LMFDB - Embedded newform 2100.2.bo.i.1349.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2100,2,Mod(1349,2100)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2100, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 3, 5]))

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

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

chi := DirichletCharacter("2100.1349");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2100.bo (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:	$16.7685844245$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1349.8
Character	$\chi$	$=$	2100.1349
Dual form			2100.2.bo.i.1949.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.134063 + 1.72685i) q^{3} +(2.52603 + 0.786875i) q^{7} +(-2.96405 - 0.463016i) q^{9} +O(q^{10})$	\(q+(-0.134063 + 1.72685i) q^{3} +(2.52603 + 0.786875i) q^{7} +(-2.96405 - 0.463016i) q^{9} +(2.34474 - 1.35373i) q^{11} -1.12489 q^{13} +(6.39336 - 3.69121i) q^{17} +(0.412264 + 0.238021i) q^{19} +(-1.69747 + 4.25660i) q^{21} +(2.79845 - 4.84706i) q^{23} +(1.19693 - 5.05642i) q^{27} -2.20372i q^{29} +(-2.07315 + 1.19693i) q^{31} +(2.02336 + 4.23051i) q^{33} +(7.53233 + 4.34879i) q^{37} +(0.150806 - 1.94251i) q^{39} +5.42336 q^{41} -4.16209i q^{43} +(-10.7600 - 6.21227i) q^{47} +(5.76166 + 3.97534i) q^{49} +(5.51707 + 11.5353i) q^{51} +(2.45559 + 4.25321i) q^{53} +(-0.466297 + 0.680011i) q^{57} +(-1.15586 - 2.00200i) q^{59} +(-2.26895 - 1.30998i) q^{61} +(-7.12295 - 3.50193i) q^{63} +(12.7169 - 7.34210i) q^{67} +(7.99501 + 5.48234i) q^{69} +9.89729i q^{71} +(-3.63180 - 6.29046i) q^{73} +(6.98810 - 1.57456i) q^{77} +(-3.47478 + 6.01850i) q^{79} +(8.57123 + 2.74481i) q^{81} +11.3005i q^{83} +(3.80550 + 0.295438i) q^{87} +(-3.48186 + 6.03075i) q^{89} +(-2.84150 - 0.885144i) q^{91} +(-1.78899 - 3.74049i) q^{93} +8.79691 q^{97} +(-7.57673 + 2.92689i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 18 q^{9}+O(q^{10}) $ 32 * q + 18 * q^9	$ 32 q + 18 q^{9} + 36 q^{19} - 22 q^{21} - 36 q^{31} - 24 q^{39} + 36 q^{49} - 2 q^{51} + 72 q^{61} + 14 q^{81} + 40 q^{91} + 60 q^{99}+O(q^{100}) $ 32 * q + 18 * q^9 + 36 * q^19 - 22 * q^21 - 36 * q^31 - 24 * q^39 + 36 * q^49 - 2 * q^51 + 72 * q^61 + 14 * q^81 + 40 * q^91 + 60 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2100\mathbb{Z}\right)^\times$.

$n$	$701$	$1051$	$1177$	$1501$
$\chi(n)$	$-1$	$1$	$-1$	$e\left(\frac{5}{6}\right)$

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
$3$	−0.134063	+	1.72685i	−0.0774015	+	0.997000i
$3$	−0.134063	+	1.72685i	−0.0774015	+	0.997000i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	2.52603	+	0.786875i	0.954750	+	0.297411i
$7$	2.52603	+	0.786875i	0.954750	+	0.297411i
$8$		0			0
$9$	−2.96405	−	0.463016i	−0.988018	−	0.154339i
$10$		0			0
$11$	2.34474	−	1.35373i	0.706965	−	0.408166i	−0.102971	−	0.994684i	$-0.532835\pi$
$11$	2.34474	−	1.35373i	0.706965	−	0.408166i	0.809936	+	0.586518i	$0.199502\pi$
$12$		0			0
$13$	−1.12489			−0.311987			−0.155994	−	0.987758i	$-0.549858\pi$
$13$	−1.12489			−0.311987			−0.155994	+	0.987758i	$0.549858\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	6.39336	−	3.69121i	1.55062	−	0.895250i	0.552527	−	0.833495i	$-0.313664\pi$
$17$	6.39336	−	3.69121i	1.55062	−	0.895250i	0.998091	−	0.0617544i	$-0.0196696\pi$
$18$		0			0
$19$	0.412264	+	0.238021i	0.0945799	+	0.0546057i	0.546544	−	0.837430i	$-0.315943\pi$
$19$	0.412264	+	0.238021i	0.0945799	+	0.0546057i	−0.451964	+	0.892036i	$0.649276\pi$
$20$		0			0
$21$	−1.69747	+	4.25660i	−0.370417	+	0.928865i
$22$		0			0
$23$	2.79845	−	4.84706i	0.583518	−	1.01068i	−0.411540	−	0.911392i	$-0.635009\pi$
$23$	2.79845	−	4.84706i	0.583518	−	1.01068i	0.995058	−	0.0992913i	$-0.0316576\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	1.19693	−	5.05642i	0.230350	−	0.973108i
$28$		0			0
$29$		−	2.20372i		−	0.409220i	−0.978844	−	0.204610i	$-0.934407\pi$
$29$		−	2.20372i		−	0.409220i	0.978844	−	0.204610i	$-0.0655926\pi$
$30$		0			0
$31$	−2.07315	+	1.19693i	−0.372348	+	0.214975i	−0.674484	−	0.738290i	$-0.735634\pi$
$31$	−2.07315	+	1.19693i	−0.372348	+	0.214975i	0.302136	+	0.953265i	$0.402300\pi$
$32$		0			0
$33$	2.02336	+	4.23051i	0.352222	+	0.736437i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	7.53233	+	4.34879i	1.23831	+	0.714937i	0.968748	−	0.248047i	$-0.0797888\pi$
$37$	7.53233	+	4.34879i	1.23831	+	0.714937i	0.269559	+	0.962984i	$0.413122\pi$
$38$		0			0
$39$	0.150806	−	1.94251i	0.0241483	−	0.311051i
$40$		0			0
$41$	5.42336			0.846986			0.423493	−	0.905899i	$-0.360804\pi$
$41$	5.42336			0.846986			0.423493	+	0.905899i	$0.360804\pi$
$42$		0			0
$43$		−	4.16209i		−	0.634712i	−0.948306	−	0.317356i	$-0.897205\pi$
$43$		−	4.16209i		−	0.634712i	0.948306	−	0.317356i	$-0.102795\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−10.7600	−	6.21227i	−1.56950	−	0.906153i	−0.996227	−	0.0867912i	$-0.972339\pi$
$47$	−10.7600	−	6.21227i	−1.56950	−	0.906153i	−0.573277	−	0.819362i	$-0.694328\pi$
$48$		0			0
$49$	5.76166	+	3.97534i	0.823094	+	0.567905i
$50$		0			0
$51$	5.51707	+	11.5353i	0.772544	+	1.61526i
$52$		0			0
$53$	2.45559	+	4.25321i	0.337302	+	0.584224i	0.983924	−	0.178586i	$-0.0571524\pi$
$53$	2.45559	+	4.25321i	0.337302	+	0.584224i	−0.646622	+	0.762810i	$0.723819\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−0.466297	+	0.680011i	−0.0617626	+	0.0900696i
$58$		0			0
$59$	−1.15586	−	2.00200i	−0.150480	−	0.260638i	0.780924	−	0.624626i	$-0.214748\pi$
$59$	−1.15586	−	2.00200i	−0.150480	−	0.260638i	−0.931404	+	0.363987i	$0.881415\pi$
$60$		0			0
$61$	−2.26895	−	1.30998i	−0.290509	−	0.167726i	0.347662	−	0.937620i	$-0.386976\pi$
$61$	−2.26895	−	1.30998i	−0.290509	−	0.167726i	−0.638172	+	0.769894i	$0.720309\pi$
$62$		0			0
$63$	−7.12295	−	3.50193i	−0.897408	−	0.441202i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	12.7169	−	7.34210i	1.55361	−	0.896980i	0.555772	−	0.831335i	$-0.312423\pi$
$67$	12.7169	−	7.34210i	1.55361	−	0.896980i	0.997843	−	0.0656452i	$-0.0209106\pi$
$68$		0			0
$69$	7.99501	+	5.48234i	0.962486	+	0.659996i
$70$		0			0
$71$			9.89729i			1.17459i	0.809372	+	0.587296i	$0.199807\pi$
$71$			9.89729i			1.17459i	−0.809372	+	0.587296i	$0.800193\pi$
$72$		0			0
$73$	−3.63180	−	6.29046i	−0.425070	−	0.736242i	0.571357	−	0.820701i	$-0.306417\pi$
