LMFDB - Embedded newform 1078.2.c.b.1077.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1078,2,Mod(1077,1078)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1078, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("1078.1077");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1078 = 2 \cdot 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1078.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:	$8.60787333789$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 6 x^{15} + 18 x^{14} - 36 x^{13} + 34 x^{12} + 18 x^{11} - 72 x^{10} + 132 x^{9} - 93 x^{8} + \cdots + 1 $ x^16 - 6x^15 + 18x^14 - 36x^13 + 34x^12 + 18x^11 - 72x^10 + 132x^9 - 93x^8 - 102x^7 + 144x^6 - 432x^5 + 502x^4 + 288x^3 + 72x^2 + 12*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{12} $
Twist minimal:	no (minimal twist has level 154)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1077.14
Root			$-0.347596 - 1.29724i$ of defining polynomial
Character	$\chi$	$=$	1078.1077
Dual form			1078.2.c.b.1077.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +1.55924i q^{3} -1.00000 q^{4} -1.01909i q^{5} -1.55924 q^{6} -1.00000i q^{8} +0.568783 q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +1.55924i q^{3} -1.00000 q^{4} -1.01909i q^{5} -1.55924 q^{6} -1.00000i q^{8} +0.568783 q^{9} +1.01909 q^{10} +(3.09335 + 1.19633i) q^{11} -1.55924i q^{12} -0.167247 q^{13} +1.58900 q^{15} +1.00000 q^{16} +2.95232 q^{17} +0.568783i q^{18} +0.311700 q^{19} +1.01909i q^{20} +(-1.19633 + 3.09335i) q^{22} -0.475438 q^{23} +1.55924 q^{24} +3.96145 q^{25} -0.167247i q^{26} +5.56458i q^{27} +1.89701i q^{29} +1.58900i q^{30} -2.54997i q^{31} +1.00000i q^{32} +(-1.86537 + 4.82325i) q^{33} +2.95232i q^{34} -0.568783 q^{36} +6.09335 q^{37} +0.311700i q^{38} -0.260777i q^{39} -1.01909 q^{40} -10.2084 q^{41} +10.1222i q^{43} +(-3.09335 - 1.19633i) q^{44} -0.579642i q^{45} -0.475438i q^{46} +3.79859i q^{47} +1.55924i q^{48} +3.96145i q^{50} +4.60336i q^{51} +0.167247 q^{52} +8.42157 q^{53} -5.56458 q^{54} +(1.21917 - 3.15240i) q^{55} +0.486014i q^{57} -1.89701 q^{58} +6.24251i q^{59} -1.58900 q^{60} -11.8792 q^{61} +2.54997 q^{62} -1.00000 q^{64} +0.170440i q^{65} +(-4.82325 - 1.86537i) q^{66} -10.3830 q^{67} -2.95232 q^{68} -0.741321i q^{69} +14.5206 q^{71} -0.568783i q^{72} +9.70771 q^{73} +6.09335i q^{74} +6.17684i q^{75} -0.311700 q^{76} +0.260777 q^{78} -7.00567i q^{79} -1.01909i q^{80} -6.97014 q^{81} -10.2084i q^{82} -14.6915 q^{83} -3.00868i q^{85} -10.1222 q^{86} -2.95789 q^{87} +(1.19633 - 3.09335i) q^{88} -6.90094i q^{89} +0.579642 q^{90} +0.475438 q^{92} +3.97600 q^{93} -3.79859 q^{94} -0.317651i q^{95} -1.55924 q^{96} -11.0218i q^{97} +(1.75944 + 0.680455i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 16 q^{4} - 32 q^{9}+O(q^{10}) $ 16 * q - 16 * q^4 - 32 * q^9	$ 16 q - 16 q^{4} - 32 q^{9} - 16 q^{11} - 8 q^{15} + 16 q^{16} - 8 q^{22} - 32 q^{23} + 32 q^{36} + 32 q^{37} + 16 q^{44} + 56 q^{53} + 24 q^{58} + 8 q^{60} - 16 q^{64} - 24 q^{67} + 8 q^{71} - 16 q^{78} + 16 q^{81} - 40 q^{86} + 8 q^{88} + 32 q^{92} + 88 q^{93} + 56 q^{99}+O(q^{100}) $ 16 * q - 16 * q^4 - 32 * q^9 - 16 * q^11 - 8 * q^15 + 16 * q^16 - 8 * q^22 - 32 * q^23 + 32 * q^36 + 32 * q^37 + 16 * q^44 + 56 * q^53 + 24 * q^58 + 8 * q^60 - 16 * q^64 - 24 * q^67 + 8 * q^71 - 16 * q^78 + 16 * q^81 - 40 * q^86 + 8 * q^88 + 32 * q^92 + 88 * q^93 + 56 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1078\mathbb{Z}\right)^\times$.

$n$	$199$	$981$
$\chi(n)$	$-1$	$-1$

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 $

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$			1.55924i			0.900225i	0.892972	+	0.450113i	$0.148616\pi$
$3$			1.55924i			0.900225i	−0.892972	+	0.450113i	$0.851384\pi$
$4$	−1.00000			−0.500000
$5$		−	1.01909i		−	0.455752i	−0.973690	−	0.227876i	$-0.926822\pi$
$5$		−	1.01909i		−	0.455752i	0.973690	−	0.227876i	$-0.0731780\pi$
$6$	−1.55924			−0.636555
$7$		0			0
$7$		0			0
$8$		−	1.00000i		−	0.353553i
$9$	0.568783			0.189594
$10$	1.01909			0.322265
$11$	3.09335	+	1.19633i	0.932679	+	0.360708i
$11$	3.09335	+	1.19633i	0.932679	+	0.360708i
$12$		−	1.55924i		−	0.450113i
$13$	−0.167247			−0.0463859			−0.0231929	−	0.999731i	$-0.507383\pi$
$13$	−0.167247			−0.0463859			−0.0231929	+	0.999731i	$0.507383\pi$
$14$		0			0
$15$	1.58900			0.410279
$16$	1.00000			0.250000
$17$	2.95232			0.716042			0.358021	−	0.933713i	$-0.383452\pi$
$17$	2.95232			0.716042			0.358021	+	0.933713i	$0.383452\pi$
$18$			0.568783i			0.134064i
$19$	0.311700			0.0715090			0.0357545	−	0.999361i	$-0.488617\pi$
$19$	0.311700			0.0715090			0.0357545	+	0.999361i	$0.488617\pi$
$20$			1.01909i			0.227876i
$21$		0			0
$22$	−1.19633	+	3.09335i	−0.255059	+	0.659503i
$23$	−0.475438			−0.0991358			−0.0495679	−	0.998771i	$-0.515784\pi$
$23$	−0.475438			−0.0991358			−0.0495679	+	0.998771i	$0.515784\pi$
$24$	1.55924			0.318278
$25$	3.96145			0.792291
$26$		−	0.167247i		−	0.0327998i
$27$			5.56458i			1.07090i
$28$		0			0
$29$			1.89701i			0.352266i	0.984366	+	0.176133i	$0.0563589\pi$
$29$			1.89701i			0.352266i	−0.984366	+	0.176133i	$0.943641\pi$
$30$			1.58900i			0.290111i
$31$		−	2.54997i		−	0.457987i	−0.973428	−	0.228994i	$-0.926456\pi$
$31$		−	2.54997i		−	0.457987i	0.973428	−	0.228994i	$-0.0735435\pi$
$32$			1.00000i			0.176777i
$33$	−1.86537	+	4.82325i	−0.324719	+	0.839621i
$34$			2.95232i			0.506318i
$35$		0			0
$36$	−0.568783			−0.0947972
$37$	6.09335			1.00174			0.500870	−	0.865523i	$-0.333014\pi$
$37$	6.09335			1.00174			0.500870	+	0.865523i	$0.333014\pi$
$38$			0.311700i			0.0505645i
$39$		−	0.260777i		−	0.0417577i
$40$	−1.01909			−0.161132
$41$	−10.2084			−1.59428			−0.797138	−	0.603797i	$-0.793654\pi$
$41$	−10.2084			−1.59428			−0.797138	+	0.603797i	$0.793654\pi$
$42$		0			0
$43$			10.1222i			1.54363i	0.635848	+	0.771814i	$0.280650\pi$
$43$			10.1222i			1.54363i	−0.635848	+	0.771814i	$0.719350\pi$
$44$	−3.09335	−	1.19633i	−0.466339	−	0.180354i
$45$		−	0.579642i		−	0.0864080i
$46$		−	0.475438i		−	0.0700996i
$47$			3.79859i			0.554082i	0.960858	+	0.277041i	$0.0893538\pi$
$47$			3.79859i			0.554082i	−0.960858	+	0.277041i	$0.910646\pi$
$48$			1.55924i			0.225056i
$49$		0			0
$50$			3.96145i			0.560234i
$51$			4.60336i			0.644599i
$52$	0.167247			0.0231929
$53$	8.42157			1.15679			0.578396	−	0.815756i	$-0.303679\pi$
$53$	8.42157			1.15679			0.578396	+	0.815756i	$0.303679\pi$
$54$	−5.56458			−0.757243
$55$	1.21917	−	3.15240i	0.164393	−	0.425070i
$56$		0			0
$57$			0.486014i			0.0643742i
$58$	−1.89701			−0.249090
$59$			6.24251i			0.812706i	0.913716	+	0.406353i	$0.133200\pi$
