi$
$198$	−79.3946			−0.400983
$199$		−	265.577i		−	1.33456i	−0.744809	−	0.667278i	$-0.767459\pi$
$199$		−	265.577i		−	1.33456i	0.744809	−	0.667278i	$-0.232541\pi$
$200$	−47.3523	−	70.9240i	−0.236761	−	0.354620i
$201$			508.602i			2.53036i
$202$		−	72.8063i		−	0.360427i
$203$	65.3283			0.321814
$204$			361.639i			1.77274i
$205$	−46.5307	−	153.493i	−0.226979	−	0.748744i
$206$			32.9299i			0.159854i
$207$	283.343	−	152.623i	1.36881	−	0.737311i
$208$		−	130.915i		−	0.629400i
$209$	363.295			1.73825
$210$	16.3574	+	53.9587i	0.0778923	+	0.256946i
$211$	190.598			0.903307			0.451654	−	0.892193i	$-0.350834\pi$
$211$	190.598			0.903307			0.451654	+	0.892193i	$0.350834\pi$
$212$	−43.5433			−0.205393
$213$		−	64.7854i		−	0.304157i
$214$		−	6.49804i		−	0.0303647i
$215$	−42.7151	−	140.906i	−0.198675	−	0.655377i
$216$	−81.6656			−0.378081
$217$	199.549			0.919583
$218$	15.9802			0.0733038
$219$	−38.0489			−0.173739
$220$	236.758	−	71.7724i	1.07617	−	0.326238i
$221$			188.554i			0.853187i
$222$	74.6634			0.336321
$223$			390.262i			1.75005i	0.484076	+	0.875026i	$0.339156\pi$
$223$			390.262i			1.75005i	−0.484076	+	0.875026i	$0.660844\pi$
$224$			105.789i			0.472272i
$225$	290.936	−	194.243i	1.29305	−	0.863300i
$226$		−	56.1613i		−	0.248501i
$227$	−41.0806			−0.180972			−0.0904859	−	0.995898i	$-0.528842\pi$
$227$	−41.0806			−0.180972			−0.0904859	+	0.995898i	$0.528842\pi$
$228$	510.852			2.24058
$229$			18.4264i			0.0804644i	0.999190	+	0.0402322i	$0.0128098\pi$
$229$			18.4264i			0.0804644i	−0.999190	+	0.0402322i	$0.987190\pi$
$230$	35.4125	−	35.6278i	0.153967	−	0.154904i
$231$	−335.337			−1.45167
$232$			41.3913i			0.178411i
$233$		−	395.794i		−	1.69869i	−0.527841	−	0.849343i	$-0.676998\pi$
$233$		−	395.794i		−	1.69869i	0.527841	−	0.849343i	$-0.323002\pi$
$234$	−58.2087			−0.248755
$235$	−395.396	+	119.863i	−1.68254	+	0.510054i
$236$	74.3603			0.315086
$237$	−592.201			−2.49874
$238$		−	46.5622i		−	0.195639i
$239$	−172.200			−0.720502			−0.360251	−	0.932855i	$-0.617309\pi$
$239$	−172.200			−0.720502			−0.360251	+	0.932855i	$0.617309\pi$
$240$	315.410	−	95.6153i	1.31421	−	0.398397i
$241$		−	41.0402i		−	0.170291i	−0.996369	−	0.0851457i	$-0.972864\pi$
$241$		−	41.0402i		−	0.170291i	0.996369	−	0.0851457i	$-0.0271356\pi$
$242$		−	20.8479i		−	0.0861483i
$243$			268.870i			1.10646i
$244$			83.1839i			0.340918i
$245$	−29.0315	−	95.7673i	−0.118496	−	0.390887i
$246$	−67.1890			−0.273126
$247$	266.352			1.07835
$248$			126.432i			0.509808i
$249$		−	620.715i		−	2.49283i
$250$	34.6620	−	42.1884i	0.138648	−	0.168754i
$251$			94.8356i			0.377831i	0.981993	+	0.188916i	$0.0604972\pi$
$251$			94.8356i			0.377831i	−0.981993	+	0.188916i	$0.939503\pi$
$252$	−286.966			−1.13875
$253$	141.680	+	263.028i	0.560001	+	1.03963i
$254$	16.0815			0.0633128
$255$	−454.277	+	137.712i	−1.78148	+	0.540049i
$256$	142.430			0.556366
$257$		−	317.943i		−	1.23713i	−0.785733	−	0.618566i	$-0.787714\pi$
$257$		−	317.943i		−	1.23713i	0.785733	−	0.618566i	$-0.212286\pi$
$258$	−61.6794			−0.239067
$259$	191.916			0.740987
$260$	173.581	−	52.6204i	0.667619	−	0.202386i
$261$	−169.790			−0.650537
$262$			64.6426i			0.246728i
$263$	253.603			0.964271			0.482136	−	0.876097i	$-0.339861\pi$
$263$	253.603			0.964271			0.482136	+	0.876097i	$0.339861\pi$
$264$		−	212.466i		−	0.804795i
$265$	−16.5813	−	54.6974i	−0.0625710	−	0.206405i
$266$	−65.7738			−0.247270
$267$	−238.809			−0.894416
$268$	−404.032			−1.50758
$269$	21.7906			0.0810058			0.0405029	−	0.999179i	$-0.487104\pi$
$269$	21.7906			0.0810058			0.0405029	+	0.999179i	$0.487104\pi$
$270$	−15.1692	−	50.0393i	−0.0561824	−	0.185331i
$271$	−212.585			−0.784448			−0.392224	−	0.919870i	$-0.628294\pi$
$271$	−212.585			−0.784448			−0.392224	+	0.919870i	$0.628294\pi$
$272$	−272.174			−1.00064
$273$	−245.855			−0.900567
$274$			44.3433i			0.161837i
$275$	180.316	+	270.076i	0.655693	+	0.982094i
$276$	199.226	+	369.860i	0.721833	+	1.34007i
$277$			115.662i			0.417552i	0.977963	+	0.208776i	$0.0669480\pi$
$277$			115.662i			0.417552i	−0.977963	+	0.208776i	$0.933052\pi$
$278$		−	30.7615i		−	0.110653i
$279$	−518.635			−1.85891
$280$	−87.8764	+	26.6394i	−0.313844	+	0.0951407i
$281$		−	170.839i		−	0.607967i	−0.952677	−	0.303984i	$-0.901683\pi$
$281$		−	170.839i		−	0.607967i	0.952677	−	0.303984i	$-0.0983168\pi$
$282$			173.078i			0.613753i
$283$	−223.105			−0.788356			−0.394178	−	0.919034i	$-0.628971\pi$
$283$	−223.105			−0.788356			−0.394178	+	0.919034i	$0.628971\pi$
$284$	51.4653			0.181216
$285$	194.533	+	641.714i	0.682572	+	2.25163i
$286$		−	54.0352i		−	0.188934i
$287$	−172.703			−0.601754
$288$		−	274.949i		−	0.954683i
$289$	103.006			0.356422
$290$	−25.3619	+	7.68836i	−0.0874548	+	0.0265116i
$291$		−	366.774i		−	1.26039i
$292$		−	30.2259i		−	0.103513i
$293$	468.687			1.59961			0.799807	−	0.600258i	$-0.204935\pi$
$293$	468.687			1.59961			0.799807	+	0.600258i	$0.204935\pi$
$294$	−41.9206			−0.142587
$295$	28.3165	+	93.4086i	0.0959881	+	0.316639i
$296$			121.596i			0.410796i
$297$	310.979			1.04707
$298$	75.6022			0.253699
$299$	103.874	+	192.841i	0.347405	+	0.644952i
$300$	253.553	+	379.771i	0.845178	+	1.26590i
$301$	−158.542			−0.526716
$302$		−	72.3386i		−	0.239532i
$303$			799.228i			2.63771i
$304$			384.474i			1.26472i
$305$	−104.493	+	31.6765i	−0.342598	+	0.103857i
$306$			121.016i			0.395479i
