Properties

 Label 3822.2.c.c.883.1 Level $3822$ Weight $2$ Character 3822.883 Analytic conductor $30.519$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

Related objects

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3822,2,Mod(883,3822)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3822, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("3822.883");

S:= CuspForms(chi, 2);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$3822 = 2 \cdot 3 \cdot 7^{2} \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 3822.c (of order $$2$$, degree $$1$$, minimal)

Newform invariants

comment: select newform

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

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

 Self dual: no Analytic conductor: $$30.5188236525$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(i)$$ comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{2} + 1$$ x^2 + 1 Coefficient ring: $$\Z[a_1, a_2]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 546) Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

 Embedding label 883.1 Root $$1.00000i$$ of defining polynomial Character $$\chi$$ $$=$$ 3822.883 Dual form 3822.2.c.c.883.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q-1.00000i q^{2} -1.00000 q^{3} -1.00000 q^{4} +2.00000i q^{5} +1.00000i q^{6} +1.00000i q^{8} +1.00000 q^{9} +O(q^{10})$$ $$q-1.00000i q^{2} -1.00000 q^{3} -1.00000 q^{4} +2.00000i q^{5} +1.00000i q^{6} +1.00000i q^{8} +1.00000 q^{9} +2.00000 q^{10} +1.00000 q^{12} +(-2.00000 + 3.00000i) q^{13} -2.00000i q^{15} +1.00000 q^{16} +2.00000 q^{17} -1.00000i q^{18} +4.00000i q^{19} -2.00000i q^{20} -6.00000 q^{23} -1.00000i q^{24} +1.00000 q^{25} +(3.00000 + 2.00000i) q^{26} -1.00000 q^{27} -2.00000 q^{30} -1.00000i q^{32} -2.00000i q^{34} -1.00000 q^{36} +2.00000i q^{37} +4.00000 q^{38} +(2.00000 - 3.00000i) q^{39} -2.00000 q^{40} +4.00000 q^{43} +2.00000i q^{45} +6.00000i q^{46} +8.00000i q^{47} -1.00000 q^{48} -1.00000i q^{50} -2.00000 q^{51} +(2.00000 - 3.00000i) q^{52} +4.00000 q^{53} +1.00000i q^{54} -4.00000i q^{57} -6.00000i q^{59} +2.00000i q^{60} -12.0000 q^{61} -1.00000 q^{64} +(-6.00000 - 4.00000i) q^{65} +2.00000i q^{67} -2.00000 q^{68} +6.00000 q^{69} +1.00000i q^{72} -14.0000i q^{73} +2.00000 q^{74} -1.00000 q^{75} -4.00000i q^{76} +(-3.00000 - 2.00000i) q^{78} +2.00000i q^{80} +1.00000 q^{81} -14.0000i q^{83} +4.00000i q^{85} -4.00000i q^{86} +4.00000i q^{89} +2.00000 q^{90} +6.00000 q^{92} +8.00000 q^{94} -8.00000 q^{95} +1.00000i q^{96} -2.00000i q^{97} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q - 2 q^{3} - 2 q^{4} + 2 q^{9}+O(q^{10})$$ 2 * q - 2 * q^3 - 2 * q^4 + 2 * q^9 $$2 q - 2 q^{3} - 2 q^{4} + 2 q^{9} + 4 q^{10} + 2 q^{12} - 4 q^{13} + 2 q^{16} + 4 q^{17} - 12 q^{23} + 2 q^{25} + 6 q^{26} - 2 q^{27} - 4 q^{30} - 2 q^{36} + 8 q^{38} + 4 q^{39} - 4 q^{40} + 8 q^{43} - 2 q^{48} - 4 q^{51} + 4 q^{52} + 8 q^{53} - 24 q^{61} - 2 q^{64} - 12 q^{65} - 4 q^{68} + 12 q^{69} + 4 q^{74} - 2 q^{75} - 6 q^{78} + 2 q^{81} + 4 q^{90} + 12 q^{92} + 16 q^{94} - 16 q^{95}+O(q^{100})$$ 2 * q - 2 * q^3 - 2 * q^4 + 2 * q^9 + 4 * q^10 + 2 * q^12 - 4 * q^13 + 2 * q^16 + 4 * q^17 - 12 * q^23 + 2 * q^25 + 6 * q^26 - 2 * q^27 - 4 * q^30 - 2 * q^36 + 8 * q^38 + 4 * q^39 - 4 * q^40 + 8 * q^43 - 2 * q^48 - 4 * q^51 + 4 * q^52 + 8 * q^53 - 24 * q^61 - 2 * q^64 - 12 * q^65 - 4 * q^68 + 12 * q^69 + 4 * q^74 - 2 * q^75 - 6 * q^78 + 2 * q^81 + 4 * q^90 + 12 * q^92 + 16 * q^94 - 16 * q^95

Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/3822\mathbb{Z}\right)^\times$$.

 $$n$$ $$1471$$ $$2549$$ $$3433$$ $$\chi(n)$$ $$-1$$ $$1$$ $$1$$

Coefficient data

For each $$n$$ we display the coefficients of the $$q$$-expansion $$a_n$$, the Satake parameters $$\alpha_p$$, and the Satake angles $$\theta_p = \textrm{Arg}(\alpha_p)$$.

