LMFDB - Embedded newform 1150.3.c.c.1149.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1150,3,Mod(1149,1150)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1150, 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("1150.1149");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 1150 = 2 \cdot 5^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	1150.c (of order $2$, degree $1$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$31.3352304014$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	no (minimal twist has level 230)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1149.3
Character	$\chi$	$=$	1150.1149
Dual form			1150.3.c.c.1149.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.41421i q^{2} +5.41949i q^{3} -2.00000 q^{4} +7.66432 q^{6} +8.24199 q^{7} +2.82843i q^{8} -20.3709 q^{9} +O(q^{10})$	\(q-1.41421i q^{2} +5.41949i q^{3} -2.00000 q^{4} +7.66432 q^{6} +8.24199 q^{7} +2.82843i q^{8} -20.3709 q^{9} -15.8246i q^{11} -10.8390i q^{12} +14.3219i q^{13} -11.6559i q^{14} +4.00000 q^{16} -10.1666 q^{17} +28.8088i q^{18} -36.5359i q^{19} +44.6674i q^{21} -22.3793 q^{22} +(-5.84663 - 22.2445i) q^{23} -15.3286 q^{24} +20.2543 q^{26} -61.6245i q^{27} -16.4840 q^{28} -6.46533 q^{29} -42.8526 q^{31} -5.65685i q^{32} +85.7611 q^{33} +14.3777i q^{34} +40.7418 q^{36} -63.6379 q^{37} -51.6696 q^{38} -77.6175 q^{39} -37.0921 q^{41} +63.1692 q^{42} -6.00126 q^{43} +31.6491i q^{44} +(-31.4584 + 8.26838i) q^{46} -32.4676i q^{47} +21.6780i q^{48} +18.9303 q^{49} -55.0977i q^{51} -28.6438i q^{52} +36.6640 q^{53} -87.1502 q^{54} +23.3119i q^{56} +198.006 q^{57} +9.14336i q^{58} -6.65851 q^{59} +55.7093i q^{61} +60.6028i q^{62} -167.897 q^{63} -8.00000 q^{64} -121.284i q^{66} +4.45984 q^{67} +20.3331 q^{68} +(120.554 - 31.6858i) q^{69} +118.412 q^{71} -57.6176i q^{72} -82.2675i q^{73} +89.9976i q^{74} +73.0718i q^{76} -130.426i q^{77} +109.768i q^{78} -133.084i q^{79} +150.636 q^{81} +52.4561i q^{82} +67.5614 q^{83} -89.3348i q^{84} +8.48707i q^{86} -35.0388i q^{87} +44.7586 q^{88} +104.729i q^{89} +118.041i q^{91} +(11.6933 + 44.4890i) q^{92} -232.240i q^{93} -45.9161 q^{94} +30.6573 q^{96} -98.6666 q^{97} -26.7715i q^{98} +322.360i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 64 q^{4} - 16 q^{6} - 128 q^{9}+O(q^{10}) $ 32 * q - 64 * q^4 - 16 * q^6 - 128 * q^9	$ 32 q - 64 q^{4} - 16 q^{6} - 128 q^{9} + 128 q^{16} + 32 q^{24} + 192 q^{26} + 216 q^{29} - 232 q^{31} + 256 q^{36} - 496 q^{39} - 312 q^{41} - 248 q^{46} + 56 q^{49} - 448 q^{54} - 408 q^{59} - 256 q^{64} + 536 q^{69} + 472 q^{71} - 272 q^{81} + 432 q^{94} - 64 q^{96}+O(q^{100}) $ 32 * q - 64 * q^4 - 16 * q^6 - 128 * q^9 + 128 * q^16 + 32 * q^24 + 192 * q^26 + 216 * q^29 - 232 * q^31 + 256 * q^36 - 496 * q^39 - 312 * q^41 - 248 * q^46 + 56 * q^49 - 448 * q^54 - 408 * q^59 - 256 * q^64 + 536 * q^69 + 472 * q^71 - 272 * q^81 + 432 * q^94 - 64 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1150\mathbb{Z}\right)^\times$.

$n$	$51$	$277$
$\chi(n)$	$-1$	$-1$

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 $

$2$		−	1.41421i		−	0.707107i
$2$		−	1.41421i		−	0.707107i
$3$			5.41949i			1.80650i	0.429117	+	0.903249i	$0.358825\pi$
$3$			5.41949i			1.80650i	−0.429117	+	0.903249i	$0.641175\pi$
$4$	−2.00000			−0.500000
$5$		0			0
$5$		0			0
$6$	7.66432			1.27739
$7$	8.24199			1.17743			0.588713	−	0.808342i	$-0.299635\pi$
$7$	8.24199			1.17743			0.588713	+	0.808342i	$0.299635\pi$
$8$			2.82843i			0.353553i
$9$	−20.3709			−2.26343
$10$		0			0
$11$		−	15.8246i		−	1.43860i	−0.694702	−	0.719298i	$-0.744464\pi$
$11$		−	15.8246i		−	1.43860i	0.694702	−	0.719298i	$-0.255536\pi$
$12$		−	10.8390i		−	0.903249i
$13$			14.3219i			1.10169i	0.834609	+	0.550843i	$0.185694\pi$
$13$			14.3219i			1.10169i	−0.834609	+	0.550843i	$0.814306\pi$
$14$		−	11.6559i		−	0.832566i
$15$		0			0
$16$	4.00000			0.250000
$17$	−10.1666			−0.598034			−0.299017	−	0.954248i	$-0.596659\pi$
$17$	−10.1666			−0.598034			−0.299017	+	0.954248i	$0.596659\pi$
$18$			28.8088i			1.60049i
$19$		−	36.5359i		−	1.92294i	−0.274904	−	0.961472i	$-0.588646\pi$
$19$		−	36.5359i		−	1.92294i	0.274904	−	0.961472i	$-0.411354\pi$
$20$		0			0
$21$			44.6674i			2.12702i
$22$	−22.3793			−1.01724
$23$	−5.84663	−	22.2445i	−0.254201	−	0.967151i
$23$	−5.84663	−	22.2445i	−0.254201	−	0.967151i
$24$	−15.3286			−0.638693
$25$		0			0
$26$	20.2543			0.779010
$27$		−	61.6245i		−	2.28239i
$28$	−16.4840			−0.588713
$29$	−6.46533			−0.222942			−0.111471	−	0.993768i	$-0.535556\pi$
$29$	−6.46533			−0.222942			−0.111471	+	0.993768i	$0.535556\pi$
$30$		0			0
$31$	−42.8526			−1.38234			−0.691172	−	0.722691i	$-0.742905\pi$
$31$	−42.8526			−1.38234			−0.691172	+	0.722691i	$0.742905\pi$
$32$		−	5.65685i		−	0.176777i
$33$	85.7611			2.59882
$34$			14.3777i			0.422874i
$35$		0			0
$36$	40.7418			1.13172
$37$	−63.6379			−1.71994			−0.859972	−	0.510341i	$-0.829519\pi$
$37$	−63.6379			−1.71994			−0.859972	+	0.510341i	$0.829519\pi$
$38$	−51.6696			−1.35973
$39$	−77.6175			−1.99019
$40$		0			0
$41$	−37.0921			−0.904685			−0.452342	−	0.891844i	$-0.649412\pi$
$41$	−37.0921			−0.904685			−0.452342	+	0.891844i	$0.649412\pi$
$42$	63.1692			1.50403
$43$	−6.00126			−0.139564			−0.0697821	−	0.997562i	$-0.522230\pi$
$43$	−6.00126			−0.139564			−0.0697821	+	0.997562i	$0.522230\pi$
$44$			31.6491i			0.719298i
$45$		0			0
$46$	−31.4584	+	8.26838i	−0.683879	+	0.179747i
$47$		−	32.4676i		−	0.690800i	−0.938455	−	0.345400i	$-0.887743\pi$
$47$		−	32.4676i		−	0.690800i	0.938455	−	0.345400i	$-0.112257\pi$
$48$			21.6780i			0.451624i
$49$	18.9303			0.386333
$50$		0			0
$51$		−	55.0977i		−	1.08035i
$52$		−	28.6438i		−	0.550843i
$53$	36.6640			0.691774			0.345887	−	0.938276i	$-0.387578\pi$
$53$	36.6640			0.691774			0.345887	+	0.938276i	$0.387578\pi$
$54$	−87.1502			−1.61389
$55$		0			0
$56$			23.3119i			0.416283i
$57$	198.006			3.47379
$58$			9.14336i			0.157644i
$59$	−6.65851			−0.112856			−0.0564280	−	0.998407i	$-0.517971\pi$
$59$	−6.65851			−0.112856			−0.0564280	+	0.998407i	$0.517971\pi$
$60$		0			0
$61$			55.7093i			0.913268i	0.889655	+	0.456634i	$0.150945\pi$
$61$			55.7093i			0.913268i	−0.889655	+	0.456634i	$0.849055\pi$