$73$	−3.63180	−	6.29046i	−0.425070	−	0.736242i	−0.996427	+	0.0844591i	$0.973084\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	6.98810	−	1.57456i	0.796368	−	0.179438i
$78$		0			0
$79$	−3.47478	+	6.01850i	−0.390944	+	0.677134i	−0.992574	−	0.121640i	$-0.961185\pi$
$79$	−3.47478	+	6.01850i	−0.390944	+	0.677134i	0.601631	+	0.798774i	$0.294518\pi$
$80$		0			0
$81$	8.57123	+	2.74481i	0.952359	+	0.304979i
$82$		0			0
$83$			11.3005i			1.24040i	0.784446	+	0.620198i	$0.212948\pi$
$83$			11.3005i			1.24040i	−0.784446	+	0.620198i	$0.787052\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	3.80550	+	0.295438i	0.407992	+	0.0316743i
$88$		0			0
$89$	−3.48186	+	6.03075i	−0.369076	+	0.639258i	−0.989421	−	0.145070i	$-0.953659\pi$
$89$	−3.48186	+	6.03075i	−0.369076	+	0.639258i	0.620345	+	0.784329i	$0.286992\pi$
$90$		0			0
$91$	−2.84150	−	0.885144i	−0.297870	−	0.0927883i
$92$		0			0
$93$	−1.78899	−	3.74049i	−0.185510	−	0.387871i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	8.79691			0.893190			0.446595	−	0.894736i	$-0.352636\pi$
$97$	8.79691			0.893190			0.446595	+	0.894736i	$0.352636\pi$
$98$		0			0
$99$	−7.57673	+	2.92689i	−0.761490	+	0.294164i
$100$		0			0
$101$	−5.23274	−	9.06338i	−0.520677	−	0.901840i	−0.999711	−	0.0240431i	$-0.992346\pi$
$101$	−5.23274	−	9.06338i	−0.520677	−	0.901840i	0.479034	−	0.877797i	$-0.340987\pi$
$102$		0			0
$103$	−1.63440	+	2.83087i	−0.161042	+	0.278934i	−0.935243	−	0.354007i	$-0.884819\pi$
$103$	−1.63440	+	2.83087i	−0.161042	+	0.278934i	0.774200	+	0.632941i	$0.218152\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	2.49305	−	4.31809i	0.241012	−	0.417445i	−0.719991	−	0.693984i	$-0.755854\pi$
$107$	2.49305	−	4.31809i	0.241012	−	0.417445i	0.961003	+	0.276538i	$0.0891873\pi$
$108$		0			0
$109$	2.40043	+	4.15767i	0.229920	+	0.398232i	0.957784	−	0.287489i	$-0.0928204\pi$
$109$	2.40043	+	4.15767i	0.229920	+	0.398232i	−0.727864	+	0.685721i	$0.759487\pi$
$110$		0			0
$111$	−8.51954	+	12.4242i	−0.808639	+	1.17925i
$112$		0			0
$113$	−18.8874			−1.77678			−0.888388	−	0.459094i	$-0.848174\pi$
$113$	−18.8874			−1.77678			−0.888388	+	0.459094i	$0.848174\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	3.33422	+	0.520840i	0.308249	+	0.0481517i
$118$		0			0
$119$	19.0543	−	4.29333i	1.74671	−	0.393569i
$120$		0			0
$121$	−1.83480	+	3.17797i	−0.166800	+	0.288907i
$122$		0			0
$123$	−0.727074	+	9.36535i	−0.0655580	+	0.844445i
$124$		0			0
$125$		0			0
$126$		0			0
$127$		−	7.77289i		−	0.689732i	−0.938652	−	0.344866i	$-0.887924\pi$
$127$		−	7.77289i		−	0.689732i	0.938652	−	0.344866i	$-0.112076\pi$
$128$		0			0
$129$	7.18732	+	0.557983i	0.632808	+	0.0491277i
$130$		0			0
$131$	−2.32600	+	4.02875i	−0.203224	+	0.351994i	−0.949565	−	0.313569i	$-0.898475\pi$
$131$	−2.32600	+	4.02875i	−0.203224	+	0.351994i	0.746342	+	0.665563i	$0.231809\pi$
$132$		0			0
$133$	0.854100	+	0.925648i	0.0740598	+	0.0802639i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−5.50592	−	9.53654i	−0.470403	−	0.814762i	0.529024	−	0.848607i	$-0.322558\pi$
$137$	−5.50592	−	9.53654i	−0.470403	−	0.814762i	−0.999427	+	0.0338451i	$0.989225\pi$
$138$		0			0
$139$			20.5928i			1.74665i	0.487134	+	0.873327i	$0.338042\pi$
$139$			20.5928i			1.74665i	−0.487134	+	0.873327i	$0.661958\pi$
$140$		0			0
$141$	12.1702	−	17.7481i	1.02492	−	1.49466i
$142$		0			0
$143$	−2.63756	+	1.52280i	−0.220564	+	0.127343i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−7.63726	+	9.41660i	−0.629910	+	0.776668i
$148$		0			0
$149$	14.8906	+	8.59708i	1.21988	+	0.704300i	0.964893	−	0.262643i	$-0.0845942\pi$
$149$	14.8906	+	8.59708i	1.21988	+	0.704300i	0.254991	+	0.966943i	$0.417928\pi$
$150$		0			0
$151$	−1.00060	−	1.73309i	−0.0814279	−	0.141037i	0.822436	−	0.568858i	$-0.192615\pi$
$151$	−1.00060	−	1.73309i	−0.0814279	−	0.141037i	−0.903863	+	0.427821i	$0.859281\pi$
$152$		0			0
$153$	−20.6594	+	7.98072i	−1.67021	+	0.645203i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	9.11856	+	15.7938i	0.727741	+	1.26048i	0.957836	+	0.287316i	$0.0927628\pi$
$157$	9.11856	+	15.7938i	0.727741	+	1.26048i	−0.230095	+	0.973168i	$0.573904\pi$
$158$		0			0
$159$	−7.67389	+	3.67025i	−0.608579	+	0.291070i
$160$		0			0
$161$	10.8830	−	10.0418i	0.857701	−	0.791405i
$162$		0			0
$163$	17.1563	+	9.90522i	1.34379	+	0.775837i	0.987361	−	0.158487i	$-0.0506615\pi$
$163$	17.1563	+	9.90522i	1.34379	+	0.775837i	0.356427	+	0.934323i	$0.383995\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$			12.5257i			0.969269i	0.874717	+	0.484634i	$0.161047\pi$
$167$			12.5257i			0.969269i	−0.874717	+	0.484634i	$0.838953\pi$
$168$		0			0
$169$	−11.7346			−0.902664
$170$		0			0
$171$	−1.11177	−	0.896392i	−0.0850189	−	0.0685488i
$172$		0			0
$173$	12.7620	+	7.36813i	0.970275	+	0.560188i	0.899320	−	0.437291i	$-0.144062\pi$
$173$	12.7620	+	7.36813i	0.970275	+	0.560188i	0.0709548	+	0.997480i	$0.477395\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	3.61212	−	1.72760i	0.271504	−	0.129854i
$178$		0			0
$179$	−1.18770	+	0.685720i	−0.0887730	+	0.0512531i	−0.543729	−	0.839261i	$-0.682988\pi$
$179$	−1.18770	+	0.685720i	−0.0887730	+	0.0512531i	0.454956	+	0.890514i	$0.349655\pi$
$180$		0			0
$181$		−	21.3843i		−	1.58949i	−0.606947	−	0.794743i	$-0.707606\pi$
$181$		−	21.3843i		−	1.58949i	0.606947	−	0.794743i	$-0.292394\pi$
$182$		0			0
$183$	2.56633	−	3.74253i	0.189708	−	0.276656i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	9.99384	−	17.3098i	0.730822	−	1.26582i
$188$		0			0
$189$	7.00225	−	11.8308i	0.509339	−	0.860566i
$190$		0			0
$191$	14.9775	+	8.64724i	1.08373	+	0.625692i	0.931900	−	0.362714i	$-0.118150\pi$
$191$	14.9775	+	8.64724i	1.08373	+	0.625692i	0.151830	+	0.988407i	$0.451483\pi$
$192$		0			0
$193$	11.0921	−	6.40401i	0.798425	−	0.460971i	−0.0444950	−	0.999010i	$-0.514168\pi$
$193$	11.0921	−	6.40401i	0.798425	−	0.460971i	0.842920	+	0.538039i	$0.180835\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−9.17207			−0.653483			−0.326741	−	0.945114i	$-0.605951\pi$
$197$	−9.17207			−0.653483			−0.326741	+	0.945114i	$0.605951\pi$
$198$		0			0
$199$	−7.16818	+	4.13855i	−0.508139	+	0.293374i	−0.732068	−	0.681231i	$-0.761445\pi$
$199$	−7.16818	+	4.13855i	−0.508139	+	0.293374i	0.223930	+	0.974605i	$0.428111\pi$
$200$		0			0
$201$	10.9739	+	22.9445i	0.774037	+	1.61838i
$202$		0			0
$203$	1.73405	−	5.56666i	0.121706	−	0.390703i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−10.5390	+	13.0712i	−0.732514	+	0.908513i