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 1.00000i 0.707107i
$$3$$ −1.00000 −0.577350
$$4$$ −1.00000 −0.500000
$$5$$ 2.00000i 0.894427i 0.894427 + 0.447214i $$0.147584\pi$$
−0.894427 + 0.447214i $$0.852416\pi$$
$$6$$ 1.00000i 0.408248i
$$7$$ 0 0
$$8$$ 1.00000i 0.353553i
$$9$$ 1.00000 0.333333
$$10$$ 2.00000 0.632456
$$11$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$12$$ 1.00000 0.288675
$$13$$ −2.00000 + 3.00000i −0.554700 + 0.832050i
$$14$$ 0 0
$$15$$ 2.00000i 0.516398i
$$16$$ 1.00000 0.250000
$$17$$ 2.00000 0.485071 0.242536 0.970143i $$-0.422021\pi$$
0.242536 + 0.970143i $$0.422021\pi$$
$$18$$ 1.00000i 0.235702i
$$19$$ 4.00000i 0.917663i 0.888523 + 0.458831i $$0.151732\pi$$
−0.888523 + 0.458831i $$0.848268\pi$$
$$20$$ 2.00000i 0.447214i
$$21$$ 0 0
$$22$$ 0 0
$$23$$ −6.00000 −1.25109 −0.625543 0.780189i $$-0.715123\pi$$
−0.625543 + 0.780189i $$0.715123\pi$$
$$24$$ 1.00000i 0.204124i
$$25$$ 1.00000 0.200000
$$26$$ 3.00000 + 2.00000i 0.588348 + 0.392232i
$$27$$ −1.00000 −0.192450
$$28$$ 0 0
$$29$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$30$$ −2.00000 −0.365148
$$31$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$32$$ 1.00000i 0.176777i
$$33$$ 0 0
$$34$$ 2.00000i 0.342997i
$$35$$ 0 0
$$36$$ −1.00000 −0.166667
$$37$$ 2.00000i 0.328798i 0.986394 + 0.164399i $$0.0525685\pi$$
−0.986394 + 0.164399i $$0.947432\pi$$
$$38$$ 4.00000 0.648886
$$39$$ 2.00000 3.00000i 0.320256 0.480384i
$$40$$ −2.00000 −0.316228
$$41$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$42$$ 0 0
$$43$$ 4.00000 0.609994 0.304997 0.952353i $$-0.401344\pi$$
0.304997 + 0.952353i $$0.401344\pi$$
$$44$$ 0 0
$$45$$ 2.00000i 0.298142i
$$46$$ 6.00000i 0.884652i
$$47$$ 8.00000i 1.16692i 0.812142 + 0.583460i $$0.198301\pi$$
−0.812142 + 0.583460i $$0.801699\pi$$
$$48$$ −1.00000 −0.144338
$$49$$ 0 0
$$50$$ 1.00000i 0.141421i
$$51$$ −2.00000 −0.280056
$$52$$ 2.00000 3.00000i 0.277350 0.416025i
$$53$$ 4.00000 0.549442 0.274721 0.961524i $$-0.411414\pi$$
0.274721 + 0.961524i $$0.411414\pi$$
$$54$$ 1.00000i 0.136083i
$$55$$ 0 0
$$56$$ 0 0
$$57$$ 4.00000i 0.529813i
$$58$$ 0 0
$$59$$ 6.00000i 0.781133i −0.920575 0.390567i $$-0.872279\pi$$
0.920575 0.390567i $$-0.127721\pi$$
$$60$$ 2.00000i 0.258199i
$$61$$ −12.0000 −1.53644 −0.768221 0.640184i $$-0.778858\pi$$
−0.768221 + 0.640184i $$0.778858\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ −1.00000 −0.125000
$$65$$ −6.00000 4.00000i −0.744208 0.496139i
$$66$$ 0 0
$$67$$ 2.00000i 0.244339i 0.992509 + 0.122169i $$0.0389851\pi$$
−0.992509 + 0.122169i $$0.961015\pi$$
$$68$$ −2.00000 −0.242536
$$69$$ 6.00000 0.722315
$$70$$ 0 0
$$71$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$72$$ 1.00000i 0.117851i
$$73$$ 14.0000i 1.63858i −0.573382 0.819288i $$-0.694369\pi$$
0.573382 0.819288i $$-0.305631\pi$$
$$74$$ 2.00000 0.232495
$$75$$ −1.00000 −0.115470
$$76$$ 4.00000i 0.458831i
$$77$$ 0 0
$$78$$ −3.00000 2.00000i −0.339683 0.226455i
$$79$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$80$$ 2.00000i 0.223607i
$$81$$ 1.00000 0.111111
$$82$$ 0 0
$$83$$ 14.0000i 1.53670i −0.640030 0.768350i $$-0.721078\pi$$
0.640030 0.768350i $$-0.278922\pi$$
$$84$$ 0 0
$$85$$ 4.00000i 0.433861i
$$86$$ 4.00000i 0.431331i
$$87$$ 0 0
$$88$$ 0 0
$$89$$ 4.00000i 0.423999i 0.977270 + 0.212000i $$0.0679975\pi$$
−0.977270 + 0.212000i $$0.932002\pi$$
$$90$$ 2.00000 0.210819
$$91$$ 0 0
$$92$$ 6.00000 0.625543
$$93$$ 0 0
$$94$$ 8.00000 0.825137
$$95$$ −8.00000 −0.820783
$$96$$ 1.00000i 0.102062i
$$97$$ 2.00000i 0.203069i −0.994832 0.101535i $$-0.967625\pi$$
0.994832 0.101535i $$-0.0323753\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ −1.00000 −0.100000
$$101$$ −2.00000 −0.199007 −0.0995037 0.995037i $$-0.531726\pi$$
−0.0995037 + 0.995037i $$0.531726\pi$$
$$102$$ 2.00000i 0.198030i
$$103$$ −14.0000 −1.37946 −0.689730 0.724066i $$-0.742271\pi$$
−0.689730 + 0.724066i $$0.742271\pi$$
$$104$$ −3.00000 2.00000i −0.294174 0.196116i
$$105$$ 0 0
$$106$$ 4.00000i 0.388514i
$$107$$ −12.0000 −1.16008 −0.580042 0.814587i $$-0.696964\pi$$
