LMFDB - Embedded newform 425.4.d.b.101.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [425,4,Mod(101,425)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(425, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("425.101");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 425 = 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	425.d (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:	$25.0758117524$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\sqrt{-19}, \sqrt{-1131})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 575x^{2} + 77284 $ x^4 + 575*x^2 + 77284
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			101.4
Root			$14.6357i$ of defining polynomial
Character	$\chi$	$=$	425.101
Dual form			425.4.d.b.101.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.00000 q^{2} +4.35890i q^{3} -7.00000 q^{4} -4.35890i q^{6} +32.0713i q^{7} +15.0000 q^{8} +8.00000 q^{9} -1.55903i q^{11} -30.5123i q^{12} +69.7956 q^{13} -32.0713i q^{14} +41.0000 q^{16} +(45.3978 + 53.4045i) q^{17} -8.00000 q^{18} +76.7956 q^{19} -139.796 q^{21} +1.55903i q^{22} -73.4968i q^{23} +65.3835i q^{24} -69.7956 q^{26} +152.561i q^{27} -224.499i q^{28} +134.521i q^{29} -54.4703i q^{31} -161.000 q^{32} +6.79563 q^{33} +(-45.3978 - 53.4045i) q^{34} -56.0000 q^{36} -112.695i q^{37} -76.7956 q^{38} +304.232i q^{39} +316.036i q^{41} +139.796 q^{42} +148.000 q^{43} +10.9132i q^{44} +73.4968i q^{46} +224.000 q^{47} +178.715i q^{48} -685.569 q^{49} +(-232.785 + 197.884i) q^{51} -488.569 q^{52} +670.569 q^{53} -152.561i q^{54} +481.070i q^{56} +334.744i q^{57} -134.521i q^{58} -334.365 q^{59} +675.725i q^{61} +54.4703i q^{62} +256.571i q^{63} -167.000 q^{64} -6.79563 q^{66} -1033.57 q^{67} +(-317.785 - 373.831i) q^{68} +320.365 q^{69} -761.248i q^{71} +120.000 q^{72} -791.188i q^{73} +112.695i q^{74} -537.569 q^{76} +50.0000 q^{77} -304.232i q^{78} -50.7796i q^{79} -449.000 q^{81} -316.036i q^{82} -608.796 q^{83} +978.569 q^{84} -148.000 q^{86} -586.365 q^{87} -23.3854i q^{88} -47.5694 q^{89} +2238.44i q^{91} +514.478i q^{92} +237.431 q^{93} -224.000 q^{94} -701.783i q^{96} -165.574i q^{97} +685.569 q^{98} -12.4722i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} - 28 q^{4} + 60 q^{8} + 32 q^{9} - 14 q^{13} + 164 q^{16} + 35 q^{17} - 32 q^{18} + 14 q^{19} - 266 q^{21} + 14 q^{26} - 644 q^{32} - 266 q^{33} - 35 q^{34} - 224 q^{36} - 14 q^{38} + 266 q^{42}+ \cdots + 690 q^{98}+O(q^{100}) $ 4 * q - 4 * q^2 - 28 * q^4 + 60 * q^8 + 32 * q^9 - 14 * q^13 + 164 * q^16 + 35 * q^17 - 32 * q^18 + 14 * q^19 - 266 * q^21 + 14 * q^26 - 644 * q^32 - 266 * q^33 - 35 * q^34 - 224 * q^36 - 14 * q^38 + 266 * q^42 + 592 * q^43 + 896 * q^47 - 690 * q^49 + 95 * q^51 + 98 * q^52 + 630 * q^53 + 1008 * q^59 - 668 * q^64 + 266 * q^66 - 2082 * q^67 - 245 * q^68 - 1064 * q^69 + 480 * q^72 - 98 * q^76 + 200 * q^77 - 1796 * q^81 - 2142 * q^83 + 1862 * q^84 - 592 * q^86 + 1862 * q^89 + 3002 * q^93 - 896 * q^94 + 690 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/425\mathbb{Z}\right)^\times$.

$n$	$52$	$326$
$\chi(n)$	$1$	$-1$

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 $

$2$	−1.00000			−0.353553			−0.176777	−	0.984251i	$-0.556567\pi$
$2$	−1.00000			−0.353553			−0.176777	+	0.984251i	$0.556567\pi$
$3$			4.35890i			0.838870i	0.907785	+	0.419435i	$0.137772\pi$
$3$			4.35890i			0.838870i	−0.907785	+	0.419435i	$0.862228\pi$
$4$	−7.00000			−0.875000
$5$		0			0
$5$		0			0
$6$		−	4.35890i		−	0.296586i
$7$			32.0713i			1.73169i	0.500314	+	0.865844i	$0.333218\pi$
$7$			32.0713i			1.73169i	−0.500314	+	0.865844i	$0.666782\pi$
$8$	15.0000			0.662913
$9$	8.00000			0.296296
$10$		0			0
$11$		−	1.55903i		−	0.0427331i	−0.999772	−	0.0213665i	$-0.993198\pi$
$11$		−	1.55903i		−	0.0427331i	0.999772	−	0.0213665i	$-0.00680170\pi$
$12$		−	30.5123i		−	0.734012i
$13$	69.7956			1.48906			0.744532	−	0.667587i	$-0.232673\pi$
$13$	69.7956			1.48906			0.744532	+	0.667587i	$0.232673\pi$
$14$		−	32.0713i		−	0.612244i
$15$		0			0
$16$	41.0000			0.640625
$17$	45.3978	+	53.4045i	0.647682	+	0.761911i
$17$	45.3978	+	53.4045i	0.647682	+	0.761911i
$18$	−8.00000			−0.104757
$19$	76.7956			0.927270			0.463635	−	0.886026i	$-0.346545\pi$
$19$	76.7956			0.927270			0.463635	+	0.886026i	$0.346545\pi$
$20$		0			0
$21$	−139.796			−1.45266
$22$			1.55903i			0.0151084i
$23$		−	73.4968i		−	0.666310i	−0.942872	−	0.333155i	$-0.891887\pi$
$23$		−	73.4968i		−	0.666310i	0.942872	−	0.333155i	$-0.108113\pi$
$24$			65.3835i			0.556098i
$25$		0			0
$26$	−69.7956			−0.526463
$27$			152.561i			1.08742i
$28$		−	224.499i		−	1.51523i
$29$			134.521i			0.861379i	0.902500	+	0.430690i	$0.141730\pi$
$29$			134.521i			0.861379i	−0.902500	+	0.430690i	$0.858270\pi$
$30$		0			0
$31$		−	54.4703i		−	0.315586i	−0.987472	−	0.157793i	$-0.949562\pi$
$31$		−	54.4703i		−	0.315586i	0.987472	−	0.157793i	$-0.0504378\pi$
$32$	−161.000			−0.889408
$33$	6.79563			0.0358475
$34$	−45.3978	−	53.4045i	−0.228990	−	0.269376i
$35$		0			0
$36$	−56.0000			−0.259259
$37$		−	112.695i		−	0.500728i	−0.968152	−	0.250364i	$-0.919450\pi$
$37$		−	112.695i		−	0.500728i	0.968152	−	0.250364i	$-0.0805503\pi$
$38$	−76.7956			−0.327839
$39$			304.232i			1.24913i
$40$		0			0
$41$			316.036i			1.20382i	0.798565	+	0.601909i	$0.205593\pi$
$41$			316.036i			1.20382i	−0.798565	+	0.601909i	$0.794407\pi$
$42$	139.796			0.513594
$43$	148.000			0.524879			0.262439	−	0.964948i	$-0.415473\pi$
$43$	148.000			0.524879			0.262439	+	0.964948i	$0.415473\pi$
$44$			10.9132i			0.0373914i
$45$		0			0
$46$			73.4968i			0.235576i
$47$	224.000			0.695186			0.347593	−	0.937645i	$-0.386999\pi$
$47$	224.000			0.695186			0.347593	+	0.937645i	$0.386999\pi$
$48$			178.715i			0.537401i
$49$	−685.569			−1.99874
$50$		0			0
$51$	−232.785	+	197.884i	−0.639145	+	0.543321i
$52$	−488.569			−1.30293
$53$	670.569			1.73792			0.868960	−	0.494882i	$-0.164789\pi$
$53$	670.569			1.73792			0.868960	+	0.494882i	$0.164789\pi$
$54$		−	152.561i		−	0.384463i
$55$		0			0
$56$			481.070i			1.14796i
$57$			334.744i			0.777859i
$58$		−	134.521i		−	0.304543i
$59$	−334.365			−0.737807			−0.368904	−	0.929468i	$-0.620267\pi$
$59$	−334.365			−0.737807			−0.368904	+	0.929468i	$0.620267\pi$