$62$			60.6028i			0.977464i
$63$	−167.897			−2.66503
$64$	−8.00000			−0.125000
$65$		0			0
$66$		−	121.284i		−	1.83764i
$67$	4.45984			0.0665648			0.0332824	−	0.999446i	$-0.489404\pi$
$67$	4.45984			0.0665648			0.0332824	+	0.999446i	$0.489404\pi$
$68$	20.3331			0.299017
$69$	120.554	−	31.6858i	1.74716	−	0.459214i
$70$		0			0
$71$	118.412			1.66777			0.833886	−	0.551937i	$-0.186111\pi$
$71$	118.412			1.66777			0.833886	+	0.551937i	$0.186111\pi$
$72$		−	57.6176i		−	0.800245i
$73$		−	82.2675i		−	1.12695i	−0.826133	−	0.563476i	$-0.809464\pi$
$73$		−	82.2675i		−	1.12695i	0.826133	−	0.563476i	$-0.190536\pi$
$74$			89.9976i			1.21618i
$75$		0			0
$76$			73.0718i			0.961472i
$77$		−	130.426i		−	1.69384i
$78$			109.768i			1.40728i
$79$		−	133.084i		−	1.68461i	−0.538999	−	0.842307i	$-0.681197\pi$
$79$		−	133.084i		−	1.68461i	0.538999	−	0.842307i	$-0.318803\pi$
$80$		0			0
$81$	150.636			1.85970
$82$			52.4561i			0.639709i
$83$	67.5614			0.813993			0.406996	−	0.913430i	$-0.366576\pi$
$83$	67.5614			0.813993			0.406996	+	0.913430i	$0.366576\pi$
$84$		−	89.3348i		−	1.06351i
$85$		0			0
$86$			8.48707i			0.0986868i
$87$		−	35.0388i		−	0.402745i
$88$	44.7586			0.508620
$89$			104.729i			1.17673i	0.808595	+	0.588365i	$0.200228\pi$
$89$			104.729i			1.17673i	−0.808595	+	0.588365i	$0.799772\pi$
$90$		0			0
$91$			118.041i			1.29715i
$92$	11.6933	+	44.4890i	0.127101	+	0.483576i
$93$		−	232.240i		−	2.49720i
$94$	−45.9161			−0.488470
$95$		0			0
$96$	30.6573			0.319347
$97$	−98.6666			−1.01718			−0.508591	−	0.861008i	$-0.669833\pi$
$97$	−98.6666			−1.01718			−0.508591	+	0.861008i	$0.669833\pi$
$98$		−	26.7715i		−	0.273179i
$99$			322.360i			3.25617i
$100$		0			0
$101$	−75.6811			−0.749318			−0.374659	−	0.927163i	$-0.622240\pi$
$101$	−75.6811			−0.749318			−0.374659	+	0.927163i	$0.622240\pi$
$102$	−77.9199			−0.763920
$103$	−86.8499			−0.843203			−0.421602	−	0.906781i	$-0.638532\pi$
$103$	−86.8499			−0.843203			−0.421602	+	0.906781i	$0.638532\pi$
$104$	−40.5085			−0.389505
$105$		0			0
$106$		−	51.8508i		−	0.489158i
$107$	−5.55552			−0.0519208			−0.0259604	−	0.999663i	$-0.508264\pi$
$107$	−5.55552			−0.0519208			−0.0259604	+	0.999663i	$0.508264\pi$
$108$			123.249i			1.14119i
$109$		−	71.0003i		−	0.651379i	−0.945477	−	0.325689i	$-0.894404\pi$
$109$		−	71.0003i		−	0.651379i	0.945477	−	0.325689i	$-0.105596\pi$
$110$		0			0
$111$		−	344.885i		−	3.10707i
$112$	32.9679			0.294357
$113$	100.763			0.891707			0.445854	−	0.895106i	$-0.352900\pi$
$113$	100.763			0.891707			0.445854	+	0.895106i	$0.352900\pi$
$114$		−	280.023i		−	2.45634i
$115$		0			0
$116$	12.9307			0.111471
$117$		−	291.750i		−	2.49359i
$118$			9.41655i			0.0798013i
$119$	−83.7927			−0.704141
$120$		0			0
$121$	−129.417			−1.06956
$122$	78.7849			0.645778
$123$		−	201.020i		−	1.63431i
$124$	85.7053			0.691172
$125$		0			0
$126$			237.442i			1.88446i
$127$		−	43.9602i		−	0.346143i	−0.984909	−	0.173072i	$-0.944631\pi$
$127$		−	43.9602i		−	0.346143i	0.984909	−	0.173072i	$-0.0553692\pi$
$128$			11.3137i			0.0883883i
$129$		−	32.5238i		−	0.252123i
$130$		0			0
$131$	−44.4134			−0.339033			−0.169517	−	0.985527i	$-0.554221\pi$
$131$	−44.4134			−0.339033			−0.169517	+	0.985527i	$0.554221\pi$
$132$	−171.522			−1.29941
$133$		−	301.129i		−	2.26412i
$134$		−	6.30717i		−	0.0470684i
$135$		0			0
$136$		−	28.7554i		−	0.211437i
$137$	44.9295			0.327953			0.163976	−	0.986464i	$-0.447568\pi$
$137$	44.9295			0.327953			0.163976	+	0.986464i	$0.447568\pi$
$138$	−44.8105	−	170.489i	−0.324713	−	1.23543i
$139$	139.796			1.00573			0.502864	−	0.864365i	$-0.332280\pi$
$139$	139.796			1.00573			0.502864	+	0.864365i	$0.332280\pi$
$140$		0			0
$141$	175.958			1.24793
$142$		−	167.460i		−	1.17929i
$143$	226.638			1.58488
$144$	−81.4836			−0.565858
$145$		0			0
$146$	−116.344			−0.796875
$147$			102.593i			0.697910i
$148$	127.276			0.859972
$149$		−	25.4227i		−	0.170622i	−0.996354	−	0.0853111i	$-0.972812\pi$
$149$		−	25.4227i		−	0.170622i	0.996354	−	0.0853111i	$-0.0271884\pi$
$150$		0			0
$151$	−52.5299			−0.347880			−0.173940	−	0.984756i	$-0.555650\pi$
$151$	−52.5299			−0.347880			−0.173940	+	0.984756i	$0.555650\pi$
$152$	103.339			0.679863
$153$	207.102			1.35361
$154$	−184.450			−1.19773
$155$		0			0
$156$	155.235			0.995097
$157$	−74.5874			−0.475079			−0.237539	−	0.971378i	$-0.576341\pi$
$157$	−74.5874			−0.475079			−0.237539	+	0.971378i	$0.576341\pi$
$158$	−188.210			−1.19120
$159$			198.700i			1.24969i
$160$		0			0
$161$	−48.1878	−	183.339i	−0.299303	−	1.13875i
$162$		−	213.031i		−	1.31501i
$163$			18.3238i			0.112416i	0.998419	+	0.0562080i	$0.0179010\pi$
$163$			18.3238i			0.112416i	−0.998419	+	0.0562080i	$0.982099\pi$
$164$	74.1842			0.452342
$165$		0			0
$166$		−	95.5462i		−	0.575580i
$167$			68.9768i			0.413035i	0.978443	+	0.206517i	$0.0662130\pi$
$167$			68.9768i			0.413035i	−0.978443	+	0.206517i	$0.933787\pi$
$168$	−126.338			−0.752014
$169$	−36.1174			−0.213712
$170$		0			0
$171$			744.270i			4.35245i
$172$	12.0025			0.0697821
$173$		−	118.707i		−	0.686166i	−0.939305	−	0.343083i	$-0.888529\pi$
$173$		−	118.707i		−	0.686166i	0.939305	−	0.343083i	$-0.111471\pi$
$174$	−49.5523			−0.284784
$175$		0			0
$176$		−	63.2982i		−	0.359649i
$177$		−	36.0857i		−	0.203874i
$178$	148.109			0.832074
$179$	278.892			1.55806			0.779029	−	0.626988i	$-0.215712\pi$
$179$	278.892			1.55806			0.779029	+	0.626988i	$0.215712\pi$
$180$		0			0
$181$		−	66.1123i		−	0.365261i	−0.983182	−	0.182631i	$-0.941539\pi$
$181$		−	66.1123i		−	0.365261i	0.983182	−	0.182631i	$-0.0584613\pi$
$182$	166.935			0.917227
$183$	−301.916			−1.64982
$184$	62.9169	−	16.5368i	0.341940	−	0.0898737i
$185$		0			0
$186$	−328.436			−1.76579
$187$			160.882i			0.860329i
$188$			64.9352i			0.345400i
$189$		−	507.908i		−	2.68735i
$190$		0			0
$191$		−	5.53406i		−	0.0289741i	−0.999895	−	0.0144871i	$-0.995388\pi$
$191$		−	5.53406i		−	0.0289741i	0.999895	−	0.0144871i	$-0.00461154\pi$
$192$		−	43.3559i		−	0.225812i
$193$			72.0460i			0.373295i	0.982427	+	0.186648i	$0.0597623\pi$
$193$			72.0460i			0.373295i	−0.982427	+	0.186648i	$0.940238\pi$
$194$			139.536i			0.719256i
$195$		0			0
$196$	−37.8606			−0.193167