$307$			566.398i			1.84495i	0.386062	+	0.922473i	$0.373835\pi$
$307$			566.398i			1.84495i	−0.386062	+	0.922473i	$0.626165\pi$
$308$		−	266.391i		−	0.864905i
$309$		−	361.486i		−	1.16986i
$310$	−77.4695	+	23.4846i	−0.249902	+	0.0757568i
$311$	575.328			1.84993			0.924965	−	0.380052i	$-0.124094\pi$
$311$	575.328			1.84993			0.924965	+	0.380052i	$0.124094\pi$
$312$		−	155.771i		−	0.499266i
$313$	−506.963			−1.61969			−0.809846	−	0.586643i	$-0.800449\pi$
$313$	−506.963			−1.61969			−0.809846	+	0.586643i	$0.800449\pi$
$314$			46.5264i			0.148173i
$315$	−109.277	−	360.476i	−0.346911	−	1.14437i
$316$		−	470.443i		−	1.48874i
$317$			80.3700i			0.253533i	0.991933	+	0.126767i	$0.0404599\pi$
$317$			80.3700i			0.253533i	−0.991933	+	0.126767i	$0.959540\pi$
$318$	−23.9430			−0.0752923
$319$		−	157.616i		−	0.494095i
$320$	67.3110	+	222.041i	0.210347	+	0.693880i
$321$			71.3320i			0.222218i
$322$	−25.6510	−	47.6206i	−0.0796614	−	0.147890i
$323$		−	553.749i		−	1.71439i
$324$	−42.4232			−0.130936
$325$	132.200	+	198.008i	0.406768	+	0.609256i
$326$	98.9226			0.303443
$327$	−175.422			−0.536460
$328$		−	109.423i		−	0.333607i
$329$			444.883i			1.35223i
$330$	130.185	−	39.4652i	0.394501	−	0.119591i
$331$	269.088			0.812953			0.406477	−	0.913661i	$-0.366757\pi$
$331$	269.088			0.812953			0.406477	+	0.913661i	$0.366757\pi$
$332$	493.094			1.48522
$333$	−498.795			−1.49788
$334$	39.1510			0.117219
$335$	−153.856	−	507.530i	−0.459271	−	1.51501i
$336$		−	354.886i		−	1.05621i
$337$	270.740			0.803383			0.401692	−	0.915775i	$-0.368422\pi$
$337$	270.740			0.803383			0.401692	+	0.915775i	$0.368422\pi$
$338$			34.2048i			0.101198i
$339$			616.508i			1.81861i
$340$	−109.398	−	360.877i	−0.321760	−	1.06140i
$341$		−	481.449i		−	1.41188i
$342$	170.948			0.499849
$343$	−371.562			−1.08327
$344$		−	100.450i		−	0.292006i
$345$	−388.739	+	391.103i	−1.12678	+	1.13363i
$346$	−18.7419			−0.0541672
$347$			149.774i			0.431626i	0.976435	+	0.215813i	$0.0692402\pi$
$347$			149.774i			0.431626i	−0.976435	+	0.215813i	$0.930760\pi$
$348$		−	221.635i		−	0.636881i
$349$	−456.824			−1.30895			−0.654475	−	0.756083i	$-0.727111\pi$
$349$	−456.824			−1.30895			−0.654475	+	0.756083i	$0.727111\pi$
$350$	−32.6458	−	48.8967i	−0.0932737	−	0.139705i
$351$	227.997			0.649563
$352$	255.235			0.725100
$353$		−	296.236i		−	0.839196i	−0.907710	−	0.419598i	$-0.862171\pi$
$353$		−	296.236i		−	0.839196i	0.907710	−	0.419598i	$-0.137829\pi$
$354$	40.8882			0.115503
$355$	19.5980	+	64.6488i	0.0552057	+	0.182109i
$356$		−	189.709i		−	0.532891i
$357$			511.134i			1.43175i
$358$			48.3286i			0.134996i
$359$		−	547.743i		−	1.52575i	−0.646547	−	0.762874i	$-0.723788\pi$
$359$		−	547.743i		−	1.52575i	0.646547	−	0.762874i	$-0.276212\pi$
$360$	228.393	−	69.2366i	0.634426	−	0.192324i
$361$	−421.227			−1.16683
$362$	−121.546			−0.335764
$363$			228.857i			0.630460i
$364$		−	195.306i		−	0.536555i
$365$	37.9686	−	11.5100i	0.104024	−	0.0315344i
$366$			45.7400i			0.124973i
$367$	625.818			1.70523			0.852613	−	0.522544i	$-0.175017\pi$
$367$	625.818			1.70523			0.852613	+	0.522544i	$0.175017\pi$
$368$	−278.361	+	149.940i	−0.756416	+	0.407445i
$369$	448.862			1.21643
$370$	−74.5059	+	22.5862i	−0.201367	+	0.0610438i
$371$	−61.5433			−0.165885
$372$		−	676.997i		−	1.81988i
$373$	−267.408			−0.716910			−0.358455	−	0.933547i	$-0.616696\pi$
$373$	−267.408			−0.716910			−0.358455	+	0.933547i	$0.616696\pi$
$374$	−112.340			−0.300374
$375$	−380.501	+	463.121i	−1.01467	+	1.23499i
$376$	−281.873			−0.749662
$377$		−	115.558i		−	0.306519i
$378$	−56.3022			−0.148948
$379$			405.070i			1.06879i	0.845236	+	0.534393i	$0.179460\pi$
$379$			405.070i			1.06879i	−0.845236	+	0.534393i	$0.820540\pi$
$380$	−509.775	+	154.536i	−1.34151	+	0.406675i
$381$	−176.533			−0.463342
$382$	−10.0571			−0.0263275
$383$	84.2618			0.220005			0.110002	−	0.993931i	$-0.464914\pi$
$383$	84.2618			0.220005			0.110002	+	0.993931i	$0.464914\pi$
$384$	474.076			1.23457
$385$	334.630	−	101.442i	0.869168	−	0.263485i
$386$	102.812			0.266353
$387$	412.054			1.06474
$388$	291.364			0.750938
$389$		−	388.293i		−	0.998181i	−0.866550	−	0.499091i	$-0.833667\pi$
$389$		−	388.293i		−	0.998181i	0.866550	−	0.499091i	$-0.166333\pi$
$390$	95.4463	−	28.9342i	0.244734	−	0.0741902i
$391$	400.917	−	215.955i	1.02536	−	0.552314i
$392$		−	68.2713i		−	0.174162i
$393$		−	709.612i		−	1.80563i
$394$	−3.65617			−0.00927961
$395$	590.952	−	179.145i	1.49608	−	0.453532i
$396$			692.357i			1.74838i
$397$			126.172i			0.317813i	0.987294	+	0.158907i	$0.0507969\pi$
$397$			126.172i			0.317813i	−0.987294	+	0.158907i	$0.949203\pi$
$398$	116.007			0.291475
$399$	722.029			1.80960
$400$	−285.820	+	190.827i	−0.714551	+	0.477068i
$401$			162.234i			0.404573i	0.979326	+	0.202287i	$0.0648372\pi$
$401$			162.234i			0.404573i	−0.979326	+	0.202287i	$0.935163\pi$
$402$	−222.163			−0.552645
$403$		−	352.978i		−	0.875876i
$404$	−634.904			−1.57154
$405$	−16.1548	−	53.2905i	−0.0398884	−	0.131581i
$406$			28.5361i			0.0702861i
$407$		−	463.032i		−	1.13767i
$408$	−323.849			−0.793747
$409$	−212.166			−0.518742			−0.259371	−	0.965778i	$-0.583515\pi$
$409$	−212.166			−0.518742			−0.259371	+	0.965778i	$0.583515\pi$
$410$	67.0473	−	20.3251i	0.163530	−	0.0495735i
$411$		−	486.777i		−	1.18437i
$412$	287.164			0.696999
$413$	105.100			0.254478
$414$	66.6676	+	123.767i	0.161033	+	0.298955i