$60$		0			0
$61$			675.725i			1.41832i	0.705046	+	0.709162i	$0.250926\pi$
$61$			675.725i			1.41832i	−0.705046	+	0.709162i	$0.749074\pi$
$62$			54.4703i			0.111576i
$63$			256.571i			0.513093i
$64$	−167.000			−0.326172
$65$		0			0
$66$	−6.79563			−0.0126740
$67$	−1033.57			−1.88464			−0.942318	−	0.334719i	$-0.891359\pi$
$67$	−1033.57			−1.88464			−0.942318	+	0.334719i	$0.891359\pi$
$68$	−317.785	−	373.831i	−0.566721	−	0.666672i
$69$	320.365			0.558948
$70$		0			0
$71$		−	761.248i		−	1.27244i	−0.771506	−	0.636222i	$-0.780496\pi$
$71$		−	761.248i		−	1.27244i	0.771506	−	0.636222i	$-0.219504\pi$
$72$	120.000			0.196419
$73$		−	791.188i		−	1.26851i	−0.773122	−	0.634257i	$-0.781306\pi$
$73$		−	791.188i		−	1.26851i	0.773122	−	0.634257i	$-0.218694\pi$
$74$			112.695i			0.177034i
$75$		0			0
$76$	−537.569			−0.811361
$77$	50.0000			0.0740004
$78$		−	304.232i		−	0.441635i
$79$		−	50.7796i		−	0.0723184i	−0.999346	−	0.0361592i	$-0.988488\pi$
$79$		−	50.7796i		−	0.0723184i	0.999346	−	0.0361592i	$-0.0115123\pi$
$80$		0			0
$81$	−449.000			−0.615912
$82$		−	316.036i		−	0.425614i
$83$	−608.796			−0.805108			−0.402554	−	0.915396i	$-0.631878\pi$
$83$	−608.796			−0.805108			−0.402554	+	0.915396i	$0.631878\pi$
$84$	978.569			1.27108
$85$		0			0
$86$	−148.000			−0.185573
$87$	−586.365			−0.722585
$88$		−	23.3854i		−	0.0283283i
$89$	−47.5694			−0.0566556			−0.0283278	−	0.999599i	$-0.509018\pi$
$89$	−47.5694			−0.0566556			−0.0283278	+	0.999599i	$0.509018\pi$
$90$		0			0
$91$			2238.44i			2.57859i
$92$			514.478i			0.583022i
$93$	237.431			0.264736
$94$	−224.000			−0.245785
$95$		0			0
$96$		−	701.783i		−	0.746098i
$97$		−	165.574i		−	0.173315i	−0.996238	−	0.0866574i	$-0.972381\pi$
$97$		−	165.574i		−	0.173315i	0.996238	−	0.0866574i	$-0.0276186\pi$
$98$	685.569			0.706663
$99$		−	12.4722i		−	0.0126617i
$100$		0			0
$101$	−336.204			−0.331224			−0.165612	−	0.986191i	$-0.552960\pi$
$101$	−336.204			−0.331224			−0.165612	+	0.986191i	$0.552960\pi$
$102$	232.785	−	197.884i	0.225972	−	0.192093i
$103$	82.3651			0.0787929			0.0393965	−	0.999224i	$-0.487456\pi$
$103$	82.3651			0.0787929			0.0393965	+	0.999224i	$0.487456\pi$
$104$	1046.93			0.987119
$105$		0			0
$106$	−670.569			−0.614448
$107$			1621.61i			1.46511i	0.680709	+	0.732554i	$0.261672\pi$
$107$			1621.61i			1.46511i	−0.680709	+	0.732554i	$0.738328\pi$
$108$		−	1067.93i		−	0.951497i
$109$		−	1064.14i		−	0.935106i	−0.883965	−	0.467553i	$-0.845136\pi$
$109$		−	1064.14i		−	0.935106i	0.883965	−	0.467553i	$-0.154864\pi$
$110$		0			0
$111$	491.226			0.420046
$112$			1314.92i			1.10936i
$113$			1858.58i			1.54726i	0.633638	+	0.773629i	$0.281561\pi$
$113$			1858.58i			1.54726i	−0.633638	+	0.773629i	$0.718439\pi$
$114$		−	334.744i		−	0.275015i
$115$		0			0
$116$		−	941.650i		−	0.753707i
$117$	558.365			0.441204
$118$	334.365			0.260854
$119$	−1712.75	+	1455.97i	−1.31939	+	1.12158i
$120$		0			0
$121$	1328.57			0.998174
$122$		−	675.725i		−	0.501453i
$123$	−1377.57			−1.00985
$124$			381.292i			0.276137i
$125$		0			0
$126$		−	256.571i		−	0.181406i
$127$	199.139			0.139140			0.0695698	−	0.997577i	$-0.477837\pi$
$127$	199.139			0.139140			0.0695698	+	0.997577i	$0.477837\pi$
$128$	1455.00			1.00473
$129$			645.117i			0.440305i
$130$		0			0
$131$		−	2103.34i		−	1.40282i	−0.712756	−	0.701412i	$-0.752553\pi$
$131$		−	2103.34i		−	1.40282i	0.712756	−	0.701412i	$-0.247447\pi$
$132$	−47.5694			−0.0313666
$133$			2462.94i			1.60574i
$134$	1033.57			0.666319
$135$		0			0
$136$	680.967	+	801.067i	0.429356	+	0.505080i
$137$	1684.14			1.05026			0.525130	−	0.851022i	$-0.324017\pi$
$137$	1684.14			1.05026			0.525130	+	0.851022i	$0.324017\pi$
$138$	−320.365			−0.197618
$139$		−	1534.30i		−	0.936242i	−0.883664	−	0.468121i	$-0.844931\pi$
$139$		−	1534.30i		−	0.936242i	0.883664	−	0.468121i	$-0.155069\pi$
$140$		0			0
$141$			976.393i			0.583171i
$142$			761.248i			0.449877i
$143$		−	108.813i		−	0.0636323i
$144$	328.000			0.189815
$145$		0			0
$146$			791.188i			0.448488i
$147$		−	2988.33i		−	1.67669i
$148$			788.865i			0.438137i
$149$	−1087.43			−0.597891			−0.298946	−	0.954270i	$-0.596635\pi$
$149$	−1087.43			−0.597891			−0.298946	+	0.954270i	$0.596635\pi$
$150$		0			0
$151$	−3183.14			−1.71550			−0.857749	−	0.514069i	$-0.828138\pi$
$151$	−3183.14			−1.71550			−0.857749	+	0.514069i	$0.828138\pi$
$152$	1151.93			0.614699
$153$	363.183	+	427.236i	0.191906	+	0.225751i
$154$	−50.0000			−0.0261631
$155$		0			0
$156$		−	2129.62i		−	1.09299i
$157$	726.569			0.369341			0.184671	−	0.982800i	$-0.440878\pi$
$157$	726.569			0.369341			0.184671	+	0.982800i	$0.440878\pi$
$158$			50.7796i			0.0255684i
$159$			2922.94i			1.45789i
$160$		0			0
$161$	2357.14			1.15384
$162$	449.000			0.217758
$163$		−	3090.65i		−	1.48514i	−0.669766	−	0.742572i	$-0.733606\pi$
$163$		−	3090.65i		−	1.48514i	0.669766	−	0.742572i	$-0.266394\pi$
$164$		−	2212.25i		−	1.05334i
$165$		0			0
$166$	608.796			0.284649
$167$		−	3020.94i		−	1.39980i	−0.714239	−	0.699902i	$-0.753227\pi$
$167$		−	3020.94i		−	1.39980i	0.714239	−	0.699902i	$-0.246773\pi$
$168$	−2096.93			−0.962988
$169$	2674.43			1.21731
$170$		0			0
$171$	614.365			0.274747
$172$	−1036.00			−0.459269
$173$			1159.79i			0.509693i	0.966982	+	0.254846i	$0.0820249\pi$
$173$			1159.79i			0.509693i	−0.966982	+	0.254846i	$0.917975\pi$
$174$	586.365			0.255473
$175$		0			0
$176$		−	63.9200i		−	0.0273759i
$177$		−	1457.46i		−	0.618925i
$178$	47.5694			0.0200308
$179$	−117.569			−0.0490925			−0.0245462	−	0.999699i	$-0.507814\pi$
$179$	−117.569			−0.0490925			−0.0245462	+	0.999699i	$0.507814\pi$
$180$		0			0
$181$		−	4686.29i		−	1.92447i	−0.272216	−	0.962236i	$-0.587756\pi$
$181$		−	4686.29i		−	1.92447i	0.272216	−	0.962236i	$-0.412244\pi$
$182$		−	2238.44i		−	0.911671i
$183$	−2945.42			−1.18979
$184$		−	1102.45i		−	0.441706i
$185$		0			0
$186$	−237.431			−0.0935981
$187$	83.2589	−	70.7764i	0.0325588	−	0.0276774i
$188$	−1568.00			−0.608288
$189$	−4892.85			−1.88308
$190$		0			0
$191$	2497.42			0.946109			0.473054	−	0.881033i	$-0.343151\pi$
$191$	2497.42			0.946109			0.473054	+	0.881033i	$0.343151\pi$
$192$		−	727.936i		−	0.273616i