$197$			191.143i			0.970271i	0.874439	+	0.485136i	$0.161230\pi$
$197$			191.143i			0.970271i	−0.874439	+	0.485136i	$0.838770\pi$
$198$	455.887			2.30246
$199$		−	172.543i		−	0.867051i	−0.901141	−	0.433525i	$-0.857269\pi$
$199$		−	172.543i		−	0.867051i	0.901141	−	0.433525i	$-0.142731\pi$
$200$		0			0
$201$			24.1701i			0.120249i
$202$			107.029i			0.529848i
$203$	−53.2871			−0.262498
$204$			110.195i			0.540173i
$205$		0			0
$206$			122.824i			0.596235i
$207$	119.101	+	453.140i	0.575368	+	2.18908i
$208$			57.2877i			0.275422i
$209$	−578.165			−2.76634
$210$		0			0
$211$	−334.039			−1.58312			−0.791561	−	0.611090i	$-0.790731\pi$
$211$	−334.039			−1.58312			−0.791561	+	0.611090i	$0.790731\pi$
$212$	−73.3281			−0.345887
$213$			641.732i			3.01282i
$214$			7.85670i			0.0367135i
$215$		0			0
$216$	174.300			0.806947
$217$	−353.191			−1.62761
$218$	−100.410			−0.460594
$219$	445.848			2.03584
$220$		0			0
$221$		−	145.605i		−	0.658845i
$222$	−487.741			−2.19703
$223$			441.580i			1.98018i	0.140440	+	0.990089i	$0.455148\pi$
$223$			441.580i			1.98018i	−0.140440	+	0.990089i	$0.544852\pi$
$224$		−	46.6237i		−	0.208142i
$225$		0			0
$226$		−	142.500i		−	0.630532i
$227$	−54.9222			−0.241948			−0.120974	−	0.992656i	$-0.538602\pi$
$227$	−54.9222			−0.241948			−0.120974	+	0.992656i	$0.538602\pi$
$228$	−396.012			−1.73690
$229$			322.300i			1.40743i	0.710485	+	0.703713i	$0.248476\pi$
$229$			322.300i			1.40743i	−0.710485	+	0.703713i	$0.751524\pi$
$230$		0			0
$231$	706.841			3.05992
$232$		−	18.2867i		−	0.0788220i
$233$		−	159.208i		−	0.683296i	−0.939828	−	0.341648i	$-0.889015\pi$
$233$		−	159.208i		−	0.683296i	0.939828	−	0.341648i	$-0.110985\pi$
$234$	−412.597			−1.76324
$235$		0			0
$236$	13.3170			0.0564280
$237$	721.250			3.04325
$238$			118.501i			0.497903i
$239$	−32.1990			−0.134724			−0.0673620	−	0.997729i	$-0.521458\pi$
$239$	−32.1990			−0.134724			−0.0673620	+	0.997729i	$0.521458\pi$
$240$		0			0
$241$		−	39.8259i		−	0.165253i	−0.996581	−	0.0826263i	$-0.973669\pi$
$241$		−	39.8259i		−	0.165253i	0.996581	−	0.0826263i	$-0.0263308\pi$
$242$			183.023i			0.756292i
$243$			261.748i			1.07715i
$244$		−	111.419i		−	0.456634i
$245$		0			0
$246$	−284.286			−1.15563
$247$	523.265			2.11848
$248$		−	121.206i		−	0.488732i
$249$			366.148i			1.47048i
$250$		0			0
$251$		−	232.529i		−	0.926410i	−0.886251	−	0.463205i	$-0.846699\pi$
$251$		−	232.529i		−	0.926410i	0.886251	−	0.463205i	$-0.153301\pi$
$252$	335.793			1.33251
$253$	−352.009	+	92.5203i	−1.39134	+	0.365693i
$254$	−62.1691			−0.244760
$255$		0			0
$256$	16.0000			0.0625000
$257$			325.160i			1.26521i	0.774473	+	0.632606i	$0.218015\pi$
$257$			325.160i			1.26521i	−0.774473	+	0.632606i	$0.781985\pi$
$258$	−45.9956			−0.178278
$259$	−524.503			−2.02511
$260$		0			0
$261$	131.705			0.504615
$262$			62.8100i			0.239733i
$263$	−4.94890			−0.0188171			−0.00940855	−	0.999956i	$-0.502995\pi$
$263$	−4.94890			−0.0188171			−0.00940855	+	0.999956i	$0.502995\pi$
$264$			242.569i			0.918822i
$265$		0			0
$266$	−425.860			−1.60098
$267$	−567.578			−2.12576
$268$	−8.91969			−0.0332824
$269$	−235.047			−0.873781			−0.436891	−	0.899515i	$-0.643920\pi$
$269$	−235.047			−0.873781			−0.436891	+	0.899515i	$0.643920\pi$
$270$		0			0
$271$	−53.5224			−0.197500			−0.0987498	−	0.995112i	$-0.531484\pi$
$271$	−53.5224			−0.197500			−0.0987498	+	0.995112i	$0.531484\pi$
$272$	−40.6663			−0.149508
$273$	−639.723			−2.34331
$274$		−	63.5399i		−	0.231898i
$275$		0			0
$276$	−241.108	+	63.3715i	−0.873578	+	0.229607i
$277$		−	143.576i		−	0.518326i	−0.965834	−	0.259163i	$-0.916553\pi$
$277$		−	143.576i		−	0.518326i	0.965834	−	0.259163i	$-0.0834468\pi$
$278$		−	197.702i		−	0.711157i
$279$	872.947			3.12884
$280$		0			0
$281$			187.330i			0.666656i	0.942811	+	0.333328i	$0.108172\pi$
$281$			187.330i			0.666656i	−0.942811	+	0.333328i	$0.891828\pi$
$282$		−	248.842i		−	0.882419i
$283$	486.156			1.71787			0.858934	−	0.512087i	$-0.171127\pi$
$283$	486.156			1.71787			0.858934	+	0.512087i	$0.171127\pi$
$284$	−236.824			−0.833886
$285$		0			0
$286$		−	320.515i		−	1.12068i
$287$	−305.712			−1.06520
$288$			115.235i			0.400122i
$289$	−185.641			−0.642356
$290$		0			0
$291$		−	534.723i		−	1.83754i
$292$			164.535i			0.563476i
$293$	−240.733			−0.821616			−0.410808	−	0.911722i	$-0.634753\pi$
$293$	−240.733			−0.821616			−0.410808	+	0.911722i	$0.634753\pi$
$294$	145.088			0.493497
$295$		0			0
$296$		−	179.995i		−	0.608092i
$297$	−975.181			−3.28344
$298$	−35.9531			−0.120648
$299$	318.584	−	83.7350i	1.06550	−	0.280050i
$300$		0			0
$301$	−49.4623			−0.164327
$302$			74.2885i			0.245988i
$303$		−	410.153i		−	1.35364i
$304$		−	146.144i		−	0.480736i
$305$		0			0
$306$		−	292.887i		−	0.957147i
$307$			338.091i			1.10127i	0.834745	+	0.550636i	$0.185615\pi$
$307$			338.091i			1.10127i	−0.834745	+	0.550636i	$0.814385\pi$
$308$			260.852i			0.846920i
$309$		−	470.683i		−	1.52324i
$310$		0			0
$311$	−131.884			−0.424066			−0.212033	−	0.977263i	$-0.568008\pi$
$311$	−131.884			−0.424066			−0.212033	+	0.977263i	$0.568008\pi$
$312$		−	219.536i		−	0.703640i
$313$	160.254			0.511994			0.255997	−	0.966678i	$-0.417596\pi$
$313$	160.254			0.511994			0.255997	+	0.966678i	$0.417596\pi$
$314$			105.482i			0.335931i
$315$		0			0
$316$			266.169i			0.842307i
$317$		−	525.687i		−	1.65832i	−0.559012	−	0.829160i	$-0.688819\pi$
$317$		−	525.687i		−	1.65832i	0.559012	−	0.829160i	$-0.311181\pi$
$318$	281.005			0.883663
$319$			102.311i			0.320724i
$320$		0			0
$321$		−	30.1081i		−	0.0937948i
$322$	−259.280	+	68.1479i	−0.805218	+	0.211639i
$323$			371.445i			1.14998i
$324$	−301.271			−0.929849
$325$		0			0
$326$	25.9138			0.0794901
$327$	384.786			1.17671
$328$		−	104.912i		−	0.319854i
$329$		−	267.598i		−	0.813367i
$330$		0			0
$331$	0.120137			0.000362953			0.000181477	−	1.00000i	$-0.499942\pi$
$331$	0.120137			0.000362953			0.000181477		1.00000i	$0.499942\pi$
$332$	−135.123			−0.406996
$333$	1296.36			3.89298
$334$	97.5480			0.292060
$335$		0			0
$336$			178.670i			0.531755i
$337$	652.946			1.93752			0.968762	−	0.247992i	$-0.0797706\pi$
$337$	652.946			1.93752			0.968762	+	0.247992i	$0.0797706\pi$