−0.580042 + 0.814587i $$0.696964\pi$$
$$108$$ 1.00000 0.0962250
$$109$$ 6.00000i 0.574696i 0.957826 + 0.287348i $$0.0927736\pi$$
−0.957826 + 0.287348i $$0.907226\pi$$
$$110$$ 0 0
$$111$$ 2.00000i 0.189832i
$$112$$ 0 0
$$113$$ 14.0000 1.31701 0.658505 0.752577i $$-0.271189\pi$$
0.658505 + 0.752577i $$0.271189\pi$$
$$114$$ −4.00000 −0.374634
$$115$$ 12.0000i 1.11901i
$$116$$ 0 0
$$117$$ −2.00000 + 3.00000i −0.184900 + 0.277350i
$$118$$ −6.00000 −0.552345
$$119$$ 0 0
$$120$$ 2.00000 0.182574
$$121$$ 11.0000 1.00000
$$122$$ 12.0000i 1.08643i
$$123$$ 0 0
$$124$$ 0 0
$$125$$ 12.0000i 1.07331i
$$126$$ 0 0
$$127$$ −12.0000 −1.06483 −0.532414 0.846484i $$-0.678715\pi$$
−0.532414 + 0.846484i $$0.678715\pi$$
$$128$$ 1.00000i 0.0883883i
$$129$$ −4.00000 −0.352180
$$130$$ −4.00000 + 6.00000i −0.350823 + 0.526235i
$$131$$ −12.0000 −1.04844 −0.524222 0.851581i $$-0.675644\pi$$
−0.524222 + 0.851581i $$0.675644\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ 2.00000 0.172774
$$135$$ 2.00000i 0.172133i
$$136$$ 2.00000i 0.171499i
$$137$$ 2.00000i 0.170872i 0.996344 + 0.0854358i $$0.0272282\pi$$
−0.996344 + 0.0854358i $$0.972772\pi$$
$$138$$ 6.00000i 0.510754i
$$139$$ −20.0000 −1.69638 −0.848189 0.529694i $$-0.822307\pi$$
−0.848189 + 0.529694i $$0.822307\pi$$
$$140$$ 0 0
$$141$$ 8.00000i 0.673722i
$$142$$ 0 0
$$143$$ 0 0
$$144$$ 1.00000 0.0833333
$$145$$ 0 0
$$146$$ −14.0000 −1.15865
$$147$$ 0 0
$$148$$ 2.00000i 0.164399i
$$149$$ 6.00000i 0.491539i 0.969328 + 0.245770i $$0.0790407\pi$$
−0.969328 + 0.245770i $$0.920959\pi$$
$$150$$ 1.00000i 0.0816497i
$$151$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$152$$ −4.00000 −0.324443
$$153$$ 2.00000 0.161690
$$154$$ 0 0
$$155$$ 0 0
$$156$$ −2.00000 + 3.00000i −0.160128 + 0.240192i
$$157$$ −8.00000 −0.638470 −0.319235 0.947676i $$-0.603426\pi$$
−0.319235 + 0.947676i $$0.603426\pi$$
$$158$$ 0 0
$$159$$ −4.00000 −0.317221
$$160$$ 2.00000 0.158114
$$161$$ 0 0
$$162$$ 1.00000i 0.0785674i
$$163$$ 14.0000i 1.09656i 0.836293 + 0.548282i $$0.184718\pi$$
−0.836293 + 0.548282i $$0.815282\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ −14.0000 −1.08661
$$167$$ 12.0000i 0.928588i −0.885681 0.464294i $$-0.846308\pi$$
0.885681 0.464294i $$-0.153692\pi$$
$$168$$ 0 0
$$169$$ −5.00000 12.0000i −0.384615 0.923077i
$$170$$ 4.00000 0.306786
$$171$$ 4.00000i 0.305888i
$$172$$ −4.00000 −0.304997
$$173$$ 6.00000 0.456172 0.228086 0.973641i $$-0.426753\pi$$
0.228086 + 0.973641i $$0.426753\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 0 0
$$177$$ 6.00000i 0.450988i
$$178$$ 4.00000 0.299813
$$179$$ −20.0000 −1.49487 −0.747435 0.664335i $$-0.768715\pi$$
−0.747435 + 0.664335i $$0.768715\pi$$
$$180$$ 2.00000i 0.149071i
$$181$$ −12.0000 −0.891953 −0.445976 0.895045i $$-0.647144\pi$$
−0.445976 + 0.895045i $$0.647144\pi$$
$$182$$ 0 0
$$183$$ 12.0000 0.887066
$$184$$ 6.00000i 0.442326i
$$185$$ −4.00000 −0.294086
$$186$$ 0 0
$$187$$ 0 0
$$188$$ 8.00000i 0.583460i
$$189$$ 0 0
$$190$$ 8.00000i 0.580381i
$$191$$ 2.00000 0.144715 0.0723575 0.997379i $$-0.476948\pi$$
0.0723575 + 0.997379i $$0.476948\pi$$
$$192$$ 1.00000 0.0721688
$$193$$ 4.00000i 0.287926i 0.989583 + 0.143963i $$0.0459847\pi$$
−0.989583 + 0.143963i $$0.954015\pi$$
$$194$$ −2.00000 −0.143592
$$195$$ 6.00000 + 4.00000i 0.429669 + 0.286446i
$$196$$ 0 0
$$197$$ 18.0000i 1.28245i −0.767354 0.641223i $$-0.778427\pi$$
0.767354 0.641223i $$-0.221573\pi$$
$$198$$ 0 0
$$199$$ 10.0000 0.708881 0.354441 0.935079i $$-0.384671\pi$$
0.354441 + 0.935079i $$0.384671\pi$$
$$200$$ 1.00000i 0.0707107i
$$201$$ 2.00000i 0.141069i
$$202$$ 2.00000i 0.140720i
$$203$$ 0 0
$$204$$ 2.00000 0.140028
$$205$$ 0 0
$$206$$ 14.0000i 0.975426i
$$207$$ −6.00000 −0.417029
$$208$$ −2.00000 + 3.00000i −0.138675 + 0.208013i
$$209$$ 0 0
$$210$$ 0 0
$$211$$ −28.0000 −1.92760 −0.963800 0.266627i $$-0.914091\pi$$
−0.963800 + 0.266627i $$0.914091\pi$$
$$212$$ −4.00000 −0.274721
$$213$$ 0 0
$$214$$ 12.0000i 0.820303i
$$215$$ 8.00000i 0.545595i
$$216$$ 1.00000i 0.0680414i
$$217$$ 0 0
$$218$$ 6.00000 0.406371
