LMFDB - Embedded newform 35.3.d.b.6.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [35,3,Mod(6,35)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(35, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("35.6");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 35 = 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	35.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:	$0.953680925261$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{-5}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 5 $ x^2 + 5
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			6.2
Root			$2.23607i$ of defining polynomial
Character	$\chi$	$=$	35.6
Dual form			35.3.d.b.6.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.00000 q^{2} +2.23607i q^{3} -2.23607i q^{5} +4.47214i q^{6} +(-2.00000 - 6.70820i) q^{7} -8.00000 q^{8} +4.00000 q^{9} +O(q^{10})$	\(q+2.00000 q^{2} +2.23607i q^{3} -2.23607i q^{5} +4.47214i q^{6} +(-2.00000 - 6.70820i) q^{7} -8.00000 q^{8} +4.00000 q^{9} -4.47214i q^{10} -1.00000 q^{11} +20.1246i q^{13} +(-4.00000 - 13.4164i) q^{14} +5.00000 q^{15} -16.0000 q^{16} +6.70820i q^{17} +8.00000 q^{18} -13.4164i q^{19} +(15.0000 - 4.47214i) q^{21} -2.00000 q^{22} +8.00000 q^{23} -17.8885i q^{24} -5.00000 q^{25} +40.2492i q^{26} +29.0689i q^{27} +41.0000 q^{29} +10.0000 q^{30} -40.2492i q^{31} -2.23607i q^{33} +13.4164i q^{34} +(-15.0000 + 4.47214i) q^{35} -28.0000 q^{37} -26.8328i q^{38} -45.0000 q^{39} +17.8885i q^{40} -13.4164i q^{41} +(30.0000 - 8.94427i) q^{42} -82.0000 q^{43} -8.94427i q^{45} +16.0000 q^{46} -20.1246i q^{47} -35.7771i q^{48} +(-41.0000 + 26.8328i) q^{49} -10.0000 q^{50} -15.0000 q^{51} +74.0000 q^{53} +58.1378i q^{54} +2.23607i q^{55} +(16.0000 + 53.6656i) q^{56} +30.0000 q^{57} +82.0000 q^{58} +93.9149i q^{59} -80.4984i q^{61} -80.4984i q^{62} +(-8.00000 - 26.8328i) q^{63} +64.0000 q^{64} +45.0000 q^{65} -4.47214i q^{66} +2.00000 q^{67} +17.8885i q^{69} +(-30.0000 + 8.94427i) q^{70} +14.0000 q^{71} -32.0000 q^{72} +67.0820i q^{73} -56.0000 q^{74} -11.1803i q^{75} +(2.00000 + 6.70820i) q^{77} -90.0000 q^{78} -19.0000 q^{79} +35.7771i q^{80} -29.0000 q^{81} -26.8328i q^{82} -93.9149i q^{83} +15.0000 q^{85} -164.000 q^{86} +91.6788i q^{87} +8.00000 q^{88} -107.331i q^{89} -17.8885i q^{90} +(135.000 - 40.2492i) q^{91} +90.0000 q^{93} -40.2492i q^{94} -30.0000 q^{95} +60.3738i q^{97} +(-82.0000 + 53.6656i) q^{98} -4.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 4 q^{2} - 4 q^{7} - 16 q^{8} + 8 q^{9}+O(q^{10}) $ 2 * q + 4 * q^2 - 4 * q^7 - 16 * q^8 + 8 * q^9	$ 2 q + 4 q^{2} - 4 q^{7} - 16 q^{8} + 8 q^{9} - 2 q^{11} - 8 q^{14} + 10 q^{15} - 32 q^{16} + 16 q^{18} + 30 q^{21} - 4 q^{22} + 16 q^{23} - 10 q^{25} + 82 q^{29} + 20 q^{30} - 30 q^{35} - 56 q^{37} - 90 q^{39} + 60 q^{42} - 164 q^{43} + 32 q^{46} - 82 q^{49} - 20 q^{50} - 30 q^{51} + 148 q^{53} + 32 q^{56} + 60 q^{57} + 164 q^{58} - 16 q^{63} + 128 q^{64} + 90 q^{65} + 4 q^{67} - 60 q^{70} + 28 q^{71} - 64 q^{72} - 112 q^{74} + 4 q^{77} - 180 q^{78} - 38 q^{79} - 58 q^{81} + 30 q^{85} - 328 q^{86} + 16 q^{88} + 270 q^{91} + 180 q^{93} - 60 q^{95} - 164 q^{98} - 8 q^{99}+O(q^{100}) $ 2 * q + 4 * q^2 - 4 * q^7 - 16 * q^8 + 8 * q^9 - 2 * q^11 - 8 * q^14 + 10 * q^15 - 32 * q^16 + 16 * q^18 + 30 * q^21 - 4 * q^22 + 16 * q^23 - 10 * q^25 + 82 * q^29 + 20 * q^30 - 30 * q^35 - 56 * q^37 - 90 * q^39 + 60 * q^42 - 164 * q^43 + 32 * q^46 - 82 * q^49 - 20 * q^50 - 30 * q^51 + 148 * q^53 + 32 * q^56 + 60 * q^57 + 164 * q^58 - 16 * q^63 + 128 * q^64 + 90 * q^65 + 4 * q^67 - 60 * q^70 + 28 * q^71 - 64 * q^72 - 112 * q^74 + 4 * q^77 - 180 * q^78 - 38 * q^79 - 58 * q^81 + 30 * q^85 - 328 * q^86 + 16 * q^88 + 270 * q^91 + 180 * q^93 - 60 * q^95 - 164 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/35\mathbb{Z}\right)^\times$.

$n$	$22$	$31$
$\chi(n)$	$1$	$-1$

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 $

$2$	2.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$2$	2.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$3$			2.23607i			0.745356i	0.927961	+	0.372678i	$0.121560\pi$
$3$			2.23607i			0.745356i	−0.927961	+	0.372678i	$0.878440\pi$
$4$		0			0
$5$		−	2.23607i		−	0.447214i
$5$		−	2.23607i		−	0.447214i
$6$			4.47214i			0.745356i
$7$	−2.00000	−	6.70820i	−0.285714	−	0.958315i
$7$	−2.00000	−	6.70820i	−0.285714	−	0.958315i
$8$	−8.00000			−1.00000
$9$	4.00000			0.444444
$10$		−	4.47214i		−	0.447214i
$11$	−1.00000			−0.0909091			−0.0454545	−	0.998966i	$-0.514474\pi$
$11$	−1.00000			−0.0909091			−0.0454545	+	0.998966i	$0.514474\pi$
$12$		0			0
$13$			20.1246i			1.54805i	0.633157	+	0.774024i	$0.281759\pi$
$13$			20.1246i			1.54805i	−0.633157	+	0.774024i	$0.718241\pi$
$14$	−4.00000	−	13.4164i	−0.285714	−	0.958315i
$15$	5.00000			0.333333
$16$	−16.0000			−1.00000
$17$			6.70820i			0.394600i	0.980343	+	0.197300i	$0.0632173\pi$
$17$			6.70820i			0.394600i	−0.980343	+	0.197300i	$0.936783\pi$
$18$	8.00000			0.444444
$19$		−	13.4164i		−	0.706127i	−0.935599	−	0.353063i	$-0.885140\pi$
$19$		−	13.4164i		−	0.706127i	0.935599	−	0.353063i	$-0.114860\pi$
$20$		0			0
$21$	15.0000	−	4.47214i	0.714286	−	0.212959i
$22$	−2.00000			−0.0909091
$23$	8.00000			0.347826			0.173913	−	0.984761i	$-0.444359\pi$
$23$	8.00000			0.347826			0.173913	+	0.984761i	$0.444359\pi$
$24$		−	17.8885i		−	0.745356i
$25$	−5.00000			−0.200000
$26$			40.2492i			1.54805i
$27$			29.0689i			1.07663i
$28$		0			0
$29$	41.0000			1.41379			0.706897	−	0.707317i	$-0.250095\pi$
$29$	41.0000			1.41379			0.706897	+	0.707317i	$0.250095\pi$
$30$	10.0000			0.333333
$31$		−	40.2492i		−	1.29836i	−0.760634	−	0.649181i	$-0.775112\pi$
$31$		−	40.2492i		−	1.29836i	0.760634	−	0.649181i	$-0.224888\pi$
$32$		0			0
$33$		−	2.23607i		−	0.0677596i
$34$			13.4164i			0.394600i
$35$	−15.0000	+	4.47214i	−0.428571	+	0.127775i
$36$		0			0
$37$	−28.0000			−0.756757			−0.378378	−	0.925651i	$-0.623518\pi$
$37$	−28.0000			−0.756757			−0.378378	+	0.925651i	$0.623518\pi$
$38$		−	26.8328i		−	0.706127i
$39$	−45.0000			−1.15385
$40$			17.8885i			0.447214i
$41$		−	13.4164i		−	0.327229i	−0.986524	−	0.163615i	$-0.947685\pi$
$41$		−	13.4164i		−	0.327229i	0.986524	−	0.163615i	$-0.0523154\pi$
$42$	30.0000	−	8.94427i	0.714286	−	0.212959i
$43$	−82.0000			−1.90698			−0.953488	−	0.301430i	$-0.902536\pi$
$43$	−82.0000			−1.90698			−0.953488	+	0.301430i	$0.902536\pi$
$44$		0			0
$45$		−	8.94427i		−	0.198762i
$46$	16.0000			0.347826
$47$		−	20.1246i		−	0.428183i	−0.976814	−	0.214092i	$-0.931321\pi$
$47$		−	20.1246i		−	0.428183i	0.976814	−	0.214092i	$-0.0686791\pi$
$48$		−	35.7771i		−	0.745356i
$49$	−41.0000	+	26.8328i	−0.836735	+	0.547608i
$50$	−10.0000			−0.200000
$51$	−15.0000			−0.294118
$52$		0			0