$208$		0			0
$209$	1.28887			0.0891529
$210$		0			0
$211$	−8.50872			−0.585765			−0.292882	−	0.956148i	$-0.594614\pi$
$211$	−8.50872			−0.585765			−0.292882	+	0.956148i	$0.594614\pi$
$212$		0			0
$213$	−17.0912	−	1.32686i	−1.17107	−	0.0909152i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−6.17867	+	1.39218i	−0.419435	+	0.0945073i
$218$		0			0
$219$	11.3496	−	5.42827i	0.766935	−	0.366808i
$220$		0			0
$221$	−7.19180	+	4.15219i	−0.483773	+	0.279306i
$222$		0			0
$223$	−5.54451			−0.371288			−0.185644	−	0.982617i	$-0.559437\pi$
$223$	−5.54451			−0.371288			−0.185644	+	0.982617i	$0.559437\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−5.36478	+	3.09736i	−0.356073	+	0.205579i	−0.667357	−	0.744738i	$-0.732574\pi$
$227$	−5.36478	+	3.09736i	−0.356073	+	0.205579i	0.311284	+	0.950317i	$0.399241\pi$
$228$		0			0
$229$	0.307553	+	0.177566i	0.0203237	+	0.0117339i	0.510127	−	0.860099i	$-0.329598\pi$
$229$	0.307553	+	0.177566i	0.0203237	+	0.0117339i	−0.489804	+	0.871833i	$0.662932\pi$
$230$		0			0
$231$	1.78219	+	12.2785i	0.117259	+	0.807867i
$232$		0			0
$233$	9.33296	−	16.1652i	0.611422	−	1.05901i	−0.379578	−	0.925160i	$-0.623931\pi$
$233$	9.33296	−	16.1652i	0.611422	−	1.05901i	0.991001	−	0.133855i	$-0.0427357\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−9.92723	−	6.80730i	−0.644843	−	0.442182i
$238$		0			0
$239$			21.1914i			1.37076i	0.728186	+	0.685379i	$0.240364\pi$
$239$			21.1914i			1.37076i	−0.728186	+	0.685379i	$0.759636\pi$
$240$		0			0
$241$	−1.92350	+	1.11053i	−0.123903	+	0.0715356i	−0.560671	−	0.828039i	$-0.689457\pi$
$241$	−1.92350	+	1.11053i	−0.123903	+	0.0715356i	0.436767	+	0.899574i	$0.356123\pi$
$242$		0			0
$243$	−5.88897	+	14.4333i	−0.377778	+	0.925896i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−0.463750	−	0.267746i	−0.0295077	−	0.0170363i
$248$		0			0
$249$	−19.5144	−	1.51499i	−1.23667	−	0.0960084i
$250$		0			0
$251$	−18.3017			−1.15519			−0.577597	−	0.816322i	$-0.696010\pi$
$251$	−18.3017			−1.15519			−0.577597	+	0.816322i	$0.696010\pi$
$252$		0			0
$253$		−	15.1535i		−	0.952690i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	9.69894	+	5.59968i	0.605003	+	0.349299i	0.771007	−	0.636826i	$-0.219753\pi$
$257$	9.69894	+	5.59968i	0.605003	+	0.349299i	−0.166004	+	0.986125i	$0.553087\pi$
$258$		0			0
$259$	15.6049	+	16.9122i	0.969643	+	1.05087i
$260$		0			0
$261$	−1.02036	+	6.53194i	−0.0631585	+	0.404317i
$262$		0			0
$263$	−6.60778	−	11.4450i	−0.407453	−	0.705730i	0.587150	−	0.809478i	$-0.300250\pi$
$263$	−6.60778	−	11.4450i	−0.407453	−	0.705730i	−0.994604	+	0.103748i	$0.966916\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−9.94744	−	6.82116i	−0.608774	−	0.417448i
$268$		0			0
$269$	−12.6657	−	21.9377i	−0.772244	−	1.33757i	−0.936330	−	0.351120i	$-0.885801\pi$
$269$	−12.6657	−	21.9377i	−0.772244	−	1.33757i	0.164086	−	0.986446i	$-0.447532\pi$
$270$		0			0
$271$	−23.9303	−	13.8162i	−1.45366	−	0.839273i	−0.454976	−	0.890504i	$-0.650352\pi$
$271$	−23.9303	−	13.8162i	−1.45366	−	0.839273i	−0.998687	+	0.0512313i	$0.983685\pi$
$272$		0			0
$273$	1.90946	−	4.78818i	0.115566	−	0.289794i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	20.4917	−	11.8309i	1.23122	−	0.710848i	0.263939	−	0.964539i	$-0.414978\pi$
$277$	20.4917	−	11.8309i	1.23122	−	0.710848i	0.967285	+	0.253691i	$0.0816448\pi$
$278$		0			0
$279$	6.69912	−	2.58787i	0.401066	−	0.154932i
$280$		0			0
$281$		−	17.3694i		−	1.03617i	−0.855329	−	0.518085i	$-0.826645\pi$
$281$		−	17.3694i		−	1.03617i	0.855329	−	0.518085i	$-0.173355\pi$
$282$		0			0
$283$	6.46037	+	11.1897i	0.384029	+	0.665158i	0.991634	−	0.129082i	$-0.0412030\pi$
$283$	6.46037	+	11.1897i	0.384029	+	0.665158i	−0.607605	+	0.794239i	$0.707870\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	13.6996	+	4.26750i	0.808660	+	0.251903i
$288$		0			0
$289$	18.7500	−	32.4760i	1.10294	−	1.91036i
$290$		0			0
$291$	−1.17934	+	15.1910i	−0.0691343	+	0.890511i
$292$		0			0
$293$			11.2345i			0.656326i	0.944621	+	0.328163i	$0.106429\pi$
$293$			11.2345i			0.656326i	−0.944621	+	0.328163i	$0.893571\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−4.03856	−	13.4763i	−0.234341	−	0.781974i
$298$		0			0
$299$	−3.14794	+	5.45239i	−0.182050	+	0.315320i
$300$		0			0
$301$	3.27504	−	10.5136i	0.188770	−	0.605991i
$302$		0			0
$303$	16.3527	−	7.82112i	0.939435	−	0.449312i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−31.0165			−1.77021			−0.885103	−	0.465395i	$-0.845912\pi$
$307$	−31.0165			−1.77021			−0.885103	+	0.465395i	$0.845912\pi$
$308$		0			0
$309$	−4.66938	−	3.20189i	−0.265632	−	0.182149i
$310$		0			0
$311$	0.771357	+	1.33603i	0.0437396	+	0.0757593i	0.887066	−	0.461642i	$-0.152739\pi$
$311$	0.771357	+	1.33603i	0.0437396	+	0.0757593i	−0.843327	+	0.537401i	$0.819406\pi$
$312$		0			0
$313$	12.8545	−	22.2646i	0.726579	−	1.25847i	−0.231742	−	0.972777i	$-0.574442\pi$
$313$	12.8545	−	22.2646i	0.726579	−	1.25847i	0.958321	−	0.285694i	$-0.0922242\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−1.55545	+	2.69412i	−0.0873629	+	0.151317i	−0.906396	−	0.422430i	$-0.861177\pi$
$317$	−1.55545	+	2.69412i	−0.0873629	+	0.151317i	0.819033	+	0.573747i	$0.194511\pi$
$318$		0			0
$319$	−2.98325	−	5.16714i	−0.167030	−	0.289304i
$320$		0			0
$321$	7.12248	+	4.88403i	0.397538	+	0.272600i
$322$		0			0
$323$	3.51434			0.195543
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−7.50150	+	3.58780i	−0.414834	+	0.198406i
$328$		0			0
$329$	−22.2917	−	24.1591i	−1.22898	−	1.33194i
$330$		0			0
$331$	0.139978	−	0.242450i	0.00769391	−	0.0133262i	−0.862153	−	0.506648i	$-0.830884\pi$
$331$	0.139978	−	0.242450i	0.00769391	−	0.0133262i	0.869847	+	0.493322i	$0.164218\pi$
$332$		0			0
$333$	−20.3127	−	16.3776i	−1.11313	−	0.897489i
$334$		0			0
$335$		0			0
$336$		0			0
$337$		−	5.96891i		−	0.325147i	−0.986696	−	0.162574i	$-0.948021\pi$
$337$		−	5.96891i		−	0.325147i	0.986696	−	0.162574i	$-0.0519795\pi$
$338$		0			0
$339$	2.53211	−	32.6158i	0.137525	−	1.77145i
$340$		0			0
$341$	−3.24066	+	5.61298i	−0.175491	+	0.303960i
$342$		0			0
$343$	11.4260	+	14.5755i	0.616947	+	0.787004i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−4.28063	−	7.41426i	−0.229796	−	0.398019i	0.727951	−	0.685629i	$-0.240473\pi$
