LMFDB - Embedded newform 425.2.e.c.251.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [425,2,Mod(251,425)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(425, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("425.251");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 425 = 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	425.e (of order $4$, degree $2$, 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:	$3.39364208590$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 18x^{10} + 119x^{8} + 364x^{6} + 519x^{4} + 278x^{2} + 1 $ x^12 + 18x^10 + 119x^8 + 364x^6 + 519x^4 + 278*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			251.6
Root			$2.69251i$ of defining polynomial
Character	$\chi$	$=$	425.251
Dual form			425.2.e.c.276.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.69251i q^{2} +(-0.494558 - 0.494558i) q^{3} -5.24959 q^{4} +(1.33160 - 1.33160i) q^{6} +(3.43326 - 3.43326i) q^{7} -8.74953i q^{8} -2.51083i q^{9} +(-1.72004 + 1.72004i) q^{11} +(2.59622 + 2.59622i) q^{12} +1.74964 q^{13} +(9.24408 + 9.24408i) q^{14} +13.0590 q^{16} +(0.515279 - 4.09078i) q^{17} +6.76041 q^{18} -0.0462547i q^{19} -3.39590 q^{21} +(-4.63121 - 4.63121i) q^{22} +(1.90172 - 1.90172i) q^{23} +(-4.32715 + 4.32715i) q^{24} +4.71093i q^{26} +(-2.72542 + 2.72542i) q^{27} +(-18.0232 + 18.0232i) q^{28} +(-1.39828 - 1.39828i) q^{29} +(-2.06252 - 2.06252i) q^{31} +17.6623i q^{32} +1.70132 q^{33} +(11.0144 + 1.38739i) q^{34} +13.1808i q^{36} +(2.43847 + 2.43847i) q^{37} +0.124541 q^{38} +(-0.865300 - 0.865300i) q^{39} +(-3.76486 + 3.76486i) q^{41} -9.14347i q^{42} -7.98228i q^{43} +(9.02949 - 9.02949i) q^{44} +(5.12039 + 5.12039i) q^{46} +9.75559 q^{47} +(-6.45842 - 6.45842i) q^{48} -16.5746i q^{49} +(-2.27796 + 1.76829i) q^{51} -9.18491 q^{52} +11.5454i q^{53} +(-7.33821 - 7.33821i) q^{54} +(-30.0394 - 30.0394i) q^{56} +(-0.0228756 + 0.0228756i) q^{57} +(3.76486 - 3.76486i) q^{58} +7.13788i q^{59} +(6.15308 - 6.15308i) q^{61} +(5.55335 - 5.55335i) q^{62} +(-8.62033 - 8.62033i) q^{63} -21.4379 q^{64} +4.58080i q^{66} +11.5883 q^{67} +(-2.70500 + 21.4749i) q^{68} -1.88102 q^{69} +(3.17202 + 3.17202i) q^{71} -21.9685 q^{72} +(-5.45257 - 5.45257i) q^{73} +(-6.56558 + 6.56558i) q^{74} +0.242818i q^{76} +11.8107i q^{77} +(2.32983 - 2.32983i) q^{78} +(2.81394 - 2.81394i) q^{79} -4.83672 q^{81} +(-10.1369 - 10.1369i) q^{82} -0.548920i q^{83} +17.8270 q^{84} +21.4923 q^{86} +1.38306i q^{87} +(15.0495 + 15.0495i) q^{88} +0.475447 q^{89} +(6.00699 - 6.00699i) q^{91} +(-9.98323 + 9.98323i) q^{92} +2.04007i q^{93} +26.2670i q^{94} +(8.73503 - 8.73503i) q^{96} +(-9.98146 - 9.98146i) q^{97} +44.6272 q^{98} +(4.31872 + 4.31872i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 2 q^{3} - 12 q^{4} + 6 q^{6} - 4 q^{11} - 4 q^{12} + 12 q^{13} + 14 q^{14} + 4 q^{16} + 6 q^{17} - 4 q^{18} + 8 q^{21} + 10 q^{22} + 12 q^{23} - 8 q^{24} + 22 q^{27} - 34 q^{28} - 6 q^{29} - 6 q^{31}+ \cdots + 30 q^{99}+O(q^{100}) $ 12 * q - 2 * q^3 - 12 * q^4 + 6 * q^6 - 4 * q^11 - 4 * q^12 + 12 * q^13 + 14 * q^14 + 4 * q^16 + 6 * q^17 - 4 * q^18 + 8 * q^21 + 10 * q^22 + 12 * q^23 - 8 * q^24 + 22 * q^27 - 34 * q^28 - 6 * q^29 - 6 * q^31 + 4 * q^33 + 30 * q^34 + 18 * q^37 - 12 * q^38 + 16 * q^39 + 6 * q^41 + 32 * q^44 + 30 * q^46 + 36 * q^47 - 10 * q^48 - 40 * q^51 - 64 * q^52 + 16 * q^54 - 56 * q^56 - 18 * q^57 - 6 * q^58 - 8 * q^61 - 22 * q^62 - 30 * q^63 - 44 * q^64 + 20 * q^67 + 10 * q^68 - 72 * q^69 - 20 * q^71 - 92 * q^72 - 18 * q^73 - 26 * q^74 + 38 * q^78 - 14 * q^79 - 8 * q^81 - 10 * q^82 + 36 * q^84 + 84 * q^86 + 66 * q^88 - 24 * q^89 + 12 * q^91 - 32 * q^92 + 22 * q^96 - 52 * q^97 + 76 * q^98 + 30 * q^99

Character values

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

$n$	$52$	$326$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$

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 $

$2$			2.69251i			1.90389i	0.306271	+	0.951944i	$0.400919\pi$
$2$			2.69251i			1.90389i	−0.306271	+	0.951944i	$0.599081\pi$
$3$	−0.494558	−	0.494558i	−0.285533	−	0.285533i	0.549778	−	0.835311i	$-0.314712\pi$
$3$	−0.494558	−	0.494558i	−0.285533	−	0.285533i	−0.835311	+	0.549778i	$0.814712\pi$
$4$	−5.24959			−2.62479
$5$		0			0
$5$		0			0
$6$	1.33160	−	1.33160i	0.543623	−	0.543623i
$7$	3.43326	−	3.43326i	1.29765	−	1.29765i	0.367713	−	0.929939i	$-0.380141\pi$
$7$	3.43326	−	3.43326i	1.29765	−	1.29765i	0.929939	−	0.367713i	$-0.119859\pi$
$8$		−	8.74953i		−	3.09342i
$9$		−	2.51083i		−	0.836942i
$10$		0			0
$11$	−1.72004	+	1.72004i	−0.518611	+	0.518611i	−0.917151	−	0.398540i	$-0.869517\pi$
$11$	−1.72004	+	1.72004i	−0.518611	+	0.518611i	0.398540	+	0.917151i	$0.369517\pi$
$12$	2.59622	+	2.59622i	0.749465	+	0.749465i
$13$	1.74964			0.485264			0.242632	−	0.970118i	$-0.421989\pi$
$13$	1.74964			0.485264			0.242632	+	0.970118i	$0.421989\pi$
$14$	9.24408	+	9.24408i	2.47059	+	2.47059i
$15$		0			0
$16$	13.0590			3.26474
$17$	0.515279	−	4.09078i	0.124973	−	0.992160i
$17$	0.515279	−	4.09078i	0.124973	−	0.992160i
$18$	6.76041			1.59344
$19$		−	0.0462547i		−	0.0106115i	−0.999986	−	0.00530577i	$-0.998311\pi$
$19$		−	0.0462547i		−	0.0106115i	0.999986	−	0.00530577i	$-0.00168889\pi$
$20$		0			0
$21$	−3.39590			−0.741045
$22$	−4.63121	−	4.63121i	−0.987378	−	0.987378i
$23$	1.90172	−	1.90172i	0.396536	−	0.396536i	−0.480474	−	0.877009i	$-0.659535\pi$
$23$	1.90172	−	1.90172i	0.396536	−	0.396536i	0.877009	+	0.480474i	$0.159535\pi$
$24$	−4.32715	+	4.32715i	−0.883275	+	0.883275i
$25$		0			0
$26$			4.71093i			0.923889i
$27$	−2.72542	+	2.72542i	−0.524508	+	0.524508i
$28$	−18.0232	+	18.0232i	−3.40607	+	3.40607i
$29$	−1.39828	−	1.39828i	−0.259653	−	0.259653i	0.565260	−	0.824913i	$-0.308776\pi$
$29$	−1.39828	−	1.39828i	−0.259653	−	0.259653i	−0.824913	+	0.565260i	$0.808776\pi$
$30$		0			0
$31$	−2.06252	−	2.06252i	−0.370440	−	0.370440i	0.497197	−	0.867637i	$-0.334362\pi$
$31$	−2.06252	−	2.06252i	−0.370440	−	0.370440i	−0.867637	+	0.497197i	$0.834362\pi$
$32$			17.6623i			3.12228i
$33$	1.70132			0.296161
$34$	11.0144	+	1.38739i	1.88896	+	0.237936i
$35$		0			0
$36$			13.1808i			2.19680i
$37$	2.43847	+	2.43847i	0.400881	+	0.400881i	0.878544	−	0.477662i	$-0.158516\pi$
$37$	2.43847	+	2.43847i	0.400881	+	0.400881i	−0.477662	+	0.878544i	$0.658516\pi$
$38$	0.124541			0.0202032
$39$	−0.865300	−	0.865300i	−0.138559	−	0.138559i
$40$		0			0
$41$	−3.76486	+	3.76486i	−0.587973	+	0.587973i	−0.937082	−	0.349109i	$-0.886484\pi$
$41$	−3.76486	+	3.76486i	−0.587973	+	0.587973i	0.349109	+	0.937082i	$0.386484\pi$
$42$		−	9.14347i		−	1.41087i
$43$		−	7.98228i		−	1.21729i	−0.793444	−	0.608643i	$-0.791714\pi$
$43$		−	7.98228i		−	1.21729i	0.793444	−	0.608643i	$-0.208286\pi$
$44$	9.02949	−	9.02949i	1.36125	−	1.36125i
$45$		0			0
$46$	5.12039	+	5.12039i	0.754960	+	0.754960i
$47$	9.75559			1.42300			0.711500	−	0.702687i	$-0.248016\pi$
$47$	9.75559			1.42300			0.711500	+	0.702687i	$0.248016\pi$
$48$	−6.45842	−	6.45842i	−0.932192	−	0.932192i
$49$		−	16.5746i		−	2.36780i
$50$		0			0
$51$	−2.27796	+	1.76829i	−0.318979	+	0.247610i
$52$	−9.18491			−1.27372
$53$			11.5454i			1.58589i	0.609296	+	0.792943i	$0.291452\pi$
$53$			11.5454i			1.58589i	−0.609296	+	0.792943i	$0.708548\pi$
$54$	−7.33821	−	7.33821i	−0.998604	−	0.998604i
$55$		0			0
$56$	−30.0394	−	30.0394i	−4.01419	−	4.01419i
$57$	−0.0228756	+	0.0228756i	−0.00302995	+	0.00302995i
$58$	3.76486	−	3.76486i	0.494351	−	0.494351i
$59$			7.13788i			0.929273i	0.885501	+	0.464637i	$0.153815\pi$