$415$	187.771	+	619.406i	0.452459	+	1.49254i
$416$	187.128			0.449826
$417$			337.682i			0.809790i
$418$			158.691i			0.379644i
$419$		−	76.5852i		−	0.182781i	−0.995815	−	0.0913905i	$-0.970869\pi$
$419$		−	76.5852i		−	0.182781i	0.995815	−	0.0913905i	$-0.0291311\pi$
$420$	470.545	−	142.644i	1.12034	−	0.339628i
$421$			657.359i			1.56142i	0.624892	+	0.780711i	$0.285143\pi$
$421$			657.359i			1.56142i	−0.624892	+	0.780711i	$0.714857\pi$
$422$			83.2553i			0.197288i
$423$		−	1156.26i		−	2.73349i
$424$		−	38.9931i		−	0.0919650i
$425$	411.661	−	274.844i	0.968613	−	0.646692i
$426$	28.2990			0.0664296
$427$			117.571i			0.275341i
$428$	−56.6659			−0.132397
$429$			593.169i			1.38268i
$430$	61.5493	−	18.6585i	0.143138	−	0.0433917i
$431$			332.608i			0.771712i	0.922559	+	0.385856i	$0.126094\pi$
$431$			332.608i			0.771712i	−0.922559	+	0.385856i	$0.873906\pi$
$432$			329.108i			0.761825i
$433$	−394.405			−0.910865			−0.455433	−	0.890270i	$-0.650515\pi$
$433$	−394.405			−0.910865			−0.455433	+	0.890270i	$0.650515\pi$
$434$			87.1655i			0.200842i
$435$	278.409	−	84.3986i	0.640021	−	0.194020i
$436$		−	139.355i		−	0.319621i
$437$	−305.059	−	566.337i	−0.698074	−	1.29597i
$438$		−	16.6202i		−	0.0379456i
$439$	94.5251			0.215319			0.107660	−	0.994188i	$-0.465664\pi$
$439$	94.5251			0.215319			0.107660	+	0.994188i	$0.465664\pi$
$440$	64.2724	+	212.018i	0.146074	+	0.481859i
$441$	280.054			0.635044
$442$	−82.3627			−0.186341
$443$			439.538i			0.992184i	0.868270	+	0.496092i	$0.165232\pi$
$443$			439.538i			0.992184i	−0.868270	+	0.496092i	$0.834768\pi$
$444$		−	651.099i		−	1.46644i
$445$	238.305	−	72.2414i	0.535518	−	0.162340i
$446$	−170.471			−0.382221
$447$	−829.920			−1.85664
$448$	249.832			0.557660
$449$	−43.4207			−0.0967054			−0.0483527	−	0.998830i	$-0.515397\pi$
$449$	−43.4207			−0.0967054			−0.0483527	+	0.998830i	$0.515397\pi$
$450$	84.8474	+	127.084i	0.188550	+	0.282409i
$451$			416.679i			0.923900i
$452$	−489.752			−1.08352
$453$			794.093i			1.75297i
$454$		−	17.9445i		−	0.0395253i
$455$	245.336	−	74.3728i	0.539201	−	0.163457i
$456$			457.470i			1.00322i
$457$	−307.020			−0.671816			−0.335908	−	0.941895i	$-0.609043\pi$
$457$	−307.020			−0.671816			−0.335908	+	0.941895i	$0.609043\pi$
$458$	−8.04884			−0.0175739
$459$		−	474.007i		−	1.03270i
$460$	−310.691	−	308.813i	−0.675415	−	0.671332i
$461$	−362.501			−0.786335			−0.393168	−	0.919467i	$-0.628621\pi$
$461$	−362.501			−0.786335			−0.393168	+	0.919467i	$0.628621\pi$
$462$		−	146.479i		−	0.317054i
$463$		−	632.518i		−	1.36613i	−0.730358	−	0.683065i	$-0.760647\pi$
$463$		−	632.518i		−	1.36613i	0.730358	−	0.683065i	$-0.239353\pi$
$464$	166.805			0.359493
$465$	850.418	−	257.801i	1.82886	−	0.554411i
$466$	172.887			0.371003
$467$	537.763			1.15153			0.575763	−	0.817616i	$-0.304705\pi$
$467$	537.763			1.15153			0.575763	+	0.817616i	$0.304705\pi$
$468$			507.607i			1.08463i
$469$	−571.051			−1.21759
$470$	−52.3574	−	172.713i	−0.111399	−	0.367476i
$471$		−	510.742i		−	1.08438i
$472$			66.5899i			0.141080i
$473$			382.510i			0.808690i
$474$		−	258.680i		−	0.545739i
$475$	−388.246	−	581.513i	−0.817359	−	1.22424i
$476$	−406.043			−0.853032
$477$	159.953			0.335331
$478$		−	75.2189i		−	0.157362i
$479$			830.923i			1.73470i	0.497695	+	0.867352i	$0.334180\pi$
$479$			830.923i			1.73470i	−0.497695	+	0.867352i	$0.665820\pi$
$480$	136.670	+	450.840i	0.284730	+	0.939250i
$481$		−	339.475i		−	0.705769i
$482$	17.9268			0.0371926
$483$	281.582	+	522.753i	0.582986	+	1.08231i
$484$	−181.803			−0.375626
$485$	110.952	+	366.000i	0.228766	+	0.754640i
$486$	−117.446			−0.241658
$487$			176.755i			0.362946i	0.983396	+	0.181473i	$0.0580865\pi$
$487$			176.755i			0.362946i	−0.983396	+	0.181473i	$0.941913\pi$
$488$	−74.4915			−0.152646
$489$	−1085.92			−2.22069
$490$	41.8322	−	12.6813i	0.0853719	−	0.0258802i
$491$	−741.442			−1.51006			−0.755032	−	0.655687i	$-0.772379\pi$
$491$	−741.442			−1.51006			−0.755032	+	0.655687i	$0.772379\pi$
$492$			585.919i			1.19089i
$493$	−240.245			−0.487313
$494$			116.346i			0.235518i
$495$	−869.713	+	263.650i	−1.75700	+	0.532627i
$496$	509.516			1.02725
$497$	72.7401			0.146358
$498$	271.135			0.544449
$499$	403.923			0.809465			0.404732	−	0.914435i	$-0.367365\pi$
$499$	403.923			0.809465			0.404732	+	0.914435i	$0.367365\pi$
$500$	−367.902	−	302.269i	−0.735804	−	0.604537i
$501$	−429.779			−0.857842
$502$	−41.4253			−0.0825205
$503$	−266.556			−0.529932			−0.264966	−	0.964258i	$-0.585361\pi$
$503$	−266.556			−0.529932			−0.264966	+	0.964258i	$0.585361\pi$
$504$		−	256.979i		−	0.509878i
$505$	−241.772	−	797.542i	−0.478756	−	1.57929i
$506$	−114.893	+	61.8876i	−0.227062	+	0.122308i
$507$		−	375.482i		−	0.740596i
$508$		−	140.238i		−	0.276058i
$509$	−74.2213			−0.145818			−0.0729089	−	0.997339i	$-0.523228\pi$
$509$	−74.2213			−0.145818			−0.0729089	+	0.997339i	$0.523228\pi$
$510$	−60.1544	−	198.434i	−0.117950	−	0.389086i
$511$		−	42.7207i		−	0.0836022i
$512$			457.683i			0.893913i
$513$	−669.584			−1.30523
$514$	138.881			0.270197
$515$	109.352	+	360.724i	0.212334	+	0.700435i
$516$			537.873i			1.04239i
$517$	1073.36			2.07613
$518$			83.8310i			0.161836i
$519$	205.738			0.396412
$520$	47.1218	+	155.442i	0.0906188	+	0.298928i
$521$			332.345i			0.637897i	0.947772	+	0.318949i	$0.103330\pi$
$521$			332.345i			0.637897i	−0.947772	+	0.318949i	$0.896670\pi$
$522$		−	74.1663i		−	0.142081i