$59$			6.24251i			0.812706i	−0.913716	+	0.406353i	$0.866800\pi$
$60$	−1.58900			−0.205140
$61$	−11.8792			−1.52098			−0.760488	−	0.649352i	$-0.775040\pi$
$61$	−11.8792			−1.52098			−0.760488	+	0.649352i	$0.775040\pi$
$62$	2.54997			0.323846
$63$		0			0
$64$	−1.00000			−0.125000
$65$			0.170440i			0.0211404i
$66$	−4.82325	−	1.86537i	−0.593702	−	0.229611i
$67$	−10.3830			−1.26849			−0.634244	−	0.773133i	$-0.718689\pi$
$67$	−10.3830			−1.26849			−0.634244	+	0.773133i	$0.718689\pi$
$68$	−2.95232			−0.358021
$69$		−	0.741321i		−	0.0892445i
$70$		0			0
$71$	14.5206			1.72328			0.861639	−	0.507522i	$-0.169439\pi$
$71$	14.5206			1.72328			0.861639	+	0.507522i	$0.169439\pi$
$72$		−	0.568783i		−	0.0670318i
$73$	9.70771			1.13620			0.568101	−	0.822959i	$-0.307678\pi$
$73$	9.70771			1.13620			0.568101	+	0.822959i	$0.307678\pi$
$74$			6.09335i			0.708337i
$75$			6.17684i			0.713240i
$76$	−0.311700			−0.0357545
$77$		0			0
$78$	0.260777			0.0295272
$79$		−	7.00567i		−	0.788200i	−0.919068	−	0.394100i	$-0.871056\pi$
$79$		−	7.00567i		−	0.788200i	0.919068	−	0.394100i	$-0.128944\pi$
$80$		−	1.01909i		−	0.113938i
$81$	−6.97014			−0.774459
$82$		−	10.2084i		−	1.12732i
$83$	−14.6915			−1.61261			−0.806303	−	0.591502i	$-0.798535\pi$
$83$	−14.6915			−1.61261			−0.806303	+	0.591502i	$0.798535\pi$
$84$		0			0
$85$		−	3.00868i		−	0.326337i
$86$	−10.1222			−1.09151
$87$	−2.95789			−0.317119
$88$	1.19633	−	3.09335i	0.127530	−	0.329752i
$89$		−	6.90094i		−	0.731498i	−0.930714	−	0.365749i	$-0.880813\pi$
$89$		−	6.90094i		−	0.731498i	0.930714	−	0.365749i	$-0.119187\pi$
$90$	0.579642			0.0610997
$91$		0			0
$92$	0.475438			0.0495679
$93$	3.97600			0.412292
$94$	−3.79859			−0.391795
$95$		−	0.317651i		−	0.0325903i
$96$	−1.55924			−0.159139
$97$		−	11.0218i		−	1.11909i	−0.828799	−	0.559547i	$-0.810975\pi$
$97$		−	11.0218i		−	1.11909i	0.828799	−	0.559547i	$-0.189025\pi$
$98$		0			0
$99$	1.75944	+	0.680455i	0.176831	+	0.0683883i
$100$	−3.96145			−0.396145
$101$	5.33504			0.530856			0.265428	−	0.964131i	$-0.414487\pi$
$101$	5.33504			0.530856			0.265428	+	0.964131i	$0.414487\pi$
$102$	−4.60336			−0.455801
$103$			12.4533i			1.22706i	0.789672	+	0.613529i	$0.210251\pi$
$103$			12.4533i			1.22706i	−0.789672	+	0.613529i	$0.789749\pi$
$104$			0.167247i			0.0163999i
$105$		0			0
$106$			8.42157i			0.817975i
$107$		−	7.25414i		−	0.701284i	−0.936510	−	0.350642i	$-0.885963\pi$
$107$		−	7.25414i		−	0.701284i	0.936510	−	0.350642i	$-0.114037\pi$
$108$		−	5.56458i		−	0.535452i
$109$			1.16743i			0.111820i	0.998436	+	0.0559098i	$0.0178059\pi$
$109$			1.16743i			0.111820i	−0.998436	+	0.0559098i	$0.982194\pi$
$110$	3.15240	+	1.21917i	0.300570	+	0.116244i
$111$			9.50096i			0.901791i
$112$		0			0
$113$	−8.40135			−0.790333			−0.395166	−	0.918610i	$-0.629313\pi$
$113$	−8.40135			−0.790333			−0.395166	+	0.918610i	$0.629313\pi$
$114$	−0.486014			−0.0455194
$115$			0.484515i			0.0451813i
$116$		−	1.89701i		−	0.176133i
$117$	−0.0951271			−0.00879450
$118$	−6.24251			−0.574670
$119$		0			0
$120$		−	1.58900i		−	0.145056i
$121$	8.13757	+	7.40135i	0.739779	+	0.672850i
$122$		−	11.8792i		−	1.07549i
$123$		−	15.9172i		−	1.43521i
$124$			2.54997i			0.228994i
$125$		−	9.13254i		−	0.816839i
$126$		0			0
$127$		−	3.53324i		−	0.313525i	−0.987636	−	0.156762i	$-0.949894\pi$
$127$		−	3.53324i		−	0.313525i	0.987636	−	0.156762i	$-0.0501057\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	−15.7830			−1.38961
$130$	−0.170440			−0.0149485
$131$	13.9797			1.22141			0.610705	−	0.791858i	$-0.290886\pi$
$131$	13.9797			1.22141			0.610705	+	0.791858i	$0.290886\pi$
$132$	1.86537	−	4.82325i	0.162359	−	0.419810i
$133$		0			0
$134$		−	10.3830i		−	0.896957i
$135$	5.67081			0.488066
$136$		−	2.95232i		−	0.253159i
$137$	−7.01058			−0.598954			−0.299477	−	0.954104i	$-0.596812\pi$
$137$	−7.01058			−0.598954			−0.299477	+	0.954104i	$0.596812\pi$
$138$	0.741321			0.0631054
$139$	11.4615			0.972148			0.486074	−	0.873918i	$-0.338429\pi$
$139$	11.4615			0.972148			0.486074	+	0.873918i	$0.338429\pi$
$140$		0			0
$141$	−5.92291			−0.498799
$142$			14.5206i			1.21854i
$143$	−0.517352	−	0.200083i	−0.0432631	−	0.0167318i
$144$	0.568783			0.0473986
$145$	1.93323			0.160546
$146$			9.70771i			0.803416i
$147$		0			0
$148$	−6.09335			−0.500870
$149$		−	14.1568i		−	1.15977i	−0.814698	−	0.579886i	$-0.803097\pi$
$149$		−	14.1568i		−	1.15977i	0.814698	−	0.579886i	$-0.196903\pi$
$150$	−6.17684			−0.504337
$151$			23.3040i			1.89646i	0.317591	+	0.948228i	$0.397126\pi$
$151$			23.3040i			1.89646i	−0.317591	+	0.948228i	$0.602874\pi$
$152$		−	0.311700i		−	0.0252822i
$153$	1.67923			0.135758
$154$		0			0
$155$	−2.59865			−0.208728
$156$			0.260777i			0.0208789i
$157$			4.03261i			0.321837i	0.986968	+	0.160919i	$0.0514456\pi$
$157$			4.03261i			0.321837i	−0.986968	+	0.160919i	$0.948554\pi$
$158$	7.00567			0.557342
$159$			13.1312i			1.04137i
$160$	1.01909			0.0805662
$161$		0			0
$162$		−	6.97014i		−	0.547626i
$163$	−5.53988			−0.433917			−0.216958	−	0.976181i	$-0.569614\pi$
$163$	−5.53988			−0.433917			−0.216958	+	0.976181i	$0.569614\pi$
$164$	10.2084			0.797138
$165$	4.91534	+	1.90098i	0.382658	+	0.147991i
$166$		−	14.6915i		−	1.14029i
$167$	21.2252			1.64245			0.821226	−	0.570603i	$-0.193291\pi$
$167$	21.2252			1.64245			0.821226	+	0.570603i	$0.193291\pi$
$168$		0			0
$169$	−12.9720			−0.997848
$170$	3.00868			0.230755
$171$	0.177290			0.0135577
$172$		−	10.1222i		−	0.771814i
$173$	15.0655			1.14541			0.572706	−	0.819761i	$-0.305894\pi$
$173$	15.0655			1.14541			0.572706	+	0.819761i	$0.305894\pi$
$174$		−	2.95789i		−	0.224237i
$175$		0			0
$176$	3.09335	+	1.19633i	0.233170	+	0.0901771i
$177$	−9.73355			−0.731618
$178$	6.90094			0.517247
$179$	−2.16176			−0.161577			−0.0807887	−	0.996731i	$-0.525744\pi$
$179$	−2.16176			−0.161577			−0.0807887	+	0.996731i	$0.525744\pi$
$180$			0.579642i			0.0432040i
$181$		−	5.39285i		−	0.400848i	−0.979709	−	0.200424i	$-0.935768\pi$
$181$		−	5.39285i		−	0.400848i	0.979709	−	0.200424i	$-0.0642319\pi$
$182$		0			0
$183$		−	18.5225i		−	1.36922i
$184$			0.475438i			0.0350498i
$185$		−	6.20968i		−	0.456544i
$186$			3.97600i			0.291534i
$187$	9.13254	+	3.53196i	0.667837	+	0.258283i
$188$		−	3.79859i		−	0.277041i
$189$		0			0
$190$	0.317651			0.0230448
$191$	6.00000			0.434145			0.217072	−	0.976156i	$-0.430349\pi$
$191$	6.00000			0.434145			0.217072	+	0.976156i	$0.430349\pi$
$192$		−	1.55924i		−	0.112528i
$193$			9.59958i			0.690993i	0.938420	+	0.345496i	$0.112289\pi$
$193$			9.59958i			0.690993i	−0.938420	+	0.345496i	$0.887711\pi$
