LMFDB - Embedded newform 700.2.r.b.149.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [700,2,Mod(149,700)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(700, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 2]))

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

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

chi := DirichletCharacter("700.149");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 700 = 2^{2} \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	700.r (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.58952814149$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 28)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			149.2
Root			$0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	700.149
Dual form			700.2.r.b.249.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{3} +(-1.73205 + 2.00000i) q^{7} +(-1.00000 + 1.73205i) q^{9} +O(q^{10})$	$q+(0.866025 - 0.500000i) q^{3} +(-1.73205 + 2.00000i) q^{7} +(-1.00000 + 1.73205i) q^{9} +(1.50000 + 2.59808i) q^{11} +2.00000i q^{13} +(-2.59808 + 1.50000i) q^{17} +(-0.500000 + 0.866025i) q^{19} +(-0.500000 + 2.59808i) q^{21} +(-2.59808 - 1.50000i) q^{23} +5.00000i q^{27} +6.00000 q^{29} +(3.50000 + 6.06218i) q^{31} +(2.59808 + 1.50000i) q^{33} +(-0.866025 - 0.500000i) q^{37} +(1.00000 + 1.73205i) q^{39} +6.00000 q^{41} -4.00000i q^{43} +(-7.79423 - 4.50000i) q^{47} +(-1.00000 - 6.92820i) q^{49} +(-1.50000 + 2.59808i) q^{51} +(2.59808 - 1.50000i) q^{53} +1.00000i q^{57} +(4.50000 + 7.79423i) q^{59} +(0.500000 - 0.866025i) q^{61} +(-1.73205 - 5.00000i) q^{63} +(6.06218 - 3.50000i) q^{67} -3.00000 q^{69} +(-0.866025 + 0.500000i) q^{73} +(-7.79423 - 1.50000i) q^{77} +(-6.50000 + 11.2583i) q^{79} +(-0.500000 - 0.866025i) q^{81} +12.0000i q^{83} +(5.19615 - 3.00000i) q^{87} +(7.50000 - 12.9904i) q^{89} +(-4.00000 - 3.46410i) q^{91} +(6.06218 + 3.50000i) q^{93} +10.0000i q^{97} -6.00000 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{9}+O(q^{10}) $ 4 * q - 4 * q^9	$ 4 q - 4 q^{9} + 6 q^{11} - 2 q^{19} - 2 q^{21} + 24 q^{29} + 14 q^{31} + 4 q^{39} + 24 q^{41} - 4 q^{49} - 6 q^{51} + 18 q^{59} + 2 q^{61} - 12 q^{69} - 26 q^{79} - 2 q^{81} + 30 q^{89} - 16 q^{91} - 24 q^{99}+O(q^{100}) $ 4 * q - 4 * q^9 + 6 * q^11 - 2 * q^19 - 2 * q^21 + 24 * q^29 + 14 * q^31 + 4 * q^39 + 24 * q^41 - 4 * q^49 - 6 * q^51 + 18 * q^59 + 2 * q^61 - 12 * q^69 - 26 * q^79 - 2 * q^81 + 30 * q^89 - 16 * q^91 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/700\mathbb{Z}\right)^\times$.

$n$	$101$	$351$	$477$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$-1$

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 $

$2$		0			0
$2$		0			0
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i	−0.228714	−	0.973494i	$-0.573452\pi$
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i	0.728714	+	0.684819i	$0.240119\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−1.73205	+	2.00000i	−0.654654	+	0.755929i
$7$	−1.73205	+	2.00000i	−0.654654	+	0.755929i
$8$		0			0
$9$	−1.00000	+	1.73205i	−0.333333	+	0.577350i
$10$		0			0
$11$	1.50000	+	2.59808i	0.452267	+	0.783349i	0.998526	−	0.0542666i	$-0.0172821\pi$
$11$	1.50000	+	2.59808i	0.452267	+	0.783349i	−0.546259	+	0.837616i	$0.683949\pi$
$12$		0			0
$13$			2.00000i			0.554700i	0.960769	+	0.277350i	$0.0894562\pi$
$13$			2.00000i			0.554700i	−0.960769	+	0.277350i	$0.910544\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−2.59808	+	1.50000i	−0.630126	+	0.363803i	−0.780801	−	0.624780i	$-0.785189\pi$
$17$	−2.59808	+	1.50000i	−0.630126	+	0.363803i	0.150675	+	0.988583i	$0.451855\pi$
$18$		0			0
$19$	−0.500000	+	0.866025i	−0.114708	+	0.198680i	−0.917663	−	0.397360i	$-0.869927\pi$
$19$	−0.500000	+	0.866025i	−0.114708	+	0.198680i	0.802955	+	0.596040i	$0.203260\pi$
$20$		0			0
$21$	−0.500000	+	2.59808i	−0.109109	+	0.566947i
$22$		0			0
$23$	−2.59808	−	1.50000i	−0.541736	−	0.312772i	0.204046	−	0.978961i	$-0.434591\pi$
$23$	−2.59808	−	1.50000i	−0.541736	−	0.312772i	−0.745782	+	0.666190i	$0.767924\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$			5.00000i			0.962250i
$28$		0			0
$29$	6.00000			1.11417			0.557086	−	0.830455i	$-0.311919\pi$
$29$	6.00000			1.11417			0.557086	+	0.830455i	$0.311919\pi$
$30$		0			0
$31$	3.50000	+	6.06218i	0.628619	+	1.08880i	0.987829	+	0.155543i	$0.0497126\pi$
$31$	3.50000	+	6.06218i	0.628619	+	1.08880i	−0.359211	+	0.933257i	$0.616954\pi$
$32$		0			0
$33$	2.59808	+	1.50000i	0.452267	+	0.261116i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−0.866025	−	0.500000i	−0.142374	−	0.0821995i	0.427121	−	0.904194i	$-0.359528\pi$
$37$	−0.866025	−	0.500000i	−0.142374	−	0.0821995i	−0.569495	+	0.821995i	$0.692861\pi$
$38$		0			0
$39$	1.00000	+	1.73205i	0.160128	+	0.277350i
$40$		0			0
$41$	6.00000			0.937043			0.468521	−	0.883452i	$-0.344787\pi$
$41$	6.00000			0.937043			0.468521	+	0.883452i	$0.344787\pi$
$42$		0			0
$43$		−	4.00000i		−	0.609994i	−0.952353	−	0.304997i	$-0.901344\pi$
$43$		−	4.00000i		−	0.609994i	0.952353	−	0.304997i	$-0.0986555\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−7.79423	−	4.50000i	−1.13691	−	0.656392i	−0.191243	−	0.981543i	$-0.561252\pi$
$47$	−7.79423	−	4.50000i	−1.13691	−	0.656392i	−0.945662	+	0.325150i	$0.894585\pi$
$48$		0			0
$49$	−1.00000	−	6.92820i	−0.142857	−	0.989743i
$50$		0			0
$51$	−1.50000	+	2.59808i	−0.210042	+	0.363803i
$52$		0			0
$53$	2.59808	−	1.50000i	0.356873	−	0.206041i	−0.310835	−	0.950464i	$-0.600609\pi$
$53$	2.59808	−	1.50000i	0.356873	−	0.206041i	0.667708	+	0.744423i	$0.267275\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$			1.00000i			0.132453i
$58$		0			0
$59$	4.50000	+	7.79423i	0.585850	+	1.01472i	0.994769	+	0.102151i	$0.0325726\pi$
$59$	4.50000	+	7.79423i	0.585850	+	1.01472i	−0.408919	+	0.912571i	$0.634094\pi$
$60$		0			0
$61$	0.500000	−	0.866025i	0.0640184	−	0.110883i	−0.832240	−	0.554416i	$-0.812942\pi$
$61$	0.500000	−	0.866025i	0.0640184	−	0.110883i	0.896258	+	0.443533i	$0.146275\pi$
$62$		0			0
$63$	−1.73205	−	5.00000i	−0.218218	−	0.629941i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	6.06218	−	3.50000i	0.740613	−	0.427593i	−0.0816792	−	0.996659i	$-0.526028\pi$
$67$	6.06218	−	3.50000i	0.740613	−	0.427593i	0.822292	+	0.569066i	$0.192695\pi$
$68$		0			0
$69$	−3.00000			−0.361158
$70$		0			0
$71$		0			0			−	1.00000i	$-0.5\pi$
$71$		0			0				1.00000i	$0.5\pi$
$72$		0			0
$73$	−0.866025	+	0.500000i	−0.101361	+	0.0585206i	−0.549823	−	0.835281i	$-0.685305\pi$