$347$	−4.28063	−	7.41426i	−0.229796	−	0.398019i	−0.957748	+	0.287610i	$0.907139\pi$
$348$		0			0
$349$			7.23833i			0.387459i	0.981055	+	0.193729i	$0.0620584\pi$
$349$			7.23833i			0.387459i	−0.981055	+	0.193729i	$0.937942\pi$
$350$		0			0
$351$	−1.34641	+	5.68789i	−0.0718661	+	0.303597i
$352$		0			0
$353$	−20.5790	+	11.8813i	−1.09531	+	0.632377i	−0.934985	−	0.354688i	$-0.884587\pi$
$353$	−20.5790	+	11.8813i	−1.09531	+	0.632377i	−0.160324	+	0.987065i	$0.551254\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	4.85947	+	33.4797i	0.257190	+	1.77193i
$358$		0			0
$359$	−31.3993	−	18.1284i	−1.65719	−	0.956780i	−0.974003	−	0.226537i	$-0.927260\pi$
$359$	−31.3993	−	18.1284i	−1.65719	−	0.956780i	−0.683188	−	0.730242i	$-0.739407\pi$
$360$		0			0
$361$	−9.38669	−	16.2582i	−0.494036	−	0.855696i
$362$		0			0
$363$	−5.24192	−	3.59449i	−0.275129	−	0.188662i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	0.730418	+	1.26512i	0.0381275	+	0.0660387i	0.884459	−	0.466617i	$-0.154527\pi$
$367$	0.730418	+	1.26512i	0.0381275	+	0.0660387i	−0.846332	+	0.532656i	$0.821194\pi$
$368$		0			0
$369$	−16.0751	−	2.51110i	−0.836838	−	0.130723i
$370$		0			0
$371$	2.85616	+	12.6760i	0.148284	+	0.658105i
$372$		0			0
$373$	18.3457	+	10.5919i	0.949907	+	0.548429i	0.893052	−	0.449954i	$-0.148559\pi$
$373$	18.3457	+	10.5919i	0.949907	+	0.548429i	0.0568547	+	0.998382i	$0.481893\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$			2.47893i			0.127671i
$378$		0			0
$379$	−24.3581			−1.25119			−0.625596	−	0.780147i	$-0.715144\pi$
$379$	−24.3581			−1.25119			−0.625596	+	0.780147i	$0.715144\pi$
$380$		0			0
$381$	13.4226	+	1.04206i	0.687663	+	0.0533863i
$382$		0			0
$383$	21.8176	+	12.5964i	1.11483	+	0.643647i	0.940076	−	0.340965i	$-0.110754\pi$
$383$	21.8176	+	12.5964i	1.11483	+	0.643647i	0.174754	+	0.984612i	$0.444087\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−1.92711	+	12.3367i	−0.0979606	+	0.627107i
$388$		0			0
$389$	−10.9380	+	6.31508i	−0.554581	+	0.320187i	−0.750967	−	0.660339i	$-0.770413\pi$
$389$	−10.9380	+	6.31508i	−0.554581	+	0.320187i	0.196387	+	0.980527i	$0.437079\pi$
$390$		0			0
$391$		−	41.3187i		−	2.08958i
$392$		0			0
$393$	−6.64524	−	4.55677i	−0.335208	−	0.229859i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−8.27166	+	14.3269i	−0.415143	+	0.719048i	−0.995443	−	0.0953542i	$-0.969602\pi$
$397$	−8.27166	+	14.3269i	−0.415143	+	0.719048i	0.580301	+	0.814402i	$0.302935\pi$
$398$		0			0
$399$	−1.71296	+	1.35081i	−0.0857555	+	0.0676251i
$400$		0			0
$401$	−9.72834	−	5.61666i	−0.485810	−	0.280482i	0.237025	−	0.971504i	$-0.423828\pi$
$401$	−9.72834	−	5.61666i	−0.485810	−	0.280482i	−0.722835	+	0.691021i	$0.757161\pi$
$402$		0			0
$403$	2.33205	−	1.34641i	0.116168	−	0.0670695i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	23.5484			1.16725
$408$		0			0
$409$	31.6764	−	18.2884i	1.56630	−	0.904303i	0.569703	−	0.821851i	$-0.307058\pi$
$409$	31.6764	−	18.2884i	1.56630	−	0.904303i	0.996595	−	0.0824520i	$-0.0262751\pi$
$410$		0			0
$411$	17.2064	−	8.22943i	0.848727	−	0.405928i
$412$		0			0
$413$	−1.34440	−	5.96663i	−0.0661537	−	0.293599i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−35.5607	−	2.76073i	−1.74141	−	0.135194i
$418$		0			0
$419$	8.29006			0.404996			0.202498	−	0.979283i	$-0.435094\pi$
$419$	8.29006			0.404996			0.202498	+	0.979283i	$0.435094\pi$
$420$		0			0
$421$	23.8826			1.16397			0.581984	−	0.813200i	$-0.302277\pi$
$421$	23.8826			1.16397			0.581984	+	0.813200i	$0.302277\pi$
$422$		0			0
$423$	29.0168	+	23.3955i	1.41084	+	1.13753i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−4.70065	−	5.09443i	−0.227480	−	0.246537i
$428$		0			0
$429$	−2.27605	−	4.75884i	−0.109889	−	0.229759i
$430$		0			0
$431$	9.93859	−	5.73805i	0.478725	−	0.276392i	−0.241160	−	0.970485i	$-0.577528\pi$
$431$	9.93859	−	5.73805i	0.478725	−	0.276392i	0.719885	+	0.694093i	$0.244194\pi$
$432$		0			0
$433$	3.31657			0.159384			0.0796920	−	0.996820i	$-0.474606\pi$
$433$	3.31657			0.159384			0.0796920	+	0.996820i	$0.474606\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	2.30741	−	1.33218i	0.110378	−	0.0637269i
$438$		0			0
$439$	−23.6144	−	13.6338i	−1.12705	−	0.650705i	−0.183862	−	0.982952i	$-0.558860\pi$
$439$	−23.6144	−	13.6338i	−1.12705	−	0.650705i	−0.943192	+	0.332247i	$0.892193\pi$
$440$		0			0
$441$	−15.2372	−	14.4509i	−0.725582	−	0.688136i
$442$		0			0
$443$	20.4555	−	35.4300i	0.971872	−	1.68333i	0.281979	−	0.959421i	$-0.409009\pi$
$443$	20.4555	−	35.4300i	0.971872	−	1.68333i	0.689893	−	0.723911i	$-0.257657\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−16.8422	+	24.5613i	−0.796608	+	1.16171i
$448$		0			0
$449$			19.6734i			0.928446i	0.885718	+	0.464223i	$0.153666\pi$
$449$			19.6734i			0.928446i	−0.885718	+	0.464223i	$0.846334\pi$
$450$		0			0
$451$	12.7164	−	7.34179i	0.598790	−	0.345711i
$452$		0			0
$453$	3.12695	−	1.49555i	0.146917	−	0.0702671i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	7.95987	+	4.59563i	0.372347	+	0.214975i	0.674483	−	0.738290i	$-0.264366\pi$
$457$	7.95987	+	4.59563i	0.372347	+	0.214975i	−0.302136	+	0.953265i	$0.597700\pi$
$458$		0			0
$459$	−11.0119	−	36.7456i	−0.513990	−	1.71514i
$460$		0			0
$461$	−28.7958			−1.34115			−0.670577	−	0.741840i	$-0.733953\pi$
$461$	−28.7958			−1.34115			−0.670577	+	0.741840i	$0.733953\pi$
$462$		0			0
$463$		−	25.0825i		−	1.16568i	−0.812586	−	0.582841i	$-0.801941\pi$
$463$		−	25.0825i		−	1.16568i	0.812586	−	0.582841i	$-0.198059\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−20.2087	−	11.6675i	−0.935145	−	0.539907i	−0.0467103	−	0.998908i	$-0.514874\pi$
$467$	−20.2087	−	11.6675i	−0.935145	−	0.539907i	−0.888435	+	0.459002i	$0.848207\pi$
$468$		0			0
$469$	37.9005	−	8.53977i	1.75008	−	0.394330i
$470$		0			0
$471$	−28.4961	+	13.6291i	−1.31303	+	0.627994i
$472$		0			0
$473$	−5.63436	−	9.75900i	−0.259068	−	0.448719i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−5.30921	−	13.7437i	−0.243092	−	0.629282i
$478$		0			0
$479$	8.12075	+	14.0655i	0.371046	+	0.642671i	0.989727	−	0.142971i	$-0.0456657\pi$
$479$	8.12075	+	14.0655i	0.371046	+	0.642671i	−0.618680	+	0.785643i	$0.712332\pi$
$480$		0			0
$481$	−8.47301	−	4.89189i	−0.386336	−	0.223051i
$482$		0			0
$483$	15.8817	+	20.1396i	0.722643	+	0.916384i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−8.79420	+	5.07733i	−0.398503	+	0.230076i	−0.685838	−	0.727754i	$-0.740564\pi$
