LMFDB - Embedded newform 1800.2.k.q.901.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1800,2,Mod(901,1800)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1800, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1800.901");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1800 = 2^{3} \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1800.k (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:	$14.3730723638$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.214798336.3
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} - 2x^{5} + 9x^{4} - 4x^{3} - 16x + 16 $ x^8 - 2x^7 - 2x^5 + 9x^4 - 4x^3 - 16*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 600)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			901.1
Root			$1.41216 - 0.0762223i$ of defining polynomial
Character	$\chi$	$=$	1800.901
Dual form			1800.2.k.q.901.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.29150 - 0.576222i) q^{2} +(1.33594 + 1.48838i) q^{4} +1.97676 q^{7} +(-0.867721 - 2.69204i) q^{8} +O(q^{10})$	\(q+(-1.29150 - 0.576222i) q^{2} +(1.33594 + 1.48838i) q^{4} +1.97676 q^{7} +(-0.867721 - 2.69204i) q^{8} +1.43055i q^{11} -0.241319i q^{13} +(-2.55298 - 1.13905i) q^{14} +(-0.430552 + 3.97676i) q^{16} -7.38407 q^{17} +3.04033i q^{19} +(0.824316 - 1.84756i) q^{22} +0.874337 q^{23} +(-0.139054 + 0.311664i) q^{26} +(2.64082 + 2.94217i) q^{28} +9.07918i q^{29} -7.44764 q^{31} +(2.84756 - 4.88789i) q^{32} +(9.53652 + 4.25487i) q^{34} +8.81463i q^{37} +(1.75191 - 3.92658i) q^{38} +1.91319 q^{41} -11.2452i q^{43} +(-2.12921 + 1.91113i) q^{44} +(-1.12921 - 0.503813i) q^{46} -3.34374 q^{47} -3.09242 q^{49} +(0.359175 - 0.322387i) q^{52} -9.20632i q^{53} +(-1.71528 - 5.32151i) q^{56} +(5.23163 - 11.7258i) q^{58} +6.43616i q^{59} +4.57331i q^{61} +(9.61862 + 4.29150i) q^{62} +(-6.49412 + 4.67187i) q^{64} +4.86671i q^{67} +(-9.86465 - 10.9903i) q^{68} +8.21808 q^{71} +4.12714 q^{73} +(5.07918 - 11.3841i) q^{74} +(-4.52517 + 4.06169i) q^{76} +2.82786i q^{77} -13.6757 q^{79} +(-2.47088 - 1.10242i) q^{82} +12.3320i q^{83} +(-6.47972 + 14.5231i) q^{86} +(3.85110 - 1.24132i) q^{88} +8.08066 q^{89} -0.477031i q^{91} +(1.16806 + 1.30135i) q^{92} +(4.31844 + 1.92674i) q^{94} -10.6757 q^{97} +(3.99385 + 1.78192i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} + 4 q^{4} - 8 q^{7} + 4 q^{8}+O(q^{10}) $ 8 * q - 2 * q^2 + 4 * q^4 - 8 * q^7 + 4 * q^8	$ 8 q - 2 q^{2} + 4 q^{4} - 8 q^{7} + 4 q^{8} + 6 q^{14} + 8 q^{16} - 12 q^{22} + 8 q^{23} + 2 q^{26} + 4 q^{28} + 8 q^{31} + 28 q^{32} + 12 q^{34} + 30 q^{38} + 12 q^{44} + 20 q^{46} + 20 q^{52} - 8 q^{56} - 12 q^{58} + 30 q^{62} - 32 q^{64} - 28 q^{68} + 40 q^{71} + 16 q^{73} - 8 q^{74} - 20 q^{76} - 16 q^{79} + 24 q^{82} + 18 q^{86} + 8 q^{88} - 36 q^{92} - 4 q^{94} + 8 q^{97} - 48 q^{98}+O(q^{100}) $ 8 * q - 2 * q^2 + 4 * q^4 - 8 * q^7 + 4 * q^8 + 6 * q^14 + 8 * q^16 - 12 * q^22 + 8 * q^23 + 2 * q^26 + 4 * q^28 + 8 * q^31 + 28 * q^32 + 12 * q^34 + 30 * q^38 + 12 * q^44 + 20 * q^46 + 20 * q^52 - 8 * q^56 - 12 * q^58 + 30 * q^62 - 32 * q^64 - 28 * q^68 + 40 * q^71 + 16 * q^73 - 8 * q^74 - 20 * q^76 - 16 * q^79 + 24 * q^82 + 18 * q^86 + 8 * q^88 - 36 * q^92 - 4 * q^94 + 8 * q^97 - 48 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1800\mathbb{Z}\right)^\times$.

$n$	$577$	$901$	$1001$	$1351$
$\chi(n)$	$1$	$-1$	$1$	$1$

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 $

$2$	−1.29150	−	0.576222i	−0.913227	−	0.407451i
$2$	−1.29150	−	0.576222i	−0.913227	−	0.407451i
$3$		0			0
$3$		0			0
$4$	1.33594	+	1.48838i	0.667968	+	0.744190i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	1.97676			0.747145			0.373573	−	0.927601i	$-0.378133\pi$
$7$	1.97676			0.747145			0.373573	+	0.927601i	$0.378133\pi$
$8$	−0.867721	−	2.69204i	−0.306786	−	0.951779i
$9$		0			0
$10$		0			0
$11$			1.43055i			0.431328i	0.976468	+	0.215664i	$0.0691915\pi$
$11$			1.43055i			0.431328i	−0.976468	+	0.215664i	$0.930808\pi$
$12$		0			0
$13$		−	0.241319i		−	0.0669300i	−0.999440	−	0.0334650i	$-0.989346\pi$
$13$		−	0.241319i		−	0.0669300i	0.999440	−	0.0334650i	$-0.0106542\pi$
$14$	−2.55298	−	1.13905i	−0.682313	−	0.304425i
$15$		0			0
$16$	−0.430552	+	3.97676i	−0.107638	+	0.994190i
$17$	−7.38407			−1.79090			−0.895450	−	0.445161i	$-0.853146\pi$
$17$	−7.38407			−1.79090			−0.895450	+	0.445161i	$0.853146\pi$
$18$		0			0
$19$			3.04033i			0.697500i	0.937216	+	0.348750i	$0.113394\pi$
$19$			3.04033i			0.697500i	−0.937216	+	0.348750i	$0.886606\pi$
$20$		0			0
$21$		0			0
$22$	0.824316	−	1.84756i	0.175745	−	0.393900i
$23$	0.874337			0.182312			0.0911560	−	0.995837i	$-0.470944\pi$
$23$	0.874337			0.182312			0.0911560	+	0.995837i	$0.470944\pi$
$24$		0			0
$25$		0			0
$26$	−0.139054	+	0.311664i	−0.0272707	+	0.0611223i
$27$		0			0
$28$	2.64082	+	2.94217i	0.499069	+	0.556018i
$29$			9.07918i			1.68596i	0.537943	+	0.842981i	$0.319201\pi$
$29$			9.07918i			1.68596i	−0.537943	+	0.842981i	$0.680799\pi$
$30$		0			0
$31$	−7.44764			−1.33764			−0.668818	−	0.743426i	$-0.733200\pi$
$31$	−7.44764			−1.33764			−0.668818	+	0.743426i	$0.733200\pi$
$32$	2.84756	−	4.88789i	0.503381	−	0.864064i
$33$		0			0
$34$	9.53652	+	4.25487i	1.63550	+	0.729704i
$35$		0			0
$36$		0			0
$37$			8.81463i			1.44912i	0.689214	+	0.724558i	$0.257956\pi$
$37$			8.81463i			1.44912i	−0.689214	+	0.724558i	$0.742044\pi$
$38$	1.75191	−	3.92658i	0.284197	−	0.636976i
$39$		0			0
$40$		0			0
$41$	1.91319			0.298790			0.149395	−	0.988778i	$-0.452267\pi$
$41$	1.91319			0.298790			0.149395	+	0.988778i	$0.452267\pi$
$42$		0			0
$43$		−	11.2452i		−	1.71487i	−0.514589	−	0.857437i	$-0.672056\pi$
$43$		−	11.2452i		−	1.71487i	0.514589	−	0.857437i	$-0.327944\pi$
$44$	−2.12921	+	1.91113i	−0.320990	+	0.288113i
$45$		0			0
$46$	−1.12921	−	0.503813i	−0.166492	−	0.0742831i
$47$	−3.34374			−0.487735			−0.243867	−	0.969809i	$-0.578416\pi$
$47$	−3.34374			−0.487735			−0.243867	+	0.969809i	$0.578416\pi$
$48$		0			0
$49$	−3.09242			−0.441774
$50$		0			0
$51$		0			0
$52$	0.359175	−	0.322387i	0.0498086	−	0.0447071i
$53$		−	9.20632i		−	1.26459i	−0.774729	−	0.632293i	$-0.782114\pi$
$53$		−	9.20632i		−	1.26459i	0.774729	−	0.632293i	$-0.217886\pi$
$54$		0			0
$55$		0			0
$56$	−1.71528	−	5.32151i	−0.229213	−	0.711117i
$57$		0			0
$58$	5.23163	−	11.7258i	0.686946	−	1.53967i
$59$			6.43616i			0.837917i	0.908005	+	0.418958i	$0.137605\pi$
$59$			6.43616i			0.837917i	−0.908005	+	0.418958i	$0.862395\pi$
$60$		0			0