$53$	74.0000			1.39623			0.698113	−	0.715987i	$-0.254023\pi$
$53$	74.0000			1.39623			0.698113	+	0.715987i	$0.254023\pi$
$54$			58.1378i			1.07663i
$55$			2.23607i			0.0406558i
$56$	16.0000	+	53.6656i	0.285714	+	0.958315i
$57$	30.0000			0.526316
$58$	82.0000			1.41379
$59$			93.9149i			1.59178i	0.605443	+	0.795889i	$0.292996\pi$
$59$			93.9149i			1.59178i	−0.605443	+	0.795889i	$0.707004\pi$
$60$		0			0
$61$		−	80.4984i		−	1.31965i	−0.751421	−	0.659823i	$-0.770631\pi$
$61$		−	80.4984i		−	1.31965i	0.751421	−	0.659823i	$-0.229369\pi$
$62$		−	80.4984i		−	1.29836i
$63$	−8.00000	−	26.8328i	−0.126984	−	0.425918i
$64$	64.0000			1.00000
$65$	45.0000			0.692308
$66$		−	4.47214i		−	0.0677596i
$67$	2.00000			0.0298507			0.0149254	−	0.999889i	$-0.495249\pi$
$67$	2.00000			0.0298507			0.0149254	+	0.999889i	$0.495249\pi$
$68$		0			0
$69$			17.8885i			0.259254i
$70$	−30.0000	+	8.94427i	−0.428571	+	0.127775i
$71$	14.0000			0.197183			0.0985915	−	0.995128i	$-0.468566\pi$
$71$	14.0000			0.197183			0.0985915	+	0.995128i	$0.468566\pi$
$72$	−32.0000			−0.444444
$73$			67.0820i			0.918932i	0.888195	+	0.459466i	$0.151959\pi$
$73$			67.0820i			0.918932i	−0.888195	+	0.459466i	$0.848041\pi$
$74$	−56.0000			−0.756757
$75$		−	11.1803i		−	0.149071i
$76$		0			0
$77$	2.00000	+	6.70820i	0.0259740	+	0.0871195i
$78$	−90.0000			−1.15385
$79$	−19.0000			−0.240506			−0.120253	−	0.992743i	$-0.538371\pi$
$79$	−19.0000			−0.240506			−0.120253	+	0.992743i	$0.538371\pi$
$80$			35.7771i			0.447214i
$81$	−29.0000			−0.358025
$82$		−	26.8328i		−	0.327229i
$83$		−	93.9149i		−	1.13150i	−0.824575	−	0.565752i	$-0.808586\pi$
$83$		−	93.9149i		−	1.13150i	0.824575	−	0.565752i	$-0.191414\pi$
$84$		0			0
$85$	15.0000			0.176471
$86$	−164.000			−1.90698
$87$			91.6788i			1.05378i
$88$	8.00000			0.0909091
$89$		−	107.331i		−	1.20597i	−0.797753	−	0.602985i	$-0.793978\pi$
$89$		−	107.331i		−	1.20597i	0.797753	−	0.602985i	$-0.206022\pi$
$90$		−	17.8885i		−	0.198762i
$91$	135.000	−	40.2492i	1.48352	−	0.442299i
$92$		0			0
$93$	90.0000			0.967742
$94$		−	40.2492i		−	0.428183i
$95$	−30.0000			−0.315789
$96$		0			0
$97$			60.3738i			0.622411i	0.950343	+	0.311205i	$0.100733\pi$
$97$			60.3738i			0.622411i	−0.950343	+	0.311205i	$0.899267\pi$
$98$	−82.0000	+	53.6656i	−0.836735	+	0.547608i
$99$	−4.00000			−0.0404040
$100$		0			0
$101$			174.413i			1.72686i	0.504465	+	0.863432i	$0.331690\pi$
$101$			174.413i			1.72686i	−0.504465	+	0.863432i	$0.668310\pi$
$102$	−30.0000			−0.294118
$103$		−	6.70820i		−	0.0651282i	−0.999470	−	0.0325641i	$-0.989633\pi$
$103$		−	6.70820i		−	0.0651282i	0.999470	−	0.0325641i	$-0.0103673\pi$
$104$		−	160.997i		−	1.54805i
$105$	−10.0000	−	33.5410i	−0.0952381	−	0.319438i
$106$	148.000			1.39623
$107$	−34.0000			−0.317757			−0.158879	−	0.987298i	$-0.550788\pi$
$107$	−34.0000			−0.317757			−0.158879	+	0.987298i	$0.550788\pi$
$108$		0			0
$109$	101.000			0.926606			0.463303	−	0.886200i	$-0.346664\pi$
$109$	101.000			0.926606			0.463303	+	0.886200i	$0.346664\pi$
$110$			4.47214i			0.0406558i
$111$		−	62.6099i		−	0.564053i
$112$	32.0000	+	107.331i	0.285714	+	0.958315i
$113$	−112.000			−0.991150			−0.495575	−	0.868565i	$-0.665043\pi$
$113$	−112.000			−0.991150			−0.495575	+	0.868565i	$0.665043\pi$
$114$	60.0000			0.526316
$115$		−	17.8885i		−	0.155553i
$116$		0			0
$117$			80.4984i			0.688021i
$118$			187.830i			1.59178i
$119$	45.0000	−	13.4164i	0.378151	−	0.112743i
$120$	−40.0000			−0.333333
$121$	−120.000			−0.991736
$122$		−	160.997i		−	1.31965i
$123$	30.0000			0.243902
$124$		0			0
$125$			11.1803i			0.0894427i
$126$	−16.0000	−	53.6656i	−0.126984	−	0.425918i
$127$	62.0000			0.488189			0.244094	−	0.969751i	$-0.421509\pi$
$127$	62.0000			0.488189			0.244094	+	0.969751i	$0.421509\pi$
$128$	128.000			1.00000
$129$		−	183.358i		−	1.42138i
$130$	90.0000			0.692308
$131$			134.164i			1.02415i	0.858940	+	0.512077i	$0.171124\pi$
$131$			134.164i			1.02415i	−0.858940	+	0.512077i	$0.828876\pi$
$132$		0			0
$133$	−90.0000	+	26.8328i	−0.676692	+	0.201750i
$134$	4.00000			0.0298507
$135$	65.0000			0.481481
$136$		−	53.6656i		−	0.394600i
$137$	−4.00000			−0.0291971			−0.0145985	−	0.999893i	$-0.504647\pi$
$137$	−4.00000			−0.0291971			−0.0145985	+	0.999893i	$0.504647\pi$
$138$			35.7771i			0.259254i
$139$			80.4984i			0.579126i	0.957159	+	0.289563i	$0.0935099\pi$
$139$			80.4984i			0.579126i	−0.957159	+	0.289563i	$0.906490\pi$
$140$		0			0
$141$	45.0000			0.319149
$142$	28.0000			0.197183
$143$		−	20.1246i		−	0.140732i
$144$	−64.0000			−0.444444
$145$		−	91.6788i		−	0.632267i
$146$			134.164i			0.918932i
$147$	−60.0000	−	91.6788i	−0.408163	−	0.623665i
$148$		0			0
$149$	−94.0000			−0.630872			−0.315436	−	0.948947i	$-0.602151\pi$
$149$	−94.0000			−0.630872			−0.315436	+	0.948947i	$0.602151\pi$
$150$		−	22.3607i		−	0.149071i
$151$	−181.000			−1.19868			−0.599338	−	0.800496i	$-0.704569\pi$
$151$	−181.000			−1.19868			−0.599338	+	0.800496i	$0.704569\pi$
$152$			107.331i			0.706127i
$153$			26.8328i			0.175378i
$154$	4.00000	+	13.4164i	0.0259740	+	0.0871195i
$155$	−90.0000			−0.580645
$156$		0			0
$157$		−	174.413i		−	1.11091i	−0.831546	−	0.555456i	$-0.812544\pi$
$157$		−	174.413i		−	1.11091i	0.831546	−	0.555456i	$-0.187456\pi$
$158$	−38.0000			−0.240506
$159$			165.469i			1.04069i
$160$		0			0
$161$	−16.0000	−	53.6656i	−0.0993789	−	0.333327i
$162$	−58.0000			−0.358025
$163$	164.000			1.00613			0.503067	−	0.864247i	$-0.332205\pi$
$163$	164.000			1.00613			0.503067	+	0.864247i	$0.332205\pi$
$164$		0			0
$165$	−5.00000			−0.0303030
$166$		−	187.830i		−	1.13150i
$167$		−	154.289i		−	0.923884i	−0.886910	−	0.461942i	$-0.847153\pi$
$167$		−	154.289i		−	0.923884i	0.886910	−	0.461942i	$-0.152847\pi$
$168$	−120.000	+	35.7771i	−0.714286	+	0.212959i
$169$	−236.000			−1.39645
$170$	30.0000			0.176471
$171$		−	53.6656i		−	0.313834i
$172$		0			0
$173$			73.7902i			0.426533i	0.976994	+	0.213267i	$0.0684103\pi$
$173$			73.7902i			0.426533i	−0.976994	+	0.213267i	$0.931590\pi$
$174$			183.358i			1.05378i
$175$	10.0000	+	33.5410i	0.0571429	+	0.191663i
$176$	16.0000			0.0909091
$177$	−210.000			−1.18644
$178$		−	214.663i		−	1.20597i
$179$	218.000			1.21788			0.608939	−	0.793217i	$-0.291596\pi$
$179$	218.000			1.21788			0.608939	+	0.793217i	$0.291596\pi$
$180$		0			0
$181$			147.580i			0.815362i	0.913124	+	0.407681i	$0.133662\pi$
$181$			147.580i			0.815362i	−0.913124	+	0.407681i	$0.866338\pi$
$182$	270.000	−	80.4984i	1.48352	−	0.442299i
$183$	180.000			0.983607
$184$	−64.0000			−0.347826
$185$			62.6099i			0.338432i
$186$	180.000			0.967742
$187$		−	6.70820i		−	0.0358727i
$188$		0			0
$189$	195.000	−	58.1378i	1.03175	−	0.307607i
$190$	−60.0000			−0.315789
$191$	167.000			0.874346			0.437173	−	0.899378i	$-0.355980\pi$