$59$			7.13788i			0.929273i	−0.885501	+	0.464637i	$0.846185\pi$
$60$		0			0
$61$	6.15308	−	6.15308i	0.787821	−	0.787821i	−0.193316	−	0.981137i	$-0.561924\pi$
$61$	6.15308	−	6.15308i	0.787821	−	0.787821i	0.981137	+	0.193316i	$0.0619242\pi$
$62$	5.55335	−	5.55335i	0.705276	−	0.705276i
$63$	−8.62033	−	8.62033i	−1.08606	−	1.08606i
$64$	−21.4379			−2.67974
$65$		0			0
$66$			4.58080i			0.563858i
$67$	11.5883			1.41574			0.707871	−	0.706342i	$-0.249656\pi$
$67$	11.5883			1.41574			0.707871	+	0.706342i	$0.249656\pi$
$68$	−2.70500	+	21.4749i	−0.328029	+	2.60421i
$69$	−1.88102			−0.226448
$70$		0			0
$71$	3.17202	+	3.17202i	0.376450	+	0.376450i	0.869820	−	0.493370i	$-0.164235\pi$
$71$	3.17202	+	3.17202i	0.376450	+	0.376450i	−0.493370	+	0.869820i	$0.664235\pi$
$72$	−21.9685			−2.58902
$73$	−5.45257	−	5.45257i	−0.638175	−	0.638175i	0.311930	−	0.950105i	$-0.399025\pi$
$73$	−5.45257	−	5.45257i	−0.638175	−	0.638175i	−0.950105	+	0.311930i	$0.899025\pi$
$74$	−6.56558	+	6.56558i	−0.763234	+	0.763234i
$75$		0			0
$76$			0.242818i			0.0278531i
$77$			11.8107i			1.34595i
$78$	2.32983	−	2.32983i	0.263801	−	0.263801i
$79$	2.81394	−	2.81394i	0.316593	−	0.316593i	−0.530864	−	0.847457i	$-0.678132\pi$
$79$	2.81394	−	2.81394i	0.316593	−	0.316593i	0.847457	+	0.530864i	$0.178132\pi$
$80$		0			0
$81$	−4.83672			−0.537413
$82$	−10.1369	−	10.1369i	−1.11944	−	1.11944i
$83$		−	0.548920i		−	0.0602518i	−0.999546	−	0.0301259i	$-0.990409\pi$
$83$		−	0.548920i		−	0.0602518i	0.999546	−	0.0301259i	$-0.00959083\pi$
$84$	17.8270			1.94509
$85$		0			0
$86$	21.4923			2.31758
$87$			1.38306i			0.148279i
$88$	15.0495	+	15.0495i	1.60428	+	1.60428i
$89$	0.475447			0.0503973			0.0251986	−	0.999682i	$-0.491978\pi$
$89$	0.475447			0.0503973			0.0251986	+	0.999682i	$0.491978\pi$
$90$		0			0
$91$	6.00699	−	6.00699i	0.629704	−	0.629704i
$92$	−9.98323	+	9.98323i	−1.04082	+	1.04082i
$93$			2.04007i			0.211546i
$94$			26.2670i			2.70923i
$95$		0			0
$96$	8.73503	−	8.73503i	0.891516	−	0.891516i
$97$	−9.98146	−	9.98146i	−1.01346	−	1.01346i	−0.999908	−	0.0135555i	$-0.995685\pi$
$97$	−9.98146	−	9.98146i	−1.01346	−	1.01346i	−0.0135555	−	0.999908i	$-0.504315\pi$
$98$	44.6272			4.50803
$99$	4.31872	+	4.31872i	0.434047	+	0.434047i
$100$		0			0
$101$	−9.72087			−0.967263			−0.483631	−	0.875272i	$-0.660682\pi$
$101$	−9.72087			−0.967263			−0.483631	+	0.875272i	$0.660682\pi$
$102$	−4.76114	−	6.13343i	−0.471423	−	0.607300i
$103$	0.810012			0.0798129			0.0399064	−	0.999203i	$-0.487294\pi$
$103$	0.810012			0.0798129			0.0399064	+	0.999203i	$0.487294\pi$
$104$		−	15.3086i		−	1.50113i
$105$		0			0
$106$	−31.0861			−3.01935
$107$	−7.04176	−	7.04176i	−0.680752	−	0.680752i	0.279417	−	0.960170i	$-0.409859\pi$
$107$	−7.04176	−	7.04176i	−0.680752	−	0.680752i	−0.960170	+	0.279417i	$0.909859\pi$
$108$	14.3073	−	14.3073i	1.37672	−	1.37672i
$109$	−6.91117	+	6.91117i	−0.661970	+	0.661970i	−0.955844	−	0.293874i	$-0.905055\pi$
$109$	−6.91117	+	6.91117i	−0.661970	+	0.661970i	0.293874	+	0.955844i	$0.405055\pi$
$110$		0			0
$111$		−	2.41193i		−	0.228930i
$112$	44.8349	−	44.8349i	4.23650	−	4.23650i
$113$	3.27807	−	3.27807i	0.308375	−	0.308375i	−0.535904	−	0.844279i	$-0.680029\pi$
$113$	3.27807	−	3.27807i	0.308375	−	0.308375i	0.844279	+	0.535904i	$0.180029\pi$
$114$	−0.0615927	−	0.0615927i	−0.00576868	−	0.00576868i
$115$		0			0
$116$	7.34037	+	7.34037i	0.681536	+	0.681536i
$117$		−	4.39305i		−	0.406138i
$118$	−19.2188			−1.76923
$119$	−12.2756	−	15.8138i	−1.12531	−	1.44965i
$120$		0			0
$121$			5.08294i			0.462085i
$122$	16.5672	+	16.5672i	1.49992	+	1.49992i
$123$	3.72389			0.335771
$124$	10.8274	+	10.8274i	0.972328	+	0.972328i
$125$		0			0
$126$	23.2103	−	23.2103i	2.06774	−	2.06774i
$127$			10.7928i			0.957708i	0.877895	+	0.478854i	$0.158948\pi$
$127$			10.7928i			0.957708i	−0.877895	+	0.478854i	$0.841052\pi$
$128$		−	22.3971i		−	1.97964i
$129$	−3.94770	+	3.94770i	−0.347576	+	0.347576i
$130$		0			0
$131$	9.21049	+	9.21049i	0.804724	+	0.804724i	0.983830	−	0.179106i	$-0.0573204\pi$
$131$	9.21049	+	9.21049i	0.804724	+	0.804724i	−0.179106	+	0.983830i	$0.557320\pi$
$132$	−8.93121			−0.777362
$133$	−0.158805	−	0.158805i	−0.0137701	−	0.0137701i
$134$			31.2017i			2.69541i
$135$		0			0
$136$	−35.7924	−	4.50845i	−3.06917	−	0.386596i
$137$	4.96853			0.424490			0.212245	−	0.977216i	$-0.431922\pi$
$137$	4.96853			0.424490			0.212245	+	0.977216i	$0.431922\pi$
$138$		−	5.06465i		−	0.431132i
$139$	1.38601	+	1.38601i	0.117560	+	0.117560i	0.763439	−	0.645880i	$-0.223509\pi$
$139$	1.38601	+	1.38601i	0.117560	+	0.117560i	−0.645880	+	0.763439i	$0.723509\pi$
$140$		0			0
$141$	−4.82470	−	4.82470i	−0.406313	−	0.406313i
$142$	−8.54069	+	8.54069i	−0.716719	+	0.716719i
$143$	−3.00946	+	3.00946i	−0.251663	+	0.251663i
$144$		−	32.7888i		−	2.73240i
$145$		0			0
$146$	14.6811	−	14.6811i	1.21501	−	1.21501i
$147$	−8.19710	+	8.19710i	−0.676086	+	0.676086i
$148$	−12.8009	−	12.8009i	−1.05223	−	1.05223i
$149$	−3.47063			−0.284325			−0.142163	−	0.989843i	$-0.545406\pi$
$149$	−3.47063			−0.284325			−0.142163	+	0.989843i	$0.545406\pi$
$150$		0			0
$151$			8.04006i			0.654291i	0.944974	+	0.327146i	$0.106087\pi$
$151$			8.04006i			0.654291i	−0.944974	+	0.327146i	$0.893913\pi$
$152$	−0.404706			−0.0328260
$153$	−10.2712	−	1.29377i	−0.830380	−	0.104596i
$154$	−31.8004			−2.56255
$155$		0			0
$156$	4.54247	+	4.54247i	0.363688	+	0.363688i
$157$	−9.48714			−0.757156			−0.378578	−	0.925569i	$-0.623587\pi$
$157$	−9.48714			−0.757156			−0.378578	+	0.925569i	$0.623587\pi$
$158$	7.57655	+	7.57655i	0.602758	+	0.602758i
$159$	5.70988	−	5.70988i	0.452823	−	0.452823i
$160$		0			0
$161$		−	13.0582i		−	1.02913i
$162$		−	13.0229i		−	1.02318i
$163$	−8.48931	+	8.48931i	−0.664934	+	0.664934i	−0.956539	−	0.291605i	$-0.905811\pi$
$163$	−8.48931	+	8.48931i	−0.664934	+	0.664934i	0.291605	+	0.956539i	$0.405811\pi$
$164$	19.7640	−	19.7640i	1.54331	−	1.54331i
$165$		0			0
$166$	1.47797			0.114713
$167$	7.23359	+	7.23359i	0.559752	+	0.559752i	0.929237	−	0.369485i	$-0.120466\pi$
$167$	7.23359	+	7.23359i	0.559752	+	0.559752i	−0.369485	+	0.929237i	$0.620466\pi$
$168$			29.7125i			2.29237i
$169$	−9.93874			−0.764519
$170$		0			0
$171$	−0.116137			−0.00888125
$172$			41.9037i			3.19512i
$173$	1.36897	+	1.36897i	0.104081	+	0.104081i	0.757230	−	0.653149i	$-0.226552\pi$
$173$	1.36897	+	1.36897i	0.104081	+	0.104081i	−0.653149	+	0.757230i	$0.726552\pi$
$174$	−3.72389			−0.282307
$175$		0			0
$176$	−22.4619	+	22.4619i	−1.69313	+	1.69313i
$177$	3.53010	−	3.53010i	0.265338	−	0.265338i
$178$			1.28014i			0.0959508i
$179$		−	2.16167i		−	0.161571i	−0.996732	−	0.0807855i	$-0.974257\pi$
$179$		−	2.16167i		−	0.161571i	0.996732	−	0.0807855i	$-0.0257429\pi$
$180$		0			0
$181$	15.8826	−	15.8826i	1.18054	−	1.18054i	0.200938	−	0.979604i	$-0.435601\pi$
$181$	15.8826	−	15.8826i	1.18054	−	1.18054i	0.979604	−	0.200938i	$-0.0643991\pi$
$182$	16.1739	+	16.1739i	1.19889	+	1.19889i
$183$	−6.08610			−0.449898
$184$	−16.6391	−	16.6391i	−1.22665	−	1.22665i
$185$		0			0
$186$	−5.49291			−0.402759
$187$	6.15000	+	7.92260i	0.449733	+	0.579358i
$188$	−51.2128			−3.73508
$189$			18.7142i			1.36126i
$190$		0			0
$191$	10.6325			0.769339			0.384669	−	0.923054i	$-0.374315\pi$
$191$	10.6325			0.769339			0.384669	+	0.923054i	$0.374315\pi$
$192$	10.6023	+	10.6023i	0.765154	+	0.765154i
$193$	7.66070	−	7.66070i	0.551429	−	0.551429i	−0.375424	−	0.926853i	$-0.622503\pi$
$193$	7.66070	−	7.66070i	0.551429	−	0.551429i	0.926853	+	0.375424i	$0.122503\pi$