$194$	11.0218			0.791319
$195$	−0.265756			−0.0190311
$196$		0			0
$197$			14.8180i			1.05574i	0.849325	+	0.527870i	$0.177009\pi$
$197$			14.8180i			1.05574i	−0.849325	+	0.527870i	$0.822991\pi$
$198$	−0.680455	+	1.75944i	−0.0483579	+	0.125038i
$199$			4.11030i			0.291371i	0.989331	+	0.145686i	$0.0465388\pi$
$199$			4.11030i			0.291371i	−0.989331	+	0.145686i	$0.953461\pi$
$200$		−	3.96145i		−	0.280117i
$201$		−	16.1896i		−	1.14193i
$202$			5.33504i			0.375372i
$203$		0			0
$204$		−	4.60336i		−	0.322300i
$205$			10.4032i			0.726594i
$206$	−12.4533			−0.867661
$207$	−0.270422			−0.0187956
$208$	−0.167247			−0.0115965
$209$	0.964197	+	0.372898i	0.0666949	+	0.0257939i
$210$		0			0
$211$		−	7.52456i		−	0.518012i	−0.965876	−	0.259006i	$-0.916605\pi$
$211$		−	7.52456i		−	0.518012i	0.965876	−	0.259006i	$-0.0833950\pi$
$212$	−8.42157			−0.578396
$213$			22.6410i			1.55134i
$214$	7.25414			0.495883
$215$	10.3155			0.703511
$216$	5.56458			0.378621
$217$		0			0
$218$	−1.16743			−0.0790685
$219$			15.1366i			1.02284i
$220$	−1.21917	+	3.15240i	−0.0821967	+	0.212535i
$221$	−0.493765			−0.0332142
$222$	−9.50096			−0.637663
$223$		−	13.5885i		−	0.909951i	−0.890504	−	0.454975i	$-0.849648\pi$
$223$		−	13.5885i		−	0.909951i	0.890504	−	0.454975i	$-0.150352\pi$
$224$		0			0
$225$	2.25321			0.150214
$226$		−	8.40135i		−	0.558850i
$227$	21.6635			1.43786			0.718929	−	0.695084i	$-0.244633\pi$
$227$	21.6635			1.43786			0.718929	+	0.695084i	$0.244633\pi$
$228$		−	0.486014i		−	0.0321871i
$229$		−	30.0632i		−	1.98663i	−0.115421	−	0.993317i	$-0.536822\pi$
$229$		−	30.0632i		−	1.98663i	0.115421	−	0.993317i	$-0.463178\pi$
$230$	−0.484515			−0.0319480
$231$		0			0
$232$	1.89701			0.124545
$233$		−	16.1916i		−	1.06075i	−0.847764	−	0.530373i	$-0.822052\pi$
$233$		−	16.1916i		−	1.06075i	0.847764	−	0.530373i	$-0.177948\pi$
$234$		−	0.0951271i		−	0.00621865i
$235$	3.87112			0.252524
$236$		−	6.24251i		−	0.406353i
$237$	10.9235			0.709558
$238$		0			0
$239$		−	26.0701i		−	1.68633i	−0.537652	−	0.843167i	$-0.680689\pi$
$239$		−	26.0701i		−	1.68633i	0.537652	−	0.843167i	$-0.319311\pi$
$240$	1.58900			0.102570
$241$	−13.2044			−0.850572			−0.425286	−	0.905059i	$-0.639827\pi$
$241$	−13.2044			−0.850572			−0.425286	+	0.905059i	$0.639827\pi$
$242$	−7.40135	+	8.13757i	−0.475777	+	0.523103i
$243$			5.82564i			0.373715i
$244$	11.8792			0.760488
$245$		0			0
$246$	15.9172			1.01485
$247$	−0.0521308			−0.00331700
$248$	−2.54997			−0.161923
$249$		−	22.9076i		−	1.45171i
$250$	9.13254			0.577593
$251$			28.9829i			1.82939i	0.404149	+	0.914693i	$0.367568\pi$
$251$			28.9829i			1.82939i	−0.404149	+	0.914693i	$0.632432\pi$
$252$		0			0
$253$	−1.47070	−	0.568783i	−0.0924618	−	0.0357591i
$254$	3.53324			0.221695
$255$	4.69125			0.293777
$256$	1.00000			0.0625000
$257$		−	6.98602i		−	0.435776i	−0.975974	−	0.217888i	$-0.930083\pi$
$257$		−	6.98602i		−	0.435776i	0.975974	−	0.217888i	$-0.0699167\pi$
$258$		−	15.7830i		−	0.982605i
$259$		0			0
$260$		−	0.170440i		−	0.0105702i
$261$			1.07899i			0.0667877i
$262$			13.9797i			0.863668i
$263$		−	4.47070i		−	0.275675i	−0.990455	−	0.137837i	$-0.955985\pi$
$263$		−	4.47070i		−	0.275675i	0.990455	−	0.137837i	$-0.0440152\pi$
$264$	4.82325	+	1.86537i	0.296851	+	0.114805i
$265$		−	8.58235i		−	0.527210i
$266$		0			0
$267$	10.7602			0.658513
$268$	10.3830			0.634244
$269$			2.21730i			0.135191i	0.997713	+	0.0675956i	$0.0215328\pi$
$269$			2.21730i			0.135191i	−0.997713	+	0.0675956i	$0.978467\pi$
$270$			5.67081i			0.345115i
$271$	−22.5122			−1.36752			−0.683759	−	0.729708i	$-0.739656\pi$
$271$	−22.5122			−1.36752			−0.683759	+	0.729708i	$0.739656\pi$
$272$	2.95232			0.179011
$273$		0			0
$274$		−	7.01058i		−	0.423524i
$275$	12.2541	+	4.73922i	0.738952	+	0.285786i
$276$			0.741321i			0.0446223i
$277$		−	24.4658i		−	1.47001i	−0.678063	−	0.735004i	$-0.737180\pi$
$277$		−	24.4658i		−	1.47001i	0.678063	−	0.735004i	$-0.262820\pi$
$278$			11.4615i			0.687413i
$279$		−	1.45038i		−	0.0868319i
$280$		0			0
$281$		−	11.3532i		−	0.677273i	−0.940917	−	0.338636i	$-0.890034\pi$
$281$		−	11.3532i		−	0.677273i	0.940917	−	0.338636i	$-0.109966\pi$
$282$		−	5.92291i		−	0.352704i
$283$	−21.6537			−1.28718			−0.643589	−	0.765371i	$-0.722555\pi$
$283$	−21.6537			−1.28718			−0.643589	+	0.765371i	$0.722555\pi$
$284$	−14.5206			−0.861639
$285$	0.495293			0.0293386
$286$	0.200083	−	0.517352i	0.0118312	−	0.0305916i
$287$		0			0
$288$			0.568783i			0.0335159i
$289$	−8.28382			−0.487283
$290$			1.93323i			0.113523i
$291$	17.1856			1.00744
$292$	−9.70771			−0.568101
$293$	12.1233			0.708249			0.354124	−	0.935198i	$-0.384779\pi$
$293$	12.1233			0.708249			0.354124	+	0.935198i	$0.384779\pi$
$294$		0			0
$295$	6.36169			0.370392
$296$		−	6.09335i		−	0.354168i
$297$	−6.65709	+	17.2132i	−0.386284	+	0.998808i
$298$	14.1568			0.820083
$299$	0.0795155			0.00459850
$300$		−	6.17684i		−	0.356620i
$301$		0			0
$302$	−23.3040			−1.34100
$303$			8.31858i			0.477890i
$304$	0.311700			0.0178772
$305$			12.1060i			0.693187i
$306$			1.67923i			0.0959952i
$307$	9.65817			0.551221			0.275610	−	0.961269i	$-0.411120\pi$
$307$	9.65817			0.551221			0.275610	+	0.961269i	$0.411120\pi$
$308$		0			0
$309$	−19.4176			−1.10463
$310$		−	2.59865i		−	0.147593i
$311$		−	17.6778i		−	1.00242i	−0.865327	−	0.501208i	$-0.832889\pi$
$311$		−	17.6778i		−	1.00242i	0.865327	−	0.501208i	$-0.167111\pi$
$312$	−0.260777			−0.0147636
$313$			28.8103i			1.62846i	0.580545	+	0.814228i	$0.302839\pi$
$313$			28.8103i			1.62846i	−0.580545	+	0.814228i	$0.697161\pi$
$314$	−4.03261			−0.227573
$315$		0			0
$316$			7.00567i			0.394100i
$317$	10.3456			0.581066			0.290533	−	0.956865i	$-0.406167\pi$
$317$	10.3456			0.581066			0.290533	+	0.956865i	$0.406167\pi$
$318$	−13.1312			−0.736362
$319$	−2.26946	+	5.86811i	−0.127065	+	0.328551i
$320$			1.01909i			0.0569689i
$321$	11.3109			0.631314
$322$		0			0
$323$	0.920239			0.0512034
$324$	6.97014			0.387230
$325$	−0.662540			−0.0367511
$326$		−	5.53988i		−	0.306826i
$327$	−1.82030			−0.100663
$328$			10.2084i			0.563662i
$329$		0			0
$330$	−1.90098	+	4.91534i	−0.104646	+	0.270580i
$331$	−26.8448			−1.47553			−0.737763	−	0.675060i	$-0.764118\pi$
$331$	−26.8448			−1.47553			−0.737763	+	0.675060i	$0.764118\pi$
$332$	14.6915			0.806303
$333$	3.46579			0.189924
$334$			21.2252i			1.16139i
$335$			10.5813i			0.578116i
$336$		0			0
$337$			14.5505i			0.792614i	0.918118	+	0.396307i	$0.129708\pi$
$337$			14.5505i			0.792614i	−0.918118	+	0.396307i	$0.870292\pi$
$338$		−	12.9720i		−	0.705585i
$339$		−	13.0997i		−	0.711477i
$340$			3.00868i			0.163169i