$191$	167.000			0.874346			0.437173	+	0.899378i	$0.355980\pi$
$192$			143.108i			0.745356i
$193$	−172.000			−0.891192			−0.445596	−	0.895234i	$-0.647008\pi$
$193$	−172.000			−0.891192			−0.445596	+	0.895234i	$0.647008\pi$
$194$			120.748i			0.622411i
$195$			100.623i			0.516016i
$196$		0			0
$197$	302.000			1.53299			0.766497	−	0.642247i	$-0.221998\pi$
$197$	302.000			1.53299			0.766497	+	0.642247i	$0.221998\pi$
$198$	−8.00000			−0.0404040
$199$			174.413i			0.876449i	0.898866	+	0.438224i	$0.144392\pi$
$199$			174.413i			0.876449i	−0.898866	+	0.438224i	$0.855608\pi$
$200$	40.0000			0.200000
$201$			4.47214i			0.0222494i
$202$			348.827i			1.72686i
$203$	−82.0000	−	275.036i	−0.403941	−	1.35486i
$204$		0			0
$205$	−30.0000			−0.146341
$206$		−	13.4164i		−	0.0651282i
$207$	32.0000			0.154589
$208$		−	321.994i		−	1.54805i
$209$			13.4164i			0.0641933i
$210$	−20.0000	−	67.0820i	−0.0952381	−	0.319438i
$211$	107.000			0.507109			0.253555	−	0.967321i	$-0.418400\pi$
$211$	107.000			0.507109			0.253555	+	0.967321i	$0.418400\pi$
$212$		0			0
$213$			31.3050i			0.146972i
$214$	−68.0000			−0.317757
$215$			183.358i			0.852826i
$216$		−	232.551i		−	1.07663i
$217$	−270.000	+	80.4984i	−1.24424	+	0.370961i
$218$	202.000			0.926606
$219$	−150.000			−0.684932
$220$		0			0
$221$	−135.000			−0.610860
$222$		−	125.220i		−	0.564053i
$223$		−	114.039i		−	0.511388i	−0.966758	−	0.255694i	$-0.917696\pi$
$223$		−	114.039i		−	0.511388i	0.966758	−	0.255694i	$-0.0823039\pi$
$224$		0			0
$225$	−20.0000			−0.0888889
$226$	−224.000			−0.991150
$227$			60.3738i			0.265964i	0.991118	+	0.132982i	$0.0424553\pi$
$227$			60.3738i			0.265964i	−0.991118	+	0.132982i	$0.957545\pi$
$228$		0			0
$229$		−	335.410i		−	1.46467i	−0.680943	−	0.732337i	$-0.738430\pi$
$229$		−	335.410i		−	1.46467i	0.680943	−	0.732337i	$-0.261570\pi$
$230$		−	35.7771i		−	0.155553i
$231$	−15.0000	+	4.47214i	−0.0649351	+	0.0193599i
$232$	−328.000			−1.41379
$233$	−52.0000			−0.223176			−0.111588	−	0.993755i	$-0.535594\pi$
$233$	−52.0000			−0.223176			−0.111588	+	0.993755i	$0.535594\pi$
$234$			160.997i			0.688021i
$235$	−45.0000			−0.191489
$236$		0			0
$237$		−	42.4853i		−	0.179263i
$238$	90.0000	−	26.8328i	0.378151	−	0.112743i
$239$	−307.000			−1.28452			−0.642259	−	0.766487i	$-0.722003\pi$
$239$	−307.000			−1.28452			−0.642259	+	0.766487i	$0.722003\pi$
$240$	−80.0000			−0.333333
$241$		−	53.6656i		−	0.222679i	−0.993782	−	0.111339i	$-0.964486\pi$
$241$		−	53.6656i		−	0.222679i	0.993782	−	0.111339i	$-0.0355141\pi$
$242$	−240.000			−0.991736
$243$			196.774i			0.809769i
$244$		0			0
$245$	60.0000	+	91.6788i	0.244898	+	0.374199i
$246$	60.0000			0.243902
$247$	270.000			1.09312
$248$			321.994i			1.29836i
$249$	210.000			0.843373
$250$			22.3607i			0.0894427i
$251$		−	26.8328i		−	0.106904i	−0.998570	−	0.0534518i	$-0.982978\pi$
$251$		−	26.8328i		−	0.106904i	0.998570	−	0.0534518i	$-0.0170224\pi$
$252$		0			0
$253$	−8.00000			−0.0316206
$254$	124.000			0.488189
$255$			33.5410i			0.131533i
$256$		0			0
$257$		−	281.745i		−	1.09628i	−0.836386	−	0.548141i	$-0.815336\pi$
$257$		−	281.745i		−	1.09628i	0.836386	−	0.548141i	$-0.184664\pi$
$258$		−	366.715i		−	1.42138i
$259$	56.0000	+	187.830i	0.216216	+	0.725211i
$260$		0			0
$261$	164.000			0.628352
$262$			268.328i			1.02415i
$263$	98.0000			0.372624			0.186312	−	0.982491i	$-0.440347\pi$
$263$	98.0000			0.372624			0.186312	+	0.982491i	$0.440347\pi$
$264$			17.8885i			0.0677596i
$265$		−	165.469i		−	0.624411i
$266$	−180.000	+	53.6656i	−0.676692	+	0.201750i
$267$	240.000			0.898876
$268$		0			0
$269$		−	187.830i		−	0.698252i	−0.937076	−	0.349126i	$-0.886479\pi$
$269$		−	187.830i		−	0.698252i	0.937076	−	0.349126i	$-0.113521\pi$
$270$	130.000			0.481481
$271$			160.997i			0.594084i	0.954864	+	0.297042i	$0.0960002\pi$
$271$			160.997i			0.594084i	−0.954864	+	0.297042i	$0.904000\pi$
$272$		−	107.331i		−	0.394600i
$273$	90.0000	+	301.869i	0.329670	+	1.10575i
$274$	−8.00000			−0.0291971
$275$	5.00000			0.0181818
$276$		0			0
$277$	176.000			0.635379			0.317690	−	0.948195i	$-0.397093\pi$
$277$	176.000			0.635379			0.317690	+	0.948195i	$0.397093\pi$
$278$			160.997i			0.579126i
$279$		−	160.997i		−	0.577050i
$280$	120.000	−	35.7771i	0.428571	−	0.127775i
$281$	−181.000			−0.644128			−0.322064	−	0.946718i	$-0.604377\pi$
$281$	−181.000			−0.644128			−0.322064	+	0.946718i	$0.604377\pi$
$282$	90.0000			0.319149
$283$		−	140.872i		−	0.497782i	−0.968532	−	0.248891i	$-0.919934\pi$
$283$		−	140.872i		−	0.497782i	0.968532	−	0.248891i	$-0.0800661\pi$
$284$		0			0
$285$		−	67.0820i		−	0.235376i
$286$		−	40.2492i		−	0.140732i
$287$	−90.0000	+	26.8328i	−0.313589	+	0.0934941i
$288$		0			0
$289$	244.000			0.844291
$290$		−	183.358i		−	0.632267i
$291$	−135.000			−0.463918
$292$		0			0
$293$			368.951i			1.25922i	0.776912	+	0.629610i	$0.216785\pi$
$293$			368.951i			1.25922i	−0.776912	+	0.629610i	$0.783215\pi$
$294$	−120.000	−	183.358i	−0.408163	−	0.623665i
$295$	210.000			0.711864
$296$	224.000			0.756757
$297$		−	29.0689i		−	0.0978750i
$298$	−188.000			−0.630872
$299$			160.997i			0.538451i
$300$		0			0
$301$	164.000	+	550.073i	0.544850	+	1.82748i
$302$	−362.000			−1.19868
$303$	−390.000			−1.28713
$304$			214.663i			0.706127i
$305$	−180.000			−0.590164
$306$			53.6656i			0.175378i
$307$		−	422.617i		−	1.37660i	−0.725425	−	0.688301i	$-0.758357\pi$
$307$		−	422.617i		−	1.37660i	0.725425	−	0.688301i	$-0.241643\pi$
$308$		0			0
$309$	15.0000			0.0485437
$310$	−180.000			−0.580645
$311$		−	254.912i		−	0.819652i	−0.912164	−	0.409826i	$-0.865589\pi$
$311$		−	254.912i		−	0.819652i	0.912164	−	0.409826i	$-0.134411\pi$
$312$	360.000			1.15385
$313$			46.9574i			0.150024i	0.997183	+	0.0750119i	$0.0238995\pi$
$313$			46.9574i			0.150024i	−0.997183	+	0.0750119i	$0.976101\pi$
$314$		−	348.827i		−	1.11091i
$315$	−60.0000	+	17.8885i	−0.190476	+	0.0567890i
$316$		0			0
$317$	122.000			0.384858			0.192429	−	0.981311i	$-0.438363\pi$
$317$	122.000			0.384858			0.192429	+	0.981311i	$0.438363\pi$
$318$			330.938i			1.04069i
$319$	−41.0000			−0.128527
$320$		−	143.108i		−	0.447214i
$321$		−	76.0263i		−	0.236842i
$322$	−32.0000	−	107.331i	−0.0993789	−	0.333327i
$323$	90.0000			0.278638
$324$		0			0
$325$		−	100.623i		−	0.309609i
$326$	328.000			1.00613
$327$			225.843i			0.690651i
$328$			107.331i			0.327229i
$329$	−135.000	+	40.2492i	−0.410334	+	0.122338i
$330$	−10.0000			−0.0303030
$331$	14.0000			0.0422961			0.0211480	−	0.999776i	$-0.493268\pi$
$331$	14.0000			0.0422961			0.0211480	+	0.999776i	$0.493268\pi$
$332$		0			0
$333$	−112.000			−0.336336
$334$		−	308.577i		−	0.923884i
$335$		−	4.47214i		−	0.0133497i
$336$	−240.000	+	71.5542i	−0.714286	+	0.212959i