$523$	−796.244			−1.52246			−0.761228	−	0.648485i	$-0.775403\pi$
$523$	−796.244			−1.52246			−0.761228	+	0.648485i	$0.775403\pi$
$524$	563.713			1.07579
$525$	358.368	+	536.762i	0.682605	+	1.02240i
$526$			110.777i			0.210602i
$527$	−733.845			−1.39249
$528$	−856.227			−1.62164
$529$	291.062	−	441.728i	0.550212	−	0.835025i
$530$	23.8925	−	7.24291i	0.0450801	−	0.0136659i
$531$	−273.157			−0.514420
$532$			573.578i			1.07815i
$533$			305.491i			0.573154i
$534$		−	104.315i		−	0.195346i
$535$	−21.5784	−	71.1815i	−0.0403335	−	0.133050i
$536$		−	361.812i		−	0.675022i
$537$		−	530.525i		−	0.987943i
$538$			9.51837i			0.0176921i
$539$			259.975i			0.482328i
$540$	−436.366	+	132.283i	−0.808085	+	0.244968i
$541$	75.8079			0.140126			0.0700628	−	0.997543i	$-0.477680\pi$
$541$	75.8079			0.140126			0.0700628	+	0.997543i	$0.477680\pi$
$542$		−	92.8597i		−	0.171328i
$543$	1334.27			2.45722
$544$		−	389.040i		−	0.715147i
$545$	175.052	−	53.0665i	0.321197	−	0.0973697i
$546$		−	107.392i		−	0.196689i
$547$		−	551.149i		−	1.00759i	−0.863824	−	0.503793i	$-0.831937\pi$
$547$		−	551.149i		−	1.00759i	0.863824	−	0.503793i	$-0.168063\pi$
$548$	386.694			0.705646
$549$		−	305.570i		−	0.556593i
$550$	−117.972	+	78.7639i	−0.214495	+	0.143207i
$551$			339.371i			0.615919i
$552$	−331.211	+	178.407i	−0.600020	+	0.323202i
$553$		−	664.915i		−	1.20238i
$554$	−50.5225			−0.0911958
$555$	817.886	−	247.939i	1.47367	−	0.446737i
$556$	−268.254			−0.482471
$557$	76.4274			0.137213			0.0686063	−	0.997644i	$-0.478145\pi$
$557$	76.4274			0.137213			0.0686063	+	0.997644i	$0.478145\pi$
$558$		−	226.546i		−	0.405996i
$559$			280.440i			0.501682i
$560$	107.355	+	354.138i	0.191706	+	0.632388i
$561$	1233.20			2.19823
$562$	74.6244			0.132784
$563$	855.822			1.52011			0.760055	−	0.649859i	$-0.225172\pi$
$563$	855.822			1.52011			0.760055	+	0.649859i	$0.225172\pi$
$564$	1509.32			2.67610
$565$	−186.498	−	615.208i	−0.330085	−	1.08886i
$566$		−	97.4548i		−	0.172182i
$567$	−59.9602			−0.105750
$568$			46.0873i			0.0811397i
$569$			290.524i			0.510587i	0.966864	+	0.255294i	$0.0821721\pi$
$569$			290.524i			0.510587i	−0.966864	+	0.255294i	$0.917828\pi$
$570$	−280.308	+	84.9743i	−0.491768	+	0.149078i
$571$			454.418i			0.795828i	0.917423	+	0.397914i	$0.130266\pi$
$571$			454.418i			0.795828i	−0.917423	+	0.397914i	$0.869734\pi$
$572$	−471.212			−0.823797
$573$	110.402			0.192673
$574$		−	75.4389i		−	0.131427i
$575$	269.608	−	507.875i	0.468883	−	0.883260i
$576$	−649.321			−1.12729
$577$			898.550i			1.55728i	0.627471	+	0.778640i	$0.284090\pi$
$577$			898.550i			1.55728i	−0.627471	+	0.778640i	$0.715910\pi$
$578$			44.9942i			0.0778446i
$579$	−1128.62			−1.94925
$580$	67.0460	+	221.167i	0.115597	+	0.381323i
$581$	696.930			1.19954
$582$	160.211			0.275277
$583$			148.484i			0.254690i
$584$	27.0674			0.0463482
$585$	−637.636	+	193.297i	−1.08998	+	0.330422i
$586$			204.728i			0.349365i
$587$		−	278.765i		−	0.474897i	−0.971400	−	0.237449i	$-0.923689\pi$
$587$		−	278.765i		−	0.474897i	0.971400	−	0.237449i	$-0.0763112\pi$
$588$			365.567i			0.621713i
$589$			1036.63i			1.75998i
$590$	−40.8020	+	12.3690i	−0.0691559	+	0.0209643i
$591$	40.1354			0.0679110
$592$	490.025			0.827744
$593$			520.625i			0.877950i	0.898499	+	0.438975i	$0.144658\pi$
$593$			520.625i			0.877950i	−0.898499	+	0.438975i	$0.855342\pi$
$594$			135.839i			0.228686i
$595$	−154.622	−	510.056i	−0.259868	−	0.857237i
$596$		−	659.286i		−	1.10618i
$597$	−1273.46			−2.13310
$598$	−84.2350	+	45.3734i	−0.140861	+	0.0758752i
$599$	791.686			1.32168			0.660839	−	0.750527i	$-0.270200\pi$
$599$	791.686			1.32168			0.660839	+	0.750527i	$0.270200\pi$
$600$	−340.086	+	227.058i	−0.566810	+	0.378430i
$601$	−17.6126			−0.0293054			−0.0146527	−	0.999893i	$-0.504664\pi$
$601$	−17.6126			−0.0293054			−0.0146527	+	0.999893i	$0.504664\pi$
$602$		−	69.2528i		−	0.115038i
$603$	1484.18			2.46133
$604$	−630.825			−1.04441
$605$	−69.2308	−	228.374i	−0.114431	−	0.377478i
$606$	−349.112			−0.576092
$607$			63.2819i			0.104254i	0.998640	+	0.0521268i	$0.0166000\pi$
$607$			63.2819i			0.104254i	−0.998640	+	0.0521268i	$0.983400\pi$
$608$	−549.559			−0.903879
$609$		−	313.254i		−	0.514375i
$610$	−13.8367	−	45.6435i	−0.0226831	−	0.0748255i
$611$	786.943			1.28796
$612$	1055.32			1.72438
$613$	−145.357			−0.237125			−0.118562	−	0.992947i	$-0.537829\pi$
$613$	−145.357			−0.237125			−0.118562	+	0.992947i	$0.537829\pi$
$614$	−247.409			−0.402947
$615$	−736.009	+	223.118i	−1.19676	+	0.362794i
$616$	238.554			0.387262
$617$	−264.551			−0.428769			−0.214385	−	0.976749i	$-0.568775\pi$
$617$	−264.551			−0.428769			−0.214385	+	0.976749i	$0.568775\pi$
$618$	157.901			0.255504
$619$			563.411i			0.910195i	0.890442	+	0.455097i	$0.150396\pi$
$619$			563.411i			0.910195i	−0.890442	+	0.455097i	$0.849604\pi$
$620$	204.796	+	675.570i	0.330317	+	1.08963i
$621$	−261.129	−	484.782i	−0.420498	−	0.780648i
$622$			251.310i			0.404035i
$623$		−	268.131i		−	0.430387i
$624$	−627.749			−1.00601
$625$	239.601	−	577.249i	0.383362	−	0.923598i
$626$		−	221.447i		−	0.353750i
$627$		−	1742.03i		−	2.77835i
$628$	405.732			0.646070
$629$	−705.771			−1.12205
$630$	157.460	−	47.7334i	0.249936	−	0.0757673i
$631$		−	485.549i		−	0.769491i	−0.923023	−	0.384746i	$-0.874289\pi$
$631$		−	485.549i		−	0.769491i	0.923023	−	0.384746i	$-0.125711\pi$
$632$	421.283			0.666587