$194$	26.8751	−	26.8751i	1.92952	−	1.92952i
$195$		0			0
$196$			87.0098i			6.21499i
$197$	−11.9582	+	11.9582i	−0.851983	+	0.851983i	−0.990377	−	0.138394i	$-0.955806\pi$
$197$	−11.9582	+	11.9582i	−0.851983	+	0.851983i	0.138394	+	0.990377i	$0.455806\pi$
$198$	−11.6282	+	11.6282i	−0.826378	+	0.826378i
$199$	12.2410	+	12.2410i	0.867738	+	0.867738i	0.992222	−	0.124483i	$-0.0397273\pi$
$199$	12.2410	+	12.2410i	0.867738	+	0.867738i	−0.124483	+	0.992222i	$0.539727\pi$
$200$		0			0
$201$	−5.73110	−	5.73110i	−0.404241	−	0.404241i
$202$		−	26.1735i		−	1.84156i
$203$	−9.60130			−0.673879
$204$	11.9584	−	9.28280i	0.837253	−	0.649926i
$205$		0			0
$206$			2.18096i			0.151955i
$207$	−4.77488	−	4.77488i	−0.331877	−	0.331877i
$208$	22.8486			1.58426
$209$	0.0795598	+	0.0795598i	0.00550327	+	0.00550327i
$210$		0			0
$211$	−13.1260	+	13.1260i	−0.903632	+	0.903632i	−0.995748	−	0.0921164i	$-0.970637\pi$
$211$	−13.1260	+	13.1260i	−0.903632	+	0.903632i	0.0921164	+	0.995748i	$0.470637\pi$
$212$		−	60.6087i		−	4.16262i
$213$		−	3.13750i		−	0.214978i
$214$	18.9600	−	18.9600i	1.29608	−	1.29608i
$215$		0			0
$216$	23.8461	+	23.8461i	1.62252	+	1.62252i
$217$	−14.1624			−0.961404
$218$	−18.6084	−	18.6084i	−1.26032	−	1.26032i
$219$			5.39322i			0.364440i
$220$		0			0
$221$	0.901555	−	7.15741i	0.0606451	−	0.481460i
$222$	6.49412			0.435857
$223$			20.9166i			1.40068i	0.713808	+	0.700341i	$0.246969\pi$
$223$			20.9166i			1.40068i	−0.713808	+	0.700341i	$0.753031\pi$
$224$	60.6394	+	60.6394i	4.05164	+	4.05164i
$225$		0			0
$226$	8.82622	+	8.82622i	0.587111	+	0.587111i
$227$	−15.5588	+	15.5588i	−1.03267	+	1.03267i	−0.0332266	+	0.999448i	$0.510578\pi$
$227$	−15.5588	+	15.5588i	−1.03267	+	1.03267i	−0.999448	+	0.0332266i	$0.989422\pi$
$228$	0.120087	−	0.120087i	0.00795298	−	0.00795298i
$229$			10.6775i			0.705589i	0.935701	+	0.352795i	$0.114769\pi$
$229$			10.6775i			0.705589i	−0.935701	+	0.352795i	$0.885231\pi$
$230$		0			0
$231$	5.84107	−	5.84107i	0.384314	−	0.384314i
$232$	−12.2342	+	12.2342i	−0.803218	+	0.803218i
$233$	10.6763	+	10.6763i	0.699426	+	0.699426i	0.964287	−	0.264860i	$-0.0853259\pi$
$233$	10.6763	+	10.6763i	0.699426	+	0.699426i	−0.264860	+	0.964287i	$0.585326\pi$
$234$	11.8283			0.773241
$235$		0			0
$236$		−	37.4709i		−	2.43915i
$237$	−2.78331			−0.180796
$238$	42.5788	−	33.0522i	2.75997	−	2.14246i
$239$	−13.2142			−0.854757			−0.427378	−	0.904073i	$-0.640563\pi$
$239$	−13.2142			−0.854757			−0.427378	+	0.904073i	$0.640563\pi$
$240$		0			0
$241$	−9.00000	−	9.00000i	−0.579741	−	0.579741i	0.355091	−	0.934832i	$-0.384450\pi$
$241$	−9.00000	−	9.00000i	−0.579741	−	0.579741i	−0.934832	+	0.355091i	$0.884450\pi$
$242$	−13.6858			−0.879759
$243$	10.5683	+	10.5683i	0.677957	+	0.677957i
$244$	−32.3011	+	32.3011i	−2.06787	+	2.06787i
$245$		0			0
$246$			10.0266i			0.639271i
$247$		−	0.0809292i		−	0.00514940i
$248$	−18.0461	+	18.0461i	−1.14593	+	1.14593i
$249$	−0.271473	+	0.271473i	−0.0172039	+	0.0172039i
$250$		0			0
$251$	2.93595			0.185316			0.0926578	−	0.995698i	$-0.470464\pi$
$251$	2.93595			0.185316			0.0926578	+	0.995698i	$0.470464\pi$
$252$	45.2531	+	45.2531i	2.85068	+	2.85068i
$253$			6.54206i			0.411296i
$254$	−29.0597			−1.82337
$255$		0			0
$256$	17.4284			1.08928
$257$		−	13.0537i		−	0.814269i	−0.913368	−	0.407135i	$-0.866528\pi$
$257$		−	13.0537i		−	0.814269i	0.913368	−	0.407135i	$-0.133472\pi$
$258$	−10.6292	−	10.6292i	−0.661745	−	0.661745i
$259$	16.7438			1.04041
$260$		0			0
$261$	−3.51083	+	3.51083i	−0.217315	+	0.217315i
$262$	−24.7993	+	24.7993i	−1.53211	+	1.53211i
$263$		−	7.27549i		−	0.448626i	−0.974517	−	0.224313i	$-0.927986\pi$
$263$		−	7.27549i		−	0.448626i	0.974517	−	0.224313i	$-0.0720138\pi$
$264$		−	14.8857i		−	0.916152i
$265$		0			0
$266$	0.427582	−	0.427582i	0.0262167	−	0.0262167i
$267$	−0.235136	−	0.235136i	−0.0143901	−	0.0143901i
$268$	−60.8340			−3.71603
$269$	−2.85304	−	2.85304i	−0.173953	−	0.173953i	0.614761	−	0.788714i	$-0.289253\pi$
$269$	−2.85304	−	2.85304i	−0.173953	−	0.173953i	−0.788714	+	0.614761i	$0.789253\pi$
$270$		0			0
$271$	25.4636			1.54680			0.773401	−	0.633918i	$-0.218554\pi$
$271$	25.4636			1.54680			0.773401	+	0.633918i	$0.218554\pi$
$272$	6.72901	−	53.4214i	0.408006	−	3.23915i
$273$	−5.94161			−0.359603
$274$			13.3778i			0.808182i
$275$		0			0
$276$	9.87457			0.594379
$277$	−5.33909	−	5.33909i	−0.320795	−	0.320795i	0.528277	−	0.849072i	$-0.322838\pi$
$277$	−5.33909	−	5.33909i	−0.320795	−	0.320795i	−0.849072	+	0.528277i	$0.822838\pi$
$278$	−3.73183	+	3.73183i	−0.223820	+	0.223820i
$279$	−5.17863	+	5.17863i	−0.310037	+	0.310037i
$280$		0			0
$281$			6.24956i			0.372818i	0.982472	+	0.186409i	$0.0596849\pi$
$281$			6.24956i			0.372818i	−0.982472	+	0.186409i	$0.940315\pi$
$282$	12.9905	−	12.9905i	0.773575	−	0.773575i
$283$	13.6812	−	13.6812i	0.813260	−	0.813260i	−0.171861	−	0.985121i	$-0.554978\pi$
$283$	13.6812	−	13.6812i	0.813260	−	0.813260i	0.985121	+	0.171861i	$0.0549781\pi$
$284$	−16.6518	−	16.6518i	−0.988103	−	0.988103i
$285$		0			0
$286$	−8.10298	−	8.10298i	−0.479139	−	0.479139i
$287$			25.8516i			1.52597i
$288$	44.3470			2.61317
$289$	−16.4690	−	4.21579i	−0.968763	−	0.247987i
$290$		0			0
$291$			9.87282i			0.578755i
$292$	28.6237	+	28.6237i	1.67508	+	1.67508i
$293$	28.6474			1.67360			0.836801	−	0.547508i	$-0.184423\pi$
$293$	28.6474			1.67360			0.836801	+	0.547508i	$0.184423\pi$
$294$	−22.0707	−	22.0707i	−1.28719	−	1.28719i
$295$		0			0
$296$	21.3354	−	21.3354i	1.24010	−	1.24010i
$297$		−	9.37566i		−	0.544031i
$298$		−	9.34470i		−	0.541324i
$299$	3.32733	−	3.32733i	0.192425	−	0.192425i
$300$		0			0
$301$	−27.4053	−	27.4053i	−1.57961	−	1.57961i
$302$	−21.6479			−1.24570
$303$	4.80753	+	4.80753i	0.276186	+	0.276186i
$304$		−	0.604039i		−	0.0346440i
$305$		0			0
$306$	3.48350	−	27.6554i	0.199138	−	1.58095i
$307$	16.8718			0.962922			0.481461	−	0.876468i	$-0.340106\pi$
$307$	16.8718			0.962922			0.481461	+	0.876468i	$0.340106\pi$
$308$		−	62.0012i		−	3.53285i
$309$	−0.400598	−	0.400598i	−0.0227892	−	0.0227892i
$310$		0			0
$311$	3.26758	+	3.26758i	0.185288	+	0.185288i	0.793655	−	0.608368i	$-0.208175\pi$
$311$	3.26758	+	3.26758i	0.185288	+	0.185288i	−0.608368	+	0.793655i	$0.708175\pi$
$312$	−7.57097	+	7.57097i	−0.428622	+	0.428622i
$313$	−6.96224	+	6.96224i	−0.393529	+	0.393529i	−0.875943	−	0.482414i	$-0.839760\pi$
$313$	−6.96224	+	6.96224i	−0.393529	+	0.393529i	0.482414	+	0.875943i	$0.339760\pi$
$314$		−	25.5442i		−	1.44154i
$315$		0			0
$316$	−14.7720	+	14.7720i	−0.830991	+	0.830991i
$317$	20.9932	−	20.9932i	1.17910	−	1.17910i	0.199123	−	0.979974i	$-0.436191\pi$
$317$	20.9932	−	20.9932i	1.17910	−	1.17910i	0.979974	−	0.199123i	$-0.0638094\pi$
$318$	15.3739	+	15.3739i	0.862124	+	0.862124i
$319$	4.81017			0.269318
$320$		0			0
$321$			6.96511i			0.388755i
$322$	35.1593			1.95935
$323$	−0.189218	−	0.0238340i	−0.0105284	−	0.00132616i
$324$	25.3908			1.41060
$325$		0			0
$326$	−22.8575	−	22.8575i	−1.26596	−	1.26596i
$327$	6.83595			0.378029
$328$	32.9408	+	32.9408i	1.81885	+	1.81885i
$329$	33.4935	−	33.4935i	1.84656	−	1.84656i
$330$		0			0
$331$			15.8142i			0.869227i	0.900617	+	0.434614i	$0.143115\pi$
$331$			15.8142i			0.869227i	−0.900617	+	0.434614i	$0.856885\pi$
$332$			2.88160i			0.158149i
$333$	6.12256	−	6.12256i	0.335514	−	0.335514i
$334$	−19.4765	+	19.4765i	−1.06571	+	1.06571i
$335$		0			0
$336$	−44.3469			−2.41932
$337$	−21.2541	−	21.2541i	−1.15779	−	1.15779i	−0.984951	−	0.172837i	$-0.944707\pi$