$337$	−64.0000			−0.189911			−0.0949555	−	0.995482i	$-0.530271\pi$
$337$	−64.0000			−0.189911			−0.0949555	+	0.995482i	$0.530271\pi$
$338$	−472.000			−1.39645
$339$		−	250.440i		−	0.738760i
$340$		0			0
$341$			40.2492i			0.118033i
$342$		−	107.331i		−	0.313834i
$343$	262.000	+	221.371i	0.763848	+	0.645396i
$344$	656.000			1.90698
$345$	40.0000			0.115942
$346$			147.580i			0.426533i
$347$	−448.000			−1.29107			−0.645533	−	0.763732i	$-0.723365\pi$
$347$	−448.000			−1.29107			−0.645533	+	0.763732i	$0.723365\pi$
$348$		0			0
$349$		−	147.580i		−	0.422867i	−0.977392	−	0.211433i	$-0.932187\pi$
$349$		−	147.580i		−	0.422867i	0.977392	−	0.211433i	$-0.0678131\pi$
$350$	20.0000	+	67.0820i	0.0571429	+	0.191663i
$351$	−585.000			−1.66667
$352$		0			0
$353$		−	248.204i		−	0.703126i	−0.936164	−	0.351563i	$-0.885650\pi$
$353$		−	248.204i		−	0.703126i	0.936164	−	0.351563i	$-0.114350\pi$
$354$	−420.000			−1.18644
$355$		−	31.3050i		−	0.0881830i
$356$		0			0
$357$	30.0000	+	100.623i	0.0840336	+	0.281857i
$358$	436.000			1.21788
$359$	−334.000			−0.930362			−0.465181	−	0.885216i	$-0.654011\pi$
$359$	−334.000			−0.930362			−0.465181	+	0.885216i	$0.654011\pi$
$360$			71.5542i			0.198762i
$361$	181.000			0.501385
$362$			295.161i			0.815362i
$363$		−	268.328i		−	0.739196i
$364$		0			0
$365$	150.000			0.410959
$366$	360.000			0.983607
$367$			60.3738i			0.164506i	0.996611	+	0.0822532i	$0.0262116\pi$
$367$			60.3738i			0.164506i	−0.996611	+	0.0822532i	$0.973788\pi$
$368$	−128.000			−0.347826
$369$		−	53.6656i		−	0.145435i
$370$			125.220i			0.338432i
$371$	−148.000	−	496.407i	−0.398922	−	1.33802i
$372$		0			0
$373$	−412.000			−1.10456			−0.552279	−	0.833659i	$-0.686242\pi$
$373$	−412.000			−1.10456			−0.552279	+	0.833659i	$0.686242\pi$
$374$		−	13.4164i		−	0.0358727i
$375$	−25.0000			−0.0666667
$376$			160.997i			0.428183i
$377$			825.109i			2.18862i
$378$	390.000	−	116.276i	1.03175	−	0.307607i
$379$	86.0000			0.226913			0.113456	−	0.993543i	$-0.463808\pi$
$379$	86.0000			0.226913			0.113456	+	0.993543i	$0.463808\pi$
$380$		0			0
$381$			138.636i			0.363875i
$382$	334.000			0.874346
$383$		−	469.574i		−	1.22604i	−0.790066	−	0.613021i	$-0.789954\pi$
$383$		−	469.574i		−	1.22604i	0.790066	−	0.613021i	$-0.210046\pi$
$384$			286.217i			0.745356i
$385$	15.0000	−	4.47214i	0.0389610	−	0.0116159i
$386$	−344.000			−0.891192
$387$	−328.000			−0.847545
$388$		0			0
$389$	221.000			0.568123			0.284062	−	0.958806i	$-0.408318\pi$
$389$	221.000			0.568123			0.284062	+	0.958806i	$0.408318\pi$
$390$			201.246i			0.516016i
$391$			53.6656i			0.137252i
$392$	328.000	−	214.663i	0.836735	−	0.547608i
$393$	−300.000			−0.763359
$394$	604.000			1.53299
$395$			42.4853i			0.107558i
$396$		0			0
$397$		−	234.787i		−	0.591403i	−0.955280	−	0.295702i	$-0.904447\pi$
$397$		−	234.787i		−	0.591403i	0.955280	−	0.295702i	$-0.0955534\pi$
$398$			348.827i			0.876449i
$399$	−60.0000	−	201.246i	−0.150376	−	0.504376i
$400$	80.0000			0.200000
$401$	599.000			1.49377			0.746883	−	0.664956i	$-0.231550\pi$
$401$	599.000			1.49377			0.746883	+	0.664956i	$0.231550\pi$
$402$			8.94427i			0.0222494i
$403$	810.000			2.00993
$404$		0			0
$405$			64.8460i			0.160114i
$406$	−164.000	−	550.073i	−0.403941	−	1.35486i
$407$	28.0000			0.0687961
$408$	120.000			0.294118
$409$		−	13.4164i		−	0.0328030i	−0.999865	−	0.0164015i	$-0.994779\pi$
$409$		−	13.4164i		−	0.0328030i	0.999865	−	0.0164015i	$-0.00522099\pi$
$410$	−60.0000			−0.146341
$411$		−	8.94427i		−	0.0217622i
$412$		0			0
$413$	630.000	−	187.830i	1.52542	−	0.454793i
$414$	64.0000			0.154589
$415$	−210.000			−0.506024
$416$		0			0
$417$	−180.000			−0.431655
$418$			26.8328i			0.0641933i
$419$			603.738i			1.44090i	0.693505	+	0.720451i	$0.256065\pi$
$419$			603.738i			1.44090i	−0.693505	+	0.720451i	$0.743935\pi$
$420$		0			0
$421$	−61.0000			−0.144893			−0.0724466	−	0.997372i	$-0.523081\pi$
$421$	−61.0000			−0.144893			−0.0724466	+	0.997372i	$0.523081\pi$
$422$	214.000			0.507109
$423$		−	80.4984i		−	0.190304i
$424$	−592.000			−1.39623
$425$		−	33.5410i		−	0.0789200i
$426$			62.6099i			0.146972i
$427$	−540.000	+	160.997i	−1.26464	+	0.377042i
$428$		0			0
$429$	45.0000			0.104895
$430$			366.715i			0.852826i
$431$	227.000			0.526682			0.263341	−	0.964703i	$-0.415176\pi$
$431$	227.000			0.526682			0.263341	+	0.964703i	$0.415176\pi$
$432$		−	465.102i		−	1.07663i
$433$			147.580i			0.340833i	0.985372	+	0.170416i	$0.0545112\pi$
$433$			147.580i			0.340833i	−0.985372	+	0.170416i	$0.945489\pi$
$434$	−540.000	+	160.997i	−1.24424	+	0.370961i
$435$	205.000			0.471264
$436$		0			0
$437$		−	107.331i		−	0.245609i
$438$	−300.000			−0.684932
$439$			724.486i			1.65031i	0.564906	+	0.825155i	$0.308912\pi$
$439$			724.486i			1.65031i	−0.564906	+	0.825155i	$0.691088\pi$
$440$		−	17.8885i		−	0.0406558i
$441$	−164.000	+	107.331i	−0.371882	+	0.243382i
$442$	−270.000			−0.610860
$443$	−526.000			−1.18736			−0.593679	−	0.804702i	$-0.702325\pi$
$443$	−526.000			−1.18736			−0.593679	+	0.804702i	$0.702325\pi$
$444$		0			0
$445$	−240.000			−0.539326
$446$		−	228.079i		−	0.511388i
$447$		−	210.190i		−	0.470225i
$448$	−128.000	−	429.325i	−0.285714	−	0.958315i
$449$	161.000			0.358575			0.179287	−	0.983797i	$-0.442621\pi$
$449$	161.000			0.358575			0.179287	+	0.983797i	$0.442621\pi$
$450$	−40.0000			−0.0888889
$451$			13.4164i			0.0297481i
$452$		0			0
$453$		−	404.728i		−	0.893440i
$454$			120.748i			0.265964i
$455$	−90.0000	−	301.869i	−0.197802	−	0.663449i
$456$	−240.000			−0.526316
$457$	602.000			1.31729			0.658643	−	0.752455i	$-0.271131\pi$
$457$	602.000			1.31729			0.658643	+	0.752455i	$0.271131\pi$
$458$		−	670.820i		−	1.46467i
$459$	−195.000			−0.424837
$460$		0			0
$461$		−	53.6656i		−	0.116411i	−0.998305	−	0.0582057i	$-0.981462\pi$
$461$		−	53.6656i		−	0.116411i	0.998305	−	0.0582057i	$-0.0185379\pi$
$462$	−30.0000	+	8.94427i	−0.0649351	+	0.0193599i
$463$	−316.000			−0.682505			−0.341253	−	0.939972i	$-0.610851\pi$
$463$	−316.000			−0.682505			−0.341253	+	0.939972i	$0.610851\pi$
$464$	−656.000			−1.41379
$465$		−	201.246i		−	0.432787i
$466$	−104.000			−0.223176
$467$			623.863i			1.33590i	0.744208	+	0.667948i	$0.232827\pi$
$467$			623.863i			1.33590i	−0.744208	+	0.667948i	$0.767173\pi$
$468$		0			0
$469$	−4.00000	−	13.4164i	−0.00852878	−	0.0286064i
$470$	−90.0000			−0.191489
$471$	390.000			0.828025
$472$		−	751.319i		−	1.59178i
$473$	82.0000			0.173362
$474$		−	84.9706i		−	0.179263i
$475$			67.0820i			0.141225i
$476$		0			0
$477$	296.000			0.620545
$478$	−614.000			−1.28452
$479$			563.489i			1.17639i	0.808720	+	0.588193i	$0.200161\pi$
$479$			563.489i			1.17639i	−0.808720	+	0.588193i	$0.799839\pi$
$480$		0			0
$481$		−	563.489i		−	1.17150i
$482$		−	107.331i		−	0.222679i