$633$		−	913.932i		−	1.44381i
$634$	−35.1066			−0.0553731
$635$	176.161	−	53.4026i	0.277419	−	0.0840986i
$636$			208.794i			0.328292i
$637$			190.602i			0.299219i
$638$	68.8487			0.107913
$639$	−189.054			−0.295859
$640$	−473.076	+	143.411i	−0.739181	+	0.224080i
$641$		−	612.917i		−	0.956189i	−0.878308	−	0.478095i	$-0.841328\pi$
$641$		−	612.917i		−	0.956189i	0.878308	−	0.478095i	$-0.158672\pi$
$642$	−31.1586			−0.0485337
$643$	1120.30			1.74229			0.871147	−	0.491022i	$-0.163376\pi$
$643$	1120.30			1.74229			0.871147	+	0.491022i	$0.163376\pi$
$644$	−415.274	+	223.688i	−0.644835	+	0.347342i
$645$	−675.655	+	204.822i	−1.04753	+	0.317554i
$646$	241.884			0.374433
$647$		−	530.564i		−	0.820038i	−0.912077	−	0.410019i	$-0.865522\pi$
$647$		−	530.564i		−	0.820038i	0.912077	−	0.410019i	$-0.134478\pi$
$648$		−	37.9901i		−	0.0586268i
$649$		−	253.572i		−	0.390711i
$650$	−86.4922	+	57.7463i	−0.133065	+	0.0888405i
$651$		−	956.855i		−	1.46982i
$652$		−	862.650i		−	1.32308i
$653$			335.088i			0.513151i	0.966524	+	0.256576i	$0.0825943\pi$
$653$			335.088i			0.513151i	−0.966524	+	0.256576i	$0.917406\pi$
$654$		−	76.6265i		−	0.117166i
$655$	214.663	+	708.115i	0.327729	+	1.08109i
$656$	−440.970			−0.672210
$657$			111.032i			0.168999i
$658$	−194.330			−0.295334
$659$			116.788i			0.177220i	0.996066	+	0.0886101i	$0.0282425\pi$
$659$			116.788i			0.177220i	−0.996066	+	0.0886101i	$0.971758\pi$
$660$	−344.154	−	1135.27i	−0.521446	−	1.72011i
$661$		−	977.384i		−	1.47864i	−0.673352	−	0.739322i	$-0.735146\pi$
$661$		−	977.384i		−	1.47864i	0.673352	−	0.739322i	$-0.264854\pi$
$662$			117.541i			0.177554i
$663$	904.133			1.36370
$664$			441.567i			0.665011i
$665$	−720.507	+	218.419i	−1.08347	+	0.328450i
$666$		−	217.879i		−	0.327146i
$667$	−245.707	+	132.350i	−0.368376	+	0.198426i
$668$		−	341.415i		−	0.511100i
$669$	1871.34			2.79721
$670$	221.695	−	67.2060i	0.330888	−	0.100307i
$671$	283.661			0.422743
$672$	507.266			0.754861
$673$		−	21.4168i		−	0.0318229i	−0.999873	−	0.0159115i	$-0.994935\pi$
$673$		−	21.4168i		−	0.0318229i	0.999873	−	0.0159115i	$-0.00506499\pi$
$674$			118.262i			0.175464i
$675$	−332.337	−	497.773i	−0.492351	−	0.737442i
$676$	298.282			0.441245
$677$	−378.998			−0.559820			−0.279910	−	0.960026i	$-0.590305\pi$
$677$	−378.998			−0.559820			−0.279910	+	0.960026i	$0.590305\pi$
$678$	−269.298			−0.397194
$679$	411.808			0.606493
$680$	323.166	−	97.9666i	0.475244	−	0.144069i
$681$			196.985i			0.289258i
$682$	210.303			0.308362
$683$			248.104i			0.363256i	0.983367	+	0.181628i	$0.0581367\pi$
$683$			248.104i			0.363256i	−0.983367	+	0.181628i	$0.941863\pi$
$684$		−	1490.75i		−	2.17945i
$685$	147.253	+	485.751i	0.214969	+	0.709125i
$686$		−	162.302i		−	0.236593i
$687$	88.3558			0.128611
$688$	−404.809			−0.588386
$689$			108.862i			0.158001i
$690$	−170.838	−	169.806i	−0.247592	−	0.246095i
$691$	68.3612			0.0989308			0.0494654	−	0.998776i	$-0.484248\pi$
$691$	68.3612			0.0989308			0.0494654	+	0.998776i	$0.484248\pi$
$692$			163.438i			0.236181i
$693$			978.565i			1.41207i
$694$	−65.4231			−0.0942696
$695$	−102.151	−	336.970i	−0.146980	−	0.484850i
$696$	198.474			0.285164
$697$	635.119			0.911217
$698$		−	199.546i		−	0.285882i
$699$	−1897.86			−2.71511
$700$	−426.402	+	284.686i	−0.609145	+	0.406694i
$701$			1138.01i			1.62341i	0.584065	+	0.811707i	$0.301461\pi$
$701$			1138.01i			1.62341i	−0.584065	+	0.811707i	$0.698539\pi$
$702$			99.5916i			0.141868i
$703$			996.975i			1.41817i
$704$		−	602.765i		−	0.856200i
$705$	574.752	+	1895.95i	0.815250	+	2.68930i
$706$	129.399			0.183285
$707$	−897.361			−1.26925
$708$		−	356.564i		−	0.503621i
$709$		−	213.151i		−	0.300636i	−0.988638	−	0.150318i	$-0.951970\pi$
$709$		−	213.151i		−	0.300636i	0.988638	−	0.150318i	$-0.0480298\pi$
$710$	−28.2393	+	8.56065i	−0.0397737	+	0.0120573i
$711$			1728.13i			2.43057i
$712$	169.885			0.238603
$713$	−750.527	+	404.273i	−1.05263	+	0.567003i
$714$	−223.269			−0.312702
$715$	−179.438	−	591.919i	−0.250962	−	0.827858i
$716$	421.448			0.588614
$717$			825.713i			1.15162i
$718$	239.261			0.333232
$719$	126.490			0.175925			0.0879627	−	0.996124i	$-0.471964\pi$
$719$	126.490			0.175925			0.0879627	+	0.996124i	$0.471964\pi$
$720$	−279.020	−	920.414i	−0.387528	−	1.27835i
$721$	405.872			0.562929
$722$		−	183.997i		−	0.254843i
$723$	−196.791			−0.272187
$724$			1059.94i			1.46401i
$725$	−252.291	+	168.441i	−0.347987	+	0.232333i
$726$	−99.9673			−0.137696
$727$	405.496			0.557766			0.278883	−	0.960325i	$-0.410036\pi$
$727$	405.496			0.557766			0.278883	+	0.960325i	$0.410036\pi$
$728$	174.897			0.240244
$729$	1189.02			1.63103
$730$	5.02772	+	16.5851i	0.00688729	+	0.0227194i
$731$	583.038			0.797589
$732$	398.874			0.544909
$733$	397.232			0.541926			0.270963	−	0.962590i	$-0.412658\pi$
$733$	397.232			0.541926			0.270963	+	0.962590i	$0.412658\pi$
$734$			273.364i			0.372431i
$735$	−459.212	+	139.208i	−0.624778	+	0.189399i
$736$	−214.321	−	397.884i	−0.291197	−	0.540603i
$737$			1377.77i			1.86942i
$738$			196.068i			0.265675i
$739$	−660.893			−0.894307			−0.447153	−	0.894457i	$-0.647562\pi$
$739$	−660.893			−0.894307			−0.447153	+	0.894457i	$0.647562\pi$
$740$	196.962	+	649.726i	0.266165	+	0.878008i
$741$		−	1277.18i		−	1.72359i
$742$		−	26.8828i		−	0.0362302i
$743$	1237.84			1.66600			0.833000	−	0.553273i	$-0.186621\pi$