$338$			51.0777i			0.151117i
$339$			546.084i			1.61087i
$340$		0			0
$341$			678.124i			1.98863i
$342$	1052.56			3.07765
$343$	−247.834			−0.722548
$344$		−	16.9741i		−	0.0493434i
$345$		0			0
$346$	−167.877			−0.485193
$347$		−	468.304i		−	1.34958i	−0.738010	−	0.674789i	$-0.764234\pi$
$347$		−	468.304i		−	1.34958i	0.738010	−	0.674789i	$-0.235766\pi$
$348$			70.0776i			0.201372i
$349$	−182.288			−0.522315			−0.261157	−	0.965296i	$-0.584104\pi$
$349$	−182.288			−0.522315			−0.261157	+	0.965296i	$0.584104\pi$
$350$		0			0
$351$	882.581			2.51448
$352$	−89.5172			−0.254310
$353$			301.039i			0.852802i	0.904534	+	0.426401i	$0.140219\pi$
$353$			301.039i			0.852802i	−0.904534	+	0.426401i	$0.859781\pi$
$354$	−51.0329			−0.144161
$355$		0			0
$356$		−	209.458i		−	0.588365i
$357$		−	454.114i		−	1.27203i
$358$		−	394.413i		−	1.10171i
$359$			24.6772i			0.0687388i	0.999409	+	0.0343694i	$0.0109423\pi$
$359$			24.6772i			0.0687388i	−0.999409	+	0.0343694i	$0.989058\pi$
$360$		0			0
$361$	−973.874			−2.69771
$362$	−93.4969			−0.258279
$363$		−	701.372i		−	1.93215i
$364$		−	236.082i		−	0.648577i
$365$		0			0
$366$			426.974i			1.16660i
$367$	−427.508			−1.16487			−0.582435	−	0.812877i	$-0.697900\pi$
$367$	−427.508			−1.16487			−0.582435	+	0.812877i	$0.697900\pi$
$368$	−23.3865	−	88.9779i	−0.0635503	−	0.241788i
$369$	755.599			2.04769
$370$		0			0
$371$	302.184			0.814513
$372$			464.479i			1.24860i
$373$	338.652			0.907913			0.453957	−	0.891024i	$-0.350012\pi$
$373$	338.652			0.907913			0.453957	+	0.891024i	$0.350012\pi$
$374$	227.521			0.608344
$375$		0			0
$376$	91.8323			0.244235
$377$		−	92.5959i		−	0.245612i
$378$	−718.291			−1.90024
$379$		−	287.157i		−	0.757671i	−0.925464	−	0.378835i	$-0.876325\pi$
$379$		−	287.157i		−	0.757671i	0.925464	−	0.378835i	$-0.123675\pi$
$380$		0			0
$381$	238.242			0.625307
$382$	−7.82634			−0.0204878
$383$	−682.661			−1.78240			−0.891202	−	0.453606i	$-0.850137\pi$
$383$	−682.661			−1.78240			−0.891202	+	0.453606i	$0.850137\pi$
$384$	−61.3146			−0.159673
$385$		0			0
$386$	101.888			0.263960
$387$	122.251			0.315894
$388$	197.333			0.508591
$389$		−	543.886i		−	1.39816i	−0.715041	−	0.699082i	$-0.753592\pi$
$389$		−	543.886i		−	1.39816i	0.715041	−	0.699082i	$-0.246408\pi$
$390$		0			0
$391$	59.4402	+	226.150i	0.152021	+	0.578389i
$392$			53.5430i			0.136589i
$393$		−	240.698i		−	0.612463i
$394$	270.318			0.686085
$395$		0			0
$396$		−	644.721i		−	1.62808i
$397$			99.6609i			0.251035i	0.992091	+	0.125517i	$0.0400591\pi$
$397$			99.6609i			0.251035i	−0.992091	+	0.125517i	$0.959941\pi$
$398$	−244.013			−0.613097
$399$	1631.96			4.09014
$400$		0			0
$401$			404.668i			1.00915i	0.863369	+	0.504573i	$0.168350\pi$
$401$			404.668i			1.00915i	−0.863369	+	0.504573i	$0.831650\pi$
$402$	34.1817			0.0850290
$403$		−	613.732i		−	1.52291i
$404$	151.362			0.374659
$405$		0			0
$406$			75.3594i			0.185614i
$407$			1007.04i			2.47430i
$408$	155.840			0.381960
$409$	−701.478			−1.71510			−0.857552	−	0.514397i	$-0.828016\pi$
$409$	−701.478			−1.71510			−0.857552	+	0.514397i	$0.828016\pi$
$410$		0			0
$411$			243.495i			0.592446i
$412$	173.700			0.421602
$413$	−54.8793			−0.132880
$414$	640.837	−	168.434i	1.54792	−	0.406847i
$415$		0			0
$416$	81.0170			0.194752
$417$			757.625i			1.81685i
$418$			817.648i			1.95610i
$419$			685.089i			1.63506i	0.575888	+	0.817529i	$0.304657\pi$
$419$			685.089i			1.63506i	−0.575888	+	0.817529i	$0.695343\pi$
$420$		0			0
$421$		−	205.326i		−	0.487711i	−0.969812	−	0.243856i	$-0.921588\pi$
$421$		−	205.326i		−	0.487711i	0.969812	−	0.243856i	$-0.0784123\pi$
$422$			472.402i			1.11944i
$423$			661.395i			1.56358i
$424$			103.702i			0.244579i
$425$		0			0
$426$	907.546			2.13039
$427$			459.156i			1.07531i
$428$	11.1110			0.0259604
$429$			1228.26i			2.86308i
$430$		0			0
$431$			355.926i			0.825814i	0.910773	+	0.412907i	$0.135487\pi$
$431$			355.926i			0.825814i	−0.910773	+	0.412907i	$0.864513\pi$
$432$		−	246.498i		−	0.570597i
$433$	−17.2870			−0.0399238			−0.0199619	−	0.999801i	$-0.506354\pi$
$433$	−17.2870			−0.0399238			−0.0199619	+	0.999801i	$0.506354\pi$
$434$			499.487i			1.15089i
$435$		0			0
$436$			142.001i			0.325689i
$437$	−812.723	+	213.612i	−1.85978	+	0.488815i
$438$		−	630.524i		−	1.43955i
$439$	458.708			1.04489			0.522447	−	0.852672i	$-0.325019\pi$
$439$	458.708			1.04489			0.522447	+	0.852672i	$0.325019\pi$
$440$		0			0
$441$	−385.628			−0.874439
$442$	−205.916			−0.465874
$443$			196.292i			0.443096i	0.975149	+	0.221548i	$0.0711110\pi$
$443$			196.292i			0.443096i	−0.975149	+	0.221548i	$0.928889\pi$
$444$			689.771i			1.55354i
$445$		0			0
$446$	624.488			1.40020
$447$	137.778			0.308228
$448$	−65.9359			−0.147178
$449$	344.536			0.767341			0.383671	−	0.923470i	$-0.374660\pi$
$449$	344.536			0.767341			0.383671	+	0.923470i	$0.374660\pi$
$450$		0			0
$451$			586.966i			1.30148i
$452$	−201.526			−0.445854
$453$		−	284.685i		−	0.628445i
$454$			77.6717i			0.171083i
$455$		0			0
$456$			560.046i			1.22817i
$457$	122.214			0.267426			0.133713	−	0.991020i	$-0.457310\pi$
$457$	122.214			0.267426			0.133713	+	0.991020i	$0.457310\pi$
$458$	455.802			0.995200
$459$			626.510i			1.36495i
$460$		0			0
$461$	218.326			0.473593			0.236796	−	0.971559i	$-0.423903\pi$
$461$	218.326			0.473593			0.236796	+	0.971559i	$0.423903\pi$
$462$		−	999.625i		−	2.16369i
$463$			455.380i			0.983542i	0.870725	+	0.491771i	$0.163650\pi$
$463$			455.380i			0.983542i	−0.870725	+	0.491771i	$0.836350\pi$
$464$	−25.8613			−0.0557356
$465$		0			0
$466$	−225.154			−0.483163
$467$	−350.332			−0.750176			−0.375088	−	0.926989i	$-0.622388\pi$
$467$	−350.332			−0.750176			−0.375088	+	0.926989i	$0.622388\pi$
$468$			583.501i			1.24680i
$469$	36.7580			0.0783752
$470$		0			0
$471$		−	404.226i		−	0.858229i
$472$		−	18.8331i		−	0.0399006i
$473$			94.9673i			0.200777i
$474$		−	1020.00i		−	2.15190i
$475$		0			0
$476$	167.585			0.352070
$477$	−746.879			−1.56578
$478$			45.5363i			0.0952643i
$479$		−	743.178i		−	1.55152i	−0.631028	−	0.775760i	$-0.717367\pi$
$479$		−	743.178i		−	1.55152i	0.631028	−	0.775760i	$-0.282633\pi$
$480$		0			0
$481$		−	911.417i		−	1.89484i
$482$	−56.3223			−0.116851