$337$	−21.2541	−	21.2541i	−1.15779	−	1.15779i	−0.172837	−	0.984951i	$-0.555293\pi$
$338$		−	26.7601i		−	1.45556i
$339$	−3.24239			−0.176102
$340$		0			0
$341$	7.09523			0.384228
$342$		−	0.312701i		−	0.0169089i
$343$	−32.8722	−	32.8722i	−1.77493	−	1.77493i
$344$	−69.8412			−3.76558
$345$		0			0
$346$	−3.68596	+	3.68596i	−0.198158	+	0.198158i
$347$	17.9011	−	17.9011i	0.960982	−	0.960982i	−0.0382850	−	0.999267i	$-0.512189\pi$
$347$	17.9011	−	17.9011i	0.960982	−	0.960982i	0.999267	+	0.0382850i	$0.0121895\pi$
$348$		−	7.26047i		−	0.389202i
$349$		−	2.52854i		−	0.135349i	−0.997707	−	0.0676747i	$-0.978442\pi$
$349$		−	2.52854i		−	0.135349i	0.997707	−	0.0676747i	$-0.0215580\pi$
$350$		0			0
$351$	−4.76852	+	4.76852i	−0.254525	+	0.254525i
$352$	−30.3798	−	30.3798i	−1.61925	−	1.61925i
$353$	0.839563			0.0446854			0.0223427	−	0.999750i	$-0.492888\pi$
$353$	0.839563			0.0446854			0.0223427	+	0.999750i	$0.492888\pi$
$354$	9.50480	+	9.50480i	0.505175	+	0.505175i
$355$		0			0
$356$	−2.49590			−0.132282
$357$	−1.74983	+	13.8919i	−0.0926110	+	0.735235i
$358$	5.82032			0.307613
$359$			14.0641i			0.742276i	0.928578	+	0.371138i	$0.121032\pi$
$359$			14.0641i			0.742276i	−0.928578	+	0.371138i	$0.878968\pi$
$360$		0			0
$361$	18.9979			0.999887
$362$	42.7639	+	42.7639i	2.24762	+	2.24762i
$363$	2.51381	−	2.51381i	0.131941	−	0.131941i
$364$	−31.5342	+	31.5342i	−1.65284	+	1.65284i
$365$		0			0
$366$		−	16.3869i		−	0.856555i
$367$	19.4035	−	19.4035i	1.01286	−	1.01286i	0.0129403	−	0.999916i	$-0.495881\pi$
$367$	19.4035	−	19.4035i	1.01286	−	1.01286i	0.999916	−	0.0129403i	$-0.00411913\pi$
$368$	24.8345	−	24.8345i	1.29459	−	1.29459i
$369$	9.45292	+	9.45292i	0.492099	+	0.492099i
$370$		0			0
$371$	39.6385	+	39.6385i	2.05793	+	2.05793i
$372$		−	10.7095i		−	0.555264i
$373$	−0.812952			−0.0420931			−0.0210465	−	0.999778i	$-0.506700\pi$
$373$	−0.812952			−0.0420931			−0.0210465	+	0.999778i	$0.506700\pi$
$374$	−21.3316	+	16.5589i	−1.10303	+	0.856241i
$375$		0			0
$376$		−	85.3568i		−	4.40194i
$377$	−2.44649	−	2.44649i	−0.126000	−	0.126000i
$378$	−50.3880			−2.59168
$379$	17.6119	+	17.6119i	0.904665	+	0.904665i	0.995835	−	0.0911706i	$-0.0290608\pi$
$379$	17.6119	+	17.6119i	0.904665	+	0.904665i	−0.0911706	+	0.995835i	$0.529061\pi$
$380$		0			0
$381$	5.33767	−	5.33767i	0.273457	−	0.273457i
$382$			28.6280i			1.46474i
$383$			14.9723i			0.765050i	0.923945	+	0.382525i	$0.124945\pi$
$383$			14.9723i			0.765050i	−0.923945	+	0.382525i	$0.875055\pi$
$384$	−11.0766	+	11.0766i	−0.565253	+	0.565253i
$385$		0			0
$386$	20.6265	+	20.6265i	1.04986	+	1.04986i
$387$	−20.0421			−1.01880
$388$	52.3985	+	52.3985i	2.66013	+	2.66013i
$389$		−	3.25025i		−	0.164794i	−0.996600	−	0.0823970i	$-0.973742\pi$
$389$		−	3.25025i		−	0.164794i	0.996600	−	0.0823970i	$-0.0262575\pi$
$390$		0			0
$391$	−6.79960	−	8.75943i	−0.343870	−	0.442983i
$392$	−145.020			−7.32462
$393$		−	9.11024i		−	0.459551i
$394$	−32.1974	−	32.1974i	−1.62208	−	1.62208i
$395$		0			0
$396$	−22.6715	−	22.6715i	−1.13928	−	1.13928i
$397$	4.23535	−	4.23535i	0.212566	−	0.212566i	−0.592790	−	0.805357i	$-0.701974\pi$
$397$	4.23535	−	4.23535i	0.212566	−	0.212566i	0.805357	+	0.592790i	$0.201974\pi$
$398$	−32.9588	+	32.9588i	−1.65208	+	1.65208i
$399$			0.157076i			0.00786364i
$400$		0			0
$401$	−17.7838	+	17.7838i	−0.888079	+	0.888079i	−0.994338	−	0.106259i	$-0.966113\pi$
$401$	−17.7838	+	17.7838i	−0.888079	+	0.888079i	0.106259	+	0.994338i	$0.466113\pi$
$402$	15.4310	−	15.4310i	0.769630	−	0.769630i
$403$	−3.60868	−	3.60868i	−0.179761	−	0.179761i
$404$	51.0305			2.53886
$405$		0			0
$406$		−	25.8516i		−	1.28299i
$407$	−8.38851			−0.415803
$408$	15.4717	+	19.9311i	0.765964	+	0.986736i
$409$	26.1116			1.29113			0.645567	−	0.763704i	$-0.276621\pi$
$409$	26.1116			1.29113			0.645567	+	0.763704i	$0.276621\pi$
$410$		0			0
$411$	−2.45723	−	2.45723i	−0.121206	−	0.121206i
$412$	−4.25223			−0.209492
$413$	24.5062	+	24.5062i	1.20587	+	1.20587i
$414$	12.8564	−	12.8564i	0.631857	−	0.631857i
$415$		0			0
$416$			30.9028i			1.51513i
$417$		−	1.37092i		−	0.0671343i
$418$	−0.214215	+	0.214215i	−0.0104776	+	0.0104776i
$419$	−12.2813	+	12.2813i	−0.599981	+	0.599981i	−0.940307	−	0.340326i	$-0.889462\pi$
$419$	−12.2813	+	12.2813i	−0.599981	+	0.599981i	0.340326	+	0.940307i	$0.389462\pi$
$420$		0			0
$421$	−1.60876			−0.0784063			−0.0392032	−	0.999231i	$-0.512482\pi$
$421$	−1.60876			−0.0784063			−0.0392032	+	0.999231i	$0.512482\pi$
$422$	−35.3419	−	35.3419i	−1.72041	−	1.72041i
$423$		−	24.4946i		−	1.19097i
$424$	101.017			4.90582
$425$		0			0
$426$	8.44773			0.409294
$427$		−	42.2503i		−	2.04463i
$428$	36.9663	+	36.9663i	1.78683	+	1.78683i
$429$	2.97670			0.143716
$430$		0			0
$431$	−19.6629	+	19.6629i	−0.947128	+	0.947128i	−0.998671	−	0.0515425i	$-0.983586\pi$
$431$	−19.6629	+	19.6629i	−0.947128	+	0.947128i	0.0515425	+	0.998671i	$0.483586\pi$
$432$	−35.5912	+	35.5912i	−1.71238	+	1.71238i
$433$			32.7970i			1.57613i	0.615595	+	0.788063i	$0.288916\pi$
$433$			32.7970i			1.57613i	−0.615595	+	0.788063i	$0.711084\pi$
$434$		−	38.1323i		−	1.83041i
$435$		0			0
$436$	36.2808	−	36.2808i	1.73754	−	1.73754i
$437$	−0.0879634	−	0.0879634i	−0.00420786	−	0.00420786i
$438$	−14.5213			−0.693854
$439$	14.9000	+	14.9000i	0.711136	+	0.711136i	0.966773	−	0.255637i	$-0.0822851\pi$
$439$	14.9000	+	14.9000i	0.711136	+	0.711136i	−0.255637	+	0.966773i	$0.582285\pi$
$440$		0			0
$441$	−41.6160			−1.98171
$442$	19.2714	+	2.42744i	0.916646	+	0.115462i
$443$	21.4940			1.02121			0.510605	−	0.859815i	$-0.329421\pi$
$443$	21.4940			1.02121			0.510605	+	0.859815i	$0.329421\pi$
$444$			12.6616i			0.600893i
$445$		0			0
$446$	−56.3182			−2.66674
$447$	1.71643	+	1.71643i	0.0811843	+	0.0811843i
$448$	−73.6020	+	73.6020i	−3.47737	+	3.47737i
$449$	−17.6314	+	17.6314i	−0.832079	+	0.832079i	−0.987801	−	0.155722i	$-0.950230\pi$
$449$	−17.6314	+	17.6314i	−0.832079	+	0.832079i	0.155722	+	0.987801i	$0.450230\pi$
$450$		0			0
$451$		−	12.9514i		−	0.609859i
$452$	−17.2085	+	17.2085i	−0.809420	+	0.809420i
$453$	3.97628	−	3.97628i	0.186822	−	0.186822i
$454$	−41.8922	−	41.8922i	−1.96610	−	1.96610i
$455$		0			0
$456$	0.200151	+	0.200151i	0.00937292	+	0.00937292i
$457$			11.3434i			0.530621i	0.964163	+	0.265311i	$0.0854745\pi$
$457$			11.3434i			0.530621i	−0.964163	+	0.265311i	$0.914526\pi$
$458$	−28.7492			−1.34336
$459$	9.74475	+	12.5535i	0.454846	+	0.585945i
$460$		0			0
$461$			40.5169i			1.88706i	0.331287	+	0.943530i	$0.392517\pi$
$461$			40.5169i			1.88706i	−0.331287	+	0.943530i	$0.607483\pi$
$462$	15.7271	+	15.7271i	0.731691	+	0.731691i
$463$	−6.91009			−0.321139			−0.160570	−	0.987025i	$-0.551333\pi$
$463$	−6.91009			−0.321139			−0.160570	+	0.987025i	$0.551333\pi$
$464$	−18.2600	−	18.2600i	−0.847701	−	0.847701i
$465$		0			0
$466$	−28.7459	+	28.7459i	−1.33163	+	1.33163i
$467$		−	13.1768i		−	0.609748i	−0.952393	−	0.304874i	$-0.901386\pi$
$467$		−	13.1768i		−	0.609748i	0.952393	−	0.304874i	$-0.0986144\pi$
$468$			23.0617i			1.06603i
$469$	39.7858	−	39.7858i	1.83714	−	1.83714i
$470$		0			0
$471$	4.69194	+	4.69194i	0.216193	+	0.216193i
$472$	62.4531			2.87464
$473$	13.7298	+	13.7298i	0.631298	+	0.631298i
$474$		−	7.49408i		−	0.344215i
$475$		0			0
$476$	64.4420	+	83.0160i	2.95370	+	3.80503i
$477$	28.9885			1.32729
$478$		−	35.5793i		−	1.62736i
$479$	−28.7306	−	28.7306i	−1.31273	−	1.31273i	−0.919392	−	0.393342i	$-0.871319\pi$
$479$	−28.7306	−	28.7306i	−1.31273	−	1.31273i	−0.393342	−	0.919392i	$-0.628681\pi$