$743$	1237.84			1.66600			0.833000	+	0.553273i	$0.186621\pi$
$744$	606.253			0.814856
$745$	828.170	−	251.057i	1.11164	−	0.336989i
$746$		−	116.807i		−	0.156577i
$747$	−1811.34			−2.42482
$748$			979.654i			1.30970i
$749$	−80.0905			−0.106930
$750$	−202.297	−	166.207i	−0.269729	−	0.221610i
$751$			729.573i			0.971469i	0.874106	+	0.485735i	$0.161448\pi$
$751$			729.573i			0.971469i	−0.874106	+	0.485735i	$0.838552\pi$
$752$			1135.93i			1.51055i
$753$	454.744			0.603910
$754$	50.4769			0.0669455
$755$	−240.219	−	792.419i	−0.318171	−	1.04956i
$756$			490.981i			0.649446i
$757$	−388.147			−0.512744			−0.256372	−	0.966578i	$-0.582527\pi$
$757$	−388.147			−0.512744			−0.256372	+	0.966578i	$0.582527\pi$
$758$	−176.939			−0.233429
$759$	1261.24	−	679.369i	1.66171	−	0.895084i
$760$	−138.388	−	456.505i	−0.182089	−	0.600665i
$761$	−1058.72			−1.39122			−0.695610	−	0.718419i	$-0.744866\pi$
$761$	−1058.72			−1.39122			−0.695610	+	0.718419i	$0.744866\pi$
$762$		−	77.1118i		−	0.101197i
$763$		−	196.962i		−	0.258141i
$764$			87.7027i			0.114794i
$765$	401.866	+	1325.65i	0.525316	+	1.73288i
$766$			36.8065i			0.0480503i
$767$		−	185.908i		−	0.242383i
$768$		−	682.961i		−	0.889272i
$769$			884.857i			1.15066i	0.817922	+	0.575330i	$0.195126\pi$
$769$			884.857i			1.15066i	−0.817922	+	0.575330i	$0.804874\pi$
$770$	44.3109	+	146.170i	0.0575467	+	0.189831i
$771$	−1524.56			−1.97738
$772$		−	896.570i		−	1.16136i
$773$	−1046.88			−1.35431			−0.677156	−	0.735840i	$-0.736788\pi$
$773$	−1046.88			−1.35431			−0.677156	+	0.735840i	$0.736788\pi$
$774$			179.990i			0.232545i
$775$	−770.638	+	514.515i	−0.994372	+	0.663890i
$776$			260.917i			0.336234i
$777$		−	920.251i		−	1.18436i
$778$	169.611			0.218009
$779$		−	897.170i		−	1.15169i
$780$	−252.319	−	832.335i	−0.323486	−	1.06710i
$781$		−	175.499i		−	0.224710i
$782$	94.3316	+	175.125i	0.120629	+	0.223945i
$783$			290.501i			0.371010i
$784$	−275.130			−0.350931
$785$	154.503	+	509.665i	0.196819	+	0.649255i
$786$	309.967			0.394359
$787$	−929.484			−1.18105			−0.590524	−	0.807020i	$-0.701079\pi$
$787$	−929.484			−1.18105			−0.590524	+	0.807020i	$0.701079\pi$
$788$			31.8834i			0.0404612i
$789$		−	1216.05i		−	1.54125i
$790$	78.2526	+	258.135i	0.0990539	+	0.326753i
$791$	−692.206			−0.875103
$792$	−620.008			−0.782839
$793$	207.968			0.262255
$794$	−55.1134			−0.0694123
$795$	−262.279	+	79.5087i	−0.329910	+	0.100011i
$796$		−	1011.63i		−	1.27090i
$797$	−504.267			−0.632707			−0.316354	−	0.948641i	$-0.602459\pi$
$797$	−504.267			−0.632707			−0.316354	+	0.948641i	$0.602459\pi$
$798$			315.391i			0.395227i
$799$		−	1636.06i		−	2.04764i
$800$	−272.765	−	408.546i	−0.340956	−	0.510682i
$801$			696.882i			0.870014i
$802$	−70.8656			−0.0883611
$803$	−103.072			−0.128358
$804$			1937.37i			2.40966i
$805$	−439.125	−	436.471i	−0.545497	−	0.542199i
$806$	154.185			0.191296
$807$		−	104.487i		−	0.129476i
$808$		−	568.558i		−	0.703661i
$809$	−969.646			−1.19857			−0.599287	−	0.800534i	$-0.704549\pi$
$809$	−969.646			−1.19857			−0.599287	+	0.800534i	$0.704549\pi$
$810$	23.2779	−	7.05661i	0.0287381	−	0.00871186i
$811$	−1329.85			−1.63976			−0.819882	−	0.572532i	$-0.805961\pi$
$811$	−1329.85			−1.63976			−0.819882	+	0.572532i	$0.805961\pi$
$812$	248.848			0.306463
$813$			1019.36i			1.25383i
$814$	202.258			0.248474
$815$	1083.63	−	328.498i	1.32961	−	0.403065i
$816$			1305.10i			1.59938i
$817$		−	823.601i		−	1.00808i
$818$		−	92.6763i		−	0.113296i
$819$			717.442i			0.875998i
$820$	−177.245	−	584.683i	−0.216152	−	0.713028i
$821$	−594.611			−0.724253			−0.362126	−	0.932129i	$-0.617949\pi$
$821$	−594.611			−0.724253			−0.362126	+	0.932129i	$0.617949\pi$
$822$	212.630			0.258674
$823$		−	303.224i		−	0.368437i	−0.982885	−	0.184219i	$-0.941025\pi$
$823$		−	303.224i		−	0.368437i	0.982885	−	0.184219i	$-0.0589755\pi$
$824$			257.156i			0.312082i
$825$	1295.04	−	864.627i	1.56974	−	1.04803i
$826$			45.9087i			0.0555795i
$827$	157.345			0.190260			0.0951299	−	0.995465i	$-0.469673\pi$
$827$	157.345			0.190260			0.0951299	+	0.995465i	$0.469673\pi$
$828$	1079.31	−	581.372i	1.30351	−	0.702140i
$829$	5.87767			0.00709008			0.00354504	−	0.999994i	$-0.498872\pi$
$829$	5.87767			0.00709008			0.00354504	+	0.999994i	$0.498872\pi$
$830$	−270.564	+	82.0204i	−0.325980	+	0.0988197i
$831$	554.608			0.667399
$832$		−	441.921i		−	0.531156i
$833$	396.264			0.475707
$834$	−147.504			−0.176863
$835$	428.872	−	130.011i	0.513620	−	0.155702i
$836$	1383.86			1.65534
$837$			887.353i			1.06016i
$838$	33.4533			0.0399204
$839$		−	772.718i		−	0.920999i	−0.887660	−	0.460500i	$-0.847670\pi$
$839$		−	772.718i		−	0.920999i	0.887660	−	0.460500i	$-0.152330\pi$
$840$	127.738	+	421.374i	0.152069	+	0.501636i
$841$	−693.763			−0.824926
$842$	−287.142			−0.341024
$843$	−819.186			−0.971750
$844$	726.025			0.860219
$845$	113.586	+	374.690i	0.134421	+	0.443420i
$846$	505.070			0.597009
$847$	−256.957			−0.303373
$848$	−157.140			−0.185307
$849$			1069.81i			1.26008i
$850$	120.055	+	179.818i	0.141241	+	0.211551i
$851$	−721.815	+	388.807i	−0.848197	+	0.456883i
$852$		−	246.780i		−	0.289648i
$853$		−	530.715i		−	0.622175i	−0.950381	−	0.311087i	$-0.899307\pi$
$853$		−	530.715i		−	0.622175i	0.950381	−	0.311087i	$-0.100693\pi$
$854$	−51.3562			−0.0601361
$855$	1872.62	−	567.678i	2.19020	−	0.663950i
$856$		−	50.7445i		−	0.0592809i
$857$		−	440.155i		−	0.513600i	−0.966465	−	0.256800i	$-0.917332\pi$