$483$	120.000	−	35.7771i	0.248447	−	0.0740726i
$484$		0			0
$485$	135.000			0.278351
$486$			393.548i			0.809769i
$487$	332.000			0.681725			0.340862	−	0.940113i	$-0.389281\pi$
$487$	332.000			0.681725			0.340862	+	0.940113i	$0.389281\pi$
$488$			643.988i			1.31965i
$489$			366.715i			0.749929i
$490$	120.000	+	183.358i	0.244898	+	0.374199i
$491$	−181.000			−0.368635			−0.184318	−	0.982867i	$-0.559008\pi$
$491$	−181.000			−0.368635			−0.184318	+	0.982867i	$0.559008\pi$
$492$		0			0
$493$			275.036i			0.557883i
$494$	540.000			1.09312
$495$			8.94427i			0.0180692i
$496$			643.988i			1.29836i
$497$	−28.0000	−	93.9149i	−0.0563380	−	0.188963i
$498$	420.000			0.843373
$499$	593.000			1.18838			0.594188	−	0.804326i	$-0.297473\pi$
$499$	593.000			1.18838			0.594188	+	0.804326i	$0.297473\pi$
$500$		0			0
$501$	345.000			0.688623
$502$		−	53.6656i		−	0.106904i
$503$		−	436.033i		−	0.866865i	−0.901186	−	0.433433i	$-0.857302\pi$
$503$		−	436.033i		−	0.866865i	0.901186	−	0.433433i	$-0.142698\pi$
$504$	64.0000	+	214.663i	0.126984	+	0.425918i
$505$	390.000			0.772277
$506$	−16.0000			−0.0316206
$507$		−	527.712i		−	1.04085i
$508$		0			0
$509$			187.830i			0.369017i	0.982831	+	0.184509i	$0.0590693\pi$
$509$			187.830i			0.369017i	−0.982831	+	0.184509i	$0.940931\pi$
$510$			67.0820i			0.131533i
$511$	450.000	−	134.164i	0.880626	−	0.262552i
$512$	−512.000			−1.00000
$513$	390.000			0.760234
$514$		−	563.489i		−	1.09628i
$515$	−15.0000			−0.0291262
$516$		0			0
$517$			20.1246i			0.0389257i
$518$	112.000	+	375.659i	0.216216	+	0.725211i
$519$	−165.000			−0.317919
$520$	−360.000			−0.692308
$521$		−	523.240i		−	1.00430i	−0.864781	−	0.502150i	$-0.832543\pi$
$521$		−	523.240i		−	1.00430i	0.864781	−	0.502150i	$-0.167457\pi$
$522$	328.000			0.628352
$523$			845.234i			1.61613i	0.589096	+	0.808063i	$0.299484\pi$
$523$			845.234i			1.61613i	−0.589096	+	0.808063i	$0.700516\pi$
$524$		0			0
$525$	−75.0000	+	22.3607i	−0.142857	+	0.0425918i
$526$	196.000			0.372624
$527$	270.000			0.512334
$528$			35.7771i			0.0677596i
$529$	−465.000			−0.879017
$530$		−	330.938i		−	0.624411i
$531$			375.659i			0.707457i
$532$		0			0
$533$	270.000			0.506567
$534$	480.000			0.898876
$535$			76.0263i			0.142105i
$536$	−16.0000			−0.0298507
$537$			487.463i			0.907752i
$538$		−	375.659i		−	0.698252i
$539$	41.0000	−	26.8328i	0.0760668	−	0.0497826i
$540$		0			0
$541$	−1081.00			−1.99815			−0.999076	−	0.0429834i	$-0.986314\pi$
$541$	−1081.00			−1.99815			−0.999076	+	0.0429834i	$0.986314\pi$
$542$			321.994i			0.594084i
$543$	−330.000			−0.607735
$544$		0			0
$545$		−	225.843i		−	0.414391i
$546$	180.000	+	603.738i	0.329670	+	1.10575i
$547$	92.0000			0.168190			0.0840951	−	0.996458i	$-0.473200\pi$
$547$	92.0000			0.168190			0.0840951	+	0.996458i	$0.473200\pi$
$548$		0			0
$549$		−	321.994i		−	0.586510i
$550$	10.0000			0.0181818
$551$		−	550.073i		−	0.998317i
$552$		−	143.108i		−	0.259254i
$553$	38.0000	+	127.456i	0.0687161	+	0.230481i
$554$	352.000			0.635379
$555$	−140.000			−0.252252
$556$		0			0
$557$	−928.000			−1.66607			−0.833034	−	0.553222i	$-0.813398\pi$
$557$	−928.000			−1.66607			−0.833034	+	0.553222i	$0.813398\pi$
$558$		−	321.994i		−	0.577050i
$559$		−	1650.22i		−	2.95209i
$560$	240.000	−	71.5542i	0.428571	−	0.127775i
$561$	15.0000			0.0267380
$562$	−362.000			−0.644128
$563$			281.745i			0.500434i	0.968190	+	0.250217i	$0.0805020\pi$
$563$			281.745i			0.500434i	−0.968190	+	0.250217i	$0.919498\pi$
$564$		0			0
$565$			250.440i			0.443256i
$566$		−	281.745i		−	0.497782i
$567$	58.0000	+	194.538i	0.102293	+	0.343100i
$568$	−112.000			−0.197183
$569$	−574.000			−1.00879			−0.504394	−	0.863474i	$-0.668284\pi$
$569$	−574.000			−1.00879			−0.504394	+	0.863474i	$0.668284\pi$
$570$		−	134.164i		−	0.235376i
$571$	−226.000			−0.395797			−0.197898	−	0.980223i	$-0.563412\pi$
$571$	−226.000			−0.395797			−0.197898	+	0.980223i	$0.563412\pi$
$572$		0			0
$573$			373.423i			0.651699i
$574$	−180.000	+	53.6656i	−0.313589	+	0.0934941i
$575$	−40.0000			−0.0695652
$576$	256.000			0.444444
$577$			623.863i			1.08122i	0.841274	+	0.540609i	$0.181806\pi$
$577$			623.863i			1.08122i	−0.841274	+	0.540609i	$0.818194\pi$
$578$	488.000			0.844291
$579$		−	384.604i		−	0.664255i
$580$		0			0
$581$	−630.000	+	187.830i	−1.08434	+	0.323287i
$582$	−270.000			−0.463918
$583$	−74.0000			−0.126930
$584$		−	536.656i		−	0.918932i
$585$	180.000			0.307692
$586$			737.902i			1.25922i
$587$			201.246i			0.342838i	0.985198	+	0.171419i	$0.0548352\pi$
$587$			201.246i			0.342838i	−0.985198	+	0.171419i	$0.945165\pi$
$588$		0			0
$589$	−540.000			−0.916808
$590$	420.000			0.711864
$591$			675.293i			1.14263i
$592$	448.000			0.756757
$593$		−	194.538i		−	0.328057i	−0.986456	−	0.164029i	$-0.947551\pi$
$593$		−	194.538i		−	0.328057i	0.986456	−	0.164029i	$-0.0524489\pi$
$594$		−	58.1378i		−	0.0978750i
$595$	−30.0000	−	100.623i	−0.0504202	−	0.169114i
$596$		0			0
$597$	−390.000			−0.653266
$598$			321.994i			0.538451i
$599$	581.000			0.969950			0.484975	−	0.874528i	$-0.338829\pi$
$599$	581.000			0.969950			0.484975	+	0.874528i	$0.338829\pi$
$600$			89.4427i			0.149071i
$601$		−	1086.73i		−	1.80820i	−0.427319	−	0.904101i	$-0.640542\pi$
$601$		−	1086.73i		−	1.80820i	0.427319	−	0.904101i	$-0.359458\pi$
$602$	328.000	+	1100.15i	0.544850	+	1.82748i
$603$	8.00000			0.0132670
$604$		0			0
$605$			268.328i			0.443518i
$606$	−780.000			−1.28713
$607$		−	342.118i		−	0.563622i	−0.959470	−	0.281811i	$-0.909065\pi$
$607$		−	342.118i		−	0.563622i	0.959470	−	0.281811i	$-0.0909351\pi$
$608$		0			0
$609$	615.000	−	183.358i	1.00985	−	0.301080i
$610$	−360.000			−0.590164
$611$	405.000			0.662848
$612$		0			0
$613$	−922.000			−1.50408			−0.752039	−	0.659118i	$-0.770930\pi$
$613$	−922.000			−1.50408			−0.752039	+	0.659118i	$0.770930\pi$
$614$		−	845.234i		−	1.37660i
$615$		−	67.0820i		−	0.109076i
$616$	−16.0000	−	53.6656i	−0.0259740	−	0.0871195i
$617$	332.000			0.538088			0.269044	−	0.963128i	$-0.413292\pi$
$617$	332.000			0.538088			0.269044	+	0.963128i	$0.413292\pi$
$618$	30.0000			0.0485437
$619$			107.331i			0.173395i	0.996235	+	0.0866973i	$0.0276313\pi$
$619$			107.331i			0.173395i	−0.996235	+	0.0866973i	$0.972369\pi$
$620$		0			0
$621$			232.551i			0.374478i
$622$		−	509.823i		−	0.819652i
$623$	−720.000	+	214.663i	−1.15570	+	0.344563i
$624$	720.000			1.15385
$625$	25.0000			0.0400000
$626$			93.9149i			0.150024i
$627$	−30.0000			−0.0478469
$628$		0			0
$629$		−	187.830i		−	0.298616i
$630$	−120.000	+	35.7771i	−0.190476	+	0.0567890i
$631$	839.000			1.32964			0.664818	−	0.747006i	$-0.268509\pi$
$631$	839.000			1.32964			0.664818	+	0.747006i	$0.268509\pi$
$632$	152.000			0.240506
$633$			239.259i			0.377977i