$480$		0			0
$481$	4.26645	+	4.26645i	0.194533	+	0.194533i
$482$	24.2325	−	24.2325i	1.10376	−	1.10376i
$483$	−6.45804	+	6.45804i	−0.293851	+	0.293851i
$484$		−	26.6833i		−	1.21288i
$485$		0			0
$486$	−28.4552	+	28.4552i	−1.29075	+	1.29075i
$487$	0.328023	−	0.328023i	0.0148641	−	0.0148641i	−0.699636	−	0.714500i	$-0.746654\pi$
$487$	0.328023	−	0.328023i	0.0148641	−	0.0148641i	0.714500	+	0.699636i	$0.246654\pi$
$488$	−53.8365	−	53.8365i	−2.43706	−	2.43706i
$489$	8.39691			0.379721
$490$		0			0
$491$		−	27.4036i		−	1.23670i	−0.785901	−	0.618352i	$-0.787800\pi$
$491$		−	27.4036i		−	1.23670i	0.785901	−	0.618352i	$-0.212200\pi$
$492$	−19.5489			−0.881330
$493$	−6.44054	+	4.99954i	−0.290067	+	0.225168i
$494$	0.217902			0.00980389
$495$		0			0
$496$	−26.9344	−	26.9344i	−1.20939	−	1.20939i
$497$	21.7808			0.977002
$498$	−0.730942	−	0.730942i	−0.0327543	−	0.0327543i
$499$	11.2441	−	11.2441i	0.503355	−	0.503355i	−0.409124	−	0.912479i	$-0.634166\pi$
$499$	11.2441	−	11.2441i	0.503355	−	0.503355i	0.912479	+	0.409124i	$0.134166\pi$
$500$		0			0
$501$		−	7.15485i		−	0.319655i
$502$			7.90507i			0.352820i
$503$	31.0421	−	31.0421i	1.38410	−	1.38410i	0.546908	−	0.837193i	$-0.315805\pi$
$503$	31.0421	−	31.0421i	1.38410	−	1.38410i	0.837193	−	0.546908i	$-0.184195\pi$
$504$	−75.4238	+	75.4238i	−3.35964	+	3.35964i
$505$		0			0
$506$	−17.6145			−0.783061
$507$	4.91528	+	4.91528i	0.218295	+	0.218295i
$508$		−	56.6578i		−	2.51378i
$509$	−31.6453			−1.40265			−0.701326	−	0.712841i	$-0.747408\pi$
$509$	−31.6453			−1.40265			−0.701326	+	0.712841i	$0.747408\pi$
$510$		0			0
$511$	−37.4402			−1.65626
$512$			2.13198i			0.0942212i
$513$	0.126063	+	0.126063i	0.00556584	+	0.00556584i
$514$	35.1472			1.55028
$515$		0			0
$516$	20.7238	−	20.7238i	0.912314	−	0.912314i
$517$	−16.7800	+	16.7800i	−0.737983	+	0.737983i
$518$			45.0828i			1.98082i
$519$		−	1.35407i		−	0.0594370i
$520$		0			0
$521$	−1.22346	+	1.22346i	−0.0536006	+	0.0536006i	−0.733399	−	0.679798i	$-0.762067\pi$
$521$	−1.22346	+	1.22346i	−0.0536006	+	0.0536006i	0.679798	+	0.733399i	$0.262067\pi$
$522$	−9.45292	−	9.45292i	−0.413743	−	0.413743i
$523$	−19.9906			−0.874130			−0.437065	−	0.899430i	$-0.643982\pi$
$523$	−19.9906			−0.874130			−0.437065	+	0.899430i	$0.643982\pi$
$524$	−48.3512	−	48.3512i	−2.11223	−	2.11223i
$525$		0			0
$526$	19.5893			0.854134
$527$	−9.50010	+	7.37455i	−0.413831	+	0.321241i
$528$	22.2175			0.966890
$529$			15.7669i			0.685519i
$530$		0			0
$531$	17.9220			0.777748
$532$	0.833658	+	0.833658i	0.0361437	+	0.0361437i
$533$	−6.58717	+	6.58717i	−0.285322	+	0.285322i
$534$	0.633105	−	0.633105i	0.0273971	−	0.0273971i
$535$		0			0
$536$		−	101.392i		−	4.37949i
$537$	−1.06907	+	1.06907i	−0.0461339	+	0.0461339i
$538$	7.68182	−	7.68182i	0.331187	−	0.331187i
$539$	28.5090	+	28.5090i	1.22797	+	1.22797i
$540$		0			0
$541$	−2.66470	−	2.66470i	−0.114564	−	0.114564i	0.647501	−	0.762065i	$-0.275814\pi$
$541$	−2.66470	−	2.66470i	−0.114564	−	0.114564i	−0.762065	+	0.647501i	$0.775814\pi$
$542$			68.5608i			2.94494i
$543$	−15.7097			−0.674168
$544$	72.2526	+	9.10101i	3.09781	+	0.390203i
$545$		0			0
$546$		−	15.9978i		−	0.684643i
$547$	4.16866	+	4.16866i	0.178239	+	0.178239i	0.790588	−	0.612349i	$-0.209775\pi$
$547$	4.16866	+	4.16866i	0.178239	+	0.178239i	−0.612349	+	0.790588i	$0.709775\pi$
$548$	−26.0827			−1.11420
$549$	−15.4493	−	15.4493i	−0.659360	−	0.659360i
$550$		0			0
$551$	−0.0646768	+	0.0646768i	−0.00275532	+	0.00275532i
$552$			16.4580i			0.700500i
$553$		−	19.3220i		−	0.821655i
$554$	14.3755	−	14.3755i	0.610758	−	0.610758i
$555$		0			0
$556$	−7.27596	−	7.27596i	−0.308569	−	0.308569i
$557$	−15.3775			−0.651564			−0.325782	−	0.945445i	$-0.605627\pi$
$557$	−15.3775			−0.651564			−0.325782	+	0.945445i	$0.605627\pi$
$558$	−13.9435	−	13.9435i	−0.590275	−	0.590275i
$559$		−	13.9662i		−	0.590705i
$560$		0			0
$561$	0.876652	−	6.95971i	0.0370123	−	0.293839i
$562$	−16.8270			−0.709803
$563$			35.0604i			1.47762i	0.673915	+	0.738809i	$0.264611\pi$
$563$			35.0604i			1.47762i	−0.673915	+	0.738809i	$0.735389\pi$
$564$	25.3277	+	25.3277i	1.06649	+	1.06649i
$565$		0			0
$566$	36.8366	+	36.8366i	1.54836	+	1.54836i
$567$	−16.6057	+	16.6057i	−0.697375	+	0.697375i
$568$	27.7537	−	27.7537i	1.16452	−	1.16452i
$569$			11.0645i			0.463849i	0.972734	+	0.231925i	$0.0745023\pi$
$569$			11.0645i			0.463849i	−0.972734	+	0.231925i	$0.925498\pi$
$570$		0			0
$571$	25.0574	−	25.0574i	1.04862	−	1.04862i	0.0498615	−	0.998756i	$-0.484122\pi$
$571$	25.0574	−	25.0574i	1.04862	−	1.04862i	0.998756	−	0.0498615i	$-0.0158780\pi$
$572$	15.7984	−	15.7984i	0.660564	−	0.660564i
$573$	−5.25837	−	5.25837i	−0.219672	−	0.219672i
$574$	−69.6054			−2.90527
$575$		0			0
$576$			53.8269i			2.24279i
$577$	11.6539			0.485158			0.242579	−	0.970132i	$-0.422007\pi$
$577$	11.6539			0.485158			0.242579	+	0.970132i	$0.422007\pi$
$578$	11.3510	−	44.3428i	0.472140	−	1.84442i
$579$	−7.57732			−0.314903
$580$		0			0
$581$	−1.88459	−	1.88459i	−0.0781859	−	0.0781859i
$582$	−26.5826			−1.10188
$583$	−19.8586	−	19.8586i	−0.822458	−	0.822458i
$584$	−47.7074	+	47.7074i	−1.97415	+	1.97415i
$585$		0			0
$586$			77.1334i			3.18635i
$587$		−	20.1225i		−	0.830545i	−0.909697	−	0.415273i	$-0.863686\pi$
$587$		−	20.1225i		−	0.830545i	0.909697	−	0.415273i	$-0.136314\pi$
$588$	43.0314	−	43.0314i	1.77458	−	1.77458i
$589$	−0.0954013	+	0.0954013i	−0.00393094	+	0.00393094i
$590$		0			0
$591$	11.8280			0.486539
$592$	31.8439	+	31.8439i	1.30878	+	1.30878i
$593$			24.0516i			0.987682i	0.869552	+	0.493841i	$0.164407\pi$
$593$			24.0516i			0.987682i	−0.869552	+	0.493841i	$0.835593\pi$
$594$	25.2440			1.03577
$595$		0			0
$596$	18.2194			0.746295
$597$		−	12.1077i		−	0.495536i
$598$	8.95886	+	8.95886i	0.366355	+	0.366355i
$599$	−6.59301			−0.269383			−0.134691	−	0.990888i	$-0.543004\pi$
$599$	−6.59301			−0.269383			−0.134691	+	0.990888i	$0.543004\pi$
$600$		0			0
$601$	17.8567	−	17.8567i	0.728391	−	0.728391i	−0.241908	−	0.970299i	$-0.577773\pi$
$601$	17.8567	−	17.8567i	0.728391	−	0.728391i	0.970299	+	0.241908i	$0.0777733\pi$
$602$	73.7889	−	73.7889i	3.00741	−	3.00741i
$603$		−	29.0963i		−	1.18489i
$604$		−	42.2070i		−	1.71738i
$605$		0			0
$606$	−12.9443	+	12.9443i	−0.525826	+	0.525826i
$607$	20.7247	+	20.7247i	0.841191	+	0.841191i	0.989014	−	0.147823i	$-0.0472267\pi$
$607$	20.7247	+	20.7247i	0.841191	+	0.841191i	−0.147823	+	0.989014i	$0.547227\pi$
$608$	0.816964			0.0331323
$609$	4.74840	+	4.74840i	0.192415	+	0.192415i
$610$		0			0
$611$	17.0688			0.690530
$612$	53.9197	+	6.79178i	2.17958	+	0.274542i
$613$	−42.5066			−1.71682			−0.858412	−	0.512961i	$-0.828549\pi$
$613$	−42.5066			−1.71682			−0.858412	+	0.512961i	$0.828549\pi$
$614$			45.4273i			1.83330i
$615$		0			0
$616$	103.338			4.16361
$617$	11.6869	+	11.6869i	0.470497	+	0.470497i	0.902075	−	0.431579i	$-0.142043\pi$
$617$	11.6869	+	11.6869i	0.470497	+	0.470497i	−0.431579	+	0.902075i	$0.642043\pi$
$618$	1.07861	−	1.07861i	0.0433881	−	0.0433881i
$619$	0.136058	−	0.136058i	0.00546862	−	0.00546862i	−0.704367	−	0.709836i	$-0.748769\pi$
$619$	0.136058	−	0.136058i	0.00546862	−	0.00546862i	0.709836	+	0.704367i	$0.248769\pi$
$620$		0			0
$621$			10.3660i			0.415972i
$622$	−8.79798	+	8.79798i	−0.352767	+	0.352767i
$623$	1.63233	−	1.63233i	0.0653981	−	0.0653981i
$624$	−11.2999	−	11.2999i	−0.452359	−	0.452359i
$625$		0			0
$626$	−18.7459	−	18.7459i	−0.749236	−	0.749236i
$627$		−	0.0786938i		−	0.00314273i
$628$	49.8035			1.98738