$857$		−	440.155i		−	0.513600i	0.966465	−	0.256800i	$-0.0826682\pi$
$858$	−259.103			−0.301985
$859$	409.847			0.477121			0.238560	−	0.971128i	$-0.423324\pi$
$859$	409.847			0.477121			0.238560	+	0.971128i	$0.423324\pi$
$860$	−162.710	−	536.738i	−0.189198	−	0.624114i
$861$			828.127i			0.961820i
$862$	−145.287			−0.168546
$863$			639.497i			0.741016i	0.928829	+	0.370508i	$0.120816\pi$
$863$			639.497i			0.741016i	−0.928829	+	0.370508i	$0.879184\pi$
$864$	−470.420			−0.544468
$865$	−205.304	+	62.2371i	−0.237346	+	0.0719505i
$866$		−	172.280i		−	0.198938i
$867$		−	493.922i		−	0.569691i
$868$	760.123			0.875718
$869$	−1604.23			−1.84606
$870$	36.8663	+	121.612i	0.0423751	+	0.139784i
$871$			1010.12i			1.15972i
$872$	124.793			0.143111
$873$	−1070.30			−1.22601
$874$	247.382	−	133.253i	0.283046	−	0.152463i
$875$	−519.986	−	427.221i	−0.594270	−	0.488253i
$876$	−144.936			−0.165452
$877$		−	435.144i		−	0.496173i	−0.968738	−	0.248087i	$-0.920198\pi$
$877$		−	435.144i		−	0.496173i	0.968738	−	0.248087i	$-0.0798018\pi$
$878$			41.2897i			0.0470269i
$879$		−	2247.39i		−	2.55676i
$880$	854.421	−	259.015i	0.970933	−	0.294335i
$881$		−	732.786i		−	0.831766i	−0.909418	−	0.415883i	$-0.863473\pi$
$881$		−	732.786i		−	0.831766i	0.909418	−	0.415883i	$-0.136527\pi$
$882$			122.331i			0.138697i
$883$			943.261i			1.06825i	0.845407	+	0.534123i	$0.179358\pi$
$883$			943.261i			1.06825i	−0.845407	+	0.534123i	$0.820642\pi$
$884$			718.240i			0.812489i
$885$	447.902	−	135.780i	0.506104	−	0.153423i
$886$	−191.995			−0.216699
$887$			1393.60i			1.57114i	0.618772	+	0.785570i	$0.287630\pi$
$887$			1393.60i			1.57114i	−0.618772	+	0.785570i	$0.712370\pi$
$888$	583.061			0.656600
$889$		−	198.209i		−	0.222958i
$890$	31.5559	+	104.095i	0.0354560	+	0.116960i
$891$			144.665i			0.162362i
$892$			1486.58i			1.66657i
$893$	−2311.10			−2.58802
$894$		−	362.519i		−	0.405502i
$895$	160.488	+	529.407i	0.179316	+	0.591516i
$896$			532.285i			0.594068i
$897$	924.686	−	498.084i	1.03086	−	0.555278i
$898$		−	18.9667i		−	0.0211210i
$899$	449.745			0.500272
$900$	1108.23	−	739.908i	1.23137	−	0.822120i
$901$	226.326			0.251194
$902$	−182.010			−0.201785
$903$			760.219i			0.841882i
$904$		−	438.574i		−	0.485149i
$905$	−1331.46	+	403.626i	−1.47122	+	0.445996i
$906$	−346.869			−0.382858
$907$	796.423			0.878085			0.439042	−	0.898466i	$-0.355318\pi$
$907$	796.423			0.878085			0.439042	+	0.898466i	$0.355318\pi$
$908$	−156.484			−0.172339
$909$	2332.27			2.56575
$910$	32.4869	+	107.166i	0.0356999	+	0.117765i
$911$			692.899i			0.760592i	0.924865	+	0.380296i	$0.124178\pi$
$911$			692.899i			0.760592i	−0.924865	+	0.380296i	$0.875822\pi$
$912$	1843.58			2.02147
$913$		−	1681.47i		−	1.84170i
$914$		−	134.110i		−	0.146728i
$915$	151.891	+	501.050i	0.166002	+	0.547596i
$916$			70.1896i			0.0766262i
$917$	796.742			0.868857
$918$	207.052			0.225547
$919$		−	688.929i		−	0.749650i	−0.927096	−	0.374825i	$-0.877703\pi$
$919$		−	688.929i		−	0.749650i	0.927096	−	0.374825i	$-0.122297\pi$
$920$	276.543	−	278.225i	0.300590	−	0.302418i
$921$	2715.92			2.94889
$922$		−	158.344i		−	0.171740i
$923$		−	128.668i		−	0.139402i
$924$	−1277.36			−1.38243
$925$	−741.158	+	494.832i	−0.801252	+	0.534954i
$926$	276.291			0.298371
$927$	−1054.87			−1.13794
$928$			238.427i			0.256926i
$929$	1149.18			1.23701			0.618505	−	0.785781i	$-0.287738\pi$
$929$	1149.18			1.23701			0.618505	+	0.785781i	$0.287738\pi$
$930$	112.610	+	371.473i	0.121087	+	0.399433i
$931$		−	559.763i		−	0.601250i
$932$		−	1507.66i		−	1.61766i
$933$		−	2758.75i		−	2.95685i
$934$			234.901i			0.251500i
$935$	−1230.60	+	373.053i	−1.31615	+	0.398987i
$936$	−454.563			−0.485645
$937$	1116.73			1.19182			0.595909	−	0.803052i	$-0.296792\pi$
$937$	1116.73			1.19182			0.595909	+	0.803052i	$0.296792\pi$
$938$		−	249.442i		−	0.265929i
$939$			2430.93i			2.58885i
$940$	−1506.14	+	456.581i	−1.60228	+	0.485724i
$941$		−	110.752i		−	0.117696i	−0.998267	−	0.0588481i	$-0.981257\pi$
$941$		−	110.752i		−	0.117696i	0.998267	−	0.0588481i	$-0.0187427\pi$
$942$	223.098			0.236834
$943$	649.556	−	349.885i	0.688819	−	0.371034i
$944$	268.354			0.284273
$945$	−616.752	+	186.966i	−0.652647	+	0.197848i
$946$	−167.085			−0.176623
$947$			587.603i			0.620489i	0.950657	+	0.310245i	$0.100411\pi$
$947$			587.603i			0.620489i	−0.950657	+	0.310245i	$0.899589\pi$
$948$	−2255.81			−2.37955
$949$	−75.5676			−0.0796287
$950$	254.011	−	169.590i	0.267381	−	0.178516i
$951$	385.381			0.405237
$952$		−	363.613i		−	0.381946i
$953$	1665.36			1.74749			0.873746	−	0.486382i	$-0.161684\pi$
$953$	1665.36			1.74749			0.873746	+	0.486382i	$0.161684\pi$
$954$			69.8693i			0.0732382i
$955$	−110.169	+	33.3973i	−0.115360	+	0.0349709i
$956$	−655.944			−0.686133
$957$	−755.783			−0.789742
$958$	−362.957			−0.378869
$959$	546.546			0.569913
$960$	1064.71	−	322.762i	1.10907	−	0.336210i
$961$	412.775			0.429526
$962$	148.287			0.154144
$963$	208.158			0.216155
$964$		−	156.330i		−	0.162168i
$965$	1126.24	−	341.414i	1.16708	−	0.353797i
$966$	−228.345	+	122.998i	−0.236382	+	0.127328i
$967$		−	789.788i		−	0.816740i	−0.912816	−	0.408370i	$-0.866097\pi$
$967$		−	789.788i		−	0.816740i	0.912816	−	0.408370i	$-0.133903\pi$
$968$		−	162.805i		−	0.168187i
$969$	−2655.27			−2.74022
$970$	−159.873	+	48.4650i	−0.164818	+	0.0499639i