$341$	3.05061	−	7.88792i	0.165200	−	0.427155i
$342$			0.177290i			0.00958674i
$343$		0			0
$344$	10.1222			0.545755
$345$	−0.755474			−0.0406733
$346$			15.0655i			0.809928i
$347$		−	28.5417i		−	1.53220i	−0.642721	−	0.766101i	$-0.722194\pi$
$347$		−	28.5417i		−	1.53220i	0.642721	−	0.766101i	$-0.277806\pi$
$348$	2.95789			0.158559
$349$	−34.6026			−1.85224			−0.926118	−	0.377235i	$-0.876875\pi$
$349$	−34.6026			−1.85224			−0.926118	+	0.377235i	$0.876875\pi$
$350$		0			0
$351$		−	0.930656i		−	0.0496748i
$352$	−1.19633	+	3.09335i	−0.0637648	+	0.164876i
$353$		−	16.9203i		−	0.900579i	−0.892883	−	0.450289i	$-0.851321\pi$
$353$		−	16.9203i		−	0.900579i	0.892883	−	0.450289i	$-0.148679\pi$
$354$		−	9.73355i		−	0.517332i
$355$		−	14.7978i		−	0.785386i
$356$			6.90094i			0.365749i
$357$		0			0
$358$		−	2.16176i		−	0.114252i
$359$		−	30.3511i		−	1.60187i	−0.598752	−	0.800934i	$-0.704337\pi$
$359$		−	30.3511i		−	1.60187i	0.598752	−	0.800934i	$-0.295663\pi$
$360$	−0.579642			−0.0305498
$361$	−18.9028			−0.994886
$362$	5.39285			0.283442
$363$	−11.5405	+	12.6884i	−0.605717	+	0.665968i
$364$		0			0
$365$		−	9.89304i		−	0.517825i
$366$	18.5225			0.968186
$367$		−	17.4215i		−	0.909395i	−0.890646	−	0.454698i	$-0.849747\pi$
$367$		−	17.4215i		−	0.909395i	0.890646	−	0.454698i	$-0.150253\pi$
$368$	−0.475438			−0.0247839
$369$	−5.80634			−0.302266
$370$	6.20968			0.322826
$371$		0			0
$372$	−3.97600			−0.206146
$373$		−	9.15211i		−	0.473878i	−0.971524	−	0.236939i	$-0.923856\pi$
$373$		−	9.15211i		−	0.473878i	0.971524	−	0.236939i	$-0.0761442\pi$
$374$	−3.53196	+	9.13254i	−0.182633	+	0.472232i
$375$	14.2398			0.735339
$376$	3.79859			0.195898
$377$		−	0.317269i		−	0.0163402i
$378$		0			0
$379$	−6.15382			−0.316100			−0.158050	−	0.987431i	$-0.550521\pi$
$379$	−6.15382			−0.316100			−0.158050	+	0.987431i	$0.550521\pi$
$380$			0.317651i			0.0162952i
$381$	5.50916			0.282243
$382$			6.00000i			0.306987i
$383$		−	12.9651i		−	0.662484i	−0.943546	−	0.331242i	$-0.892532\pi$
$383$		−	12.9651i		−	0.662484i	0.943546	−	0.331242i	$-0.107468\pi$
$384$	1.55924			0.0795694
$385$		0			0
$386$	−9.59958			−0.488606
$387$			5.75737i			0.292663i
$388$			11.0218i			0.559547i
$389$	5.16647			0.261950			0.130975	−	0.991386i	$-0.458189\pi$
$389$	5.16647			0.261950			0.130975	+	0.991386i	$0.458189\pi$
$390$		−	0.265756i		−	0.0134571i
$391$	−1.40365			−0.0709854
$392$		0			0
$393$			21.7976i			1.09954i
$394$	−14.8180			−0.746521
$395$	−7.13942			−0.359223
$396$	−1.75944	−	0.680455i	−0.0884154	−	0.0341942i
$397$		−	9.25712i		−	0.464602i	−0.972644	−	0.232301i	$-0.925375\pi$
$397$		−	9.25712i		−	0.464602i	0.972644	−	0.232301i	$-0.0746254\pi$
$398$	−4.11030			−0.206030
$399$		0			0
$400$	3.96145			0.198073
$401$	−30.9248			−1.54431			−0.772155	−	0.635435i	$-0.780821\pi$
$401$	−30.9248			−1.54431			−0.772155	+	0.635435i	$0.780821\pi$
$402$	16.1896			0.807463
$403$			0.426473i			0.0212441i
$404$	−5.33504			−0.265428
$405$			7.10320i			0.352961i
$406$		0			0
$407$	18.8488	+	7.28968i	0.934301	+	0.361336i
$408$	4.60336			0.227900
$409$	23.8397			1.17880			0.589399	−	0.807842i	$-0.299365\pi$
$409$	23.8397			1.17880			0.589399	+	0.807842i	$0.299365\pi$
$410$	−10.4032			−0.513780
$411$		−	10.9311i		−	0.539193i
$412$		−	12.4533i		−	0.613529i
$413$		0			0
$414$		−	0.270422i		−	0.0132905i
$415$			14.9720i			0.734948i
$416$		−	0.167247i		−	0.00819994i
$417$			17.8711i			0.875152i
$418$	−0.372898	+	0.964197i	−0.0182390	+	0.0471604i
$419$			5.03426i			0.245940i	0.992410	+	0.122970i	$0.0392418\pi$
$419$			5.03426i			0.245940i	−0.992410	+	0.122970i	$0.960758\pi$
$420$		0			0
$421$	−16.9250			−0.824872			−0.412436	−	0.910987i	$-0.635322\pi$
$421$	−16.9250			−0.824872			−0.412436	+	0.910987i	$0.635322\pi$
$422$	7.52456			0.366290
$423$			2.16058i			0.105051i
$424$		−	8.42157i		−	0.408988i
$425$	11.6955			0.567314
$426$	−22.6410			−1.09696
$427$		0			0
$428$			7.25414i			0.350642i
$429$	0.311976	−	0.806673i	0.0150624	−	0.0389465i
$430$			10.3155i			0.497457i
$431$		−	5.99907i		−	0.288965i	−0.989507	−	0.144482i	$-0.953848\pi$
$431$		−	5.99907i		−	0.288965i	0.989507	−	0.144482i	$-0.0461517\pi$
$432$			5.56458i			0.267726i
$433$		−	36.1175i		−	1.73570i	−0.496829	−	0.867849i	$-0.665502\pi$
$433$		−	36.1175i		−	1.73570i	0.496829	−	0.867849i	$-0.334498\pi$
$434$		0			0
$435$			3.01436i			0.144527i
$436$		−	1.16743i		−	0.0559098i
$437$	−0.148194			−0.00708909
$438$	−15.1366			−0.723255
$439$	−11.3496			−0.541688			−0.270844	−	0.962623i	$-0.587303\pi$
$439$	−11.3496			−0.541688			−0.270844	+	0.962623i	$0.587303\pi$
$440$	−3.15240	−	1.21917i	−0.150285	−	0.0581219i
$441$		0			0
$442$		−	0.493765i		−	0.0234860i
$443$	−4.75076			−0.225715			−0.112858	−	0.993611i	$-0.536000\pi$
$443$	−4.75076			−0.225715			−0.112858	+	0.993611i	$0.536000\pi$
$444$		−	9.50096i		−	0.450896i
$445$	−7.03268			−0.333381
$446$	13.5885			0.643432
$447$	22.0738			1.04406
$448$		0			0
$449$	7.33297			0.346064			0.173032	−	0.984916i	$-0.444644\pi$
$449$	7.33297			0.346064			0.173032	+	0.984916i	$0.444644\pi$
$450$			2.25321i			0.106217i
$451$	−31.5780	−	12.2126i	−1.48695	−	0.575069i
$452$	8.40135			0.395166
$453$	−36.3365			−1.70724
$454$			21.6635i			1.01672i
$455$		0			0
$456$	0.486014			0.0227597
$457$			13.5176i			0.632326i	0.948705	+	0.316163i	$0.102395\pi$
$457$			13.5176i			0.632326i	−0.948705	+	0.316163i	$0.897605\pi$
$458$	30.0632			1.40476
$459$			16.4284i			0.766812i
$460$		−	0.484515i		−	0.0225906i
$461$	−18.5730			−0.865033			−0.432516	−	0.901626i	$-0.642374\pi$
$461$	−18.5730			−0.865033			−0.432516	+	0.901626i	$0.642374\pi$
$462$		0			0
$463$	28.2849			1.31451			0.657256	−	0.753667i	$-0.271717\pi$
$463$	28.2849			1.31451			0.657256	+	0.753667i	$0.271717\pi$
$464$			1.89701i			0.0880665i
$465$		−	4.05191i		−	0.187903i
$466$	16.1916			0.750061
$467$			21.5792i			0.998564i	0.866439	+	0.499282i	$0.166403\pi$
$467$			21.5792i			0.998564i	−0.866439	+	0.499282i	$0.833597\pi$
$468$	0.0951271			0.00439725
$469$		0			0
$470$			3.87112i			0.178561i
$471$	−6.28779			−0.289726
$472$	6.24251			0.287335
$473$	−12.1096	+	31.3116i	−0.556800	+	1.43971i
$474$			10.9235i			0.501733i
$475$	1.23479			0.0566559
$476$		0			0
$477$	4.79005			0.219321
$478$	26.0701			1.19242
$479$	6.93560			0.316896			0.158448	−	0.987367i	$-0.449351\pi$
$479$	6.93560			0.316896			0.158448	+	0.987367i	$0.449351\pi$
$480$			1.58900i			0.0725278i
$481$	−1.01909			−0.0464666
$482$		−	13.2044i		−	0.601445i
$483$		0			0
$484$	−8.13757	−	7.40135i	−0.369889	−	0.336425i
$485$	−11.2322			−0.510029
$486$	−5.82564			−0.264256