$61$			4.57331i			0.585552i	0.956181	+	0.292776i	$0.0945790\pi$
$61$			4.57331i			0.585552i	−0.956181	+	0.292776i	$0.905421\pi$
$62$	9.61862	+	4.29150i	1.22157	+	0.545021i
$63$		0			0
$64$	−6.49412	+	4.67187i	−0.811765	+	0.583984i
$65$		0			0
$66$		0			0
$67$			4.86671i			0.594563i	0.954790	+	0.297282i	$0.0960801\pi$
$67$			4.86671i			0.594563i	−0.954790	+	0.297282i	$0.903920\pi$
$68$	−9.86465	−	10.9903i	−1.19626	−	1.33277i
$69$		0			0
$70$		0			0
$71$	8.21808			0.975307			0.487653	−	0.873037i	$-0.337853\pi$
$71$	8.21808			0.975307			0.487653	+	0.873037i	$0.337853\pi$
$72$		0			0
$73$	4.12714			0.483045			0.241523	−	0.970395i	$-0.422353\pi$
$73$	4.12714			0.483045			0.241523	+	0.970395i	$0.422353\pi$
$74$	5.07918	−	11.3841i	0.590443	−	1.32337i
$75$		0			0
$76$	−4.52517	+	4.06169i	−0.519072	+	0.465907i
$77$			2.82786i			0.322264i
$78$		0			0
$79$	−13.6757			−1.53864			−0.769320	−	0.638864i	$-0.779405\pi$
$79$	−13.6757			−1.53864			−0.769320	+	0.638864i	$0.779405\pi$
$80$		0			0
$81$		0			0
$82$	−2.47088	−	1.10242i	−0.272863	−	0.121742i
$83$			12.3320i			1.35361i	0.736162	+	0.676806i	$0.236636\pi$
$83$			12.3320i			1.35361i	−0.736162	+	0.676806i	$0.763364\pi$
$84$		0			0
$85$		0			0
$86$	−6.47972	+	14.5231i	−0.698726	+	1.56607i
$87$		0			0
$88$	3.85110	−	1.24132i	0.410528	−	0.132325i
$89$	8.08066			0.856548			0.428274	−	0.903649i	$-0.359122\pi$
$89$	8.08066			0.856548			0.428274	+	0.903649i	$0.359122\pi$
$90$		0			0
$91$		−	0.477031i		−	0.0500064i
$92$	1.16806	+	1.30135i	0.121779	+	0.135675i
$93$		0			0
$94$	4.31844	+	1.92674i	0.445413	+	0.198728i
$95$		0			0
$96$		0			0
$97$	−10.6757			−1.08396			−0.541978	−	0.840393i	$-0.682324\pi$
$97$	−10.6757			−1.08396			−0.541978	+	0.840393i	$0.682324\pi$
$98$	3.99385	+	1.78192i	0.403440	+	0.180001i
$99$		0			0
$100$		0			0
$101$		−	13.2063i		−	1.31408i	−0.753856	−	0.657039i	$-0.771809\pi$
$101$		−	13.2063i		−	1.31408i	0.753856	−	0.657039i	$-0.228191\pi$
$102$		0			0
$103$	−19.4244			−1.91394			−0.956972	−	0.290181i	$-0.906284\pi$
$103$	−19.4244			−1.91394			−0.956972	+	0.290181i	$0.906284\pi$
$104$	−0.649641	+	0.209398i	−0.0637025	+	0.0205331i
$105$		0			0
$106$	−5.30489	+	11.8900i	−0.515256	+	1.15485i
$107$			14.8085i			1.43159i	0.698311	+	0.715795i	$0.253935\pi$
$107$			14.8085i			1.43159i	−0.698311	+	0.715795i	$0.746065\pi$
$108$		0			0
$109$		−	15.2296i		−	1.45873i	−0.684126	−	0.729364i	$-0.739816\pi$
$109$		−	15.2296i		−	1.45873i	0.684126	−	0.729364i	$-0.260184\pi$
$110$		0			0
$111$		0			0
$112$	−0.851098	+	7.86110i	−0.0804212	+	0.742804i
$113$	−1.13890			−0.107138			−0.0535692	−	0.998564i	$-0.517060\pi$
$113$	−1.13890			−0.107138			−0.0535692	+	0.998564i	$0.517060\pi$
$114$		0			0
$115$		0			0
$116$	−13.5133	+	12.1292i	−1.25468	+	1.12617i
$117$		0			0
$118$	3.70866	−	8.31229i	0.341410	−	0.765208i
$119$	−14.5965			−1.33806
$120$		0			0
$121$	8.95352			0.813956
$122$	2.63524	−	5.90642i	0.238583	−	0.534742i
$123$		0			0
$124$	−9.94957	−	11.0849i	−0.893498	−	0.995456i
$125$		0			0
$126$		0			0
$127$	−2.43616			−0.216174			−0.108087	−	0.994141i	$-0.534473\pi$
$127$	−2.43616			−0.216174			−0.108087	+	0.994141i	$0.534473\pi$
$128$	11.0792	−	2.29166i	0.979271	−	0.202556i
$129$		0			0
$130$		0			0
$131$			6.90143i			0.602981i	0.953469	+	0.301491i	$0.0974842\pi$
$131$			6.90143i			0.602981i	−0.953469	+	0.301491i	$0.902516\pi$
$132$		0			0
$133$			6.01001i			0.521134i
$134$	2.80431	−	6.28535i	0.242255	−	0.542972i
$135$		0			0
$136$	6.40731	+	19.8782i	0.549423	+	1.70454i
$137$	−5.39022			−0.460518			−0.230259	−	0.973129i	$-0.573957\pi$
$137$	−5.39022			−0.460518			−0.230259	+	0.973129i	$0.573957\pi$
$138$		0			0
$139$			17.4244i			1.47792i	0.673750	+	0.738959i	$0.264682\pi$
$139$			17.4244i			1.47792i	−0.673750	+	0.738959i	$0.735318\pi$
$140$		0			0
$141$		0			0
$142$	−10.6136	−	4.73544i	−0.890677	−	0.397389i
$143$	0.345220			0.0288687
$144$		0			0
$145$		0			0
$146$	−5.33019	−	2.37815i	−0.441130	−	0.196817i
$147$		0			0
$148$	−13.1195	+	11.7758i	−1.07842	+	0.967962i
$149$			2.28551i			0.187236i	0.995608	+	0.0936180i	$0.0298432\pi$
$149$			2.28551i			0.187236i	−0.995608	+	0.0936180i	$0.970157\pi$
$150$		0			0
$151$	6.66425			0.542329			0.271164	−	0.962533i	$-0.412591\pi$
$151$	6.66425			0.542329			0.271164	+	0.962533i	$0.412591\pi$
$152$	8.18468	−	2.63816i	0.663865	−	0.213983i
$153$		0			0
$154$	1.62948	−	3.65217i	0.131307	−	0.294301i
$155$		0			0
$156$		0			0
$157$			17.4144i			1.38982i	0.719097	+	0.694910i	$0.244556\pi$
$157$			17.4144i			1.38982i	−0.719097	+	0.694910i	$0.755444\pi$
$158$	17.6622	+	7.88026i	1.40513	+	0.626920i
$159$		0			0
$160$		0			0
$161$	1.72836			0.136214
$162$		0			0
$163$			4.66187i			0.365145i	0.983192	+	0.182573i	$0.0584425\pi$
$163$			4.66187i			0.365145i	−0.983192	+	0.182573i	$0.941557\pi$
$164$	2.55590	+	2.84756i	0.199582	+	0.222357i
$165$		0			0
$166$	7.10597	−	15.9267i	0.551530	−	1.23615i
$167$	−0.137419			−0.0106338			−0.00531690	−	0.999986i	$-0.501692\pi$
$167$	−0.137419			−0.0106338			−0.00531690	+	0.999986i	$0.501692\pi$
$168$		0			0
$169$	12.9418			0.995520
$170$		0			0
$171$		0			0
$172$	16.7371	−	15.0228i	1.27619	−	1.14548i
$173$			3.96675i			0.301587i	0.988565	+	0.150793i	$0.0481828\pi$
$173$			3.96675i			0.301587i	−0.988565	+	0.150793i	$0.951817\pi$
$174$		0			0
$175$		0			0
$176$	−5.68896	−	0.615927i	−0.428822	−	0.0464272i
$177$		0			0
$178$	−10.4362	−	4.65626i	−0.782223	−	0.349001i
$179$		−	4.68749i		−	0.350359i	−0.984537	−	0.175180i	$-0.943949\pi$
$179$		−	4.68749i		−	0.350359i	0.984537	−	0.175180i	$-0.0560506\pi$
$180$		0			0
$181$			9.10242i			0.676578i	0.941042	+	0.338289i	$0.109848\pi$
$181$			9.10242i			0.676578i	−0.941042	+	0.338289i	$0.890152\pi$
$182$	−0.274876	+	0.616084i	−0.0203751	+	0.0456672i
$183$		0			0
$184$	−0.758681	−	2.35375i	−0.0559307	−	0.173521i
$185$		0			0
$186$		0			0
$187$		−	10.5633i		−	0.772465i
$188$	−4.46702	−	4.97676i	−0.325791	−	0.362968i
$189$		0			0
$190$		0			0
$191$	−15.2063			−1.10029			−0.550145	−	0.835069i	$-0.685428\pi$
$191$	−15.2063			−1.10029			−0.550145	+	0.835069i	$0.685428\pi$
$192$		0			0
$193$	20.7564			1.49408			0.747039	−	0.664780i	$-0.231475\pi$
$193$	20.7564			1.49408			0.747039	+	0.664780i	$0.231475\pi$
$194$	13.7877	+	6.15159i	0.989898	+	0.441659i
$195$		0			0
$196$	−4.13127	−	4.60269i	−0.295091	−	0.328764i
$197$			23.2508i			1.65655i	0.560322	+	0.828275i	$0.310677\pi$
$197$			23.2508i			1.65655i	−0.560322	+	0.828275i	$0.689323\pi$