$73$	−0.866025	+	0.500000i	−0.101361	+	0.0585206i	0.448463	+	0.893801i	$0.351972\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−7.79423	−	1.50000i	−0.888235	−	0.170941i
$78$		0			0
$79$	−6.50000	+	11.2583i	−0.731307	+	1.26666i	0.225018	+	0.974355i	$0.427756\pi$
$79$	−6.50000	+	11.2583i	−0.731307	+	1.26666i	−0.956325	+	0.292306i	$0.905577\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$		0			0
$83$			12.0000i			1.31717i	0.752506	+	0.658586i	$0.228845\pi$
$83$			12.0000i			1.31717i	−0.752506	+	0.658586i	$0.771155\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	5.19615	−	3.00000i	0.557086	−	0.321634i
$88$		0			0
$89$	7.50000	−	12.9904i	0.794998	−	1.37698i	−0.127842	−	0.991795i	$-0.540805\pi$
$89$	7.50000	−	12.9904i	0.794998	−	1.37698i	0.922840	−	0.385183i	$-0.125862\pi$
$90$		0			0
$91$	−4.00000	−	3.46410i	−0.419314	−	0.363137i
$92$		0			0
$93$	6.06218	+	3.50000i	0.628619	+	0.362933i
$94$		0			0
$95$		0			0
$96$		0			0
$97$			10.0000i			1.01535i	0.861550	+	0.507673i	$0.169494\pi$
$97$			10.0000i			1.01535i	−0.861550	+	0.507673i	$0.830506\pi$
$98$		0			0
$99$	−6.00000			−0.603023
$100$		0			0
$101$	−7.50000	−	12.9904i	−0.746278	−	1.29259i	−0.949595	−	0.313478i	$-0.898506\pi$
$101$	−7.50000	−	12.9904i	−0.746278	−	1.29259i	0.203317	−	0.979113i	$-0.434828\pi$
$102$		0			0
$103$	−9.52628	−	5.50000i	−0.938652	−	0.541931i	−0.0491146	−	0.998793i	$-0.515640\pi$
$103$	−9.52628	−	5.50000i	−0.938652	−	0.541931i	−0.889538	+	0.456862i	$0.848973\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	12.9904	+	7.50000i	1.25583	+	0.725052i	0.972261	−	0.233900i	$-0.0751489\pi$
$107$	12.9904	+	7.50000i	1.25583	+	0.725052i	0.283567	+	0.958952i	$0.408482\pi$
$108$		0			0
$109$	−0.500000	−	0.866025i	−0.0478913	−	0.0829502i	0.841086	−	0.540901i	$-0.181917\pi$
$109$	−0.500000	−	0.866025i	−0.0478913	−	0.0829502i	−0.888977	+	0.457951i	$0.848583\pi$
$110$		0			0
$111$	−1.00000			−0.0949158
$112$		0			0
$113$			6.00000i			0.564433i	0.959351	+	0.282216i	$0.0910696\pi$
$113$			6.00000i			0.564433i	−0.959351	+	0.282216i	$0.908930\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−3.46410	−	2.00000i	−0.320256	−	0.184900i
$118$		0			0
$119$	1.50000	−	7.79423i	0.137505	−	0.714496i
$120$		0			0
$121$	1.00000	−	1.73205i	0.0909091	−	0.157459i
$122$		0			0
$123$	5.19615	−	3.00000i	0.468521	−	0.270501i
$124$		0			0
$125$		0			0
$126$		0			0
$127$		−	8.00000i		−	0.709885i	−0.934888	−	0.354943i	$-0.884500\pi$
$127$		−	8.00000i		−	0.709885i	0.934888	−	0.354943i	$-0.115500\pi$
$128$		0			0
$129$	−2.00000	−	3.46410i	−0.176090	−	0.304997i
$130$		0			0
$131$	−1.50000	+	2.59808i	−0.131056	+	0.226995i	−0.924084	−	0.382190i	$-0.875170\pi$
$131$	−1.50000	+	2.59808i	−0.131056	+	0.226995i	0.793028	+	0.609185i	$0.208503\pi$
$132$		0			0
$133$	−0.866025	−	2.50000i	−0.0750939	−	0.216777i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	18.1865	−	10.5000i	1.55378	−	0.897076i	0.555952	−	0.831215i	$-0.312354\pi$
$137$	18.1865	−	10.5000i	1.55378	−	0.897076i	0.997829	−	0.0658609i	$-0.0209794\pi$
$138$		0			0
$139$	−20.0000			−1.69638			−0.848189	−	0.529694i	$-0.822307\pi$
$139$	−20.0000			−1.69638			−0.848189	+	0.529694i	$0.822307\pi$
$140$		0			0
$141$	−9.00000			−0.757937
$142$		0			0
$143$	−5.19615	+	3.00000i	−0.434524	+	0.250873i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−4.33013	−	5.50000i	−0.357143	−	0.453632i
$148$		0			0
$149$	1.50000	−	2.59808i	0.122885	−	0.212843i	−0.798019	−	0.602632i	$-0.794119\pi$
$149$	1.50000	−	2.59808i	0.122885	−	0.212843i	0.920904	+	0.389789i	$0.127452\pi$
$150$		0			0
$151$	−8.50000	−	14.7224i	−0.691720	−	1.19809i	−0.971274	−	0.237964i	$-0.923520\pi$
$151$	−8.50000	−	14.7224i	−0.691720	−	1.19809i	0.279554	−	0.960130i	$-0.409814\pi$
$152$		0			0
$153$		−	6.00000i		−	0.485071i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	11.2583	−	6.50000i	0.898513	−	0.518756i	0.0217953	−	0.999762i	$-0.493062\pi$
$157$	11.2583	−	6.50000i	0.898513	−	0.518756i	0.876717	+	0.481006i	$0.159728\pi$
$158$		0			0
$159$	1.50000	−	2.59808i	0.118958	−	0.206041i
$160$		0			0
$161$	7.50000	−	2.59808i	0.591083	−	0.204757i
$162$		0			0
$163$	−9.52628	−	5.50000i	−0.746156	−	0.430793i	0.0781474	−	0.996942i	$-0.475100\pi$
$163$	−9.52628	−	5.50000i	−0.746156	−	0.430793i	−0.824303	+	0.566149i	$0.808433\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$			12.0000i			0.928588i	0.885681	+	0.464294i	$0.153692\pi$
$167$			12.0000i			0.928588i	−0.885681	+	0.464294i	$0.846308\pi$
$168$		0			0
$169$	9.00000			0.692308
$170$		0			0
$171$	−1.00000	−	1.73205i	−0.0764719	−	0.132453i
$172$		0			0
$173$	7.79423	+	4.50000i	0.592584	+	0.342129i	0.766119	−	0.642699i	$-0.222185\pi$
$173$	7.79423	+	4.50000i	0.592584	+	0.342129i	−0.173534	+	0.984828i	$0.555519\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	7.79423	+	4.50000i	0.585850	+	0.338241i
$178$		0			0
$179$	10.5000	+	18.1865i	0.784807	+	1.35933i	0.929114	+	0.369792i	$0.120571\pi$
$179$	10.5000	+	18.1865i	0.784807	+	1.35933i	−0.144308	+	0.989533i	$0.546095\pi$
$180$		0			0
$181$	−10.0000			−0.743294			−0.371647	−	0.928374i	$-0.621207\pi$
$181$	−10.0000			−0.743294			−0.371647	+	0.928374i	$0.621207\pi$
$182$		0			0
$183$		−	1.00000i		−	0.0739221i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−7.79423	−	4.50000i	−0.569970	−	0.329073i
$188$		0			0
$189$	−10.0000	−	8.66025i	−0.727393	−	0.629941i
$190$		0			0
$191$	4.50000	−	7.79423i	0.325609	−	0.563971i	−0.656027	−	0.754738i	$-0.727764\pi$
$191$	4.50000	−	7.79423i	0.325609	−	0.563971i	0.981635	+	0.190767i	$0.0610975\pi$
$192$		0			0
$193$	9.52628	−	5.50000i	0.685717	−	0.395899i	−0.116289	−	0.993215i	$-0.537100\pi$
$193$	9.52628	−	5.50000i	0.685717	−	0.395899i	0.802005	+	0.597317i	$0.203766\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	18.0000i		−	1.28245i	−0.767354	−	0.641223i	$-0.778427\pi$
$197$		−	18.0000i		−	1.28245i	0.767354	−	0.641223i	$-0.221573\pi$
$198$		0			0
$199$	−3.50000	−	6.06218i	−0.248108	−	0.429736i	0.714893	−	0.699234i	$-0.246476\pi$
$199$	−3.50000	−	6.06218i	−0.248108	−	0.429736i	−0.963001	+	0.269498i	$0.913142\pi$
$200$		0			0
$201$	3.50000	−	6.06218i	0.246871	−	0.427593i
$202$		0			0
$203$	−10.3923	+	12.0000i	−0.729397	+	0.842235i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	5.19615	−	3.00000i	0.361158	−	0.208514i
$208$		0			0
$209$	−3.00000			−0.207514
$210$		0			0
$211$	−4.00000			−0.275371			−0.137686	−	0.990476i	$-0.543966\pi$