$193$		−	146.771i		−	0.0547399i	−0.999625	−	0.0273700i	$-0.991287\pi$
$193$		−	146.771i		−	0.0547399i	0.999625	−	0.0273700i	$-0.00871322\pi$
$194$			165.574i			0.0612760i
$195$		0			0
$196$	4798.99			1.74890
$197$			4140.32i			1.49739i	0.662916	+	0.748694i	$0.269319\pi$
$197$			4140.32i			1.49739i	−0.662916	+	0.748694i	$0.730681\pi$
$198$			12.4722i			0.00447657i
$199$			2846.33i			1.01392i	0.861968	+	0.506962i	$0.169232\pi$
$199$			2846.33i			1.01392i	−0.861968	+	0.506962i	$0.830768\pi$
$200$		0			0
$201$		−	4505.22i		−	1.58097i
$202$	336.204			0.117105
$203$	−4314.28			−1.49164
$204$	1629.49	−	1385.19i	0.559252	−	0.475406i
$205$		0			0
$206$	−82.3651			−0.0278575
$207$		−	587.974i		−	0.197425i
$208$	2861.62			0.953931
$209$		−	119.726i		−	0.0396251i
$210$		0			0
$211$		−	566.816i		−	0.184935i	−0.995716	−	0.0924674i	$-0.970525\pi$
$211$		−	566.816i		−	0.184935i	0.995716	−	0.0924674i	$-0.0294754\pi$
$212$	−4693.99			−1.52068
$213$	3318.20			1.06742
$214$		−	1621.61i		−	0.517994i
$215$		0			0
$216$			2288.42i			0.720868i
$217$	1746.93			0.546496
$218$			1064.14i			0.330610i
$219$	3448.71			1.06412
$220$		0			0
$221$	3168.57	+	3727.40i	0.964439	+	1.13453i
$222$	−491.226			−0.148509
$223$	1657.72			0.497800			0.248900	−	0.968529i	$-0.419931\pi$
$223$	1657.72			0.497800			0.248900	+	0.968529i	$0.419931\pi$
$224$		−	5163.48i		−	1.54018i
$225$		0			0
$226$		−	1858.58i		−	0.547039i
$227$		−	4295.77i		−	1.25604i	−0.778198	−	0.628019i	$-0.783866\pi$
$227$		−	4295.77i		−	1.25604i	0.778198	−	0.628019i	$-0.216134\pi$
$228$		−	2343.21i		−	0.680627i
$229$	1738.76			0.501749			0.250874	−	0.968020i	$-0.419282\pi$
$229$	1738.76			0.501749			0.250874	+	0.968020i	$0.419282\pi$
$230$		0			0
$231$			217.945i			0.0620767i
$232$			2017.82i			0.571019i
$233$			4877.51i			1.37140i	0.727884	+	0.685701i	$0.240504\pi$
$233$			4877.51i			1.37140i	−0.727884	+	0.685701i	$0.759496\pi$
$234$	−558.365			−0.155989
$235$		0			0
$236$	2340.56			0.645581
$237$	221.343			0.0606658
$238$	1712.75	−	1455.97i	0.466476	−	0.396539i
$239$	−3320.56			−0.898698			−0.449349	−	0.893356i	$-0.648344\pi$
$239$	−3320.56			−0.898698			−0.449349	+	0.893356i	$0.648344\pi$
$240$		0			0
$241$		−	1427.40i		−	0.381521i	−0.981637	−	0.190761i	$-0.938905\pi$
$241$		−	1427.40i		−	0.381521i	0.981637	−	0.190761i	$-0.0610955\pi$
$242$	−1328.57			−0.352908
$243$			2162.01i			0.570754i
$244$		−	4730.07i		−	1.24103i
$245$		0			0
$246$	1377.57			0.357035
$247$	5360.00			1.38076
$248$		−	817.055i		−	0.209206i
$249$		−	2653.68i		−	0.675382i
$250$		0			0
$251$	−1030.43			−0.259124			−0.129562	−	0.991571i	$-0.541357\pi$
$251$	−1030.43			−0.259124			−0.129562	+	0.991571i	$0.541357\pi$
$252$		−	1795.99i		−	0.448956i
$253$	−114.583			−0.0284735
$254$	−199.139			−0.0491932
$255$		0			0
$256$	−119.000			−0.0290527
$257$	4327.12			1.05027			0.525134	−	0.851020i	$-0.324015\pi$
$257$	4327.12			1.05027			0.525134	+	0.851020i	$0.324015\pi$
$258$		−	645.117i		−	0.155671i
$259$	3614.28			0.867105
$260$		0			0
$261$			1076.17i			0.255223i
$262$			2103.34i			0.495973i
$263$	663.139			0.155479			0.0777393	−	0.996974i	$-0.475230\pi$
$263$	663.139			0.155479			0.0777393	+	0.996974i	$0.475230\pi$
$264$	101.935			0.0237638
$265$		0			0
$266$		−	2462.94i		−	0.567716i
$267$		−	207.350i		−	0.0475267i
$268$	7234.99			1.64906
$269$			7663.39i			1.73697i	0.495715	+	0.868485i	$0.334906\pi$
$269$			7663.39i			1.73697i	−0.495715	+	0.868485i	$0.665094\pi$
$270$		0			0
$271$	−4319.05			−0.968132			−0.484066	−	0.875032i	$-0.660840\pi$
$271$	−4319.05			−0.968132			−0.484066	+	0.875032i	$0.660840\pi$
$272$	1861.31	+	2189.58i	0.414921	+	0.488099i
$273$	−9757.12			−2.16311
$274$	−1684.14			−0.371323
$275$		0			0
$276$	−2242.56			−0.489080
$277$		−	2258.36i		−	0.489861i	−0.969541	−	0.244930i	$-0.921235\pi$
$277$		−	2258.36i		−	0.489861i	0.969541	−	0.244930i	$-0.0787651\pi$
$278$			1534.30i			0.331012i
$279$		−	435.762i		−	0.0935069i
$280$		0			0
$281$	−7381.40			−1.56704			−0.783519	−	0.621368i	$-0.786577\pi$
$281$	−7381.40			−1.56704			−0.783519	+	0.621368i	$0.786577\pi$
$282$		−	976.393i		−	0.206182i
$283$			1018.17i			0.213865i	0.994266	+	0.106933i	$0.0341029\pi$
$283$			1018.17i			0.213865i	−0.994266	+	0.106933i	$0.965897\pi$
$284$			5328.74i			1.11339i
$285$		0			0
$286$			108.813i			0.0224974i
$287$	−10135.7			−2.08464
$288$	−1288.00			−0.263528
$289$	−791.076	+	4848.89i	−0.161017	+	0.986952i
$290$		0			0
$291$	721.722			0.145389
$292$			5538.32i			1.10995i
$293$	−7056.92			−1.40706			−0.703532	−	0.710664i	$-0.748395\pi$
$293$	−7056.92			−1.40706			−0.703532	+	0.710664i	$0.748395\pi$
$294$			2988.33i			0.592799i
$295$		0			0
$296$		−	1690.43i		−	0.331939i
$297$	237.847			0.0464690
$298$	1087.43			0.211386
$299$		−	5129.75i		−	0.992179i
$300$		0			0
$301$			4746.56i			0.908927i
$302$	3183.14			0.606520
$303$		−	1465.48i		−	0.277854i
$304$	3148.62			0.594032
$305$		0			0
$306$	−363.183	−	427.236i	−0.0678489	−	0.0798152i
$307$	−2083.29			−0.387296			−0.193648	−	0.981071i	$-0.562032\pi$
$307$	−2083.29			−0.387296			−0.193648	+	0.981071i	$0.562032\pi$
$308$	−350.000			−0.0647503
$309$			359.021i			0.0660971i
$310$		0			0
$311$			817.947i			0.149137i	0.997216	+	0.0745683i	$0.0237579\pi$
$311$			817.947i			0.149137i	−0.997216	+	0.0745683i	$0.976242\pi$
$312$			4563.48i			0.828065i
$313$		−	1717.47i		−	0.310151i	−0.987903	−	0.155075i	$-0.950438\pi$
$313$		−	1717.47i		−	0.310151i	0.987903	−	0.155075i	$-0.0495620\pi$
$314$	−726.569			−0.130582
$315$		0			0
$316$			355.457i			0.0632786i
$317$		−	613.809i		−	0.108754i	−0.998520	−	0.0543769i	$-0.982683\pi$
$317$		−	613.809i		−	0.108754i	0.998520	−	0.0543769i	$-0.0173172\pi$
$318$		−	2922.94i		−	0.515442i
$319$	209.722			0.0368094
$320$		0			0
$321$	−7068.42			−1.22904
$322$	−2357.14			−0.407945
$323$	3486.35	+	4101.23i	0.600576	+	0.706497i
$324$	3143.00			0.538923
$325$		0			0
$326$			3090.65i			0.525078i
$327$	4638.50			0.784432
$328$			4740.54i			0.798026i
$329$			7183.98i			1.20385i
$330$		0			0
$331$	−120.153			−0.0199523			−0.00997613	−	0.999950i	$-0.503176\pi$
$331$	−120.153			−0.0199523			−0.00997613	+	0.999950i	$0.503176\pi$
$332$	4261.57			0.704470
$333$		−	901.560i		−	0.148364i