$634$	244.000			0.384858
$635$		−	138.636i		−	0.218325i
$636$		0			0
$637$	−540.000	−	825.109i	−0.847724	−	1.29530i
$638$	−82.0000			−0.128527
$639$	56.0000			0.0876369
$640$		−	286.217i		−	0.447214i
$641$	614.000			0.957878			0.478939	−	0.877848i	$-0.341021\pi$
$641$	614.000			0.957878			0.478939	+	0.877848i	$0.341021\pi$
$642$		−	152.053i		−	0.236842i
$643$			476.282i			0.740719i	0.928888	+	0.370360i	$0.120766\pi$
$643$			476.282i			0.740719i	−0.928888	+	0.370360i	$0.879234\pi$
$644$		0			0
$645$	−410.000			−0.635659
$646$	180.000			0.278638
$647$			925.732i			1.43081i	0.698712	+	0.715404i	$0.253757\pi$
$647$			925.732i			1.43081i	−0.698712	+	0.715404i	$0.746243\pi$
$648$	232.000			0.358025
$649$		−	93.9149i		−	0.144707i
$650$		−	201.246i		−	0.309609i
$651$	−180.000	−	603.738i	−0.276498	−	0.927401i
$652$		0			0
$653$	314.000			0.480858			0.240429	−	0.970667i	$-0.422712\pi$
$653$	314.000			0.480858			0.240429	+	0.970667i	$0.422712\pi$
$654$			451.686i			0.690651i
$655$	300.000			0.458015
$656$			214.663i			0.327229i
$657$			268.328i			0.408414i
$658$	−270.000	+	80.4984i	−0.410334	+	0.122338i
$659$	−787.000			−1.19423			−0.597117	−	0.802154i	$-0.703687\pi$
$659$	−787.000			−1.19423			−0.597117	+	0.802154i	$0.703687\pi$
$660$		0			0
$661$			563.489i			0.852480i	0.904610	+	0.426240i	$0.140162\pi$
$661$			563.489i			0.852480i	−0.904610	+	0.426240i	$0.859838\pi$
$662$	28.0000			0.0422961
$663$		−	301.869i		−	0.455308i
$664$			751.319i			1.13150i
$665$	60.0000	+	201.246i	0.0902256	+	0.302626i
$666$	−224.000			−0.336336
$667$	328.000			0.491754
$668$		0			0
$669$	255.000			0.381166
$670$		−	8.94427i		−	0.0133497i
$671$			80.4984i			0.119968i
$672$		0			0
$673$	−76.0000			−0.112927			−0.0564636	−	0.998405i	$-0.517982\pi$
$673$	−76.0000			−0.112927			−0.0564636	+	0.998405i	$0.517982\pi$
$674$	−128.000			−0.189911
$675$		−	145.344i		−	0.215325i
$676$		0			0
$677$		−	1200.77i		−	1.77366i	−0.462095	−	0.886831i	$-0.652902\pi$
$677$		−	1200.77i		−	1.77366i	0.462095	−	0.886831i	$-0.347098\pi$
$678$		−	500.879i		−	0.738760i
$679$	405.000	−	120.748i	0.596465	−	0.177832i
$680$	−120.000			−0.176471
$681$	−135.000			−0.198238
$682$			80.4984i			0.118033i
$683$	248.000			0.363104			0.181552	−	0.983381i	$-0.441888\pi$
$683$	248.000			0.363104			0.181552	+	0.983381i	$0.441888\pi$
$684$		0			0
$685$			8.94427i			0.0130573i
$686$	524.000	+	442.741i	0.763848	+	0.645396i
$687$	750.000			1.09170
$688$	1312.00			1.90698
$689$			1489.22i			2.16142i
$690$	80.0000			0.115942
$691$			804.984i			1.16496i	0.812847	+	0.582478i	$0.197917\pi$
$691$			804.984i			1.16496i	−0.812847	+	0.582478i	$0.802083\pi$
$692$		0			0
$693$	8.00000	+	26.8328i	0.0115440	+	0.0387198i
$694$	−896.000			−1.29107
$695$	180.000			0.258993
$696$		−	733.430i		−	1.05378i
$697$	90.0000			0.129125
$698$		−	295.161i		−	0.422867i
$699$		−	116.276i		−	0.166346i
$700$		0			0
$701$	47.0000			0.0670471			0.0335235	−	0.999438i	$-0.489327\pi$
$701$	47.0000			0.0670471			0.0335235	+	0.999438i	$0.489327\pi$
$702$	−1170.00			−1.66667
$703$			375.659i			0.534366i
$704$	−64.0000			−0.0909091
$705$		−	100.623i		−	0.142728i
$706$		−	496.407i		−	0.703126i
$707$	1170.00	−	348.827i	1.65488	−	0.493390i
$708$		0			0
$709$	−247.000			−0.348378			−0.174189	−	0.984712i	$-0.555730\pi$
$709$	−247.000			−0.348378			−0.174189	+	0.984712i	$0.555730\pi$
$710$		−	62.6099i		−	0.0881830i
$711$	−76.0000			−0.106892
$712$			858.650i			1.20597i
$713$		−	321.994i		−	0.451604i
$714$	60.0000	+	201.246i	0.0840336	+	0.281857i
$715$	−45.0000			−0.0629371
$716$		0			0
$717$		−	686.473i		−	0.957424i
$718$	−668.000			−0.930362
$719$		0			0		1.00000			$0$
$719$		0			0		−1.00000			$\pi$
$720$			143.108i			0.198762i
$721$	−45.0000	+	13.4164i	−0.0624133	+	0.0186081i
$722$	362.000			0.501385
$723$	120.000			0.165975
$724$		0			0
$725$	−205.000			−0.282759
$726$		−	536.656i		−	0.739196i
$727$		−	496.407i		−	0.682816i	−0.939915	−	0.341408i	$-0.889096\pi$
$727$		−	496.407i		−	0.682816i	0.939915	−	0.341408i	$-0.110904\pi$
$728$	−1080.00	+	321.994i	−1.48352	+	0.442299i
$729$	−701.000			−0.961591
$730$	300.000			0.410959
$731$		−	550.073i		−	0.752493i
$732$		0			0
$733$		−	623.863i		−	0.851109i	−0.904933	−	0.425555i	$-0.860079\pi$
$733$		−	623.863i		−	0.851109i	0.904933	−	0.425555i	$-0.139921\pi$
$734$			120.748i			0.164506i
$735$	−205.000	+	134.164i	−0.278912	+	0.182536i
$736$		0			0
$737$	−2.00000			−0.00271370
$738$		−	107.331i		−	0.145435i
$739$	581.000			0.786198			0.393099	−	0.919496i	$-0.371403\pi$
$739$	581.000			0.786198			0.393099	+	0.919496i	$0.371403\pi$
$740$		0			0
$741$			603.738i			0.814762i
$742$	−296.000	−	992.814i	−0.398922	−	1.33802i
$743$	494.000			0.664872			0.332436	−	0.943126i	$-0.392129\pi$
$743$	494.000			0.664872			0.332436	+	0.943126i	$0.392129\pi$
$744$	−720.000			−0.967742
$745$			210.190i			0.282135i
$746$	−824.000			−1.10456
$747$		−	375.659i		−	0.502891i
$748$		0			0
$749$	68.0000	+	228.079i	0.0907877	+	0.304511i
$750$	−50.0000			−0.0666667
$751$	−1153.00			−1.53529			−0.767643	−	0.640878i	$-0.778571\pi$
$751$	−1153.00			−1.53529			−0.767643	+	0.640878i	$0.778571\pi$
$752$			321.994i			0.428183i
$753$	60.0000			0.0796813
$754$			1650.22i			2.18862i
$755$			404.728i			0.536064i
$756$		0			0
$757$	−88.0000			−0.116248			−0.0581242	−	0.998309i	$-0.518512\pi$
$757$	−88.0000			−0.116248			−0.0581242	+	0.998309i	$0.518512\pi$
$758$	172.000			0.226913
$759$		−	17.8885i		−	0.0235686i
$760$	240.000			0.315789
$761$		−	456.158i		−	0.599419i	−0.954031	−	0.299710i	$-0.903110\pi$
$761$		−	456.158i		−	0.599419i	0.954031	−	0.299710i	$-0.0968898\pi$
$762$			277.272i			0.363875i
$763$	−202.000	−	677.529i	−0.264744	−	0.887980i
$764$		0			0
$765$	60.0000			0.0784314
$766$		−	939.149i		−	1.22604i
$767$	−1890.00			−2.46415
$768$		0			0
$769$			898.899i			1.16892i	0.811423	+	0.584460i	$0.198694\pi$
$769$			898.899i			1.16892i	−0.811423	+	0.584460i	$0.801306\pi$
$770$	30.0000	−	8.94427i	0.0389610	−	0.0116159i
$771$	630.000			0.817121
$772$		0			0
$773$		−	811.693i		−	1.05006i	−0.851085	−	0.525028i	$-0.824055\pi$
$773$		−	811.693i		−	1.05006i	0.851085	−	0.525028i	$-0.175945\pi$
$774$	−656.000			−0.847545
$775$			201.246i			0.259672i
$776$		−	482.991i		−	0.622411i
$777$	−420.000	+	125.220i	−0.540541	+	0.161158i
$778$	442.000			0.568123
$779$	−180.000			−0.231065
$780$		0			0
$781$	−14.0000			−0.0179257
$782$			107.331i			0.137252i
$783$			1191.82i			1.52213i
$784$	656.000	−	429.325i	0.836735	−	0.547608i
$785$	−390.000			−0.496815
$786$	−600.000			−0.763359
$787$			275.036i			0.349474i	0.984615	+	0.174737i	$0.0559076\pi$
$787$			275.036i			0.349474i	−0.984615	+	0.174737i	$0.944092\pi$
$788$		0			0
$789$			219.135i			0.277737i