$198$		0			0
$199$	−7.21633			−0.511552			−0.255776	−	0.966736i	$-0.582331\pi$
$199$	−7.21633			−0.511552			−0.255776	+	0.966736i	$0.582331\pi$
$200$		0			0
$201$		0			0
$202$	−7.60978	+	17.0559i	−0.535422	+	1.20005i
$203$			17.9474i			1.25966i
$204$		0			0
$205$		0			0
$206$	25.0866	+	11.1928i	1.74787	+	0.779838i
$207$		0			0
$208$	0.959669	+	0.103901i	0.0665411	+	0.00720420i
$209$	−4.34935			−0.300851
$210$		0			0
$211$		−	4.38407i		−	0.301812i	−0.988548	−	0.150906i	$-0.951781\pi$
$211$		−	4.38407i		−	0.301812i	0.988548	−	0.150906i	$-0.0482191\pi$
$212$	13.7025	−	12.2991i	0.941092	−	0.844703i
$213$		0			0
$214$	8.53298	−	19.1251i	0.583302	−	1.30737i
$215$		0			0
$216$		0			0
$217$	−14.7222			−0.999409
$218$	−8.77561	+	19.6690i	−0.594360	+	1.33215i
$219$		0			0
$220$		0			0
$221$			1.78192i			0.119865i
$222$		0			0
$223$	4.98852			0.334056			0.167028	−	0.985952i	$-0.446583\pi$
$223$	4.98852			0.334056			0.167028	+	0.985952i	$0.446583\pi$
$224$	5.62894	−	9.66218i	0.376099	−	0.645582i
$225$		0			0
$226$	1.47088	+	0.656257i	0.0978416	+	0.0436536i
$227$			11.2569i			0.747149i	0.927600	+	0.373574i	$0.121868\pi$
$227$			11.2569i			0.747149i	−0.927600	+	0.373574i	$0.878132\pi$
$228$		0			0
$229$			15.8364i			1.04650i	0.852180	+	0.523249i	$0.175280\pi$
$229$			15.8364i			1.04650i	−0.852180	+	0.523249i	$0.824720\pi$
$230$		0			0
$231$		0			0
$232$	24.4415	−	7.87820i	1.60466	−	0.517229i
$233$	−10.9591			−0.717956			−0.358978	−	0.933346i	$-0.616875\pi$
$233$	−10.9591			−0.717956			−0.358978	+	0.933346i	$0.616875\pi$
$234$		0			0
$235$		0			0
$236$	−9.57945	+	8.59830i	−0.623569	+	0.559701i
$237$		0			0
$238$	18.8514	+	8.41086i	1.22196	+	0.545195i
$239$	−17.3182			−1.12022			−0.560111	−	0.828418i	$-0.689242\pi$
$239$	−17.3182			−1.12022			−0.560111	+	0.828418i	$0.689242\pi$
$240$		0			0
$241$	4.76869			0.307178			0.153589	−	0.988135i	$-0.450917\pi$
$241$	4.76869			0.307178			0.153589	+	0.988135i	$0.450917\pi$
$242$	−11.5635	−	5.15922i	−0.743327	−	0.331647i
$243$		0			0
$244$	−6.80682	+	6.10964i	−0.435762	+	0.391130i
$245$		0			0
$246$		0			0
$247$	0.733691			0.0466836
$248$	6.46247	+	20.0493i	0.410367	+	1.27313i
$249$		0			0
$250$		0			0
$251$		−	6.15837i		−	0.388713i	−0.980931	−	0.194356i	$-0.937738\pi$
$251$		−	6.15837i		−	0.388713i	0.980931	−	0.194356i	$-0.0622618\pi$
$252$		0			0
$253$			1.25079i			0.0786362i
$254$	3.14630	+	1.40377i	0.197416	+	0.0880804i
$255$		0			0
$256$	−15.6293	−	3.42440i	−0.976828	−	0.214025i
$257$	−14.1584			−0.883175			−0.441587	−	0.897218i	$-0.645584\pi$
$257$	−14.1584			−0.883175			−0.441587	+	0.897218i	$0.645584\pi$
$258$		0			0
$259$			17.4244i			1.08270i
$260$		0			0
$261$		0			0
$262$	3.97676	−	8.91319i	0.245685	−	0.550659i
$263$	−15.5960			−0.961691			−0.480845	−	0.876805i	$-0.659670\pi$
$263$	−15.5960			−0.961691			−0.480845	+	0.876805i	$0.659670\pi$
$264$		0			0
$265$		0			0
$266$	3.46310	−	7.76191i	0.212336	−	0.475913i
$267$		0			0
$268$	−7.24352	+	6.50161i	−0.442468	+	0.397149i
$269$		−	11.3182i		−	0.690084i	−0.938587	−	0.345042i	$-0.887865\pi$
$269$		−	11.3182i		−	0.690084i	0.938587	−	0.345042i	$-0.112135\pi$
$270$		0			0
$271$	−6.20485			−0.376918			−0.188459	−	0.982081i	$-0.560349\pi$
$271$	−6.20485			−0.376918			−0.188459	+	0.982081i	$0.560349\pi$
$272$	3.17923	−	29.3647i	0.192769	−	1.78050i
$273$		0			0
$274$	6.96146	+	3.10597i	0.420557	+	0.187638i
$275$		0			0
$276$		0			0
$277$		−	18.9288i		−	1.13732i	−0.822572	−	0.568661i	$-0.807462\pi$
$277$		−	18.9288i		−	1.13732i	0.822572	−	0.568661i	$-0.192538\pi$
$278$	10.0403	−	22.5036i	0.602179	−	1.34968i
$279$		0			0
$280$		0			0
$281$	21.6231			1.28993			0.644963	−	0.764214i	$-0.276873\pi$
$281$	21.6231			1.28993			0.644963	+	0.764214i	$0.276873\pi$
$282$		0			0
$283$			29.1522i			1.73292i	0.499247	+	0.866460i	$0.333610\pi$
$283$			29.1522i			1.73292i	−0.499247	+	0.866460i	$0.666390\pi$
$284$	10.9788	+	12.2316i	0.651473	+	0.725814i
$285$		0			0
$286$	−0.445851	−	0.198923i	−0.0263637	−	0.0117626i
$287$	3.78192			0.223240
$288$		0			0
$289$	37.5245			2.20733
$290$		0			0
$291$		0			0
$292$	5.51359	+	6.14275i	0.322659	+	0.359477i
$293$		−	2.32427i		−	0.135785i	−0.997693	−	0.0678927i	$-0.978372\pi$
$293$		−	2.32427i		−	0.135785i	0.997693	−	0.0678927i	$-0.0216275\pi$
$294$		0			0
$295$		0			0
$296$	23.7293	−	7.64863i	1.37924	−	0.444568i
$297$		0			0
$298$	1.31696	−	2.95173i	0.0762895	−	0.170989i
$299$		−	0.210995i		−	0.0122021i
$300$		0			0
$301$		−	22.2290i		−	1.28126i
$302$	−8.60686	−	3.84009i	−0.495269	−	0.220972i
$303$		0			0
$304$	−12.0907	−	1.30902i	−0.693447	−	0.0750775i
$305$		0			0
$306$		0			0
$307$		−	3.52297i		−	0.201066i	−0.994934	−	0.100533i	$-0.967945\pi$
$307$		−	3.52297i		−	0.201066i	0.994934	−	0.100533i	$-0.0320549\pi$
$308$	−4.20893	+	3.77784i	−0.239826	+	0.215262i
$309$		0			0
$310$		0			0
$311$	21.6757			1.22912			0.614559	−	0.788871i	$-0.289334\pi$
$311$	21.6757			1.22912			0.614559	+	0.788871i	$0.289334\pi$
$312$		0			0
$313$	12.5486			0.709288			0.354644	−	0.935001i	$-0.384602\pi$
$313$	12.5486			0.709288			0.354644	+	0.935001i	$0.384602\pi$
$314$	10.0346	−	22.4907i	0.566283	−	1.26922i
$315$		0			0
$316$	−18.2699	−	20.3547i	−1.02776	−	1.14504i
$317$		−	10.8611i		−	0.610020i	−0.952349	−	0.305010i	$-0.901340\pi$
$317$		−	10.8611i		−	0.610020i	0.952349	−	0.305010i	$-0.0986599\pi$
$318$		0			0
$319$	−12.9882			−0.727202
$320$		0			0
$321$		0			0
$322$	−2.23217	−	0.995917i	−0.124394	−	0.0555003i
$323$		−	22.4500i		−	1.24915i
$324$		0			0
$325$		0			0
$326$	2.68627	−	6.02079i	0.148779	−	0.333461i
$327$		0			0
$328$	−1.66011	−	5.15038i	−0.0916645	−	0.284382i
$329$	−6.60978			−0.364409
$330$		0			0
$331$			1.23185i			0.0677088i	0.999427	+	0.0338544i	$0.0107783\pi$
$331$			1.23185i			0.0677088i	−0.999427	+	0.0338544i	$0.989222\pi$
$332$	−18.3547	+	16.4747i	−1.00734	+	0.904169i
$333$		0			0
$334$	0.177476	+	0.0791838i	0.00971107	+	0.00433275i
$335$		0			0
$336$		0			0
$337$	−4.13890			−0.225460			−0.112730	−	0.993626i	$-0.535960\pi$
$337$	−4.13890			−0.225460			−0.112730	+	0.993626i	$0.535960\pi$
$338$	−16.7143	−	7.45733i	−0.909136	−	0.405625i
$339$		0			0
$340$		0			0
$341$		−	10.6542i		−	0.576959i
$342$		0			0
$343$	−19.9503			−1.07721
$344$	−30.2724	+	9.75767i	−1.63218	+	0.526098i
$345$		0			0
$346$	2.28573	−	5.12306i	0.122882	−	0.275417i
$347$		−	17.4586i		−	0.937226i	−0.883404	−	0.468613i	$-0.844754\pi$
$347$		−	17.4586i		−	0.937226i	0.883404	−	0.468613i	$-0.155246\pi$