$629$	11.2317	−	8.71874i	0.447838	−	0.347639i
$630$		0			0
$631$		−	29.7771i		−	1.18541i	−0.805420	−	0.592704i	$-0.798060\pi$
$631$		−	29.7771i		−	1.18541i	0.805420	−	0.592704i	$-0.201940\pi$
$632$	−24.6206	−	24.6206i	−0.979357	−	0.979357i
$633$	12.9831			0.516034
$634$	56.5244	+	56.5244i	2.24487	+	2.24487i
$635$		0			0
$636$	−29.9745	+	29.9745i	−1.18857	+	1.18857i
$637$		−	28.9997i		−	1.14901i
$638$			12.9514i			0.512752i
$639$	7.96440	−	7.96440i	0.315067	−	0.315067i
$640$		0			0
$641$	−32.2217	−	32.2217i	−1.27268	−	1.27268i	−0.944676	−	0.328004i	$-0.893624\pi$
$641$	−32.2217	−	32.2217i	−1.27268	−	1.27268i	−0.328004	−	0.944676i	$-0.606376\pi$
$642$	−18.7536			−0.740145
$643$	27.3260	+	27.3260i	1.07763	+	1.07763i	0.996721	+	0.0809091i	$0.0257824\pi$
$643$	27.3260	+	27.3260i	1.07763	+	1.07763i	0.0809091	+	0.996721i	$0.474218\pi$
$644$			68.5502i			2.70125i
$645$		0			0
$646$	0.0641733	−	0.509470i	0.00252486	−	0.0200448i
$647$	−5.31423			−0.208924			−0.104462	−	0.994529i	$-0.533312\pi$
$647$	−5.31423			−0.208924			−0.104462	+	0.994529i	$0.533312\pi$
$648$			42.3190i			1.66245i
$649$	−12.2774	−	12.2774i	−0.481931	−	0.481931i
$650$		0			0
$651$	7.00411	+	7.00411i	0.274513	+	0.274513i
$652$	44.5654	−	44.5654i	1.74531	−	1.74531i
$653$	22.6305	−	22.6305i	0.885600	−	0.885600i	−0.108497	−	0.994097i	$-0.534604\pi$
$653$	22.6305	−	22.6305i	0.885600	−	0.885600i	0.994097	+	0.108497i	$0.0346037\pi$
$654$			18.4058i			0.719725i
$655$		0			0
$656$	−49.1653	+	49.1653i	−1.91958	+	1.91958i
$657$	−13.6905	+	13.6905i	−0.534115	+	0.534115i
$658$	90.1815	+	90.1815i	3.51564	+	3.51564i
$659$	35.5696			1.38559			0.692797	−	0.721133i	$-0.256378\pi$
$659$	35.5696			1.38559			0.692797	+	0.721133i	$0.256378\pi$
$660$		0			0
$661$			30.2779i			1.17767i	0.808252	+	0.588837i	$0.200414\pi$
$661$			30.2779i			1.17767i	−0.808252	+	0.588837i	$0.799586\pi$
$662$	−42.5798			−1.65491
$663$	−3.98562	+	3.09388i	−0.154789	+	0.120156i
$664$	−4.80279			−0.186385
$665$		0			0
$666$	16.4850	+	16.4850i	0.638782	+	0.638782i
$667$	−5.31825			−0.205924
$668$	−37.9733	−	37.9733i	−1.46923	−	1.46923i
$669$	10.3445	−	10.3445i	0.399941	−	0.399941i
$670$		0			0
$671$			21.1671i			0.817145i
$672$		−	59.9794i		−	2.31375i
$673$	6.13959	−	6.13959i	0.236664	−	0.236664i	−0.578803	−	0.815467i	$-0.696480\pi$
$673$	6.13959	−	6.13959i	0.236664	−	0.236664i	0.815467	+	0.578803i	$0.196480\pi$
$674$	57.2269	−	57.2269i	2.20430	−	2.20430i
$675$		0			0
$676$	52.1743			2.00670
$677$	−17.7950	−	17.7950i	−0.683919	−	0.683919i	0.276962	−	0.960881i	$-0.410672\pi$
$677$	−17.7950	−	17.7950i	−0.683919	−	0.683919i	−0.960881	+	0.276962i	$0.910672\pi$
$678$		−	8.73015i		−	0.335279i
$679$	−68.5380			−2.63025
$680$		0			0
$681$	15.3895			0.589725
$682$			19.1040i			0.731528i
$683$	−17.2763	−	17.2763i	−0.661058	−	0.661058i	0.294571	−	0.955629i	$-0.404823\pi$
$683$	−17.2763	−	17.2763i	−0.661058	−	0.661058i	−0.955629	+	0.294571i	$0.904823\pi$
$684$	0.609673			0.0233114
$685$		0			0
$686$	88.5085	−	88.5085i	3.37927	−	3.37927i
$687$	5.28064	−	5.28064i	0.201469	−	0.201469i
$688$		−	104.240i		−	3.97413i
$689$			20.2004i			0.769574i
$690$		0			0
$691$	−13.6051	+	13.6051i	−0.517563	+	0.517563i	−0.916833	−	0.399270i	$-0.869264\pi$
$691$	−13.6051	+	13.6051i	−0.517563	+	0.517563i	0.399270	+	0.916833i	$0.369264\pi$
$692$	−7.18652	−	7.18652i	−0.273190	−	0.273190i
$693$	29.6546			1.12648
$694$	48.1988	+	48.1988i	1.82960	+	1.82960i
$695$		0			0
$696$	12.1011			0.458690
$697$	13.4613	+	17.3412i	0.509882	+	0.656844i
$698$	6.80809			0.257690
$699$		−	10.5601i		−	0.399419i
$700$		0			0
$701$	−8.54696			−0.322814			−0.161407	−	0.986888i	$-0.551603\pi$
$701$	−8.54696			−0.322814			−0.161407	+	0.986888i	$0.551603\pi$
$702$	−12.8393	−	12.8393i	−0.484587	−	0.484587i
$703$	0.112790	−	0.112790i	0.00425397	−	0.00425397i
$704$	36.8740	−	36.8740i	1.38974	−	1.38974i
$705$		0			0
$706$			2.26053i			0.0850761i
$707$	−33.3743	+	33.3743i	−1.25517	+	1.25517i
$708$	−18.5315	+	18.5315i	−0.696458	+	0.696458i
$709$	−9.78887	−	9.78887i	−0.367629	−	0.367629i	0.498983	−	0.866612i	$-0.333707\pi$
$709$	−9.78887	−	9.78887i	−0.367629	−	0.367629i	−0.866612	+	0.498983i	$0.833707\pi$
$710$		0			0
$711$	−7.06531	−	7.06531i	−0.264970	−	0.264970i
$712$		−	4.15993i		−	0.155900i
$713$	−7.84467			−0.293785
$714$	−37.4039	−	4.71143i	−1.39981	−	0.176321i
$715$		0			0
$716$			11.3479i			0.424091i
$717$	6.53519	+	6.53519i	0.244061	+	0.244061i
$718$	−37.8677			−1.41321
$719$	−14.0445	−	14.0445i	−0.523771	−	0.523771i	0.394937	−	0.918708i	$-0.370766\pi$
$719$	−14.0445	−	14.0445i	−0.523771	−	0.523771i	−0.918708	+	0.394937i	$0.870766\pi$
$720$		0			0
$721$	2.78099	−	2.78099i	0.103569	−	0.103569i
$722$			51.1518i			1.90367i
$723$			8.90204i			0.331070i
$724$	−83.3769	+	83.3769i	−3.09868	+	3.09868i
$725$		0			0
$726$	6.76844	+	6.76844i	0.251200	+	0.251200i
$727$	7.72932			0.286665			0.143332	−	0.989675i	$-0.454218\pi$
$727$	7.72932			0.286665			0.143332	+	0.989675i	$0.454218\pi$
$728$	−52.5583	−	52.5583i	−1.94794	−	1.94794i
$729$			4.05689i			0.150255i
$730$		0			0
$731$	−32.6538	−	4.11310i	−1.20774	−	0.152129i
$732$	31.9495			1.18089
$733$			12.9264i			0.477449i	0.971087	+	0.238724i	$0.0767292\pi$
$733$			12.9264i			0.477449i	−0.971087	+	0.238724i	$0.923271\pi$
$734$	52.2441	+	52.2441i	1.92837	+	1.92837i
$735$		0			0
$736$	33.5887	+	33.5887i	1.23810	+	1.23810i
$737$	−19.9324	+	19.9324i	−0.734219	+	0.734219i
$738$	−25.4520	+	25.4520i	−0.936902	+	0.936902i
$739$			24.2516i			0.892111i	0.895005	+	0.446056i	$0.147172\pi$
$739$			24.2516i			0.892111i	−0.895005	+	0.446056i	$0.852828\pi$
$740$		0			0
$741$	−0.0400242	+	0.0400242i	−0.00147032	+	0.00147032i
$742$	−106.727	+	106.727i	−3.91807	+	3.91807i
$743$	−25.2324	−	25.2324i	−0.925688	−	0.925688i	0.0717353	−	0.997424i	$-0.477146\pi$
$743$	−25.2324	−	25.2324i	−0.925688	−	0.925688i	−0.997424	+	0.0717353i	$0.977146\pi$
$744$	17.8497			0.654401
$745$		0			0
$746$		−	2.18888i		−	0.0801405i
$747$	−1.37824			−0.0504273
$748$	−32.2850	−	41.5904i	−1.18045	−	1.52069i
$749$	−48.3524			−1.76676
$750$		0			0
$751$	−6.25068	−	6.25068i	−0.228091	−	0.228091i	0.583804	−	0.811895i	$-0.301564\pi$
$751$	−6.25068	−	6.25068i	−0.228091	−	0.228091i	−0.811895	+	0.583804i	$0.801564\pi$
$752$	127.398			4.64573
$753$	−1.45200	−	1.45200i	−0.0529137	−	0.0529137i
$754$	6.58717	−	6.58717i	0.239891	−	0.239891i
$755$		0			0
$756$		−	98.2417i		−	3.57302i
$757$		−	7.60186i		−	0.276294i	−0.990412	−	0.138147i	$-0.955885\pi$
$757$		−	7.60186i		−	0.276294i	0.990412	−	0.138147i	$-0.0441147\pi$
$758$	−47.4203	+	47.4203i	−1.72238	+	1.72238i
$759$	3.23542	−	3.23542i	0.117438	−	0.117438i
$760$		0			0
$761$	21.7693			0.789136			0.394568	−	0.918867i	$-0.370894\pi$
$761$	21.7693			0.789136			0.394568	+	0.918867i	$0.370894\pi$
$762$	14.3717	+	14.3717i	0.520632	+	0.520632i
$763$			47.4558i			1.71801i
$764$	−55.8161			−2.01935
$765$		0			0
$766$	−40.3130			−1.45657
$767$			12.4888i			0.450943i
$768$	−8.61937	−	8.61937i	−0.311025	−	0.311025i
$769$	−41.1671			−1.48452			−0.742262	−	0.670110i	$-0.766247\pi$
$769$	−41.1671			−1.48452			−0.742262	+	0.670110i	$0.766247\pi$
$770$		0			0
$771$	−6.45582	+	6.45582i	−0.232501	+	0.232501i
$772$	−40.2155	+	40.2155i	−1.44739	+	1.44739i
$773$		−	5.37164i		−	0.193204i	−0.995323	−	0.0966022i	$-0.969203\pi$
$773$		−	5.37164i		−	0.193204i	0.995323	−	0.0966022i	$-0.0307975\pi$
$774$		−	53.9635i		−	1.93968i
$775$		0			0
$776$	−87.3330	+	87.3330i	−3.13507	+	3.13507i