$483$	993.603	−	261.154i	2.05715	−	0.540691i
$484$	258.833			0.534779
$485$		0			0
$486$	370.167			0.761660
$487$		−	366.770i		−	0.753122i	−0.926392	−	0.376561i	$-0.877107\pi$
$487$		−	366.770i		−	0.753122i	0.926392	−	0.376561i	$-0.122893\pi$
$488$	−157.570			−0.322889
$489$	−99.3057			−0.203079
$490$		0			0
$491$	127.024			0.258704			0.129352	−	0.991599i	$-0.458710\pi$
$491$	127.024			0.258704			0.129352	+	0.991599i	$0.458710\pi$
$492$			402.041i			0.817156i
$493$	65.7302			0.133327
$494$		−	740.008i		−	1.49799i
$495$		0			0
$496$	−171.411			−0.345586
$497$	975.948			1.96368
$498$	517.812			1.03978
$499$	−523.599			−1.04930			−0.524648	−	0.851319i	$-0.675803\pi$
$499$	−523.599			−1.04930			−0.524648	+	0.851319i	$0.675803\pi$
$500$		0			0
$501$	−373.819			−0.746147
$502$	−328.845			−0.655071
$503$	646.170			1.28463			0.642316	−	0.766440i	$-0.277974\pi$
$503$	646.170			1.28463			0.642316	+	0.766440i	$0.277974\pi$
$504$		−	474.884i		−	0.942229i
$505$		0			0
$506$	130.844	+	497.816i	0.258584	+	0.983826i
$507$		−	195.738i		−	0.386070i
$508$			87.9203i			0.173072i
$509$	605.436			1.18946			0.594731	−	0.803925i	$-0.297259\pi$
$509$	605.436			1.18946			0.594731	+	0.803925i	$0.297259\pi$
$510$		0			0
$511$		−	678.047i		−	1.32690i
$512$		−	22.6274i		−	0.0441942i
$513$	−2251.51			−4.38891
$514$	459.845			0.894641
$515$		0			0
$516$			65.0476i			0.126061i
$517$	−513.786			−0.993783
$518$			741.759i			1.43197i
$519$	643.330			1.23956
$520$		0			0
$521$		−	655.952i		−	1.25902i	−0.776990	−	0.629512i	$-0.783255\pi$
$521$		−	655.952i		−	1.25902i	0.776990	−	0.629512i	$-0.216745\pi$
$522$		−	186.258i		−	0.356817i
$523$	−317.109			−0.606328			−0.303164	−	0.952938i	$-0.598043\pi$
$523$	−317.109			−0.606328			−0.303164	+	0.952938i	$0.598043\pi$
$524$	88.8267			0.169517
$525$		0			0
$526$			6.99880i			0.0133057i
$527$	435.665			0.826688
$528$	343.044			0.649705
$529$	−460.634	+	260.111i	−0.870763	+	0.491702i
$530$		0			0
$531$	135.640			0.255442
$532$			602.257i			1.13206i
$533$		−	531.230i		−	0.996679i
$534$			802.677i			1.50314i
$535$		0			0
$536$			12.6143i			0.0235342i
$537$			1511.46i			2.81463i
$538$			332.407i			0.617856i
$539$		−	299.564i		−	0.555777i
$540$		0			0
$541$	−222.888			−0.411992			−0.205996	−	0.978553i	$-0.566043\pi$
$541$	−222.888			−0.411992			−0.205996	+	0.978553i	$0.566043\pi$
$542$			75.6921i			0.139653i
$543$	358.295			0.659844
$544$			57.5108i			0.105718i
$545$		0			0
$546$			904.704i			1.65697i
$547$		−	552.627i		−	1.01029i	−0.863035	−	0.505144i	$-0.831439\pi$
$547$		−	552.627i		−	1.01029i	0.863035	−	0.505144i	$-0.168561\pi$
$548$	−89.8590			−0.163976
$549$		−	1134.85i		−	2.06712i
$550$		0			0
$551$			236.217i			0.428706i
$552$	89.6209	+	340.978i	0.162357	+	0.617713i
$553$		−	1096.88i		−	1.98351i
$554$	−203.048			−0.366512
$555$		0			0
$556$	−279.592			−0.502864
$557$	−110.000			−0.197486			−0.0987430	−	0.995113i	$-0.531482\pi$
$557$	−110.000			−0.197486			−0.0987430	+	0.995113i	$0.531482\pi$
$558$		−	1234.53i		−	2.21243i
$559$		−	85.9496i		−	0.153756i
$560$		0			0
$561$	−871.896			−1.55418
$562$	264.925			0.471397
$563$	360.367			0.640084			0.320042	−	0.947403i	$-0.396303\pi$
$563$	360.367			0.640084			0.320042	+	0.947403i	$0.396303\pi$
$564$	−351.916			−0.623965
$565$		0			0
$566$		−	687.529i		−	1.21472i
$567$	1241.54			2.18966
$568$			334.919i			0.589646i
$569$		−	532.981i		−	0.936698i	−0.883544	−	0.468349i	$-0.844849\pi$
$569$		−	532.981i		−	0.936698i	0.883544	−	0.468349i	$-0.155151\pi$
$570$		0			0
$571$		−	582.697i		−	1.02048i	−0.860031	−	0.510242i	$-0.829556\pi$
$571$		−	582.697i		−	1.02048i	0.860031	−	0.510242i	$-0.170444\pi$
$572$	−453.276			−0.792441
$573$	29.9918			0.0523417
$574$			432.343i			0.753210i
$575$		0			0
$576$	162.967			0.282929
$577$		−	869.422i		−	1.50680i	−0.657564	−	0.753399i	$-0.728413\pi$
$577$		−	869.422i		−	1.50680i	0.657564	−	0.753399i	$-0.271587\pi$
$578$			262.536i			0.454214i
$579$	−390.453			−0.674357
$580$		0			0
$581$	556.840			0.958416
$582$	−756.212			−1.29933
$583$		−	580.192i		−	0.995183i
$584$	232.688			0.398438
$585$		0			0
$586$			340.449i			0.580970i
$587$		−	403.118i		−	0.686742i	−0.939200	−	0.343371i	$-0.888431\pi$
$587$		−	403.118i		−	0.686742i	0.939200	−	0.343371i	$-0.111569\pi$
$588$		−	205.185i		−	0.348955i
$589$			1565.66i			2.65817i
$590$		0			0
$591$	−1035.90			−1.75279
$592$	−254.552			−0.429986
$593$			668.332i			1.12703i	0.826104	+	0.563517i	$0.190552\pi$
$593$			668.332i			1.12703i	−0.826104	+	0.563517i	$0.809448\pi$
$594$			1379.11i			2.32174i
$595$		0			0
$596$			50.8454i			0.0853111i
$597$	935.096			1.56632
$598$	−118.419	−	450.545i	−0.198025	−	0.753420i
$599$	−866.946			−1.44732			−0.723661	−	0.690155i	$-0.757542\pi$
$599$	−866.946			−1.44732			−0.723661	+	0.690155i	$0.757542\pi$
$600$		0			0
$601$	544.425			0.905866			0.452933	−	0.891545i	$-0.350378\pi$
$601$	544.425			0.905866			0.452933	+	0.891545i	$0.350378\pi$
$602$			69.9503i			0.116196i
$603$	−90.8511			−0.150665
$604$	105.060			0.173940
$605$		0			0
$606$	−580.044			−0.957169
$607$			23.2820i			0.0383559i	0.999816	+	0.0191779i	$0.00610490\pi$
$607$			23.2820i			0.0383559i	−0.999816	+	0.0191779i	$0.993895\pi$
$608$	−206.678			−0.339932
$609$		−	288.789i		−	0.474202i
$610$		0			0
$611$	464.999			0.761045
$612$	−414.205			−0.676805
$613$	−559.419			−0.912592			−0.456296	−	0.889828i	$-0.650824\pi$
$613$	−559.419			−0.912592			−0.456296	+	0.889828i	$0.650824\pi$
$614$	478.133			0.778718
$615$		0			0
$616$	368.900			0.598863
$617$	1080.07			1.75052			0.875262	−	0.483649i	$-0.160689\pi$
$617$	1080.07			1.75052			0.875262	+	0.483649i	$0.160689\pi$
$618$	−665.646			−1.07710
$619$		−	729.225i		−	1.17807i	−0.808107	−	0.589035i	$-0.799508\pi$
$619$		−	729.225i		−	1.17807i	0.808107	−	0.589035i	$-0.200492\pi$
$620$		0			0
$621$	−1370.81	+	360.296i	−2.20742	+	0.580187i
$622$			186.513i			0.299860i
$623$			863.175i			1.38551i
$624$	−310.470			−0.497548
$625$		0			0
$626$		−	226.634i		−	0.362035i
$627$		−	3133.36i		−	4.99738i
$628$	149.175			0.237539
$629$	646.980			1.02858
$630$		0			0
$631$			386.633i			0.612731i	0.951914	+	0.306365i	$0.0991129\pi$