$348$		0			0
$349$		−	21.2196i		−	1.13586i	−0.823078	−	0.567928i	$-0.807745\pi$
$349$		−	21.2196i		−	1.13586i	0.823078	−	0.567928i	$-0.192255\pi$
$350$		0			0
$351$		0			0
$352$	6.99237	+	4.07358i	0.372695	+	0.217122i
$353$	21.0398			1.11984			0.559918	−	0.828548i	$-0.310833\pi$
$353$	21.0398			1.11984			0.559918	+	0.828548i	$0.310833\pi$
$354$		0			0
$355$		0			0
$356$	10.7952	+	12.0271i	0.572147	+	0.637435i
$357$		0			0
$358$	−2.70103	+	6.05388i	−0.142754	+	0.319957i
$359$	−23.5153			−1.24109			−0.620546	−	0.784170i	$-0.713089\pi$
$359$	−23.5153			−1.24109			−0.620546	+	0.784170i	$0.713089\pi$
$360$		0			0
$361$	9.75639			0.513494
$362$	5.24502	−	11.7558i	0.275672	−	0.617869i
$363$		0			0
$364$	0.710003	−	0.637282i	0.0372143	−	0.0334027i
$365$		0			0
$366$		0			0
$367$	25.4012			1.32593			0.662965	−	0.748650i	$-0.269298\pi$
$367$	25.4012			1.32593			0.662965	+	0.748650i	$0.269298\pi$
$368$	−0.376448	+	3.47703i	−0.0196237	+	0.181253i
$369$		0			0
$370$		0			0
$371$		−	18.1987i		−	0.944829i
$372$		0			0
$373$			10.0677i			0.521286i	0.965435	+	0.260643i	$0.0839345\pi$
$373$			10.0677i			0.521286i	−0.965435	+	0.260643i	$0.916065\pi$
$374$	−6.08681	+	13.6425i	−0.314741	+	0.705436i
$375$		0			0
$376$	2.90143	+	9.00148i	0.149630	+	0.464216i
$377$	2.19098			0.112841
$378$		0			0
$379$		−	18.9674i		−	0.974289i	−0.873321	−	0.487145i	$-0.838038\pi$
$379$		−	18.9674i		−	0.974289i	0.873321	−	0.487145i	$-0.161962\pi$
$380$		0			0
$381$		0			0
$382$	19.6389	+	8.76222i	1.00482	+	0.448314i
$383$	−28.7446			−1.46878			−0.734391	−	0.678727i	$-0.762532\pi$
$383$	−28.7446			−1.46878			−0.734391	+	0.678727i	$0.762532\pi$
$384$		0			0
$385$		0			0
$386$	−26.8068	−	11.9603i	−1.36443	−	0.608763i
$387$		0			0
$388$	−14.2621	−	15.8895i	−0.724048	−	0.806669i
$389$		−	29.8161i		−	1.51174i	−0.654724	−	0.755868i	$-0.727215\pi$
$389$		−	29.8161i		−	1.51174i	0.654724	−	0.755868i	$-0.272785\pi$
$390$		0			0
$391$	−6.45617			−0.326503
$392$	2.68335	+	8.32490i	0.135530	+	0.420471i
$393$		0			0
$394$	13.3976	−	30.0283i	0.674962	−	1.51281i
$395$		0			0
$396$		0			0
$397$		−	2.73167i		−	0.137099i	−0.997648	−	0.0685494i	$-0.978163\pi$
$397$		−	2.73167i		−	0.137099i	0.997648	−	0.0685494i	$-0.0218371\pi$
$398$	9.31988	+	4.15821i	0.467163	+	0.208432i
$399$		0			0
$400$		0			0
$401$	−25.8744			−1.29211			−0.646054	−	0.763292i	$-0.723582\pi$
$401$	−25.8744			−1.29211			−0.646054	+	0.763292i	$0.723582\pi$
$402$		0			0
$403$			1.79726i			0.0895279i
$404$	19.6560	−	17.6428i	0.977924	−	0.877762i
$405$		0			0
$406$	10.3417	−	23.1790i	0.513249	−	1.15035i
$407$	−12.6098			−0.625044
$408$		0			0
$409$	22.4786			1.11150			0.555748	−	0.831351i	$-0.312432\pi$
$409$	22.4786			1.11150			0.555748	+	0.831351i	$0.312432\pi$
$410$		0			0
$411$		0			0
$412$	−25.9498	−	28.9109i	−1.27845	−	1.42434i
$413$			12.7227i			0.626045i
$414$		0			0
$415$		0			0
$416$	−1.17954	−	0.687170i	−0.0578318	−	0.0336913i
$417$		0			0
$418$	5.61718	+	2.50619i	0.274745	+	0.122582i
$419$			24.5307i			1.19840i	0.800598	+	0.599201i	$0.204515\pi$
$419$			24.5307i			1.19840i	−0.800598	+	0.599201i	$0.795485\pi$
$420$		0			0
$421$		−	33.3856i		−	1.62712i	−0.581483	−	0.813558i	$-0.697527\pi$
$421$		−	33.3856i		−	1.62712i	0.581483	−	0.813558i	$-0.302473\pi$
$422$	−2.52620	+	5.66202i	−0.122974	+	0.275623i
$423$		0			0
$424$	−24.7838	+	7.98852i	−1.20361	+	0.387957i
$425$		0			0
$426$		0			0
$427$			9.04033i			0.437492i
$428$	−22.0406	+	19.7832i	−1.06537	+	0.956256i
$429$		0			0
$430$		0			0
$431$	−11.6548			−0.561391			−0.280696	−	0.959797i	$-0.590565\pi$
$431$	−11.6548			−0.561391			−0.280696	+	0.959797i	$0.590565\pi$
$432$		0			0
$433$	−19.7681			−0.949996			−0.474998	−	0.879987i	$-0.657551\pi$
$433$	−19.7681			−0.949996			−0.474998	+	0.879987i	$0.657551\pi$
$434$	19.0137	+	8.48326i	0.912687	+	0.407210i
$435$		0			0
$436$	22.6674	−	20.3457i	1.08557	−	0.974383i
$437$			2.65827i			0.127163i
$438$		0			0
$439$	−25.1699			−1.20129			−0.600646	−	0.799515i	$-0.705090\pi$
$439$	−25.1699			−1.20129			−0.600646	+	0.799515i	$0.705090\pi$
$440$		0			0
$441$		0			0
$442$	1.02678	−	2.30135i	0.0488390	−	0.109464i
$443$		−	19.5515i		−	0.928922i	−0.885594	−	0.464461i	$-0.846248\pi$
$443$		−	19.5515i		−	0.928922i	0.885594	−	0.464461i	$-0.153752\pi$
$444$		0			0
$445$		0			0
$446$	−6.44266	−	2.87449i	−0.305069	−	0.136111i
$447$		0			0
$448$	−12.8373	+	9.23517i	−0.606507	+	0.436321i
$449$	19.9612			0.942029			0.471014	−	0.882125i	$-0.343888\pi$
$449$	19.9612			0.942029			0.471014	+	0.882125i	$0.343888\pi$
$450$		0			0
$451$			2.73692i			0.128876i
$452$	−1.52149	−	1.69511i	−0.0715650	−	0.0797313i
$453$		0			0
$454$	6.48650	−	14.5383i	0.304426	−	0.682317i
$455$		0			0
$456$		0			0
$457$	5.01176			0.234440			0.117220	−	0.993106i	$-0.462602\pi$
$457$	5.01176			0.234440			0.117220	+	0.993106i	$0.462602\pi$
$458$	9.12528	−	20.4527i	0.426396	−	0.955690i
$459$		0			0
$460$		0			0
$461$			5.12566i			0.238726i	0.992851	+	0.119363i	$0.0380852\pi$
$461$			5.12566i			0.238726i	−0.992851	+	0.119363i	$0.961915\pi$
$462$		0			0
$463$	5.79515			0.269324			0.134662	−	0.990892i	$-0.457005\pi$
$463$	5.79515			0.269324			0.134662	+	0.990892i	$0.457005\pi$
$464$	−36.1057	−	3.90906i	−1.67617	−	0.181474i
$465$		0			0
$466$	14.1537	+	6.31490i	0.655657	+	0.292532i
$467$		−	16.8208i		−	0.778373i	−0.921159	−	0.389186i	$-0.872756\pi$
$467$		−	16.8208i		−	0.778373i	0.921159	−	0.389186i	$-0.127244\pi$
$468$		0			0
$469$			9.62032i			0.444225i
$470$		0			0
$471$		0			0
$472$	17.3264	−	5.58479i	0.797511	−	0.257061i
$473$	16.0868			0.739672
$474$		0			0
$475$		0			0
$476$	−19.5000	−	21.7252i	−0.893783	−	0.995773i
$477$		0			0
$478$	22.3664	+	9.97914i	1.02302	+	0.456435i
$479$	36.9065			1.68630			0.843151	−	0.537678i	$-0.180698\pi$
$479$	36.9065			1.68630			0.843151	+	0.537678i	$0.180698\pi$
$480$		0			0
$481$	2.12714			0.0969892
$482$	−6.15875	−	2.74782i	−0.280523	−	0.125160i
$483$		0			0
$484$	11.9613	+	13.3262i	0.543697	+	0.605738i
$485$		0			0
$486$		0			0
$487$	5.14984			0.233361			0.116681	−	0.993169i	$-0.462775\pi$
$487$	5.14984			0.233361			0.116681	+	0.993169i	$0.462775\pi$
$488$	12.3115	−	3.96835i	0.557316	−	0.179639i
$489$		0			0
$490$		0			0
$491$		−	23.1154i		−	1.04318i	−0.853195	−	0.521591i	$-0.825339\pi$
$491$		−	23.1154i		−	1.04318i	0.853195	−	0.521591i	$-0.174661\pi$
$492$		0			0
$493$		−	67.0414i		−	3.01939i
$494$	−0.947560	−	0.422769i	−0.0426328	−	0.0190213i