$211$	−4.00000			−0.275371			−0.137686	+	0.990476i	$0.543966\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−18.1865	−	3.50000i	−1.23458	−	0.237595i
$218$		0			0
$219$	−0.500000	+	0.866025i	−0.0337869	+	0.0585206i
$220$		0			0
$221$	−3.00000	−	5.19615i	−0.201802	−	0.349531i
$222$		0			0
$223$			8.00000i			0.535720i	0.963458	+	0.267860i	$0.0863164\pi$
$223$			8.00000i			0.535720i	−0.963458	+	0.267860i	$0.913684\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	2.59808	−	1.50000i	0.172440	−	0.0995585i	−0.411296	−	0.911502i	$-0.634924\pi$
$227$	2.59808	−	1.50000i	0.172440	−	0.0995585i	0.583736	+	0.811943i	$0.301590\pi$
$228$		0			0
$229$	5.50000	−	9.52628i	0.363450	−	0.629514i	−0.625076	−	0.780564i	$-0.714932\pi$
$229$	5.50000	−	9.52628i	0.363450	−	0.629514i	0.988526	+	0.151050i	$0.0482653\pi$
$230$		0			0
$231$	−7.50000	+	2.59808i	−0.493464	+	0.170941i
$232$		0			0
$233$	18.1865	+	10.5000i	1.19144	+	0.687878i	0.958633	−	0.284645i	$-0.0918758\pi$
$233$	18.1865	+	10.5000i	1.19144	+	0.687878i	0.232806	+	0.972523i	$0.425209\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$			13.0000i			0.844441i
$238$		0			0
$239$	12.0000			0.776215			0.388108	−	0.921614i	$-0.373129\pi$
$239$	12.0000			0.776215			0.388108	+	0.921614i	$0.373129\pi$
$240$		0			0
$241$	0.500000	+	0.866025i	0.0322078	+	0.0557856i	0.881680	−	0.471848i	$-0.156413\pi$
$241$	0.500000	+	0.866025i	0.0322078	+	0.0557856i	−0.849472	+	0.527633i	$0.823079\pi$
$242$		0			0
$243$	−13.8564	−	8.00000i	−0.888889	−	0.513200i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−1.73205	−	1.00000i	−0.110208	−	0.0636285i
$248$		0			0
$249$	6.00000	+	10.3923i	0.380235	+	0.658586i
$250$		0			0
$251$		0			0			−	1.00000i	$-0.5\pi$
$251$		0			0				1.00000i	$0.5\pi$
$252$		0			0
$253$		−	9.00000i		−	0.565825i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	2.59808	+	1.50000i	0.162064	+	0.0935674i	0.578838	−	0.815442i	$-0.303506\pi$
$257$	2.59808	+	1.50000i	0.162064	+	0.0935674i	−0.416775	+	0.909010i	$0.636840\pi$
$258$		0			0
$259$	2.50000	−	0.866025i	0.155342	−	0.0538122i
$260$		0			0
$261$	−6.00000	+	10.3923i	−0.371391	+	0.643268i
$262$		0			0
$263$	−2.59808	+	1.50000i	−0.160204	+	0.0924940i	−0.577959	−	0.816066i	$-0.696151\pi$
$263$	−2.59808	+	1.50000i	−0.160204	+	0.0924940i	0.417755	+	0.908560i	$0.362817\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		−	15.0000i		−	0.917985i
$268$		0			0
$269$	1.50000	+	2.59808i	0.0914566	+	0.158408i	0.908124	−	0.418701i	$-0.137514\pi$
$269$	1.50000	+	2.59808i	0.0914566	+	0.158408i	−0.816668	+	0.577108i	$0.804181\pi$
$270$		0			0
$271$	−5.50000	+	9.52628i	−0.334101	+	0.578680i	−0.983312	−	0.181928i	$-0.941766\pi$
$271$	−5.50000	+	9.52628i	−0.334101	+	0.578680i	0.649211	+	0.760609i	$0.275099\pi$
$272$		0			0
$273$	−5.19615	−	1.00000i	−0.314485	−	0.0605228i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	11.2583	−	6.50000i	0.676448	−	0.390547i	−0.122068	−	0.992522i	$-0.538953\pi$
$277$	11.2583	−	6.50000i	0.676448	−	0.390547i	0.798515	+	0.601975i	$0.205619\pi$
$278$		0			0
$279$	−14.0000			−0.838158
$280$		0			0
$281$	30.0000			1.78965			0.894825	−	0.446417i	$-0.147300\pi$
$281$	30.0000			1.78965			0.894825	+	0.446417i	$0.147300\pi$
$282$		0			0
$283$	25.1147	−	14.5000i	1.49292	−	0.861936i	0.492949	−	0.870058i	$-0.335919\pi$
$283$	25.1147	−	14.5000i	1.49292	−	0.861936i	0.999967	+	0.00812260i	$0.00258553\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−10.3923	+	12.0000i	−0.613438	+	0.708338i
$288$		0			0
$289$	−4.00000	+	6.92820i	−0.235294	+	0.407541i
$290$		0			0
$291$	5.00000	+	8.66025i	0.293105	+	0.507673i
$292$		0			0
$293$			6.00000i			0.350524i	0.984522	+	0.175262i	$0.0560772\pi$
$293$			6.00000i			0.350524i	−0.984522	+	0.175262i	$0.943923\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−12.9904	+	7.50000i	−0.753778	+	0.435194i
$298$		0			0
$299$	3.00000	−	5.19615i	0.173494	−	0.300501i
$300$		0			0
$301$	8.00000	+	6.92820i	0.461112	+	0.399335i
$302$		0			0
$303$	−12.9904	−	7.50000i	−0.746278	−	0.430864i
$304$		0			0
$305$		0			0
$306$		0			0
$307$			28.0000i			1.59804i	0.601302	+	0.799022i	$0.294649\pi$
$307$			28.0000i			1.59804i	−0.601302	+	0.799022i	$0.705351\pi$
$308$		0			0
$309$	−11.0000			−0.625768
$310$		0			0
$311$	13.5000	+	23.3827i	0.765515	+	1.32591i	0.939974	+	0.341246i	$0.110849\pi$
$311$	13.5000	+	23.3827i	0.765515	+	1.32591i	−0.174459	+	0.984664i	$0.555818\pi$
$312$		0			0
$313$	−19.9186	−	11.5000i	−1.12586	−	0.650018i	−0.182973	−	0.983118i	$-0.558572\pi$
$313$	−19.9186	−	11.5000i	−1.12586	−	0.650018i	−0.942892	+	0.333099i	$0.891906\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−7.79423	−	4.50000i	−0.437767	−	0.252745i	0.264883	−	0.964281i	$-0.414667\pi$
$317$	−7.79423	−	4.50000i	−0.437767	−	0.252745i	−0.702650	+	0.711535i	$0.748000\pi$
$318$		0			0
$319$	9.00000	+	15.5885i	0.503903	+	0.872786i
$320$		0			0
$321$	15.0000			0.837218
$322$		0			0
$323$		−	3.00000i		−	0.166924i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−0.866025	−	0.500000i	−0.0478913	−	0.0276501i
$328$		0			0
$329$	22.5000	−	7.79423i	1.24047	−	0.429710i
$330$		0			0
$331$	6.50000	−	11.2583i	0.357272	−	0.618814i	−0.630232	−	0.776407i	$-0.717040\pi$
$331$	6.50000	−	11.2583i	0.357272	−	0.618814i	0.987504	+	0.157593i	$0.0503735\pi$
$332$		0			0
$333$	1.73205	−	1.00000i	0.0949158	−	0.0547997i
$334$		0			0
$335$		0			0
$336$		0			0
$337$			34.0000i			1.85210i	0.377403	+	0.926049i	$0.376817\pi$
$337$			34.0000i			1.85210i	−0.377403	+	0.926049i	$0.623183\pi$
$338$		0			0
$339$	3.00000	+	5.19615i	0.162938	+	0.282216i
$340$		0			0
$341$	−10.5000	+	18.1865i	−0.568607	+	0.984856i
$342$		0			0
$343$	15.5885	+	10.0000i	0.841698	+	0.539949i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−7.79423	+	4.50000i	−0.418416	+	0.241573i	−0.694399	−	0.719590i	$-0.744330\pi$
$347$	−7.79423	+	4.50000i	−0.418416	+	0.241573i	0.275983	+	0.961162i	$0.410997\pi$
$348$		0			0
$349$	−26.0000			−1.39175			−0.695874	−	0.718164i	$-0.744983\pi$
$349$	−26.0000			−1.39175			−0.695874	+	0.718164i	$0.744983\pi$
$350$		0			0
$351$	−10.0000			−0.533761
$352$		0			0
$353$	−18.1865	+	10.5000i	−0.967972	+	0.558859i	−0.898617	−	0.438733i	$-0.855427\pi$
$353$	−18.1865	+	10.5000i	−0.967972	+	0.558859i	−0.0693543	+	0.997592i	$0.522094\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−2.59808	−	7.50000i	−0.137505	−	0.396942i
$358$		0			0
$359$	7.50000	−	12.9904i	0.395835	−	0.685606i	−0.597372	−	0.801964i	$-0.703789\pi$
$359$	7.50000	−	12.9904i	0.395835	−	0.685606i	0.993207	+	0.116358i	$0.0371219\pi$