$334$			3020.94i			0.494906i
$335$		0			0
$336$	−5731.62			−0.930612
$337$			2003.79i			0.323897i	0.986799	+	0.161949i	$0.0517779\pi$
$337$			2003.79i			0.323897i	−0.986799	+	0.161949i	$0.948222\pi$
$338$	−2674.43			−0.430384
$339$	−8101.35			−1.29795
$340$		0			0
$341$	−84.9206			−0.0134859
$342$	−614.365			−0.0971376
$343$		−	10986.7i		−	1.72951i
$344$	2220.00			0.347949
$345$		0			0
$346$		−	1159.79i		−	0.180204i
$347$			1655.90i			0.256178i	0.991763	+	0.128089i	$0.0408842\pi$
$347$			1655.90i			0.256178i	−0.991763	+	0.128089i	$0.959116\pi$
$348$	4104.56			0.632262
$349$	2207.71			0.338613			0.169306	−	0.985563i	$-0.445847\pi$
$349$	2207.71			0.338613			0.169306	+	0.985563i	$0.445847\pi$
$350$		0			0
$351$			10648.1i			1.61924i
$352$			251.003i			0.0380071i
$353$	11084.9			1.67136			0.835682	−	0.549214i	$-0.185073\pi$
$353$	11084.9			1.67136			0.835682	+	0.549214i	$0.185073\pi$
$354$			1457.46i			0.218823i
$355$		0			0
$356$	332.986			0.0495737
$357$	−6346.42	−	7465.71i	−0.940863	−	1.10680i
$358$	117.569			0.0173568
$359$	−8335.14			−1.22538			−0.612691	−	0.790323i	$-0.709913\pi$
$359$	−8335.14			−1.22538			−0.612691	+	0.790323i	$0.709913\pi$
$360$		0			0
$361$	−961.431			−0.140171
$362$			4686.29i			0.680404i
$363$			5791.10i			0.837339i
$364$		−	15669.1i		−	2.25627i
$365$		0			0
$366$	2945.42			0.420654
$367$			5185.31i			0.737523i	0.929524	+	0.368761i	$0.120218\pi$
$367$			5185.31i			0.737523i	−0.929524	+	0.368761i	$0.879782\pi$
$368$		−	3013.37i		−	0.426855i
$369$			2528.29i			0.356687i
$370$		0			0
$371$			21506.0i			3.00954i
$372$	−1662.01			−0.231644
$373$	−4059.15			−0.563472			−0.281736	−	0.959492i	$-0.590910\pi$
$373$	−4059.15			−0.563472			−0.281736	+	0.959492i	$0.590910\pi$
$374$	−83.2589	+	70.7764i	−0.0115113	+	0.00978545i
$375$		0			0
$376$	3360.00			0.460848
$377$			9389.00i			1.28265i
$378$	4892.85			0.665770
$379$		−	8500.46i		−	1.15208i	−0.817421	−	0.576041i	$-0.804597\pi$
$379$		−	8500.46i		−	1.15208i	0.817421	−	0.576041i	$-0.195403\pi$
$380$		0			0
$381$			868.026i			0.116720i
$382$	−2497.42			−0.334500
$383$	4513.42			0.602154			0.301077	−	0.953600i	$-0.402654\pi$
$383$	4513.42			0.602154			0.301077	+	0.953600i	$0.402654\pi$
$384$			6342.20i			0.842836i
$385$		0			0
$386$			146.771i			0.0193535i
$387$	1184.00			0.155520
$388$			1159.02i			0.151650i
$389$	−8881.39			−1.15759			−0.578797	−	0.815471i	$-0.696478\pi$
$389$	−8881.39			−1.15759			−0.578797	+	0.815471i	$0.696478\pi$
$390$		0			0
$391$	3925.06	−	3336.59i	0.507669	−	0.431557i
$392$	−10283.5			−1.32499
$393$	9168.26			1.17679
$394$		−	4140.32i		−	0.529407i
$395$		0			0
$396$			87.3054i			0.0110789i
$397$		−	9320.28i		−	1.17827i	−0.808036	−	0.589133i	$-0.799469\pi$
$397$		−	9320.28i		−	1.17827i	0.808036	−	0.589133i	$-0.200531\pi$
$398$		−	2846.33i		−	0.358476i
$399$	−10735.7			−1.34701
$400$		0			0
$401$		−	13773.5i		−	1.71525i	−0.514273	−	0.857627i	$-0.671938\pi$
$401$		−	13773.5i		−	1.71525i	0.514273	−	0.857627i	$-0.328062\pi$
$402$			4505.22i			0.558956i
$403$		−	3801.79i		−	0.469927i
$404$	2353.43			0.289821
$405$		0			0
$406$	4314.28			0.527374
$407$	−175.694			−0.0213977
$408$	−3491.77	+	2968.27i	−0.423697	+	0.360174i
$409$	14516.1			1.75495			0.877476	−	0.479620i	$-0.159226\pi$
$409$	14516.1			1.75495			0.877476	+	0.479620i	$0.159226\pi$
$410$		0			0
$411$			7340.99i			0.881033i
$412$	−576.556			−0.0689438
$413$		−	10723.5i		−	1.27765i
$414$			587.974i			0.0698004i
$415$		0			0
$416$	−11237.1			−1.32438
$417$	6687.86			0.785386
$418$			119.726i			0.0140096i
$419$			3075.95i			0.358640i	0.983791	+	0.179320i	$0.0573897\pi$
$419$			3075.95i			0.358640i	−0.983791	+	0.179320i	$0.942610\pi$
$420$		0			0
$421$	−3994.88			−0.462466			−0.231233	−	0.972898i	$-0.574276\pi$
$421$	−3994.88			−0.462466			−0.231233	+	0.972898i	$0.574276\pi$
$422$			566.816i			0.0653843i
$423$	1792.00			0.205981
$424$	10058.5			1.15209
$425$		0			0
$426$	−3318.20			−0.377389
$427$	−21671.4			−2.45609
$428$		−	11351.2i		−	1.28197i
$429$	474.306			0.0533792
$430$		0			0
$431$		−	3690.87i		−	0.412490i	−0.978500	−	0.206245i	$-0.933876\pi$
$431$		−	3690.87i		−	0.412490i	0.978500	−	0.206245i	$-0.0661244\pi$
$432$			6255.02i			0.696631i
$433$	−13886.3			−1.54119			−0.770593	−	0.637327i	$-0.780040\pi$
$433$	−13886.3			−1.54119			−0.770593	+	0.637327i	$0.780040\pi$
$434$	−1746.93			−0.193216
$435$		0			0
$436$			7449.01i			0.818217i
$437$		−	5644.23i		−	0.617850i
$438$	−3448.71			−0.376223
$439$			3706.34i			0.402947i	0.979494	+	0.201474i	$0.0645730\pi$
$439$			3706.34i			0.402947i	−0.979494	+	0.201474i	$0.935427\pi$
$440$		0			0
$441$	−5484.56			−0.592221
$442$	−3168.57	−	3727.40i	−0.340981	−	0.401118i
$443$	5341.82			0.572906			0.286453	−	0.958094i	$-0.407524\pi$
$443$	5341.82			0.572906			0.286453	+	0.958094i	$0.407524\pi$
$444$	−3438.58			−0.367540
$445$		0			0
$446$	−1657.72			−0.175999
$447$		−	4740.00i		−	0.501553i
$448$		−	5355.91i		−	0.564828i
$449$			13111.6i			1.37812i	0.724705	+	0.689059i	$0.241976\pi$
$449$			13111.6i			1.37812i	−0.724705	+	0.689059i	$0.758024\pi$
$450$		0			0
$451$	492.708			0.0514429
$452$		−	13010.0i		−	1.35385i
$453$		−	13875.0i		−	1.43908i
$454$			4295.77i			0.444076i
$455$		0			0
$456$			5021.17i			0.515653i
$457$	2839.83			0.290682			0.145341	−	0.989382i	$-0.453572\pi$
$457$	2839.83			0.290682			0.145341	+	0.989382i	$0.453572\pi$
$458$	−1738.76			−0.177395
$459$	−8147.47	+	6925.96i	−0.828521	+	0.704305i
$460$		0			0
$461$	3317.69			0.335185			0.167593	−	0.985856i	$-0.446401\pi$
$461$	3317.69			0.335185			0.167593	+	0.985856i	$0.446401\pi$
$462$		−	217.945i		−	0.0219474i
$463$	7078.28			0.710487			0.355243	−	0.934774i	$-0.384398\pi$
$463$	7078.28			0.710487			0.355243	+	0.934774i	$0.384398\pi$
$464$			5515.38i			0.551821i
$465$		0			0
$466$		−	4877.51i		−	0.484864i
$467$	460.468			0.0456273			0.0228136	−	0.999740i	$-0.492738\pi$
$467$	460.468			0.0456273			0.0228136	+	0.999740i	$0.492738\pi$
$468$	−3908.56			−0.386054
$469$		−	33147.9i		−	3.26360i
$470$		0			0
$471$			3167.04i			0.309829i
$472$	−5015.48			−0.489102
$473$		−	230.736i		−	0.0224297i
$474$	−221.343			−0.0214486
$475$		0			0