$631$			386.633i			0.612731i	−0.951914	+	0.306365i	$0.900887\pi$
$632$	376.420			0.595601
$633$		−	1810.32i		−	2.85991i
$634$	−743.434			−1.17261
$635$		0			0
$636$		−	397.401i		−	0.624844i
$637$			271.118i			0.425618i
$638$	144.690			0.226786
$639$	−2412.15			−3.77489
$640$		0			0
$641$		−	676.123i		−	1.05479i	−0.849619	−	0.527397i	$-0.823168\pi$
$641$		−	676.123i		−	1.05479i	0.849619	−	0.527397i	$-0.176832\pi$
$642$	−42.5793			−0.0663229
$643$	−1063.72			−1.65430			−0.827151	−	0.561980i	$-0.810040\pi$
$643$	−1063.72			−1.65430			−0.827151	+	0.561980i	$0.810040\pi$
$644$	96.3757	+	366.677i	0.149652	+	0.569375i
$645$		0			0
$646$	525.303			0.813162
$647$		−	157.776i		−	0.243857i	−0.992539	−	0.121929i	$-0.961092\pi$
$647$		−	157.776i		−	0.243857i	0.992539	−	0.121929i	$-0.0389079\pi$
$648$			426.062i			0.657503i
$649$			105.368i			0.162354i
$650$		0			0
$651$		−	1914.12i		−	2.94027i
$652$		−	36.6476i		−	0.0562080i
$653$		−	41.1895i		−	0.0630773i	−0.999503	−	0.0315386i	$-0.989959\pi$
$653$		−	41.1895i		−	0.0630773i	0.999503	−	0.0315386i	$-0.0100407\pi$
$654$		−	544.169i		−	0.832063i
$655$		0			0
$656$	−148.368			−0.226171
$657$			1675.86i			2.55078i
$658$	−378.440			−0.575137
$659$		−	19.2526i		−	0.0292149i	−0.999893	−	0.0146075i	$-0.995350\pi$
$659$		−	19.2526i		−	0.0292149i	0.999893	−	0.0146075i	$-0.00464986\pi$
$660$		0			0
$661$		−	75.8322i		−	0.114724i	−0.998353	−	0.0573618i	$-0.981731\pi$
$661$		−	75.8322i		−	0.114724i	0.998353	−	0.0573618i	$-0.0182688\pi$
$662$		−	0.169900i		−	0.000256647i
$663$	789.104			1.19020
$664$			191.092i			0.287790i
$665$		0			0
$666$		−	1833.33i		−	2.75275i
$667$	37.8004	+	143.818i	0.0566722	+	0.215619i
$668$		−	137.954i		−	0.206517i
$669$	−2393.14			−3.57719
$670$		0			0
$671$	881.576			1.31382
$672$	252.677			0.376007
$673$		−	12.6902i		−	0.0188561i	−0.999956	−	0.00942807i	$-0.996999\pi$
$673$		−	12.6902i		−	0.0188561i	0.999956	−	0.00942807i	$-0.00300109\pi$
$674$		−	923.405i		−	1.37004i
$675$		0			0
$676$	72.2347			0.106856
$677$	233.185			0.344439			0.172220	−	0.985059i	$-0.444906\pi$
$677$	233.185			0.344439			0.172220	+	0.985059i	$0.444906\pi$
$678$	772.279			1.13906
$679$	−813.209			−1.19766
$680$		0			0
$681$		−	297.650i		−	0.437078i
$682$	959.012			1.40618
$683$		−	367.020i		−	0.537364i	−0.963229	−	0.268682i	$-0.913412\pi$
$683$		−	367.020i		−	0.537364i	0.963229	−	0.268682i	$-0.0865881\pi$
$684$		−	1488.54i		−	2.17623i
$685$		0			0
$686$			350.490i			0.510918i
$687$	−1746.70			−2.54251
$688$	−24.0051			−0.0348911
$689$			525.099i			0.762118i
$690$		0			0
$691$	−1186.21			−1.71666			−0.858332	−	0.513095i	$-0.828499\pi$
$691$	−1186.21			−1.71666			−0.858332	+	0.513095i	$0.828499\pi$
$692$			237.413i			0.343083i
$693$			2656.89i			3.83390i
$694$	−662.282			−0.954296
$695$		0			0
$696$	99.1047			0.142392
$697$	377.099			0.541032
$698$			257.794i			0.369332i
$699$	862.826			1.23437
$700$		0			0
$701$			848.508i			1.21043i	0.796064	+	0.605213i	$0.206912\pi$
$701$			848.508i			1.21043i	−0.796064	+	0.605213i	$0.793088\pi$
$702$		−	1248.16i		−	1.77800i
$703$			2325.07i			3.30736i
$704$			126.596i			0.179825i
$705$		0			0
$706$	425.733			0.603022
$707$	−623.763			−0.882267
$708$			72.1715i			0.101937i
$709$		−	533.757i		−	0.752831i	−0.926451	−	0.376416i	$-0.877156\pi$
$709$		−	533.757i		−	0.752831i	0.926451	−	0.376416i	$-0.122844\pi$
$710$		0			0
$711$			2711.05i			3.81301i
$712$	−296.218			−0.416037
$713$	250.544	+	953.235i	0.351394	+	1.33694i
$714$	−642.214			−0.899460
$715$		0			0
$716$	−557.785			−0.779029
$717$		−	174.502i		−	0.243379i
$718$	34.8989			0.0486057
$719$	−1210.11			−1.68304			−0.841520	−	0.540225i	$-0.818339\pi$
$719$	−1210.11			−1.68304			−0.841520	+	0.540225i	$0.818339\pi$
$720$		0			0
$721$	−715.816			−0.992810
$722$			1377.27i			1.90757i
$723$	215.836			0.298528
$724$			132.225i			0.182631i
$725$		0			0
$726$	−991.890			−1.36624
$727$	2.43604			0.00335081			0.00167540	−	0.999999i	$-0.499467\pi$
$727$	2.43604			0.00335081			0.00167540	+	0.999999i	$0.499467\pi$
$728$	−333.870			−0.458613
$729$	−62.8190			−0.0861715
$730$		0			0
$731$	61.0123			0.0834641
$732$	603.833			0.824908
$733$	495.146			0.675506			0.337753	−	0.941235i	$-0.390333\pi$
$733$	495.146			0.675506			0.337753	+	0.941235i	$0.390333\pi$
$734$			604.587i			0.823688i
$735$		0			0
$736$	−125.834	+	33.0735i	−0.170970	+	0.0449369i
$737$		−	70.5751i		−	0.0957599i
$738$		−	1068.58i		−	1.44794i
$739$	−1235.77			−1.67222			−0.836112	−	0.548559i	$-0.815177\pi$
$739$	−1235.77			−1.67222			−0.836112	+	0.548559i	$0.815177\pi$
$740$		0			0
$741$			2835.83i			3.82703i
$742$		−	427.353i		−	0.575948i
$743$	1030.67			1.38717			0.693587	−	0.720373i	$-0.256029\pi$
$743$	1030.67			1.38717			0.693587	+	0.720373i	$0.256029\pi$
$744$	656.873			0.882894
$745$		0			0
$746$		−	478.926i		−	0.641992i
$747$	−1376.29			−1.84242
$748$		−	321.763i		−	0.430164i
$749$	−45.7885			−0.0611329
$750$		0			0
$751$			1112.44i			1.48128i	0.671903	+	0.740639i	$0.265477\pi$
$751$			1112.44i			1.48128i	−0.671903	+	0.740639i	$0.734523\pi$
$752$		−	129.870i		−	0.172700i
$753$	1260.19			1.67356
$754$	−130.950			−0.173674
$755$		0			0
$756$			1015.82i			1.34367i
$757$	483.738			0.639019			0.319510	−	0.947583i	$-0.396482\pi$
$757$	483.738			0.639019			0.319510	+	0.947583i	$0.396482\pi$
$758$	−406.102			−0.535754
$759$	−501.413	−	1907.71i	−0.660624	−	2.51345i
$760$		0			0
$761$	833.341			1.09506			0.547530	−	0.836786i	$-0.315568\pi$
$761$	833.341			1.09506			0.547530	+	0.836786i	$0.315568\pi$
$762$		−	336.925i		−	0.442158i
$763$		−	585.183i		−	0.766951i
$764$			11.0681i			0.0144871i
$765$		0			0
$766$			965.428i			1.26035i
$767$		−	95.3626i		−	0.124332i
$768$			86.7119i			0.112906i
$769$		−	356.518i		−	0.463613i	−0.972762	−	0.231806i	$-0.925536\pi$
$769$		−	356.518i		−	0.463613i	0.972762	−	0.231806i	$-0.0744636\pi$
$770$		0			0
$771$	−1762.20			−2.28560
$772$		−	144.092i		−	0.186648i
$773$	−286.633			−0.370805			−0.185403	−	0.982663i	$-0.559359\pi$
$773$	−286.633			−0.370805			−0.185403	+	0.982663i	$0.559359\pi$
$774$		−	172.889i		−	0.223371i
$775$		0			0
$776$		−	279.071i		−	0.359628i
$777$		−	2842.54i		−	3.65835i