$360$		0			0
$361$	9.00000	+	15.5885i	0.473684	+	0.820445i
$362$		0			0
$363$		−	2.00000i		−	0.104973i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−4.33013	+	2.50000i	−0.226031	+	0.130499i	−0.608740	−	0.793370i	$-0.708325\pi$
$367$	−4.33013	+	2.50000i	−0.226031	+	0.130499i	0.382709	+	0.923869i	$0.374991\pi$
$368$		0			0
$369$	−6.00000	+	10.3923i	−0.312348	+	0.541002i
$370$		0			0
$371$	−1.50000	+	7.79423i	−0.0778761	+	0.404656i
$372$		0			0
$373$	21.6506	+	12.5000i	1.12103	+	0.647225i	0.941663	−	0.336557i	$-0.109263\pi$
$373$	21.6506	+	12.5000i	1.12103	+	0.647225i	0.179364	+	0.983783i	$0.442596\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$			12.0000i			0.618031i
$378$		0			0
$379$	−8.00000			−0.410932			−0.205466	−	0.978664i	$-0.565871\pi$
$379$	−8.00000			−0.410932			−0.205466	+	0.978664i	$0.565871\pi$
$380$		0			0
$381$	−4.00000	−	6.92820i	−0.204926	−	0.354943i
$382$		0			0
$383$	28.5788	+	16.5000i	1.46031	+	0.843111i	0.999025	−	0.0441413i	$-0.0140552\pi$
$383$	28.5788	+	16.5000i	1.46031	+	0.843111i	0.461285	+	0.887252i	$0.347389\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	6.92820	+	4.00000i	0.352180	+	0.203331i
$388$		0			0
$389$	7.50000	+	12.9904i	0.380265	+	0.658638i	0.991100	−	0.133120i	$-0.0424994\pi$
$389$	7.50000	+	12.9904i	0.380265	+	0.658638i	−0.610835	+	0.791758i	$0.709166\pi$
$390$		0			0
$391$	9.00000			0.455150
$392$		0			0
$393$			3.00000i			0.151330i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−32.0429	−	18.5000i	−1.60819	−	0.928488i	−0.989775	−	0.142636i	$-0.954442\pi$
$397$	−32.0429	−	18.5000i	−1.60819	−	0.928488i	−0.618414	−	0.785853i	$-0.712224\pi$
$398$		0			0
$399$	−2.00000	−	1.73205i	−0.100125	−	0.0867110i
$400$		0			0
$401$	−1.50000	+	2.59808i	−0.0749064	+	0.129742i	−0.901046	−	0.433724i	$-0.857199\pi$
$401$	−1.50000	+	2.59808i	−0.0749064	+	0.129742i	0.826139	+	0.563466i	$0.190532\pi$
$402$		0			0
$403$	−12.1244	+	7.00000i	−0.603957	+	0.348695i
$404$		0			0
$405$		0			0
$406$		0			0
$407$		−	3.00000i		−	0.148704i
$408$		0			0
$409$	5.50000	+	9.52628i	0.271957	+	0.471044i	0.969363	−	0.245633i	$-0.0789957\pi$
$409$	5.50000	+	9.52628i	0.271957	+	0.471044i	−0.697406	+	0.716677i	$0.745662\pi$
$410$		0			0
$411$	10.5000	−	18.1865i	0.517927	−	0.897076i
$412$		0			0
$413$	−23.3827	−	4.50000i	−1.15059	−	0.221431i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−17.3205	+	10.0000i	−0.848189	+	0.489702i
$418$		0			0
$419$	12.0000			0.586238			0.293119	−	0.956076i	$-0.405307\pi$
$419$	12.0000			0.586238			0.293119	+	0.956076i	$0.405307\pi$
$420$		0			0
$421$	−22.0000			−1.07221			−0.536107	−	0.844150i	$-0.680106\pi$
$421$	−22.0000			−1.07221			−0.536107	+	0.844150i	$0.680106\pi$
$422$		0			0
$423$	15.5885	−	9.00000i	0.757937	−	0.437595i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	0.866025	+	2.50000i	0.0419099	+	0.120983i
$428$		0			0
$429$	−3.00000	+	5.19615i	−0.144841	+	0.250873i
$430$		0			0
$431$	7.50000	+	12.9904i	0.361262	+	0.625725i	0.988169	−	0.153370i	$-0.0490126\pi$
$431$	7.50000	+	12.9904i	0.361262	+	0.625725i	−0.626907	+	0.779094i	$0.715679\pi$
$432$		0			0
$433$		−	10.0000i		−	0.480569i	−0.970702	−	0.240285i	$-0.922759\pi$
$433$		−	10.0000i		−	0.480569i	0.970702	−	0.240285i	$-0.0772408\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	2.59808	−	1.50000i	0.124283	−	0.0717547i
$438$		0			0
$439$	−0.500000	+	0.866025i	−0.0238637	+	0.0413331i	−0.877711	−	0.479191i	$-0.840930\pi$
$439$	−0.500000	+	0.866025i	−0.0238637	+	0.0413331i	0.853847	+	0.520524i	$0.174263\pi$
$440$		0			0
$441$	13.0000	+	5.19615i	0.619048	+	0.247436i
$442$		0			0
$443$	7.79423	+	4.50000i	0.370315	+	0.213801i	0.673596	−	0.739100i	$-0.264749\pi$
$443$	7.79423	+	4.50000i	0.370315	+	0.213801i	−0.303281	+	0.952901i	$0.598082\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		−	3.00000i		−	0.141895i
$448$		0			0
$449$	18.0000			0.849473			0.424736	−	0.905317i	$-0.360367\pi$
$449$	18.0000			0.849473			0.424736	+	0.905317i	$0.360367\pi$
$450$		0			0
$451$	9.00000	+	15.5885i	0.423793	+	0.734032i
$452$		0			0
$453$	−14.7224	−	8.50000i	−0.691720	−	0.399365i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	19.9186	+	11.5000i	0.931752	+	0.537947i	0.887365	−	0.461067i	$-0.152533\pi$
$457$	19.9186	+	11.5000i	0.931752	+	0.537947i	0.0443868	+	0.999014i	$0.485867\pi$
$458$		0			0
$459$	−7.50000	−	12.9904i	−0.350070	−	0.606339i
$460$		0			0
$461$	−6.00000			−0.279448			−0.139724	−	0.990190i	$-0.544622\pi$
$461$	−6.00000			−0.279448			−0.139724	+	0.990190i	$0.544622\pi$
$462$		0			0
$463$		−	16.0000i		−	0.743583i	−0.928316	−	0.371792i	$-0.878744\pi$
$463$		−	16.0000i		−	0.743583i	0.928316	−	0.371792i	$-0.121256\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−18.1865	−	10.5000i	−0.841572	−	0.485882i	0.0162260	−	0.999868i	$-0.494835\pi$
$467$	−18.1865	−	10.5000i	−0.841572	−	0.485882i	−0.857798	+	0.513986i	$0.828168\pi$
$468$		0			0
$469$	−3.50000	+	18.1865i	−0.161615	+	0.839776i
$470$		0			0
$471$	6.50000	−	11.2583i	0.299504	−	0.518756i
$472$		0			0
$473$	10.3923	−	6.00000i	0.477839	−	0.275880i
$474$		0			0
$475$		0			0
$476$		0			0
$477$			6.00000i			0.274721i
$478$		0			0
$479$	−1.50000	−	2.59808i	−0.0685367	−	0.118709i	0.829721	−	0.558179i	$-0.188500\pi$
$479$	−1.50000	−	2.59808i	−0.0685367	−	0.118709i	−0.898257	+	0.439470i	$0.855166\pi$
$480$		0			0
$481$	1.00000	−	1.73205i	0.0455961	−	0.0789747i
$482$		0			0
$483$	5.19615	−	6.00000i	0.236433	−	0.273009i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	16.4545	−	9.50000i	0.745624	−	0.430486i	−0.0784867	−	0.996915i	$-0.525009\pi$
$487$	16.4545	−	9.50000i	0.745624	−	0.430486i	0.824110	+	0.566429i	$0.191675\pi$
$488$		0			0
$489$	−11.0000			−0.497437
$490$		0			0
$491$	24.0000			1.08310			0.541552	−	0.840667i	$-0.317837\pi$
$491$	24.0000			1.08310			0.541552	+	0.840667i	$0.317837\pi$
$492$		0			0
$493$	−15.5885	+	9.00000i	−0.702069	+	0.405340i
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$		0			0
$499$	5.50000	−	9.52628i	0.246214	−	0.426455i	−0.716258	−	0.697835i	$-0.754147\pi$
$499$	5.50000	−	9.52628i	0.246214	−	0.426455i	0.962472	+	0.271380i	$0.0874801\pi$
$500$		0			0
$501$	6.00000	+	10.3923i	0.268060	+	0.464294i
$502$		0			0
$503$		0			0		1.00000			$0$
$503$		0			0		−1.00000			$\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	7.79423	−	4.50000i	0.346154	−	0.199852i
$508$		0			0
$509$	1.50000	−	2.59808i	0.0664863	−	0.115158i	−0.830866	−	0.556473i	$-0.812154\pi$