$$219$$ 14.0000i 0.946032i
$$220$$ 0 0
$$221$$ −4.00000 + 6.00000i −0.269069 + 0.403604i
$$222$$ −2.00000 −0.134231
$$223$$ 16.0000i 1.07144i 0.844396 + 0.535720i $$0.179960\pi$$
−0.844396 + 0.535720i $$0.820040\pi$$
$$224$$ 0 0
$$225$$ 1.00000 0.0666667
$$226$$ 14.0000i 0.931266i
$$227$$ 22.0000i 1.46019i −0.683345 0.730096i $$-0.739475\pi$$
0.683345 0.730096i $$-0.260525\pi$$
$$228$$ 4.00000i 0.264906i
$$229$$ 14.0000i 0.925146i 0.886581 + 0.462573i $$0.153074\pi$$
−0.886581 + 0.462573i $$0.846926\pi$$
$$230$$ −12.0000 −0.791257
$$231$$ 0 0
$$232$$ 0 0
$$233$$ −6.00000 −0.393073 −0.196537 0.980497i $$-0.562969\pi$$
−0.196537 + 0.980497i $$0.562969\pi$$
$$234$$ 3.00000 + 2.00000i 0.196116 + 0.130744i
$$235$$ −16.0000 −1.04372
$$236$$ 6.00000i 0.390567i
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 16.0000i 1.03495i 0.855697 + 0.517477i $$0.173129\pi$$
−0.855697 + 0.517477i $$0.826871\pi$$
$$240$$ 2.00000i 0.129099i
$$241$$ 10.0000i 0.644157i 0.946713 + 0.322078i $$0.104381\pi$$
−0.946713 + 0.322078i $$0.895619\pi$$
$$242$$ 11.0000i 0.707107i
$$243$$ −1.00000 −0.0641500
$$244$$ 12.0000 0.768221
$$245$$ 0 0
$$246$$ 0 0
$$247$$ −12.0000 8.00000i −0.763542 0.509028i
$$248$$ 0 0
$$249$$ 14.0000i 0.887214i
$$250$$ 12.0000 0.758947
$$251$$ 28.0000 1.76734 0.883672 0.468106i $$-0.155064\pi$$
0.883672 + 0.468106i $$0.155064\pi$$
$$252$$ 0 0
$$253$$ 0 0
$$254$$ 12.0000i 0.752947i
$$255$$ 4.00000i 0.250490i
$$256$$ 1.00000 0.0625000
$$257$$ −18.0000 −1.12281 −0.561405 0.827541i $$-0.689739\pi$$
−0.561405 + 0.827541i $$0.689739\pi$$
$$258$$ 4.00000i 0.249029i
$$259$$ 0 0
$$260$$ 6.00000 + 4.00000i 0.372104 + 0.248069i
$$261$$ 0 0
$$262$$ 12.0000i 0.741362i
$$263$$ −6.00000 −0.369976 −0.184988 0.982741i $$-0.559225\pi$$
−0.184988 + 0.982741i $$0.559225\pi$$
$$264$$ 0 0
$$265$$ 8.00000i 0.491436i
$$266$$ 0 0
$$267$$ 4.00000i 0.244796i
$$268$$ 2.00000i 0.122169i
$$269$$ −10.0000 −0.609711 −0.304855 0.952399i $$-0.598608\pi$$
−0.304855 + 0.952399i $$0.598608\pi$$
$$270$$ −2.00000 −0.121716
$$271$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$272$$ 2.00000 0.121268
$$273$$ 0 0
$$274$$ 2.00000 0.120824
$$275$$ 0 0
$$276$$ −6.00000 −0.361158
$$277$$ −22.0000 −1.32185 −0.660926 0.750451i $$-0.729836\pi$$
−0.660926 + 0.750451i $$0.729836\pi$$
$$278$$ 20.0000i 1.19952i
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 30.0000i 1.78965i −0.446417 0.894825i $$-0.647300\pi$$
0.446417 0.894825i $$-0.352700\pi$$
$$282$$ −8.00000 −0.476393
$$283$$ 16.0000 0.951101 0.475551 0.879688i $$-0.342249\pi$$
0.475551 + 0.879688i $$0.342249\pi$$
$$284$$ 0 0
$$285$$ 8.00000 0.473879
$$286$$ 0 0
$$287$$ 0 0
$$288$$ 1.00000i 0.0589256i
$$289$$ −13.0000 −0.764706
$$290$$ 0 0
$$291$$ 2.00000i 0.117242i
$$292$$ 14.0000i 0.819288i
$$293$$ 6.00000i 0.350524i 0.984522 + 0.175262i $$0.0560772\pi$$
−0.984522 + 0.175262i $$0.943923\pi$$
$$294$$ 0 0
$$295$$ 12.0000 0.698667
$$296$$ −2.00000 −0.116248
$$297$$ 0 0
$$298$$ 6.00000 0.347571
$$299$$ 12.0000 18.0000i 0.693978 1.04097i
$$300$$ 1.00000 0.0577350
$$301$$ 0 0
$$302$$ 0 0
$$303$$ 2.00000 0.114897
$$304$$ 4.00000i 0.229416i
$$305$$ 24.0000i 1.37424i
$$306$$ 2.00000i 0.114332i
$$307$$ 28.0000i 1.59804i 0.601302 + 0.799022i $$0.294649\pi$$
−0.601302 + 0.799022i $$0.705351\pi$$
$$308$$ 0 0
$$309$$ 14.0000 0.796432
$$310$$ 0 0
$$311$$ −12.0000 −0.680458 −0.340229 0.940343i $$-0.610505\pi$$
−0.340229 + 0.940343i $$0.610505\pi$$
$$312$$ 3.00000 + 2.00000i 0.169842 + 0.113228i
$$313$$ 6.00000 0.339140 0.169570 0.985518i $$-0.445762\pi$$
0.169570 + 0.985518i $$0.445762\pi$$
$$314$$ 8.00000i 0.451466i
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 2.00000i 0.112331i 0.998421 + 0.0561656i $$0.0178875\pi$$
−0.998421 + 0.0561656i $$0.982113\pi$$
$$318$$ 4.00000i 0.224309i
$$319$$ 0 0
$$320$$ 2.00000i 0.111803i
$$321$$ 12.0000 0.669775
$$322$$ 0 0
$$323$$ 8.00000i 0.445132i
$$324$$ −1.00000 −0.0555556
$$325$$ −2.00000 + 3.00000i −0.110940 + 0.166410i
$$326$$ 14.0000 0.775388
$$327$$ 6.00000i 0.331801i
$$328$$ 0 0