$476$	11989.3	−	10191.8i	1.15447	−	0.981385i
$477$	5364.56			0.514939
$478$	3320.56			0.317738
$479$			1125.49i			0.107359i	0.998558	+	0.0536794i	$0.0170949\pi$
$479$			1125.49i			0.107359i	−0.998558	+	0.0536794i	$0.982905\pi$
$480$		0			0
$481$		−	7865.62i		−	0.745616i
$482$			1427.40i			0.134888i
$483$			10274.5i			0.967924i
$484$	−9299.99			−0.873402
$485$		0			0
$486$		−	2162.01i		−	0.201792i
$487$			17849.9i			1.66090i	0.557095	+	0.830449i	$0.311916\pi$
$487$			17849.9i			1.66090i	−0.557095	+	0.830449i	$0.688084\pi$
$488$			10135.9i			0.940224i
$489$	13471.8			1.24584
$490$		0			0
$491$	−19479.4			−1.79041			−0.895206	−	0.445652i	$-0.852972\pi$
$491$	−19479.4			−1.79041			−0.895206	+	0.445652i	$0.852972\pi$
$492$	9642.99			0.883617
$493$	−7184.04	+	6106.98i	−0.656294	+	0.557899i
$494$	−5360.00			−0.488174
$495$		0			0
$496$		−	2233.28i		−	0.202172i
$497$	24414.2			2.20348
$498$			2653.68i			0.238784i
$499$			3510.92i			0.314970i	0.987521	+	0.157485i	$0.0503387\pi$
$499$			3510.92i			0.314970i	−0.987521	+	0.157485i	$0.949661\pi$
$500$		0			0
$501$	13168.0			1.17425
$502$	1030.43			0.0916143
$503$			1137.77i			0.100856i	0.998728	+	0.0504280i	$0.0160585\pi$
$503$			1137.77i			0.100856i	−0.998728	+	0.0504280i	$0.983941\pi$
$504$			3848.56i			0.340136i
$505$		0			0
$506$	114.583			0.0100669
$507$			11657.6i			1.02117i
$508$	−1393.97			−0.121747
$509$	5528.26			0.481407			0.240703	−	0.970599i	$-0.422622\pi$
$509$	5528.26			0.481407			0.240703	+	0.970599i	$0.422622\pi$
$510$		0			0
$511$	25374.4			2.19667
$512$	−11521.0			−0.994455
$513$			11716.1i			1.00834i
$514$	−4327.12			−0.371325
$515$		0			0
$516$		−	4515.82i		−	0.385267i
$517$		−	349.222i		−	0.0297075i
$518$	−3614.28			−0.306568
$519$	−5055.39			−0.427566
$520$		0			0
$521$			10168.0i			0.855029i	0.904009	+	0.427514i	$0.140611\pi$
$521$			10168.0i			0.855029i	−0.904009	+	0.427514i	$0.859389\pi$
$522$		−	1076.17i		−	0.0902351i
$523$	13495.8			1.12836			0.564180	−	0.825652i	$-0.309192\pi$
$523$	13495.8			1.12836			0.564180	+	0.825652i	$0.309192\pi$
$524$			14723.4i			1.22747i
$525$		0			0
$526$	−663.139			−0.0549700
$527$	2908.96	−	2472.83i	0.240448	−	0.204399i
$528$	278.621			0.0229648
$529$	6765.22			0.556030
$530$		0			0
$531$	−2674.92			−0.218610
$532$		−	17240.6i		−	1.40502i
$533$			22057.9i			1.79256i
$534$			207.350i			0.0168032i
$535$		0			0
$536$	−15503.5			−1.24935
$537$		−	512.473i		−	0.0411822i
$538$		−	7663.39i		−	0.614112i
$539$			1068.82i			0.0854125i
$540$		0			0
$541$		−	6134.53i		−	0.487512i	−0.969837	−	0.243756i	$-0.921620\pi$
$541$		−	6134.53i		−	0.487512i	0.969837	−	0.243756i	$-0.0783796\pi$
$542$	4319.05			0.342286
$543$	20427.1			1.61438
$544$	−7309.05	−	8598.12i	−0.576053	−	0.677650i
$545$		0			0
$546$	9757.12			0.764774
$547$			3005.13i			0.234899i	0.993079	+	0.117450i	$0.0374719\pi$
$547$			3005.13i			0.234899i	−0.993079	+	0.117450i	$0.962528\pi$
$548$	−11789.0			−0.918978
$549$			5405.80i			0.420244i
$550$		0			0
$551$			10330.7i			0.798731i
$552$	4805.48			0.370534
$553$	1628.57			0.125233
$554$			2258.36i			0.173192i
$555$		0			0
$556$			10740.1i			0.819212i
$557$	12422.3			0.944970			0.472485	−	0.881339i	$-0.343357\pi$
$557$	12422.3			0.944970			0.472485	+	0.881339i	$0.343357\pi$
$558$			435.762i			0.0330597i
$559$	10329.8			0.781578
$560$		0			0
$561$	308.507	+	362.917i	0.0232178	+	0.0273126i
$562$	7381.40			0.554031
$563$	−25057.8			−1.87577			−0.937885	−	0.346947i	$-0.887219\pi$
$563$	−25057.8			−1.87577			−0.937885	+	0.346947i	$0.887219\pi$
$564$		−	6834.75i		−	0.510275i
$565$		0			0
$566$		−	1018.17i		−	0.0756128i
$567$		−	14400.0i		−	1.06657i
$568$		−	11418.7i		−	0.843519i
$569$	−10908.1			−0.803677			−0.401839	−	0.915710i	$-0.631629\pi$
$569$	−10908.1			−0.803677			−0.401839	+	0.915710i	$0.631629\pi$
$570$		0			0
$571$		−	23519.0i		−	1.72371i	−0.507155	−	0.861855i	$-0.669303\pi$
$571$		−	23519.0i		−	1.72371i	0.507155	−	0.861855i	$-0.330697\pi$
$572$			761.692i			0.0556782i
$573$			10886.0i			0.793663i
$574$	10135.7			0.737031
$575$		0			0
$576$	−1336.00			−0.0966435
$577$	10551.4			0.761280			0.380640	−	0.924723i	$-0.375704\pi$
$577$	10551.4			0.761280			0.380640	+	0.924723i	$0.375704\pi$
$578$	791.076	−	4848.89i	0.0569281	−	0.348940i
$579$	639.760			0.0459197
$580$		0			0
$581$		−	19524.9i		−	1.39420i
$582$	−721.722			−0.0514027
$583$		−	1045.43i		−	0.0742667i
$584$		−	11867.8i		−	0.840914i
$585$		0			0
$586$	7056.92			0.497472
$587$	20441.8			1.43735			0.718674	−	0.695348i	$-0.244750\pi$
$587$	20441.8			1.43735			0.718674	+	0.695348i	$0.244750\pi$
$588$			20918.3i			1.46710i
$589$		−	4183.08i		−	0.292633i
$590$		0			0
$591$	−18047.2			−1.25611
$592$		−	4620.50i		−	0.320779i
$593$	−768.111			−0.0531915			−0.0265957	−	0.999646i	$-0.508467\pi$
$593$	−768.111			−0.0531915			−0.0265957	+	0.999646i	$0.508467\pi$
$594$	−237.847			−0.0164293
$595$		0			0
$596$	7612.01			0.523155
$597$	−12406.9			−0.850551
$598$			5129.75i			0.350788i
$599$	20756.2			1.41582			0.707911	−	0.706302i	$-0.249638\pi$
$599$	20756.2			1.41582			0.707911	+	0.706302i	$0.249638\pi$
$600$		0			0
$601$		−	20609.7i		−	1.39882i	−0.714722	−	0.699408i	$-0.753447\pi$
$601$		−	20609.7i		−	1.39882i	0.714722	−	0.699408i	$-0.246553\pi$
$602$		−	4746.56i		−	0.321354i
$603$	−8268.56			−0.558411
$604$	22282.0			1.50106
$605$		0			0
$606$			1465.48i			0.0982361i
$607$		−	5057.91i		−	0.338211i	−0.985598	−	0.169106i	$-0.945912\pi$
$607$		−	5057.91i		−	0.338211i	0.985598	−	0.169106i	$-0.0540879\pi$
$608$	−12364.1			−0.824721
$609$		−	18805.5i		−	1.25129i
$610$		0			0
$611$	15634.2			1.03518
$612$	−2542.28	−	2990.65i	−0.167917	−	0.197533i
$613$	−2960.26			−0.195047			−0.0975236	−	0.995233i	$-0.531092\pi$
$613$	−2960.26			−0.195047			−0.0975236	+	0.995233i	$0.531092\pi$
$614$	2083.29			0.136930
$615$		0			0
$616$	750.000			0.0490558
$617$			12811.6i			0.835941i	0.908461	+	0.417970i	$0.137258\pi$
$617$			12811.6i			0.835941i	−0.908461	+	0.417970i	$0.862742\pi$
$618$		−	359.021i		−	0.0233688i
$619$		−	9469.50i		−	0.614881i	−0.951567	−	0.307441i	$-0.900527\pi$
$619$		−	9469.50i		−	0.614881i	0.951567	−	0.307441i	$-0.0994725\pi$
$620$		0			0
$621$	11212.8			0.724562