$509$	1.50000	−	2.59808i	0.0664863	−	0.115158i	0.897352	+	0.441315i	$0.145488\pi$
$510$		0			0
$511$	0.500000	−	2.59808i	0.0221187	−	0.114932i
$512$		0			0
$513$	−4.33013	−	2.50000i	−0.191180	−	0.110378i
$514$		0			0
$515$		0			0
$516$		0			0
$517$		−	27.0000i		−	1.18746i
$518$		0			0
$519$	9.00000			0.395056
$520$		0			0
$521$	−19.5000	−	33.7750i	−0.854311	−	1.47971i	−0.877283	−	0.479973i	$-0.840646\pi$
$521$	−19.5000	−	33.7750i	−0.854311	−	1.47971i	0.0229727	−	0.999736i	$-0.492687\pi$
$522$		0			0
$523$	0.866025	+	0.500000i	0.0378686	+	0.0218635i	0.518815	−	0.854887i	$-0.326373\pi$
$523$	0.866025	+	0.500000i	0.0378686	+	0.0218635i	−0.480946	+	0.876750i	$0.659707\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−18.1865	−	10.5000i	−0.792218	−	0.457387i
$528$		0			0
$529$	−7.00000	−	12.1244i	−0.304348	−	0.527146i
$530$		0			0
$531$	−18.0000			−0.781133
$532$		0			0
$533$			12.0000i			0.519778i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	18.1865	+	10.5000i	0.784807	+	0.453108i
$538$		0			0
$539$	16.5000	−	12.9904i	0.710705	−	0.559535i
$540$		0			0
$541$	−17.5000	+	30.3109i	−0.752384	+	1.30317i	0.194281	+	0.980946i	$0.437763\pi$
$541$	−17.5000	+	30.3109i	−0.752384	+	1.30317i	−0.946664	+	0.322221i	$0.895571\pi$
$542$		0			0
$543$	−8.66025	+	5.00000i	−0.371647	+	0.214571i
$544$		0			0
$545$		0			0
$546$		0			0
$547$		−	8.00000i		−	0.342055i	−0.985266	−	0.171028i	$-0.945291\pi$
$547$		−	8.00000i		−	0.342055i	0.985266	−	0.171028i	$-0.0547087\pi$
$548$		0			0
$549$	1.00000	+	1.73205i	0.0426790	+	0.0739221i
$550$		0			0
$551$	−3.00000	+	5.19615i	−0.127804	+	0.221364i
$552$		0			0
$553$	−11.2583	−	32.5000i	−0.478753	−	1.38204i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	28.5788	−	16.5000i	1.21092	−	0.699127i	0.247964	−	0.968769i	$-0.420239\pi$
$557$	28.5788	−	16.5000i	1.21092	−	0.699127i	0.962961	+	0.269642i	$0.0869053\pi$
$558$		0			0
$559$	8.00000			0.338364
$560$		0			0
$561$	−9.00000			−0.379980
$562$		0			0
$563$	7.79423	−	4.50000i	0.328488	−	0.189652i	−0.326682	−	0.945134i	$-0.605931\pi$
$563$	7.79423	−	4.50000i	0.328488	−	0.189652i	0.655169	+	0.755482i	$0.272597\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	2.59808	+	0.500000i	0.109109	+	0.0209980i
$568$		0			0
$569$	−4.50000	+	7.79423i	−0.188650	+	0.326751i	−0.944800	−	0.327647i	$-0.893744\pi$
$569$	−4.50000	+	7.79423i	−0.188650	+	0.326751i	0.756151	+	0.654398i	$0.227078\pi$
$570$		0			0
$571$	−14.5000	−	25.1147i	−0.606806	−	1.05102i	−0.991763	−	0.128085i	$-0.959117\pi$
$571$	−14.5000	−	25.1147i	−0.606806	−	1.05102i	0.384957	−	0.922934i	$-0.374216\pi$
$572$		0			0
$573$		−	9.00000i		−	0.375980i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	0.866025	−	0.500000i	0.0360531	−	0.0208153i	−0.481865	−	0.876245i	$-0.660040\pi$
$577$	0.866025	−	0.500000i	0.0360531	−	0.0208153i	0.517918	+	0.855430i	$0.326707\pi$
$578$		0			0
$579$	5.50000	−	9.52628i	0.228572	−	0.395899i
$580$		0			0
$581$	−24.0000	−	20.7846i	−0.995688	−	0.862291i
$582$		0			0
$583$	7.79423	+	4.50000i	0.322804	+	0.186371i
$584$		0			0
$585$		0			0
$586$		0			0
$587$		−	12.0000i		−	0.495293i	−0.968850	−	0.247647i	$-0.920343\pi$
$587$		−	12.0000i		−	0.495293i	0.968850	−	0.247647i	$-0.0796572\pi$
$588$		0			0
$589$	−7.00000			−0.288430
$590$		0			0
$591$	−9.00000	−	15.5885i	−0.370211	−	0.641223i
$592$		0			0
$593$	18.1865	+	10.5000i	0.746831	+	0.431183i	0.824548	−	0.565792i	$-0.191430\pi$
$593$	18.1865	+	10.5000i	0.746831	+	0.431183i	−0.0777165	+	0.996976i	$0.524763\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−6.06218	−	3.50000i	−0.248108	−	0.143245i
$598$		0			0
$599$	−13.5000	−	23.3827i	−0.551595	−	0.955391i	−0.998160	−	0.0606393i	$-0.980686\pi$
$599$	−13.5000	−	23.3827i	−0.551595	−	0.955391i	0.446565	−	0.894751i	$-0.352647\pi$
$600$		0			0
$601$	14.0000			0.571072			0.285536	−	0.958368i	$-0.407828\pi$
$601$	14.0000			0.571072			0.285536	+	0.958368i	$0.407828\pi$
$602$		0			0
$603$			14.0000i			0.570124i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	40.7032	+	23.5000i	1.65209	+	0.953836i	0.976210	+	0.216825i	$0.0695701\pi$
$607$	40.7032	+	23.5000i	1.65209	+	0.953836i	0.675881	+	0.737011i	$0.263763\pi$
$608$		0			0
$609$	−3.00000	+	15.5885i	−0.121566	+	0.631676i
$610$		0			0
$611$	9.00000	−	15.5885i	0.364101	−	0.630641i
$612$		0			0
$613$	−21.6506	+	12.5000i	−0.874461	+	0.504870i	−0.868828	−	0.495114i	$-0.835126\pi$
$613$	−21.6506	+	12.5000i	−0.874461	+	0.504870i	−0.00563283	+	0.999984i	$0.501793\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$		−	6.00000i		−	0.241551i	−0.992680	−	0.120775i	$-0.961462\pi$
$617$		−	6.00000i		−	0.241551i	0.992680	−	0.120775i	$-0.0385381\pi$
$618$		0			0
$619$	−15.5000	−	26.8468i	−0.622998	−	1.07906i	−0.988924	−	0.148420i	$-0.952581\pi$
$619$	−15.5000	−	26.8468i	−0.622998	−	1.07906i	0.365927	−	0.930644i	$-0.380752\pi$
$620$		0			0
$621$	7.50000	−	12.9904i	0.300965	−	0.521286i
$622$		0			0
$623$	12.9904	+	37.5000i	0.520449	+	1.50241i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−2.59808	+	1.50000i	−0.103757	+	0.0599042i
$628$		0			0
$629$	3.00000			0.119618
$630$		0			0
$631$	−16.0000			−0.636950			−0.318475	−	0.947931i	$-0.603171\pi$
$631$	−16.0000			−0.636950			−0.318475	+	0.947931i	$0.603171\pi$
$632$		0			0
$633$	−3.46410	+	2.00000i	−0.137686	+	0.0794929i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	13.8564	−	2.00000i	0.549011	−	0.0792429i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−7.50000	−	12.9904i	−0.296232	−	0.513089i	0.679039	−	0.734103i	$-0.262397\pi$
$641$	−7.50000	−	12.9904i	−0.296232	−	0.513089i	−0.975271	+	0.221013i	$0.929064\pi$
$642$		0			0
$643$			20.0000i			0.788723i	0.918955	+	0.394362i	$0.129034\pi$
$643$			20.0000i			0.788723i	−0.918955	+	0.394362i	$0.870966\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−18.1865	+	10.5000i	−0.714986	+	0.412798i	−0.812905	−	0.582397i	$-0.802115\pi$
$647$	−18.1865	+	10.5000i	−0.714986	+	0.412798i	0.0979182	+	0.995194i	$0.468782\pi$
$648$		0			0
$649$	−13.5000	+	23.3827i	−0.529921	+	0.917851i
$650$		0			0
$651$	−17.5000	+	6.06218i	−0.685879	+	0.237595i
$652$		0			0
$653$	−33.7750	−	19.5000i	−1.32172	−	0.763094i	−0.337715	−	0.941248i	$-0.609654\pi$
$653$	−33.7750	−	19.5000i	−1.32172	−	0.763094i	−0.984003	+	0.178154i	$0.942987\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		−	2.00000i		−	0.0780274i
$658$		0			0
$659$	−12.0000			−0.467454			−0.233727	−	0.972302i	$-0.575092\pi$
$659$	−12.0000			−0.467454			−0.233727	+	0.972302i	$0.575092\pi$