$$329$$ 0 0
$$330$$ 0 0
$$331$$ 10.0000i 0.549650i 0.961494 + 0.274825i $$0.0886199\pi$$
−0.961494 + 0.274825i $$0.911380\pi$$
$$332$$ 14.0000i 0.768350i
$$333$$ 2.00000i 0.109599i
$$334$$ −12.0000 −0.656611
$$335$$ −4.00000 −0.218543
$$336$$ 0 0
$$337$$ −22.0000 −1.19842 −0.599208 0.800593i $$-0.704518\pi$$
−0.599208 + 0.800593i $$0.704518\pi$$
$$338$$ −12.0000 + 5.00000i −0.652714 + 0.271964i
$$339$$ −14.0000 −0.760376
$$340$$ 4.00000i 0.216930i
$$341$$ 0 0
$$342$$ 4.00000 0.216295
$$343$$ 0 0
$$344$$ 4.00000i 0.215666i
$$345$$ 12.0000i 0.646058i
$$346$$ 6.00000i 0.322562i
$$347$$ −32.0000 −1.71785 −0.858925 0.512101i $$-0.828867\pi$$
−0.858925 + 0.512101i $$0.828867\pi$$
$$348$$ 0 0
$$349$$ 14.0000i 0.749403i 0.927146 + 0.374701i $$0.122255\pi$$
−0.927146 + 0.374701i $$0.877745\pi$$
$$350$$ 0 0
$$351$$ 2.00000 3.00000i 0.106752 0.160128i
$$352$$ 0 0
$$353$$ 24.0000i 1.27739i −0.769460 0.638696i $$-0.779474\pi$$
0.769460 0.638696i $$-0.220526\pi$$
$$354$$ 6.00000 0.318896
$$355$$ 0 0
$$356$$ 4.00000i 0.212000i
$$357$$ 0 0
$$358$$ 20.0000i 1.05703i
$$359$$ 24.0000i 1.26667i −0.773877 0.633336i $$-0.781685\pi$$
0.773877 0.633336i $$-0.218315\pi$$
$$360$$ −2.00000 −0.105409
$$361$$ 3.00000 0.157895
$$362$$ 12.0000i 0.630706i
$$363$$ −11.0000 −0.577350
$$364$$ 0 0
$$365$$ 28.0000 1.46559
$$366$$ 12.0000i 0.627250i
$$367$$ 22.0000 1.14839 0.574195 0.818718i $$-0.305315\pi$$
0.574195 + 0.818718i $$0.305315\pi$$
$$368$$ −6.00000 −0.312772
$$369$$ 0 0
$$370$$ 4.00000i 0.207950i
$$371$$ 0 0
$$372$$ 0 0
$$373$$ 34.0000 1.76045 0.880227 0.474554i $$-0.157390\pi$$
0.880227 + 0.474554i $$0.157390\pi$$
$$374$$ 0 0
$$375$$ 12.0000i 0.619677i
$$376$$ −8.00000 −0.412568
$$377$$ 0 0
$$378$$ 0 0
$$379$$ 26.0000i 1.33553i 0.744372 + 0.667765i $$0.232749\pi$$
−0.744372 + 0.667765i $$0.767251\pi$$
$$380$$ 8.00000 0.410391
$$381$$ 12.0000 0.614779
$$382$$ 2.00000i 0.102329i
$$383$$ 24.0000i 1.22634i −0.789950 0.613171i $$-0.789894\pi$$
0.789950 0.613171i $$-0.210106\pi$$
$$384$$ 1.00000i 0.0510310i
$$385$$ 0 0
$$386$$ 4.00000 0.203595
$$387$$ 4.00000 0.203331
$$388$$ 2.00000i 0.101535i
$$389$$ 20.0000 1.01404 0.507020 0.861934i $$-0.330747\pi$$
0.507020 + 0.861934i $$0.330747\pi$$
$$390$$ 4.00000 6.00000i 0.202548 0.303822i
$$391$$ −12.0000 −0.606866
$$392$$ 0 0
$$393$$ 12.0000 0.605320
$$394$$ −18.0000 −0.906827
$$395$$ 0 0
$$396$$ 0 0
$$397$$ 18.0000i 0.903394i 0.892171 + 0.451697i $$0.149181\pi$$
−0.892171 + 0.451697i $$0.850819\pi$$
$$398$$ 10.0000i 0.501255i
$$399$$ 0 0
$$400$$ 1.00000 0.0500000
$$401$$ 30.0000i 1.49813i 0.662497 + 0.749064i $$0.269497\pi$$
−0.662497 + 0.749064i $$0.730503\pi$$
$$402$$ −2.00000 −0.0997509
$$403$$ 0 0
$$404$$ 2.00000 0.0995037
$$405$$ 2.00000i 0.0993808i
$$406$$ 0 0
$$407$$ 0 0
$$408$$ 2.00000i 0.0990148i
$$409$$ 14.0000i 0.692255i 0.938187 + 0.346128i $$0.112504\pi$$
−0.938187 + 0.346128i $$0.887496\pi$$
$$410$$ 0 0
$$411$$ 2.00000i 0.0986527i
$$412$$ 14.0000 0.689730
$$413$$ 0 0
$$414$$ 6.00000i 0.294884i
$$415$$ 28.0000 1.37447
$$416$$ 3.00000 + 2.00000i 0.147087 + 0.0980581i
$$417$$ 20.0000 0.979404
$$418$$ 0 0
$$419$$ −20.0000 −0.977064 −0.488532 0.872546i $$-0.662467\pi$$
−0.488532 + 0.872546i $$0.662467\pi$$
$$420$$ 0 0
$$421$$ 30.0000i 1.46211i 0.682318 + 0.731055i $$0.260972\pi$$
−0.682318 + 0.731055i $$0.739028\pi$$
$$422$$ 28.0000i 1.36302i
$$423$$ 8.00000i 0.388973i
$$424$$ 4.00000i 0.194257i
$$425$$ 2.00000 0.0970143
$$426$$ 0 0
$$427$$ 0 0
$$428$$ 12.0000 0.580042
$$429$$ 0 0
$$430$$ 8.00000 0.385794
$$431$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$432$$ −1.00000 −0.0481125
$$433$$ 26.0000 1.24948 0.624740 0.780833i $$-0.285205\pi$$
0.624740 + 0.780833i $$0.285205\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 6.00000i 0.287348i
$$437$$ 24.0000i 1.14808i
$$438$$ 14.0000 0.668946
$$439$$ −30.0000 −1.43182 −0.715911 0.698192i $$-0.753988\pi$$
−0.715911 + 0.698192i $$0.753988\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 6.00000 + 4.00000i 0.285391 + 0.190261i
$$443$$ 4.00000 0.190046 0.0950229 0.995475i $$-0.469708\pi$$