$777$	−8.28078	−	8.28078i	−0.297071	−	0.297071i
$778$	8.75130			0.313749
$779$	0.174143	+	0.174143i	0.00623930	+	0.00623930i
$780$		0			0
$781$	−10.9120			−0.390462
$782$	23.5848	−	18.3080i	0.843391	−	0.654691i
$783$	7.62178			0.272380
$784$		−	216.447i		−	7.73027i
$785$		0			0
$786$	24.5294			0.874933
$787$	−17.5629	−	17.5629i	−0.626050	−	0.626050i	0.321021	−	0.947072i	$-0.395974\pi$
$787$	−17.5629	−	17.5629i	−0.626050	−	0.626050i	−0.947072	+	0.321021i	$0.895974\pi$
$788$	62.7753	−	62.7753i	2.23628	−	2.23628i
$789$	−3.59815	+	3.59815i	−0.128098	+	0.128098i
$790$		0			0
$791$		−	22.5090i		−	0.800327i
$792$	37.7867	−	37.7867i	1.34269	−	1.34269i
$793$	10.7657	−	10.7657i	0.382301	−	0.382301i
$794$	11.4037	+	11.4037i	0.404703	+	0.404703i
$795$		0			0
$796$	−64.2599	−	64.2599i	−2.27763	−	2.27763i
$797$		−	8.73114i		−	0.309273i	−0.987971	−	0.154636i	$-0.950579\pi$
$797$		−	8.73114i		−	0.309273i	0.987971	−	0.154636i	$-0.0494206\pi$
$798$	−0.422928			−0.0149715
$799$	5.02685	−	39.9080i	0.177837	−	1.41184i
$800$		0			0
$801$		−	1.19376i		−	0.0421796i
$802$	−47.8829	−	47.8829i	−1.69080	−	1.69080i
$803$	18.7573			0.661929
$804$	30.0859	+	30.0859i	1.06105	+	1.06105i
$805$		0			0
$806$	9.71639	−	9.71639i	0.342245	−	0.342245i
$807$			2.82198i			0.0993386i
$808$			85.0530i			2.99215i
$809$	−28.3946	+	28.3946i	−0.998302	+	0.998302i	−0.999999	−	0.00169682i	$-0.999460\pi$
$809$	−28.3946	+	28.3946i	−0.998302	+	0.998302i	0.00169682	+	0.999999i	$0.499460\pi$
$810$		0			0
$811$	22.0825	+	22.0825i	0.775423	+	0.775423i	0.979049	−	0.203626i	$-0.0652727\pi$
$811$	22.0825	+	22.0825i	0.775423	+	0.775423i	−0.203626	+	0.979049i	$0.565273\pi$
$812$	50.4028			1.76879
$813$	−12.5932	−	12.5932i	−0.441663	−	0.441663i
$814$		−	22.5861i		−	0.791643i
$815$		0			0
$816$	−29.7479	+	23.0921i	−1.04138	+	0.808385i
$817$	−0.369218			−0.0129173
$818$			70.3055i			2.45817i
$819$	−15.0825	−	15.0825i	−0.527026	−	0.527026i
$820$		0			0
$821$	−8.23585	−	8.23585i	−0.287433	−	0.287433i	0.548631	−	0.836064i	$-0.315149\pi$
$821$	−8.23585	−	8.23585i	−0.287433	−	0.287433i	−0.836064	+	0.548631i	$0.815149\pi$
$822$	6.61609	−	6.61609i	0.230763	−	0.230763i
$823$	−7.43349	+	7.43349i	−0.259115	+	0.259115i	−0.824694	−	0.565579i	$-0.808653\pi$
$823$	−7.43349	+	7.43349i	−0.259115	+	0.259115i	0.565579	+	0.824694i	$0.308653\pi$
$824$		−	7.08722i		−	0.246895i
$825$		0			0
$826$	−65.9832	+	65.9832i	−2.29585	+	2.29585i
$827$	−15.4787	+	15.4787i	−0.538249	+	0.538249i	−0.923014	−	0.384766i	$-0.874282\pi$
$827$	−15.4787	+	15.4787i	−0.538249	+	0.538249i	0.384766	+	0.923014i	$0.374282\pi$
$828$	25.0662	+	25.0662i	0.871109	+	0.871109i
$829$	35.5510			1.23474			0.617369	−	0.786674i	$-0.288199\pi$
$829$	35.5510			1.23474			0.617369	+	0.786674i	$0.288199\pi$
$830$		0			0
$831$			5.28098i			0.183195i
$832$	−37.5087			−1.30038
$833$	−67.8031	−	8.54055i	−2.34924	−	0.295912i
$834$	3.69121			0.127816
$835$		0			0
$836$	−0.417656	−	0.417656i	−0.0144449	−	0.0144449i
$837$	11.2425			0.388597
$838$	−33.0675	−	33.0675i	−1.14230	−	1.14230i
$839$	15.6461	−	15.6461i	0.540162	−	0.540162i	−0.383414	−	0.923576i	$-0.625252\pi$
$839$	15.6461	−	15.6461i	0.540162	−	0.540162i	0.923576	+	0.383414i	$0.125252\pi$
$840$		0			0
$841$		−	25.0897i		−	0.865160i
$842$		−	4.33160i		−	0.149277i
$843$	3.09077	−	3.09077i	0.106452	−	0.106452i
$844$	68.9061	−	68.9061i	2.37185	−	2.37185i
$845$		0			0
$846$	65.9518			2.26747
$847$	17.4511	+	17.4511i	0.599626	+	0.599626i
$848$			150.771i			5.17751i
$849$	−13.5322			−0.464425
$850$		0			0
$851$	9.27455			0.317928
$852$			16.4706i			0.564272i
$853$	−27.9585	−	27.9585i	−0.957281	−	0.957281i	0.0418433	−	0.999124i	$-0.486677\pi$
$853$	−27.9585	−	27.9585i	−0.957281	−	0.957281i	−0.999124	+	0.0418433i	$0.986677\pi$
$854$	113.759			3.89276
$855$		0			0
$856$	−61.6120	+	61.6120i	−2.10586	+	2.10586i
$857$	−14.5933	+	14.5933i	−0.498498	+	0.498498i	−0.910970	−	0.412472i	$-0.864665\pi$
$857$	−14.5933	+	14.5933i	−0.498498	+	0.498498i	0.412472	+	0.910970i	$0.364665\pi$
$858$			8.01478i			0.273620i
$859$			42.8019i			1.46038i	0.683243	+	0.730191i	$0.260569\pi$
$859$			42.8019i			1.46038i	−0.683243	+	0.730191i	$0.739431\pi$
$860$		0			0
$861$	12.7851	−	12.7851i	0.435715	−	0.435715i
$862$	−52.9425	−	52.9425i	−1.80323	−	1.80323i
$863$	19.5632			0.665940			0.332970	−	0.942937i	$-0.391949\pi$
$863$	19.5632			0.665940			0.332970	+	0.942937i	$0.391949\pi$
$864$	−48.1372	−	48.1372i	−1.63766	−	1.63766i
$865$		0			0
$866$	−88.3062			−3.00077
$867$	6.05991	+	10.2298i	0.205805	+	0.347423i
$868$	74.3466			2.52349
$869$			9.68017i			0.328377i
$870$		0			0
$871$	20.2755			0.687008
$872$	60.4695	+	60.4695i	2.04776	+	2.04776i
$873$	−25.0617	+	25.0617i	−0.848210	+	0.848210i
$874$	0.236842	−	0.236842i	0.00801129	−	0.00801129i
$875$		0			0
$876$		−	28.3122i		−	0.956580i
$877$	−22.6041	+	22.6041i	−0.763286	+	0.763286i	−0.976915	−	0.213629i	$-0.931472\pi$
$877$	−22.6041	+	22.6041i	−0.763286	+	0.763286i	0.213629	+	0.976915i	$0.431472\pi$
$878$	−40.1182	+	40.1182i	−1.35392	+	1.35392i
$879$	−14.1678	−	14.1678i	−0.477868	−	0.477868i
$880$		0			0
$881$	9.45655	+	9.45655i	0.318599	+	0.318599i	0.848229	−	0.529630i	$-0.177669\pi$
$881$	9.45655	+	9.45655i	0.318599	+	0.318599i	−0.529630	+	0.848229i	$0.677669\pi$
$882$		−	112.051i		−	3.77296i
$883$	8.07936			0.271892			0.135946	−	0.990716i	$-0.456593\pi$
$883$	8.07936			0.271892			0.135946	+	0.990716i	$0.456593\pi$
$884$	−4.73279	+	37.5734i	−0.159181	+	1.26373i
$885$		0			0
$886$			57.8727i			1.94427i
$887$	37.1386	+	37.1386i	1.24699	+	1.24699i	0.957041	+	0.289952i	$0.0936392\pi$
$887$	37.1386	+	37.1386i	1.24699	+	1.24699i	0.289952	+	0.957041i	$0.406361\pi$
$888$	−21.1032			−0.708177
$889$	37.0546	+	37.0546i	1.24277	+	1.24277i
$890$		0			0
$891$	8.31934	−	8.31934i	0.278708	−	0.278708i
$892$		−	109.804i		−	3.67650i
$893$		−	0.451242i		−	0.0151002i
$894$	−4.62149	+	4.62149i	−0.154566	+	0.154566i
$895$		0			0
$896$	−76.8951	−	76.8951i	−2.56889	−	2.56889i
$897$	−3.29111			−0.109887
$898$	−47.4728	−	47.4728i	−1.58419	−	1.58419i
$899$			5.76795i			0.192372i
$900$		0			0
$901$	47.2298	+	5.94911i	1.57345	+	0.198194i
$902$	34.8718			1.16110
$903$			27.1070i			0.902064i
$904$	−28.6816	−	28.6816i	−0.953934	−	0.953934i
$905$		0			0
$906$	10.7061	+	10.7061i	0.355688	+	0.355688i
$907$	−11.0571	+	11.0571i	−0.367147	+	0.367147i	−0.866436	−	0.499289i	$-0.833595\pi$
$907$	−11.0571	+	11.0571i	−0.367147	+	0.367147i	0.499289	+	0.866436i	$0.333595\pi$
$908$	81.6773	−	81.6773i	2.71056	−	2.71056i
$909$			24.4074i			0.809543i
$910$		0			0
$911$	12.0283	−	12.0283i	0.398516	−	0.398516i	−0.479194	−	0.877709i	$-0.659071\pi$
$911$	12.0283	−	12.0283i	0.398516	−	0.398516i	0.877709	+	0.479194i	$0.159071\pi$
$912$	−0.298732	+	0.298732i	−0.00989200	+	0.00989200i
$913$	0.944164	+	0.944164i	0.0312473	+	0.0312473i
$914$	−30.5421			−1.01024
$915$		0			0
$916$		−	56.0525i		−	1.85203i
$917$	63.2441			2.08850
$918$	−33.8002	+	26.2378i	−1.11557	+	0.865976i
$919$	−56.2688			−1.85614			−0.928069	−	0.372408i	$-0.878532\pi$
$919$	−56.2688			−1.85614			−0.928069	+	0.372408i	$0.878532\pi$
$920$		0			0
$921$	−8.34406	−	8.34406i	−0.274946	−	0.274946i
$922$	−109.092			−3.59275
$923$	5.54992	+	5.54992i	0.182678	+	0.182678i
$924$	−30.6632	+	30.6632i	−1.00875	+	1.00875i
$925$		0			0
$926$		−	18.6055i		−	0.611413i
$927$		−	2.03380i		−	0.0667987i
$928$	24.6968	−	24.6968i	0.810711	−	0.810711i
$929$	25.6944	−	25.6944i	0.843005	−	0.843005i	−0.146244	−	0.989249i	$-0.546718\pi$