$622$		−	817.947i		−	0.0527278i
$623$		−	1525.61i		−	0.0981099i
$624$			12473.5i			0.800225i
$625$		0			0
$626$			1717.47i			0.109655i
$627$	521.875			0.0332403
$628$	−5085.99			−0.323173
$629$	6018.42	−	5116.11i	0.381510	−	0.324313i
$630$		0			0
$631$	−2124.25			−0.134018			−0.0670088	−	0.997752i	$-0.521346\pi$
$631$	−2124.25			−0.134018			−0.0670088	+	0.997752i	$0.521346\pi$
$632$		−	761.694i		−	0.0479408i
$633$	2470.69			0.155136
$634$			613.809i			0.0384503i
$635$		0			0
$636$		−	20460.6i		−	1.27565i
$637$	−47849.8			−2.97626
$638$	−209.722			−0.0130141
$639$		−	6089.99i		−	0.377021i
$640$		0			0
$641$		−	14267.3i		−	0.879132i	−0.898210	−	0.439566i	$-0.855132\pi$
$641$		−	14267.3i		−	0.879132i	0.898210	−	0.439566i	$-0.144868\pi$
$642$	7068.42			0.434530
$643$		−	18401.0i		−	1.12856i	−0.825582	−	0.564282i	$-0.809153\pi$
$643$		−	18401.0i		−	1.12856i	0.825582	−	0.564282i	$-0.190847\pi$
$644$	−16500.0			−1.00961
$645$		0			0
$646$	−3486.35	−	4101.23i	−0.212336	−	0.249784i
$647$	−31074.7			−1.88821			−0.944105	−	0.329644i	$-0.893071\pi$
$647$	−31074.7			−1.88821			−0.944105	+	0.329644i	$0.893071\pi$
$648$	−6735.00			−0.408296
$649$			521.284i			0.0315288i
$650$		0			0
$651$			7614.71i			0.458439i
$652$			21634.6i			1.29950i
$653$			9139.88i			0.547735i	0.961767	+	0.273868i	$0.0883030\pi$
$653$			9139.88i			0.547735i	−0.961767	+	0.273868i	$0.911697\pi$
$654$	−4638.50			−0.277339
$655$		0			0
$656$			12957.5i			0.771196i
$657$		−	6329.50i		−	0.375856i
$658$		−	7183.98i		−	0.425624i
$659$	−7548.40			−0.446197			−0.223099	−	0.974796i	$-0.571617\pi$
$659$	−7548.40			−0.446197			−0.223099	+	0.974796i	$0.571617\pi$
$660$		0			0
$661$	27546.8			1.62095			0.810474	−	0.585775i	$-0.199210\pi$
$661$	27546.8			1.62095			0.810474	+	0.585775i	$0.199210\pi$
$662$	120.153			0.00705419
$663$	−16247.4	+	13811.5i	−0.951727	+	0.809040i
$664$	−9131.93			−0.533717
$665$		0			0
$666$			901.560i			0.0524546i
$667$	9886.89			0.573946
$668$			21146.6i			1.22483i
$669$			7225.84i			0.417589i
$670$		0			0
$671$	1053.47			0.0606093
$672$	22507.1			1.29201
$673$		−	21053.9i		−	1.20590i	−0.797780	−	0.602949i	$-0.793992\pi$
$673$		−	21053.9i		−	1.20590i	0.797780	−	0.602949i	$-0.206008\pi$
$674$		−	2003.79i		−	0.114515i
$675$		0			0
$676$	−18721.0			−1.06515
$677$		−	26364.3i		−	1.49669i	−0.663308	−	0.748347i	$-0.730848\pi$
$677$		−	26364.3i		−	1.49669i	0.663308	−	0.748347i	$-0.269152\pi$
$678$	8101.35			0.458895
$679$	5310.19			0.300127
$680$		0			0
$681$	18724.8			1.05365
$682$	84.9206			0.00476800
$683$		−	9790.88i		−	0.548518i	−0.961656	−	0.274259i	$-0.911567\pi$
$683$		−	9790.88i		−	0.548518i	0.961656	−	0.274259i	$-0.0884325\pi$
$684$	−4300.56			−0.240403
$685$		0			0
$686$			10986.7i			0.611476i
$687$			7579.08i			0.420902i
$688$	6068.00			0.336250
$689$	46802.8			2.58787
$690$		0			0
$691$		−	16042.1i		−	0.883171i	−0.897219	−	0.441585i	$-0.854416\pi$
$691$		−	16042.1i		−	0.883171i	0.897219	−	0.441585i	$-0.145584\pi$
$692$		−	8118.50i		−	0.445981i
$693$	400.000			0.0219260
$694$		−	1655.90i		−	0.0905724i
$695$		0			0
$696$	−8795.48			−0.479011
$697$	−16877.7	+	14347.3i	−0.917202	+	0.779691i
$698$	−2207.71			−0.119718
$699$	−21260.6			−1.15043
$700$		0			0
$701$	23409.6			1.26130			0.630649	−	0.776068i	$-0.282789\pi$
$701$	23409.6			1.26130			0.630649	+	0.776068i	$0.282789\pi$
$702$		−	10648.1i		−	0.572489i
$703$		−	8654.49i		−	0.464310i
$704$			260.357i			0.0139383i
$705$		0			0
$706$	−11084.9			−0.590916
$707$		−	10782.5i		−	0.573576i
$708$			10202.2i			0.541559i
$709$		−	28647.7i		−	1.51747i	−0.651399	−	0.758736i	$-0.725817\pi$
$709$		−	28647.7i		−	1.51747i	0.651399	−	0.758736i	$-0.274183\pi$
$710$		0			0
$711$		−	406.237i		−	0.0214277i
$712$	−713.542			−0.0375577
$713$	−4003.39			−0.210278
$714$	6346.42	+	7465.71i	0.332645	+	0.391313i
$715$		0			0
$716$	822.986			0.0429559
$717$		−	14474.0i		−	0.753891i
$718$	8335.14			0.433238
$719$		−	37028.9i		−	1.92065i	−0.278891	−	0.960323i	$-0.589967\pi$
$719$		−	37028.9i		−	1.92065i	0.278891	−	0.960323i	$-0.410033\pi$
$720$		0			0
$721$			2641.56i			0.136445i
$722$	961.431			0.0495578
$723$	6221.88			0.320047
$724$			32804.1i			1.68391i
$725$		0			0
$726$		−	5791.10i		−	0.296044i
$727$	20104.0			1.02561			0.512803	−	0.858506i	$-0.328607\pi$
$727$	20104.0			1.02561			0.512803	+	0.858506i	$0.328607\pi$
$728$			33576.6i			1.70938i
$729$	−21547.0			−1.09470
$730$		0			0
$731$	6718.88	+	7903.86i	0.339954	+	0.399911i
$732$	20617.9			1.04107
$733$	−6503.46			−0.327709			−0.163855	−	0.986485i	$-0.552393\pi$
$733$	−6503.46			−0.327709			−0.163855	+	0.986485i	$0.552393\pi$
$734$		−	5185.31i		−	0.260754i
$735$		0			0
$736$			11833.0i			0.592622i
$737$			1611.36i			0.0805363i
$738$		−	2528.29i		−	0.126108i
$739$	20453.1			1.01810			0.509051	−	0.860736i	$-0.329996\pi$
$739$	20453.1			1.01810			0.509051	+	0.860736i	$0.329996\pi$
$740$		0			0
$741$			23363.7i			1.15828i
$742$		−	21506.0i		−	1.06403i
$743$		−	21062.8i		−	1.04000i	−0.854166	−	0.520000i	$-0.825932\pi$
$743$		−	21062.8i		−	1.04000i	0.854166	−	0.520000i	$-0.174068\pi$
$744$	3561.46			0.175497
$745$		0			0
$746$	4059.15			0.199217
$747$	−4870.37			−0.238551
$748$	−582.813	+	495.434i	−0.0284890	+	0.0242178i
$749$	−52007.0			−2.53711
$750$		0			0
$751$			21729.2i			1.05581i	0.849305	+	0.527903i	$0.177021\pi$
$751$			21729.2i			1.05581i	−0.849305	+	0.527903i	$0.822979\pi$
$752$	9184.00			0.445354
$753$		−	4491.54i		−	0.217372i
$754$		−	9389.00i		−	0.453485i
$755$		0			0
$756$	34249.9			1.64770
$757$	25048.6			1.20265			0.601325	−	0.799004i	$-0.294640\pi$
$757$	25048.6			1.20265			0.601325	+	0.799004i	$0.294640\pi$
$758$			8500.46i			0.407323i
$759$		−	499.457i		−	0.0238856i
$760$		0			0
$761$	−19548.1			−0.931169			−0.465584	−	0.885003i	$-0.654156\pi$
$761$	−19548.1			−0.931169			−0.465584	+	0.885003i	$0.654156\pi$
$762$		−	868.026i		−	0.0412668i
$763$	34128.5			1.61931
$764$	−17481.9			−0.827845
$765$		0			0
$766$	−4513.42			−0.212893
$767$	−23337.2			−1.09864
$768$		−	518.709i		−	0.0243715i
$769$	10730.7			0.503197			0.251599	−	0.967832i	$-0.419044\pi$
$769$	10730.7			0.503197			0.251599	+	0.967832i	$0.419044\pi$