0.0950229 + 0.995475i $$0.469708\pi$$
$$444$$ 2.00000i 0.0949158i
$$445$$ −8.00000 −0.379236
$$446$$ 16.0000 0.757622
$$447$$ 6.00000i 0.283790i
$$448$$ 0 0
$$449$$ 14.0000i 0.660701i −0.943858 0.330350i $$-0.892833\pi$$
0.943858 0.330350i $$-0.107167\pi$$
$$450$$ 1.00000i 0.0471405i
$$451$$ 0 0
$$452$$ −14.0000 −0.658505
$$453$$ 0 0
$$454$$ −22.0000 −1.03251
$$455$$ 0 0
$$456$$ 4.00000 0.187317
$$457$$ 8.00000i 0.374224i −0.982339 0.187112i $$-0.940087\pi$$
0.982339 0.187112i $$-0.0599128\pi$$
$$458$$ 14.0000 0.654177
$$459$$ −2.00000 −0.0933520
$$460$$ 12.0000i 0.559503i
$$461$$ 10.0000i 0.465746i 0.972507 + 0.232873i $$0.0748127\pi$$
−0.972507 + 0.232873i $$0.925187\pi$$
$$462$$ 0 0
$$463$$ 16.0000i 0.743583i −0.928316 0.371792i $$-0.878744\pi$$
0.928316 0.371792i $$-0.121256\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 6.00000i 0.277945i
$$467$$ 12.0000 0.555294 0.277647 0.960683i $$-0.410445\pi$$
0.277647 + 0.960683i $$0.410445\pi$$
$$468$$ 2.00000 3.00000i 0.0924500 0.138675i
$$469$$ 0 0
$$470$$ 16.0000i 0.738025i
$$471$$ 8.00000 0.368621
$$472$$ 6.00000 0.276172
$$473$$ 0 0
$$474$$ 0 0
$$475$$ 4.00000i 0.183533i
$$476$$ 0 0
$$477$$ 4.00000 0.183147
$$478$$ 16.0000 0.731823
$$479$$ 16.0000i 0.731059i −0.930800 0.365529i $$-0.880888\pi$$
0.930800 0.365529i $$-0.119112\pi$$
$$480$$ −2.00000 −0.0912871
$$481$$ −6.00000 4.00000i −0.273576 0.182384i
$$482$$ 10.0000 0.455488
$$483$$ 0 0
$$484$$ −11.0000 −0.500000
$$485$$ 4.00000 0.181631
$$486$$ 1.00000i 0.0453609i
$$487$$ 28.0000i 1.26880i −0.773004 0.634401i $$-0.781247\pi$$
0.773004 0.634401i $$-0.218753\pi$$
$$488$$ 12.0000i 0.543214i
$$489$$ 14.0000i 0.633102i
$$490$$ 0 0
$$491$$ −8.00000 −0.361035 −0.180517 0.983572i $$-0.557777\pi$$
−0.180517 + 0.983572i $$0.557777\pi$$
$$492$$ 0 0
$$493$$ 0 0
$$494$$ −8.00000 + 12.0000i −0.359937 + 0.539906i
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 0 0
$$498$$ 14.0000 0.627355
$$499$$ 14.0000i 0.626726i −0.949633 0.313363i $$-0.898544\pi$$
0.949633 0.313363i $$-0.101456\pi$$
$$500$$ 12.0000i 0.536656i
$$501$$ 12.0000i 0.536120i
$$502$$ 28.0000i 1.24970i
$$503$$ 36.0000 1.60516 0.802580 0.596544i $$-0.203460\pi$$
0.802580 + 0.596544i $$0.203460\pi$$
$$504$$ 0 0
$$505$$ 4.00000i 0.177998i
$$506$$ 0 0
$$507$$ 5.00000 + 12.0000i 0.222058 + 0.532939i
$$508$$ 12.0000 0.532414
$$509$$ 26.0000i 1.15243i −0.817298 0.576215i $$-0.804529\pi$$
0.817298 0.576215i $$-0.195471\pi$$
$$510$$ −4.00000 −0.177123
$$511$$ 0 0
$$512$$ 1.00000i 0.0441942i
$$513$$ 4.00000i 0.176604i
$$514$$ 18.0000i 0.793946i
$$515$$ 28.0000i 1.23383i
$$516$$ 4.00000 0.176090
$$517$$ 0 0
$$518$$ 0 0
$$519$$ −6.00000 −0.263371
$$520$$ 4.00000 6.00000i 0.175412 0.263117i
$$521$$ −42.0000 −1.84005 −0.920027 0.391856i $$-0.871833\pi$$
−0.920027 + 0.391856i $$0.871833\pi$$
$$522$$ 0 0
$$523$$ −4.00000 −0.174908 −0.0874539 0.996169i $$-0.527873\pi$$
−0.0874539 + 0.996169i $$0.527873\pi$$
$$524$$ 12.0000 0.524222
$$525$$ 0 0
$$526$$ 6.00000i 0.261612i
$$527$$ 0 0
$$528$$ 0 0
$$529$$ 13.0000 0.565217
$$530$$ 8.00000 0.347498
$$531$$ 6.00000i 0.260378i
$$532$$ 0 0
$$533$$ 0 0
$$534$$ −4.00000 −0.173097
$$535$$ 24.0000i 1.03761i
$$536$$ −2.00000 −0.0863868
$$537$$ 20.0000 0.863064
$$538$$ 10.0000i 0.431131i
$$539$$ 0 0
$$540$$ 2.00000i 0.0860663i
$$541$$ 30.0000i 1.28980i 0.764267 + 0.644900i $$0.223101\pi$$
−0.764267 + 0.644900i $$0.776899\pi$$
$$542$$ 0 0
$$543$$ 12.0000 0.514969
$$544$$ 2.00000i 0.0857493i
$$545$$ −12.0000 −0.514024
$$546$$ 0 0
$$547$$ −12.0000 −0.513083 −0.256541 0.966533i $$-0.582583\pi$$
−0.256541 + 0.966533i $$0.582583\pi$$
$$548$$ 2.00000i 0.0854358i
$$549$$ −12.0000 −0.512148
$$550$$ 0 0
$$551$$ 0 0
$$552$$ 6.00000i 0.255377i
$$553$$ 0 0
$$554$$ 22.0000i 0.934690i
$$555$$ 4.00000 0.169791
$$556$$ 20.0000 0.848189
$$557$$ 18.0000i 0.762684i −0.924434 0.381342i $$-0.875462\pi$$
0.924434 0.381342i $$-0.124538\pi$$
$$558$$ 0 0
$$559$$ −8.00000 + 12.0000i −0.338364 + 0.507546i
$$560$$ 0 0
$$561$$ 0 0
$$562$$ −30.0000 −1.26547