$487$	−12.1740			−0.551658			−0.275829	−	0.961207i	$-0.588952\pi$
$487$	−12.1740			−0.551658			−0.275829	+	0.961207i	$0.588952\pi$
$488$			11.8792i			0.537746i
$489$		−	8.63798i		−	0.390623i
$490$		0			0
$491$		−	2.37152i		−	0.107025i	−0.998567	−	0.0535125i	$-0.982958\pi$
$491$		−	2.37152i		−	0.107025i	0.998567	−	0.0535125i	$-0.0170417\pi$
$492$			15.9172i			0.717604i
$493$			5.60058i			0.252237i
$494$		−	0.0521308i		−	0.00234548i
$495$	0.693446	−	1.79303i	0.0311681	−	0.0805909i
$496$		−	2.54997i		−	0.114497i
$497$		0			0
$498$	22.9076			1.02651
$499$	−3.92892			−0.175883			−0.0879413	−	0.996126i	$-0.528029\pi$
$499$	−3.92892			−0.175883			−0.0879413	+	0.996126i	$0.528029\pi$
$500$			9.13254i			0.408420i
$501$			33.0950i			1.47858i
$502$	−28.9829			−1.29357
$503$	−19.8703			−0.885971			−0.442986	−	0.896529i	$-0.646081\pi$
$503$	−19.8703			−0.885971			−0.442986	+	0.896529i	$0.646081\pi$
$504$		0			0
$505$		−	5.43689i		−	0.241938i
$506$	0.568783	−	1.47070i	0.0252855	−	0.0653804i
$507$		−	20.2265i		−	0.898288i
$508$			3.53324i			0.156762i
$509$		−	15.2927i		−	0.677836i	−0.940816	−	0.338918i	$-0.889939\pi$
$509$		−	15.2927i		−	0.677836i	0.940816	−	0.338918i	$-0.110061\pi$
$510$			4.69125i			0.207732i
$511$		0			0
$512$			1.00000i			0.0441942i
$513$			1.73448i			0.0765792i
$514$	6.98602			0.308140
$515$	12.6910			0.559234
$516$	15.7830			0.694807
$517$	−4.54439	+	11.7504i	−0.199862	+	0.516780i
$518$		0			0
$519$			23.4907i			1.03113i
$520$	0.170440			0.00747427
$521$		−	0.140713i		−	0.00616475i	−0.999995	−	0.00308237i	$-0.999019\pi$
$521$		−	0.140713i		−	0.00616475i	0.999995	−	0.00308237i	$-0.000981152\pi$
$522$	−1.07899			−0.0472260
$523$	9.12307			0.398924			0.199462	−	0.979906i	$-0.436081\pi$
$523$	9.12307			0.398924			0.199462	+	0.979906i	$0.436081\pi$
$524$	−13.9797			−0.610705
$525$		0			0
$526$	4.47070			0.194932
$527$		−	7.52831i		−	0.327938i
$528$	−1.86537	+	4.82325i	−0.0811797	+	0.209905i
$529$	−22.7740			−0.990172
$530$	8.58235			0.372794
$531$			3.55064i			0.154085i
$532$		0			0
$533$	1.70731			0.0739519
$534$			10.7602i			0.465639i
$535$	−7.39263			−0.319611
$536$			10.3830i			0.448478i
$537$		−	3.37069i		−	0.145456i
$538$	−2.21730			−0.0955946
$539$		0			0
$540$	−5.67081			−0.244033
$541$			25.0259i			1.07595i	0.842962	+	0.537973i	$0.180810\pi$
$541$			25.0259i			1.07595i	−0.842962	+	0.537973i	$0.819190\pi$
$542$		−	22.5122i		−	0.966981i
$543$	8.40873			0.360853
$544$			2.95232i			0.126580i
$545$	1.18972			0.0509620
$546$		0			0
$547$			36.7246i			1.57023i	0.619348	+	0.785116i	$0.287397\pi$
$547$			36.7246i			1.57023i	−0.619348	+	0.785116i	$0.712603\pi$
$548$	7.01058			0.299477
$549$	−6.75670			−0.288369
$550$	−4.73922	+	12.2541i	−0.202081	+	0.522518i
$551$			0.591299i			0.0251902i
$552$	−0.741321			−0.0315527
$553$		0			0
$554$	24.4658			1.03945
$555$	9.68235			0.410993
$556$	−11.4615			−0.486074
$557$		−	38.7766i		−	1.64302i	−0.570195	−	0.821509i	$-0.693132\pi$
$557$		−	38.7766i		−	1.64302i	0.570195	−	0.821509i	$-0.306868\pi$
$558$	1.45038			0.0613994
$559$		−	1.69291i		−	0.0716025i
$560$		0			0
$561$	−5.50716	+	14.2398i	−0.232512	+	0.601204i
$562$	11.3532			0.478904
$563$	43.2493			1.82274			0.911371	−	0.411586i	$-0.135025\pi$
$563$	43.2493			1.82274			0.911371	+	0.411586i	$0.135025\pi$
$564$	5.92291			0.249399
$565$			8.56175i			0.360195i
$566$		−	21.6537i		−	0.910172i
$567$		0			0
$568$		−	14.5206i		−	0.609270i
$569$			21.3369i			0.894490i	0.894412	+	0.447245i	$0.147595\pi$
$569$			21.3369i			0.894490i	−0.894412	+	0.447245i	$0.852405\pi$
$570$			0.495293i			0.0207455i
$571$			22.5948i			0.945564i	0.881179	+	0.472782i	$0.156750\pi$
$571$			22.5948i			0.945564i	−0.881179	+	0.472782i	$0.843250\pi$
$572$	0.517352	+	0.200083i	0.0216316	+	0.00836589i
$573$			9.35542i			0.390828i
$574$		0			0
$575$	−1.88343			−0.0785443
$576$	−0.568783			−0.0236993
$577$		−	33.8740i		−	1.41019i	−0.709110	−	0.705097i	$-0.750903\pi$
$577$		−	33.8740i		−	1.41019i	0.709110	−	0.705097i	$-0.249097\pi$
$578$		−	8.28382i		−	0.344561i
$579$	−14.9680			−0.622049
$580$	−1.93323			−0.0802729
$581$		0			0
$582$			17.1856i			0.712365i
$583$	26.0508	+	10.0750i	1.07892	+	0.417265i
$584$		−	9.70771i		−	0.401708i
$585$			0.0969432i			0.00400811i
$586$			12.1233i			0.500807i
$587$			6.07819i			0.250874i	0.992102	+	0.125437i	$0.0400332\pi$
$587$			6.07819i			0.250874i	−0.992102	+	0.125437i	$0.959967\pi$
$588$		0			0
$589$		−	0.794825i		−	0.0327502i
$590$			6.36169i			0.261907i
$591$	−23.1048			−0.950404
$592$	6.09335			0.250435
$593$	1.61839			0.0664594			0.0332297	−	0.999448i	$-0.489421\pi$
$593$	1.61839			0.0664594			0.0332297	+	0.999448i	$0.489421\pi$
$594$	−17.2132	−	6.65709i	−0.706264	−	0.273144i
$595$		0			0
$596$			14.1568i			0.579886i
$597$	−6.40892			−0.262300
$598$			0.0795155i			0.00325163i
$599$	5.27910			0.215698			0.107849	−	0.994167i	$-0.465604\pi$
$599$	5.27910			0.215698			0.107849	+	0.994167i	$0.465604\pi$
$600$	6.17684			0.252168
$601$	−32.7945			−1.33771			−0.668857	−	0.743391i	$-0.733216\pi$
$601$	−32.7945			−1.33771			−0.668857	+	0.743391i	$0.733216\pi$
$602$		0			0
$603$	−5.90569			−0.240498
$604$		−	23.3040i		−	0.948228i
$605$	7.54265	−	8.29292i	0.306652	−	0.337155i
$606$	−8.31858			−0.337919
$607$	−0.665819			−0.0270248			−0.0135124	−	0.999909i	$-0.504301\pi$
$607$	−0.665819			−0.0270248			−0.0135124	+	0.999909i	$0.504301\pi$
$608$			0.311700i			0.0126411i
$609$		0			0
$610$	−12.1060			−0.490158
$611$		−	0.635302i		−	0.0257016i
$612$	−1.67923			−0.0678788
$613$			4.29442i			0.173450i	0.996232	+	0.0867251i	$0.0276402\pi$
$613$			4.29442i			0.173450i	−0.996232	+	0.0867251i	$0.972360\pi$
$614$			9.65817i			0.389772i
$615$	−16.2211			−0.654098
$616$		0			0
$617$	−30.9913			−1.24766			−0.623831	−	0.781559i	$-0.714425\pi$
$617$	−30.9913			−1.24766			−0.623831	+	0.781559i	$0.714425\pi$
$618$		−	19.4176i		−	0.781091i
$619$		−	0.791382i		−	0.0318083i	−0.999874	−	0.0159042i	$-0.994937\pi$
$619$		−	0.791382i		−	0.0318083i	0.999874	−	0.0159042i	$-0.00506266\pi$
$620$	2.59865			0.104364
$621$		−	2.64561i		−	0.106165i
$622$	17.6778			0.708815
$623$		0			0
$624$		−	0.260777i		−	0.0104394i
$625$	10.5004			0.420015
$626$	−28.8103			−1.15149
$627$	−0.581436	+	1.50341i	−0.0232203	+	0.0600404i
$628$		−	4.03261i		−	0.160919i
$629$	17.9895			0.717288
$630$		0			0
$631$	−34.3677			−1.36816			−0.684078	−	0.729409i	$-0.739795\pi$
$631$	−34.3677			−1.36816			−0.684078	+	0.729409i	$0.739795\pi$
$632$	−7.00567			−0.278671
$633$	11.7326			0.466328
$634$			10.3456i			0.410876i
$635$	−3.60070			−0.142889