$487$	−8.79420	+	5.07733i	−0.398503	+	0.230076i	0.287335	+	0.957830i	$0.407231\pi$
$488$		0			0
$489$	−19.4049	+	28.2986i	−0.877520	+	1.27971i
$490$		0			0
$491$		−	25.5734i		−	1.15411i	−0.816704	−	0.577057i	$-0.804201\pi$
$491$		−	25.5734i		−	1.15411i	0.816704	−	0.577057i	$-0.195799\pi$
$492$		0			0
$493$	−8.13438	−	14.0892i	−0.366354	−	0.634544i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−7.78792	+	25.0008i	−0.349336	+	1.12144i
$498$		0			0
$499$	4.80838	−	8.32836i	0.215253	−	0.372829i	−0.738098	−	0.674693i	$-0.764276\pi$
$499$	4.80838	−	8.32836i	0.215253	−	0.372829i	0.953351	+	0.301865i	$0.0976092\pi$
$500$		0			0
$501$	−21.6301	−	1.67924i	−0.966361	−	0.0750229i
$502$		0			0
$503$		−	6.82743i		−	0.304420i	−0.988348	−	0.152210i	$-0.951361\pi$
$503$		−	6.82743i		−	0.304420i	0.988348	−	0.152210i	$-0.0486390\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	1.57318	−	20.2640i	0.0698675	−	0.899956i
$508$		0			0
$509$	7.02977	−	12.1759i	0.311589	−	0.539688i	−0.667118	−	0.744952i	$-0.732472\pi$
$509$	7.02977	−	12.1759i	0.311589	−	0.539688i	0.978707	+	0.205265i	$0.0658055\pi$
$510$		0			0
$511$	−4.22423	−	18.7477i	−0.186869	−	0.829347i
$512$		0			0
$513$	1.69699	−	1.79969i	0.0749237	−	0.0794581i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−33.6391			−1.47945
$518$		0			0
$519$	−14.4346	+	21.0503i	−0.633609	+	0.924005i
$520$		0			0
$521$	13.6122	+	23.5771i	0.596363	+	1.03293i	0.993353	+	0.115109i	$0.0367216\pi$
$521$	13.6122	+	23.5771i	0.596363	+	1.03293i	−0.396990	+	0.917823i	$0.629945\pi$
$522$		0			0
$523$	−0.528969	+	0.916202i	−0.0231302	+	0.0400627i	−0.877359	−	0.479835i	$-0.840697\pi$
$523$	−0.528969	+	0.916202i	−0.0231302	+	0.0400627i	0.854229	+	0.519898i	$0.174030\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−8.83625	+	15.3048i	−0.384913	+	0.666689i
$528$		0			0
$529$	−4.16269	−	7.20999i	−0.180987	−	0.313478i
$530$		0			0
$531$	2.49906	+	6.46922i	0.108450	+	0.280740i
$532$		0			0
$533$	−6.10066			−0.264249
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−1.02491	−	2.14292i	−0.0442282	−	0.0924738i
$538$		0			0
$539$	18.8911	+	1.52137i	0.813698	+	0.0655300i
$540$		0			0
$541$	13.1032	−	22.6953i	0.563349	−	0.975748i	−0.433853	−	0.900984i	$-0.642846\pi$
$541$	13.1032	−	22.6953i	0.563349	−	0.975748i	0.997201	−	0.0747644i	$-0.0238205\pi$
$542$		0			0
$543$	36.9276	+	2.86686i	1.58472	+	0.123029i
$544$		0			0
$545$		0			0
$546$		0			0
$547$		−	36.6385i		−	1.56655i	−0.621675	−	0.783275i	$-0.713548\pi$
$547$		−	36.6385i		−	1.56655i	0.621675	−	0.783275i	$-0.286452\pi$
$548$		0			0
$549$	6.11875	+	4.93341i	0.261142	+	0.210553i
$550$		0			0
$551$	0.524531	−	0.908514i	0.0223458	−	0.0387040i
$552$		0			0
$553$	−13.5132	+	12.4687i	−0.574640	+	0.530223i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	17.1032	+	29.6236i	0.724685	+	1.25519i	0.959104	+	0.283055i	$0.0913480\pi$
$557$	17.1032	+	29.6236i	0.724685	+	1.25519i	−0.234419	+	0.972136i	$0.575319\pi$
$558$		0			0
$559$			4.68187i			0.198022i
$560$		0			0
$561$	28.5518	+	19.5785i	1.20546	+	0.826606i
$562$		0			0
$563$	20.6666	−	11.9319i	0.870993	−	0.502868i	0.00331483	−	0.999995i	$-0.498945\pi$
$563$	20.6666	−	11.9319i	0.870993	−	0.502868i	0.867678	+	0.497127i	$0.165612\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	19.4914	+	13.6780i	0.818561	+	0.574420i
$568$		0			0
$569$	−27.8326	−	16.0692i	−1.16680	−	0.673655i	−0.213879	−	0.976860i	$-0.568610\pi$
$569$	−27.8326	−	16.0692i	−1.16680	−	0.673655i	−0.952925	+	0.303205i	$0.901943\pi$
$570$		0			0
$571$	9.85333	+	17.0665i	0.412349	+	0.714209i	0.995146	−	0.0984083i	$-0.0313751\pi$
$571$	9.85333	+	17.0665i	0.412349	+	0.714209i	−0.582797	+	0.812618i	$0.698042\pi$
$572$		0			0
$573$	−16.9405	+	24.7046i	−0.707697	+	1.03205i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	6.20731	+	10.7514i	0.258414	+	0.447586i	0.965817	−	0.259224i	$-0.0834669\pi$
$577$	6.20731	+	10.7514i	0.258414	+	0.447586i	−0.707403	+	0.706810i	$0.750134\pi$
$578$		0			0
$579$	9.57176	+	20.0129i	0.397789	+	0.831710i
$580$		0			0
$581$	−8.89211	+	28.5455i	−0.368907	+	1.18427i
$582$		0			0
$583$	11.5154	+	6.64845i	0.476921	+	0.275351i
$584$		0			0
$585$		0			0
$586$		0			0
$587$			30.6227i			1.26394i	0.774995	+	0.631968i	$0.217753\pi$
$587$			30.6227i			1.26394i	−0.774995	+	0.631968i	$0.782247\pi$
$588$		0			0
$589$	−1.13958			−0.0469556
$590$		0			0
$591$	1.22964	−	15.8388i	0.0505805	−	0.651522i
$592$		0			0
$593$	−37.6999	−	21.7660i	−1.54815	−	0.893823i	−0.998283	−	0.0585693i	$-0.981346\pi$
$593$	−37.6999	−	21.7660i	−1.54815	−	0.893823i	−0.549864	−	0.835254i	$-0.685321\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−6.18568	−	12.9332i	−0.253163	−	0.529322i
$598$		0			0
$599$	−22.8060	+	13.1670i	−0.931827	+	0.537991i	−0.887389	−	0.461022i	$-0.847483\pi$
$599$	−22.8060	+	13.1670i	−0.931827	+	0.537991i	−0.0444381	+	0.999012i	$0.514150\pi$
$600$		0			0
$601$		−	18.8846i		−	0.770317i	−0.922850	−	0.385159i	$-0.874147\pi$
$601$		−	18.8846i		−	0.770317i	0.922850	−	0.385159i	$-0.125853\pi$
$602$		0			0
$603$	−41.0930	+	15.8743i	−1.67344	+	0.646450i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−7.16622	+	12.4123i	−0.290868	+	0.503798i	−0.974015	−	0.226482i	$-0.927277\pi$
$607$	−7.16622	+	12.4123i	−0.290868	+	0.503798i	0.683147	+	0.730281i	$0.260611\pi$
$608$		0			0
$609$	9.38034	+	3.74074i	0.380110	+	0.151582i
$610$		0			0
$611$	12.1037	+	6.98810i	0.489665	+	0.282708i
$612$		0			0
$613$	16.0421	−	9.26188i	0.647932	−	0.374084i	−0.139731	−	0.990189i	$-0.544624\pi$
$613$	16.0421	−	9.26188i	0.647932	−	0.374084i	0.787664	+	0.616106i	$0.211291\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−46.6900			−1.87967			−0.939833	−	0.341633i	$-0.889020\pi$
$617$	−46.6900			−1.87967			−0.939833	+	0.341633i	$0.889020\pi$
$618$		0			0
$619$	−33.0066	+	19.0564i	−1.32665	+	0.765940i	−0.984780	−	0.173808i	$-0.944393\pi$
$619$	−33.0066	+	19.0564i	−1.32665	+	0.765940i	−0.341868	+	0.939748i	$0.611059\pi$
$620$		0			0
$621$	−21.1592	−	19.9518i	−0.849090	−	0.800636i
$622$		0			0
$623$	−13.5407	+	12.4941i	−0.542498	+	0.500565i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−0.172790	+	2.22569i	−0.00690057	+	0.0888855i
$628$		0			0
$629$	64.2092			2.56019
$630$		0			0
$631$	−17.1097			−0.681128			−0.340564	−	0.940221i	$-0.610618\pi$