$$563$$ −4.00000 −0.168580 −0.0842900 0.996441i $$-0.526862\pi$$
−0.0842900 + 0.996441i $$0.526862\pi$$
$$564$$ 8.00000i 0.336861i
$$565$$ 28.0000i 1.17797i
$$566$$ 16.0000i 0.672530i
$$567$$ 0 0
$$568$$ 0 0
$$569$$ 30.0000 1.25767 0.628833 0.777541i $$-0.283533\pi$$
0.628833 + 0.777541i $$0.283533\pi$$
$$570$$ 8.00000i 0.335083i
$$571$$ 12.0000 0.502184 0.251092 0.967963i $$-0.419210\pi$$
0.251092 + 0.967963i $$0.419210\pi$$
$$572$$ 0 0
$$573$$ −2.00000 −0.0835512
$$574$$ 0 0
$$575$$ −6.00000 −0.250217
$$576$$ −1.00000 −0.0416667
$$577$$ 22.0000i 0.915872i −0.888985 0.457936i $$-0.848589\pi$$
0.888985 0.457936i $$-0.151411\pi$$
$$578$$ 13.0000i 0.540729i
$$579$$ 4.00000i 0.166234i
$$580$$ 0 0
$$581$$ 0 0
$$582$$ 2.00000 0.0829027
$$583$$ 0 0
$$584$$ 14.0000 0.579324
$$585$$ −6.00000 4.00000i −0.248069 0.165380i
$$586$$ 6.00000 0.247858
$$587$$ 18.0000i 0.742940i 0.928445 + 0.371470i $$0.121146\pi$$
−0.928445 + 0.371470i $$0.878854\pi$$
$$588$$ 0 0
$$589$$ 0 0
$$590$$ 12.0000i 0.494032i
$$591$$ 18.0000i 0.740421i
$$592$$ 2.00000i 0.0821995i
$$593$$ 24.0000i 0.985562i −0.870153 0.492781i $$-0.835980\pi$$
0.870153 0.492781i $$-0.164020\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 6.00000i 0.245770i
$$597$$ −10.0000 −0.409273
$$598$$ −18.0000 12.0000i −0.736075 0.490716i
$$599$$ 30.0000 1.22577 0.612883 0.790173i $$-0.290010\pi$$
0.612883 + 0.790173i $$0.290010\pi$$
$$600$$ 1.00000i 0.0408248i
$$601$$ 18.0000 0.734235 0.367118 0.930175i $$-0.380345\pi$$
0.367118 + 0.930175i $$0.380345\pi$$
$$602$$ 0 0
$$603$$ 2.00000i 0.0814463i
$$604$$ 0 0
$$605$$ 22.0000i 0.894427i
$$606$$ 2.00000i 0.0812444i
$$607$$ −18.0000 −0.730597 −0.365299 0.930890i $$-0.619033\pi$$
−0.365299 + 0.930890i $$0.619033\pi$$
$$608$$ 4.00000 0.162221
$$609$$ 0 0
$$610$$ −24.0000 −0.971732
$$611$$ −24.0000 16.0000i −0.970936 0.647291i
$$612$$ −2.00000 −0.0808452
$$613$$ 34.0000i 1.37325i 0.727013 + 0.686624i $$0.240908\pi$$
−0.727013 + 0.686624i $$0.759092\pi$$
$$614$$ 28.0000 1.12999
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 18.0000i 0.724653i −0.932051 0.362326i $$-0.881983\pi$$
0.932051 0.362326i $$-0.118017\pi$$
$$618$$ 14.0000i 0.563163i
$$619$$ 16.0000i 0.643094i −0.946894 0.321547i $$-0.895797\pi$$
0.946894 0.321547i $$-0.104203\pi$$
$$620$$ 0 0
$$621$$ 6.00000 0.240772
$$622$$ 12.0000i 0.481156i
$$623$$ 0 0
$$624$$ 2.00000 3.00000i 0.0800641 0.120096i
$$625$$ −19.0000 −0.760000
$$626$$ 6.00000i 0.239808i
$$627$$ 0 0
$$628$$ 8.00000 0.319235
$$629$$ 4.00000i 0.159490i
$$630$$ 0 0
$$631$$ 20.0000i 0.796187i 0.917345 + 0.398094i $$0.130328\pi$$
−0.917345 + 0.398094i $$0.869672\pi$$
$$632$$ 0 0
$$633$$ 28.0000 1.11290
$$634$$ 2.00000 0.0794301
$$635$$ 24.0000i 0.952411i
$$636$$ 4.00000 0.158610
$$637$$ 0 0
$$638$$ 0 0
$$639$$ 0 0
$$640$$ −2.00000 −0.0790569
$$641$$ 42.0000 1.65890 0.829450 0.558581i $$-0.188654\pi$$
0.829450 + 0.558581i $$0.188654\pi$$
$$642$$ 12.0000i 0.473602i
$$643$$ 44.0000i 1.73519i −0.497271 0.867595i $$-0.665665\pi$$
0.497271 0.867595i $$-0.334335\pi$$
$$644$$ 0 0
$$645$$ 8.00000i 0.315000i
$$646$$ 8.00000 0.314756
$$647$$ −28.0000 −1.10079 −0.550397 0.834903i $$-0.685524\pi$$
−0.550397 + 0.834903i $$0.685524\pi$$
$$648$$ 1.00000i 0.0392837i
$$649$$ 0 0
$$650$$ 3.00000 + 2.00000i 0.117670 + 0.0784465i
$$651$$ 0 0
$$652$$ 14.0000i 0.548282i
$$653$$ 4.00000 0.156532 0.0782660 0.996933i $$-0.475062\pi$$
0.0782660 + 0.996933i $$0.475062\pi$$
$$654$$ −6.00000 −0.234619
$$655$$ 24.0000i 0.937758i
$$656$$ 0 0
$$657$$ 14.0000i 0.546192i
$$658$$ 0 0
$$659$$ 20.0000 0.779089 0.389545 0.921008i $$-0.372632\pi$$
0.389545 + 0.921008i $$0.372632\pi$$
$$660$$ 0 0
$$661$$ 10.0000i 0.388955i 0.980907 + 0.194477i $$0.0623011\pi$$
−0.980907 + 0.194477i $$0.937699\pi$$
$$662$$ 10.0000 0.388661
$$663$$ 4.00000 6.00000i 0.155347 0.233021i
$$664$$ 14.0000 0.543305
$$665$$ 0 0
$$666$$ 2.00000 0.0774984
$$667$$ 0 0
$$668$$ 12.0000i 0.464294i
$$669$$ 16.0000i 0.618596i
$$670$$ 4.00000i 0.154533i
$$671$$ 0 0
$$672$$ 0 0
$$673$$ −46.0000 −1.77317 −0.886585 0.462566i $$-0.846929\pi$$