$636$		−	13.1312i		−	0.520687i
$637$		0			0
$638$	−5.86811	−	2.26946i	−0.232321	−	0.0898488i
$639$	8.25907			0.326724
$640$	−1.01909			−0.0402831
$641$	4.95879			0.195860			0.0979301	−	0.995193i	$-0.468778\pi$
$641$	4.95879			0.195860			0.0979301	+	0.995193i	$0.468778\pi$
$642$			11.3109i			0.446406i
$643$			48.1404i			1.89847i	0.314562	+	0.949237i	$0.398142\pi$
$643$			48.1404i			1.89847i	−0.314562	+	0.949237i	$0.601858\pi$
$644$		0			0
$645$			16.0843i			0.633318i
$646$			0.920239i			0.0362063i
$647$		−	3.16572i		−	0.124457i	−0.998062	−	0.0622287i	$-0.980179\pi$
$647$		−	3.16572i		−	0.124457i	0.998062	−	0.0622287i	$-0.0198208\pi$
$648$			6.97014i			0.273813i
$649$	−7.46813	+	19.3102i	−0.293150	+	0.757993i
$650$		−	0.662540i		−	0.0259869i
$651$		0			0
$652$	5.53988			0.216958
$653$	−22.1211			−0.865667			−0.432833	−	0.901474i	$-0.642486\pi$
$653$	−22.1211			−0.865667			−0.432833	+	0.901474i	$0.642486\pi$
$654$		−	1.82030i		−	0.0711794i
$655$		−	14.2466i		−	0.556660i
$656$	−10.2084			−0.398569
$657$	5.52158			0.215417
$658$		0			0
$659$		−	24.6258i		−	0.959286i	−0.877464	−	0.479643i	$-0.840766\pi$
$659$		−	24.6258i		−	0.959286i	0.877464	−	0.479643i	$-0.159234\pi$
$660$	−4.91534	−	1.90098i	−0.191329	−	0.0739956i
$661$			27.7365i			1.07882i	0.842042	+	0.539412i	$0.181353\pi$
$661$			27.7365i			1.07882i	−0.842042	+	0.539412i	$0.818647\pi$
$662$		−	26.8448i		−	1.04335i
$663$		−	0.769897i		−	0.0299003i
$664$			14.6915i			0.570143i
$665$		0			0
$666$			3.46579i			0.134297i
$667$		−	0.901912i		−	0.0349222i
$668$	−21.2252			−0.821226
$669$	21.1876			0.819161
$670$	−10.5813			−0.408789
$671$	−36.7465	−	14.2115i	−1.41858	−	0.548629i
$672$		0			0
$673$		−	15.9518i		−	0.614897i	−0.951565	−	0.307449i	$-0.900525\pi$
$673$		−	15.9518i		−	0.614897i	0.951565	−	0.307449i	$-0.0994752\pi$
$674$	−14.5505			−0.560463
$675$			22.0438i			0.848466i
$676$	12.9720			0.498924
$677$	−15.0515			−0.578475			−0.289238	−	0.957257i	$-0.593402\pi$
$677$	−15.0515			−0.578475			−0.289238	+	0.957257i	$0.593402\pi$
$678$	13.0997			0.503091
$679$		0			0
$680$	−3.00868			−0.115378
$681$			33.7785i			1.29440i
$682$	7.88792	+	3.05061i	0.302044	+	0.116814i
$683$	−5.29346			−0.202549			−0.101274	−	0.994859i	$-0.532292\pi$
$683$	−5.29346			−0.202549			−0.101274	+	0.994859i	$0.532292\pi$
$684$	−0.177290			−0.00677885
$685$			7.14442i			0.272974i
$686$		0			0
$687$	46.8756			1.78842
$688$			10.1222i			0.385907i
$689$	−1.40848			−0.0536588
$690$		−	0.755474i		−	0.0287604i
$691$			27.0303i			1.02828i	0.857706	+	0.514140i	$0.171889\pi$
$691$			27.0303i			1.02828i	−0.857706	+	0.514140i	$0.828111\pi$
$692$	−15.0655			−0.572706
$693$		0			0
$694$	28.5417			1.08343
$695$		−	11.6803i		−	0.443058i
$696$			2.95789i			0.112118i
$697$	−30.1383			−1.14157
$698$		−	34.6026i		−	1.30973i
$699$	25.2465			0.954911
$700$		0			0
$701$			19.9250i			0.752555i	0.926507	+	0.376278i	$0.122796\pi$
$701$			19.9250i			0.752555i	−0.926507	+	0.376278i	$0.877204\pi$
$702$	0.930656			0.0351254
$703$	1.89930			0.0716334
$704$	−3.09335	−	1.19633i	−0.116585	−	0.0450886i
$705$			6.03598i			0.227328i
$706$	16.9203			0.636805
$707$		0			0
$708$	9.73355			0.365809
$709$	9.96825			0.374365			0.187183	−	0.982325i	$-0.440064\pi$
$709$	9.96825			0.374365			0.187183	+	0.982325i	$0.440064\pi$
$710$	14.7978			0.555352
$711$		−	3.98471i		−	0.149438i
$712$	−6.90094			−0.258623
$713$			1.21235i			0.0454029i
$714$		0			0
$715$	−0.203903	+	0.527228i	−0.00762553	+	0.0197172i
$716$	2.16176			0.0807887
$717$	40.6494			1.51808
$718$	30.3511			1.13269
$719$		−	41.2017i		−	1.53656i	−0.640112	−	0.768282i	$-0.721112\pi$
$719$		−	41.2017i		−	1.53656i	0.640112	−	0.768282i	$-0.278888\pi$
$720$		−	0.579642i		−	0.0216020i
$721$		0			0
$722$		−	18.9028i		−	0.703491i
$723$		−	20.5888i		−	0.765706i
$724$			5.39285i			0.200424i
$725$			7.51492i			0.279097i
$726$	−12.6884	−	11.5405i	−0.470910	−	0.428306i
$727$		−	0.0415718i		−	0.00154181i	−1.00000		0.000770906i	$-0.999755\pi$
$727$		−	0.0415718i		−	0.00154181i	1.00000		0.000770906i	$-0.000245387\pi$
$728$		0			0
$729$	−29.9940			−1.11089
$730$	9.89304			0.366158
$731$			29.8841i			1.10530i
$732$			18.5225i			0.684611i
$733$	−8.80809			−0.325334			−0.162667	−	0.986681i	$-0.552010\pi$
$733$	−8.80809			−0.325334			−0.162667	+	0.986681i	$0.552010\pi$
$734$	17.4215			0.643040
$735$		0			0
$736$		−	0.475438i		−	0.0175249i
$737$	−32.1183	−	12.4216i	−1.18309	−	0.457554i
$738$		−	5.80634i		−	0.213734i
$739$		−	32.7938i		−	1.20634i	−0.797612	−	0.603170i	$-0.793904\pi$
$739$		−	32.7938i		−	1.20634i	0.797612	−	0.603170i	$-0.206096\pi$
$740$			6.20968i			0.228272i
$741$		−	0.0812842i		−	0.00298605i
$742$		0			0
$743$			25.7575i			0.944952i	0.881344	+	0.472476i	$0.156640\pi$
$743$			25.7575i			0.944952i	−0.881344	+	0.472476i	$0.843360\pi$
$744$		−	3.97600i		−	0.145767i
$745$	−14.4271			−0.528568
$746$	9.15211			0.335083
$747$	−8.35631			−0.305741
$748$	−9.13254	−	3.53196i	−0.333919	−	0.129141i
$749$		0			0
$750$			14.2398i			0.519963i
$751$	11.4658			0.418393			0.209196	−	0.977874i	$-0.432915\pi$
$751$	11.4658			0.418393			0.209196	+	0.977874i	$0.432915\pi$
$752$			3.79859i			0.138521i
$753$	−45.1912			−1.64686
$754$	0.317269			0.0115542
$755$	23.7489			0.864313
$756$		0			0
$757$	21.9741			0.798661			0.399331	−	0.916807i	$-0.369243\pi$
$757$	21.9741			0.798661			0.399331	+	0.916807i	$0.369243\pi$
$758$		−	6.15382i		−	0.223517i
$759$	0.886868	−	2.29316i	0.0321913	−	0.0832365i
$760$	−0.317651			−0.0115224
$761$	−26.0095			−0.942843			−0.471421	−	0.881908i	$-0.656259\pi$
$761$	−26.0095			−0.942843			−0.471421	+	0.881908i	$0.656259\pi$
$762$			5.50916i			0.199576i
$763$		0			0
$764$	−6.00000			−0.217072
$765$		−	1.71129i		−	0.0618718i
$766$	12.9651			0.468447
$767$		−	1.04404i		−	0.0376981i
$768$			1.55924i			0.0562641i
$769$	−40.8753			−1.47400			−0.737001	−	0.675891i	$-0.763759\pi$
$769$	−40.8753			−1.47400			−0.737001	+	0.675891i	$0.763759\pi$
$770$		0			0
$771$	10.8929			0.392296
$772$		−	9.59958i		−	0.345496i
$773$			47.1382i			1.69544i	0.530441	+	0.847722i	$0.322026\pi$
$773$			47.1382i			1.69544i	−0.530441	+	0.847722i	$0.677974\pi$
$774$	−5.75737			−0.206944
$775$		−	10.1016i		−	0.362859i
$776$	−11.0218			−0.395659
$777$		0			0
$778$			5.16647i			0.185227i
$779$	−3.18195			−0.114005
$780$	0.265756			0.00951557
$781$	44.9172	+	17.3715i	1.60726	+	0.621601i
$782$		−	1.40365i		−	0.0501943i
$783$	−10.5561			−0.377243
$784$		0			0
$785$	4.10960			0.146678
$786$	−21.7976			−0.777495
$787$	−24.1491			−0.860823			−0.430411	−	0.902633i	$-0.641632\pi$