$631$	−17.1097			−0.681128			−0.340564	+	0.940221i	$0.610618\pi$
$632$		0			0
$633$	1.14071	−	14.6933i	0.0453391	−	0.584007i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−6.48121	−	4.47180i	−0.256795	−	0.177179i
$638$		0			0
$639$	4.58260	−	29.3361i	0.181285	−	1.16052i
$640$		0			0
$641$	−18.2874	+	10.5583i	−0.722310	+	0.417026i	−0.815602	−	0.578613i	$-0.803594\pi$
$641$	−18.2874	+	10.5583i	−0.722310	+	0.417026i	0.0932922	+	0.995639i	$0.470261\pi$
$642$		0			0
$643$	−6.86538			−0.270744			−0.135372	−	0.990795i	$-0.543223\pi$
$643$	−6.86538			−0.270744			−0.135372	+	0.990795i	$0.543223\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−15.4243	+	8.90522i	−0.606391	+	0.350100i	−0.771552	−	0.636167i	$-0.780519\pi$
$647$	−15.4243	+	8.90522i	−0.606391	+	0.350100i	0.165161	+	0.986267i	$0.447186\pi$
$648$		0			0
$649$	−5.42036	−	3.12944i	−0.212768	−	0.122841i
$650$		0			0
$651$	−1.57576	−	10.8563i	−0.0617589	−	0.425492i
$652$		0			0
$653$	−22.8610	+	39.5964i	−0.894619	+	1.54953i	−0.0603437	+	0.998178i	$0.519220\pi$
$653$	−22.8610	+	39.5964i	−0.894619	+	1.54953i	−0.834275	+	0.551348i	$0.814114\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	7.85226	+	20.3268i	0.306346	+	0.793025i
$658$		0			0
$659$			6.74688i			0.262821i	0.991328	+	0.131411i	$0.0419506\pi$
$659$			6.74688i			0.262821i	−0.991328	+	0.131411i	$0.958049\pi$
$660$		0			0
$661$	−43.2369	+	24.9628i	−1.68172	+	0.970942i	−0.721203	+	0.692724i	$0.756410\pi$
$661$	−43.2369	+	24.9628i	−1.68172	+	0.970942i	−0.960518	+	0.278218i	$0.910256\pi$
$662$		0			0
$663$	−6.20607	−	12.9759i	−0.241024	−	0.503940i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−10.6816	−	6.16700i	−0.413592	−	0.238787i
$668$		0			0
$669$	0.743316	−	9.57457i	0.0287383	−	0.370174i
$670$		0			0
$671$	−7.09346			−0.273840
$672$		0			0
$673$		−	20.0600i		−	0.773257i	−0.922236	−	0.386628i	$-0.873640\pi$
$673$		−	20.0600i		−	0.773257i	0.922236	−	0.386628i	$-0.126360\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	21.6076	+	12.4751i	0.830446	+	0.479458i	0.854005	−	0.520264i	$-0.174167\pi$
$677$	21.6076	+	12.4751i	0.830446	+	0.479458i	−0.0235594	+	0.999722i	$0.507500\pi$
$678$		0			0
$679$	22.2212	+	6.92206i	0.852773	+	0.265644i
$680$		0			0
$681$	−4.62947	−	9.67944i	−0.177402	−	0.370917i
$682$		0			0
$683$	15.4243	+	26.7156i	0.590194	+	1.02225i	0.994206	+	0.107492i	$0.0342820\pi$
$683$	15.4243	+	26.7156i	0.590194	+	1.02225i	−0.404012	+	0.914754i	$0.632385\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−0.347862	+	0.507294i	−0.0132718	+	0.0193545i
$688$		0			0
$689$	−2.76226	−	4.78438i	−0.105234	−	0.182270i
$690$		0			0
$691$	15.5472	+	8.97619i	0.591444	+	0.341470i	0.765668	−	0.643236i	$-0.222408\pi$
$691$	15.5472	+	8.97619i	0.591444	+	0.341470i	−0.174224	+	0.984706i	$0.555742\pi$
$692$		0			0
$693$	−21.4421	+	1.43148i	−0.814520	+	0.0543776i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	34.6735	−	20.0188i	1.31335	−	0.758264i
$698$		0			0
$699$	26.6637	+	18.2838i	1.00851	+	0.691557i
$700$		0			0
$701$		−	31.7744i		−	1.20010i	−0.799961	−	0.600052i	$-0.795147\pi$
$701$		−	31.7744i		−	1.20010i	0.799961	−	0.600052i	$-0.204853\pi$
$702$		0			0
$703$	2.07021	+	3.58570i	0.0780793	+	0.135237i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−6.08633	−	27.0119i	−0.228900	−	1.01589i
$708$		0			0
$709$	13.2201	−	22.8978i	0.496490	−	0.859946i	−0.503502	−	0.863994i	$-0.667955\pi$
$709$	13.2201	−	22.8978i	0.496490	−	0.859946i	0.999992	+	0.00404829i	$0.00128862\pi$
$710$		0			0
$711$	13.0861	−	16.2303i	0.490767	−	0.608683i
$712$		0			0
$713$			13.3982i			0.501768i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−36.5945	−	2.84099i	−1.36665	−	0.106099i
$718$		0			0
$719$	−12.2625	+	21.2393i	−0.457314	+	0.792092i	−0.998818	−	0.0486066i	$-0.984522\pi$
$719$	−12.2625	+	21.2393i	−0.457314	+	0.792092i	0.541504	+	0.840698i	$0.317855\pi$
$720$		0			0
$721$	−6.35608	+	5.86478i	−0.236713	+	0.218416i
$722$		0			0
$723$	−1.65986	−	3.47048i	−0.0617307	−	0.129069i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−49.4804			−1.83513			−0.917564	−	0.397589i	$-0.869847\pi$
$727$	−49.4804			−1.83513			−0.917564	+	0.397589i	$0.869847\pi$
$728$		0			0
$729$	−24.1347	−	12.1044i	−0.893878	−	0.448310i
$730$		0			0
$731$	−15.3631	−	26.6097i	−0.568226	−	0.984196i
$732$		0			0
$733$	−8.27642	+	14.3352i	−0.305697	+	0.529482i	−0.977416	−	0.211324i	$-0.932223\pi$
$733$	−8.27642	+	14.3352i	−0.305697	+	0.529482i	0.671720	+	0.740805i	$0.265556\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	19.8785	−	34.4306i	0.732234	−	1.26827i
$738$		0			0
$739$	8.41010	+	14.5667i	0.309371	+	0.535846i	0.978225	−	0.207548i	$-0.0665483\pi$
$739$	8.41010	+	14.5667i	0.309371	+	0.535846i	−0.668854	+	0.743394i	$0.733215\pi$
$740$		0			0
$741$	0.524531	−	0.764935i	0.0192691	−	0.0281006i
$742$		0			0
$743$	−4.76463			−0.174797			−0.0873987	−	0.996173i	$-0.527855\pi$
$743$	−4.76463			−0.174797			−0.0873987	+	0.996173i	$0.527855\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	5.23233	−	33.4954i	0.191441	−	1.22553i
$748$		0			0
$749$	9.69531	−	8.94590i	0.354259	−	0.326876i
$750$		0			0
$751$	−4.11749	+	7.13171i	−0.150249	+	0.260240i	−0.931319	−	0.364204i	$-0.881341\pi$
$751$	−4.11749	+	7.13171i	−0.150249	+	0.260240i	0.781070	+	0.624444i	$0.214674\pi$
$752$		0			0
$753$	2.45359	−	31.6044i	0.0894138	−	1.15173i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		−	3.01624i		−	0.109627i	−0.998497	−	0.0548136i	$-0.982544\pi$
$757$		−	3.01624i		−	0.109627i	0.998497	−	0.0548136i	$-0.0174565\pi$
$758$		0			0
$759$	26.1678	+	2.03152i	0.949832	+	0.0737396i
$760$		0			0
$761$	7.59504	−	13.1550i	0.275320	−	0.476868i	−0.694896	−	0.719110i	$-0.744550\pi$
$761$	7.59504	−	13.1550i	0.275320	−	0.476868i	0.970216	+	0.242242i	$0.0778829\pi$
$762$		0			0
$763$	2.79200	+	12.3912i	0.101077	+	0.448593i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	1.30021	+	2.25202i	0.0469477	+	0.0813158i
$768$		0			0
$769$			33.1611i			1.19582i	0.801563	+	0.597910i	$0.204002\pi$
$769$			33.1611i			1.19582i	−0.801563	+	0.597910i	$0.795998\pi$
$770$		0			0
$771$	−10.9701	+	15.9979i	−0.395079	+	0.576152i
$772$		0			0
$773$	8.39536	−	4.84706i	0.301960	−	0.174337i	−0.341363	−	0.939932i	$-0.610889\pi$