$790$			84.9706i			0.107558i
$791$	224.000	+	751.319i	0.283186	+	0.949834i
$792$	32.0000			0.0404040
$793$	1620.00			2.04288
$794$		−	469.574i		−	0.591403i
$795$	370.000			0.465409
$796$		0			0
$797$		−	261.620i		−	0.328256i	−0.986439	−	0.164128i	$-0.947519\pi$
$797$		−	261.620i		−	0.328256i	0.986439	−	0.164128i	$-0.0524810\pi$
$798$	−120.000	−	402.492i	−0.150376	−	0.504376i
$799$	135.000			0.168961
$800$		0			0
$801$		−	429.325i		−	0.535986i
$802$	1198.00			1.49377
$803$		−	67.0820i		−	0.0835393i
$804$		0			0
$805$	−120.000	+	35.7771i	−0.149068	+	0.0444436i
$806$	1620.00			2.00993
$807$	420.000			0.520446
$808$		−	1395.31i		−	1.72686i
$809$	941.000			1.16316			0.581582	−	0.813488i	$-0.302434\pi$
$809$	941.000			1.16316			0.581582	+	0.813488i	$0.302434\pi$
$810$			129.692i			0.160114i
$811$			1019.65i			1.25727i	0.777700	+	0.628636i	$0.216386\pi$
$811$			1019.65i			1.25727i	−0.777700	+	0.628636i	$0.783614\pi$
$812$		0			0
$813$	−360.000			−0.442804
$814$	56.0000			0.0687961
$815$		−	366.715i		−	0.449957i
$816$	240.000			0.294118
$817$			1100.15i			1.34657i
$818$		−	26.8328i		−	0.0328030i
$819$	540.000	−	160.997i	0.659341	−	0.196577i
$820$		0			0
$821$	−1273.00			−1.55055			−0.775274	−	0.631625i	$-0.782388\pi$
$821$	−1273.00			−1.55055			−0.775274	+	0.631625i	$0.782388\pi$
$822$		−	17.8885i		−	0.0217622i
$823$	818.000			0.993925			0.496962	−	0.867772i	$-0.334449\pi$
$823$	818.000			0.993925			0.496962	+	0.867772i	$0.334449\pi$
$824$			53.6656i			0.0651282i
$825$			11.1803i			0.0135519i
$826$	1260.00	−	375.659i	1.52542	−	0.454793i
$827$	−148.000			−0.178960			−0.0894800	−	0.995989i	$-0.528521\pi$
$827$	−148.000			−0.178960			−0.0894800	+	0.995989i	$0.528521\pi$
$828$		0			0
$829$		−	657.404i		−	0.793008i	−0.918033	−	0.396504i	$-0.870223\pi$
$829$		−	657.404i		−	0.793008i	0.918033	−	0.396504i	$-0.129777\pi$
$830$	−420.000			−0.506024
$831$			393.548i			0.473584i
$832$			1287.98i			1.54805i
$833$	−180.000	−	275.036i	−0.216086	−	0.330176i
$834$	−360.000			−0.431655
$835$	−345.000			−0.413174
$836$		0			0
$837$	1170.00			1.39785
$838$			1207.48i			1.44090i
$839$			321.994i			0.383783i	0.981416	+	0.191891i	$0.0614621\pi$
$839$			321.994i			0.383783i	−0.981416	+	0.191891i	$0.938538\pi$
$840$	80.0000	+	268.328i	0.0952381	+	0.319438i
$841$	840.000			0.998811
$842$	−122.000			−0.144893
$843$		−	404.728i		−	0.480105i
$844$		0			0
$845$			527.712i			0.624511i
$846$		−	160.997i		−	0.190304i
$847$	240.000	+	804.984i	0.283353	+	0.950395i
$848$	−1184.00			−1.39623
$849$	315.000			0.371025
$850$		−	67.0820i		−	0.0789200i
$851$	−224.000			−0.263220
$852$		0			0
$853$		−	1542.89i		−	1.80878i	−0.426710	−	0.904389i	$-0.640327\pi$
$853$		−	1542.89i		−	1.80878i	0.426710	−	0.904389i	$-0.359673\pi$
$854$	−1080.00	+	321.994i	−1.26464	+	0.377042i
$855$	−120.000			−0.140351
$856$	272.000			0.317757
$857$		−	872.067i		−	1.01758i	−0.860891	−	0.508790i	$-0.830093\pi$
$857$		−	872.067i		−	1.01758i	0.860891	−	0.508790i	$-0.169907\pi$
$858$	90.0000			0.104895
$859$		−	1261.14i		−	1.46815i	−0.679067	−	0.734076i	$-0.737616\pi$
$859$		−	1261.14i		−	1.46815i	0.679067	−	0.734076i	$-0.262384\pi$
$860$		0			0
$861$	−60.0000	−	201.246i	−0.0696864	−	0.233735i
$862$	454.000			0.526682
$863$	338.000			0.391657			0.195829	−	0.980638i	$-0.437260\pi$
$863$	338.000			0.391657			0.195829	+	0.980638i	$0.437260\pi$
$864$		0			0
$865$	165.000			0.190751
$866$			295.161i			0.340833i
$867$			545.601i			0.629297i
$868$		0			0
$869$	19.0000			0.0218642
$870$	410.000			0.471264
$871$			40.2492i			0.0462104i
$872$	−808.000			−0.926606
$873$			241.495i			0.276627i
$874$		−	214.663i		−	0.245609i
$875$	75.0000	−	22.3607i	0.0857143	−	0.0255551i
$876$		0			0
$877$	−514.000			−0.586089			−0.293044	−	0.956099i	$-0.594668\pi$
$877$	−514.000			−0.586089			−0.293044	+	0.956099i	$0.594668\pi$
$878$			1448.97i			1.65031i
$879$	−825.000			−0.938567
$880$		−	35.7771i		−	0.0406558i
$881$			321.994i			0.365487i	0.983161	+	0.182743i	$0.0584977\pi$
$881$			321.994i			0.365487i	−0.983161	+	0.182743i	$0.941502\pi$
$882$	−328.000	+	214.663i	−0.371882	+	0.243382i
$883$	−1252.00			−1.41789			−0.708947	−	0.705262i	$-0.750829\pi$
$883$	−1252.00			−1.41789			−0.708947	+	0.705262i	$0.750829\pi$
$884$		0			0
$885$			469.574i			0.530592i
$886$	−1052.00			−1.18736
$887$		−	925.732i		−	1.04367i	−0.853048	−	0.521833i	$-0.825248\pi$
$887$		−	925.732i		−	1.04367i	0.853048	−	0.521833i	$-0.174752\pi$
$888$			500.879i			0.564053i
$889$	−124.000	−	415.909i	−0.139483	−	0.467839i
$890$	−480.000			−0.539326
$891$	29.0000			0.0325477
$892$		0			0
$893$	−270.000			−0.302352
$894$		−	420.381i		−	0.470225i
$895$		−	487.463i		−	0.544651i
$896$	−256.000	−	858.650i	−0.285714	−	0.958315i
$897$	−360.000			−0.401338
$898$	322.000			0.358575
$899$		−	1650.22i		−	1.83562i
$900$		0			0
$901$			496.407i			0.550951i
$902$			26.8328i			0.0297481i
$903$	−1230.00	+	366.715i	−1.36213	+	0.406108i
$904$	896.000			0.991150
$905$	330.000			0.364641
$906$		−	809.457i		−	0.893440i
$907$	−1084.00			−1.19515			−0.597574	−	0.801813i	$-0.703869\pi$
$907$	−1084.00			−1.19515			−0.597574	+	0.801813i	$0.703869\pi$
$908$		0			0
$909$			697.653i			0.767495i
$910$	−180.000	−	603.738i	−0.197802	−	0.663449i
$911$	−1066.00			−1.17014			−0.585071	−	0.810982i	$-0.698934\pi$
$911$	−1066.00			−1.17014			−0.585071	+	0.810982i	$0.698934\pi$
$912$	−480.000			−0.526316
$913$			93.9149i			0.102864i
$914$	1204.00			1.31729
$915$		−	402.492i		−	0.439882i
$916$		0			0
$917$	900.000	−	268.328i	0.981461	−	0.292615i
$918$	−390.000			−0.424837
$919$	521.000			0.566921			0.283460	−	0.958984i	$-0.408518\pi$
$919$	521.000			0.566921			0.283460	+	0.958984i	$0.408518\pi$
$920$			143.108i			0.155553i
$921$	945.000			1.02606
$922$		−	107.331i		−	0.116411i
$923$			281.745i			0.305249i
$924$		0			0
$925$	140.000			0.151351
$926$	−632.000			−0.682505
$927$		−	26.8328i		−	0.0289459i
$928$		0			0
$929$			389.076i			0.418811i	0.977829	+	0.209406i	$0.0671529\pi$
$929$			389.076i			0.418811i	−0.977829	+	0.209406i	$0.932847\pi$
$930$		−	402.492i		−	0.432787i
$931$	360.000	+	550.073i	0.386681	+	0.590841i
$932$		0			0
$933$	570.000			0.610932
$934$			1247.73i			1.33590i
$935$	−15.0000			−0.0160428
$936$		−	643.988i		−	0.688021i
$937$		−	127.456i		−	0.136025i	−0.997684	−	0.0680127i	$-0.978334\pi$
$937$		−	127.456i		−	0.136025i	0.997684	−	0.0680127i	$-0.0216659\pi$
$938$	−8.00000	−	26.8328i	−0.00852878	−	0.0286064i
$939$	−105.000			−0.111821
$940$		0			0
$941$			1824.63i			1.93903i	0.245023	+	0.969517i	$0.421204\pi$
$941$			1824.63i			1.93903i	−0.245023	+	0.969517i	$0.578796\pi$
$942$	780.000			0.828025
$943$		−	107.331i		−	0.113819i
$944$		−	1502.64i		−	1.59178i