$787$	−24.1491			−0.860823			−0.430411	+	0.902633i	$0.641632\pi$
$788$		−	14.8180i		−	0.527870i
$789$	6.97087			0.248169
$790$		−	7.13942i		−	0.254009i
$791$		0			0
$792$	0.680455	−	1.75944i	0.0241789	−	0.0625191i
$793$	1.98676			0.0705518
$794$	9.25712			0.328523
$795$	13.3819			0.474607
$796$		−	4.11030i		−	0.145686i
$797$			20.3073i			0.719321i	0.933083	+	0.359660i	$0.117107\pi$
$797$			20.3073i			0.719321i	−0.933083	+	0.359660i	$0.882893\pi$
$798$		0			0
$799$			11.2147i			0.396746i
$800$			3.96145i			0.140059i
$801$		−	3.92514i		−	0.138688i
$802$		−	30.9248i		−	1.09199i
$803$	30.0293	+	11.6137i	1.05971	+	0.409837i
$804$			16.1896i			0.570963i
$805$		0			0
$806$	−0.426473			−0.0150219
$807$	−3.45729			−0.121703
$808$		−	5.33504i		−	0.187686i
$809$		−	27.0778i		−	0.952006i	−0.879444	−	0.476003i	$-0.842085\pi$
$809$		−	27.0778i		−	0.952006i	0.879444	−	0.476003i	$-0.157915\pi$
$810$	−7.10320			−0.249581
$811$	23.5808			0.828033			0.414016	−	0.910269i	$-0.364126\pi$
$811$	23.5808			0.828033			0.414016	+	0.910269i	$0.364126\pi$
$812$		0			0
$813$		−	35.1018i		−	1.23107i
$814$	−7.28968	+	18.8488i	−0.255503	+	0.660651i
$815$			5.64564i			0.197758i
$816$			4.60336i			0.161150i
$817$			3.15511i			0.110383i
$818$			23.8397i			0.833535i
$819$		0			0
$820$		−	10.4032i		−	0.363297i
$821$		−	33.9767i		−	1.18580i	−0.805277	−	0.592898i	$-0.797984\pi$
$821$		−	33.9767i		−	1.18580i	0.805277	−	0.592898i	$-0.202016\pi$
$822$	10.9311			0.381267
$823$	−11.8007			−0.411345			−0.205673	−	0.978621i	$-0.565938\pi$
$823$	−11.8007			−0.411345			−0.205673	+	0.978621i	$0.565938\pi$
$824$	12.4533			0.433831
$825$	−7.38957	+	19.1071i	−0.257272	+	0.665224i
$826$		0			0
$827$		−	17.0595i		−	0.593217i	−0.954999	−	0.296609i	$-0.904144\pi$
$827$		−	17.0595i		−	0.593217i	0.954999	−	0.296609i	$-0.0958557\pi$
$828$	0.270422			0.00939780
$829$		−	25.1016i		−	0.871816i	−0.899991	−	0.435908i	$-0.856427\pi$
$829$		−	25.1016i		−	0.871816i	0.899991	−	0.435908i	$-0.143573\pi$
$830$	−14.9720			−0.519687
$831$	38.1479			1.32334
$832$	0.167247			0.00579823
$833$		0			0
$834$	−17.8711			−0.618826
$835$		−	21.6304i		−	0.748550i
$836$	−0.964197	−	0.372898i	−0.0333474	−	0.0128969i
$837$	14.1895			0.490460
$838$	−5.03426			−0.173906
$839$		−	41.1030i		−	1.41903i	−0.704688	−	0.709517i	$-0.748913\pi$
$839$		−	41.1030i		−	1.41903i	0.704688	−	0.709517i	$-0.251087\pi$
$840$		0			0
$841$	25.4014			0.875909
$842$		−	16.9250i		−	0.583272i
$843$	17.7023			0.609698
$844$			7.52456i			0.259006i
$845$			13.2197i			0.454771i
$846$	−2.16058			−0.0742822
$847$		0			0
$848$	8.42157			0.289198
$849$		−	33.7632i		−	1.15875i
$850$			11.6955i			0.401151i
$851$	−2.89701			−0.0993082
$852$		−	22.6410i		−	0.775669i
$853$	52.7195			1.80508			0.902541	−	0.430605i	$-0.141700\pi$
$853$	52.7195			1.80508			0.902541	+	0.430605i	$0.141700\pi$
$854$		0			0
$855$		−	0.180675i		−	0.00617894i
$856$	−7.25414			−0.247941
$857$	21.8774			0.747319			0.373659	−	0.927566i	$-0.378103\pi$
$857$	21.8774			0.747319			0.373659	+	0.927566i	$0.378103\pi$
$858$	0.806673	+	0.311976i	0.0275394	+	0.0106507i
$859$		−	13.6865i		−	0.466978i	−0.972359	−	0.233489i	$-0.924986\pi$
$859$		−	13.6865i		−	0.466978i	0.972359	−	0.233489i	$-0.0750142\pi$
$860$	−10.3155			−0.351755
$861$		0			0
$862$	5.99907			0.204329
$863$	30.0480			1.02285			0.511423	−	0.859329i	$-0.329119\pi$
$863$	30.0480			1.02285			0.511423	+	0.859329i	$0.329119\pi$
$864$	−5.56458			−0.189311
$865$		−	15.3532i		−	0.522023i
$866$	36.1175			1.22732
$867$		−	12.9164i		−	0.438665i
$868$		0			0
$869$	8.38113	−	21.6710i	0.284310	−	0.735137i
$870$	−3.01436			−0.102196
$871$	1.73653			0.0588399
$872$	1.16743			0.0395342
$873$		−	6.26901i		−	0.212174i
$874$		−	0.148194i		−	0.00501275i
$875$		0			0
$876$		−	15.1366i		−	0.511418i
$877$			14.1782i			0.478762i	0.970926	+	0.239381i	$0.0769446\pi$
$877$			14.1782i			0.478762i	−0.970926	+	0.239381i	$0.923055\pi$
$878$		−	11.3496i		−	0.383031i
$879$			18.9030i			0.637583i
$880$	1.21917	−	3.15240i	0.0410984	−	0.106267i
$881$		−	22.3264i		−	0.752196i	−0.926580	−	0.376098i	$-0.877266\pi$
$881$		−	22.3264i		−	0.752196i	0.926580	−	0.376098i	$-0.122734\pi$
$882$		0			0
$883$	−4.45618			−0.149962			−0.0749812	−	0.997185i	$-0.523890\pi$
$883$	−4.45618			−0.149962			−0.0749812	+	0.997185i	$0.523890\pi$
$884$	0.493765			0.0166071
$885$			9.91938i			0.333436i
$886$		−	4.75076i		−	0.159605i
$887$	9.00141			0.302238			0.151119	−	0.988516i	$-0.451712\pi$
$887$	9.00141			0.302238			0.151119	+	0.988516i	$0.451712\pi$
$888$	9.50096			0.318831
$889$		0			0
$890$		−	7.03268i		−	0.235736i
$891$	−21.5610	−	8.33861i	−0.722322	−	0.279354i
$892$			13.5885i			0.454975i
$893$			1.18402i			0.0396218i
$894$			22.0738i			0.738259i
$895$			2.20303i			0.0736391i
$896$		0			0
$897$			0.123983i			0.00413968i
$898$			7.33297i			0.244704i
$899$	4.83731			0.161333
$900$	−2.25321			−0.0751070
$901$	24.8632			0.828312
$902$	12.2126	−	31.5780i	0.406635	−	1.05143i
$903$		0			0
$904$			8.40135i			0.279425i
$905$	−5.49581			−0.182687
$906$		−	36.3365i		−	1.20720i
$907$	21.3743			0.709723			0.354862	−	0.934919i	$-0.384528\pi$
$907$	21.3743			0.709723			0.354862	+	0.934919i	$0.384528\pi$
$908$	−21.6635			−0.718929
$909$	3.03448			0.100647
$910$		0			0
$911$	−28.4299			−0.941924			−0.470962	−	0.882153i	$-0.656093\pi$
$911$	−28.4299			−0.941924			−0.470962	+	0.882153i	$0.656093\pi$
$912$			0.486014i			0.0160935i
$913$	−45.4460	−	17.5760i	−1.50404	−	0.581681i
$914$	−13.5176			−0.447122
$915$	−18.8761			−0.624025
$916$			30.0632i			0.993317i
$917$		0			0
$918$	−16.4284			−0.542218
$919$		−	21.0525i		−	0.694459i	−0.937780	−	0.347229i	$-0.887122\pi$
$919$		−	21.0525i		−	0.694459i	0.937780	−	0.347229i	$-0.112878\pi$
$920$	0.484515			0.0159740
$921$			15.0594i			0.496223i
$922$		−	18.5730i		−	0.611670i
$923$	−2.42852			−0.0799357
$924$		0			0
$925$	24.1385			0.793669
$926$			28.2849i			0.929501i
$927$			7.08322i			0.232643i
$928$	−1.89701			−0.0622724
$929$		−	12.4772i		−	0.409363i	−0.978829	−	0.204681i	$-0.934384\pi$
$929$		−	12.4772i		−	0.409363i	0.978829	−	0.204681i	$-0.0656158\pi$
$930$	4.05191			0.132867
$931$		0			0
$932$			16.1916i			0.530373i
$933$	27.5639			0.902400
$934$	−21.5792			−0.706092
$935$	3.59939	−	9.30689i	0.117713	−	0.304368i
$936$			0.0951271i			0.00310933i
$937$	43.2128			1.41170			0.705850	−	0.708362i	$-0.250565\pi$
$937$	43.2128			1.41170			0.705850	+	0.708362i	$0.250565\pi$
$938$		0			0
$939$	−44.9221			−1.46598
$940$	−3.87112			−0.126262
$941$	−15.4751			−0.504473			−0.252236	−	0.967666i	$-0.581166\pi$