$495$		0			0
$496$	3.20660	−	29.6175i	0.143980	−	1.32986i
$497$	16.2452			0.728696
$498$		0			0
$499$		−	14.3111i		−	0.640654i	−0.947307	−	0.320327i	$-0.896207\pi$
$499$		−	14.3111i		−	0.640654i	0.947307	−	0.320327i	$-0.103793\pi$
$500$		0			0
$501$		0			0
$502$	−3.54859	+	7.95352i	−0.158381	+	0.354983i
$503$	15.4224			0.687650			0.343825	−	0.939034i	$-0.388277\pi$
$503$	15.4224			0.687650			0.343825	+	0.939034i	$0.388277\pi$
$504$		0			0
$505$		0			0
$506$	0.720730	−	1.61539i	0.0320404	−	0.0718127i
$507$		0			0
$508$	−3.25455	−	3.62593i	−0.144397	−	0.160875i
$509$			43.1578i			1.91294i	0.291835	+	0.956469i	$0.405734\pi$
$509$			43.1578i			1.91294i	−0.291835	+	0.956469i	$0.594266\pi$
$510$		0			0
$511$	8.15837			0.360905
$512$	18.2119	+	13.4285i	0.804861	+	0.593463i
$513$		0			0
$514$	18.2855	+	8.15837i	0.806539	+	0.359850i
$515$		0			0
$516$		0			0
$517$		−	4.78340i		−	0.210374i
$518$	10.0403	−	22.5036i	0.441147	−	0.988751i
$519$		0			0
$520$		0			0
$521$	17.8232			0.780848			0.390424	−	0.920635i	$-0.372328\pi$
$521$	17.8232			0.780848			0.390424	+	0.920635i	$0.372328\pi$
$522$		0			0
$523$			24.7502i			1.08225i	0.840941	+	0.541126i	$0.182002\pi$
$523$			24.7502i			1.08225i	−0.840941	+	0.541126i	$0.817998\pi$
$524$	−10.2720	+	9.21987i	−0.448733	+	0.402772i
$525$		0			0
$526$	20.1422	+	8.98677i	0.878242	+	0.391842i
$527$	54.9939			2.39557
$528$		0			0
$529$	−22.2355			−0.966762
$530$		0			0
$531$		0			0
$532$	−8.94517	+	8.02898i	−0.387822	+	0.348100i
$533$		−	0.461690i		−	0.0199980i
$534$		0			0
$535$		0			0
$536$	13.1014	−	4.22295i	0.565893	−	0.182403i
$537$		0			0
$538$	−6.52181	+	14.6175i	−0.281175	+	0.630203i
$539$		−	4.42386i		−	0.190549i
$540$		0			0
$541$		−	16.9982i		−	0.730812i	−0.930848	−	0.365406i	$-0.880930\pi$
$541$		−	16.9982i		−	0.730812i	0.930848	−	0.365406i	$-0.119070\pi$
$542$	8.01355	+	3.57537i	0.344211	+	0.153575i
$543$		0			0
$544$	−21.0266	+	36.0925i	−0.901506	+	1.54745i
$545$		0			0
$546$		0			0
$547$		−	37.2385i		−	1.59220i	−0.605163	−	0.796101i	$-0.706892\pi$
$547$		−	37.2385i		−	1.59220i	0.605163	−	0.796101i	$-0.293108\pi$
$548$	−7.20099	−	8.02270i	−0.307611	−	0.342713i
$549$		0			0
$550$		0			0
$551$	−27.6037			−1.17596
$552$		0			0
$553$	−27.0336			−1.14959
$554$	−10.9072	+	24.4465i	−0.463403	+	1.03863i
$555$		0			0
$556$	−25.9341	+	23.2779i	−1.09985	+	0.987202i
$557$		−	14.7604i		−	0.625420i	−0.949849	−	0.312710i	$-0.898763\pi$
$557$		−	14.7604i		−	0.625420i	0.949849	−	0.312710i	$-0.101237\pi$
$558$		0			0
$559$	−2.71368			−0.114776
$560$		0			0
$561$		0			0
$562$	−27.9262	−	12.4597i	−1.17800	−	0.525581i
$563$			3.00561i			0.126671i	0.997992	+	0.0633356i	$0.0201739\pi$
$563$			3.00561i			0.126671i	−0.997992	+	0.0633356i	$0.979826\pi$
$564$		0			0
$565$		0			0
$566$	16.7982	−	37.6500i	0.706079	−	1.58255i
$567$		0			0
$568$	−7.13100	−	22.1234i	−0.299210	−	0.928276i
$569$	23.1840			0.971923			0.485962	−	0.873980i	$-0.338469\pi$
$569$	23.1840			0.971923			0.485962	+	0.873980i	$0.338469\pi$
$570$		0			0
$571$		−	0.202739i		−	0.00848438i	−0.999991	−	0.00424219i	$-0.998650\pi$
$571$		−	0.202739i		−	0.00848438i	0.999991	−	0.00424219i	$-0.00135033\pi$
$572$	0.461192	+	0.513819i	0.0192834	+	0.0214838i
$573$		0			0
$574$	−4.88434	−	2.17923i	−0.203869	−	0.0909592i
$575$		0			0
$576$		0			0
$577$	−21.8023			−0.907643			−0.453821	−	0.891093i	$-0.649940\pi$
$577$	−21.8023			−0.907643			−0.453821	+	0.891093i	$0.649940\pi$
$578$	−48.4629	−	21.6225i	−2.01579	−	0.899376i
$579$		0			0
$580$		0			0
$581$			24.3774i			1.01134i
$582$		0			0
$583$	13.1701			0.545451
$584$	−3.58120	−	11.1104i	−0.148191	−	0.459752i
$585$		0			0
$586$	−1.33930	+	3.00179i	−0.0553258	+	0.124003i
$587$		−	36.7126i		−	1.51529i	−0.652667	−	0.757645i	$-0.726350\pi$
$587$		−	36.7126i		−	1.51529i	0.652667	−	0.757645i	$-0.273650\pi$
$588$		0			0
$589$		−	22.6433i		−	0.933001i
$590$		0			0
$591$		0			0
$592$	−35.0537	−	3.79515i	−1.44070	−	0.155980i
$593$	10.6036			0.435439			0.217719	−	0.976011i	$-0.430138\pi$
$593$	10.6036			0.435439			0.217719	+	0.976011i	$0.430138\pi$
$594$		0			0
$595$		0			0
$596$	−3.40170	+	3.05329i	−0.139339	+	0.125068i
$597$		0			0
$598$	−0.121580	+	0.272499i	−0.00497177	+	0.0111433i
$599$	25.7988			1.05411			0.527056	−	0.849831i	$-0.323296\pi$
$599$	25.7988			1.05411			0.527056	+	0.849831i	$0.323296\pi$
$600$		0			0
$601$	18.5021			0.754717			0.377358	−	0.926067i	$-0.376832\pi$
$601$	18.5021			0.754717			0.377358	+	0.926067i	$0.376832\pi$
$602$	−12.8089	+	28.7087i	−0.522050	+	1.17008i
$603$		0			0
$604$	8.90300	+	9.91893i	0.362258	+	0.403596i
$605$		0			0
$606$		0			0
$607$	37.5828			1.52544			0.762719	−	0.646730i	$-0.223864\pi$
$607$	37.5828			1.52544			0.762719	+	0.646730i	$0.223864\pi$
$608$	14.8608	+	8.65751i	0.602685	+	0.351108i
$609$		0			0
$610$		0			0
$611$			0.806910i			0.0326441i
$612$		0			0
$613$			4.93405i			0.199284i	0.995023	+	0.0996422i	$0.0317698\pi$
$613$			4.93405i			0.199284i	−0.995023	+	0.0996422i	$0.968230\pi$
$614$	−2.03001	+	4.54991i	−0.0819247	+	0.183619i
$615$		0			0
$616$	7.61270	−	2.45379i	0.306724	−	0.0988661i
$617$	−6.26043			−0.252035			−0.126018	−	0.992028i	$-0.540220\pi$
$617$	−6.26043			−0.252035			−0.126018	+	0.992028i	$0.540220\pi$
$618$		0			0
$619$		−	8.02562i		−	0.322577i	−0.986907	−	0.161288i	$-0.948435\pi$
$619$		−	8.02562i		−	0.322577i	0.986907	−	0.161288i	$-0.0515649\pi$
$620$		0			0
$621$		0			0
$622$	−27.9942	−	12.4900i	−1.12246	−	0.500805i
$623$	15.9735			0.639966
$624$		0			0
$625$		0			0
$626$	−16.2065	−	7.23078i	−0.647741	−	0.289000i
$627$		0			0
$628$	−25.9192	+	23.2645i	−1.03429	+	0.928355i
$629$		−	65.0878i		−	2.59522i
$630$		0			0
$631$	−26.5248			−1.05594			−0.527968	−	0.849264i	$-0.677046\pi$
$631$	−26.5248			−1.05594			−0.527968	+	0.849264i	$0.677046\pi$
$632$	11.8667	+	36.8156i	0.472032	+	1.46444i
$633$		0			0
$634$	−6.25841	+	14.0271i	−0.248553	+	0.557087i
$635$		0			0
$636$		0			0
$637$			0.746260i			0.0295679i
$638$	16.7743	+	7.48412i	0.664101	+	0.296299i
$639$		0			0
$640$		0			0
$641$	26.5863			1.05009			0.525047	−	0.851073i	$-0.324048\pi$
$641$	26.5863			1.05009			0.525047	+	0.851073i	$0.324048\pi$
$642$		0			0
$643$		−	2.89233i		−	0.114062i	−0.998372	−	0.0570312i	$-0.981837\pi$
$643$		−	2.89233i		−	0.114062i	0.998372	−	0.0570312i	$-0.0181635\pi$
$644$	2.30897	+	2.57245i	0.0909862	+	0.101369i
$645$		0			0
$646$	−12.9362	+	28.9942i	−0.508968	+	1.14076i