$778$	−769.171			−0.988651
$779$			1355.19i			1.73966i
$780$		0			0
$781$		−	1873.81i		−	2.39925i
$782$	319.825	−	84.0611i	0.408983	−	0.107495i
$783$			398.423i			0.508841i
$784$	75.7213			0.0965833
$785$		0			0
$786$	−340.398			−0.433077
$787$	930.798			1.18272			0.591359	−	0.806409i	$-0.298592\pi$
$787$	930.798			1.18272			0.591359	+	0.806409i	$0.298592\pi$
$788$		−	382.287i		−	0.485136i
$789$		−	26.8205i		−	0.0339931i
$790$		0			0
$791$	830.487			1.04992
$792$	−911.773			−1.15123
$793$	−797.865			−1.00613
$794$	140.942			0.177509
$795$		0			0
$796$			345.086i			0.433525i
$797$	−1493.90			−1.87441			−0.937203	−	0.348785i	$-0.886594\pi$
$797$	−1493.90			−1.87441			−0.937203	+	0.348785i	$0.886594\pi$
$798$		−	2307.95i		−	2.89216i
$799$			330.084i			0.413122i
$800$		0			0
$801$		−	2133.42i		−	2.66345i
$802$	572.286			0.713574
$803$	−1301.85			−1.62123
$804$		−	48.3402i		−	0.0601246i
$805$		0			0
$806$	−867.948			−1.07686
$807$		−	1273.84i		−	1.57848i
$808$		−	214.059i		−	0.264924i
$809$	850.318			1.05107			0.525537	−	0.850771i	$-0.323865\pi$
$809$	850.318			1.05107			0.525537	+	0.850771i	$0.323865\pi$
$810$		0			0
$811$	1050.33			1.29510			0.647552	−	0.762022i	$-0.275793\pi$
$811$	1050.33			1.29510			0.647552	+	0.762022i	$0.275793\pi$
$812$	106.574			0.131249
$813$		−	290.064i		−	0.356783i
$814$	1424.17			1.74960
$815$		0			0
$816$		−	220.391i		−	0.270087i
$817$			219.262i			0.268374i
$818$			992.039i			1.21276i
$819$		−	2404.60i		−	2.93602i
$820$		0			0
$821$	−461.343			−0.561929			−0.280964	−	0.959718i	$-0.590654\pi$
$821$	−461.343			−0.561929			−0.280964	+	0.959718i	$0.590654\pi$
$822$	344.354			0.418922
$823$		−	101.176i		−	0.122936i	−0.998109	−	0.0614680i	$-0.980422\pi$
$823$		−	101.176i		−	0.122936i	0.998109	−	0.0614680i	$-0.0195782\pi$
$824$		−	245.649i		−	0.298117i
$825$		0			0
$826$			77.6111i			0.0939601i
$827$	718.169			0.868403			0.434202	−	0.900816i	$-0.357031\pi$
$827$	718.169			0.868403			0.434202	+	0.900816i	$0.357031\pi$
$828$	−238.202	−	906.280i	−0.287684	−	1.09454i
$829$	−634.298			−0.765137			−0.382568	−	0.923927i	$-0.624960\pi$
$829$	−634.298			−0.765137			−0.382568	+	0.923927i	$0.624960\pi$
$830$		0			0
$831$	778.111			0.936356
$832$		−	114.575i		−	0.137711i
$833$	−192.456			−0.231040
$834$	1071.44			1.28470
$835$		0			0
$836$	1156.33			1.38317
$837$			2640.77i			3.15505i
$838$	968.862			1.15616
$839$		−	133.138i		−	0.158687i	−0.996847	−	0.0793434i	$-0.974718\pi$
$839$		−	133.138i		−	0.158687i	0.996847	−	0.0793434i	$-0.0252824\pi$
$840$		0			0
$841$	−799.200			−0.950297
$842$	−290.375			−0.344864
$843$	−1015.23			−1.20431
$844$	668.078			0.791561
$845$		0			0
$846$	935.353			1.10562
$847$	−1066.65			−1.25933
$848$	146.656			0.172944
$849$			2634.72i			3.10332i
$850$		0			0
$851$	372.068	+	1415.59i	0.437212	+	1.66345i
$852$		−	1283.46i		−	1.50641i
$853$		−	728.808i		−	0.854406i	−0.904156	−	0.427203i	$-0.859499\pi$
$853$		−	728.808i		−	0.854406i	0.904156	−	0.427203i	$-0.140501\pi$
$854$	649.344			0.760356
$855$		0			0
$856$		−	15.7134i		−	0.0183568i
$857$			1137.95i			1.32783i	0.747809	+	0.663914i	$0.231106\pi$
$857$			1137.95i			1.32783i	−0.747809	+	0.663914i	$0.768894\pi$
$858$	1737.03			2.02451
$859$	782.016			0.910379			0.455190	−	0.890395i	$-0.349571\pi$
$859$	782.016			0.910379			0.455190	+	0.890395i	$0.349571\pi$
$860$		0			0
$861$		−	1656.81i		−	1.92428i
$862$	503.355			0.583939
$863$			324.868i			0.376440i	0.982127	+	0.188220i	$0.0602718\pi$
$863$			324.868i			0.376440i	−0.982127	+	0.188220i	$0.939728\pi$
$864$	−348.601			−0.403473
$865$		0			0
$866$			24.4475i			0.0282304i
$867$		−	1006.08i		−	1.16041i
$868$	706.382			0.813804
$869$	−2106.00			−2.42348
$870$		0			0
$871$			63.8735i			0.0733336i
$872$	200.819			0.230297
$873$	2009.93			2.30232
$874$	302.093	+	1149.36i	0.345644	+	1.31506i
$875$		0			0
$876$	−891.696			−1.01792
$877$		−	411.966i		−	0.469745i	−0.972026	−	0.234872i	$-0.924533\pi$
$877$		−	411.966i		−	0.469745i	0.972026	−	0.234872i	$-0.0754672\pi$
$878$		−	648.712i		−	0.738852i
$879$		−	1304.65i		−	1.48425i
$880$		0			0
$881$			1082.39i			1.22859i	0.789076	+	0.614296i	$0.210560\pi$
$881$			1082.39i			1.22859i	−0.789076	+	0.614296i	$0.789440\pi$
$882$			545.360i			0.618322i
$883$		−	1343.48i		−	1.52149i	−0.649049	−	0.760746i	$-0.724833\pi$
$883$		−	1343.48i		−	1.52149i	0.649049	−	0.760746i	$-0.275167\pi$
$884$			291.210i			0.329423i
$885$		0			0
$886$	277.598			0.313316
$887$			377.176i			0.425227i	0.977136	+	0.212613i	$0.0681975\pi$
$887$			377.176i			0.425227i	−0.977136	+	0.212613i	$0.931803\pi$
$888$	975.483			1.09852
$889$		−	362.319i		−	0.407558i
$890$		0			0
$891$		−	2383.74i		−	2.67535i
$892$		−	883.160i		−	0.990089i
$893$	−1186.23			−1.32837
$894$		−	194.848i		−	0.217950i
$895$		0			0
$896$			93.2474i			0.104071i
$897$	453.801	+	1726.56i	0.505910	+	1.92482i
$898$		−	487.248i		−	0.542592i
$899$	277.056			0.308183
$900$		0			0
$901$	−372.748			−0.413704
$902$	830.095			0.920283
$903$		−	268.061i		−	0.296856i
$904$			285.001i			0.315266i
$905$		0			0
$906$	−402.606			−0.444378
$907$	−295.704			−0.326024			−0.163012	−	0.986624i	$-0.552121\pi$
$907$	−295.704			−0.326024			−0.163012	+	0.986624i	$0.552121\pi$
$908$	109.844			0.120974
$909$	1541.69			1.69603
$910$		0			0
$911$		−	419.625i		−	0.460620i	−0.973117	−	0.230310i	$-0.926026\pi$
$911$		−	419.625i		−	0.460620i	0.973117	−	0.230310i	$-0.0739740\pi$
$912$	792.025			0.868448
$913$		−	1069.13i		−	1.17101i
$914$		−	172.836i		−	0.189099i
$915$		0			0
$916$		−	644.601i		−	0.703713i
$917$	−366.054			−0.399187
$918$	886.019			0.965163
$919$		−	1654.94i		−	1.80080i	−0.435062	−	0.900401i	$-0.643274\pi$
$919$		−	1654.94i		−	1.80080i	0.435062	−	0.900401i	$-0.356726\pi$
$920$		0			0
$921$	−1832.28			−1.98945
$922$		−	308.760i		−	0.334881i
$923$			1695.88i			1.83736i
$924$	−1413.68			−1.52996
$925$		0			0
$926$	644.004			0.695469
$927$	1769.21			1.90853
$928$			36.5734i			0.0394110i
$929$	1291.79			1.39052			0.695260	−	0.718758i	$-0.255289\pi$
$929$	1291.79			1.39052			0.695260	+	0.718758i	$0.255289\pi$
$930$		0			0
$931$		−	691.637i		−	0.742897i
$932$			318.416i			0.341648i
$933$		−	714.747i		−	0.766074i