$770$		0			0
$771$			18861.5i			0.881038i
$772$			1027.40i			0.0478974i
$773$	11068.5			0.515014			0.257507	−	0.966276i	$-0.417099\pi$
$773$	11068.5			0.515014			0.257507	+	0.966276i	$0.417099\pi$
$774$	−1184.00			−0.0549845
$775$		0			0
$776$		−	2483.62i		−	0.114893i
$777$			15754.3i			0.727389i
$778$	8881.39			0.409271
$779$			24270.2i			1.11626i
$780$		0			0
$781$	−1186.81			−0.0543755
$782$	−3925.06	+	3336.59i	−0.179488	+	0.152578i
$783$	−20522.8			−0.936685
$784$	−28108.3			−1.28045
$785$		0			0
$786$	−9168.26			−0.416057
$787$			36768.9i			1.66540i	0.553725	+	0.832699i	$0.313206\pi$
$787$			36768.9i			1.66540i	−0.553725	+	0.832699i	$0.686794\pi$
$788$		−	28982.2i		−	1.31021i
$789$			2890.56i			0.130426i
$790$		0			0
$791$	−59607.0			−2.67937
$792$		−	187.083i		−	0.00839357i
$793$			47162.6i			2.11197i
$794$			9320.28i			0.416580i
$795$		0			0
$796$		−	19924.3i		−	0.887184i
$797$	−23834.5			−1.05930			−0.529650	−	0.848216i	$-0.677677\pi$
$797$	−23834.5			−1.05930			−0.529650	+	0.848216i	$0.677677\pi$
$798$	10735.7			0.476240
$799$	10169.1	+	11962.6i	0.450259	+	0.529670i
$800$		0			0
$801$	−380.556			−0.0167869
$802$			13773.5i			0.606434i
$803$	−1233.48			−0.0542075
$804$			31536.6i			1.38334i
$805$		0			0
$806$			3801.79i			0.166144i
$807$	−33403.9			−1.45709
$808$	−5043.07			−0.219572
$809$			22538.1i			0.979478i	0.871869	+	0.489739i	$0.162908\pi$
$809$			22538.1i			0.979478i	−0.871869	+	0.489739i	$0.837092\pi$
$810$		0			0
$811$		−	22895.4i		−	0.991325i	−0.868515	−	0.495663i	$-0.834925\pi$
$811$		−	22895.4i		−	0.991325i	0.868515	−	0.495663i	$-0.165075\pi$
$812$	30199.9			1.30519
$813$		−	18826.3i		−	0.812137i
$814$	175.694			0.00756522
$815$		0			0
$816$	−9544.17	+	8113.26i	−0.409452	+	0.348065i
$817$	11365.8			0.486704
$818$	−14516.1			−0.620469
$819$			17907.5i			0.764028i
$820$		0			0
$821$		−	13361.7i		−	0.567999i	−0.958824	−	0.283999i	$-0.908339\pi$
$821$		−	13361.7i		−	0.567999i	0.958824	−	0.283999i	$-0.0916614\pi$
$822$		−	7340.99i		−	0.311492i
$823$		−	22013.0i		−	0.932349i	−0.884693	−	0.466175i	$-0.845632\pi$
$823$		−	22013.0i		−	0.932349i	0.884693	−	0.466175i	$-0.154368\pi$
$824$	1235.48			0.0522328
$825$		0			0
$826$			10723.5i			0.451718i
$827$		−	17100.5i		−	0.719035i	−0.933138	−	0.359517i	$-0.882941\pi$
$827$		−	17100.5i		−	0.719035i	0.933138	−	0.359517i	$-0.117059\pi$
$828$			4115.82i			0.172747i
$829$	13082.8			0.548113			0.274057	−	0.961714i	$-0.411634\pi$
$829$	13082.8			0.548113			0.274057	+	0.961714i	$0.411634\pi$
$830$		0			0
$831$	9843.94			0.410930
$832$	−11655.9			−0.485691
$833$	−31123.4	−	36612.5i	−1.29455	−	1.52287i
$834$	−6687.86			−0.277676
$835$		0			0
$836$			838.084i			0.0346720i
$837$	8310.07			0.343176
$838$		−	3075.95i		−	0.126798i
$839$			26770.1i			1.10156i	0.834652	+	0.550778i	$0.185669\pi$
$839$			26770.1i			1.10156i	−0.834652	+	0.550778i	$0.814331\pi$
$840$		0			0
$841$	6293.00			0.258026
$842$	3994.88			0.163507
$843$		−	32174.8i		−	1.31454i
$844$			3967.71i			0.161818i
$845$		0			0
$846$	−1792.00			−0.0728253
$847$			42609.0i			1.72853i
$848$	27493.3			1.11336
$849$	−4438.10			−0.179405
$850$		0			0
$851$	−8282.72			−0.333640
$852$	−23227.4			−0.933989
$853$			19707.4i			0.791053i	0.918455	+	0.395526i	$0.129438\pi$
$853$			19707.4i			0.791053i	−0.918455	+	0.395526i	$0.870562\pi$
$854$	21671.4			0.868360
$855$		0			0
$856$			24324.1i			0.971239i
$857$		−	19382.1i		−	0.772556i	−0.922382	−	0.386278i	$-0.873761\pi$
$857$		−	19382.1i		−	0.772556i	0.922382	−	0.386278i	$-0.126239\pi$
$858$	−474.306			−0.0188724
$859$	37163.2			1.47613			0.738063	−	0.674732i	$-0.235741\pi$
$859$	37163.2			1.47613			0.738063	+	0.674732i	$0.235741\pi$
$860$		0			0
$861$		−	44180.5i		−	1.74874i
$862$			3690.87i			0.145837i
$863$	19130.8			0.754599			0.377300	−	0.926091i	$-0.376853\pi$
$863$	19130.8			0.754599			0.377300	+	0.926091i	$0.376853\pi$
$864$		−	24562.4i		−	0.967164i
$865$		0			0
$866$	13886.3			0.544892
$867$	−21135.8	−	3448.22i	−0.827925	−	0.135072i
$868$	−12228.5			−0.478184
$869$	−79.1667			−0.00309039
$870$		0			0
$871$	−72138.6			−2.80634
$872$		−	15962.2i		−	0.619893i
$873$		−	1324.60i		−	0.0513525i
$874$			5644.23i			0.218443i
$875$		0			0
$876$	−24141.0			−0.931104
$877$			45521.7i			1.75275i	0.481633	+	0.876373i	$0.340044\pi$
$877$			45521.7i			1.75275i	−0.481633	+	0.876373i	$0.659956\pi$
$878$		−	3706.34i		−	0.142463i
$879$		−	30760.4i		−	1.18034i
$880$		0			0
$881$		−	33610.6i		−	1.28532i	−0.766150	−	0.642662i	$-0.777830\pi$
$881$		−	33610.6i		−	1.28532i	0.766150	−	0.642662i	$-0.222170\pi$
$882$	5484.56			0.209382
$883$	42768.9			1.63000			0.814999	−	0.579462i	$-0.196737\pi$
$883$	42768.9			1.63000			0.814999	+	0.579462i	$0.196737\pi$
$884$	−22180.0	−	26091.8i	−0.843884	−	0.992717i
$885$		0			0
$886$	−5341.82			−0.202553
$887$		−	4402.36i		−	0.166648i	−0.996523	−	0.0833240i	$-0.973446\pi$
$887$		−	4402.36i		−	0.166648i	0.996523	−	0.0833240i	$-0.0265536\pi$
$888$	7368.39			0.278454
$889$			6386.65i			0.240946i
$890$		0			0
$891$			700.002i			0.0263198i
$892$	−11604.1			−0.435575
$893$	17202.2			0.644625
$894$			4740.00i			0.177326i
$895$		0			0
$896$			46663.8i			1.73987i
$897$	22360.1			0.832309
$898$		−	13111.6i		−	0.487238i
$899$	7327.42			0.271839
$900$		0			0
$901$	30442.4	+	35811.4i	1.12562	+	1.32414i
$902$	−492.708			−0.0181878
$903$	−20689.8			−0.762472
$904$			27878.7i			1.02570i
$905$		0			0
$906$			13875.0i			0.508792i
$907$			34274.0i			1.25474i	0.778721	+	0.627370i	$0.215869\pi$
$907$			34274.0i			1.25474i	−0.778721	+	0.627370i	$0.784131\pi$
$908$			30070.4i			1.09903i
$909$	−2689.63			−0.0981403
$910$		0			0
$911$			48631.3i			1.76863i	0.466887	+	0.884317i	$0.345375\pi$
$911$			48631.3i			1.76863i	−0.466887	+	0.884317i	$0.654625\pi$
$912$			13724.5i			0.498316i
$913$			949.128i			0.0344048i
$914$	−2839.83			−0.102772
$915$		0			0
$916$	−12171.3			−0.439030
$917$	67457.0			2.42926
$918$	8147.47	−	6925.96i	0.292926	−	0.249009i
$919$	−5743.19			−0.206149			−0.103074	−	0.994674i	$-0.532868\pi$
$919$	−5743.19			−0.206149			−0.103074	+	0.994674i	$0.532868\pi$
$920$		0			0
$921$		−	9080.86i		−	0.324891i
$922$	−3317.69			−0.118506