$773$	8.39536	−	4.84706i	0.301960	−	0.174337i	0.643323	+	0.765595i	$0.277555\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−31.2969	+	24.6801i	−1.12277	+	0.885395i
$778$		0			0
$779$	2.23586	+	1.29087i	0.0801079	+	0.0462503i
$780$		0			0
$781$	13.3983	+	23.2065i	0.479429	+	0.830395i
$782$		0			0
$783$	−11.1429	−	2.63770i	−0.398215	−	0.0942637i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	20.9882	+	36.3526i	0.748148	+	1.29583i	0.948710	+	0.316149i	$0.102390\pi$
$787$	20.9882	+	36.3526i	0.748148	+	1.29583i	−0.200562	+	0.979681i	$0.564277\pi$
$788$		0			0
$789$	20.6497	−	9.87632i	0.735150	−	0.351606i
$790$		0			0
$791$	−47.7101	−	14.8620i	−1.69638	−	0.528432i
$792$		0			0
$793$	2.55231	+	1.47358i	0.0906352	+	0.0523283i
$794$		0			0
$795$		0			0
$796$		0			0
$797$		−	29.8186i		−	1.05623i	−0.849173	−	0.528115i	$-0.822899\pi$
$797$		−	29.8186i		−	1.05623i	0.849173	−	0.528115i	$-0.177101\pi$
$798$		0			0
$799$	−91.7232			−3.24493
$800$		0			0
$801$	13.1127	−	16.2633i	0.463316	−	0.574636i
$802$		0			0
$803$	−17.0312	−	9.83298i	−0.601019	−	0.346998i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	39.5813	−	18.9309i	1.39333	−	0.666398i
$808$		0			0
$809$	15.5493	−	8.97739i	0.546684	−	0.315628i	−0.201099	−	0.979571i	$-0.564451\pi$
$809$	15.5493	−	8.97739i	0.546684	−	0.315628i	0.747784	+	0.663942i	$0.231118\pi$
$810$		0			0
$811$			4.42584i			0.155412i	0.996976	+	0.0777061i	$0.0247596\pi$
$811$			4.42584i			0.155412i	−0.996976	+	0.0777061i	$0.975240\pi$
$812$		0			0
$813$	27.0667	−	39.4719i	0.949270	−	1.38434i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	0.990664	−	1.71588i	0.0346589	−	0.0600311i
$818$		0			0
$819$	8.01251	+	3.93927i	0.279980	+	0.137649i
$820$		0			0
$821$	32.5257	+	18.7787i	1.13515	+	0.655381i	0.945226	−	0.326417i	$-0.105841\pi$
$821$	32.5257	+	18.7787i	1.13515	+	0.655381i	0.189927	+	0.981798i	$0.439175\pi$
$822$		0			0
$823$	−31.8982	+	18.4164i	−1.11190	+	0.641957i	−0.939321	−	0.343038i	$-0.888544\pi$
$823$	−31.8982	+	18.4164i	−1.11190	+	0.641957i	−0.172581	+	0.984995i	$0.555211\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−14.9737			−0.520686			−0.260343	−	0.965516i	$-0.583836\pi$
$827$	−14.9737			−0.520686			−0.260343	+	0.965516i	$0.583836\pi$
$828$		0			0
$829$	2.95565	−	1.70645i	0.102654	−	0.0592674i	−0.447794	−	0.894137i	$-0.647790\pi$
$829$	2.95565	−	1.70645i	0.102654	−	0.0592674i	0.550448	+	0.834869i	$0.314457\pi$
$830$		0			0
$831$	17.6830	+	36.9722i	0.613417	+	1.28255i
$832$		0			0
$833$	51.5102	+	4.14829i	1.78472	+	0.143730i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	3.57077	+	11.9153i	0.123424	+	0.411854i
$838$		0			0
$839$	−3.71578			−0.128283			−0.0641416	−	0.997941i	$-0.520431\pi$
$839$	−3.71578			−0.128283			−0.0641416	+	0.997941i	$0.520431\pi$
$840$		0			0
$841$	24.1436			0.832539
$842$		0			0
$843$	29.9944	+	2.32860i	1.03306	+	0.0802012i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−7.13544	+	6.58390i	−0.245176	+	0.226225i
$848$		0			0
$849$	−20.1891	+	9.65599i	−0.692887	+	0.331393i
$850$		0			0
$851$	42.1577	−	24.3398i	1.44515	−	0.834357i
$852$		0			0
$853$	−10.5549			−0.361393			−0.180696	−	0.983539i	$-0.557835\pi$
$853$	−10.5549			−0.361393			−0.180696	+	0.983539i	$0.557835\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	33.4229	−	19.2967i	1.14170	−	0.659163i	0.194852	−	0.980833i	$-0.437577\pi$
$857$	33.4229	−	19.2967i	1.14170	−	0.659163i	0.946852	+	0.321669i	$0.104244\pi$
$858$		0			0
$859$	25.9876	+	15.0039i	0.886685	+	0.511928i	0.872857	−	0.487977i	$-0.162265\pi$
$859$	25.9876	+	15.0039i	0.886685	+	0.511928i	0.0138282	+	0.999904i	$0.495598\pi$
$860$		0			0
$861$	−9.20597	+	23.0850i	−0.313739	+	0.786736i
$862$		0			0
$863$	−19.0643	+	33.0204i	−0.648958	+	1.12403i	0.334414	+	0.942426i	$0.391462\pi$
$863$	−19.0643	+	33.0204i	−0.648958	+	1.12403i	−0.983372	+	0.181602i	$0.941872\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	53.5677	+	36.7325i	1.81925	+	1.24750i
$868$		0			0
$869$			18.8157i			0.638280i
$870$		0			0
$871$	−14.3050	+	8.25902i	−0.484708	+	0.279846i
$872$		0			0
$873$	−26.0745	−	4.07311i	−0.882488	−	0.137854i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	28.7268	+	16.5855i	0.970037	+	0.560051i	0.899247	−	0.437440i	$-0.144115\pi$
$877$	28.7268	+	16.5855i	0.970037	+	0.560051i	0.0707893	+	0.997491i	$0.477448\pi$
$878$		0			0
$879$	−19.4003	−	1.50613i	−0.654357	−	0.0508006i
$880$		0			0
$881$	19.8093			0.667393			0.333697	−	0.942681i	$-0.391704\pi$
$881$	19.8093			0.667393			0.333697	+	0.942681i	$0.391704\pi$
$882$		0			0
$883$		−	3.37029i		−	0.113419i	−0.998391	−	0.0567096i	$-0.981939\pi$
$883$		−	3.37029i		−	0.113419i	0.998391	−	0.0567096i	$-0.0180609\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	31.3008	+	18.0715i	1.05098	+	0.606783i	0.922923	−	0.384984i	$-0.125793\pi$
$887$	31.3008	+	18.0715i	1.05098	+	0.606783i	0.128056	+	0.991767i	$0.459126\pi$
$888$		0			0
$889$	6.11629	−	19.6346i	0.205134	−	0.658522i
$890$		0			0
$891$	23.8130	−	5.16732i	0.797767	−	0.173112i
$892$		0			0
$893$	−2.95730	−	5.12220i	−0.0989623	−	0.171408i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−8.99347	−	6.16700i	−0.300283	−	0.205910i
$898$		0			0
$899$	2.63770	+	4.56863i	0.0879722	+	0.152372i
$900$		0			0
$901$	31.3990	+	18.1282i	1.04605	+	0.603939i
$902$		0			0
$903$	17.7163	+	7.06500i	0.589562	+	0.235109i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	39.9260	−	23.0513i	1.32572	−	0.765405i	0.341086	−	0.940032i	$-0.389205\pi$
$907$	39.9260	−	23.0513i	1.32572	−	0.765405i	0.984635	+	0.174627i	$0.0558718\pi$
$908$		0			0
$909$	11.3136	+	29.2872i	0.375250	+	0.971394i
$910$		0			0
$911$			58.0403i			1.92296i	0.274871	+	0.961481i	$0.411365\pi$
$911$			58.0403i			1.92296i	−0.274871	+	0.961481i	$0.588635\pi$
$912$		0			0
$913$	15.2979	+	26.4968i	0.506288	+	0.876916i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−9.04567	+	8.34648i	−0.298714	+	0.275625i
$918$		0			0
$919$	2.66148	−	4.60983i	0.0877943	−	0.152064i	−0.818784	−	0.574101i	$-0.805352\pi$
$919$	2.66148	−	4.60983i	0.0877943	−	0.152064i	0.906578	+	0.422037i	$0.138685\pi$
$920$		0			0
$921$	4.15818	−	53.5610i	0.137017	−	1.76490i
$922$		0			0
$923$		−	11.1333i		−	0.366458i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	6.15519	−	7.63409i	0.202163	−	0.250736i
$928$		0			0
$929$	−20.7113	+	35.8731i	−0.679517	+	1.17696i	0.295610	+	0.955309i	$0.404477\pi$