$934$			495.445i			0.530455i
$935$		0			0
$936$	825.195			0.881618
$937$	−212.428			−0.226711			−0.113355	−	0.993554i	$-0.536160\pi$
$937$	−212.428			−0.226711			−0.113355	+	0.993554i	$0.536160\pi$
$938$		−	51.9836i		−	0.0554196i
$939$			868.496i			0.924916i
$940$		0			0
$941$		−	980.930i		−	1.04243i	−0.853424	−	0.521217i	$-0.825478\pi$
$941$		−	980.930i		−	1.04243i	0.853424	−	0.521217i	$-0.174522\pi$
$942$	−571.661			−0.606859
$943$	216.864	+	825.094i	0.229972	+	0.874967i
$944$	−26.6340			−0.0282140
$945$		0			0
$946$	134.304			0.141970
$947$		−	953.755i		−	1.00713i	−0.863956	−	0.503567i	$-0.832021\pi$
$947$		−	953.755i		−	1.00713i	0.863956	−	0.503567i	$-0.167979\pi$
$948$	−1442.50			−1.52162
$949$	1178.23			1.24155
$950$		0			0
$951$	2848.96			2.99575
$952$		−	237.002i		−	0.248951i
$953$	248.522			0.260779			0.130389	−	0.991463i	$-0.458377\pi$
$953$	248.522			0.260779			0.130389	+	0.991463i	$0.458377\pi$
$954$			1056.25i			1.10718i
$955$		0			0
$956$	64.3981			0.0673620
$957$	−554.473			−0.579387
$958$	−1051.01			−1.09709
$959$	370.308			0.386140
$960$		0			0
$961$	875.349			0.910873
$962$	−1288.94			−1.33985
$963$	113.171			0.117519
$964$			79.6517i			0.0826263i
$965$		0			0
$966$	−369.327	−	1405.17i	−0.382326	−	1.45462i
$967$		−	1112.21i		−	1.15016i	−0.818096	−	0.575081i	$-0.804970\pi$
$967$		−	1112.21i		−	1.15016i	0.818096	−	0.575081i	$-0.195030\pi$
$968$		−	366.045i		−	0.378146i
$969$	−2013.04			−2.07745
$970$		0			0
$971$			548.535i			0.564918i	0.959279	+	0.282459i	$0.0911500\pi$
$971$			548.535i			0.564918i	−0.959279	+	0.282459i	$0.908850\pi$
$972$		−	523.495i		−	0.538575i
$973$	1152.20			1.18417
$974$	−518.692			−0.532538
$975$		0			0
$976$			222.837i			0.228317i
$977$	−262.933			−0.269122			−0.134561	−	0.990905i	$-0.542962\pi$
$977$	−262.933			−0.269122			−0.134561	+	0.990905i	$0.542962\pi$
$978$			140.439i			0.143599i
$979$	1657.29			1.69284
$980$		0			0
$981$			1446.34i			1.47435i
$982$		−	179.639i		−	0.182932i
$983$	−1516.23			−1.54245			−0.771226	−	0.636562i	$-0.780356\pi$
$983$	−1516.23			−1.54245			−0.771226	+	0.636562i	$0.780356\pi$
$984$	568.571			0.577816
$985$		0			0
$986$		−	92.9566i		−	0.0942765i
$987$	1450.24			1.46934
$988$	−1046.53			−1.05924
$989$	35.0872	+	133.495i	0.0354774	+	0.134980i
$990$		0			0
$991$	705.633			0.712042			0.356021	−	0.934478i	$-0.384133\pi$
$991$	705.633			0.712042			0.356021	+	0.934478i	$0.384133\pi$
$992$			242.411i			0.244366i
$993$			0.651084i			0.000655674i
$994$		−	1380.20i		−	1.38853i
$995$		0			0
$996$		−	732.297i		−	0.735238i
$997$			480.892i			0.482339i	0.970483	+	0.241169i	$0.0775310\pi$
$997$			480.892i			0.482339i	−0.970483	+	0.241169i	$0.922469\pi$
$998$			740.481i			0.741965i
$999$			3921.66i			3.92558i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1150.3.c.c.1149.3		32
5.2	odd	4		1150.3.d.b.551.16		16
5.3	odd	4		230.3.d.a.91.2	yes	16
5.4	even	2	inner	1150.3.c.c.1149.30		32
15.8	even	4		2070.3.c.a.91.10		16
20.3	even	4		1840.3.k.d.321.16		16
23.22	odd	2	inner	1150.3.c.c.1149.29		32
115.22	even	4		1150.3.d.b.551.15		16
115.68	even	4		230.3.d.a.91.1	✓	16
115.114	odd	2	inner	1150.3.c.c.1149.4		32
345.68	odd	4		2070.3.c.a.91.15		16
460.183	odd	4		1840.3.k.d.321.15		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.3.d.a.91.1	✓	16	115.68	even	4
230.3.d.a.91.2	yes	16	5.3	odd	4
1150.3.c.c.1149.3		32	1.1	even	1	trivial
1150.3.c.c.1149.4		32	115.114	odd	2	inner
1150.3.c.c.1149.29		32	23.22	odd	2	inner
1150.3.c.c.1149.30		32	5.4	even	2	inner
1150.3.d.b.551.15		16	115.22	even	4
1150.3.d.b.551.16		16	5.2	odd	4
1840.3.k.d.321.15		16	460.183	odd	4
1840.3.k.d.321.16		16	20.3	even	4
2070.3.c.a.91.10		16	15.8	even	4
2070.3.c.a.91.15		16	345.68	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:	\( N \)	\(=\)	\( 1150 = 2 \cdot 5^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1150.c (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-1.41421i q^{2} +5.41949i q^{3} -2.00000 q^{4} +7.66432 q^{6} +8.24199 q^{7} +2.82843i q^{8} -20.3709 q^{9} +O(q^{10})\)	\(q-1.41421i q^{2} +5.41949i q^{3} -2.00000 q^{4} +7.66432 q^{6} +8.24199 q^{7} +2.82843i q^{8} -20.3709 q^{9} -15.8246i q^{11} -10.8390i q^{12} +14.3219i q^{13} -11.6559i q^{14} +4.00000 q^{16} -10.1666 q^{17} +28.8088i q^{18} -36.5359i q^{19} +44.6674i q^{21} -22.3793 q^{22} +(-5.84663 - 22.2445i) q^{23} -15.3286 q^{24} +20.2543 q^{26} -61.6245i q^{27} -16.4840 q^{28} -6.46533 q^{29} -42.8526 q^{31} -5.65685i q^{32} +85.7611 q^{33} +14.3777i q^{34} +40.7418 q^{36} -63.6379 q^{37} -51.6696 q^{38} -77.6175 q^{39} -37.0921 q^{41} +63.1692 q^{42} -6.00126 q^{43} +31.6491i q^{44} +(-31.4584 + 8.26838i) q^{46} -32.4676i q^{47} +21.6780i q^{48} +18.9303 q^{49} -55.0977i q^{51} -28.6438i q^{52} +36.6640 q^{53} -87.1502 q^{54} +23.3119i q^{56} +198.006 q^{57} +9.14336i q^{58} -6.65851 q^{59} +55.7093i q^{61} +60.6028i q^{62} -167.897 q^{63} -8.00000 q^{64} -121.284i q^{66} +4.45984 q^{67} +20.3331 q^{68} +(120.554 - 31.6858i) q^{69} +118.412 q^{71} -57.6176i q^{72} -82.2675i q^{73} +89.9976i q^{74} +73.0718i q^{76} -130.426i q^{77} +109.768i q^{78} -133.084i q^{79} +150.636 q^{81} +52.4561i q^{82} +67.5614 q^{83} -89.3348i q^{84} +8.48707i q^{86} -35.0388i q^{87} +44.7586 q^{88} +104.729i q^{89} +118.041i q^{91} +(11.6933 + 44.4890i) q^{92} -232.240i q^{93} -45.9161 q^{94} +30.6573 q^{96} -98.6666 q^{97} -26.7715i q^{98} +322.360i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 64 q^{4} - 16 q^{6} - 128 q^{9}+O(q^{10}) \) 32 * q - 64 * q^4 - 16 * q^6 - 128 * q^9	\( 32 q - 64 q^{4} - 16 q^{6} - 128 q^{9} + 128 q^{16} + 32 q^{24} + 192 q^{26} + 216 q^{29} - 232 q^{31} + 256 q^{36} - 496 q^{39} - 312 q^{41} - 248 q^{46} + 56 q^{49} - 448 q^{54} - 408 q^{59} - 256 q^{64} + 536 q^{69} + 472 q^{71} - 272 q^{81} + 432 q^{94} - 64 q^{96}+O(q^{100}) \) 32 * q - 64 * q^4 - 16 * q^6 - 128 * q^9 + 128 * q^16 + 32 * q^24 + 192 * q^26 + 216 * q^29 - 232 * q^31 + 256 * q^36 - 496 * q^39 - 312 * q^41 - 248 * q^46 + 56 * q^49 - 448 * q^54 - 408 * q^59 - 256 * q^64 + 536 * q^69 + 472 * q^71 - 272 * q^81 + 432 * q^94 - 64 * q^96

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