$971$		−	1421.57i		−	1.46402i	−0.681293	−	0.732011i	$-0.738582\pi$
$971$		−	1421.57i		−	1.46402i	0.681293	−	0.732011i	$-0.261418\pi$
$972$			1024.18i			1.05368i
$973$	−379.145			−0.389666
$974$	−77.2085			−0.0792695
$975$	949.464	−	633.908i	0.973810	−	0.650162i
$976$			300.197i			0.307579i
$977$	264.103			0.270321			0.135160	−	0.990824i	$-0.456845\pi$
$977$	264.103			0.270321			0.135160	+	0.990824i	$0.456845\pi$
$978$		−	474.341i		−	0.485012i
$979$	−646.916			−0.660792
$980$	−110.587	−	364.796i	−0.112843	−	0.372241i
$981$			511.910i			0.521824i
$982$		−	323.870i		−	0.329807i
$983$	−291.911			−0.296959			−0.148479	−	0.988915i	$-0.547438\pi$
$983$	−291.911			−0.296959			−0.148479	+	0.988915i	$0.547438\pi$
$984$	−524.692			−0.533224
$985$	−40.0508	+	12.1412i	−0.0406607	+	0.0123261i
$986$		−	104.942i		−	0.106432i
$987$	2133.25			2.16135
$988$	1014.59			1.02691
$989$	596.292	−	321.194i	0.602924	−	0.324766i
$990$	−115.165	−	379.901i	−0.116329	−	0.383738i
$991$	−519.671			−0.524390			−0.262195	−	0.965015i	$-0.584446\pi$
$991$	−519.671			−0.524390			−0.262195	+	0.965015i	$0.584446\pi$
$992$			728.292i			0.734165i
$993$		−	1290.30i		−	1.29939i
$994$			31.7737i			0.0319655i
$995$	1270.78	−	385.231i	1.27716	−	0.387167i
$996$		−	2364.42i		−	2.37392i
$997$			597.766i			0.599564i	0.954008	+	0.299782i	$0.0969140\pi$
$997$			597.766i			0.599564i	−0.954008	+	0.299782i	$0.903086\pi$
$998$			176.438i			0.176792i
$999$			853.407i			0.854261i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	115.3.c.c.114.12	yes	20
5.2	odd	4		575.3.d.i.551.10		20
5.3	odd	4		575.3.d.i.551.11		20
5.4	even	2	inner	115.3.c.c.114.9	✓	20
23.22	odd	2	inner	115.3.c.c.114.11	yes	20
115.22	even	4		575.3.d.i.551.9		20
115.68	even	4		575.3.d.i.551.12		20
115.114	odd	2	inner	115.3.c.c.114.10	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.3.c.c.114.9	✓	20	5.4	even	2	inner
115.3.c.c.114.10	yes	20	115.114	odd	2	inner
115.3.c.c.114.11	yes	20	23.22	odd	2	inner
115.3.c.c.114.12	yes	20	1.1	even	1	trivial
575.3.d.i.551.9		20	115.22	even	4
575.3.d.i.551.10		20	5.2	odd	4
575.3.d.i.551.11		20	5.3	odd	4
575.3.d.i.551.12		20	115.68	even	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:	\( N \)	\(=\)	\( 115 = 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	115.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+0.436812i q^{2} -4.79508i q^{3} +3.80920 q^{4} +(1.45055 + 4.78497i) q^{5} +2.09455 q^{6} +5.38385 q^{7} +3.41115i q^{8} -13.9928 q^{9} +O(q^{10})\)	\(q+0.436812i q^{2} -4.79508i q^{3} +3.80920 q^{4} +(1.45055 + 4.78497i) q^{5} +2.09455 q^{6} +5.38385 q^{7} +3.41115i q^{8} -13.9928 q^{9} +(-2.09013 + 0.633615i) q^{10} -12.9895i q^{11} -18.2654i q^{12} -9.52336i q^{13} +2.35173i q^{14} +(22.9443 - 6.95548i) q^{15} +13.7468 q^{16} -19.7991 q^{17} -6.11221i q^{18} +27.9683i q^{19} +(5.52541 + 18.2269i) q^{20} -25.8160i q^{21} +5.67397 q^{22} +(-20.2492 + 10.9073i) q^{23} +16.3567 q^{24} +(-20.7918 + 13.8816i) q^{25} +4.15991 q^{26} +23.9408i q^{27} +20.5081 q^{28} +12.1341 q^{29} +(3.03823 + 10.0223i) q^{30} +37.0645 q^{31} +19.6493i q^{32} -62.2857 q^{33} -8.64849i q^{34} +(7.80951 + 25.7615i) q^{35} -53.3013 q^{36} +35.6466 q^{37} -12.2169 q^{38} -45.6652 q^{39} +(-16.3222 + 4.94802i) q^{40} -32.0781 q^{41} +11.2767 q^{42} -29.4476 q^{43} -49.4796i q^{44} +(-20.2972 - 66.9550i) q^{45} +(-4.76443 - 8.84509i) q^{46} +82.6329i q^{47} -65.9168i q^{48} -20.0142 q^{49} +(-6.06365 - 9.08211i) q^{50} +94.9384i q^{51} -36.2763i q^{52} -11.4311 q^{53} -10.4576 q^{54} +(62.1544 - 18.8419i) q^{55} +18.3651i q^{56} +134.110 q^{57} +5.30033i q^{58} +19.5213 q^{59} +(87.3993 - 26.4948i) q^{60} +21.8377i q^{61} +16.1902i q^{62} -75.3350 q^{63} +46.4040 q^{64} +(45.5690 - 13.8141i) q^{65} -27.2071i q^{66} -106.068 q^{67} -75.4188 q^{68} +(52.3013 + 97.0966i) q^{69} +(-11.2529 + 3.41129i) q^{70} +13.5108 q^{71} -47.7314i q^{72} -7.93498i q^{73} +15.5708i q^{74} +(66.5635 + 99.6985i) q^{75} +106.537i q^{76} -69.9336i q^{77} -19.9471i q^{78} -123.502i q^{79} +(19.9403 + 65.7778i) q^{80} -11.1371 q^{81} -14.0121i q^{82} +129.448 q^{83} -98.3381i q^{84} +(-28.7195 - 94.7383i) q^{85} -12.8631i q^{86} -58.1841i q^{87} +44.3091 q^{88} -49.8029i q^{89} +(29.2467 - 8.86603i) q^{90} -51.2723i q^{91} +(-77.1333 + 41.5480i) q^{92} -177.727i q^{93} -36.0950 q^{94} +(-133.828 + 40.5693i) q^{95} +94.2201 q^{96} +76.4896 q^{97} -8.74243i q^{98} +181.759i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 56 q^{4} - 8 q^{6} - 72 q^{9}+O(q^{10}) \) 20 * q - 56 * q^4 - 8 * q^6 - 72 * q^9	\( 20 q - 56 q^{4} - 8 q^{6} - 72 q^{9} + 88 q^{16} + 44 q^{24} - 12 q^{25} - 56 q^{26} + 236 q^{31} + 92 q^{35} - 32 q^{36} - 168 q^{39} + 124 q^{41} - 248 q^{46} + 88 q^{49} + 200 q^{50} - 196 q^{54} + 268 q^{55} + 56 q^{59} - 28 q^{64} + 376 q^{69} - 636 q^{70} - 196 q^{71} + 428 q^{75} - 988 q^{81} - 284 q^{85} + 276 q^{94} + 184 q^{95} - 264 q^{96}+O(q^{100}) \) 20 * q - 56 * q^4 - 8 * q^6 - 72 * q^9 + 88 * q^16 + 44 * q^24 - 12 * q^25 - 56 * q^26 + 236 * q^31 + 92 * q^35 - 32 * q^36 - 168 * q^39 + 124 * q^41 - 248 * q^46 + 88 * q^49 + 200 * q^50 - 196 * q^54 + 268 * q^55 + 56 * q^59 - 28 * q^64 + 376 * q^69 - 636 * q^70 - 196 * q^71 + 428 * q^75 - 988 * q^81 - 284 * q^85 + 276 * q^94 + 184 * q^95 - 264 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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