$941$	−15.4751			−0.504473			−0.252236	+	0.967666i	$0.581166\pi$
$942$		−	6.28779i		−	0.204867i
$943$	4.85344			0.158050
$944$			6.24251i			0.203176i
$945$		0			0
$946$	−31.3116	−	12.1096i	−1.01803	−	0.393717i
$947$	33.4977			1.08853			0.544264	−	0.838914i	$-0.316809\pi$
$947$	33.4977			1.08853			0.544264	+	0.838914i	$0.316809\pi$
$948$	−10.9235			−0.354779
$949$	−1.62358			−0.0527037
$950$			1.23479i			0.0400617i
$951$			16.1312i			0.523091i
$952$		0			0
$953$		−	25.4820i		−	0.825444i	−0.910857	−	0.412722i	$-0.864578\pi$
$953$		−	25.4820i		−	0.825444i	0.910857	−	0.412722i	$-0.135422\pi$
$954$			4.79005i			0.155084i
$955$		−	6.11455i		−	0.197862i
$956$			26.0701i			0.843167i
$957$	−9.14976	−	3.53862i	−0.295770	−	0.114387i
$958$			6.93560i			0.224079i
$959$		0			0
$960$	−1.58900			−0.0512849
$961$	24.4977			0.790248
$962$		−	1.01909i		−	0.0328568i
$963$		−	4.12603i		−	0.132960i
$964$	13.2044			0.425286
$965$	9.78285			0.314921
$966$		0			0
$967$		−	39.6417i		−	1.27479i	−0.770537	−	0.637395i	$-0.780012\pi$
$967$		−	39.6417i		−	1.27479i	0.770537	−	0.637395i	$-0.219988\pi$
$968$	7.40135	−	8.13757i	0.237888	−	0.261551i
$969$			1.43487i			0.0460946i
$970$		−	11.2322i		−	0.360645i
$971$			19.0620i			0.611730i	0.952075	+	0.305865i	$0.0989456\pi$
$971$			19.0620i			0.611730i	−0.952075	+	0.305865i	$0.901054\pi$
$972$		−	5.82564i		−	0.186858i
$973$		0			0
$974$		−	12.1740i		−	0.390081i
$975$		−	1.03306i		−	0.0330843i
$976$	−11.8792			−0.380244
$977$	47.6697			1.52509			0.762544	−	0.646936i	$-0.223950\pi$
$977$	47.6697			1.52509			0.762544	+	0.646936i	$0.223950\pi$
$978$	8.63798			0.276212
$979$	8.25583	−	21.3470i	0.263857	−	0.682252i
$980$		0			0
$981$			0.664016i			0.0212004i
$982$	2.37152			0.0756782
$983$			46.4625i			1.48192i	0.671548	+	0.740961i	$0.265630\pi$
$983$			46.4625i			1.48192i	−0.671548	+	0.740961i	$0.734370\pi$
$984$	−15.9172			−0.507423
$985$	15.1009			0.481155
$986$	−5.60058			−0.178359
$987$		0			0
$988$	0.0521308			0.00165850
$989$		−	4.81251i		−	0.153029i
$990$	1.79303	+	0.693446i	0.0569864	+	0.0220392i
$991$	−14.5718			−0.462887			−0.231444	−	0.972848i	$-0.574345\pi$
$991$	−14.5718			−0.462887			−0.231444	+	0.972848i	$0.574345\pi$
$992$	2.54997			0.0809615
$993$		−	41.8575i		−	1.32831i
$994$		0			0
$995$	4.18877			0.132793
$996$			22.9076i			0.725855i
$997$	4.11696			0.130385			0.0651927	−	0.997873i	$-0.479234\pi$
$997$	4.11696			0.130385			0.0651927	+	0.997873i	$0.479234\pi$
$998$		−	3.92892i		−	0.124368i
$999$			33.9069i			1.07277i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1078.2.c.b.1077.14		16
7.2	even	3		1078.2.i.c.1011.6		16
7.3	odd	6		1078.2.i.c.901.2		16
7.4	even	3		154.2.i.a.131.3	yes	16
7.5	odd	6		154.2.i.a.87.7	yes	16
7.6	odd	2	inner	1078.2.c.b.1077.11		16
11.10	odd	2	inner	1078.2.c.b.1077.6		16
21.5	even	6		1386.2.bk.c.703.2		16
21.11	odd	6		1386.2.bk.c.901.6		16
28.11	odd	6		1232.2.bn.b.593.3		16
28.19	even	6		1232.2.bn.b.241.4		16
77.10	even	6		1078.2.i.c.901.6		16
77.32	odd	6		154.2.i.a.131.7	yes	16
77.54	even	6		154.2.i.a.87.3	✓	16
77.65	odd	6		1078.2.i.c.1011.2		16
77.76	even	2	inner	1078.2.c.b.1077.3		16
231.32	even	6		1386.2.bk.c.901.2		16
231.131	odd	6		1386.2.bk.c.703.6		16
308.131	odd	6		1232.2.bn.b.241.3		16
308.263	even	6		1232.2.bn.b.593.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
154.2.i.a.87.3	✓	16	77.54	even	6
154.2.i.a.87.7	yes	16	7.5	odd	6
154.2.i.a.131.3	yes	16	7.4	even	3
154.2.i.a.131.7	yes	16	77.32	odd	6
1078.2.c.b.1077.3		16	77.76	even	2	inner
1078.2.c.b.1077.6		16	11.10	odd	2	inner
1078.2.c.b.1077.11		16	7.6	odd	2	inner
1078.2.c.b.1077.14		16	1.1	even	1	trivial
1078.2.i.c.901.2		16	7.3	odd	6
1078.2.i.c.901.6		16	77.10	even	6
1078.2.i.c.1011.2		16	77.65	odd	6
1078.2.i.c.1011.6		16	7.2	even	3
1232.2.bn.b.241.3		16	308.131	odd	6
1232.2.bn.b.241.4		16	28.19	even	6
1232.2.bn.b.593.3		16	28.11	odd	6
1232.2.bn.b.593.4		16	308.263	even	6
1386.2.bk.c.703.2		16	21.5	even	6
1386.2.bk.c.703.6		16	231.131	odd	6
1386.2.bk.c.901.2		16	231.32	even	6
1386.2.bk.c.901.6		16	21.11	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1078 = 2 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1078.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +1.55924i q^{3} -1.00000 q^{4} -1.01909i q^{5} -1.55924 q^{6} -1.00000i q^{8} +0.568783 q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +1.55924i q^{3} -1.00000 q^{4} -1.01909i q^{5} -1.55924 q^{6} -1.00000i q^{8} +0.568783 q^{9} +1.01909 q^{10} +(3.09335 + 1.19633i) q^{11} -1.55924i q^{12} -0.167247 q^{13} +1.58900 q^{15} +1.00000 q^{16} +2.95232 q^{17} +0.568783i q^{18} +0.311700 q^{19} +1.01909i q^{20} +(-1.19633 + 3.09335i) q^{22} -0.475438 q^{23} +1.55924 q^{24} +3.96145 q^{25} -0.167247i q^{26} +5.56458i q^{27} +1.89701i q^{29} +1.58900i q^{30} -2.54997i q^{31} +1.00000i q^{32} +(-1.86537 + 4.82325i) q^{33} +2.95232i q^{34} -0.568783 q^{36} +6.09335 q^{37} +0.311700i q^{38} -0.260777i q^{39} -1.01909 q^{40} -10.2084 q^{41} +10.1222i q^{43} +(-3.09335 - 1.19633i) q^{44} -0.579642i q^{45} -0.475438i q^{46} +3.79859i q^{47} +1.55924i q^{48} +3.96145i q^{50} +4.60336i q^{51} +0.167247 q^{52} +8.42157 q^{53} -5.56458 q^{54} +(1.21917 - 3.15240i) q^{55} +0.486014i q^{57} -1.89701 q^{58} +6.24251i q^{59} -1.58900 q^{60} -11.8792 q^{61} +2.54997 q^{62} -1.00000 q^{64} +0.170440i q^{65} +(-4.82325 - 1.86537i) q^{66} -10.3830 q^{67} -2.95232 q^{68} -0.741321i q^{69} +14.5206 q^{71} -0.568783i q^{72} +9.70771 q^{73} +6.09335i q^{74} +6.17684i q^{75} -0.311700 q^{76} +0.260777 q^{78} -7.00567i q^{79} -1.01909i q^{80} -6.97014 q^{81} -10.2084i q^{82} -14.6915 q^{83} -3.00868i q^{85} -10.1222 q^{86} -2.95789 q^{87} +(1.19633 - 3.09335i) q^{88} -6.90094i q^{89} +0.579642 q^{90} +0.475438 q^{92} +3.97600 q^{93} -3.79859 q^{94} -0.317651i q^{95} -1.55924 q^{96} -11.0218i q^{97} +(1.75944 + 0.680455i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{4} - 32 q^{9}+O(q^{10}) \) 16 * q - 16 * q^4 - 32 * q^9	\( 16 q - 16 q^{4} - 32 q^{9} - 16 q^{11} - 8 q^{15} + 16 q^{16} - 8 q^{22} - 32 q^{23} + 32 q^{36} + 32 q^{37} + 16 q^{44} + 56 q^{53} + 24 q^{58} + 8 q^{60} - 16 q^{64} - 24 q^{67} + 8 q^{71} - 16 q^{78} + 16 q^{81} - 40 q^{86} + 8 q^{88} + 32 q^{92} + 88 q^{93} + 56 q^{99}+O(q^{100}) \) 16 * q - 16 * q^4 - 32 * q^9 - 16 * q^11 - 8 * q^15 + 16 * q^16 - 8 * q^22 - 32 * q^23 + 32 * q^36 + 32 * q^37 + 16 * q^44 + 56 * q^53 + 24 * q^58 + 8 * q^60 - 16 * q^64 - 24 * q^67 + 8 * q^71 - 16 * q^78 + 16 * q^81 - 40 * q^86 + 8 * q^88 + 32 * q^92 + 88 * q^93 + 56 * q^99

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