$647$	−12.3472			−0.485420			−0.242710	−	0.970099i	$-0.578036\pi$
$647$	−12.3472			−0.485420			−0.242710	+	0.970099i	$0.578036\pi$
$648$		0			0
$649$	−9.20726			−0.361417
$650$		0			0
$651$		0			0
$652$	−6.93863	+	6.22795i	−0.271738	+	0.243905i
$653$			39.0507i			1.52817i	0.645114	+	0.764086i	$0.276810\pi$
$653$			39.0507i			1.52817i	−0.645114	+	0.764086i	$0.723190\pi$
$654$		0			0
$655$		0			0
$656$	−0.823728	+	7.60830i	−0.0321612	+	0.297054i
$657$		0			0
$658$	8.53652	+	3.80870i	0.332788	+	0.148479i
$659$			23.7738i			0.926094i	0.886334	+	0.463047i	$0.153244\pi$
$659$			23.7738i			0.926094i	−0.886334	+	0.463047i	$0.846756\pi$
$660$		0			0
$661$			21.5051i			0.836450i	0.908343	+	0.418225i	$0.137348\pi$
$661$			21.5051i			0.836450i	−0.908343	+	0.418225i	$0.862652\pi$
$662$	0.709822	−	1.59094i	0.0275880	−	0.0618335i
$663$		0			0
$664$	33.1982	−	10.7007i	1.28834	−	0.415268i
$665$		0			0
$666$		0			0
$667$			7.93827i			0.307371i
$668$	−0.183583	−	0.204532i	−0.00710303	−	0.00791356i
$669$		0			0
$670$		0			0
$671$	−6.54235			−0.252565
$672$		0			0
$673$	36.1896			1.39501			0.697503	−	0.716582i	$-0.254294\pi$
$673$	36.1896			1.39501			0.697503	+	0.716582i	$0.254294\pi$
$674$	5.34538	+	2.38492i	0.205896	+	0.0918639i
$675$		0			0
$676$	17.2894	+	19.2623i	0.664976	+	0.740856i
$677$			9.17214i			0.352514i	0.984344	+	0.176257i	$0.0563990\pi$
$677$			9.17214i			0.352514i	−0.984344	+	0.176257i	$0.943601\pi$
$678$		0			0
$679$	−21.1034			−0.809873
$680$		0			0
$681$		0			0
$682$	−6.13921	+	13.7599i	−0.235083	+	0.526895i
$683$		−	16.3974i		−	0.627429i	−0.949517	−	0.313714i	$-0.898427\pi$
$683$		−	16.3974i		−	0.627429i	0.949517	−	0.313714i	$-0.101573\pi$
$684$		0			0
$685$		0			0
$686$	25.7658	+	11.4958i	0.983742	+	0.438912i
$687$		0			0
$688$	44.7194	+	4.84163i	1.70491	+	0.184586i
$689$	−2.22166			−0.0846387
$690$		0			0
$691$			24.4904i			0.931657i	0.884875	+	0.465828i	$0.154244\pi$
$691$			24.4904i			0.931657i	−0.884875	+	0.465828i	$0.845756\pi$
$692$	−5.90404	+	5.29933i	−0.224438	+	0.201450i
$693$		0			0
$694$	−10.0600	+	22.5477i	−0.381873	+	0.855900i
$695$		0			0
$696$		0			0
$697$	−14.1271			−0.535104
$698$	−12.2272	+	27.4050i	−0.462806	+	1.03730i
$699$		0			0
$700$		0			0
$701$			12.3887i			0.467916i	0.972247	+	0.233958i	$0.0751679\pi$
$701$			12.3887i			0.467916i	−0.972247	+	0.233958i	$0.924832\pi$
$702$		0			0
$703$	−26.7994			−1.01076
$704$	−6.68335	−	9.29018i	−0.251888	−	0.350137i
$705$		0			0
$706$	−27.1729	−	12.1236i	−1.02266	−	0.456278i
$707$		−	26.1057i		−	0.981807i
$708$		0			0
$709$			33.4144i			1.25490i	0.778655	+	0.627452i	$0.215902\pi$
$709$			33.4144i			1.25490i	−0.778655	+	0.627452i	$0.784098\pi$
$710$		0			0
$711$		0			0
$712$	−7.01176	−	21.7534i	−0.262777	−	0.815244i
$713$	−6.51175			−0.243867
$714$		0			0
$715$		0			0
$716$	6.97676	−	6.26218i	0.260734	−	0.234029i
$717$		0			0
$718$	30.3700	+	13.5501i	1.13340	+	0.505684i
$719$	33.8938			1.26403			0.632013	−	0.774958i	$-0.282229\pi$
$719$	33.8938			1.26403			0.632013	+	0.774958i	$0.282229\pi$
$720$		0			0
$721$	−38.3974			−1.42999
$722$	−12.6004	−	5.62185i	−0.468937	−	0.209224i
$723$		0			0
$724$	−13.5479	+	12.1603i	−0.503503	+	0.451932i
$725$		0			0
$726$		0			0
$727$	−14.1846			−0.526076			−0.263038	−	0.964785i	$-0.584725\pi$
$727$	−14.1846			−0.526076			−0.263038	+	0.964785i	$0.584725\pi$
$728$	−1.28418	+	0.413929i	−0.0475950	+	0.0153412i
$729$		0			0
$730$		0			0
$731$			83.0352i			3.07117i
$732$		0			0
$733$		−	8.09296i		−	0.298920i	−0.988768	−	0.149460i	$-0.952246\pi$
$733$		−	8.09296i		−	0.298920i	0.988768	−	0.149460i	$-0.0477536\pi$
$734$	−32.8056	−	14.6367i	−1.21088	−	0.540251i
$735$		0			0
$736$	2.48972	−	4.27366i	0.0917725	−	0.157529i
$737$	−6.96208			−0.256452
$738$		0			0
$739$		−	22.0919i		−	0.812663i	−0.913726	−	0.406331i	$-0.866808\pi$
$739$		−	22.0919i		−	0.812663i	0.913726	−	0.406331i	$-0.133192\pi$
$740$		0			0
$741$		0			0
$742$	−10.4865	+	23.5036i	−0.384971	+	0.862844i
$743$	−8.78340			−0.322232			−0.161116	−	0.986936i	$-0.551509\pi$
$743$	−8.78340			−0.322232			−0.161116	+	0.986936i	$0.551509\pi$
$744$		0			0
$745$		0			0
$746$	5.80123	−	13.0024i	0.212398	−	0.476052i
$747$		0			0
$748$	15.7222	−	14.1119i	0.574861	−	0.515982i
$749$			29.2728i			1.06961i
$750$		0			0
$751$	13.3779			0.488167			0.244084	−	0.969754i	$-0.421513\pi$
$751$	13.3779			0.488167			0.244084	+	0.969754i	$0.421513\pi$
$752$	1.43965	−	13.2973i	0.0524988	−	0.484901i
$753$		0			0
$754$	−2.82965	−	1.26249i	−0.103050	−	0.0459773i
$755$		0			0
$756$		0			0
$757$		−	9.72450i		−	0.353443i	−0.984261	−	0.176721i	$-0.943451\pi$
$757$		−	9.72450i		−	0.353443i	0.984261	−	0.176721i	$-0.0565492\pi$
$758$	−10.9294	+	24.4963i	−0.396975	+	0.889747i
$759$		0			0
$760$		0			0
$761$	−33.8835			−1.22828			−0.614138	−	0.789198i	$-0.710496\pi$
$761$	−33.8835			−1.22828			−0.614138	+	0.789198i	$0.710496\pi$
$762$		0			0
$763$		−	30.1052i		−	1.08988i
$764$	−20.3147	−	22.6328i	−0.734959	−	0.818826i
$765$		0			0
$766$	37.1236	+	16.5633i	1.34133	+	0.598456i
$767$	1.55317			0.0560817
$768$		0			0
$769$	18.7334			0.675545			0.337772	−	0.941228i	$-0.390327\pi$
$769$	18.7334			0.675545			0.337772	+	0.941228i	$0.390327\pi$
$770$		0			0
$771$		0			0
$772$	27.7292	+	30.8934i	0.997996	+	1.11188i
$773$		−	22.5006i		−	0.809292i	−0.914474	−	0.404646i	$-0.867395\pi$
$773$		−	22.5006i		−	0.809292i	0.914474	−	0.404646i	$-0.132605\pi$
$774$		0			0
$775$		0			0
$776$	9.26355	+	28.7395i	0.332542	+	1.03169i
$777$		0			0
$778$	−17.1807	+	38.5074i	−0.615958	+	1.38056i
$779$			5.81673i			0.208406i
$780$		0			0
$781$			11.7564i			0.420677i
$782$	8.33813	+	3.72019i	0.298171	+	0.133034i
$783$		0			0
$784$	1.33145	−	12.2978i	0.0475517	−	0.439207i
$785$		0			0
$786$		0			0
$787$			28.1063i			1.00188i	0.865482	+	0.500940i	$0.167012\pi$
$787$			28.1063i			1.00188i	−0.865482	+	0.500940i	$0.832988\pi$
$788$	−34.6060	+	31.0616i	−1.23279	+	1.10652i
$789$		0			0
$790$		0			0
$791$	−2.25133			−0.0800479
$792$		0			0
$793$	1.10363			0.0391910
$794$	−1.57405	+	3.52795i	−0.0558610	+	0.125202i
$795$		0			0
$796$	−9.64055	−	10.7406i	−0.341700	−	0.380692i
$797$		−	38.1461i		−	1.35120i	−0.737267	−	0.675602i	$-0.763884\pi$
$797$		−	38.1461i		−	1.35120i	0.737267	−	0.675602i	$-0.236116\pi$
$798$		0			0
$799$	24.6904			0.873485
$800$		0			0
$801$		0			0
$802$	33.4168	+	14.9094i	1.17999	+	0.526470i
$803$			5.90409i			0.208351i
$804$		0			0
$805$		0			0
$806$	1.03562	−	2.32116i	0.0364782	−	0.0817593i