$945$	−130.000	−	436.033i	−0.137566	−	0.461411i
$946$	164.000			0.173362
$947$	626.000			0.661035			0.330517	−	0.943800i	$-0.392777\pi$
$947$	626.000			0.661035			0.330517	+	0.943800i	$0.392777\pi$
$948$		0			0
$949$	−1350.00			−1.42255
$950$			134.164i			0.141225i
$951$			272.800i			0.286856i
$952$	−360.000	+	107.331i	−0.378151	+	0.112743i
$953$	218.000			0.228751			0.114376	−	0.993438i	$-0.463513\pi$
$953$	218.000			0.228751			0.114376	+	0.993438i	$0.463513\pi$
$954$	592.000			0.620545
$955$		−	373.423i		−	0.391019i
$956$		0			0
$957$		−	91.6788i		−	0.0957981i
$958$			1126.98i			1.17639i
$959$	8.00000	+	26.8328i	0.00834202	+	0.0279800i
$960$	320.000			0.333333
$961$	−659.000			−0.685744
$962$		−	1126.98i		−	1.17150i
$963$	−136.000			−0.141225
$964$		0			0
$965$			384.604i			0.398553i
$966$	240.000	−	71.5542i	0.248447	−	0.0740726i
$967$	−514.000			−0.531541			−0.265770	−	0.964036i	$-0.585626\pi$
$967$	−514.000			−0.531541			−0.265770	+	0.964036i	$0.585626\pi$
$968$	960.000			0.991736
$969$			201.246i			0.207684i
$970$	270.000			0.278351
$971$		−	228.079i		−	0.234891i	−0.993079	−	0.117445i	$-0.962529\pi$
$971$		−	228.079i		−	0.234891i	0.993079	−	0.117445i	$-0.0374705\pi$
$972$		0			0
$973$	540.000	−	160.997i	0.554985	−	0.165464i
$974$	664.000			0.681725
$975$	225.000			0.230769
$976$			1287.98i			1.31965i
$977$	602.000			0.616172			0.308086	−	0.951359i	$-0.400312\pi$
$977$	602.000			0.616172			0.308086	+	0.951359i	$0.400312\pi$
$978$			733.430i			0.749929i
$979$			107.331i			0.109634i
$980$		0			0
$981$	404.000			0.411825
$982$	−362.000			−0.368635
$983$			1334.93i			1.35802i	0.734130	+	0.679009i	$0.237590\pi$
$983$			1334.93i			1.35802i	−0.734130	+	0.679009i	$0.762410\pi$
$984$	−240.000			−0.243902
$985$		−	675.293i		−	0.685576i
$986$			550.073i			0.557883i
$987$	−90.0000	−	301.869i	−0.0911854	−	0.305845i
$988$		0			0
$989$	−656.000			−0.663296
$990$			17.8885i			0.0180692i
$991$	−766.000			−0.772957			−0.386478	−	0.922298i	$-0.626309\pi$
$991$	−766.000			−0.772957			−0.386478	+	0.922298i	$0.626309\pi$
$992$		0			0
$993$			31.3050i			0.0315256i
$994$	−56.0000	−	187.830i	−0.0563380	−	0.188963i
$995$	390.000			0.391960
$996$		0			0
$997$			462.866i			0.464259i	0.972685	+	0.232129i	$0.0745693\pi$
$997$			462.866i			0.464259i	−0.972685	+	0.232129i	$0.925431\pi$
$998$	1186.00			1.18838
$999$		−	813.929i		−	0.814743i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	35.3.d.b.6.2	yes	2
3.2	odd	2		315.3.h.a.181.2		2
4.3	odd	2		560.3.f.b.321.1		2
5.2	odd	4		175.3.c.c.174.4		4
5.3	odd	4		175.3.c.c.174.1		4
5.4	even	2		175.3.d.c.76.1		2
7.2	even	3		245.3.h.a.31.1		4
7.3	odd	6		245.3.h.a.166.1		4
7.4	even	3		245.3.h.a.166.2		4
7.5	odd	6		245.3.h.a.31.2		4
7.6	odd	2	inner	35.3.d.b.6.1	✓	2
21.20	even	2		315.3.h.a.181.1		2
28.27	even	2		560.3.f.b.321.2		2
35.13	even	4		175.3.c.c.174.2		4
35.27	even	4		175.3.c.c.174.3		4
35.34	odd	2		175.3.d.c.76.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.3.d.b.6.1	✓	2	7.6	odd	2	inner
35.3.d.b.6.2	yes	2	1.1	even	1	trivial
175.3.c.c.174.1		4	5.3	odd	4
175.3.c.c.174.2		4	35.13	even	4
175.3.c.c.174.3		4	35.27	even	4
175.3.c.c.174.4		4	5.2	odd	4
175.3.d.c.76.1		2	5.4	even	2
175.3.d.c.76.2		2	35.34	odd	2
245.3.h.a.31.1		4	7.2	even	3
245.3.h.a.31.2		4	7.5	odd	6
245.3.h.a.166.1		4	7.3	odd	6
245.3.h.a.166.2		4	7.4	even	3
315.3.h.a.181.1		2	21.20	even	2
315.3.h.a.181.2		2	3.2	odd	2
560.3.f.b.321.1		2	4.3	odd	2
560.3.f.b.321.2		2	28.27	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:	\( N \)	\(=\)	\( 35 = 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	35.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+2.00000 q^{2} +2.23607i q^{3} -2.23607i q^{5} +4.47214i q^{6} +(-2.00000 - 6.70820i) q^{7} -8.00000 q^{8} +4.00000 q^{9} +O(q^{10})\)	\(q+2.00000 q^{2} +2.23607i q^{3} -2.23607i q^{5} +4.47214i q^{6} +(-2.00000 - 6.70820i) q^{7} -8.00000 q^{8} +4.00000 q^{9} -4.47214i q^{10} -1.00000 q^{11} +20.1246i q^{13} +(-4.00000 - 13.4164i) q^{14} +5.00000 q^{15} -16.0000 q^{16} +6.70820i q^{17} +8.00000 q^{18} -13.4164i q^{19} +(15.0000 - 4.47214i) q^{21} -2.00000 q^{22} +8.00000 q^{23} -17.8885i q^{24} -5.00000 q^{25} +40.2492i q^{26} +29.0689i q^{27} +41.0000 q^{29} +10.0000 q^{30} -40.2492i q^{31} -2.23607i q^{33} +13.4164i q^{34} +(-15.0000 + 4.47214i) q^{35} -28.0000 q^{37} -26.8328i q^{38} -45.0000 q^{39} +17.8885i q^{40} -13.4164i q^{41} +(30.0000 - 8.94427i) q^{42} -82.0000 q^{43} -8.94427i q^{45} +16.0000 q^{46} -20.1246i q^{47} -35.7771i q^{48} +(-41.0000 + 26.8328i) q^{49} -10.0000 q^{50} -15.0000 q^{51} +74.0000 q^{53} +58.1378i q^{54} +2.23607i q^{55} +(16.0000 + 53.6656i) q^{56} +30.0000 q^{57} +82.0000 q^{58} +93.9149i q^{59} -80.4984i q^{61} -80.4984i q^{62} +(-8.00000 - 26.8328i) q^{63} +64.0000 q^{64} +45.0000 q^{65} -4.47214i q^{66} +2.00000 q^{67} +17.8885i q^{69} +(-30.0000 + 8.94427i) q^{70} +14.0000 q^{71} -32.0000 q^{72} +67.0820i q^{73} -56.0000 q^{74} -11.1803i q^{75} +(2.00000 + 6.70820i) q^{77} -90.0000 q^{78} -19.0000 q^{79} +35.7771i q^{80} -29.0000 q^{81} -26.8328i q^{82} -93.9149i q^{83} +15.0000 q^{85} -164.000 q^{86} +91.6788i q^{87} +8.00000 q^{88} -107.331i q^{89} -17.8885i q^{90} +(135.000 - 40.2492i) q^{91} +90.0000 q^{93} -40.2492i q^{94} -30.0000 q^{95} +60.3738i q^{97} +(-82.0000 + 53.6656i) q^{98} -4.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 4 q^{2} - 4 q^{7} - 16 q^{8} + 8 q^{9}+O(q^{10}) \) 2 * q + 4 * q^2 - 4 * q^7 - 16 * q^8 + 8 * q^9	\( 2 q + 4 q^{2} - 4 q^{7} - 16 q^{8} + 8 q^{9} - 2 q^{11} - 8 q^{14} + 10 q^{15} - 32 q^{16} + 16 q^{18} + 30 q^{21} - 4 q^{22} + 16 q^{23} - 10 q^{25} + 82 q^{29} + 20 q^{30} - 30 q^{35} - 56 q^{37} - 90 q^{39} + 60 q^{42} - 164 q^{43} + 32 q^{46} - 82 q^{49} - 20 q^{50} - 30 q^{51} + 148 q^{53} + 32 q^{56} + 60 q^{57} + 164 q^{58} - 16 q^{63} + 128 q^{64} + 90 q^{65} + 4 q^{67} - 60 q^{70} + 28 q^{71} - 64 q^{72} - 112 q^{74} + 4 q^{77} - 180 q^{78} - 38 q^{79} - 58 q^{81} + 30 q^{85} - 328 q^{86} + 16 q^{88} + 270 q^{91} + 180 q^{93} - 60 q^{95} - 164 q^{98} - 8 q^{99}+O(q^{100}) \) 2 * q + 4 * q^2 - 4 * q^7 - 16 * q^8 + 8 * q^9 - 2 * q^11 - 8 * q^14 + 10 * q^15 - 32 * q^16 + 16 * q^18 + 30 * q^21 - 4 * q^22 + 16 * q^23 - 10 * q^25 + 82 * q^29 + 20 * q^30 - 30 * q^35 - 56 * q^37 - 90 * q^39 + 60 * q^42 - 164 * q^43 + 32 * q^46 - 82 * q^49 - 20 * q^50 - 30 * q^51 + 148 * q^53 + 32 * q^56 + 60 * q^57 + 164 * q^58 - 16 * q^63 + 128 * q^64 + 90 * q^65 + 4 * q^67 - 60 * q^70 + 28 * q^71 - 64 * q^72 - 112 * q^74 + 4 * q^77 - 180 * q^78 - 38 * q^79 - 58 * q^81 + 30 * q^85 - 328 * q^86 + 16 * q^88 + 270 * q^91 + 180 * q^93 - 60 * q^95 - 164 * q^98 - 8 * q^99

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