$929$	−20.7113	+	35.8731i	−0.679517	+	1.17696i	−0.975127	+	0.221649i	$0.928856\pi$
$930$		0			0
$931$	1.42911	+	3.01029i	0.0468373	+	0.0986581i
$932$		0			0
$933$	−2.41054	+	1.15291i	−0.0789175	+	0.0377445i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	0.523249			0.0170938			0.00854690	−	0.999963i	$-0.497279\pi$
$937$	0.523249			0.0170938			0.00854690	+	0.999963i	$0.497279\pi$
$938$		0			0
$939$	36.7245	+	25.1827i	1.19846	+	0.821807i
$940$		0			0
$941$	9.58594	+	16.6033i	0.312493	+	0.541253i	0.978901	−	0.204333i	$-0.0655026\pi$
$941$	9.58594	+	16.6033i	0.312493	+	0.541253i	−0.666409	+	0.745587i	$0.732169\pi$
$942$		0			0
$943$	15.1770	−	26.2874i	0.494232	−	0.856035i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	15.0654	−	26.0940i	0.489558	−	0.847940i	−0.510370	−	0.859955i	$-0.670491\pi$
$947$	15.0654	−	26.0940i	0.489558	−	0.847940i	0.999928	+	0.0120156i	$0.00382477\pi$
$948$		0			0
$949$	4.08536	+	7.07605i	0.132616	+	0.229698i
$950$		0			0
$951$	−4.44383	−	3.04722i	−0.144101	−	0.0988130i
$952$		0			0
$953$	17.4015			0.563691			0.281846	−	0.959460i	$-0.409053\pi$
$953$	17.4015			0.563691			0.281846	+	0.959460i	$0.409053\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	9.32285	−	4.45892i	0.301365	−	0.144136i
$958$		0			0
$959$	−6.40407	−	28.4221i	−0.206798	−	0.917796i
$960$		0			0
$961$	−12.6347	+	21.8840i	−0.407571	+	0.705934i
$962$		0			0
$963$	−9.38887	+	11.6447i	−0.302552	+	0.375246i
$964$		0			0
$965$		0			0
$966$		0			0
$967$			24.9154i			0.801224i	0.916248	+	0.400612i	$0.131203\pi$
$967$			24.9154i			0.801224i	−0.916248	+	0.400612i	$0.868797\pi$
$968$		0			0
$969$	−0.471144	+	6.06875i	−0.0151353	+	0.194956i
$970$		0			0
$971$	9.45293	−	16.3730i	0.303359	−	0.525433i	−0.673536	−	0.739155i	$-0.735225\pi$
$971$	9.45293	−	16.3730i	0.303359	−	0.525433i	0.976895	+	0.213722i	$0.0685585\pi$
$972$		0			0
$973$	−16.2039	+	52.0179i	−0.519474	+	1.66762i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−20.2411	−	35.0586i	−0.647571	−	1.12163i	−0.983701	−	0.179810i	$-0.942452\pi$
$977$	−20.2411	−	35.0586i	−0.647571	−	1.12163i	0.336131	−	0.941815i	$-0.390882\pi$
$978$		0			0
$979$			18.8540i			0.602578i
$980$		0			0
$981$	−5.18994	−	13.4350i	−0.165702	−	0.428946i
$982$		0			0
$983$	47.0341	−	27.1552i	1.50016	−	0.866116i	0.500156	−	0.865935i	$-0.333276\pi$
$983$	47.0341	−	27.1552i	1.50016	−	0.866116i	1.00000		0.000180339i	$-5.74036e-5\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	44.7078	−	35.2557i	1.42307	−	1.12220i
$988$		0			0
$989$	−20.1739	−	11.6474i	−0.641493	−	0.370366i
$990$		0			0
$991$	30.8784	+	53.4830i	0.980886	+	1.69894i	0.658957	+	0.752181i	$0.270998\pi$
$991$	30.8784	+	53.4830i	0.980886	+	1.69894i	0.321929	+	0.946764i	$0.395669\pi$
$992$		0			0
$993$	0.399910	+	0.274226i	0.0126907	+	0.00870230i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	10.2738	+	17.7948i	0.325375	+	0.563566i	0.981588	−	0.191009i	$-0.0611761\pi$
$997$	10.2738	+	17.7948i	0.325375	+	0.563566i	−0.656213	+	0.754576i	$0.727843\pi$
$998$		0			0
$999$	31.0050	−	32.8814i	0.980954	−	1.04032i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2100.2.bo.i.1349.8		32
3.2	odd	2	inner	2100.2.bo.i.1349.13		32
5.2	odd	4		2100.2.bi.m.1601.8	yes	16
5.3	odd	4		2100.2.bi.l.1601.1	yes	16
5.4	even	2	inner	2100.2.bo.i.1349.9		32
7.3	odd	6	inner	2100.2.bo.i.1949.4		32
15.2	even	4		2100.2.bi.m.1601.5	yes	16
15.8	even	4		2100.2.bi.l.1601.4	yes	16
15.14	odd	2	inner	2100.2.bo.i.1349.4		32
21.17	even	6	inner	2100.2.bo.i.1949.9		32
35.3	even	12		2100.2.bi.l.101.4	yes	16
35.17	even	12		2100.2.bi.m.101.5	yes	16
35.24	odd	6	inner	2100.2.bo.i.1949.13		32
105.17	odd	12		2100.2.bi.m.101.8	yes	16
105.38	odd	12		2100.2.bi.l.101.1	✓	16
105.59	even	6	inner	2100.2.bo.i.1949.8		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2100.2.bi.l.101.1	✓	16	105.38	odd	12
2100.2.bi.l.101.4	yes	16	35.3	even	12
2100.2.bi.l.1601.1	yes	16	5.3	odd	4
2100.2.bi.l.1601.4	yes	16	15.8	even	4
2100.2.bi.m.101.5	yes	16	35.17	even	12
2100.2.bi.m.101.8	yes	16	105.17	odd	12
2100.2.bi.m.1601.5	yes	16	15.2	even	4
2100.2.bi.m.1601.8	yes	16	5.2	odd	4
2100.2.bo.i.1349.4		32	15.14	odd	2	inner
2100.2.bo.i.1349.8		32	1.1	even	1	trivial
2100.2.bo.i.1349.9		32	5.4	even	2	inner
2100.2.bo.i.1349.13		32	3.2	odd	2	inner
2100.2.bo.i.1949.4		32	7.3	odd	6	inner
2100.2.bo.i.1949.8		32	105.59	even	6	inner
2100.2.bo.i.1949.9		32	21.17	even	6	inner
2100.2.bo.i.1949.13		32	35.24	odd	6	inner

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:	\( N \)	\(=\)	\( 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2100.bo (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.134063 + 1.72685i) q^{3} +(2.52603 + 0.786875i) q^{7} +(-2.96405 - 0.463016i) q^{9} +O(q^{10})\)	\(q+(-0.134063 + 1.72685i) q^{3} +(2.52603 + 0.786875i) q^{7} +(-2.96405 - 0.463016i) q^{9} +(2.34474 - 1.35373i) q^{11} -1.12489 q^{13} +(6.39336 - 3.69121i) q^{17} +(0.412264 + 0.238021i) q^{19} +(-1.69747 + 4.25660i) q^{21} +(2.79845 - 4.84706i) q^{23} +(1.19693 - 5.05642i) q^{27} -2.20372i q^{29} +(-2.07315 + 1.19693i) q^{31} +(2.02336 + 4.23051i) q^{33} +(7.53233 + 4.34879i) q^{37} +(0.150806 - 1.94251i) q^{39} +5.42336 q^{41} -4.16209i q^{43} +(-10.7600 - 6.21227i) q^{47} +(5.76166 + 3.97534i) q^{49} +(5.51707 + 11.5353i) q^{51} +(2.45559 + 4.25321i) q^{53} +(-0.466297 + 0.680011i) q^{57} +(-1.15586 - 2.00200i) q^{59} +(-2.26895 - 1.30998i) q^{61} +(-7.12295 - 3.50193i) q^{63} +(12.7169 - 7.34210i) q^{67} +(7.99501 + 5.48234i) q^{69} +9.89729i q^{71} +(-3.63180 - 6.29046i) q^{73} +(6.98810 - 1.57456i) q^{77} +(-3.47478 + 6.01850i) q^{79} +(8.57123 + 2.74481i) q^{81} +11.3005i q^{83} +(3.80550 + 0.295438i) q^{87} +(-3.48186 + 6.03075i) q^{89} +(-2.84150 - 0.885144i) q^{91} +(-1.78899 - 3.74049i) q^{93} +8.79691 q^{97} +(-7.57673 + 2.92689i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 18 q^{9}+O(q^{10}) \) 32 * q + 18 * q^9	\( 32 q + 18 q^{9} + 36 q^{19} - 22 q^{21} - 36 q^{31} - 24 q^{39} + 36 q^{49} - 2 q^{51} + 72 q^{61} + 14 q^{81} + 40 q^{91} + 60 q^{99}+O(q^{100}) \) 32 * q + 18 * q^9 + 36 * q^19 - 22 * q^21 - 36 * q^31 - 24 * q^39 + 36 * q^49 - 2 * q^51 + 72 * q^61 + 14 * q^81 + 40 * q^91 + 60 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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