$807$		0			0
$808$	−35.5519	+	11.4594i	−1.25071	+	0.403140i
$809$	10.0745			0.354201			0.177101	−	0.984193i	$-0.443328\pi$
$809$	10.0745			0.354201			0.177101	+	0.984193i	$0.443328\pi$
$810$		0			0
$811$			40.6001i			1.42566i	0.701335	+	0.712832i	$0.252588\pi$
$811$			40.6001i			1.42566i	−0.701335	+	0.712832i	$0.747412\pi$
$812$	−26.7125	+	23.9765i	−0.937426	+	0.841411i
$813$		0			0
$814$	16.2855	+	7.26604i	0.570807	+	0.254674i
$815$		0			0
$816$		0			0
$817$	34.1891			1.19612
$818$	−29.0311	−	12.9527i	−1.01505	−	0.452879i
$819$		0			0
$820$		0			0
$821$			10.3397i			0.360858i	0.983588	+	0.180429i	$0.0577486\pi$
$821$			10.3397i			0.360858i	−0.983588	+	0.180429i	$0.942251\pi$
$822$		0			0
$823$	28.5013			0.993493			0.496746	−	0.867896i	$-0.334528\pi$
$823$	28.5013			0.993493			0.496746	+	0.867896i	$0.334528\pi$
$824$	16.8550	+	52.2912i	0.587170	+	1.82165i
$825$		0			0
$826$	7.33113	−	16.4314i	0.255083	−	0.571722i
$827$			32.1957i			1.11956i	0.828643	+	0.559778i	$0.189114\pi$
$827$			32.1957i			1.11956i	−0.828643	+	0.559778i	$0.810886\pi$
$828$		0			0
$829$		−	31.5286i		−	1.09503i	−0.836795	−	0.547516i	$-0.815573\pi$
$829$		−	31.5286i		−	1.09503i	0.836795	−	0.547516i	$-0.184427\pi$
$830$		0			0
$831$		0			0
$832$	1.12741	+	1.56716i	0.0390860	+	0.0543314i
$833$	22.8346			0.791173
$834$		0			0
$835$		0			0
$836$	−5.81045	−	6.47349i	−0.200959	−	0.223890i
$837$		0			0
$838$	14.1351	−	31.6813i	0.488290	−	1.09441i
$839$	−54.9816			−1.89818			−0.949089	−	0.315009i	$-0.897992\pi$
$839$	−54.9816			−1.89818			−0.949089	+	0.315009i	$0.897992\pi$
$840$		0			0
$841$	−53.4316			−1.84247
$842$	−19.2376	+	43.1175i	−0.662970	+	1.48593i
$843$		0			0
$844$	6.52517	−	5.85684i	0.224606	−	0.201601i
$845$		0			0
$846$		0			0
$847$	17.6990			0.608144
$848$	36.6113	+	3.96380i	1.25724	+	0.136117i
$849$		0			0
$850$		0			0
$851$			7.70696i			0.264191i
$852$		0			0
$853$		−	4.22607i		−	0.144698i	−0.997379	−	0.0723489i	$-0.976950\pi$
$853$		−	4.22607i		−	0.144698i	0.997379	−	0.0723489i	$-0.0230495\pi$
$854$	5.20924	−	11.6756i	0.178257	−	0.399530i
$855$		0			0
$856$	39.8650	−	12.8496i	1.36256	−	0.439191i
$857$	54.8223			1.87270			0.936348	−	0.351074i	$-0.114183\pi$
$857$	54.8223			1.87270			0.936348	+	0.351074i	$0.114183\pi$
$858$		0			0
$859$			14.2126i			0.484926i	0.970161	+	0.242463i	$0.0779554\pi$
$859$			14.2126i			0.484926i	−0.970161	+	0.242463i	$0.922045\pi$
$860$		0			0
$861$		0			0
$862$	15.0521	+	6.71574i	0.512678	+	0.228739i
$863$	40.7446			1.38696			0.693482	−	0.720474i	$-0.256076\pi$
$863$	40.7446			1.38696			0.693482	+	0.720474i	$0.256076\pi$
$864$		0			0
$865$		0			0
$866$	25.5305	+	11.3908i	0.867563	+	0.387077i
$867$		0			0
$868$	−19.6679	−	21.9122i	−0.667573	−	0.743750i
$869$		−	19.5638i		−	0.663658i
$870$		0			0
$871$	1.17443			0.0397941
$872$	−40.9985	+	13.2150i	−1.38839	+	0.447517i
$873$		0			0
$874$	1.53176	−	3.43316i	0.0518125	−	0.116128i
$875$		0			0
$876$		0			0
$877$			34.4568i			1.16352i	0.813359	+	0.581762i	$0.197637\pi$
$877$			34.4568i			1.16352i	−0.813359	+	0.581762i	$0.802363\pi$
$878$	32.5068	+	14.5034i	1.09705	+	0.489467i
$879$		0			0
$880$		0			0
$881$	−23.8528			−0.803623			−0.401811	−	0.915722i	$-0.631619\pi$
$881$	−23.8528			−0.803623			−0.401811	+	0.915722i	$0.631619\pi$
$882$		0			0
$883$			24.2417i			0.815798i	0.913027	+	0.407899i	$0.133738\pi$
$883$			24.2417i			0.815798i	−0.913027	+	0.407899i	$0.866262\pi$
$884$	−2.65217	+	2.38053i	−0.0892023	+	0.0800659i
$885$		0			0
$886$	−11.2660	+	25.2508i	−0.378490	+	0.848317i
$887$	−39.1843			−1.31568			−0.657840	−	0.753158i	$-0.728530\pi$
$887$	−39.1843			−1.31568			−0.657840	+	0.753158i	$0.728530\pi$
$888$		0			0
$889$	−4.81571			−0.161514
$890$		0			0
$891$		0			0
$892$	6.66434	+	7.42481i	0.223139	+	0.248601i
$893$		−	10.1661i		−	0.340195i
$894$		0			0
$895$		0			0
$896$	21.9009	−	4.53005i	0.731658	−	0.151339i
$897$		0			0
$898$	−25.7799	−	11.5021i	−0.860286	−	0.383830i
$899$		−	67.6185i		−	2.25520i
$900$		0			0
$901$			67.9802i			2.26475i
$902$	1.57707	−	3.53473i	0.0525108	−	0.117693i
$903$		0			0
$904$	0.988244	+	3.06595i	0.0328685	+	0.101972i
$905$		0			0
$906$		0			0
$907$			18.9418i			0.628951i	0.949266	+	0.314475i	$0.101829\pi$
$907$			18.9418i			0.628951i	−0.949266	+	0.314475i	$0.898171\pi$
$908$	−16.7546	+	15.0385i	−0.556021	+	0.499071i
$909$		0			0
$910$		0			0
$911$	−17.8493			−0.591375			−0.295688	−	0.955285i	$-0.595549\pi$
$911$	−17.8493			−0.591375			−0.295688	+	0.955285i	$0.595549\pi$
$912$		0			0
$913$	−17.6415			−0.583850
$914$	−6.47267	−	2.88789i	−0.214097	−	0.0955228i
$915$		0			0
$916$	−23.5706	+	21.1564i	−0.778793	+	0.699027i
$917$			13.6425i			0.450515i
$918$		0			0
$919$	24.4983			0.808126			0.404063	−	0.914731i	$-0.367598\pi$
$919$	24.4983			0.808126			0.404063	+	0.914731i	$0.367598\pi$
$920$		0			0
$921$		0			0
$922$	2.95352	−	6.61978i	0.0972690	−	0.218011i
$923$		−	1.98318i		−	0.0652772i
$924$		0			0
$925$		0			0
$926$	−7.48443	−	3.33930i	−0.245954	−	0.109736i
$927$		0			0
$928$	44.3780	+	25.8535i	1.45678	+	0.848682i
$929$	−11.5577			−0.379196			−0.189598	−	0.981862i	$-0.560718\pi$
$929$	−11.5577			−0.379196			−0.189598	+	0.981862i	$0.560718\pi$
$930$		0			0
$931$		−	9.40197i		−	0.308137i
$932$	−14.6407	−	16.3114i	−0.479572	−	0.534296i
$933$		0			0
$934$	−9.69251	+	21.7240i	−0.317148	+	0.710831i
$935$		0			0
$936$		0			0
$937$	59.5587			1.94570			0.972849	−	0.231440i	$-0.0743436\pi$
$937$	59.5587			1.94570			0.972849	+	0.231440i	$0.0743436\pi$
$938$	5.54345	−	12.4246i	0.181000	−	0.405679i
$939$		0			0
$940$		0			0
$941$			55.9289i			1.82323i	0.411044	+	0.911615i	$0.365164\pi$
$941$			55.9289i			1.82323i	−0.411044	+	0.911615i	$0.634836\pi$
$942$		0			0
$943$	1.67277			0.0544730
$944$	−25.5951	−	2.77110i	−0.833048	−	0.0901917i
$945$		0			0
$946$	−20.7761	−	9.26958i	−0.675489	−	0.301380i
$947$			30.0945i			0.977941i	0.872300	+	0.488970i	$0.162627\pi$
$947$			30.0945i			0.977941i	−0.872300	+	0.488970i	$0.837373\pi$
$948$		0			0
$949$		−	0.995959i		−	0.0323302i
$950$		0			0
$951$		0			0
$952$	12.6657	+	39.2944i	0.410498	+	1.27354i
$953$	12.4097			0.401989			0.200995	−	0.979592i	$-0.435583\pi$
$953$	12.4097			0.401989			0.200995	+	0.979592i	$0.435583\pi$
$954$		0			0
$955$		0			0
$956$	−23.1360	−	25.7761i	−0.748272	−	0.833658i
$957$		0			0
$958$	−47.6647	−	21.2664i	−1.53998	−	0.687085i
$959$	−10.6552			−0.344074
$960$		0			0
$961$	24.4674			0.789271