−0.886585 + 0.462566i $$0.846929\pi$$
$$674$$ 22.0000i 0.847408i
$$675$$ −1.00000 −0.0384900
$$676$$ 5.00000 + 12.0000i 0.192308 + 0.461538i
$$677$$ 22.0000 0.845529 0.422764 0.906240i $$-0.361060\pi$$
0.422764 + 0.906240i $$0.361060\pi$$
$$678$$ 14.0000i 0.537667i
$$679$$ 0 0
$$680$$ −4.00000 −0.153393
$$681$$ 22.0000i 0.843042i
$$682$$ 0 0
$$683$$ 16.0000i 0.612223i −0.951996 0.306111i $$-0.900972\pi$$
0.951996 0.306111i $$-0.0990280\pi$$
$$684$$ 4.00000i 0.152944i
$$685$$ −4.00000 −0.152832
$$686$$ 0 0
$$687$$ 14.0000i 0.534133i
$$688$$ 4.00000 0.152499
$$689$$ −8.00000 + 12.0000i −0.304776 + 0.457164i
$$690$$ 12.0000 0.456832
$$691$$ 40.0000i 1.52167i −0.648944 0.760836i $$-0.724789\pi$$
0.648944 0.760836i $$-0.275211\pi$$
$$692$$ −6.00000 −0.228086
$$693$$ 0 0
$$694$$ 32.0000i 1.21470i
$$695$$ 40.0000i 1.51729i
$$696$$ 0 0
$$697$$ 0 0
$$698$$ 14.0000 0.529908
$$699$$ 6.00000 0.226941
$$700$$ 0 0
$$701$$ −48.0000 −1.81293 −0.906467 0.422276i $$-0.861231\pi$$
−0.906467 + 0.422276i $$0.861231\pi$$
$$702$$ −3.00000 2.00000i −0.113228 0.0754851i
$$703$$ −8.00000 −0.301726
$$704$$ 0 0
$$705$$ 16.0000 0.602595
$$706$$ −24.0000 −0.903252
$$707$$ 0 0
$$708$$ 6.00000i 0.225494i
$$709$$ 46.0000i 1.72757i 0.503864 + 0.863783i $$0.331911\pi$$
−0.503864 + 0.863783i $$0.668089\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ −4.00000 −0.149906
$$713$$ 0 0
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 20.0000 0.747435
$$717$$ 16.0000i 0.597531i
$$718$$ −24.0000 −0.895672
$$719$$ −20.0000 −0.745874 −0.372937 0.927857i $$-0.621649\pi$$
−0.372937 + 0.927857i $$0.621649\pi$$
$$720$$ 2.00000i 0.0745356i
$$721$$ 0 0
$$722$$ 3.00000i 0.111648i
$$723$$ 10.0000i 0.371904i
$$724$$ 12.0000 0.445976
$$725$$ 0 0
$$726$$ 11.0000i 0.408248i
$$727$$ −38.0000 −1.40934 −0.704671 0.709534i $$-0.748905\pi$$
−0.704671 + 0.709534i $$0.748905\pi$$
$$728$$ 0 0
$$729$$ 1.00000 0.0370370
$$730$$ 28.0000i 1.03633i
$$731$$ 8.00000 0.295891
$$732$$ −12.0000 −0.443533
$$733$$ 14.0000i 0.517102i −0.965998 0.258551i $$-0.916755\pi$$
0.965998 0.258551i $$-0.0832450\pi$$
$$734$$ 22.0000i 0.812035i
$$735$$ 0 0
$$736$$ 6.00000i 0.221163i
$$737$$ 0 0
$$738$$ 0 0
$$739$$ 34.0000i 1.25071i −0.780340 0.625355i $$-0.784954\pi$$
0.780340 0.625355i $$-0.215046\pi$$
$$740$$ 4.00000 0.147043
$$741$$ 12.0000 + 8.00000i 0.440831 + 0.293887i
$$742$$ 0 0
$$743$$ 16.0000i 0.586983i −0.955962 0.293492i $$-0.905183\pi$$
0.955962 0.293492i $$-0.0948173\pi$$
$$744$$ 0 0
$$745$$ −12.0000 −0.439646
$$746$$ 34.0000i 1.24483i
$$747$$ 14.0000i 0.512233i
$$748$$ 0 0
$$749$$ 0 0
$$750$$ −12.0000 −0.438178
$$751$$ 12.0000 0.437886 0.218943 0.975738i $$-0.429739\pi$$
0.218943 + 0.975738i $$0.429739\pi$$
$$752$$ 8.00000i 0.291730i
$$753$$ −28.0000 −1.02038
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 0 0
$$757$$ −42.0000 −1.52652 −0.763258 0.646094i $$-0.776401\pi$$
−0.763258 + 0.646094i $$0.776401\pi$$
$$758$$ 26.0000 0.944363
$$759$$ 0 0
$$760$$ 8.00000i 0.290191i
$$761$$ 40.0000i 1.45000i 0.688749 + 0.724999i $$0.258160\pi$$
−0.688749 + 0.724999i $$0.741840\pi$$
$$762$$ 12.0000i 0.434714i
$$763$$ 0 0
$$764$$ −2.00000 −0.0723575
$$765$$ 4.00000i 0.144620i
$$766$$ −24.0000 −0.867155
$$767$$ 18.0000 + 12.0000i 0.649942 + 0.433295i
$$768$$ −1.00000 −0.0360844
$$769$$ 26.0000i 0.937584i −0.883309 0.468792i $$-0.844689\pi$$
0.883309 0.468792i $$-0.155311\pi$$
$$770$$ 0 0
$$771$$ 18.0000 0.648254
$$772$$ 4.00000i 0.143963i
$$773$$ 26.0000i 0.935155i 0.883952 + 0.467578i $$0.154873\pi$$
−0.883952 + 0.467578i $$0.845127\pi$$
$$774$$ 4.00000i 0.143777i
$$775$$ 0 0
$$776$$ 2.00000 0.0717958
$$777$$ 0 0
$$778$$ 20.0000i 0.717035i
$$779$$ 0 0
$$780$$ −6.00000 4.00000i −0.214834 0.143223i
$$781$$ 0 0
$$782$$ 12.0000i 0.429119i
$$783$$ 0 0
$$784$$ 0 0
$$785$$ 16.0000i 0.571064i
$$786$$ 12.0000i 0.428026i
$$787$$ 48.0000i 1.71102i 0.517790 + 0.855508i $$0.326755\pi$$
−0.517790 + 0.855508i $$0.673245\pi$$
$$788$$ 18.0000i 0.641223i
$$789$$ 6.00000 0.213606
$$790$$ 0 0
$$791$$ 0 0
$$792$$ 0 0