$660$		0			0
$661$	−5.50000	−	9.52628i	−0.213925	−	0.370529i	0.739014	−	0.673690i	$-0.235292\pi$
$661$	−5.50000	−	9.52628i	−0.213925	−	0.370529i	−0.952940	+	0.303160i	$0.901958\pi$
$662$		0			0
$663$	−5.19615	−	3.00000i	−0.201802	−	0.116510i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−15.5885	−	9.00000i	−0.603587	−	0.348481i
$668$		0			0
$669$	4.00000	+	6.92820i	0.154649	+	0.267860i
$670$		0			0
$671$	3.00000			0.115814
$672$		0			0
$673$			14.0000i			0.539660i	0.962908	+	0.269830i	$0.0869676\pi$
$673$			14.0000i			0.539660i	−0.962908	+	0.269830i	$0.913032\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	23.3827	+	13.5000i	0.898670	+	0.518847i	0.876768	−	0.480913i	$-0.159695\pi$
$677$	23.3827	+	13.5000i	0.898670	+	0.518847i	0.0219013	+	0.999760i	$0.493028\pi$
$678$		0			0
$679$	−20.0000	−	17.3205i	−0.767530	−	0.664700i
$680$		0			0
$681$	1.50000	−	2.59808i	0.0574801	−	0.0995585i
$682$		0			0
$683$	18.1865	−	10.5000i	0.695888	−	0.401771i	−0.109926	−	0.993940i	$-0.535061\pi$
$683$	18.1865	−	10.5000i	0.695888	−	0.401771i	0.805814	+	0.592168i	$0.201728\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$		−	11.0000i		−	0.419676i
$688$		0			0
$689$	3.00000	+	5.19615i	0.114291	+	0.197958i
$690$		0			0
$691$	6.50000	−	11.2583i	0.247272	−	0.428287i	−0.715496	−	0.698617i	$-0.753799\pi$
$691$	6.50000	−	11.2583i	0.247272	−	0.428287i	0.962768	+	0.270330i	$0.0871327\pi$
$692$		0			0
$693$	10.3923	−	12.0000i	0.394771	−	0.455842i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−15.5885	+	9.00000i	−0.590455	+	0.340899i
$698$		0			0
$699$	21.0000			0.794293
$700$		0			0
$701$	−18.0000			−0.679851			−0.339925	−	0.940452i	$-0.610402\pi$
$701$	−18.0000			−0.679851			−0.339925	+	0.940452i	$0.610402\pi$
$702$		0			0
$703$	0.866025	−	0.500000i	0.0326628	−	0.0188579i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	38.9711	+	7.50000i	1.46566	+	0.282067i
$708$		0			0
$709$	−0.500000	+	0.866025i	−0.0187779	+	0.0325243i	−0.875262	−	0.483650i	$-0.839311\pi$
$709$	−0.500000	+	0.866025i	−0.0187779	+	0.0325243i	0.856484	+	0.516174i	$0.172644\pi$
$710$		0			0
$711$	−13.0000	−	22.5167i	−0.487538	−	0.844441i
$712$		0			0
$713$		−	21.0000i		−	0.786456i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	10.3923	−	6.00000i	0.388108	−	0.224074i
$718$		0			0
$719$	−10.5000	+	18.1865i	−0.391584	+	0.678243i	−0.992659	−	0.120950i	$-0.961406\pi$
$719$	−10.5000	+	18.1865i	−0.391584	+	0.678243i	0.601075	+	0.799193i	$0.294739\pi$
$720$		0			0
$721$	27.5000	−	9.52628i	1.02415	−	0.354777i
$722$		0			0
$723$	0.866025	+	0.500000i	0.0322078	+	0.0185952i
$724$		0			0
$725$		0			0
$726$		0			0
$727$		−	32.0000i		−	1.18681i	−0.804902	−	0.593407i	$-0.797782\pi$
$727$		−	32.0000i		−	1.18681i	0.804902	−	0.593407i	$-0.202218\pi$
$728$		0			0
$729$	−13.0000			−0.481481
$730$		0			0
$731$	6.00000	+	10.3923i	0.221918	+	0.384373i
$732$		0			0
$733$	21.6506	+	12.5000i	0.799684	+	0.461698i	0.843361	−	0.537348i	$-0.180574\pi$
$733$	21.6506	+	12.5000i	0.799684	+	0.461698i	−0.0436764	+	0.999046i	$0.513907\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	18.1865	+	10.5000i	0.669910	+	0.386772i
$738$		0			0
$739$	−9.50000	−	16.4545i	−0.349463	−	0.605288i	0.636691	−	0.771119i	$-0.280303\pi$
$739$	−9.50000	−	16.4545i	−0.349463	−	0.605288i	−0.986154	+	0.165831i	$0.946969\pi$
$740$		0			0
$741$	−2.00000			−0.0734718
$742$		0			0
$743$		−	48.0000i		−	1.76095i	−0.474093	−	0.880475i	$-0.657224\pi$
$743$		−	48.0000i		−	1.76095i	0.474093	−	0.880475i	$-0.342776\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−20.7846	−	12.0000i	−0.760469	−	0.439057i
$748$		0			0
$749$	−37.5000	+	12.9904i	−1.37022	+	0.474658i
$750$		0			0
$751$	12.5000	−	21.6506i	0.456131	−	0.790043i	−0.542621	−	0.839978i	$-0.682568\pi$
$751$	12.5000	−	21.6506i	0.456131	−	0.790043i	0.998752	+	0.0499348i	$0.0159013\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$		−	2.00000i		−	0.0726912i	−0.999339	−	0.0363456i	$-0.988428\pi$
$757$		−	2.00000i		−	0.0726912i	0.999339	−	0.0363456i	$-0.0115717\pi$
$758$		0			0
$759$	−4.50000	−	7.79423i	−0.163340	−	0.282913i
$760$		0			0
$761$	−1.50000	+	2.59808i	−0.0543750	+	0.0941802i	−0.891932	−	0.452170i	$-0.850650\pi$
$761$	−1.50000	+	2.59808i	−0.0543750	+	0.0941802i	0.837557	+	0.546350i	$0.183983\pi$
$762$		0			0
$763$	2.59808	+	0.500000i	0.0940567	+	0.0181012i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−15.5885	+	9.00000i	−0.562867	+	0.324971i
$768$		0			0
$769$	34.0000			1.22607			0.613036	−	0.790055i	$-0.289948\pi$
$769$	34.0000			1.22607			0.613036	+	0.790055i	$0.289948\pi$
$770$		0			0
$771$	3.00000			0.108042
$772$		0			0
$773$	−28.5788	+	16.5000i	−1.02791	+	0.593464i	−0.916385	−	0.400298i	$-0.868907\pi$
$773$	−28.5788	+	16.5000i	−1.02791	+	0.593464i	−0.111524	+	0.993762i	$0.535573\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	1.73205	−	2.00000i	0.0621370	−	0.0717496i
$778$		0			0
$779$	−3.00000	+	5.19615i	−0.107486	+	0.186171i
$780$		0			0
$781$		0			0
$782$		0			0
$783$			30.0000i			1.07211i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	26.8468	−	15.5000i	0.956985	−	0.552515i	0.0617409	−	0.998092i	$-0.480335\pi$
$787$	26.8468	−	15.5000i	0.956985	−	0.552515i	0.895244	+	0.445577i	$0.147001\pi$
$788$		0			0
$789$	−1.50000	+	2.59808i	−0.0534014	+	0.0924940i
$790$		0			0
$791$	−12.0000	−	10.3923i	−0.426671	−	0.369508i
$792$		0			0
$793$	1.73205	+	1.00000i	0.0615069	+	0.0355110i
$794$		0			0
$795$		0			0
$796$		0			0
$797$		−	42.0000i		−	1.48772i	−0.668338	−	0.743858i	$-0.732994\pi$
$797$		−	42.0000i		−	1.48772i	0.668338	−	0.743858i	$-0.267006\pi$
$798$		0			0
$799$	27.0000			0.955191
$800$		0			0
$801$	15.0000	+	25.9808i	0.529999	+	0.917985i
$802$		0			0
$803$	−2.59808	−	1.50000i	−0.0916841	−	0.0529339i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	2.59808	+	1.50000i	0.0914566	+	0.0528025i
$808$		0			0
$809$	−16.5000	−	28.5788i	−0.580109	−	1.00478i	−0.995466	−	0.0951198i	$-0.969677\pi$
$809$	−16.5000	−	28.5788i	−0.580109	−	1.00478i	0.415357	−	0.909659i	$-0.363657\pi$
$810$		0			0
$811$	−52.0000			−1.82597			−0.912983	−	0.407997i	$-0.866228\pi$
$811$	−52.0000			−1.82597			−0.912983	+	0.407997i	$0.866228\pi$
$812$		0			0
$813$			11.0000i			0.385787i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	3.46410	+	2.00000i	0.121194	+	0.0699711i
$818$		0			0
$819$	10.0000	−	3.46410i	0.349428	−	0.121046i
$820$		0			0
$821$	−13.5000	+	23.3827i	−0.471153	+	0.816061i	−0.999456	−	0.0329950i	$-0.989495\pi$