$929$	25.6944	−	25.6944i	0.843005	−	0.843005i	0.989249	+	0.146244i	$0.0467183\pi$
$930$		0			0
$931$	−0.766653			−0.0251260
$932$	−56.0460	−	56.0460i	−1.83585	−	1.83585i
$933$		−	3.23202i		−	0.105811i
$934$	35.4785			1.16089
$935$		0			0
$936$	−38.4371			−1.25636
$937$			40.8124i			1.33328i	0.745378	+	0.666642i	$0.232269\pi$
$937$			40.8124i			1.33328i	−0.745378	+	0.666642i	$0.767731\pi$
$938$	107.124	+	107.124i	3.49771	+	3.49771i
$939$	6.88646			0.224731
$940$		0			0
$941$	22.8191	−	22.8191i	0.743883	−	0.743883i	−0.229440	−	0.973323i	$-0.573689\pi$
$941$	22.8191	−	22.8191i	0.743883	−	0.743883i	0.973323	+	0.229440i	$0.0736894\pi$
$942$	−12.6331	+	12.6331i	−0.411608	+	0.411608i
$943$			14.3194i			0.466305i
$944$			93.2135i			3.03384i
$945$		0			0
$946$	−36.9676	+	36.9676i	−1.20192	+	1.20192i
$947$	−6.61111	−	6.61111i	−0.214832	−	0.214832i	0.591484	−	0.806316i	$-0.298542\pi$
$947$	−6.61111	−	6.61111i	−0.214832	−	0.214832i	−0.806316	+	0.591484i	$0.798542\pi$
$948$	14.6112			0.474551
$949$	−9.54006	−	9.54006i	−0.309684	−	0.309684i
$950$		0			0
$951$	−20.7647			−0.673343
$952$	−138.363	+	107.406i	−4.48439	+	3.48105i
$953$	−41.4456			−1.34256			−0.671278	−	0.741206i	$-0.734254\pi$
$953$	−41.4456			−1.34256			−0.671278	+	0.741206i	$0.734254\pi$
$954$			78.0518i			2.52702i
$955$		0			0
$956$	69.3692			2.24356
$957$	−2.37891	−	2.37891i	−0.0768992	−	0.0768992i
$958$	77.3573	−	77.3573i	2.49930	−	2.49930i
$959$	17.0583	−	17.0583i	0.550841	−	0.550841i
$960$		0			0
$961$		−	22.4920i		−	0.725549i
$962$	−11.4874	+	11.4874i	−0.370370	+	0.370370i
$963$	−17.6806	+	17.6806i	−0.569750	+	0.569750i
$964$	47.2463	+	47.2463i	1.52170	+	1.52170i
$965$		0			0
$966$	−17.3883	−	17.3883i	−0.559459	−	0.559459i
$967$		−	17.1727i		−	0.552236i	−0.961124	−	0.276118i	$-0.910952\pi$
$967$		−	17.1727i		−	0.552236i	0.961124	−	0.276118i	$-0.0890481\pi$
$968$	44.4733			1.42943
$969$	0.0817918	+	0.105366i	0.00262753	+	0.00338486i
$970$		0			0
$971$		−	33.0307i		−	1.06001i	−0.847996	−	0.530003i	$-0.822191\pi$
$971$		−	33.0307i		−	1.06001i	0.847996	−	0.530003i	$-0.177809\pi$
$972$	−55.4792	−	55.4792i	−1.77950	−	1.77950i
$973$	9.51705			0.305103
$974$	0.883204	+	0.883204i	0.0282997	+	0.0282997i
$975$		0			0
$976$	80.3529	−	80.3529i	2.57203	−	2.57203i
$977$			31.6277i			1.01186i	0.862575	+	0.505930i	$0.168851\pi$
$977$			31.6277i			1.01186i	−0.862575	+	0.505930i	$0.831149\pi$
$978$			22.6087i			0.722947i
$979$	−0.817787	+	0.817787i	−0.0261366	+	0.0261366i
$980$		0			0
$981$	17.3528	+	17.3528i	0.554031	+	0.554031i
$982$	73.7842			2.35455
$983$	−15.0952	−	15.0952i	−0.481463	−	0.481463i	0.424135	−	0.905599i	$-0.360578\pi$
$983$	−15.0952	−	15.0952i	−0.481463	−	0.481463i	−0.905599	+	0.424135i	$0.860578\pi$
$984$		−	32.5822i		−	1.03868i
$985$		0			0
$986$	−13.4613	−	17.3412i	−0.428694	−	0.552256i
$987$	−33.1290			−1.05451
$988$			0.424845i			0.0135161i
$989$	−15.1801	−	15.1801i	−0.482698	−	0.482698i
$990$		0			0
$991$	−0.883161	−	0.883161i	−0.0280545	−	0.0280545i	0.692940	−	0.720995i	$-0.256315\pi$
$991$	−0.883161	−	0.883161i	−0.0280545	−	0.0280545i	−0.720995	+	0.692940i	$0.756315\pi$
$992$	36.4289	−	36.4289i	1.15662	−	1.15662i
$993$	7.82104	−	7.82104i	0.248193	−	0.248193i
$994$			58.6449i			1.86010i
$995$		0			0
$996$	1.42512	−	1.42512i	0.0451567	−	0.0451567i
$997$	18.9898	−	18.9898i	0.601414	−	0.601414i	−0.339274	−	0.940688i	$-0.610181\pi$
$997$	18.9898	−	18.9898i	0.601414	−	0.601414i	0.940688	+	0.339274i	$0.110181\pi$
$998$	30.2748	+	30.2748i	0.958331	+	0.958331i
$999$	−13.2917			−0.420531

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	425.2.e.c.251.6	✓	12
5.2	odd	4		425.2.j.a.149.1		12
5.3	odd	4		425.2.j.d.149.6		12
5.4	even	2		425.2.e.e.251.1	yes	12
17.2	even	8		7225.2.a.bm.1.1		12
17.4	even	4	inner	425.2.e.c.276.1	yes	12
17.15	even	8		7225.2.a.bm.1.2		12
85.4	even	4		425.2.e.e.276.6	yes	12
85.19	even	8		7225.2.a.br.1.12		12
85.38	odd	4		425.2.j.a.174.1		12
85.49	even	8		7225.2.a.br.1.11		12
85.72	odd	4		425.2.j.d.174.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
425.2.e.c.251.6	✓	12	1.1	even	1	trivial
425.2.e.c.276.1	yes	12	17.4	even	4	inner
425.2.e.e.251.1	yes	12	5.4	even	2
425.2.e.e.276.6	yes	12	85.4	even	4
425.2.j.a.149.1		12	5.2	odd	4
425.2.j.a.174.1		12	85.38	odd	4
425.2.j.d.149.6		12	5.3	odd	4
425.2.j.d.174.6		12	85.72	odd	4
7225.2.a.bm.1.1		12	17.2	even	8
7225.2.a.bm.1.2		12	17.15	even	8
7225.2.a.br.1.11		12	85.49	even	8
7225.2.a.br.1.12		12	85.19	even	8

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+2.69251i q^{2} +(-0.494558 - 0.494558i) q^{3} -5.24959 q^{4} +(1.33160 - 1.33160i) q^{6} +(3.43326 - 3.43326i) q^{7} -8.74953i q^{8} -2.51083i q^{9} +(-1.72004 + 1.72004i) q^{11} +(2.59622 + 2.59622i) q^{12} +1.74964 q^{13} +(9.24408 + 9.24408i) q^{14} +13.0590 q^{16} +(0.515279 - 4.09078i) q^{17} +6.76041 q^{18} -0.0462547i q^{19} -3.39590 q^{21} +(-4.63121 - 4.63121i) q^{22} +(1.90172 - 1.90172i) q^{23} +(-4.32715 + 4.32715i) q^{24} +4.71093i q^{26} +(-2.72542 + 2.72542i) q^{27} +(-18.0232 + 18.0232i) q^{28} +(-1.39828 - 1.39828i) q^{29} +(-2.06252 - 2.06252i) q^{31} +17.6623i q^{32} +1.70132 q^{33} +(11.0144 + 1.38739i) q^{34} +13.1808i q^{36} +(2.43847 + 2.43847i) q^{37} +0.124541 q^{38} +(-0.865300 - 0.865300i) q^{39} +(-3.76486 + 3.76486i) q^{41} -9.14347i q^{42} -7.98228i q^{43} +(9.02949 - 9.02949i) q^{44} +(5.12039 + 5.12039i) q^{46} +9.75559 q^{47} +(-6.45842 - 6.45842i) q^{48} -16.5746i q^{49} +(-2.27796 + 1.76829i) q^{51} -9.18491 q^{52} +11.5454i q^{53} +(-7.33821 - 7.33821i) q^{54} +(-30.0394 - 30.0394i) q^{56} +(-0.0228756 + 0.0228756i) q^{57} +(3.76486 - 3.76486i) q^{58} +7.13788i q^{59} +(6.15308 - 6.15308i) q^{61} +(5.55335 - 5.55335i) q^{62} +(-8.62033 - 8.62033i) q^{63} -21.4379 q^{64} +4.58080i q^{66} +11.5883 q^{67} +(-2.70500 + 21.4749i) q^{68} -1.88102 q^{69} +(3.17202 + 3.17202i) q^{71} -21.9685 q^{72} +(-5.45257 - 5.45257i) q^{73} +(-6.56558 + 6.56558i) q^{74} +0.242818i q^{76} +11.8107i q^{77} +(2.32983 - 2.32983i) q^{78} +(2.81394 - 2.81394i) q^{79} -4.83672 q^{81} +(-10.1369 - 10.1369i) q^{82} -0.548920i q^{83} +17.8270 q^{84} +21.4923 q^{86} +1.38306i q^{87} +(15.0495 + 15.0495i) q^{88} +0.475447 q^{89} +(6.00699 - 6.00699i) q^{91} +(-9.98323 + 9.98323i) q^{92} +2.04007i q^{93} +26.2670i q^{94} +(8.73503 - 8.73503i) q^{96} +(-9.98146 - 9.98146i) q^{97} +44.6272 q^{98} +(4.31872 + 4.31872i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 2 q^{3} - 12 q^{4} + 6 q^{6} - 4 q^{11} - 4 q^{12} + 12 q^{13} + 14 q^{14} + 4 q^{16} + 6 q^{17} - 4 q^{18} + 8 q^{21} + 10 q^{22} + 12 q^{23} - 8 q^{24} + 22 q^{27} - 34 q^{28} - 6 q^{29} - 6 q^{31}+ \cdots + 30 q^{99}+O(q^{100}) \) 12 * q - 2 * q^3 - 12 * q^4 + 6 * q^6 - 4 * q^11 - 4 * q^12 + 12 * q^13 + 14 * q^14 + 4 * q^16 + 6 * q^17 - 4 * q^18 + 8 * q^21 + 10 * q^22 + 12 * q^23 - 8 * q^24 + 22 * q^27 - 34 * q^28 - 6 * q^29 - 6 * q^31 + 4 * q^33 + 30 * q^34 + 18 * q^37 - 12 * q^38 + 16 * q^39 + 6 * q^41 + 32 * q^44 + 30 * q^46 + 36 * q^47 - 10 * q^48 - 40 * q^51 - 64 * q^52 + 16 * q^54 - 56 * q^56 - 18 * q^57 - 6 * q^58 - 8 * q^61 - 22 * q^62 - 30 * q^63 - 44 * q^64 + 20 * q^67 + 10 * q^68 - 72 * q^69 - 20 * q^71 - 92 * q^72 - 18 * q^73 - 26 * q^74 + 38 * q^78 - 14 * q^79 - 8 * q^81 - 10 * q^82 + 36 * q^84 + 84 * q^86 + 66 * q^88 - 24 * q^89 + 12 * q^91 - 32 * q^92 + 22 * q^96 - 52 * q^97 + 76 * q^98 + 30 * q^99

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