$962$	−2.74720	−	1.22571i	−0.0885732	−	0.0395183i
$963$		0			0
$964$	6.37066	+	7.09762i	0.205185	+	0.228599i
$965$		0			0
$966$		0			0
$967$	−41.8371			−1.34539			−0.672694	−	0.739920i	$-0.734863\pi$
$967$	−41.8371			−1.34539			−0.672694	+	0.739920i	$0.734863\pi$
$968$	−7.76916	−	24.1032i	−0.249710	−	0.774706i
$969$		0			0
$970$		0			0
$971$		−	40.6875i		−	1.30572i	−0.757477	−	0.652862i	$-0.773568\pi$
$971$		−	40.6875i		−	1.30572i	0.757477	−	0.652862i	$-0.226432\pi$
$972$		0			0
$973$			34.4439i			1.10422i
$974$	−6.65101	−	2.96745i	−0.213112	−	0.0950833i
$975$		0			0
$976$	−18.1869	−	1.96905i	−0.582150	−	0.0630276i
$977$	1.67923			0.0537233			0.0268617	−	0.999639i	$-0.491449\pi$
$977$	1.67923			0.0537233			0.0268617	+	0.999639i	$0.491449\pi$
$978$		0			0
$979$			11.5598i			0.369453i
$980$		0			0
$981$		0			0
$982$	−13.3196	+	29.8535i	−0.425046	+	0.952663i
$983$	−13.4944			−0.430404			−0.215202	−	0.976570i	$-0.569041\pi$
$983$	−13.4944			−0.430404			−0.215202	+	0.976570i	$0.569041\pi$
$984$		0			0
$985$		0			0
$986$	−38.6307	+	86.5838i	−1.23025	+	2.75739i
$987$		0			0
$988$	0.980164	+	1.09201i	0.0311832	+	0.0347415i
$989$		−	9.83208i		−	0.312642i
$990$		0			0
$991$	−10.8502			−0.344667			−0.172333	−	0.985039i	$-0.555131\pi$
$991$	−10.8502			−0.344667			−0.172333	+	0.985039i	$0.555131\pi$
$992$	−21.2076	+	36.4032i	−0.673341	+	1.15580i
$993$		0			0
$994$	−20.9806	−	9.36083i	−0.665465	−	0.296908i
$995$		0			0
$996$		0			0
$997$		−	39.0972i		−	1.23822i	−0.785304	−	0.619110i	$-0.787493\pi$
$997$		−	39.0972i		−	1.23822i	0.785304	−	0.619110i	$-0.212507\pi$
$998$	−8.24639	+	18.4828i	−0.261035	+	0.585063i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1800.2.k.q.901.1		8
3.2	odd	2		600.2.k.e.301.8	yes	8
4.3	odd	2		7200.2.k.s.3601.1		8
5.2	odd	4		1800.2.d.t.1549.5		8
5.3	odd	4		1800.2.d.s.1549.4		8
5.4	even	2		1800.2.k.t.901.8		8
8.3	odd	2		7200.2.k.s.3601.2		8
8.5	even	2	inner	1800.2.k.q.901.2		8
12.11	even	2		2400.2.k.e.1201.5		8
15.2	even	4		600.2.d.g.349.4		8
15.8	even	4		600.2.d.h.349.5		8
15.14	odd	2		600.2.k.d.301.1	✓	8
20.3	even	4		7200.2.d.s.2449.7		8
20.7	even	4		7200.2.d.t.2449.2		8
20.19	odd	2		7200.2.k.r.3601.7		8
24.5	odd	2		600.2.k.e.301.7	yes	8
24.11	even	2		2400.2.k.e.1201.1		8
40.3	even	4		7200.2.d.t.2449.7		8
40.13	odd	4		1800.2.d.t.1549.6		8
40.19	odd	2		7200.2.k.r.3601.8		8
40.27	even	4		7200.2.d.s.2449.2		8
40.29	even	2		1800.2.k.t.901.7		8
40.37	odd	4		1800.2.d.s.1549.3		8
60.23	odd	4		2400.2.d.g.49.7		8
60.47	odd	4		2400.2.d.h.49.2		8
60.59	even	2		2400.2.k.d.1201.4		8
120.29	odd	2		600.2.k.d.301.2	yes	8
120.53	even	4		600.2.d.g.349.3		8
120.59	even	2		2400.2.k.d.1201.8		8
120.77	even	4		600.2.d.h.349.6		8
120.83	odd	4		2400.2.d.h.49.7		8
120.107	odd	4		2400.2.d.g.49.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
600.2.d.g.349.3		8	120.53	even	4
600.2.d.g.349.4		8	15.2	even	4
600.2.d.h.349.5		8	15.8	even	4
600.2.d.h.349.6		8	120.77	even	4
600.2.k.d.301.1	✓	8	15.14	odd	2
600.2.k.d.301.2	yes	8	120.29	odd	2
600.2.k.e.301.7	yes	8	24.5	odd	2
600.2.k.e.301.8	yes	8	3.2	odd	2
1800.2.d.s.1549.3		8	40.37	odd	4
1800.2.d.s.1549.4		8	5.3	odd	4
1800.2.d.t.1549.5		8	5.2	odd	4
1800.2.d.t.1549.6		8	40.13	odd	4
1800.2.k.q.901.1		8	1.1	even	1	trivial
1800.2.k.q.901.2		8	8.5	even	2	inner
1800.2.k.t.901.7		8	40.29	even	2
1800.2.k.t.901.8		8	5.4	even	2
2400.2.d.g.49.2		8	120.107	odd	4
2400.2.d.g.49.7		8	60.23	odd	4
2400.2.d.h.49.2		8	60.47	odd	4
2400.2.d.h.49.7		8	120.83	odd	4
2400.2.k.d.1201.4		8	60.59	even	2
2400.2.k.d.1201.8		8	120.59	even	2
2400.2.k.e.1201.1		8	24.11	even	2
2400.2.k.e.1201.5		8	12.11	even	2
7200.2.d.s.2449.2		8	40.27	even	4
7200.2.d.s.2449.7		8	20.3	even	4
7200.2.d.t.2449.2		8	20.7	even	4
7200.2.d.t.2449.7		8	40.3	even	4
7200.2.k.r.3601.7		8	20.19	odd	2
7200.2.k.r.3601.8		8	40.19	odd	2
7200.2.k.s.3601.1		8	4.3	odd	2
7200.2.k.s.3601.2		8	8.3	odd	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:	\( N \)	\(=\)	\( 1800 = 2^{3} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1800.k (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.29150 - 0.576222i) q^{2} +(1.33594 + 1.48838i) q^{4} +1.97676 q^{7} +(-0.867721 - 2.69204i) q^{8} +O(q^{10})\)	\(q+(-1.29150 - 0.576222i) q^{2} +(1.33594 + 1.48838i) q^{4} +1.97676 q^{7} +(-0.867721 - 2.69204i) q^{8} +1.43055i q^{11} -0.241319i q^{13} +(-2.55298 - 1.13905i) q^{14} +(-0.430552 + 3.97676i) q^{16} -7.38407 q^{17} +3.04033i q^{19} +(0.824316 - 1.84756i) q^{22} +0.874337 q^{23} +(-0.139054 + 0.311664i) q^{26} +(2.64082 + 2.94217i) q^{28} +9.07918i q^{29} -7.44764 q^{31} +(2.84756 - 4.88789i) q^{32} +(9.53652 + 4.25487i) q^{34} +8.81463i q^{37} +(1.75191 - 3.92658i) q^{38} +1.91319 q^{41} -11.2452i q^{43} +(-2.12921 + 1.91113i) q^{44} +(-1.12921 - 0.503813i) q^{46} -3.34374 q^{47} -3.09242 q^{49} +(0.359175 - 0.322387i) q^{52} -9.20632i q^{53} +(-1.71528 - 5.32151i) q^{56} +(5.23163 - 11.7258i) q^{58} +6.43616i q^{59} +4.57331i q^{61} +(9.61862 + 4.29150i) q^{62} +(-6.49412 + 4.67187i) q^{64} +4.86671i q^{67} +(-9.86465 - 10.9903i) q^{68} +8.21808 q^{71} +4.12714 q^{73} +(5.07918 - 11.3841i) q^{74} +(-4.52517 + 4.06169i) q^{76} +2.82786i q^{77} -13.6757 q^{79} +(-2.47088 - 1.10242i) q^{82} +12.3320i q^{83} +(-6.47972 + 14.5231i) q^{86} +(3.85110 - 1.24132i) q^{88} +8.08066 q^{89} -0.477031i q^{91} +(1.16806 + 1.30135i) q^{92} +(4.31844 + 1.92674i) q^{94} -10.6757 q^{97} +(3.99385 + 1.78192i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} + 4 q^{4} - 8 q^{7} + 4 q^{8}+O(q^{10}) \) 8 * q - 2 * q^2 + 4 * q^4 - 8 * q^7 + 4 * q^8	\( 8 q - 2 q^{2} + 4 q^{4} - 8 q^{7} + 4 q^{8} + 6 q^{14} + 8 q^{16} - 12 q^{22} + 8 q^{23} + 2 q^{26} + 4 q^{28} + 8 q^{31} + 28 q^{32} + 12 q^{34} + 30 q^{38} + 12 q^{44} + 20 q^{46} + 20 q^{52} - 8 q^{56} - 12 q^{58} + 30 q^{62} - 32 q^{64} - 28 q^{68} + 40 q^{71} + 16 q^{73} - 8 q^{74} - 20 q^{76} - 16 q^{79} + 24 q^{82} + 18 q^{86} + 8 q^{88} - 36 q^{92} - 4 q^{94} + 8 q^{97} - 48 q^{98}+O(q^{100}) \) 8 * q - 2 * q^2 + 4 * q^4 - 8 * q^7 + 4 * q^8 + 6 * q^14 + 8 * q^16 - 12 * q^22 + 8 * q^23 + 2 * q^26 + 4 * q^28 + 8 * q^31 + 28 * q^32 + 12 * q^34 + 30 * q^38 + 12 * q^44 + 20 * q^46 + 20 * q^52 - 8 * q^56 - 12 * q^58 + 30 * q^62 - 32 * q^64 - 28 * q^68 + 40 * q^71 + 16 * q^73 - 8 * q^74 - 20 * q^76 - 16 * q^79 + 24 * q^82 + 18 * q^86 + 8 * q^88 - 36 * q^92 - 4 * q^94 + 8 * q^97 - 48 * q^98

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