$821$	−13.5000	+	23.3827i	−0.471153	+	0.816061i	0.528302	+	0.849056i	$0.322829\pi$
$822$		0			0
$823$	4.33013	−	2.50000i	0.150939	−	0.0871445i	−0.422628	−	0.906303i	$-0.638892\pi$
$823$	4.33013	−	2.50000i	0.150939	−	0.0871445i	0.573567	+	0.819159i	$0.305559\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			36.0000i			1.25184i	0.779886	+	0.625921i	$0.215277\pi$
$827$			36.0000i			1.25184i	−0.779886	+	0.625921i	$0.784723\pi$
$828$		0			0
$829$	−0.500000	−	0.866025i	−0.0173657	−	0.0300783i	0.857212	−	0.514964i	$-0.172195\pi$
$829$	−0.500000	−	0.866025i	−0.0173657	−	0.0300783i	−0.874578	+	0.484885i	$0.838861\pi$
$830$		0			0
$831$	6.50000	−	11.2583i	0.225483	−	0.390547i
$832$		0			0
$833$	12.9904	+	16.5000i	0.450090	+	0.571691i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−30.3109	+	17.5000i	−1.04770	+	0.604888i
$838$		0			0
$839$	24.0000			0.828572			0.414286	−	0.910147i	$-0.364031\pi$
$839$	24.0000			0.828572			0.414286	+	0.910147i	$0.364031\pi$
$840$		0			0
$841$	7.00000			0.241379
$842$		0			0
$843$	25.9808	−	15.0000i	0.894825	−	0.516627i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	1.73205	+	5.00000i	0.0595140	+	0.171802i
$848$		0			0
$849$	14.5000	−	25.1147i	0.497639	−	0.861936i
$850$		0			0
$851$	1.50000	+	2.59808i	0.0514193	+	0.0890609i
$852$		0			0
$853$		−	22.0000i		−	0.753266i	−0.926363	−	0.376633i	$-0.877082\pi$
$853$		−	22.0000i		−	0.753266i	0.926363	−	0.376633i	$-0.122918\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−12.9904	+	7.50000i	−0.443743	+	0.256195i	−0.705184	−	0.709024i	$-0.749136\pi$
$857$	−12.9904	+	7.50000i	−0.443743	+	0.256195i	0.261441	+	0.965219i	$0.415802\pi$
$858$		0			0
$859$	11.5000	−	19.9186i	0.392375	−	0.679613i	−0.600387	−	0.799709i	$-0.704987\pi$
$859$	11.5000	−	19.9186i	0.392375	−	0.679613i	0.992762	+	0.120096i	$0.0383202\pi$
$860$		0			0
$861$	−3.00000	+	15.5885i	−0.102240	+	0.531253i
$862$		0			0
$863$	−44.1673	−	25.5000i	−1.50347	−	0.868030i	−0.999992	−	0.00402340i	$-0.998719\pi$
$863$	−44.1673	−	25.5000i	−1.50347	−	0.868030i	−0.503480	−	0.864007i	$-0.667947\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$			8.00000i			0.271694i
$868$		0			0
$869$	−39.0000			−1.32298
$870$		0			0
$871$	7.00000	+	12.1244i	0.237186	+	0.410818i
$872$		0			0
$873$	−17.3205	−	10.0000i	−0.586210	−	0.338449i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−11.2583	−	6.50000i	−0.380167	−	0.219489i	0.297724	−	0.954652i	$-0.403772\pi$
$877$	−11.2583	−	6.50000i	−0.380167	−	0.219489i	−0.677891	+	0.735163i	$0.737106\pi$
$878$		0			0
$879$	3.00000	+	5.19615i	0.101187	+	0.175262i
$880$		0			0
$881$	18.0000			0.606435			0.303218	−	0.952921i	$-0.401939\pi$
$881$	18.0000			0.606435			0.303218	+	0.952921i	$0.401939\pi$
$882$		0			0
$883$			44.0000i			1.48072i	0.672212	+	0.740359i	$0.265344\pi$
$883$			44.0000i			1.48072i	−0.672212	+	0.740359i	$0.734656\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	33.7750	+	19.5000i	1.13405	+	0.654746i	0.944951	−	0.327212i	$-0.106109\pi$
$887$	33.7750	+	19.5000i	1.13405	+	0.654746i	0.189102	+	0.981957i	$0.439442\pi$
$888$		0			0
$889$	16.0000	+	13.8564i	0.536623	+	0.464729i
$890$		0			0
$891$	1.50000	−	2.59808i	0.0502519	−	0.0870388i
$892$		0			0
$893$	7.79423	−	4.50000i	0.260824	−	0.150587i
$894$		0			0
$895$		0			0
$896$		0			0
$897$		−	6.00000i		−	0.200334i
$898$		0			0
$899$	21.0000	+	36.3731i	0.700389	+	1.21311i
$900$		0			0
$901$	−4.50000	+	7.79423i	−0.149917	+	0.259663i
$902$		0			0
$903$	10.3923	+	2.00000i	0.345834	+	0.0665558i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−35.5070	+	20.5000i	−1.17899	+	0.680691i	−0.955781	−	0.294079i	$-0.904987\pi$
$907$	−35.5070	+	20.5000i	−1.17899	+	0.680691i	−0.223211	+	0.974770i	$0.571654\pi$
$908$		0			0
$909$	30.0000			0.995037
$910$		0			0
$911$	48.0000			1.59031			0.795155	−	0.606406i	$-0.207389\pi$
$911$	48.0000			1.59031			0.795155	+	0.606406i	$0.207389\pi$
$912$		0			0
$913$	−31.1769	+	18.0000i	−1.03181	+	0.595713i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−2.59808	−	7.50000i	−0.0857960	−	0.247672i
$918$		0			0
$919$	−0.500000	+	0.866025i	−0.0164935	+	0.0285675i	−0.874154	−	0.485648i	$-0.838584\pi$
$919$	−0.500000	+	0.866025i	−0.0164935	+	0.0285675i	0.857661	+	0.514216i	$0.171917\pi$
$920$		0			0
$921$	14.0000	+	24.2487i	0.461316	+	0.799022i
$922$		0			0
$923$		0			0
$924$		0			0
$925$		0			0
$926$		0			0
$927$	19.0526	−	11.0000i	0.625768	−	0.361287i
$928$		0			0
$929$	−4.50000	+	7.79423i	−0.147640	+	0.255720i	−0.930355	−	0.366660i	$-0.880501\pi$
$929$	−4.50000	+	7.79423i	−0.147640	+	0.255720i	0.782715	+	0.622381i	$0.213834\pi$
$930$		0			0
$931$	6.50000	+	2.59808i	0.213029	+	0.0851485i
$932$		0			0
$933$	23.3827	+	13.5000i	0.765515	+	0.441970i
$934$		0			0
$935$		0			0
$936$		0			0
$937$		−	26.0000i		−	0.849383i	−0.905338	−	0.424691i	$-0.860383\pi$
$937$		−	26.0000i		−	0.849383i	0.905338	−	0.424691i	$-0.139617\pi$
$938$		0			0
$939$	−23.0000			−0.750577
$940$		0			0
$941$	−13.5000	−	23.3827i	−0.440087	−	0.762254i	0.557608	−	0.830104i	$-0.311719\pi$
$941$	−13.5000	−	23.3827i	−0.440087	−	0.762254i	−0.997695	+	0.0678506i	$0.978386\pi$
$942$		0			0
$943$	−15.5885	−	9.00000i	−0.507630	−	0.293080i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−38.9711	−	22.5000i	−1.26639	−	0.731152i	−0.292089	−	0.956391i	$-0.594350\pi$
$947$	−38.9711	−	22.5000i	−1.26639	−	0.731152i	−0.974303	+	0.225240i	$0.927684\pi$
$948$		0			0
$949$	−1.00000	−	1.73205i	−0.0324614	−	0.0562247i
$950$		0			0
$951$	−9.00000			−0.291845
$952$		0			0
$953$		−	18.0000i		−	0.583077i	−0.956559	−	0.291539i	$-0.905833\pi$
$953$		−	18.0000i		−	0.583077i	0.956559	−	0.291539i	$-0.0941672\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	15.5885	+	9.00000i	0.503903	+	0.290929i
$958$		0			0
$959$	−10.5000	+	54.5596i	−0.339063	+	1.76182i
$960$		0			0
$961$	−9.00000	+	15.5885i	−0.290323	+	0.502853i
$962$		0			0
$963$	−25.9808	+	15.0000i	−0.837218	+	0.483368i
$964$		0			0
$965$		0			0
$966$		0			0
$967$			16.0000i			0.514525i	0.966342	+	0.257263i	$0.0828206\pi$
$967$			16.0000i			0.514525i	−0.966342	+	0.257263i	$0.917179\pi$
$968$		0			0
$969$	−1.50000	−	2.59808i	−0.0481869	−	0.0834622i
$970$		0			0
$971$	−25.5000	+	44.1673i	−0.818334	+	1.41740i	0.0885751	+	0.996070i	$0.471769\pi$
$971$	−25.5000	+	44.1673i	−0.818334	+	1.41740i	−0.906909	+	0.421326i	$0.861565\pi$
$972$		0			0
$973$	34.6410	−	40.0000i	1.11054	−	1.28234i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−23.3827	+	13.5000i	−0.748078	+	0.431903i	−0.824999	−	0.565134i	$-0.808824\pi$