$923$		−	53131.8i		−	1.89475i
$924$		−	1525.61i		−	0.0543171i
$925$		0			0
$926$	−7078.28			−0.251195
$927$	658.921			0.0233461
$928$		−	21657.9i		−	0.766117i
$929$		−	23854.7i		−	0.842462i	−0.906953	−	0.421231i	$-0.861598\pi$
$929$		−	23854.7i		−	0.842462i	0.906953	−	0.421231i	$-0.138402\pi$
$930$		0			0
$931$	−52648.7			−1.85338
$932$		−	34142.6i		−	1.19998i
$933$	−3565.35			−0.125106
$934$	−460.468			−0.0161317
$935$		0			0
$936$	8375.48			0.292480
$937$	−53543.7			−1.86681			−0.933403	−	0.358830i	$-0.883176\pi$
$937$	−53543.7			−1.86681			−0.933403	+	0.358830i	$0.883176\pi$
$938$			33147.9i			1.15386i
$939$	7486.28			0.260176
$940$		0			0
$941$			9811.15i			0.339888i	0.985454	+	0.169944i	$0.0543587\pi$
$941$			9811.15i			0.339888i	−0.985454	+	0.169944i	$0.945641\pi$
$942$		−	3167.04i		−	0.109541i
$943$	23227.6			0.802117
$944$	−13709.0			−0.472658
$945$		0			0
$946$			230.736i			0.00793009i
$947$			39956.9i			1.37109i	0.728030	+	0.685546i	$0.240436\pi$
$947$			39956.9i			1.37109i	−0.728030	+	0.685546i	$0.759564\pi$
$948$	−1549.40			−0.0530826
$949$		−	55221.5i		−	1.88890i
$950$		0			0
$951$	2675.53			0.0912304
$952$	−25691.3	+	21839.5i	−0.874642	+	0.743511i
$953$	32346.1			1.09947			0.549733	−	0.835340i	$-0.314729\pi$
$953$	32346.1			1.09947			0.549733	+	0.835340i	$0.314729\pi$
$954$	−5364.56			−0.182059
$955$		0			0
$956$	23243.9			0.786361
$957$			914.158i			0.0308783i
$958$		−	1125.49i		−	0.0379571i
$959$			54012.6i			1.81872i
$960$		0			0
$961$	26824.0			0.900406
$962$			7865.62i			0.263615i
$963$			12972.8i			0.434106i
$964$			9991.77i			0.333831i
$965$		0			0
$966$		−	10274.5i		−	0.342213i
$967$	13344.6			0.443777			0.221888	−	0.975072i	$-0.428778\pi$
$967$	13344.6			0.443777			0.221888	+	0.975072i	$0.428778\pi$
$968$	19928.5			0.661702
$969$	−17876.9	+	15196.7i	−0.592660	+	0.503805i
$970$		0			0
$971$	27529.6			0.909852			0.454926	−	0.890529i	$-0.349666\pi$
$971$	27529.6			0.909852			0.454926	+	0.890529i	$0.349666\pi$
$972$		−	15134.1i		−	0.499410i
$973$	49207.0			1.62128
$974$		−	17849.9i		−	0.587216i
$975$		0			0
$976$			27704.7i			0.908613i
$977$	−39539.2			−1.29475			−0.647375	−	0.762172i	$-0.724133\pi$
$977$	−39539.2			−1.29475			−0.647375	+	0.762172i	$0.724133\pi$
$978$	−13471.8			−0.440472
$979$			74.1620i			0.00242107i
$980$		0			0
$981$		−	8513.15i		−	0.277068i
$982$	19479.4			0.633006
$983$			27892.1i			0.905006i	0.891763	+	0.452503i	$0.149469\pi$
$983$			27892.1i			0.905006i	−0.891763	+	0.452503i	$0.850531\pi$
$984$	−20663.5			−0.669441
$985$		0			0
$986$	7184.04	−	6106.98i	0.232035	−	0.197247i
$987$	−31314.2			−1.00987
$988$	−37520.0			−1.20817
$989$		−	10877.5i		−	0.349732i
$990$		0			0
$991$			25872.6i			0.829336i	0.909973	+	0.414668i	$0.136102\pi$
$991$			25872.6i			0.829336i	−0.909973	+	0.414668i	$0.863898\pi$
$992$			8769.72i			0.280684i
$993$		−	523.734i		−	0.0167374i
$994$	−24414.2			−0.779047
$995$		0			0
$996$			18575.8i			0.590959i
$997$		−	26538.1i		−	0.843000i	−0.906828	−	0.421500i	$-0.861504\pi$
$997$		−	26538.1i		−	0.843000i	0.906828	−	0.421500i	$-0.138496\pi$
$998$		−	3510.92i		−	0.111359i
$999$	17192.9			0.544504

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	425.4.d.b.101.4	yes	4
5.2	odd	4		425.4.c.d.424.3		8
5.3	odd	4		425.4.c.d.424.6		8
5.4	even	2		425.4.d.d.101.1	yes	4
17.16	even	2	inner	425.4.d.b.101.1	✓	4
85.33	odd	4		425.4.c.d.424.7		8
85.67	odd	4		425.4.c.d.424.2		8
85.84	even	2		425.4.d.d.101.4	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
425.4.c.d.424.2		8	85.67	odd	4
425.4.c.d.424.3		8	5.2	odd	4
425.4.c.d.424.6		8	5.3	odd	4
425.4.c.d.424.7		8	85.33	odd	4
425.4.d.b.101.1	✓	4	17.16	even	2	inner
425.4.d.b.101.4	yes	4	1.1	even	1	trivial
425.4.d.d.101.1	yes	4	5.4	even	2
425.4.d.d.101.4	yes	4	85.84	even	2

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:	\( N \)	\(=\)	\( 425 = 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	425.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +4.35890i q^{3} -7.00000 q^{4} -4.35890i q^{6} +32.0713i q^{7} +15.0000 q^{8} +8.00000 q^{9} -1.55903i q^{11} -30.5123i q^{12} +69.7956 q^{13} -32.0713i q^{14} +41.0000 q^{16} +(45.3978 + 53.4045i) q^{17} -8.00000 q^{18} +76.7956 q^{19} -139.796 q^{21} +1.55903i q^{22} -73.4968i q^{23} +65.3835i q^{24} -69.7956 q^{26} +152.561i q^{27} -224.499i q^{28} +134.521i q^{29} -54.4703i q^{31} -161.000 q^{32} +6.79563 q^{33} +(-45.3978 - 53.4045i) q^{34} -56.0000 q^{36} -112.695i q^{37} -76.7956 q^{38} +304.232i q^{39} +316.036i q^{41} +139.796 q^{42} +148.000 q^{43} +10.9132i q^{44} +73.4968i q^{46} +224.000 q^{47} +178.715i q^{48} -685.569 q^{49} +(-232.785 + 197.884i) q^{51} -488.569 q^{52} +670.569 q^{53} -152.561i q^{54} +481.070i q^{56} +334.744i q^{57} -134.521i q^{58} -334.365 q^{59} +675.725i q^{61} +54.4703i q^{62} +256.571i q^{63} -167.000 q^{64} -6.79563 q^{66} -1033.57 q^{67} +(-317.785 - 373.831i) q^{68} +320.365 q^{69} -761.248i q^{71} +120.000 q^{72} -791.188i q^{73} +112.695i q^{74} -537.569 q^{76} +50.0000 q^{77} -304.232i q^{78} -50.7796i q^{79} -449.000 q^{81} -316.036i q^{82} -608.796 q^{83} +978.569 q^{84} -148.000 q^{86} -586.365 q^{87} -23.3854i q^{88} -47.5694 q^{89} +2238.44i q^{91} +514.478i q^{92} +237.431 q^{93} -224.000 q^{94} -701.783i q^{96} -165.574i q^{97} +685.569 q^{98} -12.4722i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} - 28 q^{4} + 60 q^{8} + 32 q^{9} - 14 q^{13} + 164 q^{16} + 35 q^{17} - 32 q^{18} + 14 q^{19} - 266 q^{21} + 14 q^{26} - 644 q^{32} - 266 q^{33} - 35 q^{34} - 224 q^{36} - 14 q^{38} + 266 q^{42}+ \cdots + 690 q^{98}+O(q^{100}) \) 4 * q - 4 * q^2 - 28 * q^4 + 60 * q^8 + 32 * q^9 - 14 * q^13 + 164 * q^16 + 35 * q^17 - 32 * q^18 + 14 * q^19 - 266 * q^21 + 14 * q^26 - 644 * q^32 - 266 * q^33 - 35 * q^34 - 224 * q^36 - 14 * q^38 + 266 * q^42 + 592 * q^43 + 896 * q^47 - 690 * q^49 + 95 * q^51 + 98 * q^52 + 630 * q^53 + 1008 * q^59 - 668 * q^64 + 266 * q^66 - 2082 * q^67 - 245 * q^68 - 1064 * q^69 + 480 * q^72 - 98 * q^76 + 200 * q^77 - 1796 * q^81 - 2142 * q^83 + 1862 * q^84 - 592 * q^86 + 1862 * q^89 + 3002 * q^93 - 896 * q^94 + 690 * q^98

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