$977$	−23.3827	+	13.5000i	−0.748078	+	0.431903i	0.0769208	+	0.997037i	$0.475491\pi$
$978$		0			0
$979$	45.0000			1.43821
$980$		0			0
$981$	2.00000			0.0638551
$982$		0			0
$983$	28.5788	−	16.5000i	0.911523	−	0.526268i	0.0306024	−	0.999532i	$-0.490257\pi$
$983$	28.5788	−	16.5000i	0.911523	−	0.526268i	0.880921	+	0.473263i	$0.156924\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	15.5885	−	18.0000i	0.496186	−	0.572946i
$988$		0			0
$989$	−6.00000	+	10.3923i	−0.190789	+	0.330456i
$990$		0			0
$991$	9.50000	+	16.4545i	0.301777	+	0.522694i	0.976539	−	0.215342i	$-0.0690867\pi$
$991$	9.50000	+	16.4545i	0.301777	+	0.522694i	−0.674761	+	0.738036i	$0.735753\pi$
$992$		0			0
$993$		−	13.0000i		−	0.412543i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−51.0955	+	29.5000i	−1.61821	+	0.934274i	−0.630828	+	0.775923i	$0.717285\pi$
$997$	−51.0955	+	29.5000i	−1.61821	+	0.934274i	−0.987383	+	0.158352i	$0.949382\pi$
$998$		0			0
$999$	2.50000	−	4.33013i	0.0790965	−	0.136999i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	700.2.r.b.149.2		4
5.2	odd	4		28.2.e.a.9.1	✓	2
5.3	odd	4		700.2.i.c.401.1		2
5.4	even	2	inner	700.2.r.b.149.1		4
7.2	even	3		4900.2.e.i.2549.2		2
7.4	even	3	inner	700.2.r.b.249.1		4
7.5	odd	6		4900.2.e.h.2549.1		2
15.2	even	4		252.2.k.c.37.1		2
20.7	even	4		112.2.i.b.65.1		2
35.2	odd	12		196.2.a.b.1.1		1
35.4	even	6	inner	700.2.r.b.249.2		4
35.9	even	6		4900.2.e.i.2549.1		2
35.12	even	12		196.2.a.a.1.1		1
35.17	even	12		196.2.e.a.165.1		2
35.18	odd	12		700.2.i.c.501.1		2
35.19	odd	6		4900.2.e.h.2549.2		2
35.23	odd	12		4900.2.a.g.1.1		1
35.27	even	4		196.2.e.a.177.1		2
35.32	odd	12		28.2.e.a.25.1	yes	2
35.33	even	12		4900.2.a.n.1.1		1
40.27	even	4		448.2.i.c.65.1		2
40.37	odd	4		448.2.i.e.65.1		2
45.2	even	12		2268.2.i.h.2053.1		2
45.7	odd	12		2268.2.i.a.2053.1		2
45.22	odd	12		2268.2.l.h.541.1		2
45.32	even	12		2268.2.l.a.541.1		2
60.47	odd	4		1008.2.s.p.289.1		2
105.2	even	12		1764.2.a.a.1.1		1
105.17	odd	12		1764.2.k.b.361.1		2
105.32	even	12		252.2.k.c.109.1		2
105.47	odd	12		1764.2.a.j.1.1		1
105.62	odd	4		1764.2.k.b.1549.1		2
140.27	odd	4		784.2.i.d.177.1		2
140.47	odd	12		784.2.a.g.1.1		1
140.67	even	12		112.2.i.b.81.1		2
140.87	odd	12		784.2.i.d.753.1		2
140.107	even	12		784.2.a.d.1.1		1
280.37	odd	12		3136.2.a.h.1.1		1
280.67	even	12		448.2.i.c.193.1		2
280.107	even	12		3136.2.a.s.1.1		1
280.117	even	12		3136.2.a.v.1.1		1
280.187	odd	12		3136.2.a.k.1.1		1
280.277	odd	12		448.2.i.e.193.1		2
315.32	even	12		2268.2.i.h.865.1		2
315.67	odd	12		2268.2.i.a.865.1		2
315.137	even	12		2268.2.l.a.109.1		2
315.277	odd	12		2268.2.l.h.109.1		2
420.47	even	12		7056.2.a.bw.1.1		1
420.107	odd	12		7056.2.a.f.1.1		1
420.347	odd	12		1008.2.s.p.865.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
28.2.e.a.9.1	✓	2	5.2	odd	4
28.2.e.a.25.1	yes	2	35.32	odd	12
112.2.i.b.65.1		2	20.7	even	4
112.2.i.b.81.1		2	140.67	even	12
196.2.a.a.1.1		1	35.12	even	12
196.2.a.b.1.1		1	35.2	odd	12
196.2.e.a.165.1		2	35.17	even	12
196.2.e.a.177.1		2	35.27	even	4
252.2.k.c.37.1		2	15.2	even	4
252.2.k.c.109.1		2	105.32	even	12
448.2.i.c.65.1		2	40.27	even	4
448.2.i.c.193.1		2	280.67	even	12
448.2.i.e.65.1		2	40.37	odd	4
448.2.i.e.193.1		2	280.277	odd	12
700.2.i.c.401.1		2	5.3	odd	4
700.2.i.c.501.1		2	35.18	odd	12
700.2.r.b.149.1		4	5.4	even	2	inner
700.2.r.b.149.2		4	1.1	even	1	trivial
700.2.r.b.249.1		4	7.4	even	3	inner
700.2.r.b.249.2		4	35.4	even	6	inner
784.2.a.d.1.1		1	140.107	even	12
784.2.a.g.1.1		1	140.47	odd	12
784.2.i.d.177.1		2	140.27	odd	4
784.2.i.d.753.1		2	140.87	odd	12
1008.2.s.p.289.1		2	60.47	odd	4
1008.2.s.p.865.1		2	420.347	odd	12
1764.2.a.a.1.1		1	105.2	even	12
1764.2.a.j.1.1		1	105.47	odd	12
1764.2.k.b.361.1		2	105.17	odd	12
1764.2.k.b.1549.1		2	105.62	odd	4
2268.2.i.a.865.1		2	315.67	odd	12
2268.2.i.a.2053.1		2	45.7	odd	12
2268.2.i.h.865.1		2	315.32	even	12
2268.2.i.h.2053.1		2	45.2	even	12
2268.2.l.a.109.1		2	315.137	even	12
2268.2.l.a.541.1		2	45.32	even	12
2268.2.l.h.109.1		2	315.277	odd	12
2268.2.l.h.541.1		2	45.22	odd	12
3136.2.a.h.1.1		1	280.37	odd	12
3136.2.a.k.1.1		1	280.187	odd	12
3136.2.a.s.1.1		1	280.107	even	12
3136.2.a.v.1.1		1	280.117	even	12
4900.2.a.g.1.1		1	35.23	odd	12
4900.2.a.n.1.1		1	35.33	even	12
4900.2.e.h.2549.1		2	7.5	odd	6
4900.2.e.h.2549.2		2	35.19	odd	6
4900.2.e.i.2549.1		2	35.9	even	6
4900.2.e.i.2549.2		2	7.2	even	3
7056.2.a.f.1.1		1	420.107	odd	12
7056.2.a.bw.1.1		1	420.47	even	12

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:	\( N \)	\(=\)	\( 700 = 2^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	700.r (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{3} +(-1.73205 + 2.00000i) q^{7} +(-1.00000 + 1.73205i) q^{9} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{3} +(-1.73205 + 2.00000i) q^{7} +(-1.00000 + 1.73205i) q^{9} +(1.50000 + 2.59808i) q^{11} +2.00000i q^{13} +(-2.59808 + 1.50000i) q^{17} +(-0.500000 + 0.866025i) q^{19} +(-0.500000 + 2.59808i) q^{21} +(-2.59808 - 1.50000i) q^{23} +5.00000i q^{27} +6.00000 q^{29} +(3.50000 + 6.06218i) q^{31} +(2.59808 + 1.50000i) q^{33} +(-0.866025 - 0.500000i) q^{37} +(1.00000 + 1.73205i) q^{39} +6.00000 q^{41} -4.00000i q^{43} +(-7.79423 - 4.50000i) q^{47} +(-1.00000 - 6.92820i) q^{49} +(-1.50000 + 2.59808i) q^{51} +(2.59808 - 1.50000i) q^{53} +1.00000i q^{57} +(4.50000 + 7.79423i) q^{59} +(0.500000 - 0.866025i) q^{61} +(-1.73205 - 5.00000i) q^{63} +(6.06218 - 3.50000i) q^{67} -3.00000 q^{69} +(-0.866025 + 0.500000i) q^{73} +(-7.79423 - 1.50000i) q^{77} +(-6.50000 + 11.2583i) q^{79} +(-0.500000 - 0.866025i) q^{81} +12.0000i q^{83} +(5.19615 - 3.00000i) q^{87} +(7.50000 - 12.9904i) q^{89} +(-4.00000 - 3.46410i) q^{91} +(6.06218 + 3.50000i) q^{93} +10.0000i q^{97} -6.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{9}+O(q^{10}) \) 4 * q - 4 * q^9	\( 4 q - 4 q^{9} + 6 q^{11} - 2 q^{19} - 2 q^{21} + 24 q^{29} + 14 q^{31} + 4 q^{39} + 24 q^{41} - 4 q^{49} - 6 q^{51} + 18 q^{59} + 2 q^{61} - 12 q^{69} - 26 q^{79} - 2 q^{81} + 30 q^{89} - 16 q^{91} - 24 q^{99}+O(q^{100}) \) 4 * q - 4 * q^9 + 6 * q^11 - 2 * q^19 - 2 * q^21 + 24 * q^29 + 14 * q^31 + 4 * q^39 + 24 * q^41 - 4 * q^49 - 6 * q^51 + 18 * q^59 + 2 * q^61 - 12 * q^69 - 26 * q^79 - 2 * q^81 + 30 * q^89 - 16 * q^91 - 24 * q^99

Introduction

L